LMFDB - Embedded newform 312.2.bk.b.205.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(205,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.205"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.13
Character	$\chi$	$=$	312.205
Dual form			312.2.bk.b.277.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0850505 + 1.41165i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.98553 - 0.240124i) q^{4} -1.72209 q^{5} +(0.632171 + 1.26505i) q^{6} +(-4.22521 - 2.43943i) q^{7} +(0.507842 - 2.78246i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.146465 - 2.43100i) q^{10} +(-1.89993 - 3.29078i) q^{11} +(-1.83958 + 0.784813i) q^{12} +(-1.58200 + 3.23995i) q^{13} +(3.80298 - 5.75706i) q^{14} +(-1.49138 + 0.861047i) q^{15} +(3.88468 + 0.953547i) q^{16} +(2.74828 - 4.76016i) q^{17} +(1.18000 + 0.779483i) q^{18} +(-2.59127 + 4.48821i) q^{19} +(3.41927 + 0.413515i) q^{20} -4.87886 q^{21} +(4.80703 - 2.40217i) q^{22} +(1.39427 + 2.41494i) q^{23} +(-0.951427 - 2.66360i) q^{24} -2.03439 q^{25} +(-4.43914 - 2.50880i) q^{26} -1.00000i q^{27} +(7.80354 + 5.85814i) q^{28} +(-3.63649 + 2.09953i) q^{29} +(-1.08866 - 2.17854i) q^{30} -8.04936i q^{31} +(-1.67647 + 5.40273i) q^{32} +(-3.29078 - 1.89993i) q^{33} +(6.48595 + 4.28447i) q^{34} +(7.27621 + 4.20092i) q^{35} +(-1.20072 + 1.59946i) q^{36} +(2.70339 + 4.68242i) q^{37} +(-6.11541 - 4.03970i) q^{38} +(0.249921 + 3.59688i) q^{39} +(-0.874552 + 4.79166i) q^{40} +(0.996380 - 0.575260i) q^{41} +(0.414949 - 6.88726i) q^{42} +(-1.69133 - 0.976488i) q^{43} +(2.98218 + 6.99017i) q^{44} +(-0.861047 + 1.49138i) q^{45} +(-3.52765 + 1.76283i) q^{46} -10.3380i q^{47} +(3.84101 - 1.11654i) q^{48} +(8.40162 + 14.5520i) q^{49} +(0.173026 - 2.87186i) q^{50} -5.49655i q^{51} +(3.91910 - 6.05315i) q^{52} -9.45020i q^{53} +(1.41165 + 0.0850505i) q^{54} +(3.27186 + 5.66703i) q^{55} +(-8.93336 + 10.5177i) q^{56} +5.18254i q^{57} +(-2.65452 - 5.31203i) q^{58} +(0.755450 - 1.30848i) q^{59} +(3.16793 - 1.35152i) q^{60} +(2.10626 + 1.21605i) q^{61} +(11.3629 + 0.684602i) q^{62} +(-4.22521 + 2.43943i) q^{63} +(-7.48419 - 2.82610i) q^{64} +(2.72435 - 5.57949i) q^{65} +(2.96193 - 4.48385i) q^{66} +(-4.34914 - 7.53294i) q^{67} +(-6.59982 + 8.79152i) q^{68} +(2.41494 + 1.39427i) q^{69} +(-6.54909 + 9.91420i) q^{70} +(1.96941 + 1.13704i) q^{71} +(-2.15576 - 1.83104i) q^{72} +10.4863i q^{73} +(-6.83988 + 3.41802i) q^{74} +(-1.76184 + 1.01720i) q^{75} +(6.22277 - 8.28926i) q^{76} +18.5390i q^{77} +(-5.09880 + 0.0468859i) q^{78} -8.96275 q^{79} +(-6.68978 - 1.64210i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.727326 + 1.45547i) q^{82} -3.79462 q^{83} +(9.68713 + 1.17153i) q^{84} +(-4.73279 + 8.19743i) q^{85} +(1.52231 - 2.30452i) q^{86} +(-2.09953 + 3.63649i) q^{87} +(-10.1213 + 3.61529i) q^{88} +(-5.15591 + 2.97676i) q^{89} +(-2.03207 - 1.34234i) q^{90} +(14.5879 - 9.83030i) q^{91} +(-2.18848 - 5.12975i) q^{92} +(-4.02468 - 6.97095i) q^{93} +(14.5937 + 0.879252i) q^{94} +(4.46241 - 7.72911i) q^{95} +(1.24949 + 5.51713i) q^{96} +(-11.3698 - 6.56436i) q^{97} +(-21.2570 + 10.6225i) q^{98} -3.79987 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} + 6 q^{6} - 12 q^{7} + 24 q^{9} - 4 q^{10} - 8 q^{12} - 36 q^{14} - 2 q^{16} + 12 q^{17} + 54 q^{20} - 14 q^{22} + 20 q^{23} + 18 q^{24} + 48 q^{25} - 42 q^{26} + 6 q^{28} - 6 q^{30} + 12 q^{33}+ \cdots + 24 q^{98}+O(q^{100}) $ 48 * q - 2 * q^4 + 6 * q^6 - 12 * q^7 + 24 * q^9 - 4 * q^10 - 8 * q^12 - 36 * q^14 - 2 * q^16 + 12 * q^17 + 54 * q^20 - 14 * q^22 + 20 * q^23 + 18 * q^24 + 48 * q^25 - 42 * q^26 + 6 * q^28 - 6 * q^30 + 12 * q^33 + 2 * q^36 - 28 * q^38 + 28 * q^39 - 8 * q^40 - 12 * q^41 - 10 * q^42 - 30 * q^46 - 8 * q^48 + 16 * q^49 - 84 * q^50 - 28 * q^52 + 6 * q^54 - 68 * q^55 + 18 * q^56 - 24 * q^58 + 24 * q^62 - 12 * q^63 - 68 * q^64 + 12 * q^65 - 44 * q^66 + 4 * q^68 - 12 * q^71 + 54 * q^74 - 54 * q^76 + 4 * q^78 - 192 * q^79 + 78 * q^80 - 24 * q^81 - 6 * q^82 + 30 * q^84 - 10 * q^88 - 48 * q^89 - 8 * q^90 - 12 * q^92 + 54 * q^94 - 20 * q^95 + 144 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.0850505	+	1.41165i	−0.0601398	+	0.998190i
$2$	−0.0850505	+	1.41165i	−0.0601398	+	0.998190i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.98553	−	0.240124i	−0.992766	−	0.120062i
$5$	−1.72209			−0.770144			−0.385072	−	0.922887i	$-0.625823\pi$
$5$	−1.72209			−0.770144			−0.385072	+	0.922887i	$0.625823\pi$
$6$	0.632171	+	1.26505i	0.258083	+	0.516456i
$7$	−4.22521	−	2.43943i	−1.59698	−	0.922017i	−0.992065	−	0.125728i	$-0.959873\pi$
$7$	−4.22521	−	2.43943i	−1.59698	−	0.922017i	−0.604916	−	0.796289i	$-0.706793\pi$
$8$	0.507842	−	2.78246i	0.179549	−	0.983749i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.146465	−	2.43100i	0.0463163	−	0.768750i
$11$	−1.89993	−	3.29078i	−0.572851	−	0.992208i	−0.996271	−	0.0862742i	$-0.972504\pi$
$11$	−1.89993	−	3.29078i	−0.572851	−	0.992208i	0.423420	−	0.905933i	$-0.360829\pi$
$12$	−1.83958	+	0.784813i	−0.531042	+	0.226556i
$13$	−1.58200	+	3.23995i	−0.438768	+	0.898600i
$13$	−1.58200	+	3.23995i	−0.438768	+	0.898600i
$14$	3.80298	−	5.75706i	1.01639	−	1.53864i
$15$	−1.49138	+	0.861047i	−0.385072	+	0.222321i
$16$	3.88468	+	0.953547i	0.971170	+	0.238387i
$17$	2.74828	−	4.76016i	0.666555	−	1.15451i	−0.312306	−	0.949982i	$-0.601101\pi$
$17$	2.74828	−	4.76016i	0.666555	−	1.15451i	0.978861	−	0.204526i	$-0.0655652\pi$
$18$	1.18000	+	0.779483i	0.278129	+	0.183726i
$19$	−2.59127	+	4.48821i	−0.594478	+	1.02967i	0.399143	+	0.916889i	$0.369308\pi$
$19$	−2.59127	+	4.48821i	−0.594478	+	1.02967i	−0.993620	+	0.112777i	$0.964025\pi$
$20$	3.41927	+	0.413515i	0.764573	+	0.0924649i
$21$	−4.87886			−1.06465
$22$	4.80703	−	2.40217i	1.02486	−	0.512143i
$23$	1.39427	+	2.41494i	0.290725	+	0.503551i	0.973981	−	0.226628i	$-0.0727702\pi$
$23$	1.39427	+	2.41494i	0.290725	+	0.503551i	−0.683256	+	0.730179i	$0.739437\pi$
$24$	−0.951427	−	2.66360i	−0.194209	−	0.543706i
$25$	−2.03439			−0.406879
$26$	−4.43914	−	2.50880i	−0.870586	−	0.492016i
$27$		−	1.00000i		−	0.192450i
$28$	7.80354	+	5.85814i	1.47473	+	1.10708i
$29$	−3.63649	+	2.09953i	−0.675280	+	0.389873i	−0.798074	−	0.602559i	$-0.794148\pi$
$29$	−3.63649	+	2.09953i	−0.675280	+	0.389873i	0.122795	+	0.992432i	$0.460814\pi$
$30$	−1.08866	−	2.17854i	−0.198761	−	0.397745i
$31$		−	8.04936i		−	1.44571i	−0.691001	−	0.722854i	$-0.742830\pi$
$31$		−	8.04936i		−	1.44571i	0.691001	−	0.722854i	$-0.257170\pi$
$32$	−1.67647	+	5.40273i	−0.296361	+	0.955076i
$33$	−3.29078	−	1.89993i	−0.572851	−	0.330736i
$34$	6.48595	+	4.28447i	1.11233	+	0.734780i
$35$	7.27621	+	4.20092i	1.22990	+	0.710086i
$36$	−1.20072	+	1.59946i	−0.200120	+	0.266577i
$37$	2.70339	+	4.68242i	0.444435	+	0.769785i	0.998013	−	0.0630131i	$-0.0200710\pi$
$37$	2.70339	+	4.68242i	0.444435	+	0.769785i	−0.553577	+	0.832798i	$0.686738\pi$
$38$	−6.11541	−	4.03970i	−0.992050	−	0.655326i
$39$	0.249921	+	3.59688i	0.0400194	+	0.575962i
$40$	−0.874552	+	4.79166i	−0.138279	+	0.757628i
$41$	0.996380	−	0.575260i	0.155608	−	0.0898406i	−0.420174	−	0.907444i	$-0.638031\pi$
$41$	0.996380	−	0.575260i	0.155608	−	0.0898406i	0.575782	+	0.817603i	$0.304698\pi$
$42$	0.414949	−	6.88726i	0.0640280	−	1.06273i
$43$	−1.69133	−	0.976488i	−0.257925	−	0.148913i	0.365463	−	0.930826i	$-0.380911\pi$
$43$	−1.69133	−	0.976488i	−0.257925	−	0.148913i	−0.623388	+	0.781913i	$0.714244\pi$
$44$	2.98218	+	6.99017i	0.449581	+	1.05381i
$45$	−0.861047	+	1.49138i	−0.128357	+	0.222321i
$46$	−3.52765	+	1.76283i	−0.520123	+	0.259915i
$47$		−	10.3380i		−	1.50795i	−0.656902	−	0.753976i	$-0.728134\pi$
$47$		−	10.3380i		−	1.50795i	0.656902	−	0.753976i	$-0.271866\pi$
$48$	3.84101	−	1.11654i	0.554401	−	0.161159i
$49$	8.40162	+	14.5520i	1.20023	+	2.07886i
$50$	0.173026	−	2.87186i	0.0244696	−	0.406142i
$51$		−	5.49655i		−	0.769672i
$52$	3.91910	−	6.05315i	0.543482	−	0.839421i
$53$		−	9.45020i		−	1.29809i	−0.760752	−	0.649043i	$-0.775170\pi$
$53$		−	9.45020i		−	1.29809i	0.760752	−	0.649043i	$-0.224830\pi$
$54$	1.41165	+	0.0850505i	0.192102	+	0.0115739i
$55$	3.27186	+	5.66703i	0.441178	+	0.764142i
$56$	−8.93336	+	10.5177i	−1.19377	+	1.40548i
$57$			5.18254i			0.686444i
$58$	−2.65452	−	5.31203i	−0.348556	−	0.697504i
$59$	0.755450	−	1.30848i	0.0983512	−	0.170349i	−0.812651	−	0.582750i	$-0.801976\pi$
$59$	0.755450	−	1.30848i	0.0983512	−	0.170349i	0.911002	+	0.412401i	$0.135310\pi$
$60$	3.16793	−	1.35152i	0.408979	−	0.174481i
$61$	2.10626	+	1.21605i	0.269678	+	0.155699i	0.628741	−	0.777614i	$-0.283570\pi$
$61$	2.10626	+	1.21605i	0.269678	+	0.155699i	−0.359063	+	0.933313i	$0.616904\pi$
$62$	11.3629	+	0.684602i	1.44309	+	0.0869446i
$63$	−4.22521	+	2.43943i	−0.532327	+	0.307339i
$64$	−7.48419	−	2.82610i	−0.935524	−	0.353263i
$65$	2.72435	−	5.57949i	0.337915	−	0.692051i
$66$	2.96193	−	4.48385i	0.364588	−	0.551924i
$67$	−4.34914	−	7.53294i	−0.531332	−	0.920295i	−0.999331	−	0.0365657i	$-0.988358\pi$
$67$	−4.34914	−	7.53294i	−0.531332	−	0.920295i	0.467999	−	0.883729i	$-0.344975\pi$
$68$	−6.59982	+	8.79152i	−0.800346	+	1.06613i
$69$	2.41494	+	1.39427i	0.290725	+	0.167850i
$70$	−6.54909	+	9.91420i	−0.782766	+	1.18497i
$71$	1.96941	+	1.13704i	0.233726	+	0.134942i	0.612290	−	0.790633i	$-0.290249\pi$
$71$	1.96941	+	1.13704i	0.233726	+	0.134942i	−0.378564	+	0.925575i	$0.623582\pi$
$72$	−2.15576	−	1.83104i	−0.254059	−	0.215790i
$73$			10.4863i			1.22733i	0.789566	+	0.613665i	$0.210306\pi$
$73$			10.4863i			1.22733i	−0.789566	+	0.613665i	$0.789694\pi$
$74$	−6.83988	+	3.41802i	−0.795120	+	0.397336i
$75$	−1.76184	+	1.01720i	−0.203439	+	0.117456i
$76$	6.22277	−	8.28926i	0.713801	−	0.950843i
$77$			18.5390i			2.11272i
$78$	−5.09880	+	0.0468859i	−0.577326	+	0.00530878i
$79$	−8.96275			−1.00839			−0.504194	−	0.863590i	$-0.668210\pi$
$79$	−8.96275			−1.00839			−0.504194	+	0.863590i	$0.668210\pi$
$80$	−6.68978	−	1.64210i	−0.747941	−	0.183592i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.727326	+	1.45547i	0.0803197	+	0.160730i
$83$	−3.79462			−0.416513			−0.208257	−	0.978074i	$-0.566779\pi$
$83$	−3.79462			−0.416513			−0.208257	+	0.978074i	$0.566779\pi$
$84$	9.68713	+	1.17153i	1.05695	+	0.127824i
$85$	−4.73279	+	8.19743i	−0.513343	+	0.889136i
$86$	1.52231	−	2.30452i	0.164155	−	0.248503i
$87$	−2.09953	+	3.63649i	−0.225093	+	0.389873i
$88$	−10.1213	+	3.61529i	−1.07894	+	0.385392i
$89$	−5.15591	+	2.97676i	−0.546525	+	0.315536i	−0.747719	−	0.664015i	$-0.768851\pi$
$89$	−5.15591	+	2.97676i	−0.546525	+	0.315536i	0.201194	+	0.979551i	$0.435518\pi$
$90$	−2.03207	−	1.34234i	−0.214199	−	0.141495i
$91$	14.5879	−	9.83030i	1.52923	−	1.03050i
$92$	−2.18848	−	5.12975i	−0.228165	−	0.534813i
$93$	−4.02468	−	6.97095i	−0.417340	−	0.722854i
$94$	14.5937	+	0.879252i	1.50522	+	0.0906879i
$95$	4.46241	−	7.72911i	0.457833	−	0.792990i
$96$	1.24949	+	5.51713i	0.127526	+	0.563090i
$97$	−11.3698	−	6.56436i	−1.15443	−	0.666510i	−0.204466	−	0.978874i	$-0.565546\pi$
$97$	−11.3698	−	6.56436i	−1.15443	−	0.666510i	−0.949963	+	0.312364i	$0.898879\pi$
$98$	−21.2570	+	10.6225i	−2.14728	+	1.07304i
$99$	−3.79987			−0.381901
$100$	4.03936	+	0.488506i	0.403936	+	0.0488506i
$101$	−5.29490	+	3.05701i	−0.526863	+	0.304184i	−0.739738	−	0.672895i	$-0.765051\pi$
$101$	−5.29490	+	3.05701i	−0.526863	+	0.304184i	0.212875	+	0.977079i	$0.431717\pi$
$102$	7.75923	+	0.467485i	0.768278	+	0.0462879i
$103$	5.18846			0.511234			0.255617	−	0.966778i	$-0.417721\pi$
$103$	5.18846			0.511234			0.255617	+	0.966778i	$0.417721\pi$
$104$	8.21163	+	6.04724i	0.805217	+	0.592981i
$105$	8.40185			0.819936
$106$	13.3404	+	0.803745i	1.29574	+	0.0780666i
$107$	15.8280	−	9.13828i	1.53015	−	0.883431i	0.530794	−	0.847501i	$-0.321894\pi$
$107$	15.8280	−	9.13828i	1.53015	−	0.883431i	0.999354	−	0.0359302i	$-0.0114394\pi$
$108$	−0.240124	+	1.98553i	−0.0231059	+	0.191058i
$109$	−3.56605			−0.341566			−0.170783	−	0.985309i	$-0.554630\pi$
$109$	−3.56605			−0.341566			−0.170783	+	0.985309i	$0.554630\pi$
$110$	−8.27816	+	4.13675i	−0.789292	+	0.394424i
$111$	4.68242	+	2.70339i	0.444435	+	0.256595i
$112$	−14.0875	−	13.5053i	−1.33114	−	1.27613i
$113$	1.30310	−	2.25703i	0.122585	−	0.212324i	−0.798201	−	0.602391i	$-0.794215\pi$
$113$	1.30310	−	2.25703i	0.122585	−	0.212324i	0.920786	+	0.390067i	$0.127548\pi$
$114$	−7.31595	−	0.440777i	−0.685201	−	0.0412826i
$115$	−2.40106	−	4.15876i	−0.223900	−	0.387806i
$116$	7.72452	−	3.29548i	0.717204	−	0.305977i
$117$	2.01488	+	2.99003i	0.186276	+	0.276428i
$118$	1.78287	+	1.17772i	0.164126	+	0.108418i
$119$	−23.2241	+	13.4084i	−2.12895	+	1.22915i
$120$	1.63845	+	4.58697i	0.149569	+	0.418732i
$121$	−1.71949	+	2.97825i	−0.156317	+	0.270750i
$122$	−1.89578	+	2.86988i	−0.171635	+	0.259827i
$123$	0.575260	−	0.996380i	0.0518695	−	0.0898406i
$124$	−1.93284	+	15.9823i	−0.173574	+	1.43525i
$125$	12.1139			1.08350
$126$	−3.08427	−	6.17201i	−0.274769	−	0.549847i
$127$	2.27165	+	3.93461i	0.201576	+	0.349140i	0.949036	−	0.315166i	$-0.102060\pi$
$127$	2.27165	+	3.93461i	0.201576	+	0.349140i	−0.747460	+	0.664306i	$0.768727\pi$
$128$	4.62601	−	10.3247i	0.408886	−	0.912586i
$129$	−1.95298			−0.171950
$130$	7.64461	+	4.32038i	0.670476	+	0.378923i
$131$		−	3.15287i		−	0.275467i	−0.990469	−	0.137734i	$-0.956018\pi$
$131$		−	3.15287i		−	0.275467i	0.990469	−	0.137734i	$-0.0439818\pi$
$132$	6.07773	+	4.56257i	0.528999	+	0.397121i
$133$	21.8973	−	12.6424i	1.89874	−	1.09624i
$134$	11.0038	−	5.49881i	0.950583	−	0.475024i
$135$			1.72209i			0.148214i
$136$	−11.8493	−	10.0644i	−1.01607	−	0.863014i
$137$	13.8055	+	7.97062i	1.17948	+	0.680976i	0.955895	−	0.293708i	$-0.0948893\pi$
$137$	13.8055	+	7.97062i	1.17948	+	0.680976i	0.223589	+	0.974683i	$0.428223\pi$
$138$	−2.17362	+	3.29048i	−0.185031	+	0.280104i
$139$	1.91788	+	1.10729i	0.162673	+	0.0939190i	0.579126	−	0.815238i	$-0.303394\pi$
$139$	1.91788	+	1.10729i	0.162673	+	0.0939190i	−0.416454	+	0.909157i	$0.636727\pi$
$140$	−13.4384	−	10.0883i	−1.13575	−	0.852614i
$141$	−5.16900	−	8.95297i	−0.435308	−	0.753976i
$142$	−1.77261	+	2.68342i	−0.148754	+	0.225188i
$143$	13.6677	−	0.949667i	1.14295	−	0.0794152i
$144$	2.76814	−	2.88746i	0.230678	−	0.240622i
$145$	6.26238	−	3.61559i	0.520062	−	0.300258i
$146$	−14.8030	−	0.891867i	−1.22511	−	0.0738114i
$147$	14.5520	+	8.40162i	1.20023	+	0.692954i
$148$	−4.24332	−	9.94624i	−0.348799	−	0.817576i
$149$	4.81230	−	8.33515i	0.394239	−	0.682842i	−0.598765	−	0.800925i	$-0.704342\pi$
$149$	4.81230	−	8.33515i	0.394239	−	0.682842i	0.993004	+	0.118083i	$0.0376749\pi$
$150$	−1.28609	−	2.57362i	−0.105008	−	0.210135i
$151$		−	15.7457i		−	1.28137i	−0.767805	−	0.640684i	$-0.778651\pi$
$151$		−	15.7457i		−	1.28137i	0.767805	−	0.640684i	$-0.221349\pi$
$152$	11.1723	+	9.48941i	0.906195	+	0.769693i
$153$	−2.74828	−	4.76016i	−0.222185	−	0.384836i
$154$	−26.1706	−	1.57675i	−2.10889	−	0.127058i
$155$			13.8618i			1.11340i
$156$	0.367469	−	7.20173i	0.0294211	−	0.576600i
$157$		−	19.4986i		−	1.55615i	−0.628169	−	0.778077i	$-0.716195\pi$
$157$		−	19.4986i		−	1.55615i	0.628169	−	0.778077i	$-0.283805\pi$
$158$	0.762286	−	12.6523i	0.0606442	−	1.00656i
$159$	−4.72510	−	8.18412i	−0.374725	−	0.649043i
$160$	2.88704	−	9.30400i	0.228241	−	0.735546i
$161$		−	13.6049i		−	1.07221i
$162$	1.26505	−	0.632171i	0.0993920	−	0.0496680i
$163$	−5.69628	+	9.86625i	−0.446167	+	0.772785i	−0.998133	−	0.0610825i	$-0.980545\pi$
$163$	−5.69628	+	9.86625i	−0.446167	+	0.772785i	0.551965	+	0.833867i	$0.313878\pi$
$164$	−2.11648	+	0.902944i	−0.165269	+	0.0705081i
$165$	5.66703	+	3.27186i	0.441178	+	0.254714i
$166$	0.322734	−	5.35668i	0.0250490	−	0.415759i
$167$	12.4113	−	7.16568i	0.960417	−	0.554497i	0.0641155	−	0.997942i	$-0.479577\pi$
$167$	12.4113	−	7.16568i	0.960417	−	0.554497i	0.896301	+	0.443446i	$0.146244\pi$
$168$	−2.47769	+	13.5752i	−0.191158	+	1.04735i
$169$	−7.99454	−	10.2512i	−0.614965	−	0.788555i
$170$	−11.1694	−	7.37826i	−0.856655	−	0.565886i
$171$	2.59127	+	4.48821i	0.198159	+	0.343222i
$172$	3.12371	+	2.34498i	0.238180	+	0.178803i
$173$	−3.97587	−	2.29547i	−0.302280	−	0.174521i	0.341187	−	0.939996i	$-0.389171\pi$
$173$	−3.97587	−	2.29547i	−0.302280	−	0.174521i	−0.643467	+	0.765474i	$0.722504\pi$
$174$	−4.95490	−	3.27309i	−0.375630	−	0.248133i
$175$	8.59575	+	4.96276i	0.649778	+	0.375149i
$176$	−4.24272	−	14.5953i	−0.319807	−	1.10016i
$177$		−	1.51090i		−	0.113566i
$178$	−3.76365	−	7.53153i	−0.282097	−	0.564512i
$179$	−11.1431	+	6.43346i	−0.832873	+	0.480860i	−0.854835	−	0.518899i	$-0.826342\pi$
$179$	−11.1431	+	6.43346i	−0.832873	+	0.480860i	0.0219622	+	0.999759i	$0.493009\pi$
$180$	2.06775	−	2.75442i	0.154121	−	0.205302i
$181$		−	2.23699i		−	0.166274i	−0.996538	−	0.0831370i	$-0.973506\pi$
$181$		−	2.23699i		−	0.166274i	0.996538	−	0.0831370i	$-0.0264939\pi$
$182$	12.6363	+	21.4292i	0.936663	+	1.58844i
$183$	2.43209			0.179786
$184$	7.42756	−	2.65309i	0.547567	−	0.195588i
$185$	−4.65550	−	8.06356i	−0.342279	−	0.592845i
$186$	10.1829	−	5.08857i	0.746644	−	0.373112i
$187$	−20.8862			−1.52735
$188$	−2.48240	+	20.5264i	−0.181047	+	1.49704i
$189$	−2.43943	+	4.22521i	−0.177442	+	0.307339i
$190$	10.5313	+	6.95674i	0.764021	+	0.504695i
$191$	−7.65684	+	13.2620i	−0.554029	+	0.959607i	0.443949	+	0.896052i	$0.353577\pi$
$191$	−7.65684	+	13.2620i	−0.554029	+	0.959607i	−0.997978	+	0.0635547i	$0.979756\pi$
$192$	−7.89455	+	1.29462i	−0.569740	+	0.0934311i
$193$	2.57679	−	1.48771i	0.185481	−	0.107088i	−0.404384	−	0.914589i	$-0.632514\pi$
$193$	2.57679	−	1.48771i	0.185481	−	0.107088i	0.589865	+	0.807502i	$0.299181\pi$
$194$	10.2336	−	15.4919i	0.734731	−	1.11226i
$195$	−0.430388	−	6.19416i	−0.0308207	−	0.443573i
$196$	−13.1874	−	30.9110i	−0.941957	−	2.20793i
$197$	0.598593	+	1.03679i	0.0426480	+	0.0738685i	0.886561	−	0.462611i	$-0.153087\pi$
$197$	0.598593	+	1.03679i	0.0426480	+	0.0738685i	−0.843913	+	0.536479i	$0.819754\pi$
$198$	0.323181	−	5.36410i	0.0229674	−	0.381210i
$199$	5.51709	−	9.55588i	0.391096	−	0.677398i	−0.601498	−	0.798874i	$-0.705429\pi$
$199$	5.51709	−	9.55588i	0.391096	−	0.677398i	0.992594	+	0.121476i	$0.0387627\pi$
$200$	−1.03315	+	5.66063i	−0.0730548	+	0.400267i
$201$	−7.53294	−	4.34914i	−0.531332	−	0.306765i
$202$	−3.86511	−	7.73457i	−0.271948	−	0.544203i
$203$	20.4866			1.43788
$204$	−1.31985	+	10.9136i	−0.0924082	+	0.764104i
$205$	−1.71586	+	0.990652i	−0.119841	+	0.0691901i
$206$	−0.441281	+	7.32431i	−0.0307455	+	0.510309i
$207$	2.78854			0.193817
$208$	−9.23502	+	11.0777i	−0.640333	+	0.768097i
$209$	19.6929			1.36219
$210$	−0.714581	+	11.8605i	−0.0493108	+	0.818452i
$211$	−14.0830	+	8.13080i	−0.969511	+	0.559747i	−0.899087	−	0.437770i	$-0.855768\pi$
$211$	−14.0830	+	8.13080i	−0.969511	+	0.559747i	−0.0704237	+	0.997517i	$0.522435\pi$
$212$	−2.26922	+	18.7637i	−0.155851	+	1.28870i
$213$	2.27408			0.155817
$214$	11.5539	+	23.1208i	0.789809	+	1.58051i
$215$	2.91262	+	1.68160i	0.198639	+	0.114684i
$216$	−2.78246	−	0.507842i	−0.189323	−	0.0345543i
$217$	−19.6358	+	34.0103i	−1.33297	+	2.30877i
$218$	0.303295	−	5.03403i	0.0205417	−	0.340948i
$219$	5.24316	+	9.08142i	0.354300	+	0.613665i
$220$	−5.13560	−	12.0377i	−0.346242	−	0.811583i
$221$	11.0749	+	16.4349i	0.744977	+	1.10553i
$222$	−4.21450	+	6.38003i	−0.282859	+	0.428199i
$223$	3.26380	−	1.88436i	0.218560	−	0.126186i	−0.386723	−	0.922196i	$-0.626393\pi$
$223$	3.26380	−	1.88436i	0.218560	−	0.126186i	0.605283	+	0.796010i	$0.293060\pi$
$224$	20.2630	−	18.7380i	1.35388	−	1.25199i
$225$	−1.01720	+	1.76184i	−0.0678132	+	0.117456i
$226$	3.07532	+	2.03149i	0.204567	+	0.135132i
$227$	2.76574	−	4.79041i	0.183569	−	0.317951i	−0.759524	−	0.650479i	$-0.774568\pi$
$227$	2.76574	−	4.79041i	0.183569	−	0.317951i	0.943093	+	0.332528i	$0.107902\pi$
$228$	1.24445	−	10.2901i	0.0824157	−	0.681478i
$229$	−9.54211			−0.630561			−0.315280	−	0.948999i	$-0.602099\pi$
$229$	−9.54211			−0.630561			−0.315280	+	0.948999i	$0.602099\pi$
$230$	6.07494	−	3.03576i	0.400570	−	0.200172i
$231$	9.26950	+	16.0552i	0.609888	+	1.05636i
$232$	3.99510	+	11.1846i	0.262291	+	0.734307i
$233$	−10.9117			−0.714852			−0.357426	−	0.933942i	$-0.616346\pi$
$233$	−10.9117			−0.714852			−0.357426	+	0.933942i	$0.616346\pi$
$234$	−4.39225	+	2.59001i	−0.287130	+	0.169314i
$235$			17.8030i			1.16134i
$236$	−1.81417	+	2.41662i	−0.118092	+	0.157309i
$237$	−7.76197	+	4.48137i	−0.504194	+	0.291097i
$238$	−16.9529	−	33.9248i	−1.09889	−	2.19902i
$239$			15.7924i			1.02153i	0.859721	+	0.510764i	$0.170637\pi$
$239$			15.7924i			1.02153i	−0.859721	+	0.510764i	$0.829363\pi$
$240$	−6.61457	+	1.92279i	−0.426969	+	0.124116i
$241$	16.2332	+	9.37223i	1.04567	+	0.603719i	0.921434	−	0.388534i	$-0.127018\pi$
$241$	16.2332	+	9.37223i	1.04567	+	0.603719i	0.124237	+	0.992253i	$0.460352\pi$
$242$	−4.05801	−	2.68063i	−0.260859	−	0.172317i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.89004	−	2.92026i	−0.249034	−	0.186951i
$245$	−14.4684	−	25.0600i	−0.924350	−	1.60102i
$246$	1.35762	+	0.896811i	0.0865585	+	0.0571786i
$247$	−10.4422	−	15.4959i	−0.664420	−	0.985983i
$248$	−22.3970	−	4.08780i	−1.42221	−	0.259576i
$249$	−3.28623	+	1.89731i	−0.208257	+	0.120237i
$250$	−1.03029	+	17.1006i	−0.0651614	+	1.08154i
$251$	−21.9060	−	12.6475i	−1.38270	−	0.798300i	−0.390218	−	0.920722i	$-0.627600\pi$
$251$	−21.9060	−	12.6475i	−1.38270	−	0.798300i	−0.992478	+	0.122422i	$0.960934\pi$
$252$	8.97506	−	3.82899i	0.565376	−	0.241204i
$253$	5.29803	−	9.17646i	0.333085	−	0.576919i
$254$	−5.74751	+	2.87214i	−0.360631	+	0.180214i
$255$			9.46558i			0.592758i
$256$	14.1815	+	7.40845i	0.886343	+	0.463028i
$257$	−11.1746	−	19.3549i	−0.697051	−	1.20733i	−0.969484	−	0.245153i	$-0.921162\pi$
$257$	−11.1746	−	19.3549i	−0.697051	−	1.20733i	0.272433	−	0.962175i	$-0.412172\pi$
$258$	0.166102	−	2.75693i	0.0103410	−	0.171639i
$259$		−	26.3789i		−	1.63911i
$260$	−6.74906	+	10.4241i	−0.418559	+	0.646475i
$261$			4.19906i			0.259915i
$262$	4.45075	+	0.268153i	0.274969	+	0.0165665i
$263$	−2.61142	−	4.52311i	−0.161027	−	0.278907i	0.774210	−	0.632929i	$-0.218147\pi$
$263$	−2.61142	−	4.52311i	−0.161027	−	0.278907i	−0.935237	+	0.354021i	$0.884814\pi$
$264$	−6.95769	+	8.19161i	−0.428216	+	0.504159i
$265$			16.2741i			0.999712i
$266$	15.9844	+	31.9867i	0.980063	+	1.96123i
$267$	−2.97676	+	5.15591i	−0.182175	+	0.315536i
$268$	6.82653	+	16.0012i	0.416997	+	0.977431i
$269$	−4.01867	−	2.32018i	−0.245023	−	0.141464i	0.372460	−	0.928048i	$-0.378514\pi$
$269$	−4.01867	−	2.32018i	−0.245023	−	0.141464i	−0.617483	+	0.786584i	$0.711848\pi$
$270$	−2.43100	−	0.146465i	−0.147946	−	0.00891357i
$271$	−21.0062	+	12.1279i	−1.27604	+	0.736720i	−0.976117	−	0.217245i	$-0.930293\pi$
$271$	−21.0062	+	12.1279i	−1.27604	+	0.736720i	−0.299919	+	0.953965i	$0.596960\pi$
$272$	15.2152	−	15.8711i	0.922558	−	0.962325i
$273$	7.71836	−	15.8072i	0.467136	−	0.956698i
$274$	−12.4259	+	18.8107i	−0.750677	+	1.13640i
$275$	3.86521	+	6.69475i	0.233081	+	0.403708i
$276$	−4.46015	−	3.34825i	−0.268470	−	0.201541i
$277$	19.8813	+	11.4784i	1.19455	+	0.689673i	0.959335	−	0.282271i	$-0.0910876\pi$
$277$	19.8813	+	11.4784i	1.19455	+	0.689673i	0.235214	+	0.971944i	$0.424421\pi$
$278$	−1.72623	+	2.61321i	−0.103532	+	0.156730i
$279$	−6.97095	−	4.02468i	−0.417340	−	0.240951i
$280$	15.3841	−	18.1124i	0.919374	−	1.08242i
$281$		−	11.4160i		−	0.681019i	−0.940241	−	0.340509i	$-0.889401\pi$
$281$		−	11.4160i		−	0.681019i	0.940241	−	0.340509i	$-0.110599\pi$
$282$	13.0781	−	6.53538i	0.778790	−	0.389176i
$283$	−4.73809	+	2.73554i	−0.281650	+	0.162611i	−0.634170	−	0.773193i	$-0.718658\pi$
$283$	−4.73809	+	2.73554i	−0.281650	+	0.162611i	0.352520	+	0.935804i	$0.385325\pi$
$284$	−3.63730	−	2.73053i	−0.215834	−	0.162027i
$285$		−	8.92481i		−	0.528660i
$286$	0.178160	+	19.3748i	0.0105348	+	1.14565i
$287$	−5.61322			−0.331338
$288$	3.84066	+	4.15323i	0.226313	+	0.244731i
$289$	−6.60606	−	11.4420i	−0.388591	−	0.673060i
$290$	4.57134	+	9.14782i	0.268438	+	0.537178i
$291$	−13.1287			−0.769619
$292$	2.51801	−	20.8209i	0.147356	−	1.21845i
$293$	6.15125	−	10.6543i	0.359360	−	0.622429i	−0.628494	−	0.777814i	$-0.716328\pi$
$293$	6.15125	−	10.6543i	0.359360	−	0.622429i	0.987854	+	0.155385i	$0.0496618\pi$
$294$	−13.0978	+	19.8279i	−0.763881	+	1.15638i
$295$	−1.30095	+	2.25332i	−0.0757445	+	0.131193i
$296$	14.4015	−	5.14417i	0.837073	−	0.298999i
$297$	−3.29078	+	1.89993i	−0.190950	+	0.110245i
$298$	11.3571	+	7.50221i	0.657896	+	0.434591i
$299$	−10.0300	+	0.696915i	−0.580052	+	0.0403036i
$300$	3.74244	−	1.59662i	0.216070	−	0.0921809i
$301$	4.76415	+	8.25174i	0.274601	+	0.475623i
$302$	22.2275	+	1.33918i	1.27905	+	0.0770612i
$303$	−3.05701	+	5.29490i	−0.175621	+	0.304184i
$304$	−14.3460	+	14.9644i	−0.822798	+	0.858265i
$305$	−3.62717	−	2.09415i	−0.207691	−	0.119910i
$306$	6.95343	−	3.47476i	0.397501	−	0.198639i
$307$	−3.32074			−0.189524			−0.0947622	−	0.995500i	$-0.530209\pi$
$307$	−3.32074			−0.189524			−0.0947622	+	0.995500i	$0.530209\pi$
$308$	4.45165	−	36.8098i	0.253657	−	2.09743i
$309$	4.49334	−	2.59423i	0.255617	−	0.147581i
$310$	−19.5680	−	1.17895i	−1.11139	−	0.0669598i
$311$	15.1744			0.860464			0.430232	−	0.902718i	$-0.358432\pi$
$311$	15.1744			0.860464			0.430232	+	0.902718i	$0.358432\pi$
$312$	10.1351	+	1.13125i	0.573787	+	0.0640444i
$313$	1.86005			0.105136			0.0525681	−	0.998617i	$-0.483259\pi$
$313$	1.86005			0.105136			0.0525681	+	0.998617i	$0.483259\pi$
$314$	27.5252	+	1.65836i	1.55334	+	0.0935868i
$315$	7.27621	−	4.20092i	0.409968	−	0.236695i
$316$	17.7958	+	2.15217i	1.00109	+	0.121069i
$317$	1.69808			0.0953735			0.0476868	−	0.998862i	$-0.484815\pi$
$317$	1.69808			0.0953735			0.0476868	+	0.998862i	$0.484815\pi$
$318$	11.9550	−	5.97415i	0.670404	−	0.335013i
$319$	13.8182	+	7.97793i	0.773670	+	0.446678i
$320$	12.8885	+	4.86681i	0.720488	+	0.272063i
$321$	9.13828	−	15.8280i	0.510049	−	0.883431i
$322$	19.2054	+	1.15710i	1.07027	+	0.0644827i
$323$	14.2430	+	24.6697i	0.792504	+	1.37266i
$324$	0.784813	+	1.83958i	0.0436007	+	0.102199i
$325$	3.21842	−	6.59134i	0.178526	−	0.365622i
$326$	−13.4433	−	8.88031i	−0.744553	−	0.491835i
$327$	−3.08829	+	1.78303i	−0.170783	+	0.0986016i
$328$	−1.09464	−	3.06453i	−0.0604412	−	0.169210i
$329$	−25.2188	+	43.6802i	−1.39036	+	2.40817i
$330$	−5.10072	+	7.72161i	−0.280785	+	0.425061i
$331$	−13.4918	+	23.3685i	−0.741578	+	1.28445i	0.210198	+	0.977659i	$0.432589\pi$
$331$	−13.4918	+	23.3685i	−0.741578	+	1.28445i	−0.951776	+	0.306792i	$0.900744\pi$
$332$	7.53433	+	0.911177i	0.413500	+	0.0500074i
$333$	5.40679			0.296290
$334$	9.05987	+	18.1299i	0.495734	+	0.992026i
$335$	7.48963	+	12.9724i	0.409202	+	0.708759i
$336$	−18.9528	−	4.65222i	−1.03396	−	0.253799i
$337$	20.6039			1.12236			0.561182	−	0.827693i	$-0.310347\pi$
$337$	20.6039			1.12236			0.561182	+	0.827693i	$0.310347\pi$
$338$	15.1511	−	10.4137i	0.824111	−	0.566428i
$339$		−	2.60620i		−	0.141549i
$340$	11.3655	−	15.1398i	0.616381	−	0.821072i
$341$	−26.4887	+	15.2932i	−1.43444	+	0.828176i
$342$	−6.55619	+	3.27625i	−0.354518	+	0.177159i
$343$		−	47.8286i		−	2.58250i
$344$	−3.57597	+	4.21015i	−0.192803	+	0.226996i
$345$	−4.15876	−	2.40106i	−0.223900	−	0.129269i
$346$	3.57856	−	5.41732i	0.192385	−	0.291237i
$347$	−15.3893	−	8.88503i	−0.826142	−	0.476974i	0.0263876	−	0.999652i	$-0.491600\pi$
$347$	−15.3893	−	8.88503i	−0.826142	−	0.476974i	−0.852530	+	0.522678i	$0.824933\pi$
$348$	5.04189	−	6.71623i	0.270274	−	0.360028i
$349$	−0.887725	−	1.53759i	−0.0475188	−	0.0823050i	0.841288	−	0.540588i	$-0.181798\pi$
$349$	−0.887725	−	1.53759i	−0.0475188	−	0.0823050i	−0.888807	+	0.458283i	$0.848465\pi$
$350$	−7.73677	+	11.7121i	−0.413548	+	0.626040i
$351$	3.23995	+	1.58200i	0.172936	+	0.0844410i
$352$	20.9644	−	4.74791i	1.11740	−	0.253065i
$353$	−24.0830	+	13.9043i	−1.28181	+	0.740052i	−0.977179	−	0.212419i	$-0.931866\pi$
$353$	−24.0830	+	13.9043i	−1.28181	+	0.740052i	−0.304629	+	0.952471i	$0.598533\pi$
$354$	2.13287	+	0.128503i	0.113361	+	0.00682984i
$355$	−3.39151	−	1.95809i	−0.180003	−	0.103925i
$356$	10.9520	−	4.67241i	0.580455	−	0.247637i
$357$	−13.4084	+	23.2241i	−0.709650	+	1.22915i
$358$	−8.13410	−	16.2773i	−0.429900	−	0.860285i
$359$			24.5145i			1.29383i	0.762564	+	0.646913i	$0.223940\pi$
$359$			24.5145i			1.29383i	−0.762564	+	0.646913i	$0.776060\pi$
$360$	3.71242	+	3.15321i	0.195662	+	0.166189i
$361$	−3.92935	−	6.80583i	−0.206808	−	0.358201i
$362$	3.15785	+	0.190257i	0.165973	+	0.00999968i
$363$			3.43898i			0.180500i
$364$	−31.3253	+	16.0155i	−1.64189	+	0.839439i
$365$		−	18.0584i		−	0.945221i
$366$	−0.206851	+	3.43328i	−0.0108123	+	0.179460i
$367$	−2.45624	−	4.25433i	−0.128215	−	0.222074i	0.794770	−	0.606910i	$-0.207591\pi$
$367$	−2.45624	−	4.25433i	−0.128215	−	0.222074i	−0.922985	+	0.384836i	$0.874258\pi$
$368$	3.11353	+	10.7108i	0.162304	+	0.558338i
$369$		−	1.15052i		−	0.0598937i
$370$	11.7789	−	5.88614i	0.612356	−	0.306006i
$371$	−23.0531	+	39.9291i	−1.19686	+	2.07302i
$372$	6.31724	+	14.8075i	0.327534	+	0.767732i
$373$	−10.0357	−	5.79410i	−0.519628	−	0.300007i	0.217155	−	0.976137i	$-0.430322\pi$
$373$	−10.0357	−	5.79410i	−0.519628	−	0.300007i	−0.736782	+	0.676130i	$0.763656\pi$
$374$	1.77638	−	29.4840i	0.0918544	−	1.52458i
$375$	10.4909	−	6.05694i	0.541749	−	0.312779i
$376$	−28.7651	−	5.25007i	−1.48345	−	0.270752i
$377$	−1.04943	−	15.1035i	−0.0540486	−	0.777870i
$378$	−5.75706	−	3.80298i	−0.296111	−	0.195604i
$379$	0.372546	+	0.645269i	0.0191364	+	0.0331452i	0.875435	−	0.483336i	$-0.160575\pi$
$379$	0.372546	+	0.645269i	0.0191364	+	0.0331452i	−0.856299	+	0.516481i	$0.827242\pi$
$380$	−10.7162	+	14.2749i	−0.549729	+	0.732286i
$381$	3.93461	+	2.27165i	0.201576	+	0.116380i
$382$	−18.0702	−	11.9367i	−0.924551	−	0.610737i
$383$	−3.53018	−	2.03815i	−0.180384	−	0.104145i	0.407089	−	0.913388i	$-0.366544\pi$
$383$	−3.53018	−	2.03815i	−0.180384	−	0.104145i	−0.587473	+	0.809244i	$0.699877\pi$
$384$	−1.15612	−	11.2545i	−0.0589979	−	0.574328i
$385$		−	31.9259i		−	1.62709i
$386$	1.88097	+	3.76406i	0.0957390	+	0.191586i
$387$	−1.69133	+	0.976488i	−0.0859750	+	0.0496377i
$388$	20.9989	+	15.7639i	1.06606	+	0.800292i
$389$		−	0.109160i		−	0.00553463i	−0.999996	−	0.00276731i	$-0.999119\pi$
$389$		−	0.109160i		−	0.00553463i	0.999996	−	0.00276731i	$-0.000880865\pi$
$390$	8.78062	−	0.0807419i	0.444624	−	0.00408852i
$391$	15.3273			0.775137
$392$	44.7572	−	15.9871i	2.26058	−	0.807468i
$393$	−1.57643	−	2.73046i	−0.0795205	−	0.137734i
$394$	−1.51450	+	0.756826i	−0.0762996	+	0.0381284i
$395$	15.4347			0.776603
$396$	7.54476	+	0.912438i	0.379138	+	0.0458517i
$397$	7.42620	−	12.8626i	0.372710	−	0.645554i	−0.617271	−	0.786751i	$-0.711762\pi$
$397$	7.42620	−	12.8626i	0.372710	−	0.645554i	0.989982	+	0.141197i	$0.0450951\pi$
$398$	13.0204	+	8.60095i	0.652652	+	0.431127i
$399$	12.6424	−	21.8973i	0.632913	−	1.09624i
$400$	−7.90298	−	1.93989i	−0.395149	−	0.0969946i
$401$	−2.05832	+	1.18837i	−0.102788	+	0.0593444i	−0.550513	−	0.834827i	$-0.685568\pi$
$401$	−2.05832	+	1.18837i	−0.102788	+	0.0593444i	0.447725	+	0.894171i	$0.352234\pi$
$402$	6.78017	−	10.2640i	0.338164	−	0.511922i
$403$	26.0795	+	12.7341i	1.29911	+	0.634331i
$404$	11.2473	−	4.79837i	0.559573	−	0.238728i
$405$	0.861047	+	1.49138i	0.0427858	+	0.0741071i
$406$	−1.74240	+	28.9200i	−0.0864737	+	1.43528i
$407$	10.2725	−	17.7926i	0.509191	−	0.881944i
$408$	−15.2940	−	2.79138i	−0.757164	−	0.138194i
$409$	−20.4868	−	11.8281i	−1.01301	−	0.584861i	−0.100937	−	0.994893i	$-0.532184\pi$
$409$	−20.4868	−	11.8281i	−1.01301	−	0.584861i	−0.912071	+	0.410032i	$0.865518\pi$
$410$	−1.25252	−	2.50646i	−0.0618577	−	0.123785i
$411$	15.9412			0.786323
$412$	−10.3019	−	1.24587i	−0.507536	−	0.0613798i
$413$	−6.38387	+	3.68573i	−0.314130	+	0.181363i
$414$	−0.237166	+	3.93645i	−0.0116561	+	0.193466i
$415$	6.53468			0.320775
$416$	−14.8524	−	13.9788i	−0.728198	−	0.685367i
$417$	2.21458			0.108448
$418$	−1.67490	+	27.7996i	−0.0819218	+	1.35972i
$419$	−9.08687	+	5.24631i	−0.443923	+	0.256299i	−0.705260	−	0.708949i	$-0.749170\pi$
$419$	−9.08687	+	5.24631i	−0.443923	+	0.256299i	0.261337	+	0.965247i	$0.415836\pi$
$420$	−16.6821	−	2.01748i	−0.814005	−	0.0984431i
$421$	−2.63183			−0.128268			−0.0641338	−	0.997941i	$-0.520428\pi$
$421$	−2.63183			−0.128268			−0.0641338	+	0.997941i	$0.520428\pi$
$422$	−10.2801	−	20.5718i	−0.500428	−	1.00142i
$423$	−8.95297	−	5.16900i	−0.435308	−	0.251325i
$424$	−26.2948	−	4.79921i	−1.27699	−	0.233070i
$425$	−5.59108	+	9.68404i	−0.271207	+	0.469745i
$426$	−0.193412	+	3.21021i	−0.00937083	+	0.155535i
$427$	−5.93292	−	10.2761i	−0.287114	−	0.497296i
$428$	−33.6213	+	14.3437i	−1.62515	+	0.693329i
$429$	11.3617	−	7.65627i	0.548548	−	0.369648i
$430$	−2.62156	+	3.96859i	−0.126423	+	0.191383i
$431$	−13.4676	+	7.77554i	−0.648713	+	0.374534i	−0.787963	−	0.615723i	$-0.788864\pi$
$431$	−13.4676	+	7.77554i	−0.648713	+	0.374534i	0.139250	+	0.990257i	$0.455531\pi$
$432$	0.953547	−	3.88468i	0.0458776	−	0.186902i
$433$	7.54881	−	13.0749i	0.362773	−	0.628341i	−0.625643	−	0.780109i	$-0.715163\pi$
$433$	7.54881	−	13.0749i	0.362773	−	0.628341i	0.988416	+	0.151768i	$0.0484968\pi$
$434$	−46.3407	−	30.6116i	−2.22442	−	1.46940i
$435$	3.61559	−	6.26238i	0.173354	−	0.300258i
$436$	7.08051	+	0.856294i	0.339095	+	0.0410090i
$437$	−14.4517			−0.691318
$438$	−13.2658	+	6.62915i	−0.633862	+	0.316753i
$439$	14.1740	+	24.5501i	0.676490	+	1.17171i	0.976031	+	0.217631i	$0.0698330\pi$
$439$	14.1740	+	24.5501i	0.676490	+	1.17171i	−0.299541	+	0.954083i	$0.596834\pi$
$440$	17.4299	−	6.22588i	0.830937	−	0.296807i
$441$	16.8032			0.800154
$442$	−24.1422	+	14.2361i	−1.14833	+	0.677143i
$443$		−	27.9206i		−	1.32655i	−0.748377	−	0.663273i	$-0.769167\pi$
$443$		−	27.9206i		−	1.32655i	0.748377	−	0.663273i	$-0.230833\pi$
$444$	−8.64794	−	6.49204i	−0.410413	−	0.308099i
$445$	8.87895	−	5.12626i	0.420903	−	0.243008i
$446$	2.38247	+	4.76762i	0.112813	+	0.225753i
$447$		−	9.62460i		−	0.455228i
$448$	24.7282	+	30.1980i	1.16830	+	1.42672i
$449$	30.2662	+	17.4742i	1.42835	+	0.824659i	0.996991	−	0.0775206i	$-0.0247003\pi$
$449$	30.2662	+	17.4742i	1.42835	+	0.824659i	0.431361	+	0.902180i	$0.358034\pi$
$450$	−2.40059	−	1.58578i	−0.113165	−	0.0747542i
$451$	−3.78611	−	2.18591i	−0.178281	−	0.102931i
$452$	−3.12931	+	4.16851i	−0.147191	+	0.196070i
$453$	−7.87285	−	13.6362i	−0.369899	−	0.640684i
$454$	6.52717	+	4.31170i	0.306335	+	0.202358i
$455$	−25.1218	+	16.9287i	−1.17773	+	0.793629i
$456$	14.4202	+	2.63191i	0.675288	+	0.123251i
$457$	6.74386	−	3.89357i	0.315465	−	0.182134i	−0.333905	−	0.942607i	$-0.608366\pi$
$457$	6.74386	−	3.89357i	0.315465	−	0.182134i	0.649369	+	0.760473i	$0.275033\pi$
$458$	0.811561	−	13.4702i	0.0379218	−	0.629419i
$459$	−4.76016	−	2.74828i	−0.222185	−	0.128279i
$460$	3.76877	+	8.83390i	0.175720	+	0.411883i
$461$	7.68029	−	13.3026i	0.357707	−	0.619566i	−0.629871	−	0.776700i	$-0.716892\pi$
$461$	7.68029	−	13.3026i	0.357707	−	0.619566i	0.987577	+	0.157134i	$0.0502254\pi$
$462$	−23.4528	+	11.7198i	−1.09112	+	0.545255i
$463$			39.3570i			1.82907i	0.404503	+	0.914537i	$0.367444\pi$
$463$			39.3570i			1.82907i	−0.404503	+	0.914537i	$0.632556\pi$
$464$	−16.1286	+	4.68844i	−0.748752	+	0.217655i
$465$	6.93088	+	12.0046i	0.321412	+	0.556701i
$466$	0.928049	−	15.4036i	0.0429910	−	0.713558i
$467$		−	28.6326i		−	1.32496i	−0.749080	−	0.662480i	$-0.769504\pi$
$467$		−	28.6326i		−	1.32496i	0.749080	−	0.662480i	$-0.230496\pi$
$468$	−3.28263	−	6.42062i	−0.151740	−	0.296793i
$469$			42.4377i			1.95959i
$470$	−25.1317	−	1.51415i	−1.15924	−	0.0698427i
$471$	−9.74928	−	16.8862i	−0.449223	−	0.778077i
$472$	−3.25714	−	2.76651i	−0.149922	−	0.127339i
$473$			7.42105i			0.341220i
$474$	−5.66599	−	11.3384i	−0.260248	−	0.520788i
$475$	5.27166	−	9.13079i	0.241881	−	0.418949i
$476$	49.3319	−	21.0463i	2.26113	−	0.964654i
$477$	−8.18412	−	4.72510i	−0.374725	−	0.216348i
$478$	−22.2935	−	1.34316i	−1.01968	−	0.0614345i
$479$	−12.3225	+	7.11440i	−0.563030	+	0.325065i	−0.754361	−	0.656460i	$-0.772053\pi$
$479$	−12.3225	+	7.11440i	−0.563030	+	0.325065i	0.191331	+	0.981526i	$0.438720\pi$
$480$	−2.15175	−	9.50102i	−0.0982134	−	0.433660i
$481$	−19.4476	+	1.35127i	−0.886733	+	0.0616127i
$482$	−14.6110	+	22.1185i	−0.665512	+	1.00747i
$483$	−6.80244	−	11.7822i	−0.309522	−	0.536107i
$484$	4.12925	−	5.50051i	0.187693	−	0.250023i
$485$	19.5799	+	11.3044i	0.889076	+	0.513308i
$486$	0.779483	−	1.18000i	0.0353581	−	0.0535260i
$487$	8.53338	+	4.92675i	0.386684	+	0.223252i	0.680722	−	0.732541i	$-0.261666\pi$
$487$	8.53338	+	4.92675i	0.386684	+	0.223252i	−0.294038	+	0.955794i	$0.594999\pi$
$488$	4.45325	−	5.24302i	0.201589	−	0.237340i
$489$			11.3926i			0.515190i
$490$	36.6065	−	18.2930i	1.65371	−	0.826392i
$491$	−24.0866	+	13.9064i	−1.08701	+	0.627587i	−0.932780	−	0.360447i	$-0.882624\pi$
$491$	−24.0866	+	13.9064i	−1.08701	+	0.627587i	−0.154234	+	0.988034i	$0.549291\pi$
$492$	−1.38145	+	1.84021i	−0.0622807	+	0.0829632i
$493$			23.0804i			1.03949i
$494$	22.7630	−	13.4228i	1.02416	−	0.603921i
$495$	6.54372			0.294119
$496$	7.67544	−	31.2692i	0.344638	−	1.40403i
$497$	−5.54746	−	9.60848i	−0.248837	−	0.430999i
$498$	−2.39885	−	4.80039i	−0.107495	−	0.215111i
$499$	37.3081			1.67014			0.835069	−	0.550145i	$-0.185428\pi$
$499$	37.3081			1.67014			0.835069	+	0.550145i	$0.185428\pi$
$500$	−24.0525	−	2.90883i	−1.07566	−	0.130087i
$501$	7.16568	−	12.4113i	0.320139	−	0.554497i
$502$	19.7169	−	29.8481i	0.880010	−	1.33218i
$503$	12.8133	−	22.1932i	0.571315	−	0.989546i	−0.425117	−	0.905139i	$-0.639767\pi$
$503$	12.8133	−	22.1932i	0.571315	−	0.989546i	0.996431	−	0.0844074i	$-0.0268997\pi$
$504$	4.64188	+	12.9953i	0.206766	+	0.578859i
$505$	9.11832	−	5.26446i	0.405760	−	0.234266i
$506$	12.5034	+	8.25945i	0.555843	+	0.367177i
$507$	−12.0491	−	4.88054i	−0.535119	−	0.216752i
$508$	−3.56564	−	8.35777i	−0.158200	−	0.370816i
$509$	−15.3397	−	26.5691i	−0.679920	−	1.17766i	−0.975005	−	0.222185i	$-0.928681\pi$
$509$	−15.3397	−	26.5691i	−0.679920	−	1.17766i	0.295085	−	0.955471i	$-0.404652\pi$
$510$	−13.3621	−	0.805052i	−0.591685	−	0.0356483i
$511$	25.5806	−	44.3069i	1.13162	−	1.96002i
$512$	−11.6643	+	19.3893i	−0.515495	+	0.856893i
$513$	4.48821	+	2.59127i	0.198159	+	0.114407i
$514$	28.2729	−	14.1285i	1.24706	−	0.623181i
$515$	−8.93502			−0.393724
$516$	3.87770	+	0.468956i	0.170706	+	0.0206446i
$517$	−34.0201	+	19.6415i	−1.49620	+	0.863832i
$518$	37.2379	+	2.24354i	1.63614	+	0.0985756i
$519$	−4.59094			−0.201520
$520$	−14.1412	−	10.4139i	−0.620132	−	0.456680i
$521$	−17.8859			−0.783596			−0.391798	−	0.920051i	$-0.628147\pi$
$521$	−17.8859			−0.783596			−0.391798	+	0.920051i	$0.628147\pi$
$522$	−5.92762	−	0.357132i	−0.259445	−	0.0156312i
$523$	8.03954	−	4.64163i	0.351545	−	0.202964i	−0.313821	−	0.949482i	$-0.601609\pi$
$523$	8.03954	−	4.64163i	0.351545	−	0.202964i	0.665365	+	0.746518i	$0.268276\pi$
$524$	−0.757078	+	6.26012i	−0.0330731	+	0.273474i
$525$	9.92552			0.433185
$526$	6.60717	−	3.30173i	0.288086	−	0.143962i
$527$	−38.3162	−	22.1219i	−1.66908	−	0.963644i
$528$	−10.9720	−	10.5185i	−0.477493	−	0.457761i
$529$	7.61203	−	13.1844i	0.330958	−	0.573236i
$530$	−22.9734	−	1.38412i	−0.997903	−	0.0601225i
$531$	−0.755450	−	1.30848i	−0.0327837	−	0.0567831i
$532$	−46.5136	+	19.8439i	−2.01662	+	0.860342i
$533$	0.287540	+	4.13828i	0.0124547	+	0.179249i
$534$	−7.02518	−	4.64067i	−0.304009	−	0.200822i
$535$	−27.2572	+	15.7370i	−1.17843	+	0.680369i
$536$	−23.1688	+	8.27579i	−1.00074	+	0.357459i
$537$	−6.43346	+	11.1431i	−0.277624	+	0.480860i
$538$	3.61708	−	5.47564i	0.155943	−	0.236071i
$539$	31.9250	−	55.2958i	1.37511	−	2.38176i
$540$	0.413515	−	3.41927i	0.0177949	−	0.147142i
$541$	4.09602			0.176102			0.0880508	−	0.996116i	$-0.471936\pi$
$541$	4.09602			0.176102			0.0880508	+	0.996116i	$0.471936\pi$
$542$	−15.3339	−	30.6850i	−0.658646	−	1.31803i
$543$	−1.11849	−	1.93729i	−0.0479992	−	0.0831370i
$544$	21.1104	+	22.8285i	0.905101	+	0.978762i
$545$	6.14107			0.263055
$546$	21.6579	+	12.2401i	0.926873	+	0.523826i
$547$		−	5.20867i		−	0.222707i	−0.993781	−	0.111353i	$-0.964481\pi$
$547$		−	5.20867i		−	0.222707i	0.993781	−	0.111353i	$-0.0355186\pi$
$548$	−25.4974	−	19.1409i	−1.08919	−	0.817661i
$549$	2.10626	−	1.21605i	0.0898928	−	0.0518996i
$550$	−9.77940	+	4.88695i	−0.416995	+	0.208380i
$551$		−	21.7618i		−	0.927083i
$552$	5.10591	−	6.01142i	0.217322	−	0.255863i
$553$	37.8695	+	21.8640i	1.61038	+	0.929751i
$554$	−17.8945	+	27.0892i	−0.760265	+	1.15091i
$555$	−8.06356	−	4.65550i	−0.342279	−	0.197615i
$556$	−3.54213	−	2.65909i	−0.150220	−	0.112770i
$557$	18.8096	+	32.5792i	0.796988	+	1.38042i	0.921569	+	0.388214i	$0.126908\pi$
$557$	18.8096	+	32.5792i	0.796988	+	1.38042i	−0.124582	+	0.992209i	$0.539759\pi$
$558$	6.27434	−	9.49827i	0.265614	−	0.402094i
$559$	5.83945	−	3.93501i	0.246983	−	0.166433i
$560$	24.2600	+	23.2575i	1.02517	+	0.982807i
$561$	−18.0880	+	10.4431i	−0.763674	+	0.440907i
$562$	16.1154	+	0.970933i	0.679786	+	0.0409563i
$563$	−11.0392	−	6.37349i	−0.465247	−	0.268611i	0.249001	−	0.968503i	$-0.419898\pi$
$563$	−11.0392	−	6.37349i	−0.465247	−	0.268611i	−0.714248	+	0.699893i	$0.753231\pi$
$564$	8.11339	+	19.0176i	0.341636	+	0.800786i
$565$	−2.24406	+	3.88682i	−0.0944082	+	0.163520i
$566$	−3.45866	−	6.92120i	−0.145378	−	0.290920i
$567$			4.87886i			0.204893i
$568$	4.16392	−	4.90238i	0.174714	−	0.205699i
$569$	18.9960	+	32.9020i	0.796353	+	1.37932i	0.921977	+	0.387246i	$0.126573\pi$
$569$	18.9960	+	32.9020i	0.796353	+	1.37932i	−0.125624	+	0.992078i	$0.540093\pi$
$570$	12.5987	+	0.759060i	0.527703	+	0.0317935i
$571$			34.4787i			1.44289i	0.692473	+	0.721443i	$0.256521\pi$
$571$			34.4787i			1.44289i	−0.692473	+	0.721443i	$0.743479\pi$
$572$	−27.3656	−	1.39633i	−1.14421	−	0.0583836i
$573$			15.3137i			0.639738i
$574$	0.477408	−	7.92393i	0.0199266	−	0.330738i
$575$	−2.83649	−	4.91295i	−0.118290	−	0.204884i
$576$	−6.18957	+	5.06845i	−0.257899	+	0.211185i
$577$		−	11.5186i		−	0.479524i	−0.970832	−	0.239762i	$-0.922931\pi$
$577$		−	11.5186i		−	0.479524i	0.970832	−	0.239762i	$-0.0770694\pi$
$578$	16.7140	−	8.35231i	0.695212	−	0.347410i
$579$	1.48771	−	2.57679i	0.0618271	−	0.107088i
$580$	−13.3023	+	5.67512i	−0.552350	+	0.235646i
$581$	16.0331	+	9.25669i	0.665163	+	0.384032i
$582$	1.11660	−	18.5332i	0.0462847	−	0.768226i
$583$	−31.0985	+	17.9548i	−1.28797	+	0.743610i
$584$	29.1778	+	5.32539i	1.20739	+	0.220366i
$585$	−3.46981	−	5.14911i	−0.143459	−	0.212889i
$586$	14.5170	+	9.58958i	0.599691	+	0.396142i
$587$	6.53396	+	11.3172i	0.269685	+	0.467109i	0.968781	−	0.247920i	$-0.0797469\pi$
$587$	6.53396	+	11.3172i	0.269685	+	0.467109i	−0.699095	+	0.715029i	$0.746414\pi$
$588$	−26.8761	−	20.1760i	−1.10835	−	0.832043i
$589$	36.1272	+	20.8581i	1.48860	+	0.859441i
$590$	−3.07026	−	2.02814i	−0.126401	−	0.0834974i
$591$	1.03679	+	0.598593i	0.0426480	+	0.0246228i
$592$	6.03692	+	20.7675i	0.248116	+	0.853540i
$593$		−	28.5561i		−	1.17266i	−0.810073	−	0.586330i	$-0.800572\pi$
$593$		−	28.5561i		−	1.17266i	0.810073	−	0.586330i	$-0.199428\pi$
$594$	−2.40217	−	4.80703i	−0.0985620	−	0.197235i
$595$	39.9941	−	23.0906i	1.63960	−	0.946622i
$596$	−11.5564	+	15.3942i	−0.473370	+	0.630569i
$597$		−	11.0342i		−	0.451599i
$598$	−0.130743	−	14.2182i	−0.00534648	−	0.581426i
$599$	−13.0357			−0.532623			−0.266312	−	0.963887i	$-0.585805\pi$
$599$	−13.0357			−0.532623			−0.266312	+	0.963887i	$0.585805\pi$
$600$	1.93558	+	5.41882i	0.0790196	+	0.221222i
$601$	10.0148	+	17.3461i	0.408511	+	0.707562i	0.994723	−	0.102596i	$-0.0327149\pi$
$601$	10.0148	+	17.3461i	0.408511	+	0.707562i	−0.586212	+	0.810157i	$0.699382\pi$
$602$	−12.0538	+	6.02351i	−0.491276	+	0.245500i
$603$	−8.69829			−0.354222
$604$	−3.78092	+	31.2636i	−0.153843	+	1.27210i
$605$	2.96112	−	5.12882i	0.120387	−	0.208516i
$606$	−7.21457	−	4.76578i	−0.293072	−	0.193597i
$607$	−3.53922	+	6.13011i	−0.143653	+	0.248813i	−0.928869	−	0.370407i	$-0.879218\pi$
$607$	−3.53922	+	6.13011i	−0.143653	+	0.248813i	0.785217	+	0.619221i	$0.212551\pi$
$608$	−19.9044	−	21.5243i	−0.807229	−	0.872924i
$609$	17.7419	−	10.2433i	0.718939	−	0.415080i
$610$	3.26470	−	4.94220i	0.132184	−	0.200104i
$611$	33.4946	+	16.3547i	1.35505	+	0.661641i
$612$	4.31377	+	10.1114i	0.174374	+	0.408728i
$613$	−7.63880	−	13.2308i	−0.308528	−	0.534387i	0.669512	−	0.742801i	$-0.266503\pi$
$613$	−7.63880	−	13.2308i	−0.308528	−	0.534387i	−0.978041	+	0.208414i	$0.933170\pi$
$614$	0.282430	−	4.68773i	0.0113980	−	0.189181i
$615$	−0.990652	+	1.71586i	−0.0399469	+	0.0691901i
$616$	51.5841	+	9.41489i	2.07838	+	0.379337i
$617$	34.1134	+	19.6954i	1.37335	+	0.792906i	0.991349	−	0.131254i	$-0.0419004\pi$
$617$	34.1134	+	19.6954i	1.37335	+	0.792906i	0.382005	+	0.924160i	$0.375234\pi$
$618$	3.28000	+	6.56368i	0.131941	+	0.264030i
$619$	47.2069			1.89740			0.948702	−	0.316172i	$-0.102398\pi$
$619$	47.2069			1.89740			0.948702	+	0.316172i	$0.102398\pi$
$620$	3.32854	−	27.5230i	0.133677	−	1.10535i
$621$	2.41494	−	1.39427i	0.0969084	−	0.0559501i
$622$	−1.29059	+	21.4211i	−0.0517481	+	0.858906i
$623$	29.0464			1.16372
$624$	−2.45893	+	14.2110i	−0.0984360	+	0.568897i
$625$	−10.6893			−0.427571
$626$	−0.158198	+	2.62574i	−0.00632286	+	0.104946i
$627$	17.0546	−	9.84647i	0.681095	−	0.393230i
$628$	−4.68207	+	38.7150i	−0.186835	+	1.54490i
$629$	29.7187			1.18496
$630$	5.31140	+	10.6288i	0.211611	+	0.423461i
$631$	−20.9034	−	12.0686i	−0.832152	−	0.480443i	0.0224373	−	0.999748i	$-0.492857\pi$
$631$	−20.9034	−	12.0686i	−0.832152	−	0.480443i	−0.854589	+	0.519305i	$0.826191\pi$
$632$	−4.55166	+	24.9385i	−0.181055	+	0.992001i
$633$	−8.13080	+	14.0830i	−0.323170	+	0.559747i
$634$	−0.144422	+	2.39710i	−0.00573574	+	0.0952009i
$635$	−3.91199	−	6.77576i	−0.155242	−	0.268888i
$636$	7.41664	+	17.3844i	0.294089	+	0.689338i
$637$	−60.4392	+	4.19949i	−2.39469	+	0.166390i
$638$	−12.4373	+	18.8280i	−0.492398	+	0.745406i
$639$	1.96941	−	1.13704i	0.0779087	−	0.0449806i
$640$	−7.96643	+	17.7801i	−0.314901	+	0.702822i
$641$	10.2830	−	17.8107i	0.406155	−	0.703481i	−0.588300	−	0.808643i	$-0.700203\pi$
$641$	10.2830	−	17.8107i	0.406155	−	0.703481i	0.994455	+	0.105161i	$0.0335359\pi$
$642$	21.5664	+	14.2463i	0.851158	+	0.562255i
$643$	1.87110	−	3.24084i	0.0737890	−	0.127806i	−0.826770	−	0.562540i	$-0.809824\pi$
$643$	1.87110	−	3.24084i	0.0737890	−	0.127806i	0.900559	+	0.434734i	$0.143158\pi$
$644$	−3.26685	+	27.0129i	−0.128732	+	1.06446i
$645$	3.36321			0.132426
$646$	−36.0364	+	18.0081i	−1.41783	+	0.708519i
$647$	21.4763	+	37.1980i	0.844320	+	1.46240i	0.886211	+	0.463283i	$0.153329\pi$
$647$	21.4763	+	37.1980i	0.844320	+	1.46240i	−0.0418907	+	0.999122i	$0.513338\pi$
$648$	−2.66360	+	0.951427i	−0.104636	+	0.0373756i
$649$	−5.74122			−0.225362
$650$	9.03096	+	5.10388i	0.354223	+	0.200191i
$651$			39.2717i			1.53918i
$652$	13.6793	−	18.2220i	0.535722	−	0.713627i
$653$	8.50601	−	4.91095i	0.332866	−	0.192180i	−0.324247	−	0.945972i	$-0.605111\pi$
$653$	8.50601	−	4.91095i	0.332866	−	0.192180i	0.657113	+	0.753792i	$0.271778\pi$
$654$	−2.25435	−	4.51125i	−0.0881522	−	0.176404i
$655$			5.42953i			0.212149i
$656$	4.41916	−	1.28461i	0.172539	−	0.0501555i
$657$	9.08142	+	5.24316i	0.354300	+	0.204555i
$658$	−59.5165	−	39.3152i	−2.32019	−	1.53267i
$659$	−20.5045	−	11.8383i	−0.798743	−	0.461155i	0.0442882	−	0.999019i	$-0.485898\pi$
$659$	−20.5045	−	11.8383i	−0.798743	−	0.461155i	−0.843032	+	0.537864i	$0.819231\pi$
$660$	−10.4664	−	7.85718i	−0.407405	−	0.305840i
$661$	−18.3619	−	31.8038i	−0.714196	−	1.23702i	−0.963269	−	0.268538i	$-0.913459\pi$
$661$	−18.3619	−	31.8038i	−0.714196	−	1.23702i	0.249073	−	0.968485i	$-0.419874\pi$
$662$	−31.8408	−	21.0333i	−1.23753	−	0.817482i
$663$	17.8086	+	8.69556i	0.691627	+	0.337707i
$664$	−1.92707	+	10.5584i	−0.0747847	+	0.409744i
$665$	−37.7092	+	21.7714i	−1.46230	+	0.844260i
$666$	−0.459850	+	7.63252i	−0.0178188	+	0.295754i
$667$	−10.1405	−	5.85462i	−0.392641	−	0.226692i
$668$	−26.3637	+	11.2474i	−1.02004	+	0.435176i
$669$	1.88436	−	3.26380i	0.0728534	−	0.126186i
$670$	−18.9496	+	9.46946i	−0.732086	+	0.365837i
$671$		−	9.24163i		−	0.356769i
$672$	8.17927	−	26.3591i	0.315522	−	1.01683i
$673$	−4.89868	−	8.48476i	−0.188830	−	0.327064i	0.756030	−	0.654537i	$-0.227136\pi$
$673$	−4.89868	−	8.48476i	−0.188830	−	0.327064i	−0.944861	+	0.327473i	$0.893803\pi$
$674$	−1.75237	+	29.0855i	−0.0674987	+	1.12033i
$675$			2.03439i			0.0783039i
$676$	13.4119	+	22.2738i	0.515841	+	0.856684i
$677$			11.0208i			0.423564i	0.977317	+	0.211782i	$0.0679267\pi$
$677$			11.0208i			0.423564i	−0.977317	+	0.211782i	$0.932073\pi$
$678$	3.67905	+	0.221658i	0.141293	+	0.00851274i
$679$	32.0266	+	55.4717i	1.22907	+	2.12881i
$680$	20.4055	+	17.3318i	0.782517	+	0.664645i
$681$		−	5.53149i		−	0.211967i
$682$	−19.3359	−	38.6935i	−0.740410	−	1.48165i
$683$	19.6551	−	34.0437i	0.752083	−	1.30265i	−0.194728	−	0.980857i	$-0.562383\pi$
$683$	19.6551	−	34.0437i	0.752083	−	1.30265i	0.946811	−	0.321789i	$-0.104284\pi$
$684$	−4.06732	−	9.53371i	−0.155518	−	0.364531i
$685$	−23.7744	−	13.7261i	−0.908372	−	0.524449i
$686$	67.5174	+	4.06785i	2.57783	+	0.155311i
$687$	−8.26371	+	4.77106i	−0.315280	+	0.182027i
$688$	−5.63914	−	5.40611i	−0.214990	−	0.206106i
$689$	30.6182	+	14.9502i	1.16646	+	0.569559i
$690$	3.74317	−	5.66652i	0.142500	−	0.215721i
$691$	−19.8819	−	34.4364i	−0.756341	−	1.31002i	−0.944705	−	0.327922i	$-0.893652\pi$
$691$	−19.8819	−	34.4364i	−0.756341	−	1.31002i	0.188363	−	0.982099i	$-0.439682\pi$
$692$	7.34303	+	5.51243i	0.279140	+	0.209551i
$693$	16.0552	+	9.26950i	0.609888	+	0.352119i
$694$	13.8515	−	20.9687i	0.525794	−	0.795962i
$695$	−3.30277	−	1.90685i	−0.125281	−	0.0723311i
$696$	9.05217	+	7.68863i	0.343122	+	0.291437i
$697$		−	6.32390i		−	0.239535i
$698$	2.24604	−	1.12239i	0.0850138	−	0.0424830i
$699$	−9.44984	+	5.45587i	−0.357426	+	0.206360i
$700$	−15.8755	−	11.9178i	−0.600036	−	0.450449i
$701$		−	14.0325i		−	0.529999i	−0.964249	−	0.265000i	$-0.914628\pi$
$701$		−	14.0325i		−	0.529999i	0.964249	−	0.265000i	$-0.0853718\pi$
$702$	−2.50880	+	4.43914i	−0.0946885	+	0.167544i
$703$	−28.0209			−1.05683
$704$	4.91938	+	29.9982i	0.185406	+	1.13060i
$705$	8.90150	+	15.4178i	0.335250	+	0.580670i
$706$	−17.5798	−	35.1794i	−0.661625	−	1.32399i
$707$	29.8295			1.12185
$708$	−0.362803	+	2.99994i	−0.0136350	+	0.112745i
$709$	9.49155	−	16.4399i	0.356463	−	0.617412i	−0.630904	−	0.775861i	$-0.717316\pi$
$709$	9.49155	−	16.4399i	0.356463	−	0.617412i	0.987367	+	0.158449i	$0.0506493\pi$
$710$	3.05259	−	4.62110i	0.114562	−	0.173427i
$711$	−4.48137	+	7.76197i	−0.168065	+	0.291097i
$712$	5.66435	+	15.8578i	0.212280	+	0.594298i
$713$	19.4388	−	11.2230i	0.727987	−	0.420304i
$714$	−31.6440	−	20.9033i	−1.18425	−	0.782287i
$715$	−23.5370	+	1.63542i	−0.880233	+	0.0611611i
$716$	23.6698	−	10.0981i	0.884581	−	0.377385i
$717$	7.89622	+	13.6767i	0.294890	+	0.510764i
$718$	−34.6060	−	2.08497i	−1.29148	−	0.0778104i
$719$	14.7452	−	25.5395i	0.549904	−	0.952461i	−0.448377	−	0.893845i	$-0.647998\pi$
$719$	14.7452	−	25.5395i	0.549904	−	0.952461i	0.998281	−	0.0586167i	$-0.0186690\pi$
$720$	−4.76699	+	4.97247i	−0.177655	+	0.185313i
$721$	−21.9224	−	12.6569i	−0.816431	−	0.471367i
$722$	9.94167	−	4.96804i	0.369991	−	0.184891i
$723$	18.7445			0.697114
$724$	−0.537154	+	4.44161i	−0.0199632	+	0.165071i
$725$	7.39806	−	4.27127i	0.274757	−	0.158631i
$726$	−4.85465	−	0.292487i	−0.180173	−	0.0108552i
$727$	−12.3928			−0.459625			−0.229813	−	0.973235i	$-0.573811\pi$
$727$	−12.3928			−0.459625			−0.229813	+	0.973235i	$0.573811\pi$
$728$	−19.9441	−	45.5826i	−0.739177	−	1.68940i
$729$	−1.00000			−0.0370370
$730$	25.4922	+	1.53588i	0.943510	+	0.0568454i
$731$	−9.29647	+	5.36732i	−0.343842	+	0.198518i
$732$	−4.82900	−	0.584004i	−0.178485	−	0.0215854i
$733$	18.6307			0.688140			0.344070	−	0.938944i	$-0.388194\pi$
$733$	18.6307			0.688140			0.344070	+	0.938944i	$0.388194\pi$
$734$	6.21455	−	3.10553i	0.229383	−	0.114627i
$735$	−25.0600	−	14.4684i	−0.924350	−	0.533674i
$736$	−15.3847	+	3.48426i	−0.567089	+	0.128432i
$737$	−16.5262	+	28.6242i	−0.608749	+	1.05438i
$738$	1.62414	+	0.0978524i	0.0597853	+	0.00360200i
$739$	11.9209	+	20.6476i	0.438517	+	0.759534i	0.997575	−	0.0695946i	$-0.0221706\pi$
$739$	11.9209	+	20.6476i	0.438517	+	0.759534i	−0.559058	+	0.829128i	$0.688837\pi$
$740$	7.30739	+	17.1284i	0.268625	+	0.629651i
$741$	−16.7912	−	8.19878i	−0.616839	−	0.301190i
$742$	−54.4054	−	35.9390i	−1.99729	−	1.31936i
$743$	−13.6419	+	7.87615i	−0.500473	+	0.288948i	−0.728909	−	0.684611i	$-0.759972\pi$
$743$	−13.6419	+	7.87615i	−0.500473	+	0.288948i	0.228436	+	0.973559i	$0.426639\pi$
$744$	−21.4403	+	7.65838i	−0.786040	+	0.280770i
$745$	−8.28723	+	14.3539i	−0.303621	+	0.525886i
$746$	9.03280	−	13.6741i	0.330714	−	0.500645i
$747$	−1.89731	+	3.28623i	−0.0694189	+	0.120237i
$748$	41.4702	+	5.01527i	1.51630	+	0.183376i
$749$	−89.1687			−3.25816
$750$	7.65805	+	15.3247i	0.279632	+	0.559579i
$751$	0.792300	+	1.37230i	0.0289114	+	0.0500761i	0.880119	−	0.474753i	$-0.157463\pi$
$751$	0.792300	+	1.37230i	0.0289114	+	0.0500761i	−0.851208	+	0.524829i	$0.824129\pi$
$752$	9.85776	−	40.1598i	0.359476	−	1.46448i
$753$	−25.2949			−0.921798
$754$	21.4102	−	0.196877i	0.779713	−	0.00716982i
$755$			27.1156i			0.986837i
$756$	5.85814	−	7.80354i	0.213058	−	0.283812i
$757$	30.1588	−	17.4122i	1.09614	−	0.632857i	0.160936	−	0.986965i	$-0.448549\pi$
$757$	30.1588	−	17.4122i	1.09614	−	0.632857i	0.935205	+	0.354107i	$0.115215\pi$
$758$	−0.942581	+	0.471026i	−0.0342361	+	0.0171084i
$759$		−	10.5961i		−	0.384613i
$760$	−19.2398	−	16.3416i	−0.697900	−	0.592774i
$761$	−5.65870	−	3.26705i	−0.205128	−	0.118430i	0.393917	−	0.919146i	$-0.371120\pi$
$761$	−5.65870	−	3.26705i	−0.205128	−	0.118430i	−0.599045	+	0.800715i	$0.704453\pi$
$762$	−3.54142	+	5.36110i	−0.128292	+	0.194212i
$763$	15.0673	+	8.69913i	0.545474	+	0.314930i
$764$	18.3874	−	24.4936i	0.665234	−	0.886148i
$765$	4.73279	+	8.19743i	0.171114	+	0.296379i
$766$	3.17740	−	4.81004i	0.114804	−	0.173794i
$767$	3.04428	+	4.51763i	0.109922	+	0.163122i
$768$	15.9858	−	0.674840i	0.576837	−	0.0243512i
$769$	35.8319	−	20.6876i	1.29213	−	0.746012i	0.313099	−	0.949720i	$-0.398633\pi$
$769$	35.8319	−	20.6876i	1.29213	−	0.746012i	0.979032	+	0.203708i	$0.0652994\pi$
$770$	45.0683	+	2.71531i	1.62415	+	0.0978531i
$771$	−19.3549	−	11.1746i	−0.697051	−	0.402443i
$772$	−5.47353	+	2.33515i	−0.196997	+	0.0840438i
$773$	−17.6447	+	30.5615i	−0.634636	+	1.09922i	0.351957	+	0.936016i	$0.385516\pi$
$773$	−17.6447	+	30.5615i	−0.634636	+	1.09922i	−0.986592	+	0.163205i	$0.947817\pi$
$774$	−1.23462	−	2.47062i	−0.0443773	−	0.0888046i
$775$			16.3756i			0.588228i
$776$	−24.0392	+	28.3024i	−0.862955	+	1.01600i
$777$	−13.1895	−	22.8448i	−0.473170	−	0.819554i
$778$	0.154096	+	0.00928411i	0.00552461	+	0.000332851i
$779$			5.96262i			0.213633i
$780$	−0.632816	+	12.4021i	−0.0226585	+	0.444065i
$781$		−	8.64120i		−	0.309206i
$782$	−1.30360	+	21.6369i	−0.0466166	+	0.773734i
$783$	2.09953	+	3.63649i	0.0750311	+	0.129958i
$784$	18.7616	+	64.5413i	0.670056	+	2.30505i
$785$			33.5783i			1.19846i
$786$	3.98854	−	1.99315i	0.142267	−	0.0710933i
$787$	3.99149	−	6.91346i	0.142281	−	0.246438i	−0.786074	−	0.618132i	$-0.787890\pi$
$787$	3.99149	−	6.91346i	0.142281	−	0.246438i	0.928355	+	0.371694i	$0.121223\pi$
$788$	−0.939567	−	2.20232i	−0.0334707	−	0.0784545i
$789$	−4.52311	−	2.61142i	−0.161027	−	0.0929691i
$790$	−1.31273	+	21.7884i	−0.0467048	+	0.775198i
$791$	−11.0117	+	6.35763i	−0.391533	+	0.226051i
$792$	−1.92973	+	10.5730i	−0.0685700	+	0.375695i
$793$	−7.27203	+	4.90037i	−0.258237	+	0.174017i
$794$	17.5259	+	11.5772i	0.621970	+	0.410859i
$795$	8.13707	+	14.0938i	0.288592	+	0.499856i
$796$	−13.2490	+	17.6487i	−0.469597	+	0.625543i
$797$	−27.2357	−	15.7245i	−0.964738	−	0.556992i	−0.0671101	−	0.997746i	$-0.521378\pi$
$797$	−27.2357	−	15.7245i	−0.964738	−	0.556992i	−0.897628	+	0.440754i	$0.854711\pi$
$798$	29.8362	+	19.7091i	1.05619	+	0.697695i
$799$	−49.2105	−	28.4117i	−1.74094	−	1.00513i
$800$	3.41061	−	10.9913i	0.120583	−	0.388600i
$801$			5.95353i			0.210358i
$802$	−1.50251	−	3.00670i	−0.0530554	−	0.106170i
$803$	34.5082	−	19.9233i	1.21777	−	0.703078i
$804$	13.9126	+	10.4442i	0.490658	+	0.368339i
$805$			23.4289i			0.825759i
$806$	−20.1942	+	35.7322i	−0.711311	+	1.25861i
$807$	−4.64036			−0.163348
$808$	5.81705	+	16.2854i	0.204643	+	0.572917i
$809$	−15.8054	−	27.3757i	−0.555687	−	0.962477i	−0.997850	−	0.0655427i	$-0.979122\pi$
$809$	−15.8054	−	27.3757i	−0.555687	−	0.962477i	0.442163	−	0.896935i	$-0.354211\pi$
$810$	−2.17854	+	1.08866i	−0.0765461	+	0.0382515i
$811$	−25.4863			−0.894946			−0.447473	−	0.894298i	$-0.647676\pi$
$811$	−25.4863			−0.894946			−0.447473	+	0.894298i	$0.647676\pi$
$812$	−40.6768	−	4.91932i	−1.42748	−	0.172634i
$813$	−12.1279	+	21.0062i	−0.425345	+	0.736720i
$814$	24.2432	+	16.0145i	0.849725	+	0.561309i
$815$	9.80953	−	16.9906i	0.343613	−	0.595155i
$816$	5.24122	−	21.3524i	0.183480	−	0.747482i
$817$	8.76537	−	5.06069i	0.306661	−	0.177051i
$818$	18.4396	−	27.9143i	0.644724	−	0.976002i
$819$	−1.21933	−	17.5487i	−0.0426068	−	0.613200i
$820$	3.64477	−	1.55495i	0.127281	−	0.0543013i
$821$	7.50722	+	13.0029i	0.262004	+	0.453804i	0.966774	−	0.255632i	$-0.0822834\pi$
$821$	7.50722	+	13.0029i	0.262004	+	0.453804i	−0.704771	+	0.709435i	$0.748950\pi$
$822$	−1.35581	+	22.5035i	−0.0472893	+	0.784900i
$823$	−5.76572	+	9.98652i	−0.200980	+	0.348108i	−0.948845	−	0.315744i	$-0.897746\pi$
$823$	−5.76572	+	9.98652i	−0.200980	+	0.348108i	0.747864	+	0.663852i	$0.231079\pi$
$824$	2.63492	−	14.4367i	0.0917918	−	0.502926i
$825$	6.69475	+	3.86521i	0.233081	+	0.134569i
$826$	−4.66002	−	9.32529i	−0.162143	−	0.324468i
$827$	−29.0366			−1.00970			−0.504851	−	0.863206i	$-0.668453\pi$
$827$	−29.0366			−1.00970			−0.504851	+	0.863206i	$0.668453\pi$
$828$	−5.53673	−	0.669594i	−0.192415	−	0.0232700i
$829$	−21.9606	+	12.6789i	−0.762722	+	0.440358i	−0.830272	−	0.557358i	$-0.811815\pi$
$829$	−21.9606	+	12.6789i	−0.762722	+	0.440358i	0.0675499	+	0.997716i	$0.478482\pi$
$830$	−0.555778	+	9.22471i	−0.0192913	+	0.320194i
$831$	22.9569			0.796366
$832$	20.9964	−	19.7775i	0.727920	−	0.685662i
$833$	92.3599			3.20008
$834$	−0.188351	+	3.12622i	−0.00652206	+	0.108252i
$835$	−21.3735	+	12.3400i	−0.739659	+	0.427042i
$836$	−39.1010	−	4.72874i	−1.35234	−	0.163547i
$837$	−8.04936			−0.278227
$838$	−6.63313	−	13.2737i	−0.229138	−	0.458533i
$839$	9.47372	+	5.46965i	0.327069	+	0.188833i	0.654539	−	0.756028i	$-0.272863\pi$
$839$	9.47372	+	5.46965i	0.327069	+	0.188833i	−0.327470	+	0.944862i	$0.606196\pi$
$840$	4.26681	−	23.3778i	0.147219	−	0.806611i
$841$	−5.68395	+	9.84489i	−0.195998	+	0.339479i
$842$	0.223839	−	3.71524i	0.00771399	−	0.128036i
$843$	−5.70798	−	9.88651i	−0.196593	−	0.340509i
$844$	29.9146	−	12.7623i	1.02970	−	0.439297i
$845$	13.7673	+	17.6535i	0.473611	+	0.607300i
$846$	8.05829	−	12.1989i	0.277050	−	0.419406i
$847$	14.5304	−	8.38915i	0.499272	−	0.288255i
$848$	9.01121	−	36.7110i	0.309446	−	1.26066i
$849$	−2.73554	+	4.73809i	−0.0938834	+	0.162611i
$850$	−13.1950	−	8.71630i	−0.452584	−	0.298967i
$851$	−7.53852	+	13.0571i	−0.258417	+	0.447591i
$852$	−4.51526	−	0.546061i	−0.154690	−	0.0187077i
$853$	55.3736			1.89595			0.947977	−	0.318338i	$-0.103125\pi$
$853$	55.3736			1.89595			0.947977	+	0.318338i	$0.103125\pi$
$854$	15.0109	−	7.50124i	0.513663	−	0.256687i
$855$	−4.46241	−	7.72911i	−0.152611	−	0.264330i
$856$	−17.3888	−	48.6815i	−0.594338	−	1.66390i
$857$	−19.3912			−0.662392			−0.331196	−	0.943562i	$-0.607452\pi$
$857$	−19.3912			−0.662392			−0.331196	+	0.943562i	$0.607452\pi$
$858$	9.84168	+	16.6900i	0.335989	+	0.569786i
$859$			26.1648i			0.892731i	0.894851	+	0.446365i	$0.147282\pi$
$859$			26.1648i			0.892731i	−0.894851	+	0.446365i	$0.852718\pi$
$860$	−5.37932	−	4.03827i	−0.183433	−	0.137704i
$861$	−4.86120	+	2.80661i	−0.165669	+	0.0956491i
$862$	−9.83094	−	19.6729i	−0.334843	−	0.670063i
$863$			0.778784i			0.0265101i	0.999912	+	0.0132551i	$0.00421934\pi$
$863$			0.778784i			0.0265101i	−0.999912	+	0.0132551i	$0.995781\pi$
$864$	5.40273	+	1.67647i	0.183804	+	0.0570348i
$865$	6.84682	+	3.95301i	0.232799	+	0.134406i
$866$	17.8152	+	11.7683i	0.605387	+	0.399904i
$867$	−11.4420	−	6.60606i	−0.388591	−	0.224353i
$868$	47.1543	−	62.8135i	1.60052	−	2.13203i
$869$	17.0286	+	29.4944i	0.577656	+	1.00053i
$870$	8.53280	+	5.63657i	0.289289	+	0.191098i
$871$	31.2867	−	2.17389i	1.06011	−	0.0736593i
$872$	−1.81099	+	9.92241i	−0.0613279	+	0.336015i
$873$	−11.3698	+	6.56436i	−0.384810	+	0.222170i
$874$	1.22912	−	20.4008i	0.0415757	−	0.690067i
$875$	−51.1837	−	29.5509i	−1.73033	−	0.999004i
$876$	−8.22980	−	19.2905i	−0.278059	−	0.651764i
$877$	−20.7645	+	35.9652i	−0.701168	+	1.21446i	0.266889	+	0.963727i	$0.414004\pi$
$877$	−20.7645	+	35.9652i	−0.701168	+	1.21446i	−0.968057	+	0.250731i	$0.919329\pi$
$878$	−35.8618	+	17.9208i	−1.21028	+	0.604798i
$879$		−	12.3025i		−	0.414953i
$880$	7.30636	+	25.1345i	0.246297	+	0.847283i
$881$	−28.9735	−	50.1835i	−0.976141	−	1.69073i	−0.676118	−	0.736793i	$-0.736339\pi$
$881$	−28.9735	−	50.1835i	−0.976141	−	1.69073i	−0.300022	−	0.953932i	$-0.596994\pi$
$882$	−1.42912	+	23.7204i	−0.0481211	+	0.798706i
$883$		−	55.6853i		−	1.87396i	−0.349385	−	0.936979i	$-0.613610\pi$
$883$		−	55.6853i		−	1.87396i	0.349385	−	0.936979i	$-0.386390\pi$
$884$	−18.0431	−	35.2913i	−0.606857	−	1.18697i
$885$			2.60191i			0.0874622i
$886$	39.4142	+	2.37466i	1.32415	+	0.0797782i
$887$	−22.5227	−	39.0104i	−0.756237	−	1.30984i	−0.944757	−	0.327772i	$-0.893702\pi$
$887$	−22.5227	−	39.0104i	−0.756237	−	1.30984i	0.188520	−	0.982069i	$-0.439631\pi$
$888$	9.90002	−	11.6558i	0.332223	−	0.391141i
$889$		−	22.1661i		−	0.743426i
$890$	6.48135	+	12.9700i	0.217255	+	0.434755i
$891$	−1.89993	+	3.29078i	−0.0636502	+	0.110245i
$892$	−6.93286	+	2.95773i	−0.232129	+	0.0990323i
$893$	46.3991	+	26.7885i	1.55269	+	0.896444i
$894$	13.5866	+	0.818577i	0.454404	+	0.0273773i
$895$	19.1894	−	11.0790i	0.641432	−	0.370331i
$896$	−44.7323	+	32.3393i	−1.49440	+	1.08038i
$897$	−8.33780	+	5.61856i	−0.278391	+	0.187598i
$898$	−27.2417	+	41.2392i	−0.909067	+	1.37617i
$899$	16.8999	+	29.2714i	0.563642	+	0.976257i
$900$	2.44274	−	3.25393i	0.0814246	−	0.108464i
$901$	−44.9844	−	25.9718i	−1.49865	−	0.865245i
$902$	3.40776	−	5.15876i	0.113466	−	0.171768i
$903$	8.25174	+	4.76415i	0.274601	+	0.158541i
$904$	−5.61834	−	4.77204i	−0.186863	−	0.158716i
$905$			3.85230i			0.128055i
$906$	19.9192	−	9.95398i	0.661770	−	0.330699i
$907$	25.4910	−	14.7173i	0.846416	−	0.488678i	−0.0130240	−	0.999915i	$-0.504146\pi$
$907$	25.4910	−	14.7173i	0.846416	−	0.488678i	0.859440	+	0.511237i	$0.170812\pi$
$908$	−6.64177	+	8.84740i	−0.220415	+	0.293611i
$909$			6.11403i			0.202790i
$910$	−21.7608	−	36.9030i	−0.721365	−	1.22332i
$911$	9.22242			0.305552			0.152776	−	0.988261i	$-0.451179\pi$
$911$	9.22242			0.305552			0.152776	+	0.988261i	$0.451179\pi$
$912$	−4.94179	+	20.1325i	−0.163639	+	0.666654i
$913$	7.20952	+	12.4872i	0.238600	+	0.413268i
$914$	4.92280	+	9.85115i	0.162832	+	0.325847i
$915$	−4.18829			−0.138461
$916$	18.9462	+	2.29129i	0.625999	+	0.0757063i
$917$	−7.69119	+	13.3215i	−0.253985	+	0.439916i
$918$	4.28447	−	6.48595i	0.141409	−	0.214068i
$919$	−0.0583125	+	0.101000i	−0.00192355	+	0.00333169i	−0.866986	−	0.498333i	$-0.833946\pi$
$919$	−0.0583125	+	0.101000i	−0.00192355	+	0.00333169i	0.865062	+	0.501665i	$0.167279\pi$
$920$	−12.7909	+	4.56887i	−0.421705	+	0.150631i
$921$	−2.87584	+	1.66037i	−0.0947622	+	0.0547110i
$922$	18.1255	+	11.9733i	0.596932	+	0.394320i
$923$	−6.79956	+	4.58199i	−0.223810	+	0.150818i
$924$	−14.5497	−	34.1040i	−0.478648	−	1.12194i
$925$	−5.49977	−	9.52589i	−0.180831	−	0.313209i
$926$	−55.5584	−	3.34733i	−1.82576	−	0.110000i
$927$	2.59423	−	4.49334i	0.0852057	−	0.147581i
$928$	−5.24670	−	23.1668i	−0.172231	−	0.760487i
$929$	−36.5771	−	21.1178i	−1.20006	−	0.692853i	−0.239488	−	0.970899i	$-0.576980\pi$
$929$	−36.5771	−	21.1178i	−1.20006	−	0.692853i	−0.960568	+	0.278047i	$0.910313\pi$
$930$	−17.5359	+	8.76300i	−0.575023	+	0.287350i
$931$	−87.0834			−2.85404
$932$	21.6656	+	2.62017i	0.709681	+	0.0858264i
$933$	13.1415	−	7.58722i	0.430232	−	0.248395i
$934$	40.4194	+	2.43522i	1.32256	+	0.0796828i
$935$	35.9679			1.17628
$936$	9.34288	−	4.08786i	0.305382	−	0.133616i
$937$	14.2669			0.466080			0.233040	−	0.972467i	$-0.425133\pi$
$937$	14.2669			0.466080			0.233040	+	0.972467i	$0.425133\pi$
$938$	−59.9073	−	3.60935i	−1.95604	−	0.117849i
$939$	1.61085	−	0.930024i	0.0525681	−	0.0303502i
$940$	4.27492	−	35.3484i	0.139433	−	1.15294i
$941$	34.1969			1.11479			0.557393	−	0.830249i	$-0.311802\pi$
$941$	34.1969			1.11479			0.557393	+	0.830249i	$0.311802\pi$
$942$	24.6667	−	12.3264i	0.803685	−	0.401617i
$943$	2.77844	+	1.60413i	0.0904785	+	0.0522378i
$944$	4.18238	−	4.36266i	0.136125	−	0.141992i
$945$	4.20092	−	7.27621i	0.136656	−	0.236695i
$946$	−10.4760	−	0.631164i	−0.340603	−	0.0205209i
$947$	7.48563	+	12.9655i	0.243250	+	0.421322i	0.961638	−	0.274321i	$-0.0884530\pi$
$947$	7.48563	+	12.9655i	0.243250	+	0.421322i	−0.718388	+	0.695643i	$0.755120\pi$
$948$	16.4877	−	7.03408i	0.535496	−	0.228456i
$949$	−33.9751	−	16.5894i	−1.10288	−	0.538514i
$950$	12.4412	+	8.21834i	0.403644	+	0.266638i
$951$	1.47058	−	0.849039i	0.0476868	−	0.0275320i
$952$	25.5143	+	71.4296i	0.826924	+	2.31505i
$953$	6.28504	−	10.8860i	0.203592	−	0.352632i	−0.746091	−	0.665844i	$-0.768072\pi$
$953$	6.28504	−	10.8860i	0.203592	−	0.352632i	0.949683	+	0.313212i	$0.101405\pi$
$954$	7.36627	−	11.1513i	0.238492	−	0.361036i
$955$	13.1858	−	22.8384i	0.426682	−	0.739035i
$956$	3.79214	−	31.3564i	0.122647	−	1.01414i
$957$	15.9559			0.515780
$958$	−8.99504	−	18.0002i	−0.290617	−	0.581560i
$959$	−38.8875	−	67.3551i	−1.25574	−	2.17501i
$960$	13.5952	−	2.22946i	0.438782	−	0.0719554i
$961$	−33.7922			−1.09007
$962$	−0.253502	−	27.5682i	−0.00817324	−	0.888833i
$963$		−	18.2766i		−	0.588954i
$964$	−29.9810	−	22.5068i	−0.965624	−	0.724897i
$965$	−4.43747	+	2.56197i	−0.142847	+	0.0824728i
$966$	17.2109	−	8.60060i	0.553751	−	0.276720i
$967$			0.668278i			0.0214904i	0.999942	+	0.0107452i	$0.00342036\pi$
$967$			0.668278i			0.0214904i	−0.999942	+	0.0107452i	$0.996580\pi$
$968$	7.41363	+	6.29690i	0.238283	+	0.202390i
$969$	24.6697	+	14.2430i	0.792504	+	0.457553i
$970$	−17.6232	+	26.6785i	−0.565848	+	0.856597i
$971$	15.1157	+	8.72704i	0.485085	+	0.280064i	0.722533	−	0.691336i	$-0.242978\pi$
$971$	15.1157	+	8.72704i	0.485085	+	0.280064i	−0.237448	+	0.971400i	$0.576311\pi$
$972$	1.59946	+	1.20072i	0.0513027	+	0.0385131i
$973$	−5.40230	−	9.35706i	−0.173190	−	0.299974i
$974$	−7.68063	+	11.6272i	−0.246103	+	0.372558i
$975$	−0.508438	−	7.31747i	−0.0162831	−	0.234347i
$976$	7.02257	+	6.73237i	0.224787	+	0.215498i
$977$	52.7386	−	30.4487i	1.68726	−	0.974139i	0.730654	−	0.682748i	$-0.239215\pi$
$977$	52.7386	−	30.4487i	1.68726	−	0.974139i	0.956604	−	0.291390i	$-0.0941179\pi$
$978$	−16.0824	−	0.968944i	−0.514257	−	0.0309834i
$979$	19.5918	+	11.3113i	0.626155	+	0.361511i
$980$	22.7099	+	53.2316i	0.725442	+	1.70042i
$981$	−1.78303	+	3.08829i	−0.0569276	+	0.0986016i
$982$	−17.5825	−	35.1847i	−0.561079	−	1.12279i
$983$		−	53.8532i		−	1.71765i	−0.512269	−	0.858825i	$-0.671195\pi$
$983$		−	53.8532i		−	1.71765i	0.512269	−	0.858825i	$-0.328805\pi$
$984$	−2.48025	−	2.10664i	−0.0790674	−	0.0671574i
$985$	−1.03083	−	1.78546i	−0.0328451	−	0.0568893i
$986$	−32.5815	−	1.96300i	−1.03761	−	0.0625145i
$987$			50.4376i			1.60545i
$988$	17.0123	+	33.2751i	0.541235	+	1.05862i
$989$		−	5.44595i		−	0.173171i
$990$	−0.556547	+	9.23747i	−0.0176882	+	0.293586i
$991$	25.6914	+	44.4988i	0.816114	+	1.41355i	0.908525	+	0.417830i	$0.137209\pi$
$991$	25.6914	+	44.4988i	0.816114	+	1.41355i	−0.0924112	+	0.995721i	$0.529457\pi$
$992$	43.4885	+	13.4945i	1.38076	+	0.428452i
$993$			26.9837i			0.856301i
$994$	14.0357	−	7.01388i	0.445184	−	0.222467i
$995$	−9.50094	+	16.4561i	−0.301200	+	0.521694i
$996$	6.98051	−	2.97806i	0.221186	−	0.0943636i
$997$	−30.5423	−	17.6336i	−0.967285	−	0.558462i	−0.0688774	−	0.997625i	$-0.521942\pi$
$997$	−30.5423	−	17.6336i	−0.967285	−	0.558462i	−0.898407	+	0.439163i	$0.855275\pi$
$998$	−3.17307	+	52.6661i	−0.100442	+	1.66712i
$999$	4.68242	−	2.70339i	0.148145	−	0.0855316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bk.b.205.13	yes	48
3.2	odd	2		936.2.dg.e.829.12		48
4.3	odd	2		1248.2.ca.b.49.9		48
8.3	odd	2		1248.2.ca.b.49.16		48
8.5	even	2	inner	312.2.bk.b.205.5	✓	48
13.4	even	6	inner	312.2.bk.b.277.5	yes	48
24.5	odd	2		936.2.dg.e.829.20		48
39.17	odd	6		936.2.dg.e.901.20		48
52.43	odd	6		1248.2.ca.b.433.16		48
104.43	odd	6		1248.2.ca.b.433.9		48
104.69	even	6	inner	312.2.bk.b.277.13	yes	48
312.173	odd	6		936.2.dg.e.901.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.5	✓	48	8.5	even	2	inner
312.2.bk.b.205.13	yes	48	1.1	even	1	trivial
312.2.bk.b.277.5	yes	48	13.4	even	6	inner
312.2.bk.b.277.13	yes	48	104.69	even	6	inner
936.2.dg.e.829.12		48	3.2	odd	2
936.2.dg.e.829.20		48	24.5	odd	2
936.2.dg.e.901.12		48	312.173	odd	6
936.2.dg.e.901.20		48	39.17	odd	6
1248.2.ca.b.49.9		48	4.3	odd	2
1248.2.ca.b.49.16		48	8.3	odd	2
1248.2.ca.b.433.9		48	104.43	odd	6
1248.2.ca.b.433.16		48	52.43	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0850505 + 1.41165i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.98553 - 0.240124i) q^{4} -1.72209 q^{5} +(0.632171 + 1.26505i) q^{6} +(-4.22521 - 2.43943i) q^{7} +(0.507842 - 2.78246i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.146465 - 2.43100i) q^{10} +(-1.89993 - 3.29078i) q^{11} +(-1.83958 + 0.784813i) q^{12} +(-1.58200 + 3.23995i) q^{13} +(3.80298 - 5.75706i) q^{14} +(-1.49138 + 0.861047i) q^{15} +(3.88468 + 0.953547i) q^{16} +(2.74828 - 4.76016i) q^{17} +(1.18000 + 0.779483i) q^{18} +(-2.59127 + 4.48821i) q^{19} +(3.41927 + 0.413515i) q^{20} -4.87886 q^{21} +(4.80703 - 2.40217i) q^{22} +(1.39427 + 2.41494i) q^{23} +(-0.951427 - 2.66360i) q^{24} -2.03439 q^{25} +(-4.43914 - 2.50880i) q^{26} -1.00000i q^{27} +(7.80354 + 5.85814i) q^{28} +(-3.63649 + 2.09953i) q^{29} +(-1.08866 - 2.17854i) q^{30} -8.04936i q^{31} +(-1.67647 + 5.40273i) q^{32} +(-3.29078 - 1.89993i) q^{33} +(6.48595 + 4.28447i) q^{34} +(7.27621 + 4.20092i) q^{35} +(-1.20072 + 1.59946i) q^{36} +(2.70339 + 4.68242i) q^{37} +(-6.11541 - 4.03970i) q^{38} +(0.249921 + 3.59688i) q^{39} +(-0.874552 + 4.79166i) q^{40} +(0.996380 - 0.575260i) q^{41} +(0.414949 - 6.88726i) q^{42} +(-1.69133 - 0.976488i) q^{43} +(2.98218 + 6.99017i) q^{44} +(-0.861047 + 1.49138i) q^{45} +(-3.52765 + 1.76283i) q^{46} -10.3380i q^{47} +(3.84101 - 1.11654i) q^{48} +(8.40162 + 14.5520i) q^{49} +(0.173026 - 2.87186i) q^{50} -5.49655i q^{51} +(3.91910 - 6.05315i) q^{52} -9.45020i q^{53} +(1.41165 + 0.0850505i) q^{54} +(3.27186 + 5.66703i) q^{55} +(-8.93336 + 10.5177i) q^{56} +5.18254i q^{57} +(-2.65452 - 5.31203i) q^{58} +(0.755450 - 1.30848i) q^{59} +(3.16793 - 1.35152i) q^{60} +(2.10626 + 1.21605i) q^{61} +(11.3629 + 0.684602i) q^{62} +(-4.22521 + 2.43943i) q^{63} +(-7.48419 - 2.82610i) q^{64} +(2.72435 - 5.57949i) q^{65} +(2.96193 - 4.48385i) q^{66} +(-4.34914 - 7.53294i) q^{67} +(-6.59982 + 8.79152i) q^{68} +(2.41494 + 1.39427i) q^{69} +(-6.54909 + 9.91420i) q^{70} +(1.96941 + 1.13704i) q^{71} +(-2.15576 - 1.83104i) q^{72} +10.4863i q^{73} +(-6.83988 + 3.41802i) q^{74} +(-1.76184 + 1.01720i) q^{75} +(6.22277 - 8.28926i) q^{76} +18.5390i q^{77} +(-5.09880 + 0.0468859i) q^{78} -8.96275 q^{79} +(-6.68978 - 1.64210i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.727326 + 1.45547i) q^{82} -3.79462 q^{83} +(9.68713 + 1.17153i) q^{84} +(-4.73279 + 8.19743i) q^{85} +(1.52231 - 2.30452i) q^{86} +(-2.09953 + 3.63649i) q^{87} +(-10.1213 + 3.61529i) q^{88} +(-5.15591 + 2.97676i) q^{89} +(-2.03207 - 1.34234i) q^{90} +(14.5879 - 9.83030i) q^{91} +(-2.18848 - 5.12975i) q^{92} +(-4.02468 - 6.97095i) q^{93} +(14.5937 + 0.879252i) q^{94} +(4.46241 - 7.72911i) q^{95} +(1.24949 + 5.51713i) q^{96} +(-11.3698 - 6.56436i) q^{97} +(-21.2570 + 10.6225i) q^{98} -3.79987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 6 q^{6} - 12 q^{7} + 24 q^{9} - 4 q^{10} - 8 q^{12} - 36 q^{14} - 2 q^{16} + 12 q^{17} + 54 q^{20} - 14 q^{22} + 20 q^{23} + 18 q^{24} + 48 q^{25} - 42 q^{26} + 6 q^{28} - 6 q^{30} + 12 q^{33}+ \cdots + 24 q^{98}+O(q^{100}) \) 48 * q - 2 * q^4 + 6 * q^6 - 12 * q^7 + 24 * q^9 - 4 * q^10 - 8 * q^12 - 36 * q^14 - 2 * q^16 + 12 * q^17 + 54 * q^20 - 14 * q^22 + 20 * q^23 + 18 * q^24 + 48 * q^25 - 42 * q^26 + 6 * q^28 - 6 * q^30 + 12 * q^33 + 2 * q^36 - 28 * q^38 + 28 * q^39 - 8 * q^40 - 12 * q^41 - 10 * q^42 - 30 * q^46 - 8 * q^48 + 16 * q^49 - 84 * q^50 - 28 * q^52 + 6 * q^54 - 68 * q^55 + 18 * q^56 - 24 * q^58 + 24 * q^62 - 12 * q^63 - 68 * q^64 + 12 * q^65 - 44 * q^66 + 4 * q^68 - 12 * q^71 + 54 * q^74 - 54 * q^76 + 4 * q^78 - 192 * q^79 + 78 * q^80 - 24 * q^81 - 6 * q^82 + 30 * q^84 - 10 * q^88 - 48 * q^89 - 8 * q^90 - 12 * q^92 + 54 * q^94 - 20 * q^95 + 144 * q^97 + 24 * q^98

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