LMFDB - Embedded newform 195.2.o.a.161.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(86,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.86"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.20
Character	$\chi$	$=$	195.161
Dual form			195.2.o.a.86.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.90946 + 1.90946i) q^{2} +(0.460384 - 1.66974i) q^{3} +5.29209i q^{4} +(0.707107 + 0.707107i) q^{5} +(4.06740 - 2.30923i) q^{6} +(-1.58484 - 1.58484i) q^{7} +(-6.28612 + 6.28612i) q^{8} +(-2.57609 - 1.53745i) q^{9} +2.70039i q^{10} +(3.68605 - 3.68605i) q^{11} +(8.83644 + 2.43639i) q^{12} +(-3.21906 + 1.62409i) q^{13} -6.05240i q^{14} +(1.50623 - 0.855147i) q^{15} -13.4220 q^{16} -1.75794 q^{17} +(-1.98325 - 7.85465i) q^{18} +(-0.812904 + 0.812904i) q^{19} +(-3.74207 + 3.74207i) q^{20} +(-3.37592 + 1.91665i) q^{21} +14.0767 q^{22} +4.74587 q^{23} +(7.60219 + 13.3902i) q^{24} +1.00000i q^{25} +(-9.24780 - 3.04554i) q^{26} +(-3.75314 + 3.59360i) q^{27} +(8.38714 - 8.38714i) q^{28} -4.37626i q^{29} +(4.50896 + 1.24322i) q^{30} +(-0.454250 + 0.454250i) q^{31} +(-13.0566 - 13.0566i) q^{32} +(-4.45776 - 7.85176i) q^{33} +(-3.35671 - 3.35671i) q^{34} -2.24131i q^{35} +(8.13631 - 13.6329i) q^{36} +(0.906820 + 0.906820i) q^{37} -3.10442 q^{38} +(1.22980 + 6.12271i) q^{39} -8.88992 q^{40} +(-2.81924 - 2.81924i) q^{41} +(-10.1060 - 2.78643i) q^{42} +3.01033i q^{43} +(19.5069 + 19.5069i) q^{44} +(-0.734433 - 2.90871i) q^{45} +(9.06206 + 9.06206i) q^{46} +(-2.05622 + 2.05622i) q^{47} +(-6.17929 + 22.4114i) q^{48} -1.97654i q^{49} +(-1.90946 + 1.90946i) q^{50} +(-0.809326 + 2.93531i) q^{51} +(-8.59481 - 17.0356i) q^{52} +8.31773i q^{53} +(-14.0283 - 0.304629i) q^{54} +5.21286 q^{55} +19.9250 q^{56} +(0.983094 + 1.73159i) q^{57} +(8.35630 - 8.35630i) q^{58} +(0.222599 - 0.222599i) q^{59} +(4.52551 + 7.97110i) q^{60} +9.69286 q^{61} -1.73475 q^{62} +(1.64609 + 6.51932i) q^{63} -23.0182i q^{64} +(-3.42462 - 1.12782i) q^{65} +(6.48071 - 23.5046i) q^{66} +(-10.0848 + 10.0848i) q^{67} -9.30316i q^{68} +(2.18492 - 7.92439i) q^{69} +(4.27969 - 4.27969i) q^{70} +(8.02801 + 8.02801i) q^{71} +(25.8582 - 6.52905i) q^{72} +(0.537976 + 0.537976i) q^{73} +3.46308i q^{74} +(1.66974 + 0.460384i) q^{75} +(-4.30196 - 4.30196i) q^{76} -11.6836 q^{77} +(-9.34282 + 14.0393i) q^{78} +8.21258 q^{79} +(-9.49082 - 9.49082i) q^{80} +(4.27251 + 7.92122i) q^{81} -10.7664i q^{82} +(-0.470968 - 0.470968i) q^{83} +(-10.1431 - 17.8657i) q^{84} +(-1.24305 - 1.24305i) q^{85} +(-5.74811 + 5.74811i) q^{86} +(-7.30724 - 2.01476i) q^{87} +46.3419i q^{88} +(-4.20611 + 4.20611i) q^{89} +(4.15170 - 6.95645i) q^{90} +(7.67563 + 2.52779i) q^{91} +25.1156i q^{92} +(0.549352 + 0.967611i) q^{93} -7.85255 q^{94} -1.14962 q^{95} +(-27.8123 + 15.7902i) q^{96} +(-5.84813 + 5.84813i) q^{97} +(3.77413 - 3.77413i) q^{98} +(-15.1627 + 3.82850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} - 16 q^{7} + 4 q^{15} - 64 q^{16} + 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} - 24 q^{27} + 32 q^{28} + 32 q^{31} - 4 q^{33} - 16 q^{34} + 32 q^{37} - 8 q^{39} + 8 q^{42} - 8 q^{45} - 40 q^{46}+ \cdots - 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 - 16 * q^7 + 4 * q^15 - 64 * q^16 + 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 - 24 * q^27 + 32 * q^28 + 32 * q^31 - 4 * q^33 - 16 * q^34 + 32 * q^37 - 8 * q^39 + 8 * q^42 - 8 * q^45 - 40 * q^46 + 8 * q^48 - 32 * q^54 + 8 * q^55 - 36 * q^57 + 24 * q^58 + 16 * q^60 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 + 132 * q^72 - 64 * q^73 + 16 * q^76 - 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 24 * q^85 + 16 * q^87 + 8 * q^91 - 108 * q^93 - 32 * q^94 - 76 * q^96 + 24 * q^97 - 20 * q^99

Character values

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

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.90946	+	1.90946i	1.35019	+	1.35019i	0.885440	+	0.464753i	$0.153857\pi$
$2$	1.90946	+	1.90946i	1.35019	+	1.35019i	0.464753	+	0.885440i	$0.346143\pi$
$3$	0.460384	−	1.66974i	0.265803	−	0.964027i
$3$	0.460384	−	1.66974i	0.265803	−	0.964027i
$4$			5.29209i			2.64605i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	4.06740	−	2.30923i	1.66051	−	0.942738i
$7$	−1.58484	−	1.58484i	−0.599015	−	0.599015i	0.341036	−	0.940050i	$-0.389222\pi$
$7$	−1.58484	−	1.58484i	−0.599015	−	0.599015i	−0.940050	+	0.341036i	$0.889222\pi$
$8$	−6.28612	+	6.28612i	−2.22248	+	2.22248i
$9$	−2.57609	−	1.53745i	−0.858698	−	0.512483i
$10$			2.70039i			0.853937i
$11$	3.68605	−	3.68605i	1.11139	−	1.11139i	0.118422	−	0.992963i	$-0.462217\pi$
$11$	3.68605	−	3.68605i	1.11139	−	1.11139i	0.992963	−	0.118422i	$-0.0377835\pi$
$12$	8.83644	+	2.43639i	2.55086	+	0.703326i
$13$	−3.21906	+	1.62409i	−0.892807	+	0.450440i
$13$	−3.21906	+	1.62409i	−0.892807	+	0.450440i
$14$		−	6.05240i		−	1.61757i
$15$	1.50623	−	0.855147i	0.388906	−	0.220798i
$16$	−13.4220			−3.35551
$17$	−1.75794			−0.426362			−0.213181	−	0.977013i	$-0.568382\pi$
$17$	−1.75794			−0.426362			−0.213181	+	0.977013i	$0.568382\pi$
$18$	−1.98325	−	7.85465i	−0.467457	−	1.85136i
$19$	−0.812904	+	0.812904i	−0.186493	+	0.186493i	−0.794178	−	0.607685i	$-0.792098\pi$
$19$	−0.812904	+	0.812904i	−0.186493	+	0.186493i	0.607685	+	0.794178i	$0.292098\pi$
$20$	−3.74207	+	3.74207i	−0.836753	+	0.836753i
$21$	−3.37592	+	1.91665i	−0.736686	+	0.418247i
$22$	14.0767			3.00117
$23$	4.74587			0.989582			0.494791	−	0.869012i	$-0.335245\pi$
$23$	4.74587			0.989582			0.494791	+	0.869012i	$0.335245\pi$
$24$	7.60219	+	13.3902i	1.55179	+	2.73327i
$25$			1.00000i			0.200000i
$26$	−9.24780	−	3.04554i	−1.81364	−	0.597280i
$27$	−3.75314	+	3.59360i	−0.722292	+	0.691589i
$28$	8.38714	−	8.38714i	1.58502	−	1.58502i
$29$		−	4.37626i		−	0.812651i	−0.913728	−	0.406326i	$-0.866810\pi$
$29$		−	4.37626i		−	0.812651i	0.913728	−	0.406326i	$-0.133190\pi$
$30$	4.50896	+	1.24322i	0.823219	+	0.226979i
$31$	−0.454250	+	0.454250i	−0.0815857	+	0.0815857i	−0.746722	−	0.665136i	$-0.768373\pi$
$31$	−0.454250	+	0.454250i	−0.0815857	+	0.0815857i	0.665136	+	0.746722i	$0.268373\pi$
$32$	−13.0566	−	13.0566i	−2.30811	−	2.30811i
$33$	−4.45776	−	7.85176i	−0.775996	−	1.36682i
$34$	−3.35671	−	3.35671i	−0.575672	−	0.575672i
$35$		−	2.24131i		−	0.378850i
$36$	8.13631	−	13.6329i	1.35605	−	2.27215i
$37$	0.906820	+	0.906820i	0.149080	+	0.149080i	0.777707	−	0.628627i	$-0.216383\pi$
$37$	0.906820	+	0.906820i	0.149080	+	0.149080i	−0.628627	+	0.777707i	$0.716383\pi$
$38$	−3.10442			−0.503603
$39$	1.22980	+	6.12271i	0.196926	+	0.980418i
$40$	−8.88992			−1.40562
$41$	−2.81924	−	2.81924i	−0.440291	−	0.440291i	0.451819	−	0.892110i	$-0.350775\pi$
$41$	−2.81924	−	2.81924i	−0.440291	−	0.440291i	−0.892110	+	0.451819i	$0.850775\pi$
$42$	−10.1060	−	2.78643i	−1.55938	−	0.429955i
$43$			3.01033i			0.459071i	0.973300	+	0.229535i	$0.0737207\pi$
$43$			3.01033i			0.459071i	−0.973300	+	0.229535i	$0.926279\pi$
$44$	19.5069	+	19.5069i	2.94078	+	2.94078i
$45$	−0.734433	−	2.90871i	−0.109483	−	0.433605i
$46$	9.06206	+	9.06206i	1.33613	+	1.33613i
$47$	−2.05622	+	2.05622i	−0.299931	+	0.299931i	−0.840987	−	0.541056i	$-0.818025\pi$
$47$	−2.05622	+	2.05622i	−0.299931	+	0.299931i	0.541056	+	0.840987i	$0.318025\pi$
$48$	−6.17929	+	22.4114i	−0.891904	+	3.23480i
$49$		−	1.97654i		−	0.282363i
$50$	−1.90946	+	1.90946i	−0.270039	+	0.270039i
$51$	−0.809326	+	2.93531i	−0.113328	+	0.411025i
$52$	−8.59481	−	17.0356i	−1.19189	−	2.36241i
$53$			8.31773i			1.14253i	0.820766	+	0.571264i	$0.193547\pi$
$53$			8.31773i			1.14253i	−0.820766	+	0.571264i	$0.806453\pi$
$54$	−14.0283	−	0.304629i	−1.90901	−	0.0414547i
$55$	5.21286			0.702902
$56$	19.9250			2.66260
$57$	0.983094	+	1.73159i	0.130214	+	0.229355i
$58$	8.35630	−	8.35630i	1.09724	−	1.09724i
$59$	0.222599	−	0.222599i	0.0289800	−	0.0289800i	−0.692468	−	0.721448i	$-0.743477\pi$
$59$	0.222599	−	0.222599i	0.0289800	−	0.0289800i	0.721448	+	0.692468i	$0.243477\pi$
$60$	4.52551	+	7.97110i	0.584241	+	1.02906i
$61$	9.69286			1.24104			0.620522	−	0.784189i	$-0.286921\pi$
$61$	9.69286			1.24104			0.620522	+	0.784189i	$0.286921\pi$
$62$	−1.73475			−0.220313
$63$	1.64609	+	6.51932i	0.207388	+	0.821357i
$64$		−	23.0182i		−	2.87728i
$65$	−3.42462	−	1.12782i	−0.424772	−	0.139888i
$66$	6.48071	−	23.5046i	0.797720	−	2.89321i
$67$	−10.0848	+	10.0848i	−1.23206	+	1.23206i	−0.268883	+	0.963173i	$0.586654\pi$
$67$	−10.0848	+	10.0848i	−1.23206	+	1.23206i	−0.963173	+	0.268883i	$0.913346\pi$
$68$		−	9.30316i		−	1.12817i
$69$	2.18492	−	7.92439i	0.263034	−	0.953984i
$70$	4.27969	−	4.27969i	0.511521	−	0.511521i
$71$	8.02801	+	8.02801i	0.952750	+	0.952750i	0.998933	−	0.0461834i	$-0.0147059\pi$
$71$	8.02801	+	8.02801i	0.952750	+	0.952750i	−0.0461834	+	0.998933i	$0.514706\pi$
$72$	25.8582	−	6.52905i	3.04742	−	0.769456i
$73$	0.537976	+	0.537976i	0.0629653	+	0.0629653i	0.737888	−	0.674923i	$-0.235823\pi$
$73$	0.537976	+	0.537976i	0.0629653	+	0.0629653i	−0.674923	+	0.737888i	$0.735823\pi$
$74$			3.46308i			0.402575i
$75$	1.66974	+	0.460384i	0.192805	+	0.0531606i
$76$	−4.30196	−	4.30196i	−0.493469	−	0.493469i
$77$	−11.6836			−1.33147
$78$	−9.34282	+	14.0393i	−1.05787	+	1.58964i
$79$	8.21258			0.923987			0.461993	−	0.886883i	$-0.347134\pi$
$79$	8.21258			0.923987			0.461993	+	0.886883i	$0.347134\pi$
$80$	−9.49082	−	9.49082i	−1.06111	−	1.06111i
$81$	4.27251	+	7.92122i	0.474723	+	0.880135i
$82$		−	10.7664i		−	1.18896i
$83$	−0.470968	−	0.470968i	−0.0516955	−	0.0516955i	0.680786	−	0.732482i	$-0.261638\pi$
$83$	−0.470968	−	0.470968i	−0.0516955	−	0.0516955i	−0.732482	+	0.680786i	$0.761638\pi$
$84$	−10.1431	−	17.8657i	−1.10670	−	1.94931i
$85$	−1.24305	−	1.24305i	−0.134828	−	0.134828i
$86$	−5.74811	+	5.74811i	−0.619835	+	0.619835i
$87$	−7.30724	−	2.01476i	−0.783418	−	0.216005i
$88$			46.3419i			4.94006i
$89$	−4.20611	+	4.20611i	−0.445847	+	0.445847i	−0.893971	−	0.448124i	$-0.852092\pi$
$89$	−4.20611	+	4.20611i	−0.445847	+	0.445847i	0.448124	+	0.893971i	$0.352092\pi$
$90$	4.15170	−	6.95645i	0.437628	−	0.733274i
$91$	7.67563	+	2.52779i	0.804625	+	0.264984i
$92$			25.1156i			2.61848i
$93$	0.549352	+	0.967611i	0.0569651	+	0.100337i
$94$	−7.85255			−0.809929
$95$	−1.14962			−0.117949
$96$	−27.8123	+	15.7902i	−2.83858	+	1.61158i
$97$	−5.84813	+	5.84813i	−0.593787	+	0.593787i	−0.938652	−	0.344865i	$-0.887925\pi$
$97$	−5.84813	+	5.84813i	−0.593787	+	0.593787i	0.344865	+	0.938652i	$0.387925\pi$
$98$	3.77413	−	3.77413i	0.381244	−	0.381244i
$99$	−15.1627	+	3.82850i	−1.52391	+	0.384778i
$100$	−5.29209			−0.529209
$101$	−9.45053			−0.940363			−0.470182	−	0.882570i	$-0.655812\pi$
$101$	−9.45053			−0.940363			−0.470182	+	0.882570i	$0.655812\pi$
$102$	−7.15023	+	4.05948i	−0.707979	+	0.401948i
$103$		−	1.78209i		−	0.175594i	−0.996138	−	0.0877972i	$-0.972017\pi$
$103$		−	1.78209i		−	0.175594i	0.996138	−	0.0877972i	$-0.0279827\pi$
$104$	10.0262	−	30.4446i	0.983150	−	2.98534i
$105$	−3.74241	−	1.03186i	−0.365222	−	0.100699i
$106$	−15.8824	+	15.8824i	−1.54263	+	1.54263i
$107$		−	15.1884i		−	1.46832i	−0.678975	−	0.734161i	$-0.737576\pi$
$107$		−	15.1884i		−	1.46832i	0.678975	−	0.734161i	$-0.262424\pi$
$108$	−19.0177	−	19.8619i	−1.82997	−	1.91122i
$109$	−1.10487	+	1.10487i	−0.105827	+	0.105827i	−0.758038	−	0.652211i	$-0.773842\pi$
$109$	−1.10487	+	1.10487i	−0.105827	+	0.105827i	0.652211	+	0.758038i	$0.273842\pi$
$110$	9.95376	+	9.95376i	0.949053	+	0.949053i
$111$	1.93164	−	1.09667i	0.183344	−	0.104092i
$112$	21.2718	+	21.2718i	2.01000	+	2.01000i
$113$		−	7.82563i		−	0.736173i	−0.929792	−	0.368086i	$-0.880013\pi$
$113$		−	7.82563i		−	0.736173i	0.929792	−	0.368086i	$-0.119987\pi$
$114$	−1.42923	+	5.18359i	−0.133859	+	0.485487i
$115$	3.35584	+	3.35584i	0.312933	+	0.312933i
$116$	23.1596			2.15031
$117$	10.7895	+	0.765340i	0.997494	+	0.0707557i
$118$	0.850091			0.0782572
$119$	2.78606	+	2.78606i	0.255397	+	0.255397i
$120$	−4.09278	+	14.8439i	−0.373618	+	1.35506i
$121$		−	16.1739i		−	1.47035i
$122$	18.5082	+	18.5082i	1.67565	+	1.67565i
$123$	−6.00533	+	3.40947i	−0.541483	+	0.307422i
$124$	−2.40393	−	2.40393i	−0.215879	−	0.215879i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−9.30525	+	15.5915i	−0.828977	+	1.38900i
$127$		−	12.2683i		−	1.08864i	−0.838878	−	0.544320i	$-0.816788\pi$
$127$		−	12.2683i		−	1.08864i	0.838878	−	0.544320i	$-0.183212\pi$
$128$	17.8391	−	17.8391i	1.57677	−	1.57677i
$129$	5.02648	+	1.38591i	0.442557	+	0.122022i
$130$	−4.38566	−	8.69271i	−0.384648	−	0.762401i
$131$		−	19.0344i		−	1.66305i	−0.555489	−	0.831524i	$-0.687469\pi$
$131$		−	19.0344i		−	1.66305i	0.555489	−	0.831524i	$-0.312531\pi$
$132$	41.5522	−	23.5909i	3.61665	−	2.05332i
$133$	2.57665			0.223424
$134$	−38.5131			−3.32703
$135$	−5.19493	−	0.112809i	−0.447108	−	0.00970908i
$136$	11.0506	−	11.0506i	0.947582	−	0.947582i
$137$	6.05814	−	6.05814i	0.517582	−	0.517582i	−0.399257	−	0.916839i	$-0.630732\pi$
$137$	6.05814	−	6.05814i	0.517582	−	0.517582i	0.916839	+	0.399257i	$0.130732\pi$
$138$	19.3033	−	10.9593i	1.64321	−	0.932917i
$139$	−10.1580			−0.861592			−0.430796	−	0.902449i	$-0.641767\pi$
$139$	−10.1580			−0.861592			−0.430796	+	0.902449i	$0.641767\pi$
$140$	11.8612			1.00245
$141$	2.48671	+	4.38002i	0.209419	+	0.368864i
$142$			30.6584i			2.57279i
$143$	−5.87915	+	17.8521i	−0.491639	+	1.49286i
$144$	34.5764	+	20.6357i	2.88137	+	1.71964i
$145$	3.09448	−	3.09448i	0.256983	−	0.256983i
$146$			2.05449i			0.170031i
$147$	−3.30031	−	0.909967i	−0.272205	−	0.0750528i
$148$	−4.79898	+	4.79898i	−0.394473	+	0.394473i
$149$	6.79400	+	6.79400i	0.556586	+	0.556586i	0.928334	−	0.371748i	$-0.121241\pi$
$149$	6.79400	+	6.79400i	0.556586	+	0.556586i	−0.371748	+	0.928334i	$0.621241\pi$
$150$	2.30923	+	4.06740i	0.188548	+	0.332102i
$151$	14.9235	+	14.9235i	1.21445	+	1.21445i	0.969546	+	0.244908i	$0.0787577\pi$
$151$	14.9235	+	14.9235i	1.21445	+	1.21445i	0.244908	+	0.969546i	$0.421242\pi$
$152$		−	10.2200i		−	0.828954i
$153$	4.52861	+	2.70274i	0.366116	+	0.218503i
$154$	−22.3094	−	22.3094i	−1.79775	−	1.79775i
$155$	−0.642406			−0.0515993
$156$	−32.4019	+	6.50823i	−2.59423	+	0.521076i
$157$	−9.94990			−0.794089			−0.397044	−	0.917799i	$-0.629964\pi$
$157$	−9.94990			−0.794089			−0.397044	+	0.917799i	$0.629964\pi$
$158$	15.6816	+	15.6816i	1.24756	+	1.24756i
$159$	13.8885	+	3.82935i	1.10143	+	0.303687i
$160$		−	18.4649i		−	1.45978i
$161$	−7.52146	−	7.52146i	−0.592774	−	0.592774i
$162$	−6.96707	+	23.2835i	−0.547384	+	1.82932i
$163$	1.33592	+	1.33592i	0.104638	+	0.104638i	0.757487	−	0.652850i	$-0.226427\pi$
$163$	1.33592	+	1.33592i	0.104638	+	0.104638i	−0.652850	+	0.757487i	$0.726427\pi$
$164$	14.9197	−	14.9197i	1.16503	−	1.16503i
$165$	2.39992	−	8.70414i	0.186833	−	0.677617i
$166$		−	1.79859i		−	0.139598i
$167$	7.62392	−	7.62392i	0.589957	−	0.589957i	−0.347663	−	0.937620i	$-0.613025\pi$
$167$	7.62392	−	7.62392i	0.589957	−	0.589957i	0.937620	+	0.347663i	$0.113025\pi$
$168$	9.17317	−	33.2697i	0.707726	−	2.56682i
$169$	7.72469	−	10.4561i	0.594207	−	0.804312i
$170$		−	4.74711i		−	0.364087i
$171$	3.34391	−	0.844319i	0.255715	−	0.0645667i
$172$	−15.9309			−1.21472
$173$	17.3873			1.32193			0.660964	−	0.750417i	$-0.270147\pi$
$173$	17.3873			1.32193			0.660964	+	0.750417i	$0.270147\pi$
$174$	−10.1058	−	17.8000i	−0.766117	−	1.34941i
$175$	1.58484	−	1.58484i	0.119803	−	0.119803i
$176$	−49.4743	+	49.4743i	−3.72926	+	3.72926i
$177$	−0.269203	−	0.474166i	−0.0202345	−	0.0356405i
$178$	−16.0628			−1.20396
$179$	23.9770			1.79213			0.896064	−	0.443924i	$-0.146414\pi$
$179$	23.9770			1.79213			0.896064	+	0.443924i	$0.146414\pi$
$180$	15.3932	−	3.88669i	1.14734	−	0.289697i
$181$		−	9.23457i		−	0.686400i	−0.939262	−	0.343200i	$-0.888489\pi$
$181$		−	9.23457i		−	0.686400i	0.939262	−	0.343200i	$-0.111511\pi$
$182$	9.82961	+	19.4830i	0.728620	+	1.44418i
$183$	4.46244	−	16.1846i	0.329873	−	1.19640i
$184$	−29.8331	+	29.8331i	−2.19933	+	2.19933i
$185$			1.28244i			0.0942867i
$186$	−0.798649	+	2.89658i	−0.0585598	+	0.212388i
$187$	−6.47984	+	6.47984i	−0.473853	+	0.473853i
$188$	−10.8817	−	10.8817i	−0.793630	−	0.793630i
$189$	11.6434	+	0.252840i	0.846935	+	0.0183914i
$190$	−2.19516	−	2.19516i	−0.159253	−	0.159253i
$191$		−	19.0991i		−	1.38196i	−0.722874	−	0.690980i	$-0.757179\pi$
$191$		−	19.0991i		−	1.38196i	0.722874	−	0.690980i	$-0.242821\pi$
$192$	−38.4345	−	10.5972i	−2.77377	−	0.764788i
$193$	−2.86517	−	2.86517i	−0.206239	−	0.206239i	0.596428	−	0.802667i	$-0.296586\pi$
$193$	−2.86517	−	2.86517i	−0.206239	−	0.206239i	−0.802667	+	0.596428i	$0.796586\pi$
$194$	−22.3336			−1.60346
$195$	−3.45981	+	5.19901i	−0.247762	+	0.372309i
$196$	10.4600			0.747144
$197$	−15.1179	−	15.1179i	−1.07711	−	1.07711i	−0.996768	−	0.0803391i	$-0.974400\pi$
$197$	−15.1179	−	15.1179i	−1.07711	−	1.07711i	−0.0803391	−	0.996768i	$-0.525600\pi$
$198$	−36.2630	−	21.6422i	−2.57710	−	1.53805i
$199$			26.9039i			1.90717i	0.301131	+	0.953583i	$0.402636\pi$
$199$			26.9039i			1.90717i	−0.301131	+	0.953583i	$0.597364\pi$
$200$	−6.28612	−	6.28612i	−0.444496	−	0.444496i
$201$	12.1962	+	21.4819i	0.860252	+	1.51522i
$202$	−18.0454	−	18.0454i	−1.26967	−	1.26967i
$203$	−6.93569	+	6.93569i	−0.486790	+	0.486790i
$204$	−15.5339	−	4.28303i	−1.08759	−	0.299872i
$205$		−	3.98700i		−	0.278464i
$206$	3.40283	−	3.40283i	0.237086	−	0.237086i
$207$	−12.2258	−	7.29653i	−0.849752	−	0.507144i
$208$	43.2063	−	21.7985i	2.99582	−	1.51146i
$209$			5.99281i			0.414531i
$210$	−5.17569	−	9.11629i	−0.357157	−	0.629084i
$211$	5.67624			0.390769			0.195384	−	0.980727i	$-0.437405\pi$
$211$	5.67624			0.390769			0.195384	+	0.980727i	$0.437405\pi$
$212$	−44.0182			−3.02318
$213$	17.1007	−	9.70876i	1.17172	−	0.665233i
$214$	29.0018	−	29.0018i	1.98252	−	1.98252i
$215$	−2.12862	+	2.12862i	−0.145171	+	0.145171i
$216$	1.00287	−	46.1825i	0.0682364	−	3.14232i
$217$	1.43983			0.0977421
$218$	−4.21940			−0.285774
$219$	1.14596	−	0.650607i	0.0774367	−	0.0439639i
$220$			27.5869i			1.85991i
$221$	5.65891	−	2.85504i	0.380659	−	0.192051i
$222$	5.78246	+	1.59435i	0.388093	+	0.107006i
$223$	−9.19468	+	9.19468i	−0.615721	+	0.615721i	−0.944431	−	0.328710i	$-0.893386\pi$
$223$	−9.19468	+	9.19468i	−0.615721	+	0.615721i	0.328710	+	0.944431i	$0.393386\pi$
$224$			41.3855i			2.76518i
$225$	1.53745	−	2.57609i	0.102497	−	0.171740i
$226$	14.9427	−	14.9427i	0.993976	−	0.993976i
$227$	−4.28750	−	4.28750i	−0.284572	−	0.284572i	0.550358	−	0.834929i	$-0.314491\pi$
$227$	−4.28750	−	4.28750i	−0.284572	−	0.284572i	−0.834929	+	0.550358i	$0.814491\pi$
$228$	−9.16373	+	5.20262i	−0.606883	+	0.344552i
$229$	−2.06681	−	2.06681i	−0.136579	−	0.136579i	0.635512	−	0.772091i	$-0.280789\pi$
$229$	−2.06681	−	2.06681i	−0.136579	−	0.136579i	−0.772091	+	0.635512i	$0.780789\pi$
$230$			12.8157i			0.845041i
$231$	−5.37895	+	19.5087i	−0.353909	+	1.28358i
$232$	27.5097	+	27.5097i	1.80610	+	1.80610i
$233$	−9.32465			−0.610878			−0.305439	−	0.952212i	$-0.598803\pi$
$233$	−9.32465			−0.610878			−0.305439	+	0.952212i	$0.598803\pi$
$234$	19.1408	+	22.0636i	1.25128	+	1.44234i
$235$	−2.90794			−0.189693
$236$	1.17802	+	1.17802i	0.0766824	+	0.0766824i
$237$	3.78094	−	13.7129i	0.245598	−	0.890749i
$238$			10.6397i			0.689672i
$239$	−2.07865	−	2.07865i	−0.134457	−	0.134457i	0.636675	−	0.771132i	$-0.280309\pi$
$239$	−2.07865	−	2.07865i	−0.134457	−	0.134457i	−0.771132	+	0.636675i	$0.780309\pi$
$240$	−20.2167	+	11.4778i	−1.30498	+	0.740890i
$241$	−19.3708	−	19.3708i	−1.24779	−	1.24779i	−0.956696	−	0.291089i	$-0.905982\pi$
$241$	−19.3708	−	19.3708i	−1.24779	−	1.24779i	−0.291089	−	0.956696i	$-0.594018\pi$
$242$	30.8834	−	30.8834i	1.98526	−	1.98526i
$243$	15.1934	−	3.48720i	0.974657	−	0.223704i
$244$			51.2955i			3.28386i
$245$	1.39762	−	1.39762i	0.0892909	−	0.0892909i
$246$	−17.9772	−	4.95670i	−1.14619	−	0.316028i
$247$	1.29656	−	3.93701i	0.0824982	−	0.250506i
$248$		−	5.71094i		−	0.362645i
$249$	−1.00322	+	0.569570i	−0.0635766	+	0.0360950i
$250$	−2.70039			−0.170787
$251$	16.5801			1.04653			0.523265	−	0.852170i	$-0.324714\pi$
$251$	16.5801			1.04653			0.523265	+	0.852170i	$0.324714\pi$
$252$	−34.5008	+	8.71126i	−2.17335	+	0.548758i
$253$	17.4935	−	17.4935i	1.09981	−	1.09981i
$254$	23.4259	−	23.4259i	1.46987	−	1.46987i
$255$	−2.64786	+	1.50329i	−0.165815	+	0.0941400i
$256$	22.0899			1.38062
$257$	7.58331			0.473034			0.236517	−	0.971627i	$-0.423994\pi$
$257$	7.58331			0.473034			0.236517	+	0.971627i	$0.423994\pi$
$258$	6.95154	+	12.2442i	0.432784	+	0.762291i
$259$		−	2.87434i		−	0.178603i
$260$	5.96851	−	18.1234i	0.370151	−	1.12397i
$261$	−6.72827	+	11.2737i	−0.416470	+	0.697822i
$262$	36.3455	−	36.3455i	2.24544	−	2.24544i
$263$			29.6577i			1.82877i	0.404844	+	0.914386i	$0.367326\pi$
$263$			29.6577i			1.82877i	−0.404844	+	0.914386i	$0.632674\pi$
$264$	77.3791	+	21.3351i	4.76235	+	1.31308i
$265$	−5.88153	+	5.88153i	−0.361299	+	0.361299i
$266$	4.92002	+	4.92002i	0.301666	+	0.301666i
$267$	5.08671	+	8.95956i	0.311301	+	0.548316i
$268$	−53.3697	−	53.3697i	−3.26008	−	3.26008i
$269$		−	4.95529i		−	0.302129i	−0.988524	−	0.151065i	$-0.951730\pi$
$269$		−	4.95529i		−	0.302129i	0.988524	−	0.151065i	$-0.0482702\pi$
$270$	−9.70411	−	10.1349i	−0.590573	−	0.616792i
$271$	−12.2435	−	12.2435i	−0.743737	−	0.743737i	0.229558	−	0.973295i	$-0.426272\pi$
$271$	−12.2435	−	12.2435i	−0.743737	−	0.743737i	−0.973295	+	0.229558i	$0.926272\pi$
$272$	23.5951			1.43066
$273$	7.75449	−	11.6526i	0.469323	−	0.705247i
$274$	23.1356			1.39767
$275$	3.68605	+	3.68605i	0.222277	+	0.222277i
$276$	41.9366	+	11.5628i	2.52429	+	0.695999i
$277$		−	0.286481i		−	0.0172129i	−0.999963	−	0.00860647i	$-0.997260\pi$
$277$		−	0.286481i		−	0.0172129i	0.999963	−	0.00860647i	$-0.00273956\pi$
$278$	−19.3963	−	19.3963i	−1.16332	−	1.16332i
$279$	1.86858	−	0.471805i	0.111869	−	0.0282462i
$280$	14.0891	+	14.0891i	0.841987	+	0.841987i
$281$	−9.40929	+	9.40929i	−0.561311	+	0.561311i	−0.929680	−	0.368369i	$-0.879916\pi$
$281$	−9.40929	+	9.40929i	−0.561311	+	0.561311i	0.368369	+	0.929680i	$0.379916\pi$
$282$	−3.61519	+	13.1118i	−0.215281	+	0.780794i
$283$		−	28.8859i		−	1.71709i	−0.512740	−	0.858544i	$-0.671369\pi$
$283$		−	28.8859i		−	1.71709i	0.512740	−	0.858544i	$-0.328631\pi$
$284$	−42.4850	+	42.4850i	−2.52102	+	2.52102i
$285$	−0.529267	+	1.91957i	−0.0313511	+	0.113706i
$286$	−45.3139	+	22.8618i	−2.67946	+	1.35185i
$287$			8.93610i			0.527481i
$288$	13.5612	+	53.7090i	0.799102	+	3.16483i
$289$	−13.9097			−0.818215
$290$	11.8176			0.693953
$291$	7.07249	+	12.4573i	0.414597	+	0.730258i
$292$	−2.84702	+	2.84702i	−0.166609	+	0.166609i
$293$	4.71291	−	4.71291i	0.275331	−	0.275331i	−0.555911	−	0.831242i	$-0.687630\pi$
$293$	4.71291	−	4.71291i	0.275331	−	0.275331i	0.831242	+	0.555911i	$0.187630\pi$
$294$	−4.56428	−	8.03937i	−0.266194	−	0.468866i
$295$	0.314803			0.0183286
$296$	−11.4008			−0.662656
$297$	−0.588059	+	27.0804i	−0.0341226	+	1.57137i
$298$			25.9458i			1.50300i
$299$	−15.2772	+	7.70770i	−0.883505	+	0.445748i
$300$	−2.43639	+	8.83644i	−0.140665	+	0.510172i
$301$	4.77090	−	4.77090i	0.274990	−	0.274990i
$302$			56.9916i			3.27950i
$303$	−4.35087	+	15.7800i	−0.249951	+	0.906536i
$304$	10.9108	−	10.9108i	0.625779	−	0.625779i
$305$	6.85389	+	6.85389i	0.392453	+	0.392453i
$306$	3.48644	+	13.8080i	0.199306	+	0.789350i
$307$	20.7819	+	20.7819i	1.18609	+	1.18609i	0.978140	+	0.207949i	$0.0666787\pi$
$307$	20.7819	+	20.7819i	1.18609	+	1.18609i	0.207949	+	0.978140i	$0.433321\pi$
$308$		−	61.8308i		−	3.52314i
$309$	−2.97563	−	0.820445i	−0.169278	−	0.0466735i
$310$	−1.22665	−	1.22665i	−0.0696691	−	0.0696691i
$311$	−12.0971			−0.685963			−0.342981	−	0.939342i	$-0.611437\pi$
$311$	−12.0971			−0.685963			−0.342981	+	0.939342i	$0.611437\pi$
$312$	−46.2188	−	30.7574i	−2.61662	−	1.74130i
$313$	−18.4060			−1.04037			−0.520183	−	0.854055i	$-0.674136\pi$
$313$	−18.4060			−1.04037			−0.520183	+	0.854055i	$0.674136\pi$
$314$	−18.9990	−	18.9990i	−1.07217	−	1.07217i
$315$	−3.44589	+	5.77382i	−0.194154	+	0.325318i
$316$			43.4617i			2.44491i
$317$	−2.39602	−	2.39602i	−0.134574	−	0.134574i	0.636611	−	0.771185i	$-0.280336\pi$
$317$	−2.39602	−	2.39602i	−0.134574	−	0.134574i	−0.771185	+	0.636611i	$0.780336\pi$
$318$	19.2075	+	33.8315i	1.07711	+	1.89718i
$319$	−16.1311	−	16.1311i	−0.903169	−	0.903169i
$320$	16.2763	−	16.2763i	0.909874	−	0.909874i
$321$	−25.3608	−	6.99252i	−1.41550	−	0.390284i
$322$		−	28.7239i		−	1.60072i
$323$	1.42903	−	1.42903i	0.0795136	−	0.0795136i
$324$	−41.9198	+	22.6105i	−2.32888	+	1.25614i
$325$	−1.62409	−	3.21906i	−0.0900881	−	0.178561i
$326$			5.10179i			0.282562i
$327$	1.33618	+	2.35351i	0.0738910	+	0.130149i
$328$	35.4441			1.95707
$329$	6.51758			0.359326
$330$	21.2028	−	12.0377i	1.16717	−	0.662652i
$331$	5.01639	−	5.01639i	0.275726	−	0.275726i	−0.555674	−	0.831400i	$-0.687540\pi$
$331$	5.01639	−	5.01639i	0.275726	−	0.275726i	0.831400	+	0.555674i	$0.187540\pi$
$332$	2.49241	−	2.49241i	0.136789	−	0.136789i
$333$	−0.941865	−	3.73024i	−0.0516139	−	0.204416i
$334$	29.1152			1.59311
$335$	−14.2621			−0.779221
$336$	45.3118	−	25.7253i	2.47196	−	1.40343i
$337$		−	14.3651i		−	0.782518i	−0.920281	−	0.391259i	$-0.872040\pi$
$337$		−	14.3651i		−	0.782518i	0.920281	−	0.391259i	$-0.127960\pi$
$338$	34.7154	−	5.21544i	1.88827	−	0.283683i
$339$	−13.0668	−	3.60279i	−0.709691	−	0.195677i
$340$	6.57833	−	6.57833i	0.356760	−	0.356760i
$341$			3.34877i			0.181346i
$342$	7.99727	+	4.77288i	0.432443	+	0.258088i
$343$	−14.2264	+	14.2264i	−0.768154	+	0.768154i
$344$	−18.9233	−	18.9233i	−1.02028	−	1.02028i
$345$	7.14836	−	4.05842i	0.384855	−	0.218498i
$346$	33.2003	+	33.2003i	1.78486	+	1.78486i
$347$			7.59308i			0.407618i	0.979011	+	0.203809i	$0.0653321\pi$
$347$			7.59308i			0.407618i	−0.979011	+	0.203809i	$0.934668\pi$
$348$	10.6623	−	38.6706i	0.571559	−	2.07296i
$349$	10.8348	+	10.8348i	0.579974	+	0.579974i	0.934896	−	0.354922i	$-0.115493\pi$
$349$	10.8348	+	10.8348i	0.579974	+	0.579974i	−0.354922	+	0.934896i	$0.615493\pi$
$350$	6.05240			0.323514
$351$	6.24526	−	17.6634i	0.333347	−	0.942804i
$352$	−96.2547			−5.13039
$353$	−17.1557	−	17.1557i	−0.913106	−	0.913106i	0.0834091	−	0.996515i	$-0.473419\pi$
$353$	−17.1557	−	17.1557i	−0.913106	−	0.913106i	−0.996515	+	0.0834091i	$0.973419\pi$
$354$	0.391368	−	1.41943i	0.0208010	−	0.0754421i
$355$			11.3533i			0.602572i
$356$	−22.2591	−	22.2591i	−1.17973	−	1.17973i
$357$	5.93466	−	3.36935i	0.314095	−	0.178325i
$358$	45.7833	+	45.7833i	2.41972	+	2.41972i
$359$	10.4307	−	10.4307i	0.550510	−	0.550510i	−0.376078	−	0.926588i	$-0.622728\pi$
$359$	10.4307	−	10.4307i	0.550510	−	0.550510i	0.926588	+	0.376078i	$0.122728\pi$
$360$	22.9013	+	13.6678i	1.20700	+	0.720355i
$361$			17.6784i			0.930441i
$362$	17.6331	−	17.6331i	0.926773	−	0.926773i
$363$	−27.0063	−	7.44620i	−1.41746	−	0.390824i
$364$	−13.3773	+	40.6201i	−0.701159	+	2.12907i
$365$			0.760813i			0.0398228i
$366$	39.4248	−	22.3830i	2.06076	−	1.16998i
$367$	4.52740			0.236328			0.118164	−	0.992994i	$-0.462299\pi$
$367$	4.52740			0.236328			0.118164	+	0.992994i	$0.462299\pi$
$368$	−63.6992			−3.32055
$369$	2.92819	+	11.5970i	0.152435	+	0.603718i
$370$	−2.44877	+	2.44877i	−0.127305	+	0.127305i
$371$	13.1823	−	13.1823i	0.684391	−	0.684391i
$372$	−5.12068	+	2.90722i	−0.265495	+	0.150732i
$373$	28.1625			1.45820			0.729099	−	0.684408i	$-0.239939\pi$
$373$	28.1625			1.45820			0.729099	+	0.684408i	$0.239939\pi$
$374$	−24.7460			−1.27959
$375$	0.855147	+	1.50623i	0.0441596	+	0.0777813i
$376$		−	25.8513i		−	1.33318i
$377$	7.10742	+	14.0874i	0.366051	+	0.725540i
$378$	21.7499	+	22.7155i	1.11869	+	1.16836i
$379$	2.26005	−	2.26005i	0.116091	−	0.116091i	−0.646675	−	0.762766i	$-0.723841\pi$
$379$	2.26005	−	2.26005i	0.116091	−	0.116091i	0.762766	+	0.646675i	$0.223841\pi$
$380$		−	6.08389i		−	0.312097i
$381$	−20.4850	−	5.64815i	−1.04948	−	0.289364i
$382$	36.4690	−	36.4690i	1.86591	−	1.86591i
$383$	9.03101	+	9.03101i	0.461463	+	0.461463i	0.899135	−	0.437672i	$-0.144197\pi$
$383$	9.03101	+	9.03101i	0.461463	+	0.461463i	−0.437672	+	0.899135i	$0.644197\pi$
$384$	−21.5739	−	37.9996i	−1.10094	−	1.93916i
$385$	−8.26157	−	8.26157i	−0.421048	−	0.421048i
$386$		−	10.9419i		−	0.556926i
$387$	4.62822	−	7.75489i	0.235266	−	0.394203i
$388$	−30.9488	−	30.9488i	−1.57119	−	1.57119i
$389$	−17.8827			−0.906688			−0.453344	−	0.891336i	$-0.649769\pi$
$389$	−17.8827			−0.906688			−0.453344	+	0.891336i	$0.649769\pi$
$390$	−16.5337	+	3.32095i	−0.837216	+	0.168163i
$391$	−8.34294			−0.421921
$392$	12.4248	+	12.4248i	0.627545	+	0.627545i
$393$	−31.7827	−	8.76316i	−1.60322	−	0.442043i
$394$		−	57.7342i		−	2.90861i
$395$	5.80717	+	5.80717i	0.292190	+	0.292190i
$396$	−20.2607	−	80.2424i	−1.01814	−	4.03233i
$397$	20.1129	+	20.1129i	1.00944	+	1.00944i	0.999955	+	0.00948364i	$0.00301878\pi$
$397$	20.1129	+	20.1129i	1.00944	+	1.00944i	0.00948364	+	0.999955i	$0.496981\pi$
$398$	−51.3719	+	51.3719i	−2.57504	+	2.57504i
$399$	1.18625	−	4.30235i	0.0593868	−	0.215387i
$400$		−	13.4220i		−	0.671102i
$401$	−23.3806	+	23.3806i	−1.16757	+	1.16757i	−0.184796	+	0.982777i	$0.559162\pi$
$401$	−23.3806	+	23.3806i	−1.16757	+	1.16757i	−0.982777	+	0.184796i	$0.940838\pi$
$402$	−17.7308	+	64.3071i	−0.884334	+	3.20735i
$403$	0.724517	−	2.20000i	0.0360908	−	0.109590i
$404$		−	50.0131i		−	2.48824i
$405$	−2.58002	+	8.62227i	−0.128202	+	0.428444i
$406$	−26.4869			−1.31452
$407$	6.68517			0.331371
$408$	−13.3642	−	23.5392i	−0.661625	−	1.16536i
$409$	−11.3883	+	11.3883i	−0.563116	+	0.563116i	−0.930191	−	0.367075i	$-0.880359\pi$
$409$	−11.3883	+	11.3883i	−0.563116	+	0.563116i	0.367075	+	0.930191i	$0.380359\pi$
$410$	7.61303	−	7.61303i	0.375981	−	0.375981i
$411$	−7.32648	−	12.9046i	−0.361388	−	0.636538i
$412$	9.43097			0.464631
$413$	−0.705571			−0.0347189
$414$	−9.41226	−	37.2771i	−0.462588	−	1.83207i
$415$		−	0.666049i		−	0.0326951i
$416$	63.2352	+	20.8250i	3.10036	+	1.02103i
$417$	−4.67659	+	16.9613i	−0.229014	+	0.830598i
$418$	−11.4430	+	11.4430i	−0.559697	+	0.559697i
$419$		−	19.1129i		−	0.933728i	−0.884329	−	0.466864i	$-0.845384\pi$
$419$		−	19.1129i		−	0.933728i	0.884329	−	0.466864i	$-0.154616\pi$
$420$	5.46071	−	19.8052i	0.266455	−	0.966394i
$421$	−24.1154	+	24.1154i	−1.17531	+	1.17531i	−0.194389	+	0.980925i	$0.562272\pi$
$421$	−24.1154	+	24.1154i	−1.17531	+	1.17531i	−0.980925	+	0.194389i	$0.937728\pi$
$422$	10.8386	+	10.8386i	0.527613	+	0.527613i
$423$	8.45835	−	2.13568i	0.411259	−	0.103841i
$424$	−52.2863	−	52.2863i	−2.53925	−	2.53925i
$425$		−	1.75794i		−	0.0852725i
$426$	51.1916	+	14.1146i	2.48024	+	0.683856i
$427$	−15.3617	−	15.3617i	−0.743404	−	0.743404i
$428$	80.3786			3.88525
$429$	27.1017	+	18.0355i	1.30848	+	0.870761i
$430$	−8.12905			−0.392018
$431$	15.3644	+	15.3644i	0.740076	+	0.740076i	0.972592	−	0.232516i	$-0.0746960\pi$
$431$	15.3644	+	15.3644i	0.740076	+	0.740076i	−0.232516	+	0.972592i	$0.574696\pi$
$432$	50.3748	−	48.2334i	2.42366	−	2.32063i
$433$			38.5386i			1.85205i	0.377468	+	0.926023i	$0.376795\pi$
$433$			38.5386i			1.85205i	−0.377468	+	0.926023i	$0.623205\pi$
$434$	2.74930	+	2.74930i	0.131971	+	0.131971i
$435$	−3.74235	−	6.59165i	−0.179432	−	0.316045i
$436$	−5.84705	−	5.84705i	−0.280023	−	0.280023i
$437$	−3.85794	+	3.85794i	−0.184550	+	0.184550i
$438$	3.43047	+	0.945854i	0.163914	+	0.0451947i
$439$		−	6.01382i		−	0.287024i	−0.989649	−	0.143512i	$-0.954160\pi$
$439$		−	6.01382i		−	0.287024i	0.989649	−	0.143512i	$-0.0458395\pi$
$440$	−32.7687	+	32.7687i	−1.56218	+	1.56218i
$441$	−3.03882	+	5.09175i	−0.144706	+	0.242464i
$442$	16.2571	+	5.35387i	0.773269	+	0.254658i
$443$			5.02446i			0.238719i	0.992851	+	0.119360i	$0.0380842\pi$
$443$			5.02446i			0.238719i	−0.992851	+	0.119360i	$0.961916\pi$
$444$	5.80369	+	10.2224i	0.275431	+	0.485135i
$445$	−5.94834			−0.281978
$446$	−35.1138			−1.66269
$447$	14.4721	−	8.21639i	0.684507	−	0.388622i
$448$	−36.4803	+	36.4803i	−1.72353	+	1.72353i
$449$	−23.1186	+	23.1186i	−1.09103	+	1.09103i	−0.0956146	+	0.995418i	$0.530482\pi$
$449$	−23.1186	+	23.1186i	−1.09103	+	1.09103i	−0.995418	+	0.0956146i	$0.969518\pi$
$450$	7.85465	−	1.98325i	0.370272	−	0.0934915i
$451$	−20.7837			−0.978665
$452$	41.4139			1.94795
$453$	31.7889	−	18.0478i	1.49357	−	0.847962i
$454$		−	16.3736i		−	0.768453i
$455$	3.64008	+	7.21490i	0.170649	+	0.338240i
$456$	−17.0648	−	4.70514i	−0.799134	−	0.220338i
$457$	3.46957	−	3.46957i	0.162300	−	0.162300i	−0.621285	−	0.783585i	$-0.713389\pi$
$457$	3.46957	−	3.46957i	0.162300	−	0.162300i	0.783585	+	0.621285i	$0.213389\pi$
$458$		−	7.89301i		−	0.368816i
$459$	6.59778	−	6.31732i	0.307958	−	0.294867i
$460$	−17.7594	+	17.7594i	−0.828036	+	0.828036i
$461$	−0.0185220	−	0.0185220i	−0.000862656	−	0.000862656i	0.706675	−	0.707538i	$-0.250194\pi$
$461$	−0.0185220	−	0.0185220i	−0.000862656	−	0.000862656i	−0.707538	+	0.706675i	$0.750194\pi$
$462$	−47.5220	+	26.9801i	−2.21092	+	1.25523i
$463$	−22.4800	−	22.4800i	−1.04473	−	1.04473i	−0.998951	−	0.0457826i	$-0.985422\pi$
$463$	−22.4800	−	22.4800i	−1.04473	−	1.04473i	−0.0457826	−	0.998951i	$-0.514578\pi$
$464$			58.7383i			2.72686i
$465$	−0.295754	+	1.07265i	−0.0137152	+	0.0497432i
$466$	−17.8051	−	17.8051i	−0.824804	−	0.824804i
$467$	−2.56460			−0.118676			−0.0593378	−	0.998238i	$-0.518899\pi$
$467$	−2.56460			−0.118676			−0.0593378	+	0.998238i	$0.518899\pi$
$468$	−4.05025	+	57.0992i	−0.187223	+	2.63941i
$469$	31.9657			1.47604
$470$	−5.55259	−	5.55259i	−0.256122	−	0.256122i
$471$	−4.58078	+	16.6138i	−0.211071	+	0.765523i
$472$			2.79857i			0.128815i
$473$	11.0962	+	11.0962i	0.510205	+	0.510205i
$474$	33.4038	−	18.9647i	1.53429	−	0.871078i
$475$	−0.812904	−	0.812904i	−0.0372986	−	0.0372986i
$476$	−14.7441	+	14.7441i	−0.675793	+	0.675793i
$477$	12.7881	−	21.4273i	0.585526	−	0.981087i
$478$		−	7.93820i		−	0.363085i
$479$	8.28794	−	8.28794i	0.378686	−	0.378686i	−0.491942	−	0.870628i	$-0.663713\pi$
$479$	8.28794	−	8.28794i	0.378686	−	0.378686i	0.870628	+	0.491942i	$0.163713\pi$
$480$	−30.8316	−	8.50093i	−1.40726	−	0.388013i
$481$	−4.39186	−	1.44635i	−0.200252	−	0.0659481i
$482$		−	73.9757i		−	3.36950i
$483$	−16.0217	+	9.09616i	−0.729012	+	0.413890i
$484$	85.5937			3.89062
$485$	−8.27050			−0.375544
$486$	35.6699	+	22.3526i	1.61802	+	1.01393i
$487$	−0.925018	+	0.925018i	−0.0419166	+	0.0419166i	−0.727754	−	0.685838i	$-0.759436\pi$
$487$	−0.925018	+	0.925018i	−0.0419166	+	0.0419166i	0.685838	+	0.727754i	$0.259436\pi$
$488$	−60.9305	+	60.9305i	−2.75820	+	2.75820i
$489$	2.84569	−	1.61561i	0.128687	−	0.0730606i
$490$	5.33742			0.241120
$491$	4.38624			0.197948			0.0989741	−	0.995090i	$-0.468444\pi$
$491$	4.38624			0.197948			0.0989741	+	0.995090i	$0.468444\pi$
$492$	−18.0432	−	31.7808i	−0.813452	−	1.43279i
$493$			7.69319i			0.346484i
$494$	9.99331	−	5.04184i	0.449620	−	0.226843i
$495$	−13.4288	−	8.01450i	−0.603580	−	0.360225i
$496$	6.09696	−	6.09696i	0.273762	−	0.273762i
$497$		−	25.4463i		−	1.14142i
$498$	−3.00319	−	0.828043i	−0.134576	−	0.0371055i
$499$	0.439217	−	0.439217i	0.0196620	−	0.0196620i	−0.697207	−	0.716869i	$-0.745574\pi$
$499$	0.439217	−	0.439217i	0.0196620	−	0.0196620i	0.716869	+	0.697207i	$0.245574\pi$
$500$	−3.74207	−	3.74207i	−0.167351	−	0.167351i
$501$	−9.22007	−	16.2399i	−0.411922	−	0.725547i
$502$	31.6592	+	31.6592i	1.41302	+	1.41302i
$503$			27.5248i			1.22727i	0.789590	+	0.613634i	$0.210293\pi$
$503$			27.5248i			1.22727i	−0.789590	+	0.613634i	$0.789707\pi$
$504$	−51.3288	−	30.6337i	−2.28636	−	1.36453i
$505$	−6.68254	−	6.68254i	−0.297369	−	0.297369i
$506$	66.8064			2.96990
$507$	−13.9026	−	17.7121i	−0.617437	−	0.786620i
$508$	64.9252			2.88059
$509$	8.72545	+	8.72545i	0.386749	+	0.386749i	0.873526	−	0.486777i	$-0.161828\pi$
$509$	8.72545	+	8.72545i	0.386749	+	0.386749i	−0.486777	+	0.873526i	$0.661828\pi$
$510$	−7.92646	−	2.18549i	−0.350990	−	0.0967753i
$511$		−	1.70522i		−	0.0754343i
$512$	6.50149	+	6.50149i	0.287328	+	0.287328i
$513$	0.129688	−	5.97219i	0.00572586	−	0.263679i
$514$	14.4800	+	14.4800i	0.638687	+	0.638687i
$515$	1.26013	−	1.26013i	0.0555278	−	0.0555278i
$516$	−7.33435	+	26.6006i	−0.322877	+	1.17103i
$517$			15.1587i			0.666677i
$518$	5.48844	−	5.48844i	0.241148	−	0.241148i
$519$	8.00482	−	29.0323i	0.351372	−	1.27438i
$520$	28.6172	−	14.4380i	1.25495	−	0.633148i
$521$			5.01532i			0.219725i	0.993947	+	0.109863i	$0.0350411\pi$
$521$			5.01532i			0.219725i	−0.993947	+	0.109863i	$0.964959\pi$
$522$	−34.3740	+	8.67924i	−1.50451	+	0.379880i
$523$	9.38435			0.410349			0.205174	−	0.978725i	$-0.434224\pi$
$523$	9.38435			0.410349			0.205174	+	0.978725i	$0.434224\pi$
$524$	100.732			4.40050
$525$	−1.91665	−	3.37592i	−0.0836494	−	0.147337i
$526$	−56.6302	+	56.6302i	−2.46920	+	2.46920i
$527$	0.798543	−	0.798543i	0.0347851	−	0.0347851i
$528$	59.8322	+	105.387i	2.60386	+	4.58636i
$529$	−0.476723			−0.0207271
$530$	−22.4611			−0.975648
$531$	−0.915672	+	0.231202i	−0.0397368	+	0.0100333i
$532$			13.6359i			0.591190i
$533$	13.6540	+	4.49661i	0.591419	+	0.194770i
$534$	−7.39507	+	26.8208i	−0.320016	+	1.16065i
$535$	10.7399	−	10.7399i	0.464324	−	0.464324i
$536$		−	126.789i		−	5.47644i
$537$	11.0387	−	40.0355i	0.476353	−	1.72766i
$538$	9.46194	−	9.46194i	0.407933	−	0.407933i
$539$	−7.28562	−	7.28562i	−0.313814	−	0.313814i
$540$	0.596997	−	27.4920i	0.0256907	−	1.18307i
$541$	15.7319	+	15.7319i	0.676367	+	0.676367i	0.959176	−	0.282809i	$-0.0912664\pi$
$541$	15.7319	+	15.7319i	0.676367	+	0.676367i	−0.282809	+	0.959176i	$0.591266\pi$
$542$		−	46.7569i		−	2.00838i
$543$	−15.4194	−	4.25145i	−0.661708	−	0.182447i
$544$	22.9527	+	22.9527i	0.984091	+	0.984091i
$545$	−1.56252			−0.0669308
$546$	37.0571	−	7.44327i	1.58590	−	0.318542i
$547$	4.67474			0.199877			0.0999387	−	0.994994i	$-0.468135\pi$
$547$	4.67474			0.199877			0.0999387	+	0.994994i	$0.468135\pi$
$548$	32.0602	+	32.0602i	1.36955	+	1.36955i
$549$	−24.9697	−	14.9023i	−1.06568	−	0.636013i
$550$			14.0767i			0.600234i
$551$	3.55748	+	3.55748i	0.151554	+	0.151554i
$552$	36.0790	+	63.5484i	1.53562	+	2.70480i
$553$	−13.0157	−	13.0157i	−0.553482	−	0.553482i
$554$	0.547024	−	0.547024i	0.0232408	−	0.0232408i
$555$	2.14134	+	0.590414i	0.0908950	+	0.0250617i
$556$		−	53.7571i		−	2.27981i
$557$	−19.0775	+	19.0775i	−0.808338	+	0.808338i	−0.984382	−	0.176044i	$-0.943670\pi$
$557$	−19.0775	+	19.0775i	−0.808338	+	0.808338i	0.176044	+	0.984382i	$0.443670\pi$
$558$	4.46887	+	2.66708i	0.189182	+	0.112907i
$559$	−4.88903	−	9.69043i	−0.206784	−	0.409861i
$560$			30.0829i			1.27124i
$561$	7.83646	+	13.8029i	0.330856	+	0.582759i
$562$	−35.9334			−1.51576
$563$	−18.5617			−0.782281			−0.391140	−	0.920331i	$-0.627919\pi$
$563$	−18.5617			−0.782281			−0.391140	+	0.920331i	$0.627919\pi$
$564$	−23.1794	+	13.1599i	−0.976030	+	0.554132i
$565$	5.53355	−	5.53355i	0.232798	−	0.232798i
$566$	55.1565	−	55.1565i	2.31840	−	2.31840i
$567$	5.78263	−	19.3252i	0.242848	−	0.811580i
$568$	−100.930			−4.23493
$569$	9.88325			0.414327			0.207164	−	0.978306i	$-0.433577\pi$
$569$	9.88325			0.414327			0.207164	+	0.978306i	$0.433577\pi$
$570$	−4.67596	+	2.65473i	−0.195855	+	0.111195i
$571$		−	35.3312i		−	1.47857i	−0.673395	−	0.739283i	$-0.735165\pi$
$571$		−	35.3312i		−	1.47857i	0.673395	−	0.739283i	$-0.264835\pi$
$572$	−94.4747	−	31.1130i	−3.95019	−	1.30090i
$573$	−31.8906	−	8.79291i	−1.33225	−	0.367329i
$574$	−17.0631	+	17.0631i	−0.712202	+	0.712202i
$575$			4.74587i			0.197916i
$576$	−35.3893	+	59.2970i	−1.47455	+	2.47071i
$577$	−28.7178	+	28.7178i	−1.19554	+	1.19554i	−0.220050	+	0.975489i	$0.570622\pi$
$577$	−28.7178	+	28.7178i	−1.19554	+	1.19554i	−0.975489	+	0.220050i	$0.929378\pi$
$578$	−26.5600	−	26.5600i	−1.10475	−	1.10475i
$579$	−6.10318	+	3.46502i	−0.253639	+	0.144001i
$580$	16.3763	+	16.3763i	0.679988	+	0.679988i
$581$			1.49282i			0.0619327i
$582$	−10.2820	+	37.2913i	−0.426203	+	1.54578i
$583$	30.6596	+	30.6596i	1.26979	+	1.26979i
$584$	−6.76357			−0.279878
$585$	7.08818	+	8.17054i	0.293060	+	0.337810i
$586$	17.9982			0.743500
$587$	−14.5016	−	14.5016i	−0.598546	−	0.598546i	0.341379	−	0.939926i	$-0.389106\pi$
$587$	−14.5016	−	14.5016i	−0.598546	−	0.598546i	−0.939926	+	0.341379i	$0.889106\pi$
$588$	4.81563	−	17.4656i	0.198593	−	0.720268i
$589$		−	0.738523i		−	0.0304303i
$590$	0.601105	+	0.601105i	0.0247471	+	0.0247471i
$591$	−32.2031	+	18.2830i	−1.32466	+	0.752062i
$592$	−12.1714	−	12.1714i	−0.500241	−	0.500241i
$593$	16.0741	−	16.0741i	0.660084	−	0.660084i	−0.295316	−	0.955400i	$-0.595425\pi$
$593$	16.0741	−	16.0741i	0.660084	−	0.660084i	0.955400	+	0.295316i	$0.0954248\pi$
$594$	−52.8319	+	50.5862i	−2.16772	+	2.07558i
$595$			3.94008i			0.161528i
$596$	−35.9545	+	35.9545i	−1.47275	+	1.47275i
$597$	44.9226	+	12.3861i	1.83856	+	0.506930i
$598$	−43.8889	−	14.4537i	−1.79475	−	0.591058i
$599$			1.50675i			0.0615640i	0.999526	+	0.0307820i	$0.00979977\pi$
$599$			1.50675i			0.0615640i	−0.999526	+	0.0307820i	$0.990200\pi$
$600$	−13.3902	+	7.60219i	−0.546655	+	0.310358i
$601$	37.4059			1.52582			0.762910	−	0.646505i	$-0.223770\pi$
$601$	37.4059			1.52582			0.762910	+	0.646505i	$0.223770\pi$
$602$	18.2197			0.742580
$603$	41.4843	−	10.4745i	1.68937	−	0.426556i
$604$	−78.9763	+	78.9763i	−3.21350	+	3.21350i
$605$	11.4367	−	11.4367i	0.464967	−	0.464967i
$606$	−38.4391	+	21.8234i	−1.56148	+	0.886516i
$607$	4.82608			0.195884			0.0979422	−	0.995192i	$-0.468774\pi$
$607$	4.82608			0.195884			0.0979422	+	0.995192i	$0.468774\pi$
$608$	21.2276			0.860892
$609$	8.38775	+	14.7739i	0.339889	+	0.598669i
$610$			26.1745i			1.05977i
$611$	3.27962	−	9.95858i	0.132679	−	0.402881i
$612$	−14.3031	+	23.9658i	−0.578170	+	0.968761i
$613$	31.5265	−	31.5265i	1.27334	−	1.27334i	0.329020	−	0.944323i	$-0.393282\pi$
$613$	31.5265	−	31.5265i	1.27334	−	1.27334i	0.944323	−	0.329020i	$-0.106718\pi$
$614$			79.3647i			3.20290i
$615$	−6.65727	−	1.83555i	−0.268447	−	0.0740166i
$616$	73.4447	−	73.4447i	2.95917	−	2.95917i
$617$	0.339493	+	0.339493i	0.0136675	+	0.0136675i	0.713907	−	0.700240i	$-0.246924\pi$
$617$	0.339493	+	0.339493i	0.0136675	+	0.0136675i	−0.700240	+	0.713907i	$0.746924\pi$
$618$	−4.11525	−	7.24847i	−0.165540	−	0.291576i
$619$	24.3085	+	24.3085i	0.977040	+	0.977040i	0.999742	−	0.0227024i	$-0.00722701\pi$
$619$	24.3085	+	24.3085i	0.977040	+	0.977040i	−0.0227024	+	0.999742i	$0.507227\pi$
$620$		−	3.39967i		−	0.136534i
$621$	−17.8119	+	17.0548i	−0.714767	+	0.684384i
$622$	−23.0989	−	23.0989i	−0.926182	−	0.926182i
$623$	13.3321			0.534138
$624$	−16.5065	−	82.1793i	−0.660788	−	3.28980i
$625$	−1.00000			−0.0400000
$626$	−35.1455	−	35.1455i	−1.40470	−	1.40470i
$627$	10.0065	+	2.75899i	0.399619	+	0.110184i
$628$		−	52.6558i		−	2.10119i
$629$	−1.59413	−	1.59413i	−0.0635623	−	0.0635623i
$630$	−17.6047	+	4.44508i	−0.701388	+	0.177096i
$631$	−1.82450	−	1.82450i	−0.0726324	−	0.0726324i	0.669857	−	0.742490i	$-0.266355\pi$
$631$	−1.82450	−	1.82450i	−0.0726324	−	0.0726324i	−0.742490	+	0.669857i	$0.766355\pi$
$632$	−51.6252	+	51.6252i	−2.05354	+	2.05354i
$633$	2.61325	−	9.47787i	0.103867	−	0.376712i
$634$		−	9.15022i		−	0.363402i
$635$	8.67503	−	8.67503i	0.344258	−	0.344258i
$636$	−20.2653	+	73.4991i	−0.803571	+	2.91443i
$637$	3.21007	+	6.36260i	0.127188	+	0.252095i
$638$		−	61.6035i		−	2.43890i
$639$	−8.33826	−	33.0235i	−0.329856	−	1.30639i
$640$	25.2283			0.997237
$641$	−20.9541			−0.827639			−0.413819	−	0.910359i	$-0.635806\pi$
$641$	−20.9541			−0.827639			−0.413819	+	0.910359i	$0.635806\pi$
$642$	−35.0736	−	61.7775i	−1.38424	−	2.43816i
$643$	16.4365	−	16.4365i	0.648192	−	0.648192i	−0.304364	−	0.952556i	$-0.598444\pi$
$643$	16.4365	−	16.4365i	0.648192	−	0.648192i	0.952556	+	0.304364i	$0.0984439\pi$
$644$	39.8043	−	39.8043i	1.56851	−	1.56851i
$645$	2.57427	+	4.53424i	0.101362	+	0.178536i
$646$	5.45737			0.214718
$647$	44.9519			1.76724			0.883620	−	0.468204i	$-0.155099\pi$
$647$	44.9519			1.76724			0.883620	+	0.468204i	$0.155099\pi$
$648$	−76.6512	−	22.9362i	−3.01115	−	0.901019i
$649$		−	1.64102i		−	0.0644159i
$650$	3.04554	−	9.24780i	0.119456	−	0.362729i
$651$	0.662875	−	2.40415i	0.0259801	−	0.0942260i
$652$	−7.06983	+	7.06983i	−0.276876	+	0.276876i
$653$		−	13.4232i		−	0.525292i	−0.964892	−	0.262646i	$-0.915405\pi$
$653$		−	13.4232i		−	0.525292i	0.964892	−	0.262646i	$-0.0845952\pi$
$654$	−1.94254	+	7.04532i	−0.0759595	+	0.275494i
$655$	13.4594	−	13.4594i	0.525902	−	0.525902i
$656$	37.8399	+	37.8399i	1.47740	+	1.47740i
$657$	−0.558766	−	2.21299i	−0.0217995	−	0.0863368i
$658$	12.4451	+	12.4451i	0.485159	+	0.485159i
$659$			14.8367i			0.577954i	0.957336	+	0.288977i	$0.0933151\pi$
$659$			14.8367i			0.577954i	−0.957336	+	0.288977i	$0.906685\pi$
$660$	46.0631	+	12.7006i	1.79300	+	0.494369i
$661$	10.5386	+	10.5386i	0.409903	+	0.409903i	0.881705	−	0.471802i	$-0.156396\pi$
$661$	10.5386	+	10.5386i	0.409903	+	0.409903i	−0.471802	+	0.881705i	$0.656396\pi$
$662$	19.1572			0.744566
$663$	−2.16192	−	10.7633i	−0.0839620	−	0.418014i
$664$	5.92113			0.229784
$665$	1.82197	+	1.82197i	0.0706529	+	0.0706529i
$666$	5.32430	−	8.92121i	0.206312	−	0.345690i
$667$		−	20.7692i		−	0.804185i
$668$	40.3465	+	40.3465i	1.56105	+	1.56105i
$669$	11.1197	+	19.5859i	0.429912	+	0.757233i
$670$	−27.2329	−	27.2329i	−1.05210	−	1.05210i
$671$	35.7284	−	35.7284i	1.37928	−	1.37928i
$672$	69.1031	+	19.0532i	2.66571	+	0.734993i
$673$			31.1406i			1.20038i	0.799856	+	0.600192i	$0.204909\pi$
$673$			31.1406i			1.20038i	−0.799856	+	0.600192i	$0.795091\pi$
$674$	27.4297	−	27.4297i	1.05655	−	1.05655i
$675$	−3.59360	−	3.75314i	−0.138318	−	0.144458i
$676$	55.3344	+	40.8798i	2.12825	+	1.57230i
$677$		−	30.1978i		−	1.16060i	−0.814404	−	0.580298i	$-0.802936\pi$
$677$		−	30.1978i		−	1.16060i	0.814404	−	0.580298i	$-0.197064\pi$
$678$	−18.0712	−	31.8299i	−0.694018	−	1.22242i
$679$	18.5367			0.711375
$680$	15.6279			0.599303
$681$	−9.13293	+	5.18514i	−0.349975	+	0.198695i
$682$	−6.39436	+	6.39436i	−0.244853	+	0.244853i
$683$	−4.07814	+	4.07814i	−0.156046	+	0.156046i	−0.780812	−	0.624766i	$-0.785194\pi$
$683$	−4.07814	+	4.07814i	−0.156046	+	0.156046i	0.624766	+	0.780812i	$0.285194\pi$
$684$	4.46821	+	17.6963i	0.170846	+	0.676635i
$685$	8.56750			0.327348
$686$	−54.3296			−2.07431
$687$	−4.40258	+	2.49952i	−0.167969	+	0.0953628i
$688$		−	40.4048i		−	1.54042i
$689$	−13.5087	−	26.7753i	−0.514641	−	1.02006i
$690$	21.3989	+	5.90014i	0.814643	+	0.224614i
$691$	−13.3012	+	13.3012i	−0.506000	+	0.506000i	−0.913296	−	0.407296i	$-0.866472\pi$
$691$	−13.3012	+	13.3012i	−0.506000	+	0.506000i	0.407296	+	0.913296i	$0.366472\pi$
$692$			92.0149i			3.49788i
$693$	30.0981	+	17.9630i	1.14333	+	0.682356i
$694$	−14.4987	+	14.4987i	−0.550363	+	0.550363i
$695$	−7.18280	−	7.18280i	−0.272459	−	0.272459i
$696$	58.5992	−	33.2691i	2.22120	−	1.26106i
$697$	4.95604	+	4.95604i	0.187723	+	0.187723i
$698$			41.3773i			1.56615i
$699$	−4.29292	+	15.5698i	−0.162373	+	0.588903i
$700$	8.38714	+	8.38714i	0.317004	+	0.317004i
$701$	−8.80263			−0.332471			−0.166235	−	0.986086i	$-0.553161\pi$
$701$	−8.80263			−0.332471			−0.166235	+	0.986086i	$0.553161\pi$
$702$	45.6527	−	21.8026i	1.72305	−	0.822885i
$703$	−1.47432			−0.0556049
$704$	−84.8462	−	84.8462i	−3.19776	−	3.19776i
$705$	−1.33877	+	4.85551i	−0.0504209	+	0.182869i
$706$		−	65.5164i		−	2.46574i
$707$	14.9776	+	14.9776i	0.563291	+	0.563291i
$708$	2.50933	−	1.42465i	0.0943063	−	0.0535415i
$709$	−20.1751	−	20.1751i	−0.757692	−	0.757692i	0.218210	−	0.975902i	$-0.429978\pi$
$709$	−20.1751	−	20.1751i	−0.757692	−	0.757692i	−0.975902	+	0.218210i	$0.929978\pi$
$710$	−21.6787	+	21.6787i	−0.813588	+	0.813588i
$711$	−21.1564	−	12.6264i	−0.793425	−	0.473527i
$712$		−	52.8803i		−	1.98177i
$713$	−2.15581	+	2.15581i	−0.0807357	+	0.0807357i
$714$	17.7656	+	4.89837i	0.664863	+	0.183317i
$715$	−16.7805	+	8.46613i	−0.627555	+	0.316615i
$716$			126.889i			4.74205i
$717$	−4.42779	+	2.51384i	−0.165359	+	0.0938809i
$718$	39.8339			1.48659
$719$	−3.39602			−0.126650			−0.0633251	−	0.997993i	$-0.520171\pi$
$719$	−3.39602			−0.126650			−0.0633251	+	0.997993i	$0.520171\pi$
$720$	9.85759	+	39.0409i	0.367371	+	1.45497i
$721$	−2.82433	+	2.82433i	−0.105184	+	0.105184i
$722$	−33.7562	+	33.7562i	−1.25628	+	1.25628i
$723$	−41.2624	+	23.4263i	−1.53456	+	0.871234i
$724$	48.8702			1.81625
$725$	4.37626			0.162530
$726$	−37.3492	−	65.7857i	−1.38616	−	2.44154i
$727$		−	3.82751i		−	0.141954i	−0.997478	−	0.0709772i	$-0.977388\pi$
$727$		−	3.82751i		−	0.141954i	0.997478	−	0.0709772i	$-0.0226118\pi$
$728$	−64.1399	+	32.3600i	−2.37718	+	1.19934i
$729$	1.17207	−	26.9745i	0.0434101	−	0.999057i
$730$	−1.45274	+	1.45274i	−0.0537684	+	0.0537684i
$731$		−	5.29197i		−	0.195731i
$732$	85.6504	+	23.6156i	3.16573	+	0.872859i
$733$	−27.6549	+	27.6549i	−1.02146	+	1.02146i	−0.0216912	+	0.999765i	$0.506905\pi$
$733$	−27.6549	+	27.6549i	−1.02146	+	1.02146i	−0.999765	+	0.0216912i	$0.993095\pi$
$734$	8.64490	+	8.64490i	0.319089	+	0.319089i
$735$	−1.69023	−	2.97712i	−0.0623451	−	0.109813i
$736$	−61.9651	−	61.9651i	−2.28406	−	2.28406i
$737$			74.3462i			2.73858i
$738$	−16.5528	+	27.7354i	−0.609319	+	1.02095i
$739$	11.1151	+	11.1151i	0.408874	+	0.408874i	0.881346	−	0.472472i	$-0.156638\pi$
$739$	11.1151	+	11.1151i	0.408874	+	0.408874i	−0.472472	+	0.881346i	$0.656638\pi$
$740$	−6.78678			−0.249487
$741$	−5.97689	−	3.97746i	−0.219566	−	0.146116i
$742$	50.3422			1.84812
$743$	−15.2366	−	15.2366i	−0.558977	−	0.558977i	0.370039	−	0.929016i	$-0.379344\pi$
$743$	−15.2366	−	15.2366i	−0.558977	−	0.558977i	−0.929016	+	0.370039i	$0.879344\pi$
$744$	−9.53581	−	2.62923i	−0.349600	−	0.0963921i
$745$			9.60817i			0.352016i
$746$	53.7752	+	53.7752i	1.96885	+	1.96885i
$747$	0.489169	+	1.93735i	0.0178978	+	0.0708838i
$748$	−34.2919	−	34.2919i	−1.25384	−	1.25384i
$749$	−24.0713	+	24.0713i	−0.879547	+	0.879547i
$750$	−1.24322	+	4.50896i	−0.0453958	+	0.164644i
$751$		−	27.0194i		−	0.985950i	−0.870043	−	0.492975i	$-0.835909\pi$
$751$		−	27.0194i		−	0.985950i	0.870043	−	0.492975i	$-0.164091\pi$
$752$	27.5987	−	27.5987i	1.00642	−	1.00642i
$753$	7.63323	−	27.6846i	0.278171	−	1.00888i
$754$	−13.3281	+	40.4708i	−0.485380	+	1.47386i
$755$			21.1050i			0.768088i
$756$	−1.33805	+	61.6181i	−0.0486646	+	2.24103i
$757$	9.23494			0.335650			0.167825	−	0.985817i	$-0.446326\pi$
$757$	9.23494			0.335650			0.167825	+	0.985817i	$0.446326\pi$
$758$	8.63098			0.313491
$759$	−21.1559	−	37.2634i	−0.767912	−	1.35258i
$760$	7.22665	−	7.22665i	0.262138	−	0.262138i
$761$	−20.0613	+	20.0613i	−0.727222	+	0.727222i	−0.970066	−	0.242843i	$-0.921920\pi$
$761$	−20.0613	+	20.0613i	−0.727222	+	0.727222i	0.242843	+	0.970066i	$0.421920\pi$
$762$	−28.3304	−	49.9003i	−1.02630	−	1.80770i
$763$	3.50208			0.126784
$764$	101.074			3.65673
$765$	1.29109	+	5.11333i	0.0466794	+	0.184873i
$766$			34.4887i			1.24613i
$767$	−0.355040	+	1.07808i	−0.0128198	+	0.0389273i
$768$	10.1698	−	36.8844i	0.366972	−	1.33095i
$769$	−25.1637	+	25.1637i	−0.907425	+	0.907425i	−0.996064	−	0.0886386i	$-0.971748\pi$
$769$	−25.1637	+	25.1637i	−0.907425	+	0.907425i	0.0886386	+	0.996064i	$0.471748\pi$
$770$		−	31.5503i		−	1.13699i
$771$	3.49123	−	12.6622i	0.125734	−	0.456017i
$772$	15.1627	−	15.1627i	0.545719	−	0.545719i
$773$	−19.1823	−	19.1823i	−0.689941	−	0.689941i	0.272278	−	0.962219i	$-0.412223\pi$
$773$	−19.1823	−	19.1823i	−0.689941	−	0.689941i	−0.962219	+	0.272278i	$0.912223\pi$
$774$	23.6451	−	5.97025i	0.849905	−	0.214596i
$775$	−0.454250	−	0.454250i	−0.0163171	−	0.0163171i
$776$		−	73.5241i		−	2.63936i
$777$	−4.79941	−	1.32330i	−0.172178	−	0.0474731i
$778$	−34.1463	−	34.1463i	−1.22420	−	1.22420i
$779$	4.58354			0.164222
$780$	−27.5136	−	18.3096i	−0.985147	−	0.655589i
$781$	59.1833			2.11774
$782$	−15.9305	−	15.9305i	−0.569675	−	0.569675i
$783$	15.7265	+	16.4247i	0.562020	+	0.586971i
$784$			26.5292i			0.947471i
$785$	−7.03564	−	7.03564i	−0.251113	−	0.251113i
$786$	−43.9549	−	77.4207i	−1.56782	−	2.76150i
$787$	8.33052	+	8.33052i	0.296951	+	0.296951i	0.839818	−	0.542868i	$-0.182661\pi$
$787$	8.33052	+	8.33052i	0.296951	+	0.296951i	−0.542868	+	0.839818i	$0.682661\pi$
$788$	80.0054	−	80.0054i	2.85007	−	2.85007i
$789$	49.5208	+	13.6539i	1.76299	+	0.486093i
$790$			22.1771i			0.789027i
$791$	−12.4024	+	12.4024i	−0.440978	+	0.440978i
$792$	71.2482	−	119.381i	2.53170	−	4.24202i
$793$	−31.2019	+	15.7420i	−1.10801	+	0.559016i
$794$			76.8097i			2.72588i
$795$	7.11288	+	12.5284i	0.252268	+	0.444337i
$796$	−142.378			−5.04645
$797$	−26.1215			−0.925270			−0.462635	−	0.886549i	$-0.653096\pi$
$797$	−26.1215			−0.925270			−0.462635	+	0.886549i	$0.653096\pi$
$798$	10.4803	−	5.95008i	0.370998	−	0.210630i
$799$	3.61471	−	3.61471i	0.127879	−	0.127879i
$800$	13.0566	−	13.0566i	0.461622	−	0.461622i
$801$	17.3020	−	4.36866i	0.611337	−	0.154359i
$802$	−89.2888			−3.15290
$803$	3.96601			0.139957
$804$	−113.684	+	64.5432i	−4.00934	+	2.27626i
$805$		−	10.6370i		−	0.374903i
$806$	5.58425	−	2.81738i	0.196697	−	0.0992378i
$807$	−8.27407	−	2.28134i	−0.291261	−	0.0803069i
$808$	59.4072	−	59.4072i	2.08994	−	2.08994i
$809$		−	27.9566i		−	0.982902i	−0.870905	−	0.491451i	$-0.836467\pi$
$809$		−	27.9566i		−	0.982902i	0.870905	−	0.491451i	$-0.163533\pi$
$810$	−21.3903	+	11.5374i	−0.751580	+	0.405384i
$811$	17.7339	−	17.7339i	0.622720	−	0.622720i	−0.323506	−	0.946226i	$-0.604861\pi$
$811$	17.7339	−	17.7339i	0.622720	−	0.622720i	0.946226	+	0.323506i	$0.104861\pi$
$812$	−36.7043	−	36.7043i	−1.28807	−	1.28807i
$813$	−26.0801	+	14.8068i	−0.914671	+	0.519296i
$814$	12.7651	+	12.7651i	0.447415	+	0.447415i
$815$			1.88928i			0.0661787i
$816$	10.8628	−	39.3978i	0.380274	−	1.37920i
$817$	−2.44711	−	2.44711i	−0.0856135	−	0.0856135i
$818$	−43.4911			−1.52063
$819$	−15.8868	−	18.3127i	−0.555130	−	0.639897i
$820$	21.0996			0.736829
$821$	32.2090	+	32.2090i	1.12410	+	1.12410i	0.991118	+	0.132982i	$0.0424553\pi$
$821$	32.2090	+	32.2090i	1.12410	+	1.12410i	0.132982	+	0.991118i	$0.457545\pi$
$822$	10.6513	−	38.6305i	0.371505	−	1.34739i
$823$			33.0237i			1.15113i	0.817755	+	0.575566i	$0.195218\pi$
$823$			33.0237i			1.15113i	−0.817755	+	0.575566i	$0.804782\pi$
$824$	11.2024	+	11.2024i	0.390255	+	0.390255i
$825$	7.85176	−	4.45776i	0.273363	−	0.155199i
$826$	−1.34726	−	1.34726i	−0.0468772	−	0.0468772i
$827$	3.33765	−	3.33765i	0.116061	−	0.116061i	−0.646691	−	0.762752i	$-0.723848\pi$
$827$	3.33765	−	3.33765i	0.116061	−	0.116061i	0.762752	+	0.646691i	$0.223848\pi$
$828$	38.6139	−	64.7000i	1.34192	−	2.24848i
$829$		−	40.6810i		−	1.41291i	−0.707757	−	0.706456i	$-0.750293\pi$
$829$		−	40.6810i		−	1.41291i	0.707757	−	0.706456i	$-0.249707\pi$
$830$	1.27180	−	1.27180i	0.0441447	−	0.0441447i
$831$	−0.478349	−	0.131891i	−0.0165938	−	0.00457525i
$832$	37.3835	+	74.0970i	1.29604	+	2.56885i
$833$			3.47463i			0.120389i
$834$	−41.3167	+	23.4572i	−1.43068	+	0.812255i
$835$	10.7819			0.373121
$836$	−31.7145			−1.09687
$837$	0.0724694	−	3.33725i	0.00250491	−	0.115352i
$838$	36.4954	−	36.4954i	1.26071	−	1.26071i
$839$	−21.1336	+	21.1336i	−0.729614	+	0.729614i	−0.970543	−	0.240929i	$-0.922548\pi$
$839$	−21.1336	+	21.1336i	−0.729614	+	0.729614i	0.240929	+	0.970543i	$0.422548\pi$
$840$	30.0117	−	17.0388i	1.03550	−	0.587896i
$841$	9.84834			0.339598
$842$	−92.0949			−3.17380
$843$	11.3792	+	20.0430i	0.391921	+	0.690317i
$844$			30.0392i			1.03399i
$845$	12.8557	−	1.93137i	0.442251	−	0.0664411i
$846$	20.2289	+	12.0729i	0.695484	+	0.415074i
$847$	−25.6331	+	25.6331i	−0.880764	+	0.880764i
$848$		−	111.641i		−	3.83377i
$849$	−48.2321	−	13.2986i	−1.65532	−	0.456407i
$850$	3.35671	−	3.35671i	0.115134	−	0.115134i
$851$	4.30365	+	4.30365i	0.147527	+	0.147527i
$852$	51.3796	+	90.4984i	1.76024	+	3.10042i
$853$	−33.0134	−	33.0134i	−1.13036	−	1.13036i	−0.990118	−	0.140238i	$-0.955213\pi$
$853$	−33.0134	−	33.0134i	−1.13036	−	1.13036i	−0.140238	−	0.990118i	$-0.544787\pi$
$854$		−	58.6651i		−	2.00748i
$855$	2.96153	+	1.76748i	0.101282	+	0.0604466i
$856$	95.4764	+	95.4764i	3.26332	+	3.26332i
$857$	20.6052			0.703861			0.351930	−	0.936026i	$-0.385525\pi$
$857$	20.6052			0.703861			0.351930	+	0.936026i	$0.385525\pi$
$858$	17.3116	+	86.1878i	0.591009	+	2.94240i
$859$	−32.0080			−1.09210			−0.546049	−	0.837753i	$-0.683869\pi$
$859$	−32.0080			−1.09210			−0.546049	+	0.837753i	$0.683869\pi$
$860$	−11.2649	−	11.2649i	−0.384129	−	0.384129i
$861$	14.9210	+	4.11404i	0.508506	+	0.140206i
$862$			58.6754i			1.99849i
$863$	−28.4308	−	28.4308i	−0.967795	−	0.967795i	0.0317024	−	0.999497i	$-0.489907\pi$
$863$	−28.4308	−	28.4308i	−0.967795	−	0.967795i	−0.999497	+	0.0317024i	$0.989907\pi$
$864$	95.9236	+	2.08301i	3.26339	+	0.0708654i
$865$	12.2946	+	12.2946i	0.418031	+	0.418031i
$866$	−73.5879	+	73.5879i	−2.50062	+	2.50062i
$867$	−6.40378	+	23.2256i	−0.217484	+	0.788782i
$868$			7.61971i			0.258630i
$869$	30.2719	−	30.2719i	1.02691	−	1.02691i
$870$	5.44063	−	19.7324i	0.184455	−	0.668990i
$871$	16.0850	−	48.8422i	0.545020	−	1.65496i
$872$		−	13.8906i		−	0.470396i
$873$	24.0565	−	6.07413i	0.814189	−	0.205578i
$874$	−14.7332			−0.498357
$875$	2.24131			0.0757700
$876$	3.44307	+	6.06451i	0.116331	+	0.204901i
$877$	−5.56017	+	5.56017i	−0.187754	+	0.187754i	−0.794724	−	0.606971i	$-0.792385\pi$
$877$	−5.56017	+	5.56017i	−0.187754	+	0.187754i	0.606971	+	0.794724i	$0.292385\pi$
$878$	11.4832	−	11.4832i	0.387538	−	0.387538i
$879$	−5.69960	−	10.0391i	−0.192243	−	0.338610i
$880$	−69.9672			−2.35859
$881$	−16.1228			−0.543192			−0.271596	−	0.962411i	$-0.587551\pi$
$881$	−16.1228			−0.543192			−0.271596	+	0.962411i	$0.587551\pi$
$882$	−15.5250	+	3.91998i	−0.522755	+	0.131993i
$883$			36.6871i			1.23462i	0.786721	+	0.617309i	$0.211777\pi$
$883$			36.6871i			1.23462i	−0.786721	+	0.617309i	$0.788223\pi$
$884$	15.1091	+	29.9474i	0.508175	+	1.00724i
$885$	0.144930	−	0.525641i	0.00487178	−	0.0176692i
$886$	−9.59402	+	9.59402i	−0.322317	+	0.322317i
$887$			15.7845i			0.529992i	0.964249	+	0.264996i	$0.0853707\pi$
$887$			15.7845i			0.529992i	−0.964249	+	0.264996i	$0.914629\pi$
$888$	−5.24873	+	19.0364i	−0.176136	+	0.638819i
$889$	−19.4434	+	19.4434i	−0.652111	+	0.652111i
$890$	−11.3581	−	11.3581i	−0.380726	−	0.380726i
$891$	44.9467	+	13.4493i	1.50577	+	0.450569i
$892$	−48.6591	−	48.6591i	−1.62923	−	1.62923i
$893$		−	3.34302i		−	0.111870i
$894$	43.3228	+	11.9450i	1.44893	+	0.399501i
$895$	16.9543	+	16.9543i	0.566721	+	0.566721i
$896$	−56.5445			−1.88902
$897$	5.83649	+	29.0576i	0.194875	+	0.970204i
$898$	−88.2881			−2.94621
$899$	1.98792	+	1.98792i	0.0663007	+	0.0663007i
$900$	13.6329	+	8.13631i	0.454431	+	0.271210i
$901$		−	14.6221i		−	0.487131i
$902$	−39.6856	−	39.6856i	−1.32139	−	1.32139i
$903$	−5.76974	−	10.1626i	−0.192005	−	0.338191i
$904$	49.1928	+	49.1928i	1.63613	+	1.63613i
$905$	6.52983	−	6.52983i	0.217059	−	0.217059i
$906$	95.1614	+	26.2380i	3.16152	+	0.871700i
$907$		−	51.7678i		−	1.71892i	−0.511202	−	0.859460i	$-0.670800\pi$
$907$		−	51.7678i		−	1.71892i	0.511202	−	0.859460i	$-0.329200\pi$
$908$	22.6899	−	22.6899i	0.752989	−	0.752989i
$909$	24.3454	+	14.5297i	0.807488	+	0.481920i
$910$	−6.82600	+	20.7272i	−0.226280	+	0.687099i
$911$		−	13.0642i		−	0.432836i	−0.976301	−	0.216418i	$-0.930563\pi$
$911$		−	13.0642i		−	0.432836i	0.976301	−	0.216418i	$-0.0694374\pi$
$912$	−13.1951	−	23.2415i	−0.436934	−	0.769602i
$913$	−3.47202			−0.114907
$914$	13.2500			0.438271
$915$	14.5997	−	8.28882i	0.482650	−	0.274020i
$916$	10.9378	−	10.9378i	0.361394	−	0.361394i
$917$	−30.1666	+	30.1666i	−0.996190	+	0.996190i
$918$	24.6609	+	0.535518i	0.813931	+	0.0176747i
$919$	2.11295			0.0696997			0.0348498	−	0.999393i	$-0.488905\pi$
$919$	2.11295			0.0696997			0.0348498	+	0.999393i	$0.488905\pi$
$920$	−42.1904			−1.39098
$921$	44.2682	−	25.1329i	1.45869	−	0.828156i
$922$		−	0.0707342i		−	0.00232951i
$923$	−38.8808	−	12.8045i	−1.27978	−	0.421464i
$924$	−103.242	−	28.4659i	−3.39640	−	0.936460i
$925$	−0.906820	+	0.906820i	−0.0298161	+	0.0298161i
$926$		−	85.8494i		−	2.82119i
$927$	−2.73987	+	4.59083i	−0.0899891	+	0.150782i
$928$	−57.1392	+	57.1392i	−1.87569	+	1.87569i
$929$	−9.78322	−	9.78322i	−0.320977	−	0.320977i	0.528165	−	0.849142i	$-0.322880\pi$
$929$	−9.78322	−	9.78322i	−0.320977	−	0.320977i	−0.849142	+	0.528165i	$0.822880\pi$
$930$	−2.61292	+	1.48346i	−0.0856811	+	0.0486447i
$931$	1.60674	+	1.60674i	0.0526587	+	0.0526587i
$932$		−	49.3469i		−	1.61641i
$933$	−5.56930	+	20.1990i	−0.182331	+	0.661287i
$934$	−4.89701	−	4.89701i	−0.160235	−	0.160235i
$935$	−9.16388			−0.299691
$936$	−72.6354	+	63.0134i	−2.37416	+	2.05966i
$937$	6.06246			0.198052			0.0990260	−	0.995085i	$-0.468427\pi$
$937$	6.06246			0.198052			0.0990260	+	0.995085i	$0.468427\pi$
$938$	61.0373	+	61.0373i	1.99294	+	1.99294i
$939$	−8.47381	+	30.7332i	−0.276532	+	1.00294i
$940$		−	15.3891i		−	0.501936i
$941$	−18.0735	−	18.0735i	−0.589180	−	0.589180i	0.348229	−	0.937409i	$-0.386783\pi$
$941$	−18.0735	−	18.0735i	−0.589180	−	0.589180i	−0.937409	+	0.348229i	$0.886783\pi$
$942$	−40.4702	+	22.9766i	−1.31859	+	0.748618i
$943$	−13.3797	−	13.3797i	−0.435704	−	0.435704i
$944$	−2.98774	+	2.98774i	−0.0972426	+	0.0972426i
$945$	8.05437	+	8.41194i	0.262009	+	0.273640i
$946$			42.3756i			1.37775i
$947$	39.6788	−	39.6788i	1.28939	−	1.28939i	0.354226	−	0.935160i	$-0.384744\pi$
$947$	39.6788	−	39.6788i	1.28939	−	1.28939i	0.935160	−	0.354226i	$-0.115256\pi$
$948$	72.5699	+	20.0091i	2.35696	+	0.649864i
$949$	−2.60550	−	0.858058i	−0.0845780	−	0.0278537i
$950$		−	3.10442i		−	0.100721i
$951$	−5.10383	+	2.89765i	−0.165503	+	0.0939628i
$952$	−35.0270			−1.13523
$953$	14.5091			0.469996			0.234998	−	0.971996i	$-0.424492\pi$
$953$	14.5091			0.469996			0.234998	+	0.971996i	$0.424492\pi$
$954$	65.3329	−	16.4962i	2.11523	−	0.534083i
$955$	13.5051	−	13.5051i	0.437014	−	0.437014i
$956$	11.0004	−	11.0004i	0.355778	−	0.355778i
$957$	−34.3613	+	19.5083i	−1.11074	+	0.630614i
$958$	31.6510			1.02260
$959$	−19.2024			−0.620078
$960$	−19.6839	−	34.6707i	−0.635297	−	1.11899i
$961$			30.5873i			0.986688i
$962$	−5.62434	−	11.1479i	−0.181336	−	0.359421i
$963$	−23.3514	+	39.1268i	−0.752490	+	1.26084i
$964$	102.512	−	102.512i	3.30170	−	3.30170i
$965$		−	4.05196i		−	0.130437i
$966$	−47.9616	−	13.2240i	−1.54314	−	0.425476i
$967$	−15.5572	+	15.5572i	−0.500287	+	0.500287i	−0.911527	−	0.411240i	$-0.865096\pi$
$967$	−15.5572	+	15.5572i	−0.500287	+	0.500287i	0.411240	+	0.911527i	$0.365096\pi$
$968$	101.671	+	101.671i	3.26783	+	3.26783i
$969$	−1.72822	−	3.04403i	−0.0555183	−	0.0977882i
$970$	−15.7922	−	15.7922i	−0.507057	−	0.507057i
$971$			31.9328i			1.02477i	0.858755	+	0.512387i	$0.171239\pi$
$971$			31.9328i			1.02477i	−0.858755	+	0.512387i	$0.828761\pi$
$972$	18.4546	+	80.4049i	0.591930	+	2.57899i
$973$	16.0989	+	16.0989i	0.516106	+	0.516106i
$974$	−3.53257			−0.113191
$975$	−6.12271	+	1.22980i	−0.196084	+	0.0393853i
$976$	−130.098			−4.16434
$977$	31.6617	+	31.6617i	1.01295	+	1.01295i	0.999915	+	0.0130317i	$0.00414825\pi$
$977$	31.6617	+	31.6617i	1.01295	+	1.01295i	0.0130317	+	0.999915i	$0.495852\pi$
$978$	8.51869	+	2.34878i	0.272398	+	0.0751058i
$979$			31.0079i			0.991016i
$980$	7.39635	+	7.39635i	0.236268	+	0.236268i
$981$	4.54491	−	1.14756i	0.145108	−	0.0366389i
$982$	8.37536	+	8.37536i	0.267268	+	0.267268i
$983$	7.36772	−	7.36772i	0.234994	−	0.234994i	−0.579780	−	0.814773i	$-0.696861\pi$
$983$	7.36772	−	7.36772i	0.234994	−	0.234994i	0.814773	+	0.579780i	$0.196861\pi$
$984$	16.3179	−	59.1826i	0.520196	−	1.88667i
$985$		−	21.3800i		−	0.681222i
$986$	−14.6899	+	14.6899i	−0.467820	+	0.467820i
$987$	3.00059	−	10.8827i	0.0955098	−	0.346400i
$988$	20.8350	+	6.86152i	0.662850	+	0.218294i
$989$			14.2866i			0.454288i
$990$	−10.3384	−	40.9452i	−0.328577	−	1.30132i
$991$	20.5277			0.652083			0.326042	−	0.945355i	$-0.394285\pi$
$991$	20.5277			0.652083			0.326042	+	0.945355i	$0.394285\pi$
$992$	11.8619			0.376617
$993$	−6.06662	−	10.6856i	−0.192518	−	0.339096i
$994$	48.5887	−	48.5887i	1.54114	−	1.54114i
$995$	−19.0239	+	19.0239i	−0.603099	+	0.603099i
$996$	−3.01422	−	5.30914i	−0.0955091	−	0.168227i
$997$	12.6974			0.402129			0.201065	−	0.979578i	$-0.435560\pi$
$997$	12.6974			0.402129			0.201065	+	0.979578i	$0.435560\pi$
$998$	1.67733			0.0530951
$999$	−6.66217	−	0.144671i	−0.210782	−	0.00457719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.o.a.161.20	yes	40
3.2	odd	2	inner	195.2.o.a.161.1	yes	40
5.2	odd	4		975.2.n.r.824.1		40
5.3	odd	4		975.2.n.q.824.20		40
5.4	even	2		975.2.o.p.551.1		40
13.8	odd	4	inner	195.2.o.a.86.1	✓	40
15.2	even	4		975.2.n.r.824.20		40
15.8	even	4		975.2.n.q.824.1		40
15.14	odd	2		975.2.o.p.551.20		40
39.8	even	4	inner	195.2.o.a.86.20	yes	40
65.8	even	4		975.2.n.r.749.20		40
65.34	odd	4		975.2.o.p.476.20		40
65.47	even	4		975.2.n.q.749.1		40
195.8	odd	4		975.2.n.r.749.1		40
195.47	odd	4		975.2.n.q.749.20		40
195.164	even	4		975.2.o.p.476.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.1	✓	40	13.8	odd	4	inner
195.2.o.a.86.20	yes	40	39.8	even	4	inner
195.2.o.a.161.1	yes	40	3.2	odd	2	inner
195.2.o.a.161.20	yes	40	1.1	even	1	trivial
975.2.n.q.749.1		40	65.47	even	4
975.2.n.q.749.20		40	195.47	odd	4
975.2.n.q.824.1		40	15.8	even	4
975.2.n.q.824.20		40	5.3	odd	4
975.2.n.r.749.1		40	195.8	odd	4
975.2.n.r.749.20		40	65.8	even	4
975.2.n.r.824.1		40	5.2	odd	4
975.2.n.r.824.20		40	15.2	even	4
975.2.o.p.476.1		40	195.164	even	4
975.2.o.p.476.20		40	65.34	odd	4
975.2.o.p.551.1		40	5.4	even	2
975.2.o.p.551.20		40	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.90946 + 1.90946i) q^{2} +(0.460384 - 1.66974i) q^{3} +5.29209i q^{4} +(0.707107 + 0.707107i) q^{5} +(4.06740 - 2.30923i) q^{6} +(-1.58484 - 1.58484i) q^{7} +(-6.28612 + 6.28612i) q^{8} +(-2.57609 - 1.53745i) q^{9} +2.70039i q^{10} +(3.68605 - 3.68605i) q^{11} +(8.83644 + 2.43639i) q^{12} +(-3.21906 + 1.62409i) q^{13} -6.05240i q^{14} +(1.50623 - 0.855147i) q^{15} -13.4220 q^{16} -1.75794 q^{17} +(-1.98325 - 7.85465i) q^{18} +(-0.812904 + 0.812904i) q^{19} +(-3.74207 + 3.74207i) q^{20} +(-3.37592 + 1.91665i) q^{21} +14.0767 q^{22} +4.74587 q^{23} +(7.60219 + 13.3902i) q^{24} +1.00000i q^{25} +(-9.24780 - 3.04554i) q^{26} +(-3.75314 + 3.59360i) q^{27} +(8.38714 - 8.38714i) q^{28} -4.37626i q^{29} +(4.50896 + 1.24322i) q^{30} +(-0.454250 + 0.454250i) q^{31} +(-13.0566 - 13.0566i) q^{32} +(-4.45776 - 7.85176i) q^{33} +(-3.35671 - 3.35671i) q^{34} -2.24131i q^{35} +(8.13631 - 13.6329i) q^{36} +(0.906820 + 0.906820i) q^{37} -3.10442 q^{38} +(1.22980 + 6.12271i) q^{39} -8.88992 q^{40} +(-2.81924 - 2.81924i) q^{41} +(-10.1060 - 2.78643i) q^{42} +3.01033i q^{43} +(19.5069 + 19.5069i) q^{44} +(-0.734433 - 2.90871i) q^{45} +(9.06206 + 9.06206i) q^{46} +(-2.05622 + 2.05622i) q^{47} +(-6.17929 + 22.4114i) q^{48} -1.97654i q^{49} +(-1.90946 + 1.90946i) q^{50} +(-0.809326 + 2.93531i) q^{51} +(-8.59481 - 17.0356i) q^{52} +8.31773i q^{53} +(-14.0283 - 0.304629i) q^{54} +5.21286 q^{55} +19.9250 q^{56} +(0.983094 + 1.73159i) q^{57} +(8.35630 - 8.35630i) q^{58} +(0.222599 - 0.222599i) q^{59} +(4.52551 + 7.97110i) q^{60} +9.69286 q^{61} -1.73475 q^{62} +(1.64609 + 6.51932i) q^{63} -23.0182i q^{64} +(-3.42462 - 1.12782i) q^{65} +(6.48071 - 23.5046i) q^{66} +(-10.0848 + 10.0848i) q^{67} -9.30316i q^{68} +(2.18492 - 7.92439i) q^{69} +(4.27969 - 4.27969i) q^{70} +(8.02801 + 8.02801i) q^{71} +(25.8582 - 6.52905i) q^{72} +(0.537976 + 0.537976i) q^{73} +3.46308i q^{74} +(1.66974 + 0.460384i) q^{75} +(-4.30196 - 4.30196i) q^{76} -11.6836 q^{77} +(-9.34282 + 14.0393i) q^{78} +8.21258 q^{79} +(-9.49082 - 9.49082i) q^{80} +(4.27251 + 7.92122i) q^{81} -10.7664i q^{82} +(-0.470968 - 0.470968i) q^{83} +(-10.1431 - 17.8657i) q^{84} +(-1.24305 - 1.24305i) q^{85} +(-5.74811 + 5.74811i) q^{86} +(-7.30724 - 2.01476i) q^{87} +46.3419i q^{88} +(-4.20611 + 4.20611i) q^{89} +(4.15170 - 6.95645i) q^{90} +(7.67563 + 2.52779i) q^{91} +25.1156i q^{92} +(0.549352 + 0.967611i) q^{93} -7.85255 q^{94} -1.14962 q^{95} +(-27.8123 + 15.7902i) q^{96} +(-5.84813 + 5.84813i) q^{97} +(3.77413 - 3.77413i) q^{98} +(-15.1627 + 3.82850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} - 16 q^{7} + 4 q^{15} - 64 q^{16} + 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} - 24 q^{27} + 32 q^{28} + 32 q^{31} - 4 q^{33} - 16 q^{34} + 32 q^{37} - 8 q^{39} + 8 q^{42} - 8 q^{45} - 40 q^{46}+ \cdots - 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 - 16 * q^7 + 4 * q^15 - 64 * q^16 + 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 - 24 * q^27 + 32 * q^28 + 32 * q^31 - 4 * q^33 - 16 * q^34 + 32 * q^37 - 8 * q^39 + 8 * q^42 - 8 * q^45 - 40 * q^46 + 8 * q^48 - 32 * q^54 + 8 * q^55 - 36 * q^57 + 24 * q^58 + 16 * q^60 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 + 132 * q^72 - 64 * q^73 + 16 * q^76 - 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 24 * q^85 + 16 * q^87 + 8 * q^91 - 108 * q^93 - 32 * q^94 - 76 * q^96 + 24 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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