LMFDB - Embedded newform 550.2.g.c.361.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(291,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.291"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$15$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.5
Character	$\chi$	$=$	550.361
Dual form			550.2.g.c.291.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.347673 - 1.07003i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.09898 - 0.770911i) q^{5} +(0.910220 - 0.661314i) q^{6} +(0.0285107 + 0.0207142i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.40297 - 1.01932i) q^{9} +(1.38180 + 1.75802i) q^{10} +(-3.17421 - 0.961440i) q^{11} +(0.910220 + 0.661314i) q^{12} +(4.87131 - 3.53921i) q^{13} +(-0.0108901 + 0.0335163i) q^{14} +(-1.55465 - 1.97794i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.04312 + 2.93750i) q^{17} +(1.40297 + 1.01932i) q^{18} +(-1.08254 - 0.786511i) q^{19} +(-1.24498 + 1.85743i) q^{20} +(0.0122524 - 0.0377090i) q^{21} +(-0.0665022 - 3.31596i) q^{22} +(2.49922 - 1.81579i) q^{23} +(-0.347673 + 1.07003i) q^{24} +(3.81139 - 3.23625i) q^{25} +(4.87131 + 3.53921i) q^{26} +(-4.30913 - 3.13077i) q^{27} -0.0352411 q^{28} +(2.92674 - 2.12640i) q^{29} +(1.40072 - 2.08978i) q^{30} +9.14964 q^{31} +1.00000 q^{32} +(0.0748212 + 3.73076i) q^{33} +(-4.04312 - 2.93750i) q^{34} +(0.0758120 + 0.0214994i) q^{35} +(-0.535886 + 1.64929i) q^{36} +(2.75746 + 8.48658i) q^{37} +(0.413493 - 1.27260i) q^{38} +(-5.48068 - 3.98195i) q^{39} +(-2.15124 - 0.610067i) q^{40} +3.04236 q^{41} +0.0396496 q^{42} -7.85827 q^{43} +(3.13311 - 1.08793i) q^{44} +(2.15899 - 3.22108i) q^{45} +(2.49922 + 1.81579i) q^{46} +(-1.50162 - 4.62151i) q^{47} -1.12509 q^{48} +(-2.16274 - 6.65621i) q^{49} +(4.25564 + 2.62479i) q^{50} +(4.54889 + 3.30496i) q^{51} +(-1.86067 + 5.72657i) q^{52} +(4.87152 + 3.53937i) q^{53} +(1.64594 - 5.06569i) q^{54} +(-7.40378 + 0.428998i) q^{55} +(-0.0108901 - 0.0335163i) q^{56} +(-0.465219 + 1.43180i) q^{57} +(2.92674 + 2.12640i) q^{58} +(1.59374 + 4.90503i) q^{59} +(2.42034 + 0.686382i) q^{60} +(4.35394 + 3.16332i) q^{61} +(2.82740 + 8.70183i) q^{62} +0.0611138 q^{63} +(0.309017 + 0.951057i) q^{64} +(7.49634 - 11.1841i) q^{65} +(-3.52505 + 1.22403i) q^{66} +(2.82207 + 8.68544i) q^{67} +(1.54434 - 4.75297i) q^{68} +(-2.81186 - 2.04294i) q^{69} +(0.00298002 + 0.0787451i) q^{70} -1.99953 q^{71} -1.73416 q^{72} -14.7216 q^{73} +(-7.21912 + 5.24500i) q^{74} +(-4.78799 - 2.95314i) q^{75} +1.33809 q^{76} +(-0.0705834 - 0.0931626i) q^{77} +(2.09343 - 6.44293i) q^{78} +(4.29076 + 3.11742i) q^{79} +(-0.0845609 - 2.23447i) q^{80} +(-0.244181 + 0.751512i) q^{81} +(0.940141 + 2.89346i) q^{82} +(-7.62152 + 5.53736i) q^{83} +(0.0122524 + 0.0377090i) q^{84} +(-6.22186 + 9.28263i) q^{85} +(-2.42834 - 7.47366i) q^{86} +(-3.29285 - 2.39240i) q^{87} +(2.00287 + 2.64358i) q^{88} +(-7.59214 + 5.51601i) q^{89} +(3.73060 + 1.05796i) q^{90} +0.212196 q^{91} +(-0.954618 + 2.93801i) q^{92} +(-3.18109 - 9.79037i) q^{93} +(3.93130 - 2.85625i) q^{94} +(-2.87855 - 0.816325i) q^{95} +(-0.347673 - 1.07003i) q^{96} +(-11.5028 - 8.35728i) q^{97} +(5.66211 - 4.11377i) q^{98} +(-5.43333 + 1.88666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9} - 5 q^{10} + 7 q^{11} + q^{12} + 12 q^{13} - 3 q^{14} + 12 q^{15} - 15 q^{16} + q^{17} - 17 q^{18} + 3 q^{19} - 5 q^{20} - 4 q^{21}+ \cdots + 21 q^{99}+O(q^{100}) $ 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9 - 5 * q^10 + 7 * q^11 + q^12 + 12 * q^13 - 3 * q^14 + 12 * q^15 - 15 * q^16 + q^17 - 17 * q^18 + 3 * q^19 - 5 * q^20 - 4 * q^21 - 3 * q^22 - 3 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^28 + 18 * q^29 + 2 * q^30 - 20 * q^31 + 60 * q^32 + 10 * q^33 + q^34 - 19 * q^35 - 12 * q^36 - 36 * q^37 - 22 * q^38 + 13 * q^39 + 64 * q^41 + 46 * q^42 + 40 * q^43 - 8 * q^44 - 20 * q^45 - 3 * q^46 - 9 * q^47 + 6 * q^48 - 30 * q^49 + 18 * q^50 - 48 * q^51 - 8 * q^52 + 31 * q^53 - 8 * q^54 - 42 * q^55 - 3 * q^56 + 30 * q^57 + 18 * q^58 + 23 * q^59 - 8 * q^60 - 41 * q^61 - 5 * q^62 + 6 * q^63 - 15 * q^64 - 7 * q^65 - 30 * q^66 - 40 * q^67 - 4 * q^68 - 22 * q^69 - 4 * q^70 + 4 * q^71 + 58 * q^72 + 74 * q^73 - 11 * q^74 + 35 * q^75 + 38 * q^76 + 22 * q^77 - 12 * q^78 - 45 * q^79 + 10 * q^80 + 24 * q^81 - 11 * q^82 + 16 * q^83 - 4 * q^84 + 9 * q^85 - 20 * q^86 + 68 * q^87 + 7 * q^88 + q^89 + 10 * q^90 + 10 * q^91 + 2 * q^92 - 40 * q^93 - 24 * q^94 + 24 * q^95 - 4 * q^96 + 6 * q^97 - 30 * q^98 + 21 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.347673	−	1.07003i	−0.200729	−	0.617781i	−0.999862	−	0.0166261i	$-0.994707\pi$
$3$	−0.347673	−	1.07003i	−0.200729	−	0.617781i	0.799133	−	0.601155i	$-0.205293\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	2.09898	−	0.770911i	0.938690	−	0.344762i
$5$	2.09898	−	0.770911i	0.938690	−	0.344762i
$6$	0.910220	−	0.661314i	0.371596	−	0.269980i
$7$	0.0285107	+	0.0207142i	0.0107760	+	0.00782923i	0.593160	−	0.805084i	$-0.297880\pi$
$7$	0.0285107	+	0.0207142i	0.0107760	+	0.00782923i	−0.582384	+	0.812914i	$0.697880\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	1.40297	−	1.01932i	0.467656	−	0.339772i
$10$	1.38180	+	1.75802i	0.436963	+	0.555935i
$11$	−3.17421	−	0.961440i	−0.957061	−	0.289885i
$11$	−3.17421	−	0.961440i	−0.957061	−	0.289885i
$12$	0.910220	+	0.661314i	0.262758	+	0.190905i
$13$	4.87131	−	3.53921i	1.35106	−	0.981601i	0.352100	−	0.935962i	$-0.385468\pi$
$13$	4.87131	−	3.53921i	1.35106	−	0.981601i	0.998958	−	0.0456387i	$-0.0145323\pi$
$14$	−0.0108901	+	0.0335163i	−0.00291050	+	0.00895760i
$15$	−1.55465	−	1.97794i	−0.401410	−	0.510701i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−4.04312	+	2.93750i	−0.980601	+	0.712448i	−0.957843	−	0.287293i	$-0.907245\pi$
$17$	−4.04312	+	2.93750i	−0.980601	+	0.712448i	−0.0227582	+	0.999741i	$0.507245\pi$
$18$	1.40297	+	1.01932i	0.330683	+	0.240255i
$19$	−1.08254	−	0.786511i	−0.248352	−	0.180438i	0.456644	−	0.889649i	$-0.349051\pi$
$19$	−1.08254	−	0.786511i	−0.248352	−	0.180438i	−0.704996	+	0.709211i	$0.749051\pi$
$20$	−1.24498	+	1.85743i	−0.278385	+	0.415333i
$21$	0.0122524	−	0.0377090i	0.00267369	−	0.00822877i
$22$	−0.0665022	−	3.31596i	−0.0141783	−	0.706965i
$23$	2.49922	−	1.81579i	0.521124	−	0.378619i	−0.295903	−	0.955218i	$-0.595621\pi$
$23$	2.49922	−	1.81579i	0.521124	−	0.378619i	0.817027	+	0.576599i	$0.195621\pi$
$24$	−0.347673	+	1.07003i	−0.0709685	+	0.218419i
$25$	3.81139	−	3.23625i	0.762279	−	0.647249i
$26$	4.87131	+	3.53921i	0.955342	+	0.694097i
$27$	−4.30913	−	3.13077i	−0.829293	−	0.602516i
$28$	−0.0352411			−0.00665994
$29$	2.92674	−	2.12640i	0.543481	−	0.394862i	−0.281895	−	0.959445i	$-0.590963\pi$
$29$	2.92674	−	2.12640i	0.543481	−	0.394862i	0.825376	+	0.564583i	$0.190963\pi$
$30$	1.40072	−	2.08978i	0.255734	−	0.381540i
$31$	9.14964			1.64332			0.821662	−	0.569975i	$-0.193047\pi$
$31$	9.14964			1.64332			0.821662	+	0.569975i	$0.193047\pi$
$32$	1.00000			0.176777
$33$	0.0748212	+	3.73076i	0.0130247	+	0.649443i
$34$	−4.04312	−	2.93750i	−0.693390	−	0.503777i
$35$	0.0758120	+	0.0214994i	0.0128146	+	0.00363407i
$36$	−0.535886	+	1.64929i	−0.0893143	+	0.274881i
$37$	2.75746	+	8.48658i	0.453323	+	1.39519i	0.873092	+	0.487555i	$0.162111\pi$
$37$	2.75746	+	8.48658i	0.453323	+	1.39519i	−0.419769	+	0.907631i	$0.637889\pi$
$38$	0.413493	−	1.27260i	0.0670775	−	0.206443i
$39$	−5.48068	−	3.98195i	−0.877611	−	0.637622i
$40$	−2.15124	−	0.610067i	−0.340140	−	0.0964600i
$41$	3.04236			0.475137			0.237568	−	0.971371i	$-0.423650\pi$
$41$	3.04236			0.475137			0.237568	+	0.971371i	$0.423650\pi$
$42$	0.0396496			0.00611806
$43$	−7.85827			−1.19837			−0.599187	−	0.800609i	$-0.704510\pi$
$43$	−7.85827			−1.19837			−0.599187	+	0.800609i	$0.704510\pi$
$44$	3.13311	−	1.08793i	0.472335	−	0.164012i
$45$	2.15899	−	3.22108i	0.321844	−	0.480170i
$46$	2.49922	+	1.81579i	0.368490	+	0.267724i
$47$	−1.50162	−	4.62151i	−0.219034	−	0.674117i	−0.998843	−	0.0480992i	$-0.984684\pi$
$47$	−1.50162	−	4.62151i	−0.219034	−	0.674117i	0.779809	−	0.626018i	$-0.215316\pi$
$48$	−1.12509			−0.162393
$49$	−2.16274	−	6.65621i	−0.308962	−	0.950888i
$50$	4.25564	+	2.62479i	0.601838	+	0.371202i
$51$	4.54889	+	3.30496i	0.636972	+	0.462787i
$52$	−1.86067	+	5.72657i	−0.258029	+	0.794132i
$53$	4.87152	+	3.53937i	0.669155	+	0.486170i	0.869742	−	0.493506i	$-0.164285\pi$
$53$	4.87152	+	3.53937i	0.669155	+	0.486170i	−0.200587	+	0.979676i	$0.564285\pi$
$54$	1.64594	−	5.06569i	0.223984	−	0.689353i
$55$	−7.40378	+	0.428998i	−0.998326	+	0.0578460i
$56$	−0.0108901	−	0.0335163i	−0.00145525	−	0.00447880i
$57$	−0.465219	+	1.43180i	−0.0616197	+	0.189646i
$58$	2.92674	+	2.12640i	0.384299	+	0.279210i
$59$	1.59374	+	4.90503i	0.207487	+	0.638580i	0.999602	+	0.0282080i	$0.00898008\pi$
$59$	1.59374	+	4.90503i	0.207487	+	0.638580i	−0.792115	+	0.610372i	$0.791020\pi$
$60$	2.42034	+	0.686382i	0.312465	+	0.0886116i
$61$	4.35394	+	3.16332i	0.557465	+	0.405022i	0.830530	−	0.556973i	$-0.188037\pi$
$61$	4.35394	+	3.16332i	0.557465	+	0.405022i	−0.273065	+	0.961996i	$0.588037\pi$
$62$	2.82740	+	8.70183i	0.359080	+	1.10513i
$63$	0.0611138			0.00769962
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	7.49634	−	11.1841i	0.929806	−	1.38721i
$66$	−3.52505	+	1.22403i	−0.433903	+	0.150668i
$67$	2.82207	+	8.68544i	0.344771	+	1.06110i	0.961706	+	0.274082i	$0.0883739\pi$
$67$	2.82207	+	8.68544i	0.344771	+	1.06110i	−0.616936	+	0.787014i	$0.711626\pi$
$68$	1.54434	−	4.75297i	0.187278	−	0.576383i
$69$	−2.81186	−	2.04294i	−0.338508	−	0.245941i
$70$	0.00298002	+	0.0787451i	0.000356181	+	0.00941184i
$71$	−1.99953			−0.237300			−0.118650	−	0.992936i	$-0.537857\pi$
$71$	−1.99953			−0.237300			−0.118650	+	0.992936i	$0.537857\pi$
$72$	−1.73416			−0.204373
$73$	−14.7216			−1.72303			−0.861517	−	0.507729i	$-0.830485\pi$
$73$	−14.7216			−1.72303			−0.861517	+	0.507729i	$0.830485\pi$
$74$	−7.21912	+	5.24500i	−0.839206	+	0.609719i
$75$	−4.78799	−	2.95314i	−0.552870	−	0.340999i
$76$	1.33809			0.153490
$77$	−0.0705834	−	0.0931626i	−0.00804373	−	0.0106169i
$78$	2.09343	−	6.44293i	0.237035	−	0.729518i
$79$	4.29076	+	3.11742i	0.482749	+	0.350737i	0.802389	−	0.596802i	$-0.203562\pi$
$79$	4.29076	+	3.11742i	0.482749	+	0.350737i	−0.319640	+	0.947539i	$0.603562\pi$
$80$	−0.0845609	−	2.23447i	−0.00945420	−	0.249821i
$81$	−0.244181	+	0.751512i	−0.0271312	+	0.0835013i
$82$	0.940141	+	2.89346i	0.103821	+	0.319529i
$83$	−7.62152	+	5.53736i	−0.836571	+	0.607804i	−0.921411	−	0.388591i	$-0.872962\pi$
$83$	−7.62152	+	5.53736i	−0.836571	+	0.607804i	0.0848400	+	0.996395i	$0.472962\pi$
$84$	0.0122524	+	0.0377090i	0.00133685	+	0.00411439i
$85$	−6.22186	+	9.28263i	−0.674856	+	1.00684i
$86$	−2.42834	−	7.47366i	−0.261854	−	0.805905i
$87$	−3.29285	−	2.39240i	−0.353031	−	0.256492i
$88$	2.00287	+	2.64358i	0.213507	+	0.281806i
$89$	−7.59214	+	5.51601i	−0.804765	+	0.584696i	−0.912308	−	0.409504i	$-0.865702\pi$
$89$	−7.59214	+	5.51601i	−0.804765	+	0.584696i	0.107543	+	0.994200i	$0.465702\pi$
$90$	3.73060	+	1.05796i	0.393239	+	0.111518i
$91$	0.212196			0.0222442
$92$	−0.954618	+	2.93801i	−0.0995258	+	0.306309i
$93$	−3.18109	−	9.79037i	−0.329863	−	1.01521i
$94$	3.93130	−	2.85625i	0.405482	−	0.294600i
$95$	−2.87855	−	0.816325i	−0.295333	−	0.0837532i
$96$	−0.347673	−	1.07003i	−0.0354842	−	0.109209i
$97$	−11.5028	−	8.35728i	−1.16793	−	0.848553i	−0.177173	−	0.984180i	$-0.556695\pi$
$97$	−11.5028	−	8.35728i	−1.16793	−	0.848553i	−0.990760	+	0.135626i	$0.956695\pi$
$98$	5.66211	−	4.11377i	0.571960	−	0.415553i
$99$	−5.43333	+	1.88666i	−0.546070	+	0.189616i
$100$	−1.18126	+	4.85846i	−0.118126	+	0.485846i
$101$	−4.70894	+	14.4926i	−0.468557	+	1.44207i	0.385896	+	0.922542i	$0.373893\pi$
$101$	−4.70894	+	14.4926i	−0.468557	+	1.44207i	−0.854453	+	0.519529i	$0.826107\pi$
$102$	−1.73752	+	5.34754i	−0.172040	+	0.529486i
$103$	−4.92623	+	3.57912i	−0.485396	+	0.352661i	−0.803411	−	0.595425i	$-0.796984\pi$
$103$	−4.92623	+	3.57912i	−0.485396	+	0.352661i	0.318015	+	0.948086i	$0.396984\pi$
$104$	−6.02127			−0.590434
$105$	−0.00335280	−	0.0885957i	−0.000327200	−	0.00864605i
$106$	−1.86076	+	5.72682i	−0.180733	+	0.556238i
$107$	−10.7167	+	7.78611i	−1.03602	+	0.752712i	−0.969504	−	0.245074i	$-0.921188\pi$
$107$	−10.7167	+	7.78611i	−1.03602	+	0.752712i	−0.0665143	+	0.997785i	$0.521188\pi$
$108$	5.32638			0.512531
$109$	2.06653	+	1.50142i	0.197938	+	0.143810i	0.682339	−	0.731035i	$-0.260963\pi$
$109$	2.06653	+	1.50142i	0.197938	+	0.143810i	−0.484402	+	0.874846i	$0.660963\pi$
$110$	−2.69589	−	6.90885i	−0.257043	−	0.658733i
$111$	8.12219	−	5.90111i	0.770924	−	0.560109i
$112$	0.0285107	−	0.0207142i	0.00269400	−	0.00195731i
$113$	4.55949			0.428921			0.214460	−	0.976733i	$-0.431201\pi$
$113$	4.55949			0.428921			0.214460	+	0.976733i	$0.431201\pi$
$114$	−1.50548			−0.141001
$115$	3.84599	−	5.73798i	0.358641	−	0.535069i
$116$	−1.11791	+	3.44058i	−0.103796	+	0.319450i
$117$	3.22671	−	9.93080i	0.298310	−	0.918103i
$118$	−4.17247	+	3.03147i	−0.384107	+	0.279070i
$119$	−0.176120			−0.0161449
$120$	0.0951390	+	2.51399i	0.00868496	+	0.229495i
$121$	9.15127	+	6.10363i	0.831933	+	0.554876i
$122$	−1.66306	+	5.11837i	−0.150566	+	0.463395i
$123$	−1.05775	−	3.25541i	−0.0953738	−	0.293530i
$124$	−7.40222	+	5.37803i	−0.664739	+	0.482961i
$125$	5.50516	−	9.73104i	0.492397	−	0.870371i
$126$	0.0188852	+	0.0581227i	0.00168243	+	0.00517798i
$127$	6.51872	+	4.73612i	0.578443	+	0.420263i	0.838162	−	0.545421i	$-0.183630\pi$
$127$	6.51872	+	4.73612i	0.578443	+	0.420263i	−0.259720	+	0.965684i	$0.583630\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	2.73211	+	8.40857i	0.240549	+	0.740333i
$130$	12.9532	+	3.67337i	1.13607	+	0.322176i
$131$	−3.22663	−	9.93056i	−0.281912	−	0.867637i	−0.987307	−	0.158822i	$-0.949230\pi$
$131$	−3.22663	−	9.93056i	−0.281912	−	0.867637i	0.705395	−	0.708815i	$-0.250770\pi$
$132$	−2.25342	−	2.97427i	−0.196135	−	0.258877i
$133$	−0.0145720	−	0.0448479i	−0.00126355	−	0.00388881i
$134$	−7.38828	+	5.36790i	−0.638250	+	0.463716i
$135$	−11.4583	−	3.24945i	−0.986174	−	0.279668i
$136$	4.99757			0.428538
$137$	−0.317469	+	0.977070i	−0.0271232	+	0.0834767i	−0.963702	−	0.266981i	$-0.913974\pi$
$137$	−0.317469	+	0.977070i	−0.0271232	+	0.0834767i	0.936579	+	0.350458i	$0.113974\pi$
$138$	1.07404	−	3.30554i	0.0914279	−	0.281386i
$139$	16.9882			1.44092			0.720461	−	0.693495i	$-0.243930\pi$
$139$	16.9882			1.44092			0.720461	+	0.693495i	$0.243930\pi$
$140$	−0.0739702	+	0.0271678i	−0.00625162	+	0.00229609i
$141$	−4.42308	+	3.21355i	−0.372490	+	0.270630i
$142$	−0.617888	−	1.90166i	−0.0518520	−	0.159584i
$143$	−18.8653	+	6.55075i	−1.57760	+	0.547801i
$144$	−0.535886	−	1.64929i	−0.0446572	−	0.137441i
$145$	4.50388	−	6.71951i	0.374027	−	0.558025i
$146$	−4.54923	−	14.0011i	−0.376497	−	1.15874i
$147$	−6.37041	+	4.62837i	−0.525423	+	0.381742i
$148$	−7.21912	−	5.24500i	−0.593408	−	0.431136i
$149$	−5.92022	−	18.2206i	−0.485003	−	1.49269i	−0.831976	−	0.554812i	$-0.812790\pi$
$149$	−5.92022	−	18.2206i	−0.485003	−	1.49269i	0.346972	−	0.937875i	$-0.387210\pi$
$150$	1.32903	−	5.46622i	0.108515	−	0.446315i
$151$	−6.13857	+	4.45993i	−0.499550	+	0.362944i	−0.808845	−	0.588022i	$-0.799907\pi$
$151$	−6.13857	+	4.45993i	−0.499550	+	0.362944i	0.309295	+	0.950966i	$0.399907\pi$
$152$	0.413493	+	1.27260i	0.0335387	+	0.103222i
$153$	−2.67813	+	8.24244i	−0.216514	+	0.666361i
$154$	0.0667914	−	0.0959177i	0.00538220	−	0.00772927i
$155$	19.2049	−	7.05356i	1.54257	−	0.566556i
$156$	6.77449			0.542394
$157$	12.2377	−	8.89124i	0.976678	−	0.709598i	0.0197140	−	0.999806i	$-0.493724\pi$
$157$	12.2377	−	8.89124i	0.976678	−	0.709598i	0.956964	+	0.290208i	$0.0937244\pi$
$158$	−1.63893	+	5.04410i	−0.130386	+	0.401287i
$159$	2.09353	−	6.44321i	0.166027	−	0.510980i
$160$	2.09898	−	0.770911i	0.165939	−	0.0609459i
$161$	0.108867			0.00857993
$162$	−0.790187			−0.0620829
$163$	−6.80302	+	4.94269i	−0.532854	+	0.387141i	−0.821424	−	0.570318i	$-0.806820\pi$
$163$	−6.80302	+	4.94269i	−0.532854	+	0.387141i	0.288570	+	0.957459i	$0.406820\pi$
$164$	−2.46132	+	1.78825i	−0.192197	+	0.139639i
$165$	3.03314	+	7.77310i	0.236129	+	0.605135i
$166$	−7.62152	−	5.53736i	−0.591545	−	0.429782i
$167$	−18.2228			−1.41012			−0.705062	−	0.709146i	$-0.749081\pi$
$167$	−18.2228			−1.41012			−0.705062	+	0.709146i	$0.749081\pi$
$168$	−0.0320772	+	0.0233054i	−0.00247481	+	0.00179805i
$169$	7.18640	−	22.1175i	0.552800	−	1.70134i
$170$	−10.7510	−	3.04885i	−0.824561	−	0.233836i
$171$	−2.32047			−0.177451
$172$	6.35747	−	4.61897i	0.484753	−	0.352194i
$173$	−6.33728	+	19.5041i	−0.481815	+	1.48287i	0.354727	+	0.934970i	$0.384574\pi$
$173$	−6.33728	+	19.5041i	−0.481815	+	1.48287i	−0.836542	+	0.547903i	$0.815426\pi$
$174$	1.25776	−	3.87098i	0.0953504	−	0.293458i
$175$	0.175702	−	0.0133175i	0.0132818	−	0.00100671i
$176$	−1.89527	+	2.72176i	−0.142861	+	0.205160i
$177$	4.69442	−	3.41069i	0.352854	−	0.256363i
$178$	−7.59214	−	5.51601i	−0.569055	−	0.413443i
$179$	2.55115	+	7.85164i	0.190682	+	0.586859i	1.00000		0.000511743i	$-0.000162893\pi$
$179$	2.55115	+	7.85164i	0.190682	+	0.586859i	−0.809318	+	0.587371i	$0.800163\pi$
$180$	0.146642	+	3.87493i	0.0109301	+	0.288821i
$181$	10.0585	−	7.30791i	0.747640	−	0.543192i	−0.147454	−	0.989069i	$-0.547108\pi$
$181$	10.0585	−	7.30791i	0.747640	−	0.543192i	0.895095	+	0.445876i	$0.147108\pi$
$182$	0.0655722	+	0.201811i	0.00486054	+	0.0149592i
$183$	1.87110	−	5.75864i	0.138315	−	0.425691i
$184$	−3.08921			−0.227740
$185$	12.3302	+	15.6874i	0.906537	+	1.15336i
$186$	8.32819	−	6.05078i	0.610652	−	0.443665i
$187$	15.6580	−	5.43703i	1.14502	−	0.397595i
$188$	3.93130	+	2.85625i	0.286719	+	0.208314i
$189$	−0.0580048	−	0.178520i	−0.00421923	−	0.0129855i
$190$	−0.113150	−	2.98993i	−0.00820879	−	0.216912i
$191$	5.91154	+	18.1939i	0.427744	+	1.31646i	0.900342	+	0.435183i	$0.143316\pi$
$191$	5.91154	+	18.1939i	0.427744	+	1.31646i	−0.472598	+	0.881278i	$0.656684\pi$
$192$	0.910220	−	0.661314i	0.0656895	−	0.0477262i
$193$	4.56288	+	14.0431i	0.328444	+	1.01085i	0.969862	+	0.243654i	$0.0783462\pi$
$193$	4.56288	+	14.0431i	0.328444	+	1.01085i	−0.641419	+	0.767191i	$0.721654\pi$
$194$	4.39368	−	13.5224i	0.315448	−	0.970849i
$195$	−14.5735	−	4.13289i	−1.04363	−	0.295963i
$196$	5.66211	+	4.11377i	0.404437	+	0.293840i
$197$	−3.09582	+	9.52794i	−0.220568	+	0.678838i	0.778144	+	0.628087i	$0.216162\pi$
$197$	−3.09582	+	9.52794i	−0.220568	+	0.678838i	−0.998711	+	0.0507514i	$0.983838\pi$
$198$	−3.47331	−	4.58440i	−0.246837	−	0.325799i
$199$	6.87736			0.487523			0.243762	−	0.969835i	$-0.421619\pi$
$199$	6.87736			0.487523			0.243762	+	0.969835i	$0.421619\pi$
$200$	−4.98570	+	0.377897i	−0.352542	+	0.0267214i
$201$	8.31251	−	6.03939i	0.586319	−	0.425986i
$202$	−15.2385			−1.07217
$203$	0.127490			0.00894803
$204$	−5.62274			−0.393671
$205$	6.38584	−	2.34539i	0.446006	−	0.163809i
$206$	−4.92623	−	3.57912i	−0.343227	−	0.249369i
$207$	1.65546	−	5.09499i	0.115063	−	0.354127i
$208$	−1.86067	−	5.72657i	−0.129015	−	0.397066i
$209$	2.68003	+	3.53735i	0.185381	+	0.244684i
$210$	0.0832234	−	0.0305663i	0.00574296	−	0.00210927i
$211$	−3.16822	−	9.75079i	−0.218110	−	0.671272i	−0.998918	−	0.0465020i	$-0.985193\pi$
$211$	−3.16822	−	9.75079i	−0.218110	−	0.671272i	0.780809	−	0.624770i	$-0.214807\pi$
$212$	−6.02153			−0.413561
$213$	0.695183	+	2.13955i	0.0476331	+	0.146600i
$214$	−10.7167	−	7.78611i	−0.732576	−	0.532248i
$215$	−16.4943	+	6.05803i	−1.12490	+	0.413154i
$216$	1.64594	+	5.06569i	0.111992	+	0.344676i
$217$	0.260862	+	0.189528i	0.0177085	+	0.0128660i
$218$	−0.789345	+	2.42935i	−0.0534612	+	0.164537i
$219$	5.11831	+	15.7525i	0.345863	+	1.06446i
$220$	5.73763	−	4.69890i	0.386831	−	0.316800i
$221$	−9.29886	+	28.6189i	−0.625509	+	1.92512i
$222$	8.12219	+	5.90111i	0.545126	+	0.396057i
$223$	6.28745	−	19.3508i	0.421039	−	1.29582i	−0.485698	−	0.874127i	$-0.661434\pi$
$223$	6.28745	−	19.3508i	0.421039	−	1.29582i	0.906737	−	0.421698i	$-0.138566\pi$
$224$	0.0285107	+	0.0207142i	0.00190495	+	0.00138403i
$225$	2.04850	−	8.42536i	0.136567	−	0.561691i
$226$	1.40896	+	4.33633i	0.0937226	+	0.288448i
$227$	10.8360			0.719211			0.359605	−	0.933104i	$-0.382911\pi$
$227$	10.8360			0.719211			0.359605	+	0.933104i	$0.382911\pi$
$228$	−0.465219	−	1.43180i	−0.0308099	−	0.0948230i
$229$	0.133678	+	0.0971226i	0.00883367	+	0.00641804i	0.592193	−	0.805796i	$-0.298262\pi$
$229$	0.133678	+	0.0971226i	0.00883367	+	0.00641804i	−0.583360	+	0.812214i	$0.698262\pi$
$230$	6.64562	+	1.88462i	0.438199	+	0.124268i
$231$	−0.0751466	+	0.107916i	−0.00494428	+	0.00710038i
$232$	−3.61764			−0.237510
$233$	−15.1047			−0.989545			−0.494772	−	0.869023i	$-0.664749\pi$
$233$	−15.1047			−0.989545			−0.494772	+	0.869023i	$0.664749\pi$
$234$	10.4419			0.682606
$235$	−6.71464	−	8.54283i	−0.438015	−	0.557273i
$236$	−4.17247	−	3.03147i	−0.271604	−	0.197332i
$237$	1.84395	−	5.67508i	0.119777	−	0.368636i
$238$	−0.0544241	−	0.167500i	−0.00352779	−	0.0108574i
$239$	5.87083	−	18.0686i	0.379753	−	1.16876i	−0.560463	−	0.828179i	$-0.689377\pi$
$239$	5.87083	−	18.0686i	0.379753	−	1.16876i	0.940216	−	0.340579i	$-0.110623\pi$
$240$	−2.36154	+	0.867347i	−0.152437	+	0.0559870i
$241$	19.3288	+	14.0432i	1.24507	+	0.904600i	0.997926	−	0.0643775i	$-0.0205062\pi$
$241$	19.3288	+	14.0432i	1.24507	+	0.904600i	0.247149	+	0.968977i	$0.420506\pi$
$242$	−2.97700	+	10.5895i	−0.191369	+	0.680719i
$243$	−15.0901			−0.968031
$244$	−5.38177			−0.344532
$245$	−9.67088	−	12.3040i	−0.617850	−	0.786071i
$246$	2.76922	−	2.01195i	0.176559	−	0.128277i
$247$	−8.05701			−0.512656
$248$	−7.40222	−	5.37803i	−0.470041	−	0.341505i
$249$	8.57493	+	6.23005i	0.543414	+	0.394813i
$250$	10.9560	+	2.22866i	0.692916	+	0.140953i
$251$	−5.05070	+	15.5445i	−0.318797	+	0.981157i	0.655366	+	0.755312i	$0.272515\pi$
$251$	−5.05070	+	15.5445i	−0.318797	+	0.981157i	−0.974163	+	0.225846i	$0.927485\pi$
$252$	−0.0494421	+	0.0359218i	−0.00311456	+	0.00226286i
$253$	−9.67884	+	3.36086i	−0.608504	+	0.211295i
$254$	−2.48993	+	7.66321i	−0.156232	+	0.480833i
$255$	12.0958	+	3.43025i	0.757471	+	0.214810i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	9.78681	+	7.11054i	0.610485	+	0.443543i	0.849585	−	0.527452i	$-0.176852\pi$
$257$	9.78681	+	7.11054i	0.610485	+	0.443543i	−0.239100	+	0.970995i	$0.576852\pi$
$258$	−7.15275	+	5.19678i	−0.445311	+	0.323537i
$259$	−0.0971759	+	0.299077i	−0.00603822	+	0.0185837i
$260$	0.509164	+	13.4543i	0.0315770	+	0.834402i
$261$	1.93865	−	5.96654i	0.119999	−	0.369319i
$262$	8.44744	−	6.13742i	0.521884	−	0.379171i
$263$	8.07183	+	5.86452i	0.497730	+	0.361622i	0.808149	−	0.588978i	$-0.200469\pi$
$263$	8.07183	+	5.86452i	0.497730	+	0.361622i	−0.310419	+	0.950600i	$0.600469\pi$
$264$	2.13236	−	3.06223i	0.131237	−	0.188467i
$265$	12.9537	+	3.67354i	0.795742	+	0.225664i
$266$	0.0381499	−	0.0277175i	0.00233912	−	0.00169947i
$267$	8.54187	+	6.20603i	0.522754	+	0.379803i
$268$	−7.38828	−	5.36790i	−0.451311	−	0.327897i
$269$	−3.17415	+	2.30616i	−0.193531	+	0.140609i	−0.680331	−	0.732905i	$-0.738164\pi$
$269$	−3.17415	+	2.30616i	−0.193531	+	0.140609i	0.486800	+	0.873514i	$0.338164\pi$
$270$	−0.450404	−	11.9016i	−0.0274107	−	0.724310i
$271$	7.08231	−	5.14560i	0.430220	−	0.312573i	−0.351517	−	0.936182i	$-0.614334\pi$
$271$	7.08231	−	5.14560i	0.430220	−	0.312573i	0.781737	+	0.623608i	$0.214334\pi$
$272$	1.54434	+	4.75297i	0.0936391	+	0.288191i
$273$	−0.0737749	−	0.227056i	−0.00446506	−	0.0137420i
$274$	−1.02735			−0.0620646
$275$	−15.2096	+	6.60811i	−0.917175	+	0.398484i
$276$	3.47565			0.209210
$277$	7.18354	+	22.1086i	0.431617	+	1.32838i	0.896514	+	0.443015i	$0.146091\pi$
$277$	7.18354	+	22.1086i	0.431617	+	1.32838i	−0.464897	+	0.885365i	$0.653909\pi$
$278$	5.24965	+	16.1568i	0.314853	+	0.969018i
$279$	12.8367	−	9.32637i	0.768510	−	0.558355i
$280$	−0.0486961	−	0.0619545i	−0.00291015	−	0.00370249i
$281$	3.04608	−	2.21310i	0.181714	−	0.132023i	−0.493210	−	0.869910i	$-0.664177\pi$
$281$	3.04608	−	2.21310i	0.181714	−	0.132023i	0.674924	+	0.737888i	$0.264177\pi$
$282$	−4.42308	−	3.21355i	−0.263390	−	0.191364i
$283$	−4.02656	−	2.92547i	−0.239354	−	0.173901i	0.461641	−	0.887067i	$-0.347261\pi$
$283$	−4.02656	−	2.92547i	−0.239354	−	0.173901i	−0.700995	+	0.713166i	$0.747261\pi$
$284$	1.61765	−	1.17529i	0.0959900	−	0.0697408i
$285$	0.127305	+	3.36395i	0.00754088	+	0.199263i
$286$	−12.0598	−	15.9177i	−0.713113	−	0.941233i
$287$	0.0867396	+	0.0630200i	0.00512008	+	0.00371996i
$288$	1.40297	−	1.01932i	0.0826707	−	0.0600638i
$289$	2.46464	−	7.58538i	0.144979	−	0.446199i
$290$	7.78241	+	2.20700i	0.456999	+	0.129600i
$291$	−4.94331	+	15.2139i	−0.289782	+	0.891856i
$292$	11.9100	−	8.65314i	0.696982	−	0.506387i
$293$	3.94287	+	2.86466i	0.230345	+	0.167355i	0.696971	−	0.717099i	$-0.254531\pi$
$293$	3.94287	+	2.86466i	0.230345	+	0.167355i	−0.466626	+	0.884455i	$0.654531\pi$
$294$	−6.37041	−	4.62837i	−0.371530	−	0.269932i
$295$	7.12656	+	9.06690i	0.414924	+	0.527895i
$296$	2.75746	−	8.48658i	0.160274	−	0.493273i
$297$	10.6681	+	14.0807i	0.619024	+	0.817045i
$298$	15.4993	−	11.2609i	0.897853	−	0.652328i
$299$	5.74801	−	17.6906i	0.332416	−	1.02307i
$300$	5.60938	−	0.425170i	0.323858	−	0.0245472i
$301$	−0.224044	−	0.162778i	−0.0129137	−	0.00938236i
$302$	−6.13857	−	4.45993i	−0.353235	−	0.256640i
$303$	17.1447			0.984937
$304$	−1.08254	+	0.786511i	−0.0620879	+	0.0451095i
$305$	11.5775	+	3.28324i	0.662923	+	0.187998i
$306$	−8.66661			−0.495437
$307$	25.1216			1.43377			0.716883	−	0.697193i	$-0.245568\pi$
$307$	25.1216			1.43377			0.716883	+	0.697193i	$0.245568\pi$
$308$	0.111863	+	0.0338822i	0.00637398	+	0.00193062i
$309$	5.54248	+	4.02685i	0.315301	+	0.229079i
$310$	12.6430	+	16.0852i	0.718072	+	0.913581i
$311$	9.44667	−	29.0739i	0.535671	−	1.64863i	−0.206523	−	0.978442i	$-0.566215\pi$
$311$	9.44667	−	29.0739i	0.535671	−	1.64863i	0.742194	−	0.670185i	$-0.233785\pi$
$312$	2.09343	+	6.44293i	0.118517	+	0.364759i
$313$	−1.33267	+	4.10153i	−0.0753268	+	0.231832i	−0.981629	−	0.190797i	$-0.938893\pi$
$313$	−1.33267	+	4.10153i	−0.0753268	+	0.231832i	0.906303	+	0.422629i	$0.138893\pi$
$314$	12.2377	+	8.89124i	0.690615	+	0.501761i
$315$	0.128276	−	0.0471133i	0.00722756	−	0.00265454i
$316$	−5.30368			−0.298355
$317$	10.8725			0.610663			0.305331	−	0.952246i	$-0.401233\pi$
$317$	10.8725			0.610663			0.305331	+	0.952246i	$0.401233\pi$
$318$	6.77479			0.379911
$319$	−11.3345	+	3.93576i	−0.634610	+	0.220360i
$320$	1.38180	+	1.75802i	0.0772449	+	0.0982763i
$321$	12.0573	+	8.76011i	0.672970	+	0.488941i
$322$	0.0336418	+	0.103539i	0.00187478	+	0.00576999i
$323$	6.68722			0.372087
$324$	−0.244181	−	0.751512i	−0.0135656	−	0.0417507i
$325$	7.11271	−	29.2541i	0.394542	−	1.62272i
$326$	−6.80302	−	4.94269i	−0.376785	−	0.273750i
$327$	0.888087	−	2.73325i	0.0491113	−	0.151149i
$328$	−2.46132	−	1.78825i	−0.135904	−	0.0987398i
$329$	0.0529188	−	0.162867i	0.00291751	−	0.00897916i
$330$	−6.45537	+	5.28670i	−0.355356	+	0.291023i
$331$	9.83408	+	30.2662i	0.540530	+	1.66358i	0.731388	+	0.681962i	$0.238873\pi$
$331$	9.83408	+	30.2662i	0.540530	+	1.66358i	−0.190858	+	0.981618i	$0.561127\pi$
$332$	2.91116	−	8.95963i	0.159771	−	0.491724i
$333$	12.5191	+	9.09568i	0.686044	+	0.498440i
$334$	−5.63116	−	17.3309i	−0.308123	−	0.948306i
$335$	12.6192	+	16.0550i	0.689458	+	0.877176i
$336$	−0.0320772	−	0.0233054i	−0.00174995	−	0.00127142i
$337$	−0.897283	−	2.76155i	−0.0488781	−	0.150431i	0.923639	−	0.383265i	$-0.125200\pi$
$337$	−0.897283	−	2.76155i	−0.0488781	−	0.150431i	−0.972517	+	0.232833i	$0.925200\pi$
$338$	23.2557			1.26494
$339$	−1.58521	−	4.87878i	−0.0860969	−	0.264979i
$340$	−0.422599	−	11.1669i	−0.0229187	−	0.605611i
$341$	−29.0429	−	8.79683i	−1.57276	−	0.476375i
$342$	−0.717065	−	2.20690i	−0.0387744	−	0.119335i
$343$	0.152448	−	0.469186i	0.00823141	−	0.0253337i
$344$	6.35747	+	4.61897i	0.342772	+	0.249038i
$345$	−7.47695	−	2.12038i	−0.402545	−	0.114157i
$346$	−20.5079			−1.10251
$347$	−17.3324			−0.930451			−0.465225	−	0.885192i	$-0.654027\pi$
$347$	−17.3324			−0.930451			−0.465225	+	0.885192i	$0.654027\pi$
$348$	4.07019			0.218185
$349$	−22.2567	+	16.1704i	−1.19137	+	0.865583i	−0.993409	−	0.114626i	$-0.963433\pi$
$349$	−22.2567	+	16.1704i	−1.19137	+	0.865583i	−0.197964	+	0.980209i	$0.563433\pi$
$350$	0.0669605	+	0.162987i	0.00357919	+	0.00871201i
$351$	−32.0716			−1.71185
$352$	−3.17421	−	0.961440i	−0.169186	−	0.0512449i
$353$	7.96674	−	24.5191i	0.424027	−	1.30502i	−0.479896	−	0.877325i	$-0.659326\pi$
$353$	7.96674	−	24.5191i	0.424027	−	1.30502i	0.903923	−	0.427695i	$-0.140674\pi$
$354$	4.69442	+	3.41069i	0.249505	+	0.181276i
$355$	−4.19696	+	1.54146i	−0.222752	+	0.0818121i
$356$	2.89994	−	8.92509i	0.153696	−	0.473029i
$357$	0.0612322	+	0.188453i	0.00324075	+	0.00997401i
$358$	−6.67901	+	4.85258i	−0.352997	+	0.256467i
$359$	3.43423	+	10.5695i	0.181252	+	0.557836i	0.999864	−	0.0165111i	$-0.00525589\pi$
$359$	3.43423	+	10.5695i	0.181252	+	0.557836i	−0.818612	+	0.574347i	$0.805256\pi$
$360$	−3.63997	+	1.33689i	−0.191843	+	0.0704601i
$361$	−5.31803	−	16.3672i	−0.279896	−	0.861432i
$362$	10.0585	+	7.30791i	0.528662	+	0.384095i
$363$	3.34941	−	11.9142i	0.175798	−	0.625332i
$364$	−0.171670	+	0.124726i	−0.00899797	+	0.00653741i
$365$	−30.9003	+	11.3490i	−1.61739	+	0.594036i
$366$	6.05500			0.316500
$367$	10.0616	−	30.9666i	0.525214	−	1.61644i	−0.238679	−	0.971098i	$-0.576714\pi$
$367$	10.0616	−	30.9666i	0.525214	−	1.61644i	0.763893	−	0.645343i	$-0.223286\pi$
$368$	−0.954618	−	2.93801i	−0.0497629	−	0.153154i
$369$	4.26833	−	3.10112i	0.222200	−	0.161438i
$370$	−11.1093	+	16.5744i	−0.577546	+	0.861663i
$371$	0.0655751	+	0.201819i	0.00340449	+	0.0104779i
$372$	8.32819	+	6.05078i	0.431797	+	0.313719i
$373$	−4.97381	+	3.61368i	−0.257534	+	0.187109i	−0.709059	−	0.705149i	$-0.750880\pi$
$373$	−4.97381	+	3.61368i	−0.257534	+	0.187109i	0.451525	+	0.892258i	$0.350880\pi$
$374$	10.0095	+	13.2115i	0.517579	+	0.683149i
$375$	−12.3265	−	2.50745i	−0.636537	−	0.129484i
$376$	−1.50162	+	4.62151i	−0.0774402	+	0.238336i
$377$	6.73126	−	20.7167i	0.346677	−	1.06696i
$378$	0.151859	−	0.110332i	0.00781076	−	0.00567485i
$379$	−24.5826			−1.26272			−0.631361	−	0.775489i	$-0.717503\pi$
$379$	−24.5826			−1.26272			−0.631361	+	0.775489i	$0.717503\pi$
$380$	2.80862	−	1.03155i	0.144079	−	0.0529174i
$381$	2.80140	−	8.62183i	0.143520	−	0.441710i
$382$	−15.4766	+	11.2444i	−0.791853	+	0.575315i
$383$	−11.4181			−0.583439			−0.291719	−	0.956504i	$-0.594227\pi$
$383$	−11.4181			−0.583439			−0.291719	+	0.956504i	$0.594227\pi$
$384$	0.910220	+	0.661314i	0.0464495	+	0.0337475i
$385$	−0.219973	−	0.141132i	−0.0112109	−	0.00719277i
$386$	−11.9458	+	8.67912i	−0.608025	+	0.441756i
$387$	−11.0249	+	8.01006i	−0.560427	+	0.407174i
$388$	14.2183			0.721823
$389$	−24.3124			−1.23269			−0.616345	−	0.787476i	$-0.711387\pi$
$389$	−24.3124			−1.23269			−0.616345	+	0.787476i	$0.711387\pi$
$390$	−0.572858	−	15.1374i	−0.0290078	−	0.766512i
$391$	−4.77077	+	14.6829i	−0.241268	+	0.742548i
$392$	−2.16274	+	6.65621i	−0.109235	+	0.336190i
$393$	−9.50416	+	6.90518i	−0.479421	+	0.348320i
$394$	−10.0183			−0.504713
$395$	11.4095	+	3.23560i	0.574072	+	0.162800i
$396$	3.28671	−	4.71997i	0.165163	−	0.237187i
$397$	11.4108	−	35.1189i	0.572693	−	1.76257i	−0.0712114	−	0.997461i	$-0.522687\pi$
$397$	11.4108	−	35.1189i	0.572693	−	1.76257i	0.643904	−	0.765106i	$-0.277313\pi$
$398$	2.12522	+	6.54076i	0.106528	+	0.327859i
$399$	−0.0429222	+	0.0311848i	−0.00214880	+	0.00156119i
$400$	−1.90007	−	4.62490i	−0.0950034	−	0.231245i
$401$	−9.51815	−	29.2939i	−0.475314	−	1.46287i	−0.845534	−	0.533922i	$-0.820718\pi$
$401$	−9.51815	−	29.2939i	−0.475314	−	1.46287i	0.370220	−	0.928944i	$-0.379282\pi$
$402$	8.31251	+	6.03939i	0.414590	+	0.301217i
$403$	44.5707	−	32.3825i	2.22023	−	1.61309i
$404$	−4.70894	−	14.4926i	−0.234279	−	0.721036i
$405$	0.0668189	+	1.76565i	0.00332026	+	0.0877357i
$406$	0.0393965	+	0.121250i	0.00195522	+	0.00601754i
$407$	−0.593420	−	29.5894i	−0.0294148	−	1.46669i
$408$	−1.73752	−	5.34754i	−0.0860202	−	0.264743i
$409$	8.55217	−	6.21352i	0.422878	−	0.307239i	−0.355917	−	0.934518i	$-0.615831\pi$
$409$	8.55217	−	6.21352i	0.422878	−	0.307239i	0.778795	+	0.627279i	$0.215831\pi$
$410$	4.20393	+	5.34853i	0.207617	+	0.264145i
$411$	1.15587			0.0570148
$412$	1.88165	−	5.79114i	0.0927025	−	0.285309i
$413$	−0.0561652	+	0.172859i	−0.00276371	+	0.00850581i
$414$	5.35719			0.263292
$415$	−11.7286	+	17.4983i	−0.575733	+	0.858957i
$416$	4.87131	−	3.53921i	0.238836	−	0.173524i
$417$	−5.90635	−	18.1779i	−0.289235	−	0.890175i
$418$	−2.53605	+	3.64196i	−0.124042	+	0.178134i
$419$	0.601551	+	1.85138i	0.0293877	+	0.0904460i	0.964675	−	0.263444i	$-0.0848586\pi$
$419$	0.601551	+	1.85138i	0.0293877	+	0.0904460i	−0.935287	+	0.353890i	$0.884859\pi$
$420$	0.0547877	+	0.0697047i	0.00267337	+	0.00340124i
$421$	−2.41108	−	7.42054i	−0.117509	−	0.361655i	0.874953	−	0.484208i	$-0.160892\pi$
$421$	−2.41108	−	7.42054i	−0.117509	−	0.361655i	−0.992462	+	0.122552i	$0.960892\pi$
$422$	8.29452	−	6.02632i	0.403771	−	0.293357i
$423$	−6.81751	−	4.95321i	−0.331479	−	0.240833i
$424$	−1.86076	−	5.72682i	−0.0903663	−	0.278119i
$425$	−5.90345	+	24.2805i	−0.286360	+	1.17778i
$426$	−1.82001	+	1.32232i	−0.0881798	+	0.0640664i
$427$	0.0586080	+	0.180377i	0.00283624	+	0.00872905i
$428$	4.09340	−	12.5982i	0.197862	−	0.608957i
$429$	13.5684	+	17.9089i	0.655091	+	0.864650i
$430$	−10.8585	−	13.8150i	−0.523646	−	0.666218i
$431$	18.1166			0.872648			0.436324	−	0.899790i	$-0.356280\pi$
$431$	18.1166			0.872648			0.436324	+	0.899790i	$0.356280\pi$
$432$	−4.30913	+	3.13077i	−0.207323	+	0.150629i
$433$	−10.1291	+	31.1743i	−0.486775	+	1.49814i	0.342618	+	0.939475i	$0.388686\pi$
$433$	−10.1291	+	31.1743i	−0.486775	+	1.49814i	−0.829393	+	0.558665i	$0.811314\pi$
$434$	−0.0996405	+	0.306662i	−0.00478290	+	0.0147202i
$435$	−8.75594	−	2.48309i	−0.419815	−	0.119055i
$436$	−2.55437			−0.122332
$437$	−4.13365			−0.197739
$438$	−13.3999	+	9.73560i	−0.640272	+	0.465185i
$439$	23.7235	−	17.2362i	1.13226	−	0.822637i	0.146240	−	0.989249i	$-0.453283\pi$
$439$	23.7235	−	17.2362i	1.13226	−	0.822637i	0.986022	+	0.166612i	$0.0532828\pi$
$440$	6.24194	+	4.00477i	0.297573	+	0.190920i
$441$	−9.81903	−	7.13394i	−0.467573	−	0.339712i
$442$	−30.0917			−1.43132
$443$	−17.8199	+	12.9469i	−0.846648	+	0.615126i	−0.924220	−	0.381861i	$-0.875283\pi$
$443$	−17.8199	+	12.9469i	−0.846648	+	0.615126i	0.0775718	+	0.996987i	$0.475283\pi$
$444$	−3.10240	+	9.54820i	−0.147233	+	0.453138i
$445$	−11.6834	+	17.4308i	−0.553844	+	0.826301i
$446$	20.3466			0.963440
$447$	−17.4382	+	12.6696i	−0.824799	+	0.599252i
$448$	−0.0108901	+	0.0335163i	−0.000514509	+	0.00158350i
$449$	−0.150573	+	0.463417i	−0.00710600	+	0.0218700i	−0.954547	−	0.298062i	$-0.903660\pi$
$449$	−0.150573	+	0.463417i	−0.00710600	+	0.0218700i	0.947441	+	0.319932i	$0.103660\pi$
$450$	8.64602	−	0.655336i	0.407577	−	0.0308928i
$451$	−9.65710	−	2.92505i	−0.454735	−	0.137735i
$452$	−3.68870	+	2.68000i	−0.173502	+	0.126057i
$453$	6.90647	+	5.01785i	0.324494	+	0.235759i
$454$	3.34851	+	10.3057i	0.157153	+	0.483668i
$455$	0.445395	−	0.163584i	0.0208804	−	0.00766895i
$456$	1.21796	−	0.884899i	0.0570361	−	0.0414392i
$457$	−4.23129	−	13.0226i	−0.197932	−	0.609171i	−0.999930	−	0.0118443i	$-0.996230\pi$
$457$	−4.23129	−	13.0226i	−0.197932	−	0.609171i	0.801998	−	0.597326i	$-0.203770\pi$
$458$	−0.0510604	+	0.157148i	−0.00238589	+	0.00734303i
$459$	26.6190			1.24247
$460$	0.261226	+	6.90274i	0.0121797	+	0.321842i
$461$	−8.35564	+	6.07073i	−0.389161	+	0.282742i	−0.765112	−	0.643898i	$-0.777316\pi$
$461$	−8.35564	+	6.07073i	−0.389161	+	0.282742i	0.375951	+	0.926640i	$0.377316\pi$
$462$	−0.125856	−	0.0381207i	−0.00585536	−	0.00177353i
$463$	−16.2541	−	11.8093i	−0.755392	−	0.548824i	0.142102	−	0.989852i	$-0.454614\pi$
$463$	−16.2541	−	11.8093i	−0.755392	−	0.548824i	−0.897493	+	0.441028i	$0.854614\pi$
$464$	−1.11791	−	3.44058i	−0.0518978	−	0.159725i
$465$	−14.2245	−	18.0974i	−0.659647	−	0.839248i
$466$	−4.66762	−	14.3655i	−0.216223	−	0.665467i
$467$	−1.68862	+	1.22685i	−0.0781399	+	0.0567720i	−0.626169	−	0.779687i	$-0.715378\pi$
$467$	−1.68862	+	1.22685i	−0.0781399	+	0.0567720i	0.548029	+	0.836459i	$0.315378\pi$
$468$	3.22671	+	9.93080i	0.149155	+	0.459052i
$469$	−0.0994529	+	0.306085i	−0.00459231	+	0.0141337i
$470$	6.04977	−	9.02588i	0.279055	−	0.416333i
$471$	−13.7686	−	10.0035i	−0.634424	−	0.460936i
$472$	1.59374	−	4.90503i	0.0733578	−	0.225772i
$473$	24.9438	+	7.55525i	1.14692	+	0.347391i
$474$	5.96713			0.274080
$475$	−6.67133	+	0.505662i	−0.306101	+	0.0232014i
$476$	0.142484	−	0.103521i	0.00653075	−	0.00474487i
$477$	10.4423			0.478121
$478$	18.9984			0.868967
$479$	−11.4872			−0.524865			−0.262433	−	0.964950i	$-0.584525\pi$
$479$	−11.4872			−0.524865			−0.262433	+	0.964950i	$0.584525\pi$
$480$	−1.55465	−	1.97794i	−0.0709599	−	0.0902801i
$481$	43.4683	+	31.5815i	1.98198	+	1.43999i
$482$	−7.38293	+	22.7223i	−0.336283	+	1.03497i
$483$	−0.0378502	−	0.116491i	−0.00172224	−	0.00530052i
$484$	−10.9912	+	0.441037i	−0.499598	+	0.0200471i
$485$	−30.5868	−	8.67408i	−1.38888	−	0.393870i
$486$	−4.66310	−	14.3515i	−0.211522	−	0.650999i
$487$	16.8890			0.765315			0.382657	−	0.923890i	$-0.375009\pi$
$487$	16.8890			0.765315			0.382657	+	0.923890i	$0.375009\pi$
$488$	−1.66306	−	5.11837i	−0.0752831	−	0.231698i
$489$	7.65404	+	5.56099i	0.346128	+	0.251476i
$490$	8.71329	−	12.9997i	0.393626	−	0.587266i
$491$	−11.1072	−	34.1843i	−0.501259	−	1.54272i	−0.806971	−	0.590592i	$-0.798894\pi$
$491$	−11.1072	−	34.1843i	−0.501259	−	1.54272i	0.305712	−	0.952124i	$-0.401106\pi$
$492$	2.76922	+	2.01195i	0.124846	+	0.0907059i
$493$	−5.58686	+	17.1946i	−0.251619	+	0.774405i
$494$	−2.48975	−	7.66268i	−0.112019	−	0.344760i
$495$	−9.94998	+	8.14866i	−0.447218	+	0.366255i
$496$	2.82740	−	8.70183i	0.126954	−	0.390724i
$497$	−0.0570079	−	0.0414186i	−0.00255715	−	0.00185788i
$498$	−3.27533	+	10.0804i	−0.146771	+	0.451715i
$499$	−6.46836	−	4.69954i	−0.289563	−	0.210380i	0.433515	−	0.901147i	$-0.357273\pi$
$499$	−6.46836	−	4.69954i	−0.289563	−	0.210380i	−0.723078	+	0.690766i	$0.757273\pi$
$500$	1.26600	+	11.1084i	0.0566170	+	0.496784i
$501$	6.33558	+	19.4989i	0.283053	+	0.871147i
$502$	−16.3444			−0.729487
$503$	3.68798	+	11.3504i	0.164439	+	0.506091i	0.998995	−	0.0448327i	$-0.0142755\pi$
$503$	3.68798	+	11.3504i	0.164439	+	0.506091i	−0.834556	+	0.550924i	$0.814275\pi$
$504$	−0.0494421	−	0.0359218i	−0.00220233	−	0.00160008i
$505$	1.28858	+	34.0499i	0.0573410	+	1.51520i
$506$	−6.18729	−	8.16656i	−0.275059	−	0.363048i
$507$	−26.1648			−1.16202
$508$	−8.05758			−0.357497
$509$	−19.3868			−0.859306			−0.429653	−	0.902994i	$-0.641364\pi$
$509$	−19.3868			−0.859306			−0.429653	+	0.902994i	$0.641364\pi$
$510$	0.475464	+	12.5638i	0.0210539	+	0.556336i
$511$	−0.419723	−	0.304946i	−0.0185674	−	0.0134900i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	2.20242	+	6.77836i	0.0972393	+	0.299272i
$514$	−3.73823	+	11.5051i	−0.164886	+	0.507468i
$515$	−7.58086	+	11.3102i	−0.334053	+	0.498386i
$516$	−7.15275	−	5.19678i	−0.314882	−	0.228776i
$517$	0.323157	+	16.1134i	0.0142124	+	0.708666i
$518$	−0.314468			−0.0138169
$519$	23.0733			1.01280
$520$	−12.6385	+	4.64186i	−0.554235	+	0.203559i
$521$	1.08964	−	0.791670i	0.0477380	−	0.0346837i	−0.563660	−	0.826007i	$-0.690607\pi$
$521$	1.08964	−	0.791670i	0.0477380	−	0.0346837i	0.611398	+	0.791323i	$0.290607\pi$
$522$	6.27359			0.274587
$523$	−11.8636	−	8.61939i	−0.518758	−	0.376900i	0.297378	−	0.954760i	$-0.403888\pi$
$523$	−11.8636	−	8.61939i	−0.518758	−	0.376900i	−0.816136	+	0.577860i	$0.803888\pi$
$524$	8.44744	+	6.13742i	0.369028	+	0.268115i
$525$	−0.0753368	−	0.183375i	−0.00328797	−	0.00800316i
$526$	−3.08316	+	9.48900i	−0.134432	+	0.413740i
$527$	−36.9931	+	26.8771i	−1.61145	+	1.17078i
$528$	3.57129	+	1.08171i	0.155420	+	0.0470754i
$529$	−4.15838	+	12.7982i	−0.180799	+	0.556442i
$530$	0.509186	+	13.4549i	0.0221176	+	0.584445i
$531$	7.23574	+	5.25707i	0.314004	+	0.228137i
$532$	0.0381499	+	0.0277175i	0.00165401	+	0.00120171i
$533$	14.8203	−	10.7676i	0.641937	−	0.466395i
$534$	−3.26270	+	10.0416i	−0.141191	+	0.434541i
$535$	−16.4916	+	24.6044i	−0.712994	+	1.06374i
$536$	2.82207	−	8.68544i	0.121895	−	0.375154i
$537$	7.51451	−	5.45961i	0.324275	−	0.235600i
$538$	−3.17415	−	2.30616i	−0.136847	−	0.0994255i
$539$	0.465433	+	23.2076i	0.0200476	+	0.999622i
$540$	11.1799	−	4.10616i	0.481108	−	0.176701i
$541$	3.81483	−	2.77163i	0.164012	−	0.119162i	−0.502752	−	0.864431i	$-0.667679\pi$
$541$	3.81483	−	2.77163i	0.164012	−	0.119162i	0.666764	+	0.745269i	$0.267679\pi$
$542$	7.08231	+	5.14560i	0.304211	+	0.221023i
$543$	−11.3167	−	8.22208i	−0.485647	−	0.352843i
$544$	−4.04312	+	2.93750i	−0.173347	+	0.125944i
$545$	5.49506	+	1.55834i	0.235383	+	0.0667519i
$546$	0.193145	−	0.140328i	0.00826585	−	0.00600549i
$547$	−10.7869	−	33.1986i	−0.461214	−	1.41947i	−0.863682	−	0.504037i	$-0.831848\pi$
$547$	−10.7869	−	33.1986i	−0.461214	−	1.41947i	0.402468	−	0.915434i	$-0.368152\pi$
$548$	−0.317469	−	0.977070i	−0.0135616	−	0.0417384i
$549$	9.33287			0.398317
$550$	−10.9847	−	12.4232i	−0.468390	−	0.529727i
$551$	−4.84074			−0.206223
$552$	1.07404	+	3.30554i	0.0457140	+	0.140693i
$553$	0.0577576	+	0.177760i	0.00245610	+	0.00755910i
$554$	−18.8067	+	13.6639i	−0.799022	+	0.580523i
$555$	12.4990	−	18.6478i	0.530554	−	0.791554i
$556$	−13.7438	+	9.98543i	−0.582865	+	0.423477i
$557$	25.0929	+	18.2310i	1.06322	+	0.772474i	0.974681	−	0.223599i	$-0.0717807\pi$
$557$	25.0929	+	18.2310i	1.06322	+	0.772474i	0.0885374	+	0.996073i	$0.471781\pi$
$558$	12.8367	+	9.32637i	0.543419	+	0.394817i
$559$	−38.2801	+	27.8121i	−1.61907	+	1.17633i
$560$	0.0438743	−	0.0654578i	0.00185403	−	0.00276610i
$561$	−11.2616	−	14.8641i	−0.475466	−	0.627565i
$562$	3.04608	+	2.21310i	0.128491	+	0.0933541i
$563$	25.2790	−	18.3663i	1.06538	−	0.774046i	0.0903064	−	0.995914i	$-0.471215\pi$
$563$	25.2790	−	18.3663i	1.06538	−	0.774046i	0.975077	+	0.221868i	$0.0712154\pi$
$564$	1.68946	−	5.19964i	0.0711393	−	0.218944i
$565$	9.57025	−	3.51496i	0.402624	−	0.147875i
$566$	1.53801	−	4.73350i	0.0646473	−	0.198964i
$567$	−0.0225287	+	0.0163681i	−0.000946118	+	0.000687395i
$568$	1.61765	+	1.17529i	0.0678752	+	0.0493142i
$569$	−7.90977	−	5.74679i	−0.331595	−	0.240918i	0.409512	−	0.912305i	$-0.365699\pi$
$569$	−7.90977	−	5.74679i	−0.331595	−	0.240918i	−0.741107	+	0.671387i	$0.765699\pi$
$570$	−3.15996	+	1.16059i	−0.132356	+	0.0486118i
$571$	−7.03671	+	21.6568i	−0.294477	+	0.906308i	0.688919	+	0.724838i	$0.258085\pi$
$571$	−7.03671	+	21.6568i	−0.294477	+	0.906308i	−0.983397	+	0.181470i	$0.941915\pi$
$572$	11.4119	−	16.3884i	0.477157	−	0.685234i
$573$	17.4127	−	12.6510i	0.727424	−	0.528505i
$574$	−0.0331316	+	0.101969i	−0.00138289	+	0.00425609i
$575$	3.64917	−	15.0088i	0.152181	−	0.625910i
$576$	1.40297	+	1.01932i	0.0584570	+	0.0424715i
$577$	−0.0473740	−	0.0344192i	−0.00197220	−	0.00143289i	0.586799	−	0.809733i	$-0.300388\pi$
$577$	−0.0473740	−	0.0344192i	−0.00197220	−	0.00143289i	−0.588771	+	0.808300i	$0.700388\pi$
$578$	7.97574			0.331747
$579$	13.4401	−	9.76483i	0.558553	−	0.405812i
$580$	0.305911	+	8.08351i	0.0127023	+	0.335650i
$581$	−0.331997			−0.0137735
$582$	−15.9969			−0.663092
$583$	−12.0604	−	15.9184i	−0.499489	−	0.659272i
$584$	11.9100	+	8.65314i	0.492840	+	0.358070i
$585$	−0.882974	−	23.3320i	−0.0365065	−	0.964660i
$586$	−1.50604	+	4.63512i	−0.0622140	+	0.191475i
$587$	0.383684	+	1.18086i	0.0158363	+	0.0487392i	0.958662	−	0.284546i	$-0.0918428\pi$
$587$	0.383684	+	1.18086i	0.0158363	+	0.0487392i	−0.942826	+	0.333285i	$0.891843\pi$
$588$	2.43328	−	7.48887i	0.100347	−	0.308836i
$589$	−9.90485	−	7.19629i	−0.408122	−	0.296518i
$590$	−6.42090	+	9.57959i	−0.264344	+	0.394385i
$591$	11.2715			0.463648
$592$	8.92332			0.366746
$593$	14.7553			0.605929			0.302965	−	0.953002i	$-0.402024\pi$
$593$	14.7553			0.605929			0.302965	+	0.953002i	$0.402024\pi$
$594$	−10.0949	+	14.4971i	−0.414200	+	0.594823i
$595$	−0.369672	+	0.135773i	−0.0151551	+	0.00556614i
$596$	15.4993	+	11.2609i	0.634878	+	0.461266i
$597$	−2.39107	−	7.35897i	−0.0978601	−	0.301182i
$598$	18.6010			0.760650
$599$	5.20227	+	16.0109i	0.212559	+	0.654189i	0.999318	+	0.0369287i	$0.0117574\pi$
$599$	5.20227	+	16.0109i	0.212559	+	0.654189i	−0.786759	+	0.617260i	$0.788243\pi$
$600$	2.13775	+	5.20345i	0.0872735	+	0.212430i
$601$	−3.32550	−	2.41612i	−0.135650	−	0.0985555i	0.517891	−	0.855447i	$-0.326717\pi$
$601$	−3.32550	−	2.41612i	−0.135650	−	0.0985555i	−0.653541	+	0.756891i	$0.726717\pi$
$602$	0.0855773	−	0.263380i	0.00348787	−	0.0107346i
$603$	12.8125	+	9.30881i	0.521765	+	0.379084i
$604$	2.34473	−	7.21633i	0.0954056	−	0.293628i
$605$	23.9136	+	5.75656i	0.972228	+	0.234037i
$606$	5.29800	+	16.3056i	0.215217	+	0.662369i
$607$	−8.57550	+	26.3927i	−0.348069	+	1.07125i	0.611851	+	0.790973i	$0.290425\pi$
$607$	−8.57550	+	26.3927i	−0.348069	+	1.07125i	−0.959920	+	0.280273i	$0.909575\pi$
$608$	−1.08254	−	0.786511i	−0.0439028	−	0.0318972i
$609$	−0.0443248	−	0.136418i	−0.00179613	−	0.00552792i
$610$	0.455087	+	12.0254i	0.0184259	+	0.486894i
$611$	−23.6714	−	17.1983i	−0.957642	−	0.695767i
$612$	−2.67813	−	8.24244i	−0.108257	−	0.333181i
$613$	8.28272			0.334536			0.167268	−	0.985911i	$-0.446506\pi$
$613$	8.28272			0.334536			0.167268	+	0.985911i	$0.446506\pi$
$614$	7.76301	+	23.8921i	0.313290	+	0.964206i
$615$	−4.72981	−	6.01759i	−0.190725	−	0.242653i
$616$	0.00234361	+	0.116858i	9.44268e−5	+	0.00470834i
$617$	−7.89724	−	24.3052i	−0.317931	−	0.978490i	−0.974531	−	0.224252i	$-0.928006\pi$
$617$	−7.89724	−	24.3052i	−0.317931	−	0.978490i	0.656600	−	0.754239i	$-0.271994\pi$
$618$	−2.11704	+	6.51557i	−0.0851598	+	0.262095i
$619$	5.24608	+	3.81150i	0.210858	+	0.153197i	0.688202	−	0.725519i	$-0.258400\pi$
$619$	5.24608	+	3.81150i	0.210858	+	0.153197i	−0.477344	+	0.878717i	$0.658400\pi$
$620$	−11.3911	+	16.9948i	−0.457477	+	0.682527i
$621$	−16.4543			−0.660288
$622$	30.5701			1.22575
$623$	−0.330717			−0.0132499
$624$	−5.48068	+	3.98195i	−0.219403	+	0.159405i
$625$	4.05343	−	24.6692i	0.162137	−	0.986768i
$626$	−4.31260			−0.172366
$627$	2.85329	−	4.09755i	0.113949	−	0.163640i
$628$	−4.67440	+	14.3863i	−0.186529	+	0.574077i
$629$	−36.0781	−	26.2123i	−1.43853	−	1.04515i
$630$	0.0844470	+	0.107439i	0.00336445	+	0.00428048i
$631$	11.7346	−	36.1153i	0.467146	−	1.43773i	−0.389118	−	0.921188i	$-0.627220\pi$
$631$	11.7346	−	36.1153i	0.467146	−	1.43773i	0.856264	−	0.516539i	$-0.172780\pi$
$632$	−1.63893	−	5.04410i	−0.0651930	−	0.200643i
$633$	−9.33212	+	6.78018i	−0.370918	+	0.269488i
$634$	3.35980	+	10.3404i	0.133435	+	0.410670i
$635$	17.3338	+	4.91566i	0.687869	+	0.195072i
$636$	2.09353	+	6.44321i	0.0830137	+	0.255490i
$637$	−34.0931	−	24.7701i	−1.35082	−	0.981427i
$638$	−7.24568	−	9.56352i	−0.286859	−	0.378624i
$639$	−2.80527	+	2.03815i	−0.110975	+	0.0806280i
$640$	−1.24498	+	1.85743i	−0.0492120	+	0.0734212i
$641$	−39.1695			−1.54710			−0.773552	−	0.633733i	$-0.781522\pi$
$641$	−39.1695			−1.54710			−0.773552	+	0.633733i	$0.781522\pi$
$642$	−4.60546	+	14.1741i	−0.181763	+	0.559409i
$643$	12.4538	+	38.3288i	0.491130	+	1.51154i	0.822902	+	0.568183i	$0.192353\pi$
$643$	12.4538	+	38.3288i	0.491130	+	1.51154i	−0.331773	+	0.943359i	$0.607647\pi$
$644$	−0.0880754	+	0.0639905i	−0.00347066	+	0.00252158i
$645$	12.2169	+	15.5432i	0.481039	+	0.612011i
$646$	2.06646	+	6.35992i	0.0813039	+	0.250228i
$647$	28.0621	+	20.3883i	1.10324	+	0.801547i	0.981585	−	0.191026i	$-0.0611813\pi$
$647$	28.0621	+	20.3883i	1.10324	+	0.801547i	0.121650	+	0.992573i	$0.461181\pi$
$648$	0.639274	−	0.464460i	0.0251131	−	0.0182457i
$649$	−0.342982	−	17.1019i	−0.0134632	−	0.671308i
$650$	30.0202	−	2.27542i	1.17749	−	0.0892494i
$651$	0.112105	−	0.345024i	0.00439374	−	0.0135225i
$652$	2.59852	−	7.99743i	0.101766	−	0.313204i
$653$	−27.6863	+	20.1153i	−1.08345	+	0.787171i	−0.978281	−	0.207283i	$-0.933538\pi$
$653$	−27.6863	+	20.1153i	−1.08345	+	0.787171i	−0.105168	+	0.994455i	$0.533538\pi$
$654$	2.87391			0.112379
$655$	−14.4282	−	18.3565i	−0.563756	−	0.717250i
$656$	0.940141	−	2.89346i	0.0367063	−	0.112970i
$657$	−20.6539	+	15.0060i	−0.805787	+	0.585438i
$658$	0.171249			0.00667597
$659$	14.2606	+	10.3609i	0.555515	+	0.403605i	0.829815	−	0.558039i	$-0.188446\pi$
$659$	14.2606	+	10.3609i	0.555515	+	0.403605i	−0.274300	+	0.961644i	$0.588446\pi$
$660$	−7.02277	−	4.50574i	−0.273361	−	0.175386i
$661$	−33.2564	+	24.1622i	−1.29352	+	0.939800i	−0.999870	−	0.0161118i	$-0.994871\pi$
$661$	−33.2564	+	24.1622i	−1.29352	+	0.939800i	−0.293654	+	0.955912i	$0.594871\pi$
$662$	−25.7459	+	18.7055i	−1.00064	+	0.727011i
$663$	33.8560			1.31486
$664$	9.42072			0.365595
$665$	−0.0651599	−	0.0829009i	−0.00252679	−	0.00321476i
$666$	−4.78188	+	14.7171i	−0.185294	+	0.570277i
$667$	3.45347	−	10.6287i	0.133719	−	0.411544i
$668$	14.7426	−	10.7111i	0.570407	−	0.414425i
$669$	−22.8919			−0.885050
$670$	−11.3696	+	16.9628i	−0.439247	+	0.655330i
$671$	−10.7790	−	14.2271i	−0.416119	−	0.549232i
$672$	0.0122524	−	0.0377090i	0.000472646	−	0.00145466i
$673$	−11.9208	−	36.6886i	−0.459515	−	1.41424i	−0.865752	−	0.500473i	$-0.833159\pi$
$673$	−11.9208	−	36.6886i	−0.459515	−	1.41424i	0.406238	−	0.913767i	$-0.366841\pi$
$674$	2.34912	−	1.70673i	0.0904846	−	0.0657409i
$675$	−26.5557	+	2.01283i	−1.02213	+	0.0774737i
$676$	7.18640	+	22.1175i	0.276400	+	0.850672i
$677$	6.50950	+	4.72943i	0.250180	+	0.181767i	0.705807	−	0.708404i	$-0.250585\pi$
$677$	6.50950	+	4.72943i	0.250180	+	0.181767i	−0.455626	+	0.890171i	$0.650585\pi$
$678$	4.15014	−	3.01525i	0.159385	−	0.115800i
$679$	−0.154838	−	0.476543i	−0.00594215	−	0.0182880i
$680$	10.4898	−	3.85268i	0.402265	−	0.147744i
$681$	−3.76739	−	11.5948i	−0.144367	−	0.444315i
$682$	−0.608471	−	30.3398i	−0.0232996	−	1.16177i
$683$	−5.42337	−	16.6914i	−0.207520	−	0.638680i	−0.999601	−	0.0282636i	$-0.991002\pi$
$683$	−5.42337	−	16.6914i	−0.207520	−	0.638680i	0.792081	−	0.610416i	$-0.208998\pi$
$684$	1.87730	−	1.36394i	0.0717804	−	0.0521515i
$685$	0.0868739	+	2.29559i	0.00331928	+	0.0877099i
$686$	0.493332			0.0188355
$687$	0.0574477	−	0.176806i	0.00219177	−	0.00674556i
$688$	−2.42834	+	7.47366i	−0.0925795	+	0.284931i
$689$	36.2573			1.38129
$690$	−0.293904	−	7.76623i	−0.0111887	−	0.295655i
$691$	−9.01362	+	6.54878i	−0.342894	+	0.249127i	−0.745882	−	0.666078i	$-0.767972\pi$
$691$	−9.01362	+	6.54878i	−0.342894	+	0.249127i	0.402988	+	0.915205i	$0.367972\pi$
$692$	−6.33728	−	19.5041i	−0.240907	−	0.741437i
$693$	−0.193988	−	0.0587573i	−0.00736901	−	0.00223201i
$694$	−5.35600	−	16.4841i	−0.203311	−	0.625727i
$695$	35.6579	−	13.0964i	1.35258	−	0.496775i
$696$	1.25776	+	3.87098i	0.0476752	+	0.146729i
$697$	−12.3006	+	8.93693i	−0.465919	+	0.338510i
$698$	−22.2567	−	16.1704i	−0.842428	−	0.612060i
$699$	5.25151	+	16.1625i	0.198630	+	0.611322i
$700$	−0.134318	+	0.114049i	−0.00507673	+	0.00431064i
$701$	−9.66187	+	7.01976i	−0.364924	+	0.265133i	−0.755103	−	0.655606i	$-0.772413\pi$
$701$	−9.66187	+	7.01976i	−0.364924	+	0.265133i	0.390179	+	0.920739i	$0.372413\pi$
$702$	−9.91066	−	30.5019i	−0.374054	−	1.15122i
$703$	3.68973	−	11.3558i	0.139161	−	0.428293i
$704$	−0.0665022	−	3.31596i	−0.00250640	−	0.124975i
$705$	−6.80656	+	10.1550i	−0.256350	+	0.382458i
$706$	25.7809			0.970277
$707$	−0.434458	+	0.315653i	−0.0163395	+	0.0118713i
$708$	−1.79311	+	5.51862i	−0.0673891	+	0.207402i
$709$	−2.38622	+	7.34403i	−0.0896163	+	0.275811i	−0.985813	−	0.167846i	$-0.946319\pi$
$709$	−2.38622	+	7.34403i	−0.0896163	+	0.275811i	0.896197	+	0.443656i	$0.146319\pi$
$710$	−2.76295	−	3.51521i	−0.103692	−	0.131923i
$711$	9.19744			0.344931
$712$	9.38440			0.351695
$713$	22.8670	−	16.6138i	0.856376	−	0.622193i
$714$	−0.160308	+	0.116471i	−0.00599938	+	0.00435880i
$715$	−34.5478	+	28.2933i	−1.29201	+	1.05811i
$716$	−6.67901	−	4.85258i	−0.249606	−	0.181350i
$717$	−21.3750			−0.798264
$718$	−8.99094	+	6.53230i	−0.335539	+	0.243783i
$719$	−13.6612	+	42.0448i	−0.509476	+	1.56800i	0.283638	+	0.958931i	$0.408458\pi$
$719$	−13.6612	+	42.0448i	−0.509476	+	1.56800i	−0.793114	+	0.609073i	$0.791542\pi$
$720$	−2.39627	−	3.04869i	−0.0893035	−	0.113618i
$721$	−0.214589			−0.00799170
$722$	13.9228	−	10.1155i	0.518152	−	0.376460i
$723$	8.30649	−	25.5647i	0.308922	−	0.950763i
$724$	−3.84199	+	11.8244i	−0.142787	+	0.439452i
$725$	4.27339	−	17.5762i	0.158710	−	0.652763i
$726$	12.3661	−	0.496208i	0.458948	−	0.0184160i
$727$	19.1797	−	13.9349i	0.711337	−	0.516817i	−0.172268	−	0.985050i	$-0.555109\pi$
$727$	19.1797	−	13.9349i	0.711337	−	0.516817i	0.883605	+	0.468233i	$0.155109\pi$
$728$	−0.171670	−	0.124726i	−0.00636253	−	0.00462265i
$729$	5.97897	+	18.4014i	0.221443	+	0.681532i
$730$	−20.3423	−	25.8809i	−0.752902	−	0.957894i
$731$	31.7719	−	23.0837i	1.17513	−	0.853780i
$732$	1.87110	+	5.75864i	0.0691577	+	0.212846i
$733$	6.61671	−	20.3641i	0.244394	−	0.752167i	−0.751342	−	0.659913i	$-0.770593\pi$
$733$	6.61671	−	20.3641i	0.244394	−	0.752167i	0.995736	−	0.0922535i	$-0.0294070\pi$
$734$	32.5602			1.20182
$735$	−9.80327	+	14.6259i	−0.361599	+	0.539483i
$736$	2.49922	−	1.81579i	0.0921226	−	0.0669310i
$737$	−0.607326	−	30.2827i	−0.0223711	−	1.11548i
$738$	4.26833	+	3.10112i	0.157119	+	0.114154i
$739$	9.22687	+	28.3974i	0.339416	+	1.04461i	0.964506	+	0.264062i	$0.0850622\pi$
$739$	9.22687	+	28.3974i	0.339416	+	1.04461i	−0.625090	+	0.780553i	$0.714938\pi$
$740$	−19.1962	−	5.44382i	−0.705665	−	0.200119i
$741$	2.80121	+	8.62123i	0.102905	+	0.316709i
$742$	−0.171678	+	0.124731i	−0.00630249	+	0.00457903i
$743$	3.96065	+	12.1896i	0.145302	+	0.447194i	0.997050	−	0.0767581i	$-0.0244569\pi$
$743$	3.96065	+	12.1896i	0.145302	+	0.447194i	−0.851747	+	0.523952i	$0.824457\pi$
$744$	−3.18109	+	9.79037i	−0.116624	+	0.358933i
$745$	−26.4728	−	33.6806i	−0.969890	−	1.23396i
$746$	−4.97381	−	3.61368i	−0.182104	−	0.132306i
$747$	−5.04843	+	15.5375i	−0.184712	+	0.568486i
$748$	−9.47175	+	13.6022i	−0.346321	+	0.497345i
$749$	−0.466822			−0.0170573
$750$	−1.42436	−	12.4980i	−0.0520104	−	0.456364i
$751$	23.4098	−	17.0082i	0.854234	−	0.620637i	−0.0720760	−	0.997399i	$-0.522962\pi$
$751$	23.4098	−	17.0082i	0.854234	−	0.620637i	0.926310	+	0.376762i	$0.122962\pi$
$752$	−4.85935			−0.177202
$753$	18.3890			0.670132
$754$	21.7828			0.793283
$755$	−9.44650	+	14.0936i	−0.343793	+	0.512918i
$756$	0.151859	+	0.110332i	0.00552304	+	0.00401272i
$757$	9.73297	−	29.9550i	0.353751	−	1.08873i	−0.602980	−	0.797757i	$-0.706020\pi$
$757$	9.73297	−	29.9550i	0.353751	−	1.08873i	0.956730	−	0.290976i	$-0.0939801\pi$
$758$	−7.59643	−	23.3794i	−0.275915	−	0.849178i
$759$	6.96129	+	9.18815i	0.252679	+	0.333509i
$760$	1.84897	+	2.35239i	0.0670694	+	0.0853302i
$761$	−2.79996	−	8.61739i	−0.101498	−	0.312380i	0.887394	−	0.461011i	$-0.152513\pi$
$761$	−2.79996	−	8.61739i	−0.101498	−	0.312380i	−0.988893	+	0.148631i	$0.952513\pi$
$762$	9.06553			0.328410
$763$	0.0278174	+	0.0856131i	0.00100706	+	0.00309940i
$764$	−15.4766	−	11.2444i	−0.559925	−	0.406809i
$765$	0.732857	+	19.3653i	0.0264965	+	0.700153i
$766$	−3.52839	−	10.8593i	−0.127486	−	0.392362i
$767$	25.1235	+	18.2533i	0.907158	+	0.659089i
$768$	−0.347673	+	1.07003i	−0.0125456	+	0.0386113i
$769$	2.72226	+	8.37825i	0.0981672	+	0.302128i	0.988066	−	0.154030i	$-0.0492253\pi$
$769$	2.72226	+	8.37825i	0.0981672	+	0.302128i	−0.889899	+	0.456158i	$0.849225\pi$
$770$	0.0662495	−	0.252819i	0.00238747	−	0.00911097i
$771$	4.20586	−	12.9443i	0.151470	−	0.466178i
$772$	−11.9458	−	8.67912i	−0.429938	−	0.312368i
$773$	−1.61100	+	4.95816i	−0.0579437	+	0.178332i	−0.975839	−	0.218490i	$-0.929887\pi$
$773$	−1.61100	+	4.95816i	−0.0579437	+	0.178332i	0.917896	+	0.396822i	$0.129887\pi$
$774$	−11.0249	−	8.01006i	−0.396282	−	0.287916i
$775$	34.8729	−	29.6105i	1.25267	−	1.06364i
$776$	4.39368	+	13.5224i	0.157724	+	0.485425i
$777$	0.353806			0.0126927
$778$	−7.51296	−	23.1225i	−0.269353	−	0.828982i
$779$	−3.29347	−	2.39285i	−0.118001	−	0.0857327i
$780$	14.2195	−	5.22253i	0.509140	−	0.186997i
$781$	6.34693	+	1.92243i	0.227111	+	0.0687898i
$782$	−15.4385			−0.552081
$783$	−19.2689			−0.688616
$784$	−6.99876			−0.249956
$785$	18.8324	−	28.0967i	0.672155	−	1.00281i
$786$	−9.50416	−	6.90518i	−0.339002	−	0.246299i
$787$	1.61167	−	4.96021i	0.0574499	−	0.176813i	−0.918214	−	0.396085i	$-0.870368\pi$
$787$	1.61167	−	4.96021i	0.0574499	−	0.176813i	0.975664	+	0.219273i	$0.0703685\pi$
$788$	−3.09582	−	9.52794i	−0.110284	−	0.339419i
$789$	3.46885	−	10.6760i	0.123494	−	0.380076i
$790$	0.448484	+	11.8509i	0.0159563	+	0.421636i
$791$	0.129994	+	0.0944462i	0.00462205	+	0.00335812i
$792$	5.50461	+	1.66729i	0.195598	+	0.0592447i
$793$	32.4051			1.15074
$794$	36.9262			1.31046
$795$	−0.572883	−	15.1381i	−0.0203181	−	0.536892i
$796$	−5.56390	+	4.04241i	−0.197207	+	0.143279i
$797$	21.3605			0.756629			0.378315	−	0.925677i	$-0.376504\pi$
$797$	21.3605			0.756629			0.378315	+	0.925677i	$0.376504\pi$
$798$	−0.0429222	−	0.0311848i	−0.00151943	−	0.00110393i
$799$	19.6469	+	14.2743i	0.695059	+	0.504990i
$800$	3.81139	−	3.23625i	0.134753	−	0.114419i
$801$	−5.02897	+	15.4776i	−0.177690	+	0.546873i
$802$	24.9189	−	18.1046i	0.879915	−	0.639296i
$803$	46.7295	+	14.1539i	1.64905	+	0.499482i
$804$	−3.17510	+	9.77194i	−0.111977	+	0.344630i
$805$	0.228509	−	0.0839269i	0.00805390	−	0.00295803i
$806$	44.5707	+	32.3825i	1.56994	+	1.14063i
$807$	3.57122	+	2.59464i	0.125713	+	0.0913357i
$808$	12.3282	−	8.95694i	0.433704	−	0.315104i
$809$	14.6917	−	45.2165i	0.516534	−	1.58973i	−0.263940	−	0.964539i	$-0.585022\pi$
$809$	14.6917	−	45.2165i	0.516534	−	1.58973i	0.780474	−	0.625188i	$-0.214978\pi$
$810$	−1.65858	+	0.609163i	−0.0582766	+	0.0214038i
$811$	13.4542	−	41.4078i	0.472441	−	1.45402i	−0.376937	−	0.926239i	$-0.623023\pi$
$811$	13.4542	−	41.4078i	0.472441	−	1.45402i	0.849378	−	0.527785i	$-0.176977\pi$
$812$	−0.103141	+	0.0749366i	−0.00361955	+	0.00262976i
$813$	−7.96827	−	5.78929i	−0.279459	−	0.203039i
$814$	27.9578	−	9.70799i	0.979920	−	0.340265i
$815$	−10.4690	+	15.6191i	−0.366713	+	0.547113i
$816$	4.54889	−	3.30496i	0.159243	−	0.115697i
$817$	8.50689	+	6.18061i	0.297618	+	0.216232i
$818$	8.55217	+	6.21352i	0.299020	+	0.217251i
$819$	0.297704	−	0.216295i	0.0104026	−	0.00755796i
$820$	−3.78766	+	5.65096i	−0.132271	+	0.197340i
$821$	−31.2323	+	22.6916i	−1.09001	+	0.791942i	−0.979402	−	0.201922i	$-0.935281\pi$
$821$	−31.2323	+	22.6916i	−1.09001	+	0.791942i	−0.110613	+	0.993864i	$0.535281\pi$
$822$	0.357183	+	1.09930i	0.0124582	+	0.0383423i
$823$	−6.37665	−	19.6253i	−0.222276	−	0.684096i	−0.998557	−	0.0537082i	$-0.982896\pi$
$823$	−6.37665	−	19.6253i	−0.222276	−	0.684096i	0.776280	−	0.630388i	$-0.217104\pi$
$824$	6.08916			0.212126
$825$	12.3588	+	13.9773i	0.430280	+	0.486626i
$826$	−0.181754			−0.00632404
$827$	2.92936	+	9.01565i	0.101864	+	0.313505i	0.988982	−	0.148038i	$-0.0472959\pi$
$827$	2.92936	+	9.01565i	0.101864	+	0.313505i	−0.887118	+	0.461543i	$0.847296\pi$
$828$	1.65546	+	5.09499i	0.0575313	+	0.177063i
$829$	23.6401	−	17.1755i	0.821053	−	0.596530i	−0.0959610	−	0.995385i	$-0.530592\pi$
$829$	23.6401	−	17.1755i	0.821053	−	0.596530i	0.917014	+	0.398855i	$0.130592\pi$
$830$	−20.2662	−	5.74726i	−0.703450	−	0.199490i
$831$	21.1594	−	15.3732i	0.734010	−	0.533289i
$832$	4.87131	+	3.53921i	0.168882	+	0.122700i
$833$	28.2968	+	20.5589i	0.980427	+	0.712322i
$834$	15.4630	−	11.2345i	0.535441	−	0.389021i
$835$	−38.2492	+	14.0482i	−1.32367	+	0.486157i
$836$	−4.24739	−	1.28650i	−0.146899	−	0.0444944i
$837$	−39.4270	−	28.6454i	−1.36280	−	0.990130i
$838$	−1.57488	+	1.14422i	−0.0544033	+	0.0395263i
$839$	−13.6345	+	41.9626i	−0.470714	+	1.44871i	0.380938	+	0.924601i	$0.375601\pi$
$839$	−13.6345	+	41.9626i	−0.470714	+	1.44871i	−0.851652	+	0.524108i	$0.824399\pi$
$840$	−0.0493628	+	0.0736461i	−0.00170318	+	0.00254103i
$841$	−4.91728	+	15.1338i	−0.169561	+	0.521856i
$842$	6.31229	−	4.58615i	0.217536	−	0.158049i
$843$	−3.42712	−	2.48995i	−0.118036	−	0.0857584i
$844$	8.29452	+	6.02632i	0.285509	+	0.207435i
$845$	−1.96652	−	51.9641i	−0.0676504	−	1.78762i
$846$	2.60406	−	8.01446i	0.0895293	−	0.275543i
$847$	0.134477	+	0.363580i	0.00462067	+	0.0124927i
$848$	4.87152	−	3.53937i	0.167289	−	0.121542i
$849$	−1.73040	+	5.32564i	−0.0593873	+	0.182775i
$850$	−24.9164	+	1.88857i	−0.854625	+	0.0647774i
$851$	22.3014	+	16.2029i	0.764481	+	0.555428i
$852$	−1.82001	−	1.32232i	−0.0623526	−	0.0453018i
$853$	−43.4266			−1.48690			−0.743449	−	0.668793i	$-0.766811\pi$
$853$	−43.4266			−1.48690			−0.743449	+	0.668793i	$0.766811\pi$
$854$	−0.153438	+	0.111479i	−0.00525053	+	0.00381473i
$855$	−4.87061	+	1.78888i	−0.166571	+	0.0611783i
$856$	13.2465			0.452757
$857$	24.7392			0.845076			0.422538	−	0.906345i	$-0.361139\pi$
$857$	24.7392			0.845076			0.422538	+	0.906345i	$0.361139\pi$
$858$	−12.8395	+	18.4385i	−0.438333	+	0.629481i
$859$	18.7556	+	13.6267i	0.639933	+	0.464939i	0.859827	−	0.510585i	$-0.170571\pi$
$859$	18.7556	+	13.6267i	0.639933	+	0.464939i	−0.219894	+	0.975524i	$0.570571\pi$
$860$	9.78336	−	14.5962i	0.333610	−	0.497725i
$861$	0.0372762	−	0.114724i	0.00127037	−	0.00390979i
$862$	5.59835	+	17.2299i	0.190681	+	0.586854i
$863$	−2.83275	+	8.71832i	−0.0964281	+	0.296775i	−0.987623	−	0.156845i	$-0.949868\pi$
$863$	−2.83275	+	8.71832i	−0.0964281	+	0.296775i	0.891195	+	0.453620i	$0.149868\pi$
$864$	−4.30913	−	3.13077i	−0.146600	−	0.106511i
$865$	1.73417	+	45.8242i	0.0589634	+	1.55807i
$866$	−32.7786			−1.11386
$867$	−8.97346			−0.304755
$868$	−0.322444			−0.0109444
$869$	−10.6226	−	14.0207i	−0.360347	−	0.475619i
$870$	−0.344179	−	9.09471i	−0.0116688	−	0.308340i
$871$	44.4868	+	32.3216i	1.50738	+	1.09517i
$872$	−0.789345	−	2.42935i	−0.0267306	−	0.0822683i
$873$	−24.6568			−0.834506
$874$	−1.27737	−	3.93133i	−0.0432076	−	0.132979i
$875$	0.358527	−	0.163403i	0.0121204	−	0.00552404i
$876$	−13.3999	−	9.73560i	−0.452741	−	0.328935i
$877$	6.33605	−	19.5004i	0.213953	−	0.658481i	−0.785273	−	0.619150i	$-0.787477\pi$
$877$	6.33605	−	19.5004i	0.213953	−	0.658481i	0.999226	−	0.0393308i	$-0.0125226\pi$
$878$	23.7235	+	17.2362i	0.800631	+	0.581692i
$879$	1.69444	−	5.21495i	0.0571520	−	0.175896i
$880$	−1.87989	+	7.17398i	−0.0633712	+	0.241835i
$881$	2.43214	+	7.48536i	0.0819409	+	0.252188i	0.983631	−	0.180195i	$-0.0576728\pi$
$881$	2.43214	+	7.48536i	0.0819409	+	0.252188i	−0.901690	+	0.432383i	$0.857673\pi$
$882$	3.75054	−	11.5430i	0.126287	−	0.388672i
$883$	−1.53267	−	1.11355i	−0.0515785	−	0.0374740i	0.561697	−	0.827343i	$-0.310149\pi$
$883$	−1.53267	−	1.11355i	−0.0515785	−	0.0374740i	−0.613276	+	0.789869i	$0.710149\pi$
$884$	−9.29886	−	28.6189i	−0.312754	−	0.962559i
$885$	7.22412	−	10.7779i	0.242836	−	0.362296i
$886$	−17.8199	−	12.9469i	−0.598671	−	0.434960i
$887$	−14.1287	−	43.4838i	−0.474397	−	1.46004i	−0.846770	−	0.531959i	$-0.821456\pi$
$887$	−14.1287	−	43.4838i	−0.474397	−	1.46004i	0.372373	−	0.928083i	$-0.378544\pi$
$888$	−10.0396			−0.336906
$889$	0.0877478	+	0.270060i	0.00294297	+	0.00905752i
$890$	−20.1881	−	5.72511i	−0.676705	−	0.191906i
$891$	1.49762	−	2.15069i	0.0501720	−	0.0720510i
$892$	6.28745	+	19.3508i	0.210519	+	0.647912i
$893$	−2.00931	+	6.18401i	−0.0672389	+	0.206940i
$894$	−17.4382	−	12.6696i	−0.583221	−	0.423735i
$895$	11.4077	+	14.5137i	0.381318	+	0.485139i
$896$	−0.0352411			−0.00117732
$897$	−20.9278			−0.698760
$898$	−0.487266			−0.0162603
$899$	26.7786	−	19.4558i	0.893116	−	0.648887i
$900$	3.29503	+	8.02034i	0.109834	+	0.267345i
$901$	−30.0931			−1.00255
$902$	−0.202324	−	10.0883i	−0.00673664	−	0.335905i
$903$	−0.0962826	+	0.296327i	−0.00320408	+	0.00986115i
$904$	−3.68870	−	2.68000i	−0.122684	−	0.0891355i
$905$	15.4787	−	23.0933i	0.514531	−	0.767647i
$906$	−2.63804	+	8.11905i	−0.0876429	+	0.269737i
$907$	12.6738	+	39.0060i	0.420828	+	1.29517i	0.906933	+	0.421274i	$0.138417\pi$
$907$	12.6738	+	39.0060i	0.420828	+	1.29517i	−0.486106	+	0.873900i	$0.661583\pi$
$908$	−8.76651	+	6.36924i	−0.290927	+	0.211371i
$909$	8.16608	+	25.1326i	0.270852	+	0.833596i
$910$	0.293212	+	0.373045i	0.00971990	+	0.0123663i
$911$	6.01656	+	18.5171i	0.199337	+	0.613497i	0.999899	+	0.0142463i	$0.00453489\pi$
$911$	6.01656	+	18.5171i	0.199337	+	0.613497i	−0.800561	+	0.599251i	$0.795465\pi$
$912$	1.21796	+	0.884899i	0.0403306	+	0.0293019i
$913$	29.5162	−	10.2491i	0.976843	−	0.339197i
$914$	11.0777	−	8.04840i	0.366417	−	0.266217i
$915$	−0.512016	−	13.5297i	−0.0169267	−	0.447278i
$916$	−0.165235			−0.00545951
$917$	0.113710	−	0.349964i	0.00375504	−	0.0115568i
$918$	8.22571	+	25.3161i	0.271489	+	0.835557i
$919$	−7.39613	+	5.37360i	−0.243976	+	0.177259i	−0.703053	−	0.711138i	$-0.748180\pi$
$919$	−7.39613	+	5.37360i	−0.243976	+	0.177259i	0.459077	+	0.888397i	$0.348180\pi$
$920$	−6.48417	+	2.38151i	−0.213777	+	0.0785159i
$921$	−8.73411	−	26.8808i	−0.287799	−	0.885754i
$922$	−8.35564	−	6.07073i	−0.275178	−	0.199929i
$923$	−9.74032	+	7.07676i	−0.320607	+	0.232934i
$924$	−0.00263678	−	0.131476i	−8.67438e−5	−	0.00432525i
$925$	37.9744	+	23.4219i	1.24859	+	0.770107i
$926$	6.20851	−	19.1078i	0.204024	−	0.627922i
$927$	−3.26310	+	10.0428i	−0.107174	+	0.329848i
$928$	2.92674	−	2.12640i	0.0960748	−	0.0698024i
$929$	−0.183077			−0.00600656			−0.00300328	−	0.999995i	$-0.500956\pi$
$929$	−0.183077			−0.00600656			−0.00300328	+	0.999995i	$0.500956\pi$
$930$	12.8160	−	19.1207i	0.420255	−	0.626994i
$931$	−2.89394	+	8.90663i	−0.0948450	+	0.291903i
$932$	12.2200	−	8.87834i	0.400279	−	0.290820i
$933$	−34.3942			−1.12602
$934$	−1.68862	−	1.22685i	−0.0552533	−	0.0401438i
$935$	28.6742	−	23.4831i	0.937747	−	0.767979i
$936$	−8.44765	+	6.13757i	−0.276120	+	0.200613i
$937$	3.22684	−	2.34444i	0.105416	−	0.0765894i	−0.533828	−	0.845593i	$-0.679247\pi$
$937$	3.22684	−	2.34444i	0.105416	−	0.0765894i	0.639245	+	0.769004i	$0.279247\pi$
$938$	−0.321836			−0.0105083
$939$	4.85208			0.158342
$940$	10.4536	+	2.96453i	0.340959	+	0.0966922i
$941$	−5.56453	+	17.1259i	−0.181398	+	0.558287i	−0.999868	−	0.0162633i	$-0.994823\pi$
$941$	−5.56453	+	17.1259i	−0.181398	+	0.558287i	0.818469	+	0.574550i	$0.194823\pi$
$942$	5.25914	−	16.1860i	0.171352	−	0.527367i
$943$	7.60353	−	5.52429i	0.247605	−	0.179896i
$944$	5.15745			0.167861
$945$	−0.259374	−	0.329993i	−0.00843744	−	0.0107347i
$946$	0.522592	+	26.0577i	0.0169909	+	0.847209i
$947$	−11.8820	+	36.5690i	−0.386112	+	1.18833i	0.549558	+	0.835456i	$0.314796\pi$
$947$	−11.8820	+	36.5690i	−0.386112	+	1.18833i	−0.935670	+	0.352876i	$0.885204\pi$
$948$	1.84395	+	5.67508i	0.0598886	+	0.184318i
$949$	−71.7135	+	52.1029i	−2.32792	+	1.69133i
$950$	−2.54247	−	6.18855i	−0.0824885	−	0.200783i
$951$	−3.78009	−	11.6339i	−0.122578	−	0.377256i
$952$	0.142484	+	0.103521i	0.00461794	+	0.00335513i
$953$	−13.3938	+	9.73116i	−0.433867	+	0.315223i	−0.783193	−	0.621778i	$-0.786411\pi$
$953$	−13.3938	+	9.73116i	−0.433867	+	0.315223i	0.349326	+	0.937001i	$0.386411\pi$
$954$	3.22686	+	9.93124i	0.104473	+	0.321536i
$955$	26.4340	+	33.6312i	0.855385	+	1.08828i
$956$	5.87083	+	18.0686i	0.189876	+	0.584379i
$957$	8.15207	+	10.7599i	0.263519	+	0.347817i
$958$	−3.54975	−	10.9250i	−0.114687	−	0.352971i
$959$	−0.0292905	+	0.0212808i	−0.000945839	+	0.000687192i
$960$	1.40072	−	2.08978i	0.0452079	−	0.0674473i
$961$	52.7160			1.70051
$962$	−16.6034	+	51.1000i	−0.535315	+	1.64753i
$963$	−7.09863	+	21.8473i	−0.228750	+	0.704020i
$964$	−23.8917			−0.769499
$965$	20.4034	+	25.9586i	0.656808	+	0.835636i
$966$	0.0990931	−	0.0719953i	0.00318827	−	0.00231641i
$967$	4.76429	+	14.6630i	0.153209	+	0.471530i	0.997975	−	0.0636066i	$-0.0202603\pi$
$967$	4.76429	+	14.6630i	0.153209	+	0.471530i	−0.844766	+	0.535136i	$0.820260\pi$
$968$	−3.81590	−	10.3169i	−0.122648	−	0.331598i
$969$	−2.32497	−	7.15551i	−0.0746886	−	0.229868i
$970$	−1.20231	−	31.7702i	−0.0386038	−	1.02008i
$971$	−12.0762	−	37.1668i	−0.387544	−	1.19274i	−0.934618	−	0.355654i	$-0.884258\pi$
$971$	−12.0762	−	37.1668i	−0.387544	−	1.19274i	0.547073	−	0.837085i	$-0.315742\pi$
$972$	12.2081	−	8.86974i	0.391577	−	0.284497i
$973$	0.484346	+	0.351898i	0.0155274	+	0.0112813i
$974$	5.21900	+	16.0624i	0.167227	+	0.514673i
$975$	−33.7756	+	2.56006i	−1.08168	+	0.0819877i
$976$	4.35394	−	3.16332i	0.139366	−	0.101256i
$977$	−4.79527	−	14.7583i	−0.153414	−	0.472161i	0.844582	−	0.535426i	$-0.179849\pi$
$977$	−4.79527	−	14.7583i	−0.153414	−	0.472161i	−0.997997	+	0.0632647i	$0.979849\pi$
$978$	−2.92358	+	8.99786i	−0.0934859	+	0.287720i
$979$	29.4024	−	10.2096i	0.939704	−	0.326301i
$980$	15.0560	+	4.26971i	0.480946	+	0.136391i
$981$	4.42970			0.141430
$982$	29.0789	−	21.1271i	0.927945	−	0.674192i
$983$	8.16871	−	25.1407i	0.260541	−	0.801864i	−0.732146	−	0.681148i	$-0.761481\pi$
$983$	8.16871	−	25.1407i	0.260541	−	0.801864i	0.992687	−	0.120716i	$-0.0385190\pi$
$984$	−1.05775	+	3.25541i	−0.0337197	+	0.103779i
$985$	0.847155	+	22.3855i	0.0269926	+	0.713262i
$986$	−18.0794			−0.575767
$987$	−0.192671			−0.00613279
$988$	6.51826	−	4.73579i	0.207374	−	0.150666i
$989$	−19.6396	+	14.2690i	−0.624502	+	0.453727i
$990$	−10.8245	−	6.94492i	−0.344027	−	0.220724i
$991$	34.1796	+	24.8329i	1.08575	+	0.788844i	0.978677	−	0.205407i	$-0.0658518\pi$
$991$	34.1796	+	24.8329i	1.08575	+	0.788844i	0.107074	+	0.994251i	$0.465852\pi$
$992$	9.14964			0.290501
$993$	28.9666	−	21.0455i	0.919228	−	0.667858i
$994$	0.0217751	−	0.0670168i	0.000690663	−	0.00212564i
$995$	14.4354	−	5.30183i	0.457633	−	0.168079i
$996$	−10.5992			−0.335848
$997$	−38.8332	+	28.2140i	−1.22986	+	0.893546i	−0.996880	−	0.0789358i	$-0.974848\pi$
$997$	−38.8332	+	28.2140i	−1.22986	+	0.893546i	−0.232980	+	0.972481i	$0.574848\pi$
$998$	2.47069	−	7.60401i	0.0782084	−	0.240701i
$999$	14.6873	−	45.2028i	0.464685	−	1.43015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.g.c.361.5	yes	60
11.5	even	5		550.2.j.c.511.11	yes	60
25.16	even	5		550.2.j.c.141.11	yes	60
275.16	even	5	inner	550.2.g.c.291.5	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.g.c.291.5	✓	60	275.16	even	5	inner
550.2.g.c.361.5	yes	60	1.1	even	1	trivial
550.2.j.c.141.11	yes	60	25.16	even	5
550.2.j.c.511.11	yes	60	11.5	even	5

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.347673 - 1.07003i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.09898 - 0.770911i) q^{5} +(0.910220 - 0.661314i) q^{6} +(0.0285107 + 0.0207142i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.40297 - 1.01932i) q^{9} +(1.38180 + 1.75802i) q^{10} +(-3.17421 - 0.961440i) q^{11} +(0.910220 + 0.661314i) q^{12} +(4.87131 - 3.53921i) q^{13} +(-0.0108901 + 0.0335163i) q^{14} +(-1.55465 - 1.97794i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.04312 + 2.93750i) q^{17} +(1.40297 + 1.01932i) q^{18} +(-1.08254 - 0.786511i) q^{19} +(-1.24498 + 1.85743i) q^{20} +(0.0122524 - 0.0377090i) q^{21} +(-0.0665022 - 3.31596i) q^{22} +(2.49922 - 1.81579i) q^{23} +(-0.347673 + 1.07003i) q^{24} +(3.81139 - 3.23625i) q^{25} +(4.87131 + 3.53921i) q^{26} +(-4.30913 - 3.13077i) q^{27} -0.0352411 q^{28} +(2.92674 - 2.12640i) q^{29} +(1.40072 - 2.08978i) q^{30} +9.14964 q^{31} +1.00000 q^{32} +(0.0748212 + 3.73076i) q^{33} +(-4.04312 - 2.93750i) q^{34} +(0.0758120 + 0.0214994i) q^{35} +(-0.535886 + 1.64929i) q^{36} +(2.75746 + 8.48658i) q^{37} +(0.413493 - 1.27260i) q^{38} +(-5.48068 - 3.98195i) q^{39} +(-2.15124 - 0.610067i) q^{40} +3.04236 q^{41} +0.0396496 q^{42} -7.85827 q^{43} +(3.13311 - 1.08793i) q^{44} +(2.15899 - 3.22108i) q^{45} +(2.49922 + 1.81579i) q^{46} +(-1.50162 - 4.62151i) q^{47} -1.12509 q^{48} +(-2.16274 - 6.65621i) q^{49} +(4.25564 + 2.62479i) q^{50} +(4.54889 + 3.30496i) q^{51} +(-1.86067 + 5.72657i) q^{52} +(4.87152 + 3.53937i) q^{53} +(1.64594 - 5.06569i) q^{54} +(-7.40378 + 0.428998i) q^{55} +(-0.0108901 - 0.0335163i) q^{56} +(-0.465219 + 1.43180i) q^{57} +(2.92674 + 2.12640i) q^{58} +(1.59374 + 4.90503i) q^{59} +(2.42034 + 0.686382i) q^{60} +(4.35394 + 3.16332i) q^{61} +(2.82740 + 8.70183i) q^{62} +0.0611138 q^{63} +(0.309017 + 0.951057i) q^{64} +(7.49634 - 11.1841i) q^{65} +(-3.52505 + 1.22403i) q^{66} +(2.82207 + 8.68544i) q^{67} +(1.54434 - 4.75297i) q^{68} +(-2.81186 - 2.04294i) q^{69} +(0.00298002 + 0.0787451i) q^{70} -1.99953 q^{71} -1.73416 q^{72} -14.7216 q^{73} +(-7.21912 + 5.24500i) q^{74} +(-4.78799 - 2.95314i) q^{75} +1.33809 q^{76} +(-0.0705834 - 0.0931626i) q^{77} +(2.09343 - 6.44293i) q^{78} +(4.29076 + 3.11742i) q^{79} +(-0.0845609 - 2.23447i) q^{80} +(-0.244181 + 0.751512i) q^{81} +(0.940141 + 2.89346i) q^{82} +(-7.62152 + 5.53736i) q^{83} +(0.0122524 + 0.0377090i) q^{84} +(-6.22186 + 9.28263i) q^{85} +(-2.42834 - 7.47366i) q^{86} +(-3.29285 - 2.39240i) q^{87} +(2.00287 + 2.64358i) q^{88} +(-7.59214 + 5.51601i) q^{89} +(3.73060 + 1.05796i) q^{90} +0.212196 q^{91} +(-0.954618 + 2.93801i) q^{92} +(-3.18109 - 9.79037i) q^{93} +(3.93130 - 2.85625i) q^{94} +(-2.87855 - 0.816325i) q^{95} +(-0.347673 - 1.07003i) q^{96} +(-11.5028 - 8.35728i) q^{97} +(5.66211 - 4.11377i) q^{98} +(-5.43333 + 1.88666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9} - 5 q^{10} + 7 q^{11} + q^{12} + 12 q^{13} - 3 q^{14} + 12 q^{15} - 15 q^{16} + q^{17} - 17 q^{18} + 3 q^{19} - 5 q^{20} - 4 q^{21}+ \cdots + 21 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9 - 5 * q^10 + 7 * q^11 + q^12 + 12 * q^13 - 3 * q^14 + 12 * q^15 - 15 * q^16 + q^17 - 17 * q^18 + 3 * q^19 - 5 * q^20 - 4 * q^21 - 3 * q^22 - 3 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^28 + 18 * q^29 + 2 * q^30 - 20 * q^31 + 60 * q^32 + 10 * q^33 + q^34 - 19 * q^35 - 12 * q^36 - 36 * q^37 - 22 * q^38 + 13 * q^39 + 64 * q^41 + 46 * q^42 + 40 * q^43 - 8 * q^44 - 20 * q^45 - 3 * q^46 - 9 * q^47 + 6 * q^48 - 30 * q^49 + 18 * q^50 - 48 * q^51 - 8 * q^52 + 31 * q^53 - 8 * q^54 - 42 * q^55 - 3 * q^56 + 30 * q^57 + 18 * q^58 + 23 * q^59 - 8 * q^60 - 41 * q^61 - 5 * q^62 + 6 * q^63 - 15 * q^64 - 7 * q^65 - 30 * q^66 - 40 * q^67 - 4 * q^68 - 22 * q^69 - 4 * q^70 + 4 * q^71 + 58 * q^72 + 74 * q^73 - 11 * q^74 + 35 * q^75 + 38 * q^76 + 22 * q^77 - 12 * q^78 - 45 * q^79 + 10 * q^80 + 24 * q^81 - 11 * q^82 + 16 * q^83 - 4 * q^84 + 9 * q^85 - 20 * q^86 + 68 * q^87 + 7 * q^88 + q^89 + 10 * q^90 + 10 * q^91 + 2 * q^92 - 40 * q^93 - 24 * q^94 + 24 * q^95 - 4 * q^96 + 6 * q^97 - 30 * q^98 + 21 * q^99

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