LMFDB - Embedded newform 90.2.l.a.77.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,2,Mod(23,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("90.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	90.l (of order $12$, degree $4$, 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:	$0.718653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			77.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	90.77
Dual form			90.2.l.a.83.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.20711 - 0.358719i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(0.283763 - 1.05902i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.548188 + 2.94949i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.20711 - 0.358719i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(0.283763 - 1.05902i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.548188 + 2.94949i) q^{9} +(2.22474 + 0.224745i) q^{10} +(-5.44949 + 3.14626i) q^{11} +(-0.599900 - 1.62484i) q^{12} +(-0.896575 - 3.34607i) q^{13} +(0.548188 - 0.949490i) q^{14} +(-3.33694 - 1.96593i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.14626 + 3.14626i) q^{17} +(-0.233875 + 2.99087i) q^{18} +1.55051i q^{19} +(2.09077 + 0.792893i) q^{20} +(-1.55051 + 1.09638i) q^{21} +(-6.07812 + 1.62863i) q^{22} +(0.965926 - 0.258819i) q^{23} +(-0.158919 - 1.72474i) q^{24} +(4.74264 - 1.58346i) q^{25} -3.46410i q^{26} +(2.53553 - 4.53553i) q^{27} +(0.775255 - 0.775255i) q^{28} +(1.57313 + 2.72474i) q^{29} +(-2.71441 - 2.76260i) q^{30} +(2.22474 - 3.85337i) q^{31} +(0.258819 + 0.965926i) q^{32} +(10.7420 + 1.84304i) q^{33} +(-3.85337 + 2.22474i) q^{34} +(0.246405 - 2.43916i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(-3.00000 - 3.00000i) q^{37} +(-0.401302 + 1.49768i) q^{38} +(-2.51059 + 5.44949i) q^{39} +(1.81431 + 1.30701i) q^{40} +(-3.39898 - 1.96240i) q^{41} +(-1.78144 + 0.657717i) q^{42} +(-3.34607 - 0.896575i) q^{43} -6.29253 q^{44} +(2.26795 + 6.31319i) q^{45} +1.00000 q^{46} +(8.69333 + 2.32937i) q^{47} +(0.292893 - 1.70711i) q^{48} +(5.02118 + 2.89898i) q^{49} +(4.99087 - 0.302023i) q^{50} +(7.67423 - 0.707107i) q^{51} +(0.896575 - 3.34607i) q^{52} +(-6.61037 - 6.61037i) q^{53} +(3.62302 - 3.72474i) q^{54} +(-10.8990 + 8.89898i) q^{55} +(0.949490 - 0.548188i) q^{56} +(1.71673 - 2.06520i) q^{57} +(0.814313 + 3.03906i) q^{58} +(5.90326 - 10.2247i) q^{59} +(-1.90691 - 3.37101i) q^{60} +(2.72474 + 4.71940i) q^{61} +(3.14626 - 3.14626i) q^{62} +(3.27912 + 0.256415i) q^{63} +1.00000i q^{64} +(-3.17914 - 7.06350i) q^{65} +(9.89898 + 4.56048i) q^{66} +(-3.65307 + 0.978838i) q^{67} +(-4.29788 + 1.15161i) q^{68} +(-1.57313 - 0.724745i) q^{69} +(0.869309 - 2.29227i) q^{70} -0.635674i q^{71} +(-1.69798 + 2.47323i) q^{72} +(2.89898 - 2.89898i) q^{73} +(-2.12132 - 3.67423i) q^{74} +(-8.07019 - 3.14198i) q^{75} +(-0.775255 + 1.34278i) q^{76} +(1.78559 + 6.66390i) q^{77} +(-3.83548 + 4.61401i) q^{78} +(-2.12132 + 1.22474i) q^{79} +(1.41421 + 1.73205i) q^{80} +(-8.39898 + 3.23375i) q^{81} +(-2.77526 - 2.77526i) q^{82} +(-0.142483 + 0.531752i) q^{83} +(-1.89097 + 0.174235i) q^{84} +(-5.81552 + 8.07277i) q^{85} +(-3.00000 - 1.73205i) q^{86} +(0.921519 - 5.37101i) q^{87} +(-6.07812 - 1.62863i) q^{88} +2.36773 q^{89} +(0.556696 + 6.68506i) q^{90} -3.79796 q^{91} +(0.965926 + 0.258819i) q^{92} +(-7.22973 + 2.66925i) q^{93} +(7.79423 + 4.50000i) q^{94} +(0.556198 + 3.42214i) q^{95} +(0.724745 - 1.57313i) q^{96} +(-2.89123 + 10.7902i) q^{97} +(4.09978 + 4.09978i) q^{98} +(-12.2672 - 14.3485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 12 q^{5} - 8 q^{6} - 8 q^{7}+O(q^{10}) $ 8 * q + 4 * q^3 + 12 * q^5 - 8 * q^6 - 8 * q^7	$ 8 q + 4 q^{3} + 12 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{10} - 24 q^{11} - 4 q^{12} + 16 q^{15} + 4 q^{16} - 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{25} - 8 q^{27} + 16 q^{28} - 12 q^{30} + 8 q^{31} + 16 q^{33} - 8 q^{36} - 24 q^{37} + 12 q^{38} + 4 q^{40} + 12 q^{41} + 20 q^{42} + 32 q^{45} + 8 q^{46} + 8 q^{48} + 24 q^{50} + 32 q^{51} - 48 q^{55} - 12 q^{56} + 28 q^{57} - 4 q^{58} - 8 q^{60} + 12 q^{61} - 32 q^{63} - 24 q^{65} + 40 q^{66} + 4 q^{67} - 12 q^{68} - 16 q^{70} + 8 q^{72} - 16 q^{73} + 8 q^{75} - 16 q^{76} + 24 q^{77} - 24 q^{78} - 28 q^{81} - 32 q^{82} + 12 q^{83} - 20 q^{85} - 24 q^{86} - 8 q^{87} - 8 q^{88} - 20 q^{90} + 48 q^{91} - 20 q^{93} - 24 q^{95} - 4 q^{96} + 12 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 + 12 * q^5 - 8 * q^6 - 8 * q^7 + 8 * q^10 - 24 * q^11 - 4 * q^12 + 16 * q^15 + 4 * q^16 - 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^25 - 8 * q^27 + 16 * q^28 - 12 * q^30 + 8 * q^31 + 16 * q^33 - 8 * q^36 - 24 * q^37 + 12 * q^38 + 4 * q^40 + 12 * q^41 + 20 * q^42 + 32 * q^45 + 8 * q^46 + 8 * q^48 + 24 * q^50 + 32 * q^51 - 48 * q^55 - 12 * q^56 + 28 * q^57 - 4 * q^58 - 8 * q^60 + 12 * q^61 - 32 * q^63 - 24 * q^65 + 40 * q^66 + 4 * q^67 - 12 * q^68 - 16 * q^70 + 8 * q^72 - 16 * q^73 + 8 * q^75 - 16 * q^76 + 24 * q^77 - 24 * q^78 - 28 * q^81 - 32 * q^82 + 12 * q^83 - 20 * q^85 - 24 * q^86 - 8 * q^87 - 8 * q^88 - 20 * q^90 + 48 * q^91 - 20 * q^93 - 24 * q^95 - 4 * q^96 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−1.33195	−	1.10721i	−0.769002	−	0.639246i
$3$	−1.33195	−	1.10721i	−0.769002	−	0.639246i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	2.20711	−	0.358719i	0.987048	−	0.160424i
$5$	2.20711	−	0.358719i	0.987048	−	0.160424i
$6$	−1.00000	−	1.41421i	−0.408248	−	0.577350i
$7$	0.283763	−	1.05902i	0.107252	−	0.400271i	−0.891339	−	0.453338i	$-0.850233\pi$
$7$	0.283763	−	1.05902i	0.107252	−	0.400271i	0.998591	+	0.0530669i	$0.0168997\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.548188	+	2.94949i	0.182729	+	0.983163i
$10$	2.22474	+	0.224745i	0.703526	+	0.0710706i
$11$	−5.44949	+	3.14626i	−1.64308	+	0.948634i	−0.663354	+	0.748305i	$0.730868\pi$
$11$	−5.44949	+	3.14626i	−1.64308	+	0.948634i	−0.979729	+	0.200329i	$0.935799\pi$
$12$	−0.599900	−	1.62484i	−0.173176	−	0.469052i
$13$	−0.896575	−	3.34607i	−0.248665	−	0.928032i	−0.971506	−	0.237016i	$-0.923830\pi$
$13$	−0.896575	−	3.34607i	−0.248665	−	0.928032i	0.722840	−	0.691015i	$-0.242836\pi$
$14$	0.548188	−	0.949490i	0.146509	−	0.253762i
$15$	−3.33694	−	1.96593i	−0.861593	−	0.507600i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.14626	+	3.14626i	−0.763081	+	0.763081i	−0.976878	−	0.213797i	$-0.931417\pi$
$17$	−3.14626	+	3.14626i	−0.763081	+	0.763081i	0.213797	+	0.976878i	$0.431417\pi$
$18$	−0.233875	+	2.99087i	−0.0551249	+	0.704955i
$19$			1.55051i			0.355711i	0.984057	+	0.177856i	$0.0569160\pi$
$19$			1.55051i			0.355711i	−0.984057	+	0.177856i	$0.943084\pi$
$20$	2.09077	+	0.792893i	0.467510	+	0.177296i
$21$	−1.55051	+	1.09638i	−0.338349	+	0.239249i
$22$	−6.07812	+	1.62863i	−1.29586	+	0.347224i
$23$	0.965926	−	0.258819i	0.201409	−	0.0539675i	−0.156704	−	0.987646i	$-0.550087\pi$
$23$	0.965926	−	0.258819i	0.201409	−	0.0539675i	0.358113	+	0.933678i	$0.383420\pi$
$24$	−0.158919	−	1.72474i	−0.0324391	−	0.352062i
$25$	4.74264	−	1.58346i	0.948528	−	0.316693i
$26$		−	3.46410i		−	0.679366i
$27$	2.53553	−	4.53553i	0.487964	−	0.872864i
$28$	0.775255	−	0.775255i	0.146509	−	0.146509i
$29$	1.57313	+	2.72474i	0.292123	+	0.505972i	0.974312	−	0.225204i	$-0.0723049\pi$
$29$	1.57313	+	2.72474i	0.292123	+	0.505972i	−0.682188	+	0.731177i	$0.738972\pi$
$30$	−2.71441	−	2.76260i	−0.495582	−	0.504380i
$31$	2.22474	−	3.85337i	0.399576	−	0.692086i	−0.594098	−	0.804393i	$-0.702491\pi$
$31$	2.22474	−	3.85337i	0.399576	−	0.692086i	0.993674	+	0.112307i	$0.0358240\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	10.7420	+	1.84304i	1.86995	+	0.320832i
$34$	−3.85337	+	2.22474i	−0.660848	+	0.381541i
$35$	0.246405	−	2.43916i	0.0416500	−	0.412293i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$	−0.401302	+	1.49768i	−0.0650997	+	0.242955i
$39$	−2.51059	+	5.44949i	−0.402016	+	0.872617i
$40$	1.81431	+	1.30701i	0.286868	+	0.206656i
$41$	−3.39898	−	1.96240i	−0.530831	−	0.306476i	0.210524	−	0.977589i	$-0.432483\pi$
$41$	−3.39898	−	1.96240i	−0.530831	−	0.306476i	−0.741355	+	0.671113i	$0.765816\pi$
$42$	−1.78144	+	0.657717i	−0.274882	+	0.101488i
$43$	−3.34607	−	0.896575i	−0.510270	−	0.136726i	−0.00550783	−	0.999985i	$-0.501753\pi$
$43$	−3.34607	−	0.896575i	−0.510270	−	0.136726i	−0.504762	+	0.863258i	$0.668420\pi$
$44$	−6.29253			−0.948634
$45$	2.26795	+	6.31319i	0.338086	+	0.941115i
$46$	1.00000			0.147442
$47$	8.69333	+	2.32937i	1.26805	+	0.339774i	0.829285	−	0.558827i	$-0.188748\pi$
$47$	8.69333	+	2.32937i	1.26805	+	0.339774i	0.438768	+	0.898600i	$0.355415\pi$
$48$	0.292893	−	1.70711i	0.0422755	−	0.246400i
$49$	5.02118	+	2.89898i	0.717311	+	0.414140i
$50$	4.99087	−	0.302023i	0.705816	−	0.0427126i
$51$	7.67423	−	0.707107i	1.07461	−	0.0990148i
$52$	0.896575	−	3.34607i	0.124333	−	0.464016i
$53$	−6.61037	−	6.61037i	−0.908004	−	0.908004i	0.0881074	−	0.996111i	$-0.471918\pi$
$53$	−6.61037	−	6.61037i	−0.908004	−	0.908004i	−0.996111	+	0.0881074i	$0.971918\pi$
$54$	3.62302	−	3.72474i	0.493031	−	0.506874i
$55$	−10.8990	+	8.89898i	−1.46962	+	1.19994i
$56$	0.949490	−	0.548188i	0.126881	−	0.0732547i
$57$	1.71673	−	2.06520i	0.227387	−	0.273543i
$58$	0.814313	+	3.03906i	0.106925	+	0.399048i
$59$	5.90326	−	10.2247i	0.768539	−	1.33115i	−0.169816	−	0.985476i	$-0.554317\pi$
$59$	5.90326	−	10.2247i	0.768539	−	1.33115i	0.938355	−	0.345673i	$-0.112349\pi$
$60$	−1.90691	−	3.37101i	−0.246181	−	0.435195i
$61$	2.72474	+	4.71940i	0.348868	+	0.604257i	0.986049	−	0.166458i	$-0.0532329\pi$
$61$	2.72474	+	4.71940i	0.348868	+	0.604257i	−0.637181	+	0.770714i	$0.719900\pi$
$62$	3.14626	−	3.14626i	0.399576	−	0.399576i
$63$	3.27912	+	0.256415i	0.413130	+	0.0323053i
$64$			1.00000i			0.125000i
$65$	−3.17914	−	7.06350i	−0.394323	−	0.876120i
$66$	9.89898	+	4.56048i	1.21848	+	0.561356i
$67$	−3.65307	+	0.978838i	−0.446294	+	0.119584i	−0.474965	−	0.880005i	$-0.657539\pi$
$67$	−3.65307	+	0.978838i	−0.446294	+	0.119584i	0.0286709	+	0.999589i	$0.490873\pi$
$68$	−4.29788	+	1.15161i	−0.521194	+	0.139654i
$69$	−1.57313	−	0.724745i	−0.189383	−	0.0872490i
$70$	0.869309	−	2.29227i	0.103902	−	0.273979i
$71$		−	0.635674i		−	0.0754407i	−0.999288	−	0.0377203i	$-0.987990\pi$
$71$		−	0.635674i		−	0.0754407i	0.999288	−	0.0377203i	$-0.0120096\pi$
$72$	−1.69798	+	2.47323i	−0.200108	+	0.291473i
$73$	2.89898	−	2.89898i	0.339300	−	0.339300i	−0.516804	−	0.856104i	$-0.672878\pi$
$73$	2.89898	−	2.89898i	0.339300	−	0.339300i	0.856104	+	0.516804i	$0.172878\pi$
$74$	−2.12132	−	3.67423i	−0.246598	−	0.427121i
$75$	−8.07019	−	3.14198i	−0.931865	−	0.362805i
$76$	−0.775255	+	1.34278i	−0.0889279	+	0.154028i
$77$	1.78559	+	6.66390i	0.203487	+	0.759422i
$78$	−3.83548	+	4.61401i	−0.434282	+	0.522434i
$79$	−2.12132	+	1.22474i	−0.238667	+	0.137795i	−0.614564	−	0.788867i	$-0.710668\pi$
$79$	−2.12132	+	1.22474i	−0.238667	+	0.137795i	0.375897	+	0.926662i	$0.377335\pi$
$80$	1.41421	+	1.73205i	0.158114	+	0.193649i
$81$	−8.39898	+	3.23375i	−0.933220	+	0.359306i
$82$	−2.77526	−	2.77526i	−0.306476	−	0.306476i
$83$	−0.142483	+	0.531752i	−0.0156395	+	0.0583674i	−0.973305	−	0.229517i	$-0.926285\pi$
$83$	−0.142483	+	0.531752i	−0.0156395	+	0.0583674i	0.957665	+	0.287885i	$0.0929519\pi$
$84$	−1.89097	+	0.174235i	−0.206322	+	0.0190106i
$85$	−5.81552	+	8.07277i	−0.630781	+	0.875615i
$86$	−3.00000	−	1.73205i	−0.323498	−	0.186772i
$87$	0.921519	−	5.37101i	0.0987973	−	0.575833i
$88$	−6.07812	−	1.62863i	−0.647929	−	0.173612i
$89$	2.36773			0.250978			0.125489	−	0.992095i	$-0.459950\pi$
$89$	2.36773			0.250978			0.125489	+	0.992095i	$0.459950\pi$
$90$	0.556696	+	6.68506i	0.0586809	+	0.704668i
$91$	−3.79796			−0.398134
$92$	0.965926	+	0.258819i	0.100705	+	0.0269838i
$93$	−7.22973	+	2.66925i	−0.749688	+	0.276788i
$94$	7.79423	+	4.50000i	0.803913	+	0.464140i
$95$	0.556198	+	3.42214i	0.0570647	+	0.351104i
$96$	0.724745	−	1.57313i	0.0739690	−	0.160557i
$97$	−2.89123	+	10.7902i	−0.293560	+	1.09558i	0.648795	+	0.760963i	$0.275273\pi$
$97$	−2.89123	+	10.7902i	−0.293560	+	1.09558i	−0.942355	+	0.334616i	$0.891393\pi$
$98$	4.09978	+	4.09978i	0.414140	+	0.414140i
$99$	−12.2672	−	14.3485i	−1.23290	−	1.44208i
$100$	4.89898	+	1.00000i	0.489898	+	0.100000i
$101$	1.10102	−	0.635674i	0.109556	−	0.0632520i	−0.444221	−	0.895917i	$-0.646519\pi$
$101$	1.10102	−	0.635674i	0.109556	−	0.0632520i	0.553777	+	0.832665i	$0.313186\pi$
$102$	7.59575	+	1.30323i	0.752092	+	0.129039i
$103$	1.06110	+	3.96008i	0.104553	+	0.390198i	0.998294	−	0.0583855i	$-0.0185953\pi$
$103$	1.06110	+	3.96008i	0.104553	+	0.390198i	−0.893741	+	0.448584i	$0.851929\pi$
$104$	1.73205	−	3.00000i	0.169842	−	0.294174i
$105$	−3.02885	+	2.97602i	−0.295586	+	0.290430i
$106$	−4.67423	−	8.09601i	−0.454002	−	0.786354i
$107$	−3.71051	+	3.71051i	−0.358708	+	0.358708i	−0.863337	−	0.504628i	$-0.831630\pi$
$107$	−3.71051	+	3.71051i	−0.358708	+	0.358708i	0.504628	+	0.863337i	$0.331630\pi$
$108$	4.46360	−	2.66012i	0.429510	−	0.255970i
$109$		−	20.3485i		−	1.94903i	−0.224323	−	0.974515i	$-0.572017\pi$
$109$		−	20.3485i		−	1.94903i	0.224323	−	0.974515i	$-0.427983\pi$
$110$	−12.8308	+	5.77489i	−1.22337	+	0.550614i
$111$	0.674235	+	7.31747i	0.0639955	+	0.694544i
$112$	1.05902	−	0.283763i	0.100068	−	0.0268131i
$113$	−13.3278	+	3.57117i	−1.25377	+	0.335948i	−0.823793	−	0.566890i	$-0.808146\pi$
$113$	−13.3278	+	3.57117i	−1.25377	+	0.335948i	−0.429981	+	0.902838i	$0.641480\pi$
$114$	2.19275	−	1.55051i	0.205370	−	0.145219i
$115$	2.03906	−	0.917738i	0.190143	−	0.0855795i
$116$			3.14626i			0.292123i
$117$	9.37769	−	4.47871i	0.866968	−	0.414057i
$118$	8.34847	−	8.34847i	0.768539	−	0.768539i
$119$	2.43916	+	4.22474i	0.223597	+	0.387282i
$120$	−0.969450	−	3.74969i	−0.0884983	−	0.342298i
$121$	14.2980	−	24.7648i	1.29981	−	2.25134i
$122$	1.41043	+	5.26380i	0.127694	+	0.476562i
$123$	2.35449	+	6.37720i	0.212297	+	0.575012i
$124$	3.85337	−	2.22474i	0.346043	−	0.199788i
$125$	9.89949	−	5.19615i	0.885438	−	0.464758i
$126$	3.10102	+	1.09638i	0.276261	+	0.0976730i
$127$	14.1237	+	14.1237i	1.25328	+	1.25328i	0.954242	+	0.299036i	$0.0966651\pi$
$127$	14.1237	+	14.1237i	1.25328	+	1.25328i	0.299036	+	0.954242i	$0.403335\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	3.46410	+	4.89898i	0.304997	+	0.431331i
$130$	−1.24264	−	7.64564i	−0.108987	−	0.670567i
$131$	9.12372	+	5.26758i	0.797143	+	0.460231i	0.842471	−	0.538741i	$-0.181100\pi$
$131$	9.12372	+	5.26758i	0.797143	+	0.460231i	−0.0453278	+	0.998972i	$0.514433\pi$
$132$	8.38134	+	6.96713i	0.729502	+	0.606411i
$133$	1.64202	+	0.439978i	0.142381	+	0.0381509i
$134$	−3.78194			−0.326710
$135$	3.96921	−	10.9200i	0.341615	−	0.939840i
$136$	−4.44949			−0.381541
$137$	−2.12701	−	0.569930i	−0.181723	−	0.0486924i	0.166810	−	0.985989i	$-0.446653\pi$
$137$	−2.12701	−	0.569930i	−0.181723	−	0.0486924i	−0.348533	+	0.937297i	$0.613320\pi$
$138$	−1.33195	−	1.10721i	−0.113383	−	0.0942517i
$139$	−11.1708	−	6.44949i	−0.947499	−	0.547039i	−0.0551956	−	0.998476i	$-0.517578\pi$
$139$	−11.1708	−	6.44949i	−0.947499	−	0.547039i	−0.892303	+	0.451437i	$0.850912\pi$
$140$	1.43297	−	1.98917i	0.121108	−	0.168116i
$141$	−9.00000	−	12.7279i	−0.757937	−	1.07188i
$142$	0.164525	−	0.614014i	0.0138066	−	0.0515269i
$143$	15.4135	+	15.4135i	1.28894	+	1.28894i
$144$	−2.28024	+	1.94949i	−0.190020	+	0.162457i
$145$	4.44949	+	5.44949i	0.369510	+	0.452555i
$146$	3.55051	−	2.04989i	0.293842	−	0.169650i
$147$	−3.47820	−	9.42078i	−0.286877	−	0.777013i
$148$	−1.09808	−	4.09808i	−0.0902613	−	0.336860i
$149$	−6.45145	+	11.1742i	−0.528523	+	0.915429i	0.470924	+	0.882174i	$0.343921\pi$
$149$	−6.45145	+	11.1742i	−0.528523	+	0.915429i	−0.999447	+	0.0332550i	$0.989413\pi$
$150$	−6.98200	−	5.12364i	−0.570078	−	0.418344i
$151$	10.7980	+	18.7026i	0.878725	+	1.52200i	0.852741	+	0.522335i	$0.174939\pi$
$151$	10.7980	+	18.7026i	0.878725	+	1.52200i	0.0259849	+	0.999662i	$0.491728\pi$
$152$	−1.09638	+	1.09638i	−0.0889279	+	0.0889279i
$153$	−11.0046	−	7.55513i	−0.889671	−	0.610796i
$154$			6.89898i			0.555936i
$155$	3.52797	−	9.30286i	0.283373	−	0.747224i
$156$	−4.89898	+	3.46410i	−0.392232	+	0.277350i
$157$	−5.94012	+	1.59165i	−0.474073	+	0.127028i	−0.487942	−	0.872876i	$-0.662252\pi$
$157$	−5.94012	+	1.59165i	−0.474073	+	0.127028i	0.0138684	+	0.999904i	$0.495585\pi$
$158$	−2.36603	+	0.633975i	−0.188231	+	0.0504363i
$159$	1.48565	+	16.1237i	0.117819	+	1.27869i
$160$	0.917738	+	2.03906i	0.0725535	+	0.161202i
$161$		−	1.09638i		−	0.0864066i
$162$	−8.94975	+	0.949747i	−0.703159	+	0.0746192i
$163$	−0.449490	+	0.449490i	−0.0352068	+	0.0352068i	−0.724491	−	0.689284i	$-0.757925\pi$
$163$	−0.449490	+	0.449490i	−0.0352068	+	0.0352068i	0.689284	+	0.724491i	$0.257925\pi$
$164$	−1.96240	−	3.39898i	−0.153238	−	0.265416i
$165$	24.3699	+	0.214413i	1.89720	+	0.0166920i
$166$	−0.275255	+	0.476756i	−0.0213639	+	0.0370034i
$167$	−2.79472	−	10.4300i	−0.216262	−	0.807100i	−0.985719	−	0.168401i	$-0.946140\pi$
$167$	−2.79472	−	10.4300i	−0.216262	−	0.807100i	0.769457	−	0.638699i	$-0.220527\pi$
$168$	−1.87163	−	0.321121i	−0.144400	−	0.0247750i
$169$	0.866025	−	0.500000i	0.0666173	−	0.0384615i
$170$	−7.70674	+	6.29253i	−0.591080	+	0.482615i
$171$	−4.57321	+	0.849971i	−0.349722	+	0.0649989i
$172$	−2.44949	−	2.44949i	−0.186772	−	0.186772i
$173$	0.802603	−	2.99536i	0.0610208	−	0.227733i	−0.928680	−	0.370881i	$-0.879056\pi$
$173$	0.802603	−	2.99536i	0.0610208	−	0.227733i	0.989701	+	0.143148i	$0.0457225\pi$
$174$	2.28024	−	4.94949i	0.172864	−	0.375220i
$175$	−0.331131	−	5.47187i	−0.0250312	−	0.413635i
$176$	−5.44949	−	3.14626i	−0.410771	−	0.237159i
$177$	−19.1838	+	7.08274i	−1.44194	+	0.532371i
$178$	2.28705	+	0.612812i	0.171421	+	0.0459322i
$179$	17.6062			1.31595			0.657976	−	0.753039i	$-0.271413\pi$
$179$	17.6062			1.31595			0.657976	+	0.753039i	$0.271413\pi$
$180$	−1.19249	+	6.60136i	−0.0888833	+	0.492036i
$181$	−10.5505			−0.784213			−0.392107	−	0.919920i	$-0.628254\pi$
$181$	−10.5505			−0.784213			−0.392107	+	0.919920i	$0.628254\pi$
$182$	−3.66855	−	0.982984i	−0.271931	−	0.0728636i
$183$	1.59612	−	9.30286i	0.117988	−	0.687687i
$184$	0.866025	+	0.500000i	0.0638442	+	0.0368605i
$185$	−7.69748	−	5.54516i	−0.565930	−	0.407688i
$186$	−7.67423	+	0.707107i	−0.562702	+	0.0518476i
$187$	7.24656	−	27.0445i	0.529921	−	1.97769i
$188$	6.36396	+	6.36396i	0.464140	+	0.464140i
$189$	−4.08372	−	3.97219i	−0.297047	−	0.288935i
$190$	−0.348469	+	3.44949i	−0.0252806	+	0.250252i
$191$	−2.87628	+	1.66062i	−0.208120	+	0.120158i	−0.600437	−	0.799672i	$-0.705007\pi$
$191$	−2.87628	+	1.66062i	−0.208120	+	0.120158i	0.392317	+	0.919830i	$0.371673\pi$
$192$	1.10721	−	1.33195i	0.0799057	−	0.0961253i
$193$	4.48288	+	16.7303i	0.322685	+	1.20428i	0.916619	+	0.399762i	$0.130907\pi$
$193$	4.48288	+	16.7303i	0.322685	+	1.20428i	−0.593934	+	0.804513i	$0.702426\pi$
$194$	−5.58542	+	9.67423i	−0.401010	+	0.694570i
$195$	−3.58630	+	12.9282i	−0.256820	+	0.925808i
$196$	2.89898	+	5.02118i	0.207070	+	0.358656i
$197$	−6.92820	+	6.92820i	−0.493614	+	0.493614i	−0.909443	−	0.415829i	$-0.863492\pi$
$197$	−6.92820	+	6.92820i	−0.493614	+	0.493614i	0.415829	+	0.909443i	$0.363492\pi$
$198$	−8.13557	−	17.0345i	−0.578170	−	1.21059i
$199$			3.55051i			0.251689i	0.992050	+	0.125844i	$0.0401640\pi$
$199$			3.55051i			0.251689i	−0.992050	+	0.125844i	$0.959836\pi$
$200$	4.47323	+	2.23388i	0.316305	+	0.157959i
$201$	5.94949	+	2.74094i	0.419645	+	0.193331i
$202$	1.22803	−	0.329049i	0.0864038	−	0.0231518i
$203$	3.33195	−	0.892794i	0.233857	−	0.0626618i
$204$	6.99964	+	3.22474i	0.490073	+	0.225777i
$205$	−8.20586	−	3.11195i	−0.573122	−	0.217348i
$206$			4.09978i			0.285645i
$207$	1.29289	+	2.70711i	0.0898623	+	0.188157i
$208$	2.44949	−	2.44949i	0.169842	−	0.169842i
$209$	−4.87832	−	8.44949i	−0.337440	−	0.584463i
$210$	−3.69589	+	2.09069i	−0.255041	+	0.144271i
$211$	−9.44949	+	16.3670i	−0.650530	+	1.12675i	0.332465	+	0.943116i	$0.392120\pi$
$211$	−9.44949	+	16.3670i	−0.650530	+	1.12675i	−0.982995	+	0.183635i	$0.941214\pi$
$212$	−2.41956	−	9.02993i	−0.166176	−	0.620178i
$213$	−0.703823	+	0.846687i	−0.0482251	+	0.0580141i
$214$	−4.54442	+	2.62372i	−0.310650	+	0.179354i
$215$	−7.70674	−	0.778539i	−0.525595	−	0.0530959i
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$	−3.44949	−	3.44949i	−0.234167	−	0.234167i
$218$	5.26657	−	19.6551i	0.356697	−	1.33121i
$219$	−7.07107	+	0.651531i	−0.477818	+	0.0440264i
$220$	−13.8883	+	2.25725i	−0.936348	+	0.152184i
$221$	13.3485	+	7.70674i	0.897915	+	0.518412i
$222$	−1.24264	+	7.24264i	−0.0834006	+	0.486094i
$223$	−8.02714	−	2.15087i	−0.537537	−	0.144033i	−0.0201706	−	0.999797i	$-0.506421\pi$
$223$	−8.02714	−	2.15087i	−0.537537	−	0.144033i	−0.517367	+	0.855764i	$0.673088\pi$
$224$	1.09638			0.0732547
$225$	7.27027	+	13.1203i	0.484685	+	0.874689i
$226$	−13.7980			−0.917827
$227$	−14.5865	−	3.90843i	−0.968138	−	0.259412i	−0.260096	−	0.965583i	$-0.583754\pi$
$227$	−14.5865	−	3.90843i	−0.968138	−	0.259412i	−0.708041	+	0.706171i	$0.750421\pi$
$228$	2.51934	−	0.930152i	0.166847	−	0.0616008i
$229$	14.1582	+	8.17423i	0.935600	+	0.540169i	0.888578	−	0.458725i	$-0.151694\pi$
$229$	14.1582	+	8.17423i	0.935600	+	0.540169i	0.0470214	+	0.998894i	$0.485027\pi$
$230$	2.20711	−	0.358719i	0.145532	−	0.0236533i
$231$	5.00000	−	10.8530i	0.328976	−	0.714075i
$232$	−0.814313	+	3.03906i	−0.0534623	+	0.199524i
$233$	−10.9959	−	10.9959i	−0.720363	−	0.720363i	0.248316	−	0.968679i	$-0.420123\pi$
$233$	−10.9959	−	10.9959i	−0.720363	−	0.720363i	−0.968679	+	0.248316i	$0.920123\pi$
$234$	10.2173	−	1.89898i	0.667928	−	0.124140i
$235$	20.0227	+	2.02270i	1.30614	+	0.131947i
$236$	10.2247	−	5.90326i	0.665574	−	0.384269i
$237$	4.18154	+	0.717439i	0.271620	+	0.0466027i
$238$	1.26260	+	4.71209i	0.0818423	+	0.305439i
$239$	−8.48528	+	14.6969i	−0.548867	+	0.950666i	0.449485	+	0.893288i	$0.351607\pi$
$239$	−8.48528	+	14.6969i	−0.548867	+	0.950666i	−0.998353	+	0.0573782i	$0.981726\pi$
$240$	0.0340742	−	3.87283i	0.00219948	−	0.249990i
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	−0.990912	−	0.134515i	$-0.957053\pi$
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$242$	20.2204	−	20.2204i	1.29981	−	1.29981i
$243$	14.7675	+	4.99221i	0.947333	+	0.320250i
$244$			5.44949i			0.348868i
$245$	12.1222	+	4.59716i	0.774459	+	0.293702i
$246$	0.623724	+	6.76928i	0.0397672	+	0.431594i
$247$	5.18811	−	1.39015i	0.330111	−	0.0884531i
$248$	4.29788	−	1.15161i	0.272915	−	0.0731275i
$249$	0.778539	−	0.550510i	0.0493379	−	0.0348872i
$250$	10.9070	−	2.45692i	0.689822	−	0.155389i
$251$		−	11.1708i		−	0.705097i	−0.935793	−	0.352549i	$-0.885315\pi$
$251$		−	11.1708i		−	0.705097i	0.935793	−	0.352549i	$-0.114685\pi$
$252$	2.71159	+	1.86162i	0.170814	+	0.117271i
$253$	−4.44949	+	4.44949i	−0.279737	+	0.279737i
$254$	9.98698	+	17.2980i	0.626639	+	1.08537i
$255$	16.6842	−	4.31356i	1.04481	−	0.270125i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.74105	−	25.1579i	−0.420495	−	1.56931i	−0.773568	−	0.633713i	$-0.781530\pi$
$257$	−6.74105	−	25.1579i	−0.420495	−	1.56931i	0.353073	−	0.935596i	$-0.385137\pi$
$258$	2.07812	+	5.62863i	0.129378	+	0.350423i
$259$	−4.02834	+	2.32577i	−0.250309	+	0.144516i
$260$	0.778539	−	7.70674i	0.0482829	−	0.477952i
$261$	−7.17423	+	6.13361i	−0.444074	+	0.379661i
$262$	7.44949	+	7.44949i	0.460231	+	0.460231i
$263$	3.28621	−	12.2643i	0.202636	−	0.756249i	−0.787521	−	0.616288i	$-0.788636\pi$
$263$	3.28621	−	12.2643i	0.202636	−	0.756249i	0.990157	−	0.139961i	$-0.0446977\pi$
$264$	6.29253	+	8.89898i	0.387278	+	0.547694i
$265$	−16.9611	−	12.2185i	−1.04191	−	0.750578i
$266$	1.47219	+	0.849971i	0.0902660	+	0.0521151i
$267$	−3.15369	−	2.62156i	−0.193003	−	0.160437i
$268$	−3.65307	−	0.978838i	−0.223147	−	0.0597920i
$269$	−4.70334			−0.286768			−0.143384	−	0.989667i	$-0.545798\pi$
$269$	−4.70334			−0.286768			−0.143384	+	0.989667i	$0.545798\pi$
$270$	6.66025	−	9.52056i	0.405330	−	0.579403i
$271$	−16.0454			−0.974689			−0.487345	−	0.873210i	$-0.662034\pi$
$271$	−16.0454			−0.974689			−0.487345	+	0.873210i	$0.662034\pi$
$272$	−4.29788	−	1.15161i	−0.260597	−	0.0698268i
$273$	5.05870	+	4.20512i	0.306166	+	0.254506i
$274$	−1.90702	−	1.10102i	−0.115208	−	0.0665151i
$275$	−20.8630	+	23.5507i	−1.25808	+	1.42016i
$276$	−1.00000	−	1.41421i	−0.0601929	−	0.0851257i
$277$	−3.69723	+	13.7983i	−0.222145	+	0.829057i	0.761383	+	0.648302i	$0.224521\pi$
$277$	−3.69723	+	13.7983i	−0.222145	+	0.829057i	−0.983528	+	0.180754i	$0.942146\pi$
$278$	−9.12096	−	9.12096i	−0.547039	−	0.547039i
$279$	12.5851	+	4.44949i	0.753448	+	0.266384i
$280$	1.89898	−	1.55051i	0.113486	−	0.0926607i
$281$	−0.151531	+	0.0874863i	−0.00903957	+	0.00521900i	−0.504513	−	0.863404i	$-0.668328\pi$
$281$	−0.151531	+	0.0874863i	−0.00903957	+	0.00521900i	0.495473	+	0.868623i	$0.334995\pi$
$282$	−5.39910	−	14.6236i	−0.321512	−	0.870823i
$283$	1.78484	+	6.66112i	0.106098	+	0.395962i	0.998467	−	0.0553430i	$-0.0176252\pi$
$283$	1.78484	+	6.66112i	0.106098	+	0.395962i	−0.892370	+	0.451305i	$0.850959\pi$
$284$	0.317837	−	0.550510i	0.0188602	−	0.0326668i
$285$	3.04819	−	5.17395i	0.180559	−	0.306478i
$286$	10.8990	+	18.8776i	0.644470	+	1.11626i
$287$	−3.04272	+	3.04272i	−0.179606	+	0.179606i
$288$	−2.70711	+	1.29289i	−0.159518	+	0.0761845i
$289$		−	2.79796i		−	0.164586i
$290$	2.88745	+	6.41542i	0.169557	+	0.376726i
$291$	15.7980	−	11.1708i	0.926093	−	0.654846i
$292$	3.96008	−	1.06110i	0.231746	−	0.0620962i
$293$	21.2942	−	5.70577i	1.24402	−	0.333335i	0.423998	−	0.905663i	$-0.360626\pi$
$293$	21.2942	−	5.70577i	1.24402	−	0.333335i	0.820024	+	0.572329i	$0.193960\pi$
$294$	−0.921404	−	10.0000i	−0.0537374	−	0.583212i
$295$	9.36131	−	24.6847i	0.545036	−	1.43720i
$296$		−	4.24264i		−	0.246598i
$297$	0.452623	+	32.6938i	0.0262638	+	1.89709i
$298$	−9.12372	+	9.12372i	−0.528523	+	0.528523i
$299$	−1.73205	−	3.00000i	−0.100167	−	0.173494i
$300$	−5.41800	−	6.75613i	−0.312808	−	0.390065i
$301$	−1.89898	+	3.28913i	−0.109455	+	0.189582i
$302$	5.58943	+	20.8601i	0.321636	+	1.20036i
$303$	−2.17033	−	0.372369i	−0.124682	−	0.0213921i
$304$	−1.34278	+	0.775255i	−0.0770138	+	0.0444639i
$305$	7.70674	+	9.43879i	0.441287	+	0.540464i
$306$	−8.67423	−	10.1459i	−0.495873	−	0.580002i
$307$	0.674235	+	0.674235i	0.0384806	+	0.0384806i	0.726085	−	0.687605i	$-0.241338\pi$
$307$	0.674235	+	0.674235i	0.0384806	+	0.0384806i	−0.687605	+	0.726085i	$0.741338\pi$
$308$	−1.78559	+	6.66390i	−0.101743	+	0.379711i
$309$	2.97129	−	6.44949i	0.169031	−	0.366899i
$310$	5.81552	−	8.07277i	0.330299	−	0.458502i
$311$	−17.8207	−	10.2888i	−1.01052	−	0.583422i	−0.0991741	−	0.995070i	$-0.531620\pi$
$311$	−17.8207	−	10.2888i	−1.01052	−	0.583422i	−0.911343	+	0.411648i	$0.864953\pi$
$312$	−5.62863	+	2.07812i	−0.318658	+	0.117650i
$313$	−4.85009	−	1.29958i	−0.274143	−	0.0734564i	0.119128	−	0.992879i	$-0.461990\pi$
$313$	−4.85009	−	1.29958i	−0.274143	−	0.0734564i	−0.393271	+	0.919422i	$0.628657\pi$
$314$	−6.14966			−0.347046
$315$	7.32935	−	0.610348i	0.412962	−	0.0343892i
$316$	−2.44949			−0.137795
$317$	1.06350	+	0.284965i	0.0597323	+	0.0160052i	0.288561	−	0.957461i	$-0.406823\pi$
$317$	1.06350	+	0.284965i	0.0597323	+	0.0160052i	−0.228829	+	0.973467i	$0.573490\pi$
$318$	−2.73810	+	15.9588i	−0.153545	+	0.894927i
$319$	−17.1455	−	9.89898i	−0.959966	−	0.554236i
$320$	0.358719	+	2.20711i	0.0200530	+	0.123381i
$321$	9.05051	−	0.833917i	0.505150	−	0.0465447i
$322$	0.283763	−	1.05902i	0.0158135	−	0.0590168i
$323$	−4.87832	−	4.87832i	−0.271437	−	0.271437i
$324$	−8.89060	−	1.39898i	−0.493922	−	0.0777211i
$325$	−9.55051	−	14.4495i	−0.529767	−	0.801513i
$326$	−0.550510	+	0.317837i	−0.0304899	+	0.0176034i
$327$	−22.5300	+	27.1032i	−1.24591	+	1.49881i
$328$	−1.01581	−	3.79107i	−0.0560889	−	0.209327i
$329$	4.93369	−	8.54541i	0.272003	−	0.471124i
$330$	23.4840	+	6.51451i	1.29275	+	0.358612i
$331$	2.22474	+	3.85337i	0.122283	+	0.211800i	0.920668	−	0.390347i	$-0.127645\pi$
$331$	2.22474	+	3.85337i	0.122283	+	0.211800i	−0.798385	+	0.602148i	$0.794312\pi$
$332$	−0.389270	+	0.389270i	−0.0213639	+	0.0213639i
$333$	7.20390	−	10.4930i	0.394772	−	0.575015i
$334$		−	10.7980i		−	0.590838i
$335$	−7.71159	+	3.47083i	−0.421329	+	0.189632i
$336$	−1.72474	−	0.794593i	−0.0940925	−	0.0433486i
$337$	29.7766	−	7.97861i	1.62203	−	0.434622i	0.670435	−	0.741968i	$-0.266108\pi$
$337$	29.7766	−	7.97861i	1.62203	−	0.434622i	0.951598	+	0.307346i	$0.0994408\pi$
$338$	0.965926	−	0.258819i	0.0525394	−	0.0140779i
$339$	21.7060	+	10.0000i	1.17891	+	0.543125i
$340$	−9.07277	+	4.08346i	−0.492040	+	0.221457i
$341$			27.9985i			1.51621i
$342$	−4.63737	−	0.362626i	−0.250760	−	0.0196085i
$343$	9.92168	−	9.92168i	0.535721	−	0.535721i
$344$	−1.73205	−	3.00000i	−0.0933859	−	0.161749i
$345$	−3.73205	−	1.03528i	−0.200927	−	0.0557374i
$346$	1.55051	−	2.68556i	0.0833559	−	0.144377i
$347$	−1.08757	−	4.05886i	−0.0583837	−	0.217891i	0.930570	−	0.366113i	$-0.119312\pi$
$347$	−1.08757	−	4.05886i	−0.0583837	−	0.217891i	−0.988954	+	0.148222i	$0.952645\pi$
$348$	3.48356	−	4.19067i	0.186739	−	0.224644i
$349$	−13.0297	+	7.52270i	−0.697464	+	0.402681i	−0.806402	−	0.591367i	$-0.798588\pi$
$349$	−13.0297	+	7.52270i	−0.697464	+	0.402681i	0.108938	+	0.994049i	$0.465255\pi$
$350$	1.09638	−	5.37113i	0.0586038	−	0.287099i
$351$	−17.4495	−	4.41761i	−0.931385	−	0.235795i
$352$	−4.44949	−	4.44949i	−0.237159	−	0.237159i
$353$	−8.87564	+	33.1244i	−0.472403	+	1.76303i	0.158694	+	0.987328i	$0.449272\pi$
$353$	−8.87564	+	33.1244i	−0.472403	+	1.76303i	−0.631097	+	0.775704i	$0.717395\pi$
$354$	−20.3632	+	1.87628i	−1.08229	+	0.0997229i
$355$	−0.228029	−	1.40300i	−0.0121025	−	0.0744636i
$356$	2.05051	+	1.18386i	0.108677	+	0.0627446i
$357$	1.42883	−	8.32780i	0.0756215	−	0.440754i
$358$	17.0063	+	4.55683i	0.898812	+	0.240836i
$359$	−17.4634			−0.921682			−0.460841	−	0.887483i	$-0.652452\pi$
$359$	−17.4634			−0.921682			−0.460841	+	0.887483i	$0.652452\pi$
$360$	−2.86042	+	6.06778i	−0.150757	+	0.319800i
$361$	16.5959			0.873469
$362$	−10.1910	−	2.73067i	−0.535628	−	0.143521i
$363$	−46.4639	+	17.1547i	−2.43872	+	0.900388i
$364$	−3.28913	−	1.89898i	−0.172397	−	0.0995336i
$365$	5.35844	−	7.43828i	0.280473	−	0.389337i
$366$	3.94949	−	8.57277i	0.206443	−	0.448106i
$367$	2.52520	−	9.42418i	0.131814	−	0.491938i	−0.868176	−	0.496256i	$-0.834708\pi$
$367$	2.52520	−	9.42418i	0.131814	−	0.491938i	0.999991	+	0.00431778i	$0.00137440\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$	3.92480	−	11.1010i	0.204317	−	0.577896i
$370$	−6.00000	−	7.34847i	−0.311925	−	0.382029i
$371$	−8.87628	+	5.12472i	−0.460833	+	0.266062i
$372$	−7.59575	−	1.30323i	−0.393822	−	0.0675691i
$373$	5.25190	+	19.6004i	0.271933	+	1.01487i	0.957869	+	0.287206i	$0.0927266\pi$
$373$	5.25190	+	19.6004i	0.271933	+	1.01487i	−0.685935	+	0.727662i	$0.740607\pi$
$374$	13.9993	−	24.2474i	0.723885	−	1.25381i
$375$	−18.9389	−	4.03976i	−0.977998	−	0.208612i
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$	7.70674	−	7.70674i	0.396917	−	0.396917i
$378$	−2.91649	−	4.89379i	−0.150008	−	0.251709i
$379$		−	6.65153i		−	0.341666i	−0.985300	−	0.170833i	$-0.945354\pi$
$379$		−	6.65153i		−	0.341666i	0.985300	−	0.170833i	$-0.0546459\pi$
$380$	−1.22939	+	3.24176i	−0.0630663	+	0.166299i
$381$	−3.17423	−	34.4500i	−0.162621	−	1.76493i
$382$	−3.20807	+	0.859599i	−0.164139	+	0.0439809i
$383$	26.8508	−	7.19464i	1.37201	−	0.367629i	0.503798	−	0.863822i	$-0.331936\pi$
$383$	26.8508	−	7.19464i	1.37201	−	0.367629i	0.868212	+	0.496193i	$0.165269\pi$
$384$	1.41421	−	1.00000i	0.0721688	−	0.0510310i
$385$	6.33145	+	14.0674i	0.322681	+	0.716942i
$386$			17.3205i			0.881591i
$387$	0.810167	−	10.3607i	0.0411831	−	0.526663i
$388$	−7.89898	+	7.89898i	−0.401010	+	0.401010i
$389$	2.81237	+	4.87117i	0.142593	+	0.246978i	0.928472	−	0.371402i	$-0.121123\pi$
$389$	2.81237	+	4.87117i	0.142593	+	0.246978i	−0.785879	+	0.618380i	$0.787789\pi$
$390$	−6.81017	+	11.5595i	−0.344846	+	0.585337i
$391$	−2.22474	+	3.85337i	−0.112510	+	0.194873i
$392$	1.50062	+	5.60040i	0.0757929	+	0.282863i
$393$	−6.32005	−	17.1180i	−0.318804	−	0.863489i
$394$	−8.48528	+	4.89898i	−0.427482	+	0.246807i
$395$	−4.24264	+	3.46410i	−0.213470	+	0.174298i
$396$	−3.44949	−	18.5597i	−0.173343	−	0.932662i
$397$	15.4495	+	15.4495i	0.775388	+	0.775388i	0.979043	−	0.203655i	$-0.0652821\pi$
$397$	15.4495	+	15.4495i	0.775388	+	0.775388i	−0.203655	+	0.979043i	$0.565282\pi$
$398$	−0.918940	+	3.42953i	−0.0460623	+	0.171907i
$399$	−1.69994	−	2.40408i	−0.0851036	−	0.120355i
$400$	3.74264	+	3.31552i	0.187132	+	0.165776i
$401$	22.3485	+	12.9029i	1.11603	+	0.644340i	0.940384	−	0.340114i	$-0.110466\pi$
$401$	22.3485	+	12.9029i	1.11603	+	0.644340i	0.175645	+	0.984454i	$0.443799\pi$
$402$	5.03736	+	4.18739i	0.251241	+	0.208848i
$403$	−14.8883	−	3.98930i	−0.741638	−	0.198721i
$404$	1.27135			0.0632520
$405$	−17.3774	+	10.1501i	−0.863492	+	0.504363i
$406$	3.44949			0.171195
$407$	25.7873	+	6.90968i	1.27823	+	0.342500i
$408$	5.92650	+	4.92650i	0.293406	+	0.243898i
$409$	16.5420	+	9.55051i	0.817948	+	0.472242i	0.849708	−	0.527253i	$-0.176778\pi$
$409$	16.5420	+	9.55051i	0.817948	+	0.472242i	−0.0317605	+	0.999496i	$0.510111\pi$
$410$	−7.12082	−	5.12975i	−0.351672	−	0.253340i
$411$	2.20204	+	3.11416i	0.108619	+	0.153610i
$412$	−1.06110	+	3.96008i	−0.0522767	+	0.195099i
$413$	−9.15306	−	9.15306i	−0.450393	−	0.450393i
$414$	0.548188	+	2.94949i	0.0269420	+	0.144960i
$415$	−0.123724	+	1.22474i	−0.00607339	+	0.0601204i
$416$	3.00000	−	1.73205i	0.147087	−	0.0849208i
$417$	7.73810	+	20.9588i	0.378937	+	1.02636i
$418$	−2.52520	−	9.42418i	−0.123512	−	0.460952i
$419$	5.97469	−	10.3485i	0.291883	−	0.505556i	−0.682372	−	0.731005i	$-0.739052\pi$
$419$	5.97469	−	10.3485i	0.291883	−	0.505556i	0.974255	+	0.225449i	$0.0723850\pi$
$420$	−4.11107	+	1.06288i	−0.200600	+	0.0518633i
$421$	7.44949	+	12.9029i	0.363066	+	0.628849i	0.988464	−	0.151457i	$-0.0483966\pi$
$421$	7.44949	+	12.9029i	0.363066	+	0.628849i	−0.625398	+	0.780306i	$0.715063\pi$
$422$	−13.3636	+	13.3636i	−0.650530	+	0.650530i
$423$	−2.10488	+	26.9178i	−0.102343	+	1.30879i
$424$		−	9.34847i		−	0.454002i
$425$	−9.93960	+	19.9036i	−0.482142	+	0.965466i
$426$	−0.898979	+	0.635674i	−0.0435557	+	0.0307985i
$427$	5.77111	−	1.54636i	0.279284	−	0.0748338i
$428$	−5.06865	+	1.35814i	−0.245002	+	0.0656482i
$429$	−3.46410	−	37.5959i	−0.167248	−	1.81515i
$430$	−7.24264	−	2.74666i	−0.349271	−	0.132456i
$431$		−	15.5563i		−	0.749323i	−0.927162	−	0.374661i	$-0.877759\pi$
$431$		−	15.5563i		−	0.749323i	0.927162	−	0.374661i	$-0.122241\pi$
$432$	5.19565	−	0.0719302i	0.249976	−	0.00346074i
$433$	8.55051	−	8.55051i	0.410911	−	0.410911i	−0.471145	−	0.882056i	$-0.656159\pi$
$433$	8.55051	−	8.55051i	0.410911	−	0.410911i	0.882056	+	0.471145i	$0.156159\pi$
$434$	−2.43916	−	4.22474i	−0.117083	−	0.202794i
$435$	0.107206	−	12.1850i	0.00514015	−	0.584224i
$436$	10.1742	−	17.6223i	0.487257	−	0.843955i
$437$	0.401302	+	1.49768i	0.0191969	+	0.0716436i
$438$	−6.99876	−	1.20080i	−0.334413	−	0.0573763i
$439$	8.83523	−	5.10102i	0.421682	−	0.243458i	−0.274114	−	0.961697i	$-0.588385\pi$
$439$	8.83523	−	5.10102i	0.421682	−	0.243458i	0.695797	+	0.718239i	$0.255051\pi$
$440$	−13.9993	−	1.41421i	−0.667389	−	0.0674200i
$441$	−5.79796	+	16.3991i	−0.276093	+	0.780910i
$442$	10.8990	+	10.8990i	0.518412	+	0.518412i
$443$	0.142483	−	0.531752i	0.00676955	−	0.0252643i	−0.962458	−	0.271429i	$-0.912504\pi$
$443$	0.142483	−	0.531752i	0.00676955	−	0.0252643i	0.969228	+	0.246165i	$0.0791704\pi$
$444$	−3.07483	+	6.67423i	−0.145925	+	0.316745i
$445$	5.22582	−	0.849349i	0.247728	−	0.0402630i
$446$	−7.19694	−	4.15515i	−0.340785	−	0.196752i
$447$	20.9652	−	7.74045i	0.991620	−	0.366111i
$448$	1.05902	+	0.283763i	0.0500339	+	0.0134065i
$449$	21.7060			1.02437			0.512185	−	0.858875i	$-0.328836\pi$
$449$	21.7060			1.02437			0.512185	+	0.858875i	$0.328836\pi$
$450$	3.62675	+	14.5550i	0.170967	+	0.686127i
$451$	24.6969			1.16293
$452$	−13.3278	−	3.57117i	−0.626887	−	0.167974i
$453$	6.32530	−	36.8665i	0.297188	−	1.73214i
$454$	−13.0779	−	7.55051i	−0.613775	−	0.354363i
$455$	−8.38250	+	1.36240i	−0.392978	+	0.0638704i
$456$	2.67423	−	0.246405i	0.125233	−	0.0115390i
$457$	1.59165	−	5.94012i	0.0744543	−	0.277867i	−0.918655	−	0.395061i	$-0.870723\pi$
$457$	1.59165	−	5.94012i	0.0744543	−	0.277867i	0.993109	+	0.117194i	$0.0373900\pi$
$458$	11.5601	+	11.5601i	0.540169	+	0.540169i
$459$	6.29253	+	22.2474i	0.293710	+	1.03842i
$460$	2.22474	+	0.224745i	0.103729	+	0.0104788i
$461$	16.3763	−	9.45485i	0.762719	−	0.440356i	−0.0675520	−	0.997716i	$-0.521519\pi$
$461$	16.3763	−	9.45485i	0.762719	−	0.440356i	0.830271	+	0.557360i	$0.188186\pi$
$462$	7.63859	−	9.18910i	0.355380	−	0.427516i
$463$	−8.54613	−	31.8946i	−0.397172	−	1.48227i	−0.818048	−	0.575150i	$-0.804944\pi$
$463$	−8.54613	−	31.8946i	−0.397172	−	1.48227i	0.420876	−	0.907118i	$-0.361723\pi$
$464$	−1.57313	+	2.72474i	−0.0730308	+	0.126493i
$465$	−14.9993	+	8.48477i	−0.695575	+	0.393472i
$466$	−7.77526	−	13.4671i	−0.360182	−	0.623853i
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	−0.638630	−	0.769514i	$-0.720499\pi$
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	0.769514	+	0.638630i	$0.220499\pi$
$468$	10.3607	+	0.810167i	0.478922	+	0.0374500i
$469$			4.14643i			0.191464i
$470$	18.8169	+	7.13604i	0.867960	+	0.329161i
$471$	9.67423	+	4.45694i	0.445765	+	0.205365i
$472$	11.4042	−	3.05575i	0.524922	−	0.140652i
$473$	21.0552	−	5.64173i	0.968120	−	0.259407i
$474$	3.85337	+	1.77526i	0.176991	+	0.0815402i
$475$	2.45518	+	7.35351i	0.112651	+	0.337402i
$476$			4.87832i			0.223597i
$477$	15.8735	−	23.1209i	0.726797	−	1.05863i
$478$	−12.0000	+	12.0000i	−0.548867	+	0.548867i
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	0.773879	−	0.633333i	$-0.218314\pi$
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	−0.935422	+	0.353533i	$0.884980\pi$
$480$	1.03528	−	3.73205i	0.0472537	−	0.170344i
$481$	−7.34847	+	12.7279i	−0.335061	+	0.580343i
$482$	−4.91756	−	18.3526i	−0.223989	−	0.835938i
$483$	−1.21391	+	1.46032i	−0.0552350	+	0.0664469i
$484$	24.7648	−	14.2980i	1.12567	−	0.649907i
$485$	−2.51059	+	24.8523i	−0.114000	+	1.12848i
$486$	12.9722	+	8.64420i	0.588431	+	0.392109i
$487$	−12.0000	−	12.0000i	−0.543772	−	0.543772i	0.380861	−	0.924632i	$-0.375628\pi$
$487$	−12.0000	−	12.0000i	−0.543772	−	0.543772i	−0.924632	+	0.380861i	$0.875628\pi$
$488$	−1.41043	+	5.26380i	−0.0638472	+	0.238281i
$489$	1.09638	−	0.101021i	0.0495799	−	0.00456831i
$490$	10.5193	+	7.57797i	0.475214	+	0.342338i
$491$	0.247449	+	0.142865i	0.0111672	+	0.00644739i	0.505573	−	0.862784i	$-0.331281\pi$
$491$	0.247449	+	0.142865i	0.0111672	+	0.00644739i	−0.494406	+	0.869231i	$0.664614\pi$
$492$	−1.14955	+	6.70006i	−0.0518256	+	0.302062i
$493$	−13.5223	−	3.62328i	−0.609012	−	0.163184i
$494$	5.37113			0.241658
$495$	−32.2221	−	27.2681i	−1.44828	−	1.22561i
$496$	4.44949			0.199788
$497$	−0.673191	−	0.180381i	−0.0301967	−	0.00809119i
$498$	0.894494	−	0.330251i	0.0400832	−	0.0147989i
$499$	7.70674	+	4.44949i	0.345001	+	0.199187i	0.662481	−	0.749078i	$-0.269503\pi$
$499$	7.70674	+	4.44949i	0.345001	+	0.199187i	−0.317480	+	0.948265i	$0.602837\pi$
$500$	11.1713	+	0.449747i	0.499595	+	0.0201133i
$501$	−7.82577	+	16.9866i	−0.349629	+	0.758906i
$502$	2.89123	−	10.7902i	0.129042	−	0.481590i
$503$	−16.7563	−	16.7563i	−0.747125	−	0.747125i	0.226813	−	0.973938i	$-0.427169\pi$
$503$	−16.7563	−	16.7563i	−0.747125	−	0.747125i	−0.973938	+	0.226813i	$0.927169\pi$
$504$	2.13737	+	2.50000i	0.0952062	+	0.111359i
$505$	2.20204	−	1.79796i	0.0979895	−	0.0800081i
$506$	−5.44949	+	3.14626i	−0.242259	+	0.139869i
$507$	−1.70711	−	0.292893i	−0.0758153	−	0.0130078i
$508$	5.16964	+	19.2934i	0.229366	+	0.856005i
$509$	−19.8150	+	34.3207i	−0.878286	+	1.52124i	−0.0250662	+	0.999686i	$0.507980\pi$
$509$	−19.8150	+	34.3207i	−0.878286	+	1.52124i	−0.853220	+	0.521551i	$0.825354\pi$
$510$	17.2321	+	0.151613i	0.763052	+	0.00671352i
$511$	−2.24745	−	3.89270i	−0.0994213	−	0.172203i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	7.03239	+	3.93137i	0.310488	+	0.173574i
$514$		−	26.0454i		−	1.14881i
$515$	3.76252	+	8.35968i	0.165796	+	0.368372i
$516$	0.550510	+	5.97469i	0.0242349	+	0.263021i
$517$	−54.7030	+	14.6576i	−2.40584	+	0.644642i
$518$	−4.49303	+	1.20390i	−0.197413	+	0.0528965i
$519$	−4.38551	+	3.10102i	−0.192502	+	0.136120i
$520$	2.74666	−	7.24264i	0.120449	−	0.317611i
$521$		−	29.4449i		−	1.29000i	−0.764181	−	0.645001i	$-0.776857\pi$
$521$		−	29.4449i		−	1.29000i	0.764181	−	0.645001i	$-0.223143\pi$
$522$	−8.51727	+	4.06778i	−0.372791	+	0.178042i
$523$	1.77526	−	1.77526i	0.0776265	−	0.0776265i	−0.667228	−	0.744854i	$-0.732519\pi$
$523$	1.77526	−	1.77526i	0.0776265	−	0.0776265i	0.744854	+	0.667228i	$0.232519\pi$
$524$	5.26758	+	9.12372i	0.230116	+	0.398572i
$525$	−5.61744	+	7.65490i	−0.245165	+	0.334087i
$526$	6.34847	−	10.9959i	0.276806	−	0.479443i
$527$	5.12409	+	19.1234i	0.223209	+	0.833027i
$528$	3.77489	+	10.2244i	0.164281	+	0.444959i
$529$	−19.0526	+	11.0000i	−0.828372	+	0.478261i
$530$	−13.2207	−	16.1920i	−0.574272	−	0.703337i
$531$	33.3939	+	11.8065i	1.44917	+	0.512359i
$532$	1.20204	+	1.20204i	0.0521151	+	0.0521151i
$533$	−3.51888	+	13.1326i	−0.152420	+	0.568838i
$534$	−2.36773	−	3.34847i	−0.102461	−	0.144902i
$535$	−6.85845	+	9.52052i	−0.296517	+	0.411608i
$536$	−3.27526	−	1.89097i	−0.141469	−	0.0816774i
$537$	−23.4506	−	19.4937i	−1.01197	−	0.841217i
$538$	−4.54308	−	1.21731i	−0.195866	−	0.0524822i
$539$	−36.4838			−1.57147
$540$	8.89741	−	7.47235i	0.382884	−	0.321559i
$541$	−25.9444			−1.11544			−0.557718	−	0.830030i	$-0.688323\pi$
$541$	−25.9444			−1.11544			−0.557718	+	0.830030i	$0.688323\pi$
$542$	−15.4987	−	4.15286i	−0.665725	−	0.178380i
$543$	14.0528	+	11.6816i	0.603062	+	0.501305i
$544$	−3.85337	−	2.22474i	−0.165212	−	0.0953851i
$545$	−7.29939	−	44.9112i	−0.312672	−	1.92379i
$546$	3.79796	+	5.37113i	0.162538	+	0.229863i
$547$	−5.53567	+	20.6594i	−0.236688	+	0.883332i	0.740693	+	0.671844i	$0.234498\pi$
$547$	−5.53567	+	20.6594i	−0.236688	+	0.883332i	−0.977381	+	0.211488i	$0.932169\pi$
$548$	−1.55708	−	1.55708i	−0.0665151	−	0.0665151i
$549$	−12.4261	+	10.6237i	−0.530335	+	0.453410i
$550$	−26.2474	+	17.3485i	−1.11919	+	0.739741i
$551$	−4.22474	+	2.43916i	−0.179980	+	0.103912i
$552$	−0.599900	−	1.62484i	−0.0255335	−	0.0691580i
$553$	0.695075	+	2.59405i	0.0295576	+	0.110310i
$554$	−7.14250	+	12.3712i	−0.303456	+	0.525601i
$555$	4.11303	+	15.9086i	0.174588	+	0.675282i
$556$	−6.44949	−	11.1708i	−0.273519	−	0.473749i
$557$	16.3670	−	16.3670i	0.693492	−	0.693492i	−0.269507	−	0.962999i	$-0.586861\pi$
$557$	16.3670	−	16.3670i	0.693492	−	0.693492i	0.962999	+	0.269507i	$0.0868606\pi$
$558$	11.0046	+	7.55513i	0.465863	+	0.319834i
$559$			12.0000i			0.507546i
$560$	2.23557	−	1.00619i	0.0944703	−	0.0425191i
$561$	−39.5959	+	27.9985i	−1.67174	+	1.18210i
$562$	−0.169011	+	0.0452863i	−0.00712928	+	0.00191029i
$563$	−33.1781	+	8.89004i	−1.39829	+	0.374670i	−0.877730	−	0.479155i	$-0.840943\pi$
$563$	−33.1781	+	8.89004i	−1.39829	+	0.374670i	−0.520559	+	0.853826i	$0.674276\pi$
$564$	−1.43027	−	15.5227i	−0.0602251	−	0.653624i
$565$	−28.1348	+	12.6629i	−1.18364	+	0.532732i
$566$			6.89610i			0.289864i
$567$	1.04128	+	9.81229i	0.0437297	+	0.412077i
$568$	0.449490	−	0.449490i	0.0188602	−	0.0188602i
$569$	−13.0458	−	22.5959i	−0.546907	−	0.947270i	−0.998484	−	0.0550383i	$-0.982472\pi$
$569$	−13.0458	−	22.5959i	−0.546907	−	0.947270i	0.451578	−	0.892232i	$-0.350861\pi$
$570$	4.28344	−	4.20872i	0.179414	−	0.176284i
$571$	−13.5505	+	23.4702i	−0.567071	+	0.982196i	0.429782	+	0.902932i	$0.358590\pi$
$571$	−13.5505	+	23.4702i	−0.567071	+	0.982196i	−0.996854	+	0.0792637i	$0.974743\pi$
$572$	5.64173	+	21.0552i	0.235892	+	0.880363i
$573$	5.66971	+	0.972768i	0.236855	+	0.0406380i
$574$	−3.72656	+	2.15153i	−0.155544	+	0.0898032i
$575$	4.17121	−	2.75699i	0.173951	−	0.114975i
$576$	−2.94949	+	0.548188i	−0.122895	+	0.0228412i
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	0.258336	−	0.966055i	$-0.416826\pi$
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	−0.966055	+	0.258336i	$0.916826\pi$
$578$	0.724165	−	2.70262i	0.0301213	−	0.112414i
$579$	12.5529	−	27.2474i	0.521683	−	1.13237i
$580$	1.12863	+	6.94414i	0.0468637	+	0.288340i
$581$	0.522704	+	0.301783i	0.0216854	+	0.0125201i
$582$	18.1509	−	6.70139i	0.752378	−	0.277782i
$583$	56.8211	+	15.2252i	2.35329	+	0.630562i
$584$	4.09978			0.169650
$585$	19.0910	−	13.2490i	0.789314	−	0.547777i
$586$	22.0454			0.910687
$587$	29.9876	+	8.03514i	1.23772	+	0.331646i	0.817581	−	0.575814i	$-0.195315\pi$
$587$	29.9876	+	8.03514i	1.23772	+	0.331646i	0.420138	+	0.907460i	$0.361981\pi$
$588$	1.69818	−	9.89774i	0.0700319	−	0.408176i
$589$	5.97469	+	3.44949i	0.246183	+	0.142134i
$590$	15.4312	−	21.4207i	0.635293	−	0.881877i
$591$	16.8990	−	1.55708i	0.695131	−	0.0640496i
$592$	1.09808	−	4.09808i	0.0451307	−	0.168430i
$593$	10.0745	+	10.0745i	0.413709	+	0.413709i	0.883028	−	0.469320i	$-0.155501\pi$
$593$	10.0745	+	10.0745i	0.413709	+	0.413709i	−0.469320	+	0.883028i	$0.655501\pi$
$594$	−8.02458	+	31.6969i	−0.329252	+	1.30054i
$595$	6.89898	+	8.44949i	0.282831	+	0.346395i
$596$	−11.1742	+	6.45145i	−0.457714	+	0.264262i
$597$	3.93115	−	4.72911i	0.160891	−	0.193549i
$598$	−0.896575	−	3.34607i	−0.0366637	−	0.136831i
$599$	16.8991	−	29.2702i	0.690480	−	1.19595i	−0.281201	−	0.959649i	$-0.590733\pi$
$599$	16.8991	−	29.2702i	0.690480	−	1.19595i	0.971681	−	0.236297i	$-0.0759339\pi$
$600$	−3.48477	−	7.92820i	−0.142265	−	0.323668i
$601$	−17.3485	−	30.0484i	−0.707659	−	1.22570i	−0.965723	−	0.259573i	$-0.916418\pi$
$601$	−17.3485	−	30.0484i	−0.707659	−	1.22570i	0.258065	−	0.966128i	$-0.416915\pi$
$602$	−2.68556	+	2.68556i	−0.109455	+	0.109455i
$603$	−4.88964	−	10.2381i	−0.199122	−	0.416928i
$604$			21.5959i			0.878725i
$605$	22.6735	−	59.7875i	0.921809	−	2.43071i
$606$	−2.00000	−	0.921404i	−0.0812444	−	0.0374295i
$607$	−21.4114	+	5.73717i	−0.869062	+	0.232864i	−0.665682	−	0.746235i	$-0.731859\pi$
$607$	−21.4114	+	5.73717i	−0.869062	+	0.232864i	−0.203380	+	0.979100i	$0.565193\pi$
$608$	−1.49768	+	0.401302i	−0.0607389	+	0.0162749i
$609$	−5.42650	−	2.50000i	−0.219893	−	0.101305i
$610$	5.00120	+	11.1118i	0.202493	+	0.449905i
$611$		−	31.1769i		−	1.26128i
$612$	−5.75272	−	12.0452i	−0.232540	−	0.486900i
$613$	−12.7980	+	12.7980i	−0.516905	+	0.516905i	−0.916633	−	0.399729i	$-0.869104\pi$
$613$	−12.7980	+	12.7980i	−0.516905	+	0.516905i	0.399729	+	0.916633i	$0.369104\pi$
$614$	0.476756	+	0.825765i	0.0192403	+	0.0333252i
$615$	7.48424	+	13.2305i	0.301794	+	0.533507i
$616$	−3.44949	+	5.97469i	−0.138984	+	0.240727i
$617$	1.83788	+	6.85906i	0.0739902	+	0.276135i	0.993002	−	0.118094i	$-0.0376783\pi$
$617$	1.83788	+	6.85906i	0.0739902	+	0.276135i	−0.919012	+	0.394229i	$0.871012\pi$
$618$	4.53930	−	5.46070i	0.182597	−	0.219662i
$619$	21.4275	−	12.3712i	0.861244	−	0.497239i	−0.00318471	−	0.999995i	$-0.501014\pi$
$619$	21.4275	−	12.3712i	0.861244	−	0.497239i	0.864429	+	0.502756i	$0.167680\pi$
$620$	7.70674	−	6.29253i	0.309510	−	0.252714i
$621$	1.27526	−	5.03723i	0.0511742	−	0.202137i
$622$	−14.5505	−	14.5505i	−0.583422	−	0.583422i
$623$	0.671873	−	2.50746i	0.0269180	−	0.100459i
$624$	−5.97469	+	0.550510i	−0.239179	+	0.0220380i
$625$	19.9853	−	15.0196i	0.799411	−	0.600784i
$626$	−4.34847	−	2.51059i	−0.173800	−	0.100343i
$627$	−2.85765	+	16.6556i	−0.114124	+	0.665161i
$628$	−5.94012	−	1.59165i	−0.237037	−	0.0635138i
$629$	18.8776			0.752699
$630$	7.23757	+	1.30742i	0.288352	+	0.0520890i
$631$	−12.8990			−0.513500			−0.256750	−	0.966478i	$-0.582652\pi$
$631$	−12.8990			−0.513500			−0.256750	+	0.966478i	$0.582652\pi$
$632$	−2.36603	−	0.633975i	−0.0941154	−	0.0252182i
$633$	30.7079	−	11.3375i	1.22053	−	0.450625i
$634$	0.953512	+	0.550510i	0.0378688	+	0.0218636i
$635$	36.2390	+	26.1061i	1.43810	+	1.03599i
$636$	−6.77526	+	14.7064i	−0.268656	+	0.583146i
$637$	5.19831	−	19.4003i	0.205964	−	0.768670i
$638$	−13.9993	−	13.9993i	−0.554236	−	0.554236i
$639$	1.87492	−	0.348469i	0.0741705	−	0.0137852i
$640$	−0.224745	+	2.22474i	−0.00888382	+	0.0879408i
$641$	−7.74745	+	4.47299i	−0.306006	+	0.176673i	−0.645138	−	0.764066i	$-0.723200\pi$
$641$	−7.74745	+	4.47299i	−0.306006	+	0.176673i	0.339132	+	0.940739i	$0.389867\pi$
$642$	8.95796	+	1.53694i	0.353542	+	0.0606583i
$643$	−8.22539	−	30.6976i	−0.324378	−	1.21059i	−0.914936	−	0.403599i	$-0.867759\pi$
$643$	−8.22539	−	30.6976i	−0.324378	−	1.21059i	0.590558	−	0.806995i	$-0.298908\pi$
$644$	0.548188	−	0.949490i	0.0216016	−	0.0374151i
$645$	9.40300	+	9.56993i	0.370243	+	0.376816i
$646$	−3.44949	−	5.97469i	−0.135718	−	0.235071i
$647$	−24.9558	+	24.9558i	−0.981114	+	0.981114i	−0.999825	−	0.0187105i	$-0.994044\pi$
$647$	−24.9558	+	24.9558i	−0.981114	+	0.981114i	0.0187105	+	0.999825i	$0.494044\pi$
$648$	−8.22558	−	3.65237i	−0.323131	−	0.143479i
$649$			74.2929i			2.91625i
$650$	−5.48528	−	16.4290i	−0.215150	−	0.644398i
$651$	0.775255	+	8.41385i	0.0303846	+	0.329765i
$652$	−0.614014	+	0.164525i	−0.0240467	+	0.00644328i
$653$	−20.8162	+	5.57768i	−0.814601	+	0.218272i	−0.641985	−	0.766718i	$-0.721889\pi$
$653$	−20.8162	+	5.57768i	−0.814601	+	0.218272i	−0.172616	+	0.984989i	$0.555222\pi$
$654$	−28.7771	+	20.3485i	−1.12527	+	0.795688i
$655$	22.0266	+	8.35326i	0.860651	+	0.326389i
$656$		−	3.92480i		−	0.153238i
$657$	10.1397	+	6.96132i	0.395587	+	0.271587i
$658$	6.97730	−	6.97730i	0.272003	−	0.272003i
$659$	5.65685	+	9.79796i	0.220360	+	0.381674i	0.954917	−	0.296872i	$-0.0959435\pi$
$659$	5.65685	+	9.79796i	0.220360	+	0.381674i	−0.734557	+	0.678546i	$0.762610\pi$
$660$	20.9978	+	12.3706i	0.817337	+	0.481527i
$661$	15.3485	−	26.5843i	0.596986	−	1.03401i	−0.396277	−	0.918131i	$-0.629698\pi$
$661$	15.3485	−	26.5843i	0.596986	−	1.03401i	0.993263	−	0.115880i	$-0.0369687\pi$
$662$	1.15161	+	4.29788i	0.0447587	+	0.167042i
$663$	−9.24656	−	25.0445i	−0.359106	−	0.972648i
$664$	−0.476756	+	0.275255i	−0.0185017	+	0.0106820i
$665$	3.78194	+	0.382053i	0.146657	+	0.0148154i
$666$	9.67423	−	8.27098i	0.374869	−	0.320494i
$667$	2.22474	+	2.22474i	0.0861425	+	0.0861425i
$668$	2.79472	−	10.4300i	0.108131	−	0.403550i
$669$	8.31031	+	11.7526i	0.321295	+	0.454380i
$670$	−8.34714	+	1.35666i	−0.322478	+	0.0524122i
$671$	−29.6969	−	17.1455i	−1.14644	−	0.661896i
$672$	−1.46032	−	1.21391i	−0.0563331	−	0.0468278i
$673$	15.7783	+	4.22778i	0.608208	+	0.162969i	0.549762	−	0.835322i	$-0.314719\pi$
$673$	15.7783	+	4.22778i	0.608208	+	0.162969i	0.0584468	+	0.998291i	$0.481385\pi$
$674$	30.8270			1.18741
$675$	4.84327	−	25.5253i	0.186418	−	0.982471i
$676$	1.00000			0.0384615
$677$	6.18587	+	1.65750i	0.237742	+	0.0637028i	0.375723	−	0.926732i	$-0.377394\pi$
$677$	6.18587	+	1.65750i	0.237742	+	0.0637028i	−0.137981	+	0.990435i	$0.544061\pi$
$678$	18.3782	+	15.2772i	0.705811	+	0.586717i
$679$	10.6066	+	6.12372i	0.407044	+	0.235007i
$680$	−9.82050	+	1.59612i	−0.376599	+	0.0612084i
$681$	15.1010	+	21.3561i	0.578672	+	0.818366i
$682$	−7.24656	+	27.0445i	−0.277485	+	1.03559i
$683$	13.8564	+	13.8564i	0.530201	+	0.530201i	0.920632	−	0.390431i	$-0.127674\pi$
$683$	13.8564	+	13.8564i	0.530201	+	0.530201i	−0.390431	+	0.920632i	$0.627674\pi$
$684$	−4.38551	−	1.55051i	−0.167684	−	0.0592852i
$685$	−4.89898	−	0.494897i	−0.187180	−	0.0189091i
$686$	12.1515	−	7.01569i	0.463948	−	0.267860i
$687$	−9.80745	−	26.5637i	−0.374178	−	1.01347i
$688$	−0.896575	−	3.34607i	−0.0341816	−	0.127568i
$689$	−16.1920	+	28.0454i	−0.616867	+	1.06844i
$690$	−3.33694	−	1.96593i	−0.127035	−	0.0748415i
$691$	−16.4722	−	28.5307i	−0.626632	−	1.08536i	−0.988223	−	0.153021i	$-0.951100\pi$
$691$	−16.4722	−	28.5307i	−0.626632	−	1.08536i	0.361591	−	0.932337i	$-0.382234\pi$
$692$	2.19275	−	2.19275i	0.0833559	−	0.0833559i
$693$	−18.6763	+	8.91964i	−0.709453	+	0.338829i
$694$		−	4.20204i		−	0.159507i
$695$	−26.9688	−	10.2275i	−1.02299	−	0.387952i
$696$	4.44949	−	3.14626i	0.168657	−	0.119259i
$697$	16.8683	−	4.51985i	0.638933	−	0.171202i
$698$	−14.5327	+	3.89404i	−0.550073	+	0.147392i
$699$	2.47127	+	26.8207i	0.0934719	+	1.01445i
$700$	2.44917	−	4.90435i	0.0925698	−	0.185367i
$701$			23.9309i			0.903857i	0.892054	+	0.451928i	$0.149264\pi$
$701$			23.9309i			0.903857i	−0.892054	+	0.451928i	$0.850736\pi$
$702$	−15.7116	−	8.78335i	−0.592994	−	0.331506i
$703$	4.65153	−	4.65153i	0.175436	−	0.175436i
$704$	−3.14626	−	5.44949i	−0.118579	−	0.205385i
$705$	−24.4297	−	24.8634i	−0.920076	−	0.936410i
$706$	−17.1464	+	29.6985i	−0.645314	+	1.11772i
$707$	−0.360762	−	1.34638i	−0.0135678	−	0.0506359i
$708$	−20.1550	−	3.45805i	−0.757471	−	0.129961i
$709$	38.4069	−	22.1742i	1.44240	−	0.832771i	0.444392	−	0.895833i	$-0.353420\pi$
$709$	38.4069	−	22.1742i	1.44240	−	0.832771i	0.998010	+	0.0630617i	$0.0200865\pi$
$710$	0.142865	−	1.41421i	0.00536161	−	0.0530745i
$711$	−4.77526	−	5.58542i	−0.179086	−	0.209470i
$712$	1.67423	+	1.67423i	0.0627446	+	0.0627446i
$713$	1.15161	−	4.29788i	0.0431282	−	0.160957i
$714$	3.53553	−	7.67423i	0.132314	−	0.287201i
$715$	39.5483	+	28.4901i	1.47902	+	1.06547i
$716$	15.2474	+	8.80312i	0.569824	+	0.328988i
$717$	27.5745	−	10.1806i	1.02979	−	0.380203i
$718$	−16.8683	−	4.51985i	−0.629520	−	0.168679i
$719$	32.5269			1.21305			0.606525	−	0.795065i	$-0.292563\pi$
$719$	32.5269			1.21305			0.606525	+	0.795065i	$0.292563\pi$
$720$	−4.33341	+	5.12070i	−0.161497	+	0.190837i
$721$	4.49490			0.167399
$722$	16.0304	+	4.29534i	0.596591	+	0.159856i
$723$	−5.56497	+	32.4350i	−0.206964	+	1.20627i
$724$	−9.13701	−	5.27526i	−0.339574	−	0.196053i
$725$	11.7753	+	10.4315i	0.437325	+	0.387416i
$726$	−49.3207	+	4.54442i	−1.83046	+	0.168659i
$727$	−8.11447	+	30.2836i	−0.300949	+	1.12316i	0.635428	+	0.772160i	$0.280824\pi$
$727$	−8.11447	+	30.2836i	−0.300949	+	1.12316i	−0.936377	+	0.350996i	$0.885843\pi$
$728$	−2.68556	−	2.68556i	−0.0995336	−	0.0995336i
$729$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$730$	7.10102	−	5.79796i	0.262821	−	0.214592i
$731$	13.3485	−	7.70674i	0.493711	−	0.285044i
$732$	6.03371	−	7.25845i	0.223012	−	0.268280i
$733$	−3.71385	−	13.8603i	−0.137174	−	0.511941i	−0.999979	−	0.00640470i	$-0.997961\pi$
$733$	−3.71385	−	13.8603i	−0.137174	−	0.511941i	0.862805	−	0.505536i	$-0.168705\pi$
$734$	4.87832	−	8.44949i	0.180062	−	0.311876i
$735$	−11.0562	−	19.5450i	−0.407813	−	0.720927i
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	16.8277	−	16.8277i	0.619856	−	0.619856i
$738$	6.66422	−	9.70695i	0.245313	−	0.357318i
$739$		−	24.9444i		−	0.917594i	−0.888541	−	0.458797i	$-0.848280\pi$
$739$		−	24.9444i		−	0.917594i	0.888541	−	0.458797i	$-0.151720\pi$
$740$	−3.89363	−	8.65099i	−0.143133	−	0.318017i
$741$	−8.44949	−	3.89270i	−0.310400	−	0.143002i
$742$	−9.90020	+	2.65275i	−0.363448	+	0.0973855i
$743$	0.0975783	−	0.0261460i	0.00357980	−	0.000959205i	−0.257029	−	0.966404i	$-0.582743\pi$
$743$	0.0975783	−	0.0261460i	0.00357980	−	0.000959205i	0.260609	+	0.965445i	$0.416077\pi$
$744$	−6.99964	−	3.22474i	−0.256619	−	0.118225i
$745$	−10.2306	+	26.9770i	−0.374821	+	0.988360i
$746$			20.2918i			0.742936i
$747$	−1.64650	−	0.128751i	−0.0602425	−	0.00471074i
$748$	19.7980	−	19.7980i	0.723885	−	0.723885i
$749$	2.87659	+	4.98240i	0.105108	+	0.182053i
$750$	−17.2480	−	8.80385i	−0.629807	−	0.321471i
$751$	4.34847	−	7.53177i	0.158678	−	0.274838i	−0.775714	−	0.631084i	$-0.782610\pi$
$751$	4.34847	−	7.53177i	0.158678	−	0.274838i	0.934392	+	0.356246i	$0.115944\pi$
$752$	2.32937	+	8.69333i	0.0849434	+	0.317013i
$753$	−12.3684	+	14.8790i	−0.450731	+	0.542222i
$754$	9.43879	−	5.44949i	0.343741	−	0.198459i
$755$	30.5412	+	37.4052i	1.11151	+	1.36132i
$756$	−1.55051	−	5.48188i	−0.0563915	−	0.199374i
$757$	−22.0454	−	22.0454i	−0.801254	−	0.801254i	0.182038	−	0.983292i	$-0.441731\pi$
$757$	−22.0454	−	22.0454i	−0.801254	−	0.801254i	−0.983292	+	0.182038i	$0.941731\pi$
$758$	1.72154	−	6.42489i	0.0625293	−	0.233362i
$759$	10.8530	−	1.00000i	0.393939	−	0.0362977i
$760$	−2.02653	+	2.81311i	−0.0735099	+	0.102042i
$761$	−15.3990	−	8.89060i	−0.558213	−	0.322284i	0.194215	−	0.980959i	$-0.437784\pi$
$761$	−15.3990	−	8.89060i	−0.558213	−	0.322284i	−0.752428	+	0.658675i	$0.771117\pi$
$762$	5.85024	−	34.0977i	0.211932	−	1.23523i
$763$	−21.5494	−	5.77414i	−0.780141	−	0.209038i
$764$	−3.32124			−0.120158
$765$	−26.9985	−	12.7274i	−0.976134	−	0.460160i
$766$	27.7980			1.00438
$767$	−39.5054	−	10.5854i	−1.42646	−	0.382218i
$768$	1.62484	−	0.599900i	0.0586315	−	0.0216470i
$769$	−17.0580	−	9.84847i	−0.615129	−	0.355145i	0.159841	−	0.987143i	$-0.448902\pi$
$769$	−17.0580	−	9.84847i	−0.615129	−	0.355145i	−0.774970	+	0.631998i	$0.782235\pi$
$770$	2.47480	+	15.2268i	0.0891855	+	0.548735i
$771$	−18.8763	+	40.9729i	−0.679812	+	1.47560i
$772$	−4.48288	+	16.7303i	−0.161342	+	0.602138i
$773$	3.11416	+	3.11416i	0.112008	+	0.112008i	0.760890	−	0.648881i	$-0.224763\pi$
$773$	3.11416	+	3.11416i	0.112008	+	0.112008i	−0.648881	+	0.760890i	$0.724763\pi$
$774$	3.46410	−	9.79796i	0.124515	−	0.352180i
$775$	4.44949	−	21.7980i	0.159830	−	0.783006i
$776$	−9.67423	+	5.58542i	−0.347285	+	0.200505i
$777$	7.94066	+	1.36240i	0.284870	+	0.0488759i
$778$	1.45579	+	5.43309i	0.0521927	+	0.194786i
$779$	3.04272	−	5.27015i	0.109017	−	0.188823i
$780$	−9.56993	+	9.40300i	−0.342658	+	0.336681i
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	−3.14626	+	3.14626i	−0.112510	+	0.112510i
$783$	16.3469	−	0.226311i	0.584191	−	0.00808771i
$784$			5.79796i			0.207070i
$785$	−12.5395	+	5.64378i	−0.447555	+	0.201435i
$786$	−1.67423	−	18.1705i	−0.0597180	−	0.648120i
$787$	−3.96008	+	1.06110i	−0.141162	+	0.0378241i	−0.328708	−	0.944432i	$-0.606613\pi$
$787$	−3.96008	+	1.06110i	−0.141162	+	0.0378241i	0.187546	+	0.982256i	$0.439947\pi$
$788$	−9.46410	+	2.53590i	−0.337145	+	0.0903376i
$789$	−17.9562	+	12.6969i	−0.639257	+	0.452023i
$790$	−4.99465	+	2.24799i	−0.177702	+	0.0799799i
$791$			15.1278i			0.537881i
$792$	1.47167	−	18.8201i	0.0522933	−	0.668744i
$793$	13.3485	−	13.3485i	0.474018	−	0.474018i
$794$	10.9244	+	18.9217i	0.387694	+	0.671505i
$795$	9.06287	+	35.0539i	0.321427	+	1.24323i
$796$	−1.77526	+	3.07483i	−0.0629222	+	0.108985i
$797$	−5.22867	−	19.5137i	−0.185209	−	0.691210i	−0.994586	−	0.103920i	$-0.966861\pi$
$797$	−5.22867	−	19.5137i	−0.185209	−	0.691210i	0.809377	−	0.587290i	$-0.199805\pi$
$798$	−1.01980	−	2.76214i	−0.0361004	−	0.0977788i
$799$	−34.6803	+	20.0227i	−1.22690	+	0.708352i
$800$	2.75699	+	4.17121i	0.0974745	+	0.147474i
$801$	1.29796	+	6.98358i	0.0458611	+	0.246753i
$802$	18.2474	+	18.2474i	0.644340	+	0.644340i
$803$	−6.67700	+	24.9189i	−0.235626	+	0.879369i
$804$	3.78194	+	5.34847i	0.133379	+	0.188626i
$805$	−0.393292	−	2.41982i	−0.0138617	−	0.0852874i
$806$	−13.3485	−	7.70674i	−0.470180	−	0.271458i
$807$	6.26462	+	5.20757i	0.220525	+	0.183315i
$808$	1.22803	+	0.329049i	0.0432019	+	0.0115759i
$809$	−54.0901			−1.90171			−0.950853	−	0.309644i	$-0.899790\pi$
$809$	−54.0901			−1.90171			−0.950853	+	0.309644i	$0.899790\pi$
$810$	−19.4124	+	5.30664i	−0.682081	+	0.186456i
$811$	43.6413			1.53245			0.766227	−	0.642570i	$-0.222132\pi$
$811$	43.6413			1.53245			0.766227	+	0.642570i	$0.222132\pi$
$812$	3.33195	+	0.892794i	0.116929	+	0.0313309i
$813$	21.3717	+	17.7656i	0.749538	+	0.623066i
$814$	23.1202	+	13.3485i	0.810364	+	0.467864i
$815$	−0.830831	+	1.15331i	−0.0291027	+	0.0403988i
$816$	4.44949	+	6.29253i	0.155763	+	0.220283i
$817$	1.39015	−	5.18811i	0.0486352	−	0.181509i
$818$	13.5065	+	13.5065i	0.472242	+	0.472242i
$819$	−2.08200	−	11.2020i	−0.0727508	−	0.391431i
$820$	−5.55051	−	6.79796i	−0.193832	−	0.237395i
$821$	−22.3207	+	12.8868i	−0.778997	+	0.449754i	−0.836075	−	0.548616i	$-0.815155\pi$
$821$	−22.3207	+	12.8868i	−0.778997	+	0.449754i	0.0570780	+	0.998370i	$0.481822\pi$
$822$	1.32101	+	3.57797i	0.0460754	+	0.124796i
$823$	−12.5807	−	46.9519i	−0.438536	−	1.63664i	−0.732459	−	0.680811i	$-0.761627\pi$
$823$	−12.5807	−	46.9519i	−0.438536	−	1.63664i	0.293923	−	0.955829i	$-0.405039\pi$
$824$	−2.04989	+	3.55051i	−0.0714112	+	0.123688i
$825$	53.8639	−	8.26873i	1.87530	−	0.287880i
$826$	−6.47219	−	11.2102i	−0.225196	−	0.390052i
$827$	−27.3235	+	27.3235i	−0.950133	+	0.950133i	−0.998814	−	0.0486816i	$-0.984498\pi$
$827$	−27.3235	+	27.3235i	−0.950133	+	0.950133i	0.0486816	+	0.998814i	$0.484498\pi$
$828$	−0.233875	+	2.99087i	−0.00812772	+	0.103940i
$829$		−	15.4495i		−	0.536583i	−0.963338	−	0.268291i	$-0.913541\pi$
$829$		−	15.4495i		−	0.536583i	0.963338	−	0.268291i	$-0.0864590\pi$
$830$	−0.436496	+	1.15099i	−0.0151510	+	0.0399515i
$831$	20.2020	−	14.2850i	0.700801	−	0.495541i
$832$	3.34607	−	0.896575i	0.116004	−	0.0310832i
$833$	−24.9189	+	6.67700i	−0.863389	+	0.231344i
$834$	2.04989	+	22.2474i	0.0709818	+	0.770366i
$835$	−9.90969	−	22.0177i	−0.342939	−	0.761953i
$836$		−	9.75663i		−	0.337440i
$837$	−11.8362	−	19.8608i	−0.409118	−	0.686488i
$838$	8.44949	−	8.44949i	0.291883	−	0.291883i
$839$	−10.1459	−	17.5732i	−0.350275	−	0.606695i	0.636022	−	0.771671i	$-0.280579\pi$
$839$	−10.1459	−	17.5732i	−0.350275	−	0.606695i	−0.986298	+	0.164976i	$0.947245\pi$
$840$	−4.24608	−	0.0373581i	−0.146504	−	0.00128898i
$841$	9.55051	−	16.5420i	0.329328	−	0.570413i
$842$	3.85614	+	14.3913i	0.132891	+	0.495957i
$843$	0.298697	+	0.0512483i	0.0102877	+	0.00176509i
$844$	−16.3670	+	9.44949i	−0.563375	+	0.325265i
$845$	1.73205	−	1.41421i	0.0595844	−	0.0486504i
$846$	−9.00000	+	25.4558i	−0.309426	+	0.875190i
$847$	−22.1691	−	22.1691i	−0.761740	−	0.761740i
$848$	2.41956	−	9.02993i	0.0830881	−	0.310089i
$849$	4.99791	−	10.8485i	0.171528	−	0.372319i
$850$	−14.7524	+	16.6528i	−0.506001	+	0.571188i
$851$	−3.67423	−	2.12132i	−0.125951	−	0.0727179i
$852$	−1.03287	+	0.381341i	−0.0353856	+	0.0130645i
$853$	35.8547	+	9.60723i	1.22764	+	0.328945i	0.813660	−	0.581340i	$-0.197472\pi$
$853$	35.8547	+	9.60723i	1.22764	+	0.328945i	0.413980	+	0.910286i	$0.364138\pi$
$854$	5.97469			0.204450
$855$	−9.78867	+	3.51648i	−0.334765	+	0.120261i
$856$	−5.24745			−0.179354
$857$	3.66855	+	0.982984i	0.125315	+	0.0335781i	0.320932	−	0.947102i	$-0.396004\pi$
$857$	3.66855	+	0.982984i	0.125315	+	0.0335781i	−0.195616	+	0.980680i	$0.562671\pi$
$858$	6.38447	−	37.2114i	0.217962	−	1.27038i
$859$	−2.16064	−	1.24745i	−0.0737202	−	0.0425624i	0.462687	−	0.886522i	$-0.346885\pi$
$859$	−2.16064	−	1.24745i	−0.0737202	−	0.0425624i	−0.536407	+	0.843959i	$0.680219\pi$
$860$	−6.28497	−	4.52761i	−0.214316	−	0.154390i
$861$	7.42168	−	0.683837i	0.252930	−	0.0233051i
$862$	4.02628	−	15.0263i	0.137136	−	0.511797i
$863$	27.7842	+	27.7842i	0.945787	+	0.945787i	0.998604	−	0.0528175i	$-0.0168202\pi$
$863$	27.7842	+	27.7842i	0.945787	+	0.945787i	−0.0528175	+	0.998604i	$0.516820\pi$
$864$	5.03723	+	1.27526i	0.171370	+	0.0433851i
$865$	0.696938	−	6.89898i	0.0236966	−	0.234572i
$866$	10.4722	−	6.04612i	0.355860	−	0.205456i
$867$	−3.09792	+	3.72674i	−0.105211	+	0.126567i
$868$	−1.26260	−	4.71209i	−0.0428555	−	0.159939i
$869$	7.70674	−	13.3485i	0.261433	−	0.452816i
$870$	3.25725	−	11.7420i	0.110431	−	0.398092i
$871$	6.55051	+	11.3458i	0.221956	+	0.384438i
$872$	14.3885	−	14.3885i	0.487257	−	0.487257i
$873$	−33.4105	−	2.61258i	−1.13078	−	0.0884225i
$874$			1.55051i			0.0524468i
$875$	−2.69371	−	11.9582i	−0.0910640	−	0.404262i
$876$	−6.44949	−	2.97129i	−0.217908	−	0.100391i
$877$	−7.85813	+	2.10558i	−0.265350	+	0.0711004i	−0.389041	−	0.921220i	$-0.627194\pi$
$877$	−7.85813	+	2.10558i	−0.265350	+	0.0711004i	0.123691	+	0.992321i	$0.460527\pi$
$878$	9.85441	−	2.64048i	0.332570	−	0.0891120i
$879$	−34.6803	−	15.9773i	−1.16974	−	0.538901i
$880$	−13.1562	−	4.98930i	−0.443496	−	0.168189i
$881$			58.3006i			1.96420i	0.188368	+	0.982098i	$0.439680\pi$
$881$			58.3006i			1.96420i	−0.188368	+	0.982098i	$0.560320\pi$
$882$	−9.84480	+	14.3397i	−0.331492	+	0.482843i
$883$	−40.2702	+	40.2702i	−1.35520	+	1.35520i	−0.475463	+	0.879736i	$0.657719\pi$
$883$	−40.2702	+	40.2702i	−1.35520	+	1.35520i	−0.879736	+	0.475463i	$0.842281\pi$
$884$	7.70674	+	13.3485i	0.259206	+	0.448958i
$885$	−39.7999	+	22.5139i	−1.33786	+	0.756798i
$886$	0.275255	−	0.476756i	0.00924738	−	0.0160169i
$887$	7.19464	+	26.8508i	0.241572	+	0.901561i	0.975075	+	0.221874i	$0.0712174\pi$
$887$	7.19464	+	26.8508i	0.241572	+	0.901561i	−0.733503	+	0.679686i	$0.762116\pi$
$888$	−4.69748	+	5.65099i	−0.157637	+	0.189635i
$889$	18.9651	−	10.9495i	0.636068	−	0.367234i
$890$	5.26758	+	0.532134i	0.176570	+	0.0178372i
$891$	35.5959	−	44.0477i	1.19251	−	1.47565i
$892$	−5.87628	−	5.87628i	−0.196752	−	0.196752i
$893$	−3.61171	+	13.4791i	−0.120861	+	0.451061i
$894$	22.2542	−	2.05051i	0.744292	−	0.0685793i
$895$	38.8588	−	6.31570i	1.29891	−	0.211111i
$896$	0.949490	+	0.548188i	0.0317202	+	0.0183137i
$897$	−1.01461	+	5.91359i	−0.0338769	+	0.197449i
$898$	20.9664	+	5.61793i	0.699658	+	0.187473i
$899$	13.9993			0.466902
$900$	−0.263927	+	14.9977i	−0.00879757	+	0.499923i
$901$	41.5959			1.38576
$902$	23.8554	+	6.39204i	0.794298	+	0.212832i
$903$	6.17109	−	2.27840i	0.205361	−	0.0758203i
$904$	−11.9494	−	6.89898i	−0.397431	−	0.229457i
$905$	−23.2861	+	3.78467i	−0.774056	+	0.125807i
$906$	15.6515	−	33.9732i	0.519987	−	1.12869i
$907$	1.71089	−	6.38512i	0.0568091	−	0.212015i	−0.931687	−	0.363263i	$-0.881663\pi$
$907$	1.71089	−	6.38512i	0.0568091	−	0.212015i	0.988496	+	0.151248i	$0.0483293\pi$
$908$	−10.6780	−	10.6780i	−0.354363	−	0.354363i
$909$	2.47848	+	2.89898i	0.0822061	+	0.0961531i
$910$	−8.44949	−	0.853572i	−0.280098	−	0.0282956i
$911$	6.12372	−	3.53553i	0.202888	−	0.117137i	−0.395114	−	0.918632i	$-0.629295\pi$
$911$	6.12372	−	3.53553i	0.202888	−	0.117137i	0.598002	+	0.801495i	$0.295962\pi$
$912$	2.64689	+	0.454134i	0.0876472	+	0.0150379i
$913$	−0.896575	−	3.34607i	−0.0296723	−	0.110739i
$914$	3.07483	−	5.32577i	0.101706	−	0.176161i
$915$	0.185687	−	21.1050i	0.00613862	−	0.697709i
$916$	8.17423	+	14.1582i	0.270084	+	0.467800i
$917$	8.16744	−	8.16744i	0.269713	−	0.269713i
$918$	0.320053	+	23.1180i	0.0105633	+	0.763008i
$919$			27.3485i			0.902143i	0.892488	+	0.451071i	$0.148958\pi$
$919$			27.3485i			0.902143i	−0.892488	+	0.451071i	$0.851042\pi$
$920$	2.09077	+	0.792893i	0.0689307	+	0.0261409i
$921$	−0.151531	−	1.64456i	−0.00499311	−	0.0541902i
$922$	18.2654	−	4.89419i	0.601538	−	0.161182i
$923$	−2.12701	+	0.569930i	−0.0700113	+	0.0187595i
$924$	9.75663	−	6.89898i	0.320970	−	0.226960i
$925$	−18.9783	−	9.47753i	−0.624003	−	0.311619i
$926$		−	33.0197i		−	1.08510i
$927$	−11.0985	+	5.30057i	−0.364524	+	0.174094i
$928$	−2.22474	+	2.22474i	−0.0730308	+	0.0730308i
$929$	−23.9309	−	41.4495i	−0.785147	−	1.35991i	−0.928912	−	0.370302i	$-0.879254\pi$
$929$	−23.9309	−	41.4495i	−0.785147	−	1.35991i	0.143765	−	0.989612i	$-0.454079\pi$
$930$	−16.6842	+	4.31356i	−0.547097	+	0.141447i
$931$	−4.49490	+	7.78539i	−0.147314	+	0.255156i
$932$	−4.02477	−	15.0206i	−0.131836	−	0.492017i
$933$	12.3445	+	33.4353i	0.404140	+	1.09462i
$934$	3.46410	−	2.00000i	0.113349	−	0.0654420i
$935$	6.29253	−	62.2896i	0.205788	−	2.03709i
$936$	9.79796	+	3.46410i	0.320256	+	0.113228i
$937$	−12.8990	−	12.8990i	−0.421391	−	0.421391i	0.464291	−	0.885683i	$-0.346309\pi$
$937$	−12.8990	−	12.8990i	−0.421391	−	0.421391i	−0.885683	+	0.464291i	$0.846309\pi$
$938$	−1.07317	+	4.00514i	−0.0350404	+	0.130773i
$939$	5.02118	+	7.10102i	0.163860	+	0.231733i
$940$	16.3288	+	11.7631i	0.532587	+	0.383669i
$941$	5.47730	+	3.16232i	0.178555	+	0.103089i	0.586613	−	0.809867i	$-0.300461\pi$
$941$	5.47730	+	3.16232i	0.178555	+	0.103089i	−0.408059	+	0.912956i	$0.633794\pi$
$942$	8.19105	+	6.80895i	0.266879	+	0.221847i
$943$	−3.79107	−	1.01581i	−0.123454	−	0.0330795i
$944$	11.8065			0.384269
$945$	−10.4381	−	7.30214i	−0.339552	−	0.237539i
$946$	21.7980			0.708713
$947$	39.6468	+	10.6233i	1.28835	+	0.345212i	0.837033	−	0.547152i	$-0.184288\pi$
$947$	39.6468	+	10.6233i	1.28835	+	0.345212i	0.451316	+	0.892364i	$0.350955\pi$
$948$	3.26260	+	2.71209i	0.105964	+	0.0880846i
$949$	−12.2993	−	7.10102i	−0.399253	−	0.230509i
$950$	0.468290	+	7.73839i	0.0151933	+	0.251067i
$951$	−1.10102	−	1.55708i	−0.0357030	−	0.0504917i
$952$	−1.26260	+	4.71209i	−0.0409211	+	0.152720i
$953$	−19.6561	−	19.6561i	−0.636724	−	0.636724i	0.313022	−	0.949746i	$-0.398659\pi$
$953$	−19.6561	−	19.6561i	−0.636724	−	0.636724i	−0.949746	+	0.313022i	$0.898659\pi$
$954$	21.3167	−	18.2247i	0.690155	−	0.590048i
$955$	−5.75255	+	4.69694i	−0.186148	+	0.151989i
$956$	−14.6969	+	8.48528i	−0.475333	+	0.274434i
$957$	11.8768	+	32.1686i	0.383923	+	1.03986i
$958$	−1.83013	−	6.83013i	−0.0591287	−	0.220671i
$959$	−1.20713	+	2.09082i	−0.0389804	+	0.0675159i
$960$	1.96593	−	3.33694i	0.0634500	−	0.107699i
$961$	5.60102	+	9.70125i	0.180678	+	0.312944i
$962$	−10.3923	+	10.3923i	−0.335061	+	0.335061i
$963$	−12.9782	−	8.91005i	−0.418215	−	0.287122i
$964$		−	19.0000i		−	0.611949i
$965$	15.8957	+	35.3175i	0.511700	+	1.13691i
$966$	−1.55051	+	1.09638i	−0.0498868	+	0.0352753i
$967$	48.7319	−	13.0577i	1.56711	−	0.419907i	0.632206	−	0.774800i	$-0.282150\pi$
$967$	48.7319	−	13.0577i	1.56711	−	0.419907i	0.934907	+	0.354894i	$0.115483\pi$
$968$	27.6215	−	7.40117i	0.887790	−	0.237883i
$969$	1.09638	+	11.8990i	0.0352207	+	0.382250i
$970$	−8.85729	+	23.3557i	−0.284390	+	0.749905i
$971$		−	49.2117i		−	1.57928i	−0.613570	−	0.789640i	$-0.710267\pi$
$971$		−	49.2117i		−	1.57928i	0.613570	−	0.789640i	$-0.289733\pi$
$972$	10.2929	+	11.7071i	0.330145	+	0.375506i
$973$	−10.0000	+	10.0000i	−0.320585	+	0.320585i
$974$	−8.48528	−	14.6969i	−0.271886	−	0.470920i
$975$	−3.27775	+	29.8204i	−0.104972	+	0.955017i
$976$	−2.72474	+	4.71940i	−0.0872170	+	0.151064i
$977$	10.9985	+	41.0469i	0.351873	+	1.31321i	0.884374	+	0.466778i	$0.154585\pi$
$977$	10.9985	+	41.0469i	0.351873	+	1.31321i	−0.532502	+	0.846429i	$0.678748\pi$
$978$	1.08516	+	0.186185i	0.0346997	+	0.00595353i
$979$	−12.9029	+	7.44949i	−0.412378	+	0.238087i
$980$	8.19955	+	10.0424i	0.261925	+	0.320791i
$981$	60.0176	−	11.1548i	1.91621	−	0.356145i
$982$	0.202041	+	0.202041i	0.00644739	+	0.00644739i
$983$	12.1122	−	45.2034i	0.386319	−	1.44176i	−0.449757	−	0.893151i	$-0.648490\pi$
$983$	12.1122	−	45.2034i	0.386319	−	1.44176i	0.836077	−	0.548612i	$-0.184844\pi$
$984$	−2.84448	+	6.17423i	−0.0906787	+	0.196827i
$985$	−12.8060	+	17.7766i	−0.408033	+	0.566408i
$986$	−12.1237	−	6.99964i	−0.386098	−	0.222914i
$987$	−16.0330	+	5.91945i	−0.510335	+	0.188418i
$988$	5.18811	+	1.39015i	0.165056	+	0.0442265i
$989$	−3.46410			−0.110152
$990$	−24.0667	−	34.6787i	−0.764890	−	1.10216i
$991$	−56.7423			−1.80248			−0.901240	−	0.433320i	$-0.857342\pi$
$991$	−56.7423			−1.80248			−0.901240	+	0.433320i	$0.857342\pi$
$992$	4.29788	+	1.15161i	0.136458	+	0.0365637i
$993$	1.30323	−	7.59575i	0.0413566	−	0.241044i
$994$	−0.603566	−	0.348469i	−0.0191440	−	0.0110528i
$995$	1.27364	+	7.83636i	0.0403770	+	0.248429i
$996$	0.949490	−	0.0874863i	0.0300857	−	0.00277211i
$997$	−10.7053	+	39.9528i	−0.339041	+	1.26532i	0.560381	+	0.828235i	$0.310655\pi$
$997$	−10.7053	+	39.9528i	−0.339041	+	1.26532i	−0.899422	+	0.437082i	$0.856012\pi$
$998$	6.29253	+	6.29253i	0.199187	+	0.199187i
$999$	−21.2132	+	6.00000i	−0.671156	+	0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.2.l.a.77.2	yes	8
3.2	odd	2		270.2.m.a.17.1		8
4.3	odd	2		720.2.cu.a.257.2		8
5.2	odd	4		450.2.p.a.293.1		8
5.3	odd	4	inner	90.2.l.a.23.2	✓	8
5.4	even	2		450.2.p.a.257.1		8
9.2	odd	6	inner	90.2.l.a.47.2	yes	8
9.4	even	3		810.2.f.b.647.1		8
9.5	odd	6		810.2.f.b.647.4		8
9.7	even	3		270.2.m.a.197.1		8
15.2	even	4		1350.2.q.g.1043.2		8
15.8	even	4		270.2.m.a.233.1		8
15.14	odd	2		1350.2.q.g.557.2		8
20.3	even	4		720.2.cu.a.113.2		8
36.11	even	6		720.2.cu.a.497.2		8
45.2	even	12		450.2.p.a.443.1		8
45.7	odd	12		1350.2.q.g.143.2		8
45.13	odd	12		810.2.f.b.323.3		8
45.23	even	12		810.2.f.b.323.2		8
45.29	odd	6		450.2.p.a.407.1		8
45.34	even	6		1350.2.q.g.1007.2		8
45.38	even	12	inner	90.2.l.a.83.2	yes	8
45.43	odd	12		270.2.m.a.143.1		8
180.83	odd	12		720.2.cu.a.353.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.2	✓	8	5.3	odd	4	inner
90.2.l.a.47.2	yes	8	9.2	odd	6	inner
90.2.l.a.77.2	yes	8	1.1	even	1	trivial
90.2.l.a.83.2	yes	8	45.38	even	12	inner
270.2.m.a.17.1		8	3.2	odd	2
270.2.m.a.143.1		8	45.43	odd	12
270.2.m.a.197.1		8	9.7	even	3
270.2.m.a.233.1		8	15.8	even	4
450.2.p.a.257.1		8	5.4	even	2
450.2.p.a.293.1		8	5.2	odd	4
450.2.p.a.407.1		8	45.29	odd	6
450.2.p.a.443.1		8	45.2	even	12
720.2.cu.a.113.2		8	20.3	even	4
720.2.cu.a.257.2		8	4.3	odd	2
720.2.cu.a.353.2		8	180.83	odd	12
720.2.cu.a.497.2		8	36.11	even	6
810.2.f.b.323.2		8	45.23	even	12
810.2.f.b.323.3		8	45.13	odd	12
810.2.f.b.647.1		8	9.4	even	3
810.2.f.b.647.4		8	9.5	odd	6
1350.2.q.g.143.2		8	45.7	odd	12
1350.2.q.g.557.2		8	15.14	odd	2
1350.2.q.g.1007.2		8	45.34	even	6
1350.2.q.g.1043.2		8	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	90.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.20711 - 0.358719i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(0.283763 - 1.05902i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.548188 + 2.94949i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.33195 - 1.10721i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.20711 - 0.358719i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(0.283763 - 1.05902i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.548188 + 2.94949i) q^{9} +(2.22474 + 0.224745i) q^{10} +(-5.44949 + 3.14626i) q^{11} +(-0.599900 - 1.62484i) q^{12} +(-0.896575 - 3.34607i) q^{13} +(0.548188 - 0.949490i) q^{14} +(-3.33694 - 1.96593i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.14626 + 3.14626i) q^{17} +(-0.233875 + 2.99087i) q^{18} +1.55051i q^{19} +(2.09077 + 0.792893i) q^{20} +(-1.55051 + 1.09638i) q^{21} +(-6.07812 + 1.62863i) q^{22} +(0.965926 - 0.258819i) q^{23} +(-0.158919 - 1.72474i) q^{24} +(4.74264 - 1.58346i) q^{25} -3.46410i q^{26} +(2.53553 - 4.53553i) q^{27} +(0.775255 - 0.775255i) q^{28} +(1.57313 + 2.72474i) q^{29} +(-2.71441 - 2.76260i) q^{30} +(2.22474 - 3.85337i) q^{31} +(0.258819 + 0.965926i) q^{32} +(10.7420 + 1.84304i) q^{33} +(-3.85337 + 2.22474i) q^{34} +(0.246405 - 2.43916i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(-3.00000 - 3.00000i) q^{37} +(-0.401302 + 1.49768i) q^{38} +(-2.51059 + 5.44949i) q^{39} +(1.81431 + 1.30701i) q^{40} +(-3.39898 - 1.96240i) q^{41} +(-1.78144 + 0.657717i) q^{42} +(-3.34607 - 0.896575i) q^{43} -6.29253 q^{44} +(2.26795 + 6.31319i) q^{45} +1.00000 q^{46} +(8.69333 + 2.32937i) q^{47} +(0.292893 - 1.70711i) q^{48} +(5.02118 + 2.89898i) q^{49} +(4.99087 - 0.302023i) q^{50} +(7.67423 - 0.707107i) q^{51} +(0.896575 - 3.34607i) q^{52} +(-6.61037 - 6.61037i) q^{53} +(3.62302 - 3.72474i) q^{54} +(-10.8990 + 8.89898i) q^{55} +(0.949490 - 0.548188i) q^{56} +(1.71673 - 2.06520i) q^{57} +(0.814313 + 3.03906i) q^{58} +(5.90326 - 10.2247i) q^{59} +(-1.90691 - 3.37101i) q^{60} +(2.72474 + 4.71940i) q^{61} +(3.14626 - 3.14626i) q^{62} +(3.27912 + 0.256415i) q^{63} +1.00000i q^{64} +(-3.17914 - 7.06350i) q^{65} +(9.89898 + 4.56048i) q^{66} +(-3.65307 + 0.978838i) q^{67} +(-4.29788 + 1.15161i) q^{68} +(-1.57313 - 0.724745i) q^{69} +(0.869309 - 2.29227i) q^{70} -0.635674i q^{71} +(-1.69798 + 2.47323i) q^{72} +(2.89898 - 2.89898i) q^{73} +(-2.12132 - 3.67423i) q^{74} +(-8.07019 - 3.14198i) q^{75} +(-0.775255 + 1.34278i) q^{76} +(1.78559 + 6.66390i) q^{77} +(-3.83548 + 4.61401i) q^{78} +(-2.12132 + 1.22474i) q^{79} +(1.41421 + 1.73205i) q^{80} +(-8.39898 + 3.23375i) q^{81} +(-2.77526 - 2.77526i) q^{82} +(-0.142483 + 0.531752i) q^{83} +(-1.89097 + 0.174235i) q^{84} +(-5.81552 + 8.07277i) q^{85} +(-3.00000 - 1.73205i) q^{86} +(0.921519 - 5.37101i) q^{87} +(-6.07812 - 1.62863i) q^{88} +2.36773 q^{89} +(0.556696 + 6.68506i) q^{90} -3.79796 q^{91} +(0.965926 + 0.258819i) q^{92} +(-7.22973 + 2.66925i) q^{93} +(7.79423 + 4.50000i) q^{94} +(0.556198 + 3.42214i) q^{95} +(0.724745 - 1.57313i) q^{96} +(-2.89123 + 10.7902i) q^{97} +(4.09978 + 4.09978i) q^{98} +(-12.2672 - 14.3485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 12 q^{5} - 8 q^{6} - 8 q^{7}+O(q^{10}) \) 8 * q + 4 * q^3 + 12 * q^5 - 8 * q^6 - 8 * q^7	\( 8 q + 4 q^{3} + 12 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{10} - 24 q^{11} - 4 q^{12} + 16 q^{15} + 4 q^{16} - 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{25} - 8 q^{27} + 16 q^{28} - 12 q^{30} + 8 q^{31} + 16 q^{33} - 8 q^{36} - 24 q^{37} + 12 q^{38} + 4 q^{40} + 12 q^{41} + 20 q^{42} + 32 q^{45} + 8 q^{46} + 8 q^{48} + 24 q^{50} + 32 q^{51} - 48 q^{55} - 12 q^{56} + 28 q^{57} - 4 q^{58} - 8 q^{60} + 12 q^{61} - 32 q^{63} - 24 q^{65} + 40 q^{66} + 4 q^{67} - 12 q^{68} - 16 q^{70} + 8 q^{72} - 16 q^{73} + 8 q^{75} - 16 q^{76} + 24 q^{77} - 24 q^{78} - 28 q^{81} - 32 q^{82} + 12 q^{83} - 20 q^{85} - 24 q^{86} - 8 q^{87} - 8 q^{88} - 20 q^{90} + 48 q^{91} - 20 q^{93} - 24 q^{95} - 4 q^{96} + 12 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 + 12 * q^5 - 8 * q^6 - 8 * q^7 + 8 * q^10 - 24 * q^11 - 4 * q^12 + 16 * q^15 + 4 * q^16 - 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^25 - 8 * q^27 + 16 * q^28 - 12 * q^30 + 8 * q^31 + 16 * q^33 - 8 * q^36 - 24 * q^37 + 12 * q^38 + 4 * q^40 + 12 * q^41 + 20 * q^42 + 32 * q^45 + 8 * q^46 + 8 * q^48 + 24 * q^50 + 32 * q^51 - 48 * q^55 - 12 * q^56 + 28 * q^57 - 4 * q^58 - 8 * q^60 + 12 * q^61 - 32 * q^63 - 24 * q^65 + 40 * q^66 + 4 * q^67 - 12 * q^68 - 16 * q^70 + 8 * q^72 - 16 * q^73 + 8 * q^75 - 16 * q^76 + 24 * q^77 - 24 * q^78 - 28 * q^81 - 32 * q^82 + 12 * q^83 - 20 * q^85 - 24 * q^86 - 8 * q^87 - 8 * q^88 - 20 * q^90 + 48 * q^91 - 20 * q^93 - 24 * q^95 - 4 * q^96 + 12 * q^97

Introduction

L-functions

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