LMFDB - Embedded newform 150.2.g.c.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1064390625.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 3x^{6} - 5x^{5} + 36x^{4} - 35x^{3} + 23x^{2} - 171x + 361 $ x^8 - 2x^7 - 3x^6 - 5x^5 + 36x^4 - 35x^3 + 23x^2 - 171*x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			121.1
Root			$-0.815575 + 1.64827i$ of defining polynomial
Character	$\chi$	$=$	150.121
Dual form			150.2.g.c.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.12459 + 0.697217i) q^{5} +(0.809017 - 0.587785i) q^{6} -4.25729 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.12459 + 0.697217i) q^{5} +(0.809017 - 0.587785i) q^{6} -4.25729 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.00655751 - 2.23606i) q^{10} +(-1.51061 + 4.64918i) q^{11} +(0.309017 + 0.951057i) q^{12} +(-1.43361 - 4.41219i) q^{13} +(1.31557 - 4.04892i) q^{14} +(2.12864 + 0.684743i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.815575 - 0.592550i) q^{17} -1.00000 q^{18} +(1.00000 - 0.726543i) q^{19} +(2.12864 + 0.684743i) q^{20} +(3.44422 + 2.50237i) q^{21} +(-3.95483 - 2.87335i) q^{22} +(-1.38197 + 4.25325i) q^{23} -1.00000 q^{24} +(4.02778 - 2.96260i) q^{25} +4.63925 q^{26} +(0.309017 - 0.951057i) q^{27} +(3.44422 + 2.50237i) q^{28} +(-3.42049 - 2.48513i) q^{29} +(-1.30902 + 1.81286i) q^{30} +(-0.826185 + 0.600258i) q^{31} -1.00000 q^{32} +(3.95483 - 2.87335i) q^{33} +(0.311522 + 0.958765i) q^{34} +(9.04500 - 2.96825i) q^{35} +(0.309017 - 0.951057i) q^{36} +(3.31152 + 10.1918i) q^{37} +(0.381966 + 1.17557i) q^{38} +(-1.43361 + 4.41219i) q^{39} +(-1.30902 + 1.81286i) q^{40} +(1.42049 + 4.37183i) q^{41} +(-3.44422 + 2.50237i) q^{42} -10.4984 q^{43} +(3.95483 - 2.87335i) q^{44} +(-1.31963 - 1.80515i) q^{45} +(-3.61803 - 2.62866i) q^{46} +(1.63925 + 1.19099i) q^{47} +(0.309017 - 0.951057i) q^{48} +11.1245 q^{49} +(1.57295 + 4.74614i) q^{50} -1.00811 q^{51} +(-1.43361 + 4.41219i) q^{52} +(-8.94413 - 6.49829i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-0.0320560 - 10.9308i) q^{55} +(-3.44422 + 2.50237i) q^{56} -1.23607 q^{57} +(3.42049 - 2.48513i) q^{58} +(-0.656508 - 2.02052i) q^{59} +(-1.31963 - 1.80515i) q^{60} +(1.19754 - 3.68565i) q^{61} +(-0.315575 - 0.971238i) q^{62} +(-1.31557 - 4.04892i) q^{63} +(0.309017 - 0.951057i) q^{64} +(6.12209 + 8.37457i) q^{65} +(1.51061 + 4.64918i) q^{66} +(-3.03434 + 2.20457i) q^{67} -1.00811 q^{68} +(3.61803 - 2.62866i) q^{69} +(0.0279172 + 9.51955i) q^{70} +(-10.1457 - 7.37130i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.05975 - 3.26157i) q^{73} -10.7163 q^{74} +(-4.99991 + 0.0293259i) q^{75} -1.23607 q^{76} +(6.43110 - 19.7929i) q^{77} +(-3.75324 - 2.72689i) q^{78} +(-5.16968 - 3.75599i) q^{79} +(-1.31963 - 1.80515i) q^{80} +(-0.809017 + 0.587785i) q^{81} -4.59681 q^{82} +(-5.70151 + 4.14239i) q^{83} +(-1.31557 - 4.04892i) q^{84} +(-1.31963 + 1.82756i) q^{85} +(3.24417 - 9.98454i) q^{86} +(1.30651 + 4.02103i) q^{87} +(1.51061 + 4.64918i) q^{88} +(0.693488 - 2.13434i) q^{89} +(2.12459 - 0.697217i) q^{90} +(6.10328 + 18.7840i) q^{91} +(3.61803 - 2.62866i) q^{92} +1.02122 q^{93} +(-1.63925 + 1.19099i) q^{94} +(-1.61803 + 2.24082i) q^{95} +(0.809017 + 0.587785i) q^{96} +(6.49586 + 4.71952i) q^{97} +(-3.43766 + 10.5800i) q^{98} -4.88844 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 4 q^{10} - 5 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} + q^{15} - 2 q^{16} - 2 q^{17} - 8 q^{18} + 8 q^{19} + q^{20} + 3 q^{21} - 20 q^{23} - 8 q^{24} + 14 q^{25} + 14 q^{26} - 2 q^{27} + 3 q^{28} - 18 q^{29} - 6 q^{30} + 9 q^{31} - 8 q^{32} - 3 q^{34} - 4 q^{35} - 2 q^{36} + 21 q^{37} + 12 q^{38} + 6 q^{39} - 6 q^{40} + 2 q^{41} - 3 q^{42} - 32 q^{43} + q^{45} - 20 q^{46} - 10 q^{47} - 2 q^{48} + 22 q^{49} + 26 q^{50} - 2 q^{51} + 6 q^{52} + 7 q^{53} + 2 q^{54} - 40 q^{55} - 3 q^{56} + 8 q^{57} + 18 q^{58} - 25 q^{59} + q^{60} + 10 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 37 q^{65} + 5 q^{66} - 2 q^{67} - 2 q^{68} + 20 q^{69} - 11 q^{70} + 2 q^{72} - 24 q^{73} - 26 q^{74} + 14 q^{75} + 8 q^{76} + 35 q^{77} - q^{78} - 6 q^{79} + q^{80} - 2 q^{81} - 42 q^{82} + 11 q^{83} - 2 q^{84} + q^{85} + 2 q^{86} + 7 q^{87} + 5 q^{88} + 9 q^{89} + 4 q^{90} - 4 q^{91} + 20 q^{92} - 6 q^{93} + 10 q^{94} - 4 q^{95} + 2 q^{96} + q^{97} - 7 q^{98} + 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 4 * q^10 - 5 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^14 + q^15 - 2 * q^16 - 2 * q^17 - 8 * q^18 + 8 * q^19 + q^20 + 3 * q^21 - 20 * q^23 - 8 * q^24 + 14 * q^25 + 14 * q^26 - 2 * q^27 + 3 * q^28 - 18 * q^29 - 6 * q^30 + 9 * q^31 - 8 * q^32 - 3 * q^34 - 4 * q^35 - 2 * q^36 + 21 * q^37 + 12 * q^38 + 6 * q^39 - 6 * q^40 + 2 * q^41 - 3 * q^42 - 32 * q^43 + q^45 - 20 * q^46 - 10 * q^47 - 2 * q^48 + 22 * q^49 + 26 * q^50 - 2 * q^51 + 6 * q^52 + 7 * q^53 + 2 * q^54 - 40 * q^55 - 3 * q^56 + 8 * q^57 + 18 * q^58 - 25 * q^59 + q^60 + 10 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 37 * q^65 + 5 * q^66 - 2 * q^67 - 2 * q^68 + 20 * q^69 - 11 * q^70 + 2 * q^72 - 24 * q^73 - 26 * q^74 + 14 * q^75 + 8 * q^76 + 35 * q^77 - q^78 - 6 * q^79 + q^80 - 2 * q^81 - 42 * q^82 + 11 * q^83 - 2 * q^84 + q^85 + 2 * q^86 + 7 * q^87 + 5 * q^88 + 9 * q^89 + 4 * q^90 - 4 * q^91 + 20 * q^92 - 6 * q^93 + 10 * q^94 - 4 * q^95 + 2 * q^96 + q^97 - 7 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−2.12459	+	0.697217i	−0.950146	+	0.311805i
$5$	−2.12459	+	0.697217i	−0.950146	+	0.311805i
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	−4.25729			−1.60910			−0.804552	−	0.593882i	$-0.797594\pi$
$7$	−4.25729			−1.60910			−0.804552	+	0.593882i	$0.797594\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−0.00655751	−	2.23606i	−0.00207367	−	0.707104i
$11$	−1.51061	+	4.64918i	−0.455466	+	1.40178i	0.415121	+	0.909766i	$0.363739\pi$
$11$	−1.51061	+	4.64918i	−0.455466	+	1.40178i	−0.870587	+	0.492014i	$0.836261\pi$
$12$	0.309017	+	0.951057i	0.0892055	+	0.274546i
$13$	−1.43361	−	4.41219i	−0.397611	−	1.22372i	−0.926909	−	0.375286i	$-0.877544\pi$
$13$	−1.43361	−	4.41219i	−0.397611	−	1.22372i	0.529298	−	0.848436i	$-0.322456\pi$
$14$	1.31557	−	4.04892i	0.351602	−	1.08212i
$15$	2.12864	+	0.684743i	0.549614	+	0.176800i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.815575	−	0.592550i	0.197806	−	0.143714i	−0.484473	−	0.874806i	$-0.660989\pi$
$17$	0.815575	−	0.592550i	0.197806	−	0.143714i	0.682279	+	0.731092i	$0.260989\pi$
$18$	−1.00000			−0.235702
$19$	1.00000	−	0.726543i	0.229416	−	0.166680i	−0.467139	−	0.884184i	$-0.654715\pi$
$19$	1.00000	−	0.726543i	0.229416	−	0.166680i	0.696555	+	0.717504i	$0.254715\pi$
$20$	2.12864	+	0.684743i	0.475979	+	0.153113i
$21$	3.44422	+	2.50237i	0.751590	+	0.546062i
$22$	−3.95483	−	2.87335i	−0.843172	−	0.612601i
$23$	−1.38197	+	4.25325i	−0.288160	+	0.886865i	0.697274	+	0.716805i	$0.254396\pi$
$23$	−1.38197	+	4.25325i	−0.288160	+	0.886865i	−0.985434	+	0.170060i	$0.945604\pi$
$24$	−1.00000			−0.204124
$25$	4.02778	−	2.96260i	0.805556	−	0.592520i
$26$	4.63925			0.909833
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	3.44422	+	2.50237i	0.650896	+	0.472904i
$29$	−3.42049	−	2.48513i	−0.635170	−	0.461478i	0.223018	−	0.974814i	$-0.428409\pi$
$29$	−3.42049	−	2.48513i	−0.635170	−	0.461478i	−0.858187	+	0.513337i	$0.828409\pi$
$30$	−1.30902	+	1.81286i	−0.238993	+	0.330982i
$31$	−0.826185	+	0.600258i	−0.148387	+	0.107810i	−0.659502	−	0.751703i	$-0.729233\pi$
$31$	−0.826185	+	0.600258i	−0.148387	+	0.107810i	0.511115	+	0.859513i	$0.329233\pi$
$32$	−1.00000			−0.176777
$33$	3.95483	−	2.87335i	0.688447	−	0.500186i
$34$	0.311522	+	0.958765i	0.0534255	+	0.164427i
$35$	9.04500	−	2.96825i	1.52888	−	0.501726i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	3.31152	+	10.1918i	0.544411	+	1.67552i	0.722387	+	0.691489i	$0.243045\pi$
$37$	3.31152	+	10.1918i	0.544411	+	1.67552i	−0.177976	+	0.984035i	$0.556955\pi$
$38$	0.381966	+	1.17557i	0.0619631	+	0.190703i
$39$	−1.43361	+	4.41219i	−0.229561	+	0.706516i
$40$	−1.30902	+	1.81286i	−0.206974	+	0.286639i
$41$	1.42049	+	4.37183i	0.221844	+	0.682765i	0.998597	+	0.0529595i	$0.0168654\pi$
$41$	1.42049	+	4.37183i	0.221844	+	0.682765i	−0.776753	+	0.629806i	$0.783135\pi$
$42$	−3.44422	+	2.50237i	−0.531454	+	0.386124i
$43$	−10.4984			−1.60099			−0.800493	−	0.599342i	$-0.795429\pi$
$43$	−10.4984			−1.60099			−0.800493	+	0.599342i	$0.795429\pi$
$44$	3.95483	−	2.87335i	0.596213	−	0.433174i
$45$	−1.31963	−	1.80515i	−0.196718	−	0.269097i
$46$	−3.61803	−	2.62866i	−0.533450	−	0.387574i
$47$	1.63925	+	1.19099i	0.239110	+	0.173723i	0.700887	−	0.713273i	$-0.252788\pi$
$47$	1.63925	+	1.19099i	0.239110	+	0.173723i	−0.461777	+	0.886996i	$0.652788\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	11.1245			1.58922
$50$	1.57295	+	4.74614i	0.222449	+	0.671205i
$51$	−1.00811			−0.141163
$52$	−1.43361	+	4.41219i	−0.198806	+	0.611861i
$53$	−8.94413	−	6.49829i	−1.22857	−	0.892609i	−0.231789	−	0.972766i	$-0.574458\pi$
$53$	−8.94413	−	6.49829i	−1.22857	−	0.892609i	−0.996782	+	0.0801570i	$0.974458\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	−0.0320560	−	10.9308i	−0.00432242	−	1.47391i
$56$	−3.44422	+	2.50237i	−0.460253	+	0.334393i
$57$	−1.23607			−0.163721
$58$	3.42049	−	2.48513i	0.449133	−	0.326314i
$59$	−0.656508	−	2.02052i	−0.0854701	−	0.263050i	0.899183	−	0.437573i	$-0.144162\pi$
$59$	−0.656508	−	2.02052i	−0.0854701	−	0.263050i	−0.984653	+	0.174523i	$0.944162\pi$
$60$	−1.31963	−	1.80515i	−0.170363	−	0.233044i
$61$	1.19754	−	3.68565i	0.153329	−	0.471899i	−0.844658	−	0.535306i	$-0.820196\pi$
$61$	1.19754	−	3.68565i	0.153329	−	0.471899i	0.997988	+	0.0634064i	$0.0201964\pi$
$62$	−0.315575	−	0.971238i	−0.0400780	−	0.123347i
$63$	−1.31557	−	4.04892i	−0.165747	−	0.510116i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	6.12209	+	8.37457i	0.759351	+	1.03874i
$66$	1.51061	+	4.64918i	0.185943	+	0.572275i
$67$	−3.03434	+	2.20457i	−0.370703	+	0.269332i	−0.757502	−	0.652832i	$-0.773581\pi$
$67$	−3.03434	+	2.20457i	−0.370703	+	0.269332i	0.386799	+	0.922164i	$0.373581\pi$
$68$	−1.00811			−0.122251
$69$	3.61803	−	2.62866i	0.435560	−	0.316453i
$70$	0.0279172	+	9.51955i	0.00333674	+	1.13780i
$71$	−10.1457	−	7.37130i	−1.20408	−	0.874813i	−0.209397	−	0.977831i	$-0.567150\pi$
$71$	−10.1457	−	7.37130i	−1.20408	−	0.874813i	−0.994679	+	0.103018i	$0.967150\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	1.05975	−	3.26157i	0.124034	−	0.381738i	−0.869690	−	0.493599i	$-0.835681\pi$
$73$	1.05975	−	3.26157i	0.124034	−	0.381738i	0.993724	+	0.111861i	$0.0356811\pi$
$74$	−10.7163			−1.24575
$75$	−4.99991	+	0.0293259i	−0.577340	+	0.00338627i
$76$	−1.23607			−0.141787
$77$	6.43110	−	19.7929i	0.732892	−	2.25561i
$78$	−3.75324	−	2.72689i	−0.424970	−	0.308759i
$79$	−5.16968	−	3.75599i	−0.581634	−	0.422582i	0.257679	−	0.966231i	$-0.417042\pi$
$79$	−5.16968	−	3.75599i	−0.581634	−	0.422582i	−0.839313	+	0.543649i	$0.817042\pi$
$80$	−1.31963	−	1.80515i	−0.147539	−	0.201822i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−4.59681			−0.507633
$83$	−5.70151	+	4.14239i	−0.625822	+	0.454686i	−0.854950	−	0.518710i	$-0.826412\pi$
$83$	−5.70151	+	4.14239i	−0.625822	+	0.454686i	0.229128	+	0.973396i	$0.426412\pi$
$84$	−1.31557	−	4.04892i	−0.143541	−	0.441774i
$85$	−1.31963	+	1.82756i	−0.143134	+	0.198226i
$86$	3.24417	−	9.98454i	0.349828	−	1.07666i
$87$	1.30651	+	4.02103i	0.140073	+	0.431100i
$88$	1.51061	+	4.64918i	0.161032	+	0.495604i
$89$	0.693488	−	2.13434i	0.0735096	−	0.226239i	−0.907551	−	0.419943i	$-0.862050\pi$
$89$	0.693488	−	2.13434i	0.0735096	−	0.226239i	0.981060	+	0.193704i	$0.0620501\pi$
$90$	2.12459	−	0.697217i	0.223952	−	0.0734931i
$91$	6.10328	+	18.7840i	0.639798	+	1.96910i
$92$	3.61803	−	2.62866i	0.377206	−	0.274056i
$93$	1.02122			0.105896
$94$	−1.63925	+	1.19099i	−0.169076	+	0.122841i
$95$	−1.61803	+	2.24082i	−0.166007	+	0.229904i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	6.49586	+	4.71952i	0.659555	+	0.479195i	0.866513	−	0.499155i	$-0.166356\pi$
$97$	6.49586	+	4.71952i	0.659555	+	0.479195i	−0.206958	+	0.978350i	$0.566356\pi$
$98$	−3.43766	+	10.5800i	−0.347256	+	1.06874i
$99$	−4.88844			−0.491306
$100$	−4.99991	+	0.0293259i	−0.499991	+	0.00293259i
$101$	−17.6310			−1.75435			−0.877174	−	0.480173i	$-0.840574\pi$
$101$	−17.6310			−1.75435			−0.877174	+	0.480173i	$0.840574\pi$
$102$	0.311522	−	0.958765i	0.0308452	−	0.0949319i
$103$	15.9376	+	11.5793i	1.57038	+	1.14094i	0.926795	+	0.375566i	$0.122552\pi$
$103$	15.9376	+	11.5793i	1.57038	+	1.14094i	0.643580	+	0.765378i	$0.277448\pi$
$104$	−3.75324	−	2.72689i	−0.368035	−	0.267393i
$105$	−9.06225	−	2.91515i	−0.884385	−	0.284490i
$106$	8.94413	−	6.49829i	0.868731	−	0.631170i
$107$	6.16695			0.596181			0.298091	−	0.954538i	$-0.403650\pi$
$107$	6.16695			0.596181			0.298091	+	0.954538i	$0.403650\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	2.44982	+	7.53977i	0.234650	+	0.722179i	0.997168	+	0.0752113i	$0.0239631\pi$
$109$	2.44982	+	7.53977i	0.234650	+	0.722179i	−0.762517	+	0.646968i	$0.776037\pi$
$110$	10.4057	+	3.34733i	0.992149	+	0.319155i
$111$	3.31152	−	10.1918i	0.314316	−	0.967364i
$112$	−1.31557	−	4.04892i	−0.124310	−	0.382587i
$113$	2.08857	+	6.42795i	0.196476	+	0.604691i	0.999956	+	0.00935951i	$0.00297927\pi$
$113$	2.08857	+	6.42795i	0.196476	+	0.604691i	−0.803480	+	0.595332i	$0.797021\pi$
$114$	0.381966	−	1.17557i	0.0357744	−	0.110102i
$115$	−0.0293261	−	9.99996i	−0.00273467	−	0.932501i
$116$	1.30651	+	4.02103i	0.121307	+	0.373343i
$117$	3.75324	−	2.72689i	0.346987	−	0.252101i
$118$	2.12451			0.195577
$119$	−3.47214	+	2.52265i	−0.318290	+	0.231251i
$120$	2.12459	−	0.697217i	0.193948	−	0.0636469i
$121$	−10.4337	−	7.58056i	−0.948523	−	0.689142i
$122$	3.13520	+	2.27786i	0.283848	+	0.206228i
$123$	1.42049	−	4.37183i	0.128082	−	0.394195i
$124$	1.02122			0.0917083
$125$	−6.49181	+	9.10255i	−0.580645	+	0.814157i
$126$	4.25729			0.379269
$127$	3.12054	−	9.60403i	0.276903	−	0.852220i	−0.711807	−	0.702376i	$-0.752123\pi$
$127$	3.12054	−	9.60403i	0.276903	−	0.852220i	0.988710	−	0.149844i	$-0.0478773\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	8.49336	+	6.17078i	0.747798	+	0.543307i
$130$	−9.85652	+	3.23457i	−0.864474	+	0.283690i
$131$	−5.43780	+	3.95079i	−0.475103	+	0.345182i	−0.799427	−	0.600764i	$-0.794863\pi$
$131$	−5.43780	+	3.95079i	−0.475103	+	0.345182i	0.324324	+	0.945946i	$0.394863\pi$
$132$	−4.88844			−0.425484
$133$	−4.25729	+	3.09310i	−0.369154	+	0.268206i
$134$	−1.15901	−	3.56708i	−0.100123	−	0.308148i
$135$	0.00655751	+	2.23606i	0.000564380	+	0.192449i
$136$	0.311522	−	0.958765i	0.0267128	−	0.0822134i
$137$	5.44672	+	16.7633i	0.465345	+	1.43218i	0.858548	+	0.512733i	$0.171367\pi$
$137$	5.44672	+	16.7633i	0.465345	+	1.43218i	−0.393203	+	0.919452i	$0.628633\pi$
$138$	1.38197	+	4.25325i	0.117641	+	0.362061i
$139$	−2.51976	+	7.75502i	−0.213723	+	0.657772i	0.785519	+	0.618838i	$0.212396\pi$
$139$	−2.51976	+	7.75502i	−0.213723	+	0.657772i	−0.999242	+	0.0389342i	$0.987604\pi$
$140$	−9.06225	−	2.91515i	−0.765900	−	0.246375i
$141$	−0.626140	−	1.92706i	−0.0527305	−	0.162288i
$142$	10.1457	−	7.37130i	0.851410	−	0.618586i
$143$	22.6787			1.89649
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$	8.99983	+	2.89507i	0.747395	+	0.240422i
$146$	2.77446	+	2.01576i	0.229616	+	0.166826i
$147$	−8.99991	−	6.53882i	−0.742300	−	0.539313i
$148$	3.31152	−	10.1918i	0.272205	−	0.837762i
$149$	10.2230			0.837497			0.418748	−	0.908102i	$-0.362469\pi$
$149$	10.2230			0.837497			0.418748	+	0.908102i	$0.362469\pi$
$150$	1.51717	−	4.76426i	0.123876	−	0.389000i
$151$	17.2016			1.39984			0.699922	−	0.714220i	$-0.253218\pi$
$151$	17.2016			1.39984			0.699922	+	0.714220i	$0.253218\pi$
$152$	0.381966	−	1.17557i	0.0309815	−	0.0953514i
$153$	0.815575	+	0.592550i	0.0659353	+	0.0479048i
$154$	16.8368	+	12.2327i	1.35675	+	0.985738i
$155$	1.33680	−	1.85133i	0.107374	−	0.148703i
$156$	3.75324	−	2.72689i	0.300499	−	0.218326i
$157$	−18.7425			−1.49582			−0.747909	−	0.663802i	$-0.768942\pi$
$157$	−18.7425			−1.49582			−0.747909	+	0.663802i	$0.768942\pi$
$158$	5.16968	−	3.75599i	0.411277	−	0.298811i
$159$	3.41635	+	10.5145i	0.270935	+	0.833851i
$160$	2.12459	−	0.697217i	0.167964	−	0.0551198i
$161$	5.88343	−	18.1073i	0.463679	−	1.42706i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−4.32624	−	13.3148i	−0.338857	−	1.04289i	−0.964791	−	0.263019i	$-0.915282\pi$
$163$	−4.32624	−	13.3148i	−0.338857	−	1.04289i	0.625934	−	0.779876i	$-0.284718\pi$
$164$	1.42049	−	4.37183i	0.110922	−	0.341383i
$165$	−6.39905	+	8.86207i	−0.498165	+	0.689911i
$166$	−2.17778	−	6.70252i	−0.169029	−	0.520217i
$167$	10.9309	−	7.94175i	0.845857	−	0.614551i	−0.0781438	−	0.996942i	$-0.524899\pi$
$167$	10.9309	−	7.94175i	0.845857	−	0.614551i	0.924001	+	0.382391i	$0.124899\pi$
$168$	4.25729			0.328457
$169$	−6.89500	+	5.00951i	−0.530384	+	0.385347i
$170$	−1.33032	−	1.81979i	−0.102031	−	0.139571i
$171$	1.00000	+	0.726543i	0.0764719	+	0.0555601i
$172$	8.49336	+	6.17078i	0.647612	+	0.470518i
$173$	−2.77609	+	8.54393i	−0.211062	+	0.649583i	0.788348	+	0.615230i	$0.210937\pi$
$173$	−2.77609	+	8.54393i	−0.211062	+	0.649583i	−0.999410	+	0.0343526i	$0.989063\pi$
$174$	−4.22796			−0.320521
$175$	−17.1474	+	12.6126i	−1.29622	+	0.953426i
$176$	−4.88844			−0.368480
$177$	−0.656508	+	2.02052i	−0.0493462	+	0.151872i
$178$	1.81557	+	1.31909i	0.136083	+	0.0988701i
$179$	−5.68029	−	4.12697i	−0.424565	−	0.308464i	0.354907	−	0.934902i	$-0.384512\pi$
$179$	−5.68029	−	4.12697i	−0.424565	−	0.308464i	−0.779472	+	0.626437i	$0.784512\pi$
$180$	0.00655751	+	2.23606i	0.000488768	+	0.166666i
$181$	9.66968	−	7.02543i	0.718741	−	0.522196i	−0.167240	−	0.985916i	$-0.553486\pi$
$181$	9.66968	−	7.02543i	0.718741	−	0.522196i	0.885982	+	0.463720i	$0.153486\pi$
$182$	−19.7506			−1.46402
$183$	−3.13520	+	2.27786i	−0.231761	+	0.168384i
$184$	1.38197	+	4.25325i	0.101880	+	0.313554i
$185$	−14.1415	−	19.3446i	−1.03971	−	1.42224i
$186$	−0.315575	+	0.971238i	−0.0231390	+	0.0712147i
$187$	1.52285	+	4.68686i	0.111362	+	0.342737i
$188$	−0.626140	−	1.92706i	−0.0456659	−	0.140545i
$189$	−1.31557	+	4.04892i	−0.0956940	+	0.294516i
$190$	−1.63115	−	2.23129i	−0.118336	−	0.161875i
$191$	1.00000	+	3.07768i	0.0723575	+	0.222693i	0.980695	−	0.195545i	$-0.0626476\pi$
$191$	1.00000	+	3.07768i	0.0723575	+	0.222693i	−0.908337	+	0.418239i	$0.862648\pi$
$192$	−0.809017	+	0.587785i	−0.0583858	+	0.0424197i
$193$	−7.60802			−0.547637			−0.273818	−	0.961781i	$-0.588287\pi$
$193$	−7.60802			−0.547637			−0.273818	+	0.961781i	$0.588287\pi$
$194$	−6.49586	+	4.71952i	−0.466376	+	0.338842i
$195$	−0.0304219	−	10.3736i	−0.00217856	−	0.742872i
$196$	−8.99991	−	6.53882i	−0.642851	−	0.467059i
$197$	−3.81549	−	2.77211i	−0.271842	−	0.197505i	0.443509	−	0.896270i	$-0.353733\pi$
$197$	−3.81549	−	2.77211i	−0.271842	−	0.197505i	−0.715351	+	0.698765i	$0.753733\pi$
$198$	1.51061	−	4.64918i	0.107354	−	0.330403i
$199$	−15.9276			−1.12908			−0.564539	−	0.825406i	$-0.690946\pi$
$199$	−15.9276			−1.12908			−0.564539	+	0.825406i	$0.690946\pi$
$200$	1.51717	−	4.76426i	0.107280	−	0.336884i
$201$	3.75065			0.264550
$202$	5.44827	−	16.7681i	0.383339	−	1.17980i
$203$	14.5620	+	10.5799i	1.02205	+	0.742566i
$204$	0.815575	+	0.592550i	0.0571016	+	0.0414868i
$205$	−6.06608	−	8.29796i	−0.423673	−	0.579555i
$206$	−15.9376	+	11.5793i	−1.11042	+	0.806770i
$207$	−4.47214			−0.310835
$208$	3.75324	−	2.72689i	0.260240	−	0.189075i
$209$	1.86722	+	5.74670i	0.129158	+	0.397508i
$210$	5.57286	−	7.71788i	0.384564	−	0.532585i
$211$	−3.73443	+	11.4934i	−0.257089	+	0.791239i	0.736322	+	0.676631i	$0.236561\pi$
$211$	−3.73443	+	11.4934i	−0.257089	+	0.791239i	−0.993411	+	0.114607i	$0.963439\pi$
$212$	3.41635	+	10.5145i	0.234636	+	0.722136i
$213$	3.87532	+	11.9270i	0.265533	+	0.817226i
$214$	−1.90569	+	5.86511i	−0.130270	+	0.400931i
$215$	22.3047	−	7.31963i	1.52117	−	0.499195i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	3.51731	−	2.55547i	0.238770	−	0.173477i
$218$	−7.92778			−0.536937
$219$	−2.77446	+	2.01576i	−0.187480	+	0.136212i
$220$	−6.39905	+	8.86207i	−0.431424	+	0.597481i
$221$	−3.78366	−	2.74899i	−0.254516	−	0.184917i
$222$	8.66968	+	6.29889i	0.581871	+	0.422754i
$223$	−2.89258	+	8.90243i	−0.193701	+	0.596151i	0.806288	+	0.591523i	$0.201473\pi$
$223$	−2.89258	+	8.90243i	−0.193701	+	0.596151i	−0.999989	+	0.00462801i	$0.998527\pi$
$224$	4.25729			0.284452
$225$	4.06225	+	2.91515i	0.270817	+	0.194343i
$226$	−6.75875			−0.449585
$227$	3.12864	−	9.62898i	0.207655	−	0.639098i	−0.791938	−	0.610601i	$-0.790928\pi$
$227$	3.12864	−	9.62898i	0.207655	−	0.639098i	0.999594	−	0.0284967i	$-0.00907202\pi$
$228$	1.00000	+	0.726543i	0.0662266	+	0.0481165i
$229$	−5.99741	−	4.35737i	−0.396320	−	0.287943i	0.371720	−	0.928345i	$-0.378768\pi$
$229$	−5.99741	−	4.35737i	−0.396320	−	0.287943i	−0.768040	+	0.640401i	$0.778768\pi$
$230$	9.51959	+	3.06227i	0.627703	+	0.201920i
$231$	−16.8368	+	12.2327i	−1.10778	+	0.804852i
$232$	−4.22796			−0.277579
$233$	4.79568	−	3.48426i	0.314175	−	0.228262i	−0.419511	−	0.907750i	$-0.637798\pi$
$233$	4.79568	−	3.48426i	0.314175	−	0.228262i	0.733686	+	0.679489i	$0.237798\pi$
$234$	1.43361	+	4.41219i	0.0937179	+	0.288434i
$235$	−4.31312	−	1.38745i	−0.281357	−	0.0905071i
$236$	−0.656508	+	2.02052i	−0.0427351	+	0.131525i
$237$	1.97464	+	6.07732i	0.128267	+	0.394764i
$238$	−1.32624	−	4.08174i	−0.0859672	−	0.264580i
$239$	−5.10328	+	15.7063i	−0.330104	+	1.01596i	0.638980	+	0.769224i	$0.279357\pi$
$239$	−5.10328	+	15.7063i	−0.330104	+	1.01596i	−0.969084	+	0.246732i	$0.920643\pi$
$240$	0.00655751	+	2.23606i	0.000423285	+	0.144337i
$241$	−2.48120	−	7.63634i	−0.159828	−	0.491900i	0.838790	−	0.544455i	$-0.183264\pi$
$241$	−2.48120	−	7.63634i	−0.159828	−	0.491900i	−0.998618	+	0.0525550i	$0.983264\pi$
$242$	10.4337	−	7.58056i	0.670707	−	0.487297i
$243$	1.00000			0.0641500
$244$	−3.13520	+	2.27786i	−0.200711	+	0.145825i
$245$	−23.6350	+	7.75619i	−1.50999	+	0.495525i
$246$	3.71890	+	2.70194i	0.237108	+	0.172269i
$247$	−4.63925	−	3.37062i	−0.295189	−	0.214467i
$248$	−0.315575	+	0.971238i	−0.0200390	+	0.0616737i
$249$	7.04745			0.446614
$250$	−6.65096	−	8.98692i	−0.420644	−	0.568383i
$251$	14.4639			0.912951			0.456475	−	0.889736i	$-0.349112\pi$
$251$	14.4639			0.912951			0.456475	+	0.889736i	$0.349112\pi$
$252$	−1.31557	+	4.04892i	−0.0828734	+	0.255058i
$253$	−17.6865	−	12.8500i	−1.11194	−	0.807874i
$254$	8.16968	+	5.93562i	0.512611	+	0.372434i
$255$	2.14181	−	0.702868i	0.134125	−	0.0440153i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.36075			−0.0848810			−0.0424405	−	0.999099i	$-0.513513\pi$
$257$	−1.36075			−0.0848810			−0.0424405	+	0.999099i	$0.513513\pi$
$258$	−8.49336	+	6.17078i	−0.528773	+	0.384176i
$259$	−14.0981	−	43.3895i	−0.876014	−	2.69609i
$260$	−0.0304219	−	10.3736i	−0.00188669	−	0.643346i
$261$	1.30651	−	4.02103i	0.0808711	−	0.248896i
$262$	−2.07705	−	6.39252i	−0.128321	−	0.394931i
$263$	−2.09518	−	6.44830i	−0.129194	−	0.397619i	0.865448	−	0.500999i	$-0.167034\pi$
$263$	−2.09518	−	6.44830i	−0.129194	−	0.397619i	−0.994642	+	0.103380i	$0.967034\pi$
$264$	1.51061	−	4.64918i	0.0929716	−	0.286137i
$265$	23.5333	+	7.57022i	1.44564	+	0.465035i
$266$	−1.62614	−	5.00474i	−0.0997050	−	0.306860i
$267$	−1.81557	+	1.31909i	−0.111111	+	0.0807271i
$268$	3.75065			0.229107
$269$	3.19745	−	2.32309i	0.194952	−	0.141641i	−0.486027	−	0.873944i	$-0.661554\pi$
$269$	3.19745	−	2.32309i	0.194952	−	0.141641i	0.680979	+	0.732303i	$0.261554\pi$
$270$	−2.12864	−	0.684743i	−0.129545	−	0.0416722i
$271$	−8.28521	−	6.01955i	−0.503290	−	0.365662i	0.306982	−	0.951715i	$-0.400681\pi$
$271$	−8.28521	−	6.01955i	−0.503290	−	0.365662i	−0.810272	+	0.586053i	$0.800681\pi$
$272$	0.815575	+	0.592550i	0.0494515	+	0.0359286i
$273$	6.10328	−	18.7840i	0.369388	−	1.13686i
$274$	−17.6260			−1.06482
$275$	7.68926	+	23.2012i	0.463680	+	1.39909i
$276$	−4.47214			−0.269191
$277$	−3.18684	+	9.80810i	−0.191479	+	0.589311i	0.808521	+	0.588468i	$0.200269\pi$
$277$	−3.18684	+	9.80810i	−0.191479	+	0.589311i	−1.00000		0.000843804i	$0.999731\pi$
$278$	−6.59681	−	4.79287i	−0.395651	−	0.287457i
$279$	−0.826185	−	0.600258i	−0.0494624	−	0.0359365i
$280$	5.57286	−	7.71788i	0.333042	−	0.461232i
$281$	2.88602	−	2.09682i	0.172165	−	0.125086i	−0.498366	−	0.866967i	$-0.666066\pi$
$281$	2.88602	−	2.09682i	0.172165	−	0.125086i	0.670531	+	0.741881i	$0.266066\pi$
$282$	2.02623			0.120660
$283$	23.2571	−	16.8973i	1.38249	−	1.00444i	0.385850	−	0.922562i	$-0.373908\pi$
$283$	23.2571	−	16.8973i	1.38249	−	1.00444i	0.996642	−	0.0818776i	$-0.0260917\pi$
$284$	3.87532	+	11.9270i	0.229958	+	0.707738i
$285$	2.62614	−	0.861807i	0.155559	−	0.0510490i
$286$	−7.00811	+	21.5687i	−0.414398	+	1.27539i
$287$	−6.04745	−	18.6121i	−0.356970	−	1.09864i
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	−4.93924	+	15.2014i	−0.290544	+	0.894201i
$290$	−5.53447	+	7.66472i	−0.324996	+	0.450088i
$291$	−2.48120	−	7.63634i	−0.145450	−	0.447650i
$292$	−2.77446	+	2.01576i	−0.162363	+	0.117963i
$293$	1.78543			0.104306			0.0521530	−	0.998639i	$-0.483392\pi$
$293$	1.78543			0.104306			0.0521530	+	0.998639i	$0.483392\pi$
$294$	8.99991	−	6.53882i	0.524886	−	0.381352i
$295$	2.80356	+	3.83506i	0.163229	+	0.223286i
$296$	8.66968	+	6.29889i	0.503915	+	0.366115i
$297$	3.95483	+	2.87335i	0.229482	+	0.166729i
$298$	−3.15907	+	9.72261i	−0.183000	+	0.563215i
$299$	20.7474			1.19985
$300$	4.06225	+	2.91515i	0.234534	+	0.168306i
$301$	44.6946			2.57615
$302$	−5.31557	+	16.3597i	−0.305877	+	0.941392i
$303$	14.2638	+	10.3632i	0.819432	+	0.595352i
$304$	1.00000	+	0.726543i	0.0573539	+	0.0416701i
$305$	0.0254125	+	8.66545i	0.00145511	+	0.496182i
$306$	−0.815575	+	0.592550i	−0.0466233	+	0.0338738i
$307$	16.2752			0.928877			0.464439	−	0.885605i	$-0.346256\pi$
$307$	16.2752			0.928877			0.464439	+	0.885605i	$0.346256\pi$
$308$	−16.8368	+	12.2327i	−0.959368	+	0.697022i
$309$	−6.08761	−	18.7357i	−0.346312	−	1.06584i
$310$	1.34763	+	1.84346i	0.0765403	+	0.104702i
$311$	4.00501	−	12.3262i	0.227103	−	0.698952i	−0.770968	−	0.636874i	$-0.780227\pi$
$311$	4.00501	−	12.3262i	0.227103	−	0.698952i	0.998071	−	0.0620781i	$-0.0197728\pi$
$312$	1.43361	+	4.41219i	0.0811621	+	0.249791i
$313$	−1.29075	−	3.97253i	−0.0729577	−	0.224541i	0.907928	−	0.419127i	$-0.137664\pi$
$313$	−1.29075	−	3.97253i	−0.0729577	−	0.224541i	−0.980885	+	0.194586i	$0.937664\pi$
$314$	5.79176	−	17.8252i	0.326848	−	1.00594i
$315$	5.61803	+	7.68506i	0.316540	+	0.433004i
$316$	1.97464	+	6.07732i	0.111082	+	0.341876i
$317$	−24.4480	+	17.7625i	−1.37314	+	0.997643i	−0.375653	+	0.926761i	$0.622581\pi$
$317$	−24.4480	+	17.7625i	−1.37314	+	0.997643i	−0.997485	+	0.0708820i	$0.977419\pi$
$318$	−11.0556			−0.619965
$319$	16.7209	−	12.1484i	0.936189	−	0.680181i
$320$	0.00655751	+	2.23606i	0.000366576	+	0.124999i
$321$	−4.98916	−	3.62484i	−0.278468	−	0.202319i
$322$	15.4030	+	11.1909i	0.858376	+	0.623647i
$323$	0.385062	−	1.18510i	0.0214254	−	0.0659407i
$324$	1.00000			0.0555556
$325$	−18.8458	−	13.5241i	−1.04538	−	0.750183i
$326$	14.0000			0.775388
$327$	2.44982	−	7.53977i	0.135475	−	0.416950i
$328$	3.71890	+	2.70194i	0.205342	+	0.149190i
$329$	−6.97878	−	5.07038i	−0.384753	−	0.279539i
$330$	−6.45092	−	8.82439i	−0.355111	−	0.485766i
$331$	−11.3949	+	8.27889i	−0.626321	+	0.455049i	−0.855124	−	0.518424i	$-0.826519\pi$
$331$	−11.3949	+	8.27889i	−0.626321	+	0.455049i	0.228803	+	0.973473i	$0.426519\pi$
$332$	7.04745			0.386779
$333$	−8.66968	+	6.29889i	−0.475095	+	0.345177i
$334$	4.17522	+	12.8500i	0.228458	+	0.703122i
$335$	4.90966	−	6.79941i	0.268243	−	0.371491i
$336$	−1.31557	+	4.04892i	−0.0717705	+	0.220887i
$337$	4.15155	+	12.7772i	0.226149	+	0.696016i	0.998173	+	0.0604224i	$0.0192448\pi$
$337$	4.15155	+	12.7772i	0.226149	+	0.696016i	−0.772023	+	0.635594i	$0.780755\pi$
$338$	−2.63365	−	8.10555i	−0.143252	−	0.440884i
$339$	2.08857	−	6.42795i	0.113435	−	0.349119i
$340$	2.14181	−	0.702868i	0.116156	−	0.0381184i
$341$	−1.54267	−	4.74784i	−0.0835401	−	0.257110i
$342$	−1.00000	+	0.726543i	−0.0540738	+	0.0392869i
$343$	−17.5592			−0.948108
$344$	−8.49336	+	6.17078i	−0.457931	+	0.332706i
$345$	−5.85410	+	8.10737i	−0.315174	+	0.436486i
$346$	−7.26790	−	5.28044i	−0.390725	−	0.283878i
$347$	−4.55975	−	3.31285i	−0.244780	−	0.177843i	0.458630	−	0.888627i	$-0.348340\pi$
$347$	−4.55975	−	3.31285i	−0.244780	−	0.177843i	−0.703410	+	0.710784i	$0.748340\pi$
$348$	1.30651	−	4.02103i	0.0700364	−	0.215550i
$349$	24.1159			1.29090			0.645449	−	0.763804i	$-0.276670\pi$
$349$	24.1159			1.29090			0.645449	+	0.763804i	$0.276670\pi$
$350$	−6.69650	−	20.2057i	−0.357943	−	1.08004i
$351$	−4.63925			−0.247625
$352$	1.51061	−	4.64918i	0.0805158	−	0.247802i
$353$	−19.1672	−	13.9258i	−1.02017	−	0.741196i	−0.0538510	−	0.998549i	$-0.517150\pi$
$353$	−19.1672	−	13.9258i	−1.02017	−	0.741196i	−0.966317	+	0.257353i	$0.917150\pi$
$354$	−1.71876	−	1.24875i	−0.0913511	−	0.0663705i
$355$	26.6949	+	8.58724i	1.41682	+	0.455763i
$356$	−1.81557	+	1.31909i	−0.0962253	+	0.0699117i
$357$	4.29180			0.227146
$358$	5.68029	−	4.12697i	0.300212	−	0.218117i
$359$	−0.849092	−	2.61324i	−0.0448134	−	0.137921i	0.926146	−	0.377164i	$-0.123101\pi$
$359$	−0.849092	−	2.61324i	−0.0448134	−	0.137921i	−0.970960	+	0.239243i	$0.923101\pi$
$360$	−2.12864	−	0.684743i	−0.112189	−	0.0360891i
$361$	−5.39919	+	16.6170i	−0.284168	+	0.874578i
$362$	3.69349	+	11.3674i	0.194125	+	0.597457i
$363$	3.98534	+	12.2656i	0.209176	+	0.643777i
$364$	6.10328	−	18.7840i	0.319899	−	0.984548i
$365$	0.0224884	+	7.66838i	0.00117710	+	0.401381i
$366$	−1.19754	−	3.68565i	−0.0625964	−	0.192652i
$367$	4.33266	−	3.14786i	0.226163	−	0.164317i	−0.468934	−	0.883233i	$-0.655362\pi$
$367$	4.33266	−	3.14786i	0.226163	−	0.164317i	0.695096	+	0.718917i	$0.255362\pi$
$368$	−4.47214			−0.233126
$369$	−3.71890	+	2.70194i	−0.193598	+	0.140657i
$370$	22.7678	−	7.47159i	1.18364	−	0.388429i
$371$	38.0778	+	27.6651i	1.97690	+	1.43630i
$372$	−0.826185	−	0.600258i	−0.0428357	−	0.0311219i
$373$	−8.66048	+	26.6542i	−0.448422	+	1.38010i	0.430264	+	0.902703i	$0.358420\pi$
$373$	−8.66048	+	26.6542i	−0.448422	+	1.38010i	−0.878687	+	0.477399i	$0.841580\pi$
$374$	−4.92806			−0.254824
$375$	10.6023	−	3.54833i	0.547502	−	0.183235i
$376$	2.02623			0.104495
$377$	−6.06124	+	18.6546i	−0.312170	+	0.960760i
$378$	−3.44422	−	2.50237i	−0.177151	−	0.128708i
$379$	2.20145	+	1.59945i	0.113081	+	0.0821582i	0.642889	−	0.765960i	$-0.277736\pi$
$379$	2.20145	+	1.59945i	0.113081	+	0.0821582i	−0.529807	+	0.848118i	$0.677736\pi$
$380$	2.62614	−	0.861807i	0.134718	−	0.0442098i
$381$	−8.16968	+	5.93562i	−0.418545	+	0.304091i
$382$	−3.23607			−0.165572
$383$	−13.6522	+	9.91890i	−0.697595	+	0.506832i	−0.879148	−	0.476549i	$-0.841888\pi$
$383$	−13.6522	+	9.91890i	−0.697595	+	0.506832i	0.181553	+	0.983381i	$0.441888\pi$
$384$	−0.309017	−	0.951057i	−0.0157695	−	0.0485334i
$385$	0.136471	+	46.5357i	0.00695523	+	2.37168i
$386$	2.35101	−	7.23565i	0.119663	−	0.368285i
$387$	−3.24417	−	9.98454i	−0.164911	−	0.507543i
$388$	−2.48120	−	7.63634i	−0.125964	−	0.387677i
$389$	11.9654	−	36.8258i	0.606672	−	1.86714i	0.121810	−	0.992553i	$-0.461130\pi$
$389$	11.9654	−	36.8258i	0.606672	−	1.86714i	0.484862	−	0.874590i	$-0.338870\pi$
$390$	9.87532	+	3.17670i	0.500056	+	0.160858i
$391$	1.39317	+	4.28773i	0.0704555	+	0.216840i
$392$	8.99991	−	6.53882i	0.454564	−	0.330260i
$393$	6.72149			0.339054
$394$	3.81549	−	2.77211i	0.192222	−	0.139657i
$395$	13.6022	+	4.37556i	0.684400	+	0.220158i
$396$	3.95483	+	2.87335i	0.198738	+	0.144391i
$397$	−20.0261	−	14.5498i	−1.00508	−	0.730233i	−0.0419078	−	0.999121i	$-0.513344\pi$
$397$	−20.0261	−	14.5498i	−1.00508	−	0.730233i	−0.963171	+	0.268889i	$0.913344\pi$
$398$	4.92190	−	15.1481i	0.246713	−	0.759304i
$399$	5.26230			0.263444
$400$	4.06225	+	2.91515i	0.203113	+	0.145758i
$401$	−3.31830			−0.165708			−0.0828541	−	0.996562i	$-0.526404\pi$
$401$	−3.31830			−0.165708			−0.0828541	+	0.996562i	$0.526404\pi$
$402$	−1.15901	+	3.56708i	−0.0578063	+	0.177910i
$403$	3.83288	+	2.78475i	0.190929	+	0.138718i
$404$	14.2638	+	10.3632i	0.709649	+	0.515590i
$405$	1.30902	−	1.81286i	0.0650456	−	0.0900819i
$406$	−14.5620	+	10.5799i	−0.722701	+	0.525073i
$407$	−52.3860			−2.59668
$408$	−0.815575	+	0.592550i	−0.0403770	+	0.0293356i
$409$	−8.76950	−	26.9897i	−0.433624	−	1.33456i	−0.894490	−	0.447087i	$-0.852461\pi$
$409$	−8.76950	−	26.9897i	−0.433624	−	1.33456i	0.460866	−	0.887470i	$-0.347539\pi$
$410$	9.76635	−	3.20497i	0.482326	−	0.158282i
$411$	5.44672	−	16.7633i	0.268667	−	0.826872i
$412$	−6.08761	−	18.7357i	−0.299915	−	0.923044i
$413$	2.79495	+	8.60196i	0.137530	+	0.423275i
$414$	1.38197	−	4.25325i	0.0679199	−	0.209036i
$415$	9.22523	−	12.7761i	0.452849	−	0.627152i
$416$	1.43361	+	4.41219i	0.0702884	+	0.216326i
$417$	6.59681	−	4.79287i	0.323047	−	0.234708i
$418$	−6.04244			−0.295545
$419$	−11.9931	+	8.71352i	−0.585903	+	0.425683i	−0.840847	−	0.541272i	$-0.817943\pi$
$419$	−11.9931	+	8.71352i	−0.585903	+	0.425683i	0.254945	+	0.966956i	$0.417943\pi$
$420$	5.61803	+	7.68506i	0.274132	+	0.374993i
$421$	−14.7255	−	10.6987i	−0.717677	−	0.521423i	0.167964	−	0.985793i	$-0.446281\pi$
$421$	−14.7255	−	10.6987i	−0.717677	−	0.521423i	−0.885641	+	0.464370i	$0.846281\pi$
$422$	−9.77688	−	7.10332i	−0.475931	−	0.345784i
$423$	−0.626140	+	1.92706i	−0.0304439	+	0.0936968i
$424$	−11.0556			−0.536905
$425$	1.52947	−	4.80288i	0.0741900	−	0.232974i
$426$	−12.5408			−0.607604
$427$	−5.09828	+	15.6909i	−0.246723	+	0.759335i
$428$	−4.98916	−	3.62484i	−0.241160	−	0.175213i
$429$	−18.3475	−	13.3302i	−0.885824	−	0.643589i
$430$	0.0688431	+	23.4750i	0.00331991	+	1.13206i
$431$	−14.3606	+	10.4336i	−0.691724	+	0.502567i	−0.877227	−	0.480077i	$-0.840609\pi$
$431$	−14.3606	+	10.4336i	−0.691724	+	0.502567i	0.185502	+	0.982644i	$0.440609\pi$
$432$	1.00000			0.0481125
$433$	−17.5703	+	12.7656i	−0.844373	+	0.613473i	−0.923589	−	0.383384i	$-0.874758\pi$
$433$	−17.5703	+	12.7656i	−0.844373	+	0.613473i	0.0792155	+	0.996858i	$0.474758\pi$
$434$	1.34349	+	4.13484i	0.0644897	+	0.198479i
$435$	−5.57933	−	7.63213i	−0.267509	−	0.365932i
$436$	2.44982	−	7.53977i	0.117325	−	0.361089i
$437$	1.70820	+	5.25731i	0.0817145	+	0.251491i
$438$	−1.05975	−	3.26157i	−0.0506367	−	0.155844i
$439$	3.31399	−	10.1994i	0.158168	−	0.486792i	−0.840300	−	0.542122i	$-0.817621\pi$
$439$	3.31399	−	10.1994i	0.158168	−	0.486792i	0.998468	+	0.0553300i	$0.0176211\pi$
$440$	−6.45092	−	8.82439i	−0.307535	−	0.420686i
$441$	3.43766	+	10.5800i	0.163698	+	0.503811i
$442$	3.78366	−	2.74899i	0.179970	−	0.130756i
$443$	25.5092			1.21198			0.605990	−	0.795472i	$-0.292777\pi$
$443$	25.5092			1.21198			0.605990	+	0.795472i	$0.292777\pi$
$444$	−8.66968	+	6.29889i	−0.411445	+	0.298932i
$445$	0.0147162	+	5.01810i	0.000697614	+	0.237881i
$446$	−7.57286	−	5.50201i	−0.358585	−	0.260528i
$447$	−8.27054	−	6.00890i	−0.391183	−	0.284211i
$448$	−1.31557	+	4.04892i	−0.0621551	+	0.191294i
$449$	−12.5619			−0.592831			−0.296415	−	0.955059i	$-0.595791\pi$
$449$	−12.5619			−0.592831			−0.296415	+	0.955059i	$0.595791\pi$
$450$	−4.02778	+	2.96260i	−0.189871	+	0.139658i
$451$	−22.4712			−1.05813
$452$	2.08857	−	6.42795i	0.0982380	−	0.302346i
$453$	−13.9164	−	10.1108i	−0.653847	−	0.475048i
$454$	8.19090	+	5.95104i	0.384418	+	0.279296i
$455$	−26.0635	−	35.6530i	−1.22188	−	1.67144i
$456$	−1.00000	+	0.726543i	−0.0468293	+	0.0340235i
$457$	3.04289			0.142340			0.0711702	−	0.997464i	$-0.477327\pi$
$457$	3.04289			0.142340			0.0711702	+	0.997464i	$0.477327\pi$
$458$	5.99741	−	4.35737i	0.280241	−	0.203607i
$459$	−0.311522	−	0.958765i	−0.0145406	−	0.0447513i
$460$	−5.85410	+	8.10737i	−0.272949	+	0.378008i
$461$	−8.52674	+	26.2426i	−0.397130	+	1.22224i	0.530161	+	0.847897i	$0.322132\pi$
$461$	−8.52674	+	26.2426i	−0.397130	+	1.22224i	−0.927291	+	0.374342i	$0.877868\pi$
$462$	−6.43110	−	19.7929i	−0.299202	−	0.920849i
$463$	9.33417	+	28.7276i	0.433796	+	1.33509i	0.894316	+	0.447437i	$0.147663\pi$
$463$	9.33417	+	28.7276i	0.433796	+	1.33509i	−0.460520	+	0.887649i	$0.652337\pi$
$464$	1.30651	−	4.02103i	0.0606533	−	0.186672i
$465$	−2.16968	+	0.712012i	−0.100616	+	0.0330188i
$466$	1.83179	+	5.63766i	0.0848558	+	0.261159i
$467$	−24.1271	+	17.5293i	−1.11647	+	0.811161i	−0.983670	−	0.179982i	$-0.942396\pi$
$467$	−24.1271	+	17.5293i	−1.11647	+	0.811161i	−0.132797	+	0.991143i	$0.542396\pi$
$468$	−4.63925			−0.214450
$469$	12.9180	−	9.38551i	0.596500	−	0.433382i
$470$	2.65237	−	3.67328i	0.122345	−	0.169436i
$471$	15.1630	+	11.0166i	0.698676	+	0.507618i
$472$	−1.71876	−	1.24875i	−0.0791124	−	0.0574785i
$473$	15.8589	−	48.8088i	0.729195	−	2.24423i
$474$	−6.39007			−0.293506
$475$	1.87532	−	5.88895i	0.0860457	−	0.270204i
$476$	4.29180			0.196714
$477$	3.41635	−	10.5145i	0.156424	−	0.481424i
$478$	−13.3606	−	9.70702i	−0.611098	−	0.443989i
$479$	−5.27040	−	3.82917i	−0.240811	−	0.174959i	0.460834	−	0.887487i	$-0.347550\pi$
$479$	−5.27040	−	3.82917i	−0.240811	−	0.174959i	−0.701644	+	0.712527i	$0.747550\pi$
$480$	−2.12864	−	0.684743i	−0.0971589	−	0.0312541i
$481$	40.2208	−	29.2221i	1.83391	−	1.33242i
$482$	8.02933			0.365726
$483$	−15.4030	+	11.1909i	−0.700861	+	0.509206i
$484$	3.98534	+	12.2656i	0.181152	+	0.557528i
$485$	−17.0916	−	5.49803i	−0.776089	−	0.249653i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	12.4222	+	38.2315i	0.562903	+	1.73244i	0.674102	+	0.738638i	$0.264531\pi$
$487$	12.4222	+	38.2315i	0.562903	+	1.73244i	−0.111199	+	0.993798i	$0.535469\pi$
$488$	−1.19754	−	3.68565i	−0.0542101	−	0.166842i
$489$	−4.32624	+	13.3148i	−0.195639	+	0.602116i
$490$	−0.0729490	−	24.8750i	−0.00329550	−	1.12374i
$491$	−11.3187	−	34.8353i	−0.510804	−	1.57209i	−0.790788	−	0.612090i	$-0.790329\pi$
$491$	−11.3187	−	34.8353i	−0.510804	−	1.57209i	0.279984	−	0.960005i	$-0.409671\pi$
$492$	−3.71890	+	2.70194i	−0.167661	+	0.121813i
$493$	−4.26223			−0.191961
$494$	4.63925	−	3.37062i	0.208730	−	0.151651i
$495$	10.3859	−	3.40830i	0.466813	−	0.153192i
$496$	−0.826185	−	0.600258i	−0.0370968	−	0.0269524i
$497$	43.1933	+	31.3818i	1.93748	+	1.40766i
$498$	−2.17778	+	6.70252i	−0.0975887	+	0.300347i
$499$	−24.9343			−1.11621			−0.558105	−	0.829770i	$-0.688471\pi$
$499$	−24.9343			−1.11621			−0.558105	+	0.829770i	$0.688471\pi$
$500$	10.6023	−	3.54833i	0.474151	−	0.158686i
$501$	−13.5113			−0.603641
$502$	−4.46958	+	13.7559i	−0.199487	+	0.613958i
$503$	−34.9784	−	25.4133i	−1.55961	−	1.13312i	−0.936327	−	0.351128i	$-0.885798\pi$
$503$	−34.9784	−	25.4133i	−1.55961	−	1.13312i	−0.623284	−	0.781996i	$-0.714202\pi$
$504$	−3.44422	−	2.50237i	−0.153418	−	0.111464i
$505$	37.4586	−	12.2926i	1.66689	−	0.547014i
$506$	17.6865	−	12.8500i	0.786262	−	0.571253i
$507$	8.52268			0.378506
$508$	−8.16968	+	5.93562i	−0.362471	+	0.263350i
$509$	9.55465	+	29.4062i	0.423503	+	1.30341i	0.904421	+	0.426641i	$0.140303\pi$
$509$	9.55465	+	29.4062i	0.423503	+	1.30341i	−0.480918	+	0.876765i	$0.659697\pi$
$510$	0.00661066	+	2.25418i	0.000292725	+	0.0998169i
$511$	−4.51165	+	13.8854i	−0.199584	+	0.614256i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−0.381966	−	1.17557i	−0.0168642	−	0.0519027i
$514$	0.420493	−	1.29415i	0.0185472	−	0.0570823i
$515$	−41.9341	−	13.4894i	−1.84784	−	0.594414i
$516$	−3.24417	−	9.98454i	−0.142817	−	0.439545i
$517$	−8.01339	+	5.82207i	−0.352429	+	0.256054i
$518$	45.6224			2.00453
$519$	7.26790	−	5.28044i	0.319025	−	0.231785i
$520$	9.87532	+	3.17670i	0.433062	+	0.139307i
$521$	23.9548	+	17.4042i	1.04948	+	0.762491i	0.972113	−	0.234512i	$-0.0753492\pi$
$521$	23.9548	+	17.4042i	1.04948	+	0.762491i	0.0773654	+	0.997003i	$0.475349\pi$
$522$	3.42049	+	2.48513i	0.149711	+	0.108771i
$523$	3.64736	−	11.2254i	0.159488	−	0.490853i	−0.839100	−	0.543977i	$-0.816918\pi$
$523$	3.64736	−	11.2254i	0.159488	−	0.490853i	0.998588	+	0.0531238i	$0.0169178\pi$
$524$	6.72149			0.293630
$525$	21.2861	−	0.124849i	0.929001	−	0.00544886i
$526$	6.78014			0.295628
$527$	−0.318132	+	0.979111i	−0.0138581	+	0.0426507i
$528$	3.95483	+	2.87335i	0.172112	+	0.125047i
$529$	2.42705	+	1.76336i	0.105524	+	0.0766676i
$530$	−14.4719	+	20.0422i	−0.628620	+	0.870578i
$531$	1.71876	−	1.24875i	0.0745879	−	0.0541913i
$532$	5.26230			0.228150
$533$	17.2529	−	12.5350i	0.747307	−	0.542950i
$534$	−0.693488	−	2.13434i	−0.0300101	−	0.0923617i
$535$	−13.1022	+	4.29970i	−0.566459	+	0.185892i
$536$	−1.15901	+	3.56708i	−0.0500617	+	0.154074i
$537$	2.16968	+	6.67758i	0.0936285	+	0.288159i
$538$	1.22132	+	3.75883i	0.0526548	+	0.162055i
$539$	−16.8048	+	51.7198i	−0.723834	+	2.22773i
$540$	1.30902	−	1.81286i	0.0563311	−	0.0780132i
$541$	4.69039	+	14.4355i	0.201656	+	0.620632i	0.999834	+	0.0182113i	$0.00579717\pi$
$541$	4.69039	+	14.4355i	0.201656	+	0.620632i	−0.798178	+	0.602421i	$0.794203\pi$
$542$	8.28521	−	6.01955i	0.355880	−	0.258562i
$543$	−11.9524			−0.512926
$544$	−0.815575	+	0.592550i	−0.0349675	+	0.0254054i
$545$	−10.4617	−	14.3109i	−0.448131	−	0.613011i
$546$	15.9786	+	11.6091i	0.683821	+	0.496825i
$547$	−28.2147	−	20.4992i	−1.20637	−	0.876481i	−0.211476	−	0.977383i	$-0.567827\pi$
$547$	−28.2147	−	20.4992i	−1.20637	−	0.876481i	−0.994896	+	0.100902i	$0.967827\pi$
$548$	5.44672	−	16.7633i	0.232672	−	0.716092i
$549$	3.87532			0.165395
$550$	−24.4418	+	0.143358i	−1.04220	+	0.00611281i
$551$	−5.22605			−0.222637
$552$	1.38197	−	4.25325i	0.0588204	−	0.181031i
$553$	22.0088	+	15.9903i	0.935910	+	0.679978i
$554$	−8.34327	−	6.06174i	−0.354471	−	0.257539i
$555$	0.0702723	+	23.9623i	0.00298289	+	1.01714i
$556$	6.59681	−	4.79287i	0.279767	−	0.203263i
$557$	31.4820			1.33393			0.666967	−	0.745087i	$-0.267592\pi$
$557$	31.4820			1.33393			0.666967	+	0.745087i	$0.267592\pi$
$558$	0.826185	−	0.600258i	0.0349752	−	0.0254110i
$559$	15.0505	+	46.3208i	0.636570	+	1.95916i
$560$	5.61803	+	7.68506i	0.237405	+	0.324753i
$561$	1.52285	−	4.68686i	0.0642950	−	0.197880i
$562$	1.10236	+	3.39272i	0.0465003	+	0.143113i
$563$	0.272961	+	0.840089i	0.0115040	+	0.0354055i	0.956644	−	0.291261i	$-0.0940747\pi$
$563$	0.272961	+	0.840089i	0.0115040	+	0.0354055i	−0.945140	+	0.326666i	$0.894075\pi$
$564$	−0.626140	+	1.92706i	−0.0263652	+	0.0811438i
$565$	−8.91903	−	12.2006i	−0.375226	−	0.513283i
$566$	8.88343	+	27.3404i	0.373398	+	1.14920i
$567$	3.44422	−	2.50237i	0.144644	−	0.105090i
$568$	−12.5408			−0.526201
$569$	4.94008	−	3.58918i	0.207099	−	0.150466i	−0.479401	−	0.877596i	$-0.659146\pi$
$569$	4.94008	−	3.58918i	0.207099	−	0.150466i	0.686500	+	0.727130i	$0.259146\pi$
$570$	0.00810552	+	2.76392i	0.000339503	+	0.115768i
$571$	0.0293261	+	0.0213066i	0.00122726	+	0.000891655i	0.588399	−	0.808571i	$-0.299759\pi$
$571$	0.0293261	+	0.0213066i	0.00122726	+	0.000891655i	−0.587171	+	0.809463i	$0.699759\pi$
$572$	−18.3475	−	13.3302i	−0.767146	−	0.557364i
$573$	1.00000	−	3.07768i	0.0417756	−	0.128572i
$574$	19.5700			0.816834
$575$	7.03444	+	21.2254i	0.293357	+	0.885159i
$576$	1.00000			0.0416667
$577$	12.3368	−	37.9688i	0.513587	−	1.58066i	−0.272250	−	0.962227i	$-0.587768\pi$
$577$	12.3368	−	37.9688i	0.513587	−	1.58066i	0.785837	−	0.618433i	$-0.212232\pi$
$578$	−12.9311	−	9.39500i	−0.537863	−	0.390780i
$579$	6.15501	+	4.47188i	0.255794	+	0.185845i
$580$	−5.57933	−	7.63213i	−0.231669	−	0.316907i
$581$	24.2730	−	17.6353i	1.00701	−	0.731637i
$582$	8.02933			0.332826
$583$	43.7228	−	31.7665i	1.81081	−	1.31563i
$584$	−1.05975	−	3.26157i	−0.0438527	−	0.134965i
$585$	−6.07286	+	8.41034i	−0.251082	+	0.347725i
$586$	−0.551728	+	1.69805i	−0.0227917	+	0.0701456i
$587$	−5.39111	−	16.5921i	−0.222515	−	0.684831i	−0.998534	−	0.0541218i	$-0.982764\pi$
$587$	−5.39111	−	16.5921i	−0.222515	−	0.684831i	0.776019	−	0.630709i	$-0.217236\pi$
$588$	3.43766	+	10.5800i	0.141767	+	0.436313i
$589$	−0.390072	+	1.20052i	−0.0160726	+	0.0494664i
$590$	−4.51371	+	1.48124i	−0.185826	+	0.0609817i
$591$	1.45739	+	4.48538i	0.0599489	+	0.184504i
$592$	−8.66968	+	6.29889i	−0.356322	+	0.258883i
$593$	−5.43780			−0.223304			−0.111652	−	0.993747i	$-0.535614\pi$
$593$	−5.43780			−0.223304			−0.111652	+	0.993747i	$0.535614\pi$
$594$	−3.95483	+	2.87335i	−0.162269	+	0.117895i
$595$	5.61803	−	7.78044i	0.230317	−	0.318967i
$596$	−8.27054	−	6.00890i	−0.338775	−	0.246134i
$597$	12.8857	+	9.36201i	0.527377	+	0.383162i
$598$	−6.41129	+	19.7319i	−0.262177	+	0.806899i
$599$	28.7804			1.17593			0.587967	−	0.808885i	$-0.299929\pi$
$599$	28.7804			1.17593			0.587967	+	0.808885i	$0.299929\pi$
$600$	−4.02778	+	2.96260i	−0.164433	+	0.120948i
$601$	−41.4162			−1.68940			−0.844702	−	0.535237i	$-0.820222\pi$
$601$	−41.4162			−1.68940			−0.844702	+	0.535237i	$0.820222\pi$
$602$	−13.8114	+	42.5071i	−0.562910	+	1.73246i
$603$	−3.03434	−	2.20457i	−0.123568	−	0.0897772i
$604$	−13.9164	−	10.1108i	−0.566248	−	0.411404i
$605$	27.4527	+	8.83101i	1.11611	+	0.359032i
$606$	−14.2638	+	10.3632i	−0.579426	+	0.420977i
$607$	23.9868			0.973595			0.486797	−	0.873515i	$-0.338165\pi$
$607$	23.9868			0.973595			0.486797	+	0.873515i	$0.338165\pi$
$608$	−1.00000	+	0.726543i	−0.0405554	+	0.0294652i
$609$	−5.56220	−	17.1187i	−0.225392	−	0.693684i
$610$	−8.24918	−	2.65360i	−0.334000	−	0.107441i
$611$	2.90482	−	8.94012i	0.117516	−	0.361678i
$612$	−0.311522	−	0.958765i	−0.0125925	−	0.0387558i
$613$	0.131288	+	0.404063i	0.00530268	+	0.0163200i	0.953673	−	0.300846i	$-0.0972689\pi$
$613$	0.131288	+	0.404063i	0.00530268	+	0.0163200i	−0.948370	+	0.317166i	$0.897269\pi$
$614$	−5.02933	+	15.4787i	−0.202967	+	0.624668i
$615$	0.0301436	+	10.2787i	0.00121551	+	0.414479i
$616$	−6.43110	−	19.7929i	−0.259117	−	0.797479i
$617$	−26.5991	+	19.3253i	−1.07084	+	0.778009i	−0.976063	−	0.217489i	$-0.930213\pi$
$617$	−26.5991	+	19.3253i	−1.07084	+	0.778009i	−0.0947752	+	0.995499i	$0.530213\pi$
$618$	19.6999			0.792447
$619$	−9.53580	+	6.92816i	−0.383276	+	0.278466i	−0.762695	−	0.646759i	$-0.776124\pi$
$619$	−9.53580	+	6.92816i	−0.383276	+	0.278466i	0.379419	+	0.925225i	$0.376124\pi$
$620$	−2.16968	+	0.712012i	−0.0871363	+	0.0285951i
$621$	3.61803	+	2.62866i	0.145187	+	0.105484i
$622$	10.4853	+	7.61798i	0.420420	+	0.305453i
$623$	−2.95238	+	9.08648i	−0.118285	+	0.364042i
$624$	−4.63925			−0.185719
$625$	7.44599	−	23.8654i	0.297840	−	0.954616i
$626$	4.17697			0.166945
$627$	1.86722	−	5.74670i	0.0745695	−	0.229501i
$628$	15.1630	+	11.0166i	0.605071	+	0.439610i
$629$	8.73995	+	6.34994i	0.348485	+	0.253189i
$630$	−9.04500	+	2.96825i	−0.360361	+	0.118258i
$631$	−27.0900	+	19.6820i	−1.07844	+	0.783529i	−0.977410	−	0.211354i	$-0.932213\pi$
$631$	−27.0900	+	19.6820i	−1.07844	+	0.783529i	−0.101026	+	0.994884i	$0.532213\pi$
$632$	−6.39007			−0.254183
$633$	9.77688	−	7.10332i	0.388596	−	0.282331i
$634$	−9.33831	−	28.7404i	−0.370872	−	1.14143i
$635$	0.0662195	+	22.5803i	0.00262784	+	0.896073i
$636$	3.41635	−	10.5145i	0.135467	−	0.416925i
$637$	−15.9482	−	49.0835i	−0.631890	−	1.94476i
$638$	6.38680	+	19.6566i	0.252856	+	0.778211i
$639$	3.87532	−	11.9270i	0.153305	−	0.471825i
$640$	−2.12864	−	0.684743i	−0.0841421	−	0.0270669i
$641$	−5.17714	−	15.9336i	−0.204485	−	0.629339i	−0.999734	−	0.0230567i	$-0.992660\pi$
$641$	−5.17714	−	15.9336i	−0.204485	−	0.629339i	0.795250	−	0.606282i	$-0.207340\pi$
$642$	4.98916	−	3.62484i	0.196907	−	0.143061i
$643$	14.5246			0.572794			0.286397	−	0.958111i	$-0.407542\pi$
$643$	14.5246			0.572794			0.286397	+	0.958111i	$0.407542\pi$
$644$	−15.4030	+	11.1909i	−0.606964	+	0.440985i
$645$	−22.3473	−	7.18869i	−0.879924	−	0.283054i
$646$	1.00811	+	0.732432i	0.0396634	+	0.0288171i
$647$	−12.8965	−	9.36989i	−0.507015	−	0.368368i	0.304675	−	0.952456i	$-0.401452\pi$
$647$	−12.8965	−	9.36989i	−0.507015	−	0.368368i	−0.811690	+	0.584088i	$0.801452\pi$
$648$	−0.309017	+	0.951057i	−0.0121393	+	0.0373610i
$649$	10.3855			0.407667
$650$	18.6859	−	13.7443i	0.732921	−	0.539094i
$651$	−4.34763			−0.170397
$652$	−4.32624	+	13.3148i	−0.169429	+	0.521447i
$653$	20.3233	+	14.7657i	0.795312	+	0.577828i	0.909535	−	0.415627i	$-0.136438\pi$
$653$	20.3233	+	14.7657i	0.795312	+	0.577828i	−0.114223	+	0.993455i	$0.536438\pi$
$654$	6.41371	+	4.65983i	0.250796	+	0.182214i
$655$	8.79855	−	12.1851i	0.343788	−	0.476113i
$656$	−3.71890	+	2.70194i	−0.145199	+	0.105493i
$657$	3.42942			0.133794
$658$	6.97878	−	5.07038i	0.272061	−	0.197664i
$659$	−3.40766	−	10.4877i	−0.132744	−	0.408543i	0.862489	−	0.506076i	$-0.168905\pi$
$659$	−3.40766	−	10.4877i	−0.132744	−	0.408543i	−0.995232	+	0.0975338i	$0.968905\pi$
$660$	10.3859	−	3.40830i	0.404272	−	0.132668i
$661$	−4.20173	+	12.9316i	−0.163428	+	0.502981i	−0.998917	−	0.0465267i	$-0.985185\pi$
$661$	−4.20173	+	12.9316i	−0.163428	+	0.502981i	0.835489	+	0.549508i	$0.185185\pi$
$662$	−4.35247	−	13.3955i	−0.169163	−	0.520632i
$663$	1.44523	+	4.44796i	0.0561280	+	0.172744i
$664$	−2.17778	+	6.70252i	−0.0845143	+	0.260108i
$665$	6.88844	−	9.53983i	0.267122	−	0.369939i
$666$	−3.31152	−	10.1918i	−0.128319	−	0.394925i
$667$	15.2969	−	11.1139i	0.592299	−	0.430330i
$668$	−13.5113			−0.522768
$669$	7.57286	−	5.50201i	0.292784	−	0.212720i
$670$	4.94945	+	6.77049i	0.191214	+	0.261567i
$671$	15.3262	+	11.1352i	0.591663	+	0.429868i
$672$	−3.44422	−	2.50237i	−0.132864	−	0.0965311i
$673$	−6.81053	+	20.9607i	−0.262527	+	0.807974i	0.729726	+	0.683740i	$0.239648\pi$
$673$	−6.81053	+	20.9607i	−0.262527	+	0.807974i	−0.992253	+	0.124235i	$0.960352\pi$
$674$	−13.4347			−0.517485
$675$	−1.57295	−	4.74614i	−0.0605428	−	0.182679i
$676$	8.52268			0.327795
$677$	10.3185	−	31.7571i	0.396572	−	1.22052i	−0.531158	−	0.847273i	$-0.678243\pi$
$677$	10.3185	−	31.7571i	0.396572	−	1.22052i	0.927730	−	0.373251i	$-0.121757\pi$
$678$	5.46794	+	3.97269i	0.209995	+	0.152570i
$679$	−27.6548	−	20.0924i	−1.06129	−	0.771074i
$680$	0.00661066	+	2.25418i	0.000253507	+	0.0864440i
$681$	−8.19090	+	5.95104i	−0.313876	+	0.228044i
$682$	4.99217			0.191160
$683$	−2.88616	+	2.09692i	−0.110436	+	0.0802363i	−0.641632	−	0.767012i	$-0.721743\pi$
$683$	−2.88616	+	2.09692i	−0.110436	+	0.0802363i	0.531197	+	0.847249i	$0.321743\pi$
$684$	−0.381966	−	1.17557i	−0.0146048	−	0.0449491i
$685$	−23.2597	−	31.8176i	−0.888708	−	1.21569i
$686$	5.42609	−	16.6998i	0.207169	−	0.637601i
$687$	2.29081	+	7.05038i	0.0873997	+	0.268989i
$688$	−3.24417	−	9.98454i	−0.123683	−	0.380657i
$689$	−15.8493	+	48.7792i	−0.603812	+	1.85834i
$690$	−5.90155	−	8.07290i	−0.224668	−	0.307330i
$691$	−11.6129	−	35.7407i	−0.441774	−	1.35964i	−0.885983	−	0.463717i	$-0.846515\pi$
$691$	−11.6129	−	35.7407i	−0.441774	−	1.35964i	0.444210	−	0.895923i	$-0.353485\pi$
$692$	7.26790	−	5.28044i	0.276284	−	0.200732i
$693$	20.8115			0.790563
$694$	4.55975	−	3.31285i	0.173086	−	0.125754i
$695$	−0.0534706	−	18.2331i	−0.00202826	−	0.691620i
$696$	3.42049	+	2.48513i	0.129653	+	0.0941988i
$697$	3.74904	+	2.72384i	0.142005	+	0.103173i
$698$	−7.45224	+	22.9356i	−0.282071	+	0.868126i
$699$	−5.92778			−0.224209
$700$	21.2861	−	0.124849i	0.804538	−	0.00471885i
$701$	26.4948			1.00070			0.500348	−	0.865825i	$-0.333205\pi$
$701$	26.4948			1.00070			0.500348	+	0.865825i	$0.333205\pi$
$702$	1.43361	−	4.41219i	0.0541081	−	0.166528i
$703$	10.7163	+	7.78585i	0.404173	+	0.293649i
$704$	3.95483	+	2.87335i	0.149053	+	0.108294i
$705$	2.67387	+	3.65766i	0.100704	+	0.137755i
$706$	19.1672	−	13.9258i	0.721368	−	0.524105i
$707$	75.0602			2.82293
$708$	1.71876	−	1.24875i	0.0645950	−	0.0469310i
$709$	11.5055	+	35.4104i	0.432100	+	1.32987i	0.896029	+	0.443995i	$0.146439\pi$
$709$	11.5055	+	35.4104i	0.432100	+	1.32987i	−0.463930	+	0.885872i	$0.653561\pi$
$710$	−16.4161	+	22.7348i	−0.616086	+	0.853221i
$711$	1.97464	−	6.07732i	0.0740548	−	0.227917i
$712$	−0.693488	−	2.13434i	−0.0259896	−	0.0799876i
$713$	−1.41129	−	4.34351i	−0.0528533	−	0.162666i
$714$	−1.32624	+	4.08174i	−0.0496332	+	0.152755i
$715$	−48.1830	+	15.8120i	−1.80194	+	0.591334i
$716$	2.16968	+	6.67758i	0.0810846	+	0.249553i
$717$	13.3606	−	9.70702i	0.498960	−	0.362515i
$718$	2.74772			0.102544
$719$	0.501912	−	0.364661i	0.0187182	−	0.0135995i	−0.578387	−	0.815763i	$-0.696318\pi$
$719$	0.501912	−	0.364661i	0.0187182	−	0.0135995i	0.597105	+	0.802163i	$0.296318\pi$
$720$	1.30902	−	1.81286i	0.0487842	−	0.0675614i
$721$	−67.8509	−	49.2965i	−2.52690	−	1.83590i
$722$	−14.1353	−	10.2699i	−0.526060	−	0.382205i
$723$	−2.48120	+	7.63634i	−0.0922768	+	0.283999i
$724$	−11.9524			−0.444207
$725$	−21.1394	+	0.123989i	−0.785099	+	0.00460483i
$726$	−12.8968			−0.478646
$727$	−0.0770549	+	0.237151i	−0.00285781	+	0.00879543i	−0.952475	−	0.304616i	$-0.901472\pi$
$727$	−0.0770549	+	0.237151i	−0.00285781	+	0.00879543i	0.949617	+	0.313411i	$0.101472\pi$
$728$	15.9786	+	11.6091i	0.592207	+	0.430263i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−7.30001	−	2.34827i	−0.270185	−	0.0869134i
$731$	−8.56220	+	6.22080i	−0.316684	+	0.230085i
$732$	3.87532			0.143236
$733$	−34.4927	+	25.0604i	−1.27402	+	0.925628i	−0.999355	−	0.0359121i	$-0.988566\pi$
$733$	−34.4927	+	25.0604i	−1.27402	+	0.925628i	−0.274663	+	0.961540i	$0.588566\pi$
$734$	1.65493	+	5.09334i	0.0610845	+	0.187999i
$735$	23.6801	+	7.61743i	0.873454	+	0.280973i
$736$	1.38197	−	4.25325i	0.0509399	−	0.156777i
$737$	−5.66576	−	17.4374i	−0.208701	−	0.642316i
$738$	−1.42049	−	4.37183i	−0.0522891	−	0.160929i
$739$	4.86029	−	14.9584i	0.178789	−	0.550255i	−0.820997	−	0.570932i	$-0.806582\pi$
$739$	4.86029	−	14.9584i	0.178789	−	0.550255i	0.999786	+	0.0206765i	$0.00658202\pi$
$740$	0.0702723	+	23.9623i	0.00258326	+	0.880871i
$741$	1.77204	+	5.45377i	0.0650974	+	0.200349i
$742$	−38.0778	+	27.6651i	−1.39788	+	1.01562i
$743$	−45.9731			−1.68659			−0.843294	−	0.537452i	$-0.819387\pi$
$743$	−45.9731			−1.68659			−0.843294	+	0.537452i	$0.819387\pi$
$744$	0.826185	−	0.600258i	0.0302894	−	0.0220065i
$745$	−21.7196	+	7.12761i	−0.795745	+	0.261136i
$746$	−22.6734	−	16.4732i	−0.830133	−	0.603127i
$747$	−5.70151	−	4.14239i	−0.208607	−	0.151562i
$748$	1.52285	−	4.68686i	0.0556811	−	0.171369i
$749$	−26.2545			−0.959317
$750$	0.0983615	+	11.1799i	0.00359165	+	0.408232i
$751$	7.09608			0.258940			0.129470	−	0.991583i	$-0.458672\pi$
$751$	7.09608			0.258940			0.129470	+	0.991583i	$0.458672\pi$
$752$	−0.626140	+	1.92706i	−0.0228330	+	0.0702726i
$753$	−11.7015	−	8.50164i	−0.426427	−	0.309817i
$754$	−15.8685	−	11.5292i	−0.577898	−	0.419868i
$755$	−36.5463	+	11.9932i	−1.33006	+	0.436478i
$756$	3.44422	−	2.50237i	0.125265	−	0.0910104i
$757$	23.7795			0.864281			0.432141	−	0.901806i	$-0.357758\pi$
$757$	23.7795			0.864281			0.432141	+	0.901806i	$0.357758\pi$
$758$	−2.20145	+	1.59945i	−0.0799604	+	0.0580946i
$759$	6.75565	+	20.7918i	0.245215	+	0.754693i
$760$	0.00810552	+	2.76392i	0.000294018	+	0.100258i
$761$	1.62195	−	4.99184i	0.0587956	−	0.180954i	−0.917345	−	0.398093i	$-0.869672\pi$
$761$	1.62195	−	4.99184i	0.0587956	−	0.180954i	0.976141	+	0.217138i	$0.0696723\pi$
$762$	−3.12054	−	9.60403i	−0.113045	−	0.347917i
$763$	−10.4296	−	32.0990i	−0.377576	−	1.16206i
$764$	1.00000	−	3.07768i	0.0361787	−	0.111347i
$765$	−2.14590	−	0.690294i	−0.0775851	−	0.0249576i
$766$	−5.21468	−	16.0491i	−0.188414	−	0.579878i
$767$	−7.97377	+	5.79328i	−0.287916	+	0.209183i
$768$	1.00000			0.0360844
$769$	4.43639	−	3.22323i	0.159980	−	0.116233i	−0.504915	−	0.863169i	$-0.668476\pi$
$769$	4.43639	−	3.22323i	0.159980	−	0.116233i	0.664895	+	0.746937i	$0.268476\pi$
$770$	−44.3003	−	14.2505i	−1.59647	−	0.513553i
$771$	1.10087	+	0.799826i	0.0396467	+	0.0288050i
$772$	6.15501	+	4.47188i	0.221524	+	0.160946i
$773$	−3.60661	+	11.1000i	−0.129721	+	0.399239i	−0.994732	−	0.102514i	$-0.967311\pi$
$773$	−3.60661	+	11.1000i	−0.129721	+	0.399239i	0.865011	+	0.501753i	$0.167311\pi$
$774$	10.4984			0.377356
$775$	−1.54936	+	4.86536i	−0.0556548	+	0.174769i
$776$	8.02933			0.288236
$777$	−14.0981	+	43.3895i	−0.505767	+	1.55659i
$778$	31.3259	+	22.7596i	1.12309	+	0.815972i
$779$	4.59681	+	3.33978i	0.164698	+	0.119660i
$780$	−6.07286	+	8.41034i	−0.217443	+	0.301138i
$781$	49.5967	−	36.0341i	1.77471	−	1.28940i
$782$	−4.50838			−0.161220
$783$	−3.42049	+	2.48513i	−0.122238	+	0.0888114i
$784$	3.43766	+	10.5800i	0.122774	+	0.377858i
$785$	39.8202	−	13.0676i	1.42125	−	0.466403i
$786$	−2.07705	+	6.39252i	−0.0740861	+	0.228014i
$787$	−7.63108	−	23.4861i	−0.272019	−	0.837188i	−0.989993	−	0.141118i	$-0.954930\pi$
$787$	−7.63108	−	23.4861i	−0.272019	−	0.837188i	0.717974	−	0.696070i	$-0.245070\pi$
$788$	1.45739	+	4.48538i	0.0519173	+	0.159785i
$789$	−2.09518	+	6.44830i	−0.0745904	+	0.229566i
$790$	−8.36471	+	11.5843i	−0.297603	+	0.412152i
$791$	−8.89164	−	27.3657i	−0.316150	−	0.973011i
$792$	−3.95483	+	2.87335i	−0.140529	+	0.102100i
$793$	−17.9786			−0.638439
$794$	20.0261	−	14.5498i	0.710698	−	0.516352i
$795$	−14.5892	−	19.9570i	−0.517426	−	0.707802i
$796$	12.8857	+	9.36201i	0.456722	+	0.331828i
$797$	−16.7427	−	12.1643i	−0.593056	−	0.430880i	0.250351	−	0.968155i	$-0.419454\pi$
$797$	−16.7427	−	12.1643i	−0.593056	−	0.430880i	−0.843407	+	0.537275i	$0.819454\pi$
$798$	−1.62614	+	5.00474i	−0.0575647	+	0.177166i
$799$	2.04265			0.0722639
$800$	−4.02778	+	2.96260i	−0.142403	+	0.104744i
$801$	2.24417			0.0792940
$802$	1.02541	−	3.15590i	0.0362086	−	0.111439i
$803$	13.5628	+	9.85392i	0.478619	+	0.347737i
$804$	−3.03434	−	2.20457i	−0.107013	−	0.0777493i
$805$	0.124850	+	42.5727i	0.00440037	+	1.50049i
$806$	−3.83288	+	2.78475i	−0.135007	+	0.0980887i
$807$	−3.95227			−0.139127
$808$	−14.2638	+	10.3632i	−0.501797	+	0.364577i
$809$	−0.948863	−	2.92030i	−0.0333602	−	0.102672i	0.932990	−	0.359903i	$-0.117190\pi$
$809$	−0.948863	−	2.92030i	−0.0333602	−	0.102672i	−0.966350	+	0.257230i	$0.917190\pi$
$810$	1.31963	+	1.80515i	0.0463670	+	0.0634267i
$811$	−14.3668	+	44.2164i	−0.504485	+	1.55265i	0.297149	+	0.954831i	$0.403964\pi$
$811$	−14.3668	+	44.2164i	−0.504485	+	1.55265i	−0.801634	+	0.597815i	$0.796036\pi$
$812$	−5.56220	−	17.1187i	−0.195195	−	0.600748i
$813$	3.16467	+	9.73984i	0.110990	+	0.341591i
$814$	16.1882	−	49.8221i	0.567395	−	1.74626i
$815$	18.4748	+	25.2722i	0.647143	+	0.885245i
$816$	−0.311522	−	0.958765i	−0.0109054	−	0.0335635i
$817$	−10.4984	+	7.62751i	−0.367291	+	0.266853i
$818$	28.3787			0.992238
$819$	−15.9786	+	11.6091i	−0.558338	+	0.405656i
$820$	0.0301436	+	10.2787i	0.00105266	+	0.358949i
$821$	14.3885	+	10.4539i	0.502162	+	0.364842i	0.809842	−	0.586648i	$-0.199553\pi$
$821$	14.3885	+	10.4539i	0.502162	+	0.364842i	−0.307680	+	0.951490i	$0.599553\pi$
$822$	14.2597	+	10.3603i	0.497364	+	0.361356i
$823$	1.89759	−	5.84017i	0.0661457	−	0.203575i	−0.912521	−	0.409030i	$-0.865867\pi$
$823$	1.89759	−	5.84017i	0.0661457	−	0.203575i	0.978667	+	0.205454i	$0.0658672\pi$
$824$	19.6999			0.686279
$825$	7.41658	−	23.2898i	0.258212	−	0.810847i
$826$	−9.04463			−0.314703
$827$	−9.06121	+	27.8875i	−0.315089	+	0.969745i	0.660629	+	0.750713i	$0.270290\pi$
$827$	−9.06121	+	27.8875i	−0.315089	+	0.969745i	−0.975718	+	0.219032i	$0.929710\pi$
$828$	3.61803	+	2.62866i	0.125735	+	0.0913521i
$829$	40.1826	+	29.1944i	1.39560	+	1.01396i	0.995225	+	0.0976102i	$0.0311199\pi$
$829$	40.1826	+	29.1944i	1.39560	+	1.01396i	0.400374	+	0.916352i	$0.368880\pi$
$830$	9.30001	+	12.7217i	0.322808	+	0.441578i
$831$	8.34327	−	6.06174i	0.289425	−	0.210279i
$832$	−4.63925			−0.160837
$833$	9.07286	−	6.59182i	0.314356	−	0.228393i
$834$	2.51976	+	7.75502i	0.0872521	+	0.268534i
$835$	−17.6865	+	24.4942i	−0.612068	+	0.847655i
$836$	1.86722	−	5.74670i	0.0645790	−	0.198754i
$837$	0.315575	+	0.971238i	0.0109079	+	0.0335709i
$838$	−4.58097	−	14.0988i	−0.158247	−	0.487034i
$839$	8.60481	−	26.4829i	0.297071	−	0.914291i	−0.685447	−	0.728123i	$-0.740393\pi$
$839$	8.60481	−	26.4829i	0.297071	−	0.914291i	0.982518	−	0.186168i	$-0.0596069\pi$
$840$	−9.04500	+	2.96825i	−0.312082	+	0.102414i
$841$	−3.43761	−	10.5799i	−0.118538	−	0.364823i
$842$	14.7255	−	10.6987i	0.507475	−	0.368702i
$843$	−3.56732			−0.122865
$844$	9.77688	−	7.10332i	0.336534	−	0.244506i
$845$	11.1563	−	15.4505i	0.383790	−	0.531512i
$846$	−1.63925	−	1.19099i	−0.0563587	−	0.0409470i
$847$	44.4195	+	32.2726i	1.52627	+	1.10890i
$848$	3.41635	−	10.5145i	0.117318	−	0.361068i
$849$	−28.7474			−0.986607
$850$	4.09518	+	2.93878i	0.140463	+	0.100799i
$851$	−47.9248			−1.64284
$852$	3.87532	−	11.9270i	0.132766	−	0.408613i
$853$	25.8857	+	18.8070i	0.886309	+	0.643941i	0.934913	−	0.354877i	$-0.115477\pi$
$853$	25.8857	+	18.8070i	0.886309	+	0.643941i	−0.0486043	+	0.998818i	$0.515477\pi$
$854$	−13.3475	−	9.69750i	−0.456741	−	0.331841i
$855$	−2.63115	−	0.846389i	−0.0899834	−	0.0289459i
$856$	4.98916	−	3.62484i	0.170526	−	0.123894i
$857$	31.7769			1.08548			0.542739	−	0.839902i	$-0.317387\pi$
$857$	31.7769			1.08548			0.542739	+	0.839902i	$0.317387\pi$
$858$	18.3475	−	13.3302i	0.626372	−	0.455086i
$859$	2.55910	+	7.87611i	0.0873155	+	0.268729i	0.985175	−	0.171553i	$-0.0548784\pi$
$859$	2.55910	+	7.87611i	0.0873155	+	0.268729i	−0.897859	+	0.440282i	$0.854878\pi$
$860$	−22.3473	−	7.18869i	−0.762036	−	0.245132i
$861$	−6.04745	+	18.6121i	−0.206097	+	0.634300i
$862$	−5.48525	−	16.8819i	−0.186828	−	0.574999i
$863$	−5.98671	−	18.4252i	−0.203790	−	0.627201i	−0.999761	−	0.0218664i	$-0.993039\pi$
$863$	−5.98671	−	18.4252i	−0.203790	−	0.627201i	0.795971	−	0.605335i	$-0.206961\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−0.0589101	−	20.0879i	−0.00200300	−	0.683009i
$866$	−6.71125	−	20.6551i	−0.228057	−	0.701889i
$867$	12.9311	−	9.39500i	0.439163	−	0.319071i
$868$	−4.34763			−0.147568
$869$	25.2716	−	18.3609i	0.857282	−	0.622852i
$870$	8.98269	−	2.94781i	0.304542	−	0.0999400i
$871$	14.0771	+	10.2276i	0.476983	+	0.346548i
$872$	6.41371	+	4.65983i	0.217196	+	0.157802i
$873$	−2.48120	+	7.63634i	−0.0839758	+	0.258451i
$874$	−5.52786			−0.186983
$875$	27.6375	−	38.7522i	0.934318	−	1.31006i
$876$	3.42942			0.115869
$877$	−9.18634	+	28.2726i	−0.310201	+	0.954699i	0.667485	+	0.744624i	$0.267371\pi$
$877$	−9.18634	+	28.2726i	−0.310201	+	0.954699i	−0.977685	+	0.210076i	$0.932629\pi$
$878$	8.67615	+	6.30359i	0.292806	+	0.212736i
$879$	−1.44444	−	1.04945i	−0.0487199	−	0.0353971i
$880$	10.3859	−	3.40830i	0.350110	−	0.114894i
$881$	−13.8537	+	10.0653i	−0.466741	+	0.339107i	−0.796170	−	0.605073i	$-0.793144\pi$
$881$	−13.8537	+	10.0653i	−0.466741	+	0.339107i	0.329429	+	0.944180i	$0.393144\pi$
$882$	−11.1245			−0.374582
$883$	2.34718	−	1.70533i	0.0789889	−	0.0573888i	−0.547590	−	0.836747i	$-0.684455\pi$
$883$	2.34718	−	1.70533i	0.0789889	−	0.0573888i	0.626579	+	0.779358i	$0.284455\pi$
$884$	1.44523	+	4.44796i	0.0486083	+	0.149601i
$885$	−0.0139315	−	4.75052i	−0.000468301	−	0.159687i
$886$	−7.88278	+	24.2607i	−0.264827	+	0.815055i
$887$	−8.80338	−	27.0940i	−0.295589	−	0.909728i	−0.983023	−	0.183482i	$-0.941263\pi$
$887$	−8.80338	−	27.0940i	−0.295589	−	0.909728i	0.687434	−	0.726246i	$-0.258737\pi$
$888$	−3.31152	−	10.1918i	−0.111127	−	0.342015i
$889$	−13.2850	+	40.8871i	−0.445566	+	1.37131i
$890$	−4.77705	−	1.53668i	−0.160127	−	0.0515097i
$891$	−1.51061	−	4.64918i	−0.0506073	−	0.155753i
$892$	7.57286	−	5.50201i	0.253558	−	0.184221i
$893$	2.50456			0.0838118
$894$	8.27054	−	6.00890i	0.276608	−	0.200968i
$895$	14.9457	+	4.80773i	0.499579	+	0.160705i
$896$	−3.44422	−	2.50237i	−0.115063	−	0.0835984i
$897$	−16.7850	−	12.1950i	−0.560434	−	0.407179i
$898$	3.88183	−	11.9470i	0.129538	−	0.398678i
$899$	4.31768			0.144003
$900$	−1.57295	−	4.74614i	−0.0524316	−	0.158205i
$901$	−11.1452			−0.371299
$902$	6.94399	−	21.3714i	0.231210	−	0.711590i
$903$	−36.1587	−	26.2708i	−1.20329	−	0.874238i
$904$	5.46794	+	3.97269i	0.181861	+	0.132130i
$905$	−15.6459	+	21.6680i	−0.520086	+	0.720270i
$906$	13.9164	−	10.1108i	0.462340	−	0.335910i
$907$	55.7343			1.85063			0.925314	−	0.379203i	$-0.123802\pi$
$907$	55.7343			1.85063			0.925314	+	0.379203i	$0.123802\pi$
$908$	−8.19090	+	5.95104i	−0.271824	+	0.197492i
$909$	−5.44827	−	16.7681i	−0.180708	−	0.556161i
$910$	41.9621	−	13.7705i	1.39103	−	0.456487i
$911$	0.506472	−	1.55876i	0.0167801	−	0.0516440i	−0.942316	−	0.334725i	$-0.891357\pi$
$911$	0.506472	−	1.55876i	0.0167801	−	0.0516440i	0.959096	+	0.283081i	$0.0913566\pi$
$912$	−0.381966	−	1.17557i	−0.0126482	−	0.0389270i
$913$	−10.6460	−	32.7649i	−0.352330	−	1.08436i
$914$	−0.940305	+	2.89396i	−0.0311025	+	0.0957237i
$915$	5.07286	−	7.02543i	0.167704	−	0.232254i
$916$	2.29081	+	7.05038i	0.0756904	+	0.232951i
$917$	23.1503	−	16.8197i	0.764490	−	0.555434i
$918$	1.00811			0.0332724
$919$	−28.5965	+	20.7766i	−0.943310	+	0.685355i	−0.949215	−	0.314627i	$-0.898120\pi$
$919$	−28.5965	+	20.7766i	−0.943310	+	0.685355i	0.00590477	+	0.999983i	$0.498120\pi$
$920$	−5.90155	−	8.07290i	−0.194568	−	0.266156i
$921$	−13.1669	−	9.56635i	−0.433866	−	0.315222i
$922$	−22.3233	−	16.2188i	−0.735178	−	0.534138i
$923$	−17.9786	+	55.3325i	−0.591773	+	1.82129i
$924$	20.8115			0.684648
$925$	43.5324	+	31.2397i	1.43134	+	1.02715i
$926$	−30.2060			−0.992631
$927$	−6.08761	+	18.7357i	−0.199943	+	0.615363i
$928$	3.42049	+	2.48513i	0.112283	+	0.0815785i
$929$	7.50256	+	5.45093i	0.246151	+	0.178839i	0.704019	−	0.710181i	$-0.251387\pi$
$929$	7.50256	+	5.45093i	0.246151	+	0.178839i	−0.457868	+	0.889020i	$0.651387\pi$
$930$	−0.00669666	−	2.28351i	−0.000219592	−	0.0748792i
$931$	11.1245	−	8.08243i	0.364591	−	0.264891i
$932$	−5.92778			−0.194171
$933$	−10.4853	+	7.61798i	−0.343272	+	0.249401i
$934$	−9.21572	−	28.3631i	−0.301548	−	0.928068i
$935$	−6.50320	−	8.89591i	−0.212677	−	0.290927i
$936$	1.43361	−	4.41219i	0.0468590	−	0.144217i
$937$	−3.03856	−	9.35173i	−0.0992654	−	0.305508i	0.889076	−	0.457759i	$-0.151348\pi$
$937$	−3.03856	−	9.35173i	−0.0992654	−	0.305508i	−0.988342	+	0.152251i	$0.951348\pi$
$938$	4.93425	+	15.1861i	0.161109	+	0.495843i
$939$	−1.29075	+	3.97253i	−0.0421221	+	0.129639i
$940$	2.67387	+	3.65766i	0.0872120	+	0.119300i
$941$	18.0203	+	55.4607i	0.587444	+	1.80797i	0.589227	+	0.807968i	$0.299432\pi$
$941$	18.0203	+	55.4607i	0.587444	+	1.80797i	−0.00178292	+	0.999998i	$0.500568\pi$
$942$	−15.1630	+	11.0166i	−0.494038	+	0.358940i
$943$	−20.5576			−0.669447
$944$	1.71876	−	1.24875i	0.0559409	−	0.0406434i
$945$	−0.0279172	−	9.51955i	−0.000908146	−	0.309671i
$946$	41.5192	+	30.1655i	1.34991	+	0.980765i
$947$	35.0917	+	25.4956i	1.14033	+	0.828496i	0.987165	−	0.159705i	$-0.0510544\pi$
$947$	35.0917	+	25.4956i	1.14033	+	0.828496i	0.153162	+	0.988201i	$0.451054\pi$
$948$	1.97464	−	6.07732i	0.0641333	−	0.197382i
$949$	−15.9099			−0.516458
$950$	5.02122	+	3.60332i	0.162910	+	0.116907i
$951$	30.2194			0.979931
$952$	−1.32624	+	4.08174i	−0.0429836	+	0.132290i
$953$	8.14992	+	5.92126i	0.264002	+	0.191808i	0.711909	−	0.702271i	$-0.247831\pi$
$953$	8.14992	+	5.92126i	0.264002	+	0.191808i	−0.447908	+	0.894080i	$0.647831\pi$
$954$	8.94413	+	6.49829i	0.289577	+	0.210390i
$955$	−4.27040	−	5.84160i	−0.138187	−	0.189030i
$956$	13.3606	−	9.70702i	0.432112	−	0.313948i
$957$	−20.6681			−0.668106
$958$	5.27040	−	3.82917i	0.170279	−	0.123715i
$959$	−23.1883	−	71.3662i	−0.748788	−	2.30453i
$960$	1.30902	−	1.81286i	0.0422483	−	0.0585099i
$961$	−9.25726	+	28.4909i	−0.298621	+	0.919061i
$962$	15.3630	+	47.2824i	0.495323	+	1.52445i
$963$	1.90569	+	5.86511i	0.0614100	+	0.189001i
$964$	−2.48120	+	7.63634i	−0.0799140	+	0.245950i
$965$	16.1639	−	5.30443i	0.520335	−	0.170756i
$966$	−5.88343	−	18.1073i	−0.189296	−	0.582594i
$967$	11.3754	−	8.26469i	0.365807	−	0.265775i	−0.389663	−	0.920958i	$-0.627408\pi$
$967$	11.3754	−	8.26469i	0.365807	−	0.265775i	0.755470	+	0.655183i	$0.227408\pi$
$968$	−12.8968			−0.414520
$969$	−1.00811	+	0.732432i	−0.0323850	+	0.0235291i
$970$	10.5105	−	14.5561i	0.337473	−	0.467367i
$971$	24.3406	+	17.6845i	0.781127	+	0.567522i	0.905317	−	0.424737i	$-0.139633\pi$
$971$	24.3406	+	17.6845i	0.781127	+	0.567522i	−0.124190	+	0.992258i	$0.539633\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	10.7273	−	33.0154i	0.343903	−	1.05842i
$974$	−40.1990			−1.28806
$975$	7.29731	+	22.0185i	0.233701	+	0.705158i
$976$	3.87532			0.124046
$977$	−3.66766	+	11.2879i	−0.117339	+	0.361131i	−0.992428	−	0.122831i	$-0.960803\pi$
$977$	−3.66766	+	11.2879i	−0.117339	+	0.361131i	0.875089	+	0.483962i	$0.160803\pi$
$978$	−11.3262	−	8.22899i	−0.362173	−	0.263134i
$979$	8.87532	+	6.44830i	0.283657	+	0.206089i
$980$	23.6801	+	7.61743i	0.756434	+	0.243330i
$981$	−6.41371	+	4.65983i	−0.204774	+	0.148777i
$982$	36.6280			1.16885
$983$	27.7898	−	20.1905i	0.886358	−	0.643976i	−0.0485682	−	0.998820i	$-0.515466\pi$
$983$	27.7898	−	20.1905i	0.886358	−	0.643976i	0.934926	+	0.354843i	$0.115466\pi$
$984$	−1.42049	−	4.37183i	−0.0452837	−	0.139369i
$985$	10.0391	+	3.22939i	0.319873	+	0.102897i
$986$	1.31710	−	4.05362i	0.0419451	−	0.129094i
$987$	2.66566	+	8.20405i	0.0848488	+	0.261138i
$988$	1.77204	+	5.45377i	0.0563760	+	0.173508i
$989$	14.5084	−	44.6522i	0.461340	−	1.41986i
$990$	0.0320560	+	10.9308i	0.00101881	+	0.347405i
$991$	8.76632	+	26.9800i	0.278471	+	0.857046i	0.988280	+	0.152652i	$0.0487814\pi$
$991$	8.76632	+	26.9800i	0.278471	+	0.857046i	−0.709809	+	0.704394i	$0.751219\pi$
$992$	0.826185	−	0.600258i	0.0262314	−	0.0190582i
$993$	14.0849			0.446970
$994$	−43.1933	+	31.3818i	−1.37001	+	0.995369i
$995$	33.8397	−	11.1050i	1.07279	−	0.352052i
$996$	−5.70151	−	4.14239i	−0.180659	−	0.131257i
$997$	−37.0128	−	26.8914i	−1.17221	−	0.851658i	−0.180935	−	0.983495i	$-0.557912\pi$
$997$	−37.0128	−	26.8914i	−1.17221	−	0.851658i	−0.991271	+	0.131837i	$0.957912\pi$
$998$	7.70511	−	23.7139i	0.243901	−	0.750650i
$999$	10.7163			0.339049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.g.c.121.1	yes	8
3.2	odd	2		450.2.h.d.271.2		8
5.2	odd	4		750.2.h.e.649.1		16
5.3	odd	4		750.2.h.e.649.4		16
5.4	even	2		750.2.g.d.601.2		8
25.6	even	5	inner	150.2.g.c.31.1	✓	8
25.8	odd	20		750.2.h.e.349.2		16
25.9	even	10		3750.2.a.q.1.4		4
25.12	odd	20		3750.2.c.h.1249.1		8
25.13	odd	20		3750.2.c.h.1249.8		8
25.16	even	5		3750.2.a.l.1.1		4
25.17	odd	20		750.2.h.e.349.3		16
25.19	even	10		750.2.g.d.151.2		8
75.56	odd	10		450.2.h.d.181.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.c.31.1	✓	8	25.6	even	5	inner
150.2.g.c.121.1	yes	8	1.1	even	1	trivial
450.2.h.d.181.2		8	75.56	odd	10
450.2.h.d.271.2		8	3.2	odd	2
750.2.g.d.151.2		8	25.19	even	10
750.2.g.d.601.2		8	5.4	even	2
750.2.h.e.349.2		16	25.8	odd	20
750.2.h.e.349.3		16	25.17	odd	20
750.2.h.e.649.1		16	5.2	odd	4
750.2.h.e.649.4		16	5.3	odd	4
3750.2.a.l.1.1		4	25.16	even	5
3750.2.a.q.1.4		4	25.9	even	10
3750.2.c.h.1249.1		8	25.12	odd	20
3750.2.c.h.1249.8		8	25.13	odd	20

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.12459 + 0.697217i) q^{5} +(0.809017 - 0.587785i) q^{6} -4.25729 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.12459 + 0.697217i) q^{5} +(0.809017 - 0.587785i) q^{6} -4.25729 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.00655751 - 2.23606i) q^{10} +(-1.51061 + 4.64918i) q^{11} +(0.309017 + 0.951057i) q^{12} +(-1.43361 - 4.41219i) q^{13} +(1.31557 - 4.04892i) q^{14} +(2.12864 + 0.684743i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.815575 - 0.592550i) q^{17} -1.00000 q^{18} +(1.00000 - 0.726543i) q^{19} +(2.12864 + 0.684743i) q^{20} +(3.44422 + 2.50237i) q^{21} +(-3.95483 - 2.87335i) q^{22} +(-1.38197 + 4.25325i) q^{23} -1.00000 q^{24} +(4.02778 - 2.96260i) q^{25} +4.63925 q^{26} +(0.309017 - 0.951057i) q^{27} +(3.44422 + 2.50237i) q^{28} +(-3.42049 - 2.48513i) q^{29} +(-1.30902 + 1.81286i) q^{30} +(-0.826185 + 0.600258i) q^{31} -1.00000 q^{32} +(3.95483 - 2.87335i) q^{33} +(0.311522 + 0.958765i) q^{34} +(9.04500 - 2.96825i) q^{35} +(0.309017 - 0.951057i) q^{36} +(3.31152 + 10.1918i) q^{37} +(0.381966 + 1.17557i) q^{38} +(-1.43361 + 4.41219i) q^{39} +(-1.30902 + 1.81286i) q^{40} +(1.42049 + 4.37183i) q^{41} +(-3.44422 + 2.50237i) q^{42} -10.4984 q^{43} +(3.95483 - 2.87335i) q^{44} +(-1.31963 - 1.80515i) q^{45} +(-3.61803 - 2.62866i) q^{46} +(1.63925 + 1.19099i) q^{47} +(0.309017 - 0.951057i) q^{48} +11.1245 q^{49} +(1.57295 + 4.74614i) q^{50} -1.00811 q^{51} +(-1.43361 + 4.41219i) q^{52} +(-8.94413 - 6.49829i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-0.0320560 - 10.9308i) q^{55} +(-3.44422 + 2.50237i) q^{56} -1.23607 q^{57} +(3.42049 - 2.48513i) q^{58} +(-0.656508 - 2.02052i) q^{59} +(-1.31963 - 1.80515i) q^{60} +(1.19754 - 3.68565i) q^{61} +(-0.315575 - 0.971238i) q^{62} +(-1.31557 - 4.04892i) q^{63} +(0.309017 - 0.951057i) q^{64} +(6.12209 + 8.37457i) q^{65} +(1.51061 + 4.64918i) q^{66} +(-3.03434 + 2.20457i) q^{67} -1.00811 q^{68} +(3.61803 - 2.62866i) q^{69} +(0.0279172 + 9.51955i) q^{70} +(-10.1457 - 7.37130i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.05975 - 3.26157i) q^{73} -10.7163 q^{74} +(-4.99991 + 0.0293259i) q^{75} -1.23607 q^{76} +(6.43110 - 19.7929i) q^{77} +(-3.75324 - 2.72689i) q^{78} +(-5.16968 - 3.75599i) q^{79} +(-1.31963 - 1.80515i) q^{80} +(-0.809017 + 0.587785i) q^{81} -4.59681 q^{82} +(-5.70151 + 4.14239i) q^{83} +(-1.31557 - 4.04892i) q^{84} +(-1.31963 + 1.82756i) q^{85} +(3.24417 - 9.98454i) q^{86} +(1.30651 + 4.02103i) q^{87} +(1.51061 + 4.64918i) q^{88} +(0.693488 - 2.13434i) q^{89} +(2.12459 - 0.697217i) q^{90} +(6.10328 + 18.7840i) q^{91} +(3.61803 - 2.62866i) q^{92} +1.02122 q^{93} +(-1.63925 + 1.19099i) q^{94} +(-1.61803 + 2.24082i) q^{95} +(0.809017 + 0.587785i) q^{96} +(6.49586 + 4.71952i) q^{97} +(-3.43766 + 10.5800i) q^{98} -4.88844 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 4 q^{10} - 5 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} + q^{15} - 2 q^{16} - 2 q^{17} - 8 q^{18} + 8 q^{19} + q^{20} + 3 q^{21} - 20 q^{23} - 8 q^{24} + 14 q^{25} + 14 q^{26} - 2 q^{27} + 3 q^{28} - 18 q^{29} - 6 q^{30} + 9 q^{31} - 8 q^{32} - 3 q^{34} - 4 q^{35} - 2 q^{36} + 21 q^{37} + 12 q^{38} + 6 q^{39} - 6 q^{40} + 2 q^{41} - 3 q^{42} - 32 q^{43} + q^{45} - 20 q^{46} - 10 q^{47} - 2 q^{48} + 22 q^{49} + 26 q^{50} - 2 q^{51} + 6 q^{52} + 7 q^{53} + 2 q^{54} - 40 q^{55} - 3 q^{56} + 8 q^{57} + 18 q^{58} - 25 q^{59} + q^{60} + 10 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 37 q^{65} + 5 q^{66} - 2 q^{67} - 2 q^{68} + 20 q^{69} - 11 q^{70} + 2 q^{72} - 24 q^{73} - 26 q^{74} + 14 q^{75} + 8 q^{76} + 35 q^{77} - q^{78} - 6 q^{79} + q^{80} - 2 q^{81} - 42 q^{82} + 11 q^{83} - 2 q^{84} + q^{85} + 2 q^{86} + 7 q^{87} + 5 q^{88} + 9 q^{89} + 4 q^{90} - 4 q^{91} + 20 q^{92} - 6 q^{93} + 10 q^{94} - 4 q^{95} + 2 q^{96} + q^{97} - 7 q^{98} + 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 4 * q^10 - 5 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^14 + q^15 - 2 * q^16 - 2 * q^17 - 8 * q^18 + 8 * q^19 + q^20 + 3 * q^21 - 20 * q^23 - 8 * q^24 + 14 * q^25 + 14 * q^26 - 2 * q^27 + 3 * q^28 - 18 * q^29 - 6 * q^30 + 9 * q^31 - 8 * q^32 - 3 * q^34 - 4 * q^35 - 2 * q^36 + 21 * q^37 + 12 * q^38 + 6 * q^39 - 6 * q^40 + 2 * q^41 - 3 * q^42 - 32 * q^43 + q^45 - 20 * q^46 - 10 * q^47 - 2 * q^48 + 22 * q^49 + 26 * q^50 - 2 * q^51 + 6 * q^52 + 7 * q^53 + 2 * q^54 - 40 * q^55 - 3 * q^56 + 8 * q^57 + 18 * q^58 - 25 * q^59 + q^60 + 10 * q^61 + 6 * q^62 - 2 * q^63 - 2 * q^64 + 37 * q^65 + 5 * q^66 - 2 * q^67 - 2 * q^68 + 20 * q^69 - 11 * q^70 + 2 * q^72 - 24 * q^73 - 26 * q^74 + 14 * q^75 + 8 * q^76 + 35 * q^77 - q^78 - 6 * q^79 + q^80 - 2 * q^81 - 42 * q^82 + 11 * q^83 - 2 * q^84 + q^85 + 2 * q^86 + 7 * q^87 + 5 * q^88 + 9 * q^89 + 4 * q^90 - 4 * q^91 + 20 * q^92 - 6 * q^93 + 10 * q^94 - 4 * q^95 + 2 * q^96 + q^97 - 7 * q^98 + 10 * q^99

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