LMFDB - Embedded newform 714.2.bh.a.25.8

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			25.8
Character	$\chi$	$=$	714.25
Dual form			714.2.bh.a.457.8

$q$-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 $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{8}\right)$

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	−0.910152	−	0.414274i	$-0.864035\pi$
$5$	−0.309102	−	2.34786i	−0.138235	−	1.05000i	0.771917	−	0.635723i	$-0.219298\pi$
$6$	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	−0.0802707	−	0.996773i	$-0.525578\pi$
$11$	−1.37902	−	0.181551i	−0.415790	−	0.0547398i	−0.335519	+	0.942033i	$0.608912\pi$
$12$	0.130526	+	0.991445i	0.0376797	+	0.286205i
$13$			0.134336i			0.0372582i	0.999826	+	0.0186291i	$0.00593017\pi$
$13$			0.134336i			0.0372582i	−0.999826	+	0.0186291i	$0.994070\pi$
$14$	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	0.674202	−	0.738547i	$-0.264488\pi$
$19$	3.87421	+	1.03809i	0.888805	+	0.238155i	0.214603	+	0.976701i	$0.431154\pi$
$20$	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	−0.658986	−	0.752155i	$-0.729015\pi$
$23$	1.14188	−	1.48812i	0.238098	−	0.310295i	0.897084	+	0.441860i	$0.145681\pi$
$24$	−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	−0.287722	−	0.957714i	$-0.592898\pi$
$29$	−6.29191	−	2.60620i	−1.16838	−	0.483958i	−0.880656	+	0.473756i	$0.842898\pi$
$30$	2.05086	−	1.18406i	0.374433	−	0.216179i
$31$	4.41332	+	5.75155i	0.792656	+	1.03301i	0.998518	+	0.0544284i	$0.0173337\pi$
$31$	4.41332	+	5.75155i	0.792656	+	1.03301i	−0.205862	+	0.978581i	$0.566000\pi$
$32$	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	−0.125531	−	0.992090i	$-0.540064\pi$
$37$	0.0607460	−	0.00799736i	0.00998658	−	0.00131476i	0.135518	+	0.990775i	$0.456730\pi$
$38$	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	−0.970337	−	0.241754i	$-0.922277\pi$
$41$	−9.51199	+	3.94000i	−1.48552	+	0.615324i	−0.515186	+	0.857078i	$0.672277\pi$
$42$	0.408888	+	2.61396i	0.0630927	+	0.403343i
$43$	−8.37978	−	8.37978i	−1.27790	−	1.27790i	−0.941839	−	0.336065i	$-0.890904\pi$
$43$	−8.37978	−	8.37978i	−1.27790	−	1.27790i	−0.336065	−	0.941839i	$-0.609096\pi$
$44$	−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	−0.582413	−	0.812893i	$-0.697891\pi$
$47$	−1.16295	+	0.671430i	−0.169634	+	0.0979381i	0.412779	+	0.910831i	$0.364558\pi$
$48$	−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	0.978527	−	0.206117i	$-0.0660827\pi$
$53$	0.204130	+	0.761823i	0.0280394	+	0.104644i	−0.950488	+	0.310761i	$0.899416\pi$
$54$	−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	0.255490	−	0.966812i	$-0.417763\pi$
$59$	7.37511	−	1.97615i	0.960157	−	0.257273i	0.704667	+	0.709538i	$0.251096\pi$
$60$	2.28743	−	0.612916i	0.295306	−	0.0791271i
$61$	−2.15849	−	1.65627i	−0.276366	−	0.212063i	0.461273	−	0.887258i	$-0.347393\pi$
$61$	−2.15849	−	1.65627i	−0.276366	−	0.212063i	−0.737639	+	0.675195i	$0.764059\pi$
$62$	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	−0.841719	−	0.539916i	$-0.818456\pi$
$67$	0.382431	−	0.662389i	0.0467213	−	0.0809237i	0.888440	+	0.458992i	$0.151789\pi$
$68$	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	−0.649472	−	0.760386i	$-0.725010\pi$
$71$	2.92765	−	7.06797i	0.347448	−	0.838814i	0.996920	−	0.0784280i	$-0.0249901\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−8.45174	+	6.48525i	−0.989201	+	0.759041i	−0.970578	−	0.240786i	$-0.922595\pi$
$73$	−8.45174	+	6.48525i	−0.989201	+	0.759041i	−0.0186231	+	0.999827i	$0.505928\pi$
$74$	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	0.0218267	+	0.999762i	$0.493052\pi$
$79$	−8.43950	+	10.9986i	−0.949518	+	1.23744i	−0.971345	+	0.237674i	$0.923615\pi$
$80$	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	−0.946923	−	0.321461i	$-0.895826\pi$
$83$	−5.69822	+	5.69822i	−0.625461	+	0.625461i	0.321461	+	0.946923i	$0.395826\pi$
$84$	−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	−0.955363	−	0.295434i	$-0.904536\pi$
$89$	−11.1056	+	6.41182i	−1.17719	+	0.679652i	−0.221829	+	0.975086i	$0.571203\pi$
$90$	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	−0.0481435	−	0.998840i	$-0.515330\pi$
$97$	−7.76556	−	3.21660i	−0.788473	−	0.326596i	−0.740329	+	0.672244i	$0.765330\pi$
$98$	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	−0.819596	−	0.572941i	$-0.805802\pi$
$101$	0.868145	−	1.50367i	0.0863836	−	0.149621i	0.905980	+	0.423321i	$0.139136\pi$
$102$	2.12321	+	3.53440i	0.210229	+	0.349958i
$103$	2.22184	+	3.84835i	0.218925	+	0.379189i	0.954480	−	0.298276i	$-0.0964117\pi$
$103$	2.22184	+	3.84835i	0.218925	+	0.379189i	−0.735555	+	0.677465i	$0.763078\pi$
$104$	−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	−0.953846	−	0.300297i	$-0.902914\pi$
$107$	−1.14017	−	8.66043i	−0.110224	−	0.837235i	0.843622	−	0.536938i	$-0.180419\pi$
$108$	−0.991445	−	0.130526i	−0.0954018	−	0.0125599i
$109$	−0.892397	+	6.77843i	−0.0854761	+	0.649256i	0.894054	+	0.447959i	$0.147849\pi$
$109$	−0.892397	+	6.77843i	−0.0854761	+	0.649256i	−0.979530	+	0.201297i	$0.935484\pi$
$110$	−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	0.727071	−	0.686562i	$-0.240881\pi$
$113$	−2.89691	−	6.99377i	−0.272519	−	0.657919i	−0.999590	+	0.0286438i	$0.990881\pi$
$114$	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	0.594771	−	0.803896i	$-0.297243\pi$
$127$	−2.35672	−	2.35672i	−0.209125	−	0.209125i	−0.803896	+	0.594771i	$0.797243\pi$
$128$	−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	−0.946891	−	0.321556i	$-0.895794\pi$
$131$	−1.32184	−	10.0403i	−0.115489	−	0.877228i	0.831401	−	0.555672i	$-0.187539\pi$
$132$		−	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	−0.970522	−	0.241014i	$-0.922520\pi$
$137$	−3.23677	+	5.60626i	−0.276536	+	0.478975i	0.693985	+	0.719989i	$0.255853\pi$
$138$	1.81182	+	0.485476i	0.154233	+	0.0413265i
$139$	4.15870	−	10.0400i	0.352736	−	0.851581i	−0.643544	−	0.765409i	$-0.722537\pi$
$139$	4.15870	−	10.0400i	0.352736	−	0.851581i	0.996280	−	0.0861719i	$-0.0274634\pi$
$140$	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	0.650344	−	0.759640i	$-0.274625\pi$
$149$	19.9380	−	11.5112i	1.63338	−	0.943034i	0.983039	−	0.183394i	$-0.0587084\pi$
$150$	−0.370135	−	0.482369i	−0.0302214	−	0.0393853i
$151$	−3.80781	−	14.2109i	−0.309875	−	1.15647i	−0.928667	−	0.370914i	$-0.879044\pi$
$151$	−3.80781	−	14.2109i	−0.309875	−	1.15647i	0.618792	−	0.785555i	$-0.287622\pi$
$152$	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	0.896477	−	0.443091i	$-0.146118\pi$
$157$	12.0411	+	6.95195i	0.960987	+	0.554826i	0.0645100	+	0.997917i	$0.479452\pi$
$158$	−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	0.293228	−	0.956043i	$-0.405271\pi$
$163$	−7.07741	−	5.43069i	−0.554345	−	0.425364i	−0.847573	+	0.530678i	$0.821937\pi$
$164$	−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	−0.904448	−	0.426584i	$-0.859717\pi$
$167$	0.474702	−	1.14603i	0.0367335	−	0.0886826i	0.941182	+	0.337901i	$0.109717\pi$
$168$	−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	−0.0208462	−	0.999783i	$-0.506636\pi$
$173$	2.86446	−	0.377113i	0.217781	−	0.0286714i	0.238627	+	0.971111i	$0.423303\pi$
$174$		−	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	−0.904841	+	0.425749i	$0.860011\pi$
$179$	−25.4381	+	6.81611i	−1.90133	+	0.509460i	−0.996490	+	0.0837113i	$0.973323\pi$
$180$	1.87876	+	1.44162i	0.140034	+	0.107452i
$181$	3.97580	+	9.59843i	0.295519	+	0.713446i	0.999993	+	0.00371627i	$0.00118293\pi$
$181$	3.97580	+	9.59843i	0.295519	+	0.713446i	−0.704474	+	0.709730i	$0.748817\pi$
$182$	−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	−0.786740	−	0.617284i	$-0.788233\pi$
$191$	−8.92135	+	5.15074i	−0.645526	+	0.372695i	0.141214	+	0.989979i	$0.454899\pi$
$192$	−0.793353	+	0.608761i	−0.0572553	+	0.0439336i
$193$	3.50672	+	0.461668i	0.252419	+	0.0332316i	0.255674	−	0.966763i	$-0.417703\pi$
$193$	3.50672	+	0.461668i	0.252419	+	0.0332316i	−0.00325469	+	0.999995i	$0.501036\pi$
$194$	−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	−0.718706	−	0.695314i	$-0.755265\pi$
$197$	−10.3197	+	4.27455i	−0.735246	+	0.304549i	−0.0165403	+	0.999863i	$0.505265\pi$
$198$	0.846738	−	1.10349i	0.0601751	−	0.0784217i
$199$	12.8997	−	9.89826i	0.914433	−	0.701669i	−0.0402828	−	0.999188i	$-0.512826\pi$
$199$	12.8997	−	9.89826i	0.914433	−	0.701669i	0.954716	+	0.297519i	$0.0961592\pi$
$200$	−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	−0.667589	−	0.744530i	$-0.732674\pi$
$211$	−8.90702	+	3.68941i	−0.613184	+	0.253989i	0.0544051	+	0.998519i	$0.482674\pi$
$212$	−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	−0.812816	−	0.582520i	$-0.802067\pi$
$223$	−3.43906	+	3.43906i	−0.230297	+	0.230297i	0.582520	+	0.812816i	$0.302067\pi$
$224$	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	−0.284427	−	0.958698i	$-0.591803\pi$
$227$	−12.1631	−	1.60130i	−0.807292	−	0.106282i	−0.522865	+	0.852416i	$0.675137\pi$
$228$	−0.523525	+	3.97657i	−0.0346713	+	0.263355i
$229$	−6.57554	+	24.5403i	−0.434524	+	1.62167i	0.307678	+	0.951490i	$0.400448\pi$
$229$	−6.57554	+	24.5403i	−0.434524	+	1.62167i	−0.742203	+	0.670176i	$0.766219\pi$
$230$	−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	−0.999009	−	0.0445120i	$-0.985827\pi$
$233$	−0.695458	−	5.28253i	−0.0455609	−	0.346070i	0.953448	−	0.301558i	$-0.0975066\pi$
$234$	−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	0.729491	−	0.683990i	$-0.239757\pi$
$241$	−1.86288	−	2.42775i	−0.119998	−	0.156385i	−0.849490	+	0.527605i	$0.823090\pi$
$242$	−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	$0.106764\pi$
$251$			10.4296i			0.658308i	−0.944276	+	0.329154i	$0.893236\pi$
$252$	−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	0.959257	−	0.282533i	$-0.0911748\pi$
$257$	26.4312	+	7.08222i	1.64873	+	0.441776i	0.689475	+	0.724310i	$0.257841\pi$
$258$	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	−0.0581086	−	0.998310i	$-0.518507\pi$
$263$	6.33646	−	1.69785i	0.390723	−	0.104694i	0.448832	+	0.893616i	$0.351840\pi$
$264$	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	0.915455	−	0.402421i	$-0.131831\pi$
$269$	4.75321	+	6.19451i	0.289808	+	0.377686i	−0.625646	+	0.780107i	$0.715165\pi$
$270$	0.612916	+	2.28743i	0.0373009	+	0.139209i
$271$	6.11076	+	10.5841i	0.371202	+	0.642941i	0.989751	−	0.142806i	$-0.0456124\pi$
$271$	6.11076	+	10.5841i	0.371202	+	0.642941i	−0.618549	+	0.785746i	$0.712279\pi$
$272$	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	−0.865456	−	0.500986i	$-0.832971\pi$
$277$	−10.0781	+	7.73323i	−0.605537	+	0.464645i	0.259919	+	0.965631i	$0.416304\pi$
$278$	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	0.999082	−	0.0428348i	$-0.0136389\pi$
$281$	16.0296	+	16.0296i	0.956247	+	0.956247i	−0.0428348	+	0.999082i	$0.513639\pi$
$282$	−1.06536	−	0.817481i	−0.0634414	−	0.0486803i
$283$	24.4163	+	3.21446i	1.45140	+	0.191080i	0.814632	−	0.579978i	$-0.196939\pi$
$283$	24.4163	+	3.21446i	1.45140	+	0.191080i	0.636765	+	0.771058i	$0.280272\pi$
$284$	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	$-0.825726\pi$
$293$		−	17.8208i		−	1.04110i	0.853830	−	0.520552i	$-0.174274\pi$
$294$	−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	−0.272247	−	0.962227i	$-0.587767\pi$
$311$	10.3471	−	7.93962i	0.586731	−	0.450214i	0.858978	+	0.512013i	$0.171100\pi$
$312$	−0.133187	−	0.0175344i	−0.00754023	−	0.000992691i
$313$	11.6123	+	8.91046i	0.656368	+	0.503649i	0.882418	−	0.470467i	$-0.155914\pi$
$313$	11.6123	+	8.91046i	0.656368	+	0.503649i	−0.226049	+	0.974116i	$0.572581\pi$
$314$	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	−0.836665	−	0.547714i	$-0.815498\pi$
$317$	−1.62144	+	2.11310i	−0.0910692	+	0.118684i	0.745596	+	0.666398i	$0.232165\pi$
$318$	−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	−0.949262	−	0.314486i	$-0.898168\pi$
$331$	0.547004	−	2.04145i	0.0300661	−	0.112208i	0.979328	+	0.202278i	$0.0648345\pi$
$332$	−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	0.150802	+	0.988564i	$0.451815\pi$
$337$	−12.0215	+	29.0224i	−0.654852	+	1.58095i	−0.805653	+	0.592387i	$0.798185\pi$
$338$	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	−0.975671	−	0.219241i	$-0.929642\pi$
$347$	0.437730	−	3.32489i	0.0234986	−	0.178489i	0.999169	+	0.0407517i	$0.0129753\pi$
$348$	1.76264	−	6.57826i	0.0944874	−	0.352632i
$349$	19.5269	+	19.5269i	1.04525	+	1.04525i	0.998927	+	0.0463220i	$0.0147500\pi$
$349$	19.5269	+	19.5269i	1.04525	+	1.04525i	0.0463220	+	0.998927i	$0.485250\pi$
$350$	−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	0.925633	−	0.378423i	$-0.123534\pi$
$353$	19.9292	+	11.5061i	1.06072	+	0.612410i	0.135092	+	0.990833i	$0.456867\pi$
$354$	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	0.0898155	−	0.995958i	$-0.471372\pi$
$359$	−6.25983	−	1.67732i	−0.330381	−	0.0885254i	−0.420197	+	0.907433i	$0.638039\pi$
$360$	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	−0.946612	−	0.322376i	$-0.895519\pi$
$367$	0.980504	−	7.44767i	0.0511819	−	0.388765i	0.997794	−	0.0663897i	$-0.0211481\pi$
$368$	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	0.959745	−	0.280871i	$-0.0906234\pi$
$373$	4.57011	+	7.91566i	0.236631	+	0.409857i	−0.723114	+	0.690728i	$0.757290\pi$
$374$	−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	−0.640334	−	0.768097i	$-0.721204\pi$
$379$	−31.8543	−	13.1945i	−1.63624	−	0.677755i	−0.995911	+	0.0903418i	$0.971204\pi$
$380$	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	−0.0282161	+	0.999602i	$0.508983\pi$
$383$	−9.85528	+	36.7804i	−0.503581	+	1.87939i	−0.475365	+	0.879789i	$0.657684\pi$
$384$	−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	0.996813	−	0.0797732i	$-0.0254196\pi$
$389$	1.84728	+	6.89416i	0.0936610	+	0.349548i	−0.903152	+	0.429321i	$0.858753\pi$
$390$	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	−0.332934	−	0.942950i	$-0.608039\pi$
$397$	13.2312	−	17.2433i	0.664056	−	0.865414i	0.996990	+	0.0775358i	$0.0247052\pi$
$398$	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	0.434675	−	0.900587i	$-0.356863\pi$
$401$	−6.46252	−	4.95886i	−0.322723	−	0.247634i	−0.757398	+	0.652953i	$0.773530\pi$
$402$	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	−0.0283123	−	0.999599i	$-0.509013\pi$
$409$	17.2210	−	29.8276i	0.851522	−	1.47488i	0.879834	−	0.475280i	$-0.157653\pi$
$410$	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	−0.962362	−	0.271771i	$-0.912391\pi$
$419$	−9.70336	−	23.4260i	−0.474040	−	1.14443i	0.488322	−	0.872664i	$-0.337609\pi$
$420$	6.26362	−	0.152030i	0.305634	−	0.00741832i
$421$			3.62766i			0.176801i	0.996085	+	0.0884006i	$0.0281756\pi$
$421$			3.62766i			0.176801i	−0.996085	+	0.0884006i	$0.971824\pi$
$422$	−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	−0.205116	−	0.978738i	$-0.565757\pi$
$431$	−13.6305	−	1.79449i	−0.656559	−	0.0864376i	−0.451443	+	0.892300i	$0.649091\pi$
$432$	−0.793353	−	0.608761i	−0.0381702	−	0.0292890i
$433$	−12.2361	−	12.2361i	−0.588030	−	0.588030i	0.349067	−	0.937098i	$-0.386498\pi$
$433$	−12.2361	−	12.2361i	−0.588030	−	0.588030i	−0.937098	+	0.349067i	$0.886498\pi$
$434$	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	−0.440690	−	0.897659i	$-0.645266\pi$
$439$	−13.2844	+	1.74893i	−0.634032	+	0.0834719i	−0.193342	+	0.981131i	$0.561933\pi$
$440$	−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	0.999722	+	0.0235718i	$0.00750384\pi$
$443$	10.9505	+	18.9669i	0.520275	+	0.901143i	−0.479447	+	0.877571i	$0.659163\pi$
$444$	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	−0.277384	−	0.960759i	$-0.589467\pi$
$449$	4.36157	−	1.80662i	0.205835	−	0.0852598i	0.483219	+	0.875499i	$0.339467\pi$
$450$	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	−0.606074	−	0.795408i	$-0.707257\pi$
$457$	−32.6789	−	8.75628i	−1.52865	−	0.409602i	−0.922580	+	0.385807i	$0.873923\pi$
$458$	−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	−0.970605	−	0.240678i	$-0.922630\pi$
$461$	−15.6722	+	15.6722i	−0.729927	+	0.729927i	0.240678	+	0.970605i	$0.422630\pi$
$462$	−0.0892951	−	3.67894i	−0.00415439	−	0.171160i
$463$		−	33.4311i		−	1.55367i	−0.629701	−	0.776837i	$-0.716823\pi$
$463$		−	33.4311i		−	1.55367i	0.629701	−	0.776837i	$-0.283177\pi$
$464$	−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	−0.966490	−	0.256702i	$-0.917364\pi$
$467$	−0.0245044	+	0.0914515i	−0.00113393	+	0.00423187i	0.965357	+	0.260934i	$0.0840306\pi$
$468$	−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	0.992794	+	0.119836i	$0.0382368\pi$
$479$	18.6380	+	24.2895i	0.851592	+	1.10982i	−0.141201	+	0.989981i	$0.545097\pi$
$480$	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	0.566294	−	0.824203i	$-0.308377\pi$
$487$	19.8607	+	2.61470i	0.899972	+	0.118484i	0.333678	+	0.942687i	$0.391710\pi$
$488$	−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	−0.742098	−	0.670291i	$-0.766169\pi$
$491$	−1.59114	+	1.59114i	−0.0718071	+	0.0718071i	0.670291	+	0.742098i	$0.266169\pi$
$492$	−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	−0.408213	−	0.912887i	$-0.633848\pi$
$499$	12.9388	−	16.8622i	0.579221	−	0.754855i	0.987434	+	0.158031i	$0.0505147\pi$
$500$	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	0.190351	−	0.981716i	$-0.439037\pi$
$503$	22.8567	−	9.46754i	1.01913	−	0.422137i	0.828777	+	0.559579i	$0.189037\pi$
$504$	−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	0.951055	+	0.309023i	$0.100002\pi$
$509$	16.7662	+	29.0399i	0.743149	+	1.28717i	−0.207905	+	0.978149i	$0.566665\pi$
$510$	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	−0.735297	−	0.677745i	$-0.762957\pi$
$521$	−36.9989	−	4.87100i	−1.62095	−	0.213403i	−0.885656	+	0.464342i	$0.846291\pi$
$522$	5.40299	−	4.14586i	0.236482	−	0.181459i
$523$	38.3993	−	22.1698i	1.67908	−	0.969419i	0.716837	−	0.697241i	$-0.245589\pi$
$523$	38.3993	−	22.1698i	1.67908	−	0.969419i	0.962247	−	0.272179i	$-0.0877441\pi$
$524$	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	−0.0221961	−	0.999754i	$-0.507066\pi$
$541$	5.00355	−	0.658730i	0.215119	−	0.0283210i	0.237316	+	0.971433i	$0.423732\pi$
$542$	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	−0.386954	−	0.922099i	$-0.626473\pi$
$547$	12.5988	−	30.4162i	0.538686	−	1.30050i	0.925640	−	0.378405i	$-0.123527\pi$
$548$	−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	0.140300	−	0.990109i	$-0.455193\pi$
$557$	−15.2700	−	8.81612i	−0.647009	−	0.373551i	−0.787309	+	0.616558i	$0.788527\pi$
$558$	−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	0.997522	−	0.0703611i	$-0.0224152\pi$
$563$	2.33627	+	8.71907i	0.0984620	+	0.367465i	−0.899060	+	0.437826i	$0.855748\pi$
$564$	−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	−0.694679	−	0.719320i	$-0.744454\pi$
$569$	6.35918	−	23.7328i	0.266591	−	0.994930i	0.961270	−	0.275610i	$-0.0888797\pi$
$570$	9.17462	−	2.45833i	0.384282	−	0.102968i
$571$	5.10524	−	38.7782i	0.213648	−	1.62282i	−0.462895	−	0.886413i	$-0.653189\pi$
$571$	5.10524	−	38.7782i	0.213648	−	1.62282i	0.676543	−	0.736403i	$-0.263477\pi$
$572$	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	−0.658062	−	0.752964i	$-0.728624\pi$
$577$	7.76004	−	13.4408i	0.323055	−	0.559547i	0.981117	+	0.193417i	$0.0619569\pi$
$578$	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	0.438250	−	0.898853i	$-0.355598\pi$
$587$	−11.1595	−	11.1595i	−0.460602	−	0.460602i	−0.898853	+	0.438250i	$0.855598\pi$
$588$	−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	0.106158	−	0.994349i	$-0.466145\pi$
$593$	−7.28310	−	1.95150i	−0.299081	−	0.0801386i	−0.405239	+	0.914211i	$0.632812\pi$
$594$	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	0.325561	−	0.945521i	$-0.394447\pi$
$599$	−8.08889	−	4.67012i	−0.330503	−	0.190816i	−0.656064	+	0.754705i	$0.727780\pi$
$600$	−0.0793616	−	0.602811i	−0.00323992	−	0.0246097i
$601$	−15.3427	−	37.0406i	−0.625842	−	1.51092i	−0.844745	−	0.535170i	$-0.820248\pi$
$601$	−15.3427	−	37.0406i	−0.625842	−	1.51092i	0.218903	−	0.975747i	$-0.429752\pi$
$602$	−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	0.979409	−	0.201887i	$-0.0647073\pi$
$607$	−0.465143	−	3.53311i	−0.0188796	−	0.143405i	−0.998288	+	0.0584821i	$0.981374\pi$
$608$			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	−0.424547	−	0.905406i	$-0.639567\pi$
$613$	14.1579	−	24.5221i	0.571831	−	0.990440i	0.996378	−	0.0850341i	$-0.0270999\pi$
$614$	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	0.649335	−	0.760503i	$-0.275047\pi$
$617$	14.1766	+	5.87212i	0.570727	+	0.236403i	−0.0786078	+	0.996906i	$0.525047\pi$
$618$	−2.70515	+	3.52542i	−0.108817	+	0.141813i
$619$	2.10577	−	15.9949i	0.0846381	−	0.642890i	−0.895570	−	0.444921i	$-0.853232\pi$
$619$	2.10577	−	15.9949i	0.0846381	−	0.642890i	0.980208	−	0.197970i	$-0.0634347\pi$
$620$	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	−0.906860	−	0.421431i	$-0.861528\pi$
$631$	−12.1938	+	12.1938i	−0.485429	+	0.485429i	0.421431	+	0.906860i	$0.361528\pi$
$632$	−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	−0.998306	−	0.0581741i	$-0.981472\pi$
$641$	−30.3941	+	23.3222i	−1.20050	+	0.921172i	−0.202189	+	0.979347i	$0.564805\pi$
$642$	7.56487	−	4.36758i	0.298561	−	0.172375i
$643$	14.1449	−	34.1489i	0.557821	−	1.34670i	−0.353666	−	0.935372i	$-0.615065\pi$
$643$	14.1449	−	34.1489i	0.557821	−	1.34670i	0.911487	−	0.411328i	$-0.134935\pi$
$644$	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	0.436356	+	0.899774i	$0.356269\pi$
$647$	−14.2710	+	24.7180i	−0.561049	+	0.971766i	−0.997405	+	0.0719917i	$0.977064\pi$
$648$	−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	0.459683	−	0.888083i	$-0.347963\pi$
$653$	−7.13373	−	5.47390i	−0.279164	−	0.214210i	−0.738848	+	0.673873i	$0.764630\pi$
$654$	−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	$-0.880328\pi$
$659$		−	18.8511i		−	0.734333i	0.930155	−	0.367166i	$-0.119672\pi$
$660$	−3.26569	+	0.429936i	−0.127117	+	0.0167352i
$661$	−12.9945	−	48.4963i	−0.505429	−	1.88629i	−0.461266	−	0.887262i	$-0.652604\pi$
$661$	−12.9945	−	48.4963i	−0.505429	−	1.88629i	−0.0441633	−	0.999024i	$-0.514062\pi$
$662$	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	−0.753144	−	0.657856i	$-0.771464\pi$
$673$	−21.2862	+	8.81704i	−0.820523	+	0.339872i	−0.0673792	+	0.997727i	$0.521464\pi$
$674$	−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	0.124692	−	0.992195i	$-0.460206\pi$
$677$	13.0599	−	1.71937i	0.501935	−	0.0660809i	0.377242	+	0.926115i	$0.376872\pi$
$678$	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	0.987705	−	0.156328i	$-0.0499656\pi$
$683$	15.1858	+	19.7905i	0.581067	+	0.757262i	−0.406638	+	0.913589i	$0.633299\pi$
$684$	−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	−0.991240	−	0.132074i	$-0.957836\pi$
$691$	−15.9592	+	20.7984i	−0.607115	+	0.791207i	0.384125	+	0.923281i	$0.374503\pi$
$692$	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	$0.198202\pi$
$701$			30.8824i			1.16641i	−0.812325	+	0.583205i	$0.801798\pi$
$702$	−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	0.897260	+	0.441502i	$0.145554\pi$
$709$	3.85673	+	29.2948i	0.144843	+	1.10019i	−0.752418	+	0.658686i	$0.771112\pi$
$710$	−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	0.999905	+	0.0137775i	$0.00438564\pi$
$719$	1.00920	+	7.66563i	0.0376368	+	0.285880i	−0.962268	+	0.272102i	$0.912281\pi$
$720$	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	$-0.850632\pi$
$727$		−	24.3864i		−	0.904443i	0.891906	−	0.452221i	$-0.149368\pi$
$728$	−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	0.0918156	−	0.995776i	$-0.470733\pi$
$733$	−8.84122	−	2.36900i	−0.326558	−	0.0875009i	−0.418373	+	0.908275i	$0.637400\pi$
$734$	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	0.391382	−	0.920228i	$-0.371997\pi$
$739$	32.3617	−	8.67128i	1.19044	−	0.318978i	0.799061	+	0.601250i	$0.205330\pi$
$740$	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	0.975136	−	0.221609i	$-0.0711307\pi$
$743$	41.1040	+	17.0258i	1.50796	+	0.624617i	0.532824	+	0.846226i	$0.321131\pi$
$744$	−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	−0.115022	−	0.993363i	$-0.536694\pi$
$751$	0.848870	−	0.111756i	0.0309757	−	0.00407803i	0.145998	+	0.989285i	$0.453361\pi$
$752$	−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	0.824751	−	0.565496i	$-0.191315\pi$
$757$	7.13303	+	7.13303i	0.259254	+	0.259254i	−0.565496	+	0.824751i	$0.691315\pi$
$758$	−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	−0.0976767	−	0.995218i	$-0.531141\pi$
$761$	19.7343	−	11.3936i	0.715369	−	0.413019i	0.813046	+	0.582200i	$0.197808\pi$
$762$	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	$0.0337149\pi$
$769$			5.86345i			0.211441i	−0.994396	+	0.105721i	$0.966285\pi$
$770$	−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	−0.882775	−	0.469797i	$-0.844327\pi$
$773$	−39.2683	+	10.5219i	−1.41238	+	0.378446i	−0.529607	+	0.848243i	$0.677660\pi$
$774$	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	−0.180485	−	0.983578i	$-0.557767\pi$
$787$	20.2789	−	15.5605i	0.722865	−	0.554674i	0.903350	+	0.428904i	$0.141100\pi$
$788$	−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	−0.995616	−	0.0935376i	$-0.970182\pi$
$797$	−25.4667	+	25.4667i	−0.902078	+	0.902078i	0.0935376	+	0.995616i	$0.470182\pi$
$798$	−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	−0.992121	−	0.125284i	$-0.960016\pi$
$809$	−0.0392471	+	0.298111i	−0.00137985	+	0.0104810i	0.990741	+	0.135765i	$0.0433492\pi$
$810$	−1.44162	+	1.87876i	−0.0506535	+	0.0660129i
$811$	−22.2708	−	9.22486i	−0.782033	−	0.323929i	−0.0442973	−	0.999018i	$-0.514105\pi$
$811$	−22.2708	−	9.22486i	−0.782033	−	0.323929i	−0.737736	+	0.675090i	$0.764105\pi$
$812$	−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	−0.681521	−	0.731798i	$-0.738681\pi$
$821$	−6.09238	−	46.2762i	−0.212626	−	1.61505i	0.468896	−	0.883254i	$-0.344652\pi$
$822$	−6.41817	−	0.844968i	−0.223859	−	0.0294716i
$823$	−4.93919	+	37.5169i	−0.172169	+	1.30776i	0.659171	+	0.751993i	$0.270907\pi$
$823$	−4.93919	+	37.5169i	−0.172169	+	1.30776i	−0.831341	+	0.555763i	$0.812426\pi$
$824$	−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	0.969603	+	0.244684i	$0.0786841\pi$
$827$	13.1424	+	31.7287i	0.457008	+	1.10331i	−0.512595	+	0.858630i	$0.671316\pi$
$828$	0.244833	+	1.85969i	0.00850853	+	0.0646287i
$829$	27.5738	+	15.9198i	0.957679	+	0.552916i	0.895458	−	0.445146i	$-0.146848\pi$
$829$	27.5738	+	15.9198i	0.957679	+	0.552916i	0.0622213	+	0.998062i	$0.480182\pi$
$830$	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	−0.832457	−	0.554090i	$-0.813066\pi$
$839$	−18.4111	−	44.4483i	−0.635622	−	1.53453i	0.196835	−	0.980437i	$-0.436934\pi$
$840$	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	−0.706892	−	0.707322i	$-0.749903\pi$
$853$	8.56056	−	20.6670i	0.293108	−	0.707626i	1.00000		0.000303888i	$-9.67305e-5\pi$
$854$	−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	0.785886	+	0.618372i	$0.212207\pi$
$857$	−3.90136	+	29.6338i	−0.133268	+	1.01227i	−0.919154	+	0.393899i	$0.871126\pi$
$858$	0.180484	−	0.0483606i	0.00616163	−	0.00165100i
$859$	11.1352	−	41.5573i	0.379929	−	1.41792i	−0.466078	−	0.884744i	$-0.654333\pi$
$859$	11.1352	−	41.5573i	0.379929	−	1.41792i	0.846007	−	0.533172i	$-0.179000\pi$
$860$	−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	0.451159	−	0.892444i	$-0.351011\pi$
$863$	42.5852	−	24.5866i	1.44962	−	0.836937i	0.998458	+	0.0555069i	$0.0176775\pi$
$864$	−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	0.410790	−	0.911730i	$-0.365253\pi$
$877$	−10.7663	−	8.26129i	−0.363553	−	0.278964i	−0.774343	+	0.632766i	$0.781920\pi$
$878$	−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	−0.970332	−	0.241775i	$-0.922270\pi$
$881$	−3.36123	+	8.11474i	−0.113243	+	0.273392i	0.857089	+	0.515168i	$0.172270\pi$
$882$	−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	−0.329371	−	0.944201i	$-0.606837\pi$
$887$	−12.0066	+	1.58069i	−0.403141	+	0.0530745i	−0.0737705	+	0.997275i	$0.523503\pi$
$888$			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	0.185504	−	0.982643i	$-0.440608\pi$
$907$	3.32368	+	0.437571i	0.110361	+	0.0145293i	−0.0751434	+	0.997173i	$0.523941\pi$
$908$	−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	−0.663114	−	0.748518i	$-0.730766\pi$
$911$	−18.1919	+	7.53533i	−0.602724	+	0.249656i	0.0603900	+	0.998175i	$0.480766\pi$
$912$	−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	0.809501	−	0.587118i	$-0.199738\pi$
$919$	−3.14392	−	5.44544i	−0.103709	−	0.179628i	−0.913210	+	0.407490i	$0.866404\pi$
$920$	−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	−0.423853	−	0.905731i	$-0.639323\pi$
$929$	17.0904	−	22.2726i	0.560718	−	0.730742i	0.984570	+	0.174990i	$0.0559892\pi$
$930$	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	−0.558571	+	0.829457i	$0.688650\pi$
$937$	−42.4882	+	42.4882i	−1.38803	+	1.38803i	−0.829457	+	0.558571i	$0.811350\pi$
$938$	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	−0.126538	−	0.991962i	$-0.540386\pi$
$941$	−15.5066	−	2.04149i	−0.505502	−	0.0665506i	−0.378965	+	0.925411i	$0.623720\pi$
$942$	−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	0.995141	+	0.0984589i	$0.0313913\pi$
$947$	1.82768	+	13.8826i	0.0593917	+	0.451124i	−0.935749	+	0.352665i	$0.885275\pi$
$948$	−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	−0.424239	−	0.905550i	$-0.639458\pi$
$967$	14.9672	−	14.9672i	0.481311	−	0.481311i	0.905550	+	0.424239i	$0.139458\pi$
$968$	−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	0.868128	−	0.496340i	$-0.165323\pi$
$971$	42.7458	+	11.4537i	1.37178	+	0.367567i	0.503651	+	0.863907i	$0.331990\pi$
$972$	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	0.280583	−	0.959830i	$-0.409472\pi$
$977$	31.3661	−	8.40452i	1.00349	−	0.268884i	0.722907	+	0.690945i	$0.242805\pi$
$978$	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	0.966730	+	0.255799i	$0.0823384\pi$
$983$	30.2117	+	39.3727i	0.963604	+	1.25579i	−0.00312571	+	0.999995i	$0.500995\pi$
$984$	−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	−0.404307	−	0.914623i	$-0.632487\pi$
$991$	11.7896	−	9.04648i	0.374509	−	0.287371i	0.778816	+	0.627252i	$0.215821\pi$
$992$	−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	−0.567782	−	0.823179i	$-0.692198\pi$
$997$	−41.9721	−	5.52574i	−1.32927	−	0.175002i	−0.761489	+	0.648177i	$0.775532\pi$
$998$	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.25.8	✓	96
7.2	even	3	inner	714.2.bh.a.331.2	yes	96
17.15	even	8	inner	714.2.bh.a.151.2	yes	96
119.100	even	24	inner	714.2.bh.a.457.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.bh.a.25.8	✓	96	1.1	even	1	trivial
714.2.bh.a.151.2	yes	96	17.15	even	8	inner
714.2.bh.a.331.2	yes	96	7.2	even	3	inner
714.2.bh.a.457.8	yes	96	119.100	even	24	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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
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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