LMFDB - Embedded newform 294.2.e.a.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,2,Mod(67,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,-1,-1,-2] 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:	$2.34760181943$
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 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.2.e.a.79.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-0.500000 - 0.866025i) q^{12} -6.00000 q^{13} +2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} +2.00000 q^{20} -4.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-1.00000 - 1.73205i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(5.00000 + 8.66025i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(3.00000 - 5.19615i) q^{39} +(-1.00000 - 1.73205i) q^{40} +6.00000 q^{41} -4.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(-1.00000 + 1.73205i) q^{45} +(-4.00000 + 6.92820i) q^{46} +1.00000 q^{48} -1.00000 q^{50} +(1.00000 + 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-0.500000 - 0.866025i) q^{54} -8.00000 q^{55} +4.00000 q^{57} +(1.00000 + 1.73205i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(3.00000 + 5.19615i) q^{61} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(2.00000 - 3.46410i) q^{66} +(-2.00000 + 3.46410i) q^{67} +(1.00000 + 1.73205i) q^{68} +8.00000 q^{69} +8.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(5.00000 - 8.66025i) q^{73} +(5.00000 - 8.66025i) q^{74} +(0.500000 + 0.866025i) q^{75} +4.00000 q^{76} -6.00000 q^{78} +(-1.00000 + 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +4.00000 q^{83} -4.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(1.00000 - 1.73205i) q^{87} +(2.00000 - 3.46410i) q^{88} +(-3.00000 - 5.19615i) q^{89} +2.00000 q^{90} +8.00000 q^{92} +(-4.00000 + 6.92820i) q^{95} +(-0.500000 - 0.866025i) q^{96} +14.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} - q^{9} - 2 q^{10} + 4 q^{11} - q^{12} - 12 q^{13} + 4 q^{15} - q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} - 8 q^{23} - q^{24}+ \cdots - 8 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 - q^9 - 2 * q^10 + 4 * q^11 - q^12 - 12 * q^13 + 4 * q^15 - q^16 + 2 * q^17 - q^18 - 4 * q^19 + 4 * q^20 - 8 * q^22 - 8 * q^23 - q^24 + q^25 + 6 * q^26 + 2 * q^27 - 4 * q^29 - 2 * q^30 - q^32 + 4 * q^33 - 4 * q^34 + 2 * q^36 + 10 * q^37 - 4 * q^38 + 6 * q^39 - 2 * q^40 + 12 * q^41 - 8 * q^43 + 4 * q^44 - 2 * q^45 - 8 * q^46 + 2 * q^48 - 2 * q^50 + 2 * q^51 + 6 * q^52 - 6 * q^53 - q^54 - 16 * q^55 + 8 * q^57 + 2 * q^58 + 4 * q^59 - 2 * q^60 + 6 * q^61 + 2 * q^64 + 12 * q^65 + 4 * q^66 - 4 * q^67 + 2 * q^68 + 16 * q^69 + 16 * q^71 - q^72 + 10 * q^73 + 10 * q^74 + q^75 + 8 * q^76 - 12 * q^78 - 2 * q^80 - q^81 - 6 * q^82 + 8 * q^83 - 8 * q^85 + 4 * q^86 + 2 * q^87 + 4 * q^88 - 6 * q^89 + 4 * q^90 + 16 * q^92 - 8 * q^95 - q^96 + 28 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−6.00000			−1.66410			−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000			−1.66410			−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$	−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	$0.0886875\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$	−4.00000			−0.852803
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	3.00000	+	5.19615i	0.588348	+	1.01905i
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	−1.00000	−	1.73205i	−0.182574	−	0.316228i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.00000	+	3.46410i	0.348155	+	0.603023i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	0.904194	+	0.427121i	$0.140472\pi$
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$	3.00000	−	5.19615i	0.480384	−	0.832050i
$40$	−1.00000	−	1.73205i	−0.158114	−	0.273861i
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$	−4.00000	+	6.92820i	−0.589768	+	1.02151i
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$	3.00000	−	5.19615i	0.416025	−	0.720577i
$53$	−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	$0.301865\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−8.00000			−1.07872
$56$		0			0
$57$	4.00000			0.529813
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$	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	$0.0828195\pi$
$60$	−1.00000	+	1.73205i	−0.129099	+	0.223607i
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	6.00000	+	10.3923i	0.744208	+	1.28901i
$66$	2.00000	−	3.46410i	0.246183	−	0.426401i
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$	8.00000			0.963087
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$	5.00000	−	8.66025i	0.581238	−	1.00673i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	4.00000			0.458831
$77$		0			0
$78$	−6.00000			−0.679366
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$	1.00000	−	1.73205i	0.107211	−	0.185695i
$88$	2.00000	−	3.46410i	0.213201	−	0.369274i
$89$	−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	$0.936344\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$	8.00000			0.834058
$93$		0			0
$94$		0			0
$95$	−4.00000	+	6.92820i	−0.410391	+	0.710819i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	14.0000			1.42148			0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$	1.00000	−	1.73205i	0.0990148	−	0.171499i
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	−6.00000			−0.588348
$105$		0			0
$106$	6.00000			0.582772
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	4.00000	+	6.92820i	0.381385	+	0.660578i
$111$	−10.0000			−0.949158
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$	−8.00000	+	13.8564i	−0.746004	+	1.29212i
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$	−4.00000			−0.368230
$119$		0			0
$120$	2.00000			0.182574
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	3.00000	−	5.19615i	0.271607	−	0.470438i
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$	6.00000	−	10.3923i	0.526235	−	0.911465i
$131$	−10.0000	−	17.3205i	−0.873704	−	1.51330i	−0.858137	−	0.513421i	$-0.828378\pi$
$131$	−10.0000	−	17.3205i	−0.873704	−	1.51330i	−0.0155672	−	0.999879i	$-0.504955\pi$
$132$	−4.00000			−0.348155
$133$		0			0
$134$	4.00000			0.345547
$135$	−1.00000	−	1.73205i	−0.0860663	−	0.149071i
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	−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	$0.307159\pi$
$138$	−4.00000	−	6.92820i	−0.340503	−	0.589768i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$		0			0
$142$	−4.00000	−	6.92820i	−0.335673	−	0.581402i
$143$	−12.0000	+	20.7846i	−1.00349	+	1.73810i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	2.00000	+	3.46410i	0.166091	+	0.287678i
$146$	−10.0000			−0.827606
$147$		0			0
$148$	−10.0000			−0.821995
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$	−2.00000	−	3.46410i	−0.162221	−	0.280976i
$153$	−2.00000			−0.161690
$154$		0			0
$155$		0			0
$156$	3.00000	+	5.19615i	0.240192	+	0.416025i
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	−0.993608	−	0.112884i	$-0.963991\pi$
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	0.594565	+	0.804048i	$0.297324\pi$
$158$		0			0
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	2.00000			0.158114
$161$		0			0
$162$	1.00000			0.0785674
$163$	−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
$165$	4.00000	−	6.92820i	0.311400	−	0.539360i
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		0			0
$169$	23.0000			1.76923
$170$	2.00000	+	3.46410i	0.153393	+	0.265684i
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	11.0000	+	19.0526i	0.836315	+	1.44854i	0.892956	+	0.450145i	$0.148628\pi$
$173$	11.0000	+	19.0526i	0.836315	+	1.44854i	−0.0566411	+	0.998395i	$0.518039\pi$
$174$	−2.00000			−0.151620
$175$		0			0
$176$	−4.00000			−0.301511
$177$	2.00000	+	3.46410i	0.150329	+	0.260378i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$	−1.00000	−	1.73205i	−0.0745356	−	0.129099i
$181$	18.0000			1.33793			0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$		0			0
$183$	−6.00000			−0.443533
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$	10.0000	−	17.3205i	0.735215	−	1.27343i
$186$		0			0
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$		0			0
$189$		0			0
$190$	8.00000			0.580381
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$	−12.0000			−0.859338
$196$		0			0
$197$	−10.0000			−0.712470			−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000			−0.712470			−0.356235	+	0.934396i	$0.615940\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−2.00000	−	3.46410i	−0.141069	−	0.244339i
$202$	2.00000			0.140720
$203$		0			0
$204$	−2.00000			−0.140028
$205$	−6.00000	−	10.3923i	−0.419058	−	0.725830i
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$	−4.00000	+	6.92820i	−0.278019	+	0.481543i
$208$	3.00000	+	5.19615i	0.208013	+	0.360288i
$209$	−16.0000			−1.10674
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	−4.00000	+	6.92820i	−0.274075	+	0.474713i
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	4.00000	+	6.92820i	0.272798	+	0.472500i
$216$	1.00000			0.0680414
$217$		0			0
$218$	−2.00000			−0.135457
$219$	5.00000	+	8.66025i	0.337869	+	0.585206i
$220$	4.00000	−	6.92820i	0.269680	−	0.467099i
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$	5.00000	+	8.66025i	0.335578	+	0.581238i
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$	7.00000	+	12.1244i	0.465633	+	0.806500i
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$	−2.00000	+	3.46410i	−0.132453	+	0.229416i
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	0.831092	−	0.556136i	$-0.187717\pi$
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	−0.897173	+	0.441679i	$0.854383\pi$
$230$	16.0000			1.05501
$231$		0			0
$232$	−2.00000			−0.131306
$233$	11.0000	+	19.0526i	0.720634	+	1.24817i	0.960746	+	0.277429i	$0.0894825\pi$
$233$	11.0000	+	19.0526i	0.720634	+	1.24817i	−0.240112	+	0.970745i	$0.577184\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$		0			0
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−1.00000	−	1.73205i	−0.0645497	−	0.111803i
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	−0.832019	−	0.554747i	$-0.812815\pi$
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	0.896435	+	0.443176i	$0.146148\pi$
$242$	−2.50000	+	4.33013i	−0.160706	+	0.278351i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−6.00000			−0.384111
$245$		0			0
$246$	6.00000			0.382546
$247$	12.0000	+	20.7846i	0.763542	+	1.32249i
$248$		0			0
$249$	−2.00000	+	3.46410i	−0.126745	+	0.219529i
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	−32.0000			−2.01182
$254$		0			0
$255$	2.00000	−	3.46410i	0.125245	−	0.216930i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.773427	−	0.633885i	$-0.781459\pi$
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.162247	−	0.986750i	$-0.551874\pi$
$258$	−4.00000			−0.249029
$259$		0			0
$260$	−12.0000			−0.744208
$261$	1.00000	+	1.73205i	0.0618984	+	0.107211i
$262$	−10.0000	+	17.3205i	−0.617802	+	1.07006i
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$	2.00000	+	3.46410i	0.123091	+	0.213201i
$265$	12.0000			0.737154
$266$		0			0
$267$	6.00000			0.367194
$268$	−2.00000	−	3.46410i	−0.122169	−	0.211604i
$269$	11.0000	−	19.0526i	0.670682	−	1.16166i	−0.307029	−	0.951700i	$-0.599335\pi$
$269$	11.0000	−	19.0526i	0.670682	−	1.16166i	0.977711	−	0.209955i	$-0.0673317\pi$
$270$	−1.00000	+	1.73205i	−0.0608581	+	0.105409i
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$	−4.00000	+	6.92820i	−0.240772	+	0.417029i
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$	2.00000	+	3.46410i	0.119952	+	0.207763i
$279$		0			0
$280$		0			0
$281$	26.0000			1.55103			0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000			1.55103			0.775515	+	0.631329i	$0.217490\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	−4.00000	+	6.92820i	−0.237356	+	0.411113i
$285$	−4.00000	−	6.92820i	−0.236940	−	0.410391i
$286$	24.0000			1.41915
$287$		0			0
$288$	1.00000			0.0589256
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	2.00000	−	3.46410i	0.117444	−	0.203419i
$291$	−7.00000	+	12.1244i	−0.410347	+	0.710742i
$292$	5.00000	+	8.66025i	0.292603	+	0.506803i
$293$	−30.0000			−1.75262			−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000			−1.75262			−0.876309	+	0.481749i	$0.840002\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$	5.00000	+	8.66025i	0.290619	+	0.503367i
$297$	2.00000	−	3.46410i	0.116052	−	0.201008i
$298$	−3.00000	+	5.19615i	−0.173785	+	0.301005i
$299$	24.0000	+	41.5692i	1.38796	+	2.40401i
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	−8.00000			−0.460348
$303$	−1.00000	−	1.73205i	−0.0574485	−	0.0995037i
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	6.00000	−	10.3923i	0.343559	−	0.595062i
$306$	1.00000	+	1.73205i	0.0571662	+	0.0990148i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$		0			0
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	−0.956864	−	0.290537i	$-0.906166\pi$
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	0.730044	+	0.683400i	$0.239499\pi$
$312$	3.00000	−	5.19615i	0.169842	−	0.294174i
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$	10.0000			0.564333
$315$		0			0
$316$		0			0
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$	−3.00000	+	5.19615i	−0.168232	+	0.291386i
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$	−1.00000	−	1.73205i	−0.0559017	−	0.0968246i
$321$	12.0000			0.669775
$322$		0			0
$323$	−8.00000			−0.445132
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−3.00000	+	5.19615i	−0.166410	+	0.288231i
$326$	−10.0000	+	17.3205i	−0.553849	+	0.959294i
$327$	1.00000	+	1.73205i	0.0553001	+	0.0957826i
$328$	6.00000			0.331295
$329$		0			0
$330$	−8.00000			−0.440386
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−2.00000	+	3.46410i	−0.109764	+	0.190117i
$333$	5.00000	−	8.66025i	0.273998	−	0.474579i
$334$	−4.00000	−	6.92820i	−0.218870	−	0.379094i
$335$	8.00000			0.437087
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	−11.5000	−	19.9186i	−0.625518	−	1.08343i
$339$	7.00000	−	12.1244i	0.380188	−	0.658505i
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$		0			0
$342$	4.00000			0.216295
$343$		0			0
$344$	−4.00000			−0.215666
$345$	−8.00000	−	13.8564i	−0.430706	−	0.746004i
$346$	11.0000	−	19.0526i	0.591364	−	1.02427i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$	1.00000	+	1.73205i	0.0536056	+	0.0928477i
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$		0			0
$351$	−6.00000			−0.320256
$352$	2.00000	+	3.46410i	0.106600	+	0.184637i
$353$	−15.0000	+	25.9808i	−0.798369	+	1.38282i	0.122308	+	0.992492i	$0.460970\pi$
$353$	−15.0000	+	25.9808i	−0.798369	+	1.38282i	−0.920677	+	0.390324i	$0.872363\pi$
$354$	2.00000	−	3.46410i	0.106299	−	0.184115i
$355$	−8.00000	−	13.8564i	−0.424596	−	0.735422i
$356$	6.00000			0.317999
$357$		0			0
$358$	−12.0000			−0.634220
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	0.952063	−	0.305903i	$-0.0989582\pi$
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	−0.740951	+	0.671559i	$0.765625\pi$
$360$	−1.00000	+	1.73205i	−0.0527046	+	0.0912871i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−9.00000	−	15.5885i	−0.473029	−	0.819311i
$363$	5.00000			0.262432
$364$		0			0
$365$	−20.0000			−1.04685
$366$	3.00000	+	5.19615i	0.156813	+	0.271607i
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	−0.0586798	−	0.998277i	$-0.518689\pi$
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	0.893873	−	0.448320i	$-0.147978\pi$
$368$	−4.00000	+	6.92820i	−0.208514	+	0.361158i
$369$	−3.00000	−	5.19615i	−0.156174	−	0.270501i
$370$	−20.0000			−1.03975
$371$		0			0
$372$		0			0
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	−0.996610	−	0.0822766i	$-0.973781\pi$
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	0.427051	−	0.904227i	$-0.359552\pi$
$374$	−4.00000	+	6.92820i	−0.206835	+	0.358249i
$375$	6.00000	−	10.3923i	0.309839	−	0.536656i
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−4.00000	−	6.92820i	−0.205196	−	0.355409i
$381$		0			0
$382$		0			0
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	2.00000			0.101797
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	−7.00000	+	12.1244i	−0.355371	+	0.615521i
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	−0.321716	−	0.946836i	$-0.604260\pi$
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	0.980842	−	0.194804i	$-0.0624070\pi$
$390$	6.00000	+	10.3923i	0.303822	+	0.526235i
$391$	−16.0000			−0.809155
$392$		0			0
$393$	20.0000			1.00887
$394$	5.00000	+	8.66025i	0.251896	+	0.436297i
$395$		0			0
$396$	2.00000	−	3.46410i	0.100504	−	0.174078i
$397$	3.00000	+	5.19615i	0.150566	+	0.260787i	0.931436	−	0.363906i	$-0.118557\pi$
$397$	3.00000	+	5.19615i	0.150566	+	0.260787i	−0.780870	+	0.624694i	$0.785224\pi$
$398$	−8.00000			−0.401004
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	−2.00000	+	3.46410i	−0.0997509	+	0.172774i
$403$		0			0
$404$	−1.00000	−	1.73205i	−0.0497519	−	0.0861727i
$405$	2.00000			0.0993808
$406$		0			0
$407$	40.0000			1.98273
$408$	1.00000	+	1.73205i	0.0495074	+	0.0857493i
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	0.454759	+	0.890614i	$0.349725\pi$
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	−0.998674	+	0.0514740i	$0.983608\pi$
$410$	−6.00000	+	10.3923i	−0.296319	+	0.513239i
$411$	−5.00000	−	8.66025i	−0.246632	−	0.427179i
$412$	−8.00000			−0.394132
$413$		0			0
$414$	8.00000			0.393179
$415$	−4.00000	−	6.92820i	−0.196352	−	0.340092i
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$	2.00000	−	3.46410i	0.0979404	−	0.169638i
$418$	8.00000	+	13.8564i	0.391293	+	0.677739i
$419$	36.0000			1.75872			0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000			1.75872			0.879358	+	0.476162i	$0.157972\pi$
$420$		0			0
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	−10.0000	−	17.3205i	−0.486792	−	0.843149i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$	8.00000			0.387601
$427$		0			0
$428$	12.0000			0.580042
$429$	−12.0000	−	20.7846i	−0.579365	−	1.00349i
$430$	4.00000	−	6.92820i	0.192897	−	0.334108i
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	−4.00000			−0.191785
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−16.0000	+	27.7128i	−0.765384	+	1.32568i
$438$	5.00000	−	8.66025i	0.238909	−	0.413803i
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$	−8.00000			−0.381385
$441$		0			0
$442$	12.0000			0.570782
$443$	2.00000	+	3.46410i	0.0950229	+	0.164584i	0.909618	−	0.415445i	$-0.136374\pi$
$443$	2.00000	+	3.46410i	0.0950229	+	0.164584i	−0.814595	+	0.580030i	$0.803041\pi$
$444$	5.00000	−	8.66025i	0.237289	−	0.410997i
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$	6.00000			0.283790
$448$		0			0
$449$	34.0000			1.60456			0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$	0.500000	+	0.866025i	0.0235702	+	0.0408248i
$451$	12.0000	−	20.7846i	0.565058	−	0.978709i
$452$	7.00000	−	12.1244i	0.329252	−	0.570282i
$453$	4.00000	+	6.92820i	0.187936	+	0.325515i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	4.00000			0.187317
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	−1.00000	+	1.73205i	−0.0467269	+	0.0809334i
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$	−8.00000	−	13.8564i	−0.373002	−	0.646058i
$461$	−22.0000			−1.02464			−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000			−1.02464			−0.512321	+	0.858794i	$0.671214\pi$
$462$		0			0
$463$	−32.0000			−1.48717			−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000			−1.48717			−0.743583	+	0.668644i	$0.766875\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	11.0000	−	19.0526i	0.509565	−	0.882593i
$467$	14.0000	+	24.2487i	0.647843	+	1.12210i	0.983637	+	0.180161i	$0.0576619\pi$
$467$	14.0000	+	24.2487i	0.647843	+	1.12210i	−0.335794	+	0.941935i	$0.609005\pi$
$468$	−6.00000			−0.277350
$469$		0			0
$470$		0			0
$471$	−5.00000	−	8.66025i	−0.230388	−	0.399043i
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$	−8.00000	+	13.8564i	−0.367840	+	0.637118i
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	−0.988861	−	0.148842i	$-0.952445\pi$
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	0.623332	+	0.781958i	$0.285779\pi$
$480$	−1.00000	+	1.73205i	−0.0456435	+	0.0790569i
$481$	−30.0000	−	51.9615i	−1.36788	−	2.36924i
$482$	−2.00000			−0.0910975
$483$		0			0
$484$	5.00000			0.227273
$485$	−14.0000	−	24.2487i	−0.635707	−	1.10108i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−4.00000	+	6.92820i	−0.181257	+	0.313947i	−0.942309	−	0.334744i	$-0.891350\pi$
$487$	−4.00000	+	6.92820i	−0.181257	+	0.313947i	0.761052	+	0.648691i	$0.224683\pi$
$488$	3.00000	+	5.19615i	0.135804	+	0.235219i
$489$	20.0000			0.904431
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$	−3.00000	−	5.19615i	−0.135250	−	0.234261i
$493$	−2.00000	+	3.46410i	−0.0900755	+	0.156015i
$494$	12.0000	−	20.7846i	0.539906	−	0.935144i
$495$	4.00000	+	6.92820i	0.179787	+	0.311400i
$496$		0			0
$497$		0			0
$498$	4.00000			0.179244
$499$	22.0000	+	38.1051i	0.984855	+	1.70582i	0.642578	+	0.766220i	$0.277865\pi$
$499$	22.0000	+	38.1051i	0.984855	+	1.70582i	0.342277	+	0.939599i	$0.388802\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$	−4.00000	+	6.92820i	−0.178707	+	0.309529i
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	4.00000			0.177998
$506$	16.0000	+	27.7128i	0.711287	+	1.23198i
$507$	−11.5000	+	19.9186i	−0.510733	+	0.884615i
$508$		0			0
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$	−4.00000			−0.177123
$511$		0			0
$512$	1.00000			0.0441942
$513$	−2.00000	−	3.46410i	−0.0883022	−	0.152944i
$514$	−15.0000	+	25.9808i	−0.661622	+	1.14596i
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$		0			0
$518$		0			0
$519$	−22.0000			−0.965693
$520$	6.00000	+	10.3923i	0.263117	+	0.455733i
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	−0.924229	−	0.381839i	$-0.875291\pi$
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	0.792797	+	0.609486i	$0.208624\pi$
$522$	1.00000	−	1.73205i	0.0437688	−	0.0758098i
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$	20.0000			0.873704
$525$		0			0
$526$	−24.0000			−1.04645
$527$		0			0
$528$	2.00000	−	3.46410i	0.0870388	−	0.150756i
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	−6.00000	−	10.3923i	−0.260623	−	0.451413i
$531$	−4.00000			−0.173585
$532$		0			0
$533$	−36.0000			−1.55933
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$	−12.0000	+	20.7846i	−0.518805	+	0.898597i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$	−22.0000			−0.948487
$539$		0			0
$540$	2.00000			0.0860663
$541$	−15.0000	−	25.9808i	−0.644900	−	1.11700i	−0.984325	−	0.176367i	$-0.943566\pi$
$541$	−15.0000	−	25.9808i	−0.644900	−	1.11700i	0.339424	−	0.940633i	$-0.389768\pi$
$542$		0			0
$543$	−9.00000	+	15.5885i	−0.386227	+	0.668965i
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−5.00000	−	8.66025i	−0.213589	−	0.369948i
$549$	3.00000	−	5.19615i	0.128037	−	0.221766i
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$	4.00000	+	6.92820i	0.170406	+	0.295151i
$552$	8.00000			0.340503
$553$		0			0
$554$	−10.0000			−0.424859
$555$	10.0000	+	17.3205i	0.424476	+	0.735215i
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	1.00000	−	1.73205i	0.0423714	−	0.0733893i	−0.844062	−	0.536246i	$-0.819842\pi$
$557$	1.00000	−	1.73205i	0.0423714	−	0.0733893i	0.886433	+	0.462856i	$0.153175\pi$
$558$		0			0
$559$	24.0000			1.01509
$560$		0			0
$561$	8.00000			0.337760
$562$	−13.0000	−	22.5167i	−0.548372	−	0.949808i
$563$	22.0000	−	38.1051i	0.927189	−	1.60594i	0.139188	−	0.990266i	$-0.455551\pi$
$563$	22.0000	−	38.1051i	0.927189	−	1.60594i	0.788002	−	0.615673i	$-0.211116\pi$
$564$		0			0
$565$	14.0000	+	24.2487i	0.588984	+	1.02015i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	8.00000			0.335673
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	−4.00000	+	6.92820i	−0.167542	+	0.290191i
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	−0.963827	−	0.266529i	$-0.914123\pi$
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	0.712735	+	0.701434i	$0.247456\pi$
$572$	−12.0000	−	20.7846i	−0.501745	−	0.869048i
$573$		0			0
$574$		0			0
$575$	−8.00000			−0.333623
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	17.0000	−	29.4449i	0.707719	−	1.22581i	−0.257982	−	0.966150i	$-0.583058\pi$
$577$	17.0000	−	29.4449i	0.707719	−	1.22581i	0.965701	−	0.259656i	$-0.0836092\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	−1.00000	−	1.73205i	−0.0415586	−	0.0719816i
$580$	−4.00000			−0.166091
$581$		0			0
$582$	14.0000			0.580319
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$	5.00000	−	8.66025i	0.206901	−	0.358364i
$585$	6.00000	−	10.3923i	0.248069	−	0.429669i
$586$	15.0000	+	25.9808i	0.619644	+	1.07326i
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$		0			0
$589$		0			0
$590$	4.00000	+	6.92820i	0.164677	+	0.285230i
$591$	5.00000	−	8.66025i	0.205673	−	0.356235i
$592$	5.00000	−	8.66025i	0.205499	−	0.355934i
$593$	9.00000	+	15.5885i	0.369586	+	0.640141i	0.989501	−	0.144528i	$-0.0461663\pi$
$593$	9.00000	+	15.5885i	0.369586	+	0.640141i	−0.619915	+	0.784669i	$0.712833\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	6.00000			0.245770
$597$	4.00000	+	6.92820i	0.163709	+	0.283552i
$598$	24.0000	−	41.5692i	0.981433	−	1.69989i
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	4.00000			0.162893
$604$	4.00000	+	6.92820i	0.162758	+	0.281905i
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$	−1.00000	+	1.73205i	−0.0406222	+	0.0703598i
$607$	24.0000	+	41.5692i	0.974130	+	1.68724i	0.682777	+	0.730627i	$0.260772\pi$
$607$	24.0000	+	41.5692i	0.974130	+	1.68724i	0.291353	+	0.956616i	$0.405895\pi$
$608$	4.00000			0.162221
$609$		0			0
$610$	−12.0000			−0.485866
$611$		0			0
$612$	1.00000	−	1.73205i	0.0404226	−	0.0700140i
$613$	21.0000	−	36.3731i	0.848182	−	1.46909i	−0.0346469	−	0.999400i	$-0.511031\pi$
$613$	21.0000	−	36.3731i	0.848182	−	1.46909i	0.882829	−	0.469695i	$-0.155636\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$	12.0000			0.483887
$616$		0			0
$617$	−22.0000			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$618$	4.00000	+	6.92820i	0.160904	+	0.278693i
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.0376891	+	0.999290i	$0.512000\pi$
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.846566	+	0.532284i	$0.821334\pi$
$620$		0			0
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$	8.00000			0.320771
$623$		0			0
$624$	−6.00000			−0.240192
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	5.00000	−	8.66025i	0.199840	−	0.346133i
$627$	8.00000	−	13.8564i	0.319489	−	0.553372i
$628$	−5.00000	−	8.66025i	−0.199522	−	0.345582i
$629$	20.0000			0.797452
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$		0			0
$636$	6.00000			0.237915
$637$		0			0
$638$	8.00000			0.316723
$639$	−4.00000	−	6.92820i	−0.158238	−	0.274075i
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$	−6.00000	−	10.3923i	−0.236801	−	0.410152i
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$	4.00000	+	6.92820i	0.157378	+	0.272587i
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−8.00000	−	13.8564i	−0.314027	−	0.543912i
$650$	6.00000			0.235339
$651$		0			0
$652$	20.0000			0.783260
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$	−20.0000	+	34.6410i	−0.781465	+	1.35354i
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	−10.0000			−0.390137
$658$		0			0
$659$	−28.0000			−1.09073			−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000			−1.09073			−0.545363	+	0.838200i	$0.683608\pi$
$660$	4.00000	+	6.92820i	0.155700	+	0.269680i
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$	2.00000	−	3.46410i	0.0777322	−	0.134636i
$663$	−6.00000	−	10.3923i	−0.233021	−	0.403604i
$664$	4.00000			0.155230
$665$		0			0
$666$	−10.0000			−0.387492
$667$	8.00000	+	13.8564i	0.309761	+	0.536522i
$668$	−4.00000	+	6.92820i	−0.154765	+	0.268060i
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	24.0000			0.926510
$672$		0			0
$673$	2.00000			0.0770943			0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000			0.0770943			0.0385472	+	0.999257i	$0.487727\pi$
$674$	−9.00000	−	15.5885i	−0.346667	−	0.600445i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−11.5000	+	19.9186i	−0.442308	+	0.766099i
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	0.639618	−	0.768693i	$-0.279092\pi$
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	−0.985517	+	0.169580i	$0.945759\pi$
$678$	−14.0000			−0.537667
$679$		0			0
$680$	−4.00000			−0.153393
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$		0			0
$683$	−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	$0.240403\pi$
$684$	−2.00000	−	3.46410i	−0.0764719	−	0.132453i
$685$	20.0000			0.764161
$686$		0			0
$687$	2.00000			0.0763048
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$	−8.00000	+	13.8564i	−0.304555	+	0.527504i
$691$	−2.00000	−	3.46410i	−0.0760836	−	0.131781i	0.825473	−	0.564441i	$-0.190908\pi$
$691$	−2.00000	−	3.46410i	−0.0760836	−	0.131781i	−0.901557	+	0.432660i	$0.857575\pi$
$692$	−22.0000			−0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	4.00000	+	6.92820i	0.151729	+	0.262802i
$696$	1.00000	−	1.73205i	0.0379049	−	0.0656532i
$697$	6.00000	−	10.3923i	0.227266	−	0.393637i
$698$	11.0000	+	19.0526i	0.416356	+	0.721150i
$699$	−22.0000			−0.832116
$700$		0			0
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$	3.00000	+	5.19615i	0.113228	+	0.196116i
$703$	20.0000	−	34.6410i	0.754314	−	1.30651i
$704$	2.00000	−	3.46410i	0.0753778	−	0.130558i
$705$		0			0
$706$	30.0000			1.12906
$707$		0			0
$708$	−4.00000			−0.150329
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	−8.00000	+	13.8564i	−0.300235	+	0.520022i
$711$		0			0
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$		0			0
$714$		0			0
$715$	48.0000			1.79510
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	4.00000	−	6.92820i	0.149279	−	0.258558i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	2.00000			0.0745356
$721$		0			0
$722$	−3.00000			−0.111648
$723$	1.00000	+	1.73205i	0.0371904	+	0.0644157i
$724$	−9.00000	+	15.5885i	−0.334482	+	0.579340i
$725$	−1.00000	+	1.73205i	−0.0371391	+	0.0643268i
$726$	−2.50000	−	4.33013i	−0.0927837	−	0.160706i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	10.0000	+	17.3205i	0.370117	+	0.641061i
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$	3.00000	−	5.19615i	0.110883	−	0.192055i
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	0.916096	−	0.400959i	$-0.131323\pi$
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	−0.805289	+	0.592883i	$0.797990\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	8.00000			0.294884
$737$	8.00000	+	13.8564i	0.294684	+	0.510407i
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	6.00000	−	10.3923i	0.220714	−	0.382287i	−0.734311	−	0.678813i	$-0.762495\pi$
$739$	6.00000	−	10.3923i	0.220714	−	0.382287i	0.955025	+	0.296526i	$0.0958281\pi$
$740$	10.0000	+	17.3205i	0.367607	+	0.636715i
$741$	−24.0000			−0.881662
$742$		0			0
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$		0			0
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$	−11.0000	+	19.0526i	−0.402739	+	0.697564i
$747$	−2.00000	−	3.46410i	−0.0731762	−	0.126745i
$748$	8.00000			0.292509
$749$		0			0
$750$	−12.0000			−0.438178
$751$	−24.0000	−	41.5692i	−0.875772	−	1.51688i	−0.855938	−	0.517079i	$-0.827019\pi$
$751$	−24.0000	−	41.5692i	−0.875772	−	1.51688i	−0.0198348	−	0.999803i	$-0.506314\pi$
$752$		0			0
$753$	−6.00000	+	10.3923i	−0.218652	+	0.378717i
$754$	−6.00000	−	10.3923i	−0.218507	−	0.378465i
$755$	−16.0000			−0.582300
$756$		0			0
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$	16.0000	−	27.7128i	0.580763	−	1.00591i
$760$	−4.00000	+	6.92820i	−0.145095	+	0.251312i
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	0.594822	−	0.803857i	$-0.297222\pi$
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	−0.993572	+	0.113203i	$0.963889\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.00000	+	3.46410i	0.0723102	+	0.125245i
$766$	−8.00000	+	13.8564i	−0.289052	+	0.500652i
$767$	−12.0000	+	20.7846i	−0.433295	+	0.750489i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$	30.0000			1.08042
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	−1.00000	+	1.73205i	−0.0359675	+	0.0622975i	−0.883449	−	0.468528i	$-0.844785\pi$
$773$	−1.00000	+	1.73205i	−0.0359675	+	0.0622975i	0.847481	+	0.530825i	$0.178118\pi$
$774$	2.00000	−	3.46410i	0.0718885	−	0.124515i
$775$		0			0
$776$	14.0000			0.502571
$777$		0			0
$778$	−26.0000			−0.932145
$779$	−12.0000	−	20.7846i	−0.429945	−	0.744686i
$780$	6.00000	−	10.3923i	0.214834	−	0.372104i
$781$	16.0000	−	27.7128i	0.572525	−	0.991642i
$782$	8.00000	+	13.8564i	0.286079	+	0.495504i
$783$	−2.00000			−0.0714742
$784$		0			0
$785$	20.0000			0.713831
$786$	−10.0000	−	17.3205i	−0.356688	−	0.617802i
$787$	−18.0000	+	31.1769i	−0.641631	+	1.11134i	0.343438	+	0.939175i	$0.388408\pi$
$787$	−18.0000	+	31.1769i	−0.641631	+	1.11134i	−0.985069	+	0.172162i	$0.944925\pi$
$788$	5.00000	−	8.66025i	0.178118	−	0.308509i
$789$	12.0000	+	20.7846i	0.427211	+	0.739952i
$790$		0			0
$791$		0			0
$792$	−4.00000			−0.142134
$793$	−18.0000	−	31.1769i	−0.639199	−	1.10712i
$794$	3.00000	−	5.19615i	0.106466	−	0.184405i
$795$	−6.00000	+	10.3923i	−0.212798	+	0.368577i
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	−6.00000			−0.212531			−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000			−0.212531			−0.106265	+	0.994338i	$0.533889\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$	−20.0000	−	34.6410i	−0.705785	−	1.22245i
$804$	4.00000			0.141069
$805$		0			0
$806$		0			0
$807$	11.0000	+	19.0526i	0.387218	+	0.670682i
$808$	−1.00000	+	1.73205i	−0.0351799	+	0.0609333i
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	−0.940435	−	0.339975i	$-0.889582\pi$
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	0.764644	+	0.644453i	$0.222915\pi$
$810$	−1.00000	−	1.73205i	−0.0351364	−	0.0608581i
$811$	44.0000			1.54505			0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000			1.54505			0.772524	+	0.634985i	$0.218994\pi$
$812$		0			0
$813$		0			0
$814$	−20.0000	−	34.6410i	−0.701000	−	1.21417i
$815$	−20.0000	+	34.6410i	−0.700569	+	1.21342i
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	8.00000	+	13.8564i	0.279885	+	0.484774i
$818$	22.0000			0.769212
$819$		0			0
$820$	12.0000			0.419058
$821$	−19.0000	−	32.9090i	−0.663105	−	1.14853i	−0.979795	−	0.200002i	$-0.935905\pi$
$821$	−19.0000	−	32.9090i	−0.663105	−	1.14853i	0.316691	−	0.948529i	$-0.397428\pi$
$822$	−5.00000	+	8.66025i	−0.174395	+	0.302061i
$823$	28.0000	−	48.4974i	0.976019	−	1.69051i	0.299487	−	0.954100i	$-0.403185\pi$
$823$	28.0000	−	48.4974i	0.976019	−	1.69051i	0.676532	−	0.736413i	$-0.263482\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$	4.00000			0.139262
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$	−4.00000	−	6.92820i	−0.139010	−	0.240772i
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	−0.998480	−	0.0551154i	$-0.982447\pi$
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	0.546971	+	0.837151i	$0.315781\pi$
$830$	−4.00000	+	6.92820i	−0.138842	+	0.240481i
$831$	5.00000	+	8.66025i	0.173448	+	0.300421i
$832$	−6.00000			−0.208013
$833$		0			0
$834$	−4.00000			−0.138509
$835$	−8.00000	−	13.8564i	−0.276851	−	0.479521i
$836$	8.00000	−	13.8564i	0.276686	−	0.479234i
$837$		0			0
$838$	−18.0000	−	31.1769i	−0.621800	−	1.07699i
$839$	−56.0000			−1.93333			−0.966667	−	0.256036i	$-0.917584\pi$
$839$	−56.0000			−1.93333			−0.966667	+	0.256036i	$0.917584\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−3.00000	−	5.19615i	−0.103387	−	0.179071i
$843$	−13.0000	+	22.5167i	−0.447744	+	0.775515i
$844$	−10.0000	+	17.3205i	−0.344214	+	0.596196i
$845$	−23.0000	−	39.8372i	−0.791224	−	1.37044i
$846$		0			0
$847$		0			0
$848$	6.00000			0.206041
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$	−1.00000	+	1.73205i	−0.0342997	+	0.0594089i
$851$	40.0000	−	69.2820i	1.37118	−	2.37496i
$852$	−4.00000	−	6.92820i	−0.137038	−	0.237356i
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$		0			0
$855$	8.00000			0.273594
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	−0.244701	−	0.969599i	$-0.578690\pi$
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	0.962048	−	0.272882i	$-0.0879768\pi$
$858$	−12.0000	+	20.7846i	−0.409673	+	0.709575i
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	0.984655	−	0.174512i	$-0.0558348\pi$
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	−0.643459	+	0.765480i	$0.722501\pi$
$860$	−8.00000			−0.272798
$861$		0			0
$862$		0			0
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	0.998629	+	0.0523446i	$0.0166694\pi$
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	−0.453983	+	0.891010i	$0.649997\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	22.0000	−	38.1051i	0.748022	−	1.29561i
$866$	1.00000	+	1.73205i	0.0339814	+	0.0588575i
$867$	−13.0000			−0.441503
$868$		0			0
$869$		0			0
$870$	2.00000	+	3.46410i	0.0678064	+	0.117444i
$871$	12.0000	−	20.7846i	0.406604	−	0.704260i
$872$	1.00000	−	1.73205i	0.0338643	−	0.0586546i
$873$	−7.00000	−	12.1244i	−0.236914	−	0.410347i
$874$	32.0000			1.08242
$875$		0			0
$876$	−10.0000			−0.337869
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	0.882415	−	0.470471i	$-0.155916\pi$
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	−0.848648	+	0.528958i	$0.822583\pi$
$878$	−12.0000	+	20.7846i	−0.404980	+	0.701447i
$879$	15.0000	−	25.9808i	0.505937	−	0.876309i
$880$	4.00000	+	6.92820i	0.134840	+	0.233550i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$	4.00000	−	6.92820i	0.134459	−	0.232889i
$886$	2.00000	−	3.46410i	0.0671913	−	0.116379i
$887$	−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	$0.965338\pi$
$888$	−10.0000			−0.335578
$889$		0			0
$890$	12.0000			0.402241
$891$	2.00000	+	3.46410i	0.0670025	+	0.116052i
$892$	−8.00000	+	13.8564i	−0.267860	+	0.463947i
$893$		0			0
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$	−24.0000			−0.802232
$896$		0			0
$897$	−48.0000			−1.60267
$898$	−17.0000	−	29.4449i	−0.567297	−	0.982588i
$899$		0			0
$900$	0.500000	−	0.866025i	0.0166667	−	0.0288675i
$901$	6.00000	+	10.3923i	0.199889	+	0.346218i
$902$	−24.0000			−0.799113
$903$		0			0
$904$	−14.0000			−0.465633
$905$	−18.0000	−	31.1769i	−0.598340	−	1.03636i
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	6.00000	+	10.3923i	0.199117	+	0.344881i
$909$	2.00000			0.0663358
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	8.00000	−	13.8564i	0.264761	−	0.458580i
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$	6.00000	+	10.3923i	0.198354	+	0.343559i
$916$	2.00000			0.0660819
$917$		0			0
$918$	−2.00000			−0.0660098
$919$	−20.0000	−	34.6410i	−0.659739	−	1.14270i	−0.980683	−	0.195603i	$-0.937333\pi$
$919$	−20.0000	−	34.6410i	−0.659739	−	1.14270i	0.320944	−	0.947098i	$-0.396000\pi$
$920$	−8.00000	+	13.8564i	−0.263752	+	0.456832i
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$	11.0000	+	19.0526i	0.362266	+	0.627463i
$923$	−48.0000			−1.57994
$924$		0			0
$925$	10.0000			0.328798
$926$	16.0000	+	27.7128i	0.525793	+	0.910700i
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$	1.00000	−	1.73205i	0.0328266	−	0.0568574i
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	0.975050	−	0.221985i	$-0.0712536\pi$
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	−0.679770	+	0.733426i	$0.737920\pi$
$930$		0			0
$931$		0			0
$932$	−22.0000			−0.720634
$933$	−4.00000	−	6.92820i	−0.130954	−	0.226819i
$934$	14.0000	−	24.2487i	0.458094	−	0.793442i
$935$	−8.00000	+	13.8564i	−0.261628	+	0.453153i
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	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
$939$	−10.0000			−0.326338
$940$		0			0
$941$	−13.0000	+	22.5167i	−0.423788	+	0.734022i	−0.996306	−	0.0858697i	$-0.972633\pi$
$941$	−13.0000	+	22.5167i	−0.423788	+	0.734022i	0.572518	+	0.819892i	$0.305966\pi$
$942$	−5.00000	+	8.66025i	−0.162909	+	0.282166i
$943$	−24.0000	−	41.5692i	−0.781548	−	1.35368i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	16.0000			0.520205
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	0.831699	−	0.555227i	$-0.187369\pi$
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	−0.896690	+	0.442659i	$0.854035\pi$
$948$		0			0
$949$	−30.0000	+	51.9615i	−0.973841	+	1.68674i
$950$	2.00000	+	3.46410i	0.0648886	+	0.112390i
$951$	−18.0000			−0.583690
$952$		0			0
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$	−3.00000	−	5.19615i	−0.0971286	−	0.168232i
$955$		0			0
$956$		0			0
$957$	−4.00000	−	6.92820i	−0.129302	−	0.223957i
$958$	16.0000			0.516937
$959$		0			0
$960$	2.00000			0.0645497
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	−30.0000	+	51.9615i	−0.967239	+	1.67531i
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	1.00000	+	1.73205i	0.0322078	+	0.0557856i
$965$	4.00000			0.128765
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	−2.50000	−	4.33013i	−0.0803530	−	0.139176i
$969$	4.00000	−	6.92820i	0.128499	−	0.222566i
$970$	−14.0000	+	24.2487i	−0.449513	+	0.778579i
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$	1.00000			0.0320750
$973$		0			0
$974$	8.00000			0.256337
$975$	−3.00000	−	5.19615i	−0.0960769	−	0.166410i
$976$	3.00000	−	5.19615i	0.0960277	−	0.166325i
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$	−10.0000	−	17.3205i	−0.319765	−	0.553849i
$979$	−24.0000			−0.767043
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	−0.991453	−	0.130465i	$-0.958353\pi$
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	0.608712	+	0.793391i	$0.291686\pi$
$984$	−3.00000	+	5.19615i	−0.0956365	+	0.165647i
$985$	10.0000	+	17.3205i	0.318626	+	0.551877i
$986$	4.00000			0.127386
$987$		0			0
$988$	−24.0000			−0.763542
$989$	16.0000	+	27.7128i	0.508770	+	0.881216i
$990$	4.00000	−	6.92820i	0.127128	−	0.220193i
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$		0			0
$993$	−4.00000			−0.126936
$994$		0			0
$995$	−16.0000			−0.507234
$996$	−2.00000	−	3.46410i	−0.0633724	−	0.109764i
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	−0.733630	−	0.679549i	$-0.762175\pi$
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	0.955322	+	0.295567i	$0.0955086\pi$
$998$	22.0000	−	38.1051i	0.696398	−	1.20620i
$999$	5.00000	+	8.66025i	0.158193	+	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.e.a.67.1		2
3.2	odd	2		882.2.g.j.361.1		2
4.3	odd	2		2352.2.q.n.1537.1		2
7.2	even	3	inner	294.2.e.a.79.1		2
7.3	odd	6		42.2.a.a.1.1	✓	1
7.4	even	3		294.2.a.g.1.1		1
7.5	odd	6		294.2.e.c.79.1		2
7.6	odd	2		294.2.e.c.67.1		2
21.2	odd	6		882.2.g.j.667.1		2
21.5	even	6		882.2.g.h.667.1		2
21.11	odd	6		882.2.a.b.1.1		1
21.17	even	6		126.2.a.a.1.1		1
21.20	even	2		882.2.g.h.361.1		2
28.3	even	6		336.2.a.d.1.1		1
28.11	odd	6		2352.2.a.l.1.1		1
28.19	even	6		2352.2.q.i.961.1		2
28.23	odd	6		2352.2.q.n.961.1		2
28.27	even	2		2352.2.q.i.1537.1		2
35.3	even	12		1050.2.g.a.799.1		2
35.4	even	6		7350.2.a.f.1.1		1
35.17	even	12		1050.2.g.a.799.2		2
35.24	odd	6		1050.2.a.i.1.1		1
56.3	even	6		1344.2.a.i.1.1		1
56.11	odd	6		9408.2.a.bw.1.1		1
56.45	odd	6		1344.2.a.q.1.1		1
56.53	even	6		9408.2.a.n.1.1		1
63.31	odd	6		1134.2.f.g.379.1		2
63.38	even	6		1134.2.f.j.757.1		2
63.52	odd	6		1134.2.f.g.757.1		2
63.59	even	6		1134.2.f.j.379.1		2
77.10	even	6		5082.2.a.d.1.1		1
84.11	even	6		7056.2.a.k.1.1		1
84.59	odd	6		1008.2.a.j.1.1		1
91.38	odd	6		7098.2.a.f.1.1		1
105.17	odd	12		3150.2.g.r.2899.1		2
105.38	odd	12		3150.2.g.r.2899.2		2
105.59	even	6		3150.2.a.bo.1.1		1
112.3	even	12		5376.2.c.e.2689.2		2
112.45	odd	12		5376.2.c.bc.2689.1		2
112.59	even	12		5376.2.c.e.2689.1		2
112.101	odd	12		5376.2.c.bc.2689.2		2
140.59	even	6		8400.2.a.k.1.1		1
168.59	odd	6		4032.2.a.m.1.1		1
168.101	even	6		4032.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.a.a.1.1	✓	1	7.3	odd	6
126.2.a.a.1.1		1	21.17	even	6
294.2.a.g.1.1		1	7.4	even	3
294.2.e.a.67.1		2	1.1	even	1	trivial
294.2.e.a.79.1		2	7.2	even	3	inner
294.2.e.c.67.1		2	7.6	odd	2
294.2.e.c.79.1		2	7.5	odd	6
336.2.a.d.1.1		1	28.3	even	6
882.2.a.b.1.1		1	21.11	odd	6
882.2.g.h.361.1		2	21.20	even	2
882.2.g.h.667.1		2	21.5	even	6
882.2.g.j.361.1		2	3.2	odd	2
882.2.g.j.667.1		2	21.2	odd	6
1008.2.a.j.1.1		1	84.59	odd	6
1050.2.a.i.1.1		1	35.24	odd	6
1050.2.g.a.799.1		2	35.3	even	12
1050.2.g.a.799.2		2	35.17	even	12
1134.2.f.g.379.1		2	63.31	odd	6
1134.2.f.g.757.1		2	63.52	odd	6
1134.2.f.j.379.1		2	63.59	even	6
1134.2.f.j.757.1		2	63.38	even	6
1344.2.a.i.1.1		1	56.3	even	6
1344.2.a.q.1.1		1	56.45	odd	6
2352.2.a.l.1.1		1	28.11	odd	6
2352.2.q.i.961.1		2	28.19	even	6
2352.2.q.i.1537.1		2	28.27	even	2
2352.2.q.n.961.1		2	28.23	odd	6
2352.2.q.n.1537.1		2	4.3	odd	2
3150.2.a.bo.1.1		1	105.59	even	6
3150.2.g.r.2899.1		2	105.17	odd	12
3150.2.g.r.2899.2		2	105.38	odd	12
4032.2.a.e.1.1		1	168.101	even	6
4032.2.a.m.1.1		1	168.59	odd	6
5082.2.a.d.1.1		1	77.10	even	6
5376.2.c.e.2689.1		2	112.59	even	12
5376.2.c.e.2689.2		2	112.3	even	12
5376.2.c.bc.2689.1		2	112.45	odd	12
5376.2.c.bc.2689.2		2	112.101	odd	12
7056.2.a.k.1.1		1	84.11	even	6
7098.2.a.f.1.1		1	91.38	odd	6
7350.2.a.f.1.1		1	35.4	even	6
8400.2.a.k.1.1		1	140.59	even	6
9408.2.a.n.1.1		1	56.53	even	6
9408.2.a.bw.1.1		1	56.11	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-0.500000 - 0.866025i) q^{12} -6.00000 q^{13} +2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} +2.00000 q^{20} -4.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-1.00000 - 1.73205i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(5.00000 + 8.66025i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(3.00000 - 5.19615i) q^{39} +(-1.00000 - 1.73205i) q^{40} +6.00000 q^{41} -4.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(-1.00000 + 1.73205i) q^{45} +(-4.00000 + 6.92820i) q^{46} +1.00000 q^{48} -1.00000 q^{50} +(1.00000 + 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-0.500000 - 0.866025i) q^{54} -8.00000 q^{55} +4.00000 q^{57} +(1.00000 + 1.73205i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(3.00000 + 5.19615i) q^{61} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(2.00000 - 3.46410i) q^{66} +(-2.00000 + 3.46410i) q^{67} +(1.00000 + 1.73205i) q^{68} +8.00000 q^{69} +8.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(5.00000 - 8.66025i) q^{73} +(5.00000 - 8.66025i) q^{74} +(0.500000 + 0.866025i) q^{75} +4.00000 q^{76} -6.00000 q^{78} +(-1.00000 + 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +4.00000 q^{83} -4.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(1.00000 - 1.73205i) q^{87} +(2.00000 - 3.46410i) q^{88} +(-3.00000 - 5.19615i) q^{89} +2.00000 q^{90} +8.00000 q^{92} +(-4.00000 + 6.92820i) q^{95} +(-0.500000 - 0.866025i) q^{96} +14.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} - q^{9} - 2 q^{10} + 4 q^{11} - q^{12} - 12 q^{13} + 4 q^{15} - q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} - 8 q^{23} - q^{24}+ \cdots - 8 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 - q^9 - 2 * q^10 + 4 * q^11 - q^12 - 12 * q^13 + 4 * q^15 - q^16 + 2 * q^17 - q^18 - 4 * q^19 + 4 * q^20 - 8 * q^22 - 8 * q^23 - q^24 + q^25 + 6 * q^26 + 2 * q^27 - 4 * q^29 - 2 * q^30 - q^32 + 4 * q^33 - 4 * q^34 + 2 * q^36 + 10 * q^37 - 4 * q^38 + 6 * q^39 - 2 * q^40 + 12 * q^41 - 8 * q^43 + 4 * q^44 - 2 * q^45 - 8 * q^46 + 2 * q^48 - 2 * q^50 + 2 * q^51 + 6 * q^52 - 6 * q^53 - q^54 - 16 * q^55 + 8 * q^57 + 2 * q^58 + 4 * q^59 - 2 * q^60 + 6 * q^61 + 2 * q^64 + 12 * q^65 + 4 * q^66 - 4 * q^67 + 2 * q^68 + 16 * q^69 + 16 * q^71 - q^72 + 10 * q^73 + 10 * q^74 + q^75 + 8 * q^76 - 12 * q^78 - 2 * q^80 - q^81 - 6 * q^82 + 8 * q^83 - 8 * q^85 + 4 * q^86 + 2 * q^87 + 4 * q^88 - 6 * q^89 + 4 * q^90 + 16 * q^92 - 8 * q^95 - q^96 + 28 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more