LMFDB - Embedded newform 714.2.bh.a.457.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [714,2,Mod(25,714)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(714, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 16, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("714.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.bh (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,8,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			457.8
Character	$\chi$	$=$	714.457
Dual form			714.2.bh.a.25.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(0.608761 - 0.793353i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.309102 + 2.34786i) q^{5} +(0.382683 - 0.923880i) q^{6} +(2.57146 - 0.622558i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(0.309102 + 2.34786i) q^{10} +(-1.37902 + 0.181551i) q^{11} +(0.130526 - 0.991445i) q^{12} -0.134336i q^{13} +(2.32271 - 1.26689i) q^{14} +(1.67452 + 1.67452i) q^{15} +(0.500000 - 0.866025i) q^{16} +(4.07788 + 0.609038i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.87421 - 1.03809i) q^{19} +(0.906242 + 2.18786i) q^{20} +(1.07150 - 2.41907i) q^{21} +(-1.28504 + 0.532282i) q^{22} +(1.14188 + 1.48812i) q^{23} +(-0.130526 - 0.991445i) q^{24} +(-0.587295 - 0.157365i) q^{25} +(-0.0347688 - 0.129759i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(1.91567 - 1.82488i) q^{28} +(-6.29191 + 2.60620i) q^{29} +(2.05086 + 1.18406i) q^{30} +(4.41332 - 5.75155i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.695460 + 1.20457i) q^{33} +(4.09656 - 0.467147i) q^{34} +(0.666837 + 6.22988i) q^{35} +(-0.707107 - 0.707107i) q^{36} +(0.0607460 + 0.00799736i) q^{37} +(3.47352 - 2.00544i) q^{38} +(-0.106576 - 0.0817788i) q^{39} +(1.44162 + 1.87876i) q^{40} +(-9.51199 - 3.94000i) q^{41} +(0.408888 - 2.61396i) q^{42} +(-8.37978 + 8.37978i) q^{43} +(-1.10349 + 0.846738i) q^{44} +(2.34786 - 0.309102i) q^{45} +(1.48812 + 1.14188i) q^{46} +(-1.16295 - 0.671430i) q^{47} +(-0.382683 - 0.923880i) q^{48} +(6.22484 - 3.20177i) q^{49} -0.608013 q^{50} +(2.96564 - 2.86444i) q^{51} +(-0.0671682 - 0.116339i) q^{52} +(0.204130 - 0.761823i) q^{53} +(-0.991445 - 0.130526i) q^{54} -3.29387i q^{55} +(1.37808 - 2.25851i) q^{56} +(1.53490 - 3.70557i) q^{57} +(-5.40299 + 4.14586i) q^{58} +(7.37511 + 1.97615i) q^{59} +(2.28743 + 0.612916i) q^{60} +(-2.15849 + 1.65627i) q^{61} +(2.77433 - 6.69783i) q^{62} +(-1.26689 - 2.32271i) q^{63} -1.00000i q^{64} +(0.315404 + 0.0415237i) q^{65} +(-0.359996 + 1.34352i) q^{66} +(0.382431 + 0.662389i) q^{67} +(3.83606 - 1.51150i) q^{68} +1.87574 q^{69} +(2.25653 + 5.84501i) q^{70} +(2.92765 + 7.06797i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(-8.45174 - 6.48525i) q^{73} +(0.0607460 - 0.00799736i) q^{74} +(-0.482369 + 0.370135i) q^{75} +(2.83612 - 2.83612i) q^{76} +(-3.43307 + 1.32537i) q^{77} +(-0.124111 - 0.0514083i) q^{78} +(-8.43950 - 10.9986i) q^{79} +(1.87876 + 1.44162i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-10.2076 - 1.34386i) q^{82} +(-5.69822 - 5.69822i) q^{83} +(-0.281589 - 2.63072i) q^{84} +(-2.69042 + 9.38605i) q^{85} +(-5.92540 + 10.2631i) q^{86} +(-1.76264 + 6.57826i) q^{87} +(-0.846738 + 1.10349i) q^{88} +(-11.1056 - 6.41182i) q^{89} +(2.18786 - 0.906242i) q^{90} +(-0.0836322 - 0.345441i) q^{91} +(1.73296 + 0.717813i) q^{92} +(-1.87635 - 7.00265i) q^{93} +(-1.29710 - 0.347558i) q^{94} +(1.23977 + 9.41701i) q^{95} +(-0.608761 - 0.793353i) q^{96} +(-7.76556 + 3.21660i) q^{97} +(5.18406 - 4.70378i) q^{98} +(0.532282 + 1.28504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{5} - 8 q^{10} - 16 q^{11} - 16 q^{15} + 48 q^{16} + 8 q^{17} - 48 q^{18} + 8 q^{19} + 16 q^{22} - 40 q^{25} + 32 q^{29} + 48 q^{33} + 32 q^{35} + 16 q^{37} + 16 q^{39} + 16 q^{42} - 16 q^{43}+ \cdots + 32 q^{99}+O(q^{100}) $ 96 * q + 8 * q^5 - 8 * q^10 - 16 * q^11 - 16 * q^15 + 48 * q^16 + 8 * q^17 - 48 * q^18 + 8 * q^19 + 16 * q^22 - 40 * q^25 + 32 * q^29 + 48 * q^33 + 32 * q^35 + 16 * q^37 + 16 * q^39 + 16 * q^42 - 16 * q^43 + 8 * q^44 + 8 * q^46 + 16 * q^49 - 128 * q^50 - 16 * q^52 - 24 * q^53 - 16 * q^57 + 16 * q^58 + 56 * q^59 - 8 * q^60 - 64 * q^65 + 32 * q^67 + 128 * q^69 + 24 * q^70 + 64 * q^71 - 40 * q^73 + 16 * q^74 + 16 * q^76 - 16 * q^77 + 32 * q^78 + 56 * q^79 - 8 * q^80 + 16 * q^83 - 48 * q^85 - 16 * q^86 - 24 * q^87 + 16 * q^88 - 16 * q^90 + 8 * q^91 + 16 * q^92 - 8 * q^93 - 24 * q^94 + 64 * q^95 + 32 * q^97 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.608761	−	0.793353i	0.351469	−	0.458043i
$3$	0.608761	−	0.793353i	0.351469	−	0.458043i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.309102	+	2.34786i	−0.138235	+	1.05000i	0.771917	+	0.635723i	$0.219298\pi$
$5$	−0.309102	+	2.34786i	−0.138235	+	1.05000i	−0.910152	+	0.414274i	$0.864035\pi$
$6$	0.382683	−	0.923880i	0.156230	−	0.377172i
$7$	2.57146	−	0.622558i	0.971922	−	0.235305i
$7$	2.57146	−	0.622558i	0.971922	−	0.235305i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.258819	−	0.965926i	−0.0862730	−	0.321975i
$10$	0.309102	+	2.34786i	0.0977467	+	0.742460i
$11$	−1.37902	+	0.181551i	−0.415790	+	0.0547398i	−0.335519	−	0.942033i	$-0.608912\pi$
$11$	−1.37902	+	0.181551i	−0.415790	+	0.0547398i	−0.0802707	+	0.996773i	$0.525578\pi$
$12$	0.130526	−	0.991445i	0.0376797	−	0.286205i
$13$		−	0.134336i		−	0.0372582i	−0.999826	−	0.0186291i	$-0.994070\pi$
$13$		−	0.134336i		−	0.0372582i	0.999826	−	0.0186291i	$-0.00593017\pi$
$14$	2.32271	−	1.26689i	0.620771	−	0.338590i
$15$	1.67452	+	1.67452i	0.432358	+	0.432358i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	4.07788	+	0.609038i	0.989030	+	0.147713i
$17$	4.07788	+	0.609038i	0.989030	+	0.147713i
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	3.87421	−	1.03809i	0.888805	−	0.238155i	0.214603	−	0.976701i	$-0.431154\pi$
$19$	3.87421	−	1.03809i	0.888805	−	0.238155i	0.674202	+	0.738547i	$0.264488\pi$
$20$	0.906242	+	2.18786i	0.202642	+	0.489221i
$21$	1.07150	−	2.41907i	0.233820	−	0.527884i
$22$	−1.28504	+	0.532282i	−0.273972	+	0.113483i
$23$	1.14188	+	1.48812i	0.238098	+	0.310295i	0.897084	−	0.441860i	$-0.145681\pi$
$23$	1.14188	+	1.48812i	0.238098	+	0.310295i	−0.658986	+	0.752155i	$0.729015\pi$
$24$	−0.130526	−	0.991445i	−0.0266435	−	0.202378i
$25$	−0.587295	−	0.157365i	−0.117459	−	0.0314731i
$26$	−0.0347688	−	0.129759i	−0.00681872	−	0.0254478i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	1.91567	−	1.82488i	0.362028	−	0.344870i
$29$	−6.29191	+	2.60620i	−1.16838	+	0.483958i	−0.880656	−	0.473756i	$-0.842898\pi$
$29$	−6.29191	+	2.60620i	−1.16838	+	0.483958i	−0.287722	+	0.957714i	$0.592898\pi$
$30$	2.05086	+	1.18406i	0.374433	+	0.216179i
$31$	4.41332	−	5.75155i	0.792656	−	1.03301i	−0.205862	−	0.978581i	$-0.566000\pi$
$31$	4.41332	−	5.75155i	0.792656	−	1.03301i	0.998518	−	0.0544284i	$-0.0173337\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−0.695460	+	1.20457i	−0.121064	+	0.209689i
$34$	4.09656	−	0.467147i	0.702554	−	0.0801150i
$35$	0.666837	+	6.22988i	0.112716	+	1.05304i
$36$	−0.707107	−	0.707107i	−0.117851	−	0.117851i
$37$	0.0607460	+	0.00799736i	0.00998658	+	0.00131476i	0.135518	−	0.990775i	$-0.456730\pi$
$37$	0.0607460	+	0.00799736i	0.00998658	+	0.00131476i	−0.125531	+	0.992090i	$0.540064\pi$
$38$	3.47352	−	2.00544i	0.563480	−	0.325325i
$39$	−0.106576	−	0.0817788i	−0.0170658	−	0.0130951i
$40$	1.44162	+	1.87876i	0.227941	+	0.297058i
$41$	−9.51199	−	3.94000i	−1.48552	−	0.615324i	−0.515186	−	0.857078i	$-0.672277\pi$
$41$	−9.51199	−	3.94000i	−1.48552	−	0.615324i	−0.970337	+	0.241754i	$0.922277\pi$
$42$	0.408888	−	2.61396i	0.0630927	−	0.403343i
$43$	−8.37978	+	8.37978i	−1.27790	+	1.27790i	−0.336065	+	0.941839i	$0.609096\pi$
$43$	−8.37978	+	8.37978i	−1.27790	+	1.27790i	−0.941839	+	0.336065i	$0.890904\pi$
$44$	−1.10349	+	0.846738i	−0.166357	+	0.127651i
$45$	2.34786	−	0.309102i	0.349999	−	0.0460782i
$46$	1.48812	+	1.14188i	0.219412	+	0.168360i
$47$	−1.16295	−	0.671430i	−0.169634	−	0.0979381i	0.412779	−	0.910831i	$-0.364558\pi$
$47$	−1.16295	−	0.671430i	−0.169634	−	0.0979381i	−0.582413	+	0.812893i	$0.697891\pi$
$48$	−0.382683	−	0.923880i	−0.0552356	−	0.133351i
$49$	6.22484	−	3.20177i	0.889263	−	0.457396i
$50$	−0.608013			−0.0859860
$51$	2.96564	−	2.86444i	0.415272	−	0.401102i
$52$	−0.0671682	−	0.116339i	−0.00931455	−	0.0161333i
$53$	0.204130	−	0.761823i	0.0280394	−	0.104644i	−0.950488	−	0.310761i	$-0.899416\pi$
$53$	0.204130	−	0.761823i	0.0280394	−	0.104644i	0.978527	+	0.206117i	$0.0660827\pi$
$54$	−0.991445	−	0.130526i	−0.134919	−	0.0177624i
$55$		−	3.29387i		−	0.444145i
$56$	1.37808	−	2.25851i	0.184154	−	0.301807i
$57$	1.53490	−	3.70557i	0.203302	−	0.490815i
$58$	−5.40299	+	4.14586i	−0.709447	+	0.544378i
$59$	7.37511	+	1.97615i	0.960157	+	0.257273i	0.704667	−	0.709538i	$-0.251096\pi$
$59$	7.37511	+	1.97615i	0.960157	+	0.257273i	0.255490	+	0.966812i	$0.417763\pi$
$60$	2.28743	+	0.612916i	0.295306	+	0.0791271i
$61$	−2.15849	+	1.65627i	−0.276366	+	0.212063i	−0.737639	−	0.675195i	$-0.764059\pi$
$61$	−2.15849	+	1.65627i	−0.276366	+	0.212063i	0.461273	+	0.887258i	$0.347393\pi$
$62$	2.77433	−	6.69783i	0.352340	−	0.850625i
$63$	−1.26689	−	2.32271i	−0.159613	−	0.292634i
$64$		−	1.00000i		−	0.125000i
$65$	0.315404	+	0.0415237i	0.0391210	+	0.00515038i
$66$	−0.359996	+	1.34352i	−0.0443125	+	0.165376i
$67$	0.382431	+	0.662389i	0.0467213	+	0.0809237i	0.888440	−	0.458992i	$-0.151789\pi$
$67$	0.382431	+	0.662389i	0.0467213	+	0.0809237i	−0.841719	+	0.539916i	$0.818456\pi$
$68$	3.83606	−	1.51150i	0.465191	−	0.183296i
$69$	1.87574			0.225812
$70$	2.25653	+	5.84501i	0.269707	+	0.698613i
$71$	2.92765	+	7.06797i	0.347448	+	0.838814i	0.996920	+	0.0784280i	$0.0249901\pi$
$71$	2.92765	+	7.06797i	0.347448	+	0.838814i	−0.649472	+	0.760386i	$0.725010\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	−8.45174	−	6.48525i	−0.989201	−	0.759041i	−0.0186231	−	0.999827i	$-0.505928\pi$
$73$	−8.45174	−	6.48525i	−0.989201	−	0.759041i	−0.970578	+	0.240786i	$0.922595\pi$
$74$	0.0607460	−	0.00799736i	0.00706157	−	0.000929674i
$75$	−0.482369	+	0.370135i	−0.0556992	+	0.0427395i
$76$	2.83612	−	2.83612i	0.325325	−	0.325325i
$77$	−3.43307	+	1.32537i	−0.391235	+	0.151040i
$78$	−0.124111	−	0.0514083i	−0.0140528	−	0.00582084i
$79$	−8.43950	−	10.9986i	−0.949518	−	1.23744i	−0.971345	−	0.237674i	$-0.923615\pi$
$79$	−8.43950	−	10.9986i	−0.949518	−	1.23744i	0.0218267	−	0.999762i	$-0.493052\pi$
$80$	1.87876	+	1.44162i	0.210052	+	0.161178i
$81$	−0.866025	+	0.500000i	−0.0962250	+	0.0555556i
$82$	−10.2076	−	1.34386i	−1.12724	−	0.148404i
$83$	−5.69822	−	5.69822i	−0.625461	−	0.625461i	0.321461	−	0.946923i	$-0.395826\pi$
$83$	−5.69822	−	5.69822i	−0.625461	−	0.625461i	−0.946923	+	0.321461i	$0.895826\pi$
$84$	−0.281589	−	2.63072i	−0.0307239	−	0.287035i
$85$	−2.69042	+	9.38605i	−0.291817	+	1.01806i
$86$	−5.92540	+	10.2631i	−0.638952	+	1.10670i
$87$	−1.76264	+	6.57826i	−0.188975	+	0.705264i
$88$	−0.846738	+	1.10349i	−0.0902626	+	0.117632i
$89$	−11.1056	−	6.41182i	−1.17719	−	0.679652i	−0.221829	−	0.975086i	$-0.571203\pi$
$89$	−11.1056	−	6.41182i	−1.17719	−	0.679652i	−0.955363	+	0.295434i	$0.904536\pi$
$90$	2.18786	−	0.906242i	0.230621	−	0.0955263i
$91$	−0.0836322	−	0.345441i	−0.00876703	−	0.0362120i
$92$	1.73296	+	0.717813i	0.180673	+	0.0748372i
$93$	−1.87635	−	7.00265i	−0.194569	−	0.726141i
$94$	−1.29710	−	0.347558i	−0.133786	−	0.0358478i
$95$	1.23977	+	9.41701i	0.127198	+	0.966164i
$96$	−0.608761	−	0.793353i	−0.0621315	−	0.0809713i
$97$	−7.76556	+	3.21660i	−0.788473	+	0.326596i	−0.740329	−	0.672244i	$-0.765330\pi$
$97$	−7.76556	+	3.21660i	−0.788473	+	0.326596i	−0.0481435	+	0.998840i	$0.515330\pi$
$98$	5.18406	−	4.70378i	0.523669	−	0.475154i
$99$	0.532282	+	1.28504i	0.0534963	+	0.129152i
$100$	−0.587295	+	0.157365i	−0.0587295	+	0.0157365i
$101$	0.868145	+	1.50367i	0.0863836	+	0.149621i	0.905980	−	0.423321i	$-0.139136\pi$
$101$	0.868145	+	1.50367i	0.0863836	+	0.149621i	−0.819596	+	0.572941i	$0.805802\pi$
$102$	2.12321	−	3.53440i	0.210229	−	0.349958i
$103$	2.22184	−	3.84835i	0.218925	−	0.379189i	−0.735555	−	0.677465i	$-0.763078\pi$
$103$	2.22184	−	3.84835i	0.218925	−	0.379189i	0.954480	+	0.298276i	$0.0964117\pi$
$104$	−0.0949901	−	0.0949901i	−0.00931455	−	0.00931455i
$105$	5.34844	+	3.26347i	0.521954	+	0.318482i
$106$		−	0.788697i		−	0.0766050i
$107$	−1.14017	+	8.66043i	−0.110224	+	0.837235i	0.843622	+	0.536938i	$0.180419\pi$
$107$	−1.14017	+	8.66043i	−0.110224	+	0.837235i	−0.953846	+	0.300297i	$0.902914\pi$
$108$	−0.991445	+	0.130526i	−0.0954018	+	0.0125599i
$109$	−0.892397	−	6.77843i	−0.0854761	−	0.649256i	−0.979530	−	0.201297i	$-0.935484\pi$
$109$	−0.892397	−	6.77843i	−0.0854761	−	0.649256i	0.894054	−	0.447959i	$-0.147849\pi$
$110$	−0.852516	−	3.18163i	−0.0812842	−	0.303357i
$111$	0.0433245	−	0.0433245i	0.00411218	−	0.00411218i
$112$	0.746580	−	2.53823i	0.0705452	−	0.239840i
$113$	−2.89691	+	6.99377i	−0.272519	+	0.657919i	−0.999590	−	0.0286438i	$-0.990881\pi$
$113$	−2.89691	+	6.99377i	−0.272519	+	0.657919i	0.727071	+	0.686562i	$0.240881\pi$
$114$	0.523525	−	3.97657i	0.0490326	−	0.372440i
$115$	−3.84687	+	2.22099i	−0.358722	+	0.207108i
$116$	−4.14586	+	5.40299i	−0.384933	+	0.501655i
$117$	−0.129759	+	0.0347688i	−0.0119962	+	0.00321438i
$118$	7.63528			0.702884
$119$	10.8653	−	0.972597i	0.996018	−	0.0891578i
$120$	2.36812			0.216179
$121$	−8.75645	+	2.34628i	−0.796041	+	0.213299i
$122$	−1.65627	+	2.15849i	−0.149951	+	0.195420i
$123$	−8.91634	+	5.14785i	−0.803960	+	0.464166i
$124$	0.946272	−	7.18765i	0.0849778	−	0.645470i
$125$	−3.98020	+	9.60906i	−0.356000	+	0.859460i
$126$	−1.82488	−	1.91567i	−0.162573	−	0.170662i
$127$	−2.35672	+	2.35672i	−0.209125	+	0.209125i	−0.803896	−	0.594771i	$-0.797243\pi$
$127$	−2.35672	+	2.35672i	−0.209125	+	0.209125i	0.594771	+	0.803896i	$0.297243\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	1.54684	+	11.7494i	0.136192	+	1.03448i
$130$	0.315404	−	0.0415237i	0.0276627	−	0.00364187i
$131$	−1.32184	+	10.0403i	−0.115489	+	0.877228i	0.831401	+	0.555672i	$0.187539\pi$
$131$	−1.32184	+	10.0403i	−0.115489	+	0.877228i	−0.946891	+	0.321556i	$0.895794\pi$
$132$			1.39092i			0.121064i
$133$	9.31612	−	5.08134i	0.807810	−	0.440608i
$134$	0.540838	+	0.540838i	0.0467213	+	0.0467213i
$135$	1.18406	−	2.05086i	0.101908	−	0.176510i
$136$	3.31415	−	2.45284i	0.284186	−	0.210329i
$137$	−3.23677	−	5.60626i	−0.276536	−	0.478975i	0.693985	−	0.719989i	$-0.255853\pi$
$137$	−3.23677	−	5.60626i	−0.276536	−	0.478975i	−0.970522	+	0.241014i	$0.922520\pi$
$138$	1.81182	−	0.485476i	0.154233	−	0.0413265i
$139$	4.15870	+	10.0400i	0.352736	+	0.851581i	0.996280	+	0.0861719i	$0.0274634\pi$
$139$	4.15870	+	10.0400i	0.352736	+	0.851581i	−0.643544	+	0.765409i	$0.722537\pi$
$140$	3.69244	+	5.06182i	0.312068	+	0.427802i
$141$	−1.24064	+	0.513890i	−0.104481	+	0.0432774i
$142$	4.65722	+	6.06940i	0.390825	+	0.509333i
$143$	0.0243890	+	0.185252i	0.00203951	+	0.0154916i
$144$	−0.965926	−	0.258819i	−0.0804938	−	0.0215683i
$145$	−4.17415	−	15.5781i	−0.346644	−	1.29369i
$146$	−9.84226	−	4.07680i	−0.814551	−	0.337398i
$147$	1.24931	−	6.88761i	0.103041	−	0.568081i
$148$	0.0566062	−	0.0234471i	0.00465300	−	0.00192734i
$149$	19.9380	+	11.5112i	1.63338	+	0.943034i	0.983039	+	0.183394i	$0.0587084\pi$
$149$	19.9380	+	11.5112i	1.63338	+	0.943034i	0.650344	+	0.759640i	$0.274625\pi$
$150$	−0.370135	+	0.482369i	−0.0302214	+	0.0393853i
$151$	−3.80781	+	14.2109i	−0.309875	+	1.15647i	0.618792	+	0.785555i	$0.287622\pi$
$151$	−3.80781	+	14.2109i	−0.309875	+	1.15647i	−0.928667	+	0.370914i	$0.879044\pi$
$152$	2.00544	−	3.47352i	0.162663	−	0.281740i
$153$	−0.467147	−	4.09656i	−0.0377666	−	0.331187i
$154$	−2.97306	+	2.16876i	−0.239576	+	0.174763i
$155$	12.1397	+	12.1397i	0.975084	+	0.975084i
$156$	−0.133187	−	0.0175344i	−0.0106635	−	0.00140388i
$157$	12.0411	−	6.95195i	0.960987	−	0.554826i	0.0645100	−	0.997917i	$-0.479452\pi$
$157$	12.0411	−	6.95195i	0.960987	−	0.554826i	0.896477	+	0.443091i	$0.146118\pi$
$158$	−10.9986	−	8.43950i	−0.874999	−	0.671411i
$159$	−0.480128	−	0.625715i	−0.0380766	−	0.0496224i
$160$	2.18786	+	0.906242i	0.172966	+	0.0716447i
$161$	3.86274	+	3.11577i	0.304426	+	0.245557i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−7.07741	+	5.43069i	−0.554345	+	0.425364i	−0.847573	−	0.530678i	$-0.821937\pi$
$163$	−7.07741	+	5.43069i	−0.554345	+	0.425364i	0.293228	+	0.956043i	$0.405271\pi$
$164$	−10.2076	+	1.34386i	−0.797082	+	0.104938i
$165$	−2.61320	−	2.00518i	−0.203438	−	0.156103i
$166$	−6.97887	−	4.02925i	−0.541665	−	0.312731i
$167$	0.474702	+	1.14603i	0.0367335	+	0.0886826i	0.941182	−	0.337901i	$-0.109717\pi$
$167$	0.474702	+	1.14603i	0.0367335	+	0.0886826i	−0.904448	+	0.426584i	$0.859717\pi$
$168$	−0.952875	−	2.46820i	−0.0735159	−	0.190426i
$169$	12.9820			0.998612
$170$	−0.169458	+	9.76256i	−0.0129968	+	0.748754i
$171$	−2.00544	−	3.47352i	−0.153360	−	0.265627i
$172$	−3.06721	+	11.4470i	−0.233873	+	0.872825i
$173$	2.86446	+	0.377113i	0.217781	+	0.0286714i	0.238627	−	0.971111i	$-0.423303\pi$
$173$	2.86446	+	0.377113i	0.217781	+	0.0286714i	−0.0208462	+	0.999783i	$0.506636\pi$
$174$			6.81032i			0.516289i
$175$	−1.60818	−	0.0390336i	−0.121567	−	0.00295066i
$176$	−0.532282	+	1.28504i	−0.0401222	+	0.0968637i
$177$	6.05747	−	4.64806i	0.455307	−	0.349370i
$178$	−12.3867	−	3.31900i	−0.928422	−	0.248770i
$179$	−25.4381	−	6.81611i	−1.90133	−	0.509460i	−0.996490	−	0.0837113i	$-0.973323\pi$
$179$	−25.4381	−	6.81611i	−1.90133	−	0.509460i	−0.904841	−	0.425749i	$-0.860011\pi$
$180$	1.87876	−	1.44162i	0.140034	−	0.107452i
$181$	3.97580	−	9.59843i	0.295519	−	0.713446i	−0.704474	−	0.709730i	$-0.748817\pi$
$181$	3.97580	−	9.59843i	0.295519	−	0.713446i	0.999993	−	0.00371627i	$-0.00118293\pi$
$182$	−0.170189	−	0.312025i	−0.0126153	−	0.0231288i
$183$			2.72072i			0.201121i
$184$	1.85969	+	0.244833i	0.137098	+	0.0180493i
$185$	−0.0375534	+	0.140151i	−0.00276098	+	0.0103041i
$186$	−3.62484	−	6.27840i	−0.265786	−	0.460355i
$187$	−5.73404	−	0.0995311i	−0.419315	−	0.00727843i
$188$	−1.34286			−0.0979381
$189$	−2.61396	−	0.408888i	−0.190138	−	0.0297422i
$190$	3.63483	+	8.77525i	0.263698	+	0.636624i
$191$	−8.92135	−	5.15074i	−0.645526	−	0.372695i	0.141214	−	0.989979i	$-0.454899\pi$
$191$	−8.92135	−	5.15074i	−0.645526	−	0.372695i	−0.786740	+	0.617284i	$0.788233\pi$
$192$	−0.793353	−	0.608761i	−0.0572553	−	0.0439336i
$193$	3.50672	−	0.461668i	0.252419	−	0.0332316i	−0.00325469	−	0.999995i	$-0.501036\pi$
$193$	3.50672	−	0.461668i	0.252419	−	0.0332316i	0.255674	+	0.966763i	$0.417703\pi$
$194$	−6.66844	+	5.11687i	−0.478766	+	0.367370i
$195$	0.224948	−	0.224948i	0.0161089	−	0.0161089i
$196$	3.78999	−	5.88524i	0.270713	−	0.420374i
$197$	−10.3197	−	4.27455i	−0.735246	−	0.304549i	−0.0165403	−	0.999863i	$-0.505265\pi$
$197$	−10.3197	−	4.27455i	−0.735246	−	0.304549i	−0.718706	+	0.695314i	$0.755265\pi$
$198$	0.846738	+	1.10349i	0.0601751	+	0.0784217i
$199$	12.8997	+	9.89826i	0.914433	+	0.701669i	0.954716	−	0.297519i	$-0.0961592\pi$
$199$	12.8997	+	9.89826i	0.914433	+	0.701669i	−0.0402828	+	0.999188i	$0.512826\pi$
$200$	−0.526555	+	0.304006i	−0.0372330	+	0.0214965i
$201$	0.758318	+	0.0998344i	0.0534876	+	0.00704178i
$202$	1.22774	+	1.22774i	0.0863836	+	0.0863836i
$203$	−14.5569	+	10.6188i	−1.02169	+	0.745295i
$204$	1.13610	−	3.96349i	0.0795427	−	0.277500i
$205$	12.1908	−	21.1150i	0.851439	−	1.47474i
$206$	1.15011	−	4.29227i	0.0801321	−	0.299057i
$207$	1.14188	−	1.48812i	0.0793659	−	0.103432i
$208$	−0.116339	−	0.0671682i	−0.00806664	−	0.00465727i
$209$	−5.15415	+	2.13492i	−0.356520	+	0.147675i
$210$	6.01085	+	1.76800i	0.414788	+	0.122003i
$211$	−8.90702	−	3.68941i	−0.613184	−	0.253989i	0.0544051	−	0.998519i	$-0.482674\pi$
$211$	−8.90702	−	3.68941i	−0.613184	−	0.253989i	−0.667589	+	0.744530i	$0.732674\pi$
$212$	−0.204130	−	0.761823i	−0.0140197	−	0.0523222i
$213$	7.38964	+	1.98005i	0.506330	+	0.135671i
$214$	1.14017	+	8.66043i	0.0779402	+	0.592014i
$215$	−17.0844	−	22.2648i	−1.16514	−	1.51845i
$216$	−0.923880	+	0.382683i	−0.0628620	+	0.0260383i
$217$	7.76802	−	17.5375i	0.527327	−	1.19052i
$218$	−2.61638	−	6.31649i	−0.177203	−	0.427807i
$219$	−10.2902	+	2.75725i	−0.695346	+	0.186318i
$220$	−1.64693	−	2.85257i	−0.111036	−	0.192321i
$221$	0.0818159	−	0.547807i	0.00550353	−	0.0368495i
$222$	0.0306351	−	0.0530615i	0.00205609	−	0.00356125i
$223$	−3.43906	−	3.43906i	−0.230297	−	0.230297i	0.582520	−	0.812816i	$-0.302067\pi$
$223$	−3.43906	−	3.43906i	−0.230297	−	0.230297i	−0.812816	+	0.582520i	$0.802067\pi$
$224$	0.0641986	−	2.64497i	0.00428945	−	0.176725i
$225$			0.608013i			0.0405342i
$226$	−0.988084	+	7.50524i	−0.0657263	+	0.499241i
$227$	−12.1631	+	1.60130i	−0.807292	+	0.106282i	−0.522865	−	0.852416i	$-0.675137\pi$
$227$	−12.1631	+	1.60130i	−0.807292	+	0.106282i	−0.284427	+	0.958698i	$0.591803\pi$
$228$	−0.523525	−	3.97657i	−0.0346713	−	0.263355i
$229$	−6.57554	−	24.5403i	−0.434524	−	1.62167i	−0.742203	−	0.670176i	$-0.766219\pi$
$229$	−6.57554	−	24.5403i	−0.434524	−	1.62167i	0.307678	−	0.951490i	$-0.400448\pi$
$230$	−3.14095	+	3.14095i	−0.207108	+	0.207108i
$231$	−1.03843	+	3.53047i	−0.0683239	+	0.232288i
$232$	−2.60620	+	6.29191i	−0.171105	+	0.413084i
$233$	−0.695458	+	5.28253i	−0.0455609	+	0.346070i	0.953448	+	0.301558i	$0.0975066\pi$
$233$	−0.695458	+	5.28253i	−0.0455609	+	0.346070i	−0.999009	+	0.0445120i	$0.985827\pi$
$234$	−0.116339	+	0.0671682i	−0.00760530	+	0.00439092i
$235$	1.93590	−	2.52291i	0.126284	−	0.164577i
$236$	7.37511	−	1.97615i	0.480079	−	0.128637i
$237$	−13.8634			−0.900524
$238$	10.2433	−	3.75159i	0.663976	−	0.243180i
$239$	27.7139			1.79267			0.896333	−	0.443382i	$-0.146221\pi$
$239$	27.7139			1.79267			0.896333	+	0.443382i	$0.146221\pi$
$240$	2.28743	−	0.612916i	0.147653	−	0.0395635i
$241$	−1.86288	+	2.42775i	−0.119998	+	0.156385i	−0.849490	−	0.527605i	$-0.823090\pi$
$241$	−1.86288	+	2.42775i	−0.119998	+	0.156385i	0.729491	+	0.683990i	$0.239757\pi$
$242$	−7.85082	+	4.53267i	−0.504670	+	0.291371i
$243$	−0.130526	+	0.991445i	−0.00837326	+	0.0636012i
$244$	−1.04117	+	2.51361i	−0.0666543	+	0.160918i
$245$	5.59321	+	15.6048i	0.357337	+	0.996952i
$246$	−7.28016	+	7.28016i	−0.464166	+	0.464166i
$247$	−0.139454	−	0.520448i	−0.00887322	−	0.0331153i
$248$	−0.946272	−	7.18765i	−0.0600884	−	0.456416i
$249$	−7.98956	+	1.05185i	−0.506318	+	0.0666580i
$250$	−1.35757	+	10.3118i	−0.0858605	+	0.652175i
$251$		−	10.4296i		−	0.658308i	−0.944276	−	0.329154i	$-0.893236\pi$
$251$		−	10.4296i		−	0.658308i	0.944276	−	0.329154i	$-0.106764\pi$
$252$	−2.25851	−	1.37808i	−0.142273	−	0.0868111i
$253$	−1.84484	−	1.84484i	−0.115984	−	0.115984i
$254$	−1.66645	+	2.88638i	−0.104562	+	0.181108i
$255$	5.80863	+	7.84832i	0.363750	+	0.491481i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	26.4312	−	7.08222i	1.64873	−	0.441776i	0.689475	−	0.724310i	$-0.257841\pi$
$257$	26.4312	−	7.08222i	1.64873	−	0.441776i	0.959257	+	0.282533i	$0.0911748\pi$
$258$	4.53510	+	10.9487i	0.282343	+	0.681637i
$259$	0.161185	−	0.0172530i	0.0100155	−	0.00107205i
$260$	0.293909	−	0.121741i	0.0182275	−	0.00755007i
$261$	4.14586	+	5.40299i	0.256622	+	0.334437i
$262$	1.32184	+	10.0403i	0.0816632	+	0.620294i
$263$	6.33646	+	1.69785i	0.390723	+	0.104694i	0.448832	−	0.893616i	$-0.351840\pi$
$263$	6.33646	+	1.69785i	0.390723	+	0.104694i	−0.0581086	+	0.998310i	$0.518507\pi$
$264$	0.359996	+	1.34352i	0.0221562	+	0.0826882i
$265$	1.72556	+	0.714750i	0.106000	+	0.0439067i
$266$	7.68354	−	7.31939i	0.471108	−	0.448780i
$267$	−11.8475	+	4.90740i	−0.725056	+	0.300328i
$268$	0.662389	+	0.382431i	0.0404619	+	0.0233607i
$269$	4.75321	−	6.19451i	0.289808	−	0.377686i	−0.625646	−	0.780107i	$-0.715165\pi$
$269$	4.75321	−	6.19451i	0.289808	−	0.377686i	0.915455	+	0.402421i	$0.131831\pi$
$270$	0.612916	−	2.28743i	0.0373009	−	0.139209i
$271$	6.11076	−	10.5841i	0.371202	−	0.642941i	−0.618549	−	0.785746i	$-0.712279\pi$
$271$	6.11076	−	10.5841i	0.371202	−	0.642941i	0.989751	+	0.142806i	$0.0456124\pi$
$272$	2.56638	−	3.22703i	0.155610	−	0.195667i
$273$	−0.324969	−	0.143941i	−0.0196680	−	0.00871172i
$274$	−4.57749	−	4.57749i	−0.276536	−	0.276536i
$275$	0.838462	+	0.110386i	0.0505611	+	0.00665650i
$276$	1.62444	−	0.937869i	0.0977796	−	0.0564531i
$277$	−10.0781	−	7.73323i	−0.605537	−	0.464645i	0.259919	−	0.965631i	$-0.416304\pi$
$277$	−10.0781	−	7.73323i	−0.605537	−	0.464645i	−0.865456	+	0.500986i	$0.832971\pi$
$278$	6.61554	+	8.62154i	0.396774	+	0.517086i
$279$	−6.69783	−	2.77433i	−0.400988	−	0.166095i
$280$	4.87672	+	3.93367i	0.291440	+	0.235082i
$281$	16.0296	−	16.0296i	0.956247	−	0.956247i	−0.0428348	−	0.999082i	$-0.513639\pi$
$281$	16.0296	−	16.0296i	0.956247	−	0.956247i	0.999082	+	0.0428348i	$0.0136389\pi$
$282$	−1.06536	+	0.817481i	−0.0634414	+	0.0486803i
$283$	24.4163	−	3.21446i	1.45140	−	0.191080i	0.636765	−	0.771058i	$-0.280272\pi$
$283$	24.4163	−	3.21446i	1.45140	−	0.191080i	0.814632	+	0.579978i	$0.196939\pi$
$284$	6.06940	+	4.65722i	0.360153	+	0.276355i
$285$	8.22574	+	4.74913i	0.487251	+	0.281314i
$286$	0.0715048	+	0.172628i	0.00422817	+	0.0102077i
$287$	−26.9126	−	4.20979i	−1.58860	−	0.248496i
$288$	−1.00000			−0.0589256
$289$	16.2581	+	4.96716i	0.956362	+	0.292186i
$290$	−8.06384	−	13.9670i	−0.473525	−	0.820169i
$291$	−2.17547	+	8.11897i	−0.127528	+	0.475943i
$292$	−10.5620	−	1.39052i	−0.618097	−	0.0813740i
$293$			17.8208i			1.04110i	0.853830	+	0.520552i	$0.174274\pi$
$293$			17.8208i			1.04110i	−0.853830	+	0.520552i	$0.825726\pi$
$294$	−0.575906	−	6.97627i	−0.0335875	−	0.406864i
$295$	−6.91941	+	16.7049i	−0.402863	+	0.972598i
$296$	0.0486089	−	0.0372989i	0.00282533	−	0.00216795i
$297$	1.34352	+	0.359996i	0.0779592	+	0.0208891i
$298$	22.2379	+	5.95864i	1.28821	+	0.345174i
$299$	0.199909	−	0.153395i	0.0115610	−	0.00887109i
$300$	−0.232676	+	0.561731i	−0.0134336	+	0.0324315i
$301$	−16.3314	+	26.7652i	−0.941325	+	1.54272i
$302$			14.7122i			0.846594i
$303$	1.72144	+	0.226631i	0.0988939	+	0.0130196i
$304$	1.03809	−	3.87421i	0.0595387	−	0.222201i
$305$	−3.22150	−	5.57980i	−0.184462	−	0.319498i
$306$	−1.51150	−	3.83606i	−0.0864065	−	0.219293i
$307$	8.07361			0.460785			0.230393	−	0.973098i	$-0.425999\pi$
$307$	8.07361			0.460785			0.230393	+	0.973098i	$0.425999\pi$
$308$	−2.31044	+	2.86434i	−0.131650	+	0.163211i
$309$	−1.70053	−	4.10543i	−0.0967396	−	0.233550i
$310$	14.8680	+	8.58407i	0.844448	+	0.487542i
$311$	10.3471	+	7.93962i	0.586731	+	0.450214i	0.858978	−	0.512013i	$-0.171100\pi$
$311$	10.3471	+	7.93962i	0.586731	+	0.450214i	−0.272247	+	0.962227i	$0.587767\pi$
$312$	−0.133187	+	0.0175344i	−0.00754023	+	0.000992691i
$313$	11.6123	−	8.91046i	0.656368	−	0.503649i	−0.226049	−	0.974116i	$-0.572581\pi$
$313$	11.6123	−	8.91046i	0.656368	−	0.503649i	0.882418	+	0.470467i	$0.155914\pi$
$314$	9.83154	−	9.83154i	0.554826	−	0.554826i
$315$	5.84501	−	2.25653i	0.329329	−	0.127141i
$316$	−12.8081	−	5.30529i	−0.720512	−	0.298446i
$317$	−1.62144	−	2.11310i	−0.0910692	−	0.118684i	0.745596	−	0.666398i	$-0.232165\pi$
$317$	−1.62144	−	2.11310i	−0.0910692	−	0.118684i	−0.836665	+	0.547714i	$0.815498\pi$
$318$	−0.625715	−	0.480128i	−0.0350884	−	0.0269242i
$319$	8.20351	−	4.73630i	0.459309	−	0.265182i
$320$	2.34786	+	0.309102i	0.131250	+	0.0172793i
$321$	6.17669	+	6.17669i	0.344749	+	0.344749i
$322$	4.53754	+	2.00985i	0.252867	+	0.112005i
$323$	16.4308	−	1.87367i	0.914234	−	0.104254i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−0.0211399	+	0.0788951i	−0.00117263	+	0.00437631i
$326$	−5.43069	+	7.07741i	−0.300778	+	0.391981i
$327$	−5.92094	−	3.41846i	−0.327429	−	0.189041i
$328$	−9.51199	+	3.94000i	−0.525212	+	0.217550i
$329$	−3.40849	−	1.00255i	−0.187916	−	0.0552725i
$330$	−3.04314	−	1.26051i	−0.167519	−	0.0693888i
$331$	0.547004	+	2.04145i	0.0300661	+	0.112208i	0.979328	−	0.202278i	$-0.0648345\pi$
$331$	0.547004	+	2.04145i	0.0300661	+	0.112208i	−0.949262	+	0.314486i	$0.898168\pi$
$332$	−7.78392	−	2.08569i	−0.427198	−	0.114467i
$333$	−0.00799736	−	0.0607460i	−0.000438253	−	0.00332886i
$334$	0.755141	+	0.984119i	0.0413195	+	0.0538486i
$335$	−1.67341	+	0.693149i	−0.0914282	+	0.0378708i
$336$	−1.55922	−	2.13748i	−0.0850627	−	0.116609i
$337$	−12.0215	−	29.0224i	−0.654852	−	1.58095i	−0.805653	−	0.592387i	$-0.798185\pi$
$337$	−12.0215	−	29.0224i	−0.654852	−	1.58095i	0.150802	−	0.988564i	$-0.451815\pi$
$338$	12.5396	−	3.35998i	0.682065	−	0.182759i
$339$	3.78500	+	6.55581i	0.205573	+	0.356063i
$340$	2.36305	+	9.47376i	0.128154	+	0.513787i
$341$	−5.04186	+	8.73275i	−0.273032	+	0.472905i
$342$	−2.83612	−	2.83612i	−0.153360	−	0.153360i
$343$	14.0137	−	12.1086i	0.756667	−	0.653801i
$344$			11.8508i			0.638952i
$345$	−0.579795	+	4.40398i	−0.0312151	+	0.237102i
$346$	2.86446	−	0.377113i	0.153994	−	0.0202737i
$347$	0.437730	+	3.32489i	0.0234986	+	0.178489i	0.999169	−	0.0407517i	$-0.0129753\pi$
$347$	0.437730	+	3.32489i	0.0234986	+	0.178489i	−0.975671	+	0.219241i	$0.929642\pi$
$348$	1.76264	+	6.57826i	0.0944874	+	0.352632i
$349$	19.5269	−	19.5269i	1.04525	−	1.04525i	0.0463220	−	0.998927i	$-0.485250\pi$
$349$	19.5269	−	19.5269i	1.04525	−	1.04525i	0.998927	−	0.0463220i	$-0.0147500\pi$
$350$	−1.56348	+	0.378523i	−0.0835716	+	0.0202329i
$351$	−0.0514083	+	0.124111i	−0.00274397	+	0.00662453i
$352$	−0.181551	+	1.37902i	−0.00967672	+	0.0735020i
$353$	19.9292	−	11.5061i	1.06072	−	0.612410i	0.135092	−	0.990833i	$-0.456867\pi$
$353$	19.9292	−	11.5061i	1.06072	−	0.612410i	0.925633	+	0.378423i	$0.123534\pi$
$354$	4.64806	−	6.05747i	0.247042	−	0.321951i
$355$	−17.4996	+	4.68900i	−0.928781	+	0.248866i
$356$	−12.8236			−0.679652
$357$	5.84274	−	9.21208i	0.309231	−	0.487555i
$358$	−26.3354			−1.39187
$359$	−6.25983	+	1.67732i	−0.330381	+	0.0885254i	−0.420197	−	0.907433i	$-0.638039\pi$
$359$	−6.25983	+	1.67732i	−0.330381	+	0.0885254i	0.0898155	+	0.995958i	$0.471372\pi$
$360$	1.44162	−	1.87876i	0.0759802	−	0.0990193i
$361$	−2.52259	+	1.45642i	−0.132768	+	0.0766536i
$362$	1.35607	−	10.3004i	0.0712736	−	0.541376i
$363$	−3.46916	+	8.37529i	−0.182084	+	0.439588i
$364$	−0.245148	−	0.257345i	−0.0128492	−	0.0134885i
$365$	17.8389	−	17.8389i	0.933733	−	0.933733i
$366$	0.704173	+	2.62801i	0.0368077	+	0.137368i
$367$	0.980504	+	7.44767i	0.0511819	+	0.388765i	0.997794	+	0.0663897i	$0.0211481\pi$
$367$	0.980504	+	7.44767i	0.0511819	+	0.388765i	−0.946612	+	0.322376i	$0.895519\pi$
$368$	1.85969	−	0.244833i	0.0969430	−	0.0127628i
$369$	−1.34386	+	10.2076i	−0.0699585	+	0.531388i
$370$			0.145095i			0.00754315i
$371$	0.0506333	−	2.08608i	0.00262875	−	0.108304i
$372$	−5.12629	−	5.12629i	−0.265786	−	0.265786i
$373$	4.57011	−	7.91566i	0.236631	−	0.409857i	−0.723114	−	0.690728i	$-0.757290\pi$
$373$	4.57011	−	7.91566i	0.236631	−	0.409857i	0.959745	+	0.280871i	$0.0906234\pi$
$374$	−5.56442	+	1.38794i	−0.287729	+	0.0717687i
$375$	5.20039	+	9.00733i	0.268547	+	0.465137i
$376$	−1.29710	+	0.347558i	−0.0668930	+	0.0179239i
$377$	0.350107	+	0.845232i	0.0180314	+	0.0435317i
$378$	−2.63072	+	0.281589i	−0.135310	+	0.0144834i
$379$	−31.8543	+	13.1945i	−1.63624	+	0.677755i	−0.995911	−	0.0903418i	$-0.971204\pi$
$379$	−31.8543	+	13.1945i	−1.63624	+	0.677755i	−0.640334	+	0.768097i	$0.721204\pi$
$380$	5.78218	+	7.53548i	0.296619	+	0.386562i
$381$	0.435031	+	3.30439i	0.0222873	+	0.169289i
$382$	−9.95047	−	2.66622i	−0.509110	−	0.136416i
$383$	−9.85528	−	36.7804i	−0.503581	−	1.87939i	−0.475365	−	0.879789i	$-0.657684\pi$
$383$	−9.85528	−	36.7804i	−0.503581	−	1.87939i	−0.0282161	−	0.999602i	$-0.508983\pi$
$384$	−0.923880	−	0.382683i	−0.0471465	−	0.0195287i
$385$	−2.05063	−	8.47006i	−0.104510	−	0.431674i
$386$	3.26774	−	1.35354i	0.166324	−	0.0688935i
$387$	10.2631	+	5.92540i	0.521702	+	0.301205i
$388$	−5.11687	+	6.66844i	−0.259770	+	0.338539i
$389$	1.84728	−	6.89416i	0.0936610	−	0.349548i	−0.903152	−	0.429321i	$-0.858753\pi$
$389$	1.84728	−	6.89416i	0.0936610	−	0.349548i	0.996813	+	0.0797732i	$0.0254196\pi$
$390$	0.159063	−	0.275504i	0.00805445	−	0.0139507i
$391$	3.75011	+	6.76382i	0.189651	+	0.342061i
$392$	2.13764	−	6.66562i	0.107967	−	0.336665i
$393$	7.16085	+	7.16085i	0.361217	+	0.361217i
$394$	−11.0744	−	1.45797i	−0.557919	−	0.0734514i
$395$	28.4318	−	16.4151i	1.43056	−	0.825935i
$396$	1.10349	+	0.846738i	0.0554525	+	0.0425502i
$397$	13.2312	+	17.2433i	0.664056	+	0.865414i	0.996990	−	0.0775358i	$-0.0247052\pi$
$397$	13.2312	+	17.2433i	0.664056	+	0.865414i	−0.332934	+	0.942950i	$0.608039\pi$
$398$	15.0220	+	6.22231i	0.752984	+	0.311896i
$399$	1.64000	−	10.4843i	0.0821027	−	0.524872i
$400$	−0.429930	+	0.429930i	−0.0214965	+	0.0214965i
$401$	−6.46252	+	4.95886i	−0.322723	+	0.247634i	−0.757398	−	0.652953i	$-0.773530\pi$
$401$	−6.46252	+	4.95886i	−0.322723	+	0.247634i	0.434675	+	0.900587i	$0.356863\pi$
$402$	0.758318	−	0.0998344i	0.0378214	−	0.00497929i
$403$	−0.772643	−	0.592870i	−0.0384881	−	0.0295329i
$404$	1.50367	+	0.868145i	0.0748104	+	0.0431918i
$405$	−0.906242	−	2.18786i	−0.0450315	−	0.108716i
$406$	−11.3125	+	14.0246i	−0.561432	+	0.696029i
$407$	−0.0852218			−0.00422429
$408$	0.0715578	−	4.12248i	0.00354264	−	0.204093i
$409$	17.2210	+	29.8276i	0.851522	+	1.47488i	0.879834	+	0.475280i	$0.157653\pi$
$409$	17.2210	+	29.8276i	0.851522	+	1.47488i	−0.0283123	+	0.999599i	$0.509013\pi$
$410$	6.31040	−	23.5507i	0.311648	−	1.16309i
$411$	−6.41817	−	0.844968i	−0.316585	−	0.0416792i
$412$		−	4.44369i		−	0.218925i
$413$	20.1951	+	0.490174i	0.993735	+	0.0241199i
$414$	0.717813	−	1.73296i	0.0352786	−	0.0851701i
$415$	15.1400	−	11.6173i	0.743193	−	0.570272i
$416$	−0.129759	−	0.0347688i	−0.00636196	−	0.00170468i
$417$	10.4969	+	2.81264i	0.514036	+	0.137736i
$418$	−4.42597	+	3.39617i	−0.216481	+	0.166112i
$419$	−9.70336	+	23.4260i	−0.474040	+	1.14443i	0.488322	+	0.872664i	$0.337609\pi$
$419$	−9.70336	+	23.4260i	−0.474040	+	1.14443i	−0.962362	+	0.271771i	$0.912391\pi$
$420$	6.26362	+	0.152030i	0.305634	+	0.00741832i
$421$		−	3.62766i		−	0.176801i	−0.996085	−	0.0884006i	$-0.971824\pi$
$421$		−	3.62766i		−	0.176801i	0.996085	−	0.0884006i	$-0.0281756\pi$
$422$	−9.55840	−	1.25839i	−0.465296	−	0.0612574i
$423$	−0.347558	+	1.29710i	−0.0168988	+	0.0630673i
$424$	−0.394348	−	0.683031i	−0.0191512	−	0.0331709i
$425$	−2.29908	−	0.999401i	−0.111522	−	0.0484781i
$426$	7.65032			0.370659
$427$	−4.51935	+	5.60281i	−0.218707	+	0.271139i
$428$	3.34280	+	8.07023i	0.161580	+	0.390089i
$429$	0.161818	+	0.0934255i	0.00781263	+	0.00451063i
$430$	−22.2648	−	17.0844i	−1.07370	−	0.823882i
$431$	−13.6305	+	1.79449i	−0.656559	+	0.0864376i	−0.451443	−	0.892300i	$-0.649091\pi$
$431$	−13.6305	+	1.79449i	−0.656559	+	0.0864376i	−0.205116	+	0.978738i	$0.565757\pi$
$432$	−0.793353	+	0.608761i	−0.0381702	+	0.0292890i
$433$	−12.2361	+	12.2361i	−0.588030	+	0.588030i	−0.937098	−	0.349067i	$-0.886498\pi$
$433$	−12.2361	+	12.2361i	−0.588030	+	0.588030i	0.349067	+	0.937098i	$0.386498\pi$
$434$	2.96430	−	18.9504i	0.142291	−	0.909648i
$435$	−14.9000	−	6.17179i	−0.714402	−	0.295915i
$436$	−4.16205	−	5.42409i	−0.199326	−	0.259767i
$437$	5.96868	+	4.57993i	0.285521	+	0.219088i
$438$	−9.22593	+	5.32659i	−0.440832	+	0.254514i
$439$	−13.2844	−	1.74893i	−0.634032	−	0.0834719i	−0.193342	−	0.981131i	$-0.561933\pi$
$439$	−13.2844	−	1.74893i	−0.634032	−	0.0834719i	−0.440690	+	0.897659i	$0.645266\pi$
$440$	−2.32912	−	2.32912i	−0.111036	−	0.111036i
$441$	−4.70378	−	5.18406i	−0.223990	−	0.246860i
$442$	−0.0627548	−	0.550316i	−0.00298494	−	0.0261759i
$443$	10.9505	−	18.9669i	0.520275	−	0.901143i	−0.479447	−	0.877571i	$-0.659163\pi$
$443$	10.9505	−	18.9669i	0.520275	−	0.901143i	0.999722	−	0.0235718i	$-0.00750384\pi$
$444$	0.0158579	−	0.0591824i	0.000752582	−	0.00280867i
$445$	18.4869	−	24.0926i	0.876361	−	1.14210i
$446$	−4.21197	−	2.43178i	−0.199443	−	0.115148i
$447$	21.2699	−	8.81029i	1.00603	−	0.416712i
$448$	−0.622558	−	2.57146i	−0.0294131	−	0.121490i
$449$	4.36157	+	1.80662i	0.205835	+	0.0852598i	0.483219	−	0.875499i	$-0.339467\pi$
$449$	4.36157	+	1.80662i	0.205835	+	0.0852598i	−0.277384	+	0.960759i	$0.589467\pi$
$450$	0.157365	+	0.587295i	0.00741827	+	0.0276854i
$451$	13.8325	+	3.70642i	0.651349	+	0.174528i
$452$	0.988084	+	7.50524i	0.0464755	+	0.353017i
$453$	8.95624	+	11.6720i	0.420801	+	0.548398i
$454$	−11.3342	+	4.69477i	−0.531940	+	0.220337i
$455$	0.836899	−	0.0895805i	0.0392345	−	0.00419960i
$456$	−1.53490	−	3.70557i	−0.0718782	−	0.173529i
$457$	−32.6789	+	8.75628i	−1.52865	+	0.409602i	−0.922580	−	0.385807i	$-0.873923\pi$
$457$	−32.6789	+	8.75628i	−1.52865	+	0.409602i	−0.606074	+	0.795408i	$0.707257\pi$
$458$	−12.7030	−	22.0022i	−0.593571	−	1.02810i
$459$	−3.53440	−	2.12321i	−0.164972	−	0.0991031i
$460$	−2.22099	+	3.84687i	−0.103554	+	0.179361i
$461$	−15.6722	−	15.6722i	−0.729927	−	0.729927i	0.240678	−	0.970605i	$-0.422630\pi$
$461$	−15.6722	−	15.6722i	−0.729927	−	0.729927i	−0.970605	+	0.240678i	$0.922630\pi$
$462$	−0.0892951	+	3.67894i	−0.00415439	+	0.171160i
$463$			33.4311i			1.55367i	0.629701	+	0.776837i	$0.283177\pi$
$463$			33.4311i			1.55367i	−0.629701	+	0.776837i	$0.716823\pi$
$464$	−0.888925	+	6.75205i	−0.0412673	+	0.313456i
$465$	17.0213	−	2.24089i	0.789342	−	0.103919i
$466$	0.695458	+	5.28253i	0.0322165	+	0.244708i
$467$	−0.0245044	−	0.0914515i	−0.00113393	−	0.00423187i	0.965357	−	0.260934i	$-0.0840306\pi$
$467$	−0.0245044	−	0.0914515i	−0.00113393	−	0.00423187i	−0.966490	+	0.256702i	$0.917364\pi$
$468$	−0.0949901	+	0.0949901i	−0.00439092	+	0.00439092i
$469$	1.39578	+	1.46522i	0.0644512	+	0.0676578i
$470$	1.21696	−	2.93799i	0.0561340	−	0.135519i
$471$	1.81482	−	13.7849i	0.0836226	−	0.635177i
$472$	6.61234	−	3.81764i	0.304358	−	0.175721i
$473$	10.0345	−	13.0772i	0.461388	−	0.601292i
$474$	−13.3910	+	3.58811i	−0.615070	+	0.164807i
$475$	−2.43867			−0.111894
$476$	8.92330	−	6.27493i	0.408999	−	0.287611i
$477$	−0.788697			−0.0361119
$478$	26.7696	−	7.17290i	1.22441	−	0.328081i
$479$	18.6380	−	24.2895i	0.851592	−	1.10982i	−0.141201	−	0.989981i	$-0.545097\pi$
$479$	18.6380	−	24.2895i	0.851592	−	1.10982i	0.992794	−	0.119836i	$-0.0382368\pi$
$480$	2.05086	−	1.18406i	0.0936083	−	0.0540448i
$481$	0.00107434	−	0.00816039i	4.89855e−5	−	0.000372082i
$482$	−1.17105	+	2.82717i	−0.0533400	+	0.128774i
$483$	4.82339	−	1.16776i	0.219472	−	0.0531347i
$484$	−6.41017	+	6.41017i	−0.291371	+	0.291371i
$485$	−5.15179	−	19.2267i	−0.233931	−	0.873041i
$486$	0.130526	+	0.991445i	0.00592079	+	0.0449729i
$487$	19.8607	−	2.61470i	0.899972	−	0.118484i	0.333678	−	0.942687i	$-0.391710\pi$
$487$	19.8607	−	2.61470i	0.899972	−	0.118484i	0.566294	+	0.824203i	$0.308377\pi$
$488$	−0.355125	+	2.69744i	−0.0160757	+	0.122107i
$489$			8.92088i			0.403416i
$490$	9.44144	+	13.6254i	0.426521	+	0.615533i
$491$	−1.59114	−	1.59114i	−0.0718071	−	0.0718071i	0.670291	−	0.742098i	$-0.266169\pi$
$491$	−1.59114	−	1.59114i	−0.0718071	−	0.0718071i	−0.742098	+	0.670291i	$0.766169\pi$
$492$	−5.14785	+	8.91634i	−0.232083	+	0.401980i
$493$	−27.2449	+	6.79573i	−1.22705	+	0.306064i
$494$	−0.269404	−	0.466621i	−0.0121210	−	0.0209943i
$495$	−3.18163	+	0.852516i	−0.143004	+	0.0383178i
$496$	−2.77433	−	6.69783i	−0.124571	−	0.300741i
$497$	11.9286	+	16.3524i	0.535069	+	0.733505i
$498$	−7.44509	+	3.08386i	−0.333622	+	0.138191i
$499$	12.9388	+	16.8622i	0.579221	+	0.754855i	0.987434	−	0.158031i	$-0.0505147\pi$
$499$	12.9388	+	16.8622i	0.579221	+	0.754855i	−0.408213	+	0.912887i	$0.633848\pi$
$500$	1.35757	+	10.3118i	0.0607125	+	0.461157i
$501$	1.19819	+	0.321053i	0.0535311	+	0.0143436i
$502$	−2.69937	−	10.0742i	−0.120479	−	0.449633i
$503$	22.8567	+	9.46754i	1.01913	+	0.422137i	0.828777	−	0.559579i	$-0.189037\pi$
$503$	22.8567	+	9.46754i	1.01913	+	0.422137i	0.190351	+	0.981716i	$0.439037\pi$
$504$	−2.53823	−	0.746580i	−0.113062	−	0.0332553i
$505$	−3.79876	+	1.57350i	−0.169043	+	0.0700198i
$506$	−2.25946	−	1.30450i	−0.100445	−	0.0579921i
$507$	7.90291	−	10.2993i	0.350981	−	0.457407i
$508$	−0.862619	+	3.21934i	−0.0382725	+	0.142835i
$509$	16.7662	−	29.0399i	0.743149	−	1.28717i	−0.207905	−	0.978149i	$-0.566665\pi$
$509$	16.7662	−	29.0399i	0.743149	−	1.28717i	0.951055	−	0.309023i	$-0.100002\pi$
$510$	7.64200	+	6.07751i	0.338393	+	0.269117i
$511$	−25.7708	−	11.4149i	−1.14003	−	0.504964i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−3.97657	−	0.523525i	−0.175570	−	0.0231142i
$514$	23.6976	−	13.6818i	1.04525	−	0.603478i
$515$	8.34862	+	6.40612i	0.367884	+	0.282288i
$516$	7.21431	+	9.40187i	0.317592	+	0.413894i
$517$	1.72563	+	0.714780i	0.0758932	+	0.0314360i
$518$	0.151227	−	0.0583828i	0.00664454	−	0.00256519i
$519$	2.04296	−	2.04296i	0.0896758	−	0.0896758i
$520$	0.252386	−	0.193662i	0.0110678	−	0.00849265i
$521$	−36.9989	+	4.87100i	−1.62095	+	0.213403i	−0.885656	−	0.464342i	$-0.846291\pi$
$521$	−36.9989	+	4.87100i	−1.62095	+	0.213403i	−0.735297	+	0.677745i	$0.762957\pi$
$522$	5.40299	+	4.14586i	0.236482	+	0.181459i
$523$	38.3993	+	22.1698i	1.67908	+	0.969419i	0.962247	+	0.272179i	$0.0877441\pi$
$523$	38.3993	+	22.1698i	1.67908	+	0.969419i	0.716837	+	0.697241i	$0.245589\pi$
$524$	3.87542	+	9.35610i	0.169299	+	0.408723i
$525$	−1.00996	+	1.25209i	−0.0440784	+	0.0546457i
$526$	6.55999			0.286029
$527$	21.4999	−	20.7662i	0.936550	−	0.904592i
$528$	0.695460	+	1.20457i	0.0302660	+	0.0524222i
$529$	5.04221	−	18.8178i	0.219227	−	0.818165i
$530$	1.85175	+	0.243788i	0.0804350	+	0.0105895i
$531$		−	7.63528i		−	0.331343i
$532$	5.52733	−	9.05863i	0.239640	−	0.392741i
$533$	−0.529285	+	1.27781i	−0.0229259	+	0.0553479i
$534$	−10.1737	+	7.80654i	−0.440258	+	0.337822i
$535$	−19.9811	−	5.35391i	−0.863857	−	0.231470i
$536$	0.738799	+	0.197961i	0.0319113	+	0.00855060i
$537$	−20.8933	+	16.0320i	−0.901613	+	0.691832i
$538$	2.98799	−	7.21365i	0.128822	−	0.311003i
$539$	−8.00290	+	5.54543i	−0.344709	+	0.238859i
$540$		−	2.36812i		−	0.101908i
$541$	5.00355	+	0.658730i	0.215119	+	0.0283210i	0.237316	−	0.971433i	$-0.423732\pi$
$541$	5.00355	+	0.658730i	0.215119	+	0.0283210i	−0.0221961	+	0.999754i	$0.507066\pi$
$542$	3.16316	−	11.8051i	0.135869	−	0.507071i
$543$	−5.19463	−	8.99737i	−0.222923	−	0.386114i
$544$	1.64372	−	3.78130i	0.0704738	−	0.162122i
$545$	16.1907			0.693532
$546$	−0.351150	−	0.0549285i	−0.0150279	−	0.00235072i
$547$	12.5988	+	30.4162i	0.538686	+	1.30050i	0.925640	+	0.378405i	$0.123527\pi$
$547$	12.5988	+	30.4162i	0.538686	+	1.30050i	−0.386954	+	0.922099i	$0.626473\pi$
$548$	−5.60626	−	3.23677i	−0.239487	−	0.138268i
$549$	2.15849	+	1.65627i	0.0921221	+	0.0706877i
$550$	0.838462	−	0.110386i	0.0357521	−	0.00470686i
$551$	−21.6707	+	16.6285i	−0.923204	+	0.708400i
$552$	1.32635	−	1.32635i	0.0564531	−	0.0564531i
$553$	−28.5491	−	23.0283i	−1.21403	−	0.979265i
$554$	−11.7362	−	4.86131i	−0.498625	−	0.206537i
$555$	0.0883284	+	0.115112i	0.00374933	+	0.00488623i
$556$	8.62154	+	6.61554i	0.365635	+	0.280561i
$557$	−15.2700	+	8.81612i	−0.647009	+	0.373551i	−0.787309	−	0.616558i	$-0.788527\pi$
$557$	−15.2700	+	8.81612i	−0.647009	+	0.373551i	0.140300	+	0.990109i	$0.455193\pi$
$558$	−7.18765	−	0.946272i	−0.304278	−	0.0400589i
$559$	1.12571	+	1.12571i	0.0476124	+	0.0476124i
$560$	5.72865	+	2.53744i	0.242080	+	0.107227i
$561$	−3.56963	+	4.48853i	−0.150710	+	0.189506i
$562$	11.3347	−	19.6322i	0.478124	−	0.828135i
$563$	2.33627	−	8.71907i	0.0984620	−	0.367465i	−0.899060	−	0.437826i	$-0.855748\pi$
$563$	2.33627	−	8.71907i	0.0984620	−	0.367465i	0.997522	+	0.0703611i	$0.0224152\pi$
$564$	−0.817481	+	1.06536i	−0.0344222	+	0.0448598i
$565$	−15.5250	−	8.96335i	−0.653141	−	0.377091i
$566$	22.7523	−	9.42433i	0.956353	−	0.396134i
$567$	−1.91567	+	1.82488i	−0.0804507	+	0.0766379i
$568$	7.06797	+	2.92765i	0.296565	+	0.122841i
$569$	6.35918	+	23.7328i	0.266591	+	0.994930i	0.961270	+	0.275610i	$0.0888797\pi$
$569$	6.35918	+	23.7328i	0.266591	+	0.994930i	−0.694679	+	0.719320i	$0.744454\pi$
$570$	9.17462	+	2.45833i	0.384282	+	0.102968i
$571$	5.10524	+	38.7782i	0.213648	+	1.62282i	0.676543	+	0.736403i	$0.263477\pi$
$571$	5.10524	+	38.7782i	0.213648	+	1.62282i	−0.462895	+	0.886413i	$0.653189\pi$
$572$	0.113748	+	0.148239i	0.00475603	+	0.00619818i
$573$	−9.51733	+	3.94221i	−0.397592	+	0.164688i
$574$	−27.0852	+	2.89915i	−1.13051	+	0.121008i
$575$	−0.436440	−	1.05366i	−0.0182008	−	0.0439406i
$576$	−0.965926	+	0.258819i	−0.0402469	+	0.0107841i
$577$	7.76004	+	13.4408i	0.323055	+	0.559547i	0.981117	−	0.193417i	$-0.0619569\pi$
$577$	7.76004	+	13.4408i	0.323055	+	0.559547i	−0.658062	+	0.752964i	$0.728624\pi$
$578$	16.9898	+	0.589992i	0.706681	+	0.0245404i
$579$	1.76849	−	3.06311i	0.0734959	−	0.127299i
$580$	−11.4040	−	11.4040i	−0.473525	−	0.473525i
$581$	−18.2002	−	11.1053i	−0.755073	−	0.460725i
$582$			8.40538i			0.348414i
$583$	−0.143189	+	1.08763i	−0.00593028	+	0.0450450i
$584$	−10.5620	+	1.39052i	−0.437061	+	0.0575401i
$585$	−0.0415237	−	0.315404i	−0.00171679	−	0.0130403i
$586$	4.61237	+	17.2136i	0.190535	+	0.711087i
$587$	−11.1595	+	11.1595i	−0.460602	+	0.460602i	−0.898853	−	0.438250i	$-0.855598\pi$
$587$	−11.1595	+	11.1595i	−0.460602	+	0.460602i	0.438250	+	0.898853i	$0.355598\pi$
$588$	−2.36187	−	6.58950i	−0.0974020	−	0.271747i
$589$	11.1275	−	26.8642i	0.458501	−	1.10692i
$590$	−2.36008	+	17.9266i	−0.0971630	+	0.738026i
$591$	−9.67345	+	5.58497i	−0.397912	+	0.229735i
$592$	0.0372989	−	0.0486089i	0.00153298	−	0.00199781i
$593$	−7.28310	+	1.95150i	−0.299081	+	0.0801386i	−0.405239	−	0.914211i	$-0.632812\pi$
$593$	−7.28310	+	1.95150i	−0.299081	+	0.0801386i	0.106158	+	0.994349i	$0.466145\pi$
$594$	1.39092			0.0570701
$595$	−1.07495	+	25.8108i	−0.0440688	+	1.05814i
$596$	23.0224			0.943034
$597$	15.7056	−	4.20831i	0.642789	−	0.172235i
$598$	0.153395	−	0.199909i	0.00627281	−	0.00817488i
$599$	−8.08889	+	4.67012i	−0.330503	+	0.190816i	−0.656064	−	0.754705i	$-0.727780\pi$
$599$	−8.08889	+	4.67012i	−0.330503	+	0.190816i	0.325561	+	0.945521i	$0.394447\pi$
$600$	−0.0793616	+	0.602811i	−0.00323992	+	0.0246097i
$601$	−15.3427	+	37.0406i	−0.625842	+	1.51092i	0.218903	+	0.975747i	$0.429752\pi$
$601$	−15.3427	+	37.0406i	−0.625842	+	1.51092i	−0.844745	+	0.535170i	$0.820248\pi$
$602$	−8.84757	+	30.0801i	−0.360600	+	1.22597i
$603$	0.540838	−	0.540838i	0.0220246	−	0.0220246i
$604$	3.80781	+	14.2109i	0.154937	+	0.578234i
$605$	−2.80212	−	21.2842i	−0.113922	−	0.865326i
$606$	1.72144	−	0.226631i	0.0699285	−	0.00920627i
$607$	−0.465143	+	3.53311i	−0.0188796	+	0.143405i	−0.998288	−	0.0584821i	$-0.981374\pi$
$607$	−0.465143	+	3.53311i	−0.0188796	+	0.143405i	0.979409	+	0.201887i	$0.0647073\pi$
$608$		−	4.01088i		−	0.162663i
$609$	−0.437213	+	18.0131i	−0.0177168	+	0.729928i
$610$	−4.55588	−	4.55588i	−0.184462	−	0.184462i
$611$	−0.0901974	+	0.156227i	−0.00364900	+	0.00632025i
$612$	−2.45284	−	3.31415i	−0.0991501	−	0.133967i
$613$	14.1579	+	24.5221i	0.571831	+	0.990440i	0.996378	+	0.0850341i	$0.0270999\pi$
$613$	14.1579	+	24.5221i	0.571831	+	0.990440i	−0.424547	+	0.905406i	$0.639567\pi$
$614$	7.79851	−	2.08960i	0.314722	−	0.0843295i
$615$	−9.33040	−	22.5256i	−0.376238	−	0.908319i
$616$	−1.49037	+	3.36473i	−0.0600487	+	0.135569i
$617$	14.1766	−	5.87212i	0.570727	−	0.236403i	−0.0786078	−	0.996906i	$-0.525047\pi$
$617$	14.1766	−	5.87212i	0.570727	−	0.236403i	0.649335	+	0.760503i	$0.275047\pi$
$618$	−2.70515	−	3.52542i	−0.108817	−	0.141813i
$619$	2.10577	+	15.9949i	0.0846381	+	0.642890i	0.980208	+	0.197970i	$0.0634347\pi$
$619$	2.10577	+	15.9949i	0.0846381	+	0.642890i	−0.895570	+	0.444921i	$0.853232\pi$
$620$	16.5831	+	4.44344i	0.665995	+	0.178453i
$621$	−0.485476	−	1.81182i	−0.0194815	−	0.0727059i
$622$	12.0495	+	4.99105i	0.483140	+	0.200123i
$623$	−32.5494	−	9.57388i	−1.30406	−	0.383570i
$624$	−0.124111	+	0.0514083i	−0.00496840	+	0.00205798i
$625$	−23.9633	−	13.8352i	−0.958530	−	0.553408i
$626$	8.91046	−	11.6123i	0.356134	−	0.464123i
$627$	−1.44390	+	5.38872i	−0.0576639	+	0.215205i
$628$	6.95195	−	12.0411i	0.277413	−	0.480493i
$629$	0.242844	+	0.0696088i	0.00968282	+	0.00277549i
$630$	5.06182	−	3.69244i	0.201668	−	0.147110i
$631$	−12.1938	−	12.1938i	−0.485429	−	0.485429i	0.421431	−	0.906860i	$-0.361528\pi$
$631$	−12.1938	−	12.1938i	−0.485429	−	0.485429i	−0.906860	+	0.421431i	$0.861528\pi$
$632$	−13.7448	−	1.80954i	−0.546739	−	0.0719795i
$633$	−8.34925	+	4.82044i	−0.331853	+	0.191595i
$634$	−2.11310	−	1.62144i	−0.0839221	−	0.0643957i
$635$	−4.80479	−	6.26172i	−0.190672	−	0.248489i
$636$	−0.728661	−	0.301821i	−0.0288933	−	0.0119680i
$637$	−0.430114	−	0.836223i	−0.0170417	−	0.0331323i
$638$	6.69814	−	6.69814i	0.265182	−	0.265182i
$639$	6.06940	−	4.65722i	0.240102	−	0.184237i
$640$	2.34786	−	0.309102i	0.0928075	−	0.0122183i
$641$	−30.3941	−	23.3222i	−1.20050	−	0.921172i	−0.202189	−	0.979347i	$-0.564805\pi$
$641$	−30.3941	−	23.3222i	−1.20050	−	0.921172i	−0.998306	+	0.0581741i	$0.981472\pi$
$642$	7.56487	+	4.36758i	0.298561	+	0.172375i
$643$	14.1449	+	34.1489i	0.557821	+	1.34670i	0.911487	+	0.411328i	$0.134935\pi$
$643$	14.1449	+	34.1489i	0.557821	+	1.34670i	−0.353666	+	0.935372i	$0.615065\pi$
$644$	4.90311	+	0.766966i	0.193210	+	0.0302227i
$645$	−28.0642			−1.10502
$646$	15.3860	−	6.06243i	0.605354	−	0.238523i
$647$	−14.2710	−	24.7180i	−0.561049	−	0.971766i	−0.997405	−	0.0719917i	$-0.977064\pi$
$647$	−14.2710	−	24.7180i	−0.561049	−	0.971766i	0.436356	−	0.899774i	$-0.356269\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	−10.5292	−	1.38619i	−0.413307	−	0.0544129i
$650$			0.0816782i			0.00320368i
$651$	−9.18453	−	16.8389i	−0.359970	−	0.659969i
$652$	−3.41387	+	8.24182i	−0.133698	+	0.322774i
$653$	−7.13373	+	5.47390i	−0.279164	+	0.214210i	−0.738848	−	0.673873i	$-0.764630\pi$
$653$	−7.13373	+	5.47390i	−0.279164	+	0.214210i	0.459683	+	0.888083i	$0.347963\pi$
$654$	−6.60396	−	1.76952i	−0.258235	−	0.0691939i
$655$	−23.1648	−	6.20698i	−0.905122	−	0.242527i
$656$	−8.16813	+	6.26763i	−0.318912	+	0.244710i
$657$	−4.07680	+	9.84226i	−0.159051	+	0.383983i
$658$	−3.55183	−	0.0862098i	−0.138465	−	0.00336081i
$659$			18.8511i			0.734333i	0.930155	+	0.367166i	$0.119672\pi$
$659$			18.8511i			0.734333i	−0.930155	+	0.367166i	$0.880328\pi$
$660$	−3.26569	−	0.429936i	−0.127117	−	0.0167352i
$661$	−12.9945	+	48.4963i	−0.505429	+	1.88629i	−0.0441633	+	0.999024i	$0.514062\pi$
$661$	−12.9945	+	48.4963i	−0.505429	+	1.88629i	−0.461266	+	0.887262i	$0.652604\pi$
$662$	1.05673	+	1.83031i	0.0410710	+	0.0711370i
$663$	−0.384798	−	0.398393i	−0.0149443	−	0.0154723i
$664$	−8.05850			−0.312731
$665$	9.05066	+	23.4436i	0.350970	+	0.909106i
$666$	−0.0234471	−	0.0566062i	−0.000908555	−	0.00219345i
$667$	−11.0629	−	6.38718i	−0.428358	−	0.247313i
$668$	0.984119	+	0.755141i	0.0380767	+	0.0292173i
$669$	−4.82196	+	0.634823i	−0.186428	+	0.0245437i
$670$	−1.43699	+	1.10264i	−0.0555158	+	0.0425987i
$671$	2.67590	−	2.67590i	0.103302	−	0.103302i
$672$	−2.05932	−	1.66109i	−0.0794398	−	0.0640779i
$673$	−21.2862	−	8.81704i	−0.820523	−	0.339872i	−0.0673792	−	0.997727i	$-0.521464\pi$
$673$	−21.2862	−	8.81704i	−0.820523	−	0.339872i	−0.753144	+	0.657856i	$0.771464\pi$
$674$	−19.1234	−	24.9221i	−0.736606	−	0.959964i
$675$	0.482369	+	0.370135i	0.0185664	+	0.0142465i
$676$	11.2427	−	6.49098i	0.432412	−	0.249653i
$677$	13.0599	+	1.71937i	0.501935	+	0.0660809i	0.377242	−	0.926115i	$-0.376872\pi$
$677$	13.0599	+	1.71937i	0.501935	+	0.0660809i	0.124692	+	0.992195i	$0.460206\pi$
$678$	5.35280	+	5.35280i	0.205573	+	0.205573i
$679$	−17.9663	+	13.1059i	−0.689484	+	0.502957i
$680$	4.73452	+	8.53935i	0.181561	+	0.327469i
$681$	−6.13402	+	10.6244i	−0.235056	+	0.407129i
$682$	−2.60986	+	9.74012i	−0.0999366	+	0.372968i
$683$	15.1858	−	19.7905i	0.581067	−	0.757262i	−0.406638	−	0.913589i	$-0.633299\pi$
$683$	15.1858	−	19.7905i	0.581067	−	0.757262i	0.987705	+	0.156328i	$0.0499656\pi$
$684$	−3.47352	−	2.00544i	−0.132814	−	0.0766799i
$685$	14.1632	−	5.86660i	0.541149	−	0.224151i
$686$	10.4022	−	15.3230i	0.397159	−	0.585034i
$687$	−23.4720	−	9.72244i	−0.895514	−	0.370934i
$688$	3.06721	+	11.4470i	0.116936	+	0.436412i
$689$	−0.102340	−	0.0274220i	−0.00389886	−	0.00104470i
$690$	0.579795	+	4.40398i	0.0220724	+	0.167657i
$691$	−15.9592	−	20.7984i	−0.607115	−	0.791207i	0.384125	−	0.923281i	$-0.374503\pi$
$691$	−15.9592	−	20.7984i	−0.607115	−	0.791207i	−0.991240	+	0.132074i	$0.957836\pi$
$692$	2.66925	−	1.10564i	0.101470	−	0.0420301i
$693$	2.16876	+	2.97306i	0.0823842	+	0.112937i
$694$	1.28336	+	3.09830i	0.0487156	+	0.117610i
$695$	−24.8580	+	6.66068i	−0.942918	+	0.252654i
$696$	3.40516	+	5.89791i	0.129072	+	0.223560i
$697$	−36.3891	−	21.8600i	−1.37834	−	0.828006i
$698$	13.8076	−	23.9154i	0.522624	−	0.905212i
$699$	3.76754	+	3.76754i	0.142501	+	0.142501i
$700$	−1.41224	+	0.770284i	−0.0533776	+	0.0291140i
$701$		−	30.8824i		−	1.16641i	−0.812325	−	0.583205i	$-0.801798\pi$
$701$		−	30.8824i		−	1.16641i	0.812325	−	0.583205i	$-0.198202\pi$
$702$	−0.0175344	+	0.133187i	−0.000661794	+	0.00502682i
$703$	0.243645	−	0.0320764i	0.00918924	−	0.00120979i
$704$	0.181551	+	1.37902i	0.00684248	+	0.0519738i
$705$	−0.823060	−	3.07170i	−0.0309982	−	0.115687i
$706$	16.2721	−	16.2721i	0.612410	−	0.612410i
$707$	3.16852	+	3.32616i	0.119165	+	0.125093i
$708$	2.92189	−	7.05407i	0.109811	−	0.265108i
$709$	3.85673	−	29.2948i	0.144843	−	1.10019i	−0.752418	−	0.658686i	$-0.771112\pi$
$709$	3.85673	−	29.2948i	0.144843	−	1.10019i	0.897260	−	0.441502i	$-0.145554\pi$
$710$	−15.6897	+	9.05845i	−0.588824	+	0.339958i
$711$	−8.43950	+	10.9986i	−0.316506	+	0.412479i
$712$	−12.3867	+	3.31900i	−0.464211	+	0.124385i
$713$	13.5985			0.509267
$714$	3.25940	−	10.4104i	0.121980	−	0.389599i
$715$	−0.442486			−0.0165481
$716$	−25.4381	+	6.81611i	−0.950666	+	0.254730i
$717$	16.8712	−	21.9869i	0.630066	−	0.821118i
$718$	−5.61241	+	3.24033i	−0.209453	+	0.120928i
$719$	1.00920	−	7.66563i	0.0376368	−	0.285880i	−0.962268	−	0.272102i	$-0.912281\pi$
$719$	1.00920	−	7.66563i	0.0376368	−	0.285880i	0.999905	−	0.0137775i	$-0.00438564\pi$
$720$	0.906242	−	2.18786i	0.0337736	−	0.0815368i
$721$	3.31757	−	11.2791i	0.123553	−	0.420056i
$722$	−2.05969	+	2.05969i	−0.0766536	+	0.0766536i
$723$	0.792014	+	2.95584i	0.0294553	+	0.109929i
$724$	−1.35607	−	10.3004i	−0.0503980	−	0.382811i
$725$	4.10533	−	0.540478i	0.152468	−	0.0200728i
$726$	−1.18326	+	8.98779i	−0.0439151	+	0.333568i
$727$			24.3864i			0.904443i	0.891906	+	0.452221i	$0.149368\pi$
$727$			24.3864i			0.904443i	−0.891906	+	0.452221i	$0.850632\pi$
$728$	−0.303400	−	0.185127i	−0.0112448	−	0.00686125i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	12.6140	−	21.8481i	0.466866	−	0.808636i
$731$	−39.2753	+	29.0681i	−1.45265	+	1.07512i
$732$	1.36036	+	2.35621i	0.0502803	+	0.0870880i
$733$	−8.84122	+	2.36900i	−0.326558	+	0.0875009i	−0.418373	−	0.908275i	$-0.637400\pi$
$733$	−8.84122	+	2.36900i	−0.326558	+	0.0875009i	0.0918156	+	0.995776i	$0.470733\pi$
$734$	2.87469	+	6.94012i	0.106107	+	0.256165i
$735$	15.7850	+	5.06219i	0.582239	+	0.186722i
$736$	1.73296	−	0.717813i	0.0638776	−	0.0264590i
$737$	−0.647637	−	0.844017i	−0.0238560	−	0.0310898i
$738$	1.34386	+	10.2076i	0.0494681	+	0.375748i
$739$	32.3617	+	8.67128i	1.19044	+	0.318978i	0.799061	−	0.601250i	$-0.205330\pi$
$739$	32.3617	+	8.67128i	1.19044	+	0.318978i	0.391382	+	0.920228i	$0.371997\pi$
$740$	0.0375534	+	0.140151i	0.00138049	+	0.00515206i
$741$	−0.497793	−	0.206193i	−0.0182869	−	0.00757467i
$742$	−0.491010	−	2.02810i	−0.0180255	−	0.0744541i
$743$	41.1040	−	17.0258i	1.50796	−	0.624617i	0.532824	−	0.846226i	$-0.321131\pi$
$743$	41.1040	−	17.0258i	1.50796	−	0.624617i	0.975136	+	0.221609i	$0.0711307\pi$
$744$	−6.27840	−	3.62484i	−0.230177	−	0.132893i
$745$	−33.1896	+	43.2535i	−1.21597	+	1.58469i
$746$	2.36566	−	8.82877i	0.0866130	−	0.323244i
$747$	−4.02925	+	6.97887i	−0.147423	+	0.255343i
$748$	−5.01559	+	2.78083i	−0.183388	+	0.101677i
$749$	2.45972	+	22.9798i	0.0898763	+	0.839663i
$750$	7.35446	+	7.35446i	0.268547	+	0.268547i
$751$	0.848870	+	0.111756i	0.0309757	+	0.00407803i	0.145998	−	0.989285i	$-0.453361\pi$
$751$	0.848870	+	0.111756i	0.0309757	+	0.00407803i	−0.115022	+	0.993363i	$0.536694\pi$
$752$	−1.16295	+	0.671430i	−0.0424084	+	0.0244845i
$753$	−8.27433	−	6.34911i	−0.301533	−	0.231375i
$754$	0.556939	+	0.725818i	0.0202825	+	0.0264327i
$755$	−32.1883	−	13.3328i	−1.17145	−	0.485232i
$756$	−2.46820	+	0.952875i	−0.0897677	+	0.0346557i
$757$	7.13303	−	7.13303i	0.259254	−	0.259254i	−0.565496	−	0.824751i	$-0.691315\pi$
$757$	7.13303	−	7.13303i	0.259254	−	0.259254i	0.824751	+	0.565496i	$0.191315\pi$
$758$	−27.3539	+	20.9894i	−0.993538	+	0.762369i
$759$	−2.58668	+	0.340543i	−0.0938905	+	0.0123609i
$760$	7.53548	+	5.78218i	0.273341	+	0.209742i
$761$	19.7343	+	11.3936i	0.715369	+	0.413019i	0.813046	−	0.582200i	$-0.197808\pi$
$761$	19.7343	+	11.3936i	0.715369	+	0.413019i	−0.0976767	+	0.995218i	$0.531141\pi$
$762$	1.27545	+	3.07920i	0.0462046	+	0.111548i
$763$	−6.51473	−	16.8749i	−0.235849	−	0.610913i
$764$	−10.3015			−0.372695
$765$	9.76256	+	0.169458i	0.352966	+	0.00612676i
$766$	−19.0389	−	32.9764i	−0.687905	−	1.19149i
$767$	0.265469	−	0.990745i	0.00958554	−	0.0357737i
$768$	−0.991445	−	0.130526i	−0.0357757	−	0.00470996i
$769$		−	5.86345i		−	0.211441i	−0.994396	−	0.105721i	$-0.966285\pi$
$769$		−	5.86345i		−	0.211441i	0.994396	−	0.105721i	$-0.0337149\pi$
$770$	−4.17297	−	7.65071i	−0.150383	−	0.275713i
$771$	10.4716	−	25.2807i	0.377125	−	0.910460i
$772$	2.80607	−	2.15318i	0.100993	−	0.0774945i
$773$	−39.2683	−	10.5219i	−1.41238	−	0.378446i	−0.529607	−	0.848243i	$-0.677660\pi$
$773$	−39.2683	−	10.5219i	−1.41238	−	0.378446i	−0.882775	+	0.469797i	$0.844327\pi$
$774$	11.4470	+	3.06721i	0.411453	+	0.110249i
$775$	−3.49702	+	2.68336i	−0.125617	+	0.0963890i
$776$	−3.21660	+	7.76556i	−0.115469	+	0.278767i
$777$	0.0844354	−	0.138379i	0.00302910	−	0.00496434i
$778$		−	7.13736i		−	0.255887i
$779$	−40.9416	−	5.39006i	−1.46688	−	0.193119i
$780$	0.0823368	−	0.307285i	0.00294813	−	0.0110026i
$781$	−5.32049	−	9.21535i	−0.190382	−	0.329751i
$782$	5.37293	+	5.56275i	0.192136	+	0.198924i
$783$	6.81032			0.243381
$784$	0.339607	−	6.99176i	0.0121288	−	0.249706i
$785$	12.6003	+	30.4198i	0.449724	+	1.08573i
$786$	8.77021	+	5.06349i	0.312823	+	0.180609i
$787$	20.2789	+	15.5605i	0.722865	+	0.554674i	0.903350	−	0.428904i	$-0.141100\pi$
$787$	20.2789	+	15.5605i	0.722865	+	0.554674i	−0.180485	+	0.983578i	$0.557767\pi$
$788$	−11.0744	+	1.45797i	−0.394508	+	0.0519380i
$789$	5.20439	−	3.99347i	0.185281	−	0.142171i
$790$	23.2145	−	23.2145i	0.825935	−	0.825935i
$791$	−3.09528	+	19.7877i	−0.110055	+	0.703570i
$792$	1.28504	+	0.532282i	0.0456620	+	0.0189138i
$793$	0.222497	+	0.289963i	0.00790109	+	0.0102969i
$794$	17.2433	+	13.2312i	0.611940	+	0.469558i
$795$	1.61750	−	0.933866i	0.0573669	−	0.0331208i
$796$	16.1206	+	2.12231i	0.571378	+	0.0752234i
$797$	−25.4667	−	25.4667i	−0.902078	−	0.902078i	0.0935376	−	0.995616i	$-0.470182\pi$
$797$	−25.4667	−	25.4667i	−0.902078	−	0.902078i	−0.995616	+	0.0935376i	$0.970182\pi$
$798$	−1.12942	−	10.5515i	−0.0399810	−	0.373520i
$799$	−4.33344	−	3.44629i	−0.153306	−	0.121921i
$800$	−0.304006	+	0.526555i	−0.0107482	+	0.0186165i
$801$	−3.31900	+	12.3867i	−0.117271	+	0.437662i
$802$	−4.95886	+	6.46252i	−0.175104	+	0.228199i
$803$	12.8325	+	7.40886i	0.452850	+	0.261453i
$804$	0.706639	−	0.292700i	0.0249213	−	0.0103227i
$805$	−8.50938	+	8.10609i	−0.299916	+	0.285702i
$806$	−0.899761	−	0.372693i	−0.0316927	−	0.0131276i
$807$	−2.02086	−	7.54195i	−0.0711376	−	0.265489i
$808$	1.67713	+	0.449385i	0.0590011	+	0.0158093i
$809$	−0.0392471	−	0.298111i	−0.00137985	−	0.0104810i	0.990741	−	0.135765i	$-0.0433492\pi$
$809$	−0.0392471	−	0.298111i	−0.00137985	−	0.0104810i	−0.992121	+	0.125284i	$0.960016\pi$
$810$	−1.44162	−	1.87876i	−0.0506535	−	0.0660129i
$811$	−22.2708	+	9.22486i	−0.782033	+	0.323929i	−0.737736	−	0.675090i	$-0.764105\pi$
$811$	−22.2708	+	9.22486i	−0.782033	+	0.323929i	−0.0442973	+	0.999018i	$0.514105\pi$
$812$	−7.29725	+	16.4746i	−0.256083	+	0.578146i
$813$	−4.67697	−	11.2912i	−0.164028	−	0.396000i
$814$	−0.0823180	+	0.0220570i	−0.00288524	+	0.000773099i
$815$	−10.5629	−	18.2954i	−0.370001	−	0.640861i
$816$	−0.997858	−	4.00053i	−0.0349320	−	0.140047i
$817$	−23.7661	+	41.1640i	−0.831469	+	1.44015i
$818$	24.3541	+	24.3541i	0.851522	+	0.851522i
$819$	−0.312025	+	0.170189i	−0.0109030	+	0.00594689i
$820$		−	24.3815i		−	0.851439i
$821$	−6.09238	+	46.2762i	−0.212626	+	1.61505i	0.468896	+	0.883254i	$0.344652\pi$
$821$	−6.09238	+	46.2762i	−0.212626	+	1.61505i	−0.681521	+	0.731798i	$0.738681\pi$
$822$	−6.41817	+	0.844968i	−0.223859	+	0.0294716i
$823$	−4.93919	−	37.5169i	−0.172169	−	1.30776i	−0.831341	−	0.555763i	$-0.812426\pi$
$823$	−4.93919	−	37.5169i	−0.172169	−	1.30776i	0.659171	−	0.751993i	$-0.270907\pi$
$824$	−1.15011	−	4.29227i	−0.0400660	−	0.149528i
$825$	0.597998	−	0.597998i	0.0208196	−	0.0208196i
$826$	19.6338	−	4.75340i	0.683148	−	0.165392i
$827$	13.1424	−	31.7287i	0.457008	−	1.10331i	−0.512595	−	0.858630i	$-0.671316\pi$
$827$	13.1424	−	31.7287i	0.457008	−	1.10331i	0.969603	−	0.244684i	$-0.0786841\pi$
$828$	0.244833	−	1.85969i	0.00850853	−	0.0646287i
$829$	27.5738	−	15.9198i	0.957679	−	0.552916i	0.0622213	−	0.998062i	$-0.480182\pi$
$829$	27.5738	−	15.9198i	0.957679	−	0.552916i	0.895458	+	0.445146i	$0.146848\pi$
$830$	11.6173	−	15.1400i	0.403243	−	0.525517i
$831$	−12.2704	+	3.28784i	−0.425654	+	0.114054i
$832$	−0.134336			−0.00465727
$833$	27.3341	−	9.26526i	0.947072	−	0.321022i
$834$	10.8672			0.376301
$835$	−2.83746	+	0.760294i	−0.0981943	+	0.0263111i
$836$	−3.39617	+	4.42597i	−0.117459	+	0.153075i
$837$	−6.27840	+	3.62484i	−0.217013	+	0.125293i
$838$	−3.30964	+	25.1392i	−0.114329	+	0.868419i
$839$	−18.4111	+	44.4483i	−0.635622	+	1.53453i	0.196835	+	0.980437i	$0.436934\pi$
$839$	−18.4111	+	44.4483i	−0.635622	+	1.53453i	−0.832457	+	0.554090i	$0.813066\pi$
$840$	6.08954	−	1.47429i	0.210109	−	0.0508680i
$841$	12.2898	−	12.2898i	0.423786	−	0.423786i
$842$	−0.938907	−	3.50405i	−0.0323569	−	0.120758i
$843$	−2.95894	−	22.4754i	−0.101911	−	0.774093i
$844$	−9.55840	+	1.25839i	−0.329014	+	0.0433155i
$845$	−4.01275	+	30.4799i	−0.138043	+	1.04854i
$846$			1.34286i			0.0461685i
$847$	−21.0562	+	11.4848i	−0.723499	+	0.394622i
$848$	−0.557693	−	0.557693i	−0.0191512	−	0.0191512i
$849$	12.3135	−	21.3276i	0.422598	−	0.731961i
$850$	−2.47940	−	0.370303i	−0.0850427	−	0.0127013i
$851$	0.0574633	+	0.0995294i	0.00196982	+	0.00341182i
$852$	7.38964	−	1.98005i	0.253165	−	0.0678353i
$853$	8.56056	+	20.6670i	0.293108	+	0.707626i	1.00000		0.000303888i	$9.67305e-5\pi$
$853$	8.56056	+	20.6670i	0.293108	+	0.707626i	−0.706892	+	0.707322i	$0.749903\pi$
$854$	−2.91524	+	6.58160i	−0.0997576	+	0.225218i
$855$	8.77525	−	3.63483i	0.300107	−	0.124309i
$856$	5.31763	+	6.93006i	0.181753	+	0.236865i
$857$	−3.90136	−	29.6338i	−0.133268	−	1.01227i	−0.919154	−	0.393899i	$-0.871126\pi$
$857$	−3.90136	−	29.6338i	−0.133268	−	1.01227i	0.785886	−	0.618372i	$-0.212207\pi$
$858$	0.180484	+	0.0483606i	0.00616163	+	0.00165100i
$859$	11.1352	+	41.5573i	0.379929	+	1.41792i	0.846007	+	0.533172i	$0.179000\pi$
$859$	11.1352	+	41.5573i	0.379929	+	1.41792i	−0.466078	+	0.884744i	$0.654333\pi$
$860$	−25.9279	−	10.7397i	−0.884134	−	0.366220i
$861$	−19.7232	+	18.7885i	−0.672165	+	0.640309i
$862$	−12.7016	+	5.26118i	−0.432619	+	0.179197i
$863$	42.5852	+	24.5866i	1.44962	+	0.836937i	0.998458	−	0.0555069i	$-0.0176775\pi$
$863$	42.5852	+	24.5866i	1.44962	+	0.836937i	0.451159	+	0.892444i	$0.351011\pi$
$864$	−0.608761	+	0.793353i	−0.0207105	+	0.0269904i
$865$	−1.77082	+	6.60879i	−0.0602097	+	0.224706i
$866$	−8.65224	+	14.9861i	−0.294015	+	0.509249i
$867$	13.8380	−	9.87464i	0.469965	−	0.335360i
$868$	−2.04143	−	19.0719i	−0.0692905	−	0.647342i
$869$	13.6350	+	13.6350i	0.462537	+	0.462537i
$870$	−15.9897	−	2.10508i	−0.542102	−	0.0713690i
$871$	0.0889829	−	0.0513743i	0.00301507	−	0.00174075i
$872$	−5.42409	−	4.16205i	−0.183683	−	0.140945i
$873$	5.11687	+	6.66844i	0.173180	+	0.225692i
$874$	6.95068	+	2.87906i	0.235110	+	0.0973858i
$875$	−4.25275	+	27.1872i	−0.143769	+	0.919097i
$876$	−7.53294	+	7.53294i	−0.254514	+	0.254514i
$877$	−10.7663	+	8.26129i	−0.363553	+	0.278964i	−0.774343	−	0.632766i	$-0.781920\pi$
$877$	−10.7663	+	8.26129i	−0.363553	+	0.278964i	0.410790	+	0.911730i	$0.365253\pi$
$878$	−13.2844	+	1.74893i	−0.448328	+	0.0590236i
$879$	14.1382	+	10.8486i	0.476870	+	0.365915i
$880$	−2.85257	−	1.64693i	−0.0961603	−	0.0555182i
$881$	−3.36123	−	8.11474i	−0.113243	−	0.273392i	0.857089	−	0.515168i	$-0.172270\pi$
$881$	−3.36123	−	8.11474i	−0.113243	−	0.273392i	−0.970332	+	0.241775i	$0.922270\pi$
$882$	−5.88524	−	3.78999i	−0.198166	−	0.127616i
$883$	42.5131			1.43068			0.715339	−	0.698777i	$-0.246272\pi$
$883$	42.5131			1.43068			0.715339	+	0.698777i	$0.246272\pi$
$884$	−0.203049	−	0.515323i	−0.00682927	−	0.0173322i
$885$	9.04064	+	15.6588i	0.303898	+	0.526366i
$886$	5.66841	−	21.1548i	0.190434	−	0.710709i
$887$	−12.0066	−	1.58069i	−0.403141	−	0.0530745i	−0.0737705	−	0.997275i	$-0.523503\pi$
$887$	−12.0066	−	1.58069i	−0.403141	−	0.0530745i	−0.329371	+	0.944201i	$0.606837\pi$
$888$		−	0.0612701i		−	0.00205609i
$889$	−4.59302	+	7.52741i	−0.154045	+	0.252461i
$890$	11.6213	−	28.0564i	0.389548	−	0.940452i
$891$	1.10349	−	0.846738i	0.0369683	−	0.0283668i
$892$	−4.69784	−	1.25878i	−0.157295	−	0.0421472i
$893$	−5.20252	−	1.39401i	−0.174096	−	0.0466488i
$894$	18.2649	−	14.0151i	0.610870	−	0.468737i
$895$	23.8663	−	57.6183i	0.797762	−	1.92597i
$896$	−1.26689	−	2.32271i	−0.0423238	−	0.0775964i
$897$		−	0.251980i		−	0.00841336i
$898$	4.68054	+	0.616205i	0.156192	+	0.0205630i
$899$	−12.7786	+	47.6902i	−0.426189	+	1.59056i
$900$	0.304006	+	0.526555i	0.0101335	+	0.0175518i
$901$	1.29639	−	2.98230i	0.0431892	−	0.0993547i
$902$	14.3205			0.476820
$903$	11.2923	+	29.2502i	0.375785	+	0.973385i
$904$	2.89691	+	6.99377i	0.0963499	+	0.232609i
$905$	21.3069	+	12.3015i	0.708265	+	0.408917i
$906$	11.6720	+	8.95624i	0.387776	+	0.297551i
$907$	3.32368	−	0.437571i	0.110361	−	0.0145293i	−0.0751434	−	0.997173i	$-0.523941\pi$
$907$	3.32368	−	0.437571i	0.110361	−	0.0145293i	0.185504	+	0.982643i	$0.440608\pi$
$908$	−9.73289	+	7.46831i	−0.322997	+	0.247844i
$909$	1.22774	−	1.22774i	0.0407216	−	0.0407216i
$910$	0.785198	−	0.303134i	0.0260290	−	0.0100488i
$911$	−18.1919	−	7.53533i	−0.602724	−	0.249656i	0.0603900	−	0.998175i	$-0.480766\pi$
$911$	−18.1919	−	7.53533i	−0.602724	−	0.249656i	−0.663114	+	0.748518i	$0.730766\pi$
$912$	−2.44167	−	3.18205i	−0.0808518	−	0.105368i
$913$	8.89248	+	6.82344i	0.294298	+	0.225823i
$914$	−29.2991	+	16.9158i	−0.969128	+	0.559526i
$915$	−6.38787	−	0.840979i	−0.211177	−	0.0278019i
$916$	−17.9647	−	17.9647i	−0.593571	−	0.593571i
$917$	2.85164	+	26.6413i	0.0941695	+	0.879772i
$918$	−3.96349	−	1.13610i	−0.130815	−	0.0374968i
$919$	−3.14392	+	5.44544i	−0.103709	+	0.179628i	−0.913210	−	0.407490i	$-0.866404\pi$
$919$	−3.14392	+	5.44544i	−0.103709	+	0.179628i	0.809501	+	0.587118i	$0.199738\pi$
$920$	−1.14967	+	4.29062i	−0.0379035	+	0.141458i
$921$	4.91490	−	6.40522i	0.161952	−	0.211059i
$922$	−19.1945	−	11.0819i	−0.632136	−	0.364964i
$923$	0.949485	−	0.393290i	0.0312527	−	0.0129453i
$924$	0.865928	+	3.57670i	0.0284869	+	0.117665i
$925$	−0.0344173	−	0.0142561i	−0.00113163	−	0.000468738i
$926$	8.65260	+	32.2920i	0.284342	+	1.06118i
$927$	−4.29227	−	1.15011i	−0.140977	−	0.0377746i
$928$	0.888925	+	6.75205i	0.0291804	+	0.221647i
$929$	17.0904	+	22.2726i	0.560718	+	0.730742i	0.984570	−	0.174990i	$-0.0559892\pi$
$929$	17.0904	+	22.2726i	0.560718	+	0.730742i	−0.423853	+	0.905731i	$0.639323\pi$
$930$	15.8613	−	6.56996i	0.520112	−	0.215437i
$931$	20.7926	−	18.8663i	0.681451	−	0.618318i
$932$	2.03898	+	4.92253i	0.0667890	+	0.161243i
$933$	12.5978	−	3.37558i	0.412435	−	0.110512i
$934$	−0.0473388	−	0.0819932i	−0.00154897	−	0.00268290i
$935$	2.00609	−	13.4320i	0.0656062	−	0.439273i
$936$	−0.0671682	+	0.116339i	−0.00219546	+	0.00380265i
$937$	−42.4882	−	42.4882i	−1.38803	−	1.38803i	−0.829457	−	0.558571i	$-0.811350\pi$
$937$	−42.4882	−	42.4882i	−1.38803	−	1.38803i	−0.558571	−	0.829457i	$-0.688650\pi$
$938$	1.72745	+	1.05404i	0.0564032	+	0.0344157i
$939$		−	14.6370i		−	0.477662i
$940$	0.415081	−	3.15285i	0.0135384	−	0.102835i
$941$	−15.5066	+	2.04149i	−0.505502	+	0.0665506i	−0.378965	−	0.925411i	$-0.623720\pi$
$941$	−15.5066	+	2.04149i	−0.505502	+	0.0665506i	−0.126538	+	0.991962i	$0.540386\pi$
$942$	−1.81482	−	13.7849i	−0.0591301	−	0.449138i
$943$	−4.99832	−	18.6540i	−0.162768	−	0.607458i
$944$	5.39895	−	5.39895i	0.175721	−	0.175721i
$945$	1.76800	−	6.01085i	0.0575129	−	0.195533i
$946$	6.30796	−	15.2288i	0.205090	−	0.495130i
$947$	1.82768	−	13.8826i	0.0593917	−	0.451124i	−0.935749	−	0.352665i	$-0.885275\pi$
$947$	1.82768	−	13.8826i	0.0593917	−	0.451124i	0.995141	−	0.0984589i	$-0.0313913\pi$
$948$	−12.0061	+	6.93170i	−0.389939	+	0.225131i
$949$	−0.871205	+	1.13538i	−0.0282805	+	0.0368559i
$950$	−2.35557	+	0.631173i	−0.0764248	+	0.0204780i
$951$	−2.66351			−0.0863702
$952$	6.99518	−	8.37063i	0.226715	−	0.271294i
$953$	−18.1757			−0.588768			−0.294384	−	0.955687i	$-0.595114\pi$
$953$	−18.1757			−0.588768			−0.294384	+	0.955687i	$0.595114\pi$
$954$	−0.761823	+	0.204130i	−0.0246649	+	0.00660894i
$955$	14.8509	−	19.3540i	0.480562	−	0.626281i
$956$	24.0010	−	13.8570i	0.776247	−	0.448166i
$957$	1.23642	−	9.39156i	0.0399679	−	0.303586i
$958$	11.7163	−	28.2858i	0.378538	−	0.913871i
$959$	−11.8135	−	12.4012i	−0.381477	−	0.400456i
$960$	1.67452	−	1.67452i	0.0540448	−	0.0540448i
$961$	−5.57956	−	20.8232i	−0.179986	−	0.671717i
$962$	−0.00107434	−	0.00816039i	−3.46380e−5	−	0.000263102i
$963$	8.66043	−	1.14017i	0.279078	−	0.0367414i
$964$	−0.399424	+	3.03393i	−0.0128646	+	0.0977163i
$965$			8.37601i			0.269633i
$966$	4.35680	−	2.37635i	0.140178	−	0.0764578i
$967$	14.9672	+	14.9672i	0.481311	+	0.481311i	0.905550	−	0.424239i	$-0.139458\pi$
$967$	14.9672	+	14.9672i	0.481311	+	0.481311i	−0.424239	+	0.905550i	$0.639458\pi$
$968$	−4.53267	+	7.85082i	−0.145686	+	0.252335i
$969$	8.51595	−	14.1760i	0.273572	−	0.455400i
$970$	−9.95249	−	17.2382i	−0.319555	−	0.553486i
$971$	42.7458	−	11.4537i	1.37178	−	0.367567i	0.503651	−	0.863907i	$-0.331990\pi$
$971$	42.7458	−	11.4537i	1.37178	−	0.367567i	0.868128	+	0.496340i	$0.165323\pi$
$972$	0.382683	+	0.923880i	0.0122746	+	0.0296334i
$973$	16.9444	+	23.2284i	0.543213	+	0.744670i
$974$	18.5072	−	7.66593i	0.593008	−	0.245632i
$975$	0.0497225	+	0.0647997i	0.00159240	+	0.00207525i
$976$	0.355125	+	2.69744i	0.0113673	+	0.0863429i
$977$	31.3661	+	8.40452i	1.00349	+	0.268884i	0.722907	−	0.690945i	$-0.242805\pi$
$977$	31.3661	+	8.40452i	1.00349	+	0.268884i	0.280583	+	0.959830i	$0.409472\pi$
$978$	2.30889	+	8.61691i	0.0738303	+	0.275538i
$979$	16.4789	+	6.82579i	0.526669	+	0.218153i
$980$	12.6462	+	10.7175i	0.403969	+	0.342358i
$981$	−6.31649	+	2.61638i	−0.201670	+	0.0835344i
$982$	−1.94874	−	1.12511i	−0.0621868	−	0.0359036i
$983$	30.2117	−	39.3727i	0.963604	−	1.25579i	−0.00312571	−	0.999995i	$-0.500995\pi$
$983$	30.2117	−	39.3727i	0.963604	−	1.25579i	0.966730	−	0.255799i	$-0.0823384\pi$
$984$	−2.66472	+	9.94489i	−0.0849483	+	0.317031i
$985$	13.2259	−	22.9079i	0.421412	−	0.729907i
$986$	−24.5577	+	13.6157i	−0.782076	+	0.433611i
$987$	−2.87033	+	2.09382i	−0.0913638	+	0.0666470i
$988$	−0.380994	−	0.380994i	−0.0121210	−	0.0121210i
$989$	−22.0388	−	2.90146i	−0.700793	−	0.0922612i
$990$	−2.85257	+	1.64693i	−0.0906608	+	0.0523430i
$991$	11.7896	+	9.04648i	0.374509	+	0.287371i	0.778816	−	0.627252i	$-0.215821\pi$
$991$	11.7896	+	9.04648i	0.374509	+	0.287371i	−0.404307	+	0.914623i	$0.632487\pi$
$992$	−4.41332	−	5.75155i	−0.140123	−	0.182612i
$993$	1.95258	+	0.808786i	0.0619634	+	0.0256661i
$994$	15.7544	+	12.7079i	0.499700	+	0.403069i
$995$	−27.2271	+	27.2271i	−0.863157	+	0.863157i
$996$	−6.39324	+	4.90571i	−0.202578	+	0.155443i
$997$	−41.9721	+	5.52574i	−1.32927	+	0.175002i	−0.761489	−	0.648177i	$-0.775532\pi$
$997$	−41.9721	+	5.52574i	−1.32927	+	0.175002i	−0.567782	+	0.823179i	$0.692198\pi$
$998$	16.8622	+	12.9388i	0.533763	+	0.409571i
$999$	−0.0530615	−	0.0306351i	−0.00167879	−	0.000969251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.bh.a.457.8	yes	96
7.4	even	3	inner	714.2.bh.a.151.2	yes	96
17.8	even	8	inner	714.2.bh.a.331.2	yes	96
119.25	even	24	inner	714.2.bh.a.25.8	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.bh.a.25.8	✓	96	119.25	even	24	inner
714.2.bh.a.151.2	yes	96	7.4	even	3	inner
714.2.bh.a.331.2	yes	96	17.8	even	8	inner
714.2.bh.a.457.8	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.608761 - 0.793353i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.309102 + 2.34786i) q^{5} +(0.382683 - 0.923880i) q^{6} +(2.57146 - 0.622558i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(0.309102 + 2.34786i) q^{10} +(-1.37902 + 0.181551i) q^{11} +(0.130526 - 0.991445i) q^{12} -0.134336i q^{13} +(2.32271 - 1.26689i) q^{14} +(1.67452 + 1.67452i) q^{15} +(0.500000 - 0.866025i) q^{16} +(4.07788 + 0.609038i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.87421 - 1.03809i) q^{19} +(0.906242 + 2.18786i) q^{20} +(1.07150 - 2.41907i) q^{21} +(-1.28504 + 0.532282i) q^{22} +(1.14188 + 1.48812i) q^{23} +(-0.130526 - 0.991445i) q^{24} +(-0.587295 - 0.157365i) q^{25} +(-0.0347688 - 0.129759i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(1.91567 - 1.82488i) q^{28} +(-6.29191 + 2.60620i) q^{29} +(2.05086 + 1.18406i) q^{30} +(4.41332 - 5.75155i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.695460 + 1.20457i) q^{33} +(4.09656 - 0.467147i) q^{34} +(0.666837 + 6.22988i) q^{35} +(-0.707107 - 0.707107i) q^{36} +(0.0607460 + 0.00799736i) q^{37} +(3.47352 - 2.00544i) q^{38} +(-0.106576 - 0.0817788i) q^{39} +(1.44162 + 1.87876i) q^{40} +(-9.51199 - 3.94000i) q^{41} +(0.408888 - 2.61396i) q^{42} +(-8.37978 + 8.37978i) q^{43} +(-1.10349 + 0.846738i) q^{44} +(2.34786 - 0.309102i) q^{45} +(1.48812 + 1.14188i) q^{46} +(-1.16295 - 0.671430i) q^{47} +(-0.382683 - 0.923880i) q^{48} +(6.22484 - 3.20177i) q^{49} -0.608013 q^{50} +(2.96564 - 2.86444i) q^{51} +(-0.0671682 - 0.116339i) q^{52} +(0.204130 - 0.761823i) q^{53} +(-0.991445 - 0.130526i) q^{54} -3.29387i q^{55} +(1.37808 - 2.25851i) q^{56} +(1.53490 - 3.70557i) q^{57} +(-5.40299 + 4.14586i) q^{58} +(7.37511 + 1.97615i) q^{59} +(2.28743 + 0.612916i) q^{60} +(-2.15849 + 1.65627i) q^{61} +(2.77433 - 6.69783i) q^{62} +(-1.26689 - 2.32271i) q^{63} -1.00000i q^{64} +(0.315404 + 0.0415237i) q^{65} +(-0.359996 + 1.34352i) q^{66} +(0.382431 + 0.662389i) q^{67} +(3.83606 - 1.51150i) q^{68} +1.87574 q^{69} +(2.25653 + 5.84501i) q^{70} +(2.92765 + 7.06797i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(-8.45174 - 6.48525i) q^{73} +(0.0607460 - 0.00799736i) q^{74} +(-0.482369 + 0.370135i) q^{75} +(2.83612 - 2.83612i) q^{76} +(-3.43307 + 1.32537i) q^{77} +(-0.124111 - 0.0514083i) q^{78} +(-8.43950 - 10.9986i) q^{79} +(1.87876 + 1.44162i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-10.2076 - 1.34386i) q^{82} +(-5.69822 - 5.69822i) q^{83} +(-0.281589 - 2.63072i) q^{84} +(-2.69042 + 9.38605i) q^{85} +(-5.92540 + 10.2631i) q^{86} +(-1.76264 + 6.57826i) q^{87} +(-0.846738 + 1.10349i) q^{88} +(-11.1056 - 6.41182i) q^{89} +(2.18786 - 0.906242i) q^{90} +(-0.0836322 - 0.345441i) q^{91} +(1.73296 + 0.717813i) q^{92} +(-1.87635 - 7.00265i) q^{93} +(-1.29710 - 0.347558i) q^{94} +(1.23977 + 9.41701i) q^{95} +(-0.608761 - 0.793353i) q^{96} +(-7.76556 + 3.21660i) q^{97} +(5.18406 - 4.70378i) q^{98} +(0.532282 + 1.28504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{5} - 8 q^{10} - 16 q^{11} - 16 q^{15} + 48 q^{16} + 8 q^{17} - 48 q^{18} + 8 q^{19} + 16 q^{22} - 40 q^{25} + 32 q^{29} + 48 q^{33} + 32 q^{35} + 16 q^{37} + 16 q^{39} + 16 q^{42} - 16 q^{43}+ \cdots + 32 q^{99}+O(q^{100}) \) 96 * q + 8 * q^5 - 8 * q^10 - 16 * q^11 - 16 * q^15 + 48 * q^16 + 8 * q^17 - 48 * q^18 + 8 * q^19 + 16 * q^22 - 40 * q^25 + 32 * q^29 + 48 * q^33 + 32 * q^35 + 16 * q^37 + 16 * q^39 + 16 * q^42 - 16 * q^43 + 8 * q^44 + 8 * q^46 + 16 * q^49 - 128 * q^50 - 16 * q^52 - 24 * q^53 - 16 * q^57 + 16 * q^58 + 56 * q^59 - 8 * q^60 - 64 * q^65 + 32 * q^67 + 128 * q^69 + 24 * q^70 + 64 * q^71 - 40 * q^73 + 16 * q^74 + 16 * q^76 - 16 * q^77 + 32 * q^78 + 56 * q^79 - 8 * q^80 + 16 * q^83 - 48 * q^85 - 16 * q^86 - 24 * q^87 + 16 * q^88 - 16 * q^90 + 8 * q^91 + 16 * q^92 - 8 * q^93 - 24 * q^94 + 64 * q^95 + 32 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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