LMFDB - Embedded newform 539.2.q.g.410.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(214,539)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 12]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			410.3
Character	$\chi$	$=$	539.410
Dual form			539.2.q.g.422.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01812 + 0.453294i) q^{2} +(2.79635 + 0.594382i) q^{3} +(-0.507177 - 0.563277i) q^{4} +(-0.361259 + 3.43715i) q^{5} +(2.57757 + 1.87272i) q^{6} +(-0.949813 - 2.92322i) q^{8} +(4.72563 + 2.10398i) q^{9} +O(q^{10})$	\(q+(1.01812 + 0.453294i) q^{2} +(2.79635 + 0.594382i) q^{3} +(-0.507177 - 0.563277i) q^{4} +(-0.361259 + 3.43715i) q^{5} +(2.57757 + 1.87272i) q^{6} +(-0.949813 - 2.92322i) q^{8} +(4.72563 + 2.10398i) q^{9} +(-1.92584 + 3.33566i) q^{10} +(-1.73896 + 2.82418i) q^{11} +(-1.08344 - 1.87657i) q^{12} +(1.66629 - 1.21063i) q^{13} +(-3.05318 + 9.39672i) q^{15} +(0.199604 - 1.89910i) q^{16} +(1.76655 - 0.786518i) q^{17} +(3.85751 + 4.28420i) q^{18} +(1.08597 - 1.20609i) q^{19} +(2.11929 - 1.53975i) q^{20} +(-3.05065 + 2.08708i) q^{22} +(0.403568 + 0.699000i) q^{23} +(-0.918495 - 8.73890i) q^{24} +(-6.79272 - 1.44384i) q^{25} +(2.24525 - 0.477243i) q^{26} +(5.02542 + 3.65118i) q^{27} +(2.46400 - 7.58342i) q^{29} +(-7.36797 + 8.18296i) q^{30} +(-0.0824123 - 0.784101i) q^{31} +(-2.00959 + 3.48071i) q^{32} +(-6.54139 + 6.86378i) q^{33} +2.15508 q^{34} +(-1.21160 - 3.72893i) q^{36} +(-9.84189 + 2.09196i) q^{37} +(1.65236 - 0.735679i) q^{38} +(5.37911 - 2.39494i) q^{39} +(10.3907 - 2.20861i) q^{40} +(-0.657011 - 2.02207i) q^{41} +3.08043 q^{43} +(2.47276 - 0.452841i) q^{44} +(-8.93887 + 15.4826i) q^{45} +(0.0940260 + 0.894598i) q^{46} +(5.06286 - 5.62287i) q^{47} +(1.68695 - 5.19190i) q^{48} +(-6.26129 - 4.54910i) q^{50} +(5.40737 - 1.14937i) q^{51} +(-1.52703 - 0.324580i) q^{52} +(-1.13125 - 10.7632i) q^{53} +(3.46140 + 5.99532i) q^{54} +(-9.07891 - 6.99733i) q^{55} +(3.75363 - 2.72717i) q^{57} +(5.94616 - 6.60388i) q^{58} +(-2.20588 - 2.44988i) q^{59} +(6.84146 - 3.04602i) q^{60} +(0.112538 - 1.07073i) q^{61} +(0.271523 - 0.835662i) q^{62} +(-6.71351 + 4.87765i) q^{64} +(3.55916 + 6.16465i) q^{65} +(-9.77121 + 4.02295i) q^{66} +(-1.20157 + 2.08118i) q^{67} +(-1.33898 - 0.596153i) q^{68} +(0.713042 + 2.19452i) q^{69} +(2.57963 + 1.87421i) q^{71} +(1.66196 - 15.8124i) q^{72} +(0.820539 + 0.911300i) q^{73} +(-10.9685 - 2.33142i) q^{74} +(-18.1366 - 8.07494i) q^{75} -1.23015 q^{76} +6.56217 q^{78} +(-8.66208 - 3.85660i) q^{79} +(6.45538 + 1.37213i) q^{80} +(1.49869 + 1.66447i) q^{81} +(0.247681 - 2.35652i) q^{82} +(13.0004 + 9.44536i) q^{83} +(2.06520 + 6.35602i) q^{85} +(3.13623 + 1.39634i) q^{86} +(11.3976 - 19.7413i) q^{87} +(9.90740 + 2.40094i) q^{88} +(2.21915 + 3.84368i) q^{89} +(-16.1190 + 11.7111i) q^{90} +(0.189050 - 0.581837i) q^{92} +(0.235602 - 2.24160i) q^{93} +(7.70339 - 3.42977i) q^{94} +(3.75320 + 4.16836i) q^{95} +(-7.68837 + 8.53880i) q^{96} +(-5.23278 + 3.80184i) q^{97} +(-14.1597 + 9.68727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) $ 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9	$ 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9} - 12 q^{10} + 3 q^{11} - 18 q^{12} - 14 q^{13} - 36 q^{15} - 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + 2 q^{20} - 66 q^{22} - 32 q^{23} + 35 q^{24} - 7 q^{25} + 27 q^{26} + 20 q^{27} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 32 q^{32} + 26 q^{33} - 48 q^{34} + 104 q^{36} - 4 q^{37} + 5 q^{38} - 11 q^{39} + 10 q^{40} - 20 q^{41} - 16 q^{43} + 38 q^{44} - 70 q^{45} + 42 q^{46} + 23 q^{47} - 72 q^{48} + 104 q^{50} + 29 q^{51} - 33 q^{52} - 4 q^{53} - 60 q^{54} - 24 q^{55} - 22 q^{57} - 20 q^{58} - 17 q^{59} + 30 q^{60} + 7 q^{61} + 158 q^{62} + 14 q^{64} + 8 q^{65} - 8 q^{66} + 38 q^{67} + 2 q^{68} + 20 q^{69} - 28 q^{71} + 35 q^{73} + 29 q^{74} - 9 q^{75} + 104 q^{76} - 116 q^{78} - 15 q^{79} + 87 q^{80} + 14 q^{81} - 19 q^{82} + 10 q^{83} + 12 q^{85} + 52 q^{86} + 72 q^{87} - 55 q^{88} - 74 q^{89} - 28 q^{90} - 110 q^{92} - 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 40 q^{97} + 32 q^{99}+O(q^{100}) $ 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9 - 12 * q^10 + 3 * q^11 - 18 * q^12 - 14 * q^13 - 36 * q^15 - 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + 2 * q^20 - 66 * q^22 - 32 * q^23 + 35 * q^24 - 7 * q^25 + 27 * q^26 + 20 * q^27 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 32 * q^32 + 26 * q^33 - 48 * q^34 + 104 * q^36 - 4 * q^37 + 5 * q^38 - 11 * q^39 + 10 * q^40 - 20 * q^41 - 16 * q^43 + 38 * q^44 - 70 * q^45 + 42 * q^46 + 23 * q^47 - 72 * q^48 + 104 * q^50 + 29 * q^51 - 33 * q^52 - 4 * q^53 - 60 * q^54 - 24 * q^55 - 22 * q^57 - 20 * q^58 - 17 * q^59 + 30 * q^60 + 7 * q^61 + 158 * q^62 + 14 * q^64 + 8 * q^65 - 8 * q^66 + 38 * q^67 + 2 * q^68 + 20 * q^69 - 28 * q^71 + 35 * q^73 + 29 * q^74 - 9 * q^75 + 104 * q^76 - 116 * q^78 - 15 * q^79 + 87 * q^80 + 14 * q^81 - 19 * q^82 + 10 * q^83 + 12 * q^85 + 52 * q^86 + 72 * q^87 - 55 * q^88 - 74 * q^89 - 28 * q^90 - 110 * q^92 - 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 40 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.01812	+	0.453294i	0.719917	+	0.320528i	0.733790	−	0.679376i	$-0.237750\pi$
$2$	1.01812	+	0.453294i	0.719917	+	0.320528i	−0.0138735	+	0.999904i	$0.504416\pi$
$3$	2.79635	+	0.594382i	1.61447	+	0.343166i	0.924651	−	0.380815i	$-0.124356\pi$
$3$	2.79635	+	0.594382i	1.61447	+	0.343166i	0.689820	+	0.723981i	$0.257690\pi$
$4$	−0.507177	−	0.563277i	−0.253589	−	0.281639i
$5$	−0.361259	+	3.43715i	−0.161560	+	1.53714i	0.550390	+	0.834908i	$0.314479\pi$
$5$	−0.361259	+	3.43715i	−0.161560	+	1.53714i	−0.711950	+	0.702230i	$0.752188\pi$
$6$	2.57757	+	1.87272i	1.05229	+	0.764534i
$7$		0			0
$7$		0			0
$8$	−0.949813	−	2.92322i	−0.335810	−	1.03352i
$9$	4.72563	+	2.10398i	1.57521	+	0.701328i
$10$	−1.92584	+	3.33566i	−0.609005	+	1.05483i
$11$	−1.73896	+	2.82418i	−0.524318	+	0.851523i
$11$	−1.73896	+	2.82418i	−0.524318	+	0.851523i
$12$	−1.08344	−	1.87657i	−0.312762	−	0.541720i
$13$	1.66629	−	1.21063i	0.462147	−	0.335769i	−0.332226	−	0.943200i	$-0.607800\pi$
$13$	1.66629	−	1.21063i	0.462147	−	0.335769i	0.794373	+	0.607430i	$0.207800\pi$
$14$		0			0
$15$	−3.05318	+	9.39672i	−0.788328	+	2.42622i
$16$	0.199604	−	1.89910i	0.0499009	−	0.474775i
$17$	1.76655	−	0.786518i	0.428451	−	0.190759i	−0.181170	−	0.983452i	$-0.557988\pi$
$17$	1.76655	−	0.786518i	0.428451	−	0.190759i	0.609621	+	0.792693i	$0.291322\pi$
$18$	3.85751	+	4.28420i	0.909224	+	1.00980i
$19$	1.08597	−	1.20609i	0.249139	−	0.276697i	−0.605584	−	0.795782i	$-0.707060\pi$
$19$	1.08597	−	1.20609i	0.249139	−	0.276697i	0.854723	+	0.519085i	$0.173727\pi$
$20$	2.11929	−	1.53975i	0.473887	−	0.344299i
$21$		0			0
$22$	−3.05065	+	2.08708i	−0.650401	+	0.444967i
$23$	0.403568	+	0.699000i	0.0841497	+	0.145752i	0.905029	−	0.425351i	$-0.139849\pi$
$23$	0.403568	+	0.699000i	0.0841497	+	0.145752i	−0.820879	+	0.571102i	$0.806516\pi$
$24$	−0.918495	−	8.73890i	−0.187487	−	1.78382i
$25$	−6.79272	−	1.44384i	−1.35854	−	0.288767i
$26$	2.24525	−	0.477243i	0.440331	−	0.0935951i
$27$	5.02542	+	3.65118i	0.967142	+	0.702670i
$28$		0			0
$29$	2.46400	−	7.58342i	0.457554	−	1.40821i	−0.410557	−	0.911835i	$-0.634666\pi$
$29$	2.46400	−	7.58342i	0.457554	−	1.40821i	0.868111	−	0.496371i	$-0.165334\pi$
$30$	−7.36797	+	8.18296i	−1.34520	+	1.49400i
$31$	−0.0824123	−	0.784101i	−0.0148017	−	0.140829i	0.984625	−	0.174680i	$-0.0558892\pi$
$31$	−0.0824123	−	0.784101i	−0.0148017	−	0.140829i	−0.999427	+	0.0338518i	$0.989223\pi$
$32$	−2.00959	+	3.48071i	−0.355248	+	0.615308i
$33$	−6.54139	+	6.86378i	−1.13871	+	1.19483i
$34$	2.15508			0.369592
$35$		0			0
$36$	−1.21160	−	3.72893i	−0.201934	−	0.621488i
$37$	−9.84189	+	2.09196i	−1.61800	+	0.343916i	−0.925865	−	0.377854i	$-0.876662\pi$
$37$	−9.84189	+	2.09196i	−1.61800	+	0.343916i	−0.692133	+	0.721770i	$0.743329\pi$
$38$	1.65236	−	0.735679i	0.268048	−	0.119343i
$39$	5.37911	−	2.39494i	0.861347	−	0.383497i
$40$	10.3907	−	2.20861i	1.64291	−	0.349211i
$41$	−0.657011	−	2.02207i	−0.102608	−	0.315795i	0.886554	−	0.462626i	$-0.153093\pi$
$41$	−0.657011	−	2.02207i	−0.102608	−	0.315795i	−0.989162	+	0.146831i	$0.953093\pi$
$42$		0			0
$43$	3.08043			0.469761			0.234880	−	0.972024i	$-0.424530\pi$
$43$	3.08043			0.469761			0.234880	+	0.972024i	$0.424530\pi$
$44$	2.47276	−	0.452841i	0.372783	−	0.0682683i
$45$	−8.93887	+	15.4826i	−1.33253	+	2.30801i
$46$	0.0940260	+	0.894598i	0.0138634	+	0.131901i
$47$	5.06286	−	5.62287i	0.738493	−	0.820180i	−0.250504	−	0.968116i	$-0.580596\pi$
$47$	5.06286	−	5.62287i	0.738493	−	0.820180i	0.988997	+	0.147936i	$0.0472629\pi$
$48$	1.68695	−	5.19190i	0.243490	−	0.749387i
$49$		0			0
$50$	−6.26129	−	4.54910i	−0.885481	−	0.643339i
$51$	5.40737	−	1.14937i	0.757184	−	0.160944i
$52$	−1.52703	−	0.324580i	−0.211761	−	0.0450111i
$53$	−1.13125	−	10.7632i	−0.155390	−	1.47843i	−0.743001	−	0.669290i	$-0.766598\pi$
$53$	−1.13125	−	10.7632i	−0.155390	−	1.47843i	0.587611	−	0.809143i	$-0.300068\pi$
$54$	3.46140	+	5.99532i	0.471037	+	0.815859i
$55$	−9.07891	−	6.99733i	−1.22420	−	0.943520i
$56$		0			0
$57$	3.75363	−	2.72717i	0.497181	−	0.361223i
$58$	5.94616	−	6.60388i	0.780769	−	0.867132i
$59$	−2.20588	−	2.44988i	−0.287181	−	0.318947i	0.582242	−	0.813016i	$-0.302176\pi$
$59$	−2.20588	−	2.44988i	−0.287181	−	0.318947i	−0.869423	+	0.494069i	$0.835509\pi$
$60$	6.84146	−	3.04602i	0.883229	−	0.393239i
$61$	0.112538	−	1.07073i	0.0144090	−	0.137093i	−0.984952	−	0.172826i	$-0.944710\pi$
$61$	0.112538	−	1.07073i	0.0144090	−	0.137093i	0.999361	+	0.0357334i	$0.0113767\pi$
$62$	0.271523	−	0.835662i	0.0344835	−	0.106129i
$63$		0			0
$64$	−6.71351	+	4.87765i	−0.839189	+	0.609707i
$65$	3.55916	+	6.16465i	0.441459	+	0.764630i
$66$	−9.77121	+	4.02295i	−1.20275	+	0.495191i
$67$	−1.20157	+	2.08118i	−0.146795	+	0.254257i	−0.930041	−	0.367455i	$-0.880229\pi$
$67$	−1.20157	+	2.08118i	−0.146795	+	0.254257i	0.783246	+	0.621712i	$0.213562\pi$
$68$	−1.33898	−	0.596153i	−0.162375	−	0.0722941i
$69$	0.713042	+	2.19452i	0.0858402	+	0.264189i
$70$		0			0
$71$	2.57963	+	1.87421i	0.306145	+	0.222428i	0.730241	−	0.683190i	$-0.239408\pi$
$71$	2.57963	+	1.87421i	0.306145	+	0.222428i	−0.424095	+	0.905618i	$0.639408\pi$
$72$	1.66196	−	15.8124i	0.195863	−	1.86352i
$73$	0.820539	+	0.911300i	0.0960368	+	0.106660i	0.789247	−	0.614076i	$-0.210471\pi$
$73$	0.820539	+	0.911300i	0.0960368	+	0.106660i	−0.693210	+	0.720735i	$0.743804\pi$
$74$	−10.9685	−	2.33142i	−1.27506	−	0.271022i
$75$	−18.1366	−	8.07494i	−2.09424	−	0.932414i
$76$	−1.23015			−0.141107
$77$		0			0
$78$	6.56217			0.743020
$79$	−8.66208	−	3.85660i	−0.974560	−	0.433902i	−0.143235	−	0.989689i	$-0.545750\pi$
$79$	−8.66208	−	3.85660i	−0.974560	−	0.433902i	−0.831325	+	0.555787i	$0.812417\pi$
$80$	6.45538	+	1.37213i	0.721733	+	0.153409i
$81$	1.49869	+	1.66447i	0.166521	+	0.184941i
$82$	0.247681	−	2.35652i	0.0273518	−	0.260235i
$83$	13.0004	+	9.44536i	1.42698	+	1.03676i	0.990569	+	0.137016i	$0.0437511\pi$
$83$	13.0004	+	9.44536i	1.42698	+	1.03676i	0.436412	+	0.899747i	$0.356249\pi$
$84$		0			0
$85$	2.06520	+	6.35602i	0.224002	+	0.689407i
$86$	3.13623	+	1.39634i	0.338189	+	0.150571i
$87$	11.3976	−	19.7413i	1.22196	−	2.11649i
$88$	9.90740	+	2.40094i	1.05613	+	0.255941i
$89$	2.21915	+	3.84368i	0.235230	+	0.407430i	0.959339	−	0.282255i	$-0.0910825\pi$
$89$	2.21915	+	3.84368i	0.235230	+	0.407430i	−0.724110	+	0.689685i	$0.757749\pi$
$90$	−16.1190	+	11.7111i	−1.69909	+	1.23446i
$91$		0			0
$92$	0.189050	−	0.581837i	0.0197099	−	0.0606607i
$93$	0.235602	−	2.24160i	0.0244308	−	0.232443i
$94$	7.70339	−	3.42977i	0.794544	−	0.353754i
$95$	3.75320	+	4.16836i	0.385071	+	0.427664i
$96$	−7.68837	+	8.53880i	−0.784691	+	0.871488i
$97$	−5.23278	+	3.80184i	−0.531308	+	0.386018i	−0.820847	−	0.571148i	$-0.806498\pi$
$97$	−5.23278	+	3.80184i	−0.531308	+	0.386018i	0.289539	+	0.957166i	$0.406498\pi$
$98$		0			0
$99$	−14.1597	+	9.68727i	−1.42311	+	0.973607i
$100$	2.63183	+	4.55847i	0.263183	+	0.455847i
$101$	1.61443	+	15.3603i	0.160642	+	1.52841i	0.716770	+	0.697310i	$0.245620\pi$
$101$	1.61443	+	15.3603i	0.160642	+	1.52841i	−0.556128	+	0.831097i	$0.687714\pi$
$102$	6.02634	+	1.28094i	0.596696	+	0.126832i
$103$	−8.71346	+	1.85210i	−0.858563	+	0.182493i	−0.616100	−	0.787668i	$-0.711288\pi$
$103$	−8.71346	+	1.85210i	−0.858563	+	0.182493i	−0.242462	+	0.970161i	$0.577955\pi$
$104$	−5.12162	−	3.72107i	−0.502216	−	0.364881i
$105$		0			0
$106$	3.72713	−	11.4709i	0.362011	−	1.11416i
$107$	2.35011	−	2.61007i	0.227194	−	0.252325i	−0.618760	−	0.785580i	$-0.712365\pi$
$107$	2.35011	−	2.61007i	0.227194	−	0.252325i	0.845954	+	0.533255i	$0.179031\pi$
$108$	−0.492150	−	4.68250i	−0.0473572	−	0.450574i
$109$	−1.93827	+	3.35719i	−0.185653	+	0.321560i	−0.943796	−	0.330527i	$-0.892773\pi$
$109$	−1.93827	+	3.35719i	−0.185653	+	0.321560i	0.758143	+	0.652088i	$0.226107\pi$
$110$	−6.07153	−	11.2395i	−0.578897	−	1.07165i
$111$	−28.7648			−2.73023
$112$		0			0
$113$	3.29224	+	10.1325i	0.309708	+	0.953183i	0.977878	+	0.209175i	$0.0670777\pi$
$113$	3.29224	+	10.1325i	0.309708	+	0.953183i	−0.668170	+	0.744008i	$0.732922\pi$
$114$	5.05785	−	1.07508i	0.473711	−	0.100690i
$115$	−2.54836	+	1.13460i	−0.237635	+	0.105802i
$116$	−5.52125	+	2.45822i	−0.512635	+	0.228240i
$117$	10.4214	−	2.21514i	0.963462	−	0.204790i
$118$	−1.13533	−	3.49417i	−0.104515	−	0.321665i
$119$		0			0
$120$	30.3687			2.77227
$121$	−4.95200	−	9.82230i	−0.450182	−	0.892937i
$122$	0.599933	−	1.03911i	0.0543154	−	0.0940769i
$123$	−0.635348	−	6.04493i	−0.0572874	−	0.545053i
$124$	−0.399868	+	0.444099i	−0.0359092	+	0.0398813i
$125$	2.07667	−	6.39134i	0.185743	−	0.571659i
$126$		0			0
$127$	−15.7361	−	11.4330i	−1.39635	−	1.01451i	−0.995134	−	0.0985289i	$-0.968586\pi$
$127$	−15.7361	−	11.4330i	−1.39635	−	1.01451i	−0.401220	−	0.915982i	$-0.631414\pi$
$128$	−1.18346	+	0.251551i	−0.104604	+	0.0222342i
$129$	8.61394	+	1.83095i	0.758415	+	0.161206i
$130$	0.829238	+	7.88967i	0.0727290	+	0.691970i
$131$	−2.55642	−	4.42785i	−0.223355	−	0.386863i	0.732469	−	0.680800i	$-0.238368\pi$
$131$	−2.55642	−	4.42785i	−0.223355	−	0.386863i	−0.955825	+	0.293937i	$0.905034\pi$
$132$	7.18385	+	0.203464i	0.625274	+	0.0177092i
$133$		0			0
$134$	−2.16672	+	1.57422i	−0.187176	+	0.135992i
$135$	−14.3651	+	15.9541i	−1.23635	+	1.37311i
$136$	−3.97706	−	4.41697i	−0.341030	−	0.378752i
$137$	8.31374	−	3.70151i	0.710290	−	0.316242i	−0.0195980	−	0.999808i	$-0.506239\pi$
$137$	8.31374	−	3.70151i	0.710290	−	0.316242i	0.729888	+	0.683566i	$0.239572\pi$
$138$	−0.268803	+	2.55749i	−0.0228821	+	0.217708i
$139$	−4.02234	+	12.3795i	−0.341171	+	1.05002i	0.622431	+	0.782675i	$0.286145\pi$
$139$	−4.02234	+	12.3795i	−0.341171	+	1.05002i	−0.963602	+	0.267341i	$0.913855\pi$
$140$		0			0
$141$	17.4996	−	12.7142i	1.47373	−	1.07073i
$142$	1.77679	+	3.07749i	0.149105	+	0.258257i
$143$	0.521422	+	6.81117i	0.0436035	+	0.569578i
$144$	4.93893	−	8.55448i	0.411577	−	0.712873i
$145$	25.1752	+	11.2087i	2.09068	+	0.930832i
$146$	0.422316	+	1.29975i	0.0349511	+	0.107568i
$147$		0			0
$148$	6.16994	+	4.48272i	0.507166	+	0.368477i
$149$	0.328899	−	3.12926i	0.0269444	−	0.256359i	−0.972755	−	0.231836i	$-0.925527\pi$
$149$	0.328899	−	3.12926i	0.0269444	−	0.256359i	0.999699	−	0.0245229i	$-0.00780666\pi$
$150$	−14.8048	−	16.4424i	−1.20881	−	1.34252i
$151$	−2.80431	−	0.596075i	−0.228212	−	0.0485079i	0.0923863	−	0.995723i	$-0.470551\pi$
$151$	−2.80431	−	0.596075i	−0.228212	−	0.0485079i	−0.320598	+	0.947215i	$0.603884\pi$
$152$	−4.55715	−	2.02898i	−0.369634	−	0.164572i
$153$	10.0029			0.808684
$154$		0			0
$155$	2.72484			0.218864
$156$	−4.07718	−	1.81528i	−0.326435	−	0.145338i
$157$	21.0199	+	4.46792i	1.67757	+	0.356579i	0.945744	−	0.324912i	$-0.105335\pi$
$157$	21.0199	+	4.46792i	1.67757	+	0.356579i	0.731827	+	0.681491i	$0.238668\pi$
$158$	−7.07082	−	7.85294i	−0.562524	−	0.624746i
$159$	3.23405	−	30.7699i	0.256477	−	2.44021i
$160$	−11.2377	−	8.16468i	−0.888420	−	0.645475i
$161$		0			0
$162$	0.771349	+	2.37397i	0.0606029	+	0.186517i
$163$	−7.51158	−	3.34437i	−0.588353	−	0.261951i	0.0908952	−	0.995860i	$-0.471027\pi$
$163$	−7.51158	−	3.34437i	−0.588353	−	0.261951i	−0.679248	+	0.733909i	$0.737694\pi$
$164$	−0.805767	+	1.39563i	−0.0629198	+	0.108980i
$165$	−21.2287	−	24.9633i	−1.65265	−	1.94339i
$166$	8.95440	+	15.5095i	0.694997	+	1.20377i
$167$	17.5626	−	12.7600i	1.35904	−	0.987397i	0.360529	−	0.932748i	$-0.382596\pi$
$167$	17.5626	−	12.7600i	1.35904	−	0.987397i	0.998506	−	0.0546489i	$-0.0174040\pi$
$168$		0			0
$169$	−2.70632	+	8.32919i	−0.208178	+	0.640707i
$170$	−0.778540	+	7.40731i	−0.0597113	+	0.568115i
$171$	7.66950	−	3.41468i	0.586501	−	0.261127i
$172$	−1.56232	−	1.73513i	−0.119126	−	0.132303i
$173$	−5.38358	+	5.97907i	−0.409306	+	0.454580i	−0.912186	−	0.409776i	$-0.865607\pi$
$173$	−5.38358	+	5.97907i	−0.409306	+	0.454580i	0.502880	+	0.864356i	$0.332274\pi$
$174$	20.5527	−	14.9324i	1.55810	−	1.13203i
$175$		0			0
$176$	5.01630	+	3.86619i	0.378118	+	0.291425i
$177$	−4.71224	−	8.16184i	−0.354194	−	0.613482i
$178$	0.517033	+	4.91924i	0.0387533	+	0.368713i
$179$	3.54178	+	0.752829i	0.264725	+	0.0562691i	0.338362	−	0.941016i	$-0.390127\pi$
$179$	3.54178	+	0.752829i	0.264725	+	0.0562691i	−0.0736366	+	0.997285i	$0.523460\pi$
$180$	13.2546	−	2.81735i	0.987938	−	0.209993i
$181$	−12.7970	−	9.29753i	−0.951190	−	0.691080i	−0.000102207	−	1.00000i	$-0.500033\pi$
$181$	−12.7970	−	9.29753i	−0.951190	−	0.691080i	−0.951088	+	0.308920i	$0.900033\pi$
$182$		0			0
$183$	0.951118	−	2.92724i	0.0703087	−	0.216388i
$184$	1.66002	−	1.84364i	0.122378	−	0.135915i
$185$	−3.63490	−	34.5838i	−0.267243	−	2.54265i
$186$	1.25598	−	2.17541i	0.0920926	−	0.159509i
$187$	−0.850696	+	6.35678i	−0.0622091	+	0.464854i
$188$	−5.73500			−0.418268
$189$		0			0
$190$	1.93170	+	5.94518i	0.140141	+	0.431308i
$191$	−0.419704	+	0.0892109i	−0.0303687	+	0.00645508i	−0.223071	−	0.974802i	$-0.571608\pi$
$191$	−0.419704	+	0.0892109i	−0.0303687	+	0.00645508i	0.192702	+	0.981257i	$0.438275\pi$
$192$	−21.6725	+	9.64922i	−1.56408	+	0.696372i
$193$	−13.8629	+	6.17216i	−0.997873	+	0.444282i	−0.839654	−	0.543122i	$-0.817242\pi$
$193$	−13.8629	+	6.17216i	−0.997873	+	0.444282i	−0.158219	+	0.987404i	$0.550575\pi$
$194$	−7.05092	+	1.49872i	−0.506227	+	0.107602i
$195$	6.28849	+	19.3540i	0.450328	+	1.38597i
$196$		0			0
$197$	−20.8082			−1.48252			−0.741262	−	0.671216i	$-0.765772\pi$
$197$	−20.8082			−1.48252			−0.741262	+	0.671216i	$0.765772\pi$
$198$	−18.8074	+	3.44424i	−1.33659	+	0.244771i
$199$	−4.22284	+	7.31417i	−0.299349	+	0.518488i	−0.975987	−	0.217828i	$-0.930103\pi$
$199$	−4.22284	+	7.31417i	−0.299349	+	0.518488i	0.676638	+	0.736316i	$0.263436\pi$
$200$	2.23115	+	21.2280i	0.157766	+	1.50105i
$201$	−4.59702	+	5.10551i	−0.324249	+	0.360115i
$202$	−5.31906	+	16.3704i	−0.374247	+	1.15182i
$203$		0			0
$204$	−3.38991	−	2.46292i	−0.237341	−	0.172439i
$205$	7.18751	−	1.52775i	0.501998	−	0.106703i
$206$	−9.71086	−	2.06411i	−0.676588	−	0.143813i
$207$	0.436426	+	4.15231i	0.0303337	+	0.288606i
$208$	−1.96652	−	3.40611i	−0.136353	−	0.236171i
$209$	1.51776	+	5.16434i	0.104986	+	0.357225i
$210$		0			0
$211$	7.97632	−	5.79513i	0.549112	−	0.398953i	−0.278346	−	0.960481i	$-0.589786\pi$
$211$	7.97632	−	5.79513i	0.549112	−	0.398953i	0.827458	+	0.561528i	$0.189786\pi$
$212$	−5.48890	+	6.09604i	−0.376979	+	0.418678i
$213$	6.09954	+	6.77422i	0.417933	+	0.464162i
$214$	3.57582	−	1.59206i	0.244438	−	0.108831i
$215$	−1.11283	+	10.5879i	−0.0758944	+	0.722087i
$216$	5.90001	−	18.1584i	0.401445	−	1.23552i
$217$		0			0
$218$	−3.49518	+	2.53940i	−0.236724	+	0.171990i
$219$	1.75285	+	3.03602i	0.118447	+	0.205156i
$220$	0.663174	+	8.66283i	0.0447112	+	0.584048i
$221$	1.99140	−	3.44921i	0.133956	−	0.232019i
$222$	−29.2859	−	13.0389i	−1.96554	−	0.875114i
$223$	5.37562	+	16.5445i	0.359978	+	1.10790i	0.953066	+	0.302762i	$0.0979087\pi$
$223$	5.37562	+	16.5445i	0.359978	+	1.10790i	−0.593088	+	0.805138i	$0.702091\pi$
$224$		0			0
$225$	−29.0620	−	21.1148i	−1.93747	−	1.40765i
$226$	−1.24111	+	11.8084i	−0.0825575	+	0.785482i
$227$	−8.45211	−	9.38702i	−0.560986	−	0.623038i	0.394207	−	0.919022i	$-0.371019\pi$
$227$	−8.45211	−	9.38702i	−0.560986	−	0.623038i	−0.955193	+	0.295983i	$0.904353\pi$
$228$	−3.43991	−	0.731176i	−0.227814	−	0.0484233i
$229$	4.17802	+	1.86018i	0.276091	+	0.122924i	0.540112	−	0.841593i	$-0.318382\pi$
$229$	4.17802	+	1.86018i	0.276091	+	0.122924i	−0.264020	+	0.964517i	$0.585049\pi$
$230$	−3.10883			−0.204990
$231$		0			0
$232$	−24.5084			−1.60905
$233$	21.7944	+	9.70347i	1.42780	+	0.635696i	0.967684	−	0.252166i	$-0.0811428\pi$
$233$	21.7944	+	9.70347i	1.42780	+	0.635696i	0.460111	+	0.887861i	$0.347809\pi$
$234$	11.6143	+	2.46870i	0.759253	+	0.161384i
$235$	17.4976	+	19.4331i	1.14142	+	1.26767i
$236$	−0.261189	+	2.48504i	−0.0170019	+	0.161763i
$237$	−21.9299	−	15.9330i	−1.42450	−	1.03496i
$238$		0			0
$239$	2.73114	+	8.40558i	0.176663	+	0.543711i	0.999705	−	0.0242677i	$-0.00772541\pi$
$239$	2.73114	+	8.40558i	0.176663	+	0.543711i	−0.823043	+	0.567979i	$0.807725\pi$
$240$	17.2359	+	7.67392i	1.11257	+	0.495349i
$241$	−9.47322	+	16.4081i	−0.610224	+	1.05694i	0.380978	+	0.924584i	$0.375587\pi$
$241$	−9.47322	+	16.4081i	−0.610224	+	1.05694i	−0.991202	+	0.132355i	$0.957746\pi$
$242$	−0.589317	−	12.2450i	−0.0378827	−	0.787136i
$243$	−6.11610	−	10.5934i	−0.392348	−	0.679567i
$244$	−0.660194	+	0.479659i	−0.0422646	+	0.0307070i
$245$		0			0
$246$	2.09328	−	6.44244i	0.133462	−	0.410755i
$247$	0.349411	−	3.32442i	0.0222325	−	0.211528i
$248$	−2.21383	+	0.985658i	−0.140578	+	0.0625894i
$249$	30.7395	+	34.1397i	1.94804	+	2.16352i
$250$	5.01145	−	5.56578i	0.316952	−	0.352011i
$251$	2.31938	−	1.68513i	0.146398	−	0.106364i	−0.512175	−	0.858881i	$-0.671160\pi$
$251$	2.31938	−	1.68513i	0.146398	−	0.106364i	0.658573	+	0.752516i	$0.271160\pi$
$252$		0			0
$253$	−2.67589	−	0.0757876i	−0.168232	−	0.00476473i
$254$	−10.8387	−	18.7732i	−0.680080	−	1.17793i
$255$	1.99710	+	19.0012i	0.125063	+	1.18990i
$256$	14.9151	+	3.17031i	0.932195	+	0.198144i
$257$	−21.9260	+	4.66052i	−1.36771	+	0.290715i	−0.832510	−	0.554011i	$-0.813097\pi$
$257$	−21.9260	+	4.66052i	−1.36771	+	0.290715i	−0.535199	+	0.844726i	$0.679763\pi$
$258$	7.94003	+	5.76877i	0.494325	+	0.359148i
$259$		0			0
$260$	1.66728	−	5.13136i	0.103400	−	0.318234i
$261$	27.5993	−	30.6522i	1.70836	−	1.89732i
$262$	−0.595612	−	5.66687i	−0.0367970	−	0.350100i
$263$	−0.495353	+	0.857976i	−0.0305448	+	0.0529051i	−0.880894	−	0.473314i	$-0.843058\pi$
$263$	−0.495353	+	0.857976i	−0.0305448	+	0.0529051i	0.850349	+	0.526219i	$0.176391\pi$
$264$	26.2775	+	12.6026i	1.61727	+	0.775639i
$265$	37.4032			2.29766
$266$		0			0
$267$	3.92090	+	12.0673i	0.239955	+	0.738506i
$268$	1.78169	−	0.378710i	0.108834	−	0.0231334i
$269$	−6.56873	+	2.92458i	−0.400502	+	0.178315i	−0.597096	−	0.802170i	$-0.703679\pi$
$269$	−6.56873	+	2.92458i	−0.400502	+	0.178315i	0.196593	+	0.980485i	$0.437012\pi$
$270$	−21.8572	+	9.73147i	−1.33019	+	0.592238i
$271$	26.5707	−	5.64777i	1.61405	−	0.343078i	0.689546	−	0.724241i	$-0.257810\pi$
$271$	26.5707	−	5.64777i	1.61405	−	0.343078i	0.924508	+	0.381164i	$0.124477\pi$
$272$	−1.14107	−	3.51185i	−0.0691874	−	0.212937i
$273$		0			0
$274$	10.1422			0.612714
$275$	15.8900	−	16.6731i	0.958201	−	1.00543i
$276$	0.874484	−	1.51465i	0.0526377	−	0.0911712i
$277$	−2.19359	−	20.8706i	−0.131800	−	1.25400i	−0.837877	−	0.545860i	$-0.816203\pi$
$277$	−2.19359	−	20.8706i	−0.131800	−	1.25400i	0.706076	−	0.708136i	$-0.250464\pi$
$278$	−9.70677	+	10.7805i	−0.582173	+	0.646569i
$279$	1.26029	−	3.87876i	0.0754513	−	0.232215i
$280$		0			0
$281$	22.7803	+	16.5509i	1.35896	+	0.987341i	0.998510	+	0.0545621i	$0.0173763\pi$
$281$	22.7803	+	16.5509i	1.35896	+	0.987341i	0.360448	+	0.932779i	$0.382624\pi$
$282$	23.5799	−	5.01207i	1.40416	−	0.298464i
$283$	25.6194	+	5.44557i	1.52291	+	0.323705i	0.891960	−	0.452115i	$-0.149330\pi$
$283$	25.6194	+	5.44557i	1.52291	+	0.323705i	0.630954	+	0.775820i	$0.282664\pi$
$284$	−0.252629	−	2.40360i	−0.0149908	−	0.142627i
$285$	8.01766	+	13.8870i	0.474925	+	0.822595i
$286$	−2.55660	+	7.17091i	−0.151175	+	0.424025i
$287$		0			0
$288$	−16.8199	+	12.2204i	−0.991123	+	0.720093i
$289$	−8.87314	+	9.85462i	−0.521949	+	0.579683i
$290$	20.5504	+	22.8235i	1.20676	+	1.34024i
$291$	−16.8924	+	7.52098i	−0.990250	+	0.440888i
$292$	0.0971564	−	0.924381i	0.00568565	−	0.0540953i
$293$	−1.37941	+	4.24538i	−0.0805858	+	0.248017i	−0.983230	−	0.182370i	$-0.941623\pi$
$293$	−1.37941	+	4.24538i	−0.0805858	+	0.248017i	0.902644	+	0.430388i	$0.141623\pi$
$294$		0			0
$295$	9.21748	−	6.69689i	0.536663	−	0.389908i
$296$	15.4632	+	26.7831i	0.898782	+	1.55674i
$297$	−19.0506	+	7.84342i	−1.10543	+	0.455121i
$298$	1.75333	−	3.03686i	0.101568	−	0.175921i
$299$	1.51870	+	0.676167i	0.0878284	+	0.0391037i
$300$	4.65004	+	14.3114i	0.268470	+	0.826267i
$301$		0			0
$302$	−2.58492	−	1.87805i	−0.148745	−	0.108070i
$303$	−4.61537	+	43.9123i	−0.265146	+	2.52269i
$304$	−2.07373	−	2.30311i	−0.118937	−	0.132092i
$305$	3.63960	+	0.773620i	0.208403	+	0.0442974i
$306$	10.1841	+	4.53425i	0.582185	+	0.259206i
$307$	12.8841			0.735334			0.367667	−	0.929957i	$-0.380157\pi$
$307$	12.8841			0.735334			0.367667	+	0.929957i	$0.380157\pi$
$308$		0			0
$309$	−25.4667			−1.44875
$310$	2.77420	+	1.23515i	0.157564	+	0.0701521i
$311$	−26.2338	−	5.57616i	−1.48758	−	0.316195i	−0.608763	−	0.793352i	$-0.708334\pi$
$311$	−26.2338	−	5.57616i	−1.48758	−	0.316195i	−0.878818	+	0.477157i	$0.841667\pi$
$312$	−12.1101	−	13.4496i	−0.685598	−	0.761434i
$313$	−0.375120	+	3.56903i	−0.0212030	+	0.201733i	−0.999995	−	0.00312281i	$-0.999006\pi$
$313$	−0.375120	+	3.56903i	−0.0212030	+	0.201733i	0.978792	+	0.204856i	$0.0656726\pi$
$314$	19.3754	+	14.0771i	1.09342	+	0.794415i
$315$		0			0
$316$	2.22087	+	6.83513i	0.124934	+	0.384506i
$317$	−15.4554	−	6.88119i	−0.868062	−	0.386486i	−0.0761321	−	0.997098i	$-0.524257\pi$
$317$	−15.4554	−	6.88119i	−0.868062	−	0.386486i	−0.791930	+	0.610611i	$0.790924\pi$
$318$	17.2405	−	29.8614i	0.966797	−	1.67454i
$319$	17.1321	+	20.1461i	0.959216	+	1.12796i
$320$	−14.3399	−	24.8374i	−0.801624	−	1.38845i
$321$	8.12311	−	5.90178i	0.453388	−	0.329405i
$322$		0			0
$323$	0.969808	−	2.98476i	0.0539616	−	0.166077i
$324$	0.177454	−	1.68836i	0.00985854	−	0.0937977i
$325$	−13.0666	+	5.81764i	−0.724806	+	0.322704i
$326$	−6.13168	−	6.80992i	−0.339602	−	0.377166i
$327$	−7.41554	+	8.23579i	−0.410080	+	0.455440i
$328$	−5.28693	+	3.84118i	−0.291922	+	0.212094i
$329$		0			0
$330$	−10.2975	−	35.0384i	−0.566860	−	1.92880i
$331$	0.619131	+	1.07237i	0.0340305	+	0.0589426i	0.882539	−	0.470239i	$-0.155832\pi$
$331$	0.619131	+	1.07237i	0.0340305	+	0.0589426i	−0.848509	+	0.529182i	$0.822499\pi$
$332$	−1.27316	−	12.1133i	−0.0698737	−	0.664804i
$333$	−50.9106	−	10.8214i	−2.78988	−	0.593008i
$334$	23.6648	−	5.03011i	1.29488	−	0.275235i
$335$	−6.71924	−	4.88181i	−0.367111	−	0.266722i
$336$		0			0
$337$	−6.32885	+	19.4782i	−0.344754	+	1.06104i	0.616961	+	0.786994i	$0.288364\pi$
$337$	−6.32885	+	19.4782i	−0.344754	+	1.06104i	−0.961715	+	0.274051i	$0.911636\pi$
$338$	−6.53092	+	7.25332i	−0.355235	+	0.394529i
$339$	3.18369	+	30.2908i	0.172914	+	1.64517i
$340$	2.53278	−	4.38691i	0.137359	−	0.237913i
$341$	2.35775	+	1.13078i	0.127680	+	0.0612350i
$342$	9.35630			0.505931
$343$		0			0
$344$	−2.92583	−	9.00478i	−0.157750	−	0.485505i
$345$	−7.80047	+	1.65804i	−0.419963	+	0.0892660i
$346$	−8.19139	+	3.64704i	−0.440372	+	0.196066i
$347$	24.9122	−	11.0916i	1.33736	−	0.595431i	0.391551	−	0.920156i	$-0.371939\pi$
$347$	24.9122	−	11.0916i	1.33736	−	0.595431i	0.945808	+	0.324725i	$0.105272\pi$
$348$	−16.9005	+	3.59230i	−0.905959	+	0.192568i
$349$	2.46730	+	7.59356i	0.132071	+	0.406474i	0.995123	−	0.0986418i	$-0.0314498\pi$
$349$	2.46730	+	7.59356i	0.132071	+	0.406474i	−0.863052	+	0.505116i	$0.831450\pi$
$350$		0			0
$351$	12.7941			0.682897
$352$	−6.33555	−	11.7283i	−0.337686	−	0.625119i
$353$	−2.96736	+	5.13961i	−0.157937	+	0.273554i	−0.934124	−	0.356948i	$-0.883817\pi$
$353$	−2.96736	+	5.13961i	−0.157937	+	0.273554i	0.776188	+	0.630502i	$0.217151\pi$
$354$	−1.09789	−	10.4457i	−0.0583523	−	0.555185i
$355$	−7.37384	+	8.18948i	−0.391363	+	0.434652i
$356$	1.03956	−	3.19942i	0.0550964	−	0.169569i
$357$		0			0
$358$	3.26469	+	2.37194i	0.172544	+	0.125361i
$359$	−27.7992	+	5.90891i	−1.46719	+	0.311860i	−0.871118	−	0.491073i	$-0.836605\pi$
$359$	−27.7992	+	5.90891i	−1.46719	+	0.311860i	−0.596069	+	0.802933i	$0.703271\pi$
$360$	53.7493	+	11.4248i	2.83284	+	0.602138i
$361$	1.71071	+	16.2763i	0.0900375	+	0.856650i
$362$	−8.81427	−	15.2668i	−0.463267	−	0.802403i
$363$	−8.00931	−	30.4099i	−0.420380	−	1.59611i
$364$		0			0
$365$	−3.42870	+	2.49109i	−0.179466	+	0.130390i
$366$	2.29525	−	2.54913i	0.119975	−	0.133245i
$367$	−20.3425	−	22.5927i	−1.06187	−	1.17933i	−0.983220	−	0.182425i	$-0.941605\pi$
$367$	−20.3425	−	22.5927i	−1.06187	−	1.17933i	−0.0786515	−	0.996902i	$-0.525061\pi$
$368$	1.40802	−	0.626893i	0.0733984	−	0.0326791i
$369$	1.14962	−	10.9379i	0.0598468	−	0.569404i
$370$	11.9759	−	36.8580i	0.622596	−	1.91615i
$371$		0			0
$372$	−1.38213	+	1.00418i	−0.0716603	+	0.0520643i
$373$	−7.21128	−	12.4903i	−0.373386	−	0.646723i	0.616698	−	0.787200i	$-0.288470\pi$
$373$	−7.21128	−	12.4903i	−0.373386	−	0.646723i	−0.990084	+	0.140476i	$0.955137\pi$
$374$	−3.74760	+	6.08633i	−0.193784	+	0.314716i
$375$	9.60599	−	16.6381i	0.496051	−	0.859186i
$376$	−21.2457	−	9.45918i	−1.09566	−	0.487820i
$377$	−5.07499	−	15.6192i	−0.261375	−	0.804430i
$378$		0			0
$379$	18.1278	+	13.1706i	0.931163	+	0.676529i	0.946277	−	0.323356i	$-0.104811\pi$
$379$	18.1278	+	13.1706i	0.931163	+	0.676529i	−0.0151144	+	0.999886i	$0.504811\pi$
$380$	0.444401	−	4.22819i	0.0227973	−	0.216902i
$381$	−37.2081	−	41.3238i	−1.90623	−	2.11708i
$382$	−0.467747	−	0.0994226i	−0.0239320	−	0.00508690i
$383$	30.7669	+	13.6983i	1.57211	+	0.699950i	0.993306	−	0.115514i	$-0.0368514\pi$
$383$	30.7669	+	13.6983i	1.57211	+	0.699950i	0.578808	+	0.815464i	$0.303518\pi$
$384$	−3.45887			−0.176510
$385$		0			0
$386$	−16.9118			−0.860790
$387$	14.5569	+	6.48117i	0.739971	+	0.329456i
$388$	4.79543	+	1.01930i	0.243451	+	0.0517471i
$389$	1.62454	+	1.80423i	0.0823672	+	0.0914780i	0.782920	−	0.622123i	$-0.213730\pi$
$389$	1.62454	+	1.80423i	0.0823672	+	0.0914780i	−0.700552	+	0.713601i	$0.747063\pi$
$390$	−2.37064	+	22.5551i	−0.120042	+	1.14212i
$391$	1.26270	+	0.917404i	0.0638574	+	0.0463951i
$392$		0			0
$393$	−4.51680	−	13.9013i	−0.227842	−	0.701227i
$394$	−21.1852	−	9.43224i	−1.06729	−	0.475190i
$395$	16.3850	−	28.3796i	0.824417	−	1.42793i
$396$	12.6381	+	3.06269i	0.635089	+	0.153906i
$397$	2.94848	+	5.10692i	0.147980	+	0.256309i	0.930481	−	0.366341i	$-0.119390\pi$
$397$	2.94848	+	5.10692i	0.147980	+	0.256309i	−0.782501	+	0.622650i	$0.786056\pi$
$398$	−7.61481	+	5.53248i	−0.381696	+	0.277318i
$399$		0			0
$400$	−4.09784	+	12.6119i	−0.204892	+	0.630593i
$401$	−1.17486	+	11.1780i	−0.0586696	+	0.558203i	0.925221	+	0.379430i	$0.123880\pi$
$401$	−1.17486	+	11.1780i	−0.0586696	+	0.558203i	−0.983890	+	0.178774i	$0.942787\pi$
$402$	−6.99460	+	3.11420i	−0.348859	+	0.155322i
$403$	−1.08658	−	1.20677i	−0.0541265	−	0.0601136i
$404$	7.83330	−	8.69976i	0.389721	−	0.432829i
$405$	−6.26243	+	4.54992i	−0.311183	+	0.226087i
$406$		0			0
$407$	11.2066	−	31.4331i	0.555492	−	1.55808i
$408$	−8.49587	−	14.7153i	−0.420608	−	0.728515i
$409$	−3.06628	−	29.1737i	−0.151618	−	1.44255i	−0.760527	−	0.649306i	$-0.775059\pi$
$409$	−3.06628	−	29.1737i	−0.151618	−	1.44255i	0.608909	−	0.793240i	$-0.291607\pi$
$410$	8.01024	+	1.70263i	0.395598	+	0.0840869i
$411$	25.4482	−	5.40918i	1.25527	−	0.266815i
$412$	5.46251	+	3.96875i	0.269119	+	0.195526i
$413$		0			0
$414$	−1.43789	+	4.42536i	−0.0706683	+	0.217495i
$415$	−37.1616	+	41.2721i	−1.82419	+	2.02597i
$416$	0.865298	+	8.23276i	0.0424247	+	0.403644i
$417$	−18.6060	+	32.2266i	−0.911140	+	1.57814i
$418$	−0.795708	+	5.94589i	−0.0389194	+	0.290823i
$419$	−20.2858			−0.991027			−0.495514	−	0.868600i	$-0.665020\pi$
$419$	−20.2858			−0.991027			−0.495514	+	0.868600i	$0.665020\pi$
$420$		0			0
$421$	−0.945600	−	2.91026i	−0.0460857	−	0.141837i	0.925366	−	0.379075i	$-0.123758\pi$
$421$	−0.945600	−	2.91026i	−0.0460857	−	0.141837i	−0.971452	+	0.237238i	$0.923758\pi$
$422$	10.7477	−	2.28450i	0.523191	−	0.111208i
$423$	35.7556	−	15.9194i	1.73850	−	0.774028i
$424$	−30.3886	+	13.5299i	−1.47580	+	0.657070i
$425$	−13.1353	+	2.79199i	−0.637155	+	0.135431i
$426$	3.13932	+	9.66183i	0.152100	+	0.468117i
$427$		0			0
$428$	−2.66211			−0.128678
$429$	−2.59036	+	19.3563i	−0.125064	+	0.934531i
$430$	−5.93241	+	10.2752i	−0.286086	+	0.495516i
$431$	−0.788350	−	7.50065i	−0.0379735	−	0.361294i	−0.996965	−	0.0778572i	$-0.975192\pi$
$431$	−0.788350	−	7.50065i	−0.0379735	−	0.361294i	0.958991	−	0.283436i	$-0.0914745\pi$
$432$	7.93705	−	8.81499i	0.381871	−	0.424111i
$433$	−9.93848	+	30.5875i	−0.477613	+	1.46994i	0.364788	+	0.931091i	$0.381141\pi$
$433$	−9.93848	+	30.5875i	−0.477613	+	1.46994i	−0.842401	+	0.538851i	$0.818859\pi$
$434$		0			0
$435$	63.7362	+	46.3071i	3.05592	+	2.22025i
$436$	2.87408	−	0.610904i	0.137643	−	0.0292570i
$437$	1.28132	+	0.272354i	0.0612940	+	0.0130284i
$438$	0.408391	+	3.88558i	0.0195137	+	0.185660i
$439$	2.33363	+	4.04196i	0.111378	+	0.192912i	0.916326	−	0.400433i	$-0.131140\pi$
$439$	2.33363	+	4.04196i	0.111378	+	0.192912i	−0.804948	+	0.593345i	$0.797807\pi$
$440$	−11.8315	+	33.1858i	−0.564045	+	1.58207i
$441$		0			0
$442$	3.59099	−	2.60901i	0.170806	−	0.124098i
$443$	11.5607	−	12.8394i	0.549264	−	0.610020i	−0.403036	−	0.915184i	$-0.632045\pi$
$443$	11.5607	−	12.8394i	0.549264	−	0.610020i	0.952300	+	0.305165i	$0.0987116\pi$
$444$	14.5888	+	16.2025i	0.692355	+	0.768938i
$445$	−14.0130	+	6.23898i	−0.664279	+	0.295756i
$446$	−2.02651	+	19.2809i	−0.0959579	+	0.912979i
$447$	2.77969	−	8.55501i	0.131475	−	0.404638i
$448$		0			0
$449$	13.5430	−	9.83957i	0.639134	−	0.464358i	−0.220418	−	0.975405i	$-0.570742\pi$
$449$	13.5430	−	9.83957i	0.639134	−	0.464358i	0.859553	+	0.511047i	$0.170742\pi$
$450$	−20.0173	−	34.6710i	−0.943625	−	1.63441i
$451$	6.85322	+	1.66079i	0.322706	+	0.0782038i
$452$	4.03764	−	6.99340i	0.189915	−	0.328942i
$453$	−7.48753	−	3.33366i	−0.351795	−	0.156629i
$454$	−4.35015	−	13.3884i	−0.204162	−	0.628347i
$455$		0			0
$456$	−11.5374	−	8.38241i	−0.540288	−	0.392542i
$457$	2.26800	−	21.5785i	0.106092	−	1.00940i	−0.803897	−	0.594769i	$-0.797243\pi$
$457$	2.26800	−	21.5785i	0.106092	−	1.00940i	0.909989	−	0.414633i	$-0.136090\pi$
$458$	3.41050	+	3.78775i	0.159362	+	0.176990i
$459$	11.7494	+	2.49740i	0.548413	+	0.116569i
$460$	1.93156	+	0.859987i	0.0900596	+	0.0400971i
$461$	−6.07778			−0.283070			−0.141535	−	0.989933i	$-0.545204\pi$
$461$	−6.07778			−0.283070			−0.141535	+	0.989933i	$0.545204\pi$
$462$		0			0
$463$	−5.14719			−0.239210			−0.119605	−	0.992822i	$-0.538163\pi$
$463$	−5.14719			−0.239210			−0.119605	+	0.992822i	$0.538163\pi$
$464$	−13.9099	−	6.19307i	−0.645749	−	0.287506i
$465$	7.61960	+	1.61959i	0.353350	+	0.0751069i
$466$	17.7906	+	19.7585i	0.824136	+	0.915296i
$467$	0.409676	−	3.89780i	0.0189575	−	0.180369i	−0.980946	−	0.194282i	$-0.937762\pi$
$467$	0.409676	−	3.89780i	0.0189575	−	0.180369i	0.999903	+	0.0139134i	$0.00442891\pi$
$468$	−6.53325	−	4.74669i	−0.302000	−	0.219416i
$469$		0			0
$470$	9.00570	+	27.7167i	0.415402	+	1.27848i
$471$	56.1233	+	24.9877i	2.58602	+	1.15137i
$472$	−5.06637	+	8.77521i	−0.233199	+	0.403912i
$473$	−5.35675	+	8.69968i	−0.246304	+	0.400012i
$474$	−15.1048	−	26.1623i	−0.693787	−	1.20167i
$475$	−9.11811	+	6.62469i	−0.418368	+	0.303962i
$476$		0			0
$477$	17.2996	−	53.2428i	0.792096	−	2.43782i
$478$	−1.02959	+	9.79586i	−0.0470922	+	0.448052i
$479$	−13.8063	+	6.14698i	−0.630828	+	0.280863i	−0.697139	−	0.716936i	$-0.745544\pi$
$479$	−13.8063	+	6.14698i	−0.630828	+	0.280863i	0.0663109	+	0.997799i	$0.478877\pi$
$480$	−26.5716	−	29.5108i	−1.21282	−	1.34698i
$481$	−13.8669	+	15.4007i	−0.632276	+	0.702214i
$482$	−17.0825	+	12.4112i	−0.778088	+	0.565314i
$483$		0			0
$484$	−3.02114	+	7.77100i	−0.137324	+	0.353227i
$485$	−11.1771	−	19.3593i	−0.507525	−	0.879059i
$486$	−1.42497	−	13.5577i	−0.0646380	−	0.614990i
$487$	−24.5288	−	5.21376i	−1.11151	−	0.236258i	−0.384660	−	0.923058i	$-0.625681\pi$
$487$	−24.5288	−	5.21376i	−1.11151	−	0.236258i	−0.726846	+	0.686800i	$0.759015\pi$
$488$	−3.23687	+	0.688018i	−0.146526	+	0.0311451i
$489$	−19.0172	−	13.8168i	−0.859985	−	0.624816i
$490$		0			0
$491$	11.5019	−	35.3991i	0.519071	−	1.59754i	−0.256679	−	0.966497i	$-0.582628\pi$
$491$	11.5019	−	35.3991i	0.519071	−	1.59754i	0.775750	−	0.631040i	$-0.217372\pi$
$492$	−3.08274	+	3.42373i	−0.138981	+	0.154354i
$493$	−1.61172	−	15.3345i	−0.0725881	−	0.690630i
$494$	1.86268	−	3.22626i	0.0838060	−	0.145156i
$495$	−28.1812	−	52.1687i	−1.26665	−	2.34481i
$496$	−1.50554			−0.0676006
$497$		0			0
$498$	15.8211	+	48.6922i	0.708959	+	2.18195i
$499$	31.1182	−	6.61437i	1.39304	−	0.296100i	0.550546	−	0.834805i	$-0.314420\pi$
$499$	31.1182	−	6.61437i	1.39304	−	0.296100i	0.842494	+	0.538705i	$0.181086\pi$
$500$	−4.65334	+	2.07180i	−0.208104	+	0.0926537i
$501$	56.6954	−	25.2424i	2.53296	−	1.12775i
$502$	3.12526	−	0.664294i	0.139487	−	0.0296489i
$503$	−5.93493	−	18.2658i	−0.264626	−	0.814434i	−0.991779	−	0.127959i	$-0.959157\pi$
$503$	−5.93493	−	18.2658i	−0.264626	−	0.814434i	0.727154	−	0.686474i	$-0.240843\pi$
$504$		0			0
$505$	−53.3788			−2.37532
$506$	−2.69001	−	1.29013i	−0.119586	−	0.0573532i
$507$	−12.5185	+	21.6827i	−0.555967	+	0.962963i
$508$	1.54107	+	14.6623i	0.0683740	+	0.650536i
$509$	1.68319	−	1.86937i	0.0746060	−	0.0828584i	−0.704686	−	0.709519i	$-0.748912\pi$
$509$	1.68319	−	1.86937i	0.0746060	−	0.0828584i	0.779292	+	0.626661i	$0.215579\pi$
$510$	−6.57984	+	20.2506i	−0.291360	+	0.896714i
$511$		0			0
$512$	15.7059	+	11.4110i	0.694109	+	0.504300i
$513$	9.86113	−	2.09605i	0.435379	−	0.0925428i
$514$	−24.4358	−	5.19400i	−1.07782	−	0.229097i
$515$	−3.21814	−	30.6185i	−0.141808	−	1.34921i
$516$	−3.33746	−	5.78065i	−0.146924	−	0.254479i
$517$	7.07588	+	24.0764i	0.311197	+	1.05888i
$518$		0			0
$519$	−18.6082	+	13.5196i	−0.816809	+	0.593447i
$520$	14.6401	−	16.2595i	0.642011	−	0.713025i
$521$	9.96788	+	11.0705i	0.436701	+	0.485005i	0.920815	−	0.389999i	$-0.127525\pi$
$521$	9.96788	+	11.0705i	0.436701	+	0.485005i	−0.484114	+	0.875005i	$0.660858\pi$
$522$	41.9938	−	18.6968i	1.83802	−	0.818338i
$523$	1.03536	−	9.85076i	0.0452730	−	0.430744i	−0.948285	−	0.317420i	$-0.897184\pi$
$523$	1.03536	−	9.85076i	0.0452730	−	0.430744i	0.993558	−	0.113324i	$-0.0361498\pi$
$524$	−1.19755	+	3.68567i	−0.0523151	+	0.161009i
$525$		0			0
$526$	−0.893242	+	0.648979i	−0.0389472	+	0.0282968i
$527$	−0.762295	−	1.32033i	−0.0332061	−	0.0575146i
$528$	11.7293	+	13.7928i	0.510453	+	0.600254i
$529$	11.1743	−	19.3544i	0.485838	−	0.841496i
$530$	38.0808	+	16.9547i	1.65412	+	0.736464i
$531$	−5.26966	−	16.2183i	−0.228684	−	0.703816i
$532$		0			0
$533$	−3.54276	−	2.57397i	−0.153454	−	0.111491i
$534$	−1.47810	+	14.0632i	−0.0639638	+	0.608575i
$535$	8.12218	+	9.02059i	0.351152	+	0.389994i
$536$	7.22502	+	1.53573i	0.312073	+	0.0663332i
$537$	9.45659	+	4.21034i	0.408082	+	0.181690i
$538$	−8.01342			−0.345483
$539$		0			0
$540$	16.2722			0.700245
$541$	−20.1057	−	8.95161i	−0.864409	−	0.384860i	−0.0738677	−	0.997268i	$-0.523534\pi$
$541$	−20.1057	−	8.95161i	−0.864409	−	0.384860i	−0.790542	+	0.612408i	$0.790201\pi$
$542$	29.6121	+	6.29425i	1.27195	+	0.270361i
$543$	−30.2584	−	33.6054i	−1.29851	−	1.44215i
$544$	−0.812395	+	7.72942i	−0.0348311	+	0.331396i
$545$	−10.8389	−	7.87494i	−0.464289	−	0.337325i
$546$		0			0
$547$	−3.35724	−	10.3325i	−0.143545	−	0.441787i	0.853276	−	0.521460i	$-0.174612\pi$
$547$	−3.35724	−	10.3325i	−0.143545	−	0.441787i	−0.996821	+	0.0796728i	$0.974612\pi$
$548$	−6.30152	−	2.80562i	−0.269187	−	0.119850i
$549$	2.78461	−	4.82309i	0.118844	−	0.205844i
$550$	23.7356	−	9.77231i	1.01209	−	0.416693i
$551$	−6.47048	−	11.2072i	−0.275652	−	0.477443i
$552$	5.73781	−	4.16876i	0.244218	−	0.177434i
$553$		0			0
$554$	7.22721	−	22.2431i	0.307055	−	0.945018i
$555$	10.3915	−	98.8687i	0.441095	−	4.19674i
$556$	9.01313	−	4.01290i	0.382242	−	0.170185i
$557$	22.4912	+	24.9790i	0.952983	+	1.05840i	0.998233	+	0.0594193i	$0.0189249\pi$
$557$	22.4912	+	24.9790i	0.952983	+	1.05840i	−0.0452499	+	0.998976i	$0.514408\pi$
$558$	3.04134	−	3.37775i	0.128750	−	0.142991i
$559$	5.13290	−	3.72927i	0.217098	−	0.157731i
$560$		0			0
$561$	−6.15720	+	17.2701i	−0.259957	+	0.729145i
$562$	15.6906	+	27.1769i	0.661867	+	1.14639i
$563$	0.214647	+	2.04223i	0.00904631	+	0.0860699i	0.998114	−	0.0613956i	$-0.0195551\pi$
$563$	0.214647	+	2.04223i	0.00904631	+	0.0860699i	−0.989067	+	0.147465i	$0.952888\pi$
$564$	−16.0370	−	3.40878i	−0.675281	−	0.143535i
$565$	−36.0161	+	7.65547i	−1.51521	+	0.322068i
$566$	23.6151	+	17.1573i	0.992615	+	0.721177i
$567$		0			0
$568$	3.02857	−	9.32098i	0.127076	−	0.391099i
$569$	2.19084	−	2.43317i	0.0918448	−	0.102004i	−0.695470	−	0.718555i	$-0.744804\pi$
$569$	2.19084	−	2.43317i	0.0918448	−	0.102004i	0.787315	+	0.616551i	$0.211471\pi$
$570$	1.86801	+	17.7729i	0.0782424	+	0.744426i
$571$	21.9448	−	38.0096i	0.918363	−	1.59065i	0.116462	−	0.993195i	$-0.462845\pi$
$571$	21.9448	−	38.0096i	0.918363	−	1.59065i	0.801901	−	0.597457i	$-0.203822\pi$
$572$	3.57212	−	3.74817i	0.149358	−	0.156719i
$573$	−1.22666			−0.0512446
$574$		0			0
$575$	−1.73208	−	5.33080i	−0.0722328	−	0.222310i
$576$	−41.9881	+	8.92484i	−1.74950	+	0.371868i
$577$	−40.0959	+	17.8518i	−1.66921	+	0.743181i	−0.669213	+	0.743071i	$0.733369\pi$
$577$	−40.0959	+	17.8518i	−1.66921	+	0.743181i	−1.00000		0.000110759i	$0.999965\pi$
$578$	−13.5009	+	6.01100i	−0.561564	+	0.250025i
$579$	−42.4341	+	9.01964i	−1.76350	+	0.374843i
$580$	−6.45466	−	19.8654i	−0.268015	−	0.824866i
$581$		0			0
$582$	−20.6076			−0.854214
$583$	32.3643	+	15.5219i	1.34039	+	0.642851i
$584$	1.88458	−	3.26418i	0.0779843	−	0.135073i
$585$	3.84894	+	36.6202i	0.159134	+	1.51406i
$586$	−3.32880	+	3.69701i	−0.137511	+	0.152722i
$587$	0.862670	−	2.65503i	0.0356062	−	0.109585i	−0.931674	−	0.363296i	$-0.881651\pi$
$587$	0.862670	−	2.65503i	0.0356062	−	0.109585i	0.967280	+	0.253711i	$0.0816513\pi$
$588$		0			0
$589$	−1.03520	−	0.752114i	−0.0426545	−	0.0309903i
$590$	12.4201	−	2.63998i	0.511329	−	0.108686i
$591$	−58.1869	−	12.3680i	−2.39349	−	0.508752i
$592$	2.00836	+	19.1083i	0.0825433	+	0.785347i
$593$	−11.6263	−	20.1374i	−0.477435	−	0.826942i	0.522230	−	0.852805i	$-0.325100\pi$
$593$	−11.6263	−	20.1374i	−0.477435	−	0.826942i	−0.999666	+	0.0258622i	$0.991767\pi$
$594$	−22.9511	−	0.650030i	−0.941696	−	0.0266710i
$595$		0			0
$596$	−1.92945	+	1.40183i	−0.0790334	+	0.0574211i
$597$	−16.1559	+	17.9430i	−0.661218	+	0.734357i
$598$	1.23971	+	1.37683i	0.0506953	+	0.0563029i
$599$	9.55519	−	4.25424i	0.390414	−	0.173824i	−0.202135	−	0.979358i	$-0.564788\pi$
$599$	9.55519	−	4.25424i	0.390414	−	0.173824i	0.592550	+	0.805534i	$0.298121\pi$
$600$	−6.37846	+	60.6870i	−0.260400	+	2.47754i
$601$	6.89406	−	21.2177i	0.281215	−	0.865489i	−0.706293	−	0.707919i	$-0.749634\pi$
$601$	6.89406	−	21.2177i	0.281215	−	0.865489i	0.987508	−	0.157570i	$-0.0503660\pi$
$602$		0			0
$603$	−10.0569	+	7.30679i	−0.409550	+	0.297556i
$604$	1.08653	+	1.88192i	0.0442102	+	0.0765743i
$605$	35.5496	−	13.4724i	1.44530	−	0.547729i
$606$	−24.6042	+	42.6157i	−0.999476	+	1.73114i
$607$	17.3468	+	7.72328i	0.704084	+	0.313478i	0.727365	−	0.686251i	$-0.240745\pi$
$607$	17.3468	+	7.72328i	0.704084	+	0.313478i	−0.0232812	+	0.999729i	$0.507411\pi$
$608$	2.01571	+	6.20370i	0.0817477	+	0.251593i
$609$		0			0
$610$	3.35485	+	2.43744i	0.135834	+	0.0986892i
$611$	1.62897	−	15.4986i	0.0659011	−	0.627007i
$612$	−5.07323	−	5.63439i	−0.205073	−	0.227757i
$613$	−19.7211	−	4.19185i	−0.796528	−	0.169307i	−0.208366	−	0.978051i	$-0.566815\pi$
$613$	−19.7211	−	4.19185i	−0.796528	−	0.169307i	−0.588161	+	0.808744i	$0.700148\pi$
$614$	13.1175	+	5.84029i	0.529379	+	0.235695i
$615$	21.0068			0.847077
$616$		0			0
$617$	7.03919			0.283387			0.141694	−	0.989911i	$-0.454745\pi$
$617$	7.03919			0.283387			0.141694	+	0.989911i	$0.454745\pi$
$618$	−25.9281	−	11.5439i	−1.04298	−	0.464364i
$619$	30.4038	+	6.46254i	1.22203	+	0.259751i	0.773373	−	0.633951i	$-0.218568\pi$
$619$	30.4038	+	6.46254i	1.22203	+	0.259751i	0.448660	+	0.893702i	$0.351901\pi$
$620$	−1.38198	−	1.53484i	−0.0555015	−	0.0616407i
$621$	−0.524078	+	4.98626i	−0.0210305	+	0.200092i
$622$	−24.1814	−	17.5688i	−0.969585	−	0.704445i
$623$		0			0
$624$	−3.47453	−	10.6935i	−0.139093	−	0.428083i
$625$	−10.5027	−	4.67611i	−0.420108	−	0.187044i
$626$	−1.99974	+	3.46364i	−0.0799255	+	0.138435i
$627$	1.17460	+	15.3434i	0.0469090	+	0.612757i
$628$	−8.14414	−	14.1061i	−0.324986	−	0.562893i
$629$	−15.7408	+	11.4364i	−0.627628	+	0.455998i
$630$		0			0
$631$	6.78971	−	20.8966i	0.270294	−	0.831880i	−0.720132	−	0.693837i	$-0.755919\pi$
$631$	6.78971	−	20.8966i	0.270294	−	0.831880i	0.990426	−	0.138043i	$-0.0440812\pi$
$632$	−3.04637	+	28.9842i	−0.121178	+	1.15293i
$633$	25.7491	−	11.4642i	1.02343	−	0.455662i
$634$	−12.6162	−	14.0117i	−0.501053	−	0.556476i
$635$	44.9815	−	49.9570i	1.78504	−	1.98248i
$636$	−18.9722	+	13.7841i	−0.752298	+	0.546576i
$637$		0			0
$638$	8.31039	+	28.2770i	0.329012	+	1.11950i
$639$	8.24705	+	14.2843i	0.326248	+	0.565078i
$640$	−0.437085	−	4.15858i	−0.0172773	−	0.164382i
$641$	13.0005	+	2.76334i	0.513489	+	0.109145i	0.457366	−	0.889278i	$-0.348793\pi$
$641$	13.0005	+	2.76334i	0.513489	+	0.109145i	0.0561227	+	0.998424i	$0.482126\pi$
$642$	10.9455	−	2.32654i	0.431985	−	0.0918212i
$643$	−11.8848	−	8.63480i	−0.468690	−	0.340523i	0.328241	−	0.944594i	$-0.393544\pi$
$643$	−11.8848	−	8.63480i	−0.468690	−	0.340523i	−0.796930	+	0.604071i	$0.793544\pi$
$644$		0			0
$645$	−9.40510	+	28.9459i	−0.370325	+	1.13974i
$646$	2.34035	−	2.59922i	0.0920799	−	0.102265i
$647$	0.642352	+	6.11157i	0.0252534	+	0.240271i	0.999866	+	0.0163722i	$0.00521168\pi$
$647$	0.642352	+	6.11157i	0.0252534	+	0.240271i	−0.974613	+	0.223898i	$0.928122\pi$
$648$	3.44213	−	5.96195i	0.135220	−	0.234207i
$649$	10.7549	−	1.96955i	0.422165	−	0.0773118i
$650$	−15.9404			−0.625236
$651$		0			0
$652$	1.92589	+	5.92729i	0.0754238	+	0.232131i
$653$	39.7804	−	8.45558i	1.55673	−	0.330893i	0.652448	−	0.757834i	$-0.273742\pi$
$653$	39.7804	−	8.45558i	1.55673	−	0.330893i	0.904279	+	0.426941i	$0.140409\pi$
$654$	−11.2831	+	5.02357i	−0.441205	+	0.196437i
$655$	16.1427	−	7.18718i	0.630746	−	0.280826i
$656$	−3.97126	+	0.844118i	−0.155052	+	0.0329573i
$657$	1.96020	+	6.03286i	0.0764745	+	0.235364i
$658$		0			0
$659$	18.0090			0.701531			0.350765	−	0.936463i	$-0.385921\pi$
$659$	18.0090			0.701531			0.350765	+	0.936463i	$0.385921\pi$
$660$	−3.29456	+	24.6184i	−0.128241	+	0.958272i
$661$	8.57098	−	14.8454i	0.333373	−	0.577418i	−0.649798	−	0.760107i	$-0.725147\pi$
$661$	8.57098	−	14.8454i	0.333373	−	0.577418i	0.983171	+	0.182689i	$0.0584800\pi$
$662$	0.144249	+	1.37244i	0.00560641	+	0.0533415i
$663$	7.61881	−	8.46154i	0.295890	−	0.328619i
$664$	15.2629	−	46.9744i	0.592316	−	1.82296i
$665$		0			0
$666$	−46.9276	−	34.0949i	−1.81841	−	1.32115i
$667$	6.29520	−	1.33809i	0.243751	−	0.0518109i
$668$	−16.0948	−	3.42105i	−0.622725	−	0.132364i
$669$	5.19838	+	49.4592i	0.200981	+	1.91220i
$670$	−4.62807	−	8.01605i	−0.178798	−	0.309687i
$671$	2.82823	+	2.17979i	0.109183	+	0.0841498i
$672$		0			0
$673$	18.7632	−	13.6322i	0.723268	−	0.525485i	−0.164159	−	0.986434i	$-0.552491\pi$
$673$	18.7632	−	13.6322i	0.723268	−	0.525485i	0.887426	+	0.460949i	$0.152491\pi$
$674$	−15.2729	+	16.9622i	−0.588288	+	0.653361i
$675$	−28.8645	−	32.0573i	−1.11100	−	1.23389i
$676$	6.06423	−	2.69997i	0.233239	−	0.103845i
$677$	2.88191	−	27.4195i	0.110761	−	1.05382i	−0.788089	−	0.615561i	$-0.788930\pi$
$677$	2.88191	−	27.4195i	0.110761	−	1.05382i	0.898850	−	0.438256i	$-0.144404\pi$
$678$	−10.4893	+	32.2826i	−0.402838	+	1.23981i
$679$		0			0
$680$	16.6185	−	12.0741i	0.637291	−	0.463019i
$681$	−18.0556	−	31.2731i	−0.691890	−	1.19839i
$682$	1.88789	+	2.22002i	0.0722912	+	0.0850089i
$683$	−10.9675	+	18.9963i	−0.419661	+	0.726874i	−0.995905	−	0.0904032i	$-0.971184\pi$
$683$	−10.9675	+	18.9963i	−0.419661	+	0.726874i	0.576244	+	0.817278i	$0.304518\pi$
$684$	−5.81321	−	2.58821i	−0.222274	−	0.0989626i
$685$	9.71923	+	29.9127i	0.371353	+	1.14291i
$686$		0			0
$687$	10.5775	+	7.68503i	0.403558	+	0.293202i
$688$	0.614864	−	5.85004i	0.0234415	−	0.223031i
$689$	−14.9152	−	16.5651i	−0.568226	−	0.631078i
$690$	−8.69337	−	1.84783i	−0.330951	−	0.0703458i
$691$	−23.4476	−	10.4396i	−0.891990	−	0.397139i	−0.0910234	−	0.995849i	$-0.529014\pi$
$691$	−23.4476	−	10.4396i	−0.891990	−	0.397139i	−0.800966	+	0.598709i	$0.795680\pi$
$692$	6.09830			0.231823
$693$		0			0
$694$	30.3913			1.15364
$695$	−41.0970	−	18.2976i	−1.55890	−	0.694067i
$696$	−68.5339	−	14.5673i	−2.59777	−	0.552173i
$697$	−2.75104	−	3.05534i	−0.104203	−	0.115729i
$698$	−0.930124	+	8.84954i	−0.0352057	+	0.334960i
$699$	55.1770	+	40.0884i	2.08699	+	1.51628i
$700$		0			0
$701$	−5.69007	−	17.5122i	−0.214911	−	0.661428i	−0.999160	−	0.0409817i	$-0.986951\pi$
$701$	−5.69007	−	17.5122i	−0.214911	−	0.661428i	0.784249	−	0.620446i	$-0.213049\pi$
$702$	13.0258	+	5.79948i	0.491629	+	0.218887i
$703$	−8.16492	+	14.1421i	−0.307946	+	0.533378i
$704$	−2.10081	−	27.4423i	−0.0791774	−	1.03427i
$705$	37.3787	+	64.7419i	1.40776	+	2.43832i
$706$	−5.35087	+	3.88764i	−0.201383	+	0.146313i
$707$		0			0
$708$	−2.20744	+	6.79380i	−0.0829607	+	0.255327i
$709$	−2.47336	+	23.5324i	−0.0928889	+	0.883779i	0.844514	+	0.535533i	$0.179889\pi$
$709$	−2.47336	+	23.5324i	−0.0928889	+	0.883779i	−0.937403	+	0.348246i	$0.886777\pi$
$710$	−11.2197	+	4.99532i	−0.421067	+	0.187471i
$711$	−32.8195	−	36.4497i	−1.23083	−	1.36697i
$712$	9.12816	−	10.1379i	0.342092	−	0.379932i
$713$	0.514827	−	0.374044i	0.0192804	−	0.0140081i
$714$		0			0
$715$	−23.5993	−	0.668389i	−0.882565	−	0.0249963i
$716$	−1.37226	−	2.37682i	−0.0512838	−	0.0888261i
$717$	2.64108	+	25.1282i	0.0986331	+	0.938431i
$718$	−30.9813	−	6.58528i	−1.15621	−	0.245760i
$719$	−10.8792	+	2.31244i	−0.405726	+	0.0862396i	−0.406254	−	0.913760i	$-0.633165\pi$
$719$	−10.8792	+	2.31244i	−0.405726	+	0.0862396i	0.000528360		1.00000i	$0.499832\pi$
$720$	27.6187	+	20.0662i	1.02929	+	0.747823i
$721$		0			0
$722$	−5.63627	+	17.3467i	−0.209760	+	0.645576i
$723$	−36.2431	+	40.2520i	−1.34790	+	1.49699i
$724$	1.25323	+	11.9237i	0.0465761	+	0.443142i
$725$	−27.6865	+	47.9544i	−1.02825	+	1.78098i
$726$	5.63025	−	34.5914i	0.208958	−	1.28381i
$727$	42.4803			1.57551			0.787753	−	0.615991i	$-0.211244\pi$
$727$	42.4803			1.57551			0.787753	+	0.615991i	$0.211244\pi$
$728$		0			0
$729$	−12.8826	−	39.6485i	−0.477133	−	1.46846i
$730$	−4.62001	+	0.982014i	−0.170994	+	0.0363460i
$731$	5.44173	−	2.42281i	0.201269	−	0.0896109i
$732$	−2.13123	+	0.948886i	−0.0787726	+	0.0350718i
$733$	−21.7036	+	4.61323i	−0.801639	+	0.170394i	−0.590474	−	0.807057i	$-0.701059\pi$
$733$	−21.7036	+	4.61323i	−0.801639	+	0.170394i	−0.211165	+	0.977450i	$0.567726\pi$
$734$	−10.4699	−	32.2231i	−0.386452	−	1.18938i
$735$		0			0
$736$	−3.24402			−0.119576
$737$	−3.78814	−	7.01255i	−0.139538	−	0.258311i
$738$	6.12854	−	10.6149i	0.225595	−	0.390741i
$739$	−3.07817	−	29.2868i	−0.113232	−	1.07733i	−0.892626	−	0.450798i	$-0.851140\pi$
$739$	−3.07817	−	29.2868i	−0.113232	−	1.07733i	0.779394	−	0.626534i	$-0.215527\pi$
$740$	−17.6367	+	19.5875i	−0.648338	+	0.720053i
$741$	2.95305	−	9.08855i	0.108483	−	0.333876i
$742$		0			0
$743$	−13.6772	−	9.93704i	−0.501766	−	0.364555i	0.307925	−	0.951411i	$-0.400365\pi$
$743$	−13.6772	−	9.93704i	−0.501766	−	0.364555i	−0.809691	+	0.586856i	$0.800365\pi$
$744$	−6.77648	+	1.44038i	−0.248438	+	0.0528071i
$745$	10.6369	+	2.26094i	0.389706	+	0.0828346i
$746$	−1.68013	−	15.9854i	−0.0615141	−	0.585267i
$747$	41.5622	+	71.9879i	1.52068	+	2.63390i
$748$	4.01208	−	2.74484i	0.146696	−	0.100361i
$749$		0			0
$750$	17.3220	−	12.5851i	0.632508	−	0.459544i
$751$	−1.03813	+	1.15296i	−0.0378820	+	0.0420722i	−0.761788	−	0.647826i	$-0.775678\pi$
$751$	−1.03813	+	1.15296i	−0.0378820	+	0.0420722i	0.723906	+	0.689899i	$0.242345\pi$
$752$	−9.66783	−	10.7372i	−0.352550	−	0.391546i
$753$	7.48740	−	3.33361i	0.272856	−	0.121483i
$754$	1.91317	−	18.2026i	0.0696737	−	0.662901i
$755$	3.06188	−	9.42349i	0.111433	−	0.342956i
$756$		0			0
$757$	−10.1505	+	7.37474i	−0.368925	+	0.268040i	−0.756765	−	0.653687i	$-0.773221\pi$
$757$	−10.1505	+	7.37474i	−0.368925	+	0.268040i	0.387840	+	0.921727i	$0.373221\pi$
$758$	12.4860	+	21.6265i	0.453513	+	0.785508i
$759$	−7.43768	−	1.80243i	−0.269971	−	0.0654241i
$760$	8.62019	−	14.9306i	0.312687	−	0.541590i
$761$	−8.25330	−	3.67460i	−0.299182	−	0.133204i	0.251656	−	0.967817i	$-0.419025\pi$
$761$	−8.25330	−	3.67460i	−0.299182	−	0.133204i	−0.550837	+	0.834613i	$0.685692\pi$
$762$	−19.1503	−	58.9386i	−0.693742	−	2.13512i
$763$		0			0
$764$	0.263115	+	0.191164i	0.00951916	+	0.00691608i
$765$	−3.61362	+	34.3813i	−0.130651	+	1.24306i
$766$	25.1149	+	27.8929i	0.907438	+	1.00781i
$767$	−6.64155	−	1.41171i	−0.239813	−	0.0509737i
$768$	39.8235	+	17.7305i	1.43701	+	0.639796i
$769$	−16.1383			−0.581963			−0.290981	−	0.956729i	$-0.593982\pi$
$769$	−16.1383			−0.581963			−0.290981	+	0.956729i	$0.593982\pi$
$770$		0			0
$771$	−64.0829			−2.30789
$772$	10.5076	+	4.67827i	0.378176	+	0.168375i
$773$	18.0111	+	3.82837i	0.647813	+	0.137697i	0.520088	−	0.854113i	$-0.325899\pi$
$773$	18.0111	+	3.82837i	0.647813	+	0.137697i	0.127725	+	0.991810i	$0.459233\pi$
$774$	11.8828	+	13.1972i	0.427118	+	0.474362i
$775$	−0.572310	+	5.44517i	−0.0205580	+	0.195596i
$776$	16.0838	+	11.6855i	0.577374	+	0.419487i
$777$		0			0
$778$	0.836118	+	2.57331i	0.0299763	+	0.0922575i
$779$	−3.15231	−	1.40350i	−0.112943	−	0.0502855i
$780$	7.71228	−	13.3581i	0.276144	−	0.478295i
$781$	−9.77899	+	4.02615i	−0.349920	+	0.144067i
$782$	0.869719	+	1.50640i	0.0311011	+	0.0538687i
$783$	40.0711	−	29.1133i	1.43202	−	1.04043i
$784$		0			0
$785$	−22.9505	+	70.6344i	−0.819139	+	2.52105i
$786$	1.70275	−	16.2005i	0.0607349	−	0.577854i
$787$	42.9248	−	19.1113i	1.53010	−	0.681246i	0.542767	−	0.839884i	$-0.317377\pi$
$787$	42.9248	−	19.1113i	1.53010	−	0.681246i	0.987337	+	0.158638i	$0.0507101\pi$
$788$	10.5534	+	11.7208i	0.375951	+	0.417536i
$789$	−1.89514	+	2.10477i	−0.0674689	+	0.0749318i
$790$	29.5461	−	21.4665i	1.05120	−	0.763744i
$791$		0			0
$792$	41.7671	+	32.1910i	1.48413	+	1.14386i
$793$	−1.10874	−	1.92039i	−0.0393725	−	0.0681952i
$794$	0.686958	+	6.53597i	0.0243792	+	0.231953i
$795$	104.592	+	22.2318i	3.70951	+	0.788480i
$796$	6.26163	−	1.33095i	0.221938	−	0.0471743i
$797$	2.52781	+	1.83656i	0.0895395	+	0.0650543i	0.631654	−	0.775250i	$-0.282376\pi$
$797$	2.52781	+	1.83656i	0.0895395	+	0.0650543i	−0.542115	+	0.840304i	$0.682376\pi$
$798$		0			0
$799$	4.52129	−	13.9151i	0.159952	−	0.492281i
$800$	18.6761	−	20.7420i	0.660301	−	0.733339i
$801$	2.39983	+	22.8329i	0.0847938	+	0.806760i
$802$	−6.26307	+	10.8480i	−0.221157	+	0.383055i
$803$	−4.00057	+	0.732630i	−0.141177	+	0.0258540i
$804$	5.20732			0.183648
$805$		0			0
$806$	−0.559243	−	1.72117i	−0.0196985	−	0.0606258i
$807$	−20.1067	+	4.27382i	−0.707791	+	0.150446i
$808$	43.3682	−	19.3087i	1.52569	−	0.679279i
$809$	−29.8964	+	13.3107i	−1.05110	+	0.467980i	−0.858241	−	0.513246i	$-0.828443\pi$
$809$	−29.8964	+	13.3107i	−1.05110	+	0.467980i	−0.192859	+	0.981226i	$0.561776\pi$
$810$	−8.43833	+	1.79362i	−0.296493	+	0.0630215i
$811$	10.0929	+	31.0627i	0.354410	+	1.09076i	0.956351	+	0.292220i	$0.0943941\pi$
$811$	10.0929	+	31.0627i	0.354410	+	1.09076i	−0.601941	+	0.798540i	$0.705606\pi$
$812$		0			0
$813$	77.6578			2.72358
$814$	25.6581	−	26.9227i	0.899317	−	0.943639i
$815$	14.2087	−	24.6102i	0.497710	−	0.862058i
$816$	−1.10344	−	10.4986i	−0.0386283	−	0.367523i
$817$	3.34526	−	3.71529i	0.117036	−	0.129981i
$818$	10.1024	−	31.0921i	0.353224	−	1.08711i
$819$		0			0
$820$	−4.50589	−	3.27372i	−0.157352	−	0.114323i
$821$	7.26903	−	1.54508i	0.253691	−	0.0539236i	−0.0793107	−	0.996850i	$-0.525272\pi$
$821$	7.26903	−	1.54508i	0.253691	−	0.0539236i	0.333001	+	0.942926i	$0.391939\pi$
$822$	28.3612	+	6.02835i	0.989209	+	0.210263i
$823$	−0.685567	−	6.52273i	−0.0238974	−	0.227368i	−0.999952	−	0.00984082i	$-0.996868\pi$
$823$	−0.685567	−	6.52273i	−0.0238974	−	0.227368i	0.976054	−	0.217527i	$-0.0697991\pi$
$824$	13.6903	+	23.7122i	0.476923	+	0.826055i
$825$	54.3440	−	37.1790i	1.89202	−	1.29441i
$826$		0			0
$827$	−19.2982	+	14.0209i	−0.671063	+	0.487556i	−0.870381	−	0.492379i	$-0.836127\pi$
$827$	−19.2982	+	14.0209i	−0.671063	+	0.487556i	0.199318	+	0.979935i	$0.436127\pi$
$828$	2.11756	−	2.35179i	0.0735902	−	0.0817302i
$829$	−17.4932	−	19.4281i	−0.607563	−	0.674767i	0.358364	−	0.933582i	$-0.383335\pi$
$829$	−17.4932	−	19.4281i	−0.607563	−	0.674767i	−0.965927	+	0.258815i	$0.916668\pi$
$830$	−56.5432	+	25.1747i	−1.96264	+	0.873825i
$831$	6.27108	−	59.6654i	0.217541	−	2.06977i
$832$	−5.28164	+	16.2552i	−0.183108	+	0.563548i
$833$		0			0
$834$	−33.5512	+	24.3764i	−1.16178	+	0.844085i
$835$	37.5133	+	64.9749i	1.29820	+	2.24855i
$836$	2.13918	−	3.47415i	0.0739851	−	0.120156i
$837$	2.44874	−	4.24133i	0.0846407	−	0.146602i
$838$	−20.6533	−	9.19545i	−0.713457	−	0.317651i
$839$	10.5959	+	32.6107i	0.365810	+	1.12585i	0.949472	+	0.313851i	$0.101619\pi$
$839$	10.5959	+	32.6107i	0.365810	+	1.12585i	−0.583662	+	0.811997i	$0.698381\pi$
$840$		0			0
$841$	−27.9754	−	20.3253i	−0.964670	−	0.700874i
$842$	0.356473	−	3.39162i	0.0122849	−	0.116883i
$843$	53.8641	+	59.8221i	1.85518	+	2.06038i
$844$	−7.30967	−	1.55372i	−0.251609	−	0.0534812i
$845$	−27.6510	−	12.3110i	−0.951222	−	0.423511i
$846$	43.6195			1.49967
$847$		0			0
$848$	−20.6661			−0.709678
$849$	68.4039	+	30.4554i	2.34762	+	1.04523i
$850$	−14.6388	−	3.11158i	−0.502108	−	0.106726i
$851$	−5.43415	−	6.03524i	−0.186280	−	0.206885i
$852$	0.722219	−	6.87146i	0.0247428	−	0.235412i
$853$	−17.3002	−	12.5693i	−0.592347	−	0.430365i	0.250807	−	0.968037i	$-0.419304\pi$
$853$	−17.3002	−	12.5693i	−0.592347	−	0.430365i	−0.843154	+	0.537672i	$0.819304\pi$
$854$		0			0
$855$	8.96608	+	27.5948i	0.306634	+	0.943721i
$856$	−9.86197	−	4.39083i	−0.337075	−	0.150076i
$857$	−21.4348	+	37.1262i	−0.732200	+	1.26821i	0.223741	+	0.974649i	$0.428173\pi$
$857$	−21.4348	+	37.1262i	−0.732200	+	1.26821i	−0.955941	+	0.293559i	$0.905160\pi$
$858$	−11.4114	+	18.5328i	−0.389578	+	0.632698i
$859$	15.1958	+	26.3198i	0.518473	+	0.898022i	0.999770	+	0.0214638i	$0.00683266\pi$
$859$	15.1958	+	26.3198i	0.518473	+	0.898022i	−0.481297	+	0.876558i	$0.659834\pi$
$860$	6.52831	−	4.74310i	0.222614	−	0.161738i
$861$		0			0
$862$	2.59737	−	7.99389i	0.0884668	−	0.272273i
$863$	−1.23536	+	11.7537i	−0.0420522	+	0.400100i	0.953168	+	0.302442i	$0.0978018\pi$
$863$	−1.23536	+	11.7537i	−0.0420522	+	0.400100i	−0.995220	+	0.0976580i	$0.968865\pi$
$864$	−22.8077	+	10.1546i	−0.775934	+	0.345468i
$865$	−18.6061	−	20.6641i	−0.632625	−	0.702602i
$866$	−23.9837	+	26.6366i	−0.814998	+	0.905147i
$867$	−30.6698	+	22.2829i	−1.04160	+	0.756766i
$868$		0			0
$869$	25.9548	−	17.7568i	0.880456	−	0.602357i
$870$	43.9001	+	76.0373i	1.48835	+	2.57790i
$871$	0.517377	+	4.92252i	0.0175307	+	0.166793i
$872$	11.6548	+	2.47731i	0.394682	+	0.0838922i
$873$	−32.7271	+	6.95637i	−1.10765	+	0.235437i
$874$	1.18108	+	0.858104i	0.0399506	+	0.0290258i
$875$		0			0
$876$	0.821118	−	2.52714i	0.0277430	−	0.0853842i
$877$	−6.15927	+	6.84056i	−0.207984	+	0.230989i	−0.838107	−	0.545506i	$-0.816338\pi$
$877$	−6.15927	+	6.84056i	−0.207984	+	0.230989i	0.630123	+	0.776495i	$0.283004\pi$
$878$	0.543704	+	5.17300i	0.0183491	+	0.174580i
$879$	−6.38067	+	11.0516i	−0.215215	+	0.372763i
$880$	−15.1008	+	15.8451i	−0.509049	+	0.534137i
$881$	−41.9030			−1.41175			−0.705874	−	0.708338i	$-0.749445\pi$
$881$	−41.9030			−1.41175			−0.705874	+	0.708338i	$0.749445\pi$
$882$		0			0
$883$	−4.95906	−	15.2624i	−0.166886	−	0.513621i	0.832285	−	0.554348i	$-0.187032\pi$
$883$	−4.95906	−	15.2624i	−0.166886	−	0.513621i	−0.999170	+	0.0407275i	$0.987032\pi$
$884$	−2.95286	+	0.627649i	−0.0993154	+	0.0211101i
$885$	29.7558	−	13.2481i	1.00023	−	0.445331i
$886$	17.5901	−	7.83164i	0.590952	−	0.263109i
$887$	33.1087	−	7.03747i	1.11168	−	0.236295i	0.384760	−	0.923017i	$-0.374284\pi$
$887$	33.1087	−	7.03747i	1.11168	−	0.236295i	0.726921	+	0.686722i	$0.240951\pi$
$888$	27.3211	+	84.0858i	0.916838	+	2.82174i
$889$		0			0
$890$	−17.0949			−0.573024
$891$	−7.30693	+	1.33813i	−0.244791	+	0.0448291i
$892$	6.59273	−	11.4189i	0.220741	−	0.382335i
$893$	−1.28359	−	12.2126i	−0.0429538	−	0.408678i
$894$	6.70798	−	7.44997i	0.224349	−	0.249164i
$895$	−3.86708	+	11.9017i	−0.129262	+	0.397829i
$896$		0			0
$897$	3.84490	+	2.79348i	0.128377	+	0.0932716i
$898$	18.2486	−	3.87886i	0.608963	−	0.129439i
$899$	−6.14923	−	1.30706i	−0.205088	−	0.0435928i
$900$	2.84611	+	27.0789i	0.0948704	+	0.902631i
$901$	−10.4638	−	18.1239i	−0.348601	−	0.603795i
$902$	6.22455	+	4.79741i	0.207255	+	0.159736i
$903$		0			0
$904$	26.4925	−	19.2479i	0.881127	−	0.640176i
$905$	36.5800	−	40.6262i	1.21596	−	1.35046i
$906$	−6.11204	−	6.78811i	−0.203059	−	0.225520i
$907$	−40.2886	+	17.9376i	−1.33776	+	0.595609i	−0.945913	−	0.324421i	$-0.894831\pi$
$907$	−40.2886	+	17.9376i	−1.33776	+	0.595609i	−0.391848	+	0.920030i	$0.628164\pi$
$908$	−1.00078	+	9.52176i	−0.0332120	+	0.315991i
$909$	−24.6886	+	75.9837i	−0.818869	+	2.52022i
$910$		0			0
$911$	−40.1075	+	29.1398i	−1.32882	+	0.965446i	−0.329045	+	0.944314i	$0.606727\pi$
$911$	−40.1075	+	29.1398i	−1.32882	+	0.965446i	−0.999777	+	0.0211316i	$0.993273\pi$
$912$	−4.42994	−	7.67288i	−0.146690	−	0.254075i
$913$	−49.2827	+	20.2904i	−1.63102	+	0.671514i
$914$	12.0905	−	20.9414i	0.399919	−	0.692680i
$915$	9.71775	+	4.32662i	0.321259	+	0.143034i
$916$	−1.07120	−	3.29682i	−0.0353935	−	0.108930i
$917$		0			0
$918$	10.8302	+	7.86857i	0.357448	+	0.259701i
$919$	4.26399	−	40.5692i	0.140656	−	1.33825i	−0.665432	−	0.746458i	$-0.731753\pi$
$919$	4.26399	−	40.5692i	0.140656	−	1.33825i	0.806088	−	0.591795i	$-0.201581\pi$
$920$	5.73715	+	6.37176i	0.189148	+	0.210071i
$921$	36.0284	+	7.65807i	1.18718	+	0.252342i
$922$	−6.18788	−	2.75502i	−0.203787	−	0.0907319i
$923$	6.56740			0.216169
$924$		0			0
$925$	69.8737			2.29743
$926$	−5.24044	−	2.33319i	−0.172211	−	0.0766735i
$927$	−45.0733	−	9.58063i	−1.48040	−	0.314669i
$928$	21.4440	+	23.8160i	0.703935	+	0.781799i
$929$	−4.32674	+	41.1662i	−0.141956	+	1.35062i	0.659112	+	0.752044i	$0.270932\pi$
$929$	−4.32674	+	41.1662i	−0.141956	+	1.35062i	−0.801068	+	0.598573i	$0.795735\pi$
$930$	7.02348	+	5.10286i	0.230309	+	0.167329i
$931$		0			0
$932$	−5.58785	−	17.1976i	−0.183036	−	0.563327i
$933$	−70.0443	−	31.1857i	−2.29315	−	1.02098i
$934$	2.18395	−	3.78271i	0.0714610	−	0.123774i
$935$	−21.5419	−	5.22041i	−0.704494	−	0.170726i
$936$	−16.3738	−	28.3602i	−0.535194	−	0.926982i
$937$	−1.29155	+	0.938364i	−0.0421930	+	0.0306550i	−0.608682	−	0.793414i	$-0.708301\pi$
$937$	−1.29155	+	0.938364i	−0.0421930	+	0.0306550i	0.566489	+	0.824069i	$0.308301\pi$
$938$		0			0
$939$	−3.17033	+	9.75727i	−0.103460	+	0.318416i
$940$	2.07182	−	19.7120i	0.0675752	−	0.642935i
$941$	6.49336	−	2.89103i	0.211678	−	0.0942449i	−0.298159	−	0.954516i	$-0.596373\pi$
$941$	6.49336	−	2.89103i	0.211678	−	0.0942449i	0.509836	+	0.860271i	$0.329706\pi$
$942$	45.8132	+	50.8807i	1.49268	+	1.65778i
$943$	1.14828	−	1.27529i	0.0373932	−	0.0415293i
$944$	−5.09287	+	3.70019i	−0.165759	+	0.120431i
$945$		0			0
$946$	−9.39731	+	6.42910i	−0.305533	+	0.209028i
$947$	1.22993	+	2.13030i	0.0399674	+	0.0692255i	0.885317	−	0.464988i	$-0.153941\pi$
$947$	1.22993	+	2.13030i	0.0399674	+	0.0692255i	−0.845350	+	0.534213i	$0.820608\pi$
$948$	2.14764	+	20.4334i	0.0697521	+	0.663647i
$949$	2.47051	+	0.525123i	0.0801961	+	0.0170462i
$950$	−12.2862	+	2.61152i	−0.398618	+	0.0847288i
$951$	−39.1286	−	28.4286i	−1.26883	−	0.921861i
$952$		0			0
$953$	−8.83790	+	27.2003i	−0.286288	+	0.881103i	0.699722	+	0.714415i	$0.253307\pi$
$953$	−8.83790	+	27.2003i	−0.286288	+	0.881103i	−0.986010	+	0.166688i	$0.946693\pi$
$954$	41.7477	−	46.3655i	1.35163	−	1.50114i
$955$	−0.155009	−	1.47481i	−0.00501598	−	0.0477238i
$956$	3.34950	−	5.80150i	0.108331	−	0.187634i
$957$	35.9329	+	66.5185i	1.16155	+	2.15024i
$958$	−16.8428			−0.544168
$959$		0			0
$960$	−25.3364	−	77.9774i	−0.817728	−	2.51671i
$961$	29.7146	−	6.31602i	0.958534	−	0.203743i
$962$	−21.0992	+	9.39396i	−0.680265	+	0.302873i
$963$	16.5973	−	7.38959i	0.534840	−	0.238126i
$964$	14.0469	−	2.98576i	0.452421	−	0.0961650i
$965$	−16.2065	−	49.8785i	−0.521706	−	1.60565i
$966$		0			0
$967$	−0.213338			−0.00686047			−0.00343024	−	0.999994i	$-0.501092\pi$
$967$	−0.213338			−0.00686047			−0.00343024	+	0.999994i	$0.501092\pi$
$968$	−24.0093	+	23.8052i	−0.771689	+	0.765127i
$969$	4.48601	−	7.76999i	0.144111	−	0.249608i
$970$	−2.60411	−	24.7765i	−0.0836130	−	0.795525i
$971$	−0.554173	+	0.615471i	−0.0177843	+	0.0197514i	−0.751971	−	0.659196i	$-0.770897\pi$
$971$	−0.554173	+	0.615471i	−0.0177843	+	0.0197514i	0.734187	+	0.678947i	$0.237564\pi$
$972$	−2.86507	+	8.81779i	−0.0918973	+	0.282831i
$973$		0			0
$974$	−22.6098	−	16.4270i	−0.724465	−	0.526354i
$975$	−39.9967	+	8.50156i	−1.28092	+	0.272268i
$976$	−2.01096	−	0.427443i	−0.0643693	−	0.0136821i
$977$	−1.01990	−	9.70369i	−0.0326295	−	0.310449i	−0.998648	−	0.0519768i	$-0.983448\pi$
$977$	−1.01990	−	9.70369i	−0.0326295	−	0.310449i	0.966019	−	0.258472i	$-0.0832189\pi$
$978$	−13.0986	−	22.6874i	−0.418847	−	0.725464i
$979$	−14.7143	−	0.416743i	−0.470271	−	0.0133192i
$980$		0			0
$981$	−16.2230	+	11.7867i	−0.517961	+	0.376321i
$982$	27.7564	−	30.8266i	0.885743	−	0.983717i
$983$	30.1910	+	33.5305i	0.962944	+	1.06946i	0.997543	+	0.0700562i	$0.0223178\pi$
$983$	30.1910	+	33.5305i	0.962944	+	1.06946i	−0.0345993	+	0.999401i	$0.511015\pi$
$984$	−17.0672	+	7.59882i	−0.544083	+	0.242241i
$985$	7.51714	−	71.5208i	0.239516	−	2.27884i
$986$	5.31011	−	16.3428i	0.169108	−	0.520462i
$987$		0			0
$988$	−2.04978	+	1.48926i	−0.0652123	+	0.0473795i
$989$	1.24316	+	2.15322i	0.0395302	+	0.0684684i
$990$	−5.04400	−	65.8881i	−0.160309	−	2.09406i
$991$	−26.7702	+	46.3674i	−0.850384	+	1.47291i	0.0304776	+	0.999535i	$0.490297\pi$
$991$	−26.7702	+	46.3674i	−0.850384	+	1.47291i	−0.880862	+	0.473373i	$0.843036\pi$
$992$	2.89484	+	1.28887i	0.0919113	+	0.0409215i
$993$	1.09391	+	3.36671i	0.0347142	+	0.106839i
$994$		0			0
$995$	−23.6143	−	17.1568i	−0.748624	−	0.543907i
$996$	3.63973	−	34.6297i	0.115329	−	1.09729i
$997$	−20.8506	−	23.1569i	−0.660344	−	0.733387i	0.316203	−	0.948692i	$-0.397592\pi$
$997$	−20.8506	−	23.1569i	−0.660344	−	0.733387i	−0.976547	+	0.215305i	$0.930925\pi$
$998$	34.6801	+	7.37149i	1.09778	+	0.233341i
$999$	−57.0977	−	25.4216i	−1.80649	−	0.804302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.g.410.3		32
7.2	even	3	inner	539.2.q.g.520.2		32
7.3	odd	6		539.2.f.e.344.2		16
7.4	even	3		77.2.f.b.36.2	yes	16
7.5	odd	6		539.2.q.f.520.2		32
7.6	odd	2		539.2.q.f.410.3		32
11.4	even	5	inner	539.2.q.g.312.2		32
21.11	odd	6		693.2.m.i.190.3		16
77.4	even	15		77.2.f.b.15.2	✓	16
77.18	odd	30		847.2.f.x.323.3		16
77.24	even	30		5929.2.a.bs.1.3		8
77.25	even	15		847.2.f.w.148.3		16
77.26	odd	30		539.2.q.f.422.3		32
77.31	odd	30		5929.2.a.bt.1.6		8
77.32	odd	6		847.2.f.x.729.3		16
77.37	even	15	inner	539.2.q.g.422.3		32
77.39	odd	30		847.2.f.v.372.2		16
77.46	odd	30		847.2.a.o.1.3		8
77.48	odd	10		539.2.q.f.312.2		32
77.53	even	15		847.2.a.p.1.6		8
77.59	odd	30		539.2.f.e.246.2		16
77.60	even	15		847.2.f.w.372.3		16
77.74	odd	30		847.2.f.v.148.2		16
231.53	odd	30		7623.2.a.ct.1.3		8
231.158	odd	30		693.2.m.i.631.3		16
231.200	even	30		7623.2.a.cw.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.2	✓	16	77.4	even	15
77.2.f.b.36.2	yes	16	7.4	even	3
539.2.f.e.246.2		16	77.59	odd	30
539.2.f.e.344.2		16	7.3	odd	6
539.2.q.f.312.2		32	77.48	odd	10
539.2.q.f.410.3		32	7.6	odd	2
539.2.q.f.422.3		32	77.26	odd	30
539.2.q.f.520.2		32	7.5	odd	6
539.2.q.g.312.2		32	11.4	even	5	inner
539.2.q.g.410.3		32	1.1	even	1	trivial
539.2.q.g.422.3		32	77.37	even	15	inner
539.2.q.g.520.2		32	7.2	even	3	inner
693.2.m.i.190.3		16	21.11	odd	6
693.2.m.i.631.3		16	231.158	odd	30
847.2.a.o.1.3		8	77.46	odd	30
847.2.a.p.1.6		8	77.53	even	15
847.2.f.v.148.2		16	77.74	odd	30
847.2.f.v.372.2		16	77.39	odd	30
847.2.f.w.148.3		16	77.25	even	15
847.2.f.w.372.3		16	77.60	even	15
847.2.f.x.323.3		16	77.18	odd	30
847.2.f.x.729.3		16	77.32	odd	6
5929.2.a.bs.1.3		8	77.24	even	30
5929.2.a.bt.1.6		8	77.31	odd	30
7623.2.a.ct.1.3		8	231.53	odd	30
7623.2.a.cw.1.6		8	231.200	even	30

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.01812 + 0.453294i) q^{2} +(2.79635 + 0.594382i) q^{3} +(-0.507177 - 0.563277i) q^{4} +(-0.361259 + 3.43715i) q^{5} +(2.57757 + 1.87272i) q^{6} +(-0.949813 - 2.92322i) q^{8} +(4.72563 + 2.10398i) q^{9} +O(q^{10})\)	\(q+(1.01812 + 0.453294i) q^{2} +(2.79635 + 0.594382i) q^{3} +(-0.507177 - 0.563277i) q^{4} +(-0.361259 + 3.43715i) q^{5} +(2.57757 + 1.87272i) q^{6} +(-0.949813 - 2.92322i) q^{8} +(4.72563 + 2.10398i) q^{9} +(-1.92584 + 3.33566i) q^{10} +(-1.73896 + 2.82418i) q^{11} +(-1.08344 - 1.87657i) q^{12} +(1.66629 - 1.21063i) q^{13} +(-3.05318 + 9.39672i) q^{15} +(0.199604 - 1.89910i) q^{16} +(1.76655 - 0.786518i) q^{17} +(3.85751 + 4.28420i) q^{18} +(1.08597 - 1.20609i) q^{19} +(2.11929 - 1.53975i) q^{20} +(-3.05065 + 2.08708i) q^{22} +(0.403568 + 0.699000i) q^{23} +(-0.918495 - 8.73890i) q^{24} +(-6.79272 - 1.44384i) q^{25} +(2.24525 - 0.477243i) q^{26} +(5.02542 + 3.65118i) q^{27} +(2.46400 - 7.58342i) q^{29} +(-7.36797 + 8.18296i) q^{30} +(-0.0824123 - 0.784101i) q^{31} +(-2.00959 + 3.48071i) q^{32} +(-6.54139 + 6.86378i) q^{33} +2.15508 q^{34} +(-1.21160 - 3.72893i) q^{36} +(-9.84189 + 2.09196i) q^{37} +(1.65236 - 0.735679i) q^{38} +(5.37911 - 2.39494i) q^{39} +(10.3907 - 2.20861i) q^{40} +(-0.657011 - 2.02207i) q^{41} +3.08043 q^{43} +(2.47276 - 0.452841i) q^{44} +(-8.93887 + 15.4826i) q^{45} +(0.0940260 + 0.894598i) q^{46} +(5.06286 - 5.62287i) q^{47} +(1.68695 - 5.19190i) q^{48} +(-6.26129 - 4.54910i) q^{50} +(5.40737 - 1.14937i) q^{51} +(-1.52703 - 0.324580i) q^{52} +(-1.13125 - 10.7632i) q^{53} +(3.46140 + 5.99532i) q^{54} +(-9.07891 - 6.99733i) q^{55} +(3.75363 - 2.72717i) q^{57} +(5.94616 - 6.60388i) q^{58} +(-2.20588 - 2.44988i) q^{59} +(6.84146 - 3.04602i) q^{60} +(0.112538 - 1.07073i) q^{61} +(0.271523 - 0.835662i) q^{62} +(-6.71351 + 4.87765i) q^{64} +(3.55916 + 6.16465i) q^{65} +(-9.77121 + 4.02295i) q^{66} +(-1.20157 + 2.08118i) q^{67} +(-1.33898 - 0.596153i) q^{68} +(0.713042 + 2.19452i) q^{69} +(2.57963 + 1.87421i) q^{71} +(1.66196 - 15.8124i) q^{72} +(0.820539 + 0.911300i) q^{73} +(-10.9685 - 2.33142i) q^{74} +(-18.1366 - 8.07494i) q^{75} -1.23015 q^{76} +6.56217 q^{78} +(-8.66208 - 3.85660i) q^{79} +(6.45538 + 1.37213i) q^{80} +(1.49869 + 1.66447i) q^{81} +(0.247681 - 2.35652i) q^{82} +(13.0004 + 9.44536i) q^{83} +(2.06520 + 6.35602i) q^{85} +(3.13623 + 1.39634i) q^{86} +(11.3976 - 19.7413i) q^{87} +(9.90740 + 2.40094i) q^{88} +(2.21915 + 3.84368i) q^{89} +(-16.1190 + 11.7111i) q^{90} +(0.189050 - 0.581837i) q^{92} +(0.235602 - 2.24160i) q^{93} +(7.70339 - 3.42977i) q^{94} +(3.75320 + 4.16836i) q^{95} +(-7.68837 + 8.53880i) q^{96} +(-5.23278 + 3.80184i) q^{97} +(-14.1597 + 9.68727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9	\( 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9} - 12 q^{10} + 3 q^{11} - 18 q^{12} - 14 q^{13} - 36 q^{15} - 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + 2 q^{20} - 66 q^{22} - 32 q^{23} + 35 q^{24} - 7 q^{25} + 27 q^{26} + 20 q^{27} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 32 q^{32} + 26 q^{33} - 48 q^{34} + 104 q^{36} - 4 q^{37} + 5 q^{38} - 11 q^{39} + 10 q^{40} - 20 q^{41} - 16 q^{43} + 38 q^{44} - 70 q^{45} + 42 q^{46} + 23 q^{47} - 72 q^{48} + 104 q^{50} + 29 q^{51} - 33 q^{52} - 4 q^{53} - 60 q^{54} - 24 q^{55} - 22 q^{57} - 20 q^{58} - 17 q^{59} + 30 q^{60} + 7 q^{61} + 158 q^{62} + 14 q^{64} + 8 q^{65} - 8 q^{66} + 38 q^{67} + 2 q^{68} + 20 q^{69} - 28 q^{71} + 35 q^{73} + 29 q^{74} - 9 q^{75} + 104 q^{76} - 116 q^{78} - 15 q^{79} + 87 q^{80} + 14 q^{81} - 19 q^{82} + 10 q^{83} + 12 q^{85} + 52 q^{86} + 72 q^{87} - 55 q^{88} - 74 q^{89} - 28 q^{90} - 110 q^{92} - 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 40 q^{97} + 32 q^{99}+O(q^{100}) \) 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9 - 12 * q^10 + 3 * q^11 - 18 * q^12 - 14 * q^13 - 36 * q^15 - 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + 2 * q^20 - 66 * q^22 - 32 * q^23 + 35 * q^24 - 7 * q^25 + 27 * q^26 + 20 * q^27 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 32 * q^32 + 26 * q^33 - 48 * q^34 + 104 * q^36 - 4 * q^37 + 5 * q^38 - 11 * q^39 + 10 * q^40 - 20 * q^41 - 16 * q^43 + 38 * q^44 - 70 * q^45 + 42 * q^46 + 23 * q^47 - 72 * q^48 + 104 * q^50 + 29 * q^51 - 33 * q^52 - 4 * q^53 - 60 * q^54 - 24 * q^55 - 22 * q^57 - 20 * q^58 - 17 * q^59 + 30 * q^60 + 7 * q^61 + 158 * q^62 + 14 * q^64 + 8 * q^65 - 8 * q^66 + 38 * q^67 + 2 * q^68 + 20 * q^69 - 28 * q^71 + 35 * q^73 + 29 * q^74 - 9 * q^75 + 104 * q^76 - 116 * q^78 - 15 * q^79 + 87 * q^80 + 14 * q^81 - 19 * q^82 + 10 * q^83 + 12 * q^85 + 52 * q^86 + 72 * q^87 - 55 * q^88 - 74 * q^89 - 28 * q^90 - 110 * q^92 - 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 40 * q^97 + 32 * q^99

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