LMFDB - Embedded newform 560.2.cq.a.131.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(131,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 0, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cq (of order $12$, degree $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			131.13
Character	$\chi$	$=$	560.131
Dual form			560.2.cq.a.171.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13884 - 0.838476i) q^{2} +(-0.589179 + 2.19885i) q^{3} +(0.593914 + 1.90978i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(2.51466 - 2.01012i) q^{6} +(-1.24964 + 2.33204i) q^{7} +(0.924933 - 2.67292i) q^{8} +(-1.88972 - 1.09103i) q^{9} +(1.31705 + 0.515152i) q^{10} +(-1.17597 + 4.38876i) q^{11} +(-4.54924 + 0.180723i) q^{12} +(1.38652 - 1.38652i) q^{13} +(3.37850 - 1.60802i) q^{14} -2.27641i q^{15} +(-3.29453 + 2.26849i) q^{16} +(-5.68677 + 3.28326i) q^{17} +(1.23729 + 2.82699i) q^{18} +(7.37431 - 1.97594i) q^{19} +(-1.06797 - 1.69099i) q^{20} +(-4.39153 - 4.12176i) q^{21} +(5.01911 - 4.01208i) q^{22} +(0.0300112 - 0.0519810i) q^{23} +(5.33239 + 3.60862i) q^{24} +(0.866025 - 0.500000i) q^{25} +(-2.74159 + 0.416460i) q^{26} +(-1.31661 + 1.31661i) q^{27} +(-5.19586 - 1.00151i) q^{28} +(-2.86555 - 2.86555i) q^{29} +(-1.90872 + 2.59247i) q^{30} +(-1.91998 - 3.32551i) q^{31} +(5.65402 + 0.178935i) q^{32} +(-8.95737 - 5.17154i) q^{33} +(9.22926 + 1.02912i) q^{34} +(0.603485 - 2.57601i) q^{35} +(0.961297 - 4.25693i) q^{36} +(-2.13672 - 7.97435i) q^{37} +(-10.0549 - 3.93290i) q^{38} +(2.23184 + 3.86565i) q^{39} +(-0.201614 + 2.82123i) q^{40} +1.20752 q^{41} +(1.54526 + 8.37622i) q^{42} +(-4.82061 - 4.82061i) q^{43} +(-9.08000 + 0.360713i) q^{44} +(2.10771 + 0.564759i) q^{45} +(-0.0777629 + 0.0340343i) q^{46} +(-3.96450 + 6.86672i) q^{47} +(-3.04700 - 8.58072i) q^{48} +(-3.87680 - 5.82842i) q^{49} +(-1.40550 - 0.156722i) q^{50} +(-3.86886 - 14.4388i) q^{51} +(3.47142 + 1.82448i) q^{52} +(-1.87700 - 0.502941i) q^{53} +(2.60336 - 0.395462i) q^{54} -4.54358i q^{55} +(5.07751 + 5.49717i) q^{56} +17.3792i q^{57} +(0.860707 + 5.66610i) q^{58} +(4.74673 + 1.27188i) q^{59} +(4.34745 - 1.35200i) q^{60} +(1.77916 + 6.63992i) q^{61} +(-0.601806 + 5.39708i) q^{62} +(4.90579 - 3.04350i) q^{63} +(-6.28900 - 4.94454i) q^{64} +(-0.980418 + 1.69813i) q^{65} +(5.86480 + 13.4001i) q^{66} +(-6.63402 - 1.77758i) q^{67} +(-9.64777 - 8.91052i) q^{68} +(0.0966163 + 0.0966163i) q^{69} +(-2.84719 + 2.42765i) q^{70} -4.38673 q^{71} +(-4.66410 + 4.04194i) q^{72} +(1.59293 + 2.75903i) q^{73} +(-4.25292 + 10.8731i) q^{74} +(0.589179 + 2.19885i) q^{75} +(8.15332 + 12.9098i) q^{76} +(-8.76523 - 8.22678i) q^{77} +(0.699555 - 6.27370i) q^{78} +(9.58136 + 5.53180i) q^{79} +(2.59514 - 3.04388i) q^{80} +(-5.39240 - 9.33991i) q^{81} +(-1.37518 - 1.01248i) q^{82} +(3.01972 + 3.01972i) q^{83} +(5.26346 - 10.8348i) q^{84} +(4.64323 - 4.64323i) q^{85} +(1.44794 + 9.53187i) q^{86} +(7.98923 - 4.61258i) q^{87} +(10.6431 + 7.20258i) q^{88} +(-7.43260 + 12.8736i) q^{89} +(-1.92681 - 2.41043i) q^{90} +(1.50076 + 4.96607i) q^{91} +(0.117096 + 0.0264427i) q^{92} +(8.44350 - 2.26243i) q^{93} +(10.2725 - 4.49596i) q^{94} +(-6.61162 + 3.81722i) q^{95} +(-3.72468 + 12.3269i) q^{96} +16.0182i q^{97} +(-0.471941 + 9.88824i) q^{98} +(7.01052 - 7.01052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4} - 8 q^{11} - 16 q^{14} - 20 q^{16} + 40 q^{18} + 40 q^{22} + 16 q^{23} - 44 q^{28} + 32 q^{29} + 20 q^{32} - 16 q^{37} - 60 q^{42} - 16 q^{43} - 48 q^{44} - 20 q^{46} - 8 q^{50} + 40 q^{51}+ \cdots - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 - 8 * q^11 - 16 * q^14 - 20 * q^16 + 40 * q^18 + 40 * q^22 + 16 * q^23 - 44 * q^28 + 32 * q^29 + 20 * q^32 - 16 * q^37 - 60 * q^42 - 16 * q^43 - 48 * q^44 - 20 * q^46 - 8 * q^50 + 40 * q^51 - 72 * q^52 - 16 * q^53 - 84 * q^54 - 96 * q^56 - 8 * q^58 - 48 * q^59 - 28 * q^60 + 40 * q^64 - 192 * q^66 - 40 * q^67 - 60 * q^68 - 16 * q^70 + 64 * q^71 + 36 * q^72 - 60 * q^74 + 48 * q^78 + 128 * q^81 + 164 * q^84 - 52 * q^86 - 20 * q^88 + 32 * q^91 + 128 * q^92 + 72 * q^94 - 204 * q^96 + 160 * q^98 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.13884	−	0.838476i	−0.805282	−	0.592892i
$2$	−1.13884	−	0.838476i	−0.805282	−	0.592892i
$3$	−0.589179	+	2.19885i	−0.340163	+	1.26950i	0.558000	+	0.829841i	$0.311569\pi$
$3$	−0.589179	+	2.19885i	−0.340163	+	1.26950i	−0.898162	+	0.439664i	$0.855098\pi$
$4$	0.593914	+	1.90978i	0.296957	+	0.954891i
$5$	−0.965926	+	0.258819i	−0.431975	+	0.115747i
$5$	−0.965926	+	0.258819i	−0.431975	+	0.115747i
$6$	2.51466	−	2.01012i	1.02661	−	0.820629i
$7$	−1.24964	+	2.33204i	−0.472320	+	0.881427i
$7$	−1.24964	+	2.33204i	−0.472320	+	0.881427i
$8$	0.924933	−	2.67292i	0.327013	−	0.945020i
$9$	−1.88972	−	1.09103i	−0.629907	−	0.363677i
$10$	1.31705	+	0.515152i	0.416487	+	0.162906i
$11$	−1.17597	+	4.38876i	−0.354567	+	1.32326i	0.526461	+	0.850199i	$0.323518\pi$
$11$	−1.17597	+	4.38876i	−0.354567	+	1.32326i	−0.881028	+	0.473063i	$0.843148\pi$
$12$	−4.54924	+	0.180723i	−1.31325	+	0.0521703i
$13$	1.38652	−	1.38652i	0.384551	−	0.384551i	−0.488187	−	0.872739i	$-0.662342\pi$
$13$	1.38652	−	1.38652i	0.384551	−	0.384551i	0.872739	+	0.488187i	$0.162342\pi$
$14$	3.37850	−	1.60802i	0.902942	−	0.429762i
$15$		−	2.27641i		−	0.587768i
$16$	−3.29453	+	2.26849i	−0.823633	+	0.567123i
$17$	−5.68677	+	3.28326i	−1.37924	+	0.796307i	−0.992069	−	0.125698i	$-0.959883\pi$
$17$	−5.68677	+	3.28326i	−1.37924	+	0.796307i	−0.387176	+	0.922006i	$0.626550\pi$
$18$	1.23729	+	2.82699i	0.291631	+	0.666329i
$19$	7.37431	−	1.97594i	1.69178	−	0.453312i	0.720933	−	0.693004i	$-0.243713\pi$
$19$	7.37431	−	1.97594i	1.69178	−	0.453312i	0.970849	+	0.239693i	$0.0770467\pi$
$20$	−1.06797	−	1.69099i	−0.238804	−	0.378117i
$21$	−4.39153	−	4.12176i	−0.958311	−	0.899441i
$22$	5.01911	−	4.01208i	1.07008	−	0.855379i
$23$	0.0300112	−	0.0519810i	0.00625778	−	0.0108388i	−0.862880	−	0.505410i	$-0.831341\pi$
$23$	0.0300112	−	0.0519810i	0.00625778	−	0.0108388i	0.869137	+	0.494571i	$0.164675\pi$
$24$	5.33239	+	3.60862i	1.08847	+	0.736605i
$25$	0.866025	−	0.500000i	0.173205	−	0.100000i
$26$	−2.74159	+	0.416460i	−0.537670	+	0.0816746i
$27$	−1.31661	+	1.31661i	−0.253382	+	0.253382i
$28$	−5.19586	−	1.00151i	−0.981926	−	0.189268i
$29$	−2.86555	−	2.86555i	−0.532119	−	0.532119i	0.389083	−	0.921203i	$-0.372792\pi$
$29$	−2.86555	−	2.86555i	−0.532119	−	0.532119i	−0.921203	+	0.389083i	$0.872792\pi$
$30$	−1.90872	+	2.59247i	−0.348483	+	0.473318i
$31$	−1.91998	−	3.32551i	−0.344839	−	0.597279i	0.640485	−	0.767970i	$-0.278733\pi$
$31$	−1.91998	−	3.32551i	−0.344839	−	0.597279i	−0.985325	+	0.170691i	$0.945400\pi$
$32$	5.65402	+	0.178935i	0.999500	+	0.0316315i
$33$	−8.95737	−	5.17154i	−1.55928	−	0.900249i
$34$	9.22926	+	1.02912i	1.58281	+	0.176492i
$35$	0.603485	−	2.57601i	0.102008	−	0.435424i
$36$	0.961297	−	4.25693i	0.160216	−	0.709488i
$37$	−2.13672	−	7.97435i	−0.351275	−	1.31098i	−0.885108	−	0.465386i	$-0.845916\pi$
$37$	−2.13672	−	7.97435i	−0.351275	−	1.31098i	0.533833	−	0.845590i	$-0.320751\pi$
$38$	−10.0549	−	3.93290i	−1.63113	−	0.638001i
$39$	2.23184	+	3.86565i	0.357380	+	0.619000i
$40$	−0.201614	+	2.82123i	−0.0318780	+	0.446076i
$41$	1.20752			0.188584			0.0942918	−	0.995545i	$-0.469941\pi$
$41$	1.20752			0.188584			0.0942918	+	0.995545i	$0.469941\pi$
$42$	1.54526	+	8.37622i	0.238438	+	1.29248i
$43$	−4.82061	−	4.82061i	−0.735136	−	0.735136i	0.236497	−	0.971632i	$-0.424001\pi$
$43$	−4.82061	−	4.82061i	−0.735136	−	0.735136i	−0.971632	+	0.236497i	$0.924001\pi$
$44$	−9.08000	+	0.360713i	−1.36886	+	0.0543795i
$45$	2.10771	+	0.564759i	0.314199	+	0.0841893i
$46$	−0.0777629	+	0.0340343i	−0.0114655	+	0.00501809i
$47$	−3.96450	+	6.86672i	−0.578282	+	1.00161i	0.417394	+	0.908726i	$0.362943\pi$
$47$	−3.96450	+	6.86672i	−0.578282	+	1.00161i	−0.995676	+	0.0928888i	$0.970390\pi$
$48$	−3.04700	−	8.58072i	−0.439797	−	1.23852i
$49$	−3.87680	−	5.82842i	−0.553828	−	0.832631i
$50$	−1.40550	−	0.156722i	−0.198768	−	0.0221638i
$51$	−3.86886	−	14.4388i	−0.541748	−	2.02183i
$52$	3.47142	+	1.82448i	0.481400	+	0.253009i
$53$	−1.87700	−	0.502941i	−0.257826	−	0.0690843i	0.127591	−	0.991827i	$-0.459276\pi$
$53$	−1.87700	−	0.502941i	−0.257826	−	0.0690843i	−0.385417	+	0.922743i	$0.625942\pi$
$54$	2.60336	−	0.395462i	0.354272	−	0.0538156i
$55$		−	4.54358i		−	0.612657i
$56$	5.07751	+	5.49717i	0.678511	+	0.734590i
$57$			17.3792i			2.30193i
$58$	0.860707	+	5.66610i	0.113016	+	0.743995i
$59$	4.74673	+	1.27188i	0.617972	+	0.165585i	0.554206	−	0.832380i	$-0.313022\pi$
$59$	4.74673	+	1.27188i	0.617972	+	0.165585i	0.0637661	+	0.997965i	$0.479689\pi$
$60$	4.34745	−	1.35200i	0.561254	−	0.174542i
$61$	1.77916	+	6.63992i	0.227798	+	0.850155i	0.981264	+	0.192668i	$0.0617140\pi$
$61$	1.77916	+	6.63992i	0.227798	+	0.850155i	−0.753466	+	0.657487i	$0.771619\pi$
$62$	−0.601806	+	5.39708i	−0.0764295	+	0.685430i
$63$	4.90579	−	3.04350i	0.618072	−	0.383445i
$64$	−6.28900	−	4.94454i	−0.786125	−	0.618068i
$65$	−0.980418	+	1.69813i	−0.121606	+	0.210627i
$66$	5.86480	+	13.4001i	0.721907	+	1.64944i
$67$	−6.63402	−	1.77758i	−0.810474	−	0.217166i	−0.170297	−	0.985393i	$-0.554473\pi$
$67$	−6.63402	−	1.77758i	−0.810474	−	0.217166i	−0.640178	+	0.768227i	$0.721139\pi$
$68$	−9.64777	−	8.91052i	−1.16996	−	1.08056i
$69$	0.0966163	+	0.0966163i	0.0116312	+	0.0116312i
$70$	−2.84719	+	2.42765i	−0.340305	+	0.290160i
$71$	−4.38673			−0.520609			−0.260304	−	0.965527i	$-0.583823\pi$
$71$	−4.38673			−0.520609			−0.260304	+	0.965527i	$0.583823\pi$
$72$	−4.66410	+	4.04194i	−0.549669	+	0.476347i
$73$	1.59293	+	2.75903i	0.186438	+	0.322920i	0.944060	−	0.329773i	$-0.106972\pi$
$73$	1.59293	+	2.75903i	0.186438	+	0.322920i	−0.757622	+	0.652694i	$0.773639\pi$
$74$	−4.25292	+	10.8731i	−0.494392	+	1.26397i
$75$	0.589179	+	2.19885i	0.0680326	+	0.253901i
$76$	8.15332	+	12.9098i	0.935250	+	1.48085i
$77$	−8.76523	−	8.22678i	−0.998890	−	0.937528i
$78$	0.699555	−	6.27370i	0.0792090	−	0.710357i
$79$	9.58136	+	5.53180i	1.07799	+	0.622376i	0.930353	−	0.366666i	$-0.119501\pi$
$79$	9.58136	+	5.53180i	1.07799	+	0.622376i	0.147634	+	0.989042i	$0.452834\pi$
$80$	2.59514	−	3.04388i	0.290146	−	0.340317i
$81$	−5.39240	−	9.33991i	−0.599155	−	1.03777i
$82$	−1.37518	−	1.01248i	−0.151863	−	0.111810i
$83$	3.01972	+	3.01972i	0.331457	+	0.331457i	0.853140	−	0.521682i	$-0.174695\pi$
$83$	3.01972	+	3.01972i	0.331457	+	0.331457i	−0.521682	+	0.853140i	$0.674695\pi$
$84$	5.26346	−	10.8348i	0.574291	−	1.18218i
$85$	4.64323	−	4.64323i	0.503629	−	0.503629i
$86$	1.44794	+	9.53187i	0.156135	+	1.02785i
$87$	7.98923	−	4.61258i	0.856535	−	0.494521i
$88$	10.6431	+	7.20258i	1.13456	+	0.767797i
$89$	−7.43260	+	12.8736i	−0.787854	+	1.36460i	0.139425	+	0.990233i	$0.455475\pi$
$89$	−7.43260	+	12.8736i	−0.787854	+	1.36460i	−0.927279	+	0.374371i	$0.877859\pi$
$90$	−1.92681	−	2.41043i	−0.203103	−	0.254082i
$91$	1.50076	+	4.96607i	0.157323	+	0.520585i
$92$	0.117096	+	0.0264427i	0.0122082	+	0.00275684i
$93$	8.44350	−	2.26243i	0.875550	−	0.234603i
$94$	10.2725	−	4.49596i	1.05953	−	0.463723i
$95$	−6.61162	+	3.81722i	−0.678338	+	0.391639i
$96$	−3.72468	+	12.3269i	−0.380149	+	1.25811i
$97$			16.0182i			1.62640i	0.581984	+	0.813200i	$0.302277\pi$
$97$			16.0182i			1.62640i	−0.581984	+	0.813200i	$0.697723\pi$
$98$	−0.471941	+	9.88824i	−0.0476732	+	0.998863i
$99$	7.01052	−	7.01052i	0.704584	−	0.704584i
$100$	1.46924	+	1.35696i	0.146924	+	0.135696i
$101$	3.76280	−	14.0429i	0.374412	−	1.39732i	−0.479790	−	0.877383i	$-0.659287\pi$
$101$	3.76280	−	14.0429i	0.374412	−	1.39732i	0.854202	−	0.519941i	$-0.174046\pi$
$102$	−7.70056	+	19.6874i	−0.762469	+	1.94934i
$103$	9.04670	+	5.22312i	0.891398	+	0.514649i	0.874400	−	0.485207i	$-0.161256\pi$
$103$	9.04670	+	5.22312i	0.891398	+	0.514649i	0.0169985	+	0.999856i	$0.494589\pi$
$104$	−2.42362	−	4.98849i	−0.237655	−	0.489162i
$105$	5.30868	+	2.84470i	0.518074	+	0.277614i
$106$	1.71590	+	2.14659i	0.166663	+	0.208495i
$107$	5.46601	−	1.46461i	0.528420	−	0.141590i	0.0152612	−	0.999884i	$-0.495142\pi$
$107$	5.46601	−	1.46461i	0.528420	−	0.141590i	0.513158	+	0.858294i	$0.328475\pi$
$108$	−3.29639	−	1.73248i	−0.317196	−	0.166708i
$109$	0.994863	−	3.71288i	0.0952906	−	0.355629i	−0.901773	−	0.432211i	$-0.857734\pi$
$109$	0.994863	−	3.71288i	0.0952906	−	0.355629i	0.997063	+	0.0765811i	$0.0244004\pi$
$110$	−3.80969	+	5.17442i	−0.363239	+	0.493361i
$111$	18.7933			1.78378
$112$	−1.17323	−	10.5178i	−0.110860	−	0.993836i
$113$	−9.66225			−0.908948			−0.454474	−	0.890760i	$-0.650173\pi$
$113$	−9.66225			−0.908948			−0.454474	+	0.890760i	$0.650173\pi$
$114$	14.5720	−	19.7921i	1.36479	−	1.85370i
$115$	−0.0155350	+	0.0579773i	−0.00144864	+	0.00540641i
$116$	3.77068	−	7.17446i	0.350099	−	0.666132i
$117$	−4.13287	+	1.10740i	−0.382084	+	0.102379i
$118$	−4.33932	−	5.42849i	−0.399467	−	0.499733i
$119$	−0.550260	−	17.3647i	−0.0504423	−	1.59182i
$120$	−6.08467	−	2.10553i	−0.555452	−	0.192208i
$121$	−8.35208	−	4.82207i	−0.759280	−	0.438370i
$122$	3.54124	−	9.05360i	0.320609	−	0.819674i
$123$	−0.711448	+	2.65516i	−0.0641491	+	0.239408i
$124$	5.21069	−	5.64181i	0.467934	−	0.506650i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−8.13882	−	0.647331i	−0.725064	−	0.0576689i
$127$		−	8.17598i		−	0.725501i	−0.931886	−	0.362750i	$-0.881838\pi$
$127$		−	8.17598i		−	0.725501i	0.931886	−	0.362750i	$-0.118162\pi$
$128$	3.01628	+	10.9042i	0.266604	+	0.963806i
$129$	13.4400	−	7.75958i	1.18332	−	0.683193i
$130$	2.54038	−	1.11185i	0.222806	−	0.0975153i
$131$	−1.93173	+	0.517605i	−0.168776	+	0.0452233i	−0.342217	−	0.939621i	$-0.611178\pi$
$131$	−1.93173	+	0.517605i	−0.168776	+	0.0452233i	0.173442	+	0.984844i	$0.444511\pi$
$132$	4.55660	−	20.1781i	0.396601	−	1.75628i
$133$	−4.60727	+	19.6664i	−0.399501	+	1.70529i
$134$	6.06463	+	7.58685i	0.523904	+	0.655404i
$135$	0.930985	−	1.61251i	0.0801264	−	0.138783i
$136$	3.51600	+	18.2371i	0.301495	+	1.56382i
$137$	−5.17476	+	2.98765i	−0.442110	+	0.255252i	−0.704492	−	0.709712i	$-0.748825\pi$
$137$	−5.17476	+	2.98765i	−0.442110	+	0.255252i	0.262383	+	0.964964i	$0.415492\pi$
$138$	−0.0290200	−	0.191041i	−0.00247035	−	0.0162625i
$139$	−8.91972	+	8.91972i	−0.756560	+	0.756560i	−0.975695	−	0.219134i	$-0.929677\pi$
$139$	−8.91972	+	8.91972i	−0.756560	+	0.756560i	0.219134	+	0.975695i	$0.429677\pi$
$140$	5.27803	−	0.377403i	0.446075	−	0.0318964i
$141$	−12.7631	−	12.7631i	−1.07484	−	1.07484i
$142$	4.99578	+	3.67817i	0.419237	+	0.308665i
$143$	4.45461	+	7.71561i	0.372513	+	0.645212i
$144$	8.70074	−	0.692385i	0.725061	−	0.0576987i
$145$	3.50957	+	2.02625i	0.291454	+	0.168271i
$146$	0.499293	−	4.47773i	0.0413218	−	0.370580i
$147$	15.0999	−	5.09050i	1.24542	−	0.419857i
$148$	13.9602	−	8.81676i	1.14753	−	0.724733i
$149$	−5.36448	−	20.0205i	−0.439476	−	1.64014i	−0.730124	−	0.683315i	$-0.760538\pi$
$149$	−5.36448	−	20.0205i	−0.439476	−	1.64014i	0.290648	−	0.956830i	$-0.406129\pi$
$150$	1.17270	−	2.99815i	0.0957506	−	0.244798i
$151$	5.79744	+	10.0415i	0.471789	+	0.817162i	0.999479	−	0.0322745i	$-0.0102751\pi$
$151$	5.79744	+	10.0415i	0.471789	+	0.817162i	−0.527690	+	0.849437i	$0.676942\pi$
$152$	1.53921	−	21.5385i	0.124847	−	1.74701i
$153$	14.3285			1.15839
$154$	3.08424	+	16.7184i	0.248535	+	1.34721i
$155$	2.71527	+	2.71527i	0.218095	+	0.218095i
$156$	−6.05703	+	6.55819i	−0.484951	+	0.525075i
$157$	15.3427	+	4.11105i	1.22448	+	0.328098i	0.812427	−	0.583063i	$-0.198146\pi$
$157$	15.3427	+	4.11105i	1.22448	+	0.328098i	0.412051	+	0.911161i	$0.364813\pi$
$158$	−6.27335	−	14.3336i	−0.499081	−	1.14032i
$159$	2.21178	−	3.83092i	0.175406	−	0.303811i
$160$	−5.50768	+	1.29053i	−0.435420	+	0.102025i
$161$	0.0837184	+	0.134945i	0.00659793	+	0.0106352i
$162$	−1.69021	+	15.1581i	−0.132796	+	1.19093i
$163$	0.215415	+	0.803939i	0.0168726	+	0.0629694i	0.973849	−	0.227197i	$-0.0729561\pi$
$163$	0.215415	+	0.803939i	0.0168726	+	0.0629694i	−0.956976	+	0.290166i	$0.906289\pi$
$164$	0.717166	+	2.30611i	0.0560013	+	0.180077i
$165$	9.99064	+	2.67699i	0.777771	+	0.208403i
$166$	−0.907015	−	5.97095i	−0.0703980	−	0.463435i
$167$		−	3.23387i		−	0.250244i	−0.992141	−	0.125122i	$-0.960068\pi$
$167$		−	3.23387i		−	0.250244i	0.992141	−	0.125122i	$-0.0399323\pi$
$168$	−15.0790	+	7.92586i	−1.16337	+	0.611493i
$169$			9.15513i			0.704240i
$170$	−9.18114	+	1.39466i	−0.704161	+	0.106965i
$171$	−16.0912	−	4.31162i	−1.23052	−	0.329718i
$172$	6.34328	−	12.0693i	0.483671	−	0.920278i
$173$	4.90486	+	18.3052i	0.372910	+	1.39172i	0.856375	+	0.516355i	$0.172711\pi$
$173$	4.90486	+	18.3052i	0.372910	+	1.39172i	−0.483465	+	0.875364i	$0.660622\pi$
$174$	−12.9660	−	1.44578i	−0.982950	−	0.109605i
$175$	0.0837979	+	2.64442i	0.00633452	+	0.199900i
$176$	−6.08163	−	17.1266i	−0.458420	−	1.29097i
$177$	−5.59335	+	9.68797i	−0.420422	+	0.728192i
$178$	19.2588	−	8.42897i	1.44351	−	0.631778i
$179$	24.5115	+	6.56785i	1.83208	+	0.490904i	0.998141	−	0.0609547i	$-0.0194145\pi$
$179$	24.5115	+	6.56785i	1.83208	+	0.490904i	0.833938	+	0.551859i	$0.186081\pi$
$180$	0.173233	+	4.36068i	0.0129120	+	0.325026i
$181$	7.05100	+	7.05100i	0.524097	+	0.524097i	0.918806	−	0.394709i	$-0.129155\pi$
$181$	7.05100	+	7.05100i	0.524097	+	0.524097i	−0.394709	+	0.918806i	$0.629155\pi$
$182$	2.45480	−	6.91391i	0.181962	−	0.512493i
$183$	−15.6484			−1.15676
$184$	−0.111183	−	0.128297i	−0.00819649	−	0.00945815i
$185$	4.12783	+	7.14961i	0.303484	+	0.525650i
$186$	−11.5128	−	4.50313i	−0.844159	−	0.330185i
$187$	−7.72200	−	28.8189i	−0.564689	−	2.10745i
$188$	−15.4685	−	3.49309i	−1.12816	−	0.254760i
$189$	−1.42509	−	4.71568i	−0.103660	−	0.343015i
$190$	10.7302	+	1.19648i	0.778453	+	0.0868020i
$191$	−19.9342	−	11.5090i	−1.44239	−	0.832762i	−0.444378	−	0.895839i	$-0.646575\pi$
$191$	−19.9342	−	11.5090i	−1.44239	−	0.832762i	−0.998009	+	0.0630771i	$0.979909\pi$
$192$	14.5776	−	10.9153i	1.05205	−	0.787745i
$193$	2.99586	+	5.18899i	0.215647	+	0.373512i	0.953473	−	0.301480i	$-0.0974806\pi$
$193$	2.99586	+	5.18899i	0.215647	+	0.373512i	−0.737825	+	0.674992i	$0.764147\pi$
$194$	13.4309	−	18.2422i	0.964280	−	1.30971i
$195$	−3.15629	−	3.15629i	−0.226027	−	0.226027i
$196$	8.82852	−	10.8654i	0.630609	−	0.776101i
$197$	6.70827	−	6.70827i	0.477944	−	0.477944i	−0.426529	−	0.904474i	$-0.640264\pi$
$197$	6.70827	−	6.70827i	0.477944	−	0.477944i	0.904474	+	0.426529i	$0.140264\pi$
$198$	−13.8620	+	2.10571i	−0.985131	+	0.149646i
$199$	−19.2418	+	11.1092i	−1.36401	+	0.787514i	−0.990155	−	0.139972i	$-0.955299\pi$
$199$	−19.2418	+	11.1092i	−1.36401	+	0.787514i	−0.373859	+	0.927486i	$0.621965\pi$
$200$	−0.535444	−	2.77728i	−0.0378616	−	0.196384i
$201$	7.81725	−	13.5399i	0.551386	−	0.955029i
$202$	−16.0599	+	12.8377i	−1.12997	+	0.903254i
$203$	10.2635	−	3.10166i	0.720355	−	0.217694i
$204$	25.2771	−	15.9641i	1.76975	−	1.11771i
$205$	−1.16638	+	0.312530i	−0.0814634	+	0.0218281i
$206$	−5.92329	−	13.5337i	−0.412695	−	0.942940i
$207$	−0.113426	+	0.0654864i	−0.00788363	+	0.00455162i
$208$	−1.42262	+	7.71324i	−0.0986410	+	0.534817i
$209$			34.6877i			2.39940i
$210$	−3.66053	−	7.69086i	−0.252600	−	0.530720i
$211$	−16.8890	+	16.8890i	−1.16269	+	1.16269i	−0.178804	+	0.983885i	$0.557223\pi$
$211$	−16.8890	+	16.8890i	−1.16269	+	1.16269i	−0.983885	+	0.178804i	$0.942777\pi$
$212$	−0.154271	−	3.88337i	−0.0105954	−	0.266711i
$213$	2.58457	−	9.64575i	0.177092	−	0.660916i
$214$	−7.45296	−	2.91516i	−0.509474	−	0.199276i
$215$	5.90402	+	3.40868i	0.402650	+	0.232470i
$216$	2.30142	+	4.73697i	0.156592	+	0.322310i
$217$	10.1545	−	0.321781i	0.689332	−	0.0218439i
$218$	−4.24615	+	3.39421i	−0.287586	+	0.229885i
$219$	−7.00521	+	1.87704i	−0.473368	+	0.126839i
$220$	8.67725	−	2.69850i	0.585020	−	0.181933i
$221$	−3.33252	+	12.4371i	−0.224169	+	0.836612i
$222$	−21.4026	−	15.7577i	−1.43645	−	1.05759i
$223$	6.85824			0.459262			0.229631	−	0.973278i	$-0.426248\pi$
$223$	6.85824			0.459262			0.229631	+	0.973278i	$0.426248\pi$
$224$	−7.48278	+	12.9618i	−0.499964	+	0.866046i
$225$	−2.18206			−0.145471
$226$	11.0038	+	8.10157i	0.731959	+	0.538908i
$227$	−3.21785	+	12.0092i	−0.213576	+	0.797076i	0.773087	+	0.634300i	$0.218712\pi$
$227$	−3.21785	+	12.0092i	−0.213576	+	0.797076i	−0.986663	+	0.162776i	$0.947955\pi$
$228$	−33.1904	+	10.3217i	−2.19809	+	0.683573i
$229$	−7.22827	+	1.93681i	−0.477657	+	0.127988i	−0.489612	−	0.871941i	$-0.662861\pi$
$229$	−7.22827	+	1.93681i	−0.477657	+	0.127988i	0.0119543	+	0.999929i	$0.496195\pi$
$230$	0.0663044	−	0.0530012i	0.00437198	−	0.00349479i
$231$	23.2537	−	14.4263i	1.52998	−	0.949184i
$232$	−10.3098	+	5.00894i	−0.676873	+	0.328853i
$233$	−1.87303	−	1.08139i	−0.122706	−	0.0708444i	0.437391	−	0.899272i	$-0.355903\pi$
$233$	−1.87303	−	1.08139i	−0.122706	−	0.0708444i	−0.560097	+	0.828427i	$0.689236\pi$
$234$	5.63521	+	2.20416i	0.368385	+	0.144091i
$235$	2.05218	−	7.65883i	0.133869	−	0.499607i
$236$	0.390134	+	9.82061i	0.0253956	+	0.639267i
$237$	−17.8087	+	17.8087i	−1.15680	+	1.15680i
$238$	−13.9332	+	20.2370i	−0.903155	+	1.31177i
$239$			20.0237i			1.29522i	0.761970	+	0.647612i	$0.224232\pi$
$239$			20.0237i			1.29522i	−0.761970	+	0.647612i	$0.775768\pi$
$240$	5.16403	+	7.49972i	0.333337	+	0.484105i
$241$	−26.3766	+	15.2286i	−1.69907	+	0.980958i	−0.752425	+	0.658678i	$0.771116\pi$
$241$	−26.3766	+	15.2286i	−1.69907	+	0.980958i	−0.946645	+	0.322280i	$0.895551\pi$
$242$	5.46849	+	12.4946i	0.351528	+	0.803183i
$243$	18.3185	−	4.90844i	1.17513	−	0.314876i
$244$	−11.6241	+	7.34136i	−0.744159	+	0.469982i
$245$	5.25320	+	4.62643i	0.335615	+	0.295572i
$246$	3.03652	−	2.42727i	0.193601	−	0.154757i
$247$	7.48494	−	12.9643i	0.476256	−	0.824899i
$248$	−10.6647	+	2.05609i	−0.677207	+	0.130562i
$249$	−8.41906	+	4.86075i	−0.533536	+	0.308037i
$250$	1.39817	−	0.212389i	0.0884283	−	0.0134327i
$251$	−8.66247	+	8.66247i	−0.546770	+	0.546770i	−0.925505	−	0.378735i	$-0.876359\pi$
$251$	−8.66247	+	8.66247i	−0.546770	+	0.546770i	0.378735	+	0.925505i	$0.376359\pi$
$252$	8.72604	+	7.56142i	0.549689	+	0.476324i
$253$	0.192840	+	0.192840i	0.0121238	+	0.0121238i
$254$	−6.85537	+	9.31113i	−0.430144	+	0.584233i
$255$	7.47406	+	12.9454i	0.468044	+	0.810675i
$256$	5.70787	−	14.9472i	0.356742	−	0.934203i
$257$	−10.4013	−	6.00518i	−0.648814	−	0.374593i	0.139188	−	0.990266i	$-0.455551\pi$
$257$	−10.4013	−	6.00518i	−0.648814	−	0.374593i	−0.788002	+	0.615673i	$0.788884\pi$
$258$	−21.8122	−	2.43219i	−1.35797	−	0.151421i
$259$	21.2666	+	4.98216i	1.32144	+	0.309577i
$260$	−3.82535	−	0.863838i	−0.237238	−	0.0535729i
$261$	2.28868	+	8.54149i	0.141666	+	0.528705i
$262$	2.63393	+	1.03024i	0.162725	+	0.0636484i
$263$	7.30448	+	12.6517i	0.450414	+	0.780139i	0.998412	−	0.0563403i	$-0.0179432\pi$
$263$	7.30448	+	12.6517i	0.450414	+	0.780139i	−0.547998	+	0.836480i	$0.684610\pi$
$264$	−22.1081	+	19.1590i	−1.36066	+	1.17915i
$265$	1.94322			0.119371
$266$	21.7367	−	18.5338i	1.33276	−	1.13638i
$267$	−23.9280	−	23.9280i	−1.46437	−	1.46437i
$268$	−0.545250	−	13.7253i	−0.0333065	−	0.838403i
$269$	18.7665	+	5.02848i	1.14422	+	0.306592i	0.780645	−	0.624975i	$-0.214891\pi$
$269$	18.7665	+	5.02848i	1.14422	+	0.306592i	0.363571	+	0.931567i	$0.381557\pi$
$270$	−2.41230	+	1.05579i	−0.146808	+	0.0642531i
$271$	−11.5168	+	19.9476i	−0.699594	+	1.21173i	0.269014	+	0.963136i	$0.413302\pi$
$271$	−11.5168	+	19.9476i	−0.699594	+	1.21173i	−0.968607	+	0.248595i	$0.920031\pi$
$272$	11.2872	−	23.7172i	0.684387	−	1.43807i
$273$	−11.8038	+	0.374046i	−0.714401	+	0.0226383i
$274$	8.39830	+	0.936459i	0.507360	+	0.0565736i
$275$	1.17597	+	4.38876i	0.0709134	+	0.264652i
$276$	−0.127134	+	0.241898i	−0.00765258	+	0.0145605i
$277$	−12.3040	−	3.29684i	−0.739273	−	0.198088i	−0.130518	−	0.991446i	$-0.541664\pi$
$277$	−12.3040	−	3.29684i	−0.739273	−	0.198088i	−0.608755	+	0.793358i	$0.708331\pi$
$278$	17.6371	−	2.67916i	1.05780	−	0.160685i
$279$			8.37904i			0.501640i
$280$	−6.32727	−	3.99570i	−0.378127	−	0.238789i
$281$		−	9.76160i		−	0.582328i	−0.956673	−	0.291164i	$-0.905957\pi$
$281$		−	9.76160i		−	0.582328i	0.956673	−	0.291164i	$-0.0940426\pi$
$282$	3.83356	+	25.2366i	0.228285	+	1.50282i
$283$	−14.2762	−	3.82530i	−0.848633	−	0.227391i	−0.191807	−	0.981433i	$-0.561435\pi$
$283$	−14.2762	−	3.82530i	−0.848633	−	0.227391i	−0.656826	+	0.754042i	$0.728101\pi$
$284$	−2.60534	−	8.37769i	−0.154599	−	0.497125i
$285$	−4.49806	−	16.7870i	−0.266442	−	0.994375i
$286$	1.39627	−	12.5219i	0.0825631	−	0.740437i
$287$	−1.50897	+	2.81599i	−0.0890718	+	0.166223i
$288$	−10.4893	−	6.50685i	−0.618088	−	0.383420i
$289$	13.0596	−	22.6199i	0.768211	−	1.33058i
$290$	−2.29787	−	5.25026i	−0.134936	−	0.308306i
$291$	−35.2215	−	9.43758i	−2.06472	−	0.553241i
$292$	−4.32309	+	4.68078i	−0.252990	+	0.273922i
$293$	−9.74998	−	9.74998i	−0.569600	−	0.569600i	0.362417	−	0.932016i	$-0.381952\pi$
$293$	−9.74998	−	9.74998i	−0.569600	−	0.569600i	−0.932016	+	0.362417i	$0.881952\pi$
$294$	−21.4647	−	6.86367i	−1.25184	−	0.400297i
$295$	−4.91418			−0.286114
$296$	−23.2911	−	1.66446i	−1.35377	−	0.0967447i
$297$	−4.23001	−	7.32658i	−0.245450	−	0.425132i
$298$	−10.6774	+	27.2982i	−0.618528	+	1.58134i
$299$	−0.0304615	−	0.113684i	−0.00176163	−	0.00657451i
$300$	−3.84940	+	2.43113i	−0.222245	+	0.140361i
$301$	17.2659	−	5.21781i	0.995188	−	0.300749i
$302$	1.81717	−	16.2966i	0.104566	−	0.937766i
$303$	28.6613	+	16.5476i	1.64655	+	0.950636i
$304$	−19.8125	+	23.2384i	−1.13632	+	1.33281i
$305$	−3.43708	−	5.95319i	−0.196806	−	0.340879i
$306$	−16.3179	−	12.0141i	−0.932833	−	0.686803i
$307$	−13.6907	−	13.6907i	−0.781370	−	0.781370i	0.198692	−	0.980062i	$-0.436331\pi$
$307$	−13.6907	−	13.6907i	−0.781370	−	0.781370i	−0.980062	+	0.198692i	$0.936331\pi$
$308$	10.5055	−	21.6257i	0.598609	−	1.23224i
$309$	−16.8150	+	16.8150i	−0.956570	+	0.956570i
$310$	−0.815568	−	5.36894i	−0.0463211	−	0.304935i
$311$	8.76618	−	5.06116i	0.497085	−	0.286992i	−0.230424	−	0.973090i	$-0.574011\pi$
$311$	8.76618	−	5.06116i	0.497085	−	0.286992i	0.727509	+	0.686098i	$0.240678\pi$
$312$	12.3969	−	2.39005i	0.701835	−	0.135310i
$313$	10.8843	−	18.8521i	0.615216	−	1.06559i	−0.375131	−	0.926972i	$-0.622402\pi$
$313$	10.8843	−	18.8521i	0.615216	−	1.06559i	0.990347	−	0.138613i	$-0.0442645\pi$
$314$	−14.0258	−	17.5463i	−0.791523	−	0.990194i
$315$	−3.95092	+	4.20951i	−0.222609	+	0.237179i
$316$	−4.87402	+	21.5837i	−0.274185	+	1.21418i
$317$	6.48375	−	1.73732i	0.364164	−	0.0975773i	−0.0720972	−	0.997398i	$-0.522969\pi$
$317$	6.48375	−	1.73732i	0.364164	−	0.0975773i	0.436261	+	0.899820i	$0.356303\pi$
$318$	−5.73100	+	2.50828i	−0.321378	+	0.140657i
$319$	15.9460	−	9.20643i	0.892805	−	0.515461i
$320$	7.35445	+	3.14835i	0.411126	+	0.175998i
$321$			12.8819i			0.718995i
$322$	0.0178063	−	0.223877i	0.000992307	−	0.0124762i
$323$	−35.4485	+	35.4485i	−1.97241	+	1.97241i
$324$	14.6346	−	15.8454i	0.813031	−	0.880300i
$325$	0.507501	−	1.89402i	0.0281511	−	0.105061i
$326$	0.428761	−	1.09618i	0.0237469	−	0.0607117i
$327$	7.57790	+	4.37510i	0.419059	+	0.241944i
$328$	1.11688	−	3.22762i	0.0616693	−	0.178215i
$329$	−11.0592	−	17.8263i	−0.609716	−	0.982796i
$330$	−9.13316	−	11.4256i	−0.502764	−	0.628957i
$331$	−20.3196	+	5.44463i	−1.11687	+	0.299264i	−0.769616	−	0.638507i	$-0.779552\pi$
$331$	−20.3196	+	5.44463i	−1.11687	+	0.299264i	−0.347253	+	0.937771i	$0.612886\pi$
$332$	−3.97355	+	7.56046i	−0.218077	+	0.414934i
$333$	−4.66246	+	17.4005i	−0.255501	+	0.953543i
$334$	−2.71152	+	3.68286i	−0.148368	+	0.201517i
$335$	6.86804			0.375241
$336$	23.8182	+	3.61710i	1.29939	+	0.197329i
$337$	21.6942			1.18176			0.590879	−	0.806760i	$-0.298781\pi$
$337$	21.6942			1.18176			0.590879	+	0.806760i	$0.298781\pi$
$338$	7.67636	−	10.4262i	0.417539	−	0.567112i
$339$	5.69280	−	21.2458i	0.309190	−	1.15391i
$340$	11.6252	+	6.10987i	0.630467	+	0.331354i
$341$	16.8527	−	4.51567i	0.912625	−	0.244537i
$342$	14.7101	+	18.4023i	0.795431	+	0.995084i
$343$	18.4367	−	1.75740i	0.995488	−	0.0948908i
$344$	−17.3438	+	8.42636i	−0.935117	+	0.454319i
$345$	−0.118330	−	0.0683180i	−0.00637069	−	0.00367812i
$346$	9.76262	−	24.9593i	0.524842	−	1.34182i
$347$	−8.36511	+	31.2190i	−0.449062	+	1.67592i	0.255919	+	0.966698i	$0.417622\pi$
$347$	−8.36511	+	31.2190i	−0.449062	+	1.67592i	−0.704981	+	0.709226i	$0.749045\pi$
$348$	13.5539	+	12.5182i	0.726568	+	0.671046i
$349$	10.4924	−	10.4924i	0.561648	−	0.561648i	−0.368128	−	0.929775i	$-0.620001\pi$
$349$	10.4924	−	10.4924i	0.561648	−	0.561648i	0.929775	+	0.368128i	$0.120001\pi$
$350$	2.12185	−	3.08184i	0.113418	−	0.164731i
$351$			3.65101i			0.194877i
$352$	−7.43424	+	24.6038i	−0.396246	+	1.31138i
$353$	16.3978	−	9.46728i	0.872767	−	0.503893i	0.00450056	−	0.999990i	$-0.498567\pi$
$353$	16.3978	−	9.46728i	0.872767	−	0.503893i	0.868267	+	0.496097i	$0.165234\pi$
$354$	14.4931	−	6.34315i	0.770298	−	0.337135i
$355$	4.23726	−	1.13537i	0.224890	−	0.0602591i
$356$	−29.0002	−	6.54880i	−1.53701	−	0.347086i
$357$	38.5064	+	9.02096i	2.03798	+	0.477440i
$358$	−22.4077	−	28.0321i	−1.18429	−	1.48154i
$359$	−4.40482	+	7.62938i	−0.232478	+	0.402663i	−0.958537	−	0.284969i	$-0.908017\pi$
$359$	−4.40482	+	7.62938i	−0.232478	+	0.402663i	0.726059	+	0.687632i	$0.241350\pi$
$360$	3.45904	−	5.11137i	0.182308	−	0.269393i
$361$	34.0216	−	19.6424i	1.79061	−	1.03381i
$362$	−2.11787	−	13.9421i	−0.111313	−	0.732779i
$363$	15.5239	−	15.5239i	0.814792	−	0.814792i
$364$	−8.59278	+	5.81555i	−0.450384	+	0.304818i
$365$	−2.25274	−	2.25274i	−0.117914	−	0.117914i
$366$	17.8211	+	13.1208i	0.931521	+	0.685837i
$367$	−6.93838	−	12.0176i	−0.362180	−	0.627315i	0.626139	−	0.779711i	$-0.284634\pi$
$367$	−6.93838	−	12.0176i	−0.362180	−	0.627315i	−0.988319	+	0.152397i	$0.951301\pi$
$368$	0.0190456	+	0.239333i	0.000992821	+	0.0124761i
$369$	−2.28188	−	1.31745i	−0.118790	−	0.0685835i
$370$	1.29384	−	11.6034i	0.0672636	−	0.603230i
$371$	3.51846	−	3.74874i	0.182669	−	0.194625i
$372$	9.33546	+	14.7815i	0.484021	+	0.766387i
$373$	−0.923951	−	3.44823i	−0.0478404	−	0.178543i	0.937872	−	0.346983i	$-0.112794\pi$
$373$	−0.923951	−	3.44823i	−0.0478404	−	0.178543i	−0.985712	+	0.168440i	$0.946127\pi$
$374$	−15.3698	+	39.2948i	−0.794756	+	2.03189i
$375$	−1.13821	−	1.97143i	−0.0587768	−	0.101804i
$376$	14.6873	+	16.9481i	0.757439	+	0.874029i
$377$	−7.94628			−0.409254
$378$	−2.33103	+	6.56531i	−0.119895	+	0.337683i
$379$	17.4308	+	17.4308i	0.895360	+	0.895360i	0.995021	−	0.0996611i	$-0.0317759\pi$
$379$	17.4308	+	17.4308i	0.895360	+	0.895360i	−0.0996611	+	0.995021i	$0.531776\pi$
$380$	−11.2168	−	10.3597i	−0.575410	−	0.531439i
$381$	17.9777	+	4.81712i	0.921027	+	0.246788i
$382$	13.0518	+	29.8213i	0.667789	+	1.52579i
$383$	12.9587	−	22.4451i	0.662159	−	1.14689i	−0.317888	−	0.948128i	$-0.602974\pi$
$383$	12.9587	−	22.4451i	0.662159	−	1.14689i	0.980047	−	0.198765i	$-0.0636930\pi$
$384$	−25.7538	+	0.207798i	−1.31425	+	0.0106041i
$385$	10.5958	+	5.67785i	0.540012	+	0.289370i
$386$	0.939034	−	8.42139i	0.0477956	−	0.428638i
$387$	3.85017	+	14.3690i	0.195715	+	0.730419i
$388$	−30.5912	+	9.51343i	−1.55303	+	0.482971i
$389$	−15.9813	−	4.28219i	−0.810286	−	0.217116i	−0.170191	−	0.985411i	$-0.554438\pi$
$389$	−15.9813	−	4.28219i	−0.810286	−	0.217116i	−0.640095	+	0.768296i	$0.721105\pi$
$390$	0.948036	+	6.24099i	0.0480057	+	0.316025i
$391$			0.394139i			0.0199325i
$392$	−19.1647	+	4.97146i	−0.967962	+	0.251097i
$393$		−	4.55254i		−	0.229645i
$394$	−13.2644	+	2.01492i	−0.668249	+	0.101510i
$395$	−10.6866	−	2.86347i	−0.537702	−	0.144077i
$396$	17.5522	+	9.22491i	0.882032	+	0.463569i
$397$	−3.56402	−	13.3011i	−0.178873	−	0.667563i	−0.995859	−	0.0909063i	$-0.971024\pi$
$397$	−3.56402	−	13.3011i	−0.178873	−	0.667563i	0.816986	−	0.576657i	$-0.195643\pi$
$398$	31.2282	+	3.48212i	1.56533	+	0.174543i
$399$	−40.5288	−	21.7177i	−2.02898	−	1.08725i
$400$	−1.71890	+	3.61184i	−0.0859450	+	0.180592i
$401$	6.94398	−	12.0273i	0.346766	−	0.600616i	−0.638907	−	0.769284i	$-0.720613\pi$
$401$	6.94398	−	12.0273i	0.346766	−	0.600616i	0.985673	+	0.168668i	$0.0539465\pi$
$402$	−20.2555	+	8.86518i	−1.01025	+	0.442155i
$403$	−7.27298	−	1.94879i	−0.362293	−	0.0970760i
$404$	29.0537	−	1.15419i	1.44548	−	0.0574231i
$405$	7.62600	+	7.62600i	0.378939	+	0.378939i
$406$	−14.2891	−	5.07339i	−0.709158	−	0.251788i
$407$	37.5103			1.85932
$408$	−42.1721	−	3.01375i	−2.08783	−	0.149203i
$409$	−11.8912	−	20.5961i	−0.587981	−	1.01841i	−0.994497	−	0.104769i	$-0.966590\pi$
$409$	−11.8912	−	20.5961i	−0.587981	−	1.01841i	0.406516	−	0.913644i	$-0.366744\pi$
$410$	1.59037	+	0.622059i	0.0785427	+	0.0307213i
$411$	−3.52052	−	13.1388i	−0.173655	−	0.648087i
$412$	−4.60204	+	20.3793i	−0.226726	+	1.00402i
$413$	−8.89779	+	9.48016i	−0.437831	+	0.466488i
$414$	0.184083	+	0.0205263i	0.00904716	+	0.00100881i
$415$	−3.69839	−	2.13527i	−0.181547	−	0.104816i
$416$	8.08751	−	7.59132i	0.396523	−	0.372195i
$417$	−14.3578	−	24.8684i	−0.703104	−	1.21781i
$418$	29.0848	−	39.5038i	1.42259	−	1.93219i
$419$	−22.2039	−	22.2039i	−1.08473	−	1.08473i	−0.996061	−	0.0886722i	$-0.971738\pi$
$419$	−22.2039	−	22.2039i	−1.08473	−	1.08473i	−0.0886722	−	0.996061i	$-0.528262\pi$
$420$	−2.27985	+	11.8279i	−0.111245	+	0.577144i
$421$	−1.05020	+	1.05020i	−0.0511834	+	0.0511834i	−0.732235	−	0.681052i	$-0.761523\pi$
$421$	−1.05020	+	1.05020i	−0.0511834	+	0.0511834i	0.681052	+	0.732235i	$0.261523\pi$
$422$	33.3950	−	5.07285i	1.62564	−	0.246943i
$423$	14.9836	−	8.65079i	0.728528	−	0.420616i
$424$	−3.08042	+	4.55189i	−0.149599	+	0.221059i
$425$	−3.28326	+	5.68677i	−0.159261	+	0.275849i
$426$	−11.0311	+	8.81786i	−0.534461	+	0.427227i
$427$	−17.7079	−	4.14845i	−0.856943	−	0.200757i
$428$	6.04344	+	9.56904i	0.292121	+	0.462537i
$429$	−19.5900	+	5.24913i	−0.945814	+	0.253430i
$430$	−3.86563	−	8.83233i	−0.186417	−	0.425933i
$431$	−34.6068	+	19.9802i	−1.66695	+	0.962414i	−0.697682	+	0.716408i	$0.745785\pi$
$431$	−34.6068	+	19.9802i	−1.66695	+	0.962414i	−0.969268	+	0.246006i	$0.920882\pi$
$432$	1.35089	−	7.32434i	0.0649948	−	0.352392i
$433$			6.60867i			0.317593i	0.987311	+	0.158796i	$0.0507613\pi$
$433$			6.60867i			0.317593i	−0.987311	+	0.158796i	$0.949239\pi$
$434$	−11.8342	−	8.14785i	−0.568058	−	0.391109i
$435$	−6.52318	+	6.52318i	−0.312762	+	0.312762i
$436$	7.68165	−	0.305162i	0.367885	−	0.0146146i
$437$	0.118601	−	0.442624i	0.00567345	−	0.0211736i
$438$	9.55167	+	3.73606i	0.456397	+	0.178516i
$439$	−11.4841	−	6.63034i	−0.548105	−	0.316449i	0.200252	−	0.979744i	$-0.435824\pi$
$439$	−11.4841	−	6.63034i	−0.548105	−	0.316449i	−0.748358	+	0.663296i	$0.769157\pi$
$440$	−12.1446	−	4.20251i	−0.578973	−	0.200347i
$441$	0.967076	+	15.2438i	0.0460513	+	0.725894i
$442$	14.2234	−	11.3697i	0.676540	−	0.540800i
$443$	3.62568	−	0.971498i	0.172261	−	0.0461573i	−0.171657	−	0.985157i	$-0.554912\pi$
$443$	3.62568	−	0.971498i	0.172261	−	0.0461573i	0.343919	+	0.938999i	$0.388246\pi$
$444$	11.1616	+	35.8911i	0.529707	+	1.70332i
$445$	3.84740	−	14.3587i	0.182384	−	0.680667i
$446$	−7.81044	−	5.75047i	−0.369835	−	0.272293i
$447$	47.1827			2.23167
$448$	19.3898	−	8.48727i	0.916084	−	0.400986i
$449$	−12.7667			−0.602497			−0.301248	−	0.953546i	$-0.597403\pi$
$449$	−12.7667			−0.602497			−0.301248	+	0.953546i	$0.597403\pi$
$450$	2.48502	+	1.82961i	0.117145	+	0.0862485i
$451$	−1.42001	+	5.29954i	−0.0668655	+	0.249546i
$452$	−5.73855	−	18.4528i	−0.269919	−	0.867946i
$453$	−25.4954	+	6.83146i	−1.19788	+	0.320970i
$454$	13.7340	−	10.9784i	0.644569	−	0.515243i
$455$	−2.73494	−	4.40843i	−0.128216	−	0.206670i
$456$	46.4531	+	16.0746i	2.17537	+	0.752760i
$457$	−1.99979	−	1.15458i	−0.0935464	−	0.0540091i	0.452497	−	0.891766i	$-0.350533\pi$
$457$	−1.99979	−	1.15458i	−0.0935464	−	0.0540091i	−0.546043	+	0.837757i	$0.683867\pi$
$458$	9.85581	+	3.85502i	0.460532	+	0.180133i
$459$	3.16449	−	11.8100i	0.147706	−	0.551246i
$460$	−0.119950	+	0.00476516i	−0.00559272	+	0.000222177i
$461$	2.55823	−	2.55823i	0.119149	−	0.119149i	−0.645018	−	0.764167i	$-0.723150\pi$
$461$	2.55823	−	2.55823i	0.119149	−	0.119149i	0.764167	+	0.645018i	$0.223150\pi$
$462$	−38.5784	−	3.06838i	−1.79483	−	0.142754i
$463$			9.35347i			0.434692i	0.976095	+	0.217346i	$0.0697401\pi$
$463$			9.35347i			0.434692i	−0.976095	+	0.217346i	$0.930260\pi$
$464$	15.9411	+	2.94016i	0.740048	+	0.136494i
$465$	−7.57023	+	4.37068i	−0.351061	+	0.202685i
$466$	1.22636	+	2.80202i	0.0568099	+	0.129801i
$467$	27.7831	−	7.44445i	1.28565	−	0.344488i	0.449642	−	0.893209i	$-0.351552\pi$
$467$	27.7831	−	7.44445i	1.28565	−	0.344488i	0.836006	+	0.548721i	$0.184885\pi$
$468$	−4.56946	−	7.23518i	−0.211223	−	0.334446i
$469$	12.4355	−	13.2494i	0.574219	−	0.611802i
$470$	−8.75885	+	7.00148i	−0.404016	+	0.322954i
$471$	−18.0792	+	31.3140i	−0.833043	+	1.44287i
$472$	7.79005	−	11.5112i	0.358566	−	0.529847i
$473$	26.8254	−	15.4876i	1.23343	−	0.712123i
$474$	35.2135	−	5.34910i	1.61741	−	0.245692i
$475$	5.39837	−	5.39837i	0.247694	−	0.247694i
$476$	32.8359	−	11.3640i	1.50503	−	0.520868i
$477$	2.99828	+	2.99828i	0.137282	+	0.137282i
$478$	16.7894	−	22.8038i	0.767929	−	1.04302i
$479$	10.0240	+	17.3621i	0.458009	+	0.793294i	0.998856	−	0.0478268i	$-0.0152295\pi$
$479$	10.0240	+	17.3621i	0.458009	+	0.793294i	−0.540847	+	0.841121i	$0.681896\pi$
$480$	0.407329	−	12.8709i	0.0185919	−	0.587473i
$481$	−14.0192	−	8.09399i	−0.639221	−	0.369054i
$482$	42.8076	+	4.77329i	1.94983	+	0.217418i
$483$	−0.346048	+	0.104577i	−0.0157457	+	0.00475842i
$484$	4.24869	−	18.8145i	0.193122	−	0.855207i
$485$	−4.14581	−	15.4724i	−0.188252	−	0.702565i
$486$	−24.9775	−	9.76974i	−1.13300	−	0.443164i
$487$	−9.16065	−	15.8667i	−0.415108	−	0.718989i	0.580331	−	0.814380i	$-0.302923\pi$
$487$	−9.16065	−	15.8667i	−0.415108	−	0.718989i	−0.995440	+	0.0953915i	$0.969590\pi$
$488$	19.3936	+	1.38593i	0.877906	+	0.0627380i
$489$	−1.89466			−0.0856794
$490$	−2.10340	−	9.67345i	−0.0950222	−	0.437002i
$491$	25.0786	+	25.0786i	1.13178	+	1.13178i	0.989881	+	0.141902i	$0.0453219\pi$
$491$	25.0786	+	25.0786i	1.13178	+	1.13178i	0.141902	+	0.989881i	$0.454678\pi$
$492$	−5.49332	+	0.218228i	−0.247658	+	0.00983847i
$493$	25.7041	+	6.88739i	1.15765	+	0.310192i
$494$	−19.3944	+	8.48832i	−0.872596	+	0.381908i
$495$	−4.95719	+	8.58610i	−0.222809	+	0.385916i
$496$	13.8693	+	6.60052i	0.622752	+	0.296372i
$497$	5.48184	−	10.2300i	0.245894	−	0.458879i
$498$	13.6636	+	1.52357i	0.612280	+	0.0682728i
$499$	4.31084	+	16.0883i	0.192980	+	0.720210i	0.992781	+	0.119944i	$0.0382716\pi$
$499$	4.31084	+	16.0883i	0.192980	+	0.720210i	−0.799801	+	0.600265i	$0.795062\pi$
$500$	−1.77038	−	0.930459i	−0.0791738	−	0.0416114i
$501$	7.11078	+	1.90533i	0.317686	+	0.0851238i
$502$	17.1284	−	2.60189i	0.764480	−	0.116128i
$503$			13.0734i			0.582914i	0.956584	+	0.291457i	$0.0941401\pi$
$503$			13.0734i			0.582914i	−0.956584	+	0.291457i	$0.905860\pi$
$504$	−3.59750	−	15.9278i	−0.160245	−	0.709482i
$505$			14.5383i			0.646947i
$506$	−0.0579222	−	0.381306i	−0.00257496	−	0.0169511i
$507$	−20.1307	−	5.39401i	−0.894037	−	0.239556i
$508$	15.6143	−	4.85583i	0.692774	−	0.215443i
$509$	−2.35751	−	8.79836i	−0.104495	−	0.389980i	0.893792	−	0.448481i	$-0.148035\pi$
$509$	−2.35751	−	8.79836i	−0.104495	−	0.389980i	−0.998287	+	0.0585004i	$0.981368\pi$
$510$	2.34269	−	21.0096i	0.103736	−	0.930322i
$511$	−8.42476	+	0.266968i	−0.372689	+	0.0118100i
$512$	−19.0333	+	12.2366i	−0.841160	+	0.540787i
$513$	−7.10755	+	12.3106i	−0.313806	+	0.543528i
$514$	6.81019	+	15.5602i	0.300385	+	0.686330i
$515$	−10.0903	−	2.70368i	−0.444631	−	0.119139i
$516$	22.8013	+	21.0589i	1.00377	+	0.927067i
$517$	−25.4743	−	25.4743i	−1.12036	−	1.12036i
$518$	−20.0419	−	23.5055i	−0.880589	−	1.03277i
$519$	−43.1402			−1.89364
$520$	3.63215	+	4.19124i	0.159280	+	0.183798i
$521$	1.82382	+	3.15896i	0.0799032	+	0.138396i	0.903208	−	0.429203i	$-0.141206\pi$
$521$	1.82382	+	3.15896i	0.0799032	+	0.138396i	−0.823305	+	0.567599i	$0.807872\pi$
$522$	4.55539	−	11.6464i	0.199384	−	0.509749i
$523$	6.93737	+	25.8906i	0.303350	+	1.13212i	0.934356	+	0.356340i	$0.115975\pi$
$523$	6.93737	+	25.8906i	0.303350	+	1.13212i	−0.631007	+	0.775777i	$0.717358\pi$
$524$	−2.13579	−	3.38176i	−0.0933026	−	0.147733i
$525$	−5.86406	−	1.37378i	−0.255928	−	0.0599567i
$526$	2.28954	−	20.5329i	0.0998288	−	0.895279i
$527$	21.8370	+	12.6076i	0.951235	+	0.549196i
$528$	41.2419	−	3.28194i	1.79482	−	0.142828i
$529$	11.4982	+	19.9155i	0.499922	+	0.865890i
$530$	−2.21301	−	1.62934i	−0.0961271	−	0.0707740i
$531$	−7.58233	−	7.58233i	−0.329045	−	0.329045i
$532$	−40.2948	+	2.88126i	−1.74700	+	0.124919i
$533$	1.67426	−	1.67426i	0.0725201	−	0.0725201i
$534$	7.18712	+	47.3133i	0.311017	+	2.04745i
$535$	−4.90069	+	2.82942i	−0.211876	+	0.122326i
$536$	−10.8874	+	16.0881i	−0.470262	+	0.694898i
$537$	−28.8834	+	50.0275i	−1.24641	+	2.15885i
$538$	−17.1558	−	21.4619i	−0.739640	−	0.925289i
$539$	30.1385	−	10.1603i	1.29816	−	0.437636i
$540$	3.63247	+	0.820283i	0.156317	+	0.0352993i
$541$	−18.0560	+	4.83810i	−0.776289	+	0.208006i	−0.625148	−	0.780506i	$-0.714961\pi$
$541$	−18.0560	+	4.83810i	−0.776289	+	0.208006i	−0.151141	+	0.988512i	$0.548295\pi$
$542$	29.8414	−	13.0606i	1.28180	−	0.561002i
$543$	−19.6584	+	11.3498i	−0.843622	+	0.487065i
$544$	−32.7406	+	17.5461i	−1.40374	+	0.752281i
$545$			3.84386i			0.164653i
$546$	13.7563	+	9.47126i	0.588716	+	0.405333i
$547$	3.78915	−	3.78915i	0.162013	−	0.162013i	−0.621445	−	0.783458i	$-0.713454\pi$
$547$	3.78915	−	3.78915i	0.162013	−	0.162013i	0.783458	+	0.621445i	$0.213454\pi$
$548$	−8.77912	−	8.10825i	−0.375025	−	0.346367i
$549$	3.88224	−	14.4887i	0.165690	−	0.618363i
$550$	2.34064	−	5.98412i	0.0998052	−	0.255164i
$551$	−26.7936	−	15.4693i	−1.14145	−	0.659014i
$552$	0.347611	−	0.168884i	0.0147953	−	0.00718818i
$553$	−24.8736	+	15.4313i	−1.05773	+	0.656207i
$554$	11.2479	+	14.0711i	0.477879	+	0.597826i
$555$	−18.1529	+	4.86406i	−0.770549	+	0.206468i
$556$	−22.3323	−	11.7372i	−0.947099	−	0.497767i
$557$	−8.84414	+	33.0068i	−0.374738	+	1.39854i	0.478989	+	0.877821i	$0.341003\pi$
$557$	−8.84414	+	33.0068i	−0.374738	+	1.39854i	−0.853727	+	0.520721i	$0.825663\pi$
$558$	7.02563	−	9.54238i	0.297418	−	0.403961i
$559$	−13.3677			−0.565395
$560$	3.85545	+	9.85573i	0.162923	+	0.416481i
$561$	67.9180			2.86750
$562$	−8.18487	+	11.1169i	−0.345258	+	0.468938i
$563$	−1.64962	+	6.15646i	−0.0695231	+	0.259464i	−0.991936	−	0.126742i	$-0.959548\pi$
$563$	−1.64962	+	6.15646i	−0.0695231	+	0.259464i	0.922413	+	0.386206i	$0.126215\pi$
$564$	16.7945	−	31.9548i	0.707176	−	1.34554i
$565$	9.33301	−	2.50077i	0.392643	−	0.105208i
$566$	13.0509	+	16.3267i	0.548571	+	0.686261i
$567$	28.5196	−	0.903743i	1.19771	−	0.0379536i
$568$	−4.05743	+	11.7254i	−0.170246	+	0.491986i
$569$	12.2442	+	7.06920i	0.513304	+	0.296356i	0.734191	−	0.678943i	$-0.237562\pi$
$569$	12.2442	+	7.06920i	0.513304	+	0.296356i	−0.220887	+	0.975299i	$0.570895\pi$
$570$	−8.95292	+	22.8892i	−0.374996	+	0.958723i
$571$	8.30880	−	31.0089i	0.347713	−	1.29768i	−0.541699	−	0.840573i	$-0.682219\pi$
$571$	8.30880	−	31.0089i	0.347713	−	1.29768i	0.889411	−	0.457108i	$-0.151115\pi$
$572$	−12.0895	+	13.0897i	−0.505486	+	0.547310i
$573$	37.0513	−	37.0513i	1.54784	−	1.54784i
$574$	4.07962	−	1.94173i	0.170280	−	0.0810461i
$575$		−	0.0600225i		−	0.00250311i
$576$	6.48980	+	16.2053i	0.270408	+	0.675220i
$577$	−2.85679	+	1.64937i	−0.118930	+	0.0686641i	−0.558285	−	0.829649i	$-0.688540\pi$
$577$	−2.85679	+	1.64937i	−0.118930	+	0.0686641i	0.439355	+	0.898313i	$0.355207\pi$
$578$	−33.8390	+	14.8103i	−1.40752	+	0.616026i
$579$	−13.1749	+	3.53020i	−0.547530	+	0.146710i
$580$	−1.78531	+	7.90593i	−0.0741310	+	0.328276i
$581$	−10.8157	+	3.26854i	−0.448710	+	0.135602i
$582$	32.1985	+	40.2803i	1.33467	+	1.66967i
$583$	4.41458	−	7.64628i	0.182833	−	0.316676i
$584$	8.84803	−	1.70585i	0.366134	−	0.0705885i
$585$	3.70543	−	2.13933i	0.153201	−	0.0884504i
$586$	2.92854	+	19.2788i	0.120977	+	0.796399i
$587$	15.9400	−	15.9400i	0.657915	−	0.657915i	−0.296971	−	0.954886i	$-0.595977\pi$
$587$	15.9400	−	15.9400i	0.657915	−	0.657915i	0.954886	+	0.296971i	$0.0959766\pi$
$588$	18.6898	+	25.8142i	0.770754	+	1.06456i
$589$	−20.7295	−	20.7295i	−0.854146	−	0.854146i
$590$	5.59646	+	4.12042i	0.230403	+	0.169635i
$591$	10.7981	+	18.7028i	0.444174	+	0.769331i
$592$	25.1293	+	21.4246i	1.03281	+	0.880546i
$593$	−1.02539	−	0.592007i	−0.0421076	−	0.0243108i	0.478798	−	0.877925i	$-0.341072\pi$
$593$	−1.02539	−	0.592007i	−0.0421076	−	0.0243108i	−0.520906	+	0.853614i	$0.674406\pi$
$594$	−1.32587	+	11.8906i	−0.0544010	+	0.487876i
$595$	5.02582	+	16.6306i	0.206038	+	0.681786i
$596$	35.0488	−	22.1355i	1.43565	−	0.906704i
$597$	−13.0907	−	48.8551i	−0.535766	−	1.99951i
$598$	−0.0606305	+	0.155009i	−0.00247936	+	0.00633879i
$599$	−16.2765	−	28.1917i	−0.665038	−	1.15188i	−0.979275	−	0.202535i	$-0.935082\pi$
$599$	−16.2765	−	28.1917i	−0.665038	−	1.15188i	0.314237	−	0.949345i	$-0.398251\pi$
$600$	6.42229	+	0.458958i	0.262189	+	0.0187369i
$601$	16.0377			0.654190			0.327095	−	0.944991i	$-0.393930\pi$
$601$	16.0377			0.654190			0.327095	+	0.944991i	$0.393930\pi$
$602$	−24.0381	−	8.53477i	−0.979719	−	0.347851i
$603$	10.5970	+	10.5970i	0.431545	+	0.431545i
$604$	−15.7338	+	17.0356i	−0.640200	+	0.693169i
$605$	9.31553	+	2.49609i	0.378730	+	0.101480i
$606$	−18.7659	−	42.8769i	−0.762312	−	1.74176i
$607$	−12.1899	+	21.1135i	−0.494771	+	0.856969i	−0.999982	−	0.00602729i	$-0.998081\pi$
$607$	−12.1899	+	21.1135i	−0.494771	+	0.856969i	0.505211	+	0.862996i	$0.331415\pi$
$608$	42.0481	−	9.85249i	1.70527	−	0.399571i
$609$	0.773049	+	24.3952i	0.0313255	+	0.988545i
$610$	−1.07733	+	9.66164i	−0.0436198	+	0.391189i
$611$	4.02398	+	15.0177i	0.162793	+	0.607551i
$612$	8.50993	+	27.3644i	0.343993	+	1.10614i
$613$	34.8290	+	9.33240i	1.40673	+	0.376932i	0.880756	−	0.473569i	$-0.157035\pi$
$613$	34.8290	+	9.33240i	1.40673	+	0.376932i	0.525973	+	0.850501i	$0.323701\pi$
$614$	4.11219	+	27.0709i	0.165955	+	1.09249i
$615$		−	2.74883i		−	0.110843i
$616$	−30.0968	+	15.8195i	−1.21263	+	0.637387i
$617$			2.70939i			0.109076i	0.998512	+	0.0545379i	$0.0173686\pi$
$617$			2.70939i			0.109076i	−0.998512	+	0.0545379i	$0.982631\pi$
$618$	33.2485	−	5.05061i	1.33745	−	0.203165i
$619$	8.61593	+	2.30863i	0.346303	+	0.0927917i	0.427778	−	0.903884i	$-0.359296\pi$
$619$	8.61593	+	2.30863i	0.346303	+	0.0927917i	−0.0814749	+	0.996675i	$0.525963\pi$
$620$	−3.57293	+	6.79820i	−0.143492	+	0.273022i
$621$	0.0289256	+	0.107952i	0.00116075	+	0.00433196i
$622$	−14.2269	−	1.58639i	−0.570449	−	0.0636083i
$623$	−20.7337	−	33.4205i	−0.830680	−	1.33897i
$624$	−16.1221	−	7.67261i	−0.645399	−	0.307150i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−28.2025	+	12.3433i	−1.12720	+	0.493339i
$627$	−76.2730	−	20.4373i	−3.04605	−	0.816187i
$628$	1.26101	+	31.7427i	0.0503199	+	1.26667i
$629$	38.3329	+	38.3329i	1.52843	+	1.52843i
$630$	8.02904	−	1.48121i	0.319885	−	0.0590127i
$631$	−25.2411			−1.00483			−0.502415	−	0.864626i	$-0.667555\pi$
$631$	−25.2411			−1.00483			−0.502415	+	0.864626i	$0.667555\pi$
$632$	23.6482	−	20.4937i	0.940674	−	0.815194i
$633$	−27.1857	−	47.0870i	−1.08054	−	1.87154i
$634$	−8.84065	−	3.45795i	−0.351107	−	0.137333i
$635$	2.11610	+	7.89739i	0.0839748	+	0.313398i
$636$	8.62982	+	1.94878i	0.342195	+	0.0772742i
$637$	−13.4565	−	2.70596i	−0.533165	−	0.107214i
$638$	−25.8793	−	2.88570i	−1.02457	−	0.114246i
$639$	8.28969	+	4.78605i	0.327935	+	0.189333i
$640$	−5.73572	−	9.75200i	−0.226724	−	0.385482i
$641$	7.10420	+	12.3048i	0.280599	+	0.486012i	0.971532	−	0.236907i	$-0.0761336\pi$
$641$	7.10420	+	12.3048i	0.280599	+	0.486012i	−0.690933	+	0.722918i	$0.742800\pi$
$642$	10.8011	−	14.6704i	0.426287	−	0.578993i
$643$	1.94867	+	1.94867i	0.0768481	+	0.0768481i	0.744486	−	0.667638i	$-0.232695\pi$
$643$	1.94867	+	1.94867i	0.0768481	+	0.0768481i	−0.667638	+	0.744486i	$0.732695\pi$
$644$	−0.207994	+	0.240030i	−0.00819610	+	0.00945849i
$645$	−10.9737	+	10.9737i	−0.432089	+	0.432089i
$646$	70.0929	−	10.6474i	2.75777	−	0.418918i
$647$	9.62909	−	5.55936i	0.378559	−	0.218561i	−0.298632	−	0.954368i	$-0.596530\pi$
$647$	9.62909	−	5.55936i	0.378559	−	0.218561i	0.677191	+	0.735807i	$0.263197\pi$
$648$	−29.9524	+	5.77466i	−1.17664	+	0.226850i
$649$	−11.1640	+	19.3366i	−0.438225	+	0.759028i
$650$	−2.16606	+	1.73146i	−0.0849597	+	0.0679134i
$651$	−5.27527	+	22.5178i	−0.206754	+	0.882541i
$652$	−1.40741	+	0.888866i	−0.0551184	+	0.0348107i
$653$	7.56837	−	2.02794i	0.296173	−	0.0793594i	−0.107673	−	0.994186i	$-0.534340\pi$
$653$	7.56837	−	2.02794i	0.296173	−	0.0793594i	0.403846	+	0.914827i	$0.367673\pi$
$654$	−4.96160	−	11.3364i	−0.194014	−	0.443290i
$655$	1.73194	−	0.999936i	0.0676725	−	0.0390707i
$656$	−3.97823	+	2.73926i	−0.155324	+	0.106950i
$657$		−	6.95173i		−	0.271213i
$658$	−2.35222	+	29.5742i	−0.0916992	+	1.15292i
$659$	10.4403	−	10.4403i	0.406695	−	0.406695i	−0.473890	−	0.880584i	$-0.657150\pi$
$659$	10.4403	−	10.4403i	0.406695	−	0.406695i	0.880584	+	0.473890i	$0.157150\pi$
$660$	0.821132	+	20.6698i	0.0319625	+	0.804573i
$661$	0.719076	−	2.68363i	0.0279688	−	0.104381i	−0.950530	−	0.310631i	$-0.899459\pi$
$661$	0.719076	−	2.68363i	0.0279688	−	0.104381i	0.978499	+	0.206250i	$0.0661262\pi$
$662$	27.7060	+	10.8370i	1.07683	+	0.421191i
$663$	−25.3839	−	14.6554i	−0.985829	−	0.569168i
$664$	10.8645	−	5.27843i	0.421625	−	0.204843i
$665$	−0.639750	−	20.1887i	−0.0248084	−	0.782885i
$666$	19.8997	−	15.9071i	0.771099	−	0.616386i
$667$	−0.234953	+	0.0629554i	−0.00909741	+	0.00243764i
$668$	6.17598	−	1.92064i	0.238956	−	0.0743119i
$669$	−4.04073	+	15.0802i	−0.156224	+	0.583035i
$670$	−7.82160	−	5.75869i	−0.302175	−	0.222478i
$671$	−31.2333			−1.20575
$672$	−24.0923	−	24.0903i	−0.929380	−	0.929304i
$673$	38.9919			1.50303			0.751513	−	0.659719i	$-0.229325\pi$
$673$	38.9919			1.50303			0.751513	+	0.659719i	$0.229325\pi$
$674$	−24.7062	−	18.1901i	−0.951649	−	0.700656i
$675$	−0.481913	+	1.79852i	−0.0185488	+	0.0692252i
$676$	−17.4843	+	5.43736i	−0.672473	+	0.209129i
$677$	3.27882	−	0.878556i	0.126015	−	0.0337656i	−0.195260	−	0.980751i	$-0.562555\pi$
$677$	3.27882	−	0.878556i	0.126015	−	0.0337656i	0.321275	+	0.946986i	$0.395888\pi$
$678$	−24.2973	+	19.4223i	−0.933132	+	0.745909i
$679$	−37.3550	−	20.0170i	−1.43355	−	0.768181i
$680$	−8.11630	−	16.7057i	−0.311246	−	0.640633i
$681$	−24.5104	−	14.1511i	−0.939242	−	0.542271i
$682$	−22.9788	−	8.98797i	−0.879905	−	0.344167i
$683$	4.51734	−	16.8589i	0.172851	−	0.645090i	−0.824056	−	0.566508i	$-0.808294\pi$
$683$	4.51734	−	16.8589i	0.172851	−	0.645090i	0.996908	−	0.0785818i	$-0.0250392\pi$
$684$	−1.32254	−	33.2914i	−0.0505684	−	1.27293i
$685$	4.22517	−	4.22517i	0.161436	−	0.161436i
$686$	−22.4700	−	13.4573i	−0.857908	−	0.513803i
$687$		−	17.0350i		−	0.649925i
$688$	26.8172	+	4.94612i	1.02239	+	0.188569i
$689$	−3.29984	+	1.90516i	−0.125714	+	0.0725809i
$690$	0.0774762	+	0.177020i	0.00294947	+	0.00673905i
$691$	27.9730	−	7.49535i	1.06414	−	0.285137i	0.316059	−	0.948739i	$-0.397640\pi$
$691$	27.9730	−	7.49535i	1.06414	−	0.285137i	0.748085	+	0.663603i	$0.230973\pi$
$692$	−32.0459	+	20.2389i	−1.21820	+	0.769369i
$693$	7.58816	+	25.1094i	0.288250	+	0.953828i
$694$	35.7029	−	28.5395i	1.35526	−	1.08335i
$695$	6.30719	−	10.9244i	0.239245	−	0.414385i
$696$	−4.93956	−	25.6209i	−0.187234	−	0.971157i
$697$	−6.86692	+	3.96462i	−0.260103	+	0.150171i
$698$	−20.7469	+	3.15155i	−0.785281	+	0.119288i
$699$	3.48137	−	3.48137i	0.131677	−	0.131677i
$700$	−5.00050	+	1.73060i	−0.189001	+	0.0654104i
$701$	−1.82347	−	1.82347i	−0.0688714	−	0.0688714i	0.671832	−	0.740703i	$-0.265508\pi$
$701$	−1.82347	−	1.82347i	−0.0688714	−	0.0688714i	−0.740703	+	0.671832i	$0.765508\pi$
$702$	3.06129	−	4.15792i	0.115541	−	0.156931i
$703$	−31.5137	−	54.5833i	−1.18856	−	2.05865i
$704$	29.0961	−	21.7863i	1.09660	−	0.821103i
$705$	15.6315	+	9.02485i	0.588716	+	0.339896i
$706$	−26.6126	−	2.96746i	−1.00158	−	0.111682i
$707$	28.0465	+	26.3236i	1.05480	+	0.990001i
$708$	−21.8239	−	4.92825i	−0.820191	−	0.185215i
$709$	9.04292	+	33.7486i	0.339614	+	1.26746i	0.898780	+	0.438401i	$0.144455\pi$
$709$	9.04292	+	33.7486i	0.339614	+	1.26746i	−0.559166	+	0.829056i	$0.688878\pi$
$710$	−5.77754	−	2.25983i	−0.216827	−	0.0848101i
$711$	−12.0707	−	20.9071i	−0.452688	−	0.784078i
$712$	27.5356	+	31.7740i	1.03194	+	1.19078i
$713$	−0.230484			−0.00863171
$714$	−36.2888	−	42.5602i	−1.35807	−	1.59277i
$715$	−6.29977	−	6.29977i	−0.235598	−	0.235598i
$716$	2.01460	+	50.7124i	0.0752893	+	1.89521i
$717$	−44.0290	−	11.7975i	−1.64429	−	0.440587i
$718$	11.4134	−	4.99530i	0.425946	−	0.186423i
$719$	−7.42826	+	12.8661i	−0.277028	+	0.479826i	−0.970645	−	0.240518i	$-0.922683\pi$
$719$	−7.42826	+	12.8661i	−0.277028	+	0.479826i	0.693617	+	0.720344i	$0.256016\pi$
$720$	−8.22506	+	2.92071i	−0.306530	+	0.108848i
$721$	−23.4856	+	14.5702i	−0.874650	+	0.542624i
$722$	−55.2148	−	6.15677i	−2.05488	−	0.229131i
$723$	−17.9447	−	66.9706i	−0.667371	−	2.49066i
$724$	−9.27818	+	17.6536i	−0.344821	+	0.656090i
$725$	−3.91441	−	1.04886i	−0.145378	−	0.0389538i
$726$	−30.6956	+	4.66281i	−1.13922	+	0.173053i
$727$			37.4328i			1.38831i	0.719827	+	0.694153i	$0.244221\pi$
$727$			37.4328i			1.38831i	−0.719827	+	0.694153i	$0.755779\pi$
$728$	14.6620	+	0.581859i	0.543410	+	0.0215651i
$729$			10.8172i			0.400638i
$730$	0.676642	+	4.45438i	0.0250436	+	0.164864i
$731$	43.2410	+	11.5864i	1.59933	+	0.428538i
$732$	−9.29382	−	29.8851i	−0.343510	−	1.10458i
$733$	11.9901	+	44.7477i	0.442865	+	1.65279i	0.721514	+	0.692400i	$0.243447\pi$
$733$	11.9901	+	44.7477i	0.442865	+	1.65279i	−0.278649	+	0.960393i	$0.589887\pi$
$734$	−2.17479	+	19.5038i	−0.0802729	+	0.719899i
$735$	−13.2679	+	8.82519i	−0.489394	+	0.325522i
$736$	0.178985	−	0.288532i	0.00659749	−	0.0106354i
$737$	15.6028	−	27.0248i	0.574735	−	0.995470i
$738$	1.49405	+	3.41367i	0.0549968	+	0.125659i
$739$	13.4079	+	3.59263i	0.493217	+	0.132157i	0.496850	−	0.867836i	$-0.334490\pi$
$739$	13.4079	+	3.59263i	0.493217	+	0.132157i	−0.00363344	+	0.999993i	$0.501157\pi$
$740$	−11.2026	+	12.1295i	−0.411816	+	0.445890i
$741$	24.0965	+	24.0965i	0.885209	+	0.885209i
$742$	−7.15019	+	1.31908i	−0.262492	+	0.0484248i
$743$	−44.0696			−1.61676			−0.808379	−	0.588663i	$-0.799655\pi$
$743$	−44.0696			−1.61676			−0.808379	+	0.588663i	$0.799655\pi$
$744$	1.76238	−	24.6614i	0.0646120	−	0.904130i
$745$	10.3634	+	17.9499i	0.379685	+	0.657634i
$746$	−1.83903	+	4.70170i	−0.0673316	+	0.172141i
$747$	−2.41182	−	9.00103i	−0.0882439	−	0.329331i
$748$	50.4516	−	31.8633i	1.84469	−	1.16504i
$749$	−3.41502	+	14.5772i	−0.124782	+	0.532639i
$750$	−0.356764	+	3.19951i	−0.0130272	+	0.116829i
$751$	−16.7031	−	9.64353i	−0.609504	−	0.351897i	0.163267	−	0.986582i	$-0.447797\pi$
$751$	−16.7031	−	9.64353i	−0.609504	−	0.351897i	−0.772771	+	0.634684i	$0.781130\pi$
$752$	−2.51594	−	31.6161i	−0.0917467	−	1.15292i
$753$	−13.9437	−	24.1512i	−0.508136	−	0.880118i
$754$	9.04955	+	6.66277i	0.329565	+	0.242644i
$755$	−8.19882	−	8.19882i	−0.298386	−	0.298386i
$756$	8.15953	−	5.52233i	0.296759	−	0.200845i
$757$	25.9187	−	25.9187i	0.942030	−	0.942030i	−0.0563793	−	0.998409i	$-0.517956\pi$
$757$	25.9187	−	25.9187i	0.942030	−	0.942030i	0.998409	+	0.0563793i	$0.0179556\pi$
$758$	−5.23558	−	34.4662i	−0.190165	−	1.25187i
$759$	−0.537644	+	0.310409i	−0.0195152	+	0.0112671i
$760$	4.08782	+	21.2030i	0.148281	+	0.769114i
$761$	8.68104	−	15.0360i	0.314687	−	0.545054i	−0.664684	−	0.747125i	$-0.731434\pi$
$761$	8.68104	−	15.0360i	0.314687	−	0.545054i	0.979371	+	0.202071i	$0.0647670\pi$
$762$	−16.4347	−	20.5598i	−0.595367	−	0.744804i
$763$	7.41535	+	6.95983i	0.268454	+	0.251963i
$764$	10.1405	−	44.9053i	0.366870	−	1.62462i
$765$	−13.8403	+	3.70850i	−0.500397	+	0.134081i
$766$	−33.5776	+	14.6959i	−1.21321	+	0.530983i
$767$	8.34493	−	4.81795i	0.301318	−	0.173966i
$768$	29.5038	+	21.3573i	1.06462	+	0.770667i
$769$		−	19.4138i		−	0.700080i	−0.936735	−	0.350040i	$-0.886168\pi$
$769$		−	19.4138i		−	0.700080i	0.936735	−	0.350040i	$-0.113832\pi$
$770$	−7.30619	−	15.3505i	−0.263297	−	0.553193i
$771$	19.3327	−	19.3327i	0.696250	−	0.696250i
$772$	−8.13055	+	8.80326i	−0.292625	+	0.316836i
$773$	1.91417	−	7.14377i	0.0688478	−	0.256944i	−0.922920	−	0.384991i	$-0.874204\pi$
$773$	1.91417	−	7.14377i	0.0688478	−	0.256944i	0.991768	+	0.128048i	$0.0408711\pi$
$774$	7.66336	−	19.5923i	0.275454	−	0.704231i
$775$	−3.32551	−	1.91998i	−0.119456	−	0.0689678i
$776$	42.8153	+	14.8158i	1.53698	+	0.531854i
$777$	−23.4849	+	43.8267i	−0.842515	+	1.57227i
$778$	14.6097	+	18.2767i	0.523783	+	0.655252i
$779$	8.90466	−	2.38600i	0.319042	−	0.0854872i
$780$	4.15326	−	7.90240i	0.148711	−	0.282951i
$781$	5.15864	−	19.2523i	0.184591	−	0.688902i
$782$	0.330476	−	0.448861i	0.0118178	−	0.0160512i
$783$	7.54563			0.269659
$784$	25.9940	+	10.4074i	0.928355	+	0.371694i
$785$	−15.8839			−0.566920
$786$	−3.81719	+	5.18461i	−0.136155	+	0.184929i
$787$	−10.1250	+	37.7868i	−0.360916	+	1.34696i	0.511959	+	0.859010i	$0.328920\pi$
$787$	−10.1250	+	37.7868i	−0.360916	+	1.34696i	−0.872874	+	0.487945i	$0.837747\pi$
$788$	16.7955	+	8.82719i	0.598313	+	0.314455i
$789$	−32.1229	+	8.60730i	−1.14360	+	0.306428i
$790$	9.76940	+	12.2215i	0.347580	+	0.434822i
$791$	12.0743	−	22.5327i	0.429314	−	0.801171i
$792$	−12.2543	−	25.2228i	−0.435437	−	0.896254i
$793$	11.6732	+	6.73954i	0.414528	+	0.239328i
$794$	−7.09381	+	18.1362i	−0.251750	+	0.643629i
$795$	−1.14490	+	4.27283i	−0.0406055	+	0.151542i
$796$	−32.6442	−	30.1497i	−1.15704	−	1.06863i
$797$	1.44528	−	1.44528i	0.0511944	−	0.0511944i	−0.681046	−	0.732241i	$-0.738475\pi$
$797$	1.44528	−	1.44528i	0.0511944	−	0.0511944i	0.732241	+	0.681046i	$0.238475\pi$
$798$	27.9461	+	58.7155i	0.989281	+	2.07851i
$799$		−	52.0660i		−	1.84196i
$800$	4.98600	−	2.67205i	0.176282	−	0.0944712i
$801$	28.0911	−	16.2184i	0.992549	−	0.573049i
$802$	−17.9927	+	7.87484i	−0.635345	+	0.278070i
$803$	−13.9820	+	3.74646i	−0.493413	+	0.132210i
$804$	30.5010	+	6.88771i	1.07569	+	0.242911i
$805$	−0.115792	−	0.108679i	−0.00408113	−	0.00383043i
$806$	6.64875	+	8.31758i	0.234192	+	0.292974i
$807$	−22.1137	+	38.3021i	−0.778439	+	1.34830i
$808$	−34.0553	−	23.0464i	−1.19806	−	0.810771i
$809$	33.0158	−	19.0617i	1.16077	−	0.670174i	0.209285	−	0.977855i	$-0.432886\pi$
$809$	33.0158	−	19.0617i	1.16077	−	0.670174i	0.951490	+	0.307681i	$0.0995530\pi$
$810$	−2.29057	−	15.0790i	−0.0804826	−	0.529823i
$811$	−21.7252	+	21.7252i	−0.762876	+	0.762876i	−0.976841	−	0.213966i	$-0.931362\pi$
$811$	−21.7252	+	21.7252i	−0.762876	+	0.762876i	0.213966	+	0.976841i	$0.431362\pi$
$812$	12.0191	+	17.7589i	0.421788	+	0.623214i
$813$	−37.0763	−	37.0763i	−1.30032	−	1.30032i
$814$	−42.7182	−	31.4515i	−1.49727	−	1.10237i
$815$	−0.416150	−	0.720792i	−0.0145771	−	0.0252482i
$816$	45.5003	+	38.7925i	1.59283	+	1.35801i
$817$	−45.0739	−	26.0234i	−1.57694	−	0.910444i
$818$	−3.72721	+	33.4262i	−0.130319	+	1.16872i
$819$	2.58211	−	11.0219i	0.0902261	−	0.385135i
$820$	−1.28959	−	2.04191i	−0.0450346	−	0.0713067i
$821$	−4.89313	−	18.2614i	−0.170771	−	0.637328i	−0.997233	−	0.0743350i	$-0.976317\pi$
$821$	−4.89313	−	18.2614i	−0.170771	−	0.637328i	0.826462	−	0.562993i	$-0.190350\pi$
$822$	−7.00723	+	17.9148i	−0.244405	+	0.624851i
$823$	−4.92413	−	8.52884i	−0.171644	−	0.297297i	0.767351	−	0.641228i	$-0.221575\pi$
$823$	−4.92413	−	8.52884i	−0.171644	−	0.297297i	−0.938995	+	0.343931i	$0.888241\pi$
$824$	22.3286	−	19.3501i	0.777852	−	0.674092i
$825$	−10.3431			−0.360100
$826$	18.0820	−	3.33580i	0.629155	−	0.116067i
$827$	13.4192	+	13.4192i	0.466632	+	0.466632i	0.900821	−	0.434190i	$-0.142965\pi$
$827$	13.4192	+	13.4192i	0.466632	+	0.466632i	−0.434190	+	0.900821i	$0.642965\pi$
$828$	−0.192430	−	0.177725i	−0.00668740	−	0.00617637i
$829$	27.2524	+	7.30227i	0.946516	+	0.253618i	0.698883	−	0.715236i	$-0.253681\pi$
$829$	27.2524	+	7.30227i	0.946516	+	0.253618i	0.247633	+	0.968854i	$0.420347\pi$
$830$	2.42150	+	5.53274i	0.0840516	+	0.192044i
$831$	14.4985	−	25.1121i	0.502947	−	0.871129i
$832$	−15.5755	+	1.86411i	−0.539984	+	0.0646265i
$833$	41.1827	+	20.4164i	1.42689	+	0.707385i
$834$	−4.50035	+	40.3598i	−0.155834	+	1.39755i
$835$	0.836987	+	3.12368i	0.0289651	+	0.108099i
$836$	−66.2460	+	20.6015i	−2.29117	+	0.712519i
$837$	6.90627	+	1.85053i	0.238716	+	0.0639637i
$838$	6.66926	+	43.9042i	0.230386	+	1.51665i
$839$		−	10.0155i		−	0.345774i	−0.984942	−	0.172887i	$-0.944690\pi$
$839$		−	10.0155i		−	0.345774i	0.984942	−	0.172887i	$-0.0553095\pi$
$840$	12.5138	−	11.5585i	0.431768	−	0.398807i
$841$		−	12.5773i		−	0.433698i
$842$	2.07657	−	0.315441i	0.0715633	−	0.0108708i
$843$	21.4643	+	5.75133i	0.739269	+	0.198086i
$844$	−42.2850	−	22.2237i	−1.45551	−	0.764972i
$845$	−2.36952	−	8.84317i	−0.0815140	−	0.304214i
$846$	−24.3174	−	2.71153i	−0.836050	−	0.0932244i
$847$	21.6824	−	13.4515i	0.745015	−	0.462199i
$848$	7.32476	−	2.60101i	0.251533	−	0.0893191i
$849$	16.8225	−	29.1374i	0.577347	−	0.999994i
$850$	8.50733	−	3.72339i	0.291799	−	0.127711i
$851$	−0.478641	−	0.128251i	−0.0164076	−	0.00439640i
$852$	19.9563	−	0.792784i	0.683691	−	0.0271603i
$853$	−11.8888	−	11.8888i	−0.407065	−	0.407065i	0.473648	−	0.880714i	$-0.342937\pi$
$853$	−11.8888	−	11.8888i	−0.407065	−	0.407065i	−0.880714	+	0.473648i	$0.842937\pi$
$854$	16.6881	+	19.5720i	0.571053	+	0.669742i
$855$	16.6588			0.569720
$856$	1.14090	−	15.9649i	0.0389952	−	0.545669i
$857$	19.7587	+	34.2231i	0.674944	+	1.16904i	0.976485	+	0.215584i	$0.0691656\pi$
$857$	19.7587	+	34.2231i	0.674944	+	1.16904i	−0.301541	+	0.953453i	$0.597501\pi$
$858$	26.7112	+	10.4478i	0.911904	+	0.356683i
$859$	0.186524	+	0.696116i	0.00636411	+	0.0237512i	0.969035	−	0.246924i	$-0.0794198\pi$
$859$	0.186524	+	0.696116i	0.00636411	+	0.0237512i	−0.962671	+	0.270675i	$0.912753\pi$
$860$	−3.00336	+	13.2998i	−0.102414	+	0.453521i
$861$	−5.30288	−	4.97712i	−0.180722	−	0.169620i
$862$	56.1646	+	6.26267i	1.91297	+	0.213308i
$863$	6.62232	+	3.82340i	0.225427	+	0.130150i	0.608460	−	0.793584i	$-0.291787\pi$
$863$	6.62232	+	3.82340i	0.225427	+	0.130150i	−0.383034	+	0.923734i	$0.625121\pi$
$864$	−7.67974	+	7.20856i	−0.261270	+	0.245240i
$865$	−9.47547	−	16.4120i	−0.322176	−	0.558025i
$866$	5.54122	−	7.52622i	0.188298	−	0.255752i
$867$	42.0432	+	42.0432i	1.42786	+	1.42786i
$868$	6.64543	+	19.2018i	0.225561	+	0.651750i
$869$	−35.5451	+	35.5451i	−1.20579	+	1.20579i
$870$	12.8984	−	1.95933i	0.437296	−	0.0664274i
$871$	−11.6628	+	6.73355i	−0.395180	+	0.228158i
$872$	−9.00405	−	6.09336i	−0.304916	−	0.206347i
$873$	17.4763	−	30.2699i	0.591484	−	1.02448i
$874$	−0.506197	+	0.404634i	−0.0171224	+	0.0136870i
$875$	−0.765370	−	2.53263i	−0.0258742	−	0.0856185i
$876$	−7.74524	−	12.2636i	−0.261687	−	0.414349i
$877$	15.0825	−	4.04135i	0.509301	−	0.136467i	0.00498749	−	0.999988i	$-0.498412\pi$
$877$	15.0825	−	4.04135i	0.509301	−	0.136467i	0.504313	+	0.863521i	$0.331746\pi$
$878$	7.51916	+	17.1800i	0.253759	+	0.579798i
$879$	27.1832	−	15.6942i	0.916866	−	0.529353i
$880$	10.3071	+	14.9690i	0.347452	+	0.504604i
$881$			22.6975i			0.764697i	0.924018	+	0.382349i	$0.124885\pi$
$881$			22.6975i			0.764697i	−0.924018	+	0.382349i	$0.875115\pi$
$882$	11.6802	−	18.1711i	0.393293	−	0.611853i
$883$	21.8853	−	21.8853i	0.736499	−	0.736499i	−0.235399	−	0.971899i	$-0.575640\pi$
$883$	21.8853	−	21.8853i	0.736499	−	0.736499i	0.971899	+	0.235399i	$0.0756398\pi$
$884$	−25.7314	+	1.02221i	−0.865442	+	0.0343806i
$885$	2.89533	−	10.8055i	0.0973255	−	0.363224i
$886$	−4.94365	−	1.93367i	−0.166085	−	0.0649628i
$887$	31.2346	+	18.0333i	1.04876	+	0.605499i	0.922301	−	0.386473i	$-0.126307\pi$
$887$	31.2346	+	18.0333i	1.04876	+	0.605499i	0.126455	+	0.991972i	$0.459640\pi$
$888$	17.3825	−	50.2330i	0.583320	−	1.68571i
$889$	19.0667	+	10.2170i	0.639476	+	0.342668i
$890$	−16.4210	+	13.1263i	−0.550433	+	0.439995i
$891$	47.3319	−	12.6825i	1.58568	−	0.424881i
$892$	4.07321	+	13.0977i	0.136381	+	0.438545i
$893$	−15.6672	+	58.4709i	−0.524284	+	1.95666i
$894$	−53.7336	−	39.5616i	−1.79712	−	1.32314i
$895$	−25.3762			−0.848233
$896$	−29.1983	−	6.59228i	−0.975447	−	0.220233i
$897$	0.267921			0.00894561
$898$	14.5392	+	10.7046i	0.485180	+	0.357216i
$899$	−4.02760	+	15.0312i	−0.134328	+	0.501319i
$900$	−1.29596	−	4.16726i	−0.0431986	−	0.138909i
$901$	12.3254	−	3.30257i	0.410618	−	0.110025i
$902$	6.06070	−	4.84469i	0.201799	−	0.161310i
$903$	1.30047	+	41.0392i	0.0432770	+	1.36570i
$904$	−8.93693	+	25.8264i	−0.297238	+	0.858974i
$905$	−8.63568	−	4.98581i	−0.287060	−	0.165734i
$906$	34.7632	+	13.5973i	1.15493	+	0.451741i
$907$	11.9681	−	44.6657i	0.397395	−	1.48310i	−0.420267	−	0.907401i	$-0.638063\pi$
$907$	11.9681	−	44.6657i	0.397395	−	1.48310i	0.817662	−	0.575699i	$-0.195270\pi$
$908$	−24.8460	+	0.987034i	−0.824544	+	0.0327559i
$909$	−22.4319	+	22.4319i	−0.744019	+	0.744019i
$910$	−0.581703	+	7.31368i	−0.0192833	+	0.242446i
$911$			7.27312i			0.240969i	0.992715	+	0.120485i	$0.0384448\pi$
$911$			7.27312i			0.240969i	−0.992715	+	0.120485i	$0.961555\pi$
$912$	−39.4245	−	57.2562i	−1.30548	−	1.89594i
$913$	−16.8039	+	9.70176i	−0.556129	+	0.321081i
$914$	1.30936	+	2.99167i	0.0433097	+	0.0989555i
$915$	15.1152	−	4.05011i	0.499694	−	0.133892i
$916$	−7.99185	−	12.6541i	−0.264058	−	0.418104i
$917$	1.20689	−	5.15168i	0.0398551	−	0.170123i
$918$	−13.5063	+	10.7964i	−0.445774	+	0.356334i
$919$	−24.2034	+	41.9215i	−0.798397	+	1.38286i	0.122263	+	0.992498i	$0.460985\pi$
$919$	−24.2034	+	41.9215i	−0.798397	+	1.38286i	−0.920660	+	0.390366i	$0.872349\pi$
$920$	0.140600	+	0.0951488i	0.00463544	+	0.00313696i
$921$	38.1700	−	22.0375i	1.25775	−	0.726160i
$922$	−5.05844	+	0.768401i	−0.166591	+	0.0253059i
$923$	−6.08229	+	6.08229i	−0.200201	+	0.200201i
$924$	41.3619	+	35.8415i	1.36071	+	1.17910i
$925$	−5.83763	−	5.83763i	−0.191940	−	0.191940i
$926$	7.84266	−	10.6521i	0.257726	−	0.350050i
$927$	−11.3972	−	19.7404i	−0.374332	−	0.648361i
$928$	−15.6891	−	16.7146i	−0.515021	−	0.548685i
$929$	−29.0856	−	16.7926i	−0.954266	−	0.550946i	−0.0598624	−	0.998207i	$-0.519066\pi$
$929$	−29.0856	−	16.7926i	−0.954266	−	0.550946i	−0.894404	+	0.447261i	$0.852400\pi$
$930$	12.2860	+	1.36996i	0.402874	+	0.0449228i
$931$	−40.1053	−	35.3202i	−1.31440	−	1.15757i
$932$	0.952806	−	4.21933i	0.0312102	−	0.138209i
$933$	5.96386	+	22.2574i	0.195248	+	0.728676i
$934$	−37.8825	−	14.8174i	−1.23955	−	0.484841i
$935$	14.9178	+	25.8383i	0.487863	+	0.845004i
$936$	−0.862639	+	12.0711i	−0.0281962	+	0.394556i
$937$	−22.8886			−0.747739			−0.373870	−	0.927481i	$-0.621969\pi$
$937$	−22.8886			−0.747739			−0.373870	+	0.927481i	$0.621969\pi$
$938$	−25.2714	+	4.66210i	−0.825141	+	0.152223i
$939$	35.0402	+	35.0402i	1.14349	+	1.14349i
$940$	15.8455	−	0.629480i	0.516824	−	0.0205314i
$941$	−38.0767	−	10.2026i	−1.24127	−	0.332596i	−0.422310	−	0.906452i	$-0.638780\pi$
$941$	−38.0767	−	10.2026i	−1.24127	−	0.332596i	−0.818957	+	0.573855i	$0.805447\pi$
$942$	46.8453	−	20.5027i	1.52630	−	0.668014i
$943$	0.0362393	−	0.0627683i	0.00118011	−	0.00204402i
$944$	−18.5235	+	6.57767i	−0.602889	+	0.214085i
$945$	2.59704	+	4.18615i	0.0844818	+	0.136176i
$946$	−43.5359	−	4.85450i	−1.41547	−	0.157833i
$947$	12.6267	+	47.1236i	0.410314	+	1.53131i	0.794040	+	0.607865i	$0.207974\pi$
$947$	12.6267	+	47.1236i	0.410314	+	1.53131i	−0.383727	+	0.923447i	$0.625360\pi$
$948$	−44.5876	−	23.4339i	−1.44814	−	0.761098i
$949$	6.03408	+	1.61683i	0.195875	+	0.0524844i
$950$	−10.6743	+	1.62147i	−0.346319	+	0.0526076i
$951$			15.2804i			0.495500i
$952$	−46.9233	−	14.5903i	−1.52079	−	0.472876i
$953$			50.4212i			1.63330i	0.577131	+	0.816652i	$0.304172\pi$
$953$			50.4212i			1.63330i	−0.577131	+	0.816652i	$0.695828\pi$
$954$	−0.900576	−	5.92856i	−0.0291572	−	0.191944i
$955$	22.2337	+	5.95750i	0.719465	+	0.192780i
$956$	−38.2409	+	11.8924i	−1.23680	+	0.384626i
$957$	10.8485	+	40.4871i	0.350682	+	1.30876i
$958$	3.14196	−	28.1775i	0.101512	−	0.910375i
$959$	−0.500717	−	15.8012i	−0.0161690	−	0.510248i
$960$	−11.2558	+	14.3164i	−0.363280	+	0.462059i
$961$	8.12733	−	14.0770i	0.262172	−	0.454095i
$962$	9.17902	+	20.9725i	0.295943	+	0.676182i
$963$	−11.9272	−	3.19588i	−0.384348	−	0.102986i
$964$	−44.7487	−	41.3292i	−1.44126	−	1.33112i
$965$	−4.23679	−	4.23679i	−0.136387	−	0.136387i
$966$	0.481779	+	0.171057i	0.0155010	+	0.00550366i
$967$	−17.0271			−0.547555			−0.273778	−	0.961793i	$-0.588273\pi$
$967$	−17.0271			−0.547555			−0.273778	+	0.961793i	$0.588273\pi$
$968$	−20.6141	+	17.8643i	−0.662563	+	0.574182i
$969$	−57.0603	−	98.8313i	−1.83304	−	3.17492i
$970$	−8.25181	+	21.0967i	−0.264950	+	0.677375i
$971$	−1.60266	−	5.98120i	−0.0514317	−	0.191946i	0.935430	−	0.353511i	$-0.115012\pi$
$971$	−1.60266	−	5.98120i	−0.0514317	−	0.191946i	−0.986862	+	0.161565i	$0.948346\pi$
$972$	20.2537	+	32.0692i	0.649637	+	1.02862i
$973$	−9.65467	−	31.9476i	−0.309514	−	1.02419i
$974$	−2.87135	+	25.7506i	−0.0920038	+	0.825103i
$975$	3.86565	+	2.23184i	0.123800	+	0.0714760i
$976$	−20.9241	−	17.8394i	−0.669765	−	0.571026i
$977$	12.8211	+	22.2069i	0.410185	+	0.710460i	0.994910	−	0.100771i	$-0.0321310\pi$
$977$	12.8211	+	22.2069i	0.410185	+	0.710460i	−0.584725	+	0.811231i	$0.698798\pi$
$978$	2.15771	+	1.58863i	0.0689960	+	0.0507986i
$979$	−47.7589	−	47.7589i	−1.52638	−	1.52638i
$980$	−5.71552	+	12.7802i	−0.182576	+	0.408248i
$981$	−5.93088	+	5.93088i	−0.189358	+	0.189358i
$982$	−7.53272	−	49.5884i	−0.240379	−	1.58243i
$983$	38.2489	−	22.0830i	1.21995	−	0.704340i	0.255044	−	0.966929i	$-0.417910\pi$
$983$	38.2489	−	22.0830i	1.21995	−	0.704340i	0.964908	+	0.262590i	$0.0845766\pi$
$984$	6.43899	+	4.35749i	0.205268	+	0.138912i
$985$	−4.74346	+	8.21591i	−0.151139	+	0.261781i
$986$	−23.4979	−	29.3959i	−0.748326	−	0.936156i
$987$	45.7132	−	13.8147i	1.45507	−	0.439727i
$988$	29.2044	+	6.59492i	0.929116	+	0.209812i
$989$	−0.395253	+	0.105908i	−0.0125683	+	0.00336767i
$990$	12.8447	−	5.62171i	0.408231	−	0.178670i
$991$	37.3775	−	21.5799i	1.18734	−	0.685509i	0.229636	−	0.973277i	$-0.426246\pi$
$991$	37.3775	−	21.5799i	1.18734	−	0.685509i	0.957700	+	0.287768i	$0.0929130\pi$
$992$	−10.2606	−	19.1461i	−0.325774	−	0.607888i
$993$		−	47.8877i		−	1.51967i
$994$	−14.8206	+	7.05396i	−0.470080	+	0.223738i
$995$	15.7109	−	15.7109i	0.498067	−	0.498067i
$996$	−14.2832	−	13.1917i	−0.452580	−	0.417995i
$997$	−14.6836	+	54.7998i	−0.465033	+	1.73553i	0.191748	+	0.981444i	$0.438584\pi$
$997$	−14.6836	+	54.7998i	−0.465033	+	1.73553i	−0.656780	+	0.754082i	$0.728082\pi$
$998$	8.58028	−	21.9365i	0.271604	−	0.694388i
$999$	13.3124	+	7.68589i	0.421184	+	0.243171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cq.a.131.13	✓	256
7.3	odd	6	inner	560.2.cq.a.451.55	yes	256
16.11	odd	4	inner	560.2.cq.a.411.55	yes	256
112.59	even	12	inner	560.2.cq.a.171.13	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cq.a.131.13	✓	256	1.1	even	1	trivial
560.2.cq.a.171.13	yes	256	112.59	even	12	inner
560.2.cq.a.411.55	yes	256	16.11	odd	4	inner
560.2.cq.a.451.55	yes	256	7.3	odd	6	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13884 - 0.838476i) q^{2} +(-0.589179 + 2.19885i) q^{3} +(0.593914 + 1.90978i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(2.51466 - 2.01012i) q^{6} +(-1.24964 + 2.33204i) q^{7} +(0.924933 - 2.67292i) q^{8} +(-1.88972 - 1.09103i) q^{9} +(1.31705 + 0.515152i) q^{10} +(-1.17597 + 4.38876i) q^{11} +(-4.54924 + 0.180723i) q^{12} +(1.38652 - 1.38652i) q^{13} +(3.37850 - 1.60802i) q^{14} -2.27641i q^{15} +(-3.29453 + 2.26849i) q^{16} +(-5.68677 + 3.28326i) q^{17} +(1.23729 + 2.82699i) q^{18} +(7.37431 - 1.97594i) q^{19} +(-1.06797 - 1.69099i) q^{20} +(-4.39153 - 4.12176i) q^{21} +(5.01911 - 4.01208i) q^{22} +(0.0300112 - 0.0519810i) q^{23} +(5.33239 + 3.60862i) q^{24} +(0.866025 - 0.500000i) q^{25} +(-2.74159 + 0.416460i) q^{26} +(-1.31661 + 1.31661i) q^{27} +(-5.19586 - 1.00151i) q^{28} +(-2.86555 - 2.86555i) q^{29} +(-1.90872 + 2.59247i) q^{30} +(-1.91998 - 3.32551i) q^{31} +(5.65402 + 0.178935i) q^{32} +(-8.95737 - 5.17154i) q^{33} +(9.22926 + 1.02912i) q^{34} +(0.603485 - 2.57601i) q^{35} +(0.961297 - 4.25693i) q^{36} +(-2.13672 - 7.97435i) q^{37} +(-10.0549 - 3.93290i) q^{38} +(2.23184 + 3.86565i) q^{39} +(-0.201614 + 2.82123i) q^{40} +1.20752 q^{41} +(1.54526 + 8.37622i) q^{42} +(-4.82061 - 4.82061i) q^{43} +(-9.08000 + 0.360713i) q^{44} +(2.10771 + 0.564759i) q^{45} +(-0.0777629 + 0.0340343i) q^{46} +(-3.96450 + 6.86672i) q^{47} +(-3.04700 - 8.58072i) q^{48} +(-3.87680 - 5.82842i) q^{49} +(-1.40550 - 0.156722i) q^{50} +(-3.86886 - 14.4388i) q^{51} +(3.47142 + 1.82448i) q^{52} +(-1.87700 - 0.502941i) q^{53} +(2.60336 - 0.395462i) q^{54} -4.54358i q^{55} +(5.07751 + 5.49717i) q^{56} +17.3792i q^{57} +(0.860707 + 5.66610i) q^{58} +(4.74673 + 1.27188i) q^{59} +(4.34745 - 1.35200i) q^{60} +(1.77916 + 6.63992i) q^{61} +(-0.601806 + 5.39708i) q^{62} +(4.90579 - 3.04350i) q^{63} +(-6.28900 - 4.94454i) q^{64} +(-0.980418 + 1.69813i) q^{65} +(5.86480 + 13.4001i) q^{66} +(-6.63402 - 1.77758i) q^{67} +(-9.64777 - 8.91052i) q^{68} +(0.0966163 + 0.0966163i) q^{69} +(-2.84719 + 2.42765i) q^{70} -4.38673 q^{71} +(-4.66410 + 4.04194i) q^{72} +(1.59293 + 2.75903i) q^{73} +(-4.25292 + 10.8731i) q^{74} +(0.589179 + 2.19885i) q^{75} +(8.15332 + 12.9098i) q^{76} +(-8.76523 - 8.22678i) q^{77} +(0.699555 - 6.27370i) q^{78} +(9.58136 + 5.53180i) q^{79} +(2.59514 - 3.04388i) q^{80} +(-5.39240 - 9.33991i) q^{81} +(-1.37518 - 1.01248i) q^{82} +(3.01972 + 3.01972i) q^{83} +(5.26346 - 10.8348i) q^{84} +(4.64323 - 4.64323i) q^{85} +(1.44794 + 9.53187i) q^{86} +(7.98923 - 4.61258i) q^{87} +(10.6431 + 7.20258i) q^{88} +(-7.43260 + 12.8736i) q^{89} +(-1.92681 - 2.41043i) q^{90} +(1.50076 + 4.96607i) q^{91} +(0.117096 + 0.0264427i) q^{92} +(8.44350 - 2.26243i) q^{93} +(10.2725 - 4.49596i) q^{94} +(-6.61162 + 3.81722i) q^{95} +(-3.72468 + 12.3269i) q^{96} +16.0182i q^{97} +(-0.471941 + 9.88824i) q^{98} +(7.01052 - 7.01052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4} - 8 q^{11} - 16 q^{14} - 20 q^{16} + 40 q^{18} + 40 q^{22} + 16 q^{23} - 44 q^{28} + 32 q^{29} + 20 q^{32} - 16 q^{37} - 60 q^{42} - 16 q^{43} - 48 q^{44} - 20 q^{46} - 8 q^{50} + 40 q^{51}+ \cdots - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 - 8 * q^11 - 16 * q^14 - 20 * q^16 + 40 * q^18 + 40 * q^22 + 16 * q^23 - 44 * q^28 + 32 * q^29 + 20 * q^32 - 16 * q^37 - 60 * q^42 - 16 * q^43 - 48 * q^44 - 20 * q^46 - 8 * q^50 + 40 * q^51 - 72 * q^52 - 16 * q^53 - 84 * q^54 - 96 * q^56 - 8 * q^58 - 48 * q^59 - 28 * q^60 + 40 * q^64 - 192 * q^66 - 40 * q^67 - 60 * q^68 - 16 * q^70 + 64 * q^71 + 36 * q^72 - 60 * q^74 + 48 * q^78 + 128 * q^81 + 164 * q^84 - 52 * q^86 - 20 * q^88 + 32 * q^91 + 128 * q^92 + 72 * q^94 - 204 * q^96 + 160 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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