LMFDB - Embedded newform 630.2.i.d.151.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(121,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,3,2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.d.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.50000 - 0.866025i) q^{12} +(2.00000 + 3.46410i) q^{13} +(-2.00000 - 1.73205i) q^{14} -1.73205i q^{15} +1.00000 q^{16} +(1.50000 - 2.59808i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-4.50000 - 0.866025i) q^{21} +(1.50000 - 2.59808i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.00000 + 3.46410i) q^{26} -5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} -1.73205i q^{30} +2.00000 q^{31} +1.00000 q^{32} +(-2.50000 + 0.866025i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(6.00000 + 3.46410i) q^{39} +(0.500000 - 0.866025i) q^{40} +(3.00000 + 5.19615i) q^{41} +(-4.50000 - 0.866025i) q^{42} +(-5.50000 + 9.52628i) q^{43} +(-1.50000 - 2.59808i) q^{45} +(1.50000 - 2.59808i) q^{46} +3.00000 q^{47} +(1.50000 - 0.866025i) q^{48} +(1.00000 + 6.92820i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.00000 + 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} -5.19615i q^{54} +(-2.00000 - 1.73205i) q^{56} +(-3.00000 - 1.73205i) q^{57} +(-3.00000 + 5.19615i) q^{58} +12.0000 q^{59} -1.73205i q^{60} -7.00000 q^{61} +2.00000 q^{62} +(-7.50000 + 2.59808i) q^{63} +1.00000 q^{64} +4.00000 q^{65} -7.00000 q^{67} -5.19615i q^{69} +(-2.50000 + 0.866025i) q^{70} +(1.50000 - 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-1.50000 - 0.866025i) q^{75} +(-1.00000 - 1.73205i) q^{76} +(6.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(3.00000 + 5.19615i) q^{82} +(6.00000 - 10.3923i) q^{83} +(-4.50000 - 0.866025i) q^{84} +(-5.50000 + 9.52628i) q^{86} +10.3923i q^{87} +(7.50000 + 12.9904i) q^{89} +(-1.50000 - 2.59808i) q^{90} +(2.00000 - 10.3923i) q^{91} +(1.50000 - 2.59808i) q^{92} +(3.00000 - 1.73205i) q^{93} +3.00000 q^{94} -2.00000 q^{95} +(1.50000 - 0.866025i) q^{96} +(5.00000 - 8.66025i) q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + q^{5} + 3 q^{6} - 4 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} + 3 q^{12} + 4 q^{13} - 4 q^{14} + 2 q^{16} + 3 q^{18} - 2 q^{19} + q^{20} - 9 q^{21} + 3 q^{23} + 3 q^{24}+ \cdots + 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + q^5 + 3 * q^6 - 4 * q^7 + 2 * q^8 + 3 * q^9 + q^10 + 3 * q^12 + 4 * q^13 - 4 * q^14 + 2 * q^16 + 3 * q^18 - 2 * q^19 + q^20 - 9 * q^21 + 3 * q^23 + 3 * q^24 - q^25 + 4 * q^26 - 4 * q^28 - 6 * q^29 + 4 * q^31 + 2 * q^32 - 5 * q^35 + 3 * q^36 - 2 * q^37 - 2 * q^38 + 12 * q^39 + q^40 + 6 * q^41 - 9 * q^42 - 11 * q^43 - 3 * q^45 + 3 * q^46 + 6 * q^47 + 3 * q^48 + 2 * q^49 - q^50 + 4 * q^52 - 6 * q^53 - 4 * q^56 - 6 * q^57 - 6 * q^58 + 24 * q^59 - 14 * q^61 + 4 * q^62 - 15 * q^63 + 2 * q^64 + 8 * q^65 - 14 * q^67 - 5 * q^70 + 3 * q^72 - 2 * q^73 - 2 * q^74 - 3 * q^75 - 2 * q^76 + 12 * q^78 - 8 * q^79 + q^80 - 9 * q^81 + 6 * q^82 + 12 * q^83 - 9 * q^84 - 11 * q^86 + 15 * q^89 - 3 * q^90 + 4 * q^91 + 3 * q^92 + 6 * q^93 + 6 * q^94 - 4 * q^95 + 3 * q^96 + 10 * q^97 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	0.997927	+	0.0643593i	$0.0205004\pi$
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		−	1.73205i		−	0.447214i
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−4.50000	−	0.866025i	−0.981981	−	0.188982i
$22$		0			0
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$		−	5.19615i		−	1.00000i
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		−	1.73205i		−	0.316228i
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$		0			0
$35$	−2.50000	+	0.866025i	−0.422577	+	0.146385i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$	6.00000	+	3.46410i	0.960769	+	0.554700i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$	−4.50000	−	0.866025i	−0.694365	−	0.133631i
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$		0			0
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$		0			0
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		−	5.19615i		−	0.707107i
$55$		0			0
$56$	−2.00000	−	1.73205i	−0.267261	−	0.231455i
$57$	−3.00000	−	1.73205i	−0.397360	−	0.229416i
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	12.0000			1.56227			0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000			1.56227			0.781133	+	0.624364i	$0.214642\pi$
$60$		−	1.73205i		−	0.223607i
$61$	−7.00000			−0.896258			−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000			−0.896258			−0.448129	+	0.893969i	$0.647910\pi$
$62$	2.00000			0.254000
$63$	−7.50000	+	2.59808i	−0.944911	+	0.327327i
$64$	1.00000			0.125000
$65$	4.00000			0.496139
$66$		0			0
$67$	−7.00000			−0.855186			−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000			−0.855186			−0.427593	+	0.903971i	$0.640638\pi$
$68$		0			0
$69$		−	5.19615i		−	0.625543i
$70$	−2.50000	+	0.866025i	−0.298807	+	0.103510i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	−1.50000	−	0.866025i	−0.173205	−	0.100000i
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$		0			0
$78$	6.00000	+	3.46410i	0.679366	+	0.392232i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	−0.322396	−	0.946605i	$-0.604488\pi$
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	0.980982	−	0.194099i	$-0.0621783\pi$
$84$	−4.50000	−	0.866025i	−0.490990	−	0.0944911i
$85$		0			0
$86$	−5.50000	+	9.52628i	−0.593080	+	1.02725i
$87$			10.3923i			1.11417i
$88$		0			0
$89$	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	$0.540805\pi$
$90$	−1.50000	−	2.59808i	−0.158114	−	0.273861i
$91$	2.00000	−	10.3923i	0.209657	−	1.08941i
$92$	1.50000	−	2.59808i	0.156386	−	0.270868i
$93$	3.00000	−	1.73205i	0.311086	−	0.179605i
$94$	3.00000			0.309426
$95$	−2.00000			−0.205196
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	1.00000	+	6.92820i	0.101015	+	0.699854i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$		0			0
$103$	−8.50000	+	14.7224i	−0.837530	+	1.45064i	0.0544240	+	0.998518i	$0.482668\pi$
$103$	−8.50000	+	14.7224i	−0.837530	+	1.45064i	−0.891954	+	0.452126i	$0.850666\pi$
$104$	2.00000	+	3.46410i	0.196116	+	0.339683i
$105$	−3.00000	+	3.46410i	−0.292770	+	0.338062i
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$		−	5.19615i		−	0.500000i
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	−3.00000	−	1.73205i	−0.284747	−	0.164399i
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$	−3.00000	−	1.73205i	−0.280976	−	0.162221i
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	12.0000			1.10940
$118$	12.0000			1.10469
$119$		0			0
$120$		−	1.73205i		−	0.158114i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−7.00000			−0.633750
$123$	9.00000	+	5.19615i	0.811503	+	0.468521i
$124$	2.00000			0.179605
$125$	−1.00000			−0.0894427
$126$	−7.50000	+	2.59808i	−0.668153	+	0.231455i
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$	1.00000			0.0883883
$129$			19.0526i			1.67748i
$130$	4.00000			0.350823
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$	−1.00000	+	5.19615i	−0.0867110	+	0.450564i
$134$	−7.00000			−0.604708
$135$	−4.50000	−	2.59808i	−0.387298	−	0.223607i
$136$		0			0
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		−	5.19615i		−	0.442326i
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$	−2.50000	+	0.866025i	−0.211289	+	0.0731925i
$141$	4.50000	−	2.59808i	0.378968	−	0.218797i
$142$		0			0
$143$		0			0
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$	7.50000	+	9.52628i	0.618590	+	0.785714i
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$	−1.50000	−	0.866025i	−0.122474	−	0.0707107i
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	0.822464	−	0.568818i	$-0.192599\pi$
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	−0.903842	+	0.427865i	$0.859266\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$		0			0
$154$		0			0
$155$	1.00000	−	1.73205i	0.0803219	−	0.139122i
$156$	6.00000	+	3.46410i	0.480384	+	0.277350i
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$	−4.00000			−0.318223
$159$			10.3923i			0.824163i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−7.50000	+	2.59808i	−0.591083	+	0.204757i
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	−0.930033	−	0.367477i	$-0.880222\pi$
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	0.146772	−	0.989170i	$-0.453112\pi$
$164$	3.00000	+	5.19615i	0.234261	+	0.405751i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	0.918208	−	0.396098i	$-0.129636\pi$
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	−0.802135	+	0.597143i	$0.796303\pi$
$168$	−4.50000	−	0.866025i	−0.347183	−	0.0668153i
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$		0			0
$171$	−6.00000			−0.458831
$172$	−5.50000	+	9.52628i	−0.419371	+	0.726372i
$173$	24.0000			1.82469			0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000			1.82469			0.912343	+	0.409426i	$0.134271\pi$
$174$			10.3923i			0.787839i
$175$	−0.500000	+	2.59808i	−0.0377964	+	0.196396i
$176$		0			0
$177$	18.0000	−	10.3923i	1.35296	−	0.781133i
$178$	7.50000	+	12.9904i	0.562149	+	0.973670i
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	−0.304446	−	0.952529i	$-0.598471\pi$
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	2.00000	−	10.3923i	0.148250	−	0.770329i
$183$	−10.5000	+	6.06218i	−0.776182	+	0.448129i
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	−2.00000			−0.147043
$186$	3.00000	−	1.73205i	0.219971	−	0.127000i
$187$		0			0
$188$	3.00000			0.218797
$189$	−9.00000	+	10.3923i	−0.654654	+	0.755929i
$190$	−2.00000			−0.145095
$191$	18.0000			1.30243			0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000			1.30243			0.651217	+	0.758891i	$0.274259\pi$
$192$	1.50000	−	0.866025i	0.108253	−	0.0625000i
$193$	−22.0000			−1.58359			−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000			−1.58359			−0.791797	+	0.610784i	$0.790854\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$	6.00000	−	3.46410i	0.429669	−	0.248069i
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$		0			0
$199$	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	$0.121385\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−10.5000	+	6.06218i	−0.740613	+	0.427593i
$202$	−1.50000	−	2.59808i	−0.105540	−	0.182800i
$203$	15.0000	−	5.19615i	1.05279	−	0.364698i
$204$		0			0
$205$	6.00000			0.419058
$206$	−8.50000	+	14.7224i	−0.592223	+	1.02576i
$207$	−4.50000	−	7.79423i	−0.312772	−	0.541736i
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$		0			0
$210$	−3.00000	+	3.46410i	−0.207020	+	0.239046i
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$		0			0
$215$	5.50000	+	9.52628i	0.375097	+	0.649687i
$216$		−	5.19615i		−	0.353553i
$217$	−4.00000	−	3.46410i	−0.271538	−	0.235159i
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$			3.46410i			0.234082i
$220$		0			0
$221$		0			0
$222$	−3.00000	−	1.73205i	−0.201347	−	0.116248i
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	−0.350100	−	0.936713i	$-0.613852\pi$
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	0.986267	−	0.165161i	$-0.0528144\pi$
$224$	−2.00000	−	1.73205i	−0.133631	−	0.115728i
$225$	−3.00000			−0.200000
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	−0.921903	−	0.387421i	$-0.873366\pi$
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	0.125435	−	0.992102i	$-0.459967\pi$
$228$	−3.00000	−	1.73205i	−0.198680	−	0.114708i
$229$	−14.5000	+	25.1147i	−0.958187	+	1.65963i	−0.231287	+	0.972886i	$0.574293\pi$
$229$	−14.5000	+	25.1147i	−0.958187	+	1.65963i	−0.726900	+	0.686743i	$0.759040\pi$
$230$	−1.50000	−	2.59808i	−0.0989071	−	0.171312i
$231$		0			0
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$	12.0000			0.784465
$235$	1.50000	−	2.59808i	0.0978492	−	0.169480i
$236$	12.0000			0.781133
$237$	−6.00000	+	3.46410i	−0.389742	+	0.225018i
$238$		0			0
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	0.934109	+	0.356988i	$0.116196\pi$
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	−0.157893	+	0.987456i	$0.550470\pi$
$240$		−	1.73205i		−	0.111803i
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	0.990912	+	0.134515i	$0.0429475\pi$
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	−0.378963	+	0.925412i	$0.623719\pi$
$242$	5.50000	−	9.52628i	0.353553	−	0.612372i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	−7.00000			−0.448129
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$	9.00000	+	5.19615i	0.573819	+	0.331295i
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$	2.00000			0.127000
$249$		−	20.7846i		−	1.31717i
$250$	−1.00000			−0.0632456
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	−7.50000	+	2.59808i	−0.472456	+	0.163663i
$253$		0			0
$254$	−13.0000			−0.815693
$255$		0			0
$256$	1.00000			0.0625000
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$			19.0526i			1.18616i
$259$	−1.00000	+	5.19615i	−0.0621370	+	0.322873i
$260$	4.00000			0.248069
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$		0			0
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$	3.00000	+	5.19615i	0.184289	+	0.319197i
$266$	−1.00000	+	5.19615i	−0.0613139	+	0.318597i
$267$	22.5000	+	12.9904i	1.37698	+	0.794998i
$268$	−7.00000			−0.427593
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	0.985389	−	0.170321i	$-0.0544803\pi$
$270$	−4.50000	−	2.59808i	−0.273861	−	0.158114i
$271$	−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	$-0.374477\pi$
$272$		0			0
$273$	−6.00000	−	17.3205i	−0.363137	−	1.04828i
$274$	−6.00000	−	10.3923i	−0.362473	−	0.627822i
$275$		0			0
$276$		−	5.19615i		−	0.312772i
$277$	−16.0000	−	27.7128i	−0.961347	−	1.66510i	−0.719125	−	0.694881i	$-0.755457\pi$
$277$	−16.0000	−	27.7128i	−0.961347	−	1.66510i	−0.242222	−	0.970221i	$-0.577876\pi$
$278$	2.00000	+	3.46410i	0.119952	+	0.207763i
$279$	3.00000	−	5.19615i	0.179605	−	0.311086i
$280$	−2.50000	+	0.866025i	−0.149404	+	0.0517549i
$281$	−10.5000	+	18.1865i	−0.626377	+	1.08492i	0.361895	+	0.932219i	$0.382130\pi$
$281$	−10.5000	+	18.1865i	−0.626377	+	1.08492i	−0.988273	+	0.152699i	$0.951204\pi$
$282$	4.50000	−	2.59808i	0.267971	−	0.154713i
$283$	11.0000			0.653882			0.326941	−	0.945045i	$-0.393982\pi$
$283$	11.0000			0.653882			0.326941	+	0.945045i	$0.393982\pi$
$284$		0			0
$285$	−3.00000	+	1.73205i	−0.177705	+	0.102598i
$286$		0			0
$287$	3.00000	−	15.5885i	0.177084	−	0.920158i
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	3.00000	+	5.19615i	0.176166	+	0.305129i
$291$		−	17.3205i		−	1.01535i
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	15.0000	+	25.9808i	0.876309	+	1.51781i	0.855361	+	0.518032i	$0.173335\pi$
$293$	15.0000	+	25.9808i	0.876309	+	1.51781i	0.0209480	+	0.999781i	$0.493332\pi$
$294$	7.50000	+	9.52628i	0.437409	+	0.555584i
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$		0			0
$298$	−7.50000	+	12.9904i	−0.434463	+	0.752513i
$299$	12.0000			0.693978
$300$	−1.50000	−	0.866025i	−0.0866025	−	0.0500000i
$301$	27.5000	−	9.52628i	1.58507	−	0.549086i
$302$	−1.00000	−	1.73205i	−0.0575435	−	0.0996683i
$303$	−4.50000	−	2.59808i	−0.258518	−	0.149256i
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	−3.50000	+	6.06218i	−0.200409	+	0.347119i
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$			29.4449i			1.67506i
$310$	1.00000	−	1.73205i	0.0567962	−	0.0983739i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	6.00000	+	3.46410i	0.339683	+	0.196116i
$313$	26.0000			1.46961			0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000			1.46961			0.734803	+	0.678280i	$0.237274\pi$
$314$	−22.0000			−1.24153
$315$	−1.50000	+	7.79423i	−0.0845154	+	0.439155i
$316$	−4.00000			−0.225018
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$			10.3923i			0.582772i
$319$		0			0
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	−7.50000	+	2.59808i	−0.417959	+	0.144785i
$323$		0			0
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$	−10.0000	−	17.3205i	−0.553849	−	0.959294i
$327$			3.46410i			0.191565i
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	−6.00000	−	5.19615i	−0.330791	−	0.286473i
$330$		0			0
$331$	26.0000			1.42909			0.714545	−	0.699590i	$-0.246634\pi$
$331$	26.0000			1.42909			0.714545	+	0.699590i	$0.246634\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$	−6.00000			−0.328798
$334$	1.50000	+	2.59808i	0.0820763	+	0.142160i
$335$	−3.50000	+	6.06218i	−0.191225	+	0.331212i
$336$	−4.50000	−	0.866025i	−0.245495	−	0.0472456i
$337$	−16.0000	−	27.7128i	−0.871576	−	1.50961i	−0.860366	−	0.509676i	$-0.829765\pi$
$337$	−16.0000	−	27.7128i	−0.871576	−	1.50961i	−0.0112091	−	0.999937i	$-0.503568\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$	9.00000	+	5.19615i	0.488813	+	0.282216i
$340$		0			0
$341$		0			0
$342$	−6.00000			−0.324443
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−5.50000	+	9.52628i	−0.296540	+	0.513623i
$345$	−4.50000	−	2.59808i	−0.242272	−	0.139876i
$346$	24.0000			1.29025
$347$	27.0000			1.44944			0.724718	−	0.689046i	$-0.241970\pi$
$347$	27.0000			1.44944			0.724718	+	0.689046i	$0.241970\pi$
$348$			10.3923i			0.557086i
$349$	3.50000	−	6.06218i	0.187351	−	0.324501i	−0.757015	−	0.653397i	$-0.773343\pi$
$349$	3.50000	−	6.06218i	0.187351	−	0.324501i	0.944366	+	0.328896i	$0.106677\pi$
$350$	−0.500000	+	2.59808i	−0.0267261	+	0.138873i
$351$	18.0000	−	10.3923i	0.960769	−	0.554700i
$352$		0			0
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$	18.0000	−	10.3923i	0.956689	−	0.552345i
$355$		0			0
$356$	7.50000	+	12.9904i	0.397499	+	0.688489i
$357$		0			0
$358$	9.00000	−	15.5885i	0.475665	−	0.823876i
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	0.775934	−	0.630814i	$-0.217279\pi$
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	−0.934268	+	0.356572i	$0.883946\pi$
$360$	−1.50000	−	2.59808i	−0.0790569	−	0.136931i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	2.00000			0.105118
$363$		−	19.0526i		−	1.00000i
$364$	2.00000	−	10.3923i	0.104828	−	0.544705i
$365$	1.00000	+	1.73205i	0.0523424	+	0.0906597i
$366$	−10.5000	+	6.06218i	−0.548844	+	0.316875i
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	18.0000			0.937043
$370$	−2.00000			−0.103975
$371$	15.0000	−	5.19615i	0.778761	−	0.269771i
$372$	3.00000	−	1.73205i	0.155543	−	0.0898027i
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$		0			0
$375$	−1.50000	+	0.866025i	−0.0774597	+	0.0447214i
$376$	3.00000			0.154713
$377$	−24.0000			−1.23606
$378$	−9.00000	+	10.3923i	−0.462910	+	0.534522i
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	−2.00000			−0.102598
$381$	−19.5000	+	11.2583i	−0.999015	+	0.576782i
$382$	18.0000			0.920960
$383$	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	$-0.0135966\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$		0			0
$386$	−22.0000			−1.11977
$387$	16.5000	+	28.5788i	0.838742	+	1.45274i
$388$	5.00000	−	8.66025i	0.253837	−	0.439658i
$389$	−13.5000	−	23.3827i	−0.684477	−	1.18555i	−0.973601	−	0.228257i	$-0.926697\pi$
$389$	−13.5000	−	23.3827i	−0.684477	−	1.18555i	0.289124	−	0.957292i	$-0.406636\pi$
$390$	6.00000	−	3.46410i	0.303822	−	0.175412i
$391$		0			0
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$		0			0
$394$	−12.0000			−0.604551
$395$	−2.00000	+	3.46410i	−0.100631	+	0.174298i
$396$		0			0
$397$	14.0000	+	24.2487i	0.702640	+	1.21701i	0.967537	+	0.252731i	$0.0813288\pi$
$397$	14.0000	+	24.2487i	0.702640	+	1.21701i	−0.264897	+	0.964277i	$0.585338\pi$
$398$	2.00000	−	3.46410i	0.100251	−	0.173640i
$399$	3.00000	+	8.66025i	0.150188	+	0.433555i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$	−10.5000	+	6.06218i	−0.523692	+	0.302354i
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$	−9.00000			−0.447214
$406$	15.0000	−	5.19615i	0.744438	−	0.257881i
$407$		0			0
$408$		0			0
$409$	−1.00000			−0.0494468			−0.0247234	−	0.999694i	$-0.507871\pi$
$409$	−1.00000			−0.0494468			−0.0247234	+	0.999694i	$0.507871\pi$
$410$	6.00000			0.296319
$411$	−18.0000	−	10.3923i	−0.887875	−	0.512615i
$412$	−8.50000	+	14.7224i	−0.418765	+	0.725322i
$413$	−24.0000	−	20.7846i	−1.18096	−	1.02274i
$414$	−4.50000	−	7.79423i	−0.221163	−	0.383065i
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$	6.00000	+	3.46410i	0.293821	+	0.169638i
$418$		0			0
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.852047	−	0.523465i	$-0.824639\pi$
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.0273103	−	0.999627i	$-0.508694\pi$
$420$	−3.00000	+	3.46410i	−0.146385	+	0.169031i
$421$	−8.50000	+	14.7224i	−0.414265	+	0.717527i	−0.995351	−	0.0963145i	$-0.969295\pi$
$421$	−8.50000	+	14.7224i	−0.414265	+	0.717527i	0.581086	+	0.813842i	$0.302628\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$	4.50000	−	7.79423i	0.218797	−	0.378968i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$		0			0
$426$		0			0
$427$	14.0000	+	12.1244i	0.677507	+	0.586739i
$428$		0			0
$429$		0			0
$430$	5.50000	+	9.52628i	0.265234	+	0.459398i
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$		−	5.19615i		−	0.250000i
$433$	−4.00000			−0.192228			−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000			−0.192228			−0.0961139	+	0.995370i	$0.530641\pi$
$434$	−4.00000	−	3.46410i	−0.192006	−	0.166282i
$435$	9.00000	+	5.19615i	0.431517	+	0.249136i
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	−6.00000			−0.287019
$438$			3.46410i			0.165521i
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$	19.5000	+	7.79423i	0.928571	+	0.371154i
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$	−3.00000	−	1.73205i	−0.142374	−	0.0821995i
$445$	15.0000			0.711068
$446$	9.50000	−	16.4545i	0.449838	−	0.779142i
$447$			25.9808i			1.22885i
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$	−3.00000			−0.141421
$451$		0			0
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	−3.00000	−	1.73205i	−0.140952	−	0.0813788i
$454$	−12.0000	−	20.7846i	−0.563188	−	0.975470i
$455$	−8.00000	−	6.92820i	−0.375046	−	0.324799i
$456$	−3.00000	−	1.73205i	−0.140488	−	0.0811107i
$457$	26.0000			1.21623			0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000			1.21623			0.608114	+	0.793849i	$0.291926\pi$
$458$	−14.5000	+	25.1147i	−0.677541	+	1.17353i
$459$		0			0
$460$	−1.50000	−	2.59808i	−0.0699379	−	0.121136i
$461$	−13.5000	+	23.3827i	−0.628758	+	1.08904i	0.359044	+	0.933321i	$0.383103\pi$
$461$	−13.5000	+	23.3827i	−0.628758	+	1.08904i	−0.987801	+	0.155719i	$0.950230\pi$
$462$		0			0
$463$	−2.50000	−	4.33013i	−0.116185	−	0.201238i	0.802068	−	0.597233i	$-0.203733\pi$
$463$	−2.50000	−	4.33013i	−0.116185	−	0.201238i	−0.918253	+	0.395995i	$0.870400\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		−	3.46410i		−	0.160644i
$466$	−9.00000	−	15.5885i	−0.416917	−	0.722121i
$467$	−7.50000	−	12.9904i	−0.347059	−	0.601123i	0.638667	−	0.769483i	$-0.279486\pi$
$467$	−7.50000	−	12.9904i	−0.347059	−	0.601123i	−0.985726	+	0.168360i	$0.946153\pi$
$468$	12.0000			0.554700
$469$	14.0000	+	12.1244i	0.646460	+	0.559851i
$470$	1.50000	−	2.59808i	0.0691898	−	0.119840i
$471$	−33.0000	+	19.0526i	−1.52056	+	0.877896i
$472$	12.0000			0.552345
$473$		0			0
$474$	−6.00000	+	3.46410i	−0.275589	+	0.159111i
$475$	−1.00000	+	1.73205i	−0.0458831	+	0.0794719i
$476$		0			0
$477$	9.00000	+	15.5885i	0.412082	+	0.713746i
$478$	12.0000	+	20.7846i	0.548867	+	0.950666i
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$		−	1.73205i		−	0.0790569i
$481$	4.00000	−	6.92820i	0.182384	−	0.315899i
$482$	9.50000	+	16.4545i	0.432713	+	0.749481i
$483$	−9.00000	+	10.3923i	−0.409514	+	0.472866i
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	−10.0000	+	17.3205i	−0.453143	+	0.784867i	−0.998579	−	0.0532853i	$-0.983031\pi$
$487$	−10.0000	+	17.3205i	−0.453143	+	0.784867i	0.545436	+	0.838152i	$0.316364\pi$
$488$	−7.00000			−0.316875
$489$	−30.0000	−	17.3205i	−1.35665	−	0.783260i
$490$	6.50000	+	2.59808i	0.293640	+	0.117369i
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$	9.00000	+	5.19615i	0.405751	+	0.234261i
$493$		0			0
$494$	4.00000	−	6.92820i	0.179969	−	0.311715i
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$		−	20.7846i		−	0.931381i
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$	−1.00000			−0.0447214
$501$	4.50000	+	2.59808i	0.201045	+	0.116073i
$502$	−12.0000			−0.535586
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−7.50000	+	2.59808i	−0.334077	+	0.115728i
$505$	−3.00000			−0.133498
$506$		0			0
$507$			5.19615i			0.230769i
$508$	−13.0000			−0.576782
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		0			0
$511$	5.00000	−	1.73205i	0.221187	−	0.0766214i
$512$	1.00000			0.0441942
$513$	−9.00000	+	5.19615i	−0.397360	+	0.229416i
$514$	9.00000	−	15.5885i	0.396973	−	0.687577i
$515$	8.50000	+	14.7224i	0.374555	+	0.648748i
$516$			19.0526i			0.838742i
$517$		0			0
$518$	−1.00000	+	5.19615i	−0.0439375	+	0.228306i
$519$	36.0000	−	20.7846i	1.58022	−	0.912343i
$520$	4.00000			0.175412
$521$	−13.5000	+	23.3827i	−0.591446	+	1.02441i	0.402592	+	0.915379i	$0.368109\pi$
$521$	−13.5000	+	23.3827i	−0.591446	+	1.02441i	−0.994038	+	0.109035i	$0.965224\pi$
$522$	9.00000	+	15.5885i	0.393919	+	0.682288i
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	−0.986718	−	0.162446i	$-0.948062\pi$
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	0.352677	−	0.935745i	$-0.385272\pi$
$524$		0			0
$525$	1.50000	+	4.33013i	0.0654654	+	0.188982i
$526$	−4.50000	−	7.79423i	−0.196209	−	0.339845i
$527$		0			0
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$	18.0000	−	31.1769i	0.781133	−	1.35296i
$532$	−1.00000	+	5.19615i	−0.0433555	+	0.225282i
$533$	−12.0000	+	20.7846i	−0.519778	+	0.900281i
$534$	22.5000	+	12.9904i	0.973670	+	0.562149i
$535$		0			0
$536$	−7.00000			−0.302354
$537$		−	31.1769i		−	1.34538i
$538$	10.5000	−	18.1865i	0.452687	−	0.784077i
$539$		0			0
$540$	−4.50000	−	2.59808i	−0.193649	−	0.111803i
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$	−10.0000	−	17.3205i	−0.429537	−	0.743980i
$543$	3.00000	−	1.73205i	0.128742	−	0.0743294i
$544$		0			0
$545$	1.00000	+	1.73205i	0.0428353	+	0.0741929i
$546$	−6.00000	−	17.3205i	−0.256776	−	0.741249i
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	−0.938779	−	0.344519i	$-0.888042\pi$
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	0.767752	+	0.640747i	$0.221375\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$	−10.5000	+	18.1865i	−0.448129	+	0.776182i
$550$		0			0
$551$	12.0000			0.511217
$552$		−	5.19615i		−	0.221163i
$553$	8.00000	+	6.92820i	0.340195	+	0.294617i
$554$	−16.0000	−	27.7128i	−0.679775	−	1.17740i
$555$	−3.00000	+	1.73205i	−0.127343	+	0.0735215i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−3.00000	+	5.19615i	−0.127114	+	0.220168i	−0.922557	−	0.385860i	$-0.873905\pi$
$557$	−3.00000	+	5.19615i	−0.127114	+	0.220168i	0.795443	+	0.606028i	$0.207238\pi$
$558$	3.00000	−	5.19615i	0.127000	−	0.219971i
$559$	−44.0000			−1.86100
$560$	−2.50000	+	0.866025i	−0.105644	+	0.0365963i
$561$		0			0
$562$	−10.5000	+	18.1865i	−0.442916	+	0.767153i
$563$	−9.00000			−0.379305			−0.189652	−	0.981851i	$-0.560736\pi$
$563$	−9.00000			−0.379305			−0.189652	+	0.981851i	$0.560736\pi$
$564$	4.50000	−	2.59808i	0.189484	−	0.109399i
$565$	6.00000			0.252422
$566$	11.0000			0.462364
$567$	−4.50000	+	23.3827i	−0.188982	+	0.981981i
$568$		0			0
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$	−3.00000	+	1.73205i	−0.125656	+	0.0725476i
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$		0			0
$573$	27.0000	−	15.5885i	1.12794	−	0.651217i
$574$	3.00000	−	15.5885i	0.125218	−	0.650650i
$575$	−3.00000			−0.125109
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−10.0000	+	17.3205i	−0.416305	+	0.721062i	−0.995565	−	0.0940813i	$-0.970009\pi$
$577$	−10.0000	+	17.3205i	−0.416305	+	0.721062i	0.579259	+	0.815144i	$0.303342\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	−33.0000	+	19.0526i	−1.37143	+	0.791797i
$580$	3.00000	+	5.19615i	0.124568	+	0.215758i
$581$	−30.0000	+	10.3923i	−1.24461	+	0.431145i
$582$		−	17.3205i		−	0.717958i
$583$		0			0
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$	6.00000	−	10.3923i	0.248069	−	0.429669i
$586$	15.0000	+	25.9808i	0.619644	+	1.07326i
$587$	−22.5000	+	38.9711i	−0.928674	+	1.60851i	−0.143132	+	0.989704i	$0.545717\pi$
$587$	−22.5000	+	38.9711i	−0.928674	+	1.60851i	−0.785543	+	0.618808i	$0.787616\pi$
$588$	7.50000	+	9.52628i	0.309295	+	0.392857i
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$	6.00000	−	10.3923i	0.247016	−	0.427844i
$591$	−18.0000	+	10.3923i	−0.740421	+	0.427482i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$		0			0
$595$		0			0
$596$	−7.50000	+	12.9904i	−0.307212	+	0.532107i
$597$		−	6.92820i		−	0.283552i
$598$	12.0000			0.490716
$599$	6.00000			0.245153			0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000			0.245153			0.122577	+	0.992459i	$0.460884\pi$
$600$	−1.50000	−	0.866025i	−0.0612372	−	0.0353553i
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	−0.745845	−	0.666120i	$-0.767954\pi$
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	0.949799	+	0.312861i	$0.101287\pi$
$602$	27.5000	−	9.52628i	1.12082	−	0.388262i
$603$	−10.5000	+	18.1865i	−0.427593	+	0.740613i
$604$	−1.00000	−	1.73205i	−0.0406894	−	0.0704761i
$605$	−5.50000	−	9.52628i	−0.223607	−	0.387298i
$606$	−4.50000	−	2.59808i	−0.182800	−	0.105540i
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$	18.0000	−	20.7846i	0.729397	−	0.842235i
$610$	−3.50000	+	6.06218i	−0.141711	+	0.245450i
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$		0			0
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	0.171564	+	0.985173i	$0.445118\pi$
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	−0.938967	+	0.344008i	$0.888215\pi$
$614$	20.0000			0.807134
$615$	9.00000	−	5.19615i	0.362915	−	0.209529i
$616$		0			0
$617$	3.00000	+	5.19615i	0.120775	+	0.209189i	0.920074	−	0.391745i	$-0.128129\pi$
$617$	3.00000	+	5.19615i	0.120775	+	0.209189i	−0.799298	+	0.600935i	$0.794795\pi$
$618$			29.4449i			1.18445i
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$	1.00000	−	1.73205i	0.0401610	−	0.0695608i
$621$	−13.5000	−	7.79423i	−0.541736	−	0.312772i
$622$		0			0
$623$	7.50000	−	38.9711i	0.300481	−	1.56135i
$624$	6.00000	+	3.46410i	0.240192	+	0.138675i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	26.0000			1.03917
$627$		0			0
$628$	−22.0000			−0.877896
$629$		0			0
$630$	−1.50000	+	7.79423i	−0.0597614	+	0.310530i
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	−4.00000			−0.159111
$633$	−12.0000	−	6.92820i	−0.476957	−	0.275371i
$634$	−18.0000			−0.714871
$635$	−6.50000	+	11.2583i	−0.257945	+	0.446773i
$636$			10.3923i			0.412082i
$637$	−22.0000	+	17.3205i	−0.871672	+	0.686264i
$638$		0			0
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	7.50000	+	12.9904i	0.296232	+	0.513089i	0.975271	−	0.221013i	$-0.0709364\pi$
$641$	7.50000	+	12.9904i	0.296232	+	0.513089i	−0.679039	+	0.734103i	$0.737603\pi$
$642$		0			0
$643$	21.5000	+	37.2391i	0.847877	+	1.46857i	0.883099	+	0.469187i	$0.155453\pi$
$643$	21.5000	+	37.2391i	0.847877	+	1.46857i	−0.0352216	+	0.999380i	$0.511214\pi$
$644$	−7.50000	+	2.59808i	−0.295541	+	0.102379i
$645$	16.5000	+	9.52628i	0.649687	+	0.375097i
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$		0			0
$650$	2.00000	−	3.46410i	0.0784465	−	0.135873i
$651$	−9.00000	−	1.73205i	−0.352738	−	0.0678844i
$652$	−10.0000	−	17.3205i	−0.391630	−	0.678323i
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	0.407628	+	0.913148i	$0.366356\pi$
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	−0.994623	+	0.103558i	$0.966977\pi$
$654$			3.46410i			0.135457i
$655$		0			0
$656$	3.00000	+	5.19615i	0.117130	+	0.202876i
$657$	3.00000	+	5.19615i	0.117041	+	0.202721i
$658$	−6.00000	−	5.19615i	−0.233904	−	0.202567i
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	−0.999309	−	0.0371821i	$-0.988162\pi$
$659$	−12.0000	+	20.7846i	−0.467454	+	0.809653i	0.531855	+	0.846836i	$0.321495\pi$
$660$		0			0
$661$	5.00000			0.194477			0.0972387	−	0.995261i	$-0.468999\pi$
$661$	5.00000			0.194477			0.0972387	+	0.995261i	$0.468999\pi$
$662$	26.0000			1.01052
$663$		0			0
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$	4.00000	+	3.46410i	0.155113	+	0.134332i
$666$	−6.00000			−0.232495
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$		−	32.9090i		−	1.27233i
$670$	−3.50000	+	6.06218i	−0.135217	+	0.234202i
$671$		0			0
$672$	−4.50000	−	0.866025i	−0.173591	−	0.0334077i
$673$	14.0000	−	24.2487i	0.539660	−	0.934719i	−0.459262	−	0.888301i	$-0.651886\pi$
$673$	14.0000	−	24.2487i	0.539660	−	0.934719i	0.998922	−	0.0464181i	$-0.0147807\pi$
$674$	−16.0000	−	27.7128i	−0.616297	−	1.06746i
$675$	−4.50000	+	2.59808i	−0.173205	+	0.100000i
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−12.0000			−0.461197			−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000			−0.461197			−0.230599	+	0.973049i	$0.574068\pi$
$678$	9.00000	+	5.19615i	0.345643	+	0.199557i
$679$	−25.0000	+	8.66025i	−0.959412	+	0.332350i
$680$		0			0
$681$	−36.0000	−	20.7846i	−1.37952	−	0.796468i
$682$		0			0
$683$	−25.5000	+	44.1673i	−0.975730	+	1.69001i	−0.298227	+	0.954495i	$0.596395\pi$
$683$	−25.5000	+	44.1673i	−0.975730	+	1.69001i	−0.677503	+	0.735520i	$0.736938\pi$
$684$	−6.00000			−0.229416
$685$	−12.0000			−0.458496
$686$	10.0000	−	15.5885i	0.381802	−	0.595170i
$687$			50.2295i			1.91637i
$688$	−5.50000	+	9.52628i	−0.209686	+	0.363186i
$689$	−24.0000			−0.914327
$690$	−4.50000	−	2.59808i	−0.171312	−	0.0989071i
$691$	−46.0000			−1.74992			−0.874961	−	0.484193i	$-0.839113\pi$
$691$	−46.0000			−1.74992			−0.874961	+	0.484193i	$0.839113\pi$
$692$	24.0000			0.912343
$693$		0			0
$694$	27.0000			1.02491
$695$	4.00000			0.151729
$696$			10.3923i			0.393919i
$697$		0			0
$698$	3.50000	−	6.06218i	0.132477	−	0.229457i
$699$	−27.0000	−	15.5885i	−1.02123	−	0.589610i
$700$	−0.500000	+	2.59808i	−0.0188982	+	0.0981981i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	18.0000	−	10.3923i	0.679366	−	0.392232i
$703$	−2.00000	+	3.46410i	−0.0754314	+	0.130651i
$704$		0			0
$705$		−	5.19615i		−	0.195698i
$706$	−12.0000	−	20.7846i	−0.451626	−	0.782239i
$707$	−1.50000	+	7.79423i	−0.0564133	+	0.293132i
$708$	18.0000	−	10.3923i	0.676481	−	0.390567i
$709$	−19.0000			−0.713560			−0.356780	−	0.934188i	$-0.616125\pi$
$709$	−19.0000			−0.713560			−0.356780	+	0.934188i	$0.616125\pi$
$710$		0			0
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	7.50000	+	12.9904i	0.281074	+	0.486835i
$713$	3.00000	−	5.19615i	0.112351	−	0.194597i
$714$		0			0
$715$		0			0
$716$	9.00000	−	15.5885i	0.336346	−	0.582568i
$717$	36.0000	+	20.7846i	1.34444	+	0.776215i
$718$	−3.00000	−	5.19615i	−0.111959	−	0.193919i
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	0.997546	+	0.0700124i	$0.0223039\pi$
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	−0.438141	+	0.898906i	$0.644363\pi$
$720$	−1.50000	−	2.59808i	−0.0559017	−	0.0968246i
$721$	42.5000	−	14.7224i	1.58278	−	0.548292i
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$	28.5000	+	16.4545i	1.05993	+	0.611949i
$724$	2.00000			0.0743294
$725$	6.00000			0.222834
$726$		−	19.0526i		−	0.707107i
$727$	3.50000	−	6.06218i	0.129808	−	0.224834i	−0.793794	−	0.608186i	$-0.791897\pi$
$727$	3.50000	−	6.06218i	0.129808	−	0.224834i	0.923602	+	0.383353i	$0.125231\pi$
$728$	2.00000	−	10.3923i	0.0741249	−	0.385164i
$729$	−27.0000			−1.00000
$730$	1.00000	+	1.73205i	0.0370117	+	0.0641061i
$731$		0			0
$732$	−10.5000	+	6.06218i	−0.388091	+	0.224065i
$733$	−4.00000	+	6.92820i	−0.147743	+	0.255899i	−0.930393	−	0.366563i	$-0.880534\pi$
$733$	−4.00000	+	6.92820i	−0.147743	+	0.255899i	0.782650	+	0.622462i	$0.213868\pi$
$734$	−8.50000	−	14.7224i	−0.313741	−	0.543415i
$735$	12.0000	−	1.73205i	0.442627	−	0.0638877i
$736$	1.50000	−	2.59808i	0.0552907	−	0.0957664i
$737$		0			0
$738$	18.0000			0.662589
$739$	−16.0000	+	27.7128i	−0.588570	+	1.01943i	0.405851	+	0.913939i	$0.366975\pi$
$739$	−16.0000	+	27.7128i	−0.588570	+	1.01943i	−0.994420	+	0.105493i	$0.966358\pi$
$740$	−2.00000			−0.0735215
$741$		−	13.8564i		−	0.509028i
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$743$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$744$	3.00000	−	1.73205i	0.109985	−	0.0635001i
$745$	7.50000	+	12.9904i	0.274779	+	0.475931i
$746$	−7.00000	+	12.1244i	−0.256288	+	0.443904i
$747$	−18.0000	−	31.1769i	−0.658586	−	1.14070i
$748$		0			0
$749$		0			0
$750$	−1.50000	+	0.866025i	−0.0547723	+	0.0316228i
$751$	11.0000	−	19.0526i	0.401396	−	0.695238i	−0.592499	−	0.805571i	$-0.701859\pi$
$751$	11.0000	−	19.0526i	0.401396	−	0.695238i	0.993895	+	0.110333i	$0.0351919\pi$
$752$	3.00000			0.109399
$753$	−18.0000	+	10.3923i	−0.655956	+	0.378717i
$754$	−24.0000			−0.874028
$755$	−2.00000			−0.0727875
$756$	−9.00000	+	10.3923i	−0.327327	+	0.377964i
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	−4.00000			−0.145287
$759$		0			0
$760$	−2.00000			−0.0725476
$761$	−7.50000	+	12.9904i	−0.271875	+	0.470901i	−0.969342	−	0.245716i	$-0.920977\pi$
$761$	−7.50000	+	12.9904i	−0.271875	+	0.470901i	0.697467	+	0.716617i	$0.254310\pi$
$762$	−19.5000	+	11.2583i	−0.706410	+	0.407846i
$763$	5.00000	−	1.73205i	0.181012	−	0.0627044i
$764$	18.0000			0.651217
$765$		0			0
$766$	10.5000	−	18.1865i	0.379380	−	0.657106i
$767$	24.0000	+	41.5692i	0.866590	+	1.50098i
$768$	1.50000	−	0.866025i	0.0541266	−	0.0312500i
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	0.817423	−	0.576038i	$-0.195402\pi$
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	−0.907575	+	0.419890i	$0.862069\pi$
$770$		0			0
$771$		−	31.1769i		−	1.12281i
$772$	−22.0000			−0.791797
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$	16.5000	+	28.5788i	0.593080	+	1.02725i
$775$	−1.00000	−	1.73205i	−0.0359211	−	0.0622171i
$776$	5.00000	−	8.66025i	0.179490	−	0.310885i
$777$	3.00000	+	8.66025i	0.107624	+	0.310685i
$778$	−13.5000	−	23.3827i	−0.483998	−	0.838310i
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$	6.00000	−	3.46410i	0.214834	−	0.124035i
$781$		0			0
$782$		0			0
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	−11.0000	+	19.0526i	−0.392607	+	0.680015i
$786$		0			0
$787$	−1.00000			−0.0356462			−0.0178231	−	0.999841i	$-0.505674\pi$
$787$	−1.00000			−0.0356462			−0.0178231	+	0.999841i	$0.505674\pi$
$788$	−12.0000			−0.427482
$789$	−13.5000	−	7.79423i	−0.480613	−	0.277482i
$790$	−2.00000	+	3.46410i	−0.0711568	+	0.123247i
$791$	3.00000	−	15.5885i	0.106668	−	0.554262i
$792$		0			0
$793$	−14.0000	−	24.2487i	−0.497155	−	0.861097i
$794$	14.0000	+	24.2487i	0.496841	+	0.860555i
$795$	9.00000	+	5.19615i	0.319197	+	0.184289i
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	0.661441	−	0.749997i	$-0.269945\pi$
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	−0.980237	+	0.197826i	$0.936612\pi$
$798$	3.00000	+	8.66025i	0.106199	+	0.306570i
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	45.0000			1.59000
$802$	−7.50000	+	12.9904i	−0.264834	+	0.458706i
$803$		0			0
$804$	−10.5000	+	6.06218i	−0.370306	+	0.213797i
$805$	−1.50000	+	7.79423i	−0.0528681	+	0.274710i
$806$	4.00000	+	6.92820i	0.140894	+	0.244036i
$807$		−	36.3731i		−	1.28039i
$808$	−1.50000	−	2.59808i	−0.0527698	−	0.0914000i
$809$	19.5000	−	33.7750i	0.685583	−	1.18747i	−0.287670	−	0.957730i	$-0.592880\pi$
$809$	19.5000	−	33.7750i	0.685583	−	1.18747i	0.973253	−	0.229736i	$-0.0737862\pi$
$810$	−9.00000			−0.316228
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	15.0000	−	5.19615i	0.526397	−	0.182349i
$813$	−30.0000	−	17.3205i	−1.05215	−	0.607457i
$814$		0			0
$815$	−20.0000			−0.700569
$816$		0			0
$817$	22.0000			0.769683
$818$	−1.00000			−0.0349642
$819$	−24.0000	−	20.7846i	−0.838628	−	0.726273i
$820$	6.00000			0.209529
$821$	−3.00000			−0.104701			−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000			−0.104701			−0.0523504	+	0.998629i	$0.516671\pi$
$822$	−18.0000	−	10.3923i	−0.627822	−	0.362473i
$823$	8.00000			0.278862			0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000			0.278862			0.139431	+	0.990232i	$0.455473\pi$
$824$	−8.50000	+	14.7224i	−0.296112	+	0.512880i
$825$		0			0
$826$	−24.0000	−	20.7846i	−0.835067	−	0.723189i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	−4.50000	−	7.79423i	−0.156386	−	0.270868i
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	−0.563082	−	0.826401i	$-0.690385\pi$
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	0.997225	+	0.0744432i	$0.0237179\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$	−48.0000	−	27.7128i	−1.66510	−	0.961347i
$832$	2.00000	+	3.46410i	0.0693375	+	0.120096i
$833$		0			0
$834$	6.00000	+	3.46410i	0.207763	+	0.119952i
$835$	3.00000			0.103819
$836$		0			0
$837$		−	10.3923i		−	0.359211i
$838$	−18.0000	−	31.1769i	−0.621800	−	1.07699i
$839$	9.00000	−	15.5885i	0.310715	−	0.538173i	−0.667803	−	0.744338i	$-0.732765\pi$
$839$	9.00000	−	15.5885i	0.310715	−	0.538173i	0.978517	+	0.206165i	$0.0660984\pi$
$840$	−3.00000	+	3.46410i	−0.103510	+	0.119523i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−8.50000	+	14.7224i	−0.292929	+	0.507369i
$843$			36.3731i			1.25275i
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	1.50000	+	2.59808i	0.0516016	+	0.0893765i
$846$	4.50000	−	7.79423i	0.154713	−	0.267971i
$847$	−27.5000	+	9.52628i	−0.944911	+	0.327327i
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$	16.5000	−	9.52628i	0.566279	−	0.326941i
$850$		0			0
$851$	−6.00000			−0.205677
$852$		0			0
$853$	−4.00000	+	6.92820i	−0.136957	+	0.237217i	−0.926343	−	0.376680i	$-0.877066\pi$
$853$	−4.00000	+	6.92820i	−0.136957	+	0.237217i	0.789386	+	0.613897i	$0.210399\pi$
$854$	14.0000	+	12.1244i	0.479070	+	0.414887i
$855$	−3.00000	+	5.19615i	−0.102598	+	0.177705i
$856$		0			0
$857$	−15.0000	−	25.9808i	−0.512390	−	0.887486i	−0.999897	−	0.0143666i	$-0.995427\pi$
$857$	−15.0000	−	25.9808i	−0.512390	−	0.887486i	0.487507	−	0.873119i	$-0.337907\pi$
$858$		0			0
$859$	−13.0000	+	22.5167i	−0.443554	+	0.768259i	−0.997950	−	0.0639945i	$-0.979616\pi$
$859$	−13.0000	+	22.5167i	−0.443554	+	0.768259i	0.554396	+	0.832253i	$0.312949\pi$
$860$	5.50000	+	9.52628i	0.187548	+	0.324843i
$861$	−9.00000	−	25.9808i	−0.306719	−	0.885422i
$862$	−15.0000	+	25.9808i	−0.510902	+	0.884908i
$863$	10.5000	+	18.1865i	0.357424	+	0.619077i	0.987530	−	0.157433i	$-0.0503217\pi$
$863$	10.5000	+	18.1865i	0.357424	+	0.619077i	−0.630106	+	0.776509i	$0.716988\pi$
$864$		−	5.19615i		−	0.176777i
$865$	12.0000	−	20.7846i	0.408012	−	0.706698i
$866$	−4.00000			−0.135926
$867$	25.5000	+	14.7224i	0.866025	+	0.500000i
$868$	−4.00000	−	3.46410i	−0.135769	−	0.117579i
$869$		0			0
$870$	9.00000	+	5.19615i	0.305129	+	0.176166i
$871$	−14.0000	−	24.2487i	−0.474372	−	0.821636i
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$	−15.0000	−	25.9808i	−0.507673	−	0.879316i
$874$	−6.00000			−0.202953
$875$	2.00000	+	1.73205i	0.0676123	+	0.0585540i
$876$			3.46410i			0.117041i
$877$	17.0000	−	29.4449i	0.574049	−	0.994282i	−0.422095	−	0.906552i	$-0.638705\pi$
$877$	17.0000	−	29.4449i	0.574049	−	0.994282i	0.996144	−	0.0877308i	$-0.0279615\pi$
$878$	8.00000			0.269987
$879$	45.0000	+	25.9808i	1.51781	+	0.876309i
$880$		0			0
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$	19.5000	+	7.79423i	0.656599	+	0.262445i
$883$	−43.0000			−1.44707			−0.723533	−	0.690290i	$-0.757483\pi$
$883$	−43.0000			−1.44707			−0.723533	+	0.690290i	$0.757483\pi$
$884$		0			0
$885$		−	20.7846i		−	0.698667i
$886$		0			0
$887$	−4.50000	+	7.79423i	−0.151095	+	0.261705i	−0.931630	−	0.363407i	$-0.881613\pi$
$887$	−4.50000	+	7.79423i	−0.151095	+	0.261705i	0.780535	+	0.625112i	$0.214947\pi$
$888$	−3.00000	−	1.73205i	−0.100673	−	0.0581238i
$889$	26.0000	+	22.5167i	0.872012	+	0.755185i
$890$	15.0000			0.502801
$891$		0			0
$892$	9.50000	−	16.4545i	0.318084	−	0.550937i
$893$	−3.00000	−	5.19615i	−0.100391	−	0.173883i
$894$			25.9808i			0.868927i
$895$	−9.00000	−	15.5885i	−0.300837	−	0.521065i
$896$	−2.00000	−	1.73205i	−0.0668153	−	0.0578638i
$897$	18.0000	−	10.3923i	0.601003	−	0.346989i
$898$	15.0000			0.500556
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$	−3.00000			−0.100000
$901$		0			0
$902$		0			0
$903$	33.0000	−	38.1051i	1.09817	−	1.26806i
$904$	3.00000	+	5.19615i	0.0997785	+	0.172821i
$905$	1.00000	−	1.73205i	0.0332411	−	0.0575753i
$906$	−3.00000	−	1.73205i	−0.0996683	−	0.0575435i
$907$	2.00000	+	3.46410i	0.0664089	+	0.115024i	0.897318	−	0.441384i	$-0.145512\pi$
$907$	2.00000	+	3.46410i	0.0664089	+	0.115024i	−0.830909	+	0.556408i	$0.812179\pi$
$908$	−12.0000	−	20.7846i	−0.398234	−	0.689761i
$909$	−9.00000			−0.298511
$910$	−8.00000	−	6.92820i	−0.265197	−	0.229668i
$911$	21.0000	−	36.3731i	0.695761	−	1.20509i	−0.274162	−	0.961683i	$-0.588401\pi$
$911$	21.0000	−	36.3731i	0.695761	−	1.20509i	0.969923	−	0.243410i	$-0.0782661\pi$
$912$	−3.00000	−	1.73205i	−0.0993399	−	0.0573539i
$913$		0			0
$914$	26.0000			0.860004
$915$			12.1244i			0.400819i
$916$	−14.5000	+	25.1147i	−0.479093	+	0.829814i
$917$		0			0
$918$		0			0
$919$	−28.0000	−	48.4974i	−0.923635	−	1.59978i	−0.793742	−	0.608254i	$-0.791870\pi$
$919$	−28.0000	−	48.4974i	−0.923635	−	1.59978i	−0.129893	−	0.991528i	$-0.541463\pi$
$920$	−1.50000	−	2.59808i	−0.0494535	−	0.0856560i
$921$	30.0000	−	17.3205i	0.988534	−	0.570730i
$922$	−13.5000	+	23.3827i	−0.444599	+	0.770068i
$923$		0			0
$924$		0			0
$925$	−1.00000	+	1.73205i	−0.0328798	+	0.0569495i
$926$	−2.50000	−	4.33013i	−0.0821551	−	0.142297i
$927$	25.5000	+	44.1673i	0.837530	+	1.45064i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	15.0000			0.492134			0.246067	−	0.969253i	$-0.420862\pi$
$929$	15.0000			0.492134			0.246067	+	0.969253i	$0.420862\pi$
$930$		−	3.46410i		−	0.113592i
$931$	11.0000	−	8.66025i	0.360510	−	0.283828i
$932$	−9.00000	−	15.5885i	−0.294805	−	0.510617i
$933$		0			0
$934$	−7.50000	−	12.9904i	−0.245407	−	0.425058i
$935$		0			0
$936$	12.0000			0.392232
$937$	44.0000			1.43742			0.718709	−	0.695311i	$-0.244734\pi$
$937$	44.0000			1.43742			0.718709	+	0.695311i	$0.244734\pi$
$938$	14.0000	+	12.1244i	0.457116	+	0.395874i
$939$	39.0000	−	22.5167i	1.27272	−	0.734803i
$940$	1.50000	−	2.59808i	0.0489246	−	0.0847399i
$941$	15.0000			0.488986			0.244493	−	0.969651i	$-0.421378\pi$
$941$	15.0000			0.488986			0.244493	+	0.969651i	$0.421378\pi$
$942$	−33.0000	+	19.0526i	−1.07520	+	0.620766i
$943$	18.0000			0.586161
$944$	12.0000			0.390567
$945$	4.50000	+	12.9904i	0.146385	+	0.422577i
$946$		0			0
$947$	45.0000			1.46230			0.731152	−	0.682215i	$-0.238983\pi$
$947$	45.0000			1.46230			0.731152	+	0.682215i	$0.238983\pi$
$948$	−6.00000	+	3.46410i	−0.194871	+	0.112509i
$949$	−8.00000			−0.259691
$950$	−1.00000	+	1.73205i	−0.0324443	+	0.0561951i
$951$	−27.0000	+	15.5885i	−0.875535	+	0.505490i
$952$		0			0
$953$	18.0000			0.583077			0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000			0.583077			0.291539	+	0.956559i	$0.405833\pi$
$954$	9.00000	+	15.5885i	0.291386	+	0.504695i
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$		0			0
$958$	−9.00000	−	15.5885i	−0.290777	−	0.503640i
$959$	−6.00000	+	31.1769i	−0.193750	+	1.00676i
$960$		−	1.73205i		−	0.0559017i
$961$	−27.0000			−0.870968
$962$	4.00000	−	6.92820i	0.128965	−	0.223374i
$963$		0			0
$964$	9.50000	+	16.4545i	0.305974	+	0.529963i
$965$	−11.0000	+	19.0526i	−0.354103	+	0.613324i
$966$	−9.00000	+	10.3923i	−0.289570	+	0.334367i
$967$	0.500000	+	0.866025i	0.0160789	+	0.0278495i	0.873953	−	0.486011i	$-0.161548\pi$
$967$	0.500000	+	0.866025i	0.0160789	+	0.0278495i	−0.857874	+	0.513860i	$0.828215\pi$
$968$	5.50000	−	9.52628i	0.176777	−	0.306186i
$969$		0			0
$970$	−5.00000	−	8.66025i	−0.160540	−	0.278064i
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$	2.00000	−	10.3923i	0.0641171	−	0.333162i
$974$	−10.0000	+	17.3205i	−0.320421	+	0.554985i
$975$		−	6.92820i		−	0.221880i
$976$	−7.00000			−0.224065
$977$	36.0000			1.15174			0.575871	−	0.817541i	$-0.304663\pi$
$977$	36.0000			1.15174			0.575871	+	0.817541i	$0.304663\pi$
$978$	−30.0000	−	17.3205i	−0.959294	−	0.553849i
$979$		0			0
$980$	6.50000	+	2.59808i	0.207635	+	0.0829925i
$981$	3.00000	+	5.19615i	0.0957826	+	0.165900i
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	0.608712	−	0.793391i	$-0.291686\pi$
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	−0.991453	+	0.130465i	$0.958353\pi$
$984$	9.00000	+	5.19615i	0.286910	+	0.165647i
$985$	−6.00000	+	10.3923i	−0.191176	+	0.331126i
$986$		0			0
$987$	−13.5000	−	2.59808i	−0.429710	−	0.0826977i
$988$	4.00000	−	6.92820i	0.127257	−	0.220416i
$989$	16.5000	+	28.5788i	0.524669	+	0.908754i
$990$		0			0
$991$	−28.0000	+	48.4974i	−0.889449	+	1.54057i	−0.0489218	+	0.998803i	$0.515578\pi$
$991$	−28.0000	+	48.4974i	−0.889449	+	1.54057i	−0.840528	+	0.541769i	$0.817755\pi$
$992$	2.00000			0.0635001
$993$	39.0000	−	22.5167i	1.23763	−	0.714545i
$994$		0			0
$995$	−2.00000	−	3.46410i	−0.0634043	−	0.109819i
$996$		−	20.7846i		−	0.658586i
$997$	−7.00000	−	12.1244i	−0.221692	−	0.383982i	0.733630	−	0.679549i	$-0.237825\pi$
$997$	−7.00000	−	12.1244i	−0.221692	−	0.383982i	−0.955322	+	0.295567i	$0.904491\pi$
$998$	14.0000	−	24.2487i	0.443162	−	0.767580i
$999$	−9.00000	+	5.19615i	−0.284747	+	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.d.151.1	yes	2
3.2	odd	2		1890.2.i.a.991.1		2
7.2	even	3		630.2.l.b.331.1	yes	2
9.4	even	3		630.2.l.b.571.1	yes	2
9.5	odd	6		1890.2.l.d.361.1		2
21.2	odd	6		1890.2.l.d.1801.1		2
63.23	odd	6		1890.2.i.a.1171.1		2
63.58	even	3	inner	630.2.i.d.121.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.d.121.1	✓	2	63.58	even	3	inner
630.2.i.d.151.1	yes	2	1.1	even	1	trivial
630.2.l.b.331.1	yes	2	7.2	even	3
630.2.l.b.571.1	yes	2	9.4	even	3
1890.2.i.a.991.1		2	3.2	odd	2
1890.2.i.a.1171.1		2	63.23	odd	6
1890.2.l.d.361.1		2	9.5	odd	6
1890.2.l.d.1801.1		2	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.50000 - 0.866025i) q^{12} +(2.00000 + 3.46410i) q^{13} +(-2.00000 - 1.73205i) q^{14} -1.73205i q^{15} +1.00000 q^{16} +(1.50000 - 2.59808i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-4.50000 - 0.866025i) q^{21} +(1.50000 - 2.59808i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.00000 + 3.46410i) q^{26} -5.19615i q^{27} +(-2.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} -1.73205i q^{30} +2.00000 q^{31} +1.00000 q^{32} +(-2.50000 + 0.866025i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(6.00000 + 3.46410i) q^{39} +(0.500000 - 0.866025i) q^{40} +(3.00000 + 5.19615i) q^{41} +(-4.50000 - 0.866025i) q^{42} +(-5.50000 + 9.52628i) q^{43} +(-1.50000 - 2.59808i) q^{45} +(1.50000 - 2.59808i) q^{46} +3.00000 q^{47} +(1.50000 - 0.866025i) q^{48} +(1.00000 + 6.92820i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.00000 + 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} -5.19615i q^{54} +(-2.00000 - 1.73205i) q^{56} +(-3.00000 - 1.73205i) q^{57} +(-3.00000 + 5.19615i) q^{58} +12.0000 q^{59} -1.73205i q^{60} -7.00000 q^{61} +2.00000 q^{62} +(-7.50000 + 2.59808i) q^{63} +1.00000 q^{64} +4.00000 q^{65} -7.00000 q^{67} -5.19615i q^{69} +(-2.50000 + 0.866025i) q^{70} +(1.50000 - 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-1.50000 - 0.866025i) q^{75} +(-1.00000 - 1.73205i) q^{76} +(6.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(3.00000 + 5.19615i) q^{82} +(6.00000 - 10.3923i) q^{83} +(-4.50000 - 0.866025i) q^{84} +(-5.50000 + 9.52628i) q^{86} +10.3923i q^{87} +(7.50000 + 12.9904i) q^{89} +(-1.50000 - 2.59808i) q^{90} +(2.00000 - 10.3923i) q^{91} +(1.50000 - 2.59808i) q^{92} +(3.00000 - 1.73205i) q^{93} +3.00000 q^{94} -2.00000 q^{95} +(1.50000 - 0.866025i) q^{96} +(5.00000 - 8.66025i) q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + q^{5} + 3 q^{6} - 4 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} + 3 q^{12} + 4 q^{13} - 4 q^{14} + 2 q^{16} + 3 q^{18} - 2 q^{19} + q^{20} - 9 q^{21} + 3 q^{23} + 3 q^{24}+ \cdots + 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + q^5 + 3 * q^6 - 4 * q^7 + 2 * q^8 + 3 * q^9 + q^10 + 3 * q^12 + 4 * q^13 - 4 * q^14 + 2 * q^16 + 3 * q^18 - 2 * q^19 + q^20 - 9 * q^21 + 3 * q^23 + 3 * q^24 - q^25 + 4 * q^26 - 4 * q^28 - 6 * q^29 + 4 * q^31 + 2 * q^32 - 5 * q^35 + 3 * q^36 - 2 * q^37 - 2 * q^38 + 12 * q^39 + q^40 + 6 * q^41 - 9 * q^42 - 11 * q^43 - 3 * q^45 + 3 * q^46 + 6 * q^47 + 3 * q^48 + 2 * q^49 - q^50 + 4 * q^52 - 6 * q^53 - 4 * q^56 - 6 * q^57 - 6 * q^58 + 24 * q^59 - 14 * q^61 + 4 * q^62 - 15 * q^63 + 2 * q^64 + 8 * q^65 - 14 * q^67 - 5 * q^70 + 3 * q^72 - 2 * q^73 - 2 * q^74 - 3 * q^75 - 2 * q^76 + 12 * q^78 - 8 * q^79 + q^80 - 9 * q^81 + 6 * q^82 + 12 * q^83 - 9 * q^84 - 11 * q^86 + 15 * q^89 - 3 * q^90 + 4 * q^91 + 3 * q^92 + 6 * q^93 + 6 * q^94 - 4 * q^95 + 3 * q^96 + 10 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more