LMFDB - Embedded newform 792.2.bp.d.667.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(19,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.bp (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 264)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			667.5
Character	$\chi$	$=$	792.667
Dual form			792.2.bp.d.19.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.445083 + 1.34235i) q^{2} +(-1.60380 - 1.19491i) q^{4} +(-1.48262 - 2.04066i) q^{5} +(1.07225 + 3.30005i) q^{7} +(2.31782 - 1.62103i) q^{8} +(3.39916 - 1.08194i) q^{10} +(-2.55602 - 2.11348i) q^{11} +(-1.89429 - 1.37628i) q^{13} +(-4.90706 - 0.0294599i) q^{14} +(1.14437 + 3.83281i) q^{16} +(2.12874 + 2.92996i) q^{17} +(6.47486 + 2.10381i) q^{19} +(-0.0605712 + 5.04441i) q^{20} +(3.97466 - 2.49039i) q^{22} +7.17148i q^{23} +(-0.421018 + 1.29576i) q^{25} +(2.69056 - 1.93024i) q^{26} +(2.22359 - 6.57388i) q^{28} +(0.252424 + 0.776881i) q^{29} +(-3.49999 + 4.81732i) q^{31} +(-5.65431 - 0.169779i) q^{32} +(-4.88050 + 1.55344i) q^{34} +(5.14452 - 7.08083i) q^{35} +(1.96758 - 0.639306i) q^{37} +(-5.70590 + 7.75516i) q^{38} +(-6.74440 - 2.32649i) q^{40} +(4.24917 + 1.38064i) q^{41} +5.90629i q^{43} +(1.57392 + 6.44382i) q^{44} +(-9.62663 - 3.19190i) q^{46} +(6.31309 + 2.05125i) q^{47} +(-4.07750 + 2.96248i) q^{49} +(-1.55197 - 1.14187i) q^{50} +(1.39353 + 4.47079i) q^{52} +(-8.16553 + 11.2389i) q^{53} +(-0.523272 + 8.34943i) q^{55} +(7.83476 + 5.91076i) q^{56} +(-1.15520 - 0.00693530i) q^{58} +(2.47252 + 7.60962i) q^{59} +(-7.77810 + 5.65112i) q^{61} +(-4.90875 - 6.84232i) q^{62} +(2.74454 - 7.51449i) q^{64} +5.90609i q^{65} +9.83888 q^{67} +(0.0869678 - 7.24274i) q^{68} +(7.21521 + 10.0573i) q^{70} +(-3.94907 - 5.43543i) q^{71} +(4.23299 - 1.37538i) q^{73} +(-0.0175648 + 2.92573i) q^{74} +(-7.87053 - 11.1110i) q^{76} +(4.23389 - 10.7012i) q^{77} +(-10.7142 - 7.78432i) q^{79} +(6.12478 - 8.01787i) q^{80} +(-3.74453 + 5.08937i) q^{82} +(-2.34985 - 3.23429i) q^{83} +(2.82292 - 8.68806i) q^{85} +(-7.92830 - 2.62879i) q^{86} +(-9.35038 - 0.755279i) q^{88} -2.99301 q^{89} +(2.51064 - 7.72697i) q^{91} +(8.56930 - 11.5016i) q^{92} +(-5.56334 + 7.56140i) q^{94} +(-5.30663 - 16.3321i) q^{95} +(-5.74003 - 4.17037i) q^{97} +(-2.16185 - 6.79198i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{4} - 4 q^{11} + 16 q^{14} + 20 q^{16} - 25 q^{20} + 3 q^{22} - 4 q^{25} - 4 q^{26} - 25 q^{28} - 26 q^{38} - 65 q^{40} + 60 q^{41} + 43 q^{44} - 5 q^{46} - 12 q^{49} + 80 q^{50} - 15 q^{52}+ \cdots - 40 q^{97}+O(q^{100}) $ 48 * q + 4 * q^4 - 4 * q^11 + 16 * q^14 + 20 * q^16 - 25 * q^20 + 3 * q^22 - 4 * q^25 - 4 * q^26 - 25 * q^28 - 26 * q^38 - 65 * q^40 + 60 * q^41 + 43 * q^44 - 5 * q^46 - 12 * q^49 + 80 * q^50 - 15 * q^52 + 14 * q^56 + 73 * q^58 + 8 * q^59 + 45 * q^62 - 38 * q^64 + 8 * q^67 + 55 * q^68 - 40 * q^70 - 60 * q^74 - 35 * q^82 + 100 * q^83 - 81 * q^86 - 18 * q^88 - 96 * q^89 - 20 * q^91 - 59 * q^92 + 35 * q^94 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$	$-1$

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 $

$2$	−0.445083	+	1.34235i	−0.314721	+	0.949184i
$2$	−0.445083	+	1.34235i	−0.314721	+	0.949184i
$3$		0			0
$3$		0			0
$4$	−1.60380	−	1.19491i	−0.801901	−	0.597457i
$5$	−1.48262	−	2.04066i	−0.663049	−	0.912609i	0.336529	−	0.941673i	$-0.390747\pi$
$5$	−1.48262	−	2.04066i	−0.663049	−	0.912609i	−0.999578	+	0.0290646i	$0.990747\pi$
$6$		0			0
$7$	1.07225	+	3.30005i	0.405273	+	1.24730i	0.920667	+	0.390349i	$0.127646\pi$
$7$	1.07225	+	3.30005i	0.405273	+	1.24730i	−0.515394	+	0.856953i	$0.672354\pi$
$8$	2.31782	−	1.62103i	0.819472	−	0.573120i
$9$		0			0
$10$	3.39916	−	1.08194i	1.07491	−	0.342138i
$11$	−2.55602	−	2.11348i	−0.770668	−	0.637237i
$11$	−2.55602	−	2.11348i	−0.770668	−	0.637237i
$12$		0			0
$13$	−1.89429	−	1.37628i	−0.525381	−	0.381712i	0.293246	−	0.956037i	$-0.405264\pi$
$13$	−1.89429	−	1.37628i	−0.525381	−	0.381712i	−0.818627	+	0.574325i	$0.805264\pi$
$14$	−4.90706	−	0.0294599i	−1.31147	−	0.00787349i
$15$		0			0
$16$	1.14437	+	3.83281i	0.286091	+	0.958202i
$17$	2.12874	+	2.92996i	0.516296	+	0.710620i	0.984965	−	0.172753i	$-0.0552664\pi$
$17$	2.12874	+	2.92996i	0.516296	+	0.710620i	−0.468669	+	0.883374i	$0.655266\pi$
$18$		0			0
$19$	6.47486	+	2.10381i	1.48544	+	0.482647i	0.935732	−	0.352712i	$-0.114741\pi$
$19$	6.47486	+	2.10381i	1.48544	+	0.482647i	0.549704	+	0.835360i	$0.314741\pi$
$20$	−0.0605712	+	5.04441i	−0.0135441	+	1.12797i
$21$		0			0
$22$	3.97466	−	2.49039i	0.847401	−	0.530953i
$23$			7.17148i			1.49536i	0.664061	+	0.747679i	$0.268832\pi$
$23$			7.17148i			1.49536i	−0.664061	+	0.747679i	$0.731168\pi$
$24$		0			0
$25$	−0.421018	+	1.29576i	−0.0842036	+	0.259152i
$26$	2.69056	−	1.93024i	0.527663	−	0.378551i
$27$		0			0
$28$	2.22359	−	6.57388i	0.420220	−	1.24235i
$29$	0.252424	+	0.776881i	0.0468740	+	0.144263i	0.971754	−	0.235995i	$-0.0758350\pi$
$29$	0.252424	+	0.776881i	0.0468740	+	0.144263i	−0.924880	+	0.380259i	$0.875835\pi$
$30$		0			0
$31$	−3.49999	+	4.81732i	−0.628617	+	0.865217i	−0.997945	−	0.0640823i	$-0.979588\pi$
$31$	−3.49999	+	4.81732i	−0.628617	+	0.865217i	0.369328	+	0.929299i	$0.379588\pi$
$32$	−5.65431	−	0.169779i	−0.999550	−	0.0300130i
$33$		0			0
$34$	−4.88050	+	1.55344i	−0.836999	+	0.266413i
$35$	5.14452	−	7.08083i	0.869583	−	1.19688i
$36$		0			0
$37$	1.96758	−	0.639306i	0.323469	−	0.105101i	−0.142782	−	0.989754i	$-0.545605\pi$
$37$	1.96758	−	0.639306i	0.323469	−	0.105101i	0.466250	+	0.884653i	$0.345605\pi$
$38$	−5.70590	+	7.75516i	−0.925619	+	1.25805i
$39$		0			0
$40$	−6.74440	−	2.32649i	−1.06638	−	0.367850i
$41$	4.24917	+	1.38064i	0.663609	+	0.215620i	0.621405	−	0.783489i	$-0.286562\pi$
$41$	4.24917	+	1.38064i	0.663609	+	0.215620i	0.0422040	+	0.999109i	$0.486562\pi$
$42$		0			0
$43$			5.90629i			0.900700i	0.892852	+	0.450350i	$0.148701\pi$
$43$			5.90629i			0.900700i	−0.892852	+	0.450350i	$0.851299\pi$
$44$	1.57392	+	6.44382i	0.237278	+	0.971442i
$45$		0			0
$46$	−9.62663	−	3.19190i	−1.41937	−	0.470620i
$47$	6.31309	+	2.05125i	0.920859	+	0.299205i	0.730819	−	0.682571i	$-0.239138\pi$
$47$	6.31309	+	2.05125i	0.920859	+	0.299205i	0.190040	+	0.981776i	$0.439138\pi$
$48$		0			0
$49$	−4.07750	+	2.96248i	−0.582500	+	0.423211i
$50$	−1.55197	−	1.14187i	−0.219482	−	0.161485i
$51$		0			0
$52$	1.39353	+	4.47079i	0.193248	+	0.619987i
$53$	−8.16553	+	11.2389i	−1.12162	+	1.54378i	−0.318540	+	0.947909i	$0.603192\pi$
$53$	−8.16553	+	11.2389i	−1.12162	+	1.54378i	−0.803081	+	0.595870i	$0.796808\pi$
$54$		0			0
$55$	−0.523272	+	8.34943i	−0.0705580	+	1.12584i
$56$	7.83476	+	5.91076i	1.04696	+	0.789859i
$57$		0			0
$58$	−1.15520	−	0.00693530i	−0.151685	−	0.000910649i
$59$	2.47252	+	7.60962i	0.321894	+	0.990689i	0.972823	+	0.231550i	$0.0743796\pi$
$59$	2.47252	+	7.60962i	0.321894	+	0.990689i	−0.650929	+	0.759139i	$0.725620\pi$
$60$		0			0
$61$	−7.77810	+	5.65112i	−0.995883	+	0.723552i	−0.961202	−	0.275847i	$-0.911042\pi$
$61$	−7.77810	+	5.65112i	−0.995883	+	0.723552i	−0.0346817	+	0.999398i	$0.511042\pi$
$62$	−4.90875	−	6.84232i	−0.623411	−	0.868975i
$63$		0			0
$64$	2.74454	−	7.51449i	0.343067	−	0.939311i
$65$			5.90609i			0.732561i
$66$		0			0
$67$	9.83888			1.20201			0.601006	−	0.799245i	$-0.294767\pi$
$67$	9.83888			1.20201			0.601006	+	0.799245i	$0.294767\pi$
$68$	0.0869678	−	7.24274i	0.0105464	−	0.878312i
$69$		0			0
$70$	7.21521	+	10.0573i	0.862382	+	1.20208i
$71$	−3.94907	−	5.43543i	−0.468669	−	0.645067i	0.507609	−	0.861587i	$-0.330529\pi$
$71$	−3.94907	−	5.43543i	−0.468669	−	0.645067i	−0.976278	+	0.216520i	$0.930529\pi$
$72$		0			0
$73$	4.23299	−	1.37538i	0.495434	−	0.160976i	−0.0506336	−	0.998717i	$-0.516124\pi$
$73$	4.23299	−	1.37538i	0.495434	−	0.160976i	0.546068	+	0.837741i	$0.316124\pi$
$74$	−0.0175648	+	2.92573i	−0.00204187	+	0.340109i
$75$		0			0
$76$	−7.87053	−	11.1110i	−0.902812	−	1.27452i
$77$	4.23389	−	10.7012i	0.482497	−	1.21951i
$78$		0			0
$79$	−10.7142	−	7.78432i	−1.20544	−	0.875804i	−0.210632	−	0.977565i	$-0.567552\pi$
$79$	−10.7142	−	7.78432i	−1.20544	−	0.875804i	−0.994809	+	0.101761i	$0.967552\pi$
$80$	6.12478	−	8.01787i	0.684771	−	0.896425i
$81$		0			0
$82$	−3.74453	+	5.08937i	−0.413515	+	0.562027i
$83$	−2.34985	−	3.23429i	−0.257929	−	0.355009i	0.660339	−	0.750967i	$-0.270412\pi$
$83$	−2.34985	−	3.23429i	−0.257929	−	0.355009i	−0.918269	+	0.395958i	$0.870412\pi$
$84$		0			0
$85$	2.82292	−	8.68806i	0.306189	−	0.942352i
$86$	−7.92830	−	2.62879i	−0.854930	−	0.283469i
$87$		0			0
$88$	−9.35038	−	0.755279i	−0.996754	−	0.0805130i
$89$	−2.99301			−0.317259			−0.158629	−	0.987338i	$-0.550708\pi$
$89$	−2.99301			−0.317259			−0.158629	+	0.987338i	$0.550708\pi$
$90$		0			0
$91$	2.51064	−	7.72697i	0.263187	−	0.810006i
$92$	8.56930	−	11.5016i	0.893411	−	1.19913i
$93$		0			0
$94$	−5.56334	+	7.56140i	−0.573815	+	0.779899i
$95$	−5.30663	−	16.3321i	−0.544449	−	1.67564i
$96$		0			0
$97$	−5.74003	−	4.17037i	−0.582811	−	0.423437i	0.256925	−	0.966431i	$-0.417291\pi$
$97$	−5.74003	−	4.17037i	−0.582811	−	0.423437i	−0.839737	+	0.542994i	$0.817291\pi$
$98$	−2.16185	−	6.79198i	−0.218380	−	0.686094i
$99$		0			0
$100$	2.22355	−	1.57506i	0.222355	−	0.157506i
$101$	5.16038	+	3.74924i	0.513477	+	0.373063i	0.814141	−	0.580667i	$-0.197208\pi$
$101$	5.16038	+	3.74924i	0.513477	+	0.373063i	−0.300664	+	0.953730i	$0.597208\pi$
$102$		0			0
$103$	10.1308	−	3.29171i	0.998220	−	0.324341i	0.236066	−	0.971737i	$-0.424142\pi$
$103$	10.1308	−	3.29171i	0.998220	−	0.324341i	0.762154	+	0.647396i	$0.224142\pi$
$104$	−6.62160	−	0.119271i	−0.649301	−	0.0116955i
$105$		0			0
$106$	−11.4522	−	15.9632i	−1.11233	−	1.55048i
$107$	11.5148	+	3.74138i	1.11318	+	0.361693i	0.807159	−	0.590334i	$-0.201004\pi$
$107$	11.5148	+	3.74138i	1.11318	+	0.361693i	0.306016	+	0.952026i	$0.401004\pi$
$108$		0			0
$109$	3.51815			0.336977			0.168489	−	0.985704i	$-0.446111\pi$
$109$	3.51815			0.336977			0.168489	+	0.985704i	$0.446111\pi$
$110$	−10.9750	−	4.41860i	−1.04642	−	0.421297i
$111$		0			0
$112$	−11.4214	+	7.88620i	−1.07922	+	0.745176i
$113$	−5.13684	+	15.8096i	−0.483233	+	1.48724i	0.351290	+	0.936267i	$0.385743\pi$
$113$	−5.13684	+	15.8096i	−0.483233	+	1.48724i	−0.834523	+	0.550973i	$0.814257\pi$
$114$		0			0
$115$	14.6345	−	10.6326i	1.36468	−	0.991495i
$116$	0.523467	−	1.54759i	0.0486027	−	0.143690i
$117$		0			0
$118$	−11.3152	−	0.0679319i	−1.04165	−	0.00625364i
$119$	−7.38648	+	10.1666i	−0.677118	+	0.931972i
$120$		0			0
$121$	2.06643	+	10.8042i	0.187857	+	0.982196i
$122$	−4.12388	−	12.9561i	−0.373358	−	1.17299i
$123$		0			0
$124$	11.3696	−	3.54385i	1.02102	−	0.318247i
$125$	−8.72626	+	2.83533i	−0.780500	+	0.253600i
$126$		0			0
$127$	16.1834	−	11.7579i	1.43605	−	1.04335i	0.447195	−	0.894436i	$-0.352423\pi$
$127$	16.1834	−	11.7579i	1.43605	−	1.04335i	0.988850	−	0.148912i	$-0.0475771\pi$
$128$	8.86552	+	7.02870i	0.783609	+	0.621255i
$129$		0			0
$130$	−7.92804	−	2.62870i	−0.695335	−	0.230552i
$131$		−	15.4240i		−	1.34760i	−0.738914	−	0.673800i	$-0.764661\pi$
$131$		−	15.4240i		−	1.34760i	0.738914	−	0.673800i	$-0.235339\pi$
$132$		0			0
$133$			23.6232i			2.04839i
$134$	−4.37912	+	13.2072i	−0.378298	+	1.14093i
$135$		0			0
$136$	9.68358	+	3.34036i	0.830360	+	0.286434i
$137$	1.08264	−	0.786586i	0.0924965	−	0.0672026i	−0.540576	−	0.841295i	$-0.681794\pi$
$137$	1.08264	−	0.786586i	0.0924965	−	0.0672026i	0.633072	+	0.774093i	$0.281794\pi$
$138$		0			0
$139$	−3.79325	+	1.23250i	−0.321740	+	0.104540i	−0.465434	−	0.885083i	$-0.654102\pi$
$139$	−3.79325	+	1.23250i	−0.321740	+	0.104540i	0.143694	+	0.989622i	$0.454102\pi$
$140$	−16.7118	+	5.20899i	−1.41240	+	0.440240i
$141$		0			0
$142$	9.05391	−	2.88182i	0.759787	−	0.241837i
$143$	1.93309	+	7.52133i	0.161653	+	0.628965i
$144$		0			0
$145$	1.21110	−	1.66693i	0.100576	−	0.138431i
$146$	−0.0377883	+	6.29431i	−0.00312739	+	0.520921i
$147$		0			0
$148$	−3.91953	−	1.32577i	−0.322183	−	0.108978i
$149$	3.78076	−	2.74688i	0.309732	−	0.225033i	−0.422050	−	0.906573i	$-0.638689\pi$
$149$	3.78076	−	2.74688i	0.309732	−	0.225033i	0.731781	+	0.681539i	$0.238689\pi$
$150$		0			0
$151$	−0.220305	+	0.678030i	−0.0179282	+	0.0551773i	−0.959620	−	0.281298i	$-0.909235\pi$
$151$	−0.220305	+	0.678030i	−0.0179282	+	0.0551773i	0.941692	+	0.336476i	$0.109235\pi$
$152$	18.4179	−	5.61969i	1.49389	−	0.455817i
$153$		0			0
$154$	12.4803	+	10.4463i	1.00569	+	0.841784i
$155$	15.0197			1.20641
$156$		0			0
$157$	10.9722	+	3.56508i	0.875676	+	0.284524i	0.712161	−	0.702016i	$-0.247717\pi$
$157$	10.9722	+	3.56508i	0.875676	+	0.284524i	0.163515	+	0.986541i	$0.447717\pi$
$158$	15.2180	−	10.9175i	1.21068	−	0.868551i
$159$		0			0
$160$	8.03674	+	11.7902i	0.635360	+	0.932098i
$161$	−23.6663	+	7.68963i	−1.86516	+	0.606028i
$162$		0			0
$163$	−11.0431	−	8.02330i	−0.864964	−	0.628433i	0.0642670	−	0.997933i	$-0.479529\pi$
$163$	−11.0431	−	8.02330i	−0.864964	−	0.628433i	−0.929231	+	0.369500i	$0.879529\pi$
$164$	−5.16509	−	7.29167i	−0.403326	−	0.569383i
$165$		0			0
$166$	5.38742	−	1.71479i	0.418145	−	0.133094i
$167$	9.54231	+	6.93290i	0.738406	+	0.536484i	0.892212	−	0.451618i	$-0.149153\pi$
$167$	9.54231	+	6.93290i	0.738406	+	0.536484i	−0.153805	+	0.988101i	$0.549153\pi$
$168$		0			0
$169$	−2.32304	−	7.14959i	−0.178696	−	0.549968i
$170$	10.4060	+	7.65625i	0.798102	+	0.587208i
$171$		0			0
$172$	7.05750	−	9.47252i	0.538129	−	0.722273i
$173$	1.50776	−	4.64040i	0.114633	−	0.352803i	−0.877238	−	0.480057i	$-0.840616\pi$
$173$	1.50776	−	4.64040i	0.114633	−	0.352803i	0.991870	+	0.127253i	$0.0406161\pi$
$174$		0			0
$175$	−4.72751			−0.357366
$176$	5.17554	−	12.2153i	0.390121	−	0.920764i
$177$		0			0
$178$	1.33214	−	4.01767i	0.0998481	−	0.301137i
$179$	4.50804	−	13.8743i	0.336946	−	1.03701i	−0.628809	−	0.777560i	$-0.716457\pi$
$179$	4.50804	−	13.8743i	0.336946	−	1.03701i	0.965755	−	0.259455i	$-0.0835428\pi$
$180$		0			0
$181$	−4.01377	−	5.52448i	−0.298341	−	0.410631i	0.633360	−	0.773857i	$-0.281675\pi$
$181$	−4.01377	−	5.52448i	−0.298341	−	0.410631i	−0.931701	+	0.363226i	$0.881675\pi$
$182$	9.25485	+	6.80930i	0.686015	+	0.504739i
$183$		0			0
$184$	11.6252	+	16.6222i	0.857019	+	1.22540i
$185$	−4.22179	−	3.06731i	−0.310392	−	0.225513i
$186$		0			0
$187$	0.751312	−	11.9881i	0.0549414	−	0.876655i
$188$	−7.67389	−	10.8334i	−0.559676	−	0.790107i
$189$		0			0
$190$	24.2853	+	0.145798i	1.76184	+	0.0105773i
$191$	11.3228	−	3.67901i	0.819291	−	0.266204i	0.130763	−	0.991414i	$-0.458257\pi$
$191$	11.3228	−	3.67901i	0.819291	−	0.266204i	0.688528	+	0.725210i	$0.258257\pi$
$192$		0			0
$193$	6.94660	+	9.56117i	0.500027	+	0.688228i	0.982198	−	0.187849i	$-0.0601516\pi$
$193$	6.94660	+	9.56117i	0.500027	+	0.688228i	−0.482171	+	0.876077i	$0.660152\pi$
$194$	8.15288	−	5.84896i	0.585343	−	0.419931i
$195$		0			0
$196$	10.0794	+	0.121029i	0.719958	+	0.00864495i
$197$	−7.10914			−0.506505			−0.253253	−	0.967400i	$-0.581500\pi$
$197$	−7.10914			−0.506505			−0.253253	+	0.967400i	$0.581500\pi$
$198$		0			0
$199$			24.2455i			1.71872i	0.511370	+	0.859361i	$0.329138\pi$
$199$			24.2455i			1.71872i	−0.511370	+	0.859361i	$0.670862\pi$
$200$	1.12462	+	3.68581i	0.0795227	+	0.260626i
$201$		0			0
$202$	−7.32959	+	5.25832i	−0.515708	+	0.369974i
$203$	−2.29309	+	1.66603i	−0.160943	+	0.116932i
$204$		0			0
$205$	−3.48251	−	10.7181i	−0.243229	−	0.748582i
$206$	−0.0904389	+	15.0642i	−0.00630118	+	1.04957i
$207$		0			0
$208$	3.10726	−	8.83541i	0.215450	−	0.612626i
$209$	−12.1035	−	19.0619i	−0.837216	−	1.31854i
$210$		0			0
$211$	−15.0538	+	20.7198i	−1.03635	+	1.42641i	−0.136276	+	0.990671i	$0.543513\pi$
$211$	−15.0538	+	20.7198i	−1.03635	+	1.42641i	−0.900072	+	0.435741i	$0.856487\pi$
$212$	26.5254	−	8.26785i	1.82177	−	0.567839i
$213$		0			0
$214$	−10.1473	+	13.7916i	−0.693652	+	0.942776i
$215$	12.0527	−	8.75679i	0.821987	−	0.597208i
$216$		0			0
$217$	−19.6503	−	6.38477i	−1.33395	−	0.433426i
$218$	−1.56587	+	4.72258i	−0.106054	+	0.319854i
$219$		0			0
$220$	10.8161	−	12.7656i	0.729220	−	0.860655i
$221$		−	8.47994i		−	0.570422i
$222$		0			0
$223$	0.321670	+	0.104517i	0.0215406	+	0.00699897i	0.319767	−	0.947496i	$-0.396395\pi$
$223$	0.321670	+	0.104517i	0.0215406	+	0.00699897i	−0.298227	+	0.954495i	$0.596395\pi$
$224$	−5.50256	−	18.8416i	−0.367655	−	1.25890i
$225$		0			0
$226$	−18.9356	−	13.9320i	−1.25958	−	0.926743i
$227$	−6.94794	+	2.25752i	−0.461151	+	0.149837i	−0.530373	−	0.847764i	$-0.677948\pi$
$227$	−6.94794	+	2.25752i	−0.461151	+	0.149837i	0.0692224	+	0.997601i	$0.477948\pi$
$228$		0			0
$229$	−5.47704	+	7.53850i	−0.361933	+	0.498158i	−0.950686	−	0.310155i	$-0.899619\pi$
$229$	−5.47704	+	7.53850i	−0.361933	+	0.498158i	0.588753	+	0.808313i	$0.299619\pi$
$230$	7.75909	+	24.3770i	0.511619	+	1.60737i
$231$		0			0
$232$	1.84442	+	1.39148i	0.121092	+	0.0913552i
$233$	0.710006	−	0.977239i	0.0465140	−	0.0640211i	−0.785126	−	0.619335i	$-0.787402\pi$
$233$	0.710006	−	0.977239i	0.0465140	−	0.0640211i	0.831640	+	0.555314i	$0.187402\pi$
$234$		0			0
$235$	−5.17405	−	15.9241i	−0.337518	−	1.03877i
$236$	5.12741	−	15.1588i	0.333766	−	0.986752i
$237$		0			0
$238$	−10.3596	−	14.4402i	−0.671510	−	0.936021i
$239$	−5.06492	+	15.5882i	−0.327623	+	1.00832i	0.642620	+	0.766185i	$0.277847\pi$
$239$	−5.06492	+	15.5882i	−0.327623	+	1.00832i	−0.970243	+	0.242134i	$0.922153\pi$
$240$		0			0
$241$			10.8639i			0.699808i	0.936786	+	0.349904i	$0.113786\pi$
$241$			10.8639i			0.699808i	−0.936786	+	0.349904i	$0.886214\pi$
$242$	−15.4227	−	2.03488i	−0.991408	−	0.130807i
$243$		0			0
$244$	19.2271	+	0.230871i	1.23089	+	0.0147800i
$245$	12.0908	+	3.92854i	0.772452	+	0.250985i
$246$		0			0
$247$	−9.36982	−	12.8965i	−0.596188	−	0.820582i
$248$	−0.303316	+	16.8392i	−0.0192606	+	1.06929i
$249$		0			0
$250$	0.0779002	−	12.9756i	0.00492684	−	0.820652i
$251$	4.78591	+	3.47716i	0.302084	+	0.219477i	0.728492	−	0.685054i	$-0.240221\pi$
$251$	4.78591	+	3.47716i	0.302084	+	0.219477i	−0.426409	+	0.904531i	$0.640221\pi$
$252$		0			0
$253$	15.1568	−	18.3304i	0.952897	−	1.15242i
$254$	8.58030	+	26.9570i	0.538376	+	1.69144i
$255$		0			0
$256$	−13.3809	+	8.77227i	−0.836303	+	0.548267i
$257$	−5.17047	−	15.9131i	−0.322525	−	0.992630i	−0.972545	−	0.232713i	$-0.925240\pi$
$257$	−5.17047	−	15.9131i	−0.322525	−	0.992630i	0.650021	−	0.759917i	$-0.274760\pi$
$258$		0			0
$259$	4.21949	+	5.80763i	0.262186	+	0.360868i
$260$	7.05727	−	9.47221i	0.437673	−	0.587441i
$261$		0			0
$262$	20.7044	+	6.86495i	1.27912	+	0.424118i
$263$	16.8522			1.03915			0.519576	−	0.854424i	$-0.326090\pi$
$263$	16.8522			1.03915			0.519576	+	0.854424i	$0.326090\pi$
$264$		0			0
$265$	35.0411			2.15256
$266$	−31.7106	−	10.5143i	−1.94430	−	0.644672i
$267$		0			0
$268$	−15.7796	−	11.7566i	−0.963894	−	0.718149i
$269$	1.03833	+	1.42914i	0.0633083	+	0.0871365i	0.839497	−	0.543364i	$-0.182850\pi$
$269$	1.03833	+	1.42914i	0.0633083	+	0.0871365i	−0.776189	+	0.630501i	$0.782850\pi$
$270$		0			0
$271$	−1.12583	−	3.46495i	−0.0683893	−	0.210480i	0.911021	−	0.412359i	$-0.135295\pi$
$271$	−1.12583	−	3.46495i	−0.0683893	−	0.210480i	−0.979410	+	0.201879i	$0.935295\pi$
$272$	−8.79393	+	11.5120i	−0.533210	+	0.698018i
$273$		0			0
$274$	0.574008	+	1.80338i	0.0346771	+	0.108946i
$275$	3.81469	−	2.42217i	0.230034	−	0.146062i
$276$		0			0
$277$	−14.8332	−	10.7770i	−0.891242	−	0.647525i	0.0449597	−	0.998989i	$-0.485684\pi$
$277$	−14.8332	−	10.7770i	−0.891242	−	0.647525i	−0.936201	+	0.351464i	$0.885684\pi$
$278$	0.0338628	−	5.64044i	0.00203095	−	0.338291i
$279$		0			0
$280$	0.445834	−	24.7515i	0.0266437	−	1.47918i
$281$	−8.29184	−	11.4127i	−0.494650	−	0.680827i	0.486587	−	0.873632i	$-0.338242\pi$
$281$	−8.29184	−	11.4127i	−0.494650	−	0.680827i	−0.981237	+	0.192805i	$0.938242\pi$
$282$		0			0
$283$	−27.2402	−	8.85089i	−1.61926	−	0.526131i	−0.647496	−	0.762068i	$-0.724184\pi$
$283$	−27.2402	−	8.85089i	−1.61926	−	0.526131i	−0.971768	+	0.235937i	$0.924184\pi$
$284$	−0.161336	+	13.4362i	−0.00957351	+	0.797289i
$285$		0			0
$286$	−10.9566	−	0.752732i	−0.647879	−	0.0445100i
$287$			15.5029i			0.915106i
$288$		0			0
$289$	1.20015	−	3.69369i	0.0705973	−	0.217276i
$290$	1.69857	+	2.36764i	0.0997433	+	0.139033i
$291$		0			0
$292$	−8.43234	−	2.85221i	−0.493466	−	0.166913i
$293$	−5.28447	−	16.2639i	−0.308722	−	0.950149i	−0.978262	−	0.207373i	$-0.933509\pi$
$293$	−5.28447	−	16.2639i	−0.308722	−	0.950149i	0.669540	−	0.742776i	$-0.266491\pi$
$294$		0			0
$295$	11.8628	−	16.3278i	0.690679	−	0.950639i
$296$	3.52416	−	4.67130i	0.204838	−	0.271514i
$297$		0			0
$298$	2.00452	+	6.29769i	0.116119	+	0.364815i
$299$	9.86997	−	13.5848i	0.570795	−	0.785632i
$300$		0			0
$301$	−19.4911	+	6.33303i	−1.12345	+	0.365030i
$302$	−0.812100	−	0.597507i	−0.0467311	−	0.0343826i
$303$		0			0
$304$	−0.653893	+	27.2244i	−0.0375034	+	1.56143i
$305$	23.0640	+	7.49394i	1.32064	+	0.429102i
$306$		0			0
$307$			20.4466i			1.16695i	0.812131	+	0.583476i	$0.198308\pi$
$307$			20.4466i			1.16695i	−0.812131	+	0.583476i	$0.801692\pi$
$308$	−19.5773	+	12.1034i	−1.11552	+	0.689656i
$309$		0			0
$310$	−6.68499	+	20.1616i	−0.379682	+	1.14510i
$311$	−17.0796	−	5.54949i	−0.968494	−	0.314683i	−0.218286	−	0.975885i	$-0.570047\pi$
$311$	−17.0796	−	5.54949i	−0.968494	−	0.314683i	−0.750208	+	0.661202i	$0.770047\pi$
$312$		0			0
$313$	−19.0162	+	13.8161i	−1.07486	+	0.780931i	−0.976779	−	0.214248i	$-0.931270\pi$
$313$	−19.0162	+	13.8161i	−1.07486	+	0.780931i	−0.0980794	+	0.995179i	$0.531270\pi$
$314$	−9.66912	+	13.1418i	−0.545660	+	0.741632i
$315$		0			0
$316$	7.88187	+	25.2870i	0.443390	+	1.42251i
$317$	19.0205	−	26.1795i	1.06830	−	1.47039i	0.196515	−	0.980501i	$-0.437038\pi$
$317$	19.0205	−	26.1795i	1.06830	−	1.47039i	0.871785	−	0.489888i	$-0.162962\pi$
$318$		0			0
$319$	0.996722	−	2.51921i	0.0558057	−	0.141049i
$320$	−19.4036	+	5.54050i	−1.08469	+	0.309723i
$321$		0			0
$322$	0.211271	−	35.1909i	0.0117737	−	1.96111i
$323$	7.61923	+	23.4496i	0.423945	+	1.30477i
$324$		0			0
$325$	2.58086	−	1.87510i	0.143160	−	0.104012i
$326$	15.6852	−	11.2527i	0.868721	−	0.623229i
$327$		0			0
$328$	12.0869	−	3.68796i	0.667385	−	0.203633i
$329$			23.0330i			1.26985i
$330$		0			0
$331$	4.86677			0.267502			0.133751	−	0.991015i	$-0.457298\pi$
$331$	4.86677			0.267502			0.133751	+	0.991015i	$0.457298\pi$
$332$	−0.0960008	+	7.99502i	−0.00526873	+	0.438784i
$333$		0			0
$334$	−13.5535	+	9.72340i	−0.741614	+	0.532041i
$335$	−14.5874	−	20.0778i	−0.796992	−	1.09697i
$336$		0			0
$337$	−22.9644	+	7.46157i	−1.25095	+	0.406458i	−0.858261	−	0.513214i	$-0.828455\pi$
$337$	−22.9644	+	7.46157i	−1.25095	+	0.406458i	−0.392688	+	0.919672i	$0.628455\pi$
$338$	10.6312	+	0.0638251i	0.578261	+	0.00347163i
$339$		0			0
$340$	−14.9089	+	10.5608i	−0.808548	+	0.572739i
$341$	19.1273	−	4.91600i	1.03580	−	0.266216i
$342$		0			0
$343$	5.50190	+	3.99737i	0.297075	+	0.215837i
$344$	9.57425	+	13.6897i	0.516209	+	0.738098i
$345$		0			0
$346$	5.55796	+	4.08930i	0.298798	+	0.219842i
$347$	0.447412	+	0.615809i	0.0240183	+	0.0330584i	0.820857	−	0.571133i	$-0.193496\pi$
$347$	0.447412	+	0.615809i	0.0240183	+	0.0330584i	−0.796839	+	0.604192i	$0.793496\pi$
$348$		0			0
$349$	6.30428	−	19.4026i	0.337460	−	1.03860i	−0.628037	−	0.778183i	$-0.716141\pi$
$349$	6.30428	−	19.4026i	0.337460	−	1.03860i	0.965497	−	0.260413i	$-0.0838586\pi$
$350$	2.10413	−	6.34597i	0.112471	−	0.339207i
$351$		0			0
$352$	14.0937	+	12.3842i	0.751195	+	0.660080i
$353$	−8.47666			−0.451167			−0.225583	−	0.974224i	$-0.572429\pi$
$353$	−8.47666			−0.451167			−0.225583	+	0.974224i	$0.572429\pi$
$354$		0			0
$355$	−5.23686	+	16.1174i	−0.277944	+	0.855422i
$356$	4.80020	+	3.57639i	0.254410	+	0.189548i
$357$		0			0
$358$	16.6177	+	12.2266i	0.878274	+	0.646194i
$359$	0.249005	+	0.766359i	0.0131420	+	0.0404469i	0.957412	−	0.288724i	$-0.0932309\pi$
$359$	0.249005	+	0.766359i	0.0131420	+	0.0404469i	−0.944270	+	0.329171i	$0.893231\pi$
$360$		0			0
$361$	22.1265	+	16.0759i	1.16455	+	0.846098i
$362$	9.20224	−	2.92903i	0.483659	−	0.153946i
$363$		0			0
$364$	−13.2596	+	9.39253i	−0.694994	+	0.492302i
$365$	−9.08261	−	6.59890i	−0.475406	−	0.345402i
$366$		0			0
$367$	18.2008	−	5.91378i	0.950072	−	0.308697i	0.207327	−	0.978272i	$-0.433524\pi$
$367$	18.2008	−	5.91378i	0.950072	−	0.308697i	0.742745	+	0.669575i	$0.233524\pi$
$368$	−27.4869	+	8.20680i	−1.43285	+	0.427809i
$369$		0			0
$370$	5.99644	−	4.30191i	0.311740	−	0.223645i
$371$	−45.8444	−	14.8957i	−2.38012	−	0.773349i
$372$		0			0
$373$	−6.55679			−0.339498			−0.169749	−	0.985487i	$-0.554296\pi$
$373$	−6.55679			−0.339498			−0.169749	+	0.985487i	$0.554296\pi$
$374$	15.7578	+	6.34421i	0.814816	+	0.328051i
$375$		0			0
$376$	17.9577	−	5.47929i	0.926099	−	0.282573i
$377$	0.591043	−	1.81904i	0.0304403	−	0.0936855i
$378$		0			0
$379$	13.9245	−	10.1167i	0.715254	−	0.519662i	−0.169610	−	0.985511i	$-0.554251\pi$
$379$	13.9245	−	10.1167i	0.715254	−	0.519662i	0.884864	+	0.465849i	$0.154251\pi$
$380$	−11.0047	+	32.5345i	−0.564528	+	1.66898i
$381$		0			0
$382$	−0.101080	+	16.8367i	−0.00517171	+	0.861438i
$383$	−1.18431	+	1.63006i	−0.0605154	+	0.0832923i	−0.838202	−	0.545360i	$-0.816393\pi$
$383$	−1.18431	+	1.63006i	−0.0605154	+	0.0832923i	0.777687	+	0.628652i	$0.216393\pi$
$384$		0			0
$385$	−28.1147	+	7.22587i	−1.43286	+	0.368265i
$386$	−15.9262	+	5.06925i	−0.810624	+	0.258018i
$387$		0			0
$388$	4.22264	+	13.5473i	0.214372	+	0.687759i
$389$	−19.3927	+	6.30107i	−0.983249	+	0.319477i	−0.756153	−	0.654395i	$-0.772923\pi$
$389$	−19.3927	+	6.30107i	−0.983249	+	0.319477i	−0.227097	+	0.973872i	$0.572923\pi$
$390$		0			0
$391$	−21.0122	+	15.2662i	−1.06263	+	0.772047i
$392$	−4.64864	+	13.4762i	−0.234792	+	0.680652i
$393$		0			0
$394$	3.16416	−	9.54295i	0.159408	−	0.480767i
$395$			33.4052i			1.68080i
$396$		0			0
$397$		−	16.0438i		−	0.805217i	−0.915372	−	0.402608i	$-0.868104\pi$
$397$		−	16.0438i		−	0.805217i	0.915372	−	0.402608i	$-0.131896\pi$
$398$	−32.5460	−	10.7913i	−1.63138	−	0.540918i
$399$		0			0
$400$	−5.44820	−	0.130858i	−0.272410	−	0.00654291i
$401$	−10.2918	+	7.47745i	−0.513949	+	0.373406i	−0.814320	−	0.580417i	$-0.802890\pi$
$401$	−10.2918	+	7.47745i	−0.513949	+	0.373406i	0.300370	+	0.953823i	$0.402890\pi$
$402$		0			0
$403$	13.2600	−	4.30843i	0.660527	−	0.214618i
$404$	−3.79622	−	12.1792i	−0.188869	−	0.605940i
$405$		0			0
$406$	−1.21577	−	3.81964i	−0.0603379	−	0.189566i
$407$	−6.38033	−	2.52436i	−0.316261	−	0.125128i
$408$		0			0
$409$	18.7338	−	25.7849i	0.926329	−	1.27498i	−0.0349457	−	0.999389i	$-0.511126\pi$
$409$	18.7338	−	25.7849i	0.926329	−	1.27498i	0.961274	−	0.275593i	$-0.0888742\pi$
$410$	15.9374	+	0.0956812i	0.787091	+	0.00472536i
$411$		0			0
$412$	−20.1812	−	6.82621i	−0.994254	−	0.336303i
$413$	−22.4610	+	16.3189i	−1.10523	+	0.802999i
$414$		0			0
$415$	−3.11613	+	9.59045i	−0.152965	+	0.470777i
$416$	10.4772	+	8.10352i	0.513688	+	0.397308i
$417$		0			0
$418$	30.9747	−	7.76301i	1.51502	−	0.379701i
$419$	14.2948			0.698346			0.349173	−	0.937058i	$-0.386463\pi$
$419$	14.2948			0.698346			0.349173	+	0.937058i	$0.386463\pi$
$420$		0			0
$421$	7.03822	+	2.28685i	0.343022	+	0.111454i	0.475461	−	0.879737i	$-0.342281\pi$
$421$	7.03822	+	2.28685i	0.343022	+	0.111454i	−0.132440	+	0.991191i	$0.542281\pi$
$422$	−21.1130	−	29.4295i	−1.02777	−	1.43261i
$423$		0			0
$424$	−0.707640	+	39.2862i	−0.0343661	+	1.90791i
$425$	−4.69277	+	1.52477i	−0.227633	+	0.0739623i
$426$		0			0
$427$	−26.9891	−	19.6087i	−1.30609	−	0.948932i
$428$	−13.9968	−	19.7596i	−0.676561	−	0.955115i
$429$		0			0
$430$	6.39023	+	20.0764i	0.308164	+	0.968171i
$431$	−7.95812	−	5.78191i	−0.383329	−	0.278505i	0.379387	−	0.925238i	$-0.376135\pi$
$431$	−7.95812	−	5.78191i	−0.383329	−	0.278505i	−0.762716	+	0.646733i	$0.776135\pi$
$432$		0			0
$433$	−8.69388	−	26.7570i	−0.417801	−	1.28586i	−0.909721	−	0.415220i	$-0.863705\pi$
$433$	−8.69388	−	26.7570i	−0.417801	−	1.28586i	0.491920	−	0.870640i	$-0.336295\pi$
$434$	17.3166	−	23.5358i	0.831223	−	1.12975i
$435$		0			0
$436$	−5.64241	−	4.20388i	−0.270223	−	0.201329i
$437$	−15.0874	+	46.4344i	−0.721730	+	2.22126i
$438$		0			0
$439$	−32.6121			−1.55649			−0.778245	−	0.627960i	$-0.783890\pi$
$439$	−32.6121			−1.55649			−0.778245	+	0.627960i	$0.783890\pi$
$440$	12.3218	+	20.2007i	0.587420	+	0.963030i
$441$		0			0
$442$	11.3830	+	3.77428i	0.541436	+	0.179524i
$443$	5.00926	−	15.4169i	0.237997	−	0.732479i	−0.758713	−	0.651425i	$-0.774171\pi$
$443$	5.00926	−	15.4169i	0.237997	−	0.732479i	0.996710	−	0.0810540i	$-0.0258286\pi$
$444$		0			0
$445$	4.43751	+	6.10771i	0.210358	+	0.289533i
$446$	−0.283468	+	0.385275i	−0.0134226	+	0.0182433i
$447$		0			0
$448$	27.7410	+	0.999692i	1.31064	+	0.0472310i
$449$	22.1505	+	16.0933i	1.04535	+	0.759490i	0.971322	−	0.237766i	$-0.0764152\pi$
$449$	22.1505	+	16.0933i	1.04535	+	0.759490i	0.0740259	+	0.997256i	$0.476415\pi$
$450$		0			0
$451$	−7.94300	−	12.5095i	−0.374021	−	0.589048i
$452$	27.1295	−	19.2174i	1.27607	−	0.903908i
$453$		0			0
$454$	0.0620249	−	10.3313i	0.00291097	−	0.484874i
$455$	−19.4904	+	6.33282i	−0.913725	+	0.296887i
$456$		0			0
$457$	−2.48389	−	3.41878i	−0.116191	−	0.159924i	0.746960	−	0.664869i	$-0.231513\pi$
$457$	−2.48389	−	3.41878i	−0.116191	−	0.159924i	−0.863151	+	0.504945i	$0.831513\pi$
$458$	−7.68156	−	10.7074i	−0.358936	−	0.500322i
$459$		0			0
$460$	−36.1759	−	0.434385i	−1.68671	−	0.0202533i
$461$	−15.4388			−0.719059			−0.359529	−	0.933134i	$-0.617063\pi$
$461$	−15.4388			−0.719059			−0.359529	+	0.933134i	$0.617063\pi$
$462$		0			0
$463$		−	2.29618i		−	0.106712i	−0.998576	−	0.0533562i	$-0.983008\pi$
$463$		−	2.29618i		−	0.106712i	0.998576	−	0.0533562i	$-0.0169919\pi$
$464$	−2.68877	+	1.85653i	−0.124823	+	0.0861872i
$465$		0			0
$466$	0.995785	+	1.38803i	0.0461288	+	0.0642992i
$467$	−29.1415	+	21.1725i	−1.34851	+	0.979748i	−0.349422	+	0.936965i	$0.613622\pi$
$467$	−29.1415	+	21.1725i	−1.34851	+	0.979748i	−0.999084	+	0.0427822i	$0.986378\pi$
$468$		0			0
$469$	10.5498	+	32.4688i	0.487143	+	1.49927i
$470$	23.6785	+	0.142156i	1.09221	+	0.00655716i
$471$		0			0
$472$	18.0662	+	13.6297i	0.831566	+	0.627357i
$473$	12.4828	−	15.0966i	0.573960	−	0.694140i
$474$		0			0
$475$	−5.45207	+	7.50413i	−0.250158	+	0.344313i
$476$	23.9947	−	7.47905i	1.09979	−	0.342802i
$477$		0			0
$478$	−18.6705	−	13.7370i	−0.853971	−	0.628314i
$479$	9.19805	−	6.68277i	0.420270	−	0.305344i	−0.357477	−	0.933922i	$-0.616363\pi$
$479$	9.19805	−	6.68277i	0.420270	−	0.305344i	0.777746	+	0.628578i	$0.216363\pi$
$480$		0			0
$481$	−4.60703	−	1.49692i	−0.210063	−	0.0682535i
$482$	−14.5832	−	4.83535i	−0.664246	−	0.220244i
$483$		0			0
$484$	9.59589	−	19.7969i	0.436177	−	0.899861i
$485$			17.8965i			0.812638i
$486$		0			0
$487$	−6.15510	−	1.99991i	−0.278914	−	0.0906247i	0.166220	−	0.986089i	$-0.446844\pi$
$487$	−6.15510	−	1.99991i	−0.278914	−	0.0906247i	−0.445134	+	0.895464i	$0.646844\pi$
$488$	−8.86757	+	25.7068i	−0.401416	+	1.16369i
$489$		0			0
$490$	−10.6549	+	14.4815i	−0.481338	+	0.654209i
$491$	−15.3305	+	4.98117i	−0.691854	+	0.224797i	−0.633778	−	0.773515i	$-0.718497\pi$
$491$	−15.3305	+	4.98117i	−0.691854	+	0.224797i	−0.0580762	+	0.998312i	$0.518497\pi$
$492$		0			0
$493$	−1.73889	+	2.39337i	−0.0783156	+	0.107792i
$494$	21.4819	−	6.83758i	0.966516	−	0.307637i
$495$		0			0
$496$	−22.4692	−	7.90202i	−1.00889	−	0.354811i
$497$	13.7028	−	18.8603i	0.614655	−	0.846000i
$498$		0			0
$499$	5.50777	+	16.9512i	0.246562	+	0.758839i	0.995376	+	0.0960588i	$0.0306237\pi$
$499$	5.50777	+	16.9512i	0.246562	+	0.758839i	−0.748814	+	0.662780i	$0.769376\pi$
$500$	17.3832	+	5.87981i	0.777399	+	0.262953i
$501$		0			0
$502$	−6.79769	+	4.87673i	−0.303396	+	0.217659i
$503$	9.28405	−	28.5734i	0.413955	−	1.27402i	−0.499227	−	0.866471i	$-0.666382\pi$
$503$	9.28405	−	28.5734i	0.413955	−	1.27402i	0.913182	−	0.407552i	$-0.133618\pi$
$504$		0			0
$505$		−	16.0893i		−	0.715963i
$506$	17.8598	+	28.5042i	0.793965	+	1.26717i
$507$		0			0
$508$	−40.0047	−	0.480360i	−1.77492	−	0.0213125i
$509$	11.9982	+	3.89847i	0.531813	+	0.172797i	0.562600	−	0.826729i	$-0.309801\pi$
$509$	11.9982	+	3.89847i	0.531813	+	0.172797i	−0.0307867	+	0.999526i	$0.509801\pi$
$510$		0			0
$511$	9.07767	+	12.4943i	0.401572	+	0.552717i
$512$	−5.81986	−	21.8662i	−0.257204	−	0.966357i
$513$		0			0
$514$	23.6622	+	0.142058i	1.04369	+	0.00626589i
$515$	−21.7374	−	15.7932i	−0.957866	−	0.695930i
$516$		0			0
$517$	−11.8011	−	18.5856i	−0.519012	−	0.817394i
$518$	−9.67389	+	3.07915i	−0.425046	+	0.135290i
$519$		0			0
$520$	9.57394	+	13.6892i	0.419845	+	0.600313i
$521$	7.21311	+	22.1997i	0.316012	+	0.972585i	0.975336	+	0.220726i	$0.0708426\pi$
$521$	7.21311	+	22.1997i	0.316012	+	0.972585i	−0.659324	+	0.751859i	$0.729157\pi$
$522$		0			0
$523$	0.325225	+	0.447634i	0.0142211	+	0.0195737i	0.816068	−	0.577955i	$-0.196149\pi$
$523$	0.325225	+	0.447634i	0.0142211	+	0.0195737i	−0.801847	+	0.597529i	$0.796149\pi$
$524$	−18.4303	+	24.7370i	−0.805132	+	1.08064i
$525$		0			0
$526$	−7.50063	+	22.6216i	−0.327043	+	0.986347i
$527$	−21.5652			−0.939393
$528$		0			0
$529$	−28.4301			−1.23609
$530$	−15.5962	+	47.0374i	−0.677455	+	2.04317i
$531$		0			0
$532$	28.2277	−	37.8870i	1.22382	−	1.64261i
$533$	−6.14901	−	8.46338i	−0.266343	−	0.366590i
$534$		0			0
$535$	−9.43720	−	29.0447i	−0.408006	−	1.25571i
$536$	22.8047	−	15.9491i	0.985014	−	0.688896i
$537$		0			0
$538$	−2.38055	+	0.757719i	−0.102633	+	0.0326676i
$539$	16.6833	+	1.04557i	0.718600	+	0.0450358i
$540$		0			0
$541$	25.0174	+	18.1762i	1.07558	+	0.781457i	0.976908	−	0.213662i	$-0.0685392\pi$
$541$	25.0174	+	18.1762i	1.07558	+	0.781457i	0.0986763	+	0.995120i	$0.468539\pi$
$542$	5.15225	+	0.0309319i	0.221308	+	0.00132864i
$543$		0			0
$544$	−11.5391	−	16.9283i	−0.494735	−	0.725796i
$545$	−5.21608	−	7.17932i	−0.223433	−	0.307528i
$546$		0			0
$547$	23.4570	+	7.62163i	1.00295	+	0.325878i	0.764043	−	0.645165i	$-0.223212\pi$
$547$	23.4570	+	7.62163i	1.00295	+	0.325878i	0.238905	+	0.971043i	$0.423212\pi$
$548$	−2.67625	−	0.0321353i	−0.114324	−	0.00137275i
$549$		0			0
$550$	1.55355	+	6.19871i	0.0662434	+	0.264314i
$551$			5.56125i			0.236917i
$552$		0			0
$553$	14.2003	−	43.7041i	0.603860	−	1.85849i
$554$	21.0685	−	15.1147i	0.895113	−	0.642163i
$555$		0			0
$556$	7.55636	+	2.55592i	0.320461	+	0.108395i
$557$	10.6572	+	32.7996i	0.451562	+	1.38976i	0.875125	+	0.483898i	$0.160779\pi$
$557$	10.6572	+	32.7996i	0.451562	+	1.38976i	−0.423563	+	0.905867i	$0.639221\pi$
$558$		0			0
$559$	8.12871	−	11.1882i	0.343808	−	0.473211i
$560$	33.0267	+	11.6149i	1.39563	+	0.490820i
$561$		0			0
$562$	19.0104	−	6.05093i	0.801907	−	0.255243i
$563$	−1.49049	+	2.05149i	−0.0628168	+	0.0864600i	−0.839270	−	0.543716i	$-0.817017\pi$
$563$	−1.49049	+	2.05149i	−0.0628168	+	0.0864600i	0.776453	+	0.630175i	$0.217017\pi$
$564$		0			0
$565$	39.8779	−	12.9571i	1.67767	−	0.545110i
$566$	24.0052	−	32.6265i	1.00901	−	1.37140i
$567$		0			0
$568$	−17.9642	−	6.19677i	−0.753761	−	0.260011i
$569$	15.2106	+	4.94221i	0.637660	+	0.207188i	0.609965	−	0.792428i	$-0.291183\pi$
$569$	15.2106	+	4.94221i	0.637660	+	0.207188i	0.0276946	+	0.999616i	$0.491183\pi$
$570$		0			0
$571$			8.45680i			0.353906i	0.984219	+	0.176953i	$0.0566241\pi$
$571$			8.45680i			0.353906i	−0.984219	+	0.176953i	$0.943376\pi$
$572$	5.88704	−	14.3726i	0.246149	−	0.600949i
$573$		0			0
$574$	−20.8103	−	6.90007i	−0.868604	−	0.288003i
$575$	−9.29252	−	3.01932i	−0.387525	−	0.125914i
$576$		0			0
$577$	−38.8626	+	28.2353i	−1.61787	+	1.17545i	−0.800625	+	0.599166i	$0.795499\pi$
$577$	−38.8626	+	28.2353i	−1.61787	+	1.17545i	−0.817247	+	0.576287i	$0.804501\pi$
$578$	4.42406	+	3.25502i	0.184017	+	0.135391i
$579$		0			0
$580$	−3.93420	+	1.22627i	−0.163359	+	0.0509183i
$581$	8.15369	−	11.2226i	0.338272	−	0.465591i
$582$		0			0
$583$	44.6243	−	11.4691i	1.84815	−	0.475001i
$584$	7.58176	−	10.0497i	0.313735	−	0.415859i
$585$		0			0
$586$	24.1839	+	0.145190i	0.999028	+	0.00599774i
$587$	9.41855	+	28.9873i	0.388745	+	1.19644i	0.933727	+	0.357987i	$0.116537\pi$
$587$	9.41855	+	28.9873i	0.388745	+	1.19644i	−0.544981	+	0.838448i	$0.683463\pi$
$588$		0			0
$589$	−32.7967	+	23.8282i	−1.35136	+	0.981824i
$590$	16.6376	+	23.1912i	0.684960	+	0.954768i
$591$		0			0
$592$	4.70197	+	6.80977i	0.193250	+	0.279880i
$593$		−	8.98372i		−	0.368917i	−0.982840	−	0.184459i	$-0.940947\pi$
$593$		−	8.98372i		−	0.368917i	0.982840	−	0.184459i	$-0.0590532\pi$
$594$		0			0
$595$	31.6979			1.29949
$596$	−9.34587	−	0.112221i	−0.382822	−	0.00459676i
$597$		0			0
$598$	13.8427	+	19.2953i	0.566068	+	0.789045i
$599$	21.8522	+	30.0770i	0.892857	+	1.22891i	0.972691	+	0.232104i	$0.0745608\pi$
$599$	21.8522	+	30.0770i	0.892857	+	1.22891i	−0.0798345	+	0.996808i	$0.525439\pi$
$600$		0			0
$601$	11.6000	−	3.76907i	0.473175	−	0.153744i	−0.0627156	−	0.998031i	$-0.519976\pi$
$601$	11.6000	−	3.76907i	0.473175	−	0.153744i	0.535890	+	0.844288i	$0.319976\pi$
$602$	0.173999	−	28.9825i	0.00709165	−	1.18124i
$603$		0			0
$604$	1.16351	−	0.824181i	0.0473427	−	0.0335355i
$605$	18.9838	−	20.2354i	0.771803	−	0.822684i
$606$		0			0
$607$	−1.25260	−	0.910065i	−0.0508414	−	0.0369384i	0.562074	−	0.827087i	$-0.310003\pi$
$607$	−1.25260	−	0.910065i	−0.0508414	−	0.0369384i	−0.612916	+	0.790148i	$0.710003\pi$
$608$	−36.2537	−	12.9949i	−1.47028	−	0.527012i
$609$		0			0
$610$	−20.3249	+	27.6245i	−0.822929	+	1.11848i
$611$	−9.13573	−	12.5742i	−0.369592	−	0.508700i
$612$		0			0
$613$	−7.12202	+	21.9193i	−0.287656	+	0.885314i	0.697934	+	0.716162i	$0.254103\pi$
$613$	−7.12202	+	21.9193i	−0.287656	+	0.885314i	−0.985590	+	0.169152i	$0.945897\pi$
$614$	−27.4465	−	9.10045i	−1.10765	−	0.367264i
$615$		0			0
$616$	−7.53350	−	31.6666i	−0.303533	−	1.27588i
$617$	42.0365			1.69233			0.846163	−	0.532925i	$-0.178907\pi$
$617$	42.0365			1.69233			0.846163	+	0.532925i	$0.178907\pi$
$618$		0			0
$619$	−9.13452	+	28.1132i	−0.367147	+	1.12996i	0.581478	+	0.813562i	$0.302475\pi$
$619$	−9.13452	+	28.1132i	−0.367147	+	1.12996i	−0.948625	+	0.316401i	$0.897525\pi$
$620$	−24.0886	−	17.9472i	−0.967420	−	0.720776i
$621$		0			0
$622$	15.0512	−	20.4568i	0.603497	−	0.820242i
$623$	−3.20927	−	9.87710i	−0.128577	−	0.395718i
$624$		0			0
$625$	24.2349	+	17.6077i	0.969395	+	0.704307i
$626$	−10.0822	−	31.6757i	−0.402966	−	1.26601i
$627$		0			0
$628$	−13.3373	−	18.8285i	−0.532215	−	0.751339i
$629$	6.06162	+	4.40402i	0.241693	+	0.175600i
$630$		0			0
$631$	4.94570	−	1.60696i	0.196885	−	0.0639719i	−0.208915	−	0.977934i	$-0.566993\pi$
$631$	4.94570	−	1.60696i	0.196885	−	0.0639719i	0.405800	+	0.913962i	$0.366993\pi$
$632$	−37.4521	−	0.674604i	−1.48977	−	0.0268343i
$633$		0			0
$634$	26.6764	+	37.1843i	1.05945	+	1.47678i
$635$	−47.9878	−	15.5922i	−1.90434	−	0.618757i
$636$		0			0
$637$	11.8012			0.467579
$638$	2.93804	+	2.45921i	0.116318	+	0.0973609i
$639$		0			0
$640$	1.19892	−	28.5124i	0.0473916	−	1.12705i
$641$	−11.3041	+	34.7903i	−0.446484	+	1.37414i	0.434365	+	0.900737i	$0.356973\pi$
$641$	−11.3041	+	34.7903i	−0.446484	+	1.37414i	−0.880848	+	0.473398i	$0.843027\pi$
$642$		0			0
$643$	−3.35634	+	2.43852i	−0.132361	+	0.0961660i	−0.651996	−	0.758223i	$-0.726068\pi$
$643$	−3.35634	+	2.43852i	−0.132361	+	0.0961660i	0.519635	+	0.854389i	$0.326068\pi$
$644$	47.1445	+	15.9465i	1.85775	+	0.628379i
$645$		0			0
$646$	−34.8687	−	0.209337i	−1.37189	−	0.00823624i
$647$	9.87192	−	13.5875i	0.388105	−	0.534181i	−0.569604	−	0.821919i	$-0.692903\pi$
$647$	9.87192	−	13.5875i	0.388105	−	0.534181i	0.957709	+	0.287738i	$0.0929033\pi$
$648$		0			0
$649$	9.76298	−	24.6759i	0.383230	−	0.968615i
$650$	1.36835	+	4.29899i	0.0536710	+	0.168620i
$651$		0			0
$652$	8.12384	+	26.0633i	0.318154	+	1.02072i
$653$	14.1761	−	4.60608i	0.554752	−	0.180250i	−0.0182065	−	0.999834i	$-0.505796\pi$
$653$	14.1761	−	4.60608i	0.554752	−	0.180250i	0.572958	+	0.819584i	$0.305796\pi$
$654$		0			0
$655$	−31.4750	+	22.8679i	−1.22983	+	0.893524i
$656$	−0.429122	+	17.8662i	−0.0167544	+	0.697559i
$657$		0			0
$658$	−30.9183	−	10.2516i	−1.20532	−	0.399649i
$659$		−	6.39469i		−	0.249102i	−0.992213	−	0.124551i	$-0.960251\pi$
$659$		−	6.39469i		−	0.249102i	0.992213	−	0.124551i	$-0.0397490\pi$
$660$		0			0
$661$		−	4.15586i		−	0.161644i	−0.996729	−	0.0808221i	$-0.974245\pi$
$661$		−	4.15586i		−	0.161644i	0.996729	−	0.0808221i	$-0.0257546\pi$
$662$	−2.16612	+	6.53291i	−0.0841885	+	0.253909i
$663$		0			0
$664$	−10.6894	−	3.68731i	−0.414828	−	0.143095i
$665$	48.2068	−	35.0243i	1.86938	−	1.35818i
$666$		0			0
$667$	−5.57139	+	1.81025i	−0.215725	+	0.0700933i
$668$	−7.01978	−	22.5212i	−0.271603	−	0.871372i
$669$		0			0
$670$	33.4440	−	10.6451i	1.29205	−	0.411254i
$671$	31.8244	+	1.99449i	1.22857	+	0.0769964i
$672$		0			0
$673$	26.3682	−	36.2928i	1.01642	−	1.39898i	0.101739	−	0.994811i	$-0.467559\pi$
$673$	26.3682	−	36.2928i	1.01642	−	1.39898i	0.914683	−	0.404173i	$-0.132441\pi$
$674$	0.205005	−	34.1472i	0.00789650	−	1.31530i
$675$		0			0
$676$	−4.81744	+	14.2424i	−0.185286	+	0.547783i
$677$	21.4231	−	15.5648i	0.823357	−	0.598204i	−0.0943152	−	0.995542i	$-0.530066\pi$
$677$	21.4231	−	15.5648i	0.823357	−	0.598204i	0.917672	+	0.397339i	$0.130066\pi$
$678$		0			0
$679$	7.60769	−	23.4141i	0.291957	−	0.898550i
$680$	−7.54057	−	24.7133i	−0.289168	−	0.947714i
$681$		0			0
$682$	−1.91426	+	27.8636i	−0.0733007	+	1.06695i
$683$	21.1898			0.810805			0.405402	−	0.914138i	$-0.367131\pi$
$683$	21.1898			0.810805			0.405402	+	0.914138i	$0.367131\pi$
$684$		0			0
$685$	−3.21030	−	1.04309i	−0.122659	−	0.0398544i
$686$	−7.81466	+	5.60631i	−0.298365	+	0.214050i
$687$		0			0
$688$	−22.6377	+	6.75895i	−0.863053	+	0.257683i
$689$	30.9357	−	10.0516i	1.17856	−	0.382936i
$690$		0			0
$691$	14.6736	+	10.6610i	0.558210	+	0.405564i	0.830804	−	0.556566i	$-0.187881\pi$
$691$	14.6736	+	10.6610i	0.558210	+	0.405564i	−0.272593	+	0.962129i	$0.587881\pi$
$692$	−7.96302	+	5.64065i	−0.302709	+	0.214425i
$693$		0			0
$694$	−1.02577	+	0.326497i	−0.0389376	+	0.0123936i
$695$	8.13908	+	5.91338i	0.308733	+	0.224307i
$696$		0			0
$697$	5.00017	+	15.3889i	0.189395	+	0.582898i
$698$	23.2391	+	17.0983i	0.879613	+	0.647180i
$699$		0			0
$700$	7.58200	+	5.64897i	0.286573	+	0.213511i
$701$	12.5199	−	38.5324i	0.472871	−	1.45535i	−0.375937	−	0.926645i	$-0.622679\pi$
$701$	12.5199	−	38.5324i	0.472871	−	1.45535i	0.848808	−	0.528702i	$-0.177321\pi$
$702$		0			0
$703$	14.0848			0.531219
$704$	−22.8968	+	13.4066i	−0.862955	+	0.505281i
$705$		0			0
$706$	3.77281	−	11.3786i	0.141992	−	0.428241i
$707$	−6.83945	+	21.0497i	−0.257224	+	0.791654i
$708$		0			0
$709$	−21.0524	−	28.9761i	−0.790638	−	1.08822i	−0.994028	−	0.109122i	$-0.965196\pi$
$709$	−21.0524	−	28.9761i	−0.790638	−	1.08822i	0.203390	−	0.979098i	$-0.434804\pi$
$710$	−19.3043	−	14.2033i	−0.724479	−	0.533039i
$711$		0			0
$712$	−6.93726	+	4.85176i	−0.259985	+	0.181827i
$713$	−34.5473	−	25.1001i	−1.29381	−	0.940007i
$714$		0			0
$715$	12.4824	−	15.0961i	0.466815	−	0.564561i
$716$	−23.8086	+	16.8649i	−0.889769	+	0.630272i
$717$		0			0
$718$	−1.13955	−	0.00684137i	−0.0425276	−	0.000255318i
$719$	−1.96438	+	0.638267i	−0.0732592	+	0.0238034i	−0.345417	−	0.938449i	$-0.612263\pi$
$719$	−1.96438	+	0.638267i	−0.0732592	+	0.0238034i	0.272158	+	0.962253i	$0.412263\pi$
$720$		0			0
$721$	21.7256	+	29.9027i	0.809104	+	1.11364i
$722$	−31.4275	+	22.5464i	−1.16961	+	0.839091i
$723$		0			0
$724$	−0.163979	+	13.6563i	−0.00609422	+	0.507531i
$725$	−1.11293			−0.0413331
$726$		0			0
$727$			48.1161i			1.78453i	0.451514	+	0.892264i	$0.350884\pi$
$727$			48.1161i			1.78453i	−0.451514	+	0.892264i	$0.649116\pi$
$728$	−6.70642	−	21.9795i	−0.248557	−	0.814615i
$729$		0			0
$730$	12.9005	−	9.25498i	0.477471	−	0.342542i
$731$	−17.3052	+	12.5730i	−0.640056	+	0.465028i
$732$		0			0
$733$	−5.26347	−	16.1993i	−0.194411	−	0.598335i	−0.999983	−	0.00583726i	$-0.998142\pi$
$733$	−5.26347	−	16.1993i	−0.194411	−	0.598335i	0.805572	−	0.592498i	$-0.201858\pi$
$734$	−0.162480	+	27.0639i	−0.00599724	+	0.998946i
$735$		0			0
$736$	1.21757	−	40.5497i	0.0448801	−	1.49468i
$737$	−25.1483	−	20.7943i	−0.926351	−	0.765966i
$738$		0			0
$739$	−21.1621	+	29.1272i	−0.778462	+	1.07146i	0.216988	+	0.976174i	$0.430377\pi$
$739$	−21.1621	+	29.1272i	−0.778462	+	1.07146i	−0.995450	+	0.0952870i	$0.969623\pi$
$740$	3.10575	+	9.96402i	0.114170	+	0.366285i
$741$		0			0
$742$	40.3998	−	54.9093i	1.48312	−	2.01579i
$743$	22.7550	−	16.5325i	0.834801	−	0.606519i	−0.0861124	−	0.996285i	$-0.527444\pi$
$743$	22.7550	−	16.5325i	0.834801	−	0.606519i	0.920914	+	0.389767i	$0.127444\pi$
$744$		0			0
$745$	−11.2109	−	3.64263i	−0.410735	−	0.133456i
$746$	2.91831	−	8.80150i	0.106847	−	0.322246i
$747$		0			0
$748$	−15.5297	+	18.3288i	−0.567821	+	0.670166i
$749$			42.0110i			1.53505i
$750$		0			0
$751$	−11.6316	−	3.77933i	−0.424443	−	0.137910i	0.0890039	−	0.996031i	$-0.471632\pi$
$751$	−11.6316	−	3.77933i	−0.424443	−	0.137910i	−0.513447	+	0.858121i	$0.671632\pi$
$752$	−0.637556	+	26.5443i	−0.0232493	+	0.967970i
$753$		0			0
$754$	2.17873	+	1.60301i	0.0793446	+	0.0583782i
$755$	1.71026	−	0.555696i	0.0622426	−	0.0202238i
$756$		0			0
$757$	16.0896	−	22.1455i	0.584788	−	0.804891i	−0.409423	−	0.912345i	$-0.634270\pi$
$757$	16.0896	−	22.1455i	0.584788	−	0.804891i	0.994210	+	0.107454i	$0.0342698\pi$
$758$	7.38265	+	23.1943i	0.268150	+	0.842456i
$759$		0			0
$760$	−38.7746	−	29.2527i	−1.40650	−	1.06111i
$761$	19.5189	−	26.8654i	0.707559	−	0.973871i	−0.292287	−	0.956331i	$-0.594416\pi$
$761$	19.5189	−	26.8654i	0.707559	−	0.973871i	0.999846	−	0.0175405i	$-0.00558359\pi$
$762$		0			0
$763$	3.77234	+	11.6101i	0.136568	+	0.420313i
$764$	−22.5557	−	7.62939i	−0.816036	−	0.276022i
$765$		0			0
$766$	−1.66100	−	2.31527i	−0.0600143	−	0.0836541i
$767$	5.78932	−	17.8177i	0.209040	−	0.643360i
$768$		0			0
$769$			0.555847i			0.0200443i	0.999950	+	0.0100222i	$0.00319021\pi$
$769$			0.555847i			0.0200443i	−0.999950	+	0.0100222i	$0.996810\pi$
$770$	2.81370	−	40.9558i	0.101399	−	1.47594i
$771$		0			0
$772$	0.283797	−	23.6348i	0.0102141	−	0.850636i
$773$	−45.7223	−	14.8561i	−1.64452	−	0.534336i	−0.666976	−	0.745079i	$-0.732412\pi$
$773$	−45.7223	−	14.8561i	−1.64452	−	0.534336i	−0.977541	+	0.210743i	$0.932412\pi$
$774$		0			0
$775$	−4.76854	−	6.56333i	−0.171291	−	0.235762i
$776$	−20.0646	−	0.361413i	−0.720278	−	0.0129740i
$777$		0			0
$778$	0.173121	−	28.8363i	0.00620668	−	1.03383i
$779$	24.6082	+	17.8789i	0.881681	+	0.640578i
$780$		0			0
$781$	−1.39377	+	22.2393i	−0.0498731	+	0.795786i
$782$	−11.1405	−	35.0004i	−0.398382	−	1.25161i
$783$		0			0
$784$	−16.0208	−	12.2381i	−0.572170	−	0.437076i
$785$	−8.99252	−	27.6761i	−0.320957	−	0.987803i
$786$		0			0
$787$	−16.6523	−	22.9199i	−0.593589	−	0.817005i	0.401513	−	0.915853i	$-0.368484\pi$
$787$	−16.6523	−	22.9199i	−0.593589	−	0.817005i	−0.995103	+	0.0988478i	$0.968484\pi$
$788$	11.4017	+	8.49481i	0.406167	+	0.302615i
$789$		0			0
$790$	−44.8414	−	14.8681i	−1.59539	−	0.528982i
$791$	−57.6804			−2.05088
$792$		0			0
$793$	22.5115			0.799406
$794$	21.5364	+	7.14083i	0.764299	+	0.253419i
$795$		0			0
$796$	28.9713	−	38.8851i	1.02686	−	1.37824i
$797$	8.84278	+	12.1710i	0.313227	+	0.431121i	0.936384	−	0.350976i	$-0.114150\pi$
$797$	8.84278	+	12.1710i	0.313227	+	0.431121i	−0.623157	+	0.782097i	$0.714150\pi$
$798$		0			0
$799$	7.42887	+	22.8637i	0.262815	+	0.808860i
$800$	2.60056	−	7.25514i	0.0919436	−	0.256508i
$801$		0			0
$802$	−5.45663	−	17.1433i	−0.192680	−	0.605351i
$803$	−13.7264	−	5.43083i	−0.484395	−	0.191650i
$804$		0			0
$805$	50.7800	+	36.8938i	1.78976	+	1.30034i
$806$	−0.118373	+	19.7171i	−0.00416952	+	0.694506i
$807$		0			0
$808$	18.0384	+	0.324916i	0.634590	+	0.0114305i
$809$	9.96096	+	13.7101i	0.350209	+	0.482021i	0.947388	−	0.320087i	$-0.103712\pi$
$809$	9.96096	+	13.7101i	0.350209	+	0.482021i	−0.597179	+	0.802108i	$0.703712\pi$
$810$		0			0
$811$	33.3596	+	10.8392i	1.17141	+	0.380616i	0.829171	−	0.558996i	$-0.188813\pi$
$811$	33.3596	+	10.8392i	1.17141	+	0.380616i	0.342244	+	0.939611i	$0.388813\pi$
$812$	5.66841	+	0.0680639i	0.198922	+	0.00238857i
$813$		0			0
$814$	6.22835	−	7.44108i	0.218304	−	0.260810i
$815$			34.4307i			1.20606i
$816$		0			0
$817$	−12.4257	+	38.2424i	−0.434720	+	1.33793i
$818$	26.2743	+	36.6238i	0.918658	+	1.28052i
$819$		0			0
$820$	−7.22189	+	21.3510i	−0.252199	+	0.745608i
$821$	−11.1149	−	34.2081i	−0.387913	−	1.19387i	−0.934345	−	0.356369i	$-0.884015\pi$
$821$	−11.1149	−	34.2081i	−0.387913	−	1.19387i	0.546433	−	0.837503i	$-0.315985\pi$
$822$		0			0
$823$	−0.919281	+	1.26528i	−0.0320441	+	0.0441050i	−0.824738	−	0.565514i	$-0.808678\pi$
$823$	−0.919281	+	1.26528i	−0.0320441	+	0.0441050i	0.792694	+	0.609619i	$0.208678\pi$
$824$	18.1454	−	24.0519i	0.632127	−	0.837888i
$825$		0			0
$826$	−11.9086	−	37.4137i	−0.414354	−	1.30179i
$827$	−9.04149	+	12.4445i	−0.314403	+	0.432739i	−0.936748	−	0.350004i	$-0.886180\pi$
$827$	−9.04149	+	12.4445i	−0.314403	+	0.432739i	0.622345	+	0.782743i	$0.286180\pi$
$828$		0			0
$829$	−13.5176	+	4.39213i	−0.469485	+	0.152545i	−0.534199	−	0.845359i	$-0.679387\pi$
$829$	−13.5176	+	4.39213i	−0.469485	+	0.152545i	0.0647137	+	0.997904i	$0.479387\pi$
$830$	−11.4868	−	8.45148i	−0.398713	−	0.293355i
$831$		0			0
$832$	−15.5410	+	10.4573i	−0.538787	+	0.362543i
$833$	−17.3599	−	5.64057i	−0.601485	−	0.195434i
$834$		0			0
$835$		−	29.7514i		−	1.02959i
$836$	−3.36564	+	45.0341i	−0.116403	+	1.55754i
$837$		0			0
$838$	−6.36237	+	19.1886i	−0.219784	+	0.662859i
$839$	6.85229	+	2.22644i	0.236567	+	0.0768653i	0.424901	−	0.905240i	$-0.360309\pi$
$839$	6.85229	+	2.22644i	0.236567	+	0.0768653i	−0.188334	+	0.982105i	$0.560309\pi$
$840$		0			0
$841$	22.9217	−	16.6536i	0.790402	−	0.574261i
$842$	−6.20235	+	8.42990i	−0.213747	+	0.290514i
$843$		0			0
$844$	48.9018	−	15.2425i	1.68327	−	0.524668i
$845$	−11.1457	+	15.3407i	−0.383422	+	0.527735i
$846$		0			0
$847$	−33.4386	+	18.4041i	−1.14896	+	0.632372i
$848$	−52.4208	−	18.4355i	−1.80014	−	0.633078i
$849$		0			0
$850$	0.0418928	−	6.97798i	0.00143691	−	0.239343i
$851$	4.58477	+	14.1105i	0.157164	+	0.483701i
$852$		0			0
$853$	−8.69578	+	6.31785i	−0.297738	+	0.216319i	−0.726617	−	0.687043i	$-0.758909\pi$
$853$	−8.69578	+	6.31785i	−0.297738	+	0.216319i	0.428879	+	0.903362i	$0.358909\pi$
$854$	38.3341	−	27.5013i	1.31177	−	0.941074i
$855$		0			0
$856$	32.7540	−	9.99395i	1.11951	−	0.341586i
$857$		−	27.6087i		−	0.943094i	−0.881841	−	0.471547i	$-0.843696\pi$
$857$		−	27.6087i		−	0.943094i	0.881841	−	0.471547i	$-0.156304\pi$
$858$		0			0
$859$	−19.0214			−0.649002			−0.324501	−	0.945885i	$-0.605196\pi$
$859$	−19.0214			−0.649002			−0.324501	+	0.945885i	$0.605196\pi$
$860$	−29.7937	−	0.357751i	−1.01596	−	0.0121992i
$861$		0			0
$862$	11.3034	−	8.10914i	0.384994	−	0.276198i
$863$	22.7170	+	31.2673i	0.773297	+	1.06435i	0.995990	+	0.0894633i	$0.0285152\pi$
$863$	22.7170	+	31.2673i	0.773297	+	1.06435i	−0.222693	+	0.974889i	$0.571485\pi$
$864$		0			0
$865$	−11.7049	+	3.80315i	−0.397978	+	0.129311i
$866$	39.7868	+	0.238863i	1.35201	+	0.00811688i
$867$		0			0
$868$	23.8859	+	33.7203i	0.810742	+	1.14454i
$869$	10.9337	+	42.5410i	0.370899	+	1.44311i
$870$		0			0
$871$	−18.6377	−	13.5411i	−0.631514	−	0.458822i
$872$	8.15442	−	5.70301i	0.276143	−	0.193128i
$873$		0			0
$874$	−55.6160	−	40.9197i	−1.88124	−	1.38413i
$875$	−18.7135	−	25.7569i	−0.632632	−	0.870743i
$876$		0			0
$877$	−10.2280	+	31.4786i	−0.345376	+	1.06296i	0.616007	+	0.787741i	$0.288749\pi$
$877$	−10.2280	+	31.4786i	−0.345376	+	1.06296i	−0.961382	+	0.275216i	$0.911251\pi$
$878$	14.5151	−	43.7768i	0.489860	−	1.47740i
$879$		0			0
$880$	−32.6006	+	7.54920i	−1.09897	+	0.254484i
$881$	28.7554			0.968795			0.484397	−	0.874848i	$-0.339039\pi$
$881$	28.7554			0.968795			0.484397	+	0.874848i	$0.339039\pi$
$882$		0			0
$883$	6.72055	−	20.6837i	0.226164	−	0.696063i	−0.772007	−	0.635614i	$-0.780747\pi$
$883$	6.72055	−	20.6837i	0.226164	−	0.696063i	0.998171	−	0.0604484i	$-0.0192531\pi$
$884$	−10.1328	+	13.6001i	−0.340803	+	0.457423i
$885$		0			0
$886$	18.4653	+	13.5860i	0.620355	+	0.456430i
$887$	−11.9681	−	36.8340i	−0.401849	−	1.23677i	−0.923497	−	0.383605i	$-0.874683\pi$
$887$	−11.9681	−	36.8340i	−0.401849	−	1.23677i	0.521648	−	0.853161i	$-0.325317\pi$
$888$		0			0
$889$	56.1545	+	40.7986i	1.88336	+	1.36834i
$890$	−10.1737	+	3.23825i	−0.341025	+	0.108546i
$891$		0			0
$892$	−0.391006	−	0.551992i	−0.0130919	−	0.0184821i
$893$	36.5610	+	26.5631i	1.22347	+	0.888901i
$894$		0			0
$895$	−34.9964	+	11.3710i	−1.16980	+	0.380091i
$896$	−13.6890	+	36.7932i	−0.457317	+	1.22917i
$897$		0			0
$898$	−31.4617	+	22.5709i	−1.04989	+	0.753201i
$899$	−4.62597	−	1.50307i	−0.154285	−	0.0501302i
$900$		0			0
$901$	−50.3118			−1.67613
$902$	20.3274	−	5.09453i	0.676827	−	0.169629i
$903$		0			0
$904$	13.7215	+	44.9706i	0.456371	+	1.49570i
$905$	−5.32265	+	16.3814i	−0.176931	+	0.544537i
$906$		0			0
$907$	6.08306	−	4.41960i	0.201985	−	0.146751i	−0.482195	−	0.876064i	$-0.660160\pi$
$907$	6.08306	−	4.41960i	0.201985	−	0.146751i	0.684180	+	0.729313i	$0.260160\pi$
$908$	13.8407	+	4.68156i	0.459319	+	0.155363i
$909$		0			0
$910$	0.173993	−	28.9816i	0.00576781	−	0.960730i
$911$	23.6851	−	32.5998i	0.784723	−	1.08008i	−0.210022	−	0.977697i	$-0.567354\pi$
$911$	23.6851	−	32.5998i	0.784723	−	1.08008i	0.994745	−	0.102382i	$-0.0326463\pi$
$912$		0			0
$913$	−0.829348	+	13.2332i	−0.0274474	+	0.437956i
$914$	5.69473	−	1.81261i	0.188365	−	0.0599557i
$915$		0			0
$916$	17.7919	−	5.54568i	0.587862	−	0.183234i
$917$	50.8999	−	16.5384i	1.68086	−	0.546146i
$918$		0			0
$919$	33.3429	−	24.2250i	1.09988	−	0.799109i	0.118839	−	0.992913i	$-0.462083\pi$
$919$	33.3429	−	24.2250i	1.09988	−	0.799109i	0.981040	+	0.193804i	$0.0620826\pi$
$920$	16.6844	−	48.3674i	0.550067	−	1.59462i
$921$		0			0
$922$	6.87156	−	20.7243i	0.226303	−	0.682519i
$923$			15.7313i			0.517802i
$924$		0			0
$925$			2.81867i			0.0926774i
$926$	3.08227	+	1.02199i	0.101290	+	0.0335846i
$927$		0			0
$928$	−1.29538	−	4.43558i	−0.0425231	−	0.145605i
$929$	−19.2013	+	13.9506i	−0.629975	+	0.457704i	−0.856392	−	0.516327i	$-0.827299\pi$
$929$	−19.2013	+	13.9506i	−0.629975	+	0.457704i	0.226417	+	0.974031i	$0.427299\pi$
$930$		0			0
$931$	−32.6338	+	10.6034i	−1.06953	+	0.347511i
$932$	−2.30642	+	0.718904i	−0.0755495	+	0.0235485i
$933$		0			0
$934$	−15.4505	−	48.5416i	−0.505557	−	1.58833i
$935$	−25.5774	+	16.2406i	−0.836472	+	0.531125i
$936$		0			0
$937$	29.5054	−	40.6107i	0.963900	−	1.32669i	0.0188316	−	0.999823i	$-0.494005\pi$
$937$	29.5054	−	40.6107i	0.963900	−	1.32669i	0.945069	−	0.326872i	$-0.105995\pi$
$938$	−48.2800	−	0.289853i	−1.57640	−	0.00946402i
$939$		0			0
$940$	−10.7297	+	31.7216i	−0.349965	+	1.03464i
$941$	−20.7682	+	15.0890i	−0.677024	+	0.491886i	−0.872369	−	0.488848i	$-0.837417\pi$
$941$	−20.7682	+	15.0890i	−0.677024	+	0.491886i	0.195345	+	0.980735i	$0.437417\pi$
$942$		0			0
$943$	−9.90123	+	30.4729i	−0.322428	+	0.992333i
$944$	−26.3368	+	18.1849i	−0.857189	+	0.591867i
$945$		0			0
$946$	14.7090	+	23.4755i	0.478230	+	0.763254i
$947$	35.3065			1.14731			0.573653	−	0.819098i	$-0.305526\pi$
$947$	35.3065			1.14731			0.573653	+	0.819098i	$0.305526\pi$
$948$		0			0
$949$	−9.91142	−	3.22041i	−0.321738	−	0.104539i
$950$	−7.64654	−	10.6585i	−0.248086	−	0.345809i
$951$		0			0
$952$	−0.640127	+	35.5380i	−0.0207466	+	1.15179i
$953$	−8.87462	+	2.88354i	−0.287477	+	0.0934070i	−0.449206	−	0.893428i	$-0.648293\pi$
$953$	−8.87462	+	2.88354i	−0.287477	+	0.0934070i	0.161729	+	0.986835i	$0.448293\pi$
$954$		0			0
$955$	−24.2951	−	17.6514i	−0.786170	−	0.571186i
$956$	26.7497	−	18.9483i	0.865148	−	0.612832i
$957$		0			0
$958$	4.87672	+	15.3214i	0.157560	+	0.495011i
$959$	3.75664	+	2.72936i	0.121308	+	0.0881357i
$960$		0			0
$961$	−1.37715	−	4.23842i	−0.0444241	−	0.136723i
$962$	4.05989	−	5.51800i	0.130896	−	0.177907i
$963$		0			0
$964$	12.9815	−	17.4236i	0.418105	−	0.561177i
$965$	9.21187	−	28.3512i	0.296541	−	0.912658i
$966$		0			0
$967$	27.3926			0.880886			0.440443	−	0.897781i	$-0.354821\pi$
$967$	27.3926			0.880886			0.440443	+	0.897781i	$0.354821\pi$
$968$	22.3034	+	21.6923i	0.716860	+	0.697217i
$969$		0			0
$970$	−24.0234	−	7.96542i	−0.771343	−	0.255754i
$971$	3.77734	−	11.6255i	0.121221	−	0.373079i	−0.871973	−	0.489554i	$-0.837160\pi$
$971$	3.77734	−	11.6255i	0.121221	−	0.373079i	0.993194	+	0.116475i	$0.0371595\pi$
$972$		0			0
$973$	−8.13465	−	11.1964i	−0.260785	−	0.358939i
$974$	5.42411	−	7.37217i	0.173800	−	0.236219i
$975$		0			0
$976$	−30.5606	−	23.3450i	−0.978222	−	0.747256i
$977$	−2.22237	−	1.61464i	−0.0710998	−	0.0516570i	0.551668	−	0.834064i	$-0.313992\pi$
$977$	−2.22237	−	1.61464i	−0.0710998	−	0.0516570i	−0.622767	+	0.782407i	$0.713992\pi$
$978$		0			0
$979$	7.65019	+	6.32567i	0.244501	+	0.202169i
$980$	−14.6970	−	20.7480i	−0.469478	−	0.662772i
$981$		0			0
$982$	0.136857	−	22.7959i	0.00436727	−	0.727445i
$983$	−38.0558	+	12.3651i	−1.21379	+	0.394385i	−0.844817	−	0.535055i	$-0.820291\pi$
$983$	−38.0558	+	12.3651i	−1.21379	+	0.394385i	−0.368974	+	0.929440i	$0.620291\pi$
$984$		0			0
$985$	10.5402	+	14.5073i	0.335838	+	0.462241i
$986$	−2.43879	−	3.39944i	−0.0776670	−	0.108260i
$987$		0			0
$988$	−0.382795	+	31.8795i	−0.0121783	+	1.01422i
$989$	−42.3568			−1.34687
$990$		0			0
$991$		−	47.0492i		−	1.49457i	−0.664505	−	0.747284i	$-0.731357\pi$
$991$		−	47.0492i		−	1.49457i	0.664505	−	0.747284i	$-0.268643\pi$
$992$	20.6079	−	26.6444i	0.654301	−	0.845960i
$993$		0			0
$994$	19.2182	+	26.7883i	0.609565	+	0.849675i
$995$	49.4768	−	35.9470i	1.56852	−	1.13960i
$996$		0			0
$997$	−16.7250	−	51.4741i	−0.529685	−	1.63020i	−0.754862	−	0.655884i	$-0.772296\pi$
$997$	−16.7250	−	51.4741i	−0.529685	−	1.63020i	0.225177	−	0.974318i	$-0.427704\pi$
$998$	−25.2058	−	0.151325i	−0.797876	−	0.00479011i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.bp.d.667.5		48
3.2	odd	2		264.2.z.b.139.8	yes	48
8.3	odd	2	inner	792.2.bp.d.667.3		48
11.8	odd	10	inner	792.2.bp.d.19.3		48
12.11	even	2		1056.2.bp.a.271.10		48
24.5	odd	2		1056.2.bp.a.271.3		48
24.11	even	2		264.2.z.b.139.10	yes	48
33.8	even	10		264.2.z.b.19.10	yes	48
88.19	even	10	inner	792.2.bp.d.19.5		48
132.107	odd	10		1056.2.bp.a.943.3		48
264.107	odd	10		264.2.z.b.19.8	✓	48
264.173	even	10		1056.2.bp.a.943.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.z.b.19.8	✓	48	264.107	odd	10
264.2.z.b.19.10	yes	48	33.8	even	10
264.2.z.b.139.8	yes	48	3.2	odd	2
264.2.z.b.139.10	yes	48	24.11	even	2
792.2.bp.d.19.3		48	11.8	odd	10	inner
792.2.bp.d.19.5		48	88.19	even	10	inner
792.2.bp.d.667.3		48	8.3	odd	2	inner
792.2.bp.d.667.5		48	1.1	even	1	trivial
1056.2.bp.a.271.3		48	24.5	odd	2
1056.2.bp.a.271.10		48	12.11	even	2
1056.2.bp.a.943.3		48	132.107	odd	10
1056.2.bp.a.943.10		48	264.173	even	10

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:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.bp (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.445083 + 1.34235i) q^{2} +(-1.60380 - 1.19491i) q^{4} +(-1.48262 - 2.04066i) q^{5} +(1.07225 + 3.30005i) q^{7} +(2.31782 - 1.62103i) q^{8} +(3.39916 - 1.08194i) q^{10} +(-2.55602 - 2.11348i) q^{11} +(-1.89429 - 1.37628i) q^{13} +(-4.90706 - 0.0294599i) q^{14} +(1.14437 + 3.83281i) q^{16} +(2.12874 + 2.92996i) q^{17} +(6.47486 + 2.10381i) q^{19} +(-0.0605712 + 5.04441i) q^{20} +(3.97466 - 2.49039i) q^{22} +7.17148i q^{23} +(-0.421018 + 1.29576i) q^{25} +(2.69056 - 1.93024i) q^{26} +(2.22359 - 6.57388i) q^{28} +(0.252424 + 0.776881i) q^{29} +(-3.49999 + 4.81732i) q^{31} +(-5.65431 - 0.169779i) q^{32} +(-4.88050 + 1.55344i) q^{34} +(5.14452 - 7.08083i) q^{35} +(1.96758 - 0.639306i) q^{37} +(-5.70590 + 7.75516i) q^{38} +(-6.74440 - 2.32649i) q^{40} +(4.24917 + 1.38064i) q^{41} +5.90629i q^{43} +(1.57392 + 6.44382i) q^{44} +(-9.62663 - 3.19190i) q^{46} +(6.31309 + 2.05125i) q^{47} +(-4.07750 + 2.96248i) q^{49} +(-1.55197 - 1.14187i) q^{50} +(1.39353 + 4.47079i) q^{52} +(-8.16553 + 11.2389i) q^{53} +(-0.523272 + 8.34943i) q^{55} +(7.83476 + 5.91076i) q^{56} +(-1.15520 - 0.00693530i) q^{58} +(2.47252 + 7.60962i) q^{59} +(-7.77810 + 5.65112i) q^{61} +(-4.90875 - 6.84232i) q^{62} +(2.74454 - 7.51449i) q^{64} +5.90609i q^{65} +9.83888 q^{67} +(0.0869678 - 7.24274i) q^{68} +(7.21521 + 10.0573i) q^{70} +(-3.94907 - 5.43543i) q^{71} +(4.23299 - 1.37538i) q^{73} +(-0.0175648 + 2.92573i) q^{74} +(-7.87053 - 11.1110i) q^{76} +(4.23389 - 10.7012i) q^{77} +(-10.7142 - 7.78432i) q^{79} +(6.12478 - 8.01787i) q^{80} +(-3.74453 + 5.08937i) q^{82} +(-2.34985 - 3.23429i) q^{83} +(2.82292 - 8.68806i) q^{85} +(-7.92830 - 2.62879i) q^{86} +(-9.35038 - 0.755279i) q^{88} -2.99301 q^{89} +(2.51064 - 7.72697i) q^{91} +(8.56930 - 11.5016i) q^{92} +(-5.56334 + 7.56140i) q^{94} +(-5.30663 - 16.3321i) q^{95} +(-5.74003 - 4.17037i) q^{97} +(-2.16185 - 6.79198i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4} - 4 q^{11} + 16 q^{14} + 20 q^{16} - 25 q^{20} + 3 q^{22} - 4 q^{25} - 4 q^{26} - 25 q^{28} - 26 q^{38} - 65 q^{40} + 60 q^{41} + 43 q^{44} - 5 q^{46} - 12 q^{49} + 80 q^{50} - 15 q^{52}+ \cdots - 40 q^{97}+O(q^{100}) \) 48 * q + 4 * q^4 - 4 * q^11 + 16 * q^14 + 20 * q^16 - 25 * q^20 + 3 * q^22 - 4 * q^25 - 4 * q^26 - 25 * q^28 - 26 * q^38 - 65 * q^40 + 60 * q^41 + 43 * q^44 - 5 * q^46 - 12 * q^49 + 80 * q^50 - 15 * q^52 + 14 * q^56 + 73 * q^58 + 8 * q^59 + 45 * q^62 - 38 * q^64 + 8 * q^67 + 55 * q^68 - 40 * q^70 - 60 * q^74 - 35 * q^82 + 100 * q^83 - 81 * q^86 - 18 * q^88 - 96 * q^89 - 20 * q^91 - 59 * q^92 + 35 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

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Database

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