LMFDB - Embedded newform 546.2.bq.c.419.12

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			419.12
Character	$\chi$	$=$	546.419
Dual form			546.2.bq.c.503.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.22965 - 1.21982i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.88020 q^{5} +(-0.454992 + 1.67122i) q^{6} +(-1.27747 + 2.31691i) q^{7} +1.00000i q^{8} +(0.0240567 - 2.99990i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.22965 - 1.21982i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.88020 q^{5} +(-0.454992 + 1.67122i) q^{6} +(-1.27747 + 2.31691i) q^{7} +1.00000i q^{8} +(0.0240567 - 2.99990i) 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} +(-2.31198 + 2.29351i) 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} +(1.21982 + 1.22965i) q^{24} -1.46485 q^{25} +(2.28628 - 2.78800i) q^{26} +(-3.62977 - 3.71816i) q^{27} +(1.36777 + 2.26478i) q^{28} +(-2.85202 + 1.64661i) q^{29} +(0.855476 - 3.14223i) q^{30} +2.94891i q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.66396 + 6.11186i) q^{33} +5.33209i q^{34} +(2.40190 - 4.35625i) q^{35} +(-2.58596 - 1.52079i) q^{36} +(-0.930327 - 1.61137i) q^{37} +4.51011 q^{38} +(-2.59799 + 5.67895i) q^{39} -1.88020i q^{40} +(2.84478 + 4.92731i) q^{41} +(-3.29083 - 3.18911i) q^{42} +(-5.18527 + 8.98116i) q^{43} +3.65712i q^{44} +(-0.0452314 + 5.64041i) q^{45} +(1.92489 - 3.33400i) q^{46} +7.28396 q^{47} +(-1.67122 - 0.454992i) q^{48} +(-3.73613 - 5.91957i) q^{49} +(1.26860 - 0.732427i) q^{50} +(-2.35452 - 8.93028i) q^{51} +(-0.585980 + 3.55762i) q^{52} +4.50439i q^{53} +(5.00256 + 1.40514i) q^{54} +(5.95489 - 3.43806i) q^{55} +(-2.31691 - 1.27747i) 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} +(6.91977 + 3.88803i) 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} +(-1.75162 + 6.43383i) q^{69} +(0.0980162 + 4.97357i) q^{70} +(-10.1167 - 5.84088i) q^{71} +(2.99990 + 0.0240567i) q^{72} -5.08266i q^{73} +(1.61137 + 0.930327i) q^{74} +(-1.80125 + 1.78686i) q^{75} +(-3.90587 + 2.25506i) q^{76} +(-0.190649 - 9.67396i) q^{77} +(-0.589550 - 6.21711i) q^{78} +14.0285 q^{79} +(0.940099 + 1.62830i) q^{80} +(-8.99884 - 0.144336i) q^{81} +(-4.92731 - 2.84478i) q^{82} -4.75954 q^{83} +(4.44450 + 1.11644i) q^{84} +(-5.01270 + 8.68224i) q^{85} -10.3705i q^{86} +(-1.49839 + 5.50372i) q^{87} +(-1.82856 - 3.16716i) q^{88} +(-4.82669 - 8.36007i) q^{89} +(-2.78104 - 4.90736i) q^{90} +(1.36459 - 9.44129i) q^{91} +3.84978i q^{92} +(3.59716 + 3.62612i) 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} +(6.19537 + 3.25844i) 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
$3$	1.22965	−	1.21982i	0.709936	−	0.704266i
$3$	1.22965	−	1.21982i	0.709936	−	0.704266i
$4$	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	$0.638119\pi$
$6$	−0.454992	+	1.67122i	−0.185750	+	0.682273i
$7$	−1.27747	+	2.31691i	−0.482839	+	0.875709i
$7$	−1.27747	+	2.31691i	−0.482839	+	0.875709i
$8$			1.00000i			0.353553i
$9$	0.0240567	−	2.99990i	0.00801890	−	0.999968i
$10$	1.62830	−	0.940099i	0.514914	−	0.297285i
$11$	−3.16716	+	1.82856i	−0.954935	+	0.551332i	−0.894610	−	0.446847i	$-0.852547\pi$
$11$	−3.16716	+	1.82856i	−0.954935	+	0.551332i	−0.0603244	+	0.998179i	$0.519214\pi$
$12$	−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
$15$	−2.31198	+	2.29351i	−0.596950	+	0.592182i
$16$	−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	−0.0201457	−	0.999797i	$-0.506413\pi$
$19$	−3.90587	−	2.25506i	−0.896068	−	0.517345i	−0.875922	+	0.482452i	$0.839746\pi$
$20$	−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	−0.805553	−	0.592524i	$-0.798131\pi$
$23$	−3.33400	+	1.92489i	−0.695188	+	0.401367i	0.110365	+	0.993891i	$0.464798\pi$
$24$	1.21982	+	1.22965i	0.248996	+	0.251000i
$25$	−1.46485			−0.292971
$26$	2.28628	−	2.78800i	0.448377	−	0.546771i
$27$	−3.62977	−	3.71816i	−0.698550	−	0.715561i
$28$	1.36777	+	2.26478i	0.258483	+	0.428003i
$29$	−2.85202	+	1.64661i	−0.529607	+	0.305769i	−0.740856	−	0.671663i	$-0.765580\pi$
$29$	−2.85202	+	1.64661i	−0.529607	+	0.305769i	0.211249	+	0.977432i	$0.432247\pi$
$30$	0.855476	−	3.14223i	0.156188	−	0.573690i
$31$			2.94891i			0.529640i	0.964298	+	0.264820i	$0.0853126\pi$
$31$			2.94891i			0.529640i	−0.964298	+	0.264820i	$0.914687\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.66396	+	6.11186i	−0.289659	+	1.06394i
$34$			5.33209i			0.914446i
$35$	2.40190	−	4.35625i	0.405995	−	0.736340i
$36$	−2.58596	−	1.52079i	−0.430994	−	0.253464i
$37$	−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
$39$	−2.59799	+	5.67895i	−0.416011	+	0.909360i
$40$		−	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	$0.686793\pi$
$42$	−3.29083	−	3.18911i	−0.507786	−	0.492091i
$43$	−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
$45$	−0.0452314	+	5.64041i	−0.00674269	+	0.840823i
$46$	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	$0.321727\pi$
$48$	−1.67122	−	0.454992i	−0.241220	−	0.0656725i
$49$	−3.73613	−	5.91957i	−0.533733	−	0.845653i
$50$	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	$0.100116\pi$
$53$			4.50439i			0.618725i	−0.950944	+	0.309363i	$0.899884\pi$
$54$	5.00256	+	1.40514i	0.680762	+	0.191215i
$55$	5.95489	−	3.43806i	0.802957	−	0.463588i
$56$	−2.31691	−	1.27747i	−0.309610	−	0.170709i
$57$	−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	0.637274	−	0.770637i	$-0.280062\pi$
$61$	2.25341	+	1.30101i	0.288520	+	0.166577i	−0.348754	+	0.937214i	$0.613395\pi$
$62$	−1.47446	−	2.55383i	−0.187256	−	0.324337i
$63$	6.91977	+	3.88803i	0.871809	+	0.489846i
$64$	−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
$69$	−1.75162	+	6.43383i	−0.210870	+	0.774542i
$70$	0.0980162	+	4.97357i	0.0117152	+	0.594456i
$71$	−10.1167	−	5.84088i	−1.20063	−	0.693185i	−0.239936	−	0.970789i	$-0.577126\pi$
$71$	−10.1167	−	5.84088i	−1.20063	−	0.693185i	−0.960696	+	0.277604i	$0.910460\pi$
$72$	2.99990	+	0.0240567i	0.353542	+	0.00283511i
$73$		−	5.08266i		−	0.594881i	−0.954740	−	0.297440i	$-0.903867\pi$
$73$		−	5.08266i		−	0.594881i	0.954740	−	0.297440i	$-0.0961330\pi$
$74$	1.61137	+	0.930327i	0.187318	+	0.108148i
$75$	−1.80125	+	1.78686i	−0.207991	+	0.206329i
$76$	−3.90587	+	2.25506i	−0.448034	+	0.258673i
$77$	−0.190649	−	9.67396i	−0.0217264	−	1.10245i
$78$	−0.589550	−	6.21711i	−0.0667534	−	0.703949i
$79$	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
$81$	−8.99884	−	0.144336i	−0.999871	−	0.0160373i
$82$	−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	$0.584123\pi$
$84$	4.44450	+	1.11644i	0.484934	+	0.121814i
$85$	−5.01270	+	8.68224i	−0.543703	+	0.941721i
$86$		−	10.3705i		−	1.11828i
$87$	−1.49839	+	5.50372i	−0.160645	+	0.590060i
$88$	−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
$91$	1.36459	−	9.44129i	0.143048	−	0.989716i
$92$			3.84978i			0.401367i
$93$	3.59716	+	3.62612i	0.373008	+	0.376011i
$94$	−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	−0.213564	−	0.976929i	$-0.568507\pi$
$97$	−11.4876	−	6.63238i	−1.16639	−	0.673416i	−0.952827	+	0.303513i	$0.901840\pi$
$98$	6.19537	+	3.25844i	0.625827	+	0.329152i
$99$	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	$-0.416479\pi$
$102$	6.50422	+	6.55658i	0.644013	+	0.649198i
$103$			3.94251i			0.388467i	0.980955	+	0.194234i	$0.0622220\pi$
$103$			3.94251i			0.388467i	−0.980955	+	0.194234i	$0.937778\pi$
$104$	−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	$-0.288635\pi$
$107$	16.6172	−	9.59396i	1.60645	−	0.927483i	0.990157	−	0.139964i	$-0.0446987\pi$
$108$	−5.03491	+	1.28440i	−0.484485	+	0.123591i
$109$	−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
$111$	−3.10957	−	0.846583i	−0.295147	−	0.0803541i
$112$	2.64524	−	0.0521308i	0.249951	−	0.00492589i
$113$	9.32273	+	5.38248i	0.877009	+	0.506341i	0.869671	−	0.493632i	$-0.164331\pi$
$113$	9.32273	+	5.38248i	0.877009	+	0.506341i	0.00733803	+	0.999973i	$0.497664\pi$
$114$	5.54584	−	5.50154i	0.519415	−	0.515267i
$115$	6.26859	−	3.61917i	0.584549	−	0.337489i
$116$			3.29323i			0.305769i
$117$	3.73271	+	10.1522i	0.345090	+	0.938570i
$118$			4.91462i			0.452427i
$119$	7.29305	+	12.0760i	0.668553	+	1.10701i
$120$	−2.29351	−	2.31198i	−0.209368	−	0.211054i
$121$	1.18727	−	2.05641i	0.107934	−	0.186947i
$122$	−2.60201			−0.235575
$123$	9.50853	+	2.58871i	0.857355	+	0.233416i
$124$	2.55383	+	1.47446i	0.229341	+	0.132410i
$125$	12.1552			1.08719
$126$	−7.93671	+	0.0927516i	−0.707059	+	0.00826297i
$127$	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	$0.677922\pi$
$132$	4.46105	+	4.49696i	0.388284	+	0.391410i
$133$	10.2144	−	6.16877i	0.885701	−	0.534901i
$134$	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	0.996398	−	0.0847985i	$-0.0270247\pi$
$137$	16.6342	+	9.60379i	1.42116	+	0.820507i	0.424761	+	0.905305i	$0.360358\pi$
$138$	−1.69997	−	6.44767i	−0.144711	−	0.548862i
$139$	10.5865	+	6.11210i	0.897932	+	0.518421i	0.876529	−	0.481350i	$-0.159853\pi$
$139$	10.5865	+	6.11210i	0.897932	+	0.518421i	0.0214033	+	0.999771i	$0.493187\pi$
$140$	−2.57167	−	4.25823i	−0.217346	−	0.359886i
$141$	8.95669	−	8.88515i	0.754289	−	0.748265i
$142$	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
$147$	−11.8150	−	2.72155i	−0.974481	−	0.224470i
$148$	−1.86065			−0.152945
$149$	−10.8614	−	6.27084i	−0.889801	−	0.513727i	−0.0159236	−	0.999873i	$-0.505069\pi$
$149$	−10.8614	−	6.27084i	−0.889801	−	0.513727i	−0.873877	+	0.486146i	$0.838402\pi$
$150$	0.666497	−	2.44810i	0.0544192	−	0.199886i
$151$	−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
$153$	−13.7886	−	8.10897i	−1.11474	−	0.655571i
$154$	5.00209	+	8.28257i	0.403080	+	0.667428i
$155$		−	5.54454i		−	0.445348i
$156$	3.61912	+	5.08940i	0.289761	+	0.407478i
$157$		−	7.33717i		−	0.585570i	−0.956178	−	0.292785i	$-0.905418\pi$
$157$		−	7.33717i		−	0.585570i	0.956178	−	0.292785i	$-0.0945820\pi$
$158$	−12.1491	+	7.01426i	−0.966527	+	0.558025i
$159$	5.49456	+	5.53880i	0.435747	+	0.439256i
$160$	−1.62830	−	0.940099i	−0.128728	−	0.0743214i
$161$	−0.200692	−	10.1836i	−0.0158167	−	0.802578i
$162$	7.86539	−	4.37442i	0.617964	−	0.343687i
$163$	−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
$165$	3.12858	−	11.4915i	0.243560	−	0.894613i
$166$	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
$171$	−6.85891	+	11.6630i	−0.524514	+	0.891891i
$172$	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
$175$	1.87131	−	3.39393i	0.141458	−	0.256557i
$176$	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	−0.992176	−	0.124844i	$-0.960157\pi$
$179$	−18.4651	+	10.6608i	−1.38015	+	0.796828i	−0.387970	+	0.921672i	$0.626824\pi$
$180$	4.86213	+	2.85938i	0.362401	+	0.213125i
$181$		−	4.41691i		−	0.328306i	−0.986435	−	0.164153i	$-0.947511\pi$
$181$		−	4.41691i		−	0.328306i	0.986435	−	0.164153i	$-0.0524892\pi$
$182$	3.53887	+	8.85869i	0.262318	+	0.656650i
$183$	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
$186$	−4.92829	−	1.34173i	−0.361359	−	0.0983806i
$187$			19.5001i			1.42599i
$188$	3.64198	−	6.30809i	0.265619	−	0.460065i
$189$	13.2516	−	3.66000i	0.963911	−	0.266226i
$190$	−8.47990			−0.615197
$191$	−5.28436	−	3.05093i	−0.382363	−	0.220757i	0.296483	−	0.955038i	$-0.404186\pi$
$191$	−5.28436	−	3.05093i	−0.382363	−	0.220757i	−0.678846	+	0.734281i	$0.737520\pi$
$192$	−1.22965	+	1.21982i	−0.0887420	+	0.0880332i
$193$	−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
$195$	4.88474	−	10.6776i	0.349803	−	0.764635i
$196$	−6.99456	+	0.275796i	−0.499612	+	0.0196997i
$197$	1.41378	−	0.816248i	0.100728	−	0.0581553i	−0.448790	−	0.893637i	$-0.648145\pi$
$197$	1.41378	−	0.816248i	0.100728	−	0.0581553i	0.549518	+	0.835482i	$0.314811\pi$
$198$	−9.45719	−	5.56170i	−0.672093	−	0.395253i
$199$	−19.9947	−	11.5439i	−1.41738	−	0.818327i	−0.421315	−	0.906914i	$-0.638431\pi$
$199$	−19.9947	−	11.5439i	−1.41738	−	0.818327i	−0.996068	+	0.0885877i	$0.971765\pi$
$200$		−	1.46485i		−	0.103581i
$201$	−8.25934	−	2.24861i	−0.582569	−	0.158605i
$202$	12.3013	+	7.10215i	0.865515	+	0.499706i
$203$	−0.171679	−	8.71138i	−0.0120495	−	0.611419i
$204$	−8.91111	−	2.42606i	−0.623902	−	0.169858i
$205$	−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
$210$	6.18741	+	5.99617i	0.426972	+	0.413775i
$211$	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
$217$	−6.83236	−	3.76715i	−0.463811	−	0.255731i
$218$	1.24691	−	0.719902i	0.0844512	−	0.0487579i
$219$	−6.19996	−	6.24987i	−0.418954	−	0.422327i
$220$		−	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	−0.397912	−	0.917424i	$-0.630265\pi$
$223$	2.95147	−	1.70403i	0.197645	−	0.114110i	0.595556	+	0.803313i	$0.296932\pi$
$224$	−2.26478	+	1.36777i	−0.151322	+	0.0913877i
$225$	−0.0352395	+	4.39442i	−0.00234930	+	0.292961i
$226$	−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	$0.297788\pi$
$228$	−2.05206	+	7.53740i	−0.135901	+	0.499176i
$229$			16.8389i			1.11274i	0.830934	+	0.556371i	$0.187807\pi$
$229$			16.8389i			1.11274i	−0.830934	+	0.556371i	$0.812193\pi$
$230$	−3.61917	+	6.26859i	−0.238641	+	0.413338i
$231$	−12.0350	−	11.6630i	−0.791842	−	0.767368i
$232$	−1.64661	−	2.85202i	−0.108106	−	0.187244i
$233$		−	1.70806i		−	0.111899i	−0.998434	−	0.0559494i	$-0.982181\pi$
$233$		−	1.70806i		−	0.111899i	0.998434	−	0.0559494i	$-0.0178186\pi$
$234$	−8.30872	−	6.92569i	−0.543158	−	0.452747i
$235$	−13.6953			−0.893382
$236$	−2.45731	−	4.25618i	−0.159957	−	0.277054i
$237$	17.2501	−	17.1123i	1.12052	−	1.11157i
$238$	−12.3540	−	6.81160i	−0.800789	−	0.441530i
$239$			11.8939i			0.769354i	0.923051	+	0.384677i	$0.125687\pi$
$239$			11.8939i			0.769354i	−0.923051	+	0.384677i	$0.874313\pi$
$240$	3.14223	+	0.855476i	0.202830	+	0.0552207i
$241$	−13.5179	−	7.80455i	−0.870763	−	0.502735i	−0.00316139	−	0.999995i	$-0.501006\pi$
$241$	−13.5179	−	7.80455i	−0.870763	−	0.502735i	−0.867602	+	0.497260i	$0.834340\pi$
$242$			2.37454i			0.152641i
$243$	−11.2415	+	10.7995i	−0.721139	+	0.692790i
$244$	2.25341	−	1.30101i	0.144260	−	0.0832885i
$245$	7.02466	+	11.1300i	0.448789	+	0.711068i
$246$	−9.52898	+	2.51238i	−0.607546	+	0.160183i
$247$	16.0452	+	2.64283i	1.02093	+	0.168159i
$248$	−2.94891			−0.187256
$249$	−5.85255	+	5.80580i	−0.370890	+	0.367928i
$250$	−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	$-0.569641\pi$
$258$	−12.6502	−	12.7521i	−0.787570	−	0.793911i
$259$	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	−0.680131	−	0.733090i	$-0.738077\pi$
$263$	−6.24887	+	3.60779i	−0.385322	+	0.222466i	0.294809	+	0.955556i	$0.404744\pi$
$264$	−6.11186	−	1.66396i	−0.376159	−	0.102410i
$265$		−	8.46915i		−	0.520256i
$266$	−5.76154	+	10.4495i	−0.353263	+	0.640701i
$267$	−16.1329	−	4.39221i	−0.987320	−	0.268799i
$268$	−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	$0.946875\pi$
$270$	−9.40580	−	2.64194i	−0.572419	−	0.160783i
$271$	8.97137	−	5.17962i	0.544972	−	0.314640i	−0.202120	−	0.979361i	$-0.564783\pi$
$271$	8.97137	−	5.17962i	0.544972	−	0.314640i	0.747092	+	0.664721i	$0.231450\pi$
$272$	−5.33209			−0.323306
$273$	−9.83874	−	13.2740i	−0.595468	−	0.803379i
$274$	−19.2076			−1.16037
$275$	4.63943	−	2.67857i	0.279768	−	0.161524i
$276$	4.69605	+	4.73386i	0.282669	+	0.284945i
$277$	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
$279$	8.84645	+	0.0709411i	0.529623	+	0.00424713i
$280$	4.35625	+	2.40190i	0.260336	+	0.143541i
$281$			12.7301i			0.759417i	0.925106	+	0.379709i	$0.123976\pi$
$281$			12.7301i			0.759417i	−0.925106	+	0.379709i	$0.876024\pi$
$282$	−3.31414	+	12.1731i	−0.197354	+	0.724898i
$283$	20.5311	−	11.8536i	1.22045	−	0.704625i	0.255434	−	0.966827i	$-0.417782\pi$
$283$	20.5311	−	11.8536i	1.22045	−	0.704625i	0.965013	+	0.262201i	$0.0844484\pi$
$284$	−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
$288$	1.52079	−	2.58596i	0.0896131	−	0.152379i
$289$	−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
$297$	18.2950	+	5.13876i	1.06158	+	0.298181i
$298$	12.5417			0.726519
$299$	8.80167	−	10.7332i	0.509014	−	0.620714i
$300$	0.646844	+	2.45336i	0.0373456	+	0.141645i
$301$	−14.1845	−	23.4870i	−0.817580	−	1.35377i
$302$	0.906639	−	0.523448i	0.0521712	−	0.0301211i
$303$	−23.7385	−	6.46285i	−1.36374	−	0.371281i
$304$			4.51011i			0.258673i
$305$	−4.23686	−	2.44615i	−0.242602	−	0.140066i
$306$	15.9958	+	0.128272i	0.914417	+	0.00733285i
$307$			28.3173i			1.61615i	0.589077	+	0.808077i	$0.299492\pi$
$307$			28.3173i			1.61615i	−0.589077	+	0.808077i	$0.700508\pi$
$308$	−8.47322	−	4.67187i	−0.482806	−	0.266205i
$309$	4.80917	+	4.84789i	0.273584	+	0.275787i
$310$	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	$0.591064\pi$
$312$	−5.67895	−	2.59799i	−0.321507	−	0.147082i
$313$		−	34.5494i		−	1.95285i	−0.215856	−	0.976425i	$-0.569254\pi$
$313$		−	34.5494i		−	1.95285i	0.215856	−	0.976425i	$-0.430746\pi$
$314$	3.66859	+	6.35418i	0.207030	+	0.358587i
$315$	−13.0105	−	7.31027i	−0.733061	−	0.411887i
$316$	7.01426	−	12.1491i	0.394583	−	0.683438i
$317$		−	19.1192i		−	1.07384i	−0.843633	−	0.536921i	$-0.819587\pi$
$317$		−	19.1192i		−	1.07384i	0.843633	−	0.536921i	$-0.180413\pi$
$318$	−7.52783	−	2.04946i	−0.422140	−	0.114928i
$319$	6.02187	−	10.4302i	0.337160	−	0.583978i
$320$	1.88020			0.105106
$321$	8.73035	−	32.0673i	0.487281	−	1.78982i
$322$	5.26559	+	8.71888i	0.293440	+	0.485884i
$323$	−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
$327$	−1.77045	+	1.75631i	−0.0979061	+	0.0971241i
$328$	−4.92731	+	2.84478i	−0.272065	+	0.157077i
$329$	−9.30505	+	16.8763i	−0.513004	+	0.930418i
$330$	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
$336$	3.18911	−	3.29083i	0.173980	−	0.179529i
$337$	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
$342$	0.108498	−	13.5299i	0.00586692	−	0.731613i
$343$	18.4879	−	1.09418i	0.998253	−	0.0590801i
$344$	−8.98116	−	5.18527i	−0.484232	−	0.279571i
$345$	3.29339	−	12.0969i	0.177310	−	0.651274i
$346$		−	17.4113i		−	0.936037i
$347$	−1.44655	−	0.835165i	−0.0776548	−	0.0448340i	0.460670	−	0.887572i	$-0.347609\pi$
$347$	−1.44655	−	0.835165i	−0.0776548	−	0.0448340i	−0.538325	+	0.842738i	$0.680943\pi$
$348$	4.01716	+	4.04951i	0.215343	+	0.217076i
$349$	−12.6119	+	7.28149i	−0.675100	+	0.389769i	−0.798006	−	0.602649i	$-0.794112\pi$
$349$	−12.6119	+	7.28149i	−0.675100	+	0.389769i	0.122906	+	0.992418i	$0.460779\pi$
$350$	0.0763639	+	3.87489i	0.00408182	+	0.207121i
$351$	16.9738	+	7.93033i	0.905994	+	0.423290i
$352$	−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	$0.547221\pi$
$354$	5.99497	+	6.04324i	0.318629	+	0.321194i
$355$	19.0214	+	10.9820i	1.00955	+	0.582865i
$356$	−9.65338			−0.511628
$357$	23.6985	+	5.95296i	1.25426	+	0.315064i
$358$	10.6608	−	18.4651i	0.563442	−	0.975911i
$359$			9.42640i			0.497506i	0.968567	+	0.248753i	$0.0800208\pi$
$359$			9.42640i			0.497506i	−0.968567	+	0.248753i	$0.919979\pi$
$360$	−5.64041	−	0.0452314i	−0.297276	−	0.00238390i
$361$	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
$364$	−7.49410	−	5.90242i	−0.392797	−	0.309371i
$365$			9.55642i			0.500206i
$366$	−3.19956	+	3.17400i	−0.167243	+	0.165908i
$367$	−0.535195	+	0.308995i	−0.0279370	+	0.0161294i	−0.513903	−	0.857848i	$-0.671801\pi$
$367$	−0.535195	+	0.308995i	−0.0279370	+	0.0161294i	0.485966	+	0.873977i	$0.338468\pi$
$368$	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
$371$	−10.4363	−	5.75423i	−0.541824	−	0.298745i
$372$	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
$375$	14.9466	−	14.8272i	0.771839	−	0.765674i
$376$			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
$381$	27.2504	+	7.41895i	1.39608	+	0.380084i
$382$	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	$0.294895\pi$
$384$	0.454992	−	1.67122i	0.0232187	−	0.0852842i
$385$	0.358457	+	18.1890i	0.0182687	+	0.926995i
$386$	15.7646	+	9.10171i	0.802398	+	0.463265i
$387$	26.8179	+	15.7714i	1.36323	+	0.801704i
$388$	−11.4876	+	6.63238i	−0.583196	+	0.336708i
$389$			11.3388i			0.574898i	0.957796	+	0.287449i	$0.0928071\pi$
$389$			11.3388i			0.574898i	−0.957796	+	0.287449i	$0.907193\pi$
$390$	1.10847	+	11.6894i	0.0561296	+	0.591916i
$391$			20.5274i			1.03811i
$392$	5.91957	−	3.73613i	0.298984	−	0.188703i
$393$	−14.9269	+	14.8077i	−0.752965	+	0.746951i
$394$	−0.816248	+	1.41378i	−0.0411220	+	0.0712254i
$395$	−26.3764			−1.32714
$396$	10.9710	+	0.0879783i	0.551314	+	0.00442107i
$397$	−21.6176	−	12.4809i	−1.08496	−	0.626401i	−0.152728	−	0.988268i	$-0.548806\pi$
$397$	−21.6176	−	12.4809i	−1.08496	−	0.626401i	−0.932229	+	0.361868i	$0.882139\pi$
$398$	23.0878			1.15729
$399$	5.03527	−	20.0452i	0.252079	−	1.00351i
$400$	0.732427	+	1.26860i	0.0366213	+	0.0634300i
$401$	−8.62310	+	4.97855i	−0.430617	+	0.248617i	−0.699610	−	0.714525i	$-0.746643\pi$
$401$	−8.62310	+	4.97855i	−0.430617	+	0.248617i	0.268992	+	0.963142i	$0.413309\pi$
$402$	8.27710	−	2.18231i	0.412824	−	0.108844i
$403$	−3.74905	−	9.94956i	−0.186754	−	0.495623i
$404$	−14.2043			−0.706690
$405$	16.9196	+	0.271379i	0.840742	+	0.0134850i
$406$	4.50437	+	7.45843i	0.223548	+	0.370156i
$407$	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	0.408094	−	0.912940i	$-0.366194\pi$
$409$	−3.60971	−	2.08407i	−0.178489	−	0.103051i	−0.586582	+	0.809890i	$0.699527\pi$
$410$	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
$413$	6.72204	+	11.1305i	0.330770	+	0.547697i
$414$	−9.95538	−	5.85468i	−0.489280	−	0.287742i
$415$	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	$0.973269\pi$
$420$	−8.35654	−	2.09913i	−0.407757	−	0.102427i
$421$	−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
$423$	0.175228	−	21.8512i	0.00851987	−	1.06244i
$424$	−4.50439			−0.218752
$425$	−3.90537	+	6.76429i	−0.189438	+	0.328116i
$426$	14.3644	−	14.2497i	0.695958	−	0.690400i
$427$	−5.89298	+	3.55895i	−0.285182	+	0.172229i
$428$		−	19.1879i		−	0.927483i
$429$	−2.15606	−	22.7367i	−0.104095	−	1.09774i
$430$			19.4987i			0.940310i
$431$	25.7111	−	14.8443i	1.23846	−	0.715027i	0.269683	−	0.962949i	$-0.413081\pi$
$431$	25.7111	−	14.8443i	1.23846	−	0.715027i	0.968780	+	0.247923i	$0.0797479\pi$
$432$	−1.40514	+	5.00256i	−0.0676047	+	0.240686i
$433$	6.53518	+	3.77309i	0.314061	+	0.181323i	0.648742	−	0.761008i	$-0.275295\pi$
$433$	6.53518	+	3.77309i	0.314061	+	0.181323i	−0.334682	+	0.942331i	$0.608629\pi$
$434$	7.80057	−	0.153729i	0.374440	−	0.00737923i
$435$	2.81728	−	10.3481i	0.135078	−	0.496153i
$436$	−0.719902	+	1.24691i	−0.0344771	+	0.0597160i
$437$	17.3629			0.830581
$438$	8.49426	+	2.31257i	0.405871	+	0.110499i
$439$	−8.13543	+	4.69699i	−0.388283	+	0.224175i	−0.681416	−	0.731897i	$-0.738635\pi$
$439$	−8.13543	+	4.69699i	−0.388283	+	0.224175i	0.293133	+	0.956072i	$0.405302\pi$
$440$	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	$0.0967753\pi$
$443$			12.6019i			0.598733i	−0.954138	+	0.299366i	$0.903225\pi$
$444$	−2.28795	+	2.26967i	−0.108581	+	0.107714i
$445$	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
$448$	1.27747	−	2.31691i	0.0603549	−	0.109464i
$449$	−25.5271	−	14.7381i	−1.20470	−	0.695533i	−0.243102	−	0.970001i	$-0.578165\pi$
$449$	−25.5271	−	14.7381i	−1.20470	−	0.695533i	−0.961596	+	0.274468i	$0.911498\pi$
$450$	−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
$453$	−1.28731	+	1.27703i	−0.0604832	+	0.0600001i
$454$		−	12.0646i		−	0.566222i
$455$	−2.56571	+	17.7515i	−0.120282	+	0.832203i
$456$	−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
$459$	−26.8466	+	6.84851i	−1.25309	+	0.319661i
$460$		−	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	$0.838552\pi$
$462$	16.2541	+	4.08296i	0.756208	+	0.189956i
$463$	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
$465$	−6.76337	−	6.81782i	−0.313644	−	0.316169i
$466$	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	$0.483575\pi$
$468$	10.6584	+	1.84347i	0.492685	+	0.0852143i
$469$	13.0730	−	0.257635i	0.603656	−	0.0118965i
$470$	11.8605	−	6.84764i	0.547082	−	0.315858i
$471$	−8.95006	−	9.02212i	−0.412397	−	0.415717i
$472$	4.25618	+	2.45731i	0.195907	+	0.113107i
$473$		−	37.9264i		−	1.74386i
$474$	−6.38287	+	23.4448i	−0.293175	+	1.07685i
$475$	5.72153	+	3.30333i	0.262522	+	0.151567i
$476$	14.1046	−	0.277966i	0.646486	−	0.0127405i
$477$	13.5127	+	0.108361i	0.618706	+	0.00496150i
$478$	−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
$483$	−12.6689	−	12.2774i	−0.576457	−	0.558640i
$484$	−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
$490$	−11.6485	−	6.12651i	−0.526227	−	0.276767i
$491$	37.9516	−	21.9114i	1.71273	−	0.988847i	0.781899	−	0.623405i	$-0.214251\pi$
$491$	37.9516	−	21.9114i	1.71273	−	0.988847i	0.930834	−	0.365442i	$-0.119082\pi$
$492$	6.99615	−	6.94027i	0.315411	−	0.312892i
$493$			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
$497$	26.4566	−	15.9779i	1.18674	−	0.716707i
$498$	2.16555	−	7.95424i	0.0970407	−	0.356438i
$499$	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
$501$	1.18467	+	0.322528i	0.0529273	+	0.0144095i
$502$		−	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	$0.300839\pi$
$504$	−3.88803	+	6.91977i	−0.173187	+	0.308231i
$505$	13.3535	+	23.1289i	0.594221	+	1.02922i
$506$			14.0791i			0.625892i
$507$	1.54571	−	22.4635i	0.0686473	−	0.997641i
$508$	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	$-0.511502\pi$
$510$	−12.2292	−	12.3277i	−0.541519	−	0.545879i
$511$	11.7761	+	6.49296i	0.520942	+	0.287232i
$512$		−	1.00000i		−	0.0441942i
$513$	5.79277	+	22.7080i	0.255757	+	1.00258i
$514$	26.4869	+	15.2922i	1.16829	+	0.674511i
$515$		−	7.41270i		−	0.326643i
$516$	17.3315	+	4.71852i	0.762976	+	0.207721i
$517$	−23.0695	+	13.3192i	−1.01459	+	0.585776i
$518$	−4.21397	+	2.54494i	−0.185151	+	0.111818i
$519$	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	$0.600172\pi$
$522$	−8.51617	−	5.00830i	−0.372743	−	0.219207i
$523$	28.0353	−	16.1862i	1.22590	−	0.707773i	0.259729	−	0.965681i	$-0.416367\pi$
$523$	28.0353	−	16.1862i	1.22590	−	0.707773i	0.966169	+	0.257909i	$0.0830334\pi$
$524$	−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
$531$	−12.7090	−	7.47408i	−0.551525	−	0.324347i
$532$	−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
$537$	−9.70119	+	35.6332i	−0.418637	+	1.53769i
$538$		−	20.8925i		−	0.900740i
$539$	22.6572	+	11.9165i	0.975916	+	0.513280i
$540$	9.46663	−	2.41492i	0.407379	−	0.103922i
$541$	−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
$543$	−5.38786	−	5.43124i	−0.231215	−	0.233077i
$544$	4.61773	−	2.66605i	0.197983	−	0.114306i
$545$	2.70712			0.115960
$546$	15.1576	+	6.57625i	0.648686	+	0.281438i
$547$	−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
$549$	3.95711	−	6.72872i	0.168885	−	0.287175i
$550$	−2.67857	+	4.63943i	−0.114215	+	0.197826i
$551$	14.8528			0.632752
$552$	−6.43383	−	1.75162i	−0.273842	−	0.0745538i
$553$	−17.9211	+	32.5028i	−0.762081	+	1.38216i
$554$			19.8127i			0.841759i
$555$	5.84660	+	1.59174i	0.248174	+	0.0675658i
$556$	10.5865	−	6.11210i	0.448966	−	0.259211i
$557$	18.9140	−	10.9200i	0.801413	−	0.462696i	−0.0425518	−	0.999094i	$-0.513549\pi$
$557$	18.9140	−	10.9200i	0.801413	−	0.462696i	0.843965	+	0.536398i	$0.180215\pi$
$558$	−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
$561$	23.7867	+	23.9782i	1.00428	+	1.01236i
$562$	−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	−0.562508	−	0.826792i	$-0.690163\pi$
$569$	−3.04705	+	1.75922i	−0.127739	+	0.0737502i	0.434769	+	0.900542i	$0.356830\pi$
$570$	−10.4273	+	10.3440i	−0.436751	+	0.433262i
$571$	−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
$574$	12.8856	−	7.78199i	0.537835	−	0.324814i
$575$	4.88383	−	2.81968i	0.203670	−	0.117589i
$576$	−0.0240567	+	2.99990i	−0.00100236	+	0.124996i
$577$		−	16.1255i		−	0.671315i	−0.941984	−	0.335658i	$-0.891041\pi$
$577$		−	16.1255i		−	0.671315i	0.941984	−	0.335658i	$-0.108959\pi$
$578$	9.89971	+	5.71560i	0.411774	+	0.237738i
$579$	−30.4220	−	8.28241i	−1.26429	−	0.344205i
$580$		−	6.19193i		−	0.257106i
$581$	6.08018	−	11.0274i	0.252248	−	0.457494i
$582$	16.3110	−	16.1807i	0.676111	−	0.670711i
$583$	−8.23655	−	14.2661i	−0.341123	−	0.590843i
$584$	5.08266			0.210322
$585$	−7.01824	−	19.0881i	−0.290169	−	0.789197i
$586$			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	$0.609043\pi$
$588$	−8.26441	+	8.87127i	−0.340819	+	0.365845i
$589$	6.64996	−	11.5181i	0.274007	−	0.474594i
$590$		−	9.24046i		−	0.380424i
$591$	0.742773	−	2.72826i	0.0305536	−	0.112226i
$592$	−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	$0.401848\pi$
$594$	−18.4133	+	4.69719i	−0.755506	+	0.192728i
$595$	−13.7124	−	22.7053i	−0.562153	−	0.930826i
$596$	−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	$-0.825390\pi$
$599$		−	25.5246i		−	1.04290i	0.853280	−	0.521452i	$-0.174610\pi$
$600$	−1.78686	−	1.80125i	−0.0729484	−	0.0735358i
$601$	−26.1186	+	15.0796i	−1.06540	+	0.615110i	−0.926922	−	0.375255i	$-0.877555\pi$
$601$	−26.1186	+	15.0796i	−1.06540	+	0.615110i	−0.138480	+	0.990365i	$0.544222\pi$
$602$	24.0276	+	13.2481i	0.979292	+	0.539952i
$603$	−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	0.996634	−	0.0819738i	$-0.0261224\pi$
$607$	35.0826	+	20.2550i	1.42396	+	0.822124i	0.427326	+	0.904098i	$0.359456\pi$
$608$	−2.25506	−	3.90587i	−0.0914546	−	0.158404i
$609$	−10.8375	−	10.5025i	−0.439156	−	0.425582i
$610$	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
$615$	−17.8779	−	4.86728i	−0.720907	−	0.196268i
$616$	9.67396	−	0.190649i	0.389775	−	0.00768145i
$617$	−18.1108	−	10.4563i	−0.729113	−	0.420954i	0.0889845	−	0.996033i	$-0.471638\pi$
$617$	−18.1108	−	10.4563i	−0.729113	−	0.420954i	−0.818098	+	0.575079i	$0.804971\pi$
$618$	−6.58881	−	1.79381i	−0.265041	−	0.0721577i
$619$		−	0.896815i		−	0.0360460i	−0.999838	−	0.0180230i	$-0.994263\pi$
$619$		−	0.896815i		−	0.0360460i	0.999838	−	0.0180230i	$-0.00573722\pi$
$620$	−4.80171	−	2.77227i	−0.192841	−	0.111337i
$621$	19.2587	+	5.40946i	0.772826	+	0.217074i
$622$	8.61976	−	4.97662i	0.345621	−	0.199544i
$623$	25.5355	−	0.503238i	1.02306	−	0.0201618i
$624$	6.21711	−	0.589550i	0.248884	−	0.0236009i
$625$	−15.5299			−0.621197
$626$	17.2747	+	29.9207i	0.690437	+	1.19587i
$627$	20.2818	−	20.1198i	0.809977	−	0.803508i
$628$	−6.35418	−	3.66859i	−0.253559	−	0.146393i
$629$	−9.92118			−0.395583
$630$	14.9226	−	0.174391i	0.594530	−	0.00694792i
$631$	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
$633$	20.4242	+	5.56052i	0.811790	+	0.221011i
$634$	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
$637$	20.1314	+	15.2226i	0.797634	+	0.603142i
$638$			12.0437i			0.476816i
$639$	−17.7654	+	30.2086i	−0.702790	+	1.19503i
$640$	−1.62830	+	0.940099i	−0.0643642	+	0.0371607i
$641$	5.88556	+	3.39803i	0.232466	+	0.134214i	0.611709	−	0.791083i	$-0.290482\pi$
$641$	5.88556	+	3.39803i	0.232466	+	0.134214i	−0.379243	+	0.925297i	$0.623816\pi$
$642$	8.47292	+	32.1362i	0.334400	+	1.26832i
$643$	24.8365	+	14.3393i	0.979454	+	0.565488i	0.902105	−	0.431516i	$-0.142021\pi$
$643$	24.8365	+	14.3393i	0.979454	+	0.565488i	0.0773487	+	0.997004i	$0.475355\pi$
$644$	−8.91958	−	4.91798i	−0.351481	−	0.193796i
$645$	−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	$-0.509960\pi$
$648$	0.144336	−	8.99884i	0.00567003	−	0.353508i
$649$			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	−0.966368	−	0.257162i	$-0.917213\pi$
$653$	−31.3506	+	18.1003i	−1.22684	+	0.708319i	−0.260476	+	0.965480i	$0.583879\pi$
$654$	0.655100	−	2.40623i	0.0256164	−	0.0940911i
$655$	22.8241			0.891813
$656$	2.84478	−	4.92731i	0.111070	−	0.192379i
$657$	−15.2475	−	0.122272i	−0.594862	−	0.00477029i
$658$	−0.379718	−	19.2678i	−0.0148030	−	0.751137i
$659$	16.0130	+	9.24511i	0.623778	+	0.360139i	0.778339	−	0.627845i	$-0.216063\pi$
$659$	16.0130	+	9.24511i	0.623778	+	0.360139i	−0.154560	+	0.987983i	$0.549396\pi$
$660$	−8.38765	−	8.45519i	−0.326489	−	0.329118i
$661$	−6.36345	+	3.67394i	−0.247509	+	0.142900i	−0.618623	−	0.785688i	$-0.712309\pi$
$661$	−6.36345	+	3.67394i	−0.247509	+	0.142900i	0.371114	+	0.928587i	$0.378976\pi$
$662$		−	27.6900i		−	1.07620i
$663$	19.2975	+	27.1371i	0.749452	+	1.05392i
$664$		−	4.75954i		−	0.184706i
$665$	−19.2051	+	11.5985i	−0.744742	+	0.449771i
$666$	2.82966	−	4.81159i	0.109647	−	0.186445i
$667$	6.33910	−	10.9796i	0.245451	−	0.425133i
$668$	0.708866			0.0274268
$669$	1.55064	−	5.69562i	0.0599512	−	0.220205i
$670$	−8.04721	−	4.64606i	−0.310891	−	0.179493i
$671$	−9.51589			−0.367357
$672$	−1.11644	+	4.44450i	−0.0430676	+	0.171450i
$673$	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	$0.365554\pi$
$678$	−13.2371	+	13.1314i	−0.508368	+	0.504307i
$679$	30.0417	−	18.1431i	1.15290	−	0.696268i
$680$	−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	−0.100707	−	0.994916i	$-0.532110\pi$
$683$	−26.4657	−	15.2800i	−1.01268	−	0.584673i	−0.911976	+	0.410244i	$0.865444\pi$
$684$	6.67099	+	11.7715i	0.255072	+	0.450094i
$685$	−31.2757	−	18.0570i	−1.19498	−	0.689923i
$686$	−15.4639	+	10.1915i	−0.590415	+	0.389115i
$687$	20.5404	+	20.7058i	0.783667	+	0.789976i
$688$	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	$0.734915\pi$
$691$	−43.3712	+	25.0404i	−1.64992	+	0.952580i	−0.977103	+	0.212768i	$0.931752\pi$
$692$	8.70565	+	15.0786i	0.330939	+	0.573203i
$693$	−29.0255	+	0.339204i	−1.10259	+	0.0128853i
$694$	1.67033			0.0634049
$695$	−19.9047	−	11.4920i	−0.755026	−	0.435915i
$696$	−5.50372	−	1.49839i	−0.208618	−	0.0567965i
$697$	30.3373			1.14911
$698$	7.28149	−	12.6119i	0.275608	−	0.477368i
$699$	−2.08354	−	2.10031i	−0.0788066	−	0.0794411i
$700$	−2.00358	−	3.31757i	−0.0757281	−	0.125392i
$701$		−	23.8423i		−	0.900510i	−0.892900	−	0.450255i	$-0.851333\pi$
$701$		−	23.8423i		−	0.900510i	0.892900	−	0.450255i	$-0.148667\pi$
$702$	−18.6649	+	1.61903i	−0.704462	+	0.0611063i
$703$			8.39176i			0.316501i
$704$	3.16716	−	1.82856i	0.119367	−	0.0689165i
$705$	−16.8403	+	16.7058i	−0.634244	+	0.629179i
$706$	−25.4679	−	14.7039i	−0.958499	−	0.553389i
$707$	37.5738	−	0.740481i	1.41311	−	0.0278486i
$708$	−8.21342	−	2.23611i	−0.308679	−	0.0840382i
$709$	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
$711$	0.337480	−	42.0842i	0.0126565	−	1.57828i
$712$	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
$717$	14.5085	+	14.6253i	0.541830	+	0.546192i
$718$	−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
$721$	−9.13443	−	5.03645i	−0.340184	−	0.187567i
$722$	−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
$726$	2.89653	+	2.91985i	0.107500	+	0.108366i
$727$			31.1508i			1.15532i	0.816277	+	0.577660i	$0.196034\pi$
$727$			31.1508i			1.15532i	−0.816277	+	0.577660i	$0.803966\pi$
$728$	9.44129	+	1.36459i	0.349917	+	0.0505752i
$729$	−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
$732$	1.18390	−	4.34854i	0.0437581	−	0.160727i
$733$			8.10545i			0.299381i	0.988733	+	0.149691i	$0.0478278\pi$
$733$			8.10545i			0.299381i	−0.988733	+	0.149691i	$0.952172\pi$
$734$	0.308995	−	0.535195i	0.0114052	−	0.0197544i
$735$	22.2145	+	5.11706i	0.819393	+	0.188746i
$736$	−3.84978			−0.141905
$737$	15.6524	+	9.03692i	0.576564	+	0.332879i
$738$	−8.65261	+	14.7130i	−0.318507	+	0.541594i
$739$	−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
$741$	22.9538	−	16.3226i	0.843227	−	0.599627i
$742$	11.9152	−	0.234817i	0.437420	−	0.00862041i
$743$	15.4302	−	8.90864i	0.566080	−	0.326826i	−0.189502	−	0.981880i	$-0.560687\pi$
$743$	15.4302	−	8.90864i	0.566080	−	0.326826i	0.755582	+	0.655054i	$0.227354\pi$
$744$	−3.62612	+	3.59716i	−0.132940	+	0.131878i
$745$	20.4216	+	11.7904i	0.748189	+	0.431967i
$746$		−	32.9697i		−	1.20710i
$747$	−0.114499	+	14.2782i	−0.00418929	+	0.522410i
$748$	16.8876	+	9.75005i	0.617471	+	0.356497i
$749$	1.00028	+	50.7566i	0.0365494	+	1.85461i
$750$	−5.53052	+	20.3140i	−0.201946	+	0.741764i
$751$	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
$756$	3.45613	−	13.3062i	0.125698	−	0.483942i
$757$	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
$763$	1.83931	−	3.33589i	0.0665875	−	0.120767i
$764$	−5.28436	+	3.05093i	−0.191182	+	0.110379i
$765$	25.9253	+	15.2465i	0.937331	+	0.551237i
$766$		−	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	−0.230585	−	0.973052i	$-0.574064\pi$
$769$	13.7770	−	7.95414i	0.496811	−	0.286834i	0.727395	+	0.686218i	$0.240731\pi$
$770$	−9.40491	−	15.5729i	−0.338930	−	0.561207i
$771$	−51.1134	−	13.9157i	−1.84080	−	0.501161i
$772$	−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	$-0.201409\pi$
$774$	−31.1106	−	0.249481i	−1.11825	−	0.00896741i
$775$		−	4.31972i		−	0.155169i
$776$	6.63238	−	11.4876i	0.238089	−	0.412382i
$777$	5.93384	−	6.12309i	0.212875	−	0.219665i
$778$	−5.66938	−	9.81965i	−0.203257	−	0.352051i
$779$		−	25.6606i		−	0.919386i
$780$	−6.80466	−	9.56908i	−0.243646	−	0.342628i
$781$	42.7216			1.52870
$782$	−10.2637	−	17.7772i	−0.367028	−	0.635712i
$783$	16.4746	+	4.62744i	0.588753	+	0.165371i
$784$	−3.25844	+	6.19537i	−0.116373	+	0.221263i
$785$			13.7953i			0.492377i
$786$	5.52325	−	20.2873i	0.197008	−	0.723625i
$787$	−3.08887	−	1.78336i	−0.110106	−	0.0635700i	0.443935	−	0.896059i	$-0.353582\pi$
$787$	−3.08887	−	1.78336i	−0.110106	−	0.0635700i	−0.554042	+	0.832489i	$0.686915\pi$
$788$		−	1.63250i		−	0.0581553i
$789$	−3.28303	+	12.0588i	−0.116879	+	0.429306i
$790$	22.8426	−	13.1882i	0.812705	−	0.469215i
$791$	−24.3803	+	14.7239i	−0.866862	+	0.523523i
$792$	−9.54517	+	5.40932i	−0.339173	+	0.192212i
$793$	−9.25697	−	1.52473i	−0.328725	−	0.0541447i
$794$	24.9619			0.885864
$795$	−10.3309	−	10.4140i	−0.366398	−	0.369348i
$796$	−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
$804$	−6.07702	+	6.02849i	−0.214320	+	0.212608i
$805$	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	−0.526900	−	0.849927i	$-0.676646\pi$
$809$	−1.54419	+	0.891541i	−0.0542910	+	0.0313449i	0.472609	+	0.881272i	$0.343312\pi$
$810$	−14.7885	+	8.22478i	−0.519615	+	0.288989i
$811$		−	33.9033i		−	1.19051i	−0.803538	−	0.595253i	$-0.797052\pi$
$811$		−	33.9033i		−	1.19051i	0.803538	−	0.595253i	$-0.202948\pi$
$812$	−7.63011	−	4.20701i	−0.267764	−	0.147637i
$813$	4.71338	−	17.3126i	0.165305	−	0.607180i
$814$	−6.80464			−0.238503
$815$	3.49663	−	6.05635i	0.122482	−	0.212145i
$816$	−6.55658	+	6.50422i	−0.229526	+	0.227693i
$817$	40.5060	−	23.3862i	1.41713	−	0.818178i
$818$	4.16814			0.145735
$819$	−28.2901	−	4.32078i	−0.988537	−	0.150980i
$820$	−10.6975			−0.373573
$821$	−2.12966	+	1.22956i	−0.0743256	+	0.0429119i	−0.536702	−	0.843772i	$-0.680330\pi$
$821$	−2.12966	+	1.22956i	−0.0743256	+	0.0429119i	0.462377	+	0.886684i	$0.346997\pi$
$822$	−23.6185	+	23.4299i	−0.823790	+	0.817210i
$823$	−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
$825$	2.43746	−	8.95298i	0.0848615	−	0.311703i
$826$	−11.3867	−	6.27829i	−0.396195	−	0.218450i
$827$		−	5.36637i		−	0.186607i	−0.995638	−	0.0933035i	$-0.970257\pi$
$827$		−	5.36637i		−	0.186607i	0.995638	−	0.0933035i	$-0.0297427\pi$
$828$	11.5490	+	0.0926129i	0.401354	+	0.00321852i
$829$	−0.630628	+	0.364093i	−0.0219026	+	0.0126455i	−0.510911	−	0.859633i	$-0.670692\pi$
$829$	−0.630628	+	0.364093i	−0.0219026	+	0.0126455i	0.489009	+	0.872279i	$0.337359\pi$
$830$	−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
$834$	−15.0314	+	14.9114i	−0.520496	+	0.516339i
$835$	−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
$843$	15.5285	+	15.6536i	0.534832	+	0.539138i
$844$	12.2211			0.420669
$845$	−18.3647	+	16.1300i	−0.631764	+	0.554890i
$846$	10.7738	+	19.0113i	0.370412	+	0.653621i
$847$	3.24782	+	5.37781i	0.111596	+	0.184784i
$848$	3.90092	−	2.25219i	0.133958	−	0.0773407i
$849$	10.7866	−	39.6201i	0.370196	−	1.35976i
$850$		−	7.81073i		−	0.267906i
$851$	6.20343	+	3.58155i	0.212651	+	0.122774i
$852$	−5.31511	+	19.5228i	−0.182093	+	0.668840i
$853$		−	28.9236i		−	0.990324i	−0.868801	−	0.495162i	$-0.835109\pi$
$853$		−	28.9236i		−	0.990324i	0.868801	−	0.495162i	$-0.164891\pi$
$854$	3.32400	−	6.02863i	0.113745	−	0.206295i
$855$	12.8961	−	21.9287i	0.441038	−	0.749947i
$856$	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	$0.611928\pi$
$858$	13.2356	+	18.6126i	0.451855	+	0.635422i
$859$			5.08286i			0.173425i	0.996233	+	0.0867125i	$0.0276361\pi$
$859$			5.08286i			0.173425i	−0.996233	+	0.0867125i	$0.972364\pi$
$860$	−9.74934	−	16.8864i	−0.332450	−	0.575820i
$861$	−18.1447	+	18.7234i	−0.618369	+	0.638091i
$862$	−14.8443	+	25.7111i	−0.505600	+	0.875725i
$863$			52.7636i			1.79610i	0.439898	+	0.898048i	$0.355015\pi$
$863$			52.7636i			1.79610i	−0.439898	+	0.898048i	$0.644985\pi$
$864$	−1.28440	−	5.03491i	−0.0436960	−	0.171291i
$865$	16.3683	−	28.3508i	0.556540	−	0.963956i
$866$	−7.54617			−0.256429
$867$	−19.1041	−	5.20111i	−0.648808	−	0.176639i
$868$	−6.67863	+	4.03342i	−0.226687	+	0.136903i
$869$	−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
$873$	−20.1729	+	34.3022i	−0.682748	+	1.16095i
$874$	−15.0367	+	8.68146i	−0.508625	+	0.293655i
$875$	−15.5279	+	28.1625i	−0.524940	+	0.952066i
$876$	−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	$0.800799\pi$
$882$	9.92403	−	18.5071i	0.334160	−	0.623167i
$883$	−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	$-0.358557\pi$
$888$	0.846583	−	3.10957i	0.0284095	−	0.104350i
$889$	−43.1324	+	0.850027i	−1.44661	+	0.0285090i
$890$	−15.7186	−	9.07513i	−0.526888	−	0.304199i
$891$	28.7647	−	15.9978i	0.963654	−	0.535946i
$892$		−	3.40806i		−	0.114110i
$893$	−28.4502	−	16.4257i	−0.952049	−	0.549666i
$894$	15.4218	−	15.2986i	0.515782	−	0.511663i
$895$	34.7181	−	20.0445i	1.16050	−	0.670013i
$896$	0.0521308	+	2.64524i	0.00174157	+	0.0883712i
$897$	−2.26963	−	23.9345i	−0.0757809	−	0.799149i
$898$	29.4762			0.983632
$899$	−4.85572	−	8.41036i	−0.161947	−	0.280501i
$900$	3.78806	+	2.22773i	0.126269	+	0.0742576i
$901$	20.8000	+	12.0089i	0.692950	+	0.400075i
$902$	20.8074			0.692812
$903$	−46.0919	−	11.5781i	−1.53384	−	0.385295i
$904$	−5.38248	+	9.32273i	−0.179019	+	0.310070i
$905$			8.30467i			0.276057i
$906$	0.476330	−	1.74960i	0.0158250	−	0.0581264i
$907$	−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
$910$	−6.65378	−	16.6561i	−0.220571	−	0.552144i
$911$		−	11.8570i		−	0.392841i	−0.980520	−	0.196420i	$-0.937068\pi$
$911$		−	11.8570i		−	0.392841i	0.980520	−	0.196420i	$-0.0629318\pi$
$912$	5.50154	+	5.54584i	0.182174	+	0.183641i
$913$	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
$917$	15.5075	−	28.1255i	0.512103	−	0.928785i
$918$	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
$921$	34.5421	+	34.8203i	1.13820	+	1.14737i
$922$		−	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
$927$	11.8271	+	0.0948437i	0.388455	+	0.00311508i
$928$	−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	$0.0990082\pi$
$930$	9.26616	+	2.52272i	0.303849	+	0.0827233i
$931$	1.24387	+	31.5463i	0.0407663	+	1.03389i
$932$	−1.47923	−	0.854031i	−0.0484536	−	0.0279747i
$933$	−12.2390	+	12.1412i	−0.400686	+	0.397485i
$934$	−1.93053	+	1.11459i	−0.0631689	+	0.0364706i
$935$		−	36.6641i		−	1.19904i
$936$	−10.1522	+	3.73271i	−0.331835	+	0.122008i
$937$			6.10741i			0.199520i	0.995012	+	0.0997602i	$0.0318076\pi$
$937$			6.10741i			0.199520i	−0.995012	+	0.0997602i	$0.968192\pi$
$938$	−11.1927	+	6.75963i	−0.365456	+	0.220710i
$939$	−42.1443	−	42.4836i	−1.37533	−	1.38640i
$940$	−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	$0.640555\pi$
$942$	12.2620	+	3.33836i	0.399519	+	0.108769i
$943$	−18.9690	−	10.9518i	−0.617717	−	0.356639i
$944$	−4.91462			−0.159957
$945$	−24.9156	+	6.88154i	−0.810505	+	0.223856i
$946$	18.9632	+	32.8452i	0.616546	+	1.06789i
$947$	−0.247412	+	0.142844i	−0.00803982	+	0.00464179i	−0.504015	−	0.863695i	$-0.668144\pi$
$947$	−0.247412	+	0.142844i	−0.00803982	+	0.00464179i	0.495975	+	0.868337i	$0.334811\pi$
$948$	−6.19466	−	23.4952i	−0.201193	−	0.763089i
$949$	6.46177	+	17.1488i	0.209758	+	0.556673i
$950$	−6.60665			−0.214348
$951$	−23.3221	−	23.5098i	−0.756270	−	0.762359i
$952$	−12.0760	+	7.29305i	−0.391385	+	0.236369i
$953$	34.4494	+	19.8894i	1.11592	+	0.644279i	0.940357	−	0.340188i	$-0.110491\pi$
$953$	34.4494	+	19.8894i	1.11592	+	0.644279i	0.175567	+	0.984467i	$0.443824\pi$
$954$	−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
$959$	−43.5009	+	26.2715i	−1.40472	+	0.848349i
$960$	2.31198	−	2.29351i	0.0746188	−	0.0740228i
$961$	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
$966$	17.1103	+	4.29804i	0.550515	+	0.138287i
$967$	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
$969$	−10.9418	+	40.1901i	−0.351501	+	1.29109i
$970$	−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	$-0.256662\pi$
$972$	3.73194	+	15.1351i	0.119702	+	0.485460i
$973$	−27.6851	+	16.7198i	−0.887543	+	0.536013i
$974$		−	32.3409i		−	1.03627i
$975$	3.80567	−	8.31883i	0.121879	−	0.266416i
$976$		−	2.60201i		−	0.0832885i
$977$	−0.122426	+	0.0706828i	−0.00391676	+	0.00226134i	−0.501957	−	0.864893i	$-0.667386\pi$
$977$	−0.122426	+	0.0706828i	−0.00391676	+	0.00226134i	0.498040	+	0.867154i	$0.334053\pi$
$978$	−4.53705	−	4.57358i	−0.145079	−	0.146247i
$979$	30.5738	+	17.6518i	0.977143	+	0.564154i
$980$	13.1512	−	0.518552i	0.420099	−	0.0165645i
$981$	−0.0346369	+	4.31927i	−0.00110587	+	0.137904i
$982$	−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	$0.667633\pi$
$984$	−2.58871	+	9.50853i	−0.0825250	+	0.303121i
$985$	−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
$990$	17.7814	+	10.4571i	0.565130	+	0.332348i
$991$	−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
$994$	−14.9231	+	27.0656i	−0.473333	+	0.858467i
$995$	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	−0.452953	−	0.891535i	$-0.649629\pi$
$997$	−45.8322	−	26.4612i	−1.45152	−	0.838036i	−0.998568	+	0.0534988i	$0.982963\pi$
$998$	−25.0739	+	14.4764i	−0.793700	+	0.458243i
$999$	−2.61447	+	9.30803i	−0.0827183	+	0.294493i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.22965 - 1.21982i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.88020 q^{5} +(-0.454992 + 1.67122i) q^{6} +(-1.27747 + 2.31691i) q^{7} +1.00000i q^{8} +(0.0240567 - 2.99990i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.22965 - 1.21982i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.88020 q^{5} +(-0.454992 + 1.67122i) q^{6} +(-1.27747 + 2.31691i) q^{7} +1.00000i q^{8} +(0.0240567 - 2.99990i) 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} +(-2.31198 + 2.29351i) 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} +(1.21982 + 1.22965i) q^{24} -1.46485 q^{25} +(2.28628 - 2.78800i) q^{26} +(-3.62977 - 3.71816i) q^{27} +(1.36777 + 2.26478i) q^{28} +(-2.85202 + 1.64661i) q^{29} +(0.855476 - 3.14223i) q^{30} +2.94891i q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.66396 + 6.11186i) q^{33} +5.33209i q^{34} +(2.40190 - 4.35625i) q^{35} +(-2.58596 - 1.52079i) q^{36} +(-0.930327 - 1.61137i) q^{37} +4.51011 q^{38} +(-2.59799 + 5.67895i) q^{39} -1.88020i q^{40} +(2.84478 + 4.92731i) q^{41} +(-3.29083 - 3.18911i) q^{42} +(-5.18527 + 8.98116i) q^{43} +3.65712i q^{44} +(-0.0452314 + 5.64041i) q^{45} +(1.92489 - 3.33400i) q^{46} +7.28396 q^{47} +(-1.67122 - 0.454992i) q^{48} +(-3.73613 - 5.91957i) q^{49} +(1.26860 - 0.732427i) q^{50} +(-2.35452 - 8.93028i) q^{51} +(-0.585980 + 3.55762i) q^{52} +4.50439i q^{53} +(5.00256 + 1.40514i) q^{54} +(5.95489 - 3.43806i) q^{55} +(-2.31691 - 1.27747i) 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} +(6.91977 + 3.88803i) 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} +(-1.75162 + 6.43383i) q^{69} +(0.0980162 + 4.97357i) q^{70} +(-10.1167 - 5.84088i) q^{71} +(2.99990 + 0.0240567i) q^{72} -5.08266i q^{73} +(1.61137 + 0.930327i) q^{74} +(-1.80125 + 1.78686i) q^{75} +(-3.90587 + 2.25506i) q^{76} +(-0.190649 - 9.67396i) q^{77} +(-0.589550 - 6.21711i) q^{78} +14.0285 q^{79} +(0.940099 + 1.62830i) q^{80} +(-8.99884 - 0.144336i) q^{81} +(-4.92731 - 2.84478i) q^{82} -4.75954 q^{83} +(4.44450 + 1.11644i) q^{84} +(-5.01270 + 8.68224i) q^{85} -10.3705i q^{86} +(-1.49839 + 5.50372i) q^{87} +(-1.82856 - 3.16716i) q^{88} +(-4.82669 - 8.36007i) q^{89} +(-2.78104 - 4.90736i) q^{90} +(1.36459 - 9.44129i) q^{91} +3.84978i q^{92} +(3.59716 + 3.62612i) 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} +(6.19537 + 3.25844i) 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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