LMFDB - Embedded newform 288.2.bc.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 21, 8]))

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

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

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bc (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	288.13
Dual form			288.2.bc.a.133.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25694 - 0.648153i) q^{2} +(1.41818 - 0.994373i) q^{3} +(1.15979 + 1.62938i) q^{4} +(0.579315 - 4.40033i) q^{5} +(-2.42707 + 0.330671i) q^{6} +(1.20832 + 0.323768i) q^{7} +(-0.401705 - 2.79976i) q^{8} +(1.02245 - 2.82039i) q^{9} +O(q^{10})$	\(q+(-1.25694 - 0.648153i) q^{2} +(1.41818 - 0.994373i) q^{3} +(1.15979 + 1.62938i) q^{4} +(0.579315 - 4.40033i) q^{5} +(-2.42707 + 0.330671i) q^{6} +(1.20832 + 0.323768i) q^{7} +(-0.401705 - 2.79976i) q^{8} +(1.02245 - 2.82039i) q^{9} +(-3.58025 + 5.15547i) q^{10} +(-2.53108 + 3.29857i) q^{11} +(3.26500 + 1.15748i) q^{12} +(0.0758711 - 0.0582180i) q^{13} +(-1.30893 - 1.19013i) q^{14} +(-3.55400 - 6.81650i) q^{15} +(-1.30975 + 3.77949i) q^{16} +2.57648i q^{17} +(-3.11320 + 2.88236i) q^{18} +(3.07003 + 1.27165i) q^{19} +(7.84169 - 4.15956i) q^{20} +(2.03555 - 0.742359i) q^{21} +(5.31940 - 2.50558i) q^{22} +(0.507432 - 0.135966i) q^{23} +(-3.35369 - 3.57110i) q^{24} +(-14.1977 - 3.80426i) q^{25} +(-0.133100 + 0.0240004i) q^{26} +(-1.35451 - 5.01650i) q^{27} +(0.873860 + 2.34431i) q^{28} +(5.45887 - 0.718674i) q^{29} +(0.0490279 + 10.8715i) q^{30} +(-1.95771 + 3.39085i) q^{31} +(4.09597 - 3.90167i) q^{32} +(-0.309512 + 7.19480i) q^{33} +(1.66995 - 3.23848i) q^{34} +(2.12468 - 5.12943i) q^{35} +(5.78131 - 1.60512i) q^{36} +(-0.306228 + 0.126844i) q^{37} +(-3.03462 - 3.58823i) q^{38} +(0.0497082 - 0.158007i) q^{39} +(-12.5526 + 0.145697i) q^{40} +(-7.79353 + 2.08827i) q^{41} +(-3.03973 - 0.386250i) q^{42} +(5.68592 - 7.41004i) q^{43} +(-8.31017 - 0.298427i) q^{44} +(-11.8183 - 6.13299i) q^{45} +(-0.725938 - 0.157993i) q^{46} +(5.21248 - 3.00942i) q^{47} +(1.90076 + 6.66236i) q^{48} +(-4.70697 - 2.71757i) q^{49} +(15.3799 + 13.9840i) q^{50} +(2.56198 + 3.65390i) q^{51} +(0.182854 + 0.0561019i) q^{52} +(0.848306 + 2.04799i) q^{53} +(-1.54892 + 7.18337i) q^{54} +(13.0485 + 13.0485i) q^{55} +(0.421083 - 3.51305i) q^{56} +(5.61833 - 1.24933i) q^{57} +(-7.32728 - 2.63485i) q^{58} +(-1.21081 + 9.19702i) q^{59} +(6.98475 - 13.6966i) q^{60} +(13.4688 - 1.77320i) q^{61} +(4.65851 - 2.99320i) q^{62} +(2.14859 - 3.07689i) q^{63} +(-7.67727 + 2.24935i) q^{64} +(-0.212225 - 0.367585i) q^{65} +(5.05237 - 8.84282i) q^{66} +(7.53531 + 9.82021i) q^{67} +(-4.19806 + 2.98819i) q^{68} +(0.584427 - 0.697400i) q^{69} +(-5.99526 + 5.07027i) q^{70} +(1.60783 - 1.60783i) q^{71} +(-8.30713 - 1.72963i) q^{72} +(7.47247 + 7.47247i) q^{73} +(0.467124 + 0.0390476i) q^{74} +(-23.9177 + 8.72268i) q^{75} +(1.48861 + 6.47708i) q^{76} +(-4.12633 + 3.16624i) q^{77} +(-0.164893 + 0.166387i) q^{78} +(-1.18365 + 0.683378i) q^{79} +(15.8723 + 7.95285i) q^{80} +(-6.90921 - 5.76739i) q^{81} +(11.1495 + 2.42657i) q^{82} +(1.60457 + 12.1879i) q^{83} +(3.57041 + 2.45570i) q^{84} +(11.3374 + 1.49259i) q^{85} +(-11.9497 + 5.62862i) q^{86} +(7.02701 - 6.44736i) q^{87} +(10.2520 + 5.76137i) q^{88} +(-1.96743 + 1.96743i) q^{89} +(10.8798 + 15.3689i) q^{90} +(0.110526 - 0.0457812i) q^{91} +(0.810057 + 0.669106i) q^{92} +(0.595394 + 6.75551i) q^{93} +(-8.50233 + 0.404182i) q^{94} +(7.37418 - 12.7724i) q^{95} +(1.92909 - 9.60618i) q^{96} +(-5.86403 - 10.1568i) q^{97} +(4.15498 + 6.46666i) q^{98} +(6.71537 + 10.5113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.25694	−	0.648153i	−0.888791	−	0.458314i
$2$	−1.25694	−	0.648153i	−0.888791	−	0.458314i
$3$	1.41818	−	0.994373i	0.818784	−	0.574101i
$3$	1.41818	−	0.994373i	0.818784	−	0.574101i
$4$	1.15979	+	1.62938i	0.579897	+	0.814689i
$5$	0.579315	−	4.40033i	0.259077	−	1.96789i	0.00781313	−	0.999969i	$-0.497513\pi$
$5$	0.579315	−	4.40033i	0.259077	−	1.96789i	0.251264	−	0.967919i	$-0.419154\pi$
$6$	−2.42707	+	0.330671i	−0.990846	+	0.134996i
$7$	1.20832	+	0.323768i	0.456701	+	0.122373i	0.479833	−	0.877360i	$-0.340697\pi$
$7$	1.20832	+	0.323768i	0.456701	+	0.122373i	−0.0231321	+	0.999732i	$0.507364\pi$
$8$	−0.401705	−	2.79976i	−0.142024	−	0.989863i
$9$	1.02245	−	2.82039i	0.340815	−	0.940130i
$10$	−3.58025	+	5.15547i	−1.13218	+	1.63030i
$11$	−2.53108	+	3.29857i	−0.763151	+	0.994558i	0.236586	+	0.971611i	$0.423972\pi$
$11$	−2.53108	+	3.29857i	−0.763151	+	0.994558i	−0.999737	+	0.0229469i	$0.992695\pi$
$12$	3.26500	+	1.15748i	0.942525	+	0.334135i
$13$	0.0758711	−	0.0582180i	0.0210429	−	0.0161468i	−0.598186	−	0.801357i	$-0.704112\pi$
$13$	0.0758711	−	0.0582180i	0.0210429	−	0.0161468i	0.619229	+	0.785210i	$0.287445\pi$
$14$	−1.30893	−	1.19013i	−0.349827	−	0.318076i
$15$	−3.55400	−	6.81650i	−0.917639	−	1.76001i
$16$	−1.30975	+	3.77949i	−0.327438	+	0.944873i
$17$			2.57648i			0.624888i	0.949936	+	0.312444i	$0.101148\pi$
$17$			2.57648i			0.624888i	−0.949936	+	0.312444i	$0.898852\pi$
$18$	−3.11320	+	2.88236i	−0.733788	+	0.679379i
$19$	3.07003	+	1.27165i	0.704312	+	0.291736i	0.705949	−	0.708263i	$-0.250521\pi$
$19$	3.07003	+	1.27165i	0.704312	+	0.291736i	−0.00163643	+	0.999999i	$0.500521\pi$
$20$	7.84169	−	4.15956i	1.75346	−	0.930106i
$21$	2.03555	−	0.742359i	0.444194	−	0.161996i
$22$	5.31940	−	2.50558i	1.13410	−	0.534191i
$23$	0.507432	−	0.135966i	0.105807	−	0.0283509i	−0.205527	−	0.978651i	$-0.565891\pi$
$23$	0.507432	−	0.135966i	0.105807	−	0.0283509i	0.311334	+	0.950301i	$0.399224\pi$
$24$	−3.35369	−	3.57110i	−0.684569	−	0.728948i
$25$	−14.1977	−	3.80426i	−2.83954	−	0.760851i
$26$	−0.133100	+	0.0240004i	−0.0261030	+	0.00470686i
$27$	−1.35451	−	5.01650i	−0.260676	−	0.965426i
$28$	0.873860	+	2.34431i	0.165144	+	0.443033i
$29$	5.45887	−	0.718674i	1.01369	−	0.133454i	0.394662	−	0.918826i	$-0.370862\pi$
$29$	5.45887	−	0.718674i	1.01369	−	0.133454i	0.619024	+	0.785372i	$0.287528\pi$
$30$	0.0490279	+	10.8715i	0.00895123	+	1.98485i
$31$	−1.95771	+	3.39085i	−0.351615	+	0.609014i	−0.986533	−	0.163565i	$-0.947701\pi$
$31$	−1.95771	+	3.39085i	−0.351615	+	0.609014i	0.634918	+	0.772580i	$0.281034\pi$
$32$	4.09597	−	3.90167i	0.724072	−	0.689725i
$33$	−0.309512	+	7.19480i	−0.0538791	+	1.25245i
$34$	1.66995	−	3.23848i	0.286395	−	0.555395i
$35$	2.12468	−	5.12943i	0.359137	−	0.867033i
$36$	5.78131	−	1.60512i	0.963552	−	0.267521i
$37$	−0.306228	+	0.126844i	−0.0503435	+	0.0208530i	−0.407713	−	0.913110i	$-0.633674\pi$
$37$	−0.306228	+	0.126844i	−0.0503435	+	0.0208530i	0.357370	+	0.933963i	$0.383674\pi$
$38$	−3.03462	−	3.58823i	−0.492280	−	0.582088i
$39$	0.0497082	−	0.158007i	0.00795969	−	0.0253014i
$40$	−12.5526	+	0.145697i	−1.98474	+	0.0230367i
$41$	−7.79353	+	2.08827i	−1.21715	+	0.326133i	−0.809562	−	0.587035i	$-0.800295\pi$
$41$	−7.79353	+	2.08827i	−1.21715	+	0.326133i	−0.407584	+	0.913168i	$0.633629\pi$
$42$	−3.03973	−	0.386250i	−0.469040	−	0.0595997i
$43$	5.68592	−	7.41004i	0.867095	−	1.13002i	−0.123384	−	0.992359i	$-0.539375\pi$
$43$	5.68592	−	7.41004i	0.867095	−	1.13002i	0.990479	−	0.137661i	$-0.0439586\pi$
$44$	−8.31017	−	0.298427i	−1.25280	−	0.0449895i
$45$	−11.8183	−	6.13299i	−1.76177	−	0.914253i
$46$	−0.725938	−	0.157993i	−0.107034	−	0.0232947i
$47$	5.21248	−	3.00942i	0.760318	−	0.438970i	−0.0690921	−	0.997610i	$-0.522010\pi$
$47$	5.21248	−	3.00942i	0.760318	−	0.438970i	0.829410	+	0.558641i	$0.188677\pi$
$48$	1.90076	+	6.66236i	0.274352	+	0.961629i
$49$	−4.70697	−	2.71757i	−0.672425	−	0.388224i
$50$	15.3799	+	13.9840i	2.17504	+	1.97764i
$51$	2.56198	+	3.65390i	0.358749	+	0.511648i
$52$	0.182854	+	0.0561019i	0.0253573	+	0.00777993i
$53$	0.848306	+	2.04799i	0.116524	+	0.281313i	0.971371	−	0.237566i	$-0.0763495\pi$
$53$	0.848306	+	2.04799i	0.116524	+	0.281313i	−0.854848	+	0.518879i	$0.826350\pi$
$54$	−1.54892	+	7.18337i	−0.210782	+	0.977533i
$55$	13.0485	+	13.0485i	1.75946	+	1.75946i
$56$	0.421083	−	3.51305i	0.0562696	−	0.469452i
$57$	5.61833	−	1.24933i	0.744166	−	0.165478i
$58$	−7.32728	−	2.63485i	−0.962119	−	0.345973i
$59$	−1.21081	+	9.19702i	−0.157634	+	1.19735i	0.711468	+	0.702718i	$0.248030\pi$
$59$	−1.21081	+	9.19702i	−0.157634	+	1.19735i	−0.869103	+	0.494632i	$0.835303\pi$
$60$	6.98475	−	13.6966i	0.901727	−	1.76822i
$61$	13.4688	−	1.77320i	1.72450	−	0.227035i	0.797822	−	0.602893i	$-0.205986\pi$
$61$	13.4688	−	1.77320i	1.72450	−	0.227035i	0.926677	+	0.375859i	$0.122652\pi$
$62$	4.65851	−	2.99320i	0.591631	−	0.380137i
$63$	2.14859	−	3.07689i	0.270697	−	0.387652i
$64$	−7.67727	+	2.24935i	−0.959658	+	0.281169i
$65$	−0.212225	−	0.367585i	−0.0263233	−	0.0455933i
$66$	5.05237	−	8.84282i	0.621904	−	1.08848i
$67$	7.53531	+	9.82021i	0.920585	+	1.19973i	0.979495	+	0.201467i	$0.0645708\pi$
$67$	7.53531	+	9.82021i	0.920585	+	1.19973i	−0.0589102	+	0.998263i	$0.518763\pi$
$68$	−4.19806	+	2.98819i	−0.509090	+	0.362371i
$69$	0.584427	−	0.697400i	0.0703567	−	0.0839571i
$70$	−5.99526	+	5.07027i	−0.716570	+	0.606013i
$71$	1.60783	−	1.60783i	0.190815	−	0.190815i	−0.605233	−	0.796048i	$-0.706920\pi$
$71$	1.60783	−	1.60783i	0.190815	−	0.190815i	0.796048	+	0.605233i	$0.206920\pi$
$72$	−8.30713	−	1.72963i	−0.979004	−	0.203839i
$73$	7.47247	+	7.47247i	0.874587	+	0.874587i	0.992968	−	0.118381i	$-0.0377706\pi$
$73$	7.47247	+	7.47247i	0.874587	+	0.874587i	−0.118381	+	0.992968i	$0.537771\pi$
$74$	0.467124	+	0.0390476i	0.0543020	+	0.00453919i
$75$	−23.9177	+	8.72268i	−2.76177	+	1.00721i
$76$	1.48861	+	6.47708i	0.170755	+	0.742973i
$77$	−4.12633	+	3.16624i	−0.470239	+	0.360827i
$78$	−0.164893	+	0.166387i	−0.0186705	+	0.0188397i
$79$	−1.18365	+	0.683378i	−0.133171	+	0.0768861i	−0.565105	−	0.825019i	$-0.691164\pi$
$79$	−1.18365	+	0.683378i	−0.133171	+	0.0768861i	0.431935	+	0.901905i	$0.357831\pi$
$80$	15.8723	+	7.95285i	1.77457	+	0.889156i
$81$	−6.90921	−	5.76739i	−0.767690	−	0.640822i
$82$	11.1495	+	2.42657i	1.23126	+	0.267970i
$83$	1.60457	+	12.1879i	0.176124	+	1.33779i	0.819868	+	0.572553i	$0.194047\pi$
$83$	1.60457	+	12.1879i	0.176124	+	1.33779i	−0.643744	+	0.765241i	$0.722620\pi$
$84$	3.57041	+	2.45570i	0.389563	+	0.267939i
$85$	11.3374	+	1.49259i	1.22971	+	0.161894i
$86$	−11.9497	+	5.62862i	−1.28857	+	0.606950i
$87$	7.02701	−	6.44736i	0.753374	−	0.691229i
$88$	10.2520	+	5.76137i	1.09286	+	0.614164i
$89$	−1.96743	+	1.96743i	−0.208547	+	0.208547i	−0.803650	−	0.595103i	$-0.797111\pi$
$89$	−1.96743	+	1.96743i	−0.208547	+	0.208547i	0.595103	+	0.803650i	$0.297111\pi$
$90$	10.8798	+	15.3689i	1.14683	+	1.62002i
$91$	0.110526	−	0.0457812i	0.0115862	−	0.00479917i
$92$	0.810057	+	0.669106i	0.0844543	+	0.0697592i
$93$	0.595394	+	6.75551i	0.0617395	+	0.700514i
$94$	−8.50233	+	0.404182i	−0.876949	+	0.0416882i
$95$	7.37418	−	12.7724i	0.756575	−	1.31043i
$96$	1.92909	−	9.60618i	0.196886	−	0.980426i
$97$	−5.86403	−	10.1568i	−0.595402	−	1.03127i	−0.993490	−	0.113919i	$-0.963660\pi$
$97$	−5.86403	−	10.1568i	−0.595402	−	1.03127i	0.398088	−	0.917347i	$-0.369674\pi$
$98$	4.15498	+	6.46666i	0.419716	+	0.653232i
$99$	6.71537	+	10.5113i	0.674920	+	1.05642i
$100$	−10.2678	−	27.5456i	−1.02678	−	2.75456i
$101$	−7.48861	−	5.74621i	−0.745144	−	0.571769i	0.164885	−	0.986313i	$-0.447275\pi$
$101$	−7.48861	−	5.74621i	−0.745144	−	0.571769i	−0.910030	+	0.414543i	$0.863941\pi$
$102$	−0.851968	−	6.25329i	−0.0843574	−	0.619168i
$103$	1.44480	+	5.39206i	0.142360	+	0.531296i	0.999859	+	0.0168091i	$0.00535074\pi$
$103$	1.44480	+	5.39206i	0.142360	+	0.531296i	−0.857499	+	0.514486i	$0.827983\pi$
$104$	−0.193474	−	0.189034i	−0.0189717	−	0.0185363i
$105$	−2.08740	−	9.38717i	−0.203709	−	0.916094i
$106$	0.261143	−	3.12403i	0.0253644	−	0.303433i
$107$	−2.57893	−	6.22609i	−0.249315	−	0.601899i	0.748831	−	0.662760i	$-0.230615\pi$
$107$	−2.57893	−	6.22609i	−0.249315	−	0.601899i	−0.998146	+	0.0608614i	$0.980615\pi$
$108$	6.60283	−	8.02513i	0.635357	−	0.772218i
$109$	−1.85281	−	0.767459i	−0.177467	−	0.0735093i	0.292181	−	0.956363i	$-0.405619\pi$
$109$	−1.85281	−	0.767459i	−0.177467	−	0.0735093i	−0.469648	+	0.882854i	$0.655619\pi$
$110$	−7.94377	−	24.8587i	−0.757408	−	2.37018i
$111$	−0.308155	+	0.484391i	−0.0292487	+	0.0459763i
$112$	−2.80627	+	4.14277i	−0.265168	+	0.391455i
$113$	0.627382	+	0.362219i	0.0590191	+	0.0340747i	0.529219	−	0.848485i	$-0.322485\pi$
$113$	0.627382	+	0.362219i	0.0590191	+	0.0340747i	−0.470200	+	0.882560i	$0.655818\pi$
$114$	−7.87166	−	2.07120i	−0.737248	−	0.193986i
$115$	−0.304333	−	2.31164i	−0.0283792	−	0.215561i
$116$	7.50216	+	8.06105i	0.696558	+	0.748450i
$117$	−0.0866233	−	0.273511i	−0.00800832	−	0.0252861i
$118$	7.48299	−	10.7753i	0.688865	−	0.991948i
$119$	−0.834181	+	3.11321i	−0.0764692	+	0.285387i
$120$	−17.6569	+	12.6886i	−1.61184	+	1.15830i
$121$	−1.62719	−	6.07276i	−0.147926	−	0.552069i
$122$	−18.0787	−	6.50102i	−1.63677	−	0.588575i
$123$	−8.97608	+	10.7112i	−0.809346	+	0.965798i
$124$	−7.79552	+	0.742842i	−0.700058	+	0.0667092i
$125$	−16.4726	+	39.7684i	−1.47335	+	3.55699i
$126$	−4.69495	+	2.47485i	−0.418259	+	0.220477i
$127$	−1.41741			−0.125775			−0.0628875	−	0.998021i	$-0.520031\pi$
$127$	−1.41741			−0.125775			−0.0628875	+	0.998021i	$0.520031\pi$
$128$	11.1078	+	2.14874i	0.981799	+	0.189924i
$129$	0.695298	−	16.1627i	0.0612176	−	1.42304i
$130$	0.0285030	+	0.599586i	0.00249988	+	0.0525872i
$131$	−11.3164	−	14.7478i	−0.988715	−	1.28852i	−0.957326	−	0.289011i	$-0.906674\pi$
$131$	−11.3164	−	14.7478i	−0.988715	−	1.28852i	−0.0313888	−	0.999507i	$-0.509993\pi$
$132$	−12.0820	+	7.84018i	−1.05161	+	0.682400i
$133$	3.29785	+	2.53053i	0.285960	+	0.219425i
$134$	−3.10643	−	17.2275i	−0.268355	−	1.48823i
$135$	−22.8590	+	3.05417i	−1.96739	+	0.262861i
$136$	7.21351	−	1.03499i	0.618554	−	0.0887492i
$137$	−0.952444	+	3.55457i	−0.0813728	+	0.303687i	−0.994603	−	0.103757i	$-0.966913\pi$
$137$	−0.952444	+	3.55457i	−0.0813728	+	0.303687i	0.913230	+	0.407445i	$0.133580\pi$
$138$	−1.18661	+	0.497792i	−0.101011	+	0.0423749i
$139$	3.82054	+	0.502983i	0.324054	+	0.0426625i	0.290798	−	0.956784i	$-0.406079\pi$
$139$	3.82054	+	0.502983i	0.324054	+	0.0426625i	0.0332554	+	0.999447i	$0.489413\pi$
$140$	10.8220	−	2.48718i	0.914625	−	0.210205i
$141$	4.39972	−	9.45104i	0.370523	−	0.795921i
$142$	−3.06307	+	0.978828i	−0.257047	+	0.0821414i
$143$			0.397621i			0.0332507i
$144$	9.32049	+	7.55834i	0.776708	+	0.629861i
$145$		−	24.4372i		−	2.02940i
$146$	−4.54914	−	14.2358i	−0.376490	−	1.17816i
$147$	−9.37759	+	0.826490i	−0.773451	+	0.0681677i
$148$	−0.561837	−	0.351848i	−0.0461827	−	0.0289217i
$149$	1.75281	+	0.230762i	0.143596	+	0.0189047i	0.201981	−	0.979389i	$-0.435262\pi$
$149$	1.75281	+	0.230762i	0.143596	+	0.0189047i	−0.0583857	+	0.998294i	$0.518595\pi$
$150$	35.7167	+	4.53842i	2.91626	+	0.370561i
$151$	2.38241	−	8.89127i	0.193878	−	0.723561i	−0.798677	−	0.601760i	$-0.794466\pi$
$151$	2.38241	−	8.89127i	0.193878	−	0.723561i	0.992555	−	0.121801i	$-0.0388670\pi$
$152$	2.32705	−	9.10615i	0.188749	−	0.738606i
$153$	7.26668	+	2.63431i	0.587476	+	0.212971i
$154$	7.23875	−	1.30528i	0.583315	−	0.105183i
$155$	13.7867	+	10.5789i	1.10738	+	0.849720i
$156$	0.315105	−	0.102263i	0.0252286	−	0.00818757i
$157$	−3.27719	−	4.27092i	−0.261548	−	0.340856i	0.644057	−	0.764977i	$-0.277250\pi$
$157$	−3.27719	−	4.27092i	−0.261548	−	0.340856i	−0.905606	+	0.424121i	$0.860583\pi$
$158$	1.93071	−	0.0917815i	0.153599	−	0.00730174i
$159$	3.23951	+	2.06088i	0.256910	+	0.163438i
$160$	−14.7958	−	20.2839i	−1.16971	−	1.60358i
$161$	0.657161			0.0517915
$162$	4.94630	+	11.7275i	0.388618	+	0.921399i
$163$	−4.49655	+	10.8556i	−0.352197	+	0.850279i	0.644151	+	0.764898i	$0.277211\pi$
$163$	−4.49655	+	10.8556i	−0.352197	+	0.850279i	−0.996348	+	0.0853808i	$0.972789\pi$
$164$	−12.4415	−	10.2767i	−0.971517	−	0.802472i
$165$	31.4802	+	5.53001i	2.45073	+	0.430510i
$166$	5.88278	−	16.3594i	0.456592	−	1.26974i
$167$	1.61893	+	6.04195i	0.125277	+	0.467540i	0.999849	−	0.0173550i	$-0.00552455\pi$
$167$	1.61893	+	6.04195i	0.125277	+	0.467540i	−0.874572	+	0.484895i	$0.838858\pi$
$168$	−2.89611	−	5.40084i	−0.223440	−	0.416684i
$169$	−3.36228	+	12.5482i	−0.258637	+	0.965246i
$170$	−13.2830	−	9.22444i	−1.01876	−	0.707483i
$171$	6.72548	−	7.35848i	0.514310	−	0.562717i
$172$	18.6683	+	0.670397i	1.42344	+	0.0511173i
$173$	0.755257	+	5.73675i	0.0574212	+	0.436157i	0.995874	+	0.0907490i	$0.0289261\pi$
$173$	0.755257	+	5.73675i	0.0574212	+	0.436157i	−0.938453	+	0.345408i	$0.887741\pi$
$174$	−13.0114	+	3.54936i	−0.986392	+	0.269076i
$175$	−15.9236	−	9.19350i	−1.20371	−	0.694963i
$176$	−9.15184	−	13.8865i	−0.689846	−	1.04674i
$177$	7.42812	+	14.2470i	0.558332	+	1.07087i
$178$	3.74814	−	1.19774i	0.280935	−	0.0897748i
$179$	11.1115	+	4.60252i	0.830510	+	0.344009i	0.757105	−	0.653294i	$-0.226613\pi$
$179$	11.1115	+	4.60252i	0.830510	+	0.344009i	0.0734055	+	0.997302i	$0.476613\pi$
$180$	−3.71388	−	26.3696i	−0.276816	−	1.96547i
$181$	−6.51362	−	15.7253i	−0.484153	−	1.16885i	−0.957619	−	0.288037i	$-0.906997\pi$
$181$	−6.51362	−	15.7253i	−0.484153	−	1.16885i	0.473466	−	0.880812i	$-0.343003\pi$
$182$	−0.168597	−	0.0140933i	−0.0124972	−	0.00104466i
$183$	17.3379	−	15.9077i	1.28165	−	1.17593i
$184$	−0.584510	−	1.36607i	−0.0430906	−	0.100708i
$185$	0.380752	+	1.42098i	0.0279934	+	0.104473i
$186$	3.63023	−	8.87718i	0.266181	−	0.650906i
$187$	−8.49871	−	6.52129i	−0.621487	−	0.476884i
$188$	10.9489	+	5.00278i	0.798530	+	0.364865i
$189$	−0.0124987	−	6.50008i	−0.000909146	−	0.472811i
$190$	−17.5474	+	11.2746i	−1.27302	+	0.817946i
$191$	0.532783	+	0.922808i	0.0385509	+	0.0667720i	0.884657	−	0.466242i	$-0.154393\pi$
$191$	0.532783	+	0.922808i	0.0385509	+	0.0667720i	−0.846106	+	0.533014i	$0.821059\pi$
$192$	−8.65102	+	10.8240i	−0.624333	+	0.781158i
$193$	−7.00284	+	12.1293i	−0.504076	+	0.873084i	0.495913	+	0.868372i	$0.334833\pi$
$193$	−7.00284	+	12.1293i	−0.504076	+	0.873084i	−0.999989	+	0.00471241i	$0.998500\pi$
$194$	0.787571	+	16.5673i	0.0565443	+	1.18946i
$195$	−0.666488	−	0.310269i	−0.0477282	−	0.0222188i
$196$	−1.03117	−	10.8213i	−0.0736549	−	0.772948i
$197$	6.33207	−	2.62283i	0.451141	−	0.186869i	−0.145531	−	0.989354i	$-0.546489\pi$
$197$	6.33207	−	2.62283i	0.451141	−	0.186869i	0.596673	+	0.802485i	$0.296489\pi$
$198$	−1.62791	−	17.5646i	−0.115690	−	1.24826i
$199$	−6.36707	+	6.36707i	−0.451350	+	0.451350i	−0.895802	−	0.444453i	$-0.853398\pi$
$199$	−6.36707	+	6.36707i	−0.451350	+	0.451350i	0.444453	+	0.895802i	$0.353398\pi$
$200$	−4.94771	+	41.2782i	−0.349856	+	2.91881i
$201$	20.4514	+	6.43388i	1.44253	+	0.453811i
$202$	5.68830	+	12.0764i	0.400228	+	0.849693i
$203$	6.82873	+	0.899019i	0.479283	+	0.0630988i
$204$	−2.98222	+	8.41221i	−0.208797	+	0.588973i
$205$	4.67418	+	35.5039i	0.326459	+	2.47970i
$206$	1.67886	−	7.71395i	0.116971	−	0.537456i
$207$	0.135344	−	1.57017i	0.00940709	−	0.109135i
$208$	0.120662	+	0.363005i	0.00836640	+	0.0251699i
$209$	−11.9651	+	6.90806i	−0.827644	+	0.477841i
$210$	−3.46059	+	13.1521i	−0.238803	+	0.907578i
$211$	2.90515	−	2.22920i	0.199999	−	0.153464i	−0.503907	−	0.863758i	$-0.668104\pi$
$211$	2.90515	−	2.22920i	0.199999	−	0.153464i	0.703906	+	0.710294i	$0.251438\pi$
$212$	−2.35309	+	3.75746i	−0.161611	+	0.258064i
$213$	0.681405	−	3.87898i	0.0466891	−	0.265783i
$214$	−0.793900	+	9.49737i	−0.0542699	+	0.649227i
$215$	−29.3127	−	29.3127i	−1.99911	−	1.99911i
$216$	−13.5009	+	5.80746i	−0.918618	+	0.395147i
$217$	−3.46338	+	3.46338i	−0.235110	+	0.235110i
$218$	1.83144	+	2.16556i	0.124041	+	0.146670i
$219$	18.0277	+	3.16686i	1.21820	+	0.213996i
$220$	−6.12738	+	36.3946i	−0.413108	+	2.45372i
$221$	0.149997	+	0.195480i	0.0100899	+	0.0131494i
$222$	0.701291	−	0.409119i	0.0470676	−	0.0274582i
$223$	−7.22965	−	12.5221i	−0.484133	−	0.838543i	0.515701	−	0.856769i	$-0.327532\pi$
$223$	−7.22965	−	12.5221i	−0.484133	−	0.838543i	−0.999834	+	0.0182256i	$0.994198\pi$
$224$	6.21247	−	3.38832i	0.415088	−	0.226392i
$225$	−25.2459	+	36.1534i	−1.68306	+	2.41022i
$226$	−0.553808	−	0.861927i	−0.0368387	−	0.0573345i
$227$	−1.47144	+	0.193718i	−0.0976626	+	0.0128575i	−0.179199	−	0.983813i	$-0.557351\pi$
$227$	−1.47144	+	0.193718i	−0.0976626	+	0.0128575i	0.0815365	+	0.996670i	$0.474017\pi$
$228$	8.55174	+	7.70542i	0.566353	+	0.510304i
$229$	2.11700	−	16.0802i	0.139895	−	1.06261i	−0.767117	−	0.641507i	$-0.778310\pi$
$229$	2.11700	−	16.0802i	0.139895	−	1.06261i	0.907013	−	0.421104i	$-0.138357\pi$
$230$	−1.11577	+	3.10284i	−0.0735715	+	0.204595i
$231$	−2.70343	+	8.59339i	−0.177873	+	0.565404i
$232$	−4.20497	−	14.9948i	−0.276070	−	0.984457i
$233$	13.0471	+	13.0471i	0.854741	+	0.854741i	0.990713	−	0.135972i	$-0.0434157\pi$
$233$	13.0471	+	13.0471i	0.854741	+	0.854741i	−0.135972	+	0.990713i	$0.543416\pi$
$234$	−0.0683967	+	0.399932i	−0.00447123	+	0.0261444i
$235$	−10.2228	−	24.6800i	−0.666862	−	1.60995i
$236$	−16.3897	+	8.69379i	−1.06688	+	0.565917i
$237$	−0.999085	+	2.14614i	−0.0648976	+	0.139407i
$238$	3.06635	−	3.37243i	0.198762	−	0.218602i
$239$	−17.5726	−	10.1456i	−1.13668	−	0.656262i	−0.191073	−	0.981576i	$-0.561197\pi$
$239$	−17.5726	−	10.1456i	−1.13668	−	0.656262i	−0.945606	+	0.325314i	$0.894530\pi$
$240$	30.4177	−	4.50439i	1.96346	−	0.290757i
$241$	−6.95525	+	4.01561i	−0.448027	+	0.258668i	−0.706997	−	0.707217i	$-0.749950\pi$
$241$	−6.95525	+	4.01561i	−0.448027	+	0.258668i	0.258970	+	0.965885i	$0.416617\pi$
$242$	−1.89080	+	8.68776i	−0.121545	+	0.558470i
$243$	−15.5334	−	1.30885i	−0.996469	−	0.0839627i
$244$	18.5102	+	19.8892i	1.18500	+	1.27327i
$245$	−14.6850	+	19.1379i	−0.938192	+	1.22268i
$246$	18.2249	−	7.64547i	1.16198	−	0.487458i
$247$	0.306959	−	0.0822494i	0.0195313	−	0.00523340i
$248$	10.2800	+	4.11898i	0.652779	+	0.261556i
$249$	14.3949	+	15.6890i	0.912237	+	0.994252i
$250$	46.4810	−	39.3097i	2.93972	−	2.48616i
$251$	−6.63225	+	2.74717i	−0.418624	+	0.173400i	−0.582045	−	0.813157i	$-0.697747\pi$
$251$	−6.63225	+	2.74717i	−0.418624	+	0.173400i	0.163421	+	0.986556i	$0.447747\pi$
$252$	7.50535	−	0.0676963i	0.472793	−	0.00426447i
$253$	−0.835860	+	2.01794i	−0.0525500	+	0.126867i
$254$	1.78160	+	0.918700i	0.111788	+	0.0576444i
$255$	17.5626	−	9.15680i	1.09981	−	0.573421i
$256$	−12.5691	−	9.90039i	−0.785569	−	0.618774i
$257$	12.6692	−	21.9436i	0.790280	−	1.36881i	−0.135513	−	0.990776i	$-0.543268\pi$
$257$	12.6692	−	21.9436i	0.790280	−	1.36881i	0.925793	−	0.378030i	$-0.123398\pi$
$258$	−11.3498	+	19.8648i	−0.706610	+	1.23673i
$259$	−0.411088	+	0.0541208i	−0.0255438	+	0.00336290i
$260$	0.352797	−	0.772118i	0.0218795	−	0.0478847i
$261$	3.55446	−	16.1309i	0.220015	−	0.998481i
$262$	4.66517	+	25.8718i	0.288215	+	1.59836i
$263$	−18.5773	−	4.97778i	−1.14553	−	0.306943i	−0.364356	−	0.931260i	$-0.618711\pi$
$263$	−18.5773	−	4.97778i	−1.14553	−	0.306943i	−0.781171	+	0.624317i	$0.785378\pi$
$264$	20.2680	−	2.02363i	1.24741	−	0.124546i
$265$	9.50328	−	2.54640i	0.583782	−	0.156424i
$266$	−2.50503	−	5.31823i	−0.153593	−	0.326082i
$267$	−0.833803	+	4.74652i	−0.0510279	+	0.290482i
$268$	−7.26143	+	23.6673i	−0.443562	+	1.44571i
$269$	−19.0648	−	7.89688i	−1.16240	−	0.481482i	−0.283726	−	0.958905i	$-0.591571\pi$
$269$	−19.0648	−	7.89688i	−1.16240	−	0.481482i	−0.878673	+	0.477424i	$0.841571\pi$
$270$	30.7119	+	10.9772i	1.86907	+	0.668051i
$271$			16.3373i			0.992423i	0.868202	+	0.496211i	$0.165276\pi$
$271$			16.3373i			0.992423i	−0.868202	+	0.496211i	$0.834724\pi$
$272$	−9.73778	−	3.37455i	−0.590440	−	0.204612i
$273$	0.111221	−	0.174829i	0.00673141	−	0.0105811i
$274$	3.50107	−	3.85055i	0.211507	−	0.232620i
$275$	48.4842	−	37.2032i	2.92370	−	2.24344i
$276$	1.81414	+	0.143412i	0.109199	+	0.00863237i
$277$	13.4579	−	17.5387i	0.808607	−	1.05380i	−0.188814	−	0.982013i	$-0.560464\pi$
$277$	13.4579	−	17.5387i	0.808607	−	1.05380i	0.997420	−	0.0717836i	$-0.0228691\pi$
$278$	−4.47617	−	3.10851i	−0.268463	−	0.186436i
$279$	7.56187	+	8.98846i	0.452717	+	0.538125i
$280$	−15.2147	−	3.88807i	−0.909250	−	0.232357i
$281$	12.5174	+	3.35403i	0.746726	+	0.200085i	0.612065	−	0.790807i	$-0.290339\pi$
$281$	12.5174	+	3.35403i	0.746726	+	0.200085i	0.134660	+	0.990892i	$0.457006\pi$
$282$	−11.6559	+	9.02769i	−0.694099	+	0.537591i
$283$	−1.30333	+	9.89976i	−0.0774748	+	0.588480i	0.908039	+	0.418885i	$0.137579\pi$
$283$	−1.30333	+	9.89976i	−0.0774748	+	0.588480i	−0.985514	+	0.169594i	$0.945754\pi$
$284$	4.48453	+	0.755013i	0.266108	+	0.0448018i
$285$	−2.24269	−	25.4463i	−0.132846	−	1.50731i
$286$	0.257719	−	0.499786i	0.0152393	−	0.0295529i
$287$	−10.0932			−0.595782
$288$	−6.81634	−	15.5415i	−0.401657	−	0.915790i
$289$	10.3618			0.609515
$290$	−15.8390	+	30.7160i	−0.930100	+	1.80371i
$291$	−18.4159	−	8.57309i	−1.07956	−	0.502563i
$292$	−3.50895	+	20.8420i	−0.205346	+	1.21969i
$293$	−1.82530	+	13.8646i	−0.106635	+	0.809976i	0.851640	+	0.524128i	$0.175609\pi$
$293$	−1.82530	+	13.8646i	−0.106635	+	0.809976i	−0.958275	+	0.285848i	$0.907725\pi$
$294$	12.3228	+	5.03927i	0.718678	+	0.293896i
$295$	39.7685	+	10.6559i	2.31541	+	0.620413i
$296$	0.478144	+	0.806409i	0.0277916	+	0.0468715i
$297$	19.9757	+	8.22924i	1.15911	+	0.477509i
$298$	−2.05361	−	1.42614i	−0.118962	−	0.0826142i
$299$	0.0305838	−	0.0398575i	0.00176871	−	0.00230502i
$300$	−41.9521	−	28.8544i	−2.42211	−	1.66591i
$301$	9.26953	−	7.11276i	0.534287	−	0.409973i
$302$	−8.75745	+	9.63162i	−0.503934	+	0.554238i
$303$	−16.3340	−	0.702671i	−0.938366	−	0.0403674i
$304$	−8.82715	+	9.93759i	−0.506272	+	0.569960i
$305$		−	60.2943i		−	3.45244i
$306$	−7.42634	−	8.02109i	−0.424536	−	0.458535i
$307$	11.3201	+	4.68895i	0.646074	+	0.267613i	0.681565	−	0.731757i	$-0.261300\pi$
$307$	11.3201	+	4.68895i	0.646074	+	0.267613i	−0.0354914	+	0.999370i	$0.511300\pi$
$308$	−9.94470	−	3.05116i	−0.566652	−	0.173856i
$309$	7.41070	+	6.21022i	0.421580	+	0.353287i
$310$	−10.4723	−	22.2330i	−0.594788	−	1.26275i
$311$	−24.3012	+	6.51148i	−1.37799	+	0.369232i	−0.870392	−	0.492360i	$-0.836134\pi$
$311$	−24.3012	+	6.51148i	−1.37799	+	0.369232i	−0.507601	+	0.861592i	$0.669468\pi$
$312$	−0.462350	−	0.0756985i	−0.0261754	−	0.00428558i
$313$	−4.43079	−	1.18723i	−0.250443	−	0.0671061i	0.131413	−	0.991328i	$-0.458048\pi$
$313$	−4.43079	−	1.18723i	−0.250443	−	0.0671061i	−0.381857	+	0.924222i	$0.624715\pi$
$314$	1.35102	+	7.49241i	0.0762426	+	0.422821i
$315$	−12.2946	−	11.2370i	−0.692724	−	0.633133i
$316$	−2.48627	−	1.13603i	−0.139864	−	0.0639066i
$317$	25.0234	−	3.29439i	1.40545	−	0.185031i	0.610650	−	0.791900i	$-0.290908\pi$
$317$	25.0234	−	3.29439i	1.40545	−	0.185031i	0.794802	+	0.606869i	$0.207575\pi$
$318$	−2.73611	−	4.69010i	−0.153433	−	0.263008i
$319$	−11.4463	+	19.8255i	−0.640868	+	1.11002i
$320$	5.45035	+	35.0856i	0.304684	+	1.96134i
$321$	−9.84844	−	6.26528i	−0.549686	−	0.349694i
$322$	−0.826011	−	0.425941i	−0.0460318	−	0.0237367i
$323$	−3.27637	+	7.90986i	−0.182302	+	0.440116i
$324$	1.38400	−	17.9467i	0.0768891	−	0.997040i
$325$	−1.29867	+	0.537927i	−0.0720372	+	0.0298388i
$326$	12.6880	−	10.7304i	0.702724	−	0.594303i
$327$	−3.39075	+	0.753992i	−0.187509	+	0.0416959i
$328$	8.97735	+	20.9811i	0.495691	+	1.15849i
$329$	7.27268	−	1.94871i	0.400956	−	0.107436i
$330$	−35.9844	−	27.3549i	−1.98088	−	1.50584i
$331$	−5.64742	+	7.35986i	−0.310410	+	0.404535i	−0.922341	−	0.386377i	$-0.873726\pi$
$331$	−5.64742	+	7.35986i	−0.310410	+	0.404535i	0.611931	+	0.790911i	$0.290393\pi$
$332$	−17.9977	+	16.7499i	−0.987753	+	0.919270i
$333$	0.0446475	+	0.993372i	0.00244667	+	0.0544364i
$334$	1.88120	−	8.64368i	0.102935	−	0.472961i
$335$	47.5775	−	27.4689i	2.59944	−	1.50079i
$336$	0.139669	+	8.66566i	0.00761957	+	0.472750i
$337$	−9.87204	−	5.69962i	−0.537764	−	0.310478i	0.206408	−	0.978466i	$-0.433823\pi$
$337$	−9.87204	−	5.69962i	−0.537764	−	0.310478i	−0.744172	+	0.667988i	$0.767156\pi$
$338$	12.3593	−	13.5931i	0.672260	−	0.739365i
$339$	1.24992	−	0.110161i	0.0678863	−	0.00598312i
$340$	10.7170	+	20.2040i	0.581212	+	1.09571i
$341$	−6.22984	−	15.0402i	−0.337365	−	0.814471i
$342$	−13.2229	+	4.89003i	−0.715015	+	0.264423i
$343$	−10.9995	−	10.9995i	−0.593917	−	0.593917i
$344$	−23.0304	−	12.9425i	−1.24171	−	0.697815i
$345$	−2.73023	−	2.97569i	−0.146990	−	0.160206i
$346$	2.76898	−	7.70027i	0.148861	−	0.413969i
$347$	−2.40927	+	18.3003i	−0.129337	+	0.982409i	0.796541	+	0.604585i	$0.206661\pi$
$347$	−2.40927	+	18.3003i	−0.129337	+	0.982409i	−0.925877	+	0.377824i	$0.876672\pi$
$348$	18.6551	+	3.97205i	1.00002	+	0.212924i
$349$	−21.0323	+	2.76896i	−1.12583	+	0.148219i	−0.670364	−	0.742033i	$-0.733862\pi$
$349$	−21.0323	+	2.76896i	−1.12583	+	0.148219i	−0.455470	+	0.890251i	$0.650529\pi$
$350$	14.0562	+	21.8766i	0.751337	+	1.16935i
$351$	−0.394819	−	0.301751i	−0.0210739	−	0.0161063i
$352$	2.50271	+	23.3863i	0.133395	+	1.24649i
$353$	1.81403	+	3.14198i	0.0965508	+	0.167231i	0.910255	−	0.414049i	$-0.135886\pi$
$353$	1.81403	+	3.14198i	0.0965508	+	0.167231i	−0.813704	+	0.581280i	$0.802552\pi$
$354$	−0.102472	−	22.7222i	−0.00544632	−	1.20767i
$355$	−6.14356	−	8.00645i	−0.326066	−	0.424938i
$356$	−5.48750	−	0.923873i	−0.290837	−	0.0489652i
$357$	1.91267	+	5.24456i	0.101229	+	0.277572i
$358$	−10.9833	−	12.9870i	−0.580486	−	0.686386i
$359$	1.72433	−	1.72433i	0.0910068	−	0.0910068i	−0.660138	−	0.751145i	$-0.729502\pi$
$359$	1.72433	−	1.72433i	0.0910068	−	0.0910068i	0.751145	+	0.660138i	$0.229502\pi$
$360$	−12.4234	+	35.5521i	−0.654771	+	1.87376i
$361$	−5.62705	−	5.62705i	−0.296161	−	0.296161i
$362$	−2.00516	+	23.9875i	−0.105389	+	1.26076i
$363$	−8.34623	−	6.99421i	−0.438063	−	0.367101i
$364$	0.202782	+	0.126991i	0.0106287	+	0.00665615i
$365$	37.2103	−	28.5524i	1.94767	−	1.49450i
$366$	−32.1033	+	8.75740i	−1.67806	+	0.457757i
$367$	0.658261	−	0.380047i	0.0343610	−	0.0198383i	−0.482721	−	0.875774i	$-0.660352\pi$
$367$	0.658261	−	0.380047i	0.0343610	−	0.0198383i	0.517082	+	0.855936i	$0.327018\pi$
$368$	−0.150728	+	2.09592i	−0.00785722	+	0.109257i
$369$	−2.07873	+	24.1160i	−0.108214	+	1.25543i
$370$	0.442434	−	2.03288i	0.0230010	−	0.105684i
$371$	0.361949	+	2.74928i	0.0187915	+	0.142735i
$372$	−10.3168	+	8.80513i	−0.534899	+	0.456525i
$373$	−13.7418	−	1.80914i	−0.711523	−	0.0936737i	−0.233928	−	0.972254i	$-0.575158\pi$
$373$	−13.7418	−	1.80914i	−0.711523	−	0.0936737i	−0.477595	+	0.878580i	$0.658491\pi$
$374$	6.45557	+	13.7053i	0.333810	+	0.708686i
$375$	16.1835	+	72.7784i	0.835714	+	3.75826i
$376$	−10.5195	−	13.3848i	−0.542503	−	0.690266i
$377$	0.372331	−	0.372331i	0.0191760	−	0.0191760i
$378$	−4.19733	+	8.17830i	−0.215888	+	0.420647i
$379$	−17.3658	+	7.19316i	−0.892023	+	0.369488i	−0.781148	−	0.624346i	$-0.785365\pi$
$379$	−17.3658	+	7.19316i	−0.892023	+	0.369488i	−0.110875	+	0.993834i	$0.535365\pi$
$380$	29.3637	−	2.79809i	1.50633	−	0.143539i
$381$	−2.01014	+	1.40944i	−0.102983	+	0.0722076i
$382$	−0.0715557	−	1.50524i	−0.00366111	−	0.0770147i
$383$	−8.70697	+	15.0809i	−0.444905	+	0.770599i	−0.998046	−	0.0624894i	$-0.980096\pi$
$383$	−8.70697	+	15.0809i	−0.444905	+	0.770599i	0.553140	+	0.833088i	$0.313429\pi$
$384$	17.8894	−	7.99798i	0.912917	−	0.408145i
$385$	11.5421	+	19.9915i	0.588238	+	1.01886i
$386$	16.6638	−	10.7069i	0.848164	−	0.544965i
$387$	−15.0857	−	23.6129i	−0.766847	−	1.20031i
$388$	9.74819	−	21.3345i	0.494890	−	1.08310i
$389$	12.8383	+	9.85116i	0.650927	+	0.499474i	0.880641	−	0.473784i	$-0.157112\pi$
$389$	12.8383	+	9.85116i	0.650927	+	0.499474i	−0.229714	+	0.973258i	$0.573779\pi$
$390$	0.636634	+	0.821976i	0.0322372	+	0.0416224i
$391$	0.350314	+	1.30739i	0.0177161	+	0.0661175i
$392$	−5.71772	+	14.2700i	−0.288789	+	0.720746i
$393$	−30.7134	−	9.66225i	−1.54928	−	0.487396i
$394$	−9.65903	−	0.807413i	−0.486615	−	0.0406769i
$395$	2.32139	+	5.60433i	0.116802	+	0.281984i
$396$	−9.33838	+	23.1328i	−0.469271	+	1.16247i
$397$	−30.8435	−	12.7758i	−1.54799	−	0.641198i	−0.565038	−	0.825065i	$-0.691138\pi$
$397$	−30.8435	−	12.7758i	−1.54799	−	0.641198i	−0.982951	+	0.183867i	$0.941138\pi$
$398$	12.1299	−	3.87619i	0.608015	−	0.194296i
$399$	7.19322	+	0.309444i	0.360111	+	0.0154916i
$400$	32.9736	−	48.6774i	1.64868	−	2.43387i
$401$	−9.16260	−	5.29003i	−0.457558	−	0.264171i	0.253459	−	0.967346i	$-0.418432\pi$
$401$	−9.16260	−	5.29003i	−0.457558	−	0.264171i	−0.711017	+	0.703175i	$0.751765\pi$
$402$	−21.5360	−	21.3426i	−1.07412	−	1.06447i
$403$	0.0488748	+	0.371241i	0.00243463	+	0.0184928i
$404$	0.677506	−	18.8662i	0.0337072	−	0.938629i
$405$	−29.3810	+	27.0617i	−1.45996	+	1.34471i
$406$	−8.00060	−	5.55608i	−0.397063	−	0.275743i
$407$	0.356685	−	1.33117i	0.0176802	−	0.0659835i
$408$	9.20087	−	8.64071i	0.455511	−	0.427779i
$409$	−6.94590	−	25.9225i	−0.343453	−	1.28178i	−0.894409	−	0.447249i	$-0.852404\pi$
$409$	−6.94590	−	25.9225i	−0.343453	−	1.28178i	0.550957	−	0.834534i	$-0.314263\pi$
$410$	17.1368	−	47.6558i	0.846326	−	2.35355i
$411$	2.18383	+	5.98809i	0.107721	+	0.295371i
$412$	−7.11004	+	8.60781i	−0.350287	+	0.424076i
$413$	−4.44074	+	10.7209i	−0.218515	+	0.527541i
$414$	−1.18783	+	1.88589i	−0.0583788	+	0.0926865i
$415$	54.5603			2.67826
$416$	0.0836182	−	0.534483i	0.00409972	−	0.0262052i
$417$	5.91834	−	3.08572i	0.289823	−	0.151108i
$418$	19.5169	−	0.927791i	0.954603	−	0.0453797i
$419$	11.0022	+	14.3384i	0.537495	+	0.700477i	0.980606	−	0.195990i	$-0.0627920\pi$
$419$	11.0022	+	14.3384i	0.537495	+	0.700477i	−0.443111	+	0.896467i	$0.646125\pi$
$420$	12.8743	−	14.2884i	0.628201	−	0.697200i
$421$	−6.25865	−	4.80243i	−0.305028	−	0.234056i	0.444893	−	0.895584i	$-0.353242\pi$
$421$	−6.25865	−	4.80243i	−0.305028	−	0.234056i	−0.749921	+	0.661528i	$0.769908\pi$
$422$	−5.09646	+	0.918988i	−0.248092	+	0.0447356i
$423$	−3.15828	−	17.7782i	−0.153561	−	0.864405i
$424$	5.39311	−	3.19774i	0.261912	−	0.155296i
$425$	9.80159	−	36.5800i	0.475447	−	1.77439i
$426$	−3.37066	+	4.43399i	−0.163309	+	0.214827i
$427$	16.8487	+	2.21817i	0.815363	+	0.107345i
$428$	7.15363	−	11.4230i	0.345784	−	0.552154i
$429$	0.395384	+	0.563897i	0.0190893	+	0.0272252i
$430$	17.8452	+	55.8434i	0.860571	+	2.69301i
$431$			38.9561i			1.87645i	0.346025	+	0.938225i	$0.387531\pi$
$431$			38.9561i			1.87645i	−0.346025	+	0.938225i	$0.612469\pi$
$432$	20.7339	+	1.45101i	0.997560	+	0.0698116i
$433$			5.62134i			0.270145i	0.990836	+	0.135072i	$0.0431267\pi$
$433$			5.62134i			0.270145i	−0.990836	+	0.135072i	$0.956873\pi$
$434$	6.59806	−	2.10846i	0.316717	−	0.101209i
$435$	−24.2997	−	34.6562i	−1.16508	−	1.66164i
$436$	−0.898398	−	3.90903i	−0.0430255	−	0.187208i
$437$	1.73073	+	0.227855i	0.0827921	+	0.0108998i
$438$	−20.6071	−	15.6653i	−0.984647	−	0.748515i
$439$	−2.79058	+	10.4146i	−0.133187	+	0.497062i	−0.999999	−	0.00157424i	$-0.999499\pi$
$439$	−2.79058	+	10.4146i	−0.133187	+	0.497062i	0.866811	+	0.498636i	$0.166166\pi$
$440$	31.2910	−	41.7743i	1.49174	−	1.99151i
$441$	−12.4772	+	10.4969i	−0.594154	+	0.499854i
$442$	−0.0618364	−	0.342928i	−0.00294126	−	0.0163114i
$443$	−31.4895	−	24.1627i	−1.49611	−	1.14801i	−0.950814	−	0.309762i	$-0.899751\pi$
$443$	−31.4895	−	24.1627i	−1.49611	−	1.14801i	−0.545296	−	0.838243i	$-0.683583\pi$
$444$	−1.14665	+	0.0596933i	−0.0544177	+	0.00283292i
$445$	7.51758	+	9.79710i	0.356368	+	0.464427i
$446$	0.970982	+	20.4255i	0.0459773	+	0.967174i
$447$	2.71525	−	1.41568i	0.128427	−	0.0669596i
$448$	−10.0048	+	0.232282i	−0.472684	+	0.0109743i
$449$	23.0258			1.08665			0.543327	−	0.839521i	$-0.317164\pi$
$449$	23.0258			1.08665			0.543327	+	0.839521i	$0.317164\pi$
$450$	55.1654	−	29.0794i	2.60052	−	1.37082i
$451$	12.8378	−	30.9931i	0.604507	−	1.45941i
$452$	0.137442	+	1.44234i	0.00646473	+	0.0678421i
$453$	−5.46256	−	14.9784i	−0.256653	−	0.703746i
$454$	1.97507	+	0.710224i	0.0926944	+	0.0333325i
$455$	−0.137423	−	0.512871i	−0.00644250	−	0.0240437i
$456$	−5.75474	−	15.2281i	−0.269490	−	0.713120i
$457$	2.05335	−	7.66319i	0.0960515	−	0.358469i	−0.901125	−	0.433559i	$-0.857258\pi$
$457$	2.05335	−	7.66319i	0.0960515	−	0.358469i	0.997177	+	0.0750898i	$0.0239243\pi$
$458$	−13.0834	+	18.8397i	−0.611346	+	0.880322i
$459$	12.9249	−	3.48987i	0.603283	−	0.162893i
$460$	3.41357	−	3.17690i	0.159158	−	0.148124i
$461$	−0.324022	−	2.46119i	−0.0150912	−	0.114629i	0.982241	−	0.187622i	$-0.0600781\pi$
$461$	−0.324022	−	2.46119i	−0.0150912	−	0.114629i	−0.997332	+	0.0729934i	$0.976745\pi$
$462$	8.96789	−	9.04914i	0.417224	−	0.421004i
$463$	−18.1636	−	10.4867i	−0.844133	−	0.487360i	0.0145342	−	0.999894i	$-0.495373\pi$
$463$	−18.1636	−	10.4867i	−0.844133	−	0.487360i	−0.858667	+	0.512534i	$0.828707\pi$
$464$	−4.43354	+	21.5730i	−0.205822	+	1.00150i
$465$	30.0714	+	1.29364i	1.39453	+	0.0599909i
$466$	−7.94287	−	24.8558i	−0.367946	−	1.15142i
$467$	−2.29510	−	0.950660i	−0.106204	−	0.0439913i	0.328949	−	0.944348i	$-0.393306\pi$
$467$	−2.29510	−	0.950660i	−0.106204	−	0.0439913i	−0.435153	+	0.900357i	$0.643306\pi$
$468$	0.345188	−	0.458359i	0.0159563	−	0.0211876i
$469$	5.92559	+	14.3056i	0.273618	+	0.660573i
$470$	−3.14699	+	37.6472i	−0.145160	+	1.73654i
$471$	−8.89452	−	2.79817i	−0.409838	−	0.128933i
$472$	26.2358	−	0.304517i	1.20760	−	0.0140165i
$473$	10.0510	+	37.5109i	0.462146	+	1.72475i
$474$	2.64681	−	2.05000i	0.121572	−	0.0941598i
$475$	−38.7496	−	29.7336i	−1.77795	−	1.36427i
$476$	−6.04007	+	2.25148i	−0.276846	+	0.103197i
$477$	6.64348	−	0.298594i	0.304184	−	0.0136717i
$478$	15.5119	+	24.1421i	0.709496	+	1.10424i
$479$	−9.96920	−	17.2672i	−0.455504	−	0.788957i	0.543213	−	0.839595i	$-0.317208\pi$
$479$	−9.96920	−	17.2672i	−0.455504	−	0.788957i	−0.998717	+	0.0506384i	$0.983874\pi$
$480$	−41.1528	−	14.0536i	−1.87836	−	0.641457i
$481$	−0.0158492	+	0.0274517i	−0.000722664	+	0.00125169i
$482$	11.3451	−	0.539319i	0.516753	−	0.0245653i
$483$	0.931969	−	0.653462i	0.0424061	−	0.0297336i
$484$	8.00762	−	9.69446i	0.363983	−	0.440657i
$485$	−48.0904	+	19.9197i	−2.18367	+	0.904506i
$486$	18.6762	+	11.7132i	0.847171	+	0.531320i
$487$	−21.1033	+	21.1033i	−0.956283	+	0.956283i	−0.999084	−	0.0428006i	$-0.986372\pi$
$487$	−21.1033	+	21.1033i	−0.956283	+	0.956283i	0.0428006	+	0.999084i	$0.486372\pi$
$488$	−10.3750	−	36.9970i	−0.469654	−	1.67477i
$489$	4.41765	+	19.8664i	0.199773	+	0.898392i
$490$	30.8625	−	14.5370i	1.39423	−	0.656717i
$491$	−12.9939	−	1.71067i	−0.586404	−	0.0772016i	−0.168514	−	0.985699i	$-0.553897\pi$
$491$	−12.9939	−	1.71067i	−0.586404	−	0.0772016i	−0.417890	+	0.908498i	$0.637230\pi$
$492$	−27.8630	−	2.20263i	−1.25616	−	0.0993021i
$493$	1.85165	+	14.0647i	0.0833940	+	0.633440i
$494$	−0.439139	−	0.0955739i	−0.0197578	−	0.00430007i
$495$	50.1433	−	23.4605i	2.25378	−	1.05447i
$496$	−10.2516	−	11.8403i	−0.460309	−	0.531645i
$497$	2.46334	−	1.42221i	0.110496	−	0.0637948i
$498$	−7.92457	−	29.0502i	−0.355109	−	1.30177i
$499$	−17.0445	+	13.0787i	−0.763015	+	0.585482i	−0.915261	−	0.402860i	$-0.868016\pi$
$499$	−17.0445	+	13.0787i	−0.763015	+	0.585482i	0.152246	+	0.988343i	$0.451349\pi$
$500$	−83.9026	+	19.2830i	−3.75224	+	0.862364i
$501$	8.30388	+	6.95872i	0.370990	+	0.310893i
$502$	10.1169	+	0.845690i	0.451541	+	0.0377450i
$503$	29.1393	+	29.1393i	1.29926	+	1.29926i	0.928882	+	0.370377i	$0.120771\pi$
$503$	29.1393	+	29.1393i	1.29926	+	1.29926i	0.370377	+	0.928882i	$0.379229\pi$
$504$	−9.47765	−	4.77953i	−0.422168	−	0.212897i
$505$	−29.6235	+	29.6235i	−1.31823	+	1.31823i
$506$	2.35856	−	1.99467i	0.104851	−	0.0886738i
$507$	7.70928	+	21.1389i	0.342381	+	0.938812i
$508$	−1.64391	−	2.30950i	−0.0729366	−	0.102468i
$509$	−11.9320	−	15.5500i	−0.528875	−	0.689243i	0.450157	−	0.892949i	$-0.351368\pi$
$509$	−11.9320	−	15.5500i	−0.528875	−	0.689243i	−0.979032	+	0.203706i	$0.934701\pi$
$510$	−28.0101	+	0.126319i	−1.24031	+	0.00559351i
$511$	6.60977	+	11.4485i	0.292399	+	0.506450i
$512$	9.38164	+	20.5909i	0.414614	+	0.909998i
$513$	2.22083	−	17.1233i	0.0980521	−	0.756010i
$514$	−30.1472	+	19.3703i	−1.32974	+	0.854385i
$515$	24.5638	−	3.23389i	1.08241	−	0.142502i
$516$	27.1415	−	17.6125i	1.19484	−	0.775346i
$517$	−3.26641	+	24.8108i	−0.143657	+	1.09118i
$518$	0.551791	+	0.198421i	0.0242443	+	0.00871814i
$519$	6.77555	+	7.38471i	0.297414	+	0.324153i
$520$	−0.943895	+	0.741839i	−0.0413925	+	0.0325318i
$521$	−2.53175	−	2.53175i	−0.110918	−	0.110918i	0.649469	−	0.760388i	$-0.274991\pi$
$521$	−2.53175	−	2.53175i	−0.110918	−	0.110918i	−0.760388	+	0.649469i	$0.774991\pi$
$522$	−14.9231	+	17.9718i	−0.653165	+	0.786604i
$523$	10.0621	+	24.2921i	0.439986	+	1.06222i	0.975953	+	0.217982i	$0.0699473\pi$
$523$	10.0621	+	24.2921i	0.439986	+	1.06222i	−0.535967	+	0.844239i	$0.680053\pi$
$524$	10.9050	−	35.5430i	0.476389	−	1.55270i
$525$	−31.7243	+	2.79600i	−1.38456	+	0.122028i
$526$	20.1242	+	18.2977i	0.877458	+	0.797819i
$527$	−8.73645	−	5.04399i	−0.380566	−	0.219720i
$528$	−26.7873	−	10.5932i	−1.16577	−	0.461010i
$529$	−19.6796	+	11.3620i	−0.855634	+	0.494001i
$530$	−13.5955	−	2.95891i	−0.590551	−	0.128527i
$531$	24.7012	+	12.8184i	1.07194	+	0.556272i
$532$	−0.298361	+	8.30834i	−0.0129356	+	0.360212i
$533$	−0.469729	+	0.612163i	−0.0203462	+	0.0265157i
$534$	4.12451	−	5.42566i	0.178485	−	0.234791i
$535$	−28.8909	+	7.74129i	−1.24906	+	0.334685i
$536$	24.4672	−	25.0419i	1.05682	−	1.08164i
$537$	20.3346	−	4.52176i	0.877504	−	0.195128i
$538$	18.8449	+	22.2828i	0.812460	+	0.960680i
$539$	20.8779	−	8.64789i	0.899273	−	0.372491i
$540$	−31.4881	−	33.7037i	−1.35503	−	1.45038i
$541$	4.84101	−	11.6872i	0.208131	−	0.502473i	−0.784998	−	0.619499i	$-0.787336\pi$
$541$	4.84101	−	11.6872i	0.208131	−	0.502473i	0.993129	+	0.117025i	$0.0373359\pi$
$542$	10.5891	−	20.5351i	0.454841	−	0.882056i
$543$	−24.8742	−	15.8242i	−1.06746	−	0.679083i
$544$	10.0526	+	10.5532i	0.431001	+	0.452464i
$545$	−4.45044	+	7.70838i	−0.190636	+	0.330191i
$546$	−0.253114	+	0.147662i	−0.0108323	+	0.00631933i
$547$	35.4828	−	4.67140i	1.51714	−	0.199735i	0.674523	−	0.738254i	$-0.264349\pi$
$547$	35.4828	−	4.67140i	1.51714	−	0.199735i	0.842613	+	0.538519i	$0.181016\pi$
$548$	−6.89638	+	2.57068i	−0.294599	+	0.109814i
$549$	8.76998	−	39.8002i	0.374293	−	1.69863i
$550$	−85.0550	+	15.3370i	−3.62676	+	0.653973i
$551$	17.6728	+	4.73540i	0.752885	+	0.201735i
$552$	−2.18732	−	1.35610i	−0.0930984	−	0.0577196i
$553$	−1.65148	+	0.442512i	−0.0702279	+	0.0188175i
$554$	−28.2835	+	13.3223i	−1.20165	+	0.566009i
$555$	1.95296	+	1.63660i	0.0828986	+	0.0694697i
$556$	3.61149	+	6.80846i	0.153161	+	0.288743i
$557$	8.33216	+	3.45129i	0.353045	+	0.146236i	0.552156	−	0.833741i	$-0.313805\pi$
$557$	8.33216	+	3.45129i	0.353045	+	0.146236i	−0.199111	+	0.979977i	$0.563805\pi$
$558$	−3.67891	−	16.1992i	−0.155741	−	0.685767i
$559$		−	0.893231i		−	0.0377796i
$560$	16.6038	+	14.7485i	0.701641	+	0.623238i
$561$	−18.5373	−	0.797450i	−0.782643	−	0.0336684i
$562$	−13.5597	−	12.3290i	−0.571981	−	0.520068i
$563$	13.4358	−	10.3096i	0.566249	−	0.434499i	−0.285552	−	0.958363i	$-0.592177\pi$
$563$	13.4358	−	10.3096i	0.566249	−	0.434499i	0.851801	+	0.523865i	$0.175510\pi$
$564$	20.5021	−	3.79246i	0.863294	−	0.159691i
$565$	1.95734	−	2.55085i	0.0823457	−	0.107315i
$566$	8.05477	−	11.5986i	0.338567	−	0.487527i
$567$	−6.48122	−	9.20582i	−0.272186	−	0.386608i
$568$	−5.14742	−	3.85567i	−0.215981	−	0.161780i
$569$	−8.29489	−	2.22261i	−0.347740	−	0.0931766i	0.0807216	−	0.996737i	$-0.474278\pi$
$569$	−8.29489	−	2.22261i	−0.347740	−	0.0931766i	−0.428461	+	0.903560i	$0.640944\pi$
$570$	−13.6741	+	33.4380i	−0.572747	+	1.40056i
$571$	5.23465	−	39.7611i	0.219063	−	1.66395i	−0.429707	−	0.902968i	$-0.641383\pi$
$571$	5.23465	−	39.7611i	0.219063	−	1.66395i	0.648771	−	0.760984i	$-0.275283\pi$
$572$	−0.647875	+	0.461159i	−0.0270890	+	0.0192820i
$573$	1.67320	+	0.778919i	0.0698988	+	0.0325398i
$574$	12.6865	+	6.54193i	0.529525	+	0.273055i
$575$	−7.72161			−0.322013
$576$	−1.50553	+	23.9527i	−0.0627306	+	0.998030i
$577$	−25.1637			−1.04758			−0.523790	−	0.851847i	$-0.675482\pi$
$577$	−25.1637			−1.04758			−0.523790	+	0.851847i	$0.675482\pi$
$578$	−13.0241	−	6.71600i	−0.541731	−	0.279349i
$579$	2.12976	+	24.1649i	0.0885098	+	1.00426i
$580$	39.8174	−	28.3421i	1.65333	−	1.17684i
$581$	−2.00722	+	15.2463i	−0.0832735	+	0.632525i
$582$	17.5909	+	22.7122i	0.729168	+	0.941449i
$583$	−8.90259	−	2.38544i	−0.368707	−	0.0987949i
$584$	17.9194	−	23.9228i	0.741509	−	0.989934i
$585$	−1.25372	+	0.222722i	−0.0518350	+	0.00920843i
$586$	11.2807	−	16.2438i	0.465999	−	0.671027i
$587$	−7.66645	+	9.99111i	−0.316428	+	0.412377i	−0.924305	−	0.381654i	$-0.875355\pi$
$587$	−7.66645	+	9.99111i	−0.316428	+	0.412377i	0.607877	+	0.794031i	$0.292021\pi$
$588$	−12.2227	−	14.3211i	−0.504058	−	0.590592i
$589$	−10.3222	+	7.92048i	−0.425318	+	0.326358i
$590$	−43.0799	−	39.1699i	−1.77357	−	1.61260i
$591$	6.37192	−	10.0161i	0.262106	−	0.412006i
$592$	−0.0783223	−	1.32352i	−0.00321903	−	0.0543962i
$593$		−	2.54265i		−	0.104414i	−0.998636	−	0.0522070i	$-0.983374\pi$
$593$		−	2.54265i		−	0.104414i	0.998636	−	0.0522070i	$-0.0166255\pi$
$594$	−19.7744	−	23.2910i	−0.811355	−	0.955640i
$595$	13.2159	+	5.47420i	0.541798	+	0.224420i
$596$	1.65690	+	3.12363i	0.0678693	+	0.127949i
$597$	−2.69839	+	15.3609i	−0.110438	+	0.628679i
$598$	−0.0642757	+	0.0302756i	−0.00262843	+	0.00123806i
$599$	6.10924	−	1.63697i	0.249617	−	0.0668846i	−0.131841	−	0.991271i	$-0.542089\pi$
$599$	6.10924	−	1.63697i	0.249617	−	0.0668846i	0.381458	+	0.924386i	$0.375422\pi$
$600$	34.0292	+	63.4597i	1.38924	+	2.59073i
$601$	−3.35871	−	0.899964i	−0.137005	−	0.0367103i	0.189665	−	0.981849i	$-0.439260\pi$
$601$	−3.35871	−	0.899964i	−0.137005	−	0.0367103i	−0.326670	+	0.945139i	$0.605926\pi$
$602$	−16.2614	+	2.93224i	−0.662765	+	0.119509i
$603$	35.4013	−	11.2119i	1.44165	−	0.456584i
$604$	17.2503	−	6.43020i	0.701907	−	0.261641i
$605$	−27.6648	+	3.64214i	−1.12473	+	0.148074i
$606$	20.0755	+	11.4702i	0.815510	+	0.465944i
$607$	−14.8432	+	25.7092i	−0.602468	+	1.04351i	0.389978	+	0.920824i	$0.372483\pi$
$607$	−14.8432	+	25.7092i	−0.602468	+	1.04351i	−0.992446	+	0.122681i	$0.960851\pi$
$608$	17.5363	−	6.76961i	0.711190	−	0.274544i
$609$	10.5783	−	5.51534i	0.428654	−	0.223493i
$610$	−39.0799	+	75.7863i	−1.58230	+	3.06850i
$611$	0.220274	−	0.531788i	0.00891132	−	0.0215138i
$612$	4.13557	+	14.8954i	0.167170	+	0.602112i
$613$	33.6841	−	13.9524i	1.36049	−	0.563533i	0.421297	−	0.906923i	$-0.361575\pi$
$613$	33.6841	−	13.9524i	1.36049	−	0.563533i	0.939193	+	0.343390i	$0.111575\pi$
$614$	−11.1896	−	13.2309i	−0.451574	−	0.533956i
$615$	41.9329	+	45.7029i	1.69090	+	1.84292i
$616$	10.5223	+	10.2808i	0.423954	+	0.414226i
$617$	14.8886	−	3.98938i	0.599391	−	0.160606i	0.0536496	−	0.998560i	$-0.482915\pi$
$617$	14.8886	−	3.98938i	0.599391	−	0.160606i	0.545742	+	0.837953i	$0.316248\pi$
$618$	−5.28962	−	12.6091i	−0.212780	−	0.507214i
$619$	19.8516	−	25.8711i	0.797904	−	1.03985i	−0.200288	−	0.979737i	$-0.564188\pi$
$619$	19.8516	−	25.8711i	0.797904	−	1.03985i	0.998192	−	0.0601114i	$-0.0191456\pi$
$620$	−1.24731	+	34.7332i	−0.0500930	+	1.39492i
$621$	−1.36940	−	2.36137i	−0.0549520	−	0.0947584i
$622$	34.7655	+	7.56634i	1.39397	+	0.303383i
$623$	−3.01427	+	1.74029i	−0.120764	+	0.0697232i
$624$	0.532082	+	0.394822i	0.0213003	+	0.0158055i
$625$	101.805	+	58.7770i	4.07219	+	2.35108i
$626$	4.79973	+	4.36411i	0.191836	+	0.174425i
$627$	−10.0995	+	21.6946i	−0.403333	+	0.866400i
$628$	3.15808	−	10.2932i	0.126021	−	0.410743i
$629$	−0.326810	−	0.788989i	−0.0130308	−	0.0314590i
$630$	8.17032	+	22.0930i	0.325513	+	0.880208i
$631$	−12.7370	−	12.7370i	−0.507050	−	0.507050i	0.406569	−	0.913620i	$-0.366725\pi$
$631$	−12.7370	−	12.7370i	−0.507050	−	0.507050i	−0.913620	+	0.406569i	$0.866725\pi$
$632$	2.38877	+	3.03940i	0.0950201	+	0.120901i
$633$	1.90336	−	6.05020i	0.0756517	−	0.240474i
$634$	−33.5881	−	12.0781i	−1.33396	−	0.479684i
$635$	−0.821128	+	6.23708i	−0.0325855	+	0.247511i
$636$	0.399217	+	7.66859i	0.0158300	+	0.304080i
$637$	−0.515335	+	0.0678451i	−0.0204183	+	0.00268812i
$638$	27.2372	−	17.5005i	1.07833	−	0.692853i
$639$	−2.89080	−	6.17864i	−0.114358	−	0.244423i
$640$	15.8901	−	47.6331i	0.628111	−	1.88287i
$641$	9.54719	+	16.5362i	0.377091	+	0.653141i	0.990638	−	0.136518i	$-0.0435910\pi$
$641$	9.54719	+	16.5362i	0.377091	+	0.653141i	−0.613546	+	0.789659i	$0.710258\pi$
$642$	8.31803	+	14.2584i	0.328287	+	0.562733i
$643$	−15.0345	−	19.5933i	−0.592902	−	0.772685i	0.396477	−	0.918045i	$-0.370233\pi$
$643$	−15.0345	−	19.5933i	−0.592902	−	0.772685i	−0.989379	+	0.145360i	$0.953566\pi$
$644$	0.762171	+	1.07076i	0.0300338	+	0.0421940i
$645$	−70.7183	−	12.4228i	−2.78453	−	0.489148i
$646$	9.24500	−	7.81862i	0.363740	−	0.307620i
$647$	23.5792	−	23.5792i	0.926995	−	0.926995i	−0.0705153	−	0.997511i	$-0.522464\pi$
$647$	23.5792	−	23.5792i	0.926995	−	0.926995i	0.997511	+	0.0705153i	$0.0224643\pi$
$648$	−13.3718	+	21.6609i	−0.525295	+	0.850920i
$649$	−27.2724	−	27.2724i	−1.07053	−	1.07053i
$650$	1.98101	+	0.165596i	0.0777016	+	0.00649519i
$651$	−1.46779	+	8.35557i	−0.0575273	+	0.327481i
$652$	−22.9030	+	5.26372i	−0.896951	+	0.206143i
$653$	30.1532	−	23.1373i	1.17998	−	0.905434i	0.183006	−	0.983112i	$-0.441417\pi$
$653$	30.1532	−	23.1373i	1.17998	−	0.905434i	0.996979	+	0.0776774i	$0.0247504\pi$
$654$	4.75067	+	1.25000i	0.185766	+	0.0488790i
$655$	−71.4508	+	41.2521i	−2.79181	+	1.61185i
$656$	2.31499	−	32.1907i	0.0903852	−	1.25684i
$657$	28.7155	−	13.4351i	1.12030	−	0.524153i
$658$	−10.4044	−	2.26440i	−0.405605	−	0.0882756i
$659$	4.62977	+	35.1666i	0.180350	+	1.36990i	0.806980	+	0.590579i	$0.201101\pi$
$659$	4.62977	+	35.1666i	0.180350	+	1.36990i	−0.626630	+	0.779317i	$0.715566\pi$
$660$	27.5001	+	57.7068i	1.07044	+	2.24624i
$661$	44.7054	+	5.88558i	1.73884	+	0.228923i	0.932155	−	0.362060i	$-0.117926\pi$
$661$	44.7054	+	5.88558i	1.73884	+	0.228923i	0.806685	+	0.590982i	$0.201260\pi$
$662$	11.8688	−	5.59051i	0.461293	−	0.217281i
$663$	0.407103	+	0.128072i	0.0158106	+	0.00497391i
$664$	33.4785	−	9.38833i	1.29922	−	0.364338i
$665$	13.0457	−	13.0457i	0.505889	−	0.505889i
$666$	0.587738	−	1.27755i	0.0227744	−	0.0495039i
$667$	2.67229	−	1.10690i	0.103471	−	0.0428593i
$668$	−7.96699	+	9.64528i	−0.308252	+	0.373187i
$669$	−22.7046	−	10.5696i	−0.877809	−	0.408644i
$670$	−77.6061	+	3.68922i	−2.99819	+	0.142527i
$671$	−28.2416	+	48.9158i	−1.09025	+	1.88837i
$672$	5.44112	−	10.9827i	0.209896	−	0.423668i
$673$	10.1138	+	17.5177i	0.389859	+	0.675256i	0.992430	−	0.122809i	$-0.0391903\pi$
$673$	10.1138	+	17.5177i	0.389859	+	0.675256i	−0.602571	+	0.798065i	$0.705857\pi$
$674$	8.71433	+	13.5627i	0.335663	+	0.522415i
$675$	0.146859	+	76.3756i	0.00565261	+	2.93970i
$676$	−24.3453	+	9.07491i	−0.936359	+	0.349035i
$677$	−19.6052	−	15.0436i	−0.753488	−	0.578172i	0.158998	−	0.987279i	$-0.449174\pi$
$677$	−19.6052	−	15.0436i	−0.753488	−	0.578172i	−0.912486	+	0.409107i	$0.865840\pi$
$678$	−1.64247	−	0.671673i	−0.0630788	−	0.0257954i
$679$	−3.79716	−	14.1712i	−0.145722	−	0.543841i
$680$	−0.375384	−	32.3414i	−0.0143953	−	1.24024i
$681$	−1.89413	+	1.73788i	−0.0725831	+	0.0665958i
$682$	−1.91780	+	22.9425i	−0.0734362	+	0.878513i
$683$	1.02439	+	2.47310i	0.0391973	+	0.0946307i	0.942266	−	0.334866i	$-0.108691\pi$
$683$	1.02439	+	2.47310i	0.0391973	+	0.0946307i	−0.903068	+	0.429497i	$0.858691\pi$
$684$	19.7899	+	2.42402i	0.756687	+	0.0926845i
$685$	15.0895	+	6.25029i	0.576541	+	0.238811i
$686$	6.69635	+	20.9551i	0.255668	+	0.800069i
$687$	−12.9874	−	24.9097i	−0.495502	−	0.950363i
$688$	20.5590	+	31.1952i	0.783806	+	1.18931i
$689$	0.183592	+	0.105997i	0.00699429	+	0.00403815i
$690$	1.50303	+	5.50986i	0.0572193	+	0.209757i
$691$	−0.691451	−	5.25209i	−0.0263040	−	0.199799i	0.973247	−	0.229761i	$-0.0737946\pi$
$691$	−0.691451	−	5.25209i	−0.0263040	−	0.199799i	−0.999551	+	0.0299624i	$0.990461\pi$
$692$	−8.47139	+	7.88405i	−0.322034	+	0.299707i
$693$	4.71109	+	14.8752i	0.178960	+	0.565061i
$694$	14.8897	−	21.4407i	0.565204	−	0.813879i
$695$	4.42658	−	16.5202i	0.167910	−	0.626648i
$696$	−20.8738	−	17.0840i	−0.791220	−	0.647566i
$697$	−5.38039	−	20.0799i	−0.203797	−	0.760580i
$698$	28.2310	+	10.1517i	1.06856	+	0.384249i
$699$	31.4767	+	5.52938i	1.19056	+	0.209140i
$700$	−3.48843	−	36.6082i	−0.131850	−	1.38366i
$701$	12.4676	−	30.0995i	0.470895	−	1.13684i	−0.492873	−	0.870101i	$-0.664053\pi$
$701$	12.4676	−	30.0995i	0.470895	−	1.13684i	0.963768	−	0.266740i	$-0.0859466\pi$
$702$	0.300683	+	0.635186i	0.0113485	+	0.0239735i
$703$	−1.10143			−0.0415411
$704$	12.0122	−	31.0173i	0.452725	−	1.16901i
$705$	−39.0389	−	24.8353i	−1.47029	−	0.935353i
$706$	−0.243634	−	5.12505i	−0.00916927	−	0.192884i
$707$	−7.18818	−	9.36782i	−0.270339	−	0.352313i
$708$	−14.5986	+	28.6268i	−0.548651	+	1.07586i
$709$	13.4426	+	10.3149i	0.504847	+	0.387383i	0.829549	−	0.558433i	$-0.188597\pi$
$709$	13.4426	+	10.3149i	0.504847	+	0.387383i	−0.324702	+	0.945816i	$0.605264\pi$
$710$	2.53268	+	14.0456i	0.0950499	+	0.527122i
$711$	0.717180	+	4.03706i	0.0268964	+	0.151402i
$712$	6.29865	+	4.71800i	0.236052	+	0.176814i
$713$	−0.532363	+	1.98681i	−0.0199372	+	0.0744065i
$714$	0.995165	−	7.83180i	0.0372431	−	0.293098i
$715$	1.74966	+	0.230348i	0.0654337	+	0.00861452i
$716$	5.38777	+	23.4428i	0.201351	+	0.876098i
$717$	−35.0096	+	3.08555i	−1.30746	+	0.115232i
$718$	−3.28501	+	1.04975i	−0.122596	+	0.0391763i
$719$			33.2500i			1.24002i	0.784596	+	0.620008i	$0.212871\pi$
$719$			33.2500i			1.24002i	−0.784596	+	0.620008i	$0.787129\pi$
$720$	38.6587	−	36.6346i	1.44072	−	1.36529i
$721$			6.98310i			0.260064i
$722$	3.42567	+	10.7201i	0.127490	+	0.398959i
$723$	−5.87075	+	12.6110i	−0.218335	+	0.469006i
$724$	18.0680	−	28.8512i	0.671490	−	1.07225i
$725$	−80.2373	−	10.5634i	−2.97994	−	0.392316i
$726$	5.95739	+	14.2009i	0.221099	+	0.527046i
$727$	5.85311	−	21.8441i	0.217080	−	0.810153i	−0.768344	−	0.640037i	$-0.778919\pi$
$727$	5.85311	−	21.8441i	0.217080	−	0.810153i	0.985424	−	0.170116i	$-0.0544142\pi$
$728$	−0.172575	−	0.291054i	−0.00639605	−	0.0107872i
$729$	−23.3306	+	13.5898i	−0.864096	+	0.503327i
$730$	−65.2774	+	11.7707i	−2.41603	+	0.435655i
$731$	19.0918	+	14.6497i	0.706136	+	0.541837i
$732$	46.0280	+	9.80030i	1.70124	+	0.362230i
$733$	14.0686	+	18.3346i	0.519636	+	0.677203i	0.977285	−	0.211930i	$-0.0679749\pi$
$733$	14.0686	+	18.3346i	0.519636	+	0.677203i	−0.457649	+	0.889133i	$0.651308\pi$
$734$	−1.07372	+	0.0510424i	−0.0396319	+	0.00188401i
$735$	−1.79575	+	41.7433i	−0.0662371	+	1.53973i
$736$	1.54793	−	2.53675i	0.0570575	−	0.0935057i
$737$	−51.4652			−1.89575
$738$	18.2437	−	28.9650i	0.671559	−	1.06622i
$739$	−10.7055	+	25.8453i	−0.393807	+	0.950734i	0.595296	+	0.803507i	$0.297035\pi$
$739$	−10.7055	+	25.8453i	−0.393807	+	0.950734i	−0.989103	+	0.147227i	$0.952965\pi$
$740$	−1.87373	+	2.26844i	−0.0688796	+	0.0833895i
$741$	0.353535	−	0.421876i	0.0129874	−	0.0154980i
$742$	1.32700	−	3.69028i	0.0487159	−	0.135474i
$743$	−12.8588	−	47.9896i	−0.471742	−	1.76057i	−0.633507	−	0.773737i	$-0.718385\pi$
$743$	−12.8588	−	47.9896i	−0.471742	−	1.76057i	0.161765	−	0.986829i	$-0.448281\pi$
$744$	18.6746	−	4.38068i	0.684644	−	0.160604i
$745$	2.03086	−	7.57925i	0.0744048	−	0.277682i
$746$	16.1000	+	11.1808i	0.589463	+	0.409357i
$747$	36.0152	+	7.93595i	1.31773	+	0.290361i
$748$	0.768891	−	21.4110i	0.0281134	−	0.782863i
$749$	−1.10036	−	8.35807i	−0.0402063	−	0.305397i
$750$	26.8298	−	101.968i	0.979687	−	3.72333i
$751$	6.98357	+	4.03197i	0.254834	+	0.147129i	0.621976	−	0.783036i	$-0.286330\pi$
$751$	6.98357	+	4.03197i	0.254834	+	0.147129i	−0.367142	+	0.930165i	$0.619664\pi$
$752$	4.54704	+	23.6421i	0.165814	+	0.862139i
$753$	−6.67399	+	10.4909i	−0.243214	+	0.382310i
$754$	−0.709325	+	0.226670i	−0.0258321	+	0.00825483i
$755$	−37.7444	−	15.6342i	−1.37366	−	0.568988i
$756$	10.5766	−	7.55912i	0.384667	−	0.274923i
$757$	−17.1892	−	41.4984i	−0.624752	−	1.50828i	−0.846064	−	0.533081i	$-0.821034\pi$
$757$	−17.1892	−	41.4984i	−0.624752	−	1.50828i	0.221312	−	0.975203i	$-0.428966\pi$
$758$	26.4901	+	2.21435i	0.962163	+	0.0804287i
$759$	0.821192	+	3.69296i	0.0298074	+	0.134046i
$760$	−38.7220	−	15.5151i	−1.40459	−	0.562793i
$761$	11.4690	+	42.8027i	0.415749	+	1.55160i	0.783330	+	0.621606i	$0.213519\pi$
$761$	11.4690	+	42.8027i	0.415749	+	1.55160i	−0.367581	+	0.929991i	$0.619814\pi$
$762$	3.44015	−	0.468698i	0.124624	−	0.0169791i
$763$	−1.99031	−	1.52722i	−0.0720539	−	0.0552889i
$764$	−0.885684	+	1.93837i	−0.0320429	+	0.0701279i
$765$	15.8015	−	30.4497i	0.571306	−	1.10091i
$766$	20.7189	−	13.3123i	0.748604	−	0.480995i
$767$	0.443566	+	0.768279i	0.0160162	+	0.0277410i
$768$	−27.6699	−	1.54212i	−0.998451	−	0.0556464i
$769$	15.6506	−	27.1076i	0.564374	−	0.977524i	−0.432734	−	0.901522i	$-0.642451\pi$
$769$	15.6506	−	27.1076i	0.564374	−	0.977524i	0.997108	−	0.0760022i	$-0.0242156\pi$
$770$	−1.55016	−	32.6091i	−0.0558640	−	1.17515i
$771$	−3.85305	−	43.7178i	−0.138764	−	1.57446i
$772$	−27.8850	+	2.65719i	−1.00360	+	0.0956344i
$773$	32.9033	−	13.6290i	1.18345	−	0.490200i	0.297832	−	0.954618i	$-0.403737\pi$
$773$	32.9033	−	13.6290i	1.18345	−	0.490200i	0.885616	+	0.464418i	$0.153737\pi$
$774$	3.65699	+	39.4578i	0.131448	+	1.41828i
$775$	40.6946	−	40.6946i	1.46179	−	1.46179i
$776$	−26.0809	+	20.4979i	−0.936251	+	0.735831i
$777$	−0.529179	+	0.485527i	−0.0189842	+	0.0174182i
$778$	−9.75189	−	20.7035i	−0.349622	−	0.742256i
$779$	−26.5819	−	3.49957i	−0.952395	−	0.125385i
$780$	−0.267445	−	1.44581i	−0.00957605	−	0.0517683i
$781$	1.23400	+	9.37313i	0.0441558	+	0.335397i
$782$	0.407065	−	1.87036i	0.0145566	−	0.0668841i
$783$	−10.9993	−	26.4110i	−0.393084	−	0.943851i
$784$	16.4360	−	14.2306i	0.587000	−	0.508236i
$785$	−20.6920	+	11.9465i	−0.738529	+	0.426390i
$786$	32.3422	+	32.0518i	1.15361	+	1.14325i
$787$	−1.16964	+	0.897494i	−0.0416930	+	0.0319922i	−0.629398	−	0.777083i	$-0.716698\pi$
$787$	−1.16964	+	0.897494i	−0.0416930	+	0.0319922i	0.587705	+	0.809076i	$0.300032\pi$
$788$	11.6175	+	7.27540i	0.413856	+	0.259175i
$789$	−31.2957	+	11.4134i	−1.11416	+	0.406329i
$790$	0.714617	−	8.54891i	0.0254249	−	0.304157i
$791$	0.640802	+	0.640802i	0.0227843	+	0.0227843i
$792$	26.7314	−	23.0238i	0.949858	−	0.818116i
$793$	0.918658	−	0.918658i	0.0326225	−	0.0326225i
$794$	30.4877	+	36.0497i	1.08197	+	1.27936i
$795$	10.9453	−	13.0610i	0.388188	−	0.463227i
$796$	−17.7589	−	2.98988i	−0.629446	−	0.105973i
$797$	−21.0559	−	27.4405i	−0.745837	−	0.971994i	−0.999988	−	0.00482944i	$-0.998463\pi$
$797$	−21.0559	−	27.4405i	−0.745837	−	0.971994i	0.254151	−	0.967165i	$-0.418204\pi$
$798$	−8.84087	−	5.05126i	−0.312964	−	0.178813i
$799$	7.75372	+	13.4298i	0.274307	+	0.475113i
$800$	−72.9962	+	39.8126i	−2.58081	+	1.40759i
$801$	3.53733	+	7.56051i	0.124985	+	0.267137i
$802$	8.08808	+	12.5880i	0.285600	+	0.444498i
$803$	−43.5620	+	5.73504i	−1.53727	+	0.202385i
$804$	13.2361	+	40.7850i	0.466803	+	1.43838i
$805$	0.380703	−	2.89172i	0.0134180	−	0.101920i
$806$	0.179188	−	0.498306i	0.00631164	−	0.0175521i
$807$	−34.8896	+	7.75831i	−1.22817	+	0.273105i
$808$	−13.0798	+	23.2746i	−0.460145	+	0.818796i
$809$	−1.44428	−	1.44428i	−0.0507784	−	0.0507784i	0.681262	−	0.732040i	$-0.261432\pi$
$809$	−1.44428	−	1.44428i	−0.0507784	−	0.0507784i	−0.732040	+	0.681262i	$0.761432\pi$
$810$	54.4703	−	14.9715i	1.91389	−	0.526044i
$811$	0.0225622	+	0.0544699i	0.000792266	+	0.00191270i	0.924275	−	0.381727i	$-0.124671\pi$
$811$	0.0225622	+	0.0544699i	0.000792266	+	0.00191270i	−0.923483	+	0.383640i	$0.874671\pi$
$812$	6.45508	+	12.1693i	0.226529	+	0.427058i
$813$	16.2454	+	23.1692i	0.569751	+	0.812580i
$814$	−1.31113	+	1.44201i	−0.0459551	+	0.0505424i
$815$	45.1635	+	26.0751i	1.58201	+	0.913372i
$816$	−17.1654	+	4.89728i	−0.600911	+	0.171439i
$817$	26.8789	−	15.5185i	0.940373	−	0.542925i
$818$	−8.07114	+	37.0850i	−0.282201	+	1.29665i
$819$	−0.0161144	−	0.358534i	−0.000563084	−	0.0125282i
$820$	−52.4282	+	48.7932i	−1.83087	+	1.70393i
$821$	4.29003	−	5.59088i	0.149723	−	0.195123i	−0.712470	−	0.701702i	$-0.752424\pi$
$821$	4.29003	−	5.59088i	0.149723	−	0.195123i	0.862193	+	0.506579i	$0.169090\pi$
$822$	1.13625	−	8.94213i	0.0396313	−	0.311893i
$823$	39.0630	−	10.4669i	1.36165	−	0.364853i	0.497229	−	0.867620i	$-0.334351\pi$
$823$	39.0630	−	10.4669i	1.36165	−	0.364853i	0.864422	+	0.502766i	$0.167684\pi$
$824$	14.5161	−	6.21110i	0.505691	−	0.216374i
$825$	31.7652	−	100.972i	1.10592	−	3.51539i
$826$	12.5305	−	10.5972i	0.435993	−	0.368725i
$827$	2.55963	−	1.06023i	0.0890070	−	0.0368679i	−0.337736	−	0.941241i	$-0.609661\pi$
$827$	2.55963	−	1.06023i	0.0890070	−	0.0368679i	0.426743	+	0.904373i	$0.359661\pi$
$828$	2.71538	−	1.60055i	0.0943660	−	0.0556231i
$829$	−20.2938	+	48.9935i	−0.704832	+	1.70161i	0.00769626	+	0.999970i	$0.497550\pi$
$829$	−20.2938	+	48.9935i	−0.704832	+	1.70161i	−0.712528	+	0.701644i	$0.752450\pi$
$830$	−68.5790	−	35.3634i	−2.38041	−	1.22748i
$831$	1.64569	−	38.2551i	0.0570883	−	1.32705i
$832$	−0.451530	+	0.617616i	−0.0156540	+	0.0214120i
$833$	7.00177	−	12.1274i	0.242597	−	0.420190i
$834$	−9.43902	+	0.0425679i	−0.326846	+	0.00147401i
$835$	27.5244	−	3.62366i	0.952522	−	0.125402i
$836$	−25.1329	−	11.4838i	−0.869241	−	0.397175i
$837$	19.6619	+	5.22790i	0.679616	+	0.180703i
$838$	−4.53567	−	25.1536i	−0.156682	−	0.868918i
$839$	−33.3576	−	8.93815i	−1.15163	−	0.308579i	−0.368014	−	0.929820i	$-0.619962\pi$
$839$	−33.3576	−	8.93815i	−1.15163	−	0.308579i	−0.783620	+	0.621241i	$0.786629\pi$
$840$	−25.4433	+	9.61508i	−0.877876	+	0.331752i
$841$	1.27091	−	0.340538i	0.0438244	−	0.0117427i
$842$	4.75404	+	10.0929i	0.163835	+	0.347825i
$843$	21.0870	−	7.69036i	0.726276	−	0.264870i
$844$	7.00159	+	2.14817i	0.241005	+	0.0739432i
$845$	53.2684	+	22.0645i	1.83249	+	0.759042i
$846$	−7.55322	+	24.3932i	−0.259685	+	0.838654i
$847$		−	7.86465i		−	0.270233i
$848$	−8.85143	+	0.523804i	−0.303960	+	0.0179875i
$849$	7.99570	+	15.3356i	0.274412	+	0.526316i
$850$	−36.0295	+	39.6260i	−1.23580	+	1.35916i
$851$	−0.138143	+	0.106001i	−0.00473549	+	0.00363367i
$852$	7.11062	−	3.38855i	0.243606	−	0.116090i
$853$	21.6322	−	28.1917i	0.740673	−	0.965264i	−0.259327	−	0.965790i	$-0.583501\pi$
$853$	21.6322	−	28.1917i	0.740673	−	0.965264i	1.00000		0.000525544i	$0.000167286\pi$
$854$	−19.7400	−	13.7086i	−0.675490	−	0.469099i
$855$	−28.4836	−	33.8572i	−0.974119	−	1.15789i
$856$	−16.3956	+	9.72143i	−0.560389	+	0.332272i
$857$	19.7596	+	5.29457i	0.674976	+	0.180859i	0.579995	−	0.814620i	$-0.303054\pi$
$857$	19.7596	+	5.29457i	0.674976	+	0.180859i	0.0949805	+	0.995479i	$0.469721\pi$
$858$	−0.131482	−	0.965053i	−0.00448872	−	0.0329464i
$859$	2.98592	−	22.6803i	0.101878	−	0.773843i	−0.861889	−	0.507098i	$-0.830718\pi$
$859$	2.98592	−	22.6803i	0.101878	−	0.773843i	0.963767	−	0.266746i	$-0.0859483\pi$
$860$	13.7648	−	81.7582i	0.469375	−	2.78793i
$861$	−14.3139	+	10.0364i	−0.487817	+	0.342039i
$862$	25.2495	−	48.9655i	0.860003	−	1.66777i
$863$	37.7370			1.28458			0.642290	−	0.766461i	$-0.277984\pi$
$863$	37.7370			1.28458			0.642290	+	0.766461i	$0.277984\pi$
$864$	−25.1208	−	15.2626i	−0.854627	−	0.519243i
$865$	25.6811			0.873185
$866$	3.64349	−	7.06569i	0.123811	−	0.240102i
$867$	14.6948	−	10.3034i	0.499061	−	0.349923i
$868$	−9.65997	−	1.62635i	−0.327881	−	0.0552018i
$869$	0.741734	−	5.63403i	0.0251616	−	0.191121i
$870$	8.08067	+	59.3107i	0.273960	+	2.01082i
$871$	1.14343	+	0.306380i	0.0387435	+	0.0103813i
$872$	−1.40442	+	5.49571i	−0.0475595	+	0.186108i
$873$	−34.6418	+	6.15408i	−1.17245	+	0.208284i
$874$	−2.02774	−	1.40818i	−0.0685893	−	0.0476323i
$875$	−32.7798	+	42.7195i	−1.10816	+	1.44418i
$876$	15.7484	+	33.0469i	0.532090	+	1.11655i
$877$	−10.0193	+	7.68811i	−0.338329	+	0.259609i	−0.763926	−	0.645304i	$-0.776731\pi$
$877$	−10.0193	+	7.68811i	−0.338329	+	0.259609i	0.425597	+	0.904913i	$0.360064\pi$
$878$	10.2579	−	11.2818i	0.346186	−	0.380742i
$879$	11.1979	+	21.4774i	0.377697	+	0.724415i
$880$	−66.4071	+	32.2265i	−2.23858	+	1.08635i
$881$			13.4697i			0.453805i	0.973917	+	0.226903i	$0.0728599\pi$
$881$			13.4697i			0.453805i	−0.973917	+	0.226903i	$0.927140\pi$
$882$	22.4868	−	5.10685i	0.757168	−	0.171957i
$883$	3.92492	+	1.62576i	0.132084	+	0.0547111i	0.447747	−	0.894161i	$-0.352227\pi$
$883$	3.92492	+	1.62576i	0.132084	+	0.0547111i	−0.315662	+	0.948872i	$0.602227\pi$
$884$	−0.144545	+	0.471120i	−0.00486159	+	0.0158455i
$885$	66.9947	−	24.4327i	2.25200	−	0.821297i
$886$	23.9192	+	50.7811i	0.803582	+	1.70602i
$887$	8.48131	−	2.27256i	0.284775	−	0.0763051i	−0.113604	−	0.993526i	$-0.536240\pi$
$887$	8.48131	−	2.27256i	0.284775	−	0.0763051i	0.398379	+	0.917221i	$0.369573\pi$
$888$	1.47996	+	0.668176i	0.0496643	+	0.0224225i
$889$	−1.71268	−	0.458912i	−0.0574416	−	0.0153914i
$890$	−3.09912	−	17.1869i	−0.103883	−	0.576107i
$891$	36.5120	−	8.19278i	1.22320	−	0.274468i
$892$	12.0184	−	26.3029i	0.402405	−	0.880687i
$893$	19.8294	−	2.61058i	0.663564	−	0.0873599i
$894$	−4.33049	+	0.0195296i	−0.144833	+	0.000653166i
$895$	26.6897	−	46.2278i	0.892137	−	1.54523i
$896$	12.7260	+	6.19271i	0.425147	+	0.206884i
$897$	0.00373991	−	0.0869367i	0.000124872	−	0.00290273i
$898$	−28.9420	−	14.9242i	−0.965808	−	0.498028i
$899$	−8.24995	+	19.9171i	−0.275151	+	0.664274i
$900$	−88.1875	+	0.795429i	−2.93958	+	0.0265143i
$901$	−5.27661	+	2.18564i	−0.175789	+	0.0728143i
$902$	−36.2246	+	30.6357i	−1.20615	+	1.02006i
$903$	6.07309	−	19.3045i	0.202100	−	0.642414i
$904$	0.762102	−	1.90202i	0.0253471	−	0.0632603i
$905$	−72.9698	+	19.5522i	−2.42560	+	0.649937i
$906$	−2.84218	+	22.3675i	−0.0944250	+	0.743110i
$907$	7.91355	−	10.3131i	0.262765	−	0.342442i	−0.643274	−	0.765636i	$-0.722424\pi$
$907$	7.91355	−	10.3131i	0.262765	−	0.342442i	0.906039	+	0.423194i	$0.139091\pi$
$908$	−2.02220	−	2.17285i	−0.0671092	−	0.0721087i
$909$	−23.8633	+	15.2456i	−0.791494	+	0.505665i
$910$	−0.159686	+	0.733719i	−0.00529354	+	0.0243225i
$911$	−40.1326	+	23.1706i	−1.32965	+	0.767675i	−0.985246	−	0.171145i	$-0.945253\pi$
$911$	−40.1326	+	23.1706i	−1.32965	+	0.767675i	−0.344407	+	0.938821i	$0.611920\pi$
$912$	−2.63677	+	22.8707i	−0.0873123	+	0.757326i
$913$	−44.2639	−	25.5558i	−1.46492	−	0.845773i
$914$	−7.54785	+	8.30129i	−0.249661	+	0.274582i
$915$	−59.9550	−	85.5079i	−1.98205	−	2.82680i
$916$	28.6561	−	15.2004i	0.946823	−	0.502234i
$917$	−8.89890	−	21.4839i	−0.293868	−	0.709459i
$918$	−18.5078	−	3.99077i	−0.610849	−	0.131715i
$919$	−15.2252	−	15.2252i	−0.502234	−	0.502234i	0.409898	−	0.912131i	$-0.365564\pi$
$919$	−15.2252	−	15.2252i	−0.502234	−	0.502234i	−0.912131	+	0.409898i	$0.865564\pi$
$920$	−6.34976	+	1.78065i	−0.209346	+	0.0587064i
$921$	20.7165	−	4.60667i	0.682632	−	0.151795i
$922$	−1.18795	+	3.30358i	−0.0391231	+	0.108798i
$923$	0.0283834	−	0.215593i	0.000934250	−	0.00709633i
$924$	−17.1373	+	5.56166i	−0.563777	+	0.182965i
$925$	4.83027	−	0.635917i	0.158818	−	0.0209088i
$926$	16.0335	+	24.9540i	0.526893	+	0.820039i
$927$	16.6849	+	1.43819i	0.548006	+	0.0472365i
$928$	19.5553	−	24.2424i	0.641935	−	0.795795i
$929$	−28.1355	−	48.7321i	−0.923096	−	1.59885i	−0.794595	−	0.607140i	$-0.792317\pi$
$929$	−28.1355	−	48.7321i	−0.923096	−	1.59885i	−0.128501	−	0.991709i	$-0.541017\pi$
$930$	−36.9595	−	21.1169i	−1.21195	−	0.692450i
$931$	−10.9947	−	14.3286i	−0.360338	−	0.469602i
$932$	−6.12669	+	36.3905i	−0.200686	+	1.19201i
$933$	−27.9885	+	33.3988i	−0.916302	+	1.09343i
$934$	2.26862	+	2.68250i	0.0742316	+	0.0877739i
$935$	−33.6192	+	33.6192i	−1.09947	+	1.09947i
$936$	−0.730967	+	0.352395i	−0.0238924	+	0.0115184i
$937$	−6.58034	−	6.58034i	−0.214970	−	0.214970i	0.591405	−	0.806375i	$-0.298574\pi$
$937$	−6.58034	−	6.58034i	−0.214970	−	0.214970i	−0.806375	+	0.591405i	$0.798574\pi$
$938$	1.82413	−	21.8220i	0.0595601	−	0.712514i
$939$	−7.46419	+	2.72216i	−0.243585	+	0.0888344i
$940$	28.3568	−	45.2806i	0.924895	−	1.47689i
$941$	−16.4669	+	12.6355i	−0.536807	+	0.411906i	−0.841268	−	0.540618i	$-0.818190\pi$
$941$	−16.4669	+	12.6355i	−0.536807	+	0.411906i	0.304461	+	0.952525i	$0.401524\pi$
$942$	9.36624	+	9.28214i	0.305168	+	0.302428i
$943$	−3.67075	+	2.11931i	−0.119536	+	0.0690143i
$944$	−33.1742	−	16.6221i	−1.07973	−	0.541002i
$945$	−28.6097	−	3.71059i	−0.930675	−	0.120706i
$946$	11.6793	−	53.6635i	0.379726	−	1.74475i
$947$	−2.51381	−	19.0943i	−0.0816878	−	0.620481i	−0.982499	−	0.186269i	$-0.940360\pi$
$947$	−2.51381	−	19.0943i	−0.0816878	−	0.620481i	0.900811	−	0.434212i	$-0.142973\pi$
$948$	−4.65560	+	0.861189i	−0.151207	+	0.0279701i
$949$	1.00198	+	0.131913i	0.0325255	+	0.00428207i
$950$	29.4340	+	62.4890i	0.954964	+	2.02741i
$951$	32.2117	−	29.5546i	1.04454	−	0.958373i
$952$	9.05131	+	1.08491i	0.293355	+	0.0351622i
$953$	21.2848	−	21.2848i	0.689482	−	0.689482i	−0.272635	−	0.962117i	$-0.587895\pi$
$953$	21.2848	−	21.2848i	0.689482	−	0.689482i	0.962117	+	0.272635i	$0.0878952\pi$
$954$	−8.54399	−	3.93068i	−0.276622	−	0.127260i
$955$	4.36931	−	1.80983i	0.141388	−	0.0585646i
$956$	−3.84968	−	40.3993i	−0.124508	−	1.30661i
$957$	3.48113	+	39.4979i	0.112529	+	1.27679i
$958$	1.33892	+	28.1653i	0.0432585	+	0.909981i
$959$	−2.30171	+	3.98668i	−0.0743261	+	0.128737i
$960$	42.6177	+	44.3379i	1.37548	+	1.43100i
$961$	7.83476	+	13.5702i	0.252734	+	0.437749i
$962$	0.0377145	−	0.0242324i	0.00121596	−	0.000781284i
$963$	−20.1968	+	0.907754i	−0.650834	+	0.0292520i
$964$	−14.6096	−	6.67544i	−0.470544	−	0.215002i
$965$	49.3160	+	37.8415i	1.58754	+	1.21816i
$966$	−1.59497	+	0.217304i	−0.0513174	+	0.00699165i
$967$	−7.08544	−	26.4432i	−0.227852	−	0.850357i	−0.981242	−	0.192782i	$-0.938249\pi$
$967$	−7.08544	−	26.4432i	−0.227852	−	0.850357i	0.753389	−	0.657575i	$-0.228418\pi$
$968$	−16.3486	+	6.99520i	−0.525464	+	0.224834i
$969$	3.21888	+	14.4755i	0.103405	+	0.465020i
$970$	73.3577	+	6.13208i	2.35537	+	0.196889i
$971$	−6.85568	−	16.5511i	−0.220009	−	0.531149i	0.774882	−	0.632107i	$-0.217809\pi$
$971$	−6.85568	−	16.5511i	−0.220009	−	0.531149i	−0.994891	+	0.100957i	$0.967809\pi$
$972$	−15.8830	−	26.8278i	−0.509446	−	0.860502i
$973$	4.45357	+	1.84473i	0.142775	+	0.0591393i
$974$	40.2038	−	12.8474i	1.28821	−	0.411658i
$975$	−1.30684	+	2.05424i	−0.0418525	+	0.0657882i
$976$	−10.9390	+	53.2275i	−0.350147	+	1.70377i
$977$	−8.31807	−	4.80244i	−0.266119	−	0.153644i	0.361004	−	0.932564i	$-0.382434\pi$
$977$	−8.31807	−	4.80244i	−0.266119	−	0.153644i	−0.627122	+	0.778921i	$0.715767\pi$
$978$	7.32378	−	27.8342i	0.234189	−	0.890041i
$979$	−1.50998	−	11.4694i	−0.0482592	−	0.366565i
$980$	−48.2145	−	1.73143i	−1.54016	−	0.0553087i
$981$	−4.05893	+	4.44096i	−0.129592	+	0.141789i
$982$	15.2237	+	10.5722i	0.485808	+	0.337373i
$983$	−3.74798	+	13.9877i	−0.119542	+	0.446137i	−0.999587	−	0.0287541i	$-0.990846\pi$
$983$	−3.74798	+	13.9877i	−0.119542	+	0.446137i	0.880044	+	0.474891i	$0.157513\pi$
$984$	33.5945	+	20.8281i	1.07095	+	0.663975i
$985$	−7.87306	−	29.3827i	−0.250857	−	0.936209i
$986$	6.78864	−	18.8786i	0.216194	−	0.601217i
$987$	8.37620	−	9.99537i	0.266617	−	0.318156i
$988$	0.490025	+	0.404760i	0.0155898	+	0.0128771i
$989$	1.87771	−	4.53318i	0.0597076	−	0.144147i
$990$	−78.2332	−	3.01210i	−2.48641	−	0.0957308i
$991$	−19.4755			−0.618661			−0.309330	−	0.950955i	$-0.600105\pi$
$991$	−19.4755			−0.618661			−0.309330	+	0.950955i	$0.600105\pi$
$992$	5.21128	+	21.5271i	0.165458	+	0.683487i
$993$	−0.690590	+	16.0532i	−0.0219152	+	0.509434i
$994$	−4.01808	+	0.191011i	−0.127446	+	0.00605849i
$995$	24.3287	+	31.7058i	0.771271	+	1.00514i
$996$	−8.86829	+	41.6507i	−0.281003	+	1.31975i
$997$	−27.2757	−	20.9294i	−0.863830	−	0.662840i	0.0787234	−	0.996896i	$-0.474916\pi$
$997$	−27.2757	−	20.9294i	−0.863830	−	0.662840i	−0.942553	+	0.334057i	$0.891582\pi$
$998$	29.9009	−	5.39169i	0.946495	−	0.170671i
$999$	1.05110	+	1.36438i	0.0332553	+	0.0431671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.13.8	✓	368
3.2	odd	2		864.2.bk.a.685.39		368
9.2	odd	6		864.2.bk.a.397.22		368
9.7	even	3	inner	288.2.bc.a.205.25	yes	368
32.5	even	8	inner	288.2.bc.a.229.25	yes	368
96.5	odd	8		864.2.bk.a.37.22		368
288.101	odd	24		864.2.bk.a.613.39		368
288.133	even	24	inner	288.2.bc.a.133.8	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.8	✓	368	1.1	even	1	trivial
288.2.bc.a.133.8	yes	368	288.133	even	24	inner
288.2.bc.a.205.25	yes	368	9.7	even	3	inner
288.2.bc.a.229.25	yes	368	32.5	even	8	inner
864.2.bk.a.37.22		368	96.5	odd	8
864.2.bk.a.397.22		368	9.2	odd	6
864.2.bk.a.613.39		368	288.101	odd	24
864.2.bk.a.685.39		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bc (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25694 - 0.648153i) q^{2} +(1.41818 - 0.994373i) q^{3} +(1.15979 + 1.62938i) q^{4} +(0.579315 - 4.40033i) q^{5} +(-2.42707 + 0.330671i) q^{6} +(1.20832 + 0.323768i) q^{7} +(-0.401705 - 2.79976i) q^{8} +(1.02245 - 2.82039i) q^{9} +O(q^{10})\)	\(q+(-1.25694 - 0.648153i) q^{2} +(1.41818 - 0.994373i) q^{3} +(1.15979 + 1.62938i) q^{4} +(0.579315 - 4.40033i) q^{5} +(-2.42707 + 0.330671i) q^{6} +(1.20832 + 0.323768i) q^{7} +(-0.401705 - 2.79976i) q^{8} +(1.02245 - 2.82039i) q^{9} +(-3.58025 + 5.15547i) q^{10} +(-2.53108 + 3.29857i) q^{11} +(3.26500 + 1.15748i) q^{12} +(0.0758711 - 0.0582180i) q^{13} +(-1.30893 - 1.19013i) q^{14} +(-3.55400 - 6.81650i) q^{15} +(-1.30975 + 3.77949i) q^{16} +2.57648i q^{17} +(-3.11320 + 2.88236i) q^{18} +(3.07003 + 1.27165i) q^{19} +(7.84169 - 4.15956i) q^{20} +(2.03555 - 0.742359i) q^{21} +(5.31940 - 2.50558i) q^{22} +(0.507432 - 0.135966i) q^{23} +(-3.35369 - 3.57110i) q^{24} +(-14.1977 - 3.80426i) q^{25} +(-0.133100 + 0.0240004i) q^{26} +(-1.35451 - 5.01650i) q^{27} +(0.873860 + 2.34431i) q^{28} +(5.45887 - 0.718674i) q^{29} +(0.0490279 + 10.8715i) q^{30} +(-1.95771 + 3.39085i) q^{31} +(4.09597 - 3.90167i) q^{32} +(-0.309512 + 7.19480i) q^{33} +(1.66995 - 3.23848i) q^{34} +(2.12468 - 5.12943i) q^{35} +(5.78131 - 1.60512i) q^{36} +(-0.306228 + 0.126844i) q^{37} +(-3.03462 - 3.58823i) q^{38} +(0.0497082 - 0.158007i) q^{39} +(-12.5526 + 0.145697i) q^{40} +(-7.79353 + 2.08827i) q^{41} +(-3.03973 - 0.386250i) q^{42} +(5.68592 - 7.41004i) q^{43} +(-8.31017 - 0.298427i) q^{44} +(-11.8183 - 6.13299i) q^{45} +(-0.725938 - 0.157993i) q^{46} +(5.21248 - 3.00942i) q^{47} +(1.90076 + 6.66236i) q^{48} +(-4.70697 - 2.71757i) q^{49} +(15.3799 + 13.9840i) q^{50} +(2.56198 + 3.65390i) q^{51} +(0.182854 + 0.0561019i) q^{52} +(0.848306 + 2.04799i) q^{53} +(-1.54892 + 7.18337i) q^{54} +(13.0485 + 13.0485i) q^{55} +(0.421083 - 3.51305i) q^{56} +(5.61833 - 1.24933i) q^{57} +(-7.32728 - 2.63485i) q^{58} +(-1.21081 + 9.19702i) q^{59} +(6.98475 - 13.6966i) q^{60} +(13.4688 - 1.77320i) q^{61} +(4.65851 - 2.99320i) q^{62} +(2.14859 - 3.07689i) q^{63} +(-7.67727 + 2.24935i) q^{64} +(-0.212225 - 0.367585i) q^{65} +(5.05237 - 8.84282i) q^{66} +(7.53531 + 9.82021i) q^{67} +(-4.19806 + 2.98819i) q^{68} +(0.584427 - 0.697400i) q^{69} +(-5.99526 + 5.07027i) q^{70} +(1.60783 - 1.60783i) q^{71} +(-8.30713 - 1.72963i) q^{72} +(7.47247 + 7.47247i) q^{73} +(0.467124 + 0.0390476i) q^{74} +(-23.9177 + 8.72268i) q^{75} +(1.48861 + 6.47708i) q^{76} +(-4.12633 + 3.16624i) q^{77} +(-0.164893 + 0.166387i) q^{78} +(-1.18365 + 0.683378i) q^{79} +(15.8723 + 7.95285i) q^{80} +(-6.90921 - 5.76739i) q^{81} +(11.1495 + 2.42657i) q^{82} +(1.60457 + 12.1879i) q^{83} +(3.57041 + 2.45570i) q^{84} +(11.3374 + 1.49259i) q^{85} +(-11.9497 + 5.62862i) q^{86} +(7.02701 - 6.44736i) q^{87} +(10.2520 + 5.76137i) q^{88} +(-1.96743 + 1.96743i) q^{89} +(10.8798 + 15.3689i) q^{90} +(0.110526 - 0.0457812i) q^{91} +(0.810057 + 0.669106i) q^{92} +(0.595394 + 6.75551i) q^{93} +(-8.50233 + 0.404182i) q^{94} +(7.37418 - 12.7724i) q^{95} +(1.92909 - 9.60618i) q^{96} +(-5.86403 - 10.1568i) q^{97} +(4.15498 + 6.46666i) q^{98} +(6.71537 + 10.5113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

L-functions

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