LMFDB - Embedded newform 755.2.e.a.636.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [755,2,Mod(571,755)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(755, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("755.571"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 755 = 5 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	755.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.02870535261$
Analytic rank:	$0$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			636.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	755.636
Dual form			755.2.e.a.571.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} -2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{6} +3.00000 q^{8} +1.00000 q^{9} +(0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{12} +(1.00000 + 1.73205i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-4.00000 - 6.92820i) q^{17} +(0.500000 + 0.866025i) q^{18} -1.00000 q^{19} -1.00000 q^{20} +(-1.50000 + 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} -6.00000 q^{24} +(-0.500000 + 0.866025i) q^{25} +4.00000 q^{27} +9.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(2.50000 - 4.33013i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(4.00000 - 6.92820i) q^{34} +(0.500000 - 0.866025i) q^{36} +(-5.00000 - 8.66025i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(-1.50000 - 2.59808i) q^{40} -7.00000 q^{41} +(2.00000 - 3.46410i) q^{43} +3.00000 q^{44} +(-0.500000 - 0.866025i) q^{45} +(3.00000 - 5.19615i) q^{46} +(1.00000 - 1.73205i) q^{47} +(-1.00000 - 1.73205i) q^{48} +(3.50000 - 6.06218i) q^{49} -1.00000 q^{50} +(8.00000 + 13.8564i) q^{51} -4.00000 q^{53} +(2.00000 + 3.46410i) q^{54} +(1.50000 - 2.59808i) q^{55} +2.00000 q^{57} +(4.50000 + 7.79423i) q^{58} -1.00000 q^{59} +2.00000 q^{60} +(-4.50000 + 7.79423i) q^{61} +(2.00000 - 3.46410i) q^{62} +7.00000 q^{64} +(3.00000 - 5.19615i) q^{66} +8.00000 q^{67} -8.00000 q^{68} +(6.00000 + 10.3923i) q^{69} +(-1.50000 + 2.59808i) q^{71} +3.00000 q^{72} +2.00000 q^{73} +(5.00000 - 8.66025i) q^{74} +(1.00000 - 1.73205i) q^{75} +(-0.500000 + 0.866025i) q^{76} +16.0000 q^{79} +(0.500000 - 0.866025i) q^{80} -11.0000 q^{81} +(-3.50000 - 6.06218i) q^{82} -6.00000 q^{83} +(-4.00000 + 6.92820i) q^{85} +4.00000 q^{86} -18.0000 q^{87} +(4.50000 + 7.79423i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(0.500000 - 0.866025i) q^{90} -6.00000 q^{92} +(4.00000 + 6.92820i) q^{93} +2.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(-5.00000 + 8.66025i) q^{96} +(7.00000 + 12.1244i) q^{97} +7.00000 q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 4 q^{3} + q^{4} - q^{5} - 2 q^{6} + 6 q^{8} + 2 q^{9} + q^{10} + 3 q^{11} - 2 q^{12} + 2 q^{15} + q^{16} - 8 q^{17} + q^{18} - 2 q^{19} - 2 q^{20} - 3 q^{22} - 6 q^{23} - 12 q^{24} - q^{25}+ \cdots + 3 q^{99}+O(q^{100}) $ 2 * q + q^2 - 4 * q^3 + q^4 - q^5 - 2 * q^6 + 6 * q^8 + 2 * q^9 + q^10 + 3 * q^11 - 2 * q^12 + 2 * q^15 + q^16 - 8 * q^17 + q^18 - 2 * q^19 - 2 * q^20 - 3 * q^22 - 6 * q^23 - 12 * q^24 - q^25 + 8 * q^27 + 18 * q^29 - 2 * q^30 - 4 * q^31 + 5 * q^32 - 6 * q^33 + 8 * q^34 + q^36 - 10 * q^37 - q^38 - 3 * q^40 - 14 * q^41 + 4 * q^43 + 6 * q^44 - q^45 + 6 * q^46 + 2 * q^47 - 2 * q^48 + 7 * q^49 - 2 * q^50 + 16 * q^51 - 8 * q^53 + 4 * q^54 + 3 * q^55 + 4 * q^57 + 9 * q^58 - 2 * q^59 + 4 * q^60 - 9 * q^61 + 4 * q^62 + 14 * q^64 + 6 * q^66 + 16 * q^67 - 16 * q^68 + 12 * q^69 - 3 * q^71 + 6 * q^72 + 4 * q^73 + 10 * q^74 + 2 * q^75 - q^76 + 32 * q^79 + q^80 - 22 * q^81 - 7 * q^82 - 12 * q^83 - 8 * q^85 + 8 * q^86 - 36 * q^87 + 9 * q^88 - 2 * q^89 + q^90 - 12 * q^92 + 8 * q^93 + 4 * q^94 + q^95 - 10 * q^96 + 14 * q^97 + 14 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/755\mathbb{Z}\right)^\times$.

$n$	$6$	$152$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	−2.00000			−1.15470			−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000			−1.15470			−0.577350	+	0.816497i	$0.695913\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.00000	−	1.73205i	−0.408248	−	0.707107i
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$	3.00000			1.06066
$9$	1.00000			0.333333
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$13$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$14$		0			0
$15$	1.00000	+	1.73205i	0.258199	+	0.447214i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−4.00000	−	6.92820i	−0.970143	−	1.68034i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−4.00000	−	6.92820i	−0.970143	−	1.68034i	−0.275029	−	0.961436i	$-0.588688\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−1.00000			−0.229416			−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000			−0.229416			−0.114708	+	0.993399i	$0.536593\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	−6.00000			−1.22474
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$	4.00000	−	6.92820i	0.685994	−	1.18818i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	0.0821995	−	0.996616i	$-0.473806\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$		0			0
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	3.00000			0.452267
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$	−1.00000	−	1.73205i	−0.144338	−	0.250000i
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$	−1.00000			−0.141421
$51$	8.00000	+	13.8564i	1.12022	+	1.94029i
$52$		0			0
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	1.50000	−	2.59808i	0.202260	−	0.350325i
$56$		0			0
$57$	2.00000			0.264906
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	−1.00000			−0.130189			−0.0650945	−	0.997879i	$-0.520735\pi$
$59$	−1.00000			−0.130189			−0.0650945	+	0.997879i	$0.520735\pi$
$60$	2.00000			0.258199
$61$	−4.50000	+	7.79423i	−0.576166	+	0.997949i	0.419748	+	0.907641i	$0.362118\pi$
$61$	−4.50000	+	7.79423i	−0.576166	+	0.997949i	−0.995914	+	0.0903080i	$0.971215\pi$
$62$	2.00000	−	3.46410i	0.254000	−	0.439941i
$63$		0			0
$64$	7.00000			0.875000
$65$		0			0
$66$	3.00000	−	5.19615i	0.369274	−	0.639602i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	−8.00000			−0.970143
$69$	6.00000	+	10.3923i	0.722315	+	1.25109i
$70$		0			0
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	−0.941201	−	0.337846i	$-0.890302\pi$
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	0.763184	+	0.646181i	$0.223635\pi$
$72$	3.00000			0.353553
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	5.00000	−	8.66025i	0.581238	−	1.00673i
$75$	1.00000	−	1.73205i	0.115470	−	0.200000i
$76$	−0.500000	+	0.866025i	−0.0573539	+	0.0993399i
$77$		0			0
$78$		0			0
$79$	16.0000			1.80014			0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000			1.80014			0.900070	+	0.435745i	$0.143515\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−11.0000			−1.22222
$82$	−3.50000	−	6.06218i	−0.386510	−	0.669456i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	−4.00000	+	6.92820i	−0.433861	+	0.751469i
$86$	4.00000			0.431331
$87$	−18.0000			−1.92980
$88$	4.50000	+	7.79423i	0.479702	+	0.830868i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$		0			0
$92$	−6.00000			−0.625543
$93$	4.00000	+	6.92820i	0.414781	+	0.718421i
$94$	2.00000			0.206284
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	−5.00000	+	8.66025i	−0.510310	+	0.883883i
$97$	7.00000	+	12.1244i	0.710742	+	1.23104i	0.964579	+	0.263795i	$0.0849741\pi$
$97$	7.00000	+	12.1244i	0.710742	+	1.23104i	−0.253837	+	0.967247i	$0.581693\pi$
$98$	7.00000			0.707107
$99$	1.50000	+	2.59808i	0.150756	+	0.261116i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−17.0000			−1.69156			−0.845782	−	0.533529i	$-0.820865\pi$
$101$	−17.0000			−1.69156			−0.845782	+	0.533529i	$0.820865\pi$
$102$	−8.00000	+	13.8564i	−0.792118	+	1.37199i
$103$	−3.00000	−	5.19615i	−0.295599	−	0.511992i	0.679525	−	0.733652i	$-0.262186\pi$
$103$	−3.00000	−	5.19615i	−0.295599	−	0.511992i	−0.975124	+	0.221660i	$0.928852\pi$
$104$		0			0
$105$		0			0
$106$	−2.00000	−	3.46410i	−0.194257	−	0.336463i
$107$	−8.00000			−0.773389			−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000			−0.773389			−0.386695	+	0.922208i	$0.626383\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	−0.00790932	−	0.999969i	$-0.502518\pi$
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	0.869953	−	0.493135i	$-0.164149\pi$
$110$	3.00000			0.286039
$111$	10.0000	+	17.3205i	0.949158	+	1.64399i
$112$		0			0
$113$	−2.00000	−	3.46410i	−0.188144	−	0.325875i	0.756487	−	0.654008i	$-0.226914\pi$
$113$	−2.00000	−	3.46410i	−0.188144	−	0.325875i	−0.944632	+	0.328133i	$0.893581\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$	4.50000	−	7.79423i	0.417815	−	0.723676i
$117$		0			0
$118$	−0.500000	−	0.866025i	−0.0460287	−	0.0797241i
$119$		0			0
$120$	3.00000	+	5.19615i	0.273861	+	0.474342i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−9.00000			−0.814822
$123$	14.0000			1.26234
$124$	−4.00000			−0.359211
$125$	1.00000			0.0894427
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$		0			0
$131$	21.0000			1.83478			0.917389	−	0.397991i	$-0.130293\pi$
$131$	21.0000			1.83478			0.917389	+	0.397991i	$0.130293\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$	4.00000	+	6.92820i	0.345547	+	0.598506i
$135$	−2.00000	−	3.46410i	−0.172133	−	0.298142i
$136$	−12.0000	−	20.7846i	−1.02899	−	1.78227i
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$	−6.00000	+	10.3923i	−0.510754	+	0.884652i
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	−0.795373	−	0.606120i	$-0.792725\pi$
$139$	1.50000	−	2.59808i	0.127228	−	0.220366i	0.922602	+	0.385754i	$0.126059\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$	−3.00000			−0.251754
$143$		0			0
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$	−7.00000	+	12.1244i	−0.577350	+	1.00000i
$148$	−10.0000			−0.821995
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$	2.00000			0.163299
$151$	2.00000	+	12.1244i	0.162758	+	0.986666i
$151$	2.00000	+	12.1244i	0.162758	+	0.986666i
$152$	−3.00000			−0.243332
$153$	−4.00000	−	6.92820i	−0.323381	−	0.560112i
$154$		0			0
$155$	−2.00000	+	3.46410i	−0.160644	+	0.278243i
$156$		0			0
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$	8.00000	+	13.8564i	0.636446	+	1.10236i
$159$	8.00000			0.634441
$160$	−5.00000			−0.395285
$161$		0			0
$162$	−5.50000	−	9.52628i	−0.432121	−	0.748455i
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	−3.50000	+	6.06218i	−0.273304	+	0.473377i
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	0.969693	+	0.244328i	$0.0785675\pi$
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	−0.273252	+	0.961943i	$0.588099\pi$
$168$		0			0
$169$	6.50000	+	11.2583i	0.500000	+	0.866025i
$170$	−8.00000			−0.613572
$171$	−1.00000			−0.0764719
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	−0.931984	−	0.362500i	$-0.881923\pi$
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	0.779926	+	0.625871i	$0.215256\pi$
$174$	−9.00000	−	15.5885i	−0.682288	−	1.18176i
$175$		0			0
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$	2.00000			0.150329
$178$	−2.00000			−0.149906
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−1.00000			−0.0745356
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	0.706129	+	0.708083i	$0.250440\pi$
$182$		0			0
$183$	9.00000	−	15.5885i	0.665299	−	1.15233i
$184$	−9.00000	−	15.5885i	−0.663489	−	1.14920i
$185$	−5.00000	+	8.66025i	−0.367607	+	0.636715i
$186$	−4.00000	+	6.92820i	−0.293294	+	0.508001i
$187$	12.0000	−	20.7846i	0.877527	−	1.51992i
$188$	−1.00000	−	1.73205i	−0.0729325	−	0.126323i
$189$		0			0
$190$	−0.500000	+	0.866025i	−0.0362738	+	0.0628281i
$191$	5.50000	+	9.52628i	0.397966	+	0.689297i	0.993475	−	0.114051i	$-0.0363829\pi$
$191$	5.50000	+	9.52628i	0.397966	+	0.689297i	−0.595509	+	0.803349i	$0.703050\pi$
$192$	−14.0000			−1.01036
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	−7.00000	+	12.1244i	−0.502571	+	0.870478i
$195$		0			0
$196$	−3.50000	−	6.06218i	−0.250000	−	0.433013i
$197$	−12.0000	+	20.7846i	−0.854965	+	1.48084i	0.0217133	+	0.999764i	$0.493088\pi$
$197$	−12.0000	+	20.7846i	−0.854965	+	1.48084i	−0.876678	+	0.481078i	$0.840245\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	−0.500000	−	0.866025i	−0.0354441	−	0.0613909i	0.847759	−	0.530381i	$-0.177951\pi$
$199$	−0.500000	−	0.866025i	−0.0354441	−	0.0613909i	−0.883203	+	0.468990i	$0.844618\pi$
$200$	−1.50000	+	2.59808i	−0.106066	+	0.183712i
$201$	−16.0000			−1.12855
$202$	−8.50000	−	14.7224i	−0.598058	−	1.03587i
$203$		0			0
$204$	16.0000			1.12022
$205$	3.50000	+	6.06218i	0.244451	+	0.423401i
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$		0			0
$209$	−1.50000	−	2.59808i	−0.103757	−	0.179713i
$210$		0			0
$211$	13.0000			0.894957			0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000			0.894957			0.447478	+	0.894295i	$0.352322\pi$
$212$	−2.00000	+	3.46410i	−0.137361	+	0.237915i
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$	−4.00000	−	6.92820i	−0.273434	−	0.473602i
$215$	−4.00000			−0.272798
$216$	12.0000			0.816497
$217$		0			0
$218$	18.0000			1.21911
$219$	−4.00000			−0.270295
$220$	−1.50000	−	2.59808i	−0.101130	−	0.175162i
$221$		0			0
$222$	−10.0000	+	17.3205i	−0.671156	+	1.16248i
$223$	26.0000			1.74109			0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000			1.74109			0.870544	+	0.492090i	$0.163767\pi$
$224$		0			0
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	2.00000	−	3.46410i	0.133038	−	0.230429i
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	−0.125435	−	0.992102i	$-0.540033\pi$
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	0.921903	−	0.387421i	$-0.126634\pi$
$228$	1.00000	−	1.73205i	0.0662266	−	0.114708i
$229$	−6.00000			−0.396491			−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000			−0.396491			−0.198246	+	0.980152i	$0.563524\pi$
$230$	−6.00000			−0.395628
$231$		0			0
$232$	27.0000			1.77264
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	0.928312	+	0.371802i	$0.121260\pi$
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	−0.142166	+	0.989843i	$0.545407\pi$
$234$		0			0
$235$	−2.00000			−0.130466
$236$	−0.500000	+	0.866025i	−0.0325472	+	0.0563735i
$237$	−32.0000			−2.07862
$238$		0			0
$239$	−2.00000	−	3.46410i	−0.129369	−	0.224074i	0.794063	−	0.607835i	$-0.207962\pi$
$239$	−2.00000	−	3.46410i	−0.129369	−	0.224074i	−0.923432	+	0.383761i	$0.874629\pi$
$240$	−1.00000	+	1.73205i	−0.0645497	+	0.111803i
$241$	−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	$0.982234\pi$
$242$	2.00000			0.128565
$243$	10.0000			0.641500
$244$	4.50000	+	7.79423i	0.288083	+	0.498974i
$245$	−7.00000			−0.447214
$246$	7.00000	+	12.1244i	0.446304	+	0.773021i
$247$		0			0
$248$	−6.00000	−	10.3923i	−0.381000	−	0.659912i
$249$	12.0000			0.760469
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$252$		0			0
$253$	9.00000	−	15.5885i	0.565825	−	0.980038i
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$	8.00000	−	13.8564i	0.500979	−	0.867722i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.773427	−	0.633885i	$-0.781459\pi$
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.162247	−	0.986750i	$-0.551874\pi$
$258$	−8.00000			−0.498058
$259$		0			0
$260$		0			0
$261$	9.00000			0.557086
$262$	10.5000	+	18.1865i	0.648692	+	1.12357i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$	−9.00000	−	15.5885i	−0.553912	−	0.959403i
$265$	2.00000	+	3.46410i	0.122859	+	0.212798i
$266$		0			0
$267$	2.00000	−	3.46410i	0.122398	−	0.212000i
$268$	4.00000	−	6.92820i	0.244339	−	0.423207i
$269$	−9.50000	−	16.4545i	−0.579225	−	1.00325i	−0.995568	−	0.0940400i	$-0.970022\pi$
$269$	−9.50000	−	16.4545i	−0.579225	−	1.00325i	0.416343	−	0.909208i	$-0.363311\pi$
$270$	2.00000	−	3.46410i	0.121716	−	0.210819i
$271$	−9.50000	−	16.4545i	−0.577084	−	0.999539i	−0.995812	−	0.0914269i	$-0.970857\pi$
$271$	−9.50000	−	16.4545i	−0.577084	−	0.999539i	0.418728	−	0.908112i	$-0.362476\pi$
$272$	4.00000	−	6.92820i	0.242536	−	0.420084i
$273$		0			0
$274$	−6.00000			−0.362473
$275$	−3.00000			−0.180907
$276$	12.0000			0.722315
$277$	15.0000	−	25.9808i	0.901263	−	1.56103i	0.0754058	−	0.997153i	$-0.475975\pi$
$277$	15.0000	−	25.9808i	0.901263	−	1.56103i	0.825857	−	0.563880i	$-0.190692\pi$
$278$	3.00000			0.179928
$279$	−2.00000	−	3.46410i	−0.119737	−	0.207390i
$280$		0			0
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	0.998217	−	0.0596933i	$-0.0190123\pi$
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	−0.550804	+	0.834634i	$0.685679\pi$
$282$	−4.00000			−0.238197
$283$	26.0000			1.54554			0.772770	−	0.634686i	$-0.218871\pi$
$283$	26.0000			1.54554			0.772770	+	0.634686i	$0.218871\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$	−1.00000	−	1.73205i	−0.0592349	−	0.102598i
$286$		0			0
$287$		0			0
$288$	2.50000	−	4.33013i	0.147314	−	0.255155i
$289$	−23.5000	+	40.7032i	−1.38235	+	2.39431i
$290$	4.50000	−	7.79423i	0.264249	−	0.457693i
$291$	−14.0000	−	24.2487i	−0.820695	−	1.42148i
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	−14.0000			−0.816497
$295$	0.500000	+	0.866025i	0.0291111	+	0.0504219i
$296$	−15.0000	−	25.9808i	−0.871857	−	1.51010i
$297$	6.00000	+	10.3923i	0.348155	+	0.603023i
$298$	1.50000	−	2.59808i	0.0868927	−	0.150503i
$299$		0			0
$300$	−1.00000	−	1.73205i	−0.0577350	−	0.100000i
$301$		0			0
$302$	−9.50000	+	7.79423i	−0.546664	+	0.448507i
$303$	34.0000			1.95325
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	9.00000			0.515339
$306$	4.00000	−	6.92820i	0.228665	−	0.396059i
$307$	−7.00000	−	12.1244i	−0.399511	−	0.691974i	0.594154	−	0.804351i	$-0.297487\pi$
$307$	−7.00000	−	12.1244i	−0.399511	−	0.691974i	−0.993666	+	0.112377i	$0.964153\pi$
$308$		0			0
$309$	6.00000	+	10.3923i	0.341328	+	0.591198i
$310$	−4.00000			−0.227185
$311$	19.0000			1.07739			0.538696	−	0.842500i	$-0.318917\pi$
$311$	19.0000			1.07739			0.538696	+	0.842500i	$0.318917\pi$
$312$		0			0
$313$	−3.00000	−	5.19615i	−0.169570	−	0.293704i	0.768699	−	0.639611i	$-0.220905\pi$
$313$	−3.00000	−	5.19615i	−0.169570	−	0.293704i	−0.938269	+	0.345907i	$0.887571\pi$
$314$	−5.00000	+	8.66025i	−0.282166	+	0.488726i
$315$		0			0
$316$	8.00000	−	13.8564i	0.450035	−	0.779484i
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$	4.00000	+	6.92820i	0.224309	+	0.388514i
$319$	13.5000	+	23.3827i	0.755855	+	1.30918i
$320$	−3.50000	−	6.06218i	−0.195656	−	0.338886i
$321$	16.0000			0.893033
$322$		0			0
$323$	4.00000	+	6.92820i	0.222566	+	0.385496i
$324$	−5.50000	+	9.52628i	−0.305556	+	0.529238i
$325$		0			0
$326$	−4.00000			−0.221540
$327$	−18.0000	+	31.1769i	−0.995402	+	1.72409i
$328$	−21.0000			−1.15953
$329$		0			0
$330$	−6.00000			−0.330289
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$	−5.00000	−	8.66025i	−0.273998	−	0.474579i
$334$	−9.00000	+	15.5885i	−0.492458	+	0.852962i
$335$	−4.00000	−	6.92820i	−0.218543	−	0.378528i
$336$		0			0
$337$	−10.0000	+	17.3205i	−0.544735	+	0.943508i	0.453889	+	0.891058i	$0.350036\pi$
$337$	−10.0000	+	17.3205i	−0.544735	+	0.943508i	−0.998624	+	0.0524499i	$0.983297\pi$
$338$	−6.50000	+	11.2583i	−0.353553	+	0.612372i
$339$	4.00000	+	6.92820i	0.217250	+	0.376288i
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	−0.500000	−	0.866025i	−0.0270369	−	0.0468293i
$343$		0			0
$344$	6.00000	−	10.3923i	0.323498	−	0.560316i
$345$	6.00000	−	10.3923i	0.323029	−	0.559503i
$346$	−4.00000			−0.215041
$347$	10.0000	+	17.3205i	0.536828	+	0.929814i	0.999072	+	0.0430610i	$0.0137110\pi$
$347$	10.0000	+	17.3205i	0.536828	+	0.929814i	−0.462244	+	0.886753i	$0.652956\pi$
$348$	−9.00000	+	15.5885i	−0.482451	+	0.835629i
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	−0.838019	−	0.545640i	$-0.816286\pi$
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	0.891548	+	0.452926i	$0.149620\pi$
$350$		0			0
$351$		0			0
$352$	15.0000			0.799503
$353$	−14.0000	−	24.2487i	−0.745145	−	1.29063i	−0.950127	−	0.311863i	$-0.899047\pi$
$353$	−14.0000	−	24.2487i	−0.745145	−	1.29063i	0.204982	−	0.978766i	$-0.434286\pi$
$354$	1.00000	+	1.73205i	0.0531494	+	0.0920575i
$355$	3.00000			0.159223
$356$	1.00000	+	1.73205i	0.0529999	+	0.0917985i
$357$		0			0
$358$		0			0
$359$	−11.0000			−0.580558			−0.290279	−	0.956942i	$-0.593748\pi$
$359$	−11.0000			−0.580558			−0.290279	+	0.956942i	$0.593748\pi$
$360$	−1.50000	−	2.59808i	−0.0790569	−	0.136931i
$361$	−18.0000			−0.947368
$362$	−7.00000			−0.367912
$363$	−2.00000	+	3.46410i	−0.104973	+	0.181818i
$364$		0			0
$365$	−1.00000	−	1.73205i	−0.0523424	−	0.0906597i
$366$	18.0000			0.940875
$367$	24.0000			1.25279			0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000			1.25279			0.626395	+	0.779506i	$0.284530\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$	−7.00000			−0.364405
$370$	−10.0000			−0.519875
$371$		0			0
$372$	8.00000			0.414781
$373$	8.00000	−	13.8564i	0.414224	−	0.717458i	−0.581122	−	0.813816i	$-0.697386\pi$
$373$	8.00000	−	13.8564i	0.414224	−	0.717458i	0.995347	+	0.0963587i	$0.0307196\pi$
$374$	24.0000			1.24101
$375$	−2.00000			−0.103280
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$		0			0
$378$		0			0
$379$	11.5000	−	19.9186i	0.590715	−	1.02315i	−0.403421	−	0.915014i	$-0.632179\pi$
$379$	11.5000	−	19.9186i	0.590715	−	1.02315i	0.994136	−	0.108134i	$-0.0344877\pi$
$380$	1.00000			0.0512989
$381$	16.0000			0.819705
$382$	−5.50000	+	9.52628i	−0.281404	+	0.487407i
$383$	−16.0000			−0.817562			−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000			−0.817562			−0.408781	+	0.912633i	$0.634046\pi$
$384$	3.00000	+	5.19615i	0.153093	+	0.265165i
$385$		0			0
$386$	−4.00000			−0.203595
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$	14.0000			0.710742
$389$	35.0000			1.77457			0.887285	−	0.461221i	$-0.152589\pi$
$389$	35.0000			1.77457			0.887285	+	0.461221i	$0.152589\pi$
$390$		0			0
$391$	−24.0000	+	41.5692i	−1.21373	+	2.10225i
$392$	10.5000	−	18.1865i	0.530330	−	0.918559i
$393$	−42.0000			−2.11862
$394$	−24.0000			−1.20910
$395$	−8.00000	−	13.8564i	−0.402524	−	0.697191i
$396$	3.00000			0.150756
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$	0.500000	−	0.866025i	0.0250627	−	0.0434099i
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	0.615725	−	0.787961i	$-0.288863\pi$
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	−0.990257	+	0.139253i	$0.955530\pi$
$402$	−8.00000	−	13.8564i	−0.399004	−	0.691095i
$403$		0			0
$404$	−8.50000	+	14.7224i	−0.422891	+	0.732468i
$405$	5.50000	+	9.52628i	0.273297	+	0.473365i
$406$		0			0
$407$	15.0000	−	25.9808i	0.743522	−	1.28782i
$408$	24.0000	+	41.5692i	1.18818	+	2.05798i
$409$	3.00000			0.148340			0.0741702	−	0.997246i	$-0.476369\pi$
$409$	3.00000			0.148340			0.0741702	+	0.997246i	$0.476369\pi$
$410$	−3.50000	+	6.06218i	−0.172853	+	0.299390i
$411$	6.00000	−	10.3923i	0.295958	−	0.512615i
$412$	−6.00000			−0.295599
$413$		0			0
$414$	3.00000	−	5.19615i	0.147442	−	0.255377i
$415$	3.00000	+	5.19615i	0.147264	+	0.255069i
$416$		0			0
$417$	−3.00000	+	5.19615i	−0.146911	+	0.254457i
$418$	1.50000	−	2.59808i	0.0733674	−	0.127076i
$419$	−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
$421$	3.50000	−	6.06218i	0.170580	−	0.295452i	−0.768043	−	0.640398i	$-0.778769\pi$
$421$	3.50000	−	6.06218i	0.170580	−	0.295452i	0.938623	+	0.344946i	$0.112103\pi$
$422$	6.50000	+	11.2583i	0.316415	+	0.548047i
$423$	1.00000	−	1.73205i	0.0486217	−	0.0842152i
$424$	−12.0000			−0.582772
$425$	8.00000			0.388057
$426$	6.00000			0.290701
$427$		0			0
$428$	−4.00000	+	6.92820i	−0.193347	+	0.334887i
$429$		0			0
$430$	−2.00000	−	3.46410i	−0.0964486	−	0.167054i
$431$	−14.5000	+	25.1147i	−0.698440	+	1.20973i	0.270567	+	0.962701i	$0.412789\pi$
$431$	−14.5000	+	25.1147i	−0.698440	+	1.20973i	−0.969007	+	0.247033i	$0.920544\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	20.0000			0.961139			0.480569	−	0.876957i	$-0.340430\pi$
$433$	20.0000			0.961139			0.480569	+	0.876957i	$0.340430\pi$
$434$		0			0
$435$	9.00000	+	15.5885i	0.431517	+	0.747409i
$436$	−9.00000	−	15.5885i	−0.431022	−	0.746552i
$437$	3.00000	+	5.19615i	0.143509	+	0.248566i
$438$	−2.00000	−	3.46410i	−0.0955637	−	0.165521i
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	−0.853847	−	0.520524i	$-0.825737\pi$
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	0.877711	+	0.479191i	$0.159070\pi$
$440$	4.50000	−	7.79423i	0.214529	−	0.371575i
$441$	3.50000	−	6.06218i	0.166667	−	0.288675i
$442$		0			0
$443$	−10.0000	+	17.3205i	−0.475114	+	0.822922i	−0.999594	−	0.0285009i	$-0.990927\pi$
$443$	−10.0000	+	17.3205i	−0.475114	+	0.822922i	0.524479	+	0.851423i	$0.324260\pi$
$444$	20.0000			0.949158
$445$	2.00000			0.0948091
$446$	13.0000	+	22.5167i	0.615568	+	1.06619i
$447$	3.00000	+	5.19615i	0.141895	+	0.245770i
$448$		0			0
$449$	2.50000	−	4.33013i	0.117982	−	0.204351i	−0.800986	−	0.598684i	$-0.795691\pi$
$449$	2.50000	−	4.33013i	0.117982	−	0.204351i	0.918968	+	0.394332i	$0.129024\pi$
$450$	−1.00000			−0.0471405
$451$	−10.5000	−	18.1865i	−0.494426	−	0.856370i
$452$	−4.00000			−0.188144
$453$	−4.00000	−	24.2487i	−0.187936	−	1.13930i
$454$	24.0000			1.12638
$455$		0			0
$456$	6.00000			0.280976
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	0.485299	+	0.874348i	$0.338711\pi$
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	−0.999857	+	0.0168929i	$0.994623\pi$
$458$	−3.00000	−	5.19615i	−0.140181	−	0.242800i
$459$	−16.0000	−	27.7128i	−0.746816	−	1.29352i
$460$	3.00000	+	5.19615i	0.139876	+	0.242272i
$461$	−5.00000			−0.232873			−0.116437	−	0.993198i	$-0.537147\pi$
$461$	−5.00000			−0.232873			−0.116437	+	0.993198i	$0.537147\pi$
$462$		0			0
$463$	17.0000	−	29.4449i	0.790057	−	1.36842i	−0.135874	−	0.990726i	$-0.543384\pi$
$463$	17.0000	−	29.4449i	0.790057	−	1.36842i	0.925931	−	0.377693i	$-0.123282\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	9.00000	−	15.5885i	0.416470	−	0.721348i	−0.579111	−	0.815249i	$-0.696600\pi$
$467$	9.00000	−	15.5885i	0.416470	−	0.721348i	0.995582	+	0.0939008i	$0.0299336\pi$
$468$		0			0
$469$		0			0
$470$	−1.00000	−	1.73205i	−0.0461266	−	0.0798935i
$471$	−10.0000	−	17.3205i	−0.460776	−	0.798087i
$472$	−3.00000			−0.138086
$473$	12.0000			0.551761
$474$	−16.0000	−	27.7128i	−0.734904	−	1.27289i
$475$	0.500000	−	0.866025i	0.0229416	−	0.0397360i
$476$		0			0
$477$	−4.00000			−0.183147
$478$	2.00000	−	3.46410i	0.0914779	−	0.158444i
$479$	−5.00000			−0.228456			−0.114228	−	0.993455i	$-0.536439\pi$
$479$	−5.00000			−0.228456			−0.114228	+	0.993455i	$0.536439\pi$
$480$	10.0000			0.456435
$481$		0			0
$482$	−17.0000			−0.774329
$483$		0			0
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$	7.00000	−	12.1244i	0.317854	−	0.550539i
$486$	5.00000	+	8.66025i	0.226805	+	0.392837i
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	−0.842479	−	0.538730i	$-0.818904\pi$
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	0.887793	+	0.460243i	$0.152238\pi$
$488$	−13.5000	+	23.3827i	−0.611116	+	1.05848i
$489$	4.00000	−	6.92820i	0.180886	−	0.313304i
$490$	−3.50000	−	6.06218i	−0.158114	−	0.273861i
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	0.984145	−	0.177365i	$-0.0567572\pi$
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	−0.645675	+	0.763612i	$0.723424\pi$
$492$	7.00000	−	12.1244i	0.315584	−	0.546608i
$493$	−36.0000	−	62.3538i	−1.62136	−	2.80828i
$494$		0			0
$495$	1.50000	−	2.59808i	0.0674200	−	0.116775i
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$		0			0
$498$	6.00000	+	10.3923i	0.268866	+	0.465690i
$499$	1.50000	−	2.59808i	0.0671492	−	0.116306i	−0.830496	−	0.557024i	$-0.811943\pi$
$499$	1.50000	−	2.59808i	0.0671492	−	0.116306i	0.897645	+	0.440719i	$0.145276\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−18.0000	−	31.1769i	−0.804181	−	1.39288i
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	−42.0000			−1.87269			−0.936344	−	0.351085i	$-0.885813\pi$
$503$	−42.0000			−1.87269			−0.936344	+	0.351085i	$0.885813\pi$
$504$		0			0
$505$	8.50000	+	14.7224i	0.378245	+	0.655140i
$506$	18.0000			0.800198
$507$	−13.0000	−	22.5167i	−0.577350	−	1.00000i
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	−14.5000	−	25.1147i	−0.642701	−	1.11319i	−0.984827	−	0.173537i	$-0.944480\pi$
$509$	−14.5000	−	25.1147i	−0.642701	−	1.11319i	0.342126	−	0.939654i	$-0.388853\pi$
$510$	16.0000			0.708492
$511$		0			0
$512$	11.0000			0.486136
$513$	−4.00000			−0.176604
$514$	15.0000	−	25.9808i	0.661622	−	1.14596i
$515$	−3.00000	+	5.19615i	−0.132196	+	0.228970i
$516$	4.00000	+	6.92820i	0.176090	+	0.304997i
$517$	6.00000			0.263880
$518$		0			0
$519$	4.00000	−	6.92820i	0.175581	−	0.304114i
$520$		0			0
$521$	3.00000			0.131432			0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$	4.50000	+	7.79423i	0.196960	+	0.341144i
$523$	16.0000			0.699631			0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000			0.699631			0.349816	+	0.936819i	$0.386244\pi$
$524$	10.5000	−	18.1865i	0.458695	−	0.794482i
$525$		0			0
$526$	−24.0000			−1.04645
$527$	−16.0000	+	27.7128i	−0.696971	+	1.20719i
$528$	3.00000	−	5.19615i	0.130558	−	0.226134i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−2.00000	+	3.46410i	−0.0868744	+	0.150471i
$531$	−1.00000			−0.0433963
$532$		0			0
$533$		0			0
$534$	4.00000			0.173097
$535$	4.00000	+	6.92820i	0.172935	+	0.299532i
$536$	24.0000			1.03664
$537$		0			0
$538$	9.50000	−	16.4545i	0.409574	−	0.709403i
$539$	21.0000			0.904534
$540$	−4.00000			−0.172133
$541$	−7.50000	−	12.9904i	−0.322450	−	0.558500i	0.658543	−	0.752543i	$-0.271173\pi$
$541$	−7.50000	−	12.9904i	−0.322450	−	0.558500i	−0.980993	+	0.194043i	$0.937840\pi$
$542$	9.50000	−	16.4545i	0.408060	−	0.706781i
$543$	7.00000	−	12.1244i	0.300399	−	0.520306i
$544$	−40.0000			−1.71499
$545$	−18.0000			−0.771035
$546$		0			0
$547$	−16.0000			−0.684111			−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000			−0.684111			−0.342055	+	0.939680i	$0.611123\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$	−4.50000	+	7.79423i	−0.192055	+	0.332650i
$550$	−1.50000	−	2.59808i	−0.0639602	−	0.110782i
$551$	−9.00000			−0.383413
$552$	18.0000	+	31.1769i	0.766131	+	1.32698i
$553$		0			0
$554$	30.0000			1.27458
$555$	10.0000	−	17.3205i	0.424476	−	0.735215i
$556$	−1.50000	−	2.59808i	−0.0636142	−	0.110183i
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	−0.991254	−	0.131965i	$-0.957871\pi$
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	0.609912	+	0.792469i	$0.291205\pi$
$558$	2.00000	−	3.46410i	0.0846668	−	0.146647i
$559$		0			0
$560$		0			0
$561$	−24.0000	+	41.5692i	−1.01328	+	1.75505i
$562$	−7.50000	+	12.9904i	−0.316368	+	0.547966i
$563$	−16.0000			−0.674320			−0.337160	−	0.941447i	$-0.609466\pi$
$563$	−16.0000			−0.674320			−0.337160	+	0.941447i	$0.609466\pi$
$564$	2.00000	+	3.46410i	0.0842152	+	0.145865i
$565$	−2.00000	+	3.46410i	−0.0841406	+	0.145736i
$566$	13.0000	+	22.5167i	0.546431	+	0.946446i
$567$		0			0
$568$	−4.50000	+	7.79423i	−0.188816	+	0.327039i
$569$	19.0000	−	32.9090i	0.796521	−	1.37962i	−0.125347	−	0.992113i	$-0.540004\pi$
$569$	19.0000	−	32.9090i	0.796521	−	1.37962i	0.921869	−	0.387503i	$-0.126662\pi$
$570$	1.00000	−	1.73205i	0.0418854	−	0.0725476i
$571$	−16.5000	−	28.5788i	−0.690504	−	1.19599i	−0.971673	−	0.236329i	$-0.924056\pi$
$571$	−16.5000	−	28.5788i	−0.690504	−	1.19599i	0.281170	−	0.959658i	$-0.409278\pi$
$572$		0			0
$573$	−11.0000	−	19.0526i	−0.459532	−	0.795932i
$574$		0			0
$575$	6.00000			0.250217
$576$	7.00000			0.291667
$577$	−32.0000			−1.33218			−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000			−1.33218			−0.666089	+	0.745873i	$0.732033\pi$
$578$	−47.0000			−1.95494
$579$	4.00000	−	6.92820i	0.166234	−	0.287926i
$580$	−9.00000			−0.373705
$581$		0			0
$582$	14.0000	−	24.2487i	0.580319	−	1.00514i
$583$	−6.00000	−	10.3923i	−0.248495	−	0.430405i
$584$	6.00000			0.248282
$585$		0			0
$586$		0			0
$587$	21.0000	+	36.3731i	0.866763	+	1.50128i	0.865286	+	0.501278i	$0.167137\pi$
$587$	21.0000	+	36.3731i	0.866763	+	1.50128i	0.00147660	+	0.999999i	$0.499530\pi$
$588$	7.00000	+	12.1244i	0.288675	+	0.500000i
$589$	2.00000	+	3.46410i	0.0824086	+	0.142736i
$590$	−0.500000	+	0.866025i	−0.0205847	+	0.0356537i
$591$	24.0000	−	41.5692i	0.987228	−	1.70993i
$592$	5.00000	−	8.66025i	0.205499	−	0.355934i
$593$	15.0000	+	25.9808i	0.615976	+	1.06690i	0.990212	+	0.139569i	$0.0445716\pi$
$593$	15.0000	+	25.9808i	0.615976	+	1.06690i	−0.374236	+	0.927333i	$0.622095\pi$
$594$	−6.00000	+	10.3923i	−0.246183	+	0.426401i
$595$		0			0
$596$	−3.00000			−0.122885
$597$	1.00000	+	1.73205i	0.0409273	+	0.0708881i
$598$		0			0
$599$	12.5000	+	21.6506i	0.510736	+	0.884621i	0.999923	+	0.0124417i	$0.00396043\pi$
$599$	12.5000	+	21.6506i	0.510736	+	0.884621i	−0.489186	+	0.872179i	$0.662706\pi$
$600$	3.00000	−	5.19615i	0.122474	−	0.212132i
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$		0			0
$603$	8.00000			0.325785
$604$	11.5000	+	4.33013i	0.467928	+	0.176190i
$605$	−2.00000			−0.0813116
$606$	17.0000	+	29.4449i	0.690578	+	1.19612i
$607$	14.0000			0.568242			0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000			0.568242			0.284121	+	0.958788i	$0.408298\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$		0			0
$610$	4.50000	+	7.79423i	0.182200	+	0.315579i
$611$		0			0
$612$	−8.00000			−0.323381
$613$	−24.0000			−0.969351			−0.484675	−	0.874694i	$-0.661062\pi$
$613$	−24.0000			−0.969351			−0.484675	+	0.874694i	$0.661062\pi$
$614$	7.00000	−	12.1244i	0.282497	−	0.489299i
$615$	−7.00000	−	12.1244i	−0.282267	−	0.488901i
$616$		0			0
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	−0.799298	−	0.600935i	$-0.794795\pi$
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	0.920074	+	0.391745i	$0.128129\pi$
$618$	−6.00000	+	10.3923i	−0.241355	+	0.418040i
$619$	18.0000	+	31.1769i	0.723481	+	1.25311i	0.959596	+	0.281381i	$0.0907924\pi$
$619$	18.0000	+	31.1769i	0.723481	+	1.25311i	−0.236115	+	0.971725i	$0.575874\pi$
$620$	2.00000	+	3.46410i	0.0803219	+	0.139122i
$621$	−12.0000	−	20.7846i	−0.481543	−	0.834058i
$622$	9.50000	+	16.4545i	0.380915	+	0.659765i
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	10.0000			0.399043
$629$	−40.0000	+	69.2820i	−1.59490	+	2.76246i
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	48.0000			1.90934
$633$	−26.0000			−1.03341
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	4.00000	+	6.92820i	0.158735	+	0.274937i
$636$	4.00000	−	6.92820i	0.158610	−	0.274721i
$637$		0			0
$638$	−13.5000	+	23.3827i	−0.534470	+	0.925729i
$639$	−1.50000	+	2.59808i	−0.0593391	+	0.102778i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−8.50000	−	14.7224i	−0.335730	−	0.581501i	0.647895	−	0.761730i	$-0.275650\pi$
$641$	−8.50000	−	14.7224i	−0.335730	−	0.581501i	−0.983625	+	0.180229i	$0.942316\pi$
$642$	8.00000	+	13.8564i	0.315735	+	0.546869i
$643$	−7.00000	+	12.1244i	−0.276053	+	0.478138i	−0.970400	−	0.241502i	$-0.922360\pi$
$643$	−7.00000	+	12.1244i	−0.276053	+	0.478138i	0.694347	+	0.719640i	$0.255693\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$	−4.00000	+	6.92820i	−0.157378	+	0.272587i
$647$	7.00000	−	12.1244i	0.275198	−	0.476658i	−0.694987	−	0.719023i	$-0.744590\pi$
$647$	7.00000	−	12.1244i	0.275198	−	0.476658i	0.970185	+	0.242365i	$0.0779231\pi$
$648$	−33.0000			−1.29636
$649$	−1.50000	−	2.59808i	−0.0588802	−	0.101983i
$650$		0			0
$651$		0			0
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	−0.262515	−	0.964928i	$-0.584552\pi$
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	0.966910	−	0.255119i	$-0.0821147\pi$
$654$	−36.0000			−1.40771
$655$	−10.5000	−	18.1865i	−0.410269	−	0.710607i
$656$	−3.50000	−	6.06218i	−0.136652	−	0.236688i
$657$	2.00000			0.0780274
$658$		0			0
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	−0.682161	−	0.731202i	$-0.738960\pi$
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	0.974320	+	0.225168i	$0.0722932\pi$
$660$	3.00000	+	5.19615i	0.116775	+	0.202260i
$661$	6.00000			0.233373			0.116686	−	0.993169i	$-0.462773\pi$
$661$	6.00000			0.233373			0.116686	+	0.993169i	$0.462773\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$		0			0
$664$	−18.0000			−0.698535
$665$		0			0
$666$	5.00000	−	8.66025i	0.193746	−	0.335578i
$667$	−27.0000	−	46.7654i	−1.04544	−	1.81076i
$668$	18.0000			0.696441
$669$	−52.0000			−2.01044
$670$	4.00000	−	6.92820i	0.154533	−	0.267660i
$671$	−27.0000			−1.04232
$672$		0			0
$673$	11.0000	+	19.0526i	0.424019	+	0.734422i	0.996328	−	0.0856156i	$-0.0272857\pi$
$673$	11.0000	+	19.0526i	0.424019	+	0.734422i	−0.572309	+	0.820038i	$0.693952\pi$
$674$	−20.0000			−0.770371
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	13.0000			0.500000
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$	−4.00000	+	6.92820i	−0.153619	+	0.266076i
$679$		0			0
$680$	−12.0000	+	20.7846i	−0.460179	+	0.797053i
$681$	−24.0000	+	41.5692i	−0.919682	+	1.59294i
$682$	12.0000			0.459504
$683$	−24.0000			−0.918334			−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000			−0.918334			−0.459167	+	0.888350i	$0.651852\pi$
$684$	−0.500000	+	0.866025i	−0.0191180	+	0.0331133i
$685$	6.00000			0.229248
$686$		0			0
$687$	12.0000			0.457829
$688$	4.00000			0.152499
$689$		0			0
$690$	12.0000			0.456832
$691$	19.0000			0.722794			0.361397	−	0.932412i	$-0.382300\pi$
$691$	19.0000			0.722794			0.361397	+	0.932412i	$0.382300\pi$
$692$	2.00000	+	3.46410i	0.0760286	+	0.131685i
$693$		0			0
$694$	−10.0000	+	17.3205i	−0.379595	+	0.657477i
$695$	−3.00000			−0.113796
$696$	−54.0000			−2.04686
$697$	28.0000	+	48.4974i	1.06058	+	1.83697i
$698$	2.00000			0.0757011
$699$	−24.0000	−	41.5692i	−0.907763	−	1.57229i
$700$		0			0
$701$	−6.50000	−	11.2583i	−0.245502	−	0.425221i	0.716771	−	0.697309i	$-0.245619\pi$
$701$	−6.50000	−	11.2583i	−0.245502	−	0.425221i	−0.962273	+	0.272087i	$0.912286\pi$
$702$		0			0
$703$	5.00000	+	8.66025i	0.188579	+	0.326628i
$704$	10.5000	+	18.1865i	0.395734	+	0.685431i
$705$	4.00000			0.150649
$706$	14.0000	−	24.2487i	0.526897	−	0.912612i
$707$		0			0
$708$	1.00000	−	1.73205i	0.0375823	−	0.0650945i
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	−0.980326	−	0.197383i	$-0.936756\pi$
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	0.661102	+	0.750296i	$0.270089\pi$
$710$	1.50000	+	2.59808i	0.0562940	+	0.0975041i
$711$	16.0000			0.600047
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.00000	+	6.92820i	0.149383	+	0.258738i
$718$	−5.50000	−	9.52628i	−0.205258	−	0.355518i
$719$	−3.50000	+	6.06218i	−0.130528	+	0.226081i	−0.923880	−	0.382682i	$-0.875001\pi$
$719$	−3.50000	+	6.06218i	−0.130528	+	0.226081i	0.793352	+	0.608763i	$0.208334\pi$
$720$	0.500000	−	0.866025i	0.0186339	−	0.0322749i
$721$		0			0
$722$	−9.00000	−	15.5885i	−0.334945	−	0.580142i
$723$	17.0000	−	29.4449i	0.632237	−	1.09507i
$724$	3.50000	+	6.06218i	0.130076	+	0.225299i
$725$	−4.50000	+	7.79423i	−0.167126	+	0.289470i
$726$	−4.00000			−0.148454
$727$	−4.00000			−0.148352			−0.0741759	−	0.997245i	$-0.523633\pi$
$727$	−4.00000			−0.148352			−0.0741759	+	0.997245i	$0.523633\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	1.00000	−	1.73205i	0.0370117	−	0.0641061i
$731$	−32.0000			−1.18356
$732$	−9.00000	−	15.5885i	−0.332650	−	0.576166i
$733$	−9.00000	+	15.5885i	−0.332423	+	0.575773i	−0.982986	−	0.183679i	$-0.941199\pi$
$733$	−9.00000	+	15.5885i	−0.332423	+	0.575773i	0.650564	+	0.759452i	$0.274533\pi$
$734$	12.0000	+	20.7846i	0.442928	+	0.767174i
$735$	14.0000			0.516398
$736$	−30.0000			−1.10581
$737$	12.0000	+	20.7846i	0.442026	+	0.765611i
$738$	−3.50000	−	6.06218i	−0.128837	−	0.223152i
$739$	−6.00000	−	10.3923i	−0.220714	−	0.382287i	0.734311	−	0.678813i	$-0.237505\pi$
$739$	−6.00000	−	10.3923i	−0.220714	−	0.382287i	−0.955025	+	0.296526i	$0.904172\pi$
$740$	5.00000	+	8.66025i	0.183804	+	0.318357i
$741$		0			0
$742$		0			0
$743$	−11.0000	+	19.0526i	−0.403551	+	0.698971i	−0.994152	−	0.107993i	$-0.965557\pi$
$743$	−11.0000	+	19.0526i	−0.403551	+	0.698971i	0.590601	+	0.806964i	$0.298891\pi$
$744$	12.0000	+	20.7846i	0.439941	+	0.762001i
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$	16.0000			0.585802
$747$	−6.00000			−0.219529
$748$	−12.0000	−	20.7846i	−0.438763	−	0.759961i
$749$		0			0
$750$	−1.00000	−	1.73205i	−0.0365148	−	0.0632456i
$751$	−17.5000	+	30.3109i	−0.638584	+	1.10606i	0.347160	+	0.937806i	$0.387146\pi$
$751$	−17.5000	+	30.3109i	−0.638584	+	1.10606i	−0.985744	+	0.168254i	$0.946187\pi$
$752$	2.00000			0.0729325
$753$	12.0000	+	20.7846i	0.437304	+	0.757433i
$754$		0			0
$755$	9.50000	−	7.79423i	0.345740	−	0.283661i
$756$		0			0
$757$	−16.0000	−	27.7128i	−0.581530	−	1.00724i	−0.995298	−	0.0968571i	$-0.969121\pi$
$757$	−16.0000	−	27.7128i	−0.581530	−	1.00724i	0.413768	−	0.910382i	$-0.364212\pi$
$758$	23.0000			0.835398
$759$	−18.0000	+	31.1769i	−0.653359	+	1.13165i
$760$	1.50000	+	2.59808i	0.0544107	+	0.0942421i
$761$	−3.50000	−	6.06218i	−0.126875	−	0.219754i	0.795589	−	0.605836i	$-0.207161\pi$
$761$	−3.50000	−	6.06218i	−0.126875	−	0.219754i	−0.922464	+	0.386082i	$0.873828\pi$
$762$	8.00000	+	13.8564i	0.289809	+	0.501965i
$763$		0			0
$764$	11.0000			0.397966
$765$	−4.00000	+	6.92820i	−0.144620	+	0.250490i
$766$	−8.00000	−	13.8564i	−0.289052	−	0.500652i
$767$		0			0
$768$	−17.0000	+	29.4449i	−0.613435	+	1.06250i
$769$	3.50000	−	6.06218i	0.126213	−	0.218608i	−0.795993	−	0.605305i	$-0.793051\pi$
$769$	3.50000	−	6.06218i	0.126213	−	0.218608i	0.922207	+	0.386698i	$0.126384\pi$
$770$		0			0
$771$	30.0000	+	51.9615i	1.08042	+	1.87135i
$772$	2.00000	+	3.46410i	0.0719816	+	0.124676i
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	0.807018	−	0.590527i	$-0.201080\pi$
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	−0.914920	+	0.403634i	$0.867747\pi$
$774$	4.00000			0.143777
$775$	4.00000			0.143684
$776$	21.0000	+	36.3731i	0.753856	+	1.30572i
$777$		0			0
$778$	17.5000	+	30.3109i	0.627405	+	1.08670i
$779$	7.00000			0.250801
$780$		0			0
$781$	−9.00000			−0.322045
$782$	−48.0000			−1.71648
$783$	36.0000			1.28654
$784$	7.00000			0.250000
$785$	5.00000	−	8.66025i	0.178458	−	0.309098i
$786$	−21.0000	−	36.3731i	−0.749045	−	1.29738i
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	−0.999999	−	0.00110111i	$-0.999650\pi$
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	0.500953	+	0.865474i	$0.332983\pi$
$788$	12.0000	+	20.7846i	0.427482	+	0.740421i
$789$	24.0000	−	41.5692i	0.854423	−	1.47990i
$790$	8.00000	−	13.8564i	0.284627	−	0.492989i
$791$		0			0
$792$	4.50000	+	7.79423i	0.159901	+	0.276956i
$793$		0			0
$794$	7.00000	−	12.1244i	0.248421	−	0.430277i
$795$	−4.00000	−	6.92820i	−0.141865	−	0.245718i
$796$	−1.00000			−0.0354441
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	−0.807989	−	0.589197i	$-0.799444\pi$
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	0.914255	+	0.405140i	$0.132777\pi$
$798$		0			0
$799$	−16.0000			−0.566039
$800$	2.50000	+	4.33013i	0.0883883	+	0.153093i
$801$	−1.00000	+	1.73205i	−0.0353333	+	0.0611990i
$802$	7.50000	−	12.9904i	0.264834	−	0.458706i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$	−8.00000	+	13.8564i	−0.282138	+	0.488678i
$805$		0			0
$806$		0			0
$807$	19.0000	+	32.9090i	0.668832	+	1.15845i
$808$	−51.0000			−1.79417
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	0.808458	−	0.588555i	$-0.200303\pi$
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	−0.913932	+	0.405868i	$0.866969\pi$
$810$	−5.50000	+	9.52628i	−0.193250	+	0.334719i
$811$	13.5000	+	23.3827i	0.474049	+	0.821077i	0.999559	−	0.0297106i	$-0.00945858\pi$
$811$	13.5000	+	23.3827i	0.474049	+	0.821077i	−0.525509	+	0.850788i	$0.676125\pi$
$812$		0			0
$813$	19.0000	+	32.9090i	0.666359	+	1.15417i
$814$	30.0000			1.05150
$815$	4.00000			0.140114
$816$	−8.00000	+	13.8564i	−0.280056	+	0.485071i
$817$	−2.00000	+	3.46410i	−0.0699711	+	0.121194i
$818$	1.50000	+	2.59808i	0.0524463	+	0.0908396i
$819$		0			0
$820$	7.00000			0.244451
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	0.143591	+	0.989637i	$0.454135\pi$
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	−0.928846	+	0.370465i	$0.879198\pi$
$822$	12.0000			0.418548
$823$	16.0000			0.557725			0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000			0.557725			0.278862	+	0.960331i	$0.410043\pi$
$824$	−9.00000	−	15.5885i	−0.313530	−	0.543050i
$825$	6.00000			0.208893
$826$		0			0
$827$	44.0000			1.53003			0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000			1.53003			0.765015	+	0.644013i	$0.222732\pi$
$828$	−6.00000			−0.208514
$829$	−13.5000	+	23.3827i	−0.468874	+	0.812114i	−0.999367	−	0.0355753i	$-0.988674\pi$
$829$	−13.5000	+	23.3827i	−0.468874	+	0.812114i	0.530493	+	0.847690i	$0.322007\pi$
$830$	−3.00000	+	5.19615i	−0.104132	+	0.180361i
$831$	−30.0000	+	51.9615i	−1.04069	+	1.80253i
$832$		0			0
$833$	−56.0000			−1.94029
$834$	−6.00000			−0.207763
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$	−3.00000			−0.103757
$837$	−8.00000	−	13.8564i	−0.276520	−	0.478947i
$838$	−12.0000			−0.414533
$839$	−35.0000			−1.20833			−0.604167	−	0.796858i	$-0.706494\pi$
$839$	−35.0000			−1.20833			−0.604167	+	0.796858i	$0.706494\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	7.00000			0.241236
$843$	−15.0000	−	25.9808i	−0.516627	−	0.894825i
$844$	6.50000	−	11.2583i	0.223739	−	0.387528i
$845$	6.50000	−	11.2583i	0.223607	−	0.387298i
$846$	2.00000			0.0687614
$847$		0			0
$848$	−2.00000	−	3.46410i	−0.0686803	−	0.118958i
$849$	−52.0000			−1.78464
$850$	4.00000	+	6.92820i	0.137199	+	0.237635i
$851$	−30.0000	+	51.9615i	−1.02839	+	1.78122i
$852$	−3.00000	−	5.19615i	−0.102778	−	0.178017i
$853$	38.0000			1.30110			0.650548	−	0.759465i	$-0.274539\pi$
$853$	38.0000			1.30110			0.650548	+	0.759465i	$0.274539\pi$
$854$		0			0
$855$	0.500000	+	0.866025i	0.0170996	+	0.0296174i
$856$	−24.0000			−0.820303
$857$	24.0000	−	41.5692i	0.819824	−	1.41998i	−0.0859870	−	0.996296i	$-0.527404\pi$
$857$	24.0000	−	41.5692i	0.819824	−	1.41998i	0.905811	−	0.423681i	$-0.139262\pi$
$858$		0			0
$859$	−7.50000	+	12.9904i	−0.255897	+	0.443226i	−0.965139	−	0.261739i	$-0.915704\pi$
$859$	−7.50000	+	12.9904i	−0.255897	+	0.443226i	0.709242	+	0.704965i	$0.249037\pi$
$860$	−2.00000	+	3.46410i	−0.0681994	+	0.118125i
$861$		0			0
$862$	−29.0000			−0.987744
$863$	−7.00000	+	12.1244i	−0.238283	+	0.412718i	−0.960222	−	0.279239i	$-0.909918\pi$
$863$	−7.00000	+	12.1244i	−0.238283	+	0.412718i	0.721939	+	0.691957i	$0.243251\pi$
$864$	10.0000	−	17.3205i	0.340207	−	0.589256i
$865$	4.00000			0.136004
$866$	10.0000	+	17.3205i	0.339814	+	0.588575i
$867$	47.0000	−	81.4064i	1.59620	−	2.76471i
$868$		0			0
$869$	24.0000	+	41.5692i	0.814144	+	1.41014i
$870$	−9.00000	+	15.5885i	−0.305129	+	0.528498i
$871$		0			0
$872$	27.0000	−	46.7654i	0.914335	−	1.58368i
$873$	7.00000	+	12.1244i	0.236914	+	0.410347i
$874$	−3.00000	+	5.19615i	−0.101477	+	0.175762i
$875$		0			0
$876$	−2.00000	+	3.46410i	−0.0675737	+	0.117041i
$877$	10.0000			0.337676			0.168838	−	0.985644i	$-0.445999\pi$
$877$	10.0000			0.337676			0.168838	+	0.985644i	$0.445999\pi$
$878$	1.00000			0.0337484
$879$		0			0
$880$	3.00000			0.101130
$881$	7.00000	−	12.1244i	0.235836	−	0.408480i	−0.723679	−	0.690136i	$-0.757551\pi$
$881$	7.00000	−	12.1244i	0.235836	−	0.408480i	0.959515	+	0.281656i	$0.0908839\pi$
$882$	7.00000			0.235702
$883$	−13.0000	−	22.5167i	−0.437485	−	0.757746i	0.560010	−	0.828486i	$-0.310797\pi$
$883$	−13.0000	−	22.5167i	−0.437485	−	0.757746i	−0.997495	+	0.0707399i	$0.977464\pi$
$884$		0			0
$885$	−1.00000	−	1.73205i	−0.0336146	−	0.0582223i
$886$	−20.0000			−0.671913
$887$	18.0000			0.604381			0.302190	−	0.953248i	$-0.402282\pi$
$887$	18.0000			0.604381			0.302190	+	0.953248i	$0.402282\pi$
$888$	30.0000	+	51.9615i	1.00673	+	1.74371i
$889$		0			0
$890$	1.00000	+	1.73205i	0.0335201	+	0.0580585i
$891$	−16.5000	−	28.5788i	−0.552771	−	0.957427i
$892$	13.0000	−	22.5167i	0.435272	−	0.753914i
$893$	−1.00000	+	1.73205i	−0.0334637	+	0.0579609i
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	5.00000			0.166852
$899$	−18.0000	−	31.1769i	−0.600334	−	1.03981i
$900$	0.500000	+	0.866025i	0.0166667	+	0.0288675i
$901$	16.0000	+	27.7128i	0.533037	+	0.923248i
$902$	10.5000	−	18.1865i	0.349612	−	0.605545i
$903$		0			0
$904$	−6.00000	−	10.3923i	−0.199557	−	0.345643i
$905$	7.00000			0.232688
$906$	19.0000	−	15.5885i	0.631233	−	0.517892i
$907$	−8.00000			−0.265636			−0.132818	−	0.991140i	$-0.542403\pi$
$907$	−8.00000			−0.265636			−0.132818	+	0.991140i	$0.542403\pi$
$908$	−12.0000	−	20.7846i	−0.398234	−	0.689761i
$909$	−17.0000			−0.563854
$910$		0			0
$911$	−28.0000	−	48.4974i	−0.927681	−	1.60679i	−0.787191	−	0.616709i	$-0.788465\pi$
$911$	−28.0000	−	48.4974i	−0.927681	−	1.60679i	−0.140490	−	0.990082i	$-0.544868\pi$
$912$	1.00000	+	1.73205i	0.0331133	+	0.0573539i
$913$	−9.00000	−	15.5885i	−0.297857	−	0.515903i
$914$	−22.0000			−0.727695
$915$	−18.0000			−0.595062
$916$	−3.00000	+	5.19615i	−0.0991228	+	0.171686i
$917$		0			0
$918$	16.0000	−	27.7128i	0.528079	−	0.914659i
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	−0.471684	−	0.881768i	$-0.656354\pi$
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	0.999475	−	0.0323936i	$-0.0103130\pi$
$920$	−9.00000	+	15.5885i	−0.296721	+	0.513936i
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$	−2.50000	−	4.33013i	−0.0823331	−	0.142605i
$923$		0			0
$924$		0			0
$925$	10.0000			0.328798
$926$	34.0000			1.11731
$927$	−3.00000	−	5.19615i	−0.0985329	−	0.170664i
$928$	22.5000	−	38.9711i	0.738599	−	1.27929i
$929$	6.50000	+	11.2583i	0.213258	+	0.369374i	0.952732	−	0.303811i	$-0.0982592\pi$
$929$	6.50000	+	11.2583i	0.213258	+	0.369374i	−0.739474	+	0.673185i	$0.764926\pi$
$930$	8.00000			0.262330
$931$	−3.50000	+	6.06218i	−0.114708	+	0.198680i
$932$	24.0000			0.786146
$933$	−38.0000			−1.24406
$934$	18.0000			0.588978
$935$	−24.0000			−0.784884
$936$		0			0
$937$	29.0000	+	50.2295i	0.947389	+	1.64093i	0.750896	+	0.660420i	$0.229622\pi$
$937$	29.0000	+	50.2295i	0.947389	+	1.64093i	0.196492	+	0.980505i	$0.437045\pi$
$938$		0			0
$939$	6.00000	+	10.3923i	0.195803	+	0.339140i
$940$	−1.00000	+	1.73205i	−0.0326164	+	0.0564933i
$941$	−3.50000	+	6.06218i	−0.114097	+	0.197621i	−0.917418	−	0.397924i	$-0.869731\pi$
$941$	−3.50000	+	6.06218i	−0.114097	+	0.197621i	0.803322	+	0.595545i	$0.203064\pi$
$942$	10.0000	−	17.3205i	0.325818	−	0.564333i
$943$	21.0000	+	36.3731i	0.683854	+	1.18447i
$944$	−0.500000	−	0.866025i	−0.0162736	−	0.0281867i
$945$		0			0
$946$	6.00000	+	10.3923i	0.195077	+	0.337883i
$947$	−40.0000			−1.29983			−0.649913	−	0.760009i	$-0.725195\pi$
$947$	−40.0000			−1.29983			−0.649913	+	0.760009i	$0.725195\pi$
$948$	−16.0000	+	27.7128i	−0.519656	+	0.900070i
$949$		0			0
$950$	1.00000			0.0324443
$951$	−6.00000	−	10.3923i	−0.194563	−	0.336994i
$952$		0			0
$953$	19.0000	−	32.9090i	0.615470	−	1.06603i	−0.374831	−	0.927093i	$-0.622299\pi$
$953$	19.0000	−	32.9090i	0.615470	−	1.06603i	0.990302	−	0.138933i	$-0.0443673\pi$
$954$	−2.00000	−	3.46410i	−0.0647524	−	0.112154i
$955$	5.50000	−	9.52628i	0.177976	−	0.308263i
$956$	−4.00000			−0.129369
$957$	−27.0000	−	46.7654i	−0.872786	−	1.51171i
$958$	−2.50000	−	4.33013i	−0.0807713	−	0.139900i
$959$		0			0
$960$	7.00000	+	12.1244i	0.225924	+	0.391312i
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−8.00000			−0.257796
$964$	8.50000	+	14.7224i	0.273767	+	0.474178i
$965$	4.00000			0.128765
$966$		0			0
$967$	25.0000	−	43.3013i	0.803946	−	1.39247i	−0.113055	−	0.993589i	$-0.536064\pi$
$967$	25.0000	−	43.3013i	0.803946	−	1.39247i	0.917000	−	0.398886i	$-0.130603\pi$
$968$	3.00000	−	5.19615i	0.0964237	−	0.167011i
$969$	−8.00000	−	13.8564i	−0.256997	−	0.445132i
$970$	14.0000			0.449513
$971$	3.00000			0.0962746			0.0481373	−	0.998841i	$-0.484672\pi$
$971$	3.00000			0.0962746			0.0481373	+	0.998841i	$0.484672\pi$
$972$	5.00000	−	8.66025i	0.160375	−	0.277778i
$973$		0			0
$974$	2.00000			0.0640841
$975$		0			0
$976$	−9.00000			−0.288083
$977$	5.00000	−	8.66025i	0.159964	−	0.277066i	−0.774891	−	0.632094i	$-0.782195\pi$
$977$	5.00000	−	8.66025i	0.159964	−	0.277066i	0.934856	+	0.355028i	$0.115529\pi$
$978$	8.00000			0.255812
$979$	−6.00000			−0.191761
$980$	−3.50000	+	6.06218i	−0.111803	+	0.193649i
$981$	9.00000	−	15.5885i	0.287348	−	0.497701i
$982$	−7.50000	+	12.9904i	−0.239335	+	0.414540i
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	−0.686050	−	0.727554i	$-0.740657\pi$
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	0.973106	+	0.230360i	$0.0739903\pi$
$984$	42.0000			1.33891
$985$	24.0000			0.764704
$986$	36.0000	−	62.3538i	1.14647	−	1.98575i
$987$		0			0
$988$		0			0
$989$	−24.0000			−0.763156
$990$	3.00000			0.0953463
$991$	−14.5000	+	25.1147i	−0.460608	+	0.797796i	−0.998991	−	0.0449040i	$-0.985702\pi$
$991$	−14.5000	+	25.1147i	−0.460608	+	0.797796i	0.538384	+	0.842700i	$0.319035\pi$
$992$	−20.0000			−0.635001
$993$	−40.0000			−1.26936
$994$		0			0
$995$	−0.500000	+	0.866025i	−0.0158511	+	0.0274549i
$996$	6.00000	−	10.3923i	0.190117	−	0.329293i
$997$	34.0000			1.07679			0.538395	−	0.842692i	$-0.319031\pi$
$997$	34.0000			1.07679			0.538395	+	0.842692i	$0.319031\pi$
$998$	3.00000			0.0949633
$999$	−20.0000	−	34.6410i	−0.632772	−	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	755.2.e.a.636.1	yes	2
151.118	even	3	inner	755.2.e.a.571.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
755.2.e.a.571.1	✓	2	151.118	even	3	inner
755.2.e.a.636.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	755.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} -2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{6} +3.00000 q^{8} +1.00000 q^{9} +(0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{12} +(1.00000 + 1.73205i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-4.00000 - 6.92820i) q^{17} +(0.500000 + 0.866025i) q^{18} -1.00000 q^{19} -1.00000 q^{20} +(-1.50000 + 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} -6.00000 q^{24} +(-0.500000 + 0.866025i) q^{25} +4.00000 q^{27} +9.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(2.50000 - 4.33013i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(4.00000 - 6.92820i) q^{34} +(0.500000 - 0.866025i) q^{36} +(-5.00000 - 8.66025i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(-1.50000 - 2.59808i) q^{40} -7.00000 q^{41} +(2.00000 - 3.46410i) q^{43} +3.00000 q^{44} +(-0.500000 - 0.866025i) q^{45} +(3.00000 - 5.19615i) q^{46} +(1.00000 - 1.73205i) q^{47} +(-1.00000 - 1.73205i) q^{48} +(3.50000 - 6.06218i) q^{49} -1.00000 q^{50} +(8.00000 + 13.8564i) q^{51} -4.00000 q^{53} +(2.00000 + 3.46410i) q^{54} +(1.50000 - 2.59808i) q^{55} +2.00000 q^{57} +(4.50000 + 7.79423i) q^{58} -1.00000 q^{59} +2.00000 q^{60} +(-4.50000 + 7.79423i) q^{61} +(2.00000 - 3.46410i) q^{62} +7.00000 q^{64} +(3.00000 - 5.19615i) q^{66} +8.00000 q^{67} -8.00000 q^{68} +(6.00000 + 10.3923i) q^{69} +(-1.50000 + 2.59808i) q^{71} +3.00000 q^{72} +2.00000 q^{73} +(5.00000 - 8.66025i) q^{74} +(1.00000 - 1.73205i) q^{75} +(-0.500000 + 0.866025i) q^{76} +16.0000 q^{79} +(0.500000 - 0.866025i) q^{80} -11.0000 q^{81} +(-3.50000 - 6.06218i) q^{82} -6.00000 q^{83} +(-4.00000 + 6.92820i) q^{85} +4.00000 q^{86} -18.0000 q^{87} +(4.50000 + 7.79423i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(0.500000 - 0.866025i) q^{90} -6.00000 q^{92} +(4.00000 + 6.92820i) q^{93} +2.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(-5.00000 + 8.66025i) q^{96} +(7.00000 + 12.1244i) q^{97} +7.00000 q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 4 q^{3} + q^{4} - q^{5} - 2 q^{6} + 6 q^{8} + 2 q^{9} + q^{10} + 3 q^{11} - 2 q^{12} + 2 q^{15} + q^{16} - 8 q^{17} + q^{18} - 2 q^{19} - 2 q^{20} - 3 q^{22} - 6 q^{23} - 12 q^{24} - q^{25}+ \cdots + 3 q^{99}+O(q^{100}) \) 2 * q + q^2 - 4 * q^3 + q^4 - q^5 - 2 * q^6 + 6 * q^8 + 2 * q^9 + q^10 + 3 * q^11 - 2 * q^12 + 2 * q^15 + q^16 - 8 * q^17 + q^18 - 2 * q^19 - 2 * q^20 - 3 * q^22 - 6 * q^23 - 12 * q^24 - q^25 + 8 * q^27 + 18 * q^29 - 2 * q^30 - 4 * q^31 + 5 * q^32 - 6 * q^33 + 8 * q^34 + q^36 - 10 * q^37 - q^38 - 3 * q^40 - 14 * q^41 + 4 * q^43 + 6 * q^44 - q^45 + 6 * q^46 + 2 * q^47 - 2 * q^48 + 7 * q^49 - 2 * q^50 + 16 * q^51 - 8 * q^53 + 4 * q^54 + 3 * q^55 + 4 * q^57 + 9 * q^58 - 2 * q^59 + 4 * q^60 - 9 * q^61 + 4 * q^62 + 14 * q^64 + 6 * q^66 + 16 * q^67 - 16 * q^68 + 12 * q^69 - 3 * q^71 + 6 * q^72 + 4 * q^73 + 10 * q^74 + 2 * q^75 - q^76 + 32 * q^79 + q^80 - 22 * q^81 - 7 * q^82 - 12 * q^83 - 8 * q^85 + 8 * q^86 - 36 * q^87 + 9 * q^88 - 2 * q^89 + q^90 - 12 * q^92 + 8 * q^93 + 4 * q^94 + q^95 - 10 * q^96 + 14 * q^97 + 14 * q^98 + 3 * q^99

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