LMFDB - Embedded newform 637.2.f.b.393.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(295,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.295"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,3,1,6] 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:	$5.08647060876$
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:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.b.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} +(1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(1.50000 - 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +3.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} +(4.50000 + 7.79423i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +6.00000 q^{18} +(0.500000 - 0.866025i) q^{19} +(1.50000 - 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(-4.50000 - 7.79423i) q^{24} +4.00000 q^{25} +(3.50000 - 0.866025i) q^{26} -9.00000 q^{27} +(-3.50000 - 6.06218i) q^{29} +(4.50000 - 7.79423i) q^{30} +3.00000 q^{31} +(-2.50000 + 4.33013i) q^{32} +(-4.50000 + 7.79423i) q^{33} -2.00000 q^{34} +(3.00000 + 5.19615i) q^{36} +(-1.00000 - 1.73205i) q^{37} -1.00000 q^{38} +(-10.5000 + 2.59808i) q^{39} -9.00000 q^{40} +(-1.50000 - 2.59808i) q^{41} +(3.50000 - 6.06218i) q^{43} +3.00000 q^{44} +(-9.00000 + 15.5885i) q^{45} +1.00000 q^{47} +(-1.50000 + 2.59808i) q^{48} +(-2.00000 - 3.46410i) q^{50} +6.00000 q^{51} +(2.50000 + 2.59808i) q^{52} +3.00000 q^{53} +(4.50000 + 7.79423i) q^{54} +(4.50000 + 7.79423i) q^{55} +3.00000 q^{57} +(-3.50000 + 6.06218i) q^{58} +(2.00000 - 3.46410i) q^{59} +9.00000 q^{60} +(6.50000 - 11.2583i) q^{61} +(-1.50000 - 2.59808i) q^{62} +7.00000 q^{64} +(-3.00000 + 10.3923i) q^{65} +9.00000 q^{66} +(1.50000 + 2.59808i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-6.50000 + 11.2583i) q^{71} +(9.00000 - 15.5885i) q^{72} -13.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(6.00000 + 10.3923i) q^{75} +(-0.500000 - 0.866025i) q^{76} +(7.50000 + 7.79423i) q^{78} -3.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(3.00000 - 5.19615i) q^{85} -7.00000 q^{86} +(10.5000 - 18.1865i) q^{87} +(-4.50000 - 7.79423i) q^{88} +(-3.00000 - 5.19615i) q^{89} +18.0000 q^{90} +(4.50000 + 7.79423i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(1.50000 - 2.59808i) q^{95} -15.0000 q^{96} +(2.50000 - 4.33013i) q^{97} -18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 3 q^{3} + q^{4} + 6 q^{5} + 3 q^{6} - 6 q^{8} - 6 q^{9} - 3 q^{10} + 3 q^{11} + 6 q^{12} - 2 q^{13} + 9 q^{15} + q^{16} + 2 q^{17} + 12 q^{18} + q^{19} + 3 q^{20} + 3 q^{22} - 9 q^{24}+ \cdots - 36 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 + q^4 + 6 * q^5 + 3 * q^6 - 6 * q^8 - 6 * q^9 - 3 * q^10 + 3 * q^11 + 6 * q^12 - 2 * q^13 + 9 * q^15 + q^16 + 2 * q^17 + 12 * q^18 + q^19 + 3 * q^20 + 3 * q^22 - 9 * q^24 + 8 * q^25 + 7 * q^26 - 18 * q^27 - 7 * q^29 + 9 * q^30 + 6 * q^31 - 5 * q^32 - 9 * q^33 - 4 * q^34 + 6 * q^36 - 2 * q^37 - 2 * q^38 - 21 * q^39 - 18 * q^40 - 3 * q^41 + 7 * q^43 + 6 * q^44 - 18 * q^45 + 2 * q^47 - 3 * q^48 - 4 * q^50 + 12 * q^51 + 5 * q^52 + 6 * q^53 + 9 * q^54 + 9 * q^55 + 6 * q^57 - 7 * q^58 + 4 * q^59 + 18 * q^60 + 13 * q^61 - 3 * q^62 + 14 * q^64 - 6 * q^65 + 18 * q^66 + 3 * q^67 - 2 * q^68 - 13 * q^71 + 18 * q^72 - 26 * q^73 - 2 * q^74 + 12 * q^75 - q^76 + 15 * q^78 - 6 * q^79 + 3 * q^80 - 9 * q^81 - 3 * q^82 + 6 * q^85 - 14 * q^86 + 21 * q^87 - 9 * q^88 - 6 * q^89 + 36 * q^90 + 9 * q^93 - q^94 + 3 * q^95 - 30 * q^96 + 5 * q^97 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$	1.50000	−	2.59808i	0.612372	−	1.06066i
$7$		0			0
$7$		0			0
$8$	−3.00000			−1.06066
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	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	$0.683949\pi$
$12$	3.00000			0.866025
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$		0			0
$15$	4.50000	+	7.79423i	1.16190	+	2.01246i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	6.00000			1.41421
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−4.50000	−	7.79423i	−0.918559	−	1.59099i
$25$	4.00000			0.800000
$26$	3.50000	−	0.866025i	0.686406	−	0.169842i
$27$	−9.00000			−1.73205
$28$		0			0
$29$	−3.50000	−	6.06218i	−0.649934	−	1.12572i	−0.983138	−	0.182864i	$-0.941463\pi$
$29$	−3.50000	−	6.06218i	−0.649934	−	1.12572i	0.333205	−	0.942855i	$-0.391870\pi$
$30$	4.50000	−	7.79423i	0.821584	−	1.42302i
$31$	3.00000			0.538816			0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000			0.538816			0.269408	+	0.963026i	$0.413172\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$	−4.50000	+	7.79423i	−0.783349	+	1.35680i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	3.00000	+	5.19615i	0.500000	+	0.866025i
$37$	−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			−0.162221
$39$	−10.5000	+	2.59808i	−1.68135	+	0.416025i
$40$	−9.00000			−1.42302
$41$	−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			0
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	−0.465478	−	0.885059i	$-0.654118\pi$
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	0.999223	−	0.0394140i	$-0.0125491\pi$
$44$	3.00000			0.452267
$45$	−9.00000	+	15.5885i	−1.34164	+	2.32379i
$46$		0			0
$47$	1.00000			0.145865			0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000			0.145865			0.0729325	+	0.997337i	$0.476764\pi$
$48$	−1.50000	+	2.59808i	−0.216506	+	0.375000i
$49$		0			0
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$	6.00000			0.840168
$52$	2.50000	+	2.59808i	0.346688	+	0.360288i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$	4.50000	+	7.79423i	0.612372	+	1.06066i
$55$	4.50000	+	7.79423i	0.606780	+	1.05097i
$56$		0			0
$57$	3.00000			0.397360
$58$	−3.50000	+	6.06218i	−0.459573	+	0.796003i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$	9.00000			1.16190
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$	−1.50000	−	2.59808i	−0.190500	−	0.329956i
$63$		0			0
$64$	7.00000			0.875000
$65$	−3.00000	+	10.3923i	−0.372104	+	1.28901i
$66$	9.00000			1.10782
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	0.942987	−	0.332830i	$-0.108004\pi$
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$		0			0
$70$		0			0
$71$	−6.50000	+	11.2583i	−0.771408	+	1.33612i	0.165383	+	0.986229i	$0.447114\pi$
$71$	−6.50000	+	11.2583i	−0.771408	+	1.33612i	−0.936791	+	0.349889i	$0.886219\pi$
$72$	9.00000	−	15.5885i	1.06066	−	1.83712i
$73$	−13.0000			−1.52153			−0.760767	−	0.649025i	$-0.775177\pi$
$73$	−13.0000			−1.52153			−0.760767	+	0.649025i	$0.775177\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	6.00000	+	10.3923i	0.692820	+	1.20000i
$76$	−0.500000	−	0.866025i	−0.0573539	−	0.0993399i
$77$		0			0
$78$	7.50000	+	7.79423i	0.849208	+	0.882523i
$79$	−3.00000			−0.337526			−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000			−0.337526			−0.168763	+	0.985657i	$0.553977\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	−7.00000			−0.754829
$87$	10.5000	−	18.1865i	1.12572	−	1.94980i
$88$	−4.50000	−	7.79423i	−0.479702	−	0.830868i
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	18.0000			1.89737
$91$		0			0
$92$		0			0
$93$	4.50000	+	7.79423i	0.466628	+	0.808224i
$94$	−0.500000	−	0.866025i	−0.0515711	−	0.0893237i
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$	−15.0000			−1.53093
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	0.964579	+	0.263795i	$0.0849741\pi$
$98$		0			0
$99$	−18.0000			−1.80907
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	0.963182	−	0.268851i	$-0.0866439\pi$
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	−0.714423	+	0.699715i	$0.753311\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	5.00000			0.492665			0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000			0.492665			0.246332	+	0.969185i	$0.420775\pi$
$104$	3.00000	−	10.3923i	0.294174	−	1.01905i
$105$		0			0
$106$	−1.50000	−	2.59808i	−0.145693	−	0.252347i
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$	−4.50000	+	7.79423i	−0.433013	+	0.750000i
$109$	7.00000			0.670478			0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000			0.670478			0.335239	+	0.942133i	$0.391183\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$	3.00000	−	5.19615i	0.284747	−	0.493197i
$112$		0			0
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	0.260955	+	0.965351i	$0.415962\pi$
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	−0.966496	+	0.256681i	$0.917371\pi$
$114$	−1.50000	−	2.59808i	−0.140488	−	0.243332i
$115$		0			0
$116$	−7.00000			−0.649934
$117$	−15.0000	−	15.5885i	−1.38675	−	1.44115i
$118$	−4.00000			−0.368230
$119$		0			0
$120$	−13.5000	−	23.3827i	−1.23238	−	2.13454i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−13.0000			−1.17696
$123$	4.50000	−	7.79423i	0.405751	−	0.702782i
$124$	1.50000	−	2.59808i	0.134704	−	0.233314i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	0.511859	−	0.859069i	$-0.328957\pi$
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	−0.999905	+	0.0137486i	$0.995624\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$	21.0000			1.84895
$130$	10.5000	−	2.59808i	0.920911	−	0.227866i
$131$	5.00000			0.436852			0.218426	−	0.975854i	$-0.429908\pi$
$131$	5.00000			0.436852			0.218426	+	0.975854i	$0.429908\pi$
$132$	4.50000	+	7.79423i	0.391675	+	0.678401i
$133$		0			0
$134$	1.50000	−	2.59808i	0.129580	−	0.224440i
$135$	−27.0000			−2.32379
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	−0.996621	−	0.0821359i	$-0.973826\pi$
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	0.569442	+	0.822031i	$0.307159\pi$
$138$		0			0
$139$	7.50000	−	12.9904i	0.636142	−	1.10183i	−0.350130	−	0.936701i	$-0.613863\pi$
$139$	7.50000	−	12.9904i	0.636142	−	1.10183i	0.986272	−	0.165129i	$-0.0528040\pi$
$140$		0			0
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$	13.0000			1.09094
$143$	−10.5000	+	2.59808i	−0.878054	+	0.217262i
$144$	−6.00000			−0.500000
$145$	−10.5000	−	18.1865i	−0.871978	−	1.51031i
$146$	6.50000	+	11.2583i	0.537944	+	0.931746i
$147$		0			0
$148$	−2.00000			−0.164399
$149$	−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	$0.956055\pi$
$150$	6.00000	−	10.3923i	0.489898	−	0.848528i
$151$	−21.0000			−1.70896			−0.854478	−	0.519488i	$-0.826123\pi$
$151$	−21.0000			−1.70896			−0.854478	+	0.519488i	$0.826123\pi$
$152$	−1.50000	+	2.59808i	−0.121666	+	0.210732i
$153$	6.00000	+	10.3923i	0.485071	+	0.840168i
$154$		0			0
$155$	9.00000			0.722897
$156$	−3.00000	+	10.3923i	−0.240192	+	0.832050i
$157$	19.0000			1.51637			0.758183	−	0.652042i	$-0.226088\pi$
$157$	19.0000			1.51637			0.758183	+	0.652042i	$0.226088\pi$
$158$	1.50000	+	2.59808i	0.119334	+	0.206692i
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$	−7.50000	+	12.9904i	−0.592927	+	1.02698i
$161$		0			0
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	−0.845780	−	0.533533i	$-0.820864\pi$
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	0.884943	+	0.465700i	$0.154198\pi$
$164$	−3.00000			−0.234261
$165$	−13.5000	+	23.3827i	−1.05097	+	1.82034i
$166$		0			0
$167$	6.50000	+	11.2583i	0.502985	+	0.871196i	0.999994	+	0.00345033i	$0.00109828\pi$
$167$	6.50000	+	11.2583i	0.502985	+	0.871196i	−0.497009	+	0.867745i	$0.665568\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	−6.00000			−0.460179
$171$	3.00000	+	5.19615i	0.229416	+	0.397360i
$172$	−3.50000	−	6.06218i	−0.266872	−	0.462237i
$173$	−9.50000	+	16.4545i	−0.722272	+	1.25101i	0.237816	+	0.971310i	$0.423569\pi$
$173$	−9.50000	+	16.4545i	−0.722272	+	1.25101i	−0.960087	+	0.279701i	$0.909765\pi$
$174$	−21.0000			−1.59201
$175$		0			0
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$	12.0000			0.901975
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−8.50000	−	14.7224i	−0.635320	−	1.10041i	−0.986447	−	0.164079i	$-0.947535\pi$
$179$	−8.50000	−	14.7224i	−0.635320	−	1.10041i	0.351127	−	0.936328i	$-0.385798\pi$
$180$	9.00000	+	15.5885i	0.670820	+	1.16190i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	39.0000			2.88296
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$	4.50000	−	7.79423i	0.329956	−	0.571501i
$187$	6.00000			0.438763
$188$	0.500000	−	0.866025i	0.0364662	−	0.0631614i
$189$		0			0
$190$	−3.00000			−0.217643
$191$	8.50000	−	14.7224i	0.615038	−	1.06528i	−0.375339	−	0.926887i	$-0.622474\pi$
$191$	8.50000	−	14.7224i	0.615038	−	1.06528i	0.990378	−	0.138390i	$-0.0441928\pi$
$192$	10.5000	+	18.1865i	0.757772	+	1.31250i
$193$	−3.50000	−	6.06218i	−0.251936	−	0.436365i	0.712123	−	0.702055i	$-0.247734\pi$
$193$	−3.50000	−	6.06218i	−0.251936	−	0.436365i	−0.964059	+	0.265689i	$0.914400\pi$
$194$	−5.00000			−0.358979
$195$	−31.5000	+	7.79423i	−2.25576	+	0.558156i
$196$		0			0
$197$	0.500000	+	0.866025i	0.0356235	+	0.0617018i	0.883287	−	0.468832i	$-0.155325\pi$
$197$	0.500000	+	0.866025i	0.0356235	+	0.0617018i	−0.847664	+	0.530534i	$0.821992\pi$
$198$	9.00000	+	15.5885i	0.639602	+	1.10782i
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	−12.0000			−0.848528
$201$	−4.50000	+	7.79423i	−0.317406	+	0.549762i
$202$	2.50000	−	4.33013i	0.175899	−	0.304667i
$203$		0			0
$204$	3.00000	−	5.19615i	0.210042	−	0.363803i
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	−2.50000	−	4.33013i	−0.174183	−	0.301694i
$207$		0			0
$208$	−3.50000	+	0.866025i	−0.242681	+	0.0600481i
$209$	3.00000			0.207514
$210$		0			0
$211$	−3.50000	−	6.06218i	−0.240950	−	0.417338i	0.720035	−	0.693938i	$-0.244126\pi$
$211$	−3.50000	−	6.06218i	−0.240950	−	0.417338i	−0.960985	+	0.276600i	$0.910792\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	−39.0000			−2.67224
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$	10.5000	−	18.1865i	0.716094	−	1.24031i
$216$	27.0000			1.83712
$217$		0			0
$218$	−3.50000	−	6.06218i	−0.237050	−	0.410582i
$219$	−19.5000	−	33.7750i	−1.31769	−	2.28230i
$220$	9.00000			0.606780
$221$	5.00000	+	5.19615i	0.336336	+	0.349531i
$222$	−6.00000			−0.402694
$223$	4.50000	+	7.79423i	0.301342	+	0.521940i	0.976440	−	0.215788i	$-0.0692320\pi$
$223$	4.50000	+	7.79423i	0.301342	+	0.521940i	−0.675098	+	0.737728i	$0.735899\pi$
$224$		0			0
$225$	−12.0000	+	20.7846i	−0.800000	+	1.38564i
$226$	15.0000			0.997785
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	−0.791989	−	0.610535i	$-0.790954\pi$
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	0.924734	+	0.380615i	$0.124288\pi$
$228$	1.50000	−	2.59808i	0.0993399	−	0.172062i
$229$	−13.0000			−0.859064			−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000			−0.859064			−0.429532	+	0.903052i	$0.641321\pi$
$230$		0			0
$231$		0			0
$232$	10.5000	+	18.1865i	0.689359	+	1.19400i
$233$	−21.0000			−1.37576			−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000			−1.37576			−0.687878	+	0.725826i	$0.741458\pi$
$234$	−6.00000	+	20.7846i	−0.392232	+	1.35873i
$235$	3.00000			0.195698
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$	−4.50000	−	7.79423i	−0.292306	−	0.506290i
$238$		0			0
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	−4.50000	+	7.79423i	−0.290474	+	0.503115i
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	−0.0546547	−	0.998505i	$-0.517406\pi$
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	0.892058	−	0.451920i	$-0.149261\pi$
$242$	−2.00000			−0.128565
$243$		0			0
$244$	−6.50000	−	11.2583i	−0.416120	−	0.720741i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	2.50000	+	2.59808i	0.159071	+	0.165312i
$248$	−9.00000			−0.571501
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	11.5000	−	19.9186i	0.725874	−	1.25725i	−0.232740	−	0.972539i	$-0.574769\pi$
$251$	11.5000	−	19.9186i	0.725874	−	1.25725i	0.958613	−	0.284711i	$-0.0918976\pi$
$252$		0			0
$253$		0			0
$254$	−5.50000	+	9.52628i	−0.345101	+	0.597732i
$255$	18.0000			1.12720
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	0.895528	−	0.445005i	$-0.146798\pi$
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	−0.833150	+	0.553047i	$0.813465\pi$
$258$	−10.5000	−	18.1865i	−0.653701	−	1.13224i
$259$		0			0
$260$	7.50000	+	7.79423i	0.465130	+	0.483378i
$261$	42.0000			2.59973
$262$	−2.50000	−	4.33013i	−0.154451	−	0.267516i
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	0.896093	+	0.443866i	$0.146393\pi$
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	−0.0636476	+	0.997972i	$0.520273\pi$
$264$	13.5000	−	23.3827i	0.830868	−	1.43910i
$265$	9.00000			0.552866
$266$		0			0
$267$	9.00000	−	15.5885i	0.550791	−	0.953998i
$268$	3.00000			0.183254
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	13.5000	+	23.3827i	0.821584	+	1.42302i
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	0.319447	+	0.947604i	$0.396503\pi$
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	−0.980373	+	0.197153i	$0.936830\pi$
$278$	−15.0000			−0.899640
$279$	−9.00000	+	15.5885i	−0.538816	+	0.933257i
$280$		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
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	0.850782	−	0.525519i	$-0.176129\pi$
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	−0.880504	+	0.474039i	$0.842796\pi$
$284$	6.50000	+	11.2583i	0.385704	+	0.668059i
$285$	9.00000			0.533114
$286$	7.50000	+	7.79423i	0.443484	+	0.460882i
$287$		0			0
$288$	−15.0000	−	25.9808i	−0.883883	−	1.53093i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−10.5000	+	18.1865i	−0.616581	+	1.06795i
$291$	15.0000			0.879316
$292$	−6.50000	+	11.2583i	−0.380384	+	0.658844i
$293$	−5.50000	+	9.52628i	−0.321313	+	0.556531i	−0.980759	−	0.195221i	$-0.937458\pi$
$293$	−5.50000	+	9.52628i	−0.321313	+	0.556531i	0.659446	+	0.751752i	$0.270791\pi$
$294$		0			0
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$	−13.5000	−	23.3827i	−0.783349	−	1.35680i
$298$	15.0000			0.868927
$299$		0			0
$300$	12.0000			0.692820
$301$		0			0
$302$	10.5000	+	18.1865i	0.604207	+	1.04652i
$303$	−7.50000	+	12.9904i	−0.430864	+	0.746278i
$304$	1.00000			0.0573539
$305$	19.5000	−	33.7750i	1.11657	−	1.93395i
$306$	6.00000	−	10.3923i	0.342997	−	0.594089i
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$		0			0
$309$	7.50000	+	12.9904i	0.426660	+	0.738997i
$310$	−4.50000	−	7.79423i	−0.255583	−	0.442682i
$311$	−9.00000			−0.510343			−0.255172	−	0.966896i	$-0.582132\pi$
$311$	−9.00000			−0.510343			−0.255172	+	0.966896i	$0.582132\pi$
$312$	31.5000	−	7.79423i	1.78334	−	0.441261i
$313$	19.0000			1.07394			0.536972	−	0.843600i	$-0.319568\pi$
$313$	19.0000			1.07394			0.536972	+	0.843600i	$0.319568\pi$
$314$	−9.50000	−	16.4545i	−0.536116	−	0.928580i
$315$		0			0
$316$	−1.50000	+	2.59808i	−0.0843816	+	0.146153i
$317$	−9.00000			−0.505490			−0.252745	−	0.967533i	$-0.581333\pi$
$317$	−9.00000			−0.505490			−0.252745	+	0.967533i	$0.581333\pi$
$318$	4.50000	−	7.79423i	0.252347	−	0.437079i
$319$	10.5000	−	18.1865i	0.587887	−	1.01825i
$320$	21.0000			1.17394
$321$	12.0000	−	20.7846i	0.669775	−	1.16008i
$322$		0			0
$323$	−1.00000	−	1.73205i	−0.0556415	−	0.0963739i
$324$	−9.00000			−0.500000
$325$	−4.00000	+	13.8564i	−0.221880	+	0.768615i
$326$	−1.00000			−0.0553849
$327$	10.5000	+	18.1865i	0.580651	+	1.00572i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$	27.0000			1.48630
$331$	14.5000	−	25.1147i	0.796992	−	1.38043i	−0.124574	−	0.992210i	$-0.539757\pi$
$331$	14.5000	−	25.1147i	0.796992	−	1.38043i	0.921567	−	0.388221i	$-0.126910\pi$
$332$		0			0
$333$	12.0000			0.657596
$334$	6.50000	−	11.2583i	0.355664	−	0.616028i
$335$	4.50000	+	7.79423i	0.245861	+	0.425844i
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−0.500000	+	12.9904i	−0.0271964	+	0.706584i
$339$	−45.0000			−2.44406
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	4.50000	+	7.79423i	0.243689	+	0.422081i
$342$	3.00000	−	5.19615i	0.162221	−	0.280976i
$343$		0			0
$344$	−10.5000	+	18.1865i	−0.566122	+	0.980552i
$345$		0			0
$346$	19.0000			1.02145
$347$	4.00000	−	6.92820i	0.214731	−	0.371925i	−0.738458	−	0.674299i	$-0.764446\pi$
$347$	4.00000	−	6.92820i	0.214731	−	0.371925i	0.953189	+	0.302374i	$0.0977791\pi$
$348$	−10.5000	−	18.1865i	−0.562859	−	0.974901i
$349$	−11.5000	−	19.9186i	−0.615581	−	1.06622i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−11.5000	−	19.9186i	−0.615581	−	1.06622i	0.374701	−	0.927146i	$-0.377745\pi$
$350$		0			0
$351$	9.00000	−	31.1769i	0.480384	−	1.66410i
$352$	−15.0000			−0.799503
$353$	12.5000	+	21.6506i	0.665308	+	1.15235i	0.979202	+	0.202889i	$0.0650330\pi$
$353$	12.5000	+	21.6506i	0.665308	+	1.15235i	−0.313894	+	0.949458i	$0.601634\pi$
$354$	−6.00000	−	10.3923i	−0.318896	−	0.552345i
$355$	−19.5000	+	33.7750i	−1.03495	+	1.79259i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−8.50000	+	14.7224i	−0.449239	+	0.778105i
$359$	17.0000			0.897226			0.448613	−	0.893726i	$-0.351918\pi$
$359$	17.0000			0.897226			0.448613	+	0.893726i	$0.351918\pi$
$360$	27.0000	−	46.7654i	1.42302	−	2.46475i
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	11.0000	+	19.0526i	0.578147	+	1.00138i
$363$	6.00000			0.314918
$364$		0			0
$365$	−39.0000			−2.04135
$366$	−19.5000	−	33.7750i	−1.01928	−	1.76545i
$367$	15.5000	+	26.8468i	0.809093	+	1.40139i	0.913493	+	0.406855i	$0.133375\pi$
$367$	15.5000	+	26.8468i	0.809093	+	1.40139i	−0.104399	+	0.994535i	$0.533292\pi$
$368$		0			0
$369$	18.0000			0.937043
$370$	−3.00000	+	5.19615i	−0.155963	+	0.270135i
$371$		0			0
$372$	9.00000			0.466628
$373$	4.50000	−	7.79423i	0.233001	−	0.403570i	−0.725689	−	0.688023i	$-0.758479\pi$
$373$	4.50000	−	7.79423i	0.233001	−	0.403570i	0.958690	+	0.284453i	$0.0918121\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	−3.00000			−0.154713
$377$	24.5000	−	6.06218i	1.26181	−	0.312218i
$378$		0			0
$379$	16.5000	+	28.5788i	0.847548	+	1.46800i	0.883390	+	0.468639i	$0.155255\pi$
$379$	16.5000	+	28.5788i	0.847548	+	1.46800i	−0.0358418	+	0.999357i	$0.511411\pi$
$380$	−1.50000	−	2.59808i	−0.0769484	−	0.133278i
$381$	16.5000	−	28.5788i	0.845321	−	1.46414i
$382$	−17.0000			−0.869796
$383$	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	$-0.0135966\pi$
$384$	−4.50000	+	7.79423i	−0.229640	+	0.397748i
$385$		0			0
$386$	−3.50000	+	6.06218i	−0.178145	+	0.308557i
$387$	21.0000	+	36.3731i	1.06749	+	1.84895i
$388$	−2.50000	−	4.33013i	−0.126918	−	0.219829i
$389$	−33.0000			−1.67317			−0.836583	−	0.547840i	$-0.815450\pi$
$389$	−33.0000			−1.67317			−0.836583	+	0.547840i	$0.815450\pi$
$390$	22.5000	+	23.3827i	1.13933	+	1.18403i
$391$		0			0
$392$		0			0
$393$	7.50000	+	12.9904i	0.378325	+	0.655278i
$394$	0.500000	−	0.866025i	0.0251896	−	0.0436297i
$395$	−9.00000			−0.452839
$396$	−9.00000	+	15.5885i	−0.452267	+	0.783349i
$397$	0.500000	−	0.866025i	0.0250943	−	0.0434646i	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	0.500000	−	0.866025i	0.0250943	−	0.0434646i	0.878300	+	0.478110i	$0.158678\pi$
$398$	−20.0000			−1.00251
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	0.889914	−	0.456129i	$-0.150764\pi$
$401$	1.00000	+	1.73205i	0.0499376	+	0.0864945i	−0.839976	+	0.542623i	$0.817431\pi$
$402$	9.00000			0.448879
$403$	−3.00000	+	10.3923i	−0.149441	+	0.517678i
$404$	5.00000			0.248759
$405$	−13.5000	−	23.3827i	−0.670820	−	1.16190i
$406$		0			0
$407$	3.00000	−	5.19615i	0.148704	−	0.257564i
$408$	−18.0000			−0.891133
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$	−30.0000			−1.47979
$412$	2.50000	−	4.33013i	0.123166	−	0.213330i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−12.5000	−	12.9904i	−0.612863	−	0.636906i
$417$	45.0000			2.20366
$418$	−1.50000	−	2.59808i	−0.0733674	−	0.127076i
$419$	12.5000	+	21.6506i	0.610665	+	1.05770i	0.991129	+	0.132907i	$0.0424311\pi$
$419$	12.5000	+	21.6506i	0.610665	+	1.05770i	−0.380464	+	0.924796i	$0.624236\pi$
$420$		0			0
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$	−3.50000	+	6.06218i	−0.170377	+	0.295102i
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$	−9.00000			−0.437079
$425$	4.00000	−	6.92820i	0.194029	−	0.336067i
$426$	19.5000	+	33.7750i	0.944778	+	1.63640i
$427$		0			0
$428$	−8.00000			−0.386695
$429$	−22.5000	−	23.3827i	−1.08631	−	1.12893i
$430$	−21.0000			−1.01271
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	0.737057	−	0.675830i	$-0.236215\pi$
$431$	−4.50000	−	7.79423i	−0.216757	−	0.375435i	−0.953815	+	0.300395i	$0.902881\pi$
$432$	−4.50000	−	7.79423i	−0.216506	−	0.375000i
$433$	−13.5000	+	23.3827i	−0.648769	+	1.12370i	0.334649	+	0.942343i	$0.391382\pi$
$433$	−13.5000	+	23.3827i	−0.648769	+	1.12370i	−0.983417	+	0.181357i	$0.941951\pi$
$434$		0			0
$435$	31.5000	−	54.5596i	1.51031	−	2.61593i
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$		0			0
$438$	−19.5000	+	33.7750i	−0.931746	+	1.61383i
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	−13.5000	−	23.3827i	−0.643587	−	1.11473i
$441$		0			0
$442$	2.00000	−	6.92820i	0.0951303	−	0.329541i
$443$	−11.0000			−0.522626			−0.261313	−	0.965254i	$-0.584155\pi$
$443$	−11.0000			−0.522626			−0.261313	+	0.965254i	$0.584155\pi$
$444$	−3.00000	−	5.19615i	−0.142374	−	0.246598i
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$	4.50000	−	7.79423i	0.213081	−	0.369067i
$447$	−45.0000			−2.12843
$448$		0			0
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	−0.986937	−	0.161106i	$-0.948494\pi$
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	0.632990	+	0.774160i	$0.281827\pi$
$450$	24.0000			1.13137
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$	−31.5000	−	54.5596i	−1.48000	−	2.56343i
$454$	−4.00000			−0.187729
$455$		0			0
$456$	−9.00000			−0.421464
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	6.50000	+	11.2583i	0.303725	+	0.526067i
$459$	−9.00000	+	15.5885i	−0.420084	+	0.727607i
$460$		0			0
$461$	−17.5000	+	30.3109i	−0.815056	+	1.41172i	0.0942312	+	0.995550i	$0.469961\pi$
$461$	−17.5000	+	30.3109i	−0.815056	+	1.41172i	−0.909288	+	0.416169i	$0.863373\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	3.50000	−	6.06218i	0.162483	−	0.281430i
$465$	13.5000	+	23.3827i	0.626048	+	1.08435i
$466$	10.5000	+	18.1865i	0.486403	+	0.842475i
$467$	−7.00000			−0.323921			−0.161961	−	0.986797i	$-0.551782\pi$
$467$	−7.00000			−0.323921			−0.161961	+	0.986797i	$0.551782\pi$
$468$	−21.0000	+	5.19615i	−0.970725	+	0.240192i
$469$		0			0
$470$	−1.50000	−	2.59808i	−0.0691898	−	0.119840i
$471$	28.5000	+	49.3634i	1.31321	+	2.27455i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	21.0000			0.965581
$474$	−4.50000	+	7.79423i	−0.206692	+	0.358001i
$475$	2.00000	−	3.46410i	0.0917663	−	0.158944i
$476$		0			0
$477$	−9.00000	+	15.5885i	−0.412082	+	0.713746i
$478$	2.00000	+	3.46410i	0.0914779	+	0.158444i
$479$	17.5000	+	30.3109i	0.799595	+	1.38494i	0.919880	+	0.392200i	$0.128286\pi$
$479$	17.5000	+	30.3109i	0.799595	+	1.38494i	−0.120284	+	0.992739i	$0.538381\pi$
$480$	−45.0000			−2.05396
$481$	7.00000	−	1.73205i	0.319173	−	0.0789747i
$482$	−26.0000			−1.18427
$483$		0			0
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$	7.50000	−	12.9904i	0.340557	−	0.589863i
$486$		0			0
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$	−19.5000	+	33.7750i	−0.882724	+	1.52892i
$489$	3.00000			0.135665
$490$		0			0
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	0.645675	−	0.763612i	$-0.276576\pi$
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	−0.984145	+	0.177365i	$0.943243\pi$
$492$	−4.50000	−	7.79423i	−0.202876	−	0.351391i
$493$	−14.0000			−0.630528
$494$	1.00000	−	3.46410i	0.0449921	−	0.155857i
$495$	−54.0000			−2.42712
$496$	1.50000	+	2.59808i	0.0673520	+	0.116657i
$497$		0			0
$498$		0			0
$499$	−31.0000			−1.38775			−0.693875	−	0.720095i	$-0.744098\pi$
$499$	−31.0000			−1.38775			−0.693875	+	0.720095i	$0.744098\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	−19.5000	+	33.7750i	−0.871196	+	1.50896i
$502$	−23.0000			−1.02654
$503$	15.5000	−	26.8468i	0.691111	−	1.19704i	−0.280363	−	0.959894i	$-0.590455\pi$
$503$	15.5000	−	26.8468i	0.691111	−	1.19704i	0.971474	−	0.237145i	$-0.0762117\pi$
$504$		0			0
$505$	7.50000	+	12.9904i	0.333746	+	0.578064i
$506$		0			0
$507$	1.50000	−	38.9711i	0.0666173	−	1.73077i
$508$	−11.0000			−0.488046
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	0.946111	+	0.323843i	$0.104975\pi$
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	−0.192599	+	0.981278i	$0.561692\pi$
$510$	−9.00000	−	15.5885i	−0.398527	−	0.690268i
$511$		0			0
$512$	−11.0000			−0.486136
$513$	−4.50000	+	7.79423i	−0.198680	+	0.344124i
$514$	1.00000	−	1.73205i	0.0441081	−	0.0763975i
$515$	15.0000			0.660979
$516$	10.5000	−	18.1865i	0.462237	−	0.800617i
$517$	1.50000	+	2.59808i	0.0659699	+	0.114263i
$518$		0			0
$519$	−57.0000			−2.50202
$520$	9.00000	−	31.1769i	0.394676	−	1.36720i
$521$	−17.0000			−0.744784			−0.372392	−	0.928076i	$-0.621462\pi$
$521$	−17.0000			−0.744784			−0.372392	+	0.928076i	$0.621462\pi$
$522$	−21.0000	−	36.3731i	−0.919145	−	1.59201i
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	0.818980	−	0.573822i	$-0.194540\pi$
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	−0.906434	+	0.422347i	$0.861206\pi$
$524$	2.50000	−	4.33013i	0.109213	−	0.189162i
$525$		0			0
$526$	13.5000	−	23.3827i	0.588628	−	1.01953i
$527$	3.00000	−	5.19615i	0.130682	−	0.226348i
$528$	−9.00000			−0.391675
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$	12.0000	+	20.7846i	0.520756	+	0.901975i
$532$		0			0
$533$	10.5000	−	2.59808i	0.454805	−	0.112535i
$534$	−18.0000			−0.778936
$535$	−12.0000	−	20.7846i	−0.518805	−	0.898597i
$536$	−4.50000	−	7.79423i	−0.194370	−	0.336659i
$537$	25.5000	−	44.1673i	1.10041	−	1.90596i
$538$	18.0000			0.776035
$539$		0			0
$540$	−13.5000	+	23.3827i	−0.580948	+	1.00623i
$541$	−37.0000			−1.59075			−0.795377	−	0.606115i	$-0.792727\pi$
$541$	−37.0000			−1.59075			−0.795377	+	0.606115i	$0.792727\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$	−33.0000	−	57.1577i	−1.41617	−	2.45287i
$544$	5.00000	+	8.66025i	0.214373	+	0.371305i
$545$	21.0000			0.899541
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	5.00000	+	8.66025i	0.213589	+	0.369948i
$549$	39.0000	+	67.5500i	1.66448	+	2.88296i
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	−7.00000			−0.298210
$552$		0			0
$553$		0			0
$554$	22.0000			0.934690
$555$	9.00000	−	15.5885i	0.382029	−	0.661693i
$556$	−7.50000	−	12.9904i	−0.318071	−	0.550915i
$557$	−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	$0.853578\pi$
$558$	18.0000			0.762001
$559$	17.5000	+	18.1865i	0.740171	+	0.769208i
$560$		0			0
$561$	9.00000	+	15.5885i	0.379980	+	0.658145i
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	−0.905088	−	0.425223i	$-0.860196\pi$
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	0.820798	+	0.571218i	$0.193529\pi$
$564$	3.00000			0.126323
$565$	−22.5000	+	38.9711i	−0.946582	+	1.63953i
$566$	−0.500000	+	0.866025i	−0.0210166	+	0.0364018i
$567$		0			0
$568$	19.5000	−	33.7750i	0.818202	−	1.41717i
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	0.741981	−	0.670421i	$-0.233886\pi$
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	−0.951592	+	0.307364i	$0.900553\pi$
$570$	−4.50000	−	7.79423i	−0.188484	−	0.326464i
$571$	43.0000			1.79949			0.899747	−	0.436412i	$-0.143751\pi$
$571$	43.0000			1.79949			0.899747	+	0.436412i	$0.143751\pi$
$572$	−3.00000	+	10.3923i	−0.125436	+	0.434524i
$573$	51.0000			2.13056
$574$		0			0
$575$		0			0
$576$	−21.0000	+	36.3731i	−0.875000	+	1.51554i
$577$	−1.00000			−0.0416305			−0.0208153	−	0.999783i	$-0.506626\pi$
$577$	−1.00000			−0.0416305			−0.0208153	+	0.999783i	$0.506626\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	10.5000	−	18.1865i	0.436365	−	0.755807i
$580$	−21.0000			−0.871978
$581$		0			0
$582$	−7.50000	−	12.9904i	−0.310885	−	0.538469i
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	39.0000			1.61383
$585$	−45.0000	−	46.7654i	−1.86052	−	1.93351i
$586$	11.0000			0.454406
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	0.974668	+	0.223659i	$0.0718001\pi$
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	−0.293640	+	0.955916i	$0.594867\pi$
$588$		0			0
$589$	1.50000	−	2.59808i	0.0618064	−	0.107052i
$590$	−12.0000			−0.494032
$591$	−1.50000	+	2.59808i	−0.0617018	+	0.106871i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	27.0000			1.10876			0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000			1.10876			0.554379	+	0.832265i	$0.312956\pi$
$594$	−13.5000	+	23.3827i	−0.553912	+	0.959403i
$595$		0			0
$596$	7.50000	+	12.9904i	0.307212	+	0.532107i
$597$	60.0000			2.45564
$598$		0			0
$599$	−25.0000			−1.02147			−0.510736	−	0.859738i	$-0.670627\pi$
$599$	−25.0000			−1.02147			−0.510736	+	0.859738i	$0.670627\pi$
$600$	−18.0000	−	31.1769i	−0.734847	−	1.27279i
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$		0			0
$603$	−18.0000			−0.733017
$604$	−10.5000	+	18.1865i	−0.427239	+	0.740000i
$605$	3.00000	−	5.19615i	0.121967	−	0.211254i
$606$	15.0000			0.609333
$607$	−5.50000	+	9.52628i	−0.223238	+	0.386660i	−0.955789	−	0.294052i	$-0.904996\pi$
$607$	−5.50000	+	9.52628i	−0.223238	+	0.386660i	0.732551	+	0.680712i	$0.238329\pi$
$608$	2.50000	+	4.33013i	0.101388	+	0.175610i
$609$		0			0
$610$	−39.0000			−1.57906
$611$	−1.00000	+	3.46410i	−0.0404557	+	0.140143i
$612$	12.0000			0.485071
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	0.999984	+	0.00563283i	$0.00179300\pi$
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	−0.495114	+	0.868828i	$0.664874\pi$
$614$	−6.00000	−	10.3923i	−0.242140	−	0.419399i
$615$	13.5000	−	23.3827i	0.544373	−	0.942881i
$616$		0			0
$617$	16.5000	−	28.5788i	0.664265	−	1.15054i	−0.315219	−	0.949019i	$-0.602078\pi$
$617$	16.5000	−	28.5788i	0.664265	−	1.15054i	0.979484	−	0.201522i	$-0.0645887\pi$
$618$	7.50000	−	12.9904i	0.301694	−	0.522550i
$619$	11.0000			0.442127			0.221064	−	0.975259i	$-0.429047\pi$
$619$	11.0000			0.442127			0.221064	+	0.975259i	$0.429047\pi$
$620$	4.50000	−	7.79423i	0.180724	−	0.313024i
$621$		0			0
$622$	4.50000	+	7.79423i	0.180434	+	0.312520i
$623$		0			0
$624$	−7.50000	−	7.79423i	−0.300240	−	0.312019i
$625$	−29.0000			−1.16000
$626$	−9.50000	−	16.4545i	−0.379696	−	0.657653i
$627$	4.50000	+	7.79423i	0.179713	+	0.311272i
$628$	9.50000	−	16.4545i	0.379091	−	0.656605i
$629$	−4.00000			−0.159490
$630$		0			0
$631$	−12.5000	+	21.6506i	−0.497617	+	0.861898i	−0.999996	−	0.00274930i	$-0.999125\pi$
$631$	−12.5000	+	21.6506i	−0.497617	+	0.861898i	0.502379	+	0.864647i	$0.332458\pi$
$632$	9.00000			0.358001
$633$	10.5000	−	18.1865i	0.417338	−	0.722850i
$634$	4.50000	+	7.79423i	0.178718	+	0.309548i
$635$	−16.5000	−	28.5788i	−0.654783	−	1.13412i
$636$	9.00000			0.356873
$637$		0			0
$638$	−21.0000			−0.831398
$639$	−39.0000	−	67.5500i	−1.54282	−	2.67224i
$640$	4.50000	+	7.79423i	0.177878	+	0.308094i
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$	−24.0000			−0.947204
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	−0.615630	−	0.788035i	$-0.711098\pi$
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	0.990274	+	0.139134i	$0.0444318\pi$
$644$		0			0
$645$	63.0000			2.48062
$646$	−1.00000	+	1.73205i	−0.0393445	+	0.0681466i
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$	13.5000	+	23.3827i	0.530330	+	0.918559i
$649$	12.0000			0.471041
$650$	14.0000	−	3.46410i	0.549125	−	0.135873i
$651$		0			0
$652$	−0.500000	−	0.866025i	−0.0195815	−	0.0339162i
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$	10.5000	−	18.1865i	0.410582	−	0.711150i
$655$	15.0000			0.586098
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$	39.0000	−	67.5500i	1.52153	−	2.63538i
$658$		0			0
$659$	−14.5000	+	25.1147i	−0.564840	+	0.978331i	0.432225	+	0.901766i	$0.357729\pi$
$659$	−14.5000	+	25.1147i	−0.564840	+	0.978331i	−0.997065	+	0.0765653i	$0.975605\pi$
$660$	13.5000	+	23.3827i	0.525487	+	0.910170i
$661$	4.50000	+	7.79423i	0.175030	+	0.303160i	0.940172	−	0.340701i	$-0.110665\pi$
$661$	4.50000	+	7.79423i	0.175030	+	0.303160i	−0.765142	+	0.643862i	$0.777331\pi$
$662$	−29.0000			−1.12712
$663$	−6.00000	+	20.7846i	−0.233021	+	0.807207i
$664$		0			0
$665$		0			0
$666$	−6.00000	−	10.3923i	−0.232495	−	0.402694i
$667$		0			0
$668$	13.0000			0.502985
$669$	−13.5000	+	23.3827i	−0.521940	+	0.904027i
$670$	4.50000	−	7.79423i	0.173850	−	0.301117i
$671$	39.0000			1.50558
$672$		0			0
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	0.925832	+	0.377934i	$0.123365\pi$
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	−0.135615	+	0.990762i	$0.543301\pi$
$674$	−7.00000	−	12.1244i	−0.269630	−	0.467013i
$675$	−36.0000			−1.38564
$676$	−11.5000	+	6.06218i	−0.442308	+	0.233161i
$677$	7.00000			0.269032			0.134516	−	0.990911i	$-0.457052\pi$
$677$	7.00000			0.269032			0.134516	+	0.990911i	$0.457052\pi$
$678$	22.5000	+	38.9711i	0.864107	+	1.49668i
$679$		0			0
$680$	−9.00000	+	15.5885i	−0.345134	+	0.597790i
$681$	12.0000			0.459841
$682$	4.50000	−	7.79423i	0.172314	−	0.298456i
$683$	−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	$0.240403\pi$
$684$	6.00000			0.229416
$685$	−15.0000	+	25.9808i	−0.573121	+	0.992674i
$686$		0			0
$687$	−19.5000	−	33.7750i	−0.743971	−	1.28860i
$688$	7.00000			0.266872
$689$	−3.00000	+	10.3923i	−0.114291	+	0.395915i
$690$		0			0
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	0.901557	−	0.432660i	$-0.142425\pi$
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	−0.825473	+	0.564441i	$0.809092\pi$
$692$	9.50000	+	16.4545i	0.361136	+	0.625506i
$693$		0			0
$694$	−8.00000			−0.303676
$695$	22.5000	−	38.9711i	0.853474	−	1.47826i
$696$	−31.5000	+	54.5596i	−1.19400	+	2.06808i
$697$	−6.00000			−0.227266
$698$	−11.5000	+	19.9186i	−0.435281	+	0.753930i
$699$	−31.5000	−	54.5596i	−1.19144	−	2.06363i
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	−31.5000	+	7.79423i	−1.18889	+	0.294174i
$703$	−2.00000			−0.0754314
$704$	10.5000	+	18.1865i	0.395734	+	0.685431i
$705$	4.50000	+	7.79423i	0.169480	+	0.293548i
$706$	12.5000	−	21.6506i	0.470444	−	0.814832i
$707$		0			0
$708$	6.00000	−	10.3923i	0.225494	−	0.390567i
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	−0.950628	−	0.310334i	$-0.899559\pi$
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	0.744071	+	0.668101i	$0.232892\pi$
$710$	39.0000			1.46364
$711$	9.00000	−	15.5885i	0.337526	−	0.584613i
$712$	9.00000	+	15.5885i	0.337289	+	0.584202i
$713$		0			0
$714$		0			0
$715$	−31.5000	+	7.79423i	−1.17803	+	0.291488i
$716$	−17.0000			−0.635320
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$	−8.50000	−	14.7224i	−0.317217	−	0.549436i
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	−0.769832	−	0.638247i	$-0.779660\pi$
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	0.937654	+	0.347571i	$0.112993\pi$
$720$	−18.0000			−0.670820
$721$		0			0
$722$	9.00000	−	15.5885i	0.334945	−	0.580142i
$723$	78.0000			2.90085
$724$	−11.0000	+	19.0526i	−0.408812	+	0.708083i
$725$	−14.0000	−	24.2487i	−0.519947	−	0.900575i
$726$	−3.00000	−	5.19615i	−0.111340	−	0.192847i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	19.5000	+	33.7750i	0.721727	+	1.25007i
$731$	−7.00000	−	12.1244i	−0.258904	−	0.448435i
$732$	19.5000	−	33.7750i	0.720741	−	1.24836i
$733$	−9.00000			−0.332423			−0.166211	−	0.986090i	$-0.553153\pi$
$733$	−9.00000			−0.332423			−0.166211	+	0.986090i	$0.553153\pi$
$734$	15.5000	−	26.8468i	0.572115	−	0.990933i
$735$		0			0
$736$		0			0
$737$	−4.50000	+	7.79423i	−0.165760	+	0.287104i
$738$	−9.00000	−	15.5885i	−0.331295	−	0.573819i
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	0.856683	−	0.515844i	$-0.172522\pi$
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	−0.875075	+	0.483987i	$0.839188\pi$
$740$	−6.00000			−0.220564
$741$	−3.00000	+	10.3923i	−0.110208	+	0.381771i
$742$		0			0
$743$	−25.5000	−	44.1673i	−0.935504	−	1.62034i	−0.773732	−	0.633513i	$-0.781612\pi$
$743$	−25.5000	−	44.1673i	−0.935504	−	1.62034i	−0.161772	−	0.986828i	$-0.551721\pi$
$744$	−13.5000	−	23.3827i	−0.494934	−	0.857251i
$745$	−22.5000	+	38.9711i	−0.824336	+	1.42779i
$746$	−9.00000			−0.329513
$747$		0			0
$748$	3.00000	−	5.19615i	0.109691	−	0.189990i
$749$		0			0
$750$	−4.50000	+	7.79423i	−0.164317	+	0.284605i
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	−0.999921	−	0.0125942i	$-0.995991\pi$
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	0.489053	−	0.872254i	$-0.337342\pi$
$752$	0.500000	+	0.866025i	0.0182331	+	0.0315807i
$753$	69.0000			2.51450
$754$	−17.5000	−	18.1865i	−0.637312	−	0.662314i
$755$	−63.0000			−2.29280
$756$		0			0
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	0.837478	−	0.546471i	$-0.184029\pi$
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	−0.891997	+	0.452042i	$0.850696\pi$
$758$	16.5000	−	28.5788i	0.599307	−	1.03803i
$759$		0			0
$760$	−4.50000	+	7.79423i	−0.163232	+	0.282726i
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	−0.772863	−	0.634573i	$-0.781176\pi$
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	0.935988	+	0.352032i	$0.114509\pi$
$762$	−33.0000			−1.19546
$763$		0			0
$764$	−8.50000	−	14.7224i	−0.307519	−	0.532639i
$765$	18.0000	+	31.1769i	0.650791	+	1.12720i
$766$	−21.0000			−0.758761
$767$	10.0000	+	10.3923i	0.361079	+	0.375244i
$768$	51.0000			1.84030
$769$	−9.50000	−	16.4545i	−0.342579	−	0.593364i	0.642332	−	0.766426i	$-0.277967\pi$
$769$	−9.50000	−	16.4545i	−0.342579	−	0.593364i	−0.984911	+	0.173063i	$0.944634\pi$
$770$		0			0
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$	−7.00000			−0.251936
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$	21.0000	−	36.3731i	0.754829	−	1.30740i
$775$	12.0000			0.431053
$776$	−7.50000	+	12.9904i	−0.269234	+	0.466328i
$777$		0			0
$778$	16.5000	+	28.5788i	0.591554	+	1.02460i
$779$	−3.00000			−0.107486
$780$	−9.00000	+	31.1769i	−0.322252	+	1.11631i
$781$	−39.0000			−1.39553
$782$		0			0
$783$	31.5000	+	54.5596i	1.12572	+	1.94980i
$784$		0			0
$785$	57.0000			2.03442
$786$	7.50000	−	12.9904i	0.267516	−	0.463352i
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	−0.630905	−	0.775860i	$-0.717316\pi$
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	0.987367	+	0.158450i	$0.0506498\pi$
$788$	1.00000			0.0356235
$789$	−40.5000	+	70.1481i	−1.44184	+	2.49734i
$790$	4.50000	+	7.79423i	0.160103	+	0.277306i
$791$		0			0
$792$	54.0000			1.91881
$793$	32.5000	+	33.7750i	1.15411	+	1.19939i
$794$	−1.00000			−0.0354887
$795$	13.5000	+	23.3827i	0.478796	+	0.829298i
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	−1.50000	+	2.59808i	−0.0531327	+	0.0920286i	−0.891368	−	0.453279i	$-0.850254\pi$
$797$	−1.50000	+	2.59808i	−0.0531327	+	0.0920286i	0.838236	+	0.545308i	$0.183587\pi$
$798$		0			0
$799$	1.00000	−	1.73205i	0.0353775	−	0.0612756i
$800$	−10.0000	+	17.3205i	−0.353553	+	0.612372i
$801$	36.0000			1.27200
$802$	1.00000	−	1.73205i	0.0353112	−	0.0611608i
$803$	−19.5000	−	33.7750i	−0.688140	−	1.19189i
$804$	4.50000	+	7.79423i	0.158703	+	0.274881i
$805$		0			0
$806$	10.5000	−	2.59808i	0.369847	−	0.0915133i
$807$	−54.0000			−1.90089
$808$	−7.50000	−	12.9904i	−0.263849	−	0.457000i
$809$	−5.50000	−	9.52628i	−0.193370	−	0.334926i	0.752995	−	0.658026i	$-0.228608\pi$
$809$	−5.50000	−	9.52628i	−0.193370	−	0.334926i	−0.946365	+	0.323100i	$0.895275\pi$
$810$	−13.5000	+	23.3827i	−0.474342	+	0.821584i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$		0			0
$813$	−24.0000	+	41.5692i	−0.841717	+	1.45790i
$814$	−6.00000			−0.210300
$815$	1.50000	−	2.59808i	0.0525427	−	0.0910066i
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	−3.50000	−	6.06218i	−0.122449	−	0.212089i
$818$	14.0000			0.489499
$819$		0			0
$820$	−9.00000			−0.314294
$821$	27.0000	+	46.7654i	0.942306	+	1.63212i	0.761056	+	0.648686i	$0.224681\pi$
$821$	27.0000	+	46.7654i	0.942306	+	1.63212i	0.181250	+	0.983437i	$0.441986\pi$
$822$	15.0000	+	25.9808i	0.523185	+	0.906183i
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	−15.0000			−0.522550
$825$	−18.0000	+	31.1769i	−0.626680	+	1.08544i
$826$		0			0
$827$	4.00000			0.139094			0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000			0.139094			0.0695468	+	0.997579i	$0.477845\pi$
$828$		0			0
$829$	−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
$831$	−66.0000			−2.28951
$832$	−7.00000	+	24.2487i	−0.242681	+	0.840673i
$833$		0			0
$834$	−22.5000	−	38.9711i	−0.779111	−	1.34946i
$835$	19.5000	+	33.7750i	0.674825	+	1.16883i
$836$	1.50000	−	2.59808i	0.0518786	−	0.0898563i
$837$	−27.0000			−0.933257
$838$	12.5000	−	21.6506i	0.431805	−	0.747909i
$839$	−18.5000	+	32.0429i	−0.638691	+	1.10625i	0.347029	+	0.937854i	$0.387190\pi$
$839$	−18.5000	+	32.0429i	−0.638691	+	1.10625i	−0.985720	+	0.168391i	$0.946143\pi$
$840$		0			0
$841$	−10.0000	+	17.3205i	−0.344828	+	0.597259i
$842$	−9.00000	−	15.5885i	−0.310160	−	0.537214i
$843$	−27.0000	−	46.7654i	−0.929929	−	1.61068i
$844$	−7.00000			−0.240950
$845$	−33.0000	−	20.7846i	−1.13523	−	0.715012i
$846$	6.00000			0.206284
$847$		0			0
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	1.50000	−	2.59808i	0.0514799	−	0.0891657i
$850$	−8.00000			−0.274398
$851$		0			0
$852$	−19.5000	+	33.7750i	−0.668059	+	1.15711i
$853$	−6.00000			−0.205436			−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000			−0.205436			−0.102718	+	0.994711i	$0.532754\pi$
$854$		0			0
$855$	9.00000	+	15.5885i	0.307794	+	0.533114i
$856$	12.0000	+	20.7846i	0.410152	+	0.710403i
$857$	−33.0000			−1.12726			−0.563629	−	0.826028i	$-0.690595\pi$
$857$	−33.0000			−1.12726			−0.563629	+	0.826028i	$0.690595\pi$
$858$	−9.00000	+	31.1769i	−0.307255	+	1.06436i
$859$	25.0000			0.852989			0.426494	−	0.904490i	$-0.359748\pi$
$859$	25.0000			0.852989			0.426494	+	0.904490i	$0.359748\pi$
$860$	−10.5000	−	18.1865i	−0.358047	−	0.620156i
$861$		0			0
$862$	−4.50000	+	7.79423i	−0.153271	+	0.265472i
$863$	37.0000			1.25949			0.629747	−	0.776800i	$-0.283158\pi$
$863$	37.0000			1.25949			0.629747	+	0.776800i	$0.283158\pi$
$864$	22.5000	−	38.9711i	0.765466	−	1.32583i
$865$	−28.5000	+	49.3634i	−0.969029	+	1.67841i
$866$	27.0000			0.917497
$867$	−19.5000	+	33.7750i	−0.662255	+	1.14706i
$868$		0			0
$869$	−4.50000	−	7.79423i	−0.152652	−	0.264401i
$870$	−63.0000			−2.13590
$871$	−10.5000	+	2.59808i	−0.355779	+	0.0880325i
$872$	−21.0000			−0.711150
$873$	15.0000	+	25.9808i	0.507673	+	0.879316i
$874$		0			0
$875$		0			0
$876$	−39.0000			−1.31769
$877$	22.5000	−	38.9711i	0.759771	−	1.31596i	−0.183196	−	0.983076i	$-0.558644\pi$
$877$	22.5000	−	38.9711i	0.759771	−	1.31596i	0.942967	−	0.332886i	$-0.108022\pi$
$878$	8.00000	−	13.8564i	0.269987	−	0.467631i
$879$	−33.0000			−1.11306
$880$	−4.50000	+	7.79423i	−0.151695	+	0.262743i
$881$	−7.50000	−	12.9904i	−0.252681	−	0.437657i	0.711582	−	0.702603i	$-0.247979\pi$
$881$	−7.50000	−	12.9904i	−0.252681	−	0.437657i	−0.964263	+	0.264946i	$0.914646\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	7.00000	−	1.73205i	0.235435	−	0.0582552i
$885$	36.0000			1.21013
$886$	5.50000	+	9.52628i	0.184776	+	0.320042i
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$	−9.00000	+	15.5885i	−0.302020	+	0.523114i
$889$		0			0
$890$	−9.00000	+	15.5885i	−0.301681	+	0.522526i
$891$	13.5000	−	23.3827i	0.452267	−	0.783349i
$892$	9.00000			0.301342
$893$	0.500000	−	0.866025i	0.0167319	−	0.0289804i
$894$	22.5000	+	38.9711i	0.752513	+	1.30339i
$895$	−25.5000	−	44.1673i	−0.852371	−	1.47635i
$896$		0			0
$897$		0			0
$898$	15.0000			0.500556
$899$	−10.5000	−	18.1865i	−0.350195	−	0.606555i
$900$	12.0000	+	20.7846i	0.400000	+	0.692820i
$901$	3.00000	−	5.19615i	0.0999445	−	0.173109i
$902$	−9.00000			−0.299667
$903$		0			0
$904$	22.5000	−	38.9711i	0.748339	−	1.29616i
$905$	−66.0000			−2.19391
$906$	−31.5000	+	54.5596i	−1.04652	+	1.81262i
$907$	23.5000	+	40.7032i	0.780305	+	1.35153i	0.931764	+	0.363064i	$0.118269\pi$
$907$	23.5000	+	40.7032i	0.780305	+	1.35153i	−0.151460	+	0.988463i	$0.548397\pi$
$908$	−2.00000	−	3.46410i	−0.0663723	−	0.114960i
$909$	−30.0000			−0.995037
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	1.50000	+	2.59808i	0.0496700	+	0.0860309i
$913$		0			0
$914$	9.00000	−	15.5885i	0.297694	−	0.515620i
$915$	117.000			3.86790
$916$	−6.50000	+	11.2583i	−0.214766	+	0.371986i
$917$		0			0
$918$	18.0000			0.594089
$919$	12.5000	−	21.6506i	0.412337	−	0.714189i	−0.582808	−	0.812610i	$-0.698046\pi$
$919$	12.5000	−	21.6506i	0.412337	−	0.714189i	0.995145	+	0.0984214i	$0.0313793\pi$
$920$		0			0
$921$	18.0000	+	31.1769i	0.593120	+	1.02731i
$922$	35.0000			1.15266
$923$	−32.5000	−	33.7750i	−1.06975	−	1.11172i
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	4.00000	+	6.92820i	0.131448	+	0.227675i
$927$	−15.0000	+	25.9808i	−0.492665	+	0.853320i
$928$	35.0000			1.14893
$929$	6.50000	−	11.2583i	0.213258	−	0.369374i	−0.739474	−	0.673185i	$-0.764926\pi$
$929$	6.50000	−	11.2583i	0.213258	−	0.369374i	0.952732	+	0.303811i	$0.0982592\pi$
$930$	13.5000	−	23.3827i	0.442682	−	0.766748i
$931$		0			0
$932$	−10.5000	+	18.1865i	−0.343939	+	0.595720i
$933$	−13.5000	−	23.3827i	−0.441970	−	0.765515i
$934$	3.50000	+	6.06218i	0.114523	+	0.198361i
$935$	18.0000			0.588663
$936$	45.0000	+	46.7654i	1.47087	+	1.52857i
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$		0			0
$939$	28.5000	+	49.3634i	0.930062	+	1.61092i
$940$	1.50000	−	2.59808i	0.0489246	−	0.0847399i
$941$	−17.0000			−0.554184			−0.277092	−	0.960843i	$-0.589371\pi$
$941$	−17.0000			−0.554184			−0.277092	+	0.960843i	$0.589371\pi$
$942$	28.5000	−	49.3634i	0.928580	−	1.60835i
$943$		0			0
$944$	4.00000			0.130189
$945$		0			0
$946$	−10.5000	−	18.1865i	−0.341384	−	0.591295i
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$	−9.00000			−0.292306
$949$	13.0000	−	45.0333i	0.421998	−	1.46184i
$950$	−4.00000			−0.129777
$951$	−13.5000	−	23.3827i	−0.437767	−	0.758236i
$952$		0			0
$953$	16.5000	−	28.5788i	0.534487	−	0.925759i	−0.464701	−	0.885468i	$-0.653838\pi$
$953$	16.5000	−	28.5788i	0.534487	−	0.925759i	0.999188	−	0.0402915i	$-0.0128286\pi$
$954$	18.0000			0.582772
$955$	25.5000	−	44.1673i	0.825161	−	1.42922i
$956$	−2.00000	+	3.46410i	−0.0646846	+	0.112037i
$957$	63.0000			2.03650
$958$	17.5000	−	30.3109i	0.565399	−	0.979300i
$959$		0			0
$960$	31.5000	+	54.5596i	1.01666	+	1.76090i
$961$	−22.0000			−0.709677
$962$	−5.00000	−	5.19615i	−0.161206	−	0.167531i
$963$	48.0000			1.54678
$964$	−13.0000	−	22.5167i	−0.418702	−	0.725213i
$965$	−10.5000	−	18.1865i	−0.338007	−	0.585445i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−3.00000	+	5.19615i	−0.0964237	+	0.167011i
$969$	3.00000	−	5.19615i	0.0963739	−	0.166924i
$970$	−15.0000			−0.481621
$971$	0.500000	−	0.866025i	0.0160458	−	0.0277921i	−0.857891	−	0.513832i	$-0.828226\pi$
$971$	0.500000	−	0.866025i	0.0160458	−	0.0277921i	0.873937	+	0.486040i	$0.161559\pi$
$972$		0			0
$973$		0			0
$974$	16.0000			0.512673
$975$	−42.0000	+	10.3923i	−1.34508	+	0.332820i
$976$	13.0000			0.416120
$977$	2.50000	+	4.33013i	0.0799821	+	0.138533i	0.903242	−	0.429132i	$-0.141180\pi$
$977$	2.50000	+	4.33013i	0.0799821	+	0.138533i	−0.823260	+	0.567665i	$0.807847\pi$
$978$	−1.50000	−	2.59808i	−0.0479647	−	0.0830773i
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$	−21.0000	+	36.3731i	−0.670478	+	1.16130i
$982$	−7.50000	+	12.9904i	−0.239335	+	0.414540i
$983$	47.0000			1.49907			0.749534	−	0.661966i	$-0.230278\pi$
$983$	47.0000			1.49907			0.749534	+	0.661966i	$0.230278\pi$
$984$	−13.5000	+	23.3827i	−0.430364	+	0.745413i
$985$	1.50000	+	2.59808i	0.0477940	+	0.0827816i
$986$	7.00000	+	12.1244i	0.222925	+	0.386118i
$987$		0			0
$988$	3.50000	−	0.866025i	0.111350	−	0.0275519i
$989$		0			0
$990$	27.0000	+	46.7654i	0.858116	+	1.48630i
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	0.744124	−	0.668042i	$-0.232867\pi$
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	−0.950603	+	0.310409i	$0.899534\pi$
$992$	−7.50000	+	12.9904i	−0.238125	+	0.412445i
$993$	87.0000			2.76086
$994$		0			0
$995$	30.0000	−	51.9615i	0.951064	−	1.64729i
$996$		0			0
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	−0.881426	−	0.472322i	$-0.843416\pi$
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	0.849756	+	0.527176i	$0.176749\pi$
$998$	15.5000	+	26.8468i	0.490644	+	0.849820i
$999$	9.00000	+	15.5885i	0.284747	+	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.b.393.1		2
7.2	even	3		91.2.g.a.81.1	yes	2
7.3	odd	6		637.2.h.a.471.1		2
7.4	even	3		91.2.h.a.16.1	yes	2
7.5	odd	6		637.2.g.a.263.1		2
7.6	odd	2		637.2.f.a.393.1		2
13.3	even	3		8281.2.a.i.1.1		1
13.9	even	3	inner	637.2.f.b.295.1		2
13.10	even	6		8281.2.a.c.1.1		1
21.2	odd	6		819.2.n.c.172.1		2
21.11	odd	6		819.2.s.a.289.1		2
91.9	even	3		91.2.h.a.74.1	yes	2
91.16	even	3		1183.2.e.a.508.1		2
91.23	even	6		1183.2.e.c.508.1		2
91.48	odd	6		637.2.f.a.295.1		2
91.55	odd	6		8281.2.a.j.1.1		1
91.61	odd	6		637.2.h.a.165.1		2
91.62	odd	6		8281.2.a.g.1.1		1
91.74	even	3		91.2.g.a.9.1	✓	2
91.81	even	3		1183.2.e.a.170.1		2
91.87	odd	6		637.2.g.a.373.1		2
91.88	even	6		1183.2.e.c.170.1		2
273.74	odd	6		819.2.n.c.100.1		2
273.191	odd	6		819.2.s.a.802.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.a.9.1	✓	2	91.74	even	3
91.2.g.a.81.1	yes	2	7.2	even	3
91.2.h.a.16.1	yes	2	7.4	even	3
91.2.h.a.74.1	yes	2	91.9	even	3
637.2.f.a.295.1		2	91.48	odd	6
637.2.f.a.393.1		2	7.6	odd	2
637.2.f.b.295.1		2	13.9	even	3	inner
637.2.f.b.393.1		2	1.1	even	1	trivial
637.2.g.a.263.1		2	7.5	odd	6
637.2.g.a.373.1		2	91.87	odd	6
637.2.h.a.165.1		2	91.61	odd	6
637.2.h.a.471.1		2	7.3	odd	6
819.2.n.c.100.1		2	273.74	odd	6
819.2.n.c.172.1		2	21.2	odd	6
819.2.s.a.289.1		2	21.11	odd	6
819.2.s.a.802.1		2	273.191	odd	6
1183.2.e.a.170.1		2	91.81	even	3
1183.2.e.a.508.1		2	91.16	even	3
1183.2.e.c.170.1		2	91.88	even	6
1183.2.e.c.508.1		2	91.23	even	6
8281.2.a.c.1.1		1	13.10	even	6
8281.2.a.g.1.1		1	91.62	odd	6
8281.2.a.i.1.1		1	13.3	even	3
8281.2.a.j.1.1		1	91.55	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(1.50000 - 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +3.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} +(4.50000 + 7.79423i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +6.00000 q^{18} +(0.500000 - 0.866025i) q^{19} +(1.50000 - 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(-4.50000 - 7.79423i) q^{24} +4.00000 q^{25} +(3.50000 - 0.866025i) q^{26} -9.00000 q^{27} +(-3.50000 - 6.06218i) q^{29} +(4.50000 - 7.79423i) q^{30} +3.00000 q^{31} +(-2.50000 + 4.33013i) q^{32} +(-4.50000 + 7.79423i) q^{33} -2.00000 q^{34} +(3.00000 + 5.19615i) q^{36} +(-1.00000 - 1.73205i) q^{37} -1.00000 q^{38} +(-10.5000 + 2.59808i) q^{39} -9.00000 q^{40} +(-1.50000 - 2.59808i) q^{41} +(3.50000 - 6.06218i) q^{43} +3.00000 q^{44} +(-9.00000 + 15.5885i) q^{45} +1.00000 q^{47} +(-1.50000 + 2.59808i) q^{48} +(-2.00000 - 3.46410i) q^{50} +6.00000 q^{51} +(2.50000 + 2.59808i) q^{52} +3.00000 q^{53} +(4.50000 + 7.79423i) q^{54} +(4.50000 + 7.79423i) q^{55} +3.00000 q^{57} +(-3.50000 + 6.06218i) q^{58} +(2.00000 - 3.46410i) q^{59} +9.00000 q^{60} +(6.50000 - 11.2583i) q^{61} +(-1.50000 - 2.59808i) q^{62} +7.00000 q^{64} +(-3.00000 + 10.3923i) q^{65} +9.00000 q^{66} +(1.50000 + 2.59808i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-6.50000 + 11.2583i) q^{71} +(9.00000 - 15.5885i) q^{72} -13.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(6.00000 + 10.3923i) q^{75} +(-0.500000 - 0.866025i) q^{76} +(7.50000 + 7.79423i) q^{78} -3.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(3.00000 - 5.19615i) q^{85} -7.00000 q^{86} +(10.5000 - 18.1865i) q^{87} +(-4.50000 - 7.79423i) q^{88} +(-3.00000 - 5.19615i) q^{89} +18.0000 q^{90} +(4.50000 + 7.79423i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(1.50000 - 2.59808i) q^{95} -15.0000 q^{96} +(2.50000 - 4.33013i) q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} + q^{4} + 6 q^{5} + 3 q^{6} - 6 q^{8} - 6 q^{9} - 3 q^{10} + 3 q^{11} + 6 q^{12} - 2 q^{13} + 9 q^{15} + q^{16} + 2 q^{17} + 12 q^{18} + q^{19} + 3 q^{20} + 3 q^{22} - 9 q^{24}+ \cdots - 36 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 + q^4 + 6 * q^5 + 3 * q^6 - 6 * q^8 - 6 * q^9 - 3 * q^10 + 3 * q^11 + 6 * q^12 - 2 * q^13 + 9 * q^15 + q^16 + 2 * q^17 + 12 * q^18 + q^19 + 3 * q^20 + 3 * q^22 - 9 * q^24 + 8 * q^25 + 7 * q^26 - 18 * q^27 - 7 * q^29 + 9 * q^30 + 6 * q^31 - 5 * q^32 - 9 * q^33 - 4 * q^34 + 6 * q^36 - 2 * q^37 - 2 * q^38 - 21 * q^39 - 18 * q^40 - 3 * q^41 + 7 * q^43 + 6 * q^44 - 18 * q^45 + 2 * q^47 - 3 * q^48 - 4 * q^50 + 12 * q^51 + 5 * q^52 + 6 * q^53 + 9 * q^54 + 9 * q^55 + 6 * q^57 - 7 * q^58 + 4 * q^59 + 18 * q^60 + 13 * q^61 - 3 * q^62 + 14 * q^64 - 6 * q^65 + 18 * q^66 + 3 * q^67 - 2 * q^68 - 13 * q^71 + 18 * q^72 - 26 * q^73 - 2 * q^74 + 12 * q^75 - q^76 + 15 * q^78 - 6 * q^79 + 3 * q^80 - 9 * q^81 - 3 * q^82 + 6 * q^85 - 14 * q^86 + 21 * q^87 - 9 * q^88 - 6 * q^89 + 36 * q^90 + 9 * q^93 - q^94 + 3 * q^95 - 30 * q^96 + 5 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more