LMFDB - Embedded newform 147.2.e.e.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, 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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.2.e.e.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207107 + 0.358719i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(1.70711 - 2.95680i) q^{5} -0.414214 q^{6} -1.58579 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.207107 + 0.358719i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(1.70711 - 2.95680i) q^{5} -0.414214 q^{6} -1.58579 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.707107 + 1.22474i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-0.914214 + 1.58346i) q^{12} -2.58579 q^{13} +3.41421 q^{15} +(-1.50000 + 2.59808i) q^{16} +(-1.12132 - 1.94218i) q^{17} +(-0.207107 - 0.358719i) q^{18} +(-1.41421 + 2.44949i) q^{19} +6.24264 q^{20} -0.828427 q^{22} +(3.82843 - 6.63103i) q^{23} +(-0.792893 - 1.37333i) q^{24} +(-3.32843 - 5.76500i) q^{25} +(0.535534 - 0.927572i) q^{26} -1.00000 q^{27} -6.82843 q^{29} +(-0.707107 + 1.22474i) q^{30} +(-0.585786 - 1.01461i) q^{31} +(-2.20711 - 3.82282i) q^{32} +(-1.00000 + 1.73205i) q^{33} +0.928932 q^{34} -1.82843 q^{36} +(2.00000 - 3.46410i) q^{37} +(-0.585786 - 1.01461i) q^{38} +(-1.29289 - 2.23936i) q^{39} +(-2.70711 + 4.68885i) q^{40} -6.24264 q^{41} +5.65685 q^{43} +(-1.82843 + 3.16693i) q^{44} +(1.70711 + 2.95680i) q^{45} +(1.58579 + 2.74666i) q^{46} +(-1.41421 + 2.44949i) q^{47} -3.00000 q^{48} +2.75736 q^{50} +(1.12132 - 1.94218i) q^{51} +(-2.36396 - 4.09450i) q^{52} +(1.00000 + 1.73205i) q^{53} +(0.207107 - 0.358719i) q^{54} +6.82843 q^{55} -2.82843 q^{57} +(1.41421 - 2.44949i) q^{58} +(-0.585786 - 1.01461i) q^{59} +(3.12132 + 5.40629i) q^{60} +(6.12132 - 10.6024i) q^{61} +0.485281 q^{62} -4.17157 q^{64} +(-4.41421 + 7.64564i) q^{65} +(-0.414214 - 0.717439i) q^{66} +(2.82843 + 4.89898i) q^{67} +(2.05025 - 3.55114i) q^{68} +7.65685 q^{69} +9.31371 q^{71} +(0.792893 - 1.37333i) q^{72} +(6.94975 + 12.0373i) q^{73} +(0.828427 + 1.43488i) q^{74} +(3.32843 - 5.76500i) q^{75} -5.17157 q^{76} +1.07107 q^{78} +(-6.82843 + 11.8272i) q^{79} +(5.12132 + 8.87039i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.29289 - 2.23936i) q^{82} -7.31371 q^{83} -7.65685 q^{85} +(-1.17157 + 2.02922i) q^{86} +(-3.41421 - 5.91359i) q^{87} +(-1.58579 - 2.74666i) q^{88} +(-7.12132 + 12.3345i) q^{89} -1.41421 q^{90} +14.0000 q^{92} +(0.585786 - 1.01461i) q^{93} +(-0.585786 - 1.01461i) q^{94} +(4.82843 + 8.36308i) q^{95} +(2.20711 - 3.82282i) q^{96} -2.58579 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 - 12 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} - 2 q^{9} + 4 q^{11} + 2 q^{12} - 16 q^{13} + 8 q^{15} - 6 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{20} + 8 q^{22} + 4 q^{23} - 6 q^{24} - 2 q^{25} - 12 q^{26} - 4 q^{27} - 16 q^{29} - 8 q^{31} - 6 q^{32} - 4 q^{33} + 32 q^{34} + 4 q^{36} + 8 q^{37} - 8 q^{38} - 8 q^{39} - 8 q^{40} - 8 q^{41} + 4 q^{44} + 4 q^{45} + 12 q^{46} - 12 q^{48} + 28 q^{50} - 4 q^{51} + 16 q^{52} + 4 q^{53} - 2 q^{54} + 16 q^{55} - 8 q^{59} + 4 q^{60} + 16 q^{61} - 32 q^{62} - 28 q^{64} - 12 q^{65} + 4 q^{66} + 28 q^{68} + 8 q^{69} - 8 q^{71} + 6 q^{72} + 8 q^{73} - 8 q^{74} + 2 q^{75} - 32 q^{76} - 24 q^{78} - 16 q^{79} + 12 q^{80} - 2 q^{81} + 8 q^{82} + 16 q^{83} - 8 q^{85} - 16 q^{86} - 8 q^{87} - 12 q^{88} - 20 q^{89} + 56 q^{92} + 8 q^{93} - 8 q^{94} + 8 q^{95} + 6 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 - 12 * q^8 - 2 * q^9 + 4 * q^11 + 2 * q^12 - 16 * q^13 + 8 * q^15 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^20 + 8 * q^22 + 4 * q^23 - 6 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 - 16 * q^29 - 8 * q^31 - 6 * q^32 - 4 * q^33 + 32 * q^34 + 4 * q^36 + 8 * q^37 - 8 * q^38 - 8 * q^39 - 8 * q^40 - 8 * q^41 + 4 * q^44 + 4 * q^45 + 12 * q^46 - 12 * q^48 + 28 * q^50 - 4 * q^51 + 16 * q^52 + 4 * q^53 - 2 * q^54 + 16 * q^55 - 8 * q^59 + 4 * q^60 + 16 * q^61 - 32 * q^62 - 28 * q^64 - 12 * q^65 + 4 * q^66 + 28 * q^68 + 8 * q^69 - 8 * q^71 + 6 * q^72 + 8 * q^73 - 8 * q^74 + 2 * q^75 - 32 * q^76 - 24 * q^78 - 16 * q^79 + 12 * q^80 - 2 * q^81 + 8 * q^82 + 16 * q^83 - 8 * q^85 - 16 * q^86 - 8 * q^87 - 12 * q^88 - 20 * q^89 + 56 * q^92 + 8 * q^93 - 8 * q^94 + 8 * q^95 + 6 * q^96 - 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.207107	+	0.358719i	−0.146447	+	0.253653i	−0.929912	−	0.367783i	$-0.880117\pi$
$2$	−0.207107	+	0.358719i	−0.146447	+	0.253653i	0.783465	+	0.621436i	$0.213450\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.914214	+	1.58346i	0.457107	+	0.791732i
$5$	1.70711	−	2.95680i	0.763441	−	1.32232i	−0.177625	−	0.984098i	$-0.556842\pi$
$5$	1.70711	−	2.95680i	0.763441	−	1.32232i	0.941067	−	0.338221i	$-0.109825\pi$
$6$	−0.414214			−0.169102
$7$		0			0
$7$		0			0
$8$	−1.58579			−0.560660
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.707107	+	1.22474i	0.223607	+	0.387298i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	−0.914214	+	1.58346i	−0.263911	+	0.457107i
$13$	−2.58579			−0.717168			−0.358584	−	0.933497i	$-0.616740\pi$
$13$	−2.58579			−0.717168			−0.358584	+	0.933497i	$0.616740\pi$
$14$		0			0
$15$	3.41421			0.881546
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−1.12132	−	1.94218i	−0.271960	−	0.471049i	0.697404	−	0.716679i	$-0.254339\pi$
$17$	−1.12132	−	1.94218i	−0.271960	−	0.471049i	−0.969364	+	0.245630i	$0.921005\pi$
$18$	−0.207107	−	0.358719i	−0.0488155	−	0.0845510i
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	−0.981399	−	0.191977i	$-0.938510\pi$
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	0.656957	+	0.753928i	$0.271843\pi$
$20$	6.24264			1.39590
$21$		0			0
$22$	−0.828427			−0.176621
$23$	3.82843	−	6.63103i	0.798282	−	1.38267i	−0.122452	−	0.992474i	$-0.539076\pi$
$23$	3.82843	−	6.63103i	0.798282	−	1.38267i	0.920734	−	0.390191i	$-0.127591\pi$
$24$	−0.792893	−	1.37333i	−0.161849	−	0.280330i
$25$	−3.32843	−	5.76500i	−0.665685	−	1.15300i
$26$	0.535534	−	0.927572i	0.105027	−	0.181912i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−6.82843			−1.26801			−0.634004	−	0.773330i	$-0.718590\pi$
$29$	−6.82843			−1.26801			−0.634004	+	0.773330i	$0.718590\pi$
$30$	−0.707107	+	1.22474i	−0.129099	+	0.223607i
$31$	−0.585786	−	1.01461i	−0.105210	−	0.182230i	0.808614	−	0.588340i	$-0.200218\pi$
$31$	−0.585786	−	1.01461i	−0.105210	−	0.182230i	−0.913824	+	0.406110i	$0.866885\pi$
$32$	−2.20711	−	3.82282i	−0.390165	−	0.675786i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	0.928932			0.159311
$35$		0			0
$36$	−1.82843			−0.304738
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	−0.585786	−	1.01461i	−0.0950271	−	0.164592i
$39$	−1.29289	−	2.23936i	−0.207029	−	0.358584i
$40$	−2.70711	+	4.68885i	−0.428031	+	0.741372i
$41$	−6.24264			−0.974937			−0.487468	−	0.873141i	$-0.662080\pi$
$41$	−6.24264			−0.974937			−0.487468	+	0.873141i	$0.662080\pi$
$42$		0			0
$43$	5.65685			0.862662			0.431331	−	0.902194i	$-0.358044\pi$
$43$	5.65685			0.862662			0.431331	+	0.902194i	$0.358044\pi$
$44$	−1.82843	+	3.16693i	−0.275646	+	0.477432i
$45$	1.70711	+	2.95680i	0.254480	+	0.440773i
$46$	1.58579	+	2.74666i	0.233811	+	0.404973i
$47$	−1.41421	+	2.44949i	−0.206284	+	0.357295i	−0.950541	−	0.310599i	$-0.899470\pi$
$47$	−1.41421	+	2.44949i	−0.206284	+	0.357295i	0.744257	+	0.667893i	$0.232804\pi$
$48$	−3.00000			−0.433013
$49$		0			0
$50$	2.75736			0.389949
$51$	1.12132	−	1.94218i	0.157016	−	0.271960i
$52$	−2.36396	−	4.09450i	−0.327822	−	0.567805i
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$	0.207107	−	0.358719i	0.0281837	−	0.0488155i
$55$	6.82843			0.920745
$56$		0			0
$57$	−2.82843			−0.374634
$58$	1.41421	−	2.44949i	0.185695	−	0.321634i
$59$	−0.585786	−	1.01461i	−0.0762629	−	0.132091i	0.825372	−	0.564589i	$-0.190965\pi$
$59$	−0.585786	−	1.01461i	−0.0762629	−	0.132091i	−0.901635	+	0.432498i	$0.857632\pi$
$60$	3.12132	+	5.40629i	0.402961	+	0.697948i
$61$	6.12132	−	10.6024i	0.783755	−	1.35750i	−0.145985	−	0.989287i	$-0.546635\pi$
$61$	6.12132	−	10.6024i	0.783755	−	1.35750i	0.929740	−	0.368216i	$-0.120031\pi$
$62$	0.485281			0.0616308
$63$		0			0
$64$	−4.17157			−0.521447
$65$	−4.41421	+	7.64564i	−0.547516	+	0.948325i
$66$	−0.414214	−	0.717439i	−0.0509862	−	0.0883106i
$67$	2.82843	+	4.89898i	0.345547	+	0.598506i	0.985453	−	0.169948i	$-0.0543599\pi$
$67$	2.82843	+	4.89898i	0.345547	+	0.598506i	−0.639906	+	0.768453i	$0.721027\pi$
$68$	2.05025	−	3.55114i	0.248630	−	0.430639i
$69$	7.65685			0.921777
$70$		0			0
$71$	9.31371			1.10533			0.552667	−	0.833402i	$-0.313610\pi$
$71$	9.31371			1.10533			0.552667	+	0.833402i	$0.313610\pi$
$72$	0.792893	−	1.37333i	0.0934434	−	0.161849i
$73$	6.94975	+	12.0373i	0.813406	+	1.40886i	0.910467	+	0.413583i	$0.135723\pi$
$73$	6.94975	+	12.0373i	0.813406	+	1.40886i	−0.0970601	+	0.995279i	$0.530944\pi$
$74$	0.828427	+	1.43488i	0.0963027	+	0.166801i
$75$	3.32843	−	5.76500i	0.384334	−	0.665685i
$76$	−5.17157			−0.593220
$77$		0			0
$78$	1.07107			0.121275
$79$	−6.82843	+	11.8272i	−0.768258	+	1.33066i	0.170249	+	0.985401i	$0.445543\pi$
$79$	−6.82843	+	11.8272i	−0.768258	+	1.33066i	−0.938507	+	0.345261i	$0.887790\pi$
$80$	5.12132	+	8.87039i	0.572581	+	0.991739i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.29289	−	2.23936i	0.142776	−	0.247296i
$83$	−7.31371			−0.802784			−0.401392	−	0.915906i	$-0.631473\pi$
$83$	−7.31371			−0.802784			−0.401392	+	0.915906i	$0.631473\pi$
$84$		0			0
$85$	−7.65685			−0.830502
$86$	−1.17157	+	2.02922i	−0.126334	+	0.218817i
$87$	−3.41421	−	5.91359i	−0.366042	−	0.634004i
$88$	−1.58579	−	2.74666i	−0.169045	−	0.292795i
$89$	−7.12132	+	12.3345i	−0.754858	+	1.30745i	0.190586	+	0.981670i	$0.438961\pi$
$89$	−7.12132	+	12.3345i	−0.754858	+	1.30745i	−0.945445	+	0.325783i	$0.894372\pi$
$90$	−1.41421			−0.149071
$91$		0			0
$92$	14.0000			1.45960
$93$	0.585786	−	1.01461i	0.0607432	−	0.105210i
$94$	−0.585786	−	1.01461i	−0.0604193	−	0.104649i
$95$	4.82843	+	8.36308i	0.495386	+	0.858034i
$96$	2.20711	−	3.82282i	0.225262	−	0.390165i
$97$	−2.58579			−0.262547			−0.131273	−	0.991346i	$-0.541907\pi$
$97$	−2.58579			−0.262547			−0.131273	+	0.991346i	$0.541907\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	6.08579	−	10.5409i	0.608579	−	1.05409i
$101$	1.46447	+	2.53653i	0.145720	+	0.252394i	0.929641	−	0.368466i	$-0.120117\pi$
$101$	1.46447	+	2.53653i	0.145720	+	0.252394i	−0.783921	+	0.620860i	$0.786784\pi$
$102$	0.464466	+	0.804479i	0.0459890	+	0.0796553i
$103$	2.24264	−	3.88437i	0.220974	−	0.382738i	−0.734130	−	0.679009i	$-0.762410\pi$
$103$	2.24264	−	3.88437i	0.220974	−	0.382738i	0.955104	+	0.296271i	$0.0957431\pi$
$104$	4.10051			0.402088
$105$		0			0
$106$	−0.828427			−0.0804640
$107$	0.171573	−	0.297173i	0.0165866	−	0.0287288i	−0.857613	−	0.514296i	$-0.828053\pi$
$107$	0.171573	−	0.297173i	0.0165866	−	0.0287288i	0.874200	+	0.485567i	$0.161387\pi$
$108$	−0.914214	−	1.58346i	−0.0879702	−	0.152369i
$109$	2.82843	+	4.89898i	0.270914	+	0.469237i	0.969096	−	0.246683i	$-0.0793407\pi$
$109$	2.82843	+	4.89898i	0.270914	+	0.469237i	−0.698182	+	0.715920i	$0.746007\pi$
$110$	−1.41421	+	2.44949i	−0.134840	+	0.233550i
$111$	4.00000			0.379663
$112$		0			0
$113$	−5.31371			−0.499872			−0.249936	−	0.968262i	$-0.580410\pi$
$113$	−5.31371			−0.499872			−0.249936	+	0.968262i	$0.580410\pi$
$114$	0.585786	−	1.01461i	0.0548639	−	0.0950271i
$115$	−13.0711	−	22.6398i	−1.21888	−	2.11117i
$116$	−6.24264	−	10.8126i	−0.579615	−	1.00392i
$117$	1.29289	−	2.23936i	0.119528	−	0.207029i
$118$	0.485281			0.0446738
$119$		0			0
$120$	−5.41421			−0.494248
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	2.53553	+	4.39167i	0.229556	+	0.397603i
$123$	−3.12132	−	5.40629i	−0.281440	−	0.487468i
$124$	1.07107	−	1.85514i	0.0961847	−	0.166597i
$125$	−5.65685			−0.505964
$126$		0			0
$127$	−1.65685			−0.147022			−0.0735110	−	0.997294i	$-0.523420\pi$
$127$	−1.65685			−0.147022			−0.0735110	+	0.997294i	$0.523420\pi$
$128$	5.27817	−	9.14207i	0.466529	−	0.808052i
$129$	2.82843	+	4.89898i	0.249029	+	0.431331i
$130$	−1.82843	−	3.16693i	−0.160364	−	0.277758i
$131$	−7.65685	+	13.2621i	−0.668982	+	1.15871i	0.309207	+	0.950995i	$0.399937\pi$
$131$	−7.65685	+	13.2621i	−0.668982	+	1.15871i	−0.978189	+	0.207717i	$0.933397\pi$
$132$	−3.65685			−0.318288
$133$		0			0
$134$	−2.34315			−0.202417
$135$	−1.70711	+	2.95680i	−0.146924	+	0.254480i
$136$	1.77817	+	3.07989i	0.152477	+	0.264098i
$137$	−7.07107	−	12.2474i	−0.604122	−	1.04637i	−0.992190	−	0.124739i	$-0.960191\pi$
$137$	−7.07107	−	12.2474i	−0.604122	−	1.04637i	0.388067	−	0.921631i	$-0.373143\pi$
$138$	−1.58579	+	2.74666i	−0.134991	+	0.233811i
$139$	17.6569			1.49763			0.748817	−	0.662776i	$-0.230622\pi$
$139$	17.6569			1.49763			0.748817	+	0.662776i	$0.230622\pi$
$140$		0			0
$141$	−2.82843			−0.238197
$142$	−1.92893	+	3.34101i	−0.161872	+	0.280371i
$143$	−2.58579	−	4.47871i	−0.216234	−	0.374529i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	−11.6569	+	20.1903i	−0.968049	+	1.67671i
$146$	−5.75736			−0.476482
$147$		0			0
$148$	7.31371			0.601183
$149$	−8.65685	+	14.9941i	−0.709197	+	1.22837i	0.255958	+	0.966688i	$0.417609\pi$
$149$	−8.65685	+	14.9941i	−0.709197	+	1.22837i	−0.965155	+	0.261678i	$0.915724\pi$
$150$	1.37868	+	2.38794i	0.112569	+	0.194975i
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	0.511636	−	0.859202i	$-0.329040\pi$
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	−0.999909	+	0.0134886i	$0.995706\pi$
$152$	2.24264	−	3.88437i	0.181902	−	0.315064i
$153$	2.24264			0.181307
$154$		0			0
$155$	−4.00000			−0.321288
$156$	2.36396	−	4.09450i	0.189268	−	0.327822i
$157$	5.87868	+	10.1822i	0.469170	+	0.812626i	0.999379	−	0.0352411i	$-0.0112199\pi$
$157$	5.87868	+	10.1822i	0.469170	+	0.812626i	−0.530209	+	0.847867i	$0.677887\pi$
$158$	−2.82843	−	4.89898i	−0.225018	−	0.389742i
$159$	−1.00000	+	1.73205i	−0.0793052	+	0.137361i
$160$	−15.0711			−1.19147
$161$		0			0
$162$	0.414214			0.0325437
$163$	5.65685	−	9.79796i	0.443079	−	0.767435i	−0.554837	−	0.831959i	$-0.687219\pi$
$163$	5.65685	−	9.79796i	0.443079	−	0.767435i	0.997916	+	0.0645236i	$0.0205528\pi$
$164$	−5.70711	−	9.88500i	−0.445650	−	0.771889i
$165$	3.41421	+	5.91359i	0.265796	+	0.460372i
$166$	1.51472	−	2.62357i	0.117565	−	0.203628i
$167$	19.7990			1.53209			0.766046	−	0.642786i	$-0.222221\pi$
$167$	19.7990			1.53209			0.766046	+	0.642786i	$0.222221\pi$
$168$		0			0
$169$	−6.31371			−0.485670
$170$	1.58579	−	2.74666i	0.121624	−	0.210659i
$171$	−1.41421	−	2.44949i	−0.108148	−	0.187317i
$172$	5.17157	+	8.95743i	0.394329	+	0.682997i
$173$	10.5355	−	18.2481i	0.801002	−	1.38738i	−0.117956	−	0.993019i	$-0.537634\pi$
$173$	10.5355	−	18.2481i	0.801002	−	1.38738i	0.918957	−	0.394357i	$-0.129033\pi$
$174$	2.82843			0.214423
$175$		0			0
$176$	−6.00000			−0.452267
$177$	0.585786	−	1.01461i	0.0440304	−	0.0762629i
$178$	−2.94975	−	5.10911i	−0.221093	−	0.382944i
$179$	9.82843	+	17.0233i	0.734611	+	1.27238i	0.954894	+	0.296948i	$0.0959687\pi$
$179$	9.82843	+	17.0233i	0.734611	+	1.27238i	−0.220283	+	0.975436i	$0.570698\pi$
$180$	−3.12132	+	5.40629i	−0.232649	+	0.402961i
$181$	2.58579			0.192200			0.0961000	−	0.995372i	$-0.469363\pi$
$181$	2.58579			0.192200			0.0961000	+	0.995372i	$0.469363\pi$
$182$		0			0
$183$	12.2426			0.905002
$184$	−6.07107	+	10.5154i	−0.447565	+	0.775205i
$185$	−6.82843	−	11.8272i	−0.502036	−	0.869552i
$186$	0.242641	+	0.420266i	0.0177913	+	0.0308154i
$187$	2.24264	−	3.88437i	0.163998	−	0.284053i
$188$	−5.17157			−0.377176
$189$		0			0
$190$	−4.00000			−0.290191
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	−2.08579	−	3.61269i	−0.150529	−	0.260723i
$193$	−2.65685	−	4.60181i	−0.191245	−	0.331245i	0.754418	−	0.656394i	$-0.227919\pi$
$193$	−2.65685	−	4.60181i	−0.191245	−	0.331245i	−0.945663	+	0.325149i	$0.894586\pi$
$194$	0.535534	−	0.927572i	0.0384491	−	0.0665958i
$195$	−8.82843			−0.632217
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	0.414214	−	0.717439i	0.0294369	−	0.0509862i
$199$	10.8284	+	18.7554i	0.767607	+	1.32953i	0.938857	+	0.344307i	$0.111886\pi$
$199$	10.8284	+	18.7554i	0.767607	+	1.32953i	−0.171250	+	0.985228i	$0.554781\pi$
$200$	5.27817	+	9.14207i	0.373223	+	0.646442i
$201$	−2.82843	+	4.89898i	−0.199502	+	0.345547i
$202$	−1.21320			−0.0853607
$203$		0			0
$204$	4.10051			0.287093
$205$	−10.6569	+	18.4582i	−0.744307	+	1.28918i
$206$	0.928932	+	1.60896i	0.0647218	+	0.112101i
$207$	3.82843	+	6.63103i	0.266094	+	0.460888i
$208$	3.87868	−	6.71807i	0.268938	−	0.465814i
$209$	−5.65685			−0.391293
$210$		0			0
$211$	12.9706			0.892930			0.446465	−	0.894801i	$-0.352683\pi$
$211$	12.9706			0.892930			0.446465	+	0.894801i	$0.352683\pi$
$212$	−1.82843	+	3.16693i	−0.125577	+	0.217506i
$213$	4.65685	+	8.06591i	0.319082	+	0.552667i
$214$	0.0710678	+	0.123093i	0.00485810	+	0.00841447i
$215$	9.65685	−	16.7262i	0.658592	−	1.14071i
$216$	1.58579			0.107899
$217$		0			0
$218$	−2.34315			−0.158698
$219$	−6.94975	+	12.0373i	−0.469620	+	0.813406i
$220$	6.24264	+	10.8126i	0.420879	+	0.728983i
$221$	2.89949	+	5.02207i	0.195041	+	0.337821i
$222$	−0.828427	+	1.43488i	−0.0556004	+	0.0963027i
$223$	−24.9706			−1.67215			−0.836076	−	0.548613i	$-0.815156\pi$
$223$	−24.9706			−1.67215			−0.836076	+	0.548613i	$0.815156\pi$
$224$		0			0
$225$	6.65685			0.443790
$226$	1.10051	−	1.90613i	0.0732045	−	0.126794i
$227$	11.8995	+	20.6105i	0.789797	+	1.36797i	0.926091	+	0.377300i	$0.123148\pi$
$227$	11.8995	+	20.6105i	0.789797	+	1.36797i	−0.136294	+	0.990668i	$0.543519\pi$
$228$	−2.58579	−	4.47871i	−0.171248	−	0.296610i
$229$	−0.121320	+	0.210133i	−0.00801707	+	0.0138860i	−0.870006	−	0.493041i	$-0.835885\pi$
$229$	−0.121320	+	0.210133i	−0.00801707	+	0.0138860i	0.861989	+	0.506927i	$0.169219\pi$
$230$	10.8284			0.714005
$231$		0			0
$232$	10.8284			0.710921
$233$	3.07107	−	5.31925i	0.201192	−	0.348475i	−0.747721	−	0.664014i	$-0.768852\pi$
$233$	3.07107	−	5.31925i	0.201192	−	0.348475i	0.948913	+	0.315538i	$0.102185\pi$
$234$	0.535534	+	0.927572i	0.0350089	+	0.0606373i
$235$	4.82843	+	8.36308i	0.314972	+	0.545547i
$236$	1.07107	−	1.85514i	0.0697206	−	0.120760i
$237$	−13.6569			−0.887108
$238$		0			0
$239$	−15.6569			−1.01276			−0.506379	−	0.862311i	$-0.669016\pi$
$239$	−15.6569			−1.01276			−0.506379	+	0.862311i	$0.669016\pi$
$240$	−5.12132	+	8.87039i	−0.330580	+	0.572581i
$241$	−8.12132	−	14.0665i	−0.523140	−	0.906105i	−0.999637	−	0.0269294i	$-0.991427\pi$
$241$	−8.12132	−	14.0665i	−0.523140	−	0.906105i	0.476497	−	0.879176i	$-0.341906\pi$
$242$	1.44975	+	2.51104i	0.0931933	+	0.161416i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	22.3848			1.43304
$245$		0			0
$246$	2.58579			0.164864
$247$	3.65685	−	6.33386i	0.232680	−	0.403014i
$248$	0.928932	+	1.60896i	0.0589873	+	0.102169i
$249$	−3.65685	−	6.33386i	−0.231744	−	0.401392i
$250$	1.17157	−	2.02922i	0.0740968	−	0.128339i
$251$	12.4853			0.788064			0.394032	−	0.919097i	$-0.371080\pi$
$251$	12.4853			0.788064			0.394032	+	0.919097i	$0.371080\pi$
$252$		0			0
$253$	15.3137			0.962765
$254$	0.343146	−	0.594346i	0.0215309	−	0.0372926i
$255$	−3.82843	−	6.63103i	−0.239745	−	0.415251i
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	11.6066	−	20.1032i	0.724000	−	1.25400i	−0.235384	−	0.971902i	$-0.575635\pi$
$257$	11.6066	−	20.1032i	0.724000	−	1.25400i	0.959384	−	0.282102i	$-0.0910318\pi$
$258$	−2.34315			−0.145878
$259$		0			0
$260$	−16.1421			−1.00109
$261$	3.41421	−	5.91359i	0.211335	−	0.366042i
$262$	−3.17157	−	5.49333i	−0.195940	−	0.339379i
$263$	−2.65685	−	4.60181i	−0.163829	−	0.283760i	0.772410	−	0.635124i	$-0.219051\pi$
$263$	−2.65685	−	4.60181i	−0.163829	−	0.283760i	−0.936239	+	0.351365i	$0.885718\pi$
$264$	1.58579	−	2.74666i	0.0975984	−	0.169045i
$265$	6.82843			0.419467
$266$		0			0
$267$	−14.2426			−0.871635
$268$	−5.17157	+	8.95743i	−0.315904	+	0.547162i
$269$	−7.36396	−	12.7548i	−0.448989	−	0.777671i	0.549332	−	0.835604i	$-0.314882\pi$
$269$	−7.36396	−	12.7548i	−0.448989	−	0.777671i	−0.998320	+	0.0579332i	$0.981549\pi$
$270$	−0.707107	−	1.22474i	−0.0430331	−	0.0745356i
$271$	−5.07107	+	8.78335i	−0.308045	+	0.533550i	−0.977935	−	0.208911i	$-0.933008\pi$
$271$	−5.07107	+	8.78335i	−0.308045	+	0.533550i	0.669889	+	0.742461i	$0.266342\pi$
$272$	6.72792			0.407940
$273$		0			0
$274$	5.85786			0.353887
$275$	6.65685	−	11.5300i	0.401423	−	0.695286i
$276$	7.00000	+	12.1244i	0.421350	+	0.729800i
$277$	4.65685	+	8.06591i	0.279803	+	0.484633i	0.971336	−	0.237712i	$-0.0763974\pi$
$277$	4.65685	+	8.06591i	0.279803	+	0.484633i	−0.691532	+	0.722345i	$0.743064\pi$
$278$	−3.65685	+	6.33386i	−0.219324	+	0.379880i
$279$	1.17157			0.0701402
$280$		0			0
$281$	0.485281			0.0289495			0.0144747	−	0.999895i	$-0.495392\pi$
$281$	0.485281			0.0289495			0.0144747	+	0.999895i	$0.495392\pi$
$282$	0.585786	−	1.01461i	0.0348831	−	0.0604193i
$283$	−4.24264	−	7.34847i	−0.252199	−	0.436821i	0.711932	−	0.702248i	$-0.247820\pi$
$283$	−4.24264	−	7.34847i	−0.252199	−	0.436821i	−0.964131	+	0.265427i	$0.914487\pi$
$284$	8.51472	+	14.7479i	0.505256	+	0.875128i
$285$	−4.82843	+	8.36308i	−0.286011	+	0.495386i
$286$	2.14214			0.126667
$287$		0			0
$288$	4.41421			0.260110
$289$	5.98528	−	10.3668i	0.352075	−	0.609812i
$290$	−4.82843	−	8.36308i	−0.283535	−	0.491097i
$291$	−1.29289	−	2.23936i	−0.0757907	−	0.131273i
$292$	−12.7071	+	22.0094i	−0.743627	+	1.28800i
$293$	−16.5858			−0.968952			−0.484476	−	0.874805i	$-0.660990\pi$
$293$	−16.5858			−0.968952			−0.484476	+	0.874805i	$0.660990\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	−3.17157	+	5.49333i	−0.184344	+	0.319293i
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$	−3.58579	−	6.21076i	−0.207719	−	0.359780i
$299$	−9.89949	+	17.1464i	−0.572503	+	0.991604i
$300$	12.1716			0.702726
$301$		0			0
$302$	4.97056			0.286024
$303$	−1.46447	+	2.53653i	−0.0841314	+	0.145720i
$304$	−4.24264	−	7.34847i	−0.243332	−	0.421464i
$305$	−20.8995	−	36.1990i	−1.19670	−	2.07275i
$306$	−0.464466	+	0.804479i	−0.0265518	+	0.0459890i
$307$	−30.1421			−1.72030			−0.860151	−	0.510039i	$-0.829631\pi$
$307$	−30.1421			−1.72030			−0.860151	+	0.510039i	$0.829631\pi$
$308$		0			0
$309$	4.48528			0.255159
$310$	0.828427	−	1.43488i	0.0470515	−	0.0814956i
$311$	3.07107	+	5.31925i	0.174144	+	0.301627i	0.939865	−	0.341547i	$-0.110951\pi$
$311$	3.07107	+	5.31925i	0.174144	+	0.301627i	−0.765721	+	0.643173i	$0.777617\pi$
$312$	2.05025	+	3.55114i	0.116073	+	0.201044i
$313$	0.949747	−	1.64501i	0.0536829	−	0.0929815i	−0.837935	−	0.545770i	$-0.816237\pi$
$313$	0.949747	−	1.64501i	0.0536829	−	0.0929815i	0.891618	+	0.452788i	$0.149571\pi$
$314$	−4.87006			−0.274833
$315$		0			0
$316$	−24.9706			−1.40470
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	−0.971589	−	0.236675i	$-0.923942\pi$
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	0.690761	+	0.723083i	$0.257276\pi$
$318$	−0.414214	−	0.717439i	−0.0232279	−	0.0402320i
$319$	−6.82843	−	11.8272i	−0.382319	−	0.662195i
$320$	−7.12132	+	12.3345i	−0.398094	+	0.689519i
$321$	0.343146			0.0191525
$322$		0			0
$323$	6.34315			0.352942
$324$	0.914214	−	1.58346i	0.0507896	−	0.0879702i
$325$	8.60660	+	14.9071i	0.477408	+	0.826896i
$326$	2.34315	+	4.05845i	0.129775	+	0.224777i
$327$	−2.82843	+	4.89898i	−0.156412	+	0.270914i
$328$	9.89949			0.546608
$329$		0			0
$330$	−2.82843			−0.155700
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−6.68629	−	11.5810i	−0.366958	−	0.635590i
$333$	2.00000	+	3.46410i	0.109599	+	0.189832i
$334$	−4.10051	+	7.10228i	−0.224370	+	0.388620i
$335$	19.3137			1.05522
$336$		0			0
$337$	−29.6569			−1.61551			−0.807756	−	0.589517i	$-0.799318\pi$
$337$	−29.6569			−1.61551			−0.807756	+	0.589517i	$0.799318\pi$
$338$	1.30761	−	2.26485i	0.0711247	−	0.123192i
$339$	−2.65685	−	4.60181i	−0.144301	−	0.249936i
$340$	−7.00000	−	12.1244i	−0.379628	−	0.657536i
$341$	1.17157	−	2.02922i	0.0634442	−	0.109889i
$342$	1.17157			0.0633514
$343$		0			0
$344$	−8.97056			−0.483660
$345$	13.0711	−	22.6398i	0.703723	−	1.21888i
$346$	4.36396	+	7.55860i	0.234608	+	0.406353i
$347$	−16.6569	−	28.8505i	−0.894187	−	1.54878i	−0.834808	−	0.550541i	$-0.814421\pi$
$347$	−16.6569	−	28.8505i	−0.894187	−	1.54878i	−0.0593789	−	0.998236i	$-0.518912\pi$
$348$	6.24264	−	10.8126i	0.334641	−	0.579615i
$349$	9.89949			0.529908			0.264954	−	0.964261i	$-0.414643\pi$
$349$	9.89949			0.529908			0.264954	+	0.964261i	$0.414643\pi$
$350$		0			0
$351$	2.58579			0.138019
$352$	4.41421	−	7.64564i	0.235278	−	0.407514i
$353$	−7.36396	−	12.7548i	−0.391944	−	0.678867i	0.600762	−	0.799428i	$-0.294864\pi$
$353$	−7.36396	−	12.7548i	−0.391944	−	0.678867i	−0.992706	+	0.120561i	$0.961531\pi$
$354$	0.242641	+	0.420266i	0.0128962	+	0.0223369i
$355$	15.8995	−	27.5387i	0.843858	−	1.46160i
$356$	−26.0416			−1.38020
$357$		0			0
$358$	−8.14214			−0.430325
$359$	0.171573	−	0.297173i	0.00905527	−	0.0156842i	−0.861462	−	0.507822i	$-0.830451\pi$
$359$	0.171573	−	0.297173i	0.00905527	−	0.0156842i	0.870518	+	0.492137i	$0.163784\pi$
$360$	−2.70711	−	4.68885i	−0.142677	−	0.247124i
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	−0.535534	+	0.927572i	−0.0281470	+	0.0487521i
$363$	7.00000			0.367405
$364$		0			0
$365$	47.4558			2.48395
$366$	−2.53553	+	4.39167i	−0.132534	+	0.229556i
$367$	−1.65685	−	2.86976i	−0.0864871	−	0.149800i	0.819537	−	0.573027i	$-0.194231\pi$
$367$	−1.65685	−	2.86976i	−0.0864871	−	0.149800i	−0.906024	+	0.423226i	$0.860897\pi$
$368$	11.4853	+	19.8931i	0.598712	+	1.03700i
$369$	3.12132	−	5.40629i	0.162489	−	0.281440i
$370$	5.65685			0.294086
$371$		0			0
$372$	2.14214			0.111065
$373$	5.34315	−	9.25460i	0.276658	−	0.479185i	−0.693894	−	0.720077i	$-0.744107\pi$
$373$	5.34315	−	9.25460i	0.276658	−	0.479185i	0.970552	+	0.240892i	$0.0774399\pi$
$374$	0.928932	+	1.60896i	0.0480339	+	0.0831972i
$375$	−2.82843	−	4.89898i	−0.146059	−	0.252982i
$376$	2.24264	−	3.88437i	0.115655	−	0.200321i
$377$	17.6569			0.909374
$378$		0			0
$379$	8.68629			0.446185			0.223092	−	0.974797i	$-0.428385\pi$
$379$	8.68629			0.446185			0.223092	+	0.974797i	$0.428385\pi$
$380$	−8.82843	+	15.2913i	−0.452889	+	0.784426i
$381$	−0.828427	−	1.43488i	−0.0424416	−	0.0735110i
$382$	3.72792	+	6.45695i	0.190737	+	0.330366i
$383$	−9.17157	+	15.8856i	−0.468645	+	0.811718i	−0.999358	−	0.0358343i	$-0.988591\pi$
$383$	−9.17157	+	15.8856i	−0.468645	+	0.811718i	0.530712	+	0.847552i	$0.321924\pi$
$384$	10.5563			0.538701
$385$		0			0
$386$	2.20101			0.112028
$387$	−2.82843	+	4.89898i	−0.143777	+	0.249029i
$388$	−2.36396	−	4.09450i	−0.120012	−	0.207867i
$389$	9.07107	+	15.7116i	0.459921	+	0.796607i	0.998956	−	0.0456762i	$-0.0145442\pi$
$389$	9.07107	+	15.7116i	0.459921	+	0.796607i	−0.539035	+	0.842283i	$0.681211\pi$
$390$	1.82843	−	3.16693i	0.0925860	−	0.160364i
$391$	−17.1716			−0.868404
$392$		0			0
$393$	−15.3137			−0.772474
$394$	−0.414214	+	0.717439i	−0.0208678	+	0.0361441i
$395$	23.3137	+	40.3805i	1.17304	+	2.03176i
$396$	−1.82843	−	3.16693i	−0.0918819	−	0.159144i
$397$	−1.19239	+	2.06528i	−0.0598442	+	0.103653i	−0.894395	−	0.447277i	$-0.852394\pi$
$397$	−1.19239	+	2.06528i	−0.0598442	+	0.103653i	0.834551	+	0.550931i	$0.185727\pi$
$398$	−8.97056			−0.449654
$399$		0			0
$400$	19.9706			0.998528
$401$	3.07107	−	5.31925i	0.153362	−	0.265630i	−0.779100	−	0.626900i	$-0.784323\pi$
$401$	3.07107	−	5.31925i	0.153362	−	0.265630i	0.932461	+	0.361270i	$0.117657\pi$
$402$	−1.17157	−	2.02922i	−0.0584327	−	0.101208i
$403$	1.51472	+	2.62357i	0.0754535	+	0.130689i
$404$	−2.67767	+	4.63786i	−0.133219	+	0.230742i
$405$	−3.41421			−0.169654
$406$		0			0
$407$	8.00000			0.396545
$408$	−1.77817	+	3.07989i	−0.0880328	+	0.152477i
$409$	−10.7071	−	18.5453i	−0.529432	−	0.917004i	−0.999411	−	0.0343258i	$-0.989072\pi$
$409$	−10.7071	−	18.5453i	−0.529432	−	0.917004i	0.469978	−	0.882678i	$-0.344262\pi$
$410$	−4.41421	−	7.64564i	−0.218002	−	0.377591i
$411$	7.07107	−	12.2474i	0.348790	−	0.604122i
$412$	8.20101			0.404035
$413$		0			0
$414$	−3.17157			−0.155874
$415$	−12.4853	+	21.6251i	−0.612878	+	1.06154i
$416$	5.70711	+	9.88500i	0.279814	+	0.484652i
$417$	8.82843	+	15.2913i	0.432330	+	0.748817i
$418$	1.17157	−	2.02922i	0.0573035	−	0.0992526i
$419$	−33.1716			−1.62054			−0.810269	−	0.586059i	$-0.800679\pi$
$419$	−33.1716			−1.62054			−0.810269	+	0.586059i	$0.800679\pi$
$420$		0			0
$421$	16.6274			0.810371			0.405185	−	0.914235i	$-0.367207\pi$
$421$	16.6274			0.810371			0.405185	+	0.914235i	$0.367207\pi$
$422$	−2.68629	+	4.65279i	−0.130767	+	0.226494i
$423$	−1.41421	−	2.44949i	−0.0687614	−	0.119098i
$424$	−1.58579	−	2.74666i	−0.0770126	−	0.133390i
$425$	−7.46447	+	12.9288i	−0.362080	+	0.627141i
$426$	−3.85786			−0.186914
$427$		0			0
$428$	0.627417			0.0303273
$429$	2.58579	−	4.47871i	0.124843	−	0.216234i
$430$	4.00000	+	6.92820i	0.192897	+	0.334108i
$431$	13.4853	+	23.3572i	0.649563	+	1.12508i	0.983227	+	0.182384i	$0.0583815\pi$
$431$	13.4853	+	23.3572i	0.649563	+	1.12508i	−0.333664	+	0.942692i	$0.608285\pi$
$432$	1.50000	−	2.59808i	0.0721688	−	0.125000i
$433$	20.2426			0.972799			0.486400	−	0.873736i	$-0.338310\pi$
$433$	20.2426			0.972799			0.486400	+	0.873736i	$0.338310\pi$
$434$		0			0
$435$	−23.3137			−1.11781
$436$	−5.17157	+	8.95743i	−0.247673	+	0.428983i
$437$	10.8284	+	18.7554i	0.517994	+	0.897192i
$438$	−2.87868	−	4.98602i	−0.137549	−	0.238241i
$439$	6.34315	−	10.9867i	0.302742	−	0.524364i	−0.674014	−	0.738718i	$-0.735431\pi$
$439$	6.34315	−	10.9867i	0.302742	−	0.524364i	0.976756	+	0.214354i	$0.0687647\pi$
$440$	−10.8284			−0.516225
$441$		0			0
$442$	−2.40202			−0.114252
$443$	−17.4853	+	30.2854i	−0.830751	+	1.43890i	0.0666929	+	0.997774i	$0.478755\pi$
$443$	−17.4853	+	30.2854i	−0.830751	+	1.43890i	−0.897444	+	0.441129i	$0.854578\pi$
$444$	3.65685	+	6.33386i	0.173547	+	0.300592i
$445$	24.3137	+	42.1126i	1.15258	+	1.99633i
$446$	5.17157	−	8.95743i	0.244881	−	0.424146i
$447$	−17.3137			−0.818910
$448$		0			0
$449$	−5.31371			−0.250769			−0.125385	−	0.992108i	$-0.540017\pi$
$449$	−5.31371			−0.250769			−0.125385	+	0.992108i	$0.540017\pi$
$450$	−1.37868	+	2.38794i	−0.0649916	+	0.112569i
$451$	−6.24264	−	10.8126i	−0.293954	−	0.509144i
$452$	−4.85786	−	8.41407i	−0.228495	−	0.395764i
$453$	6.00000	−	10.3923i	0.281905	−	0.488273i
$454$	−9.85786			−0.462652
$455$		0			0
$456$	4.48528			0.210043
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	−0.575036	−	0.818128i	$-0.695012\pi$
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	0.996038	+	0.0889312i	$0.0283451\pi$
$458$	−0.0502525	−	0.0870399i	−0.00234815	−	0.00406711i
$459$	1.12132	+	1.94218i	0.0523388	+	0.0906534i
$460$	23.8995	−	41.3951i	1.11432	−	1.93006i
$461$	16.5858			0.772477			0.386239	−	0.922399i	$-0.373774\pi$
$461$	16.5858			0.772477			0.386239	+	0.922399i	$0.373774\pi$
$462$		0			0
$463$	−26.6274			−1.23748			−0.618741	−	0.785595i	$-0.712357\pi$
$463$	−26.6274			−1.23748			−0.618741	+	0.785595i	$0.712357\pi$
$464$	10.2426	−	17.7408i	0.475503	−	0.823595i
$465$	−2.00000	−	3.46410i	−0.0927478	−	0.160644i
$466$	1.27208	+	2.20330i	0.0589279	+	0.102066i
$467$	0.100505	−	0.174080i	0.00465082	−	0.00805546i	−0.863691	−	0.504022i	$-0.831853\pi$
$467$	0.100505	−	0.174080i	0.00465082	−	0.00805546i	0.868341	+	0.495967i	$0.165186\pi$
$468$	4.72792			0.218548
$469$		0			0
$470$	−4.00000			−0.184506
$471$	−5.87868	+	10.1822i	−0.270875	+	0.469170i
$472$	0.928932	+	1.60896i	0.0427576	+	0.0740583i
$473$	5.65685	+	9.79796i	0.260102	+	0.450511i
$474$	2.82843	−	4.89898i	0.129914	−	0.225018i
$475$	18.8284			0.863907
$476$		0			0
$477$	−2.00000			−0.0915737
$478$	3.24264	−	5.61642i	0.148315	−	0.256889i
$479$	0.928932	+	1.60896i	0.0424440	+	0.0735152i	0.886467	−	0.462792i	$-0.153152\pi$
$479$	0.928932	+	1.60896i	0.0424440	+	0.0735152i	−0.844023	+	0.536307i	$0.819819\pi$
$480$	−7.53553	−	13.0519i	−0.343948	−	0.595736i
$481$	−5.17157	+	8.95743i	−0.235803	+	0.408424i
$482$	6.72792			0.306448
$483$		0			0
$484$	12.7990			0.581772
$485$	−4.41421	+	7.64564i	−0.200439	+	0.347171i
$486$	0.207107	+	0.358719i	0.00939455	+	0.0162718i
$487$	−13.3137	−	23.0600i	−0.603302	−	1.04495i	−0.992317	−	0.123718i	$-0.960518\pi$
$487$	−13.3137	−	23.0600i	−0.603302	−	1.04495i	0.389016	−	0.921231i	$-0.372815\pi$
$488$	−9.70711	+	16.8132i	−0.439420	+	0.761098i
$489$	11.3137			0.511624
$490$		0			0
$491$	5.02944			0.226975			0.113488	−	0.993539i	$-0.463798\pi$
$491$	5.02944			0.226975			0.113488	+	0.993539i	$0.463798\pi$
$492$	5.70711	−	9.88500i	0.257296	−	0.445650i
$493$	7.65685	+	13.2621i	0.344847	+	0.597293i
$494$	1.51472	+	2.62357i	0.0681504	+	0.118040i
$495$	−3.41421	+	5.91359i	−0.153457	+	0.265796i
$496$	3.51472			0.157816
$497$		0			0
$498$	3.02944			0.135752
$499$	−1.65685	+	2.86976i	−0.0741710	+	0.128468i	−0.900725	−	0.434389i	$-0.856964\pi$
$499$	−1.65685	+	2.86976i	−0.0741710	+	0.128468i	0.826554	+	0.562857i	$0.190298\pi$
$500$	−5.17157	−	8.95743i	−0.231280	−	0.400588i
$501$	9.89949	+	17.1464i	0.442277	+	0.766046i
$502$	−2.58579	+	4.47871i	−0.115409	+	0.199895i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	−3.17157	+	5.49333i	−0.140994	+	0.244208i
$507$	−3.15685	−	5.46783i	−0.140201	−	0.242835i
$508$	−1.51472	−	2.62357i	−0.0672048	−	0.116402i
$509$	2.77817	−	4.81194i	0.123140	−	0.213285i	−0.797864	−	0.602837i	$-0.794037\pi$
$509$	2.77817	−	4.81194i	0.123140	−	0.213285i	0.921005	+	0.389552i	$0.127370\pi$
$510$	3.17157			0.140440
$511$		0			0
$512$	22.7574			1.00574
$513$	1.41421	−	2.44949i	0.0624391	−	0.108148i
$514$	4.80761	+	8.32703i	0.212055	+	0.367289i
$515$	−7.65685	−	13.2621i	−0.337401	−	0.584396i
$516$	−5.17157	+	8.95743i	−0.227666	+	0.394329i
$517$	−5.65685			−0.248788
$518$		0			0
$519$	21.0711			0.924917
$520$	7.00000	−	12.1244i	0.306970	−	0.531688i
$521$	−17.7071	−	30.6696i	−0.775762	−	1.34366i	−0.934365	−	0.356317i	$-0.884032\pi$
$521$	−17.7071	−	30.6696i	−0.775762	−	1.34366i	0.158603	−	0.987343i	$-0.449301\pi$
$522$	1.41421	+	2.44949i	0.0618984	+	0.107211i
$523$	−12.8284	+	22.2195i	−0.560948	+	0.971590i	0.436466	+	0.899721i	$0.356230\pi$
$523$	−12.8284	+	22.2195i	−0.560948	+	0.971590i	−0.997414	+	0.0718696i	$0.977103\pi$
$524$	−28.0000			−1.22319
$525$		0			0
$526$	2.20101			0.0959686
$527$	−1.31371	+	2.27541i	−0.0572260	+	0.0991184i
$528$	−3.00000	−	5.19615i	−0.130558	−	0.226134i
$529$	−17.8137	−	30.8542i	−0.774509	−	1.34149i
$530$	−1.41421	+	2.44949i	−0.0614295	+	0.106399i
$531$	1.17157			0.0508419
$532$		0			0
$533$	16.1421			0.699194
$534$	2.94975	−	5.10911i	0.127648	−	0.221093i
$535$	−0.585786	−	1.01461i	−0.0253258	−	0.0438655i
$536$	−4.48528	−	7.76874i	−0.193735	−	0.335558i
$537$	−9.82843	+	17.0233i	−0.424128	+	0.734611i
$538$	6.10051			0.263011
$539$		0			0
$540$	−6.24264			−0.268640
$541$	−8.65685	+	14.9941i	−0.372187	+	0.644647i	−0.989902	−	0.141755i	$-0.954725\pi$
$541$	−8.65685	+	14.9941i	−0.372187	+	0.644647i	0.617715	+	0.786402i	$0.288059\pi$
$542$	−2.10051	−	3.63818i	−0.0902244	−	0.156273i
$543$	1.29289	+	2.23936i	0.0554834	+	0.0961000i
$544$	−4.94975	+	8.57321i	−0.212219	+	0.367574i
$545$	19.3137			0.827308
$546$		0			0
$547$	−36.9706			−1.58075			−0.790374	−	0.612625i	$-0.790114\pi$
$547$	−36.9706			−1.58075			−0.790374	+	0.612625i	$0.790114\pi$
$548$	12.9289	−	22.3936i	0.552297	−	0.956606i
$549$	6.12132	+	10.6024i	0.261252	+	0.452501i
$550$	2.75736	+	4.77589i	0.117574	+	0.203644i
$551$	9.65685	−	16.7262i	0.411396	−	0.712558i
$552$	−12.1421			−0.516804
$553$		0			0
$554$	−3.85786			−0.163905
$555$	6.82843	−	11.8272i	0.289851	−	0.502036i
$556$	16.1421	+	27.9590i	0.684579	+	1.18573i
$557$	−13.0000	−	22.5167i	−0.550828	−	0.954062i	−0.998215	−	0.0597213i	$-0.980979\pi$
$557$	−13.0000	−	22.5167i	−0.550828	−	0.954062i	0.447387	−	0.894340i	$-0.352355\pi$
$558$	−0.242641	+	0.420266i	−0.0102718	+	0.0177913i
$559$	−14.6274			−0.618674
$560$		0			0
$561$	4.48528			0.189369
$562$	−0.100505	+	0.174080i	−0.00423955	+	0.00734312i
$563$	−0.585786	−	1.01461i	−0.0246880	−	0.0427608i	0.853417	−	0.521228i	$-0.174526\pi$
$563$	−0.585786	−	1.01461i	−0.0246880	−	0.0427608i	−0.878105	+	0.478467i	$0.841193\pi$
$564$	−2.58579	−	4.47871i	−0.108881	−	0.188588i
$565$	−9.07107	+	15.7116i	−0.381623	+	0.660990i
$566$	3.51472			0.147735
$567$		0			0
$568$	−14.7696			−0.619717
$569$	8.24264	−	14.2767i	0.345549	−	0.598509i	−0.639904	−	0.768455i	$-0.721026\pi$
$569$	8.24264	−	14.2767i	0.345549	−	0.598509i	0.985453	+	0.169946i	$0.0543592\pi$
$570$	−2.00000	−	3.46410i	−0.0837708	−	0.145095i
$571$	−11.1716	−	19.3497i	−0.467516	−	0.809761i	0.531795	−	0.846873i	$-0.321518\pi$
$571$	−11.1716	−	19.3497i	−0.467516	−	0.809761i	−0.999311	+	0.0371118i	$0.988184\pi$
$572$	4.72792	−	8.18900i	0.197684	−	0.342399i
$573$	18.0000			0.751961
$574$		0			0
$575$	−50.9706			−2.12562
$576$	2.08579	−	3.61269i	0.0869078	−	0.150529i
$577$	−16.9497	−	29.3578i	−0.705627	−	1.22218i	−0.966465	−	0.256799i	$-0.917332\pi$
$577$	−16.9497	−	29.3578i	−0.705627	−	1.22218i	0.260837	−	0.965383i	$-0.416001\pi$
$578$	2.47918	+	4.29407i	0.103120	+	0.178610i
$579$	2.65685	−	4.60181i	0.110415	−	0.191245i
$580$	−42.6274			−1.77001
$581$		0			0
$582$	1.07107			0.0443972
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$	−11.0208	−	19.0886i	−0.456045	−	0.789892i
$585$	−4.41421	−	7.64564i	−0.182505	−	0.316108i
$586$	3.43503	−	5.94964i	0.141900	−	0.245778i
$587$	22.8284			0.942230			0.471115	−	0.882072i	$-0.343852\pi$
$587$	22.8284			0.942230			0.471115	+	0.882072i	$0.343852\pi$
$588$		0			0
$589$	3.31371			0.136539
$590$	0.828427	−	1.43488i	0.0341058	−	0.0590730i
$591$	1.00000	+	1.73205i	0.0411345	+	0.0712470i
$592$	6.00000	+	10.3923i	0.246598	+	0.427121i
$593$	−3.46447	+	6.00063i	−0.142269	+	0.246416i	−0.928351	−	0.371706i	$-0.878773\pi$
$593$	−3.46447	+	6.00063i	−0.142269	+	0.246416i	0.786082	+	0.618122i	$0.212106\pi$
$594$	0.828427			0.0339908
$595$		0			0
$596$	−31.6569			−1.29672
$597$	−10.8284	+	18.7554i	−0.443178	+	0.767607i
$598$	−4.10051	−	7.10228i	−0.167682	−	0.290434i
$599$	1.00000	+	1.73205i	0.0408589	+	0.0707697i	0.885732	−	0.464198i	$-0.153657\pi$
$599$	1.00000	+	1.73205i	0.0408589	+	0.0707697i	−0.844873	+	0.534967i	$0.820324\pi$
$600$	−5.27817	+	9.14207i	−0.215481	+	0.373223i
$601$	15.0711			0.614762			0.307381	−	0.951587i	$-0.400547\pi$
$601$	15.0711			0.614762			0.307381	+	0.951587i	$0.400547\pi$
$602$		0			0
$603$	−5.65685			−0.230365
$604$	10.9706	−	19.0016i	0.446386	−	0.773163i
$605$	−11.9497	−	20.6976i	−0.485826	−	0.841476i
$606$	−0.606602	−	1.05066i	−0.0246415	−	0.0426803i
$607$	−9.17157	+	15.8856i	−0.372263	+	0.644778i	−0.989913	−	0.141675i	$-0.954751\pi$
$607$	−9.17157	+	15.8856i	−0.372263	+	0.644778i	0.617651	+	0.786453i	$0.288085\pi$
$608$	12.4853			0.506345
$609$		0			0
$610$	17.3137			0.701012
$611$	3.65685	−	6.33386i	0.147940	−	0.256240i
$612$	2.05025	+	3.55114i	0.0828765	+	0.143546i
$613$	−2.34315	−	4.05845i	−0.0946388	−	0.163919i	0.814819	−	0.579715i	$-0.196836\pi$
$613$	−2.34315	−	4.05845i	−0.0946388	−	0.163919i	−0.909458	+	0.415796i	$0.863503\pi$
$614$	6.24264	−	10.8126i	0.251932	−	0.436360i
$615$	−21.3137			−0.859452
$616$		0			0
$617$	−24.4853			−0.985740			−0.492870	−	0.870103i	$-0.664052\pi$
$617$	−24.4853			−0.985740			−0.492870	+	0.870103i	$0.664052\pi$
$618$	−0.928932	+	1.60896i	−0.0373671	+	0.0647218i
$619$	14.4853	+	25.0892i	0.582213	+	1.00842i	0.995217	+	0.0976926i	$0.0311462\pi$
$619$	14.4853	+	25.0892i	0.582213	+	1.00842i	−0.413004	+	0.910729i	$0.635520\pi$
$620$	−3.65685	−	6.33386i	−0.146863	−	0.254374i
$621$	−3.82843	+	6.63103i	−0.153629	+	0.266094i
$622$	−2.54416			−0.102011
$623$		0			0
$624$	7.75736			0.310543
$625$	6.98528	−	12.0989i	0.279411	−	0.483954i
$626$	0.393398	+	0.681386i	0.0157234	+	0.0272337i
$627$	−2.82843	−	4.89898i	−0.112956	−	0.195646i
$628$	−10.7487	+	18.6174i	−0.428921	+	0.742914i
$629$	−8.97056			−0.357680
$630$		0			0
$631$	23.3137			0.928104			0.464052	−	0.885808i	$-0.346395\pi$
$631$	23.3137			0.928104			0.464052	+	0.885808i	$0.346395\pi$
$632$	10.8284	−	18.7554i	0.430732	−	0.746049i
$633$	6.48528	+	11.2328i	0.257767	+	0.446465i
$634$	−2.07107	−	3.58719i	−0.0822526	−	0.142466i
$635$	−2.82843	+	4.89898i	−0.112243	+	0.194410i
$636$	−3.65685			−0.145004
$637$		0			0
$638$	5.65685			0.223957
$639$	−4.65685	+	8.06591i	−0.184222	+	0.319082i
$640$	−18.0208	−	31.2130i	−0.712335	−	1.23380i
$641$	5.41421	+	9.37769i	0.213849	+	0.370397i	0.952916	−	0.303235i	$-0.0980668\pi$
$641$	5.41421	+	9.37769i	0.213849	+	0.370397i	−0.739067	+	0.673632i	$0.764733\pi$
$642$	−0.0710678	+	0.123093i	−0.00280482	+	0.00485810i
$643$	34.4264			1.35764			0.678822	−	0.734302i	$-0.262491\pi$
$643$	34.4264			1.35764			0.678822	+	0.734302i	$0.262491\pi$
$644$		0			0
$645$	19.3137			0.760477
$646$	−1.31371	+	2.27541i	−0.0516872	+	0.0895248i
$647$	13.4142	+	23.2341i	0.527367	+	0.913427i	0.999491	+	0.0318946i	$0.0101541\pi$
$647$	13.4142	+	23.2341i	0.527367	+	0.913427i	−0.472124	+	0.881532i	$0.656513\pi$
$648$	0.792893	+	1.37333i	0.0311478	+	0.0539496i
$649$	1.17157	−	2.02922i	0.0459883	−	0.0796540i
$650$	−7.12994			−0.279659
$651$		0			0
$652$	20.6863			0.810138
$653$	−18.2426	+	31.5972i	−0.713890	+	1.23649i	0.249497	+	0.968376i	$0.419735\pi$
$653$	−18.2426	+	31.5972i	−0.713890	+	1.23649i	−0.963386	+	0.268118i	$0.913598\pi$
$654$	−1.17157	−	2.02922i	−0.0458121	−	0.0793489i
$655$	26.1421	+	45.2795i	1.02146	+	1.76922i
$656$	9.36396	−	16.2189i	0.365601	−	0.633240i
$657$	−13.8995			−0.542271
$658$		0			0
$659$	9.31371			0.362811			0.181405	−	0.983408i	$-0.441935\pi$
$659$	9.31371			0.362811			0.181405	+	0.983408i	$0.441935\pi$
$660$	−6.24264	+	10.8126i	−0.242994	+	0.420879i
$661$	−11.7782	−	20.4004i	−0.458118	−	0.793483i	0.540744	−	0.841187i	$-0.318143\pi$
$661$	−11.7782	−	20.4004i	−0.458118	−	0.793483i	−0.998862	+	0.0477040i	$0.984810\pi$
$662$	0.828427	+	1.43488i	0.0321977	+	0.0557681i
$663$	−2.89949	+	5.02207i	−0.112607	+	0.195041i
$664$	11.5980			0.450089
$665$		0			0
$666$	−1.65685			−0.0642018
$667$	−26.1421	+	45.2795i	−1.01223	+	1.75323i
$668$	18.1005	+	31.3510i	0.700330	+	1.21301i
$669$	−12.4853	−	21.6251i	−0.482709	−	0.836076i
$670$	−4.00000	+	6.92820i	−0.154533	+	0.267660i
$671$	24.4853			0.945244
$672$		0			0
$673$	23.3137			0.898677			0.449339	−	0.893361i	$-0.351660\pi$
$673$	23.3137			0.898677			0.449339	+	0.893361i	$0.351660\pi$
$674$	6.14214	−	10.6385i	0.236586	−	0.409779i
$675$	3.32843	+	5.76500i	0.128111	+	0.221895i
$676$	−5.77208	−	9.99753i	−0.222003	−	0.384520i
$677$	15.7071	−	27.2055i	0.603673	−	1.04559i	−0.388587	−	0.921412i	$-0.627037\pi$
$677$	15.7071	−	27.2055i	0.603673	−	1.04559i	0.992260	−	0.124180i	$-0.0396301\pi$
$678$	2.20101			0.0845293
$679$		0			0
$680$	12.1421			0.465630
$681$	−11.8995	+	20.6105i	−0.455990	+	0.789797i
$682$	0.485281	+	0.840532i	0.0185824	+	0.0321856i
$683$	9.82843	+	17.0233i	0.376074	+	0.651380i	0.990487	−	0.137605i	$-0.0439404\pi$
$683$	9.82843	+	17.0233i	0.376074	+	0.651380i	−0.614413	+	0.788985i	$0.710607\pi$
$684$	2.58579	−	4.47871i	0.0988700	−	0.171248i
$685$	−48.2843			−1.84485
$686$		0			0
$687$	−0.242641			−0.00925732
$688$	−8.48528	+	14.6969i	−0.323498	+	0.560316i
$689$	−2.58579	−	4.47871i	−0.0985106	−	0.170625i
$690$	5.41421	+	9.37769i	0.206116	+	0.357003i
$691$	−0.343146	+	0.594346i	−0.0130539	+	0.0226100i	−0.872479	−	0.488652i	$-0.837489\pi$
$691$	−0.343146	+	0.594346i	−0.0130539	+	0.0226100i	0.859425	+	0.511262i	$0.170822\pi$
$692$	38.5269			1.46457
$693$		0			0
$694$	13.7990			0.523802
$695$	30.1421	−	52.2077i	1.14336	−	1.98035i
$696$	5.41421	+	9.37769i	0.205225	+	0.355461i
$697$	7.00000	+	12.1244i	0.265144	+	0.459243i
$698$	−2.05025	+	3.55114i	−0.0776032	+	0.134413i
$699$	6.14214			0.232317
$700$		0			0
$701$	−17.1716			−0.648561			−0.324281	−	0.945961i	$-0.605122\pi$
$701$	−17.1716			−0.648561			−0.324281	+	0.945961i	$0.605122\pi$
$702$	−0.535534	+	0.927572i	−0.0202124	+	0.0350089i
$703$	5.65685	+	9.79796i	0.213352	+	0.369537i
$704$	−4.17157	−	7.22538i	−0.157222	−	0.272317i
$705$	−4.82843	+	8.36308i	−0.181849	+	0.314972i
$706$	6.10051			0.229596
$707$		0			0
$708$	2.14214			0.0805064
$709$	18.1421	−	31.4231i	0.681342	−	1.18012i	−0.293229	−	0.956042i	$-0.594730\pi$
$709$	18.1421	−	31.4231i	0.681342	−	1.18012i	0.974571	−	0.224077i	$-0.0719368\pi$
$710$	6.58579	+	11.4069i	0.247160	+	0.428094i
$711$	−6.82843	−	11.8272i	−0.256086	−	0.443554i
$712$	11.2929	−	19.5599i	0.423219	−	0.733037i
$713$	−8.97056			−0.335950
$714$		0			0
$715$	−17.6569			−0.660329
$716$	−17.9706	+	31.1259i	−0.671591	+	1.16323i
$717$	−7.82843	−	13.5592i	−0.292358	−	0.506379i
$718$	0.0710678	+	0.123093i	0.00265223	+	0.00459379i
$719$	20.9706	−	36.3221i	0.782070	−	1.35459i	−0.148664	−	0.988888i	$-0.547497\pi$
$719$	20.9706	−	36.3221i	0.782070	−	1.35459i	0.930734	−	0.365697i	$-0.119169\pi$
$720$	−10.2426			−0.381721
$721$		0			0
$722$	−4.55635			−0.169570
$723$	8.12132	−	14.0665i	0.302035	−	0.523140i
$724$	2.36396	+	4.09450i	0.0878559	+	0.152171i
$725$	22.7279	+	39.3659i	0.844094	+	1.46201i
$726$	−1.44975	+	2.51104i	−0.0538052	+	0.0931933i
$727$	−12.4853			−0.463053			−0.231527	−	0.972829i	$-0.574372\pi$
$727$	−12.4853			−0.463053			−0.231527	+	0.972829i	$0.574372\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−9.82843	+	17.0233i	−0.363766	+	0.630062i
$731$	−6.34315	−	10.9867i	−0.234610	−	0.406356i
$732$	11.1924	+	19.3858i	0.413683	+	0.716519i
$733$	24.8492	−	43.0402i	0.917828	−	1.58972i	0.115120	−	0.993352i	$-0.463275\pi$
$733$	24.8492	−	43.0402i	0.917828	−	1.58972i	0.802708	−	0.596373i	$-0.203392\pi$
$734$	1.37258			0.0506630
$735$		0			0
$736$	−33.7990			−1.24585
$737$	−5.65685	+	9.79796i	−0.208373	+	0.360912i
$738$	1.29289	+	2.23936i	0.0475921	+	0.0824319i
$739$	−2.34315	−	4.05845i	−0.0861940	−	0.149292i	0.819705	−	0.572785i	$-0.194137\pi$
$739$	−2.34315	−	4.05845i	−0.0861940	−	0.149292i	−0.905899	+	0.423493i	$0.860804\pi$
$740$	12.4853	−	21.6251i	0.458968	−	0.794956i
$741$	7.31371			0.268676
$742$		0			0
$743$	−50.9706			−1.86993			−0.934964	−	0.354742i	$-0.884569\pi$
$743$	−50.9706			−1.86993			−0.934964	+	0.354742i	$0.884569\pi$
$744$	−0.928932	+	1.60896i	−0.0340563	+	0.0589873i
$745$	29.5563	+	51.1931i	1.08286	+	1.87557i
$746$	2.21320	+	3.83338i	0.0810311	+	0.140350i
$747$	3.65685	−	6.33386i	0.133797	−	0.231744i
$748$	8.20101			0.299859
$749$		0			0
$750$	2.34315			0.0855596
$751$	−6.82843	+	11.8272i	−0.249173	+	0.431580i	−0.963297	−	0.268440i	$-0.913492\pi$
$751$	−6.82843	+	11.8272i	−0.249173	+	0.431580i	0.714124	+	0.700020i	$0.246825\pi$
$752$	−4.24264	−	7.34847i	−0.154713	−	0.267971i
$753$	6.24264	+	10.8126i	0.227494	+	0.394032i
$754$	−3.65685	+	6.33386i	−0.133175	+	0.230665i
$755$	−40.9706			−1.49107
$756$		0			0
$757$	26.3431			0.957458			0.478729	−	0.877963i	$-0.341098\pi$
$757$	26.3431			0.957458			0.478729	+	0.877963i	$0.341098\pi$
$758$	−1.79899	+	3.11594i	−0.0653423	+	0.113176i
$759$	7.65685	+	13.2621i	0.277926	+	0.481382i
$760$	−7.65685	−	13.2621i	−0.277743	−	0.481065i
$761$	−9.26346	+	16.0448i	−0.335800	+	0.581623i	−0.983638	−	0.180155i	$-0.942340\pi$
$761$	−9.26346	+	16.0448i	−0.335800	+	0.581623i	0.647838	+	0.761778i	$0.275673\pi$
$762$	0.686292			0.0248617
$763$		0			0
$764$	32.9117			1.19070
$765$	3.82843	−	6.63103i	0.138417	−	0.239745i
$766$	−3.79899	−	6.58004i	−0.137263	−	0.237747i
$767$	1.51472	+	2.62357i	0.0546933	+	0.0947316i
$768$	1.98528	−	3.43861i	0.0716377	−	0.124080i
$769$	−29.6985			−1.07095			−0.535477	−	0.844550i	$-0.679868\pi$
$769$	−29.6985			−1.07095			−0.535477	+	0.844550i	$0.679868\pi$
$770$		0			0
$771$	23.2132			0.836003
$772$	4.85786	−	8.41407i	0.174838	−	0.302829i
$773$	−4.77817	−	8.27604i	−0.171859	−	0.297669i	0.767211	−	0.641395i	$-0.221644\pi$
$773$	−4.77817	−	8.27604i	−0.171859	−	0.297669i	−0.939070	+	0.343727i	$0.888311\pi$
$774$	−1.17157	−	2.02922i	−0.0421113	−	0.0729389i
$775$	−3.89949	+	6.75412i	−0.140074	+	0.242615i
$776$	4.10051

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 + 0.358719i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(1.70711 - 2.95680i) q^{5} -0.414214 q^{6} -1.58579 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.207107 + 0.358719i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(1.70711 - 2.95680i) q^{5} -0.414214 q^{6} -1.58579 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.707107 + 1.22474i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-0.914214 + 1.58346i) q^{12} -2.58579 q^{13} +3.41421 q^{15} +(-1.50000 + 2.59808i) q^{16} +(-1.12132 - 1.94218i) q^{17} +(-0.207107 - 0.358719i) q^{18} +(-1.41421 + 2.44949i) q^{19} +6.24264 q^{20} -0.828427 q^{22} +(3.82843 - 6.63103i) q^{23} +(-0.792893 - 1.37333i) q^{24} +(-3.32843 - 5.76500i) q^{25} +(0.535534 - 0.927572i) q^{26} -1.00000 q^{27} -6.82843 q^{29} +(-0.707107 + 1.22474i) q^{30} +(-0.585786 - 1.01461i) q^{31} +(-2.20711 - 3.82282i) q^{32} +(-1.00000 + 1.73205i) q^{33} +0.928932 q^{34} -1.82843 q^{36} +(2.00000 - 3.46410i) q^{37} +(-0.585786 - 1.01461i) q^{38} +(-1.29289 - 2.23936i) q^{39} +(-2.70711 + 4.68885i) q^{40} -6.24264 q^{41} +5.65685 q^{43} +(-1.82843 + 3.16693i) q^{44} +(1.70711 + 2.95680i) q^{45} +(1.58579 + 2.74666i) q^{46} +(-1.41421 + 2.44949i) q^{47} -3.00000 q^{48} +2.75736 q^{50} +(1.12132 - 1.94218i) q^{51} +(-2.36396 - 4.09450i) q^{52} +(1.00000 + 1.73205i) q^{53} +(0.207107 - 0.358719i) q^{54} +6.82843 q^{55} -2.82843 q^{57} +(1.41421 - 2.44949i) q^{58} +(-0.585786 - 1.01461i) q^{59} +(3.12132 + 5.40629i) q^{60} +(6.12132 - 10.6024i) q^{61} +0.485281 q^{62} -4.17157 q^{64} +(-4.41421 + 7.64564i) q^{65} +(-0.414214 - 0.717439i) q^{66} +(2.82843 + 4.89898i) q^{67} +(2.05025 - 3.55114i) q^{68} +7.65685 q^{69} +9.31371 q^{71} +(0.792893 - 1.37333i) q^{72} +(6.94975 + 12.0373i) q^{73} +(0.828427 + 1.43488i) q^{74} +(3.32843 - 5.76500i) q^{75} -5.17157 q^{76} +1.07107 q^{78} +(-6.82843 + 11.8272i) q^{79} +(5.12132 + 8.87039i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.29289 - 2.23936i) q^{82} -7.31371 q^{83} -7.65685 q^{85} +(-1.17157 + 2.02922i) q^{86} +(-3.41421 - 5.91359i) q^{87} +(-1.58579 - 2.74666i) q^{88} +(-7.12132 + 12.3345i) q^{89} -1.41421 q^{90} +14.0000 q^{92} +(0.585786 - 1.01461i) q^{93} +(-0.585786 - 1.01461i) q^{94} +(4.82843 + 8.36308i) q^{95} +(2.20711 - 3.82282i) q^{96} -2.58579 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 - 12 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} - 2 q^{9} + 4 q^{11} + 2 q^{12} - 16 q^{13} + 8 q^{15} - 6 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{20} + 8 q^{22} + 4 q^{23} - 6 q^{24} - 2 q^{25} - 12 q^{26} - 4 q^{27} - 16 q^{29} - 8 q^{31} - 6 q^{32} - 4 q^{33} + 32 q^{34} + 4 q^{36} + 8 q^{37} - 8 q^{38} - 8 q^{39} - 8 q^{40} - 8 q^{41} + 4 q^{44} + 4 q^{45} + 12 q^{46} - 12 q^{48} + 28 q^{50} - 4 q^{51} + 16 q^{52} + 4 q^{53} - 2 q^{54} + 16 q^{55} - 8 q^{59} + 4 q^{60} + 16 q^{61} - 32 q^{62} - 28 q^{64} - 12 q^{65} + 4 q^{66} + 28 q^{68} + 8 q^{69} - 8 q^{71} + 6 q^{72} + 8 q^{73} - 8 q^{74} + 2 q^{75} - 32 q^{76} - 24 q^{78} - 16 q^{79} + 12 q^{80} - 2 q^{81} + 8 q^{82} + 16 q^{83} - 8 q^{85} - 16 q^{86} - 8 q^{87} - 12 q^{88} - 20 q^{89} + 56 q^{92} + 8 q^{93} - 8 q^{94} + 8 q^{95} + 6 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 - 12 * q^8 - 2 * q^9 + 4 * q^11 + 2 * q^12 - 16 * q^13 + 8 * q^15 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^20 + 8 * q^22 + 4 * q^23 - 6 * q^24 - 2 * q^25 - 12 * q^26 - 4 * q^27 - 16 * q^29 - 8 * q^31 - 6 * q^32 - 4 * q^33 + 32 * q^34 + 4 * q^36 + 8 * q^37 - 8 * q^38 - 8 * q^39 - 8 * q^40 - 8 * q^41 + 4 * q^44 + 4 * q^45 + 12 * q^46 - 12 * q^48 + 28 * q^50 - 4 * q^51 + 16 * q^52 + 4 * q^53 - 2 * q^54 + 16 * q^55 - 8 * q^59 + 4 * q^60 + 16 * q^61 - 32 * q^62 - 28 * q^64 - 12 * q^65 + 4 * q^66 + 28 * q^68 + 8 * q^69 - 8 * q^71 + 6 * q^72 + 8 * q^73 - 8 * q^74 + 2 * q^75 - 32 * q^76 - 24 * q^78 - 16 * q^79 + 12 * q^80 - 2 * q^81 + 8 * q^82 + 16 * q^83 - 8 * q^85 - 16 * q^86 - 8 * q^87 - 12 * q^88 - 20 * q^89 + 56 * q^92 + 8 * q^93 - 8 * q^94 + 8 * q^95 + 6 * q^96 - 16 * q^97 - 8 * q^99

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