LMFDB - Embedded newform 195.2.o.a.86.20

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			86.20
Character	$\chi$	$=$	195.86
Dual form			195.2.o.a.161.20

$q$-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 $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

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

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	0.464753	−	0.885440i	$-0.346143\pi$
$2$	1.90946	−	1.90946i	1.35019	−	1.35019i	0.885440	−	0.464753i	$-0.153857\pi$
$3$	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	−0.940050	−	0.341036i	$-0.889222\pi$
$7$	−1.58484	+	1.58484i	−0.599015	+	0.599015i	0.341036	+	0.940050i	$0.389222\pi$
$8$	−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	0.992963	+	0.118422i	$0.0377835\pi$
$11$	3.68605	+	3.68605i	1.11139	+	1.11139i	0.118422	+	0.992963i	$0.462217\pi$
$12$	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	0.607685	−	0.794178i	$-0.292098\pi$
$19$	−0.812904	−	0.812904i	−0.186493	−	0.186493i	−0.794178	+	0.607685i	$0.792098\pi$
$20$	−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	$0.133190\pi$
$29$			4.37626i			0.812651i	−0.913728	+	0.406326i	$0.866810\pi$
$30$	4.50896	−	1.24322i	0.823219	−	0.226979i
$31$	−0.454250	−	0.454250i	−0.0815857	−	0.0815857i	0.665136	−	0.746722i	$-0.268373\pi$
$31$	−0.454250	−	0.454250i	−0.0815857	−	0.0815857i	−0.746722	+	0.665136i	$0.768373\pi$
$32$	−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	−0.628627	−	0.777707i	$-0.716383\pi$
$37$	0.906820	−	0.906820i	0.149080	−	0.149080i	0.777707	+	0.628627i	$0.216383\pi$
$38$	−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	−0.892110	−	0.451819i	$-0.850775\pi$
$41$	−2.81924	+	2.81924i	−0.440291	+	0.440291i	0.451819	+	0.892110i	$0.350775\pi$
$42$	−10.1060	+	2.78643i	−1.55938	+	0.429955i
$43$		−	3.01033i		−	0.459071i	−0.973300	−	0.229535i	$-0.926279\pi$
$43$		−	3.01033i		−	0.459071i	0.973300	−	0.229535i	$-0.0737207\pi$
$44$	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	0.541056	−	0.840987i	$-0.318025\pi$
$47$	−2.05622	−	2.05622i	−0.299931	−	0.299931i	−0.840987	+	0.541056i	$0.818025\pi$
$48$	−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	$-0.806453\pi$
$53$		−	8.31773i		−	1.14253i	0.820766	−	0.571264i	$-0.193547\pi$
$54$	−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	0.721448	−	0.692468i	$-0.243477\pi$
$59$	0.222599	+	0.222599i	0.0289800	+	0.0289800i	−0.692468	+	0.721448i	$0.743477\pi$
$60$	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	−0.963173	−	0.268883i	$-0.913346\pi$
$67$	−10.0848	−	10.0848i	−1.23206	−	1.23206i	−0.268883	−	0.963173i	$-0.586654\pi$
$68$			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	−0.0461834	−	0.998933i	$-0.514706\pi$
$71$	8.02801	−	8.02801i	0.952750	−	0.952750i	0.998933	+	0.0461834i	$0.0147059\pi$
$72$	25.8582	+	6.52905i	3.04742	+	0.769456i
$73$	0.537976	−	0.537976i	0.0629653	−	0.0629653i	−0.674923	−	0.737888i	$-0.735823\pi$
$73$	0.537976	−	0.537976i	0.0629653	−	0.0629653i	0.737888	+	0.674923i	$0.235823\pi$
$74$		−	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	−0.732482	−	0.680786i	$-0.761638\pi$
$83$	−0.470968	+	0.470968i	−0.0516955	+	0.0516955i	0.680786	+	0.732482i	$0.261638\pi$
$84$	−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	0.448124	−	0.893971i	$-0.352092\pi$
$89$	−4.20611	−	4.20611i	−0.445847	−	0.445847i	−0.893971	+	0.448124i	$0.852092\pi$
$90$	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	0.344865	−	0.938652i	$-0.387925\pi$
$97$	−5.84813	−	5.84813i	−0.593787	−	0.593787i	−0.938652	+	0.344865i	$0.887925\pi$
$98$	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	$0.0279827\pi$
$103$			1.78209i			0.175594i	−0.996138	+	0.0877972i	$0.972017\pi$
$104$	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	$0.262424\pi$
$107$			15.1884i			1.46832i	−0.678975	+	0.734161i	$0.737576\pi$
$108$	−19.0177	+	19.8619i	−1.82997	+	1.91122i
$109$	−1.10487	−	1.10487i	−0.105827	−	0.105827i	0.652211	−	0.758038i	$-0.273842\pi$
$109$	−1.10487	−	1.10487i	−0.105827	−	0.105827i	−0.758038	+	0.652211i	$0.773842\pi$
$110$	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	$0.119987\pi$
$113$			7.82563i			0.736173i	−0.929792	+	0.368086i	$0.880013\pi$
$114$	−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	$0.183212\pi$
$127$			12.2683i			1.08864i	−0.838878	+	0.544320i	$0.816788\pi$
$128$	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	$0.312531\pi$
$131$			19.0344i			1.66305i	−0.555489	+	0.831524i	$0.687469\pi$
$132$	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	0.916839	−	0.399257i	$-0.130732\pi$
$137$	6.05814	+	6.05814i	0.517582	+	0.517582i	−0.399257	+	0.916839i	$0.630732\pi$
$138$	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	−0.371748	−	0.928334i	$-0.621241\pi$
$149$	6.79400	−	6.79400i	0.556586	−	0.556586i	0.928334	+	0.371748i	$0.121241\pi$
$150$	2.30923	−	4.06740i	0.188548	−	0.332102i
$151$	14.9235	−	14.9235i	1.21445	−	1.21445i	0.244908	−	0.969546i	$-0.421242\pi$
$151$	14.9235	−	14.9235i	1.21445	−	1.21445i	0.969546	−	0.244908i	$-0.0787577\pi$
$152$			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	−0.652850	−	0.757487i	$-0.726427\pi$
$163$	1.33592	−	1.33592i	0.104638	−	0.104638i	0.757487	+	0.652850i	$0.226427\pi$
$164$	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	0.937620	−	0.347663i	$-0.113025\pi$
$167$	7.62392	+	7.62392i	0.589957	+	0.589957i	−0.347663	+	0.937620i	$0.613025\pi$
$168$	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	$0.111511\pi$
$181$			9.23457i			0.686400i	−0.939262	+	0.343200i	$0.888489\pi$
$182$	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	$0.242821\pi$
$191$			19.0991i			1.38196i	−0.722874	+	0.690980i	$0.757179\pi$
$192$	−38.4345	+	10.5972i	−2.77377	+	0.764788i
$193$	−2.86517	+	2.86517i	−0.206239	+	0.206239i	−0.802667	−	0.596428i	$-0.796586\pi$
$193$	−2.86517	+	2.86517i	−0.206239	+	0.206239i	0.596428	+	0.802667i	$0.296586\pi$
$194$	−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	−0.0803391	+	0.996768i	$0.525600\pi$
$197$	−15.1179	+	15.1179i	−1.07711	+	1.07711i	−0.996768	+	0.0803391i	$0.974400\pi$
$198$	−36.2630	+	21.6422i	−2.57710	+	1.53805i
$199$		−	26.9039i		−	1.90717i	−0.301131	−	0.953583i	$-0.597364\pi$
$199$		−	26.9039i		−	1.90717i	0.301131	−	0.953583i	$-0.402636\pi$
$200$	−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	0.328710	−	0.944431i	$-0.393386\pi$
$223$	−9.19468	−	9.19468i	−0.615721	−	0.615721i	−0.944431	+	0.328710i	$0.893386\pi$
$224$		−	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	−0.834929	−	0.550358i	$-0.814491\pi$
$227$	−4.28750	+	4.28750i	−0.284572	+	0.284572i	0.550358	+	0.834929i	$0.314491\pi$
$228$	−9.16373	−	5.20262i	−0.606883	−	0.344552i
$229$	−2.06681	+	2.06681i	−0.136579	+	0.136579i	−0.772091	−	0.635512i	$-0.780789\pi$
$229$	−2.06681	+	2.06681i	−0.136579	+	0.136579i	0.635512	+	0.772091i	$0.280789\pi$
$230$		−	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	−0.771132	−	0.636675i	$-0.780309\pi$
$239$	−2.07865	+	2.07865i	−0.134457	+	0.134457i	0.636675	+	0.771132i	$0.280309\pi$
$240$	−20.2167	−	11.4778i	−1.30498	−	0.740890i
$241$	−19.3708	+	19.3708i	−1.24779	+	1.24779i	−0.291089	+	0.956696i	$0.594018\pi$
$241$	−19.3708	+	19.3708i	−1.24779	+	1.24779i	−0.956696	+	0.291089i	$0.905982\pi$
$242$	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	$-0.632674\pi$
$263$		−	29.6577i		−	1.82877i	0.404844	−	0.914386i	$-0.367326\pi$
$264$	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	$0.0482702\pi$
$269$			4.95529i			0.302129i	−0.988524	+	0.151065i	$0.951730\pi$
$270$	−9.70411	+	10.1349i	−0.590573	+	0.616792i
$271$	−12.2435	+	12.2435i	−0.743737	+	0.743737i	−0.973295	−	0.229558i	$-0.926272\pi$
$271$	−12.2435	+	12.2435i	−0.743737	+	0.743737i	0.229558	+	0.973295i	$0.426272\pi$
$272$	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	$0.00273956\pi$
$277$			0.286481i			0.0172129i	−0.999963	+	0.00860647i	$0.997260\pi$
$278$	−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	0.368369	−	0.929680i	$-0.379916\pi$
$281$	−9.40929	−	9.40929i	−0.561311	−	0.561311i	−0.929680	+	0.368369i	$0.879916\pi$
$282$	−3.61519	−	13.1118i	−0.215281	−	0.780794i
$283$			28.8859i			1.71709i	0.512740	+	0.858544i	$0.328631\pi$
$283$			28.8859i			1.71709i	−0.512740	+	0.858544i	$0.671369\pi$
$284$	−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	0.831242	−	0.555911i	$-0.187630\pi$
$293$	4.71291	+	4.71291i	0.275331	+	0.275331i	−0.555911	+	0.831242i	$0.687630\pi$
$294$	−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	0.207949	−	0.978140i	$-0.433321\pi$
$307$	20.7819	−	20.7819i	1.18609	−	1.18609i	0.978140	−	0.207949i	$-0.0666787\pi$
$308$			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	−0.771185	−	0.636611i	$-0.780336\pi$
$317$	−2.39602	+	2.39602i	−0.134574	+	0.134574i	0.636611	+	0.771185i	$0.280336\pi$
$318$	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	0.831400	−	0.555674i	$-0.187540\pi$
$331$	5.01639	+	5.01639i	0.275726	+	0.275726i	−0.555674	+	0.831400i	$0.687540\pi$
$332$	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	$0.127960\pi$
$337$			14.3651i			0.782518i	−0.920281	+	0.391259i	$0.872040\pi$
$338$	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	$-0.934668\pi$
$347$		−	7.59308i		−	0.407618i	0.979011	−	0.203809i	$-0.0653321\pi$
$348$	10.6623	+	38.6706i	0.571559	+	2.07296i
$349$	10.8348	−	10.8348i	0.579974	−	0.579974i	−0.354922	−	0.934896i	$-0.615493\pi$
$349$	10.8348	−	10.8348i	0.579974	−	0.579974i	0.934896	+	0.354922i	$0.115493\pi$
$350$	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	−0.996515	−	0.0834091i	$-0.973419\pi$
$353$	−17.1557	+	17.1557i	−0.913106	+	0.913106i	0.0834091	+	0.996515i	$0.473419\pi$
$354$	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	0.926588	−	0.376078i	$-0.122728\pi$
$359$	10.4307	+	10.4307i	0.550510	+	0.550510i	−0.376078	+	0.926588i	$0.622728\pi$
$360$	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	0.762766	−	0.646675i	$-0.223841\pi$
$379$	2.26005	+	2.26005i	0.116091	+	0.116091i	−0.646675	+	0.762766i	$0.723841\pi$
$380$			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	−0.437672	−	0.899135i	$-0.644197\pi$
$383$	9.03101	−	9.03101i	0.461463	−	0.461463i	0.899135	+	0.437672i	$0.144197\pi$
$384$	−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	0.00948364	−	0.999955i	$-0.496981\pi$
$397$	20.1129	−	20.1129i	1.00944	−	1.00944i	0.999955	−	0.00948364i	$-0.00301878\pi$
$398$	−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	−0.982777	−	0.184796i	$-0.940838\pi$
$401$	−23.3806	−	23.3806i	−1.16757	−	1.16757i	−0.184796	−	0.982777i	$-0.559162\pi$
$402$	−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	0.367075	−	0.930191i	$-0.380359\pi$
$409$	−11.3883	−	11.3883i	−0.563116	−	0.563116i	−0.930191	+	0.367075i	$0.880359\pi$
$410$	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	$0.154616\pi$
$419$			19.1129i			0.933728i	−0.884329	+	0.466864i	$0.845384\pi$
$420$	5.46071	+	19.8052i	0.266455	+	0.966394i
$421$	−24.1154	−	24.1154i	−1.17531	−	1.17531i	−0.980925	−	0.194389i	$-0.937728\pi$
$421$	−24.1154	−	24.1154i	−1.17531	−	1.17531i	−0.194389	−	0.980925i	$-0.562272\pi$
$422$	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	−0.232516	−	0.972592i	$-0.574696\pi$
$431$	15.3644	−	15.3644i	0.740076	−	0.740076i	0.972592	+	0.232516i	$0.0746960\pi$
$432$	50.3748	+	48.2334i	2.42366	+	2.32063i
$433$		−	38.5386i		−	1.85205i	−0.377468	−	0.926023i	$-0.623205\pi$
$433$		−	38.5386i		−	1.85205i	0.377468	−	0.926023i	$-0.376795\pi$
$434$	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	$0.0458395\pi$
$439$			6.01382i			0.287024i	−0.989649	+	0.143512i	$0.954160\pi$
$440$	−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	$-0.961916\pi$
$443$		−	5.02446i		−	0.238719i	0.992851	−	0.119360i	$-0.0380842\pi$
$444$	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	−0.995418	−	0.0956146i	$-0.969518\pi$
$449$	−23.1186	−	23.1186i	−1.09103	−	1.09103i	−0.0956146	−	0.995418i	$-0.530482\pi$
$450$	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	0.783585	−	0.621285i	$-0.213389\pi$
$457$	3.46957	+	3.46957i	0.162300	+	0.162300i	−0.621285	+	0.783585i	$0.713389\pi$
$458$			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	−0.707538	−	0.706675i	$-0.750194\pi$
$461$	−0.0185220	+	0.0185220i	−0.000862656	+	0.000862656i	0.706675	+	0.707538i	$0.250194\pi$
$462$	−47.5220	−	26.9801i	−2.21092	−	1.25523i
$463$	−22.4800	+	22.4800i	−1.04473	+	1.04473i	−0.0457826	+	0.998951i	$0.514578\pi$
$463$	−22.4800	+	22.4800i	−1.04473	+	1.04473i	−0.998951	+	0.0457826i	$0.985422\pi$
$464$		−	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	0.870628	−	0.491942i	$-0.163713\pi$
$479$	8.28794	+	8.28794i	0.378686	+	0.378686i	−0.491942	+	0.870628i	$0.663713\pi$
$480$	−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	0.685838	−	0.727754i	$-0.259436\pi$
$487$	−0.925018	−	0.925018i	−0.0419166	−	0.0419166i	−0.727754	+	0.685838i	$0.759436\pi$
$488$	−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	0.716869	−	0.697207i	$-0.245574\pi$
$499$	0.439217	+	0.439217i	0.0196620	+	0.0196620i	−0.697207	+	0.716869i	$0.745574\pi$
$500$	−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	$-0.789707\pi$
$503$		−	27.5248i		−	1.22727i	0.789590	−	0.613634i	$-0.210293\pi$
$504$	−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	−0.486777	−	0.873526i	$-0.661828\pi$
$509$	8.72545	−	8.72545i	0.386749	−	0.386749i	0.873526	+	0.486777i	$0.161828\pi$
$510$	−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	$-0.964959\pi$
$521$		−	5.01532i		−	0.219725i	0.993947	−	0.109863i	$-0.0350411\pi$
$522$	−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	−0.282809	−	0.959176i	$-0.591266\pi$
$541$	15.7319	−	15.7319i	0.676367	−	0.676367i	0.959176	+	0.282809i	$0.0912664\pi$
$542$			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	0.176044	−	0.984382i	$-0.443670\pi$
$557$	−19.0775	−	19.0775i	−0.808338	−	0.808338i	−0.984382	+	0.176044i	$0.943670\pi$
$558$	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	$0.264835\pi$
$571$			35.3312i			1.47857i	−0.673395	+	0.739283i	$0.735165\pi$
$572$	−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	−0.975489	−	0.220050i	$-0.929378\pi$
$577$	−28.7178	−	28.7178i	−1.19554	−	1.19554i	−0.220050	−	0.975489i	$-0.570622\pi$
$578$	−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	−0.939926	−	0.341379i	$-0.889106\pi$
$587$	−14.5016	+	14.5016i	−0.598546	+	0.598546i	0.341379	+	0.939926i	$0.389106\pi$
$588$	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	0.955400	−	0.295316i	$-0.0954248\pi$
$593$	16.0741	+	16.0741i	0.660084	+	0.660084i	−0.295316	+	0.955400i	$0.595425\pi$
$594$	−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	$-0.990200\pi$
$599$		−	1.50675i		−	0.0615640i	0.999526	−	0.0307820i	$-0.00979977\pi$
$600$	−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	0.944323	+	0.329020i	$0.106718\pi$
$613$	31.5265	+	31.5265i	1.27334	+	1.27334i	0.329020	+	0.944323i	$0.393282\pi$
$614$		−	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	−0.700240	−	0.713907i	$-0.746924\pi$
$617$	0.339493	−	0.339493i	0.0136675	−	0.0136675i	0.713907	+	0.700240i	$0.246924\pi$
$618$	−4.11525	+	7.24847i	−0.165540	+	0.291576i
$619$	24.3085	−	24.3085i	0.977040	−	0.977040i	−0.0227024	−	0.999742i	$-0.507227\pi$
$619$	24.3085	−	24.3085i	0.977040	−	0.977040i	0.999742	+	0.0227024i	$0.00722701\pi$
$620$			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	−0.742490	−	0.669857i	$-0.766355\pi$
$631$	−1.82450	+	1.82450i	−0.0726324	+	0.0726324i	0.669857	+	0.742490i	$0.266355\pi$
$632$	−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	0.952556	−	0.304364i	$-0.0984439\pi$
$643$	16.4365	+	16.4365i	0.648192	+	0.648192i	−0.304364	+	0.952556i	$0.598444\pi$
$644$	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	$0.0845952\pi$
$653$			13.4232i			0.525292i	−0.964892	+	0.262646i	$0.915405\pi$
$654$	−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	$-0.906685\pi$
$659$		−	14.8367i		−	0.577954i	0.957336	−	0.288977i	$-0.0933151\pi$
$660$	46.0631	−	12.7006i	1.79300	−	0.494369i
$661$	10.5386	−	10.5386i	0.409903	−	0.409903i	−0.471802	−	0.881705i	$-0.656396\pi$
$661$	10.5386	−	10.5386i	0.409903	−	0.409903i	0.881705	+	0.471802i	$0.156396\pi$
$662$	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	$-0.795091\pi$
$673$		−	31.1406i		−	1.20038i	0.799856	−	0.600192i	$-0.204909\pi$
$674$	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	$0.197064\pi$
$677$			30.1978i			1.16060i	−0.814404	+	0.580298i	$0.802936\pi$
$678$	−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	0.624766	−	0.780812i	$-0.285194\pi$
$683$	−4.07814	−	4.07814i	−0.156046	−	0.156046i	−0.780812	+	0.624766i	$0.785194\pi$
$684$	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	0.407296	−	0.913296i	$-0.366472\pi$
$691$	−13.3012	−	13.3012i	−0.506000	−	0.506000i	−0.913296	+	0.407296i	$0.866472\pi$
$692$		−	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	−0.975902	−	0.218210i	$-0.929978\pi$
$709$	−20.1751	+	20.1751i	−0.757692	+	0.757692i	0.218210	+	0.975902i	$0.429978\pi$
$710$	−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	$0.0226118\pi$
$727$			3.82751i			0.141954i	−0.997478	+	0.0709772i	$0.977388\pi$
$728$	−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	−0.999765	−	0.0216912i	$-0.993095\pi$
$733$	−27.6549	−	27.6549i	−1.02146	−	1.02146i	−0.0216912	−	0.999765i	$-0.506905\pi$
$734$	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	−0.472472	−	0.881346i	$-0.656638\pi$
$739$	11.1151	−	11.1151i	0.408874	−	0.408874i	0.881346	+	0.472472i	$0.156638\pi$
$740$	−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	−0.929016	−	0.370039i	$-0.879344\pi$
$743$	−15.2366	+	15.2366i	−0.558977	+	0.558977i	0.370039	+	0.929016i	$0.379344\pi$
$744$	−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	$0.164091\pi$
$751$			27.0194i			0.985950i	−0.870043	+	0.492975i	$0.835909\pi$
$752$	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	0.242843	−	0.970066i	$-0.421920\pi$
$761$	−20.0613	−	20.0613i	−0.727222	−	0.727222i	−0.970066	+	0.242843i	$0.921920\pi$
$762$	−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	0.0886386	−	0.996064i	$-0.471748\pi$
$769$	−25.1637	−	25.1637i	−0.907425	−	0.907425i	−0.996064	+	0.0886386i	$0.971748\pi$
$770$			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	−0.962219	−	0.272278i	$-0.912223\pi$
$773$	−19.1823	+	19.1823i	−0.689941	+	0.689941i	0.272278	+	0.962219i	$0.412223\pi$
$774$	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	−0.542868	−	0.839818i	$-0.682661\pi$
$787$	8.33052	−	8.33052i	0.296951	−	0.296951i	0.839818	+	0.542868i	$0.182661\pi$
$788$	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	$0.163533\pi$
$809$			27.9566i			0.982902i	−0.870905	+	0.491451i	$0.836467\pi$
$810$	−21.3903	−	11.5374i	−0.751580	−	0.405384i
$811$	17.7339	+	17.7339i	0.622720	+	0.622720i	0.946226	−	0.323506i	$-0.104861\pi$
$811$	17.7339	+	17.7339i	0.622720	+	0.622720i	−0.323506	+	0.946226i	$0.604861\pi$
$812$	−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	0.132982	−	0.991118i	$-0.457545\pi$
$821$	32.2090	−	32.2090i	1.12410	−	1.12410i	0.991118	−	0.132982i	$-0.0424553\pi$
$822$	10.6513	+	38.6305i	0.371505	+	1.34739i
$823$		−	33.0237i		−	1.15113i	−0.817755	−	0.575566i	$-0.804782\pi$
$823$		−	33.0237i		−	1.15113i	0.817755	−	0.575566i	$-0.195218\pi$
$824$	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	0.762752	−	0.646691i	$-0.223848\pi$
$827$	3.33765	+	3.33765i	0.116061	+	0.116061i	−0.646691	+	0.762752i	$0.723848\pi$
$828$	38.6139	+	64.7000i	1.34192	+	2.24848i
$829$			40.6810i			1.41291i	0.707757	+	0.706456i	$0.249707\pi$
$829$			40.6810i			1.41291i	−0.707757	+	0.706456i	$0.750293\pi$
$830$	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	0.240929	−	0.970543i	$-0.422548\pi$
$839$	−21.1336	−	21.1336i	−0.729614	−	0.729614i	−0.970543	+	0.240929i	$0.922548\pi$
$840$	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	−0.140238	+	0.990118i	$0.544787\pi$
$853$	−33.0134	+	33.0134i	−1.13036	+	1.13036i	−0.990118	+	0.140238i	$0.955213\pi$
$854$			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	−0.999497	−	0.0317024i	$-0.989907\pi$
$863$	−28.4308	+	28.4308i	−0.967795	+	0.967795i	0.0317024	+	0.999497i	$0.489907\pi$
$864$	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	0.606971	−	0.794724i	$-0.292385\pi$
$877$	−5.56017	−	5.56017i	−0.187754	−	0.187754i	−0.794724	+	0.606971i	$0.792385\pi$
$878$	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	$-0.788223\pi$
$883$		−	36.6871i		−	1.23462i	0.786721	−	0.617309i	$-0.211777\pi$
$884$	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	$-0.914629\pi$
$887$		−	15.7845i		−	0.529992i	0.964249	−	0.264996i	$-0.0853707\pi$
$888$	−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	$0.329200\pi$
$907$			51.7678i			1.71892i	−0.511202	+	0.859460i	$0.670800\pi$
$908$	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	$0.0694374\pi$
$911$			13.0642i			0.432836i	−0.976301	+	0.216418i	$0.930563\pi$
$912$	−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	−0.849142	−	0.528165i	$-0.822880\pi$
$929$	−9.78322	+	9.78322i	−0.320977	+	0.320977i	0.528165	+	0.849142i	$0.322880\pi$
$930$	−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	−0.937409	−	0.348229i	$-0.886783\pi$
$941$	−18.0735	+	18.0735i	−0.589180	+	0.589180i	0.348229	+	0.937409i	$0.386783\pi$
$942$	−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	0.935160	+	0.354226i	$0.115256\pi$
$947$	39.6788	+	39.6788i	1.28939	+	1.28939i	0.354226	+	0.935160i	$0.384744\pi$
$948$	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	0.411240	−	0.911527i	$-0.365096\pi$
$967$	−15.5572	−	15.5572i	−0.500287	−	0.500287i	−0.911527	+	0.411240i	$0.865096\pi$
$968$	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	$-0.828761\pi$
$971$		−	31.9328i		−	1.02477i	0.858755	−	0.512387i	$-0.171239\pi$
$972$	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	0.0130317	−	0.999915i	$-0.495852\pi$
$977$	31.6617	−	31.6617i	1.01295	−	1.01295i	0.999915	−	0.0130317i	$-0.00414825\pi$
$978$	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	0.814773	−	0.579780i	$-0.196861\pi$
$983$	7.36772	+	7.36772i	0.234994	+	0.234994i	−0.579780	+	0.814773i	$0.696861\pi$
$984$	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.86.20	yes	40
3.2	odd	2	inner	195.2.o.a.86.1	✓	40
5.2	odd	4		975.2.n.q.749.20		40
5.3	odd	4		975.2.n.r.749.1		40
5.4	even	2		975.2.o.p.476.1		40
13.5	odd	4	inner	195.2.o.a.161.1	yes	40
15.2	even	4		975.2.n.q.749.1		40
15.8	even	4		975.2.n.r.749.20		40
15.14	odd	2		975.2.o.p.476.20		40
39.5	even	4	inner	195.2.o.a.161.20	yes	40
65.18	even	4		975.2.n.q.824.1		40
65.44	odd	4		975.2.o.p.551.20		40
65.57	even	4		975.2.n.r.824.20		40
195.44	even	4		975.2.o.p.551.1		40
195.83	odd	4		975.2.n.q.824.20		40
195.122	odd	4		975.2.n.r.824.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.1	✓	40	3.2	odd	2	inner
195.2.o.a.86.20	yes	40	1.1	even	1	trivial
195.2.o.a.161.1	yes	40	13.5	odd	4	inner
195.2.o.a.161.20	yes	40	39.5	even	4	inner
975.2.n.q.749.1		40	15.2	even	4
975.2.n.q.749.20		40	5.2	odd	4
975.2.n.q.824.1		40	65.18	even	4
975.2.n.q.824.20		40	195.83	odd	4
975.2.n.r.749.1		40	5.3	odd	4
975.2.n.r.749.20		40	15.8	even	4
975.2.n.r.824.1		40	195.122	odd	4
975.2.n.r.824.20		40	65.57	even	4
975.2.o.p.476.1		40	5.4	even	2
975.2.o.p.476.20		40	15.14	odd	2
975.2.o.p.551.1		40	195.44	even	4
975.2.o.p.551.20		40	65.44	odd	4

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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