LMFDB - Embedded newform 260.2.o.a.27.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.4
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34983 - 0.421862i) q^{2} +(-1.90910 - 1.90910i) q^{3} +(1.64407 + 1.13888i) q^{4} +(-0.987103 - 2.00640i) q^{5} +(1.77158 + 3.38234i) q^{6} +(-3.15102 + 3.15102i) q^{7} +(-1.73875 - 2.23086i) q^{8} +4.28935i q^{9} +O(q^{10})$	\(q+(-1.34983 - 0.421862i) q^{2} +(-1.90910 - 1.90910i) q^{3} +(1.64407 + 1.13888i) q^{4} +(-0.987103 - 2.00640i) q^{5} +(1.77158 + 3.38234i) q^{6} +(-3.15102 + 3.15102i) q^{7} +(-1.73875 - 2.23086i) q^{8} +4.28935i q^{9} +(0.485997 + 3.12471i) q^{10} -1.76842i q^{11} +(-0.964451 - 5.31293i) q^{12} +(0.707107 - 0.707107i) q^{13} +(5.58262 - 2.92403i) q^{14} +(-1.94594 + 5.71490i) q^{15} +(1.40590 + 3.74479i) q^{16} +(2.56615 + 2.56615i) q^{17} +(1.80951 - 5.78988i) q^{18} -1.23388 q^{19} +(0.662183 - 4.42284i) q^{20} +12.0312 q^{21} +(-0.746028 + 2.38706i) q^{22} +(2.73924 + 2.73924i) q^{23} +(-0.939480 + 7.57840i) q^{24} +(-3.05126 + 3.96104i) q^{25} +(-1.25277 + 0.656171i) q^{26} +(2.46150 - 2.46150i) q^{27} +(-8.76911 + 1.59185i) q^{28} +2.75202i q^{29} +(5.03757 - 6.89321i) q^{30} +4.10776i q^{31} +(-0.317944 - 5.64791i) q^{32} +(-3.37609 + 3.37609i) q^{33} +(-2.38130 - 4.54642i) q^{34} +(9.43256 + 3.21181i) q^{35} +(-4.88506 + 7.05197i) q^{36} +(1.55050 + 1.55050i) q^{37} +(1.66552 + 0.520525i) q^{38} -2.69988 q^{39} +(-2.75966 + 5.69072i) q^{40} -11.6267 q^{41} +(-16.2401 - 5.07551i) q^{42} +(-0.431204 - 0.431204i) q^{43} +(2.01402 - 2.90740i) q^{44} +(8.60614 - 4.23403i) q^{45} +(-2.54192 - 4.85308i) q^{46} +(8.54523 - 8.54523i) q^{47} +(4.46517 - 9.83320i) q^{48} -12.8578i q^{49} +(5.78968 - 4.05951i) q^{50} -9.79809i q^{51} +(1.96784 - 0.357220i) q^{52} +(-10.2133 + 10.2133i) q^{53} +(-4.36102 + 2.28419i) q^{54} +(-3.54815 + 1.74561i) q^{55} +(12.5083 + 1.55063i) q^{56} +(2.35560 + 2.35560i) q^{57} +(1.16097 - 3.71474i) q^{58} -7.03475 q^{59} +(-9.70784 + 7.17948i) q^{60} -8.24800 q^{61} +(1.73290 - 5.54476i) q^{62} +(-13.5158 - 13.5158i) q^{63} +(-1.95347 + 7.75783i) q^{64} +(-2.11672 - 0.720749i) q^{65} +(5.98138 - 3.13290i) q^{66} +(-1.41930 + 1.41930i) q^{67} +(1.29638 + 7.14146i) q^{68} -10.4590i q^{69} +(-11.3774 - 8.31462i) q^{70} +11.4152i q^{71} +(9.56894 - 7.45813i) q^{72} +(-5.51442 + 5.51442i) q^{73} +(-1.43881 - 2.74699i) q^{74} +(13.3872 - 1.73687i) q^{75} +(-2.02857 - 1.40524i) q^{76} +(5.57231 + 5.57231i) q^{77} +(3.64437 + 1.13898i) q^{78} -6.65878 q^{79} +(6.12576 - 6.51729i) q^{80} +3.46952 q^{81} +(15.6940 + 4.90486i) q^{82} +(-3.92562 - 3.92562i) q^{83} +(19.7801 + 13.7021i) q^{84} +(2.61566 - 7.68177i) q^{85} +(0.400142 + 0.763959i) q^{86} +(5.25388 - 5.25388i) q^{87} +(-3.94509 + 3.07484i) q^{88} -8.02760i q^{89} +(-13.4030 + 2.08461i) q^{90} +4.45621i q^{91} +(1.38382 + 7.62315i) q^{92} +(7.84213 - 7.84213i) q^{93} +(-15.1395 + 7.92968i) q^{94} +(1.21796 + 2.47564i) q^{95} +(-10.1755 + 11.3894i) q^{96} +(1.20285 + 1.20285i) q^{97} +(-5.42421 + 17.3558i) q^{98} +7.58537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.34983	−	0.421862i	−0.954472	−	0.298301i
$2$	−1.34983	−	0.421862i	−0.954472	−	0.298301i
$3$	−1.90910	−	1.90910i	−1.10222	−	1.10222i	−0.994142	−	0.108079i	$-0.965530\pi$
$3$	−1.90910	−	1.90910i	−1.10222	−	1.10222i	−0.108079	−	0.994142i	$-0.534470\pi$
$4$	1.64407	+	1.13888i	0.822033	+	0.569440i
$5$	−0.987103	−	2.00640i	−0.441446	−	0.897288i
$5$	−0.987103	−	2.00640i	−0.441446	−	0.897288i
$6$	1.77158	+	3.38234i	0.723245	+	1.38083i
$7$	−3.15102	+	3.15102i	−1.19097	+	1.19097i	−0.214177	+	0.976795i	$0.568707\pi$
$7$	−3.15102	+	3.15102i	−1.19097	+	1.19097i	−0.976795	+	0.214177i	$0.931293\pi$
$8$	−1.73875	−	2.23086i	−0.614742	−	0.788728i
$9$			4.28935i			1.42978i
$10$	0.485997	+	3.12471i	0.153686	+	0.988120i
$11$		−	1.76842i		−	0.533198i	−0.963808	−	0.266599i	$-0.914100\pi$
$11$		−	1.76842i		−	0.533198i	0.963808	−	0.266599i	$-0.0858999\pi$
$12$	−0.964451	−	5.31293i	−0.278413	−	1.53371i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	5.58262	−	2.92403i	1.49202	−	0.781481i
$15$	−1.94594	+	5.71490i	−0.502439	+	1.47558i
$16$	1.40590	+	3.74479i	0.351476	+	0.936197i
$17$	2.56615	+	2.56615i	0.622383	+	0.622383i	0.946140	−	0.323757i	$-0.104946\pi$
$17$	2.56615	+	2.56615i	0.622383	+	0.622383i	−0.323757	+	0.946140i	$0.604946\pi$
$18$	1.80951	−	5.78988i	0.426506	−	1.36469i
$19$	−1.23388			−0.283071			−0.141535	−	0.989933i	$-0.545204\pi$
$19$	−1.23388			−0.283071			−0.141535	+	0.989933i	$0.545204\pi$
$20$	0.662183	−	4.42284i	0.148069	−	0.988977i
$21$	12.0312			2.62543
$22$	−0.746028	+	2.38706i	−0.159054	+	0.508923i
$23$	2.73924	+	2.73924i	0.571171	+	0.571171i	0.932456	−	0.361285i	$-0.117662\pi$
$23$	2.73924	+	2.73924i	0.571171	+	0.571171i	−0.361285	+	0.932456i	$0.617662\pi$
$24$	−0.939480	+	7.57840i	−0.191771	+	1.54693i
$25$	−3.05126	+	3.96104i	−0.610251	+	0.792208i
$26$	−1.25277	+	0.656171i	−0.245689	+	0.128686i
$27$	2.46150	−	2.46150i	0.473717	−	0.473717i
$28$	−8.76911	+	1.59185i	−1.65721	+	0.300831i
$29$			2.75202i			0.511036i	0.966804	+	0.255518i	$0.0822461\pi$
$29$			2.75202i			0.511036i	−0.966804	+	0.255518i	$0.917754\pi$
$30$	5.03757	−	6.89321i	0.919731	−	1.25852i
$31$			4.10776i			0.737775i	0.929474	+	0.368887i	$0.120261\pi$
$31$			4.10776i			0.737775i	−0.929474	+	0.368887i	$0.879739\pi$
$32$	−0.317944	−	5.64791i	−0.0562051	−	0.998419i
$33$	−3.37609	+	3.37609i	−0.587702	+	0.587702i
$34$	−2.38130	−	4.54642i	−0.408389	−	0.779704i
$35$	9.43256	+	3.21181i	1.59439	+	0.542895i
$36$	−4.88506	+	7.05197i	−0.814176	+	1.17533i
$37$	1.55050	+	1.55050i	0.254900	+	0.254900i	0.822976	−	0.568076i	$-0.192312\pi$
$37$	1.55050	+	1.55050i	0.254900	+	0.254900i	−0.568076	+	0.822976i	$0.692312\pi$
$38$	1.66552	+	0.520525i	0.270183	+	0.0844403i
$39$	−2.69988			−0.432327
$40$	−2.75966	+	5.69072i	−0.436340	+	0.899782i
$41$	−11.6267			−1.81579			−0.907893	−	0.419203i	$-0.862310\pi$
$41$	−11.6267			−1.81579			−0.907893	+	0.419203i	$0.862310\pi$
$42$	−16.2401	−	5.07551i	−2.50590	−	0.783169i
$43$	−0.431204	−	0.431204i	−0.0657580	−	0.0657580i	0.673463	−	0.739221i	$-0.264806\pi$
$43$	−0.431204	−	0.431204i	−0.0657580	−	0.0657580i	−0.739221	+	0.673463i	$0.764806\pi$
$44$	2.01402	−	2.90740i	0.303624	−	0.438306i
$45$	8.60614	−	4.23403i	1.28293	−	0.631172i
$46$	−2.54192	−	4.85308i	−0.374785	−	0.715547i
$47$	8.54523	−	8.54523i	1.24645	−	1.24645i	0.289173	−	0.957277i	$-0.406620\pi$
$47$	8.54523	−	8.54523i	1.24645	−	1.24645i	0.957277	−	0.289173i	$-0.0933804\pi$
$48$	4.46517	−	9.83320i	0.644492	−	1.41930i
$49$		−	12.8578i		−	1.83683i
$50$	5.78968	−	4.05951i	0.818784	−	0.574102i
$51$		−	9.79809i		−	1.37201i
$52$	1.96784	−	0.357220i	0.272890	−	0.0495375i
$53$	−10.2133	+	10.2133i	−1.40290	+	1.40290i	−0.612187	+	0.790713i	$0.709710\pi$
$53$	−10.2133	+	10.2133i	−1.40290	+	1.40290i	−0.790713	+	0.612187i	$0.790290\pi$
$54$	−4.36102	+	2.28419i	−0.593460	+	0.310839i
$55$	−3.54815	+	1.74561i	−0.478432	+	0.235378i
$56$	12.5083	+	1.55063i	1.67149	+	0.207212i
$57$	2.35560	+	2.35560i	0.312006	+	0.312006i
$58$	1.16097	−	3.71474i	0.152443	−	0.487770i
$59$	−7.03475			−0.915846			−0.457923	−	0.888992i	$-0.651406\pi$
$59$	−7.03475			−0.915846			−0.457923	+	0.888992i	$0.651406\pi$
$60$	−9.70784	+	7.17948i	−1.25328	+	0.926867i
$61$	−8.24800			−1.05605			−0.528024	−	0.849229i	$-0.677067\pi$
$61$	−8.24800			−1.05605			−0.528024	+	0.849229i	$0.677067\pi$
$62$	1.73290	−	5.54476i	0.220079	−	0.704185i
$63$	−13.5158	−	13.5158i	−1.70283	−	1.70283i
$64$	−1.95347	+	7.75783i	−0.244183	+	0.969729i
$65$	−2.11672	−	0.720749i	−0.262547	−	0.0893980i
$66$	5.98138	−	3.13290i	0.736258	−	0.385633i
$67$	−1.41930	+	1.41930i	−0.173395	+	0.173395i	−0.788469	−	0.615074i	$-0.789126\pi$
$67$	−1.41930	+	1.41930i	−0.173395	+	0.173395i	0.615074	+	0.788469i	$0.289126\pi$
$68$	1.29638	+	7.14146i	0.157209	+	0.866029i
$69$		−	10.4590i		−	1.25911i
$70$	−11.3774	−	8.31462i	−1.35986	−	0.993788i
$71$			11.4152i			1.35474i	0.735644	+	0.677368i	$0.236880\pi$
$71$			11.4152i			1.35474i	−0.735644	+	0.677368i	$0.763120\pi$
$72$	9.56894	−	7.45813i	1.12771	−	0.878949i
$73$	−5.51442	+	5.51442i	−0.645414	+	0.645414i	−0.951881	−	0.306467i	$-0.900853\pi$
$73$	−5.51442	+	5.51442i	−0.645414	+	0.645414i	0.306467	+	0.951881i	$0.400853\pi$
$74$	−1.43881	−	2.74699i	−0.167258	−	0.319332i
$75$	13.3872	−	1.73687i	1.54582	−	0.200557i
$76$	−2.02857	−	1.40524i	−0.232693	−	0.161192i
$77$	5.57231	+	5.57231i	0.635024	+	0.635024i
$78$	3.64437	+	1.13898i	0.412644	+	0.128964i
$79$	−6.65878			−0.749171			−0.374586	−	0.927192i	$-0.622215\pi$
$79$	−6.65878			−0.749171			−0.374586	+	0.927192i	$0.622215\pi$
$80$	6.12576	−	6.51729i	0.684881	−	0.728655i
$81$	3.46952			0.385502
$82$	15.6940	+	4.90486i	1.73312	+	0.541651i
$83$	−3.92562	−	3.92562i	−0.430893	−	0.430893i	0.458039	−	0.888932i	$-0.348552\pi$
$83$	−3.92562	−	3.92562i	−0.430893	−	0.430893i	−0.888932	+	0.458039i	$0.848552\pi$
$84$	19.7801	+	13.7021i	2.15819	+	1.49502i
$85$	2.61566	−	7.68177i	0.283708	−	0.833205i
$86$	0.400142	+	0.763959i	0.0431485	+	0.0823798i
$87$	5.25388	−	5.25388i	0.563275	−	0.563275i
$88$	−3.94509	+	3.07484i	−0.420548	+	0.327779i
$89$		−	8.02760i		−	0.850924i	−0.904976	−	0.425462i	$-0.860112\pi$
$89$		−	8.02760i		−	0.850924i	0.904976	−	0.425462i	$-0.139888\pi$
$90$	−13.4030	+	2.08461i	−1.41280	+	0.219737i
$91$			4.45621i			0.467138i
$92$	1.38382	+	7.62315i	0.144274	+	0.794769i
$93$	7.84213	−	7.84213i	0.813191	−	0.813191i
$94$	−15.1395	+	7.92968i	−1.56152	+	0.817884i
$95$	1.21796	+	2.47564i	0.124960	+	0.253996i
$96$	−10.1755	+	11.3894i	−1.03853	+	1.16243i
$97$	1.20285	+	1.20285i	0.122131	+	0.122131i	0.765531	−	0.643400i	$-0.222477\pi$
$97$	1.20285	+	1.20285i	0.122131	+	0.122131i	−0.643400	+	0.765531i	$0.722477\pi$
$98$	−5.42421	+	17.3558i	−0.547928	+	1.75320i
$99$	7.58537			0.762358
$100$	−9.52761	+	3.03720i	−0.952761	+	0.303720i
$101$	−0.373555			−0.0371701			−0.0185851	−	0.999827i	$-0.505916\pi$
$101$	−0.373555			−0.0371701			−0.0185851	+	0.999827i	$0.505916\pi$
$102$	−4.13344	+	13.2257i	−0.409271	+	1.30954i
$103$	0.262755	+	0.262755i	0.0258900	+	0.0258900i	0.719933	−	0.694043i	$-0.244172\pi$
$103$	0.262755	+	0.262755i	0.0258900	+	0.0258900i	−0.694043	+	0.719933i	$0.744172\pi$
$104$	−2.80694	−	0.347971i	−0.275243	−	0.0341214i
$105$	−11.8761	−	24.1394i	−1.15899	−	2.35577i
$106$	18.0947	−	9.47756i	1.75752	−	0.920542i
$107$	−1.30227	+	1.30227i	−0.125895	+	0.125895i	−0.767247	−	0.641352i	$-0.778374\pi$
$107$	−1.30227	+	1.30227i	−0.125895	+	0.125895i	0.641352	+	0.767247i	$0.278374\pi$
$108$	6.85023	−	1.24352i	0.659164	−	0.119657i
$109$			16.9444i			1.62298i	0.584366	+	0.811490i	$0.301343\pi$
$109$			16.9444i			1.62298i	−0.584366	+	0.811490i	$0.698657\pi$
$110$	5.52579	−	0.859445i	0.526864	−	0.0819449i
$111$		−	5.92011i		−	0.561912i
$112$	−16.2299	−	7.36986i	−1.53358	−	0.696386i
$113$	3.61951	−	3.61951i	0.340495	−	0.340495i	−0.516058	−	0.856553i	$-0.672601\pi$
$113$	3.61951	−	3.61951i	0.340495	−	0.340495i	0.856553	+	0.516058i	$0.172601\pi$
$114$	−2.18591	−	4.17338i	−0.204729	−	0.390873i
$115$	2.79209	−	8.19991i	0.260364	−	0.764646i
$116$	−3.13422	+	4.52449i	−0.291005	+	0.420089i
$117$	3.03303	+	3.03303i	0.280404	+	0.280404i
$118$	9.49569	+	2.96769i	0.874149	+	0.273198i
$119$	−16.1720			−1.48248
$120$	16.1326	−	5.59570i	1.47270	−	0.510815i
$121$	7.87270			0.715700
$122$	11.1334	+	3.47951i	1.00797	+	0.315020i
$123$	22.1966	+	22.1966i	2.00140	+	2.00140i
$124$	−4.67824	+	6.75342i	−0.420119	+	0.606475i
$125$	10.9593	+	2.21207i	0.980232	+	0.197854i
$126$	12.5422	+	23.9458i	1.11735	+	2.13326i
$127$	−4.78144	+	4.78144i	−0.424284	+	0.424284i	−0.886676	−	0.462392i	$-0.846991\pi$
$127$	−4.78144	+	4.78144i	−0.424284	+	0.424284i	0.462392	+	0.886676i	$0.346991\pi$
$128$	5.90957	−	9.64764i	0.522338	−	0.852739i
$129$			1.64643i			0.144960i
$130$	2.55315	+	1.86585i	0.223926	+	0.163646i
$131$		−	6.06174i		−	0.529617i	−0.964301	−	0.264808i	$-0.914691\pi$
$131$		−	6.06174i		−	0.529617i	0.964301	−	0.264808i	$-0.0853087\pi$
$132$	−9.39548	+	1.70555i	−0.817772	+	0.148449i
$133$	3.88796	−	3.88796i	0.337129	−	0.337129i
$134$	2.51455	−	1.31706i	0.217224	−	0.113776i
$135$	−7.36851	−	2.50900i	−0.634181	−	0.215940i
$136$	1.26282	−	10.1866i	0.108286	−	0.873496i
$137$	−12.4596	−	12.4596i	−1.06449	−	1.06449i	−0.997772	−	0.0667216i	$-0.978746\pi$
$137$	−12.4596	−	12.4596i	−1.06449	−	1.06449i	−0.0667216	−	0.997772i	$-0.521254\pi$
$138$	−4.41224	+	14.1178i	−0.375595	+	1.20179i
$139$	11.7642			0.997824			0.498912	−	0.866653i	$-0.333733\pi$
$139$	11.7642			0.997824			0.498912	+	0.866653i	$0.333733\pi$
$140$	11.8499	+	16.0230i	1.00150	+	1.35419i
$141$	−32.6275			−2.74773
$142$	4.81564	−	15.4086i	0.404119	−	1.29306i
$143$	−1.25046	−	1.25046i	−0.104569	−	0.104569i
$144$	−16.0627	+	6.03041i	−1.33856	+	0.502534i
$145$	5.52163	−	2.71652i	0.458547	−	0.225595i
$146$	9.76984	−	5.11719i	0.808558	−	0.423502i
$147$	−24.5469	+	24.5469i	−2.02459	+	2.02459i
$148$	0.783287	+	4.31494i	0.0643858	+	0.354686i
$149$		−	7.73718i		−	0.633854i	−0.948450	−	0.316927i	$-0.897349\pi$
$149$		−	7.73718i		−	0.633854i	0.948450	−	0.316927i	$-0.102651\pi$
$150$	−18.8031	−	3.30306i	−1.53527	−	0.269694i
$151$			18.7832i			1.52856i	0.644886	+	0.764279i	$0.276905\pi$
$151$			18.7832i			1.52856i	−0.644886	+	0.764279i	$0.723095\pi$
$152$	2.14541	+	2.75260i	0.174015	+	0.223266i
$153$	−11.0071	+	11.0071i	−0.889873	+	0.889873i
$154$	−5.17091	−	9.87240i	−0.416684	−	0.795541i
$155$	8.24179	−	4.05478i	0.661996	−	0.325688i
$156$	−4.43878	−	3.07484i	−0.355387	−	0.246184i
$157$	3.98679	+	3.98679i	0.318180	+	0.318180i	0.848068	−	0.529888i	$-0.177766\pi$
$157$	3.98679	+	3.98679i	0.318180	+	0.318180i	−0.529888	+	0.848068i	$0.677766\pi$
$158$	8.98820	+	2.80908i	0.715063	+	0.223479i
$159$	38.9964			3.09261
$160$	−11.0181	+	6.21299i	−0.871058	+	0.491180i
$161$	−17.2628			−1.36050
$162$	−4.68325	−	1.46366i	−0.367951	−	0.114996i
$163$	−6.93048	−	6.93048i	−0.542837	−	0.542837i	0.381522	−	0.924360i	$-0.375400\pi$
$163$	−6.93048	−	6.93048i	−0.542837	−	0.542837i	−0.924360	+	0.381522i	$0.875400\pi$
$164$	−19.1151	−	13.2414i	−1.49264	−	1.03398i
$165$	10.1063	+	3.44123i	0.786777	+	0.267899i
$166$	3.64284	+	6.95498i	0.282739	+	0.539811i
$167$	−2.14619	+	2.14619i	−0.166078	+	0.166078i	−0.785253	−	0.619175i	$-0.787467\pi$
$167$	−2.14619	+	2.14619i	−0.166078	+	0.166078i	0.619175	+	0.785253i	$0.287467\pi$
$168$	−20.9193	−	26.8400i	−1.61396	−	2.07075i
$169$		−	1.00000i		−	0.0769231i
$170$	−6.77133	+	9.26561i	−0.519337	+	0.710640i
$171$		−	5.29253i		−	0.404730i
$172$	−0.217838	−	1.20002i	−0.0166100	−	0.0915005i
$173$	1.40204	−	1.40204i	0.106595	−	0.106595i	−0.651798	−	0.758393i	$-0.725985\pi$
$173$	1.40204	−	1.40204i	0.106595	−	0.106595i	0.758393	+	0.651798i	$0.225985\pi$
$174$	−9.30824	+	4.87542i	−0.705656	+	0.369605i
$175$	−2.86675	−	22.0959i	−0.216706	−	1.67029i
$176$	6.62235	−	2.48622i	0.499178	−	0.187406i
$177$	13.4301	+	13.4301i	1.00946	+	1.00946i
$178$	−3.38654	+	10.8359i	−0.253832	+	0.812183i
$179$	−10.6942			−0.799325			−0.399662	−	0.916662i	$-0.630873\pi$
$179$	−10.6942			−0.799325			−0.399662	+	0.916662i	$0.630873\pi$
$180$	18.9711	+	2.84034i	1.41402	+	0.211706i
$181$	13.3815			0.994639			0.497319	−	0.867568i	$-0.334318\pi$
$181$	13.3815			0.994639			0.497319	+	0.867568i	$0.334318\pi$
$182$	1.87990	−	6.01511i	0.139348	−	0.445870i
$183$	15.7463	+	15.7463i	1.16400	+	1.16400i
$184$	1.34799	−	10.8737i	0.0993754	−	0.801621i
$185$	1.58041	−	4.64141i	0.116194	−	0.341243i
$186$	−13.8938	+	7.27723i	−1.01874	+	0.533592i
$187$	4.53803	−	4.53803i	0.331853	−	0.331853i
$188$	23.7809	−	4.31693i	1.73440	−	0.314844i
$189$			15.5125i			1.12837i
$190$	−0.599659	−	3.85550i	−0.0435039	−	0.279708i
$191$		−	22.0682i		−	1.59680i	−0.602128	−	0.798399i	$-0.705680\pi$
$191$		−	22.0682i		−	1.59680i	0.602128	−	0.798399i	$-0.294320\pi$
$192$	18.5399	−	11.0811i	1.33800	−	0.799712i
$193$	−11.0984	+	11.0984i	−0.798884	+	0.798884i	−0.982920	−	0.184036i	$-0.941084\pi$
$193$	−11.0984	+	11.0984i	−0.798884	+	0.798884i	0.184036	+	0.982920i	$0.441084\pi$
$194$	−1.11620	−	2.13108i	−0.0801387	−	0.153002i
$195$	2.66506	+	5.41703i	0.190849	+	0.387922i
$196$	14.6435	−	21.1391i	1.04596	−	1.50993i
$197$	4.33528	+	4.33528i	0.308876	+	0.308876i	0.844473	−	0.535598i	$-0.179914\pi$
$197$	4.33528	+	4.33528i	0.308876	+	0.308876i	−0.535598	+	0.844473i	$0.679914\pi$
$198$	−10.2389	−	3.19997i	−0.727649	−	0.227412i
$199$	19.2499			1.36459			0.682295	−	0.731077i	$-0.260982\pi$
$199$	19.2499			1.36459			0.682295	+	0.731077i	$0.260982\pi$
$200$	14.1419	−	0.0803545i	0.999984	−	0.00568192i
$201$	5.41916			0.382238
$202$	0.504234	+	0.157588i	0.0354778	+	0.0110879i
$203$	−8.67164	−	8.67164i	−0.608630	−	0.608630i
$204$	11.1589	−	16.1087i	0.781276	−	1.12783i
$205$	11.4768	+	23.3278i	0.801571	+	1.62928i
$206$	−0.243827	−	0.465519i	−0.0169882	−	0.0324343i
$207$	−11.7496	+	11.7496i	−0.816651	+	0.816651i
$208$	3.64209	+	1.65384i	0.252533	+	0.114673i
$209$			2.18201i			0.150933i
$210$	5.84714	+	37.5941i	0.403491	+	2.59424i
$211$		−	7.78507i		−	0.535946i	−0.963426	−	0.267973i	$-0.913646\pi$
$211$		−	7.78507i		−	0.535946i	0.963426	−	0.267973i	$-0.0863539\pi$
$212$	−28.4230	+	5.15959i	−1.95210	+	0.354362i
$213$	21.7928	−	21.7928i	1.49322	−	1.49322i
$214$	2.30722	−	1.20846i	0.157718	−	0.0826089i
$215$	−0.439523	+	1.29081i	−0.0299752	+	0.0880324i
$216$	−9.77122	−	1.21132i	−0.664847	−	0.0824198i
$217$	−12.9436	−	12.9436i	−0.878669	−	0.878669i
$218$	7.14820	−	22.8720i	0.484137	−	1.54909i
$219$	21.0552			1.42278
$220$	−7.82143	−	1.17102i	−0.527321	−	0.0789500i
$221$	3.62908			0.244119
$222$	−2.49747	+	7.99112i	−0.167619	+	0.536329i
$223$	−9.01350	−	9.01350i	−0.603589	−	0.603589i	0.337674	−	0.941263i	$-0.390360\pi$
$223$	−9.01350	−	9.01350i	−0.603589	−	0.603589i	−0.941263	+	0.337674i	$0.890360\pi$
$224$	18.7985	+	16.7948i	1.25603	+	1.12215i
$225$	−16.9903	−	13.0879i	−1.13269	−	0.872527i
$226$	−6.41265	+	3.35878i	−0.426563	+	0.223423i
$227$	−15.9244	+	15.9244i	−1.05694	+	1.05694i	−0.0586582	+	0.998278i	$0.518682\pi$
$227$	−15.9244	+	15.9244i	−1.05694	+	1.05694i	−0.998278	+	0.0586582i	$0.981318\pi$
$228$	1.19001	+	6.55550i	0.0788105	+	0.434148i
$229$		−	11.1968i		−	0.739908i	−0.929050	−	0.369954i	$-0.879373\pi$
$229$		−	11.1968i		−	0.739908i	0.929050	−	0.369954i	$-0.120627\pi$
$230$	−7.22806	+	9.89058i	−0.476604	+	0.652166i
$231$		−	21.2762i		−	1.39987i
$232$	6.13936	−	4.78508i	0.403069	−	0.314156i
$233$	−6.39478	+	6.39478i	−0.418936	+	0.418936i	−0.884837	−	0.465901i	$-0.845730\pi$
$233$	−6.39478	+	6.39478i	−0.418936	+	0.418936i	0.465901	+	0.884837i	$0.345730\pi$
$234$	−2.81455	−	5.37358i	−0.183993	−	0.351282i
$235$	−25.5801	−	8.71010i	−1.66866	−	0.568184i
$236$	−11.5656	−	8.01173i	−0.752855	−	0.521519i
$237$	12.7123	+	12.7123i	0.825752	+	0.825752i
$238$	21.8293	+	6.82233i	1.41499	+	0.442226i
$239$	−7.21067			−0.466419			−0.233210	−	0.972426i	$-0.574923\pi$
$239$	−7.21067			−0.466419			−0.233210	+	0.972426i	$0.574923\pi$
$240$	−24.1369	+	0.747477i	−1.55803	+	0.0482494i
$241$	12.2443			0.788728			0.394364	−	0.918954i	$-0.370965\pi$
$241$	12.2443			0.788728			0.394364	+	0.918954i	$0.370965\pi$
$242$	−10.6268	−	3.32119i	−0.683115	−	0.213494i
$243$	−14.0082	−	14.0082i	−0.898626	−	0.898626i
$244$	−13.5603	−	9.39349i	−0.868106	−	0.601356i
$245$	−25.7978	+	12.6920i	−1.64816	+	0.810860i
$246$	−20.5976	−	39.3254i	−1.31326	−	2.50730i
$247$	−0.872482	+	0.872482i	−0.0555147	+	0.0555147i
$248$	9.16383	−	7.14238i	0.581904	−	0.453541i
$249$			14.9888i			0.949879i
$250$	−13.8600	−	7.60923i	−0.876583	−	0.481250i
$251$			2.83819i			0.179145i	0.995980	+	0.0895726i	$0.0285501\pi$
$251$			2.83819i			0.179145i	−0.995980	+	0.0895726i	$0.971450\pi$
$252$	−6.82799	−	37.6138i	−0.430123	−	2.36945i
$253$	4.84412	−	4.84412i	0.304547	−	0.304547i
$254$	8.47122	−	4.43701i	0.531532	−	0.278403i
$255$	−19.6589	+	9.67172i	−1.23109	+	0.605667i
$256$	−12.0469	+	10.5296i	−0.752929	+	0.658101i
$257$	−9.01088	−	9.01088i	−0.562084	−	0.562084i	0.367815	−	0.929899i	$-0.380106\pi$
$257$	−9.01088	−	9.01088i	−0.562084	−	0.562084i	−0.929899	+	0.367815i	$0.880106\pi$
$258$	0.694564	−	2.22239i	0.0432417	−	0.138360i
$259$	−9.77127			−0.607157
$260$	−2.65919	−	3.59565i	−0.164916	−	0.222993i
$261$	−11.8044			−0.730671
$262$	−2.55722	+	8.18230i	−0.157985	+	0.505504i
$263$	−0.472686	−	0.472686i	−0.0291471	−	0.0291471i	0.692383	−	0.721530i	$-0.256561\pi$
$263$	−0.472686	−	0.472686i	−0.0291471	−	0.0291471i	−0.721530	+	0.692383i	$0.756561\pi$
$264$	13.4018	+	1.66139i	0.824823	+	0.102252i
$265$	30.5734	+	10.4103i	1.87811	+	0.639501i
$266$	−6.88826	+	3.60789i	−0.422346	+	0.221214i
$267$	−15.3255	+	15.3255i	−0.937906	+	0.937906i
$268$	−3.94982	+	0.717007i	−0.241274	+	0.0437982i
$269$		−	6.52851i		−	0.398050i	−0.979994	−	0.199025i	$-0.936222\pi$
$269$		−	6.52851i		−	0.398050i	0.979994	−	0.199025i	$-0.0637775\pi$
$270$	8.88777	+	6.49520i	0.540892	+	0.395285i
$271$			22.4977i			1.36664i	0.730119	+	0.683320i	$0.239465\pi$
$271$			22.4977i			1.36664i	−0.730119	+	0.683320i	$0.760535\pi$
$272$	−6.00193	+	13.2174i	−0.363920	+	0.801425i
$273$	8.50736	−	8.50736i	0.514889	−	0.514889i
$274$	11.5621	+	22.0745i	0.698489	+	1.33357i
$275$	7.00478	+	5.39589i	0.422404	+	0.325385i
$276$	11.9115	−	17.1952i	0.716990	−	1.03503i
$277$	−21.0843	−	21.0843i	−1.26683	−	1.26683i	−0.947716	−	0.319114i	$-0.896615\pi$
$277$	−21.0843	−	21.0843i	−1.26683	−	1.26683i	−0.319114	−	0.947716i	$-0.603385\pi$
$278$	−15.8796	−	4.96285i	−0.952395	−	0.297652i
$279$	−17.6196			−1.05486
$280$	−9.23581	−	26.6273i	−0.551945	−	1.59128i
$281$	−3.11270			−0.185688			−0.0928440	−	0.995681i	$-0.529596\pi$
$281$	−3.11270			−0.185688			−0.0928440	+	0.995681i	$0.529596\pi$
$282$	44.0414	+	13.7643i	2.62263	+	0.819650i
$283$	1.41066	+	1.41066i	0.0838550	+	0.0838550i	0.747790	−	0.663935i	$-0.231115\pi$
$283$	1.41066	+	1.41066i	0.0838550	+	0.0838550i	−0.663935	+	0.747790i	$0.731115\pi$
$284$	−13.0006	+	18.7674i	−0.771441	+	1.11364i
$285$	2.40104	−	7.05148i	0.142226	−	0.417693i
$286$	1.16038	+	2.21543i	0.0686149	+	0.131001i
$287$	36.6359	−	36.6359i	2.16255	−	2.16255i
$288$	24.2259	−	1.36377i	1.42752	−	0.0803611i
$289$		−	3.82975i		−	0.225279i
$290$	−8.59925	+	1.33747i	−0.504965	+	0.0785389i
$291$		−	4.59273i		−	0.269231i
$292$	−15.3463	+	2.78581i	−0.898077	+	0.163027i
$293$	−0.0447969	+	0.0447969i	−0.00261706	+	0.00261706i	−0.708414	−	0.705797i	$-0.750589\pi$
$293$	−0.0447969	+	0.0447969i	−0.00261706	+	0.00261706i	0.705797	+	0.708414i	$0.250589\pi$
$294$	43.4894	−	22.7786i	2.53635	−	1.32848i
$295$	6.94402	+	14.1145i	0.404296	+	0.821778i
$296$	0.763007	−	6.15487i	0.0443489	−	0.357744i
$297$	−4.35297	−	4.35297i	−0.252585	−	0.252585i
$298$	−3.26402	+	10.4438i	−0.189079	+	0.604996i
$299$	3.87387			0.224032
$300$	23.9875	+	12.3909i	1.38492	+	0.715388i
$301$	2.71746			0.156632
$302$	7.92392	−	25.3541i	0.455970	−	1.45896i
$303$	0.713155	+	0.713155i	0.0409697	+	0.0409697i
$304$	−1.73471	−	4.62060i	−0.0994925	−	0.265010i
$305$	8.14163	+	16.5488i	0.466188	+	0.947579i
$306$	19.5012	−	10.2142i	1.11481	−	0.583908i
$307$	−0.114902	+	0.114902i	−0.00655779	+	0.00655779i	−0.710378	−	0.703820i	$-0.751476\pi$
$307$	−0.114902	+	0.114902i	−0.00655779	+	0.00655779i	0.703820	+	0.710378i	$0.251476\pi$
$308$	2.81505	+	15.5074i	0.160402	+	0.883619i
$309$		−	1.00325i		−	0.0570730i
$310$	−12.8355	+	1.99636i	−0.729010	+	0.113385i
$311$			21.1090i			1.19698i	0.801129	+	0.598492i	$0.204233\pi$
$311$			21.1090i			1.19698i	−0.801129	+	0.598492i	$0.795767\pi$
$312$	4.69443	+	6.02305i	0.265770	+	0.340988i
$313$	−3.33321	+	3.33321i	−0.188404	+	0.188404i	−0.795006	−	0.606602i	$-0.792532\pi$
$313$	−3.33321	+	3.33321i	−0.188404	+	0.188404i	0.606602	+	0.795006i	$0.292532\pi$
$314$	−3.69960	−	7.06334i	−0.208780	−	0.398608i
$315$	−13.7766	+	40.4596i	−0.776222	+	2.27964i
$316$	−10.9475	−	7.58355i	−0.615843	−	0.426608i
$317$	14.6974	+	14.6974i	0.825488	+	0.825488i	0.986889	−	0.161401i	$-0.0516013\pi$
$317$	14.6974	+	14.6974i	0.825488	+	0.825488i	−0.161401	+	0.986889i	$0.551601\pi$
$318$	−52.6383	−	16.4511i	−2.95181	−	0.922530i
$319$	4.86671			0.272484
$320$	17.4936	−	3.73835i	0.977920	−	0.208980i
$321$	4.97234			0.277529
$322$	23.3017	+	7.28250i	1.29856	+	0.405838i
$323$	−3.16631	−	3.16631i	−0.176178	−	0.176178i
$324$	5.70412	+	3.95137i	0.316895	+	0.219520i
$325$	0.643315	+	4.95844i	0.0356847	+	0.275045i
$326$	6.43125	+	12.2787i	0.356194	+	0.680052i
$327$	32.3486	−	32.3486i	1.78888	−	1.78888i
$328$	20.2160	+	25.9375i	1.11624	+	1.43216i
$329$			53.8523i			2.96897i
$330$	−12.1901	−	8.90854i	−0.671042	−	0.490399i
$331$			4.25750i			0.234013i	0.993131	+	0.117007i	$0.0373299\pi$
$331$			4.25750i			0.234013i	−0.993131	+	0.117007i	$0.962670\pi$
$332$	−1.98317	−	10.9248i	−0.108840	−	0.599576i
$333$	−6.65062	+	6.65062i	−0.364452	+	0.364452i
$334$	3.80239	−	1.99159i	0.208057	−	0.108975i
$335$	4.24866	+	1.44668i	0.232129	+	0.0790405i
$336$	16.9147	+	45.0544i	0.922775	+	2.45792i
$337$	4.55389	+	4.55389i	0.248066	+	0.248066i	0.820177	−	0.572110i	$-0.193875\pi$
$337$	4.55389	+	4.55389i	0.248066	+	0.248066i	−0.572110	+	0.820177i	$0.693875\pi$
$338$	−0.421862	+	1.34983i	−0.0229462	+	0.0734209i
$339$	−13.8201			−0.750602
$340$	13.0489	−	9.65041i	0.707678	−	0.523367i
$341$	7.26423			0.393380
$342$	−2.23271	+	7.14400i	−0.120731	+	0.386303i
$343$	18.4580	+	18.4580i	0.996639	+	0.996639i
$344$	−0.212198	+	1.71171i	−0.0114409	+	0.0922894i
$345$	−20.9849	+	10.3241i	−1.12979	+	0.555830i
$346$	−2.48397	+	1.30104i	−0.133539	+	0.0699445i
$347$	−20.5579	+	20.5579i	−1.10360	+	1.10360i	−0.109633	+	0.993972i	$0.534967\pi$
$347$	−20.5579	+	20.5579i	−1.10360	+	1.10360i	−0.993972	+	0.109633i	$0.965033\pi$
$348$	14.6213	−	2.65418i	0.783782	−	0.142279i
$349$		−	25.9580i		−	1.38950i	−0.719250	−	0.694751i	$-0.755515\pi$
$349$		−	25.9580i		−	1.38950i	0.719250	−	0.694751i	$-0.244485\pi$
$350$	−5.45178	+	31.0349i	−0.291410	+	1.65889i
$351$		−	3.48109i		−	0.185807i
$352$	−9.98787	+	0.562258i	−0.532355	+	0.0299685i
$353$	−2.32243	+	2.32243i	−0.123611	+	0.123611i	−0.766206	−	0.642595i	$-0.777858\pi$
$353$	−2.32243	+	2.32243i	−0.123611	+	0.123611i	0.642595	+	0.766206i	$0.277858\pi$
$354$	−12.4626	−	23.7939i	−0.662381	−	1.26463i
$355$	22.9034	−	11.2680i	1.21559	−	0.598043i
$356$	9.14247	−	13.1979i	0.484550	−	0.699487i
$357$	30.8739	+	30.8739i	1.63402	+	1.63402i
$358$	14.4354	+	4.51149i	0.762933	+	0.238439i
$359$	16.7930			0.886300			0.443150	−	0.896448i	$-0.353861\pi$
$359$	16.7930			0.886300			0.443150	+	0.896448i	$0.353861\pi$
$360$	−24.4095	−	11.8371i	−1.28649	−	0.623872i
$361$	−17.4776			−0.919871
$362$	−18.0627	−	5.64514i	−0.949355	−	0.296702i
$363$	−15.0298	−	15.0298i	−0.788860	−	0.788860i
$364$	−5.07509	+	7.32630i	−0.266007	+	0.384002i
$365$	16.5074	+	5.62082i	0.864038	+	0.294207i
$366$	−14.6120	−	27.8975i	−0.763782	−	1.45823i
$367$	4.33130	−	4.33130i	0.226092	−	0.226092i	−0.584966	−	0.811058i	$-0.698892\pi$
$367$	4.33130	−	4.33130i	0.226092	−	0.226092i	0.811058	+	0.584966i	$0.198892\pi$
$368$	−6.40676	+	14.1090i	−0.333976	+	0.735481i
$369$		−	49.8710i		−	2.59618i
$370$	−4.09131	+	5.59838i	−0.212697	+	0.291046i
$371$		−	64.3643i		−	3.34163i
$372$	21.8242	−	3.96173i	1.13153	−	0.205406i
$373$	−15.0638	+	15.0638i	−0.779976	+	0.779976i	−0.979826	−	0.199850i	$-0.935954\pi$
$373$	−15.0638	+	15.0638i	−0.779976	+	0.779976i	0.199850	+	0.979826i	$0.435954\pi$
$374$	−8.03997	+	4.21113i	−0.415737	+	0.217752i
$375$	−16.6994	−	25.1456i	−0.862353	−	1.29851i
$376$	−33.9213	−	4.20515i	−1.74936	−	0.216864i
$377$	1.94597	+	1.94597i	0.100222	+	0.100222i
$378$	6.54412	−	20.9392i	0.336593	−	1.07699i
$379$	7.89852			0.405720			0.202860	−	0.979208i	$-0.434976\pi$
$379$	7.89852			0.405720			0.202860	+	0.979208i	$0.434976\pi$
$380$	−0.817052	+	5.45724i	−0.0419139	+	0.279950i
$381$	18.2565			0.935310
$382$	−9.30972	+	29.7882i	−0.476327	+	1.52410i
$383$	5.61005	+	5.61005i	0.286660	+	0.286660i	0.835758	−	0.549098i	$-0.185029\pi$
$383$	5.61005	+	5.61005i	0.286660	+	0.286660i	−0.549098	+	0.835758i	$0.685029\pi$
$384$	−29.7003	+	7.13635i	−1.51564	+	0.364175i
$385$	5.67982	−	16.6807i	0.289471	−	0.850128i
$386$	19.6630	−	10.2990i	1.00082	−	0.524204i
$387$	1.84959	−	1.84959i	0.0940197	−	0.0940197i
$388$	0.607662	+	3.34747i	0.0308494	+	0.169942i
$389$			1.00399i			0.0509041i	0.999676	+	0.0254520i	$0.00810251\pi$
$389$			1.00399i			0.0509041i	−0.999676	+	0.0254520i	$0.991897\pi$
$390$	−1.31213	−	8.43634i	−0.0664424	−	0.427191i
$391$			14.0586i			0.710974i
$392$	−28.6839	+	22.3565i	−1.44876	+	1.12918i
$393$	−11.5725	+	11.5725i	−0.583755	+	0.583755i
$394$	−4.02299	−	7.68076i	−0.202675	−	0.386951i
$395$	6.57290	+	13.3602i	0.330719	+	0.672222i
$396$	12.4708	+	8.63882i	0.626683	+	0.434117i
$397$	22.2875	+	22.2875i	1.11858	+	1.11858i	0.991950	+	0.126630i	$0.0404160\pi$
$397$	22.2875	+	22.2875i	1.11858	+	1.11858i	0.126630	+	0.991950i	$0.459584\pi$
$398$	−25.9840	−	8.12079i	−1.30246	−	0.407059i
$399$	−14.8450			−0.743182
$400$	−19.1230	−	5.85746i	−0.956151	−	0.292873i
$401$	−16.2164			−0.809810			−0.404905	−	0.914359i	$-0.632695\pi$
$401$	−16.2164			−0.809810			−0.404905	+	0.914359i	$0.632695\pi$
$402$	−7.31493	−	2.28614i	−0.364836	−	0.114022i
$403$	2.90462	+	2.90462i	0.144690	+	0.144690i
$404$	−0.614149	−	0.425434i	−0.0305550	−	0.0211661i
$405$	−3.42477	−	6.96123i	−0.170178	−	0.345906i
$406$	8.04698	+	15.3634i	0.399365	+	0.762475i
$407$	2.74192	−	2.74192i	0.135912	−	0.135912i
$408$	−21.8582	+	17.0365i	−1.08214	+	0.843431i
$409$		−	26.1902i		−	1.29502i	−0.762056	−	0.647511i	$-0.775810\pi$
$409$		−	26.1902i		−	1.29502i	0.762056	−	0.647511i	$-0.224190\pi$
$410$	−5.65054	−	36.3301i	−0.279060	−	1.79421i
$411$			47.5732i			2.34661i
$412$	0.132740	+	0.731232i	0.00653962	+	0.0360252i
$413$	22.1666	−	22.1666i	1.09075	−	1.09075i
$414$	20.8166	−	10.9032i	1.02308	−	0.535862i
$415$	−4.00136	+	11.7513i	−0.196419	+	0.576851i
$416$	−4.21850	−	3.76886i	−0.206829	−	0.184783i
$417$	−22.4590	−	22.4590i	−1.09982	−	1.09982i
$418$	0.920505	−	2.94533i	0.0450234	−	0.144061i
$419$	−34.7358			−1.69696			−0.848478	−	0.529231i	$-0.822480\pi$
$419$	−34.7358			−1.69696			−0.848478	+	0.529231i	$0.822480\pi$
$420$	7.96688	−	53.2122i	0.388744	−	2.59649i
$421$	−19.0536			−0.928615			−0.464307	−	0.885674i	$-0.653697\pi$
$421$	−19.0536			−0.928615			−0.464307	+	0.885674i	$0.653697\pi$
$422$	−3.28422	+	10.5085i	−0.159873	+	0.511546i
$423$	36.6535	+	36.6535i	1.78215	+	1.78215i
$424$	40.5427	+	5.02600i	1.96893	+	0.244084i
$425$	−17.9946	+	2.33465i	−0.872866	+	0.113247i
$426$	−38.6101	+	20.2230i	−1.87066	+	0.979806i
$427$	25.9896	−	25.9896i	1.25772	−	1.25772i
$428$	−3.62415	+	0.657889i	−0.175180	+	0.0318003i
$429$			4.77452i			0.230516i
$430$	1.13782	−	1.55695i	0.0548707	−	0.0750828i
$431$			26.6616i			1.28425i	0.766602	+	0.642123i	$0.221946\pi$
$431$			26.6616i			1.28425i	−0.766602	+	0.642123i	$0.778054\pi$
$432$	12.6784	+	5.75717i	0.609992	+	0.276992i
$433$	11.9113	−	11.9113i	0.572419	−	0.572419i	−0.360384	−	0.932804i	$-0.617355\pi$
$433$	11.9113	−	11.9113i	0.572419	−	0.572419i	0.932804	+	0.360384i	$0.117355\pi$
$434$	12.0112	+	22.9320i	0.576557	+	1.10077i
$435$	−15.7275	−	5.35525i	−0.754076	−	0.256764i
$436$	−19.2977	+	27.8577i	−0.924190	+	1.33414i
$437$	−3.37988	−	3.37988i	−0.161682	−	0.161682i
$438$	−28.4209	−	8.88238i	−1.35800	−	0.424417i
$439$	−28.3991			−1.35542			−0.677708	−	0.735331i	$-0.737026\pi$
$439$	−28.3991			−1.35542			−0.677708	+	0.735331i	$0.737026\pi$
$440$	10.0636	+	4.88023i	0.479762	+	0.232656i
$441$	55.1516			2.62627
$442$	−4.89864	−	1.53097i	−0.233004	−	0.0728209i
$443$	2.27026	+	2.27026i	0.107863	+	0.107863i	0.758979	−	0.651115i	$-0.225699\pi$
$443$	2.27026	+	2.27026i	0.107863	+	0.107863i	−0.651115	+	0.758979i	$0.725699\pi$
$444$	6.74230	−	9.73305i	0.319975	−	0.461910i
$445$	−16.1065	+	7.92407i	−0.763523	+	0.375637i
$446$	8.36422	+	15.9691i	0.396057	+	0.756159i
$447$	−14.7711	+	14.7711i	−0.698648	+	0.698648i
$448$	−18.2896	−	30.6005i	−0.864104	−	1.44574i
$449$			22.6117i			1.06711i	0.845764	+	0.533557i	$0.179145\pi$
$449$			22.6117i			1.06711i	−0.845764	+	0.533557i	$0.820855\pi$
$450$	17.4127	+	24.8340i	0.820841	+	1.17068i
$451$			20.5609i			0.968173i
$452$	10.0729	−	1.82852i	0.473790	−	0.0860066i
$453$	35.8591	−	35.8591i	1.68481	−	1.68481i
$454$	28.2130	−	14.7772i	1.32410	−	0.693531i
$455$	8.94092	−	4.39874i	0.419157	−	0.206216i
$456$	1.15920	−	9.35081i	0.0542846	−	0.437892i
$457$	6.14197	+	6.14197i	0.287309	+	0.287309i	0.836015	−	0.548706i	$-0.184879\pi$
$457$	6.14197	+	6.14197i	0.287309	+	0.287309i	−0.548706	+	0.836015i	$0.684879\pi$
$458$	−4.72352	+	15.1138i	−0.220715	+	0.706221i
$459$	12.6332			0.589666
$460$	13.9291	−	10.3013i	0.649447	−	0.480302i
$461$	−28.7359			−1.33836			−0.669181	−	0.743099i	$-0.733355\pi$
$461$	−28.7359			−1.33836			−0.669181	+	0.743099i	$0.733355\pi$
$462$	−8.97563	+	28.7192i	−0.417584	+	1.33614i
$463$	−16.3509	−	16.3509i	−0.759890	−	0.759890i	0.216412	−	0.976302i	$-0.430565\pi$
$463$	−16.3509	−	16.3509i	−0.759890	−	0.759890i	−0.976302	+	0.216412i	$0.930565\pi$
$464$	−10.3057	+	3.86907i	−0.478431	+	0.179617i
$465$	−23.4754	−	7.99343i	−1.08865	−	0.370687i
$466$	11.3296	−	5.93414i	0.524832	−	0.274894i
$467$	4.30118	−	4.30118i	0.199035	−	0.199035i	−0.600551	−	0.799586i	$-0.705052\pi$
$467$	4.30118	−	4.30118i	0.199035	−	0.199035i	0.799586	+	0.600551i	$0.205052\pi$
$468$	1.53224	+	8.44076i	0.0708279	+	0.390174i
$469$		−	8.94445i		−	0.413016i
$470$	30.8543	+	22.5484i	1.42320	+	1.04008i
$471$		−	15.2224i		−	0.701410i
$472$	12.2317	+	15.6935i	0.563009	+	0.722353i
$473$	−0.762549	+	0.762549i	−0.0350620	+	0.0350620i
$474$	−11.7966	−	22.5222i	−0.541834	−	1.03448i
$475$	3.76487	−	4.88743i	0.172744	−	0.224251i
$476$	−26.5878	−	18.4179i	−1.21865	−	0.844184i
$477$	−43.8083	−	43.8083i	−2.00584	−	2.00584i
$478$	9.73315	+	3.04190i	0.445184	+	0.139133i
$479$	−4.08327			−0.186569			−0.0932847	−	0.995639i	$-0.529737\pi$
$479$	−4.08327			−0.186569			−0.0932847	+	0.995639i	$0.529737\pi$
$480$	32.8960	+	9.17346i	1.50149	+	0.418709i
$481$	2.19273			0.0999799
$482$	−16.5277	−	5.16542i	−0.752818	−	0.235278i
$483$	32.9564	+	32.9564i	1.49957	+	1.49957i
$484$	12.9432	+	8.96606i	0.588329	+	0.407548i
$485$	1.22606	−	3.60073i	0.0556724	−	0.163501i
$486$	12.9991	+	24.8181i	0.589652	+	1.12577i
$487$	28.6833	−	28.6833i	1.29976	−	1.29976i	0.371219	−	0.928545i	$-0.378940\pi$
$487$	28.6833	−	28.6833i	1.29976	−	1.29976i	0.928545	−	0.371219i	$-0.121060\pi$
$488$	14.3412	+	18.4001i	0.649198	+	0.832935i
$489$			26.4620i			1.19665i
$490$	40.1769	−	6.24885i	1.81501	−	0.282294i
$491$		−	7.08151i		−	0.319584i	−0.987151	−	0.159792i	$-0.948918\pi$
$491$		−	7.08151i		−	0.319584i	0.987151	−	0.159792i	$-0.0510824\pi$
$492$	11.2134	+	61.7719i	0.505538	+	2.78489i
$493$	−7.06208	+	7.06208i	−0.318060	+	0.318060i
$494$	1.54577	−	0.809633i	0.0695473	−	0.0364271i
$495$	−7.48754	−	15.2193i	−0.336540	−	0.684055i
$496$	−15.3827	+	5.77511i	−0.690702	+	0.259310i
$497$	−35.9695	−	35.9695i	−1.61345	−	1.61345i
$498$	6.32321	−	20.2323i	0.283350	−	0.906632i
$499$	20.2512			0.906566			0.453283	−	0.891367i	$-0.350253\pi$
$499$	20.2512			0.906566			0.453283	+	0.891367i	$0.350253\pi$
$500$	15.4986	+	16.1181i	0.693117	+	0.720826i
$501$	8.19461			0.366108
$502$	1.19732	−	3.83107i	0.0534392	−	0.170989i
$503$	−6.46560	−	6.46560i	−0.288287	−	0.288287i	0.548116	−	0.836402i	$-0.315345\pi$
$503$	−6.46560	−	6.46560i	−0.288287	−	0.288287i	−0.836402	+	0.548116i	$0.815345\pi$
$504$	−6.65120	+	53.6526i	−0.296268	+	2.38987i
$505$	0.368737	+	0.749499i	0.0164086	+	0.0333523i
$506$	−8.58227	+	4.49517i	−0.381528	+	0.199835i
$507$	−1.90910	+	1.90910i	−0.0847863	+	0.0847863i
$508$	−13.3065	+	2.41551i	−0.590380	+	0.107171i
$509$		−	9.49400i		−	0.420814i	−0.977614	−	0.210407i	$-0.932521\pi$
$509$		−	9.49400i		−	0.420814i	0.977614	−	0.210407i	$-0.0674790\pi$
$510$	30.6162	−	4.76184i	1.35571	−	0.210858i
$511$		−	34.7521i		−	1.53734i
$512$	20.7032	−	9.13105i	0.914962	−	0.403539i
$513$	−3.03719	+	3.03719i	−0.134095	+	0.134095i
$514$	8.36179	+	15.9645i	0.368823	+	0.704163i
$515$	0.267824	−	0.786556i	0.0118017	−	0.0346598i
$516$	−1.87508	+	2.70683i	−0.0825459	+	0.119162i
$517$	−15.1115	−	15.1115i	−0.664605	−	0.664605i
$518$	13.1895	+	4.12212i	0.579514	+	0.181116i
$519$	−5.35327			−0.234982
$520$	2.07257	+	5.97532i	0.0908883	+	0.262035i
$521$	−9.55223			−0.418491			−0.209245	−	0.977863i	$-0.567101\pi$
$521$	−9.55223			−0.418491			−0.209245	+	0.977863i	$0.567101\pi$
$522$	15.9338	+	4.97981i	0.697405	+	0.217960i
$523$	−9.29332	−	9.29332i	−0.406368	−	0.406368i	0.474102	−	0.880470i	$-0.342773\pi$
$523$	−9.29332	−	9.29332i	−0.406368	−	0.406368i	−0.880470	+	0.474102i	$0.842773\pi$
$524$	6.90360	−	9.96590i	0.301585	−	0.435362i
$525$	−36.7103	+	47.6562i	−1.60217	+	2.07989i
$526$	0.438637	+	0.837453i	0.0191255	+	0.0365147i
$527$	−10.5411	+	10.5411i	−0.459178	+	0.459178i
$528$	−17.3892	−	7.89629i	−0.756768	−	0.343642i
$529$		−	7.99314i		−	0.347528i
$530$	−36.8771	−	26.9499i	−1.60184	−	1.17063i
$531$		−	30.1745i		−	1.30946i
$532$	10.8200	−	1.96414i	0.469106	−	0.0851563i
$533$	−8.22132	+	8.22132i	−0.356105	+	0.356105i
$534$	27.1520	−	14.2215i	1.17498	−	0.615426i
$535$	3.89835	+	1.32740i	0.168540	+	0.0573884i
$536$	5.63406	+	0.698443i	0.243354	+	0.0301681i
$537$	20.4164	+	20.4164i	0.881033	+	0.881033i
$538$	−2.75413	+	8.81236i	−0.118739	+	0.379928i
$539$	−22.7380			−0.979393
$540$	−9.25687	−	12.5168i	−0.398352	−	0.538638i
$541$	28.8757			1.24146			0.620732	−	0.784023i	$-0.286835\pi$
$541$	28.8757			1.24146			0.620732	+	0.784023i	$0.286835\pi$
$542$	9.49093	−	30.3681i	0.407670	−	1.30442i
$543$	−25.5467	−	25.5467i	−1.09631	−	1.09631i
$544$	13.6775	−	15.3093i	0.586418	−	0.656380i
$545$	33.9972	−	16.7259i	1.45628	−	0.716458i
$546$	−15.0724	+	7.89454i	−0.645039	+	0.337855i
$547$	17.8016	−	17.8016i	0.761139	−	0.761139i	−0.215389	−	0.976528i	$-0.569102\pi$
$547$	17.8016	−	17.8016i	0.761139	−	0.761139i	0.976528	+	0.215389i	$0.0691019\pi$
$548$	−6.29439	−	34.6743i	−0.268883	−	1.48121i
$549$		−	35.3786i		−	1.50992i
$550$	−7.17891	−	10.2386i	−0.306110	−	0.436574i
$551$		−	3.39564i		−	0.144659i
$552$	−23.3325	+	18.1856i	−0.993098	+	0.774030i
$553$	20.9819	−	20.9819i	0.892242	−	0.892242i
$554$	19.5655	+	37.3547i	0.831257	+	1.58705i
$555$	−11.8781	+	5.84376i	−0.504197	+	0.248054i
$556$	19.3411	+	13.3980i	0.820244	+	0.568201i
$557$	0.213360	+	0.213360i	0.00904034	+	0.00904034i	0.711613	−	0.702572i	$-0.247965\pi$
$557$	0.213360	+	0.213360i	0.00904034	+	0.00904034i	−0.702572	+	0.711613i	$0.747965\pi$
$558$	23.7834	+	7.43304i	1.00683	+	0.314666i
$559$	−0.609814			−0.0257924
$560$	1.23373	+	39.8384i	0.0521345	+	1.68348i
$561$	−17.3271			−0.731552
$562$	4.20160	+	1.31313i	0.177234	+	0.0553909i
$563$	−7.49585	−	7.49585i	−0.315912	−	0.315912i	0.531282	−	0.847195i	$-0.321710\pi$
$563$	−7.49585	−	7.49585i	−0.315912	−	0.315912i	−0.847195	+	0.531282i	$0.821710\pi$
$564$	−53.6417	−	37.1588i	−2.25872	−	1.56467i
$565$	−10.8350	−	3.68935i	−0.455832	−	0.155212i
$566$	−1.30904	−	2.49925i	−0.0550232	−	0.105051i
$567$	−10.9325	+	10.9325i	−0.459122	+	0.459122i
$568$	25.4657	−	19.8482i	1.06852	−	0.832814i
$569$			22.3444i			0.936725i	0.883536	+	0.468362i	$0.155156\pi$
$569$			22.3444i			0.936725i	−0.883536	+	0.468362i	$0.844844\pi$
$570$	−6.21574	+	8.50537i	−0.260349	+	0.356251i
$571$		−	14.2843i		−	0.597779i	−0.954288	−	0.298889i	$-0.903384\pi$
$571$		−	14.2843i		−	0.597779i	0.954288	−	0.298889i	$-0.0966161\pi$
$572$	−0.631714	−	3.47996i	−0.0264133	−	0.145505i
$573$	−42.1305	+	42.1305i	−1.76003	+	1.76003i
$574$	−64.9074	+	33.9969i	−2.70918	+	1.41900i
$575$	−19.2084	+	2.49212i	−0.801044	+	0.103929i
$576$	−33.2761	−	8.37911i	−1.38650	−	0.349130i
$577$	2.28756	+	2.28756i	0.0952324	+	0.0952324i	0.753118	−	0.657886i	$-0.228549\pi$
$577$	2.28756	+	2.28756i	0.0952324	+	0.0952324i	−0.657886	+	0.753118i	$0.728549\pi$
$578$	−1.61562	+	5.16950i	−0.0672011	+	0.215023i
$579$	42.3762			1.76109
$580$	12.1717	+	1.82234i	0.505403	+	0.0756685i
$581$	24.7394			1.02636
$582$	−1.93750	+	6.19939i	−0.0803118	+	0.256973i
$583$	18.0613	+	18.0613i	0.748024	+	0.748024i
$584$	21.8901	+	2.71368i	0.905820	+	0.112293i
$585$	3.09155	−	9.07937i	0.127820	−	0.375386i
$586$	0.0793661	−	0.0415700i	0.00327858	−	0.00171724i
$587$	12.7907	−	12.7907i	0.527928	−	0.527928i	−0.392026	−	0.919954i	$-0.628226\pi$
$587$	12.7907	−	12.7907i	0.527928	−	0.527928i	0.919954	+	0.392026i	$0.128226\pi$
$588$	−68.3126	+	12.4007i	−2.81716	+	0.511397i
$589$		−	5.06846i		−	0.208842i
$590$	−3.41886	−	21.9815i	−0.140752	−	0.904966i
$591$		−	16.5530i		−	0.680899i
$592$	−3.62643	+	7.98612i	−0.149045	+	0.328228i
$593$	20.9443	−	20.9443i	0.860077	−	0.860077i	−0.131269	−	0.991347i	$-0.541905\pi$
$593$	20.9443	−	20.9443i	0.860077	−	0.860077i	0.991347	+	0.131269i	$0.0419053\pi$
$594$	4.03940	+	7.71211i	0.165739	+	0.316432i
$595$	15.9634	+	32.4474i	0.654435	+	1.33021i
$596$	8.81172	−	12.7204i	0.360942	−	0.521049i
$597$	−36.7500	−	36.7500i	−1.50408	−	1.50408i
$598$	−5.22905	−	1.63424i	−0.213832	−	0.0668289i
$599$	−23.1160			−0.944492			−0.472246	−	0.881467i	$-0.656557\pi$
$599$	−23.1160			−0.944492			−0.472246	+	0.881467i	$0.656557\pi$
$600$	−27.1518	−	26.8450i	−1.10847	−	1.09594i
$601$	10.3817			0.423477			0.211738	−	0.977326i	$-0.432088\pi$
$601$	10.3817			0.423477			0.211738	+	0.977326i	$0.432088\pi$
$602$	−3.66810	−	1.14639i	−0.149501	−	0.0467235i
$603$	−6.08786	−	6.08786i	−0.247917	−	0.247917i
$604$	−21.3918	+	30.8809i	−0.870422	+	1.25652i
$605$	−7.77116	−	15.7958i	−0.315943	−	0.642189i
$606$	−0.661783	−	1.26349i	−0.0268831	−	0.0513257i
$607$	1.83398	−	1.83398i	0.0744389	−	0.0744389i	−0.668907	−	0.743346i	$-0.733238\pi$
$607$	1.83398	−	1.83398i	0.0744389	−	0.0744389i	0.743346	+	0.668907i	$0.233238\pi$
$608$	0.392303	+	6.96882i	0.0159100	+	0.282623i
$609$			33.1101i			1.34169i
$610$	−4.00850	−	25.7726i	−0.162299	−	1.04350i
$611$		−	12.0848i		−	0.488898i
$612$	−30.6322	+	5.56063i	−1.23823	+	0.224775i
$613$	5.33515	−	5.33515i	0.215485	−	0.215485i	−0.591108	−	0.806593i	$-0.701309\pi$
$613$	5.33515	−	5.33515i	0.215485	−	0.215485i	0.806593	+	0.591108i	$0.201309\pi$
$614$	0.203570	−	0.106625i	0.00821542	−	0.00430303i
$615$	22.6248	−	66.4454i	0.912321	−	2.67934i
$616$	2.74216	−	22.1199i	0.110485	−	0.891237i
$617$	18.8364	+	18.8364i	0.758323	+	0.758323i	0.976017	−	0.217694i	$-0.0698534\pi$
$617$	18.8364	+	18.8364i	0.758323	+	0.758323i	−0.217694	+	0.976017i	$0.569853\pi$
$618$	−0.423233	+	1.35422i	−0.0170249	+	0.0544745i
$619$	−9.61444			−0.386437			−0.193219	−	0.981156i	$-0.561893\pi$
$619$	−9.61444			−0.386437			−0.193219	+	0.981156i	$0.561893\pi$
$620$	18.1679	+	2.72009i	0.729642	+	0.109241i
$621$	13.4853			0.541146
$622$	8.90509	−	28.4935i	0.357061	−	1.14249i
$623$	25.2951	+	25.2951i	1.01343	+	1.01343i
$624$	−3.79577	−	10.1105i	−0.151952	−	0.404743i
$625$	−6.37968	−	24.1723i	−0.255187	−	0.966892i
$626$	5.90541	−	3.09310i	0.236028	−	0.123625i
$627$	4.16568	−	4.16568i	0.166361	−	0.166361i
$628$	2.01407	+	11.0950i	0.0803700	+	0.442739i
$629$			7.95761i			0.317291i
$630$	35.6643	−	48.8016i	1.42090	−	1.94430i
$631$			40.8443i			1.62599i	0.582274	+	0.812993i	$0.302163\pi$
$631$			40.8443i			1.62599i	−0.582274	+	0.812993i	$0.697837\pi$
$632$	11.5780	+	14.8548i	0.460547	+	0.590892i
$633$	−14.8625	+	14.8625i	−0.590731	+	0.590731i
$634$	−13.6387	−	26.0392i	−0.541661	−	1.03415i
$635$	14.3132	+	4.87369i	0.568004	+	0.193407i
$636$	64.1126	+	44.4122i	2.54223	+	1.76106i
$637$	−9.09184	−	9.09184i	−0.360232	−	0.360232i
$638$	−6.56922	−	2.05308i	−0.260078	−	0.0812822i
$639$	−48.9638			−1.93698
$640$	−25.1903	−	2.33374i	−0.995736	−	0.0922491i
$641$	18.6486			0.736574			0.368287	−	0.929712i	$-0.379944\pi$
$641$	18.6486			0.736574			0.368287	+	0.929712i	$0.379944\pi$
$642$	−6.71180	−	2.09764i	−0.264894	−	0.0827873i
$643$	16.1537	+	16.1537i	0.637040	+	0.637040i	0.949824	−	0.312784i	$-0.101262\pi$
$643$	16.1537	+	16.1537i	0.637040	+	0.637040i	−0.312784	+	0.949824i	$0.601262\pi$
$644$	−28.3811	−	19.6602i	−1.11837	−	0.774721i
$645$	3.30338	−	1.62519i	0.130071	−	0.0639919i
$646$	2.93823	+	5.60972i	0.115603	+	0.220711i
$647$	−2.84849	+	2.84849i	−0.111986	+	0.111986i	−0.760879	−	0.648893i	$-0.775232\pi$
$647$	−2.84849	+	2.84849i	−0.111986	+	0.111986i	0.648893	+	0.760879i	$0.275232\pi$
$648$	−6.03264	−	7.74001i	−0.236985	−	0.304056i
$649$			12.4404i			0.488327i
$650$	1.22341	−	6.96443i	0.0479862	−	0.273167i
$651$			49.4214i			1.93698i
$652$	−3.50118	−	19.2872i	−0.137117	−	0.755343i
$653$	21.9792	−	21.9792i	0.860113	−	0.860113i	−0.131238	−	0.991351i	$-0.541895\pi$
$653$	21.9792	−	21.9792i	0.860113	−	0.860113i	0.991351	+	0.131238i	$0.0418953\pi$
$654$	−57.3117	+	30.0184i	−2.24106	+	1.17381i
$655$	−12.1623	+	5.98356i	−0.475219	+	0.233797i
$656$	−16.3460	−	43.5395i	−0.638205	−	1.69993i
$657$	−23.6533	−	23.6533i	−0.922803	−	0.922803i
$658$	22.7182	−	72.6913i	0.885649	−	2.83380i
$659$	42.7307			1.66455			0.832275	−	0.554363i	$-0.187038\pi$
$659$	42.7307			1.66455			0.832275	+	0.554363i	$0.187038\pi$
$660$	12.6963	+	17.1675i	0.494204	+	0.668244i
$661$	16.6982			0.649483			0.324742	−	0.945803i	$-0.394723\pi$
$661$	16.6982			0.649483			0.324742	+	0.945803i	$0.394723\pi$
$662$	1.79608	−	5.74689i	0.0698064	−	0.223359i
$663$	−6.92830	−	6.92830i	−0.269073	−	0.269073i
$664$	−1.93182	+	15.5832i	−0.0749691	+	0.604745i
$665$	−11.6386	−	3.96297i	−0.451326	−	0.153678i
$666$	11.7828	−	6.17154i	0.456575	−	0.239142i
$667$	−7.53843	+	7.53843i	−0.291889	+	0.291889i
$668$	−5.97274	+	1.08423i	−0.231092	+	0.0419500i
$669$			34.4154i			1.33058i
$670$	−5.12466	−	3.74511i	−0.197983	−	0.144686i
$671$			14.5859i			0.563083i
$672$	−3.82526	−	67.9513i	−0.147563	−	2.62128i
$673$	−5.23052	+	5.23052i	−0.201622	+	0.201622i	−0.800695	−	0.599073i	$-0.795536\pi$
$673$	−5.23052	+	5.23052i	−0.201622	+	0.201622i	0.599073	+	0.800695i	$0.295536\pi$
$674$	−4.22585	−	8.06808i	−0.162774	−	0.310771i
$675$	2.23944	+	17.2608i	0.0861961	+	0.664368i
$676$	1.13888	−	1.64407i	0.0438031	−	0.0632333i
$677$	−8.44260	−	8.44260i	−0.324475	−	0.324475i	0.526006	−	0.850481i	$-0.323689\pi$
$677$	−8.44260	−	8.44260i	−0.324475	−	0.324475i	−0.850481	+	0.526006i	$0.823689\pi$
$678$	18.6547	+	5.83015i	0.716429	+	0.223906i
$679$	−7.58040			−0.290909
$680$	−21.6849	+	7.52154i	−0.831579	+	0.288438i
$681$	60.8025			2.32996
$682$	−9.80545	−	3.06450i	−0.375470	−	0.117346i
$683$	−9.22992	−	9.22992i	−0.353173	−	0.353173i	0.508116	−	0.861289i	$-0.330342\pi$
$683$	−9.22992	−	9.22992i	−0.353173	−	0.353173i	−0.861289	+	0.508116i	$0.830342\pi$
$684$	6.02755	−	8.70126i	0.230469	−	0.332701i
$685$	−12.7000	+	37.2977i	−0.485241	+	1.42507i
$686$	−17.1284	−	32.7018i	−0.653965	−	1.24856i
$687$	−21.3759	+	21.3759i	−0.815542	+	0.815542i
$688$	1.00854	−	2.22100i	0.0384501	−	0.0846748i
$689$			14.4437i			0.550263i
$690$	32.6813	−	5.08303i	1.24415	−	0.193508i
$691$			11.7811i			0.448175i	0.974569	+	0.224088i	$0.0719402\pi$
$691$			11.7811i			0.448175i	−0.974569	+	0.224088i	$0.928060\pi$
$692$	3.90180	−	0.708289i	0.148324	−	0.0269251i
$693$	−23.9016	+	23.9016i	−0.907947	+	0.907947i
$694$	36.4222	−	19.0770i	1.38257	−	0.724153i
$695$	−11.6125	−	23.6036i	−0.440485	−	0.895336i
$696$	−20.8559	−	2.58546i	−0.790540	−	0.0980017i
$697$	−29.8359	−	29.8359i	−1.13011	−	1.13011i
$698$	−10.9507	+	35.0389i	−0.414490	+	1.32624i
$699$	24.4166			0.923521
$700$	20.4514	−	39.5919i	0.772991	−	1.49643i
$701$	−40.8964			−1.54464			−0.772318	−	0.635236i	$-0.780903\pi$
$701$	−40.8964			−1.54464			−0.772318	+	0.635236i	$0.780903\pi$
$702$	−1.46854	+	4.69887i	−0.0554265	+	0.177348i
$703$	−1.91312	−	1.91312i	−0.0721546	−	0.0721546i
$704$	13.7191	+	3.45455i	0.517058	+	0.130198i
$705$	32.2067	+	65.4636i	1.21297	+	2.46550i
$706$	4.11462	−	2.15514i	0.154856	−	0.0811096i
$707$	1.17708	−	1.17708i	0.0442685	−	0.0442685i
$708$	6.78467	+	37.3751i	0.254983	+	1.40464i
$709$		−	10.0408i		−	0.377091i	−0.982064	−	0.188546i	$-0.939623\pi$
$709$		−	10.0408i		−	0.377091i	0.982064	−	0.188546i	$-0.0603774\pi$
$710$	−35.6692	+	5.54775i	−1.33864	+	0.208203i
$711$		−	28.5618i		−	1.07115i
$712$	−17.9084	+	13.9580i	−0.671147	+	0.523099i
$713$	−11.2521	+	11.2521i	−0.421395	+	0.421395i
$714$	−28.6499	−	54.6990i	−1.07220	−	2.04706i
$715$	−1.27459	+	3.74325i	−0.0476668	+	0.139990i
$716$	−17.5820	−	12.1795i	−0.657071	−	0.455168i
$717$	13.7659	+	13.7659i	0.514097	+	0.514097i
$718$	−22.6676	−	7.08431i	−0.845948	−	0.264384i
$719$	−27.5425			−1.02716			−0.513581	−	0.858041i	$-0.671681\pi$
$719$	−27.5425			−1.02716			−0.513581	+	0.858041i	$0.671681\pi$
$720$	27.9550	+	26.2755i	1.04182	+	0.979231i
$721$	−1.65589			−0.0616685
$722$	23.5917	+	7.37311i	0.877991	+	0.274399i
$723$	−23.3757	−	23.3757i	−0.869352	−	0.869352i
$724$	22.0001	+	15.2399i	0.817626	+	0.566387i
$725$	−10.9008	−	8.39710i	−0.404847	−	0.311860i
$726$	13.9471	+	26.6281i	0.517626	+	0.988262i
$727$	−21.2619	+	21.2619i	−0.788560	+	0.788560i	−0.981258	−	0.192698i	$-0.938276\pi$
$727$	−21.2619	+	21.2619i	−0.788560	+	0.788560i	0.192698	+	0.981258i	$0.438276\pi$
$728$	9.94118	−	7.74825i	0.368444	−	0.287169i
$729$			43.0776i			1.59547i
$730$	−19.9110	−	14.5510i	−0.736938	−	0.538556i
$731$		−	2.21307i		−	0.0818533i
$732$	7.95479	+	43.8211i	0.294018	+	1.61967i
$733$	−14.1192	+	14.1192i	−0.521503	+	0.521503i	−0.918025	−	0.396522i	$-0.870217\pi$
$733$	−14.1192	+	14.1192i	−0.521503	+	0.521503i	0.396522	+	0.918025i	$0.370217\pi$
$734$	−7.67372	+	4.01930i	−0.283242	+	0.148355i
$735$	73.4810	+	25.0205i	2.71039	+	0.922894i
$736$	14.6001	−	16.3419i	0.538165	−	0.602371i
$737$	2.50991	+	2.50991i	0.0924537	+	0.0924537i
$738$	−21.0387	+	67.3172i	−0.774444	+	2.47798i
$739$	−1.11147			−0.0408861			−0.0204430	−	0.999791i	$-0.506508\pi$
$739$	−1.11147			−0.0408861			−0.0204430	+	0.999791i	$0.506508\pi$
$740$	7.88430	−	5.83088i	0.289833	−	0.214347i
$741$	3.33132			0.122379
$742$	−27.1528	+	86.8807i	−0.996812	+	3.18949i
$743$	32.4947	+	32.4947i	1.19211	+	1.19211i	0.976472	+	0.215642i	$0.0691844\pi$
$743$	32.4947	+	32.4947i	1.19211	+	1.19211i	0.215642	+	0.976472i	$0.430816\pi$
$744$	−31.1302	−	3.85915i	−1.14129	−	0.141483i
$745$	−15.5238	+	7.63739i	−0.568750	+	0.279812i
$746$	26.6884	−	13.9787i	0.977133	−	0.511798i
$747$	16.8384	−	16.8384i	0.616084	−	0.616084i
$748$	12.6291	−	2.29254i	0.461765	−	0.0838237i
$749$		−	8.20696i		−	0.299876i
$750$	11.9334	+	40.9870i	0.435745	+	1.49663i
$751$			22.7914i			0.831668i	0.909440	+	0.415834i	$0.136510\pi$
$751$			22.7914i			0.831668i	−0.909440	+	0.415834i	$0.863490\pi$
$752$	44.0138	+	19.9863i	1.60502	+	0.728826i
$753$	5.41840	−	5.41840i	0.197458	−	0.197458i
$754$	−1.80579	−	3.44765i	−0.0657630	−	0.125556i
$755$	37.6866	−	18.5410i	1.37156	−	0.674775i
$756$	−17.6669	+	25.5035i	−0.642537	+	0.927554i
$757$	20.7548	+	20.7548i	0.754344	+	0.754344i	0.975287	−	0.220943i	$-0.0709133\pi$
$757$	20.7548	+	20.7548i	0.754344	+	0.754344i	−0.220943	+	0.975287i	$0.570913\pi$
$758$	−10.6616	−	3.33208i	−0.387248	−	0.121027i
$759$	−18.4958			−0.671357
$760$	3.40508	−	7.02164i	0.123515	−	0.254702i
$761$	40.7964			1.47887			0.739433	−	0.673230i	$-0.235093\pi$
$761$	40.7964			1.47887			0.739433	+	0.673230i	$0.235093\pi$
$762$	−24.6432	−	7.70173i	−0.892727	−	0.279004i
$763$	−53.3921	−	53.3921i	−1.93292	−	1.93292i
$764$	25.1330	−	36.2816i	0.909281	−	1.31262i
$765$	32.9498	+	11.2195i	1.19130	+	0.405641i
$766$	−5.20593	−	9.93926i	−0.188098	−	0.359120i
$767$	−4.97432	+	4.97432i	−0.179612	+	0.179612i
$768$	43.1009	+	2.89659i	1.55527	+	0.104522i
$769$			9.81657i			0.353994i	0.984211	+	0.176997i	$0.0566384\pi$
$769$			9.81657i			0.353994i	−0.984211	+	0.176997i	$0.943362\pi$
$770$	−14.7037	+	20.1200i	−0.529886	+	0.725074i
$771$			34.4054i			1.23908i
$772$	−30.8864	+	5.60677i	−1.11163	+	0.201792i
$773$	32.9413

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34983 - 0.421862i) q^{2} +(-1.90910 - 1.90910i) q^{3} +(1.64407 + 1.13888i) q^{4} +(-0.987103 - 2.00640i) q^{5} +(1.77158 + 3.38234i) q^{6} +(-3.15102 + 3.15102i) q^{7} +(-1.73875 - 2.23086i) q^{8} +4.28935i q^{9} +O(q^{10})\)	\(q+(-1.34983 - 0.421862i) q^{2} +(-1.90910 - 1.90910i) q^{3} +(1.64407 + 1.13888i) q^{4} +(-0.987103 - 2.00640i) q^{5} +(1.77158 + 3.38234i) q^{6} +(-3.15102 + 3.15102i) q^{7} +(-1.73875 - 2.23086i) q^{8} +4.28935i q^{9} +(0.485997 + 3.12471i) q^{10} -1.76842i q^{11} +(-0.964451 - 5.31293i) q^{12} +(0.707107 - 0.707107i) q^{13} +(5.58262 - 2.92403i) q^{14} +(-1.94594 + 5.71490i) q^{15} +(1.40590 + 3.74479i) q^{16} +(2.56615 + 2.56615i) q^{17} +(1.80951 - 5.78988i) q^{18} -1.23388 q^{19} +(0.662183 - 4.42284i) q^{20} +12.0312 q^{21} +(-0.746028 + 2.38706i) q^{22} +(2.73924 + 2.73924i) q^{23} +(-0.939480 + 7.57840i) q^{24} +(-3.05126 + 3.96104i) q^{25} +(-1.25277 + 0.656171i) q^{26} +(2.46150 - 2.46150i) q^{27} +(-8.76911 + 1.59185i) q^{28} +2.75202i q^{29} +(5.03757 - 6.89321i) q^{30} +4.10776i q^{31} +(-0.317944 - 5.64791i) q^{32} +(-3.37609 + 3.37609i) q^{33} +(-2.38130 - 4.54642i) q^{34} +(9.43256 + 3.21181i) q^{35} +(-4.88506 + 7.05197i) q^{36} +(1.55050 + 1.55050i) q^{37} +(1.66552 + 0.520525i) q^{38} -2.69988 q^{39} +(-2.75966 + 5.69072i) q^{40} -11.6267 q^{41} +(-16.2401 - 5.07551i) q^{42} +(-0.431204 - 0.431204i) q^{43} +(2.01402 - 2.90740i) q^{44} +(8.60614 - 4.23403i) q^{45} +(-2.54192 - 4.85308i) q^{46} +(8.54523 - 8.54523i) q^{47} +(4.46517 - 9.83320i) q^{48} -12.8578i q^{49} +(5.78968 - 4.05951i) q^{50} -9.79809i q^{51} +(1.96784 - 0.357220i) q^{52} +(-10.2133 + 10.2133i) q^{53} +(-4.36102 + 2.28419i) q^{54} +(-3.54815 + 1.74561i) q^{55} +(12.5083 + 1.55063i) q^{56} +(2.35560 + 2.35560i) q^{57} +(1.16097 - 3.71474i) q^{58} -7.03475 q^{59} +(-9.70784 + 7.17948i) q^{60} -8.24800 q^{61} +(1.73290 - 5.54476i) q^{62} +(-13.5158 - 13.5158i) q^{63} +(-1.95347 + 7.75783i) q^{64} +(-2.11672 - 0.720749i) q^{65} +(5.98138 - 3.13290i) q^{66} +(-1.41930 + 1.41930i) q^{67} +(1.29638 + 7.14146i) q^{68} -10.4590i q^{69} +(-11.3774 - 8.31462i) q^{70} +11.4152i q^{71} +(9.56894 - 7.45813i) q^{72} +(-5.51442 + 5.51442i) q^{73} +(-1.43881 - 2.74699i) q^{74} +(13.3872 - 1.73687i) q^{75} +(-2.02857 - 1.40524i) q^{76} +(5.57231 + 5.57231i) q^{77} +(3.64437 + 1.13898i) q^{78} -6.65878 q^{79} +(6.12576 - 6.51729i) q^{80} +3.46952 q^{81} +(15.6940 + 4.90486i) q^{82} +(-3.92562 - 3.92562i) q^{83} +(19.7801 + 13.7021i) q^{84} +(2.61566 - 7.68177i) q^{85} +(0.400142 + 0.763959i) q^{86} +(5.25388 - 5.25388i) q^{87} +(-3.94509 + 3.07484i) q^{88} -8.02760i q^{89} +(-13.4030 + 2.08461i) q^{90} +4.45621i q^{91} +(1.38382 + 7.62315i) q^{92} +(7.84213 - 7.84213i) q^{93} +(-15.1395 + 7.92968i) q^{94} +(1.21796 + 2.47564i) q^{95} +(-10.1755 + 11.3894i) q^{96} +(1.20285 + 1.20285i) q^{97} +(-5.42421 + 17.3558i) q^{98} +7.58537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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