LMFDB - Embedded newform 108.2.l.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(11,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("108.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.l (of order $18$, degree $6$, 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:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	108.11
Dual form			108.2.l.a.59.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37675 - 0.323366i) q^{2} +(-1.70299 - 0.315971i) q^{3} +(1.79087 - 0.890387i) q^{4} +(0.470103 - 1.29160i) q^{5} +(-2.44676 + 0.115676i) q^{6} +(1.57428 + 0.277589i) q^{7} +(2.17765 - 1.80495i) q^{8} +(2.80032 + 1.07619i) q^{9} +O(q^{10})$	\(q+(1.37675 - 0.323366i) q^{2} +(-1.70299 - 0.315971i) q^{3} +(1.79087 - 0.890387i) q^{4} +(0.470103 - 1.29160i) q^{5} +(-2.44676 + 0.115676i) q^{6} +(1.57428 + 0.277589i) q^{7} +(2.17765 - 1.80495i) q^{8} +(2.80032 + 1.07619i) q^{9} +(0.229554 - 1.93022i) q^{10} +(-3.66920 + 1.33548i) q^{11} +(-3.33116 + 0.950455i) q^{12} +(-5.10894 + 4.28691i) q^{13} +(2.25716 - 0.126901i) q^{14} +(-1.20869 + 2.05103i) q^{15} +(2.41442 - 3.18913i) q^{16} +(-2.32950 + 1.34494i) q^{17} +(4.20334 + 0.576109i) q^{18} +(3.15841 + 1.82351i) q^{19} +(-0.308129 - 2.73165i) q^{20} +(-2.59328 - 0.970158i) q^{21} +(-4.61972 + 3.02512i) q^{22} +(-0.644252 - 3.65373i) q^{23} +(-4.27882 + 2.38572i) q^{24} +(2.38300 + 1.99957i) q^{25} +(-5.64747 + 7.55405i) q^{26} +(-4.42887 - 2.71756i) q^{27} +(3.06650 - 0.904598i) q^{28} +(1.98152 - 2.36148i) q^{29} +(-1.00082 + 3.21460i) q^{30} +(1.45019 - 0.255708i) q^{31} +(2.29279 - 5.17137i) q^{32} +(6.67058 - 1.11494i) q^{33} +(-2.77223 + 2.60493i) q^{34} +(1.09861 - 1.90285i) q^{35} +(5.97324 - 0.566062i) q^{36} +(1.27577 + 2.20970i) q^{37} +(4.93800 + 1.48919i) q^{38} +(10.0550 - 5.68627i) q^{39} +(-1.30754 - 3.66116i) q^{40} +(-6.30271 - 7.51128i) q^{41} +(-3.88400 - 0.497086i) q^{42} +(1.27388 + 3.49995i) q^{43} +(-5.38197 + 5.65868i) q^{44} +(2.70644 - 3.11097i) q^{45} +(-2.06847 - 4.82194i) q^{46} +(-0.901707 + 5.11384i) q^{47} +(-5.11940 + 4.66816i) q^{48} +(-4.17653 - 1.52013i) q^{49} +(3.92738 + 1.98232i) q^{50} +(4.39208 - 1.55436i) q^{51} +(-5.33242 + 12.2262i) q^{52} -3.96045i q^{53} +(-6.97620 - 2.30924i) q^{54} +5.36695i q^{55} +(3.92928 - 2.23701i) q^{56} +(-4.80256 - 4.10338i) q^{57} +(1.96443 - 3.89192i) q^{58} +(-0.666798 - 0.242695i) q^{59} +(-0.338383 + 4.74933i) q^{60} +(0.969119 - 5.49615i) q^{61} +(1.91386 - 0.820987i) q^{62} +(4.10977 + 2.47157i) q^{63} +(1.48434 - 7.86109i) q^{64} +(3.13523 + 8.61397i) q^{65} +(8.82317 - 3.69204i) q^{66} +(-10.4714 - 12.4793i) q^{67} +(-2.97432 + 4.48277i) q^{68} +(-0.0573217 + 6.42582i) q^{69} +(0.897191 - 2.97499i) q^{70} +(7.76079 + 13.4421i) q^{71} +(8.04060 - 2.71087i) q^{72} +(4.04282 - 7.00237i) q^{73} +(2.47096 + 2.62966i) q^{74} +(-3.42640 - 4.15820i) q^{75} +(7.27993 + 0.453456i) q^{76} +(-6.14709 + 1.08390i) q^{77} +(12.0044 - 11.0800i) q^{78} +(8.37729 - 9.98366i) q^{79} +(-2.98405 - 4.61768i) q^{80} +(6.68364 + 6.02735i) q^{81} +(-11.1061 - 8.30305i) q^{82} +(0.344982 + 0.289474i) q^{83} +(-5.50803 + 0.571594i) q^{84} +(0.642014 + 3.64104i) q^{85} +(2.88558 + 4.40662i) q^{86} +(-4.12066 + 3.39547i) q^{87} +(-5.57978 + 9.53093i) q^{88} +(0.994859 + 0.574382i) q^{89} +(2.72011 - 5.15820i) q^{90} +(-9.23292 + 5.33063i) q^{91} +(-4.40701 - 5.96972i) q^{92} +(-2.55045 - 0.0227513i) q^{93} +(0.412218 + 7.33204i) q^{94} +(3.84002 - 3.22216i) q^{95} +(-5.53859 + 8.08233i) q^{96} +(-9.00157 + 3.27630i) q^{97} +(-6.24159 - 0.742291i) q^{98} +(-11.7122 - 0.208974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.37675	−	0.323366i	0.973508	−	0.228654i
$2$	1.37675	−	0.323366i	0.973508	−	0.228654i
$3$	−1.70299	−	0.315971i	−0.983220	−	0.182426i
$3$	−1.70299	−	0.315971i	−0.983220	−	0.182426i
$4$	1.79087	−	0.890387i	0.895434	−	0.445194i
$5$	0.470103	−	1.29160i	0.210236	−	0.577620i	−0.789092	−	0.614276i	$-0.789448\pi$
$5$	0.470103	−	1.29160i	0.210236	−	0.577620i	0.999328	+	0.0366558i	$0.0116705\pi$
$6$	−2.44676	+	0.115676i	−0.998884	+	0.0472245i
$7$	1.57428	+	0.277589i	0.595024	+	0.104919i	0.463046	−	0.886334i	$-0.346756\pi$
$7$	1.57428	+	0.277589i	0.595024	+	0.104919i	0.131977	+	0.991253i	$0.457867\pi$
$8$	2.17765	−	1.80495i	0.769917	−	0.638145i
$9$	2.80032	+	1.07619i	0.933442	+	0.358729i
$10$	0.229554	−	1.93022i	0.0725914	−	0.610389i
$11$	−3.66920	+	1.33548i	−1.10631	+	0.402663i	−0.829637	−	0.558303i	$-0.811453\pi$
$11$	−3.66920	+	1.33548i	−1.10631	+	0.402663i	−0.276669	+	0.960965i	$0.589231\pi$
$12$	−3.33116	+	0.950455i	−0.961623	+	0.274373i
$13$	−5.10894	+	4.28691i	−1.41696	+	1.18897i	−0.464021	+	0.885824i	$0.653594\pi$
$13$	−5.10894	+	4.28691i	−1.41696	+	1.18897i	−0.952943	+	0.303149i	$0.901962\pi$
$14$	2.25716	−	0.126901i	0.603250	−	0.0339156i
$15$	−1.20869	+	2.05103i	−0.312081	+	0.529575i
$16$	2.41442	−	3.18913i	0.603605	−	0.797283i
$17$	−2.32950	+	1.34494i	−0.564988	+	0.326196i	−0.755145	−	0.655558i	$-0.772434\pi$
$17$	−2.32950	+	1.34494i	−0.564988	+	0.326196i	0.190157	+	0.981754i	$0.439100\pi$
$18$	4.20334	+	0.576109i	0.990738	+	0.135790i
$19$	3.15841	+	1.82351i	0.724590	+	0.418342i	0.816440	−	0.577431i	$-0.195945\pi$
$19$	3.15841	+	1.82351i	0.724590	+	0.418342i	−0.0918500	+	0.995773i	$0.529278\pi$
$20$	−0.308129	−	2.73165i	−0.0688998	−	0.610817i
$21$	−2.59328	−	0.970158i	−0.565899	−	0.211706i
$22$	−4.61972	+	3.02512i	−0.984927	+	0.644957i
$23$	−0.644252	−	3.65373i	−0.134336	−	0.761856i	−0.975320	−	0.220796i	$-0.929134\pi$
$23$	−0.644252	−	3.65373i	−0.134336	−	0.761856i	0.840984	−	0.541060i	$-0.181977\pi$
$24$	−4.27882	+	2.38572i	−0.873411	+	0.486983i
$25$	2.38300	+	1.99957i	0.476599	+	0.399914i
$26$	−5.64747	+	7.55405i	−1.10756	+	1.48147i
$27$	−4.42887	−	2.71756i	−0.852336	−	0.522994i
$28$	3.06650	−	0.904598i	0.579514	−	0.170953i
$29$	1.98152	−	2.36148i	0.367959	−	0.438516i	−0.550016	−	0.835154i	$-0.685379\pi$
$29$	1.98152	−	2.36148i	0.367959	−	0.438516i	0.917975	+	0.396638i	$0.129823\pi$
$30$	−1.00082	+	3.21460i	−0.182724	+	0.586904i
$31$	1.45019	−	0.255708i	0.260462	−	0.0459264i	−0.0418922	−	0.999122i	$-0.513339\pi$
$31$	1.45019	−	0.255708i	0.260462	−	0.0459264i	0.302354	+	0.953196i	$0.402228\pi$
$32$	2.29279	−	5.17137i	0.405312	−	0.914179i
$33$	6.67058	−	1.11494i	1.16120	−	0.194087i
$34$	−2.77223	+	2.60493i	−0.475434	+	0.446741i
$35$	1.09861	−	1.90285i	0.185699	−	0.321640i
$36$	5.97324	−	0.566062i	0.995540	−	0.0943437i
$37$	1.27577	+	2.20970i	0.209736	+	0.363273i	0.951631	−	0.307243i	$-0.0994063\pi$
$37$	1.27577	+	2.20970i	0.209736	+	0.363273i	−0.741896	+	0.670515i	$0.766073\pi$
$38$	4.93800	+	1.48919i	0.801049	+	0.241579i
$39$	10.0550	−	5.68627i	1.61009	−	0.910531i
$40$	−1.30754	−	3.66116i	−0.206740	−	0.578880i
$41$	−6.30271	−	7.51128i	−0.984318	−	1.17306i	−0.984910	−	0.173065i	$-0.944633\pi$
$41$	−6.30271	−	7.51128i	−0.984318	−	1.17306i	0.000592131	−	1.00000i	$-0.499812\pi$
$42$	−3.88400	−	0.497086i	−0.599315	−	0.0767020i
$43$	1.27388	+	3.49995i	0.194265	+	0.533738i	0.998134	−	0.0610687i	$-0.0194509\pi$
$43$	1.27388	+	3.49995i	0.194265	+	0.533738i	−0.803869	+	0.594807i	$0.797229\pi$
$44$	−5.38197	+	5.65868i	−0.811362	+	0.853079i
$45$	2.70644	−	3.11097i	0.403453	−	0.463756i
$46$	−2.06847	−	4.82194i	−0.304979	−	0.710956i
$47$	−0.901707	+	5.11384i	−0.131528	+	0.745930i	0.845688	+	0.533678i	$0.179191\pi$
$47$	−0.901707	+	5.11384i	−0.131528	+	0.745930i	−0.977215	+	0.212251i	$0.931920\pi$
$48$	−5.11940	+	4.66816i	−0.738922	+	0.673792i
$49$	−4.17653	−	1.52013i	−0.596647	−	0.217162i
$50$	3.92738	+	1.98232i	0.555415	+	0.280343i
$51$	4.39208	−	1.55436i	0.615014	−	0.217654i
$52$	−5.33242	+	12.2262i	−0.739474	+	1.69547i
$53$		−	3.96045i		−	0.544009i	−0.962296	−	0.272005i	$-0.912313\pi$
$53$		−	3.96045i		−	0.544009i	0.962296	−	0.272005i	$-0.0876866\pi$
$54$	−6.97620	−	2.30924i	−0.949341	−	0.314248i
$55$			5.36695i			0.723679i
$56$	3.92928	−	2.23701i	0.525072	−	0.298932i
$57$	−4.80256	−	4.10338i	−0.636114	−	0.543506i
$58$	1.96443	−	3.89192i	0.257942	−	0.511034i
$59$	−0.666798	−	0.242695i	−0.0868098	−	0.0315962i	0.298250	−	0.954488i	$-0.403597\pi$
$59$	−0.666798	−	0.242695i	−0.0868098	−	0.0315962i	−0.385060	+	0.922892i	$0.625819\pi$
$60$	−0.338383	+	4.74933i	−0.0436851	+	0.613136i
$61$	0.969119	−	5.49615i	0.124083	−	0.703709i	−0.857765	−	0.514041i	$-0.828148\pi$
$61$	0.969119	−	5.49615i	0.124083	−	0.703709i	0.981848	−	0.189668i	$-0.0607411\pi$
$62$	1.91386	−	0.820987i	0.243060	−	0.104266i
$63$	4.10977	+	2.47157i	0.517782	+	0.311388i
$64$	1.48434	−	7.86109i	0.185543	−	0.982636i
$65$	3.13523	+	8.61397i	0.388877	+	1.06843i
$66$	8.82317	−	3.69204i	1.08606	−	0.454458i
$67$	−10.4714	−	12.4793i	−1.27928	−	1.52459i	−0.715344	−	0.698773i	$-0.753730\pi$
$67$	−10.4714	−	12.4793i	−1.27928	−	1.52459i	−0.563939	−	0.825817i	$-0.690715\pi$
$68$	−2.97432	+	4.48277i	−0.360689	+	0.543616i
$69$	−0.0573217	+	6.42582i	−0.00690072	+	0.773578i
$70$	0.897191	−	2.97499i	0.107235	−	0.355580i
$71$	7.76079	+	13.4421i	0.921036	+	1.59528i	0.797815	+	0.602903i	$0.205989\pi$
$71$	7.76079	+	13.4421i	0.921036	+	1.59528i	0.123222	+	0.992379i	$0.460677\pi$
$72$	8.04060	−	2.71087i	0.947593	−	0.319479i
$73$	4.04282	−	7.00237i	0.473176	−	0.819565i	−0.526352	−	0.850266i	$-0.676441\pi$
$73$	4.04282	−	7.00237i	0.473176	−	0.819565i	0.999529	+	0.0307013i	$0.00977408\pi$
$74$	2.47096	+	2.62966i	0.287243	+	0.305692i
$75$	−3.42640	−	4.15820i	−0.395647	−	0.480147i
$76$	7.27993	+	0.453456i	0.835066	+	0.0520150i
$77$	−6.14709	+	1.08390i	−0.700525	+	0.123522i
$78$	12.0044	−	11.0800i	1.35923	−	1.25456i
$79$	8.37729	−	9.98366i	0.942518	−	1.12325i	−0.0497030	−	0.998764i	$-0.515827\pi$
$79$	8.37729	−	9.98366i	0.942518	−	1.12325i	0.992221	−	0.124486i	$-0.0397281\pi$
$80$	−2.98405	−	4.61768i	−0.333627	−	0.516272i
$81$	6.68364	+	6.02735i	0.742626	+	0.669706i
$82$	−11.1061	−	8.30305i	−1.22647	−	0.916919i
$83$	0.344982	+	0.289474i	0.0378667	+	0.0317739i	0.661525	−	0.749923i	$-0.269910\pi$
$83$	0.344982	+	0.289474i	0.0378667	+	0.0317739i	−0.623658	+	0.781697i	$0.714354\pi$
$84$	−5.50803	+	0.571594i	−0.600976	+	0.0623660i
$85$	0.642014	+	3.64104i	0.0696362	+	0.394927i
$86$	2.88558	+	4.40662i	0.311160	+	0.475178i
$87$	−4.12066	+	3.39547i	−0.441781	+	0.364033i
$88$	−5.57978	+	9.53093i	−0.594807	+	1.01600i
$89$	0.994859	+	0.574382i	0.105455	+	0.0608844i	0.551800	−	0.833977i	$-0.313941\pi$
$89$	0.994859	+	0.574382i	0.105455	+	0.0608844i	−0.446345	+	0.894861i	$0.647275\pi$
$90$	2.72011	−	5.15820i	0.286724	−	0.543722i
$91$	−9.23292	+	5.33063i	−0.967873	+	0.558802i
$92$	−4.40701	−	5.96972i	−0.459462	−	0.622387i
$93$	−2.55045	−	0.0227513i	−0.264469	−	0.00235920i
$94$	0.412218	+	7.33204i	0.0425171	+	0.756242i
$95$	3.84002	−	3.22216i	0.393978	−	0.330587i
$96$	−5.53859	+	8.08233i	−0.565280	+	0.824899i
$97$	−9.00157	+	3.27630i	−0.913971	+	0.332658i	−0.755837	−	0.654760i	$-0.772770\pi$
$97$	−9.00157	+	3.27630i	−0.913971	+	0.332658i	−0.158134	+	0.987418i	$0.550548\pi$
$98$	−6.24159	−	0.742291i	−0.630496	−	0.0749827i
$99$	−11.7122	−	0.208974i	−1.17712	−	0.0210027i
$100$	6.04802	+	1.45918i	0.604802	+	0.145918i
$101$	12.4723	+	2.19921i	1.24104	+	0.218830i	0.755363	−	0.655306i	$-0.227460\pi$
$101$	12.4723	+	2.19921i	1.24104	+	0.218830i	0.485681	+	0.874136i	$0.338572\pi$
$102$	5.54415	−	3.56021i	0.548953	−	0.352513i
$103$	−1.92687	+	5.29404i	−0.189860	+	0.521637i	−0.997701	−	0.0677632i	$-0.978414\pi$
$103$	−1.92687	+	5.29404i	−0.189860	+	0.521637i	0.807841	+	0.589400i	$0.200636\pi$
$104$	−3.38786	+	18.5567i	−0.332207	+	1.81964i
$105$	−2.47216	+	2.89339i	−0.241258	+	0.282366i
$106$	−1.28068	−	5.45254i	−0.124390	−	0.529597i
$107$	−8.38143			−0.810264			−0.405132	−	0.914258i	$-0.632774\pi$
$107$	−8.38143			−0.810264			−0.405132	+	0.914258i	$0.632774\pi$
$108$	−10.3512	−	0.923374i	−0.996045	−	0.0888517i
$109$	6.18810			0.592713			0.296356	−	0.955077i	$-0.404228\pi$
$109$	6.18810			0.592713			0.296356	+	0.955077i	$0.404228\pi$
$110$	1.73549	+	7.38893i	0.165472	+	0.704507i
$111$	−1.47442	−	4.16620i	−0.139946	−	0.395438i
$112$	4.68625	−	4.35039i	0.442809	−	0.411073i
$113$	−4.37086	+	12.0088i	−0.411176	+	1.12970i	0.545390	+	0.838182i	$0.316382\pi$
$113$	−4.37086	+	12.0088i	−0.411176	+	1.12970i	−0.956566	+	0.291515i	$0.905841\pi$
$114$	−7.93881	−	4.09633i	−0.743537	−	0.383657i
$115$	−5.02202	−	0.885517i	−0.468305	−	0.0825749i
$116$	1.44601	−	5.99342i	0.134258	−	0.556475i
$117$	−18.9202	+	6.50655i	−1.74917	+	0.601531i
$118$	−0.996493	−	0.118509i	−0.0917346	−	0.0109097i
$119$	−4.04064	+	1.47067i	−0.370405	+	0.134816i
$120$	1.06990	+	6.64805i	0.0976685	+	0.606881i
$121$	3.25306	−	2.72964i	0.295732	−	0.248149i
$122$	−0.443036	−	7.88019i	−0.0401106	−	0.713439i
$123$	8.36009	+	14.7831i	0.753804	+	1.33295i
$124$	2.36942	−	1.74917i	0.212780	−	0.157080i
$125$	9.65461	−	5.57409i	0.863534	−	0.498562i
$126$	6.45734	+	2.07376i	0.575265	+	0.184745i
$127$	−6.61685	−	3.82024i	−0.587151	−	0.338992i	0.176819	−	0.984243i	$-0.443419\pi$
$127$	−6.61685	−	3.82024i	−0.587151	−	0.338992i	−0.763970	+	0.645252i	$0.776753\pi$
$128$	−0.498443	−	11.3027i	−0.0440565	−	0.999029i
$129$	−1.06351	−	6.36288i	−0.0936372	−	0.560220i
$130$	7.10189	+	10.8454i	0.622877	+	0.951208i
$131$	−1.87334	−	10.6242i	−0.163674	−	0.928243i	−0.950421	−	0.310967i	$-0.899347\pi$
$131$	−1.87334	−	10.6242i	−0.163674	−	0.928243i	0.786746	−	0.617276i	$-0.211764\pi$
$132$	10.9534	−	7.93612i	0.953371	−	0.690750i
$133$	4.46606	+	3.74747i	0.387256	+	0.324946i
$134$	−18.4518	−	13.7948i	−1.59400	−	1.19169i
$135$	−5.59201	+	4.44279i	−0.481284	+	0.382374i
$136$	−2.64531	+	7.13344i	−0.226833	+	0.611688i
$137$	−6.79690	+	8.10023i	−0.580699	+	0.692050i	−0.973790	−	0.227450i	$-0.926961\pi$
$137$	−6.79690	+	8.10023i	−0.580699	+	0.692050i	0.393091	+	0.919499i	$0.371406\pi$
$138$	1.99898	+	8.86527i	0.170164	+	0.754662i
$139$	1.59536	−	0.281305i	0.135317	−	0.0238600i	−0.105580	−	0.994411i	$-0.533670\pi$
$139$	1.59536	−	0.281305i	0.135317	−	0.0238600i	0.240896	+	0.970551i	$0.422559\pi$
$140$	0.273194	−	4.38594i	0.0230891	−	0.370679i
$141$	3.15142	−	8.42388i	0.265397	−	0.709419i
$142$	15.0314	+	15.9968i	1.26140	+	1.34242i
$143$	13.0206	−	22.5524i	1.08884	−	1.88593i
$144$	10.1933	−	6.33224i	0.849439	−	0.527687i
$145$	−2.11857	−	3.66946i	−0.175937	−	0.304732i
$146$	3.30161	−	10.9478i	0.273243	−	0.906047i
$147$	6.63226	+	3.90843i	0.547019	+	0.322362i
$148$	4.25223	+	2.82135i	0.349531	+	0.231914i
$149$	9.08882	+	10.8316i	0.744585	+	0.887362i	0.996769	−	0.0803176i	$-0.0255935\pi$
$149$	9.08882	+	10.8316i	0.744585	+	0.887362i	−0.252185	+	0.967679i	$0.581149\pi$
$150$	−6.06191	−	4.61681i	−0.494953	−	0.376961i
$151$	3.73181	+	10.2531i	0.303691	+	0.834384i	0.993851	+	0.110727i	$0.0353179\pi$
$151$	3.73181	+	10.2531i	0.303691	+	0.834384i	−0.690160	+	0.723657i	$0.742460\pi$
$152$	10.1693	−	1.72979i	0.824836	−	0.140304i
$153$	−7.97078	+	1.25928i	−0.644399	+	0.101807i
$154$	−8.11249	+	3.48001i	−0.653723	+	0.280427i
$155$	0.351467	−	1.99327i	0.0282305	−	0.160103i
$156$	12.9442	−	19.1362i	1.03636	−	1.53212i
$157$	9.66944	+	3.51939i	0.771705	+	0.280878i	0.697709	−	0.716381i	$-0.254203\pi$
$157$	9.66944	+	3.51939i	0.771705	+	0.280878i	0.0739957	+	0.997259i	$0.476425\pi$
$158$	8.30503	−	16.4539i	0.660713	−	1.30900i
$159$	−1.25139	+	6.74459i	−0.0992414	+	0.534881i
$160$	−5.60149	−	5.39244i	−0.442836	−	0.426310i
$161$		−	5.93085i		−	0.467417i
$162$	11.1507	+	6.13688i	0.876084	+	0.482159i
$163$			6.18193i			0.484206i	0.970251	+	0.242103i	$0.0778372\pi$
$163$			6.18193i			0.484206i	−0.970251	+	0.242103i	$0.922163\pi$
$164$	−17.9753	−	7.83986i	−1.40363	−	0.612190i
$165$	1.69580	−	9.13984i	0.132018	−	0.711535i
$166$	0.568559	+	0.286977i	0.0441288	+	0.0222738i
$167$	−0.411580	−	0.149803i	−0.0318490	−	0.0115921i	0.326047	−	0.945354i	$-0.394283\pi$
$167$	−0.411580	−	0.149803i	−0.0318490	−	0.0115921i	−0.357896	+	0.933762i	$0.616506\pi$
$168$	−7.39834	+	2.56805i	−0.570794	+	0.198130i
$169$	5.46623	−	31.0006i	0.420480	−	2.38466i
$170$	2.06128	+	4.80519i	0.158093	+	0.368541i
$171$	6.88214	+	8.50547i	0.526290	+	0.650429i
$172$	5.39766	+	5.13371i	0.411568	+	0.391442i
$173$	−2.70503	−	7.43201i	−0.205660	−	0.565045i	0.793386	−	0.608719i	$-0.208316\pi$
$173$	−2.70503	−	7.43201i	−0.205660	−	0.565045i	−0.999046	+	0.0436734i	$0.986094\pi$
$174$	−4.57513	+	6.00719i	−0.346840	+	0.455404i
$175$	3.19646	+	3.80939i	0.241629	+	0.287963i
$176$	−4.59997	+	14.9260i	−0.346736	+	1.12509i
$177$	1.05886	+	0.623995i	0.0795891	+	0.0469023i
$178$	1.55541	+	0.469076i	0.116583	+	0.0351587i
$179$	5.74464	+	9.95001i	0.429374	+	0.743698i	0.996818	−	0.0797141i	$-0.0254007\pi$
$179$	5.74464	+	9.95001i	0.429374	+	0.743698i	−0.567443	+	0.823412i	$0.692067\pi$
$180$	2.07691	−	7.98113i	0.154804	−	0.594878i
$181$	−7.34496	+	12.7218i	−0.545946	+	0.945607i	0.452600	+	0.891714i	$0.350496\pi$
$181$	−7.34496	+	12.7218i	−0.545946	+	0.945607i	−0.998547	+	0.0538935i	$0.982837\pi$
$182$	−10.9877	+	10.3245i	−0.814459	+	0.765306i
$183$	−3.38702	+	9.05365i	−0.250376	+	0.669265i
$184$	−7.99775	−	6.79372i	−0.589602	−	0.500840i
$185$	3.45379	−	0.608996i	0.253928	−	0.0447743i
$186$	−3.51868	+	0.793407i	−0.258002	+	0.0581754i
$187$	6.75129	−	8.04587i	0.493703	−	0.588372i
$188$	2.93846	+	9.96108i	0.214309	+	0.726486i
$189$	−6.21794	−	5.50761i	−0.452289	−	0.400620i
$190$	4.24480	−	5.67783i	0.307950	−	0.411913i
$191$	−10.5145	−	8.82269i	−0.760800	−	0.638387i	0.177535	−	0.984115i	$-0.443188\pi$
$191$	−10.5145	−	8.82269i	−0.760800	−	0.638387i	−0.938335	+	0.345727i	$0.887632\pi$
$192$	−5.01169	+	12.9183i	−0.361688	+	0.932299i
$193$	−1.42837	−	8.10071i	−0.102817	−	0.583102i	−0.992070	−	0.125687i	$-0.959887\pi$
$193$	−1.42837	−	8.10071i	−0.102817	−	0.583102i	0.889253	−	0.457415i	$-0.151225\pi$
$194$	−11.3334	+	7.42145i	−0.813694	+	0.532829i
$195$	−2.61749	−	15.6601i	−0.187442	−	1.12144i
$196$	−8.83313	+	0.996373i	−0.630938	+	0.0711695i
$197$	8.28713	+	4.78458i	0.590434	+	0.340887i	0.765269	−	0.643711i	$-0.222606\pi$
$197$	8.28713	+	4.78458i	0.590434	+	0.340887i	−0.174835	+	0.984598i	$0.555939\pi$
$198$	−16.1923	+	3.49962i	−1.15074	+	0.248707i
$199$	12.3825	−	7.14906i	0.877774	−	0.506783i	0.00785032	−	0.999969i	$-0.497501\pi$
$199$	12.3825	−	7.14906i	0.877774	−	0.506783i	0.869924	+	0.493186i	$0.164168\pi$
$200$	8.79845	+	0.0531943i	0.622145	+	0.00376141i
$201$	13.8895	+	24.5607i	0.979691	+	1.73238i
$202$	17.8824	−	1.00538i	1.25820	−	0.0707380i
$203$	3.77500	−	3.16760i	0.264953	−	0.222322i
$204$	6.48165	−	6.69430i	0.453806	−	0.468695i
$205$	−12.6645	+	4.60949i	−0.884525	+	0.321941i
$206$	−0.940904	+	7.91164i	−0.0655559	+	0.551230i
$207$	2.12799	−	10.9250i	0.147906	−	0.759338i
$208$	1.33640	+	26.6435i	0.0926626	+	1.84739i
$209$	−14.0241	−	2.47283i	−0.970069	−	0.171049i
$210$	−2.46792	+	4.78289i	−0.170302	+	0.330050i
$211$	5.92941	−	16.2909i	0.408197	−	1.12151i	−0.549940	−	0.835204i	$-0.685349\pi$
$211$	5.92941	−	16.2909i	0.408197	−	1.12151i	0.958137	−	0.286309i	$-0.0924284\pi$
$212$	−3.52633	−	7.09264i	−0.242190	−	0.487125i
$213$	−8.96921	−	25.3439i	−0.614560	−	1.73653i
$214$	−11.5391	+	2.71027i	−0.788798	+	0.185270i
$215$	5.11938			0.349139
$216$	−14.5496	+	2.07598i	−0.989974	+	0.141252i
$217$	2.35399			0.159800
$218$	8.51945	−	2.00102i	0.577010	−	0.135526i
$219$	−9.09741	+	10.6475i	−0.614746	+	0.719493i
$220$	4.77866	+	9.61150i	0.322177	+	0.648007i
$221$	6.13566	−	16.8576i	0.412729	−	1.13396i
$222$	−3.37711	−	5.25903i	−0.226657	−	0.352963i
$223$	−6.25203	−	1.10240i	−0.418667	−	0.0738223i	−0.0396537	−	0.999213i	$-0.512625\pi$
$223$	−6.25203	−	1.10240i	−0.418667	−	0.0738223i	−0.379013	+	0.925391i	$0.623737\pi$
$224$	5.04502	−	7.50476i	0.337085	−	0.501433i
$225$	4.52125	+	8.16400i	0.301416	+	0.544267i
$226$	−2.13432	+	17.9465i	−0.141973	+	1.19379i
$227$	14.5711	−	5.30345i	0.967119	−	0.352002i	0.190299	−	0.981726i	$-0.439054\pi$
$227$	14.5711	−	5.30345i	0.967119	−	0.352002i	0.776819	+	0.629724i	$0.216832\pi$
$228$	−12.2543	−	3.07248i	−0.811564	−	0.203480i
$229$	0.780733	−	0.655113i	0.0515923	−	0.0432911i	−0.616627	−	0.787256i	$-0.711501\pi$
$229$	0.780733	−	0.655113i	0.0515923	−	0.0432911i	0.668219	+	0.743964i	$0.267057\pi$
$230$	−7.20040	+	0.404817i	−0.474780	+	0.0266928i
$231$	10.8109	+	0.0964387i	0.711304	+	0.00634520i
$232$	0.0527141	−	8.71902i	0.00346085	−	0.572432i
$233$	−8.68625	+	5.01501i	−0.569055	+	0.328544i	−0.756772	−	0.653679i	$-0.773225\pi$
$233$	−8.68625	+	5.01501i	−0.569055	+	0.328544i	0.187717	+	0.982223i	$0.439891\pi$
$234$	−23.9443	+	15.0760i	−1.56529	+	0.985551i
$235$	6.18112	+	3.56867i	0.403212	+	0.232794i
$236$	−1.41024	+	0.159075i	−0.0917989	+	0.0103549i
$237$	−17.4210	+	14.3551i	−1.13161	+	0.932461i
$238$	−5.08738	+	3.33136i	−0.329766	+	0.215940i
$239$	3.33468	+	18.9119i	0.215702	+	1.22331i	0.879684	+	0.475560i	$0.157754\pi$
$239$	3.33468	+	18.9119i	0.215702	+	1.22331i	−0.663981	+	0.747749i	$0.731134\pi$
$240$	3.62274	+	8.80672i	0.233847	+	0.568471i
$241$	0.880417	+	0.738758i	0.0567127	+	0.0475876i	0.670703	−	0.741726i	$-0.265992\pi$
$241$	0.880417	+	0.738758i	0.0567127	+	0.0475876i	−0.613991	+	0.789313i	$0.710437\pi$
$242$	3.59596	−	4.80995i	0.231157	−	0.309195i
$243$	−9.47767	−	12.3763i	−0.607993	−	0.793942i
$244$	−3.15813	−	10.7058i	−0.202179	−	0.685366i
$245$	−3.92680	+	4.67978i	−0.250874	+	0.298980i
$246$	16.2901	+	17.6492i	1.03862	+	1.12527i
$247$	−23.9533	+	4.22362i	−1.52411	+	0.268743i
$248$	2.69647	−	3.17436i	0.171226	−	0.201572i
$249$	−0.496034	−	0.601975i	−0.0314349	−	0.0381486i
$250$	11.4895	−	10.7961i	0.726659	−	0.682805i
$251$	−11.3633	+	19.6818i	−0.717243	+	1.24230i	0.244845	+	0.969562i	$0.421263\pi$
$251$	−11.3633	+	19.6818i	−0.717243	+	1.24230i	−0.962088	+	0.272739i	$0.912070\pi$
$252$	9.56071	+	0.766962i	0.602268	+	0.0483140i
$253$	7.24338	+	12.5459i	0.455388	+	0.788754i
$254$	−10.3451	−	3.11984i	−0.649108	−	0.195756i
$255$	0.0571226	−	6.40350i	0.00357715	−	0.401003i
$256$	−4.34115	−	15.3998i	−0.271322	−	0.962489i
$257$	7.00172	+	8.34433i	0.436755	+	0.520505i	0.938859	−	0.344303i	$-0.111885\pi$
$257$	7.00172	+	8.34433i	0.436755	+	0.520505i	−0.502103	+	0.864808i	$0.667440\pi$
$258$	−3.52173	−	8.41618i	−0.219253	−	0.523968i
$259$	1.39504	+	3.83284i	0.0866836	+	0.238161i
$260$	13.2846	+	12.6349i	0.823873	+	0.783585i
$261$	8.09030	−	4.48043i	0.500777	−	0.277332i
$262$	−6.01463	−	14.0211i	−0.371585	−	0.866227i
$263$	0.0454458	−	0.257736i	0.00280231	−	0.0158927i	−0.983375	−	0.181589i	$-0.941876\pi$
$263$	0.0454458	−	0.257736i	0.00280231	−	0.0158927i	0.986177	+	0.165696i	$0.0529871\pi$
$264$	12.5138	−	14.4680i	0.770170	−	0.890443i
$265$	−5.11531	−	1.86182i	−0.314231	−	0.114371i
$266$	7.36044	+	3.71514i	0.451297	+	0.227790i
$267$	−1.51274	−	1.29251i	−0.0925784	−	0.0791004i
$268$	−29.8643	−	13.0252i	−1.82425	−	0.795641i
$269$		−	7.47642i		−	0.455845i	−0.973679	−	0.227923i	$-0.926807\pi$
$269$		−	7.47642i		−	0.455845i	0.973679	−	0.227923i	$-0.0731933\pi$
$270$	−6.26214	+	7.92486i	−0.381102	+	0.482292i
$271$		−	14.5903i		−	0.886299i	−0.896448	−	0.443150i	$-0.853861\pi$
$271$		−	14.5903i		−	0.886299i	0.896448	−	0.443150i	$-0.146139\pi$
$272$	−1.33521	+	10.6764i	−0.0809590	+	0.647349i
$273$	17.4079	−	6.16065i	1.05357	−	0.372860i
$274$	−6.73828	+	13.3499i	−0.407074	+	0.806495i
$275$	−11.4141	−	4.15439i	−0.688295	−	0.250519i
$276$	5.61882	+	11.5588i	0.338213	+	0.695761i
$277$	−0.964532	+	5.47013i	−0.0579531	+	0.328668i	−0.999976	−	0.00687933i	$-0.997810\pi$
$277$	−0.964532	+	5.47013i	−0.0579531	+	0.328668i	0.942023	+	0.335548i	$0.108921\pi$
$278$	2.10544	−	0.903171i	0.126276	−	0.0541686i
$279$	4.33619	+	0.844613i	0.259601	+	0.0505657i
$280$	−1.04214	−	6.12667i	−0.0622801	−	0.366138i
$281$	−2.82619	−	7.76489i	−0.168596	−	0.463214i	0.826405	−	0.563076i	$-0.190382\pi$
$281$	−2.82619	−	7.76489i	−0.168596	−	0.463214i	−0.995001	+	0.0998617i	$0.968160\pi$
$282$	1.61471	−	12.6166i	0.0961546	−	0.751309i
$283$	20.8899	+	24.8956i	1.24178	+	1.47989i	0.819143	+	0.573590i	$0.194450\pi$
$283$	20.8899	+	24.8956i	1.24178	+	1.47989i	0.422633	+	0.906301i	$0.361106\pi$
$284$	25.8672	+	17.1629i	1.53494	+	1.01843i
$285$	−7.55761	+	4.27396i	−0.447674	+	0.253167i
$286$	10.6335	−	35.2594i	0.628769	−	2.08493i
$287$	−7.83722	−	13.5745i	−0.462616	−	0.801275i
$288$	11.9859	−	12.0141i	0.706278	−	0.707935i
$289$	−4.88227	+	8.45634i	−0.287192	+	0.497432i
$290$	−4.10331	−	4.36685i	−0.240955	−	0.256430i
$291$	16.3648	−	2.73526i	0.959319	−	0.160344i
$292$	1.00534	−	16.1400i	0.0588329	−	0.944522i
$293$	3.37269	−	0.594697i	0.197035	−	0.0347426i	−0.0742597	−	0.997239i	$-0.523659\pi$
$293$	3.37269	−	0.594697i	0.197035	−	0.0347426i	0.271295	+	0.962496i	$0.412548\pi$
$294$	10.3948	+	3.23627i	0.606237	+	0.188743i
$295$	−0.626928	+	0.747144i	−0.0365012	+	0.0435004i
$296$	6.76658	+	2.50927i	0.393299	+	0.145848i
$297$	19.8797	+	4.05659i	1.15354	+	0.235387i
$298$	16.0156	+	11.9734i	0.927758	+	0.693601i
$299$	18.9547	+	15.9048i	1.09618	+	0.919801i
$300$	−9.83864	−	4.39596i	−0.568034	−	0.253801i
$301$	1.03390	+	5.86354i	0.0595930	+	0.337969i
$302$	8.45327	+	12.9092i	0.486431	+	0.742839i
$303$	−20.5453	−	7.68612i	−1.18030	−	0.441556i
$304$	13.4412	−	5.66988i	0.770903	−	0.325190i
$305$	−6.64322	−	3.83547i	−0.380390	−	0.219618i
$306$	−10.5665	+	4.31120i	−0.604049	+	0.246455i
$307$	−3.67167	+	2.11984i	−0.209553	+	0.120986i	−0.601104	−	0.799171i	$-0.705272\pi$
$307$	−3.67167	+	2.11984i	−0.209553	+	0.120986i	0.391550	+	0.920157i	$0.371939\pi$
$308$	−10.0435	+	7.41441i	−0.572284	+	0.422475i
$309$	4.95420	−	8.40684i	0.281835	−	0.478249i
$310$	−0.160674	−	2.85788i	−0.00912570	−	0.162317i
$311$	−17.8431	+	14.9722i	−1.01179	+	0.848994i	−0.988574	−	0.150737i	$-0.951835\pi$
$311$	−17.8431	+	14.9722i	−1.01179	+	0.848994i	−0.0232172	+	0.999730i	$0.507391\pi$
$312$	11.6329	−	30.5314i	0.658581	−	1.72850i
$313$	−7.63152	+	2.77765i	−0.431359	+	0.157002i	−0.548569	−	0.836105i	$-0.684827\pi$
$313$	−7.63152	+	2.77765i	−0.431359	+	0.157002i	0.117210	+	0.993107i	$0.462605\pi$
$314$	14.4504	+	1.71854i	0.815485	+	0.0969828i
$315$	5.12428	−	4.14628i	0.288721	−	0.233616i
$316$	6.11329	−	25.3385i	0.343900	−	1.42540i
$317$	−17.9863	−	3.17148i	−1.01021	−	0.178128i	−0.356039	−	0.934471i	$-0.615873\pi$
$317$	−17.9863	−	3.17148i	−1.01021	−	0.178128i	−0.654175	+	0.756343i	$0.726984\pi$
$318$	0.458129	+	9.69026i	0.0256906	+	0.543403i
$319$	−4.11688	+	11.3110i	−0.230501	+	0.633297i
$320$	−9.45557	−	5.61270i	−0.528582	−	0.313759i
$321$	14.2735	+	2.64829i	0.796667	+	0.147813i
$322$	−1.91784	−	8.16529i	−0.106877	−	0.455034i
$323$	−9.81005			−0.545846
$324$	17.3362	+	4.84317i	0.963122	+	0.269065i
$325$	−20.7465			−1.15081
$326$	1.99903	+	8.51096i	0.110716	+	0.471378i
$327$	−10.5382	−	1.95526i	−0.582767	−	0.108126i
$328$	−27.2826	−	4.98091i	−1.50643	−	0.275025i
$329$	−2.83909	+	7.80033i	−0.156524	+	0.430046i
$330$	−0.620827	−	13.1316i	−0.0341754	−	0.722872i
$331$	−27.7857	−	4.89938i	−1.52724	−	0.269294i	−0.653968	−	0.756522i	$-0.726897\pi$
$331$	−27.7857	−	4.89938i	−1.52724	−	0.269294i	−0.873275	+	0.487228i	$0.838008\pi$
$332$	0.875561	+	0.211243i	0.0480527	+	0.0115934i
$333$	1.19452	+	7.56085i	0.0654593	+	0.414332i
$334$	−0.615083	−	0.0731497i	−0.0336559	−	0.00400257i
$335$	−21.0409	+	7.65825i	−1.14958	+	0.418415i
$336$	−9.35522	+	5.92793i	−0.510369	+	0.323395i
$337$	9.31991	−	7.82033i	0.507688	−	0.426001i	−0.352627	−	0.935764i	$-0.614712\pi$
$337$	9.31991	−	7.82033i	0.507688	−	0.426001i	0.860315	+	0.509763i	$0.170267\pi$
$338$	−2.49891	−	44.4475i	−0.135923	−	2.41763i
$339$	11.2380	−	19.0698i	0.610362	−	1.03573i
$340$	4.39170	+	5.94899i	0.238173	+	0.322629i
$341$	−4.97955	+	2.87494i	−0.269658	+	0.155687i
$342$	12.2254	+	9.48443i	0.661071	+	0.512859i
$343$	−15.8439	−	9.14748i	−0.855490	−	0.493917i
$344$	9.09129	+	5.32240i	0.490169	+	0.286965i
$345$	8.27263	+	3.09483i	0.445383	+	0.166620i
$346$	−6.12740	−	9.35728i	−0.329411	−	0.503051i
$347$	1.12983	+	6.40758i	0.0606524	+	0.343977i	0.999999	+	0.00100899i	$0.000321173\pi$
$347$	1.12983	+	6.40758i	0.0606524	+	0.343977i	−0.939347	+	0.342968i	$0.888568\pi$
$348$	−4.35628	+	9.74982i	−0.233521	+	0.522645i
$349$	23.5937	+	19.7975i	1.26294	+	1.05974i	0.995362	+	0.0962012i	$0.0306692\pi$
$349$	23.5937	+	19.7975i	1.26294	+	1.05974i	0.267582	+	0.963535i	$0.413775\pi$
$350$	5.63254	+	4.21094i	0.301072	+	0.225084i
$351$	34.2767	−	5.10234i	1.82956	−	0.272342i
$352$	−1.50644	+	22.0368i	−0.0802935	+	1.17457i
$353$	18.3162	−	21.8284i	0.974873	−	1.16181i	−0.0119377	−	0.999929i	$-0.503800\pi$
$353$	18.3162	−	21.8284i	0.974873	−	1.16181i	0.986811	−	0.161879i	$-0.0517556\pi$
$354$	1.65957	+	0.516683i	0.0882050	+	0.0274614i
$355$	21.0101	−	3.70465i	1.11510	−	0.196623i
$356$	2.29308	+	0.142833i	0.121533	+	0.00757013i
$357$	7.34585	−	1.22781i	0.388784	−	0.0649827i
$358$	11.1264	+	11.8410i	0.588049	+	0.625818i
$359$	−1.50638	+	2.60913i	−0.0795039	+	0.137705i	−0.903036	−	0.429565i	$-0.858667\pi$
$359$	−1.50638	+	2.60913i	−0.0795039	+	0.137705i	0.823532	+	0.567270i	$0.192000\pi$
$360$	0.278558	−	11.6596i	0.0146813	−	0.614515i
$361$	−2.84962	−	4.93568i	−0.149980	−	0.259773i
$362$	−5.99834	+	19.8899i	−0.315266	+	1.04539i
$363$	−6.40240	+	3.62067i	−0.336039	+	0.190036i
$364$	−11.7886	+	17.7673i	−0.617891	+	0.931261i
$365$	−7.14370	−	8.51353i	−0.373918	−	0.445618i
$366$	−1.73543	+	13.5598i	−0.0907122	+	0.708784i
$367$	1.08161	+	2.97170i	0.0564595	+	0.155121i	0.964716	−	0.263292i	$-0.0848084\pi$
$367$	1.08161	+	2.97170i	0.0564595	+	0.155121i	−0.908257	+	0.418414i	$0.862586\pi$
$368$	−13.2077	−	6.76704i	−0.688501	−	0.352757i
$369$	−9.56609	−	27.8169i	−0.497991	−	1.44809i
$370$	4.55807	−	1.95527i	0.236963	−	0.101650i
$371$	1.09938	−	6.23487i	0.0570768	−	0.323699i
$372$	−4.58778	+	2.23014i	−0.237865	+	0.115628i
$373$	2.76041	+	1.00471i	0.142928	+	0.0520217i	0.412494	−	0.910960i	$-0.364658\pi$
$373$	2.76041	+	1.00471i	0.142928	+	0.0520217i	−0.269565	+	0.962982i	$0.586880\pi$
$374$	6.69305	−	13.2603i	0.346090	−	0.685672i
$375$	−18.2029	+	6.44202i	−0.939994	+	0.332665i
$376$	7.26659	+	12.7637i	0.374746	+	0.658237i
$377$			20.5592i			1.05886i
$378$	−10.3415	−	5.57192i	−0.531910	−	0.286589i
$379$		−	1.91457i		−	0.0983448i	−0.998790	−	0.0491724i	$-0.984342\pi$
$379$		−	1.91457i		−	0.0983448i	0.998790	−	0.0491724i	$-0.0156584\pi$
$380$	4.00800	−	9.18957i	0.205606	−	0.471415i
$381$	10.0613	+	8.59655i	0.515457	+	0.440415i
$382$	−17.3287	−	8.74659i	−0.886615	−	0.447514i
$383$	17.6014	+	6.40639i	0.899390	+	0.327351i	0.750008	−	0.661428i	$-0.230049\pi$
$383$	17.6014	+	6.40639i	0.899390	+	0.327351i	0.149382	+	0.988780i	$0.452272\pi$
$384$	−2.72249	+	19.4059i	−0.138932	+	0.990302i
$385$	−1.48980	+	8.44910i	−0.0759275	+	0.430606i
$386$	−4.58600	−	10.6907i	−0.233421	−	0.544144i
$387$	−0.199335	+	11.1719i	−0.0101328	+	0.567902i
$388$	−13.2034	+	13.8823i	−0.670303	+	0.704768i
$389$	−3.55765	−	9.77456i	−0.180380	−	0.495590i	0.816243	−	0.577709i	$-0.196053\pi$
$389$	−3.55765	−	9.77456i	−0.180380	−	0.495590i	−0.996622	+	0.0821196i	$0.973831\pi$
$390$	−8.66758	−	20.7136i	−0.438900	−	1.04888i
$391$	6.41484	+	7.64491i	0.324412	+	0.386620i
$392$	−11.8388	+	4.22809i	−0.597949	+	0.213551i
$393$	−0.166678	+	18.6848i	−0.00840782	+	0.942525i
$394$	12.9565	+	3.90738i	0.652737	+	0.196851i
$395$	−8.95668	−	15.5134i	−0.450660	−	0.780565i
$396$	−21.1611	+	10.0541i	−1.06338	+	0.505240i
$397$	7.93455	−	13.7430i	0.398224	−	0.689744i	−0.595283	−	0.803516i	$-0.702960\pi$
$397$	7.93455	−	13.7430i	0.398224	−	0.689744i	0.993507	+	0.113772i	$0.0362934\pi$
$398$	14.7359	−	13.8465i	0.738642	−	0.694064i
$399$	−6.42154	−	7.79303i	−0.321479	−	0.390139i
$400$	12.1305	−	2.77189i	0.606523	−	0.138594i
$401$	−5.87809	+	1.03647i	−0.293538	+	0.0517586i	−0.318478	−	0.947930i	$-0.603172\pi$
$401$	−5.87809	+	1.03647i	−0.293538	+	0.0517586i	0.0249400	+	0.999689i	$0.492061\pi$
$402$	27.0645	+	29.3225i	1.34985	+	1.46247i
$403$	−6.31273	+	7.52322i	−0.314460	+	0.374758i
$404$	24.2945	−	7.16672i	1.20870	−	0.356558i
$405$	10.9269	−	5.79909i	0.542963	−	0.288159i
$406$	4.17292	−	5.58169i	0.207099	−	0.277015i
$407$	−7.63208	−	6.40408i	−0.378308	−	0.317438i
$408$	6.75889	−	11.3123i	0.334615	−	0.560043i
$409$	2.36345	+	13.4038i	0.116865	+	0.662775i	0.985810	+	0.167866i	$0.0536875\pi$
$409$	2.36345	+	13.4038i	0.116865	+	0.662775i	−0.868945	+	0.494909i	$0.835201\pi$
$410$	−15.9452	+	10.4414i	−0.787479	+	0.515662i
$411$	14.1345	−	11.6470i	0.697202	−	0.574502i
$412$	1.26297	+	11.1966i	0.0622221	+	0.551617i
$413$	−0.982361	−	0.567167i	−0.0483388	−	0.0279084i
$414$	−0.603061	−	15.7291i	−0.0296388	−	0.773041i
$415$	0.536061	−	0.309495i	0.0263142	−	0.0151925i
$416$	10.4555	+	36.2492i	0.512622	+	1.77726i
$417$	−2.80576	−	0.0250288i	−0.137399	−	0.00122567i
$418$	−20.1073	+	1.13046i	−0.983481	+	0.0552928i
$419$	7.77815	−	6.52664i	0.379988	−	0.318847i	−0.432710	−	0.901533i	$-0.642443\pi$
$419$	7.77815	−	6.52664i	0.379988	−	0.318847i	0.812698	+	0.582686i	$0.197998\pi$
$420$	−1.85107	+	7.38287i	−0.0903231	+	0.360247i
$421$	−22.4900	+	8.18570i	−1.09610	+	0.398947i	−0.825876	−	0.563852i	$-0.809319\pi$
$421$	−22.4900	+	8.18570i	−1.09610	+	0.398947i	−0.270221	+	0.962798i	$0.587097\pi$
$422$	2.89537	−	24.3459i	0.140944	−	1.18514i
$423$	−8.02852	+	13.3500i	−0.390360	+	0.649099i
$424$	−7.14839	−	8.62448i	−0.347157	−	0.418842i
$425$	−8.24050	−	1.45302i	−0.399723	−	0.0704820i
$426$	−20.5437	−	31.9918i	−0.995345	−	1.55001i
$427$	3.05134	−	8.38348i	0.147665	−	0.405705i
$428$	−15.0100	+	7.46272i	−0.725538	+	0.360724i
$429$	−29.2999	+	34.2923i	−1.41461	+	1.65565i
$430$	7.04810	−	1.65544i	0.339890	−	0.0798322i
$431$	−19.6478			−0.946399			−0.473199	−	0.880955i	$-0.656901\pi$
$431$	−19.6478			−0.946399			−0.473199	+	0.880955i	$0.656901\pi$
$432$	−19.3598	+	7.56294i	−0.931449	+	0.363872i
$433$	−11.5738			−0.556202			−0.278101	−	0.960552i	$-0.589705\pi$
$433$	−11.5738			−0.556202			−0.278101	+	0.960552i	$0.589705\pi$
$434$	3.24086	−	0.761202i	0.155566	−	0.0365389i
$435$	2.44845	+	6.91845i	0.117394	+	0.331714i
$436$	11.0821	−	5.50981i	0.530735	−	0.263872i
$437$	4.62781	−	12.7148i	0.221378	−	0.608231i
$438$	−9.08179	+	17.6007i	−0.433945	+	0.840996i
$439$	11.0923	+	1.95588i	0.529408	+	0.0933490i	0.431962	−	0.901892i	$-0.357821\pi$
$439$	11.0923	+	1.95588i	0.529408	+	0.0933490i	0.0974464	+	0.995241i	$0.468933\pi$
$440$	9.68705	+	11.6873i	0.461812	+	0.557172i
$441$	−10.0597	−	8.75160i	−0.479033	−	0.416743i
$442$	2.99608	−	25.1927i	0.142509	−	1.19829i
$443$	34.5395	−	12.5713i	1.64102	−	0.597282i	0.653802	−	0.756666i	$-0.273173\pi$
$443$	34.5395	−	12.5713i	1.64102	−	0.597282i	0.987217	+	0.159383i	$0.0509506\pi$
$444$	−6.35003	−	6.14831i	−0.301359	−	0.291786i
$445$	1.20956	−	1.01494i	0.0573385	−	0.0481127i
$446$	−8.96395	+	0.503967i	−0.424455	+	0.0238635i
$447$	−12.0556	−	21.3179i	−0.570213	−	1.00830i
$448$	4.51893	−	11.9636i	0.213499	−	0.565225i
$449$	−2.77399	+	1.60156i	−0.130913	+	0.0755824i	−0.564026	−	0.825757i	$-0.690748\pi$
$449$	−2.77399	+	1.60156i	−0.130913	+	0.0755824i	0.433114	+	0.901339i	$0.357415\pi$
$450$	8.86458	+	9.77775i	0.417880	+	0.460927i
$451$	33.1571	+	19.1433i	1.56131	+	0.901421i
$452$	2.86489	+	25.3980i	0.134753	+	1.19462i
$453$	−3.11555	−	18.6400i	−0.146382	−	0.875783i
$454$	18.3458	−	12.0133i	0.861010	−	0.563813i
$455$	2.54460	+	14.4312i	0.119293	+	0.676543i
$456$	−17.8647	−	0.267384i	−0.836590	−	0.0125214i
$457$	14.8332	+	12.4465i	0.693868	+	0.582224i	0.920022	−	0.391867i	$-0.128171\pi$
$457$	14.8332	+	12.4465i	0.693868	+	0.582224i	−0.226154	+	0.974092i	$0.572615\pi$
$458$	0.863031	−	1.15439i	0.0403268	−	0.0539410i
$459$	13.9720	+	0.373993i	0.652158	+	0.0174565i
$460$	−9.78223	+	2.88570i	−0.456099	+	0.134546i
$461$	1.37982	−	1.64440i	0.0642645	−	0.0765874i	−0.732954	−	0.680278i	$-0.761859\pi$
$461$	1.37982	−	1.64440i	0.0642645	−	0.0765874i	0.797219	+	0.603690i	$0.206304\pi$
$462$	14.9150	−	3.36310i	0.693911	−	0.156466i
$463$	19.6343	−	3.46206i	0.912483	−	0.160895i	0.302352	−	0.953196i	$-0.402228\pi$
$463$	19.6343	−	3.46206i	0.912483	−	0.160895i	0.610131	+	0.792301i	$0.291117\pi$
$464$	−2.74686	−	12.0209i	−0.127520	−	0.558058i
$465$	−1.22836	+	3.28346i	−0.0569638	+	0.152267i
$466$	−10.3371	+	9.71324i	−0.478857	+	0.449957i
$467$	−4.94711	+	8.56864i	−0.228925	+	0.396509i	−0.957490	−	0.288467i	$-0.906854\pi$
$467$	−4.94711	+	8.56864i	−0.228925	+	0.396509i	0.728565	+	0.684977i	$0.240188\pi$
$468$	−28.0902	+	28.4987i	−1.29847	+	1.31735i
$469$	−13.0208	−	22.5527i	−0.601245	−	1.04139i
$470$	9.66383	+	2.91439i	0.445759	+	0.134431i
$471$	−15.3549	−	9.04873i	−0.707516	−	0.416943i
$472$	−1.89011	+	0.675030i	−0.0869992	+	0.0310708i
$473$	−9.34824	−	11.1408i	−0.429833	−	0.512254i
$474$	−19.3423	+	25.3966i	−0.888422	+	1.16651i
$475$	3.88025	+	10.6609i	0.178038	+	0.489155i
$476$	−5.92679	+	6.23152i	−0.271654	+	0.285621i
$477$	4.26219	−	11.0905i	0.195152	−	0.507801i
$478$	10.7065	+	24.9586i	0.489703	+	1.14158i
$479$	4.47267	−	25.3658i	0.204362	−	1.15899i	−0.694079	−	0.719898i	$-0.744188\pi$
$479$	4.47267	−	25.3658i	0.204362	−	1.15899i	0.898441	−	0.439094i	$-0.144701\pi$
$480$	7.83540	+	10.9532i	0.357635	+	0.499941i
$481$	−15.9906	−	5.82011i	−0.729110	−	0.265374i
$482$	1.45100	+	0.732386i	0.0660913	+	0.0333593i
$483$	−1.87398	+	10.1002i	−0.0852689	+	0.459573i
$484$	3.39536	−	7.78490i	0.154335	−	0.353859i
$485$			13.1666i			0.597865i
$486$	−17.0505	−	13.9743i	−0.773424	−	0.633889i
$487$		−	25.1669i		−	1.14042i	−0.821498	−	0.570212i	$-0.806861\pi$
$487$		−	25.1669i		−	1.14042i	0.821498	−	0.570212i	$-0.193139\pi$
$488$	−7.80984	−	13.7179i	−0.353535	−	0.620980i
$489$	1.95331	−	10.5277i	0.0883317	−	0.476081i
$490$	−3.89293	+	7.71267i	−0.175865	+	0.348423i
$491$	4.40319	+	1.60263i	0.198713	+	0.0723257i	0.439460	−	0.898262i	$-0.355170\pi$
$491$	4.40319	+	1.60263i	0.198713	+	0.0723257i	−0.240746	+	0.970588i	$0.577392\pi$
$492$	28.1345	+	19.0308i	1.26840	+	0.857976i
$493$	−1.43991	+	8.16611i	−0.0648501	+	0.367783i
$494$	−31.6119	+	13.5606i	−1.42229	+	0.610119i
$495$	−5.77585	+	15.0292i	−0.259605	+	0.675512i
$496$	2.68588	−	5.24224i	0.120600	−	0.235383i
$497$	8.48632	+	23.3160i	0.380664	+	1.04586i
$498$	−0.877572	−	0.668367i	−0.0393249	−	0.0299502i
$499$	−6.36794	−	7.58902i	−0.285068	−	0.339731i	0.604440	−	0.796651i	$-0.293397\pi$
$499$	−6.36794	−	7.58902i	−0.285068	−	0.339731i	−0.889508	+	0.456920i	$0.848953\pi$
$500$	12.3270	−	18.5788i	0.551282	−	0.830869i
$501$	0.653582	+	0.385160i	0.0291999	+	0.0172077i
$502$	−9.27994	+	30.7713i	−0.414184	+	1.37339i
$503$	−6.96764	−	12.0683i	−0.310672	−	0.538099i	0.667836	−	0.744308i	$-0.267221\pi$
$503$	−6.96764	−	12.0683i	−0.310672	−	0.538099i	−0.978508	+	0.206209i	$0.933887\pi$
$504$	13.4107	−	2.03570i	0.597360	−	0.0906772i
$505$	8.70378	−	15.0754i	0.387313	−	0.670846i
$506$	14.0292	+	14.9303i	0.623675	+	0.663732i
$507$	−19.1042	+	51.0663i	−0.848447	+	2.26794i
$508$	−15.2514	−	0.949988i	−0.676672	−	0.0421489i
$509$	29.7725	−	5.24969i	1.31964	−	0.232688i	0.530911	−	0.847428i	$-0.321850\pi$
$509$	29.7725	−	5.24969i	1.31964	−	0.232688i	0.788730	+	0.614740i	$0.210739\pi$
$510$	−1.99203	−	8.83448i	−0.0882087	−	0.391197i
$511$	8.30833	−	9.90148i	0.367539	−	0.438016i
$512$	−10.9564	−	19.7979i	−0.484211	−	0.874951i
$513$	−9.03271	−	16.6593i	−0.398804	−	0.735524i
$514$	12.3379	+	9.22391i	0.544201	+	0.406849i
$515$	5.93194	+	4.97749i	0.261392	+	0.219334i
$516$	−7.57004	−	10.4481i	−0.333253	−	0.459954i
$517$	−3.52088	−	19.9679i	−0.154848	−	0.878188i
$518$	3.16003	+	4.82575i	0.138844	+	0.212031i
$519$	2.25833	+	13.5113i	0.0991297	+	0.593081i
$520$	22.3752	+	13.0993i	0.981217	+	0.574444i
$521$	−16.1661	−	9.33349i	−0.708249	−	0.408908i	0.102164	−	0.994768i	$-0.467423\pi$
$521$	−16.1661	−	9.33349i	−0.708249	−	0.408908i	−0.810412	+	0.585860i	$0.800757\pi$
$522$	9.68948	−	8.78455i	0.424097	−	0.384489i
$523$	31.7939	−	18.3562i	1.39025	−	0.802662i	0.396909	−	0.917858i	$-0.370083\pi$
$523$	31.7939	−	18.3562i	1.39025	−	0.802662i	0.993343	+	0.115196i	$0.0367495\pi$
$524$	−12.8146	−	17.3586i	−0.559808	−	0.758314i
$525$	−4.23986	−	7.49732i	−0.185043	−	0.327210i
$526$	−0.0207757	−	0.369533i	−0.000905864	−	0.0161124i
$527$	−3.03431	+	2.54609i	−0.132177	+	0.110909i
$528$	12.5499	−	23.9653i	0.546163	−	1.04296i
$529$	8.67822	−	3.15861i	0.377314	−	0.137331i
$530$	−7.64453	−	0.909138i	−0.332057	−	0.0394904i
$531$	−1.60607	−	1.39723i	−0.0696974	−	0.0606344i
$532$	11.3348	+	2.73470i	0.491427	+	0.118564i
$533$	64.4003	+	11.3555i	2.78949	+	0.491862i
$534$	−2.50062	−	1.29029i	−0.108212	−	0.0558364i
$535$	−3.94014	+	10.8254i	−0.170347	+	0.468024i
$536$	−45.3275	−	8.27532i	−1.95785	−	0.357440i
$537$	−6.63913	−	18.7599i	−0.286500	−	0.809548i
$538$	−2.41762	−	10.2931i	−0.104231	−	0.443769i
$539$	17.3547			0.747518
$540$	−6.05876	+	12.9355i	−0.260727	+	0.556655i
$541$	12.0288			0.517156			0.258578	−	0.965990i	$-0.416746\pi$
$541$	12.0288			0.517156			0.258578	+	0.965990i	$0.416746\pi$
$542$	−4.71802	−	20.0872i	−0.202656	−	0.862819i
$543$	16.5281	−	19.3443i	0.709288	−	0.830145i
$544$	1.61413	+	15.1304i	0.0692051	+	0.648711i
$545$	2.90904	−	7.99253i	0.124610	−	0.342363i
$546$	21.9741	−	14.1108i	0.940404	−	0.603885i
$547$	−28.2762	−	4.98585i	−1.20900	−	0.213180i	−0.467416	−	0.884038i	$-0.654815\pi$
$547$	−28.2762	−	4.98585i	−1.20900	−	0.213180i	−0.741586	+	0.670858i	$0.765926\pi$
$548$	−4.96001	+	20.5583i	−0.211881	+	0.878208i
$549$	8.62874	−	14.3480i	0.368265	−	0.612359i
$550$	−17.0577	−	2.02861i	−0.727343	−	0.0865004i
$551$	10.5646	−	3.84522i	0.450069	−	0.163812i
$552$	11.4734	+	14.0967i	0.488342	+	0.599994i
$553$	15.9596	−	13.3917i	0.678671	−	0.569472i
$554$	0.440939	+	7.84289i	0.0187337	+	0.333212i
$555$	−6.07418	−	0.0541849i	−0.257835	−	0.00230002i
$556$	2.60661	−	1.92427i	0.110545	−	0.0816071i
$557$	−6.08867	+	3.51530i	−0.257985	+	0.148948i	−0.623415	−	0.781891i	$-0.714255\pi$
$557$	−6.08867	+	3.51530i	−0.257985	+	0.148948i	0.365430	+	0.930839i	$0.380922\pi$
$558$	6.24296	−	0.239359i	0.264286	−	0.0101329i
$559$	−21.5121	−	12.4200i	−0.909866	−	0.525312i
$560$	−3.41593	−	8.09788i	−0.144349	−	0.342198i
$561$	−14.0396	+	11.5688i	−0.592753	+	0.488435i
$562$	−6.40185	−	9.77640i	−0.270046	−	0.412392i
$563$	−3.67394	−	20.8360i	−0.154838	−	0.878132i	−0.958933	−	0.283631i	$-0.908461\pi$
$563$	−3.67394	−	20.8360i	−0.154838	−	0.878132i	0.804095	−	0.594501i	$-0.202650\pi$
$564$	−1.85674	−	17.8920i	−0.0781828	−	0.753391i
$565$	13.4558	+	11.2908i	0.566091	+	0.475007i
$566$	36.8105	+	27.5199i	1.54726	+	1.15675i
$567$	8.84882	+	11.3441i	0.371616	+	0.476406i
$568$	41.1625	+	15.2644i	1.72714	+	0.640480i
$569$	−1.16629	+	1.38993i	−0.0488934	+	0.0582688i	−0.789937	−	0.613188i	$-0.789887\pi$
$569$	−1.16629	+	1.38993i	−0.0488934	+	0.0582688i	0.741044	+	0.671457i	$0.234331\pi$
$570$	−9.02287	+	8.32804i	−0.377926	+	0.348823i
$571$	−20.8305	+	3.67297i	−0.871728	+	0.153709i	−0.591579	−	0.806247i	$-0.701495\pi$
$571$	−20.8305	+	3.67297i	−0.871728	+	0.153709i	−0.280149	+	0.959956i	$0.590384\pi$
$572$	3.23787	−	51.9818i	0.135382	−	2.17347i
$573$	15.1183	+	18.3472i	0.631575	+	0.766465i
$574$	−15.1794	−	16.1543i	−0.633576	−	0.674268i
$575$	5.77065	−	9.99506i	0.240653	−	0.416823i
$576$	12.6167	−	20.4162i	0.525694	−	0.850674i
$577$	−9.92984	−	17.1990i	−0.413385	−	0.716003i	0.581873	−	0.813280i	$-0.302320\pi$
$577$	−9.92984	−	17.1990i	−0.413385	−	0.716003i	−0.995257	+	0.0972766i	$0.968987\pi$
$578$	−3.98716	+	13.2210i	−0.165844	+	0.549922i
$579$	−0.127088	+	14.2467i	−0.00528160	+	0.592073i
$580$	−7.06132	−	4.68518i	−0.293205	−	0.194542i
$581$	0.462745	+	0.551478i	0.0191979	+	0.0228792i
$582$	21.6457	−	9.05758i	0.897241	−	0.375449i
$583$	5.28910	+	14.5317i	0.219052	+	0.601841i
$584$	−3.83503	−	22.5458i	−0.158695	−	0.932952i
$585$	−0.490597	+	27.4960i	−0.0202837	+	1.13682i
$586$	4.45104	−	1.90936i	0.183871	−	0.0788751i
$587$	−3.45020	+	19.5670i	−0.142405	+	0.807618i	0.827009	+	0.562188i	$0.190040\pi$
$587$	−3.45020	+	19.5670i	−0.142405	+	0.807618i	−0.969414	+	0.245430i	$0.921071\pi$
$588$	15.3575	+	1.09420i	0.633333	+	0.0451241i
$589$	5.04659	+	1.83681i	0.207941	+	0.0756843i
$590$	−0.621521	+	1.23136i	−0.0255876	+	0.0506941i
$591$	−12.6011	−	10.7666i	−0.518340	−	0.442877i
$592$	10.1273	+	1.26654i	0.416229	+	0.0520545i
$593$			25.8771i			1.06265i	0.847169	+	0.531323i	$0.178305\pi$
$593$			25.8771i			1.06265i	−0.847169	+	0.531323i	$0.821695\pi$
$594$	28.6811	−	0.843510i	1.17680	−	0.0346096i
$595$			5.91025i			0.242297i
$596$	25.9212	+	11.3055i	1.06177	+	0.463089i
$597$	−23.3462	+	8.26223i	−0.955495	+	0.338150i
$598$	31.2389	+	15.7677i	1.27745	+	0.644788i
$599$	0.696001	+	0.253324i	0.0284378	+	0.0103505i	0.356200	−	0.934410i	$-0.384072\pi$
$599$	0.696001	+	0.253324i	0.0284378	+	0.0103505i	−0.327762	+	0.944760i	$0.606294\pi$
$600$	−14.9668	−	2.87064i	−0.611019	−	0.117194i
$601$	−1.05648	+	5.99159i	−0.0430947	+	0.244402i	−0.998744	−	0.0501051i	$-0.984044\pi$
$601$	−1.05648	+	5.99159i	−0.0430947	+	0.244402i	0.955649	+	0.294507i	$0.0951555\pi$
$602$	3.31949	+	7.73828i	0.135292	+	0.315389i
$603$	−15.8932	−	46.2153i	−0.647220	−	1.88203i
$604$	15.8124	+	15.0392i	0.643397	+	0.611934i
$605$	−1.99632	−	5.48485i	−0.0811620	−	0.222991i
$606$	−30.7712	−	3.93818i	−1.24999	−	0.159978i
$607$	−2.46703	−	2.94009i	−0.100134	−	0.119335i	0.713650	−	0.700502i	$-0.247041\pi$
$607$	−2.46703	−	2.94009i	−0.100134	−	0.119335i	−0.813784	+	0.581167i	$0.802596\pi$
$608$	16.6716	−	12.1524i	0.676124	−	0.492845i
$609$	−7.42964	+	4.20159i	−0.301064	+	0.170257i
$610$	−10.3863	−	3.13228i	−0.420529	−	0.126822i
$611$	−17.3158	−	29.9918i	−0.700521	−	1.21334i
$612$	−13.1534	+	9.35229i	−0.531693	+	0.378044i
$613$	−0.245022	+	0.424390i	−0.00989633	+	0.0171409i	−0.870931	−	0.491405i	$-0.836483\pi$
$613$	−0.245022	+	0.424390i	−0.00989633	+	0.0171409i	0.861035	+	0.508546i	$0.169817\pi$
$614$	−4.36948	+	4.10578i	−0.176338	+	0.165696i
$615$	23.0239	−	3.84829i	0.928413	−	0.155178i
$616$	−11.4298	+	13.4555i	−0.460522	+	0.542138i
$617$	−13.7119	+	2.41778i	−0.552020	+	0.0973360i	−0.442699	−	0.896671i	$-0.645979\pi$
$617$	−13.7119	+	2.41778i	−0.552020	+	0.0973360i	−0.109321	+	0.994006i	$0.534868\pi$
$618$	4.10220	−	13.1761i	0.165015	−	0.530021i
$619$	−26.8642	+	32.0155i	−1.07976	+	1.28681i	−0.124124	+	0.992267i	$0.539612\pi$
$619$	−26.8642	+	32.0155i	−1.07976	+	1.28681i	−0.955638	+	0.294543i	$0.904832\pi$
$620$	−1.14535	−	3.88263i	−0.0459984	−	0.155930i
$621$	−7.07592	+	17.9327i	−0.283947	+	0.719615i
$622$	−19.7240	+	26.3828i	−0.790860	+	1.05785i
$623$	1.40675	+	1.18040i	0.0563602	+	0.0472919i
$624$	6.14269	−	45.7957i	0.245905	−	1.83330i
$625$	0.0400863	+	0.227341i	0.00160345	+	0.00909364i
$626$	−9.60848	+	6.29189i	−0.384032	+	0.251475i
$627$	23.1015	+	8.64241i	0.922587	+	0.345145i
$628$	20.4503	−	2.30679i	0.816056	−	0.0920508i
$629$	−5.94383	−	3.43167i	−0.236996	−	0.136830i
$630$	5.71408	−	7.36540i	0.227654	−	0.293445i
$631$	−34.7995	+	20.0915i	−1.38535	+	0.799831i	−0.992787	−	0.119895i	$-0.961744\pi$
$631$	−34.7995	+	20.0915i	−1.38535	+	0.799831i	−0.392562	+	0.919726i	$0.628411\pi$
$632$	0.222860	−	36.8615i	0.00886489	−	1.46627i
$633$	−15.2452	+	25.8697i	−0.605941	+	1.02823i
$634$	−25.7882	+	1.44985i	−1.02418	+	0.0575809i
$635$	−8.04482	+	6.75040i	−0.319249	+	0.267882i
$636$	3.76423	+	13.1929i	0.149261	+	0.523132i
$637$	27.8543	−	10.1381i	1.10363	−	0.401688i
$638$	−2.01030	+	16.9037i	−0.0795885	+	0.669224i
$639$	7.26652	+	45.9943i	0.287459	+	1.81951i
$640$	−14.8329	−	4.66966i	−0.586321	−	0.184584i
$641$	−27.8087	−	4.90343i	−1.09838	−	0.193674i	−0.405050	−	0.914295i	$-0.632746\pi$
$641$	−27.8087	−	4.90343i	−1.09838	−	0.193674i	−0.693330	+	0.720621i	$0.743857\pi$
$642$	20.5073	−	0.969530i	0.809360	−	0.0382643i
$643$	3.39235	−	9.32039i	0.133781	−	0.367560i	−0.854655	−	0.519196i	$-0.826232\pi$
$643$	3.39235	−	9.32039i	0.133781	−	0.367560i	0.988437	+	0.151635i	$0.0484539\pi$
$644$	−5.28076	−	10.6214i	−0.208091	−	0.418541i
$645$	−8.71824	−	1.61758i	−0.343280	−	0.0636920i
$646$	−13.5060	+	3.17224i	−0.531385	+	0.124810i
$647$	35.8829			1.41070			0.705352	−	0.708857i	$-0.250789\pi$
$647$	35.8829			1.41070			0.705352	+	0.708857i	$0.250789\pi$
$648$	25.4337	+	1.06189i	0.999130	+	0.0417148i
$649$	2.77073			0.108761
$650$	−28.5628	+	6.70873i	−1.12032	+	0.263138i
$651$	−4.00882	−	0.743794i	−0.157118	−	0.0291516i
$652$	5.50431	+	11.0710i	0.215566	+	0.433575i
$653$	−13.2180	+	36.3162i	−0.517261	+	1.42116i	0.356264	+	0.934385i	$0.384050\pi$
$653$	−13.2180	+	36.3162i	−0.517261	+	1.42116i	−0.873525	+	0.486779i	$0.838172\pi$
$654$	−15.1408	+	0.715815i	−0.592051	+	0.0279906i
$655$	−14.6029	−	2.57488i	−0.570582	−	0.100609i
$656$	−39.1719	+	1.96481i	−1.52940	+	0.0767128i
$657$	18.8571	−	15.2581i	0.735684	−	0.595274i
$658$	−1.38634	+	11.6572i	−0.0540453	+	0.454443i
$659$	−25.4346	+	9.25743i	−0.990791	+	0.360618i	−0.786026	−	0.618193i	$-0.787865\pi$
$659$	−25.4346	+	9.25743i	−0.990791	+	0.360618i	−0.204764	+	0.978811i	$0.565643\pi$
$660$	−5.10104	−	17.8782i	−0.198558	−	0.695907i
$661$	−31.8188	+	26.6991i	−1.23761	+	1.03848i	−0.239901	+	0.970797i	$0.577115\pi$
$661$	−31.8188	+	26.6991i	−1.23761	+	1.03848i	−0.997707	+	0.0676787i	$0.978441\pi$
$662$	−39.8382	+	2.23977i	−1.54836	+	0.0870510i
$663$	−15.7754	+	26.7695i	−0.612668	+	1.03964i
$664$	1.27374	+	0.00770084i	0.0494305	+	0.000298851i
$665$	6.93972	−	4.00665i	0.269111	−	0.155371i
$666$	4.08948	+	10.0231i	0.158464	+	0.388388i
$667$	−9.90482	−	5.71855i	−0.383516	−	0.221423i
$668$	−0.870469	+	0.0981885i	−0.0336794	+	0.00379903i
$669$	10.2988	+	3.85284i	0.398175	+	0.148959i
$670$	−26.4915	+	17.3474i	−1.02346	+	0.670188i
$671$	3.78410	+	21.4607i	0.146084	+	0.828482i
$672$	−10.9629	+	11.1864i	−0.422903	+	0.431526i
$673$	−12.2531	−	10.2816i	−0.472323	−	0.396326i	0.375318	−	0.926896i	$-0.377533\pi$
$673$	−12.2531	−	10.2816i	−0.472323	−	0.396326i	−0.847641	+	0.530570i	$0.821978\pi$
$674$	10.3023	−	13.7804i	0.396831	−	0.530800i
$675$	−5.12003	−	15.3318i	−0.197070	−	0.590120i
$676$	−17.8132	−	60.3850i	−0.685123	−	2.32250i
$677$	−20.2335	+	24.1133i	−0.777635	+	0.926750i	−0.998824	−	0.0484812i	$-0.984562\pi$
$677$	−20.2335	+	24.1133i	−0.777635	+	0.926750i	0.221189	+	0.975231i	$0.429006\pi$
$678$	9.30530	−	29.8883i	0.357368	−	1.14785i
$679$	−15.0805	+	2.65910i	−0.578736	+	0.102047i
$680$	7.96997	+	6.77013i	0.305634	+	0.259623i
$681$	−26.4901	+	4.42766i	−1.01510	+	0.169668i
$682$	−5.92592	+	5.56829i	−0.226915	+	0.213221i
$683$	−19.8352	+	34.3556i	−0.758973	+	1.31458i	0.184402	+	0.982851i	$0.440965\pi$
$683$	−19.8352	+	34.3556i	−0.758973	+	1.31458i	−0.943375	+	0.331729i	$0.892368\pi$
$684$	19.8982	+	9.10441i	0.760826	+	0.348116i
$685$	7.26700	+	12.5868i	0.277658	+	0.480917i
$686$	−24.7710	−	7.47039i	−0.945763	−	0.285221i
$687$	−1.53657	+	0.868959i	−0.0586239	+	0.0331528i
$688$	14.2375	+	4.38779i	0.542799	+	0.167283i
$689$	16.9781	+	20.2337i	0.646813	+	0.770842i
$690$	12.3901	+	1.58572i	0.471683	+	0.0603673i
$691$	−13.5569	−	37.2473i	−0.515729	−	1.41695i	−0.875184	−	0.483790i	$-0.839260\pi$
$691$	−13.5569	−	37.2473i	−0.515729	−	1.41695i	0.359455	−	0.933162i	$-0.382962\pi$
$692$	−11.4617	−	10.9012i	−0.435709	−	0.414402i
$693$	−18.3803	−	3.58016i	−0.698210	−	0.135999i
$694$	3.62749	+	8.45628i	0.137698	+	0.320996i
$695$	0.386650	−	2.19280i	0.0146665	−	0.0831778i
$696$	−2.84473	+	14.8317i	−0.107829	+	0.562195i
$697$	24.7844	+	9.02079i	0.938777	+	0.341687i
$698$	38.8845	+	19.6267i	1.47180	+	0.742883i
$699$	16.3772	−	5.79589i	0.619441	−	0.219221i
$700$	9.11626	+	3.97603i	0.344562	+	0.150280i
$701$			14.6338i			0.552710i	0.961056	+	0.276355i	$0.0891265\pi$
$701$			14.6338i			0.552710i	−0.961056	+	0.276355i	$0.910873\pi$
$702$	45.5405	−	18.1086i	1.71881	−	0.683464i
$703$			9.30554i			0.350965i
$704$	5.05197	+	30.8262i	0.190403	+	1.16181i
$705$	−9.39877	−	8.03045i	−0.353978	−	0.302444i
$706$	18.1582	−	35.9750i	0.683394	−	1.35394i
$707$	19.0245	+	6.92437i	0.715491	+	0.260418i
$708$	2.45188	+	0.174693i	0.0921474	+	0.00656538i
$709$	6.05391	−	34.3334i	0.227359	−	1.28942i	−0.630764	−	0.775975i	$-0.717258\pi$
$709$	6.05391	−	34.3334i	0.227359	−	1.28942i	0.858123	−	0.513444i	$-0.171630\pi$
$710$	27.7277	−	11.8943i	1.04060	−	0.446387i
$711$	34.2034	−	18.9420i	1.28273	−	0.710379i
$712$	3.20319	−	0.544861i	0.120045	−	0.0204195i
$713$	−1.86858	−	5.13387i	−0.0699787	−	0.192265i
$714$	9.71635	−	4.06579i	0.363625	−	0.152158i
$715$	−23.0076	−	27.4194i	−0.860435	−	1.02543i
$716$	19.1473	+	12.7042i	0.715566	+	0.474778i
$717$	0.296700	−	33.2604i	0.0110805	−	1.24213i
$718$	−1.23021	+	4.07923i	−0.0459109	+	0.152236i
$719$	−3.63844	−	6.30196i	−0.135691	−	0.235024i	0.790170	−	0.612887i	$-0.209992\pi$
$719$	−3.63844	−	6.30196i	−0.135691	−	0.235024i	−0.925861	+	0.377864i	$0.876659\pi$
$720$	−3.38682	−	16.1424i	−0.126219	−	0.601592i
$721$	−4.50301	+	7.79945i	−0.167701	+	0.290467i
$722$	−5.51924	−	5.87372i	−0.205405	−	0.218597i
$723$	−1.26591	−	1.53628i	−0.0470798	−	0.0571349i
$724$	−1.82649	+	29.3230i	−0.0678809	+	1.08978i
$725$	9.44390	−	1.66521i	0.350738	−	0.0618445i
$726$	−7.64368	+	7.05506i	−0.283684	+	0.261838i
$727$	25.9765	−	30.9576i	0.963414	−	1.14815i	−0.0255013	−	0.999675i	$-0.508118\pi$
$727$	25.9765	−	30.9576i	0.963414	−	1.14815i	0.988916	−	0.148478i	$-0.0474374\pi$
$728$	−10.4846	+	28.2732i	−0.388585	+	1.04787i
$729$	12.2298	+	24.0714i	0.452955	+	0.891533i
$730$	−12.5881	−	9.41095i	−0.465905	−	0.348315i
$731$	−7.67473	−	6.43987i	−0.283860	−	0.238187i
$732$	1.99555	+	19.2297i	0.0737576	+	0.710748i
$733$	−7.32008	−	41.5142i	−0.270373	−	1.53336i	−0.753285	−	0.657694i	$-0.771532\pi$
$733$	−7.32008	−	41.5142i	−0.270373	−	1.53336i	0.482912	−	0.875669i	$-0.339579\pi$
$734$	2.45005	+	3.74152i	0.0904330	+	0.138102i
$735$	8.16596	−	6.72884i	0.301206	−	0.248197i
$736$	−20.3720	−	5.04557i	−0.750920	−	0.185982i
$737$	55.0875	+	31.8048i	2.02917	+	1.17154i
$738$	−22.1651	−	35.2035i	−0.815910	−	1.29586i
$739$	7.93929	−	4.58375i	0.292052	−	0.168616i	−0.346815	−	0.937934i	$-0.612737\pi$
$739$	7.93929	−	4.58375i	0.292052	−	0.168616i	0.638867	+	0.769317i	$0.279404\pi$
$740$	5.64304	−	4.16584i	0.207442	−	0.153139i
$741$	42.1268	+	0.375793i	1.54757	+	0.0138051i
$742$	−0.502584	−	8.93935i	−0.0184504	−	0.328174i
$743$	10.4100	−	8.73505i	0.381907	−	0.320458i	−0.431544	−	0.902092i	$-0.642031\pi$
$743$	10.4100	−	8.73505i	0.381907	−	0.320458i	0.813450	+	0.581634i	$0.197586\pi$
$744$	−5.59506	+	4.55388i	−0.205125	+	0.166953i
$745$	18.2628	−	6.64711i	0.669097	−	0.243531i
$746$	4.12527	+	0.490604i	0.151037	+	0.0179623i
$747$	0.654533	+	1.18189i	0.0239481	+	0.0432430i
$748$	4.92672	−	20.4204i	0.180139	−	0.746642i
$749$	−13.1948	−	2.32659i	−0.482126	−	0.0850118i
$750$	−22.9777	+	14.7552i	−0.839026	+	0.538785i
$751$	−12.3201	+	33.8492i	−0.449567	+	1.23518i	0.483459	+	0.875367i	$0.339380\pi$
$751$	−12.3201	+	33.8492i	−0.449567	+	1.23518i	−0.933026	+	0.359809i	$0.882842\pi$
$752$	14.1316	+	15.2226i	0.515327	+	0.555112i
$753$	25.5704	−	29.9273i	0.931836	−	1.09061i
$754$	6.64817	+	28.3049i	0.242112	+	1.03080i
$755$	14.9972			0.545803
$756$	−16.0394	−	4.32703i	−0.583348	−	0.157373i
$757$	20.5853			0.748185			0.374093	−	0.927391i	$-0.377954\pi$
$757$	20.5853			0.748185			0.374093	+	0.927391i	$0.377954\pi$
$758$	−0.619107	−	2.63588i	−0.0224870	−	0.0957394i
$759$	−8.37124	−	23.6542i	−0.303857	−	0.858593i
$760$	2.54641	−	13.9478i	0.0923680	−	0.505939i
$761$	15.1391	−	41.5945i	0.548793	−	1.50780i	−0.286548	−	0.958066i	$-0.592508\pi$
$761$	15.1391	−	41.5945i	0.548793	−	1.50780i	0.835341	−	0.549732i	$-0.185270\pi$
$762$	16.6317	+	8.58179i	0.602504	+	0.310886i
$763$	9.74183	+	1.71775i	0.352678	+	0.0621866i
$764$	−26.6856	−	6.43832i	−0.965453	−	0.232930i
$765$	−2.12060	+	10.8870i	−0.0766705	+	0.393621i
$766$	26.3043	+	3.12828i	0.950413	+	0.113029i
$767$	4.44704	−	1.61859i	0.160573	−	0.0584439i
$768$	2.52702	+	27.5974i	0.0911860	+	0.995834i
$769$	−22.3866	+	18.7846i	−0.807281	+	0.677389i	−0.949957	−	0.312381i	$-0.898874\pi$
$769$	−22.3866	+	18.7846i	−0.807281	+	0.677389i	0.142677	+	0.989769i	$0.454429\pi$
$770$	0.681069	+	12.1140i	0.0245440	+	0.436560i
$771$	−9.28727	−	16.4226i	−0.334473	−	0.591446i
$772$	−9.77080	−	13.2355i	−0.351659	−	0.476356i
$773$	−2.91631	+	1.68373i	−0.104892	+	0.0605596i	−0.551528	−	0.834156i	$-0.685955\pi$
$773$	−2.91631	+	1.68373i	−0.104892	+	0.0605596i	0.446636	+	0.894716i	$0.352622\pi$
$774$	3.33819	+	15.4454i	0.119989	+	0.555173i
$775$	3.96710	+	2.29041i	0.142503	+	0.0822739i
$776$	−13.6887	+	23.3820i	−0.491397	+	0.839365i
$777$	−1.16467	−	6.96807i	−0.0417822	−	0.249978i
$778$	−8.05875	−	12.3067i	−0.288920	−	0.441216i
$779$	−6.20967	−	35.2168i	−0.222485	−	1.26177i
$780$	−18.6312	−	25.7146i	−0.667102	−	0.920732i
$781$	−46.4276	−	38.9574i	−1.66131	−	1.39400i
$782$	11.3037	+	8.45077i	0.404220	+	0.302199i
$783$	−15.1934	+	5.07381i	−0.542966	+	0.181323i
$784$	−14.9318	+	9.64928i	−0.533279	+	0.344617i
$785$	9.09126	−	10.8345i	0.324481	−	0.386701i
$786$	5.81257	+	25.7782i	0.207328	+	0.919478i
$787$	38.7602	−	6.83447i	1.38165	−	0.243622i	0.567069	−	0.823670i	$-0.308077\pi$
$787$	38.7602	−	6.83447i	1.38165	−	0.243622i	0.814582	+	0.580048i	$0.196966\pi$
$788$	19.1013	+	1.18979i	0.680456	+	0.0423846i
$789$	−0.158831	+	0.424561i	−0.00565452	+	0.0151148i
$790$	−17.3476	−	18.4618i	−0.617200	−	0.656841i
$791$	−10.2145	+	17.6920i	−0.363186	+	0.629057i
$792$	−25.8823	+	20.6848i	−0.919687	+	0.735002i
$793$	18.6103	+	32.2340i	0.660871	+	1.14466i
$794$	6.47984	−	21.4865i	0.229961	−	0.762527i
$795$	8.12301	+	4.78694i	0.288094	+	0.169775i
$796$	15.8101	−	23.8283i	0.560372	−	0.844571i
$797$	−16.5914	−	19.7729i	−0.587699	−	0.700392i	0.387463	−	0.921885i	$-0.373351\pi$
$797$	−16.5914	−	19.7729i	−0.587699	−	0.700392i	−0.975162	+	0.221493i	$0.928907\pi$
$798$	−11.3608	−	8.65252i	−0.402169	−	0.306296i
$799$	−4.77727	−	13.1254i	−0.169008	−	0.464345i
$800$	15.8042	−	7.73877i	0.558764	−	0.273607i
$801$	2.16779	+	2.67911i	0.0765949	+	0.0946618i
$802$	−7.75749	+	3.32773i	−0.273926	+	0.117506i
$803$	−5.48240	+	31.0922i	−0.193470	+	1.09722i
$804$	46.7429	+	31.6180i	1.64849	+	1.11508i
$805$	−7.66028	−	2.78811i	−0.269989	−	0.0982680i
$806$	−6.25829	+	12.3989i	−0.220439	+	0.436733i
$807$	−2.36233	+	12.7322i	−0.0831580	+	0.448196i
$808$	31.1299	−	17.7228i	1.09515	−	0.623485i
$809$		−	54.1748i		−	1.90469i	−0.305029	−	0.952343i	$-0.598666\pi$
$809$		−	54.1748i		−	1.90469i	0.305029	−	0.952343i	$-0.401334\pi$
$810$	13.1684	−	11.5173i	0.462689	−	0.404676i
$811$			25.4797i			0.894714i	0.894356	+	0.447357i	$0.147635\pi$
$811$			25.4797i			0.894714i	−0.894356	+	0.447357i	$0.852365\pi$
$812$	3.94013	−	9.03396i	0.138272	−	0.317030i
$813$	−4.61012	+	24.8471i	−0.161684	+	0.871427i
$814$	−12.5783	−	6.34884i	−0.440870	−	0.222527i
$815$	7.98456	+	2.90614i	0.279687	+	0.101798i
$816$	5.64726	−	17.7598i	0.197694	−	0.621717i
$817$	−2.35877	+	13.3772i	−0.0825228	+	0.468010i
$818$	7.58821	+	17.6894i	0.265315	+	0.618494i
$819$	−31.5919	+	4.99113i	−1.10391	+	0.174404i
$820$	−18.5762	+	19.5313i	−0.648708	+	0.682062i
$821$	−15.2379	−	41.8658i	−0.531807	−	1.46113i	−0.856919	−	0.515451i	$-0.827624\pi$
$821$	−15.2379	−	41.8658i	−0.531807	−	1.46113i	0.325112	−	0.945675i	$-0.394598\pi$
$822$	15.6934	−	20.6055i	0.547369	−	0.718701i
$823$	8.99956	+	10.7253i	0.313705	+	0.373859i	0.899740	−	0.436427i	$-0.143756\pi$
$823$	8.99956	+	10.7253i	0.313705	+	0.373859i	−0.586035	+	0.810286i	$0.699312\pi$
$824$	5.35939	+	15.0065i	0.186703	+	0.522776i
$825$	18.1254	+	10.6814i	0.631044	+	0.371878i
$826$	−1.53587	−	0.463183i	−0.0534396	−	0.0161162i
$827$	21.2656	+	36.8331i	0.739478	+	1.28081i	0.952730	+	0.303817i	$0.0982611\pi$
$827$	21.2656	+	36.8331i	0.739478	+	1.28081i	−0.213252	+	0.976997i	$0.568406\pi$
$828$	−5.91651	−	21.4599i	−0.205613	−	0.745784i
$829$	−2.02999	+	3.51605i	−0.0705046	+	0.122118i	−0.899123	−	0.437697i	$-0.855794\pi$
$829$	−2.02999	+	3.51605i	−0.0705046	+	0.122118i	0.828618	+	0.559815i	$0.189128\pi$
$830$	0.637941	−	0.599441i	0.0221432	−	0.0208069i
$831$	3.37099	−	9.01079i	0.116938	−	0.312581i
$832$	26.1163	+	46.5250i	0.905421	+	1.61297i
$833$	11.7737	−	2.07603i	0.407936	−	0.0719301i
$834$	−3.87091	+	0.872829i	−0.134039	+	0.0302236i
$835$	−0.386970	+	0.461173i	−0.0133917	+	0.0159596i
$836$	−27.3171	+	8.05839i	−0.944783	+	0.278705i
$837$	−7.11760	−	2.80848i	−0.246020	−	0.0970751i
$838$	8.59806	−	11.5007i	0.297015	−	0.397286i
$839$	−7.46280	−	6.26203i	−0.257644	−	0.216189i	0.504811	−	0.863230i	$-0.331562\pi$
$839$	−7.46280	−	6.26203i	−0.257644	−	0.216189i	−0.762456	+	0.647040i	$0.776007\pi$
$840$	−0.161091	+	10.7629i	−0.00555816	+	0.371356i
$841$	3.38562	+	19.2008i	0.116745	+	0.662096i
$842$	−28.3161	+	18.5422i	−0.975838	+	0.639005i
$843$	2.35948	+	14.1165i	0.0812648	+	0.486198i
$844$	−3.88644	−	34.4544i	−0.133777	−	1.18597i
$845$	−37.4705	−	21.6336i	−1.28903	−	0.744219i
$846$	−6.73631	+	20.9757i	−0.231599	+	0.721160i
$847$	5.87895	−	3.39422i	0.202003	−	0.116627i
$848$	−12.6304	−	9.56219i	−0.433730	−	0.328367i
$849$	−27.7089	−	48.9975i	−0.950968	−	1.68159i
$850$	−11.8150	+	0.664254i	−0.405249	+	0.0227837i
$851$	7.25174	−	6.08494i	0.248587	−	0.208589i
$852$	−38.6285	−	37.4015i	−1.32339	−	1.28135i
$853$	−15.2217	+	5.54023i	−0.521179	+	0.189694i	−0.589196	−	0.807990i	$-0.700555\pi$
$853$	−15.2217	+	5.54023i	−0.521179	+	0.189694i	0.0680162	+	0.997684i	$0.478333\pi$
$854$	1.48999	−	12.5286i	0.0509863	−	0.428721i
$855$	14.2210	−	4.89051i	0.486346	−	0.167252i
$856$	−18.2519	+	15.1280i	−0.623835	+	0.517065i
$857$	−1.64050	−	0.289264i	−0.0560383	−	0.00988106i	0.145559	−	0.989350i	$-0.453502\pi$
$857$	−1.64050	−	0.289264i	−0.0560383	−	0.00988106i	−0.201597	+	0.979469i	$0.564613\pi$
$858$	−29.2496	+	56.6865i	−0.998564	+	1.93524i
$859$	1.29836	−	3.56720i	0.0442993	−	0.121711i	−0.915570	−	0.402158i	$-0.868260\pi$
$859$	1.29836	−	3.56720i	0.0442993	−	0.121711i	0.959870	+	0.280446i	$0.0904825\pi$
$860$	9.16814	−	4.55824i	0.312631	−	0.155435i
$861$	9.05754	+	25.5934i	0.308680	+	0.872222i
$862$	−27.0500	+	6.35342i	−0.921326	+	0.216398i
$863$	50.6239			1.72326			0.861629	−	0.507538i	$-0.169444\pi$
$863$	50.6239			1.72326			0.861629	+	0.507538i	$0.169444\pi$
$864$	−24.2080	+	16.6726i	−0.823572	+	0.567212i
$865$	−10.8708			−0.369618
$866$	−15.9342	+	3.74258i	−0.541466	+	0.127178i
$867$	10.9864	−	12.8584i	0.373118	−	0.436693i
$868$	4.21569	−	2.09597i	0.143090	−	0.0711417i
$869$	−17.4050	+	47.8198i	−0.590424	+	1.62218i
$870$	5.60809	+	8.73322i	0.190132	+	0.296084i
$871$	106.995	+	18.8661i	3.62539	+	0.639255i
$872$	13.4755	−	11.1692i	0.456339	−	0.378236i
$873$	−28.7332	−	0.512672i	−0.972473	−	0.0173513i
$874$	2.25979	−	19.0015i	0.0764385	−	0.642737i
$875$	16.7464	−	6.09519i	0.566132	−	0.206055i
$876$	−6.81184	+	27.1685i	−0.230151	+	0.917940i
$877$	28.4064	−	23.8358i	0.959217	−	0.804879i	−0.0216083	−	0.999767i	$-0.506879\pi$
$877$	28.4064	−	23.8358i	0.959217	−	0.804879i	0.980826	+	0.194888i	$0.0624342\pi$
$878$	15.9038	−	0.894136i	0.536728	−	0.0301756i
$879$	−5.93156	−	0.0529126i	−0.200067	−	0.00178470i
$880$	17.1159	+	12.9581i	0.576977	+	0.436816i
$881$	32.9375	−	19.0165i	1.10969	−	0.640682i	0.170944	−	0.985281i	$-0.445318\pi$
$881$	32.9375	−	19.0165i	1.10969	−	0.640682i	0.938750	+	0.344599i	$0.111985\pi$
$882$	−16.6796	−	8.79578i	−0.561632	−	0.296169i
$883$	−19.2734	−	11.1275i	−0.648603	−	0.374471i	0.139318	−	0.990248i	$-0.455509\pi$
$883$	−19.2734	−	11.1275i	−0.648603	−	0.374471i	−0.787921	+	0.615777i	$0.788842\pi$
$884$	−4.02162	−	35.6528i	−0.135262	−	1.19913i
$885$	1.30373	−	1.07428i	0.0438242	−	0.0361117i
$886$	43.4870	−	28.4764i	1.46097	−	0.956685i
$887$	−2.07379	−	11.7610i	−0.0696309	−	0.394897i	−0.999627	−	0.0273261i	$-0.991301\pi$
$887$	−2.07379	−	11.7610i	−0.0696309	−	0.394897i	0.929996	−	0.367571i	$-0.119810\pi$
$888$	−10.7305	−	6.41129i	−0.360093	−	0.215149i
$889$	−9.35636	−	7.85091i	−0.313802	−	0.263311i
$890$	1.33706	−	1.78844i	0.0448183	−	0.0599488i
$891$	−32.5730	−	13.1897i	−1.09124	−	0.441872i
$892$	−12.1781	+	3.59247i	−0.407754	+	0.120285i
$893$	−12.1731	+	14.5073i	−0.407357	+	0.485469i
$894$	−23.4911	−	25.4510i	−0.785659	−	0.851209i
$895$	15.5520	−	2.74223i	0.519845	−	0.0916627i
$896$	2.35282	−	17.9321i	0.0786022	−	0.599068i
$897$	−27.2540	−	33.0748i	−0.909986	−	1.10434i
$898$	−3.30119	+	3.10196i	−0.110162	+	0.103514i
$899$	2.26973	−	3.93129i	0.0756997	−	0.131116i
$900$	15.3661	+	10.5950i	0.512203	+	0.353166i
$901$	5.32657	+	9.22589i	0.177454	+	0.307359i
$902$	51.8393	+	15.6336i	1.72606	+	0.520540i
$903$	0.0919902	−	10.3122i	0.00306124	−	0.343169i
$904$	12.1571	+	34.0403i	0.404339	+	1.13216i
$905$	12.9786	+	15.4673i	0.431424	+	0.514151i
$906$	−10.3169	−	24.6551i	−0.342755	−	0.819111i
$907$	2.47672	+	6.80473i	0.0822381	+	0.225947i	0.973996	−	0.226566i	$-0.0727498\pi$
$907$	2.47672	+	6.80473i	0.0822381	+	0.225947i	−0.891758	+	0.452513i	$0.850528\pi$
$908$	21.3728	−	22.4717i	0.709282	−	0.745750i
$909$	32.5598	+	19.5811i	1.07994	+	0.649464i
$910$	8.16982	+	19.0452i	0.270827	+	0.631343i
$911$	−2.01998	+	11.4559i	−0.0669251	+	0.379551i	0.932887	+	0.360169i	$0.117281\pi$
$911$	−2.01998	+	11.4559i	−0.0669251	+	0.379551i	−0.999812	+	0.0193820i	$0.993830\pi$
$912$	−24.6816	+	5.40871i	−0.817290	+	0.179100i
$913$	−1.65240	−	0.601423i	−0.0546863	−	0.0199042i
$914$	24.4464	+	12.3392i	0.808614	+	0.408144i
$915$	10.1014	+	8.63081i	0.333943	+	0.285326i
$916$	0.814886	−	1.86838i	0.0269246	−	0.0617329i
$917$		−	17.2456i		−	0.569499i
$918$	19.3569	−	4.00319i	0.638873	−	0.132125i
$919$		−	21.8452i		−	0.720605i	−0.932835	−	0.360303i	$-0.882673\pi$
$919$		−	21.8452i		−	0.720605i	0.932835	−	0.360303i	$-0.117327\pi$
$920$	−12.5345	+	7.13612i	−0.413251	+	0.235271i
$921$	6.92262	−	2.44992i	0.228108	−	0.0807275i
$922$	1.36792	−	2.71011i	0.0450499	−	0.0892528i
$923$	−97.2743	−	35.4050i	−3.20182	−	1.16537i
$924$	19.4467	−	9.45317i	0.639751	−	0.310986i
$925$	−1.37830	+	7.81671i	−0.0453181	+	0.257012i
$926$	25.9120	−	11.1154i	0.851520	−	0.365276i
$927$	−11.0933	+	12.7514i	−0.364350	+	0.418809i
$928$	−7.66890	−	15.6616i	−0.251744	−	0.514116i
$929$	18.5670	+	51.0125i	0.609164	+	1.67366i	0.732056	+	0.681244i	$0.238561\pi$
$929$	18.5670	+	51.0125i	0.609164	+	1.67366i	−0.122892	+	0.992420i	$0.539217\pi$
$930$	−0.629382	+	4.91770i	−0.0206382	+	0.161258i
$931$	−10.4192	−	12.4172i	−0.341477	−	0.406956i
$932$	−11.0906	+	16.7154i	−0.363286	+	0.547530i
$933$	35.1174	−	19.8595i	1.14969	−	0.650170i
$934$	−4.04011	+	13.3966i	−0.132196	+	0.438350i
$935$	−7.21822	−	12.5023i	−0.236061	−	0.408870i
$936$	−29.4577	+	48.3189i	−0.962854	+	1.57935i
$937$	−16.0875	+	27.8643i	−0.525555	+	0.910288i	0.474002	+	0.880524i	$0.342809\pi$
$937$	−16.0875	+	27.8643i	−0.525555	+	0.910288i	−0.999557	+	0.0297643i	$0.990524\pi$
$938$	−25.2192	−	26.8389i	−0.823435	−	0.876321i
$939$	13.8740	−	2.31895i	0.452762	−	0.0756762i
$940$	14.2471	+	0.887430i	0.464688	+	0.0289448i
$941$	−41.3860	+	7.29746i	−1.34914	+	0.237891i	−0.801086	−	0.598550i	$-0.795744\pi$
$941$	−41.3860	+	7.29746i	−1.34914	+	0.237891i	−0.548058	+	0.836440i	$0.684633\pi$
$942$	−24.0659	−	7.49256i	−0.784108	−	0.244121i
$943$	−23.3837	+	27.8676i	−0.761477	+	0.907493i
$944$	−2.38392	+	1.54054i	−0.0775899	+	0.0501404i
$945$	−10.0367	+	5.44193i	−0.326493	+	0.177026i
$946$	−16.4727	−	12.3152i	−0.535575	−	0.400401i
$947$	−0.0104289	−	0.00875091i	−0.000338895	−	0.000284366i	0.642618	−	0.766187i	$-0.277848\pi$
$947$	−0.0104289	−	0.00875091i	−0.000338895	−	0.000284366i	−0.642957	+	0.765902i	$0.722293\pi$
$948$	−18.4171	+	41.2194i	−0.598159	+	1.33874i
$949$	9.36399	+	53.1058i	0.303968	+	1.72389i
$950$	8.78949	+	13.4226i	0.285169	+	0.435487i
$951$	29.6284	+	11.0841i	0.960766	+	0.359428i
$952$	−6.14463	+	10.4958i	−0.199149	+	0.340170i
$953$	−41.1680	−	23.7683i	−1.33356	−	0.769932i	−0.347718	−	0.937599i	$-0.613043\pi$
$953$	−41.1680	−	23.7683i	−1.33356	−	0.769932i	−0.985844	+	0.167667i	$0.946377\pi$
$954$	2.28165	−	16.6471i	0.0738712	−	0.538971i
$955$	−16.3382	+	9.43289i	−0.528693	+	0.305241i
$956$	22.8109	+	30.8996i	0.737757	+	0.999363i
$957$	10.5850	−	17.9617i	0.342163	−	0.580620i
$958$	−2.04470	−	36.3686i	−0.0660612	−	1.17502i
$959$	−12.9488	+	10.8653i	−0.418138	+	0.350860i
$960$	14.3293	+	12.5460i	0.462475	+	0.404921i
$961$	−27.0928	+	9.86098i	−0.873961	+	0.318096i
$962$	−23.8971	−	2.84200i	−0.770473	−	0.0916296i
$963$	−23.4707	−	9.02000i	−0.756334	−	0.290665i
$964$	2.23449	+	0.539106i	0.0719682	+	0.0173634i
$965$	−11.1343	−	1.96328i	−0.358427	−	0.0632003i
$966$	0.686057	+	14.5114i	0.0220735	+	0.466895i
$967$	1.45894	−	4.00841i	0.0469164	−	0.128902i	−0.914022	−	0.405666i	$-0.867040\pi$
$967$	1.45894	−	4.00841i	0.0469164	−	0.128902i	0.960938	+	0.276764i	$0.0892620\pi$
$968$	2.15718	−	11.8158i	0.0693344	−	0.379774i
$969$	16.7064	+	3.09969i	0.536686	+	0.0995764i
$970$	4.25763	+	18.1271i	0.136704	+	0.582026i
$971$	−40.5152			−1.30019			−0.650097	−	0.759851i	$-0.725272\pi$
$971$	−40.5152			−1.30019			−0.650097	+	0.759851i	$0.725272\pi$
$972$	−27.9930	−	13.7256i	−0.897876	−	0.440249i
$973$	2.58964			0.0830199
$974$	−8.13814	−	34.6485i	−0.260763	−	1.11021i
$975$	35.3311	+	6.55530i	1.13150	+	0.209938i
$976$	−15.1881	−	16.3607i	−0.486159	−	0.523692i
$977$	−0.197548	+	0.542760i	−0.00632013	+	0.0173644i	−0.942813	−	0.333323i	$-0.891830\pi$
$977$	−0.197548	+	0.542760i	−0.00632013	+	0.0173644i	0.936492	+	0.350688i	$0.114052\pi$
$978$	−0.715101	−	15.1257i	−0.0228664	−	0.483666i
$979$	−4.41742	−	0.778910i	−0.141181	−	0.0248941i
$980$	−2.86557	+	11.8772i	−0.0915372	+	0.379404i
$981$	17.3287	+	6.65956i	0.553262	+	0.212623i
$982$	6.58032	+	0.782575i	0.209986	+	0.0249730i
$983$	−48.7103	+	17.7291i	−1.55362	+	0.565471i	−0.969263	−	0.246028i	$-0.920875\pi$
$983$	−48.7103	+	17.7291i	−1.55362	+	0.565471i	−0.584355	+	0.811498i	$0.698652\pi$
$984$	44.8880	+	17.1029i	1.43098	+	0.545221i
$985$	10.0756	−	8.45440i	0.321034	−	0.269379i
$986$	0.658258	+	11.7083i	0.0209632	+	0.372868i
$987$	7.29961	−	12.3868i	0.232349	−	0.394276i
$988$	−39.1366	+	28.8917i	−1.24510	+	0.919168i
$989$	11.9672	−	6.90926i	0.380535	−	0.219702i
$990$	−3.09195	+	22.5591i	−0.0982686	+	0.716976i
$991$	45.4196	+	26.2230i	1.44280	+	0.833002i	0.998036	−	0.0626443i	$-0.0199534\pi$
$991$	45.4196	+	26.2230i	1.44280	+	0.833002i	0.444766	+	0.895647i	$0.353287\pi$
$992$	2.00262	−	8.08576i	0.0635833	−	0.256723i
$993$	45.7707	+	17.1231i	1.45249	+	0.543384i
$994$	19.2231	+	29.3560i	0.609720	+	0.931117i
$995$	−3.41264	−	19.3540i	−0.108188	−	0.613564i
$996$	−1.42432	−	0.636395i	−0.0451314	−	0.0201650i
$997$	−30.7742	−	25.8226i	−0.974627	−	0.817809i	0.00864294	−	0.999963i	$-0.497249\pi$
$997$	−30.7742	−	25.8226i	−0.974627	−	0.817809i	−0.983270	+	0.182153i	$0.941693\pi$
$998$	−11.2211	−	8.38899i	−0.355197	−	0.265549i
$999$	0.354759	−	13.2535i	0.0112241	−	0.419321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.l.a.11.15	yes	96
3.2	odd	2		324.2.l.a.35.2		96
4.3	odd	2	inner	108.2.l.a.11.9	✓	96
9.2	odd	6		972.2.l.a.755.13		96
9.4	even	3		972.2.l.c.431.7		96
9.5	odd	6		972.2.l.b.431.10		96
9.7	even	3		972.2.l.d.755.4		96
12.11	even	2		324.2.l.a.35.8		96
27.4	even	9		972.2.l.a.215.15		96
27.5	odd	18	inner	108.2.l.a.59.9	yes	96
27.13	even	9		972.2.l.b.539.3		96
27.14	odd	18		972.2.l.c.539.14		96
27.22	even	9		324.2.l.a.287.8		96
27.23	odd	18		972.2.l.d.215.2		96
36.7	odd	6		972.2.l.d.755.2		96
36.11	even	6		972.2.l.a.755.15		96
36.23	even	6		972.2.l.b.431.3		96
36.31	odd	6		972.2.l.c.431.14		96
108.23	even	18		972.2.l.d.215.4		96
108.31	odd	18		972.2.l.a.215.13		96
108.59	even	18	inner	108.2.l.a.59.15	yes	96
108.67	odd	18		972.2.l.b.539.10		96
108.95	even	18		972.2.l.c.539.7		96
108.103	odd	18		324.2.l.a.287.2		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.9	✓	96	4.3	odd	2	inner
108.2.l.a.11.15	yes	96	1.1	even	1	trivial
108.2.l.a.59.9	yes	96	27.5	odd	18	inner
108.2.l.a.59.15	yes	96	108.59	even	18	inner
324.2.l.a.35.2		96	3.2	odd	2
324.2.l.a.35.8		96	12.11	even	2
324.2.l.a.287.2		96	108.103	odd	18
324.2.l.a.287.8		96	27.22	even	9
972.2.l.a.215.13		96	108.31	odd	18
972.2.l.a.215.15		96	27.4	even	9
972.2.l.a.755.13		96	9.2	odd	6
972.2.l.a.755.15		96	36.11	even	6
972.2.l.b.431.3		96	36.23	even	6
972.2.l.b.431.10		96	9.5	odd	6
972.2.l.b.539.3		96	27.13	even	9
972.2.l.b.539.10		96	108.67	odd	18
972.2.l.c.431.7		96	9.4	even	3
972.2.l.c.431.14		96	36.31	odd	6
972.2.l.c.539.7		96	108.95	even	18
972.2.l.c.539.14		96	27.14	odd	18
972.2.l.d.215.2		96	27.23	odd	18
972.2.l.d.215.4		96	108.23	even	18
972.2.l.d.755.2		96	36.7	odd	6
972.2.l.d.755.4		96	9.7	even	3

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37675 - 0.323366i) q^{2} +(-1.70299 - 0.315971i) q^{3} +(1.79087 - 0.890387i) q^{4} +(0.470103 - 1.29160i) q^{5} +(-2.44676 + 0.115676i) q^{6} +(1.57428 + 0.277589i) q^{7} +(2.17765 - 1.80495i) q^{8} +(2.80032 + 1.07619i) q^{9} +O(q^{10})\)	\(q+(1.37675 - 0.323366i) q^{2} +(-1.70299 - 0.315971i) q^{3} +(1.79087 - 0.890387i) q^{4} +(0.470103 - 1.29160i) q^{5} +(-2.44676 + 0.115676i) q^{6} +(1.57428 + 0.277589i) q^{7} +(2.17765 - 1.80495i) q^{8} +(2.80032 + 1.07619i) q^{9} +(0.229554 - 1.93022i) q^{10} +(-3.66920 + 1.33548i) q^{11} +(-3.33116 + 0.950455i) q^{12} +(-5.10894 + 4.28691i) q^{13} +(2.25716 - 0.126901i) q^{14} +(-1.20869 + 2.05103i) q^{15} +(2.41442 - 3.18913i) q^{16} +(-2.32950 + 1.34494i) q^{17} +(4.20334 + 0.576109i) q^{18} +(3.15841 + 1.82351i) q^{19} +(-0.308129 - 2.73165i) q^{20} +(-2.59328 - 0.970158i) q^{21} +(-4.61972 + 3.02512i) q^{22} +(-0.644252 - 3.65373i) q^{23} +(-4.27882 + 2.38572i) q^{24} +(2.38300 + 1.99957i) q^{25} +(-5.64747 + 7.55405i) q^{26} +(-4.42887 - 2.71756i) q^{27} +(3.06650 - 0.904598i) q^{28} +(1.98152 - 2.36148i) q^{29} +(-1.00082 + 3.21460i) q^{30} +(1.45019 - 0.255708i) q^{31} +(2.29279 - 5.17137i) q^{32} +(6.67058 - 1.11494i) q^{33} +(-2.77223 + 2.60493i) q^{34} +(1.09861 - 1.90285i) q^{35} +(5.97324 - 0.566062i) q^{36} +(1.27577 + 2.20970i) q^{37} +(4.93800 + 1.48919i) q^{38} +(10.0550 - 5.68627i) q^{39} +(-1.30754 - 3.66116i) q^{40} +(-6.30271 - 7.51128i) q^{41} +(-3.88400 - 0.497086i) q^{42} +(1.27388 + 3.49995i) q^{43} +(-5.38197 + 5.65868i) q^{44} +(2.70644 - 3.11097i) q^{45} +(-2.06847 - 4.82194i) q^{46} +(-0.901707 + 5.11384i) q^{47} +(-5.11940 + 4.66816i) q^{48} +(-4.17653 - 1.52013i) q^{49} +(3.92738 + 1.98232i) q^{50} +(4.39208 - 1.55436i) q^{51} +(-5.33242 + 12.2262i) q^{52} -3.96045i q^{53} +(-6.97620 - 2.30924i) q^{54} +5.36695i q^{55} +(3.92928 - 2.23701i) q^{56} +(-4.80256 - 4.10338i) q^{57} +(1.96443 - 3.89192i) q^{58} +(-0.666798 - 0.242695i) q^{59} +(-0.338383 + 4.74933i) q^{60} +(0.969119 - 5.49615i) q^{61} +(1.91386 - 0.820987i) q^{62} +(4.10977 + 2.47157i) q^{63} +(1.48434 - 7.86109i) q^{64} +(3.13523 + 8.61397i) q^{65} +(8.82317 - 3.69204i) q^{66} +(-10.4714 - 12.4793i) q^{67} +(-2.97432 + 4.48277i) q^{68} +(-0.0573217 + 6.42582i) q^{69} +(0.897191 - 2.97499i) q^{70} +(7.76079 + 13.4421i) q^{71} +(8.04060 - 2.71087i) q^{72} +(4.04282 - 7.00237i) q^{73} +(2.47096 + 2.62966i) q^{74} +(-3.42640 - 4.15820i) q^{75} +(7.27993 + 0.453456i) q^{76} +(-6.14709 + 1.08390i) q^{77} +(12.0044 - 11.0800i) q^{78} +(8.37729 - 9.98366i) q^{79} +(-2.98405 - 4.61768i) q^{80} +(6.68364 + 6.02735i) q^{81} +(-11.1061 - 8.30305i) q^{82} +(0.344982 + 0.289474i) q^{83} +(-5.50803 + 0.571594i) q^{84} +(0.642014 + 3.64104i) q^{85} +(2.88558 + 4.40662i) q^{86} +(-4.12066 + 3.39547i) q^{87} +(-5.57978 + 9.53093i) q^{88} +(0.994859 + 0.574382i) q^{89} +(2.72011 - 5.15820i) q^{90} +(-9.23292 + 5.33063i) q^{91} +(-4.40701 - 5.96972i) q^{92} +(-2.55045 - 0.0227513i) q^{93} +(0.412218 + 7.33204i) q^{94} +(3.84002 - 3.22216i) q^{95} +(-5.53859 + 8.08233i) q^{96} +(-9.00157 + 3.27630i) q^{97} +(-6.24159 - 0.742291i) q^{98} +(-11.7122 - 0.208974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Introduction

L-functions

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