LMFDB - Embedded newform 171.2.h.c.49.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(7,171)] 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("171.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.h (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-2,1,34,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.6
Character	$\chi$	$=$	171.49
Dual form			171.2.h.c.7.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.23359 q^{2} +(-1.68779 + 0.389075i) q^{3} -0.478252 q^{4} +(0.275772 + 0.477650i) q^{5} +(2.08204 - 0.479960i) q^{6} +(-1.62156 - 2.80862i) q^{7} +3.05715 q^{8} +(2.69724 - 1.31335i) q^{9} +(-0.340189 - 0.589225i) q^{10} +(2.68677 + 4.65363i) q^{11} +(0.807186 - 0.186076i) q^{12} +3.52389 q^{13} +(2.00034 + 3.46470i) q^{14} +(-0.651285 - 0.698875i) q^{15} -2.81477 q^{16} +(2.60168 - 4.50624i) q^{17} +(-3.32729 + 1.62014i) q^{18} +(0.164107 - 4.35581i) q^{19} +(-0.131888 - 0.228437i) q^{20} +(3.82961 + 4.10945i) q^{21} +(-3.31438 - 5.74068i) q^{22} +2.98467 q^{23} +(-5.15981 + 1.18946i) q^{24} +(2.34790 - 4.06668i) q^{25} -4.34704 q^{26} +(-4.04137 + 3.26609i) q^{27} +(0.775514 + 1.34323i) q^{28} +(-2.74921 + 4.76176i) q^{29} +(0.803420 + 0.862127i) q^{30} +(-2.54567 + 4.40923i) q^{31} -2.64202 q^{32} +(-6.34531 - 6.80897i) q^{33} +(-3.20941 + 5.55885i) q^{34} +(0.894360 - 1.54908i) q^{35} +(-1.28996 + 0.628113i) q^{36} +9.20826 q^{37} +(-0.202441 + 5.37329i) q^{38} +(-5.94757 + 1.37106i) q^{39} +(0.843075 + 1.46025i) q^{40} +(-0.855013 - 1.48093i) q^{41} +(-4.72418 - 5.06938i) q^{42} -3.59217 q^{43} +(-1.28495 - 2.22561i) q^{44} +(1.37114 + 0.926153i) q^{45} -3.68186 q^{46} +(5.31770 - 9.21053i) q^{47} +(4.75073 - 1.09516i) q^{48} +(-1.75891 + 3.04653i) q^{49} +(-2.89635 + 5.01663i) q^{50} +(-2.63781 + 8.61781i) q^{51} -1.68531 q^{52} +(0.562013 + 0.973435i) q^{53} +(4.98540 - 4.02902i) q^{54} +(-1.48187 + 2.56668i) q^{55} +(-4.95735 - 8.58639i) q^{56} +(1.41776 + 7.41552i) q^{57} +(3.39140 - 5.87407i) q^{58} +(3.88928 + 6.73644i) q^{59} +(0.311478 + 0.334238i) q^{60} +(5.68723 - 9.85058i) q^{61} +(3.14032 - 5.43919i) q^{62} +(-8.06245 - 5.44586i) q^{63} +8.88872 q^{64} +(0.971789 + 1.68319i) q^{65} +(7.82752 + 8.39949i) q^{66} +2.37259 q^{67} +(-1.24426 + 2.15512i) q^{68} +(-5.03748 + 1.16126i) q^{69} +(-1.10328 + 1.91093i) q^{70} +(-0.507763 + 0.879471i) q^{71} +(8.24587 - 4.01511i) q^{72} +(-5.98562 + 10.3674i) q^{73} -11.3592 q^{74} +(-2.38051 + 7.77720i) q^{75} +(-0.0784845 + 2.08317i) q^{76} +(8.71353 - 15.0923i) q^{77} +(7.33688 - 1.69133i) q^{78} -1.13760 q^{79} +(-0.776234 - 1.34448i) q^{80} +(5.55022 - 7.08485i) q^{81} +(1.05474 + 1.82686i) q^{82} +(-1.14372 - 1.98099i) q^{83} +(-1.83152 - 1.96535i) q^{84} +2.86987 q^{85} +4.43127 q^{86} +(2.78738 - 9.10648i) q^{87} +(8.21387 + 14.2268i) q^{88} +(1.12141 + 1.94234i) q^{89} +(-1.69143 - 1.14249i) q^{90} +(-5.71420 - 9.89729i) q^{91} -1.42742 q^{92} +(2.58102 - 8.43229i) q^{93} +(-6.55987 + 11.3620i) q^{94} +(2.12581 - 1.12282i) q^{95} +(4.45917 - 1.02795i) q^{96} +8.18199 q^{97} +(2.16978 - 3.75817i) q^{98} +(13.3587 + 9.02328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + q^{3} + 34 q^{4} + 3 q^{5} - 7 q^{6} + q^{7} - 36 q^{8} + 17 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} + 8 q^{13} + q^{14} - 14 q^{15} + 22 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20}+ \cdots - 49 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + q^3 + 34 * q^4 + 3 * q^5 - 7 * q^6 + q^7 - 36 * q^8 + 17 * q^9 - 8 * q^10 + 7 * q^11 - 3 * q^12 + 8 * q^13 + q^14 - 14 * q^15 + 22 * q^16 - 7 * q^17 + 6 * q^18 + 7 * q^19 - 3 * q^20 + 8 * q^21 - 8 * q^22 - 10 * q^23 - 39 * q^24 - 9 * q^25 - 4 * q^26 - 5 * q^27 - 10 * q^28 + 10 * q^29 - 5 * q^30 - 10 * q^31 - 34 * q^32 + q^33 - 13 * q^34 - 3 * q^35 - 19 * q^36 + 2 * q^37 - 46 * q^38 + 12 * q^40 + 6 * q^41 + 16 * q^42 - 14 * q^43 + 20 * q^44 - 35 * q^45 - 9 * q^47 - 15 * q^48 - 13 * q^49 + q^50 - 10 * q^51 - 38 * q^52 + 16 * q^53 - 40 * q^54 + 15 * q^55 - 6 * q^56 + 69 * q^57 + 37 * q^59 - 19 * q^60 - 12 * q^61 + 54 * q^62 + 21 * q^63 - 64 * q^64 + 54 * q^65 + 37 * q^66 + 22 * q^67 - 2 * q^68 + 3 * q^69 + 24 * q^70 + 9 * q^71 + 15 * q^72 - 10 * q^73 - 12 * q^74 - 76 * q^75 - 40 * q^76 + 46 * q^77 + 8 * q^78 + 16 * q^79 - 24 * q^80 + 17 * q^81 + 7 * q^82 + 3 * q^83 + 12 * q^84 + 54 * q^85 - 34 * q^86 - 9 * q^87 + 9 * q^88 + 30 * q^89 + 133 * q^90 - q^91 + 34 * q^92 + 27 * q^93 - 18 * q^94 + 3 * q^95 - 5 * q^96 + 18 * q^98 - 49 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.23359			−0.872281			−0.436140	−	0.899879i	$-0.643655\pi$
$2$	−1.23359			−0.872281			−0.436140	+	0.899879i	$0.643655\pi$
$3$	−1.68779	+	0.389075i	−0.974443	+	0.224633i
$3$	−1.68779	+	0.389075i	−0.974443	+	0.224633i
$4$	−0.478252			−0.239126
$5$	0.275772	+	0.477650i	0.123329	+	0.213612i	0.921078	−	0.389377i	$-0.127310\pi$
$5$	0.275772	+	0.477650i	0.123329	+	0.213612i	−0.797750	+	0.602989i	$0.793976\pi$
$6$	2.08204	−	0.479960i	0.849989	−	0.195943i
$7$	−1.62156	−	2.80862i	−0.612892	−	1.06156i	−0.990750	−	0.135697i	$-0.956673\pi$
$7$	−1.62156	−	2.80862i	−0.612892	−	1.06156i	0.377858	−	0.925863i	$-0.376661\pi$
$8$	3.05715			1.08087
$9$	2.69724	−	1.31335i	0.899080	−	0.437784i
$10$	−0.340189	−	0.589225i	−0.107577	−	0.186329i
$11$	2.68677	+	4.65363i	0.810093	+	1.40312i	0.912799	+	0.408410i	$0.133917\pi$
$11$	2.68677	+	4.65363i	0.810093	+	1.40312i	−0.102706	+	0.994712i	$0.532750\pi$
$12$	0.807186	−	0.186076i	0.233015	−	0.0537155i
$13$	3.52389			0.977352			0.488676	−	0.872465i	$-0.337480\pi$
$13$	3.52389			0.977352			0.488676	+	0.872465i	$0.337480\pi$
$14$	2.00034	+	3.46470i	0.534614	+	0.925979i
$15$	−0.651285	−	0.698875i	−0.168161	−	0.180449i
$16$	−2.81477			−0.703693
$17$	2.60168	−	4.50624i	0.630999	−	1.09292i	−0.356349	−	0.934353i	$-0.615978\pi$
$17$	2.60168	−	4.50624i	0.630999	−	1.09292i	0.987348	−	0.158570i	$-0.0506882\pi$
$18$	−3.32729	+	1.62014i	−0.784251	+	0.381871i
$19$	0.164107	−	4.35581i	0.0376488	−	0.999291i
$19$	0.164107	−	4.35581i	0.0376488	−	0.999291i
$20$	−0.131888	−	0.228437i	−0.0294911	−	0.0510801i
$21$	3.82961	+	4.10945i	0.835690	+	0.896755i
$22$	−3.31438	−	5.74068i	−0.706628	−	1.22392i
$23$	2.98467			0.622346			0.311173	−	0.950353i	$-0.399278\pi$
$23$	2.98467			0.622346			0.311173	+	0.950353i	$0.399278\pi$
$24$	−5.15981	+	1.18946i	−1.05324	+	0.242798i
$25$	2.34790	−	4.06668i	0.469580	−	0.813336i
$26$	−4.34704			−0.852525
$27$	−4.04137	+	3.26609i	−0.777762	+	0.628559i
$28$	0.775514	+	1.34323i	0.146558	+	0.253847i
$29$	−2.74921	+	4.76176i	−0.510515	+	0.884237i	0.489411	+	0.872053i	$0.337212\pi$
$29$	−2.74921	+	4.76176i	−0.510515	+	0.884237i	−0.999926	+	0.0121841i	$0.996122\pi$
$30$	0.803420	+	0.862127i	0.146684	+	0.157402i
$31$	−2.54567	+	4.40923i	−0.457216	+	0.791921i	−0.998813	−	0.0487176i	$-0.984487\pi$
$31$	−2.54567	+	4.40923i	−0.457216	+	0.791921i	0.541597	+	0.840638i	$0.317820\pi$
$32$	−2.64202			−0.467048
$33$	−6.34531	−	6.80897i	−1.10458	−	1.18529i
$34$	−3.20941	+	5.55885i	−0.550409	+	0.953336i
$35$	0.894360	−	1.54908i	0.151174	−	0.261842i
$36$	−1.28996	+	0.628113i	−0.214993	+	0.104685i
$37$	9.20826			1.51383			0.756914	−	0.653514i	$-0.226706\pi$
$37$	9.20826			1.51383			0.756914	+	0.653514i	$0.226706\pi$
$38$	−0.202441	+	5.37329i	−0.0328403	+	0.871663i
$39$	−5.94757	+	1.37106i	−0.952374	+	0.219545i
$40$	0.843075	+	1.46025i	0.133302	+	0.230886i
$41$	−0.855013	−	1.48093i	−0.133531	−	0.231282i	0.791505	−	0.611163i	$-0.209298\pi$
$41$	−0.855013	−	1.48093i	−0.133531	−	0.231282i	−0.925035	+	0.379881i	$0.875965\pi$
$42$	−4.72418	−	5.06938i	−0.728956	−	0.782222i
$43$	−3.59217			−0.547800			−0.273900	−	0.961758i	$-0.588314\pi$
$43$	−3.59217			−0.547800			−0.273900	+	0.961758i	$0.588314\pi$
$44$	−1.28495	−	2.22561i	−0.193714	−	0.335523i
$45$	1.37114	+	0.926153i	0.204398	+	0.138063i
$46$	−3.68186			−0.542860
$47$	5.31770	−	9.21053i	0.775666	−	1.34349i	−0.158753	−	0.987318i	$-0.550747\pi$
$47$	5.31770	−	9.21053i	0.775666	−	1.34349i	0.934419	−	0.356175i	$-0.115919\pi$
$48$	4.75073	−	1.09516i	0.685709	−	0.158072i
$49$	−1.75891	+	3.04653i	−0.251273	+	0.435218i
$50$	−2.89635	+	5.01663i	−0.409606	+	0.709458i
$51$	−2.63781	+	8.61781i	−0.369367	+	1.20673i
$52$	−1.68531			−0.233710
$53$	0.562013	+	0.973435i	0.0771985	+	0.133712i	0.902040	−	0.431652i	$-0.142069\pi$
$53$	0.562013	+	0.973435i	0.0771985	+	0.133712i	−0.824842	+	0.565364i	$0.808736\pi$
$54$	4.98540	−	4.02902i	0.678427	−	0.548280i
$55$	−1.48187	+	2.56668i	−0.199815	+	0.346091i
$56$	−4.95735	−	8.58639i	−0.662454	−	1.14740i
$57$	1.41776	+	7.41552i	0.187787	+	0.982210i
$58$	3.39140	−	5.87407i	0.445312	−	0.771303i
$59$	3.88928	+	6.73644i	0.506342	+	0.877010i	0.999973	+	0.00733829i	$0.00233587\pi$
$59$	3.88928	+	6.73644i	0.506342	+	0.877010i	−0.493631	+	0.869671i	$0.664331\pi$
$60$	0.311478	+	0.334238i	0.0402117	+	0.0431500i
$61$	5.68723	−	9.85058i	0.728176	−	1.26124i	−0.229478	−	0.973314i	$-0.573702\pi$
$61$	5.68723	−	9.85058i	0.728176	−	1.26124i	0.957653	−	0.287923i	$-0.0929648\pi$
$62$	3.14032	−	5.43919i	0.398820	−	0.690777i
$63$	−8.06245	−	5.44586i	−1.01577	−	0.686114i
$64$	8.88872			1.11109
$65$	0.971789	+	1.68319i	0.120536	+	0.208774i
$66$	7.82752	+	8.39949i	0.963501	+	1.03391i
$67$	2.37259			0.289858			0.144929	−	0.989442i	$-0.453705\pi$
$67$	2.37259			0.289858			0.144929	+	0.989442i	$0.453705\pi$
$68$	−1.24426	+	2.15512i	−0.150888	+	0.261346i
$69$	−5.03748	+	1.16126i	−0.606441	+	0.139799i
$70$	−1.10328	+	1.91093i	−0.131867	+	0.228400i
$71$	−0.507763	+	0.879471i	−0.0602604	+	0.104374i	−0.894582	−	0.446904i	$-0.852526\pi$
$71$	−0.507763	+	0.879471i	−0.0602604	+	0.104374i	0.834321	+	0.551278i	$0.185860\pi$
$72$	8.24587	−	4.01511i	0.971785	−	0.473186i
$73$	−5.98562	+	10.3674i	−0.700564	+	1.21341i	0.267704	+	0.963501i	$0.413735\pi$
$73$	−5.98562	+	10.3674i	−0.700564	+	1.21341i	−0.968269	+	0.249912i	$0.919598\pi$
$74$	−11.3592			−1.32048
$75$	−2.38051	+	7.77720i	−0.274877	+	0.898033i
$76$	−0.0784845	+	2.08317i	−0.00900279	+	0.238956i
$77$	8.71353	−	15.0923i	0.992999	−	1.71992i
$78$	7.33688	−	1.69133i	0.830738	−	0.191505i
$79$	−1.13760			−0.127990			−0.0639952	−	0.997950i	$-0.520384\pi$
$79$	−1.13760			−0.127990			−0.0639952	+	0.997950i	$0.520384\pi$
$80$	−0.776234	−	1.34448i	−0.0867856	−	0.150317i
$81$	5.55022	−	7.08485i	0.616691	−	0.787206i
$82$	1.05474	+	1.82686i	0.116476	+	0.201743i
$83$	−1.14372	−	1.98099i	−0.125540	−	0.217441i	0.796404	−	0.604765i	$-0.206733\pi$
$83$	−1.14372	−	1.98099i	−0.125540	−	0.217441i	−0.921944	+	0.387324i	$0.873400\pi$
$84$	−1.83152	−	1.96535i	−0.199835	−	0.214437i
$85$	2.86987			0.311281
$86$	4.43127			0.477836
$87$	2.78738	−	9.10648i	0.298839	−	0.976318i
$88$	8.21387	+	14.2268i	0.875601	+	1.51659i
$89$	1.12141	+	1.94234i	0.118870	+	0.205888i	0.919320	−	0.393511i	$-0.128740\pi$
$89$	1.12141	+	1.94234i	0.118870	+	0.205888i	−0.800450	+	0.599399i	$0.795406\pi$
$90$	−1.69143	−	1.14249i	−0.178293	−	0.120429i
$91$	−5.71420	−	9.89729i	−0.599011	−	1.03752i
$92$	−1.42742			−0.148819
$93$	2.58102	−	8.43229i	0.267639	−	0.874387i
$94$	−6.55987	+	11.3620i	−0.676599	+	1.17190i
$95$	2.12581	−	1.12282i	0.218103	−	0.115199i
$96$	4.45917	−	1.02795i	0.455112	−	0.104914i
$97$	8.18199			0.830756			0.415378	−	0.909649i	$-0.363649\pi$
$97$	8.18199			0.830756			0.415378	+	0.909649i	$0.363649\pi$
$98$	2.16978	−	3.75817i	0.219181	−	0.379633i
$99$	13.3587	+	9.02328i	1.34260	+	0.906873i
$100$	−1.12289	+	1.94490i	−0.112289	+	0.194490i
$101$	−2.71715	+	4.70624i	−0.270366	+	0.468288i	−0.968956	−	0.247235i	$-0.920478\pi$
$101$	−2.71715	+	4.70624i	−0.270366	+	0.468288i	0.698589	+	0.715523i	$0.253811\pi$
$102$	3.25398	−	10.6309i	0.322192	−	1.05261i
$103$	6.93864	−	12.0181i	0.683684	−	1.18418i	−0.290164	−	0.956977i	$-0.593710\pi$
$103$	6.93864	−	12.0181i	0.683684	−	1.18418i	0.973848	−	0.227199i	$-0.0729567\pi$
$104$	10.7731			1.05639
$105$	−0.906780	+	2.96248i	−0.0884927	+	0.289109i
$106$	−0.693295	−	1.20082i	−0.0673387	−	0.116634i
$107$	−15.8009			−1.52753			−0.763765	−	0.645494i	$-0.776652\pi$
$107$	−15.8009			−1.52753			−0.763765	+	0.645494i	$0.776652\pi$
$108$	1.93279	−	1.56201i	0.185983	−	0.150305i
$109$	−3.79701	+	6.57662i	−0.363688	+	0.629926i	−0.988565	−	0.150798i	$-0.951816\pi$
$109$	−3.79701	+	6.57662i	−0.363688	+	0.629926i	0.624877	+	0.780723i	$0.285149\pi$
$110$	1.82802	−	3.16623i	0.174295	−	0.301888i
$111$	−15.5416	+	3.58271i	−1.47514	+	0.340056i
$112$	4.56432	+	7.90564i	0.431288	+	0.747012i
$113$	−2.26572	+	3.92433i	−0.213141	+	0.369170i	−0.952696	−	0.303926i	$-0.901703\pi$
$113$	−2.26572	+	3.92433i	−0.213141	+	0.369170i	0.739555	+	0.673096i	$0.235036\pi$
$114$	−1.74894	−	9.14772i	−0.163803	−	0.856763i
$115$	0.823086	+	1.42563i	0.0767531	+	0.132940i
$116$	1.31481	−	2.27732i	0.122077	−	0.211444i
$117$	9.50478	−	4.62811i	0.878717	−	0.427869i
$118$	−4.79779	−	8.31001i	−0.441672	−	0.764999i
$119$	−16.8751			−1.54694
$120$	−1.99108	−	2.13657i	−0.181760	−	0.195041i
$121$	−8.93750	+	15.4802i	−0.812500	+	1.40729i
$122$	−7.01572	+	12.1516i	−0.635174	+	1.10015i
$123$	2.01927	+	2.16682i	0.182072	+	0.195376i
$124$	1.21747	−	2.10872i	0.109332	−	0.189369i
$125$	5.34765			0.478308
$126$	9.94577	+	6.71796i	0.886040	+	0.598484i
$127$	−5.24840	−	9.09049i	−0.465720	−	0.806651i	0.533514	−	0.845792i	$-0.320871\pi$
$127$	−5.24840	−	9.09049i	−0.465720	−	0.806651i	−0.999234	+	0.0391405i	$0.987538\pi$
$128$	−5.68101			−0.502135
$129$	6.06281	−	1.39762i	0.533800	−	0.123054i
$130$	−1.19879	−	2.07637i	−0.105141	−	0.182109i
$131$	0.281725	+	0.487963i	0.0246145	+	0.0426335i	0.878070	−	0.478532i	$-0.158831\pi$
$131$	0.281725	+	0.487963i	0.0246145	+	0.0426335i	−0.853456	+	0.521165i	$0.825498\pi$
$132$	3.03465	+	3.25640i	0.264133	+	0.283433i
$133$	−12.4999	+	6.60229i	−1.08388	+	0.572491i
$134$	−2.92681			−0.252838
$135$	−2.67454	−	1.02967i	−0.230188	−	0.0886198i
$136$	7.95372	−	13.7762i	0.682026	−	1.18130i
$137$	−8.61664	+	14.9245i	−0.736169	+	1.27508i	0.218040	+	0.975940i	$0.430034\pi$
$137$	−8.61664	+	14.9245i	−0.736169	+	1.27508i	−0.954209	+	0.299142i	$0.903300\pi$
$138$	6.21419	−	1.43252i	0.528987	−	0.121944i
$139$	1.45247			0.123197			0.0615986	−	0.998101i	$-0.480380\pi$
$139$	1.45247			0.123197			0.0615986	+	0.998101i	$0.480380\pi$
$140$	−0.427729	+	0.740849i	−0.0361497	+	0.0626132i
$141$	−5.39155	+	17.6144i	−0.454050	+	1.48340i
$142$	0.626372	−	1.08491i	0.0525640	−	0.0910434i
$143$	9.46790	+	16.3989i	0.791745	+	1.37134i
$144$	−7.59212	+	3.69679i	−0.632676	+	0.308065i
$145$	−3.03261			−0.251845
$146$	7.38382	−	12.7891i	0.611089	−	1.05844i
$147$	1.78334	−	5.82624i	0.147087	−	0.480540i
$148$	−4.40387			−0.361996
$149$	−2.34506	−	4.06177i	−0.192115	−	0.332753i	0.753836	−	0.657063i	$-0.228201\pi$
$149$	−2.34506	−	4.06177i	−0.192115	−	0.332753i	−0.945951	+	0.324310i	$0.894868\pi$
$150$	2.93657	−	9.59389i	0.239770	−	0.783338i
$151$	0.368885	+	0.638928i	0.0300195	+	0.0519953i	0.880645	−	0.473777i	$-0.157110\pi$
$151$	0.368885	+	0.638928i	0.0300195	+	0.0519953i	−0.850625	+	0.525772i	$0.823776\pi$
$152$	0.501700	−	13.3164i	0.0406933	−	1.08010i
$153$	1.09908	−	15.5713i	0.0888550	−	1.25887i
$154$	−10.7489	+	18.6177i	−0.866174	+	1.50026i
$155$	−2.80809			−0.225551
$156$	2.84444	−	0.655711i	0.227737	−	0.0524989i
$157$	−2.70723	−	4.68906i	−0.216060	−	0.374228i	0.737540	−	0.675304i	$-0.235988\pi$
$157$	−2.70723	−	4.68906i	−0.216060	−	0.374228i	−0.953600	+	0.301076i	$0.902654\pi$
$158$	1.40334			0.111644
$159$	−1.32730	−	1.42428i	−0.105262	−	0.112953i
$160$	−0.728594	−	1.26196i	−0.0576005	−	0.0997669i
$161$	−4.83981	−	8.38280i	−0.381431	−	0.660657i
$162$	−6.84670	+	8.73981i	−0.537927	+	0.686665i
$163$	−10.0435			−0.786669			−0.393334	−	0.919395i	$-0.628679\pi$
$163$	−10.0435			−0.786669			−0.393334	+	0.919395i	$0.628679\pi$
$164$	0.408912	+	0.708256i	0.0319306	+	0.0553055i
$165$	1.50245	−	4.90856i	0.116966	−	0.382131i
$166$	1.41089	+	2.44373i	0.109506	+	0.189670i
$167$	−14.3449			−1.11004			−0.555021	−	0.831837i	$-0.687290\pi$
$167$	−14.3449			−1.11004			−0.555021	+	0.831837i	$0.687290\pi$
$168$	11.7077	+	12.5632i	0.903269	+	0.969272i
$169$	−0.582192			−0.0447840
$170$	−3.54025			−0.271525
$171$	−5.27807	−	11.9642i	−0.403624	−	0.914925i
$172$	1.71796			0.130993
$173$	4.09478			0.311321			0.155660	−	0.987811i	$-0.450249\pi$
$173$	4.09478			0.311321			0.155660	+	0.987811i	$0.450249\pi$
$174$	−3.43849	+	11.2337i	−0.260672	+	0.851623i
$175$	−15.2290			−1.15121
$176$	−7.56265	−	13.0989i	−0.570056	−	0.987367i
$177$	−9.18526	−	9.85644i	−0.690406	−	0.740855i
$178$	−1.38337	−	2.39606i	−0.103688	−	0.179592i
$179$	1.96134			0.146597			0.0732986	−	0.997310i	$-0.476647\pi$
$179$	1.96134			0.146597			0.0732986	+	0.997310i	$0.476647\pi$
$180$	−0.655752	−	0.442934i	−0.0488769	−	0.0330144i
$181$	0.625824	+	1.08396i	0.0465172	+	0.0805701i	0.888347	−	0.459174i	$-0.151854\pi$
$181$	0.625824	+	1.08396i	0.0465172	+	0.0805701i	−0.841829	+	0.539744i	$0.818521\pi$
$182$	7.04899	+	12.2092i	0.522506	+	0.905007i
$183$	−5.76621	+	18.8384i	−0.426251	+	1.39258i
$184$	9.12457			0.672672
$185$	2.53938	+	4.39833i	0.186699	+	0.323372i
$186$	−3.18393	+	10.4020i	−0.233457	+	0.762712i
$187$	27.9605			2.04467
$188$	−2.54320	+	4.40495i	−0.185482	+	0.321264i
$189$	15.7265	+	6.05454i	1.14394	+	0.440403i
$190$	−2.62238	+	1.38510i	−0.190247	+	0.100486i
$191$	8.35232	+	14.4666i	0.604353	+	1.04677i	0.992153	+	0.125026i	$0.0399016\pi$
$191$	8.35232	+	14.4666i	0.604353	+	1.04677i	−0.387801	+	0.921743i	$0.626765\pi$
$192$	−15.0023	+	3.45838i	−1.08269	+	0.249587i
$193$	−12.3705	−	21.4263i	−0.890445	−	1.54230i	−0.839343	−	0.543602i	$-0.817060\pi$
$193$	−12.3705	−	21.4263i	−0.890445	−	1.54230i	−0.0511017	−	0.998693i	$-0.516273\pi$
$194$	−10.0932			−0.724652
$195$	−2.29506	−	2.46276i	−0.164353	−	0.176362i
$196$	0.841203	−	1.45701i	0.0600860	−	0.104072i
$197$	3.02872			0.215787			0.107894	−	0.994162i	$-0.465589\pi$
$197$	3.02872			0.215787			0.107894	+	0.994162i	$0.465589\pi$
$198$	−16.4792	−	11.1310i	−1.17113	−	0.791048i
$199$	8.82614	+	15.2873i	0.625668	+	1.08369i	0.988411	+	0.151800i	$0.0485069\pi$
$199$	8.82614	+	15.2873i	0.625668	+	1.08369i	−0.362743	+	0.931889i	$0.618160\pi$
$200$	7.17788	−	12.4325i	0.507553	−	0.879108i
$201$	−4.00443	+	0.923117i	−0.282451	+	0.0651117i
$202$	3.35185	−	5.80558i	0.235835	−	0.408479i
$203$	17.8320			1.25156
$204$	1.26154	−	4.12148i	0.0883252	−	0.288561i
$205$	0.471577	−	0.816795i	0.0329363	−	0.0570474i
$206$	−8.55944	+	14.8254i	−0.596365	+	1.03293i
$207$	8.05036	−	3.91991i	0.559539	−	0.272453i
$208$	−9.91895			−0.687755
$209$	20.7112	−	10.9394i	1.43263	−	0.756692i
$210$	1.11860	−	3.65450i	0.0771905	−	0.252184i
$211$	4.06435	+	7.03965i	0.279801	+	0.484630i	0.971335	−	0.237714i	$-0.0763981\pi$
$211$	4.06435	+	7.03965i	0.279801	+	0.484630i	−0.691534	+	0.722344i	$0.743065\pi$
$212$	−0.268784	−	0.465547i	−0.0184601	−	0.0319739i
$213$	0.514814	−	1.68192i	0.0352745	−	0.115243i
$214$	19.4919			1.33244
$215$	−0.990617	−	1.71580i	−0.0675595	−	0.117017i
$216$	−12.3551	+	9.98492i	−0.840657	+	0.679387i
$217$	16.5118			1.12090
$218$	4.68396	−	8.11286i	0.317238	−	0.549472i
$219$	6.06875	−	19.8268i	0.410088	−	1.33977i
$220$	0.708707	−	1.22752i	0.0477810	−	0.0827592i
$221$	9.16802	−	15.8795i	0.616708	−	1.06817i
$222$	19.1719	−	4.41960i	1.28674	−	0.296624i
$223$	−5.80779			−0.388919			−0.194459	−	0.980911i	$-0.562295\pi$
$223$	−5.80779			−0.388919			−0.194459	+	0.980911i	$0.562295\pi$
$224$	4.28420	+	7.42045i	0.286250	+	0.495800i
$225$	0.991868	−	14.0524i	0.0661246	−	0.936829i
$226$	2.79497	−	4.84103i	0.185918	−	0.322020i
$227$	−5.88816	−	10.1986i	−0.390811	−	0.676905i	0.601746	−	0.798688i	$-0.294472\pi$
$227$	−5.88816	−	10.1986i	−0.390811	−	0.676905i	−0.992557	+	0.121783i	$0.961139\pi$
$228$	−0.678046	−	3.54649i	−0.0449047	−	0.234872i
$229$	12.6223	−	21.8625i	0.834106	−	1.44471i	−0.0606506	−	0.998159i	$-0.519318\pi$
$229$	12.6223	−	21.8625i	0.834106	−	1.44471i	0.894756	−	0.446555i	$-0.147349\pi$
$230$	−1.01535	−	1.75864i	−0.0669503	−	0.115961i
$231$	−8.83454	+	28.8627i	−0.581270	+	1.89903i
$232$	−8.40473	+	14.5574i	−0.551798	+	0.955742i
$233$	−9.04140	+	15.6602i	−0.592322	+	1.02593i	0.401597	+	0.915816i	$0.368455\pi$
$233$	−9.04140	+	15.6602i	−0.592322	+	1.02593i	−0.993919	+	0.110115i	$0.964878\pi$
$234$	−11.7250	+	5.70919i	−0.766489	+	0.373222i
$235$	5.86588			0.382648
$236$	−1.86006	−	3.22171i	−0.121079	−	0.209716i
$237$	1.92003	−	0.442613i	0.124719	−	0.0287508i
$238$	20.8170			1.34936
$239$	−4.15871	+	7.20309i	−0.269004	+	0.465929i	−0.968605	−	0.248605i	$-0.920028\pi$
$239$	−4.15871	+	7.20309i	−0.269004	+	0.465929i	0.699601	+	0.714534i	$0.253361\pi$
$240$	1.83322	+	1.96717i	0.118334	+	0.126981i
$241$	−9.89328	+	17.1357i	−0.637282	+	1.10381i	0.348744	+	0.937218i	$0.386608\pi$
$241$	−9.89328	+	17.1357i	−0.637282	+	1.10381i	−0.986027	+	0.166588i	$0.946725\pi$
$242$	11.0252	−	19.0962i	0.708728	−	1.22755i
$243$	−6.61103	+	14.1172i	−0.424098	+	0.905616i
$244$	−2.71993	+	4.71106i	−0.174126	+	0.301594i
$245$	−1.94023			−0.123957
$246$	−2.49096	−	2.67297i	−0.158818	−	0.170423i
$247$	0.578296	−	15.3494i	0.0367961	−	0.976659i
$248$	−7.78249	+	13.4797i	−0.494189	+	0.855960i
$249$	2.70111	+	2.89849i	0.171176	+	0.183684i
$250$	−6.59682			−0.417219
$251$	5.61049	+	9.71765i	0.354131	+	0.613373i	0.986969	−	0.160912i	$-0.0514434\pi$
$251$	5.61049	+	9.71765i	0.354131	+	0.613373i	−0.632838	+	0.774284i	$0.718110\pi$
$252$	3.85588	+	2.60449i	0.242898	+	0.164067i
$253$	8.01912	+	13.8895i	0.504158	+	0.873227i
$254$	6.47438	+	11.2140i	0.406239	+	0.703626i
$255$	−4.84373	+	1.11660i	−0.303326	+	0.0699240i
$256$	−10.7694			−0.673087
$257$	−30.7735			−1.91960			−0.959800	−	0.280685i	$-0.909438\pi$
$257$	−30.7735			−1.91960			−0.959800	+	0.280685i	$0.909438\pi$
$258$	−7.47903	+	1.72410i	−0.465624	+	0.107338i
$259$	−14.9317	−	25.8625i	−0.927814	−	1.60702i
$260$	−0.464760	−	0.804987i	−0.0288232	−	0.0499232i
$261$	−1.16140	+	16.4543i	−0.0718888	+	1.01850i
$262$	−0.347534	−	0.601947i	−0.0214707	−	0.0371884i
$263$	22.0066			1.35698			0.678491	−	0.734609i	$-0.262634\pi$
$263$	22.0066			1.35698			0.678491	+	0.734609i	$0.262634\pi$
$264$	−19.3986	−	20.8160i	−1.19390	−	1.28114i
$265$	−0.309974	+	0.536892i	−0.0190416	+	0.0329810i
$266$	15.4198	−	8.14453i	0.945450	−	0.499373i
$267$	−2.64842	−	2.84195i	−0.162081	−	0.173924i
$268$	−1.13470			−0.0693126
$269$	4.69970	−	8.14012i	0.286546	−	0.496312i	−0.686437	−	0.727189i	$-0.740826\pi$
$269$	4.69970	−	8.14012i	0.286546	−	0.496312i	0.972983	+	0.230877i	$0.0741596\pi$
$270$	3.29929	+	1.27019i	0.200789	+	0.0773013i
$271$	5.10799	−	8.84729i	0.310288	−	0.537435i	−0.668137	−	0.744039i	$-0.732908\pi$
$271$	5.10799	−	8.84729i	0.310288	−	0.537435i	0.978425	+	0.206604i	$0.0662412\pi$
$272$	−7.32313	+	12.6840i	−0.444030	+	0.769082i
$273$	13.4951	+	14.4812i	0.816763	+	0.876445i
$274$	10.6294	−	18.4107i	0.642146	−	1.11223i
$275$	25.2331			1.52161
$276$	2.40918	−	0.555374i	0.145016	−	0.0334296i
$277$	−11.8449	−	20.5159i	−0.711688	−	1.23268i	−0.964223	−	0.265092i	$-0.914598\pi$
$277$	−11.8449	−	20.5159i	−0.711688	−	1.23268i	0.252535	−	0.967588i	$-0.418736\pi$
$278$	−1.79176			−0.107463
$279$	−1.07542	+	15.2361i	−0.0643834	+	0.912162i
$280$	2.73419	−	4.73576i	0.163399	−	0.283016i
$281$	2.13345	−	3.69524i	0.127271	−	0.220440i	−0.795347	−	0.606154i	$-0.792712\pi$
$281$	2.13345	−	3.69524i	0.127271	−	0.220440i	0.922618	+	0.385714i	$0.126045\pi$
$282$	6.65097	−	21.7290i	0.396060	−	1.29394i
$283$	10.9364	+	18.9424i	0.650102	+	1.12601i	0.983098	+	0.183081i	$0.0586071\pi$
$283$	10.9364	+	18.9424i	0.650102	+	1.12601i	−0.332996	+	0.942928i	$0.608060\pi$
$284$	0.242838	−	0.420608i	0.0144098	−	0.0249585i
$285$	−3.15105	+	2.72218i	−0.186652	+	0.161248i
$286$	−11.6795	−	20.2295i	−0.690624	−	1.19620i
$287$	−2.77291	+	4.80282i	−0.163680	+	0.283502i
$288$	−7.12617	+	3.46990i	−0.419914	+	0.204466i
$289$	−5.03744	−	8.72510i	−0.296320	−	0.513241i
$290$	3.74100			0.219679
$291$	−13.8095	+	3.18341i	−0.809524	+	0.186615i
$292$	2.86263	−	4.95823i	0.167523	−	0.290158i
$293$	0.0198641	−	0.0344056i	0.00116047	−	0.00201000i	−0.865445	−	0.501005i	$-0.832964\pi$
$293$	0.0198641	−	0.0344056i	0.00116047	−	0.00201000i	0.866605	+	0.498995i	$0.166297\pi$
$294$	−2.19991	+	7.18720i	−0.128302	+	0.419166i
$295$	−2.14511	+	3.71544i	−0.124893	+	0.216321i
$296$	28.1510			1.63625
$297$	−26.0574	−	10.0318i	−1.51200	−	0.582104i
$298$	2.89285	+	5.01056i	0.167578	+	0.290254i
$299$	10.5176			0.608251
$300$	1.13848	−	3.71946i	0.0657302	−	0.214743i
$301$	5.82491	+	10.0890i	0.335742	+	0.581523i
$302$	−0.455054	−	0.788177i	−0.0261854	−	0.0453545i
$303$	2.75488	−	9.00030i	0.158264	−	0.517054i
$304$	−0.461924	+	12.2606i	−0.0264932	+	0.703194i
$305$	6.27351			0.359220
$306$	−1.35581	+	19.2086i	−0.0775065	+	1.09809i
$307$	7.73434	−	13.3963i	0.441422	−	0.764566i	−0.556373	−	0.830933i	$-0.687807\pi$
$307$	7.73434	−	13.3963i	0.441422	−	0.764566i	0.997795	+	0.0663669i	$0.0211408\pi$
$308$	−4.16726	+	7.21791i	−0.237452	+	0.411278i
$309$	−7.03499	+	22.9836i	−0.400207	+	1.30749i
$310$	3.46404			0.196744
$311$	6.04377	−	10.4681i	0.342711	−	0.593593i	−0.642224	−	0.766517i	$-0.721988\pi$
$311$	6.04377	−	10.4681i	0.342711	−	0.593593i	0.984935	+	0.172924i	$0.0553215\pi$
$312$	−18.1826	+	4.19153i	−1.02939	+	0.237299i
$313$	−3.83744	+	6.64663i	−0.216905	+	0.375690i	−0.953860	−	0.300251i	$-0.902929\pi$
$313$	−3.83744	+	6.64663i	−0.216905	+	0.375690i	0.736955	+	0.675941i	$0.236263\pi$
$314$	3.33962	+	5.78439i	0.188465	+	0.326432i
$315$	0.377822	−	5.35284i	0.0212878	−	0.301599i
$316$	0.544061			0.0306058
$317$	4.76121	−	8.24665i	0.267416	−	0.463178i	−0.700778	−	0.713380i	$-0.747164\pi$
$317$	4.76121	−	8.24665i	0.267416	−	0.463178i	0.968194	+	0.250201i	$0.0804969\pi$
$318$	1.63734	+	1.75699i	0.0918176	+	0.0985269i
$319$	−29.5460			−1.65426
$320$	2.45126	+	4.24570i	0.137029	+	0.237342i
$321$	26.6685	−	6.14774i	1.48849	−	0.343133i
$322$	5.97035	+	10.3410i	0.332715	+	0.576279i
$323$	−19.2013	−	12.0719i	−1.06839	−	0.671699i
$324$	−2.65440	+	3.38834i	−0.147467	+	0.188241i
$325$	8.27374	−	14.3305i	0.458945	−	0.794916i
$326$	12.3896			0.686196
$327$	3.84974	−	12.5772i	0.212891	−	0.695523i
$328$	−2.61390	−	4.52742i	−0.144329	−	0.249985i
$329$	−34.4919			−1.90160
$330$	−1.85341	+	6.05516i	−0.102027	+	0.333325i
$331$	4.84054	+	8.38406i	0.266060	+	0.460830i	0.967841	−	0.251563i	$-0.0809447\pi$
$331$	4.84054	+	8.38406i	0.266060	+	0.460830i	−0.701781	+	0.712393i	$0.747611\pi$
$332$	0.546987	+	0.947410i	0.0300198	+	0.0519959i
$333$	24.8369	−	12.0937i	1.36105	−	0.662730i
$334$	17.6957			0.968268
$335$	0.654294	+	1.13327i	0.0357479	+	0.0619171i
$336$	−10.7795	−	11.5672i	−0.588069	−	0.631040i
$337$	15.1840	+	26.2994i	0.827123	+	1.43262i	0.900286	+	0.435299i	$0.143357\pi$
$337$	15.1840	+	26.2994i	0.827123	+	1.43262i	−0.0731634	+	0.997320i	$0.523309\pi$
$338$	0.718188			0.0390643
$339$	2.29718	−	7.50497i	0.124766	−	0.407614i
$340$	−1.37252			−0.0744354
$341$	−27.3585			−1.48155
$342$	6.51098	+	14.7589i	0.352074	+	0.798072i
$343$	−11.2931			−0.609770
$344$	−10.9818			−0.592098
$345$	−1.94387	−	2.08591i	−0.104654	−	0.112302i
$346$	−5.05129			−0.271559
$347$	4.12021	+	7.13641i	0.221184	+	0.383102i	0.955168	−	0.296065i	$-0.0956744\pi$
$347$	4.12021	+	7.13641i	0.221184	+	0.383102i	−0.733984	+	0.679167i	$0.762341\pi$
$348$	−1.33307	+	4.35519i	−0.0714601	+	0.233463i
$349$	0.121550	+	0.210531i	0.00650642	+	0.0112695i	0.869260	−	0.494355i	$-0.164596\pi$
$349$	0.121550	+	0.210531i	0.00650642	+	0.0112695i	−0.862754	+	0.505624i	$0.831262\pi$
$350$	18.7864			1.00418
$351$	−14.2414	+	11.5093i	−0.760147	+	0.614323i
$352$	−7.09851	−	12.2950i	−0.378352	−	0.655325i
$353$	5.37981	+	9.31810i	0.286338	+	0.495952i	0.972933	−	0.231088i	$-0.0742286\pi$
$353$	5.37981	+	9.31810i	0.286338	+	0.495952i	−0.686595	+	0.727040i	$0.740895\pi$
$354$	11.3309	+	12.1588i	0.602228	+	0.646234i
$355$	−0.560106			−0.0297273
$356$	−0.536318	−	0.928929i	−0.0284248	−	0.0492332i
$357$	28.4815	−	6.56568i	1.50740	−	0.347493i
$358$	−2.41949			−0.127874
$359$	−8.34473	+	14.4535i	−0.440418	+	0.762827i	−0.997720	−	0.0674831i	$-0.978503\pi$
$359$	−8.34473	+	14.4535i	−0.440418	+	0.762827i	0.557302	+	0.830310i	$0.311836\pi$
$360$	4.19180	+	2.83139i	0.220927	+	0.149227i
$361$	−18.9461	−	1.42964i	−0.997165	−	0.0752441i
$362$	−0.772012	−	1.33716i	−0.0405760	−	0.0702798i
$363$	9.06162	−	29.6046i	0.475612	−	1.55384i
$364$	2.73283	+	4.73339i	0.143239	+	0.248097i
$365$	−6.60266			−0.345599
$366$	7.11315	−	23.2389i	0.371810	−	1.21472i
$367$	7.58487	−	13.1374i	0.395927	−	0.685765i	−0.597292	−	0.802024i	$-0.703757\pi$
$367$	7.58487	−	13.1374i	0.395927	−	0.685765i	0.993219	+	0.116258i	$0.0370901\pi$
$368$	−8.40115			−0.437940
$369$	−4.25115	−	2.87148i	−0.221306	−	0.149483i
$370$	−3.13255	−	5.42574i	−0.162854	−	0.282071i
$371$	1.82268	−	3.15697i	0.0946286	−	0.163902i
$372$	−1.23438	+	4.03276i	−0.0639995	+	0.209089i
$373$	−15.4009	+	26.6751i	−0.797427	+	1.38118i	0.123860	+	0.992300i	$0.460473\pi$
$373$	−15.4009	+	26.6751i	−0.797427	+	1.38118i	−0.921287	+	0.388884i	$0.872861\pi$
$374$	−34.4918			−1.78353
$375$	−9.02569	+	2.08064i	−0.466085	+	0.107444i
$376$	16.2570	−	28.1580i	0.838391	−	1.45214i
$377$	−9.68790	+	16.7799i	−0.498952	+	0.864211i
$378$	−19.4001	−	7.46883i	−0.997835	−	0.384155i
$379$	22.2036			1.14052			0.570260	−	0.821464i	$-0.306842\pi$
$379$	22.2036			1.14052			0.570260	+	0.821464i	$0.306842\pi$
$380$	−1.01667	+	0.536992i	−0.0521542	+	0.0275471i
$381$	12.3951	+	13.3008i	0.635018	+	0.681420i
$382$	−10.3034	−	17.8459i	−0.527165	−	0.913077i
$383$	−1.55372	−	2.69112i	−0.0793913	−	0.137510i	0.823596	−	0.567177i	$-0.191964\pi$
$383$	−1.55372	−	2.69112i	−0.0793913	−	0.137510i	−0.902987	+	0.429667i	$0.858631\pi$
$384$	9.58832	−	2.21034i	0.489302	−	0.112796i
$385$	9.61177			0.489861
$386$	15.2601	+	26.4312i	0.776718	+	1.34532i
$387$	−9.68894	+	4.71778i	−0.492516	+	0.239818i
$388$	−3.91305			−0.198655
$389$	0.546994	−	0.947421i	0.0277337	−	0.0480362i	−0.851825	−	0.523826i	$-0.824504\pi$
$389$	0.546994	−	0.947421i	0.0277337	−	0.0480362i	0.879559	+	0.475790i	$0.157838\pi$
$390$	2.83116	+	3.03804i	0.143362	+	0.153837i
$391$	7.76513	−	13.4496i	0.392700	−	0.680176i
$392$	−5.37726	+	9.31369i	−0.271593	+	0.470413i
$393$	−0.665346	−	0.713964i	−0.0335623	−	0.0360147i
$394$	−3.73621			−0.188227
$395$	−0.313719	−	0.543377i	−0.0157849	−	0.0273402i
$396$	−6.38883	−	4.31540i	−0.321051	−	0.216857i
$397$	−16.6030	+	28.7572i	−0.833279	+	1.44328i	0.0621458	+	0.998067i	$0.480206\pi$
$397$	−16.6030	+	28.7572i	−0.833279	+	1.44328i	−0.895424	+	0.445214i	$0.853128\pi$
$398$	−10.8878	−	18.8583i	−0.545758	−	0.945281i
$399$	18.5284	−	16.0067i	0.927582	−	0.801336i
$400$	−6.60880	+	11.4468i	−0.330440	+	0.572339i
$401$	−5.35339	−	9.27234i	−0.267336	−	0.463039i	0.700837	−	0.713321i	$-0.252810\pi$
$401$	−5.35339	−	9.27234i	−0.267336	−	0.463039i	−0.968173	+	0.250282i	$0.919477\pi$
$402$	4.93983	−	1.13875i	0.246376	−	0.0567957i
$403$	−8.97066	+	15.5376i	−0.446860	+	0.773985i
$404$	1.29948	−	2.25077i	0.0646516	−	0.111980i
$405$	4.91467	+	0.697262i	0.244212	+	0.0346472i
$406$	−21.9974			−1.09171
$407$	24.7405	+	42.8518i	1.22634	+	2.12409i
$408$	−8.06417	+	26.3459i	−0.399236	+	1.30432i
$409$	−11.2331			−0.555443			−0.277721	−	0.960662i	$-0.589579\pi$
$409$	−11.2331			−0.555443			−0.277721	+	0.960662i	$0.589579\pi$
$410$	−0.581733	+	1.00759i	−0.0287297	+	0.0497614i
$411$	8.73630	−	28.5418i	0.430930	−	1.40786i
$412$	−3.31841	+	5.74766i	−0.163487	+	0.283167i
$413$	12.6134	−	21.8471i	0.620666	−	1.07502i
$414$	−9.93086	+	4.83557i	−0.488075	+	0.237655i
$415$	0.630812	−	1.09260i	0.0309654	−	0.0536336i
$416$	−9.31020			−0.456470
$417$	−2.45146	+	0.565122i	−0.120049	+	0.0276741i
$418$	−25.5492	+	13.4947i	−1.24965	+	0.660048i
$419$	−3.31446	+	5.74081i	−0.161922	+	0.280457i	−0.935558	−	0.353173i	$-0.885103\pi$
$419$	−3.31446	+	5.74081i	−0.161922	+	0.280457i	0.773636	+	0.633630i	$0.218436\pi$
$420$	0.433669	−	1.41681i	0.0211609	−	0.0691334i
$421$	−14.1701			−0.690609			−0.345304	−	0.938491i	$-0.612224\pi$
$421$	−14.1701			−0.690609			−0.345304	+	0.938491i	$0.612224\pi$
$422$	−5.01374	−	8.68406i	−0.244065	−	0.422733i
$423$	2.24646	−	31.8270i	0.109227	−	1.54748i
$424$	1.71816	+	2.97594i	0.0834412	+	0.144524i
$425$	−12.2170	−	21.1604i	−0.592609	−	1.02643i
$426$	−0.635071	+	2.07480i	−0.0307693	+	0.100524i
$427$	−36.8888			−1.78517
$428$	7.55681			0.365272
$429$	−22.3602	−	23.9941i	−1.07956	−	1.15844i
$430$	1.22202	+	2.11660i	0.0589309	+	0.102071i
$431$	6.14500	+	10.6434i	0.295994	+	0.512677i	0.975216	−	0.221256i	$-0.0710158\pi$
$431$	6.14500	+	10.6434i	0.295994	+	0.512677i	−0.679222	+	0.733933i	$0.737682\pi$
$432$	11.3755	−	9.19329i	0.547306	−	0.442312i
$433$	6.40711	+	11.0974i	0.307906	+	0.533309i	0.977904	−	0.209054i	$-0.0670384\pi$
$433$	6.40711	+	11.0974i	0.307906	+	0.533309i	−0.669998	+	0.742363i	$0.733705\pi$
$434$	−20.3688			−0.977736
$435$	5.11840	−	1.17991i	0.245408	−	0.0565725i
$436$	1.81593	−	3.14528i	0.0869672	−	0.150632i
$437$	0.489805	−	13.0006i	0.0234305	−	0.621905i
$438$	−7.48636	+	24.4582i	−0.357712	+	1.16866i
$439$	6.54477			0.312365			0.156182	−	0.987728i	$-0.450081\pi$
$439$	6.54477			0.312365			0.156182	+	0.987728i	$0.450081\pi$
$440$	−4.53030	+	7.84671i	−0.215974	+	0.374077i
$441$	−0.743051	+	10.5273i	−0.0353834	+	0.501300i
$442$	−11.3096	+	19.5888i	−0.537943	+	0.931744i
$443$	−2.31425	+	4.00840i	−0.109954	+	0.190445i	−0.915751	−	0.401746i	$-0.868404\pi$
$443$	−2.31425	+	4.00840i	−0.109954	+	0.190445i	0.805798	+	0.592191i	$0.201737\pi$
$444$	7.43278	−	1.71344i	0.352744	−	0.0813161i
$445$	−0.618507	+	1.07129i	−0.0293201	+	0.0507838i
$446$	7.16445			0.339246
$447$	5.53829	+	5.94298i	0.261952	+	0.281094i
$448$	−14.4136	−	24.9651i	−0.680978	−	1.17949i
$449$	16.6475			0.785642			0.392821	−	0.919615i	$-0.371499\pi$
$449$	16.6475			0.785642			0.392821	+	0.919615i	$0.371499\pi$
$450$	−1.22356	+	17.3350i	−0.0576792	+	0.817178i
$451$	4.59445	−	7.95783i	0.216344	−	0.374719i
$452$	1.08358	−	1.87682i	0.0509674	−	0.0882782i
$453$	−0.871191	−	0.934850i	−0.0409321	−	0.0439231i
$454$	7.26359	+	12.5809i	0.340897	+	0.590451i
$455$	3.15163	−	5.45878i	0.147751	−	0.255912i
$456$	4.33431	+	22.6704i	0.202972	+	1.06164i
$457$	19.2727	+	33.3814i	0.901541	+	1.56151i	0.825494	+	0.564411i	$0.190896\pi$
$457$	19.2727	+	33.3814i	0.901541	+	1.56151i	0.0760467	+	0.997104i	$0.475770\pi$
$458$	−15.5708	+	26.9694i	−0.727575	+	1.26020i
$459$	4.20341	+	26.7087i	0.196198	+	1.24665i
$460$	−0.393642	−	0.681808i	−0.0183537	−	0.0317895i
$461$	−10.2231			−0.476137			−0.238068	−	0.971248i	$-0.576514\pi$
$461$	−10.2231			−0.476137			−0.238068	+	0.971248i	$0.576514\pi$
$462$	10.8982	−	35.6048i	0.507031	−	1.65649i
$463$	4.51183	−	7.81472i	0.209683	−	0.363181i	−0.741932	−	0.670475i	$-0.766090\pi$
$463$	4.51183	−	7.81472i	0.209683	−	0.363181i	0.951615	+	0.307294i	$0.0994236\pi$
$464$	7.73839	−	13.4033i	0.359246	−	0.622232i
$465$	4.73946	−	1.09256i	0.219787	−	0.0506662i
$466$	11.1534	−	19.3182i	0.516671	−	0.894900i
$467$	−31.0166			−1.43528			−0.717639	−	0.696416i	$-0.754777\pi$
$467$	−31.0166			−1.43528			−0.717639	+	0.696416i	$0.754777\pi$
$468$	−4.54568	+	2.21340i	−0.210124	+	0.102314i
$469$	−3.84730	−	6.66372i	−0.177652	−	0.307702i
$470$	−7.23610			−0.333777
$471$	6.39362	+	6.86081i	0.294603	+	0.316130i
$472$	11.8901	+	20.5943i	0.547287	+	0.947930i
$473$	−9.65133	−	16.7166i	−0.443769	−	0.768630i
$474$	−2.36853	+	0.546004i	−0.108790	+	0.0250788i
$475$	−17.3284	−	10.8944i	−0.795081	−	0.499868i
$476$	8.07054			0.369913
$477$	2.79435	+	1.88747i	0.127944	+	0.0864213i
$478$	5.13015	−	8.88568i	0.234647	−	0.406421i
$479$	17.5539	−	30.4043i	0.802060	−	1.38921i	−0.116197	−	0.993226i	$-0.537071\pi$
$479$	17.5539	−	30.4043i	0.802060	−	1.38921i	0.918258	−	0.395983i	$-0.129596\pi$
$480$	1.72071	+	1.84644i	0.0785393	+	0.0842783i
$481$	32.4489			1.47954
$482$	12.2043	−	21.1384i	0.555889	−	0.962829i
$483$	11.4301	+	12.2653i	0.520088	+	0.558092i
$484$	4.27437	−	7.40343i	0.194290	−	0.336520i
$485$	2.25636	+	3.90813i	0.102456	+	0.177459i
$486$	8.15531	−	17.4148i	0.369933	−	0.789952i
$487$	23.8848			1.08232			0.541161	−	0.840919i	$-0.317985\pi$
$487$	23.8848			1.08232			0.541161	+	0.840919i	$0.317985\pi$
$488$	17.3867	−	30.1147i	0.787060	−	1.36323i
$489$	16.9513	−	3.90768i	0.766564	−	0.176712i
$490$	2.39346			0.108125
$491$	−17.9338	−	31.0623i	−0.809342	−	1.40182i	−0.913321	−	0.407241i	$-0.866491\pi$
$491$	−17.9338	−	31.0623i	−0.809342	−	1.40182i	0.103979	−	0.994580i	$-0.466843\pi$
$492$	−0.965720	−	1.03629i	−0.0435380	−	0.0467194i
$493$	14.3051	+	24.7771i	0.644269	+	1.11591i
$494$	−0.713381	+	18.9349i	−0.0320965	+	0.851921i
$495$	−0.626015	+	8.86916i	−0.0281373	+	0.398639i
$496$	7.16548	−	12.4110i	0.321739	−	0.557269i
$497$	3.29347			0.147732
$498$	−3.33207	−	3.57555i	−0.149314	−	0.160224i
$499$	13.9470	+	24.1570i	0.624355	+	1.08141i	0.988665	+	0.150137i	$0.0479714\pi$
$499$	13.9470	+	24.1570i	0.624355	+	1.08141i	−0.364310	+	0.931278i	$0.618695\pi$
$500$	−2.55752			−0.114376
$501$	24.2111	−	5.58125i	1.08167	−	0.249352i
$502$	−6.92105	−	11.9876i	−0.308902	−	0.535033i
$503$	−19.7196	−	34.1554i	−0.879254	−	1.52291i	−0.852161	−	0.523280i	$-0.824708\pi$
$503$	−19.7196	−	34.1554i	−0.879254	−	1.52291i	−0.0270935	−	0.999633i	$-0.508625\pi$
$504$	−24.6481	−	16.6488i	−1.09791	−	0.741597i
$505$	−2.99725			−0.133376
$506$	−9.89232	−	17.1340i	−0.439767	−	0.761699i
$507$	0.982616	−	0.226517i	0.0436395	−	0.0100600i
$508$	2.51006	+	4.34754i	0.111366	+	0.192891i
$509$	19.1292			0.847887			0.423943	−	0.905689i	$-0.360646\pi$
$509$	19.1292			0.847887			0.423943	+	0.905689i	$0.360646\pi$
$510$	5.97519	−	1.37742i	0.264586	−	0.0609934i
$511$	38.8242			1.71748
$512$	24.6471			1.08926
$513$	13.5632	+	18.1394i	0.598831	+	0.800875i
$514$	37.9620			1.67443
$515$	7.65391			0.337272
$516$	−2.89955	+	0.668416i	−0.127645	+	0.0294254i
$517$	57.1498			2.51345
$518$	18.4197	+	31.9038i	0.809314	+	1.40177i
$519$	−6.91112	+	1.59318i	−0.303364	+	0.0699328i
$520$	2.97090	+	5.14576i	0.130283	+	0.225656i
$521$	−33.0169			−1.44650			−0.723248	−	0.690589i	$-0.757352\pi$
$521$	−33.0169			−1.44650			−0.723248	+	0.690589i	$0.757352\pi$
$522$	1.43269	−	20.2979i	0.0627072	−	0.888414i
$523$	6.43545	+	11.1465i	0.281403	+	0.487404i	0.971730	−	0.236093i	$-0.0758670\pi$
$523$	6.43545	+	11.1465i	0.281403	+	0.487404i	−0.690328	+	0.723497i	$0.742534\pi$
$524$	−0.134736	−	0.233369i	−0.00588596	−	0.0101948i
$525$	25.7034	−	5.92525i	1.12179	−	0.258599i
$526$	−27.1471			−1.18367
$527$	13.2460	+	22.9428i	0.577005	+	0.999403i
$528$	17.8606	+	19.1657i	0.777283	+	0.834080i
$529$	−14.0918			−0.612686
$530$	0.382382	−	0.662305i	0.0166096	−	0.0287687i
$531$	19.3376	+	13.0618i	0.839182	+	0.566834i
$532$	5.97812	−	3.15756i	0.259184	−	0.136897i
$533$	−3.01297	−	5.21862i	−0.130506	−	0.226044i
$534$	3.26707	+	3.50580i	0.141380	+	0.151711i
$535$	−4.35744	−	7.54731i	−0.188389	−	0.326298i
$536$	7.25337			0.313298
$537$	−3.31032	+	0.763108i	−0.142851	+	0.0329305i
$538$	−5.79751	+	10.0416i	−0.249948	+	0.432923i
$539$	−18.9032			−0.814219
$540$	1.27910	+	0.492441i	0.0550439	+	0.0211913i
$541$	−1.61584	−	2.79872i	−0.0694705	−	0.120326i	0.829198	−	0.558955i	$-0.188798\pi$
$541$	−1.61584	−	2.79872i	−0.0694705	−	0.120326i	−0.898668	+	0.438629i	$0.855464\pi$
$542$	−6.30117	+	10.9139i	−0.270658	+	0.468794i
$543$	−1.47800	−	1.58600i	−0.0634270	−	0.0680617i
$544$	−6.87369	+	11.9056i	−0.294707	+	0.510447i
$545$	−4.18843			−0.179413
$546$	−16.6475	−	17.8639i	−0.712447	−	0.764506i
$547$	−14.7344	+	25.5207i	−0.629998	+	1.09119i	0.357554	+	0.933893i	$0.383611\pi$
$547$	−14.7344	+	25.5207i	−0.629998	+	1.09119i	−0.987552	+	0.157296i	$0.949722\pi$
$548$	4.12092	−	7.13764i	0.176037	−	0.304905i
$549$	2.40257	−	34.0387i	0.102539	−	1.45274i
$550$	−31.1273			−1.32727
$551$	20.2902	+	12.7565i	0.864390	+	0.543443i
$552$	−15.4003	+	3.55015i	−0.655481	+	0.151104i
$553$	1.84469	+	3.19510i	0.0784443	+	0.135869i
$554$	14.6117	+	25.3082i	0.620792	+	1.07524i
$555$	−5.99720	−	6.43543i	−0.254567	−	0.273169i
$556$	−0.694648			−0.0294596
$557$	13.2513	+	22.9520i	0.561477	+	0.972506i	0.997368	+	0.0725066i	$0.0230998\pi$
$557$	13.2513	+	22.9520i	0.561477	+	0.972506i	−0.435891	+	0.899999i	$0.643567\pi$
$558$	1.32662	−	18.7951i	0.0561604	−	0.795661i
$559$	−12.6584			−0.535393
$560$	−2.51742	+	4.36030i	−0.106380	+	0.184256i
$561$	−47.1913	+	10.8787i	−1.99242	+	0.459300i
$562$	−2.63180	+	4.55842i	−0.111016	+	0.192285i
$563$	9.60939	−	16.6440i	0.404988	−	0.701459i	−0.589332	−	0.807891i	$-0.700609\pi$
$563$	9.60939	−	16.6440i	0.404988	−	0.701459i	0.994320	+	0.106432i	$0.0339425\pi$
$564$	2.57852	−	8.42411i	0.108575	−	0.354719i
$565$	−2.49928			−0.105145
$566$	−13.4911	−	23.3672i	−0.567072	−	0.982197i
$567$	−28.8987	−	4.09996i	−1.21363	−	0.172182i
$568$	−1.55231	+	2.68867i	−0.0651334	+	0.112814i
$569$	−22.9341	−	39.7230i	−0.961446	−	1.66527i	−0.718875	−	0.695139i	$-0.755343\pi$
$569$	−22.9341	−	39.7230i	−0.961446	−	1.66527i	−0.242570	−	0.970134i	$-0.577991\pi$
$570$	3.88711	−	3.35806i	0.162813	−	0.140654i
$571$	−8.69243	+	15.0557i	−0.363767	+	0.630063i	−0.988577	−	0.150713i	$-0.951843\pi$
$571$	−8.69243	+	15.0557i	−0.363767	+	0.630063i	0.624810	+	0.780776i	$0.285176\pi$
$572$	−4.52804	−	7.84279i	−0.189327	−	0.327924i
$573$	−19.7255	−	21.1669i	−0.824046	−	0.884261i
$574$	3.42064	−	5.92472i	0.142775	−	0.247293i
$575$	7.00770	−	12.1377i	0.292241	−	0.506176i
$576$	23.9750	−	11.6740i	0.998959	−	0.486417i
$577$	11.7739			0.490155			0.245078	−	0.969503i	$-0.421187\pi$
$577$	11.7739			0.490155			0.245078	+	0.969503i	$0.421187\pi$
$578$	6.21415	+	10.7632i	0.258474	+	0.447691i
$579$	29.2151	+	31.3499i	1.21414	+	1.30286i
$580$	1.45035			0.0602226
$581$	−3.70923	+	6.42458i	−0.153885	+	0.266536i
$582$	17.0352	−	3.92703i	0.706133	−	0.162781i
$583$	−3.02000	+	5.23080i	−0.125076	+	0.216638i
$584$	−18.2990	+	31.6947i	−0.757216	+	1.31154i
$585$	4.83177	+	3.26366i	0.199769	+	0.134936i
$586$	−0.0245042	+	0.0424425i	−0.00101226	+	0.00175328i
$587$	−13.8868			−0.573171			−0.286586	−	0.958055i	$-0.592520\pi$
$587$	−13.8868			−0.573171			−0.286586	+	0.958055i	$0.592520\pi$
$588$	−0.852886	+	2.78641i	−0.0351724	+	0.114909i
$589$	18.7880	+	11.8120i	0.774146	+	0.486706i
$590$	2.64619	−	4.58333i	0.108942	−	0.188693i
$591$	−5.11183	+	1.17840i	−0.210273	+	0.0484729i
$592$	−25.9192			−1.06527
$593$	7.23610	+	12.5333i	0.297151	+	0.514681i	0.975483	−	0.220075i	$-0.0706302\pi$
$593$	7.23610	+	12.5333i	0.297151	+	0.514681i	−0.678332	+	0.734756i	$0.737297\pi$
$594$	32.1442	+	12.3752i	1.31889	+	0.507759i
$595$	−4.65367	−	8.06040i	−0.190782	−	0.330444i
$596$	1.12153	+	1.94255i	0.0459397	+	0.0795698i
$597$	−20.8445	−	22.3677i	−0.853110	−	0.915448i
$598$	−12.9745			−0.530565
$599$	−12.0904			−0.494000			−0.247000	−	0.969015i	$-0.579445\pi$
$599$	−12.0904			−0.494000			−0.247000	+	0.969015i	$0.579445\pi$
$600$	−7.27757	+	23.7761i	−0.297105	+	0.970654i
$601$	−14.0237	−	24.2898i	−0.572040	−	0.990803i	−0.996356	−	0.0852884i	$-0.972819\pi$
$601$	−14.0237	−	24.2898i	−0.572040	−	0.990803i	0.424316	−	0.905514i	$-0.360515\pi$
$602$	−7.18556	−	12.4458i	−0.292862	−	0.507251i
$603$	6.39945	−	3.11605i	0.260606	−	0.126895i
$604$	−0.176420	−	0.305569i	−0.00717843	−	0.0124334i
$605$	−9.85883			−0.400819
$606$	−3.39840	+	11.1027i	−0.138051	+	0.451016i
$607$	10.3136	−	17.8637i	0.418616	−	0.725063i	−0.577185	−	0.816613i	$-0.695849\pi$
$607$	10.3136	−	17.8637i	0.418616	−	0.725063i	0.995800	+	0.0915501i	$0.0291822\pi$
$608$	−0.433575	+	11.5081i	−0.0175838	+	0.466717i
$609$	−30.0966	+	6.93799i	−1.21958	+	0.281142i
$610$	−7.73895			−0.313341
$611$	18.7390	−	32.4569i	0.758099	−	1.31307i
$612$	−0.525635	+	7.44701i	−0.0212475	+	0.301028i
$613$	−6.15798	+	10.6659i	−0.248718	+	0.430793i	−0.963170	−	0.268891i	$-0.913343\pi$
$613$	−6.15798	+	10.6659i	−0.248718	+	0.430793i	0.714452	+	0.699684i	$0.246676\pi$
$614$	−9.54102	+	16.5255i	−0.385044	+	0.666916i
$615$	−0.478126	+	1.56205i	−0.0192799	+	0.0629881i
$616$	26.6386	−	46.1393i	1.07330	−	1.85901i
$617$	−36.4564			−1.46768			−0.733840	−	0.679322i	$-0.762274\pi$
$617$	−36.4564			−1.46768			−0.733840	+	0.679322i	$0.762274\pi$
$618$	8.67831	−	28.3523i	0.349093	−	1.14050i
$619$	19.8664	+	34.4097i	0.798500	+	1.38304i	0.920593	+	0.390523i	$0.127706\pi$
$619$	19.8664	+	34.4097i	0.798500	+	1.38304i	−0.122093	+	0.992519i	$0.538961\pi$
$620$	1.34297			0.0539352
$621$	−12.0621	+	9.74817i	−0.484037	+	0.391181i
$622$	−7.45555	+	12.9134i	−0.298940	+	0.517780i
$623$	3.63688	−	6.29925i	0.145708	−	0.252374i
$624$	16.7411	−	3.85922i	0.670179	−	0.154492i
$625$	−10.2648	−	17.7791i	−0.410591	−	0.711164i
$626$	4.73383	−	8.19923i	0.189202	−	0.327707i
$627$	−30.6999	+	26.5216i	−1.22603	+	1.05917i
$628$	1.29474	+	2.24255i	0.0516657	+	0.0894875i
$629$	23.9569	−	41.4946i	0.955225	−	1.65450i
$630$	−0.466078	+	6.60322i	−0.0185690	+	0.263079i
$631$	−14.0414	−	24.3204i	−0.558980	−	0.968181i	−0.997582	−	0.0694998i	$-0.977860\pi$
$631$	−14.0414	−	24.3204i	−0.558980	−	0.968181i	0.438602	−	0.898681i	$-0.355474\pi$
$632$	−3.47782			−0.138340
$633$	−9.59870	−	10.3001i	−0.381514	−	0.409392i
$634$	−5.87339	+	10.1730i	−0.233262	+	0.404022i
$635$	2.89472	−	5.01380i	0.114873	−	0.198967i
$636$	0.634782	+	0.681167i	0.0251708	+	0.0270100i
$637$	−6.19822	+	10.7356i	−0.245582	+	0.425361i
$638$	36.4477			1.44298
$639$	−0.214504	+	3.03902i	−0.00848564	+	0.120222i
$640$	−1.56666	−	2.71353i	−0.0619277	−	0.107262i
$641$	−28.1224			−1.11077			−0.555384	−	0.831594i	$-0.687429\pi$
$641$	−28.1224			−1.11077			−0.555384	+	0.831594i	$0.687429\pi$
$642$	−32.8981	+	7.58380i	−1.29838	+	0.299309i
$643$	−9.92546	−	17.1914i	−0.391422	−	0.677963i	0.601215	−	0.799087i	$-0.294683\pi$
$643$	−9.92546	−	17.1914i	−0.391422	−	0.677963i	−0.992637	+	0.121124i	$0.961350\pi$
$644$	2.31465	+	4.00909i	0.0912100	+	0.157980i
$645$	2.33952	+	2.51048i	0.0921187	+	0.0988499i
$646$	23.6866	+	14.8918i	0.931938	+	0.585910i
$647$	−22.5967			−0.888369			−0.444184	−	0.895935i	$-0.646506\pi$
$647$	−22.5967			−0.888369			−0.444184	+	0.895935i	$0.646506\pi$
$648$	16.9678	−	21.6595i	0.666560	−	0.850864i
$649$	−20.8992	+	36.1986i	−0.820367	+	1.42092i
$650$	−10.2064	+	17.6780i	−0.400329	+	0.693390i
$651$	−27.8684	+	6.42434i	−1.09225	+	0.251790i
$652$	4.80333			0.188113
$653$	−20.4974	+	35.5026i	−0.802127	+	1.38932i	0.116087	+	0.993239i	$0.462965\pi$
$653$	−20.4974	+	35.5026i	−0.802127	+	1.38932i	−0.918214	+	0.396085i	$0.870368\pi$
$654$	−4.74901	+	15.5152i	−0.185701	+	0.606692i
$655$	−0.155384	+	0.269132i	−0.00607134	+	0.0105159i
$656$	2.40667	+	4.16847i	0.0939646	+	0.162751i
$657$	−2.52862	+	35.8246i	−0.0986509	+	1.39765i
$658$	42.5489			1.65873
$659$	−17.6656	+	30.5978i	−0.688156	+	1.19192i	0.284278	+	0.958742i	$0.408246\pi$
$659$	−17.6656	+	30.5978i	−0.688156	+	1.19192i	−0.972434	+	0.233179i	$0.925087\pi$
$660$	−0.718549	+	2.34753i	−0.0279695	+	0.0913773i
$661$	−44.7287			−1.73974			−0.869872	−	0.493277i	$-0.835799\pi$
$661$	−44.7287			−1.73974			−0.869872	+	0.493277i	$0.835799\pi$
$662$	−5.97125	−	10.3425i	−0.232079	−	0.401973i
$663$	−9.29534	+	30.3682i	−0.361001	+	1.17940i
$664$	−3.49653	−	6.05617i	−0.135692	−	0.235025i
$665$	−6.60071	−	4.14988i	−0.255965	−	0.160925i
$666$	−30.6386	+	14.9187i	−1.18722	+	0.578087i
$667$	−8.20546	+	14.2123i	−0.317717	+	0.550301i
$668$	6.86047			0.265440
$669$	9.80231	−	2.25967i	0.378979	−	0.0873639i
$670$	−0.807131	−	1.39799i	−0.0311822	−	0.0540091i
$671$	61.1212			2.35956
$672$	−10.1179	−	10.8572i	−0.390307	−	0.418827i
$673$	−10.6195	−	18.3935i	−0.409351	−	0.709017i	0.585466	−	0.810697i	$-0.300912\pi$
$673$	−10.6195	−	18.3935i	−0.409351	−	0.709017i	−0.994817	+	0.101680i	$0.967578\pi$
$674$	−18.7308	−	32.4427i	−0.721483	−	1.24965i
$675$	3.79340	+	24.1034i	0.146008	+	0.927741i
$676$	0.278435			0.0107090
$677$	−8.69327	−	15.0572i	−0.334109	−	0.578694i	0.649204	−	0.760614i	$-0.275102\pi$
$677$	−8.69327	−	15.0572i	−0.334109	−	0.578694i	−0.983313	+	0.181920i	$0.941769\pi$
$678$	−2.83378	+	9.25807i	−0.108831	+	0.355554i
$679$	−13.2676	−	22.9801i	−0.509164	−	0.881897i
$680$	8.77363			0.336454
$681$	13.9060	+	14.9221i	0.532878	+	0.571816i
$682$	33.7493			1.29233
$683$	30.4671			1.16579			0.582896	−	0.812547i	$-0.301920\pi$
$683$	30.4671			1.16579			0.582896	+	0.812547i	$0.301920\pi$
$684$	2.52425	+	5.72190i	0.0965170	+	0.218782i
$685$	−9.50489			−0.363163
$686$	13.9311			0.531891
$687$	−12.7976	+	41.8102i	−0.488259	+	1.59516i
$688$	10.1111			0.385483
$689$	1.98047	+	3.43028i	0.0754500	+	0.130683i
$690$	2.39794	+	2.57316i	0.0912880	+	0.0979585i
$691$	3.54990	+	6.14860i	0.135044	+	0.233904i	0.925614	−	0.378468i	$-0.123549\pi$
$691$	3.54990	+	6.14860i	0.135044	+	0.233904i	−0.790570	+	0.612372i	$0.790216\pi$
$692$	−1.95834			−0.0744448
$693$	3.68102	−	52.1514i	0.139830	−	1.98107i
$694$	−5.08265	−	8.80341i	−0.192935	−	0.334173i
$695$	0.400551	+	0.693775i	0.0151938	+	0.0263164i
$696$	8.52145	−	27.8399i	0.323005	−	1.05527i
$697$	−8.89787			−0.337031
$698$	−0.149943	−	0.259709i	−0.00567543	−	0.00983013i
$699$	9.16696	−	29.9488i	0.346726	−	1.13277i
$700$	7.28332			0.275283
$701$	−7.28494	+	12.6179i	−0.275148	+	0.476571i	−0.970173	−	0.242416i	$-0.922060\pi$
$701$	−7.28494	+	12.6179i	−0.275148	+	0.476571i	0.695024	+	0.718986i	$0.255394\pi$
$702$	17.5680	−	14.1978i	0.663062	−	0.535862i
$703$	1.51114	−	40.1094i	0.0569938	−	1.51276i
$704$	23.8820	+	41.3648i	0.900086	+	1.55899i
$705$	−9.90035	+	2.28227i	−0.372869	+	0.0859553i
$706$	−6.63648	−	11.4947i	−0.249767	−	0.432610i
$707$	17.6241			0.662822
$708$	4.39287	+	4.71386i	0.165094	+	0.177158i
$709$	6.17216	−	10.6905i	0.231800	−	0.401490i	−0.726538	−	0.687127i	$-0.758872\pi$
$709$	6.17216	−	10.6905i	0.231800	−	0.401490i	0.958338	+	0.285637i	$0.0922050\pi$
$710$	0.690942			0.0259306
$711$	−3.06839	+	1.49407i	−0.115074	+	0.0560321i
$712$	3.42833	+	5.93804i	0.128482	+	0.222537i
$713$	−7.59797	+	13.1601i	−0.284546	+	0.492848i
$714$	−35.1346	+	8.09937i	−1.31488	+	0.303111i
$715$	−5.22195	+	9.04469i	−0.195290	+	0.338252i
$716$	−0.938013			−0.0350552
$717$	4.21646	−	13.7753i	0.157467	−	0.514449i
$718$	10.2940	−	17.8297i	0.384168	−	0.665399i
$719$	6.57335	−	11.3854i	0.245144	−	0.424603i	−0.717028	−	0.697045i	$-0.754498\pi$
$719$	6.57335	−	11.3854i	0.245144	−	0.424603i	0.962172	+	0.272442i	$0.0878313\pi$
$720$	−3.85946	−	2.60691i	−0.143834	−	0.0971538i
$721$	−45.0057			−1.67610
$722$	23.3718	+	1.76359i	0.869808	+	0.0656340i
$723$	10.0307	−	32.7706i	0.373045	−	1.21875i
$724$	−0.299302	−	0.518406i	−0.0111235	−	0.0192664i
$725$	12.9097	+	22.3603i	0.479455	+	0.830440i
$726$	−11.1783	+	36.5200i	−0.414867	+	1.35539i
$727$	−5.03560			−0.186760			−0.0933800	−	0.995631i	$-0.529767\pi$
$727$	−5.03560			−0.186760			−0.0933800	+	0.995631i	$0.529767\pi$
$728$	−17.4692	−	30.2575i	−0.647451	−	1.12142i
$729$	5.66537	−	26.3989i	0.209828	−	0.977738i
$730$	8.14498			0.301459
$731$	−9.34565	+	16.1871i	−0.345661	+	0.598703i
$732$	2.75770	−	9.00951i	0.101928	−	0.333001i
$733$	21.5362	−	37.3019i	0.795459	−	1.37778i	−0.127088	−	0.991891i	$-0.540563\pi$
$733$	21.5362	−	37.3019i	0.795459	−	1.37778i	0.922547	−	0.385884i	$-0.126104\pi$
$734$	−9.35663	+	16.2062i	−0.345359	+	0.598180i
$735$	3.27470	−	0.754897i	0.120789	−	0.0278448i
$736$	−7.88555			−0.290665
$737$	6.37462	+	11.0412i	0.234812	+	0.406706i
$738$	5.24419	+	3.54224i	0.193041	+	0.130392i
$739$	−5.54488	+	9.60401i	−0.203972	+	0.353289i	−0.949805	−	0.312844i	$-0.898718\pi$
$739$	−5.54488	+	9.60401i	−0.203972	+	0.353289i	0.745833	+	0.666133i	$0.232052\pi$
$740$	−1.21446	−	2.10351i	−0.0446445	−	0.0773265i
$741$	4.99603	+	26.1315i	0.183534	+	0.959964i
$742$	−2.24844	+	3.89441i	−0.0825428	+	0.142968i
$743$	3.00507	+	5.20493i	0.110245	+	0.190950i	0.915869	−	0.401477i	$-0.131503\pi$
$743$	3.00507	+	5.20493i	0.110245	+	0.190950i	−0.805624	+	0.592427i	$0.798170\pi$
$744$	7.89057	−	25.7788i	0.289282	−	0.945096i
$745$	1.29340	−	2.24024i	0.0473866	−	0.0820760i
$746$	18.9984	−	32.9062i	0.695580	−	1.20478i
$747$	−5.68663	−	3.84109i	−0.208063	−	0.140538i
$748$	−13.3721			−0.488934
$749$	25.6221	+	44.3788i	0.936212	+	1.62157i
$750$	11.1340	−	2.56666i	0.406557	−	0.0937211i
$751$	−3.51714			−0.128342			−0.0641711	−	0.997939i	$-0.520440\pi$
$751$	−3.51714			−0.128342			−0.0641711	+	0.997939i	$0.520440\pi$
$752$	−14.9681	+	25.9255i	−0.545831	+	0.945407i
$753$	−13.2502	−	14.2184i	−0.482864	−	0.518148i
$754$	11.9509	−	20.6996i	0.435227	−	0.753835i
$755$	−0.203456	+	0.352396i	−0.00740453	+	0.0128250i
$756$	−7.52124	−	2.89559i	−0.273545	−	0.105312i
$757$	−14.2947	+	24.7592i	−0.519551	+	0.899888i	0.480191	+	0.877164i	$0.340567\pi$
$757$	−14.2947	+	24.7592i	−0.519551	+	0.899888i	−0.999742	+	0.0227241i	$0.992766\pi$
$758$	−27.3901			−0.994854
$759$	−18.9386	−	20.3225i	−0.687428	−	0.737660i
$760$	6.49892	−	3.43264i	0.235741	−	0.124515i
$761$	−10.3023	+	17.8440i	−0.373457	+	0.646846i	−0.990095	−	0.140401i	$-0.955161\pi$
$761$	−10.3023	+	17.8440i	−0.373457	+	0.646846i	0.616638	+	0.787247i	$0.288494\pi$
$762$	−15.2904	−	16.4077i	−0.553914	−	0.594390i
$763$	24.6283			0.891606
$764$	−3.99451	−	6.91870i	−0.144516	−	0.250310i
$765$	7.74074	−	3.76915i	0.279867	−	0.136274i
$766$	1.91665	+	3.31974i	0.0692515	+	0.119947i
$767$	13.7054	+	23.7385i	0.494874	+	0.857147i
$768$	18.1764	−	4.19011i	0.655886	−	0.151197i
$769$	−27.1374			−0.978601			−0.489300	−	0.872115i	$-0.662748\pi$
$769$	−27.1374			−0.978601			−0.489300	+	0.872115i	$0.662748\pi$
$770$	−11.8570			−0.427297
$771$	51.9391	−	11.9732i	1.87054	−	0.431205i
$772$	5.91619	+	10.2471i	0.212928	+	0.368803i
$773$	24.5515	+	42.5244i	0.883056	+	1.52950i	0.847926	+	0.530115i	$0.177851\pi$
$773$	24.5515	+	42.5244i	0.883056	+	1.52950i	0.0351305	+	0.999383i	$0.488815\pi$
$774$	11.9522	−	5.81981i	0.429613	−	0.209189i
$775$	11.9540	+	20.7049i	0.429399	+	0.743740i
$776$	25.0136			0.897936
$777$	35.2641	+	37.8409i	1.26509	+	1.35753i
$778$	−0.674767	+	1.16873i	−0.0241916	+	0.0419010i
$779$	−6.59095	+	3.48124i	−0.236145	+	0.124729i
$780$	1.09762	+	1.17782i	0.0393009	+	0.0421727i
$781$	−5.45697			−0.195266
$782$	−9.57900	+	16.5913i	−0.342544	+	0.593304i
$783$	−4.44177	−	28.2232i	−0.158736	−	1.00861i
$784$	4.95094	−	8.57528i	0.176819	−	0.306260i
$785$	1.49315	−	2.58622i	0.0532930	−	0.0923061i
$786$	0.820766	+	0.880740i	0.0292757	+	0.0314150i
$787$	13.5510	−	23.4710i	0.483040	−	0.836650i	−0.516770	−	0.856124i	$-0.672866\pi$
$787$	13.5510	−	23.4710i	0.483040	−	0.836650i	0.999810	+	0.0194740i	$0.00619914\pi$
$788$	−1.44849			−0.0516004
$789$	−37.1424	+	8.56221i	−1.32230	+	0.304823i
$790$	0.387001	+	0.670305i	0.0137689	+	0.0238484i
$791$	14.6960			0.522529
$792$	40.8396	+	27.5855i	1.45117	+	0.980209i
$793$	20.0412	−	34.7124i	0.711684	−	1.23267i
$794$	20.4813	−	35.4746i	0.726853	−	1.25895i
$795$	0.314279	−	1.02676i	0.0111463	−	0.0364155i
$796$	−4.22111	−	7.31118i	−0.149613	−	0.259138i
$797$	−13.1487	+	22.7743i	−0.465752	+	0.806707i	−0.999235	−	0.0391042i	$-0.987550\pi$
$797$	−13.1487	+	22.7743i	−0.465752	+	0.806707i	0.533483	+	0.845811i	$0.320883\pi$
$798$	−22.8565	+	19.7457i	−0.809112	+	0.698990i
$799$	−27.6699	−	47.9256i	−0.978890	−	1.69549i
$800$	−6.20320	+	10.7443i	−0.219316	+	0.379867i
$801$	5.57570	+	3.76616i	0.197008	+	0.133071i
$802$	6.60390	+	11.4383i	0.233192	+	0.403900i
$803$	−64.3281			−2.27009
$804$	1.91512	−	0.441482i	0.0675412	−	0.0155699i
$805$	2.66937	−	4.62348i	0.0940828	−	0.162956i
$806$	11.0661	−	19.1671i	0.389788	−	0.675132i
$807$	−4.76497	+	15.5673i	−0.167735	+	0.547995i
$808$	−8.30673	+	14.3877i	−0.292230	+	0.506157i
$809$	5.16978			0.181760			0.0908799	−	0.995862i	$-0.471032\pi$
$809$	5.16978			0.181760			0.0908799	+	0.995862i	$0.471032\pi$
$810$	−6.06270	−	0.860136i	−0.213022	−	0.0302221i
$811$	−17.7354	−	30.7187i	−0.622775	−	1.07868i	−0.988967	−	0.148139i	$-0.952672\pi$
$811$	−17.7354	−	30.7187i	−0.622775	−	1.07868i	0.366191	−	0.930540i	$-0.380662\pi$
$812$	−8.52819			−0.299281
$813$	−5.17892	+	16.9197i	−0.181633	+	0.593401i
$814$	−30.5197	−	52.8616i	−1.06971	−	1.85280i
$815$	−2.76972	−	4.79729i	−0.0970189	−	0.168042i
$816$	7.42482	−	24.2572i	0.259921	−	0.849171i
$817$	−0.589500	+	15.6468i	−0.0206240	+	0.547412i
$818$	13.8571			0.484502
$819$	−28.4112	−	19.1906i	−0.992767	−	0.670574i
$820$	−0.225532	+	0.390634i	−0.00787593	+	0.0136415i
$821$	9.23095	−	15.9885i	0.322162	−	0.558001i	−0.658772	−	0.752343i	$-0.728924\pi$
$821$	9.23095	−	15.9885i	0.322162	−	0.558001i	0.980934	+	0.194342i	$0.0622570\pi$
$822$	−10.7770	+	35.2089i	−0.375892	+	1.22805i
$823$	51.3714			1.79069			0.895347	−	0.445369i	$-0.146927\pi$
$823$	51.3714			1.79069			0.895347	+	0.445369i	$0.146927\pi$
$824$	21.2125	−	36.7410i	0.738971	−	1.27993i
$825$	−42.5881	+	9.81758i	−1.48273	+	0.341804i
$826$	−15.5598	+	26.9504i	−0.541395	+	0.937723i
$827$	−13.9591	−	24.1779i	−0.485406	−	0.840748i	0.514454	−	0.857518i	$-0.327995\pi$
$827$	−13.9591	−	24.1779i	−0.485406	−	0.840748i	−0.999859	+	0.0167707i	$0.994661\pi$
$828$	−3.85010	+	1.87471i	−0.133800	+	0.0651505i
$829$	12.7112			0.441480			0.220740	−	0.975333i	$-0.429153\pi$
$829$	12.7112			0.441480			0.220740	+	0.975333i	$0.429153\pi$
$830$	−0.778165	+	1.34782i	−0.0270105	+	0.0467836i
$831$	27.9738	+	30.0179i	0.970400	+	1.04131i
$832$	31.3229			1.08593
$833$	9.15225	+	15.8522i	0.317107	+	0.549245i
$834$	3.02411	−	0.697130i	0.104716	−	0.0241396i
$835$	−3.95591	−	6.85184i	−0.136900	−	0.237118i
$836$	−9.90518	+	5.23178i	−0.342578	+	0.180945i
$837$	−4.11292	−	26.1337i	−0.142163	−	0.903313i
$838$	4.08869	−	7.08181i	0.141241	−	0.244637i
$839$	31.5580			1.08950			0.544752	−	0.838598i	$-0.316624\pi$
$839$	31.5580			1.08950			0.544752	+	0.838598i	$0.316624\pi$
$840$	−2.77216	+	9.05676i	−0.0956488	+	0.312488i
$841$	−0.616261	−	1.06740i	−0.0212504	−	0.0368067i
$842$	17.4801			0.602405
$843$	−2.16308	+	7.06685i	−0.0745003	+	0.243395i
$844$	−1.94378	−	3.36673i	−0.0669077	−	0.115888i
$845$	−0.160552	−	0.278084i	−0.00552316	−	0.00956639i
$846$	−2.77121	+	39.2615i	−0.0952762	+	1.34984i
$847$	57.9708			1.99190
$848$	−1.58194	−	2.74000i	−0.0543240	−	0.0940919i
$849$	−25.8283	−	27.7156i	−0.886426	−	0.951198i
$850$	15.0707	+	26.1033i	0.516922	+	0.895335i
$851$	27.4836			0.942125
$852$	−0.246211	+	0.804379i	−0.00843504	+	0.0275576i
$853$	−5.31542			−0.181996			−0.0909982	−	0.995851i	$-0.529006\pi$
$853$	−5.31542			−0.181996			−0.0909982	+	0.995851i	$0.529006\pi$
$854$	45.5057			1.55717
$855$	4.25916	−	5.82046i	0.145660	−	0.199055i
$856$	−48.3057			−1.65106
$857$	7.10747			0.242786			0.121393	−	0.992604i	$-0.461264\pi$
$857$	7.10747			0.242786			0.121393	+	0.992604i	$0.461264\pi$
$858$	27.5833	+	29.5989i	0.941679	+	1.01049i
$859$	3.88372			0.132511			0.0662554	−	0.997803i	$-0.478895\pi$
$859$	3.88372			0.132511			0.0662554	+	0.997803i	$0.478895\pi$
$860$	0.473764	+	0.820584i	0.0161552	+	0.0279817i
$861$	2.81142	−	9.18501i	0.0958129	−	0.313024i
$862$	−7.58042	−	13.1297i	−0.258190	−	0.447198i
$863$	48.2914			1.64386			0.821929	−	0.569589i	$-0.192898\pi$
$863$	48.2914			1.64386			0.821929	+	0.569589i	$0.192898\pi$
$864$	10.6774	−	8.62907i	0.363252	−	0.293567i
$865$	1.12922	+	1.95587i	0.0383948	+	0.0665017i
$866$	−7.90376	−	13.6897i	−0.268581	−	0.465195i
$867$	11.8968	+	12.7662i	0.404038	+	0.433562i
$868$	−7.89681			−0.268035
$869$	−3.05648	−	5.29398i	−0.103684	−	0.179586i
$870$	−6.31401	+	1.45553i	−0.214065	+	0.0493472i
$871$	8.36076			0.283293
$872$	−11.6080	+	20.1057i	−0.393098	+	0.680865i
$873$	22.0688	−	10.7458i	0.746916	−	0.363691i
$874$	−0.604219	+	16.0375i	−0.0204380	+	0.542475i
$875$	−8.67154	−	15.0195i	−0.293151	−	0.507753i
$876$	−2.90239	+	9.48221i	−0.0980626	+	0.320374i
$877$	9.56491	+	16.5669i	0.322984	+	0.559425i	0.981102	−	0.193490i	$-0.0619806\pi$
$877$	9.56491	+	16.5669i	0.322984	+	0.559425i	−0.658118	+	0.752915i	$0.728647\pi$
$878$	−8.07357			−0.272470
$879$	−0.0201399	+	0.0657979i	−0.000679303	+	0.00221931i
$880$	4.17113	−	7.22461i	0.140609	−	0.243541i
$881$	2.13502			0.0719308			0.0359654	−	0.999353i	$-0.488549\pi$
$881$	2.13502			0.0719308			0.0359654	+	0.999353i	$0.488549\pi$
$882$	0.916622	−	12.9864i	0.0308643	−	0.437274i
$883$	−12.2593	−	21.2338i	−0.412559	−	0.714573i	0.582610	−	0.812752i	$-0.302032\pi$
$883$	−12.2593	−	21.2338i	−0.412559	−	0.714573i	−0.995169	+	0.0981790i	$0.968698\pi$
$884$	−4.38462	+	7.59439i	−0.147471	+	0.255427i
$885$	2.17490	−	7.10547i	0.0731084	−	0.238848i
$886$	2.85484	−	4.94473i	0.0959103	−	0.166122i
$887$	−33.5092			−1.12513			−0.562565	−	0.826753i	$-0.690185\pi$
$887$	−33.5092			−1.12513			−0.562565	+	0.826753i	$0.690185\pi$
$888$	−47.5129	+	10.9529i	−1.59443	+	0.367554i
$889$	−17.0212	+	29.4816i	−0.570872	+	0.988780i
$890$	0.762985	−	1.32153i	0.0255753	−	0.0442978i
$891$	47.8824	+	6.79325i	1.60412	+	0.227582i
$892$	2.77759			0.0930005
$893$	−39.2466	−	24.6744i	−1.31334	−	0.825697i
$894$	−6.83199	−	7.33122i	−0.228496	−	0.245193i
$895$	0.540881	+	0.936833i	0.0180796	+	0.0313149i
$896$	9.21209	+	15.9558i	0.307754	+	0.533046i
$897$	−17.7515	+	4.09215i	−0.592706	+	0.136633i
$898$	−20.5362			−0.685301
$899$	−13.9971	−	24.2437i	−0.466830	−	0.808574i
$900$	−0.474363	+	6.72060i	−0.0158121	+	0.224020i
$901$	5.84871			0.194849
$902$	−5.66768	+	9.81671i	−0.188713	+	0.326861i
$903$	−13.7566	−	14.7618i	−0.457791	−	0.491242i
$904$	−6.92663	+	11.9973i	−0.230376	+	0.399024i
$905$	−0.345169	+	0.597850i	−0.0114738	+	0.0198732i
$906$	1.07469	+	1.15322i	0.0357043	+	0.0383133i
$907$	−16.7641			−0.556643			−0.278322	−	0.960488i	$-0.589778\pi$
$907$	−16.7641			−0.556643			−0.278322	+	0.960488i	$0.589778\pi$
$908$	2.81602	+	4.87750i	0.0934530	+	0.161865i
$909$	−1.14786	+	16.2624i	−0.0380720	+	0.539391i
$910$	−3.88782	+	6.73390i	−0.128880	+	0.223227i
$911$	24.6760	+	42.7400i	0.817551	+	1.41604i	0.907482	+	0.420092i	$0.138002\pi$
$911$	24.6760	+	42.7400i	0.817551	+	1.41604i	−0.0899306	+	0.995948i	$0.528665\pi$
$912$	−3.99067	−	20.8730i	−0.132144	−	0.691174i
$913$	6.14585	−	10.6449i	0.203398	−	0.352295i
$914$	−23.7747	−	41.1790i	−0.786397	−	1.36208i
$915$	−10.5883	+	2.44087i	−0.350040	+	0.0806926i
$916$	−6.03664	+	10.4558i	−0.199456	+	0.345468i
$917$	0.913669	−	1.58252i	0.0301720	−	0.0522595i
$918$	−5.18529	−	32.9476i	−0.171140	−	1.08743i
$919$	26.1970			0.864158			0.432079	−	0.901836i	$-0.357780\pi$
$919$	26.1970			0.864158			0.432079	+	0.901836i	$0.357780\pi$
$920$	2.51630	+	4.35835i	0.0829599	+	0.143691i
$921$	−7.84175	+	25.6193i	−0.258394	+	0.844184i
$922$	12.6111			0.415325
$923$	−1.78930	+	3.09916i	−0.0588955	+	0.102010i
$924$	4.22513	−	13.8037i	0.138997	−	0.454107i
$925$	21.6201	−	37.4471i	0.710864	−	1.23125i
$926$	−5.56576	+	9.64018i	−0.182902	+	0.316796i
$927$	2.93122	−	41.5285i	0.0962739	−	1.36397i
$928$	7.26346	−	12.5807i	0.238435	−	0.412981i
$929$	59.4958			1.95200			0.975998	−	0.217782i	$-0.0698821\pi$
$929$	59.4958			1.95200			0.975998	+	0.217782i	$0.0698821\pi$
$930$	−5.84655	+	1.34777i	−0.191716	+	0.0441952i
$931$	12.9814	+	8.16145i	0.425450	+	0.267481i
$932$	4.32406	−	7.48950i	0.141639	−	0.245327i
$933$	−6.12771	+	20.0194i	−0.200612	+	0.655407i
$934$	38.2618			1.25196
$935$	7.71070	+	13.3553i	0.252167	+	0.436766i
$936$	29.0576	−	14.1488i	0.949776	−	0.462469i
$937$	−7.96252	−	13.7915i	−0.260124	−	0.450548i	0.706150	−	0.708062i	$-0.250430\pi$
$937$	−7.96252	−	13.7915i	−0.260124	−	0.450548i	−0.966275	+	0.257513i	$0.917097\pi$
$938$	4.74600	+	8.22031i	0.154962	+	0.268403i
$939$	3.89073	−	12.7111i	0.126969	−	0.414813i
$940$	−2.80537			−0.0915010
$941$	31.5343			1.02799			0.513995	−	0.857793i	$-0.328165\pi$
$941$	31.5343			1.02799			0.513995	+	0.857793i	$0.328165\pi$
$942$	−7.88712	−	8.46344i	−0.256976	−	0.275754i
$943$	−2.55193	−	4.42007i	−0.0831022	−	0.143937i
$944$	−10.9474	−	18.9615i	−0.356309	−	0.617145i
$945$	1.44498	+	9.18145i	0.0470051	+	0.298673i
$946$	11.9058	+	20.6215i	0.387091	+	0.670461i
$947$	−48.3300			−1.57051			−0.785257	−	0.619170i	$-0.787469\pi$
$947$	−48.3300			−1.57051			−0.785257	+	0.619170i	$0.787469\pi$
$948$	−0.918258	+	0.211681i	−0.0298236	+	0.00687507i
$949$	−21.0927	+	36.5336i	−0.684698	+	1.18593i
$950$	21.3761	+	13.4392i	0.693534	+	0.436026i
$951$	−4.82733	+	15.7711i	−0.156537	+	0.511411i
$952$	−51.5897			−1.67203
$953$	24.6011	−	42.6103i	0.796907	−	1.38028i	−0.124715	−	0.992193i	$-0.539802\pi$
$953$	24.6011	−	42.6103i	0.796907	−	1.38028i	0.921621	−	0.388090i	$-0.126865\pi$
$954$	−3.44708	−	2.32837i	−0.111603	−	0.0753836i
$955$	−4.60666	+	7.97898i	−0.149068	+	0.258194i
$956$	1.98891	−	3.44489i	0.0643259	−	0.111416i
$957$	49.8673	−	11.4956i	1.61198	−	0.371600i
$958$	−21.6544	+	37.5065i	−0.699622	+	1.21178i
$959$	55.8896			1.80477
$960$	−5.78909	−	6.21211i	−0.186842	−	0.200495i
$961$	2.53914	+	4.39792i	0.0819078	+	0.141869i
$962$	−40.0287			−1.29058
$963$	−42.6188	+	20.7521i	−1.37337	+	0.668728i
$964$	4.73148	−	8.19516i	0.152391	−	0.263948i
$965$	6.82284	−	11.8175i	0.219635	−	0.380419i
$966$	−14.1001	−	15.1304i	−0.453663	−	0.486813i
$967$	−4.59111	−	7.95204i	−0.147640	−	0.255720i	0.782715	−	0.622381i	$-0.213834\pi$
$967$	−4.59111	−	7.95204i	−0.147640	−	0.255720i	−0.930355	+	0.366660i	$0.880501\pi$
$968$	−27.3233	+	47.3253i	−0.878204	+	1.52109i
$969$	37.1046	+	12.9040i	1.19197	+	0.414537i
$970$	−2.78343	−	4.82104i	−0.0893705	−	0.154794i
$971$	−18.6062	+	32.2269i	−0.597101	+	1.03421i	0.396146	+	0.918188i	$0.370347\pi$
$971$	−18.6062	+	32.2269i	−0.597101	+	1.03421i	−0.993247	+	0.116021i	$0.962986\pi$
$972$	3.16174	−	6.75156i	0.101413	−	0.216556i
$973$	−2.35527	−	4.07945i	−0.0755066	−	0.130781i
$974$	−29.4640			−0.944089
$975$	−8.38864	+	27.4060i	−0.268652	+	0.877694i
$976$	−16.0083	+	27.7271i	−0.512412	+	0.887524i
$977$	21.1242	−	36.5882i	0.675823	−	1.17056i	−0.300405	−	0.953812i	$-0.597122\pi$
$977$	21.1242	−	36.5882i	0.675823	−	1.17056i	0.976228	−	0.216748i	$-0.0695449\pi$
$978$	−20.9110	+	4.82049i	−0.668659	+	0.154142i
$979$	−6.02596	+	10.4373i	−0.192591	+	0.333577i
$980$	0.927920			0.0296413
$981$	−1.60404	+	22.7255i	−0.0512132	+	0.725571i
$982$	22.1230	+	38.3182i	0.705973	+	1.22278i
$983$	−48.8617			−1.55845			−0.779223	−	0.626747i	$-0.784386\pi$
$983$	−48.8617			−1.55845			−0.779223	+	0.626747i	$0.784386\pi$
$984$	6.17322	+	6.62430i	0.196795	+	0.211175i
$985$	0.835235	+	1.44667i	0.0266128	+	0.0460947i
$986$	−17.6466	−	30.5649i	−0.561983	−	0.973384i
$987$	58.2149	−	13.4199i	1.85300	−	0.427161i
$988$	−0.276571	+	7.34087i	−0.00879889	+	0.233544i
$989$	−10.7214			−0.340921
$990$	0.772247	−	10.9409i	0.0245436	−	0.347725i
$991$	−23.9926	+	41.5564i	−0.762150	+	1.32008i	0.179590	+	0.983742i	$0.442523\pi$
$991$	−23.9926	+	41.5564i	−0.762150	+	1.32008i	−0.941740	+	0.336342i	$0.890810\pi$
$992$	6.72571	−	11.6493i	0.213542	−	0.369865i
$993$	−11.4318	−	12.2672i	−0.362778	−	0.389287i
$994$	−4.06280			−0.128864
$995$	−4.86799	+	8.43161i	−0.154326	+	0.267300i
$996$	−1.29181	−	1.38621i	−0.0409326	−	0.0439236i
$997$	2.20984	−	3.82755i	0.0699862	−	0.121220i	−0.828909	−	0.559384i	$-0.811038\pi$
$997$	2.20984	−	3.82755i	0.0699862	−	0.121220i	0.898895	+	0.438164i	$0.144371\pi$
$998$	−17.2049	−	29.7998i	−0.544613	−	0.943297i
$999$	−37.2140	+	30.0750i	−1.17740	+	0.951530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.h.c.49.6	yes	32
3.2	odd	2		513.2.h.c.334.11		32
9.2	odd	6		513.2.g.c.505.6		32
9.7	even	3		171.2.g.c.106.11	✓	32
19.7	even	3		171.2.g.c.121.11	yes	32
57.26	odd	6		513.2.g.c.64.6		32
171.7	even	3	inner	171.2.h.c.7.6	yes	32
171.83	odd	6		513.2.h.c.235.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.11	✓	32	9.7	even	3
171.2.g.c.121.11	yes	32	19.7	even	3
171.2.h.c.7.6	yes	32	171.7	even	3	inner
171.2.h.c.49.6	yes	32	1.1	even	1	trivial
513.2.g.c.64.6		32	57.26	odd	6
513.2.g.c.505.6		32	9.2	odd	6
513.2.h.c.235.11		32	171.83	odd	6
513.2.h.c.334.11		32	3.2	odd	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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.23359 q^{2} +(-1.68779 + 0.389075i) q^{3} -0.478252 q^{4} +(0.275772 + 0.477650i) q^{5} +(2.08204 - 0.479960i) q^{6} +(-1.62156 - 2.80862i) q^{7} +3.05715 q^{8} +(2.69724 - 1.31335i) q^{9} +(-0.340189 - 0.589225i) q^{10} +(2.68677 + 4.65363i) q^{11} +(0.807186 - 0.186076i) q^{12} +3.52389 q^{13} +(2.00034 + 3.46470i) q^{14} +(-0.651285 - 0.698875i) q^{15} -2.81477 q^{16} +(2.60168 - 4.50624i) q^{17} +(-3.32729 + 1.62014i) q^{18} +(0.164107 - 4.35581i) q^{19} +(-0.131888 - 0.228437i) q^{20} +(3.82961 + 4.10945i) q^{21} +(-3.31438 - 5.74068i) q^{22} +2.98467 q^{23} +(-5.15981 + 1.18946i) q^{24} +(2.34790 - 4.06668i) q^{25} -4.34704 q^{26} +(-4.04137 + 3.26609i) q^{27} +(0.775514 + 1.34323i) q^{28} +(-2.74921 + 4.76176i) q^{29} +(0.803420 + 0.862127i) q^{30} +(-2.54567 + 4.40923i) q^{31} -2.64202 q^{32} +(-6.34531 - 6.80897i) q^{33} +(-3.20941 + 5.55885i) q^{34} +(0.894360 - 1.54908i) q^{35} +(-1.28996 + 0.628113i) q^{36} +9.20826 q^{37} +(-0.202441 + 5.37329i) q^{38} +(-5.94757 + 1.37106i) q^{39} +(0.843075 + 1.46025i) q^{40} +(-0.855013 - 1.48093i) q^{41} +(-4.72418 - 5.06938i) q^{42} -3.59217 q^{43} +(-1.28495 - 2.22561i) q^{44} +(1.37114 + 0.926153i) q^{45} -3.68186 q^{46} +(5.31770 - 9.21053i) q^{47} +(4.75073 - 1.09516i) q^{48} +(-1.75891 + 3.04653i) q^{49} +(-2.89635 + 5.01663i) q^{50} +(-2.63781 + 8.61781i) q^{51} -1.68531 q^{52} +(0.562013 + 0.973435i) q^{53} +(4.98540 - 4.02902i) q^{54} +(-1.48187 + 2.56668i) q^{55} +(-4.95735 - 8.58639i) q^{56} +(1.41776 + 7.41552i) q^{57} +(3.39140 - 5.87407i) q^{58} +(3.88928 + 6.73644i) q^{59} +(0.311478 + 0.334238i) q^{60} +(5.68723 - 9.85058i) q^{61} +(3.14032 - 5.43919i) q^{62} +(-8.06245 - 5.44586i) q^{63} +8.88872 q^{64} +(0.971789 + 1.68319i) q^{65} +(7.82752 + 8.39949i) q^{66} +2.37259 q^{67} +(-1.24426 + 2.15512i) q^{68} +(-5.03748 + 1.16126i) q^{69} +(-1.10328 + 1.91093i) q^{70} +(-0.507763 + 0.879471i) q^{71} +(8.24587 - 4.01511i) q^{72} +(-5.98562 + 10.3674i) q^{73} -11.3592 q^{74} +(-2.38051 + 7.77720i) q^{75} +(-0.0784845 + 2.08317i) q^{76} +(8.71353 - 15.0923i) q^{77} +(7.33688 - 1.69133i) q^{78} -1.13760 q^{79} +(-0.776234 - 1.34448i) q^{80} +(5.55022 - 7.08485i) q^{81} +(1.05474 + 1.82686i) q^{82} +(-1.14372 - 1.98099i) q^{83} +(-1.83152 - 1.96535i) q^{84} +2.86987 q^{85} +4.43127 q^{86} +(2.78738 - 9.10648i) q^{87} +(8.21387 + 14.2268i) q^{88} +(1.12141 + 1.94234i) q^{89} +(-1.69143 - 1.14249i) q^{90} +(-5.71420 - 9.89729i) q^{91} -1.42742 q^{92} +(2.58102 - 8.43229i) q^{93} +(-6.55987 + 11.3620i) q^{94} +(2.12581 - 1.12282i) q^{95} +(4.45917 - 1.02795i) q^{96} +8.18199 q^{97} +(2.16978 - 3.75817i) q^{98} +(13.3587 + 9.02328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + q^{3} + 34 q^{4} + 3 q^{5} - 7 q^{6} + q^{7} - 36 q^{8} + 17 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} + 8 q^{13} + q^{14} - 14 q^{15} + 22 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20}+ \cdots - 49 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + q^3 + 34 * q^4 + 3 * q^5 - 7 * q^6 + q^7 - 36 * q^8 + 17 * q^9 - 8 * q^10 + 7 * q^11 - 3 * q^12 + 8 * q^13 + q^14 - 14 * q^15 + 22 * q^16 - 7 * q^17 + 6 * q^18 + 7 * q^19 - 3 * q^20 + 8 * q^21 - 8 * q^22 - 10 * q^23 - 39 * q^24 - 9 * q^25 - 4 * q^26 - 5 * q^27 - 10 * q^28 + 10 * q^29 - 5 * q^30 - 10 * q^31 - 34 * q^32 + q^33 - 13 * q^34 - 3 * q^35 - 19 * q^36 + 2 * q^37 - 46 * q^38 + 12 * q^40 + 6 * q^41 + 16 * q^42 - 14 * q^43 + 20 * q^44 - 35 * q^45 - 9 * q^47 - 15 * q^48 - 13 * q^49 + q^50 - 10 * q^51 - 38 * q^52 + 16 * q^53 - 40 * q^54 + 15 * q^55 - 6 * q^56 + 69 * q^57 + 37 * q^59 - 19 * q^60 - 12 * q^61 + 54 * q^62 + 21 * q^63 - 64 * q^64 + 54 * q^65 + 37 * q^66 + 22 * q^67 - 2 * q^68 + 3 * q^69 + 24 * q^70 + 9 * q^71 + 15 * q^72 - 10 * q^73 - 12 * q^74 - 76 * q^75 - 40 * q^76 + 46 * q^77 + 8 * q^78 + 16 * q^79 - 24 * q^80 + 17 * q^81 + 7 * q^82 + 3 * q^83 + 12 * q^84 + 54 * q^85 - 34 * q^86 - 9 * q^87 + 9 * q^88 + 30 * q^89 + 133 * q^90 - q^91 + 34 * q^92 + 27 * q^93 - 18 * q^94 + 3 * q^95 - 5 * q^96 + 18 * q^98 - 49 * q^99

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