LMFDB - Embedded newform 546.2.u.a.185.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 2]))

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

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

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.15
Character	$\chi$	$=$	546.185
Dual form			546.2.u.a.425.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.11365 - 1.32657i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.12998 - 3.68924i) q^{5} +(-1.62773 + 0.592023i) q^{6} +(-1.07162 - 2.41901i) q^{7} -1.00000i q^{8} +(-0.519589 - 2.95466i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.11365 - 1.32657i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.12998 - 3.68924i) q^{5} +(-1.62773 + 0.592023i) q^{6} +(-1.07162 - 2.41901i) q^{7} -1.00000i q^{8} +(-0.519589 - 2.95466i) q^{9} +4.25996i q^{10} -1.48711i q^{11} +(1.70567 + 0.301159i) q^{12} +(2.41401 + 2.67816i) q^{13} +(-0.281454 + 2.63074i) q^{14} +(-7.26609 - 1.28293i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.33253 + 2.30802i) q^{17} +(-1.02735 + 2.81861i) q^{18} +4.10864i q^{19} +(2.12998 - 3.68924i) q^{20} +(-4.40240 - 1.27234i) q^{21} +(-0.743556 + 1.28788i) q^{22} +(-0.137205 - 0.0792156i) q^{23} +(-1.32657 - 1.11365i) q^{24} +(-6.57365 + 11.3859i) q^{25} +(-0.751517 - 3.52636i) q^{26} +(-4.49821 - 2.60117i) q^{27} +(1.55912 - 2.13756i) q^{28} +(-0.413684 + 0.238841i) q^{29} +(5.65115 + 4.74409i) q^{30} +(3.04646 + 1.75887i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.97276 - 1.65611i) q^{33} -2.66507i q^{34} +(-6.64178 + 9.10593i) q^{35} +(2.29902 - 1.92731i) q^{36} +(5.23854 - 9.07342i) q^{37} +(2.05432 - 3.55819i) q^{38} +(6.24113 - 0.219845i) q^{39} +(-3.68924 + 2.12998i) q^{40} +(-5.13995 - 8.90266i) q^{41} +(3.17643 + 3.30308i) q^{42} +(4.00148 - 6.93077i) q^{43} +(1.28788 - 0.743556i) q^{44} +(-9.79373 + 8.21027i) q^{45} +(0.0792156 + 0.137205i) q^{46} +(-2.27135 - 3.93409i) q^{47} +(0.592023 + 1.62773i) q^{48} +(-4.70325 + 5.18454i) q^{49} +(11.3859 - 6.57365i) q^{50} +(4.54572 + 0.802608i) q^{51} +(-1.11235 + 3.42968i) q^{52} +(3.23858 + 1.86979i) q^{53} +(2.59498 + 4.50179i) q^{54} +(-5.48631 + 3.16752i) q^{55} +(-2.41901 + 1.07162i) q^{56} +(5.45041 + 4.57557i) q^{57} +0.477682 q^{58} +(2.39384 + 4.14626i) q^{59} +(-2.52200 - 6.93408i) q^{60} -2.64025i q^{61} +(-1.75887 - 3.04646i) q^{62} +(-6.59056 + 4.42318i) q^{63} -1.00000 q^{64} +(4.73856 - 14.6103i) q^{65} +(0.880404 + 2.42062i) q^{66} -3.26889 q^{67} +(-1.33253 + 2.30802i) q^{68} +(-0.257883 + 0.0937949i) q^{69} +(10.3049 - 4.56508i) q^{70} +(7.70265 + 4.44713i) q^{71} +(-2.95466 + 0.519589i) q^{72} +(-6.03059 - 3.48176i) q^{73} +(-9.07342 + 5.23854i) q^{74} +(7.78350 + 21.4003i) q^{75} +(-3.55819 + 2.05432i) q^{76} +(-3.59734 + 1.59362i) q^{77} +(-5.51490 - 2.93017i) q^{78} +(-8.20543 - 14.2122i) q^{79} +4.25996 q^{80} +(-8.46005 + 3.07042i) q^{81} +10.2799i q^{82} -8.37013 q^{83} +(-1.09933 - 4.44876i) q^{84} +(5.67655 - 9.83207i) q^{85} +(-6.93077 + 4.00148i) q^{86} +(-0.143858 + 0.814766i) q^{87} -1.48711 q^{88} +(-5.94520 + 10.2974i) q^{89} +(12.5868 - 2.21343i) q^{90} +(3.89159 - 8.70951i) q^{91} -0.158431i q^{92} +(5.72594 - 2.08259i) q^{93} +4.54269i q^{94} +(15.1578 - 8.75134i) q^{95} +(0.301159 - 1.70567i) q^{96} +(3.13800 + 1.81173i) q^{97} +(6.66540 - 2.13832i) q^{98} +(-4.39391 + 0.772687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.11365	−	1.32657i	0.642963	−	0.765897i
$3$	1.11365	−	1.32657i	0.642963	−	0.765897i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.12998	−	3.68924i	−0.952557	−	1.64988i	−0.739862	−	0.672759i	$-0.765109\pi$
$5$	−2.12998	−	3.68924i	−0.952557	−	1.64988i	−0.212695	−	0.977119i	$-0.568224\pi$
$6$	−1.62773	+	0.592023i	−0.664518	+	0.241692i
$7$	−1.07162	−	2.41901i	−0.405035	−	0.914301i
$7$	−1.07162	−	2.41901i	−0.405035	−	0.914301i
$8$		−	1.00000i		−	0.353553i
$9$	−0.519589	−	2.95466i	−0.173196	−	0.984887i
$10$			4.25996i			1.34712i
$11$		−	1.48711i		−	0.448381i	−0.974545	−	0.224191i	$-0.928026\pi$
$11$		−	1.48711i		−	0.448381i	0.974545	−	0.224191i	$-0.0719738\pi$
$12$	1.70567	+	0.301159i	0.492384	+	0.0869370i
$13$	2.41401	+	2.67816i	0.669527	+	0.742788i
$13$	2.41401	+	2.67816i	0.669527	+	0.742788i
$14$	−0.281454	+	2.63074i	−0.0752217	+	0.703094i
$15$	−7.26609	−	1.28293i	−1.87610	−	0.331250i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.33253	+	2.30802i	0.323187	+	0.559776i	0.981144	−	0.193280i	$-0.0619124\pi$
$17$	1.33253	+	2.30802i	0.323187	+	0.559776i	−0.657957	+	0.753056i	$0.728579\pi$
$18$	−1.02735	+	2.81861i	−0.242150	+	0.664352i
$19$			4.10864i			0.942587i	0.881976	+	0.471294i	$0.156213\pi$
$19$			4.10864i			0.942587i	−0.881976	+	0.471294i	$0.843787\pi$
$20$	2.12998	−	3.68924i	0.476279	−	0.824939i
$21$	−4.40240	−	1.27234i	−0.960683	−	0.277647i
$22$	−0.743556	+	1.28788i	−0.158527	+	0.274576i
$23$	−0.137205	−	0.0792156i	−0.0286093	−	0.0165176i	0.485627	−	0.874166i	$-0.338591\pi$
$23$	−0.137205	−	0.0792156i	−0.0286093	−	0.0165176i	−0.514236	+	0.857648i	$0.671925\pi$
$24$	−1.32657	−	1.11365i	−0.270785	−	0.227322i
$25$	−6.57365	+	11.3859i	−1.31473	+	2.27718i
$26$	−0.751517	−	3.52636i	−0.147385	−	0.691576i
$27$	−4.49821	−	2.60117i	−0.865681	−	0.500596i
$28$	1.55912	−	2.13756i	0.294645	−	0.403961i
$29$	−0.413684	+	0.238841i	−0.0768193	+	0.0443516i	−0.537918	−	0.842997i	$-0.680789\pi$
$29$	−0.413684	+	0.238841i	−0.0768193	+	0.0443516i	0.461098	+	0.887349i	$0.347456\pi$
$30$	5.65115	+	4.74409i	1.03175	+	0.866148i
$31$	3.04646	+	1.75887i	0.547160	+	0.315903i	0.747976	−	0.663726i	$-0.231026\pi$
$31$	3.04646	+	1.75887i	0.547160	+	0.315903i	−0.200816	+	0.979629i	$0.564359\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.97276	−	1.65611i	−0.343414	−	0.288293i
$34$		−	2.66507i		−	0.457055i
$35$	−6.64178	+	9.10593i	−1.12267	+	1.53918i
$36$	2.29902	−	1.92731i	0.383170	−	0.321218i
$37$	5.23854	−	9.07342i	0.861211	−	1.49166i	−0.00954999	−	0.999954i	$-0.503040\pi$
$37$	5.23854	−	9.07342i	0.861211	−	1.49166i	0.870761	−	0.491707i	$-0.163627\pi$
$38$	2.05432	−	3.55819i	0.333255	−	0.577215i
$39$	6.24113	−	0.219845i	0.999380	−	0.0352033i
$40$	−3.68924	+	2.12998i	−0.583320	+	0.336780i
$41$	−5.13995	−	8.90266i	−0.802726	−	1.39036i	−0.917816	−	0.397007i	$-0.870049\pi$
$41$	−5.13995	−	8.90266i	−0.802726	−	1.39036i	0.115090	−	0.993355i	$-0.463284\pi$
$42$	3.17643	+	3.30308i	0.490133	+	0.509676i
$43$	4.00148	−	6.93077i	0.610221	−	1.05693i	−0.380982	−	0.924582i	$-0.624414\pi$
$43$	4.00148	−	6.93077i	0.610221	−	1.05693i	0.991203	−	0.132351i	$-0.0422526\pi$
$44$	1.28788	−	0.743556i	0.194155	−	0.112095i
$45$	−9.79373	+	8.21027i	−1.45996	+	1.22391i
$46$	0.0792156	+	0.137205i	0.0116797	+	0.0202298i
$47$	−2.27135	−	3.93409i	−0.331310	−	0.573846i	0.651459	−	0.758684i	$-0.274157\pi$
$47$	−2.27135	−	3.93409i	−0.331310	−	0.573846i	−0.982769	+	0.184838i	$0.940824\pi$
$48$	0.592023	+	1.62773i	0.0854512	+	0.234943i
$49$	−4.70325	+	5.18454i	−0.671893	+	0.740649i
$50$	11.3859	−	6.57365i	1.61021	−	0.929654i
$51$	4.54572	+	0.802608i	0.636528	+	0.112388i
$52$	−1.11235	+	3.42968i	−0.154255	+	0.475611i
$53$	3.23858	+	1.86979i	0.444853	+	0.256836i	0.705654	−	0.708557i	$-0.250653\pi$
$53$	3.23858	+	1.86979i	0.444853	+	0.256836i	−0.260801	+	0.965393i	$0.583987\pi$
$54$	2.59498	+	4.50179i	0.353132	+	0.612616i
$55$	−5.48631	+	3.16752i	−0.739774	+	0.427109i
$56$	−2.41901	+	1.07162i	−0.323254	+	0.143202i
$57$	5.45041	+	4.57557i	0.721925	+	0.606049i
$58$	0.477682			0.0627227
$59$	2.39384	+	4.14626i	0.311652	+	0.539797i	0.978720	−	0.205200i	$-0.0657844\pi$
$59$	2.39384	+	4.14626i	0.311652	+	0.539797i	−0.667068	+	0.744997i	$0.732451\pi$
$60$	−2.52200	−	6.93408i	−0.325588	−	0.895186i
$61$		−	2.64025i		−	0.338049i	−0.985612	−	0.169025i	$-0.945938\pi$
$61$		−	2.64025i		−	0.338049i	0.985612	−	0.169025i	$-0.0540617\pi$
$62$	−1.75887	−	3.04646i	−0.223377	−	0.386900i
$63$	−6.59056	+	4.42318i	−0.830333	+	0.557268i
$64$	−1.00000			−0.125000
$65$	4.73856	−	14.6103i	0.587746	−	1.81218i
$66$	0.880404	+	2.42062i	0.108370	+	0.297957i
$67$	−3.26889			−0.399359			−0.199679	−	0.979861i	$-0.563990\pi$
$67$	−3.26889			−0.399359			−0.199679	+	0.979861i	$0.563990\pi$
$68$	−1.33253	+	2.30802i	−0.161593	+	0.279888i
$69$	−0.257883	+	0.0937949i	−0.0310455	+	0.0112916i
$70$	10.3049	−	4.56508i	1.23167	−	0.545631i
$71$	7.70265	+	4.44713i	0.914136	+	0.527777i	0.881760	−	0.471699i	$-0.156359\pi$
$71$	7.70265	+	4.44713i	0.914136	+	0.527777i	0.0323767	+	0.999476i	$0.489692\pi$
$72$	−2.95466	+	0.519589i	−0.348210	+	0.0612342i
$73$	−6.03059	−	3.48176i	−0.705828	−	0.407510i	0.103687	−	0.994610i	$-0.466936\pi$
$73$	−6.03059	−	3.48176i	−0.705828	−	0.407510i	−0.809514	+	0.587100i	$0.800269\pi$
$74$	−9.07342	+	5.23854i	−1.05476	+	0.608968i
$75$	7.78350	+	21.4003i	0.898762	+	2.47109i
$76$	−3.55819	+	2.05432i	−0.408152	+	0.235647i
$77$	−3.59734	+	1.59362i	−0.409955	+	0.181610i
$78$	−5.51490	−	2.93017i	−0.624439	−	0.331777i
$79$	−8.20543	−	14.2122i	−0.923183	−	1.59900i	−0.794458	−	0.607320i	$-0.792245\pi$
$79$	−8.20543	−	14.2122i	−0.923183	−	1.59900i	−0.128725	−	0.991680i	$-0.541089\pi$
$80$	4.25996			0.476279
$81$	−8.46005	+	3.07042i	−0.940006	+	0.341158i
$82$			10.2799i			1.13523i
$83$	−8.37013			−0.918741			−0.459370	−	0.888245i	$-0.651925\pi$
$83$	−8.37013			−0.918741			−0.459370	+	0.888245i	$0.651925\pi$
$84$	−1.09933	−	4.44876i	−0.119946	−	0.485400i
$85$	5.67655	−	9.83207i	0.615708	−	1.06644i
$86$	−6.93077	+	4.00148i	−0.747365	+	0.431491i
$87$	−0.143858	+	0.814766i	−0.0154232	+	0.0873521i
$88$	−1.48711			−0.158527
$89$	−5.94520	+	10.2974i	−0.630190	+	1.09152i	0.357322	+	0.933981i	$0.383690\pi$
$89$	−5.94520	+	10.2974i	−0.630190	+	1.09152i	−0.987513	+	0.157540i	$0.949644\pi$
$90$	12.5868	−	2.21343i	1.32676	−	0.233316i
$91$	3.89159	−	8.70951i	0.407950	−	0.913004i
$92$		−	0.158431i		−	0.0165176i
$93$	5.72594	−	2.08259i	0.593753	−	0.215954i
$94$			4.54269i			0.468543i
$95$	15.1578	−	8.75134i	1.55515	−	0.897868i
$96$	0.301159	−	1.70567i	0.0307369	−	0.174084i
$97$	3.13800	+	1.81173i	0.318616	+	0.183953i	0.650775	−	0.759270i	$-0.274444\pi$
$97$	3.13800	+	1.81173i	0.318616	+	0.183953i	−0.332160	+	0.943223i	$0.607777\pi$
$98$	6.66540	−	2.13832i	0.673307	−	0.216003i
$99$	−4.39391	+	0.772687i	−0.441605	+	0.0776580i
$100$	−13.1473			−1.31473
$101$	−4.81906			−0.479514			−0.239757	−	0.970833i	$-0.577068\pi$
$101$	−4.81906			−0.479514			−0.239757	+	0.970833i	$0.577068\pi$
$102$	−3.53540	−	2.96794i	−0.350057	−	0.293870i
$103$	2.15332	−	1.24322i	0.212173	−	0.122498i	−0.390148	−	0.920752i	$-0.627576\pi$
$103$	2.15332	−	1.24322i	0.212173	−	0.122498i	0.602321	+	0.798254i	$0.294243\pi$
$104$	2.67816	−	2.41401i	0.262615	−	0.236713i
$105$	4.68309	+	18.9516i	0.457023	+	1.84948i
$106$	−1.86979	−	3.23858i	−0.181611	−	0.314559i
$107$	7.96591	+	4.59912i	0.770093	+	0.444614i	0.832908	−	0.553412i	$-0.186674\pi$
$107$	7.96591	+	4.59912i	0.770093	+	0.444614i	−0.0628146	+	0.998025i	$0.520008\pi$
$108$	0.00357501	−	5.19615i	0.000344005	−	0.500000i
$109$	3.36845	−	5.83432i	0.322639	−	0.558827i	−0.658393	−	0.752675i	$-0.728763\pi$
$109$	3.36845	−	5.83432i	0.322639	−	0.558827i	0.981032	+	0.193848i	$0.0620967\pi$
$110$	6.33504			0.604023
$111$	−6.20267	−	17.0539i	−0.588732	−	1.61868i
$112$	2.63074	+	0.281454i	0.248581	+	0.0265949i
$113$	14.7950	+	8.54191i	1.39180	+	0.803556i	0.993514	−	0.113706i	$-0.0362722\pi$
$113$	14.7950	+	8.54191i	1.39180	+	0.803556i	0.398285	+	0.917262i	$0.369606\pi$
$114$	−2.43241	−	6.68777i	−0.227816	−	0.626367i
$115$			0.674911i			0.0629358i
$116$	−0.413684	−	0.238841i	−0.0384096	−	0.0221758i
$117$	6.65876	−	8.52414i	0.615603	−	0.788057i
$118$		−	4.78769i		−	0.440742i
$119$	4.15515	−	5.69674i	0.380902	−	0.522219i
$120$	−1.28293	+	7.26609i	−0.117115	+	0.663300i
$121$	8.78850			0.798954
$122$	−1.32012	+	2.28652i	−0.119518	+	0.207012i
$123$	−17.5341	−	3.09588i	−1.58100	−	0.279146i
$124$			3.51775i			0.315903i
$125$	34.7072			3.10431
$126$	7.91918	−	0.535303i	0.705497	−	0.0476886i
$127$	2.85690	+	4.94830i	0.253509	+	0.439091i	0.964490	−	0.264121i	$-0.0850819\pi$
$127$	2.85690	+	4.94830i	0.253509	+	0.439091i	−0.710980	+	0.703212i	$0.751749\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−4.73794	−	13.0267i	−0.417152	−	1.14694i
$130$	−11.4089	+	10.2836i	−1.00062	+	0.901932i
$131$	−7.49454	−	12.9809i	−0.654801	−	1.13415i	−0.981944	−	0.189173i	$-0.939419\pi$
$131$	−7.49454	−	12.9809i	−0.654801	−	1.13415i	0.327143	−	0.944975i	$-0.393914\pi$
$132$	0.447857	−	2.53652i	0.0389809	−	0.220776i
$133$	9.93886	−	4.40292i	0.861809	−	0.381781i
$134$	2.83094	+	1.63445i	0.244556	+	0.141195i
$135$	−0.0152294	+	22.1354i	−0.00131074	+	1.90511i
$136$	2.30802	−	1.33253i	0.197911	−	0.114264i
$137$	−9.23788	+	5.33349i	−0.789245	+	0.455671i	−0.839697	−	0.543056i	$-0.817267\pi$
$137$	−9.23788	+	5.33349i	−0.789245	+	0.455671i	0.0504517	+	0.998727i	$0.483934\pi$
$138$	0.270231	+	0.0477129i	0.0230036	+	0.00406159i
$139$	−9.57332	−	5.52716i	−0.811998	−	0.468807i	0.0356511	−	0.999364i	$-0.488649\pi$
$139$	−9.57332	−	5.52716i	−0.811998	−	0.468807i	−0.847649	+	0.530557i	$0.821983\pi$
$140$	−11.2069	−	1.19898i	−0.947152	−	0.101333i
$141$	−7.74833	−	1.36807i	−0.652527	−	0.115212i
$142$	−4.44713	−	7.70265i	−0.373195	−	0.646392i
$143$	3.98272	−	3.58991i	0.333052	−	0.300203i
$144$	2.81861	+	1.02735i	0.234884	+	0.0856128i
$145$	1.76228	+	1.01745i	0.146349	+	0.0844949i
$146$	3.48176	+	6.03059i	0.288153	+	0.499095i
$147$	1.63992	+	12.0129i	0.135258	+	0.990810i
$148$	10.4771			0.861211
$149$			8.40462i			0.688533i	0.938872	+	0.344266i	$0.111872\pi$
$149$			8.40462i			0.688533i	−0.938872	+	0.344266i	$0.888128\pi$
$150$	3.95942	−	22.4249i	0.323286	−	1.83099i
$151$	11.2766	−	19.5317i	0.917679	−	1.58947i	0.114748	−	0.993395i	$-0.463394\pi$
$151$	11.2766	−	19.5317i	0.917679	−	1.58947i	0.802931	−	0.596072i	$-0.203273\pi$
$152$	4.10864			0.333255
$153$	6.12704	−	5.13641i	0.495342	−	0.415254i
$154$	3.91220	+	0.418553i	0.315254	+	0.0337280i
$155$		−	14.9855i		−	1.20366i
$156$	3.31095	+	5.29505i	0.265089	+	0.423943i
$157$	14.0883	+	8.13386i	1.12437	+	0.649153i	0.942512	−	0.334173i	$-0.108457\pi$
$157$	14.0883	+	8.13386i	1.12437	+	0.649153i	0.181854	+	0.983326i	$0.441790\pi$
$158$			16.4109i			1.30558i
$159$	6.08705	−	2.21392i	0.482734	−	0.175575i
$160$	−3.68924	−	2.12998i	−0.291660	−	0.168390i
$161$	−0.0445910	+	0.416791i	−0.00351427	+	0.0328477i
$162$	8.86183	+	1.57096i	0.696251	+	0.123427i
$163$	−6.98050			−0.546755			−0.273377	−	0.961907i	$-0.588141\pi$
$163$	−6.98050			−0.546755			−0.273377	+	0.961907i	$0.588141\pi$
$164$	5.13995	−	8.90266i	0.401363	−	0.695181i
$165$	−1.90785	+	10.8055i	−0.148526	+	0.841206i
$166$	7.24874	+	4.18506i	0.562612	+	0.324824i
$167$	−4.12054	−	7.13698i	−0.318857	−	0.552276i	0.661393	−	0.750039i	$-0.269965\pi$
$167$	−4.12054	−	7.13698i	−0.318857	−	0.552276i	−0.980250	+	0.197764i	$0.936632\pi$
$168$	−1.27234	+	4.40240i	−0.0981629	+	0.339653i
$169$	−1.34508	+	12.9302i	−0.103468	+	0.994633i
$170$	−9.83207	+	5.67655i	−0.754085	+	0.435371i
$171$	12.1397	−	2.13481i	0.928342	−	0.163253i
$172$	8.00297			0.610221
$173$	15.7662			1.19868			0.599342	−	0.800493i	$-0.295429\pi$
$173$	15.7662			1.19868			0.599342	+	0.800493i	$0.295429\pi$
$174$	0.531968	−	0.633679i	0.0403284	−	0.0480391i
$175$	34.5871	+	3.70036i	2.61454	+	0.279721i
$176$	1.28788	+	0.743556i	0.0970773	+	0.0560476i
$177$	8.16620	+	1.44185i	0.613809	+	0.108376i
$178$	10.2974	−	5.94520i	0.771822	−	0.445612i
$179$		−	7.52412i		−	0.562379i	−0.959652	−	0.281190i	$-0.909271\pi$
$179$		−	7.52412i		−	0.562379i	0.959652	−	0.281190i	$-0.0907290\pi$
$180$	−12.0072	−	4.37649i	−0.894961	−	0.326204i
$181$		−	3.30682i		−	0.245794i	−0.992419	−	0.122897i	$-0.960781\pi$
$181$		−	3.30682i		−	0.245794i	0.992419	−	0.122897i	$-0.0392185\pi$
$182$	−7.72497	+	5.59686i	−0.572613	+	0.414867i
$183$	−3.50248	−	2.94030i	−0.258911	−	0.217353i
$184$	−0.0792156	+	0.137205i	−0.00583985	+	0.0101149i
$185$	−44.6320			−3.28141
$186$	−6.00011	−	1.05940i	−0.439949	−	0.0776790i
$187$	3.43228	−	1.98163i	0.250993	−	0.144911i
$188$	2.27135	−	3.93409i	0.165655	−	0.286923i
$189$	−1.47188	+	13.6687i	−0.107064	+	0.994252i
$190$	−17.5027			−1.26978
$191$		−	25.9920i		−	1.88072i	−0.340186	−	0.940358i	$-0.610490\pi$
$191$		−	25.9920i		−	1.88072i	0.340186	−	0.940358i	$-0.389510\pi$
$192$	−1.11365	+	1.32657i	−0.0803704	+	0.0957371i
$193$	12.0753			0.869200			0.434600	−	0.900624i	$-0.356890\pi$
$193$	12.0753			0.869200			0.434600	+	0.900624i	$0.356890\pi$
$194$	−1.81173	−	3.13800i	−0.130074	−	0.225295i
$195$	−14.1045	−	22.5567i	−1.01005	−	1.61532i
$196$	−6.84157	−	1.48086i	−0.488683	−	0.105776i
$197$	−2.02572	+	1.16955i	−0.144326	+	0.0833268i	−0.570424	−	0.821350i	$-0.693221\pi$
$197$	−2.02572	+	1.16955i	−0.144326	+	0.0833268i	0.426098	+	0.904677i	$0.359888\pi$
$198$	4.19158	+	1.52779i	0.297883	+	0.108575i
$199$	−9.25711	+	5.34459i	−0.656219	+	0.378868i	−0.790835	−	0.612030i	$-0.790353\pi$
$199$	−9.25711	+	5.34459i	−0.656219	+	0.378868i	0.134616	+	0.990898i	$0.457020\pi$
$200$	11.3859	+	6.57365i	0.805104	+	0.464827i
$201$	−3.64038	+	4.33642i	−0.256773	+	0.305867i
$202$	4.17343	+	2.40953i	0.293641	+	0.169534i
$203$	1.02107	+	0.744761i	0.0716652	+	0.0522719i
$204$	1.57778	+	4.33801i	0.110467	+	0.303722i
$205$	−21.8960	+	37.9250i	−1.52928	+	2.64880i
$206$	−2.48644			−0.173238
$207$	−0.162765	+	0.446555i	−0.0113129	+	0.0310377i
$208$	−3.52636	+	0.751517i	−0.244509	+	0.0521083i
$209$	6.11001			0.422638
$210$	5.42011	−	18.7541i	0.374023	−	1.29415i
$211$	2.22580	+	3.85520i	0.153230	+	0.265403i	0.932413	−	0.361394i	$-0.117699\pi$
$211$	2.22580	+	3.85520i	0.153230	+	0.265403i	−0.779183	+	0.626797i	$0.784366\pi$
$212$			3.73959i			0.256836i
$213$	14.4775	−	5.26560i	0.991979	−	0.360793i
$214$	−4.59912	−	7.96591i	−0.314389	−	0.544538i
$215$	−34.0924			−2.32508
$216$	−2.60117	+	4.49821i	−0.176987	+	0.306065i
$217$	0.990083	−	9.25427i	0.0672112	−	0.628221i
$218$	−5.83432	+	3.36845i	−0.395150	+	0.228140i
$219$	−11.3348	+	4.12257i	−0.765932	+	0.278577i
$220$	−5.48631	−	3.16752i	−0.369887	−	0.213554i
$221$	−2.96448	+	9.14032i	−0.199413	+	0.614844i
$222$	−3.15526	+	17.8704i	−0.211767	+	1.19938i
$223$	3.82172	−	2.20647i	0.255921	−	0.147756i	−0.366551	−	0.930398i	$-0.619462\pi$
$223$	3.82172	−	2.20647i	0.255921	−	0.147756i	0.622473	+	0.782642i	$0.286128\pi$
$224$	−2.13756	−	1.55912i	−0.142822	−	0.104173i
$225$	37.0571	+	13.5069i	2.47047	+	0.900461i
$226$	−8.54191	−	14.7950i	−0.568200	−	0.984151i
$227$	9.82387	+	17.0154i	0.652033	+	1.12935i	0.982629	+	0.185582i	$0.0594171\pi$
$227$	9.82387	+	17.0154i	0.652033	+	1.12935i	−0.330596	+	0.943773i	$0.607250\pi$
$228$	−1.23735	+	7.00798i	−0.0819457	+	0.464115i
$229$	−11.0523	+	6.38106i	−0.730358	+	0.421672i	−0.818553	−	0.574431i	$-0.805223\pi$
$229$	−11.0523	+	6.38106i	−0.730358	+	0.421672i	0.0881953	+	0.996103i	$0.471890\pi$
$230$	0.337456	−	0.584490i	0.0222512	−	0.0385401i
$231$	−1.89211	+	6.54687i	−0.124491	+	0.430752i
$232$	0.238841	+	0.413684i	0.0156807	+	0.0271597i
$233$	−19.0288	+	10.9863i	−1.24662	+	0.719734i	−0.970433	−	0.241371i	$-0.922403\pi$
$233$	−19.0288	+	10.9863i	−1.24662	+	0.719734i	−0.276183	+	0.961105i	$0.589070\pi$
$234$	−10.0287	+	4.05274i	−0.655598	+	0.264936i
$235$	−9.67586	+	16.7591i	−0.631183	+	1.09324i
$236$	−2.39384	+	4.14626i	−0.155826	+	0.269898i
$237$	−27.9915	−	4.94227i	−1.81824	−	0.321035i
$238$	−6.44683	+	2.85595i	−0.417886	+	0.185124i
$239$		−	17.9466i		−	1.16087i	−0.814306	−	0.580436i	$-0.802882\pi$
$239$		−	17.9466i		−	1.16087i	0.814306	−	0.580436i	$-0.197118\pi$
$240$	4.74409	−	5.65115i	0.306230	−	0.364780i
$241$	14.2309	−	8.21623i	0.916695	−	0.529254i	0.0341158	−	0.999418i	$-0.489138\pi$
$241$	14.2309	−	8.21623i	0.916695	−	0.529254i	0.882579	+	0.470164i	$0.155805\pi$
$242$	−7.61106	−	4.39425i	−0.489258	−	0.282473i
$243$	−5.34836	+	14.6422i	−0.343097	+	0.939300i
$244$	2.28652	−	1.32012i	0.146380	−	0.0845123i
$245$	29.1448	+	6.30842i	1.86200	+	0.403030i
$246$	13.6370	+	11.4482i	0.869466	+	0.729909i
$247$	−11.0036	+	9.91832i	−0.700142	+	0.631088i
$248$	1.75887	−	3.04646i	0.111689	−	0.193450i
$249$	−9.32135	+	11.1036i	−0.590717	+	0.703661i
$250$	−30.0573	−	17.3536i	−1.90099	−	1.09754i
$251$	−5.60540	+	9.70884i	−0.353810	+	0.612816i	−0.986913	−	0.161251i	$-0.948447\pi$
$251$	−5.60540	+	9.70884i	−0.353810	+	0.612816i	0.633104	+	0.774067i	$0.281781\pi$
$252$	−7.12586	−	3.49601i	−0.448887	−	0.220228i
$253$	−0.117802	+	0.204040i	−0.00740617	+	0.0128279i
$254$		−	5.71380i		−	0.358516i
$255$	−6.72129	−	18.4798i	−0.420904	−	1.15725i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.23368	−	2.13679i	0.0769546	−	0.133289i	−0.824980	−	0.565162i	$-0.808814\pi$
$257$	1.23368	−	2.13679i	0.0769546	−	0.133289i	0.901935	+	0.431873i	$0.142147\pi$
$258$	−2.41016	+	13.6504i	−0.150050	+	0.849837i
$259$	−27.5625	−	2.94881i	−1.71265	−	0.183230i
$260$	15.0222	−	3.20144i	0.931636	−	0.198545i
$261$	0.920640	+	1.09820i	0.0569862	+	0.0679768i
$262$			14.9891i			0.926028i
$263$		−	16.7209i		−	1.03106i	−0.856872	−	0.515529i	$-0.827595\pi$
$263$		−	16.7209i		−	1.03106i	0.856872	−	0.515529i	$-0.172405\pi$
$264$	−1.65611	+	1.97276i	−0.101927	+	0.121415i
$265$		−	15.9305i		−	0.978604i
$266$	−10.8088	−	1.15639i	−0.662728	−	0.0709030i
$267$	7.03939	+	19.3544i	0.430804	+	1.18447i
$268$	−1.63445	−	2.83094i	−0.0998396	−	0.172927i
$269$	−1.31230	−	2.27296i	−0.0800121	−	0.138585i	0.823243	−	0.567689i	$-0.192163\pi$
$269$	−1.31230	−	2.27296i	−0.0800121	−	0.138585i	−0.903255	+	0.429104i	$0.858829\pi$
$270$	11.0809	−	19.1622i	0.674362	−	1.16618i
$271$	−7.72000	−	4.45715i	−0.468957	−	0.270752i	0.246846	−	0.969055i	$-0.420606\pi$
$271$	−7.72000	−	4.45715i	−0.468957	−	0.270752i	−0.715803	+	0.698302i	$0.753939\pi$
$272$	−2.66507			−0.161593
$273$	−7.21994	−	14.8618i	−0.436971	−	0.899476i
$274$	10.6670			0.644416
$275$	16.9321	+	9.77575i	1.02104	+	0.589500i
$276$	−0.210170	−	0.176436i	−0.0126508	−	0.0106202i
$277$	14.6154	+	25.3147i	0.878156	+	1.52101i	0.853363	+	0.521318i	$0.174559\pi$
$277$	14.6154	+	25.3147i	0.878156	+	1.52101i	0.0247930	+	0.999693i	$0.492107\pi$
$278$	5.52716	+	9.57332i	0.331497	+	0.574169i
$279$	3.61397	−	9.91514i	0.216363	−	0.593604i
$280$	9.10593	+	6.64178i	0.544183	+	0.396922i
$281$		−	18.8564i		−	1.12488i	−0.826839	−	0.562439i	$-0.809863\pi$
$281$		−	18.8564i		−	1.12488i	0.826839	−	0.562439i	$-0.190137\pi$
$282$	6.02621	+	5.05895i	0.358856	+	0.301256i
$283$		−	0.349698i		−	0.0207874i	−0.999946	−	0.0103937i	$-0.996692\pi$
$283$		−	0.349698i		−	0.0207874i	0.999946	−	0.0103937i	$-0.00330847\pi$
$284$			8.89425i			0.527777i
$285$	5.27108	−	29.8538i	0.312232	−	1.76838i
$286$	−5.24409	+	1.11759i	−0.310090	+	0.0660845i
$287$	−16.0276	+	21.9739i	−0.946077	+	1.29708i
$288$	−1.92731	−	2.29902i	−0.113568	−	0.135471i
$289$	4.94871	−	8.57141i	0.291100	−	0.504201i
$290$	−1.01745	−	1.76228i	−0.0597469	−	0.103485i
$291$	5.89801	−	2.14517i	0.345747	−	0.125752i
$292$		−	6.96353i		−	0.407510i
$293$	−5.35220	+	9.27029i	−0.312679	+	0.541576i	−0.978941	−	0.204141i	$-0.934560\pi$
$293$	−5.35220	+	9.27029i	−0.312679	+	0.541576i	0.666262	+	0.745717i	$0.267893\pi$
$294$	4.58626	−	11.2235i	0.267476	−	0.654566i
$295$	10.1977	−	17.6629i	0.593732	−	1.02837i
$296$	−9.07342	−	5.23854i	−0.527382	−	0.304484i
$297$	−3.86823	+	6.68934i	−0.224458	+	0.388155i
$298$	4.20231	−	7.27861i	0.243433	−	0.421639i
$299$	−0.119064	−	0.558685i	−0.00688563	−	0.0323096i
$300$	−14.6414	+	17.4408i	−0.845323	+	1.00695i
$301$	−21.0537	−	2.25247i	−1.21352	−	0.129830i
$302$	−19.5317	+	11.2766i	−1.12392	+	0.648897i
$303$	−5.36672	+	6.39283i	−0.308310	+	0.367259i
$304$	−3.55819	−	2.05432i	−0.204076	−	0.117823i
$305$	−9.74051	+	5.62368i	−0.557740	+	0.322011i
$306$	−7.87437	+	1.38474i	−0.450148	+	0.0791603i
$307$			4.04677i			0.230961i	0.993310	+	0.115481i	$0.0368408\pi$
$307$			4.04677i			0.230961i	−0.993310	+	0.115481i	$0.963159\pi$
$308$	−3.17879	−	2.31858i	−0.181128	−	0.132113i
$309$	0.748813	−	4.24104i	0.0425985	−	0.241264i
$310$	−7.49274	+	12.9778i	−0.425559	+	0.737090i
$311$	−8.19728	+	14.1981i	−0.464825	+	0.805101i	−0.999194	−	0.0401509i	$-0.987216\pi$
$311$	−8.19728	+	14.1981i	−0.464825	+	0.805101i	0.534369	+	0.845252i	$0.320549\pi$
$312$	−0.219845	−	6.24113i	−0.0124463	−	0.353334i
$313$	17.1202	−	9.88433i	0.967689	−	0.558696i	0.0691582	−	0.997606i	$-0.477969\pi$
$313$	17.1202	−	9.88433i	0.967689	−	0.558696i	0.898531	+	0.438910i	$0.144635\pi$
$314$	−8.13386	−	14.0883i	−0.459020	−	0.795047i
$315$	30.3559	+	14.8929i	1.71036	+	0.839118i
$316$	8.20543	−	14.2122i	0.461591	−	0.799500i
$317$	−6.98551	+	4.03309i	−0.392345	+	0.226521i	−0.683176	−	0.730254i	$-0.739402\pi$
$317$	−6.98551	+	4.03309i	−0.392345	+	0.226521i	0.290830	+	0.956775i	$0.406068\pi$
$318$	−6.37850	−	1.12621i	−0.357688	−	0.0631547i
$319$	0.355183	+	0.615195i	0.0198864	+	0.0344443i
$320$	2.12998	+	3.68924i	0.119070	+	0.206235i
$321$	14.9723	−	5.44557i	0.835670	−	0.303942i
$322$	0.247012	−	0.338656i	0.0137655	−	0.0188726i
$323$	−9.48281	+	5.47490i	−0.527638	+	0.304632i
$324$	−6.88909	−	5.79141i	−0.382727	−	0.321745i
$325$	−46.3621	+	9.88042i	−2.57171	+	0.548067i
$326$	6.04529	+	3.49025i	0.334818	+	0.193307i
$327$	−3.98840	−	10.9659i	−0.220559	−	0.606413i
$328$	−8.90266	+	5.13995i	−0.491567	+	0.283806i
$329$	−7.08258	+	9.71028i	−0.390475	+	0.535345i
$330$	7.05499	−	8.40389i	0.388364	−	0.462619i
$331$	18.4185			1.01238			0.506188	−	0.862423i	$-0.331054\pi$
$331$	18.4185			1.01238			0.506188	+	0.862423i	$0.331054\pi$
$332$	−4.18506	−	7.24874i	−0.229685	−	0.397826i
$333$	−29.5308	−	10.7637i	−1.61828	−	0.589845i
$334$			8.24107i			0.450931i
$335$	6.96268	+	12.0597i	0.380412	+	0.658893i
$336$	3.30308	−	3.17643i	0.180198	−	0.173288i
$337$	−16.8561			−0.918208			−0.459104	−	0.888383i	$-0.651829\pi$
$337$	−16.8561			−0.918208			−0.459104	+	0.888383i	$0.651829\pi$
$338$	7.62999	−	10.5254i	0.415016	−	0.572504i
$339$	27.8079	−	10.1140i	1.51032	−	0.549318i
$340$	11.3531			0.615708
$341$	2.61564	−	4.53042i	0.141645	−	0.245336i
$342$	−11.5806	−	4.22103i	−0.626210	−	0.228247i
$343$	17.5816	+	5.82135i	0.949316	+	0.314323i
$344$	−6.93077	−	4.00148i	−0.373682	−	0.215746i
$345$	0.895319	+	0.751611i	0.0482023	+	0.0404654i
$346$	−13.6540	−	7.88311i	−0.734041	−	0.423799i
$347$	13.5754	−	7.83777i	0.728766	−	0.420754i	−0.0892043	−	0.996013i	$-0.528432\pi$
$347$	13.5754	−	7.83777i	0.728766	−	0.420754i	0.817971	+	0.575260i	$0.195099\pi$
$348$	−0.777537	+	0.282798i	−0.0416804	+	0.0151596i
$349$	−16.3312	+	9.42880i	−0.874187	+	0.504712i	−0.868737	−	0.495273i	$-0.835068\pi$
$349$	−16.3312	+	9.42880i	−0.874187	+	0.504712i	−0.00544978	+	0.999985i	$0.501735\pi$
$350$	−28.1031	−	20.4982i	−1.50218	−	1.09567i
$351$	−3.89239	−	18.3262i	−0.207760	−	0.978180i
$352$	−0.743556	−	1.28788i	−0.0396317	−	0.0686441i
$353$	18.4076			0.979737			0.489868	−	0.871796i	$-0.337045\pi$
$353$	18.4076			0.979737			0.489868	+	0.871796i	$0.337045\pi$
$354$	−6.35121	−	5.33178i	−0.337563	−	0.283381i
$355$		−	37.8892i		−	2.01095i
$356$	−11.8904			−0.630190
$357$	−2.92978	−	11.8562i	−0.155060	−	0.627499i
$358$	−3.76206	+	6.51608i	−0.198831	+	0.344385i
$359$	29.2230	−	16.8719i	1.54233	−	0.890465i	0.543639	−	0.839319i	$-0.317046\pi$
$359$	29.2230	−	16.8719i	1.54233	−	0.890465i	0.998691	−	0.0511459i	$-0.0162873\pi$
$360$	8.21027	+	9.79373i	0.432719	+	0.516175i
$361$	2.11905			0.111529
$362$	−1.65341	+	2.86379i	−0.0869014	+	0.150518i
$363$	9.78727	−	11.6586i	0.513698	−	0.611917i
$364$	9.48845	−	0.984537i	0.497330	−	0.0516038i
$365$			29.6644i			1.55271i
$366$	1.56309	+	4.29762i	0.0817039	+	0.224640i
$367$		−	34.0455i		−	1.77716i	−0.458723	−	0.888579i	$-0.651693\pi$
$367$		−	34.0455i		−	1.77716i	0.458723	−	0.888579i	$-0.348307\pi$
$368$	0.137205	−	0.0792156i	0.00715233	−	0.00412940i
$369$	−23.6337	+	19.8126i	−1.23032	+	1.03140i
$370$	38.6524	+	22.3160i	2.00945	+	1.16015i
$371$	1.05252	−	9.83788i	0.0546442	−	0.510757i
$372$	4.66655	+	3.91752i	0.241949	+	0.203114i
$373$	30.8502			1.59736			0.798682	−	0.601753i	$-0.205531\pi$
$373$	30.8502			1.59736			0.798682	+	0.601753i	$0.205531\pi$
$374$	−3.96325			−0.204935
$375$	38.6515	−	46.0416i	1.99596	−	2.37758i
$376$	−3.93409	+	2.27135i	−0.202885	+	0.117136i
$377$	−1.63829	−	0.531348i	−0.0843764	−	0.0273658i
$378$	8.10904	−	11.1015i	0.417084	−	0.571000i
$379$	3.11757	+	5.39979i	0.160139	+	0.277368i	0.934918	−	0.354863i	$-0.115473\pi$
$379$	3.11757	+	5.39979i	0.160139	+	0.277368i	−0.774780	+	0.632231i	$0.782139\pi$
$380$	15.1578	+	8.75134i	0.777577	+	0.448934i
$381$	9.74585	+	1.72076i	0.499295	+	0.0881573i
$382$	−12.9960	+	22.5097i	−0.664934	+	1.15170i
$383$	5.45285			0.278628			0.139314	−	0.990248i	$-0.455510\pi$
$383$	5.45285			0.278628			0.139314	+	0.990248i	$0.455510\pi$
$384$	1.62773	−	0.592023i	0.0830648	−	0.0302115i
$385$	13.5415	+	9.87706i	0.690140	+	0.503382i
$386$	−10.4575	−	6.03765i	−0.532274	−	0.307309i
$387$	−22.5572	−	8.22188i	−1.14665	−	0.417942i
$388$			3.62345i			0.183953i
$389$	33.4019	+	19.2846i	1.69354	+	0.977768i	0.951616	+	0.307290i	$0.0994221\pi$
$389$	33.4019	+	19.2846i	1.69354	+	0.977768i	0.741929	+	0.670479i	$0.233911\pi$
$390$	0.936530	+	26.5870i	0.0474231	+	1.34628i
$391$		−	0.422230i		−	0.0213531i
$392$	5.18454	+	4.70325i	0.261859	+	0.237550i
$393$	−25.5664	−	4.51409i	−1.28965	−	0.227706i
$394$	2.33909			0.117842
$395$	−34.9548	+	60.5436i	−1.75877	+	3.04628i
$396$	−2.86612	−	3.41890i	−0.144028	−	0.171806i
$397$			26.9335i			1.35175i	0.737015	+	0.675876i	$0.236235\pi$
$397$			26.9335i			1.35175i	−0.737015	+	0.675876i	$0.763765\pi$
$398$	10.6892			0.535801
$399$	5.22758	−	18.0879i	0.261706	−	0.905528i
$400$	−6.57365	−	11.3859i	−0.328682	−	0.569295i
$401$	8.02151	+	4.63122i	0.400575	+	0.231272i	0.686732	−	0.726911i	$-0.259045\pi$
$401$	8.02151	+	4.63122i	0.400575	+	0.231272i	−0.286157	+	0.958183i	$0.592378\pi$
$402$	5.32087	−	1.93526i	0.265381	−	0.0965219i
$403$	2.64365	+	12.4048i	0.131689	+	0.617929i
$404$	−2.40953	−	4.17343i	−0.119879	−	0.207636i
$405$	29.3473	+	24.6712i	1.45828	+	1.22592i
$406$	−0.511895	−	1.15552i	−0.0254049	−	0.0573474i
$407$	−13.4932	−	7.79030i	−0.668833	−	0.386151i
$408$	0.802608	−	4.54572i	0.0397350	−	0.225047i
$409$	−13.2090	+	7.62621i	−0.653142	+	0.377092i	−0.789659	−	0.613546i	$-0.789743\pi$
$409$	−13.2090	+	7.62621i	−0.653142	+	0.377092i	0.136517	+	0.990638i	$0.456409\pi$
$410$	37.9250	−	21.8960i	1.87298	−	1.08137i
$411$	−3.21245	+	18.1943i	−0.158459	+	0.897460i
$412$	2.15332	+	1.24322i	0.106086	+	0.0612490i
$413$	7.46456	−	10.2340i	0.367307	−	0.503580i
$414$	0.364236	−	0.305346i	0.0179012	−	0.0150069i
$415$	17.8282	+	30.8794i	0.875153	+	1.51581i
$416$	3.42968	+	1.11235i	0.168154	+	0.0545373i
$417$	−17.9935	+	6.54441i	−0.881143	+	0.320481i
$418$	−5.29142	−	3.05501i	−0.258812	−	0.149425i
$419$	10.7855	+	18.6811i	0.526908	+	0.912631i	0.999508	+	0.0313545i	$0.00998208\pi$
$419$	10.7855	+	18.6811i	0.526908	+	0.912631i	−0.472600	+	0.881277i	$0.656685\pi$
$420$	−14.0710	+	13.5315i	−0.686594	+	0.660268i
$421$	−25.8262			−1.25869			−0.629345	−	0.777126i	$-0.716677\pi$
$421$	−25.8262			−1.25869			−0.629345	+	0.777126i	$0.716677\pi$
$422$		−	4.45160i		−	0.216700i
$423$	−10.4437	+	8.75517i	−0.507792	+	0.425691i
$424$	1.86979	−	3.23858i	0.0908053	−	0.157279i
$425$	−35.0384			−1.69961
$426$	−15.1706	−	2.67858i	−0.735020	−	0.129778i
$427$	−6.38680	+	2.82935i	−0.309079	+	0.136922i
$428$			9.19824i			0.444614i
$429$	−0.326933	−	9.28125i	−0.0157845	−	0.448103i
$430$	29.5249	+	17.0462i	1.42381	+	0.822040i
$431$			10.8349i			0.521900i	0.965352	+	0.260950i	$0.0840358\pi$
$431$			10.8349i			0.521900i	−0.965352	+	0.260950i	$0.915964\pi$
$432$	4.50179	−	2.59498i	0.216592	−	0.124851i
$433$	15.5101	+	8.95476i	0.745368	+	0.430338i	0.824018	−	0.566564i	$-0.191728\pi$
$433$	15.5101	+	8.95476i	0.745368	+	0.430338i	−0.0786500	+	0.996902i	$0.525061\pi$
$434$	−5.48457	+	7.51939i	−0.263268	+	0.360942i
$435$	3.31228	−	1.20471i	0.158812	−	0.0577615i
$436$	6.73690			0.322639
$437$	0.325469	−	0.563728i	0.0155693	−	0.0269668i
$438$	11.8775	+	2.09713i	0.567527	+	0.100205i
$439$	6.18229	+	3.56935i	0.295065	+	0.170356i	0.640224	−	0.768189i	$-0.278842\pi$
$439$	6.18229	+	3.56935i	0.295065	+	0.170356i	−0.345159	+	0.938544i	$0.612175\pi$
$440$	3.16752	+	5.48631i	0.151006	+	0.261550i
$441$	17.7623	+	11.2027i	0.845825	+	0.533461i
$442$	7.13748	−	6.43351i	0.339495	−	0.306011i
$443$	15.1527	−	8.74841i	0.719926	−	0.415650i	−0.0947992	−	0.995496i	$-0.530221\pi$
$443$	15.1527	−	8.74841i	0.719926	−	0.415650i	0.814726	+	0.579847i	$0.196888\pi$
$444$	11.6678	−	13.8986i	0.553727	−	0.659599i
$445$	50.6527			2.40117
$446$	−4.41294			−0.208959
$447$	11.1493	+	9.35976i	0.527345	+	0.442701i
$448$	1.07162	+	2.41901i	0.0506294	+	0.114288i
$449$	−3.24523	−	1.87364i	−0.153152	−	0.0884224i	0.421466	−	0.906844i	$-0.361516\pi$
$449$	−3.24523	−	1.87364i	−0.153152	−	0.0884224i	−0.574618	+	0.818422i	$0.694849\pi$
$450$	−25.3389	−	30.2259i	−1.19449	−	1.42486i
$451$	−13.2393	+	7.64369i	−0.623412	+	0.359927i
$452$			17.0838i			0.803556i
$453$	−13.3520	−	36.7106i	−0.627334	−	1.72482i
$454$		−	19.6477i		−	0.922114i
$455$	−40.4205	+	4.19409i	−1.89494	+	0.196622i
$456$	4.57557	−	5.45041i	0.214271	−	0.255239i
$457$	−6.27651	+	10.8712i	−0.293603	+	0.508535i	−0.974659	−	0.223696i	$-0.928188\pi$
$457$	−6.27651	+	10.8712i	−0.293603	+	0.508535i	0.681056	+	0.732231i	$0.261521\pi$
$458$	12.7621			0.596335
$459$	0.00952763	−	13.8481i	0.000444712	−	0.646374i
$460$	−0.584490	+	0.337456i	−0.0272520	+	0.0157339i
$461$	3.57386	−	6.19010i	0.166451	−	0.288302i	−0.770719	−	0.637176i	$-0.780103\pi$
$461$	3.57386	−	6.19010i	0.166451	−	0.288302i	0.937170	+	0.348874i	$0.113436\pi$
$462$	4.91205	−	4.72370i	0.228529	−	0.219766i
$463$	−6.57780			−0.305696			−0.152848	−	0.988250i	$-0.548845\pi$
$463$	−6.57780			−0.305696			−0.152848	+	0.988250i	$0.548845\pi$
$464$		−	0.477682i		−	0.0221758i
$465$	−19.8793	−	16.6885i	−0.921881	−	0.773911i
$466$	21.9725			1.01786
$467$	10.6728	+	18.4857i	0.493876	+	0.855418i	0.999975	−	0.00705702i	$-0.00224634\pi$
$467$	10.6728	+	18.4857i	0.493876	+	0.855418i	−0.506099	+	0.862475i	$0.668913\pi$
$468$	10.7115	+	1.50459i	0.495139	+	0.0695496i
$469$	3.50302	+	7.90749i	0.161754	+	0.365134i
$470$	16.7591	−	9.67586i	0.773038	−	0.446314i
$471$	26.4795	−	9.63087i	1.22011	−	0.443767i
$472$	4.14626	−	2.39384i	0.190847	−	0.110186i
$473$	−10.3068	−	5.95065i	−0.473909	−	0.273611i
$474$	21.7702	+	18.2759i	0.999938	+	0.839439i
$475$	−46.7806	−	27.0088i	−2.14644	−	1.23925i
$476$	7.01109	+	0.750093i	0.321353	+	0.0343805i
$477$	3.84188	−	10.5404i	0.175908	−	0.482613i
$478$	−8.97332	+	15.5422i	−0.410430	+	0.710886i
$479$	−25.0454			−1.14435			−0.572177	−	0.820130i	$-0.693901\pi$
$479$	−25.0454			−1.14435			−0.572177	+	0.820130i	$0.693901\pi$
$480$	−6.93408	+	2.52200i	−0.316496	+	0.115113i
$481$	36.9460	−	7.87371i	1.68459	−	0.359010i
$482$	−16.4325			−0.748478
$483$	0.503245	+	0.523310i	0.0228984	+	0.0238114i
$484$	4.39425	+	7.61106i	0.199739	+	0.345957i
$485$		−	15.4358i		−	0.700903i
$486$	11.9529	−	10.0064i	0.542196	−	0.453898i
$487$	−17.5926	−	30.4712i	−0.797195	−	1.38078i	−0.921436	−	0.388530i	$-0.872983\pi$
$487$	−17.5926	−	30.4712i	−0.797195	−	1.38078i	0.124241	−	0.992252i	$-0.460350\pi$
$488$	−2.64025			−0.119518
$489$	−7.77380	+	9.26014i	−0.351543	+	0.418758i
$490$	−22.0860	−	20.0357i	−0.997742	−	0.905119i
$491$	−27.3749	+	15.8049i	−1.23541	+	0.713265i	−0.968153	−	0.250360i	$-0.919451\pi$
$491$	−27.3749	+	15.8049i	−1.23541	+	0.713265i	−0.267258	+	0.963625i	$0.586118\pi$
$492$	−6.08594	−	16.7329i	−0.274375	−	0.754379i
$493$	−1.10250	−	0.636527i	−0.0496539	−	0.0286677i
$494$	14.4886	−	3.08772i	0.651871	−	0.138923i
$495$	12.2096	+	14.5644i	0.548780	+	0.654620i
$496$	−3.04646	+	1.75887i	−0.136790	+	0.0789757i
$497$	2.50332	−	23.3985i	0.112289	−	1.04956i
$498$	13.6243	−	4.95531i	0.610520	−	0.222053i
$499$	−8.10265	−	14.0342i	−0.362725	−	0.628257i	0.625684	−	0.780077i	$-0.284820\pi$
$499$	−8.10265	−	14.0342i	−0.362725	−	0.628257i	−0.988408	+	0.151819i	$0.951487\pi$
$500$	17.3536	+	30.0573i	0.776077	+	1.34420i
$501$	−14.0565	−	2.48187i	−0.627999	−	0.110882i
$502$	9.70884	−	5.60540i	0.433327	−	0.250181i
$503$	16.5718	−	28.7032i	0.738900	−	1.27981i	−0.214091	−	0.976814i	$-0.568679\pi$
$503$	16.5718	−	28.7032i	0.738900	−	1.27981i	0.952991	−	0.302999i	$-0.0979879\pi$
$504$	4.42318	+	6.59056i	0.197024	+	0.293567i
$505$	10.2645	+	17.7787i	0.456765	+	0.791140i
$506$	0.204040	−	0.117802i	0.00907067	−	0.00523696i
$507$	15.6549	+	16.1840i	0.695260	+	0.718758i
$508$	−2.85690	+	4.94830i	−0.126755	+	0.219545i
$509$	5.26636	−	9.12160i	0.233427	−	0.404308i	−0.725387	−	0.688341i	$-0.758339\pi$
$509$	5.26636	−	9.12160i	0.233427	−	0.404308i	0.958814	+	0.284033i	$0.0916726\pi$
$510$	−3.41908	+	19.3646i	−0.151399	+	0.857479i
$511$	−1.95991	+	18.3192i	−0.0867014	+	0.810395i
$512$			1.00000i			0.0441942i
$513$	10.6873	−	18.4815i	0.471855	−	0.815980i
$514$	−2.13679	+	1.23368i	−0.0942498	+	0.0544151i
$515$	−9.17307	−	5.29607i	−0.404214	−	0.233373i
$516$	8.91247	−	10.6165i	0.392349	−	0.467366i
$517$	−5.85043	+	3.37775i	−0.257302	+	0.148553i
$518$	22.3954	+	16.3350i	0.983997	+	0.717718i
$519$	17.5580	−	20.9150i	0.770710	−	0.918068i
$520$	−14.6103	−	4.73856i	−0.640704	−	0.207800i
$521$	9.84785	−	17.0570i	0.431442	−	0.747279i	−0.565556	−	0.824710i	$-0.691338\pi$
$521$	9.84785	−	17.0570i	0.431442	−	0.747279i	0.996998	+	0.0774306i	$0.0246716\pi$
$522$	−0.248198	−	1.41139i	−0.0108633	−	0.0617748i
$523$	2.85947	+	1.65092i	0.125036	+	0.0721896i	0.561213	−	0.827671i	$-0.310335\pi$
$523$	2.85947	+	1.65092i	0.125036	+	0.0721896i	−0.436177	+	0.899861i	$0.643668\pi$
$524$	7.49454	−	12.9809i	0.327400	−	0.567074i
$525$	43.4265	−	41.7614i	1.89529	−	1.82262i
$526$	−8.36047	+	14.4808i	−0.364534	+	0.631391i
$527$			9.37503i			0.408383i
$528$	2.42062	−	0.880404i	0.105344	−	0.0383147i
$529$	−11.4874	−	19.8968i	−0.499454	−	0.865080i
$530$	−7.96526	+	13.7962i	−0.345989	+	0.599270i
$531$	11.0070	−	9.22735i	0.477662	−	0.400433i
$532$	8.78247	+	6.40585i	0.380768	+	0.277729i
$533$	11.4348	−	35.2568i	0.495297	−	1.52714i
$534$	3.58090	−	20.2811i	0.154961	−	0.877648i
$535$		−	39.1842i		−	1.69408i
$536$			3.26889i			0.141195i
$537$	−9.98129	−	8.37920i	−0.430724	−	0.361589i
$538$			2.62459i			0.113154i
$539$	7.70999	+	6.99426i	0.332093	+	0.301264i
$540$	−19.1775	+	11.0545i	−0.825266	+	0.475711i
$541$	14.3963	+	24.9351i	0.618944	+	1.07204i	0.989679	+	0.143304i	$0.0457726\pi$
$541$	14.3963	+	24.9351i	0.618944	+	1.07204i	−0.370735	+	0.928739i	$0.620894\pi$
$542$	4.45715	+	7.72000i	0.191451	+	0.331603i
$543$	−4.38674	−	3.68263i	−0.188253	−	0.158037i
$544$	2.30802	+	1.33253i	0.0989554	+	0.0571319i
$545$	−28.6989			−1.22933
$546$	−1.17824	+	16.4806i	−0.0504238	+	0.705307i
$547$	19.4820			0.832989			0.416495	−	0.909138i	$-0.363258\pi$
$547$	19.4820			0.832989			0.416495	+	0.909138i	$0.363258\pi$
$548$	−9.23788	−	5.33349i	−0.394622	−	0.227835i
$549$	−7.80104	+	1.37185i	−0.332940	+	0.0585489i
$550$	−9.77575	−	16.9321i	−0.416839	−	0.721987i
$551$	−0.981311	−	1.69968i	−0.0418053	−	0.0724089i
$552$	0.0937949	+	0.257883i	0.00399218	+	0.0109762i
$553$	−25.5864	+	35.0792i	−1.08805	+	1.49172i
$554$		−	29.2308i		−	1.24190i
$555$	−49.7042	+	59.2076i	−2.10983	+	2.51322i
$556$		−	11.0543i		−	0.468807i
$557$			37.9692i			1.60881i	0.594083	+	0.804403i	$0.297515\pi$
$557$			37.9692i			1.60881i	−0.594083	+	0.804403i	$0.702485\pi$
$558$	−8.08736	+	6.77978i	−0.342365	+	0.287011i
$559$	28.2214	−	6.01437i	1.19364	−	0.254381i
$560$	−4.56508	−	10.3049i	−0.192910	−	0.435462i
$561$	1.19357	−	6.75999i	0.0503925	−	0.285407i
$562$	−9.42820	+	16.3301i	−0.397705	+	0.688845i
$563$	−5.46168	−	9.45991i	−0.230183	−	0.398688i	0.727679	−	0.685918i	$-0.240599\pi$
$563$	−5.46168	−	9.45991i	−0.230183	−	0.398688i	−0.957862	+	0.287230i	$0.907266\pi$
$564$	−2.68938	−	7.39428i	−0.113243	−	0.311355i
$565$		−	72.7765i		−	3.06173i
$566$	−0.174849	+	0.302847i	−0.00734944	+	0.0127296i
$567$	16.4934	+	17.1746i	0.692657	+	0.721267i
$568$	4.44713	−	7.70265i	0.186597	−	0.323196i
$569$	9.14518	+	5.27997i	0.383386	+	0.221348i	0.679290	−	0.733870i	$-0.262288\pi$
$569$	9.14518	+	5.27997i	0.383386	+	0.221348i	−0.295905	+	0.955218i	$0.595621\pi$
$570$	−19.4918	+	23.2186i	−0.816420	+	0.972519i
$571$	8.25387	−	14.2961i	0.345414	−	0.598274i	−0.640015	−	0.768362i	$-0.721072\pi$
$571$	8.25387	−	14.2961i	0.345414	−	0.598274i	0.985429	+	0.170088i	$0.0544053\pi$
$572$	5.10031	+	1.65419i	0.213255	+	0.0691650i
$573$	−34.4803	−	28.9459i	−1.44043	−	1.20923i
$574$	24.8672	−	11.0162i	1.03794	−	0.459807i
$575$	1.80388	−	1.04147i	0.0752270	−	0.0434323i
$576$	0.519589	+	2.95466i	0.0216496	+	0.123111i
$577$	5.28817	+	3.05312i	0.220149	+	0.127103i	0.606019	−	0.795450i	$-0.292765\pi$
$577$	5.28817	+	3.05312i	0.220149	+	0.127103i	−0.385870	+	0.922553i	$0.626099\pi$
$578$	−8.57141	+	4.94871i	−0.356524	+	0.205839i
$579$	13.4476	−	16.0188i	0.558864	−	0.665718i
$580$			2.03491i			0.0844949i
$581$	8.96962	+	20.2474i	0.372123	+	0.840006i
$582$	−6.18041	−	1.09123i	−0.256186	−	0.0452331i
$583$	2.78059	−	4.81613i	0.115160	−	0.199464i
$584$	−3.48176	+	6.03059i	−0.144076	+	0.249548i
$585$	−45.6306	−	6.40949i	−1.88659	−	0.265000i
$586$	9.27029	−	5.35220i	0.382952	−	0.221098i
$587$	1.08728	+	1.88323i	0.0448769	+	0.0777291i	0.887591	−	0.460632i	$-0.152377\pi$
$587$	1.08728	+	1.88323i	0.0448769	+	0.0777291i	−0.842714	+	0.538361i	$0.819044\pi$
$588$	−9.58355	+	7.42668i	−0.395219	+	0.306271i
$589$	−7.22658	+	12.5168i	−0.297766	+	0.515746i
$590$	−17.6629	+	10.1977i	−0.727171	+	0.419832i
$591$	−0.704439	+	3.98972i	−0.0289767	+	0.164115i
$592$	5.23854	+	9.07342i	0.215303	+	0.372915i
$593$	0.707096	+	1.22473i	0.0290370	+	0.0502935i	0.880179	−	0.474642i	$-0.157423\pi$
$593$	0.707096	+	1.22473i	0.0290370	+	0.0502935i	−0.851142	+	0.524936i	$0.824089\pi$
$594$	6.69466	−	3.85902i	0.274685	−	0.158338i
$595$	−29.8670	−	3.19537i	−1.22443	−	0.130997i
$596$	−7.27861	+	4.20231i	−0.298144	+	0.172133i
$597$	−3.21914	+	18.2322i	−0.131751	+	0.746195i
$598$	−0.176231	+	0.543368i	−0.00720660	+	0.0222200i
$599$	13.9159	+	8.03436i	0.568589	+	0.328275i	0.756586	−	0.653894i	$-0.226866\pi$
$599$	13.9159	+	8.03436i	0.568589	+	0.328275i	−0.187996	+	0.982170i	$0.560199\pi$
$600$	21.4003	−	7.78350i	0.873662	−	0.317760i
$601$	−26.6115	+	15.3641i	−1.08550	+	0.626716i	−0.932376	−	0.361490i	$-0.882268\pi$
$601$	−26.6115	+	15.3641i	−1.08550	+	0.626716i	−0.153128	+	0.988206i	$0.548935\pi$
$602$	17.1068	+	12.4776i	0.697222	+	0.508547i
$603$	1.69848	+	9.65847i	0.0691675	+	0.393323i
$604$	22.5533			0.917679
$605$	−18.7193	−	32.4229i	−0.761050	−	1.31818i
$606$	7.84414	−	2.85299i	0.318646	−	0.115895i
$607$			32.4993i			1.31910i	0.751659	+	0.659552i	$0.229254\pi$
$607$			32.4993i			1.31910i	−0.751659	+	0.659552i	$0.770746\pi$
$608$	2.05432	+	3.55819i	0.0833137	+	0.144304i
$609$	2.12509	−	0.525128i	0.0861130	−	0.0212793i
$610$	11.2474			0.455393
$611$	5.05305	−	15.5800i	0.204425	−	0.630298i
$612$	7.51178	+	2.73797i	0.303646	+	0.110676i
$613$	−8.70697			−0.351671			−0.175836	−	0.984420i	$-0.556263\pi$
$613$	−8.70697			−0.351671			−0.175836	+	0.984420i	$0.556263\pi$
$614$	2.02339	−	3.50461i	0.0816572	−	0.141434i
$615$	25.9259	+	71.2817i	1.04543	+	2.87435i
$616$	1.59362	+	3.59734i	0.0642089	+	0.144941i
$617$	29.1565	+	16.8335i	1.17380	+	0.677691i	0.954571	−	0.297983i	$-0.0963139\pi$
$617$	29.1565	+	16.8335i	1.17380	+	0.677691i	0.219225	+	0.975674i	$0.429647\pi$
$618$	−2.76901	+	3.29844i	−0.111386	+	0.132683i
$619$	−15.4503	−	8.92024i	−0.621001	−	0.358535i	0.156258	−	0.987716i	$-0.450057\pi$
$619$	−15.4503	−	8.92024i	−0.621001	−	0.358535i	−0.777259	+	0.629181i	$0.783390\pi$
$620$	12.9778	−	7.49274i	0.521201	−	0.300916i
$621$	0.411126	+	0.713223i	0.0164979	+	0.0286207i
$622$	14.1981	−	8.19728i	0.569292	−	0.328681i
$623$	31.2805	+	3.34660i	1.25323	+	0.134079i
$624$	−2.93017	+	5.51490i	−0.117301	+	0.220773i
$625$	−41.0575	−	71.1137i	−1.64230	−	2.84455i
$626$	−19.7687			−0.790115
$627$	6.80438	−	8.10537i	0.271741	−	0.323697i
$628$			16.2677i			0.649153i
$629$	27.9221			1.11333
$630$	−18.8426	−	28.0756i	−0.750706	−	1.11856i
$631$	−16.4881	+	28.5582i	−0.656380	+	1.13688i	0.325166	+	0.945657i	$0.394580\pi$
$631$	−16.4881	+	28.5582i	−0.656380	+	1.13688i	−0.981546	+	0.191227i	$0.938753\pi$
$632$	−14.2122	+	8.20543i	−0.565332	+	0.326394i
$633$	7.59295	+	1.34064i	0.301793	+	0.0532856i
$634$	8.06617			0.320349
$635$	12.1703	−	21.0796i	0.482964	−	0.836518i
$636$	4.96084	+	4.16457i	0.196710	+	0.165136i
$637$	−25.2387	−	0.0805006i	−0.999995	−	0.00318955i
$638$		−	0.710366i		−	0.0281237i
$639$	9.13754	−	25.0694i	0.361476	−	0.991730i
$640$		−	4.25996i		−	0.168390i
$641$	14.0185	−	8.09360i	0.553698	−	0.319678i	−0.196914	−	0.980421i	$-0.563092\pi$
$641$	14.0185	−	8.09360i	0.553698	−	0.319678i	0.750612	+	0.660743i	$0.229759\pi$
$642$	−15.6891	−	2.77013i	−0.619201	−	0.109328i
$643$	−31.2120	−	18.0203i	−1.23088	−	0.710650i	−0.263668	−	0.964613i	$-0.584932\pi$
$643$	−31.2120	−	18.0203i	−1.23088	−	0.710650i	−0.967214	+	0.253963i	$0.918266\pi$
$644$	−0.383247	+	0.169778i	−0.0151020	+	0.00669021i
$645$	−37.9668	+	45.2260i	−1.49494	+	1.78077i
$646$	10.9498			0.430814
$647$	11.1609			0.438782			0.219391	−	0.975637i	$-0.429593\pi$
$647$	11.1609			0.438782			0.219391	+	0.975637i	$0.429593\pi$
$648$	3.07042	+	8.46005i	0.120618	+	0.332342i
$649$	6.16595	−	3.55991i	0.242035	−	0.139739i
$650$	45.0910	+	14.6244i	1.76861	+	0.573615i
$651$	−11.1739	−	11.6194i	−0.437938	−	0.455400i
$652$	−3.49025	−	6.04529i	−0.136689	−	0.236752i
$653$	−25.9762	−	14.9973i	−1.01653	−	0.586892i	−0.103430	−	0.994637i	$-0.532982\pi$
$653$	−25.9762	−	14.9973i	−1.01653	−	0.586892i	−0.913096	+	0.407745i	$0.866315\pi$
$654$	−2.02887	+	11.4909i	−0.0793353	+	0.449330i
$655$	−31.9265	+	55.2982i	−1.24747	+	2.16068i
$656$	10.2799			0.401363
$657$	−7.15401	+	19.6275i	−0.279104	+	0.765740i
$658$	10.9888	−	4.86805i	0.428389	−	0.189777i
$659$	−10.5441	−	6.08763i	−0.410739	−	0.237141i	0.280368	−	0.959893i	$-0.409544\pi$
$659$	−10.5441	−	6.08763i	−0.410739	−	0.237141i	−0.691107	+	0.722752i	$0.742877\pi$
$660$	−10.3117	+	3.75049i	−0.401384	+	0.145988i
$661$		−	26.1449i		−	1.01692i	−0.861086	−	0.508460i	$-0.830215\pi$
$661$		−	26.1449i		−	1.01692i	0.861086	−	0.508460i	$-0.169785\pi$
$662$	−15.9509	−	9.20927i	−0.619951	−	0.357929i
$663$	8.82392	+	14.1117i	0.342693	+	0.548052i
$664$			8.37013i			0.324824i
$665$	−37.4130	−	27.2887i	−1.45081	−	1.05821i
$666$	20.1926	+	24.0870i	0.782446	+	0.933352i
$667$	0.0756796			0.00293033
$668$	4.12054	−	7.13698i	0.159428	−	0.276138i
$669$	1.32900	−	7.52701i	0.0513819	−	0.291011i
$670$		−	13.9254i		−	0.537984i
$671$	−3.92635			−0.151575
$672$	−4.44876	+	1.09933i	−0.171615	+	0.0424074i
$673$	−10.0870	−	17.4712i	−0.388825	−	0.673464i	0.603467	−	0.797388i	$-0.293785\pi$
$673$	−10.0870	−	17.4712i	−0.388825	−	0.673464i	−0.992292	+	0.123924i	$0.960452\pi$
$674$	14.5978	+	8.42803i	0.562285	+	0.324636i
$675$	59.1863	−	34.1170i	2.27808	−	1.31316i
$676$	−11.8704	+	5.30024i	−0.456556	+	0.203855i
$677$	−0.365307	−	0.632731i	−0.0140399	−	0.0243178i	0.858920	−	0.512110i	$-0.171136\pi$
$677$	−0.365307	−	0.632731i	−0.0140399	−	0.0243178i	−0.872960	+	0.487792i	$0.837803\pi$
$678$	−29.1393	−	5.14494i	−1.11909	−	0.197590i
$679$	1.01983	−	9.53236i	0.0391377	−	0.365818i
$680$	−9.83207	−	5.67655i	−0.377043	−	0.217686i
$681$	33.5125	+	5.91709i	1.28420	+	0.226743i
$682$	−4.53042	+	2.61564i	−0.173479	+	0.100158i
$683$	−7.13126	+	4.11724i	−0.272870	+	0.157542i	−0.630191	−	0.776440i	$-0.717024\pi$
$683$	−7.13126	+	4.11724i	−0.272870	+	0.157542i	0.357321	+	0.933982i	$0.383690\pi$
$684$	7.91862	+	9.44584i	0.302776	+	0.361171i
$685$	39.3530	+	22.7205i	1.50360	+	0.868105i
$686$	−12.3154	−	13.8322i	−0.470205	−	0.528117i
$687$	−3.84342	+	21.7679i	−0.146636	+	0.830498i
$688$	4.00148	+	6.93077i	0.152555	+	0.264233i
$689$	2.81037	+	13.1871i	0.107066	+	0.502390i
$690$	−0.399563	−	1.09857i	−0.0152111	−	0.0418220i
$691$	25.9028	+	14.9550i	0.985388	+	0.568914i	0.903892	−	0.427760i	$-0.140697\pi$
$691$	25.9028	+	14.9550i	0.985388	+	0.568914i	0.0814953	+	0.996674i	$0.474030\pi$
$692$	7.88311	+	13.6540i	0.299671	+	0.519045i
$693$	6.57776	+	9.80090i	0.249868	+	0.372305i
$694$	−15.6755			−0.595035
$695$			47.0910i			1.78626i
$696$	0.814766	+	0.143858i	0.0308836	+	0.00545292i
$697$	13.6983	−	23.7262i	0.518861	−	0.898694i
$698$	18.8576			0.713771
$699$	−6.61722	+	37.4778i	−0.250286	+	1.41754i
$700$	14.0889	+	31.8035i	0.532512	+	1.20206i
$701$			11.4510i			0.432498i	0.976338	+	0.216249i	$0.0693824\pi$
$701$			11.4510i			0.432498i	−0.976338	+	0.216249i	$0.930618\pi$
$702$	−5.79219	+	17.8171i	−0.218612	+	0.672465i
$703$	37.2794	+	21.5233i	1.40602	+	0.811767i
$704$			1.48711i			0.0560476i
$705$	11.4567	+	31.4994i	0.431483	+	1.18634i
$706$	−15.9414	−	9.20379i	−0.599964	−	0.346389i
$707$	5.16422	+	11.6574i	0.194220	+	0.438421i
$708$	2.83442	+	7.79307i	0.106524	+	0.292881i
$709$	17.0315			0.639632			0.319816	−	0.947480i	$-0.396379\pi$
$709$	17.0315			0.639632			0.319816	+	0.947480i	$0.396379\pi$
$710$	−18.9446	+	32.8130i	−0.710978	+	1.23145i
$711$	−37.7289	+	31.6288i	−1.41494	+	1.18617i
$712$	10.2974	+	5.94520i	0.385911	+	0.222806i
$713$	−0.278660	−	0.482654i	−0.0104359	−	0.0180755i
$714$	−3.39086	+	11.7327i	−0.126900	+	0.439085i
$715$	−21.7272	−	7.04677i	−0.812549	−	0.263534i
$716$	6.51608	−	3.76206i	0.243517	−	0.140595i
$717$	−23.8075	−	19.9862i	−0.889108	−	0.746398i
$718$	−33.7438			−1.25931
$719$	−16.9630			−0.632613			−0.316306	−	0.948657i	$-0.602443\pi$
$719$	−16.9630			−0.632613			−0.316306	+	0.948657i	$0.602443\pi$
$720$	−2.21343	−	12.5868i	−0.0824898	−	0.469081i
$721$	−5.31491	−	3.87665i	−0.197938	−	0.144374i
$722$	−1.83515	−	1.05953i	−0.0682973	−	0.0394315i
$723$	4.94878	−	28.0283i	0.184047	−	1.04238i
$724$	2.86379	−	1.65341i	0.106432	−	0.0614485i
$725$		−	6.28022i		−	0.233242i
$726$	−14.3053	+	5.20299i	−0.530920	+	0.193101i
$727$			35.4828i			1.31598i	0.753025	+	0.657992i	$0.228594\pi$
$727$			35.4828i			1.31598i	−0.753025	+	0.657992i	$0.771406\pi$
$728$	−8.70951	−	3.89159i	−0.322796	−	0.144232i
$729$	13.4678	+	23.4012i	0.498808	+	0.866713i
$730$	14.8322	−	25.6901i	0.548964	−	0.950834i
$731$	21.3285			0.788861
$732$	0.795134	−	4.50339i	0.0293890	−	0.166450i
$733$	7.97236	−	4.60284i	0.294466	−	0.170010i	−0.345488	−	0.938423i	$-0.612287\pi$
$733$	7.97236	−	4.60284i	0.294466	−	0.170010i	0.639954	+	0.768413i	$0.278953\pi$
$734$	−17.0227	+	29.4842i	−0.628320	+	1.08828i
$735$	40.8256	−	31.6374i	1.50587	−	1.16696i
$736$	−0.158431			−0.00583985
$737$			4.86121i			0.179065i
$738$	30.3737	−	5.34133i	1.11807	−	0.196617i
$739$	−35.7615			−1.31551			−0.657754	−	0.753232i	$-0.728494\pi$
$739$	−35.7615			−1.31551			−0.657754	+	0.753232i	$0.728494\pi$
$740$	−22.3160	−	38.6524i	−0.820353	−	1.42089i
$741$	0.903263	+	25.6426i	0.0331822	+	0.942003i
$742$	−5.83045	+	7.99359i	−0.214043	+	0.293454i
$743$	3.57295	−	2.06284i	0.131079	−	0.0756783i	−0.433027	−	0.901381i	$-0.642554\pi$
$743$	3.57295	−	2.06284i	0.131079	−	0.0756783i	0.564106	+	0.825703i	$0.309221\pi$
$744$	−2.08259	−	5.72594i	−0.0763513	−	0.209923i
$745$	31.0066	−	17.9017i	1.13599	−	0.655867i
$746$	−26.7171	−	15.4251i	−0.978182	−	0.564754i
$747$	4.34903	+	24.7309i	0.159123	+	0.904856i
$748$	3.43228	+	1.98163i	0.125496	+	0.0724554i
$749$	2.58888	−	24.1982i	0.0945956	−	0.884181i
$750$	−56.4940	+	20.5475i	−2.06287	+	0.750287i
$751$	14.4353	−	25.0028i	0.526753	−	0.912363i	−0.472761	−	0.881191i	$-0.656743\pi$
$751$	14.4353	−	25.0028i	0.526753	−	0.912363i	0.999514	−	0.0311726i	$-0.00992416\pi$
$752$	4.54269			0.165655
$753$	6.63705	+	18.2482i	0.241868	+	0.665000i
$754$	1.15313	+	1.27931i	0.0419945	+	0.0465896i
$755$	−96.0761			−3.49657
$756$	−12.5734	+	5.55967i	−0.457290	+	0.202203i
$757$	17.6464	+	30.5645i	0.641371	+	1.11089i	0.985127	+	0.171828i	$0.0549673\pi$
$757$	17.6464	+	30.5645i	0.641371	+	1.11089i	−0.343756	+	0.939059i	$0.611699\pi$
$758$		−	6.23514i		−	0.226470i
$759$	0.139483	+	0.383501i	0.00506293	+	0.0139202i
$760$	−8.75134	−	15.1578i	−0.317444	−	0.549830i
$761$	31.0291			1.12480			0.562402	−	0.826864i	$-0.309877\pi$
$761$	31.0291			1.12480			0.562402	+	0.826864i	$0.309877\pi$
$762$	−7.57978	−	6.36315i	−0.274586	−	0.230513i
$763$	−17.7230	−	1.89613i	−0.641616	−	0.0686443i
$764$	22.5097	−	12.9960i	0.814374	−	0.470179i
$765$	−31.9999	−	11.6636i	−1.15696	−	0.421700i
$766$	−4.72231	−	2.72642i	−0.170624	−	0.0985097i
$767$	−5.32557	+	16.4202i	−0.192295	+	0.592900i
$768$	−1.70567	−	0.301159i	−0.0615480	−	0.0108671i
$769$	23.8845	−	13.7897i	0.861297	−	0.497270i	−0.00314940	−	0.999995i	$-0.501002\pi$
$769$	23.8845	−	13.7897i	0.861297	−	0.497270i	0.864446	+	0.502725i	$0.167669\pi$
$770$	−6.78878	−	15.3246i	−0.244651	−	0.552259i
$771$	−1.46073	−	4.01619i	−0.0526069	−	0.144639i
$772$	6.03765	+	10.4575i	0.217300	+	0.376375i
$773$	−0.356834	−	0.618055i	−0.0128344	−	0.0222299i	0.859537	−	0.511074i	$-0.170752\pi$
$773$	−0.356834	−	0.618055i	−0.0128344	−	0.0222299i	−0.872371	+	0.488844i	$0.837419\pi$
$774$	15.4242	+	18.3990i	0.554411	+	0.661337i
$775$	−40.0527	+	23.1244i	−1.43874	+	0.830654i
$776$	1.81173	−	3.13800i	0.0650372	−	0.112648i
$777$	−34.6066	+	33.2797i	−1.24151	+	1.19390i
$778$	−19.2846	−	33.4019i	−0.691387	−	1.19752i
$779$	36.5779	−	21.1182i	1.31054	−	0.756639i
$780$	12.4824	−	23.4933i	0.446943	−	0.841194i
$781$	6.61337	−	11.4547i	0.236645	−	0.409881i
$782$	−0.211115	+	0.365662i	−0.00754945	+	0.0130760i
$783$	2.48211	+	0.00170771i	0.0887032	+	6.10287e-5i
$784$	−2.13832	−	6.66540i	−0.0763685	−	0.238050i
$785$		−	69.2999i		−	2.47342i
$786$	19.8841	+	16.6925i	0.709242	+	0.595402i
$787$	1.94781	−	1.12457i	0.0694320	−	0.0400866i	−0.464882	−	0.885373i	$-0.653903\pi$
$787$	1.94781	−	1.12457i	0.0694320	−	0.0400866i	0.534314	+	0.845286i	$0.320570\pi$
$788$	−2.02572	−	1.16955i	−0.0721631	−	0.0416634i
$789$	−22.1815	−	18.6212i	−0.789684	−	0.662932i
$790$	60.5436	−	34.9548i	2.15404	−	1.24364i
$791$	4.80831	−	44.9431i	0.170964	−	1.59799i
$792$	0.772687	+	4.39391i	0.0274563	+	0.156131i
$793$	7.07101	−	6.37360i	0.251099	−	0.226333i
$794$	13.4667	−	23.3251i	0.477917	−	0.827776i
$795$	−21.1330	−	17.7409i	−0.749510	−	0.629206i
$796$	−9.25711	−	5.34459i	−0.328110	−	0.189434i
$797$	0.0987658	−	0.171067i	0.00349846	−	0.00605952i	−0.864271	−	0.503027i	$-0.832220\pi$
$797$	0.0987658	−	0.171067i	0.00349846	−	0.00605952i	0.867769	+	0.496967i	$0.165553\pi$
$798$	−13.5712	+	13.0508i	−0.480414	+	0.461993i
$799$	6.05329	−	10.4846i	0.214150	−	0.370919i
$800$			13.1473i			0.464827i
$801$	33.5144	+	12.2156i	1.18417	+	0.431619i
$802$	−4.63122	−	8.02151i	−0.163534	−	0.283249i
$803$	−5.17777	+	8.96817i	−0.182720	+	0.316480i
$804$	−5.57564	−	0.984455i	−0.196638	−	0.0347190i
$805$	1.63262	−	0.723250i	0.0575423	−	0.0254912i
$806$	3.91296	−	12.0647i	0.137828	−	0.424962i
$807$	−4.47668	−	0.790419i	−0.157587	−	0.0278241i
$808$			4.81906i			0.169534i
$809$		−	11.8319i		−	0.415986i	−0.978130	−	0.207993i	$-0.933307\pi$
$809$		−	11.8319i		−	0.415986i	0.978130	−	0.207993i	$-0.0666932\pi$
$810$	−13.0799	−	36.0395i	−0.459580	−	1.26630i
$811$			25.6241i			0.899785i	0.893083	+	0.449893i	$0.148538\pi$
$811$			25.6241i			0.899785i	−0.893083	+	0.449893i	$0.851462\pi$
$812$	−0.134445	+	1.25666i	−0.00471810	+	0.0440999i
$813$	−14.5101	+	5.27747i	−0.508890	+	0.185089i
$814$	7.79030	+	13.4932i	0.273050	+	0.472936i
$815$	14.8683	+	25.7527i	0.520815	+	0.902078i
$816$	−2.96794	+	3.53540i	−0.103899	+	0.123764i
$817$	28.4761	+	16.4407i	0.996252	+	0.575186i
$818$	15.2524			0.533288
$819$	−27.7557	−	6.97297i	−0.969862	−	0.243655i
$820$	−43.7920			−1.52928
$821$	2.68291	+	1.54898i	0.0936344	+	0.0540598i	0.546086	−	0.837729i	$-0.316117\pi$
$821$	2.68291	+	1.54898i	0.0936344	+	0.0540598i	−0.452452	+	0.891789i	$0.649450\pi$
$822$	11.8792	−	14.1505i	0.414336	−	0.493556i
$823$	−0.233792	−	0.404940i	−0.00814948	−	0.0141153i	0.861922	−	0.507041i	$-0.169261\pi$
$823$	−0.233792	−	0.404940i	−0.00814948	−	0.0141153i	−0.870071	+	0.492926i	$0.835927\pi$
$824$	−1.24322	−	2.15332i	−0.0433096	−	0.0750145i
$825$	31.8246	−	11.5749i	1.10799	−	0.402988i
$826$	−11.5815	+	5.13060i	−0.402971	+	0.178516i
$827$			0.459061i			0.0159631i	0.999968	+	0.00798156i	$0.00254064\pi$
$827$			0.459061i			0.0159631i	−0.999968	+	0.00798156i	$0.997459\pi$
$828$	−0.468110	+	0.0823191i	−0.0162680	+	0.00286079i
$829$		−	3.30166i		−	0.114671i	−0.998355	−	0.0573357i	$-0.981739\pi$
$829$		−	3.30166i		−	0.114671i	0.998355	−	0.0573357i	$-0.0182605\pi$
$830$		−	35.6564i		−	1.23765i
$831$	49.8581	+	8.80312i	1.72956	+	0.305377i
$832$	−2.41401	−	2.67816i	−0.0836909	−	0.0928485i
$833$	−18.2332	−	3.94660i	−0.631744	−	0.136742i
$834$	18.8550	+	3.32910i	0.652895	+	0.115277i
$835$	−17.5533	+	30.4033i	−0.607458	+	1.05215i
$836$	3.05501	+	5.29142i	0.105660	+	0.183008i
$837$	−9.12848	−	15.8361i	−0.315526	−	0.547377i
$838$		−	21.5711i		−	0.745160i
$839$	−0.978193	+	1.69428i	−0.0337710	+	0.0584930i	−0.882417	−	0.470468i	$-0.844085\pi$
$839$	−0.978193	+	1.69428i	−0.0337710	+	0.0584930i	0.848646	+	0.528961i	$0.177418\pi$
$840$	18.9516	−	4.68309i	0.653891	−	0.161582i
$841$	−14.3859	+	24.9171i	−0.496066	+	0.859211i
$842$	22.3661	+	12.9131i	0.770787	+	0.445014i
$843$	−25.0144	−	20.9993i	−0.861541	−	0.723256i
$844$	−2.22580	+	3.85520i	−0.0766152	+	0.132701i
$845$	50.5677	−	22.5788i	1.73958	−	0.776736i
$846$	13.4221	−	2.36033i	0.461462	−	0.0811500i
$847$	−9.41796	−	21.2595i	−0.323605	−	0.730485i
$848$	−3.23858	+	1.86979i	−0.111213	+	0.0642090i
$849$	−0.463899	−	0.389439i	−0.0159210	−	0.0133655i
$850$	30.3442	+	17.5192i	1.04080	+	0.600904i
$851$	−1.43751	+	0.829948i	−0.0492773	+	0.0284503i
$852$	11.7989	+	9.90504i	0.404223	+	0.339341i
$853$		−	26.7743i		−	0.916734i	−0.888763	−	0.458367i	$-0.848434\pi$
$853$		−	26.7743i		−	0.916734i	0.888763	−	0.458367i	$-0.151566\pi$
$854$	6.94580	+	0.743108i	0.237681	+	0.0254286i
$855$	−33.7331	−	40.2390i	−1.15365	−	1.37614i
$856$	4.59912	−	7.96591i	0.157195	−	0.272269i
$857$	−1.29961	+	2.25099i	−0.0443938	+	0.0768923i	−0.887369	−	0.461061i	$-0.847469\pi$
$857$	−1.29961	+	2.25099i	−0.0443938	+	0.0768923i	0.842975	+	0.537953i	$0.180802\pi$
$858$	−4.35749	+	8.20127i	−0.148762	+	0.279987i
$859$	−11.5553	+	6.67144i	−0.394261	+	0.227626i	−0.684005	−	0.729478i	$-0.739763\pi$
$859$	−11.5553	+	6.67144i	−0.394261	+	0.227626i	0.289744	+	0.957104i	$0.406430\pi$
$860$	−17.0462	−	29.5249i	−0.581270	−	1.00679i
$861$	11.3010	+	45.7329i	0.385136	+	1.55857i
$862$	5.41746	−	9.38332i	0.184520	−	0.319597i
$863$	−29.7858	+	17.1968i	−1.01392	+	0.585387i	−0.912337	−	0.409440i	$-0.865724\pi$
$863$	−29.7858	+	17.1968i	−1.01392	+	0.585387i	−0.101583	+	0.994827i	$0.532391\pi$
$864$	−5.19615	−	0.00357501i	−0.176777	−	0.000121624i
$865$	−33.5818	−	58.1653i	−1.14181	−	1.97768i
$866$	−8.95476	−	15.5101i	−0.304295	−	0.527055i
$867$	−5.85950	−	16.1103i	−0.198999	−	0.547136i
$868$	8.50947	−	3.76970i	0.288830	−	0.127952i
$869$	−21.1352	+	12.2024i	−0.716961	+	0.413938i
$870$	−3.47087	−	0.612830i	−0.117674	−	0.0207769i
$871$	−7.89115	−	8.75461i	−0.267381	−	0.296639i
$872$	−5.83432	−	3.36845i	−0.197575	−	0.114070i
$873$	3.72257	−	10.2131i	0.125990	−	0.345661i
$874$	−0.563728	+	0.325469i	−0.0190684	+	0.0110091i
$875$	−37.1930	−	83.9572i	−1.25735	−	2.83827i
$876$	−9.23763	−	7.75490i	−0.312111	−	0.262014i
$877$	11.3196			0.382237			0.191119	−	0.981567i	$-0.438788\pi$
$877$	11.3196			0.382237			0.191119	+	0.981567i	$0.438788\pi$
$878$	−3.56935	−	6.18229i	−0.120460	−	0.208642i
$879$	6.33726	+	17.4239i	0.213750	+	0.587694i
$880$		−	6.33504i		−	0.213554i
$881$	−6.87833	−	11.9136i	−0.231737	−	0.401380i	0.726583	−	0.687079i	$-0.241107\pi$
$881$	−6.87833	−	11.9136i	−0.231737	−	0.401380i	−0.958319	+	0.285699i	$0.907774\pi$
$882$	−9.78128	−	18.5830i	−0.329353	−	0.625721i
$883$	−22.8717			−0.769694			−0.384847	−	0.922980i	$-0.625746\pi$
$883$	−22.8717			−0.769694			−0.384847	+	0.922980i	$0.625746\pi$
$884$	−9.39799	+	2.00284i	−0.316089	+	0.0673629i
$885$	−12.0745	−	33.1982i	−0.405881	−	1.11594i
$886$	−17.4968			−0.587817
$887$	11.4148	−	19.7711i	0.383273	−	0.663847i	−0.608255	−	0.793741i	$-0.708130\pi$
$887$	11.4148	−	19.7711i	0.383273	−	0.663847i	0.991528	+	0.129894i	$0.0414637\pi$
$888$	−17.0539	+	6.20267i	−0.572291	+	0.208148i
$889$	8.90848	−	12.2136i	0.298781	−	0.409631i
$890$	−43.8665	−	25.3264i	−1.47041	−	0.848941i
$891$	4.56606	+	12.5810i	0.152969	+	0.421481i
$892$	3.82172	+	2.20647i	0.127961	+	0.0738781i
$893$	16.1638	−	9.33215i	0.540900	−	0.312289i
$894$	−4.97573	−	13.6805i	−0.166413	−	0.457543i
$895$	−27.7583	+	16.0262i	−0.927856	+	0.535698i
$896$	0.281454	−	2.63074i	0.00940271	−	0.0878868i
$897$	−0.873731	−	0.464231i	−0.0291730	−	0.0155002i
$898$	1.87364	+	3.24523i	0.0625241	+	0.108295i
$899$	−1.68036			−0.0560432
$900$	6.83120	+	38.8458i	0.227707	+	1.29486i
$901$			9.96626i			0.332024i
$902$	15.2874			0.509014
$903$	−26.4344	+	25.4208i	−0.879683	+	0.845952i
$904$	8.54191	−	14.7950i	0.284100	−	0.492075i
$905$	−12.1997	+	7.04347i	−0.405530	+	0.234133i
$906$	−6.79211	+	38.4684i	−0.225653	+	1.27803i
$907$	−3.75091			−0.124547			−0.0622734	−	0.998059i	$-0.519835\pi$
$907$	−3.75091			−0.124547			−0.0622734	+	0.998059i	$0.519835\pi$
$908$	−9.82387	+	17.0154i	−0.326017	+	0.564677i
$909$	2.50393	+	14.2387i	0.0830502	+	0.472268i
$910$	37.1022	+	16.5780i	1.22993	+	0.549557i
$911$		−	9.38466i		−	0.310927i	−0.987842	−	0.155464i	$-0.950313\pi$
$911$		−	9.38466i		−	0.310927i	0.987842	−	0.155464i	$-0.0496872\pi$
$912$	−6.68777	+	2.43241i	−0.221454	+	0.0805452i
$913$			12.4473i			0.411946i
$914$	10.8712	−	6.27651i	0.359588	−	0.207608i
$915$	−3.38724	+	19.1843i	−0.111979	+	0.634213i
$916$	−11.0523	−	6.38106i	−0.365179	−	0.210836i
$917$	−23.3697	+	32.0400i	−0.771735	+	1.05805i
$918$	−6.93230	+	11.9880i	−0.228800	+	0.395664i
$919$	13.1513			0.433822			0.216911	−	0.976191i	$-0.430402\pi$
$919$	13.1513			0.433822			0.216911	+	0.976191i	$0.430402\pi$
$920$	0.674911			0.0222512
$921$	5.36833	+	4.50667i	0.176893	+	0.148500i
$922$	−6.19010	+	3.57386i	−0.203860	+	0.117699i
$923$	6.68418	+	31.3644i	0.220013	+	1.03237i
$924$	−6.61581	+	1.63482i	−0.217644	+	0.0537817i
$925$	68.8727	+	119.291i	2.26452	+	3.92226i
$926$	5.69655	+	3.28890i	0.187200	+	0.108080i
$927$	−4.79214	−	5.71637i	−0.157394	−	0.187750i
$928$	−0.238841	+	0.413684i	−0.00784033	+	0.0135799i
$929$	−25.6188			−0.840526			−0.420263	−	0.907402i	$-0.638062\pi$
$929$	−25.6188			−0.840526			−0.420263	+	0.907402i	$0.638062\pi$
$930$	8.87175	+	24.3923i	0.290916	+	0.799856i
$931$	−21.3014	−	19.3240i	−0.698126	−	0.633317i
$932$	−19.0288	−	10.9863i	−0.623308	−	0.359867i
$933$	9.70596	+	26.6859i	0.317759	+	0.873658i
$934$		−	21.3455i		−	0.698446i
$935$	−14.6214	−	8.44166i	−0.478170	−	0.276072i
$936$	−8.52414	−	6.65876i	−0.278620	−	0.217648i
$937$			44.0425i			1.43881i	0.694593	+	0.719403i	$0.255585\pi$
$937$			44.0425i			1.43881i	−0.694593	+	0.719403i	$0.744415\pi$
$938$	0.920042	−	8.59960i	0.0300404	−	0.280787i
$939$	5.95351	−	33.7188i	0.194285	−	1.10037i
$940$	−19.3517			−0.631183
$941$	−14.6395	+	25.3563i	−0.477234	+	0.826593i	−0.999660	−	0.0260916i	$-0.991694\pi$
$941$	−14.6395	+	25.3563i	−0.477234	+	0.826593i	0.522426	+	0.852685i	$0.325027\pi$
$942$	−27.7473	−	4.89917i	−0.904057	−	0.159623i
$943$			1.62866i			0.0530364i
$944$	−4.78769			−0.155826
$945$	53.5622	−	23.6840i	1.74238	−	0.770440i
$946$	5.95065	+	10.3068i	0.193472	+	0.335104i
$947$	50.9573	+	29.4202i	1.65589	+	0.956028i	0.974582	+	0.224032i	$0.0719219\pi$
$947$	50.9573	+	29.4202i	1.65589	+	0.956028i	0.681308	+	0.731997i	$0.261411\pi$
$948$	−9.71561	−	26.7125i	−0.315548	−	0.867581i
$949$	−5.23321	−	24.5559i	−0.169877	−	0.797119i
$950$	27.0088	+	46.7806i	0.876281	+	1.51776i
$951$	−2.42920	+	13.7582i	−0.0787721	+	0.446141i
$952$	−5.69674	−	4.15515i	−0.184632	−	0.134669i
$953$	−0.646257	−	0.373117i	−0.0209343	−	0.0120864i	0.489496	−	0.872005i	$-0.337181\pi$
$953$	−0.646257	−	0.373117i	−0.0209343	−	0.0120864i	−0.510431	+	0.859919i	$0.670514\pi$
$954$	−8.59738	+	7.20734i	−0.278350	+	0.233346i
$955$	−95.8907	+	55.3625i	−3.10295	+	1.79149i
$956$	15.5422	−	8.97332i	0.502672	−	0.290218i
$957$	1.21165	+	0.213933i	0.0391670	+	0.00691547i
$958$	21.6900	+	12.5227i	0.700771	+	0.404590i
$959$	22.8013	+	16.6311i	0.736292	+	0.537045i
$960$	7.26609	+	1.28293i	0.234512	+	0.0414062i
$961$	−9.31273	−	16.1301i	−0.300411	−	0.520327i
$962$	−35.9330	−	11.6542i	−1.15853	−	0.375745i
$963$	9.44984	−	25.9262i	0.304517	−	0.835461i
$964$	14.2309	+	8.21623i	0.458348	+	0.264627i
$965$	−25.7202	−	44.5487i	−0.827962	−	1.43407i
$966$	−0.174168	−	0.704822i	−0.00560375	−	0.0226773i
$967$	6.94251			0.223256			0.111628	−	0.993750i	$-0.464393\pi$
$967$	6.94251			0.223256			0.111628	+	0.993750i	$0.464393\pi$
$968$		−	8.78850i		−	0.282473i
$969$	−3.29763	+	18.6767i	−0.105935	+	0.599983i
$970$	−7.71789	+	13.3678i	−0.247807	+	0.429213i
$971$	58.1358			1.86567			0.932834	−	0.360307i	$-0.117328\pi$
$971$	58.1358			1.86567			0.932834	+	0.360307i	$0.117328\pi$
$972$	−15.3547	+	2.68930i	−0.492503	+	0.0862594i
$973$	−3.11128	+	29.0810i	−0.0997430	+	0.932294i
$974$			35.1851i			1.12740i
$975$	−38.5239	+	72.5060i	−1.23375	+	2.32205i
$976$	2.28652	+	1.32012i	0.0731898	+	0.0422562i
$977$			2.07892i			0.0665105i	0.999447	+	0.0332552i	$0.0105874\pi$
$977$			2.07892i			0.0665105i	−0.999447	+	0.0332552i	$0.989413\pi$
$978$	11.3624	−	4.13261i	0.363329	−	0.132146i
$979$	15.3134	+	8.84118i	0.489418	+	0.282565i
$980$	9.10916	+	28.3944i	0.290982	+	0.907025i
$981$	−18.9887	−	6.92117i	−0.606261	−	0.220976i
$982$	31.6098			1.00871
$983$	−6.74253	+	11.6784i	−0.215053	+	0.372483i	−0.953289	−	0.302060i	$-0.902326\pi$
$983$	−6.74253	+	11.6784i	−0.215053	+	0.372483i	0.738236	+	0.674543i	$0.235659\pi$
$984$	−3.09588	+	17.5341i	−0.0986931	+	0.558967i
$985$	8.62948	+	4.98223i	0.274958	+	0.158747i
$986$	0.636527	+	1.10250i	0.0202711	+	0.0351106i
$987$	4.99390	+	20.2094i	0.158958	+	0.643271i
$988$	−14.0913	−	4.57024i	−0.448305	−	0.145399i
$989$	−1.09805	+	0.633960i	−0.0349160	+	0.0201587i
$990$	−3.29162	−	18.7179i	−0.104615	−	0.594894i
$991$	22.7398			0.722353			0.361176	−	0.932498i	$-0.382375\pi$
$991$	22.7398			0.722353			0.361176	+	0.932498i	$0.382375\pi$
$992$	3.51775			0.111689
$993$	20.5117	−	24.4335i	0.650920	−	0.775375i
$994$	−13.8672	+	19.0120i	−0.439840	+	0.603024i
$995$	39.4350	+	22.7678i	1.25017	+	0.721787i
$996$	−14.2767	−	2.52074i	−0.452373	−	0.0798726i
$997$	6.47780	−	3.73996i	0.205154	−	0.118446i	−0.393903	−	0.919152i	$-0.628876\pi$
$997$	6.47780	−	3.73996i	0.205154	−	0.118446i	0.599057	+	0.800706i	$0.295542\pi$
$998$			16.2053i			0.512970i
$999$	−47.1656	+	27.1878i	−1.49225	+	0.860184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.185.15	✓	76
3.2	odd	2	inner	546.2.u.a.185.24	yes	76
7.5	odd	6		546.2.bb.a.341.27	yes	76
13.9	even	3		546.2.bb.a.269.22	yes	76
21.5	even	6		546.2.bb.a.341.3	yes	76
39.35	odd	6		546.2.bb.a.269.8	yes	76
91.61	odd	6	inner	546.2.u.a.425.24	yes	76
273.152	even	6	inner	546.2.u.a.425.15	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.15	✓	76	1.1	even	1	trivial
546.2.u.a.185.24	yes	76	3.2	odd	2	inner
546.2.u.a.425.15	yes	76	273.152	even	6	inner
546.2.u.a.425.24	yes	76	91.61	odd	6	inner
546.2.bb.a.269.8	yes	76	39.35	odd	6
546.2.bb.a.269.22	yes	76	13.9	even	3
546.2.bb.a.341.3	yes	76	21.5	even	6
546.2.bb.a.341.27	yes	76	7.5	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.11365 - 1.32657i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.12998 - 3.68924i) q^{5} +(-1.62773 + 0.592023i) q^{6} +(-1.07162 - 2.41901i) q^{7} -1.00000i q^{8} +(-0.519589 - 2.95466i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.11365 - 1.32657i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.12998 - 3.68924i) q^{5} +(-1.62773 + 0.592023i) q^{6} +(-1.07162 - 2.41901i) q^{7} -1.00000i q^{8} +(-0.519589 - 2.95466i) q^{9} +4.25996i q^{10} -1.48711i q^{11} +(1.70567 + 0.301159i) q^{12} +(2.41401 + 2.67816i) q^{13} +(-0.281454 + 2.63074i) q^{14} +(-7.26609 - 1.28293i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.33253 + 2.30802i) q^{17} +(-1.02735 + 2.81861i) q^{18} +4.10864i q^{19} +(2.12998 - 3.68924i) q^{20} +(-4.40240 - 1.27234i) q^{21} +(-0.743556 + 1.28788i) q^{22} +(-0.137205 - 0.0792156i) q^{23} +(-1.32657 - 1.11365i) q^{24} +(-6.57365 + 11.3859i) q^{25} +(-0.751517 - 3.52636i) q^{26} +(-4.49821 - 2.60117i) q^{27} +(1.55912 - 2.13756i) q^{28} +(-0.413684 + 0.238841i) q^{29} +(5.65115 + 4.74409i) q^{30} +(3.04646 + 1.75887i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.97276 - 1.65611i) q^{33} -2.66507i q^{34} +(-6.64178 + 9.10593i) q^{35} +(2.29902 - 1.92731i) q^{36} +(5.23854 - 9.07342i) q^{37} +(2.05432 - 3.55819i) q^{38} +(6.24113 - 0.219845i) q^{39} +(-3.68924 + 2.12998i) q^{40} +(-5.13995 - 8.90266i) q^{41} +(3.17643 + 3.30308i) q^{42} +(4.00148 - 6.93077i) q^{43} +(1.28788 - 0.743556i) q^{44} +(-9.79373 + 8.21027i) q^{45} +(0.0792156 + 0.137205i) q^{46} +(-2.27135 - 3.93409i) q^{47} +(0.592023 + 1.62773i) q^{48} +(-4.70325 + 5.18454i) q^{49} +(11.3859 - 6.57365i) q^{50} +(4.54572 + 0.802608i) q^{51} +(-1.11235 + 3.42968i) q^{52} +(3.23858 + 1.86979i) q^{53} +(2.59498 + 4.50179i) q^{54} +(-5.48631 + 3.16752i) q^{55} +(-2.41901 + 1.07162i) q^{56} +(5.45041 + 4.57557i) q^{57} +0.477682 q^{58} +(2.39384 + 4.14626i) q^{59} +(-2.52200 - 6.93408i) q^{60} -2.64025i q^{61} +(-1.75887 - 3.04646i) q^{62} +(-6.59056 + 4.42318i) q^{63} -1.00000 q^{64} +(4.73856 - 14.6103i) q^{65} +(0.880404 + 2.42062i) q^{66} -3.26889 q^{67} +(-1.33253 + 2.30802i) q^{68} +(-0.257883 + 0.0937949i) q^{69} +(10.3049 - 4.56508i) q^{70} +(7.70265 + 4.44713i) q^{71} +(-2.95466 + 0.519589i) q^{72} +(-6.03059 - 3.48176i) q^{73} +(-9.07342 + 5.23854i) q^{74} +(7.78350 + 21.4003i) q^{75} +(-3.55819 + 2.05432i) q^{76} +(-3.59734 + 1.59362i) q^{77} +(-5.51490 - 2.93017i) q^{78} +(-8.20543 - 14.2122i) q^{79} +4.25996 q^{80} +(-8.46005 + 3.07042i) q^{81} +10.2799i q^{82} -8.37013 q^{83} +(-1.09933 - 4.44876i) q^{84} +(5.67655 - 9.83207i) q^{85} +(-6.93077 + 4.00148i) q^{86} +(-0.143858 + 0.814766i) q^{87} -1.48711 q^{88} +(-5.94520 + 10.2974i) q^{89} +(12.5868 - 2.21343i) q^{90} +(3.89159 - 8.70951i) q^{91} -0.158431i q^{92} +(5.72594 - 2.08259i) q^{93} +4.54269i q^{94} +(15.1578 - 8.75134i) q^{95} +(0.301159 - 1.70567i) q^{96} +(3.13800 + 1.81173i) q^{97} +(6.66540 - 2.13832i) q^{98} +(-4.39391 + 0.772687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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