LMFDB - Embedded newform 756.2.ba.a.71.12

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			71.12
Character	$\chi$	$=$	756.71
Dual form			756.2.ba.a.575.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.791046 + 1.17228i) q^{2} +(-0.748493 - 1.85466i) q^{4} +(-0.795659 - 0.459374i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.76628 + 0.589674i) q^{8} +O(q^{10})$	\(q+(-0.791046 + 1.17228i) q^{2} +(-0.748493 - 1.85466i) q^{4} +(-0.795659 - 0.459374i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.76628 + 0.589674i) q^{8} +(1.16792 - 0.569351i) q^{10} +(0.582708 + 1.00928i) q^{11} +(0.0273083 - 0.0472994i) q^{13} +(0.0989244 - 1.41075i) q^{14} +(-2.87952 + 2.77640i) q^{16} -3.29574i q^{17} +0.455543i q^{19} +(-0.256436 + 1.81951i) q^{20} +(-1.64411 - 0.115288i) q^{22} +(1.77871 - 3.08081i) q^{23} +(-2.07795 - 3.59912i) q^{25} +(0.0338462 + 0.0694291i) q^{26} +(1.57554 + 1.23193i) q^{28} +(7.58443 - 4.37887i) q^{29} +(7.03218 + 4.06003i) q^{31} +(-0.976895 - 5.57186i) q^{32} +(3.86354 + 2.60708i) q^{34} +0.918747 q^{35} +1.20717 q^{37} +(-0.534026 - 0.360356i) q^{38} +(-1.93013 - 1.73993i) q^{40} +(5.27252 + 3.04409i) q^{41} +(5.64563 - 3.25951i) q^{43} +(1.43572 - 1.83616i) q^{44} +(2.20454 + 4.52221i) q^{46} +(2.82141 + 4.88682i) q^{47} +(0.500000 - 0.866025i) q^{49} +(5.86294 + 0.411120i) q^{50} +(-0.108164 - 0.0152443i) q^{52} -10.6457i q^{53} -1.07072i q^{55} +(-2.69050 + 0.872466i) q^{56} +(-0.866355 + 12.3550i) q^{58} +(0.744373 - 1.28929i) q^{59} +(-6.35962 - 11.0152i) q^{61} +(-10.3223 + 5.03204i) q^{62} +(7.30457 + 3.26240i) q^{64} +(-0.0434562 + 0.0250895i) q^{65} +(5.83071 + 3.36636i) q^{67} +(-6.11248 + 2.46684i) q^{68} +(-0.726771 + 1.07703i) q^{70} -2.97148 q^{71} +14.8214 q^{73} +(-0.954927 + 1.41514i) q^{74} +(0.844877 - 0.340971i) q^{76} +(-1.00928 - 0.582708i) q^{77} +(-10.9305 + 6.31075i) q^{79} +(3.56652 - 0.886292i) q^{80} +(-7.73934 + 3.77287i) q^{82} +(6.56004 + 11.3623i) q^{83} +(-1.51398 + 2.62229i) q^{85} +(-0.644889 + 9.19670i) q^{86} +(1.01679 + 3.13555i) q^{88} -7.95018i q^{89} +0.0546167i q^{91} +(-7.04520 - 0.992928i) q^{92} +(-7.96060 - 0.558212i) q^{94} +(0.209265 - 0.362457i) q^{95} +(-4.26325 - 7.38417i) q^{97} +(0.619704 + 1.27121i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.791046	+	1.17228i	−0.559354	+	0.828929i
$2$	−0.791046	+	1.17228i	−0.559354	+	0.828929i
$3$		0			0
$3$		0			0
$4$	−0.748493	−	1.85466i	−0.374247	−	0.927329i
$5$	−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	0.940401	−	0.340068i	$-0.110450\pi$
$11$	0.582708	+	1.00928i	0.175693	+	0.304309i	−0.764708	+	0.644377i	$0.777117\pi$
$12$		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	$0.164256\pi$
$14$	0.0989244	−	1.41075i	0.0264387	−	0.377039i
$15$		0			0
$16$	−2.87952	+	2.77640i	−0.719879	+	0.694100i
$17$		−	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	$0.0166407\pi$
$19$			0.455543i			0.104509i	−0.998634	+	0.0522544i	$0.983359\pi$
$20$	−0.256436	+	1.81951i	−0.0573409	+	0.406855i
$21$		0			0
$22$	−1.64411	−	0.115288i	−0.350525	−	0.0245795i
$23$	1.77871	−	3.08081i	0.370886	−	0.642393i	−0.618816	−	0.785536i	$-0.712387\pi$
$23$	1.77871	−	3.08081i	0.370886	−	0.642393i	0.989702	+	0.143143i	$0.0457207\pi$
$24$		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	0.973657	−	0.228017i	$-0.0732241\pi$
$31$	7.03218	+	4.06003i	1.26302	+	0.729203i	0.289360	+	0.957220i	$0.406557\pi$
$32$	−0.976895	−	5.57186i	−0.172692	−	0.984976i
$33$		0			0
$34$	3.86354	+	2.60708i	0.662592	+	0.447111i
$35$	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	$0.468362\pi$
$38$	−0.534026	−	0.360356i	−0.0866304	−	0.0584574i
$39$		0			0
$40$	−1.93013	−	1.73993i	−0.305180	−	0.275108i
$41$	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	−0.00337979	−	0.999994i	$-0.501076\pi$
$43$	5.64563	−	3.25951i	0.860951	−	0.497070i	0.864331	+	0.502924i	$0.167742\pi$
$44$	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	0.995059	−	0.0992864i	$-0.0316560\pi$
$47$	2.82141	+	4.88682i	0.411545	+	0.712817i	−0.583514	+	0.812103i	$0.698323\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	5.86294	+	0.411120i	0.829145	+	0.0581412i
$51$		0			0
$52$	−0.108164	−	0.0152443i	−0.0149997	−	0.00211401i
$53$		−	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
$56$	−2.69050	+	0.872466i	−0.359534	+	0.116588i
$57$		0			0
$58$	−0.866355	+	12.3550i	−0.113758	+	1.62229i
$59$	0.744373	−	1.28929i	0.0969092	−	0.167852i	−0.813495	−	0.581572i	$-0.802438\pi$
$59$	0.744373	−	1.28929i	0.0969092	−	0.167852i	0.910404	+	0.413721i	$0.135771\pi$
$60$		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	0.811925	−	0.583762i	$-0.198420\pi$
$67$	5.83071	+	3.36636i	0.712335	+	0.411267i	−0.0995902	+	0.995029i	$0.531753\pi$
$68$	−6.11248	+	2.46684i	−0.741247	+	0.299148i
$69$		0			0
$70$	−0.726771	+	1.07703i	−0.0868658	+	0.128730i
$71$	−2.97148			−0.352650			−0.176325	−	0.984332i	$-0.556421\pi$
$71$	−2.97148			−0.352650			−0.176325	+	0.984332i	$0.556421\pi$
$72$		0			0
$73$	14.8214			1.73471			0.867357	−	0.497686i	$-0.165817\pi$
$73$	14.8214			1.73471			0.867357	+	0.497686i	$0.165817\pi$
$74$	−0.954927	+	1.41514i	−0.111008	+	0.164507i
$75$		0			0
$76$	0.844877	−	0.340971i	0.0969141	−	0.0391121i
$77$	−1.00928	−	0.582708i	−0.115018	−	0.0664057i
$78$		0			0
$79$	−10.9305	+	6.31075i	−1.22978	+	0.710015i	−0.966984	−	0.254836i	$-0.917979\pi$
$79$	−10.9305	+	6.31075i	−1.22978	+	0.710015i	−0.262798	+	0.964851i	$0.584645\pi$
$80$	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	$0.0892182\pi$
$83$	6.56004	+	11.3623i	0.720058	+	1.24718i	−0.240918	+	0.970546i	$0.577448\pi$
$84$		0			0
$85$	−1.51398	+	2.62229i	−0.164214	+	0.284427i
$86$	−0.644889	+	9.19670i	−0.0695402	+	0.991705i
$87$		0			0
$88$	1.01679	+	3.13555i	0.108390	+	0.334251i
$89$		−	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
$92$	−7.04520	−	0.992928i	−0.734513	−	0.103520i
$93$		0			0
$94$	−7.96060	−	0.558212i	−0.821074	−	0.0575752i
$95$	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	0.593378	−	0.804924i	$-0.297794\pi$
$103$	1.95855	+	1.13077i	0.192982	+	0.111418i	−0.400396	+	0.916342i	$0.631127\pi$
$104$	0.103434	−	0.114740i	0.0101425	−	0.0112512i
$105$		0			0
$106$	12.4798	+	8.42123i	1.21214	+	0.817942i
$107$	4.66383			0.450870			0.225435	−	0.974258i	$-0.427620\pi$
$107$	4.66383			0.450870			0.225435	+	0.974258i	$0.427620\pi$
$108$		0			0
$109$	−11.1216			−1.06526			−0.532629	−	0.846349i	$-0.678796\pi$
$109$	−11.1216			−1.06526			−0.532629	+	0.846349i	$0.678796\pi$
$110$	1.25519	+	0.846991i	0.119678	+	0.0807574i
$111$		0			0
$112$	1.10553	−	3.84419i	0.104463	−	0.363242i
$113$	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
$122$	17.9437	+	1.25824i	1.62454	+	0.113916i
$123$		0			0
$124$	2.26643	−	16.0812i	0.203532	−	1.44413i
$125$			8.41196i			0.752389i
$126$		0			0
$127$		−	17.6270i		−	1.56415i	−0.623186	−	0.782073i	$-0.714162\pi$
$127$		−	17.6270i		−	1.56415i	0.623186	−	0.782073i	$-0.285838\pi$
$128$	−9.60271	+	5.98231i	−0.848767	+	0.528767i
$129$		0			0
$130$	0.00496392	−	0.0707899i	0.000435365	−	0.00620869i
$131$	−7.62368	+	13.2046i	−0.666084	+	1.15369i	0.312906	+	0.949784i	$0.398697\pi$
$131$	−7.62368	+	13.2046i	−0.666084	+	1.15369i	−0.978990	+	0.203907i	$0.934636\pi$
$132$		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	0.176152	−	0.984363i	$-0.443635\pi$
$139$	−6.93543	−	4.00417i	−0.588255	−	0.339629i	−0.764407	+	0.644734i	$0.776968\pi$
$140$	−0.687676	−	1.70396i	−0.0581193	−	0.144011i
$141$		0			0
$142$	2.35058	−	3.48341i	0.197256	−	0.292322i
$143$	0.0636512			0.00532278
$144$		0			0
$145$	−8.04616			−0.668197
$146$	−11.7244	+	17.3749i	−0.970319	+	1.43796i
$147$		0			0
$148$	−0.903559	−	2.23889i	−0.0742721	−	0.184035i
$149$	−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	−0.669465	−	0.742844i	$-0.733476\pi$
$151$	−4.43451	+	2.56026i	−0.360875	+	0.208351i	0.308589	+	0.951195i	$0.400143\pi$
$152$	−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	$0.160518\pi$
$158$	1.24857	−	17.8058i	0.0993313	−	1.41655i
$159$		0			0
$160$	−1.78229	+	4.88206i	−0.140903	+	0.385961i
$161$			3.55741i			0.280363i
$162$		0			0
$163$		−	23.8078i		−	1.86477i	−0.361466	−	0.932385i	$-0.617724\pi$
$163$		−	23.8078i		−	1.86477i	0.361466	−	0.932385i	$-0.382276\pi$
$164$	1.69930	−	12.0572i	0.132693	−	0.941510i
$165$		0			0
$166$	−18.5092	−	1.29790i	−1.43659	−	0.100736i
$167$	9.37726	−	16.2419i	0.725634	−	1.25684i	−0.233078	−	0.972458i	$-0.574880\pi$
$167$	9.37726	−	16.2419i	0.725634	−	1.25684i	0.958713	−	0.284377i	$-0.0917868\pi$
$168$		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
$176$	−4.48008	−	1.28841i	−0.337699	−	0.0971173i
$177$		0			0
$178$	9.31985	+	6.28895i	0.698553	+	0.471377i
$179$	−7.17934			−0.536609			−0.268305	−	0.963334i	$-0.586463\pi$
$179$	−7.17934			−0.536609			−0.268305	+	0.963334i	$0.586463\pi$
$180$		0			0
$181$	2.79633			0.207849			0.103925	−	0.994585i	$-0.466860\pi$
$181$	2.79633			0.207849			0.103925	+	0.994585i	$0.466860\pi$
$182$	−0.0640262	−	0.0432043i	−0.00474594	−	0.00320252i
$183$		0			0
$184$	6.73707	−	7.47352i	0.496663	−	0.550955i
$185$	−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	$-0.831734\pi$
$191$	−12.0033	−	20.7903i	−0.868527	−	1.50433i	−0.00502585	−	0.999987i	$-0.501600\pi$
$192$		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	$0.954786\pi$
$194$	12.0288	+	0.843479i	0.863615	+	0.0605583i
$195$		0			0
$196$	−1.98043	−	0.279115i	−0.141459	−	0.0199368i
$197$			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	$0.0282439\pi$
$199$			2.50012i			0.177229i	−0.996066	+	0.0886146i	$0.971756\pi$
$200$	−3.62588	−	11.1815i	−0.256389	−	0.790649i
$201$		0			0
$202$	1.28420	−	18.3138i	0.0903560	−	1.28856i
$203$	−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	0.404782	−	0.914413i	$-0.367347\pi$
$211$	−2.68339	−	1.54926i	−0.184732	−	0.106655i	−0.589514	+	0.807758i	$0.700681\pi$
$212$	−19.7441	+	7.96823i	−1.35603	+	0.547260i
$213$		0			0
$214$	−3.68930	+	5.46733i	−0.252196	+	0.373739i
$215$	−5.98933			−0.408469
$216$		0			0
$217$	−8.12007			−0.551226
$218$	8.79771	−	13.0377i	0.595856	−	0.883023i
$219$		0			0
$220$	−1.98582	+	0.801429i	−0.133884	+	0.0540323i
$221$	−0.155887	−	0.0900013i	−0.0104861	−	0.00605414i
$222$		0			0
$223$	−7.33815	+	4.23669i	−0.491399	+	0.283709i	−0.725155	−	0.688586i	$-0.758232\pi$
$223$	−7.33815	+	4.23669i	−0.491399	+	0.283709i	0.233756	+	0.972295i	$0.424898\pi$
$224$	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	0.551212	−	0.834365i	$-0.314165\pi$
$227$	−6.73436	−	11.6643i	−0.446975	−	0.774184i	−0.998187	+	0.0601814i	$0.980832\pi$
$228$		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	$0.233813\pi$
$230$	0.323321	−	4.61084i	0.0213192	−	0.304030i
$231$		0			0
$232$	23.5627	−	7.64083i	1.54697	−	0.501645i
$233$		−	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
$236$	−2.94836	−	0.415532i	−0.191922	−	0.0270488i
$237$		0			0
$238$	−4.64947	−	0.326029i	−0.301380	−	0.0211333i
$239$	9.17721	−	15.8954i	0.593624	−	1.02819i	−0.400115	−	0.916465i	$-0.631030\pi$
$239$	9.17721	−	15.8954i	0.593624	−	1.02819i	0.993739	−	0.111722i	$-0.0356368\pi$
$240$		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
$248$	17.0589	+	15.3779i	1.08324	+	0.976496i
$249$		0			0
$250$	−9.86120	−	6.65425i	−0.623677	−	0.420852i
$251$	−13.9450			−0.880199			−0.440099	−	0.897949i	$-0.645057\pi$
$251$	−13.9450			−0.880199			−0.440099	+	0.897949i	$0.645057\pi$
$252$		0			0
$253$	4.14587			0.260648
$254$	20.6639	+	13.9438i	1.29657	+	0.874912i
$255$		0			0
$256$	0.583221	−	15.9894i	0.0364513	−	0.999335i
$257$	−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	$0.000426466\pi$
$263$	8.12745	+	14.0772i	0.501160	+	0.868034i	−0.498839	+	0.866695i	$0.666240\pi$
$264$		0			0
$265$	−4.89035	+	8.47033i	−0.300412	+	0.520329i
$266$	0.642658	+	0.0450644i	0.0394039	+	0.00276307i
$267$		0			0
$268$	1.87920	−	13.3337i	0.114791	−	0.814484i
$269$			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	$0.413180\pi$
$271$			31.7070i			1.92606i	−0.269385	+	0.963032i	$0.586820\pi$
$272$	9.15029	+	9.49014i	0.554818	+	0.575424i
$273$		0			0
$274$	−0.645013	+	9.19846i	−0.0389667	+	0.555700i
$275$	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	0.929331	−	0.369249i	$-0.120385\pi$
$283$	18.0711	+	10.4334i	1.07422	+	0.620200i	0.144887	+	0.989448i	$0.453718\pi$
$284$	2.22413	+	5.51108i	0.131978	+	0.327022i
$285$		0			0
$286$	−0.0503510	+	0.0746172i	−0.00297732	+	0.00441220i
$287$	−6.08818			−0.359374
$288$		0			0
$289$	6.13809			0.361064
$290$	6.36488	−	9.43237i	0.373759	−	0.553888i
$291$		0			0
$292$	−11.0937	−	27.4886i	−0.649211	−	1.60865i
$293$	−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
$302$	0.506545	−	7.22378i	0.0291484	−	0.415682i
$303$		0			0
$304$	−1.26477	−	1.31174i	−0.0725395	−	0.0752337i
$305$			11.6858i			0.669125i
$306$		0			0
$307$		−	3.11806i		−	0.177957i	−0.996034	−	0.0889786i	$-0.971640\pi$
$307$		−	3.11806i		−	0.177957i	0.996034	−	0.0889786i	$-0.0283603\pi$
$308$	−0.325285	+	2.30802i	−0.0185348	+	0.131512i
$309$		0			0
$310$	10.5246	+	0.738005i	0.597757	+	0.0419158i
$311$	−10.5991	+	18.3581i	−0.601018	+	1.04099i	0.391649	+	0.920115i	$0.371905\pi$
$311$	−10.5991	+	18.3581i	−0.601018	+	1.04099i	−0.992667	+	0.120879i	$0.961429\pi$
$312$		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
$320$	−4.31328	−	5.95129i	−0.241120	−	0.332687i
$321$		0			0
$322$	−4.17029	−	2.81408i	−0.232401	−	0.156822i
$323$	1.50135			0.0835375
$324$		0			0
$325$	−0.226982			−0.0125907
$326$	27.9095	+	18.8331i	1.54576	+	1.04307i
$327$		0			0
$328$	12.7902	+	11.5299i	0.706222	+	0.636630i
$329$	−4.88682	−	2.82141i	−0.269419	−	0.155549i
$330$		0			0
$331$	−19.6152	+	11.3248i	−1.07815	+	0.622468i	−0.930396	−	0.366557i	$-0.880537\pi$
$331$	−19.6152	+	11.3248i	−1.07815	+	0.622468i	−0.147751	+	0.989025i	$0.547203\pi$
$332$	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	$0.120758\pi$
$338$	−18.3355	−	1.28572i	−0.997322	−	0.0699340i
$339$		0			0
$340$	5.99665	+	0.845148i	0.325214	+	0.0458346i
$341$			9.46325i			0.512464i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	17.5394	−	5.68761i	0.945662	−	0.306656i
$345$		0			0
$346$	1.75742	−	25.0623i	0.0944794	−	1.34736i
$347$	−3.73945	+	6.47693i	−0.200744	+	0.347700i	−0.948769	−	0.315972i	$-0.897669\pi$
$347$	−3.73945	+	6.47693i	−0.200744	+	0.347700i	0.748024	+	0.663672i	$0.231003\pi$
$348$		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
$356$	−14.7449	+	5.95065i	−0.781476	+	0.315384i
$357$		0			0
$358$	5.67919	−	8.41622i	0.300155	−	0.444811i
$359$	27.6893			1.46138			0.730692	−	0.682707i	$-0.239197\pi$
$359$	27.6893			1.46138			0.730692	+	0.682707i	$0.239197\pi$
$360$		0			0
$361$	18.7925			0.989078
$362$	−2.21202	+	3.27809i	−0.116261	+	0.172292i
$363$		0			0
$364$	0.101295	−	0.0408802i	0.00530932	−	0.00214271i
$365$	−11.7928	−	6.80856i	−0.617262	−	0.356377i
$366$		0			0
$367$	5.23819	−	3.02427i	0.273431	−	0.157866i	−0.357015	−	0.934099i	$-0.616205\pi$
$367$	5.23819	−	3.02427i	0.273431	−	0.157866i	0.630446	+	0.776233i	$0.282872\pi$
$368$	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	$-0.143050\pi$
$374$	−0.379960	+	5.41856i	−0.0196472	+	0.280187i
$375$		0			0
$376$	4.92317	+	15.1820i	0.253893	+	0.782953i
$377$		−	0.478319i		−	0.0246347i
$378$		0			0
$379$			4.79709i			0.246410i	0.992381	+	0.123205i	$0.0393172\pi$
$379$			4.79709i			0.246410i	−0.992381	+	0.123205i	$0.960683\pi$
$380$	−0.828867	−	0.116818i	−0.0425200	−	0.00599263i
$381$		0			0
$382$	33.8673	+	2.37484i	1.73280	+	0.121507i
$383$	−4.80699	+	8.32595i	−0.245626	+	0.425436i	−0.962307	−	0.271964i	$-0.912327\pi$
$383$	−4.80699	+	8.32595i	−0.245626	+	0.425436i	0.716682	+	0.697401i	$0.245660\pi$
$384$		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
$392$	1.89381	−	2.10083i	0.0956519	−	0.106108i
$393$		0			0
$394$	−2.81429	−	1.89906i	−0.141782	−	0.0956731i
$395$	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	$0.508711\pi$
$398$	−2.93085	−	1.97771i	−0.146910	−	0.0991338i
$399$		0			0
$400$	15.9761	+	4.59449i	0.798804	+	0.229725i
$401$	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	$0.902870\pi$
$410$	7.89103	+	0.553334i	0.389710	+	0.0273272i
$411$		0			0
$412$	0.631230	−	4.47882i	0.0310985	−	0.220656i
$413$			1.48875i			0.0732564i
$414$		0			0
$415$		−	12.0540i		−	0.591710i
$416$	−0.290224	−	0.105952i	−0.0142294	−	0.00519471i
$417$		0			0
$418$	0.0525187	−	0.748963i	0.00256877	−	0.0366330i
$419$	−1.72249	+	2.98343i	−0.0841490	+	0.145750i	−0.905028	−	0.425351i	$-0.860150\pi$
$419$	−1.72249	+	2.98343i	−0.0841490	+	0.145750i	0.820879	+	0.571102i	$0.193484\pi$
$420$		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
$428$	−3.49085	−	8.64981i	−0.168736	−	0.418105i
$429$		0			0
$430$	4.73783	−	7.02118i	0.228479	−	0.338592i
$431$	−16.9467			−0.816293			−0.408146	−	0.912917i	$-0.633825\pi$
$431$	−16.9467			−0.816293			−0.408146	+	0.912917i	$0.633825\pi$
$432$		0			0
$433$	32.7900			1.57579			0.787894	−	0.615811i	$-0.211171\pi$
$433$	32.7900			1.57579			0.787894	+	0.615811i	$0.211171\pi$
$434$	6.42334	−	9.51901i	0.308330	−	0.456927i
$435$		0			0
$436$	8.32445	+	20.6268i	0.398669	+	0.987844i
$437$	1.40344	+	0.810278i	0.0671358	+	0.0387609i
$438$		0			0
$439$	−13.3048	+	7.68154i	−0.635004	+	0.366620i	−0.782687	−	0.622415i	$-0.786152\pi$
$439$	−13.3048	+	7.68154i	−0.635004	+	0.366620i	0.147683	+	0.989035i	$0.452818\pi$
$440$	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	0.604233	−	0.796807i	$-0.293480\pi$
$443$	−8.16517	−	14.1425i	−0.387939	−	0.671930i	−0.992172	+	0.124878i	$0.960146\pi$
$444$		0			0
$445$	−3.65210	+	6.32563i	−0.173126	+	0.299863i
$446$	0.838223	−	11.9538i	0.0396910	−	0.566029i
$447$		0			0
$448$	−7.95714	+	0.826961i	−0.375940	+	0.0390703i
$449$			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
$452$	4.60856	−	32.6995i	0.216768	−	1.53805i
$453$		0			0
$454$	19.0010	+	1.33238i	0.891760	+	0.0625319i
$455$	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	0.498906	−	0.866656i	$-0.333735\pi$
$463$	−0.0470644	−	0.0271726i	−0.00218727	−	0.00126282i	−0.501093	+	0.865393i	$0.667069\pi$
$464$	−9.68199	+	33.6664i	−0.449475	+	1.56293i
$465$		0			0
$466$	3.87813	+	2.61693i	0.179651	+	0.121227i
$467$	32.8935			1.52213			0.761065	−	0.648676i	$-0.224677\pi$
$467$	32.8935			1.52213			0.761065	+	0.648676i	$0.224677\pi$
$468$		0			0
$469$	−6.73273			−0.310888
$470$	6.07750	+	4.10104i	0.280334	+	0.189167i
$471$		0			0
$472$	2.81940	−	3.12760i	0.129774	−	0.143960i
$473$	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	0.989057	−	0.147537i	$-0.0471345\pi$
$479$	8.02688	+	13.9030i	0.366758	+	0.635243i	−0.622299	+	0.782780i	$0.713801\pi$
$480$		0			0
$481$	0.0329658	−	0.0570985i	0.00150311	−	0.00260347i
$482$	−29.7895	−	2.08890i	−1.35687	−	0.0951466i
$483$		0			0
$484$	−19.0949	−	2.69117i	−0.867950	−	0.122326i
$485$			7.83370i			0.355710i
$486$		0			0
$487$		−	18.2339i		−	0.826258i	−0.910673	−	0.413129i	$-0.864436\pi$
$487$		−	18.2339i		−	0.826258i	0.910673	−	0.413129i	$-0.135564\pi$
$488$	−11.0971	−	34.2211i	−0.502342	−	1.54912i
$489$		0			0
$490$	0.0908865	−	1.29612i	0.00410583	−	0.0585528i
$491$	14.8772	−	25.7680i	0.671398	−	1.16289i	−0.306110	−	0.951996i	$-0.599028\pi$
$491$	14.8772	−	25.7680i	0.671398	−	1.16289i	0.977508	−	0.210899i	$-0.0676390\pi$
$492$		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	$-0.924853\pi$
$499$	−37.1029	−	21.4213i	−1.66095	−	0.958951i	−0.688690	−	0.725056i	$-0.741814\pi$
$500$	15.6013	−	6.29630i	0.697712	−	0.281579i
$501$		0			0
$502$	11.0311	−	16.3474i	0.492342	−	0.729622i
$503$	14.2832			0.636855			0.318427	−	0.947947i	$-0.396845\pi$
$503$	14.2832			0.636855			0.318427	+	0.947947i	$0.396845\pi$
$504$		0			0
$505$	11.9268			0.530737
$506$	−3.27957	+	4.86013i	−0.145795	+	0.216059i
$507$		0			0
$508$	−32.6921	+	13.1937i	−1.45048	+	0.585377i
$509$	−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
$518$	0.119419	−	1.70301i	0.00524695	−	0.0748262i
$519$		0			0
$520$	−0.135007	+	0.0437794i	−0.00592043	+	0.00191985i
$521$		−	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	$0.114139\pi$
$523$			16.0515i			0.701885i	−0.936397	+	0.350943i	$0.885861\pi$
$524$	30.1963	+	4.25577i	1.31913	+	0.185914i
$525$		0			0
$526$	−22.9316	−	1.60801i	−0.999864	−	0.0701124i
$527$	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
$536$	14.1443	+	12.7505i	0.610941	+	0.550738i
$537$		0			0
$538$	−10.6785	−	7.20574i	−0.460382	−	0.310661i
$539$	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	$0.662215\pi$
$542$	−37.1696	−	25.0817i	−1.59657	−	1.07735i
$543$		0			0
$544$	−18.3634	+	3.21959i	−0.787325	+	0.138039i
$545$	8.84901	+	5.10898i	0.379050	+	0.218845i
$546$		0			0
$547$	−6.24436	+	3.60518i	−0.266990	+	0.154147i	−0.627519	−	0.778601i	$-0.715929\pi$
$547$	−6.24436	+	3.60518i	−0.266990	+	0.154147i	0.360529	+	0.932748i	$0.382596\pi$
$548$	−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
$554$	2.26096	+	0.158543i	0.0960591	+	0.00673584i
$555$		0			0
$556$	−2.23525	+	15.8599i	−0.0947956	+	0.672611i
$557$			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
$560$	−2.64555	+	2.55081i	−0.111795	+	0.107791i
$561$		0			0
$562$	−2.18271	+	31.1273i	−0.0920720	+	1.31303i
$563$	−23.5052	+	40.7122i	−0.990625	+	1.71581i	−0.377006	+	0.926211i	$0.623046\pi$
$563$	−23.5052	+	40.7122i	−0.990625	+	1.71581i	−0.613619	+	0.789602i	$0.710287\pi$
$564$		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	0.872329	−	0.488919i	$-0.162609\pi$
$571$	21.1494	+	12.2106i	0.885077	+	0.510999i	0.0127478	+	0.999919i	$0.495942\pi$
$572$	−0.0476425	−	0.118051i	−0.00199203	−	0.00493597i
$573$		0			0
$574$	4.81603	−	7.13707i	0.201017	−	0.297896i
$575$	−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	$0.767211\pi$
$578$	−4.85551	+	7.19557i	−0.201962	+	0.299296i
$579$		0			0
$580$	6.02250	+	14.9229i	0.250070	+	0.619639i
$581$	−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	0.500534	−	0.865717i	$-0.333137\pi$
$587$	−12.1011	−	20.9597i	−0.499466	−	0.865100i	−1.00000		0.000616829i	$0.999804\pi$
$588$		0			0
$589$	−1.84952	+	3.20347i	−0.0762082	+	0.131996i
$590$	0.135307	−	1.92960i	0.00557050	−	0.0794403i
$591$		0			0
$592$	−3.47606	+	3.35159i	−0.142865	+	0.137749i
$593$			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
$596$	−0.454725	+	3.22645i	−0.0186263	+	0.132161i
$597$		0			0
$598$	0.274100	+	0.0192204i	0.0112088	+	0.000785982i
$599$	1.31442	−	2.27665i	0.0537059	−	0.0930213i	−0.837923	−	0.545789i	$-0.816230\pi$
$599$	1.31442	−	2.27665i	0.0537059	−	0.0930213i	0.891628	+	0.452768i	$0.149563\pi$
$600$		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	0.631578	−	0.775312i	$-0.282407\pi$
$607$	6.79813	+	3.92490i	0.275928	+	0.159307i	−0.355651	+	0.934619i	$0.615741\pi$
$608$	2.53823	−	0.445018i	0.102939	−	0.0180479i
$609$		0			0
$610$	−13.6990	−	9.24398i	−0.554657	−	0.374278i
$611$	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	$0.348575\pi$
$614$	3.65525	+	2.46653i	0.147514	+	0.0995410i
$615$		0			0
$616$	−2.44834	−	2.20708i	−0.0986464	−	0.0889257i
$617$	−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	−0.277706	−	0.960666i	$-0.589574\pi$
$619$	10.3351	−	5.96696i	0.415402	−	0.239832i	0.693108	+	0.720834i	$0.256241\pi$
$620$	−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
$626$	−33.2830	−	2.33387i	−1.33026	−	0.0932802i
$627$		0			0
$628$	−0.958554	−	0.135095i	−0.0382505	−	0.00539090i
$629$		−	3.97852i		−	0.158634i
$630$		0			0
$631$			4.63442i			0.184493i	0.995736	+	0.0922467i	$0.0294048\pi$
$631$			4.63442i			0.184493i	−0.995736	+	0.0922467i	$0.970595\pi$
$632$	−33.9582	+	11.0118i	−1.35078	+	0.438027i
$633$		0			0
$634$	1.80612	−	25.7569i	0.0717302	−	1.02294i
$635$	−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	$-0.918862\pi$
$643$	−42.3444	−	24.4476i	−1.66990	−	0.964118i	−0.702212	−	0.711968i	$-0.747804\pi$
$644$	6.59779	−	2.66270i	0.259989	−	0.104925i
$645$		0			0
$646$	−1.18764	+	1.76001i	−0.0467270	+	0.0692467i
$647$	−19.0364			−0.748397			−0.374198	−	0.927349i	$-0.622082\pi$
$647$	−19.0364			−0.748397			−0.374198	+	0.927349i	$0.622082\pi$
$648$		0			0
$649$	1.73501			0.0681051
$650$	0.179553	−	0.266087i	0.00704264	−	0.0104368i
$651$		0			0
$652$	−44.1553	+	17.8200i	−1.72926	+	0.697884i
$653$	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	0.663983	−	0.747747i	$-0.268865\pi$
$659$	−8.10116	−	14.0316i	−0.315577	−	0.546595i	−0.979560	+	0.201153i	$0.935531\pi$
$660$		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	$0.103667\pi$
$662$	2.24060	−	31.9529i	0.0870834	−	1.24189i
$663$		0			0
$664$	11.4468	+	35.2996i	0.444223	+	1.36989i
$665$			0.418529i			0.0162299i
$666$		0			0
$667$		−	31.1549i		−	1.20632i
$668$	−37.1420	−	5.23467i	−1.43707	−	0.202535i
$669$		0			0
$670$	8.72644	+	0.611914i	0.337132	+	0.0236403i
$671$	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
$680$	−5.73437	+	6.36121i	−0.219903	+	0.243941i
$681$		0			0
$682$	−11.0936	−	7.48587i	−0.424796	−	0.286649i
$683$	16.0167			0.612864			0.306432	−	0.951893i	$-0.400865\pi$
$683$	16.0167			0.612864			0.306432	+	0.951893i	$0.400865\pi$
$684$		0			0
$685$	−5.99048			−0.228884
$686$	−1.17228	−	0.791046i	−0.0447580	−	0.0302023i
$687$		0			0
$688$	−7.20699	+	25.0603i	−0.274764	+	0.955416i
$689$	−0.503535	−	0.290716i	−0.0191832	−	0.0110754i
$690$		0			0
$691$	35.2063	−	20.3264i	1.33931	−	0.773251i	0.352605	−	0.935772i	$-0.385296\pi$
$691$	35.2063	−	20.3264i	1.33931	−	0.773251i	0.986705	+	0.162521i	$0.0519625\pi$
$692$	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
$698$	25.3958	+	1.78080i	0.961246	+	0.0674044i
$699$		0			0
$700$	1.15998	−	8.23047i	0.0438429	−	0.311082i
$701$		−	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
$704$	0.963754	+	9.27338i	0.0363228	+	0.349504i
$705$		0			0
$706$	−0.433514	+	6.18229i	−0.0163155	+	0.232674i
$707$	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
$716$	5.37369	+	13.3152i	0.200824	+	0.497614i
$717$		0			0
$718$	−21.9035	+	32.4597i	−0.817431	+	1.21138i
$719$	−28.4079			−1.05944			−0.529718	−	0.848174i	$-0.677702\pi$
$719$	−28.4079			−1.05944			−0.529718	+	0.848174i	$0.677702\pi$
$720$		0			0
$721$	−2.26154			−0.0842242
$722$	−14.8657	+	22.0301i	−0.553244	+	0.819875i
$723$		0			0
$724$	−2.09303	−	5.18623i	−0.0777869	−	0.192745i
$725$	−31.5202	−	18.1982i	−1.17063	−	0.675863i
$726$		0			0
$727$	31.9367	−	18.4386i	1.18447	−	0.683852i	0.227422	−	0.973796i	$-0.426970\pi$
$727$	31.9367	−	18.4386i	1.18447	−	0.683852i	0.957043	+	0.289945i	$0.0936369\pi$
$728$	−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	$0.113387\pi$
$734$	−0.598348	+	8.53298i	−0.0220854	+	0.314958i
$735$		0			0
$736$	−18.9035	−	6.90108i	−0.696791	−	0.254377i
$737$			7.84642i			0.289027i
$738$		0			0
$739$			43.2538i			1.59112i	0.605876	+	0.795559i	$0.292823\pi$
$739$			43.2538i			1.59112i	−0.605876	+	0.795559i	$0.707177\pi$
$740$	−0.309562	+	2.19646i	−0.0113797	+	0.0807435i
$741$		0			0
$742$	−15.0184	−	1.05312i	−0.551343	−	0.0386612i
$743$	−14.3410	+	24.8394i	−0.526121	+	0.911268i	0.473416	+	0.880839i	$0.343021\pi$
$743$	−14.3410	+	24.8394i	−0.526121	+	0.911268i	−0.999537	+	0.0304290i	$0.990313\pi$
$744$		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	0.602598	−	0.798045i	$-0.294132\pi$
$751$	5.83084	+	3.36644i	0.212771	+	0.122843i	−0.389828	+	0.920888i	$0.627465\pi$
$752$	−21.6921	−	6.23833i	−0.791028	−	0.227489i
$753$		0			0
$754$	0.560725	+	0.378372i	0.0204204	+	0.0137795i
$755$	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	$0.679175\pi$
$758$	−5.62354	−	3.79472i	−0.204256	−	0.137830i
$759$		0			0
$760$	0.792615	−	0.879258i	0.0287512	−	0.0318941i
$761$	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	$0.250737\pi$
$770$	−1.51052	−	0.105921i	−0.0544354	−	0.00381711i
$771$		0			0
$772$	33.9821	+	4.78933i	1.22304	+	0.172372i
$773$		−	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
$776$	−7.43908	−	22.9406i	−0.267047	−	0.823519i
$777$		0			0
$778$	0.275715	−	3.93194i	0.00988486	−	0.140967i
$779$	−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	0.902259	−	0.431195i	$-0.141908\pi$
$787$	27.4914	+	15.8722i	0.979962	+	0.565781i	0.0777033	+	0.996977i	$0.475241\pi$
$788$	4.45246	−	1.79690i	0.158612	−	0.0640120i
$789$		0			0
$790$	−9.17295	+	13.5938i	−0.326359	+	0.483644i
$791$	−16.5113			−0.587075
$792$		0			0
$793$	−0.694683			−0.0246689
$794$	0.862566	−	1.27827i	0.0306113	−	0.0453642i
$795$		0			0
$796$	4.63688	−	1.87133i	0.164350	−	0.0663274i
$797$	−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
$806$	−0.0438721	+	0.625655i	−0.00154533	+	0.0220378i
$807$		0			0
$808$	−34.9271	+	11.3260i	−1.22873	+	0.398448i
$809$			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	$0.224334\pi$
$811$			36.8994i			1.29571i	−0.761763	+	0.647856i	$0.775666\pi$
$812$	17.3441	+	2.44442i	0.608658	+	0.0857823i
$813$		0			0
$814$	−1.98472	−	0.139172i	−0.0695644	−	0.00487799i
$815$	−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	0.0618640	−	0.998085i	$-0.480295\pi$
$823$	−22.1348	−	12.7795i	−0.771571	−	0.445466i	−0.833435	+	0.552618i	$0.813629\pi$
$824$	4.75111	+	4.28293i	0.165513	+	0.149203i
$825$		0			0
$826$	−1.74523	−	1.17767i	−0.0607244	−	0.0409763i
$827$	−12.8344			−0.446296			−0.223148	−	0.974785i	$-0.571633\pi$
$827$	−12.8344			−0.446296			−0.223148	+	0.974785i	$0.571633\pi$
$828$		0			0
$829$	−32.1144			−1.11538			−0.557689	−	0.830050i	$-0.688312\pi$
$829$	−32.1144			−1.11538			−0.557689	+	0.830050i	$0.688312\pi$
$830$	14.1307	+	9.53530i	0.490485	+	0.330975i
$831$		0			0
$832$	0.353786	−	0.256411i	0.0122653	−	0.00888946i
$833$	−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	0.878547	−	0.477655i	$-0.158513\pi$
$839$	0.741866	+	1.28495i	0.0256121	+	0.0443614i	−0.852935	+	0.522017i	$0.825180\pi$
$840$		0			0
$841$	23.8491	−	41.3078i	0.822382	−	1.42441i
$842$	−20.8722	−	1.46360i	−0.719304	−	0.0504389i
$843$		0			0
$844$	−0.864842	+	6.13639i	−0.0297691	+	0.211223i
$845$		−	11.9410i		−	0.410782i
$846$		0			0
$847$			9.64181i			0.331296i
$848$	29.5567	+	30.6544i	1.01498	+	1.05268i
$849$		0			0
$850$	1.35495	−	19.3227i	0.0464743	−	0.662764i
$851$	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	0.628589	−	0.777738i	$-0.283633\pi$
$859$	7.89410	+	4.55766i	0.269343	+	0.155505i	−0.359246	+	0.933243i	$0.616966\pi$
$860$	4.48297	+	11.1082i	0.152868	+	0.378785i
$861$		0			0
$862$	13.4056	−	19.8663i	0.456596	−	0.676649i
$863$	−14.0671			−0.478851			−0.239425	−	0.970915i	$-0.576959\pi$
$863$	−14.0671			−0.478851			−0.239425	+	0.970915i	$0.576959\pi$
$864$		0			0
$865$	16.3218			0.554958
$866$	−25.9384	+	38.4392i	−0.881423	+	1.30622i
$867$		0			0
$868$	6.07781	+	15.0599i	0.206294	+	0.511168i
$869$	−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	$-0.000292660\pi$
$878$	1.51978	−	21.6734i	0.0512902	−	0.731444i
$879$		0			0
$880$	2.97275	+	3.08316i	0.100211	+	0.103933i
$881$			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	$0.0147819\pi$
$883$			2.75888i			0.0928439i	−0.998922	+	0.0464219i	$0.985218\pi$
$884$	−0.0502414	+	0.356482i	−0.00168980	+	0.0119898i
$885$		0			0
$886$	23.0380	+	1.61547i	0.773977	+	0.0542727i
$887$	−5.47009	+	9.47448i	−0.183668	+	0.318122i	−0.943127	−	0.332433i	$-0.892130\pi$
$887$	−5.47009	+	9.47448i	−0.183668	+	0.318122i	0.759459	+	0.650555i	$0.225464\pi$
$888$		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
$896$	5.32503	−	9.98219i	0.177897	−	0.333481i
$897$		0			0
$898$	−14.9247	−	10.0711i	−0.498044	−	0.336075i
$899$	71.1135			2.37177
$900$		0			0
$901$	−35.0854			−1.16887
$902$	−8.31766	−	5.61268i	−0.276948	−	0.186882i
$903$		0			0
$904$	34.6875	+	31.2693i	1.15369	+	1.04000i
$905$	−2.22492	−	1.28456i	−0.0739589	−	0.0427002i
$906$		0			0
$907$	−3.75470	+	2.16778i	−0.124673	+	0.0719798i	−0.561039	−	0.827789i	$-0.689598\pi$
$907$	−3.75470	+	2.16778i	−0.124673	+	0.0719798i	0.436367	+	0.899769i	$0.356265\pi$
$908$	−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	$0.211958\pi$
$911$	28.0150	+	48.5233i	0.928177	+	1.60765i	0.141806	+	0.989894i	$0.454709\pi$
$912$		0			0
$913$	−7.64518	+	13.2418i	−0.253018	+	0.438241i
$914$	−25.3403	−	1.77691i	−0.838182	−	0.0587749i
$915$		0			0
$916$	12.5502	+	1.76879i	0.414671	+	0.0584424i
$917$		−	15.2474i		−	0.503512i
$918$		0			0
$919$		−	10.2488i		−	0.338077i	−0.985609	−	0.169039i	$-0.945934\pi$
$919$		−	10.2488i		−	0.338077i	0.985609	−	0.169039i	$-0.0540662\pi$
$920$	−8.79354	+	2.85154i	−0.289915	+	0.0940123i
$921$		0			0
$922$	−0.217553	+	3.10250i	−0.00716473	+	0.102175i
$923$	−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
$932$	−6.13556	+	2.47616i	−0.200977	+	0.0811092i
$933$		0			0
$934$	−26.0203	+	38.5605i	−0.851409	+	1.26174i
$935$	−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	$0.274715\pi$
$938$	5.32589	−	7.89266i	0.173897	−	0.257704i
$939$		0			0
$940$	−9.61515	+	3.88043i	−0.313612	+	0.126566i
$941$	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	0.685897	−	0.727698i	$-0.259410\pi$
$947$	−8.83985	−	15.3111i	−0.287257	−	0.497543i	−0.973154	+	0.230155i	$0.926077\pi$
$948$		0			0
$949$	0.404748	−	0.701044i	0.0131387	−	0.0227569i
$950$	−0.187283	+	2.67082i	−0.00607627	+	0.0866529i
$951$		0			0
$952$	2.87542	+	8.86720i	0.0931929	+	0.287388i
$953$			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
$956$	−36.3496	−	5.12299i	−1.17563	−	0.165689i
$957$		0			0
$958$	−22.6478	−	1.58811i	−0.731718	−	0.0513095i
$959$	−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	0.446112	−	0.894977i	$-0.352808\pi$
$967$	−3.29329	−	1.90138i	−0.105905	−	0.0611442i	−0.552017	+	0.833833i	$0.686142\pi$
$968$	18.2598	−	20.2558i	0.586891	−	0.651045i
$969$		0			0
$970$	−9.18331	−	6.19682i	−0.294858	−	0.198968i
$971$	−11.8109			−0.379029			−0.189514	−	0.981878i	$-0.560691\pi$
$971$	−11.8109			−0.379029			−0.189514	+	0.981878i	$0.560691\pi$
$972$		0			0
$973$	8.00834			0.256736
$974$	21.3753	+	14.4239i	0.684909	+	0.462170i
$975$		0			0
$976$	48.8952	+	14.0616i	1.56510	+	0.450099i
$977$	−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	0.990573	−	0.136987i	$-0.0437418\pi$
$983$	11.8091	+	20.4540i	0.376652	+	0.652381i	−0.613921	+	0.789368i	$0.710408\pi$
$984$		0			0
$985$	1.10282	−	1.91013i	0.0351386	−	0.0608619i
$986$	40.7188	+	2.85528i	1.29675	+	0.0909307i
$987$		0			0
$988$	0.00694446	−	0.0492736i	0.000220933	−	0.00156760i
$989$		−	23.1908i		−	0.737425i
$990$		0			0
$991$			38.2004i			1.21348i	0.794902	+	0.606738i	$0.207522\pi$
$991$			38.2004i			1.21348i	−0.794902	+	0.606738i	$0.792478\pi$
$992$	15.7522	−	43.1486i	0.500134	−	1.36997i
$993$		0			0
$994$	−0.293952	+	4.19201i	−0.00932358	+	0.132963i
$995$	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.71.12		72
3.2	odd	2		252.2.ba.a.239.25	yes	72
4.3	odd	2	inner	756.2.ba.a.71.1		72
9.2	odd	6	inner	756.2.ba.a.575.1		72
9.7	even	3		252.2.ba.a.155.36	yes	72
12.11	even	2		252.2.ba.a.239.36	yes	72
36.7	odd	6		252.2.ba.a.155.25	✓	72
36.11	even	6	inner	756.2.ba.a.575.12		72

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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)

\(f(q)\)	\(=\)	\(q+(-0.791046 + 1.17228i) q^{2} +(-0.748493 - 1.85466i) q^{4} +(-0.795659 - 0.459374i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.76628 + 0.589674i) q^{8} +O(q^{10})\)	\(q+(-0.791046 + 1.17228i) q^{2} +(-0.748493 - 1.85466i) q^{4} +(-0.795659 - 0.459374i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.76628 + 0.589674i) q^{8} +(1.16792 - 0.569351i) q^{10} +(0.582708 + 1.00928i) q^{11} +(0.0273083 - 0.0472994i) q^{13} +(0.0989244 - 1.41075i) q^{14} +(-2.87952 + 2.77640i) q^{16} -3.29574i q^{17} +0.455543i q^{19} +(-0.256436 + 1.81951i) q^{20} +(-1.64411 - 0.115288i) q^{22} +(1.77871 - 3.08081i) q^{23} +(-2.07795 - 3.59912i) q^{25} +(0.0338462 + 0.0694291i) q^{26} +(1.57554 + 1.23193i) q^{28} +(7.58443 - 4.37887i) q^{29} +(7.03218 + 4.06003i) q^{31} +(-0.976895 - 5.57186i) q^{32} +(3.86354 + 2.60708i) q^{34} +0.918747 q^{35} +1.20717 q^{37} +(-0.534026 - 0.360356i) q^{38} +(-1.93013 - 1.73993i) q^{40} +(5.27252 + 3.04409i) q^{41} +(5.64563 - 3.25951i) q^{43} +(1.43572 - 1.83616i) q^{44} +(2.20454 + 4.52221i) q^{46} +(2.82141 + 4.88682i) q^{47} +(0.500000 - 0.866025i) q^{49} +(5.86294 + 0.411120i) q^{50} +(-0.108164 - 0.0152443i) q^{52} -10.6457i q^{53} -1.07072i q^{55} +(-2.69050 + 0.872466i) q^{56} +(-0.866355 + 12.3550i) q^{58} +(0.744373 - 1.28929i) q^{59} +(-6.35962 - 11.0152i) q^{61} +(-10.3223 + 5.03204i) q^{62} +(7.30457 + 3.26240i) q^{64} +(-0.0434562 + 0.0250895i) q^{65} +(5.83071 + 3.36636i) q^{67} +(-6.11248 + 2.46684i) q^{68} +(-0.726771 + 1.07703i) q^{70} -2.97148 q^{71} +14.8214 q^{73} +(-0.954927 + 1.41514i) q^{74} +(0.844877 - 0.340971i) q^{76} +(-1.00928 - 0.582708i) q^{77} +(-10.9305 + 6.31075i) q^{79} +(3.56652 - 0.886292i) q^{80} +(-7.73934 + 3.77287i) q^{82} +(6.56004 + 11.3623i) q^{83} +(-1.51398 + 2.62229i) q^{85} +(-0.644889 + 9.19670i) q^{86} +(1.01679 + 3.13555i) q^{88} -7.95018i q^{89} +0.0546167i q^{91} +(-7.04520 - 0.992928i) q^{92} +(-7.96060 - 0.558212i) q^{94} +(0.209265 - 0.362457i) q^{95} +(-4.26325 - 7.38417i) q^{97} +(0.619704 + 1.27121i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 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

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