LMFDB - Embedded newform 252.2.ba.a.155.16

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			155.16
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.281995 - 1.38581i) q^{2} +(-1.72102 - 0.195202i) q^{3} +(-1.84096 + 0.781584i) q^{4} +(-1.04266 + 0.601980i) q^{5} +(0.214804 + 2.44005i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(1.60227 + 2.33082i) q^{8} +(2.92379 + 0.671890i) q^{9} +O(q^{10})$	\(q+(-0.281995 - 1.38581i) q^{2} +(-1.72102 - 0.195202i) q^{3} +(-1.84096 + 0.781584i) q^{4} +(-1.04266 + 0.601980i) q^{5} +(0.214804 + 2.44005i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(1.60227 + 2.33082i) q^{8} +(2.92379 + 0.671890i) q^{9} +(1.12826 + 1.27518i) q^{10} +(-0.181344 + 0.314097i) q^{11} +(3.32088 - 0.985761i) q^{12} +(3.19111 + 5.52716i) q^{13} +(-0.448692 + 1.34115i) q^{14} +(1.91194 - 0.832488i) q^{15} +(2.77825 - 2.87773i) q^{16} -1.61171i q^{17} +(0.106621 - 4.24130i) q^{18} +7.53867i q^{19} +(1.44899 - 1.92314i) q^{20} +(1.39284 + 1.02956i) q^{21} +(0.486417 + 0.162735i) q^{22} +(-1.72147 - 2.98168i) q^{23} +(-2.30255 - 4.32415i) q^{24} +(-1.77524 + 3.07481i) q^{25} +(6.75974 - 5.98091i) q^{26} +(-4.90074 - 1.72706i) q^{27} +(1.98511 + 0.243607i) q^{28} +(3.01496 + 1.74069i) q^{29} +(-1.69283 - 2.41484i) q^{30} +(-0.888005 + 0.512690i) q^{31} +(-4.77144 - 3.03864i) q^{32} +(0.373408 - 0.505167i) q^{33} +(-2.23352 + 0.454492i) q^{34} +1.20396 q^{35} +(-5.90772 + 1.04827i) q^{36} -2.78178 q^{37} +(10.4472 - 2.12586i) q^{38} +(-4.41304 - 10.1352i) q^{39} +(-3.07373 - 1.46572i) q^{40} +(-7.36112 + 4.24995i) q^{41} +(1.03400 - 2.22055i) q^{42} +(6.97385 + 4.02635i) q^{43} +(0.0883534 - 0.719974i) q^{44} +(-3.45298 + 1.05951i) q^{45} +(-3.64661 + 3.22646i) q^{46} +(-4.17236 + 7.22675i) q^{47} +(-5.34316 + 4.41029i) q^{48} +(0.500000 + 0.866025i) q^{49} +(4.76172 + 1.59307i) q^{50} +(-0.314608 + 2.77377i) q^{51} +(-10.1946 - 7.68116i) q^{52} -9.35345i q^{53} +(-1.01140 + 7.27853i) q^{54} -0.436661i q^{55} +(-0.222195 - 2.81969i) q^{56} +(1.47156 - 12.9742i) q^{57} +(1.56207 - 4.66904i) q^{58} +(5.87381 + 10.1737i) q^{59} +(-2.86914 + 3.02692i) q^{60} +(0.736621 - 1.27587i) q^{61} +(0.960905 + 1.08603i) q^{62} +(-2.19613 - 2.04377i) q^{63} +(-2.86546 + 7.46921i) q^{64} +(-6.65448 - 3.84196i) q^{65} +(-0.805366 - 0.375019i) q^{66} +(1.02391 - 0.591155i) q^{67} +(1.25968 + 2.96708i) q^{68} +(2.38066 + 5.46755i) q^{69} +(-0.339510 - 1.66846i) q^{70} +3.34851 q^{71} +(3.11865 + 7.89139i) q^{72} -12.3638 q^{73} +(0.784446 + 3.85502i) q^{74} +(3.65543 - 4.94526i) q^{75} +(-5.89210 - 13.8784i) q^{76} +(0.314097 - 0.181344i) q^{77} +(-12.8011 + 8.97373i) q^{78} +(3.68419 + 2.12707i) q^{79} +(-1.16444 + 4.67294i) q^{80} +(8.09713 + 3.92894i) q^{81} +(7.96543 + 9.00268i) q^{82} +(1.67751 - 2.90552i) q^{83} +(-3.36885 - 0.806749i) q^{84} +(0.970214 + 1.68046i) q^{85} +(3.61319 - 10.7999i) q^{86} +(-4.84901 - 3.58428i) q^{87} +(-1.02266 + 0.0805875i) q^{88} -5.41703i q^{89} +(2.44201 + 4.48641i) q^{90} -6.38222i q^{91} +(5.49959 + 4.14367i) q^{92} +(1.62835 - 0.709008i) q^{93} +(11.1915 + 3.74421i) q^{94} +(-4.53813 - 7.86026i) q^{95} +(7.61859 + 6.16094i) q^{96} +(6.98817 - 12.1039i) q^{97} +(1.05915 - 0.937121i) q^{98} +(-0.741250 + 0.796510i) 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 $

$2$	−0.281995	−	1.38581i	−0.199400	−	0.979918i
$2$	−0.281995	−	1.38581i	−0.199400	−	0.979918i
$3$	−1.72102	−	0.195202i	−0.993629	−	0.112700i
$3$	−1.72102	−	0.195202i	−0.993629	−	0.112700i
$4$	−1.84096	+	0.781584i	−0.920479	+	0.390792i
$5$	−1.04266	+	0.601980i	−0.466291	+	0.269213i	−0.714686	−	0.699445i	$-0.753430\pi$
$5$	−1.04266	+	0.601980i	−0.466291	+	0.269213i	0.248395	+	0.968659i	$0.420097\pi$
$6$	0.214804	+	2.44005i	0.0876935	+	0.996148i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	1.60227	+	2.33082i	0.566488	+	0.824070i
$9$	2.92379	+	0.671890i	0.974598	+	0.223963i
$10$	1.12826	+	1.27518i	0.356786	+	0.403246i
$11$	−0.181344	+	0.314097i	−0.0546772	+	0.0947037i	−0.892068	−	0.451900i	$-0.850746\pi$
$11$	−0.181344	+	0.314097i	−0.0546772	+	0.0947037i	0.837391	+	0.546604i	$0.184080\pi$
$12$	3.32088	−	0.985761i	0.958657	−	0.284565i
$13$	3.19111	+	5.52716i	0.885054	+	1.53296i	0.845651	+	0.533736i	$0.179212\pi$
$13$	3.19111	+	5.52716i	0.885054	+	1.53296i	0.0394031	+	0.999223i	$0.487454\pi$
$14$	−0.448692	+	1.34115i	−0.119918	+	0.358437i
$15$	1.91194	−	0.832488i	0.493661	−	0.214947i
$16$	2.77825	−	2.87773i	0.694563	−	0.719432i
$17$		−	1.61171i		−	0.390896i	−0.980714	−	0.195448i	$-0.937384\pi$
$17$		−	1.61171i		−	0.390896i	0.980714	−	0.195448i	$-0.0626161\pi$
$18$	0.106621	−	4.24130i	0.0251307	−	0.999684i
$19$			7.53867i			1.72949i	0.502211	+	0.864745i	$0.332520\pi$
$19$			7.53867i			1.72949i	−0.502211	+	0.864745i	$0.667480\pi$
$20$	1.44899	−	1.92314i	0.324005	−	0.430028i
$21$	1.39284	+	1.02956i	0.303943	+	0.224668i
$22$	0.486417	+	0.162735i	0.103704	+	0.0346952i
$23$	−1.72147	−	2.98168i	−0.358952	−	0.621723i	0.628834	−	0.777540i	$-0.283533\pi$
$23$	−1.72147	−	2.98168i	−0.358952	−	0.621723i	−0.987786	+	0.155816i	$0.950199\pi$
$24$	−2.30255	−	4.32415i	−0.470006	−	0.882663i
$25$	−1.77524	+	3.07481i	−0.355048	+	0.614962i
$26$	6.75974	−	5.98091i	1.32569	−	1.17295i
$27$	−4.90074	−	1.72706i	−0.943148	−	0.332373i
$28$	1.98511	+	0.243607i	0.375150	+	0.0460375i
$29$	3.01496	+	1.74069i	0.559865	+	0.323238i	0.753091	−	0.657916i	$-0.228562\pi$
$29$	3.01496	+	1.74069i	0.559865	+	0.323238i	−0.193227	+	0.981154i	$0.561895\pi$
$30$	−1.69283	−	2.41484i	−0.309067	−	0.440887i
$31$	−0.888005	+	0.512690i	−0.159490	+	0.0920818i	−0.577621	−	0.816305i	$-0.696019\pi$
$31$	−0.888005	+	0.512690i	−0.159490	+	0.0920818i	0.418131	+	0.908387i	$0.362685\pi$
$32$	−4.77144	−	3.03864i	−0.843480	−	0.537160i
$33$	0.373408	−	0.505167i	0.0650019	−	0.0879382i
$34$	−2.23352	+	0.454492i	−0.383046	+	0.0779448i
$35$	1.20396			0.203506
$36$	−5.90772	+	1.04827i	−0.984620	+	0.174711i
$37$	−2.78178			−0.457321			−0.228661	−	0.973506i	$-0.573435\pi$
$37$	−2.78178			−0.457321			−0.228661	+	0.973506i	$0.573435\pi$
$38$	10.4472	−	2.12586i	1.69476	−	0.344861i
$39$	−4.41304	−	10.1352i	−0.706652	−	1.62294i
$40$	−3.07373	−	1.46572i	−0.485999	−	0.231751i
$41$	−7.36112	+	4.24995i	−1.14961	+	0.663730i	−0.948793	−	0.315898i	$-0.897694\pi$
$41$	−7.36112	+	4.24995i	−1.14961	+	0.663730i	−0.200821	+	0.979628i	$0.564361\pi$
$42$	1.03400	−	2.22055i	0.159550	−	0.342638i
$43$	6.97385	+	4.02635i	1.06350	+	0.614013i	0.926399	−	0.376543i	$-0.122887\pi$
$43$	6.97385	+	4.02635i	1.06350	+	0.614013i	0.137103	+	0.990557i	$0.456221\pi$
$44$	0.0883534	−	0.719974i	0.0133198	−	0.108540i
$45$	−3.45298	+	1.05951i	−0.514740	+	0.157943i
$46$	−3.64661	+	3.22646i	−0.537663	+	0.475715i
$47$	−4.17236	+	7.22675i	−0.608602	+	1.05413i	0.382869	+	0.923802i	$0.374936\pi$
$47$	−4.17236	+	7.22675i	−0.608602	+	1.05413i	−0.991471	+	0.130327i	$0.958397\pi$
$48$	−5.34316	+	4.41029i	−0.771218	+	0.636571i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	4.76172	+	1.59307i	0.673409	+	0.225295i
$51$	−0.314608	+	2.77377i	−0.0440539	+	0.388406i
$52$	−10.1946	−	7.68116i	−1.41374	−	1.06518i
$53$		−	9.35345i		−	1.28480i	−0.766371	−	0.642398i	$-0.777940\pi$
$53$		−	9.35345i		−	1.28480i	0.766371	−	0.642398i	$-0.222060\pi$
$54$	−1.01140	+	7.27853i	−0.137635	+	0.990483i
$55$		−	0.436661i		−	0.0588793i
$56$	−0.222195	−	2.81969i	−0.0296921	−	0.376796i
$57$	1.47156	−	12.9742i	0.194913	−	1.71847i
$58$	1.56207	−	4.66904i	0.205110	−	0.613075i
$59$	5.87381	+	10.1737i	0.764705	+	1.32451i	0.940403	+	0.340063i	$0.110448\pi$
$59$	5.87381	+	10.1737i	0.764705	+	1.32451i	−0.175698	+	0.984444i	$0.556218\pi$
$60$	−2.86914	+	3.02692i	−0.370405	+	0.390773i
$61$	0.736621	−	1.27587i	0.0943147	−	0.163358i	−0.815008	−	0.579450i	$-0.803267\pi$
$61$	0.736621	−	1.27587i	0.0943147	−	0.163358i	0.909322	+	0.416092i	$0.136601\pi$
$62$	0.960905	+	1.08603i	0.122035	+	0.137926i
$63$	−2.19613	−	2.04377i	−0.276687	−	0.257491i
$64$	−2.86546	+	7.46921i	−0.358183	+	0.933651i
$65$	−6.65448	−	3.84196i	−0.825386	−	0.476537i
$66$	−0.805366	−	0.375019i	−0.0991337	−	0.0461617i
$67$	1.02391	−	0.591155i	0.125091	−	0.0722211i	−0.436149	−	0.899874i	$-0.643658\pi$
$67$	1.02391	−	0.591155i	0.125091	−	0.0722211i	0.561240	+	0.827653i	$0.310325\pi$
$68$	1.25968	+	2.96708i	0.152759	+	0.359812i
$69$	2.38066	+	5.46755i	0.286597	+	0.658216i
$70$	−0.339510	−	1.66846i	−0.0405792	−	0.199419i
$71$	3.34851			0.397396			0.198698	−	0.980061i	$-0.436329\pi$
$71$	3.34851			0.397396			0.198698	+	0.980061i	$0.436329\pi$
$72$	3.11865	+	7.89139i	0.367536	+	0.930009i
$73$	−12.3638			−1.44707			−0.723536	−	0.690286i	$-0.757485\pi$
$73$	−12.3638			−1.44707			−0.723536	+	0.690286i	$0.757485\pi$
$74$	0.784446	+	3.85502i	0.0911900	+	0.448137i
$75$	3.65543	−	4.94526i	0.422092	−	0.571030i
$76$	−5.89210	−	13.8784i	−0.675871	−	1.59196i
$77$	0.314097	−	0.181344i	0.0357946	−	0.0206660i
$78$	−12.8011	+	8.97373i	−1.44944	+	1.01608i
$79$	3.68419	+	2.12707i	0.414503	+	0.239314i	0.692723	−	0.721204i	$-0.256411\pi$
$79$	3.68419	+	2.12707i	0.414503	+	0.239314i	−0.278220	+	0.960518i	$0.589744\pi$
$80$	−1.16444	+	4.67294i	−0.130188	+	0.522451i
$81$	8.09713	+	3.92894i	0.899681	+	0.436548i
$82$	7.96543	+	9.00268i	0.879634	+	0.994180i
$83$	1.67751	−	2.90552i	0.184130	−	0.318923i	−0.759153	−	0.650912i	$-0.774387\pi$
$83$	1.67751	−	2.90552i	0.184130	−	0.318923i	0.943283	+	0.331990i	$0.107720\pi$
$84$	−3.36885	−	0.806749i	−0.367572	−	0.0880235i
$85$	0.970214	+	1.68046i	0.105234	+	0.182271i
$86$	3.61319	−	10.7999i	0.389620	−	1.16458i
$87$	−4.84901	−	3.58428i	−0.519869	−	0.384275i
$88$	−1.02266	+	0.0805875i	−0.109016	+	0.00859065i
$89$		−	5.41703i		−	0.574204i	−0.957900	−	0.287102i	$-0.907308\pi$
$89$		−	5.41703i		−	0.574204i	0.957900	−	0.287102i	$-0.0926918\pi$
$90$	2.44201	+	4.48641i	0.257410	+	0.472910i
$91$		−	6.38222i		−	0.669038i
$92$	5.49959	+	4.14367i	0.573372	+	0.432008i
$93$	1.62835	−	0.709008i	0.168852	−	0.0735207i
$94$	11.1915	+	3.74421i	1.15432	+	0.386186i
$95$	−4.53813	−	7.86026i	−0.465602	−	0.806446i
$96$	7.61859	+	6.16094i	0.777569	+	0.628798i
$97$	6.98817	−	12.1039i	0.709541	−	1.22896i	−0.255486	−	0.966813i	$-0.582236\pi$
$97$	6.98817	−	12.1039i	0.709541	−	1.22896i	0.965027	−	0.262149i	$-0.0844311\pi$
$98$	1.05915	−	0.937121i	0.106991	−	0.0946635i
$99$	−0.741250	+	0.796510i	−0.0744984	+	0.0800523i
$100$	0.864924	−	7.04809i	0.0864924	−	0.704809i
$101$	0.213167	+	0.123072i	0.0212109	+	0.0122461i	0.510568	−	0.859837i	$-0.329435\pi$
$101$	0.213167	+	0.123072i	0.0212109	+	0.0122461i	−0.489357	+	0.872084i	$0.662769\pi$
$102$	3.93265	−	0.346201i	0.389390	−	0.0342790i
$103$	7.30498	−	4.21753i	0.719781	−	0.415566i	−0.0948909	−	0.995488i	$-0.530250\pi$
$103$	7.30498	−	4.21753i	0.719781	−	0.415566i	0.814672	+	0.579922i	$0.196917\pi$
$104$	−7.76982	+	16.2939i	−0.761893	+	1.59775i
$105$	−2.07203	−	0.235015i	−0.202210	−	0.0229351i
$106$	−12.9621	+	2.63762i	−1.25899	+	0.256189i
$107$	−14.3821			−1.39037			−0.695185	−	0.718831i	$-0.744678\pi$
$107$	−14.3821			−1.39037			−0.695185	+	0.718831i	$0.744678\pi$
$108$	10.3719	−	0.650889i	0.998037	−	0.0626318i
$109$	−5.51288			−0.528038			−0.264019	−	0.964517i	$-0.585048\pi$
$109$	−5.51288			−0.528038			−0.264019	+	0.964517i	$0.585048\pi$
$110$	−0.605130	+	0.123136i	−0.0576969	+	0.0117406i
$111$	4.78748	+	0.543007i	0.454408	+	0.0515400i
$112$	−3.84490	+	1.10306i	−0.363309	+	0.104229i
$113$	8.43458	−	4.86971i	0.793459	−	0.458104i	−0.0477200	−	0.998861i	$-0.515196\pi$
$113$	8.43458	−	4.86971i	0.793459	−	0.458104i	0.841179	+	0.540757i	$0.181862\pi$
$114$	−18.3948	+	1.61934i	−1.72283	+	0.151665i
$115$	3.58982	+	2.07258i	0.334753	+	0.193269i
$116$	−6.91091	−	0.848090i	−0.641662	−	0.0787432i
$117$	5.61649	+	18.3044i	0.519245	+	1.69224i
$118$	12.4425	−	11.0089i	1.14543	−	1.01346i
$119$	−0.805853	+	1.39578i	−0.0738724	+	0.127951i
$120$	5.00383	+	3.12252i	0.456785	+	0.285046i
$121$	5.43423	+	9.41236i	0.494021	+	0.855669i
$122$	−1.97583	−	0.661032i	−0.178884	−	0.0598470i
$123$	13.4982	−	5.87732i	1.21709	−	0.529940i
$124$	1.23407	−	1.63789i	0.110823	−	0.147087i
$125$		−	10.2944i		−	0.920762i
$126$	−2.21299	+	3.61976i	−0.197149	+	0.322474i
$127$		−	18.7124i		−	1.66046i	−0.557420	−	0.830230i	$-0.688209\pi$
$127$		−	18.7124i		−	1.66046i	0.557420	−	0.830230i	$-0.311791\pi$
$128$	11.1590	+	1.86472i	0.986324	+	0.164819i
$129$	−11.2162	−	8.29073i	−0.987528	−	0.729958i
$130$	−3.44772	+	10.3053i	−0.302385	+	0.903833i
$131$	7.00838	+	12.1389i	0.612325	+	1.06058i	0.990848	+	0.134986i	$0.0430989\pi$
$131$	7.00838	+	12.1389i	0.612325	+	1.06058i	−0.378523	+	0.925592i	$0.623568\pi$
$132$	−0.292598	+	1.22184i	−0.0254674	+	0.106348i
$133$	3.76934	−	6.52868i	0.326843	−	0.566108i
$134$	−1.10797	−	1.25225i	−0.0957139	−	0.108178i
$135$	6.14946	−	1.14941i	0.529261	−	0.0989252i
$136$	3.75660	−	2.58239i	0.322126	−	0.221438i
$137$	13.8831	+	8.01544i	1.18612	+	0.684805i	0.957422	−	0.288693i	$-0.0932207\pi$
$137$	13.8831	+	8.01544i	1.18612	+	0.684805i	0.228695	+	0.973498i	$0.426554\pi$
$138$	6.90568	−	4.84097i	0.587850	−	0.412090i
$139$	0.334750	−	0.193268i	0.0283932	−	0.0163928i	−0.485736	−	0.874105i	$-0.661448\pi$
$139$	0.334750	−	0.193268i	0.0283932	−	0.0163928i	0.514129	+	0.857713i	$0.328115\pi$
$140$	−2.21644	+	0.940995i	−0.187323	+	0.0795286i
$141$	8.59138	−	11.6229i	0.723524	−	0.978824i
$142$	−0.944263	−	4.64042i	−0.0792408	−	0.389415i
$143$	−2.31475			−0.193569
$144$	10.0566	−	6.54719i	0.838046	−	0.545600i
$145$	−4.19144			−0.348080
$146$	3.48652	+	17.1339i	0.288547	+	1.41801i
$147$	−0.691458	−	1.58804i	−0.0570305	−	0.130980i
$148$	5.12113	−	2.17419i	0.420954	−	0.178717i
$149$	−20.2620	+	11.6982i	−1.65992	+	0.958358i	−0.687176	+	0.726491i	$0.741150\pi$
$149$	−20.2620	+	11.6982i	−1.65992	+	0.958358i	−0.972748	+	0.231867i	$0.925517\pi$
$150$	−7.88402	−	3.67120i	−0.643728	−	0.299752i
$151$	8.60631	+	4.96886i	0.700372	+	0.404360i	0.807486	−	0.589887i	$-0.200828\pi$
$151$	8.60631	+	4.96886i	0.700372	+	0.404360i	−0.107114	+	0.994247i	$0.534161\pi$
$152$	−17.5713	+	12.0790i	−1.42522	+	0.979735i
$153$	1.08289	−	4.71229i	0.0875464	−	0.380966i
$154$	−0.339882	−	0.384141i	−0.0273885	−	0.0309550i
$155$	0.617258	−	1.06912i	0.0495793	−	0.0858739i
$156$	16.0458	+	15.2094i	1.28469	+	1.21773i
$157$	0.331610	+	0.574366i	0.0264654	+	0.0458394i	0.878955	−	0.476905i	$-0.158241\pi$
$157$	0.331610	+	0.574366i	0.0264654	+	0.0458394i	−0.852489	+	0.522745i	$0.824908\pi$
$158$	1.90880	−	5.70541i	0.151856	−	0.453898i
$159$	−1.82581	+	16.0974i	−0.144796	+	1.27661i
$160$	6.80419	+	0.295951i	0.537918	+	0.0233970i
$161$			3.44295i			0.271342i
$162$	3.16143	−	12.3290i	0.248385	−	0.968661i
$163$			2.34168i			0.183415i	0.995786	+	0.0917073i	$0.0292324\pi$
$163$			2.34168i			0.183415i	−0.995786	+	0.0917073i	$0.970768\pi$
$164$	10.2298	−	13.5773i	0.798815	−	1.06021i
$165$	−0.0852369	+	0.751500i	−0.00663568	+	0.0585042i
$166$	−4.49956	−	1.50537i	−0.349234	−	0.116839i
$167$	−1.37986	−	2.38998i	−0.106776	−	0.184942i	0.807686	−	0.589613i	$-0.200720\pi$
$167$	−1.37986	−	2.38998i	−0.106776	−	0.184942i	−0.914463	+	0.404670i	$0.867386\pi$
$168$	−0.168005	+	4.89610i	−0.0129619	+	0.377742i
$169$	−13.8664	+	24.0172i	−1.06664	+	1.84748i
$170$	2.05521	−	1.81842i	0.157627	−	0.139466i
$171$	−5.06516	+	22.0415i	−0.387342	+	1.68556i
$172$	−15.9855	−	1.96170i	−1.21888	−	0.149578i
$173$	−7.97452	−	4.60409i	−0.606291	−	0.350042i	0.165221	−	0.986257i	$-0.447166\pi$
$173$	−7.97452	−	4.60409i	−0.606291	−	0.350042i	−0.771513	+	0.636214i	$0.780500\pi$
$174$	−3.59975	+	7.73058i	−0.272896	+	0.586053i
$175$	3.07481	−	1.77524i	0.232434	−	0.134196i
$176$	0.400065	+	1.39450i	0.0301560	+	0.105114i
$177$	−8.12299	−	18.6557i	−0.610561	−	1.40225i
$178$	−7.50699	+	1.52757i	−0.562673	+	0.114496i
$179$	−10.4075			−0.777891			−0.388945	−	0.921261i	$-0.627161\pi$
$179$	−10.4075			−0.777891			−0.388945	+	0.921261i	$0.627161\pi$
$180$	5.52870	−	4.64931i	0.412085	−	0.346539i
$181$	13.0797			0.972205			0.486103	−	0.873902i	$-0.338418\pi$
$181$	13.0797			0.972205			0.486103	+	0.873902i	$0.338418\pi$
$182$	−8.84456	+	1.79975i	−0.655603	+	0.133406i
$183$	−1.51679	+	2.05199i	−0.112124	+	0.151688i
$184$	4.19150	−	8.78991i	0.309001	−	0.648000i
$185$	2.90044	−	1.67457i	0.213245	−	0.123117i
$186$	−1.44174	−	2.05665i	−0.105713	−	0.150801i
$187$	0.506231	+	0.292273i	0.0370193	+	0.0213731i
$188$	2.03284	−	16.5652i	0.148260	−	1.20814i
$189$	3.38063	+	3.94605i	0.245905	+	0.287033i
$190$	−9.61313	+	8.50555i	−0.697410	+	0.617057i
$191$	3.13765	−	5.43457i	0.227032	−	0.393231i	−0.729895	−	0.683559i	$-0.760431\pi$
$191$	3.13765	−	5.43457i	0.227032	−	0.393231i	0.956927	+	0.290328i	$0.0937644\pi$
$192$	6.38951	−	12.2953i	0.461123	−	0.887336i
$193$	4.21063	+	7.29302i	0.303088	+	0.524963i	0.976834	−	0.214000i	$-0.0686492\pi$
$193$	4.21063	+	7.29302i	0.303088	+	0.524963i	−0.673746	+	0.738963i	$0.735316\pi$
$194$	−18.7443	−	6.27108i	−1.34576	−	0.450237i
$195$	10.7025	+	7.91105i	0.766422	+	0.566522i
$196$	−1.59735	−	1.20352i	−0.114096	−	0.0859660i
$197$			15.4461i			1.10049i	0.835004	+	0.550244i	$0.185465\pi$
$197$			15.4461i			1.10049i	−0.835004	+	0.550244i	$0.814535\pi$
$198$	1.31284	+	0.802622i	0.0932997	+	0.0570399i
$199$		−	3.27602i		−	0.232231i	−0.993236	−	0.116115i	$-0.962956\pi$
$199$		−	3.27602i		−	0.232231i	0.993236	−	0.116115i	$-0.0370442\pi$
$200$	−10.0112	+	0.788901i	−0.707902	+	0.0557837i
$201$	−1.87756	+	0.817519i	−0.132433	+	0.0576633i
$202$	0.110443	−	0.330115i	0.00777073	−	0.0232268i
$203$	−1.74069	−	3.01496i	−0.122172	−	0.211609i
$204$	−1.58876	−	5.35229i	−0.111235	−	0.374735i
$205$	5.11676	−	8.86249i	0.357370	−	0.618983i
$206$	−7.90468	−	8.93402i	−0.550745	−	0.622463i
$207$	−3.02987	−	9.87446i	−0.210591	−	0.686322i
$208$	24.7714	+	6.17272i	1.71759	+	0.428001i
$209$	−2.36787	−	1.36709i	−0.163789	−	0.0945636i
$210$	0.258616	+	2.93772i	0.0178462	+	0.202722i
$211$	−13.3911	+	7.73134i	−0.921879	+	0.532247i	−0.884234	−	0.467044i	$-0.845319\pi$
$211$	−13.3911	+	7.73134i	−0.921879	+	0.532247i	−0.0376452	+	0.999291i	$0.511986\pi$
$212$	7.31051	+	17.2193i	0.502088	+	1.18263i
$213$	−5.76285	−	0.653635i	−0.394864	−	0.0447864i
$214$	4.05568	+	19.9309i	0.277240	+	1.36245i
$215$	−9.69513			−0.661203
$216$	−3.82683	−	14.1900i	−0.260383	−	0.965505i
$217$	1.02538			0.0696073
$218$	1.55460	+	7.63983i	0.105291	+	0.517434i
$219$	21.2783	+	2.41343i	1.43785	+	0.163085i
$220$	0.341287	+	0.803874i	0.0230096	+	0.0541972i
$221$	8.90816	−	5.14313i	0.599228	−	0.345964i
$222$	−0.597537	−	6.78768i	−0.0401041	−	0.455559i
$223$	−9.46089	−	5.46225i	−0.633548	−	0.365779i	0.148577	−	0.988901i	$-0.452531\pi$
$223$	−9.46089	−	5.46225i	−0.633548	−	0.365779i	−0.782125	+	0.623122i	$0.785864\pi$
$224$	2.61287	+	5.01726i	0.174580	+	0.335230i
$225$	−7.25637	+	7.79733i	−0.483758	+	0.519822i
$226$	−9.12701	−	10.3155i	−0.607120	−	0.686179i
$227$	−5.68049	+	9.83889i	−0.377027	+	0.653030i	−0.990628	−	0.136586i	$-0.956387\pi$
$227$	−5.68049	+	9.83889i	−0.377027	+	0.653030i	0.613601	+	0.789616i	$0.289720\pi$
$228$	7.43132	+	25.0351i	0.492151	+	1.65799i
$229$	−13.3761	−	23.1681i	−0.883919	−	1.53099i	−0.846948	−	0.531676i	$-0.821563\pi$
$229$	−13.3761	−	23.1681i	−0.883919	−	1.53099i	−0.0369706	−	0.999316i	$-0.511771\pi$
$230$	1.85990	−	5.55928i	0.122638	−	0.366568i
$231$	−0.575964	+	0.250783i	−0.0378956	+	0.0165003i
$232$	0.773546	+	9.81640i	0.0507858	+	0.644478i
$233$			3.86780i			0.253388i	0.991942	+	0.126694i	$0.0404367\pi$
$233$			3.86780i			0.253388i	−0.991942	+	0.126694i	$0.959563\pi$
$234$	23.7826	−	12.9451i	1.55472	−	0.846250i
$235$		−	10.0467i		−	0.655375i
$236$	−18.7651	−	14.1385i	−1.22150	−	0.920341i
$237$	−5.92534	−	4.37987i	−0.384892	−	0.284503i
$238$	2.16153	+	0.723160i	0.140111	+	0.0468755i
$239$	−12.3296	−	21.3556i	−0.797538	−	1.38138i	−0.921215	−	0.389054i	$-0.872802\pi$
$239$	−12.3296	−	21.3556i	−0.797538	−	1.38138i	0.123676	−	0.992323i	$-0.460532\pi$
$240$	2.91618	−	7.81490i	0.188239	−	0.504450i
$241$	−0.173924	+	0.301245i	−0.0112034	+	0.0194049i	−0.871573	−	0.490266i	$-0.836900\pi$
$241$	−0.173924	+	0.301245i	−0.0112034	+	0.0194049i	0.860369	+	0.509671i	$0.170233\pi$
$242$	11.5114	−	10.1851i	0.739978	−	0.654721i
$243$	−13.1684	−	8.34233i	−0.844750	−	0.535161i
$244$	−0.358893	+	2.92455i	−0.0229758	+	0.187225i
$245$	−1.04266	−	0.601980i	−0.0666131	−	0.0384591i
$246$	−11.9513	−	17.0486i	−0.761987	−	1.08698i
$247$	−41.6675	+	24.0567i	−2.65124	+	1.53069i
$248$	−2.61781	−	1.24831i	−0.166231	−	0.0792680i
$249$	−3.45418	+	4.67300i	−0.218900	+	0.296139i
$250$	−14.2662	+	2.90297i	−0.902271	+	0.183600i
$251$	18.9259			1.19459			0.597297	−	0.802020i	$-0.296241\pi$
$251$	18.9259			1.19459			0.597297	+	0.802020i	$0.296241\pi$
$252$	5.64037	+	2.04603i	0.355310	+	0.128888i
$253$	1.24871			0.0785060
$254$	−25.9320	+	5.27681i	−1.62712	+	0.331096i
$255$	−1.34173	−	3.08149i	−0.0840221	−	0.192970i
$256$	−0.562620	−	15.9901i	−0.0351637	−	0.999382i
$257$	5.18682	−	2.99461i	0.323545	−	0.186799i	−0.329427	−	0.944181i	$-0.606855\pi$
$257$	5.18682	−	2.99461i	0.323545	−	0.186799i	0.652971	+	0.757383i	$0.273522\pi$
$258$	−8.32651	+	17.8814i	−0.518386	+	1.11325i
$259$	2.40909	+	1.39089i	0.149693	+	0.0864256i
$260$	15.2534	+	1.87186i	0.945978	+	0.116088i
$261$	7.64557	+	7.11514i	0.473249	+	0.440416i
$262$	14.8459	−	13.1354i	0.917182	−	0.811508i
$263$	1.44554	−	2.50374i	0.0891355	−	0.154387i	−0.818010	−	0.575203i	$-0.804923\pi$
$263$	1.44554	−	2.50374i	0.0891355	−	0.154387i	0.907146	+	0.420816i	$0.138256\pi$
$264$	1.77575	+	0.0609334i	0.109290	+	0.00375019i
$265$	5.63059	+	9.75246i	0.345884	+	0.599089i
$266$	−10.1105	−	3.38254i	−0.619912	−	0.207397i
$267$	−1.05741	+	9.32279i	−0.0647126	+	0.570545i
$268$	−1.42294	+	1.88856i	−0.0869199	+	0.115362i
$269$			9.94347i			0.606264i	0.952949	+	0.303132i	$0.0980323\pi$
$269$			9.94347i			0.606264i	−0.952949	+	0.303132i	$0.901968\pi$
$270$	−3.32698	−	8.19788i	−0.202473	−	0.498907i
$271$		−	18.7387i		−	1.13830i	−0.822235	−	0.569148i	$-0.807273\pi$
$271$		−	18.7387i		−	1.13830i	0.822235	−	0.569148i	$-0.192727\pi$
$272$	−4.63805	−	4.47773i	−0.281223	−	0.271502i
$273$	−1.24582	+	10.9839i	−0.0754004	+	0.664776i
$274$	7.19293	−	21.4998i	0.434541	−	1.29885i
$275$	−0.643858	−	1.11519i	−0.0388261	−	0.0672487i
$276$	−8.65604	−	8.20486i	−0.521032	−	0.493874i
$277$	12.2691	−	21.2506i	0.737176	−	1.27683i	−0.216586	−	0.976264i	$-0.569492\pi$
$277$	12.2691	−	21.2506i	0.737176	−	1.27683i	0.953762	−	0.300563i	$-0.0971745\pi$
$278$	−0.362232	−	0.409401i	−0.0217252	−	0.0245542i
$279$	−2.94081	+	0.902357i	−0.176062	+	0.0540227i
$280$	1.92907	+	2.80621i	0.115284	+	0.167703i
$281$	27.9153	+	16.1169i	1.66529	+	0.961455i	0.970126	+	0.242603i	$0.0780013\pi$
$281$	27.9153	+	16.1169i	1.66529	+	0.961455i	0.695163	+	0.718852i	$0.255332\pi$
$282$	−18.5299	−	8.62845i	−1.10344	−	0.513817i
$283$	2.56139	−	1.47882i	0.152259	−	0.0879067i	−0.421935	−	0.906626i	$-0.638649\pi$
$283$	2.56139	−	1.47882i	0.152259	−	0.0879067i	0.574194	+	0.818719i	$0.305316\pi$
$284$	−6.16447	+	2.61715i	−0.365794	+	0.155299i
$285$	6.27585	+	14.4135i	0.371749	+	0.853782i
$286$	0.652747	+	3.20781i	0.0385977	+	0.189682i
$287$	8.49989			0.501733
$288$	−11.9091	−	12.0902i	−0.701750	−	0.712424i
$289$	14.4024			0.847200
$290$	1.18196	+	5.80855i	0.0694073	+	0.341090i
$291$	−14.3894	+	19.4668i	−0.843524	+	1.14117i
$292$	22.7612	−	9.66334i	1.33200	−	0.565504i
$293$	−11.8235	+	6.82630i	−0.690736	+	0.398797i	−0.803888	−	0.594781i	$-0.797239\pi$
$293$	−11.8235	+	6.82630i	−0.690736	+	0.398797i	0.113152	+	0.993578i	$0.463905\pi$
$294$	−2.00575	+	1.40605i	−0.116977	+	0.0820026i
$295$	−12.2488	−	7.07182i	−0.713150	−	0.411738i
$296$	−4.45716	−	6.48382i	−0.259067	−	0.376865i
$297$	1.43118	−	1.22611i	0.0830457	−	0.0711463i
$298$	21.9253	+	24.7804i	1.27010	+	1.43549i
$299$	10.9868	−	19.0297i	0.635384	−	1.10052i
$300$	−2.86435	+	11.9610i	−0.165373	+	0.690571i
$301$	−4.02635	−	6.97385i	−0.232075	−	0.401966i
$302$	4.45897	−	13.3279i	0.256585	−	0.766936i
$303$	−0.342840	−	0.253419i	−0.0196956	−	0.0145586i
$304$	21.6942	+	20.9443i	1.24425	+	1.20124i
$305$			1.77372i			0.101563i
$306$	−6.83573	−	0.171841i	−0.390773	−	0.00982351i
$307$			4.22262i			0.240998i	0.992713	+	0.120499i	$0.0384494\pi$
$307$			4.22262i			0.240998i	−0.992713	+	0.120499i	$0.961551\pi$
$308$	−0.436503	+	0.579339i	−0.0248721	+	0.0330109i
$309$	−13.3953	+	5.83250i	−0.762030	+	0.331799i
$310$	−1.65567	−	0.553917i	−0.0940355	−	0.0314604i
$311$	7.37965	+	12.7819i	0.418462	+	0.724797i	0.995785	−	0.0917189i	$-0.0292361\pi$
$311$	7.37965	+	12.7819i	0.418462	+	0.724797i	−0.577323	+	0.816516i	$0.695903\pi$
$312$	16.5526	−	26.5254i	0.937105	−	1.50171i
$313$	4.46672	−	7.73659i	0.252474	−	0.437298i	−0.711732	−	0.702451i	$-0.752089\pi$
$313$	4.46672	−	7.73659i	0.252474	−	0.437298i	0.964206	+	0.265153i	$0.0854224\pi$
$314$	0.702451	−	0.621518i	0.0396416	−	0.0350743i
$315$	3.52013	+	0.808928i	0.198337	+	0.0455780i
$316$	−8.44491	−	1.03634i	−0.475063	−	0.0582986i
$317$	−24.6755	−	14.2464i	−1.38591	−	0.800158i	−0.393062	−	0.919512i	$-0.628584\pi$
$317$	−24.6755	−	14.2464i	−1.38591	−	0.800158i	−0.992852	+	0.119355i	$0.961917\pi$
$318$	22.8229	−	2.00916i	1.27985	−	0.112668i
$319$	−1.09349	+	0.631326i	−0.0612236	+	0.0353475i
$320$	−1.50861	−	9.51279i	−0.0843340	−	0.531781i
$321$	24.7518	+	2.80741i	1.38151	+	0.156694i
$322$	4.77128	−	0.970893i	0.265893	−	0.0541057i
$323$	12.1501			0.676051
$324$	−17.9773	−	0.904421i	−0.998737	−	0.0502456i
$325$	−22.6600			−1.25695
$326$	3.24513	−	0.660341i	0.179731	−	0.0365729i
$327$	9.48776	+	1.07612i	0.524674	+	0.0595098i
$328$	−21.7004	−	10.3479i	−1.19820	−	0.571367i
$329$	7.22675	−	4.17236i	0.398423	−	0.230030i
$330$	1.06548	−	0.0937966i	0.0586525	−	0.00516333i
$331$	8.06313	+	4.65525i	0.443190	+	0.255876i	0.704950	−	0.709257i	$-0.250970\pi$
$331$	8.06313	+	4.65525i	0.443190	+	0.255876i	−0.261760	+	0.965133i	$0.584303\pi$
$332$	−0.817306	+	6.66006i	−0.0448555	+	0.365518i
$333$	−8.13334	−	1.86905i	−0.445704	−	0.102423i
$334$	−2.92296	+	2.58619i	−0.159937	+	0.141510i
$335$	−0.711727	+	1.23275i	−0.0388858	+	0.0673522i
$336$	6.83246	−	1.14785i	0.372741	−	0.0626203i
$337$	4.56021	+	7.89852i	0.248411	+	0.430260i	0.963085	−	0.269197i	$-0.0867584\pi$
$337$	4.56021	+	7.89852i	0.248411	+	0.430260i	−0.714674	+	0.699457i	$0.753425\pi$
$338$	37.1936	+	12.4435i	2.02307	+	0.676834i
$339$	−15.4666	+	6.73440i	−0.840032	+	0.365763i
$340$	−3.09954	−	2.33535i	−0.168096	−	0.126652i
$341$		−	0.371892i		−	0.0201391i
$342$	31.9738	+	0.803779i	1.72894	+	0.0434634i
$343$		−	1.00000i		−	0.0539949i
$344$	1.78928	+	22.7061i	0.0964713	+	1.22423i
$345$	−5.77357	−	4.26769i	−0.310838	−	0.229765i
$346$	−4.13164	+	12.3495i	−0.222118	+	0.663914i
$347$	12.7018	+	22.0001i	0.681866	+	1.18103i	0.974411	+	0.224775i	$0.0721648\pi$
$347$	12.7018	+	22.0001i	0.681866	+	1.18103i	−0.292544	+	0.956252i	$0.594502\pi$
$348$	11.7282	+	2.80860i	0.628700	+	0.150557i
$349$	6.83524	−	11.8390i	0.365882	−	0.633726i	−0.623035	−	0.782194i	$-0.714101\pi$
$349$	6.83524	−	11.8390i	0.365882	−	0.633726i	0.988917	+	0.148467i	$0.0474340\pi$
$350$	−3.32723	−	3.76050i	−0.177848	−	0.201007i
$351$	−6.09304	−	32.5984i	−0.325222	−	1.73998i
$352$	1.81970	−	0.947656i	0.0969902	−	0.0505103i
$353$	22.6983	+	13.1048i	1.20811	+	0.697501i	0.962345	−	0.271830i	$-0.0876287\pi$
$353$	22.6983	+	13.1048i	1.20811	+	0.697501i	0.245761	+	0.969330i	$0.420962\pi$
$354$	−23.5627	+	16.5178i	−1.25235	+	0.877909i
$355$	−3.49136	+	2.01574i	−0.185302	+	0.106984i
$356$	4.23386	+	9.97252i	0.224394	+	0.528542i
$357$	1.65934	−	2.24485i	0.0878218	−	0.118810i
$358$	2.93485	+	14.4228i	0.155112	+	0.762269i
$359$	24.5077			1.29347			0.646734	−	0.762716i	$-0.276135\pi$
$359$	24.5077			1.29347			0.646734	+	0.762716i	$0.276135\pi$
$360$	−8.00214	−	6.35067i	−0.421750	−	0.334710i
$361$	−37.8316			−1.99113
$362$	−3.68840	−	18.1260i	−0.193858	−	0.952682i
$363$	−7.51509	−	17.2596i	−0.394440	−	0.905894i
$364$	4.98824	+	11.7494i	0.261455	+	0.615836i
$365$	12.8912	−	7.44275i	0.674757	−	0.389571i
$366$	3.27141	+	1.52333i	0.170999	+	0.0796259i
$367$	10.4112	+	6.01094i	0.543463	+	0.313768i	0.746481	−	0.665407i	$-0.231742\pi$
$367$	10.4112	+	6.01094i	0.543463	+	0.313768i	−0.203018	+	0.979175i	$0.565075\pi$
$368$	−13.3631	−	3.32993i	−0.696602	−	0.173585i
$369$	−24.3779	+	7.48009i	−1.26906	+	0.389398i
$370$	−3.13855	−	3.54725i	−0.163166	−	0.184413i
$371$	−4.67673	+	8.10033i	−0.242804	+	0.420548i
$372$	−2.44357	+	2.57794i	−0.126693	+	0.133660i
$373$	11.6823	+	20.2343i	0.604884	+	1.04769i	0.992070	+	0.125689i	$0.0401141\pi$
$373$	11.6823	+	20.2343i	0.604884	+	1.04769i	−0.387185	+	0.922002i	$0.626553\pi$
$374$	0.262281	−	0.783961i	0.0135622	−	0.0405377i
$375$	−2.00949	+	17.7169i	−0.103770	+	0.914896i
$376$	−23.5295	+	1.85416i	−1.21344	+	0.0956210i
$377$			22.2189i			1.14433i
$378$	4.51517	−	5.79769i	0.232235	−	0.298201i
$379$			28.9864i			1.48893i	0.667661	+	0.744465i	$0.267296\pi$
$379$			28.9864i			1.48893i	−0.667661	+	0.744465i	$0.732704\pi$
$380$	14.4980	+	10.9235i	0.743729	+	0.560363i
$381$	−3.65270	+	32.2044i	−0.187133	+	1.64988i
$382$	−8.41610	−	2.81568i	−0.430605	−	0.144063i
$383$	−2.83306	−	4.90700i	−0.144762	−	0.250736i	0.784522	−	0.620101i	$-0.212908\pi$
$383$	−2.83306	−	4.90700i	−0.144762	−	0.250736i	−0.929284	+	0.369365i	$0.879575\pi$
$384$	−18.8408	−	5.38746i	−0.961465	−	0.274928i
$385$	−0.218330	+	0.378159i	−0.0111271	+	0.0192728i
$386$	8.91939	−	7.89174i	0.453985	−	0.401679i
$387$	17.6848	+	16.4579i	0.898970	+	0.836601i
$388$	−3.40474	+	27.7446i	−0.172850	+	1.40852i
$389$	9.80278	+	5.65964i	0.497021	+	0.286955i	0.727482	−	0.686126i	$-0.240690\pi$
$389$	9.80278	+	5.65964i	0.497021	+	0.286955i	−0.230462	+	0.973081i	$0.574024\pi$
$390$	7.94519	−	17.0626i	0.402320	−	0.863996i
$391$	−4.80559	+	2.77451i	−0.243029	+	0.140313i
$392$	−1.21742	+	2.55302i	−0.0614888	+	0.128947i
$393$	−9.69200	−	22.2592i	−0.488897	−	1.12283i
$394$	21.4054	−	4.35572i	1.07839	−	0.219438i
$395$	−5.12180			−0.257706
$396$	0.742070	−	2.04569i	0.0372904	−	0.102800i
$397$	30.9280			1.55223			0.776115	−	0.630592i	$-0.217188\pi$
$397$	30.9280			1.55223			0.776115	+	0.630592i	$0.217188\pi$
$398$	−4.53995	+	0.923819i	−0.227567	+	0.0463069i
$399$	−7.76150	+	10.5002i	−0.388561	+	0.525667i
$400$	3.91639	+	13.6513i	0.195819	+	0.682563i
$401$	7.96674	−	4.59960i	0.397840	−	0.229693i	−0.287711	−	0.957717i	$-0.592894\pi$
$401$	7.96674	−	4.59960i	0.397840	−	0.229693i	0.685552	+	0.728024i	$0.259561\pi$
$402$	1.66239	+	2.37141i	0.0829125	+	0.118275i
$403$	−5.66744	−	3.27210i	−0.282315	−	0.162995i
$404$	−0.488622	−	0.0599625i	−0.0243099	−	0.00298325i
$405$	−10.8077	+	0.777764i	−0.537038	+	0.0386474i
$406$	−3.68731	+	3.26247i	−0.182998	+	0.161914i
$407$	0.504458	−	0.873746i	0.0250050	−	0.0433100i
$408$	−6.96925	+	3.71104i	−0.345029	+	0.183724i
$409$	−10.7787	−	18.6692i	−0.532972	−	0.923134i	−0.999259	−	0.0385004i	$-0.987742\pi$
$409$	−10.7787	−	18.6692i	−0.532972	−	0.923134i	0.466287	−	0.884634i	$-0.345591\pi$
$410$	−13.7247	−	4.59170i	−0.677812	−	0.226768i
$411$	−22.3285	−	16.5047i	−1.10138	−	0.814117i
$412$	−10.1518	+	13.4738i	−0.500144	+	0.663804i
$413$		−	11.7476i		−	0.578062i
$414$	−12.8297	+	6.98338i	−0.630548	+	0.343214i
$415$			4.03930i			0.198281i
$416$	1.56884	−	36.0692i	0.0769188	−	1.76844i
$417$	−0.613837	+	0.267274i	−0.0300597	+	0.0130885i
$418$	−1.22681	+	3.66694i	−0.0600050	+	0.179356i
$419$	−19.0824	−	33.0518i	−0.932238	−	1.61468i	−0.779486	−	0.626419i	$-0.784520\pi$
$419$	−19.0824	−	33.0518i	−0.932238	−	1.61468i	−0.152752	−	0.988265i	$-0.548814\pi$
$420$	3.99821	−	1.18682i	0.195093	−	0.0579107i
$421$	5.64583	−	9.77886i	0.275161	−	0.476592i	−0.695015	−	0.718995i	$-0.744602\pi$
$421$	5.64583	−	9.77886i	0.275161	−	0.476592i	0.970176	+	0.242403i	$0.0779356\pi$
$422$	14.4904	+	16.3773i	0.705382	+	0.797236i
$423$	−17.0547	+	18.3261i	−0.829228	+	0.891047i
$424$	21.8012	−	14.9868i	1.05876	−	0.727821i
$425$	4.95569	+	2.86117i	0.240386	+	0.138787i
$426$	0.719275	+	8.17055i	0.0348490	+	0.395865i
$427$	−1.27587	+	0.736621i	−0.0617434	+	0.0356476i
$428$	26.4768	−	11.2408i	1.27981	−	0.543345i
$429$	3.98372	+	0.451843i	0.192336	+	0.0218152i
$430$	2.73398	+	13.4356i	0.131844	+	0.647924i
$431$	34.5828			1.66579			0.832897	−	0.553429i	$-0.186681\pi$
$431$	34.5828			1.66579			0.832897	+	0.553429i	$0.186681\pi$
$432$	−18.5855	+	9.30477i	−0.894196	+	0.447676i
$433$	−11.5397			−0.554565			−0.277282	−	0.960788i	$-0.589434\pi$
$433$	−11.5397			−0.554565			−0.277282	+	0.960788i	$0.589434\pi$
$434$	−0.289152	−	1.42099i	−0.0138797	−	0.0682095i
$435$	7.21353	+	0.818175i	0.345862	+	0.0392285i
$436$	10.1490	−	4.30878i	0.486048	−	0.206353i
$437$	22.4779	−	12.9776i	1.07526	−	0.620804i
$438$	−2.65580	−	30.1683i	−0.126899	−	1.44150i
$439$	1.06625	+	0.615600i	0.0508894	+	0.0293810i	0.525229	−	0.850961i	$-0.323980\pi$
$439$	1.06625	+	0.615600i	0.0508894	+	0.0293810i	−0.474339	+	0.880342i	$0.657313\pi$
$440$	1.01778	−	0.699648i	0.0485207	−	0.0333544i
$441$	0.880022	+	2.86802i	0.0419058	+	0.136573i
$442$	−9.63947	−	10.8947i	−0.458503	−	0.518209i
$443$	17.8613	−	30.9367i	0.848616	−	1.46985i	−0.0338275	−	0.999428i	$-0.510770\pi$
$443$	17.8613	−	30.9367i	0.848616	−	1.46985i	0.882444	−	0.470418i	$-0.155897\pi$
$444$	−9.23796	+	2.74216i	−0.438414	+	0.130137i
$445$	3.26094	+	5.64811i	0.154583	+	0.267746i
$446$	−4.90174	+	14.6514i	−0.232104	+	0.693762i
$447$	37.1547	−	16.1777i	1.75736	−	0.765179i
$448$	6.21617	−	5.03580i	0.293686	−	0.237919i
$449$		−	2.39408i		−	0.112984i	−0.998403	−	0.0564918i	$-0.982009\pi$
$449$		−	2.39408i		−	0.112984i	0.998403	−	0.0564918i	$-0.0179915\pi$
$450$	12.8519	+	7.85717i	0.605845	+	0.370391i
$451$		−	3.08280i		−	0.145164i
$452$	−11.7216	+	15.5573i	−0.551339	+	0.731752i
$453$	−13.8417	−	10.2314i	−0.650338	−	0.480715i
$454$	15.2367	+	5.09758i	0.715095	+	0.239241i
$455$	3.84196	+	6.65448i	0.180114	+	0.311967i
$456$	32.5983	−	17.3582i	1.52656	−	0.812871i
$457$	−2.72057	+	4.71216i	−0.127263	+	0.220425i	−0.922615	−	0.385722i	$-0.873952\pi$
$457$	−2.72057	+	4.71216i	−0.127263	+	0.220425i	0.795352	+	0.606147i	$0.207286\pi$
$458$	−28.3347	+	25.0701i	−1.32399	+	1.17145i
$459$	−2.78352	+	7.89855i	−0.129923	+	0.368673i
$460$	−8.22861	−	1.00979i	−0.383661	−	0.0470819i
$461$	−23.3890	−	13.5036i	−1.08933	−	0.628927i	−0.155935	−	0.987767i	$-0.549839\pi$
$461$	−23.3890	−	13.5036i	−1.08933	−	0.628927i	−0.933399	+	0.358840i	$0.883172\pi$
$462$	0.509958	+	0.727459i	0.0237254	+	0.0338444i
$463$	12.8375	−	7.41174i	0.596610	−	0.344453i	−0.171097	−	0.985254i	$-0.554731\pi$
$463$	12.8375	−	7.41174i	0.596610	−	0.344453i	0.767707	+	0.640801i	$0.221398\pi$
$464$	13.3856	−	3.84016i	0.621409	−	0.178275i
$465$	−1.27100	+	1.71949i	−0.0589414	+	0.0797392i
$466$	5.36005	−	1.09070i	0.248300	−	0.0505257i
$467$	8.68837			0.402050			0.201025	−	0.979586i	$-0.435573\pi$
$467$	8.68837			0.402050			0.201025	+	0.979586i	$0.435573\pi$
$468$	−24.6461	−	29.3078i	−1.13927	−	1.35475i
$469$	−1.18231			−0.0545940
$470$	−13.9229	+	2.83312i	−0.642214	+	0.130682i
$471$	−0.458589	−	1.05322i	−0.0211307	−	0.0485300i
$472$	−14.3017	+	29.9919i	−0.658291	+	1.38049i
$473$	−2.52933	+	1.46031i	−0.116299	+	0.0671450i
$474$	−4.39877	+	9.44651i	−0.202042	+	0.433893i
$475$	−23.1800	−	13.3830i	−1.06357	−	0.614052i
$476$	0.392624	−	3.19941i	0.0179959	−	0.146645i
$477$	6.28449	−	27.3476i	0.287747	−	1.25216i
$478$	−26.1179	+	23.1087i	−1.19461	+	1.05697i
$479$	16.3320	−	28.2878i	0.746227	−	1.29250i	−0.203392	−	0.979097i	$-0.565196\pi$
$479$	16.3320	−	28.2878i	0.746227	−	1.29250i	0.949619	−	0.313406i	$-0.101470\pi$
$480$	−11.6523	−	1.83752i	−0.531854	−	0.0838711i
$481$	−8.87695	−	15.3753i	−0.404754	−	0.701055i
$482$	0.466516	+	0.156077i	0.0212492	+	0.00710910i
$483$	0.672069	−	5.92537i	0.0305802	−	0.269614i
$484$	−17.3607	−	13.0805i	−0.789124	−	0.594566i
$485$			16.8269i			0.764072i
$486$	−7.84751	+	20.6014i	−0.355970	+	0.934497i
$487$		−	8.24286i		−	0.373519i	−0.982406	−	0.186760i	$-0.940201\pi$
$487$		−	8.24286i		−	0.373519i	0.982406	−	0.186760i	$-0.0597986\pi$
$488$	4.15408	−	0.327348i	0.188046	−	0.0148183i
$489$	0.457100	−	4.03007i	0.0206708	−	0.182246i
$490$	−0.540207	+	1.61469i	−0.0244041	+	0.0729441i
$491$	−6.15386	−	10.6588i	−0.277720	−	0.481025i	0.693098	−	0.720844i	$-0.256245\pi$
$491$	−6.15386	−	10.6588i	−0.277720	−	0.481025i	−0.970818	+	0.239818i	$0.922912\pi$
$492$	−20.2560	+	21.3699i	−0.913211	+	0.963429i
$493$	2.80548	−	4.85923i	0.126352	−	0.218849i
$494$	45.0881	+	50.9595i	2.02861	+	2.29277i
$495$	0.293388	−	1.27671i	0.0131868	−	0.0573837i
$496$	−0.991721	+	3.97982i	−0.0445296	+	0.178699i
$497$	−2.89990	−	1.67426i	−0.130078	−	0.0751007i
$498$	7.44997	+	3.46908i	0.333841	+	0.155453i
$499$	−8.73096	+	5.04082i	−0.390852	+	0.225658i	−0.682529	−	0.730858i	$-0.739120\pi$
$499$	−8.73096	+	5.04082i	−0.390852	+	0.225658i	0.291677	+	0.956517i	$0.405787\pi$
$500$	8.04596	+	18.9516i	0.359826	+	0.847542i
$501$	1.90823	+	4.38255i	0.0852533	+	0.195798i
$502$	−5.33701	−	26.2278i	−0.238203	−	1.17061i
$503$	−29.9596			−1.33583			−0.667917	−	0.744236i	$-0.732814\pi$
$503$	−29.9596			−1.33583			−0.667917	+	0.744236i	$0.732814\pi$
$504$	1.24487	−	8.39347i	0.0554507	−	0.373875i
$505$	−0.296347			−0.0131873
$506$	−0.352131	−	1.73048i	−0.0156541	−	0.0769294i
$507$	28.5524	−	38.6273i	1.26806	−	1.71550i
$508$	14.6253	+	34.4488i	0.648895	+	1.52842i
$509$	−4.97957	+	2.87496i	−0.220715	+	0.127430i	−0.606282	−	0.795250i	$-0.707340\pi$
$509$	−4.97957	+	2.87496i	−0.220715	+	0.127430i	0.385566	+	0.922680i	$0.374006\pi$
$510$	−3.89200	+	2.72834i	−0.172341	+	0.120813i
$511$	10.7074	+	6.18190i	0.473666	+	0.273471i
$512$	−22.0006	+	5.28881i	−0.972300	+	0.233735i
$513$	13.0198	−	36.9451i	0.574836	−	1.63116i
$514$	−5.61262	−	6.34349i	−0.247562	−	0.279800i
$515$	−5.07774	+	8.79490i	−0.223752	+	0.387550i
$516$	27.1284	+	6.49651i	1.19426	+	0.285993i
$517$	−1.51326	−	2.62105i	−0.0665533	−	0.115274i
$518$	1.24816	−	3.73077i	0.0548411	−	0.163921i
$519$	12.8255	+	9.48035i	0.562979	+	0.416141i
$520$	−1.70733	−	21.6663i	−0.0748715	−	0.950129i
$521$		−	25.6654i		−	1.12442i	−0.826994	−	0.562210i	$-0.809951\pi$
$521$		−	25.6654i		−	1.12442i	0.826994	−	0.562210i	$-0.190049\pi$
$522$	7.70425	−	12.6018i	0.337206	−	0.551564i
$523$		−	20.0902i		−	0.878484i	−0.898369	−	0.439242i	$-0.855247\pi$
$523$		−	20.0902i		−	0.878484i	0.898369	−	0.439242i	$-0.144753\pi$
$524$	−22.3897	−	16.8695i	−0.978097	−	0.736948i
$525$	−5.63832	+	2.45501i	−0.246077	+	0.107145i
$526$	−3.87735	−	1.29720i	−0.169061	−	0.0565607i
$527$	0.826305	+	1.43120i	0.0359944	+	0.0623442i
$528$	−0.416310	−	2.47805i	−0.0181176	−	0.107843i
$529$	5.57306	−	9.65282i	0.242307	−	0.419688i
$530$	11.9273	−	10.5531i	0.518089	−	0.458397i
$531$	10.3382	+	33.6924i	0.448638	+	1.46213i
$532$	−1.83648	+	14.9651i	−0.0796214	+	0.648818i
$533$	−46.9803	−	27.1241i	−2.03494	−	1.17487i
$534$	13.2178	−	1.16360i	0.571992	−	0.0503539i
$535$	14.9956	−	8.65773i	0.648318	−	0.374306i
$536$	3.01846	+	1.43936i	0.130378	+	0.0621710i
$537$	17.9114	+	2.03156i	0.772935	+	0.0876681i
$538$	13.7798	−	2.80400i	0.594089	−	0.120889i
$539$	−0.362687			−0.0156221
$540$	−10.4225	+	6.92233i	−0.448515	+	0.297890i
$541$	41.9771			1.80473			0.902367	−	0.430968i	$-0.141828\pi$
$541$	41.9771			1.80473			0.902367	+	0.430968i	$0.141828\pi$
$542$	−25.9683	+	5.28421i	−1.11544	+	0.226976i
$543$	−22.5104	−	2.55318i	−0.966012	−	0.109567i
$544$	−4.89739	+	7.69016i	−0.209974	+	0.329713i
$545$	5.74806	−	3.31864i	0.246220	−	0.142155i
$546$	15.5730	−	1.37093i	0.666461	−	0.0586703i
$547$	5.11973	+	2.95588i	0.218904	+	0.126384i	0.605443	−	0.795889i	$-0.292996\pi$
$547$	5.11973	+	2.95588i	0.218904	+	0.126384i	−0.386539	+	0.922273i	$0.626329\pi$
$548$	−31.8230	−	3.90524i	−1.35941	−	0.166824i
$549$	3.01097	−	3.23544i	0.128505	−	0.138085i
$550$	−1.36389	+	1.20675i	−0.0581563	+	0.0514558i
$551$	−13.1225	+	22.7288i	−0.559037	+	0.968280i
$552$	−8.92944	+	14.3094i	−0.380062	+	0.609048i
$553$	−2.12707	−	3.68419i	−0.0904520	−	0.156667i
$554$	−32.9092	−	11.0101i	−1.39818	−	0.467773i
$555$	−5.31859	+	2.31579i	−0.225762	+	0.0983000i
$556$	−0.465206	+	0.617434i	−0.0197291	+	0.0261850i
$557$			9.78025i			0.414402i	0.978298	+	0.207201i	$0.0664355\pi$
$557$			9.78025i			0.414402i	−0.978298	+	0.207201i	$0.933565\pi$
$558$	2.07979	+	3.82096i	0.0880446	+	0.161754i
$559$			51.3941i			2.17374i
$560$	3.34490	−	3.46467i	0.141348	−	0.146409i
$561$	−0.814180	−	0.601823i	−0.0343747	−	0.0254090i
$562$	14.4631	−	43.2303i	0.610088	−	1.82356i
$563$	15.6966	+	27.1873i	0.661534	+	1.14581i	0.980213	+	0.197947i	$0.0634275\pi$
$563$	15.6966	+	27.1873i	0.661534	+	1.14581i	−0.318679	+	0.947863i	$0.603239\pi$
$564$	−6.73210	+	28.1121i	−0.283472	+	1.18373i
$565$	−5.86293	+	10.1549i	−0.246655	+	0.427220i
$566$	−2.77167	−	3.13259i	−0.116502	−	0.131673i
$567$	−5.04785	−	7.45112i	−0.211990	−	0.312918i
$568$	5.36522	+	7.80479i	0.225120	+	0.327482i
$569$	−11.2246	−	6.48054i	−0.470561	−	0.271678i	0.245914	−	0.969292i	$-0.420912\pi$
$569$	−11.2246	−	6.48054i	−0.470561	−	0.271678i	−0.716475	+	0.697613i	$0.754245\pi$
$570$	18.2047	−	12.7617i	0.762509	−	0.534528i
$571$	17.2624	−	9.96646i	0.722409	−	0.417083i	−0.0932294	−	0.995645i	$-0.529719\pi$
$571$	17.2624	−	9.96646i	0.722409	−	0.417083i	0.815639	+	0.578561i	$0.196386\pi$
$572$	4.26136	−	1.80917i	0.178176	−	0.0756453i
$573$	−6.46078	+	8.74050i	−0.269903	+	0.365140i
$574$	−2.39692	−	11.7793i	−0.100046	−	0.491657i
$575$	12.2241			0.509781
$576$	−13.3965	+	19.9132i	−0.558188	+	0.829715i
$577$	−12.1448			−0.505596			−0.252798	−	0.967519i	$-0.581351\pi$
$577$	−12.1448			−0.505596			−0.252798	+	0.967519i	$0.581351\pi$
$578$	−4.06140	−	19.9590i	−0.168932	−	0.830187i
$579$	−5.82295	−	13.3733i	−0.241993	−	0.555777i
$580$	7.71626	−	3.27596i	0.320400	−	0.136027i
$581$	−2.90552	+	1.67751i	−0.120541	+	0.0695946i
$582$	31.0352	+	14.4515i	1.28645	+	0.599036i
$583$	2.93789	+	1.69619i	0.121675	+	0.0702490i
$584$	−19.8101	−	28.8178i	−0.819749	−	1.19249i
$585$	−16.8749	−	15.7042i	−0.697693	−	0.649288i
$586$	12.7941	+	14.4602i	0.528521	+	0.597344i
$587$	−5.05289	+	8.75185i	−0.208555	+	0.361228i	−0.951260	−	0.308391i	$-0.900209\pi$
$587$	−5.05289	+	8.75185i	−0.208555	+	0.361228i	0.742705	+	0.669619i	$0.233543\pi$
$588$	2.51414	+	2.38309i	0.103681	+	0.0982770i
$589$	−3.86500	−	6.69438i	−0.159255	−	0.275837i
$590$	−6.34615	+	18.9687i	−0.261267	+	0.780930i
$591$	3.01510	−	26.5830i	0.124025	−	1.09348i
$592$	−7.72848	+	8.00519i	−0.317638	+	0.329011i
$593$			13.4831i			0.553685i	0.960915	+	0.276842i	$0.0892880\pi$
$593$			13.4831i			0.553685i	−0.960915	+	0.276842i	$0.910712\pi$
$594$	−2.10275	−	1.63760i	−0.0862769	−	0.0671913i
$595$		−	1.94043i		−	0.0795498i
$596$	28.1582	−	37.3724i	1.15341	−	1.53083i
$597$	−0.639484	+	5.63808i	−0.0261723	+	0.230751i
$598$	−29.4699	−	9.85940i	−1.20511	−	0.403181i
$599$	−6.09036	−	10.5488i	−0.248845	−	0.431013i	0.714360	−	0.699778i	$-0.246718\pi$
$599$	−6.09036	−	10.5488i	−0.248845	−	0.431013i	−0.963206	+	0.268765i	$0.913384\pi$
$600$	17.3835	+	0.596500i	0.709679	+	0.0243520i
$601$	−18.0691	+	31.2966i	−0.737053	+	1.27661i	0.216764	+	0.976224i	$0.430450\pi$
$601$	−18.0691	+	31.2966i	−0.737053	+	1.27661i	−0.953817	+	0.300389i	$0.902883\pi$
$602$	−8.52905	+	7.54637i	−0.347618	+	0.307567i
$603$	3.39089	−	1.04046i	0.138088	−	0.0423708i
$604$	−19.7274	−	2.42090i	−0.802698	−	0.0985050i
$605$	−11.3321	−	6.54259i	−0.460715	−	0.265994i
$606$	−0.254513	+	0.546575i	−0.0103389	+	0.0222031i
$607$	9.64755	−	5.57002i	0.391582	−	0.226080i	−0.291263	−	0.956643i	$-0.594076\pi$
$607$	9.64755	−	5.57002i	0.391582	−	0.226080i	0.682845	+	0.730563i	$0.260742\pi$
$608$	22.9073	−	35.9704i	0.929013	−	1.45879i
$609$	2.40723	+	5.52858i	0.0975458	+	0.224030i
$610$	2.45805	−	0.500180i	0.0995235	−	0.0202517i
$611$	−53.2579			−2.15458
$612$	1.68950	+	9.52150i	0.0682939	+	0.384884i
$613$	9.82335			0.396762			0.198381	−	0.980125i	$-0.436432\pi$
$613$	9.82335			0.396762			0.198381	+	0.980125i	$0.436432\pi$
$614$	5.85176	−	1.19076i	0.236158	−	0.0480550i
$615$	−10.5360	+	14.2537i	−0.424852	+	0.574764i
$616$	0.925947	+	0.441542i	0.0373075	+	0.0177902i
$617$	−30.8603	+	17.8172i	−1.24239	+	0.717293i	−0.969580	−	0.244776i	$-0.921286\pi$
$617$	−30.8603	+	17.8172i	−1.24239	+	0.717293i	−0.272808	+	0.962068i	$0.587952\pi$
$618$	11.8601	+	16.9186i	0.477085	+	0.680566i
$619$	−14.3845	−	8.30490i	−0.578162	−	0.333802i	0.182241	−	0.983254i	$-0.441665\pi$
$619$	−14.3845	−	8.30490i	−0.578162	−	0.333802i	−0.760403	+	0.649452i	$0.774998\pi$
$620$	−0.300737	+	2.45065i	−0.0120779	+	0.0984203i
$621$	3.28695	+	17.5855i	0.131901	+	0.705683i
$622$	15.6323	−	13.8313i	0.626800	−	0.554583i
$623$	−2.70851	+	4.69128i	−0.108514	+	0.187952i
$624$	−41.4270	−	15.4588i	−1.65841	−	0.618846i
$625$	−2.67917	−	4.64046i	−0.107167	−	0.185618i
$626$	−11.9811	−	4.00837i	−0.478860	−	0.160207i
$627$	3.80828	+	2.81500i	0.152088	+	0.112420i
$628$	−1.05940	−	0.798202i	−0.0422745	−	0.0318517i
$629$			4.48340i			0.178765i
$630$	0.128367	−	5.10635i	0.00511426	−	0.203442i
$631$			17.5229i			0.697576i	0.937202	+	0.348788i	$0.113407\pi$
$631$			17.5229i			0.697576i	−0.937202	+	0.348788i	$0.886593\pi$
$632$	0.945248	+	11.9953i	0.0376000	+	0.477148i
$633$	24.5554	−	10.6918i	0.975990	−	0.424961i
$634$	−12.7845	+	38.2130i	−0.507737	+	1.51763i
$635$	11.2645	+	19.5107i	0.447018	+	0.774259i
$636$	−9.22027	−	31.0617i	−0.365607	−	1.23168i
$637$	−3.19111	+	5.52716i	−0.126436	+	0.218994i
$638$	1.18326	+	1.33734i	0.0468456	+	0.0529458i
$639$	9.79036	+	2.24983i	0.387301	+	0.0890021i
$640$	−12.7575	+	4.77321i	−0.504286	+	0.188678i
$641$	−1.19025	−	0.687191i	−0.0470121	−	0.0271424i	0.476310	−	0.879278i	$-0.341974\pi$
$641$	−1.19025	−	0.687191i	−0.0470121	−	0.0271424i	−0.523322	+	0.852135i	$0.675307\pi$
$642$	−3.08934	−	35.0931i	−0.121926	−	1.38501i
$643$	23.9115	−	13.8053i	0.942979	−	0.544429i	0.0520859	−	0.998643i	$-0.483413\pi$
$643$	23.9115	−	13.8053i	0.942979	−	0.544429i	0.890893	+	0.454214i	$0.150080\pi$
$644$	−2.69095	−	6.33832i	−0.106038	−	0.249765i
$645$	16.6855	+	1.89251i	0.656990	+	0.0745173i
$646$	−3.42627	−	16.8378i	−0.134805	−	0.662474i
$647$	−42.2783			−1.66213			−0.831066	−	0.556174i	$-0.812269\pi$
$647$	−42.2783			−1.66213			−0.831066	+	0.556174i	$0.812269\pi$
$648$	3.81613	+	25.1682i	0.149912	+	0.988699i
$649$	−4.26071			−0.167248
$650$	6.38999	+	31.4025i	0.250636	+	1.23171i
$651$	−1.76470	−	0.200156i	−0.0691639	−	0.00784472i
$652$	−1.83022	−	4.31094i	−0.0716769	−	0.168829i
$653$	−34.0053	+	19.6330i	−1.33073	+	0.768297i	−0.985411	−	0.170189i	$-0.945562\pi$
$653$	−34.0053	+	19.6330i	−1.33073	+	0.768297i	−0.345318	+	0.938486i	$0.612229\pi$
$654$	−1.18419	−	13.4517i	−0.0463055	−	0.526004i
$655$	−14.6147	−	8.43780i	−0.571044	−	0.329692i
$656$	−8.22088	+	32.9907i	−0.320971	+	1.28807i
$657$	−36.1492	−	8.30711i	−1.41031	−	0.324091i
$658$	−7.82002	−	8.83834i	−0.304856	−	0.344554i
$659$	−15.9345	+	27.5994i	−0.620720	+	1.07512i	0.368632	+	0.929575i	$0.379826\pi$
$659$	−15.9345	+	27.5994i	−0.620720	+	1.07512i	−0.989352	+	0.145543i	$0.953507\pi$
$660$	−0.430443	−	1.45010i	−0.0167550	−	0.0564451i
$661$	11.9120	+	20.6323i	0.463325	+	0.802502i	0.999124	−	0.0418430i	$-0.0133229\pi$
$661$	11.9120	+	20.6323i	0.463325	+	0.802502i	−0.535799	+	0.844345i	$0.679990\pi$
$662$	4.17755	−	12.4868i	0.162365	−	0.485311i
$663$	−16.3350	+	7.11252i	−0.634400	+	0.276227i
$664$	9.46008	−	0.745468i	0.367122	−	0.0289298i
$665$			9.07625i			0.351962i
$666$	−0.296595	+	11.7983i	−0.0114928	+	0.457177i
$667$		−	11.9862i		−	0.464108i
$668$	4.40823	+	3.32138i	0.170559	+	0.128508i
$669$	15.2161	+	11.2474i	0.588289	+	0.434850i
$670$	1.90906	+	0.638692i	0.0737534	+	0.0246748i
$671$	0.267163	+	0.462740i	0.0103137	+	0.0178639i
$672$	−3.51742	−	9.14482i	−0.135687	−	0.352769i
$673$	−10.4611	+	18.1192i	−0.403247	+	0.698445i	−0.994116	−	0.108323i	$-0.965452\pi$
$673$	−10.4611	+	18.1192i	−0.403247	+	0.698445i	0.590869	+	0.806768i	$0.298785\pi$
$674$	9.65992	−	8.54695i	0.372086	−	0.329216i
$675$	14.0104	−	12.0029i	0.539260	−	0.461991i
$676$	6.75589	−	55.0524i	0.259842	−	2.11740i
$677$	23.9840	+	13.8472i	0.921779	+	0.532190i	0.884202	−	0.467104i	$-0.154703\pi$
$677$	23.9840	+	13.8472i	0.921779	+	0.532190i	0.0375770	+	0.999294i	$0.488036\pi$
$678$	13.6941	+	19.5348i	0.525920	+	0.750229i
$679$	−12.1039	+	6.98817i	−0.464504	+	0.268181i
$680$	−2.36231	+	4.95395i	−0.0905904	+	0.189975i
$681$	11.6968	−	15.8240i	0.448221	−	0.606379i
$682$	−0.515373	+	0.104872i	−0.0197347	+	0.00401574i
$683$	16.2123			0.620345			0.310172	−	0.950680i	$-0.399613\pi$
$683$	16.2123			0.620345			0.310172	+	0.950680i	$0.399613\pi$
$684$	−7.90254	−	44.5363i	−0.302161	−	1.70289i
$685$	−19.3005			−0.737435
$686$	−1.38581	+	0.281995i	−0.0529106	+	0.0107666i
$687$	18.4981	+	42.4837i	0.705745	+	1.62086i
$688$	30.9619	−	8.88260i	1.18041	−	0.338646i
$689$	51.6981	−	29.8479i	1.96954	−	1.13711i
$690$	−4.28611	+	9.20455i	−0.163169	+	0.350411i
$691$	−10.2054	−	5.89210i	−0.388233	−	0.224146i	0.293161	−	0.956063i	$-0.405293\pi$
$691$	−10.2054	−	5.89210i	−0.388233	−	0.224146i	−0.681394	+	0.731917i	$0.738626\pi$
$692$	18.2792	+	2.24318i	0.694872	+	0.0852729i
$693$	1.04020	−	0.319173i	0.0395138	−	0.0121244i
$694$	26.9062	−	23.8062i	1.02135	−	0.903670i
$695$	−0.232687	+	0.403026i	−0.00882632	+	0.0152876i
$696$	0.584890	−	17.0452i	0.0221702	−	0.646096i
$697$	6.84966	+	11.8640i	0.259449	+	0.449380i
$698$	−18.3341	−	6.13384i	−0.693957	−	0.232169i
$699$	0.755001	−	6.65655i	0.0285568	−	0.251774i
$700$	−4.27309	+	5.67137i	−0.161508	+	0.214357i
$701$		−	33.5044i		−	1.26544i	−0.774379	−	0.632721i	$-0.781938\pi$
$701$		−	33.5044i		−	1.26544i	0.774379	−	0.632721i	$-0.218062\pi$
$702$	−43.4571	+	17.6364i	−1.64018	+	0.665643i
$703$		−	20.9709i		−	0.790932i
$704$	−1.82642	−	2.25453i	−0.0688358	−	0.0849707i
$705$	−1.96113	+	17.2905i	−0.0738606	+	0.651200i
$706$	11.7601	−	35.1511i	0.442597	−	1.32293i
$707$	−0.123072	−	0.213167i	−0.00462860	−	0.00801697i
$708$	29.5351	+	27.9956i	1.11000	+	1.05214i
$709$	−13.9396	+	24.1441i	−0.523513	+	0.906751i	0.476112	+	0.879384i	$0.342046\pi$
$709$	−13.9396	+	24.1441i	−0.523513	+	0.906751i	−0.999625	+	0.0273668i	$0.991288\pi$
$710$	3.77798	+	4.26995i	0.141785	+	0.160248i
$711$	9.34264	+	8.69447i	0.350376	+	0.326068i
$712$	12.6261	−	8.67954i	0.473184	−	0.325279i
$713$	3.05735	+	1.76516i	0.114499	+	0.0661059i
$714$	−3.57887	−	1.66650i	−0.133936	−	0.0623674i
$715$	2.41350	−	1.39343i	0.0902596	−	0.0521114i
$716$	19.1597	−	8.13431i	0.716032	−	0.303994i
$717$	17.0509	+	39.1600i	0.636777	+	1.46246i
$718$	−6.91104	−	33.9631i	−0.257918	−	1.26749i
$719$	17.7949			0.663637			0.331818	−	0.943343i	$-0.392338\pi$
$719$	17.7949			0.663637			0.331818	+	0.943343i	$0.392338\pi$
$720$	−6.54428	+	12.8803i	−0.243891	+	0.480022i
$721$	−8.43507			−0.314138
$722$	10.6683	+	52.4275i	0.397033	+	1.95115i
$723$	0.358130	−	0.484498i	0.0133190	−	0.0180187i
$724$	−24.0792	+	10.2229i	−0.894895	+	0.379930i
$725$	−10.7046	+	6.18029i	−0.397558	+	0.229530i
$726$	−21.7994	+	15.2816i	−0.809050	+	0.567154i
$727$	11.4675	+	6.62076i	0.425306	+	0.245550i	0.697345	−	0.716736i	$-0.254365\pi$
$727$	11.4675	+	6.62076i	0.425306	+	0.245550i	−0.272039	+	0.962286i	$0.587698\pi$
$728$	14.8758	−	10.2260i	0.551334	−	0.379002i
$729$	21.0345	+	16.9278i	0.779056	+	0.626955i
$730$	−13.9495	−	15.7660i	−0.516295	−	0.583526i
$731$	6.48930	−	11.2398i	0.240015	−	0.415719i
$732$	1.18854	−	4.96313i	0.0439296	−	0.183443i
$733$	−1.16626	−	2.02003i	−0.0430769	−	0.0746114i	0.843683	−	0.536842i	$-0.180383\pi$
$733$	−1.16626	−	2.02003i	−0.0430769	−	0.0746114i	−0.886760	+	0.462230i	$0.847049\pi$
$734$	5.39412	−	16.1231i	0.199101	−	0.595114i
$735$	1.67693	+	1.23955i	0.0618543	+	0.0457213i
$736$	−0.846327	+	19.4579i	−0.0311960	+	0.717226i
$737$			0.428809i			0.0157954i
$738$	17.2404	+	31.6739i	0.634630	+	1.16593i
$739$			14.1252i			0.519603i	0.965662	+	0.259802i	$0.0836571\pi$
$739$			14.1252i			0.519603i	−0.965662	+	0.259802i	$0.916343\pi$
$740$	−4.03078	+	5.34976i	−0.148174	+	0.196661i
$741$	76.4063	−	33.2684i	2.80686	−	1.22215i
$742$	12.5444	+	4.19682i	0.460518	+	0.154070i
$743$	3.88960	+	6.73699i	0.142696	+	0.247156i	0.928511	−	0.371305i	$-0.121090\pi$
$743$	3.88960	+	6.73699i	0.142696	+	0.247156i	−0.785815	+	0.618461i	$0.787756\pi$
$744$	4.26162	+	2.65937i	0.156239	+	0.0974972i
$745$	14.0842	−	24.3946i	0.516005	−	0.893748i
$746$	24.7466	−	21.8954i	0.906037	−	0.801647i
$747$	6.85687	−	7.36805i	0.250880	−	0.269583i
$748$	−1.16039	−	0.142400i	−0.0424279	−	0.00520665i
$749$	12.4553	+	7.19105i	0.455105	+	0.262755i
$750$	25.1190	−	2.21129i	0.917215	−	0.0807448i
$751$	4.84206	−	2.79556i	0.176689	−	0.102012i	−0.409047	−	0.912513i	$-0.634139\pi$
$751$	4.84206	−	2.79556i	0.176689	−	0.102012i	0.585736	+	0.810502i	$0.300805\pi$
$752$	9.20472	+	32.0846i	0.335661	+	1.17001i
$753$	−32.5718	−	3.69437i	−1.18698	−	0.134630i
$754$	30.7913	−	6.26562i	1.12135	−	0.228180i
$755$	−11.9646			−0.435436
$756$	−9.30777	−	4.62226i	−0.338521	−	0.168110i
$757$	0.0291002			0.00105767			0.000528833	−	1.00000i	$-0.499832\pi$
$757$	0.0291002			0.00105767			0.000528833		1.00000i	$0.499832\pi$
$758$	40.1697	−	8.17401i	1.45903	−	0.296893i
$759$	−2.14906	−	0.243751i	−0.0780058	−	0.00884760i
$760$	11.0496	−	23.1718i	0.400810	−	0.840531i
$761$	41.3883	−	23.8955i	1.50032	−	0.866212i	0.500323	−	0.865839i	$-0.333215\pi$
$761$	41.3883	−	23.8955i	1.50032	−	0.866212i	1.00000		0.000372992i	$-0.000118727\pi$
$762$	45.6594	−	4.01951i	1.65406	−	0.145612i
$763$	4.77430	+	2.75644i	0.172841	+	0.0997899i
$764$	−1.52871	+	12.4571i	−0.0553068	+	0.450684i
$765$	1.70762	+	5.56519i	0.0617391	+	0.201210i
$766$	−6.00127	+	5.30983i	−0.216835	+	0.191852i
$767$	−37.4879	+	64.9310i	−1.35361	+	2.34452i
$768$	−2.15302	+	27.6291i	−0.0776903	+	0.996978i
$769$	18.0325	+	31.2331i	0.650267	+	1.12630i	0.983058	+	0.183295i	$0.0586763\pi$
$769$	18.0325	+	31.2331i	0.650267	+	1.12630i	−0.332791	+	0.943001i	$0.607990\pi$
$770$	0.585626	+	0.195926i	0.0211045	+	0.00706069i
$771$	−9.51115	+	4.14130i	−0.342536	+	0.149145i
$772$	−13.4517	−	10.1352i	−0.484137	−	0.364773i
$773$			44.2680i			1.59221i	0.605158	+	0.796105i	$0.293110\pi$
$773$			44.2680i			1.59221i	−0.605158	+	0.796105i	$0.706890\pi$
$774$	17.8205	−	29.1489i	0.640546	−	1.04774i
$775$		−	3.64059i		−	0.130774i
$776$	39.4089	−	3.10548i	1.41470	−	0.111480i
$777$	−3.87458	−	2.86400i	−0.139000	−	0.102745i
$778$	5.07887	−	15.1808i	0.182086	−	0.544259i
$779$	−32.0389	−	55.4931i	−1.14791	−	1.98825i
$780$	−25.8860	−	6.19900i	−0.926868	−	0.221960i
$781$	−0.607232	+	1.05176i	−0.0217285	+	0.0376348i
$782$	5.20010	+	5.87726i	0.185955	+	0.210170i
$783$	−11.7693	−	13.7377i	−0.420599	−	0.490945i
$784$	3.88131	+	0.967174i	0.138618	+	0.0345419i
$785$	−0.691513	−	0.399245i	−0.0246811	−	0.0142497i
$786$	−28.1141	+	19.7083i	−1.00279	+	0.702972i
$787$	23.3857	−	13.5017i	0.833609	−	0.481284i	−0.0214779	−	0.999769i	$-0.506837\pi$
$787$	23.3857	−	13.5017i	0.833609	−	0.481284i	0.855087	+	0.518485i	$0.173504\pi$
$788$	−12.0724	−	28.4356i	−0.430062	−	1.01298i
$789$	−2.97652	+	4.02681i	−0.105967	+	0.143358i
$790$	1.44432	+	7.09786i	0.0513866	+	0.252530i
$791$	−9.73942			−0.346294
$792$	−3.04421	−	0.451497i	−0.108171	−	0.0160433i
$793$	9.40255			0.333894
$794$	−8.72152	−	42.8604i	−0.309515	−	1.52106i
$795$	−7.78663	−	17.8832i	−0.276163	−	0.634253i
$796$	2.56048	+	6.03101i	0.0907539	+	0.213764i
$797$	−9.02396	+	5.20999i	−0.319645	+	0.184547i	−0.651234	−	0.758877i	$-0.725749\pi$
$797$	−9.02396	+	5.20999i	−0.319645	+	0.184547i	0.331589	+	0.943424i	$0.392415\pi$
$798$	16.7400	+	7.79499i	0.592589	+	0.275940i
$799$	11.6474	+	6.72462i	0.412055	+	0.237900i
$800$	17.8137	−	9.27696i	0.629809	−	0.327990i
$801$	3.63965	−	15.8383i	0.128601	−	0.559617i
$802$	−8.62077	−	9.74336i	−0.304410	−	0.344050i
$803$	2.24210	−	3.88342i	0.0791219	−	0.137043i
$804$	2.81755	−	2.97249i	0.0993674	−	0.104832i
$805$	−2.07258	−	3.58982i	−0.0730490	−	0.126525i
$806$	−2.93633	+	8.77673i	−0.103428	+	0.309147i
$807$	1.94098	−	17.1129i	0.0683258	−	0.602401i
$808$	0.0546921	+	0.694049i	0.00192406	+	0.0244165i
$809$			10.3967i			0.365527i	0.983157	+	0.182763i	$0.0585042\pi$
$809$			10.3967i			0.365527i	−0.983157	+	0.182763i	$0.941496\pi$
$810$	4.12554	+	14.7581i	0.144957	+	0.518547i
$811$			1.55175i			0.0544894i	0.999629	+	0.0272447i	$0.00867333\pi$
$811$			1.55175i			0.0544894i	−0.999629	+	0.0272447i	$0.991327\pi$
$812$	5.56098	+	4.18992i	0.195152	+	0.147038i
$813$	−3.65783	+	32.2496i	−0.128286	+	1.13104i
$814$	−1.35310	−	0.452692i	−0.0474263	−	0.0158669i
$815$	−1.40964	−	2.44157i	−0.0493777	−	0.0855246i
$816$	7.10810	+	8.61159i	0.248833	+	0.301466i
$817$	−30.3534	+	52.5736i	−1.06193	+	1.83932i
$818$	−22.8325	+	20.2019i	−0.798321	+	0.706342i
$819$	4.28815	−	18.6603i	0.149840	−	0.652043i
$820$	−2.49296	+	20.3146i	−0.0870580	+	0.709418i
$821$	36.9251	+	21.3187i	1.28869	+	0.744028i	0.978421	−	0.206619i	$-0.0662462\pi$
$821$	36.9251	+	21.3187i	1.28869	+	0.744028i	0.310273	+	0.950647i	$0.399580\pi$
$822$	−16.5759	+	35.5974i	−0.578152	+	1.24160i
$823$	27.1079	−	15.6508i	0.944924	−	0.545552i	0.0534233	−	0.998572i	$-0.482987\pi$
$823$	27.1079	−	15.6508i	0.944924	−	0.545552i	0.891500	+	0.453020i	$0.149653\pi$
$824$	21.5349	+	10.2690i	0.750203	+	0.357737i
$825$	0.890402	+	2.04495i	0.0309998	+	0.0711960i
$826$	−16.2800	+	3.31276i	−0.566454	+	0.115266i
$827$	−24.7566			−0.860871			−0.430436	−	0.902621i	$-0.641640\pi$
$827$	−24.7566			−0.860871			−0.430436	+	0.902621i	$0.641640\pi$
$828$	13.2956	+	15.8104i	0.462053	+	0.549448i
$829$	28.8502			1.00201			0.501005	−	0.865444i	$-0.332964\pi$
$829$	28.8502			1.00201			0.501005	+	0.865444i	$0.332964\pi$
$830$	5.59771	−	1.13906i	0.194299	−	0.0395373i
$831$	−25.2634	+	34.1777i	−0.876377	+	1.18561i
$832$	−50.4276	+	7.99719i	−1.74826	+	0.277253i
$833$	1.39578	−	0.805853i	0.0483608	−	0.0279211i
$834$	0.543491	+	0.775294i	0.0188195	+	0.0268462i
$835$	2.87744	+	1.66129i	0.0995779	+	0.0574913i
$836$	5.42765	+	0.666067i	0.187719	+	0.0230364i
$837$	5.23733	−	0.978919i	0.181029	−	0.0338364i
$838$	−40.4224	+	35.7651i	−1.39637	+	1.23549i
$839$	−15.2507	+	26.4150i	−0.526513	+	0.911947i	0.473010	+	0.881057i	$0.343167\pi$
$839$	−15.2507	+	26.4150i	−0.526513	+	0.911947i	−0.999523	+	0.0308899i	$0.990166\pi$
$840$	−2.77218	−	5.20610i	−0.0956492	−	0.179627i
$841$	−8.44000	−	14.6185i	−0.291034	−	0.504087i
$842$	−15.1438	−	5.06648i	−0.521889	−	0.174602i
$843$	−44.8967	−	33.1866i	−1.54632	−	1.14301i
$844$	18.6097	−	24.6993i	0.640573	−	0.850185i
$845$		−	33.3890i		−	1.14862i
$846$	30.2059	+	18.4668i	1.03850	+	0.634901i
$847$		−	10.8685i		−	0.373445i
$848$	−26.9167	−	25.9863i	−0.924323	−	0.892372i
$849$	−4.69686	+	2.04508i	−0.161196	+	0.0701871i
$850$	2.56757	−	7.67449i	0.0880668	−	0.263233i
$851$	4.78875	+	8.29437i	0.164156	+	0.284327i
$852$	11.1200	−	3.30083i	0.380966	−	0.113085i
$853$	17.7012	−	30.6595i	0.606079	−	1.04976i	−0.385801	−	0.922582i	$-0.626075\pi$
$853$	17.7012	−	30.6595i	0.606079	−	1.04976i	0.991880	−	0.127178i	$-0.0405919\pi$
$854$	1.38061	+	1.56039i	0.0472434	+	0.0533954i
$855$	−7.98730	−	26.0309i	−0.273160	−	0.890238i
$856$	−23.0440	−	33.5221i	−0.787628	−	1.14576i
$857$	−12.0301	−	6.94557i	−0.410940	−	0.237256i	0.280254	−	0.959926i	$-0.409581\pi$
$857$	−12.0301	−	6.94557i	−0.410940	−	0.237256i	−0.691193	+	0.722670i	$0.742915\pi$
$858$	−0.497218	−	5.64811i	−0.0169748	−	0.192823i
$859$	9.22404	−	5.32550i	0.314720	−	0.181704i	−0.334317	−	0.942461i	$-0.608505\pi$
$859$	9.22404	−	5.32550i	0.314720	−	0.181704i	0.649037	+	0.760757i	$0.275172\pi$
$860$	17.8483	−	7.57756i	0.608623	−	0.258393i
$861$	−14.6284	−	1.65919i	−0.498536	−	0.0565451i
$862$	−9.75215	−	47.9253i	−0.332160	−	1.63234i
$863$	−12.4233			−0.422893			−0.211446	−	0.977390i	$-0.567817\pi$
$863$	−12.4233			−0.422893			−0.211446	+	0.977390i	$0.567817\pi$
$864$	18.1357	+	23.1322i	0.616989	+	0.786972i
$865$	11.0863			0.376945
$866$	3.25415	+	15.9919i	0.110580	+	0.543428i
$867$	−24.7868	−	2.81137i	−0.841803	−	0.0954792i
$868$	−1.88768	+	0.801420i	−0.0640721	+	0.0272020i
$869$	−1.33621	+	0.771460i	−0.0453277	+	0.0261700i
$870$	−0.900339	−	10.2273i	−0.0305243	−	0.346739i
$871$	6.53482	+	3.77288i	0.221424	+	0.127839i
$872$	−8.83313	−	12.8495i	−0.299127	−	0.435141i
$873$	28.5644	−	30.6939i	0.966759	−	1.03883i
$874$	−24.3232	−	27.4906i	−0.822745	−	0.929882i
$875$	−5.14722	+	8.91524i	−0.174008	+	0.301390i
$876$	−41.0587	+	12.1877i	−1.38725	+	0.411786i
$877$	9.56050	+	16.5593i	0.322835	+	0.559167i	0.981072	−	0.193644i	$-0.0620307\pi$
$877$	9.56050	+	16.5593i	0.322835	+	0.559167i	−0.658237	+	0.752811i	$0.728697\pi$
$878$	0.552430	−	1.65122i	0.0186436	−	0.0557260i
$879$	21.6809	−	9.44020i	0.731280	−	0.318410i
$880$	−1.25659	−	1.21315i	−0.0423597	−	0.0408954i
$881$		−	20.0458i		−	0.675359i	−0.941261	−	0.337679i	$-0.890358\pi$
$881$		−	20.0458i		−	0.675359i	0.941261	−	0.337679i	$-0.109642\pi$
$882$	3.72638	−	2.02831i	0.125474	−	0.0682969i
$883$		−	14.5893i		−	0.490970i	−0.969400	−	0.245485i	$-0.921053\pi$
$883$		−	14.5893i		−	0.490970i	0.969400	−	0.245485i	$-0.0789473\pi$
$884$	−12.3798	+	16.4308i	−0.416376	+	0.552626i
$885$	19.6999	+	14.5617i	0.662204	+	0.489486i
$886$	−47.9093	−	16.0285i	−1.60954	−	0.538486i
$887$	16.6666	+	28.8673i	0.559609	+	0.969271i	0.997529	+	0.0702569i	$0.0223819\pi$
$887$	16.6666	+	28.8673i	0.559609	+	0.969271i	−0.437920	+	0.899014i	$0.644285\pi$
$888$	6.40518	+	12.0288i	0.214944	+	0.403660i
$889$	−9.35622	+	16.2055i	−0.313798	+	0.543513i
$890$	6.90766	−	6.11179i	0.231545	−	0.204868i
$891$	−2.70243	+	1.83079i	−0.0905347	+	0.0613338i
$892$	21.6863	+	2.66129i	0.726112	+	0.0891066i
$893$	−54.4801	−	31.4541i	−1.82311	−	1.05257i
$894$	−32.8967	−	46.9274i	−1.10023	−	1.56949i
$895$	10.8514	−	6.26509i	0.362724	−	0.209419i
$896$	−8.73160	−	7.19438i	−0.291702	−	0.240347i
$897$	−22.6231	+	30.6058i	−0.755364	+	1.02190i
$898$	−3.31775	+	0.675118i	−0.110715	+	0.0225290i
$899$	−3.56974			−0.119057
$900$	7.26440	−	20.0260i	0.242147	−	0.667534i
$901$	−15.0750			−0.502222
$902$	−4.27219	+	0.869334i	−0.142248	+	0.0289457i
$903$	5.56811	+	12.7881i	0.185295	+	0.425560i
$904$	24.8649	+	11.8569i	0.826994	+	0.394355i
$905$	−13.6377	+	7.87370i	−0.453331	+	0.261731i
$906$	−10.2756	+	22.0672i	−0.341384	+	0.733133i
$907$	−16.8116	−	9.70617i	−0.558219	−	0.322288i	0.194211	−	0.980960i	$-0.437785\pi$
$907$	−16.8116	−	9.70617i	−0.558219	−	0.322288i	−0.752430	+	0.658672i	$0.771119\pi$
$908$	2.76762	−	22.5528i	0.0918466	−	0.748440i
$909$	0.540565	+	0.503062i	0.0179294	+	0.0166855i
$910$	8.13845	−	7.20077i	0.269787	−	0.238703i
$911$	−9.63837	+	16.6942i	−0.319334	+	0.553102i	−0.980349	−	0.197270i	$-0.936792\pi$
$911$	−9.63837	+	16.6942i	−0.319334	+	0.553102i	0.661016	+	0.750372i	$0.270126\pi$
$912$	−33.2478	−	40.2803i	−1.10094	−	1.33381i
$913$	0.608410	+	1.05380i	0.0201354	+	0.0348756i
$914$	7.29736	+	2.44139i	0.241375	+	0.0807541i
$915$	0.346234	−	3.05261i	0.0114461	−	0.100916i
$916$	42.7327	+	32.1970i	1.41193	+	1.06382i
$917$		−	14.0168i		−	0.462874i
$918$	11.7309	+	1.63009i	0.387176	+	0.0538009i
$919$			0.268458i			0.00885561i	0.999990	+	0.00442780i	$0.00140942\pi$
$919$			0.268458i			0.00885561i	−0.999990	+	0.00442780i	$0.998591\pi$
$920$	0.921037	+	11.6881i	0.0303657	+	0.385344i
$921$	0.824262	−	7.26720i	0.0271604	−	0.239462i
$922$	−12.1180	+	36.2207i	−0.399084	+	1.19287i
$923$	10.6855	+	18.5078i	0.351717	+	0.609191i
$924$	0.864317	−	0.911846i	0.0284339	−	0.0299975i
$925$	4.93832	−	8.55343i	0.162371	−	0.281235i
$926$	−13.8914	−	15.7003i	−0.456500	−	0.515945i
$927$	24.1920	−	7.42305i	0.794569	−	0.243805i
$928$	−9.09640	−	17.4670i	−0.298604	−	0.573382i
$929$	−3.03534	−	1.75246i	−0.0995864	−	0.0574962i	0.449380	−	0.893341i	$-0.351645\pi$
$929$	−3.03534	−	1.75246i	−0.0995864	−	0.0574962i	−0.548966	+	0.835845i	$0.684978\pi$
$930$	2.74130	+	1.27649i	0.0898909	+	0.0418577i
$931$	−6.52868	+	3.76934i	−0.213969	+	0.123535i
$932$	−3.02301	−	7.12046i	−0.0990221	−	0.233238i
$933$	−10.2054	−	23.4384i	−0.334111	−	0.767340i
$934$	−2.45007	−	12.0405i	−0.0801689	−	0.393976i
$935$	−0.703769			−0.0230157
$936$	−33.6651	+	42.4196i	−1.10038	+	1.38653i
$937$	−11.9292			−0.389709			−0.194855	−	0.980832i	$-0.562424\pi$
$937$	−11.9292			−0.389709			−0.194855	+	0.980832i	$0.562424\pi$
$938$	0.333405	+	1.63846i	0.0108861	+	0.0534977i
$939$	−9.19750	+	12.4429i	−0.300149	+	0.406058i
$940$	7.85235	+	18.4956i	0.256115	+	0.603259i
$941$	−41.7557	+	24.1076i	−1.36120	+	0.785886i	−0.989783	−	0.142582i	$-0.954460\pi$
$941$	−41.7557	+	24.1076i	−1.36120	+	0.785886i	−0.371412	+	0.928468i	$0.621126\pi$
$942$	−1.33025	+	0.932522i	−0.0433419	+	0.0303832i
$943$	25.3440	+	14.6323i	0.825313	+	0.476494i
$944$	45.5961	+	11.3620i	1.48403	+	0.369801i
$945$	−5.90029	−	2.07931i	−0.191936	−	0.0676401i
$946$	2.73697	+	3.09338i	0.0889866	+	0.100574i
$947$	18.8281	−	32.6112i	0.611830	−	1.05972i	−0.379102	−	0.925355i	$-0.623767\pi$
$947$	18.8281	−	32.6112i	0.611830	−	1.05972i	0.990932	−	0.134366i	$-0.0428997\pi$
$948$	14.3315	+	3.43201i	0.465467	+	0.111467i
$949$	−39.4542	−	68.3367i	−1.28074	−	2.21830i
$950$	−12.0097	+	35.8970i	−0.389645	+	1.16465i
$951$	39.6860	+	29.3350i	1.28691	+	0.951252i
$952$	−4.54450	+	0.358114i	−0.147288	+	0.0116065i
$953$			8.65829i			0.280469i	0.990118	+	0.140235i	$0.0447857\pi$
$953$			8.65829i			0.280469i	−0.990118	+	0.140235i	$0.955214\pi$
$954$	−39.6708	−	0.997272i	−1.28439	−	0.0322879i
$955$			7.55520i			0.244481i
$956$	39.3895	+	29.6781i	1.27395	+	0.959857i
$957$	2.00515	−	0.873072i	0.0648172	−	0.0282224i
$958$	−43.8072	−	14.6561i	−1.41535	−	0.473516i
$959$	−8.01544	−	13.8831i	−0.258832	−	0.448310i
$960$	0.739433	+	16.6662i	0.0238651	+	0.537898i
$961$	−14.9743	+	25.9362i	−0.483042	+	0.836653i
$962$	−18.8041	+	16.6376i	−0.606268	+	0.536416i
$963$	−42.0503	−	9.66319i	−1.35505	−	0.311392i
$964$	0.0847384	−	0.690517i	0.00272924	−	0.0222400i
$965$	−8.78050	−	5.06942i	−0.282654	−	0.163191i
$966$	−8.40097	+	0.739560i	−0.270297	+	0.0237949i
$967$	−39.9241	+	23.0502i	−1.28387	+	0.741243i	−0.977554	−	0.210686i	$-0.932430\pi$
$967$	−39.9241	+	23.0502i	−1.28387	+	0.741243i	−0.306317	+	0.951929i	$0.599097\pi$
$968$	−13.2314	+	27.7474i	−0.425274	+	0.891834i
$969$	−20.9105	−	2.37172i	−0.671744	−	0.0761907i
$970$	23.3190	−	4.74511i	0.748728	−	0.152356i
$971$	−36.7005			−1.17778			−0.588888	−	0.808215i	$-0.700434\pi$
$971$	−36.7005			−1.17778			−0.588888	+	0.808215i	$0.700434\pi$
$972$	30.7626	+	5.06571i	0.986711	+	0.162483i
$973$	−0.386536			−0.0123918
$974$	−11.4231	+	2.32444i	−0.366019	+	0.0744799i
$975$	38.9981	+	4.42326i	1.24894	+	0.141658i
$976$	−1.62507	−	5.66447i	−0.0520173	−	0.181315i
$977$	16.3165	−	9.42035i	0.522012	−	0.301384i	−0.215746	−	0.976450i	$-0.569218\pi$
$977$	16.3165	−	9.42035i	0.522012	−	0.301384i	0.737757	+	0.675066i	$0.235885\pi$
$978$	−5.71383	+	0.503003i	−0.182708	+	0.0160843i
$979$	1.70147	+	0.982344i	0.0543792	+	0.0313958i
$980$	2.38999	+	0.293293i	0.0763454	+	0.00936891i
$981$	−16.1185	−	3.70405i	−0.514625	−	0.118261i
$982$	−13.0358	+	11.5338i	−0.415988	+	0.368059i
$983$	2.71655	−	4.70520i	0.0866445	−	0.150073i	−0.819446	−	0.573156i	$-0.805719\pi$
$983$	2.71655	−	4.70520i	0.0866445	−	0.150073i	0.906091	+	0.423083i	$0.139052\pi$
$984$	35.3268	+	22.0449i	1.12618	+	0.702764i
$985$	−9.29824	−	16.1050i	−0.296266	−	0.513148i
$986$	−7.52512	−	2.51759i	−0.239649	−	0.0801765i
$987$	−13.2518	+	5.77003i	−0.421809	+	0.183662i
$988$	57.9057	−	76.8540i	1.84223	−	2.44505i
$989$		−	27.7251i		−	0.881605i
$990$	−1.85201	−	0.0465571i	−0.0588607	−	0.00147968i
$991$			34.2742i			1.08876i	0.838840	+	0.544378i	$0.183234\pi$
$991$			34.2742i			1.08876i	−0.838840	+	0.544378i	$0.816766\pi$
$992$	5.79494	+	0.252053i	0.183990	+	0.00800270i
$993$	−12.9681	−	9.58570i	−0.411529	−	0.304193i
$994$	−1.50245	+	4.49085i	−0.0476549	+	0.142441i
$995$	1.97210	+	3.41577i	0.0625196	+	0.108287i
$996$	2.70665	−	11.3025i	0.0857635	−	0.358134i
$997$	−6.67750	+	11.5658i	−0.211479	+	0.366292i	−0.952177	−	0.305545i	$-0.901161\pi$
$997$	−6.67750	+	11.5658i	−0.211479	+	0.366292i	0.740699	+	0.671837i	$0.234495\pi$
$998$	9.44773	+	10.6780i	0.299063	+	0.338006i
$999$	13.6328	+	4.80430i	0.431321	+	0.152001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.16	yes	72
3.2	odd	2		756.2.ba.a.575.21		72
4.3	odd	2	inner	252.2.ba.a.155.3	✓	72
9.4	even	3		756.2.ba.a.71.34		72
9.5	odd	6	inner	252.2.ba.a.239.3	yes	72
12.11	even	2		756.2.ba.a.575.34		72
36.23	even	6	inner	252.2.ba.a.239.16	yes	72
36.31	odd	6		756.2.ba.a.71.21		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.3	✓	72	4.3	odd	2	inner
252.2.ba.a.155.16	yes	72	1.1	even	1	trivial
252.2.ba.a.239.3	yes	72	9.5	odd	6	inner
252.2.ba.a.239.16	yes	72	36.23	even	6	inner
756.2.ba.a.71.21		72	36.31	odd	6
756.2.ba.a.71.34		72	9.4	even	3
756.2.ba.a.575.21		72	3.2	odd	2
756.2.ba.a.575.34		72	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(-0.281995 - 1.38581i) q^{2} +(-1.72102 - 0.195202i) q^{3} +(-1.84096 + 0.781584i) q^{4} +(-1.04266 + 0.601980i) q^{5} +(0.214804 + 2.44005i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(1.60227 + 2.33082i) q^{8} +(2.92379 + 0.671890i) q^{9} +O(q^{10})\)	\(q+(-0.281995 - 1.38581i) q^{2} +(-1.72102 - 0.195202i) q^{3} +(-1.84096 + 0.781584i) q^{4} +(-1.04266 + 0.601980i) q^{5} +(0.214804 + 2.44005i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(1.60227 + 2.33082i) q^{8} +(2.92379 + 0.671890i) q^{9} +(1.12826 + 1.27518i) q^{10} +(-0.181344 + 0.314097i) q^{11} +(3.32088 - 0.985761i) q^{12} +(3.19111 + 5.52716i) q^{13} +(-0.448692 + 1.34115i) q^{14} +(1.91194 - 0.832488i) q^{15} +(2.77825 - 2.87773i) q^{16} -1.61171i q^{17} +(0.106621 - 4.24130i) q^{18} +7.53867i q^{19} +(1.44899 - 1.92314i) q^{20} +(1.39284 + 1.02956i) q^{21} +(0.486417 + 0.162735i) q^{22} +(-1.72147 - 2.98168i) q^{23} +(-2.30255 - 4.32415i) q^{24} +(-1.77524 + 3.07481i) q^{25} +(6.75974 - 5.98091i) q^{26} +(-4.90074 - 1.72706i) q^{27} +(1.98511 + 0.243607i) q^{28} +(3.01496 + 1.74069i) q^{29} +(-1.69283 - 2.41484i) q^{30} +(-0.888005 + 0.512690i) q^{31} +(-4.77144 - 3.03864i) q^{32} +(0.373408 - 0.505167i) q^{33} +(-2.23352 + 0.454492i) q^{34} +1.20396 q^{35} +(-5.90772 + 1.04827i) q^{36} -2.78178 q^{37} +(10.4472 - 2.12586i) q^{38} +(-4.41304 - 10.1352i) q^{39} +(-3.07373 - 1.46572i) q^{40} +(-7.36112 + 4.24995i) q^{41} +(1.03400 - 2.22055i) q^{42} +(6.97385 + 4.02635i) q^{43} +(0.0883534 - 0.719974i) q^{44} +(-3.45298 + 1.05951i) q^{45} +(-3.64661 + 3.22646i) q^{46} +(-4.17236 + 7.22675i) q^{47} +(-5.34316 + 4.41029i) q^{48} +(0.500000 + 0.866025i) q^{49} +(4.76172 + 1.59307i) q^{50} +(-0.314608 + 2.77377i) q^{51} +(-10.1946 - 7.68116i) q^{52} -9.35345i q^{53} +(-1.01140 + 7.27853i) q^{54} -0.436661i q^{55} +(-0.222195 - 2.81969i) q^{56} +(1.47156 - 12.9742i) q^{57} +(1.56207 - 4.66904i) q^{58} +(5.87381 + 10.1737i) q^{59} +(-2.86914 + 3.02692i) q^{60} +(0.736621 - 1.27587i) q^{61} +(0.960905 + 1.08603i) q^{62} +(-2.19613 - 2.04377i) q^{63} +(-2.86546 + 7.46921i) q^{64} +(-6.65448 - 3.84196i) q^{65} +(-0.805366 - 0.375019i) q^{66} +(1.02391 - 0.591155i) q^{67} +(1.25968 + 2.96708i) q^{68} +(2.38066 + 5.46755i) q^{69} +(-0.339510 - 1.66846i) q^{70} +3.34851 q^{71} +(3.11865 + 7.89139i) q^{72} -12.3638 q^{73} +(0.784446 + 3.85502i) q^{74} +(3.65543 - 4.94526i) q^{75} +(-5.89210 - 13.8784i) q^{76} +(0.314097 - 0.181344i) q^{77} +(-12.8011 + 8.97373i) q^{78} +(3.68419 + 2.12707i) q^{79} +(-1.16444 + 4.67294i) q^{80} +(8.09713 + 3.92894i) q^{81} +(7.96543 + 9.00268i) q^{82} +(1.67751 - 2.90552i) q^{83} +(-3.36885 - 0.806749i) q^{84} +(0.970214 + 1.68046i) q^{85} +(3.61319 - 10.7999i) q^{86} +(-4.84901 - 3.58428i) q^{87} +(-1.02266 + 0.0805875i) q^{88} -5.41703i q^{89} +(2.44201 + 4.48641i) q^{90} -6.38222i q^{91} +(5.49959 + 4.14367i) q^{92} +(1.62835 - 0.709008i) q^{93} +(11.1915 + 3.74421i) q^{94} +(-4.53813 - 7.86026i) q^{95} +(7.61859 + 6.16094i) q^{96} +(6.98817 - 12.1039i) q^{97} +(1.05915 - 0.937121i) q^{98} +(-0.741250 + 0.796510i) 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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