LMFDB - Embedded newform 546.2.u.a.425.15

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			425.15
Character	$\chi$	$=$	546.425
Dual form			546.2.u.a.185.15

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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	−0.212695	+	0.977119i	$0.568224\pi$
$5$	−2.12998	+	3.68924i	−0.952557	+	1.64988i	−0.739862	+	0.672759i	$0.765109\pi$
$6$	−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	$0.0719738\pi$
$11$			1.48711i			0.448381i	−0.974545	+	0.224191i	$0.928026\pi$
$12$	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	−0.657957	−	0.753056i	$-0.728579\pi$
$17$	1.33253	−	2.30802i	0.323187	−	0.559776i	0.981144	+	0.193280i	$0.0619124\pi$
$18$	−1.02735	−	2.81861i	−0.242150	−	0.664352i
$19$		−	4.10864i		−	0.942587i	−0.881976	−	0.471294i	$-0.843787\pi$
$19$		−	4.10864i		−	0.942587i	0.881976	−	0.471294i	$-0.156213\pi$
$20$	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	−0.514236	−	0.857648i	$-0.671925\pi$
$23$	−0.137205	+	0.0792156i	−0.0286093	+	0.0165176i	0.485627	+	0.874166i	$0.338591\pi$
$24$	−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	0.461098	−	0.887349i	$-0.347456\pi$
$29$	−0.413684	−	0.238841i	−0.0768193	−	0.0443516i	−0.537918	+	0.842997i	$0.680789\pi$
$30$	5.65115	−	4.74409i	1.03175	−	0.866148i
$31$	3.04646	−	1.75887i	0.547160	−	0.315903i	−0.200816	−	0.979629i	$-0.564359\pi$
$31$	3.04646	−	1.75887i	0.547160	−	0.315903i	0.747976	+	0.663726i	$0.231026\pi$
$32$	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	0.870761	+	0.491707i	$0.163627\pi$
$37$	5.23854	+	9.07342i	0.861211	+	1.49166i	−0.00954999	+	0.999954i	$0.503040\pi$
$38$	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	0.115090	+	0.993355i	$0.463284\pi$
$41$	−5.13995	+	8.90266i	−0.802726	+	1.39036i	−0.917816	+	0.397007i	$0.870049\pi$
$42$	3.17643	−	3.30308i	0.490133	−	0.509676i
$43$	4.00148	+	6.93077i	0.610221	+	1.05693i	0.991203	+	0.132351i	$0.0422526\pi$
$43$	4.00148	+	6.93077i	0.610221	+	1.05693i	−0.380982	+	0.924582i	$0.624414\pi$
$44$	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	−0.982769	−	0.184838i	$-0.940824\pi$
$47$	−2.27135	+	3.93409i	−0.331310	+	0.573846i	0.651459	+	0.758684i	$0.274157\pi$
$48$	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	−0.260801	−	0.965393i	$-0.583987\pi$
$53$	3.23858	−	1.86979i	0.444853	−	0.256836i	0.705654	+	0.708557i	$0.250653\pi$
$54$	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	−0.667068	−	0.744997i	$-0.732451\pi$
$59$	2.39384	−	4.14626i	0.311652	−	0.539797i	0.978720	+	0.205200i	$0.0657844\pi$
$60$	−2.52200	+	6.93408i	−0.325588	+	0.895186i
$61$			2.64025i			0.338049i	0.985612	+	0.169025i	$0.0540617\pi$
$61$			2.64025i			0.338049i	−0.985612	+	0.169025i	$0.945938\pi$
$62$	−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	0.0323767	−	0.999476i	$-0.489692\pi$
$71$	7.70265	−	4.44713i	0.914136	−	0.527777i	0.881760	+	0.471699i	$0.156359\pi$
$72$	−2.95466	−	0.519589i	−0.348210	−	0.0612342i
$73$	−6.03059	+	3.48176i	−0.705828	+	0.407510i	−0.809514	−	0.587100i	$-0.800269\pi$
$73$	−6.03059	+	3.48176i	−0.705828	+	0.407510i	0.103687	+	0.994610i	$0.466936\pi$
$74$	−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	−0.128725	+	0.991680i	$0.541089\pi$
$79$	−8.20543	+	14.2122i	−0.923183	+	1.59900i	−0.794458	+	0.607320i	$0.792245\pi$
$80$	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	−0.987513	−	0.157540i	$-0.949644\pi$
$89$	−5.94520	−	10.2974i	−0.630190	−	1.09152i	0.357322	−	0.933981i	$-0.383690\pi$
$90$	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	−0.332160	−	0.943223i	$-0.607777\pi$
$97$	3.13800	−	1.81173i	0.318616	−	0.183953i	0.650775	+	0.759270i	$0.274444\pi$
$98$	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	0.602321	−	0.798254i	$-0.294243\pi$
$103$	2.15332	+	1.24322i	0.212173	+	0.122498i	−0.390148	+	0.920752i	$0.627576\pi$
$104$	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	−0.0628146	−	0.998025i	$-0.520008\pi$
$107$	7.96591	−	4.59912i	0.770093	−	0.444614i	0.832908	+	0.553412i	$0.186674\pi$
$108$	0.00357501	+	5.19615i	0.000344005	+	0.500000i
$109$	3.36845	+	5.83432i	0.322639	+	0.558827i	0.981032	−	0.193848i	$-0.0620967\pi$
$109$	3.36845	+	5.83432i	0.322639	+	0.558827i	−0.658393	+	0.752675i	$0.728763\pi$
$110$	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	0.398285	−	0.917262i	$-0.369606\pi$
$113$	14.7950	−	8.54191i	1.39180	−	0.803556i	0.993514	+	0.113706i	$0.0362722\pi$
$114$	−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	−0.710980	−	0.703212i	$-0.751749\pi$
$127$	2.85690	−	4.94830i	0.253509	−	0.439091i	0.964490	+	0.264121i	$0.0850819\pi$
$128$	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	0.327143	+	0.944975i	$0.393914\pi$
$131$	−7.49454	+	12.9809i	−0.654801	+	1.13415i	−0.981944	+	0.189173i	$0.939419\pi$
$132$	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	0.0504517	−	0.998727i	$-0.483934\pi$
$137$	−9.23788	−	5.33349i	−0.789245	−	0.455671i	−0.839697	+	0.543056i	$0.817267\pi$
$138$	0.270231	−	0.0477129i	0.0230036	−	0.00406159i
$139$	−9.57332	+	5.52716i	−0.811998	+	0.468807i	−0.847649	−	0.530557i	$-0.821983\pi$
$139$	−9.57332	+	5.52716i	−0.811998	+	0.468807i	0.0356511	+	0.999364i	$0.488649\pi$
$140$	−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	$-0.888128\pi$
$149$		−	8.40462i		−	0.688533i	0.938872	−	0.344266i	$-0.111872\pi$
$150$	3.95942	+	22.4249i	0.323286	+	1.83099i
$151$	11.2766	+	19.5317i	0.917679	+	1.58947i	0.802931	+	0.596072i	$0.203273\pi$
$151$	11.2766	+	19.5317i	0.917679	+	1.58947i	0.114748	+	0.993395i	$0.463394\pi$
$152$	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	0.181854	−	0.983326i	$-0.441790\pi$
$157$	14.0883	−	8.13386i	1.12437	−	0.649153i	0.942512	+	0.334173i	$0.108457\pi$
$158$		−	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	−0.980250	−	0.197764i	$-0.936632\pi$
$167$	−4.12054	+	7.13698i	−0.318857	+	0.552276i	0.661393	+	0.750039i	$0.269965\pi$
$168$	−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	$0.0907290\pi$
$179$			7.52412i			0.562379i	−0.959652	+	0.281190i	$0.909271\pi$
$180$	−12.0072	+	4.37649i	−0.894961	+	0.326204i
$181$			3.30682i			0.245794i	0.992419	+	0.122897i	$0.0392185\pi$
$181$			3.30682i			0.245794i	−0.992419	+	0.122897i	$0.960781\pi$
$182$	−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	$0.389510\pi$
$191$			25.9920i			1.88072i	−0.340186	+	0.940358i	$0.610490\pi$
$192$	−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	0.426098	−	0.904677i	$-0.359888\pi$
$197$	−2.02572	−	1.16955i	−0.144326	−	0.0833268i	−0.570424	+	0.821350i	$0.693221\pi$
$198$	4.19158	−	1.52779i	0.297883	−	0.108575i
$199$	−9.25711	−	5.34459i	−0.656219	−	0.378868i	0.134616	−	0.990898i	$-0.457020\pi$
$199$	−9.25711	−	5.34459i	−0.656219	−	0.378868i	−0.790835	+	0.612030i	$0.790353\pi$
$200$	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	−0.779183	−	0.626797i	$-0.784366\pi$
$211$	2.22580	−	3.85520i	0.153230	−	0.265403i	0.932413	+	0.361394i	$0.117699\pi$
$212$		−	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	0.622473	−	0.782642i	$-0.286128\pi$
$223$	3.82172	+	2.20647i	0.255921	+	0.147756i	−0.366551	+	0.930398i	$0.619462\pi$
$224$	−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	−0.330596	−	0.943773i	$-0.607250\pi$
$227$	9.82387	−	17.0154i	0.652033	−	1.12935i	0.982629	−	0.185582i	$-0.0594171\pi$
$228$	−1.23735	−	7.00798i	−0.0819457	−	0.464115i
$229$	−11.0523	−	6.38106i	−0.730358	−	0.421672i	0.0881953	−	0.996103i	$-0.471890\pi$
$229$	−11.0523	−	6.38106i	−0.730358	−	0.421672i	−0.818553	+	0.574431i	$0.805223\pi$
$230$	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	−0.276183	−	0.961105i	$-0.589070\pi$
$233$	−19.0288	−	10.9863i	−1.24662	−	0.719734i	−0.970433	+	0.241371i	$0.922403\pi$
$234$	−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	$0.197118\pi$
$239$			17.9466i			1.16087i	−0.814306	+	0.580436i	$0.802882\pi$
$240$	4.74409	+	5.65115i	0.306230	+	0.364780i
$241$	14.2309	+	8.21623i	0.916695	+	0.529254i	0.882579	−	0.470164i	$-0.155805\pi$
$241$	14.2309	+	8.21623i	0.916695	+	0.529254i	0.0341158	+	0.999418i	$0.489138\pi$
$242$	−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	0.633104	−	0.774067i	$-0.281781\pi$
$251$	−5.60540	−	9.70884i	−0.353810	−	0.612816i	−0.986913	+	0.161251i	$0.948447\pi$
$252$	−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	0.901935	−	0.431873i	$-0.142147\pi$
$257$	1.23368	+	2.13679i	0.0769546	+	0.133289i	−0.824980	+	0.565162i	$0.808814\pi$
$258$	−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	$0.172405\pi$
$263$			16.7209i			1.03106i	−0.856872	+	0.515529i	$0.827595\pi$
$264$	−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	−0.903255	−	0.429104i	$-0.858829\pi$
$269$	−1.31230	+	2.27296i	−0.0800121	+	0.138585i	0.823243	+	0.567689i	$0.192163\pi$
$270$	11.0809	+	19.1622i	0.674362	+	1.16618i
$271$	−7.72000	+	4.45715i	−0.468957	+	0.270752i	−0.715803	−	0.698302i	$-0.753939\pi$
$271$	−7.72000	+	4.45715i	−0.468957	+	0.270752i	0.246846	+	0.969055i	$0.420606\pi$
$272$	−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	0.0247930	−	0.999693i	$-0.492107\pi$
$277$	14.6154	−	25.3147i	0.878156	−	1.52101i	0.853363	−	0.521318i	$-0.174559\pi$
$278$	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	$0.190137\pi$
$281$			18.8564i			1.12488i	−0.826839	+	0.562439i	$0.809863\pi$
$282$	6.02621	−	5.05895i	0.358856	−	0.301256i
$283$			0.349698i			0.0207874i	0.999946	+	0.0103937i	$0.00330847\pi$
$283$			0.349698i			0.0207874i	−0.999946	+	0.0103937i	$0.996692\pi$
$284$		−	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	0.666262	−	0.745717i	$-0.267893\pi$
$293$	−5.35220	−	9.27029i	−0.312679	−	0.541576i	−0.978941	+	0.204141i	$0.934560\pi$
$294$	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	$-0.963159\pi$
$307$		−	4.04677i		−	0.230961i	0.993310	−	0.115481i	$-0.0368408\pi$
$308$	−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	0.534369	−	0.845252i	$-0.320549\pi$
$311$	−8.19728	−	14.1981i	−0.464825	−	0.805101i	−0.999194	+	0.0401509i	$0.987216\pi$
$312$	−0.219845	+	6.24113i	−0.0124463	+	0.353334i
$313$	17.1202	+	9.88433i	0.967689	+	0.558696i	0.898531	−	0.438910i	$-0.144635\pi$
$313$	17.1202	+	9.88433i	0.967689	+	0.558696i	0.0691582	+	0.997606i	$0.477969\pi$
$314$	−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	0.290830	−	0.956775i	$-0.406068\pi$
$317$	−6.98551	−	4.03309i	−0.392345	−	0.226521i	−0.683176	+	0.730254i	$0.739402\pi$
$318$	−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	0.817971	−	0.575260i	$-0.195099\pi$
$347$	13.5754	+	7.83777i	0.728766	+	0.420754i	−0.0892043	+	0.996013i	$0.528432\pi$
$348$	−0.777537	−	0.282798i	−0.0416804	−	0.0151596i
$349$	−16.3312	−	9.42880i	−0.874187	−	0.504712i	−0.00544978	−	0.999985i	$-0.501735\pi$
$349$	−16.3312	−	9.42880i	−0.874187	−	0.504712i	−0.868737	+	0.495273i	$0.835068\pi$
$350$	−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	0.998691	+	0.0511459i	$0.0162873\pi$
$359$	29.2230	+	16.8719i	1.54233	+	0.890465i	0.543639	+	0.839319i	$0.317046\pi$
$360$	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	$0.348307\pi$
$367$			34.0455i			1.77716i	−0.458723	+	0.888579i	$0.651693\pi$
$368$	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	−0.774780	−	0.632231i	$-0.782139\pi$
$379$	3.11757	−	5.39979i	0.160139	−	0.277368i	0.934918	+	0.354863i	$0.115473\pi$
$380$	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	0.741929	−	0.670479i	$-0.233911\pi$
$389$	33.4019	−	19.2846i	1.69354	−	0.977768i	0.951616	−	0.307290i	$-0.0994221\pi$
$390$	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	$-0.763765\pi$
$397$		−	26.9335i		−	1.35175i	0.737015	−	0.675876i	$-0.236235\pi$
$398$	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	−0.286157	−	0.958183i	$-0.592378\pi$
$401$	8.02151	−	4.63122i	0.400575	−	0.231272i	0.686732	+	0.726911i	$0.259045\pi$
$402$	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	0.136517	−	0.990638i	$-0.456409\pi$
$409$	−13.2090	−	7.62621i	−0.653142	−	0.377092i	−0.789659	+	0.613546i	$0.789743\pi$
$410$	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	−0.472600	−	0.881277i	$-0.656685\pi$
$419$	10.7855	−	18.6811i	0.526908	−	0.912631i	0.999508	−	0.0313545i	$-0.00998208\pi$
$420$	−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	$-0.915964\pi$
$431$		−	10.8349i		−	0.521900i	0.965352	−	0.260950i	$-0.0840358\pi$
$432$	4.50179	+	2.59498i	0.216592	+	0.124851i
$433$	15.5101	−	8.95476i	0.745368	−	0.430338i	−0.0786500	−	0.996902i	$-0.525061\pi$
$433$	15.5101	−	8.95476i	0.745368	−	0.430338i	0.824018	+	0.566564i	$0.191728\pi$
$434$	−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	−0.345159	−	0.938544i	$-0.612175\pi$
$439$	6.18229	−	3.56935i	0.295065	−	0.170356i	0.640224	+	0.768189i	$0.278842\pi$
$440$	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	0.814726	−	0.579847i	$-0.196888\pi$
$443$	15.1527	+	8.74841i	0.719926	+	0.415650i	−0.0947992	+	0.995496i	$0.530221\pi$
$444$	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	−0.574618	−	0.818422i	$-0.694849\pi$
$449$	−3.24523	+	1.87364i	−0.153152	+	0.0884224i	0.421466	+	0.906844i	$0.361516\pi$
$450$	−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	0.681056	−	0.732231i	$-0.261521\pi$
$457$	−6.27651	−	10.8712i	−0.293603	−	0.508535i	−0.974659	+	0.223696i	$0.928188\pi$
$458$	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	0.937170	−	0.348874i	$-0.113436\pi$
$461$	3.57386	+	6.19010i	0.166451	+	0.288302i	−0.770719	+	0.637176i	$0.780103\pi$
$462$	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	−0.506099	−	0.862475i	$-0.668913\pi$
$467$	10.6728	−	18.4857i	0.493876	−	0.855418i	0.999975	+	0.00705702i	$0.00224634\pi$
$468$	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	0.124241	+	0.992252i	$0.460350\pi$
$487$	−17.5926	+	30.4712i	−0.797195	+	1.38078i	−0.921436	+	0.388530i	$0.872983\pi$
$488$	−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	−0.267258	−	0.963625i	$-0.586118\pi$
$491$	−27.3749	−	15.8049i	−1.23541	−	0.713265i	−0.968153	+	0.250360i	$0.919451\pi$
$492$	−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	−0.988408	−	0.151819i	$-0.951487\pi$
$499$	−8.10265	+	14.0342i	−0.362725	+	0.628257i	0.625684	+	0.780077i	$0.284820\pi$
$500$	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	0.952991	+	0.302999i	$0.0979879\pi$
$503$	16.5718	+	28.7032i	0.738900	+	1.27981i	−0.214091	+	0.976814i	$0.568679\pi$
$504$	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	0.958814	−	0.284033i	$-0.0916726\pi$
$509$	5.26636	+	9.12160i	0.233427	+	0.404308i	−0.725387	+	0.688341i	$0.758339\pi$
$510$	−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	0.996998	−	0.0774306i	$-0.0246716\pi$
$521$	9.84785	+	17.0570i	0.431442	+	0.747279i	−0.565556	+	0.824710i	$0.691338\pi$
$522$	−0.248198	+	1.41139i	−0.0108633	+	0.0617748i
$523$	2.85947	−	1.65092i	0.125036	−	0.0721896i	−0.436177	−	0.899861i	$-0.643668\pi$
$523$	2.85947	−	1.65092i	0.125036	−	0.0721896i	0.561213	+	0.827671i	$0.310335\pi$
$524$	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	−0.370735	−	0.928739i	$-0.620894\pi$
$541$	14.3963	−	24.9351i	0.618944	−	1.07204i	0.989679	−	0.143304i	$-0.0457726\pi$
$542$	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	$-0.702485\pi$
$557$		−	37.9692i		−	1.60881i	0.594083	−	0.804403i	$-0.297515\pi$
$558$	−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	−0.957862	−	0.287230i	$-0.907266\pi$
$563$	−5.46168	+	9.45991i	−0.230183	+	0.398688i	0.727679	+	0.685918i	$0.240599\pi$
$564$	−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	−0.295905	−	0.955218i	$-0.595621\pi$
$569$	9.14518	−	5.27997i	0.383386	−	0.221348i	0.679290	+	0.733870i	$0.262288\pi$
$570$	−19.4918	−	23.2186i	−0.816420	−	0.972519i
$571$	8.25387	+	14.2961i	0.345414	+	0.598274i	0.985429	−	0.170088i	$-0.0544053\pi$
$571$	8.25387	+	14.2961i	0.345414	+	0.598274i	−0.640015	+	0.768362i	$0.721072\pi$
$572$	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	−0.385870	−	0.922553i	$-0.626099\pi$
$577$	5.28817	−	3.05312i	0.220149	−	0.127103i	0.606019	+	0.795450i	$0.292765\pi$
$578$	−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	−0.842714	−	0.538361i	$-0.819044\pi$
$587$	1.08728	−	1.88323i	0.0448769	−	0.0777291i	0.887591	+	0.460632i	$0.152377\pi$
$588$	−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	−0.851142	−	0.524936i	$-0.824089\pi$
$593$	0.707096	−	1.22473i	0.0290370	−	0.0502935i	0.880179	+	0.474642i	$0.157423\pi$
$594$	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	−0.187996	−	0.982170i	$-0.560199\pi$
$599$	13.9159	−	8.03436i	0.568589	−	0.328275i	0.756586	+	0.653894i	$0.226866\pi$
$600$	21.4003	+	7.78350i	0.873662	+	0.317760i
$601$	−26.6115	−	15.3641i	−1.08550	−	0.626716i	−0.153128	−	0.988206i	$-0.548935\pi$
$601$	−26.6115	−	15.3641i	−1.08550	−	0.626716i	−0.932376	+	0.361490i	$0.882268\pi$
$602$	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	$-0.770746\pi$
$607$		−	32.4993i		−	1.31910i	0.751659	−	0.659552i	$-0.229254\pi$
$608$	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	0.219225	−	0.975674i	$-0.429647\pi$
$617$	29.1565	−	16.8335i	1.17380	−	0.677691i	0.954571	+	0.297983i	$0.0963139\pi$
$618$	−2.76901	−	3.29844i	−0.111386	−	0.132683i
$619$	−15.4503	+	8.92024i	−0.621001	+	0.358535i	−0.777259	−	0.629181i	$-0.783390\pi$
$619$	−15.4503	+	8.92024i	−0.621001	+	0.358535i	0.156258	+	0.987716i	$0.450057\pi$
$620$	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	−0.981546	−	0.191227i	$-0.938753\pi$
$631$	−16.4881	−	28.5582i	−0.656380	−	1.13688i	0.325166	−	0.945657i	$-0.394580\pi$
$632$	−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	0.750612	−	0.660743i	$-0.229759\pi$
$641$	14.0185	+	8.09360i	0.553698	+	0.319678i	−0.196914	+	0.980421i	$0.563092\pi$
$642$	−15.6891	+	2.77013i	−0.619201	+	0.109328i
$643$	−31.2120	+	18.0203i	−1.23088	+	0.710650i	−0.967214	−	0.253963i	$-0.918266\pi$
$643$	−31.2120	+	18.0203i	−1.23088	+	0.710650i	−0.263668	+	0.964613i	$0.584932\pi$
$644$	−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	−0.913096	−	0.407745i	$-0.866315\pi$
$653$	−25.9762	+	14.9973i	−1.01653	+	0.586892i	−0.103430	+	0.994637i	$0.532982\pi$
$654$	−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	−0.691107	−	0.722752i	$-0.742877\pi$
$659$	−10.5441	+	6.08763i	−0.410739	+	0.237141i	0.280368	+	0.959893i	$0.409544\pi$
$660$	−10.3117	−	3.75049i	−0.401384	−	0.145988i
$661$			26.1449i			1.01692i	0.861086	+	0.508460i	$0.169785\pi$
$661$			26.1449i			1.01692i	−0.861086	+	0.508460i	$0.830215\pi$
$662$	−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	−0.992292	−	0.123924i	$-0.960452\pi$
$673$	−10.0870	+	17.4712i	−0.388825	+	0.673464i	0.603467	+	0.797388i	$0.293785\pi$
$674$	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	−0.872960	−	0.487792i	$-0.837803\pi$
$677$	−0.365307	+	0.632731i	−0.0140399	+	0.0243178i	0.858920	+	0.512110i	$0.171136\pi$
$678$	−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	0.357321	−	0.933982i	$-0.383690\pi$
$683$	−7.13126	−	4.11724i	−0.272870	−	0.157542i	−0.630191	+	0.776440i	$0.717024\pi$
$684$	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	0.0814953	−	0.996674i	$-0.474030\pi$
$691$	25.9028	−	14.9550i	0.985388	−	0.568914i	0.903892	+	0.427760i	$0.140697\pi$
$692$	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	$-0.930618\pi$
$701$		−	11.4510i		−	0.432498i	0.976338	−	0.216249i	$-0.0693824\pi$
$702$	−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	$-0.771406\pi$
$727$		−	35.4828i		−	1.31598i	0.753025	−	0.657992i	$-0.228594\pi$
$728$	−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	0.639954	−	0.768413i	$-0.278953\pi$
$733$	7.97236	+	4.60284i	0.294466	+	0.170010i	−0.345488	+	0.938423i	$0.612287\pi$
$734$	−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	0.564106	−	0.825703i	$-0.309221\pi$
$743$	3.57295	+	2.06284i	0.131079	+	0.0756783i	−0.433027	+	0.901381i	$0.642554\pi$
$744$	−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	0.999514	+	0.0311726i	$0.00992416\pi$
$751$	14.4353	+	25.0028i	0.526753	+	0.912363i	−0.472761	+	0.881191i	$0.656743\pi$
$752$	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	−0.343756	−	0.939059i	$-0.611699\pi$
$757$	17.6464	−	30.5645i	0.641371	−	1.11089i	0.985127	−	0.171828i	$-0.0549673\pi$
$758$			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	0.864446	−	0.502725i	$-0.167669\pi$
$769$	23.8845	+	13.7897i	0.861297	+	0.497270i	−0.00314940	+	0.999995i	$0.501002\pi$
$770$	−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	−0.872371	−	0.488844i	$-0.837419\pi$
$773$	−0.356834	+	0.618055i	−0.0128344	+	0.0222299i	0.859537	+	0.511074i	$0.170752\pi$
$774$	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	0.534314	−	0.845286i	$-0.320570\pi$
$787$	1.94781	+	1.12457i	0.0694320	+	0.0400866i	−0.464882	+	0.885373i	$0.653903\pi$
$788$	−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	0.867769	−	0.496967i	$-0.165553\pi$
$797$	0.0987658	+	0.171067i	0.00349846	+	0.00605952i	−0.864271	+	0.503027i	$0.832220\pi$
$798$	−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	$0.0666932\pi$
$809$			11.8319i			0.415986i	−0.978130	+	0.207993i	$0.933307\pi$
$810$	−13.0799	+	36.0395i	−0.459580	+	1.26630i
$811$		−	25.6241i		−	0.899785i	−0.893083	−	0.449893i	$-0.851462\pi$
$811$		−	25.6241i		−	0.899785i	0.893083	−	0.449893i	$-0.148538\pi$
$812$	−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	−0.452452	−	0.891789i	$-0.649450\pi$
$821$	2.68291	−	1.54898i	0.0936344	−	0.0540598i	0.546086	+	0.837729i	$0.316117\pi$
$822$	11.8792	+	14.1505i	0.414336	+	0.493556i
$823$	−0.233792	+	0.404940i	−0.00814948	+	0.0141153i	−0.870071	−	0.492926i	$-0.835927\pi$
$823$	−0.233792	+	0.404940i	−0.00814948	+	0.0141153i	0.861922	+	0.507041i	$0.169261\pi$
$824$	−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	$-0.997459\pi$
$827$		−	0.459061i		−	0.0159631i	0.999968	−	0.00798156i	$-0.00254064\pi$
$828$	−0.468110	−	0.0823191i	−0.0162680	−	0.00286079i
$829$			3.30166i			0.114671i	0.998355	+	0.0573357i	$0.0182605\pi$
$829$			3.30166i			0.114671i	−0.998355	+	0.0573357i	$0.981739\pi$
$830$			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	0.848646	−	0.528961i	$-0.177418\pi$
$839$	−0.978193	−	1.69428i	−0.0337710	−	0.0584930i	−0.882417	+	0.470468i	$0.844085\pi$
$840$	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	$0.151566\pi$
$853$			26.7743i			0.916734i	−0.888763	+	0.458367i	$0.848434\pi$
$854$	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	0.842975	−	0.537953i	$-0.180802\pi$
$857$	−1.29961	−	2.25099i	−0.0443938	−	0.0768923i	−0.887369	+	0.461061i	$0.847469\pi$
$858$	−4.35749	−	8.20127i	−0.148762	−	0.279987i
$859$	−11.5553	−	6.67144i	−0.394261	−	0.227626i	0.289744	−	0.957104i	$-0.406430\pi$
$859$	−11.5553	−	6.67144i	−0.394261	−	0.227626i	−0.684005	+	0.729478i	$0.739763\pi$
$860$	−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	−0.101583	−	0.994827i	$-0.532391\pi$
$863$	−29.7858	−	17.1968i	−1.01392	−	0.585387i	−0.912337	+	0.409440i	$0.865724\pi$
$864$	−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	−0.958319	−	0.285699i	$-0.907774\pi$
$881$	−6.87833	+	11.9136i	−0.231737	+	0.401380i	0.726583	+	0.687079i	$0.241107\pi$
$882$	−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	0.991528	−	0.129894i	$-0.0414637\pi$
$887$	11.4148	+	19.7711i	0.383273	+	0.663847i	−0.608255	+	0.793741i	$0.708130\pi$
$888$	−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	$0.0496872\pi$
$911$			9.38466i			0.310927i	−0.987842	+	0.155464i	$0.950313\pi$
$912$	−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	$-0.744415\pi$
$937$		−	44.0425i		−	1.43881i	0.694593	−	0.719403i	$-0.255585\pi$
$938$	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	0.522426	−	0.852685i	$-0.325027\pi$
$941$	−14.6395	−	25.3563i	−0.477234	−	0.826593i	−0.999660	+	0.0260916i	$0.991694\pi$
$942$	−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	0.681308	−	0.731997i	$-0.261411\pi$
$947$	50.9573	−	29.4202i	1.65589	−	0.956028i	0.974582	−	0.224032i	$-0.0719219\pi$
$948$	−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	−0.510431	−	0.859919i	$-0.670514\pi$
$953$	−0.646257	+	0.373117i	−0.0209343	+	0.0120864i	0.489496	+	0.872005i	$0.337181\pi$
$954$	−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	$-0.989413\pi$
$977$		−	2.07892i		−	0.0665105i	0.999447	−	0.0332552i	$-0.0105874\pi$
$978$	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	0.738236	−	0.674543i	$-0.235659\pi$
$983$	−6.74253	−	11.6784i	−0.215053	−	0.372483i	−0.953289	+	0.302060i	$0.902326\pi$
$984$	−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	0.599057	−	0.800706i	$-0.295542\pi$
$997$	6.47780	+	3.73996i	0.205154	+	0.118446i	−0.393903	+	0.919152i	$0.628876\pi$
$998$		−	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.425.15	yes	76
3.2	odd	2	inner	546.2.u.a.425.24	yes	76
7.3	odd	6		546.2.bb.a.269.8	yes	76
13.3	even	3		546.2.bb.a.341.3	yes	76
21.17	even	6		546.2.bb.a.269.22	yes	76
39.29	odd	6		546.2.bb.a.341.27	yes	76
91.3	odd	6	inner	546.2.u.a.185.24	yes	76
273.185	even	6	inner	546.2.u.a.185.15	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.15	✓	76	273.185	even	6	inner
546.2.u.a.185.24	yes	76	91.3	odd	6	inner
546.2.u.a.425.15	yes	76	1.1	even	1	trivial
546.2.u.a.425.24	yes	76	3.2	odd	2	inner
546.2.bb.a.269.8	yes	76	7.3	odd	6
546.2.bb.a.269.22	yes	76	21.17	even	6
546.2.bb.a.341.3	yes	76	13.3	even	3
546.2.bb.a.341.27	yes	76	39.29	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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