LMFDB - Embedded newform 840.2.dj.a.403.81

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(67,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dj (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			403.81
Character	$\chi$	$=$	840.403
Dual form			840.2.dj.a.667.81

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25560 - 0.650742i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.15307 - 1.63414i) q^{4} +(-2.12053 + 0.709484i) q^{5} +(-1.04439 + 0.953542i) q^{6} +(-0.607466 + 2.57507i) q^{7} +(0.384392 - 2.80219i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.20085 + 2.27074i) q^{10} +(2.35319 - 4.07584i) q^{11} +(-0.690833 + 1.87690i) q^{12} +(1.44964 - 1.44964i) q^{13} +(0.912970 + 3.62857i) q^{14} +(1.86464 - 1.23414i) q^{15} +(-1.34086 - 3.76857i) q^{16} +(-0.672160 - 2.50853i) q^{17} +(0.762012 - 1.19136i) q^{18} +(5.85686 - 3.38146i) q^{19} +(-1.28572 + 4.28333i) q^{20} +(-0.0797100 - 2.64455i) q^{21} +(0.302347 - 6.64895i) q^{22} +(-5.19831 - 1.39288i) q^{23} +(0.353965 + 2.80619i) q^{24} +(3.99326 - 3.00896i) q^{25} +(0.876828 - 2.76351i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(3.50758 + 3.96192i) q^{28} +5.50415 q^{29} +(1.53814 - 2.76299i) q^{30} +(2.13639 + 1.23344i) q^{31} +(-4.13595 - 3.85927i) q^{32} +(-1.21810 + 4.54601i) q^{33} +(-2.47637 - 2.71232i) q^{34} +(-0.538823 - 5.89149i) q^{35} +(0.181516 - 1.99175i) q^{36} +(1.91433 - 7.14437i) q^{37} +(5.15343 - 8.05707i) q^{38} +(-1.02505 + 1.77544i) q^{39} +(1.17299 + 6.21483i) q^{40} -2.96457 q^{41} +(-1.82100 - 3.26863i) q^{42} +(1.62218 + 1.62218i) q^{43} +(-3.94712 - 8.54519i) q^{44} +(-1.48169 + 1.67469i) q^{45} +(-7.43342 + 1.63385i) q^{46} +(-1.30995 + 4.88880i) q^{47} +(2.27054 + 3.29312i) q^{48} +(-6.26197 - 3.12853i) q^{49} +(3.05589 - 6.37664i) q^{50} +(1.29851 + 2.24909i) q^{51} +(-0.697382 - 4.04045i) q^{52} +(-2.34462 - 8.75023i) q^{53} +(-0.427701 + 1.34799i) q^{54} +(-2.09825 + 10.3125i) q^{55} +(6.98232 + 2.69207i) q^{56} +(-4.78211 + 4.78211i) q^{57} +(6.91102 - 3.58178i) q^{58} +(11.4335 + 6.60111i) q^{59} +(0.133300 - 4.47015i) q^{60} +(-8.44371 + 4.87498i) q^{61} +(3.48510 + 0.158478i) q^{62} +(0.761454 + 2.53381i) q^{63} +(-7.70449 - 2.15427i) q^{64} +(-2.04550 + 4.10249i) q^{65} +(1.42883 + 6.50065i) q^{66} +(2.97990 + 11.1212i) q^{67} +(-4.87436 - 1.79411i) q^{68} +5.38169 q^{69} +(-4.51039 - 7.04673i) q^{70} -14.5259i q^{71} +(-1.06820 - 2.61896i) q^{72} +(-12.8678 + 3.44791i) q^{73} +(-2.24551 - 10.2162i) q^{74} +(-3.07842 + 3.93996i) q^{75} +(1.22758 - 13.4700i) q^{76} +(9.06610 + 8.53556i) q^{77} +(-0.131702 + 2.89628i) q^{78} +(6.51800 + 11.2895i) q^{79} +(5.51706 + 7.04003i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-3.72232 + 1.92917i) q^{82} +(-3.03652 - 3.03652i) q^{83} +(-4.41349 - 2.91910i) q^{84} +(3.20510 + 4.84253i) q^{85} +(3.09244 + 0.981193i) q^{86} +(-5.31660 + 1.42458i) q^{87} +(-10.5167 - 8.16079i) q^{88} +(0.0534045 - 0.0308331i) q^{89} +(-0.770616 + 3.06694i) q^{90} +(2.85231 + 4.61352i) q^{91} +(-8.27020 + 6.88870i) q^{92} +(-2.38283 - 0.638477i) q^{93} +(1.53657 + 6.99082i) q^{94} +(-10.0205 + 11.3258i) q^{95} +(4.99387 + 2.65731i) q^{96} +(8.57024 - 8.57024i) q^{97} +(-9.89841 + 0.146731i) q^{98} -4.70638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) $ 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	1.25560	−	0.650742i	0.887844	−	0.460144i
$2$	1.25560	−	0.650742i	0.887844	−	0.460144i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	1.15307	−	1.63414i	0.576535	−	0.817072i
$5$	−2.12053	+	0.709484i	−0.948328	+	0.317291i
$5$	−2.12053	+	0.709484i	−0.948328	+	0.317291i
$6$	−1.04439	+	0.953542i	−0.426372	+	0.389282i
$7$	−0.607466	+	2.57507i	−0.229601	+	0.973285i
$7$	−0.607466	+	2.57507i	−0.229601	+	0.973285i
$8$	0.384392	−	2.80219i	0.135903	−	0.990722i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−2.20085	+	2.27074i	−0.695968	+	0.718072i
$11$	2.35319	−	4.07584i	0.709513	−	1.22891i	−0.255525	−	0.966803i	$-0.582248\pi$
$11$	2.35319	−	4.07584i	0.709513	−	1.22891i	0.965038	−	0.262110i	$-0.0844185\pi$
$12$	−0.690833	+	1.87690i	−0.199426	+	0.541814i
$13$	1.44964	−	1.44964i	0.402057	−	0.402057i	−0.476900	−	0.878957i	$-0.658240\pi$
$13$	1.44964	−	1.44964i	0.402057	−	0.402057i	0.878957	+	0.476900i	$0.158240\pi$
$14$	0.912970	+	3.62857i	0.244001	+	0.969775i
$15$	1.86464	−	1.23414i	0.481449	−	0.318654i
$16$	−1.34086	−	3.76857i	−0.335214	−	0.942142i
$17$	−0.672160	−	2.50853i	−0.163023	−	0.608409i	−0.998284	−	0.0585560i	$-0.981350\pi$
$17$	−0.672160	−	2.50853i	−0.163023	−	0.608409i	0.835261	−	0.549853i	$-0.185316\pi$
$18$	0.762012	−	1.19136i	0.179608	−	0.280806i
$19$	5.85686	−	3.38146i	1.34366	−	0.775760i	0.356314	−	0.934366i	$-0.384033\pi$
$19$	5.85686	−	3.38146i	1.34366	−	0.775760i	0.987342	+	0.158606i	$0.0506999\pi$
$20$	−1.28572	+	4.28333i	−0.287495	+	0.957782i
$21$	−0.0797100	−	2.64455i	−0.0173942	−	0.577088i
$22$	0.302347	−	6.64895i	0.0644606	−	1.41756i
$23$	−5.19831	−	1.39288i	−1.08392	−	0.290436i	−0.327721	−	0.944774i	$-0.606281\pi$
$23$	−5.19831	−	1.39288i	−1.08392	−	0.290436i	−0.756202	+	0.654338i	$0.772947\pi$
$24$	0.353965	+	2.80619i	0.0722529	+	0.572811i
$25$	3.99326	−	3.00896i	0.798653	−	0.601792i
$26$	0.876828	−	2.76351i	0.171960	−	0.541968i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	3.50758	+	3.96192i	0.662871	+	0.748733i
$29$	5.50415			1.02209			0.511047	−	0.859553i	$-0.329258\pi$
$29$	5.50415			1.02209			0.511047	+	0.859553i	$0.329258\pi$
$30$	1.53814	−	2.76299i	0.280825	−	0.504451i
$31$	2.13639	+	1.23344i	0.383706	+	0.221533i	0.679430	−	0.733741i	$-0.262227\pi$
$31$	2.13639	+	1.23344i	0.383706	+	0.221533i	−0.295723	+	0.955274i	$0.595561\pi$
$32$	−4.13595	−	3.85927i	−0.731139	−	0.682229i
$33$	−1.21810	+	4.54601i	−0.212044	+	0.791359i
$34$	−2.47637	−	2.71232i	−0.424694	−	0.465159i
$35$	−0.538823	−	5.89149i	−0.0910777	−	0.995844i
$36$	0.181516	−	1.99175i	0.0302527	−	0.331958i
$37$	1.91433	−	7.14437i	0.314714	−	1.17453i	−0.609542	−	0.792754i	$-0.708647\pi$
$37$	1.91433	−	7.14437i	0.314714	−	1.17453i	0.924256	−	0.381774i	$-0.124687\pi$
$38$	5.15343	−	8.05707i	0.835996	−	1.30703i
$39$	−1.02505	+	1.77544i	−0.164139	+	0.284297i
$40$	1.17299	+	6.21483i	0.185467	+	0.982651i
$41$	−2.96457			−0.462988			−0.231494	−	0.972836i	$-0.574361\pi$
$41$	−2.96457			−0.462988			−0.231494	+	0.972836i	$0.574361\pi$
$42$	−1.82100	−	3.26863i	−0.280987	−	0.504361i
$43$	1.62218	+	1.62218i	0.247380	+	0.247380i	0.819895	−	0.572514i	$-0.194032\pi$
$43$	1.62218	+	1.62218i	0.247380	+	0.247380i	−0.572514	+	0.819895i	$0.694032\pi$
$44$	−3.94712	−	8.54519i	−0.595051	−	1.28824i
$45$	−1.48169	+	1.67469i	−0.220877	+	0.249649i
$46$	−7.43342	+	1.63385i	−1.09600	+	0.240898i
$47$	−1.30995	+	4.88880i	−0.191076	+	0.713104i	0.802172	+	0.597093i	$0.203678\pi$
$47$	−1.30995	+	4.88880i	−0.191076	+	0.713104i	−0.993248	+	0.116011i	$0.962989\pi$
$48$	2.27054	+	3.29312i	0.327725	+	0.475321i
$49$	−6.26197	−	3.12853i	−0.894567	−	0.446934i
$50$	3.05589	−	6.37664i	0.432169	−	0.901793i
$51$	1.29851	+	2.24909i	0.181828	+	0.314936i
$52$	−0.697382	−	4.04045i	−0.0967095	−	0.560310i
$53$	−2.34462	−	8.75023i	−0.322058	−	1.20194i	−0.917237	−	0.398343i	$-0.869585\pi$
$53$	−2.34462	−	8.75023i	−0.322058	−	1.20194i	0.595179	−	0.803593i	$-0.297081\pi$
$54$	−0.427701	+	1.34799i	−0.0582027	+	0.183438i
$55$	−2.09825	+	10.3125i	−0.282929	+	1.39054i
$56$	6.98232	+	2.69207i	0.933052	+	0.359743i
$57$	−4.78211	+	4.78211i	−0.633406	+	0.633406i
$58$	6.91102	−	3.58178i	0.907461	−	0.470311i
$59$	11.4335	+	6.60111i	1.48851	+	0.859392i	0.999914	−	0.0131180i	$-0.00417570\pi$
$59$	11.4335	+	6.60111i	1.48851	+	0.859392i	0.488596	+	0.872510i	$0.337509\pi$
$60$	0.133300	−	4.47015i	0.0172089	−	0.577094i
$61$	−8.44371	+	4.87498i	−1.08111	+	0.624177i	−0.931194	−	0.364523i	$-0.881232\pi$
$61$	−8.44371	+	4.87498i	−1.08111	+	0.624177i	−0.149911	+	0.988699i	$0.547899\pi$
$62$	3.48510	+	0.158478i	0.442609	+	0.0201267i
$63$	0.761454	+	2.53381i	0.0959342	+	0.319230i
$64$	−7.70449	−	2.15427i	−0.963061	−	0.269284i
$65$	−2.04550	+	4.10249i	−0.253713	+	0.508851i
$66$	1.42883	+	6.50065i	0.175877	+	0.800175i
$67$	2.97990	+	11.1212i	0.364053	+	1.35867i	0.868700	+	0.495339i	$0.164956\pi$
$67$	2.97990	+	11.1212i	0.364053	+	1.35867i	−0.504646	+	0.863326i	$0.668377\pi$
$68$	−4.87436	−	1.79411i	−0.591102	−	0.217568i
$69$	5.38169			0.647879
$70$	−4.51039	−	7.04673i	−0.539094	−	0.842245i
$71$		−	14.5259i		−	1.72391i	−0.506984	−	0.861955i	$-0.669240\pi$
$71$		−	14.5259i		−	1.72391i	0.506984	−	0.861955i	$-0.330760\pi$
$72$	−1.06820	−	2.61896i	−0.125889	−	0.308647i
$73$	−12.8678	+	3.44791i	−1.50606	+	0.403547i	−0.915124	−	0.403173i	$-0.867907\pi$
$73$	−12.8678	+	3.44791i	−1.50606	+	0.403547i	−0.590934	+	0.806720i	$0.701241\pi$
$74$	−2.24551	−	10.2162i	−0.261035	−	1.18761i
$75$	−3.07842	+	3.93996i	−0.355466	+	0.454948i
$76$	1.22758	−	13.4700i	0.140813	−	1.54512i
$77$	9.06610	+	8.53556i	1.03318	+	0.972718i
$78$	−0.131702	+	2.89628i	−0.0149124	+	0.327939i
$79$	6.51800	+	11.2895i	0.733332	+	1.27017i	0.955451	+	0.295149i	$0.0953692\pi$
$79$	6.51800	+	11.2895i	0.733332	+	1.27017i	−0.222119	+	0.975020i	$0.571297\pi$
$80$	5.51706	+	7.04003i	0.616826	+	0.787100i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−3.72232	+	1.92917i	−0.411061	+	0.213041i
$83$	−3.03652	−	3.03652i	−0.333301	−	0.333301i	0.520537	−	0.853839i	$-0.325732\pi$
$83$	−3.03652	−	3.03652i	−0.333301	−	0.333301i	−0.853839	+	0.520537i	$0.825732\pi$
$84$	−4.41349	−	2.91910i	−0.481551	−	0.318499i
$85$	3.20510	+	4.84253i	0.347642	+	0.525246i
$86$	3.09244	+	0.981193i	0.333466	+	0.105805i
$87$	−5.31660	+	1.42458i	−0.569999	+	0.152731i
$88$	−10.5167	−	8.16079i	−1.12109	−	0.869943i
$89$	0.0534045	−	0.0308331i	0.00566087	−	0.00326830i	−0.497167	−	0.867655i	$-0.665626\pi$
$89$	0.0534045	−	0.0308331i	0.00566087	−	0.00326830i	0.502828	+	0.864387i	$0.332293\pi$
$90$	−0.770616	+	3.06694i	−0.0812301	+	0.323284i
$91$	2.85231	+	4.61352i	0.299004	+	0.483629i
$92$	−8.27020	+	6.88870i	−0.862228	+	0.718197i
$93$	−2.38283	−	0.638477i	−0.247088	−	0.0662070i
$94$	1.53657	+	6.99082i	0.158485	+	0.721048i
$95$	−10.0205	+	11.3258i	−1.02809	+	1.16201i
$96$	4.99387	+	2.65731i	0.509685	+	0.271210i
$97$	8.57024	−	8.57024i	0.870176	−	0.870176i	−0.122316	−	0.992491i	$-0.539032\pi$
$97$	8.57024	−	8.57024i	0.870176	−	0.870176i	0.992491	+	0.122316i	$0.0390320\pi$
$98$	−9.89841	+	0.146731i	−0.999890	+	0.0148221i
$99$		−	4.70638i		−	0.473009i
$100$	−0.312558	−	9.99511i	−0.0312558	−	0.999511i
$101$	−1.82908	−	1.05602i	−0.182000	−	0.105078i	0.406232	−	0.913770i	$-0.366843\pi$
$101$	−1.82908	−	1.05602i	−0.182000	−	0.105078i	−0.588232	+	0.808692i	$0.700176\pi$
$102$	3.09399	+	1.97897i	0.306351	+	0.195947i
$103$	4.60616	+	1.23422i	0.453858	+	0.121611i	0.478504	−	0.878085i	$-0.341179\pi$
$103$	4.60616	+	1.23422i	0.453858	+	0.121611i	−0.0246459	+	0.999696i	$0.507846\pi$
$104$	−3.50492	−	4.61938i	−0.343686	−	0.452968i
$105$	2.04529	+	5.55129i	0.199600	+	0.541750i
$106$	−8.63804	−	9.46106i	−0.839001	−	0.918939i
$107$	−1.01350	−	0.271567i	−0.0979790	−	0.0262534i	0.209496	−	0.977809i	$-0.432818\pi$
$107$	−1.01350	−	0.271567i	−0.0979790	−	0.0262534i	−0.307475	+	0.951556i	$0.599484\pi$
$108$	0.340171	+	1.97086i	0.0327329	+	0.189646i
$109$	−1.86809	+	3.23562i	−0.178930	+	0.309916i	−0.941514	−	0.336973i	$-0.890597\pi$
$109$	−1.86809	+	3.23562i	−0.178930	+	0.309916i	0.762584	+	0.646889i	$0.223930\pi$
$110$	4.07619	+	14.3138i	0.388650	+	1.36477i
$111$			7.39640i			0.702035i
$112$	10.5189	−	1.16352i	0.993938	−	0.109942i
$113$	0.228114	+	0.228114i	0.0214591	+	0.0214591i	0.717755	−	0.696296i	$-0.245170\pi$
$113$	0.228114	+	0.228114i	0.0214591	+	0.0214591i	−0.696296	+	0.717755i	$0.745170\pi$
$114$	−2.89251	+	9.11634i	−0.270908	+	0.853823i
$115$	12.0114	−	0.734473i	1.12007	−	0.0684900i
$116$	6.34667	−	8.99457i	0.589274	−	0.835125i
$117$	0.530604	−	1.98024i	0.0490544	−	0.183073i
$118$	18.6515	+	0.848138i	1.71701	+	0.0780774i
$119$	6.86797	−	0.207009i	0.629585	−	0.0189765i
$120$	−2.74154	−	5.69947i	−0.250267	−	0.520288i
$121$	−5.57500	−	9.65618i	−0.506818	−	0.877835i
$122$	−7.42958	+	11.6157i	−0.672643	+	1.05164i
$123$	2.86355	−	0.767287i	0.258198	−	0.0691839i
$124$	4.47903	−	2.06892i	0.402229	−	0.185794i
$125$	−6.33302	+	9.21374i	−0.566442	+	0.824102i
$126$	2.60494	+	2.68594i	0.232066	+	0.239283i
$127$	11.7532	+	11.7532i	1.04293	+	1.04293i	0.999036	+	0.0438900i	$0.0139751\pi$
$127$	11.7532	+	11.7532i	1.04293	+	1.04293i	0.0438900	+	0.999036i	$0.486025\pi$
$128$	−11.0756	+	2.30872i	−0.978958	+	0.204064i
$129$	−1.98676	−	1.14706i	−0.174924	−	0.100993i
$130$	0.101328	+	6.48218i	0.00888701	+	0.568525i
$131$	−2.27304	−	3.93702i	−0.198596	−	0.343979i	0.749477	−	0.662030i	$-0.230305\pi$
$131$	−2.27304	−	3.93702i	−0.198596	−	0.343979i	−0.948073	+	0.318051i	$0.896972\pi$
$132$	6.02429	+	7.23243i	0.524347	+	0.629502i
$133$	5.14965	+	17.1360i	0.446532	+	1.48588i
$134$	10.9786	+	12.0246i	0.948404	+	1.03877i
$135$	0.997758	−	2.00112i	0.0858733	−	0.172229i
$136$	−7.28775	+	0.919257i	−0.624920	+	0.0788256i
$137$	1.51625	+	5.65872i	0.129542	+	0.483457i	0.999961	−	0.00885501i	$-0.00281867\pi$
$137$	1.51625	+	5.65872i	0.129542	+	0.483457i	−0.870419	+	0.492312i	$0.836152\pi$
$138$	6.75726	−	3.50209i	0.575216	−	0.298118i
$139$		−	20.8393i		−	1.76757i	−0.467896	−	0.883784i	$-0.654988\pi$
$139$		−	20.8393i		−	1.76757i	0.467896	−	0.883784i	$-0.345012\pi$
$140$	−10.2488	−	5.91279i	−0.866186	−	0.499722i
$141$		−	5.06125i		−	0.426234i
$142$	−9.45263	−	18.2388i	−0.793247	−	1.53056i
$143$	−2.49722	−	9.31976i	−0.208828	−	0.779358i
$144$	−3.04550	−	2.59325i	−0.253792	−	0.216104i
$145$	−11.6717	+	3.90511i	−0.969281	+	0.324301i
$146$	−13.9131	+	12.7028i	−1.15146	+	1.05129i
$147$	6.85832	+	1.40122i	0.565665	+	0.115570i
$148$	−9.46758	−	11.3663i	−0.778230	−	0.934301i
$149$	−3.15549	−	5.46546i	−0.258507	−	0.447748i	0.707335	−	0.706879i	$-0.249897\pi$
$149$	−3.15549	−	5.46546i	−0.258507	−	0.447748i	−0.965842	+	0.259131i	$0.916564\pi$
$150$	−1.30137	+	6.95028i	−0.106257	+	0.567488i
$151$	15.5775	+	8.99367i	1.26768	+	0.731895i	0.974548	−	0.224178i	$-0.0719696\pi$
$151$	15.5775	+	8.99367i	1.26768	+	0.731895i	0.293130	+	0.956072i	$0.405303\pi$
$152$	−7.22415	−	17.7118i	−0.585956	−	1.43662i
$153$	−1.83637	−	1.83637i	−0.148462	−	0.148462i
$154$	16.9379	+	4.81758i	1.36489	+	0.388212i
$155$	−5.40537	−	1.09982i	−0.434170	−	0.0883394i
$156$	1.71937	+	3.72228i	0.137659	+	0.298021i
$157$	13.8871	−	3.72103i	1.10831	−	0.296970i	0.342165	−	0.939640i	$-0.388840\pi$
$157$	13.8871	−	3.72103i	1.10831	−	0.296970i	0.766143	+	0.642670i	$0.222173\pi$
$158$	15.5306	+	9.93359i	1.23554	+	0.790274i
$159$	4.52945	+	7.84524i	0.359209	+	0.622168i
$160$	11.5085	+	5.24930i	0.909825	+	0.414993i
$161$	6.74457	−	12.5399i	0.531547	−	0.988282i
$162$	0.0642420	−	1.41275i	0.00504733	−	0.110996i
$163$	−5.05628	+	18.8703i	−0.396039	+	1.47804i	0.423965	+	0.905679i	$0.360638\pi$
$163$	−5.05628	+	18.8703i	−0.396039	+	1.47804i	−0.820004	+	0.572358i	$0.806029\pi$
$164$	−3.41836	+	4.84453i	−0.266929	+	0.378294i
$165$	−0.642309	−	10.5042i	−0.0500037	−	0.817748i
$166$	−5.78865	−	1.83667i	−0.449286	−	0.142553i
$167$	−2.13748	−	2.13748i	−0.165403	−	0.165403i	0.619552	−	0.784955i	$-0.287314\pi$
$167$	−2.13748	−	2.13748i	−0.165403	−	0.165403i	−0.784955	+	0.619552i	$0.787314\pi$
$168$	−7.44116	−	0.793181i	−0.574098	−	0.0611952i
$169$			8.79710i			0.676700i
$170$	7.17556	+	3.99459i	0.550340	+	0.306371i
$171$	3.38146	−	5.85686i	0.258587	−	0.447885i
$172$	4.52137	−	0.780389i	0.344751	−	0.0595041i
$173$	−15.3766	−	4.12015i	−1.16906	−	0.313249i	−0.378483	−	0.925608i	$-0.623554\pi$
$173$	−15.3766	−	4.12015i	−1.16906	−	0.313249i	−0.790580	+	0.612359i	$0.790221\pi$
$174$	−5.74850	+	5.24844i	−0.435793	+	0.397883i
$175$	5.32251	+	12.1108i	0.402344	+	0.915489i
$176$	−18.5154	−	3.40303i	−1.39565	−	0.256513i
$177$	−12.7524	−	3.41699i	−0.958527	−	0.256837i
$178$	0.0469904	−	0.0734666i	0.00352208	−	0.00550656i
$179$	9.28847	+	5.36270i	0.694253	+	0.400827i	0.805203	−	0.592999i	$-0.202056\pi$
$179$	9.28847	+	5.36270i	0.694253	+	0.400827i	−0.110950	+	0.993826i	$0.535389\pi$
$180$	1.02820	+	4.35233i	0.0766376	+	0.324404i
$181$		−	3.28428i		−	0.244118i	−0.992523	−	0.122059i	$-0.961050\pi$
$181$		−	3.28428i		−	0.244118i	0.992523	−	0.122059i	$-0.0389498\pi$
$182$	6.58358	+	3.93663i	0.488007	+	0.291802i
$183$	6.89426	−	6.89426i	0.509638	−	0.509638i
$184$	−5.90131	+	14.0312i	−0.435050	+	1.03440i
$185$	1.00943	+	16.5080i	0.0742150	+	1.21369i
$186$	−3.40737	+	0.748933i	−0.249840	+	0.0549145i
$187$	−11.8061	−	3.16344i	−0.863349	−	0.231334i
$188$	6.47853	+	7.77777i	0.472496	+	0.567252i
$189$	−1.39131	−	2.25039i	−0.101203	−	0.163692i
$190$	−5.21162	+	20.7415i	−0.378090	+	1.50475i
$191$	−0.546315	+	0.315415i	−0.0395299	+	0.0228226i	−0.519635	−	0.854389i	$-0.673932\pi$
$191$	−0.546315	+	0.315415i	−0.0395299	+	0.0228226i	0.480105	+	0.877211i	$0.340599\pi$
$192$	7.99953	+	0.0867999i	0.577316	+	0.00626425i
$193$	−3.29037	+	0.881651i	−0.236846	+	0.0634627i	−0.375289	−	0.926908i	$-0.622457\pi$
$193$	−3.29037	+	0.881651i	−0.236846	+	0.0634627i	0.138444	+	0.990370i	$0.455790\pi$
$194$	5.18379	−	16.3378i	0.372175	−	1.17299i
$195$	0.913999	−	4.49211i	0.0654528	−	0.321687i
$196$	−12.3330	+	6.62554i	−0.880927	+	0.473253i
$197$	−8.07539	−	8.07539i	−0.575347	−	0.575347i	0.358270	−	0.933618i	$-0.383367\pi$
$197$	−8.07539	−	8.07539i	−0.575347	−	0.575347i	−0.933618	+	0.358270i	$0.883367\pi$
$198$	−3.06264	−	5.90934i	−0.217652	−	0.419958i
$199$	−8.10365	+	14.0359i	−0.574453	+	0.994981i	0.421648	+	0.906760i	$0.361452\pi$
$199$	−8.10365	+	14.0359i	−0.574453	+	0.994981i	−0.996101	+	0.0882217i	$0.971882\pi$
$200$	−6.89668	−	12.3465i	−0.487669	−	0.873028i
$201$	−5.75673	−	9.97095i	−0.406049	−	0.703297i
$202$	−2.98379	−	0.135682i	−0.209939	−	0.00954654i
$203$	−3.34358	+	14.1736i	−0.234674	+	0.994789i
$204$	5.17262	+	0.471403i	0.362156	+	0.0330048i
$205$	6.28644	−	2.10331i	0.439064	−	0.146902i
$206$	6.58666	−	1.44774i	0.458914	−	0.100868i
$207$	−5.19831	+	1.39288i	−0.361308	+	0.0968121i
$208$	−7.40681	−	3.51930i	−0.513570	−	0.244020i
$209$		−	31.8289i		−	2.20165i
$210$	6.18053	+	5.63925i	0.426497	+	0.389145i
$211$	−17.6704			−1.21648			−0.608241	−	0.793753i	$-0.708124\pi$
$211$	−17.6704			−1.21648			−0.608241	+	0.793753i	$0.708124\pi$
$212$	−17.0026	−	6.25819i	−1.16775	−	0.429814i
$213$	3.75959	+	14.0310i	0.257603	+	0.961386i
$214$	−1.44928	+	0.318548i	−0.0990704	+	0.0217755i
$215$	−4.59079	−	2.28897i	−0.313089	−	0.156106i
$216$	1.70964	+	2.25325i	0.116326	+	0.153314i
$217$	−4.47399	+	4.75207i	−0.303714	+	0.322592i
$218$	−0.240019	+	5.27829i	−0.0162561	+	0.357491i
$219$	11.5369	−	6.66084i	0.779593	−	0.450098i
$220$	14.4327	+	15.3199i	0.973049	+	1.03287i
$221$	−4.61085	−	2.66208i	−0.310160	−	0.179071i
$222$	4.81315	+	9.28693i	0.323037	+	0.623298i
$223$	3.05117	−	3.05117i	0.204321	−	0.204321i	−0.597527	−	0.801849i	$-0.703850\pi$
$223$	3.05117	−	3.05117i	0.204321	−	0.204321i	0.801849	+	0.597527i	$0.203850\pi$
$224$	12.4503	−	8.30597i	0.831873	−	0.554966i
$225$	1.95379	−	4.60247i	0.130253	−	0.306831i
$226$	0.434863	+	0.137977i	0.0289267	+	0.00917809i
$227$	5.79680	+	21.6340i	0.384747	+	1.43590i	0.838565	+	0.544802i	$0.183395\pi$
$227$	5.79680	+	21.6340i	0.384747	+	1.43590i	−0.453818	+	0.891095i	$0.649938\pi$
$228$	2.30055	+	13.3288i	0.152357	+	0.882719i
$229$	−9.07263	−	15.7143i	−0.599536	−	1.03843i	−0.992890	−	0.119040i	$-0.962018\pi$
$229$	−9.07263	−	15.7143i	−0.599536	−	1.03843i	0.393353	−	0.919387i	$-0.371315\pi$
$230$	14.6036	−	8.73852i	0.962931	−	0.576201i
$231$	−10.9663	−	5.89824i	−0.721533	−	0.388076i
$232$	2.11575	−	15.4236i	0.138906	−	1.01261i
$233$	−2.43638	+	9.09270i	−0.159613	+	0.595683i	0.839053	+	0.544049i	$0.183109\pi$
$233$	−2.43638	+	9.09270i	−0.159613	+	0.595683i	−0.998666	+	0.0516337i	$0.983557\pi$
$234$	−0.622398	−	2.83168i	−0.0406874	−	0.185113i
$235$	−0.690741	−	11.2962i	−0.0450590	−	0.736883i
$236$	23.9708	−	11.0724i	1.56036	−	0.720751i
$237$	−9.21784	−	9.21784i	−0.598763	−	0.598763i
$238$	8.48872	−	4.72919i	0.550242	−	0.306548i
$239$	−1.86371			−0.120553			−0.0602766	−	0.998182i	$-0.519198\pi$
$239$	−1.86371			−0.120553			−0.0602766	+	0.998182i	$0.519198\pi$
$240$	−7.15116	−	5.37223i	−0.461606	−	0.346776i
$241$	−6.72470	+	11.6475i	−0.433176	+	0.750283i	−0.997145	−	0.0755134i	$-0.975940\pi$
$241$	−6.72470	+	11.6475i	−0.433176	+	0.750283i	0.563969	+	0.825796i	$0.309274\pi$
$242$	−13.2837	−	8.49643i	−0.853906	−	0.546171i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−1.76977	+	19.4194i	−0.113298	+	1.24320i
$245$	15.4983	+	2.19137i	0.990151	+	0.140002i
$246$	3.09618	−	2.82684i	0.197405	−	0.180233i
$247$	3.58843	−	13.3922i	0.228327	−	0.852126i
$248$	4.27755	−	5.51243i	0.271624	−	0.350039i
$249$	3.71896	+	2.14714i	0.235680	+	0.136070i
$250$	−1.95598	+	15.6899i	−0.123707	+	0.992319i
$251$	−16.8761			−1.06521			−0.532605	−	0.846364i	$-0.678787\pi$
$251$	−16.8761			−1.06521			−0.532605	+	0.846364i	$0.678787\pi$
$252$	5.01862	+	1.67734i	0.316143	+	0.105662i
$253$	−17.9098	+	17.9098i	−1.12598	+	1.12598i
$254$	22.4056	+	7.10903i	1.40585	+	0.446060i
$255$	−4.34923	−	3.84798i	−0.272359	−	0.240970i
$256$	−12.4042	+	10.1062i	−0.775263	+	0.631638i
$257$	8.63309	+	2.31323i	0.538517	+	0.144295i	0.517818	−	0.855491i	$-0.326744\pi$
$257$	8.63309	+	2.31323i	0.538517	+	0.144295i	0.0206986	+	0.999786i	$0.493411\pi$
$258$	−3.24102	−	0.147378i	−0.201777	−	0.00917538i
$259$	17.2344	+	9.26950i	1.07089	+	0.575978i
$260$	4.34545	+	8.07310i	0.269494	+	0.500672i
$261$	4.76673	−	2.75207i	0.295053	−	0.170349i
$262$	−5.41601	−	3.46416i	−0.334602	−	0.214017i
$263$	2.96660	+	11.0715i	0.182929	+	0.682699i	0.995064	+	0.0992305i	$0.0316381\pi$
$263$	2.96660	+	11.0715i	0.182929	+	0.682699i	−0.812136	+	0.583468i	$0.801695\pi$
$264$	12.2705	+	5.16079i	0.755200	+	0.317625i
$265$	11.1800	+	16.8916i	0.686780	+	1.03764i
$266$	17.6170	+	18.1648i	1.08017	+	1.11376i
$267$	−0.0436046	+	0.0436046i	−0.00266856	+	0.00266856i
$268$	21.6096	+	7.95388i	1.32002	+	0.485861i
$269$	−0.662600	+	1.14766i	−0.0403994	+	0.0699739i	−0.885518	−	0.464605i	$-0.846196\pi$
$269$	−0.662600	+	1.14766i	−0.0403994	+	0.0699739i	0.845119	+	0.534579i	$0.179530\pi$
$270$	−0.0494257	−	3.16189i	−0.00300795	−	0.192427i
$271$	−6.85052	+	3.95515i	−0.416140	+	0.240258i	−0.693424	−	0.720530i	$-0.743899\pi$
$271$	−6.85052	+	3.95515i	−0.416140	+	0.240258i	0.277285	+	0.960788i	$0.410565\pi$
$272$	−8.55231	+	5.89666i	−0.518560	+	0.357538i
$273$	−3.94919	−	3.71809i	−0.239016	−	0.225029i
$274$	5.58617	+	6.11841i	0.337473	+	0.369626i
$275$	−2.86714	−	23.3566i	−0.172895	−	1.40845i
$276$	6.20547	−	8.79446i	0.373525	−	0.529364i
$277$	11.0056	−	2.94895i	0.661265	−	0.177186i	0.0874483	−	0.996169i	$-0.472129\pi$
$277$	11.0056	−	2.94895i	0.661265	−	0.177186i	0.573817	+	0.818984i	$0.305462\pi$
$278$	−13.5610	−	26.1659i	−0.813335	−	1.56932i
$279$	2.46689			0.147689
$280$	−16.7162	−	0.754757i	−0.998982	−	0.0451054i
$281$	24.1127			1.43844			0.719221	−	0.694782i	$-0.244499\pi$
$281$	24.1127			1.43844			0.719221	+	0.694782i	$0.244499\pi$
$282$	−3.29357	−	6.35492i	−0.196129	−	0.378430i
$283$	11.2362	−	3.01073i	0.667923	−	0.178969i	0.0911039	−	0.995841i	$-0.470960\pi$
$283$	11.2362	−	3.01073i	0.667923	−	0.178969i	0.576819	+	0.816872i	$0.304294\pi$
$284$	−23.7375	−	16.7494i	−1.40856	−	0.993895i
$285$	6.74776	−	13.5334i	0.399703	−	0.801650i
$286$	−9.20028	−	10.0769i	−0.544024	−	0.595857i
$287$	1.80087	−	7.63397i	0.106302	−	0.450619i
$288$	−5.51147	−	1.27425i	−0.324766	−	0.0750861i
$289$	8.88148	−	5.12773i	0.522440	−	0.301631i
$290$	−12.1138	+	12.4985i	−0.711346	+	0.733938i
$291$	−6.06007	+	10.4964i	−0.355248	+	0.615307i
$292$	−9.20306	+	25.0035i	−0.538568	+	1.46322i
$293$	13.9145	−	13.9145i	0.812895	−	0.812895i	−0.172172	−	0.985067i	$-0.555078\pi$
$293$	13.9145	−	13.9145i	0.812895	−	0.812895i	0.985067	+	0.172172i	$0.0550785\pi$
$294$	9.52315	−	2.70363i	0.555401	−	0.157679i
$295$	−28.9284	−	5.88598i	−1.68427	−	0.342695i
$296$	−19.2840	−	8.11054i	−1.12086	−	0.471416i
$297$	1.21810	+	4.54601i	0.0706814	+	0.263786i
$298$	−7.51864	−	4.80904i	−0.435543	−	0.278580i
$299$	−9.55485	+	5.51649i	−0.552571	+	0.319027i
$300$	2.88883	+	9.57364i	0.166787	+	0.552735i
$301$	−5.16265	+	3.19181i	−0.297570	+	0.183973i
$302$	25.4117	+	1.15554i	1.46228	+	0.0664940i
$303$	2.04008	+	0.546636i	0.117199	+	0.0314034i
$304$	−20.5965	−	17.5379i	−1.18129	−	1.00587i
$305$	14.4464	−	16.3282i	0.827197	−	0.934949i
$306$	−3.50076	−	1.11075i	−0.200125	−	0.0634973i
$307$	18.3419	−	18.3419i	1.04683	−	1.04683i	0.0479780	−	0.998848i	$-0.484722\pi$
$307$	18.3419	−	18.3419i	1.04683	−	1.04683i	0.998848	−	0.0479780i	$-0.0152777\pi$
$308$	24.4022	−	4.97321i	1.39044	−	0.283375i
$309$	−4.76865			−0.271279
$310$	−7.50269	+	2.13657i	−0.426124	+	0.121349i
$311$	9.77084	+	5.64120i	0.554054	+	0.319883i	0.750755	−	0.660580i	$-0.229690\pi$
$311$	9.77084	+	5.64120i	0.554054	+	0.319883i	−0.196702	+	0.980463i	$0.563023\pi$
$312$	4.58108	+	3.55484i	0.259353	+	0.201253i
$313$	−4.20392	+	15.6892i	−0.237619	+	0.886808i	0.739331	+	0.673342i	$0.235142\pi$
$313$	−4.20392	+	15.6892i	−0.237619	+	0.886808i	−0.976951	+	0.213466i	$0.931525\pi$
$314$	15.0152	−	13.7090i	0.847356	−	0.773644i
$315$	−3.41238	−	4.83277i	−0.192266	−	0.272296i
$316$	25.9644	+	2.36625i	1.46061	+	0.133112i
$317$	2.20365	−	8.22414i	0.123769	−	0.461914i	−0.876023	−	0.482269i	$-0.839813\pi$
$317$	2.20365	−	8.22414i	0.123769	−	0.461914i	0.999793	+	0.0203549i	$0.00647961\pi$
$318$	10.7924	+	6.90299i	0.605208	+	0.387100i
$319$	12.9523	−	22.4340i	0.725190	−	1.25607i
$320$	17.8660	−	0.898018i	0.998739	−	0.0502007i
$321$	1.04925			0.0585637
$322$	0.308266	−	20.1341i	0.0171790	−	1.12203i
$323$	−12.4193	−	12.4193i	−0.691026	−	0.691026i
$324$	−0.838675	−	1.81566i	−0.0465931	−	0.100870i
$325$	1.42689	−	10.1507i	0.0791494	−	0.563059i
$326$	5.93102	+	26.9839i	0.328489	+	1.49450i
$327$	0.966992	−	3.60886i	0.0534748	−	0.199571i
$328$	−1.13955	+	8.30727i	−0.0629214	+	0.458692i
$329$	−11.7932	−	6.34299i	−0.650182	−	0.349700i
$330$	−7.64198	−	12.7711i	−0.420677	−	0.703024i
$331$	−9.67989	−	16.7661i	−0.532055	−	0.921546i	−0.999300	−	0.0374180i	$-0.988087\pi$
$331$	−9.67989	−	16.7661i	−0.532055	−	0.921546i	0.467245	−	0.884128i	$-0.345247\pi$
$332$	−8.46343	+	1.46079i	−0.464491	+	0.0801713i
$333$	−1.91433	−	7.14437i	−0.104905	−	0.391509i
$334$	−4.07477	−	1.29288i	−0.222962	−	0.0707431i
$335$	−14.2092	−	21.4685i	−0.776334	−	1.17295i
$336$	−9.85929	+	3.84635i	−0.537868	+	0.209836i
$337$	−18.3464	+	18.3464i	−0.999393	+	0.999393i	−1.00000		0.000606956i	$-0.999807\pi$
$337$	−18.3464	+	18.3464i	−0.999393	+	0.999393i	0.000606956		1.00000i	$0.499807\pi$
$338$	5.72464	+	11.0457i	0.311379	+	0.600805i
$339$	−0.279381	−	0.161301i	−0.0151739	−	0.00876066i
$340$	11.6091	+	0.346183i	0.629592	+	0.0187744i
$341$	10.0546	−	5.80505i	0.544490	−	0.314361i
$342$	0.434464	−	9.55434i	0.0234931	−	0.516640i
$343$	11.8601	−	14.2245i	0.640387	−	0.768053i
$344$	5.16921	−	3.92210i	0.278705	−	0.211466i
$345$	−11.4120	+	3.81822i	−0.614402	+	0.205566i
$346$	−21.9881	+	4.83294i	−1.18209	+	0.259820i
$347$	3.96856	+	14.8109i	0.213044	+	0.795089i	0.986846	+	0.161663i	$0.0516856\pi$
$347$	3.96856	+	14.8109i	0.213044	+	0.795089i	−0.773803	+	0.633427i	$0.781648\pi$
$348$	−3.80245	+	10.3307i	−0.203833	+	0.553785i
$349$	3.60952			0.193213			0.0966065	−	0.995323i	$-0.469201\pi$
$349$	3.60952			0.193213			0.0966065	+	0.995323i	$0.469201\pi$
$350$	14.5639	+	11.7427i	0.778475	+	0.627675i
$351$			2.05010i			0.109426i
$352$	−25.4624	+	7.77587i	−1.35715	+	0.414455i
$353$	−23.6649	+	6.34100i	−1.25956	+	0.337497i	−0.826021	−	0.563639i	$-0.809401\pi$
$353$	−23.6649	+	6.34100i	−1.25956	+	0.337497i	−0.433536	+	0.901136i	$0.642734\pi$
$354$	−18.2355	+	4.00812i	−0.969205	+	0.213029i
$355$	10.3059	+	30.8026i	0.546981	+	1.63483i
$356$	0.0111934	−	0.122823i	0.000593250	−	0.00650963i
$357$	−6.58037	+	1.97752i	−0.348270	+	0.104661i
$358$	15.1524	+	0.689021i	0.800827	+	0.0364159i
$359$	−15.4916	−	26.8322i	−0.817615	−	1.41615i	−0.907435	−	0.420193i	$-0.861962\pi$
$359$	−15.4916	−	26.8322i	−0.817615	−	1.41615i	0.0898196	−	0.995958i	$-0.471371\pi$
$360$	4.12326	+	4.79570i	0.217315	+	0.252756i
$361$	13.3686	−	23.1550i	0.703608	−	1.21868i
$362$	−2.13722	−	4.12374i	−0.112330	−	0.216739i
$363$	7.88424	+	7.88424i	0.413815	+	0.413815i
$364$	10.8281	+	0.658628i	0.567546	+	0.0345215i
$365$	24.8402	−	16.4408i	1.30020	−	0.860553i
$366$	4.17006	−	13.1428i	0.217973	−	0.686986i
$367$	−19.9320	+	5.34077i	−1.04044	+	0.278786i	−0.738297	−	0.674476i	$-0.764370\pi$
$367$	−19.9320	+	5.34077i	−1.04044	+	0.278786i	−0.302146	+	0.953262i	$0.597703\pi$
$368$	1.72101	+	21.4579i	0.0897140	+	1.11857i
$369$	−2.56739	+	1.48228i	−0.133653	+	0.0771646i
$370$	12.0099	+	20.0706i	0.624365	+	1.04342i
$371$	23.9567	−	0.722085i	1.24377	−	0.0374888i
$372$	−3.79094	+	3.15768i	−0.196551	+	0.163718i
$373$	23.8553	+	6.39202i	1.23518	+	0.330966i	0.816595	−	0.577210i	$-0.195859\pi$
$373$	23.8553	+	6.39202i	1.23518	+	0.330966i	0.418587	+	0.908177i	$0.362525\pi$
$374$	−16.8824	+	3.71071i	−0.872966	+	0.191876i
$375$	3.73253	−	10.5389i	0.192747	−	0.544226i
$376$	13.1958	+	5.54993i	0.680520	+	0.286216i
$377$	7.97902	−	7.97902i	0.410940	−	0.410940i
$378$	−3.21135	−	1.92022i	−0.165174	−	0.0987652i
$379$			15.7998i			0.811582i	0.913966	+	0.405791i	$0.133004\pi$
$379$			15.7998i			0.811582i	−0.913966	+	0.405791i	$0.866996\pi$
$380$	6.95365	+	29.4345i	0.356715	+	1.50996i
$381$	−14.3947	−	8.31076i	−0.737460	−	0.425773i
$382$	−0.480700	+	0.751545i	−0.0245947	+	0.0384524i
$383$	20.6086	+	5.52205i	1.05305	+	0.282164i	0.743511	−	0.668724i	$-0.233159\pi$
$383$	20.6086	+	5.52205i	1.05305	+	0.282164i	0.309538	+	0.950887i	$0.399826\pi$
$384$	10.1007	−	5.09664i	0.515449	−	0.260087i
$385$	−25.2807	−	11.6676i	−1.28843	−	0.594638i
$386$	−3.55766	+	3.24818i	−0.181080	+	0.165328i
$387$	2.21594	+	0.593760i	0.112643	+	0.0301825i
$388$	−4.12292	−	23.8871i	−0.209309	−	1.21268i
$389$	−5.03830	+	8.72660i	−0.255452	+	0.442456i	−0.965018	−	0.262183i	$-0.915558\pi$
$389$	−5.03830	+	8.72660i	−0.255452	+	0.442456i	0.709566	+	0.704639i	$0.248891\pi$
$390$	−1.77559	−	6.23508i	−0.0899104	−	0.315726i
$391$			13.9764i			0.706816i
$392$	−11.1738	+	16.3446i	−0.564361	+	0.825528i
$393$	3.21456	+	3.21456i	0.162153	+	0.162153i
$394$	−15.3945	−	4.88448i	−0.775562	−	0.246076i
$395$	−21.8313	−	19.3153i	−1.09845	−	0.971857i
$396$	−7.69090	−	5.42679i	−0.386482	−	0.272706i
$397$	4.00278	−	14.9386i	0.200894	−	0.749746i	−0.789768	−	0.613405i	$-0.789799\pi$
$397$	4.00278	−	14.9386i	0.200894	−	0.749746i	0.990662	−	0.136340i	$-0.0435341\pi$
$398$	−1.04119	+	22.8969i	−0.0521901	+	1.14772i
$399$	−9.40929	−	15.2192i	−0.471054	−	0.761914i
$400$	−16.6939	−	11.0143i	−0.834693	−	0.550715i
$401$	8.30512	+	14.3849i	0.414738	+	0.718347i	0.995401	−	0.0957969i	$-0.0305399\pi$
$401$	8.30512	+	14.3849i	0.414738	+	0.718347i	−0.580663	+	0.814144i	$0.697207\pi$
$402$	−13.7167	−	8.77340i	−0.684126	−	0.437577i
$403$	4.88503	−	1.30894i	0.243341	−	0.0652030i
$404$	−3.83475	+	1.77132i	−0.190786	+	0.0881263i
$405$	−0.445832	+	2.19117i	−0.0221536	+	0.108880i
$406$	5.02512	+	19.9722i	0.249393	+	0.991202i
$407$	−24.6146	−	24.6146i	−1.22010	−	1.22010i
$408$	6.80151	−	2.77414i	0.336725	−	0.137341i
$409$	18.7964	+	10.8521i	0.929422	+	0.536602i	0.886629	−	0.462482i	$-0.153041\pi$
$409$	18.7964	+	10.8521i	0.929422	+	0.536602i	0.0427934	+	0.999084i	$0.486374\pi$
$410$	6.52456	−	6.73178i	0.322225	−	0.332459i
$411$	−2.92917	−	5.07347i	−0.144485	−	0.250256i
$412$	7.32811	−	6.10399i	0.361030	−	0.300722i
$413$	−23.9438	+	25.4320i	−1.17820	+	1.25143i
$414$	−5.62060	+	5.13167i	−0.276238	+	0.252208i
$415$	8.59338	+	4.28466i	0.421833	+	0.210326i
$416$	−11.5902	+	0.401080i	−0.568254	+	0.0196646i
$417$	5.39361	+	20.1292i	0.264126	+	0.985733i
$418$	−20.7124	−	39.9644i	−1.01308	−	1.95472i
$419$			6.43493i			0.314367i	0.987569	+	0.157183i	$0.0502414\pi$
$419$			6.43493i			0.314367i	−0.987569	+	0.157183i	$0.949759\pi$
$420$	11.4300	+	3.05872i	0.557725	+	0.149250i
$421$		−	14.3531i		−	0.699525i	−0.936838	−	0.349763i	$-0.886262\pi$
$421$		−	14.3531i		−	0.699525i	0.936838	−	0.349763i	$-0.113738\pi$
$422$	−22.1870	+	11.4989i	−1.08005	+	0.559756i
$423$	1.30995	+	4.88880i	0.0636919	+	0.237701i
$424$	−25.4210	+	3.20654i	−1.23455	+	0.155723i
$425$	−10.2322	−	7.99474i	−0.496334	−	0.387802i
$426$	13.8511	+	15.1708i	0.671087	+	0.735027i
$427$	−7.42414	−	24.7045i	−0.359279	−	1.19554i
$428$	−1.61242	+	1.34307i	−0.0779393	+	0.0649199i
$429$	4.82427	+	8.35587i	0.232918	+	0.403425i
$430$	−7.25373	+	0.113388i	−0.349806	+	0.00546806i
$431$	11.0037	+	6.35298i	0.530029	+	0.306012i	0.741028	−	0.671474i	$-0.234338\pi$
$431$	11.0037	+	6.35298i	0.530029	+	0.306012i	−0.210999	+	0.977486i	$0.567672\pi$
$432$	3.61291	+	1.71665i	0.173826	+	0.0825924i
$433$	−17.7077	−	17.7077i	−0.850976	−	0.850976i	0.139277	−	0.990253i	$-0.455522\pi$
$433$	−17.7077	−	17.7077i	−0.850976	−	0.850976i	−0.990253	+	0.139277i	$0.955522\pi$
$434$	−2.52517	+	8.87812i	−0.121212	+	0.426163i
$435$	10.2633	−	6.79290i	0.492086	−	0.325695i
$436$	3.13343	+	6.78362i	0.150064	+	0.324876i
$437$	−35.1558	+	9.41996i	−1.68173	+	0.450618i
$438$	10.1513	−	15.8709i	0.485047	−	0.758342i
$439$	2.30467	+	3.99180i	0.109996	+	0.190518i	0.915768	−	0.401707i	$-0.131583\pi$
$439$	2.30467	+	3.99180i	0.109996	+	0.190518i	−0.805773	+	0.592225i	$0.798250\pi$
$440$	28.0909	+	9.84373i	1.33918	+	0.469281i
$441$	−6.98729	+	0.421594i	−0.332728	+	0.0200759i
$442$	−7.52172	−	0.342034i	−0.357772	−	0.0162689i
$443$	−4.87852	+	18.2069i	−0.231786	+	0.865035i	0.747786	+	0.663940i	$0.231117\pi$
$443$	−4.87852	+	18.2069i	−0.231786	+	0.865035i	−0.979572	+	0.201096i	$0.935550\pi$
$444$	12.0868	+	8.52857i	0.573613	+	0.404748i
$445$	−0.0913701	+	0.103272i	−0.00433136	+	0.00489557i
$446$	1.84553	−	5.81657i	0.0873883	−	0.275423i
$447$	4.46253	+	4.46253i	0.211070	+	0.211070i
$448$	10.2276	−	18.5309i	0.483209	−	0.875505i
$449$			36.7871i			1.73609i	0.496485	+	0.868045i	$0.334624\pi$
$449$			36.7871i			1.73609i	−0.496485	+	0.868045i	$0.665376\pi$
$450$	−0.541837	−	7.05028i	−0.0255424	−	0.332353i
$451$	−6.97619	+	12.0831i	−0.328496	+	0.568972i
$452$	0.635802	−	0.109740i	0.0299056	−	0.00516172i
$453$	−17.3744	−	4.65547i	−0.816322	−	0.218733i
$454$	21.3566	+	23.3914i	1.00231	+	1.09781i
$455$	−9.32162	−	7.75943i	−0.437004	−	0.363768i
$456$	11.5622	+	15.2386i	0.541447	+	0.713611i
$457$	16.1090	+	4.31639i	0.753547	+	0.201912i	0.615091	−	0.788456i	$-0.289119\pi$
$457$	16.1090	+	4.31639i	0.753547	+	0.201912i	0.138456	+	0.990369i	$0.455786\pi$
$458$	−21.6175	−	13.8269i	−1.01012	−	0.646089i
$459$	2.24909	+	1.29851i	0.104979	+	0.0606094i
$460$	12.6497	−	20.4752i	0.589797	−	0.954663i
$461$		−	11.0189i		−	0.513203i	−0.966517	−	0.256602i	$-0.917397\pi$
$461$		−	11.0189i		−	0.513203i	0.966517	−	0.256602i	$-0.0826028\pi$
$462$	−17.6076	−	0.269584i	−0.819179	−	0.0125422i
$463$	−16.6328	+	16.6328i	−0.772994	+	0.772994i	−0.978629	−	0.205635i	$-0.934074\pi$
$463$	−16.6328	+	16.6328i	−0.772994	+	0.772994i	0.205635	+	0.978629i	$0.434074\pi$
$464$	−7.38027	−	20.7428i	−0.342620	−	0.962958i
$465$	5.50584	−	0.336672i	0.255327	−	0.0156128i
$466$	2.85787	+	13.0023i	0.132388	+	0.602318i
$467$	−31.0851	−	8.32922i	−1.43845	−	0.385430i	−0.546457	−	0.837487i	$-0.684024\pi$
$467$	−31.0851	−	8.32922i	−1.43845	−	0.385430i	−0.891989	+	0.452057i	$0.850690\pi$
$468$	−2.62418	−	3.15044i	−0.121303	−	0.145629i
$469$	−30.4479	+	0.917739i	−1.40596	+	0.0423772i
$470$	−8.21821	−	13.7340i	−0.379078	−	0.633504i
$471$	−12.4508	+	7.18847i	−0.573702	+	0.331227i
$472$	22.8925	−	29.5013i	1.05371	−	1.35791i
$473$	10.4291	−	2.79446i	0.479529	−	0.128489i
$474$	−17.5724	−	5.57550i	−0.807126	−	0.256091i
$475$	13.2133	−	31.1261i	0.606269	−	1.42816i
$476$	7.58097	−	11.4619i	0.347473	−	0.525357i
$477$	−6.40561	−	6.40561i	−0.293293	−	0.293293i
$478$	−2.34007	+	1.21279i	−0.107032	+	0.0554718i
$479$	9.65123	−	16.7164i	0.440976	−	0.763793i	−0.556786	−	0.830656i	$-0.687966\pi$
$479$	9.65123	−	16.7164i	0.440976	−	0.763793i	0.997762	+	0.0668630i	$0.0212991\pi$
$480$	−12.4749	−	2.09182i	−0.569401	−	0.0954780i
$481$	−7.58167	−	13.1318i	−0.345694	−	0.598760i
$482$	−0.864016	+	19.0007i	−0.0393549	+	0.865457i
$483$	−3.26919	+	13.8582i	−0.148753	+	0.630571i
$484$	−22.2080	−	2.02391i	−1.00945	−	0.0919957i
$485$	−12.0930	+	24.2539i	−0.549113	+	1.10131i
$486$	0.303595	+	1.38124i	0.0137713	+	0.0626544i
$487$	−13.3121	+	3.56697i	−0.603229	+	0.161635i	−0.547492	−	0.836811i	$-0.684417\pi$
$487$	−13.3121	+	3.56697i	−0.603229	+	0.161635i	−0.0557369	+	0.998445i	$0.517751\pi$
$488$	10.4149	+	25.5347i	0.471460	+	1.15590i
$489$		−	19.5360i		−	0.883448i
$490$	20.8857	−	7.33391i	0.943521	−	0.331312i
$491$	−23.0455			−1.04003			−0.520015	−	0.854157i	$-0.674074\pi$
$491$	−23.0455			−1.04003			−0.520015	+	0.854157i	$0.674074\pi$
$492$	2.04802	−	5.56419i	0.0923319	−	0.250853i
$493$	−3.69967	−	13.8073i	−0.166625	−	0.621852i
$494$	−4.20923	−	19.1504i	−0.189382	−	0.861619i
$495$	3.33910	+	9.98000i	0.150081	+	0.448568i
$496$	1.78373	−	9.70499i	0.0800918	−	0.435767i
$497$	37.4053	+	8.82401i	1.67786	+	0.395811i
$498$	6.06677	+	0.275874i	0.271858	+	0.0123622i
$499$	34.8573	−	20.1248i	1.56043	−	0.900912i	0.563212	−	0.826313i	$-0.309566\pi$
$499$	34.8573	−	20.1248i	1.56043	−	0.900912i	0.997214	−	0.0745993i	$-0.0237678\pi$
$500$	7.75416	+	20.9731i	0.346777	+	0.937948i
$501$	2.61787	+	1.51143i	0.116958	+	0.0675256i
$502$	−21.1897	+	10.9820i	−0.945741	+	0.490150i
$503$	15.4889	−	15.4889i	0.690616	−	0.690616i	−0.271751	−	0.962368i	$-0.587603\pi$
$503$	15.4889	−	15.4889i	0.690616	−	0.690616i	0.962368	+	0.271751i	$0.0876027\pi$
$504$	7.39290	−	1.15976i	0.329306	−	0.0516598i
$505$	4.62785	+	0.941616i	0.205936	+	0.0419013i
$506$	−10.8329	+	34.1422i	−0.481582	+	1.51781i
$507$	−2.27686	−	8.49735i	−0.101119	−	0.377381i
$508$	32.7587	−	5.65415i	1.45343	−	0.250862i
$509$	21.4785	+	37.2019i	0.952020	+	1.64895i	0.741045	+	0.671455i	$0.234331\pi$
$509$	21.4785	+	37.2019i	0.952020	+	1.64895i	0.210975	+	0.977491i	$0.432336\pi$
$510$	−7.96494	−	2.00131i	−0.352693	−	0.0886195i
$511$	−1.06187	−	35.2299i	−0.0469744	−	1.55848i
$512$	−8.99821	+	20.7613i	−0.397669	+	0.917529i
$513$	−1.75037	+	6.53248i	−0.0772808	+	0.288416i
$514$	12.3450	−	2.71341i	0.544516	−	0.119684i
$515$	−10.6431	+	0.650807i	−0.468993	+	0.0286780i
$516$	−4.16533	+	1.92401i	−0.183368	+	0.0847000i
$517$	16.8434	+	16.8434i	0.740772	+	0.740772i
$518$	27.6715	+	0.423670i	1.21582	+	0.0186150i
$519$	15.9190			0.698769
$520$	10.7097	+	7.30883i	0.469650	+	0.320513i
$521$	8.22536	−	14.2467i	0.360359	−	0.624161i	−0.627661	−	0.778487i	$-0.715987\pi$
$521$	8.22536	−	14.2467i	0.360359	−	0.624161i	0.988020	+	0.154326i	$0.0493207\pi$
$522$	4.19423	−	6.55742i	0.183576	−	0.287010i
$523$	−1.68353	+	6.28304i	−0.0736158	+	0.274738i	−0.992916	−	0.118819i	$-0.962089\pi$
$523$	−1.68353	+	6.28304i	−0.0736158	+	0.274738i	0.919300	+	0.393557i	$0.128756\pi$
$524$	−9.05462	−	0.825186i	−0.395553	−	0.0360484i
$525$	−8.27565	−	10.3205i	−0.361179	−	0.450426i
$526$	10.9296	+	11.9709i	0.476552	+	0.521957i
$527$	1.65814	−	6.18827i	0.0722298	−	0.269565i
$528$	18.7653	−	1.50505i	0.816653	−	0.0654991i
$529$	5.16376	+	2.98130i	0.224511	+	0.129622i
$530$	25.0297	+	13.9339i	1.08722	+	0.605249i
$531$	13.2022			0.572928
$532$	33.9405	+	11.3437i	1.47151	+	0.491811i
$533$	−4.29755	+	4.29755i	−0.186147	+	0.186147i
$534$	−0.0263747	+	0.0831253i	−0.00114134	+	0.00359718i
$535$	2.34183	−	0.143198i	0.101246	−	0.00619101i
$536$	32.3090	−	4.07537i	1.39554	−	0.176029i
$537$	−10.3599	−	2.77594i	−0.447065	−	0.119791i
$538$	−0.0851335	+	1.87218i	−0.00367037	+	0.0807154i
$539$	−27.4870	+	18.1608i	−1.18395	+	0.782240i
$540$	−2.11963	−	3.93791i	−0.0912145	−	0.169461i
$541$	18.7758	−	10.8402i	0.807235	−	0.466058i	−0.0387595	−	0.999249i	$-0.512341\pi$
$541$	18.7758	−	10.8402i	0.807235	−	0.466058i	0.845995	+	0.533191i	$0.179007\pi$
$542$	−6.02774	+	9.42401i	−0.258914	+	0.404796i
$543$	0.850034	+	3.17237i	0.0364784	+	0.136139i
$544$	−6.90109	+	12.9692i	−0.295882	+	0.556050i
$545$	1.66570	−	8.18659i	0.0713509	−	0.350675i
$546$	−7.37812	−	2.09854i	−0.315755	−	0.0898090i
$547$	8.51539	−	8.51539i	0.364092	−	0.364092i	−0.501225	−	0.865317i	$-0.667117\pi$
$547$	8.51539	−	8.51539i	0.364092	−	0.364092i	0.865317	+	0.501225i	$0.167117\pi$
$548$	10.9955	+	4.04713i	0.469704	+	0.172885i
$549$	−4.87498	+	8.44371i	−0.208059	+	0.360369i
$550$	−18.7991	−	27.4608i	−0.801595	−	1.17093i
$551$	32.2370	−	18.6121i	1.37334	−	0.792901i
$552$	2.06868	−	15.0805i	0.0880487	−	0.641868i
$553$	−33.0307	+	9.92631i	−1.40461	+	0.422110i
$554$	11.8997	−	10.8645i	0.505570	−	0.461590i
$555$	−5.24763	−	15.6843i	−0.222749	−	0.665760i
$556$	−34.0544	−	24.0292i	−1.44423	−	1.01907i
$557$	8.76015	−	2.34727i	0.371179	−	0.0994572i	−0.0684071	−	0.997657i	$-0.521792\pi$
$557$	8.76015	−	2.34727i	0.371179	−	0.0994572i	0.439586	+	0.898200i	$0.355125\pi$
$558$	3.09743	−	1.60531i	0.131125	−	0.0679580i
$559$	4.70315			0.198922
$560$	−21.4800	+	9.93023i	−0.907696	+	0.419629i
$561$	12.2226			0.516038
$562$	30.2759	−	15.6911i	1.27711	−	0.661890i
$563$	20.3986	−	5.46578i	0.859698	−	0.230355i	0.198070	−	0.980188i	$-0.436533\pi$
$563$	20.3986	−	5.46578i	0.859698	−	0.230355i	0.661628	+	0.749833i	$0.269866\pi$
$564$	−8.27082	−	5.83598i	−0.348264	−	0.245739i
$565$	−0.645565	−	0.321878i	−0.0271591	−	0.0135415i
$566$	12.1490	−	11.0921i	0.510660	−	0.466238i
$567$	1.92634	+	1.81362i	0.0808988	+	0.0761647i
$568$	−40.7043	−	5.58364i	−1.70792	−	0.234285i
$569$	11.3988	−	6.58113i	0.477865	−	0.275895i	−0.241662	−	0.970361i	$-0.577692\pi$
$569$	11.3988	−	6.58113i	0.477865	−	0.275895i	0.719526	+	0.694465i	$0.244359\pi$
$570$	−0.334262	−	21.3836i	−0.0140007	−	0.895661i
$571$	−5.49773	+	9.52235i	−0.230073	+	0.398498i	−0.957829	−	0.287338i	$-0.907230\pi$
$571$	−5.49773	+	9.52235i	−0.230073	+	0.398498i	0.727756	+	0.685836i	$0.240563\pi$
$572$	−18.1093	−	6.66552i	−0.757189	−	0.278700i
$573$	0.446064	−	0.446064i	0.0186346	−	0.0186346i
$574$	−2.70656	−	10.7571i	−0.112970	−	0.448994i
$575$	−24.9494	+	10.0794i	−1.04046	+	0.420338i
$576$	−7.74942	+	1.98659i	−0.322892	+	0.0827745i
$577$	−2.23567	−	8.34364i	−0.0930722	−	0.347350i	0.903648	−	0.428276i	$-0.140879\pi$
$577$	−2.23567	−	8.34364i	−0.0930722	−	0.347350i	−0.996720	+	0.0809259i	$0.974212\pi$
$578$	7.81478	−	12.2179i	0.325052	−	0.508199i
$579$	2.95006	−	1.70322i	0.122600	−	0.0707834i
$580$	−7.07678	+	23.5761i	−0.293847	+	0.978944i
$581$	9.66383	−	5.97467i	0.400923	−	0.247871i
$582$	−0.778623	+	17.1228i	−0.0322749	+	0.709762i
$583$	−41.1819	−	11.0346i	−1.70558	−	0.457008i
$584$	4.71541	+	37.3832i	0.195125	+	1.54693i
$585$	0.279790	+	4.57561i	0.0115679	+	0.189178i
$586$	8.41634	−	26.5259i	0.347676	−	1.09577i
$587$	2.36935	−	2.36935i	0.0977935	−	0.0977935i	−0.656517	−	0.754311i	$-0.727971\pi$
$587$	2.36935	−	2.36935i	0.0977935	−	0.0977935i	0.754311	+	0.656517i	$0.227971\pi$
$588$	10.1979	−	9.59179i	0.420555	−	0.395559i
$589$	16.6834			0.687426
$590$	−40.1527	+	11.4344i	−1.65306	+	0.470748i
$591$	9.89029	+	5.71016i	0.406832	+	0.234885i
$592$	−29.4909	+	2.36530i	−1.21207	+	0.0972131i
$593$	3.65232	−	13.6306i	0.149983	−	0.559743i	−0.849500	−	0.527588i	$-0.823096\pi$
$593$	3.65232	−	13.6306i	0.149983	−	0.559743i	0.999483	−	0.0321547i	$-0.0102369\pi$
$594$	4.48773	+	4.91531i	0.184134	+	0.201678i
$595$	−14.4168	+	5.31168i	−0.591033	+	0.217758i
$596$	−12.5698	−	1.14554i	−0.514881	−	0.0469233i
$597$	4.19476	−	15.6551i	0.171680	−	0.640719i
$598$	−8.40727	+	13.1443i	−0.343799	+	0.537508i
$599$	7.71996	−	13.3714i	0.315429	−	0.546339i	−0.664099	−	0.747644i	$-0.731185\pi$
$599$	7.71996	−	13.3714i	0.315429	−	0.546339i	0.979529	+	0.201305i	$0.0645182\pi$
$600$	9.85719	+	10.1408i	0.402418	+	0.413996i
$601$	3.24967			0.132557			0.0662785	−	0.997801i	$-0.478887\pi$
$601$	3.24967			0.132557			0.0662785	+	0.997801i	$0.478887\pi$
$602$	−4.40519	+	7.36720i	−0.179542	+	0.300265i
$603$	8.14125	+	8.14125i	0.331537	+	0.331537i
$604$	32.6589	−	15.0855i	1.32887	−	0.613822i
$605$	18.6728	+	16.5208i	0.759159	+	0.671667i
$606$	2.91724	−	0.641204i	0.118505	−	0.0260471i
$607$	2.94901	−	11.0059i	0.119697	−	0.446714i	−0.879899	−	0.475162i	$-0.842390\pi$
$607$	2.94901	−	11.0059i	0.119697	−	0.446714i	0.999595	+	0.0284473i	$0.00905627\pi$
$608$	−37.2736	−	8.61767i	−1.51165	−	0.349493i
$609$	−0.438736	−	14.5560i	−0.0177785	−	0.589839i
$610$	7.51347	−	29.9026i	0.304211	−	1.21072i
$611$	5.18803	+	8.98593i	0.209885	+	0.363532i
$612$	−5.11837	+	0.883432i	−0.206898	+	0.0357106i
$613$	−4.08237	−	15.2356i	−0.164885	−	0.615360i	−0.998055	−	0.0623425i	$-0.980143\pi$
$613$	−4.08237	−	15.2356i	−0.164885	−	0.615360i	0.833170	−	0.553018i	$-0.186524\pi$
$614$	11.0943	−	34.9659i	0.447728	−	1.41111i
$615$	−5.52786	+	3.65870i	−0.222905	+	0.147533i
$616$	27.4032	−	22.1239i	1.10410	−	0.891397i
$617$	0.236797	−	0.236797i	0.00953310	−	0.00953310i	−0.702324	−	0.711857i	$-0.747854\pi$
$617$	0.236797	−	0.236797i	0.00953310	−	0.00953310i	0.711857	+	0.702324i	$0.247854\pi$
$618$	−5.98752	+	3.10316i	−0.240853	+	0.124827i
$619$	11.5244	+	6.65359i	0.463203	+	0.267430i	0.713390	−	0.700767i	$-0.247159\pi$
$619$	11.5244	+	6.65359i	0.463203	+	0.267430i	−0.250187	+	0.968198i	$0.580492\pi$
$620$	−8.03004	+	7.56499i	−0.322494	+	0.303817i
$621$	4.66068	−	2.69085i	0.187027	−	0.107980i
$622$	15.9392	+	0.724804i	0.639106	+	0.0290620i
$623$	0.0469560	+	0.156250i	0.00188125	+	0.00626004i
$624$	8.06529	+	1.48236i	0.322870	+	0.0593419i
$625$	6.89233	−	24.0311i	0.275693	−	0.961246i
$626$	4.93119	+	22.4351i	0.197090	+	0.896686i
$627$	8.23792	+	30.7443i	0.328991	+	1.22781i
$628$	9.93207	−	26.9841i	0.396333	−	1.07678i
$629$	−19.2086			−0.765899
$630$	−7.42947	−	3.84746i	−0.295997	−	0.153286i
$631$			34.1624i			1.35998i	0.733220	+	0.679991i	$0.238017\pi$
$631$			34.1624i			1.35998i	−0.733220	+	0.679991i	$0.761983\pi$
$632$	34.1407	−	13.9250i	1.35805	−	0.553909i
$633$	17.0683	−	4.57344i	0.678404	−	0.181778i
$634$	−2.58488	−	11.7602i	−0.102659	−	0.467059i
$635$	−33.2616	−	16.5842i	−1.31995	−	0.658126i
$636$	18.0430	+	1.64434i	0.715453	+	0.0652022i
$637$	−13.6128	+	4.54234i	−0.539360	+	0.179974i
$638$	1.66416	−	36.5968i	0.0658849	−	1.44888i
$639$	−7.26296	−	12.5798i	−0.287318	−	0.497650i
$640$	21.8482	−	12.7537i	0.863625	−	0.504134i
$641$	−5.79023	+	10.0290i	−0.228700	+	0.396121i	−0.957423	−	0.288688i	$-0.906781\pi$
$641$	−5.79023	+	10.0290i	−0.228700	+	0.396121i	0.728723	+	0.684809i	$0.240114\pi$
$642$	1.31745	−	0.682794i	0.0519955	−	0.0269477i
$643$	1.02318	+	1.02318i	0.0403504	+	0.0403504i	0.726994	−	0.686644i	$-0.240917\pi$
$643$	1.02318	+	1.02318i	0.0403504	+	0.0403504i	−0.686644	+	0.726994i	$0.740917\pi$
$644$	−12.7150	−	25.4810i	−0.501042	−	1.00409i
$645$	5.02679	+	1.02279i	0.197930	+	0.0402723i
$646$	−23.6754	−	7.51191i	−0.931495	−	0.295552i
$647$	−18.1211	+	4.85554i	−0.712415	+	0.190891i	−0.596785	−	0.802401i	$-0.703555\pi$
$647$	−18.1211	+	4.85554i	−0.712415	+	0.190891i	−0.115630	+	0.993292i	$0.536889\pi$
$648$	−2.23457	−	1.73399i	−0.0877821	−	0.0681174i
$649$	53.8102	−	31.0673i	2.11224	−	1.21950i
$650$	−4.81387	−	13.6738i	−0.188816	−	0.536329i
$651$	3.09161	−	5.74810i	0.121170	−	0.225286i
$652$	25.0066	+	30.0215i	0.979333	+	1.17573i
$653$	6.36358	+	1.70512i	0.249026	+	0.0667263i	0.381173	−	0.924504i	$-0.375520\pi$
$653$	6.36358	+	1.70512i	0.249026	+	0.0667263i	−0.132147	+	0.991230i	$0.542187\pi$
$654$	−1.13428	−	5.16056i	−0.0443539	−	0.201794i
$655$	7.61328	+	6.73586i	0.297476	+	0.263192i
$656$	3.97506	+	11.1722i	0.155200	+	0.436200i
$657$	−9.41985	+	9.41985i	−0.367504	+	0.367504i
$658$	−18.9353	−	0.289912i	−0.738173	−	0.0113019i
$659$			41.1503i			1.60299i	0.598002	+	0.801494i	$0.295961\pi$
$659$			41.1503i			1.60299i	−0.598002	+	0.801494i	$0.704039\pi$
$660$	−17.9059	−	11.0624i	−0.696988	−	0.430604i
$661$	−3.09722	−	1.78818i	−0.120468	−	0.0695522i	0.438555	−	0.898704i	$-0.355490\pi$
$661$	−3.09722	−	1.78818i	−0.120468	−	0.0695522i	−0.559023	+	0.829152i	$0.688824\pi$
$662$	−23.0645	−	14.7524i	−0.896426	−	0.573368i
$663$	5.14274	+	1.37799i	0.199727	+	0.0535168i
$664$	−9.67610	+	7.34168i	−0.375506	+	0.284912i
$665$	−23.0777	−	32.6836i	−0.894913	−	1.26742i
$666$	−7.05278	−	7.72475i	−0.273290	−	0.299328i
$667$	−28.6123	−	7.66664i	−1.10787	−	0.296854i
$668$	−5.95762	+	1.02829i	−0.230507	+	0.0397856i
$669$	−2.15750	+	3.73690i	−0.0834138	+	0.144477i
$670$	−31.8116	−	17.7093i	−1.22899	−	0.684172i
$671$			45.8870i			1.77145i
$672$	−9.87636	+	11.2453i	−0.380989	+	0.433798i
$673$	12.1451	+	12.1451i	0.468158	+	0.468158i	0.901317	−	0.433159i	$-0.142601\pi$
$673$	12.1451	+	12.1451i	0.468158	+	0.468158i	−0.433159	+	0.901317i	$0.642601\pi$
$674$	−11.0970	+	34.9746i	−0.427441	+	1.34717i
$675$	−0.696009	+	4.95132i	−0.0267894	+	0.190576i
$676$	14.3757	+	10.1437i	0.552913	+	0.390142i
$677$	−8.95299	+	33.4130i	−0.344092	+	1.28417i	0.549578	+	0.835442i	$0.314788\pi$
$677$	−8.95299	+	33.4130i	−0.344092	+	1.28417i	−0.893670	+	0.448725i	$0.851878\pi$
$678$	−0.455757	−	0.0207246i	−0.0175032	−	0.000795923i
$679$	16.8628	+	27.2751i	0.647136	+	1.04672i
$680$	14.8017	−	7.11985i	0.567618	−	0.273034i
$681$	−11.1986	−	19.3965i	−0.429130	−	0.743275i
$682$	8.84704	−	13.8318i	0.338771	−	0.529647i
$683$	35.7898	−	9.58985i	1.36946	−	0.366946i	0.502178	−	0.864764i	$-0.332532\pi$
$683$	35.7898	−	9.58985i	1.36946	−	0.366946i	0.867281	+	0.497819i	$0.165865\pi$
$684$	−5.67189	−	12.2792i	−0.216870	−	0.469506i
$685$	−7.23001	−	10.9237i	−0.276245	−	0.417373i
$686$	5.63510	−	25.5782i	0.215149	−	0.976581i
$687$	12.8306	+	12.8306i	0.489519	+	0.489519i
$688$	3.93819	−	8.28842i	0.150142	−	0.315993i
$689$	−16.0835	−	9.28581i	−0.612732	−	0.353761i
$690$	−11.8443	+	12.2204i	−0.450904	+	0.465224i
$691$	14.3894	+	24.9231i	0.547398	+	0.948121i	0.998452	+	0.0556242i	$0.0177149\pi$
$691$	14.3894	+	24.9231i	0.547398	+	0.948121i	−0.451054	+	0.892497i	$0.648952\pi$
$692$	−24.4633	+	20.3768i	−0.929953	+	0.774609i
$693$	12.1193	+	2.85896i	0.460372	+	0.108603i
$694$	14.6210	+	16.0141i	0.555005	+	0.607885i
$695$	14.7852	+	44.1903i	0.560833	+	1.67623i
$696$	1.94828	+	15.4457i	0.0738493	+	0.585467i
$697$	1.99266	+	7.43672i	0.0754775	+	0.281686i
$698$	4.53211	−	2.34886i	0.171543	−	0.0889058i
$699$		−	9.41346i		−	0.356050i
$700$	25.9280	+	5.26683i	0.979986	+	0.199068i
$701$			24.7798i			0.935921i	0.883749	+	0.467960i	$0.155011\pi$
$701$			24.7798i			0.935921i	−0.883749	+	0.467960i	$0.844989\pi$
$702$	1.33408	+	2.57410i	0.0503517	+	0.0971533i
$703$	−12.9465	−	48.3168i	−0.488285	−	1.82230i
$704$	−26.9106	+	26.3329i	−1.01423	+	0.992457i
$705$	3.59088	+	10.7325i	0.135240	+	0.404210i
$706$	−25.5874	+	23.3615i	−0.962993	+	0.879222i
$707$	3.83043	−	4.06852i	0.144058	−	0.153012i
$708$	−20.2882	+	16.8992i	−0.762479	+	0.635111i
$709$	−6.98171	−	12.0927i	−0.262204	−	0.454150i	0.704624	−	0.709581i	$-0.251116\pi$
$709$	−6.98171	−	12.0927i	−0.262204	−	0.454150i	−0.966827	+	0.255431i	$0.917783\pi$
$710$	32.9847	+	31.9693i	1.23789	+	1.19979i
$711$	11.2895	+	6.51800i	0.423389	+	0.244444i
$712$	−0.0658718	−	0.161501i	−0.00246865	−	0.00605252i
$713$	−9.38756	−	9.38756i	−0.351567	−	0.351567i
$714$	−6.97547	+	6.76509i	−0.261050	+	0.253177i
$715$	11.9077	+	17.9911i	0.445321	+	0.672828i
$716$	19.4737	−	8.99513i	0.727766	−	0.336164i
$717$	1.80020	−	0.482363i	0.0672298	−	0.0180142i
$718$	−36.9121	−	23.6096i	−1.37755	−	0.881101i
$719$	3.97223	+	6.88011i	0.148139	+	0.256585i	0.930540	−	0.366191i	$-0.119338\pi$
$719$	3.97223	+	6.88011i	0.148139	+	0.256585i	−0.782400	+	0.622776i	$0.786005\pi$
$720$	8.29793	+	3.33832i	0.309246	+	0.124412i
$721$	−5.97628	+	11.1114i	−0.222568	+	0.413812i
$722$	1.71765	−	37.7729i	0.0639241	−	1.40576i
$723$	3.48096	−	12.9911i	0.129458	−	0.483145i
$724$	−5.36698	−	3.78700i	−0.199462	−	0.140743i
$725$	21.9795	−	16.5618i	0.816299	−	0.615088i
$726$	15.0301	+	4.76886i	0.557818	+	0.176989i
$727$	12.8465	+	12.8465i	0.476449	+	0.476449i	0.903994	−	0.427545i	$-0.140621\pi$
$727$	12.8465	+	12.8465i	0.476449	+	0.476449i	−0.427545	+	0.903994i	$0.640621\pi$
$728$	14.0244	−	6.21931i	0.519777	−	0.230503i
$729$		−	1.00000i		−	0.0370370i
$730$	20.4906	−	36.8077i	0.758393	−	1.36231i
$731$	2.97893	−	5.15967i	0.110180	−	0.190837i
$732$	−3.31665	−	19.2158i	−0.122587	−	0.710236i
$733$	20.4955	+	5.49176i	0.757020	+	0.202843i	0.616630	−	0.787253i	$-0.288498\pi$
$733$	20.4955	+	5.49176i	0.757020	+	0.202843i	0.140390	+	0.990096i	$0.455164\pi$
$734$	−21.5512	+	19.6765i	−0.795470	+	0.726272i
$735$	−15.5374	+	1.89456i	−0.573105	+	0.0698817i
$736$	16.1244	+	25.8226i	0.594354	+	0.951833i
$737$	52.3404	+	14.0246i	1.92798	+	0.516601i
$738$	−2.25904	+	3.53187i	−0.0831563	+	0.130010i
$739$	−34.7517	−	20.0639i	−1.27836	−	0.738062i	−0.301814	−	0.953367i	$-0.597592\pi$
$739$	−34.7517	−	20.0639i	−1.27836	−	0.738062i	−0.976547	+	0.215305i	$0.930925\pi$
$740$	28.1404	+	17.3854i	1.03446	+	0.639098i
$741$			13.8646i			0.509330i
$742$	29.6102	−	16.4963i	1.08702	−	0.605598i
$743$	−10.5715	+	10.5715i	−0.387831	+	0.387831i	−0.873913	−	0.486082i	$-0.838426\pi$
$743$	−10.5715	+	10.5715i	−0.387831	+	0.387831i	0.486082	+	0.873913i	$0.338426\pi$
$744$	−2.70507	+	6.43171i	−0.0991727	+	0.235798i
$745$	10.5689	+	9.35089i	0.387216	+	0.342590i
$746$	34.1124	−	7.49783i	1.24894	−	0.274515i
$747$	−4.14796	−	1.11144i	−0.151766	−	0.0406656i
$748$	−18.7828	+	15.6452i	−0.686767	+	0.572046i
$749$	1.31497	−	2.44487i	0.0480481	−	0.0893337i
$750$	−2.17152	−	15.6616i	−0.0792927	−	0.571879i
$751$	1.96504	−	1.13452i	0.0717054	−	0.0413991i	−0.463719	−	0.885983i	$-0.653485\pi$
$751$	1.96504	−	1.13452i	0.0717054	−	0.0413991i	0.535424	+	0.844583i	$0.320152\pi$
$752$	20.1802	−	1.61854i	0.735897	−	0.0590221i
$753$	16.3011	−	4.36786i	0.594044	−	0.159174i
$754$	4.82619	−	15.2107i	0.175759	−	0.553943i
$755$	−39.4134	−	8.01933i	−1.43440	−	0.291853i
$756$	−5.28174	−	0.321267i	−0.192095	−	0.0116844i
$757$	8.49357	+	8.49357i	0.308704	+	0.308704i	0.844407	−	0.535703i	$-0.179953\pi$
$757$	8.49357	+	8.49357i	0.308704	+	0.308704i	−0.535703	+	0.844407i	$0.679953\pi$
$758$	10.2816	+	19.8383i	0.373445	+	0.720559i
$759$	12.6641	−	21.9349i	0.459679	−	0.796187i
$760$	27.8853	+	32.4330i	1.01150	+	1.17647i
$761$	0.811300	+	1.40521i	0.0294096	+	0.0509389i	0.880356	−	0.474314i	$-0.157304\pi$
$761$	0.811300	+	1.40521i	0.0294096	+	0.0509389i	−0.850946	+	0.525253i	$0.823971\pi$
$762$	−23.4821	−	1.06780i	−0.850667	−	0.0386823i
$763$	−7.19714	−	6.77598i	−0.260554	−	0.245307i
$764$	−0.114506	+	1.25645i	−0.00414268	+	0.0454569i
$765$	5.19696	+	2.59120i	0.187896	+	0.0936851i
$766$	29.4696	−	6.47736i	1.06478	−	0.234037i
$767$	26.1436	−	7.00516i	0.943991	−	0.252942i
$768$	9.36587	−	12.9723i	0.337962	−	0.468098i
$769$			0.380100i			0.0137068i	0.999977	+	0.00685338i	$0.00218151\pi$
$769$			0.380100i			0.0137068i	−0.999977	+	0.00685338i	$0.997818\pi$
$770$	−39.3352	+	1.80133i	−1.41754	+	0.0649156i
$771$	−8.93763			−0.321881
$772$	−2.35328	+	6.39354i	−0.0846964	+	0.230109i
$773$	11.1358	+	41.5592i	0.400525	+	1.49478i	0.812162	+	0.583433i	$0.198291\pi$
$773$	11.1358	+	41.5592i	0.400525	+	1.49478i	−0.411636	+	0.911348i	$0.635043\pi$
$774$	3.16872	−	0.696480i	0.113897	−	0.0250345i
$775$	12.2425	−	1.50283i	0.439765	−	0.0539834i
$776$	−20.7211	−	27.3097i	−0.743843	−	0.980362i
$777$	−19.0462	−	4.49306i	−0.683280	−	0.161188i
$778$	−0.647341	+	14.2358i	−0.0232083	+	0.510377i
$779$	−17.3631	+	10.0246i	−0.622096	+	0.359167i
$780$	−6.28686	−	6.67333i	−0.225106	−	0.238944i
$781$	−59.2054	−	34.1823i	−2.11854	−	1.22314i
$782$	9.09502	+	17.5488i	0.325237	+	0.627543i
$783$	−3.89202	+	3.89202i	−0.139089	+	0.139089i
$784$	−3.39370	+	27.7936i	−0.121203	+	0.992628i
$785$	−26.8079	+	17.7432i	−0.956814	+	0.633281i
$786$	6.12805	+	1.94436i	0.218580	+	0.0693530i
$787$	4.02768	+	15.0315i	0.143571	+	0.535816i	0.999815	+	0.0192431i	$0.00612565\pi$
$787$	4.02768	+	15.0315i	0.143571	+	0.535816i	−0.856243	+	0.516572i	$0.827208\pi$
$788$	−22.5078	+	3.88486i	−0.801808	+	0.138392i
$789$	−5.73104	−	9.92645i	−0.204030	−	0.353391i
$790$	−39.9807	−	10.0457i	−1.42245	−	0.357412i
$791$	−0.725981	+	0.448838i	−0.0258129	+	0.0159588i
$792$	−13.1881	−	1.80909i	−0.468620	−	0.0642833i
$793$	−5.17336	+	19.3073i	−0.183712	+	0.685621i
$794$	−4.69526	−	21.3617i	−0.166628	−	0.758098i
$795$	−15.1709	−	13.4225i	−0.538056	−	0.476046i
$796$	13.5927	+	29.4270i	0.481779	+	1.04301i
$797$	21.9104	+	21.9104i	0.776105	+	0.776105i	0.979166	−	0.203061i	$-0.0650891\pi$
$797$	21.9104	+	21.9104i	0.776105	+	0.776105i	−0.203061	+	0.979166i	$0.565089\pi$
$798$	−21.7181	−	12.9863i	−0.768813	−	0.459709i
$799$	13.1442			0.465009
$800$	−28.1283	−	2.96619i	−0.994486	−	0.104871i
$801$	0.0308331	−	0.0534045i	0.00108943	−	0.00188696i
$802$	19.7888	+	12.6572i	0.698766	+	0.446941i
$803$	−16.2272	+	60.5606i	−0.572644	+	2.13714i
$804$	−22.9319	−	2.08988i	−0.808746	−	0.0737044i
$805$	−5.40519	+	31.3763i	−0.190508	+	1.10587i
$806$	5.28187	−	4.82240i	0.186046	−	0.169862i
$807$	0.342987	−	1.28004i	0.0120737	−	0.0450597i
$808$	−3.66225	+	4.71950i	−0.128837	+	0.166031i
$809$	42.6507	+	24.6244i	1.49952	+	0.865748i	1.00000		0.000553784i	$-0.000176275\pi$
$809$	42.6507	+	24.6244i	1.49952	+	0.865748i	0.499520	+	0.866302i	$0.333510\pi$
$810$	0.866099	+	3.04136i	0.0304316	+	0.106863i
$811$	−22.7295			−0.798139			−0.399070	−	0.916921i	$-0.630667\pi$
$811$	−22.7295			−0.798139			−0.399070	+	0.916921i	$0.630667\pi$
$812$	19.3063	+	21.8070i	0.677517	+	0.765276i
$813$	5.59343	−	5.59343i	0.196170	−	0.196170i
$814$	−46.9238	−	14.8884i	−1.64468	−	0.521837i
$815$	−2.66620	−	43.6023i	−0.0933929	−	1.52732i
$816$	6.73473	−	7.90924i	0.235763	−	0.276879i
$817$	14.9862	+	4.01555i	0.524302	+	0.140486i
$818$	30.6627	+	1.39432i	1.07210	+	0.0487513i
$819$	4.77694	+	2.56927i	0.166920	+	0.0897776i
$820$	3.81160	−	12.6982i	0.133107	−	0.443441i
$821$	−35.2201	+	20.3343i	−1.22919	+	0.709672i	−0.966860	−	0.255306i	$-0.917824\pi$
$821$	−35.2201	+	20.3343i	−1.22919	+	0.709672i	−0.262328	+	0.964979i	$0.584490\pi$
$822$	−6.97938	−	4.46412i	−0.243434	−	0.155704i
$823$	−1.68452	−	6.28670i	−0.0587186	−	0.219141i	0.930332	−	0.366719i	$-0.119519\pi$
$823$	−1.68452	−	6.28670i	−0.0587186	−	0.219141i	−0.989050	+	0.147578i	$0.952852\pi$
$824$	5.22907	−	12.4329i	0.182163	−	0.433120i
$825$	8.81457	+	21.8186i	0.306884	+	0.759628i
$826$	−13.5142	+	47.5137i	−0.470218	+	1.65321i
$827$	36.0435	−	36.0435i	1.25336	−	1.25336i	0.299151	−	0.954206i	$-0.403297\pi$
$827$	36.0435	−	36.0435i	1.25336	−	1.25336i	0.954206	−	0.299151i	$-0.0967033\pi$
$828$	−3.71785	+	10.1009i	−0.129204	+	0.351030i
$829$	−20.3826	+	35.3037i	−0.707918	+	1.22615i	0.257711	+	0.966222i	$0.417032\pi$
$829$	−20.3826	+	35.3037i	−0.707918	+	1.22615i	−0.965628	+	0.259927i	$0.916301\pi$
$830$	13.5781	−	0.212248i	0.471302	−	0.00736725i
$831$	−9.86739	+	5.69694i	−0.342296	+	0.197625i
$832$	−14.2916	+	8.04580i	−0.495473	+	0.278938i
$833$	−3.63899	+	17.8112i	−0.126084	+	0.617123i
$834$	19.8712	+	21.7644i	0.688082	+	0.753641i
$835$	6.04909	+	3.01608i	0.209338	+	0.104376i
$836$	−52.0130	−	36.7009i	−1.79891	−	1.26933i
$837$	−2.38283	+	0.638477i	−0.0823626	+	0.0220690i
$838$	4.18748	+	8.07971i	0.144654	+	0.279109i
$839$	−10.0769			−0.347892			−0.173946	−	0.984755i	$-0.555652\pi$
$839$	−10.0769			−0.347892			−0.173946	+	0.984755i	$0.555652\pi$
$840$	16.3419	−	3.59742i	0.563850	−	0.124123i
$841$	1.29565			0.0446777
$842$	−9.34013	−	18.0217i	−0.321882	−	0.621069i
$843$	−23.2911	+	6.24082i	−0.802187	+	0.214945i
$844$	−20.3752	+	28.8760i	−0.701344	+	0.993953i
$845$	−6.24140	−	18.6545i	−0.214711	−	0.641734i
$846$	4.82612	+	5.28594i	0.165925	+	0.181734i
$847$	28.2520	−	8.49021i	0.970749	−	0.291727i
$848$	−29.8320	+	20.5686i	−1.02444	+	0.706330i
$849$	−10.0741	+	5.81629i	−0.345742	+	0.199614i
$850$	−18.0501	−	3.37970i	−0.619112	−	0.115923i
$851$	−19.9026	+	34.4723i	−0.682251	+	1.18169i
$852$	27.2637	+	10.0350i	0.934039	+	0.343793i
$853$	−17.0953	+	17.0953i	−0.585333	+	0.585333i	−0.936364	−	0.351031i	$-0.885831\pi$
$853$	−17.0953	+	17.0953i	−0.585333	+	0.585333i	0.351031	+	0.936364i	$0.385831\pi$
$854$	−25.3980	−	26.1878i	−0.869102	−	0.896129i
$855$	−3.01513	+	14.8187i	−0.103115	+	0.506790i
$856$	−1.15056	+	2.73563i	−0.0393254	+	0.0935020i
$857$	4.14177	+	15.4573i	0.141480	+	0.528011i	0.999887	+	0.0150413i	$0.00478797\pi$
$857$	4.14177	+	15.4573i	0.141480	+	0.528011i	−0.858407	+	0.512970i	$0.828545\pi$
$858$	11.4949	+	7.35230i	0.392428	+	0.251003i
$859$	−41.9138	+	24.1989i	−1.43008	+	0.825656i	−0.997126	−	0.0757602i	$-0.975862\pi$
$859$	−41.9138	+	24.1989i	−1.43008	+	0.825656i	−0.432953	+	0.901417i	$0.642528\pi$
$860$	−9.03401	+	4.86268i	−0.308057	+	0.165816i
$861$	0.236306	+	7.83995i	0.00805328	+	0.267185i
$862$	17.9504	+	0.816256i	0.611393	+	0.0278018i
$863$	4.63262	+	1.24131i	0.157696	+	0.0422546i	0.336803	−	0.941575i	$-0.390654\pi$
$863$	4.63262	+	1.24131i	0.157696	+	0.0422546i	−0.179107	+	0.983830i	$0.557321\pi$
$864$	5.65347	−	0.195639i	0.192335	−	0.00665579i
$865$	35.5297	−	2.17257i	1.20805	−	0.0738697i
$866$	−33.7569	−	10.7107i	−1.14711	−	0.363963i
$867$	−7.25170	+	7.25170i	−0.246281	+	0.246281i
$868$	2.60675	+	12.7906i	0.0884788	+	0.434142i
$869$	61.3523			2.08124
$870$	8.46616	−	15.2079i	0.287030	−	0.515597i
$871$	20.4414	+	11.8019i	0.692631	+	0.399891i
$872$	8.34873	+	6.47846i	0.282724	+	0.219389i
$873$	3.13692	−	11.7072i	0.106169	−	0.396227i
$874$	−38.0117	+	34.7051i	−1.28576	+	1.17392i
$875$	−19.8789	−	21.9050i	−0.672030	−	0.740524i
$876$	2.41810	−	26.5334i	0.0817001	−	0.896481i
$877$	−11.4581	+	42.7620i	−0.386911	+	1.44397i	0.448221	+	0.893923i	$0.352058\pi$
$877$	−11.4581	+	42.7620i	−0.386911	+	1.44397i	−0.835132	+	0.550049i	$0.814609\pi$
$878$	5.49138	+	3.51237i	0.185325	+	0.118537i
$879$	−9.83905	+	17.0417i	−0.331863	+	0.574804i
$880$	41.6768	−	5.92014i	1.40492	−	0.199568i
$881$	15.7780			0.531573			0.265787	−	0.964032i	$-0.414368\pi$
$881$	15.7780			0.531573			0.265787	+	0.964032i	$0.414368\pi$
$882$	−8.49891	+	5.07628i	−0.286173	+	0.170927i
$883$	−19.9690	−	19.9690i	−0.672010	−	0.672010i	0.286169	−	0.958179i	$-0.407618\pi$
$883$	−19.9690	−	19.9690i	−0.672010	−	0.672010i	−0.958179	+	0.286169i	$0.907618\pi$
$884$	−9.66686	+	4.46524i	−0.325132	+	0.150182i
$885$	29.4660	−	1.80179i	0.990490	−	0.0605666i
$886$	5.72250	+	26.0353i	0.192251	+	0.874672i
$887$	−1.23496	+	4.60894i	−0.0414660	+	0.154753i	−0.983555	−	0.180611i	$-0.942193\pi$
$887$	−1.23496	+	4.60894i	−0.0414660	+	0.154753i	0.942089	+	0.335364i	$0.108859\pi$
$888$	20.7261	+	2.84311i	0.695522	+	0.0954086i
$889$	−37.4049	+	23.1256i	−1.25452	+	0.775608i
$890$	−0.0475210	+	0.189127i	−0.00159291	+	0.00633955i
$891$	−2.35319	−	4.07584i	−0.0788348	−	0.136546i
$892$	−1.46784	−	8.50426i	−0.0491468	−	0.284744i
$893$	8.85908	+	33.0625i	0.296458	+	1.10640i
$894$	8.50711	+	2.69921i	0.284520	+	0.0902749i
$895$	−23.5012	−	4.78173i	−0.785558	−	0.159836i
$896$	0.782955	−	29.9230i	0.0261567	−	0.999658i
$897$	7.80150	−	7.80150i	0.260484	−	0.260484i
$898$	23.9389	+	46.1899i	0.798851	+	1.54138i
$899$	11.7590	+	6.78906i	0.392184	+	0.226428i
$900$	−5.26824	−	8.49974i	−0.175608	−	0.283325i
$901$	−20.3743	+	11.7631i	−0.678766	+	0.391886i
$902$	−0.896329	+	19.7113i	−0.0298445	+	0.656314i
$903$	4.16064	−	4.41925i	0.138457	−	0.147063i
$904$	0.726902	−	0.551532i	0.0241764	−	0.0183437i
$905$	2.33014	+	6.96440i	0.0774566	+	0.231504i
$906$	−24.8449	+	5.46086i	−0.825416	+	0.181425i
$907$	−9.90302	−	36.9586i	−0.328824	−	1.22719i	−0.910411	−	0.413705i	$-0.864235\pi$
$907$	−9.90302	−	36.9586i	−0.328824	−	1.22719i	0.581587	−	0.813484i	$-0.302432\pi$
$908$	42.0371	+	15.4727i	1.39505	+	0.513479i
$909$	−2.11204			−0.0700520
$910$	−16.7536	−	3.67678i	−0.555377	−	0.121884i
$911$			32.0730i			1.06262i	0.847176	+	0.531312i	$0.178301\pi$
$911$			32.0730i			1.06262i	−0.847176	+	0.531312i	$0.821699\pi$
$912$	24.4338	+	11.6096i	0.809084	+	0.384432i
$913$	−19.5219	+	5.23087i	−0.646080	+	0.173117i
$914$	23.0353	−	5.06312i	0.761941	−	0.167473i
$915$	−9.72809	+	19.5108i	−0.321601	+	0.645008i
$916$	−36.1407	−	3.29366i	−1.19412	−	0.108826i
$917$	11.5189	−	3.46163i	0.380387	−	0.114313i
$918$	3.66896	+	0.166838i	0.121094	+	0.00550648i
$919$	−21.4528	−	37.1573i	−0.707661	−	1.22570i	−0.965723	−	0.259576i	$-0.916417\pi$
$919$	−21.4528	−	37.1573i	−0.707661	−	1.22570i	0.258062	−	0.966128i	$-0.416916\pi$
$920$	2.55895	−	33.9405i	0.0843660	−	1.11898i
$921$	−12.9697	+	22.4641i	−0.427365	+	0.740218i
$922$	−7.17048	−	13.8354i	−0.236147	−	0.455644i
$923$	−21.0573	−	21.0573i	−0.693110	−	0.693110i
$924$	−22.2836	+	11.1195i	−0.733075	+	0.365805i
$925$	−13.8527	−	34.2895i	−0.455474	−	1.12743i
$926$	−10.0605	+	31.7079i	−0.330610	+	1.04199i
$927$	4.60616	−	1.23422i	0.151286	−	0.0405370i
$928$	−22.7649	−	21.2420i	−0.747293	−	0.697303i
$929$	−42.0632	+	24.2852i	−1.38005	+	0.796772i	−0.992165	−	0.124935i	$-0.960128\pi$
$929$	−42.0632	+	24.2852i	−1.38005	+	0.796772i	−0.387885	+	0.921708i	$0.626794\pi$
$930$	6.69406	−	4.00561i	0.219507	−	0.131349i
$931$	−47.2545	+	2.85121i	−1.54870	+	0.0934446i
$932$	12.0495	+	14.4659i	0.394694	+	0.473847i
$933$	−10.8980	−	2.92010i	−0.356783	−	0.0955998i
$934$	−44.4507	+	9.77017i	−1.45447	+	0.319690i
$935$	27.2796	−	1.66809i	0.892138	−	0.0545525i
$936$	−5.34504	−	2.24804i	−0.174708	−	0.0734795i
$937$	20.1049	−	20.1049i	0.656798	−	0.656798i	−0.297823	−	0.954621i	$-0.596261\pi$
$937$	20.1049	−	20.1049i	0.656798	−	0.656798i	0.954621	+	0.297823i	$0.0962605\pi$
$938$	−37.6333	+	20.9661i	−1.22877	+	0.684566i
$939$		−	16.2427i		−	0.530060i
$940$	−19.2561	−	11.8966i	−0.628065	−	0.388023i
$941$	32.8063	+	18.9407i	1.06946	+	0.617451i	0.928033	−	0.372498i	$-0.121499\pi$
$941$	32.8063	+	18.9407i	1.06946	+	0.617451i	0.141423	+	0.989949i	$0.454832\pi$
$942$	−10.9554	+	17.1281i	−0.356946	+	0.558064i
$943$	15.4108	+	4.12930i	0.501843	+	0.134468i
$944$	9.54612	−	51.9389i	0.310700	−	1.69047i
$945$	4.54692	+	3.78491i	0.147911	+	0.123123i
$946$	11.2763	−	10.2954i	0.366623	−	0.334731i
$947$	53.8897	+	14.4397i	1.75118	+	0.469227i	0.984877	−	0.173254i	$-0.0554281\pi$
$947$	53.8897	+	14.4397i	1.75118	+	0.469227i	0.766302	+	0.642481i	$0.222095\pi$
$948$	−25.6921	+	4.43446i	−0.834441	+	0.144025i
$949$	−13.6554	+	23.6518i	−0.443272	+	0.767770i
$950$	−3.66440	−	47.6805i	−0.118889	−	1.54696i
$951$			8.51426i			0.276094i
$952$	2.05991	−	19.3249i	0.0667621	−	0.626323i
$953$	−28.4799	−	28.4799i	−0.922554	−	0.922554i	0.0746556	−	0.997209i	$-0.476214\pi$
$953$	−28.4799	−	28.4799i	−0.922554	−	0.922554i	−0.997209	+	0.0746556i	$0.976214\pi$
$954$	−12.2113	−	3.87450i	−0.395355	−	0.125441i
$955$	0.934693	−	1.05645i	0.0302459	−	0.0341858i
$956$	−2.14899	+	3.04557i	−0.0695032	+	0.0985007i
$957$	−6.70461	+	25.0219i	−0.216729	+	0.808844i
$958$	1.24003	−	27.2696i	0.0400635	−	0.881042i
$959$	−15.4927	+	0.466968i	−0.500284	+	0.0150792i
$960$	−17.0248	+	5.49148i	−0.549473	+	0.177237i
$961$	−12.4572	−	21.5766i	−0.401846	−	0.696018i
$962$	−18.0650	−	11.5546i	−0.582438	−	0.372537i
$963$	−1.01350	+	0.271567i	−0.0326597	+	0.00875113i
$964$	11.2797	+	24.4195i	0.363294	+	0.786500i
$965$	6.35179	−	4.20403i	0.204471	−	0.135332i
$966$	4.91332	+	19.5278i	0.158084	+	0.628297i
$967$	27.6005	+	27.6005i	0.887571	+	0.887571i	0.994289	−	0.106718i	$-0.0340343\pi$
$967$	27.6005	+	27.6005i	0.887571	+	0.887571i	−0.106718	+	0.994289i	$0.534034\pi$
$968$	−29.2014	+	11.9104i	−0.938568	+	0.382816i
$969$	15.2104	+	8.78174i	0.488629	+	0.282110i
$970$	0.599047	+	38.3226i	0.0192342	+	1.23046i
$971$	7.55464	+	13.0850i	0.242440	+	0.419919i	0.961409	−	0.275124i	$-0.0887189\pi$
$971$	7.55464	+	13.0850i	0.242440	+	0.419919i	−0.718969	+	0.695042i	$0.755386\pi$
$972$	1.28003	+	1.53673i	0.0410568	+	0.0492906i
$973$	53.6627	+	12.6592i	1.72035	+	0.405834i
$974$	−14.3935	+	13.1414i	−0.461198	+	0.421079i
$975$	1.24892	+	10.1741i	0.0399976	+	0.325832i
$976$	29.6935	+	25.2840i	0.950465	+	0.809322i
$977$	−4.24400	−	15.8388i	−0.135778	−	0.506729i	−0.999993	−	0.00360797i	$-0.998852\pi$
$977$	−4.24400	−	15.8388i	−0.135778	−	0.506729i	0.864216	−	0.503121i	$-0.167815\pi$
$978$	−12.7129	−	24.5294i	−0.406513	−	0.784364i
$979$		−	0.290225i		−	0.00927562i
$980$	21.4517	−	22.7997i	0.685249	−	0.728309i
$981$			3.73617i			0.119287i
$982$	−28.9360	+	14.9967i	−0.923386	+	0.478564i
$983$	−10.7964	−	40.2927i	−0.344351	−	1.28514i	−0.893368	−	0.449326i	$-0.851664\pi$
$983$	−10.7964	−	40.2927i	−0.344351	−	1.28514i	0.549017	−	0.835811i	$-0.315002\pi$
$984$	−1.04935	−	8.31914i	−0.0334522	−	0.265205i
$985$	22.8534	+	11.3947i	0.728171	+	0.363066i
$986$	−13.6303	−	14.9290i	−0.434078	−	0.475436i
$987$	13.0331	+	3.07454i	0.414848	+	0.0978637i
$988$	−17.7471	−	21.3062i	−0.564610	−	0.677840i
$989$	−6.17310	−	10.6921i	−0.196293	−	0.339990i
$990$	10.6870	+	10.3580i	0.339655	+	0.329199i
$991$	−29.5256	−	17.0466i	−0.937911	−	0.541503i	−0.0486061	−	0.998818i	$-0.515478\pi$
$991$	−29.5256	−	17.0466i	−0.937911	−	0.541503i	−0.889305	+	0.457315i	$0.848811\pi$
$992$	−4.07579	−	13.3463i	−0.129406	−	0.423747i
$993$	13.6894	+	13.6894i	0.434421	+	0.434421i
$994$	52.7083	−	13.2617i	1.67181	−	0.420637i
$995$	7.22574	−	35.5130i	0.229071	−	1.12584i
$996$	7.79697	−	3.60151i	0.247056	−	0.114118i
$997$	12.2156	−	3.27315i	0.386871	−	0.103662i	−0.0601405	−	0.998190i	$-0.519155\pi$
$997$	12.2156	−	3.27315i	0.386871	−	0.103662i	0.447012	+	0.894528i	$0.352488\pi$
$998$	30.6708	−	47.9519i	0.970866	−	1.51789i
$999$	3.69820	+	6.40547i	0.117006	+	0.202660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dj.a.403.81	yes	384
5.2	odd	4	inner	840.2.dj.a.67.63	yes	384
7.2	even	3	inner	840.2.dj.a.163.17	yes	384
8.3	odd	2	inner	840.2.dj.a.403.67	yes	384
35.2	odd	12	inner	840.2.dj.a.667.67	yes	384
40.27	even	4	inner	840.2.dj.a.67.17	✓	384
56.51	odd	6	inner	840.2.dj.a.163.63	yes	384
280.107	even	12	inner	840.2.dj.a.667.81	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dj.a.67.17	✓	384	40.27	even	4	inner
840.2.dj.a.67.63	yes	384	5.2	odd	4	inner
840.2.dj.a.163.17	yes	384	7.2	even	3	inner
840.2.dj.a.163.63	yes	384	56.51	odd	6	inner
840.2.dj.a.403.67	yes	384	8.3	odd	2	inner
840.2.dj.a.403.81	yes	384	1.1	even	1	trivial
840.2.dj.a.667.67	yes	384	35.2	odd	12	inner
840.2.dj.a.667.81	yes	384	280.107	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25560 - 0.650742i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.15307 - 1.63414i) q^{4} +(-2.12053 + 0.709484i) q^{5} +(-1.04439 + 0.953542i) q^{6} +(-0.607466 + 2.57507i) q^{7} +(0.384392 - 2.80219i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.20085 + 2.27074i) q^{10} +(2.35319 - 4.07584i) q^{11} +(-0.690833 + 1.87690i) q^{12} +(1.44964 - 1.44964i) q^{13} +(0.912970 + 3.62857i) q^{14} +(1.86464 - 1.23414i) q^{15} +(-1.34086 - 3.76857i) q^{16} +(-0.672160 - 2.50853i) q^{17} +(0.762012 - 1.19136i) q^{18} +(5.85686 - 3.38146i) q^{19} +(-1.28572 + 4.28333i) q^{20} +(-0.0797100 - 2.64455i) q^{21} +(0.302347 - 6.64895i) q^{22} +(-5.19831 - 1.39288i) q^{23} +(0.353965 + 2.80619i) q^{24} +(3.99326 - 3.00896i) q^{25} +(0.876828 - 2.76351i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(3.50758 + 3.96192i) q^{28} +5.50415 q^{29} +(1.53814 - 2.76299i) q^{30} +(2.13639 + 1.23344i) q^{31} +(-4.13595 - 3.85927i) q^{32} +(-1.21810 + 4.54601i) q^{33} +(-2.47637 - 2.71232i) q^{34} +(-0.538823 - 5.89149i) q^{35} +(0.181516 - 1.99175i) q^{36} +(1.91433 - 7.14437i) q^{37} +(5.15343 - 8.05707i) q^{38} +(-1.02505 + 1.77544i) q^{39} +(1.17299 + 6.21483i) q^{40} -2.96457 q^{41} +(-1.82100 - 3.26863i) q^{42} +(1.62218 + 1.62218i) q^{43} +(-3.94712 - 8.54519i) q^{44} +(-1.48169 + 1.67469i) q^{45} +(-7.43342 + 1.63385i) q^{46} +(-1.30995 + 4.88880i) q^{47} +(2.27054 + 3.29312i) q^{48} +(-6.26197 - 3.12853i) q^{49} +(3.05589 - 6.37664i) q^{50} +(1.29851 + 2.24909i) q^{51} +(-0.697382 - 4.04045i) q^{52} +(-2.34462 - 8.75023i) q^{53} +(-0.427701 + 1.34799i) q^{54} +(-2.09825 + 10.3125i) q^{55} +(6.98232 + 2.69207i) q^{56} +(-4.78211 + 4.78211i) q^{57} +(6.91102 - 3.58178i) q^{58} +(11.4335 + 6.60111i) q^{59} +(0.133300 - 4.47015i) q^{60} +(-8.44371 + 4.87498i) q^{61} +(3.48510 + 0.158478i) q^{62} +(0.761454 + 2.53381i) q^{63} +(-7.70449 - 2.15427i) q^{64} +(-2.04550 + 4.10249i) q^{65} +(1.42883 + 6.50065i) q^{66} +(2.97990 + 11.1212i) q^{67} +(-4.87436 - 1.79411i) q^{68} +5.38169 q^{69} +(-4.51039 - 7.04673i) q^{70} -14.5259i q^{71} +(-1.06820 - 2.61896i) q^{72} +(-12.8678 + 3.44791i) q^{73} +(-2.24551 - 10.2162i) q^{74} +(-3.07842 + 3.93996i) q^{75} +(1.22758 - 13.4700i) q^{76} +(9.06610 + 8.53556i) q^{77} +(-0.131702 + 2.89628i) q^{78} +(6.51800 + 11.2895i) q^{79} +(5.51706 + 7.04003i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-3.72232 + 1.92917i) q^{82} +(-3.03652 - 3.03652i) q^{83} +(-4.41349 - 2.91910i) q^{84} +(3.20510 + 4.84253i) q^{85} +(3.09244 + 0.981193i) q^{86} +(-5.31660 + 1.42458i) q^{87} +(-10.5167 - 8.16079i) q^{88} +(0.0534045 - 0.0308331i) q^{89} +(-0.770616 + 3.06694i) q^{90} +(2.85231 + 4.61352i) q^{91} +(-8.27020 + 6.88870i) q^{92} +(-2.38283 - 0.638477i) q^{93} +(1.53657 + 6.99082i) q^{94} +(-10.0205 + 11.3258i) q^{95} +(4.99387 + 2.65731i) q^{96} +(8.57024 - 8.57024i) q^{97} +(-9.89841 + 0.146731i) q^{98} -4.70638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) \) 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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