LMFDB - Embedded newform 168.2.v.a.107.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(11,168)] 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("168.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.v (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.17
Character	$\chi$	$=$	168.107
Dual form			168.2.v.a.11.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.389211 - 1.35960i) q^{2} +(-0.987527 + 1.42295i) q^{3} +(-1.69703 - 1.05834i) q^{4} +(-1.77783 + 3.07929i) q^{5} +(1.55029 + 1.89647i) q^{6} +(-0.793456 + 2.52397i) q^{7} +(-2.09943 + 1.89537i) q^{8} +(-1.04958 - 2.81041i) q^{9} +(3.49466 + 3.61563i) q^{10} +(-0.396703 + 0.229036i) q^{11} +(3.18183 - 1.36965i) q^{12} -0.799063i q^{13} +(3.12277 + 2.06114i) q^{14} +(-2.62603 - 5.57065i) q^{15} +(1.75982 + 3.59208i) q^{16} +(5.48456 - 3.16651i) q^{17} +(-4.22954 + 0.333169i) q^{18} +(-2.61696 + 4.53272i) q^{19} +(6.27598 - 3.34410i) q^{20} +(-2.80793 - 3.62154i) q^{21} +(0.156997 + 0.628501i) q^{22} +(-1.55053 + 2.68559i) q^{23} +(-0.623772 - 4.85911i) q^{24} +(-3.82137 - 6.61880i) q^{25} +(-1.08641 - 0.311004i) q^{26} +(5.03556 + 1.28185i) q^{27} +(4.01774 - 3.44351i) q^{28} +2.60340 q^{29} +(-8.59594 + 1.40219i) q^{30} +(-4.42520 + 2.55489i) q^{31} +(5.56873 - 0.994581i) q^{32} +(0.0658472 - 0.790668i) q^{33} +(-2.17055 - 8.68926i) q^{34} +(-6.36142 - 6.93048i) q^{35} +(-1.19320 + 5.88016i) q^{36} +(2.89424 + 1.67099i) q^{37} +(5.14413 + 5.32221i) q^{38} +(1.13703 + 0.789096i) q^{39} +(-2.10396 - 9.83439i) q^{40} +10.1452i q^{41} +(-6.01672 + 2.40812i) q^{42} +3.56359 q^{43} +(0.915615 + 0.0311657i) q^{44} +(10.5200 + 1.76446i) q^{45} +(3.04785 + 3.15336i) q^{46} +(2.15923 - 3.73989i) q^{47} +(-6.84922 - 1.04314i) q^{48} +(-5.74086 - 4.00532i) q^{49} +(-10.4862 + 2.61943i) q^{50} +(-0.910362 + 10.9313i) q^{51} +(-0.845682 + 1.35603i) q^{52} +(-1.16913 - 2.02499i) q^{53} +(3.70270 - 6.34744i) q^{54} -1.62875i q^{55} +(-3.11805 - 6.80278i) q^{56} +(-3.86551 - 8.19999i) q^{57} +(1.01327 - 3.53959i) q^{58} +(-1.49741 + 0.864528i) q^{59} +(-1.43921 + 12.2328i) q^{60} +(-4.60841 - 2.66067i) q^{61} +(1.75130 + 7.01090i) q^{62} +(7.92618 - 0.419175i) q^{63} +(0.815178 - 7.95836i) q^{64} +(2.46055 + 1.42060i) q^{65} +(-1.04936 - 0.397262i) q^{66} +(0.00979145 + 0.0169593i) q^{67} +(-12.6587 - 0.430877i) q^{68} +(-2.29028 - 4.85842i) q^{69} +(-11.8986 + 5.95157i) q^{70} +9.04022 q^{71} +(7.53026 + 3.91090i) q^{72} +(4.15674 + 7.19969i) q^{73} +(3.39835 - 3.28465i) q^{74} +(13.1919 + 1.09863i) q^{75} +(9.23823 - 4.92251i) q^{76} +(-0.263315 - 1.18300i) q^{77} +(1.51540 - 1.23878i) q^{78} +(10.8825 + 6.28304i) q^{79} +(-14.1897 - 0.967099i) q^{80} +(-6.79677 + 5.89949i) q^{81} +(13.7934 + 3.94861i) q^{82} +0.694004i q^{83} +(0.932309 + 9.11761i) q^{84} +22.5181i q^{85} +(1.38699 - 4.84506i) q^{86} +(-2.57093 + 3.70452i) q^{87} +(0.398740 - 1.23274i) q^{88} +(7.02189 + 4.05409i) q^{89} +(6.49348 - 13.6163i) q^{90} +(2.01681 + 0.634021i) q^{91} +(5.47357 - 2.91654i) q^{92} +(0.734523 - 8.81987i) q^{93} +(-4.24437 - 4.39129i) q^{94} +(-9.30504 - 16.1168i) q^{95} +(-4.08404 + 8.90621i) q^{96} +7.05333 q^{97} +(-7.68004 + 6.24636i) q^{98} +(1.06006 + 0.874504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) $ 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	0.389211	−	1.35960i	0.275214	−	0.961383i
$2$	0.389211	−	1.35960i	0.275214	−	0.961383i
$3$	−0.987527	+	1.42295i	−0.570149	+	0.821541i
$3$	−0.987527	+	1.42295i	−0.570149	+	0.821541i
$4$	−1.69703	−	1.05834i	−0.848515	−	0.529171i
$5$	−1.77783	+	3.07929i	−0.795070	+	1.37710i	0.127724	+	0.991810i	$0.459233\pi$
$5$	−1.77783	+	3.07929i	−0.795070	+	1.37710i	−0.922795	+	0.385292i	$0.874101\pi$
$6$	1.55029	+	1.89647i	0.632903	+	0.774231i
$7$	−0.793456	+	2.52397i	−0.299898	+	0.953971i
$7$	−0.793456	+	2.52397i	−0.299898	+	0.953971i
$8$	−2.09943	+	1.89537i	−0.742259	+	0.670113i
$9$	−1.04958	−	2.81041i	−0.349860	−	0.936802i
$10$	3.49466	+	3.61563i	1.10511	+	1.14336i
$11$	−0.396703	+	0.229036i	−0.119610	+	0.0690571i	−0.558612	−	0.829429i	$-0.688666\pi$
$11$	−0.396703	+	0.229036i	−0.119610	+	0.0690571i	0.439001	+	0.898486i	$0.355332\pi$
$12$	3.18183	−	1.36965i	0.918516	−	0.395383i
$13$		−	0.799063i		−	0.221620i	−0.993842	−	0.110810i	$-0.964655\pi$
$13$		−	0.799063i		−	0.221620i	0.993842	−	0.110810i	$-0.0353445\pi$
$14$	3.12277	+	2.06114i	0.834596	+	0.550863i
$15$	−2.62603	−	5.57065i	−0.678037	−	1.43834i
$16$	1.75982	+	3.59208i	0.439956	+	0.898020i
$17$	5.48456	−	3.16651i	1.33020	−	0.767993i	0.344872	−	0.938650i	$-0.387922\pi$
$17$	5.48456	−	3.16651i	1.33020	−	0.767993i	0.985330	+	0.170657i	$0.0545891\pi$
$18$	−4.22954	+	0.333169i	−0.996912	+	0.0785287i
$19$	−2.61696	+	4.53272i	−0.600373	+	1.03988i	0.392392	+	0.919798i	$0.371648\pi$
$19$	−2.61696	+	4.53272i	−0.600373	+	1.03988i	−0.992764	+	0.120078i	$0.961686\pi$
$20$	6.27598	−	3.34410i	1.40335	−	0.747763i
$21$	−2.80793	−	3.62154i	−0.612740	−	0.790285i
$22$	0.156997	+	0.628501i	0.0334719	+	0.133997i
$23$	−1.55053	+	2.68559i	−0.323307	+	0.559985i	−0.981168	−	0.193155i	$-0.938128\pi$
$23$	−1.55053	+	2.68559i	−0.323307	+	0.559985i	0.657861	+	0.753139i	$0.271461\pi$
$24$	−0.623772	−	4.85911i	−0.127327	−	0.991861i
$25$	−3.82137	−	6.61880i	−0.764273	−	1.32376i
$26$	−1.08641	−	0.311004i	−0.213062	−	0.0609928i
$27$	5.03556	+	1.28185i	0.969094	+	0.246693i
$28$	4.01774	−	3.44351i	0.759282	−	0.650762i
$29$	2.60340			0.483440			0.241720	−	0.970346i	$-0.422288\pi$
$29$	2.60340			0.483440			0.241720	+	0.970346i	$0.422288\pi$
$30$	−8.59594	+	1.40219i	−1.56940	+	0.256004i
$31$	−4.42520	+	2.55489i	−0.794790	+	0.458872i	−0.841646	−	0.540030i	$-0.818413\pi$
$31$	−4.42520	+	2.55489i	−0.794790	+	0.458872i	0.0468563	+	0.998902i	$0.485080\pi$
$32$	5.56873	−	0.994581i	0.984423	−	0.175819i
$33$	0.0658472	−	0.790668i	0.0114625	−	0.137638i
$34$	−2.17055	−	8.68926i	−0.372245	−	1.49020i
$35$	−6.36142	−	6.93048i	−1.07528	−	1.17146i
$36$	−1.19320	+	5.88016i	−0.198867	+	0.980026i
$37$	2.89424	+	1.67099i	0.475810	+	0.274709i	0.718669	−	0.695352i	$-0.244752\pi$
$37$	2.89424	+	1.67099i	0.475810	+	0.274709i	−0.242859	+	0.970062i	$0.578085\pi$
$38$	5.14413	+	5.32221i	0.834489	+	0.863376i
$39$	1.13703	+	0.789096i	0.182070	+	0.126357i
$40$	−2.10396	−	9.83439i	−0.332666	−	1.55495i
$41$			10.1452i			1.58441i	0.610256	+	0.792205i	$0.291067\pi$
$41$			10.1452i			1.58441i	−0.610256	+	0.792205i	$0.708933\pi$
$42$	−6.01672	+	2.40812i	−0.928401	+	0.371581i
$43$	3.56359			0.543442			0.271721	−	0.962376i	$-0.412407\pi$
$43$	3.56359			0.543442			0.271721	+	0.962376i	$0.412407\pi$
$44$	0.915615	+	0.0311657i	0.138034	+	0.00469840i
$45$	10.5200	+	1.76446i	1.56824	+	0.263031i
$46$	3.04785	+	3.15336i	0.449381	+	0.464937i
$47$	2.15923	−	3.73989i	0.314956	−	0.545519i	−0.664472	−	0.747313i	$-0.731344\pi$
$47$	2.15923	−	3.73989i	0.314956	−	0.545519i	0.979428	+	0.201794i	$0.0646770\pi$
$48$	−6.84922	−	1.04314i	−0.988600	−	0.150564i
$49$	−5.74086	−	4.00532i	−0.820122	−	0.572188i
$50$	−10.4862	+	2.61943i	−1.48298	+	0.370443i
$51$	−0.910362	+	10.9313i	−0.127476	+	1.53069i
$52$	−0.845682	+	1.35603i	−0.117275	+	0.188048i
$53$	−1.16913	−	2.02499i	−0.160592	−	0.278154i	0.774489	−	0.632587i	$-0.218007\pi$
$53$	−1.16913	−	2.02499i	−0.160592	−	0.278154i	−0.935081	+	0.354433i	$0.884674\pi$
$54$	3.70270	−	6.34744i	0.503874	−	0.863777i
$55$		−	1.62875i		−	0.219621i
$56$	−3.11805	−	6.80278i	−0.416666	−	0.909059i
$57$	−3.86551	−	8.19999i	−0.511999	−	1.08612i
$58$	1.01327	−	3.53959i	0.133049	−	0.464771i
$59$	−1.49741	+	0.864528i	−0.194946	+	0.112552i	−0.594296	−	0.804247i	$-0.702569\pi$
$59$	−1.49741	+	0.864528i	−0.194946	+	0.112552i	0.399350	+	0.916798i	$0.369236\pi$
$60$	−1.43921	+	12.2328i	−0.185801	+	1.57925i
$61$	−4.60841	−	2.66067i	−0.590047	−	0.340664i	0.175069	−	0.984556i	$-0.443985\pi$
$61$	−4.60841	−	2.66067i	−0.590047	−	0.340664i	−0.765116	+	0.643892i	$0.777318\pi$
$62$	1.75130	+	7.01090i	0.222415	+	0.890385i
$63$	7.92618	−	0.419175i	0.998605	−	0.0528111i
$64$	0.815178	−	7.95836i	0.101897	−	0.994795i
$65$	2.46055	+	1.42060i	0.305193	+	0.176204i
$66$	−1.04936	−	0.397262i	−0.129168	−	0.0488996i
$67$	0.00979145	+	0.0169593i	0.00119622	+	0.00207191i	0.866623	−	0.498964i	$-0.166286\pi$
$67$	0.00979145	+	0.0169593i	0.00119622	+	0.00207191i	−0.865427	+	0.501036i	$0.832953\pi$
$68$	−12.6587	−	0.430877i	−1.53510	−	0.0522515i
$69$	−2.29028	−	4.85842i	−0.275717	−	0.584885i
$70$	−11.8986	+	5.95157i	−1.42216	+	0.711349i
$71$	9.04022			1.07288			0.536439	−	0.843939i	$-0.319769\pi$
$71$	9.04022			1.07288			0.536439	+	0.843939i	$0.319769\pi$
$72$	7.53026	+	3.91090i	0.887450	+	0.460904i
$73$	4.15674	+	7.19969i	0.486510	+	0.842660i	0.999880	−	0.0155078i	$-0.00493650\pi$
$73$	4.15674	+	7.19969i	0.486510	+	0.842660i	−0.513370	+	0.858167i	$0.671603\pi$
$74$	3.39835	−	3.28465i	0.395050	−	0.381832i
$75$	13.1919	+	1.09863i	1.52327	+	0.126859i
$76$	9.23823	−	4.92251i	1.05970	−	0.564651i
$77$	−0.263315	−	1.18300i	−0.0300076	−	0.134815i
$78$	1.51540	−	1.23878i	0.171585	−	0.140264i
$79$	10.8825	+	6.28304i	1.22438	+	0.706897i	0.965849	−	0.259105i	$-0.0834277\pi$
$79$	10.8825	+	6.28304i	1.22438	+	0.706897i	0.258533	+	0.966003i	$0.416761\pi$
$80$	−14.1897	−	0.967099i	−1.58646	−	0.108125i
$81$	−6.79677	+	5.89949i	−0.755196	+	0.655499i
$82$	13.7934	+	3.94861i	1.52322	+	0.436051i
$83$			0.694004i			0.0761768i	0.999274	+	0.0380884i	$0.0121268\pi$
$83$			0.694004i			0.0761768i	−0.999274	+	0.0380884i	$0.987873\pi$
$84$	0.932309	+	9.11761i	0.101723	+	0.994813i
$85$			22.5181i			2.44243i
$86$	1.38699	−	4.84506i	0.149563	−	0.522456i
$87$	−2.57093	+	3.70452i	−0.275633	+	0.397166i
$88$	0.398740	−	1.23274i	0.0425058	−	0.131411i
$89$	7.02189	+	4.05409i	0.744319	+	0.429733i	0.823638	−	0.567116i	$-0.191941\pi$
$89$	7.02189	+	4.05409i	0.744319	+	0.429733i	−0.0793185	+	0.996849i	$0.525274\pi$
$90$	6.49348	−	13.6163i	0.684473	−	1.43529i
$91$	2.01681	+	0.634021i	0.211419	+	0.0664634i
$92$	5.47357	−	2.91654i	0.570659	−	0.304070i
$93$	0.734523	−	8.81987i	0.0761664	−	0.914578i
$94$	−4.24437	−	4.39129i	−0.437773	−	0.452927i
$95$	−9.30504	−	16.1168i	−0.954677	−	1.65355i
$96$	−4.08404	+	8.90621i	−0.416825	+	0.908987i
$97$	7.05333			0.716157			0.358078	−	0.933692i	$-0.383432\pi$
$97$	7.05333			0.716157			0.358078	+	0.933692i	$0.383432\pi$
$98$	−7.68004	+	6.24636i	−0.775801	+	0.630978i
$99$	1.06006	+	0.874504i	0.106540	+	0.0878909i
$100$	−0.519985	+	15.2766i	−0.0519985	+	1.52766i
$101$	−3.34348	−	5.79108i	−0.332689	−	0.576234i	0.650349	−	0.759635i	$-0.274622\pi$
$101$	−3.34348	−	5.79108i	−0.332689	−	0.576234i	−0.983038	+	0.183402i	$0.941289\pi$
$102$	14.5079	+	5.49230i	1.43649	+	0.543819i
$103$	−5.48751	−	3.16822i	−0.540701	−	0.312174i	0.204662	−	0.978833i	$-0.434390\pi$
$103$	−5.48751	−	3.16822i	−0.540701	−	0.312174i	−0.745363	+	0.666659i	$0.767724\pi$
$104$	1.51452	+	1.67757i	0.148510	+	0.164500i
$105$	16.1438	−	2.20795i	1.57547	−	0.215474i
$106$	−3.20822	+	0.801402i	−0.311610	+	0.0778390i
$107$	−3.09681	−	1.78795i	−0.299380	−	0.172847i	0.342784	−	0.939414i	$-0.388630\pi$
$107$	−3.09681	−	1.78795i	−0.299380	−	0.172847i	−0.642164	+	0.766567i	$0.721963\pi$
$108$	−7.18885	−	7.50469i	−0.691748	−	0.722139i
$109$	−0.488061	+	0.281782i	−0.0467478	+	0.0269899i	−0.523192	−	0.852215i	$-0.675259\pi$
$109$	−0.488061	+	0.281782i	−0.0467478	+	0.0269899i	0.476444	+	0.879205i	$0.341926\pi$
$110$	−2.21445	−	0.633928i	−0.211140	−	0.0604426i
$111$	−5.23588	+	2.46821i	−0.496968	+	0.234273i
$112$	−10.4626	+	1.59159i	−0.988627	+	0.150391i
$113$		−	1.41462i		−	0.133076i	−0.997784	−	0.0665381i	$-0.978805\pi$
$113$		−	1.41462i		−	0.133076i	0.997784	−	0.0665381i	$-0.0211954\pi$
$114$	−12.6532	+	2.06402i	−1.18508	+	0.193314i
$115$	−5.51315	−	9.54906i	−0.514104	−	0.890454i
$116$	−4.41805	−	2.75529i	−0.410206	−	0.255822i
$117$	−2.24569	+	0.838680i	−0.207614	+	0.0775360i
$118$	0.592606	+	2.37236i	0.0545538	+	0.218393i
$119$	3.64043	+	16.3554i	0.333718	+	1.49929i
$120$	16.0716	+	6.71789i	1.46713	+	0.613257i
$121$	−5.39508	+	9.34456i	−0.490462	+	0.849506i
$122$	−5.41109	+	5.23004i	−0.489897	+	0.473506i
$123$	−14.4361	−	10.0186i	−1.30166	−	0.903350i
$124$	10.2137	+	0.347652i	0.917213	+	0.0312200i
$125$	9.39666			0.840463
$126$	2.51504	−	10.9396i	0.224058	−	0.974576i
$127$		−	15.7043i		−	1.39353i	−0.717299	−	0.696766i	$-0.754622\pi$
$127$		−	15.7043i		−	1.39353i	0.717299	−	0.696766i	$-0.245378\pi$
$128$	−10.5029	−	4.20580i	−0.928336	−	0.371743i
$129$	−3.51914	+	5.07081i	−0.309843	+	0.446460i
$130$	2.88912	−	2.79245i	0.253392	−	0.244914i
$131$	1.16617	+	0.673290i	0.101889	+	0.0588256i	0.550079	−	0.835113i	$-0.314598\pi$
$131$	1.16617	+	0.673290i	0.101889	+	0.0588256i	−0.448190	+	0.893938i	$0.647931\pi$
$132$	−0.948542	+	1.27210i	−0.0825600	+	0.110722i
$133$	−9.36400	−	10.2016i	−0.811961	−	0.884595i
$134$	0.0268688	−	0.00671173i	0.00232111	−	0.000579805i
$135$	−12.8996	+	13.2270i	−1.11022	+	1.13840i
$136$	−5.51273	+	17.0431i	−0.472713	+	1.46144i
$137$	−7.79136	+	4.49834i	−0.665661	+	0.384320i	−0.794431	−	0.607355i	$-0.792231\pi$
$137$	−7.79136	+	4.49834i	−0.665661	+	0.384320i	0.128770	+	0.991675i	$0.458897\pi$
$138$	−7.49691	+	1.22291i	−0.638180	+	0.104101i
$139$	−16.0176			−1.35859			−0.679296	−	0.733864i	$-0.737715\pi$
$139$	−16.0176			−1.35859			−0.679296	+	0.733864i	$0.737715\pi$
$140$	3.46070	+	18.4938i	0.292482	+	1.56301i
$141$	3.18939	+	6.76572i	0.268595	+	0.569777i
$142$	3.51855	−	12.2911i	0.295270	−	1.03145i
$143$	0.183014	+	0.316990i	0.0153044	+	0.0265081i
$144$	8.24813	−	8.71599i	0.687344	−	0.726332i
$145$	−4.62841	+	8.01664i	−0.384369	+	0.665746i
$146$	11.4065	−	2.84931i	0.944013	−	0.235811i
$147$	11.3686	−	4.21360i	0.937668	−	0.347532i
$148$	−3.14313	−	5.89882i	−0.258364	−	0.484880i
$149$	−3.34348	+	5.79108i	−0.273909	+	0.474424i	−0.969859	−	0.243666i	$-0.921650\pi$
$149$	−3.34348	+	5.79108i	−0.273909	+	0.474424i	0.695951	+	0.718090i	$0.254983\pi$
$150$	6.62814	−	17.5082i	0.541185	−	1.42954i
$151$	−3.66278	+	2.11471i	−0.298073	+	0.172093i	−0.641577	−	0.767059i	$-0.721719\pi$
$151$	−3.66278	+	2.11471i	−0.298073	+	0.172093i	0.343504	+	0.939151i	$0.388386\pi$
$152$	−3.09703	−	14.4762i	−0.251202	−	1.17418i
$153$	−14.6557	−	12.0903i	−1.18484	−	0.977446i
$154$	−1.71089	−	0.102431i	−0.137867	−	0.00825413i
$155$		−	18.1687i		−	1.45934i
$156$	−1.09443	−	2.54248i	−0.0876249	−	0.203562i
$157$	19.9382	−	11.5113i	1.59124	−	0.918702i	0.598144	−	0.801389i	$-0.295905\pi$
$157$	19.9382	−	11.5113i	1.59124	−	0.918702i	0.993095	−	0.117313i	$-0.0374281\pi$
$158$	12.7780	−	12.3505i	1.01657	−	0.982552i
$159$	4.03601	+	0.336121i	0.320077	+	0.0266561i
$160$	−6.83766	+	18.9160i	−0.540565	+	1.49544i
$161$	−5.54808	−	6.04438i	−0.437250	−	0.476364i
$162$	5.37558	+	11.5370i	0.422345	+	0.906435i
$163$	10.4009	−	18.0148i	0.814658	−	1.41103i	−0.0949145	−	0.995485i	$-0.530258\pi$
$163$	10.4009	−	18.0148i	0.814658	−	1.41103i	0.909573	−	0.415544i	$-0.136409\pi$
$164$	10.7371	−	17.2167i	0.838424	−	1.34440i
$165$	2.31763	+	1.60844i	0.180428	+	0.125217i
$166$	0.943568	+	0.270114i	0.0732351	+	0.0209649i
$167$	−7.53905			−0.583390			−0.291695	−	0.956511i	$-0.594219\pi$
$167$	−7.53905			−0.583390			−0.291695	+	0.956511i	$0.594219\pi$
$168$	12.7592	+	2.28110i	0.984392	+	0.175991i
$169$	12.3615			0.950885
$170$	30.6156	+	8.76429i	2.34811	+	0.672190i
$171$	15.4855	+	2.59729i	1.18420	+	0.198620i
$172$	−6.04751	−	3.77150i	−0.461119	−	0.287574i
$173$	−7.77603	+	13.4685i	−0.591201	+	1.02399i	0.402870	+	0.915257i	$0.368013\pi$
$173$	−7.77603	+	13.4685i	−0.591201	+	1.02399i	−0.994071	+	0.108733i	$0.965321\pi$
$174$	4.03603	+	4.93728i	0.305971	+	0.374294i
$175$	19.7377	−	4.39329i	1.49203	−	0.332102i
$176$	−1.52084	−	1.02192i	−0.114638	−	0.0770304i
$177$	0.248549	−	2.98448i	0.0186821	−	0.224327i
$178$	8.24494	−	7.96908i	0.617985	−	0.597308i
$179$	−7.81218	+	4.51037i	−0.583910	+	0.337121i	−0.762686	−	0.646769i	$-0.776120\pi$
$179$	−7.81218	+	4.51037i	−0.583910	+	0.337121i	0.178776	+	0.983890i	$0.442786\pi$
$180$	−15.9854	−	14.1282i	−1.19148	−	1.05305i
$181$		−	10.4041i		−	0.773330i	−0.922220	−	0.386665i	$-0.873627\pi$
$181$		−	10.4041i		−	0.773330i	0.922220	−	0.386665i	$-0.126373\pi$
$182$	1.64698	−	2.49529i	0.122082	−	0.184963i
$183$	8.33693	−	3.93006i	0.616284	−	0.290519i
$184$	−1.83496	−	8.57702i	−0.135275	−	0.632306i
$185$	−10.2909	+	5.94148i	−0.756605	+	0.436826i
$186$	−11.7056	−	4.43145i	−0.858298	−	0.324929i
$187$	−1.45049	+	2.51233i	−0.106071	+	0.183720i
$188$	−7.62236	+	4.06151i	−0.555918	+	0.296216i
$189$	−7.23085	+	11.6925i	−0.525967	+	0.850505i
$190$	−25.5340	+	6.37831i	−1.85243	+	0.462731i
$191$	7.33838	−	12.7104i	0.530986	−	0.919695i	−0.468360	−	0.883538i	$-0.655155\pi$
$191$	7.33838	−	12.7104i	0.530986	−	0.919695i	0.999346	−	0.0361574i	$-0.0115118\pi$
$192$	10.5193	+	9.01906i	0.759168	+	0.650894i
$193$	8.06569	+	13.9702i	0.580581	+	1.00560i	0.995411	+	0.0956969i	$0.0305080\pi$
$193$	8.06569	+	13.9702i	0.580581	+	1.00560i	−0.414829	+	0.909899i	$0.636159\pi$
$194$	2.74523	−	9.58971i	0.197096	−	0.688501i
$195$	−4.45130	+	2.09836i	−0.318764	+	0.150267i
$196$	5.50341	+	12.8729i	0.393101	+	0.919495i
$197$	−21.9480			−1.56373			−0.781863	−	0.623450i	$-0.785731\pi$
$197$	−21.9480			−1.56373			−0.781863	+	0.623450i	$0.785731\pi$
$198$	1.60156	−	1.10089i	0.113818	−	0.0782367i
$199$	−13.8171	+	7.97732i	−0.979470	+	0.565497i	−0.902110	−	0.431506i	$-0.857982\pi$
$199$	−13.8171	+	7.97732i	−0.979470	+	0.565497i	−0.0773599	+	0.997003i	$0.524649\pi$
$200$	20.5677	+	6.65279i	1.45436	+	0.470424i
$201$	−0.0338016	−	0.00281501i	−0.00238418	−	0.000198555i
$202$	−9.17487	+	2.29185i	−0.645542	+	0.161254i
$203$	−2.06568	+	6.57091i	−0.144983	+	0.461188i
$204$	13.1140	−	17.5872i	0.918161	−	1.23135i
$205$	−31.2400	−	18.0364i	−2.18189	−	1.25972i
$206$	−6.44331	+	6.22773i	−0.448927	+	0.433906i
$207$	9.17500	+	1.53887i	0.637707	+	0.106959i
$208$	2.87030	−	1.40621i	0.199019	−	0.0975030i
$209$		−	2.39752i		−	0.165840i
$210$	3.28141	−	22.8085i	0.226439	−	1.57394i
$211$	20.9923			1.44517			0.722586	−	0.691281i	$-0.242953\pi$
$211$	20.9923			1.44517			0.722586	+	0.691281i	$0.242953\pi$
$212$	−0.159087	+	4.67381i	−0.0109261	+	0.320999i
$213$	−8.92747	+	12.8638i	−0.611700	+	0.881413i
$214$	−3.63621	+	3.51454i	−0.248566	+	0.240249i
$215$	−6.33546	+	10.9733i	−0.432074	+	0.748375i
$216$	−13.0014	+	6.85307i	−0.884631	+	0.466292i
$217$	−2.93727	−	13.1963i	−0.199395	−	0.895821i
$218$	0.193153	+	0.773241i	0.0130820	+	0.0523705i
$219$	−14.3497	−	1.19505i	−0.969663	−	0.0807539i
$220$	−1.72378	+	2.76404i	−0.116217	+	0.186352i
$221$	−2.53024	−	4.38251i	−0.170203	−	0.294800i
$222$	1.31793	+	8.07936i	0.0884534	+	0.542251i
$223$			7.05072i			0.472151i	0.971735	+	0.236075i	$0.0758613\pi$
$223$			7.05072i			0.472151i	−0.971735	+	0.236075i	$0.924139\pi$
$224$	−1.90825	+	14.8445i	−0.127500	+	0.991839i
$225$	−14.5907	+	17.6865i	−0.972713	+	1.17910i
$226$	−1.92332	−	0.550585i	−0.127937	−	0.0366244i
$227$	17.9681	−	10.3739i	1.19258	−	0.688539i	0.233693	−	0.972310i	$-0.424919\pi$
$227$	17.9681	−	10.3739i	1.19258	−	0.688539i	0.958892	+	0.283771i	$0.0915856\pi$
$228$	−2.11852	+	18.0067i	−0.140302	+	1.19252i
$229$	19.0453	+	10.9958i	1.25855	+	0.726623i	0.972792	−	0.231680i	$-0.0744221\pi$
$229$	19.0453	+	10.9958i	1.25855	+	0.726623i	0.285756	+	0.958302i	$0.407755\pi$
$230$	−15.1287	+	3.77909i	−0.997556	+	0.249186i
$231$	1.94338	+	0.793556i	0.127865	+	0.0522122i
$232$	−5.46565	+	4.93440i	−0.358838	+	0.323959i
$233$	15.1401	+	8.74112i	0.991858	+	0.572650i	0.905829	−	0.423643i	$-0.139249\pi$
$233$	15.1401	+	8.74112i	0.991858	+	0.572650i	0.0860289	+	0.996293i	$0.472582\pi$
$234$	0.266223	+	3.37967i	0.0174035	+	0.220936i
$235$	7.67748	+	13.2978i	0.500824	+	0.867452i
$236$	3.45611	+	0.117639i	0.224974	+	0.00765764i
$237$	−19.6873	+	9.28065i	−1.27883	+	0.602843i
$238$	23.6537	+	1.41615i	1.53324	+	0.0917953i
$239$	6.60546			0.427271			0.213636	−	0.976913i	$-0.431469\pi$
$239$	6.60546			0.427271			0.213636	+	0.976913i	$0.431469\pi$
$240$	15.3889	−	19.2363i	0.993348	−	1.24169i
$241$	−5.27959	−	9.14453i	−0.340089	−	0.589051i	0.644360	−	0.764722i	$-0.277124\pi$
$241$	−5.27959	−	9.14453i	−0.340089	−	0.589051i	−0.984449	+	0.175671i	$0.943790\pi$
$242$	10.6051	+	10.9722i	0.681718	+	0.705318i
$243$	−1.68269	−	15.4974i	−0.107945	−	0.994157i
$244$	5.00472	+	9.39251i	0.320394	+	0.601294i
$245$	22.5398	−	10.5570i	1.44002	−	0.674462i
$246$	−19.2400	+	15.7279i	−1.22670	+	1.00278i
$247$	3.62192	+	2.09112i	0.230457	+	0.133055i
$248$	4.44793	−	13.7512i	0.282444	−	0.873201i
$249$	−0.987533	−	0.685347i	−0.0625824	−	0.0434321i
$250$	3.65728	−	12.7757i	0.231307	−	0.808007i
$251$			6.66647i			0.420784i	0.977617	+	0.210392i	$0.0674741\pi$
$251$			6.66647i			0.420784i	−0.977617	+	0.210392i	$0.932526\pi$
$252$	−13.8946	−	7.67726i	−0.875277	−	0.483622i
$253$		−	1.42051i		−	0.0893066i
$254$	−21.3516	−	6.11228i	−1.33972	−	0.383519i
$255$	−32.0422	−	22.2373i	−2.00656	−	1.39255i
$256$	−9.80605	+	12.6428i	−0.612878	+	0.790177i
$257$	−0.887844	−	0.512597i	−0.0553822	−	0.0319749i	0.472053	−	0.881570i	$-0.343513\pi$
$257$	−0.887844	−	0.512597i	−0.0553822	−	0.0319749i	−0.527435	+	0.849595i	$0.676846\pi$
$258$	5.52459	+	6.75824i	0.343946	+	0.420750i
$259$	−6.51398	+	5.97912i	−0.404759	+	0.371525i
$260$	−2.67214	−	5.01490i	−0.165719	−	0.311011i
$261$	−2.73248	−	7.31662i	−0.169136	−	0.452887i
$262$	1.36929	−	1.32348i	0.0845952	−	0.0817647i
$263$	8.60208	+	14.8992i	0.530427	+	0.918726i	0.999370	+	0.0354978i	$0.0113017\pi$
$263$	8.60208	+	14.8992i	0.530427	+	0.918726i	−0.468943	+	0.883228i	$0.655365\pi$
$264$	1.36036	+	1.78475i	0.0837246	+	0.109844i
$265$	8.31406			0.510729
$266$	−17.5147	+	8.76071i	−1.07390	+	0.537153i
$267$	−12.7031	+	5.98828i	−0.777416	+	0.366477i
$268$	0.00133235	−	0.0391431i	8.13864e−5	−	0.00239105i
$269$	3.92637	+	6.80068i	0.239395	+	0.414644i	0.960541	−	0.278139i	$-0.0897175\pi$
$269$	3.92637	+	6.80068i	0.239395	+	0.414644i	−0.721146	+	0.692783i	$0.756384\pi$
$270$	12.9629	+	22.6864i	0.788894	+	1.38065i
$271$	−15.7096	−	9.06993i	−0.954289	−	0.550959i	−0.0598783	−	0.998206i	$-0.519071\pi$
$271$	−15.7096	−	9.06993i	−0.954289	−	0.550959i	−0.894411	+	0.447247i	$0.852405\pi$
$272$	21.0262	+	14.1285i	1.27490	+	0.856665i
$273$	−2.89384	+	2.24371i	−0.175143	+	0.135796i
$274$	3.08347	+	12.3439i	0.186279	+	0.745725i
$275$	3.03189	+	1.75046i	0.182830	+	0.105557i
$276$	−1.25520	+	10.6688i	−0.0755543	+	0.642185i
$277$	19.2898	−	11.1370i	1.15901	−	0.669157i	0.207946	−	0.978140i	$-0.433322\pi$
$277$	19.2898	−	11.1370i	1.15901	−	0.669157i	0.951067	+	0.308983i	$0.0999888\pi$
$278$	−6.23421	+	21.7775i	−0.373903	+	1.30613i
$279$	11.8249	+	9.75505i	0.707937	+	0.584020i
$280$	26.4911	+	2.49281i	1.58315	+	0.148974i
$281$		−	17.9109i		−	1.06847i	−0.845335	−	0.534236i	$-0.820599\pi$
$281$		−	17.9109i		−	1.06847i	0.845335	−	0.534236i	$-0.179401\pi$
$282$	10.4400	−	1.70300i	0.621694	−	0.101412i
$283$	−2.24283	−	3.88469i	−0.133322	−	0.230921i	0.791633	−	0.610997i	$-0.209231\pi$
$283$	−2.24283	−	3.88469i	−0.133322	−	0.230921i	−0.924955	+	0.380076i	$0.875898\pi$
$284$	−15.3415	−	9.56765i	−0.910352	−	0.567736i
$285$	32.1224	+	2.67517i	1.90277	+	0.158463i
$286$	0.502211	−	0.125451i	0.0296964	−	0.00741805i
$287$	−25.6061	−	8.04974i	−1.51148	−	0.475161i
$288$	−8.64000	−	14.6065i	−0.509117	−	0.860697i
$289$	11.5536	−	20.0115i	0.679625	−	1.17715i
$290$	9.09801	+	9.41296i	0.534254	+	0.552748i
$291$	−6.96535	+	10.0365i	−0.408316	+	0.588352i
$292$	0.565620	−	16.6173i	0.0331004	−	0.972456i
$293$	24.7711			1.44714			0.723570	−	0.690251i	$-0.242500\pi$
$293$	24.7711			1.44714			0.723570	+	0.690251i	$0.242500\pi$
$294$	−1.30402	−	17.0968i	−0.0760521	−	0.997104i
$295$		−	6.14794i		−	0.357947i
$296$	−9.24338	+	1.97752i	−0.537261	+	0.114941i
$297$	−2.29121	+	0.644812i	−0.132950	+	0.0374158i
$298$	6.57224	+	6.79975i	0.380719	+	0.393899i
$299$	2.14596	+	1.23897i	0.124104	+	0.0716514i
$300$	−21.2244	−	15.8260i	−1.22539	−	0.913714i
$301$	−2.82755	+	8.99439i	−0.162977	+	0.518428i
$302$	1.44957	+	5.80299i	0.0834131	+	0.333925i
$303$	11.5422	+	0.961239i	0.663082	+	0.0552217i
$304$	−20.8873	−	1.42357i	−1.19797	−	0.0816473i
$305$	16.3860	−	9.46044i	0.938257	−	0.541703i
$306$	−22.1422	+	15.2202i	−1.26578	+	0.870080i
$307$	7.72188			0.440711			0.220355	−	0.975420i	$-0.429278\pi$
$307$	7.72188			0.440711			0.220355	+	0.975420i	$0.429278\pi$
$308$	−0.805161	+	2.28626i	−0.0458783	+	0.130272i
$309$	9.92729	−	4.67976i	0.564744	−	0.266222i
$310$	−24.7021	−	7.07144i	−1.40299	−	0.401631i
$311$	10.0093	+	17.3367i	0.567577	+	0.983072i	0.996805	+	0.0798757i	$0.0254523\pi$
$311$	10.0093	+	17.3367i	0.567577	+	0.983072i	−0.429228	+	0.903196i	$0.641214\pi$
$312$	−3.88273	+	0.498433i	−0.219816	+	0.0282182i
$313$	−8.54501	+	14.8004i	−0.482993	+	0.836568i	−0.999809	−	0.0195284i	$-0.993784\pi$
$313$	−8.54501	+	14.8004i	−0.482993	+	0.836568i	0.516817	+	0.856096i	$0.327117\pi$
$314$	−7.89063	−	31.5883i	−0.445294	−	1.78263i
$315$	−12.8006	+	25.1523i	−0.721234	+	1.41717i
$316$	−11.8184	−	22.1800i	−0.664837	−	1.24772i
$317$	7.67062	−	13.2859i	0.430825	−	0.746210i	−0.566120	−	0.824323i	$-0.691556\pi$
$317$	7.67062	−	13.2859i	0.430825	−	0.746210i	0.996945	+	0.0781127i	$0.0248894\pi$
$318$	2.02785	−	5.35655i	0.113716	−	0.300380i
$319$	−1.03278	+	0.596274i	−0.0578244	+	0.0333849i
$320$	23.0569	+	16.6588i	1.28892	+	0.931255i
$321$	5.60235	−	2.64097i	0.312693	−	0.147405i
$322$	−10.3773	+	5.19064i	−0.578305	+	0.289263i
$323$			33.1466i			1.84433i
$324$	17.7780	−	2.81830i	0.987666	−	0.156572i
$325$	−5.28884	+	3.05351i	−0.293372	+	0.169378i
$326$	−20.4448	−	21.1526i	−1.13234	−	1.17153i
$327$	0.0810115	−	0.972755i	0.00447994	−	0.0537935i
$328$	−19.2288	−	21.2990i	−1.06173	−	1.17604i
$329$	7.72613	+	8.41727i	0.425955	+	0.464059i
$330$	3.08888	−	2.52504i	0.170037	−	0.138999i
$331$	−6.86143	+	11.8844i	−0.377138	+	0.653223i	−0.990645	−	0.136467i	$-0.956425\pi$
$331$	−6.86143	+	11.8844i	−0.377138	+	0.653223i	0.613506	+	0.789690i	$0.289759\pi$
$332$	0.734493	−	1.17774i	0.0403106	−	0.0646371i
$333$	1.65843	−	9.88783i	0.0908813	−	0.541850i
$334$	−2.93428	+	10.2501i	−0.160557	+	0.560861i
$335$	−0.0696302			−0.00380430
$336$	8.06740	−	16.4596i	0.440113	−	0.897943i
$337$	−15.7338			−0.857074			−0.428537	−	0.903524i	$-0.640971\pi$
$337$	−15.7338			−0.857074			−0.428537	+	0.903524i	$0.640971\pi$
$338$	4.81123	−	16.8067i	0.261696	−	0.914164i
$339$	2.01293	+	1.39698i	0.109328	+	0.0758733i
$340$	23.8319	−	38.2139i	1.29246	−	2.07244i
$341$	1.17033	−	2.02706i	0.0633767	−	0.109772i
$342$	9.55839	−	20.0432i	0.516859	−	1.08381i
$343$	14.6644	−	11.3117i	0.791804	−	0.610775i
$344$	−7.48149	+	6.75430i	−0.403375	+	0.364167i
$345$	19.0322	+	1.58501i	1.02466	+	0.0853342i
$346$	15.2853	+	15.8144i	0.821740	+	0.850187i
$347$	18.5301	−	10.6984i	0.994748	−	0.574318i	0.0880576	−	0.996115i	$-0.471934\pi$
$347$	18.5301	−	10.6984i	0.994748	−	0.574318i	0.906690	+	0.421798i	$0.138601\pi$
$348$	8.28360	−	3.56575i	0.444047	−	0.191144i
$349$			15.7266i			0.841826i	0.907101	+	0.420913i	$0.138290\pi$
$349$			15.7266i			0.841826i	−0.907101	+	0.420913i	$0.861710\pi$
$350$	1.70901	−	28.5454i	0.0913507	−	1.52581i
$351$	1.02428	−	4.02373i	0.0546721	−	0.214771i
$352$	−1.98134	+	1.67000i	−0.105606	+	0.0890111i
$353$	10.1824	−	5.87883i	0.541956	−	0.312898i	−0.203915	−	0.978989i	$-0.565367\pi$
$353$	10.1824	−	5.87883i	0.541956	−	0.312898i	0.745871	+	0.666090i	$0.232033\pi$
$354$	−3.96096	−	1.49952i	−0.210523	−	0.0796985i
$355$	−16.0720	+	27.8375i	−0.853013	+	1.47746i
$356$	−7.62574	−	14.3115i	−0.404164	−	0.758507i
$357$	−26.8679	−	10.9712i	−1.42200	−	0.580658i
$358$	3.09171	+	12.3769i	0.163402	+	0.654141i
$359$	10.2639	−	17.7776i	0.541709	−	0.938268i	−0.457097	−	0.889417i	$-0.651111\pi$
$359$	10.2639	−	17.7776i	0.541709	−	0.938268i	0.998806	−	0.0488509i	$-0.0155559\pi$
$360$	−25.4304	+	16.2350i	−1.34030	+	0.855658i
$361$	−4.19701	−	7.26943i	−0.220895	−	0.382601i
$362$	−14.1454	−	4.04938i	−0.743466	−	0.212831i
$363$	−7.96906	−	16.9050i	−0.418267	−	0.887280i
$364$	−2.75158	−	3.21043i	−0.144222	−	0.168272i
$365$	−29.5599			−1.54724
$366$	−2.09849	−	12.8645i	−0.109690	−	0.672440i
$367$	19.9290	−	11.5060i	1.04029	−	0.600609i	0.120372	−	0.992729i	$-0.461591\pi$
$367$	19.9290	−	11.5060i	1.04029	−	0.600609i	0.919914	+	0.392120i	$0.128258\pi$
$368$	−12.3755	−	0.843451i	−0.645118	−	0.0439679i
$369$	28.5120	−	10.6482i	1.48428	−	0.554321i
$370$	4.07270	+	16.3041i	0.211729	+	0.847608i
$371$	6.03867	−	1.34411i	0.313512	−	0.0697826i
$372$	−10.5810	+	14.1902i	−0.548597	+	0.735728i
$373$	21.6640	+	12.5077i	1.12172	+	0.647624i	0.941839	−	0.336065i	$-0.109096\pi$
$373$	21.6640	+	12.5077i	1.12172	+	0.647624i	0.179878	+	0.983689i	$0.442430\pi$
$374$	2.85122	+	2.94992i	0.147433	+	0.152537i
$375$	−9.27946	+	13.3710i	−0.479189	+	0.690475i
$376$	2.55532	+	11.9442i	0.131781	+	0.615973i
$377$		−	2.08028i		−	0.107140i
$378$	13.0828	+	14.3819i	0.672908	+	0.739726i
$379$	−11.7405			−0.603071			−0.301535	−	0.953455i	$-0.597499\pi$
$379$	−11.7405			−0.603071			−0.301535	+	0.953455i	$0.597499\pi$
$380$	−1.26616	+	37.1986i	−0.0649529	+	1.90825i
$381$	22.3464	+	15.5084i	1.14484	+	0.794521i
$382$	−14.4250	−	14.9243i	−0.738045	−	0.763594i
$383$	8.93250	−	15.4715i	0.456430	−	0.790559i	−0.542340	−	0.840159i	$-0.682461\pi$
$383$	8.93250	−	15.4715i	0.456430	−	0.790559i	0.998769	+	0.0496002i	$0.0157947\pi$
$384$	16.3566	−	10.7918i	0.834692	−	0.550717i
$385$	4.11092	+	1.29234i	0.209512	+	0.0658639i
$386$	22.1331	−	5.52878i	1.12655	−	0.281407i
$387$	−3.74027	−	10.0151i	−0.190128	−	0.509098i
$388$	−11.9697	−	7.46484i	−0.607670	−	0.378970i
$389$	12.9460	+	22.4231i	0.656386	+	1.13689i	0.981544	+	0.191235i	$0.0612491\pi$
$389$	12.9460	+	22.4231i	0.656386	+	1.13689i	−0.325158	+	0.945660i	$0.605418\pi$
$390$	1.12044	+	6.86870i	0.0567356	+	0.347810i
$391$			19.6391i			0.993190i
$392$	19.6440	−	2.47216i	0.992174	−	0.124863i
$393$	−2.10969	+	0.994514i	−0.106420	+	0.0501666i
$394$	−8.54238	+	29.8405i	−0.430359	+	1.50334i
$395$	−38.6946	+	22.3404i	−1.94694	+	1.12407i
$396$	−0.873423	−	2.60596i	−0.0438911	−	0.130955i
$397$	−17.5040	−	10.1060i	−0.878502	−	0.507203i	−0.00833784	−	0.999965i	$-0.502654\pi$
$397$	−17.5040	−	10.1060i	−0.878502	−	0.507203i	−0.870164	+	0.492762i	$0.835987\pi$
$398$	5.46820	+	21.8906i	0.274096	+	1.09728i
$399$	23.7637	−	3.25010i	1.18967	−	0.162708i
$400$	17.0503	−	25.3746i	0.852516	−	1.26873i
$401$	−32.0937	−	18.5293i	−1.60268	−	0.925309i	−0.990948	−	0.134247i	$-0.957139\pi$
$401$	−32.0937	−	18.5293i	−1.60268	−	0.925309i	−0.611735	−	0.791063i	$-0.709528\pi$
$402$	−0.0169832	+	0.0448610i	−0.000847046	+	0.00223746i
$403$	2.04152	+	3.53601i	0.101695	+	0.176141i
$404$	−0.454957	+	13.3662i	−0.0226350	+	0.664992i
$405$	−6.08275	−	31.4175i	−0.302255	−	1.56115i
$406$	8.12983	+	5.36598i	0.403477	+	0.266309i
$407$	−1.53087			−0.0758825
$408$	−18.8075	−	24.6749i	−0.931112	−	1.22159i
$409$	−14.5304	−	25.1675i	−0.718484	−	1.24445i	−0.961600	−	0.274453i	$-0.911503\pi$
$409$	−14.5304	−	25.1675i	−0.718484	−	1.24445i	0.243117	−	0.969997i	$-0.421830\pi$
$410$	−36.6812	+	35.4539i	−1.81156	+	1.75094i
$411$	1.29326	−	15.5290i	0.0637918	−	0.765987i
$412$	5.95942	+	11.1842i	0.293599	+	0.551008i
$413$	−0.993917	−	4.46537i	−0.0489075	−	0.219727i
$414$	5.66326	−	11.8754i	0.278334	−	0.583644i
$415$	−2.13704	−	1.23382i	−0.104903	−	0.0605659i
$416$	−0.794732	−	4.44977i	−0.0389650	−	0.218168i
$417$	15.8178	−	22.7922i	0.774600	−	1.11614i
$418$	−3.25967	−	0.933141i	−0.159436	−	0.0456414i
$419$		−	1.27248i		−	0.0621647i	−0.999517	−	0.0310823i	$-0.990105\pi$
$419$		−	1.27248i		−	0.0621647i	0.999517	−	0.0310823i	$-0.00989541\pi$
$420$	−29.7333	−	13.3387i	−1.45084	−	0.650863i
$421$			12.1006i			0.589749i	0.955536	+	0.294875i	$0.0952779\pi$
$421$			12.1006i			0.589749i	−0.955536	+	0.294875i	$0.904722\pi$
$422$	8.17044	−	28.5412i	0.397731	−	1.38936i
$423$	−12.7769	−	2.14299i	−0.621234	−	0.104196i
$424$	6.29260	+	2.03539i	0.305596	+	0.0988474i
$425$	−41.9171	−	24.2008i	−2.03328	−	1.17391i
$426$	14.0150	+	17.1445i	0.679027	+	0.830655i
$427$	10.3720	−	9.52038i	0.501937	−	0.460723i
$428$	3.36313	+	6.31169i	0.162563	+	0.305087i
$429$	−0.631793	−	0.0526160i	−0.0305033	−	0.00254033i
$430$	12.4535	+	12.8846i	0.600562	+	0.621352i
$431$	−8.36354	−	14.4861i	−0.402858	−	0.697770i	0.591212	−	0.806516i	$-0.298650\pi$
$431$	−8.36354	−	14.4861i	−0.402858	−	0.697770i	−0.994070	+	0.108746i	$0.965316\pi$
$432$	4.25717	+	20.3440i	0.204823	+	0.978799i
$433$	−14.1708			−0.681007			−0.340503	−	0.940243i	$-0.610597\pi$
$433$	−14.1708			−0.681007			−0.340503	+	0.940243i	$0.610597\pi$
$434$	−19.0849	−	1.14261i	−0.916104	−	0.0548472i
$435$	−6.83661	−	14.5027i	−0.327790	−	0.695349i
$436$	1.12648	+	0.0383430i	0.0539485	+	0.00183630i
$437$	−8.11535	−	14.0562i	−0.388210	−	0.672399i
$438$	−7.20984	+	19.0447i	−0.344500	+	0.909993i
$439$	−22.3364	−	12.8959i	−1.06606	−	0.615489i	−0.138957	−	0.990298i	$-0.544375\pi$
$439$	−22.3364	−	12.8959i	−1.06606	−	0.615489i	−0.927102	+	0.374809i	$0.877708\pi$
$440$	3.08708	+	3.41944i	0.147171	+	0.163016i
$441$	−5.23108	+	20.3380i	−0.249099	+	0.968478i
$442$	−6.94326	+	1.73440i	−0.330257	+	0.0824971i
$443$	30.3993	+	17.5510i	1.44431	+	0.833875i	0.998134	−	0.0610673i	$-0.0194504\pi$
$443$	30.3993	+	17.5510i	1.44431	+	0.833875i	0.446181	+	0.894943i	$0.352784\pi$
$444$	11.4977	+	1.35272i	0.545655	+	0.0641973i
$445$	−24.9675	+	14.4150i	−1.18357	+	0.683336i
$446$	9.58616	+	2.74421i	0.453918	+	0.129942i
$447$	−4.93864	−	10.4765i	−0.233590	−	0.495519i
$448$	19.4399	+	8.37209i	0.918447	+	0.395544i
$449$			13.8891i			0.655467i	0.944770	+	0.327733i	$0.106285\pi$
$449$			13.8891i			0.655467i	−0.944770	+	0.327733i	$0.893715\pi$
$450$	18.3678	+	26.7213i	0.865866	+	1.25965i
$451$	−2.32361	−	4.02462i	−0.109415	−	0.189512i
$452$	−1.49715	+	2.40065i	−0.0704201	+	0.112917i
$453$	0.607972	−	7.30029i	0.0285650	−	0.342998i
$454$	−7.11097	−	28.4671i	−0.333734	−	1.33603i
$455$	−5.53788	+	5.08317i	−0.259620	+	0.238303i
$456$	23.6573	+	9.88873i	1.10786	+	0.463082i
$457$	3.77280	−	6.53468i	0.176484	−	0.305679i	−0.764190	−	0.644991i	$-0.776861\pi$
$457$	3.77280	−	6.53468i	0.176484	−	0.305679i	0.940674	+	0.339312i	$0.110194\pi$
$458$	22.3625	−	21.6143i	1.04493	−	1.00997i
$459$	31.6769	−	8.91476i	1.47855	−	0.416106i
$460$	−0.750191	+	22.0398i	−0.0349778	+	1.02761i
$461$	−17.6339			−0.821292			−0.410646	−	0.911795i	$-0.634697\pi$
$461$	−17.6339			−0.821292			−0.410646	+	0.911795i	$0.634697\pi$
$462$	1.83530	−	2.33336i	0.0853860	−	0.108558i
$463$			29.5192i			1.37187i	0.727661	+	0.685937i	$0.240607\pi$
$463$			29.5192i			1.37187i	−0.727661	+	0.685937i	$0.759393\pi$
$464$	4.58153	+	9.35163i	0.212692	+	0.434138i
$465$	25.8531	+	17.9420i	1.19891	+	0.832043i
$466$	17.7771	−	17.1823i	0.823508	−	0.795955i
$467$	−26.4319	−	15.2605i	−1.22312	−	0.706170i	−0.257539	−	0.966268i	$-0.582912\pi$
$467$	−26.4319	−	15.2605i	−1.22312	−	0.706170i	−0.965582	+	0.260098i	$0.916245\pi$
$468$	4.69861	+	0.953445i	0.217194	+	0.0440730i
$469$	−0.0505738	+	0.0112569i	−0.00233528	+	0.000519795i
$470$	21.0679	−	5.26267i	0.971788	−	0.242749i
$471$	−3.30946	+	39.7388i	−0.152492	+	1.83107i
$472$	1.50510	−	4.65314i	0.0692777	−	0.214178i
$473$	−1.41368	+	0.816191i	−0.0650013	+	0.0375285i
$474$	4.95549	+	30.3790i	0.227613	+	1.39535i
$475$	40.0015			1.83540
$476$	11.1317	−	31.6084i	0.510219	−	1.44877i
$477$	−4.46396	+	5.41112i	−0.204391	+	0.247758i
$478$	2.57091	−	8.98079i	0.117591	−	0.410772i
$479$	−0.0969618	−	0.167943i	−0.00443030	−	0.00767350i	0.863802	−	0.503832i	$-0.168077\pi$
$479$	−0.0969618	−	0.167943i	−0.00443030	−	0.00767350i	−0.868232	+	0.496158i	$0.834744\pi$
$480$	−20.1641	−	28.4097i	−0.920362	−	1.29672i
$481$	1.33523	−	2.31268i	0.0608811	−	0.105449i
$482$	−14.4878	+	3.61899i	−0.659900	+	0.164841i
$483$	14.0797	−	1.92565i	0.640650	−	0.0876203i
$484$	19.0454	−	10.1482i	0.865699	−	0.461280i
$485$	−12.5396	+	21.7193i	−0.569395	+	0.986221i
$486$	−21.7252	−	3.74396i	−0.985473	−	0.169829i
$487$	−17.4486	+	10.0740i	−0.790673	+	0.456496i	−0.840200	−	0.542277i	$-0.817562\pi$
$487$	−17.4486	+	10.0740i	−0.790673	+	0.456496i	0.0495261	+	0.998773i	$0.484229\pi$
$488$	14.7180	−	3.14875i	0.666251	−	0.142537i
$489$	15.3631	+	32.5900i	0.694742	+	1.47377i
$490$	−5.58058	−	34.7541i	−0.252105	−	1.57003i
$491$			4.30244i			0.194167i	0.995276	+	0.0970833i	$0.0309513\pi$
$491$			4.30244i			0.194167i	−0.995276	+	0.0970833i	$0.969049\pi$
$492$	13.8953	+	32.2802i	0.626449	+	1.45531i
$493$	14.2785	−	8.24371i	0.643073	−	0.371278i
$494$	4.25278	−	4.11048i	0.191342	−	0.184939i
$495$	−4.57745	+	1.70950i	−0.205741	+	0.0768365i
$496$	−16.9649	−	11.3995i	−0.761748	−	0.511853i
$497$	−7.17302	+	22.8173i	−0.321754	+	1.02349i
$498$	−1.31616	+	1.07591i	−0.0589784	+	0.0482125i
$499$	−13.0198	+	22.5510i	−0.582848	+	1.00952i	0.412292	+	0.911052i	$0.364728\pi$
$499$	−13.0198	+	22.5510i	−0.582848	+	1.00952i	−0.995140	+	0.0984710i	$0.968605\pi$
$500$	−15.9464	−	9.94489i	−0.713145	−	0.444749i
$501$	7.44502	−	10.7277i	0.332619	−	0.479279i
$502$	9.06375	+	2.59466i	0.404535	+	0.115805i
$503$	−22.7182			−1.01295			−0.506476	−	0.862254i	$-0.669052\pi$
$503$	−22.7182			−1.01295			−0.506476	+	0.862254i	$0.669052\pi$
$504$	−15.8459	+	15.9030i	−0.705834	+	0.708377i
$505$	23.7766			1.05804
$506$	−1.93132	−	0.552877i	−0.0858578	−	0.0245784i
$507$	−12.2073	+	17.5898i	−0.542146	+	0.781191i
$508$	−16.6205	+	26.6507i	−0.737417	+	1.18243i
$509$	18.1915	−	31.5087i	0.806326	−	1.39660i	−0.109067	−	0.994034i	$-0.534786\pi$
$509$	18.1915	−	31.5087i	0.806326	−	1.39660i	0.915392	−	0.402563i	$-0.131880\pi$
$510$	−42.7049	+	34.9096i	−1.89101	+	1.54582i
$511$	−21.4700	+	4.77886i	−0.949776	+	0.211404i
$512$	13.3726	+	18.2530i	0.590991	+	0.806678i
$513$	−18.9882	+	19.4702i	−0.838347	+	0.859630i
$514$	−1.04249	+	1.00761i	−0.0459821	+	0.0444436i
$515$	19.5117	−	11.2651i	0.859790	−	0.496400i
$516$	11.3387	−	4.88086i	0.499160	−	0.214868i
$517$			1.97817i			0.0869997i
$518$	5.59391	+	11.1836i	0.245782	+	0.491377i
$519$	−11.4860	−	24.3654i	−0.504177	−	1.06952i
$520$	−7.85829	+	1.68120i	−0.344609	+	0.0737254i
$521$	4.25083	−	2.45422i	0.186232	−	0.107521i	−0.403985	−	0.914765i	$-0.632375\pi$
$521$	4.25083	−	2.45422i	0.186232	−	0.107521i	0.590218	+	0.807244i	$0.299042\pi$
$522$	−11.0112	+	0.867373i	−0.481947	+	0.0379639i
$523$	20.4680	−	35.4516i	0.895002	−	1.55019i	0.0612000	−	0.998126i	$-0.480507\pi$
$523$	20.4680	−	35.4516i	0.895002	−	1.55019i	0.833802	−	0.552064i	$-0.186159\pi$
$524$	−1.26646	−	2.37680i	−0.0553255	−	0.103831i
$525$	−13.2401	+	32.4243i	−0.577846	+	1.41511i
$526$	23.6050	−	5.89645i	1.02923	−	0.257098i
$527$	−16.1802	+	28.0249i	−0.704821	+	1.22079i
$528$	2.95602	−	1.15491i	0.128644	−	0.0502609i
$529$	6.69173	+	11.5904i	0.290945	+	0.503931i
$530$	3.23592	−	11.3038i	0.140559	−	0.491006i
$531$	4.00132	+	3.30093i	0.173642	+	0.143248i
$532$	5.09414	+	27.2228i	0.220859	+	1.18026i
$533$	8.10662			0.351137
$534$	3.19750	+	19.6018i	0.138369	+	0.848254i
$535$	11.0112	−	6.35733i	0.476057	−	0.274852i
$536$	−0.0527005	−	0.0170464i	−0.00227631	−	0.000736292i
$537$	1.29671	−	15.5705i	0.0559574	−	0.671915i
$538$	10.7744	−	2.69140i	0.464517	−	0.116035i
$539$	3.19478	+	0.274055i	0.137609	+	0.0118044i
$540$	35.8897	−	8.79452i	1.54445	−	0.378456i
$541$	−7.39731	−	4.27084i	−0.318035	−	0.183618i	0.332481	−	0.943110i	$-0.392114\pi$
$541$	−7.39731	−	4.27084i	−0.318035	−	0.183618i	−0.650517	+	0.759492i	$0.725448\pi$
$542$	−18.4458	+	17.8286i	−0.792316	+	0.765806i
$543$	14.8045	+	10.2743i	0.635322	+	0.440913i
$544$	27.3927	−	23.0883i	1.17445	−	0.989904i
$545$		−	2.00385i		−	0.0858353i
$546$	1.92424	+	4.80774i	0.0823498	+	0.205752i
$547$	−0.501652			−0.0214491			−0.0107245	−	0.999942i	$-0.503414\pi$
$547$	−0.501652			−0.0214491			−0.0107245	+	0.999942i	$0.503414\pi$
$548$	17.9830	+	0.612103i	0.768194	+	0.0261478i
$549$	−2.64066	+	15.7441i	−0.112701	+	0.671942i
$550$	3.55998	−	3.44086i	0.151798	−	0.146719i
$551$	−6.81301	+	11.8005i	−0.290244	+	0.502718i
$552$	14.0167	+	5.85898i	0.596592	+	0.249375i
$553$	−24.4930	+	22.4819i	−1.04155	+	0.956028i
$554$	−7.63405	−	30.5611i	−0.324340	−	1.29842i
$555$	1.70815	−	20.5109i	0.0725071	−	0.870638i
$556$	27.1823	+	16.9521i	1.15279	+	0.718928i
$557$	8.85048	+	15.3295i	0.375007	+	0.649531i	0.990328	−	0.138745i	$-0.0443070\pi$
$557$	8.85048	+	15.3295i	0.375007	+	0.649531i	−0.615321	+	0.788277i	$0.710974\pi$
$558$	17.8654	−	12.2804i	0.756301	−	0.519869i
$559$		−	2.84753i		−	0.120438i
$560$	13.6998	−	35.0471i	0.578924	−	1.48101i
$561$	−2.14252	−	4.54498i	−0.0904572	−	0.191889i
$562$	−24.3516	−	6.97110i	−1.02721	−	0.294058i
$563$	−0.214083	+	0.123601i	−0.00902251	+	0.00520915i	−0.504504	−	0.863409i	$-0.668325\pi$
$563$	−0.214083	+	0.123601i	−0.00902251	+	0.00520915i	0.495482	+	0.868618i	$0.334991\pi$
$564$	1.74797	−	14.8571i	0.0736026	−	0.625597i
$565$	4.35603	+	2.51495i	0.183260	+	0.105805i
$566$	−6.15456	+	1.53739i	−0.258696	+	0.0646212i
$567$	−9.49720	−	21.8358i	−0.398845	−	0.917018i
$568$	−18.9793	+	17.1345i	−0.796353	+	0.718949i
$569$	−22.8950	−	13.2184i	−0.959809	−	0.554146i	−0.0636947	−	0.997969i	$-0.520288\pi$
$569$	−22.8950	−	13.2184i	−0.959809	−	0.554146i	−0.896114	+	0.443824i	$0.853622\pi$
$570$	16.1395	−	42.6325i	0.676011	−	1.78568i
$571$	−16.4357	−	28.4675i	−0.687814	−	1.19133i	−0.972544	−	0.232721i	$-0.925237\pi$
$571$	−16.4357	−	28.4675i	−0.687814	−	1.19133i	0.284730	−	0.958608i	$-0.408096\pi$
$572$	0.0249033	−	0.731634i	0.00104126	−	0.0305912i
$573$	10.8395	+	22.9941i	0.452826	+	0.960591i
$574$	−20.9106	+	31.6810i	−0.872792	+	1.32234i
$575$	23.7005			0.988380
$576$	−23.2218	+	6.06195i	−0.967576	+	0.252581i
$577$	13.3055	+	23.0459i	0.553917	+	0.959413i	0.997987	+	0.0634205i	$0.0202009\pi$
$577$	13.3055	+	23.0459i	0.553917	+	0.959413i	−0.444070	+	0.895992i	$0.646466\pi$
$578$	−22.7108	−	23.4970i	−0.944646	−	0.977347i
$579$	−27.8440	−	2.31886i	−1.15716	−	0.0963685i
$580$	16.3389	−	8.70604i	0.678436	−	0.361499i
$581$	−1.75164	−	0.550661i	−0.0726705	−	0.0228453i
$582$	10.9347	+	13.3764i	0.453258	+	0.554471i
$583$	0.927594	+	0.535547i	0.0384170	+	0.0221801i
$584$	−22.3728	−	7.23666i	−0.925793	−	0.299455i
$585$	1.40992	−	8.40617i	0.0582929	−	0.347552i
$586$	9.64116	−	33.6788i	0.398273	−	1.39126i
$587$		−	23.5447i		−	0.971792i	−0.874017	−	0.485896i	$-0.838493\pi$
$587$		−	23.5447i		−	0.971792i	0.874017	−	0.485896i	$-0.161507\pi$
$588$	−23.7523	−	4.88130i	−0.979529	−	0.201301i
$589$		−	26.7442i		−	1.10198i
$590$	−8.35874	−	2.39284i	−0.344124	−	0.0985118i
$591$	21.6742	−	31.2309i	0.891558	−	1.28467i
$592$	−0.908981	+	13.3370i	−0.0373589	+	0.548147i
$593$	4.37266	+	2.52456i	0.179564	+	0.103671i	0.587088	−	0.809523i	$-0.300274\pi$
$593$	4.37266	+	2.52456i	0.179564	+	0.103671i	−0.407524	+	0.913195i	$0.633608\pi$
$594$	−0.0150771	+	3.36610i	−0.000618622	+	0.138113i
$595$	−56.8351	−	17.8671i	−2.33001	−	0.732480i
$596$	11.8029	−	6.28908i	0.483467	−	0.257611i
$597$	2.29345	−	27.5389i	0.0938648	−	1.12709i
$598$	2.51973	−	2.43542i	0.103039	−	0.0995919i
$599$	7.88687	+	13.6605i	0.322249	+	0.558151i	0.980952	−	0.194252i	$-0.0622280\pi$
$599$	7.88687	+	13.6605i	0.322249	+	0.558151i	−0.658703	+	0.752403i	$0.728895\pi$
$600$	−29.7778	+	22.6970i	−1.21567	+	0.926603i
$601$	−3.65359			−0.149033			−0.0745165	−	0.997220i	$-0.523741\pi$
$601$	−3.65359			−0.149033			−0.0745165	+	0.997220i	$0.523741\pi$
$602$	11.1283	+	7.34505i	0.453554	+	0.299362i
$603$	0.0373856	−	0.0453181i	0.00152246	−	0.00184550i
$604$	8.45394	+	0.287755i	0.343986	+	0.0117086i
$605$	−19.1831	−	33.2261i	−0.779904	−	1.35083i
$606$	5.79925	−	15.3187i	0.235578	−	0.622278i
$607$	40.3527	+	23.2976i	1.63786	+	0.945622i	0.981567	+	0.191120i	$0.0612118\pi$
$607$	40.3527	+	23.2976i	1.63786	+	0.945622i	0.656298	+	0.754502i	$0.272122\pi$
$608$	−10.0650	+	27.8443i	−0.408191	+	1.12923i
$609$	−7.31017	−	9.42833i	−0.296223	−	0.382055i
$610$	−6.48483	−	25.9605i	−0.262563	−	1.05111i
$611$	−2.98841	−	1.72536i	−0.120898	−	0.0698005i
$612$	12.0754	+	36.0284i	0.488119	+	1.45636i
$613$	−18.5964	+	10.7366i	−0.751102	+	0.433649i	−0.826092	−	0.563536i	$-0.809441\pi$
$613$	−18.5964	+	10.7366i	−0.751102	+	0.433649i	0.0749902	+	0.997184i	$0.476107\pi$
$614$	3.00544	−	10.4987i	0.121290	−	0.423692i
$615$	56.5152	−	26.6415i	2.27891	−	1.07429i
$616$	2.79502	+	1.98453i	0.112615	+	0.0799592i
$617$		−	23.7350i		−	0.955536i	−0.878486	−	0.477768i	$-0.841446\pi$
$617$		−	23.7350i		−	0.955536i	0.878486	−	0.477768i	$-0.158554\pi$
$618$	−2.49880	−	15.3186i	−0.100517	−	0.616203i
$619$	−10.3184	−	17.8719i	−0.414730	−	0.718334i	0.580670	−	0.814139i	$-0.302791\pi$
$619$	−10.3184	−	17.8719i	−0.414730	−	0.718334i	−0.995400	+	0.0958052i	$0.969457\pi$
$620$	−19.2287	+	30.8328i	−0.772242	+	1.23827i
$621$	−11.2503	+	11.5359i	−0.451459	+	0.462920i
$622$	27.4667	−	6.86108i	1.10131	−	0.275104i
$623$	−15.8040	+	14.5063i	−0.633173	+	0.581183i
$624$	−0.833530	+	5.47296i	−0.0333679	+	0.219094i
$625$	2.40116	−	4.15892i	0.0960462	−	0.166357i
$626$	16.7968	+	17.3783i	0.671336	+	0.694576i
$627$	3.41155	+	2.36762i	0.136244	+	0.0945535i
$628$	−46.0186	−	1.56638i	−1.83634	−	0.0625053i
$629$	21.1649			0.843899
$630$	29.2149	+	27.1933i	1.16395	+	1.08341i
$631$		−	1.83946i		−	0.0732279i	−0.999329	−	0.0366139i	$-0.988343\pi$
$631$		−	1.83946i		−	0.0732279i	0.999329	−	0.0366139i	$-0.0116572\pi$
$632$	−34.7557	+	7.43562i	−1.38251	+	0.295773i
$633$	−20.7305	+	29.8711i	−0.823964	+	1.18727i
$634$	−15.0780	−	15.6000i	−0.598825	−	0.619555i
$635$	48.3581	+	27.9196i	1.91903	+	1.10796i
$636$	−6.49350	−	4.84189i	−0.257484	−	0.191994i
$637$	−3.20050	+	4.58730i	−0.126808	+	0.181756i
$638$	0.408727	+	1.63624i	0.0161817	+	0.0647794i
$639$	−9.48843	−	25.4067i	−0.375357	−	1.00507i
$640$	31.6233	−	24.8644i	1.25002	−	0.982851i
$641$	−21.1148	+	12.1906i	−0.833983	+	0.481500i	−0.855214	−	0.518274i	$-0.826575\pi$
$641$	−21.1148	+	12.1906i	−0.833983	+	0.481500i	0.0212316	+	0.999775i	$0.493241\pi$
$642$	−1.41017	−	8.64485i	−0.0556550	−	0.341185i
$643$	−7.88201			−0.310836			−0.155418	−	0.987849i	$-0.549672\pi$
$643$	−7.88201			−0.310836			−0.155418	+	0.987849i	$0.549672\pi$
$644$	3.01823	+	16.1293i	0.118935	+	0.635582i
$645$	−9.35808	−	19.8515i	−0.368474	−	0.781652i
$646$	45.0662	+	12.9010i	1.77311	+	0.507584i
$647$	2.44506	+	4.23496i	0.0961251	+	0.166494i	0.910078	−	0.414438i	$-0.136022\pi$
$647$	2.44506	+	4.23496i	0.0961251	+	0.166494i	−0.813953	+	0.580931i	$0.802688\pi$
$648$	3.08762	−	25.2679i	0.121293	−	0.992617i
$649$	0.396017	−	0.685921i	0.0155450	−	0.0269247i
$650$	2.09308	+	8.37916i	0.0820975	+	0.328658i
$651$	21.6783	+	8.85209i	0.849639	+	0.346941i
$652$	−36.7164	+	19.5640i	−1.43793	+	0.766186i
$653$	−21.3381	+	36.9587i	−0.835024	+	1.44630i	0.0589868	+	0.998259i	$0.481213\pi$
$653$	−21.3381	+	36.9587i	−0.835024	+	1.44630i	−0.894011	+	0.448045i	$0.852120\pi$
$654$	−1.29103	−	0.488750i	−0.0504832	−	0.0191116i
$655$	−4.14651	+	2.39399i	−0.162018	+	0.0935410i
$656$	−36.4422	+	17.8537i	−1.42283	+	0.697070i
$657$	15.8712	−	19.2388i	0.619195	−	0.750576i
$658$	14.4512	−	7.22836i	0.563367	−	0.281791i
$659$			33.4550i			1.30322i	0.758553	+	0.651611i	$0.225907\pi$
$659$			33.4550i			1.30322i	−0.758553	+	0.651611i	$0.774093\pi$
$660$	−2.23082	−	5.18242i	−0.0868345	−	0.201725i
$661$	−11.2595	+	6.50067i	−0.437944	+	0.252847i	−0.702725	−	0.711462i	$-0.748034\pi$
$661$	−11.2595	+	6.50067i	−0.437944	+	0.252847i	0.264781	+	0.964308i	$0.414700\pi$
$662$	13.4874	+	13.9543i	0.524204	+	0.542350i
$663$	8.73478	+	0.727436i	0.339231	+	0.0282513i
$664$	−1.31539	−	1.45701i	−0.0510470	−	0.0565429i
$665$	48.0615	−	10.6977i	1.86374	−	0.414838i
$666$	−12.7980	−	6.10325i	−0.495914	−	0.236496i
$667$	−4.03665	+	6.99168i	−0.156300	+	0.270719i
$668$	12.7940	+	7.97890i	0.495015	+	0.308713i
$669$	−10.0328	−	6.96278i	−0.387891	−	0.269197i
$670$	−0.0271008	+	0.0946693i	−0.00104700	+	0.00365739i
$671$	2.43756			0.0941009
$672$	−19.2385	−	17.3747i	−0.742142	−	0.670243i
$673$	−12.3531			−0.476179			−0.238089	−	0.971243i	$-0.576521\pi$
$673$	−12.3531			−0.476179			−0.238089	+	0.971243i	$0.576521\pi$
$674$	−6.12376	+	21.3917i	−0.235878	+	0.823977i
$675$	−10.7584	−	38.2278i	−0.414090	−	1.47139i
$676$	−20.9778	−	13.0827i	−0.806840	−	0.503181i
$677$	−2.07866	+	3.60034i	−0.0798894	+	0.138372i	−0.903202	−	0.429216i	$-0.858790\pi$
$677$	−2.07866	+	3.60034i	−0.0798894	+	0.138372i	0.823313	+	0.567588i	$0.192123\pi$
$678$	2.68279	−	2.19307i	0.103032	−	0.0842243i
$679$	−5.59650	+	17.8024i	−0.214774	+	0.683193i
$680$	−42.6801	−	47.2751i	−1.63671	−	1.81292i
$681$	−2.98246	+	35.8122i	−0.114288	+	1.37233i
$682$	−2.30050	−	2.38013i	−0.0880905	−	0.0911400i
$683$	−11.5310	+	6.65741i	−0.441221	+	0.254739i	−0.704115	−	0.710086i	$-0.748656\pi$
$683$	−11.5310	+	6.65741i	−0.441221	+	0.254739i	0.262895	+	0.964825i	$0.415323\pi$
$684$	−23.5305	−	20.7966i	−0.899711	−	0.795179i
$685$		−	31.9892i		−	1.22224i
$686$	−9.67187	−	24.3404i	−0.369274	−	0.929321i
$687$	−34.4542	+	16.2419i	−1.31451	+	0.619665i
$688$	6.27128	+	12.8007i	0.239090	+	0.488022i
$689$	−1.61810	+	0.934208i	−0.0616445	+	0.0355905i
$690$	9.56253	−	25.2593i	0.364039	−	0.961606i
$691$	7.57239	−	13.1158i	0.288067	−	0.498947i	−0.685281	−	0.728279i	$-0.740321\pi$
$691$	7.57239	−	13.1158i	0.288067	−	0.498947i	0.973348	+	0.229332i	$0.0736540\pi$
$692$	27.4504	−	14.6267i	1.04351	−	0.556024i
$693$	−3.04833	+	1.98167i	−0.115796	+	0.0752775i
$694$	−7.33338	−	29.3575i	−0.278371	−	1.11439i
$695$	28.4765	−	49.3228i	1.08018	−	1.87092i
$696$	−1.62393	−	12.6502i	−0.0615549	−	0.479505i
$697$	32.1248	+	55.6418i	1.21681	+	2.10758i
$698$	21.3819	+	6.12096i	0.809317	+	0.231682i
$699$	−27.3894	+	12.9115i	−1.03596	+	0.488357i
$700$	−38.1451	−	13.4337i	−1.44175	−	0.507748i
$701$	51.6538			1.95094			0.975468	−	0.220142i	$-0.0706520\pi$
$701$	51.6538			1.95094			0.975468	+	0.220142i	$0.0706520\pi$
$702$	−5.07200	−	2.95869i	−0.191430	−	0.111669i
$703$	−15.1483	+	8.74585i	−0.571327	+	0.329856i
$704$	1.49937	+	3.34381i	0.0565096	+	0.126024i
$705$	−26.5038	−	2.20725i	−0.998192	−	0.0831299i
$706$	−4.02975	−	16.1321i	−0.151662	−	0.607141i
$707$	17.2694	−	3.84388i	0.649483	−	0.144564i
$708$	−3.58040	+	4.80170i	−0.134560	+	0.180459i
$709$	44.7941	+	25.8619i	1.68228	+	0.971263i	0.960143	+	0.279510i	$0.0901719\pi$
$709$	44.7941	+	25.8619i	1.68228	+	0.971263i	0.722134	+	0.691753i	$0.243161\pi$
$710$	31.5925	+	32.6861i	1.18565	+	1.22669i
$711$	6.23580	−	37.1789i	0.233861	−	1.39432i
$712$	−22.4259	+	4.79779i	−0.840447	+	0.179805i
$713$		−	15.8457i		−	0.593427i
$714$	−25.3738	+	32.2595i	−0.949589	+	1.20728i
$715$	−1.30147			−0.0486724
$716$	18.0310	+	0.613739i	0.673851	+	0.0229365i
$717$	−6.52307	+	9.39924i	−0.243608	+	0.351021i
$718$	−20.1757	−	20.8741i	−0.752949	−	0.779014i
$719$	18.9896	−	32.8909i	0.708191	−	1.22662i	−0.257336	−	0.966322i	$-0.582845\pi$
$719$	18.9896	−	32.8909i	0.708191	−	1.22662i	0.965527	−	0.260302i	$-0.0838220\pi$
$720$	12.1753	+	40.8940i	0.453747	+	1.52403i
$721$	12.3506	−	11.3365i	0.459960	−	0.422193i
$722$	−11.5170	+	2.87691i	−0.428620	+	0.107068i
$723$	18.2260	+	1.51787i	0.677831	+	0.0564500i
$724$	−11.0111	+	17.6560i	−0.409224	+	0.656182i
$725$	−9.94856	−	17.2314i	−0.369480	−	0.639958i
$726$	−26.0856	+	4.25515i	−0.968129	+	0.157924i
$727$		−	15.9886i		−	0.592984i	−0.955035	−	0.296492i	$-0.904183\pi$
$727$		−	15.9886i		−	0.592984i	0.955035	−	0.296492i	$-0.0958167\pi$
$728$	−5.43585	+	2.49151i	−0.201466	+	0.0923417i
$729$	23.7137	+	12.9097i	0.878285	+	0.478137i
$730$	−11.5050	+	40.1897i	−0.425821	+	1.48749i
$731$	19.5447	−	11.2842i	0.722888	−	0.417359i
$732$	−18.3074	−	2.15390i	−0.676660	−	0.0796104i
$733$	−10.1169	−	5.84098i	−0.373675	−	0.215741i	0.301388	−	0.953502i	$-0.402550\pi$
$733$	−10.1169	−	5.84098i	−0.373675	−	0.215741i	−0.675063	+	0.737760i	$0.735883\pi$
$734$	−7.88701	−	31.5738i	−0.291115	−	1.16541i
$735$	−7.23659	+	42.4984i	−0.266925	+	1.56758i
$736$	−5.96344	+	16.4975i	−0.219815	+	0.608105i
$737$	−0.00776859	−	0.00448520i	−0.000286160	−	0.000165214i
$738$	−3.38006	−	42.9094i	−0.124422	−	1.57952i
$739$	8.47946	+	14.6869i	0.311922	+	0.540265i	0.978778	−	0.204922i	$-0.0656939\pi$
$739$	8.47946	+	14.6869i	0.311922	+	0.540265i	−0.666857	+	0.745186i	$0.732361\pi$
$740$	23.7522	+	0.808475i	0.873147	+	0.0297201i
$741$	−6.55231	+	3.08878i	−0.240705	+	0.113469i
$742$	0.522866	−	8.73333i	0.0191950	−	0.320611i
$743$	−14.5437			−0.533558			−0.266779	−	0.963758i	$-0.585959\pi$
$743$	−14.5437			−0.533558			−0.266779	+	0.963758i	$0.585959\pi$
$744$	15.1748	+	19.9089i	0.556335	+	0.729894i
$745$	−11.8883	−	20.5911i	−0.435553	−	0.754400i
$746$	25.4373	−	24.5862i	0.931326	−	0.900165i
$747$	1.95043	−	0.728412i	0.0713626	−	0.0266512i
$748$	5.12044	−	2.72838i	0.187222	−	0.0997594i
$749$	6.96991	−	6.39761i	0.254675	−	0.233764i
$750$	14.5675	+	17.8205i	0.531932	+	0.650712i
$751$	−9.37421	−	5.41220i	−0.342070	−	0.197494i	0.319117	−	0.947715i	$-0.396614\pi$
$751$	−9.37421	−	5.41220i	−0.342070	−	0.197494i	−0.661187	+	0.750221i	$0.729947\pi$
$752$	17.2338	+	1.17457i	0.628454	+	0.0428322i
$753$	−9.48607	−	6.58333i	−0.345692	−	0.239910i
$754$	−2.82835	−	0.809668i	−0.103003	−	0.0294864i
$755$		−	15.0384i		−	0.547303i
$756$	24.6457	−	12.1898i	0.896354	−	0.443340i
$757$			13.5121i			0.491105i	0.969383	+	0.245552i	$0.0789694\pi$
$757$			13.5121i			0.491105i	−0.969383	+	0.245552i	$0.921031\pi$
$758$	−4.56954	+	15.9624i	−0.165973	+	0.579782i
$759$	2.02131	+	1.40279i	0.0733690	+	0.0509181i
$760$	50.0825	+	16.1996i	1.81668	+	0.587621i
$761$	22.5165	+	12.9999i	0.816221	+	0.471245i	0.849111	−	0.528214i	$-0.177138\pi$
$761$	22.5165	+	12.9999i	0.816221	+	0.471245i	−0.0328907	+	0.999459i	$0.510471\pi$
$762$	29.7827	−	24.3462i	1.07892	−	0.881970i
$763$	−0.323955	−	1.45543i	−0.0117280	−	0.0526903i
$764$	−25.9054	+	13.8035i	−0.937226	+	0.499393i
$765$	63.2850	−	23.6345i	2.28808	−	0.854509i
$766$	−17.5585	−	18.1663i	−0.634415	−	0.656376i
$767$	0.690812	+	1.19652i	0.0249438	+	0.0432039i
$768$	−8.30639	−	26.4387i	−0.299731	−	0.954024i
$769$	3.84206			0.138548			0.0692741	−	0.997598i	$-0.477932\pi$
$769$	3.84206			0.138548			0.0692741	+	0.997598i	$0.477932\pi$
$770$	3.35708	−	5.08622i	0.120981	−	0.183295i
$771$	1.60617	−	0.757155i	0.0578449	−	0.0272683i
$772$	1.09752	−	32.2441i	0.0395007	−	1.16049i
$773$	−18.3710	−	31.8195i	−0.660760	−	1.14447i	−0.980416	−	0.196936i	$-0.936901\pi$
$773$	−18.3710	−	31.8195i	−0.660760	−	1.14447i	0.319657	−	0.947533i	$-0.396432\pi$
$774$	−15.0723	+	1.18728i	−0.541764	+	0.0426758i
$775$	33.8206	+	19.5263i	1.21487	+	0.701407i
$776$	−14.8079	+	13.3686i	−0.531574	+	0.479906i
$777$	−2.07526	−	15.1736i	−0.0744496	−	0.544351i
$778$	35.5251	−	8.87405i	1.27364	−	0.318150i
$779$	−45.9852	−	26.5495i	−1.64759	−	0.951236i
$780$	9.77477	+	1.15002i	0.349993	+	0.0411773i
$781$	−3.58628	+	2.07054i	−0.128327	+	0.0740897i
$782$	26.7013	+	7.64373i	0.954836	+	0.273339i
$783$	13.1096	+	3.33718i	0.468499	+	0.119261i
$784$	4.28453	−	27.6703i	0.153019	−	0.988223i
$785$			81.8606i			2.92173i
$786$	0.531030	+	3.25541i	0.0189412	+	0.116116i
$787$	19.1854	+	33.2301i	0.683886	+	1.18453i	0.973785	+	0.227469i	$0.0730450\pi$
$787$	19.1854	+	33.2301i	0.683886	+	1.18453i	−0.289899	+	0.957057i	$0.593622\pi$
$788$	37.2463	+	23.2285i	1.32685	+	0.827479i
$789$	−29.6957	−	2.47307i	−1.05719	−	0.0880436i
$790$	15.3136	+	61.3044i	0.544834	+	2.18111i
$791$	3.57046	+	1.12244i	0.126951	+	0.0399093i
$792$	−3.88301	+	0.173238i	−0.137977	+	0.00615575i
$793$	−2.12604	+	3.68241i	−0.0754979	+	0.130766i
$794$	−20.5528	+	19.8652i	−0.729392	+	0.704988i
$795$	−8.21036	+	11.8305i	−0.291192	+	0.419585i
$796$	31.8908	+	1.08550i	1.13034	+	0.0384745i
$797$	25.0108			0.885927			0.442964	−	0.896540i	$-0.353927\pi$
$797$	25.0108			0.885927			0.442964	+	0.896540i	$0.353927\pi$
$798$	4.83023	−	33.5741i	0.170988	−	1.18851i
$799$		−	27.3489i		−	0.967535i
$800$	−27.8631	−	33.0577i	−0.985109	−	1.16877i
$801$	4.02361	−	23.9895i	0.142167	−	0.847626i
$802$	−37.6837	+	36.4228i	−1.33066	+	1.28613i
$803$	−3.29798	−	1.90409i	−0.116383	−	0.0671939i
$804$	0.0543830	+	0.0405508i	0.00191794	+	0.00143012i
$805$	28.4760	−	6.33828i	1.00365	−	0.223395i
$806$	5.60215	−	1.39940i	0.197327	−	0.0492916i
$807$	−13.5544	−	1.12882i	−0.477138	−	0.0397363i
$808$	17.9956	+	5.82082i	0.633083	+	0.204776i
$809$	32.0756	−	18.5188i	1.12772	−	0.651087i	0.184357	−	0.982859i	$-0.440980\pi$
$809$	32.0756	−	18.5188i	1.12772	−	0.651087i	0.943360	+	0.331772i	$0.107646\pi$
$810$	−45.0828	−	3.95792i	−1.58405	−	0.139067i
$811$	1.97747			0.0694383			0.0347192	−	0.999397i	$-0.488946\pi$
$811$	1.97747			0.0694383			0.0347192	+	0.999397i	$0.488946\pi$
$812$	10.4598	−	8.96484i	0.367067	−	0.314604i
$813$	28.4197	−	13.3972i	0.996722	−	0.469859i
$814$	−0.595831	+	2.08137i	−0.0208839	+	0.0729521i
$815$	36.9820	+	64.0546i	1.29542	+	2.24374i
$816$	−40.8681	+	15.9670i	−1.43067	+	0.558958i
$817$	−9.32578	+	16.1527i	−0.326268	+	0.565112i
$818$	−39.8731	+	9.96015i	−1.39413	+	0.348249i
$819$	−0.334947	−	6.33351i	−0.0117040	−	0.221311i
$820$	33.9265	+	63.6709i	1.18476	+	2.22348i
$821$	−6.85902	+	11.8802i	−0.239382	+	0.414621i	−0.960537	−	0.278152i	$-0.910278\pi$
$821$	−6.85902	+	11.8802i	−0.239382	+	0.414621i	0.721155	+	0.692773i	$0.243611\pi$
$822$	−20.6098	−	7.80236i	−0.718851	−	0.272138i
$823$	34.0169	−	19.6397i	1.18575	−	0.684596i	0.228416	−	0.973564i	$-0.426646\pi$
$823$	34.0169	−	19.6397i	1.18575	−	0.684596i	0.957339	+	0.288968i	$0.0933122\pi$
$824$	17.5256	−	3.74941i	0.610532	−	0.130617i
$825$	−5.48490	+	2.58560i	−0.190960	+	0.0900191i
$826$	−6.45797	−	0.386639i	−0.224701	−	0.0134529i
$827$		−	26.9376i		−	0.936713i	−0.883540	−	0.468356i	$-0.844846\pi$
$827$		−	26.9376i		−	0.936713i	0.883540	−	0.468356i	$-0.155154\pi$
$828$	−13.9416	−	12.3218i	−0.484504	−	0.428212i
$829$	−17.5320	+	10.1221i	−0.608910	+	0.351554i	−0.772539	−	0.634968i	$-0.781013\pi$
$829$	−17.5320	+	10.1221i	−0.608910	+	0.351554i	0.163629	+	0.986522i	$0.447680\pi$
$830$	−2.50926	+	2.42531i	−0.0870978	+	0.0841836i
$831$	−3.20185	+	38.4466i	−0.111071	+	1.33370i
$832$	−6.35923	−	0.651378i	−0.220467	−	0.0225825i
$833$	−44.1690	−	3.78891i	−1.53036	−	0.131278i
$834$	−24.8319	−	30.3769i	−0.859857	−	1.05186i
$835$	13.4032	−	23.2150i	0.463836	−	0.803387i
$836$	−2.53740	+	4.06866i	−0.0877577	+	0.140718i
$837$	−25.5584	+	7.19285i	−0.883426	+	0.248621i
$838$	−1.73006	−	0.495263i	−0.0597641	−	0.0171086i
$839$	−45.3448			−1.56548			−0.782738	−	0.622352i	$-0.786177\pi$
$839$	−45.3448			−1.56548			−0.782738	+	0.622352i	$0.786177\pi$
$840$	−29.7078	+	35.2338i	−1.02502	+	1.21568i
$841$	−22.2223			−0.766286
$842$	16.4521	+	4.70970i	0.566975	+	0.162307i
$843$	25.4863	+	17.6875i	0.877794	+	0.609189i
$844$	−35.6246	−	22.2171i	−1.22625	−	0.764743i
$845$	−21.9767	+	38.0647i	−0.756020	+	1.30946i
$846$	−7.88652	+	16.5374i	−0.271144	+	0.568568i
$847$	−19.3046	−	21.0315i	−0.663315	−	0.722652i
$848$	5.21647	−	7.76323i	0.179134	−	0.266591i
$849$	7.74258	+	0.644805i	0.265725	+	0.0221297i
$850$	−49.2180	+	47.5712i	−1.68816	+	1.63168i
$851$	−8.97520	+	5.18183i	−0.307666	+	0.177631i
$852$	28.7645	−	12.3819i	0.985455	−	0.424198i
$853$			37.8961i			1.29754i	0.760986	+	0.648769i	$0.224716\pi$
$853$			37.8961i			1.29754i	−0.760986	+	0.648769i	$0.775284\pi$
$854$	−8.90701	−	17.8072i	−0.304792	−	0.609351i
$855$	−35.5284	+	43.0668i	−1.21505	+	1.47285i
$856$	9.89035	−	2.11593i	0.338045	−	0.0723211i
$857$	−30.1090	+	17.3834i	−1.02850	+	0.593806i	−0.916555	−	0.399908i	$-0.869042\pi$
$857$	−30.1090	+	17.3834i	−1.02850	+	0.593806i	−0.111947	+	0.993714i	$0.535709\pi$
$858$	−0.317438	+	0.838508i	−0.0108371	+	0.0286262i
$859$	−17.5062	+	30.3217i	−0.597305	+	1.03456i	0.395912	+	0.918288i	$0.370428\pi$
$859$	−17.5062	+	30.3217i	−0.597305	+	1.03456i	−0.993217	+	0.116274i	$0.962905\pi$
$860$	22.3650	−	11.9170i	0.762640	−	0.406366i
$861$	36.7411	−	28.4869i	1.25213	−	0.970831i
$862$	−22.9505	+	5.73294i	−0.781696	+	0.195265i
$863$	−11.8510	+	20.5265i	−0.403413	+	0.698732i	−0.994135	−	0.108143i	$-0.965509\pi$
$863$	−11.8510	+	20.5265i	−0.403413	+	0.698732i	0.590722	+	0.806875i	$0.298843\pi$
$864$	29.3166	+	2.13003i	0.997371	+	0.0724651i
$865$	−27.6490	−	47.8894i	−0.940093	−	1.62829i
$866$	−5.51544	+	19.2667i	−0.187422	+	0.654708i
$867$	17.0658	+	36.2021i	0.579586	+	1.22949i
$868$	−8.98154	+	25.5031i	−0.304853	+	0.865632i
$869$	−5.75618			−0.195265
$870$	−22.3787	+	3.65047i	−0.758709	+	0.123763i
$871$	0.0135515	−	0.00782398i	0.000459176	−	0.000265106i
$872$	0.490568	−	1.51664i	0.0166127	−	0.0513598i
$873$	−7.40303	−	19.8227i	−0.250554	−	0.670897i
$874$	−22.2694	+	5.56281i	−0.753274	+	0.188165i
$875$	−7.45583	+	23.7169i	−0.252053	+	0.801777i
$876$	23.0871	+	17.2149i	0.780041	+	0.581638i
$877$	−6.02275	−	3.47724i	−0.203374	−	0.117418i	0.394854	−	0.918744i	$-0.370795\pi$
$877$	−6.02275	−	3.47724i	−0.203374	−	0.117418i	−0.598228	+	0.801326i	$0.704128\pi$
$878$	−26.2269	+	25.3494i	−0.885115	+	0.855500i
$879$	−24.4621	+	35.2480i	−0.825086	+	1.18889i
$880$	5.85060	−	2.86631i	0.197224	−	0.0966234i
$881$		−	23.8500i		−	0.803528i	−0.915743	−	0.401764i	$-0.868397\pi$
$881$		−	23.8500i		−	0.803528i	0.915743	−	0.401764i	$-0.131603\pi$
$882$	25.6156	+	15.0280i	0.862523	+	0.506018i
$883$	32.0357			1.07809			0.539044	−	0.842278i	$-0.318786\pi$
$883$	32.0357			1.07809			0.539044	+	0.842278i	$0.318786\pi$
$884$	−0.344298	+	10.1151i	−0.0115800	+	0.340208i
$885$	8.74821	+	6.07125i	0.294068	+	0.204083i
$886$	35.6942	−	34.4999i	1.19917	−	1.15905i
$887$	25.4399	−	44.0633i	0.854190	−	1.47950i	−0.0232053	−	0.999731i	$-0.507387\pi$
$887$	25.4399	−	44.0633i	0.854190	−	1.47950i	0.877395	−	0.479769i	$-0.159280\pi$
$888$	6.31418	−	15.1057i	0.211890	−	0.506916i
$889$	39.6372	+	12.4607i	1.32939	+	0.417917i
$890$	9.88101	+	39.5563i	0.331212	+	1.32593i
$891$	1.34510	−	3.89705i	0.0450625	−	0.130556i
$892$	7.46207	−	11.9653i	0.249849	−	0.400627i
$893$	11.3012	+	19.5743i	0.378182	+	0.655030i
$894$	−16.1660	+	2.63703i	−0.540671	+	0.0881956i
$895$		−	32.0747i		−	1.07214i
$896$	18.9489	−	23.1719i	0.633038	−	0.774120i
$897$	−3.88218	+	1.83007i	−0.129622	+	0.0611044i
$898$	18.8836	+	5.40578i	0.630155	+	0.180393i
$899$	−11.5206	+	6.65141i	−0.384233	+	0.221837i
$900$	43.4793	−	14.5727i	1.44931	−	0.485755i
$901$	−12.8243	−	7.40413i	−0.427241	−	0.246667i
$902$	−6.37625	+	1.59276i	−0.212306	+	0.0530332i
$903$	−10.0063	−	12.9057i	−0.332989	−	0.429474i
$904$	2.68122	+	2.96989i	0.0891761	+	0.0987770i
$905$	32.0372	+	18.4967i	1.06495	+	0.614851i
$906$	−9.68886	−	3.66795i	−0.321891	−	0.121860i
$907$	5.21438	+	9.03157i	0.173141	+	0.299888i	0.939516	−	0.342504i	$-0.111275\pi$
$907$	5.21438	+	9.03157i	0.173141	+	0.299888i	−0.766376	+	0.642393i	$0.777942\pi$
$908$	−41.4715	−	1.41161i	−1.37628	−	0.0468458i
$909$	−12.7660	+	15.4747i	−0.423423	+	0.513264i
$910$	4.75568	+	9.50774i	0.157649	+	0.315178i
$911$	−9.95365			−0.329779			−0.164889	−	0.986312i	$-0.552727\pi$
$911$	−9.95365			−0.329779			−0.164889	+	0.986312i	$0.552727\pi$
$912$	22.6524	−	28.3157i	0.750096	−	0.937628i
$913$	−0.158952	−	0.275313i	−0.00526055	−	0.00911153i
$914$	−7.41614	−	7.67287i	−0.245304	−	0.253796i
$915$	−2.71984	+	32.6589i	−0.0899152	+	1.07967i
$916$	−20.6831	−	38.8166i	−0.683389	−	1.28254i
$917$	−2.62467	+	2.40916i	−0.0866742	+	0.0795574i
$918$	0.208447	−	46.5376i	0.00687977	−	1.53597i
$919$	−7.23519	−	4.17724i	−0.238667	−	0.137794i	0.375897	−	0.926661i	$-0.377335\pi$
$919$	−7.23519	−	4.17724i	−0.238667	−	0.137794i	−0.614564	+	0.788867i	$0.710668\pi$
$920$	29.6734	+	9.59810i	0.978303	+	0.316440i
$921$	−7.62556	+	10.9879i	−0.251271	+	0.362062i
$922$	−6.86329	+	23.9750i	−0.226031	+	0.789576i
$923$		−	7.22370i		−	0.237771i
$924$	−2.45811	−	3.40345i	−0.0808660	−	0.111965i
$925$		−	25.5419i		−	0.839812i
$926$	40.1343	+	11.4892i	1.31890	+	0.377558i
$927$	−3.14440	+	18.7474i	−0.103276	+	0.615747i
$928$	14.4977	−	2.58929i	0.475909	−	0.0849978i
$929$	45.0777	+	26.0256i	1.47895	+	0.853872i	0.999716	−	0.0238151i	$-0.00758131\pi$
$929$	45.0777	+	26.0256i	1.47895	+	0.853872i	0.479234	+	0.877687i	$0.340915\pi$
$930$	34.4563	−	28.1667i	1.12987	−	0.923622i
$931$	33.1786	−	15.5399i	1.08738	−	0.509300i
$932$	−16.4420	−	30.8573i	−0.538577	−	1.01076i
$933$	−34.5537	−	2.87765i	−1.13124	−	0.0942099i
$934$	−31.0357	+	29.9973i	−1.01552	+	0.981541i
$935$	−5.15747	−	8.93299i	−0.168667	−	0.292140i
$936$	3.12506	−	6.01715i	0.102146	−	0.196677i
$937$	−35.8998			−1.17280			−0.586398	−	0.810023i	$-0.699455\pi$
$937$	−35.8998			−1.17280			−0.586398	+	0.810023i	$0.699455\pi$
$938$	−0.00437899	+	0.0731416i	−0.000142979	+	0.00238816i
$939$	−12.6218	−	26.7749i	−0.411897	−	0.873767i
$940$	1.04470	−	30.6922i	0.0340743	−	1.00107i
$941$	2.74621	+	4.75657i	0.0895238	+	0.155060i	0.907310	−	0.420462i	$-0.138132\pi$
$941$	2.74621	+	4.75657i	0.0895238	+	0.155060i	−0.817786	+	0.575522i	$0.804799\pi$
$942$	52.7408	+	19.9663i	1.71839	+	0.650537i
$943$	−27.2458	−	15.7304i	−0.887245	−	0.512251i
$944$	−5.74062	−	3.85738i	−0.186841	−	0.125547i
$945$	−23.1494	−	43.0532i	−0.753051	−	1.40052i
$946$	0.559473	+	2.23972i	0.0181900	+	0.0728195i
$947$	1.99491	+	1.15176i	0.0648257	+	0.0374272i	0.532063	−	0.846705i	$-0.321417\pi$
$947$	1.99491	+	1.15176i	0.0648257	+	0.0374272i	−0.467237	+	0.884132i	$0.654750\pi$
$948$	43.2320	+	5.08632i	1.40411	+	0.165196i
$949$	5.75300	−	3.32150i	0.186750	−	0.107820i
$950$	15.5690	−	54.3861i	0.505126	−	1.76452i
$951$	11.3302	+	24.0351i	0.367408	+	0.779391i
$952$	−38.6422	−	27.4369i	−1.25240	−	0.889236i
$953$		−	27.0751i		−	0.877047i	−0.898720	−	0.438524i	$-0.855502\pi$
$953$		−	27.0751i		−	0.877047i	0.898720	−	0.438524i	$-0.144498\pi$
$954$	5.61955	+	8.17527i	0.181940	+	0.264684i
$955$	26.0928	+	45.1940i	0.844343	+	1.46244i
$956$	−11.2097	−	6.99084i	−0.362546	−	0.226100i
$957$	0.171427	−	2.05843i	0.00554144	−	0.0665395i
$958$	−0.266074	+	0.0664643i	−0.00859646	+	0.00214736i
$959$	−5.17159	−	23.2344i	−0.166999	−	0.750278i
$960$	−46.4739	+	16.3578i	−1.49994	+	0.527945i
$961$	−2.44506	+	4.23497i	−0.0788729	+	0.136612i
$962$	−2.62464	−	2.71549i	−0.0846217	−	0.0875511i
$963$	−1.77450	+	10.5799i	−0.0571826	+	0.340932i
$964$	−0.718410	+	21.1062i	−0.0231384	+	0.679783i
$965$	−57.3577			−1.84641
$966$	2.86187	−	19.8923i	0.0920790	−	0.640025i
$967$			33.0009i			1.06124i	0.847611	+	0.530618i	$0.178040\pi$
$967$			33.0009i			1.06124i	−0.847611	+	0.530618i	$0.821960\pi$
$968$	−6.38478	−	29.8439i	−0.205215	−	0.959218i
$969$	−47.1660	−	32.7332i	−1.51519	−	1.05154i
$970$	24.6490	+	25.5023i	0.791431	+	0.818828i
$971$	−31.6718	−	18.2857i	−1.01640	−	0.586817i	−0.103339	−	0.994646i	$-0.532953\pi$
$971$	−31.6718	−	18.2857i	−1.01640	−	0.586817i	−0.913058	+	0.407829i	$0.866286\pi$
$972$	−13.5460	+	28.0804i	−0.434487	+	0.900678i
$973$	12.7092	−	40.4279i	0.407439	−	1.29606i
$974$	6.90539	+	27.6441i	0.221263	+	0.885774i
$975$	0.877874	−	10.5412i	0.0281145	−	0.337588i
$976$	1.44734	−	21.2361i	0.0463283	−	0.679750i
$977$	−2.71660	+	1.56843i	−0.0869117	+	0.0501785i	−0.542826	−	0.839845i	$-0.682646\pi$
$977$	−2.71660	+	1.56843i	−0.0869117	+	0.0501785i	0.455914	+	0.890024i	$0.349312\pi$
$978$	50.2889	−	8.20326i	1.60806	−	0.262311i
$979$	−3.71414			−0.118704
$980$	−49.4237	−	5.93929i	−1.57878	−	0.189724i
$981$	1.30418	+	1.07590i	0.0416393	+	0.0343508i
$982$	5.84961	+	1.67456i	0.186668	+	0.0534373i
$983$	−5.06871	−	8.77927i	−0.161667	−	0.280015i	0.773800	−	0.633430i	$-0.218354\pi$
$983$	−5.06871	−	8.77927i	−0.161667	−	0.280015i	−0.935467	+	0.353415i	$0.885020\pi$
$984$	49.2964	−	6.32827i	1.57151	−	0.201738i
$985$	39.0197	−	67.5842i	1.24327	−	2.15341i
$986$	−5.65081	−	22.6216i	−0.179958	−	0.720420i
$987$	−19.6071	+	2.68162i	−0.624102	+	0.0853569i
$988$	−3.93339	−	7.38193i	−0.125138	−	0.234850i
$989$	−5.52544	+	9.57034i	−0.175699	+	0.304319i
$990$	0.542650	+	6.88887i	0.0172465	+	0.218943i
$991$	22.8644	−	13.2008i	0.726313	−	0.419337i	−0.0907589	−	0.995873i	$-0.528929\pi$
$991$	22.8644	−	13.2008i	0.726313	−	0.419337i	0.817072	+	0.576536i	$0.195596\pi$
$992$	−22.1017	+	18.6287i	−0.701731	+	0.591463i
$993$	−10.1350	−	21.4996i	−0.321624	−	0.682269i
$994$	28.2306	+	18.6332i	0.895419	+	0.591008i
$995$		−	56.7293i		−	1.79844i
$996$	0.950541	+	2.20820i	0.0301190	+	0.0699696i
$997$	−0.842124	+	0.486200i	−0.0266703	+	0.0153981i	−0.513276	−	0.858224i	$-0.671568\pi$
$997$	−0.842124	+	0.486200i	−0.0266703	+	0.0153981i	0.486606	+	0.873622i	$0.338235\pi$
$998$	25.5929	+	26.4789i	0.810131	+	0.838175i
$999$	12.4322	+	12.1244i	0.393336	+	0.383598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.v.a.107.17	yes	56
3.2	odd	2	inner	168.2.v.a.107.12	yes	56
4.3	odd	2		672.2.bd.a.527.19		56
7.4	even	3	inner	168.2.v.a.11.22	yes	56
8.3	odd	2	inner	168.2.v.a.107.7	yes	56
8.5	even	2		672.2.bd.a.527.20		56
12.11	even	2		672.2.bd.a.527.2		56
21.11	odd	6	inner	168.2.v.a.11.7	✓	56
24.5	odd	2		672.2.bd.a.527.1		56
24.11	even	2	inner	168.2.v.a.107.22	yes	56
28.11	odd	6		672.2.bd.a.431.1		56
56.11	odd	6	inner	168.2.v.a.11.12	yes	56
56.53	even	6		672.2.bd.a.431.2		56
84.11	even	6		672.2.bd.a.431.20		56
168.11	even	6	inner	168.2.v.a.11.17	yes	56
168.53	odd	6		672.2.bd.a.431.19		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.7	✓	56	21.11	odd	6	inner
168.2.v.a.11.12	yes	56	56.11	odd	6	inner
168.2.v.a.11.17	yes	56	168.11	even	6	inner
168.2.v.a.11.22	yes	56	7.4	even	3	inner
168.2.v.a.107.7	yes	56	8.3	odd	2	inner
168.2.v.a.107.12	yes	56	3.2	odd	2	inner
168.2.v.a.107.17	yes	56	1.1	even	1	trivial
168.2.v.a.107.22	yes	56	24.11	even	2	inner
672.2.bd.a.431.1		56	28.11	odd	6
672.2.bd.a.431.2		56	56.53	even	6
672.2.bd.a.431.19		56	168.53	odd	6
672.2.bd.a.431.20		56	84.11	even	6
672.2.bd.a.527.1		56	24.5	odd	2
672.2.bd.a.527.2		56	12.11	even	2
672.2.bd.a.527.19		56	4.3	odd	2
672.2.bd.a.527.20		56	8.5	even	2

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.389211 - 1.35960i) q^{2} +(-0.987527 + 1.42295i) q^{3} +(-1.69703 - 1.05834i) q^{4} +(-1.77783 + 3.07929i) q^{5} +(1.55029 + 1.89647i) q^{6} +(-0.793456 + 2.52397i) q^{7} +(-2.09943 + 1.89537i) q^{8} +(-1.04958 - 2.81041i) q^{9} +(3.49466 + 3.61563i) q^{10} +(-0.396703 + 0.229036i) q^{11} +(3.18183 - 1.36965i) q^{12} -0.799063i q^{13} +(3.12277 + 2.06114i) q^{14} +(-2.62603 - 5.57065i) q^{15} +(1.75982 + 3.59208i) q^{16} +(5.48456 - 3.16651i) q^{17} +(-4.22954 + 0.333169i) q^{18} +(-2.61696 + 4.53272i) q^{19} +(6.27598 - 3.34410i) q^{20} +(-2.80793 - 3.62154i) q^{21} +(0.156997 + 0.628501i) q^{22} +(-1.55053 + 2.68559i) q^{23} +(-0.623772 - 4.85911i) q^{24} +(-3.82137 - 6.61880i) q^{25} +(-1.08641 - 0.311004i) q^{26} +(5.03556 + 1.28185i) q^{27} +(4.01774 - 3.44351i) q^{28} +2.60340 q^{29} +(-8.59594 + 1.40219i) q^{30} +(-4.42520 + 2.55489i) q^{31} +(5.56873 - 0.994581i) q^{32} +(0.0658472 - 0.790668i) q^{33} +(-2.17055 - 8.68926i) q^{34} +(-6.36142 - 6.93048i) q^{35} +(-1.19320 + 5.88016i) q^{36} +(2.89424 + 1.67099i) q^{37} +(5.14413 + 5.32221i) q^{38} +(1.13703 + 0.789096i) q^{39} +(-2.10396 - 9.83439i) q^{40} +10.1452i q^{41} +(-6.01672 + 2.40812i) q^{42} +3.56359 q^{43} +(0.915615 + 0.0311657i) q^{44} +(10.5200 + 1.76446i) q^{45} +(3.04785 + 3.15336i) q^{46} +(2.15923 - 3.73989i) q^{47} +(-6.84922 - 1.04314i) q^{48} +(-5.74086 - 4.00532i) q^{49} +(-10.4862 + 2.61943i) q^{50} +(-0.910362 + 10.9313i) q^{51} +(-0.845682 + 1.35603i) q^{52} +(-1.16913 - 2.02499i) q^{53} +(3.70270 - 6.34744i) q^{54} -1.62875i q^{55} +(-3.11805 - 6.80278i) q^{56} +(-3.86551 - 8.19999i) q^{57} +(1.01327 - 3.53959i) q^{58} +(-1.49741 + 0.864528i) q^{59} +(-1.43921 + 12.2328i) q^{60} +(-4.60841 - 2.66067i) q^{61} +(1.75130 + 7.01090i) q^{62} +(7.92618 - 0.419175i) q^{63} +(0.815178 - 7.95836i) q^{64} +(2.46055 + 1.42060i) q^{65} +(-1.04936 - 0.397262i) q^{66} +(0.00979145 + 0.0169593i) q^{67} +(-12.6587 - 0.430877i) q^{68} +(-2.29028 - 4.85842i) q^{69} +(-11.8986 + 5.95157i) q^{70} +9.04022 q^{71} +(7.53026 + 3.91090i) q^{72} +(4.15674 + 7.19969i) q^{73} +(3.39835 - 3.28465i) q^{74} +(13.1919 + 1.09863i) q^{75} +(9.23823 - 4.92251i) q^{76} +(-0.263315 - 1.18300i) q^{77} +(1.51540 - 1.23878i) q^{78} +(10.8825 + 6.28304i) q^{79} +(-14.1897 - 0.967099i) q^{80} +(-6.79677 + 5.89949i) q^{81} +(13.7934 + 3.94861i) q^{82} +0.694004i q^{83} +(0.932309 + 9.11761i) q^{84} +22.5181i q^{85} +(1.38699 - 4.84506i) q^{86} +(-2.57093 + 3.70452i) q^{87} +(0.398740 - 1.23274i) q^{88} +(7.02189 + 4.05409i) q^{89} +(6.49348 - 13.6163i) q^{90} +(2.01681 + 0.634021i) q^{91} +(5.47357 - 2.91654i) q^{92} +(0.734523 - 8.81987i) q^{93} +(-4.24437 - 4.39129i) q^{94} +(-9.30504 - 16.1168i) q^{95} +(-4.08404 + 8.90621i) q^{96} +7.05333 q^{97} +(-7.68004 + 6.24636i) q^{98} +(1.06006 + 0.874504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) \) 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

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