LMFDB - Embedded newform 756.2.ba.a.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(71,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("756.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ba (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.1
Character	$\chi$	$=$	756.71
Dual form			756.2.ba.a.575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41075 + 0.0989244i) q^{2} +(1.98043 - 0.279115i) q^{4} +(-0.795659 - 0.459374i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.76628 + 0.589674i) q^{8} +O(q^{10})$	\(q+(-1.41075 + 0.0989244i) q^{2} +(1.98043 - 0.279115i) q^{4} +(-0.795659 - 0.459374i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.76628 + 0.589674i) q^{8} +(1.16792 + 0.569351i) q^{10} +(-0.582708 - 1.00928i) q^{11} +(0.0273083 - 0.0472994i) q^{13} +(-1.17228 + 0.791046i) q^{14} +(3.84419 - 1.10553i) q^{16} -3.29574i q^{17} -0.455543i q^{19} +(-1.70396 - 0.687676i) q^{20} +(0.921897 + 1.36620i) q^{22} +(-1.77871 + 3.08081i) q^{23} +(-2.07795 - 3.59912i) q^{25} +(-0.0338462 + 0.0694291i) q^{26} +(1.57554 - 1.23193i) q^{28} +(7.58443 - 4.37887i) q^{29} +(-7.03218 - 4.06003i) q^{31} +(-5.31382 + 1.93992i) q^{32} +(0.326029 + 4.64947i) q^{34} -0.918747 q^{35} +1.20717 q^{37} +(0.0450644 + 0.642658i) q^{38} +(2.47189 + 0.801575i) q^{40} +(5.27252 + 3.04409i) q^{41} +(-5.64563 + 3.25951i) q^{43} +(-1.43572 - 1.83616i) q^{44} +(2.20454 - 4.52221i) q^{46} +(-2.82141 - 4.88682i) q^{47} +(0.500000 - 0.866025i) q^{49} +(3.28751 + 4.87189i) q^{50} +(0.0408802 - 0.101295i) q^{52} -10.6457i q^{53} +1.07072i q^{55} +(-2.10083 + 1.89381i) q^{56} +(-10.2666 + 6.92778i) q^{58} +(-0.744373 + 1.28929i) q^{59} +(-6.35962 - 11.0152i) q^{61} +(10.3223 + 5.03204i) q^{62} +(7.30457 - 3.26240i) q^{64} +(-0.0434562 + 0.0250895i) q^{65} +(-5.83071 - 3.36636i) q^{67} +(-0.919891 - 6.52698i) q^{68} +(1.29612 - 0.0908865i) q^{70} +2.97148 q^{71} +14.8214 q^{73} +(-1.70301 + 0.119419i) q^{74} +(-0.127149 - 0.902171i) q^{76} +(-1.00928 - 0.582708i) q^{77} +(10.9305 - 6.31075i) q^{79} +(-3.56652 - 0.886292i) q^{80} +(-7.73934 - 3.77287i) q^{82} +(-6.56004 - 11.3623i) q^{83} +(-1.51398 + 2.62229i) q^{85} +(7.64213 - 5.15684i) q^{86} +(2.20708 + 2.44834i) q^{88} -7.95018i q^{89} -0.0546167i q^{91} +(-2.66270 + 6.59779i) q^{92} +(4.46373 + 6.61498i) q^{94} +(-0.209265 + 0.362457i) q^{95} +(-4.26325 - 7.38417i) q^{97} +(-0.619704 + 1.27121i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) $ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−1.41075	+	0.0989244i	−0.997550	+	0.0699501i
$2$	−1.41075	+	0.0989244i	−0.997550	+	0.0699501i
$3$		0			0
$3$		0			0
$4$	1.98043	−	0.279115i	0.990214	−	0.139558i
$5$	−0.795659	−	0.459374i	−0.355829	−	0.205438i	0.311420	−	0.950272i	$-0.399195\pi$
$5$	−0.795659	−	0.459374i	−0.355829	−	0.205438i	−0.667250	+	0.744834i	$0.732529\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$	−2.76628	+	0.589674i	−0.978026	+	0.208481i
$9$		0			0
$10$	1.16792	+	0.569351i	0.369328	+	0.180045i
$11$	−0.582708	−	1.00928i	−0.175693	−	0.304309i	0.764708	−	0.644377i	$-0.222883\pi$
$11$	−0.582708	−	1.00928i	−0.175693	−	0.304309i	−0.940401	+	0.340068i	$0.889550\pi$
$12$		0			0
$13$	0.0273083	−	0.0472994i	0.00757397	−	0.0131185i	−0.862214	−	0.506545i	$-0.830922\pi$
$13$	0.0273083	−	0.0472994i	0.00757397	−	0.0131185i	0.869788	+	0.493426i	$0.164256\pi$
$14$	−1.17228	+	0.791046i	−0.313306	+	0.211416i
$15$		0			0
$16$	3.84419	−	1.10553i	0.961047	−	0.276384i
$17$		−	3.29574i		−	0.799335i	−0.916660	−	0.399667i	$-0.869126\pi$
$17$		−	3.29574i		−	0.799335i	0.916660	−	0.399667i	$-0.130874\pi$
$18$		0			0
$19$		−	0.455543i		−	0.104509i	−0.998634	−	0.0522544i	$-0.983359\pi$
$19$		−	0.455543i		−	0.104509i	0.998634	−	0.0522544i	$-0.0166407\pi$
$20$	−1.70396	−	0.687676i	−0.381018	−	0.153769i
$21$		0			0
$22$	0.921897	+	1.36620i	0.196549	+	0.291274i
$23$	−1.77871	+	3.08081i	−0.370886	+	0.642393i	−0.989702	−	0.143143i	$-0.954279\pi$
$23$	−1.77871	+	3.08081i	−0.370886	+	0.642393i	0.618816	+	0.785536i	$0.287613\pi$
$24$		0			0
$25$	−2.07795	−	3.59912i	−0.415590	−	0.719824i
$26$	−0.0338462	+	0.0694291i	−0.00663778	+	0.0136162i
$27$		0			0
$28$	1.57554	−	1.23193i	0.297750	−	0.232814i
$29$	7.58443	−	4.37887i	1.40839	−	0.813136i	0.413160	−	0.910658i	$-0.364425\pi$
$29$	7.58443	−	4.37887i	1.40839	−	0.813136i	0.995233	+	0.0975219i	$0.0310916\pi$
$30$		0			0
$31$	−7.03218	−	4.06003i	−1.26302	−	0.729203i	−0.289360	−	0.957220i	$-0.593443\pi$
$31$	−7.03218	−	4.06003i	−1.26302	−	0.729203i	−0.973657	+	0.228017i	$0.926776\pi$
$32$	−5.31382	+	1.93992i	−0.939360	+	0.342932i
$33$		0			0
$34$	0.326029	+	4.64947i	0.0559135	+	0.797377i
$35$	−0.918747			−0.155297
$36$		0			0
$37$	1.20717			0.198458			0.0992288	−	0.995065i	$-0.468362\pi$
$37$	1.20717			0.198458			0.0992288	+	0.995065i	$0.468362\pi$
$38$	0.0450644	+	0.642658i	0.00731040	+	0.104253i
$39$		0			0
$40$	2.47189	+	0.801575i	0.390840	+	0.126740i
$41$	5.27252	+	3.04409i	0.823429	+	0.475407i	0.851598	−	0.524196i	$-0.175634\pi$
$41$	5.27252	+	3.04409i	0.823429	+	0.475407i	−0.0281682	+	0.999603i	$0.508967\pi$
$42$		0			0
$43$	−5.64563	+	3.25951i	−0.860951	+	0.497070i	−0.864331	−	0.502924i	$-0.832258\pi$
$43$	−5.64563	+	3.25951i	−0.860951	+	0.497070i	0.00337979	+	0.999994i	$0.498924\pi$
$44$	−1.43572	−	1.83616i	−0.216442	−	0.276812i
$45$		0			0
$46$	2.20454	−	4.52221i	0.325042	−	0.666763i
$47$	−2.82141	−	4.88682i	−0.411545	−	0.712817i	0.583514	−	0.812103i	$-0.301677\pi$
$47$	−2.82141	−	4.88682i	−0.411545	−	0.712817i	−0.995059	+	0.0992864i	$0.968344\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	3.28751	+	4.87189i	0.464924	+	0.688990i
$51$		0			0
$52$	0.0408802	−	0.101295i	0.00566907	−	0.0140471i
$53$		−	10.6457i		−	1.46230i	−0.682218	−	0.731149i	$-0.738984\pi$
$53$		−	10.6457i		−	1.46230i	0.682218	−	0.731149i	$-0.261016\pi$
$54$		0			0
$55$			1.07072i			0.144376i
$56$	−2.10083	+	1.89381i	−0.280735	+	0.253071i
$57$		0			0
$58$	−10.2666	+	6.92778i	−1.34806	+	0.909662i
$59$	−0.744373	+	1.28929i	−0.0969092	+	0.167852i	−0.910404	−	0.413721i	$-0.864229\pi$
$59$	−0.744373	+	1.28929i	−0.0969092	+	0.167852i	0.813495	+	0.581572i	$0.197562\pi$
$60$		0			0
$61$	−6.35962	−	11.0152i	−0.814266	−	1.41035i	−0.909854	−	0.414929i	$-0.863807\pi$
$61$	−6.35962	−	11.0152i	−0.814266	−	1.41035i	0.0955881	−	0.995421i	$-0.469527\pi$
$62$	10.3223	+	5.03204i	1.31093	+	0.639069i
$63$		0			0
$64$	7.30457	−	3.26240i	0.913071	−	0.407800i
$65$	−0.0434562	+	0.0250895i	−0.00539008	+	0.00311197i
$66$		0			0
$67$	−5.83071	−	3.36636i	−0.712335	−	0.411267i	0.0995902	−	0.995029i	$-0.468247\pi$
$67$	−5.83071	−	3.36636i	−0.712335	−	0.411267i	−0.811925	+	0.583762i	$0.801580\pi$
$68$	−0.919891	−	6.52698i	−0.111553	−	0.791512i
$69$		0			0
$70$	1.29612	−	0.0908865i	0.154916	−	0.0108630i
$71$	2.97148			0.352650			0.176325	−	0.984332i	$-0.443579\pi$
$71$	2.97148			0.352650			0.176325	+	0.984332i	$0.443579\pi$
$72$		0			0
$73$	14.8214			1.73471			0.867357	−	0.497686i	$-0.165817\pi$
$73$	14.8214			1.73471			0.867357	+	0.497686i	$0.165817\pi$
$74$	−1.70301	+	0.119419i	−0.197971	+	0.0138821i
$75$		0			0
$76$	−0.127149	−	0.902171i	−0.0145850	−	0.103486i
$77$	−1.00928	−	0.582708i	−0.115018	−	0.0664057i
$78$		0			0
$79$	10.9305	−	6.31075i	1.22978	−	0.710015i	0.262798	−	0.964851i	$-0.415355\pi$
$79$	10.9305	−	6.31075i	1.22978	−	0.710015i	0.966984	+	0.254836i	$0.0820214\pi$
$80$	−3.56652	−	0.886292i	−0.398749	−	0.0990904i
$81$		0			0
$82$	−7.73934	−	3.77287i	−0.854667	−	0.416644i
$83$	−6.56004	−	11.3623i	−0.720058	−	1.24718i	−0.960976	−	0.276632i	$-0.910782\pi$
$83$	−6.56004	−	11.3623i	−0.720058	−	1.24718i	0.240918	−	0.970546i	$-0.422552\pi$
$84$		0			0
$85$	−1.51398	+	2.62229i	−0.164214	+	0.284427i
$86$	7.64213	−	5.15684i	0.824072	−	0.556076i
$87$		0			0
$88$	2.20708	+	2.44834i	0.235275	+	0.260994i
$89$		−	7.95018i		−	0.842717i	−0.906894	−	0.421359i	$-0.861553\pi$
$89$		−	7.95018i		−	0.842717i	0.906894	−	0.421359i	$-0.138447\pi$
$90$		0			0
$91$		−	0.0546167i		−	0.00572539i
$92$	−2.66270	+	6.59779i	−0.277606	+	0.687867i
$93$		0			0
$94$	4.46373	+	6.61498i	0.460398	+	0.682283i
$95$	−0.209265	+	0.362457i	−0.0214701	+	0.0371873i
$96$		0			0
$97$	−4.26325	−	7.38417i	−0.432868	−	0.749749i	0.564251	−	0.825603i	$-0.309165\pi$
$97$	−4.26325	−	7.38417i	−0.432868	−	0.749749i	−0.997119	+	0.0758544i	$0.975832\pi$
$98$	−0.619704	+	1.27121i	−0.0625995	+	0.128411i
$99$		0			0
$100$	−5.11980	−	6.54781i	−0.511980	−	0.654781i
$101$	−11.2424	+	6.49081i	−1.11866	+	0.645860i	−0.941059	−	0.338242i	$-0.890168\pi$
$101$	−11.2424	+	6.49081i	−1.11866	+	0.645860i	−0.177604	+	0.984102i	$0.556834\pi$
$102$		0			0
$103$	−1.95855	−	1.13077i	−0.192982	−	0.111418i	0.400396	−	0.916342i	$-0.368873\pi$
$103$	−1.95855	−	1.13077i	−0.192982	−	0.111418i	−0.593378	+	0.804924i	$0.702206\pi$
$104$	−0.0476512	+	0.146946i	−0.00467258	+	0.0144093i
$105$		0			0
$106$	1.05312	+	15.0184i	0.102288	+	1.45872i
$107$	−4.66383			−0.450870			−0.225435	−	0.974258i	$-0.572380\pi$
$107$	−4.66383			−0.450870			−0.225435	+	0.974258i	$0.572380\pi$
$108$		0			0
$109$	−11.1216			−1.06526			−0.532629	−	0.846349i	$-0.678796\pi$
$109$	−11.1216			−1.06526			−0.532629	+	0.846349i	$0.678796\pi$
$110$	−0.105921	−	1.51052i	−0.0100991	−	0.144023i
$111$		0			0
$112$	2.77640	−	2.87952i	0.262345	−	0.272089i
$113$	14.2992	+	8.25566i	1.34516	+	0.776627i	0.987559	−	0.157248i	$-0.0502621\pi$
$113$	14.2992	+	8.25566i	1.34516	+	0.776627i	0.357599	+	0.933875i	$0.383595\pi$
$114$		0			0
$115$	2.83049	−	1.63418i	0.263944	−	0.152388i
$116$	13.7982	−	10.7890i	1.28113	−	1.00173i
$117$		0			0
$118$	0.922582	−	1.89251i	0.0849305	−	0.174219i
$119$	−1.64787	−	2.85420i	−0.151060	−	0.261644i
$120$		0			0
$121$	4.82090	−	8.35005i	0.438264	−	0.759095i
$122$	10.0615	+	14.9105i	0.910925	+	1.34994i
$123$		0			0
$124$	−15.0599	−	6.07781i	−1.35242	−	0.545804i
$125$			8.41196i			0.752389i
$126$		0			0
$127$			17.6270i			1.56415i	0.623186	+	0.782073i	$0.285838\pi$
$127$			17.6270i			1.56415i	−0.623186	+	0.782073i	$0.714162\pi$
$128$	−9.98219	+	5.32503i	−0.882309	+	0.470671i
$129$		0			0
$130$	0.0588239	−	0.0396938i	0.00515920	−	0.00348138i
$131$	7.62368	−	13.2046i	0.666084	−	1.15369i	−0.312906	−	0.949784i	$-0.601303\pi$
$131$	7.62368	−	13.2046i	0.666084	−	1.15369i	0.978990	−	0.203907i	$-0.0653641\pi$
$132$		0			0
$133$	−0.227772	−	0.394512i	−0.0197503	−	0.0342085i
$134$	8.55869	+	4.17229i	0.739358	+	0.360431i
$135$		0			0
$136$	1.94341	+	9.11693i	0.166646	+	0.781771i
$137$	5.64672	−	3.26013i	0.482432	−	0.278532i	−0.238998	−	0.971020i	$-0.576819\pi$
$137$	5.64672	−	3.26013i	0.482432	−	0.278532i	0.721429	+	0.692488i	$0.243485\pi$
$138$		0			0
$139$	6.93543	+	4.00417i	0.588255	+	0.339629i	0.764407	−	0.644734i	$-0.223032\pi$
$139$	6.93543	+	4.00417i	0.588255	+	0.339629i	−0.176152	+	0.984363i	$0.556365\pi$
$140$	−1.81951	+	0.256436i	−0.153777	+	0.0216728i
$141$		0			0
$142$	−4.19201	+	0.293952i	−0.351786	+	0.0246679i
$143$	−0.0636512			−0.00532278
$144$		0			0
$145$	−8.04616			−0.668197
$146$	−20.9093	+	1.46620i	−1.73047	+	0.121343i
$147$		0			0
$148$	2.39071	−	0.336939i	0.196515	−	0.0276962i
$149$	−1.41090	−	0.814584i	−0.115585	−	0.0667333i	0.441093	−	0.897462i	$-0.354591\pi$
$149$	−1.41090	−	0.814584i	−0.115585	−	0.0667333i	−0.556678	+	0.830728i	$0.687924\pi$
$150$		0			0
$151$	4.43451	−	2.56026i	0.360875	−	0.208351i	−0.308589	−	0.951195i	$-0.599857\pi$
$151$	4.43451	−	2.56026i	0.360875	−	0.208351i	0.669465	+	0.742844i	$0.266524\pi$
$152$	0.268622	+	1.26016i	0.0217881	+	0.102212i
$153$		0			0
$154$	1.48148	+	0.722212i	0.119381	+	0.0581975i
$155$	3.73015	+	6.46080i	0.299612	+	0.518944i
$156$		0			0
$157$	0.242007	−	0.419168i	0.0193142	−	0.0334532i	−0.856207	−	0.516633i	$-0.827185\pi$
$157$	0.242007	−	0.419168i	0.0193142	−	0.0334532i	0.875521	+	0.483180i	$0.160518\pi$
$158$	−14.7960	+	9.98419i	−1.17710	+	0.794299i
$159$		0			0
$160$	5.11914	+	0.897520i	0.404703	+	0.0709552i
$161$			3.55741i			0.280363i
$162$		0			0
$163$			23.8078i			1.86477i	0.361466	+	0.932385i	$0.382276\pi$
$163$			23.8078i			1.86477i	−0.361466	+	0.932385i	$0.617724\pi$
$164$	11.2915	+	4.55696i	0.881718	+	0.355839i
$165$		0			0
$166$	10.3786	+	15.3804i	0.805535	+	1.19375i
$167$	−9.37726	+	16.2419i	−0.725634	+	1.25684i	0.233078	+	0.972458i	$0.425120\pi$
$167$	−9.37726	+	16.2419i	−0.725634	+	1.25684i	−0.958713	+	0.284377i	$0.908213\pi$
$168$		0			0
$169$	6.49851	+	11.2557i	0.499885	+	0.865827i
$170$	1.87643	−	3.84916i	0.143916	−	0.295217i
$171$		0			0
$172$	−10.2710	+	8.03100i	−0.783156	+	0.612358i
$173$	−15.3852	+	8.88264i	−1.16971	+	0.675334i	−0.953613	−	0.301037i	$-0.902667\pi$
$173$	−15.3852	+	8.88264i	−1.16971	+	0.675334i	−0.216101	+	0.976371i	$0.569334\pi$
$174$		0			0
$175$	−3.59912	−	2.07795i	−0.272068	−	0.157078i
$176$	−3.35583	−	3.23566i	−0.252955	−	0.243897i
$177$		0			0
$178$	0.786466	+	11.2157i	0.0589481	+	0.840653i
$179$	7.17934			0.536609			0.268305	−	0.963334i	$-0.413537\pi$
$179$	7.17934			0.536609			0.268305	+	0.963334i	$0.413537\pi$
$180$		0			0
$181$	2.79633			0.207849			0.103925	−	0.994585i	$-0.466860\pi$
$181$	2.79633			0.207849			0.103925	+	0.994585i	$0.466860\pi$
$182$	0.00540292	+	0.0770505i	0.000400491	+	0.00571136i
$183$		0			0
$184$	3.10372	−	9.57123i	0.228809	−	0.705600i
$185$	−0.960495	−	0.554542i	−0.0706170	−	0.0407708i
$186$		0			0
$187$	−3.32633	+	1.92045i	−0.243245	+	0.140438i
$188$	−6.95158	−	8.89051i	−0.506996	−	0.648407i
$189$		0			0
$190$	0.259364	−	0.532037i	0.0188163	−	0.0385981i
$191$	12.0033	+	20.7903i	0.868527	+	1.50433i	0.863502	+	0.504346i	$0.168266\pi$
$191$	12.0033	+	20.7903i	0.868527	+	1.50433i	0.00502585	+	0.999987i	$0.498400\pi$
$192$		0			0
$193$	−8.57949	+	14.8601i	−0.617565	+	1.06965i	0.372363	+	0.928087i	$0.378548\pi$
$193$	−8.57949	+	14.8601i	−0.617565	+	1.06965i	−0.989929	+	0.141567i	$0.954786\pi$
$194$	6.74485	+	9.99547i	0.484252	+	0.717633i
$195$		0			0
$196$	0.748493	−	1.85466i	0.0534638	−	0.132476i
$197$			2.40069i			0.171042i	0.996336	+	0.0855211i	$0.0272555\pi$
$197$			2.40069i			0.171042i	−0.996336	+	0.0855211i	$0.972744\pi$
$198$		0			0
$199$		−	2.50012i		−	0.177229i	−0.996066	−	0.0886146i	$-0.971756\pi$
$199$		−	2.50012i		−	0.177229i	0.996066	−	0.0886146i	$-0.0282439\pi$
$200$	7.87049	+	8.73084i	0.556528	+	0.617364i
$201$		0			0
$202$	15.2181	−	10.2691i	1.07074	−	0.722529i
$203$	4.37887	−	7.58443i	0.307337	−	0.532323i
$204$		0			0
$205$	−2.79675	−	4.84412i	−0.195334	−	0.338328i
$206$	2.87489	+	1.40149i	0.200303	+	0.0976461i
$207$		0			0
$208$	0.0526873	−	0.212018i	0.00365321	−	0.0147008i
$209$	−0.459771	+	0.265449i	−0.0318030	+	0.0183615i
$210$		0			0
$211$	2.68339	+	1.54926i	0.184732	+	0.106655i	0.589514	−	0.807758i	$-0.299319\pi$
$211$	2.68339	+	1.54926i	0.184732	+	0.106655i	−0.404782	+	0.914413i	$0.632653\pi$
$212$	−2.97137	−	21.0830i	−0.204075	−	1.44799i
$213$		0			0
$214$	6.57950	−	0.461367i	0.449765	−	0.0315384i
$215$	5.98933			0.408469
$216$		0			0
$217$	−8.12007			−0.551226
$218$	15.6898	−	1.10020i	1.06265	−	0.0745149i
$219$		0			0
$220$	0.298855	+	2.12049i	0.0201488	+	0.142963i
$221$	−0.155887	−	0.0900013i	−0.0104861	−	0.00605414i
$222$		0			0
$223$	7.33815	−	4.23669i	0.491399	−	0.283709i	−0.233756	−	0.972295i	$-0.575102\pi$
$223$	7.33815	−	4.23669i	0.491399	−	0.283709i	0.725155	+	0.688586i	$0.241768\pi$
$224$	−3.63195	+	4.33693i	−0.242670	+	0.289773i
$225$		0			0
$226$	−20.9893	−	10.2321i	−1.39619	−	0.680631i
$227$	6.73436	+	11.6643i	0.446975	+	0.774184i	0.998187	−	0.0601814i	$-0.0191679\pi$
$227$	6.73436	+	11.6643i	0.446975	+	0.774184i	−0.551212	+	0.834365i	$0.685835\pi$
$228$		0			0
$229$	−3.16856	+	5.48811i	−0.209385	+	0.362665i	−0.951521	−	0.307584i	$-0.900479\pi$
$229$	−3.16856	+	5.48811i	−0.209385	+	0.362665i	0.742136	+	0.670249i	$0.233813\pi$
$230$	−3.83145	+	2.58543i	−0.252638	+	0.170478i
$231$		0			0
$232$	−18.3985	+	16.5855i	−1.20792	+	1.08889i
$233$		−	3.30819i		−	0.216727i	−0.994111	−	0.108363i	$-0.965439\pi$
$233$		−	3.30819i		−	0.216727i	0.994111	−	0.108363i	$-0.0345610\pi$
$234$		0			0
$235$			5.18433i			0.338188i
$236$	−1.11432	+	2.76112i	−0.0725359	+	0.179733i
$237$		0			0
$238$	2.60708	+	3.86354i	0.168992	+	0.250436i
$239$	−9.17721	+	15.8954i	−0.593624	+	1.02819i	0.400115	+	0.916465i	$0.368970\pi$
$239$	−9.17721	+	15.8954i	−0.593624	+	1.02819i	−0.993739	+	0.111722i	$0.964363\pi$
$240$		0			0
$241$	10.5580	+	18.2871i	0.680103	+	1.17797i	0.974949	+	0.222429i	$0.0713984\pi$
$241$	10.5580	+	18.2871i	0.680103	+	1.17797i	−0.294846	+	0.955545i	$0.595268\pi$
$242$	−5.97506	+	12.2567i	−0.384092	+	0.787893i
$243$		0			0
$244$	−15.6693	−	20.0397i	−1.00312	−	1.28291i
$245$	−0.795659	+	0.459374i	−0.0508328	+	0.0293483i
$246$		0			0
$247$	−0.0215470	−	0.0124401i	−0.00137100	−	0.000791547i
$248$	21.8471	+	7.08448i	1.38729	+	0.449865i
$249$		0			0
$250$	−0.832148	−	11.8672i	−0.0526297	−	0.750546i
$251$	13.9450			0.880199			0.440099	−	0.897949i	$-0.354943\pi$
$251$	13.9450			0.880199			0.440099	+	0.897949i	$0.354943\pi$
$252$		0			0
$253$	4.14587			0.260648
$254$	−1.74374	−	24.8673i	−0.109412	−	1.56032i
$255$		0			0
$256$	13.5556	−	8.49977i	0.847224	−	0.531235i
$257$	−9.32528	−	5.38395i	−0.581695	−	0.335842i	0.180112	−	0.983646i	$-0.442354\pi$
$257$	−9.32528	−	5.38395i	−0.581695	−	0.335842i	−0.761807	+	0.647804i	$0.775687\pi$
$258$		0			0
$259$	1.04544	−	0.603585i	0.0649605	−	0.0375049i
$260$	−0.0790591	+	0.0618172i	−0.00490304	+	0.00383374i
$261$		0			0
$262$	−9.44884	+	19.3825i	−0.583751	+	1.19746i
$263$	−8.12745	−	14.0772i	−0.501160	−	0.868034i	−0.999999	−	0.00133978i	$-0.999574\pi$
$263$	−8.12745	−	14.0772i	−0.501160	−	0.868034i	0.498839	−	0.866695i	$-0.333760\pi$
$264$		0			0
$265$	−4.89035	+	8.47033i	−0.300412	+	0.520329i
$266$	0.360356	+	0.534026i	0.0220948	+	0.0327432i
$267$		0			0
$268$	−12.4869	−	5.03940i	−0.762759	−	0.307830i
$269$			9.10913i			0.555393i	0.960669	+	0.277697i	$0.0895710\pi$
$269$			9.10913i			0.555393i	−0.960669	+	0.277697i	$0.910429\pi$
$270$		0			0
$271$		−	31.7070i		−	1.92606i	−0.269385	−	0.963032i	$-0.586820\pi$
$271$		−	31.7070i		−	1.92606i	0.269385	−	0.963032i	$-0.413180\pi$
$272$	−3.64356	−	12.6695i	−0.220923	−	0.768199i
$273$		0			0
$274$	−7.64360	+	5.15783i	−0.461767	+	0.311596i
$275$	−2.42168	+	4.19447i	−0.146033	+	0.252936i
$276$		0			0
$277$	−0.801334	−	1.38795i	−0.0481475	−	0.0833939i	0.840947	−	0.541117i	$-0.181998\pi$
$277$	−0.801334	−	1.38795i	−0.0481475	−	0.0833939i	−0.889095	+	0.457723i	$0.848665\pi$
$278$	−10.1803	−	4.96280i	−0.610571	−	0.297649i
$279$		0			0
$280$	2.54151	−	0.541761i	0.151884	−	0.0323764i
$281$	19.1083	−	11.0322i	1.13991	−	0.658126i	0.193500	−	0.981100i	$-0.438016\pi$
$281$	19.1083	−	11.0322i	1.13991	−	0.658126i	0.946408	+	0.322974i	$0.104683\pi$
$282$		0			0
$283$	−18.0711	−	10.4334i	−1.07422	−	0.620200i	−0.144887	−	0.989448i	$-0.546282\pi$
$283$	−18.0711	−	10.4334i	−1.07422	−	0.620200i	−0.929331	+	0.369249i	$0.879615\pi$
$284$	5.88480	−	0.829384i	0.349199	−	0.0492149i
$285$		0			0
$286$	0.0897958	−	0.00629665i	0.00530974	−	0.000372329i
$287$	6.08818			0.359374
$288$		0			0
$289$	6.13809			0.361064
$290$	11.3511	−	0.795961i	0.666560	−	0.0467405i
$291$		0			0
$292$	29.3527	−	4.13688i	1.71774	−	0.242092i
$293$	−16.0686	−	9.27721i	−0.938737	−	0.541980i	−0.0491729	−	0.998790i	$-0.515659\pi$
$293$	−16.0686	−	9.27721i	−0.938737	−	0.541980i	−0.889564	+	0.456810i	$0.848992\pi$
$294$		0			0
$295$	1.18453	−	0.683891i	0.0689662	−	0.0398177i
$296$	−3.33937	+	0.711837i	−0.194097	+	0.0413747i
$297$		0			0
$298$	2.07101	+	1.00960i	0.119970	+	0.0584846i
$299$	0.0971471	+	0.168264i	0.00561816	+	0.00973094i
$300$		0			0
$301$	−3.25951	+	5.64563i	−0.187875	+	0.325409i
$302$	−6.00271	+	4.05057i	−0.345417	+	0.233084i
$303$		0			0
$304$	−0.503619	−	1.75120i	−0.0288845	−	0.100438i
$305$			11.6858i			0.669125i
$306$		0			0
$307$			3.11806i			0.177957i	0.996034	+	0.0889786i	$0.0283603\pi$
$307$			3.11806i			0.177957i	−0.996034	+	0.0889786i	$0.971640\pi$
$308$	−2.16145	−	0.872306i	−0.123160	−	0.0497042i
$309$		0			0
$310$	−5.90143	−	8.74557i	−0.335179	−	0.496715i
$311$	10.5991	−	18.3581i	0.601018	−	1.04099i	−0.391649	−	0.920115i	$-0.628095\pi$
$311$	10.5991	−	18.3581i	0.601018	−	1.04099i	0.992667	−	0.120879i	$-0.0385713\pi$
$312$		0			0
$313$	11.7962	+	20.4317i	0.666762	+	1.15487i	0.978804	+	0.204798i	$0.0656536\pi$
$313$	11.7962	+	20.4317i	0.666762	+	1.15487i	−0.312042	+	0.950068i	$0.601013\pi$
$314$	−0.299945	+	0.615281i	−0.0169269	+	0.0347223i
$315$		0			0
$316$	19.8857	−	15.5489i	1.11866	−	0.874692i
$317$	−15.8115	+	9.12879i	−0.888064	+	0.512724i	−0.873309	−	0.487167i	$-0.838030\pi$
$317$	−15.8115	+	9.12879i	−0.888064	+	0.512724i	−0.0147552	+	0.999891i	$0.504697\pi$
$318$		0			0
$319$	−8.83902	−	5.10321i	−0.494890	−	0.285725i
$320$	−7.31061	−	0.759769i	−0.408675	−	0.0424724i
$321$		0			0
$322$	−0.351915	−	5.01862i	−0.0196115	−	0.279677i
$323$	−1.50135			−0.0835375
$324$		0			0
$325$	−0.226982			−0.0125907
$326$	−2.35517	−	33.5868i	−0.130441	−	1.86020i
$327$		0			0
$328$	−16.3803	−	5.31173i	−0.904449	−	0.293291i
$329$	−4.88682	−	2.82141i	−0.269419	−	0.155549i
$330$		0			0
$331$	19.6152	−	11.3248i	1.07815	−	0.622468i	0.147751	−	0.989025i	$-0.452797\pi$
$331$	19.6152	−	11.3248i	1.07815	−	0.622468i	0.930396	+	0.366557i	$0.119463\pi$
$332$	−16.1631	−	20.6713i	−0.887065	−	1.13448i
$333$		0			0
$334$	11.6222	−	23.8409i	0.635941	−	1.30451i
$335$	3.09284	+	5.35695i	0.168980	+	0.292681i
$336$		0			0
$337$	2.63847	−	4.56997i	0.143727	−	0.248942i	−0.785170	−	0.619280i	$-0.787425\pi$
$337$	2.63847	−	4.56997i	0.143727	−	0.248942i	0.928897	+	0.370338i	$0.120758\pi$
$338$	−10.2812	−	15.2362i	−0.559225	−	0.828739i
$339$		0			0
$340$	−2.26640	+	5.61582i	−0.122913	+	0.304561i
$341$			9.46325i			0.512464i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	13.6953	−	12.3458i	0.738403	−	0.665640i
$345$		0			0
$346$	20.8259	−	14.0531i	1.11961	−	0.755502i
$347$	3.73945	−	6.47693i	0.200744	−	0.347700i	−0.748024	−	0.663672i	$-0.768997\pi$
$347$	3.73945	−	6.47693i	0.200744	−	0.347700i	0.948769	+	0.315972i	$0.102331\pi$
$348$		0			0
$349$	−9.00083	−	15.5899i	−0.481803	−	0.834508i	0.517979	−	0.855393i	$-0.326685\pi$
$349$	−9.00083	−	15.5899i	−0.481803	−	0.834508i	−0.999782	+	0.0208860i	$0.993351\pi$
$350$	5.28301	+	2.57543i	0.282389	+	0.137662i
$351$		0			0
$352$	5.05432	+	4.23273i	0.269396	+	0.225605i
$353$	3.79516	−	2.19114i	0.201996	−	0.116622i	−0.395590	−	0.918427i	$-0.629460\pi$
$353$	3.79516	−	2.19114i	0.201996	−	0.116622i	0.597586	+	0.801805i	$0.296127\pi$
$354$		0			0
$355$	−2.36428	−	1.36502i	−0.125483	−	0.0724477i
$356$	−2.21901	−	15.7448i	−0.117608	−	0.834470i
$357$		0			0
$358$	−10.1283	+	0.710212i	−0.535295	+	0.0375359i
$359$	−27.6893			−1.46138			−0.730692	−	0.682707i	$-0.760803\pi$
$359$	−27.6893			−1.46138			−0.730692	+	0.682707i	$0.760803\pi$
$360$		0			0
$361$	18.7925			0.989078
$362$	−3.94492	+	0.276625i	−0.207340	+	0.0145391i
$363$		0			0
$364$	−0.0152443	−	0.108164i	−0.000799021	−	0.00566936i
$365$	−11.7928	−	6.80856i	−0.617262	−	0.356377i
$366$		0			0
$367$	−5.23819	+	3.02427i	−0.273431	+	0.157866i	−0.630446	−	0.776233i	$-0.717128\pi$
$367$	−5.23819	+	3.02427i	−0.273431	+	0.157866i	0.357015	+	0.934099i	$0.383795\pi$
$368$	−3.43174	+	13.8096i	−0.178892	+	0.719877i
$369$		0			0
$370$	1.40988	+	0.687304i	0.0732960	+	0.0357312i
$371$	−5.32284	−	9.21944i	−0.276348	−	0.478649i
$372$		0			0
$373$	15.9639	−	27.6503i	0.826579	−	1.43168i	−0.0741274	−	0.997249i	$-0.523617\pi$
$373$	15.9639	−	27.6503i	0.826579	−	1.43168i	0.900706	−	0.434428i	$-0.143050\pi$
$374$	4.50263	−	3.03834i	0.232826	−	0.157109i
$375$		0			0
$376$	10.6864	+	11.8546i	0.551111	+	0.611354i
$377$		−	0.478319i		−	0.0246347i
$378$		0			0
$379$		−	4.79709i		−	0.246410i	−0.992381	−	0.123205i	$-0.960683\pi$
$379$		−	4.79709i		−	0.246410i	0.992381	−	0.123205i	$-0.0393172\pi$
$380$	−0.313266	+	0.776229i	−0.0160702	+	0.0398197i
$381$		0			0
$382$	−18.9903	−	28.1425i	−0.971628	−	1.43990i
$383$	4.80699	−	8.32595i	0.245626	−	0.425436i	−0.716682	−	0.697401i	$-0.754340\pi$
$383$	4.80699	−	8.32595i	0.245626	−	0.425436i	0.962307	+	0.271964i	$0.0876732\pi$
$384$		0			0
$385$	0.535361	+	0.927273i	0.0272845	+	0.0472582i
$386$	10.6335	−	21.8126i	0.541230	−	1.11023i
$387$		0			0
$388$	−10.5041	−	13.4339i	−0.533265	−	0.682002i
$389$	−2.41372	+	1.39356i	−0.122381	+	0.0706565i	−0.559941	−	0.828533i	$-0.689176\pi$
$389$	−2.41372	+	1.39356i	−0.122381	+	0.0706565i	0.437560	+	0.899189i	$0.355843\pi$
$390$		0			0
$391$	10.1536	+	5.86216i	0.513487	+	0.296462i
$392$	−0.872466	+	2.69050i	−0.0440662	+	0.135891i
$393$		0			0
$394$	−0.237487	−	3.38678i	−0.0119644	−	0.170623i
$395$	−11.5960			−0.583457
$396$		0			0
$397$	−1.09041			−0.0547262			−0.0273631	−	0.999626i	$-0.508711\pi$
$397$	−1.09041			−0.0547262			−0.0273631	+	0.999626i	$0.508711\pi$
$398$	0.247323	+	3.52705i	0.0123972	+	0.176795i
$399$		0			0
$400$	−11.9670	−	11.5384i	−0.598349	−	0.576922i
$401$	16.1356	+	9.31590i	0.805774	+	0.465214i	0.845486	−	0.533997i	$-0.179311\pi$
$401$	16.1356	+	9.31590i	0.805774	+	0.465214i	−0.0397119	+	0.999211i	$0.512644\pi$
$402$		0			0
$403$	−0.384075	+	0.221746i	−0.0191321	+	0.0110459i
$404$	−20.4531	+	15.9925i	−1.01758	+	0.795658i
$405$		0			0
$406$	−5.42721	+	11.1329i	−0.269348	+	0.552517i
$407$	−0.703427	−	1.21837i	−0.0348676	−	0.0603925i
$408$		0			0
$409$	−14.9066	+	25.8189i	−0.737082	+	1.27666i	0.216722	+	0.976233i	$0.430463\pi$
$409$	−14.9066	+	25.8189i	−0.737082	+	1.27666i	−0.953804	+	0.300430i	$0.902870\pi$
$410$	4.42472	+	6.55717i	0.218521	+	0.323835i
$411$		0			0
$412$	−4.19439	−	1.69275i	−0.206643	−	0.0833957i
$413$			1.48875i			0.0732564i
$414$		0			0
$415$			12.0540i			0.591710i
$416$	−0.0533548	+	0.304317i	−0.00261593	+	0.0149204i
$417$		0			0
$418$	0.622362	−	0.419964i	0.0304407	−	0.0205411i
$419$	1.72249	−	2.98343i	0.0841490	−	0.145750i	−0.820879	−	0.571102i	$-0.806516\pi$
$419$	1.72249	−	2.98343i	0.0841490	−	0.145750i	0.905028	+	0.425351i	$0.139850\pi$
$420$		0			0
$421$	7.39756	+	12.8130i	0.360535	+	0.624465i	0.988049	−	0.154140i	$-0.0492607\pi$
$421$	7.39756	+	12.8130i	0.360535	+	0.624465i	−0.627514	+	0.778605i	$0.715927\pi$
$422$	−3.93885	−	1.92016i	−0.191740	−	0.0934720i
$423$		0			0
$424$	6.27749	+	29.4489i	0.304862	+	1.43017i
$425$	−11.8618	+	6.84839i	−0.575380	+	0.332196i
$426$		0			0
$427$	−11.0152	−	6.35962i	−0.533062	−	0.307764i
$428$	−9.23638	+	1.30175i	−0.446457	+	0.0629222i
$429$		0			0
$430$	−8.44944	+	0.592491i	−0.407468	+	0.0285724i
$431$	16.9467			0.816293			0.408146	−	0.912917i	$-0.366175\pi$
$431$	16.9467			0.816293			0.408146	+	0.912917i	$0.366175\pi$
$432$		0			0
$433$	32.7900			1.57579			0.787894	−	0.615811i	$-0.211171\pi$
$433$	32.7900			1.57579			0.787894	+	0.615811i	$0.211171\pi$
$434$	11.4554	−	0.803273i	0.549876	−	0.0385583i
$435$		0			0
$436$	−22.0256	+	3.10421i	−1.05483	+	0.148665i
$437$	1.40344	+	0.810278i	0.0671358	+	0.0387609i
$438$		0			0
$439$	13.3048	−	7.68154i	0.635004	−	0.366620i	−0.147683	−	0.989035i	$-0.547182\pi$
$439$	13.3048	−	7.68154i	0.635004	−	0.366620i	0.782687	+	0.622415i	$0.213848\pi$
$440$	−0.631377	−	2.96191i	−0.0300997	−	0.141204i
$441$		0			0
$442$	0.228820	+	0.111548i	0.0108839	+	0.00530581i
$443$	8.16517	+	14.1425i	0.387939	+	0.671930i	0.992172	−	0.124878i	$-0.0398538\pi$
$443$	8.16517	+	14.1425i	0.387939	+	0.671930i	−0.604233	+	0.796807i	$0.706520\pi$
$444$		0			0
$445$	−3.65210	+	6.32563i	−0.173126	+	0.299863i
$446$	−9.93319	+	6.70282i	−0.470350	+	0.317388i
$447$		0			0
$448$	4.69474	−	6.47761i	0.221806	−	0.306038i
$449$			12.7313i			0.600828i	0.953809	+	0.300414i	$0.0971248\pi$
$449$			12.7313i			0.600828i	−0.953809	+	0.300414i	$0.902875\pi$
$450$		0			0
$451$		−	7.09526i		−	0.334103i
$452$	30.6229	+	12.3586i	1.44038	+	0.581300i
$453$		0			0
$454$	−10.6544	−	15.7891i	−0.500034	−	0.741021i
$455$	−0.0250895	+	0.0434562i	−0.00117621	+	0.00203726i
$456$		0			0
$457$	8.98114	+	15.5558i	0.420120	+	0.727669i	0.995951	−	0.0898997i	$-0.0286546\pi$
$457$	8.98114	+	15.5558i	0.420120	+	0.727669i	−0.575831	+	0.817569i	$0.695321\pi$
$458$	3.92714	−	8.05580i	0.183503	−	0.376423i
$459$		0			0
$460$	5.14945	−	4.02641i	0.240094	−	0.187732i
$461$	1.90455	−	1.09959i	0.0887038	−	0.0512132i	−0.454992	−	0.890496i	$-0.650358\pi$
$461$	1.90455	−	1.09959i	0.0887038	−	0.0512132i	0.543696	+	0.839282i	$0.317025\pi$
$462$		0			0
$463$	0.0470644	+	0.0271726i	0.00218727	+	0.00126282i	0.501093	−	0.865393i	$-0.332931\pi$
$463$	0.0470644	+	0.0271726i	0.00218727	+	0.00126282i	−0.498906	+	0.866656i	$0.666265\pi$
$464$	24.3150	−	25.2181i	1.12880	−	1.17072i
$465$		0			0
$466$	0.327260	+	4.66702i	0.0151600	+	0.216196i
$467$	−32.8935			−1.52213			−0.761065	−	0.648676i	$-0.775323\pi$
$467$	−32.8935			−1.52213			−0.761065	+	0.648676i	$0.775323\pi$
$468$		0			0
$469$	−6.73273			−0.310888
$470$	−0.512856	−	7.31378i	−0.0236563	−	0.337360i
$471$		0			0
$472$	1.29888	−	4.00548i	0.0597858	−	0.184367i
$473$	6.57951	+	3.79868i	0.302526	+	0.174664i
$474$		0			0
$475$	−1.63955	+	0.946597i	−0.0752279	+	0.0434329i
$476$	−4.06014	−	5.19258i	−0.186096	−	0.238002i
$477$		0			0
$478$	11.3743	−	23.3323i	0.520248	−	1.06719i
$479$	−8.02688	−	13.9030i	−0.366758	−	0.635243i	0.622299	−	0.782780i	$-0.286199\pi$
$479$	−8.02688	−	13.9030i	−0.366758	−	0.635243i	−0.989057	+	0.147537i	$0.952865\pi$
$480$		0			0
$481$	0.0329658	−	0.0570985i	0.00150311	−	0.00260347i
$482$	−16.7038	−	24.7540i	−0.760837	−	1.12751i
$483$		0			0
$484$	7.21683	−	17.8823i	0.328038	−	0.812830i
$485$			7.83370i			0.355710i
$486$		0			0
$487$			18.2339i			0.826258i	0.910673	+	0.413129i	$0.135564\pi$
$487$			18.2339i			0.826258i	−0.910673	+	0.413129i	$0.864436\pi$
$488$	24.0878	+	26.7209i	1.09040	+	1.20960i
$489$		0			0
$490$	1.07703	−	0.726771i	0.0486553	−	0.0328322i
$491$	−14.8772	+	25.7680i	−0.671398	+	1.16289i	0.306110	+	0.951996i	$0.400972\pi$
$491$	−14.8772	+	25.7680i	−0.671398	+	1.16289i	−0.977508	+	0.210899i	$0.932361\pi$
$492$		0			0
$493$	−14.4316	−	24.9963i	−0.649968	−	1.12578i
$494$	0.0316280	+	0.0154184i	0.00142301	+	0.000693707i
$495$		0			0
$496$	−31.5216	−	7.83322i	−1.41536	−	0.351722i
$497$	2.57338	−	1.48574i	0.115432	−	0.0666445i
$498$		0			0
$499$	37.1029	+	21.4213i	1.66095	+	0.958951i	0.972262	+	0.233895i	$0.0751473\pi$
$499$	37.1029	+	21.4213i	1.66095	+	0.958951i	0.688690	+	0.725056i	$0.258186\pi$
$500$	2.34791	+	16.6593i	0.105002	+	0.745026i
$501$		0			0
$502$	−19.6729	+	1.37950i	−0.878043	+	0.0615700i
$503$	−14.2832			−0.636855			−0.318427	−	0.947947i	$-0.603155\pi$
$503$	−14.2832			−0.636855			−0.318427	+	0.947947i	$0.603155\pi$
$504$		0			0
$505$	11.9268			0.530737
$506$	−5.84878	+	0.410127i	−0.260010	+	0.0182324i
$507$		0			0
$508$	4.91997	+	34.9091i	0.218288	+	1.54884i
$509$	−18.9344	−	10.9318i	−0.839254	−	0.484543i	0.0177568	−	0.999842i	$-0.494348\pi$
$509$	−18.9344	−	10.9318i	−0.839254	−	0.484543i	−0.857010	+	0.515299i	$0.827681\pi$
$510$		0			0
$511$	12.8357	−	7.41070i	0.567819	−	0.327830i
$512$	−18.2827	+	13.3320i	−0.807989	+	0.589198i
$513$		0			0
$514$	13.6882	+	6.67291i	0.603762	+	0.294330i
$515$	1.03889	+	1.79941i	0.0457791	+	0.0792917i
$516$		0			0
$517$	−3.28812	+	5.69518i	−0.144611	+	0.250474i
$518$	−1.41514	+	0.954927i	−0.0621779	+	0.0419571i
$519$		0			0
$520$	0.105417	−	0.0950294i	0.00462286	−	0.00416732i
$521$		−	39.6382i		−	1.73658i	−0.496055	−	0.868291i	$-0.665219\pi$
$521$		−	39.6382i		−	1.73658i	0.496055	−	0.868291i	$-0.334781\pi$
$522$		0			0
$523$		−	16.0515i		−	0.701885i	−0.936397	−	0.350943i	$-0.885861\pi$
$523$		−	16.0515i		−	0.701885i	0.936397	−	0.350943i	$-0.114139\pi$
$524$	11.4125	−	28.2786i	0.498559	−	1.23536i
$525$		0			0
$526$	12.8584	+	19.0553i	0.560651	+	0.830852i
$527$	−13.3808	+	23.1763i	−0.582878	+	1.00957i
$528$		0			0
$529$	5.17240	+	8.95887i	0.224887	+	0.389516i
$530$	6.06114	−	12.4333i	0.263279	−	0.540068i
$531$		0			0
$532$	−0.561200	−	0.717728i	−0.0243311	−	0.0311175i
$533$	0.287968	−	0.166258i	0.0124733	−	0.00720144i
$534$		0			0
$535$	3.71082	+	2.14244i	0.160433	+	0.0926258i
$536$	18.1144	+	5.87407i	0.782424	+	0.253721i
$537$		0			0
$538$	−0.901115	−	12.8507i	−0.0388498	−	0.554033i
$539$	−1.16542			−0.0501980
$540$		0			0
$541$	−22.6938			−0.975681			−0.487841	−	0.872933i	$-0.662215\pi$
$541$	−22.6938			−0.975681			−0.487841	+	0.872933i	$0.662215\pi$
$542$	3.13660	+	44.7307i	0.134728	+	1.92135i
$543$		0			0
$544$	6.39346	+	17.5130i	0.274117	+	0.750863i
$545$	8.84901	+	5.10898i	0.379050	+	0.218845i
$546$		0			0
$547$	6.24436	−	3.60518i	0.266990	−	0.154147i	−0.360529	−	0.932748i	$-0.617404\pi$
$547$	6.24436	−	3.60518i	0.266990	−	0.154147i	0.627519	+	0.778601i	$0.284071\pi$
$548$	10.2730	−	8.03254i	0.438839	−	0.343133i
$549$		0			0
$550$	3.00144	−	6.15691i	0.127982	−	0.262531i
$551$	−1.99477	−	3.45504i	−0.0849799	−	0.147190i
$552$		0			0
$553$	6.31075	−	10.9305i	0.268361	−	0.464814i
$554$	1.26778	+	1.87878i	0.0538629	+	0.0798217i
$555$		0			0
$556$	14.8527	+	5.99419i	0.629896	+	0.254210i
$557$			20.7466i			0.879063i	0.898227	+	0.439531i	$0.144855\pi$
$557$			20.7466i			0.879063i	−0.898227	+	0.439531i	$0.855145\pi$
$558$		0			0
$559$			0.356047i			0.0150592i
$560$	−3.53184	+	1.01571i	−0.149247	+	0.0429214i
$561$		0			0
$562$	−25.8657	+	17.4540i	−1.09108	+	0.736251i
$563$	23.5052	−	40.7122i	0.990625	−	1.71581i	0.377006	−	0.926211i	$-0.376954\pi$
$563$	23.5052	−	40.7122i	0.990625	−	1.71581i	0.613619	−	0.789602i	$-0.289713\pi$
$564$		0			0
$565$	−7.58487	−	13.1374i	−0.319098	−	0.552694i
$566$	26.5260	+	12.9312i	1.11497	+	0.543539i
$567$		0			0
$568$	−8.21993	+	1.75220i	−0.344901	+	0.0735208i
$569$	27.5683	−	15.9166i	1.15572	−	0.667258i	0.205449	−	0.978668i	$-0.434135\pi$
$569$	27.5683	−	15.9166i	1.15572	−	0.667258i	0.950276	+	0.311410i	$0.100801\pi$
$570$		0			0
$571$	−21.1494	−	12.2106i	−0.885077	−	0.510999i	−0.0127478	−	0.999919i	$-0.504058\pi$
$571$	−21.1494	−	12.2106i	−0.885077	−	0.510999i	−0.872329	+	0.488919i	$0.837391\pi$
$572$	−0.126057	+	0.0177660i	−0.00527069	+	0.000742834i
$573$		0			0
$574$	−8.58890	+	0.602270i	−0.358494	+	0.0251383i
$575$	14.7843			0.616547
$576$		0			0
$577$	−35.7568			−1.48858			−0.744288	−	0.667859i	$-0.767211\pi$
$577$	−35.7568			−1.48858			−0.744288	+	0.667859i	$0.767211\pi$
$578$	−8.65930	+	0.607206i	−0.360179	+	0.0252565i
$579$		0			0
$580$	−15.9348	+	2.24580i	−0.661658	+	0.0932519i
$581$	−11.3623	−	6.56004i	−0.471389	−	0.272156i
$582$		0			0
$583$	−10.7445	+	6.20333i	−0.444991	+	0.256916i
$584$	−41.0001	+	8.73980i	−1.69660	+	0.361655i
$585$		0			0
$586$	23.5865	+	11.4982i	0.974349	+	0.474988i
$587$	12.1011	+	20.9597i	0.499466	+	0.865100i	1.00000		0.000616829i	$-0.000196343\pi$
$587$	12.1011	+	20.9597i	0.499466	+	0.865100i	−0.500534	+	0.865717i	$0.666863\pi$
$588$		0			0
$589$	−1.84952	+	3.20347i	−0.0762082	+	0.131996i
$590$	−1.60343	+	1.08198i	−0.0660121	+	0.0445443i
$591$		0			0
$592$	4.64059	−	1.33457i	0.190727	−	0.0548504i
$593$			4.63066i			0.190159i	0.995470	+	0.0950793i	$0.0303105\pi$
$593$			4.63066i			0.190159i	−0.995470	+	0.0950793i	$0.969690\pi$
$594$		0			0
$595$			3.02795i			0.124134i
$596$	−3.02155	−	1.21942i	−0.123767	−	0.0499494i
$597$		0			0
$598$	−0.153696	−	0.227768i	−0.00628508	−	0.00931411i
$599$	−1.31442	+	2.27665i	−0.0537059	+	0.0930213i	−0.891628	−	0.452768i	$-0.850437\pi$
$599$	−1.31442	+	2.27665i	−0.0537059	+	0.0930213i	0.837923	+	0.545789i	$0.183770\pi$
$600$		0			0
$601$	−16.4497	−	28.4918i	−0.670998	−	1.16220i	−0.977621	−	0.210372i	$-0.932533\pi$
$601$	−16.4497	−	28.4918i	−0.670998	−	1.16220i	0.306623	−	0.951831i	$-0.400801\pi$
$602$	4.03986	−	8.28702i	0.164652	−	0.337754i
$603$		0			0
$604$	8.06762	−	6.30816i	0.328267	−	0.256675i
$605$	−7.67159	+	4.42919i	−0.311894	+	0.180072i
$606$		0			0
$607$	−6.79813	−	3.92490i	−0.275928	−	0.159307i	0.355651	−	0.934619i	$-0.384259\pi$
$607$	−6.79813	−	3.92490i	−0.275928	−	0.159307i	−0.631578	+	0.775312i	$0.717593\pi$
$608$	0.883716	+	2.42068i	0.0358394	+	0.0981714i
$609$		0			0
$610$	−1.15601	−	16.4857i	−0.0468054	−	0.667486i
$611$	−0.308192			−0.0124681
$612$		0			0
$613$	22.6778			0.915950			0.457975	−	0.888965i	$-0.348575\pi$
$613$	22.6778			0.915950			0.457975	+	0.888965i	$0.348575\pi$
$614$	−0.308452	−	4.39880i	−0.0124481	−	0.177521i
$615$		0			0
$616$	3.13555	+	1.01679i	0.126335	+	0.0409674i
$617$	−16.7478	−	9.66936i	−0.674242	−	0.389274i	0.123440	−	0.992352i	$-0.460607\pi$
$617$	−16.7478	−	9.66936i	−0.674242	−	0.389274i	−0.797682	+	0.603078i	$0.793941\pi$
$618$		0			0
$619$	−10.3351	+	5.96696i	−0.415402	+	0.239832i	−0.693108	−	0.720834i	$-0.743759\pi$
$619$	−10.3351	+	5.96696i	−0.415402	+	0.239832i	0.277706	+	0.960666i	$0.410426\pi$
$620$	9.19059	+	11.7540i	0.369103	+	0.472052i
$621$		0			0
$622$	−13.1366	+	26.9472i	−0.526728	+	1.08049i
$623$	−3.97509	−	6.88506i	−0.159259	−	0.275844i
$624$		0			0
$625$	−6.52552	+	11.3025i	−0.261021	+	0.452102i
$626$	−18.6627	−	27.6570i	−0.745912	−	1.10540i
$627$		0			0
$628$	0.362281	−	0.897680i	0.0144566	−	0.0358213i
$629$		−	3.97852i		−	0.158634i
$630$		0			0
$631$		−	4.63442i		−	0.184493i	−0.995736	−	0.0922467i	$-0.970595\pi$
$631$		−	4.63442i		−	0.184493i	0.995736	−	0.0922467i	$-0.0294048\pi$
$632$	−26.5156	+	23.9027i	−1.05473	+	0.950800i
$633$		0			0
$634$	21.4030	−	14.4426i	0.850023	−	0.573588i
$635$	8.09740	−	14.0251i	0.321335	−	0.556569i
$636$		0			0
$637$	−0.0273083	−	0.0472994i	−0.00108200	−	0.00187407i
$638$	12.9745	+	6.32495i	0.513664	+	0.250407i
$639$		0			0
$640$	10.3886	+	0.348646i	0.410645	+	0.0137814i
$641$	−7.36518	+	4.25229i	−0.290907	+	0.167955i	−0.638351	−	0.769746i	$-0.720383\pi$
$641$	−7.36518	+	4.25229i	−0.290907	+	0.167955i	0.347444	+	0.937701i	$0.387050\pi$
$642$		0			0
$643$	42.3444	+	24.4476i	1.66990	+	0.964118i	0.967688	+	0.252150i	$0.0811376\pi$
$643$	42.3444	+	24.4476i	1.66990	+	0.964118i	0.702212	+	0.711968i	$0.252196\pi$
$644$	0.992928	+	7.04520i	0.0391268	+	0.277620i
$645$		0			0
$646$	2.11803	−	0.148520i	0.0833329	−	0.00584346i
$647$	19.0364			0.748397			0.374198	−	0.927349i	$-0.377918\pi$
$647$	19.0364			0.748397			0.374198	+	0.927349i	$0.377918\pi$
$648$		0			0
$649$	1.73501			0.0681051
$650$	0.320214	−	0.0224540i	0.0125598	−	0.000880719i
$651$		0			0
$652$	6.64511	+	47.1496i	0.260243	+	1.84652i
$653$	38.4290	+	22.1870i	1.50384	+	0.868244i	0.999990	+	0.00445434i	$0.00141786\pi$
$653$	38.4290	+	22.1870i	1.50384	+	0.868244i	0.503853	+	0.863790i	$0.331915\pi$
$654$		0			0
$655$	−12.1317	+	7.00424i	−0.474024	+	0.273678i
$656$	23.6339	+	5.87311i	0.922749	+	0.229306i
$657$		0			0
$658$	7.17319	+	3.49688i	0.279640	+	0.136322i
$659$	8.10116	+	14.0316i	0.315577	+	0.546595i	0.979560	−	0.201153i	$-0.0644688\pi$
$659$	8.10116	+	14.0316i	0.315577	+	0.546595i	−0.663983	+	0.747747i	$0.731135\pi$
$660$		0			0
$661$	5.05531	−	8.75605i	0.196629	−	0.340571i	−0.750805	−	0.660524i	$-0.770334\pi$
$661$	5.05531	−	8.75605i	0.196629	−	0.340571i	0.947433	+	0.319954i	$0.103667\pi$
$662$	−26.5518	+	17.9169i	−1.03196	+	0.696360i
$663$		0			0
$664$	24.8470	+	27.5630i	0.964249	+	1.06965i
$665$			0.418529i			0.0162299i
$666$		0			0
$667$			31.1549i			1.20632i
$668$	−14.0376	+	34.7832i	−0.543132	+	1.34580i
$669$		0			0
$670$	−4.89315	−	7.25136i	−0.189039	−	0.280144i
$671$	−7.41160	+	12.8373i	−0.286122	+	0.495577i
$672$		0			0
$673$	−6.81031	−	11.7958i	−0.262518	−	0.454694i	0.704392	−	0.709811i	$-0.251220\pi$
$673$	−6.81031	−	11.7958i	−0.262518	−	0.454694i	−0.966910	+	0.255116i	$0.917886\pi$
$674$	−3.27014	+	6.70809i	−0.125961	+	0.258386i
$675$		0			0
$676$	16.0115	+	20.4774i	0.615826	+	0.787591i
$677$	18.1315	−	10.4682i	0.696851	−	0.402327i	−0.109322	−	0.994006i	$-0.534868\pi$
$677$	18.1315	−	10.4682i	0.696851	−	0.402327i	0.806174	+	0.591679i	$0.201535\pi$
$678$		0			0
$679$	−7.38417	−	4.26325i	−0.283378	−	0.163609i
$680$	2.64179	−	8.14672i	0.101308	−	0.312412i
$681$		0			0
$682$	−0.936146	−	13.3503i	−0.0358469	−	0.511209i
$683$	−16.0167			−0.612864			−0.306432	−	0.951893i	$-0.599135\pi$
$683$	−16.0167			−0.612864			−0.306432	+	0.951893i	$0.599135\pi$
$684$		0			0
$685$	−5.99048			−0.228884
$686$	0.0989244	+	1.41075i	0.00377695	+	0.0538627i
$687$		0			0
$688$	−18.0994	+	18.7716i	−0.690032	+	0.715661i
$689$	−0.503535	−	0.290716i	−0.0191832	−	0.0110754i
$690$		0			0
$691$	−35.2063	+	20.3264i	−1.33931	+	0.773251i	−0.986705	−	0.162521i	$-0.948037\pi$
$691$	−35.2063	+	20.3264i	−1.33931	+	0.773251i	−0.352605	+	0.935772i	$0.614704\pi$
$692$	−27.9900	+	21.8857i	−1.06402	+	0.831968i
$693$		0			0
$694$	−4.63471	+	9.50724i	−0.175931	+	0.360890i
$695$	−3.67882	−	6.37190i	−0.139546	−	0.241700i
$696$		0			0
$697$	10.0325	−	17.3769i	0.380010	−	0.658196i
$698$	14.2401	+	21.1030i	0.538997	+	0.798761i
$699$		0			0
$700$	−7.70778	−	3.11067i	−0.291327	−	0.117572i
$701$		−	5.64269i		−	0.213122i	−0.994306	−	0.106561i	$-0.966016\pi$
$701$		−	5.64269i		−	0.213122i	0.994306	−	0.106561i	$-0.0339839\pi$
$702$		0			0
$703$		−	0.549918i		−	0.0207406i
$704$	−7.54911	−	5.47133i	−0.284518	−	0.206208i
$705$		0			0
$706$	−5.13726	+	3.46658i	−0.193343	+	0.130466i
$707$	−6.49081	+	11.2424i	−0.244112	+	0.422815i
$708$		0			0
$709$	−2.58052	−	4.46959i	−0.0969134	−	0.167859i	0.813492	−	0.581576i	$-0.197564\pi$
$709$	−2.58052	−	4.46959i	−0.0969134	−	0.167859i	−0.910406	+	0.413717i	$0.864230\pi$
$710$	3.47044	+	1.69182i	0.130243	+	0.0634927i
$711$		0			0
$712$	4.68801	+	21.9924i	0.175691	+	0.824200i
$713$	25.0164	−	14.4432i	0.936871	−	0.540903i
$714$		0			0
$715$	0.0506446	+	0.0292397i	0.00189400	+	0.00109350i
$716$	14.2182	−	2.00386i	0.531358	−	0.0748879i
$717$		0			0
$718$	39.0626	−	2.73915i	1.45780	−	0.102224i
$719$	28.4079			1.05944			0.529718	−	0.848174i	$-0.322298\pi$
$719$	28.4079			1.05944			0.529718	+	0.848174i	$0.322298\pi$
$720$		0			0
$721$	−2.26154			−0.0842242
$722$	−26.5115	+	1.85903i	−0.986655	+	0.0691861i
$723$		0			0
$724$	5.53792	−	0.780497i	0.205815	−	0.0290069i
$725$	−31.5202	−	18.1982i	−1.17063	−	0.675863i
$726$		0			0
$727$	−31.9367	+	18.4386i	−1.18447	+	0.683852i	−0.957043	−	0.289945i	$-0.906363\pi$
$727$	−31.9367	+	18.4386i	−1.18447	+	0.683852i	−0.227422	+	0.973796i	$0.573030\pi$
$728$	0.0322060	+	0.151085i	0.00119364	+	0.00559958i
$729$		0			0
$730$	17.3102	+	8.43859i	0.640679	+	0.312326i
$731$	10.7425	+	18.6065i	0.397325	+	0.688188i
$732$		0			0
$733$	4.51056	−	7.81251i	0.166601	−	0.288562i	−0.770622	−	0.637293i	$-0.780054\pi$
$733$	4.51056	−	7.81251i	0.166601	−	0.288562i	0.937223	+	0.348731i	$0.113387\pi$
$734$	7.09060	−	4.78467i	0.261719	−	0.176606i
$735$		0			0
$736$	3.47522	−	19.8214i	0.128098	−	0.730627i
$737$			7.84642i			0.289027i
$738$		0			0
$739$		−	43.2538i		−	1.59112i	−0.605876	−	0.795559i	$-0.707177\pi$
$739$		−	43.2538i		−	1.59112i	0.605876	−	0.795559i	$-0.292823\pi$
$740$	−2.05697	−	0.830142i	−0.0756158	−	0.0305166i
$741$		0			0
$742$	8.42123	+	12.4798i	0.309153	+	0.458146i
$743$	14.3410	−	24.8394i	0.526121	−	0.911268i	−0.473416	−	0.880839i	$-0.656979\pi$
$743$	14.3410	−	24.8394i	0.526121	−	0.911268i	0.999537	−	0.0304290i	$-0.00968733\pi$
$744$		0			0
$745$	0.748397	+	1.29626i	0.0274191	+	0.0474913i
$746$	−19.7858	+	40.5868i	−0.724408	+	1.48599i
$747$		0			0
$748$	−6.05152	+	4.73175i	−0.221265	+	0.173010i
$749$	−4.03900	+	2.33192i	−0.147582	+	0.0852063i
$750$		0			0
$751$	−5.83084	−	3.36644i	−0.212771	−	0.122843i	0.389828	−	0.920888i	$-0.372535\pi$
$751$	−5.83084	−	3.36644i	−0.212771	−	0.122843i	−0.602598	+	0.798045i	$0.705868\pi$
$752$	−16.2486	−	15.6667i	−0.592525	−	0.571306i
$753$		0			0
$754$	0.0473174	+	0.674789i	0.00172320	+	0.0245744i
$755$	−4.70447			−0.171213
$756$		0			0
$757$	−29.3645			−1.06727			−0.533636	−	0.845714i	$-0.679175\pi$
$757$	−29.3645			−1.06727			−0.533636	+	0.845714i	$0.679175\pi$
$758$	0.474549	+	6.76749i	0.0172364	+	0.245806i
$759$		0			0
$760$	0.365152	−	1.12605i	0.0132455	−	0.0408463i
$761$	37.4743	+	21.6358i	1.35844	+	0.784297i	0.989414	−	0.145121i	$-0.0463571\pi$
$761$	37.4743	+	21.6358i	1.35844	+	0.784297i	0.369029	+	0.929418i	$0.379690\pi$
$762$		0			0
$763$	−9.63160	+	5.56081i	−0.348687	+	0.201315i
$764$	29.5745	+	37.8234i	1.06997	+	1.36840i
$765$		0			0
$766$	−5.95782	+	12.2214i	−0.215265	+	0.441576i
$767$	0.0406552	+	0.0704169i	0.00146797	+	0.00254261i
$768$		0			0
$769$	−7.23929	+	12.5388i	−0.261055	+	0.452161i	−0.966523	−	0.256581i	$-0.917404\pi$
$769$	−7.23929	+	12.5388i	−0.261055	+	0.452161i	0.705467	+	0.708743i	$0.250737\pi$
$770$	−0.846991	−	1.25519i	−0.0305234	−	0.0452339i
$771$		0			0
$772$	−12.8434	+	31.8241i	−0.462243	+	1.14537i
$773$		−	14.1120i		−	0.507575i	−0.967260	−	0.253787i	$-0.918324\pi$
$773$		−	14.1120i		−	0.507575i	0.967260	−	0.253787i	$-0.0816764\pi$
$774$		0			0
$775$			33.7462i			1.21220i
$776$	16.1476	+	17.9127i	0.579664	+	0.643029i
$777$		0			0
$778$	3.26730	−	2.20475i	0.117138	−	0.0790440i
$779$	1.38672	−	2.40186i	0.0496843	−	0.0860556i
$780$		0			0
$781$	−1.73150	−	2.99905i	−0.0619581	−	0.107315i
$782$	−14.9040	−	7.26560i	−0.532967	−	0.259817i
$783$		0			0
$784$	0.964674	−	3.88193i	0.0344526	−	0.138640i
$785$	−0.385110	+	0.222343i	−0.0137451	+	0.00793577i
$786$		0			0
$787$	−27.4914	−	15.8722i	−0.979962	−	0.565781i	−0.0777033	−	0.996977i	$-0.524759\pi$
$787$	−27.4914	−	15.8722i	−0.979962	−	0.565781i	−0.902259	+	0.431195i	$0.858092\pi$
$788$	0.670069	+	4.75440i	0.0238702	+	0.169368i
$789$		0			0
$790$	16.3590	−	1.14712i	0.582028	−	0.0408129i
$791$	16.5113			0.587075
$792$		0			0
$793$	−0.694683			−0.0246689
$794$	1.53830	−	0.107868i	0.0545922	−	0.00382811i
$795$		0			0
$796$	−0.697822	−	4.95132i	−0.0247337	−	0.175495i
$797$	−12.4676	−	7.19816i	−0.441624	−	0.254972i	0.262662	−	0.964888i	$-0.415400\pi$
$797$	−12.4676	−	7.19816i	−0.441624	−	0.254972i	−0.704286	+	0.709916i	$0.748733\pi$
$798$		0			0
$799$	−16.1057	+	9.29864i	−0.569779	+	0.328962i
$800$	18.0239	+	15.0940i	0.637240	+	0.533654i
$801$		0			0
$802$	−23.6849	−	11.5462i	−0.836342	−	0.407711i
$803$	−8.63655	−	14.9589i	−0.304777	−	0.527890i
$804$		0			0
$805$	1.63418	−	2.83049i	0.0575974	−	0.0997615i
$806$	0.519897	−	0.350822i	0.0183126	−	0.0123572i
$807$		0			0
$808$	27.2722	−	24.5848i	0.959432	−	0.864889i
$809$			1.47726i			0.0519378i	0.999663	+	0.0259689i	$0.00826709\pi$
$809$			1.47726i			0.0519378i	−0.999663	+	0.0259689i	$0.991733\pi$
$810$		0			0
$811$		−	36.8994i		−	1.29571i	−0.761763	−	0.647856i	$-0.775666\pi$
$811$		−	36.8994i		−	1.29571i	0.761763	−	0.647856i	$-0.224334\pi$
$812$	6.55512	−	16.2426i	0.230039	−	0.570005i
$813$		0			0
$814$	1.11289	+	1.64923i	0.0390067	+	0.0578055i
$815$	10.9367	−	18.9429i	0.383095	−	0.663540i
$816$		0			0
$817$	1.48485	+	2.57183i	0.0519482	+	0.0899770i
$818$	18.4753	−	37.8986i	0.645973	−	1.32509i
$819$		0			0
$820$	−6.89083	−	8.81281i	−0.240638	−	0.307757i
$821$	9.12991	−	5.27116i	0.318636	−	0.183965i	−0.332148	−	0.943227i	$-0.607773\pi$
$821$	9.12991	−	5.27116i	0.318636	−	0.183965i	0.650785	+	0.759262i	$0.274440\pi$
$822$		0			0
$823$	22.1348	+	12.7795i	0.771571	+	0.445466i	0.833435	−	0.552618i	$-0.186371\pi$
$823$	22.1348	+	12.7795i	0.771571	+	0.445466i	−0.0618640	+	0.998085i	$0.519705\pi$
$824$	6.08468	+	1.97312i	0.211970	+	0.0687368i
$825$		0			0
$826$	−0.147273	−	2.10025i	−0.00512430	−	0.0730770i
$827$	12.8344			0.446296			0.223148	−	0.974785i	$-0.428367\pi$
$827$	12.8344			0.446296			0.223148	+	0.974785i	$0.428367\pi$
$828$		0			0
$829$	−32.1144			−1.11538			−0.557689	−	0.830050i	$-0.688312\pi$
$829$	−32.1144			−1.11538			−0.557689	+	0.830050i	$0.688312\pi$
$830$	−1.19244	−	17.0052i	−0.0413902	−	0.590260i
$831$		0			0
$832$	0.0451659	−	0.434593i	0.00156585	−	0.0150668i
$833$	−2.85420	−	1.64787i	−0.0988920	−	0.0570953i
$834$		0			0
$835$	14.9222	−	8.61533i	0.516404	−	0.298146i
$836$	−0.836452	+	0.654031i	−0.0289293	+	0.0226201i
$837$		0			0
$838$	−2.13486	+	4.37927i	−0.0737476	+	0.151280i
$839$	−0.741866	−	1.28495i	−0.0256121	−	0.0443614i	0.852935	−	0.522017i	$-0.174820\pi$
$839$	−0.741866	−	1.28495i	−0.0256121	−	0.0443614i	−0.878547	+	0.477655i	$0.841487\pi$
$840$		0			0
$841$	23.8491	−	41.3078i	0.822382	−	1.42441i
$842$	−11.7036	−	17.3441i	−0.403333	−	0.597716i
$843$		0			0
$844$	5.74669	+	2.31922i	0.197809	+	0.0798308i
$845$		−	11.9410i		−	0.410782i
$846$		0			0
$847$		−	9.64181i		−	0.331296i
$848$	−11.7692	−	40.9240i	−0.404155	−	1.40534i
$849$		0			0
$850$	16.0565	−	10.8348i	0.550733	−	0.371630i
$851$	−2.14720	+	3.71906i	−0.0736051	+	0.127488i
$852$		0			0
$853$	2.68864	+	4.65687i	0.0920574	+	0.159448i	0.908377	−	0.418153i	$-0.137322\pi$
$853$	2.68864	+	4.65687i	0.0920574	+	0.159448i	−0.816319	+	0.577601i	$0.803989\pi$
$854$	16.1688	+	7.88216i	0.553284	+	0.269722i
$855$		0			0
$856$	12.9014	−	2.75014i	0.440962	−	0.0939978i
$857$	13.2302	−	7.63847i	0.451936	−	0.260925i	−0.256712	−	0.966488i	$-0.582639\pi$
$857$	13.2302	−	7.63847i	0.451936	−	0.260925i	0.708647	+	0.705563i	$0.249306\pi$
$858$		0			0
$859$	−7.89410	−	4.55766i	−0.269343	−	0.155505i	0.359246	−	0.933243i	$-0.383034\pi$
$859$	−7.89410	−	4.55766i	−0.269343	−	0.155505i	−0.628589	+	0.777738i	$0.716367\pi$
$860$	11.8614	−	1.67171i	0.404471	−	0.0570049i
$861$		0			0
$862$	−23.9075	+	1.67644i	−0.814293	+	0.0570998i
$863$	14.0671			0.478851			0.239425	−	0.970915i	$-0.423041\pi$
$863$	14.0671			0.478851			0.239425	+	0.970915i	$0.423041\pi$
$864$		0			0
$865$	16.3218			0.554958
$866$	−46.2585	+	3.24373i	−1.57193	+	0.110227i
$867$		0			0
$868$	−16.0812	+	2.26643i	−0.545832	+	0.0769277i
$869$	−12.7386	−	7.35465i	−0.432128	−	0.249489i
$870$		0			0
$871$	−0.318454	+	0.183860i	−0.0107904	+	0.00622985i
$872$	30.7655	−	6.55813i	1.04185	−	0.222086i
$873$		0			0
$874$	−2.06006	−	1.00426i	−0.0696827	−	0.0339698i
$875$	4.20598	+	7.28497i	0.142188	+	0.246277i
$876$		0			0
$877$	14.8307	−	25.6875i	0.500796	−	0.867404i	−0.499204	−	0.866485i	$-0.666374\pi$
$877$	14.8307	−	25.6875i	0.500796	−	0.867404i	1.00000		0.000919420i	$-0.000292660\pi$
$878$	−18.0099	+	12.1529i	−0.607804	+	0.410140i
$879$		0			0
$880$	1.18372	+	4.11606i	0.0399032	+	0.138752i
$881$			14.6998i			0.495250i	0.968856	+	0.247625i	$0.0796502\pi$
$881$			14.6998i			0.495250i	−0.968856	+	0.247625i	$0.920350\pi$
$882$		0			0
$883$		−	2.75888i		−	0.0928439i	−0.998922	−	0.0464219i	$-0.985218\pi$
$883$		−	2.75888i		−	0.0928439i	0.998922	−	0.0464219i	$-0.0147819\pi$
$884$	−0.333843	−	0.134731i	−0.0112284	−	0.00453148i
$885$		0			0
$886$	−12.9180	−	19.1438i	−0.433990	−	0.643148i
$887$	5.47009	−	9.47448i	0.183668	−	0.318122i	−0.759459	−	0.650555i	$-0.774536\pi$
$887$	5.47009	−	9.47448i	0.183668	−	0.318122i	0.943127	+	0.332433i	$0.107870\pi$
$888$		0			0
$889$	8.81352	+	15.2655i	0.295596	+	0.511987i
$890$	4.52644	−	9.28516i	0.151727	−	0.311239i
$891$		0			0
$892$	13.3502	−	10.4386i	0.446997	−	0.349511i
$893$	−2.22616	+	1.28527i	−0.0744956	+	0.0430101i
$894$		0			0
$895$	−5.71231	−	3.29800i	−0.190941	−	0.110240i
$896$	−5.98231	+	9.60271i	−0.199855	+	0.320804i
$897$		0			0
$898$	−1.25944	−	17.9607i	−0.0420280	−	0.599356i
$899$	−71.1135			−2.37177
$900$		0			0
$901$	−35.0854			−1.16887
$902$	0.701895	+	10.0096i	0.0233705	+	0.333285i
$903$		0			0
$904$	−44.4238	−	14.4056i	−1.47751	−	0.479122i
$905$	−2.22492	−	1.28456i	−0.0739589	−	0.0427002i
$906$		0			0
$907$	3.75470	−	2.16778i	0.124673	−	0.0719798i	−0.436367	−	0.899769i	$-0.643735\pi$
$907$	3.75470	−	2.16778i	0.124673	−	0.0719798i	0.561039	+	0.827789i	$0.310402\pi$
$908$	16.5926	+	21.2206i	0.550644	+	0.704229i
$909$		0			0
$910$	0.0310961	−	0.0637878i	0.00103083	−	0.00211455i
$911$	−28.0150	−	48.5233i	−0.928177	−	1.60765i	−0.786371	−	0.617755i	$-0.788042\pi$
$911$	−28.0150	−	48.5233i	−0.928177	−	1.60765i	−0.141806	−	0.989894i	$-0.545291\pi$
$912$		0			0
$913$	−7.64518	+	13.2418i	−0.253018	+	0.438241i
$914$	−14.2090	−	21.0569i	−0.469991	−	0.696499i
$915$		0			0
$916$	−4.74330	+	11.7532i	−0.156723	+	0.388337i
$917$		−	15.2474i		−	0.503512i
$918$		0			0
$919$			10.2488i			0.338077i	0.985609	+	0.169039i	$0.0540662\pi$
$919$			10.2488i			0.338077i	−0.985609	+	0.169039i	$0.945934\pi$
$920$	−6.86627	+	6.18966i	−0.226374	+	0.204067i
$921$		0			0
$922$	−2.57807	+	1.73966i	−0.0849042	+	0.0572926i
$923$	0.0811462	−	0.140549i	0.00267096	−	0.00462624i
$924$		0			0
$925$	−2.50844	−	4.34475i	−0.0824770	−	0.142854i
$926$	−0.0690841	−	0.0336780i	−0.00227024	−	0.00110673i
$927$		0			0
$928$	−31.8077	+	37.9817i	−1.04414	+	1.24681i
$929$	21.0194	−	12.1356i	0.689624	−	0.398155i	−0.113847	−	0.993498i	$-0.536317\pi$
$929$	21.0194	−	12.1356i	0.689624	−	0.398155i	0.803471	+	0.595344i	$0.202984\pi$
$930$		0			0
$931$	−0.394512	−	0.227772i	−0.0129296	−	0.00746492i
$932$	−0.923365	−	6.55163i	−0.0302458	−	0.214606i
$933$		0			0
$934$	46.4045	−	3.25397i	1.51840	−	0.106473i
$935$	3.52883			0.115405
$936$		0			0
$937$	39.8014			1.30026			0.650128	−	0.759825i	$-0.274715\pi$
$937$	39.8014			1.30026			0.650128	+	0.759825i	$0.274715\pi$
$938$	9.49819	−	0.666031i	0.310127	−	0.0217467i
$939$		0			0
$940$	1.44702	+	10.2672i	0.0471967	+	0.334879i
$941$	34.3146	+	19.8115i	1.11862	+	0.645837i	0.941049	−	0.338271i	$-0.109842\pi$
$941$	34.3146	+	19.8115i	1.11862	+	0.645837i	0.177574	+	0.984108i	$0.443175\pi$
$942$		0			0
$943$	−18.7565	+	10.8291i	−0.610797	+	0.352644i
$944$	−1.43616	+	5.77922i	−0.0467429	+	0.188097i
$945$		0			0
$946$	−9.65782	−	4.70811i	−0.314003	−	0.153074i
$947$	8.83985	+	15.3111i	0.287257	+	0.497543i	0.973154	−	0.230155i	$-0.0739234\pi$
$947$	8.83985	+	15.3111i	0.287257	+	0.497543i	−0.685897	+	0.727698i	$0.740590\pi$
$948$		0			0
$949$	0.404748	−	0.701044i	0.0131387	−	0.0227569i
$950$	2.21936	−	1.49760i	0.0720055	−	0.0485887i
$951$		0			0
$952$	6.24151	+	6.92379i	0.202289	+	0.224401i
$953$			18.2570i			0.591403i	0.955280	+	0.295701i	$0.0955533\pi$
$953$			18.2570i			0.591403i	−0.955280	+	0.295701i	$0.904447\pi$
$954$		0			0
$955$		−	22.0560i		−	0.713715i
$956$	−13.7382	+	34.0412i	−0.444324	+	1.10097i
$957$		0			0
$958$	12.6993	+	18.8195i	0.410294	+	0.608032i
$959$	3.26013	−	5.64672i	0.105275	−	0.182342i
$960$		0			0
$961$	17.4677	+	30.2550i	0.563475	+	0.975968i
$962$	−0.0408581	+	0.0838128i	−0.00131732	+	0.00270223i
$963$		0			0
$964$	26.0136	+	33.2693i	0.837843	+	1.07153i
$965$	13.6527	−	7.88239i	0.439496	−	0.253743i
$966$		0			0
$967$	3.29329	+	1.90138i	0.105905	+	0.0611442i	0.552017	−	0.833833i	$-0.313858\pi$
$967$	3.29329	+	1.90138i	0.105905	+	0.0611442i	−0.446112	+	0.894977i	$0.647192\pi$
$968$	−8.41214	+	25.9413i	−0.270377	+	0.833785i
$969$		0			0
$970$	−0.774944	−	11.0514i	−0.0248820	−	0.354839i
$971$	11.8109			0.379029			0.189514	−	0.981878i	$-0.439309\pi$
$971$	11.8109			0.379029			0.189514	+	0.981878i	$0.439309\pi$
$972$		0			0
$973$	8.00834			0.256736
$974$	−1.80378	−	25.7235i	−0.0577968	−	0.824234i
$975$		0			0
$976$	−36.6252	−	35.3137i	−1.17235	−	1.13036i
$977$	−6.87127	−	3.96713i	−0.219831	−	0.126920i	0.386041	−	0.922482i	$-0.373842\pi$
$977$	−6.87127	−	3.96713i	−0.219831	−	0.126920i	−0.605872	+	0.795562i	$0.707176\pi$
$978$		0			0
$979$	−8.02395	+	4.63263i	−0.256447	+	0.148060i
$980$	−1.44753	+	1.13184i	−0.0462395	+	0.0361552i
$981$		0			0
$982$	18.4389	−	37.8239i	0.588408	−	1.20701i
$983$	−11.8091	−	20.4540i	−0.376652	−	0.652381i	0.613921	−	0.789368i	$-0.289592\pi$
$983$	−11.8091	−	20.4540i	−0.376652	−	0.652381i	−0.990573	+	0.136987i	$0.956258\pi$
$984$		0			0
$985$	1.10282	−	1.91013i	0.0351386	−	0.0608619i
$986$	22.8322	+	33.8359i	0.727124	+	1.07756i
$987$		0			0
$988$	−0.0461444	−	0.0186227i	−0.00146805	−	0.000592468i
$989$		−	23.1908i		−	0.737425i
$990$		0			0
$991$		−	38.2004i		−	1.21348i	−0.794902	−	0.606738i	$-0.792478\pi$
$991$		−	38.2004i		−	1.21348i	0.794902	−	0.606738i	$-0.207522\pi$
$992$	45.2439	+	7.93246i	1.43650	+	0.251856i
$993$		0			0
$994$	−3.48341	+	2.35058i	−0.110487	+	0.0745557i
$995$	−1.14849	+	1.98925i	−0.0364096	+	0.0630633i
$996$		0			0
$997$	−27.9939	−	48.4868i	−0.886575	−	1.53559i	−0.843898	−	0.536504i	$-0.819744\pi$
$997$	−27.9939	−	48.4868i	−0.886575	−	1.53559i	−0.0426776	−	0.999089i	$-0.513589\pi$
$998$	−54.4619	−	26.5498i	−1.72396	−	0.840418i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ba.a.71.1		72
3.2	odd	2		252.2.ba.a.239.36	yes	72
4.3	odd	2	inner	756.2.ba.a.71.12		72
9.2	odd	6	inner	756.2.ba.a.575.12		72
9.7	even	3		252.2.ba.a.155.25	✓	72
12.11	even	2		252.2.ba.a.239.25	yes	72
36.7	odd	6		252.2.ba.a.155.36	yes	72
36.11	even	6	inner	756.2.ba.a.575.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.25	✓	72	9.7	even	3
252.2.ba.a.155.36	yes	72	36.7	odd	6
252.2.ba.a.239.25	yes	72	12.11	even	2
252.2.ba.a.239.36	yes	72	3.2	odd	2
756.2.ba.a.71.1		72	1.1	even	1	trivial
756.2.ba.a.71.12		72	4.3	odd	2	inner
756.2.ba.a.575.1		72	36.11	even	6	inner
756.2.ba.a.575.12		72	9.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41075 + 0.0989244i) q^{2} +(1.98043 - 0.279115i) q^{4} +(-0.795659 - 0.459374i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.76628 + 0.589674i) q^{8} +O(q^{10})\)	\(q+(-1.41075 + 0.0989244i) q^{2} +(1.98043 - 0.279115i) q^{4} +(-0.795659 - 0.459374i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.76628 + 0.589674i) q^{8} +(1.16792 + 0.569351i) q^{10} +(-0.582708 - 1.00928i) q^{11} +(0.0273083 - 0.0472994i) q^{13} +(-1.17228 + 0.791046i) q^{14} +(3.84419 - 1.10553i) q^{16} -3.29574i q^{17} -0.455543i q^{19} +(-1.70396 - 0.687676i) q^{20} +(0.921897 + 1.36620i) q^{22} +(-1.77871 + 3.08081i) q^{23} +(-2.07795 - 3.59912i) q^{25} +(-0.0338462 + 0.0694291i) q^{26} +(1.57554 - 1.23193i) q^{28} +(7.58443 - 4.37887i) q^{29} +(-7.03218 - 4.06003i) q^{31} +(-5.31382 + 1.93992i) q^{32} +(0.326029 + 4.64947i) q^{34} -0.918747 q^{35} +1.20717 q^{37} +(0.0450644 + 0.642658i) q^{38} +(2.47189 + 0.801575i) q^{40} +(5.27252 + 3.04409i) q^{41} +(-5.64563 + 3.25951i) q^{43} +(-1.43572 - 1.83616i) q^{44} +(2.20454 - 4.52221i) q^{46} +(-2.82141 - 4.88682i) q^{47} +(0.500000 - 0.866025i) q^{49} +(3.28751 + 4.87189i) q^{50} +(0.0408802 - 0.101295i) q^{52} -10.6457i q^{53} +1.07072i q^{55} +(-2.10083 + 1.89381i) q^{56} +(-10.2666 + 6.92778i) q^{58} +(-0.744373 + 1.28929i) q^{59} +(-6.35962 - 11.0152i) q^{61} +(10.3223 + 5.03204i) q^{62} +(7.30457 - 3.26240i) q^{64} +(-0.0434562 + 0.0250895i) q^{65} +(-5.83071 - 3.36636i) q^{67} +(-0.919891 - 6.52698i) q^{68} +(1.29612 - 0.0908865i) q^{70} +2.97148 q^{71} +14.8214 q^{73} +(-1.70301 + 0.119419i) q^{74} +(-0.127149 - 0.902171i) q^{76} +(-1.00928 - 0.582708i) q^{77} +(10.9305 - 6.31075i) q^{79} +(-3.56652 - 0.886292i) q^{80} +(-7.73934 - 3.77287i) q^{82} +(-6.56004 - 11.3623i) q^{83} +(-1.51398 + 2.62229i) q^{85} +(7.64213 - 5.15684i) q^{86} +(2.20708 + 2.44834i) q^{88} -7.95018i q^{89} -0.0546167i q^{91} +(-2.66270 + 6.59779i) q^{92} +(4.46373 + 6.61498i) q^{94} +(-0.209265 + 0.362457i) q^{95} +(-4.26325 - 7.38417i) q^{97} +(-0.619704 + 1.27121i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more