LMFDB - Embedded newform 195.2.bf.a.17.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(17,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	195.17
Dual form			195.2.bf.a.23.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.65038 + 0.442218i) q^{2} +(-0.137150 - 1.72661i) q^{3} +(0.796141 - 0.459652i) q^{4} +(-0.908487 + 2.04320i) q^{5} +(0.989888 + 2.78891i) q^{6} +(0.109428 + 0.0293212i) q^{7} +(1.30565 - 1.30565i) q^{8} +(-2.96238 + 0.473611i) q^{9} +(0.595810 - 3.77380i) q^{10} +(-2.05447 + 3.55845i) q^{11} +(-0.902832 - 1.31159i) q^{12} +(3.24500 + 1.57162i) q^{13} -0.193564 q^{14} +(3.65241 + 1.28838i) q^{15} +(-2.49674 + 4.32449i) q^{16} +(5.04353 + 1.35141i) q^{17} +(4.67961 - 2.09165i) q^{18} +(3.97662 + 6.88771i) q^{19} +(0.215876 + 2.04426i) q^{20} +(0.0356182 - 0.192962i) q^{21} +(1.81705 - 6.78132i) q^{22} +(-6.69524 + 1.79398i) q^{23} +(-2.43343 - 2.07529i) q^{24} +(-3.34930 - 3.71244i) q^{25} +(-6.05047 - 1.15878i) q^{26} +(1.22403 + 5.04992i) q^{27} +(0.100598 - 0.0269551i) q^{28} +(2.00973 - 3.48095i) q^{29} +(-6.59760 - 0.511156i) q^{30} +6.89468i q^{31} +(1.25240 - 4.67403i) q^{32} +(6.42584 + 3.05924i) q^{33} -8.92135 q^{34} +(-0.159323 + 0.196946i) q^{35} +(-2.14078 + 1.73873i) q^{36} +(-1.09950 - 4.10339i) q^{37} +(-9.60880 - 9.60880i) q^{38} +(2.26853 - 5.81840i) q^{39} +(1.48154 + 3.85388i) q^{40} +(1.73822 - 3.01068i) q^{41} +(0.0265474 + 0.334211i) q^{42} +(-4.88872 - 1.30993i) q^{43} +3.77737i q^{44} +(1.72360 - 6.48299i) q^{45} +(10.2563 - 5.92150i) q^{46} +(0.185543 + 0.185543i) q^{47} +(7.80914 + 3.71780i) q^{48} +(-6.05106 - 3.49358i) q^{49} +(7.16932 + 4.64580i) q^{50} +(1.64164 - 8.89356i) q^{51} +(3.30587 - 0.240337i) q^{52} +(1.94409 + 1.94409i) q^{53} +(-4.25328 - 7.79300i) q^{54} +(-5.40416 - 7.43050i) q^{55} +(0.181159 - 0.104592i) q^{56} +(11.3470 - 7.81074i) q^{57} +(-1.77747 + 6.63362i) q^{58} +(0.619675 - 0.357770i) q^{59} +(3.50004 - 0.653105i) q^{60} +(2.04160 + 3.53616i) q^{61} +(-3.04895 - 11.3788i) q^{62} +(-0.338055 - 0.0350341i) q^{63} -1.71922i q^{64} +(-6.15917 + 5.20237i) q^{65} +(-11.9579 - 2.20728i) q^{66} +(-0.764792 - 2.85424i) q^{67} +(4.63654 - 1.24236i) q^{68} +(4.01577 + 11.3140i) q^{69} +(0.175851 - 0.395490i) q^{70} +(4.25380 + 7.36780i) q^{71} +(-3.24947 + 4.48621i) q^{72} +(-3.00868 - 3.00868i) q^{73} +(3.62918 + 6.28592i) q^{74} +(-5.95058 + 6.29211i) q^{75} +(6.33191 + 3.65573i) q^{76} +(-0.329156 + 0.329156i) q^{77} +(-1.17093 + 10.6057i) q^{78} +4.84485i q^{79} +(-6.56752 - 9.03008i) q^{80} +(8.55139 - 2.80603i) q^{81} +(-1.53734 + 5.73743i) q^{82} +(-2.04442 + 2.04442i) q^{83} +(-0.0603381 - 0.169997i) q^{84} +(-7.34318 + 9.07718i) q^{85} +8.64751 q^{86} +(-6.28589 - 2.99261i) q^{87} +(1.96368 + 7.32854i) q^{88} +(-2.79966 - 1.61638i) q^{89} +(0.0222950 + 11.4616i) q^{90} +(0.309013 + 0.267127i) q^{91} +(-4.50574 + 4.50574i) q^{92} +(11.9044 - 0.945607i) q^{93} +(-0.388267 - 0.224166i) q^{94} +(-17.6857 + 1.86762i) q^{95} +(-8.24201 - 1.52137i) q^{96} +(0.144327 + 0.0386722i) q^{97} +(11.5315 + 3.08985i) q^{98} +(4.40081 - 11.5145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.65038	+	0.442218i	−1.16699	+	0.312695i	−0.789756	−	0.613421i	$-0.789793\pi$
$2$	−1.65038	+	0.442218i	−1.16699	+	0.312695i	−0.377238	+	0.926116i	$0.623126\pi$
$3$	−0.137150	−	1.72661i	−0.0791838	−	0.996860i
$3$	−0.137150	−	1.72661i	−0.0791838	−	0.996860i
$4$	0.796141	−	0.459652i	0.398071	−	0.229826i
$5$	−0.908487	+	2.04320i	−0.406288	+	0.913745i
$5$	−0.908487	+	2.04320i	−0.406288	+	0.913745i
$6$	0.989888	+	2.78891i	0.404120	+	1.13857i
$7$	0.109428	+	0.0293212i	0.0413600	+	0.0110824i	0.279440	−	0.960163i	$-0.409851\pi$
$7$	0.109428	+	0.0293212i	0.0413600	+	0.0110824i	−0.238080	+	0.971246i	$0.576518\pi$
$8$	1.30565	−	1.30565i	0.461618	−	0.461618i
$9$	−2.96238	+	0.473611i	−0.987460	+	0.157870i
$10$	0.595810	−	3.77380i	0.188412	−	1.19338i
$11$	−2.05447	+	3.55845i	−0.619447	+	1.07291i	0.370139	+	0.928976i	$0.379310\pi$
$11$	−2.05447	+	3.55845i	−0.619447	+	1.07291i	−0.989587	+	0.143938i	$0.954023\pi$
$12$	−0.902832	−	1.31159i	−0.260625	−	0.378622i
$13$	3.24500	+	1.57162i	0.900000	+	0.435890i
$13$	3.24500	+	1.57162i	0.900000	+	0.435890i
$14$	−0.193564			−0.0517323
$15$	3.65241	+	1.28838i	0.943047	+	0.332658i
$16$	−2.49674	+	4.32449i	−0.624186	+	1.08112i
$17$	5.04353	+	1.35141i	1.22324	+	0.327765i	0.811942	−	0.583738i	$-0.198411\pi$
$17$	5.04353	+	1.35141i	1.22324	+	0.327765i	0.411293	+	0.911503i	$0.365077\pi$
$18$	4.67961	−	2.09165i	1.10299	−	0.493007i
$19$	3.97662	+	6.88771i	0.912300	+	1.58015i	0.810807	+	0.585313i	$0.199029\pi$
$19$	3.97662	+	6.88771i	0.912300	+	1.58015i	0.101493	+	0.994836i	$0.467638\pi$
$20$	0.215876	+	2.04426i	0.0482713	+	0.457111i
$21$	0.0356182	−	0.192962i	0.00777254	−	0.0421077i
$22$	1.81705	−	6.78132i	0.387396	−	1.44578i
$23$	−6.69524	+	1.79398i	−1.39605	+	0.374071i	−0.876926	−	0.480625i	$-0.840410\pi$
$23$	−6.69524	+	1.79398i	−1.39605	+	0.374071i	−0.519127	+	0.854697i	$0.673743\pi$
$24$	−2.43343	−	2.07529i	−0.496722	−	0.423616i
$25$	−3.34930	−	3.71244i	−0.669860	−	0.742487i
$26$	−6.05047	−	1.15878i	−1.18659	−	0.227255i
$27$	1.22403	+	5.04992i	0.235565	+	0.971858i
$28$	0.100598	−	0.0269551i	0.0190112	−	0.00509404i
$29$	2.00973	−	3.48095i	0.373197	−	0.646396i	−0.616858	−	0.787074i	$-0.711595\pi$
$29$	2.00973	−	3.48095i	0.373197	−	0.646396i	0.990055	+	0.140678i	$0.0449282\pi$
$30$	−6.59760	−	0.511156i	−1.20455	−	0.0933239i
$31$			6.89468i			1.23832i	0.785265	+	0.619160i	$0.212527\pi$
$31$			6.89468i			1.23832i	−0.785265	+	0.619160i	$0.787473\pi$
$32$	1.25240	−	4.67403i	0.221396	−	0.826260i
$33$	6.42584	+	3.05924i	1.11860	+	0.532545i
$34$	−8.92135			−1.53000
$35$	−0.159323	+	0.196946i	−0.0269305	+	0.0332899i
$36$	−2.14078	+	1.73873i	−0.356796	+	0.289788i
$37$	−1.09950	−	4.10339i	−0.180757	−	0.674593i	−0.995499	−	0.0947700i	$-0.969788\pi$
$37$	−1.09950	−	4.10339i	−0.180757	−	0.674593i	0.814743	−	0.579823i	$-0.196878\pi$
$38$	−9.60880	−	9.60880i	−1.55875	−	1.55875i
$39$	2.26853	−	5.81840i	0.363256	−	0.931690i
$40$	1.48154	+	3.85388i	0.234252	+	0.609351i
$41$	1.73822	−	3.01068i	0.271464	−	0.470189i	−0.697773	−	0.716319i	$-0.745826\pi$
$41$	1.73822	−	3.01068i	0.271464	−	0.470189i	0.969237	+	0.246130i	$0.0791589\pi$
$42$	0.0265474	+	0.334211i	0.00409636	+	0.0515698i
$43$	−4.88872	−	1.30993i	−0.745523	−	0.199762i	−0.133991	−	0.990982i	$-0.542779\pi$
$43$	−4.88872	−	1.30993i	−0.745523	−	0.199762i	−0.611531	+	0.791220i	$0.709446\pi$
$44$			3.77737i			0.569461i
$45$	1.72360	−	6.48299i	0.256940	−	0.966427i
$46$	10.2563	−	5.92150i	1.51222	−	0.873078i
$47$	0.185543	+	0.185543i	0.0270642	+	0.0270642i	0.720509	−	0.693445i	$-0.243908\pi$
$47$	0.185543	+	0.185543i	0.0270642	+	0.0270642i	−0.693445	+	0.720509i	$0.743908\pi$
$48$	7.80914	+	3.71780i	1.12715	+	0.536619i
$49$	−6.05106	−	3.49358i	−0.864438	−	0.499083i
$50$	7.16932	+	4.64580i	1.01389	+	0.657016i
$51$	1.64164	−	8.89356i	0.229875	−	1.24535i
$52$	3.30587	−	0.240337i	0.458442	−	0.0333287i
$53$	1.94409	+	1.94409i	0.267042	+	0.267042i	0.827907	−	0.560865i	$-0.189531\pi$
$53$	1.94409	+	1.94409i	0.267042	+	0.267042i	−0.560865	+	0.827907i	$0.689531\pi$
$54$	−4.25328	−	7.79300i	−0.578799	−	1.06049i
$55$	−5.40416	−	7.43050i	−0.728696	−	1.00193i
$56$	0.181159	−	0.104592i	0.0242084	−	0.0139767i
$57$	11.3470	−	7.81074i	1.50295	−	1.03456i
$58$	−1.77747	+	6.63362i	−0.233394	+	0.871037i
$59$	0.619675	−	0.357770i	0.0806749	−	0.0465777i	−0.459120	−	0.888374i	$-0.651835\pi$
$59$	0.619675	−	0.357770i	0.0806749	−	0.0465777i	0.539795	+	0.841797i	$0.318502\pi$
$60$	3.50004	−	0.653105i	0.451853	−	0.0843155i
$61$	2.04160	+	3.53616i	0.261400	+	0.452758i	0.966614	−	0.256236i	$-0.0824825\pi$
$61$	2.04160	+	3.53616i	0.261400	+	0.452758i	−0.705214	+	0.708994i	$0.749149\pi$
$62$	−3.04895	−	11.3788i	−0.387217	−	1.44511i
$63$	−0.338055	−	0.0350341i	−0.0425909	−	0.00441389i
$64$		−	1.71922i		−	0.214903i
$65$	−6.15917	+	5.20237i	−0.763951	+	0.645274i
$66$	−11.9579	−	2.20728i	−1.47192	−	0.271697i
$67$	−0.764792	−	2.85424i	−0.0934343	−	0.348701i	0.903343	−	0.428919i	$-0.141105\pi$
$67$	−0.764792	−	2.85424i	−0.0934343	−	0.348701i	−0.996777	+	0.0802172i	$0.974439\pi$
$68$	4.63654	−	1.24236i	0.562263	−	0.150658i
$69$	4.01577	+	11.3140i	0.483442	+	1.36205i
$70$	0.175851	−	0.395490i	0.0210182	−	0.0472701i
$71$	4.25380	+	7.36780i	0.504833	+	0.874397i	0.999984	+	0.00558990i	$0.00177933\pi$
$71$	4.25380	+	7.36780i	0.504833	+	0.874397i	−0.495151	+	0.868807i	$0.664887\pi$
$72$	−3.24947	+	4.48621i	−0.382954	+	0.528705i
$73$	−3.00868	−	3.00868i	−0.352139	−	0.352139i	0.508766	−	0.860905i	$-0.330102\pi$
$73$	−3.00868	−	3.00868i	−0.352139	−	0.352139i	−0.860905	+	0.508766i	$0.830102\pi$
$74$	3.62918	+	6.28592i	0.421884	+	0.730724i
$75$	−5.95058	+	6.29211i	−0.687114	+	0.726550i
$76$	6.33191	+	3.65573i	0.726319	+	0.419341i
$77$	−0.329156	+	0.329156i	−0.0375108	+	0.0375108i
$78$	−1.17093	+	10.6057i	−0.132582	+	1.20086i
$79$			4.84485i			0.545088i	0.962143	+	0.272544i	$0.0878650\pi$
$79$			4.84485i			0.545088i	−0.962143	+	0.272544i	$0.912135\pi$
$80$	−6.56752	−	9.03008i	−0.734271	−	1.00959i
$81$	8.55139	−	2.80603i	0.950154	−	0.311781i
$82$	−1.53734	+	5.73743i	−0.169771	+	0.633593i
$83$	−2.04442	+	2.04442i	−0.224405	+	0.224405i	−0.810350	−	0.585946i	$-0.800723\pi$
$83$	−2.04442	+	2.04442i	−0.224405	+	0.224405i	0.585946	+	0.810350i	$0.300723\pi$
$84$	−0.0603381	−	0.169997i	−0.00658343	−	0.0185482i
$85$	−7.34318	+	9.07718i	−0.796479	+	0.984558i
$86$	8.64751			0.932485
$87$	−6.28589	−	2.99261i	−0.673918	−	0.320841i
$88$	1.96368	+	7.32854i	0.209329	+	0.781225i
$89$	−2.79966	−	1.61638i	−0.296763	−	0.171336i	0.344225	−	0.938887i	$-0.388142\pi$
$89$	−2.79966	−	1.61638i	−0.296763	−	0.171336i	−0.640988	+	0.767551i	$0.721475\pi$
$90$	0.0222950	+	11.4616i	0.00235009	+	1.20816i
$91$	0.309013	+	0.267127i	0.0323933	+	0.0280025i
$92$	−4.50574	+	4.50574i	−0.469756	+	0.469756i
$93$	11.9044	−	0.945607i	1.23443	−	0.0980549i
$94$	−0.388267	−	0.224166i	−0.0400466	−	0.0231209i
$95$	−17.6857	+	1.86762i	−1.81451	+	0.191614i
$96$	−8.24201	−	1.52137i	−0.841196	−	0.155274i
$97$	0.144327	+	0.0386722i	0.0146542	+	0.00392657i	0.266139	−	0.963935i	$-0.414252\pi$
$97$	0.144327	+	0.0386722i	0.0146542	+	0.00392657i	−0.251485	+	0.967861i	$0.580919\pi$
$98$	11.5315	+	3.08985i	1.16485	+	0.312122i
$99$	4.40081	−	11.5145i	0.442298	−	1.15725i
$100$	−4.37295	−	1.41611i	−0.437295	−	0.141611i
$101$	10.5103	+	6.06812i	1.04581	+	0.603800i	0.921474	−	0.388440i	$-0.126986\pi$
$101$	10.5103	+	6.06812i	1.04581	+	0.603800i	0.124339	+	0.992240i	$0.460319\pi$
$102$	1.22357	+	15.4037i	0.121151	+	1.52519i
$103$	0.528320	−	0.528320i	0.0520569	−	0.0520569i	−0.680599	−	0.732656i	$-0.738280\pi$
$103$	0.528320	−	0.528320i	0.0520569	−	0.0520569i	0.732656	+	0.680599i	$0.238280\pi$
$104$	6.28884	−	2.18485i	0.616671	−	0.214242i
$105$	0.361900	+	0.248078i	0.0353178	+	0.0242100i
$106$	−4.06820	−	2.34878i	−0.395139	−	0.228133i
$107$	0.427445	+	1.59525i	0.0413227	+	0.154218i	0.983504	−	0.180884i	$-0.0578958\pi$
$107$	0.427445	+	1.59525i	0.0413227	+	0.154218i	−0.942182	+	0.335102i	$0.891229\pi$
$108$	3.29571	+	3.45782i	0.317130	+	0.332729i
$109$	−0.638870			−0.0611926			−0.0305963	−	0.999532i	$-0.509741\pi$
$109$	−0.638870			−0.0611926			−0.0305963	+	0.999532i	$0.509741\pi$
$110$	12.2048	+	9.87333i	1.16368	+	0.941385i
$111$	−6.93416	+	2.46119i	−0.658162	+	0.233606i
$112$	−0.400014	+	0.400014i	−0.0377977	+	0.0377977i
$113$	2.04834	−	7.64451i	0.192692	−	0.719135i	−0.800161	−	0.599786i	$-0.795253\pi$
$113$	2.04834	−	7.64451i	0.192692	−	0.719135i	0.992852	−	0.119349i	$-0.0380808\pi$
$114$	−15.2728	+	17.9085i	−1.43043	+	1.67729i
$115$	2.41708	−	15.3095i	0.225394	−	1.42762i
$116$		−	3.69510i		−	0.343082i
$117$	−10.3572	−	3.11888i	−0.957528	−	0.288340i
$118$	−0.864487	+	0.864487i	−0.0795825	+	0.0795825i
$119$	0.512280	+	0.295765i	0.0469606	+	0.0271127i
$120$	6.45096	−	3.08660i	0.588889	−	0.281767i
$121$	−2.94173	−	5.09522i	−0.267430	−	0.463202i
$122$	−4.93316	−	4.93316i	−0.446628	−	0.446628i
$123$	−5.43667	−	2.58831i	−0.490208	−	0.233380i
$124$	3.16915	+	5.48913i	0.284598	+	0.492939i
$125$	10.6280	−	3.47058i	0.950600	−	0.310418i
$126$	0.573411	−	0.0916742i	0.0510835	−	0.00816699i
$127$	12.3036	−	3.29674i	1.09177	−	0.292539i	0.332361	−	0.943152i	$-0.392155\pi$
$127$	12.3036	−	3.29674i	1.09177	−	0.292539i	0.759409	+	0.650614i	$0.225488\pi$
$128$	3.26508	+	12.1854i	0.288595	+	1.07705i
$129$	−1.59125	+	8.62058i	−0.140102	+	0.759000i
$130$	7.86438	−	11.3096i	0.689752	−	0.991914i
$131$		−	12.9569i		−	1.13205i	−0.824390	−	0.566023i	$-0.808481\pi$
$131$		−	12.9569i		−	1.13205i	0.824390	−	0.566023i	$-0.191519\pi$
$132$	6.52206	−	0.518068i	0.567673	−	0.0450921i
$133$	0.233199	+	0.870310i	0.0202209	+	0.0754655i
$134$	2.52439	+	4.37238i	0.218074	+	0.377716i
$135$	−11.4300	−	2.08685i	−0.983738	−	0.179607i
$136$	8.34958	−	4.82063i	0.715970	−	0.413366i
$137$	−3.22490	+	12.0355i	−0.275522	+	1.02826i	0.679969	+	0.733241i	$0.261993\pi$
$137$	−3.22490	+	12.0355i	−0.275522	+	1.02826i	−0.955491	+	0.295021i	$0.904673\pi$
$138$	−11.6308	−	16.8966i	−0.990079	−	1.43833i
$139$	3.31851	−	1.91594i	0.281472	−	0.162508i	−0.352618	−	0.935767i	$-0.614708\pi$
$139$	3.31851	−	1.91594i	0.281472	−	0.162508i	0.634090	+	0.773260i	$0.281375\pi$
$140$	−0.0363173	+	0.230030i	−0.00306937	+	0.0194411i
$141$	0.294914	−	0.345808i	0.0248362	−	0.0291223i
$142$	−10.2785	−	10.2785i	−0.862557	−	0.862557i
$143$	−12.2593	+	8.31831i	−1.02517	+	0.695612i
$144$	5.34818	−	13.9933i	0.445682	−	1.16610i
$145$	5.28645	+	7.26867i	0.439016	+	0.603630i
$146$	6.29594	+	3.63496i	0.521056	+	0.300832i
$147$	−5.20216	+	10.9270i	−0.429067	+	0.901243i
$148$	−2.76149	−	2.76149i	−0.226993	−	0.226993i
$149$	10.3032	−	5.94857i	0.844073	−	0.487326i	−0.0145735	−	0.999894i	$-0.504639\pi$
$149$	10.3032	−	5.94857i	0.844073	−	0.487326i	0.858647	+	0.512568i	$0.171306\pi$
$150$	7.03822	−	13.0158i	0.574669	−	1.06274i
$151$			11.1014i			0.903416i	0.892166	+	0.451708i	$0.149185\pi$
$151$			11.1014i			0.903416i	−0.892166	+	0.451708i	$0.850815\pi$
$152$	14.1851	+	3.80088i	1.15056	+	0.308292i
$153$	−15.5809	−	1.61472i	−1.25964	−	0.130542i
$154$	0.397673	−	0.688790i	0.0320454	−	0.0555043i
$155$	−14.0872	−	6.26372i	−1.13151	−	0.503114i
$156$	−0.868370	−	5.67500i	−0.0695253	−	0.454364i
$157$	5.53986	+	5.53986i	0.442129	+	0.442129i	0.892727	−	0.450598i	$-0.148789\pi$
$157$	5.53986	+	5.53986i	0.442129	+	0.442129i	−0.450598	+	0.892727i	$0.648789\pi$
$158$	−2.14248	−	7.99583i	−0.170446	−	0.636114i
$159$	3.09006	−	3.62333i	0.245058	−	0.287349i
$160$	8.41217	+	6.80520i	0.665041	+	0.537999i
$161$	−0.785250			−0.0618864
$162$	−12.8721	+	8.41259i	−1.01133	+	0.660955i
$163$	3.17233	−	11.8393i	0.248476	−	0.927326i	−0.723128	−	0.690714i	$-0.757296\pi$
$163$	3.17233	−	11.8393i	0.248476	−	0.927326i	0.971604	−	0.236612i	$-0.0760369\pi$
$164$		−	3.19590i		−	0.249558i
$165$	−12.0884	+	10.3500i	−0.941082	+	0.805745i
$166$	2.46999	−	4.27815i	0.191708	−	0.332049i
$167$	8.61742	−	2.30903i	0.666836	−	0.178678i	0.0905069	−	0.995896i	$-0.471151\pi$
$167$	8.61742	−	2.30903i	0.666836	−	0.178678i	0.576329	+	0.817218i	$0.304485\pi$
$168$	−0.205436	−	0.298446i	−0.0158497	−	0.0230256i
$169$	8.06000	+	10.1998i	0.620000	+	0.784602i
$170$	8.10493	−	18.2281i	0.621620	−	1.39803i
$171$	−15.0424	−	18.5206i	−1.15032	−	1.41631i
$172$	−4.49422	+	1.20422i	−0.342681	+	0.0918211i
$173$	2.27704	−	8.49801i	0.173120	−	0.646092i	−0.823744	−	0.566961i	$-0.808119\pi$
$173$	2.27704	−	8.49801i	0.173120	−	0.646092i	0.996864	−	0.0791307i	$-0.0252144\pi$
$174$	11.6975	+	2.15920i	0.886783	+	0.163689i
$175$	−0.257655	−	0.504451i	−0.0194769	−	0.0381329i
$176$	−10.2590	−	17.7691i	−0.773301	−	1.33940i
$177$	−0.702718	−	1.02087i	−0.0528196	−	0.0767334i
$178$	5.33529	+	1.42959i	0.399897	+	0.107152i
$179$	9.95273	−	17.2386i	0.743902	−	1.28848i	−0.206804	−	0.978382i	$-0.566306\pi$
$179$	9.95273	−	17.2386i	0.743902	−	1.28848i	0.950706	−	0.310094i	$-0.100360\pi$
$180$	−1.60769	−	5.95363i	−0.119830	−	0.443758i
$181$	7.45086			0.553818			0.276909	−	0.960896i	$-0.410690\pi$
$181$	7.45086			0.553818			0.276909	+	0.960896i	$0.410690\pi$
$182$	−0.628116	−	0.304210i	−0.0465590	−	0.0225496i
$183$	5.82556	−	4.01004i	0.430638	−	0.296430i
$184$	−6.39934	+	11.0840i	−0.471766	+	0.817122i
$185$	9.38291	+	1.48138i	0.689845	+	0.108913i
$186$	−19.2287	+	6.82496i	−1.40991	+	0.500430i
$187$	−15.1707	+	15.1707i	−1.10939	+	1.10939i
$188$	0.233004	+	0.0624332i	0.0169935	+	0.00455341i
$189$	−0.0141260	+	0.588495i	−0.00102752	+	0.0428067i
$190$	28.3621	−	10.9032i	2.05761	−	0.791001i
$191$	−19.8776	+	11.4763i	−1.43829	+	0.830399i	−0.997731	−	0.0673227i	$-0.978554\pi$
$191$	−19.8776	+	11.4763i	−1.43829	+	0.830399i	−0.440562	+	0.897722i	$0.645221\pi$
$192$	−2.96843	+	0.235792i	−0.214228	+	0.0170168i
$193$	−21.1680	+	5.67196i	−1.52371	+	0.408276i	−0.920961	−	0.389655i	$-0.872594\pi$
$193$	−21.1680	+	5.67196i	−1.52371	+	0.408276i	−0.602748	+	0.797932i	$0.705928\pi$
$194$	−0.255295			−0.0183291
$195$	9.82720	+	9.92099i	0.703740	+	0.710457i
$196$	−6.42333			−0.458810
$197$	−8.39781	+	2.25019i	−0.598319	+	0.160319i	−0.545253	−	0.838272i	$-0.683566\pi$
$197$	−8.39781	+	2.25019i	−0.598319	+	0.160319i	−0.0530668	+	0.998591i	$0.516900\pi$
$198$	−2.17108	+	20.9494i	−0.154292	+	1.48881i
$199$	17.5413	−	10.1275i	1.24347	−	0.717919i	0.273673	−	0.961823i	$-0.411761\pi$
$199$	17.5413	−	10.1275i	1.24347	−	0.717919i	0.969799	+	0.243904i	$0.0784282\pi$
$200$	−9.22018	−	0.474126i	−0.651965	−	0.0335258i
$201$	−4.82328	+	1.71196i	−0.340208	+	0.120752i
$202$	−20.0294	−	5.36686i	−1.40926	−	0.377611i
$203$	0.321987	−	0.321987i	0.0225990	−	0.0225990i
$204$	−2.78097	−	7.83511i	−0.194707	−	0.548568i
$205$	4.57226	+	6.28668i	0.319341	+	0.439081i
$206$	−0.638295	+	1.10556i	−0.0444721	+	0.0770280i
$207$	18.9842	−	8.48540i	1.31949	−	0.589776i
$208$	−14.8984	+	10.1090i	−1.03302	+	0.700934i
$209$	−32.6795			−2.26049
$210$	−0.706976	−	0.249385i	−0.0487860	−	0.0172092i
$211$	3.64767	−	6.31794i	0.251116	−	0.434945i	−0.712718	−	0.701451i	$-0.752536\pi$
$211$	3.64767	−	6.31794i	0.251116	−	0.434945i	0.963833	+	0.266506i	$0.0858692\pi$
$212$	2.44138	+	0.654166i	0.167675	+	0.0449283i
$213$	12.1379	−	8.35516i	0.831677	−	0.572486i
$214$	−1.41089	−	2.44374i	−0.0964466	−	0.167050i
$215$	7.11778	−	8.79856i	0.485428	−	0.600057i
$216$	8.19162	+	4.99529i	0.557369	+	0.339886i
$217$	−0.202160	+	0.754473i	−0.0137235	+	0.0512169i
$218$	1.05438	−	0.282519i	0.0714114	−	0.0191346i
$219$	−4.78218	+	5.60746i	−0.323149	+	0.378917i
$220$	−7.71792	−	3.43170i	−0.520342	−	0.231365i
$221$	14.2423	+	12.3118i	0.958043	+	0.828184i
$222$	10.3556	−	7.12830i	0.695023	−	0.478420i
$223$	−11.7287	+	3.14269i	−0.785411	+	0.210450i	−0.629169	−	0.777268i	$-0.716605\pi$
$223$	−11.7287	+	3.14269i	−0.785411	+	0.210450i	−0.156242	+	0.987719i	$0.549938\pi$
$224$	0.274097	−	0.474749i	0.0183139	−	0.0317205i
$225$	11.6802	+	9.41138i	0.778677	+	0.627425i
$226$			13.5221i			0.899479i
$227$	3.58919	−	13.3950i	0.238223	−	0.889061i	−0.738446	−	0.674312i	$-0.764440\pi$
$227$	3.58919	−	13.3950i	0.238223	−	0.889061i	0.976669	−	0.214748i	$-0.0688931\pi$
$228$	5.44360	−	11.4341i	0.360511	−	0.757244i
$229$	−8.51901			−0.562952			−0.281476	−	0.959568i	$-0.590824\pi$
$229$	−8.51901			−0.562952			−0.281476	+	0.959568i	$0.590824\pi$
$230$	2.78104	+	26.3353i	0.183376	+	1.73650i
$231$	0.613468	+	0.523181i	0.0403633	+	0.0344228i
$232$	−1.92091	−	7.16892i	−0.126114	−	0.470663i
$233$	−8.61258	−	8.61258i	−0.564229	−	0.564229i	0.366277	−	0.930506i	$-0.380632\pi$
$233$	−8.61258	−	8.61258i	−0.564229	−	0.564229i	−0.930506	+	0.366277i	$0.880632\pi$
$234$	18.4726	+	0.567169i	1.20759	+	0.0370770i
$235$	−0.547664	+	0.210537i	−0.0357257	+	0.0137339i
$236$	0.328899	−	0.569670i	0.0214095	−	0.0370824i
$237$	8.36517	−	0.664473i	0.543376	−	0.0431621i
$238$	−0.976248	−	0.261585i	−0.0632807	−	0.0169560i
$239$			11.5531i			0.747310i	0.927568	+	0.373655i	$0.121896\pi$
$239$			11.5531i			0.747310i	−0.927568	+	0.373655i	$0.878104\pi$
$240$	−14.6907	+	12.5780i	−0.948281	+	0.811909i
$241$	12.0934	−	6.98212i	0.779004	−	0.449758i	−0.0570731	−	0.998370i	$-0.518177\pi$
$241$	12.0934	−	6.98212i	0.779004	−	0.449758i	0.836077	+	0.548612i	$0.184843\pi$
$242$	7.10816	+	7.10816i	0.456930	+	0.456930i
$243$	−6.01775	−	14.3801i	−0.386039	−	0.922482i
$244$	3.25080	+	1.87685i	0.208111	+	0.120153i
$245$	12.6354	−	9.18963i	0.807245	−	0.587104i
$246$	10.1172	+	1.86750i	0.645047	+	0.119067i
$247$	2.07924	+	28.6004i	0.132299	+	1.81980i
$248$	9.00206	+	9.00206i	0.571631	+	0.571631i
$249$	3.81032	+	3.24953i	0.241469	+	0.205931i
$250$	−16.0055	+	10.4277i	−1.01228	+	0.659504i
$251$	−14.9246	+	8.61672i	−0.942032	+	0.543882i	−0.890597	−	0.454794i	$-0.849713\pi$
$251$	−14.9246	+	8.61672i	−0.942032	+	0.543882i	−0.0514354	+	0.998676i	$0.516380\pi$
$252$	−0.285243	+	0.127496i	−0.0179686	+	0.00803147i
$253$	7.37138	−	27.5104i	0.463435	−	1.72956i
$254$	−18.8477	+	10.8818i	−1.18261	+	0.682782i
$255$	16.6799	+	11.4339i	1.04454	+	0.716017i
$256$	−9.05800	−	15.6889i	−0.566125	−	0.980557i
$257$	−0.108348	−	0.404361i	−0.00675857	−	0.0252233i	0.962464	−	0.271409i	$-0.0874895\pi$
$257$	−0.108348	−	0.404361i	−0.00675857	−	0.0252233i	−0.969223	+	0.246185i	$0.920823\pi$
$258$	−1.18601	−	14.9309i	−0.0738377	−	0.929557i
$259$		−	0.481265i		−	0.0299044i
$260$	−2.51229	+	6.97289i	−0.155806	+	0.432441i
$261$	−4.30496	+	11.2637i	−0.266470	+	0.697207i
$262$	5.72975	+	21.3837i	0.353985	+	1.32109i
$263$	12.6393	−	3.38670i	0.779374	−	0.208833i	0.152865	−	0.988247i	$-0.451150\pi$
$263$	12.6393	−	3.38670i	0.779374	−	0.208833i	0.626509	+	0.779414i	$0.284483\pi$
$264$	12.3842	−	4.39562i	0.762197	−	0.270532i
$265$	−5.73835	+	2.20598i	−0.352504	+	0.135512i
$266$	−0.769733	−	1.33322i	−0.0471953	−	0.0817447i
$267$	−2.40689	+	5.05561i	−0.147299	+	0.309398i
$268$	−1.92084	−	1.92084i	−0.117334	−	0.117334i
$269$	0.403612	+	0.699076i	0.0246086	+	0.0426234i	0.878067	−	0.478537i	$-0.158833\pi$
$269$	0.403612	+	0.699076i	0.0246086	+	0.0426234i	−0.853459	+	0.521160i	$0.825499\pi$
$270$	19.7867	−	1.61046i	1.20418	−	0.0980093i
$271$	−9.22378	−	5.32535i	−0.560305	−	0.323492i	0.192963	−	0.981206i	$-0.438190\pi$
$271$	−9.22378	−	5.32535i	−0.560305	−	0.323492i	−0.753268	+	0.657714i	$0.771524\pi$
$272$	−18.4366	+	18.4366i	−1.11788	+	1.11788i
$273$	0.418844	−	0.570181i	0.0253496	−	0.0345089i
$274$		−	21.2892i		−	1.28613i
$275$	20.0916	−	4.29123i	1.21157	−	0.258771i
$276$	8.39764	+	7.16171i	0.505478	+	0.431084i
$277$	7.38713	−	27.5691i	0.443849	−	1.65647i	−0.275107	−	0.961414i	$-0.588713\pi$
$277$	7.38713	−	27.5691i	0.443849	−	1.65647i	0.718957	−	0.695055i	$-0.244620\pi$
$278$	−4.62953	+	4.62953i	−0.277661	+	0.277661i
$279$	−3.26539	−	20.4246i	−0.195494	−	1.22279i
$280$	0.0491217	+	0.465164i	0.00293558	+	0.0277988i
$281$	−13.4870			−0.804568			−0.402284	−	0.915515i	$-0.631784\pi$
$281$	−13.4870			−0.804568			−0.402284	+	0.915515i	$0.631784\pi$
$282$	−0.333797	+	0.701130i	−0.0198773	+	0.0417517i
$283$	0.294869	+	1.10046i	0.0175281	+	0.0654158i	0.974136	−	0.225963i	$-0.0725528\pi$
$283$	0.294869	+	1.10046i	0.0175281	+	0.0654158i	−0.956608	+	0.291379i	$0.905886\pi$
$284$	6.77325	+	3.91054i	0.401918	+	0.232048i
$285$	5.65025	+	30.2801i	0.334692	+	1.79364i
$286$	16.5540	−	19.1496i	0.978858	−	1.13234i
$287$	0.278487	−	0.278487i	0.0164386	−	0.0164386i
$288$	−1.49642	+	14.4394i	−0.0881774	+	0.850850i
$289$	8.88844	+	5.13174i	0.522850	+	0.301867i
$290$	−11.9390	−	9.65829i	−0.701081	−	0.567154i
$291$	0.0469775	−	0.254500i	0.00275387	−	0.0149191i
$292$	−3.77827	−	1.01239i	−0.221107	−	0.0592454i
$293$	7.29093	+	1.95360i	0.425941	+	0.114130i	0.465420	−	0.885090i	$-0.345903\pi$
$293$	7.29093	+	1.95360i	0.425941	+	0.114130i	−0.0394794	+	0.999220i	$0.512570\pi$
$294$	3.75342	−	20.3341i	0.218904	−	1.18591i
$295$	0.168027	+	1.59115i	0.00978289	+	0.0926402i
$296$	−6.79317	−	3.92204i	−0.394845	−	0.227964i
$297$	−20.4847	−	6.01927i	−1.18864	−	0.349274i
$298$	−14.3737	+	14.3737i	−0.832644	+	0.832644i
$299$	−24.5455	−	4.70092i	−1.41950	−	0.271861i
$300$	−1.84532	+	7.74460i	−0.106539	+	0.447135i
$301$	−0.496555	−	0.286686i	−0.0286210	−	0.0165243i
$302$	−4.90922	−	18.3214i	−0.282494	−	1.05428i
$303$	9.03580	−	18.9794i	0.519093	−	1.09034i
$304$	−39.7144			−2.27778
$305$	−9.07983	+	0.958838i	−0.519909	+	0.0549029i
$306$	26.4284	−	4.22525i	1.51081	−	0.241541i
$307$	−5.28300	+	5.28300i	−0.301517	+	0.301517i	−0.841607	−	0.540090i	$-0.818390\pi$
$307$	−5.28300	+	5.28300i	−0.301517	+	0.301517i	0.540090	+	0.841607i	$0.318390\pi$
$308$	−0.110757	+	0.413352i	−0.00631098	+	0.0235529i
$309$	−0.984663	−	0.839744i	−0.0560155	−	0.0477714i
$310$	26.0191	+	4.10792i	1.47779	+	0.233314i
$311$		−	2.37607i		−	0.134735i	−0.997728	−	0.0673674i	$-0.978540\pi$
$311$		−	2.37607i		−	0.134735i	0.997728	−	0.0673674i	$-0.0214599\pi$
$312$	−4.63490	−	10.5587i	−0.262400	−	0.597770i
$313$	20.5099	−	20.5099i	1.15929	−	1.15929i	0.174659	−	0.984629i	$-0.444118\pi$
$313$	20.5099	−	20.5099i	1.15929	−	1.15929i	0.984629	−	0.174659i	$-0.0558822\pi$
$314$	−11.5927	−	6.69304i	−0.654213	−	0.377710i
$315$	0.378700	−	0.658885i	0.0213373	−	0.0371239i
$316$	2.22694	+	3.85718i	0.125275	+	0.216983i
$317$	23.9045	+	23.9045i	1.34261	+	1.34261i	0.893450	+	0.449162i	$0.148277\pi$
$317$	23.9045	+	23.9045i	1.34261	+	1.34261i	0.449162	+	0.893450i	$0.351723\pi$
$318$	−3.49747	+	7.34634i	−0.196128	+	0.411962i
$319$	8.25787	+	14.3030i	0.462352	+	0.800817i
$320$	3.51271	+	1.56189i	0.196366	+	0.0873124i
$321$	2.69575	−	0.956821i	0.150462	−	0.0534045i
$322$	1.29596	−	0.347251i	0.0722210	−	0.0193516i
$323$	10.7481	+	40.1124i	0.598040	+	2.23191i
$324$	5.51831	−	6.16466i	0.306573	−	0.342481i
$325$	−5.03393	−	17.3107i	−0.279232	−	0.960224i
$326$			20.9422i			1.15988i
$327$	0.0876212	+	1.10308i	0.00484546	+	0.0610005i
$328$	−1.66140	−	6.20041i	−0.0917352	−	0.342361i
$329$	0.0148633	+	0.0257440i	0.000819441	+	0.00141931i
$330$	15.3735	−	22.4271i	0.846284	−	1.23457i
$331$	12.0767	−	6.97251i	0.663798	−	0.383244i	−0.129925	−	0.991524i	$-0.541474\pi$
$331$	12.0767	−	6.97251i	0.663798	−	0.383244i	0.793722	+	0.608280i	$0.208140\pi$
$332$	−0.687925	+	2.56737i	−0.0377548	+	0.140903i
$333$	5.20054	+	11.6351i	0.284988	+	0.637597i
$334$	−13.2009	+	7.62155i	−0.722322	+	0.417033i
$335$	6.52659	+	1.03042i	0.356585	+	0.0562980i
$336$	0.745531	+	0.635807i	0.0406720	+	0.0346861i
$337$	−2.58183	−	2.58183i	−0.140641	−	0.140641i	0.633281	−	0.773922i	$-0.281708\pi$
$337$	−2.58183	−	2.58183i	−0.140641	−	0.140641i	−0.773922	+	0.633281i	$0.781708\pi$
$338$	−17.8126	−	13.2693i	−0.968877	−	0.721754i
$339$	−13.4800	−	2.48824i	−0.732135	−	0.135143i
$340$	−1.67386	+	10.6020i	−0.0907777	+	0.574975i
$341$	−24.5344	−	14.1649i	−1.32861	−	0.767074i
$342$	33.0157	+	23.9141i	1.78529	+	1.29313i
$343$	−1.12047	−	1.12047i	−0.0604997	−	0.0604997i
$344$	−8.09329	+	4.67266i	−0.436361	+	0.251933i
$345$	−26.7651	−	2.07365i	−1.44098	−	0.111642i
$346$			15.0319i			0.808119i
$347$	−15.4146	−	4.13034i	−0.827500	−	0.221728i	−0.179877	−	0.983689i	$-0.557570\pi$
$347$	−15.4146	−	4.13034i	−0.827500	−	0.221728i	−0.647623	+	0.761961i	$0.724237\pi$
$348$	−6.38001	+	0.506785i	−0.342004	+	0.0271665i
$349$	−2.98342	+	5.16743i	−0.159699	+	0.276606i	−0.934760	−	0.355280i	$-0.884386\pi$
$349$	−2.98342	+	5.16743i	−0.159699	+	0.276606i	0.775061	+	0.631886i	$0.217719\pi$
$350$	0.648306	+	0.718595i	0.0346534	+	0.0384105i
$351$	−3.96459	+	18.3107i	−0.211614	+	0.977353i
$352$	14.0593	+	14.0593i	0.749363	+	0.749363i
$353$	3.22389	+	12.0317i	0.171590	+	0.640383i	0.997107	+	0.0760061i	$0.0242168\pi$
$353$	3.22389	+	12.0317i	0.171590	+	0.640383i	−0.825517	+	0.564377i	$0.809116\pi$
$354$	1.61120	+	1.37407i	0.0856342	+	0.0730309i
$355$	−18.9184	+	1.99780i	−1.00408	+	0.106032i
$356$	−2.97190			−0.157510
$357$	0.440412	−	0.925073i	0.0233091	−	0.0489600i
$358$	−8.80254	+	32.8515i	−0.465229	+	1.73626i
$359$			29.8863i			1.57734i	0.614816	+	0.788671i	$0.289230\pi$
$359$			29.8863i			1.57734i	−0.614816	+	0.788671i	$0.710770\pi$
$360$	−6.21411	−	10.7150i	−0.327513	−	0.564729i
$361$	−22.1271	+	38.3252i	−1.16458	+	2.01712i
$362$	−12.2967	+	3.29490i	−0.646302	+	0.173176i
$363$	−8.39402	+	5.77804i	−0.440572	+	0.303268i
$364$	0.368803	+	0.0706327i	0.0193305	+	0.00370216i
$365$	8.88066	−	3.41397i	0.464835	−	0.178695i
$366$	−7.84107	+	9.19424i	−0.409860	+	0.480591i
$367$	12.9762	−	3.47695i	0.677351	−	0.181496i	0.0962869	−	0.995354i	$-0.469303\pi$
$367$	12.9762	−	3.47695i	0.677351	−	0.181496i	0.581064	+	0.813858i	$0.302637\pi$
$368$	8.95823	−	33.4326i	0.466980	−	1.74279i
$369$	−3.72337	+	9.74201i	−0.193831	+	0.507149i
$370$	−16.1404	+	1.70445i	−0.839102	+	0.0886099i
$371$	0.155736	+	0.269742i	0.00808539	+	0.0140043i
$372$	9.04296	−	6.22474i	0.468855	−	0.322738i
$373$	19.2834	+	5.16696i	0.998455	+	0.267535i	0.720798	−	0.693145i	$-0.243776\pi$
$373$	19.2834	+	5.16696i	0.998455	+	0.267535i	0.277657	+	0.960680i	$0.410442\pi$
$374$	18.3287	−	31.7462i	0.947753	−	1.64156i
$375$	−7.44999	−	17.8745i	−0.384716	−	0.923035i
$376$	0.484510			0.0249867
$377$	11.9923	−	8.13714i	0.617635	−	0.419084i
$378$	−0.236929	−	0.977486i	−0.0121863	−	0.0502764i
$379$	16.7541	−	29.0190i	0.860601	−	1.49061i	−0.0107483	−	0.999942i	$-0.503421\pi$
$379$	16.7541	−	29.0190i	0.860601	−	1.49061i	0.871350	−	0.490663i	$-0.163245\pi$
$380$	−13.2218	+	9.61614i	−0.678265	+	0.493298i
$381$	−7.37965	−	20.7914i	−0.378071	−	1.06518i
$382$	27.7305	−	27.7305i	1.41882	−	1.41882i
$383$	2.60975	+	0.699279i	0.133352	+	0.0357315i	0.324878	−	0.945756i	$-0.394677\pi$
$383$	2.60975	+	0.699279i	0.133352	+	0.0357315i	−0.191526	+	0.981488i	$0.561344\pi$
$384$	20.5917	−	7.30876i	1.05082	−	0.372973i
$385$	−0.373496	−	0.971564i	−0.0190351	−	0.0495155i
$386$	32.4270	−	18.7218i	1.65049	−	0.952912i
$387$	15.1026	+	1.56515i	0.767710	+	0.0795612i
$388$	0.132680	−	0.0355516i	0.00673582	−	0.00180486i
$389$	38.6182			1.95802			0.979011	−	0.203807i	$-0.0653316\pi$
$389$	38.6182			1.95802			0.979011	+	0.203807i	$0.0653316\pi$
$390$	−20.6058	−	12.0276i	−1.04342	−	0.609043i
$391$	−36.1920			−1.83031
$392$	−12.4620	+	3.33918i	−0.629426	+	0.168654i
$393$	−22.3715	+	1.77704i	−1.12849	+	0.0896397i
$394$	12.8645	−	7.42732i	0.648104	−	0.374183i
$395$	−9.89897	−	4.40148i	−0.498071	−	0.221463i
$396$	−1.78901	−	11.1900i	−0.0899010	−	0.562320i
$397$	−10.9688	−	2.93908i	−0.550509	−	0.147508i	−0.0271666	−	0.999631i	$-0.508648\pi$
$397$	−10.9688	−	2.93908i	−0.550509	−	0.147508i	−0.523342	+	0.852122i	$0.675315\pi$
$398$	−24.4713	+	24.4713i	−1.22663	+	1.22663i
$399$	1.47070	−	0.522007i	0.0736273	−	0.0261331i
$400$	24.4167	−	5.21501i	1.22084	−	0.260751i
$401$	15.5856	−	26.9950i	0.778307	−	1.34807i	−0.154611	−	0.987975i	$-0.549412\pi$
$401$	15.5856	−	26.9950i	0.778307	−	1.34807i	0.932917	−	0.360091i	$-0.117254\pi$
$402$	7.20318	−	4.95832i	0.359262	−	0.247299i
$403$	−10.8358	+	22.3732i	−0.539771	+	1.11449i
$404$	11.1569			0.555076
$405$	−2.03555	+	20.0214i	−0.101147	+	0.994871i
$406$	−0.389012	+	0.673788i	−0.0193063	+	0.0334395i
$407$	16.8606	+	4.51779i	0.835749	+	0.223938i
$408$	−9.46851	−	13.7553i	−0.468761	−	0.680990i
$409$	5.22725	+	9.05386i	0.258471	+	0.447685i	0.965832	−	0.259167i	$-0.0834481\pi$
$409$	5.22725	+	9.05386i	0.258471	+	0.447685i	−0.707362	+	0.706852i	$0.750115\pi$
$410$	−10.3260	−	8.35347i	−0.509967	−	0.412548i
$411$	21.2229	+	3.91748i	1.04685	+	0.193235i
$412$	0.177774	−	0.663461i	0.00875828	−	0.0326864i
$413$	0.0783003	−	0.0209805i	0.00385290	−	0.00103238i
$414$	−27.5787	+	22.3993i	−1.35542	+	1.10086i
$415$	−2.31982	−	6.03449i	−0.113876	−	0.296221i
$416$	11.4099	−	13.1989i	0.559414	−	0.647130i
$417$	−3.76322	−	5.46700i	−0.184286	−	0.267720i
$418$	53.9335	−	14.4514i	2.63797	−	0.706843i
$419$	−10.9200	+	18.9139i	−0.533476	+	0.924007i	0.465760	+	0.884911i	$0.345781\pi$
$419$	−10.9200	+	18.9139i	−0.533476	+	0.924007i	−0.999235	+	0.0390956i	$0.987552\pi$
$420$	0.402153	+	0.0311572i	0.0196231	+	0.00152032i
$421$		−	11.3030i		−	0.550876i	−0.961319	−	0.275438i	$-0.911177\pi$
$421$		−	11.3030i		−	0.550876i	0.961319	−	0.275438i	$-0.0888229\pi$
$422$	−3.22612	+	12.0401i	−0.157045	+	0.586101i
$423$	−0.637524	−	0.461774i	−0.0309975	−	0.0224522i
$424$	5.07663			0.246543
$425$	−11.8753	−	23.2501i	−0.576036	−	1.12779i
$426$	−16.3374	+	19.1568i	−0.791548	+	0.928149i
$427$	0.119724	+	0.446818i	0.00579387	+	0.0216230i
$428$	1.07357	+	1.07357i	0.0518927	+	0.0518927i
$429$	16.0439	+	20.0262i	0.774605	+	0.966875i
$430$	−7.85615	+	17.6686i	−0.378857	+	0.852053i
$431$	1.35987	−	2.35537i	0.0655028	−	0.113454i	−0.831414	−	0.555653i	$-0.812468\pi$
$431$	1.35987	−	2.35537i	0.0655028	−	0.113454i	0.896917	+	0.442199i	$0.145802\pi$
$432$	−24.8944	−	7.31505i	−1.19773	−	0.351945i
$433$	13.6874	+	3.66753i	0.657775	+	0.176250i	0.572242	−	0.820085i	$-0.306074\pi$
$433$	13.6874	+	3.66753i	0.657775	+	0.176250i	0.0855335	+	0.996335i	$0.472741\pi$
$434$		−	1.33456i		−	0.0640611i
$435$	11.8251	−	10.1246i	0.566972	−	0.485435i
$436$	−0.508630	+	0.293658i	−0.0243590	+	0.0140637i
$437$	−38.9809	−	38.9809i	−1.86471	−	1.86471i
$438$	5.41268	−	11.3692i	0.258628	−	0.543241i
$439$	−8.10140	−	4.67735i	−0.386659	−	0.223237i	0.294053	−	0.955789i	$-0.404996\pi$
$439$	−8.10140	−	4.67735i	−0.386659	−	0.223237i	−0.680711	+	0.732552i	$0.738329\pi$
$440$	−16.7576	−	2.64571i	−0.798888	−	0.126129i
$441$	19.5801	+	7.48347i	0.932388	+	0.356356i
$442$	−28.9497	−	14.0210i	−1.37700	−	0.666910i
$443$	5.74199	+	5.74199i	0.272810	+	0.272810i	0.830230	−	0.557420i	$-0.188209\pi$
$443$	5.74199	+	5.74199i	0.272810	+	0.272810i	−0.557420	+	0.830230i	$0.688209\pi$
$444$	−4.38928	+	5.14676i	−0.208306	+	0.244254i
$445$	5.84604	−	4.25179i	0.277129	−	0.201554i
$446$	17.9670	−	10.3733i	0.850763	−	0.491188i
$447$	−11.6840	−	16.9738i	−0.552633	−	0.802835i
$448$	0.0504097	−	0.188132i	0.00238163	−	0.00888838i
$449$	−23.4891	+	13.5614i	−1.10852	+	0.640004i	−0.938446	−	0.345427i	$-0.887734\pi$
$449$	−23.4891	+	13.5614i	−1.10852	+	0.640004i	−0.170074	+	0.985431i	$0.554401\pi$
$450$	−23.4385	−	10.3672i	−1.10490	−	0.488713i
$451$	7.14224	+	12.3707i	0.336315	+	0.582515i
$452$	−1.88305	−	7.02763i	−0.0885711	−	0.330552i
$453$	19.1678	−	1.52256i	0.900579	−	0.0715359i
$454$			23.6941i			1.11202i
$455$	−0.826527	+	0.388692i	−0.0387482	+	0.0182221i
$456$	4.61715	−	25.0134i	0.216218	−	1.17136i
$457$	3.46105	+	12.9168i	0.161901	+	0.604224i	0.998415	+	0.0562781i	$0.0179233\pi$
$457$	3.46105	+	12.9168i	0.161901	+	0.604224i	−0.836514	+	0.547946i	$0.815410\pi$
$458$	14.0596	−	3.76726i	0.656962	−	0.176032i
$459$	−0.651065	+	27.1236i	−0.0303891	+	1.26602i
$460$	−5.11271	−	13.2995i	−0.238381	−	0.620094i
$461$	−17.1508	−	29.7061i	−0.798792	−	1.38355i	−0.920403	−	0.390971i	$-0.872139\pi$
$461$	−17.1508	−	29.7061i	−0.798792	−	1.38355i	0.121611	−	0.992578i	$-0.461194\pi$
$462$	−1.24381	−	0.592159i	−0.0578675	−	0.0275498i
$463$	−19.4344	−	19.4344i	−0.903191	−	0.903191i	0.0925195	−	0.995711i	$-0.470508\pi$
$463$	−19.4344	−	19.4344i	−0.903191	−	0.903191i	−0.995711	+	0.0925195i	$0.970508\pi$
$464$	10.0356	+	17.3821i	0.465889	+	0.806943i
$465$	−8.88296	+	25.1822i	−0.411938	+	1.16779i
$466$	18.0226	+	10.4054i	0.834883	+	0.482020i
$467$	19.6345	−	19.6345i	0.908575	−	0.908575i	−0.0875827	−	0.996157i	$-0.527914\pi$
$467$	19.6345	−	19.6345i	0.908575	−	0.908575i	0.996157	+	0.0875827i	$0.0279142\pi$
$468$	−9.67943	+	2.27767i	−0.447432	+	0.105285i
$469$		−	0.334760i		−	0.0154578i
$470$	0.810750	−	0.589653i	0.0373971	−	0.0271987i
$471$	8.80540	−	10.3250i	0.405731	−	0.475750i
$472$	0.341958	−	1.27621i	0.0157399	−	0.0587421i
$473$	14.7051	−	14.7051i	0.676140	−	0.676140i
$474$	−13.5119	+	4.79586i	−0.620620	+	0.220281i
$475$	12.2513	−	37.8320i	0.562127	−	1.73585i
$476$	0.543796			0.0249248
$477$	−6.67989	−	4.83840i	−0.305851	−	0.221535i
$478$	−5.10900	−	19.0670i	−0.233680	−	0.872107i
$479$	1.49161	+	0.861181i	0.0681534	+	0.0393484i	0.533689	−	0.845681i	$-0.320805\pi$
$479$	1.49161	+	0.861181i	0.0681534	+	0.0393484i	−0.465536	+	0.885029i	$0.654138\pi$
$480$	10.5962	−	15.4579i	0.483649	−	0.705553i
$481$	2.88111	−	15.0435i	0.131367	−	0.685924i
$482$	−16.8711	+	16.8711i	−0.768456	+	0.768456i
$483$	0.107697	+	1.35582i	0.00490040	+	0.0616921i
$484$	−4.68406	−	2.70434i	−0.212912	−	0.122925i
$485$	−0.210134	+	0.259755i	−0.00954169	+	0.0117948i
$486$	16.2907	+	21.0714i	0.738961	+	0.955819i
$487$	−20.1087	−	5.38812i	−0.911213	−	0.244159i	−0.227388	−	0.973804i	$-0.573018\pi$
$487$	−20.1087	−	5.38812i	−0.911213	−	0.244159i	−0.683826	+	0.729645i	$0.739685\pi$
$488$	7.28262	+	1.95137i	0.329669	+	0.0883344i
$489$	−20.8770	−	3.85362i	−0.944089	−	0.174267i
$490$	−16.7894	+	20.7540i	−0.758466	+	0.937568i
$491$	19.5711	+	11.2994i	0.883233	+	0.509935i	0.871723	−	0.489999i	$-0.163003\pi$
$491$	19.5711	+	11.2994i	0.883233	+	0.509935i	0.0115102	+	0.999934i	$0.496336\pi$
$492$	−5.51808	+	0.438319i	−0.248774	+	0.0197609i
$493$	14.8403	−	14.8403i	0.668374	−	0.668374i
$494$	−16.0791	−	46.2819i	−0.723434	−	2.08232i
$495$	19.5283	+	19.4525i	0.877733	+	0.874325i
$496$	−29.8159	−	17.2142i	−1.33878	−	0.772942i
$497$	0.249453	+	0.930972i	0.0111895	+	0.0417598i
$498$	−7.72547	−	3.67797i	−0.346186	−	0.164814i
$499$	35.8828			1.60634			0.803168	−	0.595753i	$-0.203146\pi$
$499$	35.8828			1.60634			0.803168	+	0.595753i	$0.203146\pi$
$500$	6.86615	−	7.64827i	0.307064	−	0.342041i
$501$	−5.16868	−	14.5623i	−0.230920	−	0.650594i
$502$	20.8208	−	20.8208i	0.929276	−	0.929276i
$503$	−8.55700	+	31.9352i	−0.381538	+	1.42392i	0.462015	+	0.886872i	$0.347127\pi$
$503$	−8.55700	+	31.9352i	−0.381538	+	1.42392i	−0.843553	+	0.537047i	$0.819540\pi$
$504$	−0.487125	+	0.395640i	−0.0216983	+	0.0176232i
$505$	−21.9468	+	15.9618i	−0.976621	+	0.710290i
$506$			48.6623i			2.16330i
$507$	16.5057	−	15.3154i	0.733044	−	0.680181i
$508$	8.28006	−	8.28006i	0.367368	−	0.367368i
$509$	5.25012	+	3.03116i	0.232707	+	0.134354i	0.611820	−	0.790997i	$-0.290438\pi$
$509$	5.25012	+	3.03116i	0.232707	+	0.134354i	−0.379113	+	0.925350i	$0.623771\pi$
$510$	−32.5844	−	11.4941i	−1.44286	−	0.508967i
$511$	−0.241016	−	0.417452i	−0.0106619	−	0.0184670i
$512$	4.04633	+	4.04633i	0.178824	+	0.178824i
$513$	−29.9149	+	28.5124i	−1.32078	+	1.25886i
$514$	0.357631	+	0.619435i	0.0157744	+	0.0273221i
$515$	0.599489	+	1.55943i	0.0264167	+	0.0687168i
$516$	2.69561	+	7.59462i	0.118668	+	0.334334i
$517$	−1.04144	+	0.279053i	−0.0458025	+	0.0122727i
$518$	0.212824	+	0.794270i	0.00935095	+	0.0348982i
$519$	−14.9851	−	2.76605i	−0.657772	−	0.121416i
$520$	−1.24926	+	14.8342i	−0.0547835	+	0.650524i
$521$			23.5394i			1.03128i	0.856805	+	0.515640i	$0.172446\pi$
$521$			23.5394i			1.03128i	−0.856805	+	0.515640i	$0.827554\pi$
$522$	2.12379	−	20.4931i	0.0929560	−	0.896960i
$523$	8.20158	+	30.6087i	0.358630	+	1.33843i	0.875854	+	0.482575i	$0.160299\pi$
$523$	8.20158	+	30.6087i	0.358630	+	1.33843i	−0.517225	+	0.855850i	$0.673035\pi$
$524$	−5.95565	−	10.3155i	−0.260174	−	0.450634i
$525$	−0.835654	+	0.514056i	−0.0364709	+	0.0224353i
$526$	−19.3620	+	11.1787i	−0.844224	+	0.487413i
$527$	−9.31753	+	34.7735i	−0.405878	+	1.51476i
$528$	−29.2733	+	20.1503i	−1.27396	+	0.876931i
$529$	21.6892	−	12.5223i	0.943010	−	0.544447i
$530$	8.49492	−	6.17830i	0.368996	−	0.268368i
$531$	−1.66627	+	1.35334i	−0.0723100	+	0.0587297i
$532$	0.585699	+	0.585699i	0.0253933	+	0.0253933i
$533$	10.3722	−	7.03782i	0.449268	−	0.304842i
$534$	1.73660	−	9.40804i	0.0751502	−	0.407126i
$535$	−3.64773	−	0.575907i	−0.157705	−	0.0248986i
$536$	−4.72521	−	2.72810i	−0.204098	−	0.117836i
$537$	−31.1295	−	14.8202i	−1.34334	−	0.639540i
$538$	−0.975256	−	0.975256i	−0.0420463	−	0.0420463i
$539$	24.8635	−	14.3550i	1.07095	−	0.618312i
$540$	−10.0591	+	3.59240i	−0.432876	+	0.154592i
$541$			26.7974i			1.15211i	0.817411	+	0.576055i	$0.195409\pi$
$541$			26.7974i			1.15211i	−0.817411	+	0.576055i	$0.804591\pi$
$542$	17.5777	+	4.70993i	0.755027	+	0.202309i
$543$	−1.02189	−	12.8647i	−0.0438534	−	0.552079i
$544$	12.6331	−	21.8811i	0.541638	−	0.938145i
$545$	0.580405	−	1.30534i	0.0248618	−	0.0559144i
$546$	−0.439107	+	1.12624i	−0.0187920	+	0.0481984i
$547$	6.51421	+	6.51421i	0.278528	+	0.278528i	0.832521	−	0.553993i	$-0.186897\pi$
$547$	6.51421	+	6.51421i	0.278528	+	0.278528i	−0.553993	+	0.832521i	$0.686897\pi$
$548$	2.96467	+	11.0643i	0.126644	+	0.472643i
$549$	−7.72276	−	9.50851i	−0.329599	−	0.405813i
$550$	−31.2611	+	15.9670i	−1.33298	+	0.680836i
$551$	31.9677			1.36187
$552$	20.0154	+	9.52901i	0.851912	+	0.405581i
$553$	−0.142057	+	0.530163i	−0.00604087	+	0.0225448i
$554$			48.7662i			2.07188i
$555$	1.27090	−	16.4038i	0.0539468	−	0.696303i
$556$	1.76133	−	3.05072i	0.0746971	−	0.129379i
$557$	22.7031	−	6.08328i	0.961962	−	0.257757i	0.256531	−	0.966536i	$-0.417420\pi$
$557$	22.7031	−	6.08328i	0.961962	−	0.257757i	0.705431	+	0.708779i	$0.250754\pi$
$558$	14.4213	+	32.2644i	0.610501	+	1.36586i
$559$	−13.8052	−	11.9339i	−0.583896	−	0.504752i
$560$	−0.453899	−	1.18071i	−0.0191807	−	0.0498943i
$561$	28.2746	+	24.1133i	1.19376	+	1.01806i
$562$	22.2587	−	5.96419i	0.938926	−	0.251584i
$563$	9.60782	−	35.8569i	0.404921	−	1.51119i	−0.399279	−	0.916829i	$-0.630740\pi$
$563$	9.60782	−	35.8569i	0.404921	−	1.51119i	0.804201	−	0.594358i	$-0.202594\pi$
$564$	0.0758413	−	0.410870i	0.00319350	−	0.0173007i
$565$	13.7583	+	11.1301i	0.578818	+	0.468247i
$566$	−0.973289	−	1.68579i	−0.0409104	−	0.0708589i
$567$	1.01804	−	0.0563221i	0.0427537	−	0.00236531i
$568$	15.1738	+	4.06580i	0.636678	+	0.170597i
$569$	6.61515	−	11.4578i	0.277322	−	0.480335i	−0.693397	−	0.720556i	$-0.743887\pi$
$569$	6.61515	−	11.4578i	0.277322	−	0.480335i	0.970718	+	0.240221i	$0.0772199\pi$
$570$	−22.7155	−	47.4750i	−0.951446	−	1.98851i
$571$	16.3611			0.684690			0.342345	−	0.939574i	$-0.388779\pi$
$571$	16.3611			0.684690			0.342345	+	0.939574i	$0.388779\pi$
$572$	−5.93661	+	12.2576i	−0.248222	+	0.512515i
$573$	22.5414	+	32.7469i	0.941681	+	1.36802i
$574$	−0.336457	+	0.582760i	−0.0140434	+	0.0243240i
$575$	29.0844	+	18.8470i	1.21290	+	0.785976i
$576$	0.814243	+	5.09299i	0.0339268	+	0.212208i
$577$	1.55067	−	1.55067i	0.0645553	−	0.0645553i	−0.674092	−	0.738647i	$-0.735465\pi$
$577$	1.55067	−	1.55067i	0.0645553	−	0.0645553i	0.738647	+	0.674092i	$0.235465\pi$
$578$	−16.9386	−	4.53869i	−0.704554	−	0.188785i
$579$	12.6965	+	35.7711i	0.527648	+	1.48660i
$580$	7.54982	+	3.35695i	0.313489	+	0.139390i
$581$	−0.283663	+	0.163773i	−0.0117683	+	0.00679444i
$582$	0.0350138	+	0.440796i	0.00145137	+	0.0182716i
$583$	−10.9121	+	2.92388i	−0.451931	+	0.121095i
$584$	−7.85658			−0.325107
$585$	15.7819	−	18.3284i	0.652501	−	0.757787i
$586$	−12.8967			−0.532758
$587$	−19.5193	+	5.23017i	−0.805646	+	0.215872i	−0.638061	−	0.769986i	$-0.720263\pi$
$587$	−19.5193	+	5.23017i	−0.805646	+	0.215872i	−0.167585	+	0.985858i	$0.553597\pi$
$588$	0.880963	+	11.0906i	0.0363303	+	0.457369i
$589$	−47.4885	+	27.4175i	−1.95673	+	1.12972i
$590$	−0.980941	−	2.55169i	−0.0403847	−	0.105051i
$591$	5.03696	+	14.1912i	0.207193	+	0.583746i
$592$	20.4902	+	5.49034i	0.842143	+	0.225651i
$593$	−3.08282	+	3.08282i	−0.126596	+	0.126596i	−0.767566	−	0.640970i	$-0.778532\pi$
$593$	−3.08282	+	3.08282i	−0.126596	+	0.126596i	0.640970	+	0.767566i	$0.278532\pi$
$594$	36.4693	+	0.875395i	1.49635	+	0.0359179i
$595$	−1.06971	+	0.777989i	−0.0438536	+	0.0318945i
$596$	5.46855	−	9.47180i	0.224000	−	0.387980i
$597$	−19.8921	−	28.8981i	−0.814128	−	1.18272i
$598$	42.5882	−	3.09615i	1.74156	−	0.126611i
$599$	17.9813			0.734698			0.367349	−	0.930083i	$-0.380266\pi$
$599$	17.9813			0.734698			0.367349	+	0.930083i	$0.380266\pi$
$600$	0.445919	+	15.9847i	0.0182046	+	0.652573i
$601$	−4.18909	+	7.25572i	−0.170877	+	0.295967i	−0.938727	−	0.344663i	$-0.887993\pi$
$601$	−4.18909	+	7.25572i	−0.170877	+	0.295967i	0.767850	+	0.640630i	$0.221327\pi$
$602$	0.946282	+	0.253555i	0.0385676	+	0.0103341i
$603$	3.61741	+	8.09314i	0.147312	+	0.329578i
$604$	5.10277	+	8.83825i	0.207629	+	0.359623i
$605$	13.0831	−	1.38158i	0.531902	−	0.0561694i
$606$	−6.51944	+	35.3190i	−0.264834	+	1.43474i
$607$	−4.58950	+	17.1283i	−0.186282	+	0.695214i	0.808070	+	0.589086i	$0.200512\pi$
$607$	−4.58950	+	17.1283i	−0.186282	+	0.695214i	−0.994352	+	0.106128i	$0.966155\pi$
$608$	37.1737	−	9.96067i	1.50759	−	0.403958i
$609$	−0.600107	−	0.511786i	−0.0243176	−	0.0207386i
$610$	14.5611	−	5.59770i	0.589563	−	0.226644i
$611$	0.310483	+	0.893690i	0.0125608	+	0.0361548i
$612$	−13.1468	+	5.87625i	−0.531428	+	0.237533i
$613$	−36.8917	+	9.88511i	−1.49004	+	0.399256i	−0.909752	−	0.415153i	$-0.863728\pi$
$613$	−36.8917	+	9.88511i	−1.49004	+	0.399256i	−0.580291	+	0.814409i	$0.697061\pi$
$614$	6.38272	−	11.0552i	0.257585	−	0.446151i
$615$	10.2276	−	8.75674i	0.412416	−	0.353106i
$616$			0.859527i			0.0346313i
$617$	7.27686	−	27.1576i	0.292955	−	1.09332i	−0.649872	−	0.760043i	$-0.725178\pi$
$617$	7.27686	−	27.1576i	0.292955	−	1.09332i	0.942828	−	0.333281i	$-0.108156\pi$
$618$	1.99642	+	0.950461i	0.0803076	+	0.0382331i
$619$	−34.9871			−1.40625			−0.703125	−	0.711066i	$-0.748213\pi$
$619$	−34.9871			−1.40625			−0.703125	+	0.711066i	$0.748213\pi$
$620$	−14.0945	+	1.48839i	−0.566049	+	0.0597753i
$621$	−17.2547	−	31.6145i	−0.692406	−	1.26865i
$622$	1.05074	+	3.92142i	0.0421309	+	0.157235i
$623$	−0.258967	−	0.258967i	−0.0103753	−	0.0103753i
$624$	19.4977	+	24.3373i	0.780531	+	0.974271i
$625$	−2.56435	+	24.8681i	−0.102574	+	0.994725i
$626$	−24.7792	+	42.9189i	−0.990378	+	1.71538i
$627$	4.48200	+	56.4248i	0.178994	+	2.25339i
$628$	6.95692	+	1.86410i	0.277611	+	0.0743857i
$629$		−	22.1814i		−	0.884431i
$630$	−0.333628	+	1.25488i	−0.0132921	+	0.0499955i
$631$	−10.8292	+	6.25222i	−0.431102	+	0.248897i	−0.699816	−	0.714323i	$-0.746735\pi$
$631$	−10.8292	+	6.25222i	−0.431102	+	0.248897i	0.268714	+	0.963220i	$0.413401\pi$
$632$	6.32569	+	6.32569i	0.251623	+	0.251623i
$633$	−11.4089	−	5.43160i	−0.453464	−	0.215887i
$634$	−50.0225	−	28.8805i	−1.98665	−	1.14699i
$635$	−4.44178	+	28.1338i	−0.176267	+	1.11645i
$636$	0.794654	−	4.30503i	0.0315101	−	0.170706i
$637$	−14.1451	−	20.8467i	−0.560449	−	0.825974i
$638$	−19.9537	−	19.9537i	−0.789973	−	0.789973i
$639$	−16.0908	−	19.8116i	−0.636544	−	0.783733i
$640$	−27.8635	−	4.39912i	−1.10140	−	0.173890i
$641$	3.54806	−	2.04848i	0.140140	−	0.0809099i	−0.428291	−	0.903641i	$-0.640884\pi$
$641$	3.54806	−	2.04848i	0.140140	−	0.0809099i	0.568431	+	0.822731i	$0.307551\pi$
$642$	−4.02588	+	2.77122i	−0.158889	+	0.109371i
$643$	−10.8144	+	40.3600i	−0.426479	+	1.59164i	0.334192	+	0.942505i	$0.391536\pi$
$643$	−10.8144	+	40.3600i	−0.426479	+	1.59164i	−0.760672	+	0.649137i	$0.775130\pi$
$644$	−0.625170	+	0.360942i	−0.0246351	+	0.0142231i
$645$	−16.1679	−	11.0829i	−0.636611	−	0.436389i
$646$	−35.4768	−	61.4477i	−1.39582	−	2.41763i
$647$	1.68818	+	6.30036i	0.0663691	+	0.247693i	0.991138	−	0.132836i	$-0.0424085\pi$
$647$	1.68818	+	6.30036i	0.0663691	+	0.247693i	−0.924769	+	0.380529i	$0.875742\pi$
$648$	7.50144	−	14.8289i	0.294685	−	0.582532i
$649$			2.94012i			0.115410i
$650$	15.9630	+	26.3431i	0.626119	+	1.03326i
$651$	1.33041	+	0.245576i	0.0521428	+	0.00962489i
$652$	−2.91634	−	10.8839i	−0.114213	−	0.426247i
$653$	−44.7451	+	11.9894i	−1.75101	+	0.469182i	−0.984842	−	0.173454i	$-0.944507\pi$
$653$	−44.7451	+	11.9894i	−1.75101	+	0.469182i	−0.766171	+	0.642637i	$0.777840\pi$
$654$	−0.632409	−	1.78175i	−0.0247292	−	0.0696720i
$655$	26.4734	+	11.7711i	1.03440	+	0.459936i
$656$	8.67976	+	15.0338i	0.338888	+	0.586971i
$657$	10.3378	+	7.48790i	0.403315	+	0.292131i
$658$	−0.0359145	−	0.0359145i	−0.00140009	−	0.00140009i
$659$	−12.0799	−	20.9230i	−0.470566	−	0.815045i	0.528867	−	0.848705i	$-0.322617\pi$
$659$	−12.0799	−	20.9230i	−0.470566	−	0.815045i	−0.999433	+	0.0336601i	$0.989284\pi$
$660$	−4.86669	+	13.7965i	−0.189436	+	0.537028i
$661$	35.3712	+	20.4215i	1.37578	+	0.794306i	0.991648	−	0.128973i	$-0.0411680\pi$
$661$	35.3712	+	20.4215i	1.37578	+	0.794306i	0.384130	+	0.923279i	$0.374501\pi$
$662$	−16.8478	+	16.8478i	−0.654809	+	0.654809i
$663$	19.3044	−	26.2796i	0.749722	−	1.02061i
$664$			5.33862i			0.207178i
$665$	−1.99007	−	0.314194i	−0.0771717	−	0.0121839i
$666$	−13.7281	−	16.9025i	−0.531953	−	0.654958i
$667$	−7.21084	+	26.9112i	−0.279205	+	1.04201i
$668$	5.79933	−	5.79933i	0.224383	−	0.224383i
$669$	7.03481	+	19.8199i	0.271981	+	0.766281i
$670$	−11.2270	+	1.18558i	−0.433737	+	0.0458030i
$671$	−16.7777			−0.647694
$672$	−0.857300	−	0.408147i	−0.0330711	−	0.0157446i
$673$	−3.20311	−	11.9542i	−0.123471	−	0.460799i	0.876310	−	0.481748i	$-0.159998\pi$
$673$	−3.20311	−	11.9542i	−0.123471	−	0.460799i	−0.999781	+	0.0209488i	$0.993331\pi$
$674$	5.40272	+	3.11926i	0.208105	+	0.120150i
$675$	14.6479	−	21.4579i	0.563796	−	0.825914i
$676$	11.1053	+	4.41570i	0.427126	+	0.169834i
$677$	17.7462	−	17.7462i	0.682043	−	0.682043i	−0.278418	−	0.960460i	$-0.589810\pi$
$677$	17.7462	−	17.7462i	0.682043	−	0.682043i	0.960460	+	0.278418i	$0.0898099\pi$
$678$	23.3475	−	1.85457i	0.896655	−	0.0712242i
$679$	0.0146595	+	0.00846367i	0.000562580	+	0.000324806i
$680$	2.26401	+	21.4393i	0.0868208	+	0.822160i
$681$	−23.6203	−	4.36001i	−0.905132	−	0.167076i
$682$	46.7550	+	12.5280i	1.79034	+	0.479721i
$683$	−21.3203	−	5.71276i	−0.815798	−	0.218593i	−0.173290	−	0.984871i	$-0.555440\pi$
$683$	−21.3203	−	5.71276i	−0.815798	−	0.218593i	−0.642509	+	0.766278i	$0.722106\pi$
$684$	−20.4889	−	7.83079i	−0.783413	−	0.299418i
$685$	−21.6611	−	17.5232i	−0.827628	−	0.669527i
$686$	2.34469	+	1.35371i	0.0895208	+	0.0516848i
$687$	1.16839	+	14.7090i	0.0445767	+	0.561185i
$688$	17.8706	−	17.8706i	0.681312	−	0.681312i
$689$	3.25319	+	9.36396i	0.123937	+	0.356738i
$690$	45.0895	−	8.41367i	1.71653	−	0.320303i
$691$	−7.86173	−	4.53897i	−0.299074	−	0.172671i	0.342953	−	0.939353i	$-0.388573\pi$
$691$	−7.86173	−	4.53897i	−0.299074	−	0.172671i	−0.642027	+	0.766682i	$0.721906\pi$
$692$	−2.09329	−	7.81226i	−0.0795749	−	0.296978i
$693$	0.819193	−	1.13098i	0.0311186	−	0.0429622i
$694$	27.2665			1.03502
$695$	0.899822	+	8.52096i	0.0341322	+	0.323219i
$696$	−12.1145	+	4.29988i	−0.459199	+	0.162987i
$697$	12.8354	−	12.8354i	0.486176	−	0.486176i
$698$	2.63864	−	9.84754i	0.0998740	−	0.372735i
$699$	−13.6894	+	16.0518i	−0.517779	+	0.607135i
$700$	−0.437002	−	0.283182i	−0.0165171	−	0.0107033i
$701$			31.3445i			1.18386i	0.805988	+	0.591932i	$0.201635\pi$
$701$			31.3445i			1.18386i	−0.805988	+	0.591932i	$0.798365\pi$
$702$	−1.55424	−	31.9728i	−0.0586611	−	1.20674i
$703$	23.8907	−	23.8907i	0.901053	−	0.901053i
$704$	6.11777	+	3.53210i	0.230572	+	0.133121i
$705$	0.438629	+	0.916729i	0.0165197	+	0.0345260i
$706$	−10.6413	−	18.4312i	−0.400489	−	0.693667i
$707$	0.972198	+	0.972198i	0.0365633	+	0.0365633i
$708$	−1.02871	−	0.489751i	−0.0386612	−	0.0184060i
$709$	−16.2682	−	28.1774i	−0.610967	−	1.05823i	−0.991078	−	0.133285i	$-0.957448\pi$
$709$	−16.2682	−	28.1774i	−0.610967	−	1.05823i	0.380111	−	0.924941i	$-0.375886\pi$
$710$	30.3390	−	11.6632i	1.13860	−	0.437711i
$711$	−2.29457	−	14.3523i	−0.0860532	−	0.538252i
$712$	−5.76582	+	1.54495i	−0.216083	+	0.0578993i
$713$	−12.3689	−	46.1615i	−0.463220	−	1.72876i
$714$	−0.317763	+	1.72148i	−0.0118920	+	0.0644247i
$715$	−5.85852	−	32.6053i	−0.219096	−	1.21937i
$716$		−	18.2992i		−	0.683873i
$717$	19.9478	−	1.58452i	0.744964	−	0.0591749i
$718$	−13.2163	−	49.3238i	−0.493227	−	1.84075i
$719$	−14.5548	−	25.2096i	−0.542802	−	0.940160i	−0.998742	−	0.0501495i	$-0.984030\pi$
$719$	−14.5548	−	25.2096i	−0.542802	−	0.940160i	0.455940	−	0.890010i	$-0.349303\pi$
$720$	23.7322	+	23.6401i	0.884448	+	0.881014i
$721$	0.0733041	−	0.0423222i	0.00272999	−	0.00157616i
$722$	19.5699	−	73.0360i	0.728318	−	2.71812i
$723$	−13.7140	−	19.9230i	−0.510030	−	0.740944i
$724$	5.93194	−	3.42480i	0.220459	−	0.127282i
$725$	−19.6540	+	4.19777i	−0.729931	+	0.155901i
$726$	11.2982	−	13.2479i	0.419314	−	0.491677i
$727$	12.8617	+	12.8617i	0.477014	+	0.477014i	0.904175	−	0.427161i	$-0.140486\pi$
$727$	12.8617	+	12.8617i	0.477014	+	0.477014i	−0.427161	+	0.904175i	$0.640486\pi$
$728$	0.752239	−	0.0546877i	0.0278798	−	0.00202686i
$729$	−24.0035	+	12.3626i	−0.889018	+	0.457873i
$730$	−13.1467	+	9.56153i	−0.486582	+	0.353888i
$731$	−22.8861	−	13.2133i	−0.846475	−	0.488712i
$732$	2.79475	−	5.87029i	0.103297	−	0.216972i
$733$	9.86693	+	9.86693i	0.364443	+	0.364443i	0.865446	−	0.501003i	$-0.167035\pi$
$733$	9.86693	+	9.86693i	0.364443	+	0.364443i	−0.501003	+	0.865446i	$0.667035\pi$
$734$	−19.8780	+	11.4766i	−0.733711	+	0.423608i
$735$	−17.5999	−	20.5561i	−0.649181	−	0.758222i
$736$			33.5405i			1.23632i
$737$	11.7279	+	3.14249i	0.432004	+	0.115755i
$738$	1.83687	−	17.7245i	0.0676162	−	0.652450i
$739$	12.6022	−	21.8276i	0.463578	−	0.802941i	−0.535558	−	0.844498i	$-0.679899\pi$
$739$	12.6022	−	21.8276i	0.463578	−	0.802941i	0.999136	+	0.0415576i	$0.0132320\pi$
$740$	8.15104	−	3.13349i	0.299638	−	0.115189i
$741$	49.0966	−	7.51259i	1.80361	−	0.275982i
$742$	−0.376307	−	0.376307i	−0.0138147	−	0.0138147i
$743$	−9.73165	−	36.3190i	−0.357020	−	1.33242i	−0.877924	−	0.478801i	$-0.841072\pi$
$743$	−9.73165	−	36.3190i	−0.357020	−	1.33242i	0.520904	−	0.853615i	$-0.325595\pi$
$744$	14.3084	−	16.7777i	0.524573	−	0.615100i
$745$	2.79375	+	26.4557i	0.102355	+	0.969262i
$746$	−34.1098			−1.24885
$747$	5.08809	−	7.02462i	0.186164	−	0.257017i
$748$	−5.10478	+	19.0513i	−0.186649	+	0.696584i
$749$			0.187098i			0.00683642i
$750$	20.1997	+	26.2052i	0.737589	+	0.956877i
$751$	14.1002	−	24.4223i	0.514524	−	0.891182i	−0.485334	−	0.874329i	$-0.661302\pi$
$751$	14.1002	−	24.4223i	0.514524	−	0.891182i	0.999858	−	0.0168530i	$-0.00536474\pi$
$752$	−1.26563	+	0.339125i	−0.0461529	+	0.0123666i
$753$	16.9246	+	24.5872i	0.616768	+	0.896007i
$754$	−16.1934	+	18.7326i	−0.589730	+	0.682200i
$755$	−22.6823	−	10.0854i	−0.825492	−	0.367047i
$756$	0.259257	+	0.475018i	0.00942907	+	0.0172762i
$757$	−29.1397	+	7.80797i	−1.05910	+	0.283785i	−0.746008	−	0.665937i	$-0.768032\pi$
$757$	−29.1397	+	7.80797i	−1.05910	+	0.283785i	−0.313093	+	0.949722i	$0.601365\pi$
$758$	−14.8179	+	55.3013i	−0.538211	+	2.00863i
$759$	−48.5108	−	8.95446i	−1.76083	−	0.325026i
$760$	−20.6529	+	25.5298i	−0.749159	+	0.926064i
$761$	−14.3226	−	24.8075i	−0.519195	−	0.899272i	−0.999751	−	0.0223082i	$-0.992898\pi$
$761$	−14.3226	−	24.8075i	−0.519195	−	0.899272i	0.480556	−	0.876964i	$-0.340435\pi$
$762$	21.3735	+	31.0503i	0.774282	+	1.12483i
$763$	−0.0699104	−	0.0187324i	−0.00253093	−	0.000678160i
$764$	−10.5503	+	18.2736i	−0.381695	+	0.661115i
$765$	17.4542	−	30.3679i	0.631059	−	1.09795i
$766$	−4.61630			−0.166794
$767$	2.57312	−	0.187066i	0.0929101	−	0.00675455i
$768$	−25.8464	+	17.7914i	−0.932650	+	0.641992i
$769$	26.5529	−	45.9910i	0.957522	−	1.65848i	0.229035	−	0.973418i	$-0.426443\pi$
$769$	26.5529	−	45.9910i	0.957522	−	1.65848i	0.728488	−	0.685059i	$-0.240224\pi$
$770$	1.04605	+	1.43828i	0.0376971	+	0.0518321i
$771$	−0.683314	+	0.242533i	−0.0246090	+	0.00873463i
$772$	−14.2456	+	14.2456i	−0.512711	+	0.512711i
$773$	34.1355	+	9.14659i	1.22777	+	0.328980i	0.813711	−	0.581270i	$-0.197444\pi$
$773$	34.1355	+	9.14659i	1.22777	+	0.328980i	0.414059	+	0.910250i	$0.364111\pi$
$774$	−25.6172	+	4.09555i	−0.920791	+	0.147212i
$775$	25.5960	−	23.0924i	0.919437	−	0.829502i
$776$	0.238933	−	0.137948i	0.00857720	−	0.00495205i
$777$	−0.830959	+	0.0660057i	−0.0298105	+	0.00236794i
$778$	−63.7347	+	17.0777i	−2.28500	+	0.612264i
$779$	27.6489			0.990626
$780$	12.3840	+	3.38142i	0.443420	+	0.121074i
$781$	−34.9573			−1.25087
$782$	59.7305	−	16.0047i	2.13596	−	0.572329i
$783$	20.0385	+	5.88817i	0.716118	+	0.210426i
$784$	30.2159	−	17.4452i	1.07914	−	0.623042i
$785$	−16.3519	+	6.28613i	−0.583625	+	0.224362i
$786$	36.1355	−	12.8258i	1.28891	−	0.457482i
$787$	18.5304	+	4.96521i	0.660539	+	0.176991i	0.573489	−	0.819213i	$-0.305590\pi$
$787$	18.5304	+	4.96521i	0.660539	+	0.176991i	0.0870495	+	0.996204i	$0.472256\pi$
$788$	−5.65154	+	5.65154i	−0.201328	+	0.201328i
$789$	−7.58100	−	21.3587i	−0.269891	−	0.760391i
$790$	18.2835	+	2.88661i	0.650496	+	0.102701i
$791$	0.448293	−	0.776465i	0.0159394	−	0.0276079i
$792$	−9.28803	−	20.7799i	−0.330036	−	0.738382i
$793$	1.06748	+	14.6834i	0.0379075	+	0.521424i
$794$	19.4024			0.688566
$795$	4.59589	+	9.60535i	0.162999	+	0.340667i
$796$	9.31025	−	16.1258i	0.329993	−	0.571565i
$797$	−15.1753	−	4.06620i	−0.537535	−	0.144032i	−0.0201695	−	0.999797i	$-0.506421\pi$
$797$	−15.1753	−	4.06620i	−0.537535	−	0.144032i	−0.517366	+	0.855764i	$0.673087\pi$
$798$	−2.19638	+	1.51188i	−0.0777509	+	0.0535200i
$799$	0.685047	+	1.18654i	0.0242352	+	0.0419766i
$800$	−21.5467	+	11.0053i	−0.761791	+	0.389095i
$801$	9.05919	+	3.46239i	0.320091	+	0.122338i
$802$	−13.7844	+	51.4442i	−0.486745	+	1.81656i
$803$	16.8875	−	4.52499i	0.595946	−	0.159683i
$804$	−3.05311	+	3.57999i	−0.107675	+	0.126257i
$805$	0.713390	−	1.60442i	0.0251437	−	0.0565484i
$806$	7.98939	−	41.7160i	0.281414	−	1.46938i
$807$	1.15168	−	0.792760i	0.0405410	−	0.0279065i
$808$	21.6457	−	5.79994i	0.761492	−	0.204041i
$809$	−9.50547	+	16.4640i	−0.334195	+	0.578842i	−0.983330	−	0.181831i	$-0.941798\pi$
$809$	−9.50547	+	16.4640i	−0.334195	+	0.578842i	0.649135	+	0.760673i	$0.275131\pi$
$810$	−5.49438	−	33.9430i	−0.193053	−	1.19264i
$811$		−	18.8816i		−	0.663023i	−0.943451	−	0.331512i	$-0.892441\pi$
$811$		−	18.8816i		−	0.663023i	0.943451	−	0.331512i	$-0.107559\pi$
$812$	0.108345	−	0.404349i	0.00380216	−	0.0141899i
$813$	−7.92978	+	16.6563i	−0.278109	+	0.584161i
$814$	−29.8242			−1.04534
$815$	21.3080	+	17.2375i	0.746386	+	0.603805i
$816$	34.3614	+	29.3042i	1.20289	+	1.02585i
$817$	−10.4182	−	38.8812i	−0.364486	−	1.36028i
$818$	−12.6307	−	12.6307i	−0.441623	−	0.441623i
$819$	−1.04193	−	0.644981i	−0.0364079	−	0.0225374i
$820$	6.52985	+	2.90343i	0.228032	+	0.101392i
$821$	0.931007	−	1.61255i	0.0324924	−	0.0562784i	−0.849322	−	0.527875i	$-0.822989\pi$
$821$	0.931007	−	1.61255i	0.0324924	−	0.0562784i	0.881814	+	0.471597i	$0.156322\pi$
$822$	−36.7583	+	2.91983i	−1.28209	+	0.101841i
$823$	−21.4397	−	5.74475i	−0.747341	−	0.200249i	−0.135003	−	0.990845i	$-0.543104\pi$
$823$	−21.4397	−	5.74475i	−0.747341	−	0.200249i	−0.612338	+	0.790596i	$0.709771\pi$
$824$		−	1.37961i		−	0.0480608i
$825$	−10.1649	−	34.1018i	−0.353895	−	1.18727i
$826$	−0.119947	+	0.0692515i	−0.00417349	+	0.00240957i
$827$	−5.90430	−	5.90430i	−0.205313	−	0.205313i	0.596959	−	0.802272i	$-0.296375\pi$
$827$	−5.90430	−	5.90430i	−0.205313	−	0.205313i	−0.802272	+	0.596959i	$0.796375\pi$
$828$	11.2138	−	15.4817i	0.389705	−	0.538026i
$829$	27.7895	+	16.0443i	0.965168	+	0.557240i	0.897760	−	0.440485i	$-0.145194\pi$
$829$	27.7895	+	16.0443i	0.965168	+	0.557240i	0.0674084	+	0.997725i	$0.478527\pi$
$830$	6.49714	+	8.93332i	0.225519	+	0.310080i
$831$	−48.6143	−	8.97358i	−1.68641	−	0.311290i
$832$	2.70197	−	5.57887i	0.0936739	−	0.193412i
$833$	−25.7974	−	25.7974i	−0.893829	−	0.893829i
$834$	8.62834	+	7.35846i	0.298775	+	0.254802i
$835$	−3.11101	+	19.7048i	−0.107661	+	0.681913i
$836$	−26.0175	+	15.0212i	−0.899833	+	0.519519i
$837$	−34.8176	+	8.43932i	−1.20347	+	0.291706i
$838$	9.65801	−	36.0442i	0.333630	−	1.24513i
$839$	6.21211	−	3.58656i	0.214466	−	0.123822i	−0.388919	−	0.921272i	$-0.627152\pi$
$839$	6.21211	−	3.58656i	0.214466	−	0.123822i	0.603385	+	0.797450i	$0.293818\pi$
$840$	0.796420	−	0.148612i	0.0274791	−	0.00512758i
$841$	6.42199	+	11.1232i	0.221448	+	0.383559i
$842$	4.99840	+	18.6543i	0.172256	+	0.642869i
$843$	1.84975	+	23.2868i	0.0637088	+	0.802042i
$844$		−	6.70663i		−	0.230852i
$845$	−28.1626	+	7.20177i	−0.968824	+	0.247748i
$846$	1.25636	+	0.480177i	0.0431946	+	0.0165088i
$847$	−0.172510	−	0.643817i	−0.00592752	−	0.0221218i
$848$	−13.2611	+	3.55330i	−0.455388	+	0.122021i
$849$	1.85963	−	0.660053i	0.0638225	−	0.0226530i
$850$	29.8803	+	33.1199i	1.02489	+	1.13600i
$851$	14.7228	+	25.5007i	0.504692	+	0.874152i
$852$	5.82303	−	12.2311i	0.199494	−	0.419031i
$853$	26.8806	+	26.8806i	0.920373	+	0.920373i	0.997056	−	0.0766825i	$-0.0244328\pi$
$853$	26.8806	+	26.8806i	0.920373	+	0.920373i	−0.0766825	+	0.997056i	$0.524433\pi$
$854$	−0.395181	−	0.684474i	−0.0135228	−	0.0234222i
$855$	51.5071	−	13.9087i	1.76151	−	0.475669i
$856$	2.64094	+	1.52474i	0.0902653	+	0.0521147i
$857$	−31.5042	+	31.5042i	−1.07616	+	1.07616i	−0.0793118	+	0.996850i	$0.525272\pi$
$857$	−31.5042	+	31.5042i	−1.07616	+	1.07616i	−0.996850	+	0.0793118i	$0.974728\pi$
$858$	−35.3344	−	25.9559i	−1.20630	−	0.886121i
$859$			29.9066i			1.02040i	0.860055	+	0.510201i	$0.170429\pi$
$859$			29.9066i			1.02040i	−0.860055	+	0.510201i	$0.829571\pi$
$860$	1.62248	−	10.2766i	0.0553261	−	0.350429i
$861$	−0.519033	−	0.442644i	−0.0176886	−	0.0150853i
$862$	−1.20272	+	4.48861i	−0.0409648	+	0.152883i
$863$	−9.69182	+	9.69182i	−0.329913	+	0.329913i	−0.852553	−	0.522640i	$-0.824947\pi$
$863$	−9.69182	+	9.69182i	−0.329913	+	0.329913i	0.522640	+	0.852553i	$0.324947\pi$
$864$	25.1365	+	0.603367i	0.855161	+	0.0205270i
$865$	15.2945	+	12.3728i	0.520027	+	0.420687i
$866$	−24.2113			−0.822732
$867$	7.64148	−	16.0507i	0.259518	−	0.545111i
$868$	0.185847	+	0.693590i	0.00630806	+	0.0235420i
$869$	−17.2402	−	9.95361i	−0.584832	−	0.337653i
$870$	−15.0387	+	21.9386i	−0.509859	+	0.743789i
$871$	2.00405	−	10.4640i	0.0679045	−	0.354558i
$872$	−0.834142	+	0.834142i	−0.0282476	+	0.0282476i
$873$	−0.445866	−	0.0462071i	−0.0150903	−	0.00156387i
$874$	81.5712	+	47.0952i	2.75919	+	1.59302i
$875$	1.26477	−	0.0681529i	0.0427570	−	0.00230399i
$876$	−1.22981	+	6.66246i	−0.0415513	+	0.225104i
$877$	−34.0942	−	9.13551i	−1.15128	−	0.308484i	−0.367801	−	0.929904i	$-0.619889\pi$
$877$	−34.0942	−	9.13551i	−1.15128	−	0.308484i	−0.783478	+	0.621420i	$0.786556\pi$
$878$	15.4388	+	4.13681i	0.521033	+	0.139610i
$879$	2.37315	−	12.8565i	0.0800445	−	0.433640i
$880$	45.6259	−	4.81814i	1.53805	−	0.162419i
$881$	−0.0237715	−	0.0137245i	−0.000800881	−	0.000462389i	0.499600	−	0.866257i	$-0.333481\pi$
$881$	−0.0237715	−	0.0137245i	−0.000800881	−	0.000462389i	−0.500400	+	0.865794i	$0.666814\pi$
$882$	−35.6240	−	3.69187i	−1.19952	−	0.124312i
$883$	−12.5285	+	12.5285i	−0.421617	+	0.421617i	−0.885760	−	0.464143i	$-0.846362\pi$
$883$	−12.5285	+	12.5285i	−0.421617	+	0.421617i	0.464143	+	0.885760i	$0.346362\pi$
$884$	16.9981	+	3.25545i	0.571707	+	0.109492i
$885$	2.72425	−	0.508343i	0.0915747	−	0.0170878i
$886$	−12.0157	−	6.93725i	−0.403674	−	0.233061i
$887$	0.784839	+	2.92906i	0.0263523	+	0.0983482i	0.977849	−	0.209309i	$-0.0671216\pi$
$887$	0.784839	+	2.92906i	0.0263523	+	0.0983482i	−0.951497	+	0.307658i	$0.900455\pi$
$888$	−5.84015	+	12.2671i	−0.195983	+	0.411656i
$889$	1.44303			0.0483976
$890$	−7.76796	+	9.60228i	−0.260383	+	0.321869i
$891$	−7.58347	+	36.1946i	−0.254056	+	1.21257i
$892$	−7.89315	+	7.89315i	−0.264282	+	0.264282i
$893$	−0.540132	+	2.01580i	−0.0180748	+	0.0674562i
$894$	26.7891	+	22.8464i	0.895961	+	0.764097i
$895$	26.1800	+	35.9965i	0.875100	+	1.20323i
$896$			1.42917i			0.0477451i
$897$	−4.75024	+	43.0253i	−0.158606	+	1.43657i
$898$	32.7688	−	32.7688i	1.09351	−	1.09351i
$899$	24.0000	+	13.8564i	0.800446	+	0.462138i
$900$	13.6250	+	2.12397i	0.454167	+	0.0707991i
$901$	7.17782	+	12.4324i	0.239128	+	0.414182i
$902$	−17.2580	−	17.2580i	−0.574627	−	0.574627i
$903$	−0.426893	+	0.896678i	−0.0142061	+	0.0298396i
$904$	−7.30666	−	12.6555i	−0.243016	−	0.420916i
$905$	−6.76901	+	15.2236i	−0.225010	+	0.506049i
$906$	−30.9607	+	10.9891i	−1.02860	+	0.365089i
$907$	−16.8138	+	4.50525i	−0.558294	+	0.149594i	−0.526922	−	0.849913i	$-0.676654\pi$
$907$	−16.8138	+	4.50525i	−0.558294	+	0.149594i	−0.0313715	+	0.999508i	$0.509988\pi$
$908$	−3.29956	−	12.3141i	−0.109500	−	0.408659i
$909$	−34.0094	−	12.9983i	−1.12802	−	0.431126i
$910$	1.19220	−	1.00699i	0.0395209	−	0.0333815i
$911$		−	4.78351i		−	0.158485i	−0.996855	−	0.0792423i	$-0.974750\pi$
$911$		−	4.78351i		−	0.158485i	0.996855	−	0.0792423i	$-0.0252501\pi$
$912$	5.44685	+	68.5714i	0.180363	+	2.27063i
$913$	−3.07477	−	11.4752i	−0.101760	−	0.379774i
$914$	−11.4241	−	19.7871i	−0.377876	−	0.654500i
$915$	2.90084	+	15.5458i	0.0958989	+	0.513930i
$916$	−6.78234	+	3.91578i	−0.224095	+	0.129381i
$917$	0.379911	−	1.41785i	0.0125458	−	0.0468214i
$918$	−10.9200	−	45.0521i	−0.360415	−	1.48694i
$919$	20.5581	−	11.8693i	0.678151	−	0.391530i	−0.121007	−	0.992652i	$-0.538612\pi$
$919$	20.5581	−	11.8693i	0.678151	−	0.391530i	0.799158	+	0.601121i	$0.205279\pi$
$920$	−16.8330	−	23.1448i	−0.554969	−	0.763060i
$921$	9.84626	+	8.39713i	0.324445	+	0.276695i
$922$	41.4418	+	41.4418i	1.36481	+	1.36481i
$923$	2.22417	+	30.5938i	0.0732094	+	1.00701i
$924$	0.728888	+	0.134543i	0.0239787	+	0.00442616i
$925$	−11.5510	+	17.8253i	−0.379795	+	0.586092i
$926$	40.6683	+	23.4798i	1.33644	+	0.771595i
$927$	−1.31487	+	1.81530i	−0.0431859	+	0.0596223i
$928$	−13.7531	−	13.7531i	−0.451467	−	0.451467i
$929$	−27.3742	+	15.8045i	−0.898117	+	0.518528i	−0.876589	−	0.481240i	$-0.840186\pi$
$929$	−27.3742	+	15.8045i	−0.898117	+	0.518528i	−0.0215282	+	0.999768i	$0.506853\pi$
$930$	3.52425	−	45.4883i	0.115565	−	1.49162i
$931$		−	55.5706i		−	1.82125i
$932$	−10.8156	−	2.89804i	−0.354277	−	0.0949283i
$933$	−4.10256	+	0.325879i	−0.134312	+	0.0106688i
$934$	−23.7216	+	41.0870i	−0.776194	+	1.34441i
$935$	−17.2144	−	44.7792i	−0.562970	−	1.46444i
$936$	−17.5952	+	9.45081i	−0.575116	+	0.308909i
$937$	−12.6526	−	12.6526i	−0.413344	−	0.413344i	0.469558	−	0.882902i	$-0.344413\pi$
$937$	−12.6526	−	12.6526i	−0.413344	−	0.413344i	−0.882902	+	0.469558i	$0.844413\pi$
$938$	0.148037	+	0.552480i	0.00483357	+	0.0180391i
$939$	−38.2256	−	32.5997i	−1.24744	−	1.06385i
$940$	−0.339244	+	0.419353i	−0.0110649	+	0.0136778i
$941$	49.4334			1.61148			0.805741	−	0.592268i	$-0.201767\pi$
$941$	49.4334			1.61148			0.805741	+	0.592268i	$0.201767\pi$
$942$	−9.96635	+	20.9340i	−0.324721	+	0.682068i
$943$	−6.23666	+	23.2755i	−0.203094	+	0.757956i
$944$			3.57304i			0.116293i
$945$	−1.18958	−	0.563502i	−0.0386969	−	0.0183307i
$946$	−17.7661	+	30.7718i	−0.577625	+	1.00048i
$947$	23.6300	−	6.33163i	0.767871	−	0.205750i	0.146440	−	0.989220i	$-0.453218\pi$
$947$	23.6300	−	6.33163i	0.767871	−	0.205750i	0.621431	+	0.783469i	$0.286552\pi$
$948$	6.35443	−	4.37408i	0.206382	−	0.142064i
$949$	−5.03464	−	14.4916i	−0.163431	−	0.470419i
$950$	−3.48927	+	67.8548i	−0.113207	+	2.20150i
$951$	37.9953	−	44.5524i	1.23208	−	1.44471i
$952$	1.05503	−	0.282693i	0.0341936	−	0.00916215i
$953$	−11.1821	+	41.7321i	−0.362223	+	1.35184i	0.508923	+	0.860812i	$0.330044\pi$
$953$	−11.1821	+	41.7321i	−0.362223	+	1.35184i	−0.871146	+	0.491024i	$0.836623\pi$
$954$	13.1640	+	5.03122i	0.426199	+	0.162892i
$955$	−5.38987	−	51.0400i	−0.174412	−	1.65162i
$956$	5.31043	+	9.19793i	0.171751	+	0.297482i
$957$	23.5632	−	16.2198i	0.761691	−	0.524312i
$958$	−2.84255	−	0.761659i	−0.0918386	−	0.0246081i
$959$	−0.705791	+	1.22247i	−0.0227912	+	0.0394755i
$960$	2.21501	−	6.27930i	0.0714892	−	0.202663i
$961$	−16.5366			−0.533437
$962$	1.89758	+	26.1015i	0.0611803	+	0.841546i
$963$	−2.02178	−	4.52328i	−0.0651510	−	0.145761i
$964$	6.41870	−	11.1175i	0.206732	−	0.358071i
$965$	7.64197	−	48.4034i	0.246004	−	1.55816i
$966$	−0.777310	−	2.18999i	−0.0250095	−	0.0704619i
$967$	−4.55251	+	4.55251i	−0.146399	+	0.146399i	−0.776507	−	0.630108i	$-0.783010\pi$
$967$	−4.55251	+	4.55251i	−0.146399	+	0.146399i	0.630108	+	0.776507i	$0.283010\pi$
$968$	−10.4935	−	2.81172i	−0.337273	−	0.0903721i
$969$	67.7845	−	24.0592i	2.17755	−	0.772893i
$970$	0.231932	−	0.521618i	0.00744690	−	0.0167482i
$971$	−51.2257	+	29.5752i	−1.64391	+	0.949113i	−0.664488	+	0.747299i	$0.731350\pi$
$971$	−51.2257	+	29.5752i	−1.64391	+	0.949113i	−0.979424	+	0.201814i	$0.935316\pi$
$972$	−11.4008	−	8.68250i	−0.365681	−	0.278491i
$973$	0.419316	−	0.112355i	0.0134427	−	0.00360195i
$974$	35.5697			1.13973
$975$	−29.1984	+	11.0658i	−0.935098	+	0.354389i
$976$	−20.3894			−0.652649
$977$	−55.9598	+	14.9944i	−1.79031	+	0.479713i	−0.992399	−	0.123059i	$-0.960730\pi$
$977$	−55.9598	+	14.9944i	−1.79031	+	0.479713i	−0.797914	+	0.602772i	$0.794063\pi$
$978$	36.1590	−	2.87223i	1.15624	−	0.0918437i
$979$	11.5036	−	6.64164i	0.367658	−	0.212268i
$980$	5.83552	−	13.1241i	0.186409	−	0.419235i
$981$	1.89257	−	0.302576i	0.0604252	−	0.00966050i
$982$	−37.2966	−	9.99359i	−1.19018	−	0.318908i
$983$	17.2893	−	17.2893i	0.551443	−	0.551443i	−0.375414	−	0.926857i	$-0.622500\pi$
$983$	17.2893	−	17.2893i	0.551443	−	0.551443i	0.926857	+	0.375414i	$0.122500\pi$
$984$	−10.4778	+	3.71898i	−0.334022	+	0.118557i
$985$	3.03173	−	19.2026i	0.0965990	−	0.611847i
$986$	−17.9295	+	31.0548i	−0.570991	+	0.988985i
$987$	0.0424114	−	0.0291940i	0.00134997	−	0.000929254i
$988$	14.8016	+	21.8142i	0.470901	+	0.694002i
$989$	35.0811			1.11551
$990$	−40.8314	−	23.4682i	−1.29771	−	0.745869i
$991$	6.95908	−	12.0535i	0.221063	−	0.382892i	−0.734068	−	0.679076i	$-0.762381\pi$
$991$	6.95908	−	12.0535i	0.221063	−	0.382892i	0.955131	+	0.296184i	$0.0957142\pi$
$992$	32.2259	+	8.63491i	1.02317	+	0.274159i
$993$	−13.6952	−	19.8956i	−0.434602	−	0.631367i
$994$	−0.823384	−	1.42614i	−0.0261162	−	0.0452345i
$995$	4.75638	+	45.0411i	0.150787	+	1.42790i
$996$	4.52721	+	0.835664i	0.143450	+	0.0264790i
$997$	−12.5004	+	46.6520i	−0.395891	+	1.47748i	0.424367	+	0.905490i	$0.360497\pi$
$997$	−12.5004	+	46.6520i	−0.395891	+	1.47748i	−0.820258	+	0.571994i	$0.806170\pi$
$998$	−59.2202	+	15.8680i	−1.87458	+	0.502293i
$999$	19.3760	−	10.5751i	0.613029	−	0.334581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.bf.a.17.6	✓	96
3.2	odd	2	inner	195.2.bf.a.17.19	yes	96
5.2	odd	4		975.2.bn.d.368.6		96
5.3	odd	4	inner	195.2.bf.a.173.19	yes	96
5.4	even	2		975.2.bn.d.407.19		96
13.10	even	6	inner	195.2.bf.a.62.6	yes	96
15.2	even	4		975.2.bn.d.368.19		96
15.8	even	4	inner	195.2.bf.a.173.6	yes	96
15.14	odd	2		975.2.bn.d.407.6		96
39.23	odd	6	inner	195.2.bf.a.62.19	yes	96
65.23	odd	12	inner	195.2.bf.a.23.19	yes	96
65.49	even	6		975.2.bn.d.257.19		96
65.62	odd	12		975.2.bn.d.218.6		96
195.23	even	12	inner	195.2.bf.a.23.6	yes	96
195.62	even	12		975.2.bn.d.218.19		96
195.179	odd	6		975.2.bn.d.257.6		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.6	✓	96	1.1	even	1	trivial
195.2.bf.a.17.19	yes	96	3.2	odd	2	inner
195.2.bf.a.23.6	yes	96	195.23	even	12	inner
195.2.bf.a.23.19	yes	96	65.23	odd	12	inner
195.2.bf.a.62.6	yes	96	13.10	even	6	inner
195.2.bf.a.62.19	yes	96	39.23	odd	6	inner
195.2.bf.a.173.6	yes	96	15.8	even	4	inner
195.2.bf.a.173.19	yes	96	5.3	odd	4	inner
975.2.bn.d.218.6		96	65.62	odd	12
975.2.bn.d.218.19		96	195.62	even	12
975.2.bn.d.257.6		96	195.179	odd	6
975.2.bn.d.257.19		96	65.49	even	6
975.2.bn.d.368.6		96	5.2	odd	4
975.2.bn.d.368.19		96	15.2	even	4
975.2.bn.d.407.6		96	15.14	odd	2
975.2.bn.d.407.19		96	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65038 + 0.442218i) q^{2} +(-0.137150 - 1.72661i) q^{3} +(0.796141 - 0.459652i) q^{4} +(-0.908487 + 2.04320i) q^{5} +(0.989888 + 2.78891i) q^{6} +(0.109428 + 0.0293212i) q^{7} +(1.30565 - 1.30565i) q^{8} +(-2.96238 + 0.473611i) q^{9} +(0.595810 - 3.77380i) q^{10} +(-2.05447 + 3.55845i) q^{11} +(-0.902832 - 1.31159i) q^{12} +(3.24500 + 1.57162i) q^{13} -0.193564 q^{14} +(3.65241 + 1.28838i) q^{15} +(-2.49674 + 4.32449i) q^{16} +(5.04353 + 1.35141i) q^{17} +(4.67961 - 2.09165i) q^{18} +(3.97662 + 6.88771i) q^{19} +(0.215876 + 2.04426i) q^{20} +(0.0356182 - 0.192962i) q^{21} +(1.81705 - 6.78132i) q^{22} +(-6.69524 + 1.79398i) q^{23} +(-2.43343 - 2.07529i) q^{24} +(-3.34930 - 3.71244i) q^{25} +(-6.05047 - 1.15878i) q^{26} +(1.22403 + 5.04992i) q^{27} +(0.100598 - 0.0269551i) q^{28} +(2.00973 - 3.48095i) q^{29} +(-6.59760 - 0.511156i) q^{30} +6.89468i q^{31} +(1.25240 - 4.67403i) q^{32} +(6.42584 + 3.05924i) q^{33} -8.92135 q^{34} +(-0.159323 + 0.196946i) q^{35} +(-2.14078 + 1.73873i) q^{36} +(-1.09950 - 4.10339i) q^{37} +(-9.60880 - 9.60880i) q^{38} +(2.26853 - 5.81840i) q^{39} +(1.48154 + 3.85388i) q^{40} +(1.73822 - 3.01068i) q^{41} +(0.0265474 + 0.334211i) q^{42} +(-4.88872 - 1.30993i) q^{43} +3.77737i q^{44} +(1.72360 - 6.48299i) q^{45} +(10.2563 - 5.92150i) q^{46} +(0.185543 + 0.185543i) q^{47} +(7.80914 + 3.71780i) q^{48} +(-6.05106 - 3.49358i) q^{49} +(7.16932 + 4.64580i) q^{50} +(1.64164 - 8.89356i) q^{51} +(3.30587 - 0.240337i) q^{52} +(1.94409 + 1.94409i) q^{53} +(-4.25328 - 7.79300i) q^{54} +(-5.40416 - 7.43050i) q^{55} +(0.181159 - 0.104592i) q^{56} +(11.3470 - 7.81074i) q^{57} +(-1.77747 + 6.63362i) q^{58} +(0.619675 - 0.357770i) q^{59} +(3.50004 - 0.653105i) q^{60} +(2.04160 + 3.53616i) q^{61} +(-3.04895 - 11.3788i) q^{62} +(-0.338055 - 0.0350341i) q^{63} -1.71922i q^{64} +(-6.15917 + 5.20237i) q^{65} +(-11.9579 - 2.20728i) q^{66} +(-0.764792 - 2.85424i) q^{67} +(4.63654 - 1.24236i) q^{68} +(4.01577 + 11.3140i) q^{69} +(0.175851 - 0.395490i) q^{70} +(4.25380 + 7.36780i) q^{71} +(-3.24947 + 4.48621i) q^{72} +(-3.00868 - 3.00868i) q^{73} +(3.62918 + 6.28592i) q^{74} +(-5.95058 + 6.29211i) q^{75} +(6.33191 + 3.65573i) q^{76} +(-0.329156 + 0.329156i) q^{77} +(-1.17093 + 10.6057i) q^{78} +4.84485i q^{79} +(-6.56752 - 9.03008i) q^{80} +(8.55139 - 2.80603i) q^{81} +(-1.53734 + 5.73743i) q^{82} +(-2.04442 + 2.04442i) q^{83} +(-0.0603381 - 0.169997i) q^{84} +(-7.34318 + 9.07718i) q^{85} +8.64751 q^{86} +(-6.28589 - 2.99261i) q^{87} +(1.96368 + 7.32854i) q^{88} +(-2.79966 - 1.61638i) q^{89} +(0.0222950 + 11.4616i) q^{90} +(0.309013 + 0.267127i) q^{91} +(-4.50574 + 4.50574i) q^{92} +(11.9044 - 0.945607i) q^{93} +(-0.388267 - 0.224166i) q^{94} +(-17.6857 + 1.86762i) q^{95} +(-8.24201 - 1.52137i) q^{96} +(0.144327 + 0.0386722i) q^{97} +(11.5315 + 3.08985i) q^{98} +(4.40081 - 11.5145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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