LMFDB - Embedded newform 1950.2.bc.j.751.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1950,2,Mod(751,1950)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1950, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1950.751"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,6,6,0,0,-12,0,-6,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.4
Root			$2.00607 + 1.30680i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.j.901.4

$q$-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} +(0.866025 + 0.500000i) q^{6} +(-3.76344 - 2.17283i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.04055 + 1.17811i) q^{11} +1.00000 q^{12} +(1.69144 + 3.18419i) q^{13} -4.34565 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50437 + 2.60564i) q^{17} +1.00000i q^{18} +(-0.585872 - 0.338254i) q^{19} -4.34565i q^{21} +(-1.17811 + 2.04055i) q^{22} +(3.22396 + 5.58405i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.05692 + 1.91187i) q^{26} -1.00000 q^{27} +(-3.76344 + 2.17283i) q^{28} +(-4.82620 - 8.35922i) q^{29} +7.11493i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.04055 - 1.17811i) q^{33} +3.00874i q^{34} +(0.500000 + 0.866025i) q^{36} +(-6.48073 + 3.74165i) q^{37} -0.676507 q^{38} +(-1.91187 + 3.05692i) q^{39} +(-2.60564 + 1.50437i) q^{41} +(-2.17283 - 3.76344i) q^{42} +(-3.41624 + 5.91710i) q^{43} +2.35623i q^{44} +(5.58405 + 3.22396i) q^{46} +5.61529i q^{47} +(0.500000 - 0.866025i) q^{48} +(5.94234 + 10.2924i) q^{49} -3.00874 q^{51} +(3.60330 + 0.127265i) q^{52} -9.43400 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-2.17283 + 3.76344i) q^{56} -0.676507i q^{57} +(-8.35922 - 4.82620i) q^{58} +(4.56364 + 2.63482i) q^{59} +(2.15646 - 3.73509i) q^{61} +(3.55746 + 6.16171i) q^{62} +(3.76344 - 2.17283i) q^{63} -1.00000 q^{64} -2.35623 q^{66} +(5.04596 - 2.91329i) q^{67} +(1.50437 + 2.60564i) q^{68} +(-3.22396 + 5.58405i) q^{69} +(2.52520 + 1.45793i) q^{71} +(0.866025 + 0.500000i) q^{72} +7.67804i q^{73} +(-3.74165 + 6.48073i) q^{74} +(-0.585872 + 0.338254i) q^{76} +10.2393 q^{77} +(-0.127265 + 3.60330i) q^{78} +3.74519 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.50437 + 2.60564i) q^{82} -10.3557i q^{83} +(-3.76344 - 2.17283i) q^{84} +6.83247i q^{86} +(4.82620 - 8.35922i) q^{87} +(1.17811 + 2.04055i) q^{88} +(-4.15208 + 2.39720i) q^{89} +(0.553049 - 15.6587i) q^{91} +6.44791 q^{92} +(-6.16171 + 3.55746i) q^{93} +(2.80764 + 4.86298i) q^{94} -1.00000i q^{96} +(-14.1520 - 8.17066i) q^{97} +(10.2924 + 5.94234i) q^{98} -2.35623i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{4} - 12 q^{7} - 6 q^{9} + 6 q^{11} + 12 q^{12} + 4 q^{13} - 4 q^{14} - 6 q^{16} + 8 q^{17} + 6 q^{19} - 6 q^{22} + 16 q^{23} - 2 q^{26} - 12 q^{27} - 12 q^{28} - 14 q^{29} + 6 q^{33}+ \cdots + 24 q^{98}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^4 - 12 * q^7 - 6 * q^9 + 6 * q^11 + 12 * q^12 + 4 * q^13 - 4 * q^14 - 6 * q^16 + 8 * q^17 + 6 * q^19 - 6 * q^22 + 16 * q^23 - 2 * q^26 - 12 * q^27 - 12 * q^28 - 14 * q^29 + 6 * q^33 + 6 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 18 * q^41 - 2 * q^42 + 10 * q^43 - 6 * q^46 + 6 * q^48 - 8 * q^49 + 16 * q^51 + 2 * q^52 - 2 * q^56 + 6 * q^58 + 36 * q^59 + 10 * q^61 + 16 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^66 + 24 * q^67 - 8 * q^68 - 16 * q^69 - 12 * q^71 + 12 * q^74 + 6 * q^76 + 24 * q^77 - 10 * q^78 - 4 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^84 + 14 * q^87 + 6 * q^88 - 18 * q^89 + 2 * q^91 + 32 * q^92 - 6 * q^93 + 8 * q^94 - 24 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	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
$5$		0			0
$5$		0			0
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−3.76344	−	2.17283i	−1.42245	−	0.821251i	−0.425940	−	0.904751i	$-0.640057\pi$
$7$	−3.76344	−	2.17283i	−1.42245	−	0.821251i	−0.996508	+	0.0835003i	$0.973390\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.04055	+	1.17811i	−0.615250	+	0.355215i	−0.775017	−	0.631940i	$-0.782259\pi$
$11$	−2.04055	+	1.17811i	−0.615250	+	0.355215i	0.159767	+	0.987155i	$0.448926\pi$
$12$	1.00000			0.288675
$13$	1.69144	+	3.18419i	0.469120	+	0.883134i
$13$	1.69144	+	3.18419i	0.469120	+	0.883134i
$14$	−4.34565			−1.16142
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50437	+	2.60564i	−0.364863	+	0.631962i	−0.988754	−	0.149550i	$-0.952218\pi$
$17$	−1.50437	+	2.60564i	−0.364863	+	0.631962i	0.623891	+	0.781511i	$0.285551\pi$
$18$			1.00000i			0.235702i
$19$	−0.585872	−	0.338254i	−0.134408	−	0.0776007i	0.431288	−	0.902214i	$-0.358059\pi$
$19$	−0.585872	−	0.338254i	−0.134408	−	0.0776007i	−0.565696	+	0.824614i	$0.691393\pi$
$20$		0			0
$21$		−	4.34565i		−	0.948299i
$22$	−1.17811	+	2.04055i	−0.251175	+	0.435047i
$23$	3.22396	+	5.58405i	0.672241	+	1.16436i	0.977267	+	0.212012i	$0.0680015\pi$
$23$	3.22396	+	5.58405i	0.672241	+	1.16436i	−0.305026	+	0.952344i	$0.598665\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$		0			0
$26$	3.05692	+	1.91187i	0.599511	+	0.374948i
$27$	−1.00000			−0.192450
$28$	−3.76344	+	2.17283i	−0.711224	+	0.410625i
$29$	−4.82620	−	8.35922i	−0.896202	−	1.55227i	−0.832310	−	0.554311i	$-0.812982\pi$
$29$	−4.82620	−	8.35922i	−0.896202	−	1.55227i	−0.0638921	−	0.997957i	$-0.520351\pi$
$30$		0			0
$31$			7.11493i			1.27788i	0.769257	+	0.638939i	$0.220626\pi$
$31$			7.11493i			1.27788i	−0.769257	+	0.638939i	$0.779374\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−2.04055	−	1.17811i	−0.355215	−	0.205083i
$34$			3.00874i			0.515995i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−6.48073	+	3.74165i	−1.06542	+	0.615123i	−0.926928	−	0.375240i	$-0.877560\pi$
$37$	−6.48073	+	3.74165i	−1.06542	+	0.615123i	−0.138497	+	0.990363i	$0.544227\pi$
$38$	−0.676507			−0.109744
$39$	−1.91187	+	3.05692i	−0.306144	+	0.489499i
$40$		0			0
$41$	−2.60564	+	1.50437i	−0.406933	+	0.234943i	−0.689471	−	0.724313i	$-0.742157\pi$
$41$	−2.60564	+	1.50437i	−0.406933	+	0.234943i	0.282538	+	0.959256i	$0.408824\pi$
$42$	−2.17283	−	3.76344i	−0.335274	−	0.580712i
$43$	−3.41624	+	5.91710i	−0.520971	+	0.902349i	0.478731	+	0.877961i	$0.341097\pi$
$43$	−3.41624	+	5.91710i	−0.520971	+	0.902349i	−0.999703	+	0.0243872i	$0.992237\pi$
$44$			2.35623i			0.355215i
$45$		0			0
$46$	5.58405	+	3.22396i	0.823324	+	0.475346i
$47$			5.61529i			0.819074i	0.912294	+	0.409537i	$0.134310\pi$
$47$			5.61529i			0.819074i	−0.912294	+	0.409537i	$0.865690\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	5.94234	+	10.2924i	0.848906	+	1.47035i
$50$		0			0
$51$	−3.00874			−0.421308
$52$	3.60330	+	0.127265i	0.499688	+	0.0176485i
$53$	−9.43400			−1.29586			−0.647930	−	0.761700i	$-0.724365\pi$
$53$	−9.43400			−1.29586			−0.647930	+	0.761700i	$0.724365\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−2.17283	+	3.76344i	−0.290356	+	0.502911i
$57$		−	0.676507i		−	0.0896056i
$58$	−8.35922	−	4.82620i	−1.09762	−	0.633711i
$59$	4.56364	+	2.63482i	0.594135	+	0.343024i	0.766731	−	0.641969i	$-0.221882\pi$
$59$	4.56364	+	2.63482i	0.594135	+	0.343024i	−0.172596	+	0.984993i	$0.555215\pi$
$60$		0			0
$61$	2.15646	−	3.73509i	0.276106	−	0.478230i	−0.694307	−	0.719679i	$-0.744289\pi$
$61$	2.15646	−	3.73509i	0.276106	−	0.478230i	0.970414	+	0.241449i	$0.0776225\pi$
$62$	3.55746	+	6.16171i	0.451798	+	0.782538i
$63$	3.76344	−	2.17283i	0.474149	−	0.273750i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−2.35623			−0.290032
$67$	5.04596	−	2.91329i	0.616463	−	0.355915i	−0.159028	−	0.987274i	$-0.550836\pi$
$67$	5.04596	−	2.91329i	0.616463	−	0.355915i	0.775490	+	0.631359i	$0.217503\pi$
$68$	1.50437	+	2.60564i	0.182432	+	0.315981i
$69$	−3.22396	+	5.58405i	−0.388119	+	0.672241i
$70$		0			0
$71$	2.52520	+	1.45793i	0.299686	+	0.173024i	0.642302	−	0.766452i	$-0.277980\pi$
$71$	2.52520	+	1.45793i	0.299686	+	0.173024i	−0.342616	+	0.939476i	$0.611313\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			7.67804i			0.898647i	0.893369	+	0.449323i	$0.148335\pi$
$73$			7.67804i			0.898647i	−0.893369	+	0.449323i	$0.851665\pi$
$74$	−3.74165	+	6.48073i	−0.434958	+	0.753369i
$75$		0			0
$76$	−0.585872	+	0.338254i	−0.0672042	+	0.0388004i
$77$	10.2393			1.16688
$78$	−0.127265	+	3.60330i	−0.0144099	+	0.407994i
$79$	3.74519			0.421367			0.210683	−	0.977554i	$-0.432431\pi$
$79$	3.74519			0.421367			0.210683	+	0.977554i	$0.432431\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.50437	+	2.60564i	−0.166130	+	0.287745i
$83$		−	10.3557i		−	1.13668i	−0.822793	−	0.568341i	$-0.807585\pi$
$83$		−	10.3557i		−	1.13668i	0.822793	−	0.568341i	$-0.192415\pi$
$84$	−3.76344	−	2.17283i	−0.410625	−	0.237075i
$85$		0			0
$86$			6.83247i			0.736765i
$87$	4.82620	−	8.35922i	0.517422	−	0.896202i
$88$	1.17811	+	2.04055i	0.125587	+	0.217524i
$89$	−4.15208	+	2.39720i	−0.440119	+	0.254103i	−0.703648	−	0.710549i	$-0.748447\pi$
$89$	−4.15208	+	2.39720i	−0.440119	+	0.254103i	0.263529	+	0.964651i	$0.415114\pi$
$90$		0			0
$91$	0.553049	−	15.6587i	0.0579753	−	1.64148i
$92$	6.44791			0.672241
$93$	−6.16171	+	3.55746i	−0.638939	+	0.368892i
$94$	2.80764	+	4.86298i	0.289586	+	0.501578i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−14.1520	−	8.17066i	−1.43692	−	0.829605i	−0.439283	−	0.898349i	$-0.644768\pi$
$97$	−14.1520	−	8.17066i	−1.43692	−	0.829605i	−0.997634	+	0.0687436i	$0.978101\pi$
$98$	10.2924	+	5.94234i	1.03969	+	0.600267i
$99$		−	2.35623i		−	0.236810i
$100$		0			0
$101$	−6.11911	−	10.5986i	−0.608875	−	1.05460i	−0.991426	−	0.130668i	$-0.958288\pi$
$101$	−6.11911	−	10.5986i	−0.608875	−	1.05460i	0.382552	−	0.923934i	$-0.375045\pi$
$102$	−2.60564	+	1.50437i	−0.257997	+	0.148955i
$103$	−3.75144			−0.369640			−0.184820	−	0.982772i	$-0.559170\pi$
$103$	−3.75144			−0.369640			−0.184820	+	0.982772i	$0.559170\pi$
$104$	3.18419	−	1.69144i	0.312235	−	0.165859i
$105$		0			0
$106$	−8.17008	+	4.71700i	−0.793549	+	0.458156i
$107$	8.30831	+	14.3904i	0.803194	+	1.39117i	0.917503	+	0.397728i	$0.130201\pi$
$107$	8.30831	+	14.3904i	0.803194	+	1.39117i	−0.114309	+	0.993445i	$0.536465\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$		−	11.1116i		−	1.06430i	−0.846652	−	0.532148i	$-0.821385\pi$
$109$		−	11.1116i		−	1.06430i	0.846652	−	0.532148i	$-0.178615\pi$
$110$		0			0
$111$	−6.48073	−	3.74165i	−0.615123	−	0.355142i
$112$			4.34565i			0.410625i
$113$	−7.83002	+	13.5620i	−0.736587	+	1.27581i	0.217437	+	0.976074i	$0.430230\pi$
$113$	−7.83002	+	13.5620i	−0.736587	+	1.27581i	−0.954024	+	0.299731i	$0.903103\pi$
$114$	−0.338254	−	0.585872i	−0.0316804	−	0.0548720i
$115$		0			0
$116$	−9.65239			−0.896202
$117$	−3.60330	−	0.127265i	−0.333126	−	0.0117657i
$118$	5.26964			0.485109
$119$	11.3232	−	6.53747i	1.03800	−	0.599288i
$120$		0			0
$121$	−2.72410	+	4.71827i	−0.247645	+	0.428934i
$122$		−	4.31292i		−	0.390473i
$123$	−2.60564	−	1.50437i	−0.234943	−	0.135644i
$124$	6.16171	+	3.55746i	0.553338	+	0.319470i
$125$		0			0
$126$	2.17283	−	3.76344i	0.193571	−	0.335274i
$127$	6.80236	+	11.7820i	0.603611	+	1.04549i	0.992269	+	0.124103i	$0.0396055\pi$
$127$	6.80236	+	11.7820i	0.603611	+	1.04549i	−0.388658	+	0.921382i	$0.627061\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−6.83247			−0.601566
$130$		0			0
$131$	10.2122			0.892246			0.446123	−	0.894972i	$-0.352804\pi$
$131$	10.2122			0.892246			0.446123	+	0.894972i	$0.352804\pi$
$132$	−2.04055	+	1.17811i	−0.177607	+	0.102542i
$133$	1.46993	+	2.54600i	0.127459	+	0.220766i
$134$	2.91329	−	5.04596i	0.251670	−	0.435905i
$135$		0			0
$136$	2.60564	+	1.50437i	0.223432	+	0.128999i
$137$	−10.7506	−	6.20689i	−0.918489	−	0.530290i	−0.0353365	−	0.999375i	$-0.511250\pi$
$137$	−10.7506	−	6.20689i	−0.918489	−	0.530290i	−0.883153	+	0.469085i	$0.844584\pi$
$138$			6.44791i			0.548883i
$139$	7.80915	−	13.5258i	0.662363	−	1.14725i	−0.317630	−	0.948215i	$-0.602887\pi$
$139$	7.80915	−	13.5258i	0.662363	−	1.14725i	0.979993	−	0.199032i	$-0.0637797\pi$
$140$		0			0
$141$	−4.86298	+	2.80764i	−0.409537	+	0.236446i
$142$	2.91585			0.244693
$143$	−7.20280	−	4.50479i	−0.602329	−	0.376710i
$144$	1.00000			0.0833333
$145$		0			0
$146$	3.83902	+	6.64938i	0.317720	+	0.550307i
$147$	−5.94234	+	10.2924i	−0.490116	+	0.848906i
$148$			7.48330i			0.615123i
$149$	−16.9104	−	9.76324i	−1.38536	−	0.799836i	−0.392569	−	0.919722i	$-0.628414\pi$
$149$	−16.9104	−	9.76324i	−1.38536	−	0.799836i	−0.992788	+	0.119886i	$0.961747\pi$
$150$		0			0
$151$		−	11.5027i		−	0.936079i	−0.883707	−	0.468040i	$-0.844960\pi$
$151$		−	11.5027i		−	0.936079i	0.883707	−	0.468040i	$-0.155040\pi$
$152$	−0.338254	+	0.585872i	−0.0274360	+	0.0475205i
$153$	−1.50437	−	2.60564i	−0.121621	−	0.210654i
$154$	8.86753	−	5.11967i	0.714566	−	0.412555i
$155$		0			0
$156$	1.69144	+	3.18419i	0.135423	+	0.254939i
$157$	4.47595			0.357220			0.178610	−	0.983920i	$-0.442840\pi$
$157$	4.47595			0.357220			0.178610	+	0.983920i	$0.442840\pi$
$158$	3.24343	−	1.87260i	0.258033	−	0.148976i
$159$	−4.71700	−	8.17008i	−0.374082	−	0.647930i
$160$		0			0
$161$		−	28.0204i		−	2.20831i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−6.71645	−	3.87774i	−0.526073	−	0.303728i	0.213343	−	0.976977i	$-0.431565\pi$
$163$	−6.71645	−	3.87774i	−0.526073	−	0.303728i	−0.739416	+	0.673249i	$0.764898\pi$
$164$			3.00874i			0.234943i
$165$		0			0
$166$	−5.17783	−	8.96827i	−0.401878	−	0.696073i
$167$	−0.587202	+	0.339021i	−0.0454390	+	0.0262342i	−0.522547	−	0.852610i	$-0.675018\pi$
$167$	−0.587202	+	0.339021i	−0.0454390	+	0.0262342i	0.477108	+	0.878844i	$0.341685\pi$
$168$	−4.34565			−0.335274
$169$	−7.27808	+	10.7717i	−0.559852	+	0.828593i
$170$		0			0
$171$	0.585872	−	0.338254i	0.0448028	−	0.0258669i
$172$	3.41624	+	5.91710i	0.260486	+	0.451174i
$173$	0.360974	−	0.625226i	0.0274444	−	0.0475350i	−0.851977	−	0.523579i	$-0.824596\pi$
$173$	0.360974	−	0.625226i	0.0274444	−	0.0475350i	0.879421	+	0.476044i	$0.157930\pi$
$174$		−	9.65239i		−	0.731746i
$175$		0			0
$176$	2.04055	+	1.17811i	0.153812	+	0.0888037i
$177$			5.26964i			0.396090i
$178$	−2.39720	+	4.15208i	−0.179678	+	0.311211i
$179$	−3.18673	−	5.51958i	−0.238187	−	0.412553i	0.722007	−	0.691886i	$-0.243220\pi$
$179$	−3.18673	−	5.51958i	−0.238187	−	0.412553i	−0.960194	+	0.279333i	$0.909887\pi$
$180$		0			0
$181$	22.0214			1.63683			0.818417	−	0.574624i	$-0.194852\pi$
$181$	22.0214			1.63683			0.818417	+	0.574624i	$0.194852\pi$
$182$	−7.35040	−	13.8374i	−0.544848	−	1.02569i
$183$	4.31292			0.318820
$184$	5.58405	−	3.22396i	0.411662	−	0.237673i
$185$		0			0
$186$	−3.55746	+	6.16171i	−0.260846	+	0.451798i
$187$		−	7.08928i		−	0.518419i
$188$	4.86298	+	2.80764i	0.354669	+	0.204768i
$189$	3.76344	+	2.17283i	0.273750	+	0.158050i
$190$		0			0
$191$	−0.293441	+	0.508255i	−0.0212326	+	0.0367760i	−0.876446	−	0.481499i	$-0.840092\pi$
$191$	−0.293441	+	0.508255i	−0.0212326	+	0.0367760i	0.855214	+	0.518275i	$0.173426\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	19.5955	−	11.3135i	1.41052	−	0.814363i	0.415081	−	0.909784i	$-0.363753\pi$
$193$	19.5955	−	11.3135i	1.41052	−	0.814363i	0.995437	+	0.0954215i	$0.0304199\pi$
$194$	−16.3413			−1.17324
$195$		0			0
$196$	11.8847			0.848906
$197$	1.42681	−	0.823770i	0.101656	−	0.0586912i	−0.448310	−	0.893878i	$-0.647974\pi$
$197$	1.42681	−	0.823770i	0.101656	−	0.0586912i	0.549966	+	0.835187i	$0.314641\pi$
$198$	−1.17811	−	2.04055i	−0.0837249	−	0.145016i
$199$	5.13665	−	8.89694i	0.364127	−	0.630687i	−0.624508	−	0.781018i	$-0.714701\pi$
$199$	5.13665	−	8.89694i	0.364127	−	0.630687i	0.988636	+	0.150331i	$0.0480339\pi$
$200$		0			0
$201$	5.04596	+	2.91329i	0.355915	+	0.205488i
$202$	−10.5986	−	6.11911i	−0.745716	−	0.430539i
$203$			41.9459i			2.94403i
$204$	−1.50437	+	2.60564i	−0.105327	+	0.182432i
$205$		0			0
$206$	−3.24884	+	1.87572i	−0.226357	+	0.130688i
$207$	−6.44791			−0.448161
$208$	1.91187	−	3.05692i	0.132564	−	0.211959i
$209$	1.59401			0.110260
$210$		0			0
$211$	12.1905	+	21.1145i	0.839226	+	1.45358i	0.890543	+	0.454900i	$0.150325\pi$
$211$	12.1905	+	21.1145i	0.839226	+	1.45358i	−0.0513166	+	0.998682i	$0.516342\pi$
$212$	−4.71700	+	8.17008i	−0.323965	+	0.561124i
$213$			2.91585i			0.199791i
$214$	14.3904	+	8.30831i	0.983708	+	0.567944i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	15.4595	−	26.7766i	1.04946	−	1.81772i
$218$	−5.55578	−	9.62290i	−0.376285	−	0.651745i
$219$	−6.64938	+	3.83902i	−0.449323	+	0.259417i
$220$		0			0
$221$	−10.8414	−	0.382907i	−0.729272	−	0.0257571i
$222$	−7.48330			−0.502246
$223$	4.01476	−	2.31792i	0.268848	−	0.155220i	−0.359516	−	0.933139i	$-0.617058\pi$
$223$	4.01476	−	2.31792i	0.268848	−	0.155220i	0.628364	+	0.777919i	$0.283725\pi$
$224$	2.17283	+	3.76344i	0.145178	+	0.251456i
$225$		0			0
$226$			15.6600i			1.04169i
$227$	−15.4016	−	8.89213i	−1.02224	−	0.590192i	−0.107489	−	0.994206i	$-0.534281\pi$
$227$	−15.4016	−	8.89213i	−1.02224	−	0.590192i	−0.914753	+	0.404015i	$0.867615\pi$
$228$	−0.585872	−	0.338254i	−0.0388004	−	0.0224014i
$229$		−	15.3361i		−	1.01344i	−0.862111	−	0.506720i	$-0.830858\pi$
$229$		−	15.3361i		−	1.01344i	0.862111	−	0.506720i	$-0.169142\pi$
$230$		0			0
$231$	5.11967	+	8.86753i	0.336850	+	0.583441i
$232$	−8.35922	+	4.82620i	−0.548809	+	0.316855i
$233$	7.75548			0.508079			0.254039	−	0.967194i	$-0.418241\pi$
$233$	7.75548			0.508079			0.254039	+	0.967194i	$0.418241\pi$
$234$	−3.18419	+	1.69144i	−0.208157	+	0.110573i
$235$		0			0
$236$	4.56364	−	2.63482i	0.297068	−	0.171512i
$237$	1.87260	+	3.24343i	0.121638	+	0.210683i
$238$	6.53747	−	11.3232i	0.423761	−	0.733975i
$239$			18.6409i			1.20578i	0.797824	+	0.602890i	$0.205984\pi$
$239$			18.6409i			1.20578i	−0.797824	+	0.602890i	$0.794016\pi$
$240$		0			0
$241$	−2.65884	−	1.53508i	−0.171271	−	0.0988833i	0.411914	−	0.911223i	$-0.364860\pi$
$241$	−2.65884	−	1.53508i	−0.171271	−	0.0988833i	−0.583185	+	0.812339i	$0.698194\pi$
$242$			5.44819i			0.350223i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.15646	−	3.73509i	−0.138053	−	0.239115i
$245$		0			0
$246$	−3.00874			−0.191830
$247$	0.0860957	−	2.43766i	0.00547814	−	0.155105i
$248$	7.11493			0.451798
$249$	8.96827	−	5.17783i	0.568341	−	0.328132i
$250$		0			0
$251$	−3.56404	+	6.17309i	−0.224960	+	0.389642i	−0.956307	−	0.292363i	$-0.905558\pi$
$251$	−3.56404	+	6.17309i	−0.224960	+	0.389642i	0.731347	+	0.682005i	$0.238892\pi$
$252$		−	4.34565i		−	0.273750i
$253$	−13.1573	−	7.59637i	−0.827193	−	0.477580i
$254$	11.7820	+	6.80236i	0.739270	+	0.426818i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.12178	+	12.3353i	0.444244	+	0.769454i	0.997999	−	0.0632261i	$-0.0201389\pi$
$257$	7.12178	+	12.3353i	0.444244	+	0.769454i	−0.553755	+	0.832680i	$0.686806\pi$
$258$	−5.91710	+	3.41624i	−0.368382	+	0.212686i
$259$	32.5198			2.02068
$260$		0			0
$261$	9.65239			0.597468
$262$	8.84404	−	5.10611i	0.546387	−	0.315457i
$263$	−7.70101	−	13.3385i	−0.474865	−	0.822490i	0.524721	−	0.851274i	$-0.324170\pi$
$263$	−7.70101	−	13.3385i	−0.474865	−	0.822490i	−0.999586	+	0.0287845i	$0.990836\pi$
$264$	−1.17811	+	2.04055i	−0.0725079	+	0.125587i
$265$		0			0
$266$	2.54600	+	1.46993i	0.156105	+	0.0901273i
$267$	−4.15208	−	2.39720i	−0.254103	−	0.146706i
$268$		−	5.82658i		−	0.355915i
$269$	−13.3134	+	23.0595i	−0.811732	+	1.40596i	0.0999185	+	0.994996i	$0.468142\pi$
$269$	−13.3134	+	23.0595i	−0.811732	+	1.40596i	−0.911651	+	0.410966i	$0.865192\pi$
$270$		0			0
$271$	−6.66899	+	3.85034i	−0.405112	+	0.233892i	−0.688687	−	0.725058i	$-0.741813\pi$
$271$	−6.66899	+	3.85034i	−0.405112	+	0.233892i	0.283575	+	0.958950i	$0.408479\pi$
$272$	3.00874			0.182432
$273$	13.8374	−	7.35040i	0.837475	−	0.444866i
$274$	−12.4138			−0.749943
$275$		0			0
$276$	3.22396	+	5.58405i	0.194059	+	0.336121i
$277$	−7.15114	+	12.3861i	−0.429671	+	0.744211i	−0.996844	−	0.0793871i	$-0.974704\pi$
$277$	−7.15114	+	12.3861i	−0.429671	+	0.744211i	0.567173	+	0.823599i	$0.308037\pi$
$278$		−	15.6183i		−	0.936723i
$279$	−6.16171	−	3.55746i	−0.368892	−	0.212980i
$280$		0			0
$281$		−	7.96746i		−	0.475299i	−0.971351	−	0.237649i	$-0.923623\pi$
$281$		−	7.96746i		−	0.475299i	0.971351	−	0.237649i	$-0.0763769\pi$
$282$	−2.80764	+	4.86298i	−0.167193	+	0.289586i
$283$	7.33785	+	12.7095i	0.436190	+	0.755503i	0.997392	−	0.0721756i	$-0.0229942\pi$
$283$	7.33785	+	12.7095i	0.436190	+	0.755503i	−0.561202	+	0.827679i	$0.689661\pi$
$284$	2.52520	−	1.45793i	0.149843	−	0.0865120i
$285$		0			0
$286$	−8.49021	−	0.299865i	−0.502036	−	0.0177314i
$287$	13.0749			0.771789
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	3.97374	+	6.88273i	0.233750	+	0.404866i
$290$		0			0
$291$		−	16.3413i		−	0.957945i
$292$	6.64938	+	3.83902i	0.389125	+	0.224662i
$293$	5.94436	+	3.43198i	0.347273	+	0.200498i	0.663484	−	0.748191i	$-0.269077\pi$
$293$	5.94436	+	3.43198i	0.347273	+	0.200498i	−0.316210	+	0.948689i	$0.602411\pi$
$294$			11.8847i			0.693129i
$295$		0			0
$296$	3.74165	+	6.48073i	0.217479	+	0.376685i
$297$	2.04055	−	1.17811i	0.118405	−	0.0683611i
$298$	−19.5265			−1.13114
$299$	−12.3275	+	19.7108i	−0.712921	+	1.13990i
$300$		0			0
$301$	25.7136	−	14.8458i	1.48211	−	0.855696i
$302$	−5.75137	−	9.96166i	−0.330954	−	0.573229i
$303$	6.11911	−	10.5986i	0.351534	−	0.608875i
$304$			0.676507i			0.0388004i
$305$		0			0
$306$	−2.60564	−	1.50437i	−0.148955	−	0.0859991i
$307$			10.9917i			0.627328i	0.949534	+	0.313664i	$0.101557\pi$
$307$			10.9917i			0.627328i	−0.949534	+	0.313664i	$0.898443\pi$
$308$	5.11967	−	8.86753i	0.291720	−	0.505275i
$309$	−1.87572	−	3.24884i	−0.106706	−	0.184820i
$310$		0			0
$311$	−13.9044			−0.788446			−0.394223	−	0.919015i	$-0.628986\pi$
$311$	−13.9044			−0.788446			−0.394223	+	0.919015i	$0.628986\pi$
$312$	3.05692	+	1.91187i	0.173064	+	0.108238i
$313$	14.1734			0.801130			0.400565	−	0.916268i	$-0.368814\pi$
$313$	14.1734			0.801130			0.400565	+	0.916268i	$0.368814\pi$
$314$	3.87629	−	2.23798i	0.218752	−	0.126296i
$315$		0			0
$316$	1.87260	−	3.24343i	0.105342	−	0.182457i
$317$		−	3.20808i		−	0.180184i	−0.995933	−	0.0900920i	$-0.971284\pi$
$317$		−	3.20808i		−	0.180184i	0.995933	−	0.0900920i	$-0.0287161\pi$
$318$	−8.17008	−	4.71700i	−0.458156	−	0.264516i
$319$	19.6962	+	11.3716i	1.10278	+	0.636688i
$320$		0			0
$321$	−8.30831	+	14.3904i	−0.463724	+	0.803194i
$322$	−14.0102	−	24.2664i	−0.780757	−	1.35231i
$323$	1.76274	−	1.01772i	0.0980813	−	0.0566273i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−7.75548			−0.429537
$327$	9.62290	−	5.55578i	0.532148	−	0.307236i
$328$	1.50437	+	2.60564i	0.0830649	+	0.143873i
$329$	12.2010	−	21.1328i	0.672665	−	1.16509i
$330$		0			0
$331$	−22.3066	−	12.8787i	−1.22608	−	0.707878i	−0.259873	−	0.965643i	$-0.583681\pi$
$331$	−22.3066	−	12.8787i	−1.22608	−	0.707878i	−0.966208	+	0.257765i	$0.917014\pi$
$332$	−8.96827	−	5.17783i	−0.492198	−	0.284170i
$333$		−	7.48330i		−	0.410082i
$334$	−0.339021	+	0.587202i	−0.0185504	+	0.0321302i
$335$		0			0
$336$	−3.76344	+	2.17283i	−0.205313	+	0.118537i
$337$	−0.772078			−0.0420578			−0.0210289	−	0.999779i	$-0.506694\pi$
$337$	−0.772078			−0.0420578			−0.0210289	+	0.999779i	$0.506694\pi$
$338$	−0.917149	+	12.9676i	−0.0498863	+	0.705345i
$339$	−15.6600			−0.850537
$340$		0			0
$341$	−8.38219	−	14.5184i	−0.453921	−	0.786215i
$342$	0.338254	−	0.585872i	0.0182907	−	0.0316804i
$343$		−	21.2271i		−	1.14616i
$344$	5.91710	+	3.41624i	0.319028	+	0.184191i
$345$		0			0
$346$		−	0.721948i		−	0.0388122i
$347$	−12.5779	+	21.7856i	−0.675218	+	1.16951i	0.301188	+	0.953565i	$0.402617\pi$
$347$	−12.5779	+	21.7856i	−0.675218	+	1.16951i	−0.976405	+	0.215946i	$0.930716\pi$
$348$	−4.82620	−	8.35922i	−0.258711	−	0.448101i
$349$	23.6602	−	13.6602i	1.26650	−	0.731214i	0.292176	−	0.956365i	$-0.405621\pi$
$349$	23.6602	−	13.6602i	1.26650	−	0.731214i	0.974324	+	0.225151i	$0.0722874\pi$
$350$		0			0
$351$	−1.69144	−	3.18419i	−0.0902823	−	0.169959i
$352$	2.35623			0.125587
$353$	6.51161	−	3.75948i	0.346578	−	0.200097i	−0.316599	−	0.948559i	$-0.602541\pi$
$353$	6.51161	−	3.75948i	0.346578	−	0.200097i	0.663177	+	0.748462i	$0.269208\pi$
$354$	2.63482	+	4.56364i	0.140039	+	0.242555i
$355$		0			0
$356$			4.79440i			0.254103i
$357$	11.3232	+	6.53747i	0.599288	+	0.345999i
$358$	−5.51958	−	3.18673i	−0.291719	−	0.168424i
$359$		−	10.8402i		−	0.572124i	−0.958211	−	0.286062i	$-0.907654\pi$
$359$		−	10.8402i		−	0.572124i	0.958211	−	0.286062i	$-0.0923463\pi$
$360$		0			0
$361$	−9.27117	−	16.0581i	−0.487956	−	0.845165i
$362$	19.0711	−	11.0107i	1.00235	−	0.578708i
$363$	−5.44819			−0.285956
$364$	−13.2843	−	8.30831i	−0.696287	−	0.435474i
$365$		0			0
$366$	3.73509	−	2.15646i	0.195237	−	0.112720i
$367$	3.75761	+	6.50838i	0.196146	+	0.339735i	0.947276	−	0.320420i	$-0.103824\pi$
$367$	3.75761	+	6.50838i	0.196146	+	0.339735i	−0.751130	+	0.660155i	$0.770491\pi$
$368$	3.22396	−	5.58405i	0.168060	−	0.291089i
$369$		−	3.00874i		−	0.156629i
$370$		0			0
$371$	35.5043	+	20.4984i	1.84329	+	1.06423i
$372$			7.11493i			0.368892i
$373$	11.4393	−	19.8135i	0.592305	−	1.02590i	−0.401616	−	0.915808i	$-0.631551\pi$
$373$	11.4393	−	19.8135i	0.592305	−	1.02590i	0.993921	−	0.110095i	$-0.0351154\pi$
$374$	−3.54464	−	6.13949i	−0.183289	−	0.317466i
$375$		0			0
$376$	5.61529			0.289586
$377$	18.4541	−	29.5066i	0.950434	−	1.51967i
$378$	4.34565			0.223516
$379$	22.6152	−	13.0569i	1.16166	−	0.670687i	0.209962	−	0.977710i	$-0.432666\pi$
$379$	22.6152	−	13.0569i	1.16166	−	0.670687i	0.951702	+	0.307022i	$0.0993327\pi$
$380$		0			0
$381$	−6.80236	+	11.7820i	−0.348495	+	0.603611i
$382$			0.586882i			0.0300275i
$383$	−11.8585	−	6.84652i	−0.605942	−	0.349841i	0.165434	−	0.986221i	$-0.447098\pi$
$383$	−11.8585	−	6.84652i	−0.605942	−	0.349841i	−0.771376	+	0.636380i	$0.780431\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	11.3135	−	19.5955i	0.575842	−	0.997387i
$387$	−3.41624	−	5.91710i	−0.173657	−	0.300783i
$388$	−14.1520	+	8.17066i	−0.718459	+	0.414802i
$389$	−24.9403			−1.26452			−0.632261	−	0.774755i	$-0.717873\pi$
$389$	−24.9403			−1.26452			−0.632261	+	0.774755i	$0.717873\pi$
$390$		0			0
$391$	−19.4001			−0.981104
$392$	10.2924	−	5.94234i	0.519847	−	0.300134i
$393$	5.10611	+	8.84404i	0.257569	+	0.446123i
$394$	0.823770	−	1.42681i	0.0415009	−	0.0718817i
$395$		0			0
$396$	−2.04055	−	1.17811i	−0.102542	−	0.0592025i
$397$	25.2043	+	14.5517i	1.26497	+	0.730328i	0.974031	−	0.226415i	$-0.0727005\pi$
$397$	25.2043	+	14.5517i	1.26497	+	0.730328i	0.290934	+	0.956743i	$0.406034\pi$
$398$		−	10.2733i		−	0.514954i
$399$	−1.46993	+	2.54600i	−0.0735887	+	0.127459i
$400$		0			0
$401$	−14.4596	+	8.34823i	−0.722076	+	0.416891i	−0.815516	−	0.578734i	$-0.803547\pi$
$401$	−14.4596	+	8.34823i	−0.722076	+	0.416891i	0.0934404	+	0.995625i	$0.470214\pi$
$402$	5.82658			0.290603
$403$	−22.6552	+	12.0345i	−1.12854	+	0.599479i
$404$	−12.2382			−0.608875
$405$		0			0
$406$	20.9730	+	36.3262i	1.04087	+	1.80284i
$407$	8.81618	−	15.2701i	0.437002	−	0.756909i
$408$			3.00874i			0.148955i
$409$	−21.3140	−	12.3056i	−1.05391	−	0.608475i	−0.130168	−	0.991492i	$-0.541552\pi$
$409$	−21.3140	−	12.3056i	−1.05391	−	0.608475i	−0.923741	+	0.383017i	$0.874885\pi$
$410$		0			0
$411$		−	12.4138i		−	0.612326i
$412$	−1.87572	+	3.24884i	−0.0924100	+	0.160059i
$413$	−11.4500	−	19.8320i	−0.563418	−	0.975868i
$414$	−5.58405	+	3.22396i	−0.274441	+	0.158449i
$415$		0			0
$416$	0.127265	−	3.60330i	0.00623968	−	0.176667i
$417$	15.6183			0.764831
$418$	1.38045	−	0.797003i	0.0675200	−	0.0389827i
$419$	13.5527	+	23.4739i	0.662091	+	1.14678i	0.980065	+	0.198676i	$0.0636643\pi$
$419$	13.5527	+	23.4739i	0.662091	+	1.14678i	−0.317974	+	0.948099i	$0.603002\pi$
$420$		0			0
$421$			32.9996i			1.60830i	0.594425	+	0.804151i	$0.297380\pi$
$421$			32.9996i			1.60830i	−0.594425	+	0.804151i	$0.702620\pi$
$422$	21.1145	+	12.1905i	1.02784	+	0.593422i
$423$	−4.86298	−	2.80764i	−0.236446	−	0.136512i
$424$			9.43400i			0.458156i
$425$		0			0
$426$	1.45793	+	2.52520i	0.0706367	+	0.122346i
$427$	−16.2314	+	9.37121i	−0.785493	+	0.453505i
$428$	16.6166			0.803194
$429$	0.299865	−	8.49021i	0.0144776	−	0.409911i
$430$		0			0
$431$	7.45678	−	4.30517i	0.359180	−	0.207373i	−0.309541	−	0.950886i	$-0.600175\pi$
$431$	7.45678	−	4.30517i	0.359180	−	0.207373i	0.668721	+	0.743513i	$0.266842\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−1.72744	+	2.99201i	−0.0830155	+	0.143787i	−0.904544	−	0.426381i	$-0.859788\pi$
$433$	−1.72744	+	2.99201i	−0.0830155	+	0.143787i	0.821528	+	0.570168i	$0.193122\pi$
$434$		−	30.9190i		−	1.48416i
$435$		0			0
$436$	−9.62290	−	5.55578i	−0.460853	−	0.266074i
$437$		−	4.36206i		−	0.208666i
$438$	−3.83902	+	6.64938i	−0.183436	+	0.317720i
$439$	12.1229	+	20.9974i	0.578593	+	1.00215i	0.995641	+	0.0932675i	$0.0297312\pi$
$439$	12.1229	+	20.9974i	0.578593	+	1.00215i	−0.417049	+	0.908884i	$0.636936\pi$
$440$		0			0
$441$	−11.8847			−0.565937
$442$	−9.58038	+	5.08909i	−0.455692	+	0.242064i
$443$	13.1629			0.625390			0.312695	−	0.949854i	$-0.398768\pi$
$443$	13.1629			0.625390			0.312695	+	0.949854i	$0.398768\pi$
$444$	−6.48073	+	3.74165i	−0.307562	+	0.177571i
$445$		0			0
$446$	2.31792	−	4.01476i	0.109757	−	0.190104i
$447$		−	19.5265i		−	0.923571i
$448$	3.76344	+	2.17283i	0.177806	+	0.102656i
$449$	−2.17774	−	1.25732i	−0.102774	−	0.0593365i	0.447732	−	0.894168i	$-0.352232\pi$
$449$	−2.17774	−	1.25732i	−0.102774	−	0.0593365i	−0.550506	+	0.834831i	$0.685565\pi$
$450$		0			0
$451$	3.54464	−	6.13949i	0.166910	−	0.289097i
$452$	7.83002	+	13.5620i	0.368293	+	0.637903i
$453$	9.96166	−	5.75137i	0.468040	−	0.270223i
$454$	−17.7843			−0.834657
$455$		0			0
$456$	−0.676507			−0.0316804
$457$	−9.32698	+	5.38493i	−0.436298	+	0.251897i	−0.702026	−	0.712151i	$-0.747721\pi$
$457$	−9.32698	+	5.38493i	−0.436298	+	0.251897i	0.265728	+	0.964048i	$0.414388\pi$
$458$	−7.66806	−	13.2815i	−0.358305	−	0.620602i
$459$	1.50437	−	2.60564i	0.0702180	−	0.121621i
$460$		0			0
$461$	10.2984	+	5.94576i	0.479642	+	0.276922i	0.720267	−	0.693697i	$-0.244019\pi$
$461$	10.2984	+	5.94576i	0.479642	+	0.276922i	−0.240625	+	0.970618i	$0.577352\pi$
$462$	8.86753	+	5.11967i	0.412555	+	0.238189i
$463$		−	29.9462i		−	1.39172i	−0.718178	−	0.695860i	$-0.755024\pi$
$463$		−	29.9462i		−	1.39172i	0.718178	−	0.695860i	$-0.244976\pi$
$464$	−4.82620	+	8.35922i	−0.224051	+	0.388067i
$465$		0			0
$466$	6.71645	−	3.87774i	0.311133	−	0.179633i
$467$	−21.8940			−1.01313			−0.506566	−	0.862201i	$-0.669085\pi$
$467$	−21.8940			−1.01313			−0.506566	+	0.862201i	$0.669085\pi$
$468$	−1.91187	+	3.05692i	−0.0883761	+	0.141306i
$469$	−25.3203			−1.16918
$470$		0			0
$471$	2.23798	+	3.87629i	0.103121	+	0.178610i
$472$	2.63482	−	4.56364i	0.121277	−	0.210059i
$473$		−	16.0989i		−	0.740227i
$474$	3.24343	+	1.87260i	0.148976	+	0.0860112i
$475$		0			0
$476$		−	13.0749i		−	0.599288i
$477$	4.71700	−	8.17008i	0.215977	−	0.374082i
$478$	9.32045	+	16.1435i	0.426307	+	0.738386i
$479$	7.90106	−	4.56168i	0.361009	−	0.208429i	−0.308514	−	0.951220i	$-0.599832\pi$
$479$	7.90106	−	4.56168i	0.361009	−	0.208429i	0.669523	+	0.742791i	$0.266498\pi$
$480$		0			0
$481$	−22.8758	−	14.3071i	−1.04305	−	0.652346i
$482$	−3.07016			−0.139842
$483$	24.2664	−	14.0102i	1.10416	−	0.637486i
$484$	2.72410	+	4.71827i	0.123823	+	0.214467i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−18.8079	−	10.8587i	−0.852265	−	0.492056i	0.00914916	−	0.999958i	$-0.497088\pi$
$487$	−18.8079	−	10.8587i	−0.852265	−	0.492056i	−0.861415	+	0.507902i	$0.830421\pi$
$488$	−3.73509	−	2.15646i	−0.169080	−	0.0976183i
$489$		−	7.75548i		−	0.350715i
$490$		0			0
$491$	16.5438	+	28.6548i	0.746613	+	1.29317i	0.949437	+	0.313957i	$0.101655\pi$
$491$	16.5438	+	28.6548i	0.746613	+	1.29317i	−0.202824	+	0.979215i	$0.565012\pi$
$492$	−2.60564	+	1.50437i	−0.117472	+	0.0678222i
$493$	29.0415			1.30796
$494$	−1.14427	−	2.15412i	−0.0514831	−	0.0969187i
$495$		0			0
$496$	6.16171	−	3.55746i	0.276669	−	0.159735i
$497$	−6.33564	−	10.9736i	−0.284192	−	0.492235i
$498$	5.17783	−	8.96827i	0.232024	−	0.401878i
$499$			10.4889i			0.469546i	0.972050	+	0.234773i	$0.0754347\pi$
$499$			10.4889i			0.469546i	−0.972050	+	0.234773i	$0.924565\pi$
$500$		0			0
$501$	−0.587202	−	0.339021i	−0.0262342	−	0.0151463i
$502$			7.12807i			0.318142i
$503$	4.12700	−	7.14818i	0.184014	−	0.318722i	−0.759230	−	0.650823i	$-0.774424\pi$
$503$	4.12700	−	7.14818i	0.184014	−	0.318722i	0.943244	+	0.332101i	$0.107757\pi$
$504$	−2.17283	−	3.76344i	−0.0967853	−	0.167637i
$505$		0			0
$506$	−15.1927			−0.675400
$507$	−12.9676	−	0.917149i	−0.575912	−	0.0407320i
$508$	13.6047			0.603611
$509$	−5.84526	+	3.37476i	−0.259087	+	0.149584i	−0.623918	−	0.781490i	$-0.714460\pi$
$509$	−5.84526	+	3.37476i	−0.259087	+	0.149584i	0.364831	+	0.931074i	$0.381127\pi$
$510$		0			0
$511$	16.6830	−	28.8959i	0.738014	−	1.27828i
$512$			1.00000i			0.0441942i
$513$	0.585872	+	0.338254i	0.0258669	+	0.0149343i
$514$	12.3353	+	7.12178i	0.544086	+	0.314128i
$515$		0			0
$516$	−3.41624	+	5.91710i	−0.150391	+	0.260486i
$517$	−6.61545	−	11.4583i	−0.290947	−	0.503935i
$518$	28.1630	−	16.2599i	1.23741	−	0.714419i
$519$	0.721948			0.0316900
$520$		0			0
$521$	−30.4048			−1.33206			−0.666029	−	0.745926i	$-0.732007\pi$
$521$	−30.4048			−1.33206			−0.666029	+	0.745926i	$0.732007\pi$
$522$	8.35922	−	4.82620i	0.365873	−	0.211237i
$523$	−1.57175	−	2.72235i	−0.0687279	−	0.119040i	0.829614	−	0.558338i	$-0.188561\pi$
$523$	−1.57175	−	2.72235i	−0.0687279	−	0.119040i	−0.898342	+	0.439298i	$0.855227\pi$
$524$	5.10611	−	8.84404i	0.223062	−	0.386354i
$525$		0			0
$526$	−13.3385	−	7.70101i	−0.581588	−	0.335780i
$527$	−18.5390	−	10.7035i	−0.807570	−	0.466251i
$528$			2.35623i			0.102542i
$529$	−9.28778	+	16.0869i	−0.403816	+	0.699431i
$530$		0			0
$531$	−4.56364	+	2.63482i	−0.198045	+	0.114341i
$532$	2.93986			0.127459
$533$	−9.19748	−	5.75231i	−0.398387	−	0.249160i
$534$	−4.79440			−0.207474
$535$		0			0
$536$	−2.91329	−	5.04596i	−0.125835	−	0.217952i
$537$	3.18673	−	5.51958i	0.137518	−	0.238187i
$538$			26.6268i			1.14796i
$539$	−24.2513	−	14.0015i	−1.04458	−	0.603088i
$540$		0			0
$541$			17.6144i			0.757301i	0.925540	+	0.378650i	$0.123612\pi$
$541$			17.6144i			0.757301i	−0.925540	+	0.378650i	$0.876388\pi$
$542$	−3.85034	+	6.66899i	−0.165386	+	0.286458i
$543$	11.0107	+	19.0711i	0.472513	+	0.818417i
$544$	2.60564	−	1.50437i	0.111716	−	0.0644993i
$545$		0			0
$546$	8.30831	−	13.2843i	0.355563	−	0.568516i
$547$	40.8067			1.74477			0.872385	−	0.488820i	$-0.162572\pi$
$547$	40.8067			1.74477			0.872385	+	0.488820i	$0.162572\pi$
$548$	−10.7506	+	6.20689i	−0.459245	+	0.265145i
$549$	2.15646	+	3.73509i	0.0920354	+	0.159410i
$550$		0			0
$551$			6.52991i			0.278184i
$552$	5.58405	+	3.22396i	0.237673	+	0.137221i
$553$	−14.0948	−	8.13765i	−0.599373	−	0.346048i
$554$			14.3023i			0.607646i
$555$		0			0
$556$	−7.80915	−	13.5258i	−0.331182	−	0.573623i
$557$	−21.8427	+	12.6109i	−0.925504	+	0.534340i	−0.885387	−	0.464855i	$-0.846106\pi$
$557$	−21.8427	+	12.6109i	−0.925504	+	0.534340i	−0.0401170	+	0.999195i	$0.512773\pi$
$558$	−7.11493			−0.301199
$559$	−24.6195	−	0.869535i	−1.04129	−	0.0367774i
$560$		0			0
$561$	6.13949	−	3.54464i	0.259210	−	0.149655i
$562$	−3.98373	−	6.90002i	−0.168043	−	0.291060i
$563$	−18.2071	+	31.5356i	−0.767337	+	1.32907i	0.171664	+	0.985155i	$0.445086\pi$
$563$	−18.2071	+	31.5356i	−0.767337	+	1.32907i	−0.939002	+	0.343912i	$0.888248\pi$
$564$			5.61529i			0.236446i
$565$		0			0
$566$	12.7095	+	7.33785i	0.534222	+	0.308433i
$567$			4.34565i			0.182500i
$568$	1.45793	−	2.52520i	0.0611732	−	0.105955i
$569$	13.6768	+	23.6888i	0.573360	+	0.993088i	0.996218	+	0.0868922i	$0.0276936\pi$
$569$	13.6768	+	23.6888i	0.573360	+	0.993088i	−0.422858	+	0.906196i	$0.638973\pi$
$570$		0			0
$571$	45.7020			1.91257			0.956285	−	0.292438i	$-0.0944664\pi$
$571$	45.7020			1.91257			0.956285	+	0.292438i	$0.0944664\pi$
$572$	−7.50267	+	3.98541i	−0.313702	+	0.166638i
$573$	−0.586882			−0.0245174
$574$	11.3232	−	6.53747i	0.472622	−	0.272869i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			31.1697i			1.29761i	0.760954	+	0.648806i	$0.224731\pi$
$577$			31.1697i			1.29761i	−0.760954	+	0.648806i	$0.775269\pi$
$578$	6.88273	+	3.97374i	0.286284	+	0.165286i
$579$	19.5955	+	11.3135i	0.814363	+	0.470173i
$580$		0			0
$581$	−22.5011	+	38.9730i	−0.933501	+	1.61687i
$582$	−8.17066	−	14.1520i	−0.338685	−	0.586619i
$583$	19.2506	−	11.1143i	0.797278	−	0.460308i
$584$	7.67804			0.317720
$585$		0			0
$586$	6.86396			0.283547
$587$	−13.1880	+	7.61411i	−0.544328	+	0.314268i	−0.746831	−	0.665014i	$-0.768426\pi$
$587$	−13.1880	+	7.61411i	−0.544328	+	0.314268i	0.202503	+	0.979282i	$0.435092\pi$
$588$	5.94234	+	10.2924i	0.245058	+	0.424453i
$589$	2.40665	−	4.16844i	0.0991643	−	0.171758i
$590$		0			0
$591$	1.42681	+	0.823770i	0.0586912	+	0.0338854i
$592$	6.48073	+	3.74165i	0.266356	+	0.153781i
$593$			15.1921i			0.623865i	0.950104	+	0.311933i	$0.100976\pi$
$593$			15.1921i			0.623865i	−0.950104	+	0.311933i	$0.899024\pi$
$594$	1.17811	−	2.04055i	0.0483386	−	0.0837249i
$595$		0			0
$596$	−16.9104	+	9.76324i	−0.692678	+	0.399918i
$597$	10.2733			0.420458
$598$	−0.820594	+	23.2338i	−0.0335566	+	0.950100i
$599$	−4.34655			−0.177595			−0.0887975	−	0.996050i	$-0.528302\pi$
$599$	−4.34655			−0.177595			−0.0887975	+	0.996050i	$0.528302\pi$
$600$		0			0
$601$	−5.14622	−	8.91351i	−0.209918	−	0.363590i	0.741770	−	0.670654i	$-0.233987\pi$
$601$	−5.14622	−	8.91351i	−0.209918	−	0.363590i	−0.951689	+	0.307065i	$0.900653\pi$
$602$	14.8458	−	25.7136i	0.605069	−	1.04801i
$603$			5.82658i			0.237277i
$604$	−9.96166	−	5.75137i	−0.405334	−	0.234020i
$605$		0			0
$606$		−	12.2382i		−	0.497144i
$607$	21.7138	−	37.6094i	0.881335	−	1.52652i	0.0314772	−	0.999504i	$-0.489979\pi$
$607$	21.7138	−	37.6094i	0.881335	−	1.52652i	0.849858	−	0.527012i	$-0.176688\pi$
$608$	0.338254	+	0.585872i	0.0137180	+	0.0237603i
$609$	−36.3262	+	20.9730i	−1.47201	+	0.849867i
$610$		0			0
$611$	−17.8801	+	9.49791i	−0.723352	+	0.384244i
$612$	−3.00874			−0.121621
$613$	28.2771	−	16.3258i	1.14210	−	0.659392i	0.195150	−	0.980773i	$-0.437481\pi$
$613$	28.2771	−	16.3258i	1.14210	−	0.659392i	0.946950	+	0.321382i	$0.104147\pi$
$614$	5.49584	+	9.51907i	0.221794	+	0.384159i
$615$		0			0
$616$		−	10.2393i		−	0.412555i
$617$	−8.37426	−	4.83488i	−0.337135	−	0.194645i	0.321869	−	0.946784i	$-0.395689\pi$
$617$	−8.37426	−	4.83488i	−0.337135	−	0.194645i	−0.659004	+	0.752139i	$0.729022\pi$
$618$	−3.24884	−	1.87572i	−0.130688	−	0.0754525i
$619$			5.20064i			0.209031i	0.994523	+	0.104516i	$0.0333292\pi$
$619$			5.20064i			0.209031i	−0.994523	+	0.104516i	$0.966671\pi$
$620$		0			0
$621$	−3.22396	−	5.58405i	−0.129373	−	0.224080i
$622$	−12.0416	+	6.95220i	−0.482823	+	0.278758i
$623$	20.8348			0.834729
$624$	3.60330	+	0.127265i	0.144248	+	0.00509468i
$625$		0			0
$626$	12.2746	−	7.08672i	0.490590	−	0.283242i
$627$	0.797003	+	1.38045i	0.0318292	+	0.0551298i
$628$	2.23798	−	3.87629i	0.0893050	−	0.154681i
$629$		−	22.5153i		−	0.897743i
$630$		0			0
$631$	−6.86811	−	3.96531i	−0.273415	−	0.157856i	0.357023	−	0.934095i	$-0.383792\pi$
$631$	−6.86811	−	3.96531i	−0.273415	−	0.157856i	−0.630439	+	0.776239i	$0.717125\pi$
$632$		−	3.74519i		−	0.148976i
$633$	−12.1905	+	21.1145i	−0.484527	+	0.839226i
$634$	−1.60404	−	2.77828i	−0.0637046	−	0.110340i
$635$		0			0
$636$	−9.43400			−0.374082
$637$	−22.7219	+	36.3305i	−0.900276	+	1.43947i
$638$	22.7432			0.900413
$639$	−2.52520	+	1.45793i	−0.0998954	+	0.0576746i
$640$		0			0
$641$	−1.69937	+	2.94340i	−0.0671212	+	0.116257i	−0.897633	−	0.440744i	$-0.854715\pi$
$641$	−1.69937	+	2.94340i	−0.0671212	+	0.116257i	0.830512	+	0.557001i	$0.188048\pi$
$642$			16.6166i			0.655805i
$643$	−8.13918	−	4.69916i	−0.320978	−	0.185317i	0.330851	−	0.943683i	$-0.392664\pi$
$643$	−8.13918	−	4.69916i	−0.320978	−	0.185317i	−0.651828	+	0.758367i	$0.725998\pi$
$644$	−24.2664	−	14.0102i	−0.956228	−	0.552079i
$645$		0			0
$646$	1.01772	−	1.76274i	0.0400415	−	0.0693540i
$647$	−20.0324	−	34.6972i	−0.787555	−	1.36409i	−0.927461	−	0.373921i	$-0.878013\pi$
$647$	−20.0324	−	34.6972i	−0.787555	−	1.36409i	0.139905	−	0.990165i	$-0.455320\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−12.4165			−0.487389
$650$		0			0
$651$	30.9190			1.21181
$652$	−6.71645	+	3.87774i	−0.263036	+	0.151864i
$653$	−15.6981	−	27.1900i	−0.614316	−	1.06403i	−0.990504	−	0.137483i	$-0.956099\pi$
$653$	−15.6981	−	27.1900i	−0.614316	−	1.06403i	0.376189	−	0.926543i	$-0.377234\pi$
$654$	5.55578	−	9.62290i	0.217248	−	0.376285i
$655$		0			0
$656$	2.60564	+	1.50437i	0.101733	+	0.0587358i
$657$	−6.64938	−	3.83902i	−0.259417	−	0.149774i
$658$		−	24.4021i		−	0.951292i
$659$	−9.48950	+	16.4363i	−0.369659	+	0.640268i	−0.989512	−	0.144450i	$-0.953859\pi$
$659$	−9.48950	+	16.4363i	−0.369659	+	0.640268i	0.619853	+	0.784718i	$0.287192\pi$
$660$		0			0
$661$	11.4484	−	6.60972i	0.445290	−	0.257088i	−0.260549	−	0.965461i	$-0.583904\pi$
$661$	11.4484	−	6.60972i	0.445290	−	0.257088i	0.705839	+	0.708372i	$0.250570\pi$
$662$	−25.7574			−1.00109
$663$	−5.08909	−	9.58038i	−0.197644	−	0.372071i
$664$	−10.3557			−0.401878
$665$		0			0
$666$	−3.74165	−	6.48073i	−0.144986	−	0.251123i
$667$	31.1189	−	53.8995i	1.20493	−	2.08700i
$668$			0.678042i			0.0262342i
$669$	4.01476	+	2.31792i	0.155220	+	0.0896161i
$670$		0			0
$671$			10.1622i			0.392308i
$672$	−2.17283	+	3.76344i	−0.0838186	+	0.145178i
$673$	−4.30020	−	7.44817i	−0.165761	−	0.287106i	0.771164	−	0.636636i	$-0.219675\pi$
$673$	−4.30020	−	7.44817i	−0.165761	−	0.287106i	−0.936925	+	0.349530i	$0.886341\pi$
$674$	−0.668639	+	0.386039i	−0.0257550	+	0.0148697i
$675$		0			0
$676$	5.68953	+	11.6889i	0.218828	+	0.449571i
$677$	25.8539			0.993646			0.496823	−	0.867852i	$-0.334500\pi$
$677$	25.8539			0.993646			0.496823	+	0.867852i	$0.334500\pi$
$678$	−13.5620	+	7.83002i	−0.520845	+	0.300710i
$679$	35.5068	+	61.4997i	1.36263	+	2.36014i
$680$		0			0
$681$		−	17.7843i		−	0.681495i
$682$	−14.5184	−	8.38219i	−0.555938	−	0.320971i
$683$	−18.1041	−	10.4524i	−0.692734	−	0.399950i	0.111901	−	0.993719i	$-0.464306\pi$
$683$	−18.1041	−	10.4524i	−0.692734	−	0.399950i	−0.804636	+	0.593769i	$0.797639\pi$
$684$		−	0.676507i		−	0.0258669i
$685$		0			0
$686$	−10.6136	−	18.3832i	−0.405228	−	0.701875i
$687$	13.2815	−	7.66806i	0.506720	−	0.292555i
$688$	6.83247			0.260486
$689$	−15.9570	−	30.0396i	−0.607914	−	1.14442i
$690$		0			0
$691$	−42.3440	+	24.4473i	−1.61084	+	0.930019i	−0.621665	+	0.783283i	$0.713543\pi$
$691$	−42.3440	+	24.4473i	−1.61084	+	0.930019i	−0.989176	+	0.146736i	$0.953123\pi$
$692$	−0.360974	−	0.625226i	−0.0137222	−	0.0237675i
$693$	−5.11967	+	8.86753i	−0.194480	+	0.336850i
$694$			25.1558i			0.954902i
$695$		0			0
$696$	−8.35922	−	4.82620i	−0.316855	−	0.182936i
$697$		−	9.05251i		−	0.342888i
$698$	13.6602	−	23.6602i	0.517046	−	0.895551i
$699$	3.87774	+	6.71645i	0.146670	+	0.254039i
$700$		0			0
$701$	31.9805			1.20789			0.603944	−	0.797027i	$-0.293595\pi$
$701$	31.9805			1.20789			0.603944	+	0.797027i	$0.293595\pi$
$702$	−3.05692	−	1.91187i	−0.115376	−	0.0721588i
$703$	5.06250			0.190936
$704$	2.04055	−	1.17811i	0.0769062	−	0.0444018i
$705$		0			0
$706$	3.75948	−	6.51161i	0.141490	−	0.245068i
$707$			53.1831i			2.00016i
$708$	4.56364	+	2.63482i	0.171512	+	0.0990225i
$709$	5.42026	+	3.12939i	0.203562	+	0.117527i	0.598316	−	0.801260i	$-0.295837\pi$
$709$	5.42026	+	3.12939i	0.203562	+	0.117527i	−0.394754	+	0.918787i	$0.629170\pi$
$710$		0			0
$711$	−1.87260	+	3.24343i	−0.0702278	+	0.121638i
$712$	2.39720	+	4.15208i	0.0898389	+	0.155606i
$713$	−39.7301	+	22.9382i	−1.48791	+	0.859043i
$714$	13.0749			0.489317
$715$		0			0
$716$	−6.37346			−0.238187
$717$	−16.1435	+	9.32045i	−0.602890	+	0.348079i
$718$	−5.42010	−	9.38789i	−0.202276	−	0.350353i
$719$	9.52308	−	16.4945i	0.355151	−	0.615140i	−0.631993	−	0.774974i	$-0.717763\pi$
$719$	9.52308	−	16.4945i	0.355151	−	0.615140i	0.987144	+	0.159835i	$0.0510961\pi$
$720$		0			0
$721$	14.1183	+	8.15122i	0.525794	+	0.303567i
$722$	−16.0581	−	9.27117i	−0.597622	−	0.345037i
$723$		−	3.07016i		−	0.114181i
$724$	11.0107	−	19.0711i	0.409209	−	0.708770i
$725$		0			0
$726$	−4.71827	+	2.72410i	−0.175111	+	0.101101i
$727$	−28.2602			−1.04811			−0.524056	−	0.851684i	$-0.675582\pi$
$727$	−28.2602			−1.04811			−0.524056	+	0.851684i	$0.675582\pi$
$728$	−15.6587	−	0.553049i	−0.580350	−	0.0204974i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−10.2786	−	17.8030i	−0.380166	−	0.658468i
$732$	2.15646	−	3.73509i	0.0797050	−	0.138053i
$733$			5.28165i			0.195082i	0.995232	+	0.0975410i	$0.0310977\pi$
$733$			5.28165i			0.195082i	−0.995232	+	0.0975410i	$0.968902\pi$
$734$	6.50838	+	3.75761i	0.240229	+	0.138696i
$735$		0			0
$736$		−	6.44791i		−	0.237673i
$737$	−6.86437	+	11.8894i	−0.252852	+	0.437953i
$738$	−1.50437	−	2.60564i	−0.0553766	−	0.0959151i
$739$	−34.5736	+	19.9611i	−1.27181	+	0.734280i	−0.975329	−	0.220758i	$-0.929147\pi$
$739$	−34.5736	+	19.9611i	−1.27181	+	0.734280i	−0.296482	+	0.955038i	$0.595813\pi$
$740$		0			0
$741$	2.15412	−	1.14427i	0.0791337	−	0.0420358i
$742$	40.9969			1.50504
$743$	−16.0828	+	9.28543i	−0.590022	+	0.340650i	−0.765106	−	0.643904i	$-0.777314\pi$
$743$	−16.0828	+	9.28543i	−0.590022	+	0.340650i	0.175084	+	0.984553i	$0.443980\pi$
$744$	3.55746	+	6.16171i	0.130423	+	0.225899i
$745$		0			0
$746$		−	22.8786i		−	0.837646i
$747$	8.96827	+	5.17783i	0.328132	+	0.189447i
$748$	−6.13949	−	3.54464i	−0.224482	−	0.129605i
$749$		−	72.2100i		−	2.63850i
$750$		0			0
$751$	15.1001	+	26.1541i	0.551010	+	0.954377i	0.998202	+	0.0599394i	$0.0190907\pi$
$751$	15.1001	+	26.1541i	0.551010	+	0.954377i	−0.447192	+	0.894438i	$0.647576\pi$
$752$	4.86298	−	2.80764i	0.177335	−	0.102384i
$753$	−7.12807			−0.259761
$754$	1.22841	−	34.7805i	0.0447361	−	1.26663i
$755$		0			0
$756$	3.76344	−	2.17283i	0.136875	−	0.0790249i
$757$	−2.80211	−	4.85341i	−0.101845	−	0.176400i	0.810600	−	0.585600i	$-0.199141\pi$
$757$	−2.80211	−	4.85341i	−0.101845	−	0.176400i	−0.912445	+	0.409200i	$0.865808\pi$
$758$	13.0569	−	22.6152i	0.474247	−	0.821421i
$759$		−	15.1927i		−	0.551462i
$760$		0			0
$761$	−5.77640	−	3.33501i	−0.209394	−	0.120894i	0.391635	−	0.920120i	$-0.371909\pi$
$761$	−5.77640	−	3.33501i	−0.209394	−	0.120894i	−0.601030	+	0.799227i	$0.705243\pi$
$762$			13.6047i			0.492847i
$763$	−24.1435	+	41.8178i	−0.874053	+	1.51391i
$764$	0.293441	+	0.508255i	0.0106163	+	0.0183880i
$765$		0			0
$766$	−13.6930			−0.494750
$767$	−0.670640	+	18.9881i	−0.0242154	+	0.685621i
$768$	−1.00000			−0.0360844
$769$	−6.03234	+	3.48277i	−0.217532	+	0.125592i	−0.604807	−	0.796372i	$-0.706750\pi$
$769$	−6.03234	+	3.48277i	−0.217532	+	0.125592i	0.387275	+	0.921964i	$0.373416\pi$
$770$		0			0
$771$	−7.12178	+	12.3353i	−0.256485	+	0.444244i
$772$		−	22.6270i		−	0.814363i
$773$	18.4893	+	10.6748i	0.665013	+	0.383945i	0.794184	−	0.607677i	$-0.207898\pi$
$773$	18.4893	+	10.6748i	0.665013	+	0.383945i	−0.129172	+	0.991622i	$0.541232\pi$
$774$	−5.91710	−	3.41624i	−0.212686	−	0.122794i
$775$		0			0
$776$	−8.17066	+	14.1520i	−0.293310	+	0.508027i
$777$	16.2599	+	28.1630i	0.583321	+	1.01034i
$778$	−21.5989	+	12.4701i	−0.774359	+	0.447076i
$779$	2.03543			0.0729270
$780$		0			0
$781$	−6.87041			−0.245843
$782$	−16.8010	+	9.70004i	−0.600801	+	0.346873i
$783$	4.82620	+	8.35922i	0.172474	+	0.298734i
$784$	5.94234	−	10.2924i	0.212226	−	0.367587i
$785$		0			0
$786$	8.84404	+	5.10611i	0.315457	+	0.182129i
$787$	16.6562	+	9.61648i	0.593731	+	0.342791i	0.766571	−	0.642159i	$-0.221961\pi$
$787$	16.6562	+	9.61648i	0.593731	+	0.342791i	−0.172841	+	0.984950i	$0.555295\pi$
$788$		−	1.64754i		−	0.0586912i
$789$	7.70101	−	13.3385i	0.274163	−	0.474865i
$790$		0			0
$791$	58.9357	−	34.0265i	2.09551	−	1.20984i
$792$	−2.35623			−0.0837249
$793$	15.5407	+	0.548883i	0.551868	+	0.0194914i
$794$	29.1034			1.03284
$795$		0			0
$796$	−5.13665	−	8.89694i	−0.182064	−	0.315344i
$797$	11.3784	−	19.7080i	0.403044	−	0.698094i	−0.591047	−	0.806637i	$-0.701285\pi$
$797$	11.3784	−	19.7080i	0.403044	−	0.698094i	0.994092	+	0.108543i	$0.0346187\pi$
$798$			2.93986i			0.104070i
$799$	−14.6314	−	8.44747i	−0.517623	−	0.298850i
$800$		0			0
$801$		−	4.79440i		−	0.169402i
$802$	−8.34823	+	14.4596i	−0.294786	+	0.510585i
$803$	−9.04561	−	15.6675i	−0.319213	−	0.552892i
$804$	5.04596	−	2.91329i	0.177957	−	0.102744i
$805$		0			0
$806$	−13.6028	+	21.7498i	−0.479138	+	0.766103i
$807$	−26.6268			−0.937308
$808$	−10.5986	+	6.11911i	−0.372858	+	0.215270i
$809$	17.7054	+	30.6667i	0.622490	+	1.07818i	0.989020	+	0.147779i	$0.0472123\pi$
$809$	17.7054	+	30.6667i	0.622490	+	1.07818i	−0.366530	+	0.930406i	$0.619454\pi$
$810$		0			0
$811$			1.41268i			0.0496060i	0.999692	+	0.0248030i	$0.00789586\pi$
$811$			1.41268i			0.0496060i	−0.999692	+	0.0248030i	$0.992104\pi$
$812$	36.3262	+	20.9730i	1.27480	+	0.736007i
$813$	−6.66899	−	3.85034i	−0.233892	−	0.135037i
$814$		−	17.6324i		−	0.618014i
$815$		0			0
$816$	1.50437	+	2.60564i	0.0526635	+	0.0912158i
$817$	4.00296	−	2.31111i	0.140046	−	0.0808555i
$818$	−24.6113			−0.860513
$819$	13.2843	+	8.30831i	0.464191	+	0.290316i
$820$		0			0
$821$	14.7591	−	8.52118i	0.515097	−	0.297391i	−0.219829	−	0.975538i	$-0.570550\pi$
$821$	14.7591	−	8.52118i	0.515097	−	0.297391i	0.734926	+	0.678147i	$0.237217\pi$
$822$	−6.20689	−	10.7506i	−0.216490	−	0.374972i
$823$	2.21485	−	3.83623i	0.0772047	−	0.133723i	−0.824838	−	0.565369i	$-0.808734\pi$
$823$	2.21485	−	3.83623i	0.0772047	−	0.133723i	0.902043	+	0.431646i	$0.142067\pi$
$824$			3.75144i			0.130688i
$825$		0			0
$826$	−19.8320	−	11.4500i	−0.690043	−	0.398396i
$827$			41.2574i			1.43466i	0.696734	+	0.717330i	$0.254636\pi$
$827$			41.2574i			1.43466i	−0.696734	+	0.717330i	$0.745364\pi$
$828$	−3.22396	+	5.58405i	−0.112040	+	0.194059i
$829$	−21.3857	−	37.0411i	−0.742756	−	1.28649i	−0.951236	−	0.308465i	$-0.900185\pi$
$829$	−21.3857	−	37.0411i	−0.742756	−	1.28649i	0.208479	−	0.978027i	$-0.433149\pi$
$830$		0			0
$831$	−14.3023			−0.496141
$832$	−1.69144	−	3.18419i	−0.0586400	−	0.110392i
$833$	−35.7579			−1.23894
$834$	13.5258	−	7.80915i	0.468361	−	0.270409i
$835$		0			0
$836$	0.797003	−	1.38045i	0.0275649	−	0.0477438i
$837$		−	7.11493i		−	0.245928i
$838$	23.4739	+	13.5527i	0.810893	+	0.468169i
$839$	0.249908	+	0.144284i	0.00862777	+	0.00498124i	0.504308	−	0.863524i	$-0.331748\pi$
$839$	0.249908	+	0.144284i	0.00862777	+	0.00498124i	−0.495680	+	0.868505i	$0.665081\pi$
$840$		0			0
$841$	−32.0843	+	55.5717i	−1.10636	+	1.91626i
$842$	16.4998	+	28.5785i	0.568621	+	0.984880i
$843$	6.90002	−	3.98373i	0.237649	−	0.137207i
$844$	24.3809			0.839226
$845$		0			0
$846$	−5.61529			−0.193058
$847$	20.5040	−	11.8380i	0.704524	−	0.406757i
$848$	4.71700	+	8.17008i	0.161982	+	0.280562i
$849$	−7.33785	+	12.7095i	−0.251834	+	0.436190i
$850$		0			0
$851$	−41.7871	−	24.1258i	−1.43244	−	0.827022i
$852$	2.52520	+	1.45793i	0.0865120	+	0.0499477i
$853$			42.9336i			1.47002i	0.678058	+	0.735009i	$0.262822\pi$
$853$			42.9336i			1.47002i	−0.678058	+	0.735009i	$0.737178\pi$
$854$	−9.37121	+	16.2314i	−0.320676	+	0.555428i
$855$		0			0
$856$	14.3904	−	8.30831i	0.491854	−	0.283972i
$857$	−43.6929			−1.49252			−0.746261	−	0.665654i	$-0.768153\pi$
$857$	−43.6929			−1.49252			−0.746261	+	0.665654i	$0.768153\pi$
$858$	−3.98541	−	7.50267i	−0.136060	−	0.256137i
$859$	50.5362			1.72427			0.862137	−	0.506676i	$-0.169126\pi$
$859$	50.5362			1.72427			0.862137	+	0.506676i	$0.169126\pi$
$860$		0			0
$861$	6.53747	+	11.3232i	0.222796	+	0.385894i
$862$	4.30517	−	7.45678i	0.146635	−	0.253979i
$863$			9.24937i			0.314852i	0.987531	+	0.157426i	$0.0503196\pi$
$863$			9.24937i			0.314852i	−0.987531	+	0.157426i	$0.949680\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		0			0
$866$			3.45488i			0.117402i
$867$	−3.97374	+	6.88273i	−0.134955	+	0.233750i
$868$	−15.4595	−	26.7766i	−0.524729	−	0.908858i
$869$	−7.64226	+	4.41226i	−0.259246	+	0.149676i
$870$		0			0
$871$	17.8114	+	11.1396i	0.603516	+	0.377452i
$872$	−11.1116			−0.376285
$873$	14.1520	−	8.17066i	0.478973	−	0.276535i
$874$	−2.18103	−	3.77765i	−0.0737744	−	0.127781i
$875$		0			0
$876$			7.67804i			0.259417i
$877$	49.3035	+	28.4654i	1.66486	+	0.961208i	0.970343	+	0.241731i	$0.0777153\pi$
$877$	49.3035	+	28.4654i	1.66486	+	0.961208i	0.694517	+	0.719476i	$0.255618\pi$
$878$	20.9974	+	12.1229i	0.708628	+	0.409127i
$879$			6.86396i			0.231515i
$880$		0			0
$881$	7.98900	+	13.8374i	0.269156	+	0.466192i	0.968644	−	0.248452i	$-0.0799218\pi$
$881$	7.98900	+	13.8374i	0.269156	+	0.466192i	−0.699488	+	0.714644i	$0.746588\pi$
$882$	−10.2924	+	5.94234i	−0.346564	+	0.200089i
$883$	0.189481			0.00637654			0.00318827	−	0.999995i	$-0.498985\pi$
$883$	0.189481			0.00637654			0.00318827	+	0.999995i	$0.498985\pi$
$884$	−5.75231	+	9.19748i	−0.193471	+	0.309345i
$885$		0			0
$886$	11.3994	−	6.58147i	0.382972	−	0.221109i
$887$	−8.96852	−	15.5339i	−0.301133	−	0.521578i	0.675260	−	0.737580i	$-0.264032\pi$
$887$	−8.96852	−	15.5339i	−0.301133	−	0.521578i	−0.976393	+	0.216002i	$0.930698\pi$
$888$	−3.74165	+	6.48073i	−0.125562	+	0.217479i
$889$		−	59.1213i		−	1.98287i
$890$		0			0
$891$	2.04055	+	1.17811i	0.0683611	+	0.0394683i
$892$		−	4.63585i		−	0.155220i
$893$	1.89939	−	3.28984i	0.0635607	−	0.110090i
$894$	−9.76324	−	16.9104i	−0.326532	−	0.565570i
$895$		0			0
$896$	4.34565			0.145178
$897$	−23.2338	−	0.820594i	−0.775754	−	0.0273988i
$898$	−2.51464			−0.0839145
$899$	59.4752	−	34.3380i	1.98361	−	1.14524i
$900$		0			0
$901$	14.1922	−	24.5817i	0.472812	−	0.818934i
$902$		−	7.08928i		−	0.236047i
$903$	25.7136	+	14.8458i	0.855696	+	0.494036i
$904$	13.5620	+	7.83002i	0.451065	+	0.260423i
$905$		0			0
$906$	5.75137	−	9.96166i	0.191076	−	0.330954i
$907$	16.5050	+	28.5874i	0.548038	+	0.949230i	0.998409	+	0.0563882i	$0.0179585\pi$
$907$	16.5050	+	28.5874i	0.548038	+	0.949230i	−0.450371	+	0.892842i	$0.648708\pi$
$908$	−15.4016	+	8.89213i	−0.511121	+	0.295096i
$909$	12.2382			0.405916
$910$		0			0
$911$	13.9676			0.462768			0.231384	−	0.972863i	$-0.425675\pi$
$911$	13.9676			0.462768			0.231384	+	0.972863i	$0.425675\pi$
$912$	−0.585872	+	0.338254i	−0.0194002	+	0.0112007i
$913$	12.2002	+	21.1313i	0.403766	+	0.699344i
$914$	−5.38493	+	9.32698i	−0.178118	+	0.308509i
$915$		0			0
$916$	−13.2815	−	7.66806i	−0.438832	−	0.253360i
$917$	−38.4331	−	22.1894i	−1.26917	−	0.732758i
$918$		−	3.00874i		−	0.0993032i
$919$	−9.50273	+	16.4592i	−0.313466	+	0.542939i	−0.979110	−	0.203330i	$-0.934824\pi$
$919$	−9.50273	+	16.4592i	−0.313466	+	0.542939i	0.665644	+	0.746269i	$0.268157\pi$
$920$		0			0
$921$	−9.51907	+	5.49584i	−0.313664	+	0.181094i
$922$	11.8915			0.391626
$923$	−0.371086	+	10.5067i	−0.0122144	+	0.345832i
$924$	10.2393			0.336850
$925$		0			0
$926$	−14.9731	−	25.9342i	−0.492047	−	0.852250i
$927$	1.87572	−	3.24884i	0.0616067	−	0.106706i
$928$			9.65239i			0.316855i
$929$	50.0606	+	28.9025i	1.64243	+	0.948259i	0.979965	+	0.199169i	$0.0638244\pi$
$929$	50.0606	+	28.9025i	1.64243	+	0.948259i	0.662468	+	0.749090i	$0.269509\pi$
$930$		0			0
$931$		−	8.04007i		−	0.263503i
$932$	3.87774	−	6.71645i	0.127020	−	0.220005i
$933$	−6.95220	−	12.0416i	−0.227605	−	0.394223i
$934$	−18.9607	+	10.9470i	−0.620414	+	0.358196i
$935$		0			0
$936$	−0.127265	+	3.60330i	−0.00415979	+	0.117778i
$937$	−39.7996			−1.30020			−0.650099	−	0.759850i	$-0.725273\pi$
$937$	−39.7996			−1.30020			−0.650099	+	0.759850i	$0.725273\pi$
$938$	−21.9280	+	12.6601i	−0.715974	+	0.413368i
$939$	7.08672	+	12.2746i	0.231266	+	0.400565i
$940$		0			0
$941$		−	1.26326i		−	0.0411810i	−0.999788	−	0.0205905i	$-0.993445\pi$
$941$		−	1.26326i		−	0.0411810i	0.999788	−	0.0205905i	$-0.00655462\pi$
$942$	3.87629	+	2.23798i	0.126296	+	0.0729172i
$943$	−16.8010	−	9.70004i	−0.547115	−	0.315877i
$944$		−	5.26964i		−	0.171512i
$945$		0			0
$946$	−8.04943	−	13.9420i	−0.261710	−	0.453294i
$947$	7.75545	−	4.47761i	0.252018	−	0.145503i	−0.368670	−	0.929560i	$-0.620187\pi$
$947$	7.75545	−	4.47761i	0.252018	−	0.145503i	0.620688	+	0.784058i	$0.286853\pi$
$948$	3.74519			0.121638
$949$	−24.4483	+	12.9869i	−0.793626	+	0.421574i
$950$		0			0
$951$	2.77828	−	1.60404i	0.0900920	−	0.0520146i
$952$	−6.53747	−	11.3232i	−0.211880	−	0.366988i
$953$	−6.18504	+	10.7128i	−0.200353	+	0.347022i	−0.948642	−	0.316351i	$-0.897542\pi$
$953$	−6.18504	+	10.7128i	−0.200353	+	0.347022i	0.748289	+	0.663373i	$0.230876\pi$
$954$		−	9.43400i		−	0.305437i
$955$		0			0
$956$	16.1435	+	9.32045i	0.522118	+	0.301445i
$957$			22.7432i			0.735184i
$958$	4.56168	−	7.90106i	0.147381	−	0.255272i
$959$	26.9730	+	46.7185i	0.871002	+	1.50862i
$960$		0			0
$961$	−19.6222			−0.632973
$962$	−26.9646	−	0.952362i	−0.869374	−	0.0307054i
$963$	−16.6166			−0.535463
$964$	−2.65884	+	1.53508i	−0.0856354	+	0.0494416i
$965$		0			0
$966$	14.0102	−	24.2664i	0.450770	−	0.780757i
$967$			6.35606i			0.204397i	0.994764	+	0.102198i	$0.0325877\pi$
$967$			6.35606i			0.204397i	−0.994764	+	0.102198i	$0.967412\pi$
$968$	4.71827	+	2.72410i	0.151651	+	0.0875557i
$969$	1.76274	+	1.01772i	0.0566273	+	0.0326938i
$970$		0			0
$971$	23.6660	−	40.9907i	0.759477	−	1.31545i	−0.183640	−	0.982994i	$-0.558788\pi$
$971$	23.6660	−	40.9907i	0.759477	−	1.31545i	0.943117	−	0.332460i	$-0.107879\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−58.7786	+	33.9358i	−1.88435	+	1.08793i
$974$	−21.7174			−0.695872
$975$		0			0
$976$	−4.31292			−0.138053
$977$	42.6002	−	24.5952i	1.36290	−	0.786871i	0.372891	−	0.927875i	$-0.378367\pi$
$977$	42.6002	−	24.5952i	1.36290	−	0.786871i	0.990009	+	0.141005i	$0.0450332\pi$
$978$	−3.87774	−	6.71645i	−0.123997	−	0.214768i
$979$	5.64835	−	9.78324i	0.180522	−	0.312674i
$980$		0			0
$981$	9.62290	+	5.55578i	0.307236	+	0.177383i
$982$	28.6548	+	16.5438i	0.914411	+	0.527935i
$983$			22.1542i			0.706609i	0.935508	+	0.353304i	$0.114942\pi$
$983$			22.1542i			0.706609i	−0.935508	+	0.353304i	$0.885058\pi$
$984$	−1.50437	+	2.60564i	−0.0479576	+	0.0830649i
$985$		0			0
$986$	25.1507	−	14.5208i	0.800961	−	0.462435i
$987$	24.4021			0.776727
$988$	−2.06803	−	1.29339i	−0.0657928	−	0.0411483i
$989$	−44.0552			−1.40087
$990$		0			0
$991$	24.0251	+	41.6127i	0.763182	+	1.32187i	0.941202	+	0.337843i	$0.109697\pi$
$991$	24.0251	+	41.6127i	0.763182	+	1.32187i	−0.178020	+	0.984027i	$0.556969\pi$
$992$	3.55746	−	6.16171i	0.112950	−	0.195634i
$993$		−	25.7574i		−	0.817387i
$994$	−10.9736	−	6.33564i	−0.348063	−	0.200954i
$995$		0			0
$996$		−	10.3557i		−	0.328132i
$997$	23.6919	−	41.0355i	0.750329	−	1.29961i	−0.197335	−	0.980336i	$-0.563229\pi$
$997$	23.6919	−	41.0355i	0.750329	−	1.29961i	0.947663	−	0.319271i	$-0.103438\pi$
$998$	5.24444	+	9.08363i	0.166010	+	0.287537i
$999$	6.48073	−	3.74165i	0.205041	−	0.118381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.j.751.4		12
5.2	odd	4		390.2.x.b.49.4	yes	12
5.3	odd	4		390.2.x.a.49.3	✓	12
5.4	even	2		1950.2.bc.i.751.3		12
13.4	even	6	inner	1950.2.bc.j.901.4		12
15.2	even	4		1170.2.bj.c.829.5		12
15.8	even	4		1170.2.bj.d.829.2		12
65.4	even	6		1950.2.bc.i.901.3		12
65.17	odd	12		390.2.x.a.199.3	yes	12
65.43	odd	12		390.2.x.b.199.4	yes	12
195.17	even	12		1170.2.bj.d.199.2		12
195.173	even	12		1170.2.bj.c.199.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.3	✓	12	5.3	odd	4
390.2.x.a.199.3	yes	12	65.17	odd	12
390.2.x.b.49.4	yes	12	5.2	odd	4
390.2.x.b.199.4	yes	12	65.43	odd	12
1170.2.bj.c.199.5		12	195.173	even	12
1170.2.bj.c.829.5		12	15.2	even	4
1170.2.bj.d.199.2		12	195.17	even	12
1170.2.bj.d.829.2		12	15.8	even	4
1950.2.bc.i.751.3		12	5.4	even	2
1950.2.bc.i.901.3		12	65.4	even	6
1950.2.bc.j.751.4		12	1.1	even	1	trivial
1950.2.bc.j.901.4		12	13.4	even	6	inner

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-3.76344 - 2.17283i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.04055 + 1.17811i) q^{11} +1.00000 q^{12} +(1.69144 + 3.18419i) q^{13} -4.34565 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50437 + 2.60564i) q^{17} +1.00000i q^{18} +(-0.585872 - 0.338254i) q^{19} -4.34565i q^{21} +(-1.17811 + 2.04055i) q^{22} +(3.22396 + 5.58405i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.05692 + 1.91187i) q^{26} -1.00000 q^{27} +(-3.76344 + 2.17283i) q^{28} +(-4.82620 - 8.35922i) q^{29} +7.11493i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.04055 - 1.17811i) q^{33} +3.00874i q^{34} +(0.500000 + 0.866025i) q^{36} +(-6.48073 + 3.74165i) q^{37} -0.676507 q^{38} +(-1.91187 + 3.05692i) q^{39} +(-2.60564 + 1.50437i) q^{41} +(-2.17283 - 3.76344i) q^{42} +(-3.41624 + 5.91710i) q^{43} +2.35623i q^{44} +(5.58405 + 3.22396i) q^{46} +5.61529i q^{47} +(0.500000 - 0.866025i) q^{48} +(5.94234 + 10.2924i) q^{49} -3.00874 q^{51} +(3.60330 + 0.127265i) q^{52} -9.43400 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-2.17283 + 3.76344i) q^{56} -0.676507i q^{57} +(-8.35922 - 4.82620i) q^{58} +(4.56364 + 2.63482i) q^{59} +(2.15646 - 3.73509i) q^{61} +(3.55746 + 6.16171i) q^{62} +(3.76344 - 2.17283i) q^{63} -1.00000 q^{64} -2.35623 q^{66} +(5.04596 - 2.91329i) q^{67} +(1.50437 + 2.60564i) q^{68} +(-3.22396 + 5.58405i) q^{69} +(2.52520 + 1.45793i) q^{71} +(0.866025 + 0.500000i) q^{72} +7.67804i q^{73} +(-3.74165 + 6.48073i) q^{74} +(-0.585872 + 0.338254i) q^{76} +10.2393 q^{77} +(-0.127265 + 3.60330i) q^{78} +3.74519 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.50437 + 2.60564i) q^{82} -10.3557i q^{83} +(-3.76344 - 2.17283i) q^{84} +6.83247i q^{86} +(4.82620 - 8.35922i) q^{87} +(1.17811 + 2.04055i) q^{88} +(-4.15208 + 2.39720i) q^{89} +(0.553049 - 15.6587i) q^{91} +6.44791 q^{92} +(-6.16171 + 3.55746i) q^{93} +(2.80764 + 4.86298i) q^{94} -1.00000i q^{96} +(-14.1520 - 8.17066i) q^{97} +(10.2924 + 5.94234i) q^{98} -2.35623i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{4} - 12 q^{7} - 6 q^{9} + 6 q^{11} + 12 q^{12} + 4 q^{13} - 4 q^{14} - 6 q^{16} + 8 q^{17} + 6 q^{19} - 6 q^{22} + 16 q^{23} - 2 q^{26} - 12 q^{27} - 12 q^{28} - 14 q^{29} + 6 q^{33}+ \cdots + 24 q^{98}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^4 - 12 * q^7 - 6 * q^9 + 6 * q^11 + 12 * q^12 + 4 * q^13 - 4 * q^14 - 6 * q^16 + 8 * q^17 + 6 * q^19 - 6 * q^22 + 16 * q^23 - 2 * q^26 - 12 * q^27 - 12 * q^28 - 14 * q^29 + 6 * q^33 + 6 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 18 * q^41 - 2 * q^42 + 10 * q^43 - 6 * q^46 + 6 * q^48 - 8 * q^49 + 16 * q^51 + 2 * q^52 - 2 * q^56 + 6 * q^58 + 36 * q^59 + 10 * q^61 + 16 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^66 + 24 * q^67 - 8 * q^68 - 16 * q^69 - 12 * q^71 + 12 * q^74 + 6 * q^76 + 24 * q^77 - 10 * q^78 - 4 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^84 + 14 * q^87 + 6 * q^88 - 18 * q^89 + 2 * q^91 + 32 * q^92 - 6 * q^93 + 8 * q^94 - 24 * q^97 + 24 * q^98

Introduction

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