LMFDB - Embedded newform 372.2.p.a.191.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(191,372)] 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("372.191"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.p (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:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.1
Character	$\chi$	$=$	372.191
Dual form			372.2.p.a.335.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40808 - 0.131599i) q^{2} +(-1.09284 - 1.34377i) q^{3} +(1.96536 + 0.370602i) q^{4} +(1.29603 - 0.748262i) q^{5} +(1.36196 + 2.03594i) q^{6} +(2.28079 + 1.31682i) q^{7} +(-2.71861 - 0.780475i) q^{8} +(-0.611419 + 2.93703i) q^{9} +(-1.92338 + 0.883056i) q^{10} +(1.70265 + 2.94907i) q^{11} +(-1.64982 - 3.04600i) q^{12} +(2.50638 + 4.34118i) q^{13} +(-3.03824 - 2.15433i) q^{14} +(-2.42184 - 0.923832i) q^{15} +(3.72531 + 1.45674i) q^{16} +(-4.70546 - 2.71670i) q^{17} +(1.24744 - 4.05511i) q^{18} +(0.335211 + 0.193534i) q^{19} +(2.82447 - 0.990297i) q^{20} +(-0.723038 - 4.50392i) q^{21} +(-2.00936 - 4.37658i) q^{22} +4.16528 q^{23} +(1.92222 + 4.50611i) q^{24} +(-1.38021 + 2.39059i) q^{25} +(-2.95789 - 6.44256i) q^{26} +(4.61487 - 2.38809i) q^{27} +(3.99457 + 3.43329i) q^{28} +7.03104i q^{29} +(3.28856 + 1.61954i) q^{30} +(5.32164 - 1.63712i) q^{31} +(-5.05382 - 2.54144i) q^{32} +(2.10215 - 5.51081i) q^{33} +(6.26813 + 4.44455i) q^{34} +3.94129 q^{35} +(-2.29013 + 5.54575i) q^{36} +(4.81658 - 8.34257i) q^{37} +(-0.446534 - 0.316624i) q^{38} +(3.09447 - 8.11220i) q^{39} +(-4.10740 + 1.02272i) q^{40} +(8.60743 - 4.96950i) q^{41} +(0.425384 + 6.43701i) q^{42} +(-5.80668 - 3.35249i) q^{43} +(2.25339 + 6.42700i) q^{44} +(1.40525 + 4.26398i) q^{45} +(-5.86503 - 0.548145i) q^{46} +3.55266 q^{47} +(-2.11364 - 6.59792i) q^{48} +(-0.0319916 - 0.0554111i) q^{49} +(2.25804 - 3.18450i) q^{50} +(1.49168 + 9.29194i) q^{51} +(3.31710 + 9.46088i) q^{52} +(0.615816 - 0.355541i) q^{53} +(-6.81236 + 2.75531i) q^{54} +(4.41335 + 2.54805i) q^{55} +(-5.17285 - 5.36002i) q^{56} +(-0.106266 - 0.661946i) q^{57} +(0.925276 - 9.90025i) q^{58} +(-2.60378 + 4.50988i) q^{59} +(-4.41741 - 2.71320i) q^{60} -12.0784 q^{61} +(-7.70872 + 1.60487i) q^{62} +(-5.26205 + 5.89364i) q^{63} +(6.78172 + 4.24362i) q^{64} +(6.49669 + 3.75086i) q^{65} +(-3.68520 + 7.48301i) q^{66} +(-6.77129 + 3.90940i) q^{67} +(-8.24112 - 7.08315i) q^{68} +(-4.55197 - 5.59716i) q^{69} +(-5.54965 - 0.518669i) q^{70} +(0.243916 + 0.422475i) q^{71} +(3.95450 - 7.50746i) q^{72} +(-3.90359 - 6.76121i) q^{73} +(-7.87999 + 11.1131i) q^{74} +(4.72074 - 0.757845i) q^{75} +(0.587087 + 0.504595i) q^{76} +8.96829i q^{77} +(-5.42481 + 11.0154i) q^{78} +(2.17740 + 1.25712i) q^{79} +(5.91812 - 0.899537i) q^{80} +(-8.25233 - 3.59152i) q^{81} +(-12.7739 + 5.86472i) q^{82} +(-6.77093 - 11.7276i) q^{83} +(0.248129 - 9.11979i) q^{84} -8.13121 q^{85} +(7.73507 + 5.48471i) q^{86} +(9.44808 - 7.68378i) q^{87} +(-2.32716 - 9.34625i) q^{88} +11.5548i q^{89} +(-1.41757 - 6.18894i) q^{90} +13.2018i q^{91} +(8.18629 + 1.54366i) q^{92} +(-8.01558 - 5.36194i) q^{93} +(-5.00242 - 0.467525i) q^{94} +0.579257 q^{95} +(2.10789 + 9.56853i) q^{96} +13.9329 q^{97} +(0.0377546 + 0.0822332i) q^{98} +(-9.70255 + 3.19761i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) $ 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.40808	−	0.131599i	−0.995661	−	0.0930543i
$2$	−1.40808	−	0.131599i	−0.995661	−	0.0930543i
$3$	−1.09284	−	1.34377i	−0.630949	−	0.775824i
$3$	−1.09284	−	1.34377i	−0.630949	−	0.775824i
$4$	1.96536	+	0.370602i	0.982682	+	0.185301i
$5$	1.29603	−	0.748262i	0.579601	−	0.334633i	−0.181374	−	0.983414i	$-0.558054\pi$
$5$	1.29603	−	0.748262i	0.579601	−	0.334633i	0.760975	+	0.648781i	$0.224721\pi$
$6$	1.36196	+	2.03594i	0.556018	+	0.831170i
$7$	2.28079	+	1.31682i	0.862058	+	0.497710i	0.864701	−	0.502287i	$-0.167508\pi$
$7$	2.28079	+	1.31682i	0.862058	+	0.497710i	−0.00264266	+	0.999997i	$0.500841\pi$
$8$	−2.71861	−	0.780475i	−0.961175	−	0.275940i
$9$	−0.611419	+	2.93703i	−0.203806	+	0.979011i
$10$	−1.92338	+	0.883056i	−0.608226	+	0.279247i
$11$	1.70265	+	2.94907i	0.513367	+	0.889178i	0.999880	+	0.0155044i	$0.00493542\pi$
$11$	1.70265	+	2.94907i	0.513367	+	0.889178i	−0.486513	+	0.873674i	$0.661731\pi$
$12$	−1.64982	−	3.04600i	−0.476261	−	0.879304i
$13$	2.50638	+	4.34118i	0.695146	+	1.20403i	0.970132	+	0.242580i	$0.0779936\pi$
$13$	2.50638	+	4.34118i	0.695146	+	1.20403i	−0.274986	+	0.961448i	$0.588673\pi$
$14$	−3.03824	−	2.15433i	−0.812004	−	0.575768i
$15$	−2.42184	−	0.923832i	−0.625315	−	0.238532i
$16$	3.72531	+	1.45674i	0.931327	+	0.364184i
$17$	−4.70546	−	2.71670i	−1.14124	−	0.658896i	−0.194503	−	0.980902i	$-0.562309\pi$
$17$	−4.70546	−	2.71670i	−1.14124	−	0.658896i	−0.946738	+	0.322006i	$0.895643\pi$
$18$	1.24744	−	4.05511i	0.294023	−	0.955798i
$19$	0.335211	+	0.193534i	0.0769027	+	0.0443998i	0.537958	−	0.842971i	$-0.319196\pi$
$19$	0.335211	+	0.193534i	0.0769027	+	0.0443998i	−0.461056	+	0.887371i	$0.652529\pi$
$20$	2.82447	−	0.990297i	0.631572	−	0.221437i
$21$	−0.723038	−	4.50392i	−0.157780	−	0.982835i
$22$	−2.00936	−	4.37658i	−0.428398	−	0.933091i
$23$	4.16528			0.868521			0.434260	−	0.900787i	$-0.357010\pi$
$23$	4.16528			0.868521			0.434260	+	0.900787i	$0.357010\pi$
$24$	1.92222	+	4.50611i	0.392372	+	0.919807i
$25$	−1.38021	+	2.39059i	−0.276041	+	0.478118i
$26$	−2.95789	−	6.44256i	−0.580090	−	1.26349i
$27$	4.61487	−	2.38809i	0.888132	−	0.459588i
$28$	3.99457	+	3.43329i	0.754903	+	0.648830i
$29$			7.03104i			1.30563i	0.757516	+	0.652816i	$0.226413\pi$
$29$			7.03104i			1.30563i	−0.757516	+	0.652816i	$0.773587\pi$
$30$	3.28856	+	1.61954i	0.600406	+	0.295686i
$31$	5.32164	−	1.63712i	0.955795	−	0.294035i
$31$	5.32164	−	1.63712i	0.955795	−	0.294035i
$32$	−5.05382	−	2.54144i	−0.893397	−	0.449268i
$33$	2.10215	−	5.51081i	0.365937	−	0.959309i
$34$	6.26813	+	4.44455i	1.07498	+	0.762234i
$35$	3.94129			0.666200
$36$	−2.29013	+	5.54575i	−0.381689	+	0.924291i
$37$	4.81658	−	8.34257i	0.791842	−	1.37151i	−0.132984	−	0.991118i	$-0.542456\pi$
$37$	4.81658	−	8.34257i	0.791842	−	1.37151i	0.924825	−	0.380392i	$-0.124211\pi$
$38$	−0.446534	−	0.316624i	−0.0724374	−	0.0513632i
$39$	3.09447	−	8.11220i	0.495512	−	1.29899i
$40$	−4.10740	+	1.02272i	−0.649437	+	0.161706i
$41$	8.60743	−	4.96950i	1.34426	−	0.776106i	0.356826	−	0.934171i	$-0.383859\pi$
$41$	8.60743	−	4.96950i	1.34426	−	0.776106i	0.987429	+	0.158065i	$0.0505254\pi$
$42$	0.425384	+	6.43701i	0.0656382	+	0.993253i
$43$	−5.80668	−	3.35249i	−0.885510	−	0.511249i	−0.0130389	−	0.999915i	$-0.504151\pi$
$43$	−5.80668	−	3.35249i	−0.885510	−	0.511249i	−0.872471	+	0.488665i	$0.837484\pi$
$44$	2.25339	+	6.42700i	0.339711	+	0.968906i
$45$	1.40525	+	4.26398i	0.209483	+	0.635637i
$46$	−5.86503	−	0.548145i	−0.864752	−	0.0808195i
$47$	3.55266			0.518209			0.259104	−	0.965849i	$-0.416573\pi$
$47$	3.55266			0.518209			0.259104	+	0.965849i	$0.416573\pi$
$48$	−2.11364	−	6.59792i	−0.305077	−	0.952328i
$49$	−0.0319916	−	0.0554111i	−0.00457023	−	0.00791587i
$50$	2.25804	−	3.18450i	0.319335	−	0.450357i
$51$	1.49168	+	9.29194i	0.208878	+	1.30113i
$52$	3.31710	+	9.46088i	0.460000	+	1.31199i
$53$	0.615816	−	0.355541i	0.0845888	−	0.0488374i	−0.457109	−	0.889411i	$-0.651115\pi$
$53$	0.615816	−	0.355541i	0.0845888	−	0.0488374i	0.541698	+	0.840573i	$0.317782\pi$
$54$	−6.81236	+	2.75531i	−0.927045	+	0.374950i
$55$	4.41335	+	2.54805i	0.595097	+	0.343579i
$56$	−5.17285	−	5.36002i	−0.691251	−	0.716262i
$57$	−0.106266	−	0.661946i	−0.0140752	−	0.0876769i
$58$	0.925276	−	9.90025i	0.121495	−	1.29997i
$59$	−2.60378	+	4.50988i	−0.338983	+	0.587136i	−0.984242	−	0.176828i	$-0.943416\pi$
$59$	−2.60378	+	4.50988i	−0.338983	+	0.587136i	0.645258	+	0.763964i	$0.276750\pi$
$60$	−4.41741	−	2.71320i	−0.570286	−	0.350273i
$61$	−12.0784			−1.54648			−0.773239	−	0.634114i	$-0.781365\pi$
$61$	−12.0784			−1.54648			−0.773239	+	0.634114i	$0.781365\pi$
$62$	−7.70872	+	1.60487i	−0.979009	+	0.203819i
$63$	−5.26205	+	5.89364i	−0.662956	+	0.742528i
$64$	6.78172	+	4.24362i	0.847715	+	0.530453i
$65$	6.49669	+	3.75086i	0.805815	+	0.465238i
$66$	−3.68520	+	7.48301i	−0.453617	+	0.921094i
$67$	−6.77129	+	3.90940i	−0.827244	+	0.477610i	−0.852908	−	0.522061i	$-0.825163\pi$
$67$	−6.77129	+	3.90940i	−0.827244	+	0.477610i	0.0256638	+	0.999671i	$0.491830\pi$
$68$	−8.24112	−	7.08315i	−0.999383	−	0.858958i
$69$	−4.55197	−	5.59716i	−0.547992	−	0.673819i
$70$	−5.54965	−	0.518669i	−0.663310	−	0.0619928i
$71$	0.243916	+	0.422475i	0.0289475	+	0.0501385i	0.880136	−	0.474721i	$-0.157451\pi$
$71$	0.243916	+	0.422475i	0.0289475	+	0.0501385i	−0.851189	+	0.524860i	$0.824118\pi$
$72$	3.95450	−	7.50746i	0.466042	−	0.884763i
$73$	−3.90359	−	6.76121i	−0.456880	−	0.791340i	0.541914	−	0.840434i	$-0.317700\pi$
$73$	−3.90359	−	6.76121i	−0.456880	−	0.791340i	−0.998794	+	0.0490944i	$0.984366\pi$
$74$	−7.87999	+	11.1131i	−0.916031	+	1.29187i
$75$	4.72074	−	0.757845i	0.545104	−	0.0875084i
$76$	0.587087	+	0.504595i	0.0673435	+	0.0578810i
$77$			8.96829i			1.02203i
$78$	−5.42481	+	11.0154i	−0.614239	+	1.24725i
$79$	2.17740	+	1.25712i	0.244976	+	0.141437i	0.617462	−	0.786601i	$-0.288161\pi$
$79$	2.17740	+	1.25712i	0.244976	+	0.141437i	−0.372486	+	0.928038i	$0.621494\pi$
$80$	5.91812	−	0.899537i	0.661666	−	0.100571i
$81$	−8.25233	−	3.59152i	−0.916926	−	0.399058i
$82$	−12.7739	+	5.86472i	−1.41064	+	0.647650i
$83$	−6.77093	−	11.7276i	−0.743206	−	1.28727i	−0.951028	−	0.309104i	$-0.899971\pi$
$83$	−6.77093	−	11.7276i	−0.743206	−	1.28727i	0.207822	−	0.978167i	$-0.433363\pi$
$84$	0.248129	−	9.11979i	0.0270731	−	0.995051i
$85$	−8.13121			−0.881953
$86$	7.73507	+	5.48471i	0.834094	+	0.591432i
$87$	9.44808	−	7.68378i	1.01294	−	0.823787i
$88$	−2.32716	−	9.34625i	−0.248076	−	0.996314i
$89$			11.5548i			1.22481i	0.790544	+	0.612405i	$0.209798\pi$
$89$			11.5548i			1.22481i	−0.790544	+	0.612405i	$0.790202\pi$
$90$	−1.41757	−	6.18894i	−0.149425	−	0.652372i
$91$			13.2018i			1.38392i
$92$	8.18629	+	1.54366i	0.853479	+	0.160938i
$93$	−8.01558	−	5.36194i	−0.831177	−	0.556007i
$94$	−5.00242	−	0.467525i	−0.515960	−	0.0482215i
$95$	0.579257			0.0594305
$96$	2.10789	+	9.56853i	0.215135	+	0.976584i
$97$	13.9329			1.41467			0.707333	−	0.706880i	$-0.249898\pi$
$97$	13.9329			1.41467			0.707333	+	0.706880i	$0.249898\pi$
$98$	0.0377546	+	0.0822332i	0.00381379	+	0.00830680i
$99$	−9.70255	+	3.19761i	−0.975143	+	0.321372i
$100$	−3.59857	+	4.18687i	−0.359857	+	0.418687i
$101$			0.641351i			0.0638168i	0.999491	+	0.0319084i	$0.0101585\pi$
$101$			0.641351i			0.0638168i	−0.999491	+	0.0319084i	$0.989842\pi$
$102$	−0.877601	−	13.2801i	−0.0868954	−	1.31492i
$103$	9.74072	−	5.62381i	0.959782	−	0.554130i	0.0636761	−	0.997971i	$-0.479718\pi$
$103$	9.74072	−	5.62381i	0.959782	−	0.554130i	0.896106	+	0.443840i	$0.146384\pi$
$104$	−3.42570	−	13.7582i	−0.335918	−	1.34910i
$105$	−4.30719	−	5.29618i	−0.420338	−	0.516854i
$106$	−0.913905	+	0.419589i	−0.0887663	+	0.0407541i
$107$	−4.50914	+	7.81005i	−0.435915	+	0.755026i	−0.997370	−	0.0724810i	$-0.976908\pi$
$107$	−4.50914	+	7.81005i	−0.435915	+	0.755026i	0.561455	+	0.827507i	$0.310242\pi$
$108$	9.95493	−	2.98319i	0.957913	−	0.287057i
$109$	2.31717			0.221945			0.110973	−	0.993823i	$-0.464603\pi$
$109$	2.31717			0.221945			0.110973	+	0.993823i	$0.464603\pi$
$110$	−5.87902	−	4.16864i	−0.560543	−	0.397465i
$111$	−16.4742	+	2.64469i	−1.56366	+	0.251023i
$112$	6.57840	+	8.22806i	0.621600	+	0.777478i
$113$	−1.13688	+	0.656376i	−0.106948	+	0.0617467i	−0.552520	−	0.833500i	$-0.686334\pi$
$113$	−1.13688	+	0.656376i	−0.106948	+	0.0617467i	0.445572	+	0.895246i	$0.353000\pi$
$114$	0.0625192	+	0.946056i	0.00585546	+	0.0886063i
$115$	5.39832	−	3.11672i	0.503396	−	0.290636i
$116$	−2.60572	+	13.8186i	−0.241935	+	1.28302i
$117$	−14.2827	+	4.70705i	−1.32043	+	0.435167i
$118$	4.25982	−	6.00761i	0.392148	−	0.553045i
$119$	−7.15478	−	12.3924i	−0.655877	−	1.13601i
$120$	5.86301	+	4.40173i	0.535217	+	0.401821i
$121$	−0.298008	+	0.516165i	−0.0270917	+	0.0469241i
$122$	17.0073	+	1.58950i	1.53977	+	0.143906i
$123$	−16.0844	−	6.13553i	−1.45028	−	0.553222i
$124$	11.0657	−	1.24532i	0.993727	−	0.111833i
$125$			11.6136i			1.03876i
$126$	8.18497	−	7.60622i	0.729175	−	0.677616i
$127$	−9.63316	−	5.56171i	−0.854805	−	0.493522i	0.00746444	−	0.999972i	$-0.497624\pi$
$127$	−9.63316	−	5.56171i	−0.854805	−	0.493522i	−0.862269	+	0.506450i	$0.830957\pi$
$128$	−8.99073	−	6.86781i	−0.794675	−	0.607035i
$129$	1.84078	+	11.4665i	0.162072	+	1.00957i
$130$	−8.65423	−	6.13646i	−0.759026	−	0.538203i
$131$	2.40149	−	4.15951i	0.209819	−	0.363418i	−0.741838	−	0.670579i	$-0.766046\pi$
$131$	2.40149	−	4.15951i	0.209819	−	0.363418i	0.951657	+	0.307161i	$0.0993791\pi$
$132$	6.17381	−	10.0517i	0.537361	−	0.874887i
$133$	0.509698	+	0.882822i	0.0441964	+	0.0765504i
$134$	10.0490	−	4.61365i	0.868099	−	0.398559i
$135$	4.19408	−	6.54816i	0.360969	−	0.563576i
$136$	10.6720	+	11.0581i	0.915117	+	0.948228i
$137$	1.30599	−	0.754014i	0.111578	−	0.0644198i	−0.443172	−	0.896436i	$-0.646147\pi$
$137$	1.30599	−	0.754014i	0.111578	−	0.0644198i	0.554751	+	0.832017i	$0.312814\pi$
$138$	5.67294	+	8.48027i	0.482913	+	0.721889i
$139$			12.6518i			1.07311i	0.843865	+	0.536556i	$0.180275\pi$
$139$			12.6518i			1.07311i	−0.843865	+	0.536556i	$0.819725\pi$
$140$	7.74608	+	1.46065i	0.654663	+	0.123448i
$141$	−3.88247	−	4.77395i	−0.326963	−	0.402039i
$142$	−0.287855	−	0.626976i	−0.0241563	−	0.0526146i
$143$	−8.53497	+	14.7830i	−0.713730	+	1.23622i
$144$	−6.55621	+	10.0507i	−0.546351	+	0.837557i
$145$	5.26106	+	9.11243i	0.436908	+	0.756746i
$146$	4.60678	+	10.0340i	0.381260	+	0.830421i
$147$	−0.0394980	+	0.103544i	−0.00325774	+	0.00854021i
$148$	12.5581	−	14.6111i	1.03227	−	1.20103i
$149$	1.19513	+	0.690011i	0.0979092	+	0.0565279i	0.548155	−	0.836377i	$-0.315330\pi$
$149$	1.19513	+	0.690011i	0.0979092	+	0.0565279i	−0.450246	+	0.892905i	$0.648664\pi$
$150$	−6.74689	+	0.445862i	−0.550881	+	0.0364045i
$151$		−	10.2245i		−	0.832058i	−0.909351	−	0.416029i	$-0.863421\pi$
$151$		−	10.2245i		−	0.832058i	0.909351	−	0.416029i	$-0.136579\pi$
$152$	−0.760260	−	0.787768i	−0.0616653	−	0.0638964i
$153$	10.8560	−	12.1590i	0.877659	−	0.983000i
$154$	1.18021	−	12.6280i	0.0951044	−	1.01760i
$155$	5.67200	−	6.10373i	0.455586	−	0.490264i
$156$	9.08816	−	14.7966i	0.727635	−	1.18468i
$157$	−1.06899			−0.0853150			−0.0426575	−	0.999090i	$-0.513582\pi$
$157$	−1.06899			−0.0853150			−0.0426575	+	0.999090i	$0.513582\pi$
$158$	−2.90051	−	2.05666i	−0.230752	−	0.163619i
$159$	−1.15075	−	0.438965i	−0.0912605	−	0.0348122i
$160$	−8.45155	+	0.487801i	−0.668154	+	0.0385641i
$161$	9.50013	+	5.48490i	0.748715	+	0.432271i
$162$	11.1473	+	6.14313i	0.875813	+	0.482650i
$163$			6.63351i			0.519577i	0.965666	+	0.259788i	$0.0836528\pi$
$163$			6.63351i			0.519577i	−0.965666	+	0.259788i	$0.916347\pi$
$164$	18.7584	−	6.57695i	1.46479	−	0.513574i
$165$	−1.39908	−	8.71512i	−0.108919	−	0.678471i
$166$	7.99066	+	17.4044i	0.620196	+	1.35084i
$167$	5.04396	−	8.73639i	0.390313	−	0.676043i	−0.602177	−	0.798362i	$-0.705700\pi$
$167$	5.04396	−	8.73639i	0.390313	−	0.676043i	0.992491	+	0.122320i	$0.0390334\pi$
$168$	−1.54954	+	12.8087i	−0.119549	+	0.988214i
$169$	−6.06392	+	10.5030i	−0.466456	+	0.807925i
$170$	11.4494	+	1.07006i	0.878126	+	0.0820695i
$171$	−0.773371	+	0.866195i	−0.0591411	+	0.0662396i
$172$	−10.1698	−	8.74082i	−0.775440	−	0.666481i
$173$	6.61635	−	3.81995i	0.503031	−	0.290425i	−0.226933	−	0.973910i	$-0.572870\pi$
$173$	6.61635	−	3.81995i	0.503031	−	0.290425i	0.729965	+	0.683485i	$0.239537\pi$
$174$	−14.3148	+	9.57600i	−1.08520	+	0.725955i
$175$	−6.29593	+	3.63496i	−0.475928	+	0.274777i
$176$	2.04687	+	13.4665i	0.154288	+	1.01508i
$177$	8.90573	−	1.42968i	0.669396	−	0.107462i
$178$	1.52060	−	16.2701i	0.113974	−	1.21950i
$179$	1.97328	−	3.41782i	0.147490	−	0.255460i	−0.782809	−	0.622262i	$-0.786214\pi$
$179$	1.97328	−	3.41782i	0.147490	−	0.255460i	0.930299	+	0.366802i	$0.119547\pi$
$180$	1.18160	+	8.90106i	0.0880710	+	0.663446i
$181$	−1.74784	−	3.02735i	−0.129916	−	0.225021i	0.793728	−	0.608273i	$-0.208137\pi$
$181$	−1.74784	−	3.02735i	−0.129916	−	0.225021i	−0.923644	+	0.383252i	$0.874804\pi$
$182$	1.73734	−	18.5891i	0.128780	−	1.37792i
$183$	13.1997	+	16.2305i	0.975749	+	1.19980i
$184$	−11.3238	−	3.25090i	−0.834800	−	0.239659i
$185$		−	14.4163i		−	1.05991i
$186$	10.5809	+	8.60487i	0.775832	+	0.630940i
$187$		−	18.5023i		−	1.35302i
$188$	6.98227	+	1.31662i	0.509234	+	0.0960246i
$189$	13.6702	+	0.630196i	0.994363	+	0.0458400i
$190$	−0.815639	−	0.0762294i	−0.0591727	−	0.00553026i
$191$	3.62027	+	6.27050i	0.261954	+	0.453717i	0.966761	−	0.255682i	$-0.0822999\pi$
$191$	3.62027	+	6.27050i	0.261954	+	0.453717i	−0.704807	+	0.709399i	$0.748967\pi$
$192$	−1.70886	−	13.7506i	−0.123327	−	0.992366i
$193$	4.24028	−	7.34439i	0.305222	−	0.528661i	−0.672088	−	0.740471i	$-0.734603\pi$
$193$	4.24028	−	7.34439i	0.305222	−	0.528661i	0.977311	+	0.211810i	$0.0679359\pi$
$194$	−19.6185	−	1.83354i	−1.40853	−	0.131641i
$195$	−2.05953	−	12.8291i	−0.147486	−	0.918712i
$196$	−0.0423397	−	0.120759i	−0.00302426	−	0.00862565i
$197$	−13.7155	+	7.91866i	−0.977191	+	0.564181i	−0.901421	−	0.432944i	$-0.857475\pi$
$197$	−13.7155	+	7.91866i	−0.977191	+	0.564181i	−0.0757698	+	0.997125i	$0.524141\pi$
$198$	14.0827	−	3.22564i	1.00082	−	0.229236i
$199$	−21.6724	+	12.5126i	−1.53631	+	0.886992i	−0.537265	+	0.843414i	$0.680542\pi$
$199$	−21.6724	+	12.5126i	−1.53631	+	0.886992i	−0.999050	+	0.0435782i	$0.986124\pi$
$200$	5.61805	−	5.42187i	0.397256	−	0.383384i
$201$	12.6532	+	4.82669i	0.892490	+	0.340449i
$202$	0.0844009	−	0.903072i	0.00593843	−	0.0635399i
$203$	−9.25859	+	16.0363i	−0.649826	+	1.12553i
$204$	−0.511909	+	18.8149i	−0.0358408	+	1.31730i
$205$	7.43698	−	12.8812i	0.519421	−	0.899664i
$206$	−14.4558	+	6.63689i	−1.00718	+	0.462414i
$207$	−2.54673	+	12.2336i	−0.177010	+	0.850291i
$208$	3.01310	+	19.8234i	0.208921	+	1.37450i
$209$			1.31808i			0.0911735i
$210$	5.36788	+	8.02425i	0.370419	+	0.553726i
$211$	3.59996	+	2.07844i	0.247831	+	0.143086i	0.618771	−	0.785572i	$-0.287631\pi$
$211$	3.59996	+	2.07844i	0.247831	+	0.143086i	−0.370939	+	0.928657i	$0.620964\pi$
$212$	1.34207	−	0.470546i	0.0921735	−	0.0323172i
$213$	0.301147	−	0.789461i	0.0206343	−	0.0540930i
$214$	7.37700	−	10.4038i	0.504282	−	0.711186i
$215$	−10.0342			−0.684324
$216$	−14.4099	+	2.89050i	−0.980469	+	0.196674i
$217$	14.2933	+	3.27369i	0.970295	+	0.222233i
$218$	−3.26276	−	0.304937i	−0.220982	−	0.0206529i
$219$	−4.81951	+	12.6344i	−0.325672	+	0.853754i
$220$	7.72953	+	6.64345i	0.521125	+	0.447901i
$221$		−	27.2363i		−	1.83211i
$222$	23.5450	−	1.55595i	1.58024	−	0.104428i
$223$	−12.6525	−	7.30492i	−0.847274	−	0.489174i	0.0124562	−	0.999922i	$-0.496035\pi$
$223$	−12.6525	−	7.30492i	−0.847274	−	0.489174i	−0.859730	+	0.510749i	$0.829368\pi$
$224$	−8.18010	−	12.4514i	−0.546556	−	0.831947i
$225$	−6.17736	−	5.51537i	−0.411824	−	0.367691i
$226$	1.68719	−	0.774617i	0.112230	−	0.0515268i
$227$	−2.28986	−	3.96616i	−0.151983	−	0.263243i	0.779973	−	0.625813i	$-0.215233\pi$
$227$	−2.28986	−	3.96616i	−0.151983	−	0.263243i	−0.931957	+	0.362570i	$0.881899\pi$
$228$	0.0364678	−	1.34035i	0.00241514	−	0.0887667i
$229$	−2.89232	+	5.00964i	−0.191130	+	0.331046i	−0.945625	−	0.325259i	$-0.894548\pi$
$229$	−2.89232	+	5.00964i	−0.191130	+	0.331046i	0.754495	+	0.656306i	$0.227882\pi$
$230$	−8.01140	+	3.67817i	−0.528256	+	0.242531i
$231$	12.0513	−	9.80087i	0.792916	−	0.644850i
$232$	5.48756	−	19.1147i	0.360276	−	1.25494i
$233$			27.2405i			1.78459i	0.451458	+	0.892293i	$0.350904\pi$
$233$			27.2405i			1.78459i	−0.451458	+	0.892293i	$0.649096\pi$
$234$	20.7305	−	4.74831i	1.35520	−	0.310407i
$235$	4.60435	−	2.65832i	0.300354	−	0.173410i
$236$	−6.78875	+	7.89859i	−0.441910	+	0.514154i
$237$	−0.690260	−	4.29974i	−0.0448372	−	0.279298i
$238$	8.44365	+	18.3911i	0.547321	+	1.19212i
$239$	−5.00047	−	8.66106i	−0.323453	−	0.560237i	0.657745	−	0.753241i	$-0.271510\pi$
$239$	−5.00047	−	8.66106i	−0.323453	−	0.560237i	−0.981198	+	0.193003i	$0.938177\pi$
$240$	−7.67631	−	6.96953i	−0.495503	−	0.449881i
$241$	−7.39874	+	12.8150i	−0.476595	+	0.825487i	−0.999640	−	0.0268181i	$-0.991463\pi$
$241$	−7.39874	+	12.8150i	−0.476595	+	0.825487i	0.523045	+	0.852305i	$0.324796\pi$
$242$	0.487545	−	0.687583i	0.0313406	−	0.0441995i
$243$	4.19228	+	15.0142i	0.268935	+	0.963158i
$244$	−23.7384	−	4.47627i	−1.51970	−	0.286564i
$245$	−0.0829240	−	0.0478762i	−0.00529782	−	0.00305870i
$246$	21.8406	+	10.7560i	1.39251	+	0.685777i
$247$			1.94028i			0.123457i
$248$	−15.7452	+	0.297283i	−0.999822	+	0.0188775i
$249$	−8.35964	+	21.9149i	−0.529771	+	1.38880i
$250$	1.52834	−	16.3529i	0.0966607	−	1.03425i
$251$	15.0036	−	25.9870i	0.947019	−	1.64029i	0.195362	−	0.980731i	$-0.437412\pi$
$251$	15.0036	−	25.9870i	0.947019	−	1.64029i	0.751657	−	0.659554i	$-0.229255\pi$
$252$	−12.5260	+	9.63301i	−0.789066	+	0.606823i
$253$	7.09200	+	12.2837i	0.445870	+	0.772269i
$254$	12.8323	+	9.09902i	0.805171	+	0.570924i
$255$	8.88607	+	10.9264i	0.556467	+	0.684241i
$256$	11.7558	+	10.8536i	0.734740	+	0.678349i
$257$	14.5301	−	8.38896i	0.906363	−	0.523289i	0.0271035	−	0.999633i	$-0.491372\pi$
$257$	14.5301	−	8.38896i	0.906363	−	0.523289i	0.879259	+	0.476344i	$0.158038\pi$
$258$	−1.08299	−	16.3880i	−0.0674238	−	1.02027i
$259$	21.9713	−	12.6851i	1.36523	−	0.788214i
$260$	11.3783	+	9.77950i	0.705651	+	0.606499i
$261$	−20.6504	−	4.29892i	−1.27823	−	0.266096i
$262$	−3.92887	+	5.54087i	−0.242726	+	0.342316i
$263$	−29.7663			−1.83547			−0.917734	−	0.397195i	$-0.869984\pi$
$263$	−29.7663			−1.83547			−0.917734	+	0.397195i	$0.869984\pi$
$264$	−10.0160	+	13.3411i	−0.616441	+	0.821087i
$265$	0.532076	−	0.921583i	0.0326852	−	0.0566124i
$266$	−0.601516	−	1.31016i	−0.0368813	−	0.0803309i
$267$	15.5270	−	12.6275i	0.950237	−	0.772793i
$268$	−14.7569	+	5.17395i	−0.901420	+	0.316049i
$269$	−1.29367	+	0.746898i	−0.0788762	+	0.0455392i	−0.538919	−	0.842357i	$-0.681167\pi$
$269$	−1.29367	+	0.746898i	−0.0788762	+	0.0455392i	0.460043	+	0.887897i	$0.347834\pi$
$270$	−6.76732	+	8.66839i	−0.411846	+	0.527541i
$271$		−	20.5671i		−	1.24936i	−0.780880	−	0.624681i	$-0.785229\pi$
$271$		−	20.5671i		−	1.24936i	0.780880	−	0.624681i	$-0.214771\pi$
$272$	−13.5718	−	16.9751i	−0.822909	−	1.02927i
$273$	17.7401	−	14.4274i	1.07368	−	0.873185i
$274$	−1.93816	+	0.889844i	−0.117089	+	0.0537574i
$275$	−9.40002			−0.566843
$276$	−6.87195	−	12.6874i	−0.413643	−	0.763693i
$277$	−15.1548			−0.910565			−0.455283	−	0.890347i	$-0.650462\pi$
$277$	−15.1548			−0.910565			−0.455283	+	0.890347i	$0.650462\pi$
$278$	1.66496	−	17.8147i	0.0998577	−	1.06846i
$279$	1.55452	+	16.6308i	0.0930666	+	0.995660i
$280$	−10.7149	−	3.07608i	−0.640335	−	0.183831i
$281$		−	31.1584i		−	1.85876i	−0.369129	−	0.929378i	$-0.620344\pi$
$281$		−	31.1584i		−	1.85876i	0.369129	−	0.929378i	$-0.379656\pi$
$282$	4.83858	+	7.23301i	0.288133	+	0.430720i
$283$		−	12.9952i		−	0.772486i	−0.922397	−	0.386243i	$-0.873773\pi$
$283$		−	12.9952i		−	0.772486i	0.922397	−	0.386243i	$-0.126227\pi$
$284$	0.322813	+	0.920712i	0.0191554	+	0.0546342i
$285$	−0.633033	−	0.778387i	−0.0374976	−	0.0461076i
$286$	13.9633	−	19.6924i	0.825668	−	1.16444i
$287$	26.1757			1.54510
$288$	10.5543	−	13.2893i	0.621918	−	0.783082i
$289$	6.26088	+	10.8442i	0.368287	+	0.637892i
$290$	−6.20880	−	13.5234i	−0.364593	−	0.794119i
$291$	−15.2263	−	18.7225i	−0.892583	−	1.09753i
$292$	−5.16625	−	14.7349i	−0.302332	−	0.862295i
$293$	−0.761518	−	0.439662i	−0.0444883	−	0.0256853i	0.477591	−	0.878582i	$-0.341510\pi$
$293$	−0.761518	−	0.439662i	−0.0444883	−	0.0256853i	−0.522079	+	0.852897i	$0.674843\pi$
$294$	0.0692426	−	0.140601i	0.00403831	−	0.00820000i
$295$			7.79324i			0.453740i
$296$	−19.6056	+	18.9210i	−1.13955	+	1.09976i
$297$	14.9001	+	9.54350i	0.864594	+	0.553770i
$298$	−1.59204	−	1.12887i	−0.0922242	−	0.0653935i
$299$	10.4398	+	18.0822i	0.603748	+	1.04572i
$300$	9.55882	+	0.260074i	0.551879	+	0.0150154i
$301$	−8.82922	−	15.2927i	−0.508908	−	0.881454i
$302$	−1.34553	+	14.3969i	−0.0774266	+	0.828448i
$303$	0.861827	−	0.700892i	0.0495106	−	0.0402652i
$304$	0.966836	+	1.20929i	0.0554519	+	0.0693574i
$305$	−15.6539	+	9.03780i	−0.896341	+	0.517503i
$306$	−16.8863	+	15.6922i	−0.965323	+	0.897065i
$307$	8.82942	+	5.09767i	0.503922	+	0.290939i	0.730332	−	0.683093i	$-0.239366\pi$
$307$	8.82942	+	5.09767i	0.503922	+	0.290939i	−0.226410	+	0.974032i	$0.572699\pi$
$308$	−3.32367	+	17.6259i	−0.189383	+	1.00433i
$309$	−18.2021	−	6.94336i	−1.03548	−	0.394994i
$310$	−8.78986	+	7.84810i	−0.499230	+	0.445742i
$311$	−6.65049			−0.377115			−0.188557	−	0.982062i	$-0.560381\pi$
$311$	−6.65049			−0.377115			−0.188557	+	0.982062i	$0.560381\pi$
$312$	−14.7440	+	19.6388i	−0.834717	+	1.11183i
$313$	10.8296	−	18.7575i	0.612126	−	1.06023i	−0.378755	−	0.925497i	$-0.623648\pi$
$313$	10.8296	−	18.7575i	0.612126	−	1.06023i	0.990881	−	0.134737i	$-0.0430190\pi$
$314$	1.50523	+	0.140678i	0.0849449	+	0.00793893i
$315$	−2.40978	+	11.5757i	−0.135776	+	0.652218i
$316$	3.81348	+	3.27765i	0.214525	+	0.184382i
$317$	−1.99612	−	1.15246i	−0.112113	−	0.0647286i	0.442895	−	0.896574i	$-0.353952\pi$
$317$	−1.99612	−	1.15246i	−0.112113	−	0.0647286i	−0.555008	+	0.831845i	$0.687285\pi$
$318$	1.56258	+	0.769533i	0.0876251	+	0.0431533i
$319$	−20.7350	+	11.9714i	−1.16094	+	0.670269i
$320$	11.9646	+	0.425351i	0.668844	+	0.0237778i
$321$	15.4226	−	2.47588i	0.860807	−	0.138190i
$322$	−12.6551	−	8.97337i	−0.705242	−	0.500067i
$323$	−1.05155	−	1.82133i	−0.0585096	−	0.101342i
$324$	−14.8878	−	10.1170i	−0.827101	−	0.562054i
$325$	−13.8373			−0.767556
$326$	0.872961	−	9.34050i	0.0483489	−	0.517323i
$327$	−2.53229	−	3.11374i	−0.140036	−	0.172190i
$328$	−27.2789	+	6.79227i	−1.50622	+	0.375040i
$329$	8.10288	+	4.67820i	0.446726	+	0.257917i
$330$	0.823122	+	12.4557i	0.0453114	+	0.685663i
$331$	−21.1347	+	12.2021i	−1.16167	+	0.670690i	−0.951704	−	0.307018i	$-0.900669\pi$
$331$	−21.1347	+	12.2021i	−1.16167	+	0.670690i	−0.209966	+	0.977709i	$0.567335\pi$
$332$	−8.96107	−	25.5583i	−0.491803	−	1.40269i
$333$	21.5575	+	19.2473i	1.18134	+	1.05474i
$334$	−8.25198	+	11.6377i	−0.451528	+	0.636789i
$335$	−5.85052	+	10.1334i	−0.319648	+	0.553647i
$336$	3.86748	−	17.8318i	0.210988	−	0.972802i
$337$	6.62666			0.360977			0.180489	−	0.983577i	$-0.442232\pi$
$337$	6.62666			0.360977			0.180489	+	0.983577i	$0.442232\pi$
$338$	9.92065	−	13.9911i	0.539612	−	0.761013i
$339$	2.12444	+	0.810386i	0.115384	+	0.0440141i
$340$	−15.9808	−	3.01344i	−0.866679	−	0.163427i
$341$	13.8888	+	12.9065i	0.752123	+	0.698924i
$342$	1.20296	−	1.11790i	0.0650484	−	0.0604489i
$343$		−	18.6039i		−	1.00452i
$344$	13.1696	+	13.6461i	0.710056	+	0.735748i
$345$	−10.0876	−	3.84802i	−0.543099	−	0.207170i
$346$	−9.81903	+	4.50808i	−0.527874	+	0.242356i
$347$	−1.41096	+	2.44386i	−0.0757444	+	0.131193i	−0.901410	−	0.432967i	$-0.857467\pi$
$347$	−1.41096	+	2.44386i	−0.0757444	+	0.131193i	0.825665	+	0.564160i	$0.190800\pi$
$348$	21.4165	−	11.5999i	1.14805	−	0.621822i
$349$	−26.7234			−1.43047			−0.715237	−	0.698882i	$-0.753681\pi$
$349$	−26.7234			−1.43047			−0.715237	+	0.698882i	$0.753681\pi$
$350$	9.34352	−	4.28977i	0.499432	−	0.229298i
$351$	21.9338	+	14.0485i	1.17074	+	0.749855i
$352$	−1.10998	−	19.2312i	−0.0591619	−	1.02503i
$353$	−30.6007	−	17.6673i	−1.62871	−	0.940337i	−0.984478	−	0.175509i	$-0.943843\pi$
$353$	−30.6007	−	17.6673i	−1.62871	−	0.940337i	−0.644234	−	0.764828i	$-0.722824\pi$
$354$	−12.7281	+	0.841125i	−0.676491	+	0.0447053i
$355$	0.632243	+	0.365026i	0.0335560	+	0.0193736i
$356$	−4.28224	+	22.7094i	−0.226958	+	1.20360i
$357$	−8.83355	+	23.1573i	−0.467521	+	1.22561i
$358$	−3.22831	+	4.55287i	−0.170621	+	0.240627i
$359$	16.5481	+	28.6622i	0.873377	+	1.51273i	0.858481	+	0.512845i	$0.171408\pi$
$359$	16.5481	+	28.6622i	0.873377	+	1.51273i	0.0148957	+	0.999889i	$0.495258\pi$
$360$	−0.492412	−	12.6889i	−0.0259524	−	0.668763i
$361$	−9.42509	−	16.3247i	−0.496057	−	0.859196i
$362$	2.06270	+	4.49276i	0.108413	+	0.236134i
$363$	1.01928	−	0.163630i	0.0534983	−	0.00858837i
$364$	−4.89261	+	25.9463i	−0.256442	+	1.35996i
$365$	−10.1183	−	5.84181i	−0.529617	−	0.305774i
$366$	−16.4503	−	24.5909i	−0.859869	−	1.28539i
$367$	17.1661	−	9.91085i	0.896063	−	0.517342i	0.0201421	−	0.999797i	$-0.493588\pi$
$367$	17.1661	−	9.91085i	0.896063	−	0.517342i	0.875921	+	0.482455i	$0.160255\pi$
$368$	15.5169	+	6.06771i	0.808877	+	0.316301i
$369$	9.33285	+	28.3188i	0.485849	+	1.47422i
$370$	−1.89716	+	20.2992i	−0.0986287	+	1.05531i
$371$	1.87273			0.0972273
$372$	−13.7664	−	13.5088i	−0.713754	−	0.700396i
$373$	−15.5757			−0.806479			−0.403240	−	0.915094i	$-0.632116\pi$
$373$	−15.5757			−0.806479			−0.403240	+	0.915094i	$0.632116\pi$
$374$	−2.43488	+	26.0527i	−0.125904	+	1.34715i
$375$	15.6060	−	12.6918i	0.805892	−	0.655402i
$376$	−9.65831	−	2.77276i	−0.498089	−	0.142994i
$377$	−30.5231	+	17.6225i	−1.57202	+	0.907605i
$378$	−19.1658	−	2.68635i	−0.985783	−	0.138171i
$379$	18.5687	+	10.7207i	0.953811	+	0.550683i	0.894263	−	0.447542i	$-0.147701\pi$
$379$	18.5687	+	10.7207i	0.953811	+	0.550683i	0.0595486	+	0.998225i	$0.481034\pi$
$380$	1.13845	+	0.214674i	0.0584013	+	0.0110125i
$381$	3.05382	+	19.0228i	0.156452	+	0.974565i
$382$	−4.27244	−	9.30577i	−0.218597	−	0.476125i
$383$	10.8314	+	18.7605i	0.553458	+	0.958618i	0.998022	+	0.0628706i	$0.0200255\pi$
$383$	10.8314	+	18.7605i	0.553458	+	0.958618i	−0.444563	+	0.895747i	$0.646641\pi$
$384$	0.596650	+	19.5868i	0.0304477	+	0.999536i
$385$	6.71063	+	11.6232i	0.342005	+	0.592371i
$386$	−6.93716	+	9.78345i	−0.353092	+	0.497965i
$387$	13.3967	−	15.0046i	0.680992	−	0.762728i
$388$	27.3831	+	5.16354i	1.39017	+	0.262139i
$389$	−17.5017	−	10.1046i	−0.887372	−	0.512324i	−0.0142899	−	0.999898i	$-0.504549\pi$
$389$	−17.5017	−	10.1046i	−0.887372	−	0.512324i	−0.873082	+	0.487574i	$0.837882\pi$
$390$	1.21168	+	18.3354i	0.0613557	+	0.928450i
$391$	−19.5995	−	11.3158i	−0.991191	−	0.572264i
$392$	0.0437258	+	0.175610i	0.00220849	+	0.00886964i
$393$	−8.21384	+	1.31861i	−0.414334	+	0.0665152i
$394$	20.3546	−	9.34514i	1.02545	−	0.470802i
$395$	3.76262			0.189318
$396$	−20.2541	+	2.68868i	−1.01781	+	0.135111i
$397$	−3.85843	+	6.68300i	−0.193649	+	0.335410i	−0.946457	−	0.322830i	$-0.895366\pi$
$397$	−3.85843	+	6.68300i	−0.193649	+	0.335410i	0.752808	+	0.658240i	$0.228699\pi$
$398$	32.1630	−	14.7666i	1.61219	−	0.740183i
$399$	0.629291	−	1.64969i	0.0315040	−	0.0825880i
$400$	−8.62415	+	6.89509i	−0.431208	+	0.344754i
$401$		−	25.1666i		−	1.25676i	−0.777906	−	0.628380i	$-0.783718\pi$
$401$		−	25.1666i		−	1.25676i	0.777906	−	0.628380i	$-0.216282\pi$
$402$	−17.1815	−	8.46151i	−0.856938	−	0.422022i
$403$	20.4451	+	18.9990i	1.01844	+	0.946406i
$404$	−0.237686	+	1.26049i	−0.0118253	+	0.0627116i
$405$	−13.3827	+	1.52020i	−0.664989	+	0.0755393i
$406$	15.1472	−	21.3620i	0.751742	−	1.06018i
$407$	32.8038			1.62602
$408$	3.19682	−	26.4254i	0.158266	−	1.30825i
$409$	−0.247661	+	0.428962i	−0.0122461	+	0.0212108i	−0.872083	−	0.489357i	$-0.837231\pi$
$409$	−0.247661	+	0.428962i	−0.0122461	+	0.0212108i	0.859837	+	0.510568i	$0.170565\pi$
$410$	−12.1670	+	17.1591i	−0.600885	+	0.847426i
$411$	−2.44045	−	0.930933i	−0.120379	−	0.0459196i
$412$	21.2283	−	7.44290i	1.04584	−	0.366685i
$413$	−11.8774	+	6.85740i	−0.584447	+	0.337431i
$414$	5.19592	−	16.8907i	0.255365	−	0.830130i
$415$	−17.5506	−	10.1329i	−0.861527	−	0.497403i
$416$	−1.63394	−	28.3094i	−0.0801106	−	1.38798i
$417$	17.0011	−	13.8263i	0.832546	−	0.677079i
$418$	0.173458	−	1.85596i	0.00848409	−	0.0907779i
$419$	25.8774			1.26419			0.632097	−	0.774889i	$-0.282194\pi$
$419$	25.8774			1.26419			0.632097	+	0.774889i	$0.282194\pi$
$420$	−6.50241	−	12.0052i	−0.317285	−	0.585792i
$421$	−5.04980	−	8.74651i	−0.246112	−	0.426279i	0.716332	−	0.697760i	$-0.245820\pi$
$421$	−5.04980	−	8.74651i	−0.246112	−	0.426279i	−0.962444	+	0.271481i	$0.912486\pi$
$422$	−4.79550	−	3.40035i	−0.233441	−	0.165526i
$423$	−2.17216	+	10.4343i	−0.105614	+	0.507332i
$424$	−1.95166	+	0.485951i	−0.0947808	+	0.0235998i
$425$	12.9890	−	7.49921i	0.630060	−	0.363765i
$426$	−0.527931	+	1.07199i	−0.0255783	+	0.0519382i
$427$	−27.5483	−	15.9050i	−1.33315	−	0.769697i
$428$	−11.7565	+	13.6785i	−0.568272	+	0.661175i
$429$	29.1922	−	4.68638i	1.40941	−	0.226261i
$430$	14.1289	+	1.32048i	0.681355	+	0.0636792i
$431$	16.4080	−	28.4196i	0.790348	−	1.36892i	−0.135404	−	0.990790i	$-0.543233\pi$
$431$	16.4080	−	28.4196i	0.790348	−	1.36892i	0.925752	−	0.378132i	$-0.123433\pi$
$432$	20.6706	−	2.17373i	0.994516	−	0.104584i
$433$	16.2441			0.780640			0.390320	−	0.920679i	$-0.372364\pi$
$433$	16.2441			0.780640			0.390320	+	0.920679i	$0.372364\pi$
$434$	−19.6953	−	6.49060i	−0.945405	−	0.311559i
$435$	6.49550	−	17.0280i	0.311436	−	0.816432i
$436$	4.55409	+	0.858750i	0.218101	+	0.0411266i
$437$	1.39625	+	0.806123i	0.0667915	+	0.0385621i
$438$	8.44891	−	17.1560i	0.403705	−	0.819744i
$439$	33.5420	−	19.3655i	1.60087	−	0.924264i	0.609559	−	0.792741i	$-0.291346\pi$
$439$	33.5420	−	19.3655i	1.60087	−	0.924264i	0.991313	−	0.131523i	$-0.0419869\pi$
$440$	−10.0095	−	10.3717i	−0.477185	−	0.494451i
$441$	0.182305	−	0.0600810i	0.00868117	−	0.00286100i
$442$	−3.58426	+	38.3509i	−0.170486	+	1.82417i
$443$	0.737152	+	1.27679i	0.0350232	+	0.0606619i	0.883006	−	0.469362i	$-0.155516\pi$
$443$	0.737152	+	1.27679i	0.0350232	+	0.0606619i	−0.847983	+	0.530024i	$0.822183\pi$
$444$	−33.3579	−	0.907593i	−1.58310	−	0.0430724i
$445$	8.64604	+	14.9754i	0.409862	+	0.709901i
$446$	16.8544	+	11.9509i	0.798078	+	0.565894i
$447$	−0.378872	−	2.36005i	−0.0179200	−	0.111627i
$448$	9.87962	+	18.6091i	0.466768	+	0.879197i
$449$		−	32.1161i		−	1.51565i	−0.652457	−	0.757826i	$-0.726262\pi$
$449$		−	32.1161i		−	1.51565i	0.652457	−	0.757826i	$-0.273738\pi$
$450$	7.97238	+	8.57900i	0.375822	+	0.404418i
$451$	29.3108	+	16.9226i	1.38019	+	0.796855i
$452$	−2.47763	+	0.868689i	−0.116538	+	0.0408597i
$453$	−13.7393	+	11.1737i	−0.645531	+	0.524986i
$454$	2.70236	+	5.88600i	0.126828	+	0.276244i
$455$	9.87840	+	17.1099i	0.463106	+	0.802124i
$456$	−0.227737	+	1.88251i	−0.0106648	+	0.0881568i
$457$	1.11996			0.0523896			0.0261948	−	0.999657i	$-0.491661\pi$
$457$	1.11996			0.0523896			0.0261948	+	0.999657i	$0.491661\pi$
$458$	4.73187	−	6.67333i	0.221106	−	0.311824i
$459$	−28.2028	−	1.30014i	−1.31639	−	0.0606856i
$460$	11.7647	−	4.12486i	0.548533	−	0.192323i
$461$			32.2037i			1.49988i	0.661507	+	0.749939i	$0.269917\pi$
$461$			32.2037i			1.49988i	−0.661507	+	0.749939i	$0.730083\pi$
$462$	−18.2589	+	12.2144i	−0.849482	+	0.568267i
$463$			37.8282i			1.75803i	0.476796	+	0.879014i	$0.341798\pi$
$463$			37.8282i			1.75803i	−0.476796	+	0.879014i	$0.658202\pi$
$464$	−10.2424	+	26.1928i	−0.475490	+	1.21597i
$465$	−14.4006	−	0.951468i	−0.667810	−	0.0441233i
$466$	3.58481	−	38.3567i	0.166063	−	1.77684i
$467$	−40.6297			−1.88012			−0.940060	−	0.341009i	$-0.889231\pi$
$467$	−40.6297			−1.88012			−0.940060	+	0.341009i	$0.889231\pi$
$468$	−29.8151	+	3.95788i	−1.37820	+	0.182953i
$469$	−20.5919			−0.950844
$470$	−6.83311	+	3.13720i	−0.315188	+	0.144708i
$471$	1.16824	+	1.43648i	0.0538294	+	0.0661895i
$472$	10.5985	−	10.2284i	0.487837	−	0.470802i
$473$		−	22.8324i		−	1.04983i
$474$	0.406100	+	6.14520i	0.0186528	+	0.282259i
$475$	−0.925321	+	0.534234i	−0.0424567	+	0.0245124i
$476$	−9.46908	−	27.0072i	−0.434015	−	1.23787i
$477$	0.667715	+	2.02606i	0.0305726	+	0.0927668i
$478$	5.90126	+	12.8535i	0.269917	+	0.587905i
$479$	3.56628	−	6.17698i	0.162948	−	0.282234i	−0.772977	−	0.634434i	$-0.781233\pi$
$479$	3.56628	−	6.17698i	0.162948	−	0.282234i	0.935925	+	0.352201i	$0.114567\pi$
$480$	9.89165	+	10.8238i	0.451490	+	0.494038i
$481$	48.2888			2.20178
$482$	12.1044	−	17.0708i	0.551342	−	0.777556i
$483$	−3.01165	−	18.7601i	−0.137035	−	0.853613i
$484$	−0.776986	+	0.904010i	−0.0353176	+	0.0410914i
$485$	18.0574	−	10.4254i	0.819943	−	0.473394i
$486$	−3.92721	−	21.6928i	−0.178142	−	0.984005i
$487$	−12.7060	+	7.33580i	−0.575763	+	0.332417i	−0.759448	−	0.650568i	$-0.774531\pi$
$487$	−12.7060	+	7.33580i	−0.575763	+	0.332417i	0.183685	+	0.982985i	$0.441197\pi$
$488$	32.8365	+	9.42688i	1.48644	+	0.426735i
$489$	8.91390	−	7.24934i	0.403100	−	0.327827i
$490$	0.110463	+	0.0783261i	0.00499021	+	0.00353841i
$491$	−4.62836	−	8.01655i	−0.208875	−	0.361782i	0.742485	−	0.669862i	$-0.233647\pi$
$491$	−4.62836	−	8.01655i	−0.208875	−	0.361782i	−0.951360	+	0.308080i	$0.900313\pi$
$492$	−29.3378	−	18.0195i	−1.32265	−	0.812380i
$493$	19.1012	−	33.0843i	0.860275	−	1.49004i
$494$	0.255339	−	2.73207i	0.0114882	−	0.122922i
$495$	−10.1821	+	11.4042i	−0.457652	+	0.512583i
$496$	22.2096	+	1.65345i	0.997240	+	0.0742421i
$497$			1.28477i			0.0576298i
$498$	14.6550	−	29.7577i	0.656706	−	1.33348i
$499$	26.2055	+	15.1298i	1.17312	+	0.677301i	0.954413	−	0.298490i	$-0.0964830\pi$
$499$	26.2055	+	15.1298i	1.17312	+	0.677301i	0.218706	+	0.975791i	$0.429816\pi$
$500$	−4.30404	+	22.8250i	−0.192483	+	1.02077i
$501$	−17.2519	+	2.76954i	−0.770758	+	0.123734i
$502$	−24.5461	+	34.6173i	−1.09555	+	1.54504i
$503$	−0.801519	+	1.38827i	−0.0357380	+	0.0619000i	−0.883341	−	0.468731i	$-0.844712\pi$
$503$	−0.801519	+	1.38827i	−0.0357380	+	0.0619000i	0.847603	+	0.530631i	$0.178045\pi$
$504$	18.9053	−	11.9156i	0.842110	−	0.530764i
$505$	0.479899	+	0.831209i	0.0213552	+	0.0369883i
$506$	−8.36956	−	18.2297i	−0.372072	−	0.810409i
$507$	20.7405	−	3.32958i	0.921117	−	0.147872i
$508$	−16.8715	−	14.5008i	−0.748551	−	0.643371i
$509$	12.2656	−	7.08152i	0.543661	−	0.313883i	−0.202900	−	0.979199i	$-0.565037\pi$
$509$	12.2656	−	7.08152i	0.543661	−	0.313883i	0.746561	+	0.665316i	$0.231703\pi$
$510$	−11.0744	−	16.5547i	−0.490381	−	0.733053i
$511$		−	20.5612i		−	0.909574i
$512$	−15.1248	−	16.8297i	−0.668429	−	0.743776i
$513$	2.00913	+	0.0926207i	0.0887053	+	0.00408930i
$514$	−21.5635	+	9.90016i	−0.951124	+	0.436677i
$515$	8.41617	−	14.5772i	0.370861	−	0.642350i
$516$	−0.631712	+	23.2181i	−0.0278096	+	1.02212i
$517$	6.04892	+	10.4770i	0.266031	+	0.460780i
$518$	−32.6066	+	14.9702i	−1.43265	+	0.657754i
$519$	−12.3637	−	4.71625i	−0.542706	−	0.207020i
$520$	−14.7345	−	15.2677i	−0.646152	−	0.669531i
$521$	26.4333	+	15.2613i	1.15806	+	0.668609i	0.950839	−	0.309685i	$-0.100224\pi$
$521$	26.4333	+	15.2613i	1.15806	+	0.668609i	0.207225	+	0.978293i	$0.433557\pi$
$522$	28.5116	+	8.77077i	1.24792	+	0.383886i
$523$			20.7795i			0.908626i	0.890842	+	0.454313i	$0.150115\pi$
$523$			20.7795i			0.908626i	−0.890842	+	0.454313i	$0.849885\pi$
$524$	6.26133	−	7.28494i	0.273527	−	0.318244i
$525$	11.7650	+	4.48785i	0.513465	+	0.195866i
$526$	41.9132	+	3.91720i	1.82750	+	0.170798i
$527$	−29.4883	−	6.75389i	−1.28453	−	0.294204i
$528$	15.8589	−	17.4672i	0.690172	−	0.760162i
$529$	−5.65046			−0.245672
$530$	−0.870484	+	1.22764i	−0.0378114	+	0.0533253i
$531$	−11.6537	−	10.4048i	−0.505726	−	0.451531i
$532$	0.674566	+	1.92396i	0.0292461	+	0.0834143i
$533$	43.1471	+	24.9110i	1.86891	+	1.07901i
$534$	−23.5250	+	15.7372i	−1.01803	+	0.681016i
$535$			13.4961i			0.583486i
$536$	21.4597	−	5.34334i	0.926918	−	0.230797i
$537$	−6.74922	+	1.08349i	−0.291250	+	0.0467560i
$538$	1.91987	−	0.881446i	0.0827716	−	0.0380018i
$539$	0.108941	−	0.188691i	0.00469241	−	0.00812750i
$540$	10.6697	−	11.3152i	0.459149	−	0.486928i
$541$	13.4535	−	23.3022i	0.578413	−	1.00184i	−0.417248	−	0.908792i	$-0.637005\pi$
$541$	13.4535	−	23.3022i	0.578413	−	1.00184i	0.995662	−	0.0930486i	$-0.0296612\pi$
$542$	−2.70660	+	28.9600i	−0.116258	+	1.24394i
$543$	−2.15795	+	5.65709i	−0.0926066	+	0.242769i
$544$	16.8762	+	25.6883i	0.723561	+	1.10138i
$545$	3.00312	−	1.73385i	0.128640	−	0.0742701i
$546$	−26.8781	+	17.9803i	−1.15028	+	0.769486i
$547$	−12.6843	+	7.32326i	−0.542340	+	0.313120i	−0.746027	−	0.665916i	$-0.768041\pi$
$547$	−12.6843	+	7.32326i	−0.542340	+	0.313120i	0.203687	+	0.979036i	$0.434708\pi$
$548$	2.84619	−	0.997909i	0.121583	−	0.0426286i
$549$	7.38496	−	35.4746i	0.315182	−	1.51402i
$550$	13.2360	+	1.23703i	0.564383	+	0.0527471i
$551$	−1.36075	+	2.35688i	−0.0579698	+	0.100407i
$552$	8.00659	+	18.7692i	0.340783	+	0.798871i
$553$	3.31079	+	5.73446i	0.140789	+	0.243854i
$554$	21.3392	+	1.99435i	0.906615	+	0.0847320i
$555$	−19.3721	+	15.7546i	−0.822300	+	0.668746i
$556$	−4.68878	+	24.8654i	−0.198849	+	1.05453i
$557$		−	26.5245i		−	1.12388i	−0.827178	−	0.561940i	$-0.810055\pi$
$557$		−	26.5245i		−	1.12388i	0.827178	−	0.561940i	$-0.189945\pi$
$558$	−0.000291774	−	23.6220i	−1.23518e−5	−	1.00000i
$559$		−	33.6105i		−	1.42157i
$560$	14.6825	+	5.74142i	0.620450	+	0.242619i
$561$	−24.8628	+	20.2200i	−1.04971	+	0.853688i
$562$	−4.10041	+	43.8735i	−0.172965	+	1.85069i
$563$	−0.931273	−	1.61301i	−0.0392485	−	0.0679803i	0.845734	−	0.533605i	$-0.179163\pi$
$563$	−0.931273	−	1.61301i	−0.0392485	−	0.0679803i	−0.884982	+	0.465625i	$0.845830\pi$
$564$	−5.86124	−	10.8214i	−0.246803	−	0.455663i
$565$	−0.982283	+	1.70136i	−0.0413250	+	0.0715769i
$566$	−1.71015	+	18.2983i	−0.0718831	+	0.769134i
$567$	−14.0925	−	19.0583i	−0.591829	−	0.800374i
$568$	−0.333382	−	1.33892i	−0.0139884	−	0.0561796i
$569$	−37.4704	+	21.6336i	−1.57084	+	0.906926i	−0.574776	+	0.818311i	$0.694911\pi$
$569$	−37.4704	+	21.6336i	−1.57084	+	0.906926i	−0.996066	+	0.0886156i	$0.971756\pi$
$570$	0.788925	+	1.17933i	0.0330444	+	0.0493969i
$571$	11.0139	−	6.35888i	0.460917	−	0.266111i	−0.251513	−	0.967854i	$-0.580928\pi$
$571$	11.0139	−	6.35888i	0.460917	−	0.266111i	0.712430	+	0.701743i	$0.247595\pi$
$572$	−22.2529	+	25.8909i	−0.930442	+	1.08255i
$573$	4.46972	−	11.7174i	0.186725	−	0.489503i
$574$	−36.8574	−	3.44468i	−1.53840	−	0.143778i
$575$	−5.74895	+	9.95747i	−0.239748	+	0.415255i
$576$	−16.6101	+	17.3235i	−0.692089	+	0.721812i
$577$	−9.07054	+	15.7106i	−0.377612	+	0.654043i	−0.990714	−	0.135961i	$-0.956588\pi$
$577$	−9.07054	+	15.7106i	−0.377612	+	0.654043i	0.613103	+	0.790003i	$0.289921\pi$
$578$	−7.38873	−	16.0933i	−0.307331	−	0.669395i
$579$	−14.5031	+	2.32826i	−0.602728	+	0.0967591i
$580$	6.96282	+	19.8590i	0.289115	+	0.824600i
$581$		−	35.6643i		−	1.47960i
$582$	18.9760	+	28.3665i	0.786580	+	1.17583i
$583$	2.09703	+	1.21072i	0.0868502	+	0.0501430i
$584$	5.33538	+	21.4278i	0.220780	+	0.886687i
$585$	−14.9886	+	16.7876i	−0.619703	+	0.694083i
$586$	1.01442	+	0.719293i	0.0419052	+	0.0297137i
$587$	18.6377			0.769262			0.384631	−	0.923070i	$-0.374329\pi$
$587$	18.6377			0.769262			0.384631	+	0.923070i	$0.374329\pi$
$588$	−0.116002	+	0.188865i	−0.00478383	+	0.00778864i
$589$	2.10071	+	0.481139i	0.0865582	+	0.0198250i
$590$	1.02558	−	10.9735i	0.0422225	−	0.451771i
$591$	25.6296	+	9.77667i	1.05426	+	0.402158i
$592$	30.0962	−	24.0622i	1.23695	−	0.988948i
$593$			13.1703i			0.540841i	0.962742	+	0.270420i	$0.0871627\pi$
$593$			13.1703i			0.540841i	−0.962742	+	0.270420i	$0.912837\pi$
$594$	−19.7246	−	15.3988i	−0.809311	−	0.631821i
$595$	−18.5456	−	10.7073i	−0.760295	−	0.438957i
$596$	2.09315	+	1.79904i	0.0857389	+	0.0736916i
$597$	40.4983	+	15.4485i	1.65749	+	0.632264i
$598$	−12.3204	−	26.8351i	−0.503820	−	1.09737i
$599$	−21.8400	−	37.8280i	−0.892359	−	1.54561i	−0.837040	−	0.547142i	$-0.815716\pi$
$599$	−21.8400	−	37.8280i	−0.892359	−	1.54561i	−0.0553187	−	0.998469i	$-0.517617\pi$
$600$	−13.4253	−	1.62413i	−0.548087	−	0.0663049i
$601$	−11.4342	+	19.8046i	−0.466411	+	0.807848i	−0.999264	−	0.0383603i	$-0.987787\pi$
$601$	−11.4342	+	19.8046i	−0.466411	+	0.807848i	0.532853	+	0.846208i	$0.321120\pi$
$602$	10.4197	+	22.6951i	0.424676	+	0.924985i
$603$	−7.34196	−	22.2778i	−0.298988	−	0.907221i
$604$	3.78922	−	20.0949i	0.154181	−	0.817648i
$605$			0.891953i			0.0362630i
$606$	−1.30575	+	0.873495i	−0.0530427	+	0.0354833i
$607$	−31.9281	+	18.4337i	−1.29592	+	0.748200i	−0.979697	−	0.200484i	$-0.935748\pi$
$607$	−31.9281	+	18.4337i	−1.29592	+	0.748200i	−0.316224	+	0.948685i	$0.602415\pi$
$608$	−1.20224	−	1.83001i	−0.0487572	−	0.0742165i
$609$	31.6672	−	5.08371i	1.28322	−	0.206002i
$610$	23.2313	−	10.6659i	0.940608	−	0.431849i
$611$	8.90433	+	15.4227i	0.360231	+	0.623938i
$612$	25.8422	−	19.8737i	1.04461	−	0.803346i
$613$	2.96673	−	5.13852i	0.119825	−	0.207543i	−0.799873	−	0.600169i	$-0.795100\pi$
$613$	2.96673	−	5.13852i	0.119825	−	0.207543i	0.919698	+	0.392626i	$0.128433\pi$
$614$	−11.7617	−	8.33985i	−0.474662	−	0.336569i
$615$	−25.4368	+	4.08350i	−1.02571	+	0.164663i
$616$	6.99953	−	24.3813i	0.282019	−	0.982351i
$617$	−2.01794	−	1.16506i	−0.0812394	−	0.0469036i	0.458830	−	0.888524i	$-0.348269\pi$
$617$	−2.01794	−	1.16506i	−0.0812394	−	0.0469036i	−0.540069	+	0.841620i	$0.681602\pi$
$618$	24.7162	+	12.1722i	0.994233	+	0.489636i
$619$		−	22.8837i		−	0.919774i	−0.887977	−	0.459887i	$-0.847890\pi$
$619$		−	22.8837i		−	0.919774i	0.887977	−	0.459887i	$-0.152110\pi$
$620$	13.4096	−	9.89400i	0.538542	−	0.397353i
$621$	19.2222	−	9.94706i	0.771361	−	0.399162i
$622$	9.36440	+	0.875195i	0.375478	+	0.0350921i
$623$	−15.2156	+	26.3542i	−0.609600	+	1.05586i
$624$	23.3452	−	25.7126i	0.934556	−	1.02933i
$625$	1.78902	+	3.09867i	0.0715607	+	0.123947i
$626$	−17.7174	+	24.9868i	−0.708130	+	0.998673i
$627$	1.77119	−	1.44045i	0.0707346	−	0.0575259i
$628$	−2.10096	−	0.396171i	−0.0838375	−	0.0158090i
$629$	−45.3285	+	26.1704i	−1.80736	+	1.04348i
$630$	4.91651	−	15.9824i	0.195878	−	0.636753i
$631$	6.66873	−	3.85019i	0.265478	−	0.153274i	−0.361353	−	0.932429i	$-0.617685\pi$
$631$	6.66873	−	3.85019i	0.265478	−	0.153274i	0.626831	+	0.779155i	$0.284352\pi$
$632$	−4.93835	−	5.11703i	−0.196437	−	0.203544i
$633$	−1.14123	−	7.10890i	−0.0453598	−	0.282553i
$634$	2.65903	+	1.88544i	0.105604	+	0.0748804i
$635$	−16.6465			−0.660595
$636$	−2.09896	−	1.28920i	−0.0832293	−	0.0511199i
$637$	0.160367	−	0.277763i	0.00635395	−	0.0110054i
$638$	30.7720	−	14.1279i	1.21827	−	0.559330i
$639$	−1.38996	+	0.458080i	−0.0549858	+	0.0181214i
$640$	−16.7912	−	2.17346i	−0.663729	−	0.0859134i
$641$	−1.56187	+	0.901747i	−0.0616902	+	0.0356169i	−0.530528	−	0.847667i	$-0.678006\pi$
$641$	−1.56187	+	0.901747i	−0.0616902	+	0.0356169i	0.468838	+	0.883284i	$0.344673\pi$
$642$	−22.0421	+	1.45663i	−0.869932	+	0.0574886i
$643$			27.3259i			1.07763i	0.842425	+	0.538814i	$0.181127\pi$
$643$			27.3259i			1.07763i	−0.842425	+	0.538814i	$0.818873\pi$
$644$	16.6385	+	14.3006i	0.655649	+	0.563523i
$645$	10.9657	+	13.4836i	0.431774	+	0.530915i
$646$	1.24097	+	2.70296i	0.0488255	+	0.106347i
$647$	1.94371			0.0764152			0.0382076	−	0.999270i	$-0.487835\pi$
$647$	1.94371			0.0764152			0.0382076	+	0.999270i	$0.487835\pi$
$648$	19.6318	+	16.2047i	0.771210	+	0.636580i
$649$	−17.7333			−0.696092
$650$	19.4840	+	1.82097i	0.764226	+	0.0714244i
$651$	−11.2212	−	22.7845i	−0.439793	−	0.892996i
$652$	−2.45839	+	13.0373i	−0.0962781	+	0.510579i
$653$		−	35.7859i		−	1.40041i	−0.713941	−	0.700206i	$-0.753092\pi$
$653$		−	35.7859i		−	1.40041i	0.713941	−	0.700206i	$-0.246908\pi$
$654$	3.15590	+	4.71764i	0.123405	+	0.184474i
$655$		−	7.18778i		−	0.280850i
$656$	39.3046	−	5.97418i	1.53459	−	0.233253i
$657$	22.2446	−	7.33103i	0.867845	−	0.286011i
$658$	−10.7938	−	7.65359i	−0.420787	−	0.298368i
$659$	−33.7140			−1.31331			−0.656655	−	0.754191i	$-0.728029\pi$
$659$	−33.7140			−1.31331			−0.656655	+	0.754191i	$0.728029\pi$
$660$	0.480131	−	17.6469i	0.0186891	−	0.686904i
$661$	−8.00945	−	13.8728i	−0.311532	−	0.539588i	0.667163	−	0.744912i	$-0.267509\pi$
$661$	−8.00945	−	13.8728i	−0.311532	−	0.539588i	−0.978694	+	0.205324i	$0.934175\pi$
$662$	31.3651	−	14.4003i	1.21904	−	0.559682i
$663$	−36.5993	+	29.7649i	−1.42140	+	1.15597i
$664$	9.25444	+	37.1673i	0.359142	+	1.44237i
$665$	1.32116	+	0.762775i	0.0512326	+	0.0295791i
$666$	−27.8216	−	29.9386i	−1.07807	−	1.16010i
$667$			29.2863i			1.13397i
$668$	13.1509	−	15.3009i	0.508825	−	0.592009i
$669$	4.01099	+	24.9851i	0.155074	+	0.965979i
$670$	9.57152	−	13.4987i	0.369780	−	0.521500i
$671$	−20.5652	−	35.6200i	−0.793911	−	1.37509i
$672$	−7.79234	+	24.5995i	−0.300596	+	0.948948i
$673$	14.4663	+	25.0564i	0.557636	+	0.965853i	0.997693	+	0.0678836i	$0.0216247\pi$
$673$	14.4663	+	25.0564i	0.557636	+	0.965853i	−0.440058	+	0.897969i	$0.645042\pi$
$674$	−9.33085	−	0.872059i	−0.359411	−	0.0335905i
$675$	−0.660534	+	14.3283i	−0.0254240	+	0.551497i
$676$	−15.8103	+	18.3950i	−0.608087	+	0.707498i
$677$	−14.6090	+	8.43449i	−0.561468	+	0.324164i	−0.753735	−	0.657179i	$-0.771750\pi$
$677$	−14.6090	+	8.43449i	−0.561468	+	0.324164i	0.192266	+	0.981343i	$0.438416\pi$
$678$	−2.88473	−	1.42066i	−0.110787	−	0.0545601i
$679$	31.7779	+	18.3470i	1.21953	+	0.704093i
$680$	22.1056	+	6.34621i	0.847711	+	0.243366i
$681$	−2.82715	+	7.41140i	−0.108337	+	0.284005i
$682$	−17.8581	−	20.0010i	−0.683822	−	0.765879i
$683$	−32.9908			−1.26236			−0.631178	−	0.775638i	$-0.717428\pi$
$683$	−32.9908			−1.26236			−0.631178	+	0.775638i	$0.717428\pi$
$684$	−1.84097	+	1.41578i	−0.0703912	+	0.0541335i
$685$	1.12840	−	1.95445i	0.0431140	−	0.0746756i
$686$	−2.44825	+	26.1958i	−0.0934747	+	1.00016i
$687$	9.89261	−	1.58811i	0.377427	−	0.0605903i
$688$	−16.7480	−	20.9478i	−0.638511	−	0.798629i
$689$	3.08694	+	1.78225i	0.117603	+	0.0678982i
$690$	13.6978	+	6.74582i	0.521465	+	0.256809i
$691$	24.7321	−	14.2791i	0.940854	−	0.543202i	0.0506258	−	0.998718i	$-0.483878\pi$
$691$	24.7321	−	14.2791i	0.940854	−	0.543202i	0.890228	+	0.455516i	$0.150545\pi$
$692$	14.4192	−	5.05556i	0.548136	−	0.192183i
$693$	−26.3402	−	5.48338i	−1.00058	−	0.208297i
$694$	2.30835	−	3.25546i	0.0876238	−	0.123576i
$695$	9.46687	+	16.3971i	0.359099	+	0.621977i
$696$	−31.6827	+	13.5152i	−1.20093	+	0.512293i
$697$	−54.0025			−2.04549
$698$	37.6287	+	3.51677i	1.42427	+	0.133112i
$699$	36.6049	−	29.7694i	1.38452	−	1.12598i
$700$	−13.7209	+	4.81073i	−0.518602	+	0.181828i
$701$	−31.1773	−	18.0002i	−1.17755	−	0.679859i	−0.222103	−	0.975023i	$-0.571292\pi$
$701$	−31.1773	−	18.0002i	−1.17755	−	0.679859i	−0.955446	+	0.295165i	$0.904625\pi$
$702$	−29.0357	−	22.6679i	−1.09588	−	0.855544i
$703$	3.22914	−	1.86435i	0.121789	−	0.0703152i
$704$	−0.967873	+	27.2251i	−0.0364781	+	1.02609i
$705$	−8.60396	−	3.28206i	−0.324044	−	0.123610i
$706$	40.7632	+	28.9040i	1.53414	+	1.08782i
$707$	−0.844542	+	1.46279i	−0.0317623	+	0.0550138i
$708$	18.0328	+	0.490632i	0.677716	+	0.0184391i
$709$	19.5519			0.734285			0.367143	−	0.930165i	$-0.380336\pi$
$709$	19.5519			0.734285			0.367143	+	0.930165i	$0.380336\pi$
$710$	−0.842211	−	0.597187i	−0.0316076	−	0.0224120i
$711$	−5.02351	+	5.62646i	−0.188396	+	0.211009i
$712$	9.01826	−	31.4131i	0.337974	−	1.17726i
$713$	22.1661	−	6.81905i	0.830127	−	0.255376i
$714$	15.4858	−	31.4447i	0.579541	−	1.17679i
$715$			25.5456i			0.955351i
$716$	5.14486	−	5.98595i	0.192272	−	0.223706i
$717$	−6.17376	+	16.1846i	−0.230563	+	0.604424i
$718$	−19.5291	−	42.5363i	−0.728821	−	1.58744i
$719$	12.5021	−	21.6543i	0.466249	−	0.807567i	−0.533008	−	0.846110i	$-0.678938\pi$
$719$	12.5021	−	21.6543i	0.466249	−	0.807567i	0.999257	+	0.0385430i	$0.0122716\pi$
$720$	−0.976485	+	17.9317i	−0.0363914	+	0.668276i
$721$	29.6221			1.10318
$722$	11.1229	+	24.2268i	0.413953	+	0.901629i
$723$	25.3060	−	4.06250i	0.941140	−	0.151086i
$724$	−2.31320	−	6.59760i	−0.0859695	−	0.245198i
$725$	−16.8083	−	9.70430i	−0.624246	−	0.360409i
$726$	−1.45676	+	0.0962685i	−0.0540654	+	0.00357286i
$727$	−0.258717	−	0.149370i	−0.00959527	−	0.00553983i	0.495195	−	0.868782i	$-0.335097\pi$
$727$	−0.258717	−	0.149370i	−0.00959527	−	0.00553983i	−0.504790	+	0.863242i	$0.668430\pi$
$728$	10.3037	−	35.8905i	0.381879	−	1.33019i
$729$	15.5940	−	22.0415i	0.577557	−	0.816350i
$730$	13.4786	+	9.55728i	0.498865	+	0.353731i
$731$	18.2154	+	31.5500i	0.673720	+	1.16692i
$732$	19.9271	+	36.7907i	0.736528	+	1.35982i
$733$	24.3767	+	42.2217i	0.900375	+	1.55949i	0.827008	+	0.562190i	$0.190041\pi$
$733$	24.3767	+	42.2217i	0.900375	+	1.55949i	0.0733662	+	0.997305i	$0.476626\pi$
$734$	−25.4754	+	11.6962i	−0.940316	+	0.431715i
$735$	0.0262879	+	0.163751i	0.000969643	+	0.00604006i
$736$	−21.0506	−	10.5858i	−0.775934	−	0.390198i
$737$	−23.0582	−	13.3127i	−0.849360	−	0.490378i
$738$	−9.41466	−	41.1032i	−0.346558	−	1.51303i
$739$	−4.53655	+	2.61918i	−0.166880	+	0.0963480i	−0.581114	−	0.813822i	$-0.697383\pi$
$739$	−4.53655	+	2.61918i	−0.166880	+	0.0963480i	0.414234	+	0.910170i	$0.364049\pi$
$740$	5.34270	−	28.3332i	0.196402	−	1.04155i
$741$	2.60729	−	2.12041i	0.0957811	−	0.0778953i
$742$	−2.63695	−	0.246449i	−0.0968055	−	0.00904742i
$743$	11.8661			0.435326			0.217663	−	0.976024i	$-0.430157\pi$
$743$	11.8661			0.435326			0.217663	+	0.976024i	$0.430157\pi$
$744$	17.6064	+	20.8330i	0.645482	+	0.763775i
$745$	2.06524			0.0756644
$746$	21.9318	+	2.04974i	0.802980	+	0.0750463i
$747$	38.5842	−	12.7160i	1.41172	−	0.465253i
$748$	6.85699	−	36.3637i	0.250716	−	1.32959i
$749$	−20.5688	+	11.8754i	−0.751568	+	0.433918i
$750$	−23.6447	+	15.8173i	−0.863384	+	0.577567i
$751$	9.01017	+	5.20202i	0.328786	+	0.189824i	0.655302	−	0.755367i	$-0.272541\pi$
$751$	9.01017	+	5.20202i	0.328786	+	0.189824i	−0.326516	+	0.945192i	$0.605875\pi$
$752$	13.2348	+	5.17528i	0.482622	+	0.188723i
$753$	−51.3170	+	8.23818i	−1.87009	+	0.300216i
$754$	45.2979	−	20.7970i	1.64965	−	0.757384i
$755$	−7.65061	−	13.2512i	−0.278434	−	0.482262i
$756$	26.6334	+	6.30478i	0.968648	+	0.229303i
$757$	3.41864	+	5.92126i	0.124253	+	0.215212i	0.921441	−	0.388519i	$-0.127013\pi$
$757$	3.41864	+	5.92126i	0.124253	+	0.215212i	−0.797188	+	0.603731i	$0.793680\pi$
$758$	−24.7354	−	17.5391i	−0.898429	−	0.637050i
$759$	8.75604	−	22.9541i	0.317824	−	0.833179i
$760$	−1.57478	−	0.452096i	−0.0571231	−	0.0163992i
$761$	30.3534	+	17.5245i	1.10031	+	0.635264i	0.936302	−	0.351195i	$-0.114225\pi$
$761$	30.3534	+	17.5245i	1.10031	+	0.635264i	0.164007	+	0.986459i	$0.447558\pi$
$762$	−1.79665	−	27.1874i	−0.0650858	−	0.984895i
$763$	5.28499	+	3.05129i	0.191330	+	0.110464i
$764$	4.79129	+	13.6655i	0.173343	+	0.494400i
$765$	4.97158	−	23.8816i	0.179748	−	0.863442i
$766$	−12.7826	−	27.8417i	−0.461853	−	1.00596i
$767$	−26.1043			−0.942572
$768$	1.73747	−	27.6583i	0.0626956	−	0.998033i
$769$	1.47150	−	2.54871i	0.0530636	−	0.0919088i	−0.838273	−	0.545250i	$-0.816435\pi$
$769$	1.47150	−	2.54871i	0.0530636	−	0.0919088i	0.891337	+	0.453341i	$0.149768\pi$
$770$	−7.91949	−	17.2494i	−0.285399	−	0.621625i
$771$	−27.1518	−	10.3573i	−0.977849	−	0.373010i
$772$	11.0555	−	12.8629i	0.397898	−	0.462947i
$773$		−	3.75886i		−	0.135197i	−0.997713	−	0.0675983i	$-0.978466\pi$
$773$		−	3.75886i		−	0.135197i	0.997713	−	0.0675983i	$-0.0215336\pi$
$774$	−20.8382	+	19.3647i	−0.749012	+	0.696050i
$775$	−3.43129	+	14.9814i	−0.123256	+	0.538148i
$776$	−37.8780	−	10.8742i	−1.35974	−	0.390363i
$777$	−41.0568	−	15.6615i	−1.47290	−	0.561853i
$778$	23.3140	+	16.5313i	0.835848	+	0.592675i
$779$	3.84707			0.137836
$780$	0.706778	−	25.9771i	0.0253067	−	0.930131i
$781$	−0.830605	+	1.43865i	−0.0297214	+	0.0514789i
$782$	26.1085	+	18.5128i	0.933639	+	0.662016i
$783$	16.7908	+	32.4474i	0.600053	+	1.15957i
$784$	−0.0384593	−	0.253027i	−0.00137355	−	0.00903667i
$785$	−1.38545	+	0.799888i	−0.0494487	+	0.0285492i
$786$	11.7393	−	0.775777i	0.418725	−	0.0276711i
$787$	5.42667	+	3.13309i	0.193440	+	0.111683i	0.593592	−	0.804766i	$-0.297709\pi$
$787$	5.42667	+	3.13309i	0.193440	+	0.111683i	−0.400152	+	0.916449i	$0.631043\pi$
$788$	−29.8907	+	10.4800i	−1.06481	+	0.373336i
$789$	32.5297	+	39.9990i	1.15809	+	1.42400i
$790$	−5.29806	−	0.495156i	−0.188497	−	0.0176169i
$791$	−3.45731			−0.122928
$792$	28.8731	−	1.12047i	1.02596	−	0.0398141i
$793$	−30.2731	−	52.4345i	−1.07503	−	1.86200i
$794$	6.31244	−	8.90241i	0.224020	−	0.315935i
$795$	−1.81987	+	0.292153i	−0.0645440	+	0.0103616i
$796$	−47.2313	+	16.5599i	−1.67407	+	0.586950i
$797$	24.6512	−	14.2324i	0.873192	−	0.504137i	0.00478418	−	0.999989i	$-0.498477\pi$
$797$	24.6512	−	14.2324i	0.873192	−	0.504137i	0.868408	+	0.495851i	$0.165144\pi$
$798$	−1.10319	+	2.24008i	−0.0390525	+	0.0792981i
$799$	−16.7169	−	9.65150i	−0.591401	−	0.341445i
$800$	13.0509	−	8.57389i	0.461418	−	0.303133i
$801$	−33.9369	−	7.06485i	−1.19910	−	0.249624i
$802$	−3.31189	+	35.4365i	−0.116947	+	1.25131i
$803$	13.2928	−	23.0239i	0.469094	−	0.812495i
$804$	23.0794	+	14.1755i	0.813949	+	0.499932i
$805$	16.4166			0.578609
$806$	−26.2880	−	29.4426i	−0.925957	−	1.03707i
$807$	2.41742	+	0.922148i	0.0850973	+	0.0324611i
$808$	0.500559	−	1.74359i	0.0176096	−	0.0613391i
$809$	18.7217	+	10.8090i	0.658221	+	0.380024i	0.791599	−	0.611041i	$-0.209249\pi$
$809$	18.7217	+	10.8090i	0.658221	+	0.380024i	−0.133378	+	0.991065i	$0.542582\pi$
$810$	19.0439	−	0.379420i	0.669133	−	0.0133315i
$811$	−24.3358	+	14.0503i	−0.854546	+	0.493372i	−0.862182	−	0.506599i	$-0.830903\pi$
$811$	−24.3358	+	14.0503i	−0.854546	+	0.493372i	0.00763630	+	0.999971i	$0.497569\pi$
$812$	−24.1396	+	28.0860i	−0.847134	+	0.985626i
$813$	−27.6374	+	22.4764i	−0.969285	+	0.788284i
$814$	−46.1902	−	4.31693i	−1.61897	−	0.151308i
$815$	4.96361	+	8.59722i	0.173868	+	0.301148i
$816$	−7.97891	+	36.7883i	−0.279318	+	1.28785i
$817$	−1.29764	−	2.24758i	−0.0453987	−	0.0786329i
$818$	0.405177	−	0.571419i	0.0141667	−	0.0199792i
$819$	−38.7741	−	8.07183i	−1.35488	−	0.282052i
$820$	19.3902	−	22.5601i	0.677135	−	0.787835i
$821$			44.2214i			1.54334i	0.636024	+	0.771669i	$0.280578\pi$
$821$			44.2214i			1.54334i	−0.636024	+	0.771669i	$0.719422\pi$
$822$	3.31384	+	1.63199i	0.115583	+	0.0569221i
$823$	−18.8687	−	10.8939i	−0.657722	−	0.379736i	0.133686	−	0.991024i	$-0.457319\pi$
$823$	−18.8687	−	10.8939i	−0.657722	−	0.379736i	−0.791409	+	0.611288i	$0.790652\pi$
$824$	−30.8705	+	7.68657i	−1.07543	+	0.267774i
$825$	10.2727	+	12.6314i	0.357649	+	0.439770i
$826$	17.6267	−	8.09270i	0.613310	−	0.281581i
$827$	−9.83122	−	17.0282i	−0.341865	−	0.592128i	0.642914	−	0.765938i	$-0.277725\pi$
$827$	−9.83122	−	17.0282i	−0.341865	−	0.592128i	−0.984779	+	0.173811i	$0.944392\pi$
$828$	−9.53904	+	23.0996i	−0.331504	+	0.802766i
$829$	−33.7871			−1.17347			−0.586737	−	0.809777i	$-0.699588\pi$
$829$	−33.7871			−1.17347			−0.586737	+	0.809777i	$0.699588\pi$
$830$	23.3792	+	16.5775i	0.811503	+	0.575413i
$831$	16.5617	+	20.3646i	0.574520	+	0.706439i
$832$	−1.42476	+	40.0768i	−0.0493946	+	1.38941i
$833$			0.347646i			0.0120452i
$834$	−25.7584	+	17.2312i	−0.891939	+	0.596669i
$835$		−	15.0968i		−	0.522447i
$836$	−0.488483	+	2.59051i	−0.0168945	+	0.0895946i
$837$	20.6491	−	20.2636i	0.713737	−	0.700414i
$838$	−36.4374	−	3.40543i	−1.25871	−	0.117639i
$839$	−16.8342			−0.581180			−0.290590	−	0.956848i	$-0.593852\pi$
$839$	−16.8342			−0.581180			−0.290590	+	0.956848i	$0.593852\pi$
$840$	7.57604	+	17.7599i	0.261398	+	0.612776i
$841$	−20.4356			−0.704675
$842$	5.95948	+	12.9803i	0.205377	+	0.447331i
$843$	−41.8697	+	34.0511i	−1.44207	+	1.17278i
$844$	6.30496	+	5.41904i	0.217026	+	0.186531i
$845$			18.1496i			0.624366i
$846$	4.43171	−	14.4064i	0.152365	−	0.495303i
$847$	−1.35939	+	0.784844i	−0.0467092	+	0.0269676i
$848$	2.81203	−	0.427421i	0.0965656	−	0.0146777i
$849$	−17.4626	+	14.2017i	−0.599314	+	0.487399i
$850$	−19.2764	+	8.85013i	−0.661176	+	0.303557i
$851$	20.0624	−	34.7491i	0.687731	−	1.19118i
$852$	0.884440	−	1.43997i	0.0303004	−	0.0493327i
$853$	−25.4278			−0.870630			−0.435315	−	0.900278i	$-0.643363\pi$
$853$	−25.4278			−0.870630			−0.435315	+	0.900278i	$0.643363\pi$
$854$	36.6970	+	26.0208i	1.25575	+	0.890413i
$855$	−0.354169	+	1.70130i	−0.0121123	+	0.0581831i
$856$	18.3541	−	17.7132i	0.627332	−	0.605426i
$857$	−9.49672	+	5.48294i	−0.324402	+	0.187294i	−0.653353	−	0.757053i	$-0.726638\pi$
$857$	−9.49672	+	5.48294i	−0.324402	+	0.187294i	0.328951	+	0.944347i	$0.393305\pi$
$858$	−41.7216	+	2.75713i	−1.42435	+	0.0941270i
$859$	1.29001	−	0.744790i	0.0440147	−	0.0254119i	−0.477831	−	0.878452i	$-0.658577\pi$
$859$	1.29001	−	0.744790i	0.0440147	−	0.0254119i	0.521846	+	0.853040i	$0.325244\pi$
$860$	−19.7208	−	3.71868i	−0.672473	−	0.126806i
$861$	−28.6057	−	35.1740i	−0.974881	−	1.19873i
$862$	−26.8438	+	37.8577i	−0.914302	+	1.28944i
$863$	−3.43680	−	5.95271i	−0.116990	−	0.202632i	0.801584	−	0.597883i	$-0.203991\pi$
$863$	−3.43680	−	5.95271i	−0.116990	−	0.202632i	−0.918573	+	0.395250i	$0.870658\pi$
$864$	−29.3919	+	0.340553i	−0.999933	+	0.0115858i
$865$	5.71665	−	9.90152i	0.194372	−	0.336662i
$866$	−22.8729	−	2.13770i	−0.777253	−	0.0726419i
$867$	7.72991	−	20.2641i	0.262522	−	0.688203i
$868$	26.8784	+	11.7311i	0.912311	+	0.398181i
$869$			8.56172i			0.290437i
$870$	−11.3870	+	23.1220i	−0.386057	+	0.783909i
$871$	−33.9429	−	19.5969i	−1.15011	−	0.664017i
$872$	−6.29950	−	1.80850i	−0.213328	−	0.0612435i
$873$	−8.51882	+	40.9213i	−0.288318	+	1.38497i
$874$	−1.85994	−	1.31883i	−0.0629134	−	0.0446100i
$875$	−15.2930	+	26.4883i	−0.516999	+	0.895469i
$876$	−14.1544	+	23.0451i	−0.478234	+	0.778621i
$877$	8.34605	+	14.4558i	0.281826	+	0.488137i	0.971835	−	0.235664i	$-0.0757266\pi$
$877$	8.34605	+	14.4558i	0.281826	+	0.488137i	−0.690009	+	0.723801i	$0.742393\pi$
$878$	−49.7782	+	22.8540i	−1.67993	+	0.771286i
$879$	0.241410	+	1.50378i	0.00814256	+	0.0507213i
$880$	12.7293	+	15.9214i	0.429104	+	0.536709i
$881$	16.6174	−	9.59407i	0.559855	−	0.323232i	−0.193232	−	0.981153i	$-0.561897\pi$
$881$	16.6174	−	9.59407i	0.559855	−	0.323232i	0.753087	+	0.657921i	$0.228564\pi$
$882$	−0.264605	+	0.0606077i	−0.00890973	+	0.00204077i
$883$			7.70837i			0.259407i	0.991553	+	0.129704i	$0.0414026\pi$
$883$			7.70837i			0.259407i	−0.991553	+	0.129704i	$0.958597\pi$
$884$	10.0938	−	53.5293i	0.339493	−	1.80039i
$885$	10.4723	−	8.51674i	0.352023	−	0.286287i
$886$	−0.869944	−	1.89482i	−0.0292264	−	0.0636578i
$887$	−2.51770	+	4.36078i	−0.0845360	+	0.146421i	−0.905193	−	0.425000i	$-0.860274\pi$
$887$	−2.51770	+	4.36078i	−0.0845360	+	0.146421i	0.820657	+	0.571421i	$0.193607\pi$
$888$	46.8511	+	5.66782i	1.57222	+	0.190200i
$889$	−14.6475	−	25.3702i	−0.491261	−	0.850889i
$890$	−10.2036	−	22.2243i	−0.342024	−	0.744961i
$891$	−3.45916	−	30.4518i	−0.115886	−	1.02017i
$892$	−22.1595	−	19.0459i	−0.741956	−	0.637703i
$893$	1.19089	+	0.687561i	0.0398516	+	0.0230083i
$894$	0.222901	+	3.37299i	0.00745493	+	0.112810i
$895$		−	5.90612i		−	0.197420i
$896$	−11.4623	−	27.5032i	−0.382930	−	0.918817i
$897$	12.8893	−	33.7896i	0.430363	−	1.12820i
$898$	−4.22643	+	45.2219i	−0.141038	+	1.50908i
$899$	11.5107	+	37.4167i	0.383902	+	1.24792i
$900$	−10.0967	−	13.1290i	−0.336558	−	0.437635i
$901$	−3.86359			−0.128715
$902$	−39.0449	−	27.6856i	−1.30005	−	0.921830i
$903$	−10.9009	+	28.5768i	−0.362758	+	0.950975i
$904$	3.60301	−	0.897129i	0.119834	−	0.0298381i
$905$	−4.53051	−	2.61569i	−0.150599	−	0.0869485i
$906$	20.8165	−	13.9254i	0.691582	−	0.462639i
$907$			0.0774324i			0.00257110i	0.999999	+	0.00128555i	$0.000409204\pi$
$907$			0.0774324i			0.00257110i	−0.999999	+	0.00128555i	$0.999591\pi$
$908$	−3.03054	−	8.64357i	−0.100572	−	0.286847i
$909$	−1.88367	−	0.392135i	−0.0624774	−	0.0130063i
$910$	−11.6579	−	25.3920i	−0.386456	−	0.841737i
$911$	5.48124	−	9.49379i	0.181602	−	0.314543i	−0.760825	−	0.648958i	$-0.775205\pi$
$911$	5.48124	−	9.49379i	0.181602	−	0.314543i	0.942426	+	0.334415i	$0.108539\pi$
$912$	0.568408	−	2.62076i	0.0188219	−	0.0867819i
$913$	23.0570	−	39.9359i	0.763075	−	1.32169i
$914$	−1.57699	−	0.147385i	−0.0521623	−	0.00487508i
$915$	29.2519	+	11.1584i	0.967037	+	0.368885i
$916$	−7.54103	+	8.77386i	−0.249163	+	0.289897i
$917$	10.9546	−	6.32465i	0.361753	−	0.208858i
$918$	39.5406	+	5.54215i	1.30503	+	0.182918i
$919$	8.19159	−	4.72942i	0.270216	−	0.156009i	−0.358770	−	0.933426i	$-0.616804\pi$
$919$	8.19159	−	4.72942i	0.270216	−	0.156009i	0.628986	+	0.777417i	$0.283470\pi$
$920$	−17.1085	+	4.25990i	−0.564049	+	0.140445i
$921$	−2.79903	−	17.4356i	−0.0922311	−	0.574522i
$922$	4.23797	−	45.3453i	0.139570	−	1.49337i
$923$	−1.22269	+	2.11777i	−0.0402454	+	0.0697071i
$924$	27.3174	−	14.7960i	0.898676	−	0.486754i
$925$	13.2958	+	23.0290i	0.437162	+	0.757187i
$926$	4.97814	−	53.2651i	0.163592	−	1.75040i
$927$	10.5617	+	32.0473i	0.346890	+	1.05257i
$928$	17.8690	−	35.5336i	0.586578	−	1.16645i
$929$		−	6.00792i		−	0.197113i	−0.995131	−	0.0985567i	$-0.968577\pi$
$929$		−	6.00792i		−	0.197113i	0.995131	−	0.0985567i	$-0.0314226\pi$
$930$	20.1519	+	3.23483i	0.660807	+	0.106074i
$931$		−	0.0247659i		−	0.000811669i
$932$	−10.0954	+	53.5375i	−0.330685	+	1.75368i
$933$	7.26789	+	8.93671i	0.237940	+	0.292575i
$934$	57.2098	+	5.34682i	1.87196	+	0.174953i
$935$	−13.8446	−	23.9795i	−0.452766	−	0.784213i
$936$	42.5028	−	1.64939i	1.38925	−	0.0539119i
$937$	−7.70675	+	13.3485i	−0.251769	+	0.436076i	−0.964013	−	0.265856i	$-0.914346\pi$
$937$	−7.70675	+	13.3485i	−0.251769	+	0.436076i	0.712244	+	0.701932i	$0.247679\pi$
$938$	28.9949	+	2.70986i	0.946718	+	0.0884801i
$939$	−37.0406	+	5.94633i	−1.20878	+	0.194051i
$940$	10.0344	−	3.51819i	0.327286	−	0.114751i
$941$	7.82292	−	4.51657i	0.255020	−	0.147236i	−0.367041	−	0.930205i	$-0.619629\pi$
$941$	7.82292	−	4.51657i	0.255020	−	0.147236i	0.622061	+	0.782969i	$0.286296\pi$
$942$	−1.45593	−	2.17641i	−0.0474367	−	0.0709113i
$943$	35.8524	−	20.6994i	1.16751	−	0.674064i
$944$	−16.2696	+	13.0077i	−0.529530	+	0.423364i
$945$	18.1886	−	9.41217i	0.591674	−	0.306178i
$946$	−3.00471	+	32.1498i	−0.0976916	+	1.04528i
$947$	−0.0694674	+	0.120321i	−0.00225739	+	0.00390991i	−0.867152	−	0.498044i	$-0.834052\pi$
$947$	−0.0694674	+	0.120321i	−0.00225739	+	0.00390991i	0.864895	+	0.501954i	$0.167385\pi$
$948$	0.236880	−	8.70636i	0.00769351	−	0.282770i
$949$	19.5678	−	33.8924i	0.635197	−	1.10019i
$950$	1.37323	−	0.630472i	0.0445534	−	0.0204552i
$951$	0.632793	+	3.94177i	0.0205197	+	0.127821i
$952$	9.77908	+	39.2744i	0.316942	+	1.27289i
$953$		−	18.6595i		−	0.604441i	−0.953238	−	0.302221i	$-0.902272\pi$
$953$		−	18.6595i		−	0.604441i	0.953238	−	0.302221i	$-0.0977279\pi$
$954$	−0.673569	−	2.94072i	−0.0218076	−	0.0952092i
$955$	9.38395	+	5.41783i	0.303658	+	0.175317i
$956$	−6.61793	−	18.8753i	−0.214039	−	0.610471i
$957$	38.7467	+	14.7803i	1.25250	+	0.477779i
$958$	−5.83448	+	8.22835i	−0.188504	+	0.265846i
$959$	3.97159			0.128249
$960$	−12.5038	−	16.5425i	−0.403559	−	0.533908i
$961$	25.6397	−	17.4243i	0.827087	−	0.562074i
$962$	−67.9944	−	6.35474i	−2.19223	−	0.204885i
$963$	−20.1814	−	18.0187i	−0.650337	−	0.580644i
$964$	−19.2905	+	22.4441i	−0.621305	+	0.722877i
$965$		−	12.6914i		−	0.408550i
$966$	1.77184	+	26.8120i	0.0570081	+	0.862661i
$967$	−22.2617	−	12.8528i	−0.715889	−	0.413319i	0.0973485	−	0.995250i	$-0.468964\pi$
$967$	−22.2617	−	12.8528i	−0.715889	−	0.413319i	−0.813238	+	0.581931i	$0.802297\pi$
$968$	1.21302	−	1.17067i	0.0389880	−	0.0376266i
$969$	−1.29828	+	3.40345i	−0.0417067	+	0.109335i
$970$	−26.7981	+	12.3035i	−0.860436	+	0.395041i
$971$	14.1715	+	24.5458i	0.454786	+	0.787712i	0.998676	−	0.0514442i	$-0.0163824\pi$
$971$	14.1715	+	24.5458i	0.454786	+	0.787712i	−0.543890	+	0.839157i	$0.683049\pi$
$972$	2.67508	+	31.0619i	0.0858033	+	0.996312i
$973$	−16.6601	+	28.8561i	−0.534098	+	0.925085i
$974$	18.8564	−	8.65729i	0.604197	−	0.277397i
$975$	15.1219	+	18.5941i	0.484289	+	0.595489i
$976$	−44.9957	−	17.5950i	−1.44028	−	0.563203i
$977$			4.20206i			0.134436i	0.997738	+	0.0672178i	$0.0214122\pi$
$977$			4.20206i			0.134436i	−0.997738	+	0.0672178i	$0.978588\pi$
$978$	−13.5055	+	9.03458i	−0.431857	+	0.288894i
$979$	−34.0760	+	19.6738i	−1.08907	+	0.628777i
$980$	−0.145233	−	0.124826i	−0.00463929	−	0.00398742i
$981$	−1.41677	+	6.80562i	−0.0452338	+	0.217287i
$982$	5.46212	+	11.8970i	0.174303	+	0.379649i
$983$	14.2685	+	24.7138i	0.455095	+	0.788247i	0.998694	−	0.0510979i	$-0.0162721\pi$
$983$	14.2685	+	24.7138i	0.455095	+	0.788247i	−0.543599	+	0.839345i	$0.682939\pi$
$984$	38.9385	+	29.2336i	1.24132	+	0.931933i
$985$	−11.8505	+	20.5256i	−0.377587	+	0.654000i
$986$	−31.2498	+	44.0715i	−0.995197	+	1.40352i
$987$	−2.56871	−	16.0009i	−0.0817628	−	0.509314i
$988$	−0.719073	+	3.81336i	−0.0228768	+	0.121319i
$989$	−24.1864	−	13.9640i	−0.769084	−	0.444031i
$990$	15.8380	−	14.7181i	0.503365	−	0.467772i
$991$		−	26.0363i		−	0.827072i	−0.910488	−	0.413536i	$-0.864294\pi$
$991$		−	26.0363i		−	0.827072i	0.910488	−	0.413536i	$-0.135706\pi$
$992$	−31.0552	−	5.25094i	−0.986005	−	0.166717i
$993$	39.4936	+	15.0652i	1.25329	+	0.478080i
$994$	0.169074	−	1.80905i	0.00536269	−	0.0573797i
$995$	−18.7253	+	32.4333i	−0.593633	+	1.02820i
$996$	−24.5514	+	39.9726i	−0.777942	+	1.26658i
$997$	−21.3828	−	37.0360i	−0.677199	−	1.17294i	−0.975821	−	0.218571i	$-0.929860\pi$
$997$	−21.3828	−	37.0360i	−0.677199	−	1.17294i	0.298623	−	0.954371i	$-0.403473\pi$
$998$	−34.9083	−	24.7525i	−1.10500	−	0.783526i
$999$	2.30510	−	50.0023i	0.0729301	−	1.58200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.p.a.191.1	✓	120
3.2	odd	2	inner	372.2.p.a.191.60	yes	120
4.3	odd	2	inner	372.2.p.a.191.59	yes	120
12.11	even	2	inner	372.2.p.a.191.2	yes	120
31.25	even	3	inner	372.2.p.a.335.1	yes	120
93.56	odd	6	inner	372.2.p.a.335.60	yes	120
124.87	odd	6	inner	372.2.p.a.335.59	yes	120
372.335	even	6	inner	372.2.p.a.335.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.p.a.191.1	✓	120	1.1	even	1	trivial
372.2.p.a.191.2	yes	120	12.11	even	2	inner
372.2.p.a.191.59	yes	120	4.3	odd	2	inner
372.2.p.a.191.60	yes	120	3.2	odd	2	inner
372.2.p.a.335.1	yes	120	31.25	even	3	inner
372.2.p.a.335.2	yes	120	372.335	even	6	inner
372.2.p.a.335.59	yes	120	124.87	odd	6	inner
372.2.p.a.335.60	yes	120	93.56	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40808 - 0.131599i) q^{2} +(-1.09284 - 1.34377i) q^{3} +(1.96536 + 0.370602i) q^{4} +(1.29603 - 0.748262i) q^{5} +(1.36196 + 2.03594i) q^{6} +(2.28079 + 1.31682i) q^{7} +(-2.71861 - 0.780475i) q^{8} +(-0.611419 + 2.93703i) q^{9} +(-1.92338 + 0.883056i) q^{10} +(1.70265 + 2.94907i) q^{11} +(-1.64982 - 3.04600i) q^{12} +(2.50638 + 4.34118i) q^{13} +(-3.03824 - 2.15433i) q^{14} +(-2.42184 - 0.923832i) q^{15} +(3.72531 + 1.45674i) q^{16} +(-4.70546 - 2.71670i) q^{17} +(1.24744 - 4.05511i) q^{18} +(0.335211 + 0.193534i) q^{19} +(2.82447 - 0.990297i) q^{20} +(-0.723038 - 4.50392i) q^{21} +(-2.00936 - 4.37658i) q^{22} +4.16528 q^{23} +(1.92222 + 4.50611i) q^{24} +(-1.38021 + 2.39059i) q^{25} +(-2.95789 - 6.44256i) q^{26} +(4.61487 - 2.38809i) q^{27} +(3.99457 + 3.43329i) q^{28} +7.03104i q^{29} +(3.28856 + 1.61954i) q^{30} +(5.32164 - 1.63712i) q^{31} +(-5.05382 - 2.54144i) q^{32} +(2.10215 - 5.51081i) q^{33} +(6.26813 + 4.44455i) q^{34} +3.94129 q^{35} +(-2.29013 + 5.54575i) q^{36} +(4.81658 - 8.34257i) q^{37} +(-0.446534 - 0.316624i) q^{38} +(3.09447 - 8.11220i) q^{39} +(-4.10740 + 1.02272i) q^{40} +(8.60743 - 4.96950i) q^{41} +(0.425384 + 6.43701i) q^{42} +(-5.80668 - 3.35249i) q^{43} +(2.25339 + 6.42700i) q^{44} +(1.40525 + 4.26398i) q^{45} +(-5.86503 - 0.548145i) q^{46} +3.55266 q^{47} +(-2.11364 - 6.59792i) q^{48} +(-0.0319916 - 0.0554111i) q^{49} +(2.25804 - 3.18450i) q^{50} +(1.49168 + 9.29194i) q^{51} +(3.31710 + 9.46088i) q^{52} +(0.615816 - 0.355541i) q^{53} +(-6.81236 + 2.75531i) q^{54} +(4.41335 + 2.54805i) q^{55} +(-5.17285 - 5.36002i) q^{56} +(-0.106266 - 0.661946i) q^{57} +(0.925276 - 9.90025i) q^{58} +(-2.60378 + 4.50988i) q^{59} +(-4.41741 - 2.71320i) q^{60} -12.0784 q^{61} +(-7.70872 + 1.60487i) q^{62} +(-5.26205 + 5.89364i) q^{63} +(6.78172 + 4.24362i) q^{64} +(6.49669 + 3.75086i) q^{65} +(-3.68520 + 7.48301i) q^{66} +(-6.77129 + 3.90940i) q^{67} +(-8.24112 - 7.08315i) q^{68} +(-4.55197 - 5.59716i) q^{69} +(-5.54965 - 0.518669i) q^{70} +(0.243916 + 0.422475i) q^{71} +(3.95450 - 7.50746i) q^{72} +(-3.90359 - 6.76121i) q^{73} +(-7.87999 + 11.1131i) q^{74} +(4.72074 - 0.757845i) q^{75} +(0.587087 + 0.504595i) q^{76} +8.96829i q^{77} +(-5.42481 + 11.0154i) q^{78} +(2.17740 + 1.25712i) q^{79} +(5.91812 - 0.899537i) q^{80} +(-8.25233 - 3.59152i) q^{81} +(-12.7739 + 5.86472i) q^{82} +(-6.77093 - 11.7276i) q^{83} +(0.248129 - 9.11979i) q^{84} -8.13121 q^{85} +(7.73507 + 5.48471i) q^{86} +(9.44808 - 7.68378i) q^{87} +(-2.32716 - 9.34625i) q^{88} +11.5548i q^{89} +(-1.41757 - 6.18894i) q^{90} +13.2018i q^{91} +(8.18629 + 1.54366i) q^{92} +(-8.01558 - 5.36194i) q^{93} +(-5.00242 - 0.467525i) q^{94} +0.579257 q^{95} +(2.10789 + 9.56853i) q^{96} +13.9329 q^{97} +(0.0377546 + 0.0822332i) q^{98} +(-9.70255 + 3.19761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) \) 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

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