LMFDB - Embedded newform 260.2.o.a.27.16

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			27.16
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.421862 - 1.34983i) q^{2} +(1.90910 + 1.90910i) q^{3} +(-1.64407 + 1.13888i) q^{4} +(-0.987103 - 2.00640i) q^{5} +(1.77158 - 3.38234i) q^{6} +(3.15102 - 3.15102i) q^{7} +(2.23086 + 1.73875i) q^{8} +4.28935i q^{9} +O(q^{10})$	\(q+(-0.421862 - 1.34983i) 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} +(2.23086 + 1.73875i) q^{8} +4.28935i q^{9} +(-2.29187 + 2.17884i) q^{10} +1.76842i q^{11} +(-5.31293 - 0.964451i) 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} +(5.78988 - 1.80951i) q^{18} +1.23388 q^{19} +(3.90791 + 2.17446i) q^{20} +12.0312 q^{21} +(2.38706 - 0.746028i) 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} +(-1.59185 + 8.76911i) q^{28} +2.75202i q^{29} +(-8.53504 - 0.215781i) q^{30} -4.10776i q^{31} +(-5.64791 - 0.317944i) 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} +(-0.520525 - 1.66552i) q^{38} +2.69988 q^{39} +(1.28654 - 6.19232i) q^{40} -11.6267 q^{41} +(-5.07551 - 16.2401i) 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} +(9.83320 - 4.46517i) q^{48} -12.8578i q^{49} +(6.63393 + 2.44766i) q^{50} +9.79809i q^{51} +(-0.357220 + 1.96784i) 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} +(3.71474 - 1.16097i) q^{58} +7.03475 q^{59} +(3.30934 + 11.6119i) q^{60} -8.24800 q^{61} +(-5.54476 + 1.73290i) 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} +(-7.14146 - 1.29638i) q^{68} -10.4590i q^{69} +(-0.356151 + 14.0873i) q^{70} -11.4152i q^{71} +(-7.45813 + 9.56894i) 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} +(-1.13898 - 3.64437i) q^{78} +6.65878 q^{79} +(-8.90130 + 0.875692i) q^{80} +3.46952 q^{81} +(4.90486 + 15.6940i) 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} +(-3.07484 + 3.94509i) q^{88} -8.02760i q^{89} +(-9.34581 - 9.83062i) q^{90} -4.45621i q^{91} +(7.62315 + 1.38382i) 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} +(-17.3558 + 5.42421i) 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 $

$2$	−0.421862	−	1.34983i	−0.298301	−	0.954472i
$2$	−0.421862	−	1.34983i	−0.298301	−	0.954472i
$3$	1.90910	+	1.90910i	1.10222	+	1.10222i	0.994142	+	0.108079i	$0.0344700\pi$
$3$	1.90910	+	1.90910i	1.10222	+	1.10222i	0.108079	+	0.994142i	$0.465530\pi$
$4$	−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	$-0.431293\pi$
$7$	3.15102	−	3.15102i	1.19097	−	1.19097i	0.976795	−	0.214177i	$-0.0687070\pi$
$8$	2.23086	+	1.73875i	0.788728	+	0.614742i
$9$			4.28935i			1.42978i
$10$	−2.29187	+	2.17884i	−0.724752	+	0.689010i
$11$			1.76842i			0.533198i	0.963808	+	0.266599i	$0.0858999\pi$
$11$			1.76842i			0.533198i	−0.963808	+	0.266599i	$0.914100\pi$
$12$	−5.31293	−	0.964451i	−1.53371	−	0.278413i
$13$	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	$0.604946\pi$
$18$	5.78988	−	1.80951i	1.36469	−	0.426506i
$19$	1.23388			0.283071			0.141535	−	0.989933i	$-0.454796\pi$
$19$	1.23388			0.283071			0.141535	+	0.989933i	$0.454796\pi$
$20$	3.90791	+	2.17446i	0.873835	+	0.486223i
$21$	12.0312			2.62543
$22$	2.38706	−	0.746028i	0.508923	−	0.159054i
$23$	−2.73924	−	2.73924i	−0.571171	−	0.571171i	0.361285	−	0.932456i	$-0.382338\pi$
$23$	−2.73924	−	2.73924i	−0.571171	−	0.571171i	−0.932456	+	0.361285i	$0.882338\pi$
$24$	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
$28$	−1.59185	+	8.76911i	−0.300831	+	1.65721i
$29$			2.75202i			0.511036i	0.966804	+	0.255518i	$0.0822461\pi$
$29$			2.75202i			0.511036i	−0.966804	+	0.255518i	$0.917754\pi$
$30$	−8.53504	−	0.215781i	−1.55828	−	0.0393960i
$31$		−	4.10776i		−	0.737775i	−0.929474	−	0.368887i	$-0.879739\pi$
$31$		−	4.10776i		−	0.737775i	0.929474	−	0.368887i	$-0.120261\pi$
$32$	−5.64791	−	0.317944i	−0.998419	−	0.0562051i
$33$	−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	$0.692312\pi$
$38$	−0.520525	−	1.66552i	−0.0844403	−	0.270183i
$39$	2.69988			0.432327
$40$	1.28654	−	6.19232i	0.203420	−	0.979092i
$41$	−11.6267			−1.81579			−0.907893	−	0.419203i	$-0.862310\pi$
$41$	−11.6267			−1.81579			−0.907893	+	0.419203i	$0.862310\pi$
$42$	−5.07551	−	16.2401i	−0.783169	−	2.50590i
$43$	0.431204	+	0.431204i	0.0657580	+	0.0657580i	0.739221	−	0.673463i	$-0.235194\pi$
$43$	0.431204	+	0.431204i	0.0657580	+	0.0657580i	−0.673463	+	0.739221i	$0.735194\pi$
$44$	−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	$0.593380\pi$
$47$	−8.54523	+	8.54523i	−1.24645	+	1.24645i	−0.957277	+	0.289173i	$0.906620\pi$
$48$	9.83320	−	4.46517i	1.41930	−	0.644492i
$49$		−	12.8578i		−	1.83683i
$50$	6.63393	+	2.44766i	0.938179	+	0.346151i
$51$			9.79809i			1.37201i
$52$	−0.357220	+	1.96784i	−0.0495375	+	0.272890i
$53$	−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
$58$	3.71474	−	1.16097i	0.487770	−	0.152443i
$59$	7.03475			0.915846			0.457923	−	0.888992i	$-0.348594\pi$
$59$	7.03475			0.915846			0.457923	+	0.888992i	$0.348594\pi$
$60$	3.30934	+	11.6119i	0.427234	+	1.49908i
$61$	−8.24800			−1.05605			−0.528024	−	0.849229i	$-0.677067\pi$
$61$	−8.24800			−1.05605			−0.528024	+	0.849229i	$0.677067\pi$
$62$	−5.54476	+	1.73290i	−0.704185	+	0.220079i
$63$	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	−0.615074	−	0.788469i	$-0.710874\pi$
$67$	1.41930	−	1.41930i	0.173395	−	0.173395i	0.788469	+	0.615074i	$0.210874\pi$
$68$	−7.14146	−	1.29638i	−0.866029	−	0.157209i
$69$		−	10.4590i		−	1.25911i
$70$	−0.356151	+	14.0873i	−0.0425682	+	1.68375i
$71$		−	11.4152i		−	1.35474i	−0.735644	−	0.677368i	$-0.763120\pi$
$71$		−	11.4152i		−	1.35474i	0.735644	−	0.677368i	$-0.236880\pi$
$72$	−7.45813	+	9.56894i	−0.878949	+	1.12771i
$73$	−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
$78$	−1.13898	−	3.64437i	−0.128964	−	0.412644i
$79$	6.65878			0.749171			0.374586	−	0.927192i	$-0.377785\pi$
$79$	6.65878			0.749171			0.374586	+	0.927192i	$0.377785\pi$
$80$	−8.90130	+	0.875692i	−0.995196	+	0.0979053i
$81$	3.46952			0.385502
$82$	4.90486	+	15.6940i	0.541651	+	1.73312i
$83$	3.92562	+	3.92562i	0.430893	+	0.430893i	0.888932	−	0.458039i	$-0.151448\pi$
$83$	3.92562	+	3.92562i	0.430893	+	0.430893i	−0.458039	+	0.888932i	$0.651448\pi$
$84$	−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
$88$	−3.07484	+	3.94509i	−0.327779	+	0.420548i
$89$		−	8.02760i		−	0.850924i	−0.904976	−	0.425462i	$-0.860112\pi$
$89$		−	8.02760i		−	0.850924i	0.904976	−	0.425462i	$-0.139888\pi$
$90$	−9.34581	−	9.83062i	−0.985135	−	1.03624i
$91$		−	4.45621i		−	0.467138i
$92$	7.62315	+	1.38382i	0.794769	+	0.144274i
$93$	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	$0.722477\pi$
$98$	−17.3558	+	5.42421i	−1.75320	+	0.547928i
$99$	−7.58537			−0.762358
$100$	0.505313	−	9.98722i	0.0505313	−	0.998722i
$101$	−0.373555			−0.0371701			−0.0185851	−	0.999827i	$-0.505916\pi$
$101$	−0.373555			−0.0371701			−0.0185851	+	0.999827i	$0.505916\pi$
$102$	13.2257	−	4.13344i	1.30954	−	0.409271i
$103$	−0.262755	−	0.262755i	−0.0258900	−	0.0258900i	0.694043	−	0.719933i	$-0.255828\pi$
$103$	−0.262755	−	0.262755i	−0.0258900	−	0.0258900i	−0.719933	+	0.694043i	$0.755828\pi$
$104$	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	−0.641352	−	0.767247i	$-0.721626\pi$
$107$	1.30227	−	1.30227i	0.125895	−	0.125895i	0.767247	+	0.641352i	$0.221626\pi$
$108$	1.24352	−	6.85023i	0.119657	−	0.659164i
$109$			16.9444i			1.62298i	0.584366	+	0.811490i	$0.301343\pi$
$109$			16.9444i			1.62298i	−0.584366	+	0.811490i	$0.698657\pi$
$110$	−3.85310	−	4.05298i	−0.367379	−	0.386436i
$111$			5.92011i			0.561912i
$112$	−7.36986	−	16.2299i	−0.696386	−	1.53358i
$113$	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
$118$	−2.96769	−	9.49569i	−0.273198	−	0.874149i
$119$	16.1720			1.48248
$120$	14.2779	−	9.36563i	1.30339	−	0.854961i
$121$	7.87270			0.715700
$122$	3.47951	+	11.1334i	0.315020	+	1.00797i
$123$	−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	−0.462392	−	0.886676i	$-0.653009\pi$
$127$	4.78144	−	4.78144i	0.424284	−	0.424284i	0.886676	+	0.462392i	$0.153009\pi$
$128$	9.64764	−	5.90957i	0.852739	−	0.522338i
$129$			1.64643i			0.144960i
$130$	−0.0799225	+	3.16127i	−0.00700966	+	0.277262i
$131$			6.06174i			0.529617i	0.964301	+	0.264808i	$0.0853087\pi$
$131$			6.06174i			0.529617i	−0.964301	+	0.264808i	$0.914691\pi$
$132$	1.70555	−	9.39548i	0.148449	−	0.817772i
$133$	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	$-0.521254\pi$
$138$	−14.1178	+	4.41224i	−1.20179	+	0.375595i
$139$	−11.7642			−0.997824			−0.498912	−	0.866653i	$-0.666267\pi$
$139$	−11.7642			−0.997824			−0.498912	+	0.866653i	$0.666267\pi$
$140$	19.1656	−	5.46214i	1.61979	−	0.461635i
$141$	−32.6275			−2.74773
$142$	−15.4086	+	4.81564i	−1.29306	+	0.404119i
$143$	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
$148$	−4.31494	−	0.783287i	−0.354686	−	0.0643858i
$149$		−	7.73718i		−	0.633854i	−0.948450	−	0.316927i	$-0.897349\pi$
$149$		−	7.73718i		−	0.633854i	0.948450	−	0.316927i	$-0.102651\pi$
$150$	7.99202	+	17.3377i	0.652546	+	1.41562i
$151$		−	18.7832i		−	1.52856i	−0.644886	−	0.764279i	$-0.723095\pi$
$151$		−	18.7832i		−	1.52856i	0.644886	−	0.764279i	$-0.276905\pi$
$152$	2.75260	+	2.14541i	0.223266	+	0.174015i
$153$	−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	$0.677766\pi$
$158$	−2.80908	−	8.98820i	−0.223479	−	0.715063i
$159$	−38.9964			−3.09261
$160$	4.93715	+	11.6458i	0.390316	+	0.920681i
$161$	−17.2628			−1.36050
$162$	−1.46366	−	4.68325i	−0.114996	−	0.367951i
$163$	6.93048	+	6.93048i	0.542837	+	0.542837i	0.924360	−	0.381522i	$-0.124600\pi$
$163$	6.93048	+	6.93048i	0.542837	+	0.542837i	−0.381522	+	0.924360i	$0.624600\pi$
$164$	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	−0.619175	−	0.785253i	$-0.712533\pi$
$167$	2.14619	−	2.14619i	0.166078	−	0.166078i	0.785253	+	0.619175i	$0.212533\pi$
$168$	26.8400	+	20.9193i	2.07075	+	1.61396i
$169$		−	1.00000i		−	0.0769231i
$170$	−11.4725	−	0.290045i	−0.879901	−	0.0222455i
$171$			5.29253i			0.404730i
$172$	−1.20002	−	0.217838i	−0.0915005	−	0.0166100i
$173$	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
$178$	−10.8359	+	3.38654i	−0.812183	+	0.253832i
$179$	10.6942			0.799325			0.399662	−	0.916662i	$-0.369127\pi$
$179$	10.6942			0.799325			0.399662	+	0.916662i	$0.369127\pi$
$180$	−9.32700	+	16.7624i	−0.695194	+	1.24939i
$181$	13.3815			0.994639			0.497319	−	0.867568i	$-0.334318\pi$
$181$	13.3815			0.994639			0.497319	+	0.867568i	$0.334318\pi$
$182$	−6.01511	+	1.87990i	−0.445870	+	0.139348i
$183$	−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
$188$	4.31693	−	23.7809i	0.314844	−	1.73440i
$189$			15.5125i			1.12837i
$190$	−2.82788	+	2.68842i	−0.205156	+	0.195038i
$191$			22.0682i			1.59680i	0.602128	+	0.798399i	$0.294320\pi$
$191$			22.0682i			1.59680i	−0.602128	+	0.798399i	$0.705680\pi$
$192$	−11.0811	+	18.5399i	−0.799712	+	1.33800i
$193$	−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	$0.679914\pi$
$198$	3.19997	+	10.2389i	0.227412	+	0.727649i
$199$	−19.2499			−1.36459			−0.682295	−	0.731077i	$-0.739018\pi$
$199$	−19.2499			−1.36459			−0.682295	+	0.731077i	$0.739018\pi$
$200$	−13.6942	+	3.53114i	−0.968326	+	0.249689i
$201$	5.41916			0.382238
$202$	0.157588	+	0.504234i	0.0110879	+	0.0354778i
$203$	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
$208$	−1.65384	−	3.64209i	−0.114673	−	0.252533i
$209$			2.18201i			0.150933i
$210$	−27.5740	+	26.2141i	−1.90279	+	1.80895i
$211$			7.78507i			0.535946i	0.963426	+	0.267973i	$0.0863539\pi$
$211$			7.78507i			0.535946i	−0.963426	+	0.267973i	$0.913646\pi$
$212$	5.15959	−	28.4230i	0.354362	−	1.95210i
$213$	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
$218$	22.8720	−	7.14820i	1.54909	−	0.484137i
$219$	−21.0552			−1.42278
$220$	−3.84535	+	6.91081i	−0.259253	+	0.465927i
$221$	3.62908			0.244119
$222$	7.99112	−	2.49747i	0.536329	−	0.167619i
$223$	9.01350	+	9.01350i	0.603589	+	0.603589i	0.941263	−	0.337674i	$-0.109640\pi$
$223$	9.01350	+	9.01350i	0.603589	+	0.603589i	−0.337674	+	0.941263i	$0.609640\pi$
$224$	−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	$-0.481318\pi$
$227$	15.9244	−	15.9244i	1.05694	−	1.05694i	0.998278	−	0.0586582i	$-0.0186822\pi$
$228$	−6.55550	−	1.19001i	−0.434148	−	0.0788105i
$229$		−	11.1968i		−	0.739908i	−0.929050	−	0.369954i	$-0.879373\pi$
$229$		−	11.1968i		−	0.739908i	0.929050	−	0.369954i	$-0.120627\pi$
$230$	12.2463	+	0.309609i	0.807499	+	0.0204150i
$231$			21.2762i			1.39987i
$232$	−4.78508	+	6.13936i	−0.314156	+	0.403069i
$233$	−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
$238$	−6.82233	−	21.8293i	−0.442226	−	1.41499i
$239$	7.21067			0.466419			0.233210	−	0.972426i	$-0.425077\pi$
$239$	7.21067			0.466419			0.233210	+	0.972426i	$0.425077\pi$
$240$	−18.6653	−	15.3217i	−1.20484	−	0.989013i
$241$	12.2443			0.788728			0.394364	−	0.918954i	$-0.370965\pi$
$241$	12.2443			0.788728			0.394364	+	0.918954i	$0.370965\pi$
$242$	−3.32119	−	10.6268i	−0.213494	−	0.683115i
$243$	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
$248$	7.14238	−	9.16383i	0.453541	−	0.581904i
$249$			14.9888i			0.949879i
$250$	−1.63740	−	15.7264i	−0.103558	−	0.994623i
$251$		−	2.83819i		−	0.179145i	−0.995980	−	0.0895726i	$-0.971450\pi$
$251$		−	2.83819i		−	0.179145i	0.995980	−	0.0895726i	$-0.0285501\pi$
$252$	−37.6138	−	6.82799i	−2.36945	−	0.430123i
$253$	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	$0.880106\pi$
$258$	2.22239	−	0.694564i	0.138360	−	0.0432417i
$259$	9.77127			0.607157
$260$	4.30088	−	1.22574i	0.266729	−	0.0760169i
$261$	−11.8044			−0.730671
$262$	8.18230	−	2.55722i	0.505504	−	0.157985i
$263$	0.472686	+	0.472686i	0.0291471	+	0.0291471i	0.721530	−	0.692383i	$-0.243439\pi$
$263$	0.472686	+	0.472686i	0.0291471	+	0.0291471i	−0.692383	+	0.721530i	$0.743439\pi$
$264$	−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
$268$	−0.717007	+	3.94982i	−0.0437982	+	0.241274i
$269$		−	6.52851i		−	0.398050i	−0.979994	−	0.199025i	$-0.936222\pi$
$269$		−	6.52851i		−	0.398050i	0.979994	−	0.199025i	$-0.0637775\pi$
$270$	0.278218	−	11.0047i	0.0169318	−	0.669723i
$271$		−	22.4977i		−	1.36664i	−0.730119	−	0.683320i	$-0.760535\pi$
$271$		−	22.4977i		−	1.36664i	0.730119	−	0.683320i	$-0.239465\pi$
$272$	13.2174	−	6.00193i	0.801425	−	0.363920i
$273$	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	$-0.603385\pi$
$278$	4.96285	+	15.8796i	0.297652	+	0.952395i
$279$	17.6196			1.05486
$280$	−15.4582	−	23.5660i	−0.923803	−	1.40834i
$281$	−3.11270			−0.185688			−0.0928440	−	0.995681i	$-0.529596\pi$
$281$	−3.11270			−0.185688			−0.0928440	+	0.995681i	$0.529596\pi$
$282$	13.7643	+	44.0414i	0.819650	+	2.62263i
$283$	−1.41066	−	1.41066i	−0.0838550	−	0.0838550i	0.663935	−	0.747790i	$-0.268885\pi$
$283$	−1.41066	−	1.41066i	−0.0838550	−	0.0838550i	−0.747790	+	0.663935i	$0.768885\pi$
$284$	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
$288$	1.36377	−	24.2259i	0.0803611	−	1.42752i
$289$		−	3.82975i		−	0.225279i
$290$	−5.99620	−	6.30725i	−0.352109	−	0.370375i
$291$			4.59273i			0.269231i
$292$	2.78581	−	15.3463i	0.163027	−	0.898077i
$293$	−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
$298$	−10.4438	+	3.26402i	−0.604996	+	0.189079i
$299$	−3.87387			−0.224032
$300$	20.0313	−	18.1020i	1.15651	−	1.04512i
$301$	2.71746			0.156632
$302$	−25.3541	+	7.92392i	−1.45896	+	0.455970i
$303$	−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	−0.703820	−	0.710378i	$-0.748524\pi$
$307$	0.114902	−	0.114902i	0.00655779	−	0.00655779i	0.710378	+	0.703820i	$0.248524\pi$
$308$	−15.5074	−	2.81505i	−0.883619	−	0.160402i
$309$		−	1.00325i		−	0.0570730i
$310$	8.95014	+	9.41443i	0.508334	+	0.534704i
$311$		−	21.1090i		−	1.19698i	−0.801129	−	0.598492i	$-0.795767\pi$
$311$		−	21.1090i		−	1.19698i	0.801129	−	0.598492i	$-0.204233\pi$
$312$	6.02305	+	4.69443i	0.340988	+	0.265770i
$313$	−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	$0.551601\pi$
$318$	16.4511	+	52.6383i	0.922530	+	2.95181i
$319$	−4.86671			−0.272484
$320$	13.6370	−	11.5772i	0.762332	−	0.647186i
$321$	4.97234			0.277529
$322$	7.28250	+	23.3017i	0.405838	+	1.29856i
$323$	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
$328$	−25.9375	−	20.2160i	−1.43216	−	1.11624i
$329$			53.8523i			2.96897i
$330$	0.381591	−	15.0935i	0.0210059	−	0.830871i
$331$		−	4.25750i		−	0.234013i	−0.993131	−	0.117007i	$-0.962670\pi$
$331$		−	4.25750i		−	0.234013i	0.993131	−	0.117007i	$-0.0373299\pi$
$332$	−10.9248	−	1.98317i	−0.599576	−	0.108840i
$333$	−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	$0.693875\pi$
$338$	−1.34983	+	0.421862i	−0.0734209	+	0.0229462i
$339$	13.8201			0.750602
$340$	4.44830	+	15.6083i	0.241243	+	0.846477i
$341$	7.26423			0.393380
$342$	7.14400	−	2.23271i	0.386303	−	0.120731i
$343$	−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	$-0.465033\pi$
$347$	20.5579	−	20.5579i	1.10360	−	1.10360i	0.993972	−	0.109633i	$-0.0349674\pi$
$348$	2.65418	−	14.6213i	0.142279	−	0.783782i
$349$		−	25.9580i		−	1.38950i	−0.719250	−	0.694751i	$-0.755515\pi$
$349$		−	25.9580i		−	1.38950i	0.719250	−	0.694751i	$-0.244485\pi$
$350$	28.6162	−	13.1910i	1.52960	−	0.705089i
$351$			3.48109i			0.185807i
$352$	0.562258	−	9.98787i	0.0299685	−	0.532355i
$353$	−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
$358$	−4.51149	−	14.4354i	−0.238439	−	0.762933i
$359$	−16.7930			−0.886300			−0.443150	−	0.896448i	$-0.646139\pi$
$359$	−16.7930			−0.886300			−0.443150	+	0.896448i	$0.646139\pi$
$360$	26.5610	+	5.51843i	1.39989	+	0.290847i
$361$	−17.4776			−0.919871
$362$	−5.64514	−	18.0627i	−0.296702	−	0.949355i
$363$	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	−0.811058	−	0.584966i	$-0.801108\pi$
$367$	−4.33130	+	4.33130i	−0.226092	+	0.226092i	0.584966	+	0.811058i	$0.301108\pi$
$368$	−14.1090	+	6.40676i	−0.735481	+	0.333976i
$369$		−	49.8710i		−	2.59618i
$370$	−6.93181	−	0.175248i	−0.360368	−	0.00911073i
$371$			64.3643i			3.34163i
$372$	−3.96173	+	21.8242i	−0.205406	+	1.13153i
$373$	−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
$378$	20.9392	−	6.54412i	1.07699	−	0.336593i
$379$	−7.89852			−0.405720			−0.202860	−	0.979208i	$-0.565024\pi$
$379$	−7.89852			−0.405720			−0.202860	+	0.979208i	$0.565024\pi$
$380$	4.82187	+	2.68301i	0.247357	+	0.137635i
$381$	18.2565			0.935310
$382$	29.7882	−	9.30972i	1.52410	−	0.476327i
$383$	−5.61005	−	5.61005i	−0.286660	−	0.286660i	0.549098	−	0.835758i	$-0.314971\pi$
$383$	−5.61005	−	5.61005i	−0.286660	−	0.286660i	−0.835758	+	0.549098i	$0.814971\pi$
$384$	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
$388$	−3.34747	−	0.607662i	−0.169942	−	0.0308494i
$389$			1.00399i			0.0509041i	0.999676	+	0.0254520i	$0.00810251\pi$
$389$			1.00399i			0.0509041i	−0.999676	+	0.0254520i	$0.991897\pi$
$390$	−6.18777	+	5.88261i	−0.313330	+	0.297877i
$391$		−	14.0586i		−	0.710974i
$392$	22.3565	−	28.6839i	1.12918	−	1.44876i
$393$	−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	$0.459584\pi$
$398$	8.12079	+	25.9840i	0.407059	+	1.30246i
$399$	14.8450			0.743182
$400$	10.5435	+	16.9951i	0.527174	+	0.849757i
$401$	−16.2164			−0.809810			−0.404905	−	0.914359i	$-0.632695\pi$
$401$	−16.2164			−0.809810			−0.404905	+	0.914359i	$0.632695\pi$
$402$	−2.28614	−	7.31493i	−0.114022	−	0.364836i
$403$	−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
$408$	−17.0365	+	21.8582i	−0.843431	+	1.08214i
$409$		−	26.1902i		−	1.29502i	−0.762056	−	0.647511i	$-0.775810\pi$
$409$		−	26.1902i		−	1.29502i	0.762056	−	0.647511i	$-0.224190\pi$
$410$	26.6469	−	25.3327i	1.31599	−	1.25109i
$411$		−	47.5732i		−	2.34661i
$412$	0.731232	+	0.132740i	0.0360252	+	0.00653962i
$413$	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
$418$	2.94533	−	0.920505i	0.144061	−	0.0450234i
$419$	34.7358			1.69696			0.848478	−	0.529231i	$-0.177520\pi$
$419$	34.7358			1.69696			0.848478	+	0.529231i	$0.177520\pi$
$420$	47.0169	+	26.1614i	2.29419	+	1.27654i
$421$	−19.0536			−0.928615			−0.464307	−	0.885674i	$-0.653697\pi$
$421$	−19.0536			−0.928615			−0.464307	+	0.885674i	$0.653697\pi$
$422$	10.5085	−	3.28422i	0.511546	−	0.159873i
$423$	−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
$428$	−0.657889	+	3.62415i	−0.0318003	+	0.175180i
$429$			4.77452i			0.230516i
$430$	−1.92779	−	0.0487379i	−0.0929661	−	0.00235035i
$431$		−	26.6616i		−	1.28425i	−0.766602	−	0.642123i	$-0.778054\pi$
$431$		−	26.6616i		−	1.28425i	0.766602	−	0.642123i	$-0.221946\pi$
$432$	5.75717	+	12.6784i	0.276992	+	0.609992i
$433$	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
$438$	8.88238	+	28.4209i	0.424417	+	1.35800i
$439$	28.3991			1.35542			0.677708	−	0.735331i	$-0.262974\pi$
$439$	28.3991			1.35542			0.677708	+	0.735331i	$0.262974\pi$
$440$	10.9506	+	2.27514i	0.522050	+	0.108463i
$441$	55.1516			2.62627
$442$	−1.53097	−	4.89864i	−0.0728209	−	0.233004i
$443$	−2.27026	−	2.27026i	−0.107863	−	0.107863i	0.651115	−	0.758979i	$-0.274301\pi$
$443$	−2.27026	−	2.27026i	−0.107863	−	0.107863i	−0.758979	+	0.651115i	$0.774301\pi$
$444$	−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
$448$	30.6005	+	18.2896i	1.44574	+	0.864104i
$449$			22.6117i			1.06711i	0.845764	+	0.533557i	$0.179145\pi$
$449$			22.6117i			1.06711i	−0.845764	+	0.533557i	$0.820855\pi$
$450$	−10.4989	+	28.4552i	−0.494921	+	1.34139i
$451$		−	20.5609i		−	0.968173i
$452$	−1.82852	+	10.0729i	−0.0860066	+	0.473790i
$453$	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	$0.684879\pi$
$458$	−15.1138	+	4.72352i	−0.706221	+	0.220715i
$459$	−12.6332			−0.589666
$460$	−4.74834	−	16.6610i	−0.221392	−	0.776825i
$461$	−28.7359			−1.33836			−0.669181	−	0.743099i	$-0.733355\pi$
$461$	−28.7359			−1.33836			−0.669181	+	0.743099i	$0.733355\pi$
$462$	28.7192	−	8.97563i	1.33614	−	0.417584i
$463$	16.3509	+	16.3509i	0.759890	+	0.759890i	0.976302	−	0.216412i	$-0.0694354\pi$
$463$	16.3509	+	16.3509i	0.759890	+	0.759890i	−0.216412	+	0.976302i	$0.569435\pi$
$464$	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	−0.799586	−	0.600551i	$-0.794948\pi$
$467$	−4.30118	+	4.30118i	−0.199035	+	0.199035i	0.600551	+	0.799586i	$0.294948\pi$
$468$	−8.44076	−	1.53224i	−0.390174	−	0.0708279i
$469$		−	8.94445i		−	0.413016i
$470$	0.965845	−	38.2032i	0.0445511	−	1.76218i
$471$			15.2224i			0.701410i
$472$	15.6935	+	12.2317i	0.722353	+	0.563009i
$473$	−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
$478$	−3.04190	−	9.73315i	−0.139133	−	0.445184i
$479$	4.08327			0.186569			0.0932847	−	0.995639i	$-0.470263\pi$
$479$	4.08327			0.186569			0.0932847	+	0.995639i	$0.470263\pi$
$480$	−12.8075	+	31.6586i	−0.584580	+	1.44501i
$481$	2.19273			0.0999799
$482$	−5.16542	−	16.5277i	−0.235278	−	0.752818i
$483$	−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	$0.621060\pi$
$487$	−28.6833	+	28.6833i	−1.29976	+	1.29976i	−0.928545	+	0.371219i	$0.878940\pi$
$488$	−18.4001	−	14.3412i	−0.832935	−	0.649198i
$489$			26.4620i			1.19665i
$490$	28.0151	+	29.4684i	1.26559	+	1.33125i
$491$			7.08151i			0.319584i	0.987151	+	0.159792i	$0.0510824\pi$
$491$			7.08151i			0.319584i	−0.987151	+	0.159792i	$0.948918\pi$
$492$	61.7719	+	11.2134i	2.78489	+	0.505538i
$493$	−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
$498$	20.2323	−	6.32321i	0.906632	−	0.283350i
$499$	−20.2512			−0.906566			−0.453283	−	0.891367i	$-0.649747\pi$
$499$	−20.2512			−0.906566			−0.453283	+	0.891367i	$0.649747\pi$
$500$	−20.5371	+	8.84456i	−0.918448	+	0.395541i
$501$	8.19461			0.366108
$502$	−3.83107	+	1.19732i	−0.170989	+	0.0534392i
$503$	6.46560	+	6.46560i	0.288287	+	0.288287i	0.836402	−	0.548116i	$-0.184655\pi$
$503$	6.46560	+	6.46560i	0.288287	+	0.288287i	−0.548116	+	0.836402i	$0.684655\pi$
$504$	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
$508$	−2.41551	+	13.3065i	−0.107171	+	0.590380i
$509$		−	9.49400i		−	0.420814i	−0.977614	−	0.210407i	$-0.932521\pi$
$509$		−	9.49400i		−	0.420814i	0.977614	−	0.210407i	$-0.0674790\pi$
$510$	−21.3485	−	22.4559i	−0.945326	−	0.994365i
$511$			34.7521i			1.53734i
$512$	−9.13105	+	20.7032i	−0.403539	+	0.914962i
$513$	−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
$518$	−4.12212	−	13.1895i	−0.181116	−	0.579514i
$519$	5.35327			0.234982
$520$	−3.46891	−	5.28835i	−0.152122	−	0.231910i
$521$	−9.55223			−0.418491			−0.209245	−	0.977863i	$-0.567101\pi$
$521$	−9.55223			−0.418491			−0.209245	+	0.977863i	$0.567101\pi$
$522$	4.97981	+	15.9338i	0.217960	+	0.697405i
$523$	9.29332	+	9.29332i	0.406368	+	0.406368i	0.880470	−	0.474102i	$-0.157227\pi$
$523$	9.29332	+	9.29332i	0.406368	+	0.406368i	−0.474102	+	0.880470i	$0.657227\pi$
$524$	−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
$528$	7.89629	+	17.3892i	0.343642	+	0.756768i
$529$		−	7.99314i		−	0.347528i
$530$	1.15438	−	45.6605i	0.0501430	−	1.98337i
$531$			30.1745i			1.30946i
$532$	−1.96414	+	10.8200i	−0.0851563	+	0.469106i
$533$	−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
$538$	−8.81236	+	2.75413i	−0.379928	+	0.118739i
$539$	22.7380			0.979393
$540$	−14.9718	+	4.26690i	−0.644282	+	0.183618i
$541$	28.8757			1.24146			0.620732	−	0.784023i	$-0.286835\pi$
$541$	28.8757			1.24146			0.620732	+	0.784023i	$0.286835\pi$
$542$	−30.3681	+	9.49093i	−1.30442	+	0.407670i
$543$	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	−0.976528	−	0.215389i	$-0.930898\pi$
$547$	−17.8016	+	17.8016i	−0.761139	+	0.761139i	0.215389	+	0.976528i	$0.430898\pi$
$548$	34.6743	+	6.29439i	1.48121	+	0.268883i
$549$		−	35.3786i		−	1.50992i
$550$	−4.32848	+	11.7316i	−0.184567	+	0.500235i
$551$			3.39564i			0.144659i
$552$	18.1856	−	23.3325i	0.774030	−	0.993098i
$553$	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	$0.747965\pi$
$558$	−7.43304	−	23.7834i	−0.314666	−	1.00683i
$559$	0.609814			0.0257924
$560$	−25.2888	+	30.8075i	−1.06865	+	1.30185i
$561$	−17.3271			−0.731552
$562$	1.31313	+	4.20160i	0.0553909	+	0.177234i
$563$	7.49585	+	7.49585i	0.315912	+	0.315912i	0.847195	−	0.531282i	$-0.178290\pi$
$563$	7.49585	+	7.49585i	0.315912	+	0.315912i	−0.531282	+	0.847195i	$0.678290\pi$
$564$	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
$568$	19.8482	−	25.4657i	0.832814	−	1.06852i
$569$			22.3444i			0.936725i	0.883536	+	0.468362i	$0.155156\pi$
$569$			22.3444i			0.936725i	−0.883536	+	0.468362i	$0.844844\pi$
$570$	−10.5312	−	0.266247i	−0.441103	−	0.0111519i
$571$			14.2843i			0.597779i	0.954288	+	0.298889i	$0.0966161\pi$
$571$			14.2843i			0.597779i	−0.954288	+	0.298889i	$0.903384\pi$
$572$	−3.47996	−	0.631714i	−0.145505	−	0.0264133i
$573$	−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	$0.728549\pi$
$578$	−5.16950	+	1.61562i	−0.215023	+	0.0672011i
$579$	−42.3762			−1.76109
$580$	−5.98413	+	10.7546i	−0.248478	+	0.446561i
$581$	24.7394			1.02636
$582$	6.19939	−	1.93750i	0.256973	−	0.0803118i
$583$	−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	−0.919954	−	0.392026i	$-0.871774\pi$
$587$	−12.7907	+	12.7907i	−0.527928	+	0.527928i	0.392026	+	0.919954i	$0.371774\pi$
$588$	−12.4007	+	68.3126i	−0.511397	+	2.81716i
$589$		−	5.06846i		−	0.208842i
$590$	−16.1227	+	15.3276i	−0.663761	+	0.631027i
$591$			16.5530i			0.680899i
$592$	7.98612	−	3.62643i	0.328228	−	0.149045i
$593$	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
$598$	1.63424	+	5.22905i	0.0668289	+	0.213832i
$599$	23.1160			0.944492			0.472246	−	0.881467i	$-0.343443\pi$
$599$	23.1160			0.944492			0.472246	+	0.881467i	$0.343443\pi$
$600$	−32.8850	−	19.4023i	−1.34252	−	0.792096i
$601$	10.3817			0.423477			0.211738	−	0.977326i	$-0.432088\pi$
$601$	10.3817			0.423477			0.211738	+	0.977326i	$0.432088\pi$
$602$	−1.14639	−	3.66810i	−0.0467235	−	0.149501i
$603$	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	−0.743346	−	0.668907i	$-0.766762\pi$
$607$	−1.83398	+	1.83398i	−0.0744389	+	0.0744389i	0.668907	+	0.743346i	$0.266762\pi$
$608$	−6.96882	−	0.392303i	−0.282623	−	0.0159100i
$609$			33.1101i			1.34169i
$610$	18.9033	−	17.9711i	0.765373	−	0.727627i
$611$			12.0848i			0.488898i
$612$	5.56063	−	30.6322i	0.224775	−	1.23823i
$613$	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	$0.569853\pi$
$618$	−1.35422	+	0.423233i	−0.0544745	+	0.0170249i
$619$	9.61444			0.386437			0.193219	−	0.981156i	$-0.438107\pi$
$619$	9.61444			0.386437			0.193219	+	0.981156i	$0.438107\pi$
$620$	8.93213	−	16.0527i	0.358723	−	0.644693i
$621$	13.4853			0.541146
$622$	−28.4935	+	8.90509i	−1.14249	+	0.357061i
$623$	−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
$628$	−11.0950	−	2.01407i	−0.442739	−	0.0803700i
$629$			7.95761i			0.317291i
$630$	−60.4252	−	1.52766i	−2.40740	−	0.0608633i
$631$		−	40.8443i		−	1.62599i	−0.582274	−	0.812993i	$-0.697837\pi$
$631$		−	40.8443i		−	1.62599i	0.582274	−	0.812993i	$-0.302163\pi$
$632$	14.8548	+	11.5780i	0.590892	+	0.460547i
$633$	−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
$638$	2.05308	+	6.56922i	0.0812822	+	0.260078i
$639$	48.9638			1.93698
$640$	−21.3802	−	13.5236i	−0.845125	−	0.534568i
$641$	18.6486			0.736574			0.368287	−	0.929712i	$-0.379944\pi$
$641$	18.6486			0.736574			0.368287	+	0.929712i	$0.379944\pi$
$642$	−2.09764	−	6.71180i	−0.0827873	−	0.264894i
$643$	−16.1537	−	16.1537i	−0.637040	−	0.637040i	0.312784	−	0.949824i	$-0.398738\pi$
$643$	−16.1537	−	16.1537i	−0.637040	−	0.637040i	−0.949824	+	0.312784i	$0.898738\pi$
$644$	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	−0.648893	−	0.760879i	$-0.724768\pi$
$647$	2.84849	−	2.84849i	0.111986	−	0.111986i	0.760879	+	0.648893i	$0.224768\pi$
$648$	7.74001	+	6.03264i	0.304056	+	0.236985i
$649$			12.4404i			0.488327i
$650$	6.42165	−	2.96014i	0.251878	−	0.116106i
$651$		−	49.4214i		−	1.93698i
$652$	−19.2872	−	3.50118i	−0.755343	−	0.137117i
$653$	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
$658$	72.6913	−	22.7182i	2.83380	−	0.885649i
$659$	−42.7307			−1.66455			−0.832275	−	0.554363i	$-0.812962\pi$
$659$	−42.7307			−1.66455			−0.832275	+	0.554363i	$0.812962\pi$
$660$	−20.5346	+	5.85230i	−0.799309	+	0.227800i
$661$	16.6982			0.649483			0.324742	−	0.945803i	$-0.394723\pi$
$661$	16.6982			0.649483			0.324742	+	0.945803i	$0.394723\pi$
$662$	−5.74689	+	1.79608i	−0.223359	+	0.0698064i
$663$	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
$668$	−1.08423	+	5.97274i	−0.0419500	+	0.231092i
$669$			34.4154i			1.33058i
$670$	−0.160419	+	6.34526i	−0.00619754	+	0.245139i
$671$		−	14.5859i		−	0.563083i
$672$	−67.9513	−	3.82526i	−2.62128	−	0.147563i
$673$	−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	$0.823689\pi$
$678$	−5.83015	−	18.6547i	−0.223906	−	0.716429i
$679$	7.58040			0.290909
$680$	19.1919	−	12.5890i	0.735975	−	0.482764i
$681$	60.8025			2.32996
$682$	−3.06450	−	9.80545i	−0.117346	−	0.375470i
$683$	9.22992	+	9.22992i	0.353173	+	0.353173i	0.861289	−	0.508116i	$-0.169658\pi$
$683$	9.22992	+	9.22992i	0.353173	+	0.353173i	−0.508116	+	0.861289i	$0.669658\pi$
$684$	−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
$688$	2.22100	−	1.00854i	0.0846748	−	0.0384501i
$689$			14.4437i			0.550263i
$690$	22.7884	+	23.9706i	0.867541	+	0.912545i
$691$		−	11.7811i		−	0.448175i	−0.974569	−	0.224088i	$-0.928060\pi$
$691$		−	11.7811i		−	0.448175i	0.974569	−	0.224088i	$-0.0719402\pi$
$692$	−0.708289	+	3.90180i	−0.0269251	+	0.148324i
$693$	−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
$698$	−35.0389	+	10.9507i	−1.32624	+	0.414490i
$699$	−24.4166			−0.923521
$700$	−29.8777	−	33.0621i	−1.12927	−	1.24963i
$701$	−40.8964			−1.54464			−0.772318	−	0.635236i	$-0.780903\pi$
$701$	−40.8964			−1.54464			−0.772318	+	0.635236i	$0.780903\pi$
$702$	4.69887	−	1.46854i	0.177348	−	0.0554265i
$703$	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
$708$	−37.3751	−	6.78467i	−1.40464	−	0.254983i
$709$		−	10.0408i		−	0.377091i	−0.982064	−	0.188546i	$-0.939623\pi$
$709$		−	10.0408i		−	0.377091i	0.982064	−	0.188546i	$-0.0603774\pi$
$710$	24.8719	+	26.1621i	0.933426	+	0.981848i
$711$			28.5618i			1.07115i
$712$	13.9580	−	17.9084i	0.523099	−	0.671147i
$713$	−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
$718$	7.08431	+	22.6676i	0.264384	+	0.845948i
$719$	27.5425			1.02716			0.513581	−	0.858041i	$-0.328319\pi$
$719$	27.5425			1.02716			0.513581	+	0.858041i	$0.328319\pi$
$720$	−3.75615	−	38.1808i	−0.139983	−	1.42291i
$721$	−1.65589			−0.0616685
$722$	7.37311	+	23.5917i	0.274399	+	0.877991i
$723$	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	−0.192698	−	0.981258i	$-0.561724\pi$
$727$	21.2619	−	21.2619i	0.788560	−	0.788560i	0.981258	+	0.192698i	$0.0617238\pi$
$728$	7.74825	−	9.94118i	0.287169	−	0.368444i
$729$			43.0776i			1.59547i
$730$	0.623281	−	24.6534i	0.0230687	−	0.912462i
$731$			2.21307i			0.0818533i
$732$	43.8211	+	7.95479i	1.61967	+	0.294018i
$733$	−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
$738$	−67.3172	+	21.0387i	−2.47798	+	0.774444i
$739$	1.11147			0.0408861			0.0204430	−	0.999791i	$-0.493492\pi$
$739$	1.11147			0.0408861			0.0204430	+	0.999791i	$0.493492\pi$
$740$	2.68771	+	9.43067i	0.0988022	+	0.346678i
$741$	3.33132			0.122379
$742$	86.8807	−	27.1528i	3.18949	−	0.996812i
$743$	−32.4947	−	32.4947i	−1.19211	−	1.19211i	−0.976472	−	0.215642i	$-0.930816\pi$
$743$	−32.4947	−	32.4947i	−1.19211	−	1.19211i	−0.215642	−	0.976472i	$-0.569184\pi$
$744$	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
$748$	2.29254	−	12.6291i	0.0838237	−	0.461765i
$749$		−	8.20696i		−	0.299876i
$750$	26.8973	−	33.1492i	0.982151	−	1.21044i
$751$		−	22.7914i		−	0.831668i	−0.909440	−	0.415834i	$-0.863490\pi$
$751$		−	22.7914i		−	0.831668i	0.909440	−	0.415834i	$-0.136510\pi$
$752$	19.9863	+	44.0138i	0.728826	+	1.60502i
$753$	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	$0.570913\pi$
$758$	3.33208	+	10.6616i	0.121027	+	0.387248i
$759$	18.4958			0.671357
$760$	1.58743	−	7.64055i	0.0575823	−	0.277152i
$761$	40.7964			1.47887			0.739433	−	0.673230i	$-0.235093\pi$
$761$	40.7964			1.47887			0.739433	+	0.673230i	$0.235093\pi$
$762$	−7.70173	−	24.6432i	−0.279004	−	0.892727i
$763$	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
$768$	−2.89659	−	43.1009i	−0.104522	−	1.55527i
$769$			9.81657i			0.353994i	0.984211	+	0.176997i	$0.0566384\pi$
$769$			9.81657i			0.353994i	−0.984211	+	0.176997i	$0.943362\pi$
$770$	−24.9122	−	0.629824i	−0.897773	−	0.0226973i
$771$		−	34.4054i		−	1.23908i
$772$	5.60677	−	30.8864i	0.201792	−	1.11163i
$773$	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)

\(f(q)\)	\(=\)	\(q+(-0.421862 - 1.34983i) q^{2} +(1.90910 + 1.90910i) q^{3} +(-1.64407 + 1.13888i) q^{4} +(-0.987103 - 2.00640i) q^{5} +(1.77158 - 3.38234i) q^{6} +(3.15102 - 3.15102i) q^{7} +(2.23086 + 1.73875i) q^{8} +4.28935i q^{9} +O(q^{10})\)	\(q+(-0.421862 - 1.34983i) 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} +(2.23086 + 1.73875i) q^{8} +4.28935i q^{9} +(-2.29187 + 2.17884i) q^{10} +1.76842i q^{11} +(-5.31293 - 0.964451i) 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} +(5.78988 - 1.80951i) q^{18} +1.23388 q^{19} +(3.90791 + 2.17446i) q^{20} +12.0312 q^{21} +(2.38706 - 0.746028i) 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} +(-1.59185 + 8.76911i) q^{28} +2.75202i q^{29} +(-8.53504 - 0.215781i) q^{30} -4.10776i q^{31} +(-5.64791 - 0.317944i) 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} +(-0.520525 - 1.66552i) q^{38} +2.69988 q^{39} +(1.28654 - 6.19232i) q^{40} -11.6267 q^{41} +(-5.07551 - 16.2401i) 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} +(9.83320 - 4.46517i) q^{48} -12.8578i q^{49} +(6.63393 + 2.44766i) q^{50} +9.79809i q^{51} +(-0.357220 + 1.96784i) 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} +(3.71474 - 1.16097i) q^{58} +7.03475 q^{59} +(3.30934 + 11.6119i) q^{60} -8.24800 q^{61} +(-5.54476 + 1.73290i) 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} +(-7.14146 - 1.29638i) q^{68} -10.4590i q^{69} +(-0.356151 + 14.0873i) q^{70} -11.4152i q^{71} +(-7.45813 + 9.56894i) 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} +(-1.13898 - 3.64437i) q^{78} +6.65878 q^{79} +(-8.90130 + 0.875692i) q^{80} +3.46952 q^{81} +(4.90486 + 15.6940i) 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} +(-3.07484 + 3.94509i) q^{88} -8.02760i q^{89} +(-9.34581 - 9.83062i) q^{90} -4.45621i q^{91} +(7.62315 + 1.38382i) 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} +(-17.3558 + 5.42421i) 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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