LMFDB - Embedded newform 525.2.bg.a.466.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (of order $15$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			466.10
Character	$\chi$	$=$	525.466
Dual form			525.2.bg.a.436.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0119875 + 0.114053i) q^{2} +(0.978148 + 0.207912i) q^{3} +(1.94343 + 0.413089i) q^{4} +(-2.12162 - 0.706211i) q^{5} +(-0.0354385 + 0.109069i) q^{6} +(2.46049 - 0.972613i) q^{7} +(-0.141288 + 0.434840i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.0119875 + 0.114053i) q^{2} +(0.978148 + 0.207912i) q^{3} +(1.94343 + 0.413089i) q^{4} +(-2.12162 - 0.706211i) q^{5} +(-0.0354385 + 0.109069i) q^{6} +(2.46049 - 0.972613i) q^{7} +(-0.141288 + 0.434840i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.105978 - 0.233512i) q^{10} +(1.95181 - 0.869003i) q^{11} +(1.81508 + 0.808124i) q^{12} +(-1.25719 + 0.913401i) q^{13} +(0.0814346 + 0.292286i) q^{14} +(-1.92843 - 1.13189i) q^{15} +(3.58225 + 1.59492i) q^{16} +(-0.734799 - 0.816077i) q^{17} +(-0.0573407 + 0.0993171i) q^{18} +(1.44890 - 0.307974i) q^{19} +(-3.83149 - 2.24889i) q^{20} +(2.60894 - 0.439794i) q^{21} +(0.0757153 + 0.233028i) q^{22} +(0.294224 - 2.79936i) q^{23} +(-0.228609 + 0.395962i) q^{24} +(4.00253 + 2.99662i) q^{25} +(-0.0891058 - 0.154336i) q^{26} +(0.809017 + 0.587785i) q^{27} +(5.18357 - 0.873804i) q^{28} +(0.663276 + 2.04135i) q^{29} +(0.152212 - 0.206375i) q^{30} +(-1.02974 - 1.14365i) q^{31} +(-0.682066 + 1.18137i) q^{32} +(2.08984 - 0.444209i) q^{33} +(0.101885 - 0.0740235i) q^{34} +(-5.90710 + 0.325888i) q^{35} +(1.60739 + 1.16784i) q^{36} +(3.68100 + 1.63889i) q^{37} +(0.0177567 + 0.168944i) q^{38} +(-1.41962 + 0.632057i) q^{39} +(0.606848 - 0.822785i) q^{40} +(-5.26454 + 3.82491i) q^{41} +(0.0188853 + 0.302830i) q^{42} -9.54777 q^{43} +(4.15219 - 0.882575i) q^{44} +(-1.65095 - 1.50810i) q^{45} +(0.315749 + 0.0671144i) q^{46} +(-1.86347 + 2.06959i) q^{47} +(3.17237 + 2.30486i) q^{48} +(5.10805 - 4.78621i) q^{49} +(-0.389754 + 0.420580i) q^{50} +(-0.549070 - 0.951017i) q^{51} +(-2.82057 + 1.25580i) q^{52} +(2.59581 + 0.551756i) q^{53} +(-0.0767369 + 0.0852249i) q^{54} +(-4.75470 + 0.465302i) q^{55} +(0.0752927 + 1.20734i) q^{56} +1.48127 q^{57} +(-0.240774 + 0.0511781i) q^{58} +(-0.928642 - 8.83544i) q^{59} +(-3.28019 - 2.99636i) q^{60} +(-0.721040 + 6.86024i) q^{61} +(0.142781 - 0.103736i) q^{62} +(2.64337 + 0.112246i) q^{63} +(6.21817 + 4.51777i) q^{64} +(3.31233 - 1.05005i) q^{65} +(0.0256115 + 0.243678i) q^{66} +(-9.36005 - 10.3954i) q^{67} +(-1.09092 - 1.88953i) q^{68} +(0.869814 - 2.67701i) q^{69} +(0.0336426 - 0.677630i) q^{70} +(3.60505 + 11.0952i) q^{71} +(-0.305938 + 0.339779i) q^{72} +(-10.3165 + 4.59321i) q^{73} +(-0.231046 + 0.400184i) q^{74} +(3.29204 + 3.76331i) q^{75} +2.94306 q^{76} +(3.95722 - 4.03653i) q^{77} +(-0.0550704 - 0.169489i) q^{78} +(2.99263 - 3.32365i) q^{79} +(-6.47382 - 5.91364i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.373135 - 0.646289i) q^{82} +(-0.0653066 + 0.200993i) q^{83} +(5.25197 + 0.223016i) q^{84} +(0.982641 + 2.25033i) q^{85} +(0.114454 - 1.08895i) q^{86} +(0.224360 + 2.13465i) q^{87} +(0.102109 + 0.971506i) q^{88} +(-0.653077 + 6.21361i) q^{89} +(0.191794 - 0.170218i) q^{90} +(-2.20492 + 3.47017i) q^{91} +(1.72819 - 5.31881i) q^{92} +(-0.769464 - 1.33275i) q^{93} +(-0.213706 - 0.237344i) q^{94} +(-3.29151 - 0.369828i) q^{95} +(-0.912782 + 1.01375i) q^{96} +(-5.03322 - 15.4907i) q^{97} +(0.484651 + 0.639964i) q^{98} +2.13653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0119875	+	0.114053i	−0.00847643	+	0.0806478i	−0.997942	−	0.0641186i	$-0.979576\pi$
$2$	−0.0119875	+	0.114053i	−0.00847643	+	0.0806478i	0.989466	+	0.144766i	$0.0462431\pi$
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$4$	1.94343	+	0.413089i	0.971715	+	0.206544i
$5$	−2.12162	−	0.706211i	−0.948817	−	0.315827i
$5$	−2.12162	−	0.706211i	−0.948817	−	0.315827i
$6$	−0.0354385	+	0.109069i	−0.0144677	+	0.0445271i
$7$	2.46049	−	0.972613i	0.929979	−	0.367613i
$7$	2.46049	−	0.972613i	0.929979	−	0.367613i
$8$	−0.141288	+	0.434840i	−0.0499529	+	0.153739i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	0.105978	−	0.233512i	0.0335133	−	0.0738429i
$11$	1.95181	−	0.869003i	0.588494	−	0.262014i	−0.0908139	−	0.995868i	$-0.528947\pi$
$11$	1.95181	−	0.869003i	0.588494	−	0.262014i	0.679308	+	0.733854i	$0.262280\pi$
$12$	1.81508	+	0.808124i	0.523967	+	0.233285i
$13$	−1.25719	+	0.913401i	−0.348681	+	0.253332i	−0.748316	−	0.663343i	$-0.769137\pi$
$13$	−1.25719	+	0.913401i	−0.348681	+	0.253332i	0.399634	+	0.916675i	$0.369137\pi$
$14$	0.0814346	+	0.292286i	0.0217643	+	0.0781168i
$15$	−1.92843	−	1.13189i	−0.497918	−	0.292252i
$16$	3.58225	+	1.59492i	0.895563	+	0.398730i
$17$	−0.734799	−	0.816077i	−0.178215	−	0.197928i	0.647418	−	0.762135i	$-0.275849\pi$
$17$	−0.734799	−	0.816077i	−0.178215	−	0.197928i	−0.825633	+	0.564207i	$0.809182\pi$
$18$	−0.0573407	+	0.0993171i	−0.0135153	+	0.0234093i
$19$	1.44890	−	0.307974i	0.332401	−	0.0706540i	−0.0386879	−	0.999251i	$-0.512318\pi$
$19$	1.44890	−	0.307974i	0.332401	−	0.0706540i	0.371089	+	0.928597i	$0.378984\pi$
$20$	−3.83149	−	2.24889i	−0.856748	−	0.502867i
$21$	2.60894	−	0.439794i	0.569318	−	0.0959709i
$22$	0.0757153	+	0.233028i	0.0161426	+	0.0496817i
$23$	0.294224	−	2.79936i	0.0613500	−	0.583706i	−0.920059	−	0.391779i	$-0.871860\pi$
$23$	0.294224	−	2.79936i	0.0613500	−	0.583706i	0.981409	−	0.191927i	$-0.0614736\pi$
$24$	−0.228609	+	0.395962i	−0.0466646	+	0.0808254i
$25$	4.00253	+	2.99662i	0.800507	+	0.599324i
$26$	−0.0891058	−	0.154336i	−0.0174751	−	0.0302677i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	5.18357	−	0.873804i	0.979603	−	0.165133i
$29$	0.663276	+	2.04135i	0.123167	+	0.379070i	0.993563	−	0.113283i	$-0.0361368\pi$
$29$	0.663276	+	2.04135i	0.123167	+	0.379070i	−0.870395	+	0.492353i	$0.836137\pi$
$30$	0.152212	−	0.206375i	0.0277901	−	0.0376787i
$31$	−1.02974	−	1.14365i	−0.184947	−	0.205405i	0.643540	−	0.765412i	$-0.277465\pi$
$31$	−1.02974	−	1.14365i	−0.184947	−	0.205405i	−0.828488	+	0.560007i	$0.810798\pi$
$32$	−0.682066	+	1.18137i	−0.120573	+	0.208839i
$33$	2.08984	−	0.444209i	0.363794	−	0.0773268i
$34$	0.101885	−	0.0740235i	0.0174731	−	0.0126949i
$35$	−5.90710	+	0.325888i	−0.998482	+	0.0550851i
$36$	1.60739	+	1.16784i	0.267899	+	0.194640i
$37$	3.68100	+	1.63889i	0.605152	+	0.269431i	0.686355	−	0.727266i	$-0.259210\pi$
$37$	3.68100	+	1.63889i	0.605152	+	0.269431i	−0.0812030	+	0.996698i	$0.525876\pi$
$38$	0.0177567	+	0.168944i	0.00288052	+	0.0274063i
$39$	−1.41962	+	0.632057i	−0.227322	+	0.101210i
$40$	0.606848	−	0.822785i	0.0959511	−	0.130094i
$41$	−5.26454	+	3.82491i	−0.822184	+	0.597351i	−0.917337	−	0.398111i	$-0.869666\pi$
$41$	−5.26454	+	3.82491i	−0.822184	+	0.597351i	0.0951536	+	0.995463i	$0.469666\pi$
$42$	0.0188853	+	0.302830i	0.00291406	+	0.0467277i
$43$	−9.54777			−1.45602			−0.728011	−	0.685566i	$-0.759555\pi$
$43$	−9.54777			−1.45602			−0.728011	+	0.685566i	$0.759555\pi$
$44$	4.15219	−	0.882575i	0.625966	−	0.133053i
$45$	−1.65095	−	1.50810i	−0.246110	−	0.224814i
$46$	0.315749	+	0.0671144i	0.0465546	+	0.00989548i
$47$	−1.86347	+	2.06959i	−0.271815	+	0.301881i	−0.863562	−	0.504242i	$-0.831772\pi$
$47$	−1.86347	+	2.06959i	−0.271815	+	0.301881i	0.591747	+	0.806124i	$0.298438\pi$
$48$	3.17237	+	2.30486i	0.457892	+	0.332678i
$49$	5.10805	−	4.78621i	0.729721	−	0.683745i
$50$	−0.389754	+	0.420580i	−0.0551196	+	0.0594790i
$51$	−0.549070	−	0.951017i	−0.0768851	−	0.133169i
$52$	−2.82057	+	1.25580i	−0.391143	+	0.174148i
$53$	2.59581	+	0.551756i	0.356562	+	0.0757895i	0.382710	−	0.923869i	$-0.374991\pi$
$53$	2.59581	+	0.551756i	0.356562	+	0.0757895i	−0.0261483	+	0.999658i	$0.508324\pi$
$54$	−0.0767369	+	0.0852249i	−0.0104426	+	0.0115976i
$55$	−4.75470	+	0.465302i	−0.641124	+	0.0627413i
$56$	0.0752927	+	1.20734i	0.0100614	+	0.161337i
$57$	1.48127			0.196199
$58$	−0.240774	+	0.0511781i	−0.0316152	+	0.00672001i
$59$	−0.928642	−	8.83544i	−0.120899	−	1.15028i	−0.871800	−	0.489862i	$-0.837047\pi$
$59$	−0.928642	−	8.83544i	−0.120899	−	1.15028i	0.750901	−	0.660414i	$-0.229619\pi$
$60$	−3.28019	−	2.99636i	−0.423471	−	0.386828i
$61$	−0.721040	+	6.86024i	−0.0923197	+	0.878363i	0.846137	+	0.532966i	$0.178923\pi$
$61$	−0.721040	+	6.86024i	−0.0923197	+	0.878363i	−0.938456	+	0.345398i	$0.887744\pi$
$62$	0.142781	−	0.103736i	0.0181332	−	0.0131745i
$63$	2.64337	+	0.112246i	0.333033	+	0.0141417i
$64$	6.21817	+	4.51777i	0.777272	+	0.564721i
$65$	3.31233	−	1.05005i	0.410844	−	0.130242i
$66$	0.0256115	+	0.243678i	0.00315256	+	0.0299946i
$67$	−9.36005	−	10.3954i	−1.14351	−	1.27000i	−0.957813	−	0.287393i	$-0.907211\pi$
$67$	−9.36005	−	10.3954i	−1.14351	−	1.27000i	−0.185700	−	0.982607i	$-0.559455\pi$
$68$	−1.09092	−	1.88953i	−0.132293	−	0.229139i
$69$	0.869814	−	2.67701i	0.104713	−	0.322274i
$70$	0.0336426	−	0.677630i	0.00402106	−	0.0809923i
$71$	3.60505	+	11.0952i	0.427841	+	1.31676i	0.900247	+	0.435379i	$0.143386\pi$
$71$	3.60505	+	11.0952i	0.427841	+	1.31676i	−0.472406	+	0.881381i	$0.656614\pi$
$72$	−0.305938	+	0.339779i	−0.0360552	+	0.0400433i
$73$	−10.3165	+	4.59321i	−1.20746	+	0.537595i	−0.908987	−	0.416824i	$-0.863143\pi$
$73$	−10.3165	+	4.59321i	−1.20746	+	0.537595i	−0.298471	+	0.954419i	$0.596476\pi$
$74$	−0.231046	+	0.400184i	−0.0268586	+	0.0465204i
$75$	3.29204	+	3.76331i	0.380132	+	0.434550i
$76$	2.94306			0.337592
$77$	3.95722	−	4.03653i	0.450967	−	0.460006i
$78$	−0.0550704	−	0.169489i	−0.00623550	−	0.0191909i
$79$	2.99263	−	3.32365i	0.336697	−	0.373940i	−0.550892	−	0.834577i	$-0.685712\pi$
$79$	2.99263	−	3.32365i	0.336697	−	0.373940i	0.887589	+	0.460637i	$0.152379\pi$
$80$	−6.47382	−	5.91364i	−0.723795	−	0.661165i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	−0.373135	−	0.646289i	−0.0412059	−	0.0713707i
$83$	−0.0653066	+	0.200993i	−0.00716833	+	0.0220619i	−0.954577	−	0.297965i	$-0.903692\pi$
$83$	−0.0653066	+	0.200993i	−0.00716833	+	0.0220619i	0.947408	+	0.320027i	$0.103692\pi$
$84$	5.25197	+	0.223016i	0.573037	+	0.0243331i
$85$	0.982641	+	2.25033i	0.106582	+	0.244082i
$86$	0.114454	−	1.08895i	0.0123419	−	0.117425i
$87$	0.224360	+	2.13465i	0.0240540	+	0.228858i
$88$	0.102109	+	0.971506i	0.0108849	+	0.103563i
$89$	−0.653077	+	6.21361i	−0.0692260	+	0.658642i	0.903801	+	0.427952i	$0.140765\pi$
$89$	−0.653077	+	6.21361i	−0.0692260	+	0.658642i	−0.973027	+	0.230689i	$0.925902\pi$
$90$	0.191794	−	0.170218i	0.0202169	−	0.0179426i
$91$	−2.20492	+	3.47017i	−0.231138	+	0.363773i
$92$	1.72819	−	5.31881i	0.180176	−	0.554525i
$93$	−0.769464	−	1.33275i	−0.0797897	−	0.138200i
$94$	−0.213706	−	0.237344i	−0.0220421	−	0.0244802i
$95$	−3.29151	−	0.369828i	−0.337702	−	0.0379435i
$96$	−0.912782	+	1.01375i	−0.0931604	+	0.103465i
$97$	−5.03322	−	15.4907i	−0.511046	−	1.57284i	−0.790363	−	0.612639i	$-0.790108\pi$
$97$	−5.03322	−	15.4907i	−0.511046	−	1.57284i	0.279317	−	0.960199i	$-0.409892\pi$
$98$	0.484651	+	0.639964i	0.0489571	+	0.0646461i
$99$	2.13653			0.214729
$100$	6.54077	+	7.47713i	0.654077	+	0.747713i
$101$	4.70206	−	8.14421i	0.467872	−	0.810379i	−0.531454	−	0.847087i	$-0.678354\pi$
$101$	4.70206	−	8.14421i	0.467872	−	0.810379i	0.999326	+	0.0367086i	$0.0116873\pi$
$102$	0.115048	−	0.0512229i	0.0113915	−	0.00507182i
$103$	−3.70615	+	4.11610i	−0.365178	+	0.405571i	−0.897531	−	0.440951i	$-0.854641\pi$
$103$	−3.70615	+	4.11610i	−0.365178	+	0.405571i	0.532353	+	0.846522i	$0.321308\pi$
$104$	−0.219557	−	0.675728i	−0.0215294	−	0.0662606i
$105$	−5.84577	−	0.909388i	−0.570489	−	0.0887472i
$106$	−0.0940467	+	0.289446i	−0.00913463	+	0.0281135i
$107$	−5.67715	−	9.83312i	−0.548831	−	0.950603i	−0.998355	−	0.0573350i	$-0.981740\pi$
$107$	−5.67715	−	9.83312i	−0.548831	−	0.950603i	0.449524	−	0.893268i	$-0.351594\pi$
$108$	1.32946	+	1.47652i	0.127927	+	0.142078i
$109$	−0.523405	−	4.97987i	−0.0501332	−	0.476985i	−0.990569	−	0.137014i	$-0.956249\pi$
$109$	−0.523405	−	4.97987i	−0.0501332	−	0.476985i	0.940436	−	0.339971i	$-0.110417\pi$
$110$	0.00392767	−	0.547867i	0.000374489	−	0.0522371i
$111$	3.25982	+	2.36839i	0.309408	+	0.224798i
$112$	10.3653	+	0.440147i	0.979433	+	0.0415900i
$113$	−14.5118	+	10.5434i	−1.36516	+	0.991844i	−0.367058	+	0.930198i	$0.619635\pi$
$113$	−14.5118	+	10.5434i	−1.36516	+	0.991844i	−0.998098	+	0.0616463i	$0.980365\pi$
$114$	−0.0177567	+	0.168944i	−0.00166307	+	0.0158230i
$115$	−2.60117	+	5.73138i	−0.242560	+	0.534454i
$116$	0.445770	+	4.24122i	0.0413887	+	0.393787i
$117$	−1.52001	+	0.323089i	−0.140525	+	0.0298696i
$118$	1.01884			0.0937920
$119$	−2.60169	−	1.29328i	−0.238497	−	0.118554i
$120$	0.764653	−	0.678635i	0.0698030	−	0.0619506i
$121$	−4.30603	+	4.78233i	−0.391457	+	0.434757i
$122$	−0.773789	−	0.164474i	−0.0700555	−	0.0148908i
$123$	−5.94474	+	2.64677i	−0.536020	+	0.238651i
$124$	−1.52881	−	2.64797i	−0.137291	−	0.237795i
$125$	−6.37560	−	9.18432i	−0.570251	−	0.821470i
$126$	−0.0444894	+	0.300139i	−0.00396343	+	0.0267385i
$127$	−3.40304	−	2.47245i	−0.301971	−	0.219395i	0.426473	−	0.904500i	$-0.359756\pi$
$127$	−3.40304	−	2.47245i	−0.301971	−	0.219395i	−0.728444	+	0.685106i	$0.759756\pi$
$128$	−2.41537	+	2.68254i	−0.213491	+	0.237105i
$129$	−9.33913	−	1.98509i	−0.822264	−	0.174778i
$130$	0.0800550	+	0.390369i	0.00702129	+	0.0342376i
$131$	−20.5168	+	4.36098i	−1.79256	+	0.381020i	−0.979545	−	0.201224i	$-0.935508\pi$
$131$	−20.5168	+	4.36098i	−1.79256	+	0.381020i	−0.813014	+	0.582244i	$0.802175\pi$
$132$	4.24495			0.369476
$133$	3.26548	−	2.16699i	0.283153	−	0.187902i
$134$	1.29783	−	0.942930i	0.112116	−	0.0814567i
$135$	−1.30133	−	1.81839i	−0.112000	−	0.156502i
$136$	0.458681	−	0.204218i	0.0393316	−	0.0175115i
$137$	0.313558	+	2.98330i	0.0267890	+	0.254881i	0.999717	+	0.0237736i	$0.00756810\pi$
$137$	0.313558	+	2.98330i	0.0267890	+	0.254881i	−0.972928	+	0.231107i	$0.925765\pi$
$138$	0.294895	+	0.131296i	0.0251031	+	0.0111766i
$139$	9.20763	+	6.68973i	0.780981	+	0.567416i	0.905273	−	0.424830i	$-0.139666\pi$
$139$	9.20763	+	6.68973i	0.780981	+	0.567416i	−0.124292	+	0.992246i	$0.539666\pi$
$140$	−11.6147	−	1.80682i	−0.981618	−	0.152704i
$141$	−2.25304	+	1.63693i	−0.189740	+	0.137855i
$142$	−1.30866	+	0.278164i	−0.109820	+	0.0233430i
$143$	−1.66005	+	2.87529i	−0.138820	+	0.240444i
$144$	2.62384	+	2.91407i	0.218653	+	0.242839i
$145$	0.0344069	−	4.79939i	0.00285734	−	0.398567i
$146$	−0.400202	−	1.23169i	−0.0331209	−	0.101936i
$147$	5.99153	−	3.61960i	0.494173	−	0.298540i
$148$	6.47676	+	4.70564i	0.532386	+	0.386801i
$149$	−5.05508	−	8.75566i	−0.414129	−	0.717292i	0.581208	−	0.813755i	$-0.302580\pi$
$149$	−5.05508	−	8.75566i	−0.414129	−	0.717292i	−0.995337	+	0.0964634i	$0.969247\pi$
$150$	−0.468681	+	0.330355i	−0.0382676	+	0.0269733i
$151$	−1.66515	+	2.88412i	−0.135508	+	0.234707i	−0.925791	−	0.378035i	$-0.876600\pi$
$151$	−1.66515	+	2.88412i	−0.135508	+	0.234707i	0.790283	+	0.612741i	$0.209933\pi$
$152$	−0.0707933	+	0.673554i	−0.00574210	+	0.0546324i
$153$	−0.339344	−	1.04439i	−0.0274343	−	0.0844342i
$154$	0.412943	+	0.499721i	0.0332759	+	0.0402687i
$155$	1.37707	+	3.15360i	0.110609	+	0.253303i
$156$	−3.02003	+	0.641928i	−0.241796	+	0.0513954i
$157$	−1.95530	+	3.38667i	−0.156050	+	0.270286i	−0.933441	−	0.358732i	$-0.883209\pi$
$157$	−1.95530	+	3.38667i	−0.156050	+	0.270286i	0.777391	+	0.629018i	$0.216543\pi$
$158$	0.343199	+	0.381161i	0.0273034	+	0.0303235i
$159$	2.42437	+	1.07940i	0.192265	+	0.0856018i
$160$	2.28138	−	2.02474i	0.180359	−	0.160070i
$161$	−1.99875	−	7.17396i	−0.157524	−	0.565387i
$162$	−0.0927793	+	0.0674081i	−0.00728943	+	0.00529608i
$163$	−20.2471	−	9.01457i	−1.58587	−	0.706076i	−0.590948	−	0.806709i	$-0.701246\pi$
$163$	−20.2471	−	9.01457i	−1.58587	−	0.706076i	−0.994924	+	0.100634i	$0.967913\pi$
$164$	−11.8113	+	5.25873i	−0.922308	+	0.410638i
$165$	−4.74754	−	0.533424i	−0.369596	−	0.0415270i
$166$	−0.0221410	−	0.00985783i	−0.00171848	−	0.000765116i
$167$	4.99235	−	15.3649i	0.386320	−	1.18897i	−0.549199	−	0.835692i	$-0.685067\pi$
$167$	4.99235	−	15.3649i	0.386320	−	1.18897i	0.935518	−	0.353278i	$-0.114933\pi$
$168$	−0.177372	+	1.19661i	−0.0136846	+	0.0923204i
$169$	−3.27100	+	10.0671i	−0.251615	+	0.774392i
$170$	−0.268436	+	0.0850976i	−0.0205881	+	0.00652669i
$171$	1.44890	+	0.307974i	0.110800	+	0.0235513i
$172$	−18.5554	−	3.94408i	−1.41484	−	0.300733i
$173$	−2.28097	+	21.7020i	−0.173419	+	1.64997i	0.468695	+	0.883360i	$0.344724\pi$
$173$	−2.28097	+	21.7020i	−0.173419	+	1.64997i	−0.642114	+	0.766609i	$0.721942\pi$
$174$	−0.246153			−0.0186608
$175$	12.7628	+	3.48025i	0.964774	+	0.263082i
$176$	8.37787			0.631506
$177$	0.928642	−	8.83544i	0.0698010	−	0.664112i
$178$	−0.700854	−	0.148971i	−0.0525312	−	0.0111659i
$179$	2.13570	+	0.453957i	0.159630	+	0.0339304i	0.287033	−	0.957921i	$-0.407331\pi$
$179$	2.13570	+	0.453957i	0.159630	+	0.0339304i	−0.127403	+	0.991851i	$0.540664\pi$
$180$	−2.58554	−	3.61287i	−0.192714	−	0.269287i
$181$	1.38946	−	4.27633i	0.103278	−	0.317857i	−0.886044	−	0.463600i	$-0.846557\pi$
$181$	1.38946	−	4.27633i	0.103278	−	0.317857i	0.989322	+	0.145743i	$0.0465574\pi$
$182$	−0.369353	−	0.293077i	−0.0273783	−	0.0217243i
$183$	−2.13161	+	6.56041i	−0.157573	+	0.484960i
$184$	1.17570	+	0.523456i	0.0866738	+	0.0385897i
$185$	−6.65227	−	6.07665i	−0.489085	−	0.446764i
$186$	0.161228	−	0.0717835i	0.0118218	−	0.00526342i
$187$	−2.14336	−	0.954287i	−0.156738	−	0.0697844i
$188$	−4.47645	+	3.25233i	−0.326479	+	0.237201i
$189$	2.56227	+	0.659381i	0.186378	+	0.0479629i
$190$	0.0816370	−	0.370975i	0.00592257	−	0.0269133i
$191$	15.5506	+	6.92355i	1.12520	+	0.500971i	0.883055	−	0.469270i	$-0.155483\pi$
$191$	15.5506	+	6.92355i	1.12520	+	0.500971i	0.242144	+	0.970240i	$0.422149\pi$
$192$	5.14299	+	5.71187i	0.371164	+	0.412219i
$193$	6.38090	−	11.0520i	0.459307	−	0.795544i	−0.539617	−	0.841911i	$-0.681431\pi$
$193$	6.38090	−	11.0520i	0.459307	−	0.795544i	0.998924	+	0.0463668i	$0.0147643\pi$
$194$	1.82709	−	0.388361i	0.131178	−	0.0278827i
$195$	3.45826	−	0.338431i	0.247651	−	0.0242355i
$196$	11.9043	−	7.19160i	0.850305	−	0.513686i
$197$	2.97095	+	9.14363i	0.211671	+	0.651457i	0.999373	+	0.0354003i	$0.0112706\pi$
$197$	2.97095	+	9.14363i	0.211671	+	0.651457i	−0.787702	+	0.616056i	$0.788729\pi$
$198$	−0.0256115	+	0.243678i	−0.00182013	+	0.0173174i
$199$	6.04814	−	10.4757i	0.428741	−	0.742601i	−0.568021	−	0.823014i	$-0.692291\pi$
$199$	6.04814	−	10.4757i	0.428741	−	0.742601i	0.996762	+	0.0804132i	$0.0256240\pi$
$200$	−1.86856	+	1.31707i	−0.132127	+	0.0931312i
$201$	−6.99419	−	12.1143i	−0.493332	−	0.854476i
$202$	0.872507	+	0.633914i	0.0613894	+	0.0446020i
$203$	3.61743	+	4.37762i	0.253894	+	0.307249i
$204$	−0.674225	−	2.07505i	−0.0472052	−	0.145283i
$205$	13.8706	−	4.39713i	0.968761	−	0.307109i
$206$	−0.425027	−	0.472040i	−0.0296130	−	0.0328886i
$207$	1.40739	−	2.43767i	0.0978202	−	0.169430i
$208$	−5.96037	+	1.26692i	−0.413277	+	0.0878448i
$209$	2.56036	−	1.86021i	0.177104	−	0.128673i
$210$	0.173795	−	0.655828i	0.0119930	−	0.0452564i
$211$	11.4658	+	8.33039i	0.789338	+	0.573488i	0.907767	−	0.419475i	$-0.137786\pi$
$211$	11.4658	+	8.33039i	0.789338	+	0.573488i	−0.118429	+	0.992963i	$0.537786\pi$
$212$	4.81685	+	2.14460i	0.330823	+	0.147292i
$213$	1.21945	+	11.6023i	0.0835553	+	0.794976i
$214$	1.18955	−	0.529623i	0.0813162	−	0.0362043i
$215$	20.2567	+	6.74274i	1.38150	+	0.459851i
$216$	−0.369897	+	0.268746i	−0.0251683	+	0.0182858i
$217$	−3.64600	−	1.81239i	−0.247507	−	0.123033i
$218$	0.574245			0.0388928
$219$	−11.0461	+	2.34791i	−0.746424	+	0.158657i
$220$	−9.43265	−	1.05983i	−0.635949	−	0.0714539i
$221$	1.66919	+	0.354796i	0.112282	+	0.0238662i
$222$	−0.309200	+	0.343401i	−0.0207521	+	0.0230476i
$223$	7.35881	+	5.34649i	0.492783	+	0.358028i	0.806253	−	0.591570i	$-0.201492\pi$
$223$	7.35881	+	5.34649i	0.492783	+	0.358028i	−0.313471	+	0.949598i	$0.601492\pi$
$224$	−0.529199	+	3.57014i	−0.0353586	+	0.238540i
$225$	2.43766	+	4.36553i	0.162511	+	0.291035i
$226$	−1.02855	−	1.78151i	−0.0684184	−	0.118504i
$227$	20.2316	−	9.00769i	1.34282	−	0.597861i	0.395592	−	0.918426i	$-0.370539\pi$
$227$	20.2316	−	9.00769i	1.34282	−	0.597861i	0.947227	+	0.320565i	$0.103873\pi$
$228$	2.87875	+	0.611897i	0.190650	+	0.0405239i
$229$	14.5720	−	16.1838i	0.962942	−	1.06946i	−0.0346015	−	0.999401i	$-0.511016\pi$
$229$	14.5720	−	16.1838i	0.962942	−	1.06946i	0.997543	−	0.0700539i	$-0.0223171\pi$
$230$	−0.622501	−	0.365376i	−0.0410465	−	0.0240922i
$231$	4.70999	−	3.12557i	0.309894	−	0.205648i
$232$	−0.981374			−0.0644304
$233$	25.7724	−	5.47809i	1.68840	−	0.358881i	0.739186	−	0.673501i	$-0.235210\pi$
$233$	25.7724	−	5.47809i	1.68840	−	0.358881i	0.949218	+	0.314620i	$0.101877\pi$
$234$	−0.0186282	−	0.177235i	−0.00121776	−	0.0115862i
$235$	5.41515	−	3.07489i	0.353245	−	0.200584i
$236$	1.84507	−	17.5547i	0.120104	−	1.14271i
$237$	3.61826	−	2.62882i	0.235031	−	0.170760i
$238$	0.178690	−	0.281228i	0.0115828	−	0.0182293i
$239$	19.7391	+	14.3413i	1.27682	+	0.927661i	0.999452	−	0.0331036i	$-0.0105391\pi$
$239$	19.7391	+	14.3413i	1.27682	+	0.927661i	0.277364	+	0.960765i	$0.410539\pi$
$240$	−5.10284	−	7.13039i	−0.329387	−	0.460265i
$241$	2.91975	+	27.7796i	0.188078	+	1.78944i	0.528261	+	0.849082i	$0.322844\pi$
$241$	2.91975	+	27.7796i	0.188078	+	1.78944i	−0.340183	+	0.940359i	$0.610489\pi$
$242$	−0.493822	−	0.548445i	−0.0317441	−	0.0352554i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.23518	+	13.0345i	−0.271130	+	0.834451i
$245$	−14.2174	+	6.54716i	−0.908317	+	0.418283i
$246$	−0.230610	−	0.709745i	−0.0147032	−	0.0452517i
$247$	−1.54024	+	1.71061i	−0.0980031	+	0.108844i
$248$	0.642793	−	0.286190i	0.0408174	−	0.0181731i
$249$	−0.105668	+	0.183023i	−0.00669646	+	0.0115986i
$250$	1.12393	−	0.617061i	0.0710835	−	0.0390264i
$251$	7.15044			0.451332			0.225666	−	0.974205i	$-0.427544\pi$
$251$	7.15044			0.451332			0.225666	+	0.974205i	$0.427544\pi$
$252$	5.09084	+	1.31009i	0.320693	+	0.0825279i
$253$	−1.85838	−	5.71950i	−0.116835	−	0.359582i
$254$	0.322785	−	0.358489i	0.0202533	−	0.0224936i
$255$	0.493299	+	2.40545i	0.0308916	+	0.150635i
$256$	10.0090	+	11.1161i	0.625562	+	0.694757i
$257$	4.70166	+	8.14352i	0.293282	+	0.507979i	0.974584	−	0.224024i	$-0.0719193\pi$
$257$	4.70166	+	8.14352i	0.293282	+	0.507979i	−0.681302	+	0.732002i	$0.738586\pi$
$258$	0.338359	−	1.04136i	0.0210653	−	0.0648323i
$259$	10.6511	+	0.452280i	0.661825	+	0.0281033i
$260$	6.87104	−	0.672410i	0.426124	−	0.0417011i
$261$	−0.224360	+	2.13465i	−0.0138876	+	0.132131i
$262$	−0.251439	−	2.39228i	−0.0155340	−	0.147796i
$263$	1.13676	+	10.8155i	0.0700956	+	0.666915i	0.972000	+	0.234980i	$0.0755024\pi$
$263$	1.13676	+	10.8155i	0.0700956	+	0.666915i	−0.901905	+	0.431935i	$0.857831\pi$
$264$	−0.102109	+	0.971506i	−0.00628440	+	0.0597920i
$265$	−5.11766	−	3.00380i	−0.314375	−	0.184522i
$266$	0.208007	+	0.398415i	0.0127537	+	0.0244284i
$267$	−1.93069	+	5.94205i	−0.118156	+	0.363647i
$268$	−13.8964	−	24.0693i	−0.848857	−	1.47026i
$269$	−19.6335	−	21.8052i	−1.19707	−	1.32948i	−0.930774	−	0.365595i	$-0.880866\pi$
$269$	−19.6335	−	21.8052i	−1.19707	−	1.32948i	−0.266299	−	0.963890i	$-0.585801\pi$
$270$	0.222993	−	0.126622i	0.0135709	−	0.00770600i
$271$	−8.97386	+	9.96648i	−0.545123	+	0.605420i	−0.951259	−	0.308392i	$-0.900209\pi$
$271$	−8.97386	+	9.96648i	−0.545123	+	0.605420i	0.406136	+	0.913813i	$0.366876\pi$
$272$	−1.33066	−	4.09534i	−0.0806829	−	0.248316i
$273$	−2.87822	+	2.93591i	−0.174198	+	0.177690i
$274$	−0.344014			−0.0207826
$275$	10.4163	+	2.37063i	0.628125	+	0.142954i
$276$	2.79627	−	4.84327i	0.168315	−	0.291531i
$277$	−4.23193	+	1.88418i	−0.254272	+	0.113209i	−0.529915	−	0.848051i	$-0.677776\pi$
$277$	−4.23193	+	1.88418i	−0.254272	+	0.113209i	0.275643	+	0.961260i	$0.411109\pi$
$278$	−0.873362	+	0.969967i	−0.0523808	+	0.0581747i
$279$	−0.475555	−	1.46361i	−0.0284707	−	0.0876239i
$280$	0.692893	−	2.61468i	0.0414083	−	0.156257i
$281$	6.39924	−	19.6948i	0.381747	−	1.17490i	−0.557066	−	0.830468i	$-0.688073\pi$
$281$	6.39924	−	19.6948i	0.381747	−	1.17490i	0.938813	−	0.344427i	$-0.111927\pi$
$282$	−0.159689	−	0.276590i	−0.00950934	−	0.0164707i
$283$	−5.39944	−	5.99668i	−0.320963	−	0.356466i	0.560973	−	0.827834i	$-0.310427\pi$
$283$	−5.39944	−	5.99668i	−0.320963	−	0.356466i	−0.881937	+	0.471368i	$0.843760\pi$
$284$	2.42286	+	23.0520i	0.143770	+	1.36788i
$285$	−3.14270	−	1.04609i	−0.186157	−	0.0619650i
$286$	−0.308036	−	0.223801i	−0.0182146	−	0.0132337i
$287$	−9.23321	+	14.5315i	−0.545019	+	0.857770i
$288$	−1.10361	+	0.801816i	−0.0650306	+	0.0472475i
$289$	1.65093	−	15.7076i	0.0971136	−	0.923975i
$290$	0.546973	+	0.0614567i	0.0321194	+	0.00360886i
$291$	−1.70254	−	16.1986i	−0.0998048	−	0.949579i
$292$	−21.9469	+	4.66495i	−1.28434	+	0.272995i
$293$	−12.4659			−0.728268			−0.364134	−	0.931346i	$-0.618635\pi$
$293$	−12.4659			−0.728268			−0.364134	+	0.931346i	$0.618635\pi$
$294$	0.341004	+	0.726744i	0.0198877	+	0.0423846i
$295$	−4.26946	+	19.4012i	−0.248577	+	1.12958i
$296$	−1.23273	+	1.36909i	−0.0716512	+	0.0795767i
$297$	2.08984	+	0.444209i	0.121265	+	0.0257756i
$298$	1.05921	−	0.471590i	0.0613583	−	0.0273185i
$299$	2.18704	+	3.78806i	0.126480	+	0.219069i
$300$	4.84326	+	8.67364i	0.279626	+	0.500773i
$301$	−23.4922	+	9.28629i	−1.35407	+	0.535253i
$302$	−0.308983	−	0.224489i	−0.0177799	−	0.0129179i
$303$	6.29258	−	6.98862i	0.361500	−	0.401486i
$304$	5.68153	+	1.20765i	0.325858	+	0.0692632i
$305$	6.37454	−	14.0456i	0.365005	−	0.804249i
$306$	0.123184	−	0.0261836i	0.00704197	−	0.00149682i
$307$	−1.30687			−0.0745868			−0.0372934	−	0.999304i	$-0.511874\pi$
$307$	−1.30687			−0.0745868			−0.0372934	+	0.999304i	$0.511874\pi$
$308$	9.35803	−	6.21004i	0.533223	−	0.353850i
$309$	−4.48095	+	3.25560i	−0.254912	+	0.185205i
$310$	−0.376186	+	0.119255i	−0.0213659	+	0.00677325i
$311$	9.61945	−	4.28286i	0.545469	−	0.242859i	−0.115453	−	0.993313i	$-0.536832\pi$
$311$	9.61945	−	4.28286i	0.545469	−	0.242859i	0.660922	+	0.750454i	$0.270165\pi$
$312$	−0.0742677	−	0.706610i	−0.00420458	−	0.0400039i
$313$	11.7832	+	5.24622i	0.666027	+	0.296534i	0.711763	−	0.702419i	$-0.247897\pi$
$313$	11.7832	+	5.24622i	0.666027	+	0.296534i	−0.0457368	+	0.998954i	$0.514564\pi$
$314$	−0.362822	−	0.263606i	−0.0204752	−	0.0148761i
$315$	−5.52895	−	2.10492i	−0.311521	−	0.118599i
$316$	7.18893	−	5.22306i	0.404409	−	0.293820i
$317$	13.4591	−	2.86082i	0.755939	−	0.160680i	0.186207	−	0.982511i	$-0.440381\pi$
$317$	13.4591	−	2.86082i	0.755939	−	0.160680i	0.569732	+	0.821831i	$0.307047\pi$
$318$	−0.152171	+	0.263568i	−0.00853332	+	0.0147801i
$319$	3.06853	+	3.40795i	0.171805	+	0.190809i
$320$	−10.0021	−	13.9763i	−0.559134	−	0.781300i
$321$	−3.50867	−	10.7986i	−0.195835	−	0.602718i
$322$	0.842174	−	0.141967i	0.0469325	−	0.00791149i
$323$	−1.31598	−	0.956117i	−0.0732232	−	0.0531998i
$324$	0.993424	+	1.72066i	0.0551902	+	0.0955923i
$325$	−7.76905	−	0.111399i	−0.430950	−	0.00617929i
$326$	1.27085	−	2.20118i	0.0703860	−	0.121912i
$327$	0.523405	−	4.97987i	0.0289444	−	0.275387i
$328$	−0.919408	−	2.82965i	−0.0507658	−	0.156241i
$329$	−2.57214	+	6.90466i	−0.141807	+	0.380666i
$330$	0.117750	−	0.535078i	0.00648191	−	0.0294551i
$331$	−3.58462	+	0.761934i	−0.197028	+	0.0418797i	−0.305369	−	0.952234i	$-0.598780\pi$
$331$	−3.58462	+	0.761934i	−0.197028	+	0.0418797i	0.108340	+	0.994114i	$0.465446\pi$
$332$	−0.209947	+	0.363639i	−0.0115223	+	0.0199573i
$333$	2.69616	+	2.99439i	0.147749	+	0.164092i
$334$	1.69257	+	0.753580i	0.0926132	+	0.0412341i
$335$	12.5171	+	28.6652i	0.683884	+	1.56615i
$336$	10.0473	+	2.58561i	0.548126	+	0.141056i
$337$	−8.31014	+	6.03767i	−0.452682	+	0.328893i	−0.790654	−	0.612263i	$-0.790259\pi$
$337$	−8.31014	+	6.03767i	−0.452682	+	0.328893i	0.337972	+	0.941156i	$0.390259\pi$
$338$	−1.10897	−	0.493747i	−0.0603203	−	0.0268563i
$339$	−16.3868	+	7.29587i	−0.890009	+	0.396257i
$340$	0.980109	+	4.77927i	0.0531539	+	0.259192i
$341$	−3.00370	−	1.33733i	−0.162659	−	0.0724207i
$342$	−0.0524941	+	0.161560i	−0.00283856	+	0.00873618i
$343$	7.91318	−	16.7446i	0.427272	−	0.904123i
$344$	1.34899	−	4.15175i	0.0727324	−	0.223847i
$345$	−3.73595	+	5.06533i	−0.201137	+	0.272708i
$346$	−2.44784	−	0.520303i	−0.131596	−	0.0279717i
$347$	10.0609	+	2.13850i	0.540096	+	0.114801i	0.469879	−	0.882731i	$-0.344298\pi$
$347$	10.0609	+	2.13850i	0.540096	+	0.114801i	0.0702169	+	0.997532i	$0.477631\pi$
$348$	−0.445770	+	4.24122i	−0.0238958	+	0.227353i
$349$	7.88396			0.422019			0.211009	−	0.977484i	$-0.432325\pi$
$349$	7.88396			0.422019			0.211009	+	0.977484i	$0.432325\pi$
$350$	−0.549926	+	1.41391i	−0.0293948	+	0.0755769i
$351$	−1.55397			−0.0829448
$352$	−0.304648	+	2.89853i	−0.0162378	+	0.154492i
$353$	−1.09277	−	0.232276i	−0.0581625	−	0.0123628i	0.178739	−	0.983897i	$-0.442798\pi$
$353$	−1.09277	−	0.232276i	−0.0581625	−	0.0123628i	−0.236901	+	0.971534i	$0.576132\pi$
$354$	0.996578	+	0.211829i	0.0529675	+	0.0112586i
$355$	0.187009	−	26.0858i	0.00992543	−	1.38449i
$356$	−3.83598	+	11.8059i	−0.203307	+	0.625714i
$357$	−2.27595	−	1.80594i	−0.120456	−	0.0955803i
$358$	−0.0773770	+	0.238142i	−0.00408950	+	0.0125862i
$359$	32.1396	+	14.3095i	1.69627	+	0.755226i	0.999272	+	0.0381479i	$0.0121458\pi$
$359$	32.1396	+	14.3095i	1.69627	+	0.755226i	0.696993	+	0.717078i	$0.254521\pi$
$360$	0.889040	−	0.504824i	0.0468565	−	0.0266066i
$361$	−15.3529	+	6.83555i	−0.808047	+	0.359766i
$362$	0.471073	+	0.209735i	0.0247590	+	0.0110234i
$363$	−5.20623	+	3.78255i	−0.273256	+	0.198532i
$364$	−5.71859	+	5.83322i	−0.299736	+	0.305744i
$365$	25.1315	−	2.45941i	1.31544	−	0.128731i
$366$	−0.722684	−	0.321759i	−0.0377753	−	0.0168186i
$367$	14.9391	+	16.5916i	0.779816	+	0.866073i	0.993848	−	0.110754i	$-0.0353264\pi$
$367$	14.9391	+	16.5916i	0.779816	+	0.866073i	−0.214032	+	0.976827i	$0.568660\pi$
$368$	5.51874	−	9.55873i	0.287684	−	0.498283i
$369$	−6.36513	+	1.35295i	−0.331356	+	0.0704318i
$370$	0.772806	−	0.685870i	0.0401763	−	0.0356567i
$371$	6.92361	−	1.16712i	0.359456	−	0.0605941i
$372$	−0.944855	−	2.90797i	−0.0489885	−	0.150771i
$373$	−1.28370	+	12.2136i	−0.0664677	+	0.632397i	0.909683	+	0.415303i	$0.136325\pi$
$373$	−1.28370	+	12.2136i	−0.0664677	+	0.632397i	−0.976151	+	0.217094i	$0.930342\pi$
$374$	0.134533	−	0.233018i	0.00695654	−	0.0120491i
$375$	−4.32676	−	10.3092i	−0.223433	−	0.532364i
$376$	−0.636656	−	1.10272i	−0.0328330	−	0.0568685i
$377$	−2.69844	−	1.96053i	−0.138977	−	0.100972i
$378$	−0.105920	+	0.284331i	−0.00544792	+	0.0146244i
$379$	−6.12572	−	18.8530i	−0.314657	−	0.968416i	−0.975895	−	0.218239i	$-0.929969\pi$
$379$	−6.12572	−	18.8530i	−0.314657	−	0.968416i	0.661238	−	0.750176i	$-0.270031\pi$
$380$	−6.24406	−	2.07842i	−0.320313	−	0.106621i
$381$	−2.81462	−	3.12595i	−0.144197	−	0.160148i
$382$	−0.976066	+	1.69060i	−0.0499399	+	0.0864984i
$383$	32.9351	−	7.00057i	1.68290	−	0.357712i	0.735444	−	0.677585i	$-0.236974\pi$
$383$	32.9351	−	7.00057i	1.68290	−	0.357712i	0.947460	+	0.319873i	$0.103640\pi$
$384$	−2.92032	+	2.12174i	−0.149027	+	0.108274i
$385$	−11.2464	+	5.76936i	−0.573167	+	0.294034i
$386$	1.18403	+	0.860249i	0.0602656	+	0.0437855i
$387$	−8.72232	−	3.88343i	−0.443381	−	0.197406i
$388$	−3.38269	−	32.1842i	−0.171730	−	1.63390i
$389$	−0.801804	+	0.356986i	−0.0406531	+	0.0180999i	−0.426962	−	0.904269i	$-0.640416\pi$
$389$	−0.801804	+	0.356986i	−0.0406531	+	0.0180999i	0.386309	+	0.922369i	$0.373750\pi$
$390$	−0.00285673	+	0.398483i	−0.000144656	+	0.0201780i
$391$	−2.50069	+	1.81685i	−0.126465	+	0.0918823i
$392$	1.35953	+	2.89742i	0.0686667	+	0.146342i
$393$	−20.9751			−1.05806
$394$	−1.07847	+	0.229237i	−0.0543328	+	0.0115488i
$395$	−8.69641	+	4.93809i	−0.437564	+	0.248462i
$396$	4.15219	+	0.882575i	0.208655	+	0.0443511i
$397$	−19.8499	+	22.0455i	−0.996236	+	1.10643i	−0.00191595	+	0.999998i	$0.500610\pi$
$397$	−19.8499	+	22.0455i	−0.996236	+	1.10643i	−0.994320	+	0.106434i	$0.966057\pi$
$398$	1.12228	+	0.815386i	0.0562550	+	0.0408716i
$399$	3.64466	−	1.44070i	0.182461	−	0.0721254i
$400$	9.55871	+	17.1184i	0.477935	+	0.855918i
$401$	13.8130	+	23.9248i	0.689787	+	1.19475i	0.971907	+	0.235367i	$0.0756293\pi$
$401$	13.8130	+	23.9248i	0.689787	+	1.19475i	−0.282119	+	0.959379i	$0.591037\pi$
$402$	1.46552	−	0.652490i	0.0730933	−	0.0325433i
$403$	2.33919	+	0.497210i	0.116523	+	0.0247678i
$404$	12.5024	−	13.8853i	0.622018	−	0.690821i
$405$	−0.894823	−	2.04922i	−0.0444641	−	0.101826i
$406$	−0.542646	+	0.360103i	−0.0269311	+	0.0178716i
$407$	8.60882			0.426723
$408$	0.491117	−	0.104390i	0.0243139	−	0.00516808i
$409$	−0.692417	−	6.58791i	−0.0342378	−	0.325751i	−0.998213	−	0.0597584i	$-0.980967\pi$
$409$	−0.692417	−	6.58791i	−0.0342378	−	0.325751i	0.963975	−	0.265993i	$-0.0856997\pi$
$410$	0.335234	+	1.63469i	0.0165560	+	0.0807317i
$411$	−0.313558	+	2.98330i	−0.0154667	+	0.147155i
$412$	−8.90296	+	6.46838i	−0.438618	+	0.318674i
$413$	−10.8784	−	20.8363i	−0.535290	−	1.02529i
$414$	0.261153	+	0.189739i	0.0128350	+	0.00932514i
$415$	0.280499	−	0.380310i	0.0137692	−	0.0186687i
$416$	−0.221581	−	2.10821i	−0.0108639	−	0.103363i
$417$	7.61554	+	8.45792i	0.372935	+	0.414186i
$418$	0.181471	+	0.314316i	0.00887601	+	0.0153737i
$419$	−3.98611	+	12.2680i	−0.194734	+	0.599330i	0.805245	+	0.592942i	$0.202034\pi$
$419$	−3.98611	+	12.2680i	−0.194734	+	0.599330i	−0.999980	+	0.00638867i	$0.997966\pi$
$420$	−10.9852	−	4.18216i	−0.536022	−	0.204068i
$421$	−5.68104	−	17.4844i	−0.276877	−	0.852140i	−0.988717	−	0.149798i	$-0.952138\pi$
$421$	−5.68104	−	17.4844i	−0.276877	−	0.852140i	0.711840	−	0.702342i	$-0.247862\pi$
$422$	−1.08755	+	1.20785i	−0.0529413	+	0.0587973i
$423$	−2.54415	+	1.13273i	−0.123701	+	0.0550751i
$424$	−0.606682	+	1.05080i	−0.0294631	+	0.0510316i
$425$	−0.495585	−	5.46829i	−0.0240394	−	0.265251i
$426$	−1.33790			−0.0648213
$427$	4.89824	+	17.5809i	0.237043	+	0.850797i
$428$	−6.97120	−	21.4551i	−0.336966	−	1.03707i
$429$	−2.22158	+	2.46731i	−0.107259	+	0.119123i
$430$	−1.01186	+	2.22952i	−0.0487961	+	0.107517i
$431$	−8.92738	−	9.91486i	−0.430017	−	0.477582i	0.488727	−	0.872437i	$-0.337461\pi$
$431$	−8.92738	−	9.91486i	−0.430017	−	0.477582i	−0.918743	+	0.394855i	$0.870795\pi$
$432$	1.96063	+	3.39591i	0.0943309	+	0.163386i
$433$	12.0663	−	37.1363i	0.579870	−	1.78466i	−0.0390903	−	0.999236i	$-0.512446\pi$
$433$	12.0663	−	37.1363i	0.579870	−	1.78466i	0.618961	−	0.785422i	$-0.287554\pi$
$434$	0.250415	−	0.394112i	0.0120203	−	0.0189180i
$435$	1.03150	−	4.68735i	0.0494568	−	0.224741i
$436$	1.03993	−	9.89425i	0.0498035	−	0.473848i
$437$	−0.435826	−	4.14661i	−0.0208484	−	0.198359i
$438$	−0.135373	−	1.28799i	−0.00646836	−	0.0615423i
$439$	1.69665	−	16.1425i	0.0809767	−	0.770442i	−0.876397	−	0.481589i	$-0.840060\pi$
$439$	1.69665	−	16.1425i	0.0809767	−	0.770442i	0.957374	−	0.288852i	$-0.0932737\pi$
$440$	0.469451	−	2.13328i	0.0223802	−	0.101700i
$441$	6.61316	−	2.29479i	0.314913	−	0.109276i
$442$	−0.0604750	+	0.186123i	−0.00287650	+	0.00885296i
$443$	12.0420	+	20.8574i	0.572135	+	0.990967i	0.996346	+	0.0854038i	$0.0272180\pi$
$443$	12.0420	+	20.8574i	0.572135	+	0.990967i	−0.424211	+	0.905563i	$0.639449\pi$
$444$	5.35687	+	5.94940i	0.254226	+	0.282346i
$445$	5.77370	−	12.7217i	0.273700	−	0.603067i
$446$	−0.697998	+	0.775206i	−0.0330512	+	0.0367071i
$447$	−3.12421	−	9.61534i	−0.147770	−	0.454790i
$448$	19.6938	+	5.06806i	0.930445	+	0.239443i
$449$	−29.6674			−1.40009			−0.700046	−	0.714098i	$-0.746837\pi$
$449$	−29.6674			−1.40009			−0.700046	+	0.714098i	$0.746837\pi$
$450$	−0.527124	+	0.225691i	−0.0248488	+	0.0106392i
$451$	−6.95154	+	12.0404i	−0.327335	+	0.566961i
$452$	−32.5581	+	14.4958i	−1.53140	+	0.681825i
$453$	−2.22840	+	2.47489i	−0.104700	+	0.116281i
$454$	0.784830	+	2.41546i	0.0368339	+	0.113363i
$455$	7.12867	−	5.80525i	0.334197	−	0.272154i
$456$	−0.209286	+	0.644116i	−0.00980072	+	0.0301635i
$457$	8.05191	+	13.9463i	0.376652	+	0.652381i	0.990573	−	0.136987i	$-0.0437418\pi$
$457$	8.05191	+	13.9463i	0.376652	+	0.652381i	−0.613920	+	0.789368i	$0.710408\pi$
$458$	1.67113	+	1.85598i	0.0780869	+	0.0867243i
$459$	−0.114787	−	1.09212i	−0.00535779	−	0.0509760i
$460$	−7.42276	+	10.0640i	−0.346088	+	0.469238i
$461$	−23.2026	−	16.8577i	−1.08065	−	0.785139i	−0.102855	−	0.994696i	$-0.532798\pi$
$461$	−23.2026	−	16.8577i	−1.08065	−	0.785139i	−0.977796	+	0.209557i	$0.932798\pi$
$462$	0.300021	+	0.574657i	0.0139582	+	0.0267355i
$463$	4.95781	−	3.60206i	0.230409	−	0.167402i	−0.466591	−	0.884473i	$-0.654518\pi$
$463$	4.95781	−	3.60206i	0.230409	−	0.167402i	0.697000	+	0.717071i	$0.254518\pi$
$464$	−0.879776	+	8.37051i	−0.0408426	+	0.388591i
$465$	0.691307	+	3.37099i	0.0320586	+	0.156326i
$466$	0.315848	+	3.00509i	0.0146314	+	0.139208i
$467$	3.55841	−	0.756363i	0.164663	−	0.0350003i	−0.124842	−	0.992177i	$-0.539842\pi$
$467$	3.55841	−	0.756363i	0.164663	−	0.0350003i	0.289506	+	0.957176i	$0.406509\pi$
$468$	−3.08750			−0.142720
$469$	−33.1410	−	16.4741i	−1.53031	−	0.760702i
$470$	0.285787	+	0.654475i	0.0131824	+	0.0301887i
$471$	−2.61670	+	2.90614i	−0.120571	+	0.133908i
$472$	3.97321	+	0.844531i	0.182882	+	0.0388727i
$473$	−18.6355	+	8.29704i	−0.856859	+	0.381498i
$474$	0.256451	+	0.444187i	0.0117792	+	0.0204022i
$475$	6.72216	+	3.10914i	0.308434	+	0.142657i
$476$	−4.52197	−	3.58812i	−0.207264	−	0.164461i
$477$	2.14697	+	1.55986i	0.0983030	+	0.0714213i
$478$	−1.87229	+	2.07939i	−0.0856367	+	0.0951092i
$479$	−9.45703	−	2.01015i	−0.432103	−	0.0918463i	−0.0132749	−	0.999912i	$-0.504226\pi$
$479$	−9.45703	−	2.01015i	−0.432103	−	0.0918463i	−0.418828	+	0.908066i	$0.637559\pi$
$480$	2.65249	−	1.50617i	0.121069	−	0.0687469i
$481$	−6.12467	+	1.30184i	−0.279261	+	0.0593587i
$482$	−3.20335			−0.145909
$483$	−0.463526	−	7.43276i	−0.0210911	−	0.338202i
$484$	−10.3440	+	7.51535i	−0.470182	+	0.341607i
$485$	−0.261094	+	36.4198i	−0.0118557	+	1.65374i
$486$	−0.104767	+	0.0466452i	−0.00475232	+	0.00211587i
$487$	−3.23756	−	30.8034i	−0.146708	−	1.39583i	−0.781864	−	0.623450i	$-0.785731\pi$
$487$	−3.23756	−	30.8034i	−0.146708	−	1.39583i	0.635156	−	0.772384i	$-0.280936\pi$
$488$	−2.88123	−	1.28281i	−0.130427	−	0.0580699i
$489$	−17.9304	−	13.0272i	−0.810840	−	0.589110i
$490$	−0.576294	−	1.70003i	−0.0260343	−	0.0767993i
$491$	17.4571	−	12.6833i	0.787829	−	0.572391i	−0.119490	−	0.992835i	$-0.538126\pi$
$491$	17.4571	−	12.6833i	0.787829	−	0.572391i	0.907318	+	0.420444i	$0.138126\pi$
$492$	−12.6466	+	2.68811i	−0.570151	+	0.121189i
$493$	1.17853	−	2.04127i	0.0530782	−	0.0919341i
$494$	−0.176637	−	0.196175i	−0.00794728	−	0.00882634i
$495$	−4.53289	−	1.50884i	−0.203738	−	0.0678172i
$496$	−1.86478	−	5.73919i	−0.0837309	−	0.257697i
$497$	19.6616	+	23.7934i	0.881942	+	1.06728i
$498$	−0.0196077	−	0.0142458i	−0.000878640	−	0.000638369i
$499$	−14.3147	−	24.7938i	−0.640813	−	1.10992i	−0.985252	−	0.171112i	$-0.945264\pi$
$499$	−14.3147	−	24.7938i	−0.640813	−	1.10992i	0.344438	−	0.938809i	$-0.388069\pi$
$500$	−8.59661	−	20.4828i	−0.384452	−	0.916018i
$501$	8.07779	−	13.9911i	0.360889	−	0.625078i
$502$	−0.0857157	+	0.815531i	−0.00382568	+	0.0363989i
$503$	7.69924	+	23.6958i	0.343292	+	1.05654i	0.962492	+	0.271311i	$0.0874570\pi$
$503$	7.69924	+	23.6958i	0.343292	+	1.05654i	−0.619200	+	0.785233i	$0.712543\pi$
$504$	−0.422286	+	1.13358i	−0.0188101	+	0.0504938i
$505$	−15.7275	+	13.9583i	−0.699865	+	0.621134i
$506$	0.674605	−	0.143392i	0.0299898	−	0.00637454i
$507$	−5.29259	+	9.16703i	−0.235052	+	0.407122i
$508$	−5.59223	−	6.21080i	−0.248115	−	0.275560i
$509$	2.74864	+	1.22377i	0.121831	+	0.0542427i	0.466747	−	0.884391i	$-0.345426\pi$
$509$	2.74864	+	1.22377i	0.121831	+	0.0542427i	−0.344916	+	0.938634i	$0.612093\pi$
$510$	−0.280263	+	0.0274270i	−0.0124103	+	0.00121449i
$511$	−20.9163	+	21.3356i	−0.925283	+	0.943829i
$512$	−7.22845	+	5.25178i	−0.319455	+	0.232098i
$513$	1.35321	+	0.602488i	0.0597457	+	0.0266005i
$514$	−0.985155	+	0.438619i	−0.0434533	+	0.0193467i
$515$	10.7699	−	6.11547i	0.474577	−	0.269480i
$516$	−17.3299	−	7.71578i	−0.762908	−	0.339668i
$517$	−1.83866	+	5.65882i	−0.0808643	+	0.248875i
$518$	−0.179263	+	1.20937i	−0.00787638	+	0.0531365i
$519$	−6.74321	+	20.7535i	−0.295994	+	0.910976i
$520$	−0.0113894	+	1.58869i	−0.000499457	+	0.0696687i
$521$	−19.5824	−	4.16236i	−0.857919	−	0.182356i	−0.242107	−	0.970249i	$-0.577839\pi$
$521$	−19.5824	−	4.16236i	−0.857919	−	0.182356i	−0.615812	+	0.787893i	$0.711172\pi$
$522$	−0.240774	−	0.0511781i	−0.0105384	−	0.00224000i
$523$	−3.85291	+	36.6580i	−0.168476	+	1.60294i	0.504591	+	0.863359i	$0.331643\pi$
$523$	−3.85291	+	36.6580i	−0.168476	+	1.60294i	−0.673066	+	0.739582i	$0.735023\pi$
$524$	−41.6744			−1.82056
$525$	11.7603	+	6.05772i	0.513260	+	0.264381i
$526$	−1.24717			−0.0543794
$527$	−0.176649	+	1.68070i	−0.00769494	+	0.0732124i
$528$	8.19480	+	1.74186i	0.356633	+	0.0758046i
$529$	14.7476	+	3.13469i	0.641199	+	0.136291i
$530$	0.403941	−	0.547677i	0.0175461	−	0.0237896i
$531$	2.74534	−	8.44929i	0.119138	−	0.366668i
$532$	7.24138	−	2.86246i	0.313954	−	0.124103i
$533$	3.12484	−	9.61728i	0.135352	−	0.416570i
$534$	−0.654566	−	0.291431i	−0.0283258	−	0.0126115i
$535$	5.10050	+	24.8714i	0.220514	+	1.07528i
$536$	5.84279	−	2.60138i	0.252370	−	0.112362i
$537$	1.99465	+	0.888075i	0.0860754	+	0.0383232i
$538$	2.72231	−	1.97787i	0.117367	−	0.0852721i
$539$	5.81072	−	13.7807i	0.250285	−	0.593577i
$540$	−1.77788	−	4.07148i	−0.0765077	−	0.175209i
$541$	−27.1111	−	12.0706i	−1.16560	−	0.518956i	−0.269579	−	0.962978i	$-0.586885\pi$
$541$	−27.1111	−	12.0706i	−1.16560	−	0.518956i	−0.896016	+	0.444022i	$0.853551\pi$
$542$	−1.02914	−	1.14297i	−0.0442051	−	0.0490948i
$543$	2.24820	−	3.89400i	0.0964795	−	0.167107i
$544$	1.46527	−	0.311453i	0.0628230	−	0.0133534i
$545$	−2.40637	+	10.9350i	−0.103078	+	0.468405i
$546$	−0.300348	−	0.363465i	−0.0128537	−	0.0155549i
$547$	2.08920	+	6.42989i	0.0893276	+	0.274922i	0.985734	−	0.168311i	$-0.0538313\pi$
$547$	2.08920	+	6.42989i	0.0893276	+	0.274922i	−0.896406	+	0.443233i	$0.853831\pi$
$548$	−0.622992	+	5.92737i	−0.0266129	+	0.253205i
$549$	−3.44901	+	5.97386i	−0.147200	+	0.254958i
$550$	−0.395243	+	1.15959i	−0.0168532	+	0.0494451i
$551$	1.58971	+	2.75345i	0.0677237	+	0.117301i
$552$	1.04118	+	0.756459i	0.0443154	+	0.0321970i
$553$	4.13071	−	11.0885i	0.175656	−	0.471530i
$554$	−0.164166	−	0.505252i	−0.00697475	−	0.0214661i
$555$	−5.24350	−	7.32695i	−0.222574	−	0.311012i
$556$	15.1309	+	16.8046i	0.641694	+	0.712674i
$557$	2.55888	−	4.43211i	0.108423	−	0.187795i	−0.806708	−	0.590950i	$-0.798753\pi$
$557$	2.55888	−	4.43211i	0.108423	−	0.187795i	0.915132	+	0.403155i	$0.132086\pi$
$558$	0.172630	−	0.0366936i	0.00730801	−	0.00155336i
$559$	12.0033	−	8.72094i	0.507687	−	0.368857i
$560$	−21.6805	−	8.25394i	−0.916167	−	0.348793i
$561$	−1.89812	−	1.37906i	−0.0801386	−	0.0582241i
$562$	2.16955	+	0.965945i	0.0915169	+	0.0407459i
$563$	−2.54464	−	24.2106i	−0.107244	−	1.02036i	−0.907315	−	0.420451i	$-0.861872\pi$
$563$	−2.54464	−	24.2106i	−0.107244	−	1.02036i	0.800071	−	0.599905i	$-0.204795\pi$
$564$	−5.05483	+	2.25056i	−0.212847	+	0.0947655i
$565$	38.2344	−	12.1208i	1.60853	−	0.509925i
$566$	0.748667	−	0.543938i	0.0314688	−	0.0228634i
$567$	2.36918	+	1.17770i	0.0994963	+	0.0494586i
$568$	−5.33399			−0.223809
$569$	−41.2844	+	8.77527i	−1.73073	+	0.367879i	−0.962287	−	0.272037i	$-0.912303\pi$
$569$	−41.2844	+	8.77527i	−1.73073	+	0.367879i	−0.768446	+	0.639915i	$0.778970\pi$
$570$	0.156983	−	0.345895i	0.00657529	−	0.0144879i
$571$	−28.4015	−	6.03692i	−1.18856	−	0.252637i	−0.429143	−	0.903236i	$-0.641185\pi$
$571$	−28.4015	−	6.03692i	−1.18856	−	0.252637i	−0.759421	+	0.650599i	$0.774518\pi$
$572$	−4.41394	+	4.90218i	−0.184556	+	0.204970i
$573$	13.7713	+	10.0054i	0.575302	+	0.417982i
$574$	−1.54669	−	1.22727i	−0.0645574	−	0.0512254i
$575$	9.56625	−	10.3228i	0.398940	−	0.430492i
$576$	3.84304	+	6.65634i	0.160127	+	0.277348i
$577$	13.5927	−	6.05185i	0.565871	−	0.251942i	−0.103802	−	0.994598i	$-0.533101\pi$
$577$	13.5927	−	6.05185i	0.565871	−	0.251942i	0.669673	+	0.742656i	$0.266434\pi$
$578$	1.77171	+	0.376588i	0.0736934	+	0.0156640i
$579$	8.53931	−	9.48387i	0.354882	−	0.394136i
$580$	2.04944	−	9.31306i	0.0850984	−	0.386704i
$581$	0.0348020	+	0.558060i	0.00144383	+	0.0231522i
$582$	1.86791			0.0774275
$583$	5.54601	−	1.17884i	0.229692	−	0.0488226i
$584$	−0.539710	−	5.13500i	−0.0223334	−	0.212488i
$585$	3.45306	+	0.387978i	0.142766	+	0.0160409i
$586$	0.149435	−	1.42178i	0.00617311	−	0.0587333i
$587$	−10.6224	+	7.71760i	−0.438432	+	0.318539i	−0.785011	−	0.619481i	$-0.787343\pi$
$587$	−10.6224	+	7.71760i	−0.438432	+	0.318539i	0.346580	+	0.938021i	$0.387343\pi$
$588$	13.1394	−	4.55941i	0.541858	−	0.188027i
$589$	−1.84421	−	1.33990i	−0.0759894	−	0.0552096i
$590$	−2.16159	−	0.719517i	−0.0889915	−	0.0296221i
$591$	1.00496	+	9.56151i	0.0413383	+	0.393308i
$592$	10.5724	+	11.7418i	0.434521	+	0.482585i
$593$	7.34117	+	12.7153i	0.301466	+	0.522154i	0.976468	−	0.215661i	$-0.0691907\pi$
$593$	7.34117	+	12.7153i	0.301466	+	0.522154i	−0.675002	+	0.737816i	$0.735857\pi$
$594$	−0.0757153	+	0.233028i	−0.00310664	+	0.00956124i
$595$	4.60648	+	4.58118i	0.188847	+	0.187810i
$596$	−6.20734	−	19.1042i	−0.254262	−	0.782539i
$597$	8.09399	−	8.98928i	0.331265	−	0.367907i
$598$	−0.458258	+	0.204030i	−0.0187396	+	0.00834339i
$599$	−18.0452	+	31.2553i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$599$	−18.0452	+	31.2553i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$600$	−2.10156	+	0.899797i	−0.0857959	+	0.0367341i
$601$	9.48350			0.386840			0.193420	−	0.981116i	$-0.438042\pi$
$601$	9.48350			0.386840			0.193420	+	0.981116i	$0.438042\pi$
$602$	−0.777518	−	2.79068i	−0.0316893	−	0.113740i
$603$	−4.32265	−	13.3037i	−0.176032	−	0.541770i
$604$	−4.42750	+	4.91724i	−0.180152	+	0.200080i
$605$	12.5131	−	7.10532i	0.508729	−	0.288872i
$606$	0.721643	+	0.801466i	0.0293147	+	0.0325573i
$607$	1.47397	+	2.55299i	0.0598267	+	0.103623i	0.894387	−	0.447293i	$-0.147612\pi$
$607$	1.47397	+	2.55299i	0.0598267	+	0.103623i	−0.834561	+	0.550916i	$0.814279\pi$
$608$	−0.624415	+	1.92175i	−0.0253234	+	0.0779373i
$609$	2.62822	+	5.03407i	0.106501	+	0.203991i
$610$	1.52553	+	0.895409i	0.0617670	+	0.0362540i
$611$	0.452365	−	4.30397i	0.0183007	−	0.174120i
$612$	−0.228064	−	2.16988i	−0.00921894	−	0.0877124i
$613$	0.902863	+	8.59017i	0.0364663	+	0.346954i	0.997508	+	0.0705509i	$0.0224757\pi$
$613$	0.902863	+	8.59017i	0.0364663	+	0.346954i	−0.961042	+	0.276403i	$0.910858\pi$
$614$	0.0156660	−	0.149052i	0.000632230	−	0.00601526i
$615$	14.4817	−	1.41720i	0.583957	−	0.0571469i
$616$	1.19614	+	2.29107i	0.0481938	+	0.0923098i
$617$	12.8306	−	39.4885i	0.516541	−	1.58975i	−0.263921	−	0.964544i	$-0.585016\pi$
$617$	12.8306	−	39.4885i	0.516541	−	1.58975i	0.780461	−	0.625204i	$-0.214984\pi$
$618$	−0.317596	−	0.550093i	−0.0127756	−	0.0221280i
$619$	17.8749	+	19.8521i	0.718454	+	0.797924i	0.986199	−	0.165566i	$-0.0529450\pi$
$619$	17.8749	+	19.8521i	0.718454	+	0.797924i	−0.267745	+	0.963490i	$0.586278\pi$
$620$	1.37352	+	6.69765i	0.0551619	+	0.268984i
$621$	1.88345	−	2.09179i	0.0755804	−	0.0839405i
$622$	0.373161	+	1.14847i	0.0149624	+	0.0460495i
$623$	4.43655	+	15.9237i	0.177747	+	0.637971i
$624$	−6.09352			−0.243936
$625$	7.04054	+	23.9881i	0.281622	+	0.959526i
$626$	−0.739600	+	1.28102i	−0.0295604	+	0.0512000i
$627$	2.89117	−	1.28723i	0.115462	−	0.0514070i
$628$	−5.19898	+	5.77405i	−0.207462	+	0.230410i
$629$	−1.36734	−	4.20823i	−0.0545193	−	0.167793i
$630$	0.306351	−	0.605362i	0.0122053	−	0.0241182i
$631$	13.8725	−	42.6952i	0.552255	−	1.69967i	−0.150828	−	0.988560i	$-0.548194\pi$
$631$	13.8725	−	42.6952i	0.552255	−	1.69967i	0.703083	−	0.711107i	$-0.251806\pi$
$632$	1.02243	+	1.77091i	0.0406702	+	0.0704428i
$633$	9.48326	+	10.5322i	0.376926	+	0.418618i
$634$	0.164945	+	1.56935i	0.00655081	+	0.0623268i
$635$	5.47388	+	7.64886i	0.217224	+	0.303536i
$636$	4.26570	+	3.09921i	0.169146	+	0.122892i
$637$	−2.05005	+	10.6829i	−0.0812258	+	0.423271i
$638$	−0.425472	+	0.309123i	−0.0168446	+	0.0122383i
$639$	−1.21945	+	11.6023i	−0.0482407	+	0.458980i
$640$	7.01893	−	3.98557i	0.277448	−	0.157543i
$641$	−4.44125	−	42.2557i	−0.175419	−	1.66900i	−0.628713	−	0.777638i	$-0.716418\pi$
$641$	−4.44125	−	42.2557i	−0.175419	−	1.66900i	0.453294	−	0.891361i	$-0.350249\pi$
$642$	1.27367	−	0.270728i	0.0502679	−	0.0106848i
$643$	12.4114			0.489459			0.244730	−	0.969591i	$-0.421301\pi$
$643$	12.4114			0.489459			0.244730	+	0.969591i	$0.421301\pi$
$644$	−0.920955	−	14.7678i	−0.0362907	−	0.581931i
$645$	18.4122	+	10.8070i	0.724979	+	0.425525i
$646$	0.124824	−	0.138631i	0.00491112	−	0.00545435i
$647$	44.3005	+	9.41636i	1.74163	+	0.370195i	0.965506	−	0.260382i	$-0.0838485\pi$
$647$	44.3005	+	9.41636i	1.74163	+	0.370195i	0.776126	+	0.630577i	$0.217182\pi$
$648$	−0.417689	+	0.185967i	−0.0164084	+	0.00730548i
$649$	−9.49056	−	16.4381i	−0.372537	−	0.645253i
$650$	0.105837	−	0.884750i	0.00415126	−	0.0347028i
$651$	−3.18951	−	2.53083i	−0.125007	−	0.0991912i
$652$	−35.6249	−	25.8830i	−1.39518	−	1.01366i
$653$	0.119714	−	0.132956i	0.00468476	−	0.00520296i	−0.740798	−	0.671728i	$-0.765552\pi$
$653$	0.119714	−	0.132956i	0.00468476	−	0.00520296i	0.745483	+	0.666525i	$0.232219\pi$
$654$	0.561696	+	0.119392i	0.0219641	+	0.00466860i
$655$	46.6086	+	5.23684i	1.82115	+	0.204620i
$656$	−24.9594	+	5.30527i	−0.974499	+	0.207136i
$657$	−11.2928			−0.440576
$658$	−0.756665	−	0.376131i	−0.0294979	−	0.0146631i
$659$	−29.7455	+	21.6114i	−1.15872	+	0.841860i	−0.989616	−	0.143738i	$-0.954088\pi$
$659$	−29.7455	+	21.6114i	−1.15872	+	0.841860i	−0.169105	+	0.985598i	$0.554088\pi$
$660$	−9.00617	−	2.99783i	−0.350565	−	0.116690i
$661$	−13.0692	+	5.81878i	−0.508332	+	0.226324i	−0.644844	−	0.764314i	$-0.723078\pi$
$661$	−13.0692	+	5.81878i	−0.508332	+	0.226324i	0.136511	+	0.990638i	$0.456411\pi$
$662$	−0.0439305	−	0.417971i	−0.00170741	−	0.0162449i
$663$	1.55894	+	0.694086i	0.0605444	+	0.0269561i
$664$	−0.0781727	−	0.0567958i	−0.00303369	−	0.00220411i
$665$	−8.45845	+	2.29141i	−0.328004	+	0.0888571i
$666$	−0.373840	+	0.271611i	−0.0144860	+	0.0105247i
$667$	5.90963	−	1.25613i	0.228822	−	0.0486375i
$668$	16.0493	−	27.7983i	0.620968	−	1.07555i
$669$	6.08641	+	6.75964i	0.235314	+	0.261343i
$670$	−3.41941	+	1.08400i	−0.132103	+	0.0418784i
$671$	4.55423	+	14.0165i	0.175814	+	0.541100i
$672$	−1.25991	+	3.38210i	−0.0486021	+	0.130467i
$673$	13.6047	+	9.88440i	0.524423	+	0.381015i	0.818267	−	0.574838i	$-0.194935\pi$
$673$	13.6047	+	9.88440i	0.524423	+	0.381015i	−0.293845	+	0.955853i	$0.594935\pi$
$674$	−0.588998	−	1.02017i	−0.0226874	−	0.0392957i
$675$	1.47675	+	4.77695i	0.0568401	+	0.183865i
$676$	−10.5156	+	18.2135i	−0.404445	+	0.700519i
$677$	−0.412052	+	3.92041i	−0.0158364	+	0.150674i	−0.999583	−	0.0288913i	$-0.990802\pi$
$677$	−0.412052	+	3.92041i	−0.0158364	+	0.150674i	0.983746	+	0.179565i	$0.0574690\pi$
$678$	−0.635682	−	1.95643i	−0.0244132	−	0.0751361i
$679$	−27.4506	−	33.2193i	−1.05346	−	1.27484i
$680$	−1.11737	+	0.109347i	−0.0428491	+	0.00419327i
$681$	21.6623	−	4.60446i	0.830101	−	0.176443i
$682$	0.188534	−	0.326550i	0.00721934	−	0.0125043i
$683$	−5.49709	−	6.10514i	−0.210340	−	0.233607i	0.628738	−	0.777617i	$-0.283572\pi$
$683$	−5.49709	−	6.10514i	−0.210340	−	0.233607i	−0.839078	+	0.544011i	$0.816905\pi$
$684$	2.68862	+	1.19705i	0.102802	+	0.0457704i
$685$	1.44159	−	6.55087i	0.0550803	−	0.250296i
$686$	1.81492	+	1.10325i	0.0692938	+	0.0421223i
$687$	17.6183	−	12.8005i	0.672181	−	0.488368i
$688$	−34.2025	−	15.2279i	−1.30396	−	0.580560i
$689$	−3.76739	+	1.67735i	−0.143526	+	0.0639020i
$690$	−0.532932	−	0.486817i	−0.0202884	−	0.0185328i
$691$	−8.07718	−	3.59619i	−0.307270	−	0.136806i	0.247308	−	0.968937i	$-0.420454\pi$
$691$	−8.07718	−	3.59619i	−0.307270	−	0.136806i	−0.554579	+	0.832131i	$0.687121\pi$
$692$	−13.3977	+	41.2340i	−0.509306	+	1.56748i
$693$	5.25690	−	2.07801i	0.199693	−	0.0789372i
$694$	−0.364508	+	1.12184i	−0.0138365	+	0.0425845i
$695$	−14.8107	−	20.6956i	−0.561802	−	0.785028i
$696$	−0.959929	−	0.204039i	−0.0363860	−	0.00773409i
$697$	6.98980	+	1.48573i	0.264758	+	0.0562760i
$698$	−0.0945088	+	0.899192i	−0.00357721	+	0.0340349i
$699$	26.3481			0.996578
$700$	23.3659	+	12.0358i	0.883147	+	0.454909i
$701$	−23.4163			−0.884422			−0.442211	−	0.896911i	$-0.645806\pi$
$701$	−23.4163			−0.884422			−0.442211	+	0.896911i	$0.645806\pi$
$702$	0.0186282	−	0.177235i	0.000703076	−	0.00668932i
$703$	5.83814	+	1.24094i	0.220190	+	0.0468028i
$704$	16.0627	+	3.41422i	0.605384	+	0.128678i
$705$	5.93612	−	1.88182i	0.223567	−	0.0708735i
$706$	0.0395915	−	0.121850i	0.00149004	−	0.00458589i
$707$	3.64822	−	24.6120i	0.137206	−	0.925631i
$708$	5.45457	−	16.7874i	0.204995	−	0.630911i
$709$	1.78538	+	0.794904i	0.0670515	+	0.0298532i	0.439988	−	0.898003i	$-0.354983\pi$
$709$	1.78538	+	0.794904i	0.0670515	+	0.0298532i	−0.372937	+	0.927857i	$0.621649\pi$
$710$	2.97292	+	0.334031i	0.111572	+	0.0125360i
$711$	4.08575	−	1.81909i	0.153228	−	0.0682213i
$712$	−2.60965	−	1.16189i	−0.0978009	−	0.0435438i
$713$	−3.50445	+	2.54613i	−0.131243	+	0.0953534i
$714$	0.233256	−	0.237931i	0.00872938	−	0.00890435i
$715$	5.55255	−	4.92792i	0.207654	−	0.184294i
$716$	3.96306	+	1.76447i	0.148107	+	0.0659413i
$717$	16.3260	+	18.1319i	0.609707	+	0.677148i
$718$	−2.01732	+	3.49409i	−0.0752856	+	0.130398i
$719$	40.4199	−	8.59152i	1.50741	−	0.320410i	0.621184	−	0.783665i	$-0.286652\pi$
$719$	40.4199	−	8.59152i	1.50741	−	0.320410i	0.886225	+	0.463255i	$0.153319\pi$
$720$	−3.50884	−	8.03552i	−0.130767	−	0.299466i
$721$	−5.11559	+	13.7323i	−0.190514	+	0.511417i
$722$	−0.595574	−	1.83299i	−0.0221650	−	0.0682167i
$723$	−2.91975	+	27.7796i	−0.108587	+	1.03313i
$724$	4.46683	−	7.73678i	0.166008	−	0.287535i
$725$	−3.46238	+	10.1582i	−0.128589	+	0.377265i
$726$	−0.369003	−	0.639131i	−0.0136950	−	0.0237204i
$727$	25.2119	+	18.3175i	0.935058	+	0.679359i	0.947226	−	0.320567i	$-0.103873\pi$
$727$	25.2119	+	18.3175i	0.935058	+	0.679359i	−0.0121682	+	0.999926i	$0.503873\pi$
$728$	−1.19744	−	1.44908i	−0.0443801	−	0.0537065i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−0.0207601	+	2.89581i	−0.000768368	+	0.107179i
$731$	7.01569	+	7.79171i	0.259485	+	0.288187i
$732$	−6.85266	+	11.8692i	−0.253282	+	0.438697i
$733$	42.7372	−	9.08408i	1.57854	−	0.335528i	0.666457	−	0.745543i	$-0.267810\pi$
$733$	42.7372	−	9.08408i	1.57854	−	0.335528i	0.912079	+	0.410015i	$0.134477\pi$
$734$	−2.07140	+	1.50496i	−0.0764569	+	0.0555492i
$735$	−15.2680	+	3.44813i	−0.563167	+	0.127186i
$736$	3.10640	+	2.25693i	0.114503	+	0.0831917i
$737$	−27.3027	−	12.1559i	−1.00571	−	0.447770i
$738$	−0.0780065	−	0.742182i	−0.00287146	−	0.0273201i
$739$	−18.7537	+	8.34969i	−0.689866	+	0.307148i	−0.721563	−	0.692349i	$-0.756576\pi$
$739$	−18.7537	+	8.34969i	−0.689866	+	0.307148i	0.0316961	+	0.999498i	$0.489909\pi$
$740$	−10.4180	−	14.5575i	−0.382975	−	0.535145i
$741$	−1.86224	+	1.35300i	−0.0684110	+	0.0497035i
$742$	0.0501177	+	0.803651i	0.00183988	+	0.0295030i
$743$	−42.6740			−1.56556			−0.782779	−	0.622300i	$-0.786198\pi$
$743$	−42.6740			−1.56556			−0.782779	+	0.622300i	$0.786198\pi$
$744$	0.688249	−	0.146292i	0.0252324	−	0.00536332i
$745$	4.54162	+	22.1461i	0.166392	+	0.811371i
$746$	−1.37761	−	0.292821i	−0.0504381	−	0.0107209i
$747$	−0.141412	+	0.157054i	−0.00517399	+	0.00574629i
$748$	−3.77127	−	2.73999i	−0.137891	−	0.100184i
$749$	−23.5324	−	18.6726i	−0.859855	−	0.682283i
$750$	1.22766	−	0.369899i	0.0448279	−	0.0135068i
$751$	−4.25602	−	7.37164i	−0.155304	−	0.268995i	0.777866	−	0.628431i	$-0.216302\pi$
$751$	−4.25602	−	7.37164i	−0.155304	−	0.268995i	−0.933170	+	0.359436i	$0.882969\pi$
$752$	−9.97626	+	4.44172i	−0.363797	+	0.161973i
$753$	6.99419	+	1.48666i	0.254882	+	0.0541769i
$754$	0.255952	−	0.284264i	0.00932123	−	0.0103523i
$755$	5.56961	−	4.94306i	0.202699	−	0.179896i
$756$	4.70721	+	2.33991i	0.171199	+	0.0851015i
$757$	−43.7447			−1.58993			−0.794963	−	0.606657i	$-0.792510\pi$
$757$	−43.7447			−1.58993			−0.794963	+	0.606657i	$0.792510\pi$
$758$	2.22368	−	0.472658i	0.0807678	−	0.0171677i
$759$	−0.628617	−	5.98090i	−0.0228174	−	0.217093i
$760$	0.625867	−	1.37903i	0.0227026	−	0.0500226i
$761$	2.75822	−	26.2427i	0.0999855	−	0.951298i	−0.823410	−	0.567447i	$-0.807931\pi$
$761$	2.75822	−	26.2427i	0.0999855	−	0.951298i	0.923395	−	0.383851i	$-0.125402\pi$
$762$	0.390265	−	0.283544i	0.0141378	−	0.0102717i
$763$	−6.13132	−	11.7439i	−0.221969	−	0.425156i
$764$	27.3614	+	19.8792i	0.989900	+	0.719205i
$765$	−0.0176032	+	2.45545i	−0.000636445	+	0.0887770i
$766$	0.403629	+	3.84027i	0.0145837	+	0.138755i
$767$	9.23777	+	10.2596i	0.333557	+	0.370452i
$768$	7.47910	+	12.9542i	0.269879	+	0.467444i
$769$	−11.3505	+	34.9334i	−0.409311	+	1.25973i	0.507930	+	0.861398i	$0.330411\pi$
$769$	−11.3505	+	34.9334i	−0.409311	+	1.25973i	−0.917241	+	0.398332i	$0.869589\pi$
$770$	−0.523199	−	1.35184i	−0.0188548	−	0.0487170i
$771$	2.90579	+	8.94309i	0.104649	+	0.322078i
$772$	16.9663	−	18.8430i	0.610631	−	0.678175i
$773$	46.2667	−	20.5993i	1.66410	−	0.740904i	0.664121	−	0.747625i	$-0.268806\pi$
$773$	46.2667	−	20.5993i	1.66410	−	0.740904i	0.999977	+	0.00672084i	$0.00213933\pi$
$774$	0.547476	−	0.948257i	0.0196786	−	0.0340844i
$775$	−0.694510	−	7.66323i	−0.0249475	−	0.275271i
$776$	7.44708			0.267335
$777$	10.3243	+	2.65688i	0.370382	+	0.0953150i
$778$	−0.0311038	−	0.0957277i	−0.00111513	−	0.00343200i
$779$	−6.44984	+	7.16327i	−0.231089	+	0.256651i
$780$	6.86070	+	0.770854i	0.245652	+	0.0276010i
$781$	16.6782	+	18.5230i	0.596792	+	0.662805i
$782$	−0.177241	−	0.306991i	−0.00633813	−	0.0109780i
$783$	−0.663276	+	2.04135i	−0.0237035	+	0.0729520i
$784$	25.9319	−	8.99849i	0.926141	−	0.321375i
$785$	6.54010	−	5.80438i	0.233426	−	0.207167i
$786$	0.251439	−	2.39228i	0.00896853	−	0.0853299i
$787$	−2.85386	−	27.1527i	−0.101729	−	0.967888i	−0.919698	−	0.392626i	$-0.871567\pi$
$787$	−2.85386	−	27.1527i	−0.101729	−	0.967888i	0.817969	−	0.575262i	$-0.195100\pi$
$788$	1.99669	+	18.9973i	0.0711293	+	0.676750i
$789$	−1.13676	+	10.8155i	−0.0404697	+	0.385043i
$790$	−0.458957	−	1.05105i	−0.0163290	−	0.0373947i
$791$	−25.4515	+	40.0565i	−0.904952	+	1.42424i
$792$	−0.301865	+	0.929046i	−0.0107263	+	0.0330122i
$793$	−5.35966	−	9.28321i	−0.190327	−	0.329656i
$794$	−2.27641	−	2.52821i	−0.0807868	−	0.0897228i
$795$	−4.38130	−	4.00218i	−0.155389	−	0.141943i
$796$	16.0815	−	17.8603i	0.569994	−	0.633043i
$797$	1.74674	+	5.37591i	0.0618727	+	0.190425i	0.977215	−	0.212252i	$-0.0680798\pi$
$797$	1.74674	+	5.37591i	0.0618727	+	0.190425i	−0.915342	+	0.402677i	$0.868080\pi$
$798$	0.120627	+	0.432956i	0.00427014	+	0.0153265i
$799$	3.05822			0.108192
$800$	−6.27011	+	2.68459i	−0.221682	+	0.0949146i
$801$	−3.12392	+	5.41079i	−0.110378	+	0.191181i
$802$	−2.89428	+	1.28862i	−0.102201	+	0.0455026i
$803$	−16.1444	+	17.9302i	−0.569724	+	0.632742i
$804$	−8.58844	−	26.4325i	−0.302891	−	0.932203i
$805$	−0.825735	+	16.6320i	−0.0291033	+	0.586199i
$806$	−0.0847494	+	0.260832i	−0.00298517	+	0.00918741i
$807$	−14.6709	−	25.4107i	−0.516439	−	0.894499i
$808$	2.87708	+	3.19532i	0.101215	+	0.112411i
$809$	−2.42891	−	23.1096i	−0.0853960	−	0.812489i	−0.950464	−	0.310834i	$-0.899392\pi$
$809$	−2.42891	−	23.1096i	−0.0853960	−	0.812489i	0.865068	−	0.501655i	$-0.167275\pi$
$810$	0.244447	−	0.0774925i	0.00858898	−	0.00272281i
$811$	5.05939	+	3.67586i	0.177659	+	0.129077i	0.673061	−	0.739587i	$-0.264979\pi$
$811$	5.05939	+	3.67586i	0.177659	+	0.129077i	−0.495402	+	0.868664i	$0.664979\pi$
$812$	5.22188	+	10.0019i	0.183252	+	0.350999i
$813$	−10.8499	+	7.88292i	−0.380523	+	0.276466i
$814$	−0.103198	+	0.981863i	−0.00361709	+	0.0344143i
$815$	36.5904	+	33.4242i	1.28170	+	1.17080i
$816$	−0.450109	−	4.28250i	−0.0157570	−	0.149918i
$817$	−13.8338	+	2.94046i	−0.483983	+	0.102874i
$818$	0.759673			0.0265613
$819$	−3.42574	+	2.27334i	−0.119705	+	0.0794370i
$820$	28.7729	−	2.81575i	1.00479	−	0.0983304i
$821$	19.8201	−	22.0125i	0.691727	−	0.768241i	−0.290309	−	0.956933i	$-0.593758\pi$
$821$	19.8201	−	22.0125i	0.691727	−	0.768241i	0.982036	+	0.188692i	$0.0604249\pi$
$822$	−0.336496	−	0.0715245i	−0.0117367	−	0.00249470i
$823$	−25.9215	+	11.5410i	−0.903567	+	0.402294i	−0.805301	−	0.592866i	$-0.797996\pi$
$823$	−25.9215	+	11.5410i	−0.903567	+	0.402294i	−0.0982658	+	0.995160i	$0.531330\pi$
$824$	−1.26621	−	2.19314i	−0.0441105	−	0.0764016i
$825$	9.69577	+	4.48449i	0.337563	+	0.156130i
$826$	2.50685	−	0.990939i	0.0872246	−	0.0344792i
$827$	−32.4388	−	23.5681i	−1.12801	−	0.819545i	−0.142603	−	0.989780i	$-0.545547\pi$
$827$	−32.4388	−	23.5681i	−1.12801	−	0.819545i	−0.985403	+	0.170235i	$0.945547\pi$
$828$	3.74213	−	4.15606i	0.130048	−	0.144433i
$829$	47.0604	+	10.0030i	1.63448	+	0.347419i	0.931485	−	0.363780i	$-0.118514\pi$
$829$	47.0604	+	10.0030i	1.63448	+	0.347419i	0.702991	+	0.711199i	$0.251847\pi$
$830$	0.0400132	+	0.0365508i	0.00138888	+	0.00126870i
$831$	−4.53119	+	0.963135i	−0.157185	+	0.0334108i
$832$	−11.9439			−0.414082
$833$	−7.65931	−	0.651655i	−0.265379	−	0.0225785i
$834$	−1.05594	+	0.767188i	−0.0365644	+	0.0265656i
$835$	−21.4427	+	29.0728i	−0.742055	+	1.00610i
$836$	5.74431	−	2.55753i	0.198671	−	0.0884541i
$837$	−0.160862	−	1.53050i	−0.00556020	−	0.0529017i
$838$	−1.35142	−	0.601691i	−0.0466840	−	0.0207851i
$839$	24.7923	+	18.0126i	0.855924	+	0.621865i	0.926773	−	0.375622i	$-0.122571\pi$
$839$	24.7923	+	18.0126i	0.855924	+	0.621865i	−0.0708490	+	0.997487i	$0.522571\pi$
$840$	1.22138	−	2.41349i	0.0421414	−	0.0832732i
$841$	19.7343	−	14.3378i	0.680493	−	0.494407i
$842$	2.06226	−	0.438347i	0.0710701	−	0.0151064i
$843$	10.3542	−	17.9340i	0.356617	−	0.617679i
$844$	18.8418	+	20.9259i	0.648561	+	0.720300i
$845$	14.0493	−	19.0485i	0.483311	−	0.655290i
$846$	−0.0986932	−	0.303747i	−0.00339314	−	0.0104430i
$847$	−5.94360	+	15.9550i	−0.204224	+	0.548220i
$848$	8.41883	+	6.11664i	0.289104	+	0.210046i
$849$	−4.03467	−	6.98825i	−0.138469	−	0.239836i
$850$	0.629617	+	0.00902794i	0.0215957	+	0.000309656i
$851$	5.67086	−	9.82222i	0.194395	−	0.336701i
$852$	−2.42286	+	23.0520i	−0.0830059	+	0.789748i
$853$	−10.8592	−	33.4212i	−0.371812	−	1.14432i	−0.945604	−	0.325319i	$-0.894528\pi$
$853$	−10.8592	−	33.4212i	−0.371812	−	1.14432i	0.573792	−	0.819001i	$-0.305472\pi$
$854$	−2.06387	+	0.347910i	−0.0706242	+	0.0119052i
$855$	−2.85653	−	1.67663i	−0.0976911	−	0.0573397i
$856$	5.07794	−	1.07935i	0.173561	−	0.0368914i
$857$	−4.88439	+	8.46001i	−0.166848	+	0.288989i	−0.937310	−	0.348497i	$-0.886692\pi$
$857$	−4.88439	+	8.46001i	−0.166848	+	0.288989i	0.770462	+	0.637486i	$0.220025\pi$
$858$	−0.254774	−	0.282955i	−0.00869784	−	0.00965993i
$859$	34.9812	+	15.5746i	1.19354	+	0.531400i	0.904730	−	0.425986i	$-0.140073\pi$
$859$	34.9812	+	15.5746i	1.19354	+	0.531400i	0.288813	+	0.957385i	$0.406739\pi$
$860$	36.5822	+	21.4719i	1.24744	+	0.732185i
$861$	−12.0527	+	12.2943i	−0.410756	+	0.418989i
$862$	1.23784	−	0.899342i	0.0421609	−	0.0306317i
$863$	−25.1645	−	11.2039i	−0.856608	−	0.381386i	−0.0690397	−	0.997614i	$-0.521994\pi$
$863$	−25.1645	−	11.2039i	−0.856608	−	0.381386i	−0.787568	+	0.616227i	$0.788660\pi$
$864$	−1.24620	+	0.554842i	−0.0423964	+	0.0188761i
$865$	20.1655	−	44.4324i	0.685647	−	1.51075i
$866$	4.09087	+	1.82137i	0.139014	+	0.0618928i
$867$	4.88064	−	15.0211i	0.165755	−	0.510142i
$868$	−6.33707	−	5.02838i	−0.215094	−	0.170674i
$869$	2.95279	−	9.08774i	0.100166	−	0.308281i
$870$	0.522243	+	0.173836i	0.0177057	+	0.00589359i
$871$	21.2625	+	4.51949i	0.720453	+	0.153137i
$872$	2.23940	+	0.475998i	0.0758355	+	0.0161193i
$873$	1.70254	−	16.1986i	0.0576223	−	0.548240i
$874$	0.478159			0.0161740
$875$	−24.6199	−	16.3969i	−0.832305	−	0.554318i
$876$	−22.4372			−0.758081
$877$	−2.80322	+	26.6708i	−0.0946580	+	0.900610i	0.839406	+	0.543505i	$0.182903\pi$
$877$	−2.80322	+	26.6708i	−0.0946580	+	0.900610i	−0.934064	+	0.357106i	$0.883764\pi$
$878$	1.82077	+	0.387017i	0.0614481	+	0.0130612i
$879$	−12.1935	−	2.59182i	−0.411278	−	0.0874198i
$880$	−17.7747	−	5.91654i	−0.599184	−	0.199447i
$881$	1.35227	−	4.16186i	0.0455592	−	0.140217i	−0.925689	−	0.378285i	$-0.876514\pi$
$881$	1.35227	−	4.16186i	0.0455592	−	0.140217i	0.971249	+	0.238068i	$0.0765141\pi$
$882$	0.182454	+	0.781761i	0.00614353	+	0.0263233i
$883$	−0.201608	+	0.620485i	−0.00678465	+	0.0208810i	−0.954392	−	0.298558i	$-0.903494\pi$
$883$	−0.201608	+	0.620485i	−0.00678465	+	0.0208810i	0.947607	+	0.319439i	$0.103494\pi$
$884$	3.09738	+	1.37904i	0.104176	+	0.0463823i
$885$	−8.20990	+	18.0896i	−0.275973	+	0.608076i
$886$	−2.52321	+	1.12341i	−0.0847690	+	0.0377416i
$887$	−9.54625	−	4.25026i	−0.320532	−	0.142710i	0.240163	−	0.970733i	$-0.422799\pi$
$887$	−9.54625	−	4.25026i	−0.320532	−	0.142710i	−0.560695	+	0.828023i	$0.689466\pi$
$888$	−1.49044	+	1.08287i	−0.0500161	+	0.0363388i
$889$	−10.7779	−	2.77361i	−0.361479	−	0.0930239i
$890$	1.38174	+	0.811010i	0.0463160	+	0.0271851i
$891$	1.95181	+	0.869003i	0.0653882	+	0.0291127i
$892$	12.0928	+	13.4304i	0.404896	+	0.449682i
$893$	−2.06261	+	3.57254i	−0.0690225	+	0.119551i
$894$	1.13411	−	0.241063i	0.0379304	−	0.00806235i
$895$	−4.21055	−	2.47138i	−0.140743	−	0.0826091i
$896$	−3.33393	+	8.94959i	−0.111379	+	0.298985i
$897$	1.35166	+	4.16000i	0.0451308	+	0.138898i
$898$	0.355637	−	3.38366i	0.0118678	−	0.112914i
$899$	1.65158	−	2.86062i	0.0550833	−	0.0954072i
$900$	2.93407	+	9.49107i	0.0978025	+	0.316369i
$901$	−1.45712	−	2.52381i	−0.0485437	−	0.0840802i
$902$	−1.28992	−	0.937180i	−0.0429496	−	0.0312047i
$903$	−24.9096	+	4.19905i	−0.828939	+	0.139736i
$904$	−2.53437	−	7.79998i	−0.0842918	−	0.259423i
$905$	−5.96790	+	8.09149i	−0.198380	+	0.268970i
$906$	−0.255557	−	0.283824i	−0.00849030	−	0.00942943i
$907$	2.58119	−	4.47075i	0.0857069	−	0.148449i	−0.819985	−	0.572385i	$-0.806018\pi$
$907$	2.58119	−	4.47075i	0.0857069	−	0.148449i	0.905692	+	0.423936i	$0.139352\pi$
$908$	43.0397	−	9.14837i	1.42832	−	0.303599i
$909$	7.60809	−	5.52760i	0.252345	−	0.183339i
$910$	0.576653	+	0.882638i	0.0191159	+	0.0292592i
$911$	−6.26367	−	4.55082i	−0.207525	−	0.150775i	0.479168	−	0.877723i	$-0.340938\pi$
$911$	−6.26367	−	4.55082i	−0.207525	−	0.150775i	−0.686693	+	0.726948i	$0.740938\pi$
$912$	5.30629	+	2.36251i	0.175709	+	0.0782306i
$913$	0.0471973	+	0.449052i	0.00156200	+	0.0148615i
$914$	−1.68714	+	0.751165i	−0.0558058	+	0.0248463i
$915$	9.15549	−	12.4133i	0.302671	−	0.410372i
$916$	35.0049	−	25.4326i	1.15660	−	0.840316i
$917$	−46.2398	+	30.6850i	−1.52697	+	1.01331i
$918$	0.125936			0.00415652
$919$	−26.0463	+	5.53632i	−0.859189	+	0.182626i	−0.616381	−	0.787448i	$-0.711402\pi$
$919$	−26.0463	+	5.53632i	−0.859189	+	0.182626i	−0.242808	+	0.970074i	$0.578068\pi$
$920$	−2.12472	−	1.94087i	−0.0700499	−	0.0639885i
$921$	−1.27831	−	0.271713i	−0.0421217	−	0.00895324i
$922$	2.20081	−	2.44425i	0.0724798	−	0.0804970i
$923$	−14.6666	−	10.6559i	−0.482757	−	0.350744i
$924$	10.4447	−	4.12869i	0.343604	−	0.135824i
$925$	9.82220	+	17.5902i	0.322952	+	0.578364i
$926$	0.351395	+	0.608634i	0.0115476	+	0.0200010i
$927$	−5.05991	+	2.25282i	−0.166189	+	0.0739922i
$928$	−2.86400	−	0.608761i	−0.0940153	−	0.0199836i
$929$	2.34257	−	2.60169i	0.0768573	−	0.0853587i	−0.703490	−	0.710706i	$-0.748376\pi$
$929$	2.34257	−	2.60169i	0.0768573	−	0.0853587i	0.780347	+	0.625347i	$0.215043\pi$
$930$	−0.392760	+	0.0384360i	−0.0128791	+	0.00126037i
$931$	5.92704	−	8.50790i	0.194251	−	0.278835i
$932$	52.3497			1.71477
$933$	10.2997	−	2.18927i	0.337197	−	0.0716735i
$934$	0.0436093	+	0.414915i	0.00142694	+	0.0135764i
$935$	3.87347	+	3.53830i	0.126676	+	0.115715i
$936$	0.0742677	−	0.706610i	0.00242752	−	0.0230963i
$937$	8.91977	−	6.48060i	0.291396	−	0.211712i	−0.432477	−	0.901645i	$-0.642360\pi$
$937$	8.91977	−	6.48060i	0.291396	−	0.211712i	0.723873	+	0.689933i	$0.242360\pi$
$938$	2.27620	−	3.58236i	0.0743205	−	0.116968i
$939$	10.4350	+	7.58145i	0.340532	+	0.247411i
$940$	11.7942	−	3.73889i	0.384683	−	0.121949i
$941$	−2.44128	−	23.2272i	−0.0795834	−	0.757186i	−0.959434	−	0.281935i	$-0.909024\pi$
$941$	−2.44128	−	23.2272i	−0.0795834	−	0.757186i	0.879850	−	0.475251i	$-0.157643\pi$
$942$	−0.300087	−	0.333280i	−0.00977735	−	0.0108588i
$943$	9.15834	+	15.8627i	0.298237	+	0.516561i
$944$	10.7652	−	33.1319i	0.350377	−	1.07835i
$945$	−4.97049	−	3.20846i	−0.161690	−	0.104371i
$946$	−0.722912	−	2.22490i	−0.0235039	−	0.0723376i
$947$	21.6637	−	24.0599i	0.703974	−	0.781843i	−0.280029	−	0.959991i	$-0.590344\pi$
$947$	21.6637	−	24.0599i	0.703974	−	0.781843i	0.984004	+	0.178149i	$0.0570109\pi$
$948$	8.11777	−	3.61426i	0.263653	−	0.117386i
$949$	8.77437	−	15.1977i	0.284828	−	0.493337i
$950$	−0.435189	+	0.729414i	−0.0141194	+	0.0236653i
$951$	13.7598			0.446192
$952$	0.929956	−	0.948596i	0.0301400	−	0.0307442i
$953$	−5.99560	−	18.4526i	−0.194217	−	0.597737i	−0.999985	−	0.00550620i	$-0.998247\pi$
$953$	−5.99560	−	18.4526i	−0.194217	−	0.597737i	0.805768	−	0.592231i	$-0.201753\pi$
$954$	−0.203644	+	0.226170i	−0.00659323	+	0.00732252i
$955$	−28.1029	−	25.6711i	−0.909387	−	0.830698i
$956$	32.4373	+	36.0253i	1.04910	+	1.16514i
$957$	2.29292	+	3.97146i	0.0741197	+	0.128379i
$958$	0.342631	−	1.05451i	0.0110699	−	0.0340696i
$959$	3.67310	+	7.03542i	0.118611	+	0.227186i
$960$	−6.87769	−	15.7505i	−0.221976	−	0.508344i
$961$	2.99283	−	28.4749i	0.0965428	−	0.918544i
$962$	−0.0750595	−	0.714144i	−0.00242002	−	0.0230249i
$963$	−1.18685	−	11.2921i	−0.0382456	−	0.363883i
$964$	−5.80111	+	55.1938i	−0.186841	+	1.77767i
$965$	−21.3429	+	18.9420i	−0.687053	+	0.609764i
$966$	0.853287	+	0.0362334i	0.0274540	+	0.00116579i
$967$	9.99007	−	30.7463i	0.321259	−	0.988733i	−0.651842	−	0.758355i	$-0.726003\pi$
$967$	9.99007	−	30.7463i	0.321259	−	0.988733i	0.973101	−	0.230379i	$-0.0739965\pi$
$968$	−1.47116	−	2.54812i	−0.0472848	−	0.0818996i
$969$	−1.08844	−	1.20883i	−0.0349656	−	0.0388333i
$970$	−4.15066	−	0.466360i	−0.133270	−	0.0149739i
$971$	−7.64456	+	8.49014i	−0.245325	+	0.272462i	−0.853214	−	0.521561i	$-0.825350\pi$
$971$	−7.64456	+	8.49014i	−0.245325	+	0.272462i	0.607889	+	0.794022i	$0.292017\pi$
$972$	0.613970	+	1.88960i	0.0196931	+	0.0606091i
$973$	29.1618	+	7.50458i	0.934885	+	0.240586i
$974$	3.55203			0.113815
$975$	−7.57612	−	1.72424i	−0.242630	−	0.0552199i
$976$	−13.5245	+	23.4251i	−0.432908	+	0.749819i
$977$	−5.88656	+	2.62087i	−0.188328	+	0.0838489i	−0.498734	−	0.866755i	$-0.666202\pi$
$977$	−5.88656	+	2.62087i	−0.188328	+	0.0838489i	0.310406	+	0.950604i	$0.399535\pi$
$978$	1.70073	−	1.88885i	0.0543834	−	0.0603989i
$979$	4.12496	+	12.6953i	0.131834	+	0.405745i
$980$	−30.3351	+	6.85091i	−0.969019	+	0.218844i
$981$	1.54734	−	4.76223i	0.0494028	−	0.152046i
$982$	1.23731	+	2.14308i	0.0394841	+	0.0683885i
$983$	−2.72949	−	3.03141i	−0.0870573	−	0.0966869i	0.698042	−	0.716057i	$-0.254055\pi$
$983$	−2.72949	−	3.03141i	−0.0870573	−	0.0966869i	−0.785099	+	0.619370i	$0.787388\pi$
$984$	−0.311000	−	2.95897i	−0.00991432	−	0.0943285i
$985$	0.154115	−	21.4974i	0.00491053	−	0.684964i
$986$	0.218686	+	0.158884i	0.00696437	+	0.00505991i
$987$	−3.95149	+	6.21900i	−0.125777	+	0.197953i
$988$	−3.69998	+	2.68820i	−0.117712	+	0.0855229i
$989$	−2.80919	+	26.7276i	−0.0893269	+	0.849889i
$990$	0.226426	−	0.498904i	0.00719628	−	0.0158562i
$991$	−3.55264	−	33.8011i	−0.112853	−	1.07373i	−0.893595	−	0.448874i	$-0.851825\pi$
$991$	−3.55264	−	33.8011i	−0.112853	−	1.07373i	0.780741	−	0.624854i	$-0.214842\pi$
$992$	2.05343	−	0.436469i	0.0651963	−	0.0138579i
$993$	−3.66470			−0.116296
$994$	−2.94940	+	1.95724i	−0.0935494	+	0.0620800i
$995$	−20.2299	+	17.9541i	−0.641330	+	0.569184i
$996$	−0.280964	+	0.312042i	−0.00890268	+	0.00988742i
$997$	−7.43890	−	1.58119i	−0.235592	−	0.0500767i	0.0886024	−	0.996067i	$-0.471760\pi$
$997$	−7.43890	−	1.58119i	−0.235592	−	0.0500767i	−0.324195	+	0.945990i	$0.605093\pi$
$998$	2.99941	−	1.33542i	0.0949445	−	0.0422720i
$999$	2.01468	+	3.48952i	0.0637415	+	0.110404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.a.466.10	yes	160
7.2	even	3	inner	525.2.bg.a.16.11	✓	160
25.11	even	5	inner	525.2.bg.a.361.11	yes	160
175.86	even	15	inner	525.2.bg.a.436.10	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.a.16.11	✓	160	7.2	even	3	inner
525.2.bg.a.361.11	yes	160	25.11	even	5	inner
525.2.bg.a.436.10	yes	160	175.86	even	15	inner
525.2.bg.a.466.10	yes	160	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0119875 + 0.114053i) q^{2} +(0.978148 + 0.207912i) q^{3} +(1.94343 + 0.413089i) q^{4} +(-2.12162 - 0.706211i) q^{5} +(-0.0354385 + 0.109069i) q^{6} +(2.46049 - 0.972613i) q^{7} +(-0.141288 + 0.434840i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.0119875 + 0.114053i) q^{2} +(0.978148 + 0.207912i) q^{3} +(1.94343 + 0.413089i) q^{4} +(-2.12162 - 0.706211i) q^{5} +(-0.0354385 + 0.109069i) q^{6} +(2.46049 - 0.972613i) q^{7} +(-0.141288 + 0.434840i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.105978 - 0.233512i) q^{10} +(1.95181 - 0.869003i) q^{11} +(1.81508 + 0.808124i) q^{12} +(-1.25719 + 0.913401i) q^{13} +(0.0814346 + 0.292286i) q^{14} +(-1.92843 - 1.13189i) q^{15} +(3.58225 + 1.59492i) q^{16} +(-0.734799 - 0.816077i) q^{17} +(-0.0573407 + 0.0993171i) q^{18} +(1.44890 - 0.307974i) q^{19} +(-3.83149 - 2.24889i) q^{20} +(2.60894 - 0.439794i) q^{21} +(0.0757153 + 0.233028i) q^{22} +(0.294224 - 2.79936i) q^{23} +(-0.228609 + 0.395962i) q^{24} +(4.00253 + 2.99662i) q^{25} +(-0.0891058 - 0.154336i) q^{26} +(0.809017 + 0.587785i) q^{27} +(5.18357 - 0.873804i) q^{28} +(0.663276 + 2.04135i) q^{29} +(0.152212 - 0.206375i) q^{30} +(-1.02974 - 1.14365i) q^{31} +(-0.682066 + 1.18137i) q^{32} +(2.08984 - 0.444209i) q^{33} +(0.101885 - 0.0740235i) q^{34} +(-5.90710 + 0.325888i) q^{35} +(1.60739 + 1.16784i) q^{36} +(3.68100 + 1.63889i) q^{37} +(0.0177567 + 0.168944i) q^{38} +(-1.41962 + 0.632057i) q^{39} +(0.606848 - 0.822785i) q^{40} +(-5.26454 + 3.82491i) q^{41} +(0.0188853 + 0.302830i) q^{42} -9.54777 q^{43} +(4.15219 - 0.882575i) q^{44} +(-1.65095 - 1.50810i) q^{45} +(0.315749 + 0.0671144i) q^{46} +(-1.86347 + 2.06959i) q^{47} +(3.17237 + 2.30486i) q^{48} +(5.10805 - 4.78621i) q^{49} +(-0.389754 + 0.420580i) q^{50} +(-0.549070 - 0.951017i) q^{51} +(-2.82057 + 1.25580i) q^{52} +(2.59581 + 0.551756i) q^{53} +(-0.0767369 + 0.0852249i) q^{54} +(-4.75470 + 0.465302i) q^{55} +(0.0752927 + 1.20734i) q^{56} +1.48127 q^{57} +(-0.240774 + 0.0511781i) q^{58} +(-0.928642 - 8.83544i) q^{59} +(-3.28019 - 2.99636i) q^{60} +(-0.721040 + 6.86024i) q^{61} +(0.142781 - 0.103736i) q^{62} +(2.64337 + 0.112246i) q^{63} +(6.21817 + 4.51777i) q^{64} +(3.31233 - 1.05005i) q^{65} +(0.0256115 + 0.243678i) q^{66} +(-9.36005 - 10.3954i) q^{67} +(-1.09092 - 1.88953i) q^{68} +(0.869814 - 2.67701i) q^{69} +(0.0336426 - 0.677630i) q^{70} +(3.60505 + 11.0952i) q^{71} +(-0.305938 + 0.339779i) q^{72} +(-10.3165 + 4.59321i) q^{73} +(-0.231046 + 0.400184i) q^{74} +(3.29204 + 3.76331i) q^{75} +2.94306 q^{76} +(3.95722 - 4.03653i) q^{77} +(-0.0550704 - 0.169489i) q^{78} +(2.99263 - 3.32365i) q^{79} +(-6.47382 - 5.91364i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.373135 - 0.646289i) q^{82} +(-0.0653066 + 0.200993i) q^{83} +(5.25197 + 0.223016i) q^{84} +(0.982641 + 2.25033i) q^{85} +(0.114454 - 1.08895i) q^{86} +(0.224360 + 2.13465i) q^{87} +(0.102109 + 0.971506i) q^{88} +(-0.653077 + 6.21361i) q^{89} +(0.191794 - 0.170218i) q^{90} +(-2.20492 + 3.47017i) q^{91} +(1.72819 - 5.31881i) q^{92} +(-0.769464 - 1.33275i) q^{93} +(-0.213706 - 0.237344i) q^{94} +(-3.29151 - 0.369828i) q^{95} +(-0.912782 + 1.01375i) q^{96} +(-5.03322 - 15.4907i) q^{97} +(0.484651 + 0.639964i) q^{98} +2.13653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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