LMFDB - Embedded newform 1014.2.i.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(361,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("1014.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.09683076496$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.361
Dual form			1014.2.i.c.823.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} -1.00000 q^{12} +2.00000 q^{14} +(-1.73205 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -1.00000i q^{18} +(-5.19615 - 3.00000i) q^{19} +(-1.73205 - 1.00000i) q^{20} +2.00000i q^{21} +(-2.00000 - 3.46410i) q^{23} +(0.866025 - 0.500000i) q^{24} +1.00000 q^{25} +1.00000 q^{27} +(-1.73205 + 1.00000i) q^{28} +(5.00000 + 8.66025i) q^{29} +(1.00000 - 1.73205i) q^{30} -10.0000i q^{31} +(0.866025 + 0.500000i) q^{32} +2.00000i q^{34} +(-2.00000 + 3.46410i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-6.92820 + 4.00000i) q^{37} +6.00000 q^{38} +2.00000 q^{40} +(-8.66025 + 5.00000i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(-2.00000 + 3.46410i) q^{43} +(1.73205 + 1.00000i) q^{45} +(3.46410 + 2.00000i) q^{46} +12.0000i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-0.866025 + 0.500000i) q^{50} -2.00000 q^{51} -6.00000 q^{53} +(-0.866025 + 0.500000i) q^{54} +(1.00000 - 1.73205i) q^{56} +6.00000i q^{57} +(-8.66025 - 5.00000i) q^{58} +(3.46410 + 2.00000i) q^{59} +2.00000i q^{60} +(-1.00000 + 1.73205i) q^{61} +(5.00000 + 8.66025i) q^{62} +(1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +(1.73205 - 1.00000i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-2.00000 + 3.46410i) q^{69} -4.00000i q^{70} +(-0.866025 - 0.500000i) q^{72} +4.00000i q^{73} +(4.00000 - 6.92820i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-5.19615 + 3.00000i) q^{76} +(-1.73205 + 1.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.00000 - 8.66025i) q^{82} +4.00000i q^{83} +(1.73205 + 1.00000i) q^{84} +(-3.46410 - 2.00000i) q^{85} -4.00000i q^{86} +(5.00000 - 8.66025i) q^{87} +(5.19615 - 3.00000i) q^{89} -2.00000 q^{90} -4.00000 q^{92} +(-8.66025 + 5.00000i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(-6.00000 + 10.3923i) q^{95} -1.00000i q^{96} +(-10.3923 - 6.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} + 8 q^{14} - 2 q^{16} + 4 q^{17} - 8 q^{23} + 4 q^{25} + 4 q^{27} + 20 q^{29} + 4 q^{30} - 8 q^{35} + 2 q^{36} + 24 q^{38} + 8 q^{40} - 4 q^{42} - 8 q^{43} - 2 q^{48} - 6 q^{49} - 8 q^{51} - 24 q^{53} + 4 q^{56} - 4 q^{61} + 20 q^{62} - 4 q^{64} - 4 q^{68} - 8 q^{69} + 16 q^{74} - 2 q^{75} - 2 q^{81} + 20 q^{82} + 20 q^{87} - 8 q^{90} - 16 q^{92} - 24 q^{94} - 24 q^{95}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 + 8 * q^14 - 2 * q^16 + 4 * q^17 - 8 * q^23 + 4 * q^25 + 4 * q^27 + 20 * q^29 + 4 * q^30 - 8 * q^35 + 2 * q^36 + 24 * q^38 + 8 * q^40 - 4 * q^42 - 8 * q^43 - 2 * q^48 - 6 * q^49 - 8 * q^51 - 24 * q^53 + 4 * q^56 - 4 * q^61 + 20 * q^62 - 4 * q^64 - 4 * q^68 - 8 * q^69 + 16 * q^74 - 2 * q^75 - 2 * q^81 + 20 * q^82 + 20 * q^87 - 8 * q^90 - 16 * q^92 - 24 * q^94 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−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
$5$		−	2.00000i		−	0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$		−	2.00000i		−	0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	0.135583	−	0.990766i	$-0.456709\pi$
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	−0.790237	+	0.612801i	$0.790043\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	2.00000			0.534522
$15$	−1.73205	+	1.00000i	−0.447214	+	0.258199i
$16$	−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	$0.0886875\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−5.19615	−	3.00000i	−1.19208	−	0.688247i	−0.233301	−	0.972404i	$-0.574953\pi$
$19$	−5.19615	−	3.00000i	−1.19208	−	0.688247i	−0.958778	+	0.284157i	$0.908286\pi$
$20$	−1.73205	−	1.00000i	−0.387298	−	0.223607i
$21$			2.00000i			0.436436i
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$	−1.73205	+	1.00000i	−0.327327	+	0.188982i
$29$	5.00000	+	8.66025i	0.928477	+	1.60817i	0.785872	+	0.618389i	$0.212214\pi$
$29$	5.00000	+	8.66025i	0.928477	+	1.60817i	0.142605	+	0.989780i	$0.454452\pi$
$30$	1.00000	−	1.73205i	0.182574	−	0.316228i
$31$		−	10.0000i		−	1.79605i	−0.439941	−	0.898027i	$-0.645001\pi$
$31$		−	10.0000i		−	1.79605i	0.439941	−	0.898027i	$-0.354999\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			2.00000i			0.342997i
$35$	−2.00000	+	3.46410i	−0.338062	+	0.585540i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.946180	−	0.323640i	$-0.895093\pi$
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.192809	+	0.981236i	$0.561760\pi$
$38$	6.00000			0.973329
$39$		0			0
$40$	2.00000			0.316228
$41$	−8.66025	+	5.00000i	−1.35250	+	0.780869i	−0.988600	−	0.150567i	$-0.951890\pi$
$41$	−8.66025	+	5.00000i	−1.35250	+	0.780869i	−0.363905	+	0.931436i	$0.618557\pi$
$42$	−1.00000	−	1.73205i	−0.154303	−	0.267261i
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$		0			0
$45$	1.73205	+	1.00000i	0.258199	+	0.149071i
$46$	3.46410	+	2.00000i	0.510754	+	0.294884i
$47$			12.0000i			1.75038i	0.483779	+	0.875190i	$0.339264\pi$
$47$			12.0000i			1.75038i	−0.483779	+	0.875190i	$0.660736\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−2.00000			−0.280056
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$			6.00000i			0.794719i
$58$	−8.66025	−	5.00000i	−1.13715	−	0.656532i
$59$	3.46410	+	2.00000i	0.450988	+	0.260378i	0.708247	−	0.705965i	$-0.249486\pi$
$59$	3.46410	+	2.00000i	0.450988	+	0.260378i	−0.257260	+	0.966342i	$0.582820\pi$
$60$			2.00000i			0.258199i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	5.00000	+	8.66025i	0.635001	+	1.09985i
$63$	1.73205	−	1.00000i	0.218218	−	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	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	$0.294348\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$	−2.00000	+	3.46410i	−0.240772	+	0.417029i
$70$		−	4.00000i		−	0.478091i
$71$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$71$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−5.19615	+	3.00000i	−0.596040	+	0.344124i
$77$		0			0
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−1.73205	+	1.00000i	−0.193649	+	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.00000	−	8.66025i	0.552158	−	0.956365i
$83$			4.00000i			0.439057i	0.975606	+	0.219529i	$0.0704519\pi$
$83$			4.00000i			0.439057i	−0.975606	+	0.219529i	$0.929548\pi$
$84$	1.73205	+	1.00000i	0.188982	+	0.109109i
$85$	−3.46410	−	2.00000i	−0.375735	−	0.216930i
$86$		−	4.00000i		−	0.431331i
$87$	5.00000	−	8.66025i	0.536056	−	0.928477i
$88$		0			0
$89$	5.19615	−	3.00000i	0.550791	−	0.317999i	−0.198650	−	0.980071i	$-0.563656\pi$
$89$	5.19615	−	3.00000i	0.550791	−	0.317999i	0.749441	+	0.662071i	$0.230322\pi$
$90$	−2.00000			−0.210819
$91$		0			0
$92$	−4.00000			−0.417029
$93$	−8.66025	+	5.00000i	−0.898027	+	0.518476i
$94$	−6.00000	−	10.3923i	−0.618853	−	1.07188i
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$		−	1.00000i		−	0.102062i
$97$	−10.3923	−	6.00000i	−1.05518	−	0.609208i	−0.131084	−	0.991371i	$-0.541846\pi$
$97$	−10.3923	−	6.00000i	−1.05518	−	0.609208i	−0.924095	+	0.382164i	$0.875179\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$	1.73205	−	1.00000i	0.171499	−	0.0990148i
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$		0			0
$105$	4.00000			0.390360
$106$	5.19615	−	3.00000i	0.504695	−	0.291386i
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$	6.92820	+	4.00000i	0.657596	+	0.379663i
$112$			2.00000i			0.188982i
$113$	−7.00000	+	12.1244i	−0.658505	+	1.14056i	0.322498	+	0.946570i	$0.395477\pi$
$113$	−7.00000	+	12.1244i	−0.658505	+	1.14056i	−0.981003	+	0.193993i	$0.937856\pi$
$114$	−3.00000	−	5.19615i	−0.280976	−	0.486664i
$115$	−6.92820	+	4.00000i	−0.646058	+	0.373002i
$116$	10.0000			0.928477
$117$		0			0
$118$	−4.00000			−0.368230
$119$	−3.46410	+	2.00000i	−0.317554	+	0.183340i
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$		−	2.00000i		−	0.181071i
$123$	8.66025	+	5.00000i	0.780869	+	0.450835i
$124$	−8.66025	−	5.00000i	−0.777714	−	0.449013i
$125$		−	12.0000i		−	1.07331i
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	0.632166	−	0.774833i	$-0.282166\pi$
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	−0.987108	+	0.160055i	$0.948833\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	4.00000			0.352180
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$		0			0
$133$	6.00000	+	10.3923i	0.520266	+	0.901127i
$134$	−1.00000	+	1.73205i	−0.0863868	+	0.149626i
$135$		−	2.00000i		−	0.172133i
$136$	1.73205	+	1.00000i	0.148522	+	0.0857493i
$137$	−1.73205	−	1.00000i	−0.147979	−	0.0854358i	0.424182	−	0.905577i	$-0.360562\pi$
$137$	−1.73205	−	1.00000i	−0.147979	−	0.0854358i	−0.572161	+	0.820141i	$0.693895\pi$
$138$		−	4.00000i		−	0.340503i
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	−0.0346338	−	0.999400i	$-0.511026\pi$
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	0.882823	−	0.469706i	$-0.155640\pi$
$140$	2.00000	+	3.46410i	0.169031	+	0.292770i
$141$	10.3923	−	6.00000i	0.875190	−	0.505291i
$142$		0			0
$143$		0			0
$144$	1.00000			0.0833333
$145$	17.3205	−	10.0000i	1.43839	−	0.830455i
$146$	−2.00000	−	3.46410i	−0.165521	−	0.286691i
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$			8.00000i			0.657596i
$149$	12.1244	+	7.00000i	0.993266	+	0.573462i	0.906249	−	0.422744i	$-0.138933\pi$
$149$	12.1244	+	7.00000i	0.993266	+	0.573462i	0.0870170	+	0.996207i	$0.472267\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$		−	10.0000i		−	0.813788i	−0.913475	−	0.406894i	$-0.866612\pi$
$151$		−	10.0000i		−	0.813788i	0.913475	−	0.406894i	$-0.133388\pi$
$152$	3.00000	−	5.19615i	0.243332	−	0.421464i
$153$	1.00000	+	1.73205i	0.0808452	+	0.140028i
$154$		0			0
$155$	−20.0000			−1.60644
$156$		0			0
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$		0			0
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$	1.00000	−	1.73205i	0.0790569	−	0.136931i
$161$			8.00000i			0.630488i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−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	$0.851385\pi$
$164$			10.0000i			0.780869i
$165$		0			0
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	10.3923	−	6.00000i	0.804181	−	0.464294i	−0.0407502	−	0.999169i	$-0.512975\pi$
$167$	10.3923	−	6.00000i	0.804181	−	0.464294i	0.844931	+	0.534875i	$0.179641\pi$
$168$	−2.00000			−0.154303
$169$		0			0
$170$	4.00000			0.306786
$171$	5.19615	−	3.00000i	0.397360	−	0.229416i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$			10.0000i			0.758098i
$175$	−1.73205	−	1.00000i	−0.130931	−	0.0755929i
$176$		0			0
$177$		−	4.00000i		−	0.300658i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	1.73205	−	1.00000i	0.129099	−	0.0745356i
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$	3.46410	−	2.00000i	0.255377	−	0.147442i
$185$	8.00000	+	13.8564i	0.588172	+	1.01874i
$186$	5.00000	−	8.66025i	0.366618	−	0.635001i
$187$		0			0
$188$	10.3923	+	6.00000i	0.757937	+	0.437595i
$189$	−1.73205	−	1.00000i	−0.125988	−	0.0727393i
$190$		−	12.0000i		−	0.870572i
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−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	$0.528663\pi$
$194$	12.0000			0.861550
$195$		0			0
$196$	−3.00000			−0.214286
$197$	19.0526	−	11.0000i	1.35744	−	0.783718i	0.368161	−	0.929762i	$-0.379988\pi$
$197$	19.0526	−	11.0000i	1.35744	−	0.783718i	0.989278	+	0.146045i	$0.0466543\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$			1.00000i			0.0707107i
$201$	−1.73205	−	1.00000i	−0.122169	−	0.0705346i
$202$	1.73205	+	1.00000i	0.121867	+	0.0703598i
$203$		−	20.0000i		−	1.40372i
$204$	−1.00000	+	1.73205i	−0.0700140	+	0.121268i
$205$	10.0000	+	17.3205i	0.698430	+	1.20972i
$206$	13.8564	−	8.00000i	0.965422	−	0.557386i
$207$	4.00000			0.278019
$208$		0			0
$209$		0			0
$210$	−3.46410	+	2.00000i	−0.239046	+	0.138013i
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	0.582165	−	0.813070i	$-0.302206\pi$
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	−0.995222	+	0.0976347i	$0.968872\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$	6.92820	+	4.00000i	0.473602	+	0.273434i
$215$	6.92820	+	4.00000i	0.472500	+	0.272798i
$216$			1.00000i			0.0680414i
$217$	−10.0000	+	17.3205i	−0.678844	+	1.17579i
$218$	2.00000	+	3.46410i	0.135457	+	0.234619i
$219$	3.46410	−	2.00000i	0.234082	−	0.135147i
$220$		0			0
$221$		0			0
$222$	−8.00000			−0.536925
$223$	12.1244	−	7.00000i	0.811907	−	0.468755i	−0.0357107	−	0.999362i	$-0.511370\pi$
$223$	12.1244	−	7.00000i	0.811907	−	0.468755i	0.847618	+	0.530607i	$0.178036\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$		−	14.0000i		−	0.931266i
$227$	6.92820	+	4.00000i	0.459841	+	0.265489i	0.711977	−	0.702202i	$-0.247800\pi$
$227$	6.92820	+	4.00000i	0.459841	+	0.265489i	−0.252136	+	0.967692i	$0.581133\pi$
$228$	5.19615	+	3.00000i	0.344124	+	0.198680i
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$	4.00000	−	6.92820i	0.263752	−	0.456832i
$231$		0			0
$232$	−8.66025	+	5.00000i	−0.568574	+	0.328266i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	24.0000			1.56559
$236$	3.46410	−	2.00000i	0.225494	−	0.130189i
$237$		0			0
$238$	2.00000	−	3.46410i	0.129641	−	0.224544i
$239$			16.0000i			1.03495i	0.855697	+	0.517477i	$0.173129\pi$
$239$			16.0000i			1.03495i	−0.855697	+	0.517477i	$0.826871\pi$
$240$	1.73205	+	1.00000i	0.111803	+	0.0645497i
$241$	17.3205	+	10.0000i	1.11571	+	0.644157i	0.940303	−	0.340339i	$-0.110542\pi$
$241$	17.3205	+	10.0000i	1.11571	+	0.644157i	0.175409	+	0.984496i	$0.443875\pi$
$242$		−	11.0000i		−	0.707107i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	−5.19615	+	3.00000i	−0.331970	+	0.191663i
$246$	−10.0000			−0.637577
$247$		0			0
$248$	10.0000			0.635001
$249$	3.46410	−	2.00000i	0.219529	−	0.126745i
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	14.0000	−	24.2487i	0.883672	−	1.53057i	0.0364441	−	0.999336i	$-0.488397\pi$
$251$	14.0000	−	24.2487i	0.883672	−	1.53057i	0.847228	−	0.531229i	$-0.178270\pi$
$252$		−	2.00000i		−	0.125988i
$253$		0			0
$254$	6.92820	+	4.00000i	0.434714	+	0.250982i
$255$			4.00000i			0.250490i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$	−3.46410	+	2.00000i	−0.215666	+	0.124515i
$259$	16.0000			0.994192
$260$		0			0
$261$	−10.0000			−0.618984
$262$	6.92820	−	4.00000i	0.428026	−	0.247121i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$		0			0
$265$			12.0000i			0.737154i
$266$	−10.3923	−	6.00000i	−0.637193	−	0.367884i
$267$	−5.19615	−	3.00000i	−0.317999	−	0.183597i
$268$		−	2.00000i		−	0.122169i
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	−0.672374	−	0.740212i	$-0.734725\pi$
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	0.977229	+	0.212187i	$0.0680585\pi$
$270$	1.00000	+	1.73205i	0.0608581	+	0.105409i
$271$	8.66025	−	5.00000i	0.526073	−	0.303728i	−0.213343	−	0.976977i	$-0.568435\pi$
$271$	8.66025	−	5.00000i	0.526073	−	0.303728i	0.739416	+	0.673249i	$0.235102\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	2.00000			0.120824
$275$		0			0
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$			20.0000i			1.19952i
$279$	8.66025	+	5.00000i	0.518476	+	0.299342i
$280$	−3.46410	−	2.00000i	−0.207020	−	0.119523i
$281$			10.0000i			0.596550i	0.954480	+	0.298275i	$0.0964112\pi$
$281$			10.0000i			0.596550i	−0.954480	+	0.298275i	$0.903589\pi$
$282$	−6.00000	+	10.3923i	−0.357295	+	0.618853i
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$		0			0
$285$	12.0000			0.710819
$286$		0			0
$287$	20.0000			1.18056
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−10.0000	+	17.3205i	−0.587220	+	1.01710i
$291$			12.0000i			0.703452i
$292$	3.46410	+	2.00000i	0.202721	+	0.117041i
$293$	−12.1244	−	7.00000i	−0.708312	−	0.408944i	0.102123	−	0.994772i	$-0.467436\pi$
$293$	−12.1244	−	7.00000i	−0.708312	−	0.408944i	−0.810436	+	0.585827i	$0.800770\pi$
$294$		−	3.00000i		−	0.174964i
$295$	4.00000	−	6.92820i	0.232889	−	0.403376i
$296$	−4.00000	−	6.92820i	−0.232495	−	0.402694i
$297$		0			0
$298$	−14.0000			−0.810998
$299$		0			0
$300$	−1.00000			−0.0577350
$301$	6.92820	−	4.00000i	0.399335	−	0.230556i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$	−1.00000	+	1.73205i	−0.0574485	+	0.0995037i
$304$			6.00000i			0.344124i
$305$	3.46410	+	2.00000i	0.198354	+	0.114520i
$306$	−1.73205	−	1.00000i	−0.0990148	−	0.0571662i
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$		0			0
$309$	8.00000	+	13.8564i	0.455104	+	0.788263i
$310$	17.3205	−	10.0000i	0.983739	−	0.567962i
$311$	−28.0000			−1.58773			−0.793867	−	0.608091i	$-0.791935\pi$
$311$	−28.0000			−1.58773			−0.793867	+	0.608091i	$0.791935\pi$
$312$		0			0
$313$	−26.0000			−1.46961			−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000			−1.46961			−0.734803	+	0.678280i	$0.762726\pi$
$314$	1.73205	−	1.00000i	0.0977453	−	0.0564333i
$315$	−2.00000	−	3.46410i	−0.112687	−	0.195180i
$316$		0			0
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$	−5.19615	−	3.00000i	−0.291386	−	0.168232i
$319$		0			0
$320$			2.00000i			0.111803i
$321$	−4.00000	+	6.92820i	−0.223258	+	0.386695i
$322$	−4.00000	−	6.92820i	−0.222911	−	0.386094i
$323$	−10.3923	+	6.00000i	−0.578243	+	0.333849i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	14.0000			0.775388
$327$	−3.46410	+	2.00000i	−0.191565	+	0.110600i
$328$	−5.00000	−	8.66025i	−0.276079	−	0.478183i
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	−8.66025	−	5.00000i	−0.476011	−	0.274825i	0.242742	−	0.970091i	$-0.421953\pi$
$331$	−8.66025	−	5.00000i	−0.476011	−	0.274825i	−0.718752	+	0.695266i	$0.755287\pi$
$332$	3.46410	+	2.00000i	0.190117	+	0.109764i
$333$		−	8.00000i		−	0.438397i
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	−2.00000	−	3.46410i	−0.109272	−	0.189264i
$336$	1.73205	−	1.00000i	0.0944911	−	0.0545545i
$337$	−2.00000			−0.108947			−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000			−0.108947			−0.0544735	+	0.998515i	$0.517348\pi$
$338$		0			0
$339$	14.0000			0.760376
$340$	−3.46410	+	2.00000i	−0.187867	+	0.108465i
$341$		0			0
$342$	−3.00000	+	5.19615i	−0.162221	+	0.280976i
$343$			20.0000i			1.07990i
$344$	−3.46410	−	2.00000i	−0.186772	−	0.107833i
$345$	6.92820	+	4.00000i	0.373002	+	0.215353i
$346$			6.00000i			0.322562i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	−5.00000	−	8.66025i	−0.268028	−	0.464238i
$349$	13.8564	−	8.00000i	0.741716	−	0.428230i	−0.0809766	−	0.996716i	$-0.525804\pi$
$349$	13.8564	−	8.00000i	0.741716	−	0.428230i	0.822693	+	0.568486i	$0.192471\pi$
$350$	2.00000			0.106904
$351$		0			0
$352$		0			0
$353$	−22.5167	+	13.0000i	−1.19844	+	0.691920i	−0.960207	−	0.279288i	$-0.909902\pi$
$353$	−22.5167	+	13.0000i	−1.19844	+	0.691920i	−0.238233	+	0.971208i	$0.576568\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$		0			0
$356$		−	6.00000i		−	0.317999i
$357$	3.46410	+	2.00000i	0.183340	+	0.105851i
$358$		0			0
$359$		−	4.00000i		−	0.211112i	−0.994413	−	0.105556i	$-0.966338\pi$
$359$		−	4.00000i		−	0.211112i	0.994413	−	0.105556i	$-0.0336622\pi$
$360$	−1.00000	+	1.73205i	−0.0527046	+	0.0912871i
$361$	8.50000	+	14.7224i	0.447368	+	0.774865i
$362$	−19.0526	+	11.0000i	−1.00138	+	0.578147i
$363$	11.0000			0.577350
$364$		0			0
$365$	8.00000			0.418739
$366$	−1.73205	+	1.00000i	−0.0905357	+	0.0522708i
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$		−	10.0000i		−	0.520579i
$370$	−13.8564	−	8.00000i	−0.720360	−	0.415900i
$371$	10.3923	+	6.00000i	0.539542	+	0.311504i
$372$			10.0000i			0.518476i
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	−0.777847	−	0.628454i	$-0.783688\pi$
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	0.933181	+	0.359408i	$0.117021\pi$
$374$		0			0
$375$	−10.3923	+	6.00000i	−0.536656	+	0.309839i
$376$	−12.0000			−0.618853
$377$		0			0
$378$	2.00000			0.102869
$379$	−29.4449	+	17.0000i	−1.51248	+	0.873231i	−0.512588	+	0.858635i	$0.671313\pi$
$379$	−29.4449	+	17.0000i	−1.51248	+	0.873231i	−0.999893	+	0.0145964i	$0.995354\pi$
$380$	6.00000	+	10.3923i	0.307794	+	0.533114i
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$		−	12.0000i		−	0.613973i
$383$	−3.46410	−	2.00000i	−0.177007	−	0.102195i	0.408879	−	0.912589i	$-0.365920\pi$
$383$	−3.46410	−	2.00000i	−0.177007	−	0.102195i	−0.585886	+	0.810394i	$0.699253\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	8.00000	−	13.8564i	0.407189	−	0.705273i
$387$	−2.00000	−	3.46410i	−0.101666	−	0.176090i
$388$	−10.3923	+	6.00000i	−0.527589	+	0.304604i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$	4.00000	+	6.92820i	0.201773	+	0.349482i
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$		0			0
$396$		0			0
$397$	6.92820	+	4.00000i	0.347717	+	0.200754i	0.663679	−	0.748017i	$-0.268994\pi$
$397$	6.92820	+	4.00000i	0.347717	+	0.200754i	−0.315963	+	0.948772i	$0.602327\pi$
$398$		0			0
$399$	6.00000	−	10.3923i	0.300376	−	0.520266i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	25.9808	−	15.0000i	1.29742	−	0.749064i	0.317460	−	0.948272i	$-0.397170\pi$
$401$	25.9808	−	15.0000i	1.29742	−	0.749064i	0.979957	+	0.199207i	$0.0638367\pi$
$402$	2.00000			0.0997509
$403$		0			0
$404$	−2.00000			−0.0995037
$405$	−1.73205	+	1.00000i	−0.0860663	+	0.0496904i
$406$	10.0000	+	17.3205i	0.496292	+	0.859602i
$407$		0			0
$408$		−	2.00000i		−	0.0990148i
$409$	3.46410	+	2.00000i	0.171289	+	0.0988936i	0.583193	−	0.812333i	$-0.301803\pi$
$409$	3.46410	+	2.00000i	0.171289	+	0.0988936i	−0.411905	+	0.911227i	$0.635136\pi$
$410$	−17.3205	−	10.0000i	−0.855399	−	0.493865i
$411$			2.00000i			0.0986527i
$412$	−8.00000	+	13.8564i	−0.394132	+	0.682656i
$413$	−4.00000	−	6.92820i	−0.196827	−	0.340915i
$414$	−3.46410	+	2.00000i	−0.170251	+	0.0982946i
$415$	8.00000			0.392705
$416$		0			0
$417$	−20.0000			−0.979404
$418$		0			0
$419$	−20.0000	−	34.6410i	−0.977064	−	1.69232i	−0.672949	−	0.739689i	$-0.734973\pi$
$419$	−20.0000	−	34.6410i	−0.977064	−	1.69232i	−0.304115	−	0.952635i	$-0.598361\pi$
$420$	2.00000	−	3.46410i	0.0975900	−	0.169031i
$421$		−	20.0000i		−	0.974740i	−0.873195	−	0.487370i	$-0.837956\pi$
$421$		−	20.0000i		−	0.974740i	0.873195	−	0.487370i	$-0.162044\pi$
$422$	10.3923	+	6.00000i	0.505889	+	0.292075i
$423$	−10.3923	−	6.00000i	−0.505291	−	0.291730i
$424$		−	6.00000i		−	0.291386i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$	3.46410	−	2.00000i	0.167640	−	0.0967868i
$428$	−8.00000			−0.386695
$429$		0			0
$430$	−8.00000			−0.385794
$431$	17.3205	−	10.0000i	0.834300	−	0.481683i	−0.0210230	−	0.999779i	$-0.506692\pi$
$431$	17.3205	−	10.0000i	0.834300	−	0.481683i	0.855323	+	0.518096i	$0.173359\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	13.0000	−	22.5167i	0.624740	−	1.08208i	−0.363851	−	0.931457i	$-0.618538\pi$
$433$	13.0000	−	22.5167i	0.624740	−	1.08208i	0.988591	−	0.150624i	$-0.0481284\pi$
$434$		−	20.0000i		−	0.960031i
$435$	−17.3205	−	10.0000i	−0.830455	−	0.479463i
$436$	−3.46410	−	2.00000i	−0.165900	−	0.0957826i
$437$			24.0000i			1.14808i
$438$	−2.00000	+	3.46410i	−0.0955637	+	0.165521i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$		0			0
$443$	−16.0000			−0.760183			−0.380091	−	0.924949i	$-0.624107\pi$
$443$	−16.0000			−0.760183			−0.380091	+	0.924949i	$0.624107\pi$
$444$	6.92820	−	4.00000i	0.328798	−	0.189832i
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	−7.00000	+	12.1244i	−0.331460	+	0.574105i
$447$		−	14.0000i		−	0.662177i
$448$	1.73205	+	1.00000i	0.0818317	+	0.0472456i
$449$	−5.19615	−	3.00000i	−0.245222	−	0.141579i	0.372353	−	0.928091i	$-0.378551\pi$
$449$	−5.19615	−	3.00000i	−0.245222	−	0.141579i	−0.617574	+	0.786513i	$0.711885\pi$
$450$		−	1.00000i		−	0.0471405i
$451$		0			0
$452$	7.00000	+	12.1244i	0.329252	+	0.570282i
$453$	−8.66025	+	5.00000i	−0.406894	+	0.234920i
$454$	−8.00000			−0.375459
$455$		0			0
$456$	−6.00000			−0.280976
$457$	−24.2487	+	14.0000i	−1.13431	+	0.654892i	−0.945015	−	0.327028i	$-0.893953\pi$
$457$	−24.2487	+	14.0000i	−1.13431	+	0.654892i	−0.189292	+	0.981921i	$0.560619\pi$
$458$	2.00000	+	3.46410i	0.0934539	+	0.161867i
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$			8.00000i			0.373002i
$461$	−25.9808	−	15.0000i	−1.21004	−	0.698620i	−0.247276	−	0.968945i	$-0.579535\pi$
$461$	−25.9808	−	15.0000i	−1.21004	−	0.698620i	−0.962769	+	0.270326i	$0.912869\pi$
$462$		0			0
$463$		−	6.00000i		−	0.278844i	−0.990233	−	0.139422i	$-0.955476\pi$
$463$		−	6.00000i		−	0.278844i	0.990233	−	0.139422i	$-0.0445244\pi$
$464$	5.00000	−	8.66025i	0.232119	−	0.402042i
$465$	10.0000	+	17.3205i	0.463739	+	0.803219i
$466$	5.19615	−	3.00000i	0.240707	−	0.138972i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$	−20.7846	+	12.0000i	−0.958723	+	0.553519i
$471$	1.00000	+	1.73205i	0.0460776	+	0.0798087i
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$		0			0
$474$		0			0
$475$	−5.19615	−	3.00000i	−0.238416	−	0.137649i
$476$			4.00000i			0.183340i
$477$	3.00000	−	5.19615i	0.137361	−	0.237915i
$478$	−8.00000	−	13.8564i	−0.365911	−	0.633777i
$479$	−20.7846	+	12.0000i	−0.949673	+	0.548294i	−0.892979	−	0.450098i	$-0.851389\pi$
$479$	−20.7846	+	12.0000i	−0.949673	+	0.548294i	−0.0566937	+	0.998392i	$0.518056\pi$
$480$	−2.00000			−0.0912871
$481$		0			0
$482$	−20.0000			−0.910975
$483$	6.92820	−	4.00000i	0.315244	−	0.182006i
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	−12.0000	+	20.7846i	−0.544892	+	0.943781i
$486$		−	1.00000i		−	0.0453609i
$487$	15.5885	+	9.00000i	0.706380	+	0.407829i	0.809719	−	0.586817i	$-0.199619\pi$
$487$	15.5885	+	9.00000i	0.706380	+	0.407829i	−0.103339	+	0.994646i	$0.532953\pi$
$488$	−1.73205	−	1.00000i	−0.0784063	−	0.0452679i
$489$			14.0000i			0.633102i
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	14.0000	+	24.2487i	0.631811	+	1.09433i	0.987181	+	0.159603i	$0.0510215\pi$
$491$	14.0000	+	24.2487i	0.631811	+	1.09433i	−0.355370	+	0.934726i	$0.615645\pi$
$492$	8.66025	−	5.00000i	0.390434	−	0.225417i
$493$	20.0000			0.900755
$494$		0			0
$495$		0			0
$496$	−8.66025	+	5.00000i	−0.388857	+	0.224507i
$497$		0			0
$498$	−2.00000	+	3.46410i	−0.0896221	+	0.155230i
$499$		−	14.0000i		−	0.626726i	−0.949633	−	0.313363i	$-0.898544\pi$
$499$		−	14.0000i		−	0.626726i	0.949633	−	0.313363i	$-0.101456\pi$
$500$	−10.3923	−	6.00000i	−0.464758	−	0.268328i
$501$	−10.3923	−	6.00000i	−0.464294	−	0.268060i
$502$			28.0000i			1.24970i
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	0.464107	+	0.885779i	$0.346375\pi$
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	−0.999161	+	0.0409609i	$0.986958\pi$
$504$	1.00000	+	1.73205i	0.0445435	+	0.0771517i
$505$	−3.46410	+	2.00000i	−0.154150	+	0.0889988i
$506$		0			0
$507$		0			0
$508$	−8.00000			−0.354943
$509$	5.19615	−	3.00000i	0.230315	−	0.132973i	−0.380402	−	0.924821i	$-0.624214\pi$
$509$	5.19615	−	3.00000i	0.230315	−	0.132973i	0.610718	+	0.791849i	$0.290881\pi$
$510$	−2.00000	−	3.46410i	−0.0885615	−	0.153393i
$511$	4.00000	−	6.92820i	0.176950	−	0.306486i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.19615	−	3.00000i	−0.229416	−	0.132453i
$514$	15.5885	+	9.00000i	0.687577	+	0.396973i
$515$			32.0000i			1.41009i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$		0			0
$518$	−13.8564	+	8.00000i	−0.608816	+	0.351500i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$	8.66025	−	5.00000i	0.379049	−	0.218844i
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	0.818980	−	0.573822i	$-0.194540\pi$
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	−0.906434	+	0.422347i	$0.861206\pi$
$524$	−4.00000	+	6.92820i	−0.174741	+	0.302660i
$525$			2.00000i			0.0872872i
$526$	20.7846	+	12.0000i	0.906252	+	0.523225i
$527$	−17.3205	−	10.0000i	−0.754493	−	0.435607i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−6.00000	−	10.3923i	−0.260623	−	0.451413i
$531$	−3.46410	+	2.00000i	−0.150329	+	0.0867926i
$532$	12.0000			0.520266
$533$		0			0
$534$	6.00000			0.259645
$535$	−13.8564	+	8.00000i	−0.599065	+	0.345870i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$		0			0
$538$			10.0000i			0.431131i
$539$		0			0
$540$	−1.73205	−	1.00000i	−0.0745356	−	0.0430331i
$541$			20.0000i			0.859867i	0.902861	+	0.429934i	$0.141463\pi$
$541$			20.0000i			0.859867i	−0.902861	+	0.429934i	$0.858537\pi$
$542$	−5.00000	+	8.66025i	−0.214768	+	0.371990i
$543$	−11.0000	−	19.0526i	−0.472055	−	0.817624i
$544$	1.73205	−	1.00000i	0.0742611	−	0.0428746i
$545$	−8.00000			−0.342682
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	−1.73205	+	1.00000i	−0.0739895	+	0.0427179i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$		0			0
$551$		−	60.0000i		−	2.55609i
$552$	−3.46410	−	2.00000i	−0.147442	−	0.0851257i
$553$		0			0
$554$			2.00000i			0.0849719i
$555$	8.00000	−	13.8564i	0.339581	−	0.588172i
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	−0.792469	−	0.609912i	$-0.791205\pi$
$557$	−15.5885	+	9.00000i	−0.660504	+	0.381342i	0.131965	+	0.991254i	$0.457871\pi$
$558$	−10.0000			−0.423334
$559$		0			0
$560$	4.00000			0.169031
$561$		0			0
$562$	−5.00000	−	8.66025i	−0.210912	−	0.365311i
$563$	8.00000	−	13.8564i	0.337160	−	0.583978i	−0.646737	−	0.762713i	$-0.723867\pi$
$563$	8.00000	−	13.8564i	0.337160	−	0.583978i	0.983897	+	0.178735i	$0.0572004\pi$
$564$		−	12.0000i		−	0.505291i
$565$	24.2487	+	14.0000i	1.02015	+	0.588984i
$566$	3.46410	+	2.00000i	0.145607	+	0.0840663i
$567$			2.00000i			0.0839921i
$568$		0			0
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	0.741981	−	0.670421i	$-0.233886\pi$
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	−0.951592	+	0.307364i	$0.900553\pi$
$570$	−10.3923	+	6.00000i	−0.435286	+	0.251312i
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$		0			0
$573$	12.0000			0.501307
$574$	−17.3205	+	10.0000i	−0.722944	+	0.417392i
$575$	−2.00000	−	3.46410i	−0.0834058	−	0.144463i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	8.00000i		−	0.333044i	−0.986038	−	0.166522i	$-0.946746\pi$
$577$		−	8.00000i		−	0.333044i	0.986038	−	0.166522i	$-0.0532537\pi$
$578$	−11.2583	−	6.50000i	−0.468285	−	0.270364i
$579$	13.8564	+	8.00000i	0.575853	+	0.332469i
$580$		−	20.0000i		−	0.830455i
$581$	4.00000	−	6.92820i	0.165948	−	0.287430i
$582$	−6.00000	−	10.3923i	−0.248708	−	0.430775i
$583$		0			0
$584$	−4.00000			−0.165521
$585$		0			0
$586$	14.0000			0.578335
$587$	−24.2487	+	14.0000i	−1.00085	+	0.577842i	−0.908500	−	0.417885i	$-0.862772\pi$
$587$	−24.2487	+	14.0000i	−1.00085	+	0.577842i	−0.0923513	+	0.995726i	$0.529438\pi$
$588$	1.50000	+	2.59808i	0.0618590	+	0.107143i
$589$	−30.0000	+	51.9615i	−1.23613	+	2.14104i
$590$			8.00000i			0.329355i
$591$	−19.0526	−	11.0000i	−0.783718	−	0.452480i
$592$	6.92820	+	4.00000i	0.284747	+	0.164399i
$593$		−	26.0000i		−	1.06769i	−0.845582	−	0.533846i	$-0.820746\pi$
$593$		−	26.0000i		−	1.06769i	0.845582	−	0.533846i	$-0.179254\pi$
$594$		0			0
$595$	4.00000	+	6.92820i	0.163984	+	0.284029i
$596$	12.1244	−	7.00000i	0.496633	−	0.286731i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	0.866025	−	0.500000i	0.0353553	−	0.0204124i
$601$	−11.0000	−	19.0526i	−0.448699	−	0.777170i	0.549602	−	0.835426i	$-0.314779\pi$
$601$	−11.0000	−	19.0526i	−0.448699	−	0.777170i	−0.998302	+	0.0582563i	$0.981446\pi$
$602$	−4.00000	+	6.92820i	−0.163028	+	0.282372i
$603$			2.00000i			0.0814463i
$604$	−8.66025	−	5.00000i	−0.352381	−	0.203447i
$605$	19.0526	+	11.0000i	0.774597	+	0.447214i
$606$		−	2.00000i		−	0.0812444i
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	−0.333842	−	0.942629i	$-0.608345\pi$
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	0.983262	−	0.182199i	$-0.0583216\pi$
$608$	−3.00000	−	5.19615i	−0.121666	−	0.210732i
$609$	−17.3205	+	10.0000i	−0.701862	+	0.405220i
$610$	−4.00000			−0.161955
$611$		0			0
$612$	2.00000			0.0808452
$613$	−13.8564	+	8.00000i	−0.559655	+	0.323117i	−0.753007	−	0.658012i	$-0.771397\pi$
$613$	−13.8564	+	8.00000i	−0.559655	+	0.323117i	0.193352	+	0.981129i	$0.438064\pi$
$614$	−1.00000	−	1.73205i	−0.0403567	−	0.0698999i
$615$	10.0000	−	17.3205i	0.403239	−	0.698430i
$616$		0			0
$617$	−19.0526	−	11.0000i	−0.767027	−	0.442843i	0.0647859	−	0.997899i	$-0.479364\pi$
$617$	−19.0526	−	11.0000i	−0.767027	−	0.442843i	−0.831813	+	0.555056i	$0.812697\pi$
$618$	−13.8564	−	8.00000i	−0.557386	−	0.321807i
$619$			26.0000i			1.04503i	0.852631	+	0.522514i	$0.175006\pi$
$619$			26.0000i			1.04503i	−0.852631	+	0.522514i	$0.824994\pi$
$620$	−10.0000	+	17.3205i	−0.401610	+	0.695608i
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$	24.2487	−	14.0000i	0.972285	−	0.561349i
$623$	−12.0000			−0.480770
$624$		0			0
$625$	−19.0000			−0.760000
$626$	22.5167	−	13.0000i	0.899947	−	0.519584i
$627$		0			0
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$			16.0000i			0.637962i
$630$	3.46410	+	2.00000i	0.138013	+	0.0796819i
$631$	8.66025	+	5.00000i	0.344759	+	0.199047i	0.662375	−	0.749173i	$-0.269549\pi$
$631$	8.66025	+	5.00000i	0.344759	+	0.199047i	−0.317615	+	0.948220i	$0.602882\pi$
$632$		0			0
$633$	−6.00000	+	10.3923i	−0.238479	+	0.413057i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−13.8564	+	8.00000i	−0.549875	+	0.317470i
$636$	6.00000			0.237915
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−1.00000	−	1.73205i	−0.0395285	−	0.0684653i
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$		−	8.00000i		−	0.315735i
$643$	5.19615	+	3.00000i	0.204916	+	0.118308i	0.598947	−	0.800789i	$-0.295586\pi$
$643$	5.19615	+	3.00000i	0.204916	+	0.118308i	−0.394030	+	0.919097i	$0.628920\pi$
$644$	6.92820	+	4.00000i	0.273009	+	0.157622i
$645$		−	8.00000i		−	0.315000i
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	16.0000	+	27.7128i	0.629025	+	1.08950i	0.987748	+	0.156059i	$0.0498790\pi$
$647$	16.0000	+	27.7128i	0.629025	+	1.08950i	−0.358723	+	0.933444i	$0.616788\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$		0			0
$650$		0			0
$651$	20.0000			0.783862
$652$	−12.1244	+	7.00000i	−0.474826	+	0.274141i
$653$	13.0000	+	22.5167i	0.508729	+	0.881145i	0.999949	+	0.0101092i	$0.00321793\pi$
$653$	13.0000	+	22.5167i	0.508729	+	0.881145i	−0.491220	+	0.871036i	$0.663449\pi$
$654$	2.00000	−	3.46410i	0.0782062	−	0.135457i
$655$			16.0000i			0.625172i
$656$	8.66025	+	5.00000i	0.338126	+	0.195217i
$657$	−3.46410	−	2.00000i	−0.135147	−	0.0780274i
$658$			24.0000i			0.935617i
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	−0.992388	−	0.123148i	$-0.960701\pi$
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	0.602844	+	0.797859i	$0.294034\pi$
$660$		0			0
$661$	34.6410	−	20.0000i	1.34738	−	0.777910i	0.359502	−	0.933144i	$-0.382947\pi$
$661$	34.6410	−	20.0000i	1.34738	−	0.777910i	0.987878	+	0.155235i	$0.0496133\pi$
$662$	10.0000			0.388661
$663$		0			0
$664$	−4.00000			−0.155230
$665$	20.7846	−	12.0000i	0.805993	−	0.465340i
$666$	4.00000	+	6.92820i	0.154997	+	0.268462i
$667$	20.0000	−	34.6410i	0.774403	−	1.34131i
$668$		−	12.0000i		−	0.464294i
$669$	−12.1244	−	7.00000i	−0.468755	−	0.270636i
$670$	3.46410	+	2.00000i	0.133830	+	0.0772667i
$671$		0			0
$672$	−1.00000	+	1.73205i	−0.0385758	+	0.0668153i
$673$	3.00000	+	5.19615i	0.115642	+	0.200297i	0.918036	−	0.396497i	$-0.129774\pi$
$673$	3.00000	+	5.19615i	0.115642	+	0.200297i	−0.802395	+	0.596794i	$0.796441\pi$
$674$	1.73205	−	1.00000i	0.0667161	−	0.0385186i
$675$	1.00000			0.0384900
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	−12.1244	+	7.00000i	−0.465633	+	0.268833i
$679$	12.0000	+	20.7846i	0.460518	+	0.797640i
$680$	2.00000	−	3.46410i	0.0766965	−	0.132842i
$681$		−	8.00000i		−	0.306561i
$682$		0			0
$683$	−20.7846	−	12.0000i	−0.795301	−	0.459167i	0.0465244	−	0.998917i	$-0.485185\pi$
$683$	−20.7846	−	12.0000i	−0.795301	−	0.459167i	−0.841825	+	0.539750i	$0.818519\pi$
$684$		−	6.00000i		−	0.229416i
$685$	−2.00000	+	3.46410i	−0.0764161	+	0.132357i
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	−3.46410	+	2.00000i	−0.132164	+	0.0763048i
$688$	4.00000			0.152499
$689$		0			0
$690$	−8.00000			−0.304555
$691$	8.66025	−	5.00000i	0.329452	−	0.190209i	−0.326146	−	0.945319i	$-0.605750\pi$
$691$	8.66025	−	5.00000i	0.329452	−	0.190209i	0.655598	+	0.755110i	$0.272417\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$		0			0
$694$			12.0000i			0.455514i
$695$	−34.6410	−	20.0000i	−1.31401	−	0.758643i
$696$	8.66025	+	5.00000i	0.328266	+	0.189525i
$697$			20.0000i			0.757554i
$698$	−8.00000	+	13.8564i	−0.302804	+	0.524473i
$699$	3.00000	+	5.19615i	0.113470	+	0.196537i
$700$	−1.73205	+	1.00000i	−0.0654654	+	0.0377964i
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$		0			0
$703$	48.0000			1.81035
$704$		0			0
$705$	−12.0000	−	20.7846i	−0.451946	−	0.782794i
$706$	13.0000	−	22.5167i	0.489261	−	0.847426i
$707$			4.00000i			0.150435i
$708$	−3.46410	−	2.00000i	−0.130189	−	0.0751646i
$709$	−31.1769	−	18.0000i	−1.17087	−	0.676004i	−0.216988	−	0.976174i	$-0.569623\pi$
$709$	−31.1769	−	18.0000i	−1.17087	−	0.676004i	−0.953886	+	0.300170i	$0.902957\pi$
$710$		0			0
$711$		0			0
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	−34.6410	+	20.0000i	−1.29732	+	0.749006i
$714$	−4.00000			−0.149696
$715$		0			0
$716$		0			0
$717$	13.8564	−	8.00000i	0.517477	−	0.298765i
$718$	2.00000	+	3.46410i	0.0746393	+	0.129279i
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	−0.990016	−	0.140955i	$-0.954983\pi$
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	0.617079	+	0.786901i	$0.288316\pi$
$720$		−	2.00000i		−	0.0745356i
$721$	27.7128	+	16.0000i	1.03208	+	0.595871i
$722$	−14.7224	−	8.50000i	−0.547912	−	0.316337i
$723$		−	20.0000i		−	0.743808i
$724$	11.0000	−	19.0526i	0.408812	−	0.708083i
$725$	5.00000	+	8.66025i	0.185695	+	0.321634i
$726$	−9.52628	+	5.50000i	−0.353553	+	0.204124i
$727$	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
$730$	−6.92820	+	4.00000i	−0.256424	+	0.148047i
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$	1.00000	−	1.73205i	0.0369611	−	0.0640184i
$733$			44.0000i			1.62518i	0.582838	+	0.812589i	$0.301942\pi$
$733$			44.0000i			1.62518i	−0.582838	+	0.812589i	$0.698058\pi$
$734$	6.92820	+	4.00000i	0.255725	+	0.147643i
$735$	5.19615	+	3.00000i	0.191663	+	0.110657i
$736$		−	4.00000i		−	0.147442i
$737$		0			0
$738$	5.00000	+	8.66025i	0.184053	+	0.318788i
$739$	22.5167	−	13.0000i	0.828289	−	0.478213i	−0.0249776	−	0.999688i	$-0.507951\pi$
$739$	22.5167	−	13.0000i	0.828289	−	0.478213i	0.853266	+	0.521475i	$0.174618\pi$
$740$	16.0000			0.588172
$741$		0			0
$742$	−12.0000			−0.440534
$743$	−13.8564	+	8.00000i	−0.508342	+	0.293492i	−0.732152	−	0.681141i	$-0.761484\pi$
$743$	−13.8564	+	8.00000i	−0.508342	+	0.293492i	0.223810	+	0.974633i	$0.428151\pi$
$744$	−5.00000	−	8.66025i	−0.183309	−	0.317500i
$745$	14.0000	−	24.2487i	0.512920	−	0.888404i
$746$			6.00000i			0.219676i
$747$	−3.46410	−	2.00000i	−0.126745	−	0.0731762i
$748$		0			0
$749$			16.0000i			0.584627i
$750$	6.00000	−	10.3923i	0.219089	−	0.379473i
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	−0.995018	−	0.0996961i	$-0.968213\pi$
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	0.411170	−	0.911559i	$-0.365120\pi$
$752$	10.3923	−	6.00000i	0.378968	−	0.218797i
$753$	−28.0000			−1.02038
$754$		0			0
$755$	−20.0000			−0.727875
$756$	−1.73205	+	1.00000i	−0.0629941	+	0.0363696i
$757$	11.0000	+	19.0526i	0.399802	+	0.692477i	0.993701	−	0.112062i	$-0.0357456\pi$
$757$	11.0000	+	19.0526i	0.399802	+	0.692477i	−0.593899	+	0.804539i	$0.702412\pi$
$758$	17.0000	−	29.4449i	0.617468	−	1.06949i
$759$		0			0
$760$	−10.3923	−	6.00000i	−0.376969	−	0.217643i
$761$	25.9808	+	15.0000i	0.941802	+	0.543750i	0.890525	−	0.454935i	$-0.150337\pi$
$761$	25.9808	+	15.0000i	0.941802	+	0.543750i	0.0512772	+	0.998684i	$0.483671\pi$
$762$		−	8.00000i		−	0.289809i
$763$	−4.00000	+	6.92820i	−0.144810	+	0.250818i
$764$	6.00000	+	10.3923i	0.217072	+	0.375980i
$765$	3.46410	−	2.00000i	0.125245	−	0.0723102i
$766$	4.00000			0.144526
$767$		0			0
$768$	1.00000			0.0360844
$769$	−20.7846	+	12.0000i	−0.749512	+	0.432731i	−0.825518	−	0.564376i	$-0.809117\pi$
$769$	−20.7846	+	12.0000i	−0.749512	+	0.432731i	0.0760054	+	0.997107i	$0.475783\pi$
$770$		0			0
$771$	−9.00000	+	15.5885i	−0.324127	+	0.561405i
$772$			16.0000i			0.575853i
$773$	5.19615	+	3.00000i	0.186893	+	0.107903i	0.590527	−	0.807018i	$-0.298920\pi$
$773$	5.19615	+	3.00000i	0.186893	+	0.107903i	−0.403634	+	0.914920i	$0.632253\pi$
$774$	3.46410	+	2.00000i	0.124515	+	0.0718885i
$775$		−	10.0000i		−	0.359211i
$776$	6.00000	−	10.3923i	0.215387	−	0.373062i
$777$	−8.00000	−	13.8564i	−0.286998	−	0.497096i
$778$	−25.9808	+	15.0000i	−0.931455	+	0.537776i
$779$	60.0000			2.14972
$780$		0			0
$781$		0			0
$782$	6.92820	−	4.00000i	0.247752	−	0.143040i
$783$	5.00000	+	8.66025i	0.178685	+	0.309492i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$			4.00000i			0.142766i
$786$	−6.92820	−	4.00000i	−0.247121	−	0.142675i
$787$	32.9090	+	19.0000i	1.17308	+	0.677277i	0.954403	−	0.298521i	$-0.0964933\pi$
$787$	32.9090	+	19.0000i	1.17308	+	0.677277i	0.218675	+	0.975798i	$0.429827\pi$
$788$		−	22.0000i		−	0.783718i
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$		0			0
$791$	24.2487	−	14.0000i	0.862185	−	0.497783i
$792$		0			0
$793$		0			0
$794$	−8.00000			−0.283909
$795$	10.3923	−	6.00000i	0.368577	−	0.212798i
$796$		0			0
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	−0.847771	−	0.530362i	$-0.822056\pi$
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	0.883193	+	0.469010i	$0.155389\pi$
$798$			12.0000i			0.424795i
$799$	20.7846	+	12.0000i	0.735307	+	0.424529i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$			6.00000i			0.212000i
$802$	−15.0000	+	25.9808i	−0.529668	+	0.917413i
$803$		0			0
$804$	−1.73205	+	1.00000i	−0.0610847	+	0.0352673i
$805$	16.0000			0.563926
$806$		0			0
$807$	−10.0000			−0.352017
$808$	1.73205	−	1.00000i	0.0609333	−	0.0351799i
$809$	25.0000	+	43.3013i	0.878953	+	1.52239i	0.852491	+	0.522742i	$0.175091\pi$
$809$	25.0000	+	43.3013i	0.878953	+	1.52239i	0.0264621	+	0.999650i	$0.491576\pi$
$810$	1.00000	−	1.73205i	0.0351364	−	0.0608581i
$811$		−	10.0000i		−	0.351147i	−0.984466	−	0.175574i	$-0.943822\pi$
$811$		−	10.0000i		−	0.351147i	0.984466	−	0.175574i	$-0.0561780\pi$
$812$	−17.3205	−	10.0000i	−0.607831	−	0.350931i
$813$	−8.66025	−	5.00000i	−0.303728	−	0.175358i
$814$		0			0
$815$	−14.0000	+	24.2487i	−0.490399	+	0.849395i
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	20.7846	−	12.0000i	0.727161	−	0.419827i
$818$	−4.00000			−0.139857
$819$		0			0
$820$	20.0000			0.698430
$821$	−25.9808	+	15.0000i	−0.906735	+	0.523504i	−0.879379	−	0.476122i	$-0.842042\pi$
$821$	−25.9808	+	15.0000i	−0.906735	+	0.523504i	−0.0273557	+	0.999626i	$0.508709\pi$
$822$	−1.00000	−	1.73205i	−0.0348790	−	0.0604122i
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	−0.995768	−	0.0919029i	$-0.970705\pi$
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	0.577474	+	0.816409i	$0.304038\pi$
$824$		−	16.0000i		−	0.557386i
$825$		0			0
$826$	6.92820	+	4.00000i	0.241063	+	0.139178i
$827$		−	48.0000i		−	1.66912i	−0.550914	−	0.834562i	$-0.685721\pi$
$827$		−	48.0000i		−	1.66912i	0.550914	−	0.834562i	$-0.314279\pi$
$828$	2.00000	−	3.46410i	0.0695048	−	0.120386i
$829$	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	$0.658903\pi$
$830$	−6.92820	+	4.00000i	−0.240481	+	0.138842i
$831$	−2.00000			−0.0693792
$832$		0			0
$833$	−6.00000			−0.207888
$834$	17.3205	−	10.0000i	0.599760	−	0.346272i
$835$	−12.0000	−	20.7846i	−0.415277	−	0.719281i
$836$		0			0
$837$		−	10.0000i		−	0.345651i
$838$	34.6410	+	20.0000i	1.19665	+	0.690889i
$839$	−13.8564	−	8.00000i	−0.478376	−	0.276191i	0.241363	−	0.970435i	$-0.422405\pi$
$839$	−13.8564	−	8.00000i	−0.478376	−	0.276191i	−0.719740	+	0.694244i	$0.755739\pi$
$840$			4.00000i			0.138013i
$841$	−35.5000	+	61.4878i	−1.22414	+	2.12027i
$842$	10.0000	+	17.3205i	0.344623	+	0.596904i
$843$	8.66025	−	5.00000i	0.298275	−	0.172209i
$844$	−12.0000			−0.413057
$845$		0			0
$846$	12.0000			0.412568
$847$	19.0526	−	11.0000i	0.654654	−	0.377964i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$			2.00000i			0.0685994i
$851$	27.7128	+	16.0000i	0.949983	+	0.548473i
$852$		0			0
$853$		−	56.0000i		−	1.91740i	−0.284413	−	0.958702i	$-0.591799\pi$
$853$		−	56.0000i		−	1.91740i	0.284413	−	0.958702i	$-0.408201\pi$
$854$	−2.00000	+	3.46410i	−0.0684386	+	0.118539i
$855$	−6.00000	−	10.3923i	−0.205196	−	0.355409i
$856$	6.92820	−	4.00000i	0.236801	−	0.136717i
$857$	−22.0000			−0.751506			−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000			−0.751506			−0.375753	+	0.926720i	$0.622616\pi$
$858$		0			0
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$	6.92820	−	4.00000i	0.236250	−	0.136399i
$861$	−10.0000	−	17.3205i	−0.340799	−	0.590281i
$862$	−10.0000	+	17.3205i	−0.340601	+	0.589939i
$863$			44.0000i			1.49778i	0.662696	+	0.748889i	$0.269412\pi$
$863$			44.0000i			1.49778i	−0.662696	+	0.748889i	$0.730588\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−10.3923	−	6.00000i	−0.353349	−	0.204006i
$866$			26.0000i			0.883516i
$867$	6.50000	−	11.2583i	0.220752	−	0.382353i
$868$	10.0000	+	17.3205i	0.339422	+	0.587896i
$869$		0			0
$870$	20.0000			0.678064
$871$		0			0
$872$	4.00000			0.135457
$873$	10.3923	−	6.00000i	0.351726	−	0.203069i
$874$	−12.0000	−	20.7846i	−0.405906	−	0.703050i
$875$	−12.0000	+	20.7846i	−0.405674	+	0.702648i
$876$		−	4.00000i		−	0.135147i
$877$	6.92820	+	4.00000i	0.233949	+	0.135070i	0.612392	−	0.790554i	$-0.290207\pi$
$877$	6.92820	+	4.00000i	0.233949	+	0.135070i	−0.378444	+	0.925624i	$0.623541\pi$
$878$		0			0
$879$			14.0000i			0.472208i
$880$		0			0
$881$	−21.0000	−	36.3731i	−0.707508	−	1.22544i	−0.965779	−	0.259367i	$-0.916486\pi$
$881$	−21.0000	−	36.3731i	−0.707508	−	1.22544i	0.258271	−	0.966073i	$-0.416847\pi$
$882$	−2.59808	+	1.50000i	−0.0874818	+	0.0505076i
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$		0			0
$885$	−8.00000			−0.268917
$886$	13.8564	−	8.00000i	0.465515	−	0.268765i
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$	−4.00000	+	6.92820i	−0.134231	+	0.232495i
$889$			16.0000i			0.536623i
$890$	10.3923	+	6.00000i	0.348351	+	0.201120i
$891$		0			0
$892$		−	14.0000i		−	0.468755i
$893$	36.0000	−	62.3538i	1.20469	−	2.08659i
$894$	7.00000	+	12.1244i	0.234115	+	0.405499i
$895$		0			0
$896$	−2.00000			−0.0668153
$897$		0			0
$898$	6.00000			0.200223
$899$	86.6025	−	50.0000i	2.88836	−	1.66759i
$900$	0.500000	+	0.866025i	0.0166667	+	0.0288675i
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$		0			0
$903$	−6.92820	−	4.00000i	−0.230556	−	0.133112i
$904$	−12.1244	−	7.00000i	−0.403250	−	0.232817i
$905$		−	44.0000i		−	1.46261i
$906$	5.00000	−	8.66025i	0.166114	−	0.287718i
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$	6.92820	−	4.00000i	0.229920	−	0.132745i
$909$	2.00000			0.0663358
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	5.19615	−	3.00000i	0.172062	−	0.0993399i
$913$		0			0
$914$	14.0000	−	24.2487i	0.463079	−	0.802076i
$915$		−	4.00000i		−	0.132236i
$916$	−3.46410	−	2.00000i	−0.114457	−	0.0660819i
$917$	13.8564	+	8.00000i	0.457579	+	0.264183i
$918$			2.00000i			0.0660098i
$919$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$919$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$920$	−4.00000	−	6.92820i	−0.131876	−	0.228416i
$921$	1.73205	−	1.00000i	0.0570730	−	0.0329511i
$922$	30.0000			0.987997
$923$		0			0
$924$		0			0
$925$	−6.92820	+	4.00000i	−0.227798	+	0.131519i
$926$	3.00000	+	5.19615i	0.0985861	+	0.170756i
$927$	8.00000	−	13.8564i	0.262754	−	0.455104i
$928$			10.0000i			0.328266i
$929$	−5.19615	−	3.00000i	−0.170480	−	0.0984268i	0.412332	−	0.911034i	$-0.364714\pi$
$929$	−5.19615	−	3.00000i	−0.170480	−	0.0984268i	−0.582812	+	0.812607i	$0.698048\pi$
$930$	−17.3205	−	10.0000i	−0.567962	−	0.327913i
$931$			18.0000i			0.589926i
$932$	−3.00000	+	5.19615i	−0.0982683	+	0.170206i
$933$	14.0000	+	24.2487i	0.458339	+	0.793867i
$934$	10.3923	−	6.00000i	0.340047	−	0.196326i
$935$		0			0
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$	3.46410	−	2.00000i	0.113107	−	0.0653023i
$939$	13.0000	+	22.5167i	0.424239	+	0.734803i
$940$	12.0000	−	20.7846i	0.391397	−	0.677919i
$941$			10.0000i			0.325991i	0.986627	+	0.162995i	$0.0521156\pi$
$941$			10.0000i			0.325991i	−0.986627	+	0.162995i	$0.947884\pi$
$942$	−1.73205	−	1.00000i	−0.0564333	−	0.0325818i
$943$	34.6410	+	20.0000i	1.12807	+	0.651290i
$944$		−	4.00000i		−	0.130189i
$945$	−2.00000	+	3.46410i	−0.0650600	+	0.112687i
$946$		0			0
$947$	45.0333	−	26.0000i	1.46339	−	0.844886i	0.464220	−	0.885720i	$-0.346335\pi$
$947$	45.0333	−	26.0000i	1.46339	−	0.844886i	0.999166	+	0.0408333i	$0.0130013\pi$
$948$		0			0
$949$		0			0
$950$	6.00000			0.194666
$951$	−15.5885	+	9.00000i	−0.505490	+	0.291845i
$952$	−2.00000	−	3.46410i	−0.0648204	−	0.112272i
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	−0.813337	−	0.581793i	$-0.802351\pi$
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	0.910516	+	0.413473i	$0.135685\pi$
$954$			6.00000i			0.194257i
$955$	20.7846	+	12.0000i	0.672574	+	0.388311i
$956$	13.8564	+	8.00000i	0.448148	+	0.258738i
$957$		0			0
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	2.00000	+	3.46410i	0.0645834	+	0.111862i
$960$	1.73205	−	1.00000i	0.0559017	−	0.0322749i
$961$	−69.0000			−2.22581
$962$		0			0
$963$	8.00000			0.257796
$964$	17.3205	−	10.0000i	0.557856	−	0.322078i
$965$	16.0000	+	27.7128i	0.515058	+	0.892107i
$966$	−4.00000	+	6.92820i	−0.128698	+	0.222911i
$967$			22.0000i			0.707472i	0.935345	+	0.353736i	$0.115089\pi$
$967$			22.0000i			0.707472i	−0.935345	+	0.353736i	$0.884911\pi$
$968$	−9.52628	−	5.50000i	−0.306186	−	0.176777i
$969$	10.3923	+	6.00000i	0.333849	+	0.192748i
$970$		−	24.0000i		−	0.770594i
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−34.6410	+	20.0000i	−1.11054	+	0.641171i
$974$	−18.0000			−0.576757
$975$		0			0
$976$	2.00000			0.0640184
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.211495	−	0.977379i	$-0.432167\pi$
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.952183	+	0.305530i	$0.0988335\pi$
$978$	−7.00000	−	12.1244i	−0.223835	−	0.387694i
$979$		0			0
$980$			6.00000i			0.191663i
$981$	3.46410	+	2.00000i	0.110600	+	0.0638551i
$982$	−24.2487	−	14.0000i	−0.773807	−	0.446758i
$983$			24.0000i			0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$			24.0000i			0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$	−5.00000	+	8.66025i	−0.159394	+	0.276079i
$985$	−22.0000	−	38.1051i	−0.700978	−	1.21413i
$986$	−17.3205	+	10.0000i	−0.551597	+	0.318465i
$987$	−24.0000			−0.763928
$988$		0			0
$989$	16.0000			0.508770
$990$		0			0
$991$	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	$0.792778\pi$
$992$	5.00000	−	8.66025i	0.158750	−	0.274963i
$993$			10.0000i			0.317340i
$994$		0			0
$995$		0			0
$996$		−	4.00000i		−	0.126745i
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	−0.314188	−	0.949361i	$-0.601732\pi$
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	0.979265	−	0.202586i	$-0.0649345\pi$
$998$	7.00000	+	12.1244i	0.221581	+	0.383790i
$999$	−6.92820	+	4.00000i	−0.219199	+	0.126554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.i.c.361.1		4
13.2	odd	12		1014.2.a.b.1.1		1
13.3	even	3		78.2.b.a.25.1	✓	2
13.4	even	6	inner	1014.2.i.c.823.1		4
13.5	odd	4		1014.2.e.e.991.1		2
13.6	odd	12		1014.2.e.e.529.1		2
13.7	odd	12		1014.2.e.b.529.1		2
13.8	odd	4		1014.2.e.b.991.1		2
13.9	even	3	inner	1014.2.i.c.823.2		4
13.10	even	6		78.2.b.a.25.2	yes	2
13.11	odd	12		1014.2.a.g.1.1		1
13.12	even	2	inner	1014.2.i.c.361.2		4
39.2	even	12		3042.2.a.n.1.1		1
39.11	even	12		3042.2.a.c.1.1		1
39.23	odd	6		234.2.b.a.181.1		2
39.29	odd	6		234.2.b.a.181.2		2
52.3	odd	6		624.2.c.a.337.1		2
52.11	even	12		8112.2.a.j.1.1		1
52.15	even	12		8112.2.a.g.1.1		1
52.23	odd	6		624.2.c.a.337.2		2
65.3	odd	12		1950.2.f.d.649.2		2
65.23	odd	12		1950.2.f.g.649.2		2
65.29	even	6		1950.2.b.c.1351.2		2
65.42	odd	12		1950.2.f.g.649.1		2
65.49	even	6		1950.2.b.c.1351.1		2
65.62	odd	12		1950.2.f.d.649.1		2
91.55	odd	6		3822.2.c.d.883.1		2
91.62	odd	6		3822.2.c.d.883.2		2
104.3	odd	6		2496.2.c.m.961.2		2
104.29	even	6		2496.2.c.f.961.2		2
104.75	odd	6		2496.2.c.m.961.1		2
104.101	even	6		2496.2.c.f.961.1		2
156.23	even	6		1872.2.c.b.1585.1		2
156.107	even	6		1872.2.c.b.1585.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.b.a.25.1	✓	2	13.3	even	3
78.2.b.a.25.2	yes	2	13.10	even	6
234.2.b.a.181.1		2	39.23	odd	6
234.2.b.a.181.2		2	39.29	odd	6
624.2.c.a.337.1		2	52.3	odd	6
624.2.c.a.337.2		2	52.23	odd	6
1014.2.a.b.1.1		1	13.2	odd	12
1014.2.a.g.1.1		1	13.11	odd	12
1014.2.e.b.529.1		2	13.7	odd	12
1014.2.e.b.991.1		2	13.8	odd	4
1014.2.e.e.529.1		2	13.6	odd	12
1014.2.e.e.991.1		2	13.5	odd	4
1014.2.i.c.361.1		4	1.1	even	1	trivial
1014.2.i.c.361.2		4	13.12	even	2	inner
1014.2.i.c.823.1		4	13.4	even	6	inner
1014.2.i.c.823.2		4	13.9	even	3	inner
1872.2.c.b.1585.1		2	156.23	even	6
1872.2.c.b.1585.2		2	156.107	even	6
1950.2.b.c.1351.1		2	65.49	even	6
1950.2.b.c.1351.2		2	65.29	even	6
1950.2.f.d.649.1		2	65.62	odd	12
1950.2.f.d.649.2		2	65.3	odd	12
1950.2.f.g.649.1		2	65.42	odd	12
1950.2.f.g.649.2		2	65.23	odd	12
2496.2.c.f.961.1		2	104.101	even	6
2496.2.c.f.961.2		2	104.29	even	6
2496.2.c.m.961.1		2	104.75	odd	6
2496.2.c.m.961.2		2	104.3	odd	6
3042.2.a.c.1.1		1	39.11	even	12
3042.2.a.n.1.1		1	39.2	even	12
3822.2.c.d.883.1		2	91.55	odd	6
3822.2.c.d.883.2		2	91.62	odd	6
8112.2.a.g.1.1		1	52.15	even	12
8112.2.a.j.1.1		1	52.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} -1.00000 q^{12} +2.00000 q^{14} +(-1.73205 + 1.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -1.00000i q^{18} +(-5.19615 - 3.00000i) q^{19} +(-1.73205 - 1.00000i) q^{20} +2.00000i q^{21} +(-2.00000 - 3.46410i) q^{23} +(0.866025 - 0.500000i) q^{24} +1.00000 q^{25} +1.00000 q^{27} +(-1.73205 + 1.00000i) q^{28} +(5.00000 + 8.66025i) q^{29} +(1.00000 - 1.73205i) q^{30} -10.0000i q^{31} +(0.866025 + 0.500000i) q^{32} +2.00000i q^{34} +(-2.00000 + 3.46410i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-6.92820 + 4.00000i) q^{37} +6.00000 q^{38} +2.00000 q^{40} +(-8.66025 + 5.00000i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(-2.00000 + 3.46410i) q^{43} +(1.73205 + 1.00000i) q^{45} +(3.46410 + 2.00000i) q^{46} +12.0000i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-0.866025 + 0.500000i) q^{50} -2.00000 q^{51} -6.00000 q^{53} +(-0.866025 + 0.500000i) q^{54} +(1.00000 - 1.73205i) q^{56} +6.00000i q^{57} +(-8.66025 - 5.00000i) q^{58} +(3.46410 + 2.00000i) q^{59} +2.00000i q^{60} +(-1.00000 + 1.73205i) q^{61} +(5.00000 + 8.66025i) q^{62} +(1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +(1.73205 - 1.00000i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-2.00000 + 3.46410i) q^{69} -4.00000i q^{70} +(-0.866025 - 0.500000i) q^{72} +4.00000i q^{73} +(4.00000 - 6.92820i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-5.19615 + 3.00000i) q^{76} +(-1.73205 + 1.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.00000 - 8.66025i) q^{82} +4.00000i q^{83} +(1.73205 + 1.00000i) q^{84} +(-3.46410 - 2.00000i) q^{85} -4.00000i q^{86} +(5.00000 - 8.66025i) q^{87} +(5.19615 - 3.00000i) q^{89} -2.00000 q^{90} -4.00000 q^{92} +(-8.66025 + 5.00000i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(-6.00000 + 10.3923i) q^{95} -1.00000i q^{96} +(-10.3923 - 6.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} + 8 q^{14} - 2 q^{16} + 4 q^{17} - 8 q^{23} + 4 q^{25} + 4 q^{27} + 20 q^{29} + 4 q^{30} - 8 q^{35} + 2 q^{36} + 24 q^{38} + 8 q^{40} - 4 q^{42} - 8 q^{43} - 2 q^{48} - 6 q^{49} - 8 q^{51} - 24 q^{53} + 4 q^{56} - 4 q^{61} + 20 q^{62} - 4 q^{64} - 4 q^{68} - 8 q^{69} + 16 q^{74} - 2 q^{75} - 2 q^{81} + 20 q^{82} + 20 q^{87} - 8 q^{90} - 16 q^{92} - 24 q^{94} - 24 q^{95}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 + 8 * q^14 - 2 * q^16 + 4 * q^17 - 8 * q^23 + 4 * q^25 + 4 * q^27 + 20 * q^29 + 4 * q^30 - 8 * q^35 + 2 * q^36 + 24 * q^38 + 8 * q^40 - 4 * q^42 - 8 * q^43 - 2 * q^48 - 6 * q^49 - 8 * q^51 - 24 * q^53 + 4 * q^56 - 4 * q^61 + 20 * q^62 - 4 * q^64 - 4 * q^68 - 8 * q^69 + 16 * q^74 - 2 * q^75 - 2 * q^81 + 20 * q^82 + 20 * q^87 - 8 * q^90 - 16 * q^92 - 24 * q^94 - 24 * q^95

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