LMFDB - Embedded newform 539.2.q.f.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.f.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	−0.689820	−	0.723981i	$-0.742310\pi$
$3$	−2.79635	−	0.594382i	−1.61447	−	0.343166i	−0.924651	+	0.380815i	$0.875644\pi$
$4$	−0.507177	−	0.563277i	−0.253589	−	0.281639i
$5$	0.361259	−	3.43715i	0.161560	−	1.53714i	−0.550390	−	0.834908i	$-0.685521\pi$
$5$	0.361259	−	3.43715i	0.161560	−	1.53714i	0.711950	−	0.702230i	$-0.247812\pi$
$6$	−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	$-0.792200\pi$
$13$	−1.66629	+	1.21063i	−0.462147	+	0.335769i	0.332226	+	0.943200i	$0.392200\pi$
$14$		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	$-0.708678\pi$
$17$	−1.76655	+	0.786518i	−0.428451	+	0.190759i	0.181170	+	0.983452i	$0.442012\pi$
$18$	3.85751	+	4.28420i	0.909224	+	1.00980i
$19$	−1.08597	+	1.20609i	−0.249139	+	0.276697i	−0.854723	−	0.519085i	$-0.826273\pi$
$19$	−1.08597	+	1.20609i	−0.249139	+	0.276697i	0.605584	+	0.795782i	$0.292940\pi$
$20$	−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	0.999427	−	0.0338518i	$-0.0107774\pi$
$31$	0.0824123	+	0.784101i	0.0148017	+	0.140829i	−0.984625	+	0.174680i	$0.944111\pi$
$32$	−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	0.989162	−	0.146831i	$-0.0469074\pi$
$41$	0.657011	+	2.02207i	0.102608	+	0.315795i	−0.886554	+	0.462626i	$0.846907\pi$
$42$		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	$-0.952737\pi$
$47$	−5.06286	+	5.62287i	−0.738493	+	0.820180i	0.250504	+	0.968116i	$0.419404\pi$
$48$	−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	0.869423	−	0.494069i	$-0.164491\pi$
$59$	2.20588	+	2.44988i	0.287181	+	0.318947i	−0.582242	+	0.813016i	$0.697824\pi$
$60$	6.84146	−	3.04602i	0.883229	−	0.393239i
$61$	−0.112538	+	1.07073i	−0.0144090	+	0.137093i	−0.999361	−	0.0357334i	$-0.988623\pi$
$61$	−0.112538	+	1.07073i	−0.0144090	+	0.137093i	0.984952	+	0.172826i	$0.0552899\pi$
$62$	−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	0.693210	−	0.720735i	$-0.256196\pi$
$73$	−0.820539	−	0.911300i	−0.0960368	−	0.106660i	−0.789247	+	0.614076i	$0.789529\pi$
$74$	−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	$-0.956249\pi$
$83$	−13.0004	−	9.44536i	−1.42698	−	1.03676i	−0.436412	−	0.899747i	$-0.643751\pi$
$84$		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	$-0.242251\pi$
$89$	−2.21915	−	3.84368i	−0.235230	−	0.407430i	−0.959339	+	0.282255i	$0.908918\pi$
$90$	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	$-0.593502\pi$
$97$	5.23278	−	3.80184i	0.531308	−	0.386018i	0.820847	+	0.571148i	$0.193502\pi$
$98$		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	$-0.754380\pi$
$101$	−1.61443	−	15.3603i	−0.160642	−	1.52841i	0.556128	−	0.831097i	$-0.312286\pi$
$102$	6.02634	+	1.28094i	0.596696	+	0.126832i
$103$	8.71346	−	1.85210i	0.858563	−	0.182493i	0.242462	−	0.970161i	$-0.422045\pi$
$103$	8.71346	−	1.85210i	0.858563	−	0.182493i	0.616100	+	0.787668i	$0.288712\pi$
$104$	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	0.955825	−	0.293937i	$-0.0949657\pi$
$131$	2.55642	+	4.42785i	0.223355	+	0.386863i	−0.732469	+	0.680800i	$0.761632\pi$
$132$	−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	$-0.713855\pi$
$139$	4.02234	−	12.3795i	0.341171	−	1.05002i	0.963602	−	0.267341i	$-0.0861450\pi$
$140$		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	−0.731827	−	0.681491i	$-0.761332\pi$
$157$	−21.0199	−	4.46792i	−1.67757	−	0.356579i	−0.945744	+	0.324912i	$0.894665\pi$
$158$	−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	$0.617404\pi$
$167$	−17.5626	+	12.7600i	−1.35904	+	0.987397i	−0.998506	+	0.0546489i	$0.982596\pi$
$168$		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	$-0.667726\pi$
$173$	5.38358	−	5.97907i	0.409306	−	0.454580i	0.912186	+	0.409776i	$0.134393\pi$
$174$	−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	0.951088	−	0.308920i	$-0.0999675\pi$
$181$	12.7970	+	9.29753i	0.951190	+	0.691080i	0.000102207		1.00000i	$0.499967\pi$
$182$		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	−0.676638	−	0.736316i	$-0.736564\pi$
$199$	4.22284	−	7.31417i	0.299349	−	0.518488i	0.975987	+	0.217828i	$0.0698972\pi$
$200$	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	$-0.902091\pi$
$223$	−5.37562	−	16.5445i	−0.359978	−	1.10790i	0.593088	−	0.805138i	$-0.297909\pi$
$224$		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	$-0.0956473\pi$
$227$	8.45211	+	9.38702i	0.560986	+	0.623038i	−0.394207	+	0.919022i	$0.628981\pi$
$228$	−3.43991	−	0.731176i	−0.227814	−	0.0484233i
$229$	−4.17802	−	1.86018i	−0.276091	−	0.122924i	0.264020	−	0.964517i	$-0.414951\pi$
$229$	−4.17802	−	1.86018i	−0.276091	−	0.122924i	−0.540112	+	0.841593i	$0.681618\pi$
$230$	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	$-0.624413\pi$
$241$	9.47322	−	16.4081i	0.610224	−	1.05694i	0.991202	−	0.132355i	$-0.0422539\pi$
$242$	−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	$-0.728840\pi$
$251$	−2.31938	+	1.68513i	−0.146398	+	0.106364i	0.512175	+	0.858881i	$0.328840\pi$
$252$		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	$-0.320237\pi$
$257$	21.9260	−	4.66052i	1.36771	−	0.290715i	0.832510	+	0.554011i	$0.186903\pi$
$258$	−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	−0.196593	−	0.980485i	$-0.562988\pi$
$269$	6.56873	−	2.92458i	0.400502	−	0.178315i	0.597096	+	0.802170i	$0.296321\pi$
$270$	−21.8572	+	9.73147i	−1.33019	+	0.592238i
$271$	−26.5707	+	5.64777i	−1.61405	+	0.343078i	−0.924508	−	0.381164i	$-0.875523\pi$
$271$	−26.5707	+	5.64777i	−1.61405	+	0.343078i	−0.689546	+	0.724241i	$0.742190\pi$
$272$	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	−0.630954	−	0.775820i	$-0.717336\pi$
$283$	−25.6194	−	5.44557i	−1.52291	−	0.323705i	−0.891960	+	0.452115i	$0.850670\pi$
$284$	−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	$-0.858377\pi$
$293$	1.37941	−	4.24538i	0.0805858	−	0.248017i	0.983230	+	0.182370i	$0.0583769\pi$
$294$		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	$-0.619843\pi$
$307$	−12.8841			−0.735334			−0.367667	+	0.929957i	$0.619843\pi$
$308$		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	$-0.158333\pi$
$311$	26.2338	+	5.57616i	1.48758	+	0.316195i	0.608763	+	0.793352i	$0.291666\pi$
$312$	−12.1101	−	13.4496i	−0.685598	−	0.761434i
$313$	0.375120	−	3.56903i	0.0212030	−	0.201733i	−0.978792	−	0.204856i	$-0.934327\pi$
$313$	0.375120	−	3.56903i	0.0212030	−	0.201733i	0.999995	+	0.00312281i	$0.000994021\pi$
$314$	−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	0.863052	−	0.505116i	$-0.168550\pi$
$349$	−2.46730	−	7.59356i	−0.132071	−	0.406474i	−0.995123	+	0.0986418i	$0.968550\pi$
$350$		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	$-0.782849\pi$
$353$	2.96736	−	5.13961i	0.157937	−	0.273554i	0.934124	+	0.356948i	$0.116183\pi$
$354$	−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	$0.0583948\pi$
$367$	20.3425	+	22.5927i	1.06187	+	1.17933i	0.0786515	+	0.996902i	$0.474939\pi$
$368$	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	−0.578808	−	0.815464i	$-0.696482\pi$
$383$	−30.7669	−	13.6983i	−1.57211	−	0.699950i	−0.993306	+	0.115514i	$0.963149\pi$
$384$	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	0.782501	−	0.622650i	$-0.213944\pi$
$397$	−2.94848	−	5.10692i	−0.147980	−	0.256309i	−0.930481	+	0.366341i	$0.880610\pi$
$398$	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	$0.224941\pi$
$409$	3.06628	+	29.1737i	0.151618	+	1.44255i	−0.608909	+	0.793240i	$0.708393\pi$
$410$	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	$-0.334980\pi$
$419$	20.2858			0.991027			0.495514	+	0.868600i	$0.334980\pi$
$420$		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	$-0.618859\pi$
$433$	9.93848	−	30.5875i	0.477613	−	1.46994i	0.842401	−	0.538851i	$-0.181141\pi$
$434$		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	$-0.202193\pi$
$439$	−2.33363	−	4.04196i	−0.111378	−	0.192912i	−0.916326	+	0.400433i	$0.868860\pi$
$440$	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	$-0.454796\pi$
$461$	6.07778			0.283070			0.141535	+	0.989933i	$0.454796\pi$
$462$		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	$-0.995571\pi$
$467$	−0.409676	+	3.89780i	−0.0189575	+	0.180369i	0.980946	+	0.194282i	$0.0622378\pi$
$468$	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	$-0.521123\pi$
$479$	13.8063	−	6.14698i	0.630828	−	0.280863i	0.697139	+	0.716936i	$0.254456\pi$
$480$	−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	$0.0408426\pi$
$503$	5.93493	+	18.2658i	0.264626	+	0.814434i	−0.727154	+	0.686474i	$0.759157\pi$
$504$		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	$-0.784421\pi$
$509$	−1.68319	+	1.86937i	−0.0746060	+	0.0828584i	0.704686	+	0.709519i	$0.251088\pi$
$510$	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	$-0.339142\pi$
$521$	−9.96788	−	11.0705i	−0.436701	−	0.485005i	−0.920815	+	0.389999i	$0.872475\pi$
$522$	41.9938	−	18.6968i	1.83802	−	0.818338i
$523$	−1.03536	+	9.85076i	−0.0452730	+	0.430744i	0.948285	+	0.317420i	$0.102816\pi$
$523$	−1.03536	+	9.85076i	−0.0452730	+	0.430744i	−0.993558	+	0.113324i	$0.963850\pi$
$524$	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	0.989067	−	0.147465i	$-0.0471115\pi$
$563$	−0.214647	−	2.04223i	−0.00904631	−	0.0860699i	−0.998114	+	0.0613956i	$0.980445\pi$
$564$	−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	$-0.266631\pi$
$577$	40.0959	−	17.8518i	1.66921	−	0.743181i	1.00000		0.000110759i	$-3.52556e-5\pi$
$578$	−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	$-0.918349\pi$
$587$	−0.862670	+	2.65503i	−0.0356062	+	0.109585i	0.931674	+	0.363296i	$0.118349\pi$
$588$		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	$-0.00823311\pi$
$593$	11.6263	+	20.1374i	0.477435	+	0.826942i	−0.522230	+	0.852805i	$0.674900\pi$
$594$	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	$0.250366\pi$
$601$	−6.89406	+	21.2177i	−0.281215	+	0.865489i	−0.987508	+	0.157570i	$0.949634\pi$
$602$		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	$-0.492589\pi$
$607$	−17.3468	−	7.72328i	−0.704084	−	0.313478i	−0.727365	+	0.686251i	$0.759255\pi$
$608$	−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	−0.448660	−	0.893702i	$-0.648099\pi$
$619$	−30.4038	−	6.46254i	−1.22203	−	0.259751i	−0.773373	+	0.633951i	$0.781432\pi$
$620$	−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	0.796930	−	0.604071i	$-0.206456\pi$
$643$	11.8848	+	8.63480i	0.468690	+	0.340523i	−0.328241	+	0.944594i	$0.606456\pi$
$644$		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	$-0.994788\pi$
$647$	−0.642352	−	6.11157i	−0.0252534	−	0.240271i	0.974613	−	0.223898i	$-0.0718783\pi$
$648$	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	−0.983171	−	0.182689i	$-0.941520\pi$
$661$	−8.57098	+	14.8454i	−0.333373	+	0.577418i	0.649798	+	0.760107i	$0.274853\pi$
$662$	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	$0.211070\pi$
$677$	−2.88191	+	27.4195i	−0.110761	+	1.05382i	−0.898850	+	0.438256i	$0.855596\pi$
$678$	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	0.800966	−	0.598709i	$-0.204320\pi$
$691$	23.4476	+	10.4396i	0.891990	+	0.397139i	0.0910234	+	0.995849i	$0.470986\pi$
$692$	−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	−0.000528360	−	1.00000i	$-0.500168\pi$
$719$	10.8792	−	2.31244i	0.405726	−	0.0862396i	0.406254	+	0.913760i	$0.366835\pi$
$720$	−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	$-0.788756\pi$
$727$	−42.4803			−1.57551			−0.787753	+	0.615991i	$0.788756\pi$
$728$		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	$-0.432274\pi$
$733$	21.7036	−	4.61323i	0.801639	−	0.170394i	0.590474	+	0.807057i	$0.298941\pi$
$734$	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	0.550837	−	0.834613i	$-0.314308\pi$
$761$	8.25330	+	3.67460i	0.299182	+	0.133204i	−0.251656	+	0.967817i	$0.580975\pi$
$762$	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	$-0.406018\pi$
$769$	16.1383			0.581963			0.290981	+	0.956729i	$0.406018\pi$
$770$		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	$-0.540767\pi$
$773$	−18.0111	−	3.82837i	−0.647813	−	0.137697i	−0.520088	+	0.854113i	$0.674101\pi$
$774$	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	$-0.949290\pi$
$787$	−42.9248	+	19.1113i	−1.53010	+	0.681246i	−0.542767	+	0.839884i	$0.682623\pi$
$788$	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	$-0.317624\pi$
$797$	−2.52781	−	1.83656i	−0.0895395	−	0.0650543i	−0.631654	+	0.775250i	$0.717624\pi$
$798$		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	$-0.905606\pi$
$811$	−10.0929	−	31.0627i	−0.354410	−	1.09076i	0.601941	−	0.798540i	$-0.294394\pi$
$812$		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	0.965927	−	0.258815i	$-0.0833320\pi$
$829$	17.4932	+	19.4281i	0.607563	+	0.674767i	−0.358364	+	0.933582i	$0.616665\pi$
$830$	−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	$-0.898381\pi$
$839$	−10.5959	−	32.6107i	−0.365810	−	1.12585i	0.583662	−	0.811997i	$-0.301619\pi$
$840$		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	$-0.180696\pi$
$853$	17.3002	+	12.5693i	0.592347	+	0.430365i	−0.250807	+	0.968037i	$0.580696\pi$
$854$		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	$-0.571827\pi$
$857$	21.4348	−	37.1262i	0.732200	−	1.26821i	0.955941	−	0.293559i	$-0.0948396\pi$
$858$	−11.4114	+	18.5328i	−0.389578	+	0.632698i
$859$	−15.1958	−	26.3198i	−0.518473	−	0.898022i	−0.999770	−	0.0214638i	$-0.993167\pi$
$859$	−15.1958	−	26.3198i	−0.518473	−	0.898022i	0.481297	−	0.876558i	$-0.340166\pi$
$860$	−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	$-0.250555\pi$
$881$	41.9030			1.41175			0.705874	+	0.708338i	$0.250555\pi$
$882$		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	−0.726921	−	0.686722i	$-0.759049\pi$
$887$	−33.1087	+	7.03747i	−1.11168	+	0.236295i	−0.384760	+	0.923017i	$0.625716\pi$
$888$	−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	$-0.729068\pi$
$929$	4.32674	−	41.1662i	0.141956	−	1.35062i	0.801068	−	0.598573i	$-0.204265\pi$
$930$	−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	$-0.691699\pi$
$937$	1.29155	−	0.938364i	0.0421930	−	0.0306550i	0.608682	+	0.793414i	$0.291699\pi$
$938$		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	$-0.670294\pi$
$941$	−6.49336	+	2.89103i	−0.211678	+	0.0942449i	0.298159	+	0.954516i	$0.403627\pi$
$942$	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	−0.734187	−	0.678947i	$-0.762436\pi$
$971$	0.554173	−	0.615471i	0.0177843	−	0.0197514i	0.751971	+	0.659196i	$0.229103\pi$
$972$	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	$-0.977682\pi$
$983$	−30.1910	−	33.5305i	−0.962944	−	1.06946i	0.0345993	−	0.999401i	$-0.488985\pi$
$984$	−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	0.976547	−	0.215305i	$-0.0690746\pi$
$997$	20.8506	+	23.1569i	0.660344	+	0.733387i	−0.316203	+	0.948692i	$0.602408\pi$
$998$	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.f.410.3		32
7.2	even	3	inner	539.2.q.f.520.2		32
7.3	odd	6		77.2.f.b.36.2	yes	16
7.4	even	3		539.2.f.e.344.2		16
7.5	odd	6		539.2.q.g.520.2		32
7.6	odd	2		539.2.q.g.410.3		32
11.4	even	5	inner	539.2.q.f.312.2		32
21.17	even	6		693.2.m.i.190.3		16
77.3	odd	30		847.2.f.w.148.3		16
77.4	even	15		539.2.f.e.246.2		16
77.10	even	6		847.2.f.x.729.3		16
77.17	even	30		847.2.f.v.372.2		16
77.24	even	30		847.2.a.o.1.3		8
77.26	odd	30		539.2.q.g.422.3		32
77.31	odd	30		847.2.a.p.1.6		8
77.37	even	15	inner	539.2.q.f.422.3		32
77.38	odd	30		847.2.f.w.372.3		16
77.46	odd	30		5929.2.a.bs.1.3		8
77.48	odd	10		539.2.q.g.312.2		32
77.52	even	30		847.2.f.v.148.2		16
77.53	even	15		5929.2.a.bt.1.6		8
77.59	odd	30		77.2.f.b.15.2	✓	16
77.73	even	30		847.2.f.x.323.3		16
231.59	even	30		693.2.m.i.631.3		16
231.101	odd	30		7623.2.a.cw.1.6		8
231.185	even	30		7623.2.a.ct.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.2	✓	16	77.59	odd	30
77.2.f.b.36.2	yes	16	7.3	odd	6
539.2.f.e.246.2		16	77.4	even	15
539.2.f.e.344.2		16	7.4	even	3
539.2.q.f.312.2		32	11.4	even	5	inner
539.2.q.f.410.3		32	1.1	even	1	trivial
539.2.q.f.422.3		32	77.37	even	15	inner
539.2.q.f.520.2		32	7.2	even	3	inner
539.2.q.g.312.2		32	77.48	odd	10
539.2.q.g.410.3		32	7.6	odd	2
539.2.q.g.422.3		32	77.26	odd	30
539.2.q.g.520.2		32	7.5	odd	6
693.2.m.i.190.3		16	21.17	even	6
693.2.m.i.631.3		16	231.59	even	30
847.2.a.o.1.3		8	77.24	even	30
847.2.a.p.1.6		8	77.31	odd	30
847.2.f.v.148.2		16	77.52	even	30
847.2.f.v.372.2		16	77.17	even	30
847.2.f.w.148.3		16	77.3	odd	30
847.2.f.w.372.3		16	77.38	odd	30
847.2.f.x.323.3		16	77.73	even	30
847.2.f.x.729.3		16	77.10	even	6
5929.2.a.bs.1.3		8	77.46	odd	30
5929.2.a.bt.1.6		8	77.53	even	15
7623.2.a.ct.1.3		8	231.185	even	30
7623.2.a.cw.1.6		8	231.101	odd	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more