LMFDB - Embedded newform 539.2.q.g.422.3

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			422.3
Character	$\chi$	$=$	539.422
Dual form			539.2.q.g.410.3

$q$-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 $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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	−0.0138735	−	0.999904i	$-0.504416\pi$
$2$	1.01812	−	0.453294i	0.719917	−	0.320528i	0.733790	+	0.679376i	$0.237750\pi$
$3$	2.79635	−	0.594382i	1.61447	−	0.343166i	0.689820	−	0.723981i	$-0.257690\pi$
$3$	2.79635	−	0.594382i	1.61447	−	0.343166i	0.924651	+	0.380815i	$0.124356\pi$
$4$	−0.507177	+	0.563277i	−0.253589	+	0.281639i
$5$	−0.361259	−	3.43715i	−0.161560	−	1.53714i	−0.711950	−	0.702230i	$-0.752188\pi$
$5$	−0.361259	−	3.43715i	−0.161560	−	1.53714i	0.550390	−	0.834908i	$-0.314479\pi$
$6$	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	0.794373	−	0.607430i	$-0.207800\pi$
$13$	1.66629	+	1.21063i	0.462147	+	0.335769i	−0.332226	+	0.943200i	$0.607800\pi$
$14$		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	0.609621	−	0.792693i	$-0.291322\pi$
$17$	1.76655	+	0.786518i	0.428451	+	0.190759i	−0.181170	+	0.983452i	$0.557988\pi$
$18$	3.85751	−	4.28420i	0.909224	−	1.00980i
$19$	1.08597	+	1.20609i	0.249139	+	0.276697i	0.854723	−	0.519085i	$-0.173727\pi$
$19$	1.08597	+	1.20609i	0.249139	+	0.276697i	−0.605584	+	0.795782i	$0.707060\pi$
$20$	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	−0.820879	−	0.571102i	$-0.806516\pi$
$23$	0.403568	−	0.699000i	0.0841497	−	0.145752i	0.905029	+	0.425351i	$0.139849\pi$
$24$	−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	0.868111	+	0.496371i	$0.165334\pi$
$29$	2.46400	+	7.58342i	0.457554	+	1.40821i	−0.410557	+	0.911835i	$0.634666\pi$
$30$	−7.36797	−	8.18296i	−1.34520	−	1.49400i
$31$	−0.0824123	+	0.784101i	−0.0148017	+	0.140829i	−0.999427	−	0.0338518i	$-0.989223\pi$
$31$	−0.0824123	+	0.784101i	−0.0148017	+	0.140829i	0.984625	+	0.174680i	$0.0558892\pi$
$32$	−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	−0.692133	−	0.721770i	$-0.743329\pi$
$37$	−9.84189	−	2.09196i	−1.61800	−	0.343916i	−0.925865	+	0.377854i	$0.876662\pi$
$38$	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	−0.989162	−	0.146831i	$-0.953093\pi$
$41$	−0.657011	+	2.02207i	−0.102608	+	0.315795i	0.886554	+	0.462626i	$0.153093\pi$
$42$		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	0.988997	−	0.147936i	$-0.0472629\pi$
$47$	5.06286	+	5.62287i	0.738493	+	0.820180i	−0.250504	+	0.968116i	$0.580596\pi$
$48$	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	0.587611	+	0.809143i	$0.300068\pi$
$53$	−1.13125	+	10.7632i	−0.155390	+	1.47843i	−0.743001	+	0.669290i	$0.766598\pi$
$54$	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	−0.869423	−	0.494069i	$-0.835509\pi$
$59$	−2.20588	+	2.44988i	−0.287181	+	0.318947i	0.582242	+	0.813016i	$0.302176\pi$
$60$	6.84146	+	3.04602i	0.883229	+	0.393239i
$61$	0.112538	+	1.07073i	0.0144090	+	0.137093i	0.999361	−	0.0357334i	$-0.0113767\pi$
$61$	0.112538	+	1.07073i	0.0144090	+	0.137093i	−0.984952	+	0.172826i	$0.944710\pi$
$62$	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	0.783246	−	0.621712i	$-0.213562\pi$
$67$	−1.20157	−	2.08118i	−0.146795	−	0.254257i	−0.930041	+	0.367455i	$0.880229\pi$
$68$	−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	−0.424095	−	0.905618i	$-0.639408\pi$
$71$	2.57963	−	1.87421i	0.306145	−	0.222428i	0.730241	+	0.683190i	$0.239408\pi$
$72$	1.66196	+	15.8124i	0.195863	+	1.86352i
$73$	0.820539	−	0.911300i	0.0960368	−	0.106660i	−0.693210	−	0.720735i	$-0.743804\pi$
$73$	0.820539	−	0.911300i	0.0960368	−	0.106660i	0.789247	+	0.614076i	$0.210471\pi$
$74$	−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	−0.831325	−	0.555787i	$-0.812417\pi$
$79$	−8.66208	+	3.85660i	−0.974560	+	0.433902i	−0.143235	+	0.989689i	$0.545750\pi$
$80$	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	0.436412	−	0.899747i	$-0.356249\pi$
$83$	13.0004	−	9.44536i	1.42698	−	1.03676i	0.990569	−	0.137016i	$-0.0437511\pi$
$84$		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	−0.724110	−	0.689685i	$-0.757749\pi$
$89$	2.21915	−	3.84368i	0.235230	−	0.407430i	0.959339	+	0.282255i	$0.0910825\pi$
$90$	−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	0.289539	−	0.957166i	$-0.406498\pi$
$97$	−5.23278	−	3.80184i	−0.531308	−	0.386018i	−0.820847	+	0.571148i	$0.806498\pi$
$98$		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	−0.556128	−	0.831097i	$-0.687714\pi$
$101$	1.61443	−	15.3603i	0.160642	−	1.52841i	0.716770	−	0.697310i	$-0.245620\pi$
$102$	6.02634	−	1.28094i	0.596696	−	0.126832i
$103$	−8.71346	−	1.85210i	−0.858563	−	0.182493i	−0.242462	−	0.970161i	$-0.577955\pi$
$103$	−8.71346	−	1.85210i	−0.858563	−	0.182493i	−0.616100	+	0.787668i	$0.711288\pi$
$104$	−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	0.845954	−	0.533255i	$-0.179031\pi$
$107$	2.35011	+	2.61007i	0.227194	+	0.252325i	−0.618760	+	0.785580i	$0.712365\pi$
$108$	−0.492150	+	4.68250i	−0.0473572	+	0.450574i
$109$	−1.93827	−	3.35719i	−0.185653	−	0.321560i	0.758143	−	0.652088i	$-0.226107\pi$
$109$	−1.93827	−	3.35719i	−0.185653	−	0.321560i	−0.943796	+	0.330527i	$0.892773\pi$
$110$	−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	−0.668170	−	0.744008i	$-0.732922\pi$
$113$	3.29224	−	10.1325i	0.309708	−	0.953183i	0.977878	−	0.209175i	$-0.0670777\pi$
$114$	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	−0.401220	+	0.915982i	$0.631414\pi$
$127$	−15.7361	+	11.4330i	−1.39635	+	1.01451i	−0.995134	+	0.0985289i	$0.968586\pi$
$128$	−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	−0.955825	−	0.293937i	$-0.905034\pi$
$131$	−2.55642	+	4.42785i	−0.223355	+	0.386863i	0.732469	+	0.680800i	$0.238368\pi$
$132$	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	0.729888	−	0.683566i	$-0.239572\pi$
$137$	8.31374	+	3.70151i	0.710290	+	0.316242i	−0.0195980	+	0.999808i	$0.506239\pi$
$138$	−0.268803	−	2.55749i	−0.0228821	−	0.217708i
$139$	−4.02234	−	12.3795i	−0.341171	−	1.05002i	−0.963602	−	0.267341i	$-0.913855\pi$
$139$	−4.02234	−	12.3795i	−0.341171	−	1.05002i	0.622431	−	0.782675i	$-0.286145\pi$
$140$		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	0.999699	+	0.0245229i	$0.00780666\pi$
$149$	0.328899	+	3.12926i	0.0269444	+	0.256359i	−0.972755	+	0.231836i	$0.925527\pi$
$150$	−14.8048	+	16.4424i	−1.20881	+	1.34252i
$151$	−2.80431	+	0.596075i	−0.228212	+	0.0485079i	−0.320598	−	0.947215i	$-0.603884\pi$
$151$	−2.80431	+	0.596075i	−0.228212	+	0.0485079i	0.0923863	+	0.995723i	$0.470551\pi$
$152$	−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	0.731827	−	0.681491i	$-0.238668\pi$
$157$	21.0199	−	4.46792i	1.67757	−	0.356579i	0.945744	+	0.324912i	$0.105335\pi$
$158$	−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	−0.679248	−	0.733909i	$-0.737694\pi$
$163$	−7.51158	+	3.34437i	−0.588353	+	0.261951i	0.0908952	+	0.995860i	$0.471027\pi$
$164$	−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	0.998506	+	0.0546489i	$0.0174040\pi$
$167$	17.5626	+	12.7600i	1.35904	+	0.987397i	0.360529	+	0.932748i	$0.382596\pi$
$168$		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	0.502880	−	0.864356i	$-0.332274\pi$
$173$	−5.38358	−	5.97907i	−0.409306	−	0.454580i	−0.912186	+	0.409776i	$0.865607\pi$
$174$	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	−0.0736366	−	0.997285i	$-0.523460\pi$
$179$	3.54178	−	0.752829i	0.264725	−	0.0562691i	0.338362	+	0.941016i	$0.390127\pi$
$180$	13.2546	+	2.81735i	0.987938	+	0.209993i
$181$	−12.7970	+	9.29753i	−0.951190	+	0.691080i	−0.951088	−	0.308920i	$-0.900033\pi$
$181$	−12.7970	+	9.29753i	−0.951190	+	0.691080i	−0.000102207		1.00000i	$0.500033\pi$
$182$		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	0.192702	−	0.981257i	$-0.438275\pi$
$191$	−0.419704	−	0.0892109i	−0.0303687	−	0.00645508i	−0.223071	+	0.974802i	$0.571608\pi$
$192$	−21.6725	−	9.64922i	−1.56408	−	0.696372i
$193$	−13.8629	−	6.17216i	−0.997873	−	0.444282i	−0.158219	−	0.987404i	$-0.550575\pi$
$193$	−13.8629	−	6.17216i	−0.997873	−	0.444282i	−0.839654	+	0.543122i	$0.817242\pi$
$194$	−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	0.676638	−	0.736316i	$-0.263436\pi$
$199$	−4.22284	−	7.31417i	−0.299349	−	0.518488i	−0.975987	+	0.217828i	$0.930103\pi$
$200$	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	0.827458	−	0.561528i	$-0.189786\pi$
$211$	7.97632	+	5.79513i	0.549112	+	0.398953i	−0.278346	+	0.960481i	$0.589786\pi$
$212$	−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	−0.593088	−	0.805138i	$-0.702091\pi$
$223$	5.37562	−	16.5445i	0.359978	−	1.10790i	0.953066	−	0.302762i	$-0.0979087\pi$
$224$		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	−0.955193	−	0.295983i	$-0.904353\pi$
$227$	−8.45211	+	9.38702i	−0.560986	+	0.623038i	0.394207	+	0.919022i	$0.371019\pi$
$228$	−3.43991	+	0.731176i	−0.227814	+	0.0484233i
$229$	4.17802	−	1.86018i	0.276091	−	0.122924i	−0.264020	−	0.964517i	$-0.585049\pi$
$229$	4.17802	−	1.86018i	0.276091	−	0.122924i	0.540112	+	0.841593i	$0.318382\pi$
$230$	−3.10883			−0.204990
$231$		0			0
$232$	−24.5084			−1.60905
$233$	21.7944	−	9.70347i	1.42780	−	0.635696i	0.460111	−	0.887861i	$-0.347809\pi$
$233$	21.7944	−	9.70347i	1.42780	−	0.635696i	0.967684	+	0.252166i	$0.0811428\pi$
$234$	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	−0.823043	−	0.567979i	$-0.807725\pi$
$239$	2.73114	−	8.40558i	0.176663	−	0.543711i	0.999705	+	0.0242677i	$0.00772541\pi$
$240$	17.2359	−	7.67392i	1.11257	−	0.495349i
$241$	−9.47322	−	16.4081i	−0.610224	−	1.05694i	−0.991202	−	0.132355i	$-0.957746\pi$
$241$	−9.47322	−	16.4081i	−0.610224	−	1.05694i	0.380978	−	0.924584i	$-0.375587\pi$
$242$	−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	0.658573	−	0.752516i	$-0.271160\pi$
$251$	2.31938	+	1.68513i	0.146398	+	0.106364i	−0.512175	+	0.858881i	$0.671160\pi$
$252$		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	−0.535199	−	0.844726i	$-0.679763\pi$
$257$	−21.9260	−	4.66052i	−1.36771	−	0.290715i	−0.832510	+	0.554011i	$0.813097\pi$
$258$	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	0.850349	−	0.526219i	$-0.176391\pi$
$263$	−0.495353	−	0.857976i	−0.0305448	−	0.0529051i	−0.880894	+	0.473314i	$0.843058\pi$
$264$	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	0.196593	−	0.980485i	$-0.437012\pi$
$269$	−6.56873	−	2.92458i	−0.400502	−	0.178315i	−0.597096	+	0.802170i	$0.703679\pi$
$270$	−21.8572	−	9.73147i	−1.33019	−	0.592238i
$271$	26.5707	+	5.64777i	1.61405	+	0.343078i	0.924508	−	0.381164i	$-0.124477\pi$
$271$	26.5707	+	5.64777i	1.61405	+	0.343078i	0.689546	+	0.724241i	$0.257810\pi$
$272$	−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	0.706076	+	0.708136i	$0.250464\pi$
$277$	−2.19359	+	20.8706i	−0.131800	+	1.25400i	−0.837877	+	0.545860i	$0.816203\pi$
$278$	−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	0.360448	−	0.932779i	$-0.382624\pi$
$281$	22.7803	−	16.5509i	1.35896	−	0.987341i	0.998510	−	0.0545621i	$-0.0173763\pi$
$282$	23.5799	+	5.01207i	1.40416	+	0.298464i
$283$	25.6194	−	5.44557i	1.52291	−	0.323705i	0.630954	−	0.775820i	$-0.282664\pi$
$283$	25.6194	−	5.44557i	1.52291	−	0.323705i	0.891960	+	0.452115i	$0.149330\pi$
$284$	−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	0.902644	−	0.430388i	$-0.141623\pi$
$293$	−1.37941	−	4.24538i	−0.0805858	−	0.248017i	−0.983230	+	0.182370i	$0.941623\pi$
$294$		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	−0.878818	−	0.477157i	$-0.841667\pi$
$311$	−26.2338	+	5.57616i	−1.48758	+	0.316195i	−0.608763	+	0.793352i	$0.708334\pi$
$312$	−12.1101	+	13.4496i	−0.685598	+	0.761434i
$313$	−0.375120	−	3.56903i	−0.0212030	−	0.201733i	0.978792	−	0.204856i	$-0.0656726\pi$
$313$	−0.375120	−	3.56903i	−0.0212030	−	0.201733i	−0.999995	+	0.00312281i	$0.999006\pi$
$314$	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	−0.791930	−	0.610611i	$-0.790924\pi$
$317$	−15.4554	+	6.88119i	−0.868062	+	0.386486i	−0.0761321	+	0.997098i	$0.524257\pi$
$318$	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	−0.848509	−	0.529182i	$-0.822499\pi$
$331$	0.619131	−	1.07237i	0.0340305	−	0.0589426i	0.882539	+	0.470239i	$0.155832\pi$
$332$	−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	−0.961715	−	0.274051i	$-0.911636\pi$
$337$	−6.32885	−	19.4782i	−0.344754	−	1.06104i	0.616961	−	0.786994i	$-0.288364\pi$
$338$	−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	0.945808	−	0.324725i	$-0.105272\pi$
$347$	24.9122	+	11.0916i	1.33736	+	0.595431i	0.391551	+	0.920156i	$0.371939\pi$
$348$	−16.9005	−	3.59230i	−0.905959	−	0.192568i
$349$	2.46730	−	7.59356i	0.132071	−	0.406474i	−0.863052	−	0.505116i	$-0.831450\pi$
$349$	2.46730	−	7.59356i	0.132071	−	0.406474i	0.995123	+	0.0986418i	$0.0314498\pi$
$350$		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	0.776188	−	0.630502i	$-0.217151\pi$
$353$	−2.96736	−	5.13961i	−0.157937	−	0.273554i	−0.934124	+	0.356948i	$0.883817\pi$
$354$	−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	−0.596069	−	0.802933i	$-0.703271\pi$
$359$	−27.7992	−	5.90891i	−1.46719	−	0.311860i	−0.871118	+	0.491073i	$0.836605\pi$
$360$	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	−0.0786515	+	0.996902i	$0.525061\pi$
$367$	−20.3425	+	22.5927i	−1.06187	+	1.17933i	−0.983220	+	0.182425i	$0.941605\pi$
$368$	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	−0.990084	−	0.140476i	$-0.955137\pi$
$373$	−7.21128	+	12.4903i	−0.373386	+	0.646723i	0.616698	+	0.787200i	$0.288470\pi$
$374$	−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	−0.0151144	−	0.999886i	$-0.504811\pi$
$379$	18.1278	−	13.1706i	0.931163	−	0.676529i	0.946277	+	0.323356i	$0.104811\pi$
$380$	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	0.578808	−	0.815464i	$-0.303518\pi$
$383$	30.7669	−	13.6983i	1.57211	−	0.699950i	0.993306	+	0.115514i	$0.0368514\pi$
$384$	−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	−0.700552	−	0.713601i	$-0.747063\pi$
$389$	1.62454	−	1.80423i	0.0823672	−	0.0914780i	0.782920	+	0.622123i	$0.213730\pi$
$390$	−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	−0.782501	−	0.622650i	$-0.786056\pi$
$397$	2.94848	−	5.10692i	0.147980	−	0.256309i	0.930481	+	0.366341i	$0.119390\pi$
$398$	−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	−0.983890	−	0.178774i	$-0.942787\pi$
$401$	−1.17486	−	11.1780i	−0.0586696	−	0.558203i	0.925221	−	0.379430i	$-0.123880\pi$
$402$	−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	0.608909	+	0.793240i	$0.291607\pi$
$409$	−3.06628	+	29.1737i	−0.151618	+	1.44255i	−0.760527	+	0.649306i	$0.775059\pi$
$410$	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	−0.971452	−	0.237238i	$-0.923758\pi$
$421$	−0.945600	+	2.91026i	−0.0460857	+	0.141837i	0.925366	+	0.379075i	$0.123758\pi$
$422$	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	0.958991	+	0.283436i	$0.0914745\pi$
$431$	−0.788350	+	7.50065i	−0.0379735	+	0.361294i	−0.996965	+	0.0778572i	$0.975192\pi$
$432$	7.93705	+	8.81499i	0.381871	+	0.424111i
$433$	−9.93848	−	30.5875i	−0.477613	−	1.46994i	−0.842401	−	0.538851i	$-0.818859\pi$
$433$	−9.93848	−	30.5875i	−0.477613	−	1.46994i	0.364788	−	0.931091i	$-0.381141\pi$
$434$		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	−0.804948	−	0.593345i	$-0.797807\pi$
$439$	2.33363	−	4.04196i	0.111378	−	0.192912i	0.916326	+	0.400433i	$0.131140\pi$
$440$	−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	0.952300	−	0.305165i	$-0.0987116\pi$
$443$	11.5607	+	12.8394i	0.549264	+	0.610020i	−0.403036	+	0.915184i	$0.632045\pi$
$444$	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	0.859553	−	0.511047i	$-0.170742\pi$
$449$	13.5430	+	9.83957i	0.639134	+	0.464358i	−0.220418	+	0.975405i	$0.570742\pi$
$450$	−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	0.909989	+	0.414633i	$0.136090\pi$
$457$	2.26800	+	21.5785i	0.106092	+	1.00940i	−0.803897	+	0.594769i	$0.797243\pi$
$458$	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	0.999903	−	0.0139134i	$-0.00442891\pi$
$467$	0.409676	+	3.89780i	0.0189575	+	0.180369i	−0.980946	+	0.194282i	$0.937762\pi$
$468$	−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	0.0663109	−	0.997799i	$-0.478877\pi$
$479$	−13.8063	−	6.14698i	−0.630828	−	0.280863i	−0.697139	+	0.716936i	$0.745544\pi$
$480$	−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	−0.726846	−	0.686800i	$-0.759015\pi$
$487$	−24.5288	+	5.21376i	−1.11151	+	0.236258i	−0.384660	+	0.923058i	$0.625681\pi$
$488$	−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	0.775750	+	0.631040i	$0.217372\pi$
$491$	11.5019	+	35.3991i	0.519071	+	1.59754i	−0.256679	+	0.966497i	$0.582628\pi$
$492$	−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	0.842494	−	0.538705i	$-0.181086\pi$
$499$	31.1182	+	6.61437i	1.39304	+	0.296100i	0.550546	+	0.834805i	$0.314420\pi$
$500$	−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	0.727154	+	0.686474i	$0.240843\pi$
$503$	−5.93493	+	18.2658i	−0.264626	+	0.814434i	−0.991779	+	0.127959i	$0.959157\pi$
$504$		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	0.779292	−	0.626661i	$-0.215579\pi$
$509$	1.68319	+	1.86937i	0.0746060	+	0.0828584i	−0.704686	+	0.709519i	$0.748912\pi$
$510$	−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	−0.484114	−	0.875005i	$-0.660858\pi$
$521$	9.96788	−	11.0705i	0.436701	−	0.485005i	0.920815	+	0.389999i	$0.127525\pi$
$522$	41.9938	+	18.6968i	1.83802	+	0.818338i
$523$	1.03536	+	9.85076i	0.0452730	+	0.430744i	0.993558	+	0.113324i	$0.0361498\pi$
$523$	1.03536	+	9.85076i	0.0452730	+	0.430744i	−0.948285	+	0.317420i	$0.897184\pi$
$524$	−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	−0.790542	−	0.612408i	$-0.790201\pi$
$541$	−20.1057	+	8.95161i	−0.864409	+	0.384860i	−0.0738677	+	0.997268i	$0.523534\pi$
$542$	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	−0.996821	−	0.0796728i	$-0.974612\pi$
$547$	−3.35724	+	10.3325i	−0.143545	+	0.441787i	0.853276	+	0.521460i	$0.174612\pi$
$548$	−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	−0.0452499	−	0.998976i	$-0.514408\pi$
$557$	22.4912	−	24.9790i	0.952983	−	1.05840i	0.998233	−	0.0594193i	$-0.0189249\pi$
$558$	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	−0.989067	−	0.147465i	$-0.952888\pi$
$563$	0.214647	−	2.04223i	0.00904631	−	0.0860699i	0.998114	+	0.0613956i	$0.0195551\pi$
$564$	−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	0.787315	−	0.616551i	$-0.211471\pi$
$569$	2.19084	+	2.43317i	0.0918448	+	0.102004i	−0.695470	+	0.718555i	$0.744804\pi$
$570$	1.86801	−	17.7729i	0.0782424	−	0.744426i
$571$	21.9448	+	38.0096i	0.918363	+	1.59065i	0.801901	+	0.597457i	$0.203822\pi$
$571$	21.9448	+	38.0096i	0.918363	+	1.59065i	0.116462	+	0.993195i	$0.462845\pi$
$572$	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	−1.00000		0.000110759i	$-0.999965\pi$
$577$	−40.0959	−	17.8518i	−1.66921	−	0.743181i	−0.669213	−	0.743071i	$-0.733369\pi$
$578$	−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	0.967280	−	0.253711i	$-0.0816513\pi$
$587$	0.862670	+	2.65503i	0.0356062	+	0.109585i	−0.931674	+	0.363296i	$0.881651\pi$
$588$		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	−0.999666	−	0.0258622i	$-0.991767\pi$
$593$	−11.6263	+	20.1374i	−0.477435	+	0.826942i	0.522230	+	0.852805i	$0.325100\pi$
$594$	−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	0.592550	−	0.805534i	$-0.298121\pi$
$599$	9.55519	+	4.25424i	0.390414	+	0.173824i	−0.202135	+	0.979358i	$0.564788\pi$
$600$	−6.37846	−	60.6870i	−0.260400	−	2.47754i
$601$	6.89406	+	21.2177i	0.281215	+	0.865489i	0.987508	+	0.157570i	$0.0503660\pi$
$601$	6.89406	+	21.2177i	0.281215	+	0.865489i	−0.706293	+	0.707919i	$0.749634\pi$
$602$		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	−0.0232812	−	0.999729i	$-0.507411\pi$
$607$	17.3468	−	7.72328i	0.704084	−	0.313478i	0.727365	+	0.686251i	$0.240745\pi$
$608$	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	−0.588161	−	0.808744i	$-0.700148\pi$
$613$	−19.7211	+	4.19185i	−0.796528	+	0.169307i	−0.208366	+	0.978051i	$0.566815\pi$
$614$	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	0.448660	−	0.893702i	$-0.351901\pi$
$619$	30.4038	−	6.46254i	1.22203	−	0.259751i	0.773373	+	0.633951i	$0.218568\pi$
$620$	−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	0.990426	+	0.138043i	$0.0440812\pi$
$631$	6.78971	+	20.8966i	0.270294	+	0.831880i	−0.720132	+	0.693837i	$0.755919\pi$
$632$	−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	0.0561227	−	0.998424i	$-0.482126\pi$
$641$	13.0005	−	2.76334i	0.513489	−	0.109145i	0.457366	+	0.889278i	$0.348793\pi$
$642$	10.9455	+	2.32654i	0.431985	+	0.0918212i
$643$	−11.8848	+	8.63480i	−0.468690	+	0.340523i	−0.796930	−	0.604071i	$-0.793544\pi$
$643$	−11.8848	+	8.63480i	−0.468690	+	0.340523i	0.328241	+	0.944594i	$0.393544\pi$
$644$		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	−0.974613	−	0.223898i	$-0.928122\pi$
$647$	0.642352	−	6.11157i	0.0252534	−	0.240271i	0.999866	−	0.0163722i	$-0.00521168\pi$
$648$	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	0.904279	−	0.426941i	$-0.140409\pi$
$653$	39.7804	+	8.45558i	1.55673	+	0.330893i	0.652448	+	0.757834i	$0.273742\pi$
$654$	−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	0.983171	−	0.182689i	$-0.0584800\pi$
$661$	8.57098	+	14.8454i	0.333373	+	0.577418i	−0.649798	+	0.760107i	$0.725147\pi$
$662$	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	0.887426	−	0.460949i	$-0.152491\pi$
$673$	18.7632	+	13.6322i	0.723268	+	0.525485i	−0.164159	+	0.986434i	$0.552491\pi$
$674$	−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	0.898850	+	0.438256i	$0.144404\pi$
$677$	2.88191	+	27.4195i	0.110761	+	1.05382i	−0.788089	+	0.615561i	$0.788930\pi$
$678$	−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	0.576244	−	0.817278i	$-0.304518\pi$
$683$	−10.9675	−	18.9963i	−0.419661	−	0.726874i	−0.995905	+	0.0904032i	$0.971184\pi$
$684$	−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	−0.800966	−	0.598709i	$-0.795680\pi$
$691$	−23.4476	+	10.4396i	−0.891990	+	0.397139i	−0.0910234	+	0.995849i	$0.529014\pi$
$692$	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	0.784249	+	0.620446i	$0.213049\pi$
$701$	−5.69007	+	17.5122i	−0.214911	+	0.661428i	−0.999160	+	0.0409817i	$0.986951\pi$
$702$	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	−0.937403	−	0.348246i	$-0.886777\pi$
$709$	−2.47336	−	23.5324i	−0.0928889	−	0.883779i	0.844514	−	0.535533i	$-0.179889\pi$
$710$	−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	0.000528360	−	1.00000i	$-0.499832\pi$
$719$	−10.8792	−	2.31244i	−0.405726	−	0.0862396i	−0.406254	+	0.913760i	$0.633165\pi$
$720$	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	−0.211165	−	0.977450i	$-0.567726\pi$
$733$	−21.7036	−	4.61323i	−0.801639	−	0.170394i	−0.590474	+	0.807057i	$0.701059\pi$
$734$	−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	0.779394	+	0.626534i	$0.215527\pi$
$739$	−3.07817	+	29.2868i	−0.113232	+	1.07733i	−0.892626	+	0.450798i	$0.851140\pi$
$740$	−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	−0.809691	−	0.586856i	$-0.800365\pi$
$743$	−13.6772	+	9.93704i	−0.501766	+	0.364555i	0.307925	+	0.951411i	$0.400365\pi$
$744$	−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	0.723906	−	0.689899i	$-0.242345\pi$
$751$	−1.03813	−	1.15296i	−0.0378820	−	0.0420722i	−0.761788	+	0.647826i	$0.775678\pi$
$752$	−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	0.387840	−	0.921727i	$-0.373221\pi$
$757$	−10.1505	−	7.37474i	−0.368925	−	0.268040i	−0.756765	+	0.653687i	$0.773221\pi$
$758$	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	−0.550837	−	0.834613i	$-0.685692\pi$
$761$	−8.25330	+	3.67460i	−0.299182	+	0.133204i	0.251656	+	0.967817i	$0.419025\pi$
$762$	−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	0.127725	−	0.991810i	$-0.459233\pi$
$773$	18.0111	−	3.82837i	0.647813	−	0.137697i	0.520088	+	0.854113i	$0.325899\pi$
$774$	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	0.987337	−	0.158638i	$-0.0507101\pi$
$787$	42.9248	+	19.1113i	1.53010	+	0.681246i	0.542767	+	0.839884i	$0.317377\pi$
$788$	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	−0.542115	−	0.840304i	$-0.682376\pi$
$797$	2.52781	−	1.83656i	0.0895395	−	0.0650543i	0.631654	+	0.775250i	$0.282376\pi$
$798$		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	−0.192859	−	0.981226i	$-0.561776\pi$
$809$	−29.8964	−	13.3107i	−1.05110	−	0.467980i	−0.858241	+	0.513246i	$0.828443\pi$
$810$	−8.43833	−	1.79362i	−0.296493	−	0.0630215i
$811$	10.0929	−	31.0627i	0.354410	−	1.09076i	−0.601941	−	0.798540i	$-0.705606\pi$
$811$	10.0929	−	31.0627i	0.354410	−	1.09076i	0.956351	−	0.292220i	$-0.0943941\pi$
$812$		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	0.333001	−	0.942926i	$-0.391939\pi$
$821$	7.26903	+	1.54508i	0.253691	+	0.0539236i	−0.0793107	+	0.996850i	$0.525272\pi$
$822$	28.3612	−	6.02835i	0.989209	−	0.210263i
$823$	−0.685567	+	6.52273i	−0.0238974	+	0.227368i	0.976054	+	0.217527i	$0.0697991\pi$
$823$	−0.685567	+	6.52273i	−0.0238974	+	0.227368i	−0.999952	+	0.00984082i	$0.996868\pi$
$824$	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	0.199318	−	0.979935i	$-0.436127\pi$
$827$	−19.2982	−	14.0209i	−0.671063	−	0.487556i	−0.870381	+	0.492379i	$0.836127\pi$
$828$	2.11756	+	2.35179i	0.0735902	+	0.0817302i
$829$	−17.4932	+	19.4281i	−0.607563	+	0.674767i	−0.965927	−	0.258815i	$-0.916668\pi$
$829$	−17.4932	+	19.4281i	−0.607563	+	0.674767i	0.358364	+	0.933582i	$0.383335\pi$
$830$	−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	−0.583662	−	0.811997i	$-0.698381\pi$
$839$	10.5959	−	32.6107i	0.365810	−	1.12585i	0.949472	−	0.313851i	$-0.101619\pi$
$840$		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	−0.843154	−	0.537672i	$-0.819304\pi$
$853$	−17.3002	+	12.5693i	−0.592347	+	0.430365i	0.250807	+	0.968037i	$0.419304\pi$
$854$		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	−0.955941	−	0.293559i	$-0.905160\pi$
$857$	−21.4348	−	37.1262i	−0.732200	−	1.26821i	0.223741	−	0.974649i	$-0.428173\pi$
$858$	−11.4114	−	18.5328i	−0.389578	−	0.632698i
$859$	15.1958	−	26.3198i	0.518473	−	0.898022i	−0.481297	−	0.876558i	$-0.659834\pi$
$859$	15.1958	−	26.3198i	0.518473	−	0.898022i	0.999770	−	0.0214638i	$-0.00683266\pi$
$860$	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	−0.995220	−	0.0976580i	$-0.968865\pi$
$863$	−1.23536	−	11.7537i	−0.0420522	−	0.400100i	0.953168	−	0.302442i	$-0.0978018\pi$
$864$	−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	0.630123	−	0.776495i	$-0.283004\pi$
$877$	−6.15927	−	6.84056i	−0.207984	−	0.230989i	−0.838107	+	0.545506i	$0.816338\pi$
$878$	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	−0.999170	−	0.0407275i	$-0.987032\pi$
$883$	−4.95906	+	15.2624i	−0.166886	+	0.513621i	0.832285	+	0.554348i	$0.187032\pi$
$884$	−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	0.726921	−	0.686722i	$-0.240951\pi$
$887$	33.1087	+	7.03747i	1.11168	+	0.236295i	0.384760	+	0.923017i	$0.374284\pi$
$888$	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	−0.391848	−	0.920030i	$-0.628164\pi$
$907$	−40.2886	−	17.9376i	−1.33776	−	0.595609i	−0.945913	+	0.324421i	$0.894831\pi$
$908$	−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	−0.999777	−	0.0211316i	$-0.993273\pi$
$911$	−40.1075	−	29.1398i	−1.32882	−	0.965446i	−0.329045	−	0.944314i	$-0.606727\pi$
$912$	−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	0.806088	+	0.591795i	$0.201581\pi$
$919$	4.26399	+	40.5692i	0.140656	+	1.33825i	−0.665432	+	0.746458i	$0.731753\pi$
$920$	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	−0.801068	−	0.598573i	$-0.795735\pi$
$929$	−4.32674	−	41.1662i	−0.141956	−	1.35062i	0.659112	−	0.752044i	$-0.270932\pi$
$930$	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	0.566489	−	0.824069i	$-0.308301\pi$
$937$	−1.29155	−	0.938364i	−0.0421930	−	0.0306550i	−0.608682	+	0.793414i	$0.708301\pi$
$938$		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	0.509836	−	0.860271i	$-0.329706\pi$
$941$	6.49336	+	2.89103i	0.211678	+	0.0942449i	−0.298159	+	0.954516i	$0.596373\pi$
$942$	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	−0.845350	−	0.534213i	$-0.820608\pi$
$947$	1.22993	−	2.13030i	0.0399674	−	0.0692255i	0.885317	+	0.464988i	$0.153941\pi$
$948$	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	−0.986010	−	0.166688i	$-0.946693\pi$
$953$	−8.83790	−	27.2003i	−0.286288	−	0.881103i	0.699722	−	0.714415i	$-0.253307\pi$
$954$	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	0.734187	−	0.678947i	$-0.237564\pi$
$971$	−0.554173	−	0.615471i	−0.0177843	−	0.0197514i	−0.751971	+	0.659196i	$0.770897\pi$
$972$	−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	0.966019	+	0.258472i	$0.0832189\pi$
$977$	−1.01990	+	9.70369i	−0.0326295	+	0.310449i	−0.998648	+	0.0519768i	$0.983448\pi$
$978$	−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	−0.0345993	−	0.999401i	$-0.511015\pi$
$983$	30.1910	−	33.5305i	0.962944	−	1.06946i	0.997543	−	0.0700562i	$-0.0223178\pi$
$984$	−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	−0.880862	−	0.473373i	$-0.843036\pi$
$991$	−26.7702	−	46.3674i	−0.850384	−	1.47291i	0.0304776	−	0.999535i	$-0.490297\pi$
$992$	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	−0.976547	−	0.215305i	$-0.930925\pi$
$997$	−20.8506	+	23.1569i	−0.660344	+	0.733387i	0.316203	+	0.948692i	$0.397592\pi$
$998$	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.422.3		32
7.2	even	3		77.2.f.b.15.2	✓	16
7.3	odd	6		539.2.q.f.312.2		32
7.4	even	3	inner	539.2.q.g.312.2		32
7.5	odd	6		539.2.f.e.246.2		16
7.6	odd	2		539.2.q.f.422.3		32
11.3	even	5	inner	539.2.q.g.520.2		32
21.2	odd	6		693.2.m.i.631.3		16
77.2	odd	30		847.2.f.v.148.2		16
77.3	odd	30		539.2.q.f.410.3		32
77.5	odd	30		5929.2.a.bt.1.6		8
77.9	even	15		847.2.f.w.148.3		16
77.16	even	15		847.2.a.p.1.6		8
77.25	even	15	inner	539.2.q.g.410.3		32
77.30	odd	30		847.2.f.x.729.3		16
77.37	even	15		847.2.f.w.372.3		16
77.47	odd	30		539.2.f.e.344.2		16
77.51	odd	30		847.2.f.v.372.2		16
77.58	even	15		77.2.f.b.36.2	yes	16
77.61	even	30		5929.2.a.bs.1.3		8
77.65	odd	6		847.2.f.x.323.3		16
77.69	odd	10		539.2.q.f.520.2		32
77.72	odd	30		847.2.a.o.1.3		8
231.149	even	30		7623.2.a.cw.1.6		8
231.170	odd	30		7623.2.a.ct.1.3		8
231.212	odd	30		693.2.m.i.190.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.2	✓	16	7.2	even	3
77.2.f.b.36.2	yes	16	77.58	even	15
539.2.f.e.246.2		16	7.5	odd	6
539.2.f.e.344.2		16	77.47	odd	30
539.2.q.f.312.2		32	7.3	odd	6
539.2.q.f.410.3		32	77.3	odd	30
539.2.q.f.422.3		32	7.6	odd	2
539.2.q.f.520.2		32	77.69	odd	10
539.2.q.g.312.2		32	7.4	even	3	inner
539.2.q.g.410.3		32	77.25	even	15	inner
539.2.q.g.422.3		32	1.1	even	1	trivial
539.2.q.g.520.2		32	11.3	even	5	inner
693.2.m.i.190.3		16	231.212	odd	30
693.2.m.i.631.3		16	21.2	odd	6
847.2.a.o.1.3		8	77.72	odd	30
847.2.a.p.1.6		8	77.16	even	15
847.2.f.v.148.2		16	77.2	odd	30
847.2.f.v.372.2		16	77.51	odd	30
847.2.f.w.148.3		16	77.9	even	15
847.2.f.w.372.3		16	77.37	even	15
847.2.f.x.323.3		16	77.65	odd	6
847.2.f.x.729.3		16	77.30	odd	30
5929.2.a.bs.1.3		8	77.61	even	30
5929.2.a.bt.1.6		8	77.5	odd	30
7623.2.a.ct.1.3		8	231.170	odd	30
7623.2.a.cw.1.6		8	231.149	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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