LMFDB - Embedded newform 462.2.n.e.65.4

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			65.4
Character	$\chi$	$=$	462.65
Dual form			462.2.n.e.263.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.993776 + 1.41859i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.246102 + 0.142087i) q^{5} +(-0.731651 - 1.56993i) q^{6} +(2.09441 + 1.61662i) q^{7} +1.00000 q^{8} +(-1.02482 - 2.81953i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.993776 + 1.41859i) 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} +(-1.02482 - 2.81953i) q^{9} +(-0.246102 + 0.142087i) q^{10} +(-3.25335 + 0.644763i) q^{11} +(1.72543 + 0.151338i) 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} +(2.95419 + 0.522246i) q^{18} +(-4.70688 - 2.71752i) q^{19} -0.284174i q^{20} +(-4.37470 + 1.36455i) q^{21} +(1.06829 - 3.13986i) q^{22} +(-1.55587 - 0.898282i) q^{23} +(-0.993776 + 1.41859i) 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} +(0.0430064 - 0.490322i) q^{30} +(-3.64386 - 6.31135i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.31844 - 5.25593i) 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} +(-8.54989 - 5.98951i) q^{39} +(0.246102 + 0.142087i) q^{40} -0.326715 q^{41} +(1.00561 - 4.47088i) q^{42} +2.29940i q^{43} +(2.18506 + 2.49510i) q^{44} +(0.148409 - 0.839506i) 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} +(-10.7904 - 0.946432i) q^{51} +(5.21955 - 3.01351i) q^{52} +(-1.66437 + 0.960923i) q^{53} +(-3.67666 + 3.67181i) 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} +(0.403128 + 0.282406i) q^{60} +(3.37831 + 1.95047i) q^{61} +7.28772 q^{62} +(2.41173 - 7.56198i) q^{63} +1.00000 q^{64} +(-0.856362 + 1.48326i) q^{65} +(3.39255 + 4.63580i) 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} +(-1.02482 - 2.81953i) q^{72} +(-3.80459 + 2.19658i) q^{73} +(-5.57207 - 9.65112i) q^{74} +(8.48780 + 0.744470i) q^{75} +5.43503i q^{76} +(-7.85617 - 3.90904i) q^{77} +(9.46201 - 4.40967i) q^{78} +(-4.63260 - 2.67463i) q^{79} +(-0.246102 + 0.142087i) q^{80} +(-6.89949 + 5.77901i) q^{81} +(0.163357 - 0.282943i) q^{82} +1.61235 q^{83} +(3.36909 + 3.10633i) q^{84} +1.77716i q^{85} +(-1.99134 - 1.14970i) q^{86} +(-0.431742 + 0.616303i) q^{87} +(-3.25335 + 0.644763i) q^{88} +(14.8319 + 8.56318i) q^{89} +(0.652829 + 0.548279i) q^{90} +(-9.74341 + 12.6230i) q^{91} +1.79656i q^{92} +(12.5744 + 1.10291i) q^{93} +(3.52794 - 2.03685i) q^{94} +(-0.772248 - 1.33757i) q^{95} +(1.72543 + 0.151338i) 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
$3$	−0.993776	+	1.41859i	−0.573757	+	0.819026i
$3$	−0.993776	+	1.41859i	−0.573757	+	0.819026i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.246102	+	0.142087i	0.110060	+	0.0635433i	0.554020	−	0.832504i	$-0.313093\pi$
$5$	0.246102	+	0.142087i	0.110060	+	0.0635433i	−0.443959	+	0.896047i	$0.646427\pi$
$6$	−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
$9$	−1.02482	−	2.81953i	−0.341606	−	0.939843i
$10$	−0.246102	+	0.142087i	−0.0778243	+	0.0449319i
$11$	−3.25335	+	0.644763i	−0.980922	+	0.194403i
$11$	−3.25335	+	0.644763i	−0.980922	+	0.194403i
$12$	1.72543	+	0.151338i	0.498088	+	0.0436876i
$13$			6.02702i			1.67159i	0.549039	+	0.835797i	$0.314994\pi$
$13$			6.02702i			1.67159i	−0.549039	+	0.835797i	$0.685006\pi$
$14$	−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	$0.559325\pi$
$18$	2.95419	+	0.522246i	0.696310	+	0.123095i
$19$	−4.70688	−	2.71752i	−1.07983	−	0.623441i	−0.148981	−	0.988840i	$-0.547599\pi$
$19$	−4.70688	−	2.71752i	−1.07983	−	0.623441i	−0.930851	+	0.365399i	$0.880933\pi$
$20$		−	0.284174i		−	0.0635433i
$21$	−4.37470	+	1.36455i	−0.954638	+	0.297770i
$22$	1.06829	−	3.13986i	0.227761	−	0.669421i
$23$	−1.55587	−	0.898282i	−0.324421	−	0.187305i	0.328940	−	0.944351i	$-0.393309\pi$
$23$	−1.55587	−	0.898282i	−0.324421	−	0.187305i	−0.653362	+	0.757046i	$0.726642\pi$
$24$	−0.993776	+	1.41859i	−0.202854	+	0.289569i
$25$	−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	$0.487157\pi$
$30$	0.0430064	−	0.490322i	0.00785186	−	0.0895201i
$31$	−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
$33$	2.31844	−	5.25593i	0.403589	−	0.914940i
$34$	−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
$39$	−8.54989	−	5.98951i	−1.36908	−	0.959089i
$40$	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	$0.508122\pi$
$42$	1.00561	−	4.47088i	0.155170	−	0.689871i
$43$			2.29940i			0.350655i	0.984510	+	0.175327i	$0.0560984\pi$
$43$			2.29940i			0.350655i	−0.984510	+	0.175327i	$0.943902\pi$
$44$	2.18506	+	2.49510i	0.329410	+	0.376151i
$45$	0.148409	−	0.839506i	0.0221235	−	0.125146i
$46$	1.55587	−	0.898282i	0.229401	−	0.132444i
$47$	−3.52794	−	2.03685i	−0.514602	−	0.297106i	0.220121	−	0.975473i	$-0.429355\pi$
$47$	−3.52794	−	2.03685i	−0.514602	−	0.297106i	−0.734723	+	0.678367i	$0.762688\pi$
$48$	−0.731651	−	1.56993i	−0.105605	−	0.226600i
$49$	1.77307	+	6.77172i	0.253296	+	0.967389i
$50$	4.91924			0.695686
$51$	−10.7904	−	0.946432i	−1.51096	−	0.132527i
$52$	5.21955	−	3.01351i	0.723821	−	0.417899i
$53$	−1.66437	+	0.960923i	−0.228618	+	0.131993i	−0.609935	−	0.792452i	$-0.708804\pi$
$53$	−1.66437	+	0.960923i	−0.228618	+	0.131993i	0.381316	+	0.924445i	$0.375471\pi$
$54$	−3.67666	+	3.67181i	−0.500330	+	0.499670i
$55$	−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	0.157437	−	0.987529i	$-0.449677\pi$
$59$	8.38305	−	4.83996i	1.09138	−	0.630109i	0.933944	+	0.357420i	$0.116344\pi$
$60$	0.403128	+	0.282406i	0.0520436	+	0.0364584i
$61$	3.37831	+	1.95047i	0.432548	+	0.249732i	0.700432	−	0.713719i	$-0.252991\pi$
$61$	3.37831	+	1.95047i	0.432548	+	0.249732i	−0.267883	+	0.963451i	$0.586324\pi$
$62$	7.28772			0.925541
$63$	2.41173	−	7.56198i	0.303849	−	0.952720i
$64$	1.00000			0.125000
$65$	−0.856362	+	1.48326i	−0.106219	+	0.183976i
$66$	3.39255	+	4.63580i	0.417594	+	0.570627i
$67$	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	$0.0740344\pi$
$71$			3.88436i			0.460989i	−0.973074	+	0.230495i	$0.925966\pi$
$72$	−1.02482	−	2.81953i	−0.120776	−	0.332285i
$73$	−3.80459	+	2.19658i	−0.445294	+	0.257091i	−0.705841	−	0.708371i	$-0.749431\pi$
$73$	−3.80459	+	2.19658i	−0.445294	+	0.257091i	0.260547	+	0.965461i	$0.416097\pi$
$74$	−5.57207	−	9.65112i	−0.647740	−	1.12192i
$75$	8.48780	+	0.744470i	0.980086	+	0.0859639i
$76$			5.43503i			0.623441i
$77$	−7.85617	−	3.90904i	−0.895294	−	0.445476i
$78$	9.46201	−	4.40967i	1.07136	−	0.499297i
$79$	−4.63260	−	2.67463i	−0.521208	−	0.300920i	0.216221	−	0.976345i	$-0.430627\pi$
$79$	−4.63260	−	2.67463i	−0.521208	−	0.300920i	−0.737429	+	0.675425i	$0.763960\pi$
$80$	−0.246102	+	0.142087i	−0.0275151	+	0.0158858i
$81$	−6.89949	+	5.77901i	−0.766610	+	0.642113i
$82$	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	$0.471796\pi$
$84$	3.36909	+	3.10633i	0.367597	+	0.338928i
$85$			1.77716i			0.192760i
$86$	−1.99134	−	1.14970i	−0.214731	−	0.123975i
$87$	−0.431742	+	0.616303i	−0.0462876	+	0.0660746i
$88$	−3.25335	+	0.644763i	−0.346808	+	0.0687320i
$89$	14.8319	+	8.56318i	1.57217	+	0.907695i	0.995902	+	0.0904364i	$0.0288262\pi$
$89$	14.8319	+	8.56318i	1.57217	+	0.907695i	0.576271	+	0.817258i	$0.304507\pi$
$90$	0.652829	+	0.548279i	0.0688142	+	0.0577936i
$91$	−9.74341	+	12.6230i	−1.02139	+	1.32325i
$92$			1.79656i			0.187305i
$93$	12.5744	+	1.10291i	1.30391	+	0.114366i
$94$	3.52794	−	2.03685i	0.363879	−	0.210086i
$95$	−0.772248	−	1.33757i	−0.0792310	−	0.137232i
$96$	1.72543	+	0.151338i	0.176101	+	0.0154459i
$97$	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	$0.648813\pi$
$102$	6.21483	−	8.87154i	0.615360	−	0.878414i
$103$	−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
$105$	−1.27051	−	0.285769i	−0.123989	−	0.0278882i
$106$		−	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	$0.916221\pi$
$108$	−1.34155	−	5.01999i	−0.129090	−	0.483048i
$109$	13.7850	−	7.95877i	1.32036	−	0.762312i	0.336577	−	0.941656i	$-0.390731\pi$
$109$	13.7850	−	7.95877i	1.32036	−	0.762312i	0.983786	+	0.179344i	$0.0573975\pi$
$110$	0.709044	−	0.620937i	0.0676046	−	0.0592040i
$111$	−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	$-0.804200\pi$
$113$		−	12.2685i		−	1.15412i	0.816702	−	0.577060i	$-0.195800\pi$
$114$	−0.822528	+	9.37775i	−0.0770368	+	0.878307i
$115$	−0.255269	−	0.442138i	−0.0238039	−	0.0412296i
$116$	−0.217223	−	0.376241i	−0.0201687	−	0.0349331i
$117$	16.9934	−	6.17660i	1.57104	−	0.571027i
$118$			9.67991i			0.891108i
$119$	−2.20653	+	16.3981i	−0.202272	+	1.50321i
$120$	−0.446134	+	0.207916i	−0.0407263	+	0.0189801i
$121$	10.1686	−	4.19528i	0.924415	−	0.381389i
$122$	−3.37831	+	1.95047i	−0.305858	+	0.176587i
$123$	0.324681	−	0.463476i	0.0292755	−	0.0417902i
$124$	−3.64386	+	6.31135i	−0.327228	+	0.566776i
$125$		−	2.81879i		−	0.252121i
$126$	5.34301	+	5.86961i	0.475993	+	0.522906i
$127$			5.55609i			0.493023i	0.969140	+	0.246511i	$0.0792843\pi$
$127$			5.55609i			0.493023i	−0.969140	+	0.246511i	$0.920716\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.26191	−	2.28509i	−0.287195	−	0.201191i
$130$	−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
$135$	1.04343	+	1.04481i	0.0898044	+	0.0899231i
$136$	3.12688	+	5.41591i	0.268128	+	0.464411i
$137$	14.6388	−	8.45173i	1.25068	−	0.722080i	0.279435	−	0.960165i	$-0.409853\pi$
$137$	14.6388	−	8.45173i	1.25068	−	0.722080i	0.971244	+	0.238084i	$0.0765195\pi$
$138$	−0.271889	+	3.09984i	−0.0231447	+	0.263876i
$139$			12.1306i			1.02890i	0.857519	+	0.514452i	$0.172005\pi$
$139$			12.1306i			1.02890i	−0.857519	+	0.514452i	$0.827995\pi$
$140$	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
$143$	−3.88600	−	19.6080i	−0.324964	−	1.63970i
$144$	2.95419	+	0.522246i	0.246183	+	0.0435205i
$145$	0.106918	+	0.0617292i	0.00887907	+	0.00512633i
$146$		−	4.39317i		−	0.363581i
$147$	−11.3684	−	4.21431i	−0.937646	−	0.347590i
$148$	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	$0.328436\pi$
$150$	−4.88863	+	6.97841i	−0.399155	+	0.569785i
$151$	−1.49875	+	0.865305i	−0.121967	+	0.0704175i	−0.559742	−	0.828667i	$-0.689100\pi$
$151$	−1.49875	+	0.865305i	−0.121967	+	0.0704175i	0.437775	+	0.899084i	$0.355766\pi$
$152$	−4.70688	−	2.71752i	−0.381778	−	0.220420i
$153$	12.0658	−	14.3667i	0.975466	−	1.16148i
$154$	7.31341	−	4.84912i	0.589332	−	0.390754i
$155$		−	2.07098i		−	0.166345i
$156$	−0.912118	+	10.3992i	−0.0730279	+	0.832601i
$157$	−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
$159$	0.290849	−	3.31600i	0.0230658	−	0.262976i
$160$		−	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
$165$	1.31737	−	0.964075i	0.102557	−	0.0750532i
$166$	−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	$0.234575\pi$
$168$	−4.37470	+	1.36455i	−0.337515	+	0.105277i
$169$	−23.3249			−1.79423
$170$	−1.53906	−	0.888578i	−0.118041	−	0.0681509i
$171$	−2.83842	+	16.0561i	−0.217060	+	1.22784i
$172$	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
$177$	−1.46494	+	16.7020i	−0.110112	+	1.25540i
$178$	−14.8319	+	8.56318i	−1.11169	+	0.641837i
$179$	−7.84070	+	4.52683i	−0.586041	+	0.338351i	−0.763531	−	0.645772i	$-0.776536\pi$
$179$	−7.84070	+	4.52683i	−0.586041	+	0.338351i	0.177489	+	0.984123i	$0.443202\pi$
$180$	−0.801238	+	0.291227i	−0.0597207	+	0.0217068i
$181$	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
$186$	−7.24236	+	10.3383i	−0.531035	+	0.758042i
$187$	−13.6648	−	15.6038i	−0.999270	−	1.14106i
$188$			4.07371i			0.297106i
$189$	8.33067	+	10.9362i	0.605967	+	0.795490i
$190$	1.54450			0.112050
$191$	−10.7800	−	6.22381i	−0.780010	−	0.450339i	0.0564238	−	0.998407i	$-0.482030\pi$
$191$	−10.7800	−	6.22381i	−0.780010	−	0.450339i	−0.836434	+	0.548068i	$0.815364\pi$
$192$	−0.993776	+	1.41859i	−0.0717196	+	0.102378i
$193$	12.9542	−	7.47910i	0.932463	−	0.538357i	0.0448730	−	0.998993i	$-0.485712\pi$
$193$	12.9542	−	7.47910i	0.932463	−	0.538357i	0.887590	+	0.460635i	$0.152378\pi$
$194$	−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	$0.594908\pi$
$198$	−9.94775	+	0.205708i	−0.706956	+	0.0146190i
$199$	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
$201$	−14.9822	−	1.31409i	−1.05676	−	0.0926891i
$202$	−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
$207$	−0.938248	+	5.30740i	−0.0652127	+	0.368890i
$208$	−5.21955	−	3.01351i	−0.361911	−	0.208949i
$209$	17.0653	+	5.80621i	1.18043	+	0.401624i
$210$	0.882738	−	0.957408i	0.0609147	−	0.0660674i
$211$		−	16.7368i		−	1.15221i	−0.817376	−	0.576105i	$-0.804572\pi$
$211$		−	16.7368i		−	1.15221i	0.817376	−	0.576105i	$-0.195428\pi$
$212$	1.66437	+	0.960923i	0.114309	+	0.0659964i
$213$	−5.51034	−	3.86019i	−0.377562	−	0.264496i
$214$	−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
$219$	0.664854	−	7.58009i	0.0449267	−	0.512215i
$220$	0.183225	+	0.924518i	0.0123530	+	0.0623310i
$221$	−32.6418	+	18.8458i	−2.19573	+	1.26770i
$222$	19.2284	+	1.68653i	1.29053	+	0.113193i
$223$	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	$0.737155\pi$
$228$	−7.71011	−	5.40121i	−0.510614	−	0.357704i
$229$	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
$231$	13.3526	−	7.26001i	0.878537	−	0.477674i
$232$	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	$0.960936\pi$
$234$	−3.14758	+	17.8050i	−0.205764	+	1.16395i
$235$	−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	$0.203041\pi$
$240$	0.0430064	−	0.490322i	0.00277605	−	0.0316501i
$241$	7.62307	−	4.40118i	0.491045	−	0.283505i	−0.233963	−	0.972246i	$-0.575169\pi$
$241$	7.62307	−	4.40118i	0.491045	−	0.283505i	0.725008	+	0.688741i	$0.241836\pi$
$242$	−1.45106	+	10.9039i	−0.0932777	+	0.700927i
$243$	−1.34152	−	15.5306i	−0.0860587	−	0.996290i
$244$		−	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
$249$	−1.60231	+	2.28727i	−0.101543	+	0.144950i
$250$	2.44115	+	1.40940i	0.154392	+	0.0891381i
$251$		−	14.0216i		−	0.885034i	−0.896760	−	0.442517i	$-0.854086\pi$
$251$		−	14.0216i		−	0.885034i	0.896760	−	0.442517i	$-0.145914\pi$
$252$	−7.75473	+	1.69237i	−0.488502	+	0.106610i
$253$	5.64097	+	1.91926i	0.354645	+	0.120663i
$254$	−4.81171	−	2.77804i	−0.301914	−	0.174310i
$255$	−2.52106	−	1.76610i	−0.157875	−	0.110597i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.60623	−	4.39146i	−0.474464	−	0.273932i	0.243643	−	0.969865i	$-0.421658\pi$
$257$	−7.60623	−	4.39146i	−0.474464	−	0.273932i	−0.718106	+	0.695933i	$0.754991\pi$
$258$	3.60990	−	1.68236i	0.224743	−	0.104739i
$259$	−27.2724	+	11.2054i	−1.69462	+	0.696271i
$260$	1.71272			0.106219
$261$	−0.445229	−	1.22493i	−0.0275590	−	0.0758215i
$262$	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	$0.755243\pi$
$264$	2.31844	−	5.25593i	0.142690	−	0.323480i
$265$	−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	−0.651143	−	0.758955i	$-0.725710\pi$
$269$	−5.23920	+	3.02485i	−0.319440	+	0.184429i	0.331703	+	0.943384i	$0.392377\pi$
$270$	−1.42655	+	0.381233i	−0.0868171	+	0.0232011i
$271$	0.886543	+	0.511846i	0.0538536	+	0.0310924i	0.526685	−	0.850060i	$-0.323435\pi$
$271$	0.886543	+	0.511846i	0.0538536	+	0.0310924i	−0.472831	+	0.881153i	$0.656768\pi$
$272$	−6.25376			−0.379190
$273$	−8.22418	−	26.3664i	−0.497750	−	1.59577i
$274$			16.9035i			1.02118i
$275$	10.7488	+	12.2740i	0.648179	+	0.740151i
$276$	−2.54860	−	1.78538i	−0.153407	−	0.107467i
$277$	−0.717044	+	0.413986i	−0.0430830	+	0.0248740i	−0.521387	−	0.853320i	$-0.674585\pi$
$277$	−0.717044	+	0.413986i	−0.0430830	+	0.0248740i	0.478304	+	0.878194i	$0.341252\pi$
$278$	−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	$0.724432\pi$
$282$	−0.616508	+	7.02889i	−0.0367125	+	0.418564i
$283$	−12.2598	+	7.07821i	−0.728770	+	0.420756i	−0.817972	−	0.575258i	$-0.804902\pi$
$283$	−12.2598	+	7.07821i	−0.728770	+	0.420756i	0.0892018	+	0.996014i	$0.471568\pi$
$284$	3.36396	−	1.94218i	0.199614	−	0.115247i
$285$	2.66492	+	0.233741i	0.157856	+	0.0138456i
$286$	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
$291$	−6.94361	+	9.91186i	−0.407042	+	0.581043i
$292$	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	$0.553801\pi$
$294$	9.33388	−	7.73813i	0.544363	−	0.451297i
$295$	2.75078			0.160157
$296$	−5.57207	+	9.65112i	−0.323870	+	0.560960i
$297$	−17.1952	−	1.15054i	−0.997769	−	0.0667611i
$298$	−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
$303$	−18.9967	−	1.66622i	−1.09133	−	0.0957216i
$304$	4.70688	−	2.71752i	0.269958	−	0.155860i
$305$	0.554273	+	0.960029i	0.0317376	+	0.0549711i
$306$	6.40897	+	17.6327i	0.366376	+	1.00799i
$307$			10.5810i			0.603888i	0.953326	+	0.301944i	$0.0976355\pi$
$307$			10.5810i			0.603888i	−0.953326	+	0.301944i	$0.902364\pi$
$308$	0.542759	+	8.75816i	0.0309265	+	0.499043i
$309$	−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	−0.323165	−	0.946343i	$-0.604747\pi$
$311$	5.90443	−	3.40892i	0.334809	−	0.193302i	0.657974	+	0.753040i	$0.271414\pi$
$312$	−8.54989	−	5.98951i	−0.484042	−	0.339089i
$313$	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
$315$	1.66799	−	1.51834i	0.0939807	−	0.0855490i
$316$			5.34926i			0.300920i
$317$	11.6116	+	6.70397i	0.652173	+	0.376533i	0.789288	−	0.614023i	$-0.210450\pi$
$317$	11.6116	+	6.70397i	0.652173	+	0.376533i	−0.137115	+	0.990555i	$0.543783\pi$
$318$	2.72632	+	1.90988i	0.152884	+	0.107101i
$319$	−1.41341	+	0.280115i	−0.0791355	+	0.0156834i
$320$	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
$324$	8.45452	+	3.08563i	0.469695	+	0.171424i
$325$	25.6762	−	14.8242i	1.42426	−	0.822298i
$326$	0.415887	+	0.720337i	0.0230338	+	0.0398958i
$327$	−2.40893	+	27.4646i	−0.133214	+	1.51879i
$328$	−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
$333$	32.9220	+	5.81998i	1.80411	+	0.318933i
$334$	−9.56974	+	16.5753i	−0.523633	+	0.906959i
$335$			2.46753i			0.134816i
$336$	1.00561	−	4.47088i	0.0548607	−	0.243906i
$337$		−	7.11663i		−	0.387668i	−0.981034	−	0.193834i	$-0.937908\pi$
$337$		−	7.11663i		−	0.387668i	0.981034	−	0.193834i	$-0.0620923\pi$
$338$	11.6625	−	20.2000i	0.634355	−	1.09874i
$339$	17.4040	+	12.1921i	0.945254	+	0.662184i
$340$	1.53906	−	0.888578i	0.0834674	−	0.0481899i
$341$	15.9241	+	18.1836i	0.862337	+	0.984697i
$342$	−12.4858	−	10.4862i	−0.675156	−	0.567030i
$343$	−7.23379	+	17.0491i	−0.390588	+	0.920566i
$344$			2.29940i			0.123975i
$345$	0.880894	+	0.0772638i	0.0474258	+	0.00415974i
$346$	−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	$0.841898\pi$
$348$	0.749605	+	0.0657483i	0.0401830	+	0.00352448i
$349$			18.5808i			0.994607i	0.867577	+	0.497304i	$0.165677\pi$
$349$			18.5808i			0.994607i	−0.867577	+	0.497304i	$0.834323\pi$
$350$	10.3029	+	7.95256i	0.550713	+	0.425082i
$351$	−8.12550	+	30.2448i	−0.433707	+	1.61435i
$352$	2.18506	+	2.49510i	0.116464	+	0.132989i
$353$	−3.11174	+	1.79656i	−0.165621	+	0.0956215i	−0.580519	−	0.814246i	$-0.697150\pi$
$353$	−3.11174	+	1.79656i	−0.165621	+	0.0956215i	0.414898	+	0.909868i	$0.363817\pi$
$354$	−13.7319	−	9.61966i	−0.729841	−	0.511279i
$355$	−0.551918	+	0.955950i	−0.0292928	+	0.0507366i
$356$		−	17.1264i		−	0.907695i
$357$	−21.0695	−	19.4262i	−1.11511	−	1.02814i
$358$		−	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	$0.0779402\pi$
$360$	0.148409	−	0.839506i	0.00782183	−	0.0442458i
$361$	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
$366$	0.590361	−	6.73078i	0.0308587	−	0.351824i
$367$	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
$369$	0.334823	+	0.921182i	0.0174302	+	0.0479548i
$370$		−	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	0.511426	−	0.859327i	$-0.329117\pi$
$373$	0.443041	+	0.255790i	0.0229398	+	0.0132443i	−0.488486	+	0.872572i	$0.662451\pi$
$374$	20.3457	−	4.03219i	1.05205	−	0.208500i
$375$	3.99872	+	2.80125i	0.206493	+	0.144656i
$376$	−3.52794	−	2.03685i	−0.181939	−	0.105043i
$377$			2.61842i			0.134855i
$378$	−13.6363	+	1.74648i	−0.701378	+	0.0898293i
$379$	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
$381$	−7.88183	−	5.52151i	−0.403799	−	0.282875i
$382$	10.7800	−	6.22381i	0.551550	−	0.318438i
$383$	−4.59160	−	2.65096i	−0.234620	−	0.135458i	0.378082	−	0.925772i	$-0.376584\pi$
$383$	−4.59160	−	2.65096i	−0.234620	−	0.135458i	−0.612702	+	0.790314i	$0.709917\pi$
$384$	−0.731651	−	1.56993i	−0.0373369	−	0.0801153i
$385$	−1.37800	−	2.07828i	−0.0702292	−	0.105919i
$386$			14.9582i			0.761352i
$387$	6.48322	−	2.35647i	0.329561	−	0.119786i
$388$	−3.49355	−	6.05100i	−0.177358	−	0.307193i
$389$	25.9986	−	15.0103i	1.31818	−	0.761053i	0.334747	−	0.942308i	$-0.391349\pi$
$389$	25.9986	−	15.0103i	1.31818	−	0.761053i	0.983436	+	0.181255i	$0.0580159\pi$
$390$	2.95518	+	0.259200i	0.149641	+	0.0131251i
$391$		−	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
$396$	4.79573	−	8.71786i	0.240994	−	0.438089i
$397$	−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
$399$	24.2994	+	5.46554i	1.21649	+	0.273619i
$400$	4.91924			0.245962
$401$	−12.6464	−	7.30138i	−0.631529	−	0.364614i	0.149815	−	0.988714i	$-0.452132\pi$
$401$	−12.6464	−	7.30138i	−0.631529	−	0.364614i	−0.781344	+	0.624100i	$0.785466\pi$
$402$	8.62912	−	12.3179i	0.430381	−	0.614360i
$403$	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
$408$	−10.7904	−	0.946432i	−0.534204	−	0.0468554i
$409$	−21.6325	+	12.4895i	−1.06966	+	0.617566i	−0.928087	−	0.372362i	$-0.878548\pi$
$409$	−21.6325	+	12.4895i	−1.06966	+	0.617566i	−0.141568	+	0.989928i	$0.545215\pi$
$410$	0.0804052	−	0.0464220i	0.00397093	−	0.00229262i
$411$	−2.55814	+	29.1657i	−0.126184	+	1.43864i
$412$	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
$417$	−17.2084	−	12.0551i	−0.842699	−	0.590341i
$418$	−13.5610	+	11.8759i	−0.663288	+	0.580867i
$419$			35.4041i			1.72960i	0.502113	+	0.864802i	$0.332556\pi$
$419$			35.4041i			1.72960i	−0.502113	+	0.864802i	$0.667444\pi$
$420$	0.387770	+	1.24318i	0.0189213	+	0.0606608i
$421$	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
$423$	−2.12748	+	12.0345i	−0.103442	+	0.585139i
$424$	−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
$429$	31.6776	+	13.9733i	1.52941	+	0.674637i
$430$	−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	$0.992457\pi$
$432$	−3.67666	+	3.67181i	−0.176893	+	0.176660i
$433$	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
$438$	6.23212	+	4.36582i	0.297782	+	0.208607i
$439$	9.43561	+	5.44765i	0.450337	+	0.260002i	0.707973	−	0.706240i	$-0.249610\pi$
$439$	9.43561	+	5.44765i	0.450337	+	0.260002i	−0.257635	+	0.966242i	$0.582943\pi$
$440$	−0.892269	−	0.303581i	−0.0425372	−	0.0144727i
$441$	17.2760	−	11.9390i	0.822667	−	0.568524i
$442$		−	37.6915i		−	1.79280i
$443$	−12.2275	−	7.05956i	−0.580947	−	0.335410i	0.180563	−	0.983563i	$-0.442208\pi$
$443$	−12.2275	−	7.05956i	−0.580947	−	0.335410i	−0.761510	+	0.648154i	$0.775541\pi$
$444$	−11.0748	+	15.8090i	−0.525586	+	0.750263i
$445$	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	$0.314490\pi$
$449$			35.3836i			1.66985i	−0.550361	+	0.834927i	$0.685510\pi$
$450$	−5.04133	−	13.8700i	−0.237651	−	0.653836i
$451$	1.06292	−	0.210654i	0.0500508	−	0.00991930i
$452$	−10.6248	+	6.13423i	−0.499749	+	0.288530i
$453$	0.261907	−	2.98604i	0.0123055	−	0.140296i
$454$	−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	0.429115	−	0.903250i	$-0.358826\pi$
$457$	−2.96219	−	1.71022i	−0.138565	−	0.0800007i	−0.567680	+	0.823249i	$0.692159\pi$
$458$	6.22490	+	10.7818i	0.290871	+	0.503803i
$459$	8.38971	+	31.3938i	0.391598	+	1.46534i
$460$	−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	$0.598298\pi$
$462$	−0.388954	+	15.1937i	−0.0180958	+	0.706875i
$463$	−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
$465$	2.93788	+	2.05809i	0.136241	+	0.0954417i
$466$	−9.19303	−	15.9228i	−0.425859	−	0.737609i
$467$	5.31873	+	3.07077i	0.246122	+	0.142098i	0.617987	−	0.786188i	$-0.287948\pi$
$467$	5.31873	+	3.07077i	0.246122	+	0.142098i	−0.371865	+	0.928287i	$0.621282\pi$
$468$	−13.8458	−	11.6284i	−0.640021	−	0.537522i
$469$	−3.06370	+	22.7683i	−0.141469	+	1.05134i
$470$	1.15764			0.0533981
$471$	19.2228	+	1.68605i	0.885742	+	0.0776889i
$472$	8.38305	−	4.83996i	0.385861	−	0.222777i
$473$	−1.48257	−	7.48074i	−0.0681685	−	0.343965i
$474$	−0.809548	+	9.22976i	−0.0371838	+	0.423937i
$475$			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	$0.780257\pi$
$480$	0.403128	+	0.282406i	0.0184002	+	0.0128900i
$481$	−58.1674	−	33.5830i	−2.65221	−	1.53125i
$482$			8.80236i			0.400937i
$483$	8.03222	+	1.80665i	0.365479	+	0.0822054i
$484$	−8.71750	−	6.70859i	−0.396250	−	0.304936i
$485$	1.71954	+	0.992777i	0.0780803	+	0.0450797i
$486$	14.1207	+	6.60352i	0.640527	+	0.299542i
$487$	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	$0.800744\pi$
$492$	−0.563722	−	0.0494444i	−0.0254146	−	0.00222913i
$493$	1.35846	+	2.35292i	0.0611820	+	0.105970i
$494$	16.3785	+	28.3684i	0.736905	+	1.27636i
$495$	0.0584568	+	2.82689i	0.00262744	+	0.127059i
$496$	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
$501$	−19.0204	+	27.1512i	−0.849767	+	1.21302i
$502$	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	$0.518833\pi$
$504$	2.41173	−	7.56198i	0.107427	−	0.336837i
$505$			3.12872i			0.139226i
$506$	−4.48261	+	3.92559i	−0.199276	+	0.174514i
$507$	23.1798	−	33.0886i	1.02945	−	1.46952i
$508$	4.81171	−	2.77804i	0.213485	−	0.123256i
$509$	10.6064	+	6.12359i	0.470119	+	0.271423i	0.716289	−	0.697803i	$-0.245839\pi$
$509$	10.6064	+	6.12359i	0.470119	+	0.271423i	−0.246171	+	0.969226i	$0.579172\pi$
$510$	2.79002	−	1.30026i	0.123544	−	0.0575764i
$511$	−11.5194	−	1.55005i	−0.509589	−	0.0685703i
$512$	1.00000			0.0441942
$513$	−19.9564	−	19.9828i	−0.881096	−	0.882261i
$514$	7.60623	−	4.39146i	0.335497	−	0.193699i
$515$	−1.90774	+	1.10144i	−0.0840652	+	0.0485351i
$516$	−0.347987	+	3.96744i	−0.0153193	+	0.174657i
$517$	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	−0.466381	−	0.884584i	$-0.654442\pi$
$521$	1.51792	−	0.876371i	0.0665012	−	0.0383945i	0.532882	+	0.846190i	$0.321109\pi$
$522$	1.28344	+	0.226888i	0.0561746	+	0.00993060i
$523$	10.9425	+	6.31768i	0.478484	+	0.276253i	0.719784	−	0.694198i	$-0.244241\pi$
$523$	10.9425	+	6.31768i	0.478484	+	0.276253i	−0.241301	+	0.970450i	$0.577574\pi$
$524$	−18.8874			−0.825099
$525$	16.5734	+	15.2808i	0.723321	+	0.666908i
$526$	−7.87749			−0.343475
$527$	22.7878	−	39.4696i	0.992653	−	1.71932i
$528$	3.39255	+	4.63580i	0.147642	+	0.201747i
$529$	−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
$534$	2.59187	−	29.5503i	0.112161	−	1.27876i
$535$	−3.60520	+	2.08146i	−0.155866	+	0.0899895i
$536$	4.34158	+	7.51984i	0.187528	+	0.324808i
$537$	1.37016	−	15.6214i	0.0591269	−	0.674114i
$538$		−	6.04971i		−	0.260822i
$539$	−10.1346	−	20.8876i	−0.436527	−	0.899691i
$540$	0.383118	−	1.42605i	0.0164868	−	0.0613672i
$541$	28.9602	+	16.7202i	1.24510	+	0.718856i	0.970127	−	0.242597i	$-0.0779992\pi$
$541$	28.9602	+	16.7202i	1.24510	+	0.718856i	0.274969	+	0.961453i	$0.411333\pi$
$542$	−0.886543	+	0.511846i	−0.0380803	+	0.0219857i
$543$	−21.0630	+	30.0669i	−0.903898	+	1.29030i
$544$	3.12688	−	5.41591i	0.134064	−	0.232205i
$545$	4.52336			0.193759
$546$	26.9461	+	6.06085i	1.15318	+	0.259380i
$547$		−	18.9288i		−	0.809336i	−0.914464	−	0.404668i	$-0.867387\pi$
$547$		−	18.9288i		−	0.809336i	0.914464	−	0.404668i	$-0.132613\pi$
$548$	−14.6388	−	8.45173i	−0.625340	−	0.361040i
$549$	2.03725	−	11.5241i	0.0869476	−	0.491838i
$550$	−16.0040	+	3.17175i	−0.682414	+	0.135244i
$551$	−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
$555$	0.479270	−	5.46422i	0.0203439	−	0.231943i
$556$	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	$0.946834\pi$
$558$	−7.46859	−	20.5479i	−0.316171	−	0.869863i
$559$	−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	$-0.367788\pi$
$564$	−5.77894	−	4.04835i	−0.243337	−	0.170466i
$565$	1.74319	−	3.01930i	0.0733366	−	0.127023i
$566$		−	14.1564i		−	0.595038i
$567$	−23.7928	+	0.949727i	−0.999204	+	0.0398848i
$568$			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	$-0.0308696\pi$
$570$	−1.53488	+	2.19101i	−0.0642892	+	0.0917715i
$571$	−1.71070	+	0.987670i	−0.0715904	+	0.0413327i	−0.535368	−	0.844619i	$-0.679827\pi$
$571$	−1.71070	+	0.987670i	−0.0715904	+	0.0413327i	0.463778	+	0.885952i	$0.346494\pi$
$572$	−15.0380	+	13.1694i	−0.628771	+	0.550639i
$573$	19.5419	−	9.10731i	0.816375	−	0.380463i
$574$	0.799549	−	0.328511i	0.0333725	−	0.0137118i
$575$			8.83774i			0.368559i
$576$	−1.02482	−	2.81953i	−0.0427008	−	0.117480i
$577$	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
$579$	−2.26375	+	25.8093i	−0.0940781	+	1.07260i
$580$		−	0.123458i		−	0.00512633i
$581$	3.37691	+	2.60656i	0.140098	+	0.108138i
$582$	−5.11211	−	10.9693i	−0.211904	−	0.454691i
$583$	4.79520	−	4.19934i	0.198597	−	0.173919i
$584$	−3.80459	+	2.19658i	−0.157435	+	0.0908953i
$585$	5.05972	+	0.894463i	0.209194	+	0.0369815i
$586$	2.87941	−	4.98728i	0.118947	−	0.206023i
$587$			13.5713i			0.560148i	0.959978	+	0.280074i	$0.0903590\pi$
$587$			13.5713i			0.560148i	−0.959978	+	0.280074i	$0.909641\pi$
$588$	2.03448	+	11.9524i	0.0839006	+	0.492910i
$589$			39.6090i			1.63206i
$590$	−1.37539	+	2.38225i	−0.0566239	+	0.0980756i
$591$	8.19501	−	11.6982i	0.337098	−	0.481200i
$592$	−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
$597$	−24.6196	−	2.15940i	−1.00761	−	0.0883782i
$598$	5.41396	+	9.37726i	0.221393	+	0.383465i
$599$	24.6430	−	14.2276i	1.00688	−	0.581325i	0.0966066	−	0.995323i	$-0.469201\pi$
$599$	24.6430	−	14.2276i	1.00688	−	0.581325i	0.910278	+	0.413998i	$0.135868\pi$
$600$	8.48780	+	0.744470i	0.346513	+	0.0303928i
$601$			4.98600i			0.203383i	0.994816	+	0.101692i	$0.0324255\pi$
$601$			4.98600i			0.203383i	−0.994816	+	0.101692i	$0.967575\pi$
$602$	−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
$605$	3.09860	+	0.412354i	0.125976	+	0.0167646i
$606$	10.9414	−	15.6186i	0.444462	−	0.634460i
$607$	5.30947	+	3.06542i	0.215505	+	0.124422i	0.603867	−	0.797085i	$-0.293626\pi$
$607$	5.30947	+	3.06542i	0.215505	+	0.124422i	−0.388362	+	0.921507i	$0.626959\pi$
$608$			5.43503i			0.220420i
$609$	−1.90057	+	0.592824i	−0.0770150	+	0.0240225i
$610$	−1.10855			−0.0448837
$611$	12.2762	−	21.2629i	0.496640	−	0.860206i
$612$	−18.4748	−	3.26600i	−0.746800	−	0.132020i
$613$	−18.9061	+	10.9154i	−0.763609	+	0.440870i	−0.830590	−	0.556884i	$-0.811997\pi$
$613$	−18.9061	+	10.9154i	−0.763609	+	0.440870i	0.0669808	+	0.997754i	$0.478663\pi$
$614$	−9.16339	−	5.29048i	−0.369804	−	0.213507i
$615$	0.145759	−	0.0679293i	0.00587756	−	0.00273917i
$616$	−7.85617	−	3.90904i	−0.316534	−	0.157500i
$617$		−	8.66345i		−	0.348777i	−0.984677	−	0.174389i	$-0.944205\pi$
$617$		−	8.66345i		−	0.348777i	0.984677	−	0.174389i	$-0.0557949\pi$
$618$	13.3752	+	1.17315i	0.538030	+	0.0471909i
$619$	−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
$621$	−6.59664	−	6.60536i	−0.264714	−	0.265064i
$622$			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
$627$	−25.1957	+	18.4386i	−1.00622	+	0.736368i
$628$	−5.57046	+	9.64832i	−0.222286	+	0.385010i
$629$	−69.6928			−2.77883
$630$	0.480929	+	2.20370i	0.0191607	+	0.0877973i
$631$	−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
$633$	23.7427	+	16.6326i	0.943689	+	0.661088i
$634$	−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
$639$	10.9521	−	3.98077i	0.433258	−	0.157477i
$640$	−0.246102	+	0.142087i	−0.00972804	+	0.00561649i
$641$	6.94573	−	4.01012i	0.274340	−	0.158390i	−0.356518	−	0.934288i	$-0.616036\pi$
$641$	6.94573	−	4.01012i	0.274340	−	0.158390i	0.630858	+	0.775898i	$0.282703\pi$
$642$	25.2761	+	2.21698i	0.997569	+	0.0874974i
$643$	−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	−0.937274	−	0.348593i	$-0.886660\pi$
$647$	−28.0821	+	16.2132i	−1.10402	+	0.637407i	−0.166747	+	0.986000i	$0.553326\pi$
$648$	−6.89949	+	5.77901i	−0.271038	+	0.227021i
$649$	−24.1524	+	21.1512i	−0.948063	+	0.830255i
$650$			29.6484i			1.16291i
$651$	24.5529	+	22.6380i	0.962306	+	0.887254i
$652$	−0.831773			−0.0325748
$653$	−27.2177	−	15.7141i	−1.06511	−	0.614942i	−0.138269	−	0.990395i	$-0.544154\pi$
$653$	−27.2177	−	15.7141i	−1.06511	−	0.614942i	−0.926842	+	0.375453i	$0.877487\pi$
$654$	−22.5805	−	15.8185i	−0.882969	−	0.618551i
$655$	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	$0.366098\pi$
$660$	−1.49360	−	0.658842i	−0.0581383	−	0.0256454i
$661$	−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
$663$	5.70416	−	65.0339i	0.221531	−	2.52571i
$664$	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
$669$	−1.08094	+	1.54302i	−0.0417915	+	0.0596565i
$670$	−2.13695	−	1.23377i	−0.0825574	−	0.0476645i
$671$	−12.2484	−	4.16735i	−0.472845	−	0.160879i
$672$	3.36909	+	3.10633i	0.129965	+	0.119829i
$673$		−	38.4311i		−	1.48141i	−0.671829	−	0.740706i	$-0.734491\pi$
$673$		−	38.4311i		−	1.48141i	0.671829	−	0.740706i	$-0.265509\pi$
$674$	6.16319	+	3.55832i	0.237397	+	0.137061i
$675$	−6.59940	−	24.6945i	−0.254011	−	0.950493i
$676$	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
$681$	−15.4718	−	1.35704i	−0.592879	−	0.0520018i
$682$	−23.7095	+	4.69885i	−0.907883	+	0.179928i
$683$	−22.5996	+	13.0479i	−0.864751	+	0.499264i	−0.865600	−	0.500735i	$-0.833063\pi$
$683$	−22.5996	+	13.0479i	−0.864751	+	0.499264i	0.000849280		1.00000i	$0.499730\pi$
$684$	15.3242	−	5.56992i	0.585937	−	0.212971i
$685$	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
$690$	−0.507360	+	0.724245i	−0.0193149	+	0.0275715i
$691$	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
$693$	−2.97050	+	26.1568i	−0.112840	+	0.993613i
$694$	1.00232			0.0380475
$695$	−1.72360	+	2.98537i	−0.0653799	+	0.113241i
$696$	−0.431742	+	0.616303i	−0.0163651	+	0.0233609i
$697$	−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	$0.602032\pi$
$702$	−22.1300	−	22.1593i	−0.835245	−	0.836349i
$703$	52.4541	−	30.2844i	1.97835	−	1.14220i
$704$	−3.25335	+	0.644763i	−0.122615	+	0.0243004i
$705$	1.99743	+	0.175196i	0.0752275	+	0.00659825i
$706$		−	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
$711$	−2.79363	+	15.8028i	−0.104769	+	0.592650i
$712$	14.8319	+	8.56318i	0.555847	+	0.320919i
$713$			13.0929i			0.490331i
$714$	27.3583	−	8.53358i	1.02386	−	0.319361i
$715$	1.82969	−	5.37772i	0.0684266	−	0.201115i
$716$	7.84070	+	4.52683i	0.293021	+	0.169176i
$717$	−24.6848	+	35.2371i	−0.921872	+	1.31595i
$718$	5.21329	+	9.02968i	0.194558	+	0.336985i
$719$	13.2458	+	7.64744i	0.493983	+	0.285201i	0.726225	−	0.687457i	$-0.241273\pi$
$719$	13.2458	+	7.64744i	0.493983	+	0.285201i	−0.232242	+	0.972658i	$0.574606\pi$
$720$	0.652829	+	0.548279i	0.0243295	+	0.0204331i
$721$	−18.9706	+	7.79445i	−0.706501	+	0.290280i
$722$	−10.5396			−0.392243
$723$	−1.33213	+	15.1878i	−0.0495426	+	0.564841i
$724$	−10.5974	−	18.3553i	−0.393851	−	0.682169i
$725$	−1.06857	−	1.85082i	−0.0396858	−	0.0687379i
$726$	−14.0261	−	12.8945i	−0.520559	−	0.478559i
$727$	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
$732$	5.53385	+	3.87666i	0.204537	+	0.143285i
$733$	20.6665	+	11.9318i	0.763336	+	0.440712i	0.830492	−	0.557030i	$-0.188059\pi$
$733$	20.6665	+	11.9318i	0.763336	+	0.440712i	−0.0671561	+	0.997742i	$0.521393\pi$
$734$	−1.60455			−0.0592251
$735$	−2.19898	−	2.65245i	−0.0811105	−	0.0978370i
$736$			1.79656i			0.0662222i
$737$	−18.9732	−	21.6654i	−0.698887	−	0.798054i
$738$	−0.965179	−	0.170625i	−0.0355287	−	0.00628081i
$739$	13.0082	−	7.51031i	0.478516	−	0.276271i	−0.241282	−	0.970455i	$-0.577568\pi$
$739$	13.0082	−	7.51031i	0.478516	−	0.276271i	0.719798	+	0.694184i	$0.244235\pi$
$740$	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	$0.679633\pi$
$744$	12.5744	+	1.10291i	0.461001	+	0.0404346i
$745$	−2.92365	+	1.68797i	−0.107114	+	0.0618423i
$746$	−0.443041	+	0.255790i	−0.0162209	+	0.00936513i
$747$	−1.65237	−	4.54607i	−0.0604569	−	0.166332i
$748$	−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
$753$	19.8909	+	13.9343i	0.724866	+	0.507794i
$754$	−2.26761	−	1.30921i	−0.0825816	−	0.0476785i
$755$	−0.491795			−0.0178982
$756$	5.30567	−	12.6827i	0.192965	−	0.461264i
$757$	−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
$759$	−8.32851	+	6.09493i	−0.302306	+	0.221232i
$760$	−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
$765$	5.01075	−	1.82126i	0.181164	−	0.0658479i
$766$	4.59160	−	2.65096i	0.165901	−	0.0957832i
$767$	29.1705	+	50.5248i	1.05329	+	1.82434i
$768$	1.72543	+	0.151338i	0.0622610	+	0.00546095i
$769$		−	5.30858i		−	0.191432i	−0.995409	−	0.0957161i	$-0.969486\pi$
$769$		−	5.30858i		−	0.191432i	0.995409	−	0.0957161i	$-0.0305141\pi$
$770$	2.48884	−	0.154238i	0.0896917	−	0.00555835i
$771$	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	−0.909174	−	0.416415i	$-0.863286\pi$
$773$	−27.8900	+	16.1023i	−1.00314	+	0.579160i	−0.0939608	+	0.995576i	$0.529953\pi$
$774$	−1.20085	+	6.79287i	−0.0431637	+	0.244165i
$775$	−17.9250	+	31.0471i	−0.643886	+	1.11524i
$776$	6.98710			0.250822
$777$	11.2067	−	49.8241i	0.402038	−	1.78743i
$778$			30.0206i			1.07629i
$779$	1.53781	+	0.887853i	0.0550976	+	0.0318106i
$780$	−1.70206	+	2.42966i	−0.0609436	+	0.0869958i
$781$	−2.50450	−	12.6372i	−0.0896179	−	0.452194i
$782$	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
$786$	−32.5888	−	2.85838i	−1.16240	−	0.101955i
$787$	25.9819	−	15.0006i	0.926153	−	0.534715i	0.0405602	−	0.999177i	$-0.487086\pi$
$787$	25.9819	−	15.0006i	0.926153	−	0.534715i	0.885593	+	0.464462i	$0.153752\pi$
$788$	4.12317	+	7.14153i	0.146882	+	0.254407i
$789$	−13.5920	−	1.19216i	−0.483889	−	0.0424422i
$790$	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
$795$	0.542740	−	0.774749i	0.0192490	−	0.0274775i
$796$	7.13434	−	12.3570i	0.252870	−	0.437984i
$797$		−	35.9024i		−	1.27173i	−0.771802	−	0.635864i	$-0.780644\pi$
$797$		−	35.9024i		−	1.27173i	0.771802	−	0.635864i	$-0.219356\pi$
$798$	−16.8830	+	18.3111i	−0.597651	+	0.648206i
$799$		−	25.4760i		−	0.901276i
$800$	−2.45962	+	4.26019i	−0.0869608	+	0.150621i
$801$	8.94416	−	50.5946i	0.316027	−	1.78767i
$802$	12.6464	−	7.30138i	0.446559	−	0.257821i
$803$	10.9614	−	9.59931i	0.386819	−	0.338752i
$804$	6.35304	+	13.6320i	0.224055	+	0.480763i
$805$	0.180134	−	1.33869i	0.00634889	−	0.0471826i
$806$			43.9232i			1.54713i
$807$	0.915552	−	10.4383i	0.0322290	−	0.367447i
$808$	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	$0.538386\pi$
$810$	0.876857	−	2.40256i	0.0308096	−	0.0844172i
$811$			15.4966i			0.544160i	0.962275	+	0.272080i	$0.0877115\pi$
$811$			15.4966i			0.544160i	−0.962275	+	0.272080i	$0.912288\pi$
$812$	0.153287	−	1.13917i	0.00537931	−	0.0399770i
$813$	−1.60713	+	0.748985i	−0.0563644	+	0.0262680i
$814$	24.3506	+	27.8058i	0.853488	+	0.974592i
$815$	0.204701	−	0.118184i	0.00717037	−	0.00413982i
$816$	6.21483	−	8.87154i	0.217563	−	0.310566i
$817$	6.24865	−	10.8230i	0.218613	−	0.378648i
$818$		−	24.9790i		−	0.873370i
$819$	45.5762	+	14.5355i	1.59256	+	0.507912i
$820$			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	$-0.0719120\pi$
$822$	−23.9792	−	16.7983i	−0.836369	−	0.585906i
$823$	−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	$0.482270\pi$
$828$	5.06547	−	1.84115i	0.176037	−	0.0639845i
$829$	−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
$831$	0.125304	−	1.42860i	0.00434674	−	0.0495577i
$832$			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
$836$	−3.50431	−	17.6821i	−0.121199	−	0.611547i
$837$	−9.77681	−	36.5842i	−0.337936	−	1.26454i
$838$	−30.6609	−	17.7021i	−1.05916	−	0.611507i
$839$		−	22.7217i		−	0.784439i	−0.919872	−	0.392220i	$-0.871707\pi$
$839$		−	22.7217i		−	0.784439i	0.919872	−	0.392220i	$-0.128293\pi$
$840$	−1.27051	−	0.285769i	−0.0438367	−	0.00985998i
$841$	−28.8113			−0.993492
$842$	−0.438979	+	0.760334i	−0.0151282	+	0.0262028i
$843$	21.5927	−	30.8231i	0.743691	−	1.06160i
$844$	−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
$847$	28.0793	+	7.65210i	0.964815	+	0.262929i
$848$		−	1.92185i		−	0.0659964i
$849$	2.14241	−	24.4259i	0.0735272	−	0.838293i
$850$	15.3819	+	26.6422i	0.527594	+	0.913820i
$851$	17.3388	−	10.0106i	0.594368	−	0.343159i
$852$	−0.587853	+	6.70219i	−0.0201395	+	0.229613i
$853$		−	21.8003i		−	0.746428i	−0.927745	−	0.373214i	$-0.878256\pi$
$853$		−	21.8003i		−	0.746428i	0.927745	−	0.373214i	$-0.121744\pi$
$854$	−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	$0.992732\pi$
$858$	−27.9400	+	20.4470i	−0.953857	+	0.698048i
$859$	−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
$861$	1.42928	−	0.445819i	0.0487097	−	0.0151935i
$862$	19.9026			0.677886
$863$	11.3331	+	6.54315i	0.385782	+	0.222731i	0.680331	−	0.732905i	$-0.261836\pi$
$863$	11.3331	+	6.54315i	0.385782	+	0.222731i	−0.294549	+	0.955636i	$0.595169\pi$
$864$	−1.34155	−	5.01999i	−0.0456404	−	0.170783i
$865$	−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
$870$	0.0186840	−	0.213018i	0.000633446	−	0.00722200i
$871$	−45.3222	+	26.1668i	−1.53569	+	0.886628i
$872$	13.7850	−	7.95877i	0.466819	−	0.269518i
$873$	−7.16051	−	19.7003i	−0.242346	−	0.666755i
$874$	−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	0.891484	−	0.453052i	$-0.149665\pi$
$877$	27.9816	+	16.1552i	0.944872	+	0.545522i	0.0533875	+	0.998574i	$0.482998\pi$
$878$	−9.43561	+	5.44765i	−0.318436	+	0.183849i
$879$	5.72297	−	8.16942i	0.193031	−	0.275548i
$880$	0.709044	−	0.620937i	0.0239019	−	0.0209318i
$881$		−	16.1735i		−	0.544899i	−0.962170	−	0.272450i	$-0.912166\pi$
$881$		−	16.1735i		−	0.544899i	0.962170	−	0.272450i	$-0.0878338\pi$
$882$	1.70149	+	20.9310i	0.0572920	+	0.704782i
$883$	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
$885$	−2.73366	+	3.90224i	−0.0918910	+	0.131172i
$886$	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
$891$	18.7204	−	23.2497i	0.627156	−	0.778894i
$892$	−0.543854	−	0.941983i	−0.0182096	−	0.0315399i
$893$	11.0704	+	19.1745i	0.370456	+	0.641649i
$894$	20.4977	+	1.79787i	0.685547	+	0.0601297i
$895$	−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
$900$	14.5324	+	2.56905i	0.484413	+	0.0856352i
$901$	−10.4085	−	6.00938i	−0.346759	−	0.200201i
$902$	−0.349027	+	1.02584i	−0.0116213	+	0.0341567i
$903$	−3.13765	−	10.0592i	−0.104414	−	0.334748i
$904$		−	12.2685i		−	0.408043i
$905$	5.21610	+	3.01152i	0.173389	+	0.100106i
$906$	2.45503	+	1.71984i	0.0815630	+	0.0571378i
$907$	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	$-0.876829\pi$
$911$		−	22.7800i		−	0.754734i	0.926064	−	0.377367i	$-0.123171\pi$
$912$	−0.822528	+	9.37775i	−0.0272366	+	0.310528i
$913$	−5.24554	+	1.03958i	−0.173602	+	0.0344052i
$914$	2.96219	−	1.71022i	0.0979805	−	0.0565690i
$915$	−1.91271	−	0.167765i	−0.0632324	−	0.00554615i
$916$	−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	−0.0147535	−	0.999891i	$-0.504696\pi$
$919$	−26.9216	−	15.5432i	−0.888061	−	0.512722i	−0.873308	+	0.487169i	$0.838030\pi$
$920$	−0.255269	−	0.442138i	−0.00841596	−	0.0145769i
$921$	−15.0101	−	10.5151i	−0.494600	−	0.346485i
$922$	6.52560	−	11.3027i	0.214909	−	0.372234i
$923$	−23.4111			−0.770587
$924$	−12.9637	−	7.93370i	−0.426473	−	0.260999i
$925$	54.8208			1.80250
$926$	9.04932	−	15.6739i	0.297379	−	0.515076i
$927$	22.9004	+	4.04836i	0.752148	+	0.132966i
$928$	−0.217223	−	0.376241i	−0.00713070	−	0.0123507i
$929$	9.05995	+	5.23076i	0.297247	+	0.171616i	0.641206	−	0.767369i	$-0.278435\pi$
$929$	9.05995	+	5.23076i	0.297247	+	0.171616i	−0.343958	+	0.938985i	$0.611768\pi$
$930$	−3.25130	+	1.51523i	−0.106614	+	0.0496865i
$931$	10.0567	−	36.6920i	0.329593	−	1.20253i
$932$	18.3861			0.602255
$933$	−1.03180	+	11.7637i	−0.0337796	+	0.385126i
$934$	−5.31873	+	3.07077i	−0.174034	+	0.100479i
$935$	−1.14585	−	5.78171i	−0.0374732	−	0.189082i
$936$	16.9934	−	6.17660i	0.555445	−	0.201889i
$937$		−	27.1309i		−	0.886328i	−0.896441	−	0.443164i	$-0.853856\pi$
$937$		−	27.1309i		−	0.886328i	0.896441	−	0.443164i	$-0.146144\pi$
$938$	−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	$0.937909\pi$
$942$	−11.0716	+	15.8044i	−0.360732	+	0.514937i
$943$	0.508326	+	0.293482i	0.0165534	+	0.00955709i
$944$			9.67991i			0.315054i
$945$	0.496305	+	3.87510i	0.0161448	+	0.126057i
$946$	7.21980	+	2.45643i	0.234736	+	0.0798655i
$947$	31.4053	+	18.1318i	1.02053	+	0.589205i	0.914258	−	0.405131i	$-0.132774\pi$
$947$	31.4053	+	18.1318i	1.02053	+	0.589205i	0.106275	+	0.994337i	$0.466108\pi$
$948$	−7.58843	−	5.31597i	−0.246461	−	0.172655i
$949$	−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	$0.281621\pi$
$954$	−5.41870	+	1.96954i	−0.175437	+	0.0637663i
$955$	−1.76865	−	3.06338i	−0.0572320	−	0.0991288i
$956$	−12.4197	−	21.5116i	−0.401683	−	0.695735i
$957$	1.00724	−	2.28342i	0.0325594	−	0.0738125i
$958$	−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
$963$	43.2766	+	7.65049i	1.39457	+	0.246533i
$964$	−7.62307	−	4.40118i	−0.245522	−	0.141752i
$965$	4.25074			0.136836
$966$	−5.58071	+	6.05278i	−0.179556	+	0.194745i
$967$			50.7537i			1.63213i	0.577961	+	0.816064i	$0.303849\pi$
$967$			50.7537i			1.63213i	−0.577961	+	0.816064i	$0.696151\pi$
$968$	10.1686	−	4.19528i	0.326830	−	0.134841i
$969$	48.2171	+	33.7778i	1.54896	+	1.08510i
$970$	−1.71954	+	0.992777i	−0.0552111	+	0.0318761i
$971$	−0.389942	−	0.225133i	−0.0125138	−	0.00722486i	0.493730	−	0.869615i	$-0.335633\pi$
$971$	−0.389942	−	0.225133i	−0.0125138	−	0.00722486i	−0.506244	+	0.862390i	$0.668966\pi$
$972$	−12.7792	+	8.92711i	−0.409892	+	0.286337i
$973$	−19.6106	+	25.4064i	−0.628686	+	0.814491i
$974$	−41.0670			−1.31587
$975$	−4.48693	+	51.1561i	−0.143697	+	1.63831i
$976$	−3.37831	+	1.95047i	−0.108137	+	0.0624330i
$977$	4.01364	−	2.31728i	0.128408	−	0.0741363i	−0.434420	−	0.900710i	$-0.643047\pi$
$977$	4.01364	−	2.31728i	0.128408	−	0.0741363i	0.562828	+	0.826574i	$0.309713\pi$
$978$	−1.43516	−	0.125879i	−0.0458915	−	0.00402517i
$979$	−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	0.0361291	−	0.999347i	$-0.488497\pi$
$983$	28.8337	−	16.6472i	0.919654	−	0.530962i	0.883525	+	0.468385i	$0.155164\pi$
$984$	0.324681	−	0.463476i	0.0103505	−	0.0147751i
$985$	−2.02944	−	1.17170i	−0.0646633	−	0.0373334i
$986$	−2.71692			−0.0865244
$987$	18.2131	+	4.09658i	0.579728	+	0.130395i
$988$	−32.7570			−1.04214
$989$	2.06551	−	3.57756i	0.0656793	−	0.113760i
$990$	−2.47739	−	1.36282i	−0.0787366	−	0.0433133i
$991$	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
$996$	2.78199	+	0.244010i	0.0881507	+	0.00773175i
$997$	−27.9874	+	16.1585i	−0.886368	+	0.511745i	−0.872753	−	0.488162i	$-0.837667\pi$
$997$	−27.9874	+	16.1585i	−0.886368	+	0.511745i	−0.0136154	+	0.999907i	$0.504334\pi$
$998$	6.45040	+	11.1724i	0.204184	+	0.353657i
$999$	−40.9733	+	40.9192i	−1.29634	+	1.29462i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.993776 + 1.41859i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.246102 + 0.142087i) q^{5} +(-0.731651 - 1.56993i) q^{6} +(2.09441 + 1.61662i) q^{7} +1.00000 q^{8} +(-1.02482 - 2.81953i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.993776 + 1.41859i) 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} +(-1.02482 - 2.81953i) q^{9} +(-0.246102 + 0.142087i) q^{10} +(-3.25335 + 0.644763i) q^{11} +(1.72543 + 0.151338i) 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} +(2.95419 + 0.522246i) q^{18} +(-4.70688 - 2.71752i) q^{19} -0.284174i q^{20} +(-4.37470 + 1.36455i) q^{21} +(1.06829 - 3.13986i) q^{22} +(-1.55587 - 0.898282i) q^{23} +(-0.993776 + 1.41859i) 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} +(0.0430064 - 0.490322i) q^{30} +(-3.64386 - 6.31135i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.31844 - 5.25593i) 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} +(-8.54989 - 5.98951i) q^{39} +(0.246102 + 0.142087i) q^{40} -0.326715 q^{41} +(1.00561 - 4.47088i) q^{42} +2.29940i q^{43} +(2.18506 + 2.49510i) q^{44} +(0.148409 - 0.839506i) 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} +(-10.7904 - 0.946432i) q^{51} +(5.21955 - 3.01351i) q^{52} +(-1.66437 + 0.960923i) q^{53} +(-3.67666 + 3.67181i) 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} +(0.403128 + 0.282406i) q^{60} +(3.37831 + 1.95047i) q^{61} +7.28772 q^{62} +(2.41173 - 7.56198i) q^{63} +1.00000 q^{64} +(-0.856362 + 1.48326i) q^{65} +(3.39255 + 4.63580i) 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} +(-1.02482 - 2.81953i) q^{72} +(-3.80459 + 2.19658i) q^{73} +(-5.57207 - 9.65112i) q^{74} +(8.48780 + 0.744470i) q^{75} +5.43503i q^{76} +(-7.85617 - 3.90904i) q^{77} +(9.46201 - 4.40967i) q^{78} +(-4.63260 - 2.67463i) q^{79} +(-0.246102 + 0.142087i) q^{80} +(-6.89949 + 5.77901i) q^{81} +(0.163357 - 0.282943i) q^{82} +1.61235 q^{83} +(3.36909 + 3.10633i) q^{84} +1.77716i q^{85} +(-1.99134 - 1.14970i) q^{86} +(-0.431742 + 0.616303i) q^{87} +(-3.25335 + 0.644763i) q^{88} +(14.8319 + 8.56318i) q^{89} +(0.652829 + 0.548279i) q^{90} +(-9.74341 + 12.6230i) q^{91} +1.79656i q^{92} +(12.5744 + 1.10291i) q^{93} +(3.52794 - 2.03685i) q^{94} +(-0.772248 - 1.33757i) q^{95} +(1.72543 + 0.151338i) 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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