LMFDB - Embedded newform 544.2.bd.b.69.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(69,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.bd (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,0,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			69.19
Character	$\chi$	$=$	544.69
Dual form			544.2.bd.b.205.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.569875 + 1.29431i) q^{2} +(1.11923 + 2.70207i) q^{3} +(-1.35049 + 1.47519i) q^{4} +(3.06285 + 1.26868i) q^{5} +(-2.85950 + 2.98848i) q^{6} +(-2.11503 - 2.11503i) q^{7} +(-2.67896 - 0.907275i) q^{8} +(-3.92717 + 3.92717i) q^{9} +(0.103382 + 4.68727i) q^{10} +(1.08903 - 2.62915i) q^{11} +(-5.49758 - 1.99802i) q^{12} +(-2.29976 + 0.952593i) q^{13} +(1.53221 - 3.94282i) q^{14} +9.69599i q^{15} +(-0.352379 - 3.98445i) q^{16} +1.00000i q^{17} +(-7.32099 - 2.84499i) q^{18} +(4.29095 - 1.77737i) q^{19} +(-6.00788 + 2.80497i) q^{20} +(3.34775 - 8.08218i) q^{21} +(4.02356 - 0.0887429i) q^{22} +(-4.80341 + 4.80341i) q^{23} +(-0.546869 - 8.25420i) q^{24} +(4.23600 + 4.23600i) q^{25} +(-2.54353 - 2.43375i) q^{26} +(-6.90072 - 2.85837i) q^{27} +(5.97640 - 0.263757i) q^{28} +(3.20710 + 7.74262i) q^{29} +(-12.5496 + 5.52550i) q^{30} +9.57921 q^{31} +(4.95631 - 2.72672i) q^{32} +8.32304 q^{33} +(-1.29431 + 0.569875i) q^{34} +(-3.79475 - 9.16133i) q^{35} +(-0.489742 - 11.0969i) q^{36} +(1.22704 + 0.508255i) q^{37} +(4.74578 + 4.54095i) q^{38} +(-5.14794 - 5.14794i) q^{39} +(-7.05424 - 6.17759i) q^{40} +(4.09672 - 4.09672i) q^{41} +(12.3687 - 0.272801i) q^{42} +(3.85929 - 9.31715i) q^{43} +(2.40779 + 5.15717i) q^{44} +(-17.0107 + 7.04605i) q^{45} +(-8.95446 - 3.47977i) q^{46} +0.338949i q^{47} +(10.3719 - 5.41168i) q^{48} +1.94673i q^{49} +(-3.06871 + 7.89669i) q^{50} +(-2.70207 + 1.11923i) q^{51} +(1.70054 - 4.67905i) q^{52} +(-3.92653 + 9.47948i) q^{53} +(-0.232923 - 10.5606i) q^{54} +(6.67109 - 6.67109i) q^{55} +(3.74718 + 7.58502i) q^{56} +(9.60516 + 9.60516i) q^{57} +(-8.19372 + 8.56331i) q^{58} +(-6.75078 - 2.79626i) q^{59} +(-14.3034 - 13.0943i) q^{60} +(-1.98630 - 4.79534i) q^{61} +(5.45895 + 12.3985i) q^{62} +16.6122 q^{63} +(6.35371 + 4.86111i) q^{64} -8.25236 q^{65} +(4.74309 + 10.7726i) q^{66} +(-4.46462 - 10.7785i) q^{67} +(-1.47519 - 1.35049i) q^{68} +(-18.3553 - 7.60301i) q^{69} +(9.69508 - 10.1324i) q^{70} +(-5.05068 - 5.05068i) q^{71} +(14.0838 - 6.95774i) q^{72} +(-3.19064 + 3.19064i) q^{73} +(0.0414166 + 1.87781i) q^{74} +(-6.70489 + 16.1870i) q^{75} +(-3.17291 + 8.73029i) q^{76} +(-7.86409 + 3.25741i) q^{77} +(3.72936 - 9.59672i) q^{78} +5.67437i q^{79} +(3.97569 - 12.6508i) q^{80} -5.18381i q^{81} +(7.63705 + 2.96782i) q^{82} +(12.3181 - 5.10231i) q^{83} +(7.40168 + 15.8534i) q^{84} +(-1.26868 + 3.06285i) q^{85} +(14.2586 - 0.314485i) q^{86} +(-17.3316 + 17.3316i) q^{87} +(-5.30284 + 6.05536i) q^{88} +(1.66801 + 1.66801i) q^{89} +(-18.8137 - 18.0017i) q^{90} +(6.87884 + 2.84931i) q^{91} +(-0.599014 - 13.5729i) q^{92} +(10.7214 + 25.8837i) q^{93} +(-0.438706 + 0.193158i) q^{94} +15.3975 q^{95} +(12.9151 + 10.3404i) q^{96} -0.0922091 q^{97} +(-2.51968 + 1.10939i) q^{98} +(6.04833 + 14.6020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 20 q^{6} - 24 q^{8} - 16 q^{12} - 20 q^{16} - 20 q^{18} - 48 q^{22} - 8 q^{23} + 68 q^{24} + 20 q^{26} - 24 q^{27} + 20 q^{30} + 48 q^{31} - 24 q^{35} + 8 q^{36} + 68 q^{38} - 24 q^{39} - 36 q^{40}+ \cdots - 136 q^{99}+O(q^{100}) $ 128 * q + 20 * q^6 - 24 * q^8 - 16 * q^12 - 20 * q^16 - 20 * q^18 - 48 * q^22 - 8 * q^23 + 68 * q^24 + 20 * q^26 - 24 * q^27 + 20 * q^30 + 48 * q^31 - 24 * q^35 + 8 * q^36 + 68 * q^38 - 24 * q^39 - 36 * q^40 - 16 * q^42 - 8 * q^43 - 40 * q^44 - 80 * q^45 + 12 * q^50 + 56 * q^52 - 16 * q^53 - 136 * q^54 + 32 * q^55 + 128 * q^56 - 32 * q^58 + 20 * q^60 - 12 * q^62 - 80 * q^63 + 12 * q^64 - 8 * q^66 + 40 * q^67 - 4 * q^68 + 100 * q^70 - 44 * q^72 + 84 * q^74 + 32 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 44 * q^80 + 40 * q^82 + 84 * q^84 - 120 * q^86 - 56 * q^87 + 128 * q^88 - 68 * q^90 - 56 * q^91 - 40 * q^92 + 32 * q^95 - 72 * q^96 - 12 * q^98 - 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$1$

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 $

$2$	0.569875	+	1.29431i	0.402962	+	0.915217i
$2$	0.569875	+	1.29431i	0.402962	+	0.915217i
$3$	1.11923	+	2.70207i	0.646190	+	1.56004i	0.818193	+	0.574944i	$0.194976\pi$
$3$	1.11923	+	2.70207i	0.646190	+	1.56004i	−0.172003	+	0.985096i	$0.555024\pi$
$4$	−1.35049	+	1.47519i	−0.675243	+	0.737596i
$5$	3.06285	+	1.26868i	1.36975	+	0.567369i	0.941721	−	0.336396i	$-0.109208\pi$
$5$	3.06285	+	1.26868i	1.36975	+	0.567369i	0.428029	+	0.903765i	$0.359208\pi$
$6$	−2.85950	+	2.98848i	−1.16738	+	1.22004i
$7$	−2.11503	−	2.11503i	−0.799407	−	0.799407i	0.183595	−	0.983002i	$-0.441227\pi$
$7$	−2.11503	−	2.11503i	−0.799407	−	0.799407i	−0.983002	+	0.183595i	$0.941227\pi$
$8$	−2.67896	−	0.907275i	−0.947157	−	0.320770i
$9$	−3.92717	+	3.92717i	−1.30906	+	1.30906i
$10$	0.103382	+	4.68727i	0.0326922	+	1.48225i
$11$	1.08903	−	2.62915i	0.328355	−	0.792720i	−0.670359	−	0.742037i	$-0.733860\pi$
$11$	1.08903	−	2.62915i	0.328355	−	0.792720i	0.998715	−	0.0506835i	$-0.0161400\pi$
$12$	−5.49758	−	1.99802i	−1.58701	−	0.576779i
$13$	−2.29976	+	0.952593i	−0.637839	+	0.264202i	−0.678080	−	0.734988i	$-0.737188\pi$
$13$	−2.29976	+	0.952593i	−0.637839	+	0.264202i	0.0402405	+	0.999190i	$0.487188\pi$
$14$	1.53221	−	3.94282i	0.409500	−	1.05376i
$15$			9.69599i			2.50349i
$16$	−0.352379	−	3.98445i	−0.0880947	−	0.996112i
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$	−7.32099	−	2.84499i	−1.72557	−	0.670571i
$19$	4.29095	−	1.77737i	0.984412	−	0.407757i	0.168354	−	0.985727i	$-0.446155\pi$
$19$	4.29095	−	1.77737i	0.984412	−	0.407757i	0.816058	+	0.577970i	$0.196155\pi$
$20$	−6.00788	+	2.80497i	−1.34340	+	0.627210i
$21$	3.34775	−	8.08218i	0.730539	−	1.76368i
$22$	4.02356	−	0.0887429i	0.857825	−	0.0189201i
$23$	−4.80341	+	4.80341i	−1.00158	+	1.00158i	−0.00158191	+	0.999999i	$0.500504\pi$
$23$	−4.80341	+	4.80341i	−1.00158	+	1.00158i	−0.999999	+	0.00158191i	$0.999496\pi$
$24$	−0.546869	−	8.25420i	−0.111629	−	1.68488i
$25$	4.23600	+	4.23600i	0.847200	+	0.847200i
$26$	−2.54353	−	2.43375i	−0.498827	−	0.477298i
$27$	−6.90072	−	2.85837i	−1.32804	−	0.550094i
$28$	5.97640	−	0.263757i	1.12943	−	0.0498454i
$29$	3.20710	+	7.74262i	0.595543	+	1.43777i	0.878081	+	0.478512i	$0.158824\pi$
$29$	3.20710	+	7.74262i	0.595543	+	1.43777i	−0.282538	+	0.959256i	$0.591176\pi$
$30$	−12.5496	+	5.52550i	−2.29124	+	1.00881i
$31$	9.57921			1.72048			0.860238	−	0.509892i	$-0.170315\pi$
$31$	9.57921			1.72048			0.860238	+	0.509892i	$0.170315\pi$
$32$	4.95631	−	2.72672i	0.876159	−	0.482021i
$33$	8.32304			1.44886
$34$	−1.29431	+	0.569875i	−0.221973	+	0.0977327i
$35$	−3.79475	−	9.16133i	−0.641429	−	1.54855i
$36$	−0.489742	−	11.0969i	−0.0816237	−	1.84949i
$37$	1.22704	+	0.508255i	0.201723	+	0.0835566i	0.481258	−	0.876579i	$-0.340180\pi$
$37$	1.22704	+	0.508255i	0.201723	+	0.0835566i	−0.279534	+	0.960136i	$0.590180\pi$
$38$	4.74578	+	4.54095i	0.769867	+	0.736639i
$39$	−5.14794	−	5.14794i	−0.824331	−	0.824331i
$40$	−7.05424	−	6.17759i	−1.11537	−	0.976762i
$41$	4.09672	−	4.09672i	0.639800	−	0.639800i	−0.310706	−	0.950506i	$-0.600565\pi$
$41$	4.09672	−	4.09672i	0.639800	−	0.639800i	0.950506	+	0.310706i	$0.100565\pi$
$42$	12.3687	−	0.272801i	1.90853	−	0.0420941i
$43$	3.85929	−	9.31715i	0.588536	−	1.42085i	−0.296366	−	0.955075i	$-0.595775\pi$
$43$	3.85929	−	9.31715i	0.588536	−	1.42085i	0.884902	−	0.465778i	$-0.154225\pi$
$44$	2.40779	+	5.15717i	0.362987	+	0.777472i
$45$	−17.0107	+	7.04605i	−2.53580	+	1.05036i
$46$	−8.95446	−	3.47977i	−1.32026	−	0.513064i
$47$			0.338949i			0.0494408i	0.999694	+	0.0247204i	$0.00786955\pi$
$47$			0.338949i			0.0494408i	−0.999694	+	0.0247204i	$0.992130\pi$
$48$	10.3719	−	5.41168i	1.49705	−	0.781109i
$49$			1.94673i			0.278104i
$50$	−3.06871	+	7.89669i	−0.433982	+	1.11676i
$51$	−2.70207	+	1.11923i	−0.378365	+	0.156724i
$52$	1.70054	−	4.67905i	0.235822	−	0.648868i
$53$	−3.92653	+	9.47948i	−0.539350	+	1.30211i	0.385827	+	0.922571i	$0.373916\pi$
$53$	−3.92653	+	9.47948i	−0.539350	+	1.30211i	−0.925177	+	0.379535i	$0.876084\pi$
$54$	−0.232923	−	10.5606i	−0.0316968	−	1.43711i
$55$	6.67109	−	6.67109i	0.899529	−	0.899529i
$56$	3.74718	+	7.58502i	0.500739	+	1.01359i
$57$	9.60516	+	9.60516i	1.27223	+	1.27223i
$58$	−8.19372	+	8.56331i	−1.07589	+	1.12442i
$59$	−6.75078	−	2.79626i	−0.878876	−	0.364042i	−0.102815	−	0.994700i	$-0.532785\pi$
$59$	−6.75078	−	2.79626i	−0.878876	−	0.364042i	−0.776061	+	0.630658i	$0.782785\pi$
$60$	−14.3034	−	13.0943i	−1.84657	−	1.69047i
$61$	−1.98630	−	4.79534i	−0.254319	−	0.613980i	0.744225	−	0.667929i	$-0.232819\pi$
$61$	−1.98630	−	4.79534i	−0.254319	−	0.613980i	−0.998544	+	0.0539489i	$0.982819\pi$
$62$	5.45895	+	12.3985i	0.693287	+	1.57461i
$63$	16.6122			2.09294
$64$	6.35371	+	4.86111i	0.794213	+	0.607639i
$65$	−8.25236			−1.02358
$66$	4.74309	+	10.7726i	0.583834	+	1.32602i
$67$	−4.46462	−	10.7785i	−0.545440	−	1.31681i	−0.920838	−	0.389945i	$-0.872494\pi$
$67$	−4.46462	−	10.7785i	−0.545440	−	1.31681i	0.375398	−	0.926864i	$-0.377506\pi$
$68$	−1.47519	−	1.35049i	−0.178893	−	0.163770i
$69$	−18.3553	−	7.60301i	−2.20972	−	0.915295i
$70$	9.69508	−	10.1324i	1.15878	−	1.21105i
$71$	−5.05068	−	5.05068i	−0.599406	−	0.599406i	0.340749	−	0.940154i	$-0.389320\pi$
$71$	−5.05068	−	5.05068i	−0.599406	−	0.599406i	−0.940154	+	0.340749i	$0.889320\pi$
$72$	14.0838	−	6.95774i	1.65979	−	0.819977i
$73$	−3.19064	+	3.19064i	−0.373436	+	0.373436i	−0.868727	−	0.495291i	$-0.835061\pi$
$73$	−3.19064	+	3.19064i	−0.373436	+	0.373436i	0.495291	+	0.868727i	$0.335061\pi$
$74$	0.0414166	+	1.87781i	0.00481458	+	0.218291i
$75$	−6.70489	+	16.1870i	−0.774214	+	1.86912i
$76$	−3.17291	+	8.73029i	−0.363957	+	1.00143i
$77$	−7.86409	+	3.25741i	−0.896196	+	0.371217i
$78$	3.72936	−	9.59672i	0.422267	−	1.08662i
$79$			5.67437i			0.638416i	0.947685	+	0.319208i	$0.103417\pi$
$79$			5.67437i			0.638416i	−0.947685	+	0.319208i	$0.896583\pi$
$80$	3.97569	−	12.6508i	0.444495	−	1.41441i
$81$		−	5.18381i		−	0.575979i
$82$	7.63705	+	2.96782i	0.843371	+	0.327740i
$83$	12.3181	−	5.10231i	1.35208	−	0.560051i	0.415211	−	0.909725i	$-0.363708\pi$
$83$	12.3181	−	5.10231i	1.35208	−	0.560051i	0.936871	+	0.349674i	$0.113708\pi$
$84$	7.40168	+	15.8534i	0.807589	+	1.72975i
$85$	−1.26868	+	3.06285i	−0.137607	+	0.332213i
$86$	14.2586	−	0.314485i	1.53755	−	0.0339118i
$87$	−17.3316	+	17.3316i	−1.85814	+	1.85814i
$88$	−5.30284	+	6.05536i	−0.565285	+	0.645504i
$89$	1.66801	+	1.66801i	0.176808	+	0.176808i	0.789963	−	0.613155i	$-0.210100\pi$
$89$	1.66801	+	1.66801i	0.176808	+	0.176808i	−0.613155	+	0.789963i	$0.710100\pi$
$90$	−18.8137	−	18.0017i	−1.98314	−	1.89755i
$91$	6.87884	+	2.84931i	0.721098	+	0.298689i
$92$	−0.599014	−	13.5729i	−0.0624515	−	1.41507i
$93$	10.7214	+	25.8837i	1.11175	+	2.68401i
$94$	−0.438706	+	0.193158i	−0.0452490	+	0.0199228i
$95$	15.3975			1.57975
$96$	12.9151	+	10.3404i	1.31814	+	1.05537i
$97$	−0.0922091			−0.00936241			−0.00468121	−	0.999989i	$-0.501490\pi$
$97$	−0.0922091			−0.00936241			−0.00468121	+	0.999989i	$0.501490\pi$
$98$	−2.51968	+	1.10939i	−0.254526	+	0.112066i
$99$	6.04833	+	14.6020i	0.607880	+	1.46755i
$100$	−11.9696	+	0.528254i	−1.19696	+	0.0528254i
$101$	2.23744	+	0.926779i	0.222634	+	0.0922180i	0.491212	−	0.871040i	$-0.336554\pi$
$101$	2.23744	+	0.926779i	0.222634	+	0.0922180i	−0.268579	+	0.963258i	$0.586554\pi$
$102$	−2.98848	−	2.85950i	−0.295903	−	0.283132i
$103$	−7.04303	−	7.04303i	−0.693971	−	0.693971i	0.269133	−	0.963103i	$-0.413263\pi$
$103$	−7.04303	−	7.04303i	−0.693971	−	0.693971i	−0.963103	+	0.269133i	$0.913263\pi$
$104$	7.02524	−	0.465447i	0.688882	−	0.0456408i
$105$	20.5073	−	20.5073i	2.00131	−	2.00131i
$106$	−14.5070	+	0.319965i	−1.40905	+	0.0310777i
$107$	−0.0422354	+	0.101965i	−0.00408305	+	0.00985735i	−0.925908	−	0.377749i	$-0.876698\pi$
$107$	−0.0422354	+	0.101965i	−0.00408305	+	0.00985735i	0.921825	+	0.387607i	$0.126698\pi$
$108$	13.5360	−	6.31969i	1.30250	−	0.608112i
$109$	16.3737	−	6.78222i	1.56832	−	0.649619i	0.581810	−	0.813325i	$-0.302345\pi$
$109$	16.3737	−	6.78222i	1.56832	−	0.649619i	0.986509	+	0.163706i	$0.0523448\pi$
$110$	12.4362	+	4.83278i	1.18574	+	0.460788i
$111$			3.88439i			0.368690i
$112$	−7.68195	+	9.17253i	−0.725876	+	0.866723i
$113$		−	12.6685i		−	1.19175i	−0.803077	−	0.595876i	$-0.796805\pi$
$113$		−	12.6685i		−	1.19175i	0.803077	−	0.595876i	$-0.203195\pi$
$114$	−6.95833	+	17.9058i	−0.651707	+	1.67703i
$115$	−20.8061	+	8.61818i	−1.94018	+	0.803649i
$116$	−15.7530	−	5.72521i	−1.46263	−	0.531572i
$117$	5.29057	−	12.7726i	0.489113	−	1.18082i
$118$	−0.227862	−	10.3311i	−0.0209764	−	0.951057i
$119$	2.11503	−	2.11503i	0.193885	−	0.193885i
$120$	8.79692	−	25.9752i	0.803045	−	2.37120i
$121$	2.05171	+	2.05171i	0.186519	+	0.186519i
$122$	5.07473	−	5.30363i	0.459444	−	0.480168i
$123$	15.6548	+	6.48444i	1.41155	+	0.584682i
$124$	−12.9366	+	14.1312i	−1.16174	+	1.26902i
$125$	1.25676	+	3.03409i	0.112408	+	0.271377i
$126$	9.46688	+	21.5014i	0.843377	+	1.91549i
$127$	−16.5455			−1.46817			−0.734087	−	0.679055i	$-0.762390\pi$
$127$	−16.5455			−1.46817			−0.734087	+	0.679055i	$0.762390\pi$
$128$	−2.67098	+	10.9939i	−0.236083	+	0.971733i
$129$	29.4950			2.59689
$130$	−4.70281	−	10.6811i	−0.412464	−	0.936797i
$131$	1.16147	+	2.80403i	0.101478	+	0.244989i	0.966462	−	0.256810i	$-0.0826716\pi$
$131$	1.16147	+	2.80403i	0.101478	+	0.244989i	−0.864984	+	0.501799i	$0.832672\pi$
$132$	−11.2401	+	12.2781i	−0.978329	+	1.06867i
$133$	−12.8347	−	5.31631i	−1.11291	−	0.460982i
$134$	11.4065	−	11.9210i	0.985373	−	1.02982i
$135$	−17.5095	−	17.5095i	−1.50698	−	1.50698i
$136$	0.907275	−	2.67896i	0.0777981	−	0.229719i
$137$	−1.66715	+	1.66715i	−0.142434	+	0.142434i	−0.774728	−	0.632294i	$-0.782113\pi$
$137$	−1.66715	+	1.66715i	−0.142434	+	0.142434i	0.632294	+	0.774728i	$0.282113\pi$
$138$	−0.619553	−	28.0902i	−0.0527399	−	2.39120i
$139$	−0.0109113	+	0.0263422i	−0.000925485	+	0.00223432i	−0.924342	−	0.381566i	$-0.875385\pi$
$139$	−0.0109113	+	0.0263422i	−0.000925485	+	0.00223432i	0.923416	+	0.383800i	$0.125385\pi$
$140$	18.6395	+	6.77426i	1.57532	+	0.572530i
$141$	−0.915863	+	0.379363i	−0.0771296	+	0.0319481i
$142$	3.65890	−	9.41542i	0.307048	−	0.790124i
$143$			7.08383i			0.592380i
$144$	17.0315	+	14.2638i	1.41929	+	1.18865i
$145$			27.7833i			2.30727i
$146$	−5.94795	−	2.31142i	−0.492255	−	0.191294i
$147$	−5.26020	+	2.17885i	−0.433854	+	0.179708i
$148$	−2.40687	+	1.12372i	−0.197843	+	0.0923693i
$149$	0.989851	−	2.38971i	0.0810917	−	0.195773i	−0.878133	−	0.478416i	$-0.841211\pi$
$149$	0.989851	−	2.38971i	0.0810917	−	0.195773i	0.959225	+	0.282643i	$0.0912112\pi$
$150$	−24.7720	+	0.546368i	−2.02263	+	0.0446107i
$151$	7.70576	−	7.70576i	0.627086	−	0.627086i	−0.320248	−	0.947334i	$-0.603766\pi$
$151$	7.70576	−	7.70576i	0.627086	−	0.627086i	0.947334	+	0.320248i	$0.103766\pi$
$152$	−13.1079	+	0.868442i	−1.06319	+	0.0704399i
$153$	−3.92717	−	3.92717i	−0.317493	−	0.317493i
$154$	−8.69765	−	8.32226i	−0.700877	−	0.670627i
$155$	29.3397	+	12.1529i	2.35662	+	0.976145i
$156$	14.5464	−	0.641979i	1.16465	−	0.0513995i
$157$	−7.34162	−	17.7242i	−0.585925	−	1.41455i	−0.887367	−	0.461064i	$-0.847468\pi$
$157$	−7.34162	−	17.7242i	−0.585925	−	1.41455i	0.301442	−	0.953484i	$-0.402532\pi$
$158$	−7.34440	+	3.23368i	−0.584289	+	0.257258i
$159$	−30.0089			−2.37986
$160$	18.6398	−	2.06361i	1.47360	−	0.163143i
$161$	20.3188			1.60134
$162$	6.70947	−	2.95412i	0.527146	−	0.232098i
$163$	2.11275	+	5.10062i	0.165483	+	0.399512i	0.984768	−	0.173876i	$-0.0556291\pi$
$163$	2.11275	+	5.10062i	0.165483	+	0.399512i	−0.819285	+	0.573387i	$0.805629\pi$
$164$	0.510885	+	11.5760i	0.0398934	+	0.903934i
$165$	25.4923	+	10.5592i	1.98457	+	0.822035i
$166$	13.6237	+	13.0357i	1.05741	+	1.01177i
$167$	−16.8005	−	16.8005i	−1.30006	−	1.30006i	−0.928347	−	0.371715i	$-0.878770\pi$
$167$	−16.8005	−	16.8005i	−1.30006	−	1.30006i	−0.371715	−	0.928347i	$-0.621230\pi$
$168$	−16.3013	+	18.6146i	−1.25767	+	1.43614i
$169$	−4.81092	+	4.81092i	−0.370070	+	0.370070i
$170$	−4.68727	+	0.103382i	−0.359497	+	0.00792901i
$171$	−9.87127	+	23.8314i	−0.754875	+	1.82243i
$172$	8.53266	+	18.2759i	0.650610	+	1.39352i
$173$	−15.4488	+	6.39910i	−1.17455	+	0.486515i	−0.882694	−	0.469947i	$-0.844273\pi$
$173$	−15.4488	+	6.39910i	−1.17455	+	0.486515i	−0.291856	+	0.956462i	$0.594273\pi$
$174$	−32.3093	−	12.5556i	−2.44936	−	0.951841i
$175$		−	17.9186i		−	1.35452i
$176$	−10.8595	−	3.41273i	−0.818564	−	0.257244i
$177$		−	21.3707i		−	1.60632i
$178$	−1.20836	+	3.10947i	−0.0905707	+	0.233065i
$179$	−18.4901	+	7.65887i	−1.38202	+	0.572451i	−0.945020	−	0.327012i	$-0.893958\pi$
$179$	−18.4901	+	7.65887i	−1.38202	+	0.572451i	−0.436998	+	0.899462i	$0.643958\pi$
$180$	12.5784	−	34.6096i	0.937538	−	2.57965i
$181$	−1.60166	+	3.86675i	−0.119050	+	0.287413i	−0.972160	−	0.234319i	$-0.924714\pi$
$181$	−1.60166	+	3.86675i	−0.119050	+	0.287413i	0.853109	+	0.521732i	$0.174714\pi$
$182$	0.232184	+	10.5271i	0.0172106	+	0.780321i
$183$	10.7342	−	10.7342i	0.793496	−	0.793496i
$184$	17.2262	−	8.51016i	1.26993	−	0.627377i
$185$	3.11342	+	3.11342i	0.228903	+	0.228903i
$186$	−27.3917	+	28.6273i	−2.00846	+	2.09905i
$187$	2.62915	+	1.08903i	0.192263	+	0.0796379i
$188$	−0.500014	−	0.457746i	−0.0364673	−	0.0333845i
$189$	8.54970	+	20.6408i	0.621899	+	1.50140i
$190$	8.77463	+	19.9291i	0.636578	+	1.44581i
$191$	−0.503134			−0.0364055			−0.0182027	−	0.999834i	$-0.505794\pi$
$191$	−0.503134			−0.0364055			−0.0182027	+	0.999834i	$0.505794\pi$
$192$	−6.02378	+	22.6089i	−0.434729	+	1.63166i
$193$	−1.99629			−0.143696			−0.0718482	−	0.997416i	$-0.522890\pi$
$193$	−1.99629			−0.143696			−0.0718482	+	0.997416i	$0.522890\pi$
$194$	−0.0525476	−	0.119347i	−0.00377270	−	0.00856864i
$195$	−9.23633	−	22.2985i	−0.661427	−	1.59683i
$196$	−2.87180	−	2.62903i	−0.205129	−	0.187788i
$197$	10.0204	+	4.15057i	0.713921	+	0.295716i	0.709926	−	0.704276i	$-0.248728\pi$
$197$	10.0204	+	4.15057i	0.713921	+	0.295716i	0.00399525	+	0.999992i	$0.498728\pi$
$198$	−15.4527	+	16.1497i	−1.09818	+	1.14771i
$199$	8.44850	+	8.44850i	0.598899	+	0.598899i	0.940019	−	0.341121i	$-0.110807\pi$
$199$	8.44850	+	8.44850i	0.598899	+	0.598899i	−0.341121	+	0.940019i	$0.610807\pi$
$200$	−7.50488	−	15.1913i	−0.530675	−	1.07419i
$201$	24.1274	−	24.1274i	1.70182	−	1.70182i
$202$	0.0755213	+	3.42410i	0.00531366	+	0.240919i
$203$	9.59278	−	23.1590i	0.673281	−	1.62544i
$204$	1.99802	−	5.49758i	0.139889	−	0.384907i
$205$	17.7451	−	7.35025i	1.23937	−	0.513363i
$206$	5.10223	−	13.1295i	0.355489	−	0.914777i
$207$		−	37.7277i		−	2.62225i
$208$	4.60594	+	8.82761i	0.319365	+	0.612085i
$209$		−	13.2172i		−	0.914252i
$210$	38.2295	+	14.8563i	2.63809	+	1.02518i
$211$	−3.25506	+	1.34829i	−0.224088	+	0.0928202i	−0.491903	−	0.870650i	$-0.663698\pi$
$211$	−3.25506	+	1.34829i	−0.224088	+	0.0928202i	0.267815	+	0.963470i	$0.413698\pi$
$212$	−8.68132	−	18.5943i	−0.596236	−	1.27706i
$213$	7.99440	−	19.3002i	0.547767	−	1.32243i
$214$	−0.156044	+	0.00344167i	−0.0106669	+	0.000235268i
$215$	23.6409	−	23.6409i	1.61229	−	1.61229i
$216$	15.8935	+	13.9183i	1.08141	+	0.947022i
$217$	−20.2603	−	20.2603i	−1.37536	−	1.37536i
$218$	18.1093	+	17.3277i	1.22652	+	1.17358i
$219$	−12.1924	−	5.05026i	−0.823886	−	0.341265i
$220$	0.831924	+	18.8503i	0.0560883	+	1.27089i
$221$	−0.952593	−	2.29976i	−0.0640783	−	0.154699i
$222$	−5.02761	+	2.21362i	−0.337431	+	0.148568i
$223$	−7.20142			−0.482243			−0.241121	−	0.970495i	$-0.577515\pi$
$223$	−7.20142			−0.482243			−0.241121	+	0.970495i	$0.577515\pi$
$224$	−16.2499	−	4.71564i	−1.08574	−	0.315077i
$225$	−33.2710			−2.21807
$226$	16.3970	−	7.21945i	1.09071	−	0.480231i
$227$	5.14755	+	12.4273i	0.341655	+	0.824827i	0.997549	+	0.0699743i	$0.0222917\pi$
$227$	5.14755	+	12.4273i	0.341655	+	0.824827i	−0.655894	+	0.754853i	$0.727708\pi$
$228$	−27.1411	+	1.19782i	−1.79746	+	0.0793276i
$229$	5.28264	+	2.18814i	0.349087	+	0.144597i	0.550335	−	0.834944i	$-0.314500\pi$
$229$	5.28264	+	2.18814i	0.349087	+	0.144597i	−0.201248	+	0.979540i	$0.564500\pi$
$230$	−23.0115	−	22.0183i	−1.51733	−	1.45184i
$231$	−17.6035	−	17.6035i	−1.15823	−	1.15823i
$232$	−1.56702	−	23.6519i	−0.102880	−	1.55282i
$233$	10.7125	−	10.7125i	0.701797	−	0.701797i	−0.262999	−	0.964796i	$-0.584712\pi$
$233$	10.7125	−	10.7125i	0.701797	−	0.701797i	0.964796	+	0.262999i	$0.0847115\pi$
$234$	19.5466	−	0.431117i	1.27780	−	0.0281830i
$235$	−0.430016	+	1.03815i	−0.0280512	+	0.0677215i
$236$	13.2418	−	6.18237i	0.861971	−	0.402438i
$237$	−15.3325	+	6.35094i	−0.995955	+	0.412538i
$238$	3.94282	+	1.53221i	0.255575	+	0.0993183i
$239$			10.5790i			0.684299i	0.939645	+	0.342150i	$0.111155\pi$
$239$			10.5790i			0.684299i	−0.939645	+	0.342150i	$0.888845\pi$
$240$	38.6332	−	3.41666i	2.49376	−	0.220544i
$241$		−	16.0770i		−	1.03561i	−0.855499	−	0.517804i	$-0.826750\pi$
$241$		−	16.0770i		−	1.03561i	0.855499	−	0.517804i	$-0.173250\pi$
$242$	−1.48633	+	3.82477i	−0.0955451	+	0.245865i
$243$	−6.69513	+	2.77322i	−0.429493	+	0.177902i
$244$	9.75651	+	3.54587i	0.624596	+	0.227001i
$245$	−2.46977	+	5.96255i	−0.157788	+	0.380933i
$246$	0.528403	+	23.9575i	0.0336897	+	1.52748i
$247$	−8.17506	+	8.17506i	−0.520166	+	0.520166i
$248$	−25.6624	−	8.69097i	−1.62956	−	0.551877i
$249$	27.5736	+	27.5736i	1.74740	+	1.74740i
$250$	−3.21086	+	3.35569i	−0.203073	+	0.212232i
$251$	12.1687	+	5.04043i	0.768079	+	0.318149i	0.732094	−	0.681203i	$-0.238543\pi$
$251$	12.1687	+	5.04043i	0.768079	+	0.318149i	0.0359851	+	0.999352i	$0.488543\pi$
$252$	−22.4345	+	24.5062i	−1.41324	+	1.54374i
$253$	7.39785	+	17.8600i	0.465099	+	1.12285i
$254$	−9.42885	−	21.4150i	−0.591619	−	1.34370i
$255$	−9.69599			−0.607186
$256$	−15.7517	+	2.80807i	−0.984479	+	0.175504i
$257$	−5.87162			−0.366262			−0.183131	−	0.983089i	$-0.558623\pi$
$257$	−5.87162			−0.366262			−0.183131	+	0.983089i	$0.558623\pi$
$258$	16.8085	+	38.1758i	1.04645	+	2.37672i
$259$	−1.52024	−	3.67020i	−0.0944634	−	0.228055i
$260$	11.1447	−	12.1738i	0.691165	−	0.754988i
$261$	−43.0014	−	17.8118i	−2.66172	−	1.10252i
$262$	−2.96740	+	3.10124i	−0.183326	+	0.191596i
$263$	11.8806	+	11.8806i	0.732590	+	0.732590i	0.971132	−	0.238542i	$-0.0766695\pi$
$263$	11.8806	+	11.8806i	0.732590	+	0.732590i	−0.238542	+	0.971132i	$0.576670\pi$
$264$	−22.2971	−	7.55128i	−1.37229	−	0.464749i
$265$	−24.0528	+	24.0528i	−1.47755	+	1.47755i
$266$	−0.433215	−	19.6417i	−0.0265621	−	1.20431i
$267$	−2.64018	+	6.37395i	−0.161576	+	0.390080i
$268$	21.9298	+	7.97010i	1.33958	+	0.486851i
$269$	−7.72957	+	3.20169i	−0.471280	+	0.195211i	−0.605667	−	0.795718i	$-0.707094\pi$
$269$	−7.72957	+	3.20169i	−0.471280	+	0.195211i	0.134387	+	0.990929i	$0.457094\pi$
$270$	12.6846	−	32.6410i	0.771957	−	1.98647i
$271$			0.968638i			0.0588406i	0.999567	+	0.0294203i	$0.00936612\pi$
$271$			0.968638i			0.0588406i	−0.999567	+	0.0294203i	$0.990634\pi$
$272$	3.98445	−	0.352379i	0.241593	−	0.0213661i
$273$			21.7761i			1.31795i
$274$	−3.10788	−	1.20775i	−0.187754	−	0.0729626i
$275$	15.7502	−	6.52396i	0.949775	−	0.393410i
$276$	36.0045	−	16.8098i	2.16721	−	1.01183i
$277$	−1.90521	+	4.59957i	−0.114473	+	0.276362i	−0.970724	−	0.240198i	$-0.922788\pi$
$277$	−1.90521	+	4.59957i	−0.114473	+	0.276362i	0.856251	+	0.516560i	$0.172788\pi$
$278$	−0.0403131		0.000889139i	−0.00241782		5.33270e-5i
$279$	−37.6192	+	37.6192i	−2.25220	+	2.25220i
$280$	1.85415	+	27.9857i	0.110807	+	1.67247i
$281$	−2.82692	−	2.82692i	−0.168640	−	0.168640i	0.617741	−	0.786381i	$-0.288048\pi$
$281$	−2.82692	−	2.82692i	−0.168640	−	0.168640i	−0.786381	+	0.617741i	$0.788048\pi$
$282$	−1.01294	−	0.969223i	−0.0603198	−	0.0577164i
$283$	−27.2108	−	11.2711i	−1.61751	−	0.669995i	−0.623761	−	0.781615i	$-0.714396\pi$
$283$	−27.2108	−	11.2711i	−1.61751	−	0.669995i	−0.993751	+	0.111620i	$0.964396\pi$
$284$	14.2716	−	0.629850i	0.846864	−	0.0373747i
$285$	17.2334	+	41.6050i	1.02082	+	2.46447i
$286$	−9.16869	+	4.03690i	−0.542156	+	0.238707i
$287$	−17.3294			−1.02292
$288$	−8.75596	+	30.1726i	−0.515950	+	1.77794i
$289$	−1.00000			−0.0588235
$290$	−35.9602	+	15.8330i	−2.11166	+	0.929745i
$291$	−0.103204	−	0.249155i	−0.00604990	−	0.0146057i
$292$	−0.397892	−	9.01571i	−0.0232848	−	0.527605i
$293$	4.09549	+	1.69641i	0.239261	+	0.0991051i	0.499092	−	0.866549i	$-0.333667\pi$
$293$	4.09549	+	1.69641i	0.239261	+	0.0991051i	−0.259831	+	0.965654i	$0.583667\pi$
$294$	−5.81776	−	5.56667i	−0.339299	−	0.324655i
$295$	−17.1291	−	17.1291i	−0.997294	−	0.997294i
$296$	−2.82606	−	2.47485i	−0.164261	−	0.143848i
$297$	−15.0302	+	15.0302i	−0.872141	+	0.872141i
$298$	3.65712	−	0.0806609i	0.211851	−	0.00467256i
$299$	6.47101	−	15.6224i	0.374228	−	0.903467i
$300$	−14.8241	−	31.7514i	−0.855871	−	1.83317i
$301$	−27.8686	+	11.5436i	−1.60632	+	0.665359i
$302$	14.3650	+	5.58234i	0.826611	+	0.321227i
$303$			7.08301i			0.406908i
$304$	−8.59388	−	16.4708i	−0.492893	−	0.944663i
$305$		−	17.2074i		−	0.985292i
$306$	2.84499	−	7.32099i	0.162637	−	0.418513i
$307$	4.01224	−	1.66193i	0.228991	−	0.0948511i	−0.265238	−	0.964183i	$-0.585451\pi$
$307$	4.01224	−	1.66193i	0.228991	−	0.0948511i	0.494229	+	0.869332i	$0.335451\pi$
$308$	5.81503	−	16.0001i	0.331342	−	0.911692i
$309$	11.1480	−	26.9136i	0.634185	−	1.53106i
$310$	0.990315	+	44.9004i	0.0562461	+	2.55017i
$311$	−7.53360	+	7.53360i	−0.427191	+	0.427191i	−0.887670	−	0.460479i	$-0.847678\pi$
$311$	−7.53360	+	7.53360i	−0.427191	+	0.427191i	0.460479	+	0.887670i	$0.347678\pi$
$312$	9.12056	+	18.4618i	0.516350	+	1.04519i
$313$	−17.3586	−	17.3586i	−0.981169	−	0.981169i	0.0186572	−	0.999826i	$-0.494061\pi$
$313$	−17.3586	−	17.3586i	−0.981169	−	0.981169i	−0.999826	+	0.0186572i	$0.994061\pi$
$314$	18.7569	−	19.6029i	1.05851	−	1.10626i
$315$	50.8808	+	21.0755i	2.86681	+	1.18747i
$316$	−8.37078	−	7.66315i	−0.470893	−	0.431086i
$317$	−8.07018	−	19.4831i	−0.453267	−	1.09428i	−0.971073	−	0.238785i	$-0.923251\pi$
$317$	−8.07018	−	19.4831i	−0.453267	−	1.09428i	0.517806	−	0.855498i	$-0.326749\pi$
$318$	−17.1013	−	38.8409i	−0.958995	−	2.17809i
$319$	23.8492			1.33530
$320$	13.2933	+	22.9497i	0.743118	+	1.28293i
$321$	−0.322788			−0.0180163
$322$	11.5791	+	26.2988i	0.645281	+	1.46557i
$323$	1.77737	+	4.29095i	0.0988955	+	0.238755i
$324$	7.64711	+	7.00066i	0.424840	+	0.388926i
$325$	−13.7770	−	5.70661i	−0.764209	−	0.316546i
$326$	−5.39779	+	5.64127i	−0.298956	+	0.312441i
$327$	36.6521	+	36.6521i	2.02686	+	2.02686i
$328$	−14.6918	+	7.25812i	−0.811220	+	0.400763i
$329$	0.716888	−	0.716888i	0.0395233	−	0.0395233i
$330$	0.860450	+	39.0124i	0.0473662	+	2.14756i
$331$	−8.75121	+	21.1273i	−0.481010	+	1.16126i	0.478120	+	0.878295i	$0.341318\pi$
$331$	−8.75121	+	21.1273i	−0.481010	+	1.16126i	−0.959130	+	0.282966i	$0.908682\pi$
$332$	−9.10848	+	25.0621i	−0.499893	+	1.37546i
$333$	−6.81479	+	2.82278i	−0.373448	+	0.154687i
$334$	12.1709	−	31.3193i	0.665962	−	1.71371i
$335$		−	38.6772i		−	2.11316i
$336$	−33.3827	−	10.4909i	−1.82118	−	0.572328i
$337$			9.28714i			0.505902i	0.967479	+	0.252951i	$0.0814012\pi$
$337$			9.28714i			0.505902i	−0.967479	+	0.252951i	$0.918599\pi$
$338$	−8.96844	−	3.48520i	−0.487819	−	0.189570i
$339$	34.2311	−	14.1790i	1.85918	−	0.770098i
$340$	−2.80497	−	6.00788i	−0.152121	−	0.325823i
$341$	10.4321	−	25.1852i	0.564928	−	1.36386i
$342$	−36.4706	+	0.804389i	−1.97210	+	0.0434964i
$343$	−10.6878	+	10.6878i	−0.577089	+	0.577089i
$344$	−18.7921	+	21.4589i	−1.01320	+	1.15699i
$345$	−46.5738	−	46.5738i	−2.50745	−	2.50745i
$346$	−17.0863	−	16.3489i	−0.918566	−	0.878921i
$347$	−12.1539	−	5.03430i	−0.652455	−	0.270256i	0.0318048	−	0.999494i	$-0.489875\pi$
$347$	−12.1539	−	5.03430i	−0.652455	−	0.270256i	−0.684260	+	0.729238i	$0.739875\pi$
$348$	−2.16135	−	48.9735i	−0.115861	−	2.62525i
$349$	−11.9362	−	28.8165i	−0.638930	−	1.54251i	−0.828106	−	0.560571i	$-0.810582\pi$
$349$	−11.9362	−	28.8165i	−0.638930	−	1.54251i	0.189176	−	0.981943i	$-0.439418\pi$
$350$	23.1922	−	10.2113i	1.23968	−	0.545819i
$351$	18.5929			0.992414
$352$	−1.77141	−	16.0004i	−0.0944163	−	0.852823i
$353$	6.30169			0.335405			0.167703	−	0.985838i	$-0.446365\pi$
$353$	6.30169			0.335405			0.167703	+	0.985838i	$0.446365\pi$
$354$	27.6604	−	12.1786i	1.47013	−	0.647288i
$355$	−9.06183	−	21.8772i	−0.480952	−	1.16112i
$356$	−4.71324	+	0.208010i	−0.249801	+	0.0110245i
$357$	8.08218	+	3.34775i	0.427754	+	0.177182i
$358$	−20.4500	−	19.5674i	−1.08082	−	1.03417i
$359$	7.50286	+	7.50286i	0.395986	+	0.395986i	0.876814	−	0.480829i	$-0.159664\pi$
$359$	7.50286	+	7.50286i	0.395986	+	0.395986i	−0.480829	+	0.876814i	$0.659664\pi$
$360$	51.9637	−	3.44277i	2.73873	−	0.181450i
$361$	1.81819	−	1.81819i	0.0956944	−	0.0956944i
$362$	−5.91753	+	0.130516i	−0.311018	+	0.00685977i
$363$	−3.24752	+	7.84020i	−0.170450	+	0.411504i
$364$	−13.4930	+	6.29965i	−0.707228	+	0.330192i
$365$	−13.8203	+	5.72457i	−0.723390	+	0.299638i
$366$	20.0106	+	7.77626i	1.04597	+	0.406472i
$367$			6.61860i			0.345488i	0.984967	+	0.172744i	$0.0552633\pi$
$367$			6.61860i			0.345488i	−0.984967	+	0.172744i	$0.944737\pi$
$368$	20.8316	+	17.4463i	1.08592	+	0.909453i
$369$			32.1771i			1.67507i
$370$	−2.25548	+	5.80399i	−0.117257	+	0.301735i
$371$	28.3541	−	11.7447i	1.47207	−	0.609753i
$372$	−52.6625	−	19.1395i	−2.73042	−	0.992335i
$373$	−6.27625	+	15.1522i	−0.324972	+	0.784552i	0.673979	+	0.738751i	$0.264584\pi$
$373$	−6.27625	+	15.1522i	−0.324972	+	0.784552i	−0.998951	+	0.0458009i	$0.985416\pi$
$374$	0.0887429	+	4.02356i	0.00458879	+	0.208053i
$375$	−6.79171	+	6.79171i	−0.350722	+	0.350722i
$376$	0.307520	−	0.908032i	0.0158591	−	0.0468282i
$377$	−14.7511	−	14.7511i	−0.759721	−	0.759721i
$378$	−21.8434	+	22.8286i	−1.12350	+	1.17418i
$379$	1.63040	+	0.675336i	0.0837482	+	0.0346897i	0.424164	−	0.905585i	$-0.360568\pi$
$379$	1.63040	+	0.675336i	0.0837482	+	0.0346897i	−0.340416	+	0.940275i	$0.610568\pi$
$380$	−20.7940	+	22.7142i	−1.06671	+	1.16521i
$381$	−18.5183	−	44.7070i	−0.948719	−	2.29041i
$382$	−0.286723	−	0.651212i	−0.0146700	−	0.0333189i
$383$	30.6059			1.56389			0.781944	−	0.623349i	$-0.214228\pi$
$383$	30.6059			1.56389			0.781944	+	0.623349i	$0.214228\pi$
$384$	−32.6957	+	5.08758i	−1.66850	+	0.259624i
$385$	−28.2191			−1.43818
$386$	−1.13764	−	2.58383i	−0.0579042	−	0.131513i
$387$	21.4340	+	51.7462i	1.08955	+	2.63041i
$388$	0.124527	−	0.136026i	0.00632190	−	0.00690568i
$389$	30.2942	+	12.5483i	1.53598	+	0.636223i	0.980713	−	0.195452i	$-0.0626173\pi$
$389$	30.2942	+	12.5483i	1.53598	+	0.636223i	0.555264	+	0.831674i	$0.312617\pi$
$390$	23.5976	−	24.6620i	1.19491	−	1.24881i
$391$	−4.80341	−	4.80341i	−0.242919	−	0.242919i
$392$	1.76622	−	5.21522i	0.0892075	−	0.263409i
$393$	−6.27673	+	6.27673i	−0.316619	+	0.316619i
$394$	0.338221	+	15.3348i	0.0170393	+	0.772555i
$395$	−7.19893	+	17.3798i	−0.362217	+	0.874470i
$396$	−29.7089	−	10.7973i	−1.49293	−	0.542585i
$397$	9.66384	−	4.00289i	0.485014	−	0.200900i	−0.126758	−	0.991934i	$-0.540457\pi$
$397$	9.66384	−	4.00289i	0.485014	−	0.200900i	0.611772	+	0.791034i	$0.290457\pi$
$398$	−6.12041	+	15.7496i	−0.306788	+	0.789456i
$399$		−	40.6304i		−	2.03407i
$400$	15.3854	−	18.3708i	0.769272	−	0.918540i
$401$		−	11.8646i		−	0.592489i	−0.955112	−	0.296244i	$-0.904266\pi$
$401$		−	11.8646i		−	0.592489i	0.955112	−	0.296244i	$-0.0957342\pi$
$402$	44.9780	+	17.4788i	2.24330	+	0.871763i
$403$	−22.0299	+	9.12508i	−1.09739	+	0.454553i
$404$	−4.38881	+	2.04905i	−0.218351	+	0.101944i
$405$	6.57657	−	15.8773i	0.326793	−	0.788947i
$406$	35.4417	−	0.781695i	1.75894	−	0.0387949i
$407$	2.67256	−	2.67256i	0.132474	−	0.132474i
$408$	8.25420	−	0.546869i	0.408644	−	0.0270741i
$409$	16.4706	+	16.4706i	0.814416	+	0.814416i	0.985293	−	0.170876i	$-0.0546598\pi$
$409$	16.4706	+	16.4706i	0.814416	+	0.814416i	−0.170876	+	0.985293i	$0.554660\pi$
$410$	19.6260	+	18.7789i	0.969258	+	0.927425i
$411$	−6.37069	−	2.63883i	−0.314243	−	0.130164i
$412$	19.9013	−	0.878308i	0.980468	−	0.0432711i
$413$	8.36393	+	20.1923i	0.411562	+	0.993598i
$414$	48.8314	−	21.5001i	2.39993	−	1.05667i
$415$	44.2016			2.16977
$416$	−8.80087	+	10.9922i	−0.431498	+	0.538935i
$417$	−0.0833908			−0.00408366
$418$	17.1072	−	7.53214i	0.836739	−	0.368409i
$419$	−14.1927	−	34.2642i	−0.693359	−	1.67392i	−0.737901	−	0.674909i	$-0.764183\pi$
$419$	−14.1927	−	34.2642i	−0.693359	−	1.67392i	0.0445420	−	0.999008i	$-0.485817\pi$
$420$	2.55739	+	57.9471i	0.124788	+	2.82753i
$421$	−16.6196	−	6.88406i	−0.809990	−	0.335509i	−0.0610398	−	0.998135i	$-0.519442\pi$
$421$	−16.6196	−	6.88406i	−0.809990	−	0.335509i	−0.748950	+	0.662627i	$0.769442\pi$
$422$	−3.60009	−	3.44471i	−0.175250	−	0.167686i
$423$	−1.33111	−	1.33111i	−0.0647209	−	0.0647209i
$424$	19.1195	−	21.8328i	0.928526	−	1.06029i
$425$	−4.23600	+	4.23600i	−0.205476	+	0.205476i
$426$	29.5363	−	0.651447i	1.43104	−	0.0315627i
$427$	−5.94122	+	14.3434i	−0.287516	+	0.694125i
$428$	−0.0933800	−	0.200008i	−0.00451369	−	0.00966774i
$429$	−19.1410	+	7.92847i	−0.924137	+	0.382790i
$430$	44.0710	+	17.1263i	2.12529	+	0.825905i
$431$		−	13.4339i		−	0.647090i	−0.946213	−	0.323545i	$-0.895125\pi$
$431$		−	13.4339i		−	0.647090i	0.946213	−	0.323545i	$-0.104875\pi$
$432$	−8.95736	+	28.5028i	−0.430961	+	1.37134i
$433$			26.5256i			1.27474i	0.770558	+	0.637369i	$0.219977\pi$
$433$			26.5256i			1.27474i	−0.770558	+	0.637369i	$0.780023\pi$
$434$	14.6773	−	37.7691i	0.704535	−	1.81297i
$435$	−75.0723	+	31.0960i	−3.59944	+	1.49094i
$436$	−12.1074	+	33.3137i	−0.579840	+	1.59544i
$437$	−12.0738	+	29.1487i	−0.577567	+	1.39437i
$438$	−0.411535	−	18.6588i	−0.0196639	−	0.891551i
$439$	11.2900	−	11.2900i	0.538840	−	0.538840i	−0.384348	−	0.923188i	$-0.625574\pi$
$439$	11.2900	−	11.2900i	0.538840	−	0.538840i	0.923188	+	0.384348i	$0.125574\pi$
$440$	−23.9241	+	11.8191i	−1.14054	+	0.563454i
$441$	−7.64515	−	7.64515i	−0.364055	−	0.364055i
$442$	2.43375	−	2.54353i	0.115762	−	0.120983i
$443$	37.4460	+	15.5107i	1.77911	+	0.736933i	0.992896	+	0.118984i	$0.0379637\pi$
$443$	37.4460	+	15.5107i	1.77911	+	0.736933i	0.786218	+	0.617949i	$0.212036\pi$
$444$	−5.73022	−	5.24581i	−0.271944	−	0.248955i
$445$	2.99270	+	7.22501i	0.141868	+	0.342498i
$446$	−4.10391	−	9.32089i	−0.194326	−	0.441357i
$447$	7.56504			0.357814
$448$	−3.15688	−	23.7197i	−0.149149	−	1.12065i
$449$	28.9054			1.36413			0.682066	−	0.731291i	$-0.261082\pi$
$449$	28.9054			1.36413			0.682066	+	0.731291i	$0.261082\pi$
$450$	−18.9603	−	43.0631i	−0.893798	−	2.03001i
$451$	−6.30945	−	15.2324i	−0.297101	−	0.717264i
$452$	18.6884	+	17.1086i	0.879030	+	0.804721i
$453$	29.4460	+	12.1970i	1.38350	+	0.573063i
$454$	−13.1513	+	13.7445i	−0.617222	+	0.645062i
$455$	17.4540	+	17.4540i	0.818257	+	0.818257i
$456$	−17.0174	−	34.4464i	−0.796911	−	1.61310i
$457$	26.2328	−	26.2328i	1.22712	−	1.22712i	0.262068	−	0.965049i	$-0.415595\pi$
$457$	26.2328	−	26.2328i	1.22712	−	1.22712i	0.965049	−	0.262068i	$-0.0844046\pi$
$458$	0.178307	+	8.08436i	0.00833175	+	0.377757i
$459$	2.85837	−	6.90072i	0.133417	−	0.322098i
$460$	15.3849	−	42.3317i	0.717325	−	1.97373i
$461$	−27.9412	+	11.5736i	−1.30135	+	0.539037i	−0.922348	−	0.386359i	$-0.873732\pi$
$461$	−27.9412	+	11.5736i	−1.30135	+	0.539037i	−0.379001	+	0.925396i	$0.623732\pi$
$462$	12.7526	−	32.8162i	0.593306	−	1.52675i
$463$		−	17.9680i		−	0.835045i	−0.908666	−	0.417523i	$-0.862898\pi$
$463$		−	17.9680i		−	0.835045i	0.908666	−	0.417523i	$-0.137102\pi$
$464$	29.7199	−	15.5068i	1.37971	−	0.719887i
$465$			92.8799i			4.30720i
$466$	19.9700	+	7.76051i	0.925094	+	0.359499i
$467$	30.5330	−	12.6472i	1.41290	−	0.585241i	0.459831	−	0.888006i	$-0.347910\pi$
$467$	30.5330	−	12.6472i	1.41290	−	0.585241i	0.953065	+	0.302765i	$0.0979098\pi$
$468$	11.6971	+	25.0538i	0.540700	+	1.15811i
$469$	−13.3542	+	32.2398i	−0.616638	+	1.48869i
$470$	−1.58875	+	0.0350411i	−0.0732834	+	0.00161633i
$471$	39.6751	−	39.6751i	1.82813	−	1.82813i
$472$	15.5481	+	13.6159i	0.715660	+	0.626722i
$473$	−20.2933	−	20.2933i	−0.933089	−	0.933089i
$474$	−16.9577	−	16.2258i	−0.778894	−	0.745277i
$475$	25.7054	+	10.6475i	1.17945	+	0.488542i
$476$	0.263757	+	5.97640i	0.0120893	+	0.273928i
$477$	−21.8074	−	52.6477i	−0.998492	−	2.41057i
$478$	−13.6925	+	6.02871i	−0.626282	+	0.275747i
$479$	12.9555			0.591951			0.295975	−	0.955196i	$-0.404355\pi$
$479$	12.9555			0.591951			0.295975	+	0.955196i	$0.404355\pi$
$480$	26.4383	+	48.0563i	1.20674	+	2.19346i
$481$	−3.30605			−0.150743
$482$	20.8086	−	9.16185i	0.947805	−	0.417311i
$483$	22.7414	+	54.9027i	1.03477	+	2.49816i
$484$	−5.79747	+	0.255860i	−0.263521	+	0.0116300i
$485$	−0.282423	−	0.116983i	−0.0128242	−	0.00531194i
$486$	−7.40479	−	7.08520i	−0.335888	−	0.321391i
$487$	−16.8608	−	16.8608i	−0.764037	−	0.764037i	0.213012	−	0.977049i	$-0.431673\pi$
$487$	−16.8608	−	16.8608i	−0.764037	−	0.764037i	−0.977049	+	0.213012i	$0.931673\pi$
$488$	0.970525	+	14.6487i	0.0439336	+	0.663114i
$489$	−11.4176	+	11.4176i	−0.516321	+	0.516321i
$490$	−9.12486	+	0.201256i	−0.412219	+	0.00909183i
$491$	−8.41495	+	20.3155i	−0.379762	+	0.916825i	0.612248	+	0.790666i	$0.290265\pi$
$491$	−8.41495	+	20.3155i	−0.379762	+	0.916825i	−0.992010	+	0.126160i	$0.959735\pi$
$492$	−30.7074	+	14.3367i	−1.38440	+	0.646349i
$493$	−7.74262	+	3.20710i	−0.348710	+	0.144440i
$494$	−15.2398	−	5.92231i	−0.685672	−	0.266457i
$495$			52.3971i			2.35507i
$496$	−3.37551	−	38.1679i	−0.151565	−	1.71379i
$497$			21.3647i			0.958339i
$498$	−19.9753	+	51.4023i	−0.895115	+	2.30339i
$499$	18.1211	−	7.50600i	0.811212	−	0.336015i	0.0617742	−	0.998090i	$-0.480324\pi$
$499$	18.1211	−	7.50600i	0.811212	−	0.336015i	0.749437	+	0.662075i	$0.230324\pi$
$500$	−6.17310	−	2.24353i	−0.276069	−	0.100334i
$501$	26.5924	−	64.1998i	1.18806	−	2.86824i
$502$	0.410734	+	18.6225i	0.0183319	+	0.831161i
$503$	1.65737	−	1.65737i	0.0738984	−	0.0738984i	−0.669192	−	0.743090i	$-0.733359\pi$
$503$	1.65737	−	1.65737i	0.0738984	−	0.0738984i	0.743090	+	0.669192i	$0.233359\pi$
$504$	−44.5035	−	15.0718i	−1.98234	−	0.671353i
$505$	5.67718	+	5.67718i	0.252631	+	0.252631i
$506$	−18.9005	+	19.7531i	−0.840231	+	0.878131i
$507$	−18.3840	−	7.61489i	−0.816461	−	0.338189i
$508$	22.3444	−	24.4078i	0.991374	−	1.08292i
$509$	10.1513	+	24.5075i	0.449951	+	1.08628i	0.972340	+	0.233570i	$0.0750407\pi$
$509$	10.1513	+	24.5075i	0.449951	+	1.08628i	−0.522389	+	0.852707i	$0.674959\pi$
$510$	−5.52550	−	12.5496i	−0.244673	−	0.555707i
$511$	13.4966			0.597055
$512$	−12.6110	−	18.7873i	−0.557332	−	0.830290i
$513$	−34.6910			−1.53165
$514$	−3.34609	−	7.59971i	−0.147590	−	0.335209i
$515$	−12.6365	−	30.5071i	−0.556829	−	1.34430i
$516$	−39.8326	+	43.5108i	−1.75353	+	1.91546i
$517$	0.891149	+	0.369126i	0.0391927	+	0.0162341i
$518$	3.88403	−	4.05922i	0.170654	−	0.178352i
$519$	−34.5816	−	34.5816i	−1.51797	−	1.51797i
$520$	22.1078	+	7.48716i	0.969491	+	0.328334i
$521$	−15.0099	+	15.0099i	−0.657595	+	0.657595i	−0.954810	−	0.297216i	$-0.903942\pi$
$521$	−15.0099	+	15.0099i	−0.657595	+	0.657595i	0.297216	+	0.954810i	$0.403942\pi$
$522$	−1.45144	−	65.8078i	−0.0635280	−	2.88033i
$523$	−15.7139	+	37.9366i	−0.687119	+	1.65885i	0.0633868	+	0.997989i	$0.479810\pi$
$523$	−15.7139	+	37.9366i	−0.687119	+	1.65885i	−0.750506	+	0.660864i	$0.770190\pi$
$524$	−5.70502	−	2.07341i	−0.249225	−	0.0905775i
$525$	48.4172	−	20.0551i	2.11310	−	0.875274i
$526$	−8.60675	+	22.1477i	−0.375272	+	0.965685i
$527$			9.57921i			0.417277i
$528$	−2.93286	−	33.1627i	−0.127636	−	1.44322i
$529$		−	23.1455i		−	1.00633i
$530$	−44.8388	−	17.4247i	−1.94767	−	0.756881i
$531$	37.4929	−	15.5301i	1.62705	−	0.673947i
$532$	25.1756	−	11.7540i	1.09150	−	0.509603i
$533$	−5.51898	+	13.3240i	−0.239053	+	0.577126i
$534$	−9.75445	+	0.215143i	−0.422116	+	0.00931013i
$535$	−0.258722	+	0.258722i	−0.0111855	+	0.0111855i
$536$	2.18146	+	32.9260i	0.0942247	+	1.42219i
$537$	−41.3896	−	41.3896i	−1.78609	−	1.78609i
$538$	−8.54887	−	8.17990i	−0.368568	−	0.352661i
$539$	5.11826	+	2.12005i	0.220459	+	0.0913171i
$540$	49.4763	−	2.18354i	2.12912	−	0.0939648i
$541$	2.79078	+	6.73755i	0.119985	+	0.289670i	0.972449	−	0.233117i	$-0.0748924\pi$
$541$	2.79078	+	6.73755i	0.119985	+	0.289670i	−0.852464	+	0.522787i	$0.824892\pi$
$542$	−1.25372	+	0.552002i	−0.0538518	+	0.0237105i
$543$	−12.2409			−0.525306
$544$	2.72672	+	4.95631i	0.116907	+	0.212500i
$545$	58.7548			2.51678
$546$	−28.1851	+	12.4097i	−1.20621	+	0.531085i
$547$	−9.86296	−	23.8113i	−0.421710	−	1.01810i	−0.981843	−	0.189695i	$-0.939250\pi$
$547$	−9.86296	−	23.8113i	−0.421710	−	1.01810i	0.560134	−	0.828402i	$-0.310750\pi$
$548$	−0.207904	−	4.71083i	−0.00888121	−	0.201237i
$549$	26.6327	+	11.0316i	1.13665	+	0.470818i
$550$	17.4197	+	16.6679i	0.742779	+	0.710721i
$551$	27.5230	+	27.5230i	1.17252	+	1.17252i
$552$	42.2752	+	37.0215i	1.79935	+	1.57574i
$553$	12.0015	−	12.0015i	0.510354	−	0.510354i
$554$	−7.03901	+	0.155251i	−0.299059	+	0.00659599i
$555$	−4.92803	+	11.8973i	−0.209183	+	0.505013i
$556$	−0.0241243	−	0.0516710i	−0.00102310	−	0.00219134i
$557$	−19.5293	+	8.08932i	−0.827485	+	0.342755i	−0.755906	−	0.654680i	$-0.772804\pi$
$557$	−19.5293	+	8.08932i	−0.827485	+	0.342755i	−0.0715781	+	0.997435i	$0.522804\pi$
$558$	−70.1293	−	27.2528i	−2.96881	−	1.15370i
$559$			25.1036i			1.06177i
$560$	−35.1656	+	18.3482i	−1.48602	+	0.775354i
$561$			8.32304i			0.351399i
$562$	2.04793	−	5.26991i	0.0863865	−	0.222298i
$563$	−1.46703	+	0.607665i	−0.0618281	+	0.0256100i	−0.413383	−	0.910557i	$-0.635653\pi$
$563$	−1.46703	+	0.607665i	−0.0618281	+	0.0256100i	0.351555	+	0.936167i	$0.385653\pi$
$564$	0.677227	−	1.86340i	0.0285164	−	0.0784632i
$565$	16.0722	−	38.8017i	0.676163	−	1.63240i
$566$	−0.918455	−	41.6423i	−0.0386056	−	1.75036i
$567$	−10.9639	+	10.9639i	−0.460442	+	0.460442i
$568$	8.94825	+	18.1130i	0.375460	+	0.760003i
$569$	2.10600	+	2.10600i	0.0882880	+	0.0882880i	0.749871	−	0.661584i	$-0.230115\pi$
$569$	2.10600	+	2.10600i	0.0882880	+	0.0882880i	−0.661584	+	0.749871i	$0.730115\pi$
$570$	−44.0290	+	46.0150i	−1.84417	+	1.92736i
$571$	−34.7247	−	14.3835i	−1.45318	−	0.601929i	−0.490230	−	0.871593i	$-0.663087\pi$
$571$	−34.7247	−	14.3835i	−1.45318	−	0.601929i	−0.962954	+	0.269664i	$0.913087\pi$
$572$	−10.4500	−	9.56661i	−0.436937	−	0.400000i
$573$	−0.563124	−	1.35950i	−0.0235249	−	0.0567940i
$574$	−9.87559	−	22.4296i	−0.412199	−	0.936195i
$575$	−40.6945			−1.69708
$576$	−44.0426	+	5.86167i	−1.83511	+	0.244236i
$577$	14.2211			0.592033			0.296017	−	0.955183i	$-0.404342\pi$
$577$	14.2211			0.592033			0.296017	+	0.955183i	$0.404342\pi$
$578$	−0.569875	−	1.29431i	−0.0237037	−	0.0538363i
$579$	−2.23432	−	5.39412i	−0.0928551	−	0.224172i
$580$	−40.9856	−	37.5209i	−1.70184	−	1.55797i
$581$	−36.8446	−	15.2615i	−1.52857	−	0.633156i
$582$	0.263672	−	0.275565i	0.0109295	−	0.0114225i
$583$	20.6469	+	20.6469i	0.855107	+	0.855107i
$584$	11.4424	−	5.65282i	0.473490	−	0.233916i
$585$	32.4085	−	32.4085i	1.33993	−	1.33993i
$586$	0.138237	+	6.26757i	0.00571050	+	0.258911i
$587$	5.52683	−	13.3429i	0.228117	−	0.550722i	−0.767831	−	0.640652i	$-0.778664\pi$
$587$	5.52683	−	13.3429i	0.228117	−	0.550722i	0.995948	+	0.0899296i	$0.0286642\pi$
$588$	3.88961	−	10.7023i	0.160405	−	0.441356i
$589$	41.1039	−	17.0258i	1.69366	−	0.701536i
$590$	12.4089	−	31.9318i	0.510868	−	1.31461i
$591$			31.7212i			1.30484i
$592$	1.59273	−	5.06816i	0.0654609	−	0.208300i
$593$		−	8.14279i		−	0.334384i	−0.985924	−	0.167192i	$-0.946530\pi$
$593$		−	8.14279i		−	0.334384i	0.985924	−	0.167192i	$-0.0534700\pi$
$594$	−28.0191	−	10.8884i	−1.14964	−	0.446758i
$595$	9.16133	−	3.79475i	0.375578	−	0.155569i
$596$	2.18850	+	4.68749i	0.0896445	+	0.192007i
$597$	−13.3726	+	32.2843i	−0.547304	+	1.32131i
$598$	23.9079	−	0.527309i	0.977667	−	0.0215633i
$599$	−18.2818	+	18.2818i	−0.746972	+	0.746972i	−0.973909	−	0.226937i	$-0.927129\pi$
$599$	−18.2818	+	18.2818i	−0.746972	+	0.746972i	0.226937	+	0.973909i	$0.427129\pi$
$600$	32.6483	−	37.2813i	1.33286	−	1.52200i
$601$	27.5717	+	27.5717i	1.12467	+	1.12467i	0.991029	+	0.133645i	$0.0426683\pi$
$601$	27.5717	+	27.5717i	1.12467	+	1.12467i	0.133645	+	0.991029i	$0.457332\pi$
$602$	−30.8226	−	29.4923i	−1.25623	−	1.20202i
$603$	59.8625	+	24.7959i	2.43779	+	1.00977i
$604$	0.960954	+	21.7740i	0.0391007	+	0.885971i
$605$	3.68113	+	8.88704i	0.149659	+	0.361309i
$606$	−9.16762	+	4.03643i	−0.372409	+	0.163969i
$607$	0.932516			0.0378497			0.0189248	−	0.999821i	$-0.493976\pi$
$607$	0.932516			0.0378497			0.0189248	+	0.999821i	$0.493976\pi$
$608$	16.4209	−	20.5094i	0.665954	−	0.831767i
$609$	73.3138			2.97083
$610$	22.2717	−	9.80606i	0.901756	−	0.397036i
$611$	−0.322880	−	0.779502i	−0.0130623	−	0.0315353i
$612$	11.0969	−	0.489742i	0.448567	−	0.0197966i
$613$	−7.71780	−	3.19682i	−0.311719	−	0.129118i	0.221339	−	0.975197i	$-0.428957\pi$
$613$	−7.71780	−	3.19682i	−0.311719	−	0.129118i	−0.533058	+	0.846079i	$0.678957\pi$
$614$	4.43753	+	4.24600i	0.179084	+	0.171355i
$615$	39.7217	+	39.7217i	1.60174	+	1.60174i
$616$	24.0230	−	1.59161i	0.967914	−	0.0641276i
$617$	−5.46622	+	5.46622i	−0.220062	+	0.220062i	−0.808524	−	0.588463i	$-0.799733\pi$
$617$	−5.46622	+	5.46622i	−0.220062	+	0.220062i	0.588463	+	0.808524i	$0.299733\pi$
$618$	41.1875	−	0.908424i	1.65680	−	0.0365422i
$619$	3.51937	−	8.49651i	0.141455	−	0.341504i	−0.837236	−	0.546842i	$-0.815830\pi$
$619$	3.51937	−	8.49651i	0.141455	−	0.341504i	0.978691	+	0.205339i	$0.0658297\pi$
$620$	−57.5507	+	26.8694i	−2.31129	+	1.07910i
$621$	46.8769	−	19.4171i	1.88111	−	0.779180i
$622$	−14.0440	−	5.45761i	−0.563114	−	0.218830i
$623$		−	7.05577i		−	0.282684i
$624$	−18.6977	+	22.3257i	−0.748506	+	0.893745i
$625$		−	19.0657i		−	0.762626i
$626$	12.5752	−	32.3598i	0.502608	−	1.29336i
$627$	35.7138	−	14.7931i	1.42627	−	0.590781i
$628$	36.0614	+	13.1060i	1.43901	+	0.522988i
$629$	−0.508255	+	1.22704i	−0.0202654	+	0.0489251i
$630$	1.71740	+	77.8660i	0.0684228	+	3.10225i
$631$	−29.4108	+	29.4108i	−1.17082	+	1.17082i	−0.188811	+	0.982013i	$0.560463\pi$
$631$	−29.4108	+	29.4108i	−1.17082	+	1.17082i	−0.982013	+	0.188811i	$0.939537\pi$
$632$	5.14821	−	15.2014i	0.204785	−	0.604680i
$633$	−7.28635	−	7.28635i	−0.289607	−	0.289607i
$634$	20.6183	−	21.5483i	0.818856	−	0.855792i
$635$	−50.6764	−	20.9908i	−2.01103	−	0.832996i
$636$	40.5266	−	44.2689i	1.60698	−	1.75538i
$637$	−1.85444	−	4.47702i	−0.0734756	−	0.177386i
$638$	13.5910	+	30.8683i	0.538075	+	1.22209i
$639$	39.6698			1.56931
$640$	−22.1285	+	30.2841i	−0.874706	+	1.19708i
$641$	15.1121			0.596894			0.298447	−	0.954426i	$-0.403531\pi$
$641$	15.1121			0.596894			0.298447	+	0.954426i	$0.403531\pi$
$642$	−0.183949	−	0.417789i	−0.00725989	−	0.0164888i
$643$	11.6391	+	28.0993i	0.459002	+	1.10813i	0.968802	+	0.247836i	$0.0797193\pi$
$643$	11.6391	+	28.0993i	0.459002	+	1.10813i	−0.509800	+	0.860293i	$0.670281\pi$
$644$	−27.4402	+	29.9740i	−1.08129	+	1.18114i
$645$	90.3390	+	37.4196i	3.55709	+	1.47340i
$646$	−4.54095	+	4.74578i	−0.178661	+	0.186720i
$647$	10.8335	+	10.8335i	0.425908	+	0.425908i	0.887232	−	0.461324i	$-0.152625\pi$
$647$	10.8335	+	10.8335i	0.425908	+	0.425908i	−0.461324	+	0.887232i	$0.652625\pi$
$648$	−4.70314	+	13.8872i	−0.184757	+	0.545543i
$649$	−14.7036	+	14.7036i	−0.577167	+	0.577167i
$650$	−0.465020	−	21.0837i	−0.0182396	−	0.826973i
$651$	32.0688	−	77.4209i	1.25688	−	3.03437i
$652$	−10.3776	−	3.77161i	−0.406419	−	0.147708i
$653$	1.60102	−	0.663163i	0.0626527	−	0.0259516i	−0.351137	−	0.936324i	$-0.614205\pi$
$653$	1.60102	−	0.663163i	0.0626527	−	0.0259516i	0.413790	+	0.910372i	$0.364205\pi$
$654$	−26.5521	+	68.3263i	−1.03827	+	2.67177i
$655$			10.0619i			0.393149i
$656$	−17.7668	−	14.8796i	−0.693676	−	0.580950i
$657$		−	25.0604i		−	0.977699i
$658$	1.33641	+	0.519340i	0.0520988	+	0.0202460i
$659$	−33.6857	+	13.9531i	−1.31221	+	0.543534i	−0.925528	−	0.378680i	$-0.876378\pi$
$659$	−33.6857	+	13.9531i	−1.31221	+	0.543534i	−0.386680	+	0.922214i	$0.626378\pi$
$660$	−50.0038	+	23.3459i	−1.94640	+	0.908736i
$661$	−13.5202	+	32.6407i	−0.525876	+	1.26958i	0.408327	+	0.912836i	$0.366112\pi$
$661$	−13.5202	+	32.6407i	−0.525876	+	1.26958i	−0.934203	+	0.356741i	$0.883888\pi$
$662$	−32.3324	+	0.713118i	−1.25663	+	0.0277161i
$663$	5.14794	−	5.14794i	0.199930	−	0.199930i
$664$	−37.6288	+	2.49304i	−1.46028	+	0.0967487i
$665$	−32.5661	−	32.5661i	−1.26286	−	1.26286i
$666$	−7.53713	−	7.21183i	−0.292058	−	0.279453i
$667$	−52.5960	−	21.7860i	−2.03653	−	0.843556i
$668$	47.4728	−	2.09512i	1.83678	−	0.0810627i
$669$	−8.06008	−	19.4587i	−0.311621	−	0.752319i
$670$	50.0604	−	22.0412i	1.93400	−	0.851525i
$671$	−14.7708			−0.570222
$672$	−5.44541	−	49.1862i	−0.210061	−	1.89740i
$673$	39.2554			1.51318			0.756592	−	0.653888i	$-0.226863\pi$
$673$	39.2554			1.51318			0.756592	+	0.653888i	$0.226863\pi$
$674$	−12.0204	+	5.29250i	−0.463010	+	0.203860i
$675$	−17.1234	−	41.3395i	−0.659079	−	1.59116i
$676$	−0.599950	−	13.5941i	−0.0230750	−	0.522850i
$677$	27.4150	+	11.3557i	1.05364	+	0.436434i	0.841191	−	0.540738i	$-0.181855\pi$
$677$	27.4150	+	11.3557i	1.05364	+	0.436434i	0.212453	+	0.977171i	$0.431855\pi$
$678$	37.8595	+	36.2255i	1.45399	+	1.39123i
$679$	0.195025	+	0.195025i	0.00748438	+	0.00748438i
$680$	6.17759	−	7.05424i	0.236900	−	0.270518i
$681$	−27.8181	+	27.8181i	−1.06599	+	1.06599i
$682$	38.5425	−	0.850087i	1.47587	−	0.0325515i
$683$	−16.4205	+	39.6425i	−0.628311	+	1.51688i	0.213409	+	0.976963i	$0.431543\pi$
$683$	−16.4205	+	39.6425i	−0.628311	+	1.51688i	−0.841720	+	0.539915i	$0.818457\pi$
$684$	−21.8248	−	46.7459i	−0.834492	−	1.78737i
$685$	−7.22131	+	2.99117i	−0.275912	+	0.114287i
$686$	−19.9241	−	7.74266i	−0.760706	−	0.295616i
$687$			16.7231i			0.638027i
$688$	−38.4836	−	12.0940i	−1.46717	−	0.461079i
$689$		−	25.5409i		−	0.973032i
$690$	33.7398	−	86.8223i	1.28445	−	3.30527i
$691$	−22.5483	+	9.33980i	−0.857777	+	0.355303i	−0.767838	−	0.640645i	$-0.778667\pi$
$691$	−22.5483	+	9.33980i	−0.857777	+	0.355303i	−0.0899391	+	0.995947i	$0.528667\pi$
$692$	11.4235	−	31.4318i	0.434255	−	1.19486i
$693$	18.0912	−	43.6761i	0.687229	−	1.65912i
$694$	−0.410235	−	18.5998i	−0.0155723	−	0.706040i
$695$	−0.0668394	+	0.0668394i	−0.00253536	+	0.00253536i
$696$	62.1553	−	30.7062i	2.35599	−	1.16392i
$697$	4.09672	+	4.09672i	0.155174	+	0.155174i
$698$	30.4954	−	31.8710i	1.15427	−	1.20633i
$699$	40.9356	+	16.9561i	1.54833	+	0.641338i
$700$	26.4333	+	24.1988i	0.999085	+	0.914627i
$701$	−1.56900	−	3.78789i	−0.0592602	−	0.143067i	0.891476	−	0.453068i	$-0.149671\pi$
$701$	−1.56900	−	3.78789i	−0.0592602	−	0.143067i	−0.950736	+	0.310001i	$0.899671\pi$
$702$	10.5956	+	24.0650i	0.399905	+	0.908274i
$703$	6.16851			0.232650
$704$	19.7000	−	11.4110i	0.742472	−	0.430067i
$705$	−3.28644			−0.123775
$706$	3.59118	+	8.15635i	0.135156	+	0.306968i
$707$	−2.77210	−	6.69243i	−0.104255	−	0.251695i
$708$	31.5259	+	28.8609i	1.18482	+	1.08466i
$709$	−24.9108	−	10.3184i	−0.935545	−	0.387515i	−0.137766	−	0.990465i	$-0.543992\pi$
$709$	−24.9108	−	10.3184i	−0.935545	−	0.387515i	−0.797779	+	0.602950i	$0.793992\pi$
$710$	23.1518	−	24.1961i	0.868871	−	0.908063i
$711$	−22.2842	−	22.2842i	−0.835724	−	0.835724i
$712$	−2.95519	−	5.98187i	−0.110750	−	0.224180i
$713$	−46.0129	+	46.0129i	−1.72320	+	1.72320i
$714$	0.272801	+	12.3687i	0.0102093	+	0.462886i
$715$	−8.98709	+	21.6967i	−0.336098	+	0.811412i
$716$	13.6724	−	37.6197i	0.510961	−	1.40591i
$717$	−28.5852	+	11.8404i	−1.06753	+	0.442187i
$718$	−5.43534	+	13.9867i	−0.202845	+	0.521980i
$719$		−	10.6164i		−	0.395923i	−0.980210	−	0.197962i	$-0.936568\pi$
$719$		−	10.6164i		−	0.395923i	0.980210	−	0.197962i	$-0.0634321\pi$
$720$	34.0688	+	65.2953i	1.26967	+	2.43341i
$721$			29.7925i			1.10953i
$722$	3.38945	+	1.31717i	0.126142	+	0.0490198i
$723$	43.4410	−	17.9939i	1.61559	−	0.669199i
$724$	−3.54118	−	7.58475i	−0.131607	−	0.281885i
$725$	−19.2125	+	46.3830i	−0.713533	+	1.72262i
$726$	−11.9983	+	0.264633i	−0.445300	+	0.00982147i
$727$	−19.5805	+	19.5805i	−0.726200	+	0.726200i	−0.969861	−	0.243660i	$-0.921652\pi$
$727$	−19.5805	+	19.5805i	−0.726200	+	0.726200i	0.243660	+	0.969861i	$0.421652\pi$
$728$	−15.8431	−	13.8742i	−0.587183	−	0.514212i
$729$	−25.9834	−	25.9834i	−0.962347	−	0.962347i
$730$	−15.2852	−	14.6255i	−0.565732	−	0.541316i
$731$	9.31715	+	3.85929i	0.344607	+	0.142741i
$732$	1.33862	+	30.3314i	0.0494768	+	1.12108i
$733$	−10.5729	−	25.5252i	−0.390519	−	0.942796i	−0.989827	−	0.142277i	$-0.954558\pi$
$733$	−10.5729	−	25.5252i	−0.390519	−	0.942796i	0.599308	−	0.800518i	$-0.295442\pi$
$734$	−8.56653	+	3.77177i	−0.316196	+	0.139219i
$735$	−18.8755			−0.696232
$736$	−10.7096	+	36.9048i	−0.394761	+	1.36033i
$737$	−33.2006			−1.22296
$738$	−41.6472	+	18.3369i	−1.53305	+	0.674991i
$739$	−20.3913	−	49.2289i	−0.750105	−	1.81091i	−0.558633	−	0.829415i	$-0.688674\pi$
$739$	−20.3913	−	49.2289i	−0.750105	−	1.81091i	−0.191472	−	0.981498i	$-0.561326\pi$
$740$	−8.79752	+	0.388262i	−0.323403	+	0.0142728i
$741$	−31.2394	−	12.9398i	−1.14761	−	0.475354i
$742$	31.3596	+	30.0061i	1.15125	+	1.10156i
$743$	14.8288	+	14.8288i	0.544015	+	0.544015i	0.924703	−	0.380689i	$-0.124313\pi$
$743$	14.8288	+	14.8288i	0.544015	+	0.544015i	−0.380689	+	0.924703i	$0.624313\pi$
$744$	−5.23858	−	79.0687i	−0.192056	−	2.89880i
$745$	6.06353	−	6.06353i	0.222151	−	0.222151i
$746$	−23.1884	+	0.511439i	−0.848986	+	0.0187251i
$747$	−28.3375	+	68.4128i	−1.03682	+	2.50309i
$748$	−5.15717	+	2.40779i	−0.188565	+	0.0880373i
$749$	0.304989	−	0.126331i	0.0111441	−	0.00461602i
$750$	−12.6610	−	4.92016i	−0.462315	−	0.179659i
$751$			12.2724i			0.447827i	0.974609	+	0.223913i	$0.0718833\pi$
$751$			12.2724i			0.447827i	−0.974609	+	0.223913i	$0.928117\pi$
$752$	1.35052	−	0.119438i	0.0492486	−	0.00435547i
$753$			38.5220i			1.40382i
$754$	10.6863	−	27.4988i	0.389170	−	1.00145i
$755$	33.3777	−	13.8255i	1.21474	−	0.503162i
$756$	−41.9954	−	15.2627i	−1.52736	−	0.555097i
$757$	−17.8650	+	43.1299i	−0.649314	+	1.56758i	0.164449	+	0.986386i	$0.447415\pi$
$757$	−17.8650	+	43.1299i	−0.649314	+	1.56758i	−0.813763	+	0.581197i	$0.802585\pi$
$758$	0.0550317	+	2.49511i	0.00199884	+	0.0906264i
$759$	−39.9790	+	39.9790i	−1.45115	+	1.45115i
$760$	−41.2493	−	13.9697i	−1.49627	−	0.506735i
$761$	19.3533	+	19.3533i	0.701557	+	0.701557i	0.964745	−	0.263187i	$-0.0847737\pi$
$761$	19.3533	+	19.3533i	0.701557	+	0.701557i	−0.263187	+	0.964745i	$0.584774\pi$
$762$	47.3118	−	49.4458i	1.71392	−	1.79123i
$763$	−48.9756	−	20.2864i	−1.77304	−	0.734416i
$764$	0.679475	−	0.742218i	0.0245825	−	0.0268525i
$765$	−7.04605	−	17.0107i	−0.254750	−	0.615022i
$766$	17.4415	+	39.6136i	0.630188	+	1.43130i
$767$	18.1889			0.656762
$768$	−25.2174	−	39.4192i	−0.909954	−	1.42242i
$769$	22.2128			0.801014			0.400507	−	0.916294i	$-0.368834\pi$
$769$	22.2128			0.801014			0.400507	+	0.916294i	$0.368834\pi$
$770$	−16.0814	−	36.5244i	−0.579533	−	1.31625i
$771$	−6.57172	−	15.8655i	−0.236675	−	0.571383i
$772$	2.69597	−	2.94491i	0.0970299	−	0.105990i
$773$	−41.0693	−	17.0115i	−1.47716	−	0.611860i	−0.508682	−	0.860954i	$-0.669867\pi$
$773$	−41.0693	−	17.0115i	−1.47716	−	0.611860i	−0.968479	+	0.249094i	$0.919867\pi$
$774$	−54.7610	+	57.2311i	−1.96834	+	2.05713i
$775$	40.5775	+	40.5775i	1.45759	+	1.45759i
$776$	0.247025	+	0.0836589i	0.00886768	+	0.00300318i
$777$	8.21561	−	8.21561i	0.294734	−	0.294734i
$778$	1.02253	+	46.3611i	0.0366596	+	1.66213i
$779$	10.2974	−	24.8602i	0.368944	−	0.890710i
$780$	45.3680	+	16.4884i	1.62444	+	0.590379i
$781$	−18.7794	+	7.77868i	−0.671979	+	0.278343i
$782$	3.47977	−	8.95446i	0.124436	−	0.320211i
$783$		−	62.5967i		−	2.23702i
$784$	7.75665	−	0.685986i	0.277023	−	0.0244995i
$785$		−	63.6009i		−	2.27001i
$786$	−11.7010	−	4.54709i	−0.417360	−	0.162189i
$787$	22.1840	−	9.18890i	0.790773	−	0.327549i	0.0495186	−	0.998773i	$-0.484231\pi$
$787$	22.1840	−	9.18890i	0.790773	−	0.327549i	0.741254	+	0.671224i	$0.234231\pi$
$788$	−19.6552	+	9.17667i	−0.700189	+	0.326905i
$789$	−18.8051	+	45.3994i	−0.669478	+	1.61626i
$790$	−26.5973	+	0.586626i	−0.946290	+	0.0208712i
$791$	−26.7943	+	26.7943i	−0.952695	+	0.952695i
$792$	−2.95528	−	44.6057i	−0.105011	−	1.58499i
$793$	9.13601	+	9.13601i	0.324429	+	0.324429i
$794$	10.6882	+	10.2269i	0.379309	+	0.362938i
$795$	−91.9129	−	38.0716i	−3.25981	−	1.35026i
$796$	−23.8727	+	1.05358i	−0.846147	+	0.0373431i
$797$	17.6567	+	42.6270i	0.625431	+	1.50992i	0.845243	+	0.534382i	$0.179456\pi$
$797$	17.6567	+	42.6270i	0.625431	+	1.50992i	−0.219812	+	0.975542i	$0.570544\pi$
$798$	52.5885	−	23.1543i	1.86161	−	0.819652i
$799$	−0.338949			−0.0119911
$800$	32.5453	+	9.44451i	1.15065	+	0.333914i
$801$	−13.1011			−0.462904
$802$	15.3565	−	6.76132i	0.542255	−	0.238751i
$803$	4.91398	+	11.8634i	0.173410	+	0.418650i
$804$	3.00883	+	68.1763i	0.106113	+	2.40439i
$805$	62.2334	+	25.7779i	2.19344	+	0.908552i
$806$	−24.3650	−	23.3134i	−0.858220	−	0.821180i
$807$	−17.3024	−	17.3024i	−0.609073	−	0.609073i
$808$	−5.15319	−	4.51278i	−0.181288	−	0.158759i
$809$	−16.2354	+	16.2354i	−0.570807	+	0.570807i	−0.932354	−	0.361547i	$-0.882249\pi$
$809$	−16.2354	+	16.2354i	−0.570807	+	0.570807i	0.361547	+	0.932354i	$0.382249\pi$
$810$	24.2979	−	0.535911i	0.853743	−	0.0188300i
$811$	−7.36884	+	17.7900i	−0.258755	+	0.624690i	−0.998857	−	0.0478052i	$-0.984777\pi$
$811$	−7.36884	+	17.7900i	−0.258755	+	0.624690i	0.740102	+	0.672495i	$0.234777\pi$
$812$	21.2091	+	45.4271i	0.744292	+	1.59418i
$813$	−2.61733	+	1.08413i	−0.0917936	+	0.0380222i
$814$	4.98215	+	1.93610i	0.174624	+	0.0678603i
$815$			18.3028i			0.641121i
$816$	5.41168	+	10.3719i	0.189447	+	0.363088i
$817$		−	46.8388i		−	1.63868i
$818$	−11.9319	+	30.7042i	−0.417188	+	1.07355i
$819$	−38.2041	+	15.8247i	−1.33496	+	0.552959i
$820$	−13.1214	+	36.1038i	−0.458220	+	1.26080i
$821$	13.3674	−	32.2719i	0.466527	−	1.12630i	−0.499142	−	0.866520i	$-0.666351\pi$
$821$	13.3674	−	32.2719i	0.466527	−	1.12630i	0.965669	−	0.259776i	$-0.0836487\pi$
$822$	−0.215032	−	9.74946i	−0.00750012	−	0.340052i
$823$	22.4412	−	22.4412i	0.782252	−	0.782252i	−0.197959	−	0.980210i	$-0.563431\pi$
$823$	22.4412	−	22.4412i	0.782252	−	0.782252i	0.980210	+	0.197959i	$0.0634312\pi$
$824$	12.4781	+	25.2580i	0.434694	+	0.879904i
$825$	35.2564	+	35.2564i	1.22747	+	1.22747i
$826$	−21.3687	+	22.3326i	−0.743514	+	0.777051i
$827$	1.56221	+	0.647090i	0.0543235	+	0.0225015i	0.409680	−	0.912229i	$-0.365640\pi$
$827$	1.56221	+	0.647090i	0.0543235	+	0.0225015i	−0.355356	+	0.934731i	$0.615640\pi$
$828$	55.6555	+	50.9507i	1.93416	+	1.77066i
$829$	−9.22670	−	22.2752i	−0.320457	−	0.773651i	−0.999227	−	0.0393005i	$-0.987487\pi$
$829$	−9.22670	−	22.2752i	−0.320457	−	0.773651i	0.678771	−	0.734350i	$-0.262513\pi$
$830$	25.1894	+	57.2106i	0.874335	+	1.98581i
$831$	−14.5607			−0.505106
$832$	−19.2427	−	5.12691i	−0.667120	−	0.177744i
$833$	−1.94673			−0.0674502
$834$	−0.0475223	−	0.107934i	−0.00164556	−	0.00373744i
$835$	−30.1431	−	72.7719i	−1.04314	−	2.51837i
$836$	19.4979	+	17.8496i	0.674348	+	0.617342i
$837$	−66.1034	−	27.3809i	−2.28487	−	0.946423i
$838$	36.2605	−	37.8961i	1.25260	−	1.30910i
$839$	9.70463	+	9.70463i	0.335041	+	0.335041i	0.854497	−	0.519456i	$-0.173865\pi$
$839$	9.70463	+	9.70463i	0.335041	+	0.335041i	−0.519456	+	0.854497i	$0.673865\pi$
$840$	−73.5442	+	36.3326i	−2.53752	+	1.25360i
$841$	−29.1566	+	29.1566i	−1.00540	+	1.00540i
$842$	−0.560968	−	25.4340i	−0.0193322	−	0.876513i
$843$	4.47455	−	10.8025i	0.154112	−	0.372059i
$844$	2.40693	−	6.62269i	0.0828499	−	0.227962i
$845$	−20.8386	+	8.63164i	−0.716870	+	0.296937i
$846$	0.964306	−	2.48144i	0.0331535	−	0.0853137i
$847$		−	8.67886i		−	0.298209i
$848$	39.1541	+	12.3047i	1.34456	+	0.422545i
$849$		−	86.1403i		−	2.95633i
$850$	−7.89669	−	3.06871i	−0.270854	−	0.105256i
$851$	−8.33531	+	3.45260i	−0.285731	+	0.118354i
$852$	17.6752	+	37.8579i	0.605541	+	1.29699i
$853$	2.66043	−	6.42284i	0.0910914	−	0.219914i	−0.871767	−	0.489920i	$-0.837026\pi$
$853$	2.66043	−	6.42284i	0.0910914	−	0.219914i	0.962859	+	0.270006i	$0.0870258\pi$
$854$	−21.9506	+	0.484138i	−0.751133	+	0.0165669i
$855$	−60.4685	+	60.4685i	−2.06798	+	2.06798i
$856$	0.205658	−	0.234842i	0.00702923	−	0.00802674i
$857$	−29.7633	−	29.7633i	−1.01669	−	1.01669i	−0.999858	−	0.0168351i	$-0.994641\pi$
$857$	−29.7633	−	29.7633i	−1.01669	−	1.01669i	−0.0168351	−	0.999858i	$-0.505359\pi$
$858$	−21.1699	−	20.2562i	−0.722728	−	0.691535i
$859$	12.2182	+	5.06094i	0.416879	+	0.172677i	0.581256	−	0.813721i	$-0.302561\pi$
$859$	12.2182	+	5.06094i	0.416879	+	0.172677i	−0.164377	+	0.986398i	$0.552561\pi$
$860$	2.94816	+	66.8015i	0.100531	+	2.27791i
$861$	−19.3956	−	46.8252i	−0.661002	−	1.59580i
$862$	17.3877	−	7.65566i	0.592227	−	0.260753i
$863$	−41.0543			−1.39750			−0.698752	−	0.715364i	$-0.746261\pi$
$863$	−41.0543			−1.39750			−0.698752	+	0.715364i	$0.746261\pi$
$864$	−41.9961	+	4.64940i	−1.42873	+	0.158176i
$865$	−55.4358			−1.88487
$866$	−34.3324	+	15.1163i	−1.16666	+	0.513672i
$867$	−1.11923	−	2.70207i	−0.0380112	−	0.0917671i
$868$	57.2492	−	2.52659i	1.94316	−	0.0857579i
$869$	14.9188	+	6.17956i	0.506085	+	0.209627i
$870$	−83.0297	−	79.4462i	−2.81497	−	2.69348i
$871$	20.5351	+	20.5351i	0.695806	+	0.695806i
$872$	−50.0180	+	3.31386i	−1.69382	+	0.112222i
$873$	0.362121	−	0.362121i	0.0122559	−	0.0122559i
$874$	−44.6080	+	0.983866i	−1.50889	+	0.0332798i
$875$	3.75911	−	9.07529i	0.127081	−	0.306801i
$876$	23.9158	−	11.1658i	0.808038	−	0.377258i
$877$	20.5932	−	8.53000i	0.695384	−	0.288038i	−0.00685702	−	0.999976i	$-0.502183\pi$
$877$	20.5932	−	8.53000i	0.695384	−	0.288038i	0.702242	+	0.711939i	$0.252183\pi$
$878$	21.0466	+	8.17886i	0.710288	+	0.276023i
$879$			12.9650i			0.437297i
$880$	−28.9314	−	24.2299i	−0.975276	−	0.816788i
$881$			9.49199i			0.319793i	0.987134	+	0.159897i	$0.0511161\pi$
$881$			9.49199i			0.319793i	−0.987134	+	0.159897i	$0.948884\pi$
$882$	5.53843	−	14.2520i	0.186489	−	0.479889i
$883$	−36.6446	+	15.1787i	−1.23319	+	0.510804i	−0.901580	−	0.432613i	$-0.857592\pi$
$883$	−36.6446	+	15.1787i	−1.23319	+	0.510804i	−0.331609	+	0.943417i	$0.607592\pi$
$884$	4.67905	+	1.70054i	0.157374	+	0.0571953i
$885$	27.1125	−	65.4554i	0.911378	−	2.20026i
$886$	1.26393	+	57.3060i	0.0424626	+	1.92523i
$887$	−23.4861	+	23.4861i	−0.788587	+	0.788587i	−0.981263	−	0.192676i	$-0.938284\pi$
$887$	−23.4861	+	23.4861i	−0.788587	+	0.788587i	0.192676	+	0.981263i	$0.438284\pi$
$888$	3.52421	−	10.4061i	0.118265	−	0.349207i
$889$	34.9942	+	34.9942i	1.17367	+	1.17367i
$890$	−7.64595	+	7.99084i	−0.256293	+	0.267853i
$891$	−13.6290	−	5.64533i	−0.456590	−	0.189126i
$892$	9.72542	−	10.6235i	0.325631	−	0.355700i
$893$	0.602438	+	1.45441i	0.0201598	+	0.0486701i
$894$	4.31113	+	9.79152i	0.144186	+	0.327477i
$895$	−66.3492			−2.21781
$896$	28.9017	−	17.6033i	0.965537	−	0.588084i
$897$	49.4554			1.65127
$898$	16.4725	+	37.4126i	0.549694	+	1.24848i
$899$	30.7215	+	74.1682i	1.02462	+	2.47365i
$900$	44.9320	−	49.0811i	1.49773	−	1.63604i
$901$	−9.47948	−	3.92653i	−0.315807	−	0.130812i
$902$	16.1198	−	16.8469i	0.536732	−	0.560942i
$903$	−62.3830	−	62.3830i	−2.07598	−	2.07598i
$904$	−11.4938	+	33.9384i	−0.382278	+	1.12878i
$905$	−9.81130	+	9.81130i	−0.326139	+	0.326139i
$906$	0.993904	+	45.0631i	0.0330203	+	1.49712i
$907$	−3.43887	+	8.30216i	−0.114186	+	0.275669i	−0.970633	−	0.240566i	$-0.922667\pi$
$907$	−3.43887	+	8.30216i	−0.114186	+	0.275669i	0.856447	+	0.516235i	$0.172667\pi$
$908$	−25.2843	−	9.18924i	−0.839089	−	0.304956i
$909$	−12.4265	+	5.14720i	−0.412159	+	0.170722i
$910$	−12.6443	+	32.5376i	−0.419156	+	1.07861i
$911$		−	34.5269i		−	1.14393i	−0.820279	−	0.571964i	$-0.806182\pi$
$911$		−	34.5269i		−	1.14393i	0.820279	−	0.571964i	$-0.193818\pi$
$912$	34.8866	−	41.6559i	1.15521	−	1.37936i
$913$		−	37.9426i		−	1.25572i
$914$	48.9028	+	19.0040i	1.61756	+	0.628596i
$915$	46.4956	−	19.2591i	1.53710	−	0.636686i
$916$	−10.3621	+	4.83786i	−0.342372	+	0.159847i
$917$	3.47407	−	8.38715i	0.114724	−	0.276968i
$918$	10.5606	−	0.232923i	0.348551	−	0.00768759i
$919$	7.49436	−	7.49436i	0.247216	−	0.247216i	−0.572611	−	0.819827i	$-0.694069\pi$
$919$	7.49436	−	7.49436i	0.247216	−	0.247216i	0.819827	+	0.572611i	$0.194069\pi$
$920$	63.5579	−	4.21093i	2.09544	−	0.138830i
$921$	8.98128	+	8.98128i	0.295943	+	0.295943i
$922$	−30.9028	−	29.5691i	−1.01773	−	0.973805i
$923$	16.4266	+	6.80413i	0.540689	+	0.223961i
$924$	49.7418	−	2.19526i	1.63639	−	0.0722188i
$925$	3.04475	+	7.35069i	0.100111	+	0.241689i
$926$	23.2562	−	10.2395i	0.764247	−	0.336492i
$927$	55.3184			1.81690
$928$	37.0073	+	29.6299i	1.21483	+	0.972650i
$929$	−17.2980			−0.567530			−0.283765	−	0.958894i	$-0.591584\pi$
$929$	−17.2980			−0.567530			−0.283765	+	0.958894i	$0.591584\pi$
$930$	−120.216	+	52.9299i	−3.94202	+	1.73564i
$931$	3.46006	+	8.35333i	0.113399	+	0.273769i
$932$	1.33591	+	30.2700i	0.0437592	+	0.991526i
$933$	−28.7882	−	11.9244i	−0.942482	−	0.390389i
$934$	33.7693	+	32.3119i	1.10497	+	1.05728i
$935$	6.67109	+	6.67109i	0.218168	+	0.218168i
$936$	−25.7615	+	29.4173i	−0.842040	+	0.961533i
$937$	7.69787	−	7.69787i	0.251479	−	0.251479i	−0.570098	−	0.821577i	$-0.693095\pi$
$937$	7.69787	−	7.69787i	0.251479	−	0.251479i	0.821577	+	0.570098i	$0.193095\pi$
$938$	−49.3385	+	1.08820i	−1.61096	+	0.0355311i
$939$	27.4759	−	66.3327i	0.896642	−	2.16468i
$940$	−0.950740	−	2.03636i	−0.0310097	−	0.0664189i
$941$	−5.96668	+	2.47148i	−0.194508	+	0.0805680i	−0.477811	−	0.878462i	$-0.658570\pi$
$941$	−5.96668	+	2.47148i	−0.194508	+	0.0805680i	0.283303	+	0.959030i	$0.408570\pi$
$942$	73.9618	+	28.7421i	2.40981	+	0.936469i
$943$			39.3565i			1.28162i
$944$	−8.76274	+	27.8835i	−0.285203	+	0.907529i
$945$			74.0665i			2.40938i
$946$	14.7012	−	37.8306i	0.477979	−	1.22998i
$947$	25.7772	−	10.6773i	0.837646	−	0.346964i	0.0777210	−	0.996975i	$-0.475236\pi$
$947$	25.7772	−	10.6773i	0.837646	−	0.346964i	0.759925	+	0.650011i	$0.225236\pi$
$948$	11.3375	−	31.1953i	0.368225	−	1.01318i
$949$	4.29833	−	10.3771i	0.139530	−	0.336855i
$950$	0.867645	+	39.3386i	0.0281501	+	1.27631i
$951$	43.6124	−	43.6124i	1.41423	−	1.41423i
$952$	−7.58502	+	3.74718i	−0.245832	+	0.121447i
$953$	−17.0103	−	17.0103i	−0.551017	−	0.551017i	0.375717	−	0.926734i	$-0.377396\pi$
$953$	−17.0103	−	17.0103i	−0.551017	−	0.551017i	−0.926734	+	0.375717i	$0.877396\pi$
$954$	55.7151	−	58.2282i	1.80384	−	1.88521i
$955$	−1.54102	−	0.638313i	−0.0498664	−	0.0206553i
$956$	−15.6061	−	14.2868i	−0.504736	−	0.462068i
$957$	26.6928	+	64.4421i	0.862856	+	2.08312i
$958$	7.38300	+	16.7684i	0.238534	+	0.541763i
$959$	7.05216			0.227726
$960$	−47.1333	+	61.6054i	−1.52122	+	1.98831i
$961$	60.7613			1.96004
$962$	−1.88403	−	4.27906i	−0.0607437	−	0.137962i
$963$	−0.234570	−	0.566301i	−0.00755890	−	0.0182488i
$964$	23.7166	+	21.7117i	0.763860	+	0.699286i
$965$	−6.11435	−	2.53265i	−0.196828	−	0.0815288i
$966$	−58.1014	+	60.7222i	−1.86938	+	1.95370i
$967$	−2.98327	−	2.98327i	−0.0959354	−	0.0959354i	0.657510	−	0.753446i	$-0.271610\pi$
$967$	−2.98327	−	2.98327i	−0.0959354	−	0.0959354i	−0.753446	+	0.657510i	$0.771610\pi$
$968$	−3.63499	−	7.35792i	−0.116833	−	0.236492i
$969$	−9.60516	+	9.60516i	−0.308562	+	0.308562i
$970$	−0.00953273	−	0.432209i	−0.000306078	−	0.0138774i
$971$	5.91100	−	14.2704i	0.189693	−	0.457960i	−0.800207	−	0.599723i	$-0.795277\pi$
$971$	5.91100	−	14.2704i	0.189693	−	0.457960i	0.989901	+	0.141764i	$0.0452773\pi$
$972$	4.95066	−	13.6218i	0.158792	−	0.436919i
$973$	0.0787924	−	0.0326369i	0.00252597	−	0.00104629i
$974$	12.2146	−	31.4317i	0.391381	−	1.00714i
$975$		−	43.6134i		−	1.39675i
$976$	−18.4069	+	9.60407i	−0.589189	+	0.307419i
$977$			15.2880i			0.489105i	0.969636	+	0.244552i	$0.0786410\pi$
$977$			15.2880i			0.489105i	−0.969636	+	0.244552i	$0.921359\pi$
$978$	−21.2845	−	8.27131i	−0.680603	−	0.264487i
$979$	6.20195	−	2.56893i	0.198215	−	0.0821035i
$980$	−5.46051	−	11.6957i	−0.174430	−	0.373606i
$981$	−37.6675	+	90.9375i	−1.20263	+	2.90341i
$982$	−31.0901	+	0.685717i	−0.992123	+	0.0218821i
$983$	15.8192	−	15.8192i	0.504554	−	0.504554i	−0.408296	−	0.912850i	$-0.633877\pi$
$983$	15.8192	−	15.8192i	0.504554	−	0.504554i	0.912850	+	0.408296i	$0.133877\pi$
$984$	−36.0555	−	31.5748i	−1.14941	−	1.00657i
$985$	25.4252	+	25.4252i	0.810114	+	0.810114i
$986$	−8.56331	−	8.19372i	−0.272711	−	0.260941i
$987$	2.73945	+	1.13472i	0.0871976	+	0.0361184i
$988$	−1.01948	−	23.1001i	−0.0324339	−	0.734911i
$989$	26.2164	+	63.2919i	0.833632	+	2.01256i
$990$	−67.8181	+	29.8598i	−2.15540	+	0.949006i
$991$	−17.3291			−0.550477			−0.275239	−	0.961376i	$-0.588757\pi$
$991$	−17.3291			−0.550477			−0.275239	+	0.961376i	$0.588757\pi$
$992$	47.4775	−	26.1199i	1.50741	−	0.829307i
$993$	−66.8821			−2.12244
$994$	−27.6526	+	12.1752i	−0.877088	+	0.386175i
$995$	15.1581	+	36.5949i	0.480545	+	1.16014i
$996$	−77.9140	+	3.43859i	−2.46880	+	0.108956i
$997$	15.8384	+	6.56047i	0.501606	+	0.207772i	0.619116	−	0.785300i	$-0.287491\pi$
$997$	15.8384	+	6.56047i	0.501606	+	0.207772i	−0.117510	+	0.993072i	$0.537491\pi$
$998$	20.0419	+	19.1769i	0.634414	+	0.607033i
$999$	−7.01464	−	7.01464i	−0.221933	−	0.221933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.bd.b.69.19	✓	128
32.13	even	8	inner	544.2.bd.b.205.19	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.bd.b.69.19	✓	128	1.1	even	1	trivial
544.2.bd.b.205.19	yes	128	32.13	even	8	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:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.569875 + 1.29431i) q^{2} +(1.11923 + 2.70207i) q^{3} +(-1.35049 + 1.47519i) q^{4} +(3.06285 + 1.26868i) q^{5} +(-2.85950 + 2.98848i) q^{6} +(-2.11503 - 2.11503i) q^{7} +(-2.67896 - 0.907275i) q^{8} +(-3.92717 + 3.92717i) q^{9} +(0.103382 + 4.68727i) q^{10} +(1.08903 - 2.62915i) q^{11} +(-5.49758 - 1.99802i) q^{12} +(-2.29976 + 0.952593i) q^{13} +(1.53221 - 3.94282i) q^{14} +9.69599i q^{15} +(-0.352379 - 3.98445i) q^{16} +1.00000i q^{17} +(-7.32099 - 2.84499i) q^{18} +(4.29095 - 1.77737i) q^{19} +(-6.00788 + 2.80497i) q^{20} +(3.34775 - 8.08218i) q^{21} +(4.02356 - 0.0887429i) q^{22} +(-4.80341 + 4.80341i) q^{23} +(-0.546869 - 8.25420i) q^{24} +(4.23600 + 4.23600i) q^{25} +(-2.54353 - 2.43375i) q^{26} +(-6.90072 - 2.85837i) q^{27} +(5.97640 - 0.263757i) q^{28} +(3.20710 + 7.74262i) q^{29} +(-12.5496 + 5.52550i) q^{30} +9.57921 q^{31} +(4.95631 - 2.72672i) q^{32} +8.32304 q^{33} +(-1.29431 + 0.569875i) q^{34} +(-3.79475 - 9.16133i) q^{35} +(-0.489742 - 11.0969i) q^{36} +(1.22704 + 0.508255i) q^{37} +(4.74578 + 4.54095i) q^{38} +(-5.14794 - 5.14794i) q^{39} +(-7.05424 - 6.17759i) q^{40} +(4.09672 - 4.09672i) q^{41} +(12.3687 - 0.272801i) q^{42} +(3.85929 - 9.31715i) q^{43} +(2.40779 + 5.15717i) q^{44} +(-17.0107 + 7.04605i) q^{45} +(-8.95446 - 3.47977i) q^{46} +0.338949i q^{47} +(10.3719 - 5.41168i) q^{48} +1.94673i q^{49} +(-3.06871 + 7.89669i) q^{50} +(-2.70207 + 1.11923i) q^{51} +(1.70054 - 4.67905i) q^{52} +(-3.92653 + 9.47948i) q^{53} +(-0.232923 - 10.5606i) q^{54} +(6.67109 - 6.67109i) q^{55} +(3.74718 + 7.58502i) q^{56} +(9.60516 + 9.60516i) q^{57} +(-8.19372 + 8.56331i) q^{58} +(-6.75078 - 2.79626i) q^{59} +(-14.3034 - 13.0943i) q^{60} +(-1.98630 - 4.79534i) q^{61} +(5.45895 + 12.3985i) q^{62} +16.6122 q^{63} +(6.35371 + 4.86111i) q^{64} -8.25236 q^{65} +(4.74309 + 10.7726i) q^{66} +(-4.46462 - 10.7785i) q^{67} +(-1.47519 - 1.35049i) q^{68} +(-18.3553 - 7.60301i) q^{69} +(9.69508 - 10.1324i) q^{70} +(-5.05068 - 5.05068i) q^{71} +(14.0838 - 6.95774i) q^{72} +(-3.19064 + 3.19064i) q^{73} +(0.0414166 + 1.87781i) q^{74} +(-6.70489 + 16.1870i) q^{75} +(-3.17291 + 8.73029i) q^{76} +(-7.86409 + 3.25741i) q^{77} +(3.72936 - 9.59672i) q^{78} +5.67437i q^{79} +(3.97569 - 12.6508i) q^{80} -5.18381i q^{81} +(7.63705 + 2.96782i) q^{82} +(12.3181 - 5.10231i) q^{83} +(7.40168 + 15.8534i) q^{84} +(-1.26868 + 3.06285i) q^{85} +(14.2586 - 0.314485i) q^{86} +(-17.3316 + 17.3316i) q^{87} +(-5.30284 + 6.05536i) q^{88} +(1.66801 + 1.66801i) q^{89} +(-18.8137 - 18.0017i) q^{90} +(6.87884 + 2.84931i) q^{91} +(-0.599014 - 13.5729i) q^{92} +(10.7214 + 25.8837i) q^{93} +(-0.438706 + 0.193158i) q^{94} +15.3975 q^{95} +(12.9151 + 10.3404i) q^{96} -0.0922091 q^{97} +(-2.51968 + 1.10939i) q^{98} +(6.04833 + 14.6020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 20 q^{6} - 24 q^{8} - 16 q^{12} - 20 q^{16} - 20 q^{18} - 48 q^{22} - 8 q^{23} + 68 q^{24} + 20 q^{26} - 24 q^{27} + 20 q^{30} + 48 q^{31} - 24 q^{35} + 8 q^{36} + 68 q^{38} - 24 q^{39} - 36 q^{40}+ \cdots - 136 q^{99}+O(q^{100}) \) 128 * q + 20 * q^6 - 24 * q^8 - 16 * q^12 - 20 * q^16 - 20 * q^18 - 48 * q^22 - 8 * q^23 + 68 * q^24 + 20 * q^26 - 24 * q^27 + 20 * q^30 + 48 * q^31 - 24 * q^35 + 8 * q^36 + 68 * q^38 - 24 * q^39 - 36 * q^40 - 16 * q^42 - 8 * q^43 - 40 * q^44 - 80 * q^45 + 12 * q^50 + 56 * q^52 - 16 * q^53 - 136 * q^54 + 32 * q^55 + 128 * q^56 - 32 * q^58 + 20 * q^60 - 12 * q^62 - 80 * q^63 + 12 * q^64 - 8 * q^66 + 40 * q^67 - 4 * q^68 + 100 * q^70 - 44 * q^72 + 84 * q^74 + 32 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 44 * q^80 + 40 * q^82 + 84 * q^84 - 120 * q^86 - 56 * q^87 + 128 * q^88 - 68 * q^90 - 56 * q^91 - 40 * q^92 + 32 * q^95 - 72 * q^96 - 12 * q^98 - 136 * q^99

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