LMFDB - Embedded newform 147.2.m.b.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(4,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("147.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.m (of order $21$, degree $12$, 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:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	147.4
Dual form			147.2.m.b.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190250 + 0.129710i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(-0.711312 - 1.81239i) q^{4} +(1.13743 - 0.350851i) q^{5} +(-0.0512377 - 0.224487i) q^{6} +(-2.33995 - 1.23477i) q^{7} +(0.202234 - 0.886046i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})$	\(q+(0.190250 + 0.129710i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(-0.711312 - 1.81239i) q^{4} +(1.13743 - 0.350851i) q^{5} +(-0.0512377 - 0.224487i) q^{6} +(-2.33995 - 1.23477i) q^{7} +(0.202234 - 0.886046i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(0.261905 + 0.0807869i) q^{10} +(0.276984 - 3.69610i) q^{11} +(-0.711312 + 1.81239i) q^{12} +(1.00902 - 0.485919i) q^{13} +(-0.285013 - 0.538429i) q^{14} +(-1.07243 - 0.516457i) q^{15} +(-2.70107 + 2.50623i) q^{16} +(6.63269 - 0.999717i) q^{17} +(-0.115130 + 0.199411i) q^{18} +(2.49731 + 4.32547i) q^{19} +(-1.44495 - 1.81191i) q^{20} +(0.875449 + 2.49672i) q^{21} +(0.532118 - 0.667255i) q^{22} +(-1.09199 - 0.164591i) q^{23} +(-0.750913 + 0.511964i) q^{24} +(-2.96054 + 2.01846i) q^{25} +(0.254995 + 0.0384343i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-0.573448 + 5.11921i) q^{28} +(4.32808 + 5.42724i) q^{29} +(-0.137041 - 0.237362i) q^{30} +(-1.42347 + 2.46552i) q^{31} +(-2.63632 + 0.397362i) q^{32} +(-2.71703 + 2.52103i) q^{33} +(1.39154 + 0.670131i) q^{34} +(-3.09474 - 0.583487i) q^{35} +(1.75417 - 0.844763i) q^{36} +(0.893462 - 2.27650i) q^{37} +(-0.0859442 + 1.14685i) q^{38} +(-1.07017 - 0.330105i) q^{39} +(-0.0808426 - 1.07877i) q^{40} +(0.970126 - 4.25040i) q^{41} +(-0.157295 + 0.588555i) q^{42} +(-2.16553 - 9.48782i) q^{43} +(-6.89580 + 2.12707i) q^{44} +(0.434870 + 1.10803i) q^{45} +(-0.186401 - 0.172955i) q^{46} +(6.47433 + 4.41412i) q^{47} +3.68469 q^{48} +(3.95071 + 5.77857i) q^{49} -0.825059 q^{50} +(-5.54209 - 3.77853i) q^{51} +(-1.59841 - 1.48310i) q^{52} +(-1.47372 - 3.75499i) q^{53} +(0.220030 - 0.0678704i) q^{54} +(-0.981728 - 4.30123i) q^{55} +(-1.56728 + 1.82359i) q^{56} +(1.11141 - 4.86939i) q^{57} +(0.119448 + 1.59393i) q^{58} +(13.6406 + 4.20757i) q^{59} +(-0.173188 + 2.31103i) q^{60} +(-2.75362 + 7.01611i) q^{61} +(-0.590618 + 0.284426i) q^{62} +(1.05645 - 2.42568i) q^{63} +(6.08648 + 2.93110i) q^{64} +(0.977206 - 0.906715i) q^{65} +(-0.843918 + 0.127200i) q^{66} +(1.69953 - 2.94368i) q^{67} +(-6.52979 - 11.3099i) q^{68} +(0.688533 + 0.863394i) q^{69} +(-0.513091 - 0.512428i) q^{70} +(-3.49266 + 4.37965i) q^{71} +(0.898682 + 0.135454i) q^{72} +(1.17183 - 0.798940i) q^{73} +(0.465267 - 0.317213i) q^{74} +(3.54314 + 0.534042i) q^{75} +(6.06308 - 7.60286i) q^{76} +(-5.21194 + 8.30666i) q^{77} +(-0.160783 - 0.201615i) q^{78} +(-8.37241 - 14.5014i) q^{79} +(-2.19297 + 3.79833i) q^{80} +(-0.988831 + 0.149042i) q^{81} +(0.735886 - 0.682803i) q^{82} +(-12.1399 - 5.84627i) q^{83} +(3.90231 - 3.36260i) q^{84} +(7.19347 - 3.46419i) q^{85} +(0.818675 - 2.08595i) q^{86} +(0.518754 - 6.92229i) q^{87} +(-3.21890 - 0.992898i) q^{88} +(-0.460090 - 6.13948i) q^{89} +(-0.0609889 + 0.267210i) q^{90} +(-2.96105 - 0.108880i) q^{91} +(0.478441 + 2.09619i) q^{92} +(2.72045 - 0.839149i) q^{93} +(0.659183 + 1.67957i) q^{94} +(4.35811 + 4.04373i) q^{95} +(2.20284 + 1.50187i) q^{96} -2.94332 q^{97} +(0.00208186 + 1.61182i) q^{98} +3.70646 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9} - 34 q^{10} - 11 q^{11} + 5 q^{12} - 2 q^{13} + 40 q^{14} - 3 q^{15} - 31 q^{16} - 9 q^{17} - 6 q^{18} - 29 q^{19} - 43 q^{20} - 11 q^{21} + 9 q^{22} - 4 q^{23} - 24 q^{24} + 55 q^{25} + 36 q^{26} - 10 q^{27} - 57 q^{28} + 4 q^{29} - 20 q^{30} - 39 q^{31} - 92 q^{32} - 18 q^{33} - 36 q^{34} - 33 q^{35} - 10 q^{36} - 24 q^{37} + 118 q^{38} - 6 q^{39} + 35 q^{41} + 38 q^{42} + 2 q^{43} + 40 q^{44} + 12 q^{45} - 40 q^{46} - 5 q^{47} + 76 q^{48} + 129 q^{49} - 176 q^{50} + 54 q^{51} - 6 q^{52} + 26 q^{53} + q^{54} + 2 q^{55} + 63 q^{56} - 12 q^{57} + 11 q^{58} - 41 q^{59} + 32 q^{60} + 6 q^{61} + 36 q^{62} - q^{63} + 74 q^{64} - 51 q^{65} - 15 q^{66} - 55 q^{67} - 22 q^{68} + 8 q^{69} - 68 q^{70} - 66 q^{71} - 24 q^{72} + 24 q^{73} + 28 q^{74} + 41 q^{75} + 3 q^{76} - 34 q^{77} - 30 q^{78} - 51 q^{79} - 5 q^{80} + 5 q^{81} - 41 q^{82} + 30 q^{83} - 30 q^{84} + 68 q^{85} + 110 q^{86} + 19 q^{87} + 129 q^{88} + 75 q^{89} - 16 q^{90} + 5 q^{91} - 4 q^{93} + 38 q^{94} + 36 q^{95} - 57 q^{96} - 168 q^{97} + 227 q^{98} + 36 q^{99}+O(q^{100}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9 - 34 * q^10 - 11 * q^11 + 5 * q^12 - 2 * q^13 + 40 * q^14 - 3 * q^15 - 31 * q^16 - 9 * q^17 - 6 * q^18 - 29 * q^19 - 43 * q^20 - 11 * q^21 + 9 * q^22 - 4 * q^23 - 24 * q^24 + 55 * q^25 + 36 * q^26 - 10 * q^27 - 57 * q^28 + 4 * q^29 - 20 * q^30 - 39 * q^31 - 92 * q^32 - 18 * q^33 - 36 * q^34 - 33 * q^35 - 10 * q^36 - 24 * q^37 + 118 * q^38 - 6 * q^39 + 35 * q^41 + 38 * q^42 + 2 * q^43 + 40 * q^44 + 12 * q^45 - 40 * q^46 - 5 * q^47 + 76 * q^48 + 129 * q^49 - 176 * q^50 + 54 * q^51 - 6 * q^52 + 26 * q^53 + q^54 + 2 * q^55 + 63 * q^56 - 12 * q^57 + 11 * q^58 - 41 * q^59 + 32 * q^60 + 6 * q^61 + 36 * q^62 - q^63 + 74 * q^64 - 51 * q^65 - 15 * q^66 - 55 * q^67 - 22 * q^68 + 8 * q^69 - 68 * q^70 - 66 * q^71 - 24 * q^72 + 24 * q^73 + 28 * q^74 + 41 * q^75 + 3 * q^76 - 34 * q^77 - 30 * q^78 - 51 * q^79 - 5 * q^80 + 5 * q^81 - 41 * q^82 + 30 * q^83 - 30 * q^84 + 68 * q^85 + 110 * q^86 + 19 * q^87 + 129 * q^88 + 75 * q^89 - 16 * q^90 + 5 * q^91 - 4 * q^93 + 38 * q^94 + 36 * q^95 - 57 * q^96 - 168 * q^97 + 227 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

Coefficient data

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

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

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

$2$	0.190250	+	0.129710i	0.134527	+	0.0917190i	0.628714	−	0.777637i	$-0.283582\pi$
$2$	0.190250	+	0.129710i	0.134527	+	0.0917190i	−0.494187	+	0.869356i	$0.664534\pi$
$3$	−0.733052	−	0.680173i	−0.423228	−	0.392698i
$3$	−0.733052	−	0.680173i	−0.423228	−	0.392698i
$4$	−0.711312	−	1.81239i	−0.355656	−	0.906196i
$5$	1.13743	−	0.350851i	0.508674	−	0.156905i	−0.0297859	−	0.999556i	$-0.509483\pi$
$5$	1.13743	−	0.350851i	0.508674	−	0.156905i	0.538460	+	0.842651i	$0.319006\pi$
$6$	−0.0512377	−	0.224487i	−0.0209177	−	0.0916465i
$7$	−2.33995	−	1.23477i	−0.884417	−	0.466698i
$7$	−2.33995	−	1.23477i	−0.884417	−	0.466698i
$8$	0.202234	−	0.886046i	0.0715006	−	0.313265i
$9$	0.0747301	+	0.997204i	0.0249100	+	0.332401i
$10$	0.261905	+	0.0807869i	0.0828216	+	0.0255471i
$11$	0.276984	−	3.69610i	0.0835139	−	1.11442i	−0.785247	−	0.619183i	$-0.787464\pi$
$11$	0.276984	−	3.69610i	0.0835139	−	1.11442i	0.868761	−	0.495232i	$-0.164917\pi$
$12$	−0.711312	+	1.81239i	−0.205338	+	0.523193i
$13$	1.00902	−	0.485919i	0.279852	−	0.134770i	−0.288693	−	0.957422i	$-0.593221\pi$
$13$	1.00902	−	0.485919i	0.279852	−	0.134770i	0.568545	+	0.822652i	$0.307506\pi$
$14$	−0.285013	−	0.538429i	−0.0761730	−	0.143901i
$15$	−1.07243	−	0.516457i	−0.276901	−	0.133349i
$16$	−2.70107	+	2.50623i	−0.675268	+	0.626557i
$17$	6.63269	−	0.999717i	1.60866	−	0.242467i	0.717637	−	0.696418i	$-0.245224\pi$
$17$	6.63269	−	0.999717i	1.60866	−	0.242467i	0.891027	+	0.453950i	$0.149986\pi$
$18$	−0.115130	+	0.199411i	−0.0271364	+	0.0470017i
$19$	2.49731	+	4.32547i	0.572922	+	0.992330i	0.996264	+	0.0863600i	$0.0275235\pi$
$19$	2.49731	+	4.32547i	0.572922	+	0.992330i	−0.423342	+	0.905970i	$0.639143\pi$
$20$	−1.44495	−	1.81191i	−0.323100	−	0.405154i
$21$	0.875449	+	2.49672i	0.191039	+	0.544828i
$22$	0.532118	−	0.667255i	0.113448	−	0.142259i
$23$	−1.09199	−	0.164591i	−0.227695	−	0.0343195i	0.0342036	−	0.999415i	$-0.489111\pi$
$23$	−1.09199	−	0.164591i	−0.227695	−	0.0343195i	−0.261899	+	0.965095i	$0.584349\pi$
$24$	−0.750913	+	0.511964i	−0.153279	+	0.104504i
$25$	−2.96054	+	2.01846i	−0.592109	+	0.403693i
$26$	0.254995	+	0.0384343i	0.0500086	+	0.00753759i
$27$	0.623490	−	0.781831i	0.119991	−	0.150464i
$28$	−0.573448	+	5.11921i	−0.108372	+	0.967439i
$29$	4.32808	+	5.42724i	0.803704	+	1.00781i	0.999630	+	0.0271942i	$0.00865726\pi$
$29$	4.32808	+	5.42724i	0.803704	+	1.00781i	−0.195926	+	0.980619i	$0.562771\pi$
$30$	−0.137041	−	0.237362i	−0.0250201	−	0.0433361i
$31$	−1.42347	+	2.46552i	−0.255662	+	0.442820i	−0.965075	−	0.261973i	$-0.915627\pi$
$31$	−1.42347	+	2.46552i	−0.255662	+	0.442820i	0.709413	+	0.704793i	$0.248960\pi$
$32$	−2.63632	+	0.397362i	−0.466041	+	0.0702444i
$33$	−2.71703	+	2.52103i	−0.472974	+	0.438856i
$34$	1.39154	+	0.670131i	0.238648	+	0.114927i
$35$	−3.09474	−	0.583487i	−0.523107	−	0.0986273i
$36$	1.75417	−	0.844763i	0.292361	−	0.140794i
$37$	0.893462	−	2.27650i	0.146884	−	0.374255i	−0.838429	−	0.545011i	$-0.816526\pi$
$37$	0.893462	−	2.27650i	0.146884	−	0.374255i	0.985313	+	0.170756i	$0.0546209\pi$
$38$	−0.0859442	+	1.14685i	−0.0139420	+	0.186043i
$39$	−1.07017	−	0.330105i	−0.171365	−	0.0528591i
$40$	−0.0808426	−	1.07877i	−0.0127823	−	0.170568i
$41$	0.970126	−	4.25040i	0.151508	−	0.663801i	−0.840939	−	0.541130i	$-0.817997\pi$
$41$	0.970126	−	4.25040i	0.151508	−	0.663801i	0.992447	−	0.122671i	$-0.0391460\pi$
$42$	−0.157295	+	0.588555i	−0.0242712	+	0.0908159i
$43$	−2.16553	−	9.48782i	−0.330241	−	1.44688i	−0.818664	−	0.574273i	$-0.805285\pi$
$43$	−2.16553	−	9.48782i	−0.330241	−	1.44688i	0.488423	−	0.872607i	$-0.337572\pi$
$44$	−6.89580	+	2.12707i	−1.03958	+	0.320668i
$45$	0.434870	+	1.10803i	0.0648266	+	0.165175i
$46$	−0.186401	−	0.172955i	−0.0274834	−	0.0255009i
$47$	6.47433	+	4.41412i	0.944377	+	0.643866i	0.934454	−	0.356085i	$-0.115889\pi$
$47$	6.47433	+	4.41412i	0.944377	+	0.643866i	0.00992387	+	0.999951i	$0.496841\pi$
$48$	3.68469			0.531840
$49$	3.95071	+	5.77857i	0.564387	+	0.825510i
$50$	−0.825059			−0.116681
$51$	−5.54209	−	3.77853i	−0.776047	−	0.529100i
$52$	−1.59841	−	1.48310i	−0.221659	−	0.205669i
$53$	−1.47372	−	3.75499i	−0.202431	−	0.515787i	0.793221	−	0.608934i	$-0.208403\pi$
$53$	−1.47372	−	3.75499i	−0.202431	−	0.515787i	−0.995652	+	0.0931471i	$0.970307\pi$
$54$	0.220030	−	0.0678704i	0.0299423	−	0.00923599i
$55$	−0.981728	−	4.30123i	−0.132376	−	0.579978i
$56$	−1.56728	+	1.82359i	−0.209436	+	0.243687i
$57$	1.11141	−	4.86939i	0.147209	−	0.644967i
$58$	0.119448	+	1.59393i	0.0156843	+	0.209293i
$59$	13.6406	+	4.20757i	1.77585	+	0.547779i	0.996855	−	0.0792458i	$-0.0252512\pi$
$59$	13.6406	+	4.20757i	1.77585	+	0.547779i	0.779000	+	0.627024i	$0.215727\pi$
$60$	−0.173188	+	2.31103i	−0.0223585	+	0.298353i
$61$	−2.75362	+	7.01611i	−0.352565	+	0.898321i	0.639059	+	0.769158i	$0.279324\pi$
$61$	−2.75362	+	7.01611i	−0.352565	+	0.898321i	−0.991623	+	0.129163i	$0.958771\pi$
$62$	−0.590618	+	0.284426i	−0.0750085	+	0.0361222i
$63$	1.05645	−	2.42568i	0.133100	−	0.305607i
$64$	6.08648	+	2.93110i	0.760810	+	0.366387i
$65$	0.977206	−	0.906715i	0.121208	−	0.112464i
$66$	−0.843918	+	0.127200i	−0.103879	+	0.0156573i
$67$	1.69953	−	2.94368i	0.207631	−	0.359628i	−0.743337	−	0.668917i	$-0.766758\pi$
$67$	1.69953	−	2.94368i	0.207631	−	0.359628i	0.950968	+	0.309290i	$0.100091\pi$
$68$	−6.52979	−	11.3099i	−0.791853	−	1.37153i
$69$	0.688533	+	0.863394i	0.0828897	+	0.103940i
$70$	−0.513091	−	0.512428i	−0.0613260	−	0.0612469i
$71$	−3.49266	+	4.37965i	−0.414502	+	0.519769i	−0.944625	−	0.328151i	$-0.893574\pi$
$71$	−3.49266	+	4.37965i	−0.414502	+	0.519769i	0.530123	+	0.847921i	$0.322146\pi$
$72$	0.898682	+	0.135454i	0.105911	+	0.0159635i
$73$	1.17183	−	0.798940i	0.137152	−	0.0935088i	−0.492800	−	0.870142i	$-0.664027\pi$
$73$	1.17183	−	0.798940i	0.137152	−	0.0935088i	0.629953	+	0.776634i	$0.283074\pi$
$74$	0.465267	−	0.317213i	0.0540862	−	0.0368753i
$75$	3.54314	+	0.534042i	0.409126	+	0.0616659i
$76$	6.06308	−	7.60286i	0.695483	−	0.872108i
$77$	−5.21194	+	8.30666i	−0.593956	+	0.946632i
$78$	−0.160783	−	0.201615i	−0.0182050	−	0.0228284i
$79$	−8.37241	−	14.5014i	−0.941970	−	1.63154i	−0.761707	−	0.647922i	$-0.775638\pi$
$79$	−8.37241	−	14.5014i	−0.941970	−	1.63154i	−0.180263	−	0.983618i	$-0.557695\pi$
$80$	−2.19297	+	3.79833i	−0.245181	+	0.424666i
$81$	−0.988831	+	0.149042i	−0.109870	+	0.0165603i
$82$	0.735886	−	0.682803i	0.0812650	−	0.0754029i
$83$	−12.1399	−	5.84627i	−1.33253	−	0.641711i	−0.374190	−	0.927352i	$-0.622079\pi$
$83$	−12.1399	−	5.84627i	−1.33253	−	0.641711i	−0.958337	+	0.285641i	$0.907794\pi$
$84$	3.90231	−	3.36260i	0.425777	−	0.366890i
$85$	7.19347	−	3.46419i	0.780241	−	0.375744i
$86$	0.818675	−	2.08595i	0.0882800	−	0.224934i
$87$	0.518754	−	6.92229i	0.0556162	−	0.742147i
$88$	−3.21890	−	0.992898i	−0.343136	−	0.105843i
$89$	−0.460090	−	6.13948i	−0.0487695	−	0.650783i	−0.967006	−	0.254752i	$-0.918006\pi$
$89$	−0.460090	−	6.13948i	−0.0487695	−	0.650783i	0.918237	−	0.396031i	$-0.129613\pi$
$90$	−0.0609889	+	0.267210i	−0.00642879	+	0.0281664i
$91$	−2.96105	−	0.108880i	−0.310403	−	0.0114137i
$92$	0.478441	+	2.09619i	0.0498809	+	0.218542i
$93$	2.72045	−	0.839149i	0.282098	−	0.0870157i
$94$	0.659183	+	1.67957i	0.0679896	+	0.173235i
$95$	4.35811	+	4.04373i	0.447132	+	0.414878i
$96$	2.20284	+	1.50187i	0.224826	+	0.153284i
$97$	−2.94332			−0.298849			−0.149424	−	0.988773i	$-0.547742\pi$
$97$	−2.94332			−0.298849			−0.149424	+	0.988773i	$0.547742\pi$
$98$	0.00208186	+	1.61182i	0.000210300	+	0.162818i
$99$	3.70646			0.372513
$100$	5.76412	+	3.92991i	0.576412	+	0.392991i
$101$	0.438721	+	0.407073i	0.0436543	+	0.0405053i	0.701698	−	0.712474i	$-0.252425\pi$
$101$	0.438721	+	0.407073i	0.0436543	+	0.0405053i	−0.658044	+	0.752979i	$0.728616\pi$
$102$	−0.564268	−	1.43773i	−0.0558708	−	0.142357i
$103$	−3.03228	+	0.935334i	−0.298779	+	0.0921612i	−0.440520	−	0.897743i	$-0.645206\pi$
$103$	−3.03228	+	0.935334i	−0.298779	+	0.0921612i	0.141741	+	0.989904i	$0.454730\pi$
$104$	−0.226488	−	0.992309i	−0.0222090	−	0.0973040i
$105$	1.87174	+	2.53269i	0.182663	+	0.247165i
$106$	0.206684	−	0.905543i	0.0200749	−	0.0879541i
$107$	1.30777	+	17.4510i	0.126427	+	1.68705i	0.595079	+	0.803667i	$0.297121\pi$
$107$	1.30777	+	17.4510i	0.126427	+	1.68705i	−0.468653	+	0.883383i	$0.655260\pi$
$108$	−1.86048	−	0.573882i	−0.179025	−	0.0552219i
$109$	−0.535242	+	7.14230i	−0.0512668	+	0.684109i	0.911071	+	0.412251i	$0.135257\pi$
$109$	−0.535242	+	7.14230i	−0.0512668	+	0.684109i	−0.962337	+	0.271858i	$0.912362\pi$
$110$	0.371140	−	0.945649i	0.0353868	−	0.0901641i
$111$	−2.20337	+	1.06109i	−0.209135	+	0.100714i
$112$	9.41497	−	2.52925i	0.889631	−	0.238992i
$113$	−7.62512	−	3.67206i	−0.717311	−	0.345439i	0.0393687	−	0.999225i	$-0.487465\pi$
$113$	−7.62512	−	3.67206i	−0.717311	−	0.345439i	−0.756679	+	0.653786i	$0.773180\pi$
$114$	0.843055	−	0.782241i	0.0789593	−	0.0732635i
$115$	−1.29981	+	0.195914i	−0.121207	+	0.0182691i
$116$	6.75767	−	11.7046i	0.627434	−	1.08675i
$117$	0.559965	+	0.969888i	0.0517688	+	0.0896661i
$118$	2.04936	+	2.56981i	0.188659	+	0.236571i
$119$	−16.7546	−	5.85053i	−1.53589	−	0.536317i
$120$	−0.674488	+	0.845781i	−0.0615720	+	0.0772089i
$121$	−2.70728	−	0.408056i	−0.246116	−	0.0370960i
$122$	−1.43394	+	0.977642i	−0.129823	+	0.0885115i
$123$	−3.60216	+	2.45591i	−0.324796	+	0.221442i
$124$	5.48102	+	0.826130i	0.492210	+	0.0741887i
$125$	−6.36997	+	7.98769i	−0.569747	+	0.714440i
$126$	0.515624	−	0.324453i	0.0459355	−	0.0289046i
$127$	4.69902	+	5.89238i	0.416970	+	0.522864i	0.945312	−	0.326168i	$-0.105757\pi$
$127$	4.69902	+	5.89238i	0.416970	+	0.522864i	−0.528342	+	0.849032i	$0.677186\pi$
$128$	3.44386	+	5.96495i	0.304397	+	0.527232i
$129$	−4.86591	+	8.42800i	−0.428419	+	0.742044i
$130$	0.303524	−	0.0457488i	0.0266208	−	0.00401244i
$131$	−8.07194	+	7.48967i	−0.705249	+	0.654375i	−0.948932	−	0.315479i	$-0.897835\pi$
$131$	−8.07194	+	7.48967i	−0.705249	+	0.654375i	0.243684	+	0.969855i	$0.421644\pi$
$132$	6.50176	+	3.13108i	0.565905	+	0.272526i
$133$	−0.502635	−	13.2050i	−0.0435839	−	1.14501i
$134$	0.705161	−	0.339588i	0.0609167	−	0.0293359i
$135$	0.434870	−	1.10803i	0.0374276	−	0.0953640i
$136$	0.455562	−	6.07905i	0.0390641	−	0.521274i
$137$	5.92527	+	1.82770i	0.506230	+	0.156151i	0.537342	−	0.843365i	$-0.319429\pi$
$137$	5.92527	+	1.82770i	0.506230	+	0.156151i	−0.0311117	+	0.999516i	$0.509905\pi$
$138$	0.0190025	+	0.253570i	0.00161760	+	0.0215853i
$139$	−4.36141	+	19.1086i	−0.369930	+	1.62077i	0.357031	+	0.934093i	$0.383789\pi$
$139$	−4.36141	+	19.1086i	−0.369930	+	1.62077i	−0.726961	+	0.686678i	$0.759068\pi$
$140$	1.14382	+	6.02393i	0.0966704	+	0.509115i
$141$	−1.74365	−	7.63944i	−0.146842	−	0.643357i
$142$	−1.23256	+	0.380196i	−0.103434	+	0.0319053i
$143$	−1.51652	−	3.86403i	−0.126818	−	0.323127i
$144$	−2.70107	−	2.50623i	−0.225089	−	0.208852i
$145$	6.82703	+	4.65459i	0.566954	+	0.386543i
$146$	0.326571			0.0270272
$147$	1.03435	−	6.92316i	0.0853121	−	0.571012i
$148$	−4.76145			−0.391389
$149$	16.6449	+	11.3483i	1.36361	+	0.929691i	0.999998	−	0.00186111i	$-0.000592411\pi$
$149$	16.6449	+	11.3483i	1.36361	+	0.929691i	0.363608	+	0.931552i	$0.381545\pi$
$150$	0.604811	+	0.561182i	0.0493826	+	0.0458204i
$151$	−0.779366	−	1.98579i	−0.0634239	−	0.161601i	0.895648	−	0.444763i	$-0.146712\pi$
$151$	−0.779366	−	1.98579i	−0.0634239	−	0.161601i	−0.959072	+	0.283161i	$0.908617\pi$
$152$	4.33760	−	1.33797i	0.351826	−	0.108524i
$153$	1.49258	+	6.53944i	0.120668	+	0.528682i
$154$	−2.06903	+	0.904300i	−0.166727	+	0.0728706i
$155$	−0.754066	+	3.30378i	−0.0605680	+	0.265366i
$156$	0.162948	+	2.17438i	0.0130462	+	0.174090i
$157$	−6.18985	−	1.90932i	−0.494004	−	0.152380i	0.0377358	−	0.999288i	$-0.487985\pi$
$157$	−6.18985	−	1.90932i	−0.494004	−	0.152380i	−0.531740	+	0.846908i	$0.678462\pi$
$158$	0.288134	−	3.84489i	0.0229227	−	0.305883i
$159$	−1.47372	+	3.75499i	−0.116874	+	0.297790i
$160$	−2.85922	+	1.37693i	−0.226041	+	0.108856i
$161$	2.35196	+	1.73348i	0.185361	+	0.136618i
$162$	−0.207457	−	0.0999062i	−0.0162994	−	0.00784937i
$163$	2.49089	−	2.31121i	0.195101	−	0.181028i	−0.576573	−	0.817046i	$-0.695610\pi$
$163$	2.49089	−	2.31121i	0.195101	−	0.181028i	0.771674	+	0.636018i	$0.219420\pi$
$164$	−8.39345	+	1.26511i	−0.655419	+	0.0987884i
$165$	−2.20592	+	3.82077i	−0.171731	+	0.297447i
$166$	−1.55129	−	2.68692i	−0.120404	−	0.208546i
$167$	−1.44643	−	1.81377i	−0.111928	−	0.140354i	0.722711	−	0.691150i	$-0.242896\pi$
$167$	−1.44643	−	1.81377i	−0.111928	−	0.140354i	−0.834640	+	0.550796i	$0.814324\pi$
$168$	2.38925	−	0.270767i	0.184335	−	0.0208901i
$169$	−7.32336	+	9.18320i	−0.563335	+	0.706400i
$170$	1.81790	+	0.274004i	0.139426	+	0.0210151i
$171$	−4.12675	+	2.81357i	−0.315580	+	0.215159i
$172$	−15.6553	+	10.6736i	−1.19370	+	0.813854i
$173$	−1.84311	−	0.277804i	−0.140129	−	0.0211211i	0.0786031	−	0.996906i	$-0.474954\pi$
$173$	−1.84311	−	0.277804i	−0.140129	−	0.0211211i	−0.218732	+	0.975785i	$0.570192\pi$
$174$	0.996584	−	1.24968i	0.0755509	−	0.0947378i
$175$	9.41985	−	1.06752i	0.712074	−	0.0806972i
$176$	8.51511	+	10.6776i	0.641850	+	0.804855i
$177$	−7.13739	−	12.3623i	−0.536479	−	0.929210i
$178$	0.708821	−	1.22771i	0.0531284	−	0.0920210i
$179$	14.3861	−	2.16835i	1.07526	−	0.162070i	0.412545	−	0.910937i	$-0.364640\pi$
$179$	14.3861	−	2.16835i	1.07526	−	0.162070i	0.662720	+	0.748867i	$0.269402\pi$
$180$	1.69886	−	1.57631i	0.126625	−	0.117491i
$181$	8.09337	+	3.89756i	0.601576	+	0.289704i	0.709778	−	0.704425i	$-0.248795\pi$
$181$	8.09337	+	3.89756i	0.601576	+	0.289704i	−0.108202	+	0.994129i	$0.534509\pi$
$182$	−0.549218	−	0.404793i	−0.0407107	−	0.0300053i
$183$	6.79071	−	3.27023i	0.501984	−	0.241743i
$184$	−0.366672	+	0.934265i	−0.0270314	+	0.0688750i
$185$	0.217537	−	2.90283i	0.0159937	−	0.213421i
$186$	0.626412	+	0.193223i	0.0459308	+	0.0141678i
$187$	−1.85790	−	24.7920i	−0.135863	−	1.81297i
$188$	3.39486	−	14.8738i	0.247595	−	1.08479i
$189$	−2.42431	+	1.05958i	−0.176343	+	0.0770732i
$190$	0.304616	+	1.33461i	0.0220992	+	0.0968228i
$191$	13.5189	−	4.17002i	0.978191	−	0.301732i	0.235876	−	0.971783i	$-0.424204\pi$
$191$	13.5189	−	4.17002i	0.978191	−	0.301732i	0.742315	+	0.670051i	$0.233728\pi$
$192$	−2.46806	−	6.28851i	−0.178117	−	0.453834i
$193$	12.2377	+	11.3549i	0.880890	+	0.817347i	0.984156	−	0.177307i	$-0.0567386\pi$
$193$	12.2377	+	11.3549i	0.880890	+	0.817347i	−0.103265	+	0.994654i	$0.532929\pi$
$194$	−0.559966	−	0.381779i	−0.0402032	−	0.0274101i
$195$	−1.33307			−0.0954628
$196$	7.66286	−	11.2706i	0.547347	−	0.805043i
$197$	−26.2060			−1.86710			−0.933549	−	0.358450i	$-0.883305\pi$
$197$	−26.2060			−1.86710			−0.933549	+	0.358450i	$0.883305\pi$
$198$	0.705154	+	0.480766i	0.0501131	+	0.0341665i
$199$	−3.17203	−	2.94321i	−0.224859	−	0.208639i	0.559696	−	0.828698i	$-0.310918\pi$
$199$	−3.17203	−	2.94321i	−0.224859	−	0.208639i	−0.784555	+	0.620059i	$0.787108\pi$
$200$	1.18973	+	3.03138i	0.0841266	+	0.214351i
$201$	−3.24806	+	1.00189i	−0.229100	+	0.0706681i
$202$	0.0306650	+	0.134352i	0.00215758	+	0.00945299i
$203$	−3.42611	−	18.0436i	−0.240466	−	1.26641i
$204$	−2.90603	+	12.7322i	−0.203463	+	0.891429i
$205$	−0.387805	−	5.17490i	−0.0270855	−	0.361431i
$206$	−0.698213	−	0.215370i	−0.0486468	−	0.0150056i
$207$	0.0825261	−	1.10123i	0.00573596	−	0.0765410i
$208$	−1.50762	+	3.84134i	−0.104534	+	0.266349i
$209$	16.6791	−	8.03221i	1.15371	−	0.555600i
$210$	0.0275823	+	0.724627i	0.00190336	+	0.0500040i
$211$	−23.4337	−	11.2851i	−1.61325	−	0.776898i	−0.613329	−	0.789827i	$-0.710170\pi$
$211$	−23.4337	−	11.2851i	−1.61325	−	0.776898i	−0.999916	+	0.0129291i	$0.995884\pi$
$212$	−5.75723	+	5.34193i	−0.395408	+	0.366885i
$213$	5.53922	−	0.834903i	0.379541	−	0.0572066i
$214$	−2.01477	+	3.48968i	−0.137727	+	0.238549i
$215$	−5.79195	−	10.0320i	−0.395008	−	0.684173i
$216$	−0.566648	−	0.710554i	−0.0385555	−	0.0483471i
$217$	6.37518	−	4.01153i	0.432775	−	0.272321i
$218$	−1.02826	+	1.28940i	−0.0696425	+	0.0873289i
$219$	−1.40243	−	0.211382i	−0.0947673	−	0.0142839i
$220$	−7.09720	+	4.83879i	−0.478493	+	0.326231i
$221$	6.20675	−	4.23169i	0.417511	−	0.284654i
$222$	−0.556825	−	0.0839278i	−0.0373716	−	0.00563287i
$223$	−4.40502	+	5.52372i	−0.294982	+	0.369896i	−0.907132	−	0.420846i	$-0.861733\pi$
$223$	−4.40502	+	5.52372i	−0.294982	+	0.369896i	0.612150	+	0.790741i	$0.290305\pi$
$224$	6.65951	+	2.32544i	0.444957	+	0.155375i
$225$	−2.23406	−	2.80143i	−0.148937	−	0.186762i
$226$	−0.974374	−	1.68767i	−0.0648144	−	0.112262i
$227$	8.67496	−	15.0255i	0.575777	−	0.997275i	−0.420180	−	0.907441i	$-0.638033\pi$
$227$	8.67496	−	15.0255i	0.575777	−	0.997275i	0.995957	−	0.0898344i	$-0.0286338\pi$
$228$	−9.61581	+	1.44935i	−0.636822	+	0.0959855i
$229$	−21.4800	+	19.9306i	−1.41944	+	1.31705i	−0.539483	+	0.841996i	$0.681380\pi$
$229$	−21.4800	+	19.9306i	−1.41944	+	1.31705i	−0.879958	+	0.475052i	$0.842429\pi$
$230$	−0.272700	−	0.131325i	−0.0179813	−	0.00865934i
$231$	9.47059	−	2.54419i	0.623119	−	0.167396i
$232$	5.68407	−	2.73730i	0.373177	−	0.179713i
$233$	10.2180	−	26.0349i	0.669400	−	1.70560i	−0.0384684	−	0.999260i	$-0.512248\pi$
$233$	10.2180	−	26.0349i	0.669400	−	1.70560i	0.707869	−	0.706344i	$-0.249657\pi$
$234$	−0.0192710	+	0.257154i	−0.00125979	+	0.0168107i
$235$	8.91279	+	2.74923i	0.581406	+	0.179340i
$236$	−2.07695	−	27.7150i	−0.135198	−	1.80409i
$237$	−3.72608	+	16.3250i	−0.242035	+	1.06042i
$238$	−2.42868	−	3.28630i	−0.157428	−	0.213019i
$239$	−0.681307	−	2.98500i	−0.0440701	−	0.193084i	0.948101	−	0.317969i	$-0.103001\pi$
$239$	−0.681307	−	2.98500i	−0.0440701	−	0.193084i	−0.992171	+	0.124885i	$0.960144\pi$
$240$	4.19108	−	1.29278i	0.270533	−	0.0834484i
$241$	−0.574566	−	1.46397i	−0.0370110	−	0.0943025i	0.911173	−	0.412023i	$-0.135178\pi$
$241$	−0.574566	−	1.46397i	−0.0370110	−	0.0943025i	−0.948184	+	0.317721i	$0.897083\pi$
$242$	−0.462130	−	0.428794i	−0.0297068	−	0.0275639i
$243$	0.826239	+	0.563320i	0.0530032	+	0.0361370i
$244$	14.6746			0.939447
$245$	6.52107	+	5.18661i	0.416616	+	0.331361i
$246$	−1.00387			−0.0640042
$247$	4.62167	+	3.15100i	0.294070	+	0.200493i
$248$	1.89669	+	1.75987i	0.120440	+	0.111752i
$249$	4.92270	+	12.5428i	0.311964	+	0.794871i
$250$	−2.24797	+	0.693407i	−0.142174	+	0.0438549i
$251$	2.42089	+	10.6066i	0.152805	+	0.669484i	0.992062	+	0.125749i	$0.0401333\pi$
$251$	2.42089	+	10.6066i	0.152805	+	0.669484i	−0.839257	+	0.543735i	$0.817010\pi$
$252$	−5.14775	−	0.189286i	−0.324278	−	0.0119239i
$253$	−0.910806	+	3.99050i	−0.0572619	+	0.250881i
$254$	0.129686	+	1.73054i	0.00813720	+	0.108583i
$255$	−7.62943	−	2.35337i	−0.477774	−	0.147374i
$256$	0.891157	−	11.8917i	0.0556973	−	0.743229i
$257$	5.36648	−	13.6736i	0.334752	−	0.852934i	−0.660061	−	0.751212i	$-0.729470\pi$
$257$	5.36648	−	13.6736i	0.334752	−	0.852934i	0.994813	−	0.101722i	$-0.0324352\pi$
$258$	−2.01894	+	0.972269i	−0.125694	+	0.0605308i
$259$	−4.90160	+	4.22368i	−0.304571	+	0.262447i
$260$	−2.33842	−	1.12612i	−0.145023	−	0.0698393i
$261$	−5.08863	+	4.72155i	−0.314978	+	0.292257i
$262$	−2.50717	+	0.377895i	−0.154894	+	0.0233465i
$263$	−5.71663	+	9.90149i	−0.352502	+	0.610552i	−0.986687	−	0.162630i	$-0.948002\pi$
$263$	−5.71663	+	9.90149i	−0.352502	+	0.610552i	0.634185	+	0.773181i	$0.281336\pi$
$264$	1.68428	+	2.91725i	0.103660	+	0.179544i
$265$	−2.99370	−	3.75397i	−0.183901	−	0.230605i
$266$	1.61719	−	2.57744i	0.0991563	−	0.158033i
$267$	−3.83864	+	4.81350i	−0.234921	+	0.294581i
$268$	−6.54400	−	0.986349i	−0.399738	−	0.0602509i
$269$	12.0801	−	8.23610i	0.736539	−	0.502164i	−0.135999	−	0.990709i	$-0.543425\pi$
$269$	12.0801	−	8.23610i	0.736539	−	0.502164i	0.872539	+	0.488545i	$0.162472\pi$
$270$	0.226457	−	0.154396i	0.0137817	−	0.00939622i
$271$	24.7952	+	3.73728i	1.50620	+	0.227024i	0.849686	−	0.527288i	$-0.176791\pi$
$271$	24.7952	+	3.73728i	1.50620	+	0.227024i	0.656516	+	0.754312i	$0.272029\pi$
$272$	−15.4098	+	19.3233i	−0.934359	+	1.17165i
$273$	2.09655	+	2.09384i	0.126889	+	0.126725i
$274$	0.890210	+	1.11629i	0.0537796	+	0.0674375i
$275$	6.64042	+	11.5015i	0.400432	+	0.693569i
$276$	1.07505	−	1.86203i	0.0647102	−	0.112081i
$277$	−7.39918	+	1.11525i	−0.444574	+	0.0670087i	−0.367514	−	0.930018i	$-0.619791\pi$
$277$	−7.39918	+	1.11525i	−0.444574	+	0.0670087i	−0.0770592	+	0.997027i	$0.524553\pi$
$278$	−3.30834	+	3.06969i	−0.198421	+	0.184108i
$279$	−2.56500	−	1.23524i	−0.153563	−	0.0739518i
$280$	−1.14286	+	2.62408i	−0.0682989	+	0.156819i
$281$	0.115260	−	0.0555061i	0.00687581	−	0.00331121i	−0.430443	−	0.902618i	$-0.641643\pi$
$281$	0.115260	−	0.0555061i	0.00687581	−	0.00331121i	0.437318	+	0.899307i	$0.355928\pi$
$282$	0.659183	−	1.67957i	0.0392538	−	0.100017i
$283$	−0.866464	+	11.5622i	−0.0515059	+	0.687299i	0.910367	+	0.413802i	$0.135799\pi$
$283$	−0.866464	+	11.5622i	−0.0515059	+	0.687299i	−0.961873	+	0.273497i	$0.911820\pi$
$284$	10.4220	+	3.21477i	0.618433	+	0.190761i
$285$	−0.444282	−	5.92853i	−0.0263170	−	0.351176i
$286$	0.212687	−	0.931841i	0.0125764	−	0.0551009i
$287$	−7.51829	+	8.74783i	−0.443791	+	0.516368i
$288$	−0.593264	−	2.59926i	−0.0349584	−	0.153163i
$289$	26.7484	−	8.25079i	1.57344	−	0.485341i
$290$	0.695095	+	1.77107i	0.0408174	+	0.104001i
$291$	2.15761	+	2.00197i	0.126481	+	0.117357i
$292$	−2.28153	−	1.55552i	−0.133516	−	0.0910299i
$293$	−13.0790			−0.764085			−0.382042	−	0.924145i	$-0.624779\pi$
$293$	−13.0790			−0.764085			−0.382042	+	0.924145i	$0.624779\pi$
$294$	1.09479	−	1.18296i	0.0638495	−	0.0689919i
$295$	16.9914			0.989280
$296$	−1.83640	−	1.25204i	−0.106739	−	0.0727731i
$297$	−2.71703	−	2.52103i	−0.157658	−	0.146285i
$298$	1.69470	+	4.31804i	0.0981716	+	0.250137i
$299$	−1.18182	+	0.364542i	−0.0683462	+	0.0210820i
$300$	−1.55238	−	6.80143i	−0.0896268	−	0.392681i
$301$	−6.64800	+	24.8749i	−0.383185	+	1.43377i
$302$	0.109303	−	0.478888i	0.00628969	−	0.0275569i
$303$	−0.0447248	−	0.596812i	−0.00256938	−	0.0342859i
$304$	−17.5860	−	5.42457i	−1.00863	−	0.311120i
$305$	−0.670443	+	8.94644i	−0.0383895	+	0.512272i
$306$	−0.564268	+	1.43773i	−0.0322570	+	0.0821896i
$307$	−6.35216	+	3.05904i	−0.362537	+	0.174588i	−0.606280	−	0.795251i	$-0.707339\pi$
$307$	−6.35216	+	3.05904i	−0.362537	+	0.174588i	0.243743	+	0.969840i	$0.421625\pi$
$308$	18.7623	+	3.53746i	1.06908	+	0.201566i
$309$	2.85901	+	1.37682i	0.162643	+	0.0783248i
$310$	−0.571995	+	0.530734i	−0.0324871	+	0.0301436i
$311$	−24.3600	+	3.67167i	−1.38133	+	0.208202i	−0.797325	−	0.603550i	$-0.793752\pi$
$311$	−24.3600	+	3.67167i	−1.38133	+	0.208202i	−0.584002	+	0.811752i	$0.698514\pi$
$312$	−0.508914	+	0.881465i	−0.0288116	+	0.0499032i
$313$	−13.2094	−	22.8793i	−0.746638	−	1.29321i	−0.949426	−	0.313992i	$-0.898333\pi$
$313$	−13.2094	−	22.8793i	−0.746638	−	1.29321i	0.202788	−	0.979223i	$-0.435000\pi$
$314$	−0.929961	−	1.16613i	−0.0524808	−	0.0658088i
$315$	0.350585	−	3.12969i	0.0197532	−	0.176338i
$316$	−20.3269	+	25.4892i	−1.14348	+	1.43388i
$317$	−16.8687	−	2.54255i	−0.947443	−	0.142804i	−0.342896	−	0.939373i	$-0.611408\pi$
$317$	−16.8687	−	2.54255i	−0.947443	−	0.142804i	−0.604547	+	0.796569i	$0.706646\pi$
$318$	−0.767436	+	0.523229i	−0.0430357	+	0.0293412i
$319$	21.2584	−	14.4937i	1.19024	−	0.811494i
$320$	7.95132	+	1.19847i	0.444493	+	0.0669965i
$321$	10.9110	−	13.6820i	0.608993	−	0.763654i
$322$	0.222610	+	0.634868i	0.0124056	+	0.0353798i
$323$	20.8881	+	26.1929i	1.16225	+	1.45741i
$324$	0.973490	+	1.68613i	0.0540828	+	0.0936741i
$325$	−2.00644	+	3.47526i	−0.111297	+	0.192773i
$326$	0.773678	−	0.116613i	0.0428501	−	0.00645861i
$327$	5.25036	−	4.87162i	0.290346	−	0.269401i
$328$	−3.56986	−	1.71915i	−0.197112	−	0.0949243i
$329$	−9.69918	−	18.3231i	−0.534733	−	1.01018i
$330$	−0.915269	+	0.440770i	−0.0503839	+	0.0242636i
$331$	−4.35015	+	11.0840i	−0.239106	+	0.609232i	−0.999175	−	0.0406102i	$-0.987070\pi$
$331$	−4.35015	+	11.0840i	−0.239106	+	0.609232i	0.760069	+	0.649842i	$0.225165\pi$
$332$	−1.96048	+	26.1608i	−0.107595	+	1.43576i
$333$	2.33691	+	0.720840i	0.128062	+	0.0395018i
$334$	−0.0399193	−	0.532686i	−0.00218429	−	0.0291473i
$335$	0.900309	−	3.94451i	0.0491891	−	0.215512i
$336$	−8.62199	−	4.54973i	−0.470368	−	0.248208i
$337$	−6.35533	−	27.8445i	−0.346197	−	1.51679i	−0.785735	−	0.618563i	$-0.787715\pi$
$337$	−6.35533	−	27.8445i	−0.346197	−	1.51679i	0.439538	−	0.898224i	$-0.355142\pi$
$338$	−2.58442	+	0.797189i	−0.140574	+	0.0433614i
$339$	3.09197	+	7.87821i	0.167933	+	0.427886i
$340$	−11.3953	−	10.5733i	−0.617995	−	0.573416i
$341$	8.71852	+	5.94419i	0.472134	+	0.321896i
$342$	−1.15006			−0.0621882
$343$	−2.10926	−	18.3998i	−0.113890	−	0.993493i
$344$	−8.84459			−0.476869
$345$	1.08608	+	0.740477i	0.0584726	+	0.0398659i
$346$	−0.314617	−	0.291922i	−0.0169139	−	0.0156938i
$347$	3.45745	+	8.80945i	0.185606	+	0.472916i	0.993144	−	0.116900i	$-0.0372956\pi$
$347$	3.45745	+	8.80945i	0.185606	+	0.472916i	−0.807538	+	0.589816i	$0.799200\pi$
$348$	−12.9149	+	3.98372i	−0.692311	+	0.213550i
$349$	3.65715	+	16.0230i	0.195763	+	0.857692i	0.973424	+	0.229009i	$0.0735486\pi$
$349$	3.65715	+	16.0230i	0.195763	+	0.857692i	−0.777662	+	0.628683i	$0.783594\pi$
$350$	1.93059	+	1.01875i	0.103195	+	0.0544547i
$351$	0.249208	−	1.09185i	0.0133017	−	0.0582787i
$352$	0.738468	+	9.85418i	0.0393605	+	0.525229i
$353$	16.0177	+	4.94082i	0.852538	+	0.262973i	0.690072	−	0.723741i	$-0.257579\pi$
$353$	16.0177	+	4.94082i	0.852538	+	0.262973i	0.162466	+	0.986714i	$0.448055\pi$
$354$	0.245632	−	3.27772i	0.0130552	−	0.174209i
$355$	−2.43605	+	6.20695i	−0.129292	+	0.329431i
$356$	−10.7999	+	5.20095i	−0.572392	+	0.275650i
$357$	8.30259	+	15.6847i	0.439420	+	0.830125i
$358$	3.01820	+	1.45349i	0.159517	+	0.0768193i
$359$	−17.2997	+	16.0518i	−0.913045	+	0.847182i	−0.988693	−	0.149952i	$-0.952088\pi$
$359$	−17.2997	+	16.0518i	−0.913045	+	0.847182i	0.0756480	+	0.997135i	$0.475897\pi$
$360$	1.06971	−	0.161233i	0.0563787	−	0.00849773i
$361$	−2.97310	+	5.14956i	−0.156479	+	0.271030i
$362$	1.03421	+	1.79130i	0.0543569	+	0.0941488i
$363$	1.70702	+	2.14054i	0.0895956	+	0.112349i
$364$	1.90890	+	5.44404i	0.100054	+	0.285345i
$365$	1.05256	−	1.31987i	0.0550938	−	0.0690854i
$366$	1.71612	+	0.258663i	0.0897028	+	0.0135205i
$367$	20.6308	−	14.0659i	1.07692	−	0.734232i	0.111196	−	0.993799i	$-0.464532\pi$
$367$	20.6308	−	14.0659i	1.07692	−	0.734232i	0.965725	+	0.259566i	$0.0835796\pi$
$368$	3.36204	−	2.29220i	0.175258	−	0.119489i
$369$	4.31101	+	0.649780i	0.224422	+	0.0338262i
$370$	0.417914	−	0.524047i	0.0217263	−	0.0272439i
$371$	−1.18809	+	10.6062i	−0.0616827	+	0.550645i
$372$	−3.45596	−	4.33364i	−0.179183	−	0.224689i
$373$	3.91904	+	6.78798i	0.202920	+	0.351468i	0.949468	−	0.313864i	$-0.101623\pi$
$373$	3.91904	+	6.78798i	0.202920	+	0.351468i	−0.746548	+	0.665332i	$0.768290\pi$
$374$	2.86231	−	4.95766i	0.148006	−	0.256354i
$375$	10.1025	−	1.52271i	0.521692	−	0.0786324i
$376$	5.22044	−	4.84386i	0.269224	−	0.249803i
$377$	7.00433	+	3.37311i	0.360741	+	0.173724i
$378$	−0.598664	−	0.112873i	−0.0307919	−	0.00580555i
$379$	21.6880	−	10.4444i	1.11404	−	0.536492i	0.215992	−	0.976395i	$-0.430702\pi$
$379$	21.6880	−	10.4444i	1.11404	−	0.536492i	0.898045	+	0.439903i	$0.144987\pi$
$380$	4.22886	−	10.7750i	0.216936	−	0.552743i
$381$	0.563214	−	7.51556i	0.0288543	−	0.385034i
$382$	3.11286	+	0.960189i	0.159268	+	0.0491275i
$383$	2.22748	+	29.7236i	0.113819	+	1.51880i	0.703225	+	0.710968i	$0.251743\pi$
$383$	2.22748	+	29.7236i	0.113819	+	1.51880i	−0.589406	+	0.807837i	$0.700638\pi$
$384$	1.53266	−	6.71504i	0.0782134	−	0.342675i
$385$	−3.01382	+	11.2769i	−0.153599	+	0.574722i
$386$	0.855373	+	3.74763i	0.0435373	+	0.190750i
$387$	9.29946	−	2.86850i	0.472718	−	0.145814i
$388$	2.09362	+	5.33445i	0.106287	+	0.270816i
$389$	−22.0653	−	20.4736i	−1.11876	−	1.03805i	−0.998976	−	0.0452536i	$-0.985590\pi$
$389$	−22.0653	−	20.4736i	−1.11876	−	1.03805i	−0.119781	−	0.992800i	$-0.538219\pi$
$390$	−0.253616	−	0.172912i	−0.0128423	−	0.00875575i
$391$	−7.40736			−0.374606
$392$	5.91905	−	2.33188i	0.298957	−	0.117778i
$393$	11.0114			0.555453
$394$	−4.98568	−	3.39918i	−0.251175	−	0.171248i
$395$	−14.6109	−	13.5569i	−0.735153	−	0.682122i
$396$	−2.63645	−	6.71756i	−0.132487	−	0.337570i
$397$	5.79883	−	1.78870i	0.291035	−	0.0897724i	−0.145800	−	0.989314i	$-0.546576\pi$
$397$	5.79883	−	1.78870i	0.291035	−	0.0897724i	0.436835	+	0.899542i	$0.356099\pi$
$398$	−0.221714	−	0.971390i	−0.0111135	−	0.0486914i
$399$	−8.61319	+	10.0218i	−0.431199	+	0.501717i
$400$	2.93791	−	12.8718i	0.146895	−	0.643591i
$401$	−1.90623	−	25.4368i	−0.0951924	−	1.27025i	−0.816380	−	0.577515i	$-0.804023\pi$
$401$	−1.90623	−	25.4368i	−0.0951924	−	1.27025i	0.721188	−	0.692739i	$-0.243596\pi$
$402$	−0.747898	−	0.230696i	−0.0373018	−	0.0115061i
$403$	−0.238267	+	3.17945i	−0.0118689	+	0.158380i
$404$	0.425709	−	1.08469i	0.0211798	−	0.0539653i
$405$	−1.07243	+	0.516457i	−0.0532897	+	0.0256630i
$406$	1.68862	−	3.87720i	0.0838050	−	0.192422i
$407$	−8.16670	−	3.93288i	−0.404808	−	0.194945i
$408$	−4.46875	+	4.14640i	−0.221236	+	0.205277i
$409$	4.23974	−	0.639038i	0.209641	−	0.0315984i	−0.0433818	−	0.999059i	$-0.513813\pi$
$409$	4.23974	−	0.639038i	0.209641	−	0.0315984i	0.253023	+	0.967460i	$0.418575\pi$
$410$	0.597457	−	1.03483i	0.0295063	−	0.0511064i
$411$	−3.10038	−	5.37001i	−0.152930	−	0.264883i
$412$	3.85209	+	4.83036i	0.189779	+	0.237975i
$413$	−26.7229	−	26.6884i	−1.31495	−	1.31325i
$414$	0.158542	−	0.198805i	0.00779191	−	0.00977074i
$415$	−15.8594	−	2.39043i	−0.778510	−	0.117341i
$416$	−2.46702	+	1.68199i	−0.120956	+	0.0824663i
$417$	16.1943	−	11.0411i	0.793038	−	0.540684i
$418$	4.21505	+	0.635316i	0.206165	+	0.0310743i
$419$	4.11418	−	5.15902i	0.200991	−	0.252035i	−0.671113	−	0.741355i	$-0.734184\pi$
$419$	4.11418	−	5.15902i	0.200991	−	0.252035i	0.872104	+	0.489320i	$0.162755\pi$
$420$	3.25884	−	5.19385i	0.159015	−	0.253434i
$421$	1.74087	+	2.18298i	0.0848448	+	0.106392i	0.822442	−	0.568849i	$-0.192611\pi$
$421$	1.74087	+	2.18298i	0.0848448	+	0.106392i	−0.737597	+	0.675241i	$0.764040\pi$
$422$	−2.99448	−	5.18659i	−0.145769	−	0.252479i
$423$	−3.91795	+	6.78609i	−0.190497	+	0.329951i
$424$	−3.62513	+	0.546400i	−0.176052	+	0.0265355i
$425$	−17.6185	+	16.3476i	−0.854622	+	0.792973i
$426$	1.16213	+	0.559653i	0.0563055	+	0.0271153i
$427$	15.1066	−	13.0173i	0.731059	−	0.629949i
$428$	30.6978	−	14.7833i	1.48383	−	0.714577i
$429$	−1.51652	+	3.86403i	−0.0732184	+	0.186557i
$430$	0.199328	−	2.65985i	0.00961247	−	0.128269i
$431$	−25.5749	−	7.88882i	−1.23190	−	0.379991i	−0.390601	−	0.920560i	$-0.627733\pi$
$431$	−25.5749	−	7.88882i	−1.23190	−	0.379991i	−0.841300	+	0.540569i	$0.818209\pi$
$432$	0.275357	+	3.67439i	0.0132481	+	0.176784i
$433$	4.70415	−	20.6102i	0.226067	−	0.990464i	−0.726746	−	0.686906i	$-0.758968\pi$
$433$	4.70415	−	20.6102i	0.226067	−	0.990464i	0.952813	−	0.303558i	$-0.0981745\pi$
$434$	1.73321	+	0.0637314i	0.0831969	+	0.00305921i
$435$	−1.83864	−	8.05562i	−0.0881562	−	0.386237i
$436$	13.3254	−	4.11034i	0.638170	−	0.196849i
$437$	−2.01510	−	5.13439i	−0.0963952	−	0.245611i
$438$	−0.239394	−	0.222125i	−0.0114387	−	0.0106135i
$439$	12.4528	+	8.49015i	0.594338	+	0.405213i	0.822792	−	0.568342i	$-0.192415\pi$
$439$	12.4528	+	8.49015i	0.594338	+	0.405213i	−0.228455	+	0.973555i	$0.573367\pi$
$440$	−4.00963			−0.191152
$441$	−5.46718	+	4.37149i	−0.260342	+	0.208166i
$442$	1.72973			0.0822747
$443$	6.25764	+	4.26638i	0.297309	+	0.202702i	0.702782	−	0.711405i	$-0.251941\pi$
$443$	6.25764	+	4.26638i	0.297309	+	0.202702i	−0.405473	+	0.914107i	$0.632893\pi$
$444$	3.49039	+	3.23861i	0.165647	+	0.153698i
$445$	−2.67736	−	6.82180i	−0.126919	−	0.323384i
$446$	−1.55454	+	0.479511i	−0.0736095	+	0.0227055i
$447$	−4.48278	−	19.6403i	−0.212028	−	0.928956i
$448$	−10.6228	−	14.3740i	−0.501882	−	0.679107i
$449$	3.06450	−	13.4265i	0.144623	−	0.633634i	−0.849703	−	0.527261i	$-0.823219\pi$
$449$	3.06450	−	13.4265i	0.144623	−	0.633634i	0.994326	−	0.106373i	$-0.0339238\pi$
$450$	−0.0616567	−	0.822752i	−0.00290653	−	0.0387849i
$451$	−15.4412	−	4.76297i	−0.727097	−	0.224280i
$452$	−1.23138	+	16.4317i	−0.0579195	+	0.772882i
$453$	−0.779366	+	1.98579i	−0.0366178	+	0.0933006i
$454$	3.59937	−	1.73336i	0.168927	−	0.0813508i
$455$	−3.40619	+	0.915044i	−0.159685	+	0.0428979i
$456$	−4.08974	−	1.96952i	−0.191520	−	0.0922310i
$457$	−6.97792	+	6.47456i	−0.326413	+	0.302867i	−0.826308	−	0.563219i	$-0.809563\pi$
$457$	−6.97792	+	6.47456i	−0.326413	+	0.302867i	0.499894	+	0.866086i	$0.333372\pi$
$458$	−6.67177	+	1.00561i	−0.311751	+	0.0469890i
$459$	3.35380	−	5.80896i	0.156542	−	0.271139i
$460$	1.27964	+	2.21640i	0.0596635	+	0.103340i
$461$	3.84992	+	4.82765i	0.179309	+	0.224846i	0.863361	−	0.504587i	$-0.168355\pi$
$461$	3.84992	+	4.82765i	0.179309	+	0.224846i	−0.684052	+	0.729433i	$0.739784\pi$
$462$	2.13179	+	0.744399i	0.0991797	+	0.0346326i
$463$	5.91446	−	7.41650i	0.274868	−	0.344674i	−0.625167	−	0.780491i	$-0.714969\pi$
$463$	5.91446	−	7.41650i	0.274868	−	0.344674i	0.900035	+	0.435817i	$0.143541\pi$
$464$	−25.2923	−	3.81221i	−1.17417	−	0.176977i
$465$	2.79991	−	1.90895i	0.129843	−	0.0885252i
$466$	5.32096	−	3.62777i	0.246489	−	0.168053i
$467$	30.6778	+	4.62394i	1.41960	+	0.213970i	0.813568	−	0.581470i	$-0.197522\pi$
$467$	30.6778	+	4.62394i	1.41960	+	0.213970i	0.606032	+	0.795440i	$0.292760\pi$
$468$	1.35951	−	1.70477i	0.0628433	−	0.0788030i
$469$	−7.61157	+	4.78953i	−0.351470	+	0.221160i
$470$	1.33905	+	1.67912i	0.0617659	+	0.0774520i
$471$	3.23882	+	5.60980i	0.149237	+	0.258486i
$472$	6.48670	−	11.2353i	0.298574	−	0.517146i
$473$	−35.6677	+	5.37605i	−1.64000	+	0.247191i
$474$	−2.82640	+	2.62252i	−0.129821	+	0.120456i
$475$	−16.1242	−	7.76500i	−0.739829	−	0.356283i
$476$	1.31425	+	34.5274i	0.0602387	+	1.58256i
$477$	3.63435	−	1.75021i	0.166406	−	0.0801367i
$478$	0.257567	−	0.656269i	0.0117808	−	0.0300170i
$479$	−1.80930	+	24.1434i	−0.0826688	+	1.10314i	0.789440	+	0.613827i	$0.210371\pi$
$479$	−1.80930	+	24.1434i	−0.0826688	+	1.10314i	−0.872109	+	0.489311i	$0.837248\pi$
$480$	3.03250	+	0.935404i	0.138414	+	0.0426951i
$481$	−0.204675	−	2.73119i	−0.00933236	−	0.124532i
$482$	0.0805807	−	0.353047i	0.00367035	−	0.0160809i
$483$	−0.545043	−	2.87047i	−0.0248003	−	0.130611i
$484$	1.18616	+	5.19690i	0.0539163	+	0.236223i
$485$	−3.34782	+	1.03267i	−0.152017	+	0.0468909i
$486$	0.0841235	+	0.214343i	0.00381592	+	0.00972280i
$487$	−7.60487	−	7.05629i	−0.344610	−	0.319751i	0.488811	−	0.872389i	$-0.337431\pi$
$487$	−7.60487	−	7.05629i	−0.344610	−	0.319751i	−0.833421	+	0.552638i	$0.813621\pi$
$488$	5.65972	+	3.85873i	0.256204	+	0.174677i
$489$	−3.39797			−0.153661
$490$	0.567876	+	1.83260i	0.0256540	+	0.0827885i
$491$	−18.0610			−0.815083			−0.407541	−	0.913187i	$-0.633614\pi$
$491$	−18.0610			−0.815083			−0.407541	+	0.913187i	$0.633614\pi$
$492$	7.01333	+	4.78161i	0.316185	+	0.215571i
$493$	34.1325	+	31.6703i	1.53725	+	1.42636i
$494$	0.470555	+	1.19895i	0.0211713	+	0.0539435i
$495$	4.21584	−	1.30041i	0.189488	−	0.0584493i
$496$	−2.33426	−	10.2271i	−0.104812	−	0.459209i
$497$	13.5805	−	5.93555i	0.609168	−	0.266246i
$498$	−0.690391	+	3.02480i	−0.0309372	+	0.135545i
$499$	1.33757	+	17.8487i	0.0598780	+	0.799016i	0.943618	+	0.331037i	$0.107399\pi$
$499$	1.33757	+	17.8487i	0.0598780	+	0.799016i	−0.883740	+	0.467979i	$0.844982\pi$
$500$	19.0079	+	5.86315i	0.850057	+	0.262208i
$501$	−0.173366	+	2.31341i	−0.00774542	+	0.103355i
$502$	−0.915212	+	2.33192i	−0.0408479	+	0.104079i
$503$	24.1448	−	11.6275i	1.07656	−	0.518445i	0.190346	−	0.981717i	$-0.439039\pi$
$503$	24.1448	−	11.6275i	1.07656	−	0.518445i	0.886216	+	0.463273i	$0.153325\pi$
$504$	−1.93561	−	1.42662i	−0.0862191	−	0.0635466i
$505$	0.641836	+	0.309092i	0.0285613	+	0.0137544i
$506$	−0.690890	+	0.641052i	−0.0307138	+	0.0284982i
$507$	11.6146	−	1.75061i	0.515821	−	0.0777475i
$508$	7.33684	−	12.7078i	0.325520	−	0.563817i
$509$	−3.91971	−	6.78913i	−0.173738	−	0.300923i	0.765986	−	0.642857i	$-0.222251\pi$
$509$	−3.91971	−	6.78913i	−0.173738	−	0.300923i	−0.939724	+	0.341934i	$0.888918\pi$
$510$	−1.14624	−	1.43734i	−0.0507565	−	0.0636466i
$511$	−3.72852	+	0.422542i	−0.164940	+	0.0186922i
$512$	10.3009	−	12.9169i	0.455238	−	0.570851i
$513$	4.93883	+	0.744409i	0.218055	+	0.0328665i
$514$	2.79458	−	1.90531i	0.123263	−	0.0840396i
$515$	−3.12084	+	2.12775i	−0.137521	+	0.0937600i
$516$	18.7360	+	2.82400i	0.824808	+	0.124320i
$517$	18.1083	−	22.7071i	0.796402	−	0.998657i
$518$	−1.48038	+	0.167767i	−0.0650443	+	0.00737128i
$519$	1.16214	+	1.45728i	0.0510123	+	0.0639674i
$520$	−0.605767	−	1.04922i	−0.0265646	−	0.0460113i
$521$	13.6714	−	23.6795i	0.598953	−	1.03742i	−0.394023	−	0.919100i	$-0.628917\pi$
$521$	13.6714	−	23.6795i	0.598953	−	1.03742i	0.992976	−	0.118316i	$-0.0377496\pi$
$522$	−1.58054	+	0.238229i	−0.0691785	+	0.0104270i
$523$	−22.1090	+	20.5142i	−0.966760	+	0.897023i	−0.994724	−	0.102586i	$-0.967288\pi$
$523$	−22.1090	+	20.5142i	−0.966760	+	0.897023i	0.0279637	+	0.999609i	$0.491098\pi$
$524$	19.3159	+	9.30204i	0.843818	+	0.406362i
$525$	−7.63134	−	5.62457i	−0.333059	−	0.245477i
$526$	−2.37191	+	1.14225i	−0.103420	+	0.0498046i
$527$	−6.97660	+	17.7761i	−0.303905	+	0.774339i
$528$	1.02060	−	13.6190i	0.0444160	−	0.592690i
$529$	−20.8128	−	6.41991i	−0.904906	−	0.279126i
$530$	−0.0826214	−	1.10251i	−0.00358885	−	0.0478898i
$531$	−3.17644	+	13.9169i	−0.137846	+	0.603942i
$532$	−23.5750	+	10.3038i	−1.02211	+	0.446727i
$533$	−1.08647	−	4.76015i	−0.0470603	−	0.206185i
$534$	−1.35466	+	0.417857i	−0.0586219	+	0.0180825i
$535$	7.61018	+	19.3904i	0.329017	+	0.838321i
$536$	−2.26453	−	2.10118i	−0.0978129	−	0.0907571i
$537$	−12.0206	−	8.19549i	−0.518726	−	0.353662i
$538$	3.36655			0.145142
$539$	22.4525	−	13.0016i	0.967096	−	0.560020i
$540$	−2.31751			−0.0997299
$541$	−16.2272	−	11.0635i	−0.697664	−	0.475659i	0.161821	−	0.986820i	$-0.448263\pi$
$541$	−16.2272	−	11.0635i	−0.697664	−	0.475659i	−0.859485	+	0.511161i	$0.829216\pi$
$542$	4.23253	+	3.92721i	0.181803	+	0.168688i
$543$	−3.28185	−	8.36201i	−0.140837	−	0.358848i
$544$	−17.0887	+	5.27116i	−0.732671	+	0.225999i
$545$	1.89708	+	8.31166i	0.0812620	+	0.356032i
$546$	0.127276	+	0.670297i	0.00544689	+	0.0286861i
$547$	−8.66645	+	37.9702i	−0.370551	+	1.62349i	0.354683	+	0.934987i	$0.384589\pi$
$547$	−8.66645	+	37.9702i	−0.370551	+	1.62349i	−0.725234	+	0.688503i	$0.758268\pi$
$548$	−0.902197	−	12.0390i	−0.0385400	−	0.514280i
$549$	−7.20227	−	2.22161i	−0.307385	−	0.0948158i
$550$	−0.228528	+	3.04950i	−0.00974448	+	0.130031i
$551$	−12.6668	+	32.2744i	−0.539623	+	1.37494i
$552$	0.904252	−	0.435465i	0.0384875	−	0.0185346i
$553$	1.68512	+	44.2706i	0.0716586	+	1.88258i
$554$	−1.55235	−	0.747573i	−0.0659531	−	0.0317613i
$555$	−2.13389	+	1.97996i	−0.0905788	+	0.0840448i
$556$	37.7346	−	5.68758i	1.60030	−	0.241207i
$557$	−15.7975	+	27.3620i	−0.669360	+	1.15937i	0.308723	+	0.951152i	$0.400098\pi$
$557$	−15.7975	+	27.3620i	−0.669360	+	1.15937i	−0.978083	+	0.208214i	$0.933235\pi$
$558$	−0.327768	−	0.567711i	−0.0138755	−	0.0240331i
$559$	−6.79539	−	8.52115i	−0.287414	−	0.360406i
$560$	9.82147	−	6.18009i	0.415033	−	0.261157i
$561$	−15.5009	+	19.4375i	−0.654448	+	0.820652i
$562$	0.0291278	+	0.00439031i	0.00122868	+	0.000185194i
$563$	−10.1391	+	6.91273i	−0.427313	+	0.291337i	−0.757817	−	0.652468i	$-0.773734\pi$
$563$	−10.1391	+	6.91273i	−0.427313	+	0.291337i	0.330504	+	0.943805i	$0.392781\pi$
$564$	−12.6054	+	8.59420i	−0.530782	+	0.361881i
$565$	−9.96138	−	1.50144i	−0.419078	−	0.0631659i
$566$	−1.66457	+	2.08731i	−0.0699672	+	0.0877362i
$567$	2.49784	+	0.872223i	0.104900	+	0.0366299i
$568$	3.17424	+	3.98037i	0.133188	+	0.167013i
$569$	−15.6049	−	27.0285i	−0.654191	−	1.13309i	−0.982096	−	0.188381i	$-0.939676\pi$
$569$	−15.6049	−	27.0285i	−0.654191	−	1.13309i	0.327905	−	0.944711i	$-0.393657\pi$
$570$	0.684466	−	1.18553i	0.0286691	−	0.0496564i
$571$	28.8905	−	4.35454i	1.20903	−	0.182232i	0.486567	−	0.873643i	$-0.338249\pi$
$571$	28.8905	−	4.35454i	1.20903	−	0.182232i	0.722461	+	0.691412i	$0.243011\pi$
$572$	−5.92443	+	5.49707i	−0.247713	+	0.229844i
$573$	−12.7464	−	6.13832i	−0.532487	−	0.256432i
$574$	−2.56504	+	0.689075i	−0.107063	+	0.0287614i
$575$	3.56510	−	1.71686i	0.148675	−	0.0715980i
$576$	−2.46806	+	6.28851i	−0.102836	+	0.262021i
$577$	2.03753	−	27.1890i	0.0848236	−	1.13189i	−0.778637	−	0.627475i	$-0.784088\pi$
$577$	2.03753	−	27.1890i	0.0848236	−	1.13189i	0.863460	−	0.504417i	$-0.168293\pi$
$578$	6.15909	+	1.89983i	0.256185	+	0.0790225i
$579$	−1.24756	−	16.6475i	−0.0518468	−	0.691848i
$580$	3.57980	−	15.6841i	0.148643	−	0.651248i
$581$	21.1880	+	28.6699i	0.879025	+	1.18943i
$582$	0.150809	+	0.660737i	0.00625123	+	0.0273884i
$583$	−14.2870	+	4.40695i	−0.591707	+	0.182517i
$584$	−0.470913	−	1.19987i	−0.0194865	−	0.0496509i
$585$	0.977206	+	0.906715i	0.0404025	+	0.0374880i
$586$	−2.48828	−	1.69648i	−0.102790	−	0.0700811i
$587$	5.13774			0.212057			0.106029	−	0.994363i	$-0.466187\pi$
$587$	5.13774			0.212057			0.106029	+	0.994363i	$0.466187\pi$
$588$	−13.2832	+	3.04987i	−0.547791	+	0.125774i
$589$	−14.2194			−0.585898
$590$	3.23262	+	2.20396i	0.133085	+	0.0907358i
$591$	19.2103	+	17.8246i	0.790207	+	0.733205i
$592$	3.29213	+	8.38822i	0.135306	+	0.344754i
$593$	−7.13101	+	2.19963i	−0.292836	+	0.0903278i	−0.437692	−	0.899125i	$-0.644204\pi$
$593$	−7.13101	+	2.19963i	−0.292836	+	0.0903278i	0.144857	+	0.989453i	$0.453728\pi$
$594$	−0.189911	−	0.832053i	−0.00779213	−	0.0341395i
$595$	−21.1098	−	0.776221i	−0.865417	−	0.0318220i
$596$	8.72788	−	38.2394i	0.357508	−	1.56635i
$597$	0.323369	+	4.31506i	0.0132346	+	0.176603i
$598$	−0.272125	−	0.0839396i	−0.0111280	−	0.00343254i
$599$	1.83455	−	24.4803i	0.0749576	−	1.00024i	−0.825247	−	0.564772i	$-0.808964\pi$
$599$	1.83455	−	24.4803i	0.0749576	−	1.00024i	0.900204	−	0.435467i	$-0.143417\pi$
$600$	1.18973	−	3.03138i	0.0485705	−	0.123756i
$601$	0.240286	−	0.115716i	0.00980149	−	0.00472015i	−0.428977	−	0.903316i	$-0.641126\pi$
$601$	0.240286	−	0.115716i	0.00980149	−	0.00472015i	0.438778	+	0.898595i	$0.355411\pi$
$602$	−4.49131	+	3.87014i	−0.183052	+	0.157735i
$603$	3.06245	+	1.47480i	0.124713	+	0.0600585i
$604$	−3.04466	+	2.82503i	−0.123886	+	0.114949i
$605$	−3.22250	+	0.485714i	−0.131013	+	0.0197471i
$606$	0.0689037	−	0.119345i	0.00279902	−	0.00484804i
$607$	13.1877	+	22.8417i	0.535271	+	0.927117i	0.999150	+	0.0412183i	$0.0131239\pi$
$607$	13.1877	+	22.8417i	0.535271	+	0.927117i	−0.463879	+	0.885899i	$0.653543\pi$
$608$	−8.30249	−	10.4110i	−0.336711	−	0.422222i
$609$	−9.76126	+	15.5573i	−0.395546	+	0.630412i
$610$	−1.28800	+	1.61510i	−0.0521494	+	0.0653933i
$611$	8.67764	+	1.30794i	0.351060	+	0.0529138i
$612$	10.7903	−	7.35672i	0.436173	−	0.297378i
$613$	−15.7701	+	10.7519i	−0.636950	+	0.434265i	−0.838266	−	0.545261i	$-0.816430\pi$
$613$	−15.7701	+	10.7519i	−0.636950	+	0.434265i	0.201317	+	0.979526i	$0.435478\pi$
$614$	−1.60529	−	0.241958i	−0.0647841	−	0.00976462i
$615$	−3.23554	+	4.05724i	−0.130470	+	0.163604i
$616$	6.30605	+	6.29791i	0.254078	+	0.253750i
$617$	21.6921	+	27.2011i	0.873293	+	1.09507i	0.994735	+	0.102476i	$0.0326765\pi$
$617$	21.6921	+	27.2011i	0.873293	+	1.09507i	−0.121443	+	0.992598i	$0.538752\pi$
$618$	0.365337	+	0.632783i	0.0146960	+	0.0254543i
$619$	−2.80634	+	4.86072i	−0.112796	+	0.195369i	−0.916897	−	0.399125i	$-0.869314\pi$
$619$	−2.80634	+	4.86072i	−0.112796	+	0.195369i	0.804100	+	0.594494i	$0.202647\pi$
$620$	6.52412	−	0.983353i	0.262015	−	0.0394924i
$621$	−0.809525	+	0.751130i	−0.0324851	+	0.0301418i
$622$	−5.11074	−	2.46120i	−0.204922	−	0.0986852i
$623$	−6.50423	+	14.9342i	−0.260587	+	0.598325i
$624$	3.71794	−	1.79046i	0.148837	−	0.0716759i
$625$	2.10247	−	5.35700i	0.0840987	−	0.214280i
$626$	0.454597	−	6.06618i	0.0181694	−	0.242453i
$627$	−17.6899	−	5.45661i	−0.706467	−	0.217916i
$628$	0.942484	+	12.5766i	0.0376092	+	0.501860i
$629$	3.65020	−	15.9926i	0.145543	−	0.637665i
$630$	0.472652	−	0.549950i	0.0188309	−	0.0219105i
$631$	−0.166820	−	0.730886i	−0.00664100	−	0.0290961i	0.971499	−	0.237044i	$-0.0761786\pi$
$631$	−0.166820	−	0.730886i	−0.00664100	−	0.0290961i	−0.978140	+	0.207948i	$0.933321\pi$
$632$	−14.5421	+	4.48566i	−0.578455	+	0.178430i
$633$	9.50234	+	24.2116i	0.377684	+	0.962323i
$634$	−2.87948	−	2.67177i	−0.114359	−	0.106110i
$635$	7.41215	+	5.05352i	0.294142	+	0.200543i
$636$	7.85379			0.311423
$637$	6.79427	+	3.91098i	0.269199	+	0.154959i
$638$	5.92440			0.234549
$639$	−4.62841	−	3.15560i	−0.183097	−	0.124834i
$640$	6.00996	+	5.57642i	0.237564	+	0.220428i
$641$	−8.65988	−	22.0650i	−0.342045	−	0.871516i	−0.993604	−	0.112918i	$-0.963980\pi$
$641$	−8.65988	−	22.0650i	−0.342045	−	0.871516i	0.651560	−	0.758597i	$-0.274115\pi$
$642$	3.85051	−	1.18773i	0.151968	−	0.0468758i
$643$	−6.65591	−	29.1614i	−0.262483	−	1.15001i	−0.918548	−	0.395310i	$-0.870637\pi$
$643$	−6.65591	−	29.1614i	−0.262483	−	1.15001i	0.656065	−	0.754705i	$-0.272220\pi$
$644$	1.46877	−	5.49573i	0.0578777	−	0.216562i
$645$	−2.57766	+	11.2935i	−0.101495	+	0.444680i
$646$	0.576480	+	7.69259i	0.0226813	+	0.302661i
$647$	−17.6525	−	5.44507i	−0.693991	−	0.214068i	−0.0723605	−	0.997379i	$-0.523053\pi$
$647$	−17.6525	−	5.44507i	−0.693991	−	0.214068i	−0.621630	+	0.783311i	$0.713529\pi$
$648$	−0.0679171	+	0.906291i	−0.00266804	+	0.0356025i
$649$	19.3298	−	49.2516i	0.758761	−	1.93329i
$650$	−0.832502	+	0.400912i	−0.0326534	+	0.0157251i
$651$	−7.40187	−	1.39556i	−0.290102	−	0.0546963i
$652$	−5.96061	−	2.87048i	−0.233436	−	0.112417i
$653$	21.9331	−	20.3509i	0.858307	−	0.796392i	−0.122276	−	0.992496i	$-0.539019\pi$
$653$	21.9331	−	20.3509i	0.858307	−	0.796392i	0.980583	+	0.196104i	$0.0628290\pi$
$654$	1.63078	−	0.245800i	0.0637685	−	0.00961156i
$655$	−6.55351	+	11.3510i	−0.256067	+	0.443521i
$656$	8.03209	+	13.9120i	0.313600	+	0.543172i
$657$	0.884277	+	1.10885i	0.0344989	+	0.0432603i
$658$	0.531423	−	4.74405i	0.0207170	−	0.184942i
$659$	23.7799	−	29.8190i	0.926333	−	1.16159i	−0.0602266	−	0.998185i	$-0.519182\pi$
$659$	23.7799	−	29.8190i	0.926333	−	1.16159i	0.986560	−	0.163400i	$-0.0522463\pi$
$660$	8.49383	+	1.28024i	0.330622	+	0.0498333i
$661$	−40.2243	+	27.4244i	−1.56454	+	1.06669i	−0.600958	+	0.799280i	$0.705214\pi$
$661$	−40.2243	+	27.4244i	−1.56454	+	1.06669i	−0.963584	+	0.267406i	$0.913833\pi$
$662$	−2.26532	+	1.54447i	−0.0880443	+	0.0600276i
$663$	−7.42815	−	1.11961i	−0.288485	−	0.0434822i
$664$	−7.63517	+	9.57420i	−0.296302	+	0.371551i
$665$	−5.20468	−	14.8434i	−0.201829	−	0.575601i
$666$	0.351096	+	0.440260i	0.0136047	+	0.0170597i
$667$	−3.83293	−	6.63884i	−0.148412	−	0.257057i
$668$	−2.25840	+	3.91166i	−0.0873799	+	0.151346i
$669$	6.98619	−	1.05300i	0.270102	−	0.0407113i
$670$	0.682927	−	0.633663i	0.0263838	−	0.0244806i
$671$	25.1695	+	12.1210i	0.971658	+	0.467926i
$672$	−3.30007	−	6.23428i	−0.127303	−	0.240493i
$673$	9.84987	−	4.74345i	0.379684	−	0.182846i	−0.234300	−	0.972164i	$-0.575280\pi$
$673$	9.84987	−	4.74345i	0.379684	−	0.182846i	0.613985	+	0.789318i	$0.289566\pi$
$674$	2.40262	−	6.12177i	0.0925453	−	0.235802i
$675$	−0.267770	+	3.57314i	−0.0103065	+	0.137530i
$676$	21.8528	+	6.74068i	0.840491	+	0.259257i
$677$	0.480262	+	6.40865i	0.0184580	+	0.246304i	0.998799	+	0.0489941i	$0.0156016\pi$
$677$	0.480262	+	6.40865i	0.0184580	+	0.246304i	−0.980341	+	0.197310i	$0.936779\pi$
$678$	−0.433637	+	1.89989i	−0.0166537	+	0.0729648i
$679$	6.88721	+	3.63431i	0.264307	+	0.139472i
$680$	−1.61467	−	7.07432i	−0.0619197	−	0.271288i
$681$	−16.5791	+	5.11398i	−0.635313	+	0.195968i
$682$	0.887676	+	2.26176i	0.0339909	+	0.0866073i
$683$	24.0087	+	22.2769i	0.918669	+	0.852400i	0.989418	−	0.145094i	$-0.0463484\pi$
$683$	24.0087	+	22.2769i	0.918669	+	0.852400i	−0.0707487	+	0.997494i	$0.522539\pi$
$684$	8.03469	+	5.47796i	0.307214	+	0.209455i
$685$	7.38083			0.282007
$686$	1.98535	−	3.77414i	0.0758010	−	0.144098i
$687$	29.3022			1.11795
$688$	29.6279	+	20.2000i	1.12955	+	0.770116i
$689$	−3.31164	−	3.07275i	−0.126163	−	0.117063i
$690$	0.110579	+	0.281751i	0.00420968	+	0.0107261i
$691$	30.4917	−	9.40545i	1.15996	−	0.357800i	0.345725	−	0.938336i	$-0.387633\pi$
$691$	30.4917	−	9.40545i	1.15996	−	0.357800i	0.814235	+	0.580536i	$0.197157\pi$
$692$	0.807535	+	3.53804i	0.0306979	+	0.134496i
$693$	−8.67292	−	4.57661i	−0.329457	−	0.173851i
$694$	−0.484895	+	2.12446i	−0.0184064	+	0.0806435i
$695$	1.74346	+	23.2649i	0.0661333	+	0.882488i
$696$	−6.02856	−	1.85956i	−0.228512	−	0.0704866i
$697$	2.18535	−	29.1614i	0.0827759	−	1.10457i
$698$	−1.38258	+	3.52275i	−0.0523313	+	0.133338i
$699$	−25.1985	+	12.1350i	−0.953096	+	0.458987i
$700$	−8.63522	−	16.3131i	−0.326381	−	0.616578i
$701$	−7.81264	−	3.76237i	−0.295079	−	0.142103i	0.280487	−	0.959858i	$-0.409504\pi$
$701$	−7.81264	−	3.76237i	−0.295079	−	0.142103i	−0.575566	+	0.817755i	$0.695218\pi$
$702$	0.189036	−	0.175400i	0.00713470	−	0.00662004i
$703$	12.0782	−	1.82049i	0.455537	−	0.0686612i
$704$	12.5195	−	21.6844i	0.471846	−	0.817260i
$705$	−4.66358	−	8.07756i	−0.175641	−	0.304219i
$706$	2.40650	+	3.01765i	0.0905698	+	0.113571i
$707$	−0.523943	−	1.49425i	−0.0197049	−	0.0561969i
$708$	−17.3285	+	21.7292i	−0.651244	+	0.816635i
$709$	−11.0565	−	1.66651i	−0.415237	−	0.0625869i	−0.0618986	−	0.998082i	$-0.519716\pi$
$709$	−11.0565	−	1.66651i	−0.415237	−	0.0625869i	−0.353339	+	0.935496i	$0.614954\pi$
$710$	−1.26856	+	0.864891i	−0.0476083	+	0.0324588i
$711$	13.8352	−	9.43270i	0.518862	−	0.353754i
$712$	−5.53291	−	0.833952i	−0.207354	−	0.0312537i
$713$	1.96021	−	2.45803i	0.0734105	−	0.0920538i
$714$	−0.454904	+	4.06095i	−0.0170243	+	0.151977i
$715$	−3.08064	−	3.86300i	−0.115209	−	0.144468i
$716$	−14.1629	−	24.5308i	−0.529291	−	0.916760i
$717$	−1.53088	+	2.65157i	−0.0571719	+	0.0990246i
$718$	−5.37336	+	0.809903i	−0.200532	+	0.0302253i
$719$	−1.28925	+	1.19625i	−0.0480811	+	0.0446127i	−0.703847	−	0.710351i	$-0.748536\pi$
$719$	−1.28925	+	1.19625i	−0.0480811	+	0.0446127i	0.655766	+	0.754964i	$0.272346\pi$
$720$	−3.95159	−	1.90299i	−0.147267	−	0.0709201i
$721$	8.25029	+	1.55552i	0.307257	+	0.0579306i
$722$	−1.23358	+	0.594063i	−0.0459092	+	0.0221087i
$723$	−0.574566	+	1.46397i	−0.0213683	+	0.0544456i
$724$	1.30700	−	17.4408i	0.0485744	−	0.648180i
$725$	−23.7682	−	7.33150i	−0.882727	−	0.272285i
$726$	0.0471113	+	0.628656i	0.00174846	+	0.0233316i
$727$	−10.6997	+	46.8784i	−0.396830	+	1.73862i	0.242924	+	0.970045i	$0.421893\pi$
$727$	−10.6997	+	46.8784i	−0.396830	+	1.73862i	−0.639754	+	0.768580i	$0.720964\pi$
$728$	−0.695299	+	2.60161i	−0.0257695	+	0.0964221i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	0.371452	−	0.114578i	0.0137480	−	0.00424071i
$731$	−23.8485	−	60.7649i	−0.882067	−	2.24747i
$732$	−10.7573	−	9.98128i	−0.397600	−	0.368919i
$733$	−24.5597	−	16.7445i	−0.907135	−	0.618474i	0.0172850	−	0.999851i	$-0.494498\pi$
$733$	−24.5597	−	16.7445i	−0.907135	−	0.618474i	−0.924420	+	0.381377i	$0.875450\pi$
$734$	5.74950			0.212218
$735$	−1.25249	−	8.23751i	−0.0461987	−	0.303845i
$736$	2.94424			0.108526
$737$	−10.4094	−	7.09699i	−0.383434	−	0.261421i
$738$	0.735886	+	0.682803i	0.0270883	+	0.0251343i
$739$	−8.03459	−	20.4718i	−0.295557	−	0.753067i	−0.999100	−	0.0424145i	$-0.986495\pi$
$739$	−8.03459	−	20.4718i	−0.295557	−	0.753067i	0.703543	−	0.710653i	$-0.251600\pi$
$740$	−5.41581	+	1.67056i	−0.199089	+	0.0614109i
$741$	−1.24470	−	5.45338i	−0.0457251	−	0.200335i
$742$	−1.60176	+	1.86372i	−0.0588026	+	0.0684191i
$743$	11.3345	−	49.6595i	0.415821	−	1.82183i	−0.139535	−	0.990217i	$-0.544561\pi$
$743$	11.3345	−	49.6595i	0.415821	−	1.82183i	0.555356	−	0.831613i	$-0.312582\pi$
$744$	−0.193356	−	2.58015i	−0.00708876	−	0.0945930i
$745$	22.9140	+	7.06804i	0.839504	+	0.258953i
$746$	−0.134873	+	1.79975i	−0.00493804	+	0.0658936i
$747$	4.92270	−	12.5428i	0.180112	−	0.458919i
$748$	−43.6112	+	21.0021i	−1.59459	+	0.767912i
$749$	18.4878	−	42.4492i	0.675528	−	1.55106i
$750$	2.11952	+	1.02070i	0.0773938	+	0.0372709i
$751$	−14.9242	+	13.8476i	−0.544592	+	0.505308i	−0.903803	−	0.427949i	$-0.859236\pi$
$751$	−14.9242	+	13.8476i	−0.544592	+	0.505308i	0.359211	+	0.933256i	$0.383046\pi$
$752$	−28.5504	+	4.30328i	−1.04113	+	0.156924i
$753$	5.43969	−	9.42183i	0.198234	−	0.343350i
$754$	0.895046	+	1.55027i	0.0325957	+	0.0564573i
$755$	−1.58319	−	1.98526i	−0.0576182	−	0.0722509i
$756$	3.64482	+	3.64011i	0.132561	+	0.132390i
$757$	−7.20271	+	9.03191i	−0.261787	+	0.328270i	−0.895302	−	0.445460i	$-0.853040\pi$
$757$	−7.20271	+	9.03191i	−0.261787	+	0.328270i	0.633515	+	0.773731i	$0.281612\pi$
$758$	5.48088	+	0.826110i	0.199075	+	0.0300057i
$759$	3.38190	−	2.30574i	0.122755	−	0.0836931i
$760$	4.46429	−	3.04370i	0.161937	−	0.110407i
$761$	25.3941	+	3.82754i	0.920535	+	0.138748i	0.592180	−	0.805806i	$-0.298268\pi$
$761$	25.3941	+	3.82754i	0.920535	+	0.138748i	0.328355	+	0.944554i	$0.393506\pi$
$762$	1.08200	−	1.35678i	0.0391966	−	0.0491510i
$763$	10.0715	−	16.0517i	0.364613	−	0.581111i
$764$	−17.1738	−	21.5353i	−0.621328	−	0.779120i
$765$	3.99207	+	6.91447i	0.144334	+	0.249993i
$766$	−3.43168	+	5.94384i	−0.123991	+	0.214760i
$767$	15.8082	−	2.38270i	0.570801	−	0.0860344i
$768$	−8.74165	+	8.11106i	−0.315437	+	0.292683i
$769$	−33.0825	−	15.9317i	−1.19299	−	0.574512i	−0.271317	−	0.962490i	$-0.587459\pi$
$769$	−33.0825	−	15.9317i	−1.19299	−	0.574512i	−0.921668	+	0.387978i	$0.873174\pi$
$770$	−2.03610	+	1.75450i	−0.0733760	+	0.0632277i
$771$	−13.2343	+	6.37330i	−0.476622	+	0.229529i
$772$	11.8748	−	30.2565i	0.427383	−	1.08895i
$773$	−3.15843	+	42.1463i	−0.113601	+	1.51590i	0.591219	+	0.806511i	$0.298647\pi$
$773$	−3.15843	+	42.1463i	−0.113601	+	1.51590i	−0.704819	+	0.709387i	$0.748972\pi$
$774$	2.14130	+	0.660502i	0.0769673	+	0.0237413i
$775$	−0.762323	−	10.1725i	−0.0273835	−	0.365407i
$776$	−0.595240	+	2.60792i	−0.0213679	+	0.0936188i
$777$	6.46596	+	0.237758i	0.231965	+	0.00852951i
$778$	−1.54229	−	6.75720i	−0.0552937	−	0.242257i
$779$	20.8077	−	6.41831i	0.745512	−	0.229960i
$780$	0.948225	+	2.41604i	0.0339519	+	0.0865081i
$781$	15.2202	+	14.1223i	0.544622	+	0.505336i
$782$	−1.40925	−	0.960810i	−0.0503947	−	0.0343585i
$783$	6.94170			0.248076
$784$	−25.1536	−	5.70696i	−0.898341	−	0.203820i
$785$	−7.71041			−0.275196
$786$	2.09492	+	1.42829i	0.0747234	+	0.0509455i
$787$	−31.4022	−	29.1370i	−1.11937	−	1.03862i	−0.998946	−	0.0458987i	$-0.985385\pi$
$787$	−31.4022	−	29.1370i	−1.11937	−	1.03862i	−0.120422	−	0.992723i	$-0.538425\pi$
$788$	18.6406	+	47.4955i	0.664044	+	1.69196i
$789$	10.9253	−	3.37001i	0.388951	−	0.119976i
$790$	−1.02125	−	4.47438i	−0.0363344	−	0.159191i
$791$	13.3082	+	18.0077i	0.473186	+	0.640279i
$792$	0.749573	−	3.28410i	0.0266349	−	0.116695i
$793$	0.630800	+	8.41744i	0.0224004	+	0.298912i
$794$	1.33524	+	0.411867i	0.0473859	+	0.0146166i
$795$	−0.358818	+	4.78809i	−0.0127259	+	0.169816i
$796$	−3.07796	+	7.84250i	−0.109095	+	0.277970i
$797$	43.8793	−	21.1312i	1.55429	−	0.748504i	0.557620	−	0.830097i	$-0.311715\pi$
$797$	43.8793	−	21.1312i	1.55429	−	0.748504i	0.996666	+	0.0815923i	$0.0260005\pi$
$798$	−2.93859	+	0.789427i	−0.104025	+	0.0279454i
$799$	47.3551	+	22.8050i	1.67530	+	0.806783i
$800$	7.00289	−	6.49774i	0.247590	−	0.229730i
$801$	6.08793	−	0.917608i	0.215106	−	0.0324221i
$802$	2.93675	−	5.08661i	0.103700	−	0.179614i
$803$	−2.62838	−	4.55249i	−0.0927535	−	0.160654i
$804$	4.12620	+	5.17410i	0.145520	+	0.182476i
$805$	3.28338	+	1.14653i	0.115724	+	0.0404097i
$806$	−0.457738	+	0.573985i	−0.0161231	+	0.0202178i
$807$	−14.4573	−	2.17909i	−0.508923	−	0.0767078i
$808$	0.449410	−	0.306403i	0.0158102	−	0.0107792i
$809$	−14.1052	+	9.61676i	−0.495912	+	0.338107i	−0.785311	−	0.619101i	$-0.787497\pi$
$809$	−14.1052	+	9.61676i	−0.495912	+	0.338107i	0.289399	+	0.957209i	$0.406545\pi$
$810$	−0.271020	−	0.0408497i	−0.00952268	−	0.00143531i
$811$	−0.102516	+	0.128551i	−0.00359983	+	0.00451405i	−0.783628	−	0.621230i	$-0.786633\pi$
$811$	−0.102516	+	0.128551i	−0.00359983	+	0.00451405i	0.780028	+	0.625744i	$0.215205\pi$
$812$	−30.2651	+	19.0441i	−1.06210	+	0.668316i
$813$	−15.6342	−	19.6047i	−0.548315	−	0.687565i
$814$	−1.04358	−	1.80753i	−0.0365775	−	0.0633540i
$815$	2.02232	−	3.50276i	0.0708388	−	0.122696i
$816$	24.4394	−	3.68365i	0.855551	−	0.128954i
$817$	35.6312	−	33.0610i	1.24658	−	1.15666i
$818$	0.889499	+	0.428360i	0.0311006	+	0.0149773i
$819$	−0.112704	−	2.96091i	−0.00393821	−	0.103463i
$820$	−9.10310	+	4.38382i	−0.317894	+	0.153090i
$821$	−6.70480	+	17.0836i	−0.233999	+	0.596220i	−0.998848	−	0.0479898i	$-0.984719\pi$
$821$	−6.70480	+	17.0836i	−0.233999	+	0.596220i	0.764849	+	0.644210i	$0.222814\pi$
$822$	0.106699	−	1.42379i	0.00372154	−	0.0496605i
$823$	−7.00189	−	2.15980i	−0.244070	−	0.0752858i	0.170306	−	0.985391i	$-0.445524\pi$
$823$	−7.00189	−	2.15980i	−0.244070	−	0.0752858i	−0.414377	+	0.910105i	$0.636000\pi$
$824$	0.215519	+	2.87589i	0.00750794	+	0.100187i
$825$	2.95526	−	12.9479i	0.102889	−	0.450787i
$826$	−1.62227	−	8.54371i	−0.0564461	−	0.297274i
$827$	3.21753	+	14.0969i	0.111885	+	0.490198i	0.999558	+	0.0297249i	$0.00946314\pi$
$827$	3.21753	+	14.0969i	0.111885	+	0.490198i	−0.887674	+	0.460473i	$0.847680\pi$
$828$	−2.05457	+	0.633751i	−0.0714012	+	0.0220244i
$829$	0.0303865	+	0.0774234i	0.00105537	+	0.00268903i	0.931400	−	0.363996i	$-0.118588\pi$
$829$	0.0303865	+	0.0774234i	0.00105537	+	0.00268903i	−0.930345	+	0.366685i	$0.880493\pi$
$830$	−2.70720	−	2.51191i	−0.0939681	−	0.0871897i
$831$	6.18254	+	4.21519i	0.214470	+	0.146223i
$832$	7.56567			0.262292
$833$	31.9808	+	34.3779i	1.10807	+	1.19112i
$834$	4.51310			0.156276
$835$	−2.28157	−	1.55555i	−0.0789572	−	0.0538321i
$836$	−26.4215	−	24.5156i	−0.913808	−	0.847890i
$837$	1.04010	+	2.65014i	0.0359512	+	0.0916022i
$838$	1.45190	−	0.447852i	0.0501551	−	0.0154708i
$839$	9.68047	+	42.4129i	0.334207	+	1.46426i	0.810899	+	0.585186i	$0.198979\pi$
$839$	9.68047	+	42.4129i	0.334207	+	1.46426i	−0.476692	+	0.879070i	$0.658164\pi$
$840$	2.62261	−	1.14625i	0.0904885	−	0.0395493i
$841$	−4.26955	+	18.7061i	−0.147226	+	0.645038i
$842$	0.0480454	+	0.641121i	0.00165575	+	0.0220945i
$843$	−0.122245	−	0.0377076i	−0.00421034	−	0.00129872i
$844$	−3.78433	+	50.4984i	−0.130262	+	1.73823i
$845$	−5.10787	+	13.0147i	−0.175716	+	0.447718i
$846$	−1.62561	+	0.782855i	−0.0558898	+	0.0269151i
$847$	5.83103	+	4.29768i	0.200357	+	0.147670i
$848$	13.3915	+	6.44900i	0.459865	+	0.221459i
$849$	8.49942	−	7.88631i	0.291699	−	0.270658i
$850$	−5.47236	+	0.824825i	−0.187700	+	0.0282913i
$851$	−1.35034	+	2.33886i	−0.0462891	+	0.0801750i
$852$	−5.45329	−	9.44537i	−0.186826	−	0.323593i
$853$	15.0264	+	18.8425i	0.514493	+	0.645154i	0.969430	−	0.245370i	$-0.0789094\pi$
$853$	15.0264	+	18.8425i	0.514493	+	0.645154i	−0.454936	+	0.890524i	$0.650338\pi$
$854$	4.56250	−	0.517054i	0.156125	−	0.0176932i
$855$	−3.70674	+	4.64811i	−0.126768	+	0.158962i
$856$	15.7268	+	2.37044i	0.537533	+	0.0810200i
$857$	−26.9888	+	18.4006i	−0.921918	+	0.628553i	−0.928463	−	0.371425i	$-0.878869\pi$
$857$	−26.9888	+	18.4006i	−0.921918	+	0.628553i	0.00654460	+	0.999979i	$0.497917\pi$
$858$	−0.789723	+	0.538424i	−0.0269607	+	0.0183815i
$859$	−1.16051	−	0.174919i	−0.0395961	−	0.00596816i	0.129214	−	0.991617i	$-0.458754\pi$
$859$	−1.16051	−	0.174919i	−0.0395961	−	0.00596816i	−0.168810	+	0.985649i	$0.553993\pi$
$860$	−14.0620	+	17.6331i	−0.479509	+	0.601285i
$861$	11.4613	−	1.29888i	0.390601	−	0.0442657i
$862$	−3.84237	−	4.81818i	−0.130872	−	0.164108i
$863$	7.72452	+	13.3793i	0.262946	+	0.455435i	0.967023	−	0.254688i	$-0.0819726\pi$
$863$	7.72452	+	13.3793i	0.262946	+	0.455435i	−0.704078	+	0.710123i	$0.748639\pi$
$864$	−1.33305	+	2.30891i	−0.0453513	+	0.0785508i
$865$	−2.19388	+	0.330673i	−0.0745940	+	0.0112432i
$866$	3.56832	−	3.31092i	0.121256	−	0.112510i
$867$	−25.2199	−	12.1453i	−0.856514	−	0.412475i
$868$	−11.8052	−	8.70087i	−0.400695	−	0.295327i
$869$	−55.9178	+	26.9286i	−1.89688	+	0.913490i
$870$	0.695095	−	1.77107i	0.0235659	−	0.0600450i
$871$	0.284476	−	3.79607i	0.00963911	−	0.128625i
$872$	6.22017	+	1.91867i	0.210641	+	0.0649743i
$873$	−0.219955	−	2.93509i	−0.00744434	−	0.0993378i
$874$	0.282610	−	1.23820i	0.00955943	−	0.0418826i
$875$	24.7683	−	10.8253i	0.837322	−	0.365964i
$876$	0.614457	+	2.69211i	0.0207606	+	0.0909580i
$877$	−8.31700	+	2.56546i	−0.280845	+	0.0866293i	−0.431978	−	0.901884i	$-0.642184\pi$
$877$	−8.31700	+	2.56546i	−0.280845	+	0.0866293i	0.151133	+	0.988513i	$0.451708\pi$
$878$	1.26788	+	3.23050i	0.0427888	+	0.109024i
$879$	9.58761	+	8.89600i	0.323382	+	0.300055i
$880$	13.4316	+	9.15749i	0.452778	+	0.308699i
$881$	−11.8364			−0.398778			−0.199389	−	0.979920i	$-0.563896\pi$
$881$	−11.8364			−0.398778			−0.199389	+	0.979920i	$0.563896\pi$
$882$	−1.60716	+	0.122528i	−0.0541158	+	0.00412572i
$883$	9.93404			0.334307			0.167153	−	0.985931i	$-0.446542\pi$
$883$	9.93404			0.334307			0.167153	+	0.985931i	$0.446542\pi$
$884$	−12.0844	−	8.23901i	−0.406443	−	0.277108i
$885$	−12.4556	−	11.5571i	−0.418691	−	0.388488i
$886$	0.637121	+	1.62336i	0.0214045	+	0.0545378i
$887$	−38.9760	+	12.0225i	−1.30868	+	0.403676i	−0.869149	−	0.494550i	$-0.835333\pi$
$887$	−38.9760	+	12.0225i	−1.30868	+	0.403676i	−0.439535	+	0.898225i	$0.644857\pi$
$888$	0.494575	+	2.16688i	0.0165969	+	0.0727156i
$889$	−3.71974	−	19.5900i	−0.124756	−	0.657029i
$890$	0.375490	−	1.64513i	0.0125864	−	0.0551448i
$891$	0.276984	+	3.69610i	0.00927932	+	0.123824i
$892$	13.1445	+	4.05454i	0.440110	+	0.135756i
$893$	−2.92474	+	39.0279i	−0.0978726	+	1.30602i
$894$	1.69470	−	4.31804i	0.0566794	−	0.144417i
$895$	15.6024	−	7.51370i	0.521529	−	0.251155i
$896$	−0.693148	−	18.2100i	−0.0231564	−	0.608354i
$897$	1.11428	+	0.536611i	0.0372049	+	0.0179169i
$898$	2.32457	−	2.15689i	0.0775720	−	0.0719763i
$899$	−19.5418	+	2.94546i	−0.651757	+	0.0982365i
$900$	−3.48817	+	6.04169i	−0.116272	+	0.201390i
$901$	−13.5287	−	23.4323i	−0.450705	−	0.780645i
$902$	−2.31988	−	2.90903i	−0.0772434	−	0.0968602i
$903$	21.7926	−	13.7128i	0.725212	−	0.456334i
$904$	−4.79568	+	6.01359i	−0.159502	+	0.200009i
$905$	10.5731	+	1.59364i	0.351462	+	0.0529744i
$906$	−0.405852	+	0.276705i	−0.0134835	+	0.00919291i
$907$	19.4586	−	13.2666i	0.646112	−	0.440512i	−0.195419	−	0.980720i	$-0.562607\pi$
$907$	19.4586	−	13.2666i	0.646112	−	0.440512i	0.841532	+	0.540208i	$0.181654\pi$
$908$	−33.4027	−	5.03464i	−1.10851	−	0.167080i
$909$	−0.373149	+	0.467914i	−0.0123766	+	0.0155197i
$910$	−0.766718	−	0.267731i	−0.0254165	−	0.00887519i
$911$	24.8640	+	31.1785i	0.823781	+	1.03299i	0.998827	+	0.0484288i	$0.0154214\pi$
$911$	24.8640	+	31.1785i	0.823781	+	1.03299i	−0.175045	+	0.984560i	$0.556007\pi$
$912$	9.20181	+	15.9380i	0.304703	+	0.527760i
$913$	−24.9709	+	43.2509i	−0.826417	+	1.43140i
$914$	−2.16737	+	0.326678i	−0.0716901	+	0.0108055i
$915$	6.57659	−	6.10219i	0.217415	−	0.201732i
$916$	51.4010	+	24.7534i	1.69834	+	0.817876i
$917$	28.1359	−	7.55847i	0.929129	−	0.249603i
$918$	1.39154	−	0.670131i	0.0459277	−	0.0221176i
$919$	4.98770	−	12.7085i	0.164529	−	0.419213i	−0.824703	−	0.565565i	$-0.808658\pi$
$919$	4.98770	−	12.7085i	0.164529	−	0.419213i	0.989233	+	0.146352i	$0.0467532\pi$
$920$	−0.0892762	+	1.19131i	−0.00294335	+	0.0392763i
$921$	6.73713	+	2.07813i	0.221996	+	0.0684767i
$922$	0.106252	+	1.41783i	0.00349922	+	0.0466938i
$923$	−1.39601	+	6.11632i	−0.0459502	+	0.201321i
$924$	−11.3476	−	15.3547i	−0.373309	−	0.505133i
$925$	1.94991	+	8.54311i	0.0641126	+	0.280896i
$926$	2.08722	−	0.643823i	0.0685904	−	0.0211573i
$927$	−1.15932	−	2.95390i	−0.0380771	−	0.0970189i
$928$	−13.5668	−	12.5882i	−0.445352	−	0.413226i
$929$	0.681947	+	0.464944i	0.0223740	+	0.0152543i	0.574455	−	0.818536i	$-0.305214\pi$
$929$	0.681947	+	0.464944i	0.0223740	+	0.0152543i	−0.552081	+	0.833790i	$0.686166\pi$
$930$	0.780292			0.0255868
$931$	−15.1289	+	31.5195i	−0.495829	+	1.03301i
$932$	−54.4536			−1.78369
$933$	20.3545	+	13.8775i	0.666376	+	0.454328i
$934$	5.23668	+	4.85893i	0.171349	+	0.158989i
$935$	−10.8115	−	27.5473i	−0.353574	−	0.900892i
$936$	0.972609	−	0.300010i	0.0317907	−	0.00980614i
$937$	4.41379	+	19.3381i	0.144192	+	0.631748i	0.994435	+	0.105356i	$0.0335983\pi$
$937$	4.41379	+	19.3381i	0.144192	+	0.631748i	−0.850242	+	0.526392i	$0.823545\pi$
$938$	−2.06935	−	0.0760914i	−0.0675667	−	0.00248447i
$939$	−5.87872	+	25.7564i	−0.191845	+	0.840527i
$940$	−1.35708	−	18.1090i	−0.0442632	−	0.590651i
$941$	28.1377	+	8.67935i	0.917264	+	0.282939i	0.717219	−	0.696848i	$-0.245415\pi$
$941$	28.1377	+	8.67935i	0.917264	+	0.282939i	0.200046	+	0.979787i	$0.435891\pi$
$942$	−0.111463	+	1.48737i	−0.00363166	+	0.0484612i
$943$	−1.75894	+	4.48171i	−0.0572790	+	0.145944i
$944$	−47.3893	+	22.8215i	−1.54239	+	0.742777i
$945$	−2.38573	+	2.05577i	−0.0776078	+	0.0668742i
$946$	−7.48311	−	3.60368i	−0.243297	−	0.117166i
$947$	1.46127	−	1.35586i	0.0474849	−	0.0440595i	−0.656073	−	0.754697i	$-0.727784\pi$
$947$	1.46127	−	1.35586i	0.0474849	−	0.0440595i	0.703558	+	0.710638i	$0.251593\pi$
$948$	32.2377	−	4.85905i	1.04703	−	0.157815i
$949$	0.794181	−	1.37556i	0.0257802	−	0.0446526i
$950$	−2.06043	−	3.56876i	−0.0668491	−	0.115786i
$951$	10.6363	+	13.3375i	0.344905	+	0.432498i
$952$	−8.57219	+	13.6621i	−0.277826	+	0.442792i
$953$	9.00489	−	11.2918i	0.291697	−	0.365777i	−0.614291	−	0.789079i	$-0.710558\pi$
$953$	9.00489	−	11.2918i	0.291697	−	0.365777i	0.905988	+	0.423303i	$0.139129\pi$
$954$	0.918456	+	0.138435i	0.0297361	+	0.00448200i
$955$	13.9137	−	9.48620i	0.450237	−	0.306966i
$956$	−4.92537	+	3.35806i	−0.159298	+	0.108608i
$957$	−25.4418	−	3.83473i	−0.822415	−	0.123959i
$958$	−3.47586	+	4.35859i	−0.112300	+	0.140820i
$959$	−11.6080	−	11.5931i	−0.374843	−	0.374359i
$960$	−5.01357	−	6.28681i	−0.161812	−	0.202906i
$961$	11.4475	+	19.8276i	0.369274	+	0.639600i
$962$	0.315324	−	0.546157i	0.0101665	−	0.0176088i
$963$	−17.3044	+	2.60823i	−0.557628	+	0.0840489i
$964$	−2.24459	+	2.08268i	−0.0722934	+	0.0670785i
$965$	17.9034	+	8.62184i	0.576332	+	0.277547i
$966$	0.268635	−	0.616805i	0.00864320	−	0.0198454i
$967$	−28.9134	+	13.9240i	−0.929793	+	0.447765i	−0.836558	−	0.547879i	$-0.815435\pi$
$967$	−28.9134	+	13.9240i	−0.929793	+	0.447765i	−0.0932360	+	0.995644i	$0.529721\pi$
$968$	−0.909060	+	2.31625i	−0.0292183	+	0.0744470i
$969$	2.50360	−	33.4083i	0.0804273	−	1.07323i
$970$	−0.770870	−	0.237782i	−0.0247511	−	0.00763471i
$971$	−0.364565	−	4.86478i	−0.0116994	−	0.156118i	−0.999994	−	0.00355830i	$-0.998867\pi$
$971$	−0.364565	−	4.86478i	−0.0116994	−	0.156118i	0.988294	−	0.152560i	$-0.0487517\pi$
$972$	0.433244	−	1.89817i	0.0138963	−	0.0608837i
$973$	33.8001	−	39.3278i	1.08358	−	1.26079i
$974$	−0.531554	−	2.32889i	−0.0170321	−	0.0746224i
$975$	3.83460	−	1.18282i	0.122806	−	0.0378805i
$976$	−10.1462	−	25.8522i	−0.324773	−	0.827509i
$977$	13.4991	+	12.5253i	0.431875	+	0.400721i	0.865930	−	0.500165i	$-0.166727\pi$
$977$	13.4991	+	12.5253i	0.431875	+	0.400721i	−0.434055	+	0.900886i	$0.642918\pi$
$978$	−0.646463	−	0.440751i	−0.0206716	−	0.0140937i
$979$	−22.8195			−0.729316
$980$	4.76167	−	15.5080i	0.152106	−	0.495386i
$981$	−7.16233			−0.228676
$982$	−3.43611	−	2.34270i	−0.109651	−	0.0747585i
$983$	−24.0688	−	22.3325i	−0.767674	−	0.712297i	0.195639	−	0.980676i	$-0.437322\pi$
$983$	−24.0688	−	22.3325i	−0.767674	−	0.712297i	−0.963314	+	0.268378i	$0.913512\pi$
$984$	1.44757	+	3.68835i	0.0461468	+	0.117580i
$985$	−29.8074	+	9.19438i	−0.949744	+	0.292957i
$986$	2.38574	+	10.4526i	0.0759775	+	0.332879i
$987$	−5.35286	+	20.0289i	−0.170383	+	0.637526i
$988$	2.42340	−	10.6176i	0.0770987	−	0.337791i
$989$	0.803129	+	10.7170i	0.0255380	+	0.340781i
$990$	0.970740	+	0.299434i	0.0308521	+	0.00951663i
$991$	2.77132	−	36.9807i	0.0880339	−	1.17473i	−0.761848	−	0.647756i	$-0.775707\pi$
$991$	2.77132	−	36.9807i	0.0880339	−	1.17473i	0.849881	−	0.526974i	$-0.176673\pi$
$992$	2.77302	−	7.06554i	0.0880435	−	0.224331i
$993$	10.7279	−	5.16630i	0.340440	−	0.163947i
$994$	3.35359	+	0.632290i	0.106369	+	0.0200550i
$995$	−4.64059	−	2.23479i	−0.147117	−	0.0708476i
$996$	19.2310	−	17.8437i	0.609357	−	0.565401i
$997$	34.7619	−	5.23952i	1.10092	−	0.165937i	0.426647	−	0.904418i	$-0.359695\pi$
$997$	34.7619	−	5.23952i	1.10092	−	0.165937i	0.674274	+	0.738481i	$0.264457\pi$
$998$	−2.06068	+	3.56921i	−0.0652297	+	0.112981i
$999$	−1.22278	−	2.11791i	−0.0386870	−	0.0670078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.m.b.4.3	✓	60
3.2	odd	2		441.2.bb.e.298.3		60
49.24	odd	42		7203.2.a.m.1.16		30
49.25	even	21		7203.2.a.n.1.16		30
49.37	even	21	inner	147.2.m.b.37.3	yes	60
147.86	odd	42		441.2.bb.e.37.3		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.4.3	✓	60	1.1	even	1	trivial
147.2.m.b.37.3	yes	60	49.37	even	21	inner
441.2.bb.e.37.3		60	147.86	odd	42
441.2.bb.e.298.3		60	3.2	odd	2
7203.2.a.m.1.16		30	49.24	odd	42
7203.2.a.n.1.16		30	49.25	even	21

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190250 + 0.129710i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(-0.711312 - 1.81239i) q^{4} +(1.13743 - 0.350851i) q^{5} +(-0.0512377 - 0.224487i) q^{6} +(-2.33995 - 1.23477i) q^{7} +(0.202234 - 0.886046i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})\)	\(q+(0.190250 + 0.129710i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(-0.711312 - 1.81239i) q^{4} +(1.13743 - 0.350851i) q^{5} +(-0.0512377 - 0.224487i) q^{6} +(-2.33995 - 1.23477i) q^{7} +(0.202234 - 0.886046i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(0.261905 + 0.0807869i) q^{10} +(0.276984 - 3.69610i) q^{11} +(-0.711312 + 1.81239i) q^{12} +(1.00902 - 0.485919i) q^{13} +(-0.285013 - 0.538429i) q^{14} +(-1.07243 - 0.516457i) q^{15} +(-2.70107 + 2.50623i) q^{16} +(6.63269 - 0.999717i) q^{17} +(-0.115130 + 0.199411i) q^{18} +(2.49731 + 4.32547i) q^{19} +(-1.44495 - 1.81191i) q^{20} +(0.875449 + 2.49672i) q^{21} +(0.532118 - 0.667255i) q^{22} +(-1.09199 - 0.164591i) q^{23} +(-0.750913 + 0.511964i) q^{24} +(-2.96054 + 2.01846i) q^{25} +(0.254995 + 0.0384343i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-0.573448 + 5.11921i) q^{28} +(4.32808 + 5.42724i) q^{29} +(-0.137041 - 0.237362i) q^{30} +(-1.42347 + 2.46552i) q^{31} +(-2.63632 + 0.397362i) q^{32} +(-2.71703 + 2.52103i) q^{33} +(1.39154 + 0.670131i) q^{34} +(-3.09474 - 0.583487i) q^{35} +(1.75417 - 0.844763i) q^{36} +(0.893462 - 2.27650i) q^{37} +(-0.0859442 + 1.14685i) q^{38} +(-1.07017 - 0.330105i) q^{39} +(-0.0808426 - 1.07877i) q^{40} +(0.970126 - 4.25040i) q^{41} +(-0.157295 + 0.588555i) q^{42} +(-2.16553 - 9.48782i) q^{43} +(-6.89580 + 2.12707i) q^{44} +(0.434870 + 1.10803i) q^{45} +(-0.186401 - 0.172955i) q^{46} +(6.47433 + 4.41412i) q^{47} +3.68469 q^{48} +(3.95071 + 5.77857i) q^{49} -0.825059 q^{50} +(-5.54209 - 3.77853i) q^{51} +(-1.59841 - 1.48310i) q^{52} +(-1.47372 - 3.75499i) q^{53} +(0.220030 - 0.0678704i) q^{54} +(-0.981728 - 4.30123i) q^{55} +(-1.56728 + 1.82359i) q^{56} +(1.11141 - 4.86939i) q^{57} +(0.119448 + 1.59393i) q^{58} +(13.6406 + 4.20757i) q^{59} +(-0.173188 + 2.31103i) q^{60} +(-2.75362 + 7.01611i) q^{61} +(-0.590618 + 0.284426i) q^{62} +(1.05645 - 2.42568i) q^{63} +(6.08648 + 2.93110i) q^{64} +(0.977206 - 0.906715i) q^{65} +(-0.843918 + 0.127200i) q^{66} +(1.69953 - 2.94368i) q^{67} +(-6.52979 - 11.3099i) q^{68} +(0.688533 + 0.863394i) q^{69} +(-0.513091 - 0.512428i) q^{70} +(-3.49266 + 4.37965i) q^{71} +(0.898682 + 0.135454i) q^{72} +(1.17183 - 0.798940i) q^{73} +(0.465267 - 0.317213i) q^{74} +(3.54314 + 0.534042i) q^{75} +(6.06308 - 7.60286i) q^{76} +(-5.21194 + 8.30666i) q^{77} +(-0.160783 - 0.201615i) q^{78} +(-8.37241 - 14.5014i) q^{79} +(-2.19297 + 3.79833i) q^{80} +(-0.988831 + 0.149042i) q^{81} +(0.735886 - 0.682803i) q^{82} +(-12.1399 - 5.84627i) q^{83} +(3.90231 - 3.36260i) q^{84} +(7.19347 - 3.46419i) q^{85} +(0.818675 - 2.08595i) q^{86} +(0.518754 - 6.92229i) q^{87} +(-3.21890 - 0.992898i) q^{88} +(-0.460090 - 6.13948i) q^{89} +(-0.0609889 + 0.267210i) q^{90} +(-2.96105 - 0.108880i) q^{91} +(0.478441 + 2.09619i) q^{92} +(2.72045 - 0.839149i) q^{93} +(0.659183 + 1.67957i) q^{94} +(4.35811 + 4.04373i) q^{95} +(2.20284 + 1.50187i) q^{96} -2.94332 q^{97} +(0.00208186 + 1.61182i) q^{98} +3.70646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9	\( 60 q + q^{2} + 5 q^{3} + 5 q^{4} - 2 q^{5} - 2 q^{6} + 5 q^{7} + 6 q^{8} + 5 q^{9} - 34 q^{10} - 11 q^{11} + 5 q^{12} - 2 q^{13} + 40 q^{14} - 3 q^{15} - 31 q^{16} - 9 q^{17} - 6 q^{18} - 29 q^{19} - 43 q^{20} - 11 q^{21} + 9 q^{22} - 4 q^{23} - 24 q^{24} + 55 q^{25} + 36 q^{26} - 10 q^{27} - 57 q^{28} + 4 q^{29} - 20 q^{30} - 39 q^{31} - 92 q^{32} - 18 q^{33} - 36 q^{34} - 33 q^{35} - 10 q^{36} - 24 q^{37} + 118 q^{38} - 6 q^{39} + 35 q^{41} + 38 q^{42} + 2 q^{43} + 40 q^{44} + 12 q^{45} - 40 q^{46} - 5 q^{47} + 76 q^{48} + 129 q^{49} - 176 q^{50} + 54 q^{51} - 6 q^{52} + 26 q^{53} + q^{54} + 2 q^{55} + 63 q^{56} - 12 q^{57} + 11 q^{58} - 41 q^{59} + 32 q^{60} + 6 q^{61} + 36 q^{62} - q^{63} + 74 q^{64} - 51 q^{65} - 15 q^{66} - 55 q^{67} - 22 q^{68} + 8 q^{69} - 68 q^{70} - 66 q^{71} - 24 q^{72} + 24 q^{73} + 28 q^{74} + 41 q^{75} + 3 q^{76} - 34 q^{77} - 30 q^{78} - 51 q^{79} - 5 q^{80} + 5 q^{81} - 41 q^{82} + 30 q^{83} - 30 q^{84} + 68 q^{85} + 110 q^{86} + 19 q^{87} + 129 q^{88} + 75 q^{89} - 16 q^{90} + 5 q^{91} - 4 q^{93} + 38 q^{94} + 36 q^{95} - 57 q^{96} - 168 q^{97} + 227 q^{98} + 36 q^{99}+O(q^{100}) \) 60 * q + q^2 + 5 * q^3 + 5 * q^4 - 2 * q^5 - 2 * q^6 + 5 * q^7 + 6 * q^8 + 5 * q^9 - 34 * q^10 - 11 * q^11 + 5 * q^12 - 2 * q^13 + 40 * q^14 - 3 * q^15 - 31 * q^16 - 9 * q^17 - 6 * q^18 - 29 * q^19 - 43 * q^20 - 11 * q^21 + 9 * q^22 - 4 * q^23 - 24 * q^24 + 55 * q^25 + 36 * q^26 - 10 * q^27 - 57 * q^28 + 4 * q^29 - 20 * q^30 - 39 * q^31 - 92 * q^32 - 18 * q^33 - 36 * q^34 - 33 * q^35 - 10 * q^36 - 24 * q^37 + 118 * q^38 - 6 * q^39 + 35 * q^41 + 38 * q^42 + 2 * q^43 + 40 * q^44 + 12 * q^45 - 40 * q^46 - 5 * q^47 + 76 * q^48 + 129 * q^49 - 176 * q^50 + 54 * q^51 - 6 * q^52 + 26 * q^53 + q^54 + 2 * q^55 + 63 * q^56 - 12 * q^57 + 11 * q^58 - 41 * q^59 + 32 * q^60 + 6 * q^61 + 36 * q^62 - q^63 + 74 * q^64 - 51 * q^65 - 15 * q^66 - 55 * q^67 - 22 * q^68 + 8 * q^69 - 68 * q^70 - 66 * q^71 - 24 * q^72 + 24 * q^73 + 28 * q^74 + 41 * q^75 + 3 * q^76 - 34 * q^77 - 30 * q^78 - 51 * q^79 - 5 * q^80 + 5 * q^81 - 41 * q^82 + 30 * q^83 - 30 * q^84 + 68 * q^85 + 110 * q^86 + 19 * q^87 + 129 * q^88 + 75 * q^89 - 16 * q^90 + 5 * q^91 - 4 * q^93 + 38 * q^94 + 36 * q^95 - 57 * q^96 - 168 * q^97 + 227 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

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Database

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