LMFDB - Embedded newform 252.2.ba.a.155.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.25
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.791046 + 1.17228i) q^{2} +(1.72015 + 0.202657i) q^{3} +(-0.748493 + 1.85466i) q^{4} +(0.795659 - 0.459374i) q^{5} +(1.12315 + 2.17682i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-2.76628 + 0.589674i) q^{8} +(2.91786 + 0.697202i) q^{9} +O(q^{10})$	\(q+(0.791046 + 1.17228i) q^{2} +(1.72015 + 0.202657i) q^{3} +(-0.748493 + 1.85466i) q^{4} +(0.795659 - 0.459374i) q^{5} +(1.12315 + 2.17682i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-2.76628 + 0.589674i) q^{8} +(2.91786 + 0.697202i) q^{9} +(1.16792 + 0.569351i) q^{10} +(-0.582708 + 1.00928i) q^{11} +(-1.66338 + 3.03861i) q^{12} +(0.0273083 + 0.0472994i) q^{13} +(-0.0989244 - 1.41075i) q^{14} +(1.46175 - 0.628948i) q^{15} +(-2.87952 - 2.77640i) q^{16} -3.29574i q^{17} +(1.49084 + 3.97208i) q^{18} -0.455543i q^{19} +(0.256436 + 1.81951i) q^{20} +(-1.38837 - 1.03558i) q^{21} +(-1.64411 + 0.115288i) q^{22} +(-1.77871 - 3.08081i) q^{23} +(-4.87792 + 0.453726i) q^{24} +(-2.07795 + 3.59912i) q^{25} +(-0.0338462 + 0.0694291i) q^{26} +(4.87788 + 1.79062i) q^{27} +(1.57554 - 1.23193i) q^{28} +(-7.58443 - 4.37887i) q^{29} +(1.89362 + 1.21606i) q^{30} +(7.03218 - 4.06003i) q^{31} +(0.976895 - 5.57186i) q^{32} +(-1.20688 + 1.61803i) q^{33} +(3.86354 - 2.60708i) q^{34} -0.918747 q^{35} +(-3.47707 + 4.88978i) q^{36} +1.20717 q^{37} +(0.534026 - 0.360356i) q^{38} +(0.0373890 + 0.0868966i) q^{39} +(-1.93013 + 1.73993i) q^{40} +(-5.27252 + 3.04409i) q^{41} +(0.115733 - 2.44675i) q^{42} +(5.64563 + 3.25951i) q^{43} +(-1.43572 - 1.83616i) q^{44} +(2.64190 - 0.785654i) q^{45} +(2.20454 - 4.52221i) q^{46} +(-2.82141 + 4.88682i) q^{47} +(-4.39056 - 5.35939i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-5.86294 + 0.411120i) q^{50} +(0.667904 - 5.66918i) q^{51} +(-0.108164 + 0.0152443i) q^{52} -10.6457i q^{53} +(1.75951 + 7.13471i) q^{54} +1.07072i q^{55} +(2.69050 + 0.872466i) q^{56} +(0.0923189 - 0.783605i) q^{57} +(-0.866355 - 12.3550i) q^{58} +(-0.744373 - 1.28929i) q^{59} +(0.0723733 + 3.18181i) q^{60} +(-6.35962 + 11.0152i) q^{61} +(10.3223 + 5.03204i) q^{62} +(-2.17834 - 2.06272i) q^{63} +(7.30457 - 3.26240i) q^{64} +(0.0434562 + 0.0250895i) q^{65} +(-2.85149 - 0.134877i) q^{66} +(5.83071 - 3.36636i) q^{67} +(6.11248 + 2.46684i) q^{68} +(-2.43530 - 5.65994i) q^{69} +(-0.726771 - 1.07703i) q^{70} +2.97148 q^{71} +(-8.48273 - 0.208066i) q^{72} +14.8214 q^{73} +(0.954927 + 1.41514i) q^{74} +(-4.30378 + 5.76993i) q^{75} +(0.844877 + 0.340971i) q^{76} +(1.00928 - 0.582708i) q^{77} +(-0.0722909 + 0.112570i) q^{78} +(-10.9305 - 6.31075i) q^{79} +(-3.56652 - 0.886292i) q^{80} +(8.02782 + 4.06867i) q^{81} +(-7.73934 - 3.77287i) q^{82} +(-6.56004 + 11.3623i) q^{83} +(2.95984 - 1.79982i) q^{84} +(-1.51398 - 2.62229i) q^{85} +(0.644889 + 9.19670i) q^{86} +(-12.1590 - 9.06937i) q^{87} +(1.01679 - 3.13555i) q^{88} -7.95018i q^{89} +(3.01087 + 2.47556i) q^{90} -0.0546167i q^{91} +(7.04520 - 0.992928i) q^{92} +(12.9192 - 5.55876i) q^{93} +(-7.96060 + 0.558212i) q^{94} +(-0.209265 - 0.362457i) q^{95} +(2.80959 - 9.38649i) q^{96} +(-4.26325 + 7.38417i) q^{97} +(-0.619704 + 1.27121i) q^{98} +(-2.40393 + 2.53867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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
$3$	1.72015	+	0.202657i	0.993131	+	0.117004i
$3$	1.72015	+	0.202657i	0.993131	+	0.117004i
$4$	−0.748493	+	1.85466i	−0.374247	+	0.927329i
$5$	0.795659	−	0.459374i	0.355829	−	0.205438i	−0.311420	−	0.950272i	$-0.600805\pi$
$5$	0.795659	−	0.459374i	0.355829	−	0.205438i	0.667250	+	0.744834i	$0.267471\pi$
$6$	1.12315	+	2.17682i	0.458524	+	0.888682i
$7$	−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
$9$	2.91786	+	0.697202i	0.972620	+	0.232401i
$10$	1.16792	+	0.569351i	0.369328	+	0.180045i
$11$	−0.582708	+	1.00928i	−0.175693	+	0.304309i	−0.940401	−	0.340068i	$-0.889550\pi$
$11$	−0.582708	+	1.00928i	−0.175693	+	0.304309i	0.764708	+	0.644377i	$0.222883\pi$
$12$	−1.66338	+	3.03861i	−0.480177	+	0.877171i
$13$	0.0273083	+	0.0472994i	0.00757397	+	0.0131185i	0.869788	−	0.493426i	$-0.164256\pi$
$13$	0.0273083	+	0.0472994i	0.00757397	+	0.0131185i	−0.862214	+	0.506545i	$0.830922\pi$
$14$	−0.0989244	−	1.41075i	−0.0264387	−	0.377039i
$15$	1.46175	−	0.628948i	0.377422	−	0.162394i
$16$	−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	$-0.130874\pi$
$18$	1.49084	+	3.97208i	0.351395	+	0.936227i
$19$		−	0.455543i		−	0.104509i	−0.998634	−	0.0522544i	$-0.983359\pi$
$19$		−	0.455543i		−	0.104509i	0.998634	−	0.0522544i	$-0.0166407\pi$
$20$	0.256436	+	1.81951i	0.0573409	+	0.406855i
$21$	−1.38837	−	1.03558i	−0.302967	−	0.225983i
$22$	−1.64411	+	0.115288i	−0.350525	+	0.0245795i
$23$	−1.77871	−	3.08081i	−0.370886	−	0.642393i	0.618816	−	0.785536i	$-0.287613\pi$
$23$	−1.77871	−	3.08081i	−0.370886	−	0.642393i	−0.989702	+	0.143143i	$0.954279\pi$
$24$	−4.87792	+	0.453726i	−0.995702	+	0.0926164i
$25$	−2.07795	+	3.59912i	−0.415590	+	0.719824i
$26$	−0.0338462	+	0.0694291i	−0.00663778	+	0.0136162i
$27$	4.87788	+	1.79062i	0.938748	+	0.344605i
$28$	1.57554	−	1.23193i	0.297750	−	0.232814i
$29$	−7.58443	−	4.37887i	−1.40839	−	0.813136i	−0.413160	−	0.910658i	$-0.635575\pi$
$29$	−7.58443	−	4.37887i	−1.40839	−	0.813136i	−0.995233	+	0.0975219i	$0.968908\pi$
$30$	1.89362	+	1.21606i	0.345725	+	0.222021i
$31$	7.03218	−	4.06003i	1.26302	−	0.729203i	0.289360	−	0.957220i	$-0.406557\pi$
$31$	7.03218	−	4.06003i	1.26302	−	0.729203i	0.973657	+	0.228017i	$0.0732241\pi$
$32$	0.976895	−	5.57186i	0.172692	−	0.984976i
$33$	−1.20688	+	1.61803i	−0.210092	+	0.281662i
$34$	3.86354	−	2.60708i	0.662592	−	0.447111i
$35$	−0.918747			−0.155297
$36$	−3.47707	+	4.88978i	−0.579512	+	0.814964i
$37$	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
$39$	0.0373890	+	0.0868966i	0.00598703	+	0.0139146i
$40$	−1.93013	+	1.73993i	−0.305180	+	0.275108i
$41$	−5.27252	+	3.04409i	−0.823429	+	0.475407i	−0.851598	−	0.524196i	$-0.824366\pi$
$41$	−5.27252	+	3.04409i	−0.823429	+	0.475407i	0.0281682	+	0.999603i	$0.491033\pi$
$42$	0.115733	−	2.44675i	0.0178579	−	0.377542i
$43$	5.64563	+	3.25951i	0.860951	+	0.497070i	0.864331	−	0.502924i	$-0.167742\pi$
$43$	5.64563	+	3.25951i	0.860951	+	0.497070i	−0.00337979	+	0.999994i	$0.501076\pi$
$44$	−1.43572	−	1.83616i	−0.216442	−	0.276812i
$45$	2.64190	−	0.785654i	0.393831	−	0.117118i
$46$	2.20454	−	4.52221i	0.325042	−	0.666763i
$47$	−2.82141	+	4.88682i	−0.411545	+	0.712817i	−0.995059	−	0.0992864i	$-0.968344\pi$
$47$	−2.82141	+	4.88682i	−0.411545	+	0.712817i	0.583514	+	0.812103i	$0.301677\pi$
$48$	−4.39056	−	5.35939i	−0.633722	−	0.773561i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−5.86294	+	0.411120i	−0.829145	+	0.0581412i
$51$	0.667904	−	5.66918i	0.0935253	−	0.793845i
$52$	−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	$-0.261016\pi$
$54$	1.75951	+	7.13471i	0.239439	+	0.970911i
$55$			1.07072i			0.144376i
$56$	2.69050	+	0.872466i	0.359534	+	0.116588i
$57$	0.0923189	−	0.783605i	0.0122279	−	0.103791i
$58$	−0.866355	−	12.3550i	−0.113758	−	1.62229i
$59$	−0.744373	−	1.28929i	−0.0969092	−	0.167852i	0.813495	−	0.581572i	$-0.197562\pi$
$59$	−0.744373	−	1.28929i	−0.0969092	−	0.167852i	−0.910404	+	0.413721i	$0.864229\pi$
$60$	0.0723733	+	3.18181i	0.00934335	+	0.410770i
$61$	−6.35962	+	11.0152i	−0.814266	+	1.41035i	0.0955881	+	0.995421i	$0.469527\pi$
$61$	−6.35962	+	11.0152i	−0.814266	+	1.41035i	−0.909854	+	0.414929i	$0.863807\pi$
$62$	10.3223	+	5.03204i	1.31093	+	0.639069i
$63$	−2.17834	−	2.06272i	−0.274445	−	0.259879i
$64$	7.30457	−	3.26240i	0.913071	−	0.407800i
$65$	0.0434562	+	0.0250895i	0.00539008	+	0.00311197i
$66$	−2.85149	−	0.134877i	−0.350994	−	0.0166022i
$67$	5.83071	−	3.36636i	0.712335	−	0.411267i	−0.0995902	−	0.995029i	$-0.531753\pi$
$67$	5.83071	−	3.36636i	0.712335	−	0.411267i	0.811925	+	0.583762i	$0.198420\pi$
$68$	6.11248	+	2.46684i	0.741247	+	0.299148i
$69$	−2.43530	−	5.65994i	−0.293176	−	0.681376i
$70$	−0.726771	−	1.07703i	−0.0868658	−	0.128730i
$71$	2.97148			0.352650			0.176325	−	0.984332i	$-0.443579\pi$
$71$	2.97148			0.352650			0.176325	+	0.984332i	$0.443579\pi$
$72$	−8.48273	−	0.208066i	−0.999699	−	0.0245208i
$73$	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
$75$	−4.30378	+	5.76993i	−0.496958	+	0.666254i
$76$	0.844877	+	0.340971i	0.0969141	+	0.0391121i
$77$	1.00928	−	0.582708i	0.115018	−	0.0664057i
$78$	−0.0722909	+	0.112570i	−0.00818533	+	0.0127460i
$79$	−10.9305	−	6.31075i	−1.22978	−	0.710015i	−0.262798	−	0.964851i	$-0.584645\pi$
$79$	−10.9305	−	6.31075i	−1.22978	−	0.710015i	−0.966984	+	0.254836i	$0.917979\pi$
$80$	−3.56652	−	0.886292i	−0.398749	−	0.0990904i
$81$	8.02782	+	4.06867i	0.891980	+	0.452075i
$82$	−7.73934	−	3.77287i	−0.854667	−	0.416644i
$83$	−6.56004	+	11.3623i	−0.720058	+	1.24718i	0.240918	+	0.970546i	$0.422552\pi$
$83$	−6.56004	+	11.3623i	−0.720058	+	1.24718i	−0.960976	+	0.276632i	$0.910782\pi$
$84$	2.95984	−	1.79982i	0.322945	−	0.196377i
$85$	−1.51398	−	2.62229i	−0.164214	−	0.284427i
$86$	0.644889	+	9.19670i	0.0695402	+	0.991705i
$87$	−12.1590	−	9.06937i	−1.30358	−	0.972339i
$88$	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	$-0.138447\pi$
$90$	3.01087	+	2.47556i	0.317374	+	0.260947i
$91$		−	0.0546167i		−	0.00572539i
$92$	7.04520	−	0.992928i	0.734513	−	0.103520i
$93$	12.9192	−	5.55876i	1.33966	−	0.576417i
$94$	−7.96060	+	0.558212i	−0.821074	+	0.0575752i
$95$	−0.209265	−	0.362457i	−0.0214701	−	0.0371873i
$96$	2.80959	−	9.38649i	0.286752	−	0.958005i
$97$	−4.26325	+	7.38417i	−0.432868	+	0.749749i	−0.997119	−	0.0758544i	$-0.975832\pi$
$97$	−4.26325	+	7.38417i	−0.432868	+	0.749749i	0.564251	+	0.825603i	$0.309165\pi$
$98$	−0.619704	+	1.27121i	−0.0625995	+	0.128411i
$99$	−2.40393	+	2.53867i	−0.241604	+	0.255146i
$100$	−5.11980	−	6.54781i	−0.511980	−	0.654781i
$101$	11.2424	+	6.49081i	1.11866	+	0.645860i	0.941059	−	0.338242i	$-0.109832\pi$
$101$	11.2424	+	6.49081i	1.11866	+	0.645860i	0.177604	+	0.984102i	$0.443166\pi$
$102$	7.17423	−	3.70161i	0.710354	−	0.366514i
$103$	1.95855	−	1.13077i	0.192982	−	0.111418i	−0.400396	−	0.916342i	$-0.631127\pi$
$103$	1.95855	−	1.13077i	0.192982	−	0.111418i	0.593378	+	0.804924i	$0.297794\pi$
$104$	−0.103434	−	0.114740i	−0.0101425	−	0.0112512i
$105$	−1.58039	−	0.186190i	−0.154230	−	0.0181703i
$106$	12.4798	−	8.42123i	1.21214	−	0.817942i
$107$	−4.66383			−0.450870			−0.225435	−	0.974258i	$-0.572380\pi$
$107$	−4.66383			−0.450870			−0.225435	+	0.974258i	$0.572380\pi$
$108$	−6.97204	+	7.70653i	−0.670885	+	0.741561i
$109$	−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
$111$	2.07652	+	0.244641i	0.197094	+	0.0232203i
$112$	1.10553	+	3.84419i	0.104463	+	0.363242i
$113$	−14.2992	+	8.25566i	−1.34516	+	0.776627i	−0.987559	−	0.157248i	$-0.949738\pi$
$113$	−14.2992	+	8.25566i	−1.34516	+	0.776627i	−0.357599	+	0.933875i	$0.616405\pi$
$114$	0.991635	−	0.511643i	0.0928751	−	0.0479198i
$115$	−2.83049	−	1.63418i	−0.263944	−	0.152388i
$116$	13.7982	−	10.7890i	1.28113	−	1.00173i
$117$	0.0467047	+	0.157053i	0.00431785	+	0.0145195i
$118$	0.922582	−	1.89251i	0.0849305	−	0.174219i
$119$	−1.64787	+	2.85420i	−0.151060	+	0.261644i
$120$	−3.67273	+	2.60180i	−0.335273	+	0.237511i
$121$	4.82090	+	8.35005i	0.438264	+	0.759095i
$122$	−17.9437	+	1.25824i	−1.62454	+	0.113916i
$123$	−9.68645	+	4.16779i	−0.873398	+	0.375797i
$124$	2.26643	+	16.0812i	0.203532	+	1.44413i
$125$			8.41196i			0.752389i
$126$	0.694929	−	4.18534i	0.0619092	−	0.372860i
$127$			17.6270i			1.56415i	0.623186	+	0.782073i	$0.285838\pi$
$127$			17.6270i			1.56415i	−0.623186	+	0.782073i	$0.714162\pi$
$128$	9.60271	+	5.98231i	0.848767	+	0.528767i
$129$	9.05080	+	6.75098i	0.796878	+	0.594391i
$130$	0.00496392	+	0.0707899i	0.000435365	+	0.00620869i
$131$	7.62368	+	13.2046i	0.666084	+	1.15369i	0.978990	+	0.203907i	$0.0653641\pi$
$131$	7.62368	+	13.2046i	0.666084	+	1.15369i	−0.312906	+	0.949784i	$0.601303\pi$
$132$	−2.09754	−	3.44944i	−0.182568	−	0.300235i
$133$	−0.227772	+	0.394512i	−0.0197503	+	0.0342085i
$134$	8.55869	+	4.17229i	0.739358	+	0.360431i
$135$	4.70369	−	0.816048i	0.404829	−	0.0702342i
$136$	1.94341	+	9.11693i	0.166646	+	0.781771i
$137$	−5.64672	−	3.26013i	−0.482432	−	0.278532i	0.238998	−	0.971020i	$-0.423181\pi$
$137$	−5.64672	−	3.26013i	−0.482432	−	0.278532i	−0.721429	+	0.692488i	$0.756515\pi$
$138$	4.70861	−	7.33213i	0.400823	−	0.624152i
$139$	−6.93543	+	4.00417i	−0.588255	+	0.339629i	−0.764407	−	0.644734i	$-0.776968\pi$
$139$	−6.93543	+	4.00417i	−0.588255	+	0.339629i	0.176152	+	0.984363i	$0.443635\pi$
$140$	0.687676	−	1.70396i	0.0581193	−	0.144011i
$141$	−5.84361	+	7.83431i	−0.492121	+	0.659768i
$142$	2.35058	+	3.48341i	0.197256	+	0.292322i
$143$	−0.0636512			−0.00532278
$144$	−6.46632	−	10.1087i	−0.538860	−	0.842396i
$145$	−8.04616			−0.668197
$146$	11.7244	+	17.3749i	0.970319	+	1.43796i
$147$	0.684571	+	1.59103i	0.0564625	+	0.131226i
$148$	−0.903559	+	2.23889i	−0.0742721	+	0.184035i
$149$	1.41090	−	0.814584i	0.115585	−	0.0667333i	−0.441093	−	0.897462i	$-0.645409\pi$
$149$	1.41090	−	0.814584i	0.115585	−	0.0667333i	0.556678	+	0.830728i	$0.312076\pi$
$150$	−10.1685	−	0.480974i	−0.830252	−	0.0392713i
$151$	−4.43451	−	2.56026i	−0.360875	−	0.208351i	0.308589	−	0.951195i	$-0.400143\pi$
$151$	−4.43451	−	2.56026i	−0.360875	−	0.208351i	−0.669465	+	0.742844i	$0.733476\pi$
$152$	0.268622	+	1.26016i	0.0217881	+	0.102212i
$153$	2.29780	−	9.61651i	0.185766	−	0.777449i
$154$	1.48148	+	0.722212i	0.119381	+	0.0581975i
$155$	3.73015	−	6.46080i	0.299612	−	0.518944i
$156$	−0.189149	+	0.00430237i	−0.0151440	+	0.000344465i
$157$	0.242007	+	0.419168i	0.0193142	+	0.0334532i	0.875521	−	0.483180i	$-0.160518\pi$
$157$	0.242007	+	0.419168i	0.0193142	+	0.0334532i	−0.856207	+	0.516633i	$0.827185\pi$
$158$	−1.24857	−	17.8058i	−0.0993313	−	1.41655i
$159$	2.15742	−	18.3122i	0.171095	−	1.45225i
$160$	−1.78229	−	4.88206i	−0.140903	−	0.385961i
$161$			3.55741i			0.280363i
$162$	1.58074	+	12.6294i	0.124194	+	0.992258i
$163$			23.8078i			1.86477i	0.361466	+	0.932385i	$0.382276\pi$
$163$			23.8078i			1.86477i	−0.361466	+	0.932385i	$0.617724\pi$
$164$	−1.69930	−	12.0572i	−0.132693	−	0.941510i
$165$	−0.216989	+	1.84181i	−0.0168926	+	0.143385i
$166$	−18.5092	+	1.29790i	−1.43659	+	0.100736i
$167$	−9.37726	−	16.2419i	−0.725634	−	1.25684i	−0.958713	−	0.284377i	$-0.908213\pi$
$167$	−9.37726	−	16.2419i	−0.725634	−	1.25684i	0.233078	−	0.972458i	$-0.425120\pi$
$168$	4.45127	+	2.04602i	0.343423	+	0.157854i
$169$	6.49851	−	11.2557i	0.499885	−	0.865827i
$170$	1.87643	−	3.84916i	0.143916	−	0.295217i
$171$	0.317606	−	1.32921i	0.0242879	−	0.101647i
$172$	−10.2710	+	8.03100i	−0.783156	+	0.612358i
$173$	15.3852	+	8.88264i	1.16971	+	0.675334i	0.953613	−	0.301037i	$-0.0973327\pi$
$173$	15.3852	+	8.88264i	1.16971	+	0.675334i	0.216101	+	0.976371i	$0.430666\pi$
$174$	1.01356	−	21.4281i	0.0768376	−	1.62446i
$175$	3.59912	−	2.07795i	0.272068	−	0.157078i
$176$	4.48008	−	1.28841i	0.337699	−	0.0971173i
$177$	−1.01915	−	2.36863i	−0.0766042	−	0.178037i
$178$	9.31985	−	6.28895i	0.698553	−	0.471377i
$179$	7.17934			0.536609			0.268305	−	0.963334i	$-0.413537\pi$
$179$	7.17934			0.536609			0.268305	+	0.963334i	$0.413537\pi$
$180$	−0.520322	+	5.48787i	−0.0387825	+	0.409042i
$181$	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
$183$	−13.1718	+	17.6590i	−0.973689	+	1.30539i
$184$	6.73707	+	7.47352i	0.496663	+	0.550955i
$185$	0.960495	−	0.554542i	0.0706170	−	0.0407708i
$186$	16.7361	+	10.7478i	1.22715	+	0.788064i
$187$	3.32633	+	1.92045i	0.243245	+	0.140438i
$188$	−6.95158	−	8.89051i	−0.506996	−	0.648407i
$189$	−3.32906	−	3.98966i	−0.242153	−	0.290205i
$190$	0.259364	−	0.532037i	0.0188163	−	0.0385981i
$191$	12.0033	−	20.7903i	0.868527	−	1.50433i	0.00502585	−	0.999987i	$-0.498400\pi$
$191$	12.0033	−	20.7903i	0.868527	−	1.50433i	0.863502	−	0.504346i	$-0.168266\pi$
$192$	13.2261	−	4.13151i	0.954514	−	0.298166i
$193$	−8.57949	−	14.8601i	−0.617565	−	1.06965i	−0.989929	−	0.141567i	$-0.954786\pi$
$193$	−8.57949	−	14.8601i	−0.617565	−	1.06965i	0.372363	−	0.928087i	$-0.378548\pi$
$194$	−12.0288	+	0.843479i	−0.863615	+	0.0605583i
$195$	0.0696669	+	0.0519645i	0.00498895	+	0.00372125i
$196$	−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	$0.972744\pi$
$198$	−4.87766	−	0.809881i	−0.346640	−	0.0575558i
$199$		−	2.50012i		−	0.177229i	−0.996066	−	0.0886146i	$-0.971756\pi$
$199$		−	2.50012i		−	0.177229i	0.996066	−	0.0886146i	$-0.0282439\pi$
$200$	3.62588	−	11.1815i	0.256389	−	0.790649i
$201$	10.7119	−	4.60903i	0.755562	−	0.325096i
$202$	1.28420	+	18.3138i	0.0903560	+	1.28856i
$203$	4.37887	+	7.58443i	0.307337	+	0.532323i
$204$	10.0145	+	5.48208i	0.701154	+	0.383822i
$205$	−2.79675	+	4.84412i	−0.195334	+	0.338328i
$206$	2.87489	+	1.40149i	0.200303	+	0.0976461i
$207$	−3.04207	−	10.2295i	−0.211439	−	0.710999i
$208$	0.0526873	−	0.212018i	0.00365321	−	0.0147008i
$209$	0.459771	+	0.265449i	0.0318030	+	0.0183615i
$210$	−1.03189	−	1.99995i	−0.0712072	−	0.138009i
$211$	−2.68339	+	1.54926i	−0.184732	+	0.106655i	−0.589514	−	0.807758i	$-0.700681\pi$
$211$	−2.68339	+	1.54926i	−0.184732	+	0.106655i	0.404782	+	0.914413i	$0.367347\pi$
$212$	19.7441	+	7.96823i	1.35603	+	0.547260i
$213$	5.11140	+	0.602190i	0.350227	+	0.0412614i
$214$	−3.68930	−	5.46733i	−0.252196	−	0.373739i
$215$	5.98933			0.408469
$216$	−14.5494	−	2.07699i	−0.989964	−	0.141321i
$217$	−8.12007			−0.551226
$218$	−8.79771	−	13.0377i	−0.595856	−	0.883023i
$219$	25.4951	+	3.00366i	1.72280	+	0.202968i
$220$	−1.98582	−	0.801429i	−0.133884	−	0.0540323i
$221$	0.155887	−	0.0900013i	0.0104861	−	0.00605414i
$222$	1.35583	+	2.62779i	0.0909975	+	0.176366i
$223$	−7.33815	−	4.23669i	−0.491399	−	0.283709i	0.233756	−	0.972295i	$-0.424898\pi$
$223$	−7.33815	−	4.23669i	−0.491399	−	0.283709i	−0.725155	+	0.688586i	$0.758232\pi$
$224$	−3.63195	+	4.33693i	−0.242670	+	0.289773i
$225$	−8.57248	+	9.05297i	−0.571499	+	0.603531i
$226$	−20.9893	−	10.2321i	−1.39619	−	0.680631i
$227$	6.73436	−	11.6643i	0.446975	−	0.774184i	−0.551212	−	0.834365i	$-0.685835\pi$
$227$	6.73436	−	11.6643i	0.446975	−	0.774184i	0.998187	+	0.0601814i	$0.0191679\pi$
$228$	1.38422	+	0.757743i	0.0916722	+	0.0501828i
$229$	−3.16856	−	5.48811i	−0.209385	−	0.362665i	0.742136	−	0.670249i	$-0.233813\pi$
$229$	−3.16856	−	5.48811i	−0.209385	−	0.362665i	−0.951521	+	0.307584i	$0.900479\pi$
$230$	−0.323321	−	4.61084i	−0.0213192	−	0.304030i
$231$	1.85421	−	0.797810i	0.121998	−	0.0524920i
$232$	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	$-0.0345610\pi$
$234$	−0.147164	+	0.178987i	−0.00962044	+	0.0117007i
$235$			5.18433i			0.338188i
$236$	2.94836	−	0.415532i	0.191922	−	0.0270488i
$237$	−17.5233	−	13.0706i	−1.13826	−	0.849028i
$238$	−4.64947	+	0.326029i	−0.301380	+	0.0211333i
$239$	−9.17721	−	15.8954i	−0.593624	−	1.02819i	−0.993739	−	0.111722i	$-0.964363\pi$
$239$	−9.17721	−	15.8954i	−0.593624	−	1.02819i	0.400115	−	0.916465i	$-0.368970\pi$
$240$	−5.95534	−	2.24734i	−0.384416	−	0.145065i
$241$	10.5580	−	18.2871i	0.680103	−	1.17797i	−0.294846	−	0.955545i	$-0.595268\pi$
$241$	10.5580	−	18.2871i	0.680103	−	1.17797i	0.974949	−	0.222429i	$-0.0713984\pi$
$242$	−5.97506	+	12.2567i	−0.384092	+	0.787893i
$243$	12.9845	+	8.62564i	0.832959	+	0.553335i
$244$	−15.6693	−	20.0397i	−1.00312	−	1.28291i
$245$	0.795659	+	0.459374i	0.0508328	+	0.0293483i
$246$	−12.5483	−	8.05835i	−0.800048	−	0.513781i
$247$	0.0215470	−	0.0124401i	0.00137100	−	0.000791547i
$248$	−17.0589	+	15.3779i	−1.08324	+	0.976496i
$249$	−13.5869	+	18.2155i	−0.861037	+	1.15436i
$250$	−9.86120	+	6.65425i	−0.623677	+	0.420852i
$251$	13.9450			0.880199			0.440099	−	0.897949i	$-0.354943\pi$
$251$	13.9450			0.880199			0.440099	+	0.897949i	$0.354943\pi$
$252$	5.45612	−	2.49614i	0.343703	−	0.157242i
$253$	4.14587			0.260648
$254$	−20.6639	+	13.9438i	−1.29657	+	0.874912i
$255$	−2.07285	−	4.81755i	−0.129807	−	0.301687i
$256$	0.583221	+	15.9894i	0.0364513	+	0.999335i
$257$	9.32528	−	5.38395i	0.581695	−	0.335842i	−0.180112	−	0.983646i	$-0.557646\pi$
$257$	9.32528	−	5.38395i	0.581695	−	0.335842i	0.761807	+	0.647804i	$0.224313\pi$
$258$	−0.754463	+	15.9504i	−0.0469708	+	0.993030i
$259$	−1.04544	−	0.603585i	−0.0649605	−	0.0375049i
$260$	−0.0790591	+	0.0618172i	−0.00490304	+	0.00383374i
$261$	−19.0774	−	18.0648i	−1.18086	−	1.11818i
$262$	−9.44884	+	19.3825i	−0.583751	+	1.19746i
$263$	−8.12745	+	14.0772i	−0.501160	+	0.868034i	0.498839	+	0.866695i	$0.333760\pi$
$263$	−8.12745	+	14.0772i	−0.501160	+	0.868034i	−0.999999	+	0.00133978i	$0.999574\pi$
$264$	2.38447	−	5.18758i	0.146754	−	0.319273i
$265$	−4.89035	−	8.47033i	−0.300412	−	0.520329i
$266$	−0.642658	+	0.0450644i	−0.0394039	+	0.00276307i
$267$	1.61116	−	13.6755i	0.0986012	−	0.836929i
$268$	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	$0.910429\pi$
$270$	4.67747	+	4.86852i	0.284662	+	0.296289i
$271$		−	31.7070i		−	1.92606i	−0.269385	−	0.963032i	$-0.586820\pi$
$271$		−	31.7070i		−	1.92606i	0.269385	−	0.963032i	$-0.413180\pi$
$272$	−9.15029	+	9.49014i	−0.554818	+	0.575424i
$273$	0.0110684	−	0.0939491i	0.000669892	−	0.00568606i
$274$	−0.645013	−	9.19846i	−0.0389667	−	0.555700i
$275$	−2.42168	−	4.19447i	−0.146033	−	0.252936i
$276$	12.3201	−	0.280231i	0.741580	−	0.0168679i
$277$	−0.801334	+	1.38795i	−0.0481475	+	0.0833939i	−0.889095	−	0.457723i	$-0.848665\pi$
$277$	−0.801334	+	1.38795i	−0.0481475	+	0.0833939i	0.840947	+	0.541117i	$0.181998\pi$
$278$	−10.1803	−	4.96280i	−0.610571	−	0.297649i
$279$	23.3496	−	6.94376i	1.39790	−	0.415712i
$280$	2.54151	−	0.541761i	0.151884	−	0.0323764i
$281$	−19.1083	−	11.0322i	−1.13991	−	0.658126i	−0.193500	−	0.981100i	$-0.561984\pi$
$281$	−19.1083	−	11.0322i	−1.13991	−	0.658126i	−0.946408	+	0.322974i	$0.895317\pi$
$282$	−13.8066	−	0.653058i	−0.822171	−	0.0388891i
$283$	18.0711	−	10.4334i	1.07422	−	0.620200i	0.144887	−	0.989448i	$-0.453718\pi$
$283$	18.0711	−	10.4334i	1.07422	−	0.620200i	0.929331	+	0.369249i	$0.120385\pi$
$284$	−2.22413	+	5.51108i	−0.131978	+	0.327022i
$285$	−0.286513	−	0.665891i	−0.0169716	−	0.0394440i
$286$	−0.0503510	−	0.0746172i	−0.00297732	−	0.00441220i
$287$	6.08818			0.359374
$288$	6.73516	−	15.5768i	0.396873	−	0.917874i
$289$	6.13809			0.361064
$290$	−6.36488	−	9.43237i	−0.373759	−	0.553888i
$291$	−8.82990	+	11.8379i	−0.517618	+	0.693952i
$292$	−11.0937	+	27.4886i	−0.649211	+	1.60865i
$293$	16.0686	−	9.27721i	0.938737	−	0.541980i	0.0491729	−	0.998790i	$-0.484341\pi$
$293$	16.0686	−	9.27721i	0.938737	−	0.541980i	0.889564	+	0.456810i	$0.151008\pi$
$294$	−1.32360	+	2.06108i	−0.0771942	+	0.120205i
$295$	−1.18453	−	0.683891i	−0.0689662	−	0.0398177i
$296$	−3.33937	+	0.711837i	−0.194097	+	0.0413747i
$297$	−4.64961	+	3.87974i	−0.269798	+	0.225125i
$298$	2.07101	+	1.00960i	0.119970	+	0.0584846i
$299$	0.0971471	−	0.168264i	0.00561816	−	0.00973094i
$300$	−7.47989	−	12.3008i	−0.431852	−	0.710187i
$301$	−3.25951	−	5.64563i	−0.187875	−	0.325409i
$302$	−0.506545	−	7.22378i	−0.0291484	−	0.415682i
$303$	18.0233	+	13.4436i	1.03541	+	0.772312i
$304$	−1.26477	+	1.31174i	−0.0725395	+	0.0752337i
$305$			11.6858i			0.669125i
$306$	13.0909	−	4.91344i	0.748359	−	0.280882i
$307$			3.11806i			0.177957i	0.996034	+	0.0889786i	$0.0283603\pi$
$307$			3.11806i			0.177957i	−0.996034	+	0.0889786i	$0.971640\pi$
$308$	0.325285	+	2.30802i	0.0185348	+	0.131512i
$309$	3.59817	−	1.54819i	0.204693	−	0.0880732i
$310$	10.5246	−	0.738005i	0.597757	−	0.0419158i
$311$	10.5991	+	18.3581i	0.601018	+	1.04099i	0.992667	+	0.120879i	$0.0385713\pi$
$311$	10.5991	+	18.3581i	0.601018	+	1.04099i	−0.391649	+	0.920115i	$0.628095\pi$
$312$	−0.154669	−	0.218333i	−0.00875641	−	0.0123606i
$313$	11.7962	−	20.4317i	0.666762	−	1.15487i	−0.312042	−	0.950068i	$-0.601013\pi$
$313$	11.7962	−	20.4317i	0.666762	−	1.15487i	0.978804	−	0.204798i	$-0.0656536\pi$
$314$	−0.299945	+	0.615281i	−0.0169269	+	0.0347223i
$315$	−2.68078	−	0.640552i	−0.151045	−	0.0360910i
$316$	19.8857	−	15.5489i	1.11866	−	0.874692i
$317$	15.8115	+	9.12879i	0.888064	+	0.512724i	0.873309	−	0.487167i	$-0.161970\pi$
$317$	15.8115	+	9.12879i	0.888064	+	0.512724i	0.0147552	+	0.999891i	$0.495303\pi$
$318$	23.1737	−	11.9567i	1.29952	−	0.670499i
$319$	8.83902	−	5.10321i	0.494890	−	0.285725i
$320$	4.31328	−	5.95129i	0.241120	−	0.332687i
$321$	−8.02251	−	0.945157i	−0.447773	−	0.0527535i
$322$	−4.17029	+	2.81408i	−0.232401	+	0.156822i
$323$	−1.50135			−0.0835375
$324$	−13.5548	+	11.8435i	−0.753043	+	0.657972i
$325$	−0.226982			−0.0125907
$326$	−27.9095	+	18.8331i	−1.54576	+	1.04307i
$327$	−19.1309	−	2.25387i	−1.05794	−	0.124639i
$328$	12.7902	−	11.5299i	0.706222	−	0.636630i
$329$	4.88682	−	2.82141i	0.269419	−	0.155549i
$330$	−2.33077	+	1.20258i	−0.128305	+	0.0662000i
$331$	−19.6152	−	11.3248i	−1.07815	−	0.622468i	−0.147751	−	0.989025i	$-0.547203\pi$
$331$	−19.6152	−	11.3248i	−1.07815	−	0.622468i	−0.930396	+	0.366557i	$0.880537\pi$
$332$	−16.1631	−	20.6713i	−0.887065	−	1.13448i
$333$	3.52235	+	0.841641i	0.193024	+	0.0461216i
$334$	11.6222	−	23.8409i	0.635941	−	1.30451i
$335$	3.09284	−	5.35695i	0.168980	−	0.292681i
$336$	1.12264	+	6.83664i	0.0612450	+	0.372969i
$337$	2.63847	+	4.56997i	0.143727	+	0.248942i	0.928897	−	0.370338i	$-0.120758\pi$
$337$	2.63847	+	4.56997i	0.143727	+	0.248942i	−0.785170	+	0.619280i	$0.787425\pi$
$338$	18.3355	−	1.28572i	0.997322	−	0.0699340i
$339$	−26.2699	+	11.3032i	−1.42679	+	0.613904i
$340$	5.99665	−	0.845148i	0.325214	−	0.0458346i
$341$			9.46325i			0.512464i
$342$	1.80945	−	0.679144i	0.0978440	−	0.0367239i
$343$		−	1.00000i		−	0.0539949i
$344$	−17.5394	−	5.68761i	−0.945662	−	0.306656i
$345$	−4.53770	−	3.38466i	−0.244301	−	0.182224i
$346$	1.75742	+	25.0623i	0.0944794	+	1.34736i
$347$	3.73945	+	6.47693i	0.200744	+	0.347700i	0.948769	−	0.315972i	$-0.102331\pi$
$347$	3.73945	+	6.47693i	0.200744	+	0.347700i	−0.748024	+	0.663672i	$0.768997\pi$
$348$	25.9215	−	15.7624i	1.38954	−	0.844953i
$349$	−9.00083	+	15.5899i	−0.481803	+	0.834508i	−0.999782	−	0.0208860i	$-0.993351\pi$
$349$	−9.00083	+	15.5899i	−0.481803	+	0.834508i	0.517979	+	0.855393i	$0.326685\pi$
$350$	5.28301	+	2.57543i	0.282389	+	0.137662i
$351$	0.0485115	+	0.279620i	0.00258935	+	0.0149250i
$352$	5.05432	+	4.23273i	0.269396	+	0.225605i
$353$	−3.79516	−	2.19114i	−0.201996	−	0.116622i	0.395590	−	0.918427i	$-0.370540\pi$
$353$	−3.79516	−	2.19114i	−0.201996	−	0.116622i	−0.597586	+	0.801805i	$0.703873\pi$
$354$	1.97051	−	3.06843i	0.104732	−	0.163085i
$355$	2.36428	−	1.36502i	0.125483	−	0.0724477i
$356$	14.7449	+	5.95065i	0.781476	+	0.315384i
$357$	−3.41301	+	4.57571i	−0.180636	+	0.242172i
$358$	5.67919	+	8.41622i	0.300155	+	0.444811i
$359$	−27.6893			−1.46138			−0.730692	−	0.682707i	$-0.760803\pi$
$359$	−27.6893			−1.46138			−0.730692	+	0.682707i	$0.760803\pi$
$360$	−6.84494	+	3.73119i	−0.360760	+	0.196651i
$361$	18.7925			0.989078
$362$	2.21202	+	3.27809i	0.116261	+	0.172292i
$363$	6.60050	+	15.3404i	0.346437	+	0.805160i
$364$	0.101295	+	0.0408802i	0.00530932	+	0.00214271i
$365$	11.7928	−	6.80856i	0.617262	−	0.356377i
$366$	−31.1208	−	1.47203i	−1.62671	−	0.0769443i
$367$	5.23819	+	3.02427i	0.273431	+	0.157866i	0.630446	−	0.776233i	$-0.282872\pi$
$367$	5.23819	+	3.02427i	0.273431	+	0.157866i	−0.357015	+	0.934099i	$0.616205\pi$
$368$	−3.43174	+	13.8096i	−0.178892	+	0.719877i
$369$	−17.5068	+	5.20622i	−0.911369	+	0.271025i
$370$	1.40988	+	0.687304i	0.0732960	+	0.0357312i
$371$	−5.32284	+	9.21944i	−0.276348	+	0.478649i
$372$	0.639649	+	28.1215i	0.0331643	+	1.45803i
$373$	15.9639	+	27.6503i	0.826579	+	1.43168i	0.900706	+	0.434428i	$0.143050\pi$
$373$	15.9639	+	27.6503i	0.826579	+	1.43168i	−0.0741274	+	0.997249i	$0.523617\pi$
$374$	0.379960	+	5.41856i	0.0196472	+	0.280187i
$375$	−1.70474	+	14.4699i	−0.0880324	+	0.747221i
$376$	4.92317	−	15.1820i	0.253893	−	0.782953i
$377$		−	0.478319i		−	0.0246347i
$378$	2.04357	−	7.05860i	0.105110	−	0.363055i
$379$		−	4.79709i		−	0.246410i	−0.992381	−	0.123205i	$-0.960683\pi$
$379$		−	4.79709i		−	0.246410i	0.992381	−	0.123205i	$-0.0393172\pi$
$380$	0.828867	−	0.116818i	0.0425200	−	0.00599263i
$381$	−3.57224	+	30.3212i	−0.183011	+	1.55340i
$382$	33.8673	−	2.37484i	1.73280	−	0.121507i
$383$	4.80699	+	8.32595i	0.245626	+	0.425436i	0.962307	−	0.271964i	$-0.0876732\pi$
$383$	4.80699	+	8.32595i	0.245626	+	0.425436i	−0.716682	+	0.697401i	$0.754340\pi$
$384$	15.3058	+	12.2365i	0.781070	+	0.624444i
$385$	0.535361	−	0.927273i	0.0272845	−	0.0472582i
$386$	10.6335	−	21.8126i	0.541230	−	1.11023i
$387$	14.2006	+	13.4469i	0.721859	+	0.683546i
$388$	−10.5041	−	13.4339i	−0.533265	−	0.682002i
$389$	2.41372	+	1.39356i	0.122381	+	0.0706565i	0.559941	−	0.828533i	$-0.310824\pi$
$389$	2.41372	+	1.39356i	0.122381	+	0.0706565i	−0.437560	+	0.899189i	$0.644157\pi$
$390$	−0.00580734	+	0.122776i	−0.000294066	+	0.00621698i
$391$	−10.1536	+	5.86216i	−0.513487	+	0.296462i
$392$	−1.89381	−	2.10083i	−0.0956519	−	0.106108i
$393$	10.4379	+	24.2589i	0.526522	+	1.22370i
$394$	−2.81429	+	1.89906i	−0.141782	+	0.0956731i
$395$	−11.5960			−0.583457
$396$	−2.90904	−	6.35865i	−0.146185	−	0.319534i
$397$	−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
$399$	−0.471753	+	0.632462i	−0.0236172	+	0.0316627i
$400$	15.9761	−	4.59449i	0.798804	−	0.229725i
$401$	−16.1356	+	9.31590i	−0.805774	+	0.465214i	−0.845486	−	0.533997i	$-0.820689\pi$
$401$	−16.1356	+	9.31590i	−0.805774	+	0.465214i	0.0397119	+	0.999211i	$0.487356\pi$
$402$	13.8767	+	8.91147i	0.692108	+	0.444463i
$403$	0.384075	+	0.221746i	0.0191321	+	0.0110459i
$404$	−20.4531	+	15.9925i	−1.01758	+	0.795658i
$405$	8.25645	−	0.450494i	0.410266	−	0.0223852i
$406$	−5.42721	+	11.1329i	−0.269348	+	0.552517i
$407$	−0.703427	+	1.21837i	−0.0348676	+	0.0603925i
$408$	1.49536	+	16.0764i	0.0740315	+	0.795899i
$409$	−14.9066	−	25.8189i	−0.737082	−	1.27666i	−0.953804	−	0.300430i	$-0.902870\pi$
$409$	−14.9066	−	25.8189i	−0.737082	−	1.27666i	0.216722	−	0.976233i	$-0.430463\pi$
$410$	−7.89103	+	0.553334i	−0.389710	+	0.0273272i
$411$	−9.05254	−	6.75228i	−0.446529	−	0.333065i
$412$	0.631230	+	4.47882i	0.0310985	+	0.220656i
$413$			1.48875i			0.0732564i
$414$	9.58544	−	11.6582i	0.471099	−	0.572968i
$415$			12.0540i			0.591710i
$416$	0.290224	−	0.105952i	0.0142294	−	0.00519471i
$417$	−12.7415	+	5.48228i	−0.623953	+	0.268468i
$418$	0.0525187	+	0.748963i	0.00256877	+	0.0366330i
$419$	1.72249	+	2.98343i	0.0841490	+	0.145750i	0.905028	−	0.425351i	$-0.139850\pi$
$419$	1.72249	+	2.98343i	0.0841490	+	0.145750i	−0.820879	+	0.571102i	$0.806516\pi$
$420$	1.52823	−	2.79172i	0.0745699	−	0.136222i
$421$	7.39756	−	12.8130i	0.360535	−	0.624465i	−0.627514	−	0.778605i	$-0.715927\pi$
$421$	7.39756	−	12.8130i	0.360535	−	0.624465i	0.988049	+	0.154140i	$0.0492607\pi$
$422$	−3.93885	−	1.92016i	−0.191740	−	0.0934720i
$423$	−11.6396	+	12.2920i	−0.565936	+	0.597657i
$424$	6.27749	+	29.4489i	0.304862	+	1.43017i
$425$	11.8618	+	6.84839i	0.575380	+	0.332196i
$426$	3.33742	+	6.46837i	0.161698	+	0.313393i
$427$	11.0152	−	6.35962i	0.533062	−	0.307764i
$428$	3.49085	−	8.64981i	0.168736	−	0.418105i
$429$	−0.109490	−	0.0128993i	−0.00528622	−	0.000622786i
$430$	4.73783	+	7.02118i	0.228479	+	0.338592i
$431$	16.9467			0.816293			0.408146	−	0.912917i	$-0.366175\pi$
$431$	16.9467			0.816293			0.408146	+	0.912917i	$0.366175\pi$
$432$	−9.07445	−	18.6990i	−0.436595	−	0.899658i
$433$	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
$435$	−13.8406	−	1.63061i	−0.663608	−	0.0781817i
$436$	8.32445	−	20.6268i	0.398669	−	0.987844i
$437$	−1.40344	+	0.810278i	−0.0671358	+	0.0387609i
$438$	16.6467	+	32.2635i	0.795408	+	1.54161i
$439$	−13.3048	−	7.68154i	−0.635004	−	0.366620i	0.147683	−	0.989035i	$-0.452818\pi$
$439$	−13.3048	−	7.68154i	−0.635004	−	0.366620i	−0.782687	+	0.622415i	$0.786152\pi$
$440$	−0.631377	−	2.96191i	−0.0300997	−	0.141204i
$441$	0.855136	+	2.87554i	0.0407208	+	0.136931i
$442$	0.228820	+	0.111548i	0.0108839	+	0.00530581i
$443$	8.16517	−	14.1425i	0.387939	−	0.671930i	−0.604233	−	0.796807i	$-0.706520\pi$
$443$	8.16517	−	14.1425i	0.387939	−	0.671930i	0.992172	+	0.124878i	$0.0398538\pi$
$444$	−2.00799	+	3.66812i	−0.0952948	+	0.174081i
$445$	−3.65210	−	6.32563i	−0.173126	−	0.299863i
$446$	−0.838223	−	11.9538i	−0.0396910	−	0.566029i
$447$	2.59205	−	1.11528i	0.122600	−	0.0527510i
$448$	−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	$0.902875\pi$
$450$	−17.3939	−	2.88806i	−0.819955	−	0.136144i
$451$		−	7.09526i		−	0.334103i
$452$	−4.60856	−	32.6995i	−0.216768	−	1.53805i
$453$	−7.10918	−	5.30273i	−0.334019	−	0.249144i
$454$	19.0010	−	1.33238i	0.891760	−	0.0625319i
$455$	−0.0250895	−	0.0434562i	−0.00117621	−	0.00203726i
$456$	0.206692	+	2.22211i	0.00967923	+	0.104060i
$457$	8.98114	−	15.5558i	0.420120	−	0.727669i	−0.575831	−	0.817569i	$-0.695321\pi$
$457$	8.98114	−	15.5558i	0.420120	−	0.727669i	0.995951	+	0.0898997i	$0.0286546\pi$
$458$	3.92714	−	8.05580i	0.183503	−	0.376423i
$459$	5.90141	−	16.0762i	0.275454	−	0.750374i
$460$	5.14945	−	4.02641i	0.240094	−	0.187732i
$461$	−1.90455	−	1.09959i	−0.0887038	−	0.0512132i	0.454992	−	0.890496i	$-0.349642\pi$
$461$	−1.90455	−	1.09959i	−0.0887038	−	0.0512132i	−0.543696	+	0.839282i	$0.682975\pi$
$462$	2.40202	+	1.54255i	0.111752	+	0.0717659i
$463$	−0.0470644	+	0.0271726i	−0.00218727	+	0.00126282i	−0.501093	−	0.865393i	$-0.667069\pi$
$463$	−0.0470644	+	0.0271726i	−0.00218727	+	0.00126282i	0.498906	+	0.866656i	$0.333735\pi$
$464$	9.68199	+	33.6664i	0.449475	+	1.56293i
$465$	7.72575	−	10.3576i	0.358273	−	0.480324i
$466$	3.87813	−	2.61693i	0.179651	−	0.121227i
$467$	−32.8935			−1.52213			−0.761065	−	0.648676i	$-0.775323\pi$
$467$	−32.8935			−1.52213			−0.761065	+	0.648676i	$0.775323\pi$
$468$	−0.326237	−	0.0309315i	−0.0150803	−	0.00142981i
$469$	−6.73273			−0.310888
$470$	−6.07750	+	4.10104i	−0.280334	+	0.189167i
$471$	0.331342	+	0.770078i	0.0152674	+	0.0354833i
$472$	2.81940	+	3.12760i	0.129774	+	0.143960i
$473$	−6.57951	+	3.79868i	−0.302526	+	0.174664i
$474$	1.46072	−	30.8817i	0.0670931	−	1.41844i
$475$	1.63955	+	0.946597i	0.0752279	+	0.0434329i
$476$	−4.06014	−	5.19258i	−0.186096	−	0.238002i
$477$	7.42219	−	31.0626i	0.339839	−	1.42226i
$478$	11.3743	−	23.3323i	0.520248	−	1.06719i
$479$	−8.02688	+	13.9030i	−0.366758	+	0.635243i	−0.989057	−	0.147537i	$-0.952865\pi$
$479$	−8.02688	+	13.9030i	−0.366758	+	0.635243i	0.622299	+	0.782780i	$0.286199\pi$
$480$	−2.07644	−	8.75909i	−0.0947759	−	0.399796i
$481$	0.0329658	+	0.0570985i	0.00150311	+	0.00260347i
$482$	29.7895	−	2.08890i	1.35687	−	0.0951466i
$483$	−0.720934	+	6.11930i	−0.0328036	+	0.278438i
$484$	−19.0949	+	2.69117i	−0.867950	+	0.122326i
$485$			7.83370i			0.355710i
$486$	0.159683	+	22.0448i	0.00724337	+	0.999974i
$487$			18.2339i			0.826258i	0.910673	+	0.413129i	$0.135564\pi$
$487$			18.2339i			0.826258i	−0.910673	+	0.413129i	$0.864436\pi$
$488$	11.0971	−	34.2211i	0.502342	−	1.54912i
$489$	−4.82481	+	40.9531i	−0.218185	+	1.85196i
$490$	0.0908865	+	1.29612i	0.00410583	+	0.0585528i
$491$	−14.8772	−	25.7680i	−0.671398	−	1.16289i	−0.977508	−	0.210899i	$-0.932361\pi$
$491$	−14.8772	−	25.7680i	−0.671398	−	1.16289i	0.306110	−	0.951996i	$-0.400972\pi$
$492$	−0.479590	−	21.0846i	−0.0216216	−	0.950569i
$493$	−14.4316	+	24.9963i	−0.649968	+	1.12578i
$494$	0.0316280	+	0.0154184i	0.00142301	+	0.000693707i
$495$	−0.746510	+	3.12422i	−0.0335531	+	0.140423i
$496$	−31.5216	−	7.83322i	−1.41536	−	0.351722i
$497$	−2.57338	−	1.48574i	−0.115432	−	0.0666445i
$498$	−32.1016	−	1.51842i	−1.43851	−	0.0680421i
$499$	−37.1029	+	21.4213i	−1.66095	+	0.958951i	−0.688690	+	0.725056i	$0.741814\pi$
$499$	−37.1029	+	21.4213i	−1.66095	+	0.958951i	−0.972262	+	0.233895i	$0.924853\pi$
$500$	−15.6013	−	6.29630i	−0.697712	−	0.281579i
$501$	−12.8388	−	29.8389i	−0.573595	−	1.33310i
$502$	11.0311	+	16.3474i	0.492342	+	0.729622i
$503$	−14.2832			−0.636855			−0.318427	−	0.947947i	$-0.603155\pi$
$503$	−14.2832			−0.636855			−0.318427	+	0.947947i	$0.603155\pi$
$504$	7.24223	+	4.42156i	0.322594	+	0.196952i
$505$	11.9268			0.530737
$506$	3.27957	+	4.86013i	0.145795	+	0.216059i
$507$	13.4595	−	18.0447i	0.597757	−	0.801391i
$508$	−32.6921	−	13.1937i	−1.45048	−	0.585377i
$509$	18.9344	−	10.9318i	0.839254	−	0.484543i	−0.0177568	−	0.999842i	$-0.505652\pi$
$509$	18.9344	−	10.9318i	0.839254	−	0.484543i	0.857010	+	0.515299i	$0.172319\pi$
$510$	4.00781	−	6.24087i	0.177469	−	0.276350i
$511$	−12.8357	−	7.41070i	−0.567819	−	0.327830i
$512$	−18.2827	+	13.3320i	−0.807989	+	0.589198i
$513$	0.815704	−	2.22208i	0.0360142	−	0.0981074i
$514$	13.6882	+	6.67291i	0.603762	+	0.294330i
$515$	1.03889	−	1.79941i	0.0457791	−	0.0792917i
$516$	−19.2952	+	11.7331i	−0.849425	+	0.516520i
$517$	−3.28812	−	5.69518i	−0.144611	−	0.250474i
$518$	−0.119419	−	1.70301i	−0.00524695	−	0.0748262i
$519$	24.6648	+	18.3974i	1.08266	+	0.807557i
$520$	−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	$-0.334781\pi$
$522$	6.08601	−	36.6542i	0.266378	−	1.60431i
$523$		−	16.0515i		−	0.701885i	−0.936397	−	0.350943i	$-0.885861\pi$
$523$		−	16.0515i		−	0.701885i	0.936397	−	0.350943i	$-0.114139\pi$
$524$	−30.1963	+	4.25577i	−1.31913	+	0.185914i
$525$	6.61215	−	2.84501i	0.288578	−	0.124166i
$526$	−22.9316	+	1.60801i	−0.999864	+	0.0701124i
$527$	−13.3808	−	23.1763i	−0.582878	−	1.00957i
$528$	7.96753	−	1.30834i	0.346742	−	0.0569382i
$529$	5.17240	−	8.95887i	0.224887	−	0.389516i
$530$	6.06114	−	12.4333i	0.263279	−	0.540068i
$531$	−1.27308	−	4.28095i	−0.0552470	−	0.185778i
$532$	−0.561200	−	0.717728i	−0.0243311	−	0.0311175i
$533$	−0.287968	−	0.166258i	−0.0124733	−	0.00720144i
$534$	17.3061	−	8.92924i	0.748908	−	0.386406i
$535$	−3.71082	+	2.14244i	−0.160433	+	0.0926258i
$536$	−14.1443	+	12.7505i	−0.610941	+	0.550738i
$537$	12.3496	+	1.45494i	0.532924	+	0.0627854i
$538$	−10.6785	+	7.20574i	−0.460382	+	0.310661i
$539$	−1.16542			−0.0501980
$540$	−2.00719	+	9.33454i	−0.0863756	+	0.401695i
$541$	−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
$543$	4.81011	+	0.566694i	0.206422	+	0.0243192i
$544$	−18.3634	−	3.21959i	−0.787325	−	0.138039i
$545$	−8.84901	+	5.10898i	−0.379050	+	0.218845i
$546$	0.118891	−	0.0613427i	0.00508805	−	0.00262523i
$547$	−6.24436	−	3.60518i	−0.266990	−	0.154147i	0.360529	−	0.932748i	$-0.382596\pi$
$547$	−6.24436	−	3.60518i	−0.266990	−	0.154147i	−0.627519	+	0.778601i	$0.715929\pi$
$548$	10.2730	−	8.03254i	0.438839	−	0.343133i
$549$	−26.2363	+	27.7068i	−1.11974	+	1.18250i
$550$	3.00144	−	6.15691i	0.127982	−	0.262531i
$551$	−1.99477	+	3.45504i	−0.0849799	+	0.147190i
$552$	10.0742	+	14.2209i	0.428788	+	0.605282i
$553$	6.31075	+	10.9305i	0.268361	+	0.464814i
$554$	−2.26096	+	0.158543i	−0.0960591	+	0.00673584i
$555$	1.76458	−	0.759247i	0.0749023	−	0.0322282i
$556$	−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	$0.855145\pi$
$558$	26.6106	+	21.8795i	1.12652	+	0.926233i
$559$			0.356047i			0.0150592i
$560$	2.64555	+	2.55081i	0.111795	+	0.107791i
$561$	5.33260	+	3.97758i	0.225143	+	0.167934i
$562$	−2.18271	−	31.1273i	−0.0920720	−	1.31303i
$563$	23.5052	+	40.7122i	0.990625	+	1.71581i	0.613619	+	0.789602i	$0.289713\pi$
$563$	23.5052	+	40.7122i	0.990625	+	1.71581i	0.377006	+	0.926211i	$0.376954\pi$
$564$	−10.1561	−	16.7018i	−0.427648	−	0.703274i
$565$	−7.58487	+	13.1374i	−0.319098	+	0.552694i
$566$	26.5260	+	12.9312i	1.11497	+	0.543539i
$567$	−4.91796	−	7.53748i	−0.206535	−	0.316545i
$568$	−8.21993	+	1.75220i	−0.344901	+	0.0735208i
$569$	−27.5683	−	15.9166i	−1.15572	−	0.667258i	−0.205449	−	0.978668i	$-0.565865\pi$
$569$	−27.5683	−	15.9166i	−1.15572	−	0.667258i	−0.950276	+	0.311410i	$0.899199\pi$
$570$	0.553967	−	0.862625i	0.0232031	−	0.0361314i
$571$	21.1494	−	12.2106i	0.885077	−	0.510999i	0.0127478	−	0.999919i	$-0.495942\pi$
$571$	21.1494	−	12.2106i	0.885077	−	0.510999i	0.872329	+	0.488919i	$0.162609\pi$
$572$	0.0476425	−	0.118051i	0.00199203	−	0.00493597i
$573$	24.8608	−	33.3300i	1.03857	−	1.39238i
$574$	4.81603	+	7.13707i	0.201017	+	0.297896i
$575$	14.7843			0.616547
$576$	23.5883	−	4.42648i	0.982844	−	0.184437i
$577$	−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
$579$	−11.7465	−	27.3004i	−0.488170	−	1.13457i
$580$	6.02250	−	14.9229i	0.250070	−	0.619639i
$581$	11.3623	−	6.56004i	0.471389	−	0.272156i
$582$	−20.8623	−	0.986795i	−0.864768	−	0.0409040i
$583$	10.7445	+	6.20333i	0.444991	+	0.256916i
$584$	−41.0001	+	8.73980i	−1.69660	+	0.361655i
$585$	0.109307	+	0.103505i	0.00451928	+	0.00427942i
$586$	23.5865	+	11.4982i	0.974349	+	0.474988i
$587$	12.1011	−	20.9597i	0.499466	−	0.865100i	−0.500534	−	0.865717i	$-0.666863\pi$
$587$	12.1011	−	20.9597i	0.499466	−	0.865100i	1.00000		0.000616829i	$0.000196343\pi$
$588$	−3.46321	+	0.0787739i	−0.142820	+	0.00324858i
$589$	−1.84952	−	3.20347i	−0.0762082	−	0.131996i
$590$	−0.135307	−	1.92960i	−0.00557050	−	0.0794403i
$591$	−0.486516	+	4.12956i	−0.0200126	+	0.169867i
$592$	−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	$0.969690\pi$
$594$	−8.22620	−	2.38161i	−0.337525	−	0.0977187i
$595$			3.02795i			0.124134i
$596$	0.454725	+	3.22645i	0.0186263	+	0.132161i
$597$	0.506667	−	4.30060i	0.0207365	−	0.176012i
$598$	0.274100	−	0.0192204i	0.0112088	−	0.000785982i
$599$	−1.31442	−	2.27665i	−0.0537059	−	0.0930213i	0.837923	−	0.545789i	$-0.183770\pi$
$599$	−1.31442	−	2.27665i	−0.0537059	−	0.0930213i	−0.891628	+	0.452768i	$0.850437\pi$
$600$	8.50308	−	18.4990i	0.347137	−	0.755220i
$601$	−16.4497	+	28.4918i	−0.670998	+	1.16220i	0.306623	+	0.951831i	$0.400801\pi$
$601$	−16.4497	+	28.4918i	−0.670998	+	1.16220i	−0.977621	+	0.210372i	$0.932533\pi$
$602$	4.03986	−	8.28702i	0.164652	−	0.337754i
$603$	19.3602	−	5.75740i	0.788410	−	0.234459i
$604$	8.06762	−	6.30816i	0.328267	−	0.256675i
$605$	7.67159	+	4.42919i	0.311894	+	0.180072i
$606$	−1.50240	+	31.7629i	−0.0610308	+	1.29028i
$607$	6.79813	−	3.92490i	0.275928	−	0.159307i	−0.355651	−	0.934619i	$-0.615741\pi$
$607$	6.79813	−	3.92490i	0.275928	−	0.159307i	0.631578	+	0.775312i	$0.282407\pi$
$608$	−2.53823	−	0.445018i	−0.102939	−	0.0180479i
$609$	5.99530	+	13.9338i	0.242942	+	0.564626i
$610$	−13.6990	+	9.24398i	−0.554657	+	0.374278i
$611$	−0.308192			−0.0124681
$612$	16.1155	+	11.4595i	0.651429	+	0.463224i
$613$	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
$615$	−5.79254	+	7.76584i	−0.233578	+	0.313149i
$616$	−2.44834	+	2.20708i	−0.0986464	+	0.0889257i
$617$	16.7478	−	9.66936i	0.674242	−	0.389274i	−0.123440	−	0.992352i	$-0.539393\pi$
$617$	16.7478	−	9.66936i	0.674242	−	0.389274i	0.797682	+	0.603078i	$0.206059\pi$
$618$	4.66123	+	2.99339i	0.187502	+	0.120412i
$619$	10.3351	+	5.96696i	0.415402	+	0.239832i	0.693108	−	0.720834i	$-0.256241\pi$
$619$	10.3351	+	5.96696i	0.415402	+	0.239832i	−0.277706	+	0.960666i	$0.589574\pi$
$620$	9.19059	+	11.7540i	0.369103	+	0.472052i
$621$	−3.15976	−	18.2128i	−0.126797	−	0.730854i
$622$	−13.1366	+	26.9472i	−0.526728	+	1.08049i
$623$	−3.97509	+	6.88506i	−0.159259	+	0.275844i
$624$	0.133597	−	0.354027i	0.00534817	−	0.0141724i
$625$	−6.52552	−	11.3025i	−0.261021	−	0.452102i
$626$	33.2830	−	2.33387i	1.33026	−	0.0932802i
$627$	0.737082	+	0.549788i	0.0294362	+	0.0219564i
$628$	−0.958554	+	0.135095i	−0.0382505	+	0.00539090i
$629$		−	3.97852i		−	0.158634i
$630$	−1.36971	−	3.64933i	−0.0545705	−	0.145393i
$631$		−	4.63442i		−	0.184493i	−0.995736	−	0.0922467i	$-0.970595\pi$
$631$		−	4.63442i		−	0.184493i	0.995736	−	0.0922467i	$-0.0294048\pi$
$632$	33.9582	+	11.0118i	1.35078	+	0.438027i
$633$	−4.92982	+	2.12115i	−0.195943	+	0.0843083i
$634$	1.80612	+	25.7569i	0.0717302	+	1.02294i
$635$	8.09740	+	14.0251i	0.321335	+	0.556569i
$636$	32.3481	+	17.7079i	1.28269	+	0.702162i
$637$	−0.0273083	+	0.0472994i	−0.00108200	+	0.00187407i
$638$	12.9745	+	6.32495i	0.513664	+	0.250407i
$639$	8.67036	+	2.07172i	0.342994	+	0.0819560i
$640$	10.3886	+	0.348646i	0.410645	+	0.0137814i
$641$	7.36518	+	4.25229i	0.290907	+	0.167955i	0.638351	−	0.769746i	$-0.279617\pi$
$641$	7.36518	+	4.25229i	0.290907	+	0.167955i	−0.347444	+	0.937701i	$0.612950\pi$
$642$	−5.23818	−	10.1523i	−0.206734	−	0.400680i
$643$	−42.3444	+	24.4476i	−1.66990	+	0.964118i	−0.702212	+	0.711968i	$0.747804\pi$
$643$	−42.3444	+	24.4476i	−1.66990	+	0.964118i	−0.967688	+	0.252150i	$0.918862\pi$
$644$	−6.59779	−	2.66270i	−0.259989	−	0.104925i
$645$	10.3026	+	1.21378i	0.405663	+	0.0477924i
$646$	−1.18764	−	1.76001i	−0.0467270	−	0.0692467i
$647$	19.0364			0.748397			0.374198	−	0.927349i	$-0.377918\pi$
$647$	19.0364			0.748397			0.374198	+	0.927349i	$0.377918\pi$
$648$	−24.6064	−	6.52128i	−0.966629	−	0.256180i
$649$	1.73501			0.0681051
$650$	−0.179553	−	0.266087i	−0.00704264	−	0.0104368i
$651$	−13.9678	−	1.64559i	−0.547440	−	0.0644956i
$652$	−44.1553	−	17.8200i	−1.72926	−	0.697884i
$653$	−38.4290	+	22.1870i	−1.50384	+	0.868244i	−0.503853	+	0.863790i	$0.668085\pi$
$653$	−38.4290	+	22.1870i	−1.50384	+	0.868244i	−0.999990	+	0.00445434i	$0.998582\pi$
$654$	−12.4912	−	24.2097i	−0.488446	−	0.946675i
$655$	12.1317	+	7.00424i	0.474024	+	0.273678i
$656$	23.6339	+	5.87311i	0.922749	+	0.229306i
$657$	43.2468	+	10.3335i	1.68722	+	0.403149i
$658$	7.17319	+	3.49688i	0.279640	+	0.136322i
$659$	8.10116	−	14.0316i	0.315577	−	0.546595i	−0.663983	−	0.747747i	$-0.731135\pi$
$659$	8.10116	−	14.0316i	0.315577	−	0.546595i	0.979560	+	0.201153i	$0.0644688\pi$
$660$	−3.25351	−	1.78102i	−0.126643	−	0.0693262i
$661$	5.05531	+	8.75605i	0.196629	+	0.340571i	0.947433	−	0.319954i	$-0.103667\pi$
$661$	5.05531	+	8.75605i	0.196629	+	0.340571i	−0.750805	+	0.660524i	$0.770334\pi$
$662$	−2.24060	−	31.9529i	−0.0870834	−	1.24189i
$663$	0.286389	−	0.123225i	0.0111224	−	0.00478565i
$664$	11.4468	−	35.2996i	0.444223	−	1.36989i
$665$			0.418529i			0.0162299i
$666$	1.79970	+	4.79497i	0.0697370	+	0.185801i
$667$			31.1549i			1.20632i
$668$	37.1420	−	5.23467i	1.43707	−	0.202535i
$669$	−11.7642	−	8.77488i	−0.454829	−	0.339256i
$670$	8.72644	−	0.611914i	0.337132	−	0.0236403i
$671$	−7.41160	−	12.8373i	−0.286122	−	0.495577i
$672$	−7.12642	+	6.72415i	−0.274908	+	0.259390i
$673$	−6.81031	+	11.7958i	−0.262518	+	0.454694i	−0.966910	−	0.255116i	$-0.917886\pi$
$673$	−6.81031	+	11.7958i	−0.262518	+	0.454694i	0.704392	+	0.709811i	$0.251220\pi$
$674$	−3.27014	+	6.70809i	−0.125961	+	0.258386i
$675$	−16.5806	+	13.8352i	−0.638189	+	0.532519i
$676$	16.0115	+	20.4774i	0.615826	+	0.787591i
$677$	−18.1315	−	10.4682i	−0.696851	−	0.402327i	0.109322	−	0.994006i	$-0.465132\pi$
$677$	−18.1315	−	10.4682i	−0.696851	−	0.402327i	−0.806174	+	0.591679i	$0.798465\pi$
$678$	−34.0312	−	21.8545i	−1.30696	−	0.839316i
$679$	7.38417	−	4.26325i	0.283378	−	0.163609i
$680$	5.73437	+	6.36121i	0.219903	+	0.243941i
$681$	13.9480	−	18.6995i	0.534488	−	0.716568i
$682$	−11.0936	+	7.48587i	−0.424796	+	0.286649i
$683$	−16.0167			−0.612864			−0.306432	−	0.951893i	$-0.599135\pi$
$683$	−16.0167			−0.612864			−0.306432	+	0.951893i	$0.599135\pi$
$684$	2.22751	+	1.58396i	0.0851709	+	0.0605641i
$685$	−5.99048			−0.228884
$686$	1.17228	−	0.791046i	0.0447580	−	0.0302023i
$687$	−4.33821	−	10.0825i	−0.165513	−	0.384672i
$688$	−7.20699	−	25.0603i	−0.274764	−	0.955416i
$689$	0.503535	−	0.290716i	0.0191832	−	0.0110754i
$690$	0.378256	−	7.99688i	0.0144000	−	0.304436i
$691$	35.2063	+	20.3264i	1.33931	+	0.773251i	0.986705	−	0.162521i	$-0.0519625\pi$
$691$	35.2063	+	20.3264i	1.33931	+	0.773251i	0.352605	+	0.935772i	$0.385296\pi$
$692$	−27.9900	+	21.8857i	−1.06402	+	0.831968i
$693$	3.35120	−	0.996589i	0.127302	−	0.0378573i
$694$	−4.63471	+	9.50724i	−0.175931	+	0.360890i
$695$	−3.67882	+	6.37190i	−0.139546	+	0.241700i
$696$	38.9831	+	17.9186i	1.47765	+	0.679201i
$697$	10.0325	+	17.3769i	0.380010	+	0.658196i
$698$	−25.3958	+	1.78080i	−0.961246	+	0.0674044i
$699$	0.670426	−	5.69059i	0.0253579	−	0.215238i
$700$	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	$-0.0339839\pi$
$702$	−0.289419	+	0.278061i	−0.0109234	+	0.0104947i
$703$		−	0.549918i		−	0.0207406i
$704$	−0.963754	+	9.27338i	−0.0363228	+	0.349504i
$705$	−1.05064	+	8.91784i	−0.0395693	+	0.335865i
$706$	−0.433514	−	6.18229i	−0.0163155	−	0.232674i
$707$	−6.49081	−	11.2424i	−0.244112	−	0.422815i
$708$	5.15584	−	0.117274i	0.193768	−	0.00440744i
$709$	−2.58052	+	4.46959i	−0.0969134	+	0.167859i	−0.910406	−	0.413717i	$-0.864230\pi$
$709$	−2.58052	+	4.46959i	−0.0969134	+	0.167859i	0.813492	+	0.581576i	$0.197564\pi$
$710$	3.47044	+	1.69182i	0.130243	+	0.0634927i
$711$	−27.4939	−	26.0347i	−1.03110	−	0.976377i
$712$	4.68801	+	21.9924i	0.175691	+	0.824200i
$713$	−25.0164	−	14.4432i	−0.936871	−	0.540903i
$714$	−8.06387	−	0.381425i	−0.301783	−	0.0142745i
$715$	−0.0506446	+	0.0292397i	−0.00189400	+	0.00109350i
$716$	−5.37369	+	13.3152i	−0.200824	+	0.497614i
$717$	−12.5649	−	29.2023i	−0.469245	−	1.09058i
$718$	−21.9035	−	32.4597i	−0.817431	−	1.21138i
$719$	28.4079			1.05944			0.529718	−	0.848174i	$-0.322298\pi$
$719$	28.4079			1.05944			0.529718	+	0.848174i	$0.322298\pi$
$720$	−9.78867	−	5.07266i	−0.364802	−	0.189047i
$721$	−2.26154			−0.0842242
$722$	14.8657	+	22.0301i	0.553244	+	0.819875i
$723$	21.8675	−	29.3169i	0.813259	−	1.09031i
$724$	−2.09303	+	5.18623i	−0.0777869	+	0.192745i
$725$	31.5202	−	18.1982i	1.17063	−	0.675863i
$726$	−12.7619	+	19.8726i	−0.473640	+	0.737541i
$727$	31.9367	+	18.4386i	1.18447	+	0.683852i	0.957043	−	0.289945i	$-0.0936369\pi$
$727$	31.9367	+	18.4386i	1.18447	+	0.683852i	0.227422	+	0.973796i	$0.426970\pi$
$728$	0.0322060	+	0.151085i	0.00119364	+	0.00559958i
$729$	20.5874	+	17.4688i	0.762495	+	0.646994i
$730$	17.3102	+	8.43859i	0.640679	+	0.312326i
$731$	10.7425	−	18.6065i	0.397325	−	0.688188i
$732$	−22.8924	−	37.6469i	−0.846127	−	1.39147i
$733$	4.51056	+	7.81251i	0.166601	+	0.288562i	0.937223	−	0.348731i	$-0.113387\pi$
$733$	4.51056	+	7.81251i	0.166601	+	0.288562i	−0.770622	+	0.637293i	$0.780054\pi$
$734$	0.598348	+	8.53298i	0.0220854	+	0.314958i
$735$	1.27556	+	0.951439i	0.0470498	+	0.0350944i
$736$	−18.9035	+	6.90108i	−0.696791	+	0.254377i
$737$			7.84642i			0.289027i
$738$	−19.9519	−	16.4046i	−0.734438	−	0.603861i
$739$		−	43.2538i		−	1.59112i	−0.605876	−	0.795559i	$-0.707177\pi$
$739$		−	43.2538i		−	1.59112i	0.605876	−	0.795559i	$-0.292823\pi$
$740$	0.309562	+	2.19646i	0.0113797	+	0.0807435i
$741$	0.0395852	−	0.0170323i	0.00145420	−	0.000625698i
$742$	−15.0184	+	1.05312i	−0.551343	+	0.0386612i
$743$	14.3410	+	24.8394i	0.526121	+	0.911268i	0.999537	+	0.0304290i	$0.00968733\pi$
$743$	14.3410	+	24.8394i	0.526121	+	0.911268i	−0.473416	+	0.880839i	$0.656979\pi$
$744$	−32.4603	+	22.9952i	−1.19005	+	0.843045i
$745$	0.748397	−	1.29626i	0.0274191	−	0.0474913i
$746$	−19.7858	+	40.5868i	−0.724408	+	1.48599i
$747$	−27.0631	+	28.5800i	−0.990188	+	1.04569i
$748$	−6.05152	+	4.73175i	−0.221265	+	0.173010i
$749$	4.03900	+	2.33192i	0.147582	+	0.0852063i
$750$	−18.3113	+	9.44789i	−0.668634	+	0.344988i
$751$	5.83084	−	3.36644i	0.212771	−	0.122843i	−0.389828	−	0.920888i	$-0.627465\pi$
$751$	5.83084	−	3.36644i	0.212771	−	0.122843i	0.602598	+	0.798045i	$0.294132\pi$
$752$	21.6921	−	6.23833i	0.791028	−	0.227489i
$753$	23.9875	+	2.82604i	0.874153	+	0.102987i
$754$	0.560725	−	0.378372i	0.0204204	−	0.0137795i
$755$	−4.70447			−0.171213
$756$	9.89123	−	3.18803i	0.359741	−	0.115948i
$757$	−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
$759$	7.13153	+	0.840187i	0.258858	+	0.0304969i
$760$	0.792615	+	0.879258i	0.0287512	+	0.0318941i
$761$	−37.4743	+	21.6358i	−1.35844	+	0.784297i	−0.989414	−	0.145121i	$-0.953643\pi$
$761$	−37.4743	+	21.6358i	−1.35844	+	0.784297i	−0.369029	+	0.929418i	$0.620310\pi$
$762$	−38.3709	+	19.7978i	−1.39003	+	0.717199i
$763$	9.63160	+	5.56081i	0.348687	+	0.201315i
$764$	29.5745	+	37.8234i	1.06997	+	1.36840i
$765$	−2.58931	−	8.70701i	−0.0936168	−	0.314803i
$766$	−5.95782	+	12.2214i	−0.215265	+	0.441576i
$767$	0.0406552	−	0.0704169i	0.00146797	−	0.00254261i
$768$	−2.23712	+	27.6224i	−0.0807252	+	0.996736i
$769$	−7.23929	−	12.5388i	−0.261055	−	0.452161i	0.705467	−	0.708743i	$-0.250737\pi$
$769$	−7.23929	−	12.5388i	−0.261055	−	0.452161i	−0.966523	+	0.256581i	$0.917404\pi$
$770$	1.51052	−	0.105921i	0.0544354	−	0.00381711i
$771$	17.1320	−	7.37140i	0.616995	−	0.265475i
$772$	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	$-0.0816764\pi$
$774$	−4.53025	+	27.2843i	−0.162837	+	0.980714i
$775$			33.7462i			1.21220i
$776$	7.43908	−	22.9406i	0.267047	−	0.823519i
$777$	−1.67600	−	1.25012i	−0.0601261	−	0.0448480i
$778$	0.275715	+	3.93194i	0.00988486	+	0.140967i
$779$	1.38672	+	2.40186i	0.0496843	+	0.0860556i
$780$	−0.148522	+	0.0903132i	−0.00531792	+	0.00323373i
$781$	−1.73150	+	2.99905i	−0.0619581	+	0.107315i
$782$	−14.9040	−	7.26560i	−0.532967	−	0.259817i
$783$	−29.1550	−	34.9404i	−1.04192	−	1.24867i
$784$	0.964674	−	3.88193i	0.0344526	−	0.138640i
$785$	0.385110	+	0.222343i	0.0137451	+	0.00793577i
$786$	−20.1815	+	31.4261i	−0.719849	+	1.12093i
$787$	27.4914	−	15.8722i	0.979962	−	0.565781i	0.0777033	−	0.996977i	$-0.475241\pi$
$787$	27.4914	−	15.8722i	0.979962	−	0.565781i	0.902259	+	0.431195i	$0.141908\pi$
$788$	−4.45246	−	1.79690i	−0.158612	−	0.0640120i
$789$	−16.8333	+	22.5678i	−0.599281	+	0.803435i
$790$	−9.17295	−	13.5938i	−0.326359	−	0.483644i
$791$	16.5113			0.587075
$792$	5.15295	−	8.44021i	0.183102	−	0.299910i
$793$	−0.694683			−0.0246689
$794$	−0.862566	−	1.27827i	−0.0306113	−	0.0453642i
$795$	−6.69559	−	15.5613i	−0.237468	−	0.551904i
$796$	4.63688	+	1.87133i	0.164350	+	0.0663274i
$797$	12.4676	−	7.19816i	0.441624	−	0.254972i	−0.262662	−	0.964888i	$-0.584600\pi$
$797$	12.4676	−	7.19816i	0.441624	−	0.254972i	0.704286	+	0.709916i	$0.251267\pi$
$798$	−1.11460	−	0.0527212i	−0.0394565	−	0.00186631i
$799$	16.1057	+	9.29864i	0.569779	+	0.328962i
$800$	18.0239	+	15.0940i	0.637240	+	0.533654i
$801$	5.54288	−	23.1975i	0.195848	−	0.819644i
$802$	−23.6849	−	11.5462i	−0.836342	−	0.407711i
$803$	−8.63655	+	14.9589i	−0.304777	+	0.527890i
$804$	0.530363	+	23.3168i	0.0187045	+	0.822321i
$805$	1.63418	+	2.83049i	0.0575974	+	0.0997615i
$806$	0.0438721	+	0.625655i	0.00154533	+	0.0220378i
$807$	−1.84603	+	15.6691i	−0.0649832	+	0.551579i
$808$	−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	$0.991733\pi$
$810$	7.05933	+	9.32253i	0.248040	+	0.327560i
$811$		−	36.8994i		−	1.29571i	−0.761763	−	0.647856i	$-0.775666\pi$
$811$		−	36.8994i		−	1.29571i	0.761763	−	0.647856i	$-0.224334\pi$
$812$	−17.3441	+	2.44442i	−0.608658	+	0.0857823i
$813$	6.42564	−	54.5410i	0.225357	−	1.91284i
$814$	−1.98472	+	0.139172i	−0.0695644	+	0.00487799i
$815$	10.9367	+	18.9429i	0.383095	+	0.663540i
$816$	−17.6632	+	14.4701i	−0.618334	+	0.506556i
$817$	1.48485	−	2.57183i	0.0519482	−	0.0899770i
$818$	18.4753	−	37.8986i	0.645973	−	1.32509i
$819$	0.0380788	−	0.159364i	0.00133058	−	0.00556863i
$820$	−6.89083	−	8.81281i	−0.240638	−	0.307757i
$821$	−9.12991	−	5.27116i	−0.318636	−	0.183965i	0.332148	−	0.943227i	$-0.392227\pi$
$821$	−9.12991	−	5.27116i	−0.318636	−	0.183965i	−0.650785	+	0.759262i	$0.725560\pi$
$822$	0.754608	−	15.9535i	0.0263200	−	0.556442i
$823$	−22.1348	+	12.7795i	−0.771571	+	0.445466i	−0.833435	−	0.552618i	$-0.813629\pi$
$823$	−22.1348	+	12.7795i	−0.771571	+	0.445466i	0.0618640	+	0.998085i	$0.480295\pi$
$824$	−4.75111	+	4.28293i	−0.165513	+	0.149203i
$825$	−3.31562	−	7.70590i	−0.115435	−	0.268285i
$826$	−1.74523	+	1.17767i	−0.0607244	+	0.0409763i
$827$	12.8344			0.446296			0.223148	−	0.974785i	$-0.428367\pi$
$827$	12.8344			0.446296			0.223148	+	0.974785i	$0.428367\pi$
$828$	21.2492	+	2.01470i	0.738460	+	0.0700157i
$829$	−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
$831$	−1.65969	+	2.22509i	−0.0575742	+	0.0771876i
$832$	0.353786	+	0.256411i	0.0122653	+	0.00888946i
$833$	2.85420	−	1.64787i	0.0988920	−	0.0570953i
$834$	−16.5059	−	10.5999i	−0.571552	−	0.367044i
$835$	−14.9222	−	8.61533i	−0.516404	−	0.298146i
$836$	−0.836452	+	0.654031i	−0.0289293	+	0.0226201i
$837$	41.5721	−	7.21239i	1.43694	−	0.249297i
$838$	−2.13486	+	4.37927i	−0.0737476	+	0.151280i
$839$	−0.741866	+	1.28495i	−0.0256121	+	0.0443614i	−0.878547	−	0.477655i	$-0.841487\pi$
$839$	−0.741866	+	1.28495i	−0.0256121	+	0.0443614i	0.852935	+	0.522017i	$0.174820\pi$
$840$	4.48158	−	0.416859i	0.154629	−	0.0143830i
$841$	23.8491	+	41.3078i	0.822382	+	1.42441i
$842$	20.8722	−	1.46360i	0.719304	−	0.0504389i
$843$	−30.6335	−	22.8495i	−1.05507	−	0.786979i
$844$	−0.864842	−	6.13639i	−0.0297691	−	0.211223i
$845$		−	11.9410i		−	0.410782i
$846$	−23.6171	−	3.92136i	−0.811973	−	0.134819i
$847$		−	9.64181i		−	0.331296i
$848$	−29.5567	+	30.6544i	−1.01498	+	1.05268i
$849$	33.1995	−	14.2848i	1.13940	−	0.490252i
$850$	1.35495	+	19.3227i	0.0464743	+	0.662764i
$851$	−2.14720	−	3.71906i	−0.0736051	−	0.127488i
$852$	−4.94271	+	9.02917i	−0.169334	+	0.309334i
$853$	2.68864	−	4.65687i	0.0920574	−	0.159448i	−0.816319	−	0.577601i	$-0.803989\pi$
$853$	2.68864	−	4.65687i	0.0920574	−	0.159448i	0.908377	+	0.418153i	$0.137322\pi$
$854$	16.1688	+	7.88216i	0.553284	+	0.269722i
$855$	−0.357900	−	1.20350i	−0.0122399	−	0.0411588i
$856$	12.9014	−	2.75014i	0.440962	−	0.0939978i
$857$	−13.2302	−	7.63847i	−0.451936	−	0.260925i	0.256712	−	0.966488i	$-0.417361\pi$
$857$	−13.2302	−	7.63847i	−0.451936	−	0.260925i	−0.708647	+	0.705563i	$0.750694\pi$
$858$	−0.0714898	−	0.138557i	−0.00244062	−	0.00473026i
$859$	7.89410	−	4.55766i	0.269343	−	0.155505i	−0.359246	−	0.933243i	$-0.616966\pi$
$859$	7.89410	−	4.55766i	0.269343	−	0.155505i	0.628589	+	0.777738i	$0.283633\pi$
$860$	−4.48297	+	11.1082i	−0.152868	+	0.378785i
$861$	10.4726	+	1.23381i	0.356906	+	0.0420482i
$862$	13.4056	+	19.8663i	0.456596	+	0.676649i
$863$	14.0671			0.478851			0.239425	−	0.970915i	$-0.423041\pi$
$863$	14.0671			0.478851			0.239425	+	0.970915i	$0.423041\pi$
$864$	14.7423	−	25.4296i	0.501542	−	0.865133i
$865$	16.3218			0.554958
$866$	25.9384	+	38.4392i	0.881423	+	1.30622i
$867$	10.5585	+	1.24392i	0.358584	+	0.0422459i
$868$	6.07781	−	15.0599i	0.206294	−	0.511168i
$869$	12.7386	−	7.35465i	0.432128	−	0.249489i
$870$	−9.03704	−	17.5150i	−0.306384	−	0.593815i
$871$	0.318454	+	0.183860i	0.0107904	+	0.00622985i
$872$	30.7655	−	6.55813i	1.04185	−	0.222086i
$873$	−17.5878	+	18.5736i	−0.595258	+	0.628622i
$874$	−2.06006	−	1.00426i	−0.0696827	−	0.0339698i
$875$	4.20598	−	7.28497i	0.142188	−	0.246277i
$876$	−24.6537	+	45.0365i	−0.832970	+	1.52164i
$877$	14.8307	+	25.6875i	0.500796	+	0.867404i	1.00000		0.000919420i	$0.000292660\pi$
$877$	14.8307	+	25.6875i	0.500796	+	0.867404i	−0.499204	+	0.866485i	$0.666374\pi$
$878$	−1.51978	−	21.6734i	−0.0512902	−	0.731444i
$879$	29.5205	−	12.7018i	0.995703	−	0.428422i
$880$	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	$0.920350\pi$
$882$	−2.69450	+	3.27715i	−0.0907284	+	0.110347i
$883$		−	2.75888i		−	0.0928439i	−0.998922	−	0.0464219i	$-0.985218\pi$
$883$		−	2.75888i		−	0.0928439i	0.998922	−	0.0464219i	$-0.0147819\pi$
$884$	0.0502414	+	0.356482i	0.00168980	+	0.0119898i
$885$	−1.89899	−	1.41645i	−0.0638337	−	0.0476135i
$886$	23.0380	−	1.61547i	0.773977	−	0.0542727i
$887$	5.47009	+	9.47448i	0.183668	+	0.318122i	0.943127	−	0.332433i	$-0.107870\pi$
$887$	5.47009	+	9.47448i	0.183668	+	0.318122i	−0.759459	+	0.650555i	$0.774536\pi$
$888$	−5.88848	+	0.547724i	−0.197605	+	0.0183804i
$889$	8.81352	−	15.2655i	0.295596	−	0.511987i
$890$	4.52644	−	9.28516i	0.151727	−	0.311239i
$891$	−8.78430	+	5.73147i	−0.294285	+	0.192011i
$892$	13.3502	−	10.4386i	0.446997	−	0.349511i
$893$	2.22616	+	1.28527i	0.0744956	+	0.0430101i
$894$	3.35785	+	2.15637i	0.112303	+	0.0721199i
$895$	5.71231	−	3.29800i	0.190941	−	0.110240i
$896$	−5.32503	−	9.98219i	−0.177897	−	0.333481i
$897$	0.201208	−	0.269752i	0.00671813	−	0.00900676i
$898$	−14.9247	+	10.0711i	−0.498044	+	0.336075i
$899$	−71.1135			−2.37177
$900$	−10.3737	−	22.6751i	−0.345791	−	0.755837i
$901$	−35.0854			−1.16887
$902$	8.31766	−	5.61268i	0.276948	−	0.186882i
$903$	−4.46273	−	10.3719i	−0.148510	−	0.345156i
$904$	34.6875	−	31.2693i	1.15369	−	1.04000i
$905$	2.22492	−	1.28456i	0.0739589	−	0.0427002i
$906$	0.592612	−	12.5287i	0.0196882	−	0.416237i
$907$	−3.75470	−	2.16778i	−0.124673	−	0.0719798i	0.436367	−	0.899769i	$-0.356265\pi$
$907$	−3.75470	−	2.16778i	−0.124673	−	0.0719798i	−0.561039	+	0.827789i	$0.689598\pi$
$908$	16.5926	+	21.2206i	0.550644	+	0.704229i
$909$	28.2784	+	26.7775i	0.937936	+	0.888154i
$910$	0.0310961	−	0.0637878i	0.00103083	−	0.00211455i
$911$	−28.0150	+	48.5233i	−0.928177	+	1.60765i	−0.141806	+	0.989894i	$0.545291\pi$
$911$	−28.0150	+	48.5233i	−0.928177	+	1.60765i	−0.786371	+	0.617755i	$0.788042\pi$
$912$	−2.44143	+	2.00009i	−0.0808439	+	0.0662295i
$913$	−7.64518	−	13.2418i	−0.253018	−	0.438241i
$914$	25.3403	−	1.77691i	0.838182	−	0.0587749i
$915$	−2.36820	+	20.1013i	−0.0782902	+	0.664529i
$916$	12.5502	−	1.76879i	0.414671	−	0.0584424i
$917$		−	15.2474i		−	0.503512i
$918$	23.5142	−	5.79890i	0.776083	−	0.191392i
$919$			10.2488i			0.338077i	0.985609	+	0.169039i	$0.0540662\pi$
$919$			10.2488i			0.338077i	−0.985609	+	0.169039i	$0.945934\pi$
$920$	8.79354	+	2.85154i	0.289915	+	0.0940123i
$921$	−0.631896	+	5.36355i	−0.0208217	+	0.176735i
$922$	−0.217553	−	3.10250i	−0.00716473	−	0.102175i
$923$	0.0811462	+	0.140549i	0.00267096	+	0.00462624i
$924$	0.0918043	+	4.03607i	0.00302014	+	0.132777i
$925$	−2.50844	+	4.34475i	−0.0824770	+	0.142854i
$926$	−0.0690841	−	0.0336780i	−0.00227024	−	0.00110673i
$927$	6.50316	−	1.93393i	0.213592	−	0.0635184i
$928$	−31.8077	+	37.9817i	−1.04414	+	1.24681i
$929$	−21.0194	−	12.1356i	−0.689624	−	0.398155i	0.113847	−	0.993498i	$-0.463683\pi$
$929$	−21.0194	−	12.1356i	−0.689624	−	0.398155i	−0.803471	+	0.595344i	$0.797016\pi$
$930$	18.2535	+	0.863399i	0.598556	+	0.0283120i
$931$	0.394512	−	0.227772i	0.0129296	−	0.00746492i
$932$	6.13556	+	2.47616i	0.200977	+	0.0811092i
$933$	14.5116	+	33.7268i	0.475090	+	1.10417i
$934$	−26.0203	−	38.5605i	−0.851409	−	1.26174i
$935$	3.52883			0.115405
$936$	−0.221808	−	0.406910i	−0.00725002	−	0.0133003i
$937$	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
$939$	24.4319	−	32.7550i	0.797306	−	1.06892i
$940$	−9.61515	−	3.88043i	−0.313612	−	0.126566i
$941$	−34.3146	+	19.8115i	−1.11862	+	0.645837i	−0.941049	−	0.338271i	$-0.890158\pi$
$941$	−34.3146	+	19.8115i	−1.11862	+	0.645837i	−0.177574	+	0.984108i	$0.556825\pi$
$942$	−0.640642	+	0.997593i	−0.0208733	+	0.0325033i
$943$	18.7565	+	10.8291i	0.610797	+	0.352644i
$944$	−1.43616	+	5.77922i	−0.0467429	+	0.188097i
$945$	−4.48154	−	1.64513i	−0.145784	−	0.0535159i
$946$	−9.65782	−	4.70811i	−0.314003	−	0.153074i
$947$	8.83985	−	15.3111i	0.287257	−	0.497543i	−0.685897	−	0.727698i	$-0.740590\pi$
$947$	8.83985	−	15.3111i	0.287257	−	0.497543i	0.973154	+	0.230155i	$0.0739234\pi$
$948$	37.3576	−	22.7165i	1.21332	−	0.737797i
$949$	0.404748	+	0.701044i	0.0131387	+	0.0227569i
$950$	0.187283	+	2.67082i	0.00607627	+	0.0866529i
$951$	25.3483	+	18.9072i	0.821973	+	0.613109i
$952$	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	$0.904447\pi$
$954$	42.2855	−	15.8711i	1.36904	−	0.513845i
$955$		−	22.0560i		−	0.713715i
$956$	36.3496	−	5.12299i	1.17563	−	0.165689i
$957$	16.2387	−	6.98702i	0.524922	−	0.225858i
$958$	−22.6478	+	1.58811i	−0.731718	+	0.0513095i
$959$	3.26013	+	5.64672i	0.105275	+	0.182342i
$960$	8.62558	−	9.36301i	0.278389	−	0.302190i
$961$	17.4677	−	30.2550i	0.563475	−	0.975968i
$962$	−0.0408581	+	0.0838128i	−0.00131732	+	0.00270223i
$963$	−13.6084	−	3.25163i	−0.438525	−	0.104782i
$964$	26.0136	+	33.2693i	0.837843	+	1.07153i
$965$	−13.6527	−	7.88239i	−0.439496	−	0.253743i
$966$	−7.74384	+	3.99551i	−0.249154	+	0.128553i
$967$	−3.29329	+	1.90138i	−0.105905	+	0.0611442i	−0.552017	−	0.833833i	$-0.686142\pi$
$967$	−3.29329	+	1.90138i	−0.105905	+	0.0611442i	0.446112	+	0.894977i	$0.352808\pi$
$968$	−18.2598	−	20.2558i	−0.586891	−	0.651045i
$969$	−2.58256	−	0.304259i	−0.0829638	−	0.00977422i
$970$	−9.18331	+	6.19682i	−0.294858	+	0.198968i
$971$	11.8109			0.379029			0.189514	−	0.981878i	$-0.439309\pi$
$971$	11.8109			0.379029			0.189514	+	0.981878i	$0.439309\pi$
$972$	−25.7165	+	17.6257i	−0.824856	+	0.565343i
$973$	8.00834			0.256736
$974$	−21.3753	+	14.4239i	−0.684909	+	0.462170i
$975$	−0.390444	−	0.0459994i	−0.0125042	−	0.00147316i
$976$	48.8952	−	14.0616i	1.56510	−	0.450099i
$977$	6.87127	−	3.96713i	0.219831	−	0.126920i	−0.386041	−	0.922482i	$-0.626158\pi$
$977$	6.87127	−	3.96713i	0.219831	−	0.126920i	0.605872	+	0.795562i	$0.292824\pi$
$978$	−51.8252	+	26.7397i	−1.65719	+	0.855042i
$979$	8.02395	+	4.63263i	0.256447	+	0.148060i
$980$	−1.44753	+	1.13184i	−0.0462395	+	0.0361552i
$981$	−32.4513	−	7.75401i	−1.03609	−	0.247566i
$982$	18.4389	−	37.8239i	0.588408	−	1.20701i
$983$	−11.8091	+	20.4540i	−0.376652	+	0.652381i	−0.990573	−	0.136987i	$-0.956258\pi$
$983$	−11.8091	+	20.4540i	−0.376652	+	0.652381i	0.613921	+	0.789368i	$0.289592\pi$
$984$	24.3378	−	17.2411i	0.775860	−	0.549627i
$985$	1.10282	+	1.91013i	0.0351386	+	0.0608619i
$986$	−40.7188	+	2.85528i	−1.29675	+	0.0909307i
$987$	8.97787	−	3.86291i	0.285769	−	0.122958i
$988$	0.00694446	+	0.0492736i	0.000220933	+	0.00156760i
$989$		−	23.1908i		−	0.737425i
$990$	−4.25299	+	1.59628i	−0.135169	+	0.0507331i
$991$		−	38.2004i		−	1.21348i	−0.794902	−	0.606738i	$-0.792478\pi$
$991$		−	38.2004i		−	1.21348i	0.794902	−	0.606738i	$-0.207522\pi$
$992$	−15.7522	−	43.1486i	−0.500134	−	1.36997i
$993$	−31.4460	−	23.4556i	−0.997910	−	0.744340i
$994$	−0.293952	−	4.19201i	−0.00932358	−	0.132963i
$995$	−1.14849	−	1.98925i	−0.0364096	−	0.0630633i
$996$	−23.6138	−	38.8333i	−0.748233	−	1.23048i
$997$	−27.9939	+	48.4868i	−0.886575	+	1.53559i	−0.0426776	+	0.999089i	$0.513589\pi$
$997$	−27.9939	+	48.4868i	−0.886575	+	1.53559i	−0.843898	+	0.536504i	$0.819744\pi$
$998$	−54.4619	−	26.5498i	−1.72396	−	0.840418i
$999$	5.88843	+	2.16158i	0.186302	+	0.0683894i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.25	✓	72	1.1	even	1	trivial
252.2.ba.a.155.36	yes	72	4.3	odd	2	inner
252.2.ba.a.239.25	yes	72	36.23	even	6	inner
252.2.ba.a.239.36	yes	72	9.5	odd	6	inner
756.2.ba.a.71.1		72	9.4	even	3
756.2.ba.a.71.12		72	36.31	odd	6
756.2.ba.a.575.1		72	12.11	even	2
756.2.ba.a.575.12		72	3.2	odd	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.791046 + 1.17228i) q^{2} +(1.72015 + 0.202657i) q^{3} +(-0.748493 + 1.85466i) q^{4} +(0.795659 - 0.459374i) q^{5} +(1.12315 + 2.17682i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-2.76628 + 0.589674i) q^{8} +(2.91786 + 0.697202i) q^{9} +O(q^{10})\)	\(q+(0.791046 + 1.17228i) q^{2} +(1.72015 + 0.202657i) q^{3} +(-0.748493 + 1.85466i) q^{4} +(0.795659 - 0.459374i) q^{5} +(1.12315 + 2.17682i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-2.76628 + 0.589674i) q^{8} +(2.91786 + 0.697202i) q^{9} +(1.16792 + 0.569351i) q^{10} +(-0.582708 + 1.00928i) q^{11} +(-1.66338 + 3.03861i) q^{12} +(0.0273083 + 0.0472994i) q^{13} +(-0.0989244 - 1.41075i) q^{14} +(1.46175 - 0.628948i) q^{15} +(-2.87952 - 2.77640i) q^{16} -3.29574i q^{17} +(1.49084 + 3.97208i) q^{18} -0.455543i q^{19} +(0.256436 + 1.81951i) q^{20} +(-1.38837 - 1.03558i) q^{21} +(-1.64411 + 0.115288i) q^{22} +(-1.77871 - 3.08081i) q^{23} +(-4.87792 + 0.453726i) q^{24} +(-2.07795 + 3.59912i) q^{25} +(-0.0338462 + 0.0694291i) q^{26} +(4.87788 + 1.79062i) q^{27} +(1.57554 - 1.23193i) q^{28} +(-7.58443 - 4.37887i) q^{29} +(1.89362 + 1.21606i) q^{30} +(7.03218 - 4.06003i) q^{31} +(0.976895 - 5.57186i) q^{32} +(-1.20688 + 1.61803i) q^{33} +(3.86354 - 2.60708i) q^{34} -0.918747 q^{35} +(-3.47707 + 4.88978i) q^{36} +1.20717 q^{37} +(0.534026 - 0.360356i) q^{38} +(0.0373890 + 0.0868966i) q^{39} +(-1.93013 + 1.73993i) q^{40} +(-5.27252 + 3.04409i) q^{41} +(0.115733 - 2.44675i) q^{42} +(5.64563 + 3.25951i) q^{43} +(-1.43572 - 1.83616i) q^{44} +(2.64190 - 0.785654i) q^{45} +(2.20454 - 4.52221i) q^{46} +(-2.82141 + 4.88682i) q^{47} +(-4.39056 - 5.35939i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-5.86294 + 0.411120i) q^{50} +(0.667904 - 5.66918i) q^{51} +(-0.108164 + 0.0152443i) q^{52} -10.6457i q^{53} +(1.75951 + 7.13471i) q^{54} +1.07072i q^{55} +(2.69050 + 0.872466i) q^{56} +(0.0923189 - 0.783605i) q^{57} +(-0.866355 - 12.3550i) q^{58} +(-0.744373 - 1.28929i) q^{59} +(0.0723733 + 3.18181i) q^{60} +(-6.35962 + 11.0152i) q^{61} +(10.3223 + 5.03204i) q^{62} +(-2.17834 - 2.06272i) q^{63} +(7.30457 - 3.26240i) q^{64} +(0.0434562 + 0.0250895i) q^{65} +(-2.85149 - 0.134877i) q^{66} +(5.83071 - 3.36636i) q^{67} +(6.11248 + 2.46684i) q^{68} +(-2.43530 - 5.65994i) q^{69} +(-0.726771 - 1.07703i) q^{70} +2.97148 q^{71} +(-8.48273 - 0.208066i) q^{72} +14.8214 q^{73} +(0.954927 + 1.41514i) q^{74} +(-4.30378 + 5.76993i) q^{75} +(0.844877 + 0.340971i) q^{76} +(1.00928 - 0.582708i) q^{77} +(-0.0722909 + 0.112570i) q^{78} +(-10.9305 - 6.31075i) q^{79} +(-3.56652 - 0.886292i) q^{80} +(8.02782 + 4.06867i) q^{81} +(-7.73934 - 3.77287i) q^{82} +(-6.56004 + 11.3623i) q^{83} +(2.95984 - 1.79982i) q^{84} +(-1.51398 - 2.62229i) q^{85} +(0.644889 + 9.19670i) q^{86} +(-12.1590 - 9.06937i) q^{87} +(1.01679 - 3.13555i) q^{88} -7.95018i q^{89} +(3.01087 + 2.47556i) q^{90} -0.0546167i q^{91} +(7.04520 - 0.992928i) q^{92} +(12.9192 - 5.55876i) q^{93} +(-7.96060 + 0.558212i) q^{94} +(-0.209265 - 0.362457i) q^{95} +(2.80959 - 9.38649i) q^{96} +(-4.26325 + 7.38417i) q^{97} +(-0.619704 + 1.27121i) q^{98} +(-2.40393 + 2.53867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

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