LMFDB - Embedded newform 546.2.bq.c.419.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(419,546)]

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, 3, 2]))

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

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

chi := DirichletCharacter("546.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bq (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:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			419.17
Character	$\chi$	$=$	546.419
Dual form			546.2.bq.c.503.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.67122 + 0.454992i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.88020 q^{5} +(-1.21982 + 1.22965i) q^{6} +(-1.36777 + 2.26478i) q^{7} -1.00000i q^{8} +(2.58596 - 1.52079i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.67122 + 0.454992i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.88020 q^{5} +(-1.21982 + 1.22965i) q^{6} +(-1.36777 + 2.26478i) q^{7} -1.00000i q^{8} +(2.58596 - 1.52079i) q^{9} +(-1.62830 + 0.940099i) q^{10} +(3.16716 - 1.82856i) q^{11} +(-0.441576 + 1.67482i) q^{12} +(3.37398 - 1.27133i) q^{13} +(-0.0521308 + 2.64524i) q^{14} +(3.14223 - 0.855476i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.66605 - 4.61773i) q^{17} +(1.47912 - 2.61002i) q^{18} +(3.90587 + 2.25506i) q^{19} +(-0.940099 + 1.62830i) q^{20} +(1.25538 - 4.40727i) q^{21} +(1.82856 - 3.16716i) q^{22} +(3.33400 - 1.92489i) q^{23} +(0.454992 + 1.67122i) q^{24} -1.46485 q^{25} +(2.28628 - 2.78800i) q^{26} +(-3.62977 + 3.71816i) q^{27} +(1.27747 + 2.31691i) q^{28} +(2.85202 - 1.64661i) q^{29} +(2.29351 - 2.31198i) q^{30} -2.94891i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.46105 + 4.49696i) q^{33} -5.33209i q^{34} +(2.57167 - 4.25823i) q^{35} +(-0.0240567 - 2.99990i) q^{36} +(-0.930327 - 1.61137i) q^{37} +4.51011 q^{38} +(-5.06021 + 3.65981i) q^{39} +1.88020i q^{40} +(2.84478 + 4.92731i) q^{41} +(-1.11644 - 4.44450i) q^{42} +(-5.18527 + 8.98116i) q^{43} -3.65712i q^{44} +(-4.86213 + 2.85938i) q^{45} +(1.92489 - 3.33400i) q^{46} +7.28396 q^{47} +(1.22965 + 1.21982i) q^{48} +(-3.25844 - 6.19537i) q^{49} +(-1.26860 + 0.732427i) q^{50} +(-2.35452 + 8.93028i) q^{51} +(0.585980 - 3.55762i) q^{52} -4.50439i q^{53} +(-1.28440 + 5.03491i) q^{54} +(-5.95489 + 3.43806i) q^{55} +(2.26478 + 1.36777i) q^{56} +(-7.55361 - 1.99156i) q^{57} +(1.64661 - 2.85202i) q^{58} +(2.45731 - 4.25618i) q^{59} +(0.830251 - 3.14899i) q^{60} +(-2.25341 - 1.30101i) q^{61} +(-1.47446 - 2.55383i) q^{62} +(-0.0927516 + 7.93671i) q^{63} -1.00000 q^{64} +(-6.34374 + 2.39036i) q^{65} +(-1.61490 + 6.12501i) q^{66} +(-2.47105 - 4.27998i) q^{67} +(-2.66605 - 4.61773i) q^{68} +(-4.69605 + 4.73386i) q^{69} +(0.0980162 - 4.97357i) q^{70} +(10.1167 + 5.84088i) q^{71} +(-1.52079 - 2.58596i) q^{72} +5.08266i q^{73} +(-1.61137 - 0.930327i) q^{74} +(2.44810 - 0.666497i) q^{75} +(3.90587 - 2.25506i) q^{76} +(-0.190649 + 9.67396i) q^{77} +(-2.55237 + 5.69960i) q^{78} +14.0285 q^{79} +(0.940099 + 1.62830i) q^{80} +(4.37442 - 7.86539i) q^{81} +(4.92731 + 2.84478i) q^{82} -4.75954 q^{83} +(-3.18911 - 3.29083i) q^{84} +(-5.01270 + 8.68224i) q^{85} +10.3705i q^{86} +(-4.01716 + 4.04951i) q^{87} +(-1.82856 - 3.16716i) q^{88} +(-4.82669 - 8.36007i) q^{89} +(-2.78104 + 4.90736i) q^{90} +(-1.73552 + 9.38019i) q^{91} -3.84978i q^{92} +(1.34173 + 4.92829i) q^{93} +(6.30809 - 3.64198i) q^{94} +(-7.34381 - 4.23995i) q^{95} +(1.67482 + 0.441576i) q^{96} +(11.4876 + 6.63238i) q^{97} +(-5.91957 - 3.73613i) q^{98} +(5.40932 - 9.54517i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.67122	+	0.454992i	−0.964880	+	0.262690i
$3$	−1.67122	+	0.454992i	−0.964880	+	0.262690i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.88020			−0.840850			−0.420425	−	0.907327i	$-0.638119\pi$
$5$	−1.88020			−0.840850			−0.420425	+	0.907327i	$0.638119\pi$
$6$	−1.21982	+	1.22965i	−0.497991	+	0.502001i
$7$	−1.36777	+	2.26478i	−0.516967	+	0.856005i
$7$	−1.36777	+	2.26478i	−0.516967	+	0.856005i
$8$		−	1.00000i		−	0.353553i
$9$	2.58596	−	1.52079i	0.861988	−	0.506928i
$10$	−1.62830	+	0.940099i	−0.514914	+	0.297285i
$11$	3.16716	−	1.82856i	0.954935	−	0.551332i	0.0603244	−	0.998179i	$-0.480786\pi$
$11$	3.16716	−	1.82856i	0.954935	−	0.551332i	0.894610	+	0.446847i	$0.147453\pi$
$12$	−0.441576	+	1.67482i	−0.127472	+	0.483478i
$13$	3.37398	−	1.27133i	0.935772	−	0.352605i
$13$	3.37398	−	1.27133i	0.935772	−	0.352605i
$14$	−0.0521308	+	2.64524i	−0.0139325	+	0.706970i
$15$	3.14223	−	0.855476i	0.811320	−	0.220883i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.66605	−	4.61773i	0.646611	−	1.11996i	−0.337316	−	0.941392i	$-0.609519\pi$
$17$	2.66605	−	4.61773i	0.646611	−	1.11996i	0.983927	−	0.178572i	$-0.0571476\pi$
$18$	1.47912	−	2.61002i	0.348631	−	0.615188i
$19$	3.90587	+	2.25506i	0.896068	+	0.517345i	0.875922	−	0.482452i	$-0.160254\pi$
$19$	3.90587	+	2.25506i	0.896068	+	0.517345i	0.0201457	+	0.999797i	$0.493587\pi$
$20$	−0.940099	+	1.62830i	−0.210213	+	0.364099i
$21$	1.25538	−	4.40727i	0.273947	−	0.961745i
$22$	1.82856	−	3.16716i	0.389851	−	0.675241i
$23$	3.33400	−	1.92489i	0.695188	−	0.401367i	−0.110365	−	0.993891i	$-0.535202\pi$
$23$	3.33400	−	1.92489i	0.695188	−	0.401367i	0.805553	+	0.592524i	$0.201869\pi$
$24$	0.454992	+	1.67122i	0.0928749	+	0.341137i
$25$	−1.46485			−0.292971
$26$	2.28628	−	2.78800i	0.448377	−	0.546771i
$27$	−3.62977	+	3.71816i	−0.698550	+	0.715561i
$28$	1.27747	+	2.31691i	0.241420	+	0.437855i
$29$	2.85202	−	1.64661i	0.529607	−	0.305769i	−0.211249	−	0.977432i	$-0.567753\pi$
$29$	2.85202	−	1.64661i	0.529607	−	0.305769i	0.740856	+	0.671663i	$0.234420\pi$
$30$	2.29351	−	2.31198i	0.418736	−	0.422107i
$31$		−	2.94891i		−	0.529640i	−0.964298	−	0.264820i	$-0.914687\pi$
$31$		−	2.94891i		−	0.529640i	0.964298	−	0.264820i	$-0.0853126\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−4.46105	+	4.49696i	−0.776569	+	0.782821i
$34$		−	5.33209i		−	0.914446i
$35$	2.57167	−	4.25823i	0.434692	−	0.719773i
$36$	−0.0240567	−	2.99990i	−0.00400945	−	0.499984i
$37$	−0.930327	−	1.61137i	−0.152945	−	0.264908i	0.779364	−	0.626571i	$-0.215542\pi$
$37$	−0.930327	−	1.61137i	−0.152945	−	0.264908i	−0.932309	+	0.361663i	$0.882209\pi$
$38$	4.51011			0.731637
$39$	−5.06021	+	3.65981i	−0.810283	+	0.586039i
$40$			1.88020i			0.297285i
$41$	2.84478	+	4.92731i	0.444280	+	0.769516i	0.998002	−	0.0631857i	$-0.0201260\pi$
$41$	2.84478	+	4.92731i	0.444280	+	0.769516i	−0.553721	+	0.832702i	$0.686793\pi$
$42$	−1.11644	−	4.44450i	−0.172270	−	0.685801i
$43$	−5.18527	+	8.98116i	−0.790747	+	1.36961i	0.134758	+	0.990878i	$0.456974\pi$
$43$	−5.18527	+	8.98116i	−0.790747	+	1.36961i	−0.925505	+	0.378735i	$0.876359\pi$
$44$		−	3.65712i		−	0.551332i
$45$	−4.86213	+	2.85938i	−0.724803	+	0.426251i
$46$	1.92489	−	3.33400i	0.283809	−	0.491572i
$47$	7.28396			1.06247			0.531237	−	0.847223i	$-0.321727\pi$
$47$	7.28396			1.06247			0.531237	+	0.847223i	$0.321727\pi$
$48$	1.22965	+	1.21982i	0.177484	+	0.176066i
$49$	−3.25844	−	6.19537i	−0.465491	−	0.885053i
$50$	−1.26860	+	0.732427i	−0.179407	+	0.103581i
$51$	−2.35452	+	8.93028i	−0.329699	+	1.25049i
$52$	0.585980	−	3.55762i	0.0812608	−	0.493353i
$53$		−	4.50439i		−	0.618725i	−0.950944	−	0.309363i	$-0.899884\pi$
$53$		−	4.50439i		−	0.618725i	0.950944	−	0.309363i	$-0.100116\pi$
$54$	−1.28440	+	5.03491i	−0.174784	+	0.685165i
$55$	−5.95489	+	3.43806i	−0.802957	+	0.463588i
$56$	2.26478	+	1.36777i	0.302644	+	0.182775i
$57$	−7.55361	−	1.99156i	−1.00050	−	0.263788i
$58$	1.64661	−	2.85202i	0.216211	−	0.374489i
$59$	2.45731	−	4.25618i	0.319914	−	0.554108i	−0.660556	−	0.750777i	$-0.729679\pi$
$59$	2.45731	−	4.25618i	0.319914	−	0.554108i	0.980470	+	0.196669i	$0.0630125\pi$
$60$	0.830251	−	3.14899i	0.107185	−	0.406533i
$61$	−2.25341	−	1.30101i	−0.288520	−	0.166577i	0.348754	−	0.937214i	$-0.386605\pi$
$61$	−2.25341	−	1.30101i	−0.288520	−	0.166577i	−0.637274	+	0.770637i	$0.719938\pi$
$62$	−1.47446	−	2.55383i	−0.187256	−	0.324337i
$63$	−0.0927516	+	7.93671i	−0.0116856	+	0.999932i
$64$	−1.00000			−0.125000
$65$	−6.34374	+	2.39036i	−0.786845	+	0.296488i
$66$	−1.61490	+	6.12501i	−0.198780	+	0.753936i
$67$	−2.47105	−	4.27998i	−0.301886	−	0.522883i	0.674677	−	0.738113i	$-0.264283\pi$
$67$	−2.47105	−	4.27998i	−0.301886	−	0.522883i	−0.976563	+	0.215231i	$0.930950\pi$
$68$	−2.66605	−	4.61773i	−0.323306	−	0.559982i
$69$	−4.69605	+	4.73386i	−0.565338	+	0.569890i
$70$	0.0980162	−	4.97357i	0.0117152	−	0.594456i
$71$	10.1167	+	5.84088i	1.20063	+	0.693185i	0.960696	−	0.277604i	$-0.0895403\pi$
$71$	10.1167	+	5.84088i	1.20063	+	0.693185i	0.239936	+	0.970789i	$0.422874\pi$
$72$	−1.52079	−	2.58596i	−0.179226	−	0.304759i
$73$			5.08266i			0.594881i	0.954740	+	0.297440i	$0.0961330\pi$
$73$			5.08266i			0.594881i	−0.954740	+	0.297440i	$0.903867\pi$
$74$	−1.61137	−	0.930327i	−0.187318	−	0.108148i
$75$	2.44810	−	0.666497i	0.282682	−	0.0769604i
$76$	3.90587	−	2.25506i	0.448034	−	0.258673i
$77$	−0.190649	+	9.67396i	−0.0217264	+	1.10245i
$78$	−2.55237	+	5.69960i	−0.288999	+	0.645352i
$79$	14.0285			1.57833			0.789166	−	0.614180i	$-0.210513\pi$
$79$	14.0285			1.57833			0.789166	+	0.614180i	$0.210513\pi$
$80$	0.940099	+	1.62830i	0.105106	+	0.182049i
$81$	4.37442	−	7.86539i	0.486047	−	0.873933i
$82$	4.92731	+	2.84478i	0.544130	+	0.314154i
$83$	−4.75954			−0.522427			−0.261214	−	0.965281i	$-0.584123\pi$
$83$	−4.75954			−0.522427			−0.261214	+	0.965281i	$0.584123\pi$
$84$	−3.18911	−	3.29083i	−0.347961	−	0.359059i
$85$	−5.01270	+	8.68224i	−0.543703	+	0.941721i
$86$			10.3705i			1.11828i
$87$	−4.01716	+	4.04951i	−0.430685	+	0.434153i
$88$	−1.82856	−	3.16716i	−0.194925	−	0.337620i
$89$	−4.82669	−	8.36007i	−0.511628	−	0.886166i	−0.999909	−	0.0134794i	$-0.995709\pi$
$89$	−4.82669	−	8.36007i	−0.511628	−	0.886166i	0.488281	−	0.872686i	$-0.337624\pi$
$90$	−2.78104	+	4.90736i	−0.293147	+	0.517281i
$91$	−1.73552	+	9.38019i	−0.181932	+	0.983311i
$92$		−	3.84978i		−	0.401367i
$93$	1.34173	+	4.92829i	0.139131	+	0.511039i
$94$	6.30809	−	3.64198i	0.650630	−	0.375641i
$95$	−7.34381	−	4.23995i	−0.753459	−	0.435010i
$96$	1.67482	+	0.441576i	0.170935	+	0.0450682i
$97$	11.4876	+	6.63238i	1.16639	+	0.673416i	0.952827	−	0.303513i	$-0.0981595\pi$
$97$	11.4876	+	6.63238i	1.16639	+	0.673416i	0.213564	+	0.976929i	$0.431493\pi$
$98$	−5.91957	−	3.73613i	−0.597967	−	0.377406i
$99$	5.40932	−	9.54517i	0.543657	−	0.959325i
$100$	−0.732427	+	1.26860i	−0.0732427	+	0.126860i
$101$	−7.10215	−	12.3013i	−0.706690	−	1.22402i	−0.966078	−	0.258250i	$-0.916854\pi$
$101$	−7.10215	−	12.3013i	−0.706690	−	1.22402i	0.259388	−	0.965773i	$-0.416479\pi$
$102$	2.42606	+	8.91111i	0.240216	+	0.882331i
$103$		−	3.94251i		−	0.388467i	−0.980955	−	0.194234i	$-0.937778\pi$
$103$		−	3.94251i		−	0.388467i	0.980955	−	0.194234i	$-0.0622220\pi$
$104$	−1.27133	−	3.37398i	−0.124665	−	0.330845i
$105$	−2.36037	+	8.28654i	−0.230349	+	0.808683i
$106$	−2.25219	−	3.90092i	−0.218752	−	0.378890i
$107$	−16.6172	+	9.59396i	−1.60645	+	0.927483i	−0.616291	+	0.787519i	$0.711365\pi$
$107$	−16.6172	+	9.59396i	−1.60645	+	0.927483i	−0.990157	+	0.139964i	$0.955301\pi$
$108$	1.40514	+	5.00256i	0.135209	+	0.481371i
$109$	−1.43980			−0.137908			−0.0689541	−	0.997620i	$-0.521966\pi$
$109$	−1.43980			−0.137908			−0.0689541	+	0.997620i	$0.521966\pi$
$110$	−3.43806	+	5.95489i	−0.327806	+	0.567777i
$111$	2.28795	+	2.26967i	0.217162	+	0.215428i
$112$	2.64524	+	0.0521308i	0.249951	+	0.00492589i
$113$	−9.32273	−	5.38248i	−0.877009	−	0.506341i	−0.00733803	−	0.999973i	$-0.502336\pi$
$113$	−9.32273	−	5.38248i	−0.877009	−	0.506341i	−0.869671	+	0.493632i	$0.835669\pi$
$114$	−7.53740	+	2.05206i	−0.705942	+	0.192193i
$115$	−6.26859	+	3.61917i	−0.584549	+	0.337489i
$116$		−	3.29323i		−	0.305769i
$117$	6.79155	−	8.41872i	0.627879	−	0.778311i
$118$		−	4.91462i		−	0.452427i
$119$	6.81160	+	12.3540i	0.624418	+	1.13249i
$120$	−0.855476	−	3.14223i	−0.0780939	−	0.286845i
$121$	1.18727	−	2.05641i	0.107934	−	0.186947i
$122$	−2.60201			−0.235575
$123$	−6.99615	−	6.94027i	−0.630822	−	0.625783i
$124$	−2.55383	−	1.47446i	−0.229341	−	0.132410i
$125$	12.1552			1.08719
$126$	3.88803	+	6.91977i	0.346373	+	0.616462i
$127$	8.15283	+	14.1211i	0.723447	+	1.25305i	0.959610	+	0.281334i	$0.0907768\pi$
$127$	8.15283	+	14.1211i	0.723447	+	1.25305i	−0.236163	+	0.971713i	$0.575890\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	4.57939	−	17.3688i	0.403192	−	1.52923i
$130$	−4.29866	+	5.24199i	−0.377018	+	0.459753i
$131$	−12.1392			−1.06061			−0.530304	−	0.847807i	$-0.677922\pi$
$131$	−12.1392			−1.06061			−0.530304	+	0.847807i	$0.677922\pi$
$132$	1.66396	+	6.11186i	0.144829	+	0.531969i
$133$	−10.4495	+	5.76154i	−0.906088	+	0.499589i
$134$	−4.27998	−	2.47105i	−0.369734	−	0.213466i
$135$	6.82470	−	6.99088i	0.587376	−	0.601680i
$136$	−4.61773	−	2.66605i	−0.395967	−	0.228612i
$137$	−16.6342	−	9.60379i	−1.42116	−	0.820507i	−0.424761	−	0.905305i	$-0.639642\pi$
$137$	−16.6342	−	9.60379i	−1.42116	−	0.820507i	−0.996398	+	0.0847985i	$0.972975\pi$
$138$	−1.69997	+	6.44767i	−0.144711	+	0.548862i
$139$	−10.5865	−	6.11210i	−0.897932	−	0.518421i	−0.0214033	−	0.999771i	$-0.506813\pi$
$139$	−10.5865	−	6.11210i	−0.897932	−	0.518421i	−0.876529	+	0.481350i	$0.840147\pi$
$140$	−2.40190	−	4.35625i	−0.202998	−	0.368170i
$141$	−12.1731	+	3.31414i	−1.02516	+	0.279101i
$142$	11.6818			0.980311
$143$	8.36121	−	10.1960i	0.699199	−	0.852636i
$144$	−2.61002	−	1.47912i	−0.217502	−	0.123260i
$145$	−5.36237	+	3.09596i	−0.445320	+	0.257106i
$146$	2.54133	+	4.40172i	0.210322	+	0.364289i
$147$	8.26441	+	8.87127i	0.681637	+	0.731690i
$148$	−1.86065			−0.152945
$149$	10.8614	+	6.27084i	0.889801	+	0.513727i	0.873877	−	0.486146i	$-0.161598\pi$
$149$	10.8614	+	6.27084i	0.889801	+	0.513727i	0.0159236	+	0.999873i	$0.494931\pi$
$150$	1.78686	−	1.80125i	0.145897	−	0.147072i
$151$	−1.04690			−0.0851952			−0.0425976	−	0.999092i	$-0.513563\pi$
$151$	−1.04690			−0.0851952			−0.0425976	+	0.999092i	$0.513563\pi$
$152$	2.25506	−	3.90587i	0.182909	−	0.316808i
$153$	−0.128272	−	15.9958i	−0.0103702	−	1.29318i
$154$	4.67187	+	8.47322i	0.376470	+	0.682791i
$155$			5.54454i			0.445348i
$156$	0.639385	+	6.21218i	0.0511918	+	0.497372i
$157$			7.33717i			0.585570i	0.956178	+	0.292785i	$0.0945820\pi$
$157$			7.33717i			0.585570i	−0.956178	+	0.292785i	$0.905418\pi$
$158$	12.1491	−	7.01426i	0.966527	−	0.558025i
$159$	2.04946	+	7.52783i	0.162533	+	0.596996i
$160$	1.62830	+	0.940099i	0.128728	+	0.0743214i
$161$	−0.200692	+	10.1836i	−0.0158167	+	0.802578i
$162$	−0.144336	−	8.99884i	−0.0113401	−	0.707016i
$163$	−1.85972	+	3.22112i	−0.145664	+	0.252298i	−0.929621	−	0.368518i	$-0.879865\pi$
$163$	−1.85972	+	3.22112i	−0.145664	+	0.252298i	0.783956	+	0.620816i	$0.213199\pi$
$164$	5.68957			0.444280
$165$	8.38765	−	8.45519i	0.652978	−	0.658235i
$166$	−4.12188	+	2.37977i	−0.319920	+	0.184706i
$167$	0.354433	+	0.613896i	0.0274268	+	0.0475047i	0.879413	−	0.476060i	$-0.157935\pi$
$167$	0.354433	+	0.613896i	0.0274268	+	0.0475047i	−0.851986	+	0.523564i	$0.824602\pi$
$168$	−4.40727	−	1.25538i	−0.340028	−	0.0968549i
$169$	9.76742	−	8.57890i	0.751340	−	0.659916i
$170$			10.0254i			0.768912i
$171$	13.5299	−	0.108498i	1.03466	−	0.00829708i
$172$	5.18527	+	8.98116i	0.395373	+	0.684807i
$173$	−8.70565	+	15.0786i	−0.661878	+	1.14641i	0.318244	+	0.948009i	$0.396907\pi$
$173$	−8.70565	+	15.0786i	−0.661878	+	1.14641i	−0.980122	+	0.198398i	$0.936426\pi$
$174$	−1.45421	+	5.51556i	−0.110244	+	0.418133i
$175$	2.00358	−	3.31757i	0.151456	−	0.250785i
$176$	−3.16716	−	1.82856i	−0.238734	−	0.137833i
$177$	−2.17018	+	8.23108i	−0.163121	+	0.618686i
$178$	−8.36007	−	4.82669i	−0.626614	−	0.361776i
$179$	18.4651	−	10.6608i	1.38015	−	0.796828i	0.387970	−	0.921672i	$-0.373176\pi$
$179$	18.4651	−	10.6608i	1.38015	−	0.796828i	0.992176	+	0.124844i	$0.0398430\pi$
$180$	0.0452314	+	5.64041i	0.00337135	+	0.420412i
$181$			4.41691i			0.328306i	0.986435	+	0.164153i	$0.0524892\pi$
$181$			4.41691i			0.328306i	−0.986435	+	0.164153i	$0.947511\pi$
$182$	3.18709	+	8.99124i	0.236243	+	0.666475i
$183$	4.35790	+	1.14899i	0.322145	+	0.0849356i
$184$	−1.92489	−	3.33400i	−0.141905	−	0.245786i
$185$	1.74920	+	3.02970i	0.128604	+	0.222748i
$186$	3.62612	+	3.59716i	0.265880	+	0.263756i
$187$		−	19.5001i		−	1.42599i
$188$	3.64198	−	6.30809i	0.265619	−	0.460065i
$189$	−3.45613	−	13.3062i	−0.251397	−	0.967884i
$190$	−8.47990			−0.615197
$191$	5.28436	+	3.05093i	0.382363	+	0.220757i	0.678846	−	0.734281i	$-0.262480\pi$
$191$	5.28436	+	3.05093i	0.382363	+	0.220757i	−0.296483	+	0.955038i	$0.595814\pi$
$192$	1.67122	−	0.454992i	0.120610	−	0.0328362i
$193$	−9.10171	−	15.7646i	−0.655156	−	1.13476i	−0.981855	−	0.189634i	$-0.939270\pi$
$193$	−9.10171	−	15.7646i	−0.655156	−	1.13476i	0.326699	−	0.945128i	$-0.394064\pi$
$194$	13.2648			0.952354
$195$	9.51421	−	6.88118i	0.681326	−	0.492771i
$196$	−6.99456	−	0.275796i	−0.499612	−	0.0196997i
$197$	−1.41378	+	0.816248i	−0.100728	+	0.0581553i	−0.549518	−	0.835482i	$-0.685189\pi$
$197$	−1.41378	+	0.816248i	−0.100728	+	0.0581553i	0.448790	+	0.893637i	$0.351855\pi$
$198$	−0.0879783	−	10.9710i	−0.00625234	−	0.779676i
$199$	19.9947	+	11.5439i	1.41738	+	0.818327i	0.996068	−	0.0885877i	$-0.0282354\pi$
$199$	19.9947	+	11.5439i	1.41738	+	0.818327i	0.421315	+	0.906914i	$0.361569\pi$
$200$			1.46485i			0.103581i
$201$	6.07702	+	6.02849i	0.428640	+	0.425217i
$202$	−12.3013	−	7.10215i	−0.865515	−	0.499706i
$203$	−0.171679	+	8.71138i	−0.0120495	+	0.611419i
$204$	6.55658	+	6.50422i	0.459053	+	0.455386i
$205$	−5.34876	−	9.26432i	−0.373573	−	0.647048i
$206$	−1.97125	−	3.41431i	−0.137344	−	0.237886i
$207$	5.69427	−	10.0480i	0.395779	−	0.698384i
$208$	−2.78800	−	2.28628i	−0.193313	−	0.158525i
$209$	16.4940			1.14092
$210$	2.09913	+	8.35654i	0.144854	+	0.576656i
$211$	6.11057	+	10.5838i	0.420669	+	0.728620i	0.996005	−	0.0892971i	$-0.0284621\pi$
$211$	6.11057	+	10.5838i	0.420669	+	0.728620i	−0.575336	+	0.817917i	$0.695129\pi$
$212$	−3.90092	−	2.25219i	−0.267916	−	0.154681i
$213$	−19.5648	−	5.15839i	−1.34056	−	0.353447i
$214$	−9.59396	+	16.6172i	−0.655829	+	1.13593i
$215$	9.74934	−	16.8864i	0.664900	−	1.15164i
$216$	3.71816	+	3.62977i	0.252989	+	0.246975i
$217$	6.67863	+	4.03342i	0.453375	+	0.273806i
$218$	−1.24691	+	0.719902i	−0.0844512	+	0.0487579i
$219$	−2.31257	−	8.49426i	−0.156269	−	0.573989i
$220$			6.87612i			0.463588i
$221$	3.12450	−	18.9695i	0.210176	−	1.27603i
$222$	3.11625	+	0.821621i	0.209149	+	0.0551436i
$223$	−2.95147	+	1.70403i	−0.197645	+	0.114110i	−0.595556	−	0.803313i	$-0.703068\pi$
$223$	−2.95147	+	1.70403i	−0.197645	+	0.114110i	0.397912	+	0.917424i	$0.369735\pi$
$224$	2.31691	−	1.27747i	0.154805	−	0.0853547i
$225$	−3.78806	+	2.22773i	−0.252537	+	0.148515i
$226$	−10.7650			−0.716075
$227$	−6.03232	+	10.4483i	−0.400379	+	0.693477i	−0.993772	−	0.111436i	$-0.964455\pi$
$227$	−6.03232	+	10.4483i	−0.400379	+	0.693477i	0.593392	+	0.804913i	$0.297788\pi$
$228$	−5.50154	+	5.54584i	−0.364349	+	0.367282i
$229$		−	16.8389i		−	1.11274i	−0.830934	−	0.556371i	$-0.812193\pi$
$229$		−	16.8389i		−	1.11274i	0.830934	−	0.556371i	$-0.187807\pi$
$230$	−3.61917	+	6.26859i	−0.238641	+	0.413338i
$231$	−4.08296	−	16.2541i	−0.268639	−	1.06944i
$232$	−1.64661	−	2.85202i	−0.108106	−	0.187244i
$233$			1.70806i			0.111899i	0.998434	+	0.0559494i	$0.0178186\pi$
$233$			1.70806i			0.111899i	−0.998434	+	0.0559494i	$0.982181\pi$
$234$	1.67230	−	10.6866i	0.109322	−	0.698605i
$235$	−13.6953			−0.893382
$236$	−2.45731	−	4.25618i	−0.159957	−	0.277054i
$237$	−23.4448	+	6.38287i	−1.52290	+	0.414612i
$238$	12.0760	+	7.29305i	0.782771	+	0.472738i
$239$		−	11.8939i		−	0.769354i	−0.923051	−	0.384677i	$-0.874313\pi$
$239$		−	11.8939i		−	0.769354i	0.923051	−	0.384677i	$-0.125687\pi$
$240$	−2.31198	−	2.29351i	−0.149238	−	0.148046i
$241$	13.5179	+	7.80455i	0.870763	+	0.502735i	0.867602	−	0.497260i	$-0.165660\pi$
$241$	13.5179	+	7.80455i	0.870763	+	0.502735i	0.00316139	+	0.999995i	$0.498994\pi$
$242$		−	2.37454i		−	0.152641i
$243$	−3.73194	+	15.1351i	−0.239404	+	0.970920i
$244$	−2.25341	+	1.30101i	−0.144260	+	0.0832885i
$245$	6.12651	+	11.6485i	0.391408	+	0.744197i
$246$	−9.52898	−	2.51238i	−0.607546	−	0.160183i
$247$	16.0452	+	2.64283i	1.02093	+	0.168159i
$248$	−2.94891			−0.187256
$249$	7.95424	−	2.16555i	0.504080	−	0.137236i
$250$	10.5267	−	6.07760i	0.665768	−	0.384381i
$251$	−12.7766	+	22.1297i	−0.806451	+	1.39681i	0.108857	+	0.994057i	$0.465281\pi$
$251$	−12.7766	+	22.1297i	−0.806451	+	1.39681i	−0.915307	+	0.402756i	$0.868052\pi$
$252$	6.82702	+	4.04868i	0.430062	+	0.255043i
$253$	7.03955	−	12.1929i	0.442573	−	0.766558i
$254$	14.1211	+	8.15283i	0.886038	+	0.511554i
$255$	4.42697	−	16.7907i	0.277228	−	1.05147i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.2922	−	26.4869i	−0.953902	−	1.65221i	−0.736860	−	0.676045i	$-0.763692\pi$
$257$	−15.2922	−	26.4869i	−0.953902	−	1.65221i	−0.217042	−	0.976162i	$-0.569641\pi$
$258$	−4.71852	−	17.3315i	−0.293762	−	1.07901i
$259$	4.92187	+	0.0969973i	0.305830	+	0.00602712i
$260$	−1.10176	+	6.68902i	−0.0683281	+	0.414836i
$261$	4.87108	−	8.59540i	0.301512	−	0.532042i
$262$	−10.5129	+	6.06961i	−0.649488	+	0.374982i
$263$	6.24887	−	3.60779i	0.385322	−	0.222466i	−0.294809	−	0.955556i	$-0.595256\pi$
$263$	6.24887	−	3.60779i	0.385322	−	0.222466i	0.680131	+	0.733090i	$0.261923\pi$
$264$	4.49696	+	4.46105i	0.276769	+	0.274558i
$265$			8.46915i			0.520256i
$266$	−6.16877	+	10.2144i	−0.378232	+	0.626285i
$267$	11.8702	+	11.7754i	0.726447	+	0.720644i
$268$	−4.94209			−0.301886
$269$	−10.4463	+	18.0935i	−0.636920	+	1.10318i	0.349185	+	0.937054i	$0.386458\pi$
$269$	−10.4463	+	18.0935i	−0.636920	+	1.10318i	−0.986105	+	0.166124i	$0.946875\pi$
$270$	2.41492	−	9.46663i	0.146967	−	0.576121i
$271$	−8.97137	+	5.17962i	−0.544972	+	0.314640i	−0.747092	−	0.664721i	$-0.768550\pi$
$271$	−8.97137	+	5.17962i	−0.544972	+	0.314640i	0.202120	+	0.979361i	$0.435217\pi$
$272$	−5.33209			−0.323306
$273$	−1.36748	−	16.4660i	−0.0827637	−	0.996569i
$274$	−19.2076			−1.16037
$275$	−4.63943	+	2.67857i	−0.279768	+	0.161524i
$276$	1.75162	+	6.43383i	0.105435	+	0.387271i
$277$	9.90633	−	17.1583i	0.595214	−	1.03094i	−0.398303	−	0.917254i	$-0.630401\pi$
$277$	9.90633	−	17.1583i	0.595214	−	1.03094i	0.993517	−	0.113686i	$-0.0362659\pi$
$278$	−12.2242			−0.733158
$279$	−4.48466	−	7.62578i	−0.268490	−	0.456544i
$280$	−4.25823	−	2.57167i	−0.254478	−	0.153687i
$281$		−	12.7301i		−	0.759417i	−0.925106	−	0.379709i	$-0.876024\pi$
$281$		−	12.7301i		−	0.759417i	0.925106	−	0.379709i	$-0.123976\pi$
$282$	−8.88515	+	8.95669i	−0.529103	+	0.533363i
$283$	−20.5311	+	11.8536i	−1.22045	+	0.704625i	−0.965013	−	0.262201i	$-0.915552\pi$
$283$	−20.5311	+	11.8536i	−1.22045	+	0.704625i	−0.255434	+	0.966827i	$0.582218\pi$
$284$	10.1167	−	5.84088i	0.600316	−	0.346592i
$285$	14.2023	+	3.74452i	0.841271	+	0.221806i
$286$	2.14300	−	13.0106i	0.126718	−	0.769335i
$287$	−15.0503	−	0.296601i	−0.888388	−	0.0175078i
$288$	−2.99990	+	0.0240567i	−0.176771	+	0.00141755i
$289$	−5.71560	−	9.89971i	−0.336212	−	0.582336i
$290$	−3.09596	+	5.36237i	−0.181801	+	0.314889i
$291$	−22.2160	−	5.85740i	−1.30233	−	0.343367i
$292$	4.40172	+	2.54133i	0.257591	+	0.148720i
$293$	3.70943	−	6.42492i	0.216707	−	0.375348i	−0.737092	−	0.675792i	$-0.763802\pi$
$293$	3.70943	−	6.42492i	0.216707	−	0.375348i	0.953799	+	0.300444i	$0.0971350\pi$
$294$	11.5928	+	3.55054i	0.676107	+	0.207072i
$295$	−4.62023	+	8.00247i	−0.269000	+	0.465922i
$296$	−1.61137	+	0.930327i	−0.0936592	+	0.0540742i
$297$	−4.69719	+	18.4133i	−0.272559	+	1.06845i
$298$	12.5417			0.726519
$299$	8.80167	−	10.7332i	0.509014	−	0.620714i
$300$	0.646844	−	2.45336i	0.0373456	−	0.141645i
$301$	−13.2481	−	24.0276i	−0.763607	−	1.38493i
$302$	−0.906639	+	0.523448i	−0.0521712	+	0.0301211i
$303$	17.4663	+	17.3268i	1.00341	+	0.995396i
$304$		−	4.51011i		−	0.258673i
$305$	4.23686	+	2.44615i	0.242602	+	0.140066i
$306$	−8.10897	−	13.7886i	−0.463559	−	0.788242i
$307$		−	28.3173i		−	1.61615i	−0.589077	−	0.808077i	$-0.700508\pi$
$307$		−	28.3173i		−	1.61615i	0.589077	−	0.808077i	$-0.299492\pi$
$308$	8.28257	+	5.00209i	0.471943	+	0.285020i
$309$	1.79381	+	6.58881i	0.102046	+	0.374824i
$310$	2.77227	+	4.80171i	0.157454	+	0.272719i
$311$	−9.95325			−0.564397			−0.282198	−	0.959356i	$-0.591064\pi$
$311$	−9.95325			−0.564397			−0.282198	+	0.959356i	$0.591064\pi$
$312$	3.65981	+	5.06021i	0.207196	+	0.286478i
$313$			34.5494i			1.95285i	0.215856	+	0.976425i	$0.430746\pi$
$313$			34.5494i			1.95285i	−0.215856	+	0.976425i	$0.569254\pi$
$314$	3.66859	+	6.35418i	0.207030	+	0.358587i
$315$	0.174391	−	14.9226i	0.00982584	−	0.840793i
$316$	7.01426	−	12.1491i	0.394583	−	0.683438i
$317$			19.1192i			1.07384i	0.843633	+	0.536921i	$0.180413\pi$
$317$			19.1192i			1.07384i	−0.843633	+	0.536921i	$0.819587\pi$
$318$	5.53880	+	5.49456i	0.310601	+	0.308120i
$319$	6.02187	−	10.4302i	0.337160	−	0.583978i
$320$	1.88020			0.105106
$321$	23.4059	−	23.5943i	1.30639	−	1.31691i
$322$	4.91798	+	8.91958i	0.274068	+	0.497069i
$323$	20.8265	−	12.0242i	1.15882	−	0.669042i
$324$	−4.62442	−	7.72106i	−0.256912	−	0.428948i
$325$	−4.94238	+	1.86232i	−0.274154	+	0.103303i
$326$			3.71943i			0.206000i
$327$	2.40623	−	0.655100i	0.133065	−	0.0362271i
$328$	4.92731	−	2.84478i	0.272065	−	0.157077i
$329$	−9.96274	+	16.4965i	−0.549264	+	0.909484i
$330$	3.03633	−	11.5162i	0.167144	−	0.633948i
$331$	−13.8450	+	23.9803i	−0.760991	+	1.31807i	0.181350	+	0.983419i	$0.441953\pi$
$331$	−13.8450	+	23.9803i	−0.760991	+	1.31807i	−0.942340	+	0.334656i	$0.891380\pi$
$332$	−2.37977	+	4.12188i	−0.130607	+	0.226218i
$333$	−4.85635	−	2.75213i	−0.266126	−	0.150816i
$334$	0.613896	+	0.354433i	0.0335909	+	0.0193937i
$335$	4.64606	+	8.04721i	0.253841	+	0.439666i
$336$	−4.44450	+	1.11644i	−0.242467	+	0.0609068i
$337$	11.3641			0.619042			0.309521	−	0.950893i	$-0.399831\pi$
$337$	11.3641			0.619042			0.309521	+	0.950893i	$0.399831\pi$
$338$	4.16938	−	12.3133i	0.226784	−	0.669753i
$339$	18.0293	+	4.75355i	0.979220	+	0.258178i
$340$	5.01270	+	8.68224i	0.271852	+	0.470861i
$341$	−5.39227	−	9.33968i	−0.292008	−	0.505772i
$342$	11.6630	−	6.85891i	0.630662	−	0.370887i
$343$	18.4879	+	1.09418i	0.998253	+	0.0590801i
$344$	8.98116	+	5.18527i	0.484232	+	0.279571i
$345$	8.82951	−	8.90059i	0.475365	−	0.479192i
$346$			17.4113i			0.936037i
$347$	1.44655	+	0.835165i	0.0776548	+	0.0448340i	0.538325	−	0.842738i	$-0.319057\pi$
$347$	1.44655	+	0.835165i	0.0776548	+	0.0448340i	−0.460670	+	0.887572i	$0.652391\pi$
$348$	1.49839	+	5.50372i	0.0803223	+	0.295030i
$349$	12.6119	−	7.28149i	0.675100	−	0.389769i	−0.122906	−	0.992418i	$-0.539221\pi$
$349$	12.6119	−	7.28149i	0.675100	−	0.389769i	0.798006	+	0.602649i	$0.205888\pi$
$350$	0.0763639	−	3.87489i	0.00408182	−	0.207121i
$351$	−7.51974	+	17.1596i	−0.401374	+	0.915914i
$352$	−3.65712			−0.194925
$353$	14.7039	+	25.4679i	0.782611	+	1.35552i	0.930416	+	0.366505i	$0.119446\pi$
$353$	14.7039	+	25.4679i	0.782611	+	1.35552i	−0.147805	+	0.989016i	$0.547221\pi$
$354$	2.23611	+	8.21342i	0.118848	+	0.436538i
$355$	−19.0214	−	10.9820i	−1.00955	−	0.582865i
$356$	−9.65338			−0.511628
$357$	−17.0047	−	17.5470i	−0.899982	−	0.928685i
$358$	10.6608	−	18.4651i	0.563442	−	0.975911i
$359$		−	9.42640i		−	0.497506i	−0.968567	−	0.248753i	$-0.919979\pi$
$359$		−	9.42640i		−	0.497506i	0.968567	−	0.248753i	$-0.0800208\pi$
$360$	2.85938	+	4.86213i	0.150702	+	0.256257i
$361$	0.670550	+	1.16143i	0.0352921	+	0.0611277i
$362$	2.20846	+	3.82516i	0.116074	+	0.201046i
$363$	−1.04854	+	3.97692i	−0.0550341	+	0.208734i
$364$	7.25573	+	6.19310i	0.380303	+	0.324606i
$365$		−	9.55642i		−	0.500206i
$366$	4.34854	−	1.18390i	0.227302	−	0.0618832i
$367$	0.535195	−	0.308995i	0.0279370	−	0.0161294i	−0.485966	−	0.873977i	$-0.661532\pi$
$367$	0.535195	−	0.308995i	0.0279370	−	0.0161294i	0.513903	+	0.857848i	$0.328199\pi$
$368$	−3.33400	−	1.92489i	−0.173797	−	0.100342i
$369$	14.8499	+	8.41554i	0.773054	+	0.438096i
$370$	3.02970	+	1.74920i	0.157507	+	0.0909366i
$371$	10.2014	+	6.16095i	0.529632	+	0.319860i
$372$	4.93889	+	1.30217i	0.256069	+	0.0675143i
$373$	−16.4848	+	28.5526i	−0.853552	+	1.47840i	0.0244298	+	0.999702i	$0.492223\pi$
$373$	−16.4848	+	28.5526i	−0.853552	+	1.47840i	−0.877982	+	0.478694i	$0.841110\pi$
$374$	−9.75005	−	16.8876i	−0.504163	−	0.873237i
$375$	−20.3140	+	5.53052i	−1.04901	+	0.285595i
$376$		−	7.28396i		−	0.375641i
$377$	7.52925	−	9.18151i	0.387776	−	0.472872i
$378$	−9.64620	−	9.79545i	−0.496147	−	0.503823i
$379$	−8.03496	−	13.9170i	−0.412728	−	0.714866i	0.582459	−	0.812860i	$-0.302091\pi$
$379$	−8.03496	−	13.9170i	−0.412728	−	0.714866i	−0.995187	+	0.0979941i	$0.968757\pi$
$380$	−7.34381	+	4.23995i	−0.376730	+	0.217505i
$381$	−20.0502	−	19.8901i	−1.02720	−	1.01900i
$382$	6.10186			0.312198
$383$	−7.67226	+	13.2887i	−0.392034	+	0.679023i	−0.992718	−	0.120464i	$-0.961562\pi$
$383$	−7.67226	+	13.2887i	−0.392034	+	0.679023i	0.600684	+	0.799487i	$0.294895\pi$
$384$	1.21982	−	1.22965i	0.0622489	−	0.0627501i
$385$	0.358457	−	18.1890i	0.0182687	−	0.926995i
$386$	−15.7646	−	9.10171i	−0.802398	−	0.463265i
$387$	0.249481	+	31.1106i	0.0126818	+	1.58144i
$388$	11.4876	−	6.63238i	0.583196	−	0.336708i
$389$		−	11.3388i		−	0.574898i	−0.957796	−	0.287449i	$-0.907193\pi$
$389$		−	11.3388i		−	0.574898i	0.957796	−	0.287449i	$-0.0928071\pi$
$390$	4.79896	−	10.7164i	0.243005	−	0.542645i
$391$		−	20.5274i		−	1.03811i
$392$	−6.19537	+	3.25844i	−0.312913	+	0.164576i
$393$	20.2873	−	5.52325i	1.02336	−	0.278611i
$394$	−0.816248	+	1.41378i	−0.0411220	+	0.0712254i
$395$	−26.3764			−1.32714
$396$	−5.56170	−	9.45719i	−0.279486	−	0.475242i
$397$	21.6176	+	12.4809i	1.08496	+	0.626401i	0.932229	−	0.361868i	$-0.117861\pi$
$397$	21.6176	+	12.4809i	1.08496	+	0.626401i	0.152728	+	0.988268i	$0.451194\pi$
$398$	23.0878			1.15729
$399$	14.8420	−	14.3833i	0.743029	−	0.720064i
$400$	0.732427	+	1.26860i	0.0366213	+	0.0634300i
$401$	8.62310	−	4.97855i	0.430617	−	0.248617i	−0.268992	−	0.963142i	$-0.586691\pi$
$401$	8.62310	−	4.97855i	0.430617	−	0.248617i	0.699610	+	0.714525i	$0.253357\pi$
$402$	8.27710	+	2.18231i	0.412824	+	0.108844i
$403$	−3.74905	−	9.94956i	−0.186754	−	0.495623i
$404$	−14.2043			−0.706690
$405$	−8.22478	+	14.7885i	−0.408693	+	0.734847i
$406$	4.20701	+	7.63011i	0.208790	+	0.378676i
$407$	−5.89299	−	3.40232i	−0.292105	−	0.168647i
$408$	8.93028	+	2.35452i	0.442114	+	0.116566i
$409$	3.60971	+	2.08407i	0.178489	+	0.103051i	0.586582	−	0.809890i	$-0.300473\pi$
$409$	3.60971	+	2.08407i	0.178489	+	0.103051i	−0.408094	+	0.912940i	$0.633806\pi$
$410$	−9.26432	−	5.34876i	−0.457532	−	0.264156i
$411$	32.1692	+	8.48161i	1.58679	+	0.418367i
$412$	−3.41431	−	1.97125i	−0.168211	−	0.0971168i
$413$	6.27829	+	11.3867i	0.308934	+	0.560304i
$414$	−0.0926129	−	11.5490i	−0.00455167	−	0.567600i
$415$	8.94888			0.439283
$416$	−3.55762	−	0.585980i	−0.174426	−	0.0287300i
$417$	20.4733	+	5.39791i	1.00258	+	0.264337i
$418$	14.2842	−	8.24701i	0.698665	−	0.403375i
$419$	−8.71172	−	15.0891i	−0.425596	−	0.737153i	0.570880	−	0.821033i	$-0.306602\pi$
$419$	−8.71172	−	15.0891i	−0.425596	−	0.737153i	−0.996476	+	0.0838802i	$0.973269\pi$
$420$	5.99617	+	6.18741i	0.292583	+	0.301915i
$421$	−10.8698			−0.529763			−0.264882	−	0.964281i	$-0.585333\pi$
$421$	−10.8698			−0.529763			−0.264882	+	0.964281i	$0.585333\pi$
$422$	10.5838	+	6.11057i	0.515212	+	0.297458i
$423$	18.8361	−	11.0773i	0.915840	−	0.538599i
$424$	−4.50439			−0.218752
$425$	−3.90537	+	6.76429i	−0.189438	+	0.328116i
$426$	−19.5228	+	5.31511i	−0.945883	+	0.257518i
$427$	6.02863	−	3.32400i	0.291746	−	0.160860i
$428$			19.1879i			0.927483i
$429$	−9.33432	+	20.8441i	−0.450665	+	1.00636i
$430$		−	19.4987i		−	0.940310i
$431$	−25.7111	+	14.8443i	−1.23846	+	0.715027i	−0.968780	−	0.247923i	$-0.920252\pi$
$431$	−25.7111	+	14.8443i	−1.23846	+	0.715027i	−0.269683	+	0.962949i	$0.586919\pi$
$432$	5.03491	+	1.28440i	0.242242	+	0.0617955i
$433$	−6.53518	−	3.77309i	−0.314061	−	0.181323i	0.334682	−	0.942331i	$-0.391371\pi$
$433$	−6.53518	−	3.77309i	−0.314061	−	0.181323i	−0.648742	+	0.761008i	$0.724705\pi$
$434$	7.80057	+	0.153729i	0.374440	+	0.00737923i
$435$	7.55306	−	7.61387i	0.362142	−	0.365057i
$436$	−0.719902	+	1.24691i	−0.0344771	+	0.0597160i
$437$	17.3629			0.830581
$438$	−6.24987	−	6.19996i	−0.298631	−	0.296245i
$439$	8.13543	−	4.69699i	0.388283	−	0.224175i	−0.293133	−	0.956072i	$-0.594698\pi$
$439$	8.13543	−	4.69699i	0.388283	−	0.224175i	0.681416	+	0.731897i	$0.261365\pi$
$440$	3.43806	+	5.95489i	0.163903	+	0.283888i
$441$	−17.8480	−	11.0656i	−0.849906	−	0.526934i
$442$	−6.77887	−	17.9903i	−0.322438	−	0.855713i
$443$		−	12.6019i		−	0.598733i	−0.954138	−	0.299366i	$-0.903225\pi$
$443$		−	12.6019i		−	0.598733i	0.954138	−	0.299366i	$-0.0967753\pi$
$444$	3.10957	−	0.846583i	0.147573	−	0.0401771i
$445$	9.07513	+	15.7186i	0.430203	+	0.745133i
$446$	−1.70403	+	2.95147i	−0.0806881	+	0.139756i
$447$	−21.0050	−	5.53810i	−0.993502	−	0.261943i
$448$	1.36777	−	2.26478i	0.0646208	−	0.107001i
$449$	25.5271	+	14.7381i	1.20470	+	0.695533i	0.961596	−	0.274468i	$-0.0885017\pi$
$449$	25.5271	+	14.7381i	1.20470	+	0.695533i	0.243102	+	0.970001i	$0.421835\pi$
$450$	−2.16669	+	3.82330i	−0.102139	+	0.180232i
$451$	18.0198	+	10.4037i	0.848518	+	0.489892i
$452$	−9.32273	+	5.38248i	−0.438505	+	0.253171i
$453$	1.74960	−	0.476330i	0.0822032	−	0.0223799i
$454$			12.0646i			0.566222i
$455$	3.26312	−	17.6366i	0.152977	−	0.826818i
$456$	−1.99156	+	7.55361i	−0.0932632	+	0.353730i
$457$	6.58219	+	11.4007i	0.307902	+	0.533302i	0.977903	−	0.209058i	$-0.0670398\pi$
$457$	6.58219	+	11.4007i	0.307902	+	0.533302i	−0.670001	+	0.742360i	$0.733707\pi$
$458$	−8.41943	−	14.5829i	−0.393414	−	0.681413i
$459$	7.49232	+	26.6741i	0.349711	+	1.24504i
$460$			7.23834i			0.337489i
$461$	−18.4159	+	31.8972i	−0.857712	+	1.48560i	0.0163943	+	0.999866i	$0.494781\pi$
$461$	−18.4159	+	31.8972i	−0.857712	+	1.48560i	−0.874106	+	0.485735i	$0.838552\pi$
$462$	−11.6630	−	12.0350i	−0.542611	−	0.559917i
$463$	19.2982			0.896865			0.448432	−	0.893817i	$-0.351983\pi$
$463$	19.2982			0.896865			0.448432	+	0.893817i	$0.351983\pi$
$464$	−2.85202	−	1.64661i	−0.132402	−	0.0764422i
$465$	−2.52272	−	9.26616i	−0.116988	−	0.429708i
$466$	0.854031	+	1.47923i	0.0395622	+	0.0685238i
$467$	2.22919			0.103154			0.0515772	−	0.998669i	$-0.483575\pi$
$467$	2.22919			0.103154			0.0515772	+	0.998669i	$0.483575\pi$
$468$	−3.89505	−	10.0910i	−0.180049	−	0.466457i
$469$	13.0730	+	0.257635i	0.603656	+	0.0118965i
$470$	−11.8605	+	6.84764i	−0.547082	+	0.315858i
$471$	−3.33836	−	12.2620i	−0.153823	−	0.565005i
$472$	−4.25618	−	2.45731i	−0.195907	−	0.113107i
$473$			37.9264i			1.74386i
$474$	−17.1123	+	17.2501i	−0.785996	+	0.792324i
$475$	−5.72153	−	3.30333i	−0.262522	−	0.151567i
$476$	14.1046	+	0.277966i	0.646486	+	0.0127405i
$477$	−6.85021	−	11.6482i	−0.313650	−	0.533334i
$478$	−5.94696	−	10.3004i	−0.272008	−	0.471131i
$479$	7.14492	+	12.3754i	0.326460	+	0.565445i	0.981807	−	0.189883i	$-0.0608109\pi$
$479$	7.14492	+	12.3754i	0.326460	+	0.565445i	−0.655347	+	0.755328i	$0.727478\pi$
$480$	−3.14899	−	0.830251i	−0.143731	−	0.0378956i
$481$	−5.18750	−	4.25398i	−0.236529	−	0.193965i
$482$	15.6091			0.710975
$483$	−4.29804	−	17.1103i	−0.195568	−	0.778546i
$484$	−1.18727	−	2.05641i	−0.0539669	−	0.0934734i
$485$	−21.5990	−	12.4702i	−0.980760	−	0.566242i
$486$	4.33562	+	14.9734i	0.196668	+	0.679207i
$487$	−16.1705	+	28.0081i	−0.732754	+	1.26917i	0.222948	+	0.974830i	$0.428432\pi$
$487$	−16.1705	+	28.0081i	−0.732754	+	1.26917i	−0.955702	+	0.294337i	$0.904901\pi$
$488$	−1.30101	+	2.25341i	−0.0588938	+	0.102007i
$489$	1.64241	−	6.22936i	0.0742724	−	0.281702i
$490$	11.1300	+	7.02466i	0.502801	+	0.317342i
$491$	−37.9516	+	21.9114i	−1.71273	+	0.988847i	−0.781899	+	0.623405i	$0.785749\pi$
$491$	−37.9516	+	21.9114i	−1.71273	+	0.988847i	−0.930834	+	0.365442i	$0.880918\pi$
$492$	−9.50853	+	2.58871i	−0.428678	+	0.116708i
$493$		−	17.5598i		−	0.790854i
$494$	15.2170	−	5.73386i	0.684645	−	0.257979i
$495$	−10.1706	+	17.9468i	−0.457134	+	0.806649i
$496$	−2.55383	+	1.47446i	−0.114670	+	0.0662050i
$497$	−27.0656	+	14.9231i	−1.21406	+	0.669393i
$498$	5.80580	−	5.85255i	0.260164	−	0.262259i
$499$	28.9528			1.29611			0.648054	−	0.761595i	$-0.275583\pi$
$499$	28.9528			1.29611			0.648054	+	0.761595i	$0.275583\pi$
$500$	6.07760	−	10.5267i	0.271799	−	0.470769i
$501$	−0.871654	−	0.864692i	−0.0389426	−	0.0386316i
$502$			25.5532i			1.14049i
$503$	−9.17611	+	15.8935i	−0.409143	+	0.708656i	−0.994794	−	0.101907i	$-0.967505\pi$
$503$	−9.17611	+	15.8935i	−0.409143	+	0.708656i	0.585651	+	0.810563i	$0.300839\pi$
$504$	7.93671	+	0.0927516i	0.353529	+	0.00413148i
$505$	13.3535	+	23.1289i	0.594221	+	1.02922i
$506$		−	14.0791i		−	0.625892i
$507$	−12.4202	+	18.7813i	−0.551600	+	0.834109i
$508$	16.3057			0.723447
$509$	−19.9332	−	34.5253i	−0.883523	−	1.53031i	−0.847397	−	0.530960i	$-0.821832\pi$
$509$	−19.9332	−	34.5253i	−0.883523	−	1.53031i	−0.0361262	−	0.999347i	$-0.511502\pi$
$510$	−4.56147	−	16.7547i	−0.201985	−	0.741908i
$511$	−11.5111	−	6.95189i	−0.509221	−	0.307534i
$512$			1.00000i			0.0441942i
$513$	−22.5621	+	6.33732i	−0.996141	+	0.279800i
$514$	−26.4869	−	15.2922i	−1.16829	−	0.674511i
$515$			7.41270i			0.326643i
$516$	−12.7521	−	12.6502i	−0.561380	−	0.556896i
$517$	23.0695	−	13.3192i	1.01459	−	0.585776i
$518$	4.31097	−	2.37693i	0.189413	−	0.104437i
$519$	7.68841	−	29.1607i	0.337484	−	1.28001i
$520$	2.39036	+	6.34374i	0.104824	+	0.278192i
$521$	−14.1304			−0.619063			−0.309531	−	0.950889i	$-0.600172\pi$
$521$	−14.1304			−0.619063			−0.309531	+	0.950889i	$0.600172\pi$
$522$	−0.0792242	−	9.87937i	−0.00346755	−	0.432408i
$523$	−28.0353	+	16.1862i	−1.22590	+	0.707773i	−0.966169	−	0.257909i	$-0.916967\pi$
$523$	−28.0353	+	16.1862i	−1.22590	+	0.707773i	−0.259729	+	0.965681i	$0.583633\pi$
$524$	−6.06961	+	10.5129i	−0.265152	+	0.459257i
$525$	−1.83895	+	6.45600i	−0.0802585	+	0.281763i
$526$	3.60779	−	6.24887i	0.157307	−	0.272464i
$527$	−13.6173	−	7.86194i	−0.593178	−	0.342471i
$528$	6.12501	+	1.61490i	0.266557	+	0.0702794i
$529$	−4.08962	+	7.08342i	−0.177809	+	0.307975i
$530$	4.23457	+	7.33450i	0.183938	+	0.318590i
$531$	−0.118229	−	14.7434i	−0.00513072	−	0.639808i
$532$	−0.235115	+	11.9303i	−0.0101935	+	0.517245i
$533$	15.8625	+	13.0079i	0.687081	+	0.563437i
$534$	16.1676	+	4.26270i	0.699642	+	0.184465i
$535$	31.2437	−	18.0385i	1.35078	−	0.779874i
$536$	−4.27998	+	2.47105i	−0.184867	+	0.106733i
$537$	−26.0087	+	26.2181i	−1.12236	+	1.13139i
$538$			20.8925i			0.900740i
$539$	−21.6486	−	13.6635i	−0.932471	−	0.588528i
$540$	−2.64194	−	9.40580i	−0.113691	−	0.404761i
$541$	−31.4192			−1.35082			−0.675409	−	0.737444i	$-0.736033\pi$
$541$	−31.4192			−1.35082			−0.675409	+	0.737444i	$0.736033\pi$
$542$	−5.17962	+	8.97137i	−0.222484	+	0.385353i
$543$	−2.00966	−	7.38164i	−0.0862428	−	0.316776i
$544$	−4.61773	+	2.66605i	−0.197983	+	0.114306i
$545$	2.70712			0.115960
$546$	−9.41729	−	13.5763i	−0.403023	−	0.581010i
$547$	−43.4777			−1.85897			−0.929485	−	0.368859i	$-0.879749\pi$
$547$	−43.4777			−1.85897			−0.929485	+	0.368859i	$0.879749\pi$
$548$	−16.6342	+	9.60379i	−0.710580	+	0.410253i
$549$	−7.80579	+	0.0625959i	−0.333143	+	0.00267153i
$550$	−2.67857	+	4.63943i	−0.114215	+	0.197826i
$551$	14.8528			0.632752
$552$	4.73386	+	4.69605i	0.201486	+	0.199877i
$553$	−19.1877	+	31.7715i	−0.815945	+	1.35106i
$554$		−	19.8127i		−	0.841759i
$555$	−4.30179	−	4.26743i	−0.182601	−	0.181142i
$556$	−10.5865	+	6.11210i	−0.448966	+	0.259211i
$557$	−18.9140	+	10.9200i	−0.801413	+	0.462696i	−0.843965	−	0.536398i	$-0.819785\pi$
$557$	−18.9140	+	10.9200i	−0.801413	+	0.462696i	0.0425518	+	0.999094i	$0.486451\pi$
$558$	−7.69672	−	4.36179i	−0.325828	−	0.184649i
$559$	−6.07693	+	36.8944i	−0.257027	+	1.56047i
$560$	−4.97357	−	0.0980162i	−0.210172	−	0.00414194i
$561$	8.87240	+	32.5890i	0.374593	+	1.37591i
$562$	−6.36507	−	11.0246i	−0.268494	−	0.465046i
$563$	21.3261	−	36.9379i	0.898788	−	1.55675i	0.0697416	−	0.997565i	$-0.477783\pi$
$563$	21.3261	−	36.9379i	0.898788	−	1.55675i	0.829046	−	0.559181i	$-0.188884\pi$
$564$	−3.21642	+	12.1993i	−0.135436	+	0.513683i
$565$	17.5286	+	10.1201i	0.737433	+	0.425757i
$566$	−11.8536	+	20.5311i	−0.498245	+	0.862986i
$567$	11.8302	+	20.6651i	0.496821	+	0.867853i
$568$	5.84088	−	10.1167i	0.245078	−	0.424487i
$569$	3.04705	−	1.75922i	0.127739	−	0.0737502i	−0.434769	−	0.900542i	$-0.643170\pi$
$569$	3.04705	−	1.75922i	0.127739	−	0.0737502i	0.562508	+	0.826792i	$0.309837\pi$
$570$	14.1718	−	3.85829i	0.593591	−	0.161606i
$571$	−42.4925			−1.77825			−0.889127	−	0.457660i	$-0.848688\pi$
$571$	−42.4925			−1.77825			−0.889127	+	0.457660i	$0.848688\pi$
$572$	−4.64943	−	12.3390i	−0.194402	−	0.515921i
$573$	−10.2195	−	2.69443i	−0.426925	−	0.112562i
$574$	−13.1822	+	7.26826i	−0.550215	+	0.303371i
$575$	−4.88383	+	2.81968i	−0.203670	+	0.117589i
$576$	−2.58596	+	1.52079i	−0.107749	+	0.0633661i
$577$			16.1255i			0.671315i	0.941984	+	0.335658i	$0.108959\pi$
$577$			16.1255i			0.671315i	−0.941984	+	0.335658i	$0.891041\pi$
$578$	−9.89971	−	5.71560i	−0.411774	−	0.237738i
$579$	22.3838	+	22.2050i	0.930237	+	0.922808i
$580$			6.19193i			0.257106i
$581$	6.50993	−	10.7793i	0.270078	−	0.447201i
$582$	−22.1684	+	6.03536i	−0.918908	+	0.250174i
$583$	−8.23655	−	14.2661i	−0.341123	−	0.590843i
$584$	5.08266			0.210322
$585$	−12.7695	+	15.8289i	−0.527952	+	0.654443i
$586$		−	7.41886i		−	0.306470i
$587$	15.6938	+	27.1824i	0.647750	+	1.12194i	0.983659	+	0.180042i	$0.0576234\pi$
$587$	15.6938	+	27.1824i	0.647750	+	1.12194i	−0.335909	+	0.941895i	$0.609043\pi$
$588$	11.8150	−	2.72155i	0.487240	−	0.112235i
$589$	6.64996	−	11.5181i	0.274007	−	0.474594i
$590$			9.24046i			0.380424i
$591$	1.99136	−	2.00739i	0.0819136	−	0.0825731i
$592$	−0.930327	+	1.61137i	−0.0382362	+	0.0662271i
$593$	14.7809			0.606979			0.303489	−	0.952835i	$-0.401848\pi$
$593$	14.7809			0.606979			0.303489	+	0.952835i	$0.401848\pi$
$594$	5.13876	+	18.2950i	0.210846	+	0.750652i
$595$	−12.8072	−	23.2279i	−0.525042	−	0.952252i
$596$	10.8614	−	6.27084i	0.444900	−	0.256863i
$597$	−38.6679	−	10.1950i	−1.58257	−	0.417255i
$598$	2.25589	−	13.6960i	0.0922502	−	0.560072i
$599$			25.5246i			1.04290i	0.853280	+	0.521452i	$0.174610\pi$
$599$			25.5246i			1.04290i	−0.853280	+	0.521452i	$0.825390\pi$
$600$	−0.666497	−	2.44810i	−0.0272096	−	0.0999431i
$601$	26.1186	−	15.0796i	1.06540	−	0.615110i	0.138480	−	0.990365i	$-0.455778\pi$
$601$	26.1186	−	15.0796i	1.06540	−	0.615110i	0.926922	+	0.375255i	$0.122445\pi$
$602$	−23.4870	−	14.1845i	−0.957258	−	0.578116i
$603$	−12.8990	−	7.30994i	−0.525287	−	0.297684i
$604$	−0.523448	+	0.906639i	−0.0212988	+	0.0368906i
$605$	−2.23231	+	3.86647i	−0.0907561	+	0.157194i
$606$	23.7896	+	6.27228i	0.966386	+	0.254794i
$607$	−35.0826	−	20.2550i	−1.42396	−	0.822124i	−0.427326	−	0.904098i	$-0.640544\pi$
$607$	−35.0826	−	20.2550i	−1.42396	−	0.822124i	−0.996634	+	0.0819738i	$0.973878\pi$
$608$	−2.25506	−	3.90587i	−0.0914546	−	0.158404i
$609$	−3.67669	−	14.6368i	−0.148987	−	0.593111i
$610$	4.89230			0.198084
$611$	24.5759	−	9.26035i	0.994234	−	0.374634i
$612$	−13.9169	−	7.88679i	−0.562556	−	0.318805i
$613$	8.80698	+	15.2541i	0.355711	+	0.616109i	0.987239	−	0.159244i	$-0.0509055\pi$
$613$	8.80698	+	15.2541i	0.355711	+	0.616109i	−0.631529	+	0.775352i	$0.717572\pi$
$614$	−14.1587	−	24.5235i	−0.571397	−	0.989688i
$615$	13.1542	+	13.0491i	0.530427	+	0.526190i
$616$	9.67396	+	0.190649i	0.389775	+	0.00768145i
$617$	18.1108	+	10.4563i	0.729113	+	0.420954i	0.818098	−	0.575079i	$-0.195029\pi$
$617$	18.1108	+	10.4563i	0.729113	+	0.420954i	−0.0889845	+	0.996033i	$0.528362\pi$
$618$	4.84789	+	4.80917i	0.195011	+	0.193453i
$619$			0.896815i			0.0360460i	0.999838	+	0.0180230i	$0.00573722\pi$
$619$			0.896815i			0.0360460i	−0.999838	+	0.0180230i	$0.994263\pi$
$620$	4.80171	+	2.77227i	0.192841	+	0.111337i
$621$	−4.94463	+	19.3833i	−0.198421	+	0.777824i
$622$	−8.61976	+	4.97662i	−0.345621	+	0.199544i
$623$	25.5355	+	0.503238i	1.02306	+	0.0201618i
$624$	5.69960	+	2.55237i	0.228167	+	0.102176i
$625$	−15.5299			−0.621197
$626$	17.2747	+	29.9207i	0.690437	+	1.19587i
$627$	−27.5652	+	7.50465i	−1.10085	+	0.299707i
$628$	6.35418	+	3.66859i	0.253559	+	0.146393i
$629$	−9.92118			−0.395583
$630$	−7.31027	−	13.0105i	−0.291248	−	0.518352i
$631$	6.46286	−	11.1940i	0.257282	−	0.445626i	−0.708231	−	0.705981i	$-0.750506\pi$
$631$	6.46286	−	11.1940i	0.257282	−	0.445626i	0.965513	+	0.260355i	$0.0838397\pi$
$632$		−	14.0285i		−	0.558025i
$633$	−15.0277	−	14.9076i	−0.597296	−	0.592526i
$634$	9.55960	+	16.5577i	0.379660	+	0.657591i
$635$	−15.3289	−	26.5505i	−0.608311	−	1.05363i
$636$	7.54403	+	1.98903i	0.299140	+	0.0788702i
$637$	−18.8703	−	16.7605i	−0.747667	−	0.664074i
$638$		−	12.0437i		−	0.476816i
$639$	35.0441	−	0.281024i	1.38632	−	0.0111172i
$640$	1.62830	−	0.940099i	0.0643642	−	0.0371607i
$641$	−5.88556	−	3.39803i	−0.232466	−	0.134214i	0.379243	−	0.925297i	$-0.376184\pi$
$641$	−5.88556	−	3.39803i	−0.232466	−	0.134214i	−0.611709	+	0.791083i	$0.709518\pi$
$642$	8.47292	−	32.1362i	0.334400	−	1.26832i
$643$	−24.8365	−	14.3393i	−0.979454	−	0.565488i	−0.0773487	−	0.997004i	$-0.524645\pi$
$643$	−24.8365	−	14.3393i	−0.979454	−	0.565488i	−0.902105	+	0.431516i	$0.857979\pi$
$644$	8.71888	+	5.26559i	0.343572	+	0.207493i
$645$	−8.61015	+	32.6567i	−0.339025	+	1.28586i
$646$	12.0242	−	20.8265i	0.473084	−	0.819406i
$647$	−22.4155	−	38.8248i	−0.881244	−	1.52636i	−0.849959	−	0.526849i	$-0.823373\pi$
$647$	−22.4155	−	38.8248i	−0.881244	−	1.52636i	−0.0312853	−	0.999510i	$-0.509960\pi$
$648$	−7.86539	−	4.37442i	−0.308982	−	0.171844i
$649$		−	17.9734i		−	0.705516i
$650$	−3.34907	+	4.08401i	−0.131361	+	0.160188i
$651$	−12.9966	−	3.70202i	−0.509379	−	0.145093i
$652$	1.85972	+	3.22112i	0.0728321	+	0.126149i
$653$	31.3506	−	18.1003i	1.22684	−	0.708319i	0.260476	−	0.965480i	$-0.416121\pi$
$653$	31.3506	−	18.1003i	1.22684	−	0.708319i	0.966368	+	0.257162i	$0.0827873\pi$
$654$	1.75631	−	1.77045i	0.0686771	−	0.0692300i
$655$	22.8241			0.891813
$656$	2.84478	−	4.92731i	0.111070	−	0.192379i
$657$	7.72964	+	13.1436i	0.301562	+	0.512780i
$658$	−0.379718	+	19.2678i	−0.0148030	+	0.751137i
$659$	−16.0130	−	9.24511i	−0.623778	−	0.360139i	0.154560	−	0.987983i	$-0.450604\pi$
$659$	−16.0130	−	9.24511i	−0.623778	−	0.360139i	−0.778339	+	0.627845i	$0.783937\pi$
$660$	−3.12858	−	11.4915i	−0.121780	−	0.447307i
$661$	6.36345	−	3.67394i	0.247509	−	0.142900i	−0.371114	−	0.928587i	$-0.621024\pi$
$661$	6.36345	−	3.67394i	0.247509	−	0.142900i	0.618623	+	0.785688i	$0.287691\pi$
$662$			27.6900i			1.07620i
$663$	3.40926	+	33.1239i	0.132405	+	1.28643i
$664$			4.75954i			0.184706i
$665$	19.6472	−	10.8328i	0.761884	−	0.420080i
$666$	−5.58178	+	0.0447612i	−0.216290	+	0.00173446i
$667$	6.33910	−	10.9796i	0.245451	−	0.425133i
$668$	0.708866			0.0274268
$669$	4.15723	−	4.19070i	0.160728	−	0.162022i
$670$	8.04721	+	4.64606i	0.310891	+	0.179493i
$671$	−9.51589			−0.367357
$672$	−3.29083	+	3.18911i	−0.126946	+	0.123023i
$673$	3.97107	+	6.87810i	0.153074	+	0.265131i	0.932356	−	0.361542i	$-0.117749\pi$
$673$	3.97107	+	6.87810i	0.153074	+	0.265131i	−0.779282	+	0.626673i	$0.784416\pi$
$674$	9.84160	−	5.68205i	0.379084	−	0.218864i
$675$	5.31709	−	5.44656i	0.204655	−	0.209638i
$676$	−2.54584	−	12.7483i	−0.0979169	−	0.490319i
$677$	21.3321			0.819857			0.409929	−	0.912118i	$-0.365554\pi$
$677$	21.3321			0.819857			0.409929	+	0.912118i	$0.365554\pi$
$678$	17.9906	−	4.89798i	0.690927	−	0.188106i
$679$	−30.7332	+	16.9454i	−1.17943	+	0.650303i
$680$	8.68224	+	5.01270i	0.332949	+	0.192228i
$681$	5.32746	−	20.2061i	0.204149	−	0.774298i
$682$	−9.33968	−	5.39227i	−0.357635	−	0.206481i
$683$	26.4657	+	15.2800i	1.01268	+	0.584673i	0.911976	−	0.410244i	$-0.134556\pi$
$683$	26.4657	+	15.2800i	1.01268	+	0.584673i	0.100707	+	0.994916i	$0.467890\pi$
$684$	6.67099	−	11.7715i	0.255072	−	0.450094i
$685$	31.2757	+	18.0570i	1.19498	+	0.689923i
$686$	16.5581	−	8.29637i	0.632191	−	0.316757i
$687$	7.66155	+	28.1415i	0.292306	+	1.07366i
$688$	10.3705			0.395373
$689$	−5.72659	−	15.1977i	−0.218166	−	0.578986i
$690$	3.19628	−	12.1229i	0.121680	−	0.461511i
$691$	43.3712	−	25.0404i	1.64992	−	0.952580i	0.672814	−	0.739812i	$-0.265085\pi$
$691$	43.3712	−	25.0404i	1.64992	−	0.952580i	0.977103	−	0.212768i	$-0.0682480\pi$
$692$	8.70565	+	15.0786i	0.330939	+	0.573203i
$693$	14.2190	+	25.3064i	0.540135	+	0.961312i
$694$	1.67033			0.0634049
$695$	19.9047	+	11.4920i	0.755026	+	0.435915i
$696$	4.04951	+	4.01716i	0.153496	+	0.152270i
$697$	30.3373			1.14911
$698$	7.28149	−	12.6119i	0.275608	−	0.477368i
$699$	−0.777155	−	2.85455i	−0.0293947	−	0.107969i
$700$	−1.87131	−	3.39393i	−0.0707289	−	0.128279i
$701$			23.8423i			0.900510i	0.892900	+	0.450255i	$0.148667\pi$
$701$			23.8423i			0.900510i	−0.892900	+	0.450255i	$0.851333\pi$
$702$	2.06754	+	18.6206i	0.0780342	+	0.702788i
$703$		−	8.39176i		−	0.316501i
$704$	−3.16716	+	1.82856i	−0.119367	+	0.0689165i
$705$	22.8879	−	6.23125i	0.862007	−	0.234682i
$706$	25.4679	+	14.7039i	0.958499	+	0.553389i
$707$	37.5738	+	0.740481i	1.41311	+	0.0278486i
$708$	6.04324	+	5.99497i	0.227119	+	0.225305i
$709$	4.91229	−	8.50834i	0.184485	−	0.319537i	−0.758918	−	0.651186i	$-0.774272\pi$
$709$	4.91229	−	8.50834i	0.184485	−	0.319537i	0.943403	+	0.331649i	$0.107605\pi$
$710$	−21.9640			−0.824295
$711$	36.2773	−	21.3344i	1.36050	−	0.800102i
$712$	−8.36007	+	4.82669i	−0.313307	+	0.180888i
$713$	−5.67632	−	9.83168i	−0.212580	−	0.368199i
$714$	−23.5000	−	6.69382i	−0.879464	−	0.250510i
$715$	−15.7207	+	19.1706i	−0.587922	+	0.716939i
$716$		−	21.3217i		−	0.796828i
$717$	5.41164	+	19.8774i	0.202101	+	0.742334i
$718$	−4.71320	−	8.16350i	−0.175895	−	0.304659i
$719$	−10.0304	+	17.3732i	−0.374073	+	0.647913i	−0.990188	−	0.139743i	$-0.955372\pi$
$719$	−10.0304	+	17.3732i	−0.374073	+	0.647913i	0.616115	+	0.787656i	$0.288706\pi$
$720$	4.90736	+	2.78104i	0.182886	+	0.103643i
$721$	8.92891	+	5.39243i	0.332530	+	0.200825i
$722$	1.16143	+	0.670550i	0.0432238	+	0.0249553i
$723$	−26.1424	−	6.89261i	−0.972246	−	0.256339i
$724$	3.82516	+	2.20846i	0.142161	+	0.0820766i
$725$	−4.17779	+	2.41205i	−0.155159	+	0.0895813i
$726$	1.08040	+	3.96839i	0.0400973	+	0.147281i
$727$		−	31.1508i		−	1.15532i	−0.816277	−	0.577660i	$-0.803966\pi$
$727$		−	31.1508i		−	1.15532i	0.816277	−	0.577660i	$-0.196034\pi$
$728$	9.38019	+	1.73552i	0.347653	+	0.0643225i
$729$	−0.649475	−	26.9922i	−0.0240546	−	0.999711i
$730$	−4.77821	−	8.27610i	−0.176849	−	0.306312i
$731$	27.6484	+	47.8884i	1.02261	+	1.77121i
$732$	3.17400	−	3.19956i	0.117314	−	0.118259i
$733$		−	8.10545i		−	0.299381i	−0.988733	−	0.149691i	$-0.952172\pi$
$733$		−	8.10545i		−	0.299381i	0.988733	−	0.149691i	$-0.0478278\pi$
$734$	0.308995	−	0.535195i	0.0114052	−	0.0197544i
$735$	−15.5387	−	16.6798i	−0.573155	−	0.615242i
$736$	−3.84978			−0.141905
$737$	−15.6524	−	9.03692i	−0.576564	−	0.332879i
$738$	17.0682	−	0.136872i	0.628287	−	0.00503833i
$739$	−13.6636	−	23.6661i	−0.502624	−	0.870571i	−0.999995	−	0.00303311i	$-0.999035\pi$
$739$	−13.6636	−	23.6661i	−0.502624	−	0.870571i	0.497371	−	0.867538i	$-0.334299\pi$
$740$	3.49840			0.128604
$741$	−28.0176	+	2.88370i	−1.02925	+	0.105935i
$742$	11.9152	+	0.234817i	0.437420	+	0.00862041i
$743$	−15.4302	+	8.90864i	−0.566080	+	0.326826i	−0.755582	−	0.655054i	$-0.772646\pi$
$743$	−15.4302	+	8.90864i	−0.566080	+	0.326826i	0.189502	+	0.981880i	$0.439313\pi$
$744$	4.92829	−	1.34173i	0.180680	−	0.0491903i
$745$	−20.4216	−	11.7904i	−0.748189	−	0.431967i
$746$			32.9697i			1.20710i
$747$	−12.3080	+	7.23824i	−0.450326	+	0.264833i
$748$	−16.8876	−	9.75005i	−0.617471	−	0.356497i
$749$	1.00028	−	50.7566i	0.0365494	−	1.85461i
$750$	−14.8272	+	14.9466i	−0.541414	+	0.545773i
$751$	4.80280	+	8.31870i	0.175257	+	0.303554i	0.940250	−	0.340485i	$-0.110591\pi$
$751$	4.80280	+	8.31870i	0.175257	+	0.303554i	−0.764993	+	0.644038i	$0.777258\pi$
$752$	−3.64198	−	6.30809i	−0.132809	−	0.230032i
$753$	11.2837	−	42.7969i	0.411200	−	1.55960i
$754$	1.92977	−	11.7160i	0.0702779	−	0.426673i
$755$	1.96837			0.0716364
$756$	−13.2516	−	3.66000i	−0.481955	−	0.133113i
$757$	12.3404	+	21.3742i	0.448519	+	0.776857i	0.998290	−	0.0584582i	$-0.0186184\pi$
$757$	12.3404	+	21.3742i	0.448519	+	0.776857i	−0.549771	+	0.835315i	$0.685285\pi$
$758$	−13.9170	−	8.03496i	−0.505487	−	0.291843i
$759$	−6.21699	+	23.5799i	−0.225663	+	0.855896i
$760$	−4.23995	+	7.34381i	−0.153799	+	0.266388i
$761$	13.7476	−	23.8116i	0.498351	−	0.863169i	−0.501648	−	0.865072i	$-0.667273\pi$
$761$	13.7476	−	23.8116i	0.498351	−	0.863169i	0.999998	+	0.00190348i	$0.000605897\pi$
$762$	−27.3090	−	7.20019i	−0.989301	−	0.260836i
$763$	1.96931	−	3.26084i	0.0712940	−	0.118050i
$764$	5.28436	−	3.05093i	0.191182	−	0.110379i
$765$	0.241178	+	30.0752i	0.00871980	+	1.08737i
$766$			15.3445i			0.554420i
$767$	2.87987	−	17.4843i	0.103986	−	0.631322i
$768$	0.441576	−	1.67482i	0.0159340	−	0.0604347i
$769$	−13.7770	+	7.95414i	−0.496811	+	0.286834i	−0.727395	−	0.686218i	$-0.759269\pi$
$769$	−13.7770	+	7.95414i	−0.496811	+	0.286834i	0.230585	+	0.973052i	$0.425936\pi$
$770$	−8.78405	−	15.9313i	−0.316555	−	0.574125i
$771$	37.6080	+	37.3076i	1.35442	+	1.34360i
$772$	−18.2034			−0.655156
$773$	25.4490	−	44.0790i	0.915337	−	1.58541i	0.108931	−	0.994049i	$-0.465257\pi$
$773$	25.4490	−	44.0790i	0.915337	−	1.58541i	0.806407	−	0.591361i	$-0.201409\pi$
$774$	15.7714	+	26.8179i	0.566890	+	0.963948i
$775$			4.31972i			0.155169i
$776$	6.63238	−	11.4876i	0.238089	−	0.412382i
$777$	−8.26967	+	2.07731i	−0.296673	+	0.0745231i
$778$	−5.66938	−	9.81965i	−0.203257	−	0.352051i
$779$			25.6606i			0.919386i
$780$	−1.20217	−	11.6801i	−0.0430446	−	0.418216i
$781$	42.7216			1.52870
$782$	−10.2637	−	17.7772i	−0.367028	−	0.635712i
$783$	−4.22981	+	16.5811i	−0.151161	+	0.592561i
$784$	−3.73613	+	5.91957i	−0.133433	+	0.211413i
$785$		−	13.7953i		−	0.492377i
$786$	14.8077	−	14.9269i	0.528174	−	0.532426i
$787$	3.08887	+	1.78336i	0.110106	+	0.0635700i	0.554042	−	0.832489i	$-0.313085\pi$
$787$	3.08887	+	1.78336i	0.110106	+	0.0635700i	−0.443935	+	0.896059i	$0.646418\pi$
$788$			1.63250i			0.0581553i
$789$	−8.80174	+	8.87260i	−0.313350	+	0.315873i
$790$	−22.8426	+	13.1882i	−0.812705	+	0.469215i
$791$	24.9414	−	13.7519i	0.886816	−	0.488963i
$792$	−9.54517	−	5.40932i	−0.339173	−	0.192212i
$793$	−9.25697	−	1.52473i	−0.328725	−	0.0541447i
$794$	24.9619			0.885864
$795$	−3.85339	−	14.1538i	−0.136666	−	0.501984i
$796$	19.9947	−	11.5439i	0.708692	−	0.409163i
$797$	4.20104	−	7.27641i	0.148808	−	0.257744i	−0.781979	−	0.623305i	$-0.785790\pi$
$797$	4.20104	−	7.27641i	0.148808	−	0.257744i	0.930787	+	0.365561i	$0.119123\pi$
$798$	5.66192	−	19.8773i	0.200430	−	0.703648i
$799$	19.4194	−	33.6353i	0.687008	−	1.18993i
$800$	1.26860	+	0.732427i	0.0448518	+	0.0258952i
$801$	−25.1955	−	14.2785i	−0.890240	−	0.504506i
$802$	4.97855	−	8.62310i	0.175799	−	0.304492i
$803$	9.29396	+	16.0976i	0.327977	+	0.568072i
$804$	8.25934	−	2.24861i	0.291284	−	0.0793025i
$805$	0.377340	−	19.1471i	0.0132995	−	0.674848i
$806$	−8.22155	−	6.74204i	−0.289592	−	0.237478i
$807$	9.22564	−	34.9911i	0.324758	−	1.23175i
$808$	−12.3013	+	7.10215i	−0.432758	+	0.249853i
$809$	1.54419	−	0.891541i	0.0542910	−	0.0313449i	−0.472609	−	0.881272i	$-0.656688\pi$
$809$	1.54419	−	0.891541i	0.0542910	−	0.0313449i	0.526900	+	0.849927i	$0.323354\pi$
$810$	0.271379	+	16.9196i	0.00953530	+	0.594495i
$811$			33.9033i			1.19051i	0.803538	+	0.595253i	$0.202948\pi$
$811$			33.9033i			1.19051i	−0.803538	+	0.595253i	$0.797052\pi$
$812$	7.45843	+	4.50437i	0.261740	+	0.158072i
$813$	12.6365	−	12.7382i	0.443180	−	0.446748i
$814$	−6.80464			−0.238503
$815$	3.49663	−	6.05635i	0.122482	−	0.212145i
$816$	8.91111	−	2.42606i	0.311951	−	0.0849291i
$817$	−40.5060	+	23.3862i	−1.41713	+	0.818178i
$818$	4.16814			0.145735
$819$	9.77727	+	26.8962i	0.341646	+	0.939829i
$820$	−10.6975			−0.373573
$821$	2.12966	−	1.22956i	0.0743256	−	0.0429119i	−0.462377	−	0.886684i	$-0.653003\pi$
$821$	2.12966	−	1.22956i	0.0743256	−	0.0429119i	0.536702	+	0.843772i	$0.319670\pi$
$822$	32.1001	−	8.73929i	1.11962	−	0.304818i
$823$	−3.56733	+	6.17880i	−0.124349	+	0.215379i	−0.921478	−	0.388430i	$-0.873018\pi$
$823$	−3.56733	+	6.17880i	−0.124349	+	0.215379i	0.797129	+	0.603809i	$0.206351\pi$
$824$	−3.94251			−0.137344
$825$	6.53478	−	6.58739i	0.227512	−	0.229344i
$826$	11.1305	+	6.72204i	0.387280	+	0.233890i
$827$			5.36637i			0.186607i	0.995638	+	0.0933035i	$0.0297427\pi$
$827$			5.36637i			0.186607i	−0.995638	+	0.0933035i	$0.970257\pi$
$828$	−5.85468	−	9.95538i	−0.203464	−	0.345973i
$829$	0.630628	−	0.364093i	0.0219026	−	0.0126455i	−0.489009	−	0.872279i	$-0.662641\pi$
$829$	0.630628	−	0.364093i	0.0219026	−	0.0126455i	0.510911	+	0.859633i	$0.329308\pi$
$830$	7.74996	−	4.47444i	0.269005	−	0.155310i
$831$	−8.74880	+	33.1826i	−0.303492	+	1.15109i
$832$	−3.37398	+	1.27133i	−0.116972	+	0.0440756i
$833$	−37.2957	−	1.47057i	−1.29222	−	0.0509523i
$834$	20.4293	−	5.56191i	0.707410	−	0.192593i
$835$	−0.666404	−	1.15425i	−0.0230619	−	0.0399443i
$836$	8.24701	−	14.2842i	0.285229	−	0.494031i
$837$	10.9645	+	10.7039i	0.378990	+	0.369980i
$838$	−15.0891	−	8.71172i	−0.521246	−	0.300941i
$839$	−0.904515	+	1.56667i	−0.0312273	+	0.0540873i	−0.881217	−	0.472712i	$-0.843275\pi$
$839$	−0.904515	+	1.56667i	−0.0312273	+	0.0540873i	0.849989	+	0.526800i	$0.176608\pi$
$840$	8.28654	+	2.36037i	0.285913	+	0.0814405i
$841$	−9.07732	+	15.7224i	−0.313011	+	0.542151i
$842$	−9.41355	+	5.43491i	−0.324412	+	0.187300i
$843$	5.79212	+	21.2749i	0.199491	+	0.732747i
$844$	12.2211			0.420669
$845$	−18.3647	+	16.1300i	−0.631764	+	0.554890i
$846$	10.7738	−	19.0113i	0.370412	−	0.653621i
$847$	3.03341	+	5.50160i	0.104229	+	0.189037i
$848$	−3.90092	+	2.25219i	−0.133958	+	0.0773407i
$849$	28.9187	−	29.1515i	0.992487	−	1.00048i
$850$			7.81073i			0.267906i
$851$	−6.20343	−	3.58155i	−0.212651	−	0.122774i
$852$	−14.2497	+	14.3644i	−0.488186	+	0.492117i
$853$			28.9236i			0.990324i	0.868801	+	0.495162i	$0.164891\pi$
$853$			28.9236i			0.990324i	−0.868801	+	0.495162i	$0.835109\pi$
$854$	3.55895	−	5.89298i	0.121785	−	0.201654i
$855$	−25.4389	+	0.203998i	−0.869992	+	0.00697660i
$856$	9.59396	+	16.6172i	0.327915	+	0.567965i
$857$	−20.1662			−0.688863			−0.344431	−	0.938811i	$-0.611928\pi$
$857$	−20.1662			−0.688863			−0.344431	+	0.938811i	$0.611928\pi$
$858$	2.33831	+	22.7187i	0.0798286	+	0.775604i
$859$		−	5.08286i		−	0.173425i	−0.996233	−	0.0867125i	$-0.972364\pi$
$859$		−	5.08286i		−	0.173425i	0.996233	−	0.0867125i	$-0.0276361\pi$
$860$	−9.74934	−	16.8864i	−0.332450	−	0.575820i
$861$	25.2873	−	6.35206i	0.861788	−	0.216478i
$862$	−14.8443	+	25.7111i	−0.505600	+	0.875725i
$863$		−	52.7636i		−	1.79610i	−0.439898	−	0.898048i	$-0.644985\pi$
$863$		−	52.7636i		−	1.79610i	0.439898	−	0.898048i	$-0.355015\pi$
$864$	5.00256	−	1.40514i	0.170190	−	0.0478037i
$865$	16.3683	−	28.3508i	0.556540	−	0.963956i
$866$	−7.54617			−0.256429
$867$	14.0563	+	13.9441i	0.477378	+	0.473565i
$868$	6.83236	−	3.76715i	0.231905	−	0.127866i
$869$	44.4306	−	25.6520i	1.50720	−	0.870185i
$870$	2.73421	−	10.3703i	0.0926983	−	0.351587i
$871$	−13.7785	−	11.2990i	−0.466868	−	0.382853i
$872$			1.43980i			0.0487579i
$873$	39.7930	−	0.319106i	1.34679	−	0.0108001i
$874$	15.0367	−	8.68146i	0.508625	−	0.293655i
$875$	−16.6255	+	27.5288i	−0.562044	+	0.930645i
$876$	−8.51253	−	2.24438i	−0.287612	−	0.0758307i
$877$	11.7057	−	20.2748i	0.395272	−	0.684631i	−0.597864	−	0.801598i	$-0.703984\pi$
$877$	11.7057	−	20.2748i	0.395272	−	0.684631i	0.993136	+	0.116966i	$0.0373170\pi$
$878$	4.69699	−	8.13543i	0.158516	−	0.274557i
$879$	−3.27599	+	12.4252i	−0.110496	+	0.419092i
$880$	5.95489	+	3.43806i	0.200739	+	0.115897i
$881$	3.02845	+	5.24543i	0.102031	+	0.176723i	0.912521	−	0.409029i	$-0.134133\pi$
$881$	3.02845	+	5.24543i	0.102031	+	0.176723i	−0.810490	+	0.585752i	$0.800799\pi$
$882$	−20.9897	−	0.659097i	−0.706758	−	0.0221929i
$883$	−6.83252			−0.229933			−0.114966	−	0.993369i	$-0.536676\pi$
$883$	−6.83252			−0.229933			−0.114966	+	0.993369i	$0.536676\pi$
$884$	−14.8658	−	12.1907i	−0.499993	−	0.410016i
$885$	4.08036	−	15.4761i	0.137160	−	0.520222i
$886$	−6.30093	−	10.9135i	−0.211684	−	0.366647i
$887$	−16.8862	−	29.2478i	−0.566984	−	0.982046i	−0.996862	−	0.0791587i	$-0.974777\pi$
$887$	−16.8862	−	29.2478i	−0.566984	−	0.982046i	0.429878	−	0.902887i	$-0.358557\pi$
$888$	2.26967	−	2.28795i	0.0761652	−	0.0767784i
$889$	−43.1324	−	0.850027i	−1.44661	−	0.0285090i
$890$	15.7186	+	9.07513i	0.526888	+	0.304199i
$891$	−0.527853	−	32.9099i	−0.0176837	−	1.10252i
$892$			3.40806i			0.114110i
$893$	28.4502	+	16.4257i	0.952049	+	0.549666i
$894$	−20.9599	+	5.70636i	−0.701004	+	0.190849i
$895$	−34.7181	+	20.0445i	−1.16050	+	0.670013i
$896$	0.0521308	−	2.64524i	0.00174157	−	0.0883712i
$897$	−9.82604	+	21.9422i	−0.328082	+	0.732628i
$898$	29.4762			0.983632
$899$	−4.85572	−	8.41036i	−0.161947	−	0.280501i
$900$	0.0352395	+	4.39442i	0.00117465	+	0.146481i
$901$	−20.8000	−	12.0089i	−0.692950	−	0.400075i
$902$	20.8074			0.692812
$903$	33.0729	+	34.1277i	1.10060	+	1.13570i
$904$	−5.38248	+	9.32273i	−0.179019	+	0.310070i
$905$		−	8.30467i		−	0.276057i
$906$	1.27703	−	1.28731i	0.0424265	−	0.0427681i
$907$	−9.41810	−	16.3126i	−0.312723	−	0.541652i	0.666228	−	0.745748i	$-0.267908\pi$
$907$	−9.41810	−	16.3126i	−0.312723	−	0.541652i	−0.978951	+	0.204096i	$0.934574\pi$
$908$	6.03232	+	10.4483i	0.200190	+	0.346739i
$909$	−37.0735	−	21.0098i	−1.22965	−	0.696852i
$910$	−5.99237	−	16.9053i	−0.198645	−	0.560406i
$911$			11.8570i			0.392841i	0.980520	+	0.196420i	$0.0629318\pi$
$911$			11.8570i			0.392841i	−0.980520	+	0.196420i	$0.937068\pi$
$912$	2.05206	+	7.53740i	0.0679507	+	0.249588i
$913$	−15.0742	+	8.70311i	−0.498884	+	0.288031i
$914$	11.4007	+	6.58219i	0.377101	+	0.217719i
$915$	−8.19371	−	2.16032i	−0.270876	−	0.0714181i
$916$	−14.5829	−	8.41943i	−0.481832	−	0.278186i
$917$	16.6036	−	27.4926i	0.548299	−	0.907887i
$918$	19.8256	+	19.3543i	0.654342	+	0.638787i
$919$	−3.08230	+	5.33869i	−0.101676	+	0.176107i	−0.912375	−	0.409355i	$-0.865754\pi$
$919$	−3.08230	+	5.33869i	−0.101676	+	0.176107i	0.810700	+	0.585462i	$0.199087\pi$
$920$	3.61917	+	6.26859i	0.119321	+	0.206669i
$921$	12.8842	+	47.3245i	0.424547	+	1.55940i
$922$			36.8317i			1.21299i
$923$	41.5592	+	6.84527i	1.36794	+	0.225315i
$924$	−16.1179	−	4.59109i	−0.530241	−	0.151036i
$925$	1.36279	+	2.36043i	0.0448084	+	0.0776104i
$926$	16.7128	−	9.64911i	0.549215	−	0.317090i
$927$	−5.99571	−	10.1952i	−0.196925	−	0.334854i
$928$	−3.29323			−0.108106
$929$	6.42991	−	11.1369i	0.210959	−	0.365391i	−0.741056	−	0.671443i	$-0.765675\pi$
$929$	6.42991	−	11.1369i	0.210959	−	0.365391i	0.952015	+	0.306052i	$0.0990082\pi$
$930$	−6.81782	−	6.76337i	−0.223565	−	0.221780i
$931$	1.24387	−	31.5463i	0.0407663	−	1.03389i
$932$	1.47923	+	0.854031i	0.0484536	+	0.0279747i
$933$	16.6341	−	4.52865i	0.544575	−	0.148261i
$934$	1.93053	−	1.11459i	0.0631689	−	0.0364706i
$935$			36.6641i			1.19904i
$936$	−8.41872	−	6.79155i	−0.275174	−	0.221989i
$937$		−	6.10741i		−	0.199520i	−0.995012	−	0.0997602i	$-0.968192\pi$
$937$		−	6.10741i		−	0.199520i	0.995012	−	0.0997602i	$-0.0318076\pi$
$938$	11.4504	−	6.31339i	0.373868	−	0.206139i
$939$	−15.7197	−	57.7398i	−0.512994	−	1.88427i
$940$	−6.84764	+	11.8605i	−0.223345	+	0.386846i
$941$	−26.2189			−0.854712			−0.427356	−	0.904083i	$-0.640555\pi$
$941$	−26.2189			−0.854712			−0.427356	+	0.904083i	$0.640555\pi$
$942$	−9.02212	−	8.95006i	−0.293957	−	0.291609i
$943$	18.9690	+	10.9518i	0.617717	+	0.356639i
$944$	−4.91462			−0.159957
$945$	6.49822	+	25.0183i	0.211387	+	0.813846i
$946$	18.9632	+	32.8452i	0.616546	+	1.06789i
$947$	0.247412	−	0.142844i	0.00803982	−	0.00464179i	−0.495975	−	0.868337i	$-0.665189\pi$
$947$	0.247412	−	0.142844i	0.00803982	−	0.00464179i	0.504015	+	0.863695i	$0.331856\pi$
$948$	−6.19466	+	23.4952i	−0.201193	+	0.763089i
$949$	6.46177	+	17.1488i	0.209758	+	0.556673i
$950$	−6.60665			−0.214348
$951$	−8.69909	−	31.9524i	−0.282087	−	1.03613i
$952$	12.3540	−	6.81160i	0.400394	−	0.220765i
$953$	−34.4494	−	19.8894i	−1.11592	−	0.644279i	−0.175567	−	0.984467i	$-0.556176\pi$
$953$	−34.4494	−	19.8894i	−1.11592	−	0.644279i	−0.940357	+	0.340188i	$0.889509\pi$
$954$	−11.7566	−	6.66252i	−0.380632	−	0.215707i
$955$	−9.93565	−	5.73635i	−0.321510	−	0.185624i
$956$	−10.3004	−	5.94696i	−0.333140	−	0.192338i
$957$	−5.31823	+	20.1711i	−0.171914	+	0.652038i
$958$	12.3754	+	7.14492i	0.399830	+	0.230842i
$959$	44.5022	−	24.5371i	1.43705	−	0.792346i
$960$	−3.14223	+	0.855476i	−0.101415	+	0.0276104i
$961$	22.3039			0.719481
$962$	−6.61949	−	1.09031i	−0.213421	−	0.0351529i
$963$	−28.3812	+	50.0809i	−0.914571	+	1.61383i
$964$	13.5179	−	7.80455i	0.435382	−	0.251368i
$965$	17.1130	+	29.6406i	0.550888	+	0.954166i
$966$	−12.2774	−	12.6689i	−0.395018	−	0.407617i
$967$	1.60093			0.0514823			0.0257412	−	0.999669i	$-0.491805\pi$
$967$	1.60093			0.0514823			0.0257412	+	0.999669i	$0.491805\pi$
$968$	−2.05641	−	1.18727i	−0.0660957	−	0.0381603i
$969$	−29.3347	+	29.5709i	−0.942367	+	0.949955i
$970$	−24.9404			−0.800788
$971$	30.2613	−	52.4141i	0.971131	−	1.68205i	0.278977	−	0.960298i	$-0.410005\pi$
$971$	30.2613	−	52.4141i	0.971131	−	1.68205i	0.692154	−	0.721750i	$-0.256662\pi$
$972$	11.2415	+	10.7995i	0.360570	+	0.346395i
$973$	28.3223	−	15.6161i	0.907972	−	0.500628i
$974$			32.3409i			1.03627i
$975$	7.41247	−	5.36109i	0.237389	−	0.171692i
$976$			2.60201i			0.0832885i
$977$	0.122426	−	0.0706828i	0.00391676	−	0.00226134i	−0.498040	−	0.867154i	$-0.665947\pi$
$977$	0.122426	−	0.0706828i	0.00391676	−	0.00226134i	0.501957	+	0.864893i	$0.332614\pi$
$978$	−1.69231	−	6.21599i	−0.0541142	−	0.198766i
$979$	−30.5738	−	17.6518i	−0.977143	−	0.564154i
$980$	13.1512	+	0.518552i	0.420099	+	0.0165645i
$981$	−3.72328	+	2.18963i	−0.118875	+	0.0699096i
$982$	−21.9114	+	37.9516i	−0.699220	+	1.21109i
$983$	−31.5175			−1.00525			−0.502626	−	0.864504i	$-0.667633\pi$
$983$	−31.5175			−1.00525			−0.502626	+	0.864504i	$0.667633\pi$
$984$	−6.94027	+	6.99615i	−0.221248	+	0.223029i
$985$	2.65819	−	1.53471i	0.0846971	−	0.0488999i
$986$	−8.77990	−	15.2072i	−0.279609	−	0.484297i
$987$	9.14416	−	32.1024i	0.291062	−	1.02183i
$988$	10.3114	−	12.5742i	0.328049	−	0.400038i
$989$			39.9243i			1.26952i
$990$	0.165417	+	20.6277i	0.00525728	+	0.655591i
$991$	−5.79173	−	10.0316i	−0.183980	−	0.318663i	0.759252	−	0.650797i	$-0.225565\pi$
$991$	−5.79173	−	10.0316i	−0.183980	−	0.318663i	−0.943232	+	0.332133i	$0.892232\pi$
$992$	−1.47446	+	2.55383i	−0.0468140	+	0.0810843i
$993$	12.2273	−	46.3757i	0.388020	−	1.47169i
$994$	−15.9779	+	26.4566i	−0.506788	+	0.839152i
$995$	−37.5939	−	21.7049i	−1.19181	−	0.688090i
$996$	2.10170	−	7.97135i	0.0665949	−	0.252582i
$997$	45.8322	+	26.4612i	1.45152	+	0.838036i	0.998568	−	0.0534988i	$-0.0170373\pi$
$997$	45.8322	+	26.4612i	1.45152	+	0.838036i	0.452953	+	0.891535i	$0.350371\pi$
$998$	25.0739	−	14.4764i	0.793700	−	0.458243i
$999$	9.36823	+	2.38982i	0.296398	+	0.0756104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bq.c.419.17	yes	64
3.2	odd	2	inner	546.2.bq.c.419.5	✓	64
7.6	odd	2	inner	546.2.bq.c.419.32	yes	64
13.9	even	3	inner	546.2.bq.c.503.12	yes	64
21.20	even	2	inner	546.2.bq.c.419.12	yes	64
39.35	odd	6	inner	546.2.bq.c.503.32	yes	64
91.48	odd	6	inner	546.2.bq.c.503.5	yes	64
273.230	even	6	inner	546.2.bq.c.503.17	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bq.c.419.5	✓	64	3.2	odd	2	inner
546.2.bq.c.419.12	yes	64	21.20	even	2	inner
546.2.bq.c.419.17	yes	64	1.1	even	1	trivial
546.2.bq.c.419.32	yes	64	7.6	odd	2	inner
546.2.bq.c.503.5	yes	64	91.48	odd	6	inner
546.2.bq.c.503.12	yes	64	13.9	even	3	inner
546.2.bq.c.503.17	yes	64	273.230	even	6	inner
546.2.bq.c.503.32	yes	64	39.35	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.67122 + 0.454992i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.88020 q^{5} +(-1.21982 + 1.22965i) q^{6} +(-1.36777 + 2.26478i) q^{7} -1.00000i q^{8} +(2.58596 - 1.52079i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.67122 + 0.454992i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.88020 q^{5} +(-1.21982 + 1.22965i) q^{6} +(-1.36777 + 2.26478i) q^{7} -1.00000i q^{8} +(2.58596 - 1.52079i) q^{9} +(-1.62830 + 0.940099i) q^{10} +(3.16716 - 1.82856i) q^{11} +(-0.441576 + 1.67482i) q^{12} +(3.37398 - 1.27133i) q^{13} +(-0.0521308 + 2.64524i) q^{14} +(3.14223 - 0.855476i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.66605 - 4.61773i) q^{17} +(1.47912 - 2.61002i) q^{18} +(3.90587 + 2.25506i) q^{19} +(-0.940099 + 1.62830i) q^{20} +(1.25538 - 4.40727i) q^{21} +(1.82856 - 3.16716i) q^{22} +(3.33400 - 1.92489i) q^{23} +(0.454992 + 1.67122i) q^{24} -1.46485 q^{25} +(2.28628 - 2.78800i) q^{26} +(-3.62977 + 3.71816i) q^{27} +(1.27747 + 2.31691i) q^{28} +(2.85202 - 1.64661i) q^{29} +(2.29351 - 2.31198i) q^{30} -2.94891i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.46105 + 4.49696i) q^{33} -5.33209i q^{34} +(2.57167 - 4.25823i) q^{35} +(-0.0240567 - 2.99990i) q^{36} +(-0.930327 - 1.61137i) q^{37} +4.51011 q^{38} +(-5.06021 + 3.65981i) q^{39} +1.88020i q^{40} +(2.84478 + 4.92731i) q^{41} +(-1.11644 - 4.44450i) q^{42} +(-5.18527 + 8.98116i) q^{43} -3.65712i q^{44} +(-4.86213 + 2.85938i) q^{45} +(1.92489 - 3.33400i) q^{46} +7.28396 q^{47} +(1.22965 + 1.21982i) q^{48} +(-3.25844 - 6.19537i) q^{49} +(-1.26860 + 0.732427i) q^{50} +(-2.35452 + 8.93028i) q^{51} +(0.585980 - 3.55762i) q^{52} -4.50439i q^{53} +(-1.28440 + 5.03491i) q^{54} +(-5.95489 + 3.43806i) q^{55} +(2.26478 + 1.36777i) q^{56} +(-7.55361 - 1.99156i) q^{57} +(1.64661 - 2.85202i) q^{58} +(2.45731 - 4.25618i) q^{59} +(0.830251 - 3.14899i) q^{60} +(-2.25341 - 1.30101i) q^{61} +(-1.47446 - 2.55383i) q^{62} +(-0.0927516 + 7.93671i) q^{63} -1.00000 q^{64} +(-6.34374 + 2.39036i) q^{65} +(-1.61490 + 6.12501i) q^{66} +(-2.47105 - 4.27998i) q^{67} +(-2.66605 - 4.61773i) q^{68} +(-4.69605 + 4.73386i) q^{69} +(0.0980162 - 4.97357i) q^{70} +(10.1167 + 5.84088i) q^{71} +(-1.52079 - 2.58596i) q^{72} +5.08266i q^{73} +(-1.61137 - 0.930327i) q^{74} +(2.44810 - 0.666497i) q^{75} +(3.90587 - 2.25506i) q^{76} +(-0.190649 + 9.67396i) q^{77} +(-2.55237 + 5.69960i) q^{78} +14.0285 q^{79} +(0.940099 + 1.62830i) q^{80} +(4.37442 - 7.86539i) q^{81} +(4.92731 + 2.84478i) q^{82} -4.75954 q^{83} +(-3.18911 - 3.29083i) q^{84} +(-5.01270 + 8.68224i) q^{85} +10.3705i q^{86} +(-4.01716 + 4.04951i) q^{87} +(-1.82856 - 3.16716i) q^{88} +(-4.82669 - 8.36007i) q^{89} +(-2.78104 + 4.90736i) q^{90} +(-1.73552 + 9.38019i) q^{91} -3.84978i q^{92} +(1.34173 + 4.92829i) q^{93} +(6.30809 - 3.64198i) q^{94} +(-7.34381 - 4.23995i) q^{95} +(1.67482 + 0.441576i) q^{96} +(11.4876 + 6.63238i) q^{97} +(-5.91957 - 3.73613i) q^{98} +(5.40932 - 9.54517i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

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