LMFDB - Embedded newform 567.2.h.b.352.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(298,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("567.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.h (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:	$4.52751779461$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	567.352
Dual form			567.2.h.b.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000 q^{4} +(-2.00000 - 3.46410i) q^{5} +(-2.50000 - 0.866025i) q^{7} +3.00000 q^{8} +(2.00000 + 3.46410i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(2.50000 + 0.866025i) q^{14} -1.00000 q^{16} +(-3.00000 - 5.19615i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(2.00000 + 3.46410i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-5.50000 + 9.52628i) q^{25} +(0.500000 - 0.866025i) q^{26} +(2.50000 + 0.866025i) q^{28} +(1.00000 + 1.73205i) q^{29} +3.00000 q^{31} -5.00000 q^{32} +(3.00000 + 5.19615i) q^{34} +(2.00000 + 10.3923i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(2.00000 - 3.46410i) q^{38} +(-6.00000 - 10.3923i) q^{40} +(-1.00000 + 1.73205i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-3.00000 - 5.19615i) q^{46} -6.00000 q^{47} +(5.50000 + 4.33013i) q^{49} +(5.50000 - 9.52628i) q^{50} +(0.500000 - 0.866025i) q^{52} +(-3.00000 - 5.19615i) q^{53} -8.00000 q^{55} +(-7.50000 - 2.59808i) q^{56} +(-1.00000 - 1.73205i) q^{58} -6.00000 q^{59} -5.00000 q^{61} -3.00000 q^{62} +7.00000 q^{64} +4.00000 q^{65} +7.00000 q^{67} +(3.00000 + 5.19615i) q^{68} +(-2.00000 - 10.3923i) q^{70} +(3.00000 + 5.19615i) q^{73} +(1.50000 - 2.59808i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-4.00000 + 3.46410i) q^{77} +11.0000 q^{79} +(2.00000 + 3.46410i) q^{80} +(1.00000 - 1.73205i) q^{82} +(3.00000 + 5.19615i) q^{83} +(-12.0000 + 20.7846i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{88} +(-2.00000 + 3.46410i) q^{89} +(2.00000 - 1.73205i) q^{91} +(-3.00000 - 5.19615i) q^{92} +6.00000 q^{94} +16.0000 q^{95} +(-4.50000 - 7.79423i) q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{4} - 4 q^{5} - 5 q^{7} + 6 q^{8} + 4 q^{10} + 2 q^{11} - q^{13} + 5 q^{14} - 2 q^{16} - 6 q^{17} - 4 q^{19} + 4 q^{20} - 2 q^{22} + 6 q^{23} - 11 q^{25} + q^{26} + 5 q^{28} + 2 q^{29}+ \cdots - 11 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 - 5 * q^7 + 6 * q^8 + 4 * q^10 + 2 * q^11 - q^13 + 5 * q^14 - 2 * q^16 - 6 * q^17 - 4 * q^19 + 4 * q^20 - 2 * q^22 + 6 * q^23 - 11 * q^25 + q^26 + 5 * q^28 + 2 * q^29 + 6 * q^31 - 10 * q^32 + 6 * q^34 + 4 * q^35 - 3 * q^37 + 4 * q^38 - 12 * q^40 - 2 * q^41 + q^43 - 2 * q^44 - 6 * q^46 - 12 * q^47 + 11 * q^49 + 11 * q^50 + q^52 - 6 * q^53 - 16 * q^55 - 15 * q^56 - 2 * q^58 - 12 * q^59 - 10 * q^61 - 6 * q^62 + 14 * q^64 + 8 * q^65 + 14 * q^67 + 6 * q^68 - 4 * q^70 + 6 * q^73 + 3 * q^74 + 4 * q^76 - 8 * q^77 + 22 * q^79 + 4 * q^80 + 2 * q^82 + 6 * q^83 - 24 * q^85 - q^86 + 6 * q^88 - 4 * q^89 + 4 * q^91 - 6 * q^92 + 12 * q^94 + 32 * q^95 - 9 * q^97 - 11 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107			−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000			−0.707107			−0.353553	+	0.935414i	$0.615027\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.834512	−	0.550990i	$-0.814250\pi$
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.0599153	−	0.998203i	$-0.519083\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$	3.00000			1.06066
$9$		0			0
$10$	2.00000	+	3.46410i	0.632456	+	1.09545i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$	2.50000	+	0.866025i	0.668153	+	0.231455i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$	2.00000	+	3.46410i	0.447214	+	0.774597i
$21$		0			0
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$		0			0
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	0.943811	−	0.330487i	$-0.107213\pi$
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	−0.758115	+	0.652121i	$0.773880\pi$
$30$		0			0
$31$	3.00000			0.538816			0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000			0.538816			0.269408	+	0.963026i	$0.413172\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$	2.00000	+	10.3923i	0.338062	+	1.75662i
$36$		0			0
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$		0			0
$40$	−6.00000	−	10.3923i	−0.948683	−	1.64317i
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	−0.933486	−	0.358614i	$-0.883249\pi$
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	0.777312	+	0.629115i	$0.216583\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	5.50000	−	9.52628i	0.777817	−	1.34722i
$51$		0			0
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	−8.00000			−1.07872
$56$	−7.50000	−	2.59808i	−1.00223	−	0.347183i
$57$		0			0
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$		0			0
$61$	−5.00000			−0.640184			−0.320092	−	0.947386i	$-0.603714\pi$
$61$	−5.00000			−0.640184			−0.320092	+	0.947386i	$0.603714\pi$
$62$	−3.00000			−0.381000
$63$		0			0
$64$	7.00000			0.875000
$65$	4.00000			0.496139
$66$		0			0
$67$	7.00000			0.855186			0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000			0.855186			0.427593	+	0.903971i	$0.359362\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$		0			0
$70$	−2.00000	−	10.3923i	−0.239046	−	1.24212i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	0.986447	−	0.164083i	$-0.0524664\pi$
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	−0.635323	+	0.772246i	$0.719133\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−4.00000	+	3.46410i	−0.455842	+	0.394771i
$78$		0			0
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$		0			0
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$		0			0
$85$	−12.0000	+	20.7846i	−1.30158	+	2.25441i
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$		0			0
$88$	3.00000	−	5.19615i	0.319801	−	0.553912i
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	−0.952340	−	0.305038i	$-0.901331\pi$
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	0.740341	+	0.672232i	$0.234664\pi$
$90$		0			0
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$	−3.00000	−	5.19615i	−0.312772	−	0.541736i
$93$		0			0
$94$	6.00000			0.618853
$95$	16.0000			1.64157
$96$		0			0
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	0.541890	−	0.840450i	$-0.317709\pi$
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	−0.998796	+	0.0490655i	$0.984376\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$		0			0
$100$	5.50000	−	9.52628i	0.550000	−	0.952628i
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	−0.993481	−	0.113998i	$-0.963634\pi$
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	0.595466	+	0.803380i	$0.296967\pi$
$102$		0			0
$103$	−8.50000	−	14.7224i	−0.837530	−	1.45064i	−0.891954	−	0.452126i	$-0.850666\pi$
$103$	−8.50000	−	14.7224i	−0.837530	−	1.45064i	0.0544240	−	0.998518i	$-0.482668\pi$
$104$	−1.50000	+	2.59808i	−0.147087	+	0.254762i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	−0.813632	−	0.581380i	$-0.802513\pi$
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	0.910306	+	0.413936i	$0.135846\pi$
$108$		0			0
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	0.565940	−	0.824447i	$-0.308513\pi$
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	−0.996962	+	0.0778949i	$0.975180\pi$
$110$	8.00000			0.762770
$111$		0			0
$112$	2.50000	+	0.866025i	0.236228	+	0.0818317i
$113$	−8.00000	+	13.8564i	−0.752577	+	1.30350i	0.193993	+	0.981003i	$0.437856\pi$
$113$	−8.00000	+	13.8564i	−0.752577	+	1.30350i	−0.946570	+	0.322498i	$0.895477\pi$
$114$		0			0
$115$	12.0000	−	20.7846i	1.11901	−	1.93817i
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$		0			0
$118$	6.00000			0.552345
$119$	3.00000	+	15.5885i	0.275010	+	1.42899i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	5.00000			0.452679
$123$		0			0
$124$	−3.00000			−0.269408
$125$	24.0000			2.14663
$126$		0			0
$127$	−9.00000			−0.798621			−0.399310	−	0.916816i	$-0.630750\pi$
$127$	−9.00000			−0.798621			−0.399310	+	0.916816i	$0.630750\pi$
$128$	3.00000			0.265165
$129$		0			0
$130$	−4.00000			−0.350823
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	0.765331	−	0.643637i	$-0.222575\pi$
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	−0.940072	+	0.340977i	$0.889242\pi$
$132$		0			0
$133$	8.00000	−	6.92820i	0.693688	−	0.600751i
$134$	−7.00000			−0.604708
$135$		0			0
$136$	−9.00000	−	15.5885i	−0.771744	−	1.33670i
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$		0			0
$139$	−4.50000	+	7.79423i	−0.381685	+	0.661098i	−0.991303	−	0.131597i	$-0.957989\pi$
$139$	−4.50000	+	7.79423i	−0.381685	+	0.661098i	0.609618	+	0.792695i	$0.291323\pi$
$140$	−2.00000	−	10.3923i	−0.169031	−	0.878310i
$141$		0			0
$142$		0			0
$143$	1.00000	+	1.73205i	0.0836242	+	0.144841i
$144$		0			0
$145$	4.00000	−	6.92820i	0.332182	−	0.575356i
$146$	−3.00000	−	5.19615i	−0.248282	−	0.430037i
$147$		0			0
$148$	1.50000	−	2.59808i	0.123299	−	0.213561i
$149$	−12.0000	−	20.7846i	−0.983078	−	1.70274i	−0.650183	−	0.759778i	$-0.725308\pi$
$149$	−12.0000	−	20.7846i	−0.983078	−	1.70274i	−0.332896	−	0.942964i	$-0.608026\pi$
$150$		0			0
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	−0.949637	−	0.313353i	$-0.898548\pi$
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	0.746190	+	0.665733i	$0.231881\pi$
$152$	−6.00000	+	10.3923i	−0.486664	+	0.842927i
$153$		0			0
$154$	4.00000	−	3.46410i	0.322329	−	0.279145i
$155$	−6.00000	−	10.3923i	−0.481932	−	0.834730i
$156$		0			0
$157$	10.0000			0.798087			0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000			0.798087			0.399043	+	0.916932i	$0.369342\pi$
$158$	−11.0000			−0.875113
$159$		0			0
$160$	10.0000	+	17.3205i	0.790569	+	1.36931i
$161$	−3.00000	−	15.5885i	−0.236433	−	1.22854i
$162$		0			0
$163$	−9.50000	+	16.4545i	−0.744097	+	1.28881i	0.206518	+	0.978443i	$0.433787\pi$
$163$	−9.50000	+	16.4545i	−0.744097	+	1.28881i	−0.950615	+	0.310372i	$0.899546\pi$
$164$	1.00000	−	1.73205i	0.0780869	−	0.135250i
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	7.00000	−	12.1244i	0.541676	−	0.938211i	−0.457132	−	0.889399i	$-0.651123\pi$
$167$	7.00000	−	12.1244i	0.541676	−	0.938211i	0.998808	−	0.0488118i	$-0.0155435\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	12.0000	−	20.7846i	0.920358	−	1.59411i
$171$		0			0
$172$	−0.500000	−	0.866025i	−0.0381246	−	0.0660338i
$173$	−16.0000			−1.21646			−0.608229	−	0.793762i	$-0.708120\pi$
$173$	−16.0000			−1.21646			−0.608229	+	0.793762i	$0.708120\pi$
$174$		0			0
$175$	22.0000	−	19.0526i	1.66304	−	1.44024i
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$		0			0
$178$	2.00000	−	3.46410i	0.149906	−	0.259645i
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	−2.00000	+	1.73205i	−0.148250	+	0.128388i
$183$		0			0
$184$	9.00000	+	15.5885i	0.663489	+	1.14920i
$185$	12.0000			0.882258
$186$		0			0
$187$	−12.0000			−0.877527
$188$	6.00000			0.437595
$189$		0			0
$190$	−16.0000			−1.16076
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$		0			0
$193$	−25.0000			−1.79954			−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−25.0000			−1.79954			−0.899770	+	0.436365i	$0.856266\pi$
$194$	4.50000	+	7.79423i	0.323081	+	0.559593i
$195$		0			0
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$	−20.0000			−1.42494			−0.712470	−	0.701702i	$-0.752424\pi$
$197$	−20.0000			−1.42494			−0.712470	+	0.701702i	$0.752424\pi$
$198$		0			0
$199$	4.50000	+	7.79423i	0.318997	+	0.552518i	0.980279	−	0.197619i	$-0.0633208\pi$
$199$	4.50000	+	7.79423i	0.318997	+	0.552518i	−0.661282	+	0.750137i	$0.729987\pi$
$200$	−16.5000	+	28.5788i	−1.16673	+	2.02083i
$201$		0			0
$202$	4.00000	−	6.92820i	0.281439	−	0.487467i
$203$	−1.00000	−	5.19615i	−0.0701862	−	0.364698i
$204$		0			0
$205$	8.00000			0.558744
$206$	8.50000	+	14.7224i	0.592223	+	1.02576i
$207$		0			0
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	4.00000	+	6.92820i	0.276686	+	0.479234i
$210$		0			0
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$	−1.00000	+	1.73205i	−0.0683586	+	0.118401i
$215$	2.00000	−	3.46410i	0.136399	−	0.236250i
$216$		0			0
$217$	−7.50000	−	2.59808i	−0.509133	−	0.176369i
$218$	4.50000	+	7.79423i	0.304778	+	0.527892i
$219$		0			0
$220$	8.00000			0.539360
$221$	6.00000			0.403604
$222$		0			0
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	−0.999128	−	0.0417488i	$-0.986707\pi$
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	0.463409	−	0.886145i	$-0.346626\pi$
$224$	12.5000	+	4.33013i	0.835191	+	0.289319i
$225$		0			0
$226$	8.00000	−	13.8564i	0.532152	−	0.921714i
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$		0			0
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	−0.726900	+	0.686743i	$0.759040\pi$
$230$	−12.0000	+	20.7846i	−0.791257	+	1.37050i
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	0.142166	+	0.989843i	$0.454593\pi$
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	−0.928312	+	0.371802i	$0.878740\pi$
$234$		0			0
$235$	12.0000	+	20.7846i	0.782794	+	1.35584i
$236$	6.00000			0.390567
$237$		0			0
$238$	−3.00000	−	15.5885i	−0.194461	−	1.01045i
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	−0.992195	−	0.124696i	$-0.960204\pi$
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	0.604087	+	0.796918i	$0.293538\pi$
$240$		0			0
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	0.450910	+	0.892570i	$0.351100\pi$
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	5.00000			0.320092
$245$	4.00000	−	27.7128i	0.255551	−	1.77051i
$246$		0			0
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$	9.00000			0.571501
$249$		0			0
$250$	−24.0000			−1.51789
$251$	−26.0000			−1.64111			−0.820553	−	0.571571i	$-0.806334\pi$
$251$	−26.0000			−1.64111			−0.820553	+	0.571571i	$0.806334\pi$
$252$		0			0
$253$	12.0000			0.754434
$254$	9.00000			0.564710
$255$		0			0
$256$	−17.0000			−1.06250
$257$	5.00000	+	8.66025i	0.311891	+	0.540212i	0.978772	−	0.204953i	$-0.0657041\pi$
$257$	5.00000	+	8.66025i	0.311891	+	0.540212i	−0.666880	+	0.745165i	$0.732371\pi$
$258$		0			0
$259$	6.00000	−	5.19615i	0.372822	−	0.322873i
$260$	−4.00000			−0.248069
$261$		0			0
$262$	2.00000	+	3.46410i	0.123560	+	0.214013i
$263$	1.00000	−	1.73205i	0.0616626	−	0.106803i	−0.833546	−	0.552450i	$-0.813693\pi$
$263$	1.00000	−	1.73205i	0.0616626	−	0.106803i	0.895209	+	0.445647i	$0.147026\pi$
$264$		0			0
$265$	−12.0000	+	20.7846i	−0.737154	+	1.27679i
$266$	−8.00000	+	6.92820i	−0.490511	+	0.424795i
$267$		0			0
$268$	−7.00000			−0.427593
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	−0.649211	−	0.760609i	$-0.724901\pi$
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	0.983312	+	0.181928i	$0.0582339\pi$
$272$	3.00000	+	5.19615i	0.181902	+	0.315063i
$273$		0			0
$274$	−9.00000	+	15.5885i	−0.543710	+	0.941733i
$275$	11.0000	+	19.0526i	0.663325	+	1.14891i
$276$		0			0
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	−0.992522	−	0.122068i	$-0.961047\pi$
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	0.601975	+	0.798515i	$0.294381\pi$
$278$	4.50000	−	7.79423i	0.269892	−	0.467467i
$279$		0			0
$280$	6.00000	+	31.1769i	0.358569	+	1.86318i
$281$	8.00000	+	13.8564i	0.477240	+	0.826604i	0.999660	−	0.0260845i	$-0.00830391\pi$
$281$	8.00000	+	13.8564i	0.477240	+	0.826604i	−0.522420	+	0.852688i	$0.674971\pi$
$282$		0			0
$283$	−5.00000			−0.297219			−0.148610	−	0.988896i	$-0.547480\pi$
$283$	−5.00000			−0.297219			−0.148610	+	0.988896i	$0.547480\pi$
$284$		0			0
$285$		0			0
$286$	−1.00000	−	1.73205i	−0.0591312	−	0.102418i
$287$	4.00000	−	3.46410i	0.236113	−	0.204479i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	−4.00000	+	6.92820i	−0.234888	+	0.406838i
$291$		0			0
$292$	−3.00000	−	5.19615i	−0.175562	−	0.304082i
$293$	11.0000	−	19.0526i	0.642627	−	1.11306i	−0.342217	−	0.939621i	$-0.611178\pi$
$293$	11.0000	−	19.0526i	0.642627	−	1.11306i	0.984844	−	0.173442i	$-0.0554888\pi$
$294$		0			0
$295$	12.0000	+	20.7846i	0.698667	+	1.21013i
$296$	−4.50000	+	7.79423i	−0.261557	+	0.453030i
$297$		0			0
$298$	12.0000	+	20.7846i	0.695141	+	1.20402i
$299$	−6.00000			−0.346989
$300$		0			0
$301$	−0.500000	−	2.59808i	−0.0288195	−	0.149751i
$302$	2.50000	−	4.33013i	0.143859	−	0.249171i
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	10.0000	+	17.3205i	0.572598	+	0.991769i
$306$		0			0
$307$	25.0000			1.42683			0.713413	−	0.700744i	$-0.247149\pi$
$307$	25.0000			1.42683			0.713413	+	0.700744i	$0.247149\pi$
$308$	4.00000	−	3.46410i	0.227921	−	0.197386i
$309$		0			0
$310$	6.00000	+	10.3923i	0.340777	+	0.590243i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	−22.0000			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	−11.0000			−0.618798
$317$	−30.0000			−1.68497			−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000			−1.68497			−0.842484	+	0.538721i	$0.818908\pi$
$318$		0			0
$319$	4.00000			0.223957
$320$	−14.0000	−	24.2487i	−0.782624	−	1.35554i
$321$		0			0
$322$	3.00000	+	15.5885i	0.167183	+	0.868711i
$323$	24.0000			1.33540
$324$		0			0
$325$	−5.50000	−	9.52628i	−0.305085	−	0.528423i
$326$	9.50000	−	16.4545i	0.526156	−	0.911330i
$327$		0			0
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	15.0000	+	5.19615i	0.826977	+	0.286473i
$330$		0			0
$331$	−28.0000			−1.53902			−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000			−1.53902			−0.769510	+	0.638635i	$0.779499\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$		0			0
$334$	−7.00000	+	12.1244i	−0.383023	+	0.663415i
$335$	−14.0000	−	24.2487i	−0.764902	−	1.32485i
$336$		0			0
$337$	−5.00000	+	8.66025i	−0.272367	+	0.471754i	−0.969468	−	0.245220i	$-0.921140\pi$
$337$	−5.00000	+	8.66025i	−0.272367	+	0.471754i	0.697100	+	0.716974i	$0.254473\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$		0			0
$340$	12.0000	−	20.7846i	0.650791	−	1.12720i
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	1.50000	+	2.59808i	0.0808746	+	0.140079i
$345$		0			0
$346$	16.0000			0.860165
$347$	−16.0000			−0.858925			−0.429463	−	0.903085i	$-0.641297\pi$
$347$	−16.0000			−0.858925			−0.429463	+	0.903085i	$0.641297\pi$
$348$		0			0
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$350$	−22.0000	+	19.0526i	−1.17595	+	1.01840i
$351$		0			0
$352$	−5.00000	+	8.66025i	−0.266501	+	0.461593i
$353$	−14.0000	+	24.2487i	−0.745145	+	1.29063i	0.204982	+	0.978766i	$0.434286\pi$
$353$	−14.0000	+	24.2487i	−0.745145	+	1.29063i	−0.950127	+	0.311863i	$0.899047\pi$
$354$		0			0
$355$		0			0
$356$	2.00000	−	3.46410i	0.106000	−	0.183597i
$357$		0			0
$358$	−2.00000	−	3.46410i	−0.105703	−	0.183083i
$359$	11.0000	−	19.0526i	0.580558	−	1.00556i	−0.414855	−	0.909887i	$-0.636168\pi$
$359$	11.0000	−	19.0526i	0.580558	−	1.00556i	0.995413	−	0.0956683i	$-0.0304988\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	2.00000			0.105118
$363$		0			0
$364$	−2.00000	+	1.73205i	−0.104828	+	0.0907841i
$365$	12.0000	−	20.7846i	0.628109	−	1.08792i
$366$		0			0
$367$	−6.00000	+	10.3923i	−0.313197	+	0.542474i	−0.979053	−	0.203607i	$-0.934733\pi$
$367$	−6.00000	+	10.3923i	−0.313197	+	0.542474i	0.665855	+	0.746081i	$0.268067\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$		0			0
$370$	−12.0000			−0.623850
$371$	3.00000	+	15.5885i	0.155752	+	0.809312i
$372$		0			0
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$	12.0000			0.620505
$375$		0			0
$376$	−18.0000			−0.928279
$377$	−2.00000			−0.103005
$378$		0			0
$379$	−9.00000			−0.462299			−0.231149	−	0.972918i	$-0.574249\pi$
$379$	−9.00000			−0.462299			−0.231149	+	0.972918i	$0.574249\pi$
$380$	−16.0000			−0.820783
$381$		0			0
$382$	−4.00000			−0.204658
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$		0			0
$385$	20.0000	+	6.92820i	1.01929	+	0.353094i
$386$	25.0000			1.27247
$387$		0			0
$388$	4.50000	+	7.79423i	0.228453	+	0.395692i
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	−0.977086	−	0.212847i	$-0.931726\pi$
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	0.672874	+	0.739758i	$0.265060\pi$
$390$		0			0
$391$	18.0000	−	31.1769i	0.910299	−	1.57668i
$392$	16.5000	+	12.9904i	0.833376	+	0.656113i
$393$		0			0
$394$	20.0000			1.00759
$395$	−22.0000	−	38.1051i	−1.10694	−	1.91728i
$396$		0			0
$397$	16.5000	−	28.5788i	0.828111	−	1.43433i	−0.0714068	−	0.997447i	$-0.522749\pi$
$397$	16.5000	−	28.5788i	0.828111	−	1.43433i	0.899518	−	0.436884i	$-0.143918\pi$
$398$	−4.50000	−	7.79423i	−0.225565	−	0.390689i
$399$		0			0
$400$	5.50000	−	9.52628i	0.275000	−	0.476314i
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	0.948272	+	0.317460i	$0.102830\pi$
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	−0.199207	+	0.979957i	$0.563837\pi$
$402$		0			0
$403$	−1.50000	+	2.59808i	−0.0747203	+	0.129419i
$404$	4.00000	−	6.92820i	0.199007	−	0.344691i
$405$		0			0
$406$	1.00000	+	5.19615i	0.0496292	+	0.257881i
$407$	3.00000	+	5.19615i	0.148704	+	0.257564i
$408$		0			0
$409$	5.00000			0.247234			0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000			0.247234			0.123617	+	0.992330i	$0.460551\pi$
$410$	−8.00000			−0.395092
$411$		0			0
$412$	8.50000	+	14.7224i	0.418765	+	0.725322i
$413$	15.0000	+	5.19615i	0.738102	+	0.255686i
$414$		0			0
$415$	12.0000	−	20.7846i	0.589057	−	1.02028i
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$		0			0
$418$	−4.00000	−	6.92820i	−0.195646	−	0.338869i
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	−0.974546	−	0.224189i	$-0.928027\pi$
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	0.681426	+	0.731887i	$0.261360\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$	−2.50000	+	4.33013i	−0.121698	+	0.210787i
$423$		0			0
$424$	−9.00000	−	15.5885i	−0.437079	−	0.757042i
$425$	66.0000			3.20147
$426$		0			0
$427$	12.5000	+	4.33013i	0.604917	+	0.209550i
$428$	−1.00000	+	1.73205i	−0.0483368	+	0.0837218i
$429$		0			0
$430$	−2.00000	+	3.46410i	−0.0964486	+	0.167054i
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$		0			0
$433$	−17.0000			−0.816968			−0.408484	−	0.912766i	$-0.633942\pi$
$433$	−17.0000			−0.816968			−0.408484	+	0.912766i	$0.633942\pi$
$434$	7.50000	+	2.59808i	0.360012	+	0.124712i
$435$		0			0
$436$	4.50000	+	7.79423i	0.215511	+	0.373276i
$437$	−24.0000			−1.14808
$438$		0			0
$439$	24.0000			1.14546			0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000			1.14546			0.572729	+	0.819745i	$0.305885\pi$
$440$	−24.0000			−1.14416
$441$		0			0
$442$	−6.00000			−0.285391
$443$	24.0000			1.14027			0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000			1.14027			0.570137	+	0.821549i	$0.306890\pi$
$444$		0			0
$445$	16.0000			0.758473
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$		0			0
$448$	−17.5000	−	6.06218i	−0.826797	−	0.286411i
$449$	36.0000			1.69895			0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000			1.69895			0.849473	+	0.527633i	$0.176920\pi$
$450$		0			0
$451$	2.00000	+	3.46410i	0.0941763	+	0.163118i
$452$	8.00000	−	13.8564i	0.376288	−	0.651751i
$453$		0			0
$454$	−9.00000	+	15.5885i	−0.422391	+	0.731603i
$455$	−10.0000	−	3.46410i	−0.468807	−	0.162400i
$456$		0			0
$457$	13.0000			0.608114			0.304057	−	0.952654i	$-0.401659\pi$
$457$	13.0000			0.608114			0.304057	+	0.952654i	$0.401659\pi$
$458$	−3.50000	−	6.06218i	−0.163544	−	0.283267i
$459$		0			0
$460$	−12.0000	+	20.7846i	−0.559503	+	0.969087i
$461$	−1.00000	−	1.73205i	−0.0465746	−	0.0806696i	0.841798	−	0.539792i	$-0.181497\pi$
$461$	−1.00000	−	1.73205i	−0.0465746	−	0.0806696i	−0.888373	+	0.459123i	$0.848164\pi$
$462$		0			0
$463$	16.0000	−	27.7128i	0.743583	−	1.28792i	−0.207271	−	0.978284i	$-0.566458\pi$
$463$	16.0000	−	27.7128i	0.743583	−	1.28792i	0.950854	−	0.309640i	$-0.100209\pi$
$464$	−1.00000	−	1.73205i	−0.0464238	−	0.0804084i
$465$		0			0
$466$	12.0000	−	20.7846i	0.555889	−	0.962828i
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$		0			0
$469$	−17.5000	−	6.06218i	−0.808075	−	0.279925i
$470$	−12.0000	−	20.7846i	−0.553519	−	0.958723i
$471$		0			0
$472$	−18.0000			−0.828517
$473$	2.00000			0.0919601
$474$		0			0
$475$	−22.0000	−	38.1051i	−1.00943	−	1.74838i
$476$	−3.00000	−	15.5885i	−0.137505	−	0.714496i
$477$		0			0
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	8.00000	−	13.8564i	0.365529	−	0.633115i	−0.623332	−	0.781958i	$-0.714221\pi$
$479$	8.00000	−	13.8564i	0.365529	−	0.633115i	0.988861	+	0.148842i	$0.0475547\pi$
$480$		0			0
$481$	−1.50000	−	2.59808i	−0.0683941	−	0.118462i
$482$	8.50000	−	14.7224i	0.387164	−	0.670588i
$483$		0			0
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	−18.0000	+	31.1769i	−0.817338	+	1.41567i
$486$		0			0
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	0.625859	−	0.779936i	$-0.284748\pi$
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	−0.988374	+	0.152042i	$0.951415\pi$
$488$	−15.0000			−0.679018
$489$		0			0
$490$	−4.00000	+	27.7128i	−0.180702	+	1.25194i
$491$	17.0000	−	29.4449i	0.767199	−	1.32883i	−0.171877	−	0.985118i	$-0.554983\pi$
$491$	17.0000	−	29.4449i	0.767199	−	1.32883i	0.939076	−	0.343710i	$-0.111684\pi$
$492$		0			0
$493$	6.00000	−	10.3923i	0.270226	−	0.468046i
$494$	2.00000	+	3.46410i	0.0899843	+	0.155857i
$495$		0			0
$496$	−3.00000			−0.134704
$497$		0			0
$498$		0			0
$499$	8.50000	+	14.7224i	0.380512	+	0.659067i	0.991136	−	0.132855i	$-0.0424144\pi$
$499$	8.50000	+	14.7224i	0.380512	+	0.659067i	−0.610623	+	0.791921i	$0.709081\pi$
$500$	−24.0000			−1.07331
$501$		0			0
$502$	26.0000			1.16044
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$	32.0000			1.42398
$506$	−12.0000			−0.533465
$507$		0			0
$508$	9.00000			0.399310
$509$	11.0000	+	19.0526i	0.487566	+	0.844490i	0.999898	−	0.0142980i	$-0.00455136\pi$
$509$	11.0000	+	19.0526i	0.487566	+	0.844490i	−0.512331	+	0.858788i	$0.671218\pi$
$510$		0			0
$511$	−3.00000	−	15.5885i	−0.132712	−	0.689593i
$512$	11.0000			0.486136
$513$		0			0
$514$	−5.00000	−	8.66025i	−0.220541	−	0.381987i
$515$	−34.0000	+	58.8897i	−1.49822	+	2.59499i
$516$		0			0
$517$	−6.00000	+	10.3923i	−0.263880	+	0.457053i
$518$	−6.00000	+	5.19615i	−0.263625	+	0.228306i
$519$		0			0
$520$	12.0000			0.526235
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$		0			0
$523$	8.50000	−	14.7224i	0.371679	−	0.643767i	−0.618145	−	0.786064i	$-0.712116\pi$
$523$	8.50000	−	14.7224i	0.371679	−	0.643767i	0.989824	+	0.142297i	$0.0454489\pi$
$524$	2.00000	+	3.46410i	0.0873704	+	0.151330i
$525$		0			0
$526$	−1.00000	+	1.73205i	−0.0436021	+	0.0755210i
$527$	−9.00000	−	15.5885i	−0.392046	−	0.679044i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	12.0000	−	20.7846i	0.521247	−	0.902826i
$531$		0			0
$532$	−8.00000	+	6.92820i	−0.346844	+	0.300376i
$533$	−1.00000	−	1.73205i	−0.0433148	−	0.0750234i
$534$		0			0
$535$	−8.00000			−0.345870
$536$	21.0000			0.907062
$537$		0			0
$538$		0			0
$539$	13.0000	−	5.19615i	0.559950	−	0.223814i
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−5.50000	+	9.52628i	−0.236245	+	0.409189i
$543$		0			0
$544$	15.0000	+	25.9808i	0.643120	+	1.11392i
$545$	−18.0000	+	31.1769i	−0.771035	+	1.33547i
$546$		0			0
$547$	−21.5000	−	37.2391i	−0.919274	−	1.59223i	−0.800521	−	0.599305i	$-0.795444\pi$
$547$	−21.5000	−	37.2391i	−0.919274	−	1.59223i	−0.118753	−	0.992924i	$-0.537890\pi$
$548$	−9.00000	+	15.5885i	−0.384461	+	0.665906i
$549$		0			0
$550$	−11.0000	−	19.0526i	−0.469042	−	0.812404i
$551$	−8.00000			−0.340811
$552$		0			0
$553$	−27.5000	−	9.52628i	−1.16942	−	0.405099i
$554$	6.50000	−	11.2583i	0.276159	−	0.478321i
$555$		0			0
$556$	4.50000	−	7.79423i	0.190843	−	0.330549i
$557$	−14.0000	−	24.2487i	−0.593199	−	1.02745i	−0.993798	−	0.111198i	$-0.964531\pi$
$557$	−14.0000	−	24.2487i	−0.593199	−	1.02745i	0.400599	−	0.916253i	$-0.368802\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$	−2.00000	−	10.3923i	−0.0845154	−	0.439155i
$561$		0			0
$562$	−8.00000	−	13.8564i	−0.337460	−	0.584497i
$563$	10.0000			0.421450			0.210725	−	0.977545i	$-0.432418\pi$
$563$	10.0000			0.421450			0.210725	+	0.977545i	$0.432418\pi$
$564$		0			0
$565$	64.0000			2.69250
$566$	5.00000			0.210166
$567$		0			0
$568$		0			0
$569$	−32.0000			−1.34151			−0.670755	−	0.741679i	$-0.734030\pi$
$569$	−32.0000			−1.34151			−0.670755	+	0.741679i	$0.734030\pi$
$570$		0			0
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$	−1.00000	−	1.73205i	−0.0418121	−	0.0724207i
$573$		0			0
$574$	−4.00000	+	3.46410i	−0.166957	+	0.144589i
$575$	−66.0000			−2.75239
$576$		0			0
$577$	8.50000	+	14.7224i	0.353860	+	0.612903i	0.986922	−	0.161198i	$-0.0515357\pi$
$577$	8.50000	+	14.7224i	0.353860	+	0.612903i	−0.633062	+	0.774101i	$0.718202\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$		0			0
$580$	−4.00000	+	6.92820i	−0.166091	+	0.287678i
$581$	−3.00000	−	15.5885i	−0.124461	−	0.646718i
$582$		0			0
$583$	−12.0000			−0.496989
$584$	9.00000	+	15.5885i	0.372423	+	0.645055i
$585$		0			0
$586$	−11.0000	+	19.0526i	−0.454406	+	0.787054i
$587$	−14.0000	−	24.2487i	−0.577842	−	1.00085i	−0.995726	−	0.0923513i	$-0.970562\pi$
$587$	−14.0000	−	24.2487i	−0.577842	−	1.00085i	0.417885	−	0.908500i	$-0.362772\pi$
$588$		0			0
$589$	−6.00000	+	10.3923i	−0.247226	+	0.428207i
$590$	−12.0000	−	20.7846i	−0.494032	−	0.855689i
$591$		0			0
$592$	1.50000	−	2.59808i	0.0616496	−	0.106780i
$593$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$593$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$594$		0			0
$595$	48.0000	−	41.5692i	1.96781	−	1.70417i
$596$	12.0000	+	20.7846i	0.491539	+	0.851371i
$597$		0			0
$598$	6.00000			0.245358
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$		0			0
$601$	16.5000	+	28.5788i	0.673049	+	1.16576i	0.977035	+	0.213079i	$0.0683491\pi$
$601$	16.5000	+	28.5788i	0.673049	+	1.16576i	−0.303986	+	0.952676i	$0.598318\pi$
$602$	0.500000	+	2.59808i	0.0203785	+	0.105890i
$603$		0			0
$604$	2.50000	−	4.33013i	0.101724	−	0.176190i
$605$	14.0000	−	24.2487i	0.569181	−	0.985850i
$606$		0			0
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$	10.0000	−	17.3205i	0.405554	−	0.702439i
$609$		0			0
$610$	−10.0000	−	17.3205i	−0.404888	−	0.701287i
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$		0			0
$613$	−3.50000	−	6.06218i	−0.141364	−	0.244849i	0.786647	−	0.617403i	$-0.211815\pi$
$613$	−3.50000	−	6.06218i	−0.141364	−	0.244849i	−0.928010	+	0.372554i	$0.878482\pi$
$614$	−25.0000			−1.00892
$615$		0			0
$616$	−12.0000	+	10.3923i	−0.483494	+	0.418718i
$617$	−9.00000	+	15.5885i	−0.362326	+	0.627568i	−0.988343	−	0.152242i	$-0.951351\pi$
$617$	−9.00000	+	15.5885i	−0.362326	+	0.627568i	0.626017	+	0.779809i	$0.284684\pi$
$618$		0			0
$619$	20.5000	−	35.5070i	0.823965	−	1.42715i	−0.0787435	−	0.996895i	$-0.525091\pi$
$619$	20.5000	−	35.5070i	0.823965	−	1.42715i	0.902708	−	0.430254i	$-0.141576\pi$
$620$	6.00000	+	10.3923i	0.240966	+	0.417365i
$621$		0			0
$622$	24.0000			0.962312
$623$	8.00000	−	6.92820i	0.320513	−	0.277573i
$624$		0			0
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	22.0000			0.879297
$627$		0			0
$628$	−10.0000			−0.399043
$629$	18.0000			0.717707
$630$		0			0
$631$	5.00000			0.199047			0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000			0.199047			0.0995234	+	0.995035i	$0.468268\pi$
$632$	33.0000			1.31267
$633$		0			0
$634$	30.0000			1.19145
$635$	18.0000	+	31.1769i	0.714308	+	1.23722i
$636$		0			0
$637$	−6.50000	+	2.59808i	−0.257539	+	0.102940i
$638$	−4.00000			−0.158362
$639$		0			0
$640$	−6.00000	−	10.3923i	−0.237171	−	0.410792i
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	−0.800678	−	0.599095i	$-0.795527\pi$
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	0.919171	+	0.393860i	$0.128860\pi$
$642$		0			0
$643$	12.5000	−	21.6506i	0.492952	−	0.853818i	−0.507015	−	0.861937i	$-0.669251\pi$
$643$	12.5000	−	21.6506i	0.492952	−	0.853818i	0.999967	+	0.00811944i	$0.00258453\pi$
$644$	3.00000	+	15.5885i	0.118217	+	0.614271i
$645$		0			0
$646$	−24.0000			−0.944267
$647$	14.0000	+	24.2487i	0.550397	+	0.953315i	0.998246	+	0.0592060i	$0.0188569\pi$
$647$	14.0000	+	24.2487i	0.550397	+	0.953315i	−0.447849	+	0.894109i	$0.647810\pi$
$648$		0			0
$649$	−6.00000	+	10.3923i	−0.235521	+	0.407934i
$650$	5.50000	+	9.52628i	0.215728	+	0.373651i
$651$		0			0
$652$	9.50000	−	16.4545i	0.372049	−	0.644407i
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$	−8.00000	+	13.8564i	−0.312586	+	0.541415i
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$		0			0
$658$	−15.0000	−	5.19615i	−0.584761	−	0.202567i
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	0.958902	−	0.283738i	$-0.0915745\pi$
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	−0.725175	+	0.688565i	$0.758241\pi$
$660$		0			0
$661$	−14.0000			−0.544537			−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$	28.0000			1.08825
$663$		0			0
$664$	9.00000	+	15.5885i	0.349268	+	0.604949i
$665$	−40.0000	−	13.8564i	−1.55113	−	0.537328i
$666$		0			0
$667$	−6.00000	+	10.3923i	−0.232321	+	0.402392i
$668$	−7.00000	+	12.1244i	−0.270838	+	0.469105i
$669$		0			0
$670$	14.0000	+	24.2487i	0.540867	+	0.936809i
$671$	−5.00000	+	8.66025i	−0.193023	+	0.334325i
$672$		0			0
$673$	−11.0000	−	19.0526i	−0.424019	−	0.734422i	0.572309	−	0.820038i	$-0.306048\pi$
$673$	−11.0000	−	19.0526i	−0.424019	−	0.734422i	−0.996328	+	0.0856156i	$0.972714\pi$
$674$	5.00000	−	8.66025i	0.192593	−	0.333581i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	−12.0000			−0.461197			−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000			−0.461197			−0.230599	+	0.973049i	$0.574068\pi$
$678$		0			0
$679$	4.50000	+	23.3827i	0.172694	+	0.897345i
$680$	−36.0000	+	62.3538i	−1.38054	+	2.39116i
$681$		0			0
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$683$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$684$		0			0
$685$	−72.0000			−2.75098
$686$	10.0000	+	15.5885i	0.381802	+	0.595170i
$687$		0			0
$688$	−0.500000	−	0.866025i	−0.0190623	−	0.0330169i
$689$	6.00000			0.228582
$690$		0			0
$691$	41.0000			1.55971			0.779857	−	0.625958i	$-0.215292\pi$
$691$	41.0000			1.55971			0.779857	+	0.625958i	$0.215292\pi$
$692$	16.0000			0.608229
$693$		0			0
$694$	16.0000			0.607352
$695$	36.0000			1.36556
$696$		0			0
$697$	12.0000			0.454532
$698$	−2.50000	−	4.33013i	−0.0946264	−	0.163898i
$699$		0			0
$700$	−22.0000	+	19.0526i	−0.831522	+	0.720119i
$701$	−24.0000			−0.906467			−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000			−0.906467			−0.453234	+	0.891392i	$0.649730\pi$
$702$		0			0
$703$	−6.00000	−	10.3923i	−0.226294	−	0.391953i
$704$	7.00000	−	12.1244i	0.263822	−	0.456954i
$705$		0			0
$706$	14.0000	−	24.2487i	0.526897	−	0.912612i
$707$	16.0000	−	13.8564i	0.601742	−	0.521124i
$708$		0			0
$709$	21.0000			0.788672			0.394336	−	0.918966i	$-0.370975\pi$
$709$	21.0000			0.788672			0.394336	+	0.918966i	$0.370975\pi$
$710$		0			0
$711$		0			0
$712$	−6.00000	+	10.3923i	−0.224860	+	0.389468i
$713$	9.00000	+	15.5885i	0.337053	+	0.583792i
$714$		0			0
$715$	4.00000	−	6.92820i	0.149592	−	0.259100i
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$		0			0
$718$	−11.0000	+	19.0526i	−0.410516	+	0.711035i
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.0613050	+	0.998119i	$0.519526\pi$
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.833744	+	0.552151i	$0.813807\pi$
$720$		0			0
$721$	8.50000	+	44.1673i	0.316557	+	1.64488i
$722$	−1.50000	−	2.59808i	−0.0558242	−	0.0966904i
$723$		0			0
$724$	2.00000			0.0743294
$725$	−22.0000			−0.817059
$726$		0			0
$727$	−20.5000	−	35.5070i	−0.760303	−	1.31688i	−0.942694	−	0.333657i	$-0.891717\pi$
$727$	−20.5000	−	35.5070i	−0.760303	−	1.31688i	0.182392	−	0.983226i	$-0.441616\pi$
$728$	6.00000	−	5.19615i	0.222375	−	0.192582i
$729$		0			0
$730$	−12.0000	+	20.7846i	−0.444140	+	0.769273i
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$		0			0
$733$	−10.5000	−	18.1865i	−0.387826	−	0.671735i	0.604331	−	0.796734i	$-0.293441\pi$
$733$	−10.5000	−	18.1865i	−0.387826	−	0.671735i	−0.992157	+	0.124999i	$0.960107\pi$
$734$	6.00000	−	10.3923i	0.221464	−	0.383587i
$735$		0			0
$736$	−15.0000	−	25.9808i	−0.552907	−	0.957664i
$737$	7.00000	−	12.1244i	0.257848	−	0.446606i
$738$		0			0
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	0.936845	−	0.349744i	$-0.113732\pi$
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	−0.771310	+	0.636460i	$0.780398\pi$
$740$	−12.0000			−0.441129
$741$		0			0
$742$	−3.00000	−	15.5885i	−0.110133	−	0.572270i
$743$	−21.0000	+	36.3731i	−0.770415	+	1.33440i	0.166920	+	0.985970i	$0.446618\pi$
$743$	−21.0000	+	36.3731i	−0.770415	+	1.33440i	−0.937336	+	0.348428i	$0.886716\pi$
$744$		0			0
$745$	−48.0000	+	83.1384i	−1.75858	+	3.04596i
$746$	13.0000	+	22.5167i	0.475964	+	0.824394i
$747$		0			0
$748$	12.0000			0.438763
$749$	−4.00000	+	3.46410i	−0.146157	+	0.126576i
$750$		0			0
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	0.929731	−	0.368238i	$-0.120039\pi$
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	−0.783769	+	0.621052i	$0.786706\pi$
$752$	6.00000			0.218797
$753$		0			0
$754$	2.00000			0.0728357
$755$	20.0000			0.727875
$756$		0			0
$757$	17.0000			0.617876			0.308938	−	0.951082i	$-0.400027\pi$
$757$	17.0000			0.617876			0.308938	+	0.951082i	$0.400027\pi$
$758$	9.00000			0.326895
$759$		0			0
$760$	48.0000			1.74114
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.861996	−	0.506915i	$-0.830786\pi$
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.00800331	−	0.999968i	$-0.502548\pi$
$762$		0			0
$763$	4.50000	+	23.3827i	0.162911	+	0.846510i
$764$	−4.00000			−0.144715
$765$		0			0
$766$	9.00000	+	15.5885i	0.325183	+	0.563234i
$767$	3.00000	−	5.19615i	0.108324	−	0.187622i
$768$		0			0
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	−0.761680	−	0.647954i	$-0.775625\pi$
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	0.941984	+	0.335657i	$0.108958\pi$
$770$	−20.0000	−	6.92820i	−0.720750	−	0.249675i
$771$		0			0
$772$	25.0000			0.899770
$773$	8.00000	+	13.8564i	0.287740	+	0.498380i	0.973270	−	0.229664i	$-0.0737628\pi$
$773$	8.00000	+	13.8564i	0.287740	+	0.498380i	−0.685530	+	0.728044i	$0.740429\pi$
$774$		0			0
$775$	−16.5000	+	28.5788i	−0.592697	+	1.02658i
$776$	−13.5000	−	23.3827i	−0.484622	−	0.839390i
$777$		0			0
$778$	6.00000	−	10.3923i	0.215110	−	0.372582i
$779$	−4.00000	−	6.92820i	−0.143315	−	0.248229i
$780$		0			0
$781$		0			0
$782$	−18.0000	+	31.1769i	−0.643679	+	1.11488i
$783$		0			0
$784$	−5.50000	−	4.33013i	−0.196429	−	0.154647i
$785$	−20.0000	−	34.6410i	−0.713831	−	1.23639i
$786$		0			0
$787$	−47.0000			−1.67537			−0.837685	−	0.546154i	$-0.816091\pi$
$787$	−47.0000			−1.67537			−0.837685	+	0.546154i	$0.816091\pi$
$788$	20.0000			0.712470
$789$		0			0
$790$	22.0000	+	38.1051i	0.782725	+	1.35572i
$791$	32.0000	−	27.7128i	1.13779	−	0.985354i
$792$		0			0
$793$	2.50000	−	4.33013i	0.0887776	−	0.153767i
$794$	−16.5000	+	28.5788i	−0.585563	+	1.01423i
$795$		0			0
$796$	−4.50000	−	7.79423i	−0.159498	−	0.276259i
$797$	7.00000	−	12.1244i	0.247953	−	0.429467i	−0.715005	−	0.699119i	$-0.753576\pi$
$797$	7.00000	−	12.1244i	0.247953	−	0.429467i	0.962958	+	0.269653i	$0.0869089\pi$
$798$		0			0
$799$	18.0000	+	31.1769i	0.636794	+	1.10296i
$800$	27.5000	−	47.6314i	0.972272	−	1.68402i
$801$		0			0
$802$	−15.0000	−	25.9808i	−0.529668	−	0.917413i
$803$	12.0000			0.423471
$804$		0			0
$805$	−48.0000	+	41.5692i	−1.69178	+	1.46512i
$806$	1.50000	−	2.59808i	0.0528352	−	0.0915133i
$807$		0			0
$808$	−12.0000	+	20.7846i	−0.422159	+	0.731200i
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$		0			0
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$	1.00000	+	5.19615i	0.0350931	+	0.182349i
$813$		0			0
$814$	−3.00000	−	5.19615i	−0.105150	−	0.182125i
$815$	76.0000			2.66216
$816$		0			0
$817$	−4.00000			−0.139942
$818$	−5.00000			−0.174821
$819$		0			0
$820$	−8.00000			−0.279372
$821$	−22.0000			−0.767805			−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000			−0.767805			−0.383903	+	0.923374i	$0.625420\pi$
$822$		0			0
$823$	45.0000			1.56860			0.784301	−	0.620381i	$-0.213022\pi$
$823$	45.0000			1.56860			0.784301	+	0.620381i	$0.213022\pi$
$824$	−25.5000	−	44.1673i	−0.888335	−	1.53864i
$825$		0			0
$826$	−15.0000	−	5.19615i	−0.521917	−	0.180797i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	0.939696	−	0.342012i	$-0.111108\pi$
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	−0.766039	+	0.642795i	$0.777775\pi$
$830$	−12.0000	+	20.7846i	−0.416526	+	0.721444i
$831$		0			0
$832$	−3.50000	+	6.06218i	−0.121341	+	0.210168i
$833$	6.00000	−	41.5692i	0.207888	−	1.44029i
$834$		0			0
$835$	−56.0000			−1.93796
$836$	−4.00000	−	6.92820i	−0.138343	−	0.239617i
$837$		0			0
$838$	6.00000	−	10.3923i	0.207267	−	0.358996i
$839$	13.0000	+	22.5167i	0.448810	+	0.777361i	0.998309	−	0.0581329i	$-0.0185147\pi$
$839$	13.0000	+	22.5167i	0.448810	+	0.777361i	−0.549499	+	0.835494i	$0.685181\pi$
$840$		0			0
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	−5.00000	−	8.66025i	−0.172311	−	0.298452i
$843$		0			0
$844$	−2.50000	+	4.33013i	−0.0860535	+	0.149049i
$845$	24.0000	−	41.5692i	0.825625	−	1.43002i
$846$		0			0
$847$	−3.50000	−	18.1865i	−0.120261	−	0.624897i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$		0			0
$850$	−66.0000			−2.26378
$851$	−18.0000			−0.617032
$852$		0			0
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	0.552948	−	0.833215i	$-0.313503\pi$
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	−0.998060	+	0.0622597i	$0.980169\pi$
$854$	−12.5000	−	4.33013i	−0.427741	−	0.148174i
$855$		0			0
$856$	3.00000	−	5.19615i	0.102538	−	0.177601i
$857$	−8.00000	+	13.8564i	−0.273275	+	0.473326i	−0.969698	−	0.244305i	$-0.921440\pi$
$857$	−8.00000	+	13.8564i	−0.273275	+	0.473326i	0.696424	+	0.717631i	$0.254773\pi$
$858$		0			0
$859$	12.5000	+	21.6506i	0.426494	+	0.738710i	0.996559	−	0.0828900i	$-0.0264150\pi$
$859$	12.5000	+	21.6506i	0.426494	+	0.738710i	−0.570064	+	0.821600i	$0.693082\pi$
$860$	−2.00000	+	3.46410i	−0.0681994	+	0.118125i
$861$		0			0
$862$	−9.00000	−	15.5885i	−0.306541	−	0.530945i
$863$	18.0000	−	31.1769i	0.612727	−	1.06127i	−0.378052	−	0.925785i	$-0.623406\pi$
$863$	18.0000	−	31.1769i	0.612727	−	1.06127i	0.990779	−	0.135490i	$-0.0432609\pi$
$864$		0			0
$865$	32.0000	+	55.4256i	1.08803	+	1.88453i
$866$	17.0000			0.577684
$867$		0			0
$868$	7.50000	+	2.59808i	0.254567	+	0.0881845i
$869$	11.0000	−	19.0526i	0.373149	−	0.646314i
$870$		0			0
$871$	−3.50000	+	6.06218i	−0.118593	+	0.205409i
$872$	−13.5000	−	23.3827i	−0.457168	−	0.791838i
$873$		0			0
$874$	24.0000			0.811812
$875$	−60.0000	−	20.7846i	−2.02837	−	0.702648i
$876$		0			0
$877$	−3.50000	−	6.06218i	−0.118187	−	0.204705i	0.800862	−	0.598848i	$-0.204375\pi$
$877$	−3.50000	−	6.06218i	−0.118187	−	0.204705i	−0.919049	+	0.394143i	$0.871041\pi$
$878$	−24.0000			−0.809961
$879$		0			0
$880$	8.00000			0.269680
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	−6.00000			−0.201802
$885$		0			0
$886$	−24.0000			−0.806296
$887$	11.0000	+	19.0526i	0.369344	+	0.639722i	0.989463	−	0.144785i	$-0.0462491\pi$
$887$	11.0000	+	19.0526i	0.369344	+	0.639722i	−0.620119	+	0.784508i	$0.712916\pi$
$888$		0			0
$889$	22.5000	+	7.79423i	0.754626	+	0.261410i
$890$	−16.0000			−0.536321
$891$		0			0
$892$	8.00000	+	13.8564i	0.267860	+	0.463947i
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$		0			0
$895$	8.00000	−	13.8564i	0.267411	−	0.463169i
$896$	−7.50000	−	2.59808i	−0.250557	−	0.0867956i
$897$		0			0
$898$	−36.0000			−1.20134
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$	−2.00000	−	3.46410i	−0.0665927	−	0.115342i
$903$		0			0
$904$	−24.0000	+	41.5692i	−0.798228	+	1.38257i
$905$	4.00000	+	6.92820i	0.132964	+	0.230301i
$906$		0			0
$907$	6.50000	−	11.2583i	0.215829	−	0.373827i	−0.737700	−	0.675129i	$-0.764088\pi$
$907$	6.50000	−	11.2583i	0.215829	−	0.373827i	0.953529	+	0.301302i	$0.0974213\pi$
$908$	−9.00000	+	15.5885i	−0.298675	+	0.517321i
$909$		0			0
$910$	10.0000	+	3.46410i	0.331497	+	0.114834i
$911$	−9.00000	−	15.5885i	−0.298183	−	0.516469i	0.677537	−	0.735489i	$-0.263047\pi$
$911$	−9.00000	−	15.5885i	−0.298183	−	0.516469i	−0.975720	+	0.219020i	$0.929714\pi$
$912$		0			0
$913$	12.0000			0.397142
$914$	−13.0000			−0.430002
$915$		0			0
$916$	−3.50000	−	6.06218i	−0.115643	−	0.200300i
$917$	2.00000	+	10.3923i	0.0660458	+	0.343184i
$918$		0			0
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	−0.999691	−	0.0248659i	$-0.992084\pi$
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	0.521380	+	0.853325i	$0.325417\pi$
$920$	36.0000	−	62.3538i	1.18688	−	2.05574i
$921$		0			0
$922$	1.00000	+	1.73205i	0.0329332	+	0.0570421i
$923$		0			0
$924$		0			0
$925$	−16.5000	−	28.5788i	−0.542517	−	0.939666i
$926$	−16.0000	+	27.7128i	−0.525793	+	0.910700i
$927$		0			0
$928$	−5.00000	−	8.66025i	−0.164133	−	0.284287i
$929$	−4.00000			−0.131236			−0.0656179	−	0.997845i	$-0.520902\pi$
$929$	−4.00000			−0.131236			−0.0656179	+	0.997845i	$0.520902\pi$
$930$		0			0
$931$	−26.0000	+	10.3923i	−0.852116	+	0.340594i
$932$	12.0000	−	20.7846i	0.393073	−	0.680823i
$933$		0			0
$934$		0			0
$935$	24.0000	+	41.5692i	0.784884	+	1.35946i
$936$		0			0
$937$	−21.0000			−0.686040			−0.343020	−	0.939328i	$-0.611450\pi$
$937$	−21.0000			−0.686040			−0.343020	+	0.939328i	$0.611450\pi$
$938$	17.5000	+	6.06218i	0.571395	+	0.197937i
$939$		0			0
$940$	−12.0000	−	20.7846i	−0.391397	−	0.677919i
$941$	−46.0000			−1.49956			−0.749779	−	0.661689i	$-0.769840\pi$
$941$	−46.0000			−1.49956			−0.749779	+	0.661689i	$0.769840\pi$
$942$		0			0
$943$	−12.0000			−0.390774
$944$	6.00000			0.195283
$945$		0			0
$946$	−2.00000			−0.0650256
$947$	26.0000			0.844886			0.422443	−	0.906389i	$-0.361173\pi$
$947$	26.0000			0.844886			0.422443	+	0.906389i	$0.361173\pi$
$948$		0			0
$949$	−6.00000			−0.194768
$950$	22.0000	+	38.1051i	0.713774	+	1.23629i
$951$		0			0
$952$	9.00000	+	46.7654i	0.291692	+	1.51567i
$953$	14.0000			0.453504			0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000			0.453504			0.226752	+	0.973952i	$0.427189\pi$
$954$		0			0
$955$	−8.00000	−	13.8564i	−0.258874	−	0.448383i
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$		0			0
$958$	−8.00000	+	13.8564i	−0.258468	+	0.447680i
$959$	−36.0000	+	31.1769i	−1.16250	+	1.00676i
$960$		0			0
$961$	−22.0000			−0.709677
$962$	1.50000	+	2.59808i	0.0483619	+	0.0837653i
$963$		0			0
$964$	8.50000	−	14.7224i	0.273767	−	0.474178i
$965$	50.0000	+	86.6025i	1.60956	+	2.78783i
$966$		0			0
$967$	8.50000	−	14.7224i	0.273342	−	0.473441i	−0.696374	−	0.717679i	$-0.745204\pi$
$967$	8.50000	−	14.7224i	0.273342	−	0.473441i	0.969715	+	0.244238i	$0.0785377\pi$
$968$	10.5000	+	18.1865i	0.337483	+	0.584537i
$969$		0			0
$970$	18.0000	−	31.1769i	0.577945	−	1.00103i
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$		0			0
$973$	18.0000	−	15.5885i	0.577054	−	0.499743i
$974$	8.00000	+	13.8564i	0.256337	+	0.443988i
$975$		0			0
$976$	5.00000			0.160046
$977$	−6.00000			−0.191957			−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000			−0.191957			−0.0959785	+	0.995383i	$0.530598\pi$
$978$		0			0
$979$	4.00000	+	6.92820i	0.127841	+	0.221426i
$980$	−4.00000	+	27.7128i	−0.127775	+	0.885253i
$981$		0			0
$982$	−17.0000	+	29.4449i	−0.542492	+	0.939623i
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	40.0000	+	69.2820i	1.27451	+	2.20751i
$986$	−6.00000	+	10.3923i	−0.191079	+	0.330958i
$987$		0			0
$988$	2.00000	+	3.46410i	0.0636285	+	0.110208i
$989$	−3.00000	+	5.19615i	−0.0953945	+	0.165228i
$990$		0			0
$991$	27.5000	+	47.6314i	0.873566	+	1.51306i	0.858282	+	0.513178i	$0.171532\pi$
$991$	27.5000	+	47.6314i	0.873566	+	1.51306i	0.0152841	+	0.999883i	$0.495135\pi$
$992$	−15.0000			−0.476250
$993$		0			0
$994$		0			0
$995$	18.0000	−	31.1769i	0.570638	−	0.988375i
$996$		0			0
$997$	14.5000	−	25.1147i	0.459220	−	0.795392i	−0.539700	−	0.841857i	$-0.681462\pi$
$997$	14.5000	−	25.1147i	0.459220	−	0.795392i	0.998920	+	0.0464655i	$0.0147958\pi$
$998$	−8.50000	−	14.7224i	−0.269063	−	0.466030i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.b.352.1		2
3.2	odd	2		567.2.h.e.352.1		2
7.4	even	3		567.2.g.e.109.1		2
9.2	odd	6		567.2.g.b.541.1		2
9.4	even	3		189.2.e.c.163.1	yes	2
9.5	odd	6		189.2.e.a.163.1	yes	2
9.7	even	3		567.2.g.e.541.1		2
21.11	odd	6		567.2.g.b.109.1		2
63.4	even	3		189.2.e.c.109.1	yes	2
63.5	even	6		1323.2.a.p.1.1		1
63.11	odd	6		567.2.h.e.298.1		2
63.23	odd	6		1323.2.a.m.1.1		1
63.25	even	3	inner	567.2.h.b.298.1		2
63.32	odd	6		189.2.e.a.109.1	✓	2
63.40	odd	6		1323.2.a.d.1.1		1
63.58	even	3		1323.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.a.109.1	✓	2	63.32	odd	6
189.2.e.a.163.1	yes	2	9.5	odd	6
189.2.e.c.109.1	yes	2	63.4	even	3
189.2.e.c.163.1	yes	2	9.4	even	3
567.2.g.b.109.1		2	21.11	odd	6
567.2.g.b.541.1		2	9.2	odd	6
567.2.g.e.109.1		2	7.4	even	3
567.2.g.e.541.1		2	9.7	even	3
567.2.h.b.298.1		2	63.25	even	3	inner
567.2.h.b.352.1		2	1.1	even	1	trivial
567.2.h.e.298.1		2	63.11	odd	6
567.2.h.e.352.1		2	3.2	odd	2
1323.2.a.d.1.1		1	63.40	odd	6
1323.2.a.g.1.1		1	63.58	even	3
1323.2.a.m.1.1		1	63.23	odd	6
1323.2.a.p.1.1		1	63.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{4} +(-2.00000 - 3.46410i) q^{5} +(-2.50000 - 0.866025i) q^{7} +3.00000 q^{8} +(2.00000 + 3.46410i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(2.50000 + 0.866025i) q^{14} -1.00000 q^{16} +(-3.00000 - 5.19615i) q^{17} +(-2.00000 + 3.46410i) q^{19} +(2.00000 + 3.46410i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-5.50000 + 9.52628i) q^{25} +(0.500000 - 0.866025i) q^{26} +(2.50000 + 0.866025i) q^{28} +(1.00000 + 1.73205i) q^{29} +3.00000 q^{31} -5.00000 q^{32} +(3.00000 + 5.19615i) q^{34} +(2.00000 + 10.3923i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(2.00000 - 3.46410i) q^{38} +(-6.00000 - 10.3923i) q^{40} +(-1.00000 + 1.73205i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-3.00000 - 5.19615i) q^{46} -6.00000 q^{47} +(5.50000 + 4.33013i) q^{49} +(5.50000 - 9.52628i) q^{50} +(0.500000 - 0.866025i) q^{52} +(-3.00000 - 5.19615i) q^{53} -8.00000 q^{55} +(-7.50000 - 2.59808i) q^{56} +(-1.00000 - 1.73205i) q^{58} -6.00000 q^{59} -5.00000 q^{61} -3.00000 q^{62} +7.00000 q^{64} +4.00000 q^{65} +7.00000 q^{67} +(3.00000 + 5.19615i) q^{68} +(-2.00000 - 10.3923i) q^{70} +(3.00000 + 5.19615i) q^{73} +(1.50000 - 2.59808i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-4.00000 + 3.46410i) q^{77} +11.0000 q^{79} +(2.00000 + 3.46410i) q^{80} +(1.00000 - 1.73205i) q^{82} +(3.00000 + 5.19615i) q^{83} +(-12.0000 + 20.7846i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{88} +(-2.00000 + 3.46410i) q^{89} +(2.00000 - 1.73205i) q^{91} +(-3.00000 - 5.19615i) q^{92} +6.00000 q^{94} +16.0000 q^{95} +(-4.50000 - 7.79423i) q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{4} - 4 q^{5} - 5 q^{7} + 6 q^{8} + 4 q^{10} + 2 q^{11} - q^{13} + 5 q^{14} - 2 q^{16} - 6 q^{17} - 4 q^{19} + 4 q^{20} - 2 q^{22} + 6 q^{23} - 11 q^{25} + q^{26} + 5 q^{28} + 2 q^{29}+ \cdots - 11 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 - 5 * q^7 + 6 * q^8 + 4 * q^10 + 2 * q^11 - q^13 + 5 * q^14 - 2 * q^16 - 6 * q^17 - 4 * q^19 + 4 * q^20 - 2 * q^22 + 6 * q^23 - 11 * q^25 + q^26 + 5 * q^28 + 2 * q^29 + 6 * q^31 - 10 * q^32 + 6 * q^34 + 4 * q^35 - 3 * q^37 + 4 * q^38 - 12 * q^40 - 2 * q^41 + q^43 - 2 * q^44 - 6 * q^46 - 12 * q^47 + 11 * q^49 + 11 * q^50 + q^52 - 6 * q^53 - 16 * q^55 - 15 * q^56 - 2 * q^58 - 12 * q^59 - 10 * q^61 - 6 * q^62 + 14 * q^64 + 8 * q^65 + 14 * q^67 + 6 * q^68 - 4 * q^70 + 6 * q^73 + 3 * q^74 + 4 * q^76 - 8 * q^77 + 22 * q^79 + 4 * q^80 + 2 * q^82 + 6 * q^83 - 24 * q^85 - q^86 + 6 * q^88 - 4 * q^89 + 4 * q^91 - 6 * q^92 + 12 * q^94 + 32 * q^95 - 9 * q^97 - 11 * q^98

Introduction

L-functions

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Database

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