LMFDB - Embedded newform 117.2.z.b.47.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(5,117)] 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("117.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.8
Character	$\chi$	$=$	117.47
Dual form			117.2.z.b.5.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.359097 + 1.34017i) q^{2} +(-0.694508 - 1.58671i) q^{3} +(0.0649546 - 0.0375016i) q^{4} +(1.79870 + 0.481960i) q^{5} +(1.87706 - 1.50054i) q^{6} +(-0.653846 - 2.44019i) q^{7} +(2.03572 + 2.03572i) q^{8} +(-2.03532 + 2.20397i) q^{9} +2.58363i q^{10} +(0.560908 - 0.150295i) q^{11} +(-0.104616 - 0.0770192i) q^{12} +(-0.116440 + 3.60367i) q^{13} +(3.03546 - 1.75253i) q^{14} +(-0.484480 - 3.18875i) q^{15} +(-1.92218 + 3.32932i) q^{16} -2.47718 q^{17} +(-3.68456 - 1.93622i) q^{18} +(-5.94048 - 5.94048i) q^{19} +(0.134908 - 0.0361485i) q^{20} +(-3.41777 + 2.73220i) q^{21} +(0.402841 + 0.697740i) q^{22} +(2.66773 + 4.62064i) q^{23} +(1.81628 - 4.64394i) q^{24} +(-1.32709 - 0.766195i) q^{25} +(-4.87133 + 1.13802i) q^{26} +(4.91061 + 1.69879i) q^{27} +(-0.133981 - 0.133981i) q^{28} +(-3.78595 - 2.18582i) q^{29} +(4.09948 - 1.79435i) q^{30} +(-0.416610 + 1.55481i) q^{31} +(0.409606 + 0.109754i) q^{32} +(-0.628030 - 0.785620i) q^{33} +(-0.889546 - 3.31983i) q^{34} -4.70429i q^{35} +(-0.0495508 + 0.219486i) q^{36} +(0.0912609 - 0.0912609i) q^{37} +(5.82803 - 10.0944i) q^{38} +(5.79886 - 2.31802i) q^{39} +(2.68052 + 4.64280i) q^{40} +(1.86543 + 0.499840i) q^{41} +(-4.88891 - 3.59927i) q^{42} +(5.23622 + 3.02313i) q^{43} +(0.0307973 - 0.0307973i) q^{44} +(-4.72315 + 2.98334i) q^{45} +(-5.23446 + 5.23446i) q^{46} +(-11.4764 + 3.07508i) q^{47} +(6.61765 + 0.737714i) q^{48} +(0.535180 - 0.308986i) q^{49} +(0.550276 - 2.05366i) q^{50} +(1.72042 + 3.93057i) q^{51} +(0.127580 + 0.238442i) q^{52} +10.8009i q^{53} +(-0.513274 + 7.19107i) q^{54} +1.08134 q^{55} +(3.63650 - 6.29860i) q^{56} +(-5.30013 + 13.5516i) q^{57} +(1.56984 - 5.85873i) q^{58} +(0.657543 - 2.45398i) q^{59} +(-0.151052 - 0.188955i) q^{60} +(1.05320 - 1.82419i) q^{61} -2.23330 q^{62} +(6.70888 + 3.52550i) q^{63} +8.27709i q^{64} +(-1.94627 + 6.42581i) q^{65} +(0.827337 - 1.12378i) q^{66} +(1.72857 - 6.45111i) q^{67} +(-0.160904 + 0.0928980i) q^{68} +(5.47887 - 7.44199i) q^{69} +(6.30454 - 1.68930i) q^{70} +(3.69628 - 3.69628i) q^{71} +(-8.63002 + 0.343333i) q^{72} +(10.1636 - 10.1636i) q^{73} +(0.155076 + 0.0895333i) q^{74} +(-0.294058 + 2.63784i) q^{75} +(-0.608639 - 0.163084i) q^{76} +(-0.733496 - 1.27045i) q^{77} +(5.18889 + 6.93904i) q^{78} +(4.35439 - 7.54202i) q^{79} +(-5.06203 + 5.06203i) q^{80} +(-0.714974 - 8.97156i) q^{81} +2.67948i q^{82} +(-0.983416 - 3.67016i) q^{83} +(-0.119539 + 0.305641i) q^{84} +(-4.45570 - 1.19390i) q^{85} +(-2.17119 + 8.10301i) q^{86} +(-0.838895 + 7.52529i) q^{87} +(1.44781 + 0.835895i) q^{88} +(-0.410551 - 0.410551i) q^{89} +(-5.69424 - 5.25850i) q^{90} +(8.86976 - 2.07211i) q^{91} +(0.346563 + 0.200088i) q^{92} +(2.75637 - 0.418787i) q^{93} +(-8.24224 - 14.2760i) q^{94} +(-7.82207 - 13.5482i) q^{95} +(-0.110327 - 0.726152i) q^{96} +(2.78216 - 0.745477i) q^{97} +(0.606275 + 0.606275i) q^{98} +(-0.810380 + 1.54212i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.359097	+	1.34017i	0.253920	+	0.947641i	0.968688	+	0.248280i	$0.0798653\pi$
$2$	0.359097	+	1.34017i	0.253920	+	0.947641i	−0.714769	+	0.699361i	$0.753468\pi$
$3$	−0.694508	−	1.58671i	−0.400975	−	0.916089i
$3$	−0.694508	−	1.58671i	−0.400975	−	0.916089i
$4$	0.0649546	−	0.0375016i	0.0324773	−	0.0187508i
$5$	1.79870	+	0.481960i	0.804403	+	0.215539i	0.637516	−	0.770437i	$-0.279962\pi$
$5$	1.79870	+	0.481960i	0.804403	+	0.215539i	0.166887	+	0.985976i	$0.446628\pi$
$6$	1.87706	−	1.50054i	0.766308	−	0.612593i
$7$	−0.653846	−	2.44019i	−0.247131	−	0.922304i	−0.972301	−	0.233734i	$-0.924905\pi$
$7$	−0.653846	−	2.44019i	−0.247131	−	0.922304i	0.725170	−	0.688570i	$-0.241761\pi$
$8$	2.03572	+	2.03572i	0.719737	+	0.719737i
$9$	−2.03532	+	2.20397i	−0.678439	+	0.734657i
$10$			2.58363i			0.817015i
$11$	0.560908	−	0.150295i	0.169120	−	0.0453156i	−0.173265	−	0.984875i	$-0.555432\pi$
$11$	0.560908	−	0.150295i	0.169120	−	0.0453156i	0.342385	+	0.939560i	$0.388765\pi$
$12$	−0.104616	−	0.0770192i	−0.0302000	−	0.0222335i
$13$	−0.116440	+	3.60367i	−0.0322946	+	0.999478i
$13$	−0.116440	+	3.60367i	−0.0322946	+	0.999478i
$14$	3.03546	−	1.75253i	0.811262	−	0.468382i
$15$	−0.484480	−	3.18875i	−0.125092	−	0.823331i
$16$	−1.92218	+	3.32932i	−0.480546	+	0.832330i
$17$	−2.47718			−0.600804			−0.300402	−	0.953813i	$-0.597121\pi$
$17$	−2.47718			−0.600804			−0.300402	+	0.953813i	$0.597121\pi$
$18$	−3.68456	−	1.93622i	−0.868460	−	0.456373i
$19$	−5.94048	−	5.94048i	−1.36284	−	1.36284i	−0.870276	−	0.492565i	$-0.836059\pi$
$19$	−5.94048	−	5.94048i	−1.36284	−	1.36284i	−0.492565	−	0.870276i	$-0.663941\pi$
$20$	0.134908	−	0.0361485i	0.0301664	−	0.00808306i
$21$	−3.41777	+	2.73220i	−0.745820	+	0.596214i
$22$	0.402841	+	0.697740i	0.0858859	+	0.148759i
$23$	2.66773	+	4.62064i	0.556260	+	0.963470i	0.997804	+	0.0662309i	$0.0210974\pi$
$23$	2.66773	+	4.62064i	0.556260	+	0.963470i	−0.441544	+	0.897239i	$0.645569\pi$
$24$	1.81628	−	4.64394i	0.370747	−	0.947939i
$25$	−1.32709	−	0.766195i	−0.265418	−	0.153239i
$26$	−4.87133	+	1.13802i	−0.955347	+	0.223183i
$27$	4.91061	+	1.69879i	0.945048	+	0.326932i
$28$	−0.133981	−	0.133981i	−0.0253201	−	0.0253201i
$29$	−3.78595	−	2.18582i	−0.703034	−	0.405897i	0.105443	−	0.994425i	$-0.466374\pi$
$29$	−3.78595	−	2.18582i	−0.703034	−	0.405897i	−0.808476	+	0.588529i	$0.799707\pi$
$30$	4.09948	−	1.79435i	0.748459	−	0.327602i
$31$	−0.416610	+	1.55481i	−0.0748253	+	0.279252i	−0.993194	−	0.116475i	$-0.962841\pi$
$31$	−0.416610	+	1.55481i	−0.0748253	+	0.279252i	0.918368	+	0.395727i	$0.129507\pi$
$32$	0.409606	+	0.109754i	0.0724088	+	0.0194019i
$33$	−0.628030	−	0.785620i	−0.109326	−	0.136759i
$34$	−0.889546	−	3.31983i	−0.152556	−	0.569346i
$35$		−	4.70429i		−	0.795171i
$36$	−0.0495508	+	0.219486i	−0.00825847	+	0.0365809i
$37$	0.0912609	−	0.0912609i	0.0150032	−	0.0150032i	−0.699565	−	0.714569i	$-0.746623\pi$
$37$	0.0912609	−	0.0912609i	0.0150032	−	0.0150032i	0.714569	+	0.699565i	$0.246623\pi$
$38$	5.82803	−	10.0944i	0.945431	−	1.63754i
$39$	5.79886	−	2.31802i	0.928561	−	0.371181i
$40$	2.68052	+	4.64280i	0.423827	+	0.734090i
$41$	1.86543	+	0.499840i	0.291331	+	0.0780620i	0.401525	−	0.915848i	$-0.368480\pi$
$41$	1.86543	+	0.499840i	0.291331	+	0.0780620i	−0.110193	+	0.993910i	$0.535147\pi$
$42$	−4.88891	−	3.59927i	−0.754375	−	0.555379i
$43$	5.23622	+	3.02313i	0.798516	+	0.461024i	0.842952	−	0.537989i	$-0.180816\pi$
$43$	5.23622	+	3.02313i	0.798516	+	0.461024i	−0.0444358	+	0.999012i	$0.514149\pi$
$44$	0.0307973	−	0.0307973i	0.00464287	−	0.00464287i
$45$	−4.72315	+	2.98334i	−0.704086	+	0.444730i
$46$	−5.23446	+	5.23446i	−0.771779	+	0.771779i
$47$	−11.4764	+	3.07508i	−1.67400	+	0.448547i	−0.966185	−	0.257851i	$-0.916986\pi$
$47$	−11.4764	+	3.07508i	−1.67400	+	0.448547i	−0.707815	+	0.706398i	$0.750319\pi$
$48$	6.61765	+	0.737714i	0.955175	+	0.106480i
$49$	0.535180	−	0.308986i	0.0764543	−	0.0441409i
$50$	0.550276	−	2.05366i	0.0778208	−	0.290431i
$51$	1.72042	+	3.93057i	0.240907	+	0.550390i
$52$	0.127580	+	0.238442i	0.0176922	+	0.0330659i
$53$			10.8009i			1.48362i	0.670610	+	0.741810i	$0.266032\pi$
$53$			10.8009i			1.48362i	−0.670610	+	0.741810i	$0.733968\pi$
$54$	−0.513274	+	7.19107i	−0.0698477	+	0.978580i
$55$	1.08134			0.145808
$56$	3.63650	−	6.29860i	0.485947	−	0.841685i
$57$	−5.30013	+	13.5516i	−0.702019	+	1.79495i
$58$	1.56984	−	5.85873i	0.206130	−	0.769288i
$59$	0.657543	−	2.45398i	0.0856048	−	0.319481i	−0.909823	−	0.414996i	$-0.863783\pi$
$59$	0.657543	−	2.45398i	0.0856048	−	0.319481i	0.995428	+	0.0955145i	$0.0304496\pi$
$60$	−0.151052	−	0.188955i	−0.0195008	−	0.0243940i
$61$	1.05320	−	1.82419i	0.134848	−	0.233563i	−0.790691	−	0.612215i	$-0.790279\pi$
$61$	1.05320	−	1.82419i	0.134848	−	0.233563i	0.925539	+	0.378651i	$0.123612\pi$
$62$	−2.23330			−0.283630
$63$	6.70888	+	3.52550i	0.845240	+	0.444171i
$64$			8.27709i			1.03464i
$65$	−1.94627	+	6.42581i	−0.241405	+	0.797023i
$66$	0.827337	−	1.12378i	0.101838	−	0.138328i
$67$	1.72857	−	6.45111i	0.211178	−	0.788129i	−0.776298	−	0.630366i	$-0.782905\pi$
$67$	1.72857	−	6.45111i	0.211178	−	0.788129i	0.987477	−	0.157763i	$-0.0504283\pi$
$68$	−0.160904	+	0.0928980i	−0.0195125	+	0.0112655i
$69$	5.47887	−	7.44199i	0.659579	−	0.895911i
$70$	6.30454	−	1.68930i	0.753536	−	0.201909i
$71$	3.69628	−	3.69628i	0.438668	−	0.438668i	−0.452896	−	0.891564i	$-0.649609\pi$
$71$	3.69628	−	3.69628i	0.438668	−	0.438668i	0.891564	+	0.452896i	$0.149609\pi$
$72$	−8.63002	+	0.343333i	−1.01706	+	0.0404622i
$73$	10.1636	−	10.1636i	1.18956	−	1.18956i	0.212376	−	0.977188i	$-0.431880\pi$
$73$	10.1636	−	10.1636i	1.18956	−	1.18956i	0.977188	−	0.212376i	$-0.0681201\pi$
$74$	0.155076	+	0.0895333i	0.0180272	+	0.0104080i
$75$	−0.294058	+	2.63784i	−0.0339548	+	0.304591i
$76$	−0.608639	−	0.163084i	−0.0698157	−	0.0187071i
$77$	−0.733496	−	1.27045i	−0.0835896	−	0.144781i
$78$	5.18889	+	6.93904i	0.587526	+	0.785692i
$79$	4.35439	−	7.54202i	0.489907	−	0.848543i	−0.510026	−	0.860159i	$-0.670364\pi$
$79$	4.35439	−	7.54202i	0.489907	−	0.848543i	0.999933	+	0.0116158i	$0.00369750\pi$
$80$	−5.06203	+	5.06203i	−0.565953	+	0.565953i
$81$	−0.714974	−	8.97156i	−0.0794415	−	0.996840i
$82$			2.67948i			0.295899i
$83$	−0.983416	−	3.67016i	−0.107944	−	0.402852i	0.890719	−	0.454555i	$-0.150202\pi$
$83$	−0.983416	−	3.67016i	−0.107944	−	0.402852i	−0.998663	+	0.0517031i	$0.983535\pi$
$84$	−0.119539	+	0.305641i	−0.0130427	+	0.0333481i
$85$	−4.45570	−	1.19390i	−0.483288	−	0.129497i
$86$	−2.17119	+	8.10301i	−0.234126	+	0.873770i
$87$	−0.838895	+	7.52529i	−0.0899389	+	0.806796i
$88$	1.44781	+	0.835895i	0.154337	+	0.0891067i
$89$	−0.410551	−	0.410551i	−0.0435184	−	0.0435184i	0.685013	−	0.728531i	$-0.259797\pi$
$89$	−0.410551	−	0.410551i	−0.0435184	−	0.0435184i	−0.728531	+	0.685013i	$0.759797\pi$
$90$	−5.69424	−	5.25850i	−0.600226	−	0.554295i
$91$	8.86976	−	2.07211i	0.929804	−	0.217216i
$92$	0.346563	+	0.200088i	0.0361316	+	0.0208606i
$93$	2.75637	−	0.418787i	0.285823	−	0.0434262i
$94$	−8.24224	−	14.2760i	−0.850123	−	1.47246i
$95$	−7.82207	−	13.5482i	−0.802528	−	1.39002i
$96$	−0.110327	−	0.726152i	−0.0112602	−	0.0741125i
$97$	2.78216	−	0.745477i	0.282485	−	0.0756917i	−0.114794	−	0.993389i	$-0.536621\pi$
$97$	2.78216	−	0.745477i	0.282485	−	0.0756917i	0.397280	+	0.917698i	$0.369954\pi$
$98$	0.606275	+	0.606275i	0.0612430	+	0.0612430i
$99$	−0.810380	+	1.54212i	−0.0814463	+	0.154989i
$100$	−0.114934			−0.0114934
$101$	9.41703	−	16.3108i	0.937030	−	1.62298i	0.166056	−	0.986116i	$-0.446897\pi$
$101$	9.41703	−	16.3108i	0.937030	−	1.62298i	0.770974	−	0.636867i	$-0.219770\pi$
$102$	−4.64982	+	3.71710i	−0.460401	+	0.368048i
$103$	4.08607	−	2.35910i	0.402613	−	0.232449i	−0.284998	−	0.958528i	$-0.591993\pi$
$103$	4.08607	−	2.35910i	0.402613	−	0.232449i	0.687611	+	0.726080i	$0.258660\pi$
$104$	−7.57312	+	7.09904i	−0.742605	+	0.696118i
$105$	−7.46436	+	3.26717i	−0.728447	+	0.318843i
$106$	−14.4750	+	3.87857i	−1.40594	+	0.376720i
$107$			15.4911i			1.49759i	0.662804	+	0.748793i	$0.269366\pi$
$107$			15.4911i			1.49759i	−0.662804	+	0.748793i	$0.730634\pi$
$108$	0.382674	−	0.0738116i	0.0368228	−	0.00710252i
$109$	6.53217	+	6.53217i	0.625668	+	0.625668i	0.946975	−	0.321307i	$-0.104122\pi$
$109$	6.53217	+	6.53217i	0.625668	+	0.625668i	−0.321307	+	0.946975i	$0.604122\pi$
$110$	0.388306	+	1.44918i	0.0370236	+	0.138174i
$111$	−0.208186	−	0.0814234i	−0.0197602	−	0.00772837i
$112$	9.38098	+	2.51363i	0.886419	+	0.237515i
$113$	−0.593927	+	0.342904i	−0.0558720	+	0.0322577i	−0.527676	−	0.849446i	$-0.676936\pi$
$113$	−0.593927	+	0.342904i	−0.0558720	+	0.0322577i	0.471804	+	0.881704i	$0.343603\pi$
$114$	−20.0646	−	2.23674i	−1.87922	−	0.209490i
$115$	2.57148	+	9.59689i	0.239792	+	0.894915i
$116$	−0.327887			−0.0304435
$117$	−7.70539	−	7.59124i	−0.712364	−	0.701810i
$118$	3.52487			0.324490
$119$	1.61969	+	6.04477i	0.148477	+	0.554123i
$120$	5.50514	−	7.47767i	0.502548	−	0.682615i
$121$	−9.23425	+	5.33140i	−0.839477	+	0.484672i
$122$	2.82292	+	0.756398i	0.255575	+	0.0684811i
$123$	−0.502453	−	3.30705i	−0.0453047	−	0.298186i
$124$	0.0312470	+	0.116615i	0.00280606	+	0.0104724i
$125$	−8.60146	−	8.60146i	−0.769338	−	0.769338i
$126$	−2.31561	+	10.2570i	−0.206291	+	0.913768i
$127$		−	11.3573i		−	1.00780i	−0.863762	−	0.503901i	$-0.831898\pi$
$127$		−	11.3573i		−	1.00780i	0.863762	−	0.503901i	$-0.168102\pi$
$128$	−10.2735	+	2.75277i	−0.908055	+	0.243313i
$129$	1.16025	−	10.4080i	0.102154	−	0.916371i
$130$	−9.31055	−	0.300838i	−0.816589	−	0.0263852i
$131$	−6.16432	+	3.55897i	−0.538579	+	0.310949i	−0.744503	−	0.667619i	$-0.767314\pi$
$131$	−6.16432	+	3.55897i	−0.538579	+	0.310949i	0.205924	+	0.978568i	$0.433980\pi$
$132$	−0.0702554	−	0.0274775i	−0.00611495	−	0.00239161i
$133$	−10.6117	+	18.3801i	−0.920154	+	1.59375i
$134$	9.26629			0.800486
$135$	8.01398	+	5.42233i	0.689733	+	0.466680i
$136$	−5.04285	−	5.04285i	−0.432420	−	0.432420i
$137$	−10.5596	+	2.82943i	−0.902167	+	0.241735i	−0.679947	−	0.733262i	$-0.737997\pi$
$137$	−10.5596	+	2.82943i	−0.902167	+	0.241735i	−0.222220	+	0.974996i	$0.571330\pi$
$138$	11.9410	+	4.67021i	1.01648	+	0.397554i
$139$	−4.54414	−	7.87068i	−0.385429	−	0.667582i	0.606400	−	0.795160i	$-0.292613\pi$
$139$	−4.54414	−	7.87068i	−0.385429	−	0.667582i	−0.991829	+	0.127578i	$0.959280\pi$
$140$	−0.176418	−	0.305566i	−0.0149101	−	0.0258250i
$141$	12.8497	+	16.0740i	1.08214	+	1.35368i
$142$	6.28096	+	3.62631i	0.527086	+	0.304313i
$143$	0.476301	+	2.03883i	0.0398303	+	0.170495i
$144$	−3.42547	−	11.0127i	−0.285456	−	0.917722i
$145$	−5.75631	−	5.75631i	−0.478036	−	0.478036i
$146$	17.2707	+	9.97124i	1.42933	+	0.825226i
$147$	−0.861960	−	0.634584i	−0.0710932	−	0.0523396i
$148$	0.00250539	−	0.00935024i	0.000205942	−	0.000768585i
$149$	15.3575	+	4.11502i	1.25813	+	0.337116i	0.825473	−	0.564441i	$-0.190908\pi$
$149$	15.3575	+	4.11502i	1.25813	+	0.337116i	0.432660	+	0.901557i	$0.357575\pi$
$150$	−3.64074	+	0.553152i	−0.297265	+	0.0451647i
$151$	−2.92070	−	10.9002i	−0.237683	−	0.887047i	−0.976921	−	0.213602i	$-0.931481\pi$
$151$	−2.92070	−	10.9002i	−0.237683	−	0.887047i	0.739237	−	0.673445i	$-0.235186\pi$
$152$		−	24.1864i		−	1.96177i
$153$	5.04184	−	5.45962i	0.407608	−	0.441384i
$154$	1.43922	−	1.43922i	0.115976	−	0.115976i
$155$	−1.49871	+	2.59584i	−0.120379	+	0.208503i
$156$	0.289733	−	0.368033i	0.0231972	−	0.0294662i
$157$	9.86279	+	17.0829i	0.787137	+	1.36336i	0.927714	+	0.373291i	$0.121771\pi$
$157$	9.86279	+	17.0829i	0.787137	+	1.36336i	−0.140578	+	0.990070i	$0.544896\pi$
$158$	11.6712	+	3.12729i	0.928511	+	0.248794i
$159$	17.1380	−	7.50133i	1.35913	−	0.594894i
$160$	0.683861	+	0.394828i	0.0540640	+	0.0312139i
$161$	9.53094	−	9.53094i	0.751144	−	0.751144i
$162$	11.7666	−	4.17984i	0.924474	−	0.328399i
$163$	−14.9232	+	14.9232i	−1.16887	+	1.16887i	−0.186399	+	0.982474i	$0.559682\pi$
$163$	−14.9232	+	14.9232i	−1.16887	+	1.16887i	−0.982474	+	0.186399i	$0.940318\pi$
$164$	0.139913	−	0.0374896i	0.0109254	−	0.00292745i
$165$	−0.751001	−	1.71578i	−0.0584654	−	0.133573i
$166$	4.56548	−	2.63588i	0.354350	−	0.204584i
$167$	5.59173	−	20.8686i	0.432701	−	1.61486i	−0.313807	−	0.949487i	$-0.601604\pi$
$167$	5.59173	−	20.8686i	0.432701	−	1.61486i	0.746508	−	0.665377i	$-0.231729\pi$
$168$	−12.5196	−	1.39565i	−0.965911	−	0.107677i
$169$	−12.9729	−	0.839222i	−0.997914	−	0.0645556i
$170$		−	6.40010i		−	0.490866i
$171$	25.1834	−	1.00189i	1.92582	−	0.0766163i
$172$	0.453489			0.0345782
$173$	−2.73891	+	4.74393i	−0.208235	+	0.360674i	−0.951159	−	0.308702i	$-0.900105\pi$
$173$	−2.73891	+	4.74393i	−0.208235	+	0.360674i	0.742923	+	0.669376i	$0.233439\pi$
$174$	−10.3864	+	1.57805i	−0.787390	+	0.119631i
$175$	−1.00195	+	3.73932i	−0.0757401	+	0.282666i
$176$	−0.577789	+	2.15634i	−0.0435525	+	0.162540i
$177$	−4.35044	+	0.660980i	−0.326999	+	0.0496823i
$178$	0.402780	−	0.697635i	0.0301896	−	0.0522900i
$179$	0.978949			0.0731701			0.0365850	−	0.999331i	$-0.488352\pi$
$179$	0.978949			0.0731701			0.0365850	+	0.999331i	$0.488352\pi$
$180$	−0.194911	+	0.370907i	−0.0145278	+	0.0276458i
$181$			19.5295i			1.45162i	0.687896	+	0.725809i	$0.258534\pi$
$181$			19.5295i			1.45162i	−0.687896	+	0.725809i	$0.741466\pi$
$182$	5.96208	+	11.1429i	0.441938	+	0.825965i
$183$	−3.62592	−	0.404205i	−0.268036	−	0.0298797i
$184$	−3.97559	+	14.8371i	−0.293084	+	1.09381i
$185$	0.208135	−	0.120167i	0.0153024	−	0.00883484i
$186$	1.55105	+	3.54361i	0.113728	+	0.259830i
$187$	−1.38947	+	0.372307i	−0.101608	+	0.0272258i
$188$	−0.630122	+	0.630122i	−0.0459564	+	0.0459564i
$189$	0.934573	−	13.0936i	0.0679802	−	0.952416i
$190$	15.3480	−	15.3480i	1.11346	−	1.11346i
$191$	2.56922	+	1.48334i	0.185902	+	0.107331i	0.590063	−	0.807357i	$-0.299103\pi$
$191$	2.56922	+	1.48334i	0.185902	+	0.107331i	−0.404161	+	0.914688i	$0.632436\pi$
$192$	13.1334	−	5.74851i	0.947819	−	0.414863i
$193$	−14.2562	−	3.81994i	−1.02618	−	0.274965i	−0.293808	−	0.955865i	$-0.594923\pi$
$193$	−14.2562	−	3.81994i	−1.02618	−	0.274965i	−0.732377	+	0.680899i	$0.761589\pi$
$194$	1.99813	+	3.46086i	0.143457	+	0.248475i
$195$	11.5476	−	1.37461i	0.826941	−	0.0984377i
$196$	0.0231749	−	0.0401402i	0.00165535	−	0.00286716i
$197$	1.86253	−	1.86253i	0.132700	−	0.132700i	−0.637637	−	0.770337i	$-0.720088\pi$
$197$	1.86253	−	1.86253i	0.132700	−	0.132700i	0.770337	+	0.637637i	$0.220088\pi$
$198$	−2.35771	−	0.532274i	−0.167555	−	0.0378270i
$199$			7.56229i			0.536077i	0.963408	+	0.268038i	$0.0863754\pi$
$199$			7.56229i			0.536077i	−0.963408	+	0.268038i	$0.913625\pi$
$200$	−1.14182	−	4.26135i	−0.0807392	−	0.301323i
$201$	−11.4366	+	1.73761i	−0.806674	+	0.122561i
$202$	25.2408	+	6.76325i	1.77594	+	0.475861i
$203$	−2.85838	+	10.6676i	−0.200619	+	0.748720i
$204$	0.259152	+	0.190790i	0.0181442	+	0.0133580i
$205$	3.11445	+	1.79813i	0.217522	+	0.125587i
$206$	4.62888	+	4.62888i	0.322509	+	0.322509i
$207$	−15.6134	−	3.52487i	−1.08521	−	0.244996i
$208$	−11.7740	−	7.31458i	−0.816377	−	0.507175i
$209$	−4.22489	−	2.43924i	−0.292242	−	0.168726i
$210$	−7.05898	−	8.83026i	−0.487116	−	0.609346i
$211$	2.62836	+	4.55246i	0.180944	+	0.313404i	0.942202	−	0.335045i	$-0.108751\pi$
$211$	2.62836	+	4.55246i	0.180944	+	0.313404i	−0.761258	+	0.648449i	$0.775418\pi$
$212$	0.405051	+	0.701570i	0.0278190	+	0.0481840i
$213$	−8.43204	−	3.29784i	−0.577754	−	0.225964i
$214$	−20.7607	+	5.56282i	−1.41917	+	0.380266i
$215$	7.96136	+	7.96136i	0.542961	+	0.542961i
$216$	6.53839	+	13.4549i	0.444881	+	0.915491i
$217$	4.06642			0.276047
$218$	−6.40851	+	11.0999i	−0.434039	+	0.751778i
$219$	−23.1855	−	9.06805i	−1.56673	−	0.612762i
$220$	0.0702382	−	0.0405520i	0.00473546	−	0.00273402i
$221$	0.288442	−	8.92693i	0.0194027	−	0.600490i
$222$	0.0343619	−	0.308243i	0.00230622	−	0.0206879i
$223$	15.4587	−	4.14213i	1.03519	−	0.277378i	0.299070	−	0.954231i	$-0.403324\pi$
$223$	15.4587	−	4.14213i	1.03519	−	0.277378i	0.736118	+	0.676853i	$0.236657\pi$
$224$		−	1.07128i		−	0.0715777i
$225$	4.38972	−	1.36542i	0.292648	−	0.0910277i
$226$	−0.672826	−	0.672826i	−0.0447557	−	0.0447557i
$227$	6.16612	+	23.0123i	0.409260	+	1.52738i	0.796062	+	0.605215i	$0.206913\pi$
$227$	6.16612	+	23.0123i	0.409260	+	1.52738i	−0.386802	+	0.922163i	$0.626420\pi$
$228$	0.163937	+	1.07900i	0.0108570	+	0.0714585i
$229$	−2.25011	−	0.602914i	−0.148691	−	0.0398417i	0.183706	−	0.982981i	$-0.441191\pi$
$229$	−2.25011	−	0.602914i	−0.148691	−	0.0398417i	−0.332397	+	0.943140i	$0.607857\pi$
$230$	−11.9380	+	6.89242i	−0.787170	+	0.454473i
$231$	−1.50642	+	2.04619i	−0.0991154	+	0.134629i
$232$	−3.25742	−	12.1569i	−0.213860	−	0.798138i
$233$	19.7159			1.29163			0.645817	−	0.763492i	$-0.276517\pi$
$233$	19.7159			1.29163			0.645817	+	0.763492i	$0.276517\pi$
$234$	7.40655	−	13.0525i	0.484181	−	0.853268i
$235$	−22.1246			−1.44325
$236$	−0.0493178	−	0.184056i	−0.00321031	−	0.0119811i
$237$	−14.9912	−	1.67117i	−0.973781	−	0.108554i
$238$	−7.51938	+	4.34131i	−0.487409	+	0.281406i
$239$	−25.9095	−	6.94244i	−1.67595	−	0.449069i	−0.709244	−	0.704963i	$-0.750963\pi$
$239$	−25.9095	−	6.94244i	−1.67595	−	0.449069i	−0.966705	+	0.255894i	$0.917630\pi$
$240$	11.5476	+	4.51637i	0.745396	+	0.291531i
$241$	−1.82813	−	6.82268i	−0.117760	−	0.439488i	0.881718	−	0.471776i	$-0.156387\pi$
$241$	−1.82813	−	6.82268i	−0.117760	−	0.439488i	−0.999479	+	0.0322888i	$0.989720\pi$
$242$	−10.4609	−	10.4609i	−0.672455	−	0.672455i
$243$	−13.7387	+	7.36528i	−0.881340	+	0.472483i
$244$		−	0.157986i		−	0.0101140i
$245$	1.11155	−	0.297838i	0.0710142	−	0.0190282i
$246$	4.25156	−	1.86092i	0.271070	−	0.118648i
$247$	22.0993	−	20.7158i	1.40614	−	1.31812i
$248$	−4.01326	+	2.31706i	−0.254842	+	0.147133i
$249$	−5.14050	+	4.10935i	−0.325766	+	0.260420i
$250$	8.43864	−	14.6161i	0.533706	−	0.924406i
$251$	−11.3132			−0.714084			−0.357042	−	0.934088i	$-0.616215\pi$
$251$	−11.3132			−0.714084			−0.357042	+	0.934088i	$0.616215\pi$
$252$	0.567985	−	0.0225965i	0.0357797	−	0.00142344i
$253$	2.19081	+	2.19081i	0.137735	+	0.137735i
$254$	15.2207	−	4.07838i	0.955034	−	0.255901i
$255$	1.20014	+	7.89909i	0.0751558	+	0.494660i
$256$	0.898756	+	1.55669i	0.0561722	+	0.0972932i
$257$	2.57789	+	4.46503i	0.160804	+	0.278521i	0.935157	−	0.354233i	$-0.115258\pi$
$257$	2.57789	+	4.46503i	0.160804	+	0.278521i	−0.774353	+	0.632754i	$0.781925\pi$
$258$	14.3651	−	2.18254i	0.894329	−	0.135879i
$259$	−0.282364	−	0.163023i	−0.0175453	−	0.0101298i
$260$	0.114559	+	0.490374i	0.00710463	+	0.0304117i
$261$	12.5231	−	3.89529i	0.775160	−	0.241112i
$262$	−6.98321	−	6.98321i	−0.431424	−	0.431424i
$263$	13.1228	+	7.57645i	0.809186	+	0.467184i	0.846673	−	0.532113i	$-0.178602\pi$
$263$	13.1228	+	7.57645i	0.809186	+	0.467184i	−0.0374869	+	0.999297i	$0.511935\pi$
$264$	0.320808	−	2.87780i	0.0197444	−	0.177116i
$265$	−5.20562	+	19.4276i	−0.319778	+	1.19343i
$266$	−28.4430	−	7.62127i	−1.74395	−	0.467290i
$267$	−0.366296	+	0.936559i	−0.0224170	+	0.0573165i
$268$	−0.129648	−	0.483854i	−0.00791952	−	0.0295561i
$269$			7.15433i			0.436207i	0.975926	+	0.218104i	$0.0699870\pi$
$269$			7.15433i			0.436207i	−0.975926	+	0.218104i	$0.930013\pi$
$270$	−4.38904	+	12.6872i	−0.267108	+	0.772119i
$271$	8.75359	−	8.75359i	0.531743	−	0.531743i	−0.389348	−	0.921091i	$-0.627300\pi$
$271$	8.75359	−	8.75359i	0.531743	−	0.531743i	0.921091	+	0.389348i	$0.127300\pi$
$272$	4.76159	−	8.24731i	0.288714	−	0.500067i
$273$	−9.44797	−	12.6347i	−0.571817	−	0.764685i
$274$	−7.58383	−	13.1356i	−0.458156	−	0.793549i
$275$	−0.859530	−	0.230310i	−0.0518316	−	0.0138882i
$276$	0.0767916	−	0.688858i	0.00462231	−	0.0414644i
$277$	8.10357	+	4.67860i	0.486897	+	0.281110i	0.723286	−	0.690549i	$-0.242631\pi$
$277$	8.10357	+	4.67860i	0.486897	+	0.281110i	−0.236390	+	0.971658i	$0.575964\pi$
$278$	8.91623	−	8.91623i	0.534760	−	0.534760i
$279$	−2.57882	−	4.08272i	−0.154390	−	0.244426i
$280$	9.57664	−	9.57664i	0.572314	−	0.572314i
$281$	−1.59694	+	0.427898i	−0.0952653	+	0.0255263i	−0.306137	−	0.951988i	$-0.599037\pi$
$281$	−1.59694	+	0.427898i	−0.0952653	+	0.0255263i	0.210871	+	0.977514i	$0.432370\pi$
$282$	−16.9276	+	22.9929i	−1.00802	+	1.36921i
$283$	−18.0723	+	10.4340i	−1.07429	+	0.620239i	−0.929349	−	0.369202i	$-0.879631\pi$
$283$	−18.0723	+	10.4340i	−1.07429	+	0.620239i	−0.144937	+	0.989441i	$0.546298\pi$
$284$	0.101474	−	0.378707i	0.00602139	−	0.0224721i
$285$	−16.0647	+	21.8207i	−0.951588	+	1.29255i
$286$	−2.56133	+	1.37046i	−0.151455	+	0.0810370i
$287$		−	4.87882i		−	0.287987i
$288$	−1.07557	+	0.679376i	−0.0633786	+	0.0400326i
$289$	−10.8636			−0.639035
$290$	5.64735	−	9.78149i	0.331624	−	0.574389i
$291$	−3.11509	−	3.89675i	−0.182610	−	0.228431i
$292$	0.279023	−	1.04133i	0.0163286	−	0.0609391i
$293$	3.22539	−	12.0373i	0.188430	−	0.703228i	−0.805441	−	0.592676i	$-0.798071\pi$
$293$	3.22539	−	12.0373i	0.188430	−	0.703228i	0.993870	−	0.110552i	$-0.0352620\pi$
$294$	0.540921	−	1.38305i	0.0315472	−	0.0806609i
$295$	2.36545	−	4.09707i	0.137722	−	0.238541i
$296$	0.371564			0.0215967
$297$	3.00972	+	0.214824i	0.174642	+	0.0124653i
$298$			22.0593i			1.27786i
$299$	−16.9619	+	9.07559i	−0.980932	+	0.524855i
$300$	0.0798226	+	0.182367i	0.00460856	+	0.0105290i
$301$	3.95333	−	14.7540i	0.227866	−	0.850408i
$302$	13.5593	−	7.82846i	0.780249	−	0.450477i
$303$	−32.4207	−	3.61416i	−1.86252	−	0.207628i
$304$	31.1965	−	8.35907i	1.78924	−	0.479426i
$305$	2.77357	−	2.77357i	0.158814	−	0.158814i
$306$	9.12731	+	4.79637i	0.521774	+	0.274190i
$307$	1.75829	−	1.75829i	0.100351	−	0.100351i	−0.655149	−	0.755500i	$-0.727394\pi$
$307$	1.75829	−	1.75829i	0.100351	−	0.100351i	0.755500	+	0.655149i	$0.227394\pi$
$308$	−0.0952878	−	0.0550145i	−0.00542953	−	0.00313474i
$309$	−6.58102	−	4.84501i	−0.374381	−	0.275623i
$310$	−4.01705	−	1.07636i	−0.228153	−	0.0611334i
$311$	−4.59266	−	7.95471i	−0.260426	−	0.451070i	0.705929	−	0.708282i	$-0.250530\pi$
$311$	−4.59266	−	7.95471i	−0.260426	−	0.451070i	−0.966355	+	0.257212i	$0.917196\pi$
$312$	16.5237	+	7.08602i	0.935472	+	0.401167i
$313$	6.90548	−	11.9606i	0.390321	−	0.676056i	−0.602171	−	0.798367i	$-0.705697\pi$
$313$	6.90548	−	11.9606i	0.390321	−	0.676056i	0.992492	+	0.122312i	$0.0390307\pi$
$314$	−19.3522	+	19.3522i	−1.09211	+	1.09211i
$315$	10.3681	+	9.57473i	0.584178	+	0.539475i
$316$		−	0.653185i		−	0.0367445i
$317$	−3.88035	−	14.4817i	−0.217942	−	0.813372i	−0.985110	−	0.171925i	$-0.945001\pi$
$317$	−3.88035	−	14.4817i	−0.217942	−	0.813372i	0.767168	−	0.641447i	$-0.221665\pi$
$318$	16.2072	+	20.2740i	0.908855	+	1.13691i
$319$	−2.45209	−	0.657035i	−0.137291	−	0.0367869i
$320$	−3.98923	+	14.8880i	−0.223005	+	0.832265i
$321$	24.5800	−	10.7587i	1.37192	−	0.600494i
$322$	16.1956	+	9.35052i	0.902545	+	0.521084i
$323$	14.7156	+	14.7156i	0.818799	+	0.818799i
$324$	−0.382888	−	0.555931i	−0.0212716	−	0.0308851i
$325$	2.91564	−	4.69317i	0.161731	−	0.260330i
$326$	−25.3584	−	14.6407i	−1.40447	−	0.810872i
$327$	5.82803	−	14.9013i	0.322291	−	0.824045i
$328$	2.77996	+	4.81504i	0.153498	+	0.265866i
$329$	15.0076	+	25.9938i	0.827393	+	1.43309i
$330$	2.02975	−	1.62260i	0.111734	−	0.0893211i
$331$	4.99190	−	1.33757i	0.274379	−	0.0735198i	−0.119006	−	0.992894i	$-0.537971\pi$
$331$	4.99190	−	1.33757i	0.274379	−	0.0735198i	0.393385	+	0.919374i	$0.371304\pi$
$332$	−0.201514	−	0.201514i	−0.0110595	−	0.0110595i
$333$	0.0153915	+	0.386881i	0.000843451	+	0.0212010i
$334$	29.9754			1.64018
$335$	6.21836	−	10.7705i	0.339745	−	0.588456i
$336$	−2.52676	−	16.6307i	−0.137846	−	0.907276i
$337$	26.9201	−	15.5423i	1.46643	−	0.846644i	0.467135	−	0.884186i	$-0.345286\pi$
$337$	26.9201	−	15.5423i	1.46643	−	0.846644i	0.999295	+	0.0375421i	$0.0119528\pi$
$338$	−3.53382	−	17.6872i	−0.192214	−	0.962056i
$339$	0.956578	+	0.704242i	0.0519542	+	0.0382492i
$340$	−0.334191	+	0.0895463i	−0.0181241	+	0.00485633i
$341$			0.934719i			0.0506179i
$342$	10.3860	+	33.3902i	0.561609	+	1.80554i
$343$	−13.6083	−	13.6083i	−0.734779	−	0.734779i
$344$	4.50523	+	16.8138i	0.242906	+	0.906537i
$345$	13.4416	−	10.7453i	0.723671	−	0.578509i
$346$	−7.34119	−	1.96707i	−0.394665	−	0.105750i
$347$	−21.9784	+	12.6892i	−1.17986	+	0.681193i	−0.955982	−	0.293424i	$-0.905205\pi$
$347$	−21.9784	+	12.6892i	−1.17986	+	0.681193i	−0.223879	+	0.974617i	$0.571872\pi$
$348$	0.227720	+	0.520262i	0.0122071	+	0.0278890i
$349$	2.97003	+	11.0843i	0.158982	+	0.593330i	0.998731	+	0.0503551i	$0.0160353\pi$
$349$	2.97003	+	11.0843i	0.158982	+	0.593330i	−0.839749	+	0.542974i	$0.817298\pi$
$350$	−5.37111			−0.287098
$351$	−6.69366	+	17.4984i	−0.357281	+	0.933997i
$352$	0.246247			0.0131250
$353$	−2.53473	−	9.45974i	−0.134910	−	0.503491i	−0.999998	−	0.00187142i	$-0.999404\pi$
$353$	−2.53473	−	9.45974i	−0.134910	−	0.503491i	0.865088	−	0.501620i	$-0.167262\pi$
$354$	−2.44805	−	5.59296i	−0.130112	−	0.297262i
$355$	8.42997	−	4.86704i	0.447416	−	0.258316i
$356$	−0.0420635	−	0.0112709i	−0.00222936	−	0.000597356i
$357$	8.46643	−	6.76813i	0.448091	−	0.358208i
$358$	0.351537	+	1.31195i	0.0185793	+	0.0693389i
$359$	−2.89742	−	2.89742i	−0.152920	−	0.152920i	0.626501	−	0.779421i	$-0.284487\pi$
$359$	−2.89742	−	2.89742i	−0.152920	−	0.152920i	−0.779421	+	0.626501i	$0.784487\pi$
$360$	−15.6883	−	3.54177i	−0.826845	−	0.186668i
$361$			51.5787i			2.71467i
$362$	−26.1728	+	7.01298i	−1.37561	+	0.368594i
$363$	14.8727	+	10.9494i	0.780612	+	0.574695i
$364$	0.498425	−	0.467223i	0.0261246	−	0.0244891i
$365$	23.1798	−	13.3829i	1.21329	−	0.700492i
$366$	−0.760352	−	5.00448i	−0.0397442	−	0.261588i
$367$	−15.2555	+	26.4233i	−0.796330	+	1.37928i	0.125661	+	0.992073i	$0.459895\pi$
$367$	−15.2555	+	26.4233i	−0.796330	+	1.37928i	−0.921991	+	0.387211i	$0.873438\pi$
$368$	−20.5115			−1.06923
$369$	−4.89837	+	3.09402i	−0.254999	+	0.161068i
$370$	0.235784	+	0.235784i	0.0122578	+	0.0122578i
$371$	26.3563	−	7.06214i	1.36835	−	0.366648i
$372$	0.163334	−	0.130570i	0.00846847	−	0.00676976i
$373$	5.28160	+	9.14799i	0.273471	+	0.473665i	0.969748	−	0.244108i	$-0.0784950\pi$
$373$	5.28160	+	9.14799i	0.273471	+	0.473665i	−0.696277	+	0.717773i	$0.745162\pi$
$374$	−0.997907	−	1.72843i	−0.0516005	−	0.0893748i
$375$	−7.67426	+	19.6218i	−0.396297	+	1.01327i
$376$	−29.6227	−	17.1027i	−1.52767	−	0.882004i
$377$	8.31781	−	13.3888i	0.428389	−	0.689559i
$378$	17.8832	−	3.44937i	0.919810	−	0.177416i
$379$	−5.66843	−	5.66843i	−0.291168	−	0.291168i	0.546374	−	0.837541i	$-0.316008\pi$
$379$	−5.66843	−	5.66843i	−0.291168	−	0.291168i	−0.837541	+	0.546374i	$0.816008\pi$
$380$	−1.01616	−	0.586680i	−0.0521279	−	0.0300961i
$381$	−18.0208	+	7.88777i	−0.923236	+	0.404103i
$382$	−1.06532	+	3.97584i	−0.0545067	+	0.203422i
$383$	−16.5127	−	4.42456i	−0.843759	−	0.226085i	−0.189052	−	0.981967i	$-0.560541\pi$
$383$	−16.5127	−	4.42456i	−0.843759	−	0.226085i	−0.654707	+	0.755882i	$0.727208\pi$
$384$	11.5029	+	14.3892i	0.587003	+	0.734297i
$385$	−0.707032	−	2.63868i	−0.0360337	−	0.134479i
$386$		−	20.4774i		−	1.04227i
$387$	−17.3203	+	5.38744i	−0.880439	+	0.273859i
$388$	0.152757	−	0.152757i	0.00775508	−	0.00775508i
$389$	6.23895	−	10.8062i	0.316327	−	0.547895i	−0.663392	−	0.748272i	$-0.730884\pi$
$389$	6.23895	−	10.8062i	0.316327	−	0.547895i	0.979719	+	0.200378i	$0.0642169\pi$
$390$	5.98891	+	14.9821i	0.303260	+	0.758648i
$391$	−6.60843	−	11.4461i	−0.334203	−	0.578856i
$392$	1.71849	+	0.460468i	0.0867968	+	0.0232571i
$393$	9.92824	+	7.30928i	0.500814	+	0.368704i
$394$	3.16492	+	1.82727i	0.159447	+	0.0920565i
$395$	11.4672	−	11.4672i	0.576977	−	0.576977i
$396$	0.00519409	+	0.130559i	0.000261013	+	0.00656081i
$397$	10.1001	−	10.1001i	0.506908	−	0.506908i	−0.406668	−	0.913576i	$-0.633310\pi$
$397$	10.1001	−	10.1001i	0.506908	−	0.506908i	0.913576	+	0.406668i	$0.133310\pi$
$398$	−10.1347	+	2.71559i	−0.508008	+	0.136120i
$399$	36.5338	+	4.07267i	1.82898	+	0.203888i
$400$	5.10182	−	2.94554i	0.255091	−	0.147277i
$401$	−3.39506	+	12.6705i	−0.169541	+	0.632736i	0.827876	+	0.560911i	$0.189549\pi$
$401$	−3.39506	+	12.6705i	−0.169541	+	0.632736i	−0.997417	+	0.0718250i	$0.977118\pi$
$402$	−6.43551	−	14.7029i	−0.320974	−	0.733316i
$403$	−5.55451	−	1.68237i	−0.276690	−	0.0838046i
$404$		−	1.41261i		−	0.0702802i
$405$	3.03791	−	16.4817i	0.150955	−	0.818984i
$406$	−15.3228			−0.760459
$407$	0.0374729	−	0.0649050i	0.00185746	−	0.00321722i
$408$	−4.49925	+	11.5038i	−0.222746	+	0.569525i
$409$	−1.02921	+	3.84105i	−0.0508910	+	0.189928i	−0.986692	−	0.162601i	$-0.948012\pi$
$409$	−1.02921	+	3.84105i	−0.0508910	+	0.189928i	0.935801	+	0.352529i	$0.114678\pi$
$410$	−1.29140	+	4.81958i	−0.0637778	+	0.238022i
$411$	11.8232	+	14.7900i	0.583197	+	0.729536i
$412$	0.176940	−	0.306468i	0.00871719	−	0.0150986i
$413$	−6.41811			−0.315815
$414$	−0.882813	−	22.1904i	−0.0433879	−	1.09060i
$415$		−	7.07548i		−	0.347322i
$416$	−0.443210	+	1.46330i	−0.0217302	+	0.0717444i
$417$	−9.33256	+	12.6765i	−0.457018	+	0.620770i
$418$	1.75185	−	6.53798i	0.0856856	−	0.319783i
$419$	−14.6526	+	8.45967i	−0.715826	+	0.413282i	−0.813214	−	0.581964i	$-0.802284\pi$
$419$	−14.6526	+	8.45967i	−0.715826	+	0.413282i	0.0973888	+	0.995246i	$0.468951\pi$
$420$	−0.362321	+	0.492143i	−0.0176794	+	0.0240141i
$421$	11.1833	−	2.99656i	0.545040	−	0.146043i	0.0242157	−	0.999707i	$-0.492291\pi$
$421$	11.1833	−	2.99656i	0.545040	−	0.146043i	0.520825	+	0.853664i	$0.325624\pi$
$422$	−5.15721	+	5.15721i	−0.251049	+	0.251049i
$423$	16.5806	−	31.5523i	0.806178	−	1.53413i
$424$	−21.9877	+	21.9877i	−1.06782	+	1.06782i
$425$	3.28743	+	1.89800i	0.159464	+	0.0920665i
$426$	1.39174	−	12.4846i	0.0674300	−	0.604880i
$427$	−5.13999	−	1.37726i	−0.248742	−	0.0666501i
$428$	0.580942	+	1.00622i	0.0280809	+	0.0486376i
$429$	2.90424	−	2.17174i	0.140218	−	0.104852i
$430$	−7.81066	+	13.5285i	−0.376663	+	0.652400i
$431$	−1.33558	+	1.33558i	−0.0643328	+	0.0643328i	−0.738541	−	0.674208i	$-0.764485\pi$
$431$	−1.33558	+	1.33558i	−0.0643328	+	0.0643328i	0.674208	+	0.738541i	$0.264485\pi$
$432$	−15.0949	+	13.0836i	−0.726254	+	0.629486i
$433$		−	17.9232i		−	0.861335i	−0.902511	−	0.430668i	$-0.858278\pi$
$433$		−	17.9232i		−	0.861335i	0.902511	−	0.430668i	$-0.141722\pi$
$434$	1.46024	+	5.44968i	0.0700936	+	0.261593i
$435$	−5.13581	+	13.1314i	−0.246243	+	0.629604i
$436$	0.669261	+	0.179328i	0.0320518	+	0.00858825i
$437$	11.6012	−	43.2964i	0.554963	−	2.07115i
$438$	3.82686	−	34.3287i	0.182854	−	1.64029i
$439$	−20.5855	−	11.8850i	−0.982491	−	0.567241i	−0.0794696	−	0.996837i	$-0.525323\pi$
$439$	−20.5855	−	11.8850i	−0.982491	−	0.567241i	−0.903021	+	0.429596i	$0.858656\pi$
$440$	2.20131	+	2.20131i	0.104944	+	0.104944i
$441$	−0.408264	+	1.80841i	−0.0194411	+	0.0861146i
$442$	12.0671	−	2.81907i	0.573976	−	0.134089i
$443$	10.0212	+	5.78573i	0.476121	+	0.274889i	0.718799	−	0.695218i	$-0.244692\pi$
$443$	10.0212	+	5.78573i	0.476121	+	0.274889i	−0.242678	+	0.970107i	$0.578026\pi$
$444$	−0.0165762	+	0.00251849i	−0.000786670	+	0.000119522i
$445$	−0.540590	−	0.936329i	−0.0256264	−	0.0443862i
$446$	11.1023	+	19.2297i	0.525709	+	0.910555i
$447$	−4.13653	−	27.2258i	−0.195651	−	1.28774i
$448$	20.1976	−	5.41194i	0.954249	−	0.255690i
$449$	13.0185	+	13.0185i	0.614380	+	0.614380i	0.944084	−	0.329704i	$-0.106949\pi$
$449$	13.0185	+	13.0185i	0.614380	+	0.614380i	−0.329704	+	0.944084i	$0.606949\pi$
$450$	3.40622	+	5.39264i	0.160571	+	0.254211i
$451$	1.12146			0.0528074
$452$	−0.0257189	+	0.0445464i	−0.00120971	+	0.00209529i
$453$	−15.2671	+	12.2046i	−0.717309	+	0.573422i
$454$	−28.6260	+	16.5273i	−1.34349	+	0.775662i
$455$	16.9527	+	0.547768i	0.794756	+	0.0256797i
$456$	−38.3768	+	16.7976i	−1.79716	+	0.786621i
$457$	−12.1771	+	3.26284i	−0.569620	+	0.152629i	−0.532122	−	0.846668i	$-0.678605\pi$
$457$	−12.1771	+	3.26284i	−0.569620	+	0.152629i	−0.0374975	+	0.999297i	$0.511939\pi$
$458$		−	3.23202i		−	0.151022i
$459$	−12.1645	−	4.20820i	−0.567788	−	0.196422i
$460$	0.526928	+	0.526928i	0.0245681	+	0.0245681i
$461$	−0.673315	−	2.51285i	−0.0313594	−	0.117035i	0.948472	−	0.316861i	$-0.102629\pi$
$461$	−0.673315	−	2.51285i	−0.0313594	−	0.117035i	−0.979831	+	0.199826i	$0.935962\pi$
$462$	−3.28318	−	1.28408i	−0.152747	−	0.0597408i
$463$	1.84699	+	0.494900i	0.0858370	+	0.0229999i	0.301482	−	0.953472i	$-0.402519\pi$
$463$	1.84699	+	0.494900i	0.0858370	+	0.0229999i	−0.215645	+	0.976472i	$0.569185\pi$
$464$	14.5546	−	8.40310i	0.675680	−	0.390104i
$465$	5.15973	+	0.575190i	0.239277	+	0.0266738i
$466$	7.07993	+	26.4226i	0.327971	+	1.22401i
$467$	−32.4561			−1.50189			−0.750945	−	0.660364i	$-0.770402\pi$
$467$	−32.4561			−1.50189			−0.750945	+	0.660364i	$0.770402\pi$
$468$	−0.785184	−	0.204122i	−0.0362952	−	0.00943554i
$469$	−16.8721			−0.779083
$470$	−7.94487	−	29.6507i	−0.366470	−	1.36768i
$471$	20.2558	−	27.5136i	0.933338	−	1.26776i
$472$	6.33421	−	3.65706i	0.291556	−	0.168330i
$473$	3.39140	+	0.908723i	0.155937	+	0.0417831i
$474$	−3.14364	−	20.6908i	−0.144392	−	0.950359i
$475$	3.33198	+	12.4351i	0.152882	+	0.570562i
$476$	0.331895	+	0.331895i	0.0152124	+	0.0152124i
$477$	−23.8049	−	21.9833i	−1.08995	−	1.00655i
$478$		−	37.2161i		−	1.70222i
$479$	−21.8311	+	5.84963i	−0.997489	+	0.267276i	−0.720393	−	0.693566i	$-0.756039\pi$
$479$	−21.8311	+	5.84963i	−0.997489	+	0.267276i	−0.277096	+	0.960842i	$0.589372\pi$
$480$	0.151531	−	1.35930i	0.00691640	−	0.0620434i
$481$	0.318248	+	0.339501i	0.0145108	+	0.0154799i
$482$	8.48705	−	4.90000i	0.386575	−	0.223189i
$483$	−21.7422	−	8.50355i	−0.989304	−	0.386925i
$484$	−0.399871	+	0.692598i	−0.0181760	+	0.0314817i
$485$	5.36356			0.243547
$486$	−14.8042	−	15.7673i	−0.671533	−	0.715221i
$487$	19.7664	+	19.7664i	0.895702	+	0.895702i	0.995052	−	0.0993507i	$-0.0316766\pi$
$487$	19.7664	+	19.7664i	0.895702	+	0.895702i	−0.0993507	+	0.995052i	$0.531677\pi$
$488$	5.85756	−	1.56953i	0.265159	−	0.0710492i
$489$	34.0431	+	13.3145i	1.53948	+	0.602104i
$490$	0.798306	+	1.38271i	0.0360638	+	0.0624643i
$491$	10.6371	+	18.4241i	0.480047	+	0.831467i	0.999738	−	0.0228880i	$-0.00728611\pi$
$491$	10.6371	+	18.4241i	0.480047	+	0.831467i	−0.519691	+	0.854355i	$0.673953\pi$
$492$	−0.156656	−	0.195965i	−0.00706260	−	0.00883479i
$493$	9.37847	+	5.41466i	0.422385	+	0.243864i
$494$	35.6984	+	22.1777i	1.60615	+	0.997822i
$495$	−2.20087	+	2.38325i	−0.0989219	+	0.107119i
$496$	−4.37565	−	4.37565i	−0.196473	−	0.196473i
$497$	−11.4364	−	6.60282i	−0.512993	−	0.296177i
$498$	−7.35315	−	5.41347i	−0.329503	−	0.242583i
$499$	1.63212	−	6.09117i	0.0730639	−	0.272678i	−0.919723	−	0.392567i	$-0.871587\pi$
$499$	1.63212	−	6.09117i	0.0730639	−	0.272678i	0.992787	+	0.119889i	$0.0382538\pi$
$500$	−0.881273	−	0.236136i	−0.0394117	−	0.0105603i
$501$	−36.9960	+	5.62096i	−1.65286	+	0.251126i
$502$	−4.06254	−	15.1616i	−0.181320	−	0.676695i
$503$			26.0031i			1.15942i	0.814823	+	0.579710i	$0.196834\pi$
$503$			26.0031i			1.15942i	−0.814823	+	0.579710i	$0.803166\pi$
$504$	6.48050	+	20.8344i	0.288664	+	0.928036i
$505$	24.7996	−	24.7996i	1.10357	−	1.10357i
$506$	−2.14934	+	3.72276i	−0.0955497	+	0.165497i
$507$	7.67817	+	21.1671i	0.340999	+	0.940063i
$508$	−0.425918	−	0.737712i	−0.0188971	−	0.0327307i
$509$	14.5263	+	3.89230i	0.643865	+	0.172523i	0.565954	−	0.824437i	$-0.308508\pi$
$509$	14.5263	+	3.89230i	0.643865	+	0.172523i	0.0779116	+	0.996960i	$0.475175\pi$
$510$	−10.1551	+	4.44493i	−0.449677	+	0.196825i
$511$	−31.4466	−	18.1557i	−1.39112	−	0.803162i
$512$	−16.8049	+	16.8049i	−0.742678	+	0.742678i
$513$	−19.0798	−	39.2630i	−0.842394	−	1.73351i
$514$	−5.05818	+	5.05818i	−0.223107	+	0.223107i
$515$	8.48661	−	2.27398i	0.373965	−	0.100204i
$516$	−0.314952	−	0.719557i	−0.0138650	−	0.0316767i
$517$	−5.97502	+	3.44968i	−0.262781	+	0.151717i
$518$	0.117082	−	0.436956i	0.00514429	−	0.0191987i
$519$	9.42945	+	1.05116i	0.413907	+	0.0461410i
$520$	−17.0432	+	9.11910i	−0.747395	+	0.399899i
$521$			39.3731i			1.72497i	0.506086	+	0.862483i	$0.331092\pi$
$521$			39.3731i			1.72497i	−0.506086	+	0.862483i	$0.668908\pi$
$522$	9.71734	+	15.3842i	0.425316	+	0.673350i
$523$	22.2613			0.973418			0.486709	−	0.873564i	$-0.338197\pi$
$523$	22.2613			0.973418			0.486709	+	0.873564i	$0.338197\pi$
$524$	−0.266934	+	0.462344i	−0.0116611	+	0.0201976i
$525$	6.62909	−	1.00718i	0.289317	−	0.0439571i
$526$	−5.44135	+	20.3074i	−0.237254	+	0.885445i
$527$	1.03202	−	3.85153i	0.0449553	−	0.167775i
$528$	3.82277	−	0.580809i	0.166365	−	0.0252765i
$529$	−2.73355	+	4.73465i	−0.118850	+	0.205854i
$530$	−27.9056			−1.21214
$531$	4.07020	+	6.44384i	0.176632	+	0.279639i
$532$			1.59183i			0.0690144i
$533$	−2.01847	+	6.66419i	−0.0874297	+	0.288658i
$534$	−1.38668	−	0.154583i	−0.0600075	−	0.00668944i
$535$	−7.46612	+	27.8639i	−0.322789	+	1.20466i
$536$	16.6516	−	9.61379i	0.719238	−	0.415252i
$537$	−0.679888	−	1.55331i	−0.0293393	−	0.0670303i
$538$	−9.58799	+	2.56909i	−0.413368	+	0.110762i
$539$	0.253748	−	0.253748i	0.0109297	−	0.0109297i
$540$	0.723891	+	0.0516688i	0.0311513	+	0.00222347i
$541$	−1.29549	+	1.29549i	−0.0556976	+	0.0556976i	−0.734407	−	0.678709i	$-0.762540\pi$
$541$	−1.29549	+	1.29549i	−0.0556976	+	0.0556976i	0.678709	+	0.734407i	$0.262540\pi$
$542$	14.8747	+	8.58788i	0.638921	+	0.368881i
$543$	30.9877	−	13.5634i	1.32981	−	0.582062i
$544$	−1.01467	−	0.271879i	−0.0435034	−	0.0116567i
$545$	8.60117	+	14.8977i	0.368434	+	0.638146i
$546$	13.5398	−	17.1989i	0.579451	−	0.736046i
$547$	0.758155	−	1.31316i	0.0324164	−	0.0561468i	−0.849362	−	0.527811i	$-0.823013\pi$
$547$	0.758155	−	1.31316i	0.0324164	−	0.0561468i	0.881778	+	0.471664i	$0.156346\pi$
$548$	−0.579786	+	0.579786i	−0.0247672	+	0.0247672i
$549$	1.87687	+	6.03401i	0.0801029	+	0.257525i
$550$		−	1.23462i		−	0.0526443i
$551$	9.50556	+	35.4752i	0.404950	+	1.51129i
$552$	26.3033	−	3.99637i	1.11954	−	0.170097i
$553$	−21.2510	−	5.69420i	−0.903686	−	0.242142i
$554$	−3.36014	+	12.5402i	−0.142759	+	0.532782i
$555$	−0.335222	−	0.246794i	−0.0142294	−	0.0104758i
$556$	−0.590325	−	0.340824i	−0.0250354	−	0.0144542i
$557$	2.26150	+	2.26150i	0.0958227	+	0.0958227i	0.753393	−	0.657570i	$-0.228416\pi$
$557$	2.26150	+	2.26150i	0.0958227	+	0.0958227i	−0.657570	+	0.753393i	$0.728416\pi$
$558$	4.54548	−	4.92214i	0.192426	−	0.208371i
$559$	−11.5041	+	18.5176i	−0.486571	+	0.783211i
$560$	15.6621	+	9.04252i	0.661845	+	0.382116i
$561$	1.55574	+	1.94612i	0.0656835	+	0.0821652i
$562$	−1.14691	−	1.98651i	−0.0483795	−	0.0837957i
$563$	13.3642	+	23.1475i	0.563234	+	0.975550i	0.997212	+	0.0746266i	$0.0237765\pi$
$563$	13.3642	+	23.1475i	0.563234	+	0.975550i	−0.433977	+	0.900924i	$0.642890\pi$
$564$	1.43745	+	0.562198i	0.0605275	+	0.0236728i
$565$	−1.23356	+	0.330532i	−0.0518964	+	0.0139056i
$566$	−20.4730	−	20.4730i	−0.860546	−	0.860546i
$567$	−21.4248	+	7.61069i	−0.899757	+	0.319619i
$568$	15.0492			0.631451
$569$	11.5338	−	19.9772i	0.483523	−	0.837487i	−0.516298	−	0.856409i	$-0.672690\pi$
$569$	11.5338	−	19.9772i	0.483523	−	0.837487i	0.999821	+	0.0189222i	$0.00602348\pi$
$570$	−35.0122	−	13.6936i	−1.46650	−	0.573560i
$571$	22.8795	−	13.2095i	0.957477	−	0.552800i	0.0620817	−	0.998071i	$-0.480226\pi$
$571$	22.8795	−	13.2095i	0.957477	−	0.552800i	0.895396	+	0.445271i	$0.146893\pi$
$572$	0.107397	+	0.114569i	0.00449050	+	0.00479038i
$573$	0.569289	−	5.10680i	0.0237824	−	0.213340i
$574$	6.53843	−	1.75197i	0.272909	−	0.0731257i
$575$		−	8.17600i		−	0.340963i
$576$	−18.2425	−	16.8465i	−0.760103	−	0.701937i
$577$	10.5178	+	10.5178i	0.437860	+	0.437860i	0.891291	−	0.453431i	$-0.149800\pi$
$577$	10.5178	+	10.5178i	0.437860	+	0.437860i	−0.453431	+	0.891291i	$0.649800\pi$
$578$	−3.90108	−	14.5590i	−0.162264	−	0.605576i
$579$	3.83991	+	25.2735i	0.159581	+	1.05033i
$580$	−0.589770	−	0.158028i	−0.0244889	−	0.00656177i
$581$	−8.31287	+	4.79944i	−0.344876	+	0.199114i
$582$	4.10367	−	5.57405i	0.170103	−	0.231052i
$583$	1.62332	+	6.05833i	0.0672312	+	0.250910i
$584$	41.3807			1.71235
$585$	−10.2010	−	17.3681i	−0.421760	−	0.718081i
$586$	17.2903			0.714254
$587$	−3.48982	−	13.0242i	−0.144040	−	0.537566i	−0.999796	−	0.0201860i	$-0.993574\pi$
$587$	−3.48982	−	13.0242i	−0.144040	−	0.537566i	0.855756	−	0.517380i	$-0.173093\pi$
$588$	−0.0797861	−	0.00889430i	−0.00329033	−	0.000366795i
$589$	11.7112	−	6.76145i	0.482551	−	0.278601i
$590$	6.34018	+	1.69885i	0.261021	+	0.0699404i
$591$	−4.24884	−	1.66176i	−0.174774	−	0.0683555i
$592$	0.128417	+	0.479257i	0.00527789	+	0.0196973i
$593$	−25.0781	−	25.0781i	−1.02983	−	1.02983i	−0.999541	−	0.0302931i	$-0.990356\pi$
$593$	−25.0781	−	25.0781i	−1.02983	−	1.02983i	−0.0302931	−	0.999541i	$-0.509644\pi$
$594$	0.792882	+	4.11067i	0.0325323	+	0.168663i
$595$			11.6534i			0.477741i
$596$	1.15186	−	0.308640i	0.0471820	−	0.0126424i
$597$	11.9992	−	5.25207i	0.491094	−	0.214953i
$598$	−18.2538	−	19.4728i	−0.746452	−	0.796300i
$599$	23.6772	−	13.6700i	0.967424	−	0.558543i	0.0689743	−	0.997618i	$-0.478027\pi$
$599$	23.6772	−	13.6700i	0.967424	−	0.558543i	0.898450	+	0.439076i	$0.144694\pi$
$600$	−5.96853	+	4.77129i	−0.243664	+	0.194787i
$601$	16.1113	−	27.9056i	0.657194	−	1.13829i	−0.324145	−	0.946007i	$-0.605077\pi$
$601$	16.1113	−	27.9056i	0.657194	−	1.13829i	0.981339	−	0.192285i	$-0.0615899\pi$
$602$	21.1925			0.863741
$603$	10.6999	+	16.9398i	0.435733	+	0.689841i
$604$	−0.598488	−	0.598488i	−0.0243521	−	0.0243521i
$605$	−19.1792	+	5.13904i	−0.779744	+	0.208932i
$606$	−6.79860	−	44.7470i	−0.276174	−	1.81772i
$607$	−3.41216	−	5.91003i	−0.138495	−	0.239881i	0.788432	−	0.615122i	$-0.210893\pi$
$607$	−3.41216	−	5.91003i	−0.138495	−	0.239881i	−0.926927	+	0.375241i	$0.877560\pi$
$608$	−1.78127	−	3.08525i	−0.0722399	−	0.125123i
$609$	18.9116	−	2.87332i	0.766337	−	0.116433i
$610$	4.71303	+	2.72107i	0.190825	+	0.110173i
$611$	−9.74528	−	41.7151i	−0.394252	−	1.68761i
$612$	0.122746	−	0.543705i	0.00496172	−	0.0219780i
$613$	3.21162	+	3.21162i	0.129716	+	0.129716i	0.768984	−	0.639268i	$-0.220763\pi$
$613$	3.21162	+	3.21162i	0.129716	+	0.129716i	−0.639268	+	0.768984i	$0.720763\pi$
$614$	2.98779	+	1.72500i	0.120578	+	0.0696155i
$615$	0.690102	−	6.19055i	0.0278276	−	0.249627i
$616$	1.09309	−	4.07948i	0.0440420	−	0.164367i
$617$	26.5681	+	7.11890i	1.06959	+	0.286596i	0.750325	−	0.661069i	$-0.229897\pi$
$617$	26.5681	+	7.11890i	1.06959	+	0.286596i	0.319266	+	0.947665i	$0.396564\pi$
$618$	4.12991	−	10.5595i	0.166129	−	0.424765i
$619$	10.4331	+	38.9370i	0.419343	+	1.56501i	0.775975	+	0.630764i	$0.217258\pi$
$619$	10.4331	+	38.9370i	0.419343	+	1.56501i	−0.356632	+	0.934245i	$0.616075\pi$
$620$			0.224816i			0.00902883i
$621$	5.25070	+	27.2221i	0.210703	+	1.09238i
$622$	9.01144	−	9.01144i	0.361326	−	0.361326i
$623$	−0.733385	+	1.27026i	−0.0293824	+	0.0508919i
$624$	−3.42904	+	23.7619i	−0.137271	+	0.951238i
$625$	−7.49492	−	12.9816i	−0.299797	−	0.519263i
$626$	18.5090	+	4.95947i	0.739768	+	0.198220i
$627$	−0.936155	+	8.39777i	−0.0373864	+	0.335374i
$628$	1.28127	+	0.739740i	0.0511282	+	0.0295189i
$629$	−0.226069	+	0.226069i	−0.00901397	+	0.00901397i
$630$	−9.10857	+	17.3333i	−0.362894	+	0.690574i
$631$	0.816658	−	0.816658i	0.0325107	−	0.0325107i	−0.690665	−	0.723175i	$-0.742682\pi$
$631$	0.816658	−	0.816658i	0.0325107	−	0.0325107i	0.723175	+	0.690665i	$0.242682\pi$
$632$	24.2178	−	6.48914i	0.963332	−	0.258124i
$633$	5.39802	−	7.33218i	0.214552	−	0.291428i
$634$	18.0144	−	10.4006i	0.715444	−	0.413062i
$635$	5.47379	−	20.4285i	0.217221	−	0.810679i
$636$	0.831878	−	1.12995i	0.0329861	−	0.0448053i
$637$	1.05117	+	1.96459i	0.0416488	+	0.0778399i
$638$		−	3.52215i		−	0.139443i
$639$	0.623393	+	15.6696i	0.0246611	+	0.619880i
$640$	−19.8056			−0.782886
$641$	4.43780	−	7.68649i	0.175283	−	0.303598i	−0.764976	−	0.644058i	$-0.777249\pi$
$641$	4.43780	−	7.68649i	0.175283	−	0.303598i	0.940259	+	0.340460i	$0.110583\pi$
$642$	23.2451	+	29.0779i	0.917411	+	1.14761i
$643$	−6.18198	+	23.0715i	−0.243794	+	0.909850i	0.730192	+	0.683242i	$0.239430\pi$
$643$	−6.18198	+	23.0715i	−0.243794	+	0.909850i	−0.973986	+	0.226609i	$0.927236\pi$
$644$	0.261654	−	0.976504i	0.0103106	−	0.0384797i
$645$	7.10317	−	18.1616i	0.279687	−	0.715114i
$646$	−14.4371	+	25.0057i	−0.568019	+	0.983837i
$647$	−24.8027			−0.975094			−0.487547	−	0.873097i	$-0.662108\pi$
$647$	−24.8027			−0.975094			−0.487547	+	0.873097i	$0.662108\pi$
$648$	16.8081	−	19.7191i	0.660285	−	0.774639i
$649$		−	1.47529i		−	0.0579100i
$650$	7.33663	+	2.22214i	0.287766	+	0.0871595i
$651$	−2.82416	−	6.45224i	−0.110688	−	0.252883i
$652$	−0.409687	+	1.52897i	−0.0160446	+	0.0598792i
$653$	−12.0674	+	6.96711i	−0.472233	+	0.272644i	−0.717174	−	0.696894i	$-0.754565\pi$
$653$	−12.0674	+	6.96711i	−0.472233	+	0.272644i	0.244941	+	0.969538i	$0.421231\pi$
$654$	22.0631	+	2.45952i	0.862735	+	0.0961748i
$655$	−12.8031	+	3.43057i	−0.500257	+	0.134043i
$656$	−5.24983	+	5.24983i	−0.204971	+	0.204971i
$657$	1.71414	+	43.0866i	0.0668750	+	1.68097i
$658$	−29.4469	+	29.4469i	−1.14796	+	1.14796i
$659$	−25.3331	−	14.6261i	−0.986837	−	0.569750i	−0.0825093	−	0.996590i	$-0.526293\pi$
$659$	−25.3331	−	14.6261i	−0.986837	−	0.569750i	−0.904327	+	0.426840i	$0.859627\pi$
$660$	−0.113125	−	0.0832841i	−0.00440340	−	0.00324183i
$661$	13.9045	+	3.72571i	0.540824	+	0.144913i	0.518882	−	0.854846i	$-0.326348\pi$
$661$	13.9045	+	3.72571i	0.540824	+	0.144913i	0.0219422	+	0.999759i	$0.493015\pi$
$662$	3.58515	+	6.20966i	0.139341	+	0.241345i
$663$	−14.3648	+	5.74215i	−0.557883	+	0.223007i
$664$	5.46946	−	9.47339i	0.212256	−	0.367639i
$665$	−27.9458	+	27.9458i	−1.08369	+	1.08369i
$666$	−0.512958	+	0.159555i	−0.0198767	+	0.00618263i
$667$		−	23.3247i		−	0.903136i
$668$	−0.419398	−	1.56521i	−0.0162270	−	0.0605599i
$669$	−17.3085	−	21.6517i	−0.669187	−	0.837103i
$670$	16.6673	+	4.46598i	0.643913	+	0.172536i
$671$	0.316580	−	1.18149i	0.0122214	−	0.0456110i
$672$	−1.69981	+	0.744011i	−0.0655715	+	0.0287008i
$673$	−24.8379	−	14.3402i	−0.957430	−	0.552773i	−0.0620491	−	0.998073i	$-0.519764\pi$
$673$	−24.8379	−	14.3402i	−0.957430	−	0.552773i	−0.895381	+	0.445300i	$0.853097\pi$
$674$	30.4962	+	30.4962i	1.17467	+	1.17467i
$675$	−5.21522	−	6.01693i	−0.200734	−	0.231592i
$676$	−0.874121	+	0.431992i	−0.0336200	+	0.0166151i
$677$	−42.5345	−	24.5573i	−1.63473	−	0.943813i	−0.982606	−	0.185702i	$-0.940544\pi$
$677$	−42.5345	−	24.5573i	−1.63473	−	0.943813i	−0.652126	−	0.758111i	$-0.726123\pi$
$678$	−0.600298	+	1.53486i	−0.0230543	+	0.0589461i
$679$	−3.63821	−	6.30156i	−0.139622	−	0.241832i
$680$	−6.64012	−	11.5010i	−0.254637	−	0.441044i
$681$	32.2314	−	25.7661i	1.23511	−	0.987358i
$682$	−1.25268	+	0.335654i	−0.0479676	+	0.0128529i
$683$	−10.5535	−	10.5535i	−0.403820	−	0.403820i	0.475757	−	0.879577i	$-0.342174\pi$
$683$	−10.5535	−	10.5535i	−0.403820	−	0.403820i	−0.879577	+	0.475757i	$0.842174\pi$
$684$	1.59821	−	1.00949i	0.0611090	−	0.0385990i
$685$	−20.3572			−0.777810
$686$	13.3507	−	23.1241i	0.509732	−	0.882881i
$687$	0.606066	+	3.98900i	0.0231229	+	0.152190i
$688$	−20.1300	+	11.6220i	−0.767448	+	0.443086i
$689$	−38.9230	−	1.25766i	−1.48285	−	0.0479130i
$690$	19.2273	+	14.1554i	0.731973	+	0.538886i
$691$	12.1723	−	3.26156i	0.463057	−	0.124076i	−0.0197455	−	0.999805i	$-0.506286\pi$
$691$	12.1723	−	3.26156i	0.463057	−	0.124076i	0.482802	+	0.875729i	$0.339619\pi$
$692$			0.410853i			0.0156183i
$693$	4.29293	+	0.969168i	0.163075	+	0.0368157i
$694$	−24.8980	−	24.8980i	−0.945116	−	0.945116i
$695$	−4.38019	−	16.3471i	−0.166150	−	0.620080i
$696$	−17.0272	+	13.6116i	−0.645413	+	0.515948i
$697$	−4.62100	−	1.23819i	−0.175033	−	0.0468999i
$698$	−13.7883	+	7.96068i	−0.521895	+	0.301316i
$699$	−13.6929	−	31.2835i	−0.517912	−	1.18325i
$700$	0.0751492	+	0.280461i	0.00284037	+	0.0106004i
$701$	−37.1825			−1.40437			−0.702183	−	0.711997i	$-0.747791\pi$
$701$	−37.1825			−1.40437			−0.702183	+	0.711997i	$0.747791\pi$
$702$	−25.8545	−	2.68700i	−0.975814	−	0.101414i
$703$	−1.08427			−0.0408939
$704$	1.24400	+	4.64269i	0.0468852	+	0.174978i
$705$	15.3657	+	35.1054i	0.578707	+	1.32215i
$706$	11.7674	−	6.79392i	0.442873	−	0.255693i
$707$	−45.9586	−	12.3146i	−1.72845	−	0.463138i
$708$	−0.257793	+	0.206082i	−0.00968846	+	0.00774503i
$709$	−4.18990	−	15.6369i	−0.157355	−	0.587257i	−0.998892	−	0.0470577i	$-0.985016\pi$
$709$	−4.18990	−	15.6369i	−0.157355	−	0.587257i	0.841537	−	0.540199i	$-0.181651\pi$
$710$	9.54982	+	9.54982i	0.358398	+	0.358398i
$711$	7.75983	+	24.9473i	0.291016	+	0.935598i
$712$		−	1.67154i		−	0.0626436i
$713$	−8.29561	+	2.22280i	−0.310673	+	0.0832446i
$714$	12.1107	+	8.91602i	0.453231	+	0.333674i
$715$	−0.125911	+	3.89680i	−0.00470882	+	0.145732i
$716$	0.0635872	−	0.0367121i	0.00237637	−	0.00137200i
$717$	6.97873	+	45.9326i	0.260625	+	1.71538i
$718$	2.84258	−	4.92348i	0.106084	−	0.183743i
$719$	21.1369			0.788272			0.394136	−	0.919052i	$-0.371044\pi$
$719$	21.1369			0.788272			0.394136	+	0.919052i	$0.371044\pi$
$720$	−0.853733	−	21.4594i	−0.0318168	−	0.799745i
$721$	−8.42830	−	8.42830i	−0.313886	−	0.313886i
$722$	−69.1241	+	18.5217i	−2.57253	+	0.689308i
$723$	−9.55598	+	7.63913i	−0.355391	+	0.284102i
$724$	0.732388	+	1.26853i	0.0272190	+	0.0471446i
$725$	3.34953	+	5.80155i	0.124398	+	0.215464i
$726$	−9.33331	+	23.8637i	−0.346391	+	0.885666i
$727$	−12.6008	−	7.27507i	−0.467337	−	0.269817i	0.247787	−	0.968815i	$-0.420297\pi$
$727$	−12.6008	−	7.27507i	−0.467337	−	0.269817i	−0.715124	+	0.698997i	$0.753630\pi$
$728$	22.2746	+	13.8381i	0.825553	+	0.512876i
$729$	21.2282	+	16.6842i	0.786231	+	0.617932i
$730$	26.2591	+	26.2591i	0.971892	+	0.971892i
$731$	−12.9710	−	7.48884i	−0.479751	−	0.276985i
$732$	−0.250678	+	0.109723i	−0.00926534	+	0.00405546i
$733$	−5.19118	+	19.3737i	−0.191741	+	0.715586i	0.801346	+	0.598201i	$0.204118\pi$
$733$	−5.19118	+	19.3737i	−0.191741	+	0.715586i	−0.993087	+	0.117384i	$0.962549\pi$
$734$	−40.8898	−	10.9564i	−1.50927	−	0.404408i
$735$	−1.24456	−	1.55686i	−0.0459064	−	0.0574255i
$736$	0.585585	+	2.18543i	0.0215850	+	0.0805562i
$737$		−	3.87828i		−	0.142858i
$738$	−5.90549	−	5.45359i	−0.217384	−	0.200749i
$739$	−10.3490	+	10.3490i	−0.380693	+	0.380693i	−0.871352	−	0.490659i	$-0.836756\pi$
$739$	−10.3490	+	10.3490i	−0.380693	+	0.380693i	0.490659	+	0.871352i	$0.336756\pi$
$740$	0.00901289	−	0.0156108i	0.000331320	−	0.000573864i
$741$	−48.2182	−	20.6779i	−1.77134	−	0.759620i
$742$	18.9289	+	32.7858i	0.694901	+	1.20360i
$743$	12.1675	+	3.26027i	0.446382	+	0.119608i	0.475006	−	0.879983i	$-0.342446\pi$
$743$	12.1675	+	3.26027i	0.446382	+	0.119608i	−0.0286240	+	0.999590i	$0.509113\pi$
$744$	6.46375	+	4.75868i	0.236972	+	0.174462i
$745$	25.6402	+	14.8034i	0.939385	+	0.542354i
$746$	−10.3632	+	10.3632i	−0.379425	+	0.379425i
$747$	10.0905	+	5.30251i	0.369191	+	0.194009i
$748$	−0.0762903	+	0.0762903i	−0.00278945	+	0.00278945i
$749$	37.8013	−	10.1288i	1.38123	−	0.370099i
$750$	−29.0523	−	3.23866i	−1.06084	−	0.118259i
$751$	32.9571	−	19.0278i	1.20262	−	0.694335i	0.241486	−	0.970404i	$-0.422365\pi$
$751$	32.9571	−	19.0278i	1.20262	−	0.694335i	0.961138	+	0.276070i	$0.0890320\pi$
$752$	11.8217	−	44.1194i	0.431095	−	1.60887i
$753$	7.85712	+	17.9508i	0.286329	+	0.654164i
$754$	20.9301	+	6.33938i	0.762230	+	0.230867i
$755$		−	21.0139i		−	0.764774i
$756$	−0.430324	−	0.885535i	−0.0156507	−	0.0322066i
$757$	−10.9910			−0.399476			−0.199738	−	0.979849i	$-0.564009\pi$
$757$	−10.9910			−0.399476			−0.199738	+	0.979849i	$0.564009\pi$
$758$	5.56112	−	9.63215i	0.201989	−	0.349855i
$759$	1.95465	−	4.99772i	0.0709493	−	0.181406i
$760$	11.6569	−	43.5040i	0.422839	−	1.57806i
$761$	−11.8082	+	44.0689i	−0.428048	+	1.59750i	0.329128	+	0.944285i	$0.393245\pi$
$761$	−11.8082	+	44.0689i	−0.428048	+	1.59750i	−0.757176	+	0.653211i	$0.773421\pi$
$762$	−17.0422	−	21.3185i	−0.617372	−	0.772287i
$763$	11.6687	−	20.2107i	0.422434	−	0.731678i
$764$	0.222510			0.00805013
$765$	11.7001	−	7.39026i	0.423017	−	0.267196i
$766$		−	23.7186i		−	0.856988i
$767$	8.76679	+	2.65531i	0.316550	+	0.0958777i
$768$	1.84583	−	2.50720i	0.0666056	−	0.0904709i
$769$	−1.65173	+	6.16433i	−0.0595628	+	0.222291i	−0.989291	−	0.145954i	$-0.953375\pi$
$769$	−1.65173	+	6.16433i	−0.0595628	+	0.222291i	0.929729	+	0.368246i	$0.120041\pi$
$770$	3.28238	−	1.89508i	0.118289	−	0.0682940i
$771$	5.29436	−	7.19137i	0.190672	−	0.258991i
$772$	−1.06926	+	0.286508i	−0.0384835	+	0.0103116i
$773$	18.2003	−	18.2003i	0.654621	−	0.654621i	−0.299482	−	0.954102i	$-0.596814\pi$
$773$	18.2003	−	18.2003i	0.654621	−	0.654621i	0.954102	+	0.299482i	$0.0968137\pi$
$774$	−13.4397	−	21.2774i	−0.483081	−	0.764801i
$775$	1.74416	−	1.74416i	0.0626522	−	0.0626522i
$776$	7.18129	+	4.14612i	0.257793	+	0.148837i
$777$	−0.0625665	+	0.561252i	−0.00224456	+	0.0201348i
$778$	16.7225	+	4.48077i	0.599529	+	0.160643i
$779$	−8.11226	−	14.0509i	−0.290652	−	0.503424i
$780$	0.698520	−	0.522340i	0.0250110	−	0.0187028i
$781$	1.51774	−	2.62881i	0.0543091	−	0.0940661i
$782$	12.9667	−	12.9667i	0.463687	−	0.463687i
$783$	−14.8781	−	17.1652i	−0.531700	−	0.613436i
$784$			2.37572i			0.0848470i
$785$	9.50695	+	35.4804i	0.339318	+	1.26635i
$786$	−6.23045	+	15.9302i	−0.222233	+	0.568213i
$787$	−35.2325	−	9.44053i	−1.25590	−	0.336519i	−0.431290	−	0.902213i	$-0.641941\pi$
$787$	−35.2325	−	9.44053i	−1.25590	−	0.336519i	−0.824615	+	0.565695i	$0.808608\pi$
$788$	0.0511320	−	0.190827i	0.00182150	−	0.00679794i
$789$	2.90776	−	26.0840i	0.103519	−	0.928616i
$790$	19.4858	+	11.2501i	0.693273	+	0.400261i
$791$	1.22509	+	1.22509i	0.0435591	+	0.0435591i
$792$	−4.78905	+	1.48963i	−0.170171	+	0.0529316i
$793$	6.45114	+	4.00778i	0.229087	+	0.142320i
$794$	17.1627	+	9.90887i	0.609080	+	0.351653i
$795$	34.4414	−	5.23283i	1.22151	−	0.185589i
$796$	0.283598	+	0.491206i	0.0100519	+	0.0174103i
$797$	−19.8552	−	34.3902i	−0.703306	−	1.21816i	−0.967299	−	0.253637i	$-0.918373\pi$
$797$	−19.8552	−	34.3902i	−0.703306	−	1.21816i	0.263993	−	0.964524i	$-0.414960\pi$
$798$	7.66111	+	50.4239i	0.271200	+	1.78499i
$799$	28.4290	−	7.61752i	1.00574	−	0.269489i
$800$	−0.459491	−	0.459491i	−0.0162454	−	0.0162454i
$801$	1.74045	−	0.0692412i	0.0614956	−	0.00244652i
$802$	−18.1998			−0.642656
$803$	4.17333	−	7.22841i	0.147273	−	0.255085i
$804$	−0.677695	+	0.541755i	−0.0239005	+	0.0191062i
$805$	21.7369	−	12.5498i	0.766123	−	0.442322i
$806$	0.260046	−	8.04809i	0.00915972	−	0.283482i
$807$	11.3519	−	4.96874i	0.399605	−	0.174908i
$808$	52.3747	−	14.0338i	1.84254	−	0.493706i
$809$		−	16.2621i		−	0.571744i	−0.958268	−	0.285872i	$-0.907717\pi$
$809$		−	16.2621i		−	0.571744i	0.958268	−	0.285872i	$-0.0922831\pi$
$810$	23.1792	−	1.84723i	0.814433	−	0.0649049i
$811$	14.1443	+	14.1443i	0.496673	+	0.496673i	0.910401	−	0.413728i	$-0.135774\pi$
$811$	14.1443	+	14.1443i	0.496673	+	0.496673i	−0.413728	+	0.910401i	$0.635774\pi$
$812$	0.214387	+	0.800105i	0.00752352	+	0.0280782i
$813$	−19.9689	−	7.80999i	−0.700339	−	0.273908i
$814$	0.100440	+	0.0269128i	0.00352042	+	0.000943293i
$815$	−34.0347	+	19.6499i	−1.19218	+	0.688308i
$816$	−16.3931	−	1.82745i	−0.573873	−	0.0639735i
$817$	−13.1468	−	49.0646i	−0.459949	−	1.71655i
$818$	−5.51723			−0.192905
$819$	−13.4859	+	23.7661i	−0.471236	+	0.830455i
$820$	0.269730			0.00941939
$821$	1.00290	+	3.74286i	0.0350013	+	0.130627i	0.981216	−	0.192913i	$-0.0617936\pi$
$821$	1.00290	+	3.74286i	0.0350013	+	0.130627i	−0.946214	+	0.323540i	$0.895127\pi$
$822$	−15.5754	+	21.1561i	−0.543253	+	0.737905i
$823$	−10.5722	+	6.10384i	−0.368522	+	0.212766i	−0.672813	−	0.739813i	$-0.734914\pi$
$823$	−10.5722	+	6.10384i	−0.368522	+	0.212766i	0.304290	+	0.952579i	$0.401581\pi$
$824$	13.1206	+	3.51565i	0.457077	+	0.122473i
$825$	0.231514	+	1.52378i	0.00806029	+	0.0530512i
$826$	−2.30472	−	8.60134i	−0.0801915	−	0.299279i
$827$	30.8023	+	30.8023i	1.07110	+	1.07110i	0.997271	+	0.0738304i	$0.0235224\pi$
$827$	30.8023	+	30.8023i	1.07110	+	1.07110i	0.0738304	+	0.997271i	$0.476478\pi$
$828$	−1.14635	+	0.356571i	−0.0398385	+	0.0123917i
$829$			3.44885i			0.119783i	0.998205	+	0.0598917i	$0.0190755\pi$
$829$			3.44885i			0.119783i	−0.998205	+	0.0598917i	$0.980924\pi$
$830$	9.48232	−	2.54078i	0.329136	−	0.0881918i
$831$	1.79560	−	16.1074i	0.0622886	−	0.558759i
$832$	−29.8279	−	0.963784i	−1.03410	−	0.0334132i
$833$	−1.32574	+	0.765414i	−0.0459340	+	0.0265200i
$834$	−20.3399	−	7.95510i	−0.704313	−	0.275463i
$835$	20.1157	−	34.8414i	0.696133	−	1.20574i
$836$	−0.365902			−0.0126550
$837$	−4.68710	+	6.92733i	−0.162010	+	0.239444i
$838$	−16.5991	−	16.5991i	−0.573405	−	0.573405i
$839$	8.31138	−	2.22703i	0.286941	−	0.0768855i	−0.112478	−	0.993654i	$-0.535879\pi$
$839$	8.31138	−	2.22703i	0.286941	−	0.0768855i	0.399419	+	0.916769i	$0.369212\pi$
$840$	−21.8464	−	8.54432i	−0.753774	−	0.294807i
$841$	−4.94438	−	8.56392i	−0.170496	−	0.295308i
$842$	8.03177	+	13.9114i	0.276793	+	0.479419i
$843$	1.78804	+	2.23670i	0.0615833	+	0.0770362i
$844$	0.341448	+	0.197135i	0.0117531	+	0.00678568i
$845$	−22.9299	−	7.76193i	−0.788811	−	0.267018i
$846$	48.2394	+	10.8905i	1.65851	+	0.374423i
$847$	19.0474	+	19.0474i	0.654476	+	0.654476i
$848$	−35.9597	−	20.7614i	−1.23486	−	0.712948i
$849$	29.1072	+	21.4290i	0.998956	+	0.735442i
$850$	−1.36313	+	5.08727i	−0.0467550	+	0.174492i
$851$	0.665143	+	0.178225i	0.0228008	+	0.00610946i
$852$	−0.671374	+	0.102005i	−0.0230009	+	0.00349462i
$853$	−2.33520	−	8.71509i	−0.0799557	−	0.298399i	0.914356	−	0.404912i	$-0.132698\pi$
$853$	−2.33520	−	8.71509i	−0.0799557	−	0.298399i	−0.994311	+	0.106513i	$0.966031\pi$
$854$		−	7.38301i		−	0.252641i
$855$	45.7803	+	10.3353i	1.56565	+	0.353460i
$856$	−31.5357	+	31.5357i	−1.07787	+	1.07787i
$857$	−16.7193	+	28.9586i	−0.571119	+	0.989208i	0.425332	+	0.905037i	$0.360157\pi$
$857$	−16.7193	+	28.9586i	−0.571119	+	0.989208i	−0.996451	+	0.0841703i	$0.973176\pi$
$858$	3.95339	+	3.11230i	0.134967	+	0.106252i
$859$	14.8413	+	25.7059i	0.506379	+	0.877075i	0.999973	+	0.00738198i	$0.00234978\pi$
$859$	14.8413	+	25.7059i	0.506379	+	0.877075i	−0.493593	+	0.869693i	$0.664317\pi$
$860$	0.815691	+	0.218564i	0.0278148	+	0.00745296i
$861$	−7.74128	+	3.38838i	−0.263822	+	0.115476i
$862$	−2.26951	−	1.31030i	−0.0772998	−	0.0446290i
$863$	14.5403	−	14.5403i	0.494958	−	0.494958i	−0.414906	−	0.909864i	$-0.636186\pi$
$863$	14.5403	−	14.5403i	0.494958	−	0.494958i	0.909864	+	0.414906i	$0.136186\pi$
$864$	1.82497	+	1.23479i	0.0620867	+	0.0420084i
$865$	−7.21286	+	7.21286i	−0.245245	+	0.245245i
$866$	24.0201	−	6.43617i	0.816236	−	0.218710i
$867$	7.54486	+	17.2374i	0.256237	+	0.585413i
$868$	0.264133	−	0.152497i	0.00896525	−	0.00517609i
$869$	1.30888	−	4.88482i	0.0444009	−	0.165706i
$870$	−19.4426	−	2.16739i	−0.659164	−	0.0734815i
$871$	23.0464	+	6.98037i	0.780898	+	0.236521i
$872$			26.5954i			0.900633i
$873$	−4.01956	+	7.64907i	−0.136042	+	0.258882i
$874$	62.1904			2.10362
$875$	−15.3651	+	26.6132i	−0.519437	+	0.899691i
$876$	−1.84607	+	0.280481i	−0.0623730	+	0.00947659i
$877$	−3.39820	+	12.6822i	−0.114749	+	0.428249i	−0.999268	−	0.0382552i	$-0.987820\pi$
$877$	−3.39820	+	12.6822i	−0.114749	+	0.428249i	0.884519	+	0.466504i	$0.154487\pi$
$878$	8.53574	−	31.8558i	0.288067	−	1.07508i
$879$	−21.3399	+	3.24225i	−0.719775	+	0.109358i
$880$	−2.07854	+	3.60014i	−0.0700675	+	0.121361i
$881$	−17.1547			−0.577956			−0.288978	−	0.957336i	$-0.593315\pi$
$881$	−17.1547			−0.577956			−0.288978	+	0.957336i	$0.593315\pi$
$882$	−2.57017	+	0.102251i	−0.0865422	+	0.00344296i
$883$		−	50.8183i		−	1.71017i	−0.518486	−	0.855086i	$-0.673504\pi$
$883$		−	50.8183i		−	1.71017i	0.518486	−	0.855086i	$-0.326496\pi$
$884$	−0.316038	−	0.590662i	−0.0106295	−	0.0198661i
$885$	−8.14370	−	0.907833i	−0.273748	−	0.0305165i
$886$	−4.15527	+	15.5077i	−0.139599	+	0.520991i
$887$	5.22557	−	3.01699i	0.175458	−	0.101300i	−0.409699	−	0.912221i	$-0.634366\pi$
$887$	5.22557	−	3.01699i	0.175458	−	0.101300i	0.585157	+	0.810920i	$0.301033\pi$
$888$	−0.258054	−	0.589565i	−0.00865973	−	0.0197845i
$889$	−27.7140	+	7.42596i	−0.929499	+	0.249059i
$890$	1.06071	−	1.06071i	0.0355552	−	0.0355552i
$891$	−1.74941	−	4.92476i	−0.0586076	−	0.164986i
$892$	0.848774	−	0.848774i	0.0284191	−	0.0284191i
$893$	86.4426	+	49.9077i	2.89269	+	1.67010i
$894$	35.0017	−	15.3203i	1.17063	−	0.512389i
$895$	1.76084	+	0.471815i	0.0588582	+	0.0157710i
$896$	13.4345	+	23.2693i	0.448816	+	0.777372i
$897$	26.1805	+	20.6106i	0.874143	+	0.688168i
$898$	−12.7720	+	22.1218i	−0.426209	+	0.738215i
$899$	4.97579	−	4.97579i	0.165952	−	0.165952i
$900$	0.233927	−	0.253311i	0.00779757	−	0.00844371i
$901$		−	26.7558i		−	0.891364i
$902$	0.402712	+	1.50294i	0.0134088	+	0.0500425i
$903$	−26.1560	+	3.97399i	−0.870418	+	0.132246i
$904$	−1.90713	−	0.511014i	−0.0634302	−	0.0169961i
$905$	−9.41245	+	35.1278i	−0.312881	+	1.16769i
$906$	−21.8386	−	16.0778i	−0.725537	−	0.534148i
$907$	−16.7652	−	9.67937i	−0.556678	−	0.321398i	0.195133	−	0.980777i	$-0.437486\pi$
$907$	−16.7652	−	9.67937i	−0.556678	−	0.321398i	−0.751811	+	0.659378i	$0.770820\pi$
$908$	1.26351	+	1.26351i	0.0419312	+	0.0419312i
$909$	16.7818	+	53.9525i	0.556618	+	1.78949i
$910$	5.35357	+	22.9162i	0.177469	+	0.759664i
$911$	5.50989	+	3.18114i	0.182551	+	0.105396i	0.588491	−	0.808504i	$-0.299722\pi$
$911$	5.50989	+	3.18114i	0.182551	+	0.105396i	−0.405940	+	0.913900i	$0.633056\pi$
$912$	−34.9297	−	43.6944i	−1.15664	−	1.44687i
$913$	−1.10321	−	1.91082i	−0.0365110	−	0.0632389i
$914$	−8.74549	−	15.1476i	−0.289275	−	0.501039i
$915$	−6.32713	−	2.47459i	−0.209168	−	0.0818075i
$916$	−0.168765	+	0.0452205i	−0.00557615	+	0.00149413i
$917$	12.7151	+	12.7151i	0.419889	+	0.419889i
$918$	1.27147	−	17.8135i	0.0419647	−	0.587935i
$919$	−33.5884			−1.10798			−0.553989	−	0.832524i	$-0.686895\pi$
$919$	−33.5884			−1.10798			−0.553989	+	0.832524i	$0.686895\pi$
$920$	−14.3018	+	24.7714i	−0.471516	+	0.816690i
$921$	−4.01104	−	1.56875i	−0.132168	−	0.0516921i
$922$	3.12585	−	1.80471i	0.102944	−	0.0594349i
$923$	12.8898	+	13.7506i	0.424273	+	0.452606i
$924$	−0.0211140	+	0.189402i	−0.000694598	+	0.00623088i
$925$	−0.191035	+	0.0511876i	−0.00628119	+	0.00168304i
$926$			2.65299i			0.0871827i
$927$	−3.11708	+	13.8071i	−0.102378	+	0.453484i
$928$	−1.31085	−	1.31085i	−0.0430306	−	0.0430306i
$929$	−9.26760	−	34.5872i	−0.304060	−	1.13477i	−0.933751	−	0.357922i	$-0.883485\pi$
$929$	−9.26760	−	34.5872i	−0.304060	−	1.13477i	0.629691	−	0.776845i	$-0.283181\pi$
$930$	1.08199	+	7.12144i	0.0354799	+	0.233521i
$931$	−5.01476	−	1.34370i	−0.164352	−	0.0440380i
$932$	1.28064	−	0.739379i	0.0419488	−	0.0242192i
$933$	−9.43221	+	12.8118i	−0.308797	+	0.419441i
$934$	−11.6549	−	43.4966i	−0.381359	−	1.42325i
$935$	−2.67868			−0.0876021
$936$	−0.232381	−	31.1397i	−0.00759563	−	1.01783i
$937$	9.21461			0.301028			0.150514	−	0.988608i	$-0.451907\pi$
$937$	9.21461			0.301028			0.150514	+	0.988608i	$0.451907\pi$
$938$	−6.05873	−	22.6115i	−0.197824	−	0.738291i
$939$	−23.7740	−	2.65025i	−0.775836	−	0.0864877i
$940$	−1.43710	+	0.829707i	−0.0468729	+	0.0270621i
$941$	33.1984	+	8.89549i	1.08224	+	0.289985i	0.755512	−	0.655135i	$-0.227388\pi$
$941$	33.1984	+	8.89549i	1.08224	+	0.289985i	0.326725	+	0.945119i	$0.394055\pi$
$942$	44.1466	+	17.2661i	1.43837	+	0.562560i
$943$	2.66688	+	9.95292i	0.0868455	+	0.324112i
$944$	6.90618	+	6.90618i	0.224777	+	0.224777i
$945$	7.99159	−	23.1010i	0.259967	−	0.751475i
$946$			4.87136i			0.158382i
$947$	42.7727	−	11.4609i	1.38993	−	0.372429i	0.515209	−	0.857064i	$-0.327714\pi$
$947$	42.7727	−	11.4609i	1.38993	−	0.372429i	0.874717	+	0.484635i	$0.161048\pi$
$948$	−1.03642	+	0.453642i	−0.0336613	+	0.0147336i
$949$	35.4430	+	37.8099i	1.15053	+	1.22736i
$950$	−15.4686	+	8.93082i	−0.501869	+	0.289754i
$951$	−20.2833	+	16.2146i	−0.657732	+	0.525796i
$952$	−9.00824	+	15.6027i	−0.291959	+	0.505687i
$953$	−42.2017			−1.36705			−0.683523	−	0.729929i	$-0.739553\pi$
$953$	−42.2017			−1.36705			−0.683523	+	0.729929i	$0.739553\pi$
$954$	20.9130	−	39.7967i	0.677084	−	1.28846i
$955$	3.90634	+	3.90634i	0.126406	+	0.126406i
$956$	−1.94330	+	0.520705i	−0.0628507	+	0.0168408i
$957$	0.660470	+	4.34708i	0.0213500	+	0.140521i
$958$	−15.6790	−	27.1568i	−0.506564	−	0.877395i
$959$	13.8087	+	23.9174i	0.445906	+	0.772332i
$960$	26.3935	−	4.01008i	0.851848	−	0.129425i
$961$	24.6029	+	14.2045i	0.793643	+	0.458210i
$962$	−0.340706	+	0.548418i	−0.0109848	+	0.0176817i
$963$	−34.1420	−	31.5294i	−1.10021	−	1.01602i
$964$	−0.374607	−	0.374607i	−0.0120653	−	0.0120653i
$965$	−23.8016	−	13.7419i	−0.766201	−	0.442366i
$966$	3.58863	−	32.1918i	0.115462	−	1.03575i
$967$	5.94903	−	22.2021i	0.191308	−	0.713971i	−0.801884	−	0.597480i	$-0.796169\pi$
$967$	5.94903	−	22.2021i	0.191308	−	0.713971i	0.993192	−	0.116491i	$-0.0371646\pi$
$968$	−29.6516	−	7.94513i	−0.953039	−	0.255366i
$969$	13.1294	−	33.5696i	0.421776	−	1.07841i
$970$	1.92604	+	7.18806i	0.0618413	+	0.230795i
$971$		−	40.4677i		−	1.29867i	−0.760503	−	0.649335i	$-0.775047\pi$
$971$		−	40.4677i		−	1.29867i	0.760503	−	0.649335i	$-0.224953\pi$
$972$	−0.616184	+	0.993633i	−0.0197641	+	0.0318708i
$973$	−16.2348	+	16.2348i	−0.520462	+	0.520462i
$974$	−19.3922	+	33.5883i	−0.621367	+	1.07624i
$975$	−9.47166	−	1.36684i	−0.303336	−	0.0437738i
$976$	4.04887	+	7.01285i	0.129601	+	0.224476i
$977$	−46.9130	−	12.5703i	−1.50088	−	0.402160i	−0.587486	−	0.809234i	$-0.699882\pi$
$977$	−46.9130	−	12.5703i	−1.50088	−	0.402160i	−0.913395	+	0.407075i	$0.866549\pi$
$978$	−5.61894	+	50.4046i	−0.179674	+	1.61176i
$979$	−0.291986	−	0.168578i	−0.00933190	−	0.00538777i
$980$	0.0610308	−	0.0610308i	0.00194956	−	0.00194956i
$981$	−27.6917	+	1.10168i	−0.884129	+	0.0351739i
$982$	−20.8716	+	20.8716i	−0.666038	+	0.666038i
$983$	−12.8749	+	3.44981i	−0.410645	+	0.110032i	−0.458227	−	0.888835i	$-0.651515\pi$
$983$	−12.8749	+	3.44981i	−0.410645	+	0.110032i	0.0475818	+	0.998867i	$0.484849\pi$
$984$	5.70937	−	7.75509i	0.182008	−	0.247223i
$985$	4.24779	−	2.45246i	0.135346	−	0.0781420i
$986$	−3.88877	+	14.5131i	−0.123844	+	0.462191i
$987$	30.8219	−	41.8656i	0.981072	−	1.33260i
$988$	0.658572	−	2.17435i	0.0209520	−	0.0691752i
$989$			32.2596i			1.02580i
$990$	−3.98427	−	2.09372i	−0.126629	−	0.0665429i
$991$	36.7939			1.16880			0.584398	−	0.811467i	$-0.301331\pi$
$991$	36.7939			1.16880			0.584398	+	0.811467i	$0.301331\pi$
$992$	−0.341291	+	0.591134i	−0.0108360	+	0.0187685i
$993$	−5.58926	−	6.99175i	−0.177370	−	0.221877i
$994$	4.74210	−	17.6978i	0.150410	−	0.561339i
$995$	−3.64472	+	13.6023i	−0.115546	+	0.431222i
$996$	−0.179792	+	0.459698i	−0.00569692	+	0.0145661i
$997$	−19.1997	+	33.2548i	−0.608059	+	1.05319i	0.383501	+	0.923541i	$0.374718\pi$
$997$	−19.1997	+	33.2548i	−0.608059	+	1.05319i	−0.991560	+	0.129649i	$0.958615\pi$
$998$	8.74928			0.276954
$999$	0.603180	−	0.293114i	0.0190838	−	0.00927372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.z.b.47.8	yes	44
3.2	odd	2		351.2.bc.b.8.4		44
9.4	even	3		351.2.bc.b.125.4		44
9.5	odd	6	inner	117.2.z.b.86.8	yes	44
13.5	odd	4	inner	117.2.z.b.83.8	yes	44
39.5	even	4		351.2.bc.b.278.4		44
117.5	even	12	inner	117.2.z.b.5.8	✓	44
117.31	odd	12		351.2.bc.b.44.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.z.b.5.8	✓	44	117.5	even	12	inner
117.2.z.b.47.8	yes	44	1.1	even	1	trivial
117.2.z.b.83.8	yes	44	13.5	odd	4	inner
117.2.z.b.86.8	yes	44	9.5	odd	6	inner
351.2.bc.b.8.4		44	3.2	odd	2
351.2.bc.b.44.4		44	117.31	odd	12
351.2.bc.b.125.4		44	9.4	even	3
351.2.bc.b.278.4		44	39.5	even	4

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.359097 + 1.34017i) q^{2} +(-0.694508 - 1.58671i) q^{3} +(0.0649546 - 0.0375016i) q^{4} +(1.79870 + 0.481960i) q^{5} +(1.87706 - 1.50054i) q^{6} +(-0.653846 - 2.44019i) q^{7} +(2.03572 + 2.03572i) q^{8} +(-2.03532 + 2.20397i) q^{9} +2.58363i q^{10} +(0.560908 - 0.150295i) q^{11} +(-0.104616 - 0.0770192i) q^{12} +(-0.116440 + 3.60367i) q^{13} +(3.03546 - 1.75253i) q^{14} +(-0.484480 - 3.18875i) q^{15} +(-1.92218 + 3.32932i) q^{16} -2.47718 q^{17} +(-3.68456 - 1.93622i) q^{18} +(-5.94048 - 5.94048i) q^{19} +(0.134908 - 0.0361485i) q^{20} +(-3.41777 + 2.73220i) q^{21} +(0.402841 + 0.697740i) q^{22} +(2.66773 + 4.62064i) q^{23} +(1.81628 - 4.64394i) q^{24} +(-1.32709 - 0.766195i) q^{25} +(-4.87133 + 1.13802i) q^{26} +(4.91061 + 1.69879i) q^{27} +(-0.133981 - 0.133981i) q^{28} +(-3.78595 - 2.18582i) q^{29} +(4.09948 - 1.79435i) q^{30} +(-0.416610 + 1.55481i) q^{31} +(0.409606 + 0.109754i) q^{32} +(-0.628030 - 0.785620i) q^{33} +(-0.889546 - 3.31983i) q^{34} -4.70429i q^{35} +(-0.0495508 + 0.219486i) q^{36} +(0.0912609 - 0.0912609i) q^{37} +(5.82803 - 10.0944i) q^{38} +(5.79886 - 2.31802i) q^{39} +(2.68052 + 4.64280i) q^{40} +(1.86543 + 0.499840i) q^{41} +(-4.88891 - 3.59927i) q^{42} +(5.23622 + 3.02313i) q^{43} +(0.0307973 - 0.0307973i) q^{44} +(-4.72315 + 2.98334i) q^{45} +(-5.23446 + 5.23446i) q^{46} +(-11.4764 + 3.07508i) q^{47} +(6.61765 + 0.737714i) q^{48} +(0.535180 - 0.308986i) q^{49} +(0.550276 - 2.05366i) q^{50} +(1.72042 + 3.93057i) q^{51} +(0.127580 + 0.238442i) q^{52} +10.8009i q^{53} +(-0.513274 + 7.19107i) q^{54} +1.08134 q^{55} +(3.63650 - 6.29860i) q^{56} +(-5.30013 + 13.5516i) q^{57} +(1.56984 - 5.85873i) q^{58} +(0.657543 - 2.45398i) q^{59} +(-0.151052 - 0.188955i) q^{60} +(1.05320 - 1.82419i) q^{61} -2.23330 q^{62} +(6.70888 + 3.52550i) q^{63} +8.27709i q^{64} +(-1.94627 + 6.42581i) q^{65} +(0.827337 - 1.12378i) q^{66} +(1.72857 - 6.45111i) q^{67} +(-0.160904 + 0.0928980i) q^{68} +(5.47887 - 7.44199i) q^{69} +(6.30454 - 1.68930i) q^{70} +(3.69628 - 3.69628i) q^{71} +(-8.63002 + 0.343333i) q^{72} +(10.1636 - 10.1636i) q^{73} +(0.155076 + 0.0895333i) q^{74} +(-0.294058 + 2.63784i) q^{75} +(-0.608639 - 0.163084i) q^{76} +(-0.733496 - 1.27045i) q^{77} +(5.18889 + 6.93904i) q^{78} +(4.35439 - 7.54202i) q^{79} +(-5.06203 + 5.06203i) q^{80} +(-0.714974 - 8.97156i) q^{81} +2.67948i q^{82} +(-0.983416 - 3.67016i) q^{83} +(-0.119539 + 0.305641i) q^{84} +(-4.45570 - 1.19390i) q^{85} +(-2.17119 + 8.10301i) q^{86} +(-0.838895 + 7.52529i) q^{87} +(1.44781 + 0.835895i) q^{88} +(-0.410551 - 0.410551i) q^{89} +(-5.69424 - 5.25850i) q^{90} +(8.86976 - 2.07211i) q^{91} +(0.346563 + 0.200088i) q^{92} +(2.75637 - 0.418787i) q^{93} +(-8.24224 - 14.2760i) q^{94} +(-7.82207 - 13.5482i) q^{95} +(-0.110327 - 0.726152i) q^{96} +(2.78216 - 0.745477i) q^{97} +(0.606275 + 0.606275i) q^{98} +(-0.810380 + 1.54212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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