LMFDB - Embedded newform 520.2.ca.a.101.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.17
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.a.381.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.237097 - 1.39420i) q^{2} +(-0.158158 + 0.0913126i) q^{3} +(-1.88757 - 0.661121i) q^{4} -1.00000 q^{5} +(0.0898089 + 0.242153i) q^{6} +(2.61251 + 1.50833i) q^{7} +(-1.36927 + 2.47489i) q^{8} +(-1.48332 + 2.56919i) q^{9} +O(q^{10})$	\(q+(0.237097 - 1.39420i) q^{2} +(-0.158158 + 0.0913126i) q^{3} +(-1.88757 - 0.661121i) q^{4} -1.00000 q^{5} +(0.0898089 + 0.242153i) q^{6} +(2.61251 + 1.50833i) q^{7} +(-1.36927 + 2.47489i) q^{8} +(-1.48332 + 2.56919i) q^{9} +(-0.237097 + 1.39420i) q^{10} +(1.37951 + 2.38937i) q^{11} +(0.358903 - 0.0677973i) q^{12} +(2.87612 + 2.17438i) q^{13} +(2.72233 - 3.28473i) q^{14} +(0.158158 - 0.0913126i) q^{15} +(3.12584 + 2.49582i) q^{16} +(1.19349 - 2.06718i) q^{17} +(3.23027 + 2.67719i) q^{18} +(0.343257 - 0.594539i) q^{19} +(1.88757 + 0.661121i) q^{20} -0.550919 q^{21} +(3.65833 - 1.35679i) q^{22} +(-1.16108 - 2.01104i) q^{23} +(-0.00942771 - 0.516456i) q^{24} +1.00000 q^{25} +(3.71343 - 3.49434i) q^{26} -1.08966i q^{27} +(-3.93410 - 4.57427i) q^{28} +(-2.86720 + 1.65538i) q^{29} +(-0.0898089 - 0.242153i) q^{30} +2.49707i q^{31} +(4.22080 - 3.76628i) q^{32} +(-0.436360 - 0.251932i) q^{33} +(-2.59909 - 2.15408i) q^{34} +(-2.61251 - 1.50833i) q^{35} +(4.49842 - 3.86887i) q^{36} +(3.59508 + 6.22686i) q^{37} +(-0.747519 - 0.619532i) q^{38} +(-0.653430 - 0.0812692i) q^{39} +(1.36927 - 2.47489i) q^{40} +(8.68199 - 5.01255i) q^{41} +(-0.130622 + 0.768090i) q^{42} +(-1.97971 - 1.14299i) q^{43} +(-1.02425 - 5.42213i) q^{44} +(1.48332 - 2.56919i) q^{45} +(-3.07908 + 1.14196i) q^{46} +8.99189i q^{47} +(-0.722277 - 0.109306i) q^{48} +(1.05014 + 1.81889i) q^{49} +(0.237097 - 1.39420i) q^{50} +0.435922i q^{51} +(-3.99135 - 6.00575i) q^{52} +6.03671i q^{53} +(-1.51920 - 0.258356i) q^{54} +(-1.37951 - 2.38937i) q^{55} +(-7.31020 + 4.40037i) q^{56} +0.125375i q^{57} +(1.62812 + 4.38992i) q^{58} +(0.982788 - 1.70224i) q^{59} +(-0.358903 + 0.0677973i) q^{60} +(12.4956 + 7.21434i) q^{61} +(3.48140 + 0.592048i) q^{62} +(-7.75040 + 4.47469i) q^{63} +(-4.25019 - 6.77760i) q^{64} +(-2.87612 - 2.17438i) q^{65} +(-0.454703 + 0.548639i) q^{66} +(-0.739960 - 1.28165i) q^{67} +(-3.61945 + 3.11291i) q^{68} +(0.367267 + 0.212042i) q^{69} +(-2.72233 + 3.28473i) q^{70} +(-13.5810 - 7.84102i) q^{71} +(-4.32741 - 7.18899i) q^{72} +4.24432i q^{73} +(9.53386 - 3.53588i) q^{74} +(-0.158158 + 0.0913126i) q^{75} +(-1.04098 + 0.895299i) q^{76} +8.32301i q^{77} +(-0.268232 + 0.891741i) q^{78} -5.23394 q^{79} +(-3.12584 - 2.49582i) q^{80} +(-4.35047 - 7.53524i) q^{81} +(-4.93000 - 13.2929i) q^{82} -14.6966 q^{83} +(1.03990 + 0.364224i) q^{84} +(-1.19349 + 2.06718i) q^{85} +(-2.06293 + 2.48911i) q^{86} +(0.302314 - 0.523623i) q^{87} +(-7.80236 + 0.142429i) q^{88} +(10.0722 - 5.81518i) q^{89} +(-3.23027 - 2.67719i) q^{90} +(4.23421 + 10.0187i) q^{91} +(0.862070 + 4.56360i) q^{92} +(-0.228014 - 0.394931i) q^{93} +(12.5365 + 2.13195i) q^{94} +(-0.343257 + 0.594539i) q^{95} +(-0.323645 + 0.981080i) q^{96} +(-6.21257 - 3.58683i) q^{97} +(2.78488 - 1.03284i) q^{98} -8.18501 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	0.237097	−	1.39420i	0.167653	−	0.985846i
$2$	0.237097	−	1.39420i	0.167653	−	0.985846i
$3$	−0.158158	+	0.0913126i	−0.0913126	+	0.0527194i	−0.544961	−	0.838461i	$-0.683456\pi$
$3$	−0.158158	+	0.0913126i	−0.0913126	+	0.0527194i	0.453648	+	0.891181i	$0.350122\pi$
$4$	−1.88757	−	0.661121i	−0.943785	−	0.330561i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.0898089	+	0.242153i	0.0366643	+	0.0988587i
$7$	2.61251	+	1.50833i	0.987436	+	0.570096i	0.904507	−	0.426459i	$-0.140239\pi$
$7$	2.61251	+	1.50833i	0.987436	+	0.570096i	0.0829290	+	0.996555i	$0.473573\pi$
$8$	−1.36927	+	2.47489i	−0.484110	+	0.875007i
$9$	−1.48332	+	2.56919i	−0.494441	+	0.856398i
$10$	−0.237097	+	1.39420i	−0.0749768	+	0.440884i
$11$	1.37951	+	2.38937i	0.415936	+	0.720423i	0.995526	−	0.0944853i	$-0.0301205\pi$
$11$	1.37951	+	2.38937i	0.415936	+	0.720423i	−0.579590	+	0.814908i	$0.696787\pi$
$12$	0.358903	−	0.0677973i	0.103606	−	0.0195714i
$13$	2.87612	+	2.17438i	0.797693	+	0.603064i
$13$	2.87612	+	2.17438i	0.797693	+	0.603064i
$14$	2.72233	−	3.28473i	0.727574	−	0.877881i
$15$	0.158158	−	0.0913126i	0.0408362	−	0.0235768i
$16$	3.12584	+	2.49582i	0.781459	+	0.623956i
$17$	1.19349	−	2.06718i	0.289463	−	0.501365i	−0.684218	−	0.729277i	$-0.739857\pi$
$17$	1.19349	−	2.06718i	0.289463	−	0.501365i	0.973682	+	0.227912i	$0.0731898\pi$
$18$	3.23027	+	2.67719i	0.761381	+	0.631021i
$19$	0.343257	−	0.594539i	0.0787486	−	0.136397i	−0.823962	−	0.566646i	$-0.808241\pi$
$19$	0.343257	−	0.594539i	0.0787486	−	0.136397i	0.902710	+	0.430249i	$0.141574\pi$
$20$	1.88757	+	0.661121i	0.422073	+	0.147831i
$21$	−0.550919			−0.120220
$22$	3.65833	−	1.35679i	0.779959	−	0.289268i
$23$	−1.16108	−	2.01104i	−0.242101	−	0.419332i	0.719211	−	0.694791i	$-0.244503\pi$
$23$	−1.16108	−	2.01104i	−0.242101	−	0.419332i	−0.961313	+	0.275460i	$0.911170\pi$
$24$	−0.00942771	−	0.516456i	−0.00192442	−	0.105421i
$25$	1.00000			0.200000
$26$	3.71343	−	3.49434i	0.728264	−	0.685297i
$27$		−	1.08966i		−	0.209705i
$28$	−3.93410	−	4.57427i	−0.743476	−	0.864456i
$29$	−2.86720	+	1.65538i	−0.532425	+	0.307396i	−0.742004	−	0.670396i	$-0.766124\pi$
$29$	−2.86720	+	1.65538i	−0.532425	+	0.307396i	0.209578	+	0.977792i	$0.432791\pi$
$30$	−0.0898089	−	0.242153i	−0.0163968	−	0.0442110i
$31$			2.49707i			0.448486i	0.974533	+	0.224243i	$0.0719910\pi$
$31$			2.49707i			0.448486i	−0.974533	+	0.224243i	$0.928009\pi$
$32$	4.22080	−	3.76628i	0.746139	−	0.665790i
$33$	−0.436360	−	0.251932i	−0.0759605	−	0.0438558i
$34$	−2.59909	−	2.15408i	−0.445739	−	0.369422i
$35$	−2.61251	−	1.50833i	−0.441595	−	0.254955i
$36$	4.49842	−	3.86887i	0.749737	−	0.644812i
$37$	3.59508	+	6.22686i	0.591028	+	1.02369i	0.994094	+	0.108519i	$0.0346109\pi$
$37$	3.59508	+	6.22686i	0.591028	+	1.02369i	−0.403067	+	0.915171i	$0.632056\pi$
$38$	−0.747519	−	0.619532i	−0.121264	−	0.100501i
$39$	−0.653430	−	0.0812692i	−0.104633	−	0.0130135i
$40$	1.36927	−	2.47489i	0.216501	−	0.391315i
$41$	8.68199	−	5.01255i	1.35590	−	0.782828i	0.366830	−	0.930288i	$-0.380443\pi$
$41$	8.68199	−	5.01255i	1.35590	−	0.782828i	0.989068	+	0.147459i	$0.0471096\pi$
$42$	−0.130622	+	0.768090i	−0.0201553	+	0.118519i
$43$	−1.97971	−	1.14299i	−0.301903	−	0.174304i	0.341394	−	0.939920i	$-0.389101\pi$
$43$	−1.97971	−	1.14299i	−0.301903	−	0.174304i	−0.643298	+	0.765616i	$0.722434\pi$
$44$	−1.02425	−	5.42213i	−0.154411	−	0.817417i
$45$	1.48332	−	2.56919i	0.221121	−	0.382993i
$46$	−3.07908	+	1.14196i	−0.453986	+	0.168372i
$47$			8.99189i			1.31160i	0.754934	+	0.655801i	$0.227669\pi$
$47$			8.99189i			1.31160i	−0.754934	+	0.655801i	$0.772331\pi$
$48$	−0.722277	−	0.109306i	−0.104252	−	0.0157770i
$49$	1.05014	+	1.81889i	0.150020	+	0.259842i
$50$	0.237097	−	1.39420i	0.0335306	−	0.197169i
$51$			0.435922i			0.0610413i
$52$	−3.99135	−	6.00575i	−0.553501	−	0.832848i
$53$			6.03671i			0.829206i	0.910002	+	0.414603i	$0.136080\pi$
$53$			6.03671i			0.829206i	−0.910002	+	0.414603i	$0.863920\pi$
$54$	−1.51920	−	0.258356i	−0.206737	−	0.0351578i
$55$	−1.37951	−	2.38937i	−0.186012	−	0.322183i
$56$	−7.31020	+	4.40037i	−0.976866	+	0.588024i
$57$			0.125375i			0.0166063i
$58$	1.62812	+	4.38992i	0.213782	+	0.576425i
$59$	0.982788	−	1.70224i	0.127948	−	0.221613i	−0.794933	−	0.606697i	$-0.792494\pi$
$59$	0.982788	−	1.70224i	0.127948	−	0.221613i	0.922881	+	0.385084i	$0.125828\pi$
$60$	−0.358903	+	0.0677973i	−0.0463342	+	0.00875259i
$61$	12.4956	+	7.21434i	1.59990	+	0.923701i	0.991506	+	0.130065i	$0.0415185\pi$
$61$	12.4956	+	7.21434i	1.59990	+	0.923701i	0.608392	+	0.793637i	$0.291815\pi$
$62$	3.48140	+	0.592048i	0.442139	+	0.0751902i
$63$	−7.75040	+	4.47469i	−0.976458	+	0.563758i
$64$	−4.25019	−	6.77760i	−0.531274	−	0.847200i
$65$	−2.87612	−	2.17438i	−0.356739	−	0.269698i
$66$	−0.454703	+	0.548639i	−0.0559701	+	0.0675328i
$67$	−0.739960	−	1.28165i	−0.0904005	−	0.156578i	0.817279	−	0.576242i	$-0.195481\pi$
$67$	−0.739960	−	1.28165i	−0.0904005	−	0.156578i	−0.907680	+	0.419664i	$0.862148\pi$
$68$	−3.61945	+	3.11291i	−0.438923	+	0.377496i
$69$	0.367267	+	0.212042i	0.0442138	+	0.0255269i
$70$	−2.72233	+	3.28473i	−0.325381	+	0.392600i
$71$	−13.5810	−	7.84102i	−1.61177	−	0.930558i	−0.988959	−	0.148188i	$-0.952656\pi$
$71$	−13.5810	−	7.84102i	−1.61177	−	0.930558i	−0.622814	−	0.782370i	$-0.714011\pi$
$72$	−4.32741	−	7.18899i	−0.509990	−	0.847231i
$73$			4.24432i			0.496760i	0.968663	+	0.248380i	$0.0798982\pi$
$73$			4.24432i			0.496760i	−0.968663	+	0.248380i	$0.920102\pi$
$74$	9.53386	−	3.53588i	1.10829	−	0.411037i
$75$	−0.158158	+	0.0913126i	−0.0182625	+	0.0105439i
$76$	−1.04098	+	0.895299i	−0.119409	+	0.102698i
$77$			8.32301i			0.948495i
$78$	−0.268232	+	0.891741i	−0.0303713	+	0.100970i
$79$	−5.23394			−0.588865			−0.294432	−	0.955672i	$-0.595131\pi$
$79$	−5.23394			−0.588865			−0.294432	+	0.955672i	$0.595131\pi$
$80$	−3.12584	−	2.49582i	−0.349479	−	0.279042i
$81$	−4.35047	−	7.53524i	−0.483386	−	0.837249i
$82$	−4.93000	−	13.2929i	−0.544427	−	1.46795i
$83$	−14.6966			−1.61316			−0.806578	−	0.591127i	$-0.798683\pi$
$83$	−14.6966			−1.61316			−0.806578	+	0.591127i	$0.798683\pi$
$84$	1.03990	+	0.364224i	0.113462	+	0.0397401i
$85$	−1.19349	+	2.06718i	−0.129452	+	0.224217i
$86$	−2.06293	+	2.48911i	−0.222452	+	0.268408i
$87$	0.302314	−	0.523623i	0.0324114	−	0.0561382i
$88$	−7.80236	+	0.142429i	−0.831734	+	0.0151830i
$89$	10.0722	−	5.81518i	1.06765	−	0.616408i	0.140112	−	0.990136i	$-0.455254\pi$
$89$	10.0722	−	5.81518i	1.06765	−	0.616408i	0.927539	+	0.373728i	$0.121920\pi$
$90$	−3.23027	−	2.67719i	−0.340500	−	0.282201i
$91$	4.23421	+	10.0187i	0.443866	+	1.05025i
$92$	0.862070	+	4.56360i	0.0898770	+	0.475788i
$93$	−0.228014	−	0.394931i	−0.0236439	−	0.0409525i
$94$	12.5365	+	2.13195i	1.29304	+	0.219894i
$95$	−0.343257	+	0.594539i	−0.0352175	+	0.0609984i
$96$	−0.323645	+	0.981080i	−0.0330318	+	0.100131i
$97$	−6.21257	−	3.58683i	−0.630791	−	0.364188i	0.150267	−	0.988645i	$-0.451987\pi$
$97$	−6.21257	−	3.58683i	−0.630791	−	0.364188i	−0.781059	+	0.624458i	$0.785320\pi$
$98$	2.78488	−	1.03284i	0.281315	−	0.104333i
$99$	−8.18501			−0.822625
$100$	−1.88757	−	0.661121i	−0.188757	−	0.0661121i
$101$	3.89828	−	2.25068i	0.387894	−	0.223951i	−0.293353	−	0.956004i	$-0.594771\pi$
$101$	3.89828	−	2.25068i	0.387894	−	0.223951i	0.681247	+	0.732054i	$0.261438\pi$
$102$	0.607761	+	0.103356i	0.0601773	+	0.0102338i
$103$	2.65866			0.261966			0.130983	−	0.991385i	$-0.458187\pi$
$103$	2.65866			0.261966			0.130983	+	0.991385i	$0.458187\pi$
$104$	−9.31954	+	4.14078i	−0.913857	+	0.406037i
$105$	0.550919			0.0537642
$106$	8.41636	+	1.43129i	0.817469	+	0.139019i
$107$	5.45713	−	3.15068i	0.527561	−	0.304587i	−0.212462	−	0.977169i	$-0.568148\pi$
$107$	5.45713	−	3.15068i	0.527561	−	0.304587i	0.740023	+	0.672582i	$0.234815\pi$
$108$	−0.720397	+	2.05681i	−0.0693203	+	0.197917i
$109$	6.90407			0.661290			0.330645	−	0.943755i	$-0.392734\pi$
$109$	6.90407			0.661290			0.330645	+	0.943755i	$0.392734\pi$
$110$	−3.65833	+	1.35679i	−0.348808	+	0.129365i
$111$	−1.13718	−	0.656552i	−0.107937	−	0.0623172i
$112$	4.40175	+	11.2352i	0.415926	+	1.06162i
$113$	−4.48541	+	7.76896i	−0.421952	+	0.730842i	−0.996130	−	0.0878878i	$-0.971988\pi$
$113$	−4.48541	+	7.76896i	−0.421952	+	0.730842i	0.574178	+	0.818730i	$0.305322\pi$
$114$	0.174797	+	0.0297261i	0.0163713	+	0.00278410i
$115$	1.16108	+	2.01104i	0.108271	+	0.187531i
$116$	6.50644	−	1.22908i	0.604108	−	0.114117i
$117$	−9.85262	+	4.16401i	−0.910875	+	0.384962i
$118$	−2.14024	−	1.77380i	−0.197025	−	0.163291i
$119$	6.23600	−	3.60035i	0.571653	−	0.330044i
$120$	0.00942771	+	0.516456i	0.000860628	+	0.0471458i
$121$	1.69393	−	2.93397i	0.153994	−	0.266725i
$122$	13.0209	−	15.7108i	1.17886	−	1.42239i
$123$	−0.915418	+	1.58555i	−0.0825404	+	0.142964i
$124$	1.65086	−	4.71339i	0.148252	−	0.423275i
$125$	−1.00000			−0.0894427
$126$	4.40100	+	11.8665i	0.392073	+	1.05715i
$127$	7.65597	+	13.2605i	0.679357	+	1.17668i	0.975175	+	0.221437i	$0.0710747\pi$
$127$	7.65597	+	13.2605i	0.679357	+	1.17668i	−0.295817	+	0.955245i	$0.595592\pi$
$128$	−10.4570	+	4.31866i	−0.924278	+	0.381719i
$129$	0.417477			0.0367568
$130$	−3.71343	+	3.49434i	−0.325690	+	0.306474i
$131$		−	9.90697i		−	0.865576i	−0.901496	−	0.432788i	$-0.857530\pi$
$131$		−	9.90697i		−	0.865576i	0.901496	−	0.432788i	$-0.142470\pi$
$132$	0.657102	+	0.764027i	0.0571933	+	0.0665000i
$133$	1.79353	−	1.03549i	0.155518	−	0.0897886i
$134$	−1.96231	+	0.727774i	−0.169518	+	0.0628701i
$135$			1.08966i			0.0937830i
$136$	3.48185	+	5.78429i	0.298566	+	0.495999i
$137$	−4.31063	−	2.48875i	−0.368282	−	0.212628i	0.304425	−	0.952536i	$-0.401536\pi$
$137$	−4.31063	−	2.48875i	−0.368282	−	0.212628i	−0.672708	+	0.739908i	$0.734869\pi$
$138$	0.382706	−	0.461769i	0.0325781	−	0.0393083i
$139$	−6.80566	−	3.92925i	−0.577249	−	0.333275i	0.182790	−	0.983152i	$-0.441487\pi$
$139$	−6.80566	−	3.92925i	−0.577249	−	0.333275i	−0.760039	+	0.649877i	$0.774820\pi$
$140$	3.93410	+	4.57427i	0.332492	+	0.386596i
$141$	−0.821073	−	1.42214i	−0.0691468	−	0.119766i
$142$	−14.1520	+	17.0756i	−1.18761	+	1.43295i
$143$	−1.22777	+	9.87169i	−0.102672	+	0.825513i
$144$	−11.0489	+	4.32876i	−0.920740	+	0.360730i
$145$	2.86720	−	1.65538i	0.238108	−	0.137472i
$146$	5.91742	+	1.00632i	0.489729	+	0.0832834i
$147$	−0.332176	−	0.191782i	−0.0273974	−	0.0158179i
$148$	−2.66925	−	14.1304i	−0.219411	−	1.16151i
$149$	4.00913	−	6.94401i	0.328440	−	0.568875i	−0.653762	−	0.756700i	$-0.726810\pi$
$149$	4.00913	−	6.94401i	0.328440	−	0.568875i	0.982203	+	0.187825i	$0.0601437\pi$
$150$	0.0898089	+	0.242153i	0.00733286	+	0.0197717i
$151$		−	18.3109i		−	1.49012i	−0.666996	−	0.745061i	$-0.732420\pi$
$151$		−	18.3109i		−	1.49012i	0.666996	−	0.745061i	$-0.267580\pi$
$152$	1.00141	+	1.66361i	0.0812250	+	0.134937i
$153$	3.54066	+	6.13260i	0.286245	+	0.495791i
$154$	11.6039	+	1.97337i	0.935070	+	0.159018i
$155$		−	2.49707i		−	0.200569i
$156$	1.17967	+	0.585398i	0.0944489	+	0.0468693i
$157$			2.83853i			0.226539i	0.993564	+	0.113269i	$0.0361323\pi$
$157$			2.83853i			0.226539i	−0.993564	+	0.113269i	$0.963868\pi$
$158$	−1.24095	+	7.29715i	−0.0987251	+	0.580530i
$159$	−0.551228	−	0.954755i	−0.0437152	−	0.0757170i
$160$	−4.22080	+	3.76628i	−0.333683	+	0.297751i
$161$		−	7.00517i		−	0.552084i
$162$	−11.5371	+	4.27883i	−0.906440	+	0.336177i
$163$	7.68284	−	13.3071i	0.601766	−	1.04229i	−0.390787	−	0.920481i	$-0.627797\pi$
$163$	7.68284	−	13.3071i	0.601766	−	1.04229i	0.992554	−	0.121809i	$-0.0388695\pi$
$164$	−19.7018	+	3.72169i	−1.53845	+	0.290615i
$165$	0.436360	+	0.251932i	0.0339706	+	0.0196129i
$166$	−3.48452	+	20.4899i	−0.270451	+	1.59032i
$167$	−15.5996	+	9.00642i	−1.20713	+	0.696938i	−0.962132	−	0.272585i	$-0.912121\pi$
$167$	−15.5996	+	9.00642i	−1.20713	+	0.696938i	−0.245000	+	0.969523i	$0.578788\pi$
$168$	0.754358	−	1.36347i	0.0582000	−	0.105194i
$169$	3.54416	+	12.5076i	0.272628	+	0.962120i
$170$	2.59909	+	2.15408i	0.199341	+	0.165210i
$171$	1.01832	+	1.76379i	0.0778732	+	0.134880i
$172$	2.98119	+	3.46630i	0.227314	+	0.264303i
$173$	−20.5307	−	11.8534i	−1.56092	−	0.901199i	−0.997164	−	0.0752598i	$-0.976021\pi$
$173$	−20.5307	−	11.8534i	−1.56092	−	0.901199i	−0.563759	−	0.825939i	$-0.690645\pi$
$174$	−0.658355	−	0.545634i	−0.0499098	−	0.0413644i
$175$	2.61251	+	1.50833i	0.197487	+	0.114019i
$176$	−1.65135	+	10.9118i	−0.124475	+	0.822507i
$177$			0.358964i			0.0269814i
$178$	−5.71942	−	15.4214i	−0.428689	−	1.15588i
$179$	−6.15302	+	3.55245i	−0.459898	+	0.265522i	−0.712001	−	0.702178i	$-0.752211\pi$
$179$	−6.15302	+	3.55245i	−0.459898	+	0.265522i	0.252103	+	0.967700i	$0.418878\pi$
$180$	−4.49842	+	3.86887i	−0.335293	+	0.288369i
$181$			5.97715i			0.444278i	0.975015	+	0.222139i	$0.0713039\pi$
$181$			5.97715i			0.444278i	−0.975015	+	0.222139i	$0.928696\pi$
$182$	14.9720	−	3.52791i	1.10980	−	0.261506i
$183$	−2.63504			−0.194788
$184$	6.56695	−	0.119877i	0.484122	−	0.00883747i
$185$	−3.59508	−	6.22686i	−0.264316	−	0.457808i
$186$	−0.604673	+	0.224259i	−0.0443368	+	0.0164434i
$187$	6.58569			0.481593
$188$	5.94473	−	16.9728i	0.433564	−	1.23787i
$189$	1.64357	−	2.84675i	0.119552	−	0.207070i
$190$	0.747519	+	0.619532i	0.0542307	+	0.0449456i
$191$	9.57885	−	16.5911i	0.693101	−	1.20049i	−0.277715	−	0.960663i	$-0.589577\pi$
$191$	9.57885	−	16.5911i	0.693101	−	1.20049i	0.970817	−	0.239823i	$-0.0770895\pi$
$192$	1.29108	+	0.683836i	0.0931759	+	0.0493516i
$193$	9.75992	−	5.63489i	0.702534	−	0.405608i	−0.105756	−	0.994392i	$-0.533726\pi$
$193$	9.75992	−	5.63489i	0.702534	−	0.405608i	0.808291	+	0.588784i	$0.200393\pi$
$194$	−6.47374	+	7.81112i	−0.464787	+	0.560806i
$195$	0.653430	+	0.0812692i	0.0467931	+	0.00581981i
$196$	−0.779700	−	4.12755i	−0.0556929	−	0.294825i
$197$	−5.09423	−	8.82346i	−0.362949	−	0.628645i	0.625496	−	0.780227i	$-0.284897\pi$
$197$	−5.09423	−	8.82346i	−0.362949	−	0.628645i	−0.988445	+	0.151582i	$0.951563\pi$
$198$	−1.94065	+	11.4115i	−0.137916	+	0.810981i
$199$	−7.73321	+	13.3943i	−0.548193	+	0.949497i	0.450206	+	0.892925i	$0.351351\pi$
$199$	−7.73321	+	13.3943i	−0.548193	+	0.949497i	−0.998398	+	0.0565726i	$0.981983\pi$
$200$	−1.36927	+	2.47489i	−0.0968221	+	0.175001i
$201$	0.234061	+	0.135135i	0.0165094	+	0.00953171i
$202$	−2.21361	−	5.96860i	−0.155749	−	0.419950i
$203$	−9.98745			−0.700981
$204$	0.288197	−	0.822833i	0.0201778	−	0.0576098i
$205$	−8.68199	+	5.01255i	−0.606376	+	0.350091i
$206$	0.630362	−	3.70670i	0.0439194	−	0.258258i
$207$	6.88902			0.478820
$208$	3.56343	+	13.9750i	0.247079	+	0.968995i
$209$	1.89410			0.131018
$210$	0.130622	−	0.768090i	0.00901375	−	0.0530032i
$211$	14.9430	−	8.62737i	1.02872	−	0.593932i	0.112103	−	0.993697i	$-0.464241\pi$
$211$	14.9430	−	8.62737i	1.02872	−	0.593932i	0.916618	+	0.399764i	$0.130908\pi$
$212$	3.99100	−	11.3947i	0.274103	−	0.782592i
$213$	2.86394			0.196234
$214$	−3.09879	−	8.35533i	−0.211829	−	0.571159i
$215$	1.97971	+	1.14299i	0.135015	+	0.0779511i
$216$	2.69679	+	1.49204i	0.183494	+	0.101520i
$217$	−3.76641	+	6.52361i	−0.255680	+	0.442852i
$218$	1.63694	−	9.62563i	0.110867	−	0.651930i
$219$	−0.387560	−	0.671273i	−0.0261889	−	0.0453604i
$220$	1.02425	+	5.42213i	0.0690547	+	0.365560i
$221$	7.92745	−	3.35037i	0.533258	−	0.225371i
$222$	−1.18499	+	1.42979i	−0.0795311	+	0.0959611i
$223$	2.51774	−	1.45362i	0.168600	−	0.0973415i	−0.413325	−	0.910583i	$-0.635633\pi$
$223$	2.51774	−	1.45362i	0.168600	−	0.0973415i	0.581926	+	0.813242i	$0.302299\pi$
$224$	16.7077	−	3.47307i	1.11633	−	0.232054i
$225$	−1.48332	+	2.56919i	−0.0988883	+	0.171280i
$226$	9.76798	+	8.09555i	0.649756	+	0.538508i
$227$	12.7908	−	22.1543i	0.848955	−	1.47043i	−0.0331859	−	0.999449i	$-0.510565\pi$
$227$	12.7908	−	22.1543i	0.848955	−	1.47043i	0.882141	−	0.470985i	$-0.156101\pi$
$228$	0.0828880	−	0.236654i	0.00548939	−	0.0156728i
$229$	12.8262			0.847580			0.423790	−	0.905760i	$-0.360699\pi$
$229$	12.8262			0.847580			0.423790	+	0.905760i	$0.360699\pi$
$230$	3.07908	−	1.14196i	0.203029	−	0.0752984i
$231$	−0.759996	−	1.31635i	−0.0500041	−	0.0866096i
$232$	−0.170912	−	9.36267i	−0.0112209	−	0.614689i
$233$	22.9064			1.50065			0.750323	−	0.661071i	$-0.229898\pi$
$233$	22.9064			1.50065			0.750323	+	0.661071i	$0.229898\pi$
$234$	3.46941	+	14.7238i	0.226803	+	0.962522i
$235$		−	8.99189i		−	0.586566i
$236$	−2.98047	+	2.56335i	−0.194012	+	0.166860i
$237$	0.827791	−	0.477925i	0.0537708	−	0.0310446i
$238$	−3.54106	−	9.54784i	−0.229533	−	0.618895i
$239$			4.63652i			0.299912i	0.988693	+	0.149956i	$0.0479132\pi$
$239$			4.63652i			0.299912i	−0.988693	+	0.149956i	$0.952087\pi$
$240$	0.722277	+	0.109306i	0.0466228	+	0.00705569i
$241$	−12.7795	−	7.37824i	−0.823199	−	0.475274i	0.0283193	−	0.999599i	$-0.490984\pi$
$241$	−12.7795	−	7.37824i	−0.823199	−	0.475274i	−0.851518	+	0.524325i	$0.824318\pi$
$242$	−3.68891	−	3.05731i	−0.237132	−	0.196531i
$243$	4.20715	+	2.42900i	0.269888	+	0.155820i
$244$	−18.8168	−	21.8787i	−1.20462	−	1.40064i
$245$	−1.05014	−	1.81889i	−0.0670908	−	0.116205i
$246$	1.99353	+	1.65220i	0.127103	+	0.105341i
$247$	2.28000	−	0.963596i	0.145073	−	0.0613122i
$248$	−6.17997	−	3.41916i	−0.392429	−	0.217117i
$249$	2.32438	−	1.34198i	0.147302	−	0.0850446i
$250$	−0.237097	+	1.39420i	−0.0149954	+	0.0881767i
$251$	−23.1377	−	13.3586i	−1.46044	−	0.843184i	−0.461407	−	0.887189i	$-0.652655\pi$
$251$	−23.1377	−	13.3586i	−1.46044	−	0.843184i	−0.999031	+	0.0440042i	$0.985989\pi$
$252$	17.5877	−	3.32234i	1.10792	−	0.209288i
$253$	3.20342	−	5.54849i	0.201398	−	0.348831i
$254$	20.3030	−	7.52989i	1.27392	−	0.472467i
$255$		−	0.435922i		−	0.0272985i
$256$	3.54172	+	15.6031i	0.221358	+	0.975193i
$257$	7.84501	+	13.5880i	0.489359	+	0.847594i	0.999925	−	0.0122445i	$-0.00389763\pi$
$257$	7.84501	+	13.5880i	0.489359	+	0.847594i	−0.510567	+	0.859838i	$0.670564\pi$
$258$	0.0989826	−	0.582045i	0.00616239	−	0.0362365i
$259$			21.6903i			1.34777i
$260$	3.99135	+	6.00575i	0.247533	+	0.372461i
$261$		−	9.82185i		−	0.607957i
$262$	−13.8123	−	2.34892i	−0.853324	−	0.145117i
$263$	0.0113076	+	0.0195853i	0.000697255	+	0.00120768i	0.866374	−	0.499396i	$-0.166445\pi$
$263$	0.0113076	+	0.0195853i	0.000697255	+	0.00120768i	−0.865677	+	0.500604i	$0.833111\pi$
$264$	1.22100	−	0.734980i	0.0751474	−	0.0452349i
$265$		−	6.03671i		−	0.370832i
$266$	−1.01844	−	2.74604i	−0.0624446	−	0.168371i
$267$	−1.06200	+	1.83944i	−0.0649933	+	0.112572i
$268$	0.549401	+	2.90840i	0.0335600	+	0.177659i
$269$	15.0105	+	8.66631i	0.915205	+	0.528394i	0.882102	−	0.471058i	$-0.156128\pi$
$269$	15.0105	+	8.66631i	0.915205	+	0.528394i	0.0331029	+	0.999452i	$0.489461\pi$
$270$	1.51920	+	0.258356i	0.0924556	+	0.0157230i
$271$	−3.75659	+	2.16887i	−0.228197	+	0.131749i	−0.609740	−	0.792602i	$-0.708726\pi$
$271$	−3.75659	+	2.16887i	−0.228197	+	0.131749i	0.381543	+	0.924351i	$0.375393\pi$
$272$	8.88997	−	3.48294i	0.539034	−	0.211184i
$273$	−1.58451	−	1.19791i	−0.0958990	−	0.0725006i
$274$	−4.49184	+	5.41980i	−0.271362	+	0.327422i
$275$	1.37951	+	2.38937i	0.0831873	+	0.144085i
$276$	−0.553057	−	0.643052i	−0.0332901	−	0.0387072i
$277$	−15.5109	−	8.95522i	−0.931959	−	0.538067i	−0.0445287	−	0.999008i	$-0.514179\pi$
$277$	−15.5109	−	8.95522i	−0.931959	−	0.538067i	−0.887431	+	0.460941i	$0.847512\pi$
$278$	−7.09176	+	8.55682i	−0.425335	+	0.513204i
$279$	−6.41545	−	3.70396i	−0.384083	−	0.221750i
$280$	7.31020	−	4.40037i	0.436868	−	0.262972i
$281$		−	23.5494i		−	1.40484i	−0.711762	−	0.702421i	$-0.752102\pi$
$281$		−	23.5494i		−	1.40484i	0.711762	−	0.702421i	$-0.247898\pi$
$282$	−2.17742	+	0.807551i	−0.129663	+	0.0480890i
$283$	−1.10387	+	0.637319i	−0.0656182	+	0.0378847i	−0.532450	−	0.846461i	$-0.678729\pi$
$283$	−1.10387	+	0.637319i	−0.0656182	+	0.0378847i	0.466832	+	0.884346i	$0.345395\pi$
$284$	20.4513	+	23.7792i	1.21356	+	1.41103i
$285$		−	0.125375i		−	0.00742657i
$286$	13.4720	+	4.05231i	0.796615	+	0.239618i
$287$	30.2424			1.78515
$288$	3.41549	+	16.4307i	0.201259	+	0.968186i
$289$	5.65117	+	9.78812i	0.332422	+	0.575772i
$290$	−1.62812	−	4.38992i	−0.0956063	−	0.257785i
$291$	1.31009			0.0767989
$292$	2.80601	−	8.01145i	0.164209	−	0.468834i
$293$	12.6078	−	21.8373i	0.736553	−	1.27575i	−0.217486	−	0.976063i	$-0.569786\pi$
$293$	12.6078	−	21.8373i	0.736553	−	1.27575i	0.954039	−	0.299684i	$-0.0968811\pi$
$294$	−0.346139	+	0.417647i	−0.0201873	+	0.0243577i
$295$	−0.982788	+	1.70224i	−0.0572201	+	0.0991082i
$296$	−20.3335	+	0.371180i	−1.18186	+	0.0215744i
$297$	2.60361	−	1.50319i	0.151076	−	0.0872240i
$298$	−8.73076	−	7.23592i	−0.505759	−	0.419165i
$299$	1.03337	−	8.30863i	0.0597614	−	0.480501i
$300$	0.358903	−	0.0677973i	0.0207213	−	0.00391428i
$301$	−3.44801	−	5.97213i	−0.198740	−	0.344228i
$302$	−25.5290	−	4.34147i	−1.46903	−	0.249824i
$303$	−0.411030	+	0.711925i	−0.0236131	+	0.0408990i
$304$	2.55683	−	1.00172i	0.146644	−	0.0574528i
$305$	−12.4956	−	7.21434i	−0.715496	−	0.413092i
$306$	9.38953	−	3.48235i	0.536764	−	0.199073i
$307$	−9.29261			−0.530357			−0.265179	−	0.964199i	$-0.585431\pi$
$307$	−9.29261			−0.530357			−0.265179	+	0.964199i	$0.585431\pi$
$308$	5.50252	−	15.7103i	0.313535	−	0.895176i
$309$	−0.420489	+	0.242769i	−0.0239208	+	0.0138107i
$310$	−3.48140	−	0.592048i	−0.197730	−	0.0336261i
$311$	24.7618			1.40411			0.702057	−	0.712121i	$-0.252265\pi$
$311$	24.7618			1.40411			0.702057	+	0.712121i	$0.252265\pi$
$312$	1.09586	−	1.50589i	0.0620406	−	0.0852543i
$313$	−30.8589			−1.74425			−0.872125	−	0.489284i	$-0.837258\pi$
$313$	−30.8589			−1.74425			−0.872125	+	0.489284i	$0.837258\pi$
$314$	3.95746	+	0.673007i	0.223333	+	0.0379800i
$315$	7.75040	−	4.47469i	0.436685	−	0.252120i
$316$	9.87943	+	3.46027i	0.555762	+	0.194655i
$317$	5.42116			0.304483			0.152241	−	0.988343i	$-0.451351\pi$
$317$	5.42116			0.304483			0.152241	+	0.988343i	$0.451351\pi$
$318$	−1.46181	+	0.542150i	−0.0819743	+	0.0304023i
$319$	−7.91063	−	4.56720i	−0.442910	−	0.255714i
$320$	4.25019	+	6.77760i	0.237593	+	0.378879i
$321$	−0.575393	+	0.996610i	−0.0321153	+	0.0556253i
$322$	−9.76658	−	1.66091i	−0.544270	−	0.0925587i
$323$	−0.819347	−	1.41915i	−0.0455897	−	0.0789637i
$324$	3.23011	+	17.0995i	0.179451	+	0.949971i
$325$	2.87612	+	2.17438i	0.159539	+	0.120613i
$326$	−16.7311	−	13.8665i	−0.926649	−	0.767992i
$327$	−1.09193	+	0.630428i	−0.0603841	+	0.0348628i
$328$	0.517528	+	28.3505i	0.0285757	+	1.56540i
$329$	−13.5628	+	23.4914i	−0.747739	+	1.29512i
$330$	0.454703	−	0.548639i	0.0250306	−	0.0302016i
$331$	5.51248	−	9.54789i	0.302993	−	0.524799i	−0.673819	−	0.738896i	$-0.735347\pi$
$331$	5.51248	−	9.54789i	0.302993	−	0.524799i	0.976812	+	0.214097i	$0.0686807\pi$
$332$	27.7408	+	9.71621i	1.52247	+	0.533246i
$333$	−21.3307			−1.16891
$334$	8.85810	+	23.8843i	0.484694	+	1.30689i
$335$	0.739960	+	1.28165i	0.0404283	+	0.0700239i
$336$	−1.72208	−	1.37500i	−0.0939474	−	0.0750123i
$337$	11.9950			0.653411			0.326705	−	0.945126i	$-0.394061\pi$
$337$	11.9950			0.653411			0.326705	+	0.945126i	$0.394061\pi$
$338$	18.2783	−	1.97575i	0.994209	−	0.107467i
$339$		−	1.63830i		−	0.0889802i
$340$	3.61945	−	3.11291i	0.196292	−	0.168821i
$341$	−5.96642	+	3.44472i	−0.323100	+	0.186542i
$342$	2.70051	−	1.00155i	0.146027	−	0.0541578i
$343$		−	14.7808i		−	0.798090i
$344$	5.53953	−	3.33452i	0.298672	−	0.179785i
$345$	−0.367267	−	0.212042i	−0.0197730	−	0.0114160i
$346$	−21.3938	+	25.8135i	−1.15014	+	1.38774i
$347$	−7.81102	−	4.50970i	−0.419318	−	0.242093i	0.275468	−	0.961310i	$-0.411167\pi$
$347$	−7.81102	−	4.50970i	−0.419318	−	0.242093i	−0.694785	+	0.719217i	$0.744501\pi$
$348$	−0.916816	+	0.788508i	−0.0491465	+	0.0422685i
$349$	−14.3432	−	24.8431i	−0.767771	−	1.32982i	−0.938769	−	0.344548i	$-0.888032\pi$
$349$	−14.3432	−	24.8431i	−0.767771	−	1.32982i	0.170997	−	0.985271i	$-0.445301\pi$
$350$	2.72233	−	3.28473i	0.145515	−	0.175576i
$351$	2.36933	−	3.13400i	0.126466	−	0.167280i
$352$	14.8217	+	4.88946i	0.789997	+	0.260609i
$353$	20.1621	−	11.6406i	1.07312	−	0.619566i	0.144088	−	0.989565i	$-0.453975\pi$
$353$	20.1621	−	11.6406i	1.07312	−	0.619566i	0.929032	+	0.369999i	$0.120642\pi$
$354$	0.500466	+	0.0851094i	0.0265995	+	0.00452351i
$355$	13.5810	+	7.84102i	0.720807	+	0.416158i
$356$	−22.8565	+	4.31762i	−1.21139	+	0.228834i
$357$	−0.657516	+	1.13885i	−0.0347994	+	0.0602744i
$358$	3.49394	+	9.42079i	0.184661	+	0.497904i
$359$		−	24.7065i		−	1.30396i	−0.758237	−	0.651979i	$-0.773939\pi$
$359$		−	24.7065i		−	1.30396i	0.758237	−	0.651979i	$-0.226061\pi$
$360$	4.32741	+	7.18899i	0.228074	+	0.378893i
$361$	9.26435	+	16.0463i	0.487597	+	0.844543i
$362$	8.33332	+	1.41717i	0.437990	+	0.0744847i
$363$			0.618709i			0.0324738i
$364$	−1.36877	−	21.7104i	−0.0717432	−	1.13793i
$365$		−	4.24432i		−	0.222158i
$366$	−0.624761	+	3.67376i	−0.0326568	+	0.192031i
$367$	18.1111	+	31.3693i	0.945389	+	1.63746i	0.754970	+	0.655759i	$0.227651\pi$
$367$	18.1111	+	31.3693i	0.945389	+	1.63746i	0.190419	+	0.981703i	$0.439015\pi$
$368$	1.38987	−	9.18404i	0.0724522	−	0.478751i
$369$			29.7409i			1.54825i
$370$	−9.53386	+	3.53588i	−0.495642	+	0.183821i
$371$	−9.10537	+	15.7710i	−0.472727	+	0.818788i
$372$	0.169294	+	0.896205i	0.00877750	+	0.0464661i
$373$	12.6773	+	7.31927i	0.656408	+	0.378977i	0.790907	−	0.611937i	$-0.209609\pi$
$373$	12.6773	+	7.31927i	0.656408	+	0.378977i	−0.134499	+	0.990914i	$0.542943\pi$
$374$	1.56145	−	9.18175i	0.0807407	−	0.474777i
$375$	0.158158	−	0.0913126i	0.00816725	−	0.00471536i
$376$	−22.2540	−	12.3123i	−1.14766	−	0.634960i
$377$	−11.8458	−	1.47330i	−0.610091	−	0.0758790i
$378$	−3.57924	−	2.96642i	−0.184096	−	0.152576i
$379$	16.4373	+	28.4702i	0.844326	+	1.46242i	0.886205	+	0.463293i	$0.153332\pi$
$379$	16.4373	+	28.4702i	0.844326	+	1.46242i	−0.0418791	+	0.999123i	$0.513334\pi$
$380$	1.04098	−	0.895299i	0.0534014	−	0.0459279i
$381$	−2.42171	−	1.39817i	−0.124068	−	0.0716306i
$382$	−20.8601	−	17.2885i	−1.06729	−	0.884557i
$383$	11.2143	+	6.47459i	0.573025	+	0.330836i	0.758357	−	0.651840i	$-0.226003\pi$
$383$	11.2143	+	6.47459i	0.573025	+	0.330836i	−0.185332	+	0.982676i	$0.559336\pi$
$384$	1.25951	−	1.63789i	0.0642743	−	0.0835831i
$385$		−	8.32301i		−	0.424180i
$386$	−5.54210	−	14.9433i	−0.282085	−	0.760592i
$387$	5.87311	−	3.39084i	0.298547	−	0.172366i
$388$	9.35534	+	10.8777i	0.474945	+	0.552229i
$389$		−	11.8371i		−	0.600165i	−0.953913	−	0.300083i	$-0.902986\pi$
$389$		−	11.8371i		−	0.600165i	0.953913	−	0.300083i	$-0.0970142\pi$
$390$	0.268232	−	0.891741i	0.0135824	−	0.0451551i
$391$	−5.54293			−0.280318
$392$	−5.93949	+	0.108423i	−0.299989	+	0.00547619i
$393$	0.904631	+	1.56687i	0.0456326	+	0.0790380i
$394$	−13.5095	+	5.01033i	−0.680597	+	0.252417i
$395$	5.23394			0.263348
$396$	15.4498	+	5.41128i	0.776381	+	0.271927i
$397$	−7.59767	+	13.1595i	−0.381316	+	0.660459i	−0.991251	−	0.131993i	$-0.957862\pi$
$397$	−7.59767	+	13.1595i	−0.381316	+	0.660459i	0.609935	+	0.792452i	$0.291196\pi$
$398$	16.8408	+	13.9574i	0.844152	+	0.699620i
$399$	−0.189107	+	0.327543i	−0.00946720	+	0.0163977i
$400$	3.12584	+	2.49582i	0.156292	+	0.124791i
$401$	−8.88365	+	5.12898i	−0.443628	+	0.256129i	−0.705136	−	0.709073i	$-0.749114\pi$
$401$	−8.88365	+	5.12898i	−0.443628	+	0.256129i	0.261507	+	0.965202i	$0.415781\pi$
$402$	0.243901	−	0.294287i	0.0121647	−	0.0146777i
$403$	−5.42957	+	7.18187i	−0.270466	+	0.357754i
$404$	−8.84625	+	1.67107i	−0.440117	+	0.0831388i
$405$	4.35047	+	7.53524i	0.216177	+	0.374429i
$406$	−2.36800	+	13.9245i	−0.117522	+	0.691060i
$407$	−9.91886	+	17.1800i	−0.491660	+	0.851580i
$408$	−1.07886	−	0.596895i	−0.0534115	−	0.0295507i
$409$	−6.23811	−	3.60157i	−0.308455	−	0.178086i	0.337780	−	0.941225i	$-0.390324\pi$
$409$	−6.23811	−	3.60157i	−0.308455	−	0.178086i	−0.646235	+	0.763139i	$0.723657\pi$
$410$	4.93000	+	13.2929i	0.243475	+	0.656488i
$411$	0.909015			0.0448384
$412$	−5.01841	−	1.75770i	−0.247239	−	0.0865955i
$413$	5.13509	−	2.96474i	0.252681	−	0.145886i
$414$	1.63337	−	9.60464i	0.0802757	−	0.472042i
$415$	14.6966			0.721426
$416$	20.3288	−	1.65467i	0.996704	−	0.0811269i
$417$	1.43516			0.0702801
$418$	0.449087	−	2.64075i	0.0219655	−	0.129163i
$419$	−29.6861	+	17.1393i	−1.45026	+	0.837307i	−0.998496	−	0.0548305i	$-0.982538\pi$
$419$	−29.6861	+	17.1393i	−1.45026	+	0.837307i	−0.451763	+	0.892138i	$0.649205\pi$
$420$	−1.03990	−	0.364224i	−0.0507419	−	0.0177723i
$421$	−17.5416			−0.854927			−0.427463	−	0.904033i	$-0.640593\pi$
$421$	−17.5416			−0.854927			−0.427463	+	0.904033i	$0.640593\pi$
$422$	−8.48529	−	22.8791i	−0.413057	−	1.11374i
$423$	−23.1019	−	13.3379i	−1.12325	−	0.648510i
$424$	−14.9402	−	8.26589i	−0.725561	−	0.401427i
$425$	1.19349	−	2.06718i	0.0578927	−	0.100273i
$426$	0.679032	−	3.99289i	0.0328992	−	0.193456i
$427$	21.7632	+	37.6951i	1.05320	+	1.82419i
$428$	−12.3837	+	2.33930i	−0.598588	+	0.113074i
$429$	−0.707228	−	1.67340i	−0.0341453	−	0.0807925i
$430$	2.06293	−	2.48911i	0.0994835	−	0.120035i
$431$	2.97455	−	1.71736i	0.143279	−	0.0827222i	−0.426647	−	0.904418i	$-0.640305\pi$
$431$	2.97455	−	1.71736i	0.143279	−	0.0827222i	0.569926	+	0.821696i	$0.306972\pi$
$432$	2.71960	−	3.40610i	0.130847	−	0.163876i
$433$	−12.8277	+	22.2182i	−0.616460	+	1.06774i	0.373667	+	0.927563i	$0.378100\pi$
$433$	−12.8277	+	22.2182i	−0.616460	+	1.06774i	−0.990127	+	0.140176i	$0.955233\pi$
$434$	8.20219	+	6.79785i	0.393718	+	0.326307i
$435$	−0.302314	+	0.523623i	−0.0144948	+	0.0251058i
$436$	−13.0319	−	4.56442i	−0.624115	−	0.218596i
$437$	−1.59419			−0.0762606
$438$	−1.02778	+	0.381177i	−0.0491091	+	0.0182134i
$439$	−13.6386	−	23.6228i	−0.650935	−	1.12745i	−0.982896	−	0.184160i	$-0.941044\pi$
$439$	−13.6386	−	23.6228i	−0.650935	−	1.12745i	0.331961	−	0.943293i	$-0.392290\pi$
$440$	7.80236	−	0.142429i	0.371963	−	0.00679004i
$441$	−6.23078			−0.296704
$442$	−2.79150	−	11.8468i	−0.132778	−	0.563494i
$443$			37.0463i			1.76012i	0.474859	+	0.880062i	$0.342499\pi$
$443$			37.0463i			1.76012i	−0.474859	+	0.880062i	$0.657501\pi$
$444$	1.71245	+	1.99110i	0.0812693	+	0.0944936i
$445$	−10.0722	+	5.81518i	−0.477468	+	0.275666i
$446$	−1.42968	−	3.85488i	−0.0676973	−	0.182534i
$447$			1.46433i			0.0692607i
$448$	−0.880796	−	24.1173i	−0.0416137	−	1.13943i
$449$	20.2515	+	11.6922i	0.955729	+	0.551790i	0.894856	−	0.446355i	$-0.147278\pi$
$449$	20.2515	+	11.6922i	0.955729	+	0.551790i	0.0608731	+	0.998146i	$0.480612\pi$
$450$	3.23027	+	2.67719i	0.152276	+	0.126204i
$451$	23.9537	+	13.8297i	1.12794	+	0.651214i
$452$	13.6028	−	11.6991i	0.639820	−	0.550277i
$453$	1.67202	+	2.89602i	0.0785583	+	0.136067i
$454$	−27.8548	−	23.0856i	−1.30729	−	1.08346i
$455$	−4.23421	−	10.0187i	−0.198503	−	0.469686i
$456$	−0.310290	−	0.171672i	−0.0145306	−	0.00803929i
$457$	−21.0652	+	12.1620i	−0.985386	+	0.568913i	−0.903892	−	0.427761i	$-0.859303\pi$
$457$	−21.0652	+	12.1620i	−0.985386	+	0.568913i	−0.0814943	+	0.996674i	$0.525969\pi$
$458$	3.04106	−	17.8823i	0.142100	−	0.835584i
$459$	−2.25253	−	1.30050i	−0.105139	−	0.0607020i
$460$	−0.862070	−	4.56360i	−0.0401942	−	0.212779i
$461$	−10.7228	+	18.5725i	−0.499412	+	0.865008i	−1.00000		0.000678318i	$-0.999784\pi$
$461$	−10.7228	+	18.5725i	−0.499412	+	0.865008i	0.500587	+	0.865686i	$0.333117\pi$
$462$	−2.01545	+	0.747480i	−0.0937671	+	0.0347759i
$463$		−	32.5598i		−	1.51318i	−0.653888	−	0.756591i	$-0.726863\pi$
$463$		−	32.5598i		−	1.51318i	0.653888	−	0.756591i	$-0.273137\pi$
$464$	−13.0939	−	1.98158i	−0.607870	−	0.0919926i
$465$	0.228014	+	0.394931i	0.0105739	+	0.0183145i
$466$	5.43104	−	31.9360i	0.251588	−	1.47941i
$467$			3.66427i			0.169562i	0.996400	+	0.0847810i	$0.0270191\pi$
$467$			3.66427i			0.169562i	−0.996400	+	0.0847810i	$0.972981\pi$
$468$	21.3504	−	1.34608i	0.986923	−	0.0622225i
$469$		−	4.46442i		−	0.206148i
$470$	−12.5365	−	2.13195i	−0.578264	−	0.0983397i
$471$	−0.259193	−	0.448936i	−0.0119430	−	0.0206859i
$472$	2.86716	+	4.76312i	0.131972	+	0.219240i
$473$		−	6.30703i		−	0.289997i
$474$	−0.470055	−	1.26742i	−0.0215903	−	0.0582144i
$475$	0.343257	−	0.594539i	0.0157497	−	0.0272793i
$476$	−14.1511	+	2.67317i	−0.648617	+	0.122525i
$477$	−15.5095	−	8.95440i	−0.710130	−	0.409994i
$478$	6.46423	+	1.09931i	0.295667	+	0.0502812i
$479$	−7.97967	+	4.60707i	−0.364601	+	0.210502i	−0.671097	−	0.741370i	$-0.734177\pi$
$479$	−7.97967	+	4.60707i	−0.364601	+	0.210502i	0.306496	+	0.951872i	$0.400843\pi$
$480$	0.323645	−	0.981080i	0.0147723	−	0.0447800i
$481$	−3.19966	+	25.7263i	−0.145892	+	1.17302i
$482$	−13.3167	+	16.0678i	−0.606559	+	0.731866i
$483$	0.639660	+	1.10792i	0.0291055	+	0.0504123i
$484$	−5.13713	+	4.41819i	−0.233506	+	0.200827i
$485$	6.21257	+	3.58683i	0.282098	+	0.162870i
$486$	4.38400	−	5.28968i	0.198862	−	0.239945i
$487$	−7.20298	−	4.15865i	−0.326398	−	0.188446i	0.327843	−	0.944732i	$-0.393678\pi$
$487$	−7.20298	−	4.15865i	−0.326398	−	0.188446i	−0.654241	+	0.756286i	$0.727012\pi$
$488$	−34.9646	+	21.0469i	−1.58277	+	0.952748i
$489$			2.80616i			0.126899i
$490$	−2.78488	+	1.03284i	−0.125808	+	0.0466591i
$491$	−11.7583	+	6.78864i	−0.530643	+	0.306367i	−0.741278	−	0.671198i	$-0.765780\pi$
$491$	−11.7583	+	6.78864i	−0.530643	+	0.306367i	0.210635	+	0.977565i	$0.432447\pi$
$492$	2.77615	−	2.38763i	0.125159	−	0.107643i
$493$			7.90269i			0.355919i
$494$	−0.802860	−	3.40724i	−0.0361224	−	0.153299i
$495$	8.18501			0.367889
$496$	−6.23224	+	7.80543i	−0.279836	+	0.350474i
$497$	−23.6537	−	40.9695i	−1.06102	−	1.83773i
$498$	−1.31988	−	3.55882i	−0.0591453	−	0.159475i
$499$	26.9915			1.20831			0.604153	−	0.796869i	$-0.293512\pi$
$499$	26.9915			1.20831			0.604153	+	0.796869i	$0.293512\pi$
$500$	1.88757	+	0.661121i	0.0844147	+	0.0295662i
$501$	1.64480	−	2.84888i	0.0734842	−	0.127278i
$502$	−24.1103	+	29.0912i	−1.07610	+	1.29840i
$503$	4.78038	−	8.27985i	0.213146	−	0.369180i	−0.739551	−	0.673100i	$-0.764962\pi$
$503$	4.78038	−	8.27985i	0.213146	−	0.369180i	0.952698	+	0.303920i	$0.0982955\pi$
$504$	−0.461997	−	25.3085i	−0.0205790	−	1.12733i
$505$	−3.89828	+	2.25068i	−0.173471	+	0.100154i
$506$	−6.97617	−	5.78174i	−0.310128	−	0.257030i
$507$	−1.70264	−	1.65454i	−0.0756167	−	0.0734809i
$508$	−5.68436	−	30.0917i	−0.252203	−	1.33510i
$509$	0.735494	+	1.27391i	0.0326002	+	0.0564652i	0.881865	−	0.471502i	$-0.156288\pi$
$509$	0.735494	+	1.27391i	0.0326002	+	0.0564652i	−0.849265	+	0.527967i	$0.822955\pi$
$510$	−0.607761	−	0.103356i	−0.0269121	−	0.00457668i
$511$	−6.40185	+	11.0883i	−0.283201	+	0.490519i
$512$	22.5935	−	1.23841i	0.998501	−	0.0547304i
$513$	−0.647846	−	0.374034i	−0.0286031	−	0.0165140i
$514$	20.8043	−	7.71582i	0.917640	−	0.340330i
$515$	−2.65866			−0.117155
$516$	−0.788016	−	0.276003i	−0.0346905	−	0.0121503i
$517$	−21.4850	+	12.4044i	−0.944908	+	0.545543i
$518$	30.2406	+	5.14272i	1.32869	+	0.225958i
$519$	4.32947			0.190043
$520$	9.31954	−	4.14078i	0.408689	−	0.181585i
$521$	−17.1591			−0.751752			−0.375876	−	0.926670i	$-0.622658\pi$
$521$	−17.1591			−0.751752			−0.375876	+	0.926670i	$0.622658\pi$
$522$	−13.6936	−	2.32874i	−0.599352	−	0.101926i
$523$	21.0272	−	12.1400i	0.919453	−	0.530847i	0.0359926	−	0.999352i	$-0.488541\pi$
$523$	21.0272	−	12.1400i	0.919453	−	0.530847i	0.883461	+	0.468505i	$0.155207\pi$
$524$	−6.54970	+	18.7001i	−0.286125	+	0.816917i
$525$	−0.550919			−0.0240441
$526$	0.0299868	−	0.0111214i	0.00130748	−	0.000484914i
$527$	5.16189	+	2.98022i	0.224856	+	0.129820i
$528$	−0.735211	−	1.87658i	−0.0319959	−	0.0816675i
$529$	8.80380	−	15.2486i	0.382774	−	0.662984i
$530$	−8.41636	−	1.43129i	−0.365583	−	0.0621712i
$531$	2.91559	+	5.04994i	0.126526	+	0.219149i
$532$	−4.06999	+	0.768827i	−0.176457	+	0.0333329i
$533$	35.8696	+	4.46122i	1.55369	+	0.193237i
$534$	2.31274	+	1.91676i	0.100082	+	0.0829464i
$535$	−5.45713	+	3.15068i	−0.235932	+	0.136216i
$536$	4.18515	−	0.0763983i	0.180771	−	0.00329990i
$537$	0.648766	−	1.12370i	0.0279963	−	0.0484911i
$538$	15.6415	−	18.8728i	0.674352	−	0.813664i
$539$	−2.89734	+	5.01834i	−0.124797	+	0.216155i
$540$	0.720397	−	2.05681i	0.0310010	−	0.0885110i
$541$	39.2553			1.68772			0.843858	−	0.536566i	$-0.180279\pi$
$541$	39.2553			1.68772			0.843858	+	0.536566i	$0.180279\pi$
$542$	2.13315	+	5.75166i	0.0916267	+	0.247055i
$543$	−0.545789	−	0.945335i	−0.0234221	−	0.0405682i
$544$	−2.74811	−	13.2202i	−0.117824	−	0.566810i
$545$	−6.90407			−0.295738
$546$	−2.04580	+	1.92510i	−0.0875522	+	0.0823867i
$547$		−	24.6557i		−	1.05420i	−0.849803	−	0.527101i	$-0.823279\pi$
$547$		−	24.6557i		−	1.05420i	0.849803	−	0.527101i	$-0.176721\pi$
$548$	6.49126	+	7.54753i	0.277293	+	0.322415i
$549$	−37.0700	+	21.4024i	−1.58211	+	0.913432i
$550$	3.65833	−	1.35679i	0.155992	−	0.0578536i
$551$			2.27288i			0.0968281i
$552$	−1.02767	+	0.618605i	−0.0437405	+	0.0263296i
$553$	−13.6737	−	7.89453i	−0.581466	−	0.335710i
$554$	−16.1629	+	19.5020i	−0.686697	+	0.828560i
$555$	1.13718	+	0.656552i	0.0482707	+	0.0278691i
$556$	10.2485	+	11.9161i	0.434631	+	0.505355i
$557$	−5.16907	−	8.95309i	−0.219020	−	0.379355i	0.735488	−	0.677537i	$-0.236953\pi$
$557$	−5.16907	−	8.95309i	−0.219020	−	0.379355i	−0.954509	+	0.298183i	$0.903619\pi$
$558$	−6.68513	+	8.06619i	−0.283004	+	0.341469i
$559$	−3.20861	−	7.59201i	−0.135710	−	0.321108i
$560$	−4.40175	−	11.2352i	−0.186008	−	0.474773i
$561$	−1.04158	+	0.601357i	−0.0439755	+	0.0253893i
$562$	−32.8326	−	5.58351i	−1.38496	−	0.235526i
$563$	24.1304	+	13.9317i	1.01698	+	0.587151i	0.913226	−	0.407453i	$-0.133583\pi$
$563$	24.1304	+	13.9317i	1.01698	+	0.587151i	0.103749	+	0.994604i	$0.466916\pi$
$564$	0.609625	+	3.22722i	0.0256699	+	0.135890i
$565$	4.48541	−	7.76896i	0.188703	−	0.326843i
$566$	0.626824	+	1.69012i	0.0263474	+	0.0710409i
$567$		−	26.2478i		−	1.10231i
$568$	38.0018	−	22.8752i	1.59452	−	0.959820i
$569$	−3.52255	−	6.10124i	−0.147673	−	0.255777i	0.782694	−	0.622407i	$-0.213845\pi$
$569$	−3.52255	−	6.10124i	−0.147673	−	0.255777i	−0.930367	+	0.366630i	$0.880512\pi$
$570$	−0.174797	−	0.0297261i	−0.00732145	−	0.00124509i
$571$		−	13.1670i		−	0.551020i	−0.961298	−	0.275510i	$-0.911153\pi$
$571$		−	13.1670i		−	0.551020i	0.961298	−	0.275510i	$-0.0888467\pi$
$572$	8.84389	−	17.8218i	0.369782	−	0.745167i
$573$			3.49868i			0.146159i
$574$	7.17039	−	42.1638i	0.299286	−	1.75988i
$575$	−1.16108	−	2.01104i	−0.0484203	−	0.0838664i
$576$	23.7174	−	0.866192i	0.988224	−	0.0360913i
$577$			6.18178i			0.257351i	0.991687	+	0.128675i	$0.0410725\pi$
$577$			6.18178i			0.257351i	−0.991687	+	0.128675i	$0.958927\pi$
$578$	14.9864	−	5.55811i	0.623354	−	0.231187i
$579$	−1.02907	+	1.78241i	−0.0427668	+	0.0740743i
$580$	−6.50644	+	1.22908i	−0.270165	+	0.0510346i
$581$	−38.3949	−	22.1673i	−1.59289	−	0.919655i
$582$	0.310619	−	1.82653i	0.0128756	−	0.0757119i
$583$	−14.4240	+	8.32767i	−0.597379	+	0.344897i
$584$	−10.5042	−	5.81162i	−0.434668	−	0.240487i
$585$	9.85262	−	4.16401i	0.407356	−	0.172160i
$586$	−27.4562	−	22.7553i	−1.13420	−	0.940011i
$587$	0.325591	+	0.563940i	0.0134386	+	0.0232763i	0.872666	−	0.488317i	$-0.162389\pi$
$587$	0.325591	+	0.563940i	0.0134386	+	0.0232763i	−0.859228	+	0.511593i	$0.829056\pi$
$588$	0.500214	+	0.581609i	0.0206285	+	0.0239852i
$589$	1.48460	+	0.857137i	0.0611721	+	0.0353177i
$590$	2.14024	+	1.77380i	0.0881123	+	0.0730261i
$591$	1.61139	+	0.930334i	0.0662836	+	0.0382688i
$592$	−4.30351	+	28.4369i	−0.176873	+	1.16875i
$593$			16.6654i			0.684365i	0.939634	+	0.342182i	$0.111166\pi$
$593$			16.6654i			0.684365i	−0.939634	+	0.342182i	$0.888834\pi$
$594$	−1.47844	−	3.98634i	−0.0606610	−	0.163562i
$595$	−6.23600	+	3.60035i	−0.255651	+	0.147600i
$596$	−12.1583	+	10.4568i	−0.498025	+	0.428326i
$597$		−	2.82456i		−	0.115601i
$598$	−11.3389	−	3.41068i	−0.463680	−	0.139473i
$599$	17.0368			0.696104			0.348052	−	0.937475i	$-0.386843\pi$
$599$	17.0368			0.696104			0.348052	+	0.937475i	$0.386843\pi$
$600$	−0.00942771	−	0.516456i	−0.000384885	−	0.0210842i
$601$	−6.05576	−	10.4889i	−0.247020	−	0.427850i	0.715678	−	0.698430i	$-0.246118\pi$
$601$	−6.05576	−	10.4889i	−0.247020	−	0.427850i	−0.962697	+	0.270580i	$0.912785\pi$
$602$	−9.14384	+	3.39123i	−0.372675	+	0.138216i
$603$	4.39040			0.178791
$604$	−12.1057	+	34.5631i	−0.492576	+	1.40635i
$605$	−1.69393	+	2.93397i	−0.0688681	+	0.119283i
$606$	0.895109	+	0.741852i	0.0363613	+	0.0301357i
$607$	−16.1534	+	27.9785i	−0.655645	+	1.13561i	0.326086	+	0.945340i	$0.394270\pi$
$607$	−16.1534	+	27.9785i	−0.655645	+	1.13561i	−0.981732	+	0.190271i	$0.939063\pi$
$608$	−0.790381	−	3.80223i	−0.0320542	−	0.154201i
$609$	1.57960	−	0.911980i	0.0640084	−	0.0369553i
$610$	−13.0209	+	15.7108i	−0.527200	+	0.636113i
$611$	−19.5518	+	25.8618i	−0.790980	+	1.04626i
$612$	−2.62885	−	13.9165i	−0.106265	−	0.562542i
$613$	20.0857	+	34.7895i	0.811255	+	1.40514i	0.911986	+	0.410221i	$0.134549\pi$
$613$	20.0857	+	34.7895i	0.811255	+	1.40514i	−0.100731	+	0.994914i	$0.532118\pi$
$614$	−2.20325	+	12.9557i	−0.0889161	+	0.522851i
$615$	0.915418	−	1.58555i	0.0369132	−	0.0639355i
$616$	−20.5986	−	11.3965i	−0.829940	−	0.459176i
$617$	−30.4689	−	17.5912i	−1.22663	−	0.708195i	−0.260307	−	0.965526i	$-0.583824\pi$
$617$	−30.4689	−	17.5912i	−1.22663	−	0.708195i	−0.966323	+	0.257331i	$0.917157\pi$
$618$	0.238771	+	0.643804i	0.00960479	+	0.0258976i
$619$	−6.18200			−0.248475			−0.124238	−	0.992252i	$-0.539649\pi$
$619$	−6.18200			−0.248475			−0.124238	+	0.992252i	$0.539649\pi$
$620$	−1.65086	+	4.71339i	−0.0663003	+	0.189294i
$621$	−2.19136	+	1.26518i	−0.0879361	+	0.0507699i
$622$	5.87096	−	34.5228i	0.235404	−	1.38424i
$623$	35.0849			1.40565
$624$	−1.83968	−	1.88488i	−0.0736463	−	0.0754556i
$625$	1.00000			0.0400000
$626$	−7.31657	+	43.0234i	−0.292429	+	1.71956i
$627$	−0.299567	+	0.172955i	−0.0119636	+	0.00690717i
$628$	1.87661	−	5.35791i	0.0748848	−	0.213804i
$629$	17.1627			0.684323
$630$	−4.40100	−	11.8665i	−0.175340	−	0.472773i
$631$	−40.8056	−	23.5592i	−1.62445	−	0.937875i	−0.985710	−	0.168450i	$-0.946124\pi$
$631$	−40.8056	−	23.5592i	−1.62445	−	0.937875i	−0.638737	−	0.769425i	$-0.720543\pi$
$632$	7.16669	−	12.9535i	0.285076	−	0.515261i
$633$	−1.57557	+	2.72897i	−0.0626235	+	0.108467i
$634$	1.28534	−	7.55816i	0.0510475	−	0.300173i
$635$	−7.65597	−	13.2605i	−0.303818	−	0.526228i
$636$	0.409272	+	2.16659i	0.0162287	+	0.0859110i
$637$	−0.934634	+	7.51475i	−0.0370315	+	0.297745i
$638$	−8.24317	+	9.94610i	−0.326350	+	0.393770i
$639$	40.2902	−	23.2615i	1.59385	−	0.920212i
$640$	10.4570	−	4.31866i	0.413350	−	0.170710i
$641$	14.2517	−	24.6847i	0.562910	−	0.974989i	−0.434331	−	0.900753i	$-0.643015\pi$
$641$	14.2517	−	24.6847i	0.562910	−	0.974989i	0.997241	−	0.0742354i	$-0.0236516\pi$
$642$	1.25305	+	1.03850i	0.0494538	+	0.0409865i
$643$	3.92131	−	6.79191i	0.154641	−	0.267847i	−0.778287	−	0.627909i	$-0.783911\pi$
$643$	3.92131	−	6.79191i	0.154641	−	0.267847i	0.932928	+	0.360062i	$0.117244\pi$
$644$	−4.63126	+	13.2227i	−0.182497	+	0.521049i
$645$	−0.417477			−0.0164381
$646$	−2.17284	+	0.805854i	−0.0854893	+	0.0317059i
$647$	16.1046	+	27.8939i	0.633136	+	1.09662i	0.986907	+	0.161292i	$0.0515661\pi$
$647$	16.1046	+	27.8939i	0.633136	+	1.09662i	−0.353770	+	0.935332i	$0.615101\pi$
$648$	24.6059	−	0.449171i	0.966611	−	0.0176451i
$649$	5.42305			0.212873
$650$	3.71343	−	3.49434i	0.145653	−	0.137059i
$651$		−	1.37568i		−	0.0539172i
$652$	−23.2995	+	20.0387i	−0.912478	+	0.784777i
$653$	12.3946	−	7.15601i	0.485037	−	0.280036i	−0.237476	−	0.971393i	$-0.576320\pi$
$653$	12.3946	−	7.15601i	0.485037	−	0.280036i	0.722513	+	0.691357i	$0.242987\pi$
$654$	0.620046	+	1.67184i	0.0242457	+	0.0653743i
$655$			9.90697i			0.387097i
$656$	39.6489	+	6.00030i	1.54803	+	0.234272i
$657$	−10.9045	−	6.29570i	−0.425424	−	0.245619i
$658$	29.5359	+	24.4789i	1.15143	+	0.954288i
$659$	−25.8144	−	14.9040i	−1.00559	−	0.580576i	−0.0956904	−	0.995411i	$-0.530506\pi$
$659$	−25.8144	−	14.9040i	−1.00559	−	0.580576i	−0.909897	+	0.414835i	$0.863839\pi$
$660$	−0.657102	−	0.764027i	−0.0255776	−	0.0297397i
$661$	−6.66973	−	11.5523i	−0.259422	−	0.449333i	0.706665	−	0.707548i	$-0.250199\pi$
$661$	−6.66973	−	11.5523i	−0.259422	−	0.449333i	−0.966087	+	0.258216i	$0.916866\pi$
$662$	−12.0046	−	9.94926i	−0.466574	−	0.386689i
$663$	−0.947859	+	1.25376i	−0.0368118	+	0.0486922i
$664$	20.1236	−	36.3724i	0.780946	−	1.41152i
$665$	−1.79353	+	1.03549i	−0.0695500	+	0.0401547i
$666$	−5.05745	+	29.7392i	−0.195972	+	1.15237i
$667$	6.65808	+	3.84404i	0.257802	+	0.148842i
$668$	35.3996	−	6.68704i	1.36965	−	0.258729i
$669$	−0.265467	+	0.459803i	−0.0102636	+	0.0177770i
$670$	1.96231	−	0.727774i	0.0758107	−	0.0281164i
$671$			39.8089i			1.53680i
$672$	−2.32532	+	2.07492i	−0.0897011	+	0.0800416i
$673$	7.99575	+	13.8490i	0.308213	+	0.533841i	0.977972	−	0.208738i	$-0.0669356\pi$
$673$	7.99575	+	13.8490i	0.308213	+	0.533841i	−0.669758	+	0.742579i	$0.733602\pi$
$674$	2.84399	−	16.7234i	0.109546	−	0.644163i
$675$		−	1.08966i		−	0.0419410i
$676$	1.57916	−	25.9520i	0.0607368	−	0.998154i
$677$			34.6980i			1.33355i	0.745258	+	0.666777i	$0.232326\pi$
$677$			34.6980i			1.33355i	−0.745258	+	0.666777i	$0.767674\pi$
$678$	−2.28411	−	0.388436i	−0.0877207	−	0.0149178i
$679$	−10.8203	−	18.7413i	−0.415244	−	0.719224i
$680$	−3.48185	−	5.78429i	−0.133523	−	0.221817i
$681$			4.67185i			0.179026i
$682$	3.38799	+	9.13510i	0.129733	+	0.349801i
$683$	−23.8298	+	41.2745i	−0.911823	+	1.57932i	−0.100335	+	0.994954i	$0.531992\pi$
$683$	−23.8298	+	41.2745i	−0.911823	+	1.57932i	−0.811488	+	0.584370i	$0.801342\pi$
$684$	−0.756079	−	4.00251i	−0.0289094	−	0.153040i
$685$	4.31063	+	2.48875i	0.164701	+	0.0950901i
$686$	−20.6074	−	3.50450i	−0.786794	−	0.133802i
$687$	−2.02857	+	1.17120i	−0.0773948	+	0.0446839i
$688$	−3.33556	−	8.51381i	−0.127167	−	0.324586i
$689$	−13.1261	+	17.3623i	−0.500064	+	0.661452i
$690$	−0.382706	+	0.461769i	−0.0145694	+	0.0175792i
$691$	6.05912	+	10.4947i	0.230500	+	0.399237i	0.957955	−	0.286917i	$-0.0926305\pi$
$691$	6.05912	+	10.4947i	0.230500	+	0.399237i	−0.727455	+	0.686155i	$0.759297\pi$
$692$	30.9166	+	35.9475i	1.17527	+	1.36652i
$693$	−21.3834	−	12.3457i	−0.812289	−	0.468975i
$694$	−8.13938	+	9.82087i	−0.308967	+	0.372795i
$695$	6.80566	+	3.92925i	0.258154	+	0.149045i
$696$	0.881961	+	1.46518i	0.0334306	+	0.0555373i
$697$		−	23.9297i		−	0.906400i
$698$	−38.0369	+	14.1069i	−1.43972	+	0.533956i
$699$	−3.62283	+	2.09164i	−0.137028	+	0.0791131i
$700$	−3.93410	−	4.57427i	−0.148695	−	0.172891i
$701$			17.3047i			0.653590i	0.945095	+	0.326795i	$0.105969\pi$
$701$			17.3047i			0.653590i	−0.945095	+	0.326795i	$0.894031\pi$
$702$	−3.80765	−	4.04638i	−0.143710	−	0.152721i
$703$	4.93615			0.186171
$704$	10.3310	−	19.5050i	0.389366	−	0.735124i
$705$	0.821073	+	1.42214i	0.0309234	+	0.0535609i
$706$	−11.4489	−	30.8699i	−0.430885	−	1.16180i
$707$	13.5791			0.510694
$708$	0.237319	−	0.677569i	0.00891898	−	0.0254646i
$709$	19.5172	−	33.8048i	0.732984	−	1.26956i	−0.222619	−	0.974906i	$-0.571460\pi$
$709$	19.5172	−	33.8048i	0.732984	−	1.26956i	0.955602	−	0.294659i	$-0.0952062\pi$
$710$	14.1520	−	17.0756i	0.531113	−	0.640834i
$711$	7.76364	−	13.4470i	0.291159	−	0.504302i
$712$	0.600398	+	32.8902i	0.0225009	+	1.23261i
$713$	5.02171	−	2.89929i	0.188065	−	0.108579i
$714$	1.43189	+	1.18672i	0.0535870	+	0.0444121i
$715$	1.22777	−	9.87169i	0.0459161	−	0.369180i
$716$	13.9628	−	2.63760i	0.521816	−	0.0985717i
$717$	−0.423373	−	0.733304i	−0.0158112	−	0.0273857i
$718$	−34.4457	−	5.85785i	−1.28550	−	0.218613i
$719$	−25.4352	+	44.0551i	−0.948573	+	1.64298i	−0.200140	+	0.979767i	$0.564140\pi$
$719$	−25.4352	+	44.0551i	−0.948573	+	1.64298i	−0.748433	+	0.663210i	$0.769194\pi$
$720$	11.0489	−	4.32876i	0.411768	−	0.161323i
$721$	6.94578	+	4.01015i	0.258674	+	0.149346i
$722$	24.5683	−	9.11178i	0.914337	−	0.339105i
$723$	2.69491			0.100225
$724$	3.95162	−	11.2823i	0.146861	−	0.419303i
$725$	−2.86720	+	1.65538i	−0.106485	+	0.0614792i
$726$	0.862602	+	0.146694i	0.0320142	+	0.00544434i
$727$	38.9624			1.44504			0.722518	−	0.691352i	$-0.242985\pi$
$727$	38.9624			1.44504			0.722518	+	0.691352i	$0.242985\pi$
$728$	−30.5931	−	3.23914i	−1.13386	−	0.120050i
$729$	25.2156			0.933913
$730$	−5.91742	−	1.00632i	−0.219013	−	0.0372455i
$731$	−4.72552	+	2.72828i	−0.174780	+	0.100909i
$732$	4.97382	+	1.74208i	0.183838	+	0.0643891i
$733$	4.59290			0.169643			0.0848213	−	0.996396i	$-0.472968\pi$
$733$	4.59290			0.169643			0.0848213	+	0.996396i	$0.472968\pi$
$734$	48.0290	−	17.8128i	1.77278	−	0.657482i
$735$	0.332176	+	0.191782i	0.0122525	+	0.00707397i
$736$	−12.4748	−	4.11527i	−0.459828	−	0.151691i
$737$	2.04156	−	3.53608i	0.0752017	−	0.130253i
$738$	41.4647	+	7.05150i	1.52634	+	0.259569i
$739$	−0.0458654	−	0.0794413i	−0.00168719	−	0.00292229i	0.865181	−	0.501460i	$-0.167204\pi$
$739$	−0.0458654	−	0.0794413i	−0.00168719	−	0.00292229i	−0.866868	+	0.498538i	$0.833870\pi$
$740$	2.66925	+	14.1304i	0.0981238	+	0.519445i
$741$	−0.272612	+	0.360594i	−0.0100147	+	0.0132467i
$742$	19.8290	+	16.4339i	0.727944	+	0.603309i
$743$	−14.9877	+	8.65317i	−0.549847	+	0.317454i	−0.749060	−	0.662502i	$-0.769495\pi$
$743$	−14.9877	+	8.65317i	−0.549847	+	0.317454i	0.199213	+	0.979956i	$0.436161\pi$
$744$	1.28963	−	0.0235416i	0.0472800	−	0.000863078i
$745$	−4.00913	+	6.94401i	−0.146883	+	0.254409i
$746$	13.2103	−	15.9393i	0.483662	−	0.583580i
$747$	21.7998	−	37.7583i	0.797611	−	1.38150i
$748$	−12.4309	−	4.35394i	−0.454521	−	0.159196i
$749$	19.0091			0.694576
$750$	−0.0898089	−	0.242153i	−0.00327936	−	0.00884219i
$751$	4.95629	+	8.58454i	0.180857	+	0.313254i	0.942173	−	0.335128i	$-0.108779\pi$
$751$	4.95629	+	8.58454i	0.180857	+	0.313254i	−0.761315	+	0.648382i	$0.775446\pi$
$752$	−22.4422	+	28.1072i	−0.818382	+	1.02496i
$753$	4.87922			0.177809
$754$	−4.86269	+	16.1661i	−0.177089	+	0.588735i
$755$			18.3109i			0.666403i
$756$	−4.98440	+	4.28684i	−0.181281	+	0.155911i
$757$	−8.66016	+	4.99995i	−0.314759	+	0.181726i	−0.649054	−	0.760742i	$-0.724835\pi$
$757$	−8.66016	+	4.99995i	−0.314759	+	0.181726i	0.334295	+	0.942468i	$0.391502\pi$
$758$	43.5903	−	16.1666i	1.58327	−	0.587197i
$759$			1.17005i			0.0424702i
$760$	−1.00141	−	1.66361i	−0.0363249	−	0.0603455i
$761$	43.2856	+	24.9909i	1.56910	+	0.905921i	0.996274	+	0.0862452i	$0.0274869\pi$
$761$	43.2856	+	24.9909i	1.56910	+	0.905921i	0.572828	+	0.819676i	$0.305846\pi$
$762$	−2.52351	+	3.04483i	−0.0914171	+	0.110303i
$763$	18.0369	+	10.4136i	0.652981	+	0.376999i
$764$	−29.0494	+	24.9840i	−1.05097	+	0.903889i
$765$	−3.54066	−	6.13260i	−0.128013	−	0.221725i
$766$	11.6857	−	14.0999i	0.422223	−	0.509449i
$767$	6.52793	−	2.75890i	0.235710	−	0.0996179i
$768$	−1.98491	−	2.14435i	−0.0716243	−	0.0773775i
$769$

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.237097 - 1.39420i) q^{2} +(-0.158158 + 0.0913126i) q^{3} +(-1.88757 - 0.661121i) q^{4} -1.00000 q^{5} +(0.0898089 + 0.242153i) q^{6} +(2.61251 + 1.50833i) q^{7} +(-1.36927 + 2.47489i) q^{8} +(-1.48332 + 2.56919i) q^{9} +O(q^{10})\)	\(q+(0.237097 - 1.39420i) q^{2} +(-0.158158 + 0.0913126i) q^{3} +(-1.88757 - 0.661121i) q^{4} -1.00000 q^{5} +(0.0898089 + 0.242153i) q^{6} +(2.61251 + 1.50833i) q^{7} +(-1.36927 + 2.47489i) q^{8} +(-1.48332 + 2.56919i) q^{9} +(-0.237097 + 1.39420i) q^{10} +(1.37951 + 2.38937i) q^{11} +(0.358903 - 0.0677973i) q^{12} +(2.87612 + 2.17438i) q^{13} +(2.72233 - 3.28473i) q^{14} +(0.158158 - 0.0913126i) q^{15} +(3.12584 + 2.49582i) q^{16} +(1.19349 - 2.06718i) q^{17} +(3.23027 + 2.67719i) q^{18} +(0.343257 - 0.594539i) q^{19} +(1.88757 + 0.661121i) q^{20} -0.550919 q^{21} +(3.65833 - 1.35679i) q^{22} +(-1.16108 - 2.01104i) q^{23} +(-0.00942771 - 0.516456i) q^{24} +1.00000 q^{25} +(3.71343 - 3.49434i) q^{26} -1.08966i q^{27} +(-3.93410 - 4.57427i) q^{28} +(-2.86720 + 1.65538i) q^{29} +(-0.0898089 - 0.242153i) q^{30} +2.49707i q^{31} +(4.22080 - 3.76628i) q^{32} +(-0.436360 - 0.251932i) q^{33} +(-2.59909 - 2.15408i) q^{34} +(-2.61251 - 1.50833i) q^{35} +(4.49842 - 3.86887i) q^{36} +(3.59508 + 6.22686i) q^{37} +(-0.747519 - 0.619532i) q^{38} +(-0.653430 - 0.0812692i) q^{39} +(1.36927 - 2.47489i) q^{40} +(8.68199 - 5.01255i) q^{41} +(-0.130622 + 0.768090i) q^{42} +(-1.97971 - 1.14299i) q^{43} +(-1.02425 - 5.42213i) q^{44} +(1.48332 - 2.56919i) q^{45} +(-3.07908 + 1.14196i) q^{46} +8.99189i q^{47} +(-0.722277 - 0.109306i) q^{48} +(1.05014 + 1.81889i) q^{49} +(0.237097 - 1.39420i) q^{50} +0.435922i q^{51} +(-3.99135 - 6.00575i) q^{52} +6.03671i q^{53} +(-1.51920 - 0.258356i) q^{54} +(-1.37951 - 2.38937i) q^{55} +(-7.31020 + 4.40037i) q^{56} +0.125375i q^{57} +(1.62812 + 4.38992i) q^{58} +(0.982788 - 1.70224i) q^{59} +(-0.358903 + 0.0677973i) q^{60} +(12.4956 + 7.21434i) q^{61} +(3.48140 + 0.592048i) q^{62} +(-7.75040 + 4.47469i) q^{63} +(-4.25019 - 6.77760i) q^{64} +(-2.87612 - 2.17438i) q^{65} +(-0.454703 + 0.548639i) q^{66} +(-0.739960 - 1.28165i) q^{67} +(-3.61945 + 3.11291i) q^{68} +(0.367267 + 0.212042i) q^{69} +(-2.72233 + 3.28473i) q^{70} +(-13.5810 - 7.84102i) q^{71} +(-4.32741 - 7.18899i) q^{72} +4.24432i q^{73} +(9.53386 - 3.53588i) q^{74} +(-0.158158 + 0.0913126i) q^{75} +(-1.04098 + 0.895299i) q^{76} +8.32301i q^{77} +(-0.268232 + 0.891741i) q^{78} -5.23394 q^{79} +(-3.12584 - 2.49582i) q^{80} +(-4.35047 - 7.53524i) q^{81} +(-4.93000 - 13.2929i) q^{82} -14.6966 q^{83} +(1.03990 + 0.364224i) q^{84} +(-1.19349 + 2.06718i) q^{85} +(-2.06293 + 2.48911i) q^{86} +(0.302314 - 0.523623i) q^{87} +(-7.80236 + 0.142429i) q^{88} +(10.0722 - 5.81518i) q^{89} +(-3.23027 - 2.67719i) q^{90} +(4.23421 + 10.0187i) q^{91} +(0.862070 + 4.56360i) q^{92} +(-0.228014 - 0.394931i) q^{93} +(12.5365 + 2.13195i) q^{94} +(-0.343257 + 0.594539i) q^{95} +(-0.323645 + 0.981080i) q^{96} +(-6.21257 - 3.58683i) q^{97} +(2.78488 - 1.03284i) q^{98} -8.18501 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more