LMFDB - Embedded newform 195.2.bf.a.62.19

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			62.19
Character	$\chi$	$=$	195.62
Dual form			195.2.bf.a.173.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.442218 - 1.65038i) q^{2} +(1.72661 + 0.137150i) q^{3} +(-0.796141 - 0.459652i) q^{4} +(-0.908487 + 2.04320i) q^{5} +(0.989888 - 2.78891i) q^{6} +(0.0293212 + 0.109428i) q^{7} +(1.30565 - 1.30565i) q^{8} +(2.96238 + 0.473611i) q^{9} +(2.97030 + 2.40288i) q^{10} +(-2.05447 - 3.55845i) q^{11} +(-1.31159 - 0.902832i) q^{12} +(-1.57162 - 3.24500i) q^{13} +0.193564 q^{14} +(-1.84883 + 3.40321i) q^{15} +(-2.49674 - 4.32449i) q^{16} +(1.35141 + 5.04353i) q^{17} +(2.09165 - 4.67961i) q^{18} +(-3.97662 + 6.88771i) q^{19} +(1.66244 - 1.20908i) q^{20} +(0.0356182 + 0.192962i) q^{21} +(-6.78132 + 1.81705i) q^{22} +(-1.79398 + 6.69524i) q^{23} +(2.43343 - 2.07529i) q^{24} +(-3.34930 - 3.71244i) q^{25} +(-6.05047 + 1.15878i) q^{26} +(5.04992 + 1.22403i) q^{27} +(0.0269551 - 0.100598i) q^{28} +(-2.00973 - 3.48095i) q^{29} +(4.79900 + 4.55623i) q^{30} -6.89468i q^{31} +(-4.67403 + 1.25240i) q^{32} +(-3.05924 - 6.42584i) q^{33} +8.92135 q^{34} +(-0.250221 - 0.0395052i) q^{35} +(-2.14078 - 1.73873i) q^{36} +(-4.10339 - 1.09950i) 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} +(0.334211 + 0.0265474i) q^{42} +(1.30993 + 4.88872i) q^{43} +3.77737i q^{44} +(-3.65896 + 5.62245i) q^{45} +(10.2563 + 5.92150i) q^{46} +(0.185543 + 0.185543i) q^{47} +(-3.71780 - 7.80914i) q^{48} +(6.05106 - 3.49358i) q^{49} +(-7.60804 + 3.88591i) q^{50} +(1.64164 + 8.89356i) q^{51} +(-0.240337 + 3.30587i) q^{52} +(-1.94409 - 1.94409i) q^{53} +(4.25328 - 7.79300i) q^{54} +(9.13708 - 0.964884i) q^{55} +(0.181159 + 0.104592i) q^{56} +(-7.81074 + 11.3470i) q^{57} +(-6.63362 + 1.77747i) q^{58} +(-0.619675 - 0.357770i) q^{59} +(3.03622 - 1.85961i) q^{60} +(2.04160 - 3.53616i) q^{61} +(-11.3788 - 3.04895i) q^{62} +(0.0350341 + 0.338055i) q^{63} -1.71922i q^{64} +(8.05796 - 0.263096i) q^{65} +(-11.9579 + 2.20728i) q^{66} +(-2.85424 - 0.764792i) q^{67} +(1.24236 - 4.63654i) q^{68} +(-4.01577 + 11.3140i) q^{69} +(-0.175851 + 0.395490i) q^{70} +(4.25380 - 7.36780i) q^{71} +(4.48621 - 3.24947i) q^{72} +(3.00868 + 3.00868i) q^{73} +(-3.62918 + 6.28592i) q^{74} +(-5.27378 - 6.86929i) q^{75} +(6.33191 - 3.65573i) q^{76} +(0.329156 - 0.329156i) q^{77} +(-10.6057 + 1.17093i) q^{78} +4.84485i q^{79} +(11.1040 - 1.17260i) q^{80} +(8.55139 + 2.80603i) q^{81} +(5.73743 - 1.53734i) q^{82} +(-2.04442 + 2.04442i) q^{83} +(0.0603381 - 0.169997i) q^{84} +(-11.5327 - 1.82079i) q^{85} +8.64751 q^{86} +(-2.99261 - 6.28589i) q^{87} +(-7.32854 - 1.96368i) q^{88} +(2.79966 - 1.61638i) q^{89} +(7.66112 + 8.52502i) q^{90} +(0.309013 - 0.267127i) q^{91} +(4.50574 - 4.50574i) q^{92} +(0.945607 - 11.9044i) q^{93} +(0.388267 - 0.224166i) q^{94} +(-10.4602 - 14.3824i) q^{95} +(-8.24201 + 1.52137i) q^{96} +(0.0386722 + 0.144327i) q^{97} +(-3.08985 - 11.5315i) 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 $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.442218	−	1.65038i	0.312695	−	1.16699i	−0.613421	−	0.789756i	$-0.710207\pi$
$2$	0.442218	−	1.65038i	0.312695	−	1.16699i	0.926116	−	0.377238i	$-0.123126\pi$
$3$	1.72661	+	0.137150i	0.996860	+	0.0791838i
$3$	1.72661	+	0.137150i	0.996860	+	0.0791838i
$4$	−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
$7$	0.0293212	+	0.109428i	0.0110824	+	0.0413600i	0.971246	−	0.238080i	$-0.0765180\pi$
$7$	0.0293212	+	0.109428i	0.0110824	+	0.0413600i	−0.960163	+	0.279440i	$0.909851\pi$
$8$	1.30565	−	1.30565i	0.461618	−	0.461618i
$9$	2.96238	+	0.473611i	0.987460	+	0.157870i
$10$	2.97030	+	2.40288i	0.939291	+	0.759859i
$11$	−2.05447	−	3.55845i	−0.619447	−	1.07291i	−0.989587	−	0.143938i	$-0.954023\pi$
$11$	−2.05447	−	3.55845i	−0.619447	−	1.07291i	0.370139	−	0.928976i	$-0.379310\pi$
$12$	−1.31159	−	0.902832i	−0.378622	−	0.260625i
$13$	−1.57162	−	3.24500i	−0.435890	−	0.900000i
$13$	−1.57162	−	3.24500i	−0.435890	−	0.900000i
$14$	0.193564			0.0517323
$15$	−1.84883	+	3.40321i	−0.477366	+	0.878705i
$16$	−2.49674	−	4.32449i	−0.624186	−	1.08112i
$17$	1.35141	+	5.04353i	0.327765	+	1.22324i	0.911503	+	0.411293i	$0.134923\pi$
$17$	1.35141	+	5.04353i	0.327765	+	1.22324i	−0.583738	+	0.811942i	$0.698411\pi$
$18$	2.09165	−	4.67961i	0.493007	−	1.10299i
$19$	−3.97662	+	6.88771i	−0.912300	+	1.58015i	−0.101493	+	0.994836i	$0.532362\pi$
$19$	−3.97662	+	6.88771i	−0.912300	+	1.58015i	−0.810807	+	0.585313i	$0.800971\pi$
$20$	1.66244	−	1.20908i	0.371734	−	0.270359i
$21$	0.0356182	+	0.192962i	0.00777254	+	0.0421077i
$22$	−6.78132	+	1.81705i	−1.44578	+	0.387396i
$23$	−1.79398	+	6.69524i	−0.374071	+	1.39605i	0.480625	+	0.876926i	$0.340410\pi$
$23$	−1.79398	+	6.69524i	−0.374071	+	1.39605i	−0.854697	+	0.519127i	$0.826257\pi$
$24$	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
$27$	5.04992	+	1.22403i	0.971858	+	0.235565i
$28$	0.0269551	−	0.100598i	0.00509404	−	0.0190112i
$29$	−2.00973	−	3.48095i	−0.373197	−	0.646396i	0.616858	−	0.787074i	$-0.288405\pi$
$29$	−2.00973	−	3.48095i	−0.373197	−	0.646396i	−0.990055	+	0.140678i	$0.955072\pi$
$30$	4.79900	+	4.55623i	0.876173	+	0.831850i
$31$		−	6.89468i		−	1.23832i	−0.785265	−	0.619160i	$-0.787473\pi$
$31$		−	6.89468i		−	1.23832i	0.785265	−	0.619160i	$-0.212527\pi$
$32$	−4.67403	+	1.25240i	−0.826260	+	0.221396i
$33$	−3.05924	−	6.42584i	−0.532545	−	1.11860i
$34$	8.92135			1.53000
$35$	−0.250221	−	0.0395052i	−0.0422951	−	0.00667760i
$36$	−2.14078	−	1.73873i	−0.356796	−	0.289788i
$37$	−4.10339	−	1.09950i	−0.674593	−	0.180757i	−0.0947700	−	0.995499i	$-0.530212\pi$
$37$	−4.10339	−	1.09950i	−0.674593	−	0.180757i	−0.579823	+	0.814743i	$0.696878\pi$
$38$	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	0.969237	−	0.246130i	$-0.0791589\pi$
$41$	1.73822	+	3.01068i	0.271464	+	0.470189i	−0.697773	+	0.716319i	$0.745826\pi$
$42$	0.334211	+	0.0265474i	0.0515698	+	0.00409636i
$43$	1.30993	+	4.88872i	0.199762	+	0.745523i	0.990982	+	0.133991i	$0.0427794\pi$
$43$	1.30993	+	4.88872i	0.199762	+	0.745523i	−0.791220	+	0.611531i	$0.790554\pi$
$44$			3.77737i			0.569461i
$45$	−3.65896	+	5.62245i	−0.545446	+	0.838146i
$46$	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	$0.743908\pi$
$48$	−3.71780	−	7.80914i	−0.536619	−	1.12715i
$49$	6.05106	−	3.49358i	0.864438	−	0.499083i
$50$	−7.60804	+	3.88591i	−1.07594	+	0.549551i
$51$	1.64164	+	8.89356i	0.229875	+	1.24535i
$52$	−0.240337	+	3.30587i	−0.0333287	+	0.458442i
$53$	−1.94409	−	1.94409i	−0.267042	−	0.267042i	0.560865	−	0.827907i	$-0.310469\pi$
$53$	−1.94409	−	1.94409i	−0.267042	−	0.267042i	−0.827907	+	0.560865i	$0.810469\pi$
$54$	4.25328	−	7.79300i	0.578799	−	1.06049i
$55$	9.13708	−	0.964884i	1.23204	−	0.130105i
$56$	0.181159	+	0.104592i	0.0242084	+	0.0139767i
$57$	−7.81074	+	11.3470i	−1.03456	+	1.50295i
$58$	−6.63362	+	1.77747i	−0.871037	+	0.233394i
$59$	−0.619675	−	0.357770i	−0.0806749	−	0.0465777i	0.459120	−	0.888374i	$-0.348165\pi$
$59$	−0.619675	−	0.357770i	−0.0806749	−	0.0465777i	−0.539795	+	0.841797i	$0.681498\pi$
$60$	3.03622	−	1.85961i	0.391975	−	0.240075i
$61$	2.04160	−	3.53616i	0.261400	−	0.452758i	−0.705214	−	0.708994i	$-0.749149\pi$
$61$	2.04160	−	3.53616i	0.261400	−	0.452758i	0.966614	+	0.256236i	$0.0824825\pi$
$62$	−11.3788	−	3.04895i	−1.44511	−	0.387217i
$63$	0.0350341	+	0.338055i	0.00441389	+	0.0425909i
$64$		−	1.71922i		−	0.214903i
$65$	8.05796	−	0.263096i	0.999467	−	0.0326330i
$66$	−11.9579	+	2.20728i	−1.47192	+	0.271697i
$67$	−2.85424	−	0.764792i	−0.348701	−	0.0934343i	0.0802172	−	0.996777i	$-0.474439\pi$
$67$	−2.85424	−	0.764792i	−0.348701	−	0.0934343i	−0.428919	+	0.903343i	$0.641105\pi$
$68$	1.24236	−	4.63654i	0.150658	−	0.562263i
$69$	−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	−0.495151	−	0.868807i	$-0.664887\pi$
$71$	4.25380	−	7.36780i	0.504833	−	0.874397i	0.999984	−	0.00558990i	$-0.00177933\pi$
$72$	4.48621	−	3.24947i	0.528705	−	0.382954i
$73$	3.00868	+	3.00868i	0.352139	+	0.352139i	0.860905	−	0.508766i	$-0.169898\pi$
$73$	3.00868	+	3.00868i	0.352139	+	0.352139i	−0.508766	+	0.860905i	$0.669898\pi$
$74$	−3.62918	+	6.28592i	−0.421884	+	0.730724i
$75$	−5.27378	−	6.86929i	−0.608964	−	0.793198i
$76$	6.33191	−	3.65573i	0.726319	−	0.419341i
$77$	0.329156	−	0.329156i	0.0375108	−	0.0375108i
$78$	−10.6057	+	1.17093i	−1.20086	+	0.132582i
$79$			4.84485i			0.545088i	0.962143	+	0.272544i	$0.0878650\pi$
$79$			4.84485i			0.545088i	−0.962143	+	0.272544i	$0.912135\pi$
$80$	11.1040	−	1.17260i	1.24147	−	0.131100i
$81$	8.55139	+	2.80603i	0.950154	+	0.311781i
$82$	5.73743	−	1.53734i	0.633593	−	0.169771i
$83$	−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
$85$	−11.5327	−	1.82079i	−1.25089	−	0.197492i
$86$	8.64751			0.932485
$87$	−2.99261	−	6.28589i	−0.320841	−	0.673918i
$88$	−7.32854	−	1.96368i	−0.781225	−	0.209329i
$89$	2.79966	−	1.61638i	0.296763	−	0.171336i	−0.344225	−	0.938887i	$-0.611858\pi$
$89$	2.79966	−	1.61638i	0.296763	−	0.171336i	0.640988	+	0.767551i	$0.278525\pi$
$90$	7.66112	+	8.52502i	0.807553	+	0.898616i
$91$	0.309013	−	0.267127i	0.0323933	−	0.0280025i
$92$	4.50574	−	4.50574i	0.469756	−	0.469756i
$93$	0.945607	−	11.9044i	0.0980549	−	1.23443i
$94$	0.388267	−	0.224166i	0.0400466	−	0.0231209i
$95$	−10.4602	−	14.3824i	−1.07320	−	1.47561i
$96$	−8.24201	+	1.52137i	−0.841196	+	0.155274i
$97$	0.0386722	+	0.144327i	0.00392657	+	0.0146542i	0.967861	−	0.251485i	$-0.0809188\pi$
$97$	0.0386722	+	0.144327i	0.00392657	+	0.0146542i	−0.963935	+	0.266139i	$0.914252\pi$
$98$	−3.08985	−	11.5315i	−0.312122	−	1.16485i
$99$	−4.40081	−	11.5145i	−0.442298	−	1.15725i
$100$	0.960088	+	4.49514i	0.0960088	+	0.449514i
$101$	10.5103	−	6.06812i	1.04581	−	0.603800i	0.124339	−	0.992240i	$-0.460319\pi$
$101$	10.5103	−	6.06812i	1.04581	−	0.603800i	0.921474	+	0.388440i	$0.126986\pi$
$102$	15.4037	+	1.22357i	1.52519	+	0.121151i
$103$	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
$105$	−0.426617	−	0.102528i	−0.0416336	−	0.0100057i
$106$	−4.06820	+	2.34878i	−0.395139	+	0.228133i
$107$	1.59525	+	0.427445i	0.154218	+	0.0413227i	0.335102	−	0.942182i	$-0.391229\pi$
$107$	1.59525	+	0.427445i	0.154218	+	0.0413227i	−0.180884	+	0.983504i	$0.557896\pi$
$108$	−3.45782	−	3.29571i	−0.332729	−	0.317130i
$109$	0.638870			0.0611926			0.0305963	−	0.999532i	$-0.490259\pi$
$109$	0.638870			0.0611926			0.0305963	+	0.999532i	$0.490259\pi$
$110$	2.44815	−	15.5063i	0.233422	−	1.47847i
$111$	−6.93416	−	2.46119i	−0.658162	−	0.233606i
$112$	0.400014	−	0.400014i	0.0377977	−	0.0377977i
$113$	7.64451	−	2.04834i	0.719135	−	0.192692i	0.119349	−	0.992852i	$-0.461919\pi$
$113$	7.64451	−	2.04834i	0.719135	−	0.192692i	0.599786	+	0.800161i	$0.295253\pi$
$114$	15.2728	+	17.9085i	1.43043	+	1.67729i
$115$	−12.0499	−	9.74800i	−1.12366	−	0.909005i
$116$			3.69510i			0.343082i
$117$	−3.11888	−	10.3572i	−0.288340	−	0.957528i
$118$	−0.864487	+	0.864487i	−0.0795825	+	0.0795825i
$119$	−0.512280	+	0.295765i	−0.0469606	+	0.0271127i
$120$	2.02948	+	6.85734i	0.185265	+	0.625987i
$121$	−2.94173	+	5.09522i	−0.267430	+	0.463202i
$122$	−4.93316	−	4.93316i	−0.446628	−	0.446628i
$123$	2.58831	+	5.43667i	0.233380	+	0.490208i
$124$	−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
$127$	−3.29674	+	12.3036i	−0.292539	+	1.09177i	0.650614	+	0.759409i	$0.274512\pi$
$127$	−3.29674	+	12.3036i	−0.292539	+	1.09177i	−0.943152	+	0.332361i	$0.892155\pi$
$128$	−12.1854	−	3.26508i	−1.07705	−	0.288595i
$129$	1.59125	+	8.62058i	0.140102	+	0.759000i
$130$	3.12917	−	13.4150i	0.274446	−	1.17658i
$131$			12.9569i			1.13205i	0.824390	+	0.566023i	$0.191519\pi$
$131$			12.9569i			1.13205i	−0.824390	+	0.566023i	$0.808481\pi$
$132$	−0.518068	+	6.52206i	−0.0450921	+	0.567673i
$133$	−0.870310	−	0.233199i	−0.0754655	−	0.0202209i
$134$	−2.52439	+	4.37238i	−0.218074	+	0.377716i
$135$	−7.08873	+	9.20597i	−0.610101	+	0.792324i
$136$	8.34958	+	4.82063i	0.715970	+	0.413366i
$137$	12.0355	−	3.22490i	1.02826	−	0.275522i	0.295021	−	0.955491i	$-0.404673\pi$
$137$	12.0355	−	3.22490i	1.02826	−	0.275522i	0.733241	+	0.679969i	$0.238007\pi$
$138$	16.8966	+	11.6308i	1.43833	+	0.990079i
$139$	−3.31851	−	1.91594i	−0.281472	−	0.162508i	0.352618	−	0.935767i	$-0.385292\pi$
$139$	−3.31851	−	1.91594i	−0.281472	−	0.162508i	−0.634090	+	0.773260i	$0.718625\pi$
$140$	0.181053	+	0.146467i	0.0153018	+	0.0123787i
$141$	0.294914	+	0.345808i	0.0248362	+	0.0291223i
$142$	−10.2785	−	10.2785i	−0.862557	−	0.862557i
$143$	−8.31831	+	12.2593i	−0.695612	+	1.02517i
$144$	−5.34818	−	13.9933i	−0.445682	−	1.16610i
$145$	8.93808	−	0.943869i	0.742267	−	0.0783841i
$146$	6.29594	−	3.63496i	0.521056	−	0.300832i
$147$	10.9270	−	5.20216i	0.901243	−	0.429067i
$148$	2.76149	+	2.76149i	0.226993	+	0.226993i
$149$	−10.3032	−	5.94857i	−0.844073	−	0.487326i	0.0145735	−	0.999894i	$-0.495361\pi$
$149$	−10.3032	−	5.94857i	−0.844073	−	0.487326i	−0.858647	+	0.512568i	$0.828694\pi$
$150$	−13.6691	+	5.66602i	−1.11608	+	0.462628i
$151$		−	11.1014i		−	0.903416i	−0.892166	−	0.451708i	$-0.850815\pi$
$151$		−	11.1014i		−	0.903416i	0.892166	−	0.451708i	$-0.149185\pi$
$152$	3.80088	+	14.1851i	0.308292	+	1.15056i
$153$	1.61472	+	15.5809i	0.130542	+	1.25964i
$154$	−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	$0.648789\pi$
$158$	7.99583	+	2.14248i	0.636114	+	0.170446i
$159$	−3.09006	−	3.62333i	−0.245058	−	0.287349i
$160$	1.68739	−	10.6878i	0.133400	−	0.844941i
$161$	−0.785250			−0.0618864
$162$	8.41259	−	12.8721i	0.660955	−	1.01133i
$163$	11.8393	−	3.17233i	0.927326	−	0.248476i	0.236612	−	0.971604i	$-0.423963\pi$
$163$	11.8393	−	3.17233i	0.927326	−	0.248476i	0.690714	+	0.723128i	$0.257296\pi$
$164$		−	3.19590i		−	0.249558i
$165$	15.9085	−	0.412827i	1.23848	−	0.0321385i
$166$	2.46999	+	4.27815i	0.191708	+	0.332049i
$167$	−2.30903	+	8.61742i	−0.178678	+	0.666836i	0.817218	+	0.576329i	$0.195515\pi$
$167$	−2.30903	+	8.61742i	−0.178678	+	0.666836i	−0.995896	+	0.0905069i	$0.971151\pi$
$168$	0.298446	+	0.205436i	0.0230256	+	0.0158497i
$169$	−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
$172$	1.20422	−	4.49422i	0.0918211	−	0.342681i
$173$	8.49801	−	2.27704i	0.646092	−	0.173120i	0.0791307	−	0.996864i	$-0.474786\pi$
$173$	8.49801	−	2.27704i	0.646092	−	0.173120i	0.566961	+	0.823744i	$0.308119\pi$
$174$	−11.6975	+	2.15920i	−0.886783	+	0.163689i
$175$	0.308040	−	0.475362i	0.0232856	−	0.0359340i
$176$	−10.2590	+	17.7691i	−0.773301	+	1.33940i
$177$	−1.02087	−	0.702718i	−0.0767334	−	0.0528196i
$178$	−1.42959	−	5.33529i	−0.107152	−	0.399897i
$179$	−9.95273	−	17.2386i	−0.743902	−	1.28848i	−0.950706	−	0.310094i	$-0.899640\pi$
$179$	−9.95273	−	17.2386i	−0.743902	−	1.28848i	0.206804	−	0.978382i	$-0.433694\pi$
$180$	5.49743	−	2.79441i	0.409754	−	0.208283i
$181$	7.45086			0.553818			0.276909	−	0.960896i	$-0.410690\pi$
$181$	7.45086			0.553818			0.276909	+	0.960896i	$0.410690\pi$
$182$	−0.304210	−	0.628116i	−0.0225496	−	0.0465590i
$183$	4.01004	−	5.82556i	0.296430	−	0.430638i
$184$	6.39934	+	11.0840i	0.471766	+	0.817122i
$185$	5.97437	−	7.38515i	0.439244	−	0.542967i
$186$	−19.2287	−	6.82496i	−1.40991	−	0.500430i
$187$	15.1707	−	15.1707i	1.10939	−	1.10939i
$188$	−0.0624332	−	0.233004i	−0.00455341	−	0.0169935i
$189$	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	−0.440562	−	0.897722i	$-0.645221\pi$
$191$	−19.8776	−	11.4763i	−1.43829	−	0.830399i	−0.997731	+	0.0673227i	$0.978554\pi$
$192$	0.235792	−	2.96843i	0.0170168	−	0.214228i
$193$	−5.67196	+	21.1680i	−0.408276	+	1.52371i	0.389655	+	0.920961i	$0.372594\pi$
$193$	−5.67196	+	21.1680i	−0.408276	+	1.52371i	−0.797932	+	0.602748i	$0.794072\pi$
$194$	0.255295			0.0183291
$195$	13.9491	+	0.650889i	0.998913	+	0.0466111i
$196$	−6.42333			−0.458810
$197$	2.25019	−	8.39781i	0.160319	−	0.598319i	−0.838272	−	0.545253i	$-0.816434\pi$
$197$	2.25019	−	8.39781i	0.160319	−	0.598319i	0.998591	−	0.0530668i	$-0.0168996\pi$
$198$	−20.9494	+	2.17108i	−1.48881	+	0.154292i
$199$	−17.5413	−	10.1275i	−1.24347	−	0.717919i	−0.273673	−	0.961823i	$-0.588239\pi$
$199$	−17.5413	−	10.1275i	−1.24347	−	0.717919i	−0.969799	+	0.243904i	$0.921572\pi$
$200$	−9.22018	−	0.474126i	−0.651965	−	0.0335258i
$201$	−4.82328	−	1.71196i	−0.340208	−	0.120752i
$202$	−5.36686	−	20.0294i	−0.377611	−	1.40926i
$203$	0.321987	−	0.321987i	0.0225990	−	0.0225990i
$204$	2.78097	−	7.83511i	0.194707	−	0.548568i
$205$	−7.73056	+	0.816354i	−0.539925	+	0.0570166i
$206$	−0.638295	−	1.10556i	−0.0444721	−	0.0770280i
$207$	−8.48540	+	18.9842i	−0.589776	+	1.31949i
$208$	−10.1090	+	14.8984i	−0.700934	+	1.03302i
$209$	32.6795			2.26049
$210$	−0.357868	+	0.658740i	−0.0246952	+	0.0454574i
$211$	3.64767	+	6.31794i	0.251116	+	0.434945i	0.963833	−	0.266506i	$-0.0858692\pi$
$211$	3.64767	+	6.31794i	0.251116	+	0.434945i	−0.712718	+	0.701451i	$0.752536\pi$
$212$	0.654166	+	2.44138i	0.0449283	+	0.167675i
$213$	8.35516	−	12.1379i	0.572486	−	0.831677i
$214$	1.41089	−	2.44374i	0.0964466	−	0.167050i
$215$	−11.1787	−	1.76490i	−0.762379	−	0.120365i
$216$	8.19162	−	4.99529i	0.557369	−	0.339886i
$217$	0.754473	−	0.202160i	0.0512169	−	0.0137235i
$218$	0.282519	−	1.05438i	0.0191346	−	0.0714114i
$219$	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
$222$	−7.12830	+	10.3556i	−0.478420	+	0.695023i
$223$	−3.14269	+	11.7287i	−0.210450	+	0.785411i	0.777268	+	0.629169i	$0.216605\pi$
$223$	−3.14269	+	11.7287i	−0.210450	+	0.785411i	−0.987719	+	0.156242i	$0.950062\pi$
$224$	−0.274097	−	0.474749i	−0.0183139	−	0.0317205i
$225$	−8.16365	−	12.5839i	−0.544244	−	0.838927i
$226$		−	13.5221i		−	0.899479i
$227$	−13.3950	+	3.58919i	−0.889061	+	0.238223i	−0.674312	−	0.738446i	$-0.735560\pi$
$227$	−13.3950	+	3.58919i	−0.889061	+	0.238223i	−0.214748	+	0.976669i	$0.568893\pi$
$228$	11.4341	−	5.44360i	0.757244	−	0.360511i
$229$	8.51901			0.562952			0.281476	−	0.959568i	$-0.409176\pi$
$229$	8.51901			0.562952			0.281476	+	0.959568i	$0.409176\pi$
$230$	−21.4165	+	15.5761i	−1.41217	+	1.02706i
$231$	0.613468	−	0.523181i	0.0403633	−	0.0344228i
$232$	−7.16892	−	1.92091i	−0.470663	−	0.126114i
$233$	8.61258	+	8.61258i	0.564229	+	0.564229i	0.930506	−	0.366277i	$-0.119368\pi$
$233$	8.61258	+	8.61258i	0.564229	+	0.564229i	−0.366277	+	0.930506i	$0.619368\pi$
$234$	−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
$237$	−0.664473	+	8.36517i	−0.0431621	+	0.543376i
$238$	0.261585	+	0.976248i	0.0169560	+	0.0632807i
$239$			11.5531i			0.747310i	0.927568	+	0.373655i	$0.121896\pi$
$239$			11.5531i			0.747310i	−0.927568	+	0.373655i	$0.878104\pi$
$240$	19.3332	−	0.501697i	1.24795	−	0.0323844i
$241$	12.0934	+	6.98212i	0.779004	+	0.449758i	0.836077	−	0.548612i	$-0.184843\pi$
$241$	12.0934	+	6.98212i	0.779004	+	0.449758i	−0.0570731	+	0.998370i	$0.518177\pi$
$242$	7.10816	+	7.10816i	0.456930	+	0.456930i
$243$	14.3801	+	6.01775i	0.922482	+	0.386039i
$244$	−3.25080	+	1.87685i	−0.208111	+	0.120153i
$245$	1.64076	+	15.5374i	0.104824	+	0.992647i
$246$	10.1172	−	1.86750i	0.645047	−	0.119067i
$247$	28.6004	+	2.07924i	1.81980	+	0.132299i
$248$	−9.00206	−	9.00206i	−0.571631	−	0.571631i
$249$	−3.81032	+	3.24953i	−0.241469	+	0.205931i
$250$	−1.02787	−	19.0750i	−0.0650082	−	1.20641i
$251$	−14.9246	−	8.61672i	−0.942032	−	0.543882i	−0.0514354	−	0.998676i	$-0.516380\pi$
$251$	−14.9246	−	8.61672i	−0.942032	−	0.543882i	−0.890597	+	0.454794i	$0.849713\pi$
$252$	0.127496	−	0.285243i	0.00803147	−	0.0179686i
$253$	27.5104	−	7.37138i	1.72956	−	0.463435i
$254$	18.8477	+	10.8818i	1.18261	+	0.682782i
$255$	−19.6627	−	4.72550i	−1.23133	−	0.295922i
$256$	−9.05800	+	15.6889i	−0.566125	+	0.980557i
$257$	−0.404361	−	0.108348i	−0.0252233	−	0.00675857i	0.246185	−	0.969223i	$-0.420823\pi$
$257$	−0.404361	−	0.108348i	−0.0252233	−	0.00675857i	−0.271409	+	0.962464i	$0.587489\pi$
$258$	14.9309	+	1.18601i	0.929557	+	0.0738377i
$259$		−	0.481265i		−	0.0299044i
$260$	−6.53621	−	3.49440i	−0.405358	−	0.216713i
$261$	−4.30496	−	11.2637i	−0.266470	−	0.697207i
$262$	21.3837	+	5.72975i	1.32109	+	0.353985i
$263$	3.38670	−	12.6393i	0.208833	−	0.779374i	−0.779414	−	0.626509i	$-0.784483\pi$
$263$	3.38670	−	12.6393i	0.208833	−	0.779374i	0.988247	−	0.152865i	$-0.0488501\pi$
$264$	−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
$267$	5.05561	−	2.40689i	0.309398	−	0.147299i
$268$	1.92084	+	1.92084i	0.117334	+	0.117334i
$269$	−0.403612	+	0.699076i	−0.0246086	+	0.0426234i	−0.878067	−	0.478537i	$-0.841167\pi$
$269$	−0.403612	+	0.699076i	−0.0246086	+	0.0426234i	0.853459	+	0.521160i	$0.174501\pi$
$270$	12.0586	+	15.7701i	0.733861	+	0.959740i
$271$	−9.22378	+	5.32535i	−0.560305	+	0.323492i	−0.753268	−	0.657714i	$-0.771524\pi$
$271$	−9.22378	+	5.32535i	−0.560305	+	0.323492i	0.192963	+	0.981206i	$0.438190\pi$
$272$	18.4366	−	18.4366i	1.11788	−	1.11788i
$273$	0.570181	−	0.418844i	0.0345089	−	0.0253496i
$274$		−	21.2892i		−	1.28613i
$275$	−6.32947	+	19.5454i	−0.381682	+	1.17863i
$276$	8.39764	−	7.16171i	0.505478	−	0.431084i
$277$	−27.5691	+	7.38713i	−1.65647	+	0.443849i	−0.961414	−	0.275107i	$-0.911287\pi$
$277$	−27.5691	+	7.38713i	−1.65647	+	0.443849i	−0.695055	+	0.718957i	$0.744620\pi$
$278$	−4.62953	+	4.62953i	−0.277661	+	0.277661i
$279$	3.26539	−	20.4246i	0.195494	−	1.22279i
$280$	−0.378283	+	0.275122i	−0.0226067	+	0.0164417i
$281$	−13.4870			−0.804568			−0.402284	−	0.915515i	$-0.631784\pi$
$281$	−13.4870			−0.804568			−0.402284	+	0.915515i	$0.631784\pi$
$282$	0.701130	−	0.333797i	0.0417517	−	0.0198773i
$283$	−1.10046	−	0.294869i	−0.0654158	−	0.0175281i	0.225963	−	0.974136i	$-0.427447\pi$
$283$	−1.10046	−	0.294869i	−0.0654158	−	0.0175281i	−0.291379	+	0.956608i	$0.594114\pi$
$284$	−6.77325	+	3.91054i	−0.401918	+	0.232048i
$285$	−16.0882	−	26.2675i	−0.952984	−	1.55595i
$286$	16.5540	+	19.1496i	0.978858	+	1.13234i
$287$	−0.278487	+	0.278487i	−0.0164386	+	0.0164386i
$288$	−14.4394	+	1.49642i	−0.850850	+	0.0881774i
$289$	−8.88844	+	5.13174i	−0.522850	+	0.301867i
$290$	2.39483	−	15.1686i	0.140629	−	0.890731i
$291$	0.0469775	+	0.254500i	0.00275387	+	0.0149191i
$292$	−1.01239	−	3.77827i	−0.0592454	−	0.221107i
$293$	−1.95360	−	7.29093i	−0.114130	−	0.425941i	0.885090	−	0.465420i	$-0.154097\pi$
$293$	−1.95360	−	7.29093i	−0.114130	−	0.425941i	−0.999220	+	0.0394794i	$0.987430\pi$
$294$	−3.75342	−	20.3341i	−0.218904	−	1.18591i
$295$	1.29396	−	0.941089i	0.0753373	−	0.0547923i
$296$	−6.79317	+	3.92204i	−0.394845	+	0.227964i
$297$	−6.01927	−	20.4847i	−0.349274	−	1.18864i
$298$	−14.3737	+	14.3737i	−0.832644	+	0.832644i
$299$	24.5455	−	4.70092i	1.41950	−	0.271861i
$300$	1.04119	+	7.89303i	0.0601131	+	0.455705i
$301$	−0.496555	+	0.286686i	−0.0286210	+	0.0165243i
$302$	−18.3214	−	4.90922i	−1.05428	−	0.282494i
$303$	18.9794	−	9.03580i	1.09034	−	0.519093i
$304$	39.7144			2.27778
$305$	5.37029	+	7.38394i	0.307502	+	0.422803i
$306$	26.4284	+	4.22525i	1.51081	+	0.241541i
$307$	5.28300	−	5.28300i	0.301517	−	0.301517i	−0.540090	−	0.841607i	$-0.681610\pi$
$307$	5.28300	−	5.28300i	0.301517	−	0.301517i	0.841607	+	0.540090i	$0.181610\pi$
$308$	−0.413352	+	0.110757i	−0.0235529	+	0.00631098i
$309$	0.984663	−	0.839744i	0.0560155	−	0.0477714i
$310$	16.5671	−	20.4792i	0.940949	−	1.16314i
$311$			2.37607i			0.134735i	0.997728	+	0.0673674i	$0.0214599\pi$
$311$			2.37607i			0.134735i	−0.997728	+	0.0673674i	$0.978540\pi$
$312$	−10.5587	−	4.63490i	−0.597770	−	0.262400i
$313$	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
$315$	−0.722541	−	0.235537i	−0.0407106	−	0.0132710i
$316$	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	$0.351723\pi$
$318$	−7.34634	+	3.49747i	−0.411962	+	0.196128i
$319$	−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
$322$	−0.347251	+	1.29596i	−0.0193516	+	0.0722210i
$323$	−40.1124	−	10.7481i	−2.23191	−	0.598040i
$324$	−5.51831	−	6.16466i	−0.306573	−	0.342481i
$325$	−6.78300	+	16.7030i	−0.376253	+	0.926517i
$326$		−	20.9422i		−	1.15988i
$327$	1.10308	+	0.0876212i	0.0610005	+	0.00484546i
$328$	6.20041	+	1.66140i	0.342361	+	0.0917352i
$329$	−0.0148633	+	0.0257440i	−0.000819441	+	0.00141931i
$330$	6.35371	−	26.4377i	0.349760	−	1.45535i
$331$	12.0767	+	6.97251i	0.663798	+	0.383244i	0.793722	−	0.608280i	$-0.208140\pi$
$331$	12.0767	+	6.97251i	0.663798	+	0.383244i	−0.129925	+	0.991524i	$0.541474\pi$
$332$	2.56737	−	0.687925i	0.140903	−	0.0377548i
$333$	−11.6351	−	5.20054i	−0.637597	−	0.284988i
$334$	13.2009	+	7.62155i	0.722322	+	0.417033i
$335$	4.15567	−	5.13698i	0.227048	−	0.280663i
$336$	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	$0.781708\pi$
$338$	13.2693	+	17.8126i	0.721754	+	0.968877i
$339$	13.4800	−	2.48824i	0.732135	−	0.135143i
$340$	8.34469	+	6.75061i	0.452555	+	0.366103i
$341$	−24.5344	+	14.1649i	−1.32861	+	0.767074i
$342$	23.9141	+	33.0157i	1.29313	+	1.78529i
$343$	1.12047	+	1.12047i	0.0604997	+	0.0604997i
$344$	8.09329	+	4.67266i	0.436361	+	0.251933i
$345$	−19.4685	−	18.4837i	−1.04815	−	0.995127i
$346$		−	15.0319i		−	0.808119i
$347$	−4.13034	−	15.4146i	−0.221728	−	0.827500i	−0.983689	−	0.179877i	$-0.942430\pi$
$347$	−4.13034	−	15.4146i	−0.221728	−	0.827500i	0.761961	−	0.647623i	$-0.224237\pi$
$348$	−0.506785	+	6.38001i	−0.0271665	+	0.342004i
$349$	2.98342	+	5.16743i	0.159699	+	0.276606i	0.934760	−	0.355280i	$-0.115614\pi$
$349$	2.98342	+	5.16743i	0.159699	+	0.276606i	−0.775061	+	0.631886i	$0.782281\pi$
$350$	−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
$353$	−12.0317	−	3.22389i	−0.640383	−	0.171590i	−0.0760061	−	0.997107i	$-0.524217\pi$
$353$	−12.0317	−	3.22389i	−0.640383	−	0.171590i	−0.564377	+	0.825517i	$0.690884\pi$
$354$	−1.61120	+	1.37407i	−0.0856342	+	0.0730309i
$355$	11.1893	+	15.3849i	0.593868	+	0.816546i
$356$	−2.97190			−0.157510
$357$	−0.925073	+	0.440412i	−0.0489600	+	0.0233091i
$358$	−32.8515	+	8.80254i	−1.73626	+	0.465229i
$359$			29.8863i			1.57734i	0.614816	+	0.788671i	$0.289230\pi$
$359$			29.8863i			1.57734i	−0.614816	+	0.788671i	$0.710770\pi$
$360$	2.56364	+	12.1183i	0.135116	+	0.638691i
$361$	−22.1271	−	38.3252i	−1.16458	−	2.01712i
$362$	3.29490	−	12.2967i	0.173176	−	0.646302i
$363$	−5.77804	+	8.39402i	−0.303268	+	0.440572i
$364$	−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
$367$	−3.47695	+	12.9762i	−0.181496	+	0.677351i	0.813858	+	0.581064i	$0.197363\pi$
$367$	−3.47695	+	12.9762i	−0.181496	+	0.677351i	−0.995354	+	0.0962869i	$0.969303\pi$
$368$	33.4326	−	8.95823i	1.74279	−	0.466980i
$369$	3.72337	+	9.74201i	0.193831	+	0.507149i
$370$	−9.54631	−	13.1258i	−0.496289	−	0.682378i
$371$	0.155736	−	0.269742i	0.00808539	−	0.0140043i
$372$	−6.22474	+	9.04296i	−0.322738	+	0.468855i
$373$	−5.16696	−	19.2834i	−0.267535	−	0.998455i	−0.960680	−	0.277657i	$-0.910442\pi$
$373$	−5.16696	−	19.2834i	−0.267535	−	0.998455i	0.693145	−	0.720798i	$-0.256224\pi$
$374$	−18.3287	−	31.7462i	−0.947753	−	1.64156i
$375$	18.8265	−	4.53471i	0.972195	−	0.234171i
$376$	0.484510			0.0249867
$377$	−8.13714	+	11.9923i	−0.419084	+	0.617635i
$378$	0.977486	+	0.236929i	0.0502764	+	0.0121863i
$379$	−16.7541	−	29.0190i	−0.860601	−	1.49061i	−0.871350	−	0.490663i	$-0.836755\pi$
$379$	−16.7541	−	29.0190i	−0.860601	−	1.49061i	0.0107483	−	0.999942i	$-0.496579\pi$
$380$	1.71691	+	16.2585i	0.0880758	+	0.834044i
$381$	−7.37965	+	20.7914i	−0.378071	+	1.06518i
$382$	−27.7305	+	27.7305i	−1.41882	+	1.41882i
$383$	−0.699279	−	2.60975i	−0.0357315	−	0.133352i	0.945756	−	0.324878i	$-0.105323\pi$
$383$	−0.699279	−	2.60975i	−0.0357315	−	0.133352i	−0.981488	+	0.191526i	$0.938656\pi$
$384$	−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
$387$	1.56515	+	15.1026i	0.0795612	+	0.767710i
$388$	0.0355516	−	0.132680i	0.00180486	−	0.00673582i
$389$	−38.6182			−1.95802			−0.979011	−	0.203807i	$-0.934668\pi$
$389$	−38.6182			−1.95802			−0.979011	+	0.203807i	$0.934668\pi$
$390$	7.24273	−	22.7334i	0.366750	−	1.15115i
$391$	−36.1920			−1.83031
$392$	3.33918	−	12.4620i	0.168654	−	0.629426i
$393$	−1.77704	+	22.3715i	−0.0896397	+	1.12849i
$394$	−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
$397$	−2.93908	−	10.9688i	−0.147508	−	0.550509i	−0.999631	−	0.0271666i	$-0.991352\pi$
$397$	−2.93908	−	10.9688i	−0.147508	−	0.550509i	0.852122	−	0.523342i	$-0.175315\pi$
$398$	−24.4713	+	24.4713i	−1.22663	+	1.22663i
$399$	−1.47070	−	0.522007i	−0.0736273	−	0.0261331i
$400$	−7.69203	+	23.7530i	−0.384602	+	1.18765i
$401$	15.5856	+	26.9950i	0.778307	+	1.34807i	0.932917	+	0.360091i	$0.117254\pi$
$401$	15.5856	+	26.9950i	0.778307	+	1.34807i	−0.154611	+	0.987975i	$0.549412\pi$
$402$	−4.95832	+	7.20318i	−0.247299	+	0.359262i
$403$	−22.3732	+	10.8358i	−1.11449	+	0.539771i
$404$	−11.1569			−0.555076
$405$	−13.5021	+	14.9229i	−0.670925	+	0.741526i
$406$	−0.389012	−	0.673788i	−0.0193063	−	0.0334395i
$407$	4.51779	+	16.8606i	0.223938	+	0.835749i
$408$	13.7553	+	9.46851i	0.680990	+	0.468761i
$409$	−5.22725	+	9.05386i	−0.258471	+	0.447685i	−0.965832	−	0.259167i	$-0.916552\pi$
$409$	−5.22725	+	9.05386i	−0.258471	+	0.447685i	0.707362	+	0.706852i	$0.249885\pi$
$410$	−2.07129	+	13.1193i	−0.102294	+	0.647918i
$411$	21.2229	−	3.91748i	1.04685	−	0.193235i
$412$	−0.663461	+	0.177774i	−0.0326864	+	0.00875828i
$413$	0.0209805	−	0.0783003i	0.00103238	−	0.00385290i
$414$	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
$417$	−5.46700	−	3.76322i	−0.267720	−	0.184286i
$418$	14.4514	−	53.9335i	0.706843	−	2.63797i
$419$	10.9200	+	18.9139i	0.533476	+	0.924007i	0.999235	+	0.0390956i	$0.0124477\pi$
$419$	10.9200	+	18.9139i	0.533476	+	0.924007i	−0.465760	+	0.884911i	$0.654219\pi$
$420$	0.292520	+	0.277722i	0.0142735	+	0.0135515i
$421$			11.3030i			0.550876i	0.961319	+	0.275438i	$0.0888229\pi$
$421$			11.3030i			0.550876i	−0.961319	+	0.275438i	$0.911177\pi$
$422$	12.0401	−	3.22612i	0.586101	−	0.157045i
$423$	0.461774	+	0.637524i	0.0224522	+	0.0309975i
$424$	−5.07663			−0.246543
$425$	14.1975	−	21.9093i	0.688680	−	1.06276i
$426$	−16.3374	−	19.1568i	−0.791548	−	0.928149i
$427$	0.446818	+	0.119724i	0.0216230	+	0.00579387i
$428$	−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	0.896917	−	0.442199i	$-0.145802\pi$
$431$	1.35987	+	2.35537i	0.0655028	+	0.113454i	−0.831414	+	0.555653i	$0.812468\pi$
$432$	−7.31505	−	24.8944i	−0.351945	−	1.19773i
$433$	−3.66753	−	13.6874i	−0.176250	−	0.657775i	−0.996335	−	0.0855335i	$-0.972741\pi$
$433$	−3.66753	−	13.6874i	−0.176250	−	0.657775i	0.820085	−	0.572242i	$-0.193926\pi$
$434$		−	1.33456i		−	0.0640611i
$435$	15.5620	−	0.403835i	0.746143	−	0.0193624i
$436$	−0.508630	−	0.293658i	−0.0243590	−	0.0140637i
$437$	−38.9809	−	38.9809i	−1.86471	−	1.86471i
$438$	11.3692	−	5.41268i	0.543241	−	0.258628i
$439$	8.10140	−	4.67735i	0.386659	−	0.223237i	−0.294053	−	0.955789i	$-0.595004\pi$
$439$	8.10140	−	4.67735i	0.386659	−	0.223237i	0.680711	+	0.732552i	$0.261671\pi$
$440$	10.6701	−	13.1897i	0.508675	−	0.628793i
$441$	19.5801	−	7.48347i	0.932388	−	0.356356i
$442$	−14.0210	−	28.9497i	−0.666910	−	1.37700i
$443$	−5.74199	−	5.74199i	−0.272810	−	0.272810i	0.557420	−	0.830230i	$-0.311791\pi$
$443$	−5.74199	−	5.74199i	−0.272810	−	0.272810i	−0.830230	+	0.557420i	$0.811791\pi$
$444$	4.38928	+	5.14676i	0.208306	+	0.244254i
$445$	0.759135	+	7.18871i	0.0359864	+	0.340778i
$446$	17.9670	+	10.3733i	0.850763	+	0.491188i
$447$	−16.9738	−	11.6840i	−0.802835	−	0.552633i
$448$	0.188132	−	0.0504097i	0.00888838	−	0.00238163i
$449$	23.4891	+	13.5614i	1.10852	+	0.640004i	0.938446	−	0.345427i	$-0.112266\pi$
$449$	23.4891	+	13.5614i	1.10852	+	0.640004i	0.170074	+	0.985431i	$0.445599\pi$
$450$	−24.3783	+	7.90829i	−1.14920	+	0.372800i
$451$	7.14224	−	12.3707i	0.336315	−	0.582515i
$452$	−7.02763	−	1.88305i	−0.330552	−	0.0885711i
$453$	1.52256	−	19.1678i	0.0715359	−	0.900579i
$454$			23.6941i			1.11202i
$455$	0.265059	+	0.874055i	0.0124262	+	0.0409763i
$456$	4.61715	+	25.0134i	0.216218	+	1.17136i
$457$	12.9168	+	3.46105i	0.604224	+	0.161901i	0.547946	−	0.836514i	$-0.315410\pi$
$457$	12.9168	+	3.46105i	0.604224	+	0.161901i	0.0562781	+	0.998415i	$0.482077\pi$
$458$	3.76726	−	14.0596i	0.176032	−	0.656962i
$459$	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	0.121611	+	0.992578i	$0.461194\pi$
$461$	−17.1508	+	29.7061i	−0.798792	+	1.38355i	−0.920403	+	0.390971i	$0.872139\pi$
$462$	−0.592159	−	1.24381i	−0.0275498	−	0.0578675i
$463$	19.4344	+	19.4344i	0.903191	+	0.903191i	0.995711	−	0.0925195i	$-0.0294920\pi$
$463$	19.4344	+	19.4344i	0.903191	+	0.903191i	−0.0925195	+	0.995711i	$0.529492\pi$
$464$	−10.0356	+	17.3821i	−0.465889	+	0.806943i
$465$	23.4640	+	12.7471i	1.08812	+	0.591132i
$466$	18.0226	−	10.4054i	0.834883	−	0.482020i
$467$	−19.6345	+	19.6345i	−0.908575	+	0.908575i	−0.996157	−	0.0875827i	$-0.972086\pi$
$467$	−19.6345	+	19.6345i	−0.908575	+	0.908575i	0.0875827	+	0.996157i	$0.472086\pi$
$468$	−2.27767	+	9.67943i	−0.105285	+	0.447432i
$469$		−	0.334760i		−	0.0154578i
$470$	0.105280	+	0.996957i	0.00485618	+	0.0459862i
$471$	8.80540	+	10.3250i	0.405731	+	0.475750i
$472$	−1.27621	+	0.341958i	−0.0587421	+	0.0157399i
$473$	14.7051	−	14.7051i	0.676140	−	0.676140i
$474$	13.5119	+	4.79586i	0.620620	+	0.220281i
$475$	38.8891	−	8.30608i	1.78435	−	0.381109i
$476$	0.543796			0.0249248
$477$	−4.83840	−	6.67989i	−0.221535	−	0.305851i
$478$	19.0670	+	5.10900i	0.872107	+	0.233680i
$479$	−1.49161	+	0.861181i	−0.0681534	+	0.0393484i	−0.533689	−	0.845681i	$-0.679195\pi$
$479$	−1.49161	+	0.861181i	−0.0681534	+	0.0393484i	0.465536	+	0.885029i	$0.345862\pi$
$480$	4.37930	−	18.2222i	0.199887	−	0.831725i
$481$	2.88111	+	15.0435i	0.131367	+	0.685924i
$482$	16.8711	−	16.8711i	0.768456	−	0.768456i
$483$	−1.35582	−	0.107697i	−0.0616921	−	0.00490040i
$484$	4.68406	−	2.70434i	0.212912	−	0.122925i
$485$	−0.330021	−	0.0521040i	−0.0149855	−	0.00236592i
$486$	16.2907	−	21.0714i	0.738961	−	0.955819i
$487$	−5.38812	−	20.1087i	−0.244159	−	0.911213i	−0.973804	−	0.227388i	$-0.926982\pi$
$487$	−5.38812	−	20.1087i	−0.244159	−	0.911213i	0.729645	−	0.683826i	$-0.239685\pi$
$488$	−1.95137	−	7.28262i	−0.0883344	−	0.329669i
$489$	20.8770	−	3.85362i	0.944089	−	0.174267i
$490$	26.3681	+	4.16303i	1.19119	+	0.188066i
$491$	19.5711	−	11.2994i	0.883233	−	0.509935i	0.0115102	−	0.999934i	$-0.496336\pi$
$491$	19.5711	−	11.2994i	0.883233	−	0.509935i	0.871723	+	0.489999i	$0.163003\pi$
$492$	0.438319	−	5.51808i	0.0197609	−	0.248774i
$493$	14.8403	−	14.8403i	0.668374	−	0.668374i
$494$	16.0791	−	46.2819i	0.723434	−	2.08232i
$495$	27.5245	+	1.46907i	1.23713	+	0.0660298i
$496$	−29.8159	+	17.2142i	−1.33878	+	0.772942i
$497$	0.930972	+	0.249453i	0.0417598	+	0.0111895i
$498$	3.67797	+	7.72547i	0.164814	+	0.346186i
$499$	−35.8828			−1.60634			−0.803168	−	0.595753i	$-0.796854\pi$
$499$	−35.8828			−1.60634			−0.803168	+	0.595753i	$0.796854\pi$
$500$	−10.0567	−	2.12213i	−0.449748	−	0.0949044i
$501$	−5.16868	+	14.5623i	−0.230920	+	0.650594i
$502$	−20.8208	+	20.8208i	−0.929276	+	0.929276i
$503$	−31.9352	+	8.55700i	−1.42392	+	0.381538i	−0.886872	−	0.462015i	$-0.847127\pi$
$503$	−31.9352	+	8.55700i	−1.42392	+	0.381538i	−0.537047	+	0.843553i	$0.680460\pi$
$504$	0.487125	+	0.395640i	0.0216983	+	0.0176232i
$505$	2.84989	+	26.9874i	0.126819	+	1.20092i
$506$		−	48.6623i		−	2.16330i
$507$	−15.3154	+	16.5057i	−0.680181	+	0.733044i
$508$	8.28006	−	8.28006i	0.367368	−	0.367368i
$509$	−5.25012	+	3.03116i	−0.232707	+	0.134354i	−0.611820	−	0.790997i	$-0.709562\pi$
$509$	−5.25012	+	3.03116i	−0.232707	+	0.134354i	0.379113	+	0.925350i	$0.376229\pi$
$510$	−16.4941	+	30.3612i	−0.730369	+	1.34442i
$511$	−0.241016	+	0.417452i	−0.0106619	+	0.0184670i
$512$	4.04633	+	4.04633i	0.178824	+	0.178824i
$513$	−28.5124	+	29.9149i	−1.25886	+	1.32078i
$514$	−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
$517$	0.279053	−	1.04144i	0.0122727	−	0.0458025i
$518$	−0.794270	−	0.212824i	−0.0348982	−	0.00935095i
$519$	14.9851	−	2.76605i	0.657772	−	0.121416i
$520$	10.1774	−	10.8644i	0.446308	−	0.476436i
$521$		−	23.5394i		−	1.03128i	−0.856805	−	0.515640i	$-0.827554\pi$
$521$		−	23.5394i		−	1.03128i	0.856805	−	0.515640i	$-0.172446\pi$
$522$	−20.4931	+	2.12379i	−0.896960	+	0.0929560i
$523$	−30.6087	−	8.20158i	−1.33843	−	0.358630i	−0.482575	−	0.875854i	$-0.660299\pi$
$523$	−30.6087	−	8.20158i	−1.33843	−	0.358630i	−0.855850	+	0.517225i	$0.826965\pi$
$524$	5.95565	−	10.3155i	0.260174	−	0.450634i
$525$	0.597061	−	0.778517i	0.0260579	−	0.0339773i
$526$	−19.3620	−	11.1787i	−0.844224	−	0.487413i
$527$	34.7735	−	9.31753i	1.51476	−	0.405878i
$528$	−20.1503	+	29.2733i	−0.876931	+	1.27396i
$529$	−21.6892	−	12.5223i	−0.943010	−	0.544447i
$530$	−1.10310	−	10.4460i	−0.0479158	−	0.453744i
$531$	−1.66627	−	1.35334i	−0.0723100	−	0.0587297i
$532$	0.585699	+	0.585699i	0.0253933	+	0.0253933i
$533$	7.03782	−	10.3722i	0.304842	−	0.449268i
$534$	−1.73660	−	9.40804i	−0.0751502	−	0.407126i
$535$	−2.32262	+	2.87107i	−0.100415	+	0.124127i
$536$	−4.72521	+	2.72810i	−0.204098	+	0.117836i
$537$	−14.8202	−	31.1295i	−0.639540	−	1.34334i
$538$	0.975256	+	0.975256i	0.0420463	+	0.0420463i
$539$	−24.8635	−	14.3550i	−1.07095	−	0.618312i
$540$	9.87518	−	4.07090i	0.424960	−	0.175184i
$541$		−	26.7974i		−	1.15211i	−0.817411	−	0.576055i	$-0.804591\pi$
$541$		−	26.7974i		−	1.15211i	0.817411	−	0.576055i	$-0.195409\pi$
$542$	4.70993	+	17.5777i	0.202309	+	0.755027i
$543$	12.8647	+	1.02189i	0.552079	+	0.0438534i
$544$	−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	$0.686897\pi$
$548$	−11.0643	−	2.96467i	−0.472643	−	0.126644i
$549$	7.72276	−	9.50851i	0.329599	−	0.405813i
$550$	29.4584	+	19.0894i	1.25611	+	0.813973i
$551$	31.9677			1.36187
$552$	9.52901	+	20.0154i	0.405581	+	0.851912i
$553$	−0.530163	+	0.142057i	−0.0225448	+	0.00604087i
$554$			48.7662i			2.07188i
$555$	11.3283	−	11.9319i	0.480859	−	0.506481i
$556$	1.76133	+	3.05072i	0.0746971	+	0.129379i
$557$	−6.08328	+	22.7031i	−0.257757	+	0.961962i	0.708779	+	0.705431i	$0.249246\pi$
$557$	−6.08328	+	22.7031i	−0.257757	+	0.961962i	−0.966536	+	0.256531i	$0.917420\pi$
$558$	−32.2644	−	14.4213i	−1.36586	−	0.610501i
$559$	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
$562$	−5.96419	+	22.2587i	−0.251584	+	0.938926i
$563$	35.8569	−	9.60782i	1.51119	−	0.404921i	0.594358	−	0.804201i	$-0.297406\pi$
$563$	35.8569	−	9.60782i	1.51119	−	0.404921i	0.916829	+	0.399279i	$0.130740\pi$
$564$	−0.0758413	−	0.410870i	−0.00319350	−	0.0173007i
$565$	−2.75978	+	17.4801i	−0.116105	+	0.735394i
$566$	−0.973289	+	1.68579i	−0.0409104	+	0.0708589i
$567$	−0.0563221	+	1.01804i	−0.00236531	+	0.0427537i
$568$	−4.06580	−	15.1738i	−0.170597	−	0.636678i
$569$	−6.61515	−	11.4578i	−0.277322	−	0.480335i	0.693397	−	0.720556i	$-0.256113\pi$
$569$	−6.61515	−	11.4578i	−0.277322	−	0.480335i	−0.970718	+	0.240221i	$0.922780\pi$
$570$	−50.4658	+	14.9357i	−2.11378	+	0.625588i
$571$	16.3611			0.684690			0.342345	−	0.939574i	$-0.388779\pi$
$571$	16.3611			0.684690			0.342345	+	0.939574i	$0.388779\pi$
$572$	12.2576	−	5.93661i	0.512515	−	0.248222i
$573$	−32.7469	−	22.5414i	−1.36802	−	0.941681i
$574$	0.336457	+	0.582760i	0.0140434	+	0.0243240i
$575$	30.8642	−	15.7643i	1.28713	−	0.657418i
$576$	0.814243	−	5.09299i	0.0339268	−	0.212208i
$577$	−1.55067	+	1.55067i	−0.0645553	+	0.0645553i	−0.738647	−	0.674092i	$-0.764535\pi$
$577$	−1.55067	+	1.55067i	−0.0645553	+	0.0645553i	0.674092	+	0.738647i	$0.264535\pi$
$578$	4.53869	+	16.9386i	0.188785	+	0.704554i
$579$	−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
$582$	0.440796	+	0.0350138i	0.0182716	+	0.00145137i
$583$	−2.92388	+	10.9121i	−0.121095	+	0.451931i
$584$	7.85658			0.325107
$585$	23.9954	+	3.03695i	0.992086	+	0.125562i
$586$	−12.8967			−0.532758
$587$	5.23017	−	19.5193i	0.215872	−	0.805646i	−0.769986	−	0.638061i	$-0.779737\pi$
$587$	5.23017	−	19.5193i	0.215872	−	0.805646i	0.985858	−	0.167585i	$-0.0535967\pi$
$588$	−11.0906	−	0.880963i	−0.457369	−	0.0363303i
$589$	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
$592$	5.49034	+	20.4902i	0.225651	+	0.842143i
$593$	−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
$595$	−0.138906	−	1.31539i	−0.00569459	−	0.0539256i
$596$	5.46855	+	9.47180i	0.224000	+	0.387980i
$597$	−28.8981	−	19.8921i	−1.18272	−	0.814128i
$598$	3.09615	−	42.5882i	0.126611	−	1.74156i
$599$	−17.9813			−0.734698			−0.367349	−	0.930083i	$-0.619734\pi$
$599$	−17.9813			−0.734698			−0.367349	+	0.930083i	$0.619734\pi$
$600$	−15.8547	−	2.08318i	−0.647264	−	0.0850456i
$601$	−4.18909	−	7.25572i	−0.170877	−	0.295967i	0.767850	−	0.640630i	$-0.221327\pi$
$601$	−4.18909	−	7.25572i	−0.170877	−	0.295967i	−0.938727	+	0.344663i	$0.887993\pi$
$602$	0.253555	+	0.946282i	0.0103341	+	0.0385676i
$603$	−8.09314	−	3.61741i	−0.329578	−	0.147312i
$604$	−5.10277	+	8.83825i	−0.207629	+	0.359623i
$605$	−7.73802	−	10.6395i	−0.314595	−	0.432556i
$606$	−6.51944	−	35.3190i	−0.264834	−	1.43474i
$607$	17.1283	−	4.58950i	0.695214	−	0.186282i	0.106128	−	0.994352i	$-0.466155\pi$
$607$	17.1283	−	4.58950i	0.695214	−	0.186282i	0.589086	+	0.808070i	$0.299488\pi$
$608$	9.96067	−	37.1737i	0.403958	−	1.50759i
$609$	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
$612$	5.87625	−	13.1468i	0.237533	−	0.531428i
$613$	−9.88511	+	36.8917i	−0.399256	+	1.49004i	0.415153	+	0.909752i	$0.363728\pi$
$613$	−9.88511	+	36.8917i	−0.399256	+	1.49004i	−0.814409	+	0.580291i	$0.802939\pi$
$614$	−6.38272	−	11.0552i	−0.257585	−	0.446151i
$615$	−13.4596	+	0.349278i	−0.542745	+	0.0140842i
$616$		−	0.859527i		−	0.0346313i
$617$	−27.1576	+	7.27686i	−1.09332	+	0.292955i	−0.760043	−	0.649872i	$-0.774822\pi$
$617$	−27.1576	+	7.27686i	−1.09332	+	0.292955i	−0.333281	+	0.942828i	$0.608156\pi$
$618$	−0.950461	−	1.99642i	−0.0382331	−	0.0803076i
$619$	34.9871			1.40625			0.703125	−	0.711066i	$-0.251787\pi$
$619$	34.9871			1.40625			0.703125	+	0.711066i	$0.251787\pi$
$620$	−8.33624	−	11.4620i	−0.334792	−	0.460325i
$621$	−17.2547	+	31.6145i	−0.692406	+	1.26865i
$622$	3.92142	+	1.05074i	0.157235	+	0.0421309i
$623$	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
$627$	56.4248	+	4.48200i	2.25339	+	0.178994i
$628$	−1.86410	−	6.95692i	−0.0743857	−	0.277611i
$629$		−	22.1814i		−	0.884431i
$630$	−0.708245	+	1.08831i	−0.0282172	+	0.0433592i
$631$	−10.8292	−	6.25222i	−0.431102	−	0.248897i	0.268714	−	0.963220i	$-0.413401\pi$
$631$	−10.8292	−	6.25222i	−0.431102	−	0.248897i	−0.699816	+	0.714323i	$0.746735\pi$
$632$	6.32569	+	6.32569i	0.251623	+	0.251623i
$633$	5.43160	+	11.4089i	0.215887	+	0.453464i
$634$	50.0225	−	28.8805i	1.98665	−	1.14699i
$635$	−22.1437	−	17.9136i	−0.878744	−	0.710879i
$636$	0.794654	+	4.30503i	0.0315101	+	0.170706i
$637$	−20.8467	−	14.1451i	−0.825974	−	0.560449i
$638$	19.9537	+	19.9537i	0.789973	+	0.789973i
$639$	16.0908	−	19.8116i	0.636544	−	0.783733i
$640$	17.7415	−	21.9309i	0.701294	−	0.866897i
$641$	3.54806	+	2.04848i	0.140140	+	0.0809099i	0.568431	−	0.822731i	$-0.307551\pi$
$641$	3.54806	+	2.04848i	0.140140	+	0.0809099i	−0.428291	+	0.903641i	$0.640884\pi$
$642$	2.77122	−	4.02588i	0.109371	−	0.158889i
$643$	−40.3600	+	10.8144i	−1.59164	+	0.426479i	−0.942505	−	0.334192i	$-0.891536\pi$
$643$	−40.3600	+	10.8144i	−1.59164	+	0.426479i	−0.649137	+	0.760672i	$0.724870\pi$
$644$	0.625170	+	0.360942i	0.0246351	+	0.0142231i
$645$	−19.0592	−	4.58045i	−0.750454	−	0.180355i
$646$	−35.4768	+	61.4477i	−1.39582	+	2.41763i
$647$	6.30036	+	1.68818i	0.247693	+	0.0663691i	0.380529	−	0.924769i	$-0.375742\pi$
$647$	6.30036	+	1.68818i	0.247693	+	0.0663691i	−0.132836	+	0.991138i	$0.542409\pi$
$648$	14.8289	−	7.50144i	0.582532	−	0.294685i
$649$			2.94012i			0.115410i
$650$	24.5667	+	18.5809i	0.963587	+	0.728802i
$651$	1.33041	−	0.245576i	0.0521428	−	0.00962489i
$652$	−10.8839	−	2.91634i	−0.426247	−	0.114213i
$653$	−11.9894	+	44.7451i	−0.469182	+	1.75101i	0.173454	+	0.984842i	$0.444507\pi$
$653$	−11.9894	+	44.7451i	−0.469182	+	1.75101i	−0.642637	+	0.766171i	$0.722160\pi$
$654$	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
$657$	7.48790	+	10.3378i	0.292131	+	0.403315i
$658$	0.0359145	+	0.0359145i	0.00140009	+	0.00140009i
$659$	12.0799	−	20.9230i	0.470566	−	0.815045i	−0.528867	−	0.848705i	$-0.677383\pi$
$659$	12.0799	−	20.9230i	0.470566	−	0.815045i	0.999433	+	0.0336601i	$0.0107164\pi$
$660$	−12.8552	−	6.98372i	−0.500388	−	0.271841i
$661$	35.3712	−	20.4215i	1.37578	−	0.794306i	0.384130	−	0.923279i	$-0.374501\pi$
$661$	35.3712	−	20.4215i	1.37578	−	0.794306i	0.991648	+	0.128973i	$0.0411680\pi$
$662$	16.8478	−	16.8478i	0.654809	−	0.654809i
$663$	26.2796	−	19.3044i	1.02061	−	0.749722i
$664$			5.33862i			0.207178i
$665$	1.26714	−	1.56636i	0.0491375	−	0.0607407i
$666$	−13.7281	+	16.9025i	−0.531953	+	0.654958i
$667$	26.9112	−	7.21084i	1.04201	−	0.279205i
$668$	5.79933	−	5.79933i	0.224383	−	0.224383i
$669$	−7.03481	+	19.8199i	−0.271981	+	0.766281i
$670$	−6.64025	−	9.13008i	−0.256535	−	0.352726i
$671$	−16.7777			−0.647694
$672$	−0.408147	−	0.857300i	−0.0157446	−	0.0330711i
$673$	11.9542	+	3.20311i	0.460799	+	0.123471i	0.481748	−	0.876310i	$-0.340002\pi$
$673$	11.9542	+	3.20311i	0.460799	+	0.123471i	−0.0209488	+	0.999781i	$0.506669\pi$
$674$	−5.40272	+	3.11926i	−0.208105	+	0.120150i
$675$	−12.3696	−	22.8472i	−0.476105	−	0.879388i
$676$	11.1053	−	4.41570i	0.427126	−	0.169834i
$677$	−17.7462	+	17.7462i	−0.682043	+	0.682043i	−0.960460	−	0.278418i	$-0.910190\pi$
$677$	−17.7462	+	17.7462i	−0.682043	+	0.682043i	0.278418	+	0.960460i	$0.410190\pi$
$678$	1.85457	−	23.3475i	0.0712242	−	0.896655i
$679$	−0.0146595	+	0.00846367i	−0.000562580	+	0.000324806i
$680$	−17.4350	+	12.6803i	−0.668601	+	0.486269i
$681$	−23.6203	+	4.36001i	−0.905132	+	0.167076i
$682$	12.5280	+	46.7550i	0.479721	+	1.79034i
$683$	5.71276	+	21.3203i	0.218593	+	0.815798i	0.984871	+	0.173290i	$0.0554397\pi$
$683$	5.71276	+	21.3203i	0.218593	+	0.815798i	−0.766278	+	0.642509i	$0.777894\pi$
$684$	20.4889	−	7.83079i	0.783413	−	0.299418i
$685$	−4.34499	+	27.5207i	−0.166013	+	1.05151i
$686$	2.34469	−	1.35371i	0.0895208	−	0.0516848i
$687$	14.7090	+	1.16839i	0.561185	+	0.0445767i
$688$	17.8706	−	17.8706i	0.681312	−	0.681312i
$689$	−3.25319	+	9.36396i	−0.123937	+	0.356738i
$690$	−39.1143	+	23.9566i	−1.48906	+	0.912013i
$691$	−7.86173	+	4.53897i	−0.299074	+	0.172671i	−0.642027	−	0.766682i	$-0.721906\pi$
$691$	−7.86173	+	4.53897i	−0.299074	+	0.172671i	0.342953	+	0.939353i	$0.388573\pi$
$692$	−7.81226	−	2.09329i	−0.296978	−	0.0795749i
$693$	1.13098	−	0.819193i	0.0429622	−	0.0311186i
$694$	−27.2665			−1.03502
$695$	6.92946	−	5.03975i	0.262849	−	0.191169i
$696$	−12.1145	−	4.29988i	−0.459199	−	0.162987i
$697$	−12.8354	+	12.8354i	−0.486176	+	0.486176i
$698$	9.84754	−	2.63864i	0.372735	−	0.0998740i
$699$	13.6894	+	16.0518i	0.517779	+	0.607135i
$700$	−0.463744	+	0.236864i	−0.0175279	+	0.00895260i
$701$		−	31.3445i		−	1.18386i	−0.805988	−	0.591932i	$-0.798365\pi$
$701$		−	31.3445i		−	1.18386i	0.805988	−	0.591932i	$-0.201635\pi$
$702$	−31.9728	−	1.55424i	−1.20674	−	0.0586611i
$703$	23.8907	−	23.8907i	0.901053	−	0.901053i
$704$	−6.11777	+	3.53210i	−0.230572	+	0.133121i
$705$	−0.974479	+	0.288404i	−0.0367010	+	0.0108619i
$706$	−10.6413	+	18.4312i	−0.400489	+	0.693667i
$707$	0.972198	+	0.972198i	0.0365633	+	0.0365633i
$708$	0.489751	+	1.02871i	0.0184060	+	0.0386612i
$709$	16.2682	−	28.1774i	0.610967	−	1.05823i	−0.380111	−	0.924941i	$-0.624114\pi$
$709$	16.2682	−	28.1774i	0.610967	−	1.05823i	0.991078	−	0.133285i	$-0.0425524\pi$
$710$	30.3390	−	11.6632i	1.13860	−	0.437711i
$711$	−2.29457	+	14.3523i	−0.0860532	+	0.538252i
$712$	1.54495	−	5.76582i	0.0578993	−	0.216083i
$713$	46.1615	+	12.3689i	1.72876	+	0.463220i
$714$	0.317763	+	1.72148i	0.0118920	+	0.0644247i
$715$	−17.4911	−	28.1334i	−0.654130	−	1.05213i
$716$			18.2992i			0.683873i
$717$	−1.58452	+	19.9478i	−0.0591749	+	0.744964i
$718$	49.3238	+	13.2163i	1.84075	+	0.493227i
$719$	14.5548	−	25.2096i	0.542802	−	0.940160i	−0.455940	−	0.890010i	$-0.650697\pi$
$719$	14.5548	−	25.2096i	0.542802	−	0.940160i	0.998742	−	0.0501495i	$-0.0159698\pi$
$720$	33.4497	+	1.78532i	1.24660	+	0.0665349i
$721$	0.0733041	+	0.0423222i	0.00272999	+	0.00157616i
$722$	−73.0360	+	19.5699i	−2.71812	+	0.728318i
$723$	19.9230	+	13.7140i	0.740944	+	0.510030i
$724$	−5.93194	−	3.42480i	−0.220459	−	0.127282i
$725$	−6.19162	+	19.1197i	−0.229951	+	0.710089i
$726$	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	$0.640486\pi$
$728$	0.0546877	−	0.752239i	0.00202686	−	0.0278798i
$729$	24.0035	+	12.3626i	0.889018	+	0.457873i
$730$	1.70716	+	16.1662i	0.0631849	+	0.598337i
$731$	−22.8861	+	13.2133i	−0.846475	+	0.488712i
$732$	−5.87029	+	2.79475i	−0.216972	+	0.103297i
$733$	−9.86693	−	9.86693i	−0.364443	−	0.364443i	0.501003	−	0.865446i	$-0.332965\pi$
$733$	−9.86693	−	9.86693i	−0.364443	−	0.364443i	−0.865446	+	0.501003i	$0.832965\pi$
$734$	19.8780	+	11.4766i	0.733711	+	0.423608i
$735$	0.702002	+	27.0521i	0.0258937	+	0.997831i
$736$		−	33.5405i		−	1.23632i
$737$	3.14249	+	11.7279i	0.115755	+	0.432004i
$738$	17.7245	−	1.83687i	0.652450	−	0.0676162i
$739$	−12.6022	−	21.8276i	−0.463578	−	0.802941i	0.535558	−	0.844498i	$-0.320101\pi$
$739$	−12.6022	−	21.8276i	−0.463578	−	0.802941i	−0.999136	+	0.0415576i	$0.986768\pi$
$740$	−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
$743$	36.3190	+	9.73165i	1.33242	+	0.357020i	0.853615	−	0.520904i	$-0.174405\pi$
$743$	36.3190	+	9.73165i	1.33242	+	0.357020i	0.478801	+	0.877924i	$0.341072\pi$
$744$	−14.3084	−	16.7777i	−0.524573	−	0.615100i
$745$	21.5144	−	15.6473i	0.788228	−	0.573273i
$746$	−34.1098			−1.24885
$747$	−7.02462	+	5.08809i	−0.257017	+	0.186164i
$748$	−19.0513	+	5.10478i	−0.696584	+	0.186649i
$749$			0.187098i			0.00683642i
$750$	0.841413	−	33.0761i	0.0307241	−	1.20777i
$751$	14.1002	+	24.4223i	0.514524	+	0.891182i	0.999858	+	0.0168530i	$0.00536474\pi$
$751$	14.1002	+	24.4223i	0.514524	+	0.891182i	−0.485334	+	0.874329i	$0.661302\pi$
$752$	0.339125	−	1.26563i	0.0123666	−	0.0461529i
$753$	−24.5872	−	16.9246i	−0.896007	−	0.616768i
$754$	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
$757$	7.80797	−	29.1397i	0.283785	−	1.05910i	−0.665937	−	0.746008i	$-0.731968\pi$
$757$	7.80797	−	29.1397i	0.283785	−	1.05910i	0.949722	−	0.313093i	$-0.101365\pi$
$758$	−55.3013	+	14.8179i	−2.00863	+	0.538211i
$759$	48.5108	−	8.95446i	1.76083	−	0.325026i
$760$	−32.4359	−	5.12101i	−1.17657	−	0.185759i
$761$	−14.3226	+	24.8075i	−0.519195	+	0.899272i	0.480556	+	0.876964i	$0.340435\pi$
$761$	−14.3226	+	24.8075i	−0.519195	+	0.899272i	−0.999751	+	0.0223082i	$0.992898\pi$
$762$	31.0503	+	21.3735i	1.12483	+	0.774282i
$763$	0.0187324	+	0.0699104i	0.000678160	+	0.00253093i
$764$	10.5503	+	18.2736i	0.381695	+	0.661115i
$765$	−33.3018	−	10.8559i	−1.20403	−	0.392494i
$766$	−4.61630			−0.166794
$767$	−0.187066	+	2.57312i	−0.00675455	+	0.0929101i
$768$	−17.7914	+	25.8464i	−0.641992	+	0.932650i
$769$	−26.5529	−	45.9910i	−0.957522	−	1.65848i	−0.728488	−	0.685059i	$-0.759776\pi$
$769$	−26.5529	−	45.9910i	−0.957522	−	1.65848i	−0.229035	−	0.973418i	$-0.573557\pi$
$770$	1.76861	−	0.186767i	0.0637364	−	0.00673063i
$771$	−0.683314	−	0.242533i	−0.0246090	−	0.00873463i
$772$	14.2456	−	14.2456i	0.512711	−	0.512711i
$773$	−9.14659	−	34.1355i	−0.328980	−	1.22777i	−0.910250	−	0.414059i	$-0.864111\pi$
$773$	−9.14659	−	34.1355i	−0.328980	−	1.22777i	0.581270	−	0.813711i	$-0.302556\pi$
$774$	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
$777$	0.0660057	−	0.830959i	0.00236794	−	0.0298105i
$778$	−17.0777	+	63.7347i	−0.612264	+	2.28500i
$779$	−27.6489			−0.990626
$780$	−10.8062	−	6.92992i	−0.386925	−	0.248131i
$781$	−34.9573			−1.25087
$782$	−16.0047	+	59.7305i	−0.572329	+	2.13596i
$783$	−5.88817	−	20.0385i	−0.210426	−	0.716118i
$784$	−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
$787$	4.96521	+	18.5304i	0.176991	+	0.660539i	0.996204	+	0.0870495i	$0.0277438\pi$
$787$	4.96521	+	18.5304i	0.176991	+	0.660539i	−0.819213	+	0.573489i	$0.805590\pi$
$788$	−5.65154	+	5.65154i	−0.201328	+	0.201328i
$789$	7.58100	−	21.3587i	0.269891	−	0.760391i
$790$	−11.6416	+	14.3906i	−0.414190	+	0.511996i
$791$	0.448293	+	0.776465i	0.0159394	+	0.0276079i
$792$	−20.7799	−	9.28803i	−0.738382	−	0.330036i
$793$	−14.6834	−	1.06748i	−0.521424	−	0.0379075i
$794$	−19.4024			−0.688566
$795$	10.2105	−	3.02186i	0.362127	−	0.107174i
$796$	9.31025	+	16.1258i	0.329993	+	0.571565i
$797$	−4.06620	−	15.1753i	−0.144032	−	0.537535i	−0.999797	−	0.0201695i	$-0.993579\pi$
$797$	−4.06620	−	15.1753i	−0.144032	−	0.537535i	0.855764	−	0.517366i	$-0.173087\pi$
$798$	−1.51188	+	2.19638i	−0.0535200	+	0.0777509i
$799$	−0.685047	+	1.18654i	−0.0242352	+	0.0419766i
$800$	20.3042	+	13.1574i	0.717862	+	0.465183i
$801$	9.05919	−	3.46239i	0.320091	−	0.122338i
$802$	51.4442	−	13.7844i	1.81656	−	0.486745i
$803$	4.52499	−	16.8875i	0.159683	−	0.595946i
$804$	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
$807$	−0.792760	+	1.15168i	−0.0279065	+	0.0405410i
$808$	5.79994	−	21.6457i	0.204041	−	0.761492i
$809$	9.50547	+	16.4640i	0.334195	+	0.578842i	0.983330	−	0.181831i	$-0.0582024\pi$
$809$	9.50547	+	16.4640i	0.334195	+	0.578842i	−0.649135	+	0.760673i	$0.724869\pi$
$810$	18.6576	+	28.8827i	0.655561	+	1.01484i
$811$			18.8816i			0.663023i	0.943451	+	0.331512i	$0.107559\pi$
$811$			18.8816i			0.663023i	−0.943451	+	0.331512i	$0.892441\pi$
$812$	−0.404349	+	0.108345i	−0.0141899	+	0.00380216i
$813$	−16.6563	+	7.92978i	−0.584161	+	0.278109i
$814$	29.8242			1.04534
$815$	−4.27416	+	27.0720i	−0.149717	+	0.948292i
$816$	34.3614	−	29.3042i	1.20289	−	1.02585i
$817$	−38.8812	−	10.4182i	−1.36028	−	0.364486i
$818$	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	0.881814	−	0.471597i	$-0.156322\pi$
$821$	0.931007	+	1.61255i	0.0324924	+	0.0562784i	−0.849322	+	0.527875i	$0.822989\pi$
$822$	2.91983	−	36.7583i	0.101841	−	1.28209i
$823$	5.74475	+	21.4397i	0.200249	+	0.747341i	0.990845	+	0.135003i	$0.0431043\pi$
$823$	5.74475	+	21.4397i	0.200249	+	0.747341i	−0.790596	+	0.612338i	$0.790229\pi$
$824$		−	1.37961i		−	0.0480608i
$825$	−13.6092	+	32.8793i	−0.473812	+	1.14471i
$826$	−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	$0.796375\pi$
$828$	15.4817	−	11.2138i	0.538026	−	0.389705i
$829$	−27.7895	+	16.0443i	−0.965168	+	0.557240i	−0.897760	−	0.440485i	$-0.854806\pi$
$829$	−27.7895	+	16.0443i	−0.965168	+	0.557240i	−0.0674084	+	0.997725i	$0.521473\pi$
$830$	−10.9851	+	1.16003i	−0.381297	+	0.0402653i
$831$	−48.6143	+	8.97358i	−1.68641	+	0.311290i
$832$	−5.57887	+	2.70197i	−0.193412	+	0.0936739i
$833$	25.7974	+	25.7974i	0.893829	+	0.893829i
$834$	−8.62834	+	7.35846i	−0.298775	+	0.254802i
$835$	−15.5094	−	12.5466i	−0.536723	−	0.434194i
$836$	−26.0175	−	15.0212i	−0.899833	−	0.519519i
$837$	8.43932	−	34.8176i	0.291706	−	1.20347i
$838$	36.0442	−	9.65801i	1.24513	−	0.333630i
$839$	−6.21211	−	3.58656i	−0.214466	−	0.123822i	0.388919	−	0.921272i	$-0.372848\pi$
$839$	−6.21211	−	3.58656i	−0.214466	−	0.123822i	−0.603385	+	0.797450i	$0.706182\pi$
$840$	−0.690881	+	0.423148i	−0.0238376	+	0.0146000i
$841$	6.42199	−	11.1232i	0.221448	−	0.383559i
$842$	18.6543	+	4.99840i	0.642869	+	0.172256i
$843$	−23.2868	−	1.84975i	−0.802042	−	0.0637088i
$844$		−	6.70663i		−	0.230852i
$845$	−13.5178	−	25.7346i	−0.465027	−	0.885296i
$846$	1.25636	−	0.480177i	0.0431946	−	0.0165088i
$847$	−0.643817	−	0.172510i	−0.0221218	−	0.00592752i
$848$	−3.55330	+	13.2611i	−0.122021	+	0.455388i
$849$	−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
$852$	−12.2311	+	5.82303i	−0.419031	+	0.199494i
$853$	−26.8806	−	26.8806i	−0.920373	−	0.920373i	0.0766825	−	0.997056i	$-0.475567\pi$
$853$	−26.8806	−	26.8806i	−0.920373	−	0.920373i	−0.997056	+	0.0766825i	$0.975567\pi$
$854$	0.395181	−	0.684474i	0.0135228	−	0.0234222i
$855$	−24.1755	−	47.5603i	−0.826785	−	1.62653i
$856$	2.64094	−	1.52474i	0.0902653	−	0.0521147i
$857$	31.5042	−	31.5042i	1.07616	−	1.07616i	0.0793118	−	0.996850i	$-0.474728\pi$
$857$	31.5042	−	31.5042i	1.07616	−	1.07616i	0.996850	−	0.0793118i	$-0.0252723\pi$
$858$	25.9559	+	35.3344i	0.886121	+	1.20630i
$859$			29.9066i			1.02040i	0.860055	+	0.510201i	$0.170429\pi$
$859$			29.9066i			1.02040i	−0.860055	+	0.510201i	$0.829571\pi$
$860$	8.08855	+	6.54341i	0.275817	+	0.223128i
$861$	−0.519033	+	0.442644i	−0.0176886	+	0.0150853i
$862$	4.48861	−	1.20272i	0.152883	−	0.0409648i
$863$	−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
$865$	−3.06791	+	19.4318i	−0.104312	+	0.660700i
$866$	−24.2113			−0.822732
$867$	−16.0507	+	7.64148i	−0.545111	+	0.259518i
$868$	−0.693590	−	0.185847i	−0.0235420	−	0.00630806i
$869$	17.2402	−	9.95361i	0.584832	−	0.337653i
$870$	6.21533	−	25.8618i	0.210719	−	0.876799i
$871$	2.00405	+	10.4640i	0.0679045	+	0.354558i
$872$	0.834142	−	0.834142i	0.0282476	−	0.0282476i
$873$	0.0462071	+	0.445866i	0.00156387	+	0.0150903i
$874$	−81.5712	+	47.0952i	−2.75919	+	1.59302i
$875$	0.691407	+	1.06125i	0.0233738	+	0.0358767i
$876$	−1.22981	−	6.66246i	−0.0415513	−	0.225104i
$877$	−9.13551	−	34.0942i	−0.308484	−	1.15128i	−0.929904	−	0.367801i	$-0.880111\pi$
$877$	−9.13551	−	34.0942i	−0.308484	−	1.15128i	0.621420	−	0.783478i	$-0.286556\pi$
$878$	−4.13681	−	15.4388i	−0.139610	−	0.521033i
$879$	−2.37315	−	12.8565i	−0.0800445	−	0.433640i
$880$	−26.9856	−	37.1041i	−0.909684	−	1.25078i
$881$	−0.0237715	+	0.0137245i	−0.000800881	+	0.000462389i	−0.500400	−	0.865794i	$-0.666814\pi$
$881$	−0.0237715	+	0.0137245i	−0.000800881	+	0.000462389i	0.499600	+	0.866257i	$0.333481\pi$
$882$	−3.69187	−	35.6240i	−0.124312	−	1.19952i
$883$	−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
$885$	2.36324	−	1.44743i	0.0794394	−	0.0486548i
$886$	−12.0157	+	6.93725i	−0.403674	+	0.233061i
$887$	2.92906	+	0.784839i	0.0983482	+	0.0263523i	0.307658	−	0.951497i	$-0.400455\pi$
$887$	2.92906	+	0.784839i	0.0983482	+	0.0263523i	−0.209309	+	0.977849i	$0.567122\pi$
$888$	−12.2671	+	5.84015i	−0.411656	+	0.195983i
$889$	−1.44303			−0.0483976
$890$	12.1998	+	1.92612i	0.408938	+	0.0645635i
$891$	−7.58347	−	36.1946i	−0.254056	−	1.21257i
$892$	7.89315	−	7.89315i	0.264282	−	0.264282i
$893$	−2.01580	+	0.540132i	−0.0674562	+	0.0180748i
$894$	−26.7891	+	22.8464i	−0.895961	+	0.764097i
$895$	44.2638	−	4.67430i	1.47958	−	0.156245i
$896$		−	1.42917i		−	0.0477451i
$897$	43.0253	−	4.75024i	1.43657	−	0.158606i
$898$	32.7688	−	32.7688i	1.09351	−	1.09351i
$899$	−24.0000	+	13.8564i	−0.800446	+	0.462138i
$900$	0.715198	+	13.7710i	0.0238399	+	0.459034i
$901$	7.17782	−	12.4324i	0.239128	−	0.414182i
$902$	−17.2580	−	17.2580i	−0.574627	−	0.574627i
$903$	−0.896678	+	0.426893i	−0.0298396	+	0.0142061i
$904$	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
$907$	4.50525	−	16.8138i	0.149594	−	0.558294i	−0.849913	−	0.526922i	$-0.823346\pi$
$907$	4.50525	−	16.8138i	0.149594	−	0.558294i	0.999508	−	0.0313715i	$-0.00998751\pi$
$908$	12.3141	+	3.29956i	0.408659	+	0.109500i
$909$	34.0094	−	12.9983i	1.12802	−	0.431126i
$910$	1.55974	−	0.0509260i	0.0517047	−	0.00168818i
$911$			4.78351i			0.158485i	0.996855	+	0.0792423i	$0.0252501\pi$
$911$			4.78351i			0.158485i	−0.996855	+	0.0792423i	$0.974750\pi$
$912$	68.5714	+	5.44685i	2.27063	+	0.180363i
$913$	11.4752	+	3.07477i	0.379774	+	0.101760i
$914$	11.4241	−	19.7871i	0.377876	−	0.654500i
$915$	8.25970	+	13.4857i	0.273057	+	0.445825i
$916$	−6.78234	−	3.91578i	−0.224095	−	0.129381i
$917$	−1.41785	+	0.379911i	−0.0468214	+	0.0125458i
$918$	45.0521	+	10.9200i	1.48694	+	0.360415i
$919$	−20.5581	−	11.8693i	−0.678151	−	0.391530i	0.121007	−	0.992652i	$-0.461388\pi$
$919$	−20.5581	−	11.8693i	−0.678151	−	0.391530i	−0.799158	+	0.601121i	$0.794721\pi$
$920$	−28.4605	+	3.00545i	−0.938314	+	0.0990868i
$921$	9.84626	−	8.39713i	0.324445	−	0.276695i
$922$	41.4418	+	41.4418i	1.36481	+	1.36481i
$923$	−30.5938	−	2.22417i	−1.00701	−	0.0732094i
$924$	−0.728888	+	0.134543i	−0.0239787	+	0.00442616i
$925$	9.66166	+	18.9161i	0.317674	+	0.621958i
$926$	40.6683	−	23.4798i	1.33644	−	0.771595i
$927$	1.81530	−	1.31487i	0.0596223	−	0.0431859i
$928$	13.7531	+	13.7531i	0.451467	+	0.451467i
$929$	27.3742	+	15.8045i	0.898117	+	0.518528i	0.876589	−	0.481240i	$-0.159814\pi$
$929$	27.3742	+	15.8045i	0.898117	+	0.518528i	0.0215282	+	0.999768i	$0.493147\pi$
$930$	31.4137	−	33.0875i	1.03010	−	1.08498i
$931$			55.5706i			1.82125i
$932$	−2.89804	−	10.8156i	−0.0949283	−	0.354277i
$933$	−0.325879	+	4.10256i	−0.0106688	+	0.134312i
$934$	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	$0.844413\pi$
$938$	−0.552480	−	0.148037i	−0.0180391	−	0.00483357i
$939$	38.2256	−	32.5997i	1.24744	−	1.06385i
$940$	0.532792	+	0.0841177i	0.0173778	+	0.00274362i
$941$	49.4334			1.61148			0.805741	−	0.592268i	$-0.201767\pi$
$941$	49.4334			1.61148			0.805741	+	0.592268i	$0.201767\pi$
$942$	20.9340	−	9.96635i	0.682068	−	0.324721i
$943$	−23.2755	+	6.23666i	−0.757956	+	0.203094i
$944$			3.57304i			0.116293i
$945$	−1.21524	−	0.505778i	−0.0395319	−	0.0164530i
$946$	−17.7661	−	30.7718i	−0.577625	−	1.00048i
$947$	−6.33163	+	23.6300i	−0.205750	+	0.767871i	0.783469	+	0.621431i	$0.213448\pi$
$947$	−6.33163	+	23.6300i	−0.205750	+	0.767871i	−0.989220	+	0.146440i	$0.953218\pi$
$948$	4.37408	−	6.35443i	0.142064	−	0.206382i
$949$	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
$952$	−0.282693	+	1.05503i	−0.00916215	+	0.0341936i
$953$	−41.7321	+	11.1821i	−1.35184	+	0.362223i	−0.860812	−	0.508923i	$-0.830044\pi$
$953$	−41.7321	+	11.1821i	−1.35184	+	0.362223i	−0.491024	+	0.871146i	$0.663377\pi$
$954$	−13.1640	+	5.03122i	−0.426199	+	0.162892i
$955$	41.5070	−	30.1878i	1.34313	−	0.976853i
$956$	5.31043	−	9.19793i	0.171751	−	0.297482i
$957$	−16.2198	+	23.5632i	−0.524312	+	0.761691i
$958$	0.761659	+	2.84255i	0.0246081	+	0.0918386i
$959$	0.705791	+	1.22247i	0.0227912	+	0.0394755i
$960$	5.85087	+	3.17855i	0.188836	+	0.102587i
$961$	−16.5366			−0.533437
$962$	26.1015	+	1.89758i	0.841546	+	0.0611803i
$963$	4.52328	+	2.02178i	0.145761	+	0.0651510i
$964$	−6.41870	−	11.1175i	−0.206732	−	0.358071i
$965$	−38.0976	−	30.8198i	−1.22640	−	0.992125i
$966$	−0.777310	+	2.18999i	−0.0250095	+	0.0704619i
$967$	4.55251	−	4.55251i	0.146399	−	0.146399i	−0.630108	−	0.776507i	$-0.716990\pi$
$967$	4.55251	−	4.55251i	0.146399	−	0.146399i	0.776507	+	0.630108i	$0.216990\pi$
$968$	2.81172	+	10.4935i	0.0903721	+	0.337273i
$969$	−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	−0.979424	−	0.201814i	$-0.935316\pi$
$971$	−51.2257	−	29.5752i	−1.64391	−	0.949113i	−0.664488	−	0.747299i	$-0.731350\pi$
$972$	−8.68250	−	11.4008i	−0.278491	−	0.365681i
$973$	0.112355	−	0.419316i	0.00360195	−	0.0134427i
$974$	−35.5697			−1.13973
$975$	−14.0024	+	27.9093i	−0.448437	+	0.893814i
$976$	−20.3894			−0.652649
$977$	14.9944	−	55.9598i	0.479713	−	1.79031i	−0.123059	−	0.992399i	$-0.539270\pi$
$977$	14.9944	−	55.9598i	0.479713	−	1.79031i	0.602772	−	0.797914i	$-0.294063\pi$
$978$	2.87223	−	36.1590i	0.0918437	−	1.15624i
$979$	−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
$982$	−9.99359	−	37.2966i	−0.318908	−	1.19018i
$983$	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
$985$	15.1141	+	12.2269i	0.481576	+	0.389581i
$986$	−17.9295	−	31.0548i	−0.570991	−	0.988985i
$987$	−0.0291940	+	0.0424114i	−0.000929254	+	0.00134997i
$988$	−21.8142	−	14.8016i	−0.694002	−	0.470901i
$989$	−35.0811			−1.11551
$990$	14.5963	−	44.7762i	0.463902	−	1.42308i
$991$	6.95908	+	12.0535i	0.221063	+	0.382892i	0.955131	−	0.296184i	$-0.0957142\pi$
$991$	6.95908	+	12.0535i	0.221063	+	0.382892i	−0.734068	+	0.679076i	$0.762381\pi$
$992$	8.63491	+	32.2259i	0.274159	+	1.02317i
$993$	19.8956	+	13.6952i	0.631367	+	0.434602i
$994$	0.823384	−	1.42614i	0.0261162	−	0.0452345i
$995$	36.6285	−	26.6397i	1.16120	−	0.844535i
$996$	4.52721	−	0.835664i	0.143450	−	0.0264790i
$997$	46.6520	−	12.5004i	1.47748	−	0.395891i	0.571994	−	0.820258i	$-0.306170\pi$
$997$	46.6520	−	12.5004i	1.47748	−	0.395891i	0.905490	+	0.424367i	$0.139503\pi$
$998$	−15.8680	+	59.2202i	−0.502293	+	1.87458i
$999$	−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.62.19	yes	96
3.2	odd	2	inner	195.2.bf.a.62.6	yes	96
5.2	odd	4		975.2.bn.d.218.19		96
5.3	odd	4	inner	195.2.bf.a.23.6	yes	96
5.4	even	2		975.2.bn.d.257.6		96
13.4	even	6	inner	195.2.bf.a.17.19	yes	96
15.2	even	4		975.2.bn.d.218.6		96
15.8	even	4	inner	195.2.bf.a.23.19	yes	96
15.14	odd	2		975.2.bn.d.257.19		96
39.17	odd	6	inner	195.2.bf.a.17.6	✓	96
65.4	even	6		975.2.bn.d.407.6		96
65.17	odd	12		975.2.bn.d.368.19		96
65.43	odd	12	inner	195.2.bf.a.173.6	yes	96
195.17	even	12		975.2.bn.d.368.6		96
195.134	odd	6		975.2.bn.d.407.19		96
195.173	even	12	inner	195.2.bf.a.173.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.6	✓	96	39.17	odd	6	inner
195.2.bf.a.17.19	yes	96	13.4	even	6	inner
195.2.bf.a.23.6	yes	96	5.3	odd	4	inner
195.2.bf.a.23.19	yes	96	15.8	even	4	inner
195.2.bf.a.62.6	yes	96	3.2	odd	2	inner
195.2.bf.a.62.19	yes	96	1.1	even	1	trivial
195.2.bf.a.173.6	yes	96	65.43	odd	12	inner
195.2.bf.a.173.19	yes	96	195.173	even	12	inner
975.2.bn.d.218.6		96	15.2	even	4
975.2.bn.d.218.19		96	5.2	odd	4
975.2.bn.d.257.6		96	5.4	even	2
975.2.bn.d.257.19		96	15.14	odd	2
975.2.bn.d.368.6		96	195.17	even	12
975.2.bn.d.368.19		96	65.17	odd	12
975.2.bn.d.407.6		96	65.4	even	6
975.2.bn.d.407.19		96	195.134	odd	6

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+(0.442218 - 1.65038i) q^{2} +(1.72661 + 0.137150i) q^{3} +(-0.796141 - 0.459652i) q^{4} +(-0.908487 + 2.04320i) q^{5} +(0.989888 - 2.78891i) q^{6} +(0.0293212 + 0.109428i) q^{7} +(1.30565 - 1.30565i) q^{8} +(2.96238 + 0.473611i) q^{9} +(2.97030 + 2.40288i) q^{10} +(-2.05447 - 3.55845i) q^{11} +(-1.31159 - 0.902832i) q^{12} +(-1.57162 - 3.24500i) q^{13} +0.193564 q^{14} +(-1.84883 + 3.40321i) q^{15} +(-2.49674 - 4.32449i) q^{16} +(1.35141 + 5.04353i) q^{17} +(2.09165 - 4.67961i) q^{18} +(-3.97662 + 6.88771i) q^{19} +(1.66244 - 1.20908i) q^{20} +(0.0356182 + 0.192962i) q^{21} +(-6.78132 + 1.81705i) q^{22} +(-1.79398 + 6.69524i) q^{23} +(2.43343 - 2.07529i) q^{24} +(-3.34930 - 3.71244i) q^{25} +(-6.05047 + 1.15878i) q^{26} +(5.04992 + 1.22403i) q^{27} +(0.0269551 - 0.100598i) q^{28} +(-2.00973 - 3.48095i) q^{29} +(4.79900 + 4.55623i) q^{30} -6.89468i q^{31} +(-4.67403 + 1.25240i) q^{32} +(-3.05924 - 6.42584i) q^{33} +8.92135 q^{34} +(-0.250221 - 0.0395052i) q^{35} +(-2.14078 - 1.73873i) q^{36} +(-4.10339 - 1.09950i) 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} +(0.334211 + 0.0265474i) q^{42} +(1.30993 + 4.88872i) q^{43} +3.77737i q^{44} +(-3.65896 + 5.62245i) q^{45} +(10.2563 + 5.92150i) q^{46} +(0.185543 + 0.185543i) q^{47} +(-3.71780 - 7.80914i) q^{48} +(6.05106 - 3.49358i) q^{49} +(-7.60804 + 3.88591i) q^{50} +(1.64164 + 8.89356i) q^{51} +(-0.240337 + 3.30587i) q^{52} +(-1.94409 - 1.94409i) q^{53} +(4.25328 - 7.79300i) q^{54} +(9.13708 - 0.964884i) q^{55} +(0.181159 + 0.104592i) q^{56} +(-7.81074 + 11.3470i) q^{57} +(-6.63362 + 1.77747i) q^{58} +(-0.619675 - 0.357770i) q^{59} +(3.03622 - 1.85961i) q^{60} +(2.04160 - 3.53616i) q^{61} +(-11.3788 - 3.04895i) q^{62} +(0.0350341 + 0.338055i) q^{63} -1.71922i q^{64} +(8.05796 - 0.263096i) q^{65} +(-11.9579 + 2.20728i) q^{66} +(-2.85424 - 0.764792i) q^{67} +(1.24236 - 4.63654i) q^{68} +(-4.01577 + 11.3140i) q^{69} +(-0.175851 + 0.395490i) q^{70} +(4.25380 - 7.36780i) q^{71} +(4.48621 - 3.24947i) q^{72} +(3.00868 + 3.00868i) q^{73} +(-3.62918 + 6.28592i) q^{74} +(-5.27378 - 6.86929i) q^{75} +(6.33191 - 3.65573i) q^{76} +(0.329156 - 0.329156i) q^{77} +(-10.6057 + 1.17093i) q^{78} +4.84485i q^{79} +(11.1040 - 1.17260i) q^{80} +(8.55139 + 2.80603i) q^{81} +(5.73743 - 1.53734i) q^{82} +(-2.04442 + 2.04442i) q^{83} +(0.0603381 - 0.169997i) q^{84} +(-11.5327 - 1.82079i) q^{85} +8.64751 q^{86} +(-2.99261 - 6.28589i) q^{87} +(-7.32854 - 1.96368i) q^{88} +(2.79966 - 1.61638i) q^{89} +(7.66112 + 8.52502i) q^{90} +(0.309013 - 0.267127i) q^{91} +(4.50574 - 4.50574i) q^{92} +(0.945607 - 11.9044i) q^{93} +(0.388267 - 0.224166i) q^{94} +(-10.4602 - 14.3824i) q^{95} +(-8.24201 + 1.52137i) q^{96} +(0.0386722 + 0.144327i) q^{97} +(-3.08985 - 11.5315i) 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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