LMFDB - Embedded newform 245.2.j.d.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(79,245)] 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("245.79"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,4,-4] 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:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	245.79
Dual form			245.2.j.d.214.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 - 1.00000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.86603 + 1.23205i) q^{5} -2.00000 q^{6} +(-1.00000 + 1.73205i) q^{9} +(4.46410 - 0.267949i) q^{10} +(1.50000 + 2.59808i) q^{11} +(1.73205 + 1.00000i) q^{12} +1.00000i q^{13} +(-1.00000 + 2.00000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-6.06218 + 3.50000i) q^{17} +(3.46410 - 2.00000i) q^{18} +(-4.00000 - 2.00000i) q^{20} -6.00000i q^{22} +(5.19615 + 3.00000i) q^{23} +(1.96410 - 4.59808i) q^{25} +(1.00000 - 1.73205i) q^{26} +5.00000i q^{27} +5.00000 q^{29} +(3.73205 - 2.46410i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-6.92820 + 4.00000i) q^{32} +(2.59808 + 1.50000i) q^{33} +14.0000 q^{34} -4.00000 q^{36} +(-1.73205 - 1.00000i) q^{37} +(0.500000 + 0.866025i) q^{39} -2.00000 q^{41} +4.00000i q^{43} +(-3.00000 + 5.19615i) q^{44} +(-0.267949 - 4.46410i) q^{45} +(-6.00000 - 10.3923i) q^{46} +(-2.59808 - 1.50000i) q^{47} -4.00000i q^{48} +(-8.00000 + 6.00000i) q^{50} +(-3.50000 + 6.06218i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(5.00000 - 8.66025i) q^{54} +(-6.00000 - 3.00000i) q^{55} +(-8.66025 - 5.00000i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(-4.46410 + 0.267949i) q^{60} +(-4.00000 + 6.92820i) q^{61} -4.00000i q^{62} +8.00000 q^{64} +(-1.23205 - 1.86603i) q^{65} +(-3.00000 - 5.19615i) q^{66} +(1.73205 - 1.00000i) q^{67} +(-12.1244 - 7.00000i) q^{68} +6.00000 q^{69} -8.00000 q^{71} +(5.19615 - 3.00000i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.598076 - 4.96410i) q^{75} -2.00000i q^{78} +(-2.50000 + 4.33013i) q^{79} +(0.535898 + 8.92820i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.46410 + 2.00000i) q^{82} -4.00000i q^{83} +(7.00000 - 14.0000i) q^{85} +(4.00000 - 6.92820i) q^{86} +(4.33013 - 2.50000i) q^{87} +(-4.00000 + 8.00000i) q^{90} +12.0000i q^{92} +(1.73205 + 1.00000i) q^{93} +(3.00000 + 5.19615i) q^{94} +(-4.00000 + 6.92820i) q^{96} -7.00000i q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{15} + 8 q^{16} - 16 q^{20} - 6 q^{25} + 4 q^{26} + 20 q^{29} + 8 q^{30} + 4 q^{31} + 56 q^{34} - 16 q^{36} + 2 q^{39} - 8 q^{41}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q + 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^15 + 8 * q^16 - 16 * q^20 - 6 * q^25 + 4 * q^26 + 20 * q^29 + 8 * q^30 + 4 * q^31 + 56 * q^34 - 16 * q^36 + 2 * q^39 - 8 * q^41 - 12 * q^44 - 8 * q^45 - 24 * q^46 - 32 * q^50 - 14 * q^51 + 20 * q^54 - 24 * q^55 - 20 * q^59 - 4 * q^60 - 16 * q^61 + 32 * q^64 + 2 * q^65 - 12 * q^66 + 24 * q^69 - 32 * q^71 + 8 * q^74 + 8 * q^75 - 10 * q^79 + 16 * q^80 - 2 * q^81 + 28 * q^85 + 16 * q^86 - 16 * q^90 + 12 * q^94 - 16 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.73205	−	1.00000i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	−1.73205	−	1.00000i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i	−0.228714	−	0.973494i	$-0.573452\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i	0.728714	+	0.684819i	$0.240119\pi$
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$6$	−2.00000			−0.816497
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$	4.46410	−	0.267949i	1.41167	−	0.0847330i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	1.73205	+	1.00000i	0.500000	+	0.288675i
$13$			1.00000i			0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$			1.00000i			0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$		0			0
$15$	−1.00000	+	2.00000i	−0.258199	+	0.516398i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−6.06218	+	3.50000i	−1.47029	+	0.848875i	−0.999444	−	0.0333386i	$-0.989386\pi$
$17$	−6.06218	+	3.50000i	−1.47029	+	0.848875i	−0.470850	+	0.882213i	$0.656053\pi$
$18$	3.46410	−	2.00000i	0.816497	−	0.471405i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	−4.00000	−	2.00000i	−0.894427	−	0.447214i
$21$		0			0
$22$		−	6.00000i		−	1.27920i
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.931831	−	0.362892i	$-0.118211\pi$
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.151642	+	0.988436i	$0.451544\pi$
$24$		0			0
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$			5.00000i			0.962250i
$28$		0			0
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$	3.73205	−	2.46410i	0.681376	−	0.449881i
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−6.92820	+	4.00000i	−1.22474	+	0.707107i
$33$	2.59808	+	1.50000i	0.452267	+	0.261116i
$34$	14.0000			2.40098
$35$		0			0
$36$	−4.00000			−0.666667
$37$	−1.73205	−	1.00000i	−0.284747	−	0.164399i	0.350823	−	0.936442i	$-0.385902\pi$
$37$	−1.73205	−	1.00000i	−0.284747	−	0.164399i	−0.635571	+	0.772043i	$0.719235\pi$
$38$		0			0
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−3.00000	+	5.19615i	−0.452267	+	0.783349i
$45$	−0.267949	−	4.46410i	−0.0399435	−	0.665469i
$46$	−6.00000	−	10.3923i	−0.884652	−	1.53226i
$47$	−2.59808	−	1.50000i	−0.378968	−	0.218797i	0.298401	−	0.954441i	$-0.403547\pi$
$47$	−2.59808	−	1.50000i	−0.378968	−	0.218797i	−0.677369	+	0.735643i	$0.736880\pi$
$48$		−	4.00000i		−	0.577350i
$49$		0			0
$50$	−8.00000	+	6.00000i	−1.13137	+	0.848528i
$51$	−3.50000	+	6.06218i	−0.490098	+	0.848875i
$52$	−1.73205	+	1.00000i	−0.240192	+	0.138675i
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	−0.812447	−	0.583036i	$-0.801865\pi$
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	0.0987002	+	0.995117i	$0.468532\pi$
$54$	5.00000	−	8.66025i	0.680414	−	1.17851i
$55$	−6.00000	−	3.00000i	−0.809040	−	0.404520i
$56$		0			0
$57$		0			0
$58$	−8.66025	−	5.00000i	−1.13715	−	0.656532i
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$	−4.46410	+	0.267949i	−0.576313	+	0.0345921i
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$		−	4.00000i		−	0.508001i
$63$		0			0
$64$	8.00000			1.00000
$65$	−1.23205	−	1.86603i	−0.152817	−	0.231452i
$66$	−3.00000	−	5.19615i	−0.369274	−	0.639602i
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	−0.390453	−	0.920623i	$-0.627682\pi$
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	0.602056	+	0.798454i	$0.294348\pi$
$68$	−12.1244	−	7.00000i	−1.47029	−	0.848875i
$69$	6.00000			0.722315
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	5.19615	−	3.00000i	0.608164	−	0.351123i	−0.164083	−	0.986447i	$-0.552466\pi$
$73$	5.19615	−	3.00000i	0.608164	−	0.351123i	0.772246	+	0.635323i	$0.219133\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	−0.598076	−	4.96410i	−0.0690599	−	0.573205i
$76$		0			0
$77$		0			0
$78$		−	2.00000i		−	0.226455i
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$	0.535898	+	8.92820i	0.0599153	+	0.998203i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.46410	+	2.00000i	0.382546	+	0.220863i
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$		0			0
$85$	7.00000	−	14.0000i	0.759257	−	1.51851i
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	4.33013	−	2.50000i	0.464238	−	0.268028i
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	−4.00000	+	8.00000i	−0.421637	+	0.843274i
$91$		0			0
$92$			12.0000i			1.25109i
$93$	1.73205	+	1.00000i	0.179605	+	0.103695i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$	−4.00000	+	6.92820i	−0.408248	+	0.707107i
$97$		−	7.00000i		−	0.710742i	−0.934725	−	0.355371i	$-0.884354\pi$
$97$		−	7.00000i		−	0.710742i	0.934725	−	0.355371i	$-0.115646\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$	9.92820	−	1.19615i	0.992820	−	0.119615i
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$	12.1244	−	7.00000i	1.20049	−	0.693103i
$103$	16.4545	+	9.50000i	1.62131	+	0.936063i	0.986571	+	0.163335i	$0.0522252\pi$
$103$	16.4545	+	9.50000i	1.62131	+	0.936063i	0.634738	+	0.772728i	$0.281108\pi$
$104$		0			0
$105$		0			0
$106$	12.0000			1.16554
$107$	6.92820	+	4.00000i	0.669775	+	0.386695i	0.795991	−	0.605308i	$-0.206950\pi$
$107$	6.92820	+	4.00000i	0.669775	+	0.386695i	−0.126217	+	0.992003i	$0.540283\pi$
$108$	−8.66025	+	5.00000i	−0.833333	+	0.481125i
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	0.960558	−	0.278078i	$-0.0896974\pi$
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	−0.721102	+	0.692829i	$0.756364\pi$
$110$	7.39230	+	11.1962i	0.704829	+	1.06751i
$111$	−2.00000			−0.189832
$112$		0			0
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$		0			0
$115$	−13.3923	+	0.803848i	−1.24884	+	0.0749592i
$116$	5.00000	+	8.66025i	0.464238	+	0.804084i
$117$	−1.73205	−	1.00000i	−0.160128	−	0.0924500i
$118$			20.0000i			1.84115i
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	13.8564	−	8.00000i	1.25450	−	0.724286i
$123$	−1.73205	+	1.00000i	−0.156174	+	0.0901670i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$		0			0
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	0.267949	+	4.46410i	0.0235007	+	0.391528i
$131$	11.0000	−	19.0526i	0.961074	−	1.66463i	0.241264	−	0.970460i	$-0.422438\pi$
$131$	11.0000	−	19.0526i	0.961074	−	1.66463i	0.719811	−	0.694170i	$-0.244228\pi$
$132$			6.00000i			0.522233i
$133$		0			0
$134$	−4.00000			−0.345547
$135$	−6.16025	−	9.33013i	−0.530190	−	0.803009i
$136$		0			0
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.0146279	−	0.999893i	$-0.495344\pi$
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.873247	+	0.487278i	$0.162010\pi$
$138$	−10.3923	−	6.00000i	−0.884652	−	0.510754i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	13.8564	+	8.00000i	1.16280	+	0.671345i
$143$	−2.59808	+	1.50000i	−0.217262	+	0.125436i
$144$	4.00000	+	6.92820i	0.333333	+	0.577350i
$145$	−9.33013	+	6.16025i	−0.774825	+	0.511581i
$146$	−12.0000			−0.993127
$147$		0			0
$148$		−	4.00000i		−	0.328798i
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	−3.92820	+	9.19615i	−0.320736	+	0.750863i
$151$	6.50000	+	11.2583i	0.528962	+	0.916190i	0.999430	+	0.0337724i	$0.0107521\pi$
$151$	6.50000	+	11.2583i	0.528962	+	0.916190i	−0.470467	+	0.882418i	$0.655915\pi$
$152$		0			0
$153$		−	14.0000i		−	1.13183i
$154$		0			0
$155$	−4.00000	−	2.00000i	−0.321288	−	0.160644i
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	15.5885	−	9.00000i	1.24409	−	0.718278i	0.274169	−	0.961681i	$-0.411597\pi$
$157$	15.5885	−	9.00000i	1.24409	−	0.718278i	0.969925	+	0.243403i	$0.0782638\pi$
$158$	8.66025	−	5.00000i	0.688973	−	0.397779i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$	8.00000	−	16.0000i	0.632456	−	1.26491i
$161$		0			0
$162$			2.00000i			0.157135i
$163$	−12.1244	−	7.00000i	−0.949653	−	0.548282i	−0.0566798	−	0.998392i	$-0.518051\pi$
$163$	−12.1244	−	7.00000i	−0.949653	−	0.548282i	−0.892973	+	0.450110i	$0.851385\pi$
$164$	−2.00000	−	3.46410i	−0.156174	−	0.270501i
$165$	−6.69615	+	0.401924i	−0.521295	+	0.0312897i
$166$	−4.00000	+	6.92820i	−0.310460	+	0.537733i
$167$			3.00000i			0.232147i	0.993241	+	0.116073i	$0.0370308\pi$
$167$			3.00000i			0.232147i	−0.993241	+	0.116073i	$0.962969\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	−26.1244	+	17.2487i	−2.00365	+	1.32292i
$171$		0			0
$172$	−6.92820	+	4.00000i	−0.528271	+	0.304997i
$173$	7.79423	+	4.50000i	0.592584	+	0.342129i	0.766119	−	0.642699i	$-0.222185\pi$
$173$	7.79423	+	4.50000i	0.592584	+	0.342129i	−0.173534	+	0.984828i	$0.555519\pi$
$174$	−10.0000			−0.758098
$175$		0			0
$176$	12.0000			0.904534
$177$	−8.66025	−	5.00000i	−0.650945	−	0.375823i
$178$		0			0
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	−0.949048	−	0.315130i	$-0.897952\pi$
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	0.201613	−	0.979465i	$-0.435382\pi$
$180$	7.46410	−	4.92820i	0.556341	−	0.367327i
$181$	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
$183$			8.00000i			0.591377i
$184$		0			0
$185$	4.46410	−	0.267949i	0.328207	−	0.0197000i
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$	−18.1865	−	10.5000i	−1.32993	−	0.767836i
$188$		−	6.00000i		−	0.437595i
$189$		0			0
$190$		0			0
$191$	1.50000	−	2.59808i	0.108536	−	0.187990i	−0.806641	−	0.591041i	$-0.798717\pi$
$191$	1.50000	−	2.59808i	0.108536	−	0.187990i	0.915177	+	0.403051i	$0.132050\pi$
$192$	6.92820	−	4.00000i	0.500000	−	0.288675i
$193$	−13.8564	+	8.00000i	−0.997406	+	0.575853i	−0.907480	−	0.420096i	$-0.861996\pi$
$193$	−13.8564	+	8.00000i	−0.997406	+	0.575853i	−0.0899262	+	0.995948i	$0.528663\pi$
$194$	−7.00000	+	12.1244i	−0.502571	+	0.870478i
$195$	−2.00000	−	1.00000i	−0.143223	−	0.0716115i
$196$		0			0
$197$			2.00000i			0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$			2.00000i			0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$	10.3923	+	6.00000i	0.738549	+	0.426401i
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$		0			0
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$		−	24.0000i		−	1.68863i
$203$		0			0
$204$	−14.0000			−0.980196
$205$	3.73205	−	2.46410i	0.260658	−	0.172100i
$206$	−19.0000	−	32.9090i	−1.32379	−	2.29288i
$207$	−10.3923	+	6.00000i	−0.722315	+	0.417029i
$208$	3.46410	+	2.00000i	0.240192	+	0.138675i
$209$		0			0
$210$		0			0
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$	−10.3923	−	6.00000i	−0.713746	−	0.412082i
$213$	−6.92820	+	4.00000i	−0.474713	+	0.274075i
$214$	−8.00000	−	13.8564i	−0.546869	−	0.947204i
$215$	−4.92820	−	7.46410i	−0.336101	−	0.509048i
$216$		0			0
$217$		0			0
$218$		−	10.0000i		−	0.677285i
$219$	3.00000	−	5.19615i	0.202721	−	0.351123i
$220$	−0.803848	−	13.3923i	−0.0541954	−	0.902909i
$221$	−3.50000	−	6.06218i	−0.235435	−	0.407786i
$222$	3.46410	+	2.00000i	0.232495	+	0.134231i
$223$			21.0000i			1.40626i	0.711059	+	0.703132i	$0.248216\pi$
$223$			21.0000i			1.40626i	−0.711059	+	0.703132i	$0.751784\pi$
$224$		0			0
$225$	6.00000	+	8.00000i	0.400000	+	0.533333i
$226$	−6.00000	+	10.3923i	−0.399114	+	0.691286i
$227$	−14.7224	+	8.50000i	−0.977162	+	0.564165i	−0.901412	−	0.432962i	$-0.857468\pi$
$227$	−14.7224	+	8.50000i	−0.977162	+	0.564165i	−0.0757500	+	0.997127i	$0.524135\pi$
$228$		0			0
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$	24.0000	+	12.0000i	1.58251	+	0.791257i
$231$		0			0
$232$		0			0
$233$	13.8564	+	8.00000i	0.907763	+	0.524097i	0.879711	−	0.475509i	$-0.157736\pi$
$233$	13.8564	+	8.00000i	0.907763	+	0.524097i	0.0280525	+	0.999606i	$0.491069\pi$
$234$	2.00000	+	3.46410i	0.130744	+	0.226455i
$235$	6.69615	−	0.401924i	0.436809	−	0.0262186i
$236$	10.0000	−	17.3205i	0.650945	−	1.12747i
$237$			5.00000i			0.324785i
$238$		0			0
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$	4.92820	+	7.46410i	0.318114	+	0.481806i
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	0.965387	+	0.260822i	$0.0839937\pi$
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	−0.256814	+	0.966461i	$0.582673\pi$
$242$	−3.46410	+	2.00000i	−0.222681	+	0.128565i
$243$	−13.8564	−	8.00000i	−0.888889	−	0.513200i
$244$	−16.0000			−1.02430
$245$		0			0
$246$	4.00000			0.255031
$247$		0			0
$248$		0			0
$249$	−2.00000	−	3.46410i	−0.126745	−	0.219529i
$250$	7.53590	−	21.0526i	0.476612	−	1.33148i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$			18.0000i			1.13165i
$254$	2.00000	−	3.46410i	0.125491	−	0.217357i
$255$	−0.937822	−	15.6244i	−0.0587287	−	0.978435i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	19.0526	+	11.0000i	1.18847	+	0.686161i	0.957958	−	0.286909i	$-0.0926278\pi$
$257$	19.0526	+	11.0000i	1.18847	+	0.686161i	0.230508	+	0.973070i	$0.425961\pi$
$258$		−	8.00000i		−	0.498058i
$259$		0			0
$260$	2.00000	−	4.00000i	0.124035	−	0.248069i
$261$	−5.00000	+	8.66025i	−0.309492	+	0.536056i
$262$	−38.1051	+	22.0000i	−2.35414	+	1.35916i
$263$	20.7846	−	12.0000i	1.28163	−	0.739952i	0.304487	−	0.952517i	$-0.401515\pi$
$263$	20.7846	−	12.0000i	1.28163	−	0.739952i	0.977147	+	0.212565i	$0.0681817\pi$
$264$		0			0
$265$	6.00000	−	12.0000i	0.368577	−	0.737154i
$266$		0			0
$267$		0			0
$268$	3.46410	+	2.00000i	0.211604	+	0.122169i
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	0.672374	−	0.740212i	$-0.265275\pi$
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	−0.977229	+	0.212187i	$0.931941\pi$
$270$	1.33975	+	22.3205i	0.0815343	+	1.35838i
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$			28.0000i			1.69775i
$273$		0			0
$274$	−24.0000			−1.44989
$275$	14.8923	−	1.79423i	0.898040	−	0.108196i
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	1.73205	−	1.00000i	0.104069	−	0.0600842i	−0.447062	−	0.894503i	$-0.647530\pi$
$277$	1.73205	−	1.00000i	0.104069	−	0.0600842i	0.551131	+	0.834419i	$0.314196\pi$
$278$	17.3205	+	10.0000i	1.03882	+	0.599760i
$279$	−4.00000			−0.239474
$280$		0			0
$281$	7.00000			0.417585			0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000			0.417585			0.208792	+	0.977960i	$0.433047\pi$
$282$	5.19615	+	3.00000i	0.309426	+	0.178647i
$283$	9.52628	−	5.50000i	0.566279	−	0.326941i	−0.189383	−	0.981903i	$-0.560649\pi$
$283$	9.52628	−	5.50000i	0.566279	−	0.326941i	0.755662	+	0.654962i	$0.227315\pi$
$284$	−8.00000	−	13.8564i	−0.474713	−	0.822226i
$285$		0			0
$286$	6.00000			0.354787
$287$		0			0
$288$		−	16.0000i		−	0.942809i
$289$	16.0000	−	27.7128i	0.941176	−	1.63017i
$290$	22.3205	−	1.33975i	1.31071	−	0.0786726i
$291$	−3.50000	−	6.06218i	−0.205174	−	0.355371i
$292$	10.3923	+	6.00000i	0.608164	+	0.351123i
$293$		−	9.00000i		−	0.525786i	−0.964825	−	0.262893i	$-0.915323\pi$
$293$		−	9.00000i		−	0.525786i	0.964825	−	0.262893i	$-0.0846766\pi$
$294$		0			0
$295$	20.0000	+	10.0000i	1.16445	+	0.582223i
$296$		0			0
$297$	−12.9904	+	7.50000i	−0.753778	+	0.435194i
$298$	−17.3205	+	10.0000i	−1.00335	+	0.579284i
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$	8.00000	−	6.00000i	0.461880	−	0.346410i
$301$		0			0
$302$		−	26.0000i		−	1.49613i
$303$	10.3923	+	6.00000i	0.597022	+	0.344691i
$304$		0			0
$305$	−1.07180	−	17.8564i	−0.0613709	−	1.02245i
$306$	−14.0000	+	24.2487i	−0.800327	+	1.38621i
$307$		−	7.00000i		−	0.399511i	−0.979846	−	0.199756i	$-0.935985\pi$
$307$		−	7.00000i		−	0.399511i	0.979846	−	0.199756i	$-0.0640148\pi$
$308$		0			0
$309$	19.0000			1.08087
$310$	4.92820	+	7.46410i	0.279903	+	0.423932i
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	−18.1865	−	10.5000i	−1.02796	−	0.593495i	−0.111563	−	0.993757i	$-0.535586\pi$
$313$	−18.1865	−	10.5000i	−1.02796	−	0.593495i	−0.916401	+	0.400262i	$0.868919\pi$
$314$	−36.0000			−2.03160
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−10.3923	−	6.00000i	−0.583690	−	0.336994i	0.178908	−	0.983866i	$-0.442743\pi$
$317$	−10.3923	−	6.00000i	−0.583690	−	0.336994i	−0.762598	+	0.646872i	$0.776077\pi$
$318$	10.3923	−	6.00000i	0.582772	−	0.336463i
$319$	7.50000	+	12.9904i	0.419919	+	0.727322i
$320$	−14.9282	+	9.85641i	−0.834512	+	0.550990i
$321$	8.00000			0.446516
$322$		0			0
$323$		0			0
$324$	1.00000	−	1.73205i	0.0555556	−	0.0962250i
$325$	4.59808	+	1.96410i	0.255055	+	0.108949i
$326$	14.0000	+	24.2487i	0.775388	+	1.34301i
$327$	4.33013	+	2.50000i	0.239457	+	0.138250i
$328$		0			0
$329$		0			0
$330$	12.0000	+	6.00000i	0.660578	+	0.330289i
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	−0.982470	−	0.186421i	$-0.940311\pi$
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	0.652680	+	0.757634i	$0.273645\pi$
$332$	6.92820	−	4.00000i	0.380235	−	0.219529i
$333$	3.46410	−	2.00000i	0.189832	−	0.109599i
$334$	3.00000	−	5.19615i	0.164153	−	0.284321i
$335$	−2.00000	+	4.00000i	−0.109272	+	0.218543i
$336$		0			0
$337$		−	18.0000i		−	0.980522i	−0.871576	−	0.490261i	$-0.836901\pi$
$337$		−	18.0000i		−	0.980522i	0.871576	−	0.490261i	$-0.163099\pi$
$338$	−20.7846	−	12.0000i	−1.13053	−	0.652714i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$	31.2487	−	1.87564i	1.69470	−	0.101721i
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−11.1962	+	7.39230i	−0.602781	+	0.397988i
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	−0.856186	−	0.516667i	$-0.827172\pi$
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	0.0193540	+	0.999813i	$0.493839\pi$
$348$	8.66025	+	5.00000i	0.464238	+	0.268028i
$349$	−20.0000			−1.07058			−0.535288	−	0.844670i	$-0.679797\pi$
$349$	−20.0000			−1.07058			−0.535288	+	0.844670i	$0.679797\pi$
$350$		0			0
$351$	−5.00000			−0.266880
$352$	−20.7846	−	12.0000i	−1.10782	−	0.639602i
$353$	9.52628	−	5.50000i	0.507033	−	0.292735i	−0.224580	−	0.974456i	$-0.572101\pi$
$353$	9.52628	−	5.50000i	0.507033	−	0.292735i	0.731613	+	0.681720i	$0.238768\pi$
$354$	10.0000	+	17.3205i	0.531494	+	0.920575i
$355$	14.9282	−	9.85641i	0.792307	−	0.523124i
$356$		0			0
$357$		0			0
$358$			40.0000i			2.11407i
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	0.471696	+	0.881761i	$0.343642\pi$
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	−0.999476	+	0.0323801i	$0.989691\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	−31.1769	−	18.0000i	−1.63862	−	0.946059i
$363$		−	2.00000i		−	0.104973i
$364$		0			0
$365$	−6.00000	+	12.0000i	−0.314054	+	0.628109i
$366$	8.00000	−	13.8564i	0.418167	−	0.724286i
$367$	2.59808	−	1.50000i	0.135618	−	0.0782994i	−0.430656	−	0.902516i	$-0.641718\pi$
$367$	2.59808	−	1.50000i	0.135618	−	0.0782994i	0.566274	+	0.824217i	$0.308384\pi$
$368$	20.7846	−	12.0000i	1.08347	−	0.625543i
$369$	2.00000	−	3.46410i	0.104116	−	0.180334i
$370$	−8.00000	−	4.00000i	−0.415900	−	0.207950i
$371$		0			0
$372$			4.00000i			0.207390i
$373$	−20.7846	−	12.0000i	−1.07619	−	0.621336i	−0.146321	−	0.989237i	$-0.546743\pi$
$373$	−20.7846	−	12.0000i	−1.07619	−	0.621336i	−0.929865	+	0.367901i	$0.880077\pi$
$374$	21.0000	+	36.3731i	1.08588	+	1.88081i
$375$	7.23205	+	8.52628i	0.373461	+	0.440295i
$376$		0			0
$377$			5.00000i			0.257513i
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$	1.00000	+	1.73205i	0.0512316	+	0.0887357i
$382$	−5.19615	+	3.00000i	−0.265858	+	0.153493i
$383$	−13.8564	−	8.00000i	−0.708029	−	0.408781i	0.102302	−	0.994753i	$-0.467379\pi$
$383$	−13.8564	−	8.00000i	−0.708029	−	0.408781i	−0.810331	+	0.585973i	$0.800713\pi$
$384$		0			0
$385$		0			0
$386$	32.0000			1.62876
$387$	−6.92820	−	4.00000i	−0.352180	−	0.203331i
$388$	12.1244	−	7.00000i	0.615521	−	0.355371i
$389$	2.50000	+	4.33013i	0.126755	+	0.219546i	0.922418	−	0.386194i	$-0.126210\pi$
$389$	2.50000	+	4.33013i	0.126755	+	0.219546i	−0.795663	+	0.605740i	$0.792877\pi$
$390$	2.46410	+	3.73205i	0.124775	+	0.188980i
$391$	−42.0000			−2.12403
$392$		0			0
$393$		−	22.0000i		−	1.10975i
$394$	2.00000	−	3.46410i	0.100759	−	0.174519i
$395$	−0.669873	−	11.1603i	−0.0337050	−	0.561533i
$396$	−6.00000	−	10.3923i	−0.301511	−	0.522233i
$397$	6.06218	+	3.50000i	0.304252	+	0.175660i	0.644351	−	0.764730i	$-0.277127\pi$
$397$	6.06218	+	3.50000i	0.304252	+	0.175660i	−0.340099	+	0.940389i	$0.610461\pi$
$398$		−	20.0000i		−	1.00251i
$399$		0			0
$400$	−12.0000	−	16.0000i	−0.600000	−	0.800000i
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$	−3.46410	+	2.00000i	−0.172774	+	0.0997509i
$403$	−1.73205	+	1.00000i	−0.0862796	+	0.0498135i
$404$	−12.0000	+	20.7846i	−0.597022	+	1.03407i
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$		0			0
$407$		−	6.00000i		−	0.297409i
$408$		0			0
$409$	−10.0000	−	17.3205i	−0.494468	−	0.856444i	0.505511	−	0.862820i	$-0.331304\pi$
$409$	−10.0000	−	17.3205i	−0.494468	−	0.856444i	−0.999980	+	0.00637586i	$0.997970\pi$
$410$	−8.92820	+	0.535898i	−0.440933	+	0.0264661i
$411$	6.00000	−	10.3923i	0.295958	−	0.512615i
$412$			38.0000i			1.87213i
$413$		0			0
$414$	24.0000			1.17954
$415$	4.92820	+	7.46410i	0.241916	+	0.366398i
$416$	−4.00000	−	6.92820i	−0.196116	−	0.339683i
$417$	−8.66025	+	5.00000i	−0.424094	+	0.244851i
$418$		0			0
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$		0			0
$421$	−3.00000			−0.146211			−0.0731055	−	0.997324i	$-0.523291\pi$
$421$	−3.00000			−0.146211			−0.0731055	+	0.997324i	$0.523291\pi$
$422$	22.5167	+	13.0000i	1.09609	+	0.632830i
$423$	5.19615	−	3.00000i	0.252646	−	0.145865i
$424$		0			0
$425$	4.18653	+	34.7487i	0.203077	+	1.68556i
$426$	16.0000			0.775203
$427$		0			0
$428$			16.0000i			0.773389i
$429$	−1.50000	+	2.59808i	−0.0724207	+	0.125436i
$430$	1.07180	+	17.8564i	0.0516866	+	0.861112i
$431$	11.5000	+	19.9186i	0.553936	+	0.959444i	0.997985	+	0.0634424i	$0.0202079\pi$
$431$	11.5000	+	19.9186i	0.553936	+	0.959444i	−0.444050	+	0.896002i	$0.646459\pi$
$432$	17.3205	+	10.0000i	0.833333	+	0.481125i
$433$			26.0000i			1.24948i	0.780833	+	0.624740i	$0.214795\pi$
$433$			26.0000i			1.24948i	−0.780833	+	0.624740i	$0.785205\pi$
$434$		0			0
$435$	−5.00000	+	10.0000i	−0.239732	+	0.479463i
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$		0			0
$438$	−10.3923	+	6.00000i	−0.496564	+	0.286691i
$439$	−15.0000	+	25.9808i	−0.715911	+	1.23999i	0.246696	+	0.969093i	$0.420655\pi$
$439$	−15.0000	+	25.9808i	−0.715911	+	1.23999i	−0.962607	+	0.270901i	$0.912678\pi$
$440$		0			0
$441$		0			0
$442$			14.0000i			0.665912i
$443$	−3.46410	−	2.00000i	−0.164584	−	0.0950229i	0.415445	−	0.909618i	$-0.363626\pi$
$443$	−3.46410	−	2.00000i	−0.164584	−	0.0950229i	−0.580030	+	0.814595i	$0.696959\pi$
$444$	−2.00000	−	3.46410i	−0.0949158	−	0.164399i
$445$		0			0
$446$	21.0000	−	36.3731i	0.994379	−	1.72231i
$447$		−	10.0000i		−	0.472984i
$448$		0			0
$449$	5.00000			0.235965			0.117982	−	0.993016i	$-0.462357\pi$
$449$	5.00000			0.235965			0.117982	+	0.993016i	$0.462357\pi$
$450$	−2.39230	−	19.8564i	−0.112774	−	0.936040i
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$	10.3923	−	6.00000i	0.488813	−	0.282216i
$453$	11.2583	+	6.50000i	0.528962	+	0.305397i
$454$	34.0000			1.59570
$455$		0			0
$456$		0			0
$457$	32.9090	+	19.0000i	1.53942	+	0.888783i	0.998873	+	0.0474665i	$0.0151147\pi$
$457$	32.9090	+	19.0000i	1.53942	+	0.888783i	0.540544	+	0.841316i	$0.318219\pi$
$458$	−17.3205	+	10.0000i	−0.809334	+	0.467269i
$459$	−17.5000	−	30.3109i	−0.816830	−	1.41479i
$460$	−14.7846	−	22.3923i	−0.689336	−	1.04405i
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$		−	36.0000i		−	1.67306i	−0.547920	−	0.836531i	$-0.684580\pi$
$463$		−	36.0000i		−	1.67306i	0.547920	−	0.836531i	$-0.315420\pi$
$464$	10.0000	−	17.3205i	0.464238	−	0.804084i
$465$	−4.46410	+	0.267949i	−0.207018	+	0.0124258i
$466$	−16.0000	−	27.7128i	−0.741186	−	1.28377i
$467$	23.3827	+	13.5000i	1.08202	+	0.624705i	0.931441	−	0.363892i	$-0.118552\pi$
$467$	23.3827	+	13.5000i	1.08202	+	0.624705i	0.150581	+	0.988598i	$0.451886\pi$
$468$		−	4.00000i		−	0.184900i
$469$		0			0
$470$	−12.0000	−	6.00000i	−0.553519	−	0.276759i
$471$	9.00000	−	15.5885i	0.414698	−	0.718278i
$472$		0			0
$473$	−10.3923	+	6.00000i	−0.477839	+	0.275880i
$474$	5.00000	−	8.66025i	0.229658	−	0.397779i
$475$		0			0
$476$		0			0
$477$		−	12.0000i		−	0.549442i
$478$	25.9808	+	15.0000i	1.18833	+	0.686084i
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	0.973321	+	0.229447i	$0.0736918\pi$
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	−0.287954	+	0.957644i	$0.592975\pi$
$480$	−1.07180	−	17.8564i	−0.0489206	−	0.815030i
$481$	1.00000	−	1.73205i	0.0455961	−	0.0789747i
$482$		−	44.0000i		−	2.00415i
$483$		0			0
$484$	4.00000			0.181818
$485$	8.62436	+	13.0622i	0.391612	+	0.593123i
$486$	16.0000	+	27.7128i	0.725775	+	1.25708i
$487$	36.3731	−	21.0000i	1.64822	−	0.951601i	0.670442	−	0.741962i	$-0.266104\pi$
$487$	36.3731	−	21.0000i	1.64822	−	0.951601i	0.977779	−	0.209639i	$-0.0672289\pi$
$488$		0			0
$489$	−14.0000			−0.633102
$490$		0			0
$491$	7.00000			0.315906			0.157953	−	0.987447i	$-0.449511\pi$
$491$	7.00000			0.315906			0.157953	+	0.987447i	$0.449511\pi$
$492$	−3.46410	−	2.00000i	−0.156174	−	0.0901670i
$493$	−30.3109	+	17.5000i	−1.36513	+	0.788160i
$494$		0			0
$495$	11.1962	−	7.39230i	0.503230	−	0.332259i
$496$	8.00000			0.359211
$497$		0			0
$498$			8.00000i			0.358489i
$499$	−17.5000	+	30.3109i	−0.783408	+	1.35690i	0.146538	+	0.989205i	$0.453187\pi$
$499$	−17.5000	+	30.3109i	−0.783408	+	1.35690i	−0.929946	+	0.367697i	$0.880146\pi$
$500$	−17.0526	+	14.4641i	−0.762614	+	0.646854i
$501$	1.50000	+	2.59808i	0.0670151	+	0.116073i
$502$	−31.1769	−	18.0000i	−1.39149	−	0.803379i
$503$		−	9.00000i		−	0.401290i	−0.979664	−	0.200645i	$-0.935696\pi$
$503$		−	9.00000i		−	0.401290i	0.979664	−	0.200645i	$-0.0643038\pi$
$504$		0			0
$505$	−24.0000	−	12.0000i	−1.06799	−	0.533993i
$506$	18.0000	−	31.1769i	0.800198	−	1.38598i
$507$	10.3923	−	6.00000i	0.461538	−	0.266469i
$508$	−3.46410	+	2.00000i	−0.153695	+	0.0887357i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$	−14.0000	+	28.0000i	−0.619930	+	1.23986i
$511$		0			0
$512$			32.0000i			1.41421i
$513$		0			0
$514$	−22.0000	−	38.1051i	−0.970378	−	1.68074i
$515$	−42.4090	+	2.54552i	−1.86876	+	0.112169i
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$		−	9.00000i		−	0.395820i
$518$		0			0
$519$	9.00000			0.395056
$520$		0			0
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	−0.990671	−	0.136272i	$-0.956488\pi$
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	0.377320	−	0.926083i	$-0.376846\pi$
$522$	17.3205	−	10.0000i	0.758098	−	0.437688i
$523$	3.46410	+	2.00000i	0.151475	+	0.0874539i	0.573822	−	0.818980i	$-0.305460\pi$
$523$	3.46410	+	2.00000i	0.151475	+	0.0874539i	−0.422347	+	0.906434i	$0.638794\pi$
$524$	44.0000			1.92215
$525$		0			0
$526$	−48.0000			−2.09290
$527$	−12.1244	−	7.00000i	−0.528145	−	0.304925i
$528$	10.3923	−	6.00000i	0.452267	−	0.261116i
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$	−22.3923	+	14.7846i	−0.972660	+	0.642202i
$531$	20.0000			0.867926
$532$		0			0
$533$		−	2.00000i		−	0.0866296i
$534$		0			0
$535$	−17.8564	+	1.07180i	−0.772000	+	0.0463378i
$536$		0			0
$537$	−17.3205	−	10.0000i	−0.747435	−	0.431532i
$538$			20.0000i			0.862261i
$539$		0			0
$540$	10.0000	−	20.0000i	0.430331	−	0.860663i
$541$	−13.5000	+	23.3827i	−0.580410	+	1.00530i	0.415020	+	0.909812i	$0.363774\pi$
$541$	−13.5000	+	23.3827i	−0.580410	+	1.00530i	−0.995431	+	0.0954880i	$0.969559\pi$
$542$	13.8564	−	8.00000i	0.595184	−	0.343629i
$543$	15.5885	−	9.00000i	0.668965	−	0.386227i
$544$	28.0000	−	48.4974i	1.20049	−	2.07931i
$545$	−10.0000	−	5.00000i	−0.428353	−	0.214176i
$546$		0			0
$547$			32.0000i			1.36822i	0.729378	+	0.684111i	$0.239809\pi$
$547$			32.0000i			1.36822i	−0.729378	+	0.684111i	$0.760191\pi$
$548$	20.7846	+	12.0000i	0.887875	+	0.512615i
$549$	−8.00000	−	13.8564i	−0.341432	−	0.591377i
$550$	−27.5885	−	11.7846i	−1.17638	−	0.502497i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−4.00000			−0.169944
$555$	3.73205	−	2.46410i	0.158417	−	0.104595i
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	−24.2487	+	14.0000i	−1.02745	+	0.593199i	−0.916253	−	0.400599i	$-0.868802\pi$
$557$	−24.2487	+	14.0000i	−1.02745	+	0.593199i	−0.111198	+	0.993798i	$0.535469\pi$
$558$	6.92820	+	4.00000i	0.293294	+	0.169334i
$559$	−4.00000			−0.169182
$560$		0			0
$561$	−21.0000			−0.886621
$562$	−12.1244	−	7.00000i	−0.511435	−	0.295277i
$563$	−20.7846	+	12.0000i	−0.875967	+	0.505740i	−0.869326	−	0.494238i	$-0.835447\pi$
$563$	−20.7846	+	12.0000i	−0.875967	+	0.505740i	−0.00664037	+	0.999978i	$0.502114\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$	7.39230	+	11.1962i	0.310997	+	0.471026i
$566$	−22.0000			−0.924729
$567$		0			0
$568$		0			0
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		0			0
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	0.712735	−	0.701434i	$-0.247456\pi$
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	−0.963827	+	0.266529i	$0.914123\pi$
$572$	−5.19615	−	3.00000i	−0.217262	−	0.125436i
$573$		−	3.00000i		−	0.125327i
$574$		0			0
$575$	24.0000	−	18.0000i	1.00087	−	0.750652i
$576$	−8.00000	+	13.8564i	−0.333333	+	0.577350i
$577$	37.2391	−	21.5000i	1.55028	−	0.895057i	0.552166	−	0.833734i	$-0.313802\pi$
$577$	37.2391	−	21.5000i	1.55028	−	0.895057i	0.998118	−	0.0613223i	$-0.0195318\pi$
$578$	−55.4256	+	32.0000i	−2.30540	+	1.33102i
$579$	−8.00000	+	13.8564i	−0.332469	+	0.575853i
$580$	−20.0000	−	10.0000i	−0.830455	−	0.415227i
$581$		0			0
$582$			14.0000i			0.580319i
$583$	−15.5885	−	9.00000i	−0.645608	−	0.372742i
$584$		0			0
$585$	4.46410	−	0.267949i	0.184568	−	0.0110783i
$586$	−9.00000	+	15.5885i	−0.371787	+	0.643953i
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$		0			0
$589$		0			0
$590$	−24.6410	−	37.3205i	−1.01445	−	1.53646i
$591$	1.00000	+	1.73205i	0.0411345	+	0.0712470i
$592$	−6.92820	+	4.00000i	−0.284747	+	0.164399i
$593$	−35.5070	−	20.5000i	−1.45810	−	0.841834i	−0.459182	−	0.888342i	$-0.651857\pi$
$593$	−35.5070	−	20.5000i	−1.45810	−	0.841834i	−0.998918	+	0.0465084i	$0.985191\pi$
$594$	30.0000			1.23091
$595$		0			0
$596$	20.0000			0.819232
$597$	8.66025	+	5.00000i	0.354441	+	0.204636i
$598$	10.3923	−	6.00000i	0.424973	−	0.245358i
$599$	12.5000	+	21.6506i	0.510736	+	0.884621i	0.999923	+	0.0124417i	$0.00396043\pi$
$599$	12.5000	+	21.6506i	0.510736	+	0.884621i	−0.489186	+	0.872179i	$0.662706\pi$
$600$		0			0
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$		0			0
$603$			4.00000i			0.162893i
$604$	−13.0000	+	22.5167i	−0.528962	+	0.916190i
$605$	0.267949	+	4.46410i	0.0108937	+	0.181492i
$606$	−12.0000	−	20.7846i	−0.487467	−	0.844317i
$607$	23.3827	+	13.5000i	0.949074	+	0.547948i	0.892793	−	0.450467i	$-0.148742\pi$
$607$	23.3827	+	13.5000i	0.949074	+	0.547948i	0.0562808	+	0.998415i	$0.482076\pi$
$608$		0			0
$609$		0			0
$610$	−16.0000	+	32.0000i	−0.647821	+	1.29564i
$611$	1.50000	−	2.59808i	0.0606835	−	0.105107i
$612$	24.2487	−	14.0000i	0.980196	−	0.565916i
$613$	38.1051	−	22.0000i	1.53905	−	0.888572i	0.540157	−	0.841564i	$-0.318365\pi$
$613$	38.1051	−	22.0000i	1.53905	−	0.888572i	0.998895	−	0.0470071i	$-0.0149684\pi$
$614$	−7.00000	+	12.1244i	−0.282497	+	0.489299i
$615$	2.00000	−	4.00000i	0.0806478	−	0.161296i
$616$		0			0
$617$			22.0000i			0.885687i	0.896599	+	0.442843i	$0.146030\pi$
$617$			22.0000i			0.885687i	−0.896599	+	0.442843i	$0.853970\pi$
$618$	−32.9090	−	19.0000i	−1.32379	−	0.764292i
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	0.747873	−	0.663842i	$-0.231075\pi$
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	−0.948840	+	0.315757i	$0.897742\pi$
$620$	−0.535898	−	8.92820i	−0.0215222	−	0.358565i
$621$	−15.0000	+	25.9808i	−0.601929	+	1.04257i
$622$		−	24.0000i		−	0.962312i
$623$		0			0
$624$	4.00000			0.160128
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	21.0000	+	36.3731i	0.839329	+	1.45376i
$627$		0			0
$628$	31.1769	+	18.0000i	1.24409	+	0.718278i
$629$	14.0000			0.558217
$630$		0			0
$631$	37.0000			1.47295			0.736473	−	0.676467i	$-0.236490\pi$
$631$	37.0000			1.47295			0.736473	+	0.676467i	$0.236490\pi$
$632$		0			0
$633$	−11.2583	+	6.50000i	−0.447478	+	0.258352i
$634$	12.0000	+	20.7846i	0.476581	+	0.825462i
$635$	−2.46410	−	3.73205i	−0.0977849	−	0.148102i
$636$	−12.0000			−0.475831
$637$		0			0
$638$		−	30.0000i		−	1.18771i
$639$	8.00000	−	13.8564i	0.316475	−	0.548151i
$640$		0			0
$641$	−11.0000	−	19.0526i	−0.434474	−	0.752531i	0.562779	−	0.826608i	$-0.309732\pi$
$641$	−11.0000	−	19.0526i	−0.434474	−	0.752531i	−0.997253	+	0.0740768i	$0.976399\pi$
$642$	−13.8564	−	8.00000i	−0.546869	−	0.315735i
$643$			1.00000i			0.0394362i	0.999806	+	0.0197181i	$0.00627687\pi$
$643$			1.00000i			0.0394362i	−0.999806	+	0.0197181i	$0.993723\pi$
$644$		0			0
$645$	−8.00000	−	4.00000i	−0.315000	−	0.157500i
$646$		0			0
$647$	6.92820	−	4.00000i	0.272376	−	0.157256i	−0.357591	−	0.933878i	$-0.616402\pi$
$647$	6.92820	−	4.00000i	0.272376	−	0.157256i	0.629967	+	0.776622i	$0.283068\pi$
$648$		0			0
$649$	15.0000	−	25.9808i	0.588802	−	1.01983i
$650$	−6.00000	−	8.00000i	−0.235339	−	0.313786i
$651$		0			0
$652$		−	28.0000i		−	1.09656i
$653$	−3.46410	−	2.00000i	−0.135561	−	0.0782660i	0.430686	−	0.902502i	$-0.358272\pi$
$653$	−3.46410	−	2.00000i	−0.135561	−	0.0782660i	−0.566247	+	0.824236i	$0.691605\pi$
$654$	−5.00000	−	8.66025i	−0.195515	−	0.338643i
$655$	2.94744	+	49.1051i	0.115166	+	1.91870i
$656$	−4.00000	+	6.92820i	−0.156174	+	0.270501i
$657$			12.0000i			0.468165i
$658$		0			0
$659$	15.0000			0.584317			0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000			0.584317			0.292159	+	0.956370i	$0.405627\pi$
$660$	−7.39230	−	11.1962i	−0.287745	−	0.435810i
$661$	6.00000	+	10.3923i	0.233373	+	0.404214i	0.958799	−	0.284087i	$-0.0916904\pi$
$661$	6.00000	+	10.3923i	0.233373	+	0.404214i	−0.725426	+	0.688301i	$0.758357\pi$
$662$	20.7846	−	12.0000i	0.807817	−	0.466393i
$663$	−6.06218	−	3.50000i	−0.235435	−	0.135929i
$664$		0			0
$665$		0			0
$666$	−8.00000			−0.309994
$667$	25.9808	+	15.0000i	1.00598	+	0.580802i
$668$	−5.19615	+	3.00000i	−0.201045	+	0.116073i
$669$	10.5000	+	18.1865i	0.405953	+	0.703132i
$670$	7.46410	−	4.92820i	0.288363	−	0.190393i
$671$	−24.0000			−0.926510
$672$		0			0
$673$			24.0000i			0.925132i	0.886585	+	0.462566i	$0.153071\pi$
$673$			24.0000i			0.925132i	−0.886585	+	0.462566i	$0.846929\pi$
$674$	−18.0000	+	31.1769i	−0.693334	+	1.20089i
$675$	22.9904	+	9.82051i	0.884900	+	0.377992i
$676$	12.0000	+	20.7846i	0.461538	+	0.799408i
$677$	−37.2391	−	21.5000i	−1.43121	−	0.826312i	−0.434001	−	0.900912i	$-0.642899\pi$
$677$	−37.2391	−	21.5000i	−1.43121	−	0.826312i	−0.997214	+	0.0746002i	$0.976232\pi$
$678$			12.0000i			0.460857i
$679$		0			0
$680$		0			0
$681$	−8.50000	+	14.7224i	−0.325721	+	0.564165i
$682$	10.3923	−	6.00000i	0.397942	−	0.229752i
$683$	−13.8564	+	8.00000i	−0.530201	+	0.306111i	−0.741098	−	0.671397i	$-0.765695\pi$
$683$	−13.8564	+	8.00000i	−0.530201	+	0.306111i	0.210898	+	0.977508i	$0.432361\pi$
$684$		0			0
$685$	−12.0000	+	24.0000i	−0.458496	+	0.916993i
$686$		0			0
$687$		−	10.0000i		−	0.381524i
$688$	13.8564	+	8.00000i	0.528271	+	0.304997i
$689$	−3.00000	−	5.19615i	−0.114291	−	0.197958i
$690$	26.7846	−	1.60770i	1.01967	−	0.0612039i
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$			18.0000i			0.684257i
$693$		0			0
$694$	36.0000			1.36654
$695$	18.6603	−	12.3205i	0.707824	−	0.467344i
$696$		0			0
$697$	12.1244	−	7.00000i	0.459243	−	0.265144i
$698$	34.6410	+	20.0000i	1.31118	+	0.757011i
$699$	16.0000			0.605176
$700$		0			0
$701$	−13.0000			−0.491003			−0.245502	−	0.969396i	$-0.578953\pi$
$701$	−13.0000			−0.491003			−0.245502	+	0.969396i	$0.578953\pi$
$702$	8.66025	+	5.00000i	0.326860	+	0.188713i
$703$		0			0
$704$	12.0000	+	20.7846i	0.452267	+	0.783349i
$705$	5.59808	−	3.69615i	0.210836	−	0.139205i
$706$	−22.0000			−0.827981
$707$		0			0
$708$		−	20.0000i		−	0.751646i
$709$	17.5000	−	30.3109i	0.657226	−	1.13835i	−0.324104	−	0.946021i	$-0.605063\pi$
$709$	17.5000	−	30.3109i	0.657226	−	1.13835i	0.981331	−	0.192328i	$-0.0616038\pi$
$710$	−35.7128	+	2.14359i	−1.34028	+	0.0804476i
$711$	−5.00000	−	8.66025i	−0.187515	−	0.324785i
$712$		0			0
$713$			12.0000i			0.449404i
$714$		0			0
$715$	3.00000	−	6.00000i	0.112194	−	0.224387i
$716$	20.0000	−	34.6410i	0.747435	−	1.29460i
$717$	−12.9904	+	7.50000i	−0.485135	+	0.280093i
$718$	34.6410	−	20.0000i	1.29279	−	0.746393i
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	0.438141	+	0.898906i	$0.355637\pi$
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	−0.997546	+	0.0700124i	$0.977696\pi$
$720$	−16.0000	−	8.00000i	−0.596285	−	0.298142i
$721$		0			0
$722$		−	38.0000i		−	1.41421i
$723$	19.0526	+	11.0000i	0.708572	+	0.409094i
$724$	18.0000	+	31.1769i	0.668965	+	1.15868i
$725$	9.82051	−	22.9904i	0.364725	−	0.853841i
$726$	−2.00000	+	3.46410i	−0.0742270	+	0.128565i
$727$			28.0000i			1.03846i	0.854634	+	0.519231i	$0.173782\pi$
$727$			28.0000i			1.03846i	−0.854634	+	0.519231i	$0.826218\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$	22.3923	−	14.7846i	0.828776	−	0.547203i
$731$	−14.0000	−	24.2487i	−0.517809	−	0.896871i
$732$	−13.8564	+	8.00000i	−0.512148	+	0.295689i
$733$	−0.866025	−	0.500000i	−0.0319874	−	0.0184679i	0.483921	−	0.875112i	$-0.339212\pi$
$733$	−0.866025	−	0.500000i	−0.0319874	−	0.0184679i	−0.515908	+	0.856644i	$0.672546\pi$
$734$	−6.00000			−0.221464
$735$		0			0
$736$	−48.0000			−1.76930
$737$	5.19615	+	3.00000i	0.191403	+	0.110506i
$738$	−6.92820	+	4.00000i	−0.255031	+	0.147242i
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	−0.984589	−	0.174883i	$-0.944045\pi$
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	0.340841	−	0.940121i	$-0.389288\pi$
$740$	4.92820	+	7.46410i	0.181164	+	0.274386i
$741$		0			0
$742$		0			0
$743$			14.0000i			0.513610i	0.966463	+	0.256805i	$0.0826698\pi$
$743$			14.0000i			0.513610i	−0.966463	+	0.256805i	$0.917330\pi$
$744$		0			0
$745$	1.33975	+	22.3205i	0.0490845	+	0.817760i
$746$	24.0000	+	41.5692i	0.878702	+	1.52196i
$747$	6.92820	+	4.00000i	0.253490	+	0.146352i
$748$		−	42.0000i		−	1.53567i
$749$		0			0
$750$	−4.00000	−	22.0000i	−0.146059	−	0.803326i
$751$	16.5000	−	28.5788i	0.602094	−	1.04286i	−0.390410	−	0.920641i	$-0.627667\pi$
$751$	16.5000	−	28.5788i	0.602094	−	1.04286i	0.992504	−	0.122216i	$-0.0389999\pi$
$752$	−10.3923	+	6.00000i	−0.378968	+	0.218797i
$753$	15.5885	−	9.00000i	0.568075	−	0.327978i
$754$	5.00000	−	8.66025i	0.182089	−	0.315388i
$755$	−26.0000	−	13.0000i	−0.946237	−	0.473118i
$756$		0			0
$757$			32.0000i			1.16306i	0.813525	+	0.581530i	$0.197546\pi$
$757$			32.0000i			1.16306i	−0.813525	+	0.581530i	$0.802454\pi$
$758$	34.6410	+	20.0000i	1.25822	+	0.726433i
$759$	9.00000	+	15.5885i	0.326679	+	0.565825i
$760$		0			0
$761$	1.00000	−	1.73205i	0.0362500	−	0.0627868i	−0.847331	−	0.531065i	$-0.821792\pi$
$761$	1.00000	−	1.73205i	0.0362500	−	0.0627868i	0.883581	+	0.468278i	$0.155125\pi$
$762$		−	4.00000i		−	0.144905i
$763$		0			0
$764$	6.00000			0.217072
$765$	17.2487	+	26.1244i	0.623628	+	0.944528i
$766$	16.0000	+	27.7128i	0.578103	+	1.00130i
$767$	8.66025	−	5.00000i	0.312704	−	0.180540i
$768$	−13.8564	−	8.00000i	−0.500000	−	0.288675i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$	22.0000			0.792311
$772$	−27.7128	−	16.0000i	−0.997406	−	0.575853i
$773$	18.1865	−	10.5000i	0.654124	−	0.377659i	−0.135910	−	0.990721i	$-0.543396\pi$
$773$	18.1865	−	10.5000i	0.654124	−	0.377659i	0.790034	+	0.613062i	$0.210063\pi$
$774$	8.00000	+	13.8564i	0.287554	+	0.498058i
$775$	9.92820	−	1.19615i	0.356632	−	0.0429671i
$776$		0			0
$777$		0			0
$778$		−	10.0000i		−	0.358517i
$779$		0			0
$780$	−0.267949	−	4.46410i	−0.00959412	−	0.159840i
$781$	−12.0000	−	20.7846i	−0.429394	−	0.743732i
$782$	72.7461	+	42.0000i	2.60140	+	1.50192i
$783$			25.0000i			0.893427i
$784$		0			0
$785$	−18.0000	+	36.0000i	−0.642448	+	1.28490i
$786$	−22.0000	+	38.1051i	−0.784714	+	1.35916i
$787$	−14.7224	+	8.50000i	−0.524798	+	0.302992i	−0.738896	−	0.673820i	$-0.764652\pi$
$787$	−14.7224	+	8.50000i	−0.524798	+	0.302992i	0.214097	+	0.976812i	$0.431319\pi$
$788$	−3.46410	+	2.00000i	−0.123404	+	0.0712470i
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$	−10.0000	+	20.0000i	−0.355784	+	0.711568i
$791$		0			0
$792$		0			0
$793$	−6.92820	−	4.00000i	−0.246028	−	0.142044i
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$	−0.803848	−	13.3923i	−0.0285095	−	0.474976i
$796$	−10.0000	+	17.3205i	−0.354441	+	0.613909i
$797$			13.0000i			0.460484i	0.973133	+	0.230242i	$0.0739517\pi$
$797$			13.0000i			0.460484i	−0.973133	+	0.230242i	$0.926048\pi$
$798$		0			0
$799$	21.0000			0.742927
$800$	4.78461	+	39.7128i	0.169161	+	1.40406i
$801$		0			0
$802$	−5.19615	+	3.00000i	−0.183483	+	0.105934i
$803$	15.5885	+	9.00000i	0.550105	+	0.317603i
$804$	4.00000			0.141069
$805$		0			0
$806$	4.00000			0.140894
$807$	−8.66025	−	5.00000i	−0.304855	−	0.176008i
$808$		0			0
$809$	22.5000	+	38.9711i	0.791058	+	1.37015i	0.925312	+	0.379206i	$0.123803\pi$
$809$	22.5000	+	38.9711i	0.791058	+	1.37015i	−0.134255	+	0.990947i	$0.542864\pi$
$810$	−2.46410	−	3.73205i	−0.0865797	−	0.131131i
$811$	38.0000			1.33436			0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000			1.33436			0.667180	+	0.744896i	$0.267501\pi$
$812$		0			0
$813$			8.00000i			0.280572i
$814$	−6.00000	+	10.3923i	−0.210300	+	0.364250i
$815$	31.2487	−	1.87564i	1.09459	−	0.0657010i
$816$	14.0000	+	24.2487i	0.490098	+	0.848875i
$817$		0			0
$818$			40.0000i			1.39857i
$819$		0			0
$820$	8.00000	+	4.00000i	0.279372	+	0.139686i
$821$	11.5000	−	19.9186i	0.401353	−	0.695163i	−0.592537	−	0.805543i	$-0.701873\pi$
$821$	11.5000	−	19.9186i	0.401353	−	0.695163i	0.993889	+	0.110380i	$0.0352068\pi$
$822$	−20.7846	+	12.0000i	−0.724947	+	0.418548i
$823$	−22.5167	+	13.0000i	−0.784881	+	0.453152i	−0.838157	−	0.545428i	$-0.816367\pi$
$823$	−22.5167	+	13.0000i	−0.784881	+	0.453152i	0.0532760	+	0.998580i	$0.483034\pi$
$824$		0			0
$825$	12.0000	−	9.00000i	0.417786	−	0.313340i
$826$		0			0
$827$		−	18.0000i		−	0.625921i	−0.949766	−	0.312961i	$-0.898679\pi$
$827$		−	18.0000i		−	0.625921i	0.949766	−	0.312961i	$-0.101321\pi$
$828$	−20.7846	−	12.0000i	−0.722315	−	0.417029i
$829$	15.0000	+	25.9808i	0.520972	+	0.902349i	0.999703	+	0.0243876i	$0.00776357\pi$
$829$	15.0000	+	25.9808i	0.520972	+	0.902349i	−0.478731	+	0.877962i	$0.658903\pi$
$830$	−1.07180	−	17.8564i	−0.0372026	−	0.619805i
$831$	1.00000	−	1.73205i	0.0346896	−	0.0600842i
$832$			8.00000i			0.277350i
$833$		0			0
$834$	20.0000			0.692543
$835$	−3.69615	−	5.59808i	−0.127911	−	0.193729i
$836$		0			0
$837$	−8.66025	+	5.00000i	−0.299342	+	0.172825i
$838$	−51.9615	−	30.0000i	−1.79498	−	1.03633i
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	5.19615	+	3.00000i	0.179071	+	0.103387i
$843$	6.06218	−	3.50000i	0.208792	−	0.120546i
$844$	−13.0000	−	22.5167i	−0.447478	−	0.775055i
$845$	−22.3923	+	14.7846i	−0.770319	+	0.508606i
$846$	−12.0000			−0.412568
$847$		0			0
$848$			24.0000i			0.824163i
$849$	5.50000	−	9.52628i	0.188760	−	0.326941i
$850$	27.4974	−	64.3731i	0.943154	−	2.20798i
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$	−13.8564	−	8.00000i	−0.474713	−	0.274075i
$853$		−	54.0000i		−	1.84892i	−0.381273	−	0.924462i	$-0.624514\pi$
$853$		−	54.0000i		−	1.84892i	0.381273	−	0.924462i	$-0.375486\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−36.3731	+	21.0000i	−1.24248	+	0.717346i	−0.969599	−	0.244701i	$-0.921310\pi$
$857$	−36.3731	+	21.0000i	−1.24248	+	0.717346i	−0.272882	+	0.962048i	$0.587977\pi$
$858$	5.19615	−	3.00000i	0.177394	−	0.102418i
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	0.291858	+	0.956462i	$0.405727\pi$
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	−0.974249	+	0.225475i	$0.927607\pi$
$860$	8.00000	−	16.0000i	0.272798	−	0.545595i
$861$		0			0
$862$		−	46.0000i		−	1.56677i
$863$	−46.7654	−	27.0000i	−1.59191	−	0.919091i	−0.992979	−	0.118291i	$-0.962258\pi$
$863$	−46.7654	−	27.0000i	−1.59191	−	0.919091i	−0.598933	−	0.800799i	$-0.704408\pi$
$864$	−20.0000	−	34.6410i	−0.680414	−	1.17851i
$865$	−20.0885	+	1.20577i	−0.683028	+	0.0409975i
$866$	26.0000	−	45.0333i	0.883516	−	1.53029i
$867$		−	32.0000i		−	1.08678i
$868$		0			0
$869$	−15.0000			−0.508840
$870$	18.6603	−	12.3205i	0.632642	−	0.417704i
$871$	1.00000	+	1.73205i	0.0338837	+	0.0586883i
$872$		0			0
$873$	12.1244	+	7.00000i	0.410347	+	0.236914i
$874$		0			0
$875$		0			0
$876$	12.0000			0.405442
$877$	−27.7128	−	16.0000i	−0.935795	−	0.540282i	−0.0471555	−	0.998888i	$-0.515016\pi$
$877$	−27.7128	−	16.0000i	−0.935795	−	0.540282i	−0.888640	+	0.458606i	$0.848349\pi$
$878$	51.9615	−	30.0000i	1.75362	−	1.01245i
$879$	−4.50000	−	7.79423i	−0.151781	−	0.262893i
$880$	−22.3923	+	14.7846i	−0.754844	+	0.498389i
$881$	−32.0000			−1.07811			−0.539054	−	0.842271i	$-0.681218\pi$
$881$	−32.0000			−1.07811			−0.539054	+	0.842271i	$0.681218\pi$
$882$		0			0
$883$		−	36.0000i		−	1.21150i	−0.795656	−	0.605748i	$-0.792874\pi$
$883$		−	36.0000i		−	1.21150i	0.795656	−	0.605748i	$-0.207126\pi$
$884$	7.00000	−	12.1244i	0.235435	−	0.407786i
$885$	22.3205	−	1.33975i	0.750296	−	0.0450351i
$886$	4.00000	+	6.92820i	0.134383	+	0.232758i
$887$	−24.2487	−	14.0000i	−0.814192	−	0.470074i	0.0342175	−	0.999414i	$-0.489106\pi$
$887$	−24.2487	−	14.0000i	−0.814192	−	0.470074i	−0.848410	+	0.529340i	$0.822439\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	−36.3731	+	21.0000i	−1.21786	+	0.703132i
$893$		0			0
$894$	−10.0000	+	17.3205i	−0.334450	+	0.579284i
$895$	40.0000	+	20.0000i	1.33705	+	0.668526i
$896$		0			0
$897$			6.00000i			0.200334i
$898$	−8.66025	−	5.00000i	−0.288996	−	0.166852i
$899$	5.00000	+	8.66025i	0.166759	+	0.288836i
$900$	−7.85641	+	18.3923i	−0.261880	+	0.613077i
$901$	21.0000	−	36.3731i	0.699611	−	1.21176i
$902$			12.0000i			0.399556i
$903$		0			0
$904$		0			0
$905$	−33.5885	+	22.1769i	−1.11652	+	0.737186i
$906$	−13.0000	−	22.5167i	−0.431896	−	0.748066i
$907$	−32.9090	+	19.0000i	−1.09272	+	0.630885i	−0.934300	−	0.356487i	$-0.883975\pi$
$907$	−32.9090	+	19.0000i	−1.09272	+	0.630885i	−0.158424	+	0.987371i	$0.550641\pi$
$908$	−29.4449	−	17.0000i	−0.977162	−	0.564165i
$909$	−24.0000			−0.796030
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	10.3923	−	6.00000i	0.343935	−	0.198571i
$914$	−38.0000	−	65.8179i	−1.25693	−	2.17706i
$915$	−9.85641	−	14.9282i	−0.325843	−	0.493511i
$916$	20.0000			0.660819
$917$		0			0
$918$			70.0000i			2.31034i
$919$	−2.50000	+	4.33013i	−0.0824674	+	0.142838i	−0.904309	−	0.426878i	$-0.859613\pi$
$919$	−2.50000	+	4.33013i	−0.0824674	+	0.142838i	0.821842	+	0.569716i	$0.192947\pi$
$920$		0			0
$921$	−3.50000	−	6.06218i	−0.115329	−	0.199756i
$922$	20.7846	+	12.0000i	0.684505	+	0.395199i
$923$		−	8.00000i		−	0.263323i
$924$		0			0
$925$	−8.00000	+	6.00000i	−0.263038	+	0.197279i
$926$	−36.0000	+	62.3538i	−1.18303	+	2.04907i
$927$	−32.9090	+	19.0000i	−1.08087	+	0.624042i
$928$	−34.6410	+	20.0000i	−1.13715	+	0.656532i
$929$	25.0000	−	43.3013i	0.820223	−	1.42067i	−0.0852924	−	0.996356i	$-0.527182\pi$
$929$	25.0000	−	43.3013i	0.820223	−	1.42067i	0.905516	−	0.424313i	$-0.139484\pi$
$930$	8.00000	+	4.00000i	0.262330	+	0.131165i
$931$		0			0
$932$			32.0000i			1.04819i
$933$	10.3923	+	6.00000i	0.340229	+	0.196431i
$934$	−27.0000	−	46.7654i	−0.883467	−	1.53021i
$935$	46.8731	−	2.81347i	1.53291	−	0.0920102i
$936$		0			0
$937$			13.0000i			0.424691i	0.977195	+	0.212346i	$0.0681103\pi$
$937$			13.0000i			0.424691i	−0.977195	+	0.212346i	$0.931890\pi$
$938$		0			0
$939$	−21.0000			−0.685309
$940$	7.39230	+	11.1962i	0.241110	+	0.365178i
$941$	−24.0000	−	41.5692i	−0.782378	−	1.35512i	−0.930553	−	0.366157i	$-0.880673\pi$
$941$	−24.0000	−	41.5692i	−0.782378	−	1.35512i	0.148176	−	0.988961i	$-0.452660\pi$
$942$	−31.1769	+	18.0000i	−1.01580	+	0.586472i
$943$	−10.3923	−	6.00000i	−0.338420	−	0.195387i
$944$	−40.0000			−1.30189
$945$		0			0
$946$	24.0000			0.780307
$947$	−36.3731	−	21.0000i	−1.18197	−	0.682408i	−0.225497	−	0.974244i	$-0.572401\pi$
$947$	−36.3731	−	21.0000i	−1.18197	−	0.682408i	−0.956469	+	0.291835i	$0.905734\pi$
$948$	−8.66025	+	5.00000i	−0.281272	+	0.162392i
$949$	3.00000	+	5.19615i	0.0973841	+	0.168674i
$950$		0			0
$951$	−12.0000			−0.389127
$952$		0			0
$953$		−	6.00000i		−	0.194359i	−0.995267	−	0.0971795i	$-0.969018\pi$
$953$		−	6.00000i		−	0.194359i	0.995267	−	0.0971795i	$-0.0309821\pi$
$954$	−12.0000	+	20.7846i	−0.388514	+	0.672927i
$955$	0.401924	+	6.69615i	0.0130059	+	0.216682i
$956$	−15.0000	−	25.9808i	−0.485135	−	0.840278i
$957$	12.9904	+	7.50000i	0.419919	+	0.242441i
$958$		−	60.0000i		−	1.93851i
$959$		0			0
$960$	−8.00000	+	16.0000i	−0.258199	+	0.516398i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−3.46410	+	2.00000i	−0.111687	+	0.0644826i
$963$	−13.8564	+	8.00000i	−0.446516	+	0.257796i
$964$	−22.0000	+	38.1051i	−0.708572	+	1.22728i
$965$	16.0000	−	32.0000i	0.515058	−	1.03012i
$966$		0			0
$967$		−	8.00000i		−	0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$		−	8.00000i		−	0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$		0			0
$969$		0			0
$970$	−1.87564	−	31.2487i	−0.0602233	−	1.00334i
$971$	11.0000	−	19.0526i	0.353007	−	0.611426i	−0.633768	−	0.773523i	$-0.718493\pi$
$971$	11.0000	−	19.0526i	0.353007	−	0.611426i	0.986775	+	0.162098i	$0.0518259\pi$
$972$		−	32.0000i		−	1.02640i
$973$		0			0
$974$	−84.0000			−2.69153
$975$	4.96410	−	0.598076i	0.158978	−	0.0191538i
$976$	16.0000	+	27.7128i	0.512148	+	0.887066i
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	−0.324462	−	0.945899i	$-0.605183\pi$
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	0.656941	+	0.753942i	$0.271850\pi$
$978$	24.2487	+	14.0000i	0.775388	+	0.447671i
$979$		0			0
$980$		0			0
$981$	−10.0000			−0.319275
$982$	−12.1244	−	7.00000i	−0.386904	−	0.223379i
$983$	44.1673	−	25.5000i	1.40872	−	0.813324i	0.413453	−	0.910525i	$-0.364323\pi$
$983$	44.1673	−	25.5000i	1.40872	−	0.813324i	0.995265	+	0.0972017i	$0.0309892\pi$
$984$		0			0
$985$	−2.46410	−	3.73205i	−0.0785128	−	0.118913i
$986$	70.0000			2.22925
$987$		0			0
$988$		0			0
$989$	−12.0000	+	20.7846i	−0.381578	+	0.660912i
$990$	−26.7846	+	1.60770i	−0.851271	+	0.0510959i
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$	−13.8564	−	8.00000i	−0.439941	−	0.254000i
$993$			12.0000i			0.380808i
$994$		0			0
$995$	−20.0000	−	10.0000i	−0.634043	−	0.317021i
$996$	4.00000	−	6.92820i	0.126745	−	0.219529i
$997$	11.2583	−	6.50000i	0.356555	−	0.205857i	−0.311014	−	0.950405i	$-0.600668\pi$
$997$	11.2583	−	6.50000i	0.356555	−	0.205857i	0.667568	+	0.744548i	$0.267335\pi$
$998$	60.6218	−	35.0000i	1.91895	−	1.10791i
$999$	5.00000	−	8.66025i	0.158193	−	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.j.d.79.1		4
5.4	even	2	inner	245.2.j.d.79.2		4
7.2	even	3		245.2.b.a.99.2		2
7.3	odd	6		245.2.j.e.214.2		4
7.4	even	3	inner	245.2.j.d.214.2		4
7.5	odd	6		35.2.b.a.29.2	yes	2
7.6	odd	2		245.2.j.e.79.1		4
21.2	odd	6		2205.2.d.b.1324.1		2
21.5	even	6		315.2.d.a.64.1		2
28.19	even	6		560.2.g.b.449.2		2
35.2	odd	12		1225.2.a.a.1.1		1
35.4	even	6	inner	245.2.j.d.214.1		4
35.9	even	6		245.2.b.a.99.1		2
35.12	even	12		175.2.a.a.1.1		1
35.19	odd	6		35.2.b.a.29.1	✓	2
35.23	odd	12		1225.2.a.i.1.1		1
35.24	odd	6		245.2.j.e.214.1		4
35.33	even	12		175.2.a.c.1.1		1
35.34	odd	2		245.2.j.e.79.2		4
56.5	odd	6		2240.2.g.h.449.2		2
56.19	even	6		2240.2.g.g.449.1		2
84.47	odd	6		5040.2.t.p.1009.2		2
105.44	odd	6		2205.2.d.b.1324.2		2
105.47	odd	12		1575.2.a.k.1.1		1
105.68	odd	12		1575.2.a.a.1.1		1
105.89	even	6		315.2.d.a.64.2		2
140.19	even	6		560.2.g.b.449.1		2
140.47	odd	12		2800.2.a.w.1.1		1
140.103	odd	12		2800.2.a.l.1.1		1
280.19	even	6		2240.2.g.g.449.2		2
280.229	odd	6		2240.2.g.h.449.1		2
420.299	odd	6		5040.2.t.p.1009.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.b.a.29.1	✓	2	35.19	odd	6
35.2.b.a.29.2	yes	2	7.5	odd	6
175.2.a.a.1.1		1	35.12	even	12
175.2.a.c.1.1		1	35.33	even	12
245.2.b.a.99.1		2	35.9	even	6
245.2.b.a.99.2		2	7.2	even	3
245.2.j.d.79.1		4	1.1	even	1	trivial
245.2.j.d.79.2		4	5.4	even	2	inner
245.2.j.d.214.1		4	35.4	even	6	inner
245.2.j.d.214.2		4	7.4	even	3	inner
245.2.j.e.79.1		4	7.6	odd	2
245.2.j.e.79.2		4	35.34	odd	2
245.2.j.e.214.1		4	35.24	odd	6
245.2.j.e.214.2		4	7.3	odd	6
315.2.d.a.64.1		2	21.5	even	6
315.2.d.a.64.2		2	105.89	even	6
560.2.g.b.449.1		2	140.19	even	6
560.2.g.b.449.2		2	28.19	even	6
1225.2.a.a.1.1		1	35.2	odd	12
1225.2.a.i.1.1		1	35.23	odd	12
1575.2.a.a.1.1		1	105.68	odd	12
1575.2.a.k.1.1		1	105.47	odd	12
2205.2.d.b.1324.1		2	21.2	odd	6
2205.2.d.b.1324.2		2	105.44	odd	6
2240.2.g.g.449.1		2	56.19	even	6
2240.2.g.g.449.2		2	280.19	even	6
2240.2.g.h.449.1		2	280.229	odd	6
2240.2.g.h.449.2		2	56.5	odd	6
2800.2.a.l.1.1		1	140.103	odd	12
2800.2.a.w.1.1		1	140.47	odd	12
5040.2.t.p.1009.1		2	420.299	odd	6
5040.2.t.p.1009.2		2	84.47	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.86603 + 1.23205i) q^{5} -2.00000 q^{6} +(-1.00000 + 1.73205i) q^{9} +(4.46410 - 0.267949i) q^{10} +(1.50000 + 2.59808i) q^{11} +(1.73205 + 1.00000i) q^{12} +1.00000i q^{13} +(-1.00000 + 2.00000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-6.06218 + 3.50000i) q^{17} +(3.46410 - 2.00000i) q^{18} +(-4.00000 - 2.00000i) q^{20} -6.00000i q^{22} +(5.19615 + 3.00000i) q^{23} +(1.96410 - 4.59808i) q^{25} +(1.00000 - 1.73205i) q^{26} +5.00000i q^{27} +5.00000 q^{29} +(3.73205 - 2.46410i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-6.92820 + 4.00000i) q^{32} +(2.59808 + 1.50000i) q^{33} +14.0000 q^{34} -4.00000 q^{36} +(-1.73205 - 1.00000i) q^{37} +(0.500000 + 0.866025i) q^{39} -2.00000 q^{41} +4.00000i q^{43} +(-3.00000 + 5.19615i) q^{44} +(-0.267949 - 4.46410i) q^{45} +(-6.00000 - 10.3923i) q^{46} +(-2.59808 - 1.50000i) q^{47} -4.00000i q^{48} +(-8.00000 + 6.00000i) q^{50} +(-3.50000 + 6.06218i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(5.00000 - 8.66025i) q^{54} +(-6.00000 - 3.00000i) q^{55} +(-8.66025 - 5.00000i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(-4.46410 + 0.267949i) q^{60} +(-4.00000 + 6.92820i) q^{61} -4.00000i q^{62} +8.00000 q^{64} +(-1.23205 - 1.86603i) q^{65} +(-3.00000 - 5.19615i) q^{66} +(1.73205 - 1.00000i) q^{67} +(-12.1244 - 7.00000i) q^{68} +6.00000 q^{69} -8.00000 q^{71} +(5.19615 - 3.00000i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.598076 - 4.96410i) q^{75} -2.00000i q^{78} +(-2.50000 + 4.33013i) q^{79} +(0.535898 + 8.92820i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.46410 + 2.00000i) q^{82} -4.00000i q^{83} +(7.00000 - 14.0000i) q^{85} +(4.00000 - 6.92820i) q^{86} +(4.33013 - 2.50000i) q^{87} +(-4.00000 + 8.00000i) q^{90} +12.0000i q^{92} +(1.73205 + 1.00000i) q^{93} +(3.00000 + 5.19615i) q^{94} +(-4.00000 + 6.92820i) q^{96} -7.00000i q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{15} + 8 q^{16} - 16 q^{20} - 6 q^{25} + 4 q^{26} + 20 q^{29} + 8 q^{30} + 4 q^{31} + 56 q^{34} - 16 q^{36} + 2 q^{39} - 8 q^{41}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q + 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^15 + 8 * q^16 - 16 * q^20 - 6 * q^25 + 4 * q^26 + 20 * q^29 + 8 * q^30 + 4 * q^31 + 56 * q^34 - 16 * q^36 + 2 * q^39 - 8 * q^41 - 12 * q^44 - 8 * q^45 - 24 * q^46 - 32 * q^50 - 14 * q^51 + 20 * q^54 - 24 * q^55 - 20 * q^59 - 4 * q^60 - 16 * q^61 + 32 * q^64 + 2 * q^65 - 12 * q^66 + 24 * q^69 - 32 * q^71 + 8 * q^74 + 8 * q^75 - 10 * q^79 + 16 * q^80 - 2 * q^81 + 28 * q^85 + 16 * q^86 - 16 * q^90 + 12 * q^94 - 16 * q^96 - 24 * q^99

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