LMFDB - Embedded newform 546.2.l.e.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.l (of order $3$, degree $2$, 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:	$4.35983195036$
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			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.211
Dual form			546.2.l.e.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(2.50000 + 2.59808i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} -1.00000 q^{18} +(-2.50000 + 4.33013i) q^{19} +1.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} -5.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(4.50000 + 7.79423i) q^{29} +8.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +3.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-4.00000 - 6.92820i) q^{37} -5.00000 q^{38} +(1.00000 - 3.46410i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} -3.00000 q^{44} +(-3.00000 + 5.19615i) q^{46} +3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.50000 - 4.33013i) q^{50} -3.00000 q^{51} +(-3.50000 + 0.866025i) q^{52} -3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(0.500000 - 0.866025i) q^{56} +5.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(3.00000 - 5.19615i) q^{59} +(3.50000 - 6.06218i) q^{61} +(4.00000 + 6.92820i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(3.00000 - 5.19615i) q^{69} +(3.00000 - 5.19615i) q^{71} +(0.500000 - 0.866025i) q^{72} -16.0000 q^{73} +(4.00000 - 6.92820i) q^{74} +(2.50000 + 4.33013i) q^{75} +(-2.50000 - 4.33013i) q^{76} -3.00000 q^{77} +(3.50000 - 0.866025i) q^{78} -13.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} +18.0000 q^{83} +(-0.500000 + 0.866025i) q^{84} -8.00000 q^{86} +(4.50000 - 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(7.50000 + 12.9904i) q^{89} +(-3.50000 + 0.866025i) q^{91} -6.00000 q^{92} +(-4.00000 - 6.92820i) q^{93} +(1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(8.00000 - 13.8564i) q^{97} +(0.500000 - 0.866025i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 + q^6 - q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} + q^{6} - q^{7} - 2 q^{8} - q^{9} + 3 q^{11} + 2 q^{12} + 5 q^{13} - 2 q^{14} - q^{16} + 3 q^{17} - 2 q^{18} - 5 q^{19} + 2 q^{21} - 3 q^{22} + 6 q^{23} + q^{24} - 10 q^{25} - 2 q^{26} + 2 q^{27} - q^{28} + 9 q^{29} + 16 q^{31} + q^{32} + 3 q^{33} + 6 q^{34} - q^{36} - 8 q^{37} - 10 q^{38} + 2 q^{39} - 3 q^{41} + q^{42} - 8 q^{43} - 6 q^{44} - 6 q^{46} + 6 q^{47} - q^{48} - q^{49} - 5 q^{50} - 6 q^{51} - 7 q^{52} - 6 q^{53} + q^{54} + q^{56} + 10 q^{57} - 9 q^{58} + 6 q^{59} + 7 q^{61} + 8 q^{62} - q^{63} + 2 q^{64} + 6 q^{66} - 2 q^{67} + 3 q^{68} + 6 q^{69} + 6 q^{71} + q^{72} - 32 q^{73} + 8 q^{74} + 5 q^{75} - 5 q^{76} - 6 q^{77} + 7 q^{78} - 26 q^{79} - q^{81} + 3 q^{82} + 36 q^{83} - q^{84} - 16 q^{86} + 9 q^{87} - 3 q^{88} + 15 q^{89} - 7 q^{91} - 12 q^{92} - 8 q^{93} + 3 q^{94} - 2 q^{96} + 16 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + q^6 - q^7 - 2 * q^8 - q^9 + 3 * q^11 + 2 * q^12 + 5 * q^13 - 2 * q^14 - q^16 + 3 * q^17 - 2 * q^18 - 5 * q^19 + 2 * q^21 - 3 * q^22 + 6 * q^23 + q^24 - 10 * q^25 - 2 * q^26 + 2 * q^27 - q^28 + 9 * q^29 + 16 * q^31 + q^32 + 3 * q^33 + 6 * q^34 - q^36 - 8 * q^37 - 10 * q^38 + 2 * q^39 - 3 * q^41 + q^42 - 8 * q^43 - 6 * q^44 - 6 * q^46 + 6 * q^47 - q^48 - q^49 - 5 * q^50 - 6 * q^51 - 7 * q^52 - 6 * q^53 + q^54 + q^56 + 10 * q^57 - 9 * q^58 + 6 * q^59 + 7 * q^61 + 8 * q^62 - q^63 + 2 * q^64 + 6 * q^66 - 2 * q^67 + 3 * q^68 + 6 * q^69 + 6 * q^71 + q^72 - 32 * q^73 + 8 * q^74 + 5 * q^75 - 5 * q^76 - 6 * q^77 + 7 * q^78 - 26 * q^79 - q^81 + 3 * q^82 + 36 * q^83 - q^84 - 16 * q^86 + 9 * q^87 - 3 * q^88 + 15 * q^89 - 7 * q^91 - 12 * q^92 - 8 * q^93 + 3 * q^94 - 2 * q^96 + 16 * q^97 + q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	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			0.288675
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	−1.00000			−0.235702
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$		0			0
$21$	1.00000			0.218218
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	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	$0.618211\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−5.00000			−1.00000
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$	1.00000			0.192450
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	0.893517	+	0.449029i	$0.148230\pi$
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	−0.0578882	+	0.998323i	$0.518437\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$	3.00000			0.514496
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	−5.00000			−0.811107
$39$	1.00000	−	3.46410i	0.160128	−	0.554700i
$40$		0			0
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.50000	−	4.33013i	−0.353553	−	0.612372i
$51$	−3.00000			−0.420084
$52$	−3.50000	+	0.866025i	−0.485363	+	0.120096i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	5.00000			0.662266
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	4.00000	+	6.92820i	0.508001	+	0.879883i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.00000			0.369274
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−16.0000			−1.87266			−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000			−1.87266			−0.936329	+	0.351123i	$0.885800\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$	2.50000	+	4.33013i	0.288675	+	0.500000i
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	−3.00000			−0.341882
$78$	3.50000	−	0.866025i	0.396297	−	0.0980581i
$79$	−13.0000			−1.46261			−0.731307	−	0.682048i	$-0.761089\pi$
$79$	−13.0000			−1.46261			−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	18.0000			1.97576			0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000			1.97576			0.987878	+	0.155230i	$0.0496119\pi$
$84$	−0.500000	+	0.866025i	−0.0545545	+	0.0944911i
$85$		0			0
$86$	−8.00000			−0.862662
$87$	4.50000	−	7.79423i	0.482451	−	0.835629i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	0.922840	+	0.385183i	$0.125862\pi$
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	−0.127842	+	0.991795i	$0.540805\pi$
$90$		0			0
$91$	−3.50000	+	0.866025i	−0.366900	+	0.0907841i
$92$	−6.00000			−0.625543
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	8.00000	−	13.8564i	0.812277	−	1.40690i	−0.0989899	−	0.995088i	$-0.531561\pi$
$97$	8.00000	−	13.8564i	0.812277	−	1.40690i	0.911267	−	0.411816i	$-0.135106\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	−3.00000			−0.301511
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$	−1.50000	−	2.59808i	−0.148522	−	0.257248i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	−2.50000	−	2.59808i	−0.245145	−	0.254762i
$105$		0			0
$106$	−1.50000	−	2.59808i	−0.145693	−	0.252347i
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	0.562267	−	0.826956i	$-0.309929\pi$
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	−0.997298	+	0.0734594i	$0.976596\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	−4.00000	+	6.92820i	−0.379663	+	0.657596i
$112$	1.00000			0.0944911
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	−0.432670	−	0.901553i	$-0.642428\pi$
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	0.997102	−	0.0760733i	$-0.0242383\pi$
$114$	2.50000	+	4.33013i	0.234146	+	0.405554i
$115$		0			0
$116$	−9.00000			−0.835629
$117$	−3.50000	+	0.866025i	−0.323575	+	0.0800641i
$118$	6.00000			0.552345
$119$	1.50000	+	2.59808i	0.137505	+	0.238165i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	7.00000			0.633750
$123$	−1.50000	+	2.59808i	−0.135250	+	0.234261i
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$		0			0
$126$	0.500000	−	0.866025i	0.0445435	−	0.0771517i
$127$	8.00000	+	13.8564i	0.709885	+	1.22956i	0.964899	+	0.262620i	$0.0845865\pi$
$127$	8.00000	+	13.8564i	0.709885	+	1.22956i	−0.255014	+	0.966937i	$0.582080\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	8.00000			0.704361
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$	1.50000	+	2.59808i	0.130558	+	0.226134i
$133$	−2.50000	−	4.33013i	−0.216777	−	0.375470i
$134$	1.00000	−	1.73205i	0.0863868	−	0.149626i
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$	6.00000			0.510754
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	−0.999268	−	0.0382553i	$-0.987820\pi$
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	0.532764	+	0.846264i	$0.321153\pi$
$140$		0			0
$141$	−1.50000	−	2.59808i	−0.126323	−	0.218797i
$142$	6.00000			0.503509
$143$	−3.00000	+	10.3923i	−0.250873	+	0.869048i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−8.00000	−	13.8564i	−0.662085	−	1.14676i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$	8.00000			0.657596
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	−2.50000	+	4.33013i	−0.204124	+	0.353553i
$151$	−19.0000			−1.54620			−0.773099	−	0.634285i	$-0.781294\pi$
$151$	−19.0000			−1.54620			−0.773099	+	0.634285i	$0.781294\pi$
$152$	2.50000	−	4.33013i	0.202777	−	0.351220i
$153$	1.50000	+	2.59808i	0.121268	+	0.210042i
$154$	−1.50000	−	2.59808i	−0.120873	−	0.209359i
$155$		0			0
$156$	2.50000	+	2.59808i	0.200160	+	0.208013i
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$	−6.50000	−	11.2583i	−0.517112	−	0.895665i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$		0			0
$161$	−6.00000			−0.472866
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	9.00000	+	15.5885i	0.698535	+	1.20990i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$	−1.00000			−0.0771517
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$	−2.50000	−	4.33013i	−0.191180	−	0.331133i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	9.00000			0.682288
$175$	2.50000	−	4.33013i	0.188982	−	0.327327i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−6.00000			−0.450988
$178$	−7.50000	+	12.9904i	−0.562149	+	0.973670i
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.831408	+	0.555663i	$0.187536\pi$
$179$	12.0000	+	20.7846i	0.896922	+	1.55351i	0.0655145	+	0.997852i	$0.479131\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	−2.50000	−	2.59808i	−0.185312	−	0.192582i
$183$	−7.00000			−0.517455
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$	9.00000			0.658145
$188$	−1.50000	+	2.59808i	−0.109399	+	0.189484i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	16.0000			1.14873
$195$		0			0
$196$	1.00000			0.0714286
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	0.914501	−	0.404584i	$-0.132584\pi$
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	−0.807630	+	0.589689i	$0.799250\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	5.00000			0.353553
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$	9.00000	−	15.5885i	0.633238	−	1.09680i
$203$	−9.00000			−0.631676
$204$	1.50000	−	2.59808i	0.105021	−	0.181902i
$205$		0			0
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$	−6.00000			−0.417029
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$	−15.0000			−1.03757
$210$		0			0
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	0.944237	+	0.329266i	$0.106801\pi$
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	−6.00000			−0.411113
$214$	4.50000	−	7.79423i	0.307614	−	0.532803i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−4.00000	+	6.92820i	−0.271538	+	0.470317i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$	8.00000	+	13.8564i	0.540590	+	0.936329i
$220$		0			0
$221$	10.5000	−	2.59808i	0.706306	−	0.174766i
$222$	−8.00000			−0.536925
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	2.50000	−	4.33013i	0.166667	−	0.288675i
$226$	12.0000			0.798228
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	−0.749125	−	0.662428i	$-0.769526\pi$
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	0.948242	+	0.317547i	$0.102859\pi$
$228$	−2.50000	+	4.33013i	−0.165567	+	0.286770i
$229$	5.00000			0.330409			0.165205	−	0.986259i	$-0.447172\pi$
$229$	5.00000			0.330409			0.165205	+	0.986259i	$0.447172\pi$
$230$		0			0
$231$	1.50000	+	2.59808i	0.0986928	+	0.170941i
$232$	−4.50000	−	7.79423i	−0.295439	−	0.511716i
$233$	−24.0000			−1.57229			−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000			−1.57229			−0.786146	+	0.618041i	$0.787927\pi$
$234$	−2.50000	−	2.59808i	−0.163430	−	0.169842i
$235$		0			0
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	6.50000	+	11.2583i	0.422220	+	0.731307i
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	0.707953	+	0.706260i	$0.249619\pi$
$242$	2.00000			0.128565
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.50000	+	6.06218i	0.224065	+	0.388091i
$245$		0			0
$246$	−3.00000			−0.191273
$247$	−17.5000	+	4.33013i	−1.11350	+	0.275519i
$248$	−8.00000			−0.508001
$249$	−9.00000	−	15.5885i	−0.570352	−	0.987878i
$250$		0			0
$251$	−9.00000	+	15.5885i	−0.568075	+	0.983935i	0.428681	+	0.903456i	$0.358978\pi$
$251$	−9.00000	+	15.5885i	−0.568075	+	0.983935i	−0.996756	+	0.0804789i	$0.974355\pi$
$252$	1.00000			0.0629941
$253$	−9.00000	+	15.5885i	−0.565825	+	0.980038i
$254$	−8.00000	+	13.8564i	−0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$	4.00000	+	6.92820i	0.249029	+	0.431331i
$259$	8.00000			0.497096
$260$		0			0
$261$	−9.00000			−0.557086
$262$	6.00000	+	10.3923i	0.370681	+	0.642039i
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	0.758585	−	0.651575i	$-0.225891\pi$
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	−0.943572	+	0.331166i	$0.892558\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$		0			0
$266$	2.50000	−	4.33013i	0.153285	−	0.265497i
$267$	7.50000	−	12.9904i	0.458993	−	0.794998i
$268$	2.00000			0.122169
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	−0.991658	−	0.128897i	$-0.958856\pi$
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	0.384201	−	0.923249i	$-0.374477\pi$
$272$	−3.00000			−0.181902
$273$	2.50000	+	2.59808i	0.151307	+	0.157243i
$274$	6.00000			0.362473
$275$	−7.50000	−	12.9904i	−0.452267	−	0.783349i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$	−11.0000			−0.659736
$279$	−4.00000	+	6.92820i	−0.239474	+	0.414781i
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	−10.5000	+	2.59808i	−0.620878	+	0.153627i
$287$	3.00000			0.177084
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−16.0000			−0.937937
$292$	8.00000	−	13.8564i	0.468165	−	0.810885i
$293$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$293$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$294$	−1.00000			−0.0583212
$295$		0			0
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$	1.50000	+	2.59808i	0.0870388	+	0.150756i
$298$	6.00000			0.347571
$299$	−6.00000	+	20.7846i	−0.346989	+	1.20201i
$300$	−5.00000			−0.288675
$301$	−4.00000	−	6.92820i	−0.230556	−	0.399335i
$302$	−9.50000	−	16.4545i	−0.546664	−	0.946849i
$303$	−9.00000	+	15.5885i	−0.517036	+	0.895533i
$304$	5.00000			0.286770
$305$		0			0
$306$	−1.50000	+	2.59808i	−0.0857493	+	0.148522i
$307$	−13.0000			−0.741949			−0.370975	−	0.928643i	$-0.620976\pi$
$307$	−13.0000			−0.741949			−0.370975	+	0.928643i	$0.620976\pi$
$308$	1.50000	−	2.59808i	0.0854704	−	0.148039i
$309$	2.00000	+	3.46410i	0.113776	+	0.197066i
$310$		0			0
$311$	−21.0000			−1.19080			−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000			−1.19080			−0.595400	+	0.803429i	$0.703007\pi$
$312$	−1.00000	+	3.46410i	−0.0566139	+	0.196116i
$313$	26.0000			1.46961			0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000			1.46961			0.734803	+	0.678280i	$0.237274\pi$
$314$	1.00000	+	1.73205i	0.0564333	+	0.0977453i
$315$		0			0
$316$	6.50000	−	11.2583i	0.365654	−	0.633331i
$317$	30.0000			1.68497			0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000			1.68497			0.842484	+	0.538721i	$0.181092\pi$
$318$	−1.50000	+	2.59808i	−0.0841158	+	0.145693i
$319$	−13.5000	+	23.3827i	−0.755855	+	1.30918i
$320$		0			0
$321$	−4.50000	+	7.79423i	−0.251166	+	0.435031i
$322$	−3.00000	−	5.19615i	−0.167183	−	0.289570i
$323$	7.50000	+	12.9904i	0.417311	+	0.722804i
$324$	1.00000			0.0555556
$325$	−12.5000	−	12.9904i	−0.693375	−	0.720577i
$326$	16.0000			0.886158
$327$	−1.00000	−	1.73205i	−0.0553001	−	0.0957826i
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	−1.50000	+	2.59808i	−0.0826977	+	0.143237i
$330$		0			0
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	−0.695266	−	0.718752i	$-0.744713\pi$
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	0.970091	+	0.242742i	$0.0780468\pi$
$332$	−9.00000	+	15.5885i	−0.493939	+	0.855528i
$333$	8.00000			0.438397
$334$		0			0
$335$		0			0
$336$	−0.500000	−	0.866025i	−0.0272772	−	0.0472456i
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$	−11.5000	+	6.06218i	−0.625518	+	0.329739i
$339$	−12.0000			−0.651751
$340$		0			0
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$	2.50000	−	4.33013i	0.135185	−	0.234146i
$343$	1.00000			0.0539949
$344$	4.00000	−	6.92820i	0.215666	−	0.373544i
$345$		0			0
$346$	6.00000			0.322562
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	−0.903475	−	0.428640i	$-0.858993\pi$
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	0.822951	+	0.568112i	$0.192326\pi$
$348$	4.50000	+	7.79423i	0.241225	+	0.417815i
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	0.838019	−	0.545640i	$-0.183714\pi$
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	−0.891548	+	0.452926i	$0.850380\pi$
$350$	5.00000			0.267261
$351$	2.50000	+	2.59808i	0.133440	+	0.138675i
$352$	3.00000			0.159901
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$		0			0
$356$	−15.0000			−0.794998
$357$	1.50000	−	2.59808i	0.0793884	−	0.137505i
$358$	−12.0000	+	20.7846i	−0.634220	+	1.09850i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	2.50000	+	4.33013i	0.131397	+	0.227586i
$363$	−2.00000			−0.104973
$364$	1.00000	−	3.46410i	0.0524142	−	0.181568i
$365$		0			0
$366$	−3.50000	−	6.06218i	−0.182948	−	0.316875i
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	0.966507	−	0.256639i	$-0.0826151\pi$
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	−0.705509	+	0.708700i	$0.749282\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$	3.00000			0.156174
$370$		0			0
$371$	1.50000	−	2.59808i	0.0778761	−	0.134885i
$372$	8.00000			0.414781
$373$	11.0000	−	19.0526i	0.569558	−	0.986504i	−0.427051	−	0.904227i	$-0.640448\pi$
$373$	11.0000	−	19.0526i	0.569558	−	0.986504i	0.996610	−	0.0822766i	$-0.0262191\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$		0			0
$376$	−3.00000			−0.154713
$377$	−9.00000	+	31.1769i	−0.463524	+	1.60569i
$378$	−1.00000			−0.0514344
$379$	5.00000	+	8.66025i	0.256833	+	0.444847i	0.965392	−	0.260804i	$-0.0839877\pi$
$379$	5.00000	+	8.66025i	0.256833	+	0.444847i	−0.708559	+	0.705652i	$0.750654\pi$
$380$		0			0
$381$	8.00000	−	13.8564i	0.409852	−	0.709885i
$382$	−6.00000			−0.306987
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	2.50000	−	4.33013i	0.127247	−	0.220398i
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$	8.00000	+	13.8564i	0.406138	+	0.703452i
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$	−6.00000	−	10.3923i	−0.302660	−	0.524222i
$394$	−1.50000	+	2.59808i	−0.0755689	+	0.130889i
$395$		0			0
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	12.5000	−	21.6506i	0.627357	−	1.08661i	−0.360723	−	0.932673i	$-0.617470\pi$
$397$	12.5000	−	21.6506i	0.627357	−	1.08661i	0.988080	−	0.153941i	$-0.0491966\pi$
$398$	4.00000			0.200502
$399$	−2.50000	+	4.33013i	−0.125157	+	0.216777i
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$	−2.00000			−0.0997509
$403$	20.0000	+	20.7846i	0.996271	+	1.03536i
$404$	18.0000			0.895533
$405$		0			0
$406$	−4.50000	−	7.79423i	−0.223331	−	0.386821i
$407$	12.0000	−	20.7846i	0.594818	−	1.03025i
$408$	3.00000			0.148522
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	0.998674	−	0.0514740i	$-0.0163919\pi$
$410$		0			0
$411$	−6.00000			−0.295958
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	3.00000	+	5.19615i	0.147620	+	0.255686i
$414$	−3.00000	−	5.19615i	−0.147442	−	0.255377i
$415$		0			0
$416$	3.50000	−	0.866025i	0.171602	−	0.0424604i
$417$	11.0000			0.538672
$418$	−7.50000	−	12.9904i	−0.366837	−	0.635380i
$419$	3.00000	+	5.19615i	0.146560	+	0.253849i	0.929954	−	0.367677i	$-0.119847\pi$
$419$	3.00000	+	5.19615i	0.146560	+	0.253849i	−0.783394	+	0.621525i	$0.786513\pi$
$420$		0			0
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	−11.0000	+	19.0526i	−0.535472	+	0.927464i
$423$	−1.50000	+	2.59808i	−0.0729325	+	0.126323i
$424$	3.00000			0.145693
$425$	−7.50000	+	12.9904i	−0.363803	+	0.630126i
$426$	−3.00000	−	5.19615i	−0.145350	−	0.251754i
$427$	3.50000	+	6.06218i	0.169377	+	0.293369i
$428$	9.00000			0.435031
$429$	10.5000	−	2.59808i	0.506945	−	0.125436i
$430$		0			0
$431$	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	$0.690607\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−7.00000	+	12.1244i	−0.336399	+	0.582659i	−0.983752	−	0.179530i	$-0.942542\pi$
$433$	−7.00000	+	12.1244i	−0.336399	+	0.582659i	0.647354	+	0.762190i	$0.275876\pi$
$434$	−8.00000			−0.384012
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	−30.0000			−1.43509
$438$	−8.00000	+	13.8564i	−0.382255	+	0.662085i
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	−0.940963	−	0.338508i	$-0.890078\pi$
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	0.177325	−	0.984152i	$-0.443256\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$	7.50000	+	7.79423i	0.356739	+	0.370734i
$443$	33.0000			1.56788			0.783939	−	0.620838i	$-0.213208\pi$
$443$	33.0000			1.56788			0.783939	+	0.620838i	$0.213208\pi$
$444$	−4.00000	−	6.92820i	−0.189832	−	0.328798i
$445$		0			0
$446$	4.00000	−	6.92820i	0.189405	−	0.328060i
$447$	−6.00000			−0.283790
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−12.0000	+	20.7846i	−0.566315	+	0.980886i	0.430611	+	0.902538i	$0.358298\pi$
$449$	−12.0000	+	20.7846i	−0.566315	+	0.980886i	−0.996926	+	0.0783487i	$0.975035\pi$
$450$	5.00000			0.235702
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	9.50000	+	16.4545i	0.446349	+	0.773099i
$454$	6.00000			0.281594
$455$		0			0
$456$	−5.00000			−0.234146
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.841316	−	0.540544i	$-0.818219\pi$
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.0474665	−	0.998873i	$-0.515115\pi$
$458$	2.50000	+	4.33013i	0.116817	+	0.202334i
$459$	1.50000	−	2.59808i	0.0700140	−	0.121268i
$460$		0			0
$461$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$461$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$462$	−1.50000	+	2.59808i	−0.0697863	+	0.120873i
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$		0			0
$466$	−12.0000	−	20.7846i	−0.555889	−	0.962828i
$467$	−24.0000			−1.11059			−0.555294	−	0.831654i	$-0.687394\pi$
$467$	−24.0000			−1.11059			−0.555294	+	0.831654i	$0.687394\pi$
$468$	1.00000	−	3.46410i	0.0462250	−	0.160128i
$469$	2.00000			0.0923514
$470$		0			0
$471$	−1.00000	−	1.73205i	−0.0460776	−	0.0798087i
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$	−24.0000			−1.10352
$474$	−6.50000	+	11.2583i	−0.298555	+	0.517112i
$475$	12.5000	−	21.6506i	0.573539	−	0.993399i
$476$	−3.00000			−0.137505
$477$	1.50000	−	2.59808i	0.0686803	−	0.118958i
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	−4.50000	−	7.79423i	−0.205610	−	0.356127i	0.744717	−	0.667381i	$-0.232585\pi$
$479$	−4.50000	−	7.79423i	−0.205610	−	0.356127i	−0.950327	+	0.311253i	$0.899251\pi$
$480$		0			0
$481$	8.00000	−	27.7128i	0.364769	−	1.26360i
$482$	−8.00000			−0.364390
$483$	3.00000	+	5.19615i	0.136505	+	0.236433i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	−0.680335	−	0.732901i	$-0.738166\pi$
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	0.974879	+	0.222737i	$0.0714992\pi$
$488$	−3.50000	+	6.06218i	−0.158438	+	0.274422i
$489$	−16.0000			−0.723545
$490$		0			0
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	0.969061	−	0.246822i	$-0.0793863\pi$
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	−0.698285	+	0.715820i	$0.746053\pi$
$492$	−1.50000	−	2.59808i	−0.0676252	−	0.117130i
$493$	27.0000			1.21602
$494$	−12.5000	−	12.9904i	−0.562402	−	0.584465i
$495$		0			0
$496$	−4.00000	−	6.92820i	−0.179605	−	0.311086i
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$	9.00000	−	15.5885i	0.403300	−	0.698535i
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$		0			0
$501$		0			0
$502$	−18.0000			−0.803379
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	−0.464107	−	0.885779i	$-0.653625\pi$
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	0.999161	−	0.0409609i	$-0.0130419\pi$
$504$	0.500000	+	0.866025i	0.0222718	+	0.0385758i
$505$		0			0
$506$	−18.0000			−0.800198
$507$	11.5000	−	6.06218i	0.510733	−	0.269231i
$508$	−16.0000			−0.709885
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$	8.00000	−	13.8564i	0.353899	−	0.612971i
$512$	−1.00000			−0.0441942
$513$	−2.50000	+	4.33013i	−0.110378	+	0.191180i
$514$	−7.50000	+	12.9904i	−0.330811	+	0.572981i
$515$		0			0
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$	4.50000	+	7.79423i	0.197910	+	0.342790i
$518$	4.00000	+	6.92820i	0.175750	+	0.304408i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	21.0000			0.920027			0.460013	−	0.887912i	$-0.347845\pi$
$521$	21.0000			0.920027			0.460013	+	0.887912i	$0.347845\pi$
$522$	−4.50000	−	7.79423i	−0.196960	−	0.341144i
$523$	9.50000	+	16.4545i	0.415406	+	0.719504i	0.995471	−	0.0950659i	$-0.0303062\pi$
$523$	9.50000	+	16.4545i	0.415406	+	0.719504i	−0.580065	+	0.814570i	$0.696973\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$	−5.00000			−0.218218
$526$	3.00000	−	5.19615i	0.130806	−	0.226563i
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$	−3.00000			−0.130558
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	3.00000	+	5.19615i	0.130189	+	0.225494i
$532$	5.00000			0.216777
$533$	3.00000	−	10.3923i	0.129944	−	0.450141i
$534$	15.0000			0.649113
$535$		0			0
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	12.0000	−	20.7846i	0.517838	−	0.896922i
$538$		0			0
$539$	1.50000	−	2.59808i	0.0646096	−	0.111907i
$540$		0			0
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	10.0000	−	17.3205i	0.429537	−	0.743980i
$543$	−2.50000	−	4.33013i	−0.107285	−	0.185824i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$	−1.00000	+	3.46410i	−0.0427960	+	0.148250i
$547$	−34.0000			−1.45374			−0.726868	−	0.686778i	$-0.759025\pi$
$547$	−34.0000			−1.45374			−0.726868	+	0.686778i	$0.759025\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$	3.50000	+	6.06218i	0.149376	+	0.258727i
$550$	7.50000	−	12.9904i	0.319801	−	0.553912i
$551$	−45.0000			−1.91706
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	6.50000	−	11.2583i	0.276408	−	0.478753i
$554$	10.0000			0.424859
$555$		0			0
$556$	−5.50000	−	9.52628i	−0.233252	−	0.404004i
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$	−8.00000			−0.338667
$559$	−28.0000	+	6.92820i	−1.18427	+	0.293032i
$560$		0			0
$561$	−4.50000	−	7.79423i	−0.189990	−	0.329073i
$562$	−9.00000	−	15.5885i	−0.379642	−	0.657559i
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$	3.00000			0.126323
$565$		0			0
$566$	−2.00000	+	3.46410i	−0.0840663	+	0.145607i
$567$	1.00000			0.0419961
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$	−7.50000	−	7.79423i	−0.313591	−	0.325893i
$573$	6.00000			0.250654
$574$	1.50000	+	2.59808i	0.0626088	+	0.108442i
$575$	−15.0000	−	25.9808i	−0.625543	−	1.08347i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	−2.50000	+	4.33013i	−0.103896	+	0.179954i
$580$		0			0
$581$	−9.00000	+	15.5885i	−0.373383	+	0.646718i
$582$	−8.00000	−	13.8564i	−0.331611	−	0.574367i
$583$	−4.50000	−	7.79423i	−0.186371	−	0.322804i
$584$	16.0000			0.662085
$585$		0			0
$586$		0			0
$587$	−12.0000	−	20.7846i	−0.495293	−	0.857873i	0.504692	−	0.863299i	$-0.331606\pi$
$587$	−12.0000	−	20.7846i	−0.495293	−	0.857873i	−0.999985	+	0.00542667i	$0.998273\pi$
$588$	−0.500000	−	0.866025i	−0.0206197	−	0.0357143i
$589$	−20.0000	+	34.6410i	−0.824086	+	1.42736i
$590$		0			0
$591$	1.50000	−	2.59808i	0.0617018	−	0.106871i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	15.0000			0.615976			0.307988	−	0.951390i	$-0.400344\pi$
$593$	15.0000			0.615976			0.307988	+	0.951390i	$0.400344\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$		0			0
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	−4.00000			−0.163709
$598$	−21.0000	+	5.19615i	−0.858754	+	0.212486i
$599$	6.00000			0.245153			0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000			0.245153			0.122577	+	0.992459i	$0.460884\pi$
$600$	−2.50000	−	4.33013i	−0.102062	−	0.176777i
$601$	−4.00000	−	6.92820i	−0.163163	−	0.282607i	0.772838	−	0.634603i	$-0.218836\pi$
$601$	−4.00000	−	6.92820i	−0.163163	−	0.282607i	−0.936002	+	0.351996i	$0.885503\pi$
$602$	4.00000	−	6.92820i	0.163028	−	0.282372i
$603$	2.00000			0.0814463
$604$	9.50000	−	16.4545i	0.386550	−	0.669523i
$605$		0			0
$606$	−18.0000			−0.731200
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$	2.50000	+	4.33013i	0.101388	+	0.175610i
$609$	4.50000	+	7.79423i	0.182349	+	0.315838i
$610$		0			0
$611$	7.50000	+	7.79423i	0.303418	+	0.315321i
$612$	−3.00000			−0.121268
$613$	20.0000	+	34.6410i	0.807792	+	1.39914i	0.914390	+	0.404835i	$0.132671\pi$
$613$	20.0000	+	34.6410i	0.807792	+	1.39914i	−0.106597	+	0.994302i	$0.533996\pi$
$614$	−6.50000	−	11.2583i	−0.262319	−	0.454349i
$615$		0			0
$616$	3.00000			0.120873
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	−0.0398207	−	0.999207i	$-0.512679\pi$
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	0.885249	−	0.465118i	$-0.153988\pi$
$618$	−2.00000	+	3.46410i	−0.0804518	+	0.139347i
$619$	−1.00000			−0.0401934			−0.0200967	−	0.999798i	$-0.506397\pi$
$619$	−1.00000			−0.0401934			−0.0200967	+	0.999798i	$0.506397\pi$
$620$		0			0
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$	−10.5000	−	18.1865i	−0.421012	−	0.729214i
$623$	−15.0000			−0.600962
$624$	−3.50000	+	0.866025i	−0.140112	+	0.0346688i
$625$	25.0000			1.00000
$626$	13.0000	+	22.5167i	0.519584	+	0.899947i
$627$	7.50000	+	12.9904i	0.299521	+	0.518786i
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	−24.0000			−0.956943
$630$		0			0
$631$	6.50000	−	11.2583i	0.258761	−	0.448187i	−0.707149	−	0.707064i	$-0.750019\pi$
$631$	6.50000	−	11.2583i	0.258761	−	0.448187i	0.965910	+	0.258877i	$0.0833525\pi$
$632$	13.0000			0.517112
$633$	11.0000	−	19.0526i	0.437211	−	0.757271i
$634$	15.0000	+	25.9808i	0.595726	+	1.03183i
$635$		0			0
$636$	−3.00000			−0.118958
$637$	1.00000	−	3.46410i	0.0396214	−	0.137253i
$638$	−27.0000			−1.06894
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$	−9.00000			−0.355202
$643$	15.5000	−	26.8468i	0.611260	−	1.05873i	−0.379768	−	0.925082i	$-0.623996\pi$
$643$	15.5000	−	26.8468i	0.611260	−	1.05873i	0.991028	−	0.133652i	$-0.0426705\pi$
$644$	3.00000	−	5.19615i	0.118217	−	0.204757i
$645$		0			0
$646$	−7.50000	+	12.9904i	−0.295084	+	0.511100i
$647$	−16.5000	−	28.5788i	−0.648682	−	1.12355i	−0.983438	−	0.181245i	$-0.941987\pi$
$647$	−16.5000	−	28.5788i	−0.648682	−	1.12355i	0.334756	−	0.942305i	$-0.391346\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	18.0000			0.706562
$650$	5.00000	−	17.3205i	0.196116	−	0.679366i
$651$	8.00000			0.313545
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	0.584091	−	0.811688i	$-0.301451\pi$
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	−0.994988	+	0.0999939i	$0.968118\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$		0			0
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$	8.00000	−	13.8564i	0.312110	−	0.540590i
$658$	−3.00000			−0.116952
$659$	16.5000	−	28.5788i	0.642749	−	1.11327i	−0.342068	−	0.939675i	$-0.611127\pi$
$659$	16.5000	−	28.5788i	0.642749	−	1.11327i	0.984817	−	0.173598i	$-0.0555394\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	10.0000			0.388661
$663$	−7.50000	−	7.79423i	−0.291276	−	0.302703i
$664$	−18.0000			−0.698535
$665$		0			0
$666$	4.00000	+	6.92820i	0.154997	+	0.268462i
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$		0			0
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$	21.0000			0.810696
$672$	0.500000	−	0.866025i	0.0192879	−	0.0334077i
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$	11.5000	+	19.9186i	0.442963	+	0.767235i
$675$	−5.00000			−0.192450
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	−6.00000	−	10.3923i	−0.230429	−	0.399114i
$679$	8.00000	+	13.8564i	0.307012	+	0.531760i
$680$		0			0
$681$	−6.00000			−0.229920
$682$	−12.0000	+	20.7846i	−0.459504	+	0.795884i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	5.00000			0.191180
$685$		0			0
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	−2.50000	−	4.33013i	−0.0953809	−	0.165205i
$688$	8.00000			0.304997
$689$	−7.50000	−	7.79423i	−0.285727	−	0.296936i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	3.00000	+	5.19615i	0.114043	+	0.197528i
$693$	1.50000	−	2.59808i	0.0569803	−	0.0986928i
$694$	−3.00000			−0.113878
$695$		0			0
$696$	−4.50000	+	7.79423i	−0.170572	+	0.295439i
$697$	−9.00000			−0.340899
$698$	1.00000	−	1.73205i	0.0378506	−	0.0655591i
$699$	12.0000	+	20.7846i	0.453882	+	0.786146i
$700$	2.50000	+	4.33013i	0.0944911	+	0.163663i
$701$	−21.0000			−0.793159			−0.396580	−	0.918000i	$-0.629803\pi$
$701$	−21.0000			−0.793159			−0.396580	+	0.918000i	$0.629803\pi$
$702$	−1.00000	+	3.46410i	−0.0377426	+	0.130744i
$703$	40.0000			1.50863
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	9.00000	−	15.5885i	0.338719	−	0.586679i
$707$	18.0000			0.676960
$708$	3.00000	−	5.19615i	0.112747	−	0.195283i
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$		0			0
$711$	6.50000	−	11.2583i	0.243769	−	0.422220i
$712$	−7.50000	−	12.9904i	−0.281074	−	0.486835i
$713$	24.0000	+	41.5692i	0.898807	+	1.55678i
$714$	3.00000			0.112272
$715$		0			0
$716$	−24.0000			−0.896922
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	−4.50000	+	7.79423i	−0.167822	+	0.290676i	−0.937654	−	0.347571i	$-0.887007\pi$
$719$	−4.50000	+	7.79423i	−0.167822	+	0.290676i	0.769832	+	0.638247i	$0.220340\pi$
$720$		0			0
$721$	2.00000	−	3.46410i	0.0744839	−	0.129010i
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$	8.00000			0.297523
$724$	−2.50000	+	4.33013i	−0.0929118	+	0.160928i
$725$	−22.5000	−	38.9711i	−0.835629	−	1.44735i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	−16.0000			−0.593407			−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000			−0.593407			−0.296704	+	0.954970i	$0.595887\pi$
$728$	3.50000	−	0.866025i	0.129719	−	0.0320970i
$729$	1.00000			0.0370370
$730$		0			0
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	3.50000	−	6.06218i	0.129364	−	0.224065i
$733$	−37.0000			−1.36663			−0.683313	−	0.730125i	$-0.739462\pi$
$733$	−37.0000			−1.36663			−0.683313	+	0.730125i	$0.739462\pi$
$734$	−5.00000	+	8.66025i	−0.184553	+	0.319656i
$735$		0			0
$736$	6.00000			0.221163
$737$	3.00000	−	5.19615i	0.110506	−	0.191403i
$738$	1.50000	+	2.59808i	0.0552158	+	0.0956365i
$739$	−1.00000	−	1.73205i	−0.0367856	−	0.0637145i	0.847046	−	0.531519i	$-0.178379\pi$
$739$	−1.00000	−	1.73205i	−0.0367856	−	0.0637145i	−0.883832	+	0.467804i	$0.845045\pi$
$740$		0			0
$741$	12.5000	+	12.9904i	0.459199	+	0.477214i
$742$	3.00000			0.110133
$743$	6.00000	+	10.3923i	0.220119	+	0.381257i	0.954844	−	0.297108i	$-0.0960222\pi$
$743$	6.00000	+	10.3923i	0.220119	+	0.381257i	−0.734725	+	0.678365i	$0.762689\pi$
$744$	4.00000	+	6.92820i	0.146647	+	0.254000i
$745$		0			0
$746$	22.0000			0.805477
$747$	−9.00000	+	15.5885i	−0.329293	+	0.570352i
$748$	−4.50000	+	7.79423i	−0.164536	+	0.284985i
$749$	9.00000			0.328853
$750$		0			0
$751$	0.500000	+	0.866025i	0.0182453	+	0.0316017i	0.875004	−	0.484116i	$-0.160859\pi$
$751$	0.500000	+	0.866025i	0.0182453	+	0.0316017i	−0.856759	+	0.515718i	$0.827525\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$	18.0000			0.655956
$754$	−31.5000	+	7.79423i	−1.14716	+	0.283849i
$755$		0			0
$756$	−0.500000	−	0.866025i	−0.0181848	−	0.0314970i
$757$	17.0000	+	29.4449i	0.617876	+	1.07019i	0.989873	+	0.141958i	$0.0453398\pi$
$757$	17.0000	+	29.4449i	0.617876	+	1.07019i	−0.371997	+	0.928234i	$0.621327\pi$
$758$	−5.00000	+	8.66025i	−0.181608	+	0.314555i
$759$	18.0000			0.653359
$760$		0			0
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$	16.0000			0.579619
$763$	−1.00000	+	1.73205i	−0.0362024	+	0.0627044i
$764$	−3.00000	−	5.19615i	−0.108536	−	0.187990i
$765$		0			0
$766$	21.0000			0.758761
$767$	21.0000	−	5.19615i	0.758266	−	0.187622i
$768$	1.00000			0.0360844
$769$	−4.00000	−	6.92820i	−0.144244	−	0.249837i	0.784847	−	0.619690i	$-0.212742\pi$
$769$	−4.00000	−	6.92820i	−0.144244	−	0.249837i	−0.929091	+	0.369852i	$0.879408\pi$
$770$		0			0
$771$	7.50000	−	12.9904i	0.270106	−	0.467837i
$772$	5.00000			0.179954
$773$	−21.0000	+	36.3731i	−0.755318	+	1.30825i	0.189899	+	0.981804i	$0.439184\pi$
$773$	−21.0000	+	36.3731i	−0.755318	+	1.30825i	−0.945216	+	0.326445i	$0.894149\pi$
$774$	4.00000	−	6.92820i	0.143777	−	0.249029i
$775$	−40.0000			−1.43684
$776$	−8.00000	+	13.8564i	−0.287183	+	0.497416i
$777$	−4.00000	−	6.92820i	−0.143499	−	0.248548i
$778$	−9.00000	−	15.5885i	−0.322666	−	0.558873i
$779$	15.0000			0.537431
$780$		0			0
$781$	18.0000			0.644091
$782$	9.00000	+	15.5885i	0.321839	+	0.557442i
$783$	4.50000	+	7.79423i	0.160817	+	0.278543i
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$		0			0
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	−17.5000	+	30.3109i	−0.623808	+	1.08047i	0.364963	+	0.931022i	$0.381082\pi$
$787$	−17.5000	+	30.3109i	−0.623808	+	1.08047i	−0.988770	+	0.149444i	$0.952252\pi$
$788$	−3.00000			−0.106871
$789$	−3.00000	+	5.19615i	−0.106803	+	0.184988i
$790$		0			0
$791$	6.00000	+	10.3923i	0.213335	+	0.369508i
$792$	3.00000			0.106600
$793$	24.5000	−	6.06218i	0.870021	−	0.215274i
$794$	25.0000			0.887217
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	27.0000	−	46.7654i	0.956389	−	1.65651i	0.225232	−	0.974305i	$-0.427686\pi$
$797$	27.0000	−	46.7654i	0.956389	−	1.65651i	0.731157	−	0.682209i	$-0.238981\pi$
$798$	−5.00000			−0.176998
$799$	4.50000	−	7.79423i	0.159199	−	0.275740i
$800$	−2.50000	+	4.33013i	−0.0883883	+	0.153093i
$801$	−15.0000			−0.529999
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	−24.0000	−	41.5692i	−0.846942	−	1.46695i
$804$	−1.00000	−	1.73205i	−0.0352673	−	0.0610847i
$805$		0			0
$806$	−8.00000	+	27.7128i	−0.281788	+	0.976142i
$807$		0			0
$808$	9.00000	+	15.5885i	0.316619	+	0.548400i
$809$	27.0000	+	46.7654i	0.949269	+	1.64418i	0.746968	+	0.664860i	$0.231509\pi$
$809$	27.0000	+	46.7654i	0.949269	+	1.64418i	0.202301	+	0.979323i	$0.435158\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$	4.50000	−	7.79423i	0.157919	−	0.273524i
$813$	−10.0000	+	17.3205i	−0.350715	+	0.607457i
$814$	24.0000			0.841200
$815$		0			0
$816$	1.50000	+	2.59808i	0.0525105	+	0.0909509i
$817$	−20.0000	−	34.6410i	−0.699711	−	1.21194i
$818$	22.0000			0.769212
$819$	1.00000	−	3.46410i	0.0349428	−	0.121046i
$820$		0			0
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$	−3.00000	−	5.19615i	−0.104637	−	0.181237i
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$	4.00000			0.139347
$825$	−7.50000	+	12.9904i	−0.261116	+	0.452267i
$826$	−3.00000	+	5.19615i	−0.104383	+	0.180797i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	3.00000	−	5.19615i	0.104257	−	0.180579i
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	0.754567	−	0.656223i	$-0.227847\pi$
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	−0.945589	+	0.325362i	$0.894514\pi$
$830$		0			0
$831$	−10.0000			−0.346896
$832$	2.50000	+	2.59808i	0.0866719	+	0.0900721i
$833$	−3.00000			−0.103944
$834$	5.50000	+	9.52628i	0.190449	+	0.329868i
$835$		0			0
$836$	7.50000	−	12.9904i	0.259393	−	0.449282i
$837$	8.00000			0.276520
$838$	−3.00000	+	5.19615i	−0.103633	+	0.179498i
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$	13.0000	+	22.5167i	0.448010	+	0.775975i
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$	−22.0000			−0.757271
$845$		0			0
$846$	−3.00000			−0.103142
$847$	1.00000	+	1.73205i	0.0343604	+	0.0595140i
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$	−15.0000			−0.514496
$851$	24.0000	−	41.5692i	0.822709	−	1.42497i
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	−1.00000			−0.0342393			−0.0171197	−	0.999853i	$-0.505450\pi$
$853$	−1.00000			−0.0342393			−0.0171197	+	0.999853i	$0.505450\pi$
$854$	−3.50000	+	6.06218i	−0.119768	+	0.207443i
$855$		0			0
$856$	4.50000	+	7.79423i	0.153807	+	0.266401i
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$	7.50000	+	7.79423i	0.256046	+	0.266091i
$859$	5.00000			0.170598			0.0852989	−	0.996355i	$-0.472815\pi$
$859$	5.00000			0.170598			0.0852989	+	0.996355i	$0.472815\pi$
$860$		0			0
$861$	−1.50000	−	2.59808i	−0.0511199	−	0.0885422i
$862$	−9.00000	+	15.5885i	−0.306541	+	0.530945i
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−14.0000			−0.475739
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	−4.00000	−	6.92820i	−0.135769	−	0.235159i
$869$	−19.5000	−	33.7750i	−0.661492	−	1.14574i
$870$		0			0
$871$	2.00000	−	6.92820i	0.0677674	−	0.234753i
$872$	−2.00000			−0.0677285
$873$	8.00000	+	13.8564i	0.270759	+	0.468968i
$874$	−15.0000	−	25.9808i	−0.507383	−	0.878812i
$875$		0			0
$876$	−16.0000			−0.540590
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	0.0421327	+	0.999112i	$0.486585\pi$
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	−0.886323	+	0.463068i	$0.846749\pi$
$878$	16.0000	−	27.7128i	0.539974	−	0.935262i
$879$		0			0
$880$		0			0
$881$	−3.00000	−	5.19615i	−0.101073	−	0.175063i	0.811054	−	0.584971i	$-0.198894\pi$
$881$	−3.00000	−	5.19615i	−0.101073	−	0.175063i	−0.912127	+	0.409908i	$0.865561\pi$
$882$	0.500000	+	0.866025i	0.0168359	+	0.0291606i
$883$	−16.0000			−0.538443			−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000			−0.538443			−0.269221	+	0.963078i	$0.586766\pi$
$884$	−3.00000	+	10.3923i	−0.100901	+	0.349531i
$885$		0			0
$886$	16.5000	+	28.5788i	0.554328	+	0.960125i
$887$	−28.5000	−	49.3634i	−0.956936	−	1.65746i	−0.729873	−	0.683582i	$-0.760421\pi$
$887$	−28.5000	−	49.3634i	−0.956936	−	1.65746i	−0.227063	−	0.973880i	$-0.572912\pi$
$888$	4.00000	−	6.92820i	0.134231	−	0.232495i
$889$	−16.0000			−0.536623
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	8.00000			0.267860
$893$	−7.50000	+	12.9904i	−0.250978	+	0.434707i
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$		0			0
$896$	−1.00000			−0.0334077
$897$	21.0000	−	5.19615i	0.701170	−	0.173494i
$898$	−24.0000			−0.800890
$899$	36.0000	+	62.3538i	1.20067	+	2.07962i
$900$	2.50000	+	4.33013i	0.0833333	+	0.144338i
$901$	−4.50000	+	7.79423i	−0.149917	+	0.259663i
$902$	9.00000			0.299667
$903$	−4.00000	+	6.92820i	−0.133112	+	0.230556i
$904$	−6.00000	+	10.3923i	−0.199557	+	0.345643i
$905$		0			0
$906$	−9.50000	+	16.4545i	−0.315616	+	0.546664i
$907$	11.0000	+	19.0526i	0.365249	+	0.632630i	0.988816	−	0.149140i	$-0.0476505\pi$
$907$	11.0000	+	19.0526i	0.365249	+	0.632630i	−0.623567	+	0.781770i	$0.714317\pi$
$908$	3.00000	+	5.19615i	0.0995585	+	0.172440i
$909$	18.0000			0.597022
$910$		0			0
$911$	−42.0000			−1.39152			−0.695761	−	0.718273i	$-0.744933\pi$
$911$	−42.0000			−1.39152			−0.695761	+	0.718273i	$0.744933\pi$
$912$	−2.50000	−	4.33013i	−0.0827833	−	0.143385i
$913$	27.0000	+	46.7654i	0.893570	+	1.54771i
$914$	19.0000	−	32.9090i	0.628464	−	1.08853i
$915$		0			0
$916$	−2.50000	+	4.33013i	−0.0826023	+	0.143071i
$917$	−6.00000	+	10.3923i	−0.198137	+	0.343184i
$918$	3.00000			0.0990148
$919$	−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	$0.325417\pi$
$920$		0			0
$921$	6.50000	+	11.2583i	0.214182	+	0.370975i
$922$		0			0
$923$	21.0000	−	5.19615i	0.691223	−	0.171033i
$924$	−3.00000			−0.0986928
$925$	20.0000	+	34.6410i	0.657596	+	1.13899i
$926$	−15.5000	−	26.8468i	−0.509362	−	0.882240i
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$	9.00000			0.295439
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	0.345708	+	0.938342i	$0.387639\pi$
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	−0.985482	+	0.169779i	$0.945695\pi$
$930$		0			0
$931$	5.00000			0.163868
$932$	12.0000	−	20.7846i	0.393073	−	0.680823i
$933$	10.5000	+	18.1865i	0.343755	+	0.595400i
$934$	−12.0000	−	20.7846i	−0.392652	−	0.680093i
$935$		0			0
$936$	3.50000	−	0.866025i	0.114401	−	0.0283069i
$937$	−28.0000			−0.914720			−0.457360	−	0.889282i	$-0.651205\pi$
$937$	−28.0000			−0.914720			−0.457360	+	0.889282i	$0.651205\pi$
$938$	1.00000	+	1.73205i	0.0326512	+	0.0565535i
$939$	−13.0000	−	22.5167i	−0.424239	−	0.734803i
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	1.00000	−	1.73205i	0.0325818	−	0.0564333i
$943$	9.00000	−	15.5885i	0.293080	−	0.507630i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	−12.0000	−	20.7846i	−0.390154	−	0.675766i
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	0.840624	−	0.541619i	$-0.182188\pi$
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	−0.889368	+	0.457193i	$0.848855\pi$
$948$	−13.0000			−0.422220
$949$	−40.0000	−	41.5692i	−1.29845	−	1.34939i
$950$	25.0000			0.811107
$951$	−15.0000	−	25.9808i	−0.486408	−	0.842484i
$952$	−1.50000	−	2.59808i	−0.0486153	−	0.0842041i
$953$	18.0000	−	31.1769i	0.583077	−	1.00992i	−0.412035	−	0.911168i	$-0.635182\pi$
$953$	18.0000	−	31.1769i	0.583077	−	1.00992i	0.995112	−	0.0987513i	$-0.0314848\pi$
$954$	3.00000			0.0971286
$955$		0			0
$956$	3.00000	−	5.19615i	0.0970269	−	0.168056i
$957$	27.0000			0.872786
$958$	4.50000	−	7.79423i	0.145388	−	0.251820i
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		0			0
$961$	33.0000			1.06452
$962$	28.0000	−	6.92820i	0.902756	−	0.223374i
$963$	9.00000			0.290021
$964$	−4.00000	−	6.92820i	−0.128831	−	0.223142i
$965$		0			0
$966$	−3.00000	+	5.19615i	−0.0965234	+	0.167183i
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	7.50000	−	12.9904i	0.240935	−	0.417311i
$970$		0			0
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	−0.910140	−	0.414301i	$-0.864026\pi$
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	0.813865	+	0.581054i	$0.197359\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−5.50000	−	9.52628i	−0.176322	−	0.305398i
$974$	13.0000			0.416547
$975$	−5.00000	+	17.3205i	−0.160128	+	0.554700i
$976$	−7.00000			−0.224065
$977$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$977$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$978$	−8.00000	−	13.8564i	−0.255812	−	0.443079i
$979$	−22.5000	+	38.9711i	−0.719103	+	1.24552i
$980$		0			0
$981$	−1.00000	+	1.73205i	−0.0319275	+	0.0553001i
$982$	−6.00000	+	10.3923i	−0.191468	+	0.331632i
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$	1.50000	−	2.59808i	0.0478183	−	0.0828236i
$985$		0			0
$986$	13.5000	+	23.3827i	0.429928	+	0.744656i
$987$	3.00000			0.0954911
$988$	5.00000	−	17.3205i	0.159071	−	0.551039i
$989$	−48.0000			−1.52631
$990$		0			0
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	0.698853	−	0.715265i	$-0.253694\pi$
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	−0.968864	+	0.247592i	$0.920361\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$	−10.0000			−0.317340
$994$	−3.00000	+	5.19615i	−0.0951542	+	0.164812i
$995$		0			0
$996$	18.0000			0.570352
$997$	9.50000	−	16.4545i	0.300868	−	0.521119i	−0.675465	−	0.737392i	$-0.736057\pi$
$997$	9.50000	−	16.4545i	0.300868	−	0.521119i	0.976333	+	0.216274i	$0.0693903\pi$
$998$	16.0000	+	27.7128i	0.506471	+	0.877234i
$999$	−4.00000	−	6.92820i	−0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.e.211.1	✓	2
3.2	odd	2		1638.2.r.f.757.1		2
13.3	even	3		7098.2.a.m.1.1		1
13.9	even	3	inner	546.2.l.e.295.1	yes	2
13.10	even	6		7098.2.a.ba.1.1		1
39.35	odd	6		1638.2.r.f.1387.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.e.211.1	✓	2	1.1	even	1	trivial
546.2.l.e.295.1	yes	2	13.9	even	3	inner
1638.2.r.f.757.1		2	3.2	odd	2
1638.2.r.f.1387.1		2	39.35	odd	6
7098.2.a.m.1.1		1	13.3	even	3
7098.2.a.ba.1.1		1	13.10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(2.50000 + 2.59808i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} -1.00000 q^{18} +(-2.50000 + 4.33013i) q^{19} +1.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} -5.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(4.50000 + 7.79423i) q^{29} +8.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +3.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-4.00000 - 6.92820i) q^{37} -5.00000 q^{38} +(1.00000 - 3.46410i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} -3.00000 q^{44} +(-3.00000 + 5.19615i) q^{46} +3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.50000 - 4.33013i) q^{50} -3.00000 q^{51} +(-3.50000 + 0.866025i) q^{52} -3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(0.500000 - 0.866025i) q^{56} +5.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(3.00000 - 5.19615i) q^{59} +(3.50000 - 6.06218i) q^{61} +(4.00000 + 6.92820i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(3.00000 - 5.19615i) q^{69} +(3.00000 - 5.19615i) q^{71} +(0.500000 - 0.866025i) q^{72} -16.0000 q^{73} +(4.00000 - 6.92820i) q^{74} +(2.50000 + 4.33013i) q^{75} +(-2.50000 - 4.33013i) q^{76} -3.00000 q^{77} +(3.50000 - 0.866025i) q^{78} -13.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} +18.0000 q^{83} +(-0.500000 + 0.866025i) q^{84} -8.00000 q^{86} +(4.50000 - 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(7.50000 + 12.9904i) q^{89} +(-3.50000 + 0.866025i) q^{91} -6.00000 q^{92} +(-4.00000 - 6.92820i) q^{93} +(1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(8.00000 - 13.8564i) q^{97} +(0.500000 - 0.866025i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + q^6 - q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} + q^{6} - q^{7} - 2 q^{8} - q^{9} + 3 q^{11} + 2 q^{12} + 5 q^{13} - 2 q^{14} - q^{16} + 3 q^{17} - 2 q^{18} - 5 q^{19} + 2 q^{21} - 3 q^{22} + 6 q^{23} + q^{24} - 10 q^{25} - 2 q^{26} + 2 q^{27} - q^{28} + 9 q^{29} + 16 q^{31} + q^{32} + 3 q^{33} + 6 q^{34} - q^{36} - 8 q^{37} - 10 q^{38} + 2 q^{39} - 3 q^{41} + q^{42} - 8 q^{43} - 6 q^{44} - 6 q^{46} + 6 q^{47} - q^{48} - q^{49} - 5 q^{50} - 6 q^{51} - 7 q^{52} - 6 q^{53} + q^{54} + q^{56} + 10 q^{57} - 9 q^{58} + 6 q^{59} + 7 q^{61} + 8 q^{62} - q^{63} + 2 q^{64} + 6 q^{66} - 2 q^{67} + 3 q^{68} + 6 q^{69} + 6 q^{71} + q^{72} - 32 q^{73} + 8 q^{74} + 5 q^{75} - 5 q^{76} - 6 q^{77} + 7 q^{78} - 26 q^{79} - q^{81} + 3 q^{82} + 36 q^{83} - q^{84} - 16 q^{86} + 9 q^{87} - 3 q^{88} + 15 q^{89} - 7 q^{91} - 12 q^{92} - 8 q^{93} + 3 q^{94} - 2 q^{96} + 16 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + q^6 - q^7 - 2 * q^8 - q^9 + 3 * q^11 + 2 * q^12 + 5 * q^13 - 2 * q^14 - q^16 + 3 * q^17 - 2 * q^18 - 5 * q^19 + 2 * q^21 - 3 * q^22 + 6 * q^23 + q^24 - 10 * q^25 - 2 * q^26 + 2 * q^27 - q^28 + 9 * q^29 + 16 * q^31 + q^32 + 3 * q^33 + 6 * q^34 - q^36 - 8 * q^37 - 10 * q^38 + 2 * q^39 - 3 * q^41 + q^42 - 8 * q^43 - 6 * q^44 - 6 * q^46 + 6 * q^47 - q^48 - q^49 - 5 * q^50 - 6 * q^51 - 7 * q^52 - 6 * q^53 + q^54 + q^56 + 10 * q^57 - 9 * q^58 + 6 * q^59 + 7 * q^61 + 8 * q^62 - q^63 + 2 * q^64 + 6 * q^66 - 2 * q^67 + 3 * q^68 + 6 * q^69 + 6 * q^71 + q^72 - 32 * q^73 + 8 * q^74 + 5 * q^75 - 5 * q^76 - 6 * q^77 + 7 * q^78 - 26 * q^79 - q^81 + 3 * q^82 + 36 * q^83 - q^84 - 16 * q^86 + 9 * q^87 - 3 * q^88 + 15 * q^89 - 7 * q^91 - 12 * q^92 - 8 * q^93 + 3 * q^94 - 2 * q^96 + 16 * q^97 + q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more