LMFDB - Embedded newform 462.2.n.e.65.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(65,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("462.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.n (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.12
Character	$\chi$	$=$	462.65
Dual form			462.2.n.e.263.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.72543 - 0.151338i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.246102 - 0.142087i) q^{5} +(-0.731651 + 1.56993i) q^{6} +(-2.09441 - 1.61662i) q^{7} +1.00000 q^{8} +(2.95419 - 0.522246i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.72543 - 0.151338i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.246102 - 0.142087i) q^{5} +(-0.731651 + 1.56993i) q^{6} +(-2.09441 - 1.61662i) q^{7} +1.00000 q^{8} +(2.95419 - 0.522246i) q^{9} +(0.246102 - 0.142087i) q^{10} +(2.18506 - 2.49510i) q^{11} +(-0.993776 - 1.41859i) q^{12} -6.02702i q^{13} +(2.44724 - 1.00550i) q^{14} +(-0.446134 - 0.207916i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.12688 + 5.41591i) q^{17} +(-1.02482 + 2.81953i) q^{18} +(4.70688 + 2.71752i) q^{19} +0.284174i q^{20} +(-3.85840 - 2.47240i) q^{21} +(1.06829 + 3.13986i) q^{22} +(1.55587 + 0.898282i) q^{23} +(1.72543 - 0.151338i) q^{24} +(-2.45962 - 4.26019i) q^{25} +(5.21955 + 3.01351i) q^{26} +(5.01821 - 1.34818i) q^{27} +(-0.352833 + 2.62212i) q^{28} +0.434446 q^{29} +(0.403128 - 0.282406i) q^{30} +(-3.64386 - 6.31135i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.39255 - 4.63580i) q^{33} -6.25376 q^{34} +(0.285737 + 0.695442i) q^{35} +(-1.92937 - 2.29728i) q^{36} +(-5.57207 + 9.65112i) q^{37} +(-4.70688 + 2.71752i) q^{38} +(-0.912118 - 10.3992i) q^{39} +(-0.246102 - 0.142087i) q^{40} -0.326715 q^{41} +(4.07036 - 2.10527i) q^{42} -2.29940i q^{43} +(-3.25335 - 0.644763i) q^{44} +(-0.801238 - 0.291227i) q^{45} +(-1.55587 + 0.898282i) q^{46} +(3.52794 + 2.03685i) q^{47} +(-0.731651 + 1.56993i) q^{48} +(1.77307 + 6.77172i) q^{49} +4.91924 q^{50} +(6.21483 + 8.87154i) q^{51} +(-5.21955 + 3.01351i) q^{52} +(1.66437 - 0.960923i) q^{53} +(-1.34155 + 5.01999i) q^{54} +(-0.892269 + 0.303581i) q^{55} +(-2.09441 - 1.61662i) q^{56} +(8.53264 + 3.97655i) q^{57} +(-0.217223 + 0.376241i) q^{58} +(-8.38305 + 4.83996i) q^{59} +(0.0430064 + 0.490322i) q^{60} +(-3.37831 - 1.95047i) q^{61} +7.28772 q^{62} +(-7.03155 - 3.68202i) q^{63} +1.00000 q^{64} +(-0.856362 + 1.48326i) q^{65} +(2.31844 + 5.25593i) q^{66} +(4.34158 + 7.51984i) q^{67} +(3.12688 - 5.41591i) q^{68} +(2.82048 + 1.31446i) q^{69} +(-0.745139 - 0.100266i) q^{70} -3.88436i q^{71} +(2.95419 - 0.522246i) q^{72} +(3.80459 - 2.19658i) q^{73} +(-5.57207 - 9.65112i) q^{74} +(-4.88863 - 6.97841i) q^{75} -5.43503i q^{76} +(-8.61003 + 1.69335i) q^{77} +(9.46201 + 4.40967i) q^{78} +(4.63260 + 2.67463i) q^{79} +(0.246102 - 0.142087i) q^{80} +(8.45452 - 3.08563i) q^{81} +(0.163357 - 0.282943i) q^{82} +1.61235 q^{83} +(-0.211960 + 4.57767i) q^{84} -1.77716i q^{85} +(1.99134 + 1.14970i) q^{86} +(0.749605 - 0.0657483i) q^{87} +(2.18506 - 2.49510i) q^{88} +(-14.8319 - 8.56318i) q^{89} +(0.652829 - 0.548279i) q^{90} +(-9.74341 + 12.6230i) q^{91} -1.79656i q^{92} +(-7.24236 - 10.3383i) q^{93} +(-3.52794 + 2.03685i) q^{94} +(-0.772248 - 1.33757i) q^{95} +(-0.993776 - 1.41859i) q^{96} +6.98710 q^{97} +(-6.75102 - 1.85034i) q^{98} +(5.15202 - 8.51215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9 - 4 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^17 - 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 + 40 * q^29 - 2 * q^30 - 28 * q^31 - 12 * q^32 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^36 - 16 * q^37 - 8 * q^41 + 6 * q^42 - 4 * q^44 - 28 * q^45 - 8 * q^49 - 40 * q^50 - 34 * q^51 + 6 * q^54 + 8 * q^55 + 40 * q^57 - 20 * q^58 - 2 * q^60 + 56 * q^62 - 14 * q^63 + 24 * q^64 - 44 * q^65 + 32 * q^66 + 4 * q^68 - 20 * q^69 + 64 * q^70 - 8 * q^72 - 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 + 144 * q^83 - 6 * q^84 + 8 * q^87 - 4 * q^88 + 56 * q^90 - 32 * q^91 - 22 * q^93 - 44 * q^95 + 64 * q^97 - 8 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.72543	−	0.151338i	0.996175	−	0.0873751i
$3$	1.72543	−	0.151338i	0.996175	−	0.0873751i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.246102	−	0.142087i	−0.110060	−	0.0635433i	0.443959	−	0.896047i	$-0.353573\pi$
$5$	−0.246102	−	0.142087i	−0.110060	−	0.0635433i	−0.554020	+	0.832504i	$0.686907\pi$
$6$	−0.731651	+	1.56993i	−0.298695	+	0.640922i
$7$	−2.09441	−	1.61662i	−0.791611	−	0.611026i
$7$	−2.09441	−	1.61662i	−0.791611	−	0.611026i
$8$	1.00000			0.353553
$9$	2.95419	−	0.522246i	0.984731	−	0.174082i
$10$	0.246102	−	0.142087i	0.0778243	−	0.0449319i
$11$	2.18506	−	2.49510i	0.658819	−	0.752301i
$11$	2.18506	−	2.49510i	0.658819	−	0.752301i
$12$	−0.993776	−	1.41859i	−0.286878	−	0.409513i
$13$		−	6.02702i		−	1.67159i	−0.549039	−	0.835797i	$-0.685006\pi$
$13$		−	6.02702i		−	1.67159i	0.549039	−	0.835797i	$-0.314994\pi$
$14$	2.44724	−	1.00550i	0.654052	−	0.268731i
$15$	−0.446134	−	0.207916i	−0.115191	−	0.0536837i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.12688	+	5.41591i	0.758380	+	1.31355i	0.943677	+	0.330869i	$0.107342\pi$
$17$	3.12688	+	5.41591i	0.758380	+	1.31355i	−0.185297	+	0.982683i	$0.559325\pi$
$18$	−1.02482	+	2.81953i	−0.241552	+	0.664569i
$19$	4.70688	+	2.71752i	1.07983	+	0.623441i	0.930851	−	0.365399i	$-0.119067\pi$
$19$	4.70688	+	2.71752i	1.07983	+	0.623441i	0.148981	+	0.988840i	$0.452401\pi$
$20$			0.284174i			0.0635433i
$21$	−3.85840	−	2.47240i	−0.841972	−	0.539522i
$22$	1.06829	+	3.13986i	0.227761	+	0.669421i
$23$	1.55587	+	0.898282i	0.324421	+	0.187305i	0.653362	−	0.757046i	$-0.273358\pi$
$23$	1.55587	+	0.898282i	0.324421	+	0.187305i	−0.328940	+	0.944351i	$0.606691\pi$
$24$	1.72543	−	0.151338i	0.352201	−	0.0308918i
$25$	−2.45962	−	4.26019i	−0.491924	−	0.852038i
$26$	5.21955	+	3.01351i	1.02364	+	0.590998i
$27$	5.01821	−	1.34818i	0.965755	−	0.259457i
$28$	−0.352833	+	2.62212i	−0.0666791	+	0.495534i
$29$	0.434446			0.0806746			0.0403373	−	0.999186i	$-0.487157\pi$
$29$	0.434446			0.0806746			0.0403373	+	0.999186i	$0.487157\pi$
$30$	0.403128	−	0.282406i	0.0736008	−	0.0515600i
$31$	−3.64386	−	6.31135i	−0.654456	−	1.13355i	−0.982030	−	0.188726i	$-0.939564\pi$
$31$	−3.64386	−	6.31135i	−0.654456	−	1.13355i	0.327573	−	0.944826i	$-0.393769\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.39255	−	4.63580i	0.590567	−	0.806989i
$34$	−6.25376			−1.07251
$35$	0.285737	+	0.695442i	0.0482983	+	0.117551i
$36$	−1.92937	−	2.29728i	−0.321562	−	0.382881i
$37$	−5.57207	+	9.65112i	−0.916043	+	1.58663i	−0.110677	+	0.993856i	$0.535302\pi$
$37$	−5.57207	+	9.65112i	−0.916043	+	1.58663i	−0.805367	+	0.592777i	$0.798032\pi$
$38$	−4.70688	+	2.71752i	−0.763556	+	0.440839i
$39$	−0.912118	−	10.3992i	−0.146056	−	1.66520i
$40$	−0.246102	−	0.142087i	−0.0389122	−	0.0224659i
$41$	−0.326715			−0.0510243			−0.0255121	−	0.999675i	$-0.508122\pi$
$41$	−0.326715			−0.0510243			−0.0255121	+	0.999675i	$0.508122\pi$
$42$	4.07036	−	2.10527i	0.628070	−	0.324851i
$43$		−	2.29940i		−	0.350655i	−0.984510	−	0.175327i	$-0.943902\pi$
$43$		−	2.29940i		−	0.350655i	0.984510	−	0.175327i	$-0.0560984\pi$
$44$	−3.25335	−	0.644763i	−0.490461	−	0.0972017i
$45$	−0.801238	−	0.291227i	−0.119441	−	0.0434136i
$46$	−1.55587	+	0.898282i	−0.229401	+	0.132444i
$47$	3.52794	+	2.03685i	0.514602	+	0.297106i	0.734723	−	0.678367i	$-0.237312\pi$
$47$	3.52794	+	2.03685i	0.514602	+	0.297106i	−0.220121	+	0.975473i	$0.570645\pi$
$48$	−0.731651	+	1.56993i	−0.105605	+	0.226600i
$49$	1.77307	+	6.77172i	0.253296	+	0.967389i
$50$	4.91924			0.695686
$51$	6.21483	+	8.87154i	0.870251	+	1.24226i
$52$	−5.21955	+	3.01351i	−0.723821	+	0.417899i
$53$	1.66437	−	0.960923i	0.228618	−	0.131993i	−0.381316	−	0.924445i	$-0.624529\pi$
$53$	1.66437	−	0.960923i	0.228618	−	0.131993i	0.609935	+	0.792452i	$0.291196\pi$
$54$	−1.34155	+	5.01999i	−0.182561	+	0.683133i
$55$	−0.892269	+	0.303581i	−0.120313	+	0.0409349i
$56$	−2.09441	−	1.61662i	−0.279877	−	0.216030i
$57$	8.53264	+	3.97655i	1.13018	+	0.526706i
$58$	−0.217223	+	0.376241i	−0.0285228	+	0.0494029i
$59$	−8.38305	+	4.83996i	−1.09138	+	0.630109i	−0.933944	−	0.357420i	$-0.883656\pi$
$59$	−8.38305	+	4.83996i	−1.09138	+	0.630109i	−0.157437	+	0.987529i	$0.550323\pi$
$60$	0.0430064	+	0.490322i	0.00555210	+	0.0633003i
$61$	−3.37831	−	1.95047i	−0.432548	−	0.249732i	0.267883	−	0.963451i	$-0.413676\pi$
$61$	−3.37831	−	1.95047i	−0.432548	−	0.249732i	−0.700432	+	0.713719i	$0.747009\pi$
$62$	7.28772			0.925541
$63$	−7.03155	−	3.68202i	−0.885892	−	0.463891i
$64$	1.00000			0.125000
$65$	−0.856362	+	1.48326i	−0.106219	+	0.183976i
$66$	2.31844	+	5.25593i	0.285381	+	0.646961i
$67$	4.34158	+	7.51984i	0.530409	+	0.918695i	0.999371	+	0.0354765i	$0.0112949\pi$
$67$	4.34158	+	7.51984i	0.530409	+	0.918695i	−0.468962	+	0.883218i	$0.655372\pi$
$68$	3.12688	−	5.41591i	0.379190	−	0.656776i
$69$	2.82048	+	1.31446i	0.339546	+	0.158242i
$70$	−0.745139	−	0.100266i	−0.0890611	−	0.0119841i
$71$		−	3.88436i		−	0.460989i	−0.973074	−	0.230495i	$-0.925966\pi$
$71$		−	3.88436i		−	0.460989i	0.973074	−	0.230495i	$-0.0740344\pi$
$72$	2.95419	−	0.522246i	0.348155	−	0.0615473i
$73$	3.80459	−	2.19658i	0.445294	−	0.257091i	−0.260547	−	0.965461i	$-0.583903\pi$
$73$	3.80459	−	2.19658i	0.445294	−	0.257091i	0.705841	+	0.708371i	$0.250569\pi$
$74$	−5.57207	−	9.65112i	−0.647740	−	1.12192i
$75$	−4.88863	−	6.97841i	−0.564490	−	0.805798i
$76$		−	5.43503i		−	0.623441i
$77$	−8.61003	+	1.69335i	−0.981204	+	0.192975i
$78$	9.46201	+	4.40967i	1.07136	+	0.499297i
$79$	4.63260	+	2.67463i	0.521208	+	0.300920i	0.737429	−	0.675425i	$-0.236040\pi$
$79$	4.63260	+	2.67463i	0.521208	+	0.300920i	−0.216221	+	0.976345i	$0.569373\pi$
$80$	0.246102	−	0.142087i	0.0275151	−	0.0158858i
$81$	8.45452	−	3.08563i	0.939391	−	0.342848i
$82$	0.163357	−	0.282943i	0.0180398	−	0.0312459i
$83$	1.61235			0.176978			0.0884892	−	0.996077i	$-0.471796\pi$
$83$	1.61235			0.176978			0.0884892	+	0.996077i	$0.471796\pi$
$84$	−0.211960	+	4.57767i	−0.0231267	+	0.499465i
$85$		−	1.77716i		−	0.192760i
$86$	1.99134	+	1.14970i	0.214731	+	0.123975i
$87$	0.749605	−	0.0657483i	0.0803661	−	0.00704896i
$88$	2.18506	−	2.49510i	0.232928	−	0.265979i
$89$	−14.8319	−	8.56318i	−1.57217	−	0.907695i	−0.995902	−	0.0904364i	$-0.971174\pi$
$89$	−14.8319	−	8.56318i	−1.57217	−	0.907695i	−0.576271	−	0.817258i	$-0.695493\pi$
$90$	0.652829	−	0.548279i	0.0688142	−	0.0577936i
$91$	−9.74341	+	12.6230i	−1.02139	+	1.32325i
$92$		−	1.79656i		−	0.187305i
$93$	−7.24236	−	10.3383i	−0.750998	−	1.07203i
$94$	−3.52794	+	2.03685i	−0.363879	+	0.210086i
$95$	−0.772248	−	1.33757i	−0.0792310	−	0.137232i
$96$	−0.993776	−	1.41859i	−0.101427	−	0.144785i
$97$	6.98710			0.709432			0.354716	−	0.934974i	$-0.384578\pi$
$97$	6.98710			0.709432			0.354716	+	0.934974i	$0.384578\pi$
$98$	−6.75102	−	1.85034i	−0.681956	−	0.186912i
$99$	5.15202	−	8.51215i	0.517798	−	0.855503i
$100$	−2.45962	+	4.26019i	−0.245962	+	0.426019i
$101$	5.50494	+	9.53484i	0.547762	+	0.948752i	0.998427	+	0.0560587i	$0.0178534\pi$
$101$	5.50494	+	9.53484i	0.547762	+	0.948752i	−0.450665	+	0.892693i	$0.648813\pi$
$102$	−10.7904	+	0.946432i	−1.06841	+	0.0937108i
$103$	−3.87592	+	6.71328i	−0.381905	+	0.661480i	−0.991335	−	0.131361i	$-0.958065\pi$
$103$	−3.87592	+	6.71328i	−0.381905	+	0.661480i	0.609429	+	0.792840i	$0.291399\pi$
$104$		−	6.02702i		−	0.590998i
$105$	0.598264	+	1.15669i	0.0583846	+	0.112882i
$106$			1.92185i			0.186666i
$107$	−7.32460	+	12.6866i	−0.708096	+	1.22646i	0.257466	+	0.966287i	$0.417112\pi$
$107$	−7.32460	+	12.6866i	−0.708096	+	1.22646i	−0.965563	+	0.260171i	$0.916221\pi$
$108$	−3.67666	−	3.67181i	−0.353787	−	0.353320i
$109$	−13.7850	+	7.95877i	−1.32036	+	0.762312i	−0.983786	−	0.179344i	$-0.942603\pi$
$109$	−13.7850	+	7.95877i	−1.32036	+	0.762312i	−0.336577	+	0.941656i	$0.609269\pi$
$110$	0.183225	−	0.924518i	0.0174698	−	0.0881493i
$111$	−8.15362	+	17.4956i	−0.773908	+	1.66060i
$112$	2.44724	−	1.00550i	0.231242	−	0.0950106i
$113$			12.2685i			1.15412i	0.816702	+	0.577060i	$0.195800\pi$
$113$			12.2685i			1.15412i	−0.816702	+	0.577060i	$0.804200\pi$
$114$	−7.71011	+	5.40121i	−0.722118	+	0.505869i
$115$	−0.255269	−	0.442138i	−0.0238039	−	0.0412296i
$116$	−0.217223	−	0.376241i	−0.0201687	−	0.0349331i
$117$	−3.14758	−	17.8050i	−0.290994	−	1.64607i
$118$		−	9.67991i		−	0.891108i
$119$	2.20653	−	16.3981i	0.202272	−	1.50321i
$120$	−0.446134	−	0.207916i	−0.0407263	−	0.0189801i
$121$	−1.45106	−	10.9039i	−0.131915	−	0.991261i
$122$	3.37831	−	1.95047i	0.305858	−	0.176587i
$123$	−0.563722	+	0.0494444i	−0.0508291	+	0.00445825i
$124$	−3.64386	+	6.31135i	−0.327228	+	0.566776i
$125$			2.81879i			0.252121i
$126$	6.70450	−	4.24849i	0.597284	−	0.378486i
$127$		−	5.55609i		−	0.493023i	−0.969140	−	0.246511i	$-0.920716\pi$
$127$		−	5.55609i		−	0.493023i	0.969140	−	0.246511i	$-0.0792843\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−0.347987	−	3.96744i	−0.0306385	−	0.349314i
$130$	−0.856362	−	1.48326i	−0.0751079	−	0.130091i
$131$	9.44368	−	16.3569i	0.825099	−	1.42911i	−0.0767455	−	0.997051i	$-0.524453\pi$
$131$	9.44368	−	16.3569i	0.825099	−	1.42911i	0.901844	−	0.432062i	$-0.142214\pi$
$132$	−5.71099	−	0.620136i	−0.497078	−	0.0539759i
$133$	−5.46491	−	13.3008i	−0.473868	−	1.15333i
$134$	−8.68317			−0.750111
$135$	−1.42655	−	0.381233i	−0.122778	−	0.0328113i
$136$	3.12688	+	5.41591i	0.268128	+	0.464411i
$137$	−14.6388	+	8.45173i	−1.25068	+	0.722080i	−0.971244	−	0.238084i	$-0.923481\pi$
$137$	−14.6388	+	8.45173i	−1.25068	+	0.722080i	−0.279435	+	0.960165i	$0.590147\pi$
$138$	−2.54860	+	1.78538i	−0.216951	+	0.151982i
$139$		−	12.1306i		−	1.02890i	−0.857519	−	0.514452i	$-0.827995\pi$
$139$		−	12.1306i		−	1.02890i	0.857519	−	0.514452i	$-0.172005\pi$
$140$	0.459402	−	0.595176i	0.0388266	−	0.0503016i
$141$	6.39545	+	2.98053i	0.538594	+	0.251006i
$142$	3.36396	+	1.94218i	0.282297	+	0.162984i
$143$	−15.0380	−	13.1694i	−1.25754	−	1.10128i
$144$	−1.02482	+	2.81953i	−0.0854016	+	0.234961i
$145$	−0.106918	−	0.0617292i	−0.00887907	−	0.00512633i
$146$			4.39317i			0.363581i
$147$	4.08412	+	11.4158i	0.336853	+	0.941557i
$148$	11.1441			0.916043
$149$	−5.93990	+	10.2882i	−0.486616	+	0.842843i	−0.999882	−	0.0153863i	$-0.995102\pi$
$149$	−5.93990	+	10.2882i	−0.486616	+	0.842843i	0.513266	+	0.858230i	$0.328436\pi$
$150$	8.48780	−	0.744470i	0.693026	−	0.0607857i
$151$	1.49875	−	0.865305i	0.121967	−	0.0704175i	−0.437775	−	0.899084i	$-0.644234\pi$
$151$	1.49875	−	0.865305i	0.121967	−	0.0704175i	0.559742	+	0.828667i	$0.310900\pi$
$152$	4.70688	+	2.71752i	0.381778	+	0.220420i
$153$	12.0658	+	14.3667i	0.975466	+	1.16148i
$154$	2.83853	−	8.30318i	0.228736	−	0.669089i
$155$			2.07098i			0.166345i
$156$	−8.54989	+	5.98951i	−0.684539	+	0.479544i
$157$	−5.57046	−	9.64832i	−0.444571	−	0.770020i	0.553451	−	0.832882i	$-0.313311\pi$
$157$	−5.57046	−	9.64832i	−0.444571	−	0.770020i	−0.998022	+	0.0628618i	$0.979977\pi$
$158$	−4.63260	+	2.67463i	−0.368550	+	0.212782i
$159$	2.72632	−	1.90988i	0.216211	−	0.151464i
$160$			0.284174i			0.0224659i
$161$	−1.80644	−	4.39662i	−0.142367	−	0.346502i
$162$	−1.55503	+	8.86464i	−0.122174	+	0.696472i
$163$	0.415887	−	0.720337i	0.0325748	−	0.0564211i	−0.849278	−	0.527945i	$-0.822963\pi$
$163$	0.415887	−	0.720337i	0.0325748	−	0.0564211i	0.881853	+	0.471524i	$0.156296\pi$
$164$	0.163357	+	0.282943i	0.0127561	+	0.0220942i
$165$	−1.49360	+	0.658842i	−0.116277	+	0.0512908i
$166$	−0.806175	+	1.39634i	−0.0625713	+	0.108377i
$167$	19.1395			1.48106			0.740529	−	0.672025i	$-0.234575\pi$
$167$	19.1395			1.48106			0.740529	+	0.672025i	$0.234575\pi$
$168$	−3.85840	−	2.47240i	−0.297682	−	0.190750i
$169$	−23.3249			−1.79423
$170$	1.53906	+	0.888578i	0.118041	+	0.0681509i
$171$	15.3242	+	5.56992i	1.17187	+	0.425943i
$172$	−1.99134	+	1.14970i	−0.151838	+	0.0876637i
$173$	−8.80633	+	15.2530i	−0.669533	+	1.15967i	0.308502	+	0.951224i	$0.400172\pi$
$173$	−8.80633	+	15.2530i	−0.669533	+	1.15967i	−0.978035	+	0.208442i	$0.933161\pi$
$174$	−0.317863	+	0.682051i	−0.0240971	+	0.0517062i
$175$	−1.73567	+	12.8988i	−0.131204	+	0.975061i
$176$	1.06829	+	3.13986i	0.0805256	+	0.236676i
$177$	−13.7319	+	9.61966i	−1.03215	+	0.723058i
$178$	14.8319	−	8.56318i	1.11169	−	0.641837i
$179$	7.84070	−	4.52683i	0.586041	−	0.338351i	−0.177489	−	0.984123i	$-0.556798\pi$
$179$	7.84070	−	4.52683i	0.586041	−	0.338351i	0.763531	+	0.645772i	$0.223464\pi$
$180$	0.148409	+	0.839506i	0.0110617	+	0.0625731i
$181$	21.1949			1.57540			0.787701	−	0.616057i	$-0.211271\pi$
$181$	21.1949			1.57540			0.787701	+	0.616057i	$0.211271\pi$
$182$	−6.06015	−	14.7495i	−0.449208	−	1.09331i
$183$	−6.12421	−	2.85412i	−0.452715	−	0.210983i
$184$	1.55587	+	0.898282i	0.114700	+	0.0662222i
$185$	2.74260	−	1.58344i	0.201640	−	0.116417i
$186$	12.5744	−	1.10291i	0.922001	−	0.0808693i
$187$	20.3457	+	4.03219i	1.48782	+	0.294863i
$188$		−	4.07371i		−	0.297106i
$189$	−12.6897	−	5.28891i	−0.923037	−	0.384712i
$190$	1.54450			0.112050
$191$	10.7800	+	6.22381i	0.780010	+	0.450339i	0.836434	−	0.548068i	$-0.184636\pi$
$191$	10.7800	+	6.22381i	0.780010	+	0.450339i	−0.0564238	+	0.998407i	$0.517970\pi$
$192$	1.72543	−	0.151338i	0.124522	−	0.0109219i
$193$	−12.9542	+	7.47910i	−0.932463	+	0.538357i	−0.887590	−	0.460635i	$-0.847622\pi$
$193$	−12.9542	+	7.47910i	−0.932463	+	0.538357i	−0.0448730	+	0.998993i	$0.514288\pi$
$194$	−3.49355	+	6.05100i	−0.250822	+	0.434437i
$195$	−1.25312	+	2.68886i	−0.0897374	+	0.192553i
$196$	4.97795	−	4.92138i	0.355568	−	0.351527i
$197$	−8.24633			−0.587527			−0.293763	−	0.955878i	$-0.594908\pi$
$197$	−8.24633			−0.587527			−0.293763	+	0.955878i	$0.594908\pi$
$198$	4.79573	+	8.71786i	0.340817	+	0.619551i
$199$	7.13434	+	12.3570i	0.505740	+	0.875967i	0.999978	+	0.00664051i	$0.00211376\pi$
$199$	7.13434	+	12.3570i	0.505740	+	0.875967i	−0.494238	+	0.869327i	$0.664553\pi$
$200$	−2.45962	−	4.26019i	−0.173922	−	0.301241i
$201$	8.62912	+	12.3179i	0.608651	+	0.868837i
$202$	−11.0099			−0.774652
$203$	−0.909907	−	0.702335i	−0.0638629	−	0.0492943i
$204$	4.57557	−	9.81798i	0.320354	−	0.687396i
$205$	0.0804052	+	0.0464220i	0.00561574	+	0.00324225i
$206$	−3.87592	−	6.71328i	−0.270048	−	0.467737i
$207$	5.06547	+	1.84115i	0.352074	+	0.127969i
$208$	5.21955	+	3.01351i	0.361911	+	0.208949i
$209$	17.0653	−	5.80621i	1.18043	−	0.401624i
$210$	−1.30086	−	0.0602336i	−0.0897676	−	0.00415651i
$211$			16.7368i			1.15221i	0.817376	+	0.576105i	$0.195428\pi$
$211$			16.7368i			1.15221i	−0.817376	+	0.576105i	$0.804572\pi$
$212$	−1.66437	−	0.960923i	−0.114309	−	0.0659964i
$213$	−0.587853	−	6.70219i	−0.0402790	−	0.459226i
$214$	−7.32460	−	12.6866i	−0.500700	−	0.867237i
$215$	−0.326715	+	0.565887i	−0.0222818	+	0.0385932i
$216$	5.01821	−	1.34818i	0.341446	−	0.0917320i
$217$	−2.57134	+	19.1093i	−0.174554	+	1.29722i
$218$		−	15.9175i		−	1.07807i
$219$	6.23212	−	4.36582i	0.421128	−	0.295015i
$220$	0.709044	+	0.620937i	0.0478037	+	0.0418635i
$221$	32.6418	−	18.8458i	2.19573	−	1.26770i
$222$	−11.0748	−	15.8090i	−0.743291	−	1.06103i
$223$	1.08771			0.0728383			0.0364192	−	0.999337i	$-0.488405\pi$
$223$	1.08771			0.0728383			0.0364192	+	0.999337i	$0.488405\pi$
$224$	−0.352833	+	2.62212i	−0.0235746	+	0.175198i
$225$	−9.49107	−	11.3009i	−0.632738	−	0.753393i
$226$	−10.6248	−	6.13423i	−0.706751	−	0.408043i
$227$	4.48346	+	7.76558i	0.297578	+	0.515420i	0.975581	−	0.219639i	$-0.0704879\pi$
$227$	4.48346	+	7.76558i	0.297578	+	0.515420i	−0.678003	+	0.735059i	$0.737155\pi$
$228$	−0.822528	−	9.37775i	−0.0544733	−	0.621057i
$229$	6.22490	−	10.7818i	0.411353	−	0.712485i	−0.583685	−	0.811980i	$-0.698390\pi$
$229$	6.22490	−	10.7818i	0.411353	−	0.712485i	0.995038	+	0.0994957i	$0.0317230\pi$
$230$	0.510537			0.0336638
$231$	−14.5997	+	4.22477i	−0.960590	+	0.277969i
$232$	0.434446			0.0285228
$233$	−9.19303	+	15.9228i	−0.602255	+	1.04314i	0.390224	+	0.920720i	$0.372398\pi$
$233$	−9.19303	+	15.9228i	−0.602255	+	1.04314i	−0.992479	+	0.122417i	$0.960936\pi$
$234$	16.9934	+	6.17660i	1.11089	+	0.403777i
$235$	−0.578822	−	1.00255i	−0.0377582	−	0.0653991i
$236$	8.38305	+	4.83996i	0.545690	+	0.315054i
$237$	8.39798	+	3.91379i	0.545508	+	0.254228i
$238$	13.0979	+	10.1100i	0.849011	+	0.655331i
$239$	24.8394			1.60673			0.803365	−	0.595487i	$-0.203041\pi$
$239$	24.8394			1.60673			0.803365	+	0.595487i	$0.203041\pi$
$240$	0.403128	−	0.282406i	0.0260218	−	0.0182292i
$241$	−7.62307	+	4.40118i	−0.491045	+	0.283505i	−0.725008	−	0.688741i	$-0.758164\pi$
$241$	−7.62307	+	4.40118i	−0.491045	+	0.283505i	0.233963	+	0.972246i	$0.424831\pi$
$242$	10.1686	+	4.19528i	0.653660	+	0.269683i
$243$	14.1207	−	6.60352i	0.905842	−	0.423616i
$244$			3.90094i			0.249732i
$245$	0.525818	−	1.91847i	0.0335933	−	0.122566i
$246$	0.239041	−	0.512920i	0.0152407	−	0.0327026i
$247$	16.3785	−	28.3684i	1.04214	−	1.80504i
$248$	−3.64386	−	6.31135i	−0.231385	−	0.400771i
$249$	2.78199	−	0.244010i	0.176301	−	0.0154635i
$250$	−2.44115	−	1.40940i	−0.154392	−	0.0891381i
$251$			14.0216i			0.885034i	0.896760	+	0.442517i	$0.145914\pi$
$251$			14.0216i			0.885034i	−0.896760	+	0.442517i	$0.854086\pi$
$252$	0.327055	+	7.93051i	0.0206025	+	0.499575i
$253$	5.64097	−	1.91926i	0.354645	−	0.120663i
$254$	4.81171	+	2.77804i	0.301914	+	0.174310i
$255$	−0.268952	−	3.06635i	−0.0168424	−	0.192023i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.60623	+	4.39146i	0.474464	+	0.273932i	0.718106	−	0.695933i	$-0.245009\pi$
$257$	7.60623	+	4.39146i	0.474464	+	0.273932i	−0.243643	+	0.969865i	$0.578342\pi$
$258$	3.60990	+	1.68236i	0.224743	+	0.104739i
$259$	27.2724	−	11.2054i	1.69462	−	0.696271i
$260$	1.71272			0.106219
$261$	1.28344	−	0.226888i	0.0794428	−	0.0140440i
$262$	9.44368	+	16.3569i	0.583433	+	1.01054i
$263$	3.93874	+	6.82210i	0.242873	+	0.420669i	0.961532	−	0.274695i	$-0.0885767\pi$
$263$	3.93874	+	6.82210i	0.242873	+	0.420669i	−0.718658	+	0.695363i	$0.755243\pi$
$264$	3.39255	−	4.63580i	0.208797	−	0.285314i
$265$	−0.546139			−0.0335490
$266$	14.2513	+	1.91766i	0.873804	+	0.117579i
$267$	−26.8872	−	12.5305i	−1.64547	−	0.766854i
$268$	4.34158	−	7.51984i	0.265204	−	0.459347i
$269$	5.23920	−	3.02485i	0.319440	−	0.184429i	−0.331703	−	0.943384i	$-0.607623\pi$
$269$	5.23920	−	3.02485i	0.319440	−	0.184429i	0.651143	+	0.758955i	$0.274290\pi$
$270$	1.04343	−	1.04481i	0.0635013	−	0.0635853i
$271$	−0.886543	−	0.511846i	−0.0538536	−	0.0310924i	0.472831	−	0.881153i	$-0.343232\pi$
$271$	−0.886543	−	0.511846i	−0.0538536	−	0.0310924i	−0.526685	+	0.850060i	$0.676565\pi$
$272$	−6.25376			−0.379190
$273$	−14.9012	+	23.2546i	−0.901861	+	1.40744i
$274$		−	16.9035i		−	1.02118i
$275$	−16.0040	−	3.17175i	−0.965079	−	0.191264i
$276$	−0.271889	−	3.09984i	−0.0163658	−	0.186588i
$277$	0.717044	−	0.413986i	0.0430830	−	0.0248740i	−0.478304	−	0.878194i	$-0.658748\pi$
$277$	0.717044	−	0.413986i	0.0430830	−	0.0248740i	0.521387	+	0.853320i	$0.325415\pi$
$278$	10.5054	+	6.06530i	0.630072	+	0.363772i
$279$	−14.0607	−	16.7420i	−0.841794	−	1.00231i
$280$	0.285737	+	0.695442i	0.0170760	+	0.0415606i
$281$	−21.7279			−1.29618			−0.648089	−	0.761564i	$-0.724432\pi$
$281$	−21.7279			−1.29618			−0.648089	+	0.761564i	$0.724432\pi$
$282$	−5.77894	+	4.04835i	−0.344131	+	0.241076i
$283$	12.2598	−	7.07821i	0.728770	−	0.420756i	−0.0892018	−	0.996014i	$-0.528432\pi$
$283$	12.2598	−	7.07821i	0.728770	−	0.420756i	0.817972	+	0.575258i	$0.195098\pi$
$284$	−3.36396	+	1.94218i	−0.199614	+	0.115247i
$285$	−1.53488	−	2.19101i	−0.0909187	−	0.129784i
$286$	18.9240	−	6.43862i	1.11900	−	0.380724i
$287$	0.684273	+	0.528174i	0.0403914	+	0.0311771i
$288$	−1.92937	−	2.29728i	−0.113690	−	0.135369i
$289$	−11.0547	+	19.1474i	−0.650279	+	1.12632i
$290$	0.106918	−	0.0617292i	0.00627845	−	0.00362486i
$291$	12.0557	−	1.05741i	0.706719	−	0.0619867i
$292$	−3.80459	−	2.19658i	−0.222647	−	0.128545i
$293$	−5.75882			−0.336434			−0.168217	−	0.985750i	$-0.553801\pi$
$293$	−5.75882			−0.336434			−0.168217	+	0.985750i	$0.553801\pi$
$294$	−11.9284	−	2.17094i	−0.695679	−	0.126612i
$295$	2.75078			0.160157
$296$	−5.57207	+	9.65112i	−0.323870	+	0.560960i
$297$	7.60122	−	15.4668i	0.441068	−	0.897474i
$298$	−5.93990	−	10.2882i	−0.344089	−	0.595980i
$299$	5.41396	−	9.37726i	0.313098	−	0.542301i
$300$	−3.59917	+	7.72288i	−0.207798	+	0.445881i
$301$	−3.71726	+	4.81587i	−0.214259	+	0.277582i
$302$			1.73061i			0.0995854i
$303$	10.9414	+	15.6186i	0.628564	+	0.897262i
$304$	−4.70688	+	2.71752i	−0.269958	+	0.155860i
$305$	0.554273	+	0.960029i	0.0317376	+	0.0549711i
$306$	−18.4748	+	3.26600i	−1.05613	+	0.186705i
$307$		−	10.5810i		−	0.603888i	−0.953326	−	0.301944i	$-0.902364\pi$
$307$		−	10.5810i		−	0.603888i	0.953326	−	0.301944i	$-0.0976355\pi$
$308$	5.77149	+	6.60983i	0.328861	+	0.376630i
$309$	−5.67163	+	12.1699i	−0.322648	+	0.692319i
$310$	−1.79352	−	1.03549i	−0.101865	−	0.0588119i
$311$	−5.90443	+	3.40892i	−0.334809	+	0.193302i	−0.657974	−	0.753040i	$-0.728586\pi$
$311$	−5.90443	+	3.40892i	−0.334809	+	0.193302i	0.323165	+	0.946343i	$0.395253\pi$
$312$	−0.912118	−	10.3992i	−0.0516385	−	0.588737i
$313$	13.6258	−	23.6005i	0.770174	−	1.33398i	−0.167293	−	0.985907i	$-0.553503\pi$
$313$	13.6258	−	23.6005i	0.770174	−	1.33398i	0.937467	−	0.348074i	$-0.113164\pi$
$314$	11.1409			0.628719
$315$	1.20731	+	1.90525i	0.0680244	+	0.107348i
$316$		−	5.34926i		−	0.300920i
$317$	−11.6116	−	6.70397i	−0.652173	−	0.376533i	0.137115	−	0.990555i	$-0.456217\pi$
$317$	−11.6116	−	6.70397i	−0.652173	−	0.376533i	−0.789288	+	0.614023i	$0.789550\pi$
$318$	0.290849	+	3.31600i	0.0163100	+	0.185952i
$319$	0.949289	−	1.08399i	0.0531500	−	0.0606916i
$320$	−0.246102	−	0.142087i	−0.0137575	−	0.00794291i
$321$	−10.7181	+	22.9983i	−0.598226	+	1.28364i
$322$	4.71081	+	0.633886i	0.262523	+	0.0353251i
$323$			33.9894i			1.89122i
$324$	−6.89949	−	5.77901i	−0.383305	−	0.321056i
$325$	−25.6762	+	14.8242i	−1.42426	+	0.822298i
$326$	0.415887	+	0.720337i	0.0230338	+	0.0398958i
$327$	−22.5805	+	15.8185i	−1.24871	+	0.874763i
$328$	−0.326715			−0.0180398
$329$	−4.09611	−	9.96934i	−0.225826	−	0.549627i
$330$	0.176227	−	1.62292i	0.00970096	−	0.0893386i
$331$	5.97956	−	10.3569i	0.328666	−	0.569267i	−0.653581	−	0.756857i	$-0.726734\pi$
$331$	5.97956	−	10.3569i	0.328666	−	0.569267i	0.982248	+	0.187590i	$0.0600675\pi$
$332$	−0.806175	−	1.39634i	−0.0442446	−	0.0766339i
$333$	−11.4207	+	31.4213i	−0.625852	+	1.72187i
$334$	−9.56974	+	16.5753i	−0.523633	+	0.906959i
$335$		−	2.46753i		−	0.134816i
$336$	4.07036	−	2.10527i	0.222056	−	0.114852i
$337$			7.11663i			0.387668i	0.981034	+	0.193834i	$0.0620923\pi$
$337$			7.11663i			0.387668i	−0.981034	+	0.193834i	$0.937908\pi$
$338$	11.6625	−	20.2000i	0.634355	−	1.09874i
$339$	1.85669	+	21.1683i	0.100841	+	1.14971i
$340$	−1.53906	+	0.888578i	−0.0834674	+	0.0481899i
$341$	−23.7095	−	4.69885i	−1.28394	−	0.254457i
$342$	−12.4858	+	10.4862i	−0.675156	+	0.567030i
$343$	7.23379	−	17.0491i	0.390588	−	0.920566i
$344$		−	2.29940i		−	0.123975i
$345$	−0.507360	−	0.724245i	−0.0273153	−	0.0389920i
$346$	−8.80633	−	15.2530i	−0.473431	−	0.820007i
$347$	−0.501160	−	0.868034i	−0.0269037	−	0.0465985i	0.852260	−	0.523118i	$-0.175231\pi$
$347$	−0.501160	−	0.868034i	−0.0269037	−	0.0465985i	−0.879164	+	0.476520i	$0.841898\pi$
$348$	−0.431742	−	0.616303i	−0.0231438	−	0.0330373i
$349$		−	18.5808i		−	0.994607i	−0.867577	−	0.497304i	$-0.834323\pi$
$349$		−	18.5808i		−	0.994607i	0.867577	−	0.497304i	$-0.165677\pi$
$350$	−10.3029	−	7.95256i	−0.550713	−	0.425082i
$351$	−8.12550	−	30.2448i	−0.433707	−	1.61435i
$352$	−3.25335	−	0.644763i	−0.173404	−	0.0343660i
$353$	3.11174	−	1.79656i	0.165621	−	0.0956215i	−0.414898	−	0.909868i	$-0.636183\pi$
$353$	3.11174	−	1.79656i	0.165621	−	0.0956215i	0.580519	+	0.814246i	$0.302850\pi$
$354$	−1.46494	−	16.7020i	−0.0778607	−	0.887700i
$355$	−0.551918	+	0.955950i	−0.0292928	+	0.0507366i
$356$			17.1264i			0.907695i
$357$	1.32555	−	28.6276i	0.0701553	−	1.51514i
$358$			9.05366i			0.478501i
$359$	5.21329	−	9.02968i	0.275147	−	0.476569i	−0.695025	−	0.718985i	$-0.744607\pi$
$359$	5.21329	−	9.02968i	0.275147	−	0.476569i	0.970172	+	0.242417i	$0.0779402\pi$
$360$	−0.801238	−	0.291227i	−0.0422289	−	0.0153490i
$361$	5.26980	+	9.12756i	0.277358	+	0.480398i
$362$	−10.5974	+	18.3553i	−0.556989	+	0.964733i
$363$	−4.15387	−	18.5942i	−0.218022	−	0.975944i
$364$	15.8036	+	2.12653i	0.828332	+	0.111460i
$365$	−1.24842			−0.0653455
$366$	5.53385	−	3.87666i	0.289259	−	0.202636i
$367$	0.802276	+	1.38958i	0.0418785	+	0.0725356i	0.886205	−	0.463294i	$-0.153332\pi$
$367$	0.802276	+	1.38958i	0.0418785	+	0.0725356i	−0.844326	+	0.535829i	$0.819999\pi$
$368$	−1.55587	+	0.898282i	−0.0811053	+	0.0468262i
$369$	−0.965179	+	0.170625i	−0.0502452	+	0.00888241i
$370$			3.16688i			0.164638i
$371$	−5.03931	−	0.678090i	−0.261628	−	0.0352047i
$372$	−5.33206	+	11.4412i	−0.276455	+	0.593200i
$373$	−0.443041	−	0.255790i	−0.0229398	−	0.0132443i	0.488486	−	0.872572i	$-0.337549\pi$
$373$	−0.443041	−	0.255790i	−0.0229398	−	0.0132443i	−0.511426	+	0.859327i	$0.670883\pi$
$374$	−13.6648	+	15.6038i	−0.706591	+	0.806851i
$375$	0.426591	+	4.86362i	0.0220291	+	0.251156i
$376$	3.52794	+	2.03685i	0.181939	+	0.105043i
$377$		−	2.61842i		−	0.134855i
$378$	10.9252	−	8.34511i	0.561930	−	0.429226i
$379$	5.08365			0.261130			0.130565	−	0.991440i	$-0.458321\pi$
$379$	5.08365			0.261130			0.130565	+	0.991440i	$0.458321\pi$
$380$	−0.772248	+	1.33757i	−0.0396155	+	0.0686161i
$381$	−0.840848	−	9.58662i	−0.0430779	−	0.491137i
$382$	−10.7800	+	6.22381i	−0.551550	+	0.318438i
$383$	4.59160	+	2.65096i	0.234620	+	0.135458i	0.612702	−	0.790314i	$-0.290083\pi$
$383$	4.59160	+	2.65096i	0.234620	+	0.135458i	−0.378082	+	0.925772i	$0.623416\pi$
$384$	−0.731651	+	1.56993i	−0.0373369	+	0.0801153i
$385$	2.35955	+	0.806638i	0.120254	+	0.0411101i
$386$		−	14.9582i		−	0.761352i
$387$	−1.20085	−	6.79287i	−0.0610427	−	0.345301i
$388$	−3.49355	−	6.05100i	−0.177358	−	0.307193i
$389$	−25.9986	+	15.0103i	−1.31818	+	0.761053i	−0.983436	−	0.181255i	$-0.941984\pi$
$389$	−25.9986	+	15.0103i	−1.31818	+	0.761053i	−0.334747	+	0.942308i	$0.608651\pi$
$390$	−1.70206	−	2.42966i	−0.0861873	−	0.123031i
$391$			11.2353i			0.568192i
$392$	1.77307	+	6.77172i	0.0895535	+	0.342024i
$393$	13.8190	−	29.6519i	0.697074	−	1.49574i
$394$	4.12317	−	7.14153i	0.207722	−	0.359785i
$395$	−0.760061	−	1.31647i	−0.0382428	−	0.0662385i
$396$	−9.94775	−	0.205708i	−0.499893	−	0.0103372i
$397$	−5.20199	+	9.01011i	−0.261080	+	0.452204i	−0.966529	−	0.256556i	$-0.917412\pi$
$397$	−5.20199	+	9.01011i	−0.261080	+	0.452204i	0.705449	+	0.708761i	$0.250745\pi$
$398$	−14.2687			−0.715224
$399$	−11.4422	−	22.1225i	−0.572828	−	1.10751i
$400$	4.91924			0.245962
$401$	12.6464	+	7.30138i	0.631529	+	0.364614i	0.781344	−	0.624100i	$-0.214534\pi$
$401$	12.6464	+	7.30138i	0.631529	+	0.364614i	−0.149815	+	0.988714i	$0.547868\pi$
$402$	−14.9822	+	1.31409i	−0.747242	+	0.0655411i
$403$	−38.0386	+	21.9616i	−1.89484	+	1.09399i
$404$	5.50494	−	9.53484i	0.273881	−	0.474376i
$405$	−2.51910	−	0.441898i	−0.125175	−	0.0219581i
$406$	1.06319	−	0.436835i	0.0527654	−	0.0216797i
$407$	11.9052	+	34.9911i	0.590120	+	1.73445i
$408$	6.21483	+	8.87154i	0.307680	+	0.439207i
$409$	21.6325	−	12.4895i	1.06966	−	0.617566i	0.141568	−	0.989928i	$-0.454785\pi$
$409$	21.6325	−	12.4895i	1.06966	−	0.617566i	0.928087	+	0.372362i	$0.121452\pi$
$410$	−0.0804052	+	0.0464220i	−0.00397093	+	0.00229262i
$411$	−23.9792	+	16.7983i	−1.18280	+	0.828597i
$412$	7.75183			0.381905
$413$	25.3819	+	3.41539i	1.24896	+	0.168060i
$414$	−4.12722	+	3.46625i	−0.202842	+	0.170357i
$415$	−0.396803	−	0.229094i	−0.0194783	−	0.0112458i
$416$	−5.21955	+	3.01351i	−0.255910	+	0.147749i
$417$	−1.83582	−	20.9305i	−0.0899006	−	1.02497i
$418$	−3.50431	+	17.6821i	−0.171401	+	0.864858i
$419$		−	35.4041i		−	1.72960i	−0.502113	−	0.864802i	$-0.667444\pi$
$419$		−	35.4041i		−	1.72960i	0.502113	−	0.864802i	$-0.332556\pi$
$420$	0.702592	−	1.09646i	0.0342830	−	0.0535017i
$421$	0.877958			0.0427891			0.0213945	−	0.999771i	$-0.493189\pi$
$421$	0.877958			0.0427891			0.0213945	+	0.999771i	$0.493189\pi$
$422$	−14.4945	−	8.36841i	−0.705581	−	0.407368i
$423$	11.4859	+	4.17481i	0.558466	+	0.202986i
$424$	1.66437	−	0.960923i	0.0808288	−	0.0466665i
$425$	15.3819	−	26.6422i	0.746131	−	1.29234i
$426$	6.09819	+	2.84200i	0.295458	+	0.137695i
$427$	3.92238	+	9.54652i	0.189817	+	0.461989i
$428$	14.6492			0.708096
$429$	−27.9400	−	20.4470i	−1.34896	−	0.987188i
$430$	−0.326715	−	0.565887i	−0.0157556	−	0.0272895i
$431$	−9.95132	−	17.2362i	−0.479338	−	0.830238i	0.520381	−	0.853934i	$-0.325790\pi$
$431$	−9.95132	−	17.2362i	−0.479338	−	0.830238i	−0.999719	+	0.0236962i	$0.992457\pi$
$432$	−1.34155	+	5.01999i	−0.0645452	+	0.241524i
$433$	13.8697			0.666538			0.333269	−	0.942832i	$-0.391848\pi$
$433$	13.8697			0.666538			0.333269	+	0.942832i	$0.391848\pi$
$434$	−15.2634	−	11.7815i	−0.732668	−	0.565529i
$435$	−0.193821	−	0.0903284i	−0.00929302	−	0.00433092i
$436$	13.7850	+	7.95877i	0.660182	+	0.381156i
$437$	4.88219	+	8.45621i	0.233547	+	0.404515i
$438$	0.664854	+	7.58009i	0.0317679	+	0.362191i
$439$	−9.43561	−	5.44765i	−0.450337	−	0.260002i	0.257635	−	0.966242i	$-0.417057\pi$
$439$	−9.43561	−	5.44765i	−0.450337	−	0.260002i	−0.707973	+	0.706240i	$0.750390\pi$
$440$	−0.892269	+	0.303581i	−0.0425372	+	0.0144727i
$441$	8.77449	+	19.0790i	0.417833	+	0.908524i
$442$			37.6915i			1.79280i
$443$	12.2275	+	7.05956i	0.580947	+	0.335410i	0.761510	−	0.648154i	$-0.224459\pi$
$443$	12.2275	+	7.05956i	0.580947	+	0.335410i	−0.180563	+	0.983563i	$0.557792\pi$
$444$	19.2284	−	1.68653i	0.912540	−	0.0800394i
$445$	2.43343	+	4.21483i	0.115356	+	0.199802i
$446$	−0.543854	+	0.941983i	−0.0257522	+	0.0446042i
$447$	−8.69187	+	18.6505i	−0.411111	+	0.882138i
$448$	−2.09441	−	1.61662i	−0.0989514	−	0.0763782i
$449$		−	35.3836i		−	1.66985i	−0.550361	−	0.834927i	$-0.685510\pi$
$449$		−	35.3836i		−	1.66985i	0.550361	−	0.834927i	$-0.314490\pi$
$450$	14.5324	−	2.56905i	0.685064	−	0.121106i
$451$	−0.713890	+	0.815187i	−0.0336158	+	0.0383856i
$452$	10.6248	−	6.13423i	0.499749	−	0.288530i
$453$	2.45503	−	1.71984i	0.115348	−	0.0808051i
$454$	−8.96692			−0.420838
$455$	4.19144	−	1.72214i	0.196498	−	0.0807351i
$456$	8.53264	+	3.97655i	0.399577	+	0.186219i
$457$	2.96219	+	1.71022i	0.138565	+	0.0800007i	0.567680	−	0.823249i	$-0.307841\pi$
$457$	2.96219	+	1.71022i	0.138565	+	0.0800007i	−0.429115	+	0.903250i	$0.641174\pi$
$458$	6.22490	+	10.7818i	0.290871	+	0.503803i
$459$	22.9929	+	22.9626i	1.07322	+	1.07180i
$460$	−0.255269	+	0.442138i	−0.0119020	+	0.0206148i
$461$	−13.0512			−0.607855			−0.303927	−	0.952695i	$-0.598298\pi$
$461$	−13.0512			−0.607855			−0.303927	+	0.952695i	$0.598298\pi$
$462$	3.64109	−	14.7561i	0.169399	−	0.686516i
$463$	−18.0986			−0.841115			−0.420558	−	0.907266i	$-0.638166\pi$
$463$	−18.0986			−0.841115			−0.420558	+	0.907266i	$0.638166\pi$
$464$	−0.217223	+	0.376241i	−0.0100843	+	0.0174666i
$465$	0.313419	+	3.57333i	0.0145344	+	0.165709i
$466$	−9.19303	−	15.9228i	−0.425859	−	0.737609i
$467$	−5.31873	−	3.07077i	−0.246122	−	0.142098i	0.371865	−	0.928287i	$-0.378718\pi$
$467$	−5.31873	−	3.07077i	−0.246122	−	0.142098i	−0.617987	+	0.786188i	$0.712052\pi$
$468$	−13.8458	+	11.6284i	−0.640021	+	0.537522i
$469$	3.06370	−	22.7683i	0.141469	−	1.05134i
$470$	1.15764			0.0533981
$471$	−11.0716	−	15.8044i	−0.510151	−	0.728230i
$472$	−8.38305	+	4.83996i	−0.385861	+	0.222777i
$473$	−5.73723	−	5.02431i	−0.263798	−	0.231018i
$474$	−7.58843	+	5.31597i	−0.348548	+	0.244171i
$475$		−	26.7363i		−	1.22674i
$476$	−15.3044	+	6.28814i	−0.701478	+	0.288216i
$477$	4.41502	−	3.70796i	0.202150	−	0.169776i
$478$	−12.4197	+	21.5116i	−0.568065	+	0.983917i
$479$	3.63249	+	6.29166i	0.165973	+	0.287473i	0.937000	−	0.349329i	$-0.113590\pi$
$479$	3.63249	+	6.29166i	0.165973	+	0.287473i	−0.771028	+	0.636802i	$0.780257\pi$
$480$	0.0430064	+	0.490322i	0.00196297	+	0.0223800i
$481$	58.1674	+	33.5830i	2.65221	+	1.53125i
$482$		−	8.80236i		−	0.400937i
$483$	−3.78226	−	7.31266i	−0.172099	−	0.332738i
$484$	−8.71750	+	6.70859i	−0.396250	+	0.304936i
$485$	−1.71954	−	0.992777i	−0.0780803	−	0.0450797i
$486$	−1.34152	+	15.5306i	−0.0608527	+	0.704483i
$487$	20.5335	+	35.5650i	0.930461	+	1.61161i	0.782535	+	0.622607i	$0.213926\pi$
$487$	20.5335	+	35.5650i	0.930461	+	1.61161i	0.147926	+	0.988998i	$0.452740\pi$
$488$	−3.37831	−	1.95047i	−0.152929	−	0.0882936i
$489$	0.608567	−	1.30583i	0.0275204	−	0.0590516i
$490$	1.39853	+	1.41460i	0.0631792	+	0.0639053i
$491$	−35.9140			−1.62078			−0.810389	−	0.585892i	$-0.800744\pi$
$491$	−35.9140			−1.62078			−0.810389	+	0.585892i	$0.800744\pi$
$492$	0.324681	+	0.463476i	0.0146378	+	0.0208951i
$493$	1.35846	+	2.35292i	0.0611820	+	0.105970i
$494$	16.3785	+	28.3684i	0.736905	+	1.27636i
$495$	−2.47739	+	1.36282i	−0.111350	+	0.0612543i
$496$	7.28772			0.327228
$497$	−6.27955	+	8.13543i	−0.281676	+	0.364924i
$498$	−1.17968	+	2.53128i	−0.0528626	+	0.113429i
$499$	6.45040	−	11.1724i	0.288760	−	0.500146i	−0.684754	−	0.728774i	$-0.740091\pi$
$499$	6.45040	−	11.1724i	0.288760	−	0.500146i	0.973514	+	0.228628i	$0.0734239\pi$
$500$	2.44115	−	1.40940i	0.109171	−	0.0630301i
$501$	33.0238	−	2.89653i	1.47539	−	0.129408i
$502$	−12.1430	−	7.01079i	−0.541971	−	0.312907i
$503$	−2.65238			−0.118264			−0.0591319	−	0.998250i	$-0.518833\pi$
$503$	−2.65238			−0.118264			−0.0591319	+	0.998250i	$0.518833\pi$
$504$	−7.03155	−	3.68202i	−0.313210	−	0.164010i
$505$		−	3.12872i		−	0.139226i
$506$	−1.15836	+	5.84485i	−0.0514953	+	0.259835i
$507$	−40.2455	+	3.52995i	−1.78736	+	0.156771i
$508$	−4.81171	+	2.77804i	−0.213485	+	0.123256i
$509$	−10.6064	−	6.12359i	−0.470119	−	0.271423i	0.246171	−	0.969226i	$-0.420828\pi$
$509$	−10.6064	−	6.12359i	−0.470119	−	0.271423i	−0.716289	+	0.697803i	$0.754161\pi$
$510$	2.79002	+	1.30026i	0.123544	+	0.0575764i
$511$	−11.5194	−	1.55005i	−0.509589	−	0.0685703i
$512$	1.00000			0.0441942
$513$	27.2838	+	7.29135i	1.20461	+	0.321921i
$514$	−7.60623	+	4.39146i	−0.335497	+	0.193699i
$515$	1.90774	−	1.10144i	0.0840652	−	0.0485351i
$516$	−3.26191	+	2.28509i	−0.143598	+	0.100595i
$517$	12.7909	−	4.35192i	0.562543	−	0.191397i
$518$	−3.93202	+	29.2213i	−0.172763	+	1.28391i
$519$	−12.8863	+	27.6507i	−0.565647	+	1.21373i
$520$	−0.856362	+	1.48326i	−0.0375539	+	0.0650453i
$521$	−1.51792	+	0.876371i	−0.0665012	+	0.0383945i	−0.532882	−	0.846190i	$-0.678891\pi$
$521$	−1.51792	+	0.876371i	−0.0665012	+	0.0383945i	0.466381	+	0.884584i	$0.345558\pi$
$522$	−0.445229	+	1.22493i	−0.0194871	+	0.0536139i
$523$	−10.9425	−	6.31768i	−0.478484	−	0.276253i	0.241301	−	0.970450i	$-0.422426\pi$
$523$	−10.9425	−	6.31768i	−0.478484	−	0.276253i	−0.719784	+	0.694198i	$0.755759\pi$
$524$	−18.8874			−0.825099
$525$	−1.04268	+	22.5187i	−0.0455064	+	0.982796i
$526$	−7.87749			−0.343475
$527$	22.7878	−	39.4696i	0.992653	−	1.71932i
$528$	2.31844	+	5.25593i	0.100897	+	0.228735i
$529$	−9.88618	−	17.1234i	−0.429834	−	0.744494i
$530$	0.273069	−	0.472970i	0.0118614	−	0.0205445i
$531$	−22.2375	+	18.6762i	−0.965026	+	0.810477i
$532$	−8.78639	+	11.3832i	−0.380938	+	0.493523i
$533$			1.96912i			0.0852919i
$534$	24.2953	−	17.0198i	1.05136	−	0.736517i
$535$	3.60520	−	2.08146i	0.155866	−	0.0899895i
$536$	4.34158	+	7.51984i	0.187528	+	0.324808i
$537$	12.8435	−	8.99731i	0.554236	−	0.388262i
$538$			6.04971i			0.260822i
$539$	20.7704	+	10.3726i	0.894644	+	0.446780i
$540$	0.383118	+	1.42605i	0.0164868	+	0.0613672i
$541$	−28.9602	−	16.7202i	−1.24510	−	0.718856i	−0.274969	−	0.961453i	$-0.588667\pi$
$541$	−28.9602	−	16.7202i	−1.24510	−	0.718856i	−0.970127	+	0.242597i	$0.922001\pi$
$542$	0.886543	−	0.511846i	0.0380803	−	0.0219857i
$543$	36.5702	−	3.20759i	1.56938	−	0.137651i
$544$	3.12688	−	5.41591i	0.134064	−	0.232205i
$545$	4.52336			0.193759
$546$	−12.6885	−	24.5321i	−0.543018	−	1.04988i
$547$			18.9288i			0.809336i	0.914464	+	0.404668i	$0.132613\pi$
$547$			18.9288i			0.809336i	−0.914464	+	0.404668i	$0.867387\pi$
$548$	14.6388	+	8.45173i	0.625340	+	0.361040i
$549$	−10.9988	−	3.99775i	−0.469418	−	0.170620i
$550$	10.7488	−	12.2740i	0.458331	−	0.523366i
$551$	2.04489	+	1.18061i	0.0871150	+	0.0502959i
$552$	2.82048	+	1.31446i	0.120048	+	0.0559470i
$553$	−5.37867	−	13.0909i	−0.228724	−	0.556683i
$554$			0.827971i			0.0351771i
$555$	4.49252	−	3.14717i	0.190697	−	0.133590i
$556$	−10.5054	+	6.06530i	−0.445528	+	0.257226i
$557$	−8.23820	−	14.2690i	−0.349064	−	0.604596i	0.637020	−	0.770848i	$-0.280167\pi$
$557$	−8.23820	−	14.2690i	−0.349064	−	0.604596i	−0.986083	+	0.166251i	$0.946834\pi$
$558$	21.5293	−	3.80598i	0.911409	−	0.161120i
$559$	−13.8585			−0.586153
$560$	−0.745139	−	0.100266i	−0.0314879	−	0.00423701i
$561$	35.7152	+	3.87818i	1.50790	+	0.163737i
$562$	10.8640	−	18.8169i	0.458268	−	0.793744i
$563$	−14.0143	−	24.2734i	−0.590631	−	1.02300i	−0.994148	−	0.108031i	$-0.965545\pi$
$563$	−14.0143	−	24.2734i	−0.590631	−	1.02300i	0.403516	−	0.914972i	$-0.367788\pi$
$564$	−0.616508	−	7.02889i	−0.0259597	−	0.295970i
$565$	1.74319	−	3.01930i	0.0733366	−	0.127023i
$566$			14.1564i			0.595038i
$567$	−22.6955	−	7.20520i	−0.953121	−	0.302590i
$568$		−	3.88436i		−	0.162984i
$569$	13.8711	−	24.0254i	0.581506	−	1.00720i	−0.413795	−	0.910370i	$-0.635797\pi$
$569$	13.8711	−	24.0254i	0.581506	−	1.00720i	0.995301	−	0.0968278i	$-0.0308696\pi$
$570$	2.66492	−	0.233741i	0.111621	−	0.00979035i
$571$	1.71070	−	0.987670i	0.0715904	−	0.0413327i	−0.463778	−	0.885952i	$-0.653506\pi$
$571$	1.71070	−	0.987670i	0.0715904	−	0.0413327i	0.535368	+	0.844619i	$0.320173\pi$
$572$	−3.88600	+	19.6080i	−0.162482	+	0.819851i
$573$	19.5419	+	9.10731i	0.816375	+	0.380463i
$574$	−0.799549	+	0.328511i	−0.0333725	+	0.0137118i
$575$		−	8.83774i		−	0.368559i
$576$	2.95419	−	0.522246i	0.123091	−	0.0217602i
$577$	9.70603	+	16.8113i	0.404067	+	0.699865i	0.994212	−	0.107432i	$-0.0342628\pi$
$577$	9.70603	+	16.8113i	0.404067	+	0.699865i	−0.590145	+	0.807297i	$0.700929\pi$
$578$	−11.0547	−	19.1474i	−0.459817	−	0.796426i
$579$	−21.2196	+	14.8651i	−0.881857	+	0.617773i
$580$			0.123458i			0.00512633i
$581$	−3.37691	−	2.60656i	−0.140098	−	0.108138i
$582$	−5.11211	+	10.9693i	−0.211904	+	0.454691i
$583$	1.23914	−	6.25243i	0.0513197	−	0.258949i
$584$	3.80459	−	2.19658i	0.157435	−	0.0908953i
$585$	−1.75523	+	4.82907i	−0.0725699	+	0.199658i
$586$	2.87941	−	4.98728i	0.118947	−	0.206023i
$587$		−	13.5713i		−	0.560148i	−0.959978	−	0.280074i	$-0.909641\pi$
$587$		−	13.5713i		−	0.560148i	0.959978	−	0.280074i	$-0.0903590\pi$
$588$	7.84429	−	9.24484i	0.323493	−	0.381251i
$589$		−	39.6090i		−	1.63206i
$590$	−1.37539	+	2.38225i	−0.0566239	+	0.0980756i
$591$	−14.2284	+	1.24799i	−0.585280	+	0.0513352i
$592$	−5.57207	−	9.65112i	−0.229011	−	0.396658i
$593$	−18.6257	+	32.2607i	−0.764867	+	1.32479i	0.175450	+	0.984488i	$0.443862\pi$
$593$	−18.6257	+	32.2607i	−0.764867	+	1.32479i	−0.940317	+	0.340300i	$0.889471\pi$
$594$	9.59402	+	14.3162i	0.393647	+	0.587403i
$595$	−2.87299	+	3.72209i	−0.117781	+	0.152591i
$596$	11.8798			0.486616
$597$	14.1799	+	20.2415i	0.580343	+	0.828428i
$598$	5.41396	+	9.37726i	0.221393	+	0.383465i
$599$	−24.6430	+	14.2276i	−1.00688	+	0.581325i	−0.910278	−	0.413998i	$-0.864132\pi$
$599$	−24.6430	+	14.2276i	−1.00688	+	0.581325i	−0.0966066	+	0.995323i	$0.530799\pi$
$600$	−4.88863	−	6.97841i	−0.199577	−	0.284892i
$601$		−	4.98600i		−	0.203383i	−0.994816	−	0.101692i	$-0.967575\pi$
$601$		−	4.98600i		−	0.203383i	0.994816	−	0.101692i	$-0.0324255\pi$
$602$	−2.31204	−	5.62717i	−0.0942317	−	0.229347i
$603$	16.7531	+	19.9477i	0.682238	+	0.812333i
$604$	−1.49875	−	0.865305i	−0.0609834	−	0.0352088i
$605$	−1.19219	+	2.88964i	−0.0484694	+	0.117481i
$606$	−18.9967	+	1.66622i	−0.771690	+	0.0676854i
$607$	−5.30947	−	3.06542i	−0.215505	−	0.124422i	0.388362	−	0.921507i	$-0.373041\pi$
$607$	−5.30947	−	3.06542i	−0.215505	−	0.124422i	−0.603867	+	0.797085i	$0.706374\pi$
$608$		−	5.43503i		−	0.220420i
$609$	−1.67627	−	1.07412i	−0.0679258	−	0.0435257i
$610$	−1.10855			−0.0448837
$611$	12.2762	−	21.2629i	0.496640	−	0.860206i
$612$	6.40897	−	17.6327i	0.259067	−	0.712758i
$613$	18.9061	−	10.9154i	0.763609	−	0.440870i	−0.0669808	−	0.997754i	$-0.521337\pi$
$613$	18.9061	−	10.9154i	0.763609	−	0.440870i	0.830590	+	0.556884i	$0.188003\pi$
$614$	9.16339	+	5.29048i	0.369804	+	0.213507i
$615$	0.145759	+	0.0679293i	0.00587756	+	0.00273917i
$616$	−8.61003	+	1.69335i	−0.346908	+	0.0682268i
$617$			8.66345i			0.348777i	0.984677	+	0.174389i	$0.0557949\pi$
$617$			8.66345i			0.348777i	−0.984677	+	0.174389i	$0.944205\pi$
$618$	−7.70359	−	10.9967i	−0.309884	−	0.442352i
$619$	−15.3069	−	26.5123i	−0.615236	−	1.06562i	−0.990343	−	0.138639i	$-0.955727\pi$
$619$	−15.3069	−	26.5123i	−0.615236	−	1.06562i	0.375107	−	0.926982i	$-0.377606\pi$
$620$	1.79352	−	1.03549i	0.0720296	−	0.0415863i
$621$	9.01872	+	2.41017i	0.361909	+	0.0967170i
$622$		−	6.81785i		−	0.273371i
$623$	17.2205	+	41.9123i	0.689925	+	1.67918i
$624$	9.46201	+	4.40967i	0.378784	+	0.176528i
$625$	−11.8976	+	20.6072i	−0.475904	+	0.824290i
$626$	13.6258	+	23.6005i	0.544596	+	0.943267i
$627$	28.5662	−	12.6008i	1.14082	−	0.503228i
$628$	−5.57046	+	9.64832i	−0.222286	+	0.385010i
$629$	−69.6928			−2.77883
$630$	−2.25365	+	0.0929406i	−0.0897875	+	0.00370284i
$631$	−12.7107			−0.506006			−0.253003	−	0.967465i	$-0.581418\pi$
$631$	−12.7107			−0.506006			−0.253003	+	0.967465i	$0.581418\pi$
$632$	4.63260	+	2.67463i	0.184275	+	0.106391i
$633$	2.53292	+	28.8781i	0.100674	+	1.14780i
$634$	11.6116	−	6.70397i	0.461156	−	0.266249i
$635$	−0.789448	+	1.36736i	−0.0313283	+	0.0542622i
$636$	−3.01717	−	1.40612i	−0.119638	−	0.0557563i
$637$	40.8133	−	10.6863i	1.61708	−	0.423407i
$638$	0.464116	+	1.36410i	0.0183745	+	0.0540053i
$639$	−2.02859	−	11.4752i	−0.0802499	−	0.453951i
$640$	0.246102	−	0.142087i	0.00972804	−	0.00561649i
$641$	−6.94573	+	4.01012i	−0.274340	+	0.158390i	−0.630858	−	0.775898i	$-0.717297\pi$
$641$	−6.94573	+	4.01012i	−0.274340	+	0.158390i	0.356518	+	0.934288i	$0.383964\pi$
$642$	−14.5580	−	20.7813i	−0.574560	−	0.820172i
$643$	−46.2342			−1.82330			−0.911649	−	0.410969i	$-0.865190\pi$
$643$	−46.2342			−1.82330			−0.911649	+	0.410969i	$0.865190\pi$
$644$	−2.90436	+	3.76273i	−0.114448	+	0.148272i
$645$	−0.478082	+	1.02584i	−0.0188245	+	0.0403924i
$646$	−29.4357	−	16.9947i	−1.15813	−	0.668647i
$647$	28.0821	−	16.2132i	1.10402	−	0.637407i	0.166747	−	0.986000i	$-0.446674\pi$
$647$	28.0821	−	16.2132i	1.10402	−	0.637407i	0.937274	+	0.348593i	$0.113340\pi$
$648$	8.45452	−	3.08563i	0.332125	−	0.121215i
$649$	−6.24125	+	31.4921i	−0.244991	+	1.23617i
$650$		−	29.6484i		−	1.16291i
$651$	−1.54470	+	33.3608i	−0.0605417	+	1.30751i
$652$	−0.831773			−0.0325748
$653$	27.2177	+	15.7141i	1.06511	+	0.614942i	0.926842	−	0.375453i	$-0.122513\pi$
$653$	27.2177	+	15.7141i	1.06511	+	0.614942i	0.138269	+	0.990395i	$0.455846\pi$
$654$	−2.40893	−	27.4646i	−0.0941967	−	1.07395i
$655$	−4.64822	+	2.68365i	−0.181621	+	0.104859i
$656$	0.163357	−	0.282943i	0.00637804	−	0.0110471i
$657$	10.0923	−	8.47606i	0.393740	−	0.330683i
$658$	10.6818	+	1.43734i	0.416418	+	0.0560332i
$659$	20.9664			0.816737			0.408368	−	0.912817i	$-0.366098\pi$
$659$	20.9664			0.816737			0.408368	+	0.912817i	$0.366098\pi$
$660$	1.31737	+	0.964075i	0.0512787	+	0.0375266i
$661$	−0.654442	−	1.13353i	−0.0254548	−	0.0440891i	0.853017	−	0.521883i	$-0.174770\pi$
$661$	−0.654442	−	1.13353i	−0.0254548	−	0.0440891i	−0.878472	+	0.477793i	$0.841437\pi$
$662$	5.97956	+	10.3569i	0.232402	+	0.402533i
$663$	53.4690	−	37.4569i	2.07656	−	1.45471i
$664$	1.61235			0.0625713
$665$	−0.544949	+	4.04985i	−0.0211322	+	0.157047i
$666$	−21.5012	−	25.6013i	−0.833156	−	0.992029i
$667$	0.675942	+	0.390255i	0.0261726	+	0.0151107i
$668$	−9.56974	−	16.5753i	−0.370264	−	0.641317i
$669$	1.87676	−	0.164612i	0.0725597	−	0.00636426i
$670$	2.13695	+	1.23377i	0.0825574	+	0.0476645i
$671$	−12.2484	+	4.16735i	−0.472845	+	0.160879i
$672$	−0.211960	+	4.57767i	−0.00817653	+	0.176587i
$673$			38.4311i			1.48141i	0.671829	+	0.740706i	$0.265509\pi$
$673$			38.4311i			1.48141i	−0.671829	+	0.740706i	$0.734491\pi$
$674$	−6.16319	−	3.55832i	−0.237397	−	0.137061i
$675$	−18.0864	−	18.0625i	−0.696146	−	0.695227i
$676$	11.6625	+	20.2000i	0.448557	+	0.776923i
$677$	−4.01555	+	6.95514i	−0.154330	+	0.267308i	−0.932815	−	0.360356i	$-0.882655\pi$
$677$	−4.01555	+	6.95514i	−0.154330	+	0.267308i	0.778485	+	0.627664i	$0.215989\pi$
$678$	−19.2607	−	8.97623i	−0.739701	−	0.344730i
$679$	−14.6338	−	11.2955i	−0.561594	−	0.433481i
$680$		−	1.77716i		−	0.0681509i
$681$	8.91111	+	12.7204i	0.341475	+	0.487448i
$682$	15.9241	−	18.1836i	0.609764	−	0.696286i
$683$	22.5996	−	13.0479i	0.864751	−	0.499264i	−0.000849280	−	1.00000i	$-0.500270\pi$
$683$	22.5996	−	13.0479i	0.864751	−	0.499264i	0.865600	+	0.500735i	$0.166937\pi$
$684$	−2.83842	−	16.0561i	−0.108530	−	0.613922i
$685$	4.80353			0.183533
$686$	11.1481	+	14.7892i	0.425635	+	0.564654i
$687$	9.10891	−	19.5454i	0.347526	−	0.745702i
$688$	1.99134	+	1.14970i	0.0759190	+	0.0438319i
$689$	−5.79150	−	10.0312i	−0.220638	−	0.382157i
$690$	0.880894	−	0.0772638i	0.0335351	−	0.00294138i
$691$	6.88382	−	11.9231i	0.261873	−	0.453577i	−0.704867	−	0.709340i	$-0.748993\pi$
$691$	6.88382	−	11.9231i	0.261873	−	0.453577i	0.966740	+	0.255762i	$0.0823265\pi$
$692$	17.6127			0.669533
$693$	−24.5513	+	9.49902i	−0.932629	+	0.360838i
$694$	1.00232			0.0380475
$695$	−1.72360	+	2.98537i	−0.0653799	+	0.113241i
$696$	0.749605	−	0.0657483i	0.0284137	−	0.00249218i
$697$	−1.02160	−	1.76946i	−0.0386958	−	0.0670230i
$698$	16.0914	+	9.29040i	0.609070	+	0.351647i
$699$	−13.4522	+	28.8649i	−0.508808	+	1.09177i
$700$	12.0386	−	4.94629i	0.455015	−	0.186952i
$701$	−16.6844			−0.630162			−0.315081	−	0.949065i	$-0.602032\pi$
$701$	−16.6844			−0.630162			−0.315081	+	0.949065i	$0.602032\pi$
$702$	30.2555	+	8.08553i	1.14192	+	0.305169i
$703$	−52.4541	+	30.2844i	−1.97835	+	1.14220i
$704$	2.18506	−	2.49510i	0.0823524	−	0.0940377i
$705$	−1.15044	−	1.64223i	−0.0433280	−	0.0618498i
$706$			3.59313i			0.135229i
$707$	3.88464	−	28.8692i	0.146097	−	1.08574i
$708$	15.1968	+	7.08231i	0.571131	+	0.266170i
$709$	−9.07757	+	15.7228i	−0.340915	+	0.590483i	−0.984603	−	0.174806i	$-0.944070\pi$
$709$	−9.07757	+	15.7228i	−0.340915	+	0.590483i	0.643688	+	0.765288i	$0.277404\pi$
$710$	−0.551918	−	0.955950i	−0.0207131	−	0.0358762i
$711$	15.0824	+	5.48203i	0.565634	+	0.205592i
$712$	−14.8319	−	8.56318i	−0.555847	−	0.320919i
$713$		−	13.0929i		−	0.490331i
$714$	24.1295	+	15.4618i	0.903024	+	0.578643i
$715$	1.82969	+	5.37772i	0.0684266	+	0.201115i
$716$	−7.84070	−	4.52683i	−0.293021	−	0.169176i
$717$	42.8586	−	3.75916i	1.60059	−	0.140388i
$718$	5.21329	+	9.02968i	0.194558	+	0.336985i
$719$	−13.2458	−	7.64744i	−0.493983	−	0.285201i	0.232242	−	0.972658i	$-0.425394\pi$
$719$	−13.2458	−	7.64744i	−0.493983	−	0.285201i	−0.726225	+	0.687457i	$0.758727\pi$
$720$	0.652829	−	0.548279i	0.0243295	−	0.0204331i
$721$	18.9706	−	7.79445i	0.706501	−	0.290280i
$722$	−10.5396			−0.392243
$723$	−12.4870	+	8.74757i	−0.464396	+	0.325326i
$724$	−10.5974	−	18.3553i	−0.393851	−	0.682169i
$725$	−1.06857	−	1.85082i	−0.0396858	−	0.0687379i
$726$	18.1800	+	5.69976i	0.674723	+	0.211538i
$727$	9.71636			0.360360			0.180180	−	0.983634i	$-0.442332\pi$
$727$	9.71636			0.360360			0.180180	+	0.983634i	$0.442332\pi$
$728$	−9.74341	+	12.6230i	−0.361115	+	0.467840i
$729$	23.3648	−	13.5309i	0.865364	−	0.501144i
$730$	0.624212	−	1.08117i	0.0231031	−	0.0400158i
$731$	12.4533	−	7.18994i	0.460603	−	0.265929i
$732$	0.590361	+	6.73078i	0.0218204	+	0.248777i
$733$	−20.6665	−	11.9318i	−0.763336	−	0.440712i	0.0671561	−	0.997742i	$-0.478607\pi$
$733$	−20.6665	−	11.9318i	−0.763336	−	0.440712i	−0.830492	+	0.557030i	$0.811941\pi$
$734$	−1.60455			−0.0592251
$735$	0.616924	−	3.38975i	0.0227556	−	0.125033i
$736$		−	1.79656i		−	0.0662222i
$737$	28.2494	+	5.59859i	1.04058	+	0.206227i
$738$	0.334823	−	0.921182i	0.0123250	−	0.0339092i
$739$	−13.0082	+	7.51031i	−0.478516	+	0.276271i	−0.719798	−	0.694184i	$-0.755765\pi$
$739$	−13.0082	+	7.51031i	−0.478516	+	0.276271i	0.241282	+	0.970455i	$0.422432\pi$
$740$	−2.74260	−	1.58344i	−0.100820	−	0.0582084i
$741$	23.9667	−	51.4264i	0.880439	−	1.88919i
$742$	3.10690	−	4.02512i	0.114058	−	0.147767i
$743$	−29.1581			−1.06971			−0.534853	−	0.844945i	$-0.679633\pi$
$743$	−29.1581			−1.06971			−0.534853	+	0.844945i	$0.679633\pi$
$744$	−7.24236	−	10.3383i	−0.265518	−	0.379021i
$745$	2.92365	−	1.68797i	0.107114	−	0.0618423i
$746$	0.443041	−	0.255790i	0.0162209	−	0.00936513i
$747$	4.76319	−	0.842043i	0.174276	−	0.0308087i
$748$	−6.68085	−	19.6360i	−0.244276	−	0.717962i
$749$	35.8501	−	14.7297i	1.30993	−	0.538213i
$750$	−4.42532	−	2.06237i	−0.161590	−	0.0753072i
$751$	10.3432	−	17.9150i	0.377430	−	0.653728i	−0.613257	−	0.789883i	$-0.710141\pi$
$751$	10.3432	−	17.9150i	0.377430	−	0.653728i	0.990688	+	0.136155i	$0.0434745\pi$
$752$	−3.52794	+	2.03685i	−0.128651	+	0.0742765i
$753$	2.12200	+	24.1932i	0.0773300	+	0.881649i
$754$	2.26761	+	1.30921i	0.0825816	+	0.0476785i
$755$	−0.491795			−0.0178982
$756$	1.76450	+	13.6340i	0.0641742	+	0.495865i
$757$	−19.7101			−0.716375			−0.358188	−	0.933650i	$-0.616605\pi$
$757$	−19.7101			−0.716375			−0.358188	+	0.933650i	$0.616605\pi$
$758$	−2.54183	+	4.40257i	−0.0923233	+	0.159909i
$759$	9.44262	−	4.16523i	0.342745	−	0.151188i
$760$	−0.772248	−	1.33757i	−0.0280124	−	0.0485189i
$761$	20.8209	−	36.0628i	0.754757	−	1.30728i	−0.190738	−	0.981641i	$-0.561088\pi$
$761$	20.8209	−	36.0628i	0.754757	−	1.30728i	0.945495	−	0.325636i	$-0.105578\pi$
$762$	8.72268	+	4.06511i	0.315989	+	0.147264i
$763$	41.7377	+	5.61623i	1.51101	+	0.203321i
$764$		−	12.4476i		−	0.450339i
$765$	−0.928113	−	5.25007i	−0.0335560	−	0.189817i
$766$	−4.59160	+	2.65096i	−0.165901	+	0.0957832i
$767$	29.1705	+	50.5248i	1.05329	+	1.82434i
$768$	−0.993776	−	1.41859i	−0.0358598	−	0.0511891i
$769$			5.30858i			0.191432i	0.995409	+	0.0957161i	$0.0305141\pi$
$769$			5.30858i			0.191432i	−0.995409	+	0.0957161i	$0.969486\pi$
$770$	−1.87834	+	1.64011i	−0.0676908	+	0.0591055i
$771$	13.7886	+	6.42603i	0.496584	+	0.231428i
$772$	12.9542	+	7.47910i	0.466231	+	0.269179i
$773$	27.8900	−	16.1023i	1.00314	−	0.579160i	0.0939608	−	0.995576i	$-0.470047\pi$
$773$	27.8900	−	16.1023i	1.00314	−	0.579160i	0.909174	+	0.416415i	$0.136714\pi$
$774$	6.48322	+	2.35647i	0.233035	+	0.0847014i
$775$	−17.9250	+	31.0471i	−0.643886	+	1.11524i
$776$	6.98710			0.250822
$777$	45.3607	−	23.4615i	1.62731	−	0.841676i
$778$		−	30.0206i		−	1.07629i
$779$	−1.53781	−	0.887853i	−0.0550976	−	0.0318106i
$780$	2.95518	−	0.259200i	0.105812	−	0.00928086i
$781$	−9.69188	−	8.48755i	−0.346803	−	0.303709i
$782$	−9.73003	−	5.61764i	−0.347945	−	0.200886i
$783$	2.18014	−	0.585711i	0.0779119	−	0.0209316i
$784$	−6.75102	−	1.85034i	−0.241108	−	0.0660835i
$785$			3.16596i			0.112998i
$786$	18.7698	+	26.7935i	0.669497	+	0.955693i
$787$	−25.9819	+	15.0006i	−0.926153	+	0.534715i	−0.885593	−	0.464462i	$-0.846248\pi$
$787$	−25.9819	+	15.0006i	−0.926153	+	0.534715i	−0.0405602	+	0.999177i	$0.512914\pi$
$788$	4.12317	+	7.14153i	0.146882	+	0.254407i
$789$	7.82846	+	11.1750i	0.278700	+	0.397839i
$790$	1.52012			0.0540835
$791$	19.8335	−	25.6951i	0.705197	−	0.913614i
$792$	5.15202	−	8.51215i	0.183069	−	0.302466i
$793$	−11.7555	+	20.3611i	−0.417450	+	0.723045i
$794$	−5.20199	−	9.01011i	−0.184612	−	0.319757i
$795$	−0.942323	+	0.0826517i	−0.0334207	+	0.00293135i
$796$	7.13434	−	12.3570i	0.252870	−	0.437984i
$797$			35.9024i			1.27173i	0.771802	+	0.635864i	$0.219356\pi$
$797$			35.9024i			1.27173i	−0.771802	+	0.635864i	$0.780644\pi$
$798$	24.8798	+	1.15201i	0.880735	+	0.0407807i
$799$			25.4760i			0.901276i
$800$	−2.45962	+	4.26019i	−0.0869608	+	0.150621i
$801$	−48.2883	−	17.5514i	−1.70618	−	0.620148i
$802$	−12.6464	+	7.30138i	−0.446559	+	0.257821i
$803$	2.83255	−	14.2925i	0.0999586	−	0.504371i
$804$	6.35304	−	13.6320i	0.224055	−	0.480763i
$805$	−0.180134	+	1.33869i	−0.00634889	+	0.0471826i
$806$		−	43.9232i		−	1.54713i
$807$	8.58208	−	6.01206i	0.302104	−	0.211634i
$808$	5.50494	+	9.53484i	0.193663	+	0.335434i
$809$	22.7425	+	39.3912i	0.799585	+	1.38492i	0.919887	+	0.392184i	$0.128280\pi$
$809$	22.7425	+	39.3912i	0.799585	+	1.38492i	−0.120302	+	0.992737i	$0.538386\pi$
$810$	1.64225	−	1.96066i	0.0577027	−	0.0688905i
$811$		−	15.4966i		−	0.544160i	−0.962275	−	0.272080i	$-0.912288\pi$
$811$		−	15.4966i		−	0.544160i	0.962275	−	0.272080i	$-0.0877115\pi$
$812$	−0.153287	+	1.13917i	−0.00537931	+	0.0399770i
$813$	−1.60713	−	0.748985i	−0.0563644	−	0.0262680i
$814$	−36.2558	−	7.18534i	−1.27077	−	0.251846i
$815$	−0.204701	+	0.118184i	−0.00717037	+	0.00413982i
$816$	−10.7904	+	0.946432i	−0.377740	+	0.0331318i
$817$	6.24865	−	10.8230i	0.218613	−	0.378648i
$818$			24.9790i			0.873370i
$819$	−22.1916	+	42.3793i	−0.775437	+	1.48085i
$820$		−	0.0928439i		−	0.00324225i
$821$	19.5209	−	33.8113i	0.681285	−	1.18002i	−0.293303	−	0.956019i	$-0.594755\pi$
$821$	19.5209	−	33.8113i	0.681285	−	1.18002i	0.974589	−	0.224001i	$-0.0719120\pi$
$822$	−2.55814	−	29.1657i	−0.0892253	−	1.01727i
$823$	−20.0995	−	34.8133i	−0.700624	−	1.21352i	−0.968248	−	0.249992i	$-0.919572\pi$
$823$	−20.0995	−	34.8133i	−0.700624	−	1.21352i	0.267624	−	0.963523i	$-0.413761\pi$
$824$	−3.87592	+	6.71328i	−0.135024	+	0.233868i
$825$	−28.0938	−	3.05060i	−0.978100	−	0.106208i
$826$	−15.6488	+	20.2737i	−0.544490	+	0.705411i
$827$	3.20205			0.111346			0.0556732	−	0.998449i	$-0.482270\pi$
$827$	3.20205			0.111346			0.0556732	+	0.998449i	$0.482270\pi$
$828$	−0.938248	−	5.30740i	−0.0326064	−	0.184445i
$829$	−6.56231	−	11.3662i	−0.227918	−	0.394766i	0.729273	−	0.684223i	$-0.239859\pi$
$829$	−6.56231	−	11.3662i	−0.227918	−	0.394766i	−0.957191	+	0.289457i	$0.906525\pi$
$830$	0.396803	−	0.229094i	0.0137732	−	0.00795197i
$831$	1.17456	−	0.822818i	0.0407449	−	0.0285432i
$832$		−	6.02702i		−	0.208949i
$833$	−31.1309	+	30.7771i	−1.07862	+	1.06636i
$834$	19.0442	+	8.87536i	0.659447	+	0.307328i
$835$	−4.71027	−	2.71947i	−0.163006	−	0.0941113i
$836$	−13.5610	−	11.8759i	−0.469016	−	0.410735i
$837$	−26.7945	−	26.7591i	−0.926152	−	0.924929i
$838$	30.6609	+	17.7021i	1.05916	+	0.611507i
$839$			22.7217i			0.784439i	0.919872	+	0.392220i	$0.128293\pi$
$839$			22.7217i			0.784439i	−0.919872	+	0.392220i	$0.871707\pi$
$840$	0.598264	+	1.15669i	0.0206421	+	0.0399096i
$841$	−28.8113			−0.993492
$842$	−0.438979	+	0.760334i	−0.0151282	+	0.0262028i
$843$	−37.4899	+	3.28826i	−1.29122	+	0.113254i
$844$	14.4945	−	8.36841i	0.498921	−	0.288052i
$845$	5.74032	+	3.31417i	0.197473	+	0.114011i
$846$	−9.35847	+	7.85971i	−0.321751	+	0.270223i
$847$	−14.5883	+	25.1829i	−0.501261	+	0.865296i
$848$			1.92185i			0.0659964i
$849$	20.0822	−	14.0683i	0.689220	−	0.482823i
$850$	15.3819	+	26.6422i	0.527594	+	0.913820i
$851$	−17.3388	+	10.0106i	−0.594368	+	0.343159i
$852$	−5.51034	+	3.86019i	−0.188781	+	0.132248i
$853$			21.8003i			0.746428i	0.927745	+	0.373214i	$0.121744\pi$
$853$			21.8003i			0.746428i	−0.927745	+	0.373214i	$0.878256\pi$
$854$	−10.2287	−	1.37638i	−0.350020	−	0.0470987i
$855$	−2.97991	−	3.54815i	−0.101911	−	0.121344i
$856$	−7.32460	+	12.6866i	−0.250350	+	0.433619i
$857$	−14.0547	−	24.3434i	−0.480098	−	0.831554i	0.519641	−	0.854384i	$-0.326066\pi$
$857$	−14.0547	−	24.3434i	−0.480098	−	0.831554i	−0.999739	+	0.0228304i	$0.992732\pi$
$858$	31.6776	−	13.9733i	1.08146	−	0.477040i
$859$	−12.9428	+	22.4176i	−0.441603	+	0.764879i	−0.997809	−	0.0661656i	$-0.978923\pi$
$859$	−12.9428	+	22.4176i	−0.441603	+	0.764879i	0.556205	+	0.831045i	$0.312257\pi$
$860$	0.653430			0.0222818
$861$	1.26060	+	0.807769i	0.0429610	+	0.0275287i
$862$	19.9026			0.677886
$863$	−11.3331	−	6.54315i	−0.385782	−	0.222731i	0.294549	−	0.955636i	$-0.404831\pi$
$863$	−11.3331	−	6.54315i	−0.385782	−	0.222731i	−0.680331	+	0.732905i	$0.738164\pi$
$864$	−3.67666	−	3.67181i	−0.125083	−	0.124917i
$865$	4.33451	−	2.50253i	0.147378	−	0.0850887i
$866$	−6.93487	+	12.0116i	−0.235657	+	0.408169i
$867$	−16.1764	+	34.7104i	−0.549380	+	1.17883i
$868$	17.8348	−	7.32778i	0.605352	−	0.248721i
$869$	16.7960	−	5.71458i	0.569764	−	0.193854i
$870$	0.175137	−	0.122690i	0.00593771	−	0.00415958i
$871$	45.3222	−	26.1668i	1.53569	−	0.886628i
$872$	−13.7850	+	7.95877i	−0.466819	+	0.269518i
$873$	20.6412	−	3.64898i	0.698600	−	0.123499i
$874$	−9.76439			−0.330285
$875$	4.55692	−	5.90370i	0.154052	−	0.199581i
$876$	−6.89697	−	3.21426i	−0.233027	−	0.108600i
$877$	−27.9816	−	16.1552i	−0.944872	−	0.545522i	−0.0533875	−	0.998574i	$-0.517002\pi$
$877$	−27.9816	−	16.1552i	−0.944872	−	0.545522i	−0.891484	+	0.453052i	$0.850335\pi$
$878$	9.43561	−	5.44765i	0.318436	−	0.183849i
$879$	−9.93641	+	0.871529i	−0.335147	+	0.0293959i
$880$	0.183225	−	0.924518i	0.00617652	−	0.0311655i
$881$			16.1735i			0.544899i	0.962170	+	0.272450i	$0.0878338\pi$
$881$			16.1735i			0.544899i	−0.962170	+	0.272450i	$0.912166\pi$
$882$	−20.9101	−	1.94057i	−0.704081	−	0.0653423i
$883$	9.98793			0.336121			0.168060	−	0.985777i	$-0.446250\pi$
$883$	9.98793			0.336121			0.168060	+	0.985777i	$0.446250\pi$
$884$	−32.6418	−	18.8458i	−1.09786	−	0.633851i
$885$	4.74627	−	0.416298i	0.159544	−	0.0139937i
$886$	−12.2275	+	7.05956i	−0.410791	+	0.237171i
$887$	−16.1800	+	28.0247i	−0.543273	+	0.940976i	0.455441	+	0.890266i	$0.349482\pi$
$887$	−16.1800	+	28.0247i	−0.543273	+	0.940976i	−0.998713	+	0.0507096i	$0.983852\pi$
$888$	−8.15362	+	17.4956i	−0.273618	+	0.587112i
$889$	−8.98209	+	11.6367i	−0.301250	+	0.390282i
$890$	−4.86687			−0.163138
$891$	10.7746	−	27.8372i	0.360964	−	0.932580i
$892$	−0.543854	−	0.941983i	−0.0182096	−	0.0315399i
$893$	11.0704	+	19.1745i	0.370456	+	0.641649i
$894$	−11.8059	−	16.8526i	−0.394847	−	0.563636i
$895$	−2.57282			−0.0859998
$896$	2.44724	−	1.00550i	0.0817565	−	0.0335913i
$897$	7.92226	−	16.9991i	0.264516	−	0.567584i
$898$	30.6431	+	17.6918i	1.02257	+	0.590382i
$899$	−1.58306	−	2.74194i	−0.0527980	−	0.0914489i
$900$	−5.04133	+	13.8700i	−0.168044	+	0.462332i
$901$	10.4085	+	6.00938i	0.346759	+	0.200201i
$902$	−0.349027	−	1.02584i	−0.0116213	−	0.0341567i
$903$	−5.68503	+	8.87200i	−0.189186	+	0.295242i
$904$			12.2685i			0.408043i
$905$	−5.21610	−	3.01152i	−0.173389	−	0.100106i
$906$	0.261907	+	2.98604i	0.00870129	+	0.0992046i
$907$	8.02681	+	13.9028i	0.266526	+	0.461636i	0.967962	−	0.251096i	$-0.0807909\pi$
$907$	8.02681	+	13.9028i	0.266526	+	0.461636i	−0.701436	+	0.712732i	$0.747458\pi$
$908$	4.48346	−	7.76558i	0.148789	−	0.257710i
$909$	21.2422	+	25.2928i	0.704559	+	0.838910i
$910$	−0.604305	+	4.49096i	−0.0200325	+	0.148874i
$911$			22.7800i			0.754734i	0.926064	+	0.377367i	$0.123171\pi$
$911$			22.7800i			0.754734i	−0.926064	+	0.377367i	$0.876829\pi$
$912$	−7.71011	+	5.40121i	−0.255307	+	0.178852i
$913$	3.52307	−	4.02297i	0.116597	−	0.133141i
$914$	−2.96219	+	1.71022i	−0.0979805	+	0.0565690i
$915$	1.10165	+	1.57258i	0.0364193	+	0.0519878i
$916$	−12.4498			−0.411353
$917$	−46.2219	+	18.9912i	−1.52638	+	0.627145i
$918$	−31.3827	+	8.43118i	−1.03578	+	0.278271i
$919$	26.9216	+	15.5432i	0.888061	+	0.512722i	0.873308	−	0.487169i	$-0.161970\pi$
$919$	26.9216	+	15.5432i	0.888061	+	0.512722i	0.0147535	+	0.999891i	$0.495304\pi$
$920$	−0.255269	−	0.442138i	−0.00841596	−	0.0145769i
$921$	−1.60130	−	18.2567i	−0.0527648	−	0.601578i
$922$	6.52560	−	11.3027i	0.214909	−	0.372234i
$923$	−23.4111			−0.770587
$924$	10.9586	+	10.5313i	0.360512	+	0.346455i
$925$	54.8208			1.80250
$926$	9.04932	−	15.6739i	0.297379	−	0.515076i
$927$	−7.94422	+	21.8565i	−0.260923	+	0.717862i
$928$	−0.217223	−	0.376241i	−0.00713070	−	0.0123507i
$929$	−9.05995	−	5.23076i	−0.297247	−	0.171616i	0.343958	−	0.938985i	$-0.388232\pi$
$929$	−9.05995	−	5.23076i	−0.297247	−	0.171616i	−0.641206	+	0.767369i	$0.721565\pi$
$930$	−3.25130	−	1.51523i	−0.106614	−	0.0496865i
$931$	−10.0567	+	36.6920i	−0.329593	+	1.20253i
$932$	18.3861			0.602255
$933$	−9.67176	+	6.77541i	−0.316639	+	0.221817i
$934$	5.31873	−	3.07077i	0.174034	−	0.100479i
$935$	−4.43419	−	3.88319i	−0.145013	−	0.126994i
$936$	−3.14758	−	17.8050i	−0.102882	−	0.581974i
$937$			27.1309i			0.886328i	0.896441	+	0.443164i	$0.146144\pi$
$937$			27.1309i			0.886328i	−0.896441	+	0.443164i	$0.853856\pi$
$938$	18.1861	+	14.0374i	0.593796	+	0.458337i
$939$	19.9386	−	42.7831i	0.650672	−	1.39617i
$940$	−0.578822	+	1.00255i	−0.0188791	+	0.0326995i
$941$	−9.89770	−	17.1433i	−0.322656	−	0.558856i	0.658379	−	0.752686i	$-0.271242\pi$
$941$	−9.89770	−	17.1433i	−0.322656	−	0.558856i	−0.981035	+	0.193830i	$0.937909\pi$
$942$	19.2228	−	1.68605i	0.626314	−	0.0549344i
$943$	−0.508326	−	0.293482i	−0.0165534	−	0.00955709i
$944$		−	9.67991i		−	0.315054i
$945$	2.37147	+	3.10465i	0.0771438	+	0.100994i
$946$	7.21980	−	2.45643i	0.234736	−	0.0798655i
$947$	−31.4053	−	18.1318i	−1.02053	−	0.589205i	−0.106275	−	0.994337i	$-0.533892\pi$
$947$	−31.4053	−	18.1318i	−1.02053	−	0.589205i	−0.914258	+	0.405131i	$0.867226\pi$
$948$	−0.809548	−	9.22976i	−0.0262929	−	0.299769i
$949$	−13.2388	−	22.9304i	−0.429751	−	0.744351i
$950$	23.1543	+	13.3681i	0.751224	+	0.433719i
$951$	−21.0496	−	9.80993i	−0.682579	−	0.318109i
$952$	2.20653	−	16.3981i	0.0715140	−	0.531465i
$953$	39.1127			1.26699			0.633493	−	0.773749i	$-0.281621\pi$
$953$	39.1127			1.26699			0.633493	+	0.773749i	$0.281621\pi$
$954$	1.00368	+	5.67750i	0.0324952	+	0.183816i
$955$	−1.76865	−	3.06338i	−0.0572320	−	0.0991288i
$956$	−12.4197	−	21.5116i	−0.401683	−	0.695735i
$957$	1.47388	−	2.01400i	0.0476438	−	0.0651035i
$958$	−7.26498			−0.234721
$959$	44.3229	+	5.96409i	1.43126	+	0.192591i
$960$	−0.446134	−	0.207916i	−0.0143989	−	0.00671047i
$961$	−11.0554	+	19.1485i	−0.356626	+	0.617695i
$962$	−58.1674	+	33.5830i	−1.87539	+	1.08276i
$963$	−15.0128	+	41.3039i	−0.483780	+	1.33100i
$964$	7.62307	+	4.40118i	0.245522	+	0.141752i
$965$	4.25074			0.136836
$966$	8.22408	+	0.380800i	0.264605	+	0.0122520i
$967$		−	50.7537i		−	1.63213i	−0.577961	−	0.816064i	$-0.696151\pi$
$967$		−	50.7537i		−	1.63213i	0.577961	−	0.816064i	$-0.303849\pi$
$968$	−1.45106	−	10.9039i	−0.0466389	−	0.350464i
$969$	5.14389	+	58.6462i	0.165246	+	1.88399i
$970$	1.71954	−	0.992777i	0.0552111	−	0.0318761i
$971$	0.389942	+	0.225133i	0.0125138	+	0.00722486i	0.506244	−	0.862390i	$-0.331034\pi$
$971$	0.389942	+	0.225133i	0.0125138	+	0.00722486i	−0.493730	+	0.869615i	$0.664367\pi$
$972$	−12.7792	−	8.92711i	−0.409892	−	0.286337i
$973$	−19.6106	+	25.4064i	−0.628686	+	0.814491i
$974$	−41.0670			−1.31587
$975$	−42.0590	+	29.4638i	−1.34697	+	0.943598i
$976$	3.37831	−	1.95047i	0.108137	−	0.0624330i
$977$	−4.01364	+	2.31728i	−0.128408	+	0.0741363i	−0.562828	−	0.826574i	$-0.690287\pi$
$977$	−4.01364	+	2.31728i	−0.128408	+	0.0741363i	0.434420	+	0.900710i	$0.356953\pi$
$978$	0.826596	+	1.17995i	0.0264316	+	0.0377306i
$979$	−53.7744	+	18.2960i	−1.71864	+	0.584742i
$980$	−1.92435	+	0.503861i	−0.0614711	+	0.0160952i
$981$	−36.5671	+	30.7109i	−1.16750	+	0.980524i
$982$	17.9570	−	31.1025i	0.573031	−	0.992520i
$983$	−28.8337	+	16.6472i	−0.919654	+	0.530962i	−0.883525	−	0.468385i	$-0.844836\pi$
$983$	−28.8337	+	16.6472i	−0.919654	+	0.530962i	−0.0361291	+	0.999347i	$0.511503\pi$
$984$	−0.563722	+	0.0494444i	−0.0179708	+	0.00157623i
$985$	2.02944	+	1.17170i	0.0646633	+	0.0373334i
$986$	−2.71692			−0.0865244
$987$	−8.57627	−	16.5815i	−0.272986	−	0.527794i
$988$	−32.7570			−1.04214
$989$	2.06551	−	3.57756i	0.0656793	−	0.113760i
$990$	0.0584568	−	2.82689i	0.00185788	−	0.0898446i
$991$	0.378039	+	0.654782i	0.0120088	+	0.0207998i	0.871967	−	0.489564i	$-0.162844\pi$
$991$	0.378039	+	0.654782i	0.0120088	+	0.0207998i	−0.859959	+	0.510364i	$0.829511\pi$
$992$	−3.64386	+	6.31135i	−0.115693	+	0.200386i
$993$	8.74990	−	18.7750i	0.277670	−	0.595807i
$994$	−3.90572	−	9.50597i	−0.123882	−	0.301511i
$995$		−	4.05479i		−	0.128545i
$996$	−1.60231	−	2.28727i	−0.0507713	−	0.0724749i
$997$	27.9874	−	16.1585i	0.886368	−	0.511745i	0.0136154	−	0.999907i	$-0.495666\pi$
$997$	27.9874	−	16.1585i	0.886368	−	0.511745i	0.872753	+	0.488162i	$0.162333\pi$
$998$	6.45040	+	11.1724i	0.204184	+	0.353657i
$999$	−14.9504	+	55.9435i	−0.473010	+	1.76997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.n.e.65.12	yes	24
3.2	odd	2		462.2.n.f.65.4	yes	24
7.4	even	3	inner	462.2.n.e.263.4	yes	24
11.10	odd	2		462.2.n.f.65.12	yes	24
21.11	odd	6		462.2.n.f.263.12	yes	24
33.32	even	2	inner	462.2.n.e.65.4	✓	24
77.32	odd	6		462.2.n.f.263.4	yes	24
231.32	even	6	inner	462.2.n.e.263.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.e.65.4	✓	24	33.32	even	2	inner
462.2.n.e.65.12	yes	24	1.1	even	1	trivial
462.2.n.e.263.4	yes	24	7.4	even	3	inner
462.2.n.e.263.12	yes	24	231.32	even	6	inner
462.2.n.f.65.4	yes	24	3.2	odd	2
462.2.n.f.65.12	yes	24	11.10	odd	2
462.2.n.f.263.4	yes	24	77.32	odd	6
462.2.n.f.263.12	yes	24	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.72543 - 0.151338i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.246102 - 0.142087i) q^{5} +(-0.731651 + 1.56993i) q^{6} +(-2.09441 - 1.61662i) q^{7} +1.00000 q^{8} +(2.95419 - 0.522246i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.72543 - 0.151338i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.246102 - 0.142087i) q^{5} +(-0.731651 + 1.56993i) q^{6} +(-2.09441 - 1.61662i) q^{7} +1.00000 q^{8} +(2.95419 - 0.522246i) q^{9} +(0.246102 - 0.142087i) q^{10} +(2.18506 - 2.49510i) q^{11} +(-0.993776 - 1.41859i) q^{12} -6.02702i q^{13} +(2.44724 - 1.00550i) q^{14} +(-0.446134 - 0.207916i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.12688 + 5.41591i) q^{17} +(-1.02482 + 2.81953i) q^{18} +(4.70688 + 2.71752i) q^{19} +0.284174i q^{20} +(-3.85840 - 2.47240i) q^{21} +(1.06829 + 3.13986i) q^{22} +(1.55587 + 0.898282i) q^{23} +(1.72543 - 0.151338i) q^{24} +(-2.45962 - 4.26019i) q^{25} +(5.21955 + 3.01351i) q^{26} +(5.01821 - 1.34818i) q^{27} +(-0.352833 + 2.62212i) q^{28} +0.434446 q^{29} +(0.403128 - 0.282406i) q^{30} +(-3.64386 - 6.31135i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.39255 - 4.63580i) q^{33} -6.25376 q^{34} +(0.285737 + 0.695442i) q^{35} +(-1.92937 - 2.29728i) q^{36} +(-5.57207 + 9.65112i) q^{37} +(-4.70688 + 2.71752i) q^{38} +(-0.912118 - 10.3992i) q^{39} +(-0.246102 - 0.142087i) q^{40} -0.326715 q^{41} +(4.07036 - 2.10527i) q^{42} -2.29940i q^{43} +(-3.25335 - 0.644763i) q^{44} +(-0.801238 - 0.291227i) q^{45} +(-1.55587 + 0.898282i) q^{46} +(3.52794 + 2.03685i) q^{47} +(-0.731651 + 1.56993i) q^{48} +(1.77307 + 6.77172i) q^{49} +4.91924 q^{50} +(6.21483 + 8.87154i) q^{51} +(-5.21955 + 3.01351i) q^{52} +(1.66437 - 0.960923i) q^{53} +(-1.34155 + 5.01999i) q^{54} +(-0.892269 + 0.303581i) q^{55} +(-2.09441 - 1.61662i) q^{56} +(8.53264 + 3.97655i) q^{57} +(-0.217223 + 0.376241i) q^{58} +(-8.38305 + 4.83996i) q^{59} +(0.0430064 + 0.490322i) q^{60} +(-3.37831 - 1.95047i) q^{61} +7.28772 q^{62} +(-7.03155 - 3.68202i) q^{63} +1.00000 q^{64} +(-0.856362 + 1.48326i) q^{65} +(2.31844 + 5.25593i) q^{66} +(4.34158 + 7.51984i) q^{67} +(3.12688 - 5.41591i) q^{68} +(2.82048 + 1.31446i) q^{69} +(-0.745139 - 0.100266i) q^{70} -3.88436i q^{71} +(2.95419 - 0.522246i) q^{72} +(3.80459 - 2.19658i) q^{73} +(-5.57207 - 9.65112i) q^{74} +(-4.88863 - 6.97841i) q^{75} -5.43503i q^{76} +(-8.61003 + 1.69335i) q^{77} +(9.46201 + 4.40967i) q^{78} +(4.63260 + 2.67463i) q^{79} +(0.246102 - 0.142087i) q^{80} +(8.45452 - 3.08563i) q^{81} +(0.163357 - 0.282943i) q^{82} +1.61235 q^{83} +(-0.211960 + 4.57767i) q^{84} -1.77716i q^{85} +(1.99134 + 1.14970i) q^{86} +(0.749605 - 0.0657483i) q^{87} +(2.18506 - 2.49510i) q^{88} +(-14.8319 - 8.56318i) q^{89} +(0.652829 - 0.548279i) q^{90} +(-9.74341 + 12.6230i) q^{91} -1.79656i q^{92} +(-7.24236 - 10.3383i) q^{93} +(-3.52794 + 2.03685i) q^{94} +(-0.772248 - 1.33757i) q^{95} +(-0.993776 - 1.41859i) q^{96} +6.98710 q^{97} +(-6.75102 - 1.85034i) q^{98} +(5.15202 - 8.51215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9 - 4 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^17 - 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 + 40 * q^29 - 2 * q^30 - 28 * q^31 - 12 * q^32 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^36 - 16 * q^37 - 8 * q^41 + 6 * q^42 - 4 * q^44 - 28 * q^45 - 8 * q^49 - 40 * q^50 - 34 * q^51 + 6 * q^54 + 8 * q^55 + 40 * q^57 - 20 * q^58 - 2 * q^60 + 56 * q^62 - 14 * q^63 + 24 * q^64 - 44 * q^65 + 32 * q^66 + 4 * q^68 - 20 * q^69 + 64 * q^70 - 8 * q^72 - 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 + 144 * q^83 - 6 * q^84 + 8 * q^87 - 4 * q^88 + 56 * q^90 - 32 * q^91 - 22 * q^93 - 44 * q^95 + 64 * q^97 - 8 * q^98 - 52 * q^99

Introduction

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