LMFDB - Embedded newform 861.2.d.b.83.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(83,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("861.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.d (of order $2$, degree $1$, 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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4x^{2} + 1 $ x^4 + 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			83.3
Root			$0.517638i$ of defining polynomial
Character	$\chi$	$=$	861.83
Dual form			861.2.d.b.83.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.517638i q^{2} +(1.00000 - 1.41421i) q^{3} +1.73205 q^{4} +1.73205 q^{5} +(0.732051 + 0.517638i) q^{6} +(1.00000 + 2.44949i) q^{7} +1.93185i q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+0.517638i q^{2} +(1.00000 - 1.41421i) q^{3} +1.73205 q^{4} +1.73205 q^{5} +(0.732051 + 0.517638i) q^{6} +(1.00000 + 2.44949i) q^{7} +1.93185i q^{8} +(-1.00000 - 2.82843i) q^{9} +0.896575i q^{10} -1.03528i q^{11} +(1.73205 - 2.44949i) q^{12} -5.79555i q^{13} +(-1.26795 + 0.517638i) q^{14} +(1.73205 - 2.44949i) q^{15} +2.46410 q^{16} -1.26795 q^{17} +(1.46410 - 0.517638i) q^{18} -4.24264i q^{19} +3.00000 q^{20} +(4.46410 + 1.03528i) q^{21} +0.535898 q^{22} +7.20977i q^{23} +(2.73205 + 1.93185i) q^{24} -2.00000 q^{25} +3.00000 q^{26} +(-5.00000 - 1.41421i) q^{27} +(1.73205 + 4.24264i) q^{28} +7.20977i q^{29} +(1.26795 + 0.896575i) q^{30} +0.656339i q^{31} +5.13922i q^{32} +(-1.46410 - 1.03528i) q^{33} -0.656339i q^{34} +(1.73205 + 4.24264i) q^{35} +(-1.73205 - 4.89898i) q^{36} -3.19615 q^{37} +2.19615 q^{38} +(-8.19615 - 5.79555i) q^{39} +3.34607i q^{40} +1.00000 q^{41} +(-0.535898 + 2.31079i) q^{42} +9.26795 q^{43} -1.79315i q^{44} +(-1.73205 - 4.89898i) q^{45} -3.73205 q^{46} -6.46410 q^{47} +(2.46410 - 3.48477i) q^{48} +(-5.00000 + 4.89898i) q^{49} -1.03528i q^{50} +(-1.26795 + 1.79315i) q^{51} -10.0382i q^{52} -6.83083i q^{53} +(0.732051 - 2.58819i) q^{54} -1.79315i q^{55} +(-4.73205 + 1.93185i) q^{56} +(-6.00000 - 4.24264i) q^{57} -3.73205 q^{58} +11.6603 q^{59} +(3.00000 - 4.24264i) q^{60} +6.03579i q^{61} -0.339746 q^{62} +(5.92820 - 5.27792i) q^{63} +2.26795 q^{64} -10.0382i q^{65} +(0.535898 - 0.757875i) q^{66} -1.00000 q^{67} -2.19615 q^{68} +(10.1962 + 7.20977i) q^{69} +(-2.19615 + 0.896575i) q^{70} +9.41902i q^{71} +(5.46410 - 1.93185i) q^{72} -9.14162i q^{73} -1.65445i q^{74} +(-2.00000 + 2.82843i) q^{75} -7.34847i q^{76} +(2.53590 - 1.03528i) q^{77} +(3.00000 - 4.24264i) q^{78} -11.3923 q^{79} +4.26795 q^{80} +(-7.00000 + 5.65685i) q^{81} +0.517638i q^{82} -13.8564 q^{83} +(7.73205 + 1.79315i) q^{84} -2.19615 q^{85} +4.79744i q^{86} +(10.1962 + 7.20977i) q^{87} +2.00000 q^{88} -2.53590 q^{89} +(2.53590 - 0.896575i) q^{90} +(14.1962 - 5.79555i) q^{91} +12.4877i q^{92} +(0.928203 + 0.656339i) q^{93} -3.34607i q^{94} -7.34847i q^{95} +(7.26795 + 5.13922i) q^{96} -5.13922i q^{97} +(-2.53590 - 2.58819i) q^{98} +(-2.92820 + 1.03528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 - 4 * q^9	$ 4 q + 4 q^{3} - 4 q^{6} + 4 q^{7} - 4 q^{9} - 12 q^{14} - 4 q^{16} - 12 q^{17} - 8 q^{18} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 4 q^{24} - 8 q^{25} + 12 q^{26} - 20 q^{27} + 12 q^{30} + 8 q^{33} + 8 q^{37} - 12 q^{38} - 12 q^{39} + 4 q^{41} - 16 q^{42} + 44 q^{43} - 8 q^{46} - 12 q^{47} - 4 q^{48} - 20 q^{49} - 12 q^{51} - 4 q^{54} - 12 q^{56} - 24 q^{57} - 8 q^{58} + 12 q^{59} + 12 q^{60} - 36 q^{62} - 4 q^{63} + 16 q^{64} + 16 q^{66} - 4 q^{67} + 12 q^{68} + 20 q^{69} + 12 q^{70} + 8 q^{72} - 8 q^{75} + 24 q^{77} + 12 q^{78} - 4 q^{79} + 24 q^{80} - 28 q^{81} + 24 q^{84} + 12 q^{85} + 20 q^{87} + 8 q^{88} - 24 q^{89} + 24 q^{90} + 36 q^{91} - 24 q^{93} + 36 q^{96} - 24 q^{98} + 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 - 4 * q^9 - 12 * q^14 - 4 * q^16 - 12 * q^17 - 8 * q^18 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 4 * q^24 - 8 * q^25 + 12 * q^26 - 20 * q^27 + 12 * q^30 + 8 * q^33 + 8 * q^37 - 12 * q^38 - 12 * q^39 + 4 * q^41 - 16 * q^42 + 44 * q^43 - 8 * q^46 - 12 * q^47 - 4 * q^48 - 20 * q^49 - 12 * q^51 - 4 * q^54 - 12 * q^56 - 24 * q^57 - 8 * q^58 + 12 * q^59 + 12 * q^60 - 36 * q^62 - 4 * q^63 + 16 * q^64 + 16 * q^66 - 4 * q^67 + 12 * q^68 + 20 * q^69 + 12 * q^70 + 8 * q^72 - 8 * q^75 + 24 * q^77 + 12 * q^78 - 4 * q^79 + 24 * q^80 - 28 * q^81 + 24 * q^84 + 12 * q^85 + 20 * q^87 + 8 * q^88 - 24 * q^89 + 24 * q^90 + 36 * q^91 - 24 * q^93 + 36 * q^96 - 24 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$			0.517638i			0.366025i	0.983111	+	0.183013i	$0.0585849\pi$
$2$			0.517638i			0.366025i	−0.983111	+	0.183013i	$0.941415\pi$
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$4$	1.73205			0.866025
$5$	1.73205			0.774597			0.387298	−	0.921954i	$-0.373408\pi$
$5$	1.73205			0.774597			0.387298	+	0.921954i	$0.373408\pi$
$6$	0.732051	+	0.517638i	0.298858	+	0.211325i
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$8$			1.93185i			0.683013i
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$			0.896575i			0.283522i
$11$		−	1.03528i		−	0.312148i	−0.987745	−	0.156074i	$-0.950116\pi$
$11$		−	1.03528i		−	0.312148i	0.987745	−	0.156074i	$-0.0498838\pi$
$12$	1.73205	−	2.44949i	0.500000	−	0.707107i
$13$		−	5.79555i		−	1.60740i	−0.595036	−	0.803699i	$-0.702862\pi$
$13$		−	5.79555i		−	1.60740i	0.595036	−	0.803699i	$-0.297138\pi$
$14$	−1.26795	+	0.517638i	−0.338874	+	0.138345i
$15$	1.73205	−	2.44949i	0.447214	−	0.632456i
$16$	2.46410			0.616025
$17$	−1.26795			−0.307523			−0.153761	−	0.988108i	$-0.549139\pi$
$17$	−1.26795			−0.307523			−0.153761	+	0.988108i	$0.549139\pi$
$18$	1.46410	−	0.517638i	0.345092	−	0.122008i
$19$		−	4.24264i		−	0.973329i	−0.873589	−	0.486664i	$-0.838214\pi$
$19$		−	4.24264i		−	0.973329i	0.873589	−	0.486664i	$-0.161786\pi$
$20$	3.00000			0.670820
$21$	4.46410	+	1.03528i	0.974147	+	0.225916i
$22$	0.535898			0.114254
$23$			7.20977i			1.50334i	0.659539	+	0.751670i	$0.270752\pi$
$23$			7.20977i			1.50334i	−0.659539	+	0.751670i	$0.729248\pi$
$24$	2.73205	+	1.93185i	0.557678	+	0.394338i
$25$	−2.00000			−0.400000
$26$	3.00000			0.588348
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$	1.73205	+	4.24264i	0.327327	+	0.801784i
$29$			7.20977i			1.33882i	0.742893	+	0.669410i	$0.233453\pi$
$29$			7.20977i			1.33882i	−0.742893	+	0.669410i	$0.766547\pi$
$30$	1.26795	+	0.896575i	0.231495	+	0.163692i
$31$			0.656339i			0.117882i	0.998261	+	0.0589410i	$0.0187724\pi$
$31$			0.656339i			0.117882i	−0.998261	+	0.0589410i	$0.981228\pi$
$32$			5.13922i			0.908494i
$33$	−1.46410	−	1.03528i	−0.254867	−	0.180218i
$34$		−	0.656339i		−	0.112561i
$35$	1.73205	+	4.24264i	0.292770	+	0.717137i
$36$	−1.73205	−	4.89898i	−0.288675	−	0.816497i
$37$	−3.19615			−0.525444			−0.262722	−	0.964872i	$-0.584620\pi$
$37$	−3.19615			−0.525444			−0.262722	+	0.964872i	$0.584620\pi$
$38$	2.19615			0.356263
$39$	−8.19615	−	5.79555i	−1.31243	−	0.928032i
$40$			3.34607i			0.529059i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−0.535898	+	2.31079i	−0.0826909	+	0.356562i
$43$	9.26795			1.41335			0.706675	−	0.707539i	$-0.250195\pi$
$43$	9.26795			1.41335			0.706675	+	0.707539i	$0.250195\pi$
$44$		−	1.79315i		−	0.270328i
$45$	−1.73205	−	4.89898i	−0.258199	−	0.730297i
$46$	−3.73205			−0.550261
$47$	−6.46410			−0.942886			−0.471443	−	0.881897i	$-0.656267\pi$
$47$	−6.46410			−0.942886			−0.471443	+	0.881897i	$0.656267\pi$
$48$	2.46410	−	3.48477i	0.355662	−	0.502983i
$49$	−5.00000	+	4.89898i	−0.714286	+	0.699854i
$50$		−	1.03528i		−	0.146410i
$51$	−1.26795	+	1.79315i	−0.177548	+	0.251091i
$52$		−	10.0382i		−	1.39205i
$53$		−	6.83083i		−	0.938287i	−0.883122	−	0.469143i	$-0.844563\pi$
$53$		−	6.83083i		−	0.938287i	0.883122	−	0.469143i	$-0.155437\pi$
$54$	0.732051	−	2.58819i	0.0996195	−	0.352208i
$55$		−	1.79315i		−	0.241788i
$56$	−4.73205	+	1.93185i	−0.632347	+	0.258155i
$57$	−6.00000	−	4.24264i	−0.794719	−	0.561951i
$58$	−3.73205			−0.490042
$59$	11.6603			1.51804			0.759018	−	0.651070i	$-0.225679\pi$
$59$	11.6603			1.51804			0.759018	+	0.651070i	$0.225679\pi$
$60$	3.00000	−	4.24264i	0.387298	−	0.547723i
$61$			6.03579i			0.772804i	0.922330	+	0.386402i	$0.126282\pi$
$61$			6.03579i			0.772804i	−0.922330	+	0.386402i	$0.873718\pi$
$62$	−0.339746			−0.0431478
$63$	5.92820	−	5.27792i	0.746883	−	0.664955i
$64$	2.26795			0.283494
$65$		−	10.0382i		−	1.24508i
$66$	0.535898	−	0.757875i	0.0659645	−	0.0932879i
$67$	−1.00000			−0.122169			−0.0610847	−	0.998133i	$-0.519456\pi$
$67$	−1.00000			−0.122169			−0.0610847	+	0.998133i	$0.519456\pi$
$68$	−2.19615			−0.266323
$69$	10.1962	+	7.20977i	1.22747	+	0.867954i
$70$	−2.19615	+	0.896575i	−0.262490	+	0.107161i
$71$			9.41902i			1.11783i	0.829224	+	0.558916i	$0.188783\pi$
$71$			9.41902i			1.11783i	−0.829224	+	0.558916i	$0.811217\pi$
$72$	5.46410	−	1.93185i	0.643951	−	0.227671i
$73$		−	9.14162i		−	1.06995i	−0.844869	−	0.534973i	$-0.820322\pi$
$73$		−	9.14162i		−	1.06995i	0.844869	−	0.534973i	$-0.179678\pi$
$74$		−	1.65445i		−	0.192326i
$75$	−2.00000	+	2.82843i	−0.230940	+	0.326599i
$76$		−	7.34847i		−	0.842927i
$77$	2.53590	−	1.03528i	0.288992	−	0.117981i
$78$	3.00000	−	4.24264i	0.339683	−	0.480384i
$79$	−11.3923			−1.28173			−0.640867	−	0.767652i	$-0.721425\pi$
$79$	−11.3923			−1.28173			−0.640867	+	0.767652i	$0.721425\pi$
$80$	4.26795			0.477171
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$			0.517638i			0.0571636i
$83$	−13.8564			−1.52094			−0.760469	−	0.649374i	$-0.775031\pi$
$83$	−13.8564			−1.52094			−0.760469	+	0.649374i	$0.775031\pi$
$84$	7.73205	+	1.79315i	0.843636	+	0.195649i
$85$	−2.19615			−0.238206
$86$			4.79744i			0.517322i
$87$	10.1962	+	7.20977i	1.09314	+	0.772968i
$88$	2.00000			0.213201
$89$	−2.53590			−0.268805			−0.134402	−	0.990927i	$-0.542911\pi$
$89$	−2.53590			−0.268805			−0.134402	+	0.990927i	$0.542911\pi$
$90$	2.53590	−	0.896575i	0.267307	−	0.0945074i
$91$	14.1962	−	5.79555i	1.48816	−	0.607539i
$92$			12.4877i			1.30193i
$93$	0.928203	+	0.656339i	0.0962502	+	0.0680592i
$94$		−	3.34607i		−	0.345120i
$95$		−	7.34847i		−	0.753937i
$96$	7.26795	+	5.13922i	0.741782	+	0.524519i
$97$		−	5.13922i		−	0.521808i	−0.965365	−	0.260904i	$-0.915979\pi$
$97$		−	5.13922i		−	0.521808i	0.965365	−	0.260904i	$-0.0840207\pi$
$98$	−2.53590	−	2.58819i	−0.256164	−	0.261447i
$99$	−2.92820	+	1.03528i	−0.294295	+	0.104049i
$100$	−3.46410			−0.346410
$101$	−9.46410			−0.941713			−0.470857	−	0.882210i	$-0.656055\pi$
$101$	−9.46410			−0.941713			−0.470857	+	0.882210i	$0.656055\pi$
$102$	−0.928203	−	0.656339i	−0.0919058	−	0.0649872i
$103$			10.6945i			1.05376i	0.849939	+	0.526882i	$0.176639\pi$
$103$			10.6945i			1.05376i	−0.849939	+	0.526882i	$0.823361\pi$
$104$	11.1962			1.09787
$105$	7.73205	+	1.79315i	0.754571	+	0.174994i
$106$	3.53590			0.343437
$107$		−	5.51815i		−	0.533460i	−0.963771	−	0.266730i	$-0.914057\pi$
$107$		−	5.51815i		−	0.533460i	0.963771	−	0.266730i	$-0.0859432\pi$
$108$	−8.66025	−	2.44949i	−0.833333	−	0.235702i
$109$	10.1962			0.976614			0.488307	−	0.872672i	$-0.337615\pi$
$109$	10.1962			0.976614			0.488307	+	0.872672i	$0.337615\pi$
$110$	0.928203			0.0885007
$111$	−3.19615	+	4.52004i	−0.303365	+	0.429023i
$112$	2.46410	+	6.03579i	0.232836	+	0.570329i
$113$			5.65685i			0.532152i	0.963952	+	0.266076i	$0.0857272\pi$
$113$			5.65685i			0.532152i	−0.963952	+	0.266076i	$0.914273\pi$
$114$	2.19615	−	3.10583i	0.205689	−	0.290887i
$115$			12.4877i			1.16448i
$116$			12.4877i			1.15945i
$117$	−16.3923	+	5.79555i	−1.51547	+	0.535799i
$118$			6.03579i			0.555640i
$119$	−1.26795	−	3.10583i	−0.116233	−	0.284711i
$120$	4.73205	+	3.34607i	0.431975	+	0.305453i
$121$	9.92820			0.902564
$122$	−3.12436			−0.282866
$123$	1.00000	−	1.41421i	0.0901670	−	0.127515i
$124$			1.13681i			0.102089i
$125$	−12.1244			−1.08444
$126$	2.73205	+	3.06866i	0.243390	+	0.273378i
$127$	−12.5359			−1.11238			−0.556191	−	0.831055i	$-0.687738\pi$
$127$	−12.5359			−1.11238			−0.556191	+	0.831055i	$0.687738\pi$
$128$			11.4524i			1.01226i
$129$	9.26795	−	13.1069i	0.815997	−	1.15399i
$130$	5.19615			0.455733
$131$	7.26795			0.635004			0.317502	−	0.948258i	$-0.397156\pi$
$131$	7.26795			0.635004			0.317502	+	0.948258i	$0.397156\pi$
$132$	−2.53590	−	1.79315i	−0.220722	−	0.156074i
$133$	10.3923	−	4.24264i	0.901127	−	0.367884i
$134$		−	0.517638i		−	0.0447171i
$135$	−8.66025	−	2.44949i	−0.745356	−	0.210819i
$136$		−	2.44949i		−	0.210042i
$137$		−	12.8666i		−	1.09927i	−0.835405	−	0.549635i	$-0.814767\pi$
$137$		−	12.8666i		−	1.09927i	0.835405	−	0.549635i	$-0.185233\pi$
$138$	−3.73205	+	5.27792i	−0.317693	+	0.449286i
$139$		−	13.6245i		−	1.15561i	−0.816173	−	0.577807i	$-0.803908\pi$
$139$		−	13.6245i		−	1.15561i	0.816173	−	0.577807i	$-0.196092\pi$
$140$	3.00000	+	7.34847i	0.253546	+	0.621059i
$141$	−6.46410	+	9.14162i	−0.544376	+	0.769863i
$142$	−4.87564			−0.409155
$143$	−6.00000			−0.501745
$144$	−2.46410	−	6.96953i	−0.205342	−	0.580794i
$145$			12.4877i			1.03705i
$146$	4.73205			0.391627
$147$	1.92820	+	11.9700i	0.159036	+	0.987273i
$148$	−5.53590			−0.455048
$149$		−	3.96524i		−	0.324845i	−0.986721	−	0.162423i	$-0.948069\pi$
$149$		−	3.96524i		−	0.324845i	0.986721	−	0.162423i	$-0.0519308\pi$
$150$	−1.46410	−	1.03528i	−0.119543	−	0.0845299i
$151$	−10.9282			−0.889325			−0.444662	−	0.895698i	$-0.646676\pi$
$151$	−10.9282			−0.889325			−0.444662	+	0.895698i	$0.646676\pi$
$152$	8.19615			0.664796
$153$	1.26795	+	3.58630i	0.102508	+	0.289935i
$154$	0.535898	+	1.31268i	0.0431839	+	0.105779i
$155$			1.13681i			0.0913109i
$156$	−14.1962	−	10.0382i	−1.13660	−	0.803699i
$157$			3.76217i			0.300254i	0.988667	+	0.150127i	$0.0479682\pi$
$157$			3.76217i			0.300254i	−0.988667	+	0.150127i	$0.952032\pi$
$158$		−	5.89709i		−	0.469147i
$159$	−9.66025	−	6.83083i	−0.766108	−	0.541720i
$160$			8.90138i			0.703716i
$161$	−17.6603	+	7.20977i	−1.39182	+	0.568209i
$162$	−2.92820	−	3.62347i	−0.230061	−	0.284686i
$163$	7.66025			0.599997			0.299999	−	0.953940i	$-0.403014\pi$
$163$	7.66025			0.599997			0.299999	+	0.953940i	$0.403014\pi$
$164$	1.73205			0.135250
$165$	−2.53590	−	1.79315i	−0.197419	−	0.139597i
$166$		−	7.17260i		−	0.556702i
$167$	17.1962			1.33068			0.665339	−	0.746541i	$-0.268287\pi$
$167$	17.1962			1.33068			0.665339	+	0.746541i	$0.268287\pi$
$168$	−2.00000	+	8.62398i	−0.154303	+	0.665355i
$169$	−20.5885			−1.58373
$170$		−	1.13681i		−	0.0871895i
$171$	−12.0000	+	4.24264i	−0.917663	+	0.324443i
$172$	16.0526			1.22400
$173$	−18.4641			−1.40380			−0.701900	−	0.712276i	$-0.747665\pi$
$173$	−18.4641			−1.40380			−0.701900	+	0.712276i	$0.747665\pi$
$174$	−3.73205	+	5.27792i	−0.282926	+	0.400118i
$175$	−2.00000	−	4.89898i	−0.151186	−	0.370328i
$176$		−	2.55103i		−	0.192291i
$177$	11.6603	−	16.4901i	0.876438	−	1.23947i
$178$		−	1.31268i		−	0.0983893i
$179$		−	3.96524i		−	0.296376i	−0.988959	−	0.148188i	$-0.952656\pi$
$179$		−	3.96524i		−	0.296376i	0.988959	−	0.148188i	$-0.0473441\pi$
$180$	−3.00000	−	8.48528i	−0.223607	−	0.632456i
$181$			19.4201i			1.44348i	0.692164	+	0.721741i	$0.256658\pi$
$181$			19.4201i			1.44348i	−0.692164	+	0.721741i	$0.743342\pi$
$182$	3.00000	+	7.34847i	0.222375	+	0.544705i
$183$	8.53590	+	6.03579i	0.630992	+	0.446179i
$184$	−13.9282			−1.02680
$185$	−5.53590			−0.407007
$186$	−0.339746	+	0.480473i	−0.0249114	+	0.0352300i
$187$			1.31268i			0.0959925i
$188$	−11.1962			−0.816563
$189$	−1.53590	−	13.6617i	−0.111720	−	0.993740i
$190$	3.80385			0.275960
$191$		−	13.2827i		−	0.961104i	−0.876966	−	0.480552i	$-0.840436\pi$
$191$		−	13.2827i		−	0.961104i	0.876966	−	0.480552i	$-0.159564\pi$
$192$	2.26795	−	3.20736i	0.163675	−	0.231472i
$193$	10.1962			0.733935			0.366968	−	0.930234i	$-0.380396\pi$
$193$	10.1962			0.733935			0.366968	+	0.930234i	$0.380396\pi$
$194$	2.66025			0.190995
$195$	−14.1962	−	10.0382i	−1.01661	−	0.718850i
$196$	−8.66025	+	8.48528i	−0.618590	+	0.606092i
$197$			22.1469i			1.57790i	0.614455	+	0.788952i	$0.289376\pi$
$197$			22.1469i			1.57790i	−0.614455	+	0.788952i	$0.710624\pi$
$198$	−0.535898	−	1.51575i	−0.0380846	−	0.107720i
$199$		−	5.55532i		−	0.393806i	−0.980423	−	0.196903i	$-0.936912\pi$
$199$		−	5.55532i		−	0.393806i	0.980423	−	0.196903i	$-0.0630884\pi$
$200$		−	3.86370i		−	0.273205i
$201$	−1.00000	+	1.41421i	−0.0705346	+	0.0997509i
$202$		−	4.89898i		−	0.344691i
$203$	−17.6603	+	7.20977i	−1.23951	+	0.506027i
$204$	−2.19615	+	3.10583i	−0.153761	+	0.217451i
$205$	1.73205			0.120972
$206$	−5.53590			−0.385704
$207$	20.3923	−	7.20977i	1.41736	−	0.501114i
$208$		−	14.2808i		−	0.990198i
$209$	−4.39230			−0.303822
$210$	−0.928203	+	4.00240i	−0.0640521	+	0.276192i
$211$	23.9282			1.64729			0.823643	−	0.567109i	$-0.191938\pi$
$211$	23.9282			1.64729			0.823643	+	0.567109i	$0.191938\pi$
$212$		−	11.8313i		−	0.812580i
$213$	13.3205	+	9.41902i	0.912706	+	0.645381i
$214$	2.85641			0.195260
$215$	16.0526			1.09478
$216$	2.73205	−	9.65926i	0.185893	−	0.657229i
$217$	−1.60770	+	0.656339i	−0.109137	+	0.0445552i
$218$			5.27792i			0.357466i
$219$	−12.9282	−	9.14162i	−0.873607	−	0.617733i
$220$		−	3.10583i		−	0.209395i
$221$			7.34847i			0.494312i
$222$	−2.33975	−	1.65445i	−0.157033	−	0.111039i
$223$			18.5235i			1.24042i	0.784434	+	0.620212i	$0.212953\pi$
$223$			18.5235i			1.24042i	−0.784434	+	0.620212i	$0.787047\pi$
$224$	−12.5885	+	5.13922i	−0.841102	+	0.343378i
$225$	2.00000	+	5.65685i	0.133333	+	0.377124i
$226$	−2.92820			−0.194781
$227$	−14.3205			−0.950486			−0.475243	−	0.879855i	$-0.657640\pi$
$227$	−14.3205			−0.950486			−0.475243	+	0.879855i	$0.657640\pi$
$228$	−10.3923	−	7.34847i	−0.688247	−	0.486664i
$229$			16.7303i			1.10557i	0.833324	+	0.552786i	$0.186435\pi$
$229$			16.7303i			1.10557i	−0.833324	+	0.552786i	$0.813565\pi$
$230$	−6.46410			−0.426230
$231$	1.07180	−	4.62158i	0.0705191	−	0.304078i
$232$	−13.9282			−0.914431
$233$		−	27.1475i		−	1.77849i	−0.457432	−	0.889245i	$-0.651231\pi$
$233$		−	27.1475i		−	1.77849i	0.457432	−	0.889245i	$-0.348769\pi$
$234$	−3.00000	−	8.48528i	−0.196116	−	0.554700i
$235$	−11.1962			−0.730356
$236$	20.1962			1.31466
$237$	−11.3923	+	16.1112i	−0.740010	+	1.04653i
$238$	1.60770	−	0.656339i	0.104211	−	0.0425441i
$239$		−	13.1069i		−	0.847812i	−0.905706	−	0.423906i	$-0.860659\pi$
$239$		−	13.1069i		−	0.847812i	0.905706	−	0.423906i	$-0.139341\pi$
$240$	4.26795	−	6.03579i	0.275495	−	0.389609i
$241$			15.1774i			0.977663i	0.872378	+	0.488832i	$0.162577\pi$
$241$			15.1774i			0.977663i	−0.872378	+	0.488832i	$0.837423\pi$
$242$			5.13922i			0.330361i
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$			10.4543i			0.669268i
$245$	−8.66025	+	8.48528i	−0.553283	+	0.542105i
$246$	0.732051	+	0.517638i	0.0466739	+	0.0330034i
$247$	−24.5885			−1.56453
$248$	−1.26795			−0.0805149
$249$	−13.8564	+	19.5959i	−0.878114	+	1.24184i
$250$		−	6.27603i		−	0.396931i
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$	10.2679	−	9.14162i	0.646820	−	0.575868i
$253$	7.46410			0.469264
$254$		−	6.48906i		−	0.407160i
$255$	−2.19615	+	3.10583i	−0.137528	+	0.194495i
$256$	−1.39230			−0.0870191
$257$	−19.8564			−1.23861			−0.619304	−	0.785151i	$-0.712585\pi$
$257$	−19.8564			−1.23861			−0.619304	+	0.785151i	$0.712585\pi$
$258$	6.78461	+	4.79744i	0.422391	+	0.298676i
$259$	−3.19615	−	7.82894i	−0.198599	−	0.486467i
$260$		−	17.3867i		−	1.07828i
$261$	20.3923	−	7.20977i	1.26225	−	0.446273i
$262$			3.76217i			0.232427i
$263$		−	4.14110i		−	0.255351i	−0.991816	−	0.127676i	$-0.959248\pi$
$263$		−	4.14110i		−	0.255351i	0.991816	−	0.127676i	$-0.0407517\pi$
$264$	2.00000	−	2.82843i	0.123091	−	0.174078i
$265$		−	11.8313i		−	0.726794i
$266$	2.19615	+	5.37945i	0.134655	+	0.329835i
$267$	−2.53590	+	3.58630i	−0.155194	+	0.219478i
$268$	−1.73205			−0.105802
$269$	−10.8564			−0.661927			−0.330963	−	0.943644i	$-0.607374\pi$
$269$	−10.8564			−0.661927			−0.330963	+	0.943644i	$0.607374\pi$
$270$	1.26795	−	4.48288i	0.0771649	−	0.272819i
$271$		−	19.8362i		−	1.20496i	−0.798134	−	0.602480i	$-0.794179\pi$
$271$		−	19.8362i		−	1.20496i	0.798134	−	0.602480i	$-0.205821\pi$
$272$	−3.12436			−0.189442
$273$	6.00000	−	25.8719i	0.363137	−	1.56584i
$274$	6.66025			0.402361
$275$			2.07055i			0.124859i
$276$	17.6603	+	12.4877i	1.06302	+	0.751670i
$277$	−18.0718			−1.08583			−0.542915	−	0.839788i	$-0.682679\pi$
$277$	−18.0718			−1.08583			−0.542915	+	0.839788i	$0.682679\pi$
$278$	7.05256			0.422984
$279$	1.85641	−	0.656339i	0.111140	−	0.0392940i
$280$	−8.19615	+	3.34607i	−0.489814	+	0.199966i
$281$			4.76028i			0.283974i	0.989868	+	0.141987i	$0.0453492\pi$
$281$			4.76028i			0.283974i	−0.989868	+	0.141987i	$0.954651\pi$
$282$	−4.73205	−	3.34607i	−0.281790	−	0.199255i
$283$		−	8.66115i		−	0.514852i	−0.966298	−	0.257426i	$-0.917126\pi$
$283$		−	8.66115i		−	0.514852i	0.966298	−	0.257426i	$-0.0828743\pi$
$284$			16.3142i			0.968071i
$285$	−10.3923	−	7.34847i	−0.615587	−	0.435286i
$286$		−	3.10583i		−	0.183651i
$287$	1.00000	+	2.44949i	0.0590281	+	0.144589i
$288$	14.5359	−	5.13922i	0.856536	−	0.302831i
$289$	−15.3923			−0.905430
$290$	−6.46410			−0.379585
$291$	−7.26795	−	5.13922i	−0.426055	−	0.301266i
$292$		−	15.8338i		−	0.926600i
$293$	−20.1962			−1.17987			−0.589936	−	0.807450i	$-0.700847\pi$
$293$	−20.1962			−1.17987			−0.589936	+	0.807450i	$0.700847\pi$
$294$	−6.19615	+	0.998111i	−0.361367	+	0.0582110i
$295$	20.1962			1.17587
$296$		−	6.17449i		−	0.358885i
$297$	−1.46410	+	5.17638i	−0.0849558	+	0.300364i
$298$	2.05256			0.118902
$299$	41.7846			2.41647
$300$	−3.46410	+	4.89898i	−0.200000	+	0.282843i
$301$	9.26795	+	22.7017i	0.534196	+	1.30851i
$302$		−	5.65685i		−	0.325515i
$303$	−9.46410	+	13.3843i	−0.543698	+	0.768906i
$304$		−	10.4543i		−	0.599595i
$305$			10.4543i			0.598611i
$306$	−1.85641	+	0.656339i	−0.106124	+	0.0375204i
$307$		−	12.4877i		−	0.712710i	−0.934351	−	0.356355i	$-0.884019\pi$
$307$		−	12.4877i		−	0.712710i	0.934351	−	0.356355i	$-0.115981\pi$
$308$	4.39230	−	1.79315i	0.250275	−	0.102174i
$309$	15.1244	+	10.6945i	0.860395	+	0.608391i
$310$	−0.588457			−0.0334221
$311$	9.00000			0.510343			0.255172	−	0.966896i	$-0.417868\pi$
$311$	9.00000			0.510343			0.255172	+	0.966896i	$0.417868\pi$
$312$	11.1962	−	15.8338i	0.633857	−	0.896410i
$313$			14.2808i			0.807201i	0.914935	+	0.403600i	$0.132241\pi$
$313$			14.2808i			0.807201i	−0.914935	+	0.403600i	$0.867759\pi$
$314$	−1.94744			−0.109900
$315$	10.2679	−	9.14162i	0.578533	−	0.515072i
$316$	−19.7321			−1.11001
$317$			25.3171i			1.42195i	0.703216	+	0.710976i	$0.251747\pi$
$317$			25.3171i			1.42195i	−0.703216	+	0.710976i	$0.748253\pi$
$318$	3.53590	−	5.00052i	0.198283	−	0.280415i
$319$	7.46410			0.417909
$320$	3.92820			0.219593
$321$	−7.80385	−	5.51815i	−0.435568	−	0.307993i
$322$	−3.73205	−	9.14162i	−0.207979	−	0.509443i
$323$			5.37945i			0.299321i
$324$	−12.1244	+	9.79796i	−0.673575	+	0.544331i
$325$			11.5911i			0.642959i
$326$			3.96524i			0.219614i
$327$	10.1962	−	14.4195i	0.563849	−	0.797402i
$328$			1.93185i			0.106669i
$329$	−6.46410	−	15.8338i	−0.356377	−	0.872943i
$330$	0.928203	−	1.31268i	0.0510959	−	0.0722605i
$331$	−15.1962			−0.835256			−0.417628	−	0.908618i	$-0.637138\pi$
$331$	−15.1962			−0.835256			−0.417628	+	0.908618i	$0.637138\pi$
$332$	−24.0000			−1.31717
$333$	3.19615	+	9.04008i	0.175148	+	0.495394i
$334$			8.90138i			0.487062i
$335$	−1.73205			−0.0946320
$336$	11.0000	+	2.55103i	0.600099	+	0.139170i
$337$	21.7321			1.18382			0.591910	−	0.806004i	$-0.298374\pi$
$337$	21.7321			1.18382			0.591910	+	0.806004i	$0.298374\pi$
$338$		−	10.6574i		−	0.579684i
$339$	8.00000	+	5.65685i	0.434500	+	0.307238i
$340$	−3.80385			−0.206293
$341$	0.679492			0.0367966
$342$	−2.19615	−	6.21166i	−0.118754	−	0.335888i
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$			17.9043i			0.965335i
$345$	17.6603	+	12.4877i	0.950796	+	0.672314i
$346$		−	9.55772i		−	0.513826i
$347$		−	5.27792i		−	0.283333i	−0.989914	−	0.141667i	$-0.954754\pi$
$347$		−	5.27792i		−	0.283333i	0.989914	−	0.141667i	$-0.0452461\pi$
$348$	17.6603	+	12.4877i	0.946689	+	0.669410i
$349$		−	5.55532i		−	0.297369i	−0.988885	−	0.148685i	$-0.952496\pi$
$349$		−	5.55532i		−	0.297369i	0.988885	−	0.148685i	$-0.0475039\pi$
$350$	2.53590	−	1.03528i	0.135549	−	0.0553378i
$351$	−8.19615	+	28.9778i	−0.437478	+	1.54672i
$352$	5.32051			0.283584
$353$	6.92820			0.368751			0.184376	−	0.982856i	$-0.440974\pi$
$353$	6.92820			0.368751			0.184376	+	0.982856i	$0.440974\pi$
$354$	8.53590	+	6.03579i	0.453678	+	0.320799i
$355$			16.3142i			0.865869i
$356$	−4.39230			−0.232792
$357$	−5.66025	−	1.31268i	−0.299572	−	0.0694743i
$358$	2.05256			0.108481
$359$		−	6.83083i		−	0.360517i	−0.983619	−	0.180259i	$-0.942306\pi$
$359$		−	6.83083i		−	0.360517i	0.983619	−	0.180259i	$-0.0576935\pi$
$360$	9.46410	−	3.34607i	0.498802	−	0.176353i
$361$	1.00000			0.0526316
$362$	−10.0526			−0.528351
$363$	9.92820	−	14.0406i	0.521096	−	0.736940i
$364$	24.5885	−	10.0382i	1.28879	−	0.526144i
$365$		−	15.8338i		−	0.828776i
$366$	−3.12436	+	4.41851i	−0.163313	+	0.230959i
$367$		−	2.20925i		−	0.115322i	−0.998336	−	0.0576610i	$-0.981636\pi$
$367$		−	2.20925i		−	0.115322i	0.998336	−	0.0576610i	$-0.0183643\pi$
$368$			17.7656i			0.926096i
$369$	−1.00000	−	2.82843i	−0.0520579	−	0.147242i
$370$		−	2.86559i		−	0.148975i
$371$	16.7321	−	6.83083i	0.868685	−	0.354639i
$372$	1.60770	+	1.13681i	0.0833551	+	0.0589410i
$373$	−16.8038			−0.870070			−0.435035	−	0.900413i	$-0.643264\pi$
$373$	−16.8038			−0.870070			−0.435035	+	0.900413i	$0.643264\pi$
$374$	−0.679492			−0.0351357
$375$	−12.1244	+	17.1464i	−0.626099	+	0.885438i
$376$		−	12.4877i		−	0.644003i
$377$	41.7846			2.15202
$378$	7.07180	−	0.795040i	0.363734	−	0.0408924i
$379$	11.8038			0.606323			0.303161	−	0.952939i	$-0.401958\pi$
$379$	11.8038			0.606323			0.303161	+	0.952939i	$0.401958\pi$
$380$		−	12.7279i		−	0.652929i
$381$	−12.5359	+	17.7284i	−0.642234	+	0.908255i
$382$	6.87564			0.351789
$383$	13.3923			0.684315			0.342157	−	0.939643i	$-0.388842\pi$
$383$	13.3923			0.684315			0.342157	+	0.939643i	$0.388842\pi$
$384$	16.1962	+	11.4524i	0.826506	+	0.584428i
$385$	4.39230	−	1.79315i	0.223853	−	0.0913874i
$386$			5.27792i			0.268639i
$387$	−9.26795	−	26.2137i	−0.471116	−	1.33252i
$388$		−	8.90138i		−	0.451899i
$389$		−	20.9358i		−	1.06149i	−0.847532	−	0.530744i	$-0.821913\pi$
$389$		−	20.9358i		−	1.06149i	0.847532	−	0.530744i	$-0.178087\pi$
$390$	5.19615	−	7.34847i	0.263117	−	0.372104i
$391$		−	9.14162i		−	0.462312i
$392$	−9.46410	−	9.65926i	−0.478009	−	0.487866i
$393$	7.26795	−	10.2784i	0.366620	−	0.518478i
$394$	−11.4641			−0.577553
$395$	−19.7321			−0.992827
$396$	−5.07180	+	1.79315i	−0.254867	+	0.0901092i
$397$		−	13.5601i		−	0.680563i	−0.940324	−	0.340282i	$-0.889478\pi$
$397$		−	13.5601i		−	0.680563i	0.940324	−	0.340282i	$-0.110522\pi$
$398$	2.87564			0.144143
$399$	4.39230	−	18.9396i	0.219890	−	0.948165i
$400$	−4.92820			−0.246410
$401$		−	22.4243i		−	1.11982i	−0.828554	−	0.559909i	$-0.810836\pi$
$401$		−	22.4243i		−	1.11982i	0.828554	−	0.559909i	$-0.189164\pi$
$402$	−0.732051	−	0.517638i	−0.0365114	−	0.0258174i
$403$	3.80385			0.189483
$404$	−16.3923			−0.815548
$405$	−12.1244	+	9.79796i	−0.602464	+	0.486864i
$406$	−3.73205	−	9.14162i	−0.185219	−	0.453691i
$407$			3.30890i			0.164016i
$408$	−3.46410	−	2.44949i	−0.171499	−	0.121268i
$409$		−	1.31268i		−	0.0649077i	−0.999473	−	0.0324539i	$-0.989668\pi$
$409$		−	1.31268i		−	0.0649077i	0.999473	−	0.0324539i	$-0.0103322\pi$
$410$			0.896575i			0.0442787i
$411$	−18.1962	−	12.8666i	−0.897550	−	0.634664i
$412$			18.5235i			0.912586i
$413$	11.6603	+	28.5617i	0.573764	+	1.40543i
$414$	3.73205	+	10.5558i	0.183420	+	0.518791i
$415$	−24.0000			−1.17811
$416$	29.7846			1.46031
$417$	−19.2679	−	13.6245i	−0.943556	−	0.667195i
$418$		−	2.27362i		−	0.111207i
$419$	34.9808			1.70892			0.854461	−	0.519515i	$-0.173888\pi$
$419$	34.9808			1.70892			0.854461	+	0.519515i	$0.173888\pi$
$420$	13.3923	+	3.10583i	0.653478	+	0.151549i
$421$	26.5885			1.29584			0.647921	−	0.761707i	$-0.275639\pi$
$421$	26.5885			1.29584			0.647921	+	0.761707i	$0.275639\pi$
$422$			12.3861i			0.602948i
$423$	6.46410	+	18.2832i	0.314295	+	0.888962i
$424$	13.1962			0.640862
$425$	2.53590			0.123009
$426$	−4.87564	+	6.89520i	−0.236226	+	0.334074i
$427$	−14.7846	+	6.03579i	−0.715477	+	0.292092i
$428$		−	9.55772i		−	0.461990i
$429$	−6.00000	+	8.48528i	−0.289683	+	0.409673i
$430$			8.30942i			0.400716i
$431$			30.8081i			1.48397i	0.670415	+	0.741987i	$0.266116\pi$
$431$			30.8081i			1.48397i	−0.670415	+	0.741987i	$0.733884\pi$
$432$	−12.3205	−	3.48477i	−0.592771	−	0.167661i
$433$			21.3891i			1.02789i	0.857822	+	0.513947i	$0.171817\pi$
$433$			21.3891i			1.02789i	−0.857822	+	0.513947i	$0.828183\pi$
$434$	−0.339746	−	0.832204i	−0.0163083	−	0.0399471i
$435$	17.6603	+	12.4877i	0.846744	+	0.598739i
$436$	17.6603			0.845773
$437$	30.5885			1.46324
$438$	4.73205	−	6.69213i	0.226106	−	0.319762i
$439$		−	29.2180i		−	1.39450i	−0.716828	−	0.697250i	$-0.754407\pi$
$439$		−	29.2180i		−	1.39450i	0.716828	−	0.697250i	$-0.245593\pi$
$440$	3.46410			0.165145
$441$	18.8564	+	9.24316i	0.897924	+	0.440150i
$442$	−3.80385			−0.180931
$443$		−	15.5563i		−	0.739104i	−0.929210	−	0.369552i	$-0.879511\pi$
$443$		−	15.5563i		−	0.739104i	0.929210	−	0.369552i	$-0.120489\pi$
$444$	−5.53590	+	7.82894i	−0.262722	+	0.371545i
$445$	−4.39230			−0.208215
$446$	−9.58846			−0.454027
$447$	−5.60770	−	3.96524i	−0.265235	−	0.187549i
$448$	2.26795	+	5.55532i	0.107151	+	0.262464i
$449$			29.9759i			1.41465i	0.706889	+	0.707325i	$0.250098\pi$
$449$			29.9759i			1.41465i	−0.706889	+	0.707325i	$0.749902\pi$
$450$	−2.92820	+	1.03528i	−0.138037	+	0.0488034i
$451$		−	1.03528i		−	0.0487493i
$452$			9.79796i			0.460857i
$453$	−10.9282	+	15.4548i	−0.513452	+	0.726130i
$454$		−	7.41284i		−	0.347902i
$455$	24.5885	−	10.0382i	1.15272	−	0.470598i
$456$	8.19615	−	11.5911i	0.383820	−	0.542803i
$457$	−0.784610			−0.0367025			−0.0183512	−	0.999832i	$-0.505842\pi$
$457$	−0.784610			−0.0367025			−0.0183512	+	0.999832i	$0.505842\pi$
$458$	−8.66025			−0.404667
$459$	6.33975	+	1.79315i	0.295914	+	0.0836971i
$460$			21.6293i			1.00847i
$461$	24.4641			1.13941			0.569703	−	0.821850i	$-0.307058\pi$
$461$	24.4641			1.13941			0.569703	+	0.821850i	$0.307058\pi$
$462$	2.39230	+	0.554803i	0.111300	+	0.0258118i
$463$	17.9282			0.833194			0.416597	−	0.909091i	$-0.363223\pi$
$463$	17.9282			0.833194			0.416597	+	0.909091i	$0.363223\pi$
$464$			17.7656i			0.824747i
$465$	1.60770	+	1.13681i	0.0745551	+	0.0527184i
$466$	14.0526			0.650972
$467$	−3.80385			−0.176021			−0.0880105	−	0.996120i	$-0.528051\pi$
$467$	−3.80385			−0.176021			−0.0880105	+	0.996120i	$0.528051\pi$
$468$	−28.3923	+	10.0382i	−1.31243	+	0.464016i
$469$	−1.00000	−	2.44949i	−0.0461757	−	0.113107i
$470$		−	5.79555i		−	0.267329i
$471$	5.32051	+	3.76217i	0.245156	+	0.173352i
$472$			22.5259i			1.03684i
$473$		−	9.59489i		−	0.441173i
$474$	−8.33975	−	5.89709i	−0.383057	−	0.270862i
$475$			8.48528i			0.389331i
$476$	−2.19615	−	5.37945i	−0.100660	−	0.246567i
$477$	−19.3205	+	6.83083i	−0.884625	+	0.312762i
$478$	6.78461			0.310321
$479$	−17.0718			−0.780030			−0.390015	−	0.920808i	$-0.627530\pi$
$479$	−17.0718			−0.780030			−0.390015	+	0.920808i	$0.627530\pi$
$480$	12.5885	+	8.90138i	0.574582	+	0.406291i
$481$			18.5235i			0.844598i
$482$	−7.85641			−0.357850
$483$	−7.46410	+	32.1851i	−0.339628	+	1.46447i
$484$	17.1962			0.781643
$485$		−	8.90138i		−	0.404191i
$486$	−8.05256	+	0.517638i	−0.365271	+	0.0234805i
$487$	3.60770			0.163480			0.0817401	−	0.996654i	$-0.473952\pi$
$487$	3.60770			0.163480			0.0817401	+	0.996654i	$0.473952\pi$
$488$	−11.6603			−0.527835
$489$	7.66025	−	10.8332i	0.346409	−	0.489896i
$490$	−4.39230	−	4.48288i	−0.198424	−	0.202516i
$491$		−	39.5708i		−	1.78580i	−0.450251	−	0.892902i	$-0.648666\pi$
$491$		−	39.5708i		−	1.78580i	0.450251	−	0.892902i	$-0.351334\pi$
$492$	1.73205	−	2.44949i	0.0780869	−	0.110432i
$493$		−	9.14162i		−	0.411718i
$494$		−	12.7279i		−	0.572656i
$495$	−5.07180	+	1.79315i	−0.227960	+	0.0805961i
$496$			1.61729i			0.0726183i
$497$	−23.0718	+	9.41902i	−1.03491	+	0.422501i
$498$	−10.1436	−	7.17260i	−0.454545	−	0.321412i
$499$	40.7846			1.82577			0.912885	−	0.408217i	$-0.133849\pi$
$499$	40.7846			1.82577			0.912885	+	0.408217i	$0.133849\pi$
$500$	−21.0000			−0.939149
$501$	17.1962	−	24.3190i	0.768267	−	1.08649i
$502$			12.4233i			0.554480i
$503$	7.73205			0.344755			0.172378	−	0.985031i	$-0.444855\pi$
$503$	7.73205			0.344755			0.172378	+	0.985031i	$0.444855\pi$
$504$	10.1962	+	11.4524i	0.454173	+	0.510131i
$505$	−16.3923			−0.729448
$506$			3.86370i			0.171763i
$507$	−20.5885	+	29.1165i	−0.914365	+	1.29311i
$508$	−21.7128			−0.963350
$509$	9.80385			0.434548			0.217274	−	0.976111i	$-0.430284\pi$
$509$	9.80385			0.434548			0.217274	+	0.976111i	$0.430284\pi$
$510$	−1.60770	−	1.13681i	−0.0711899	−	0.0503389i
$511$	22.3923	−	9.14162i	0.990577	−	0.404401i
$512$			22.1841i			0.980408i
$513$	−6.00000	+	21.2132i	−0.264906	+	0.936586i
$514$		−	10.2784i		−	0.453362i
$515$			18.5235i			0.816242i
$516$	16.0526	−	22.7017i	0.706675	−	0.999389i
$517$			6.69213i			0.294320i
$518$	4.05256	−	1.65445i	0.178059	−	0.0726924i
$519$	−18.4641	+	26.1122i	−0.810484	+	1.14620i
$520$	19.3923			0.850409
$521$	−21.7128			−0.951256			−0.475628	−	0.879647i	$-0.657779\pi$
$521$	−21.7128			−0.951256			−0.475628	+	0.879647i	$0.657779\pi$
$522$	3.73205	+	10.5558i	0.163347	+	0.462016i
$523$		−	15.3533i		−	0.671352i	−0.941978	−	0.335676i	$-0.891035\pi$
$523$		−	15.3533i		−	0.671352i	0.941978	−	0.335676i	$-0.108965\pi$
$524$	12.5885			0.549929
$525$	−8.92820	−	2.07055i	−0.389659	−	0.0903663i
$526$	2.14359			0.0934651
$527$		−	0.832204i		−	0.0362514i
$528$	−3.60770	−	2.55103i	−0.157005	−	0.111019i
$529$	−28.9808			−1.26003
$530$	6.12436			0.266025
$531$	−11.6603	−	32.9802i	−0.506012	−	1.43122i
$532$	18.0000	−	7.34847i	0.780399	−	0.318597i
$533$		−	5.79555i		−	0.251033i
$534$	−1.85641	−	1.31268i	−0.0803346	−	0.0568051i
$535$		−	9.55772i		−	0.413216i
$536$		−	1.93185i		−	0.0834433i
$537$	−5.60770	−	3.96524i	−0.241990	−	0.171113i
$538$		−	5.61969i		−	0.242282i
$539$	5.07180	+	5.17638i	0.218458	+	0.222963i
$540$	−15.0000	−	4.24264i	−0.645497	−	0.182574i
$541$	38.1244			1.63909			0.819547	−	0.573012i	$-0.194225\pi$
$541$	38.1244			1.63909			0.819547	+	0.573012i	$0.194225\pi$
$542$	10.2679			0.441046
$543$	27.4641	+	19.4201i	1.17860	+	0.833394i
$544$		−	6.51626i		−	0.279383i
$545$	17.6603			0.756482
$546$	13.3923	+	3.10583i	0.573138	+	0.132917i
$547$	27.0526			1.15668			0.578342	−	0.815794i	$-0.303700\pi$
$547$	27.0526			1.15668			0.578342	+	0.815794i	$0.303700\pi$
$548$		−	22.2856i		−	0.951996i
$549$	17.0718	−	6.03579i	0.728607	−	0.257601i
$550$	−1.07180			−0.0457016
$551$	30.5885			1.30311
$552$	−13.9282	+	19.6975i	−0.592824	+	0.838379i
$553$	−11.3923	−	27.9053i	−0.484450	−	1.18666i
$554$		−	9.35465i		−	0.397441i
$555$	−5.53590	+	7.82894i	−0.234986	+	0.332320i
$556$		−	23.5983i		−	1.00079i
$557$		−	41.8444i		−	1.77300i	−0.462725	−	0.886502i	$-0.653128\pi$
$557$		−	41.8444i		−	1.77300i	0.462725	−	0.886502i	$-0.346872\pi$
$558$	0.339746	+	0.960947i	0.0143826	+	0.0406801i
$559$		−	53.7129i		−	2.27181i
$560$	4.26795	+	10.4543i	0.180354	+	0.441775i
$561$	1.85641	+	1.31268i	0.0783775	+	0.0554213i
$562$	−2.46410			−0.103942
$563$	30.3731			1.28007			0.640036	−	0.768345i	$-0.278919\pi$
$563$	30.3731			1.28007			0.640036	+	0.768345i	$0.278919\pi$
$564$	−11.1962	+	15.8338i	−0.471443	+	0.666721i
$565$			9.79796i			0.412203i
$566$	4.48334			0.188449
$567$	−20.8564	−	11.4896i	−0.875887	−	0.482517i
$568$	−18.1962			−0.763494
$569$		−	35.1523i		−	1.47366i	−0.676078	−	0.736830i	$-0.736322\pi$
$569$		−	35.1523i		−	1.47366i	0.676078	−	0.736830i	$-0.263678\pi$
$570$	3.80385	−	5.37945i	0.159326	−	0.225320i
$571$	−29.1769			−1.22102			−0.610508	−	0.792010i	$-0.709035\pi$
$571$	−29.1769			−1.22102			−0.610508	+	0.792010i	$0.709035\pi$
$572$	−10.3923			−0.434524
$573$	−18.7846	−	13.2827i	−0.784738	−	0.554894i
$574$	−1.26795	+	0.517638i	−0.0529232	+	0.0216058i
$575$		−	14.4195i		−	0.601336i
$576$	−2.26795	−	6.41473i	−0.0944979	−	0.267280i
$577$			17.1464i			0.713815i	0.934140	+	0.356908i	$0.116169\pi$
$577$			17.1464i			0.713815i	−0.934140	+	0.356908i	$0.883831\pi$
$578$		−	7.96764i		−	0.331410i
$579$	10.1962	−	14.4195i	0.423738	−	0.599256i
$580$			21.6293i			0.898108i
$581$	−13.8564	−	33.9411i	−0.574861	−	1.40812i
$582$	2.66025	−	3.76217i	0.110271	−	0.155947i
$583$	−7.07180			−0.292884
$584$	17.6603			0.730787
$585$	−28.3923	+	10.0382i	−1.17388	+	0.415028i
$586$		−	10.4543i		−	0.431863i
$587$	3.46410			0.142979			0.0714894	−	0.997441i	$-0.477225\pi$
$587$	3.46410			0.142979			0.0714894	+	0.997441i	$0.477225\pi$
$588$	3.33975	+	20.7327i	0.137729	+	0.855003i
$589$	2.78461			0.114738
$590$			10.4543i			0.430397i
$591$	31.3205	+	22.1469i	1.28835	+	0.911004i
$592$	−7.87564			−0.323687
$593$	−18.2487			−0.749385			−0.374692	−	0.927149i	$-0.622252\pi$
$593$	−18.2487			−0.749385			−0.374692	+	0.927149i	$0.622252\pi$
$594$	−2.67949	−	0.757875i	−0.109941	−	0.0310960i
$595$	−2.19615	−	5.37945i	−0.0900335	−	0.220536i
$596$		−	6.86800i		−	0.281324i
$597$	−7.85641	−	5.55532i	−0.321541	−	0.227364i
$598$			21.6293i			0.884488i
$599$		−	3.90087i		−	0.159385i	−0.996819	−	0.0796926i	$-0.974606\pi$
$599$		−	3.90087i		−	0.159385i	0.996819	−	0.0796926i	$-0.0253939\pi$
$600$	−5.46410	−	3.86370i	−0.223071	−	0.157735i
$601$			18.0430i			0.735989i	0.929828	+	0.367995i	$0.119956\pi$
$601$			18.0430i			0.735989i	−0.929828	+	0.367995i	$0.880044\pi$
$602$	−11.7513	+	4.79744i	−0.478947	+	0.195529i
$603$	1.00000	+	2.82843i	0.0407231	+	0.115182i
$604$	−18.9282			−0.770178
$605$	17.1962			0.699123
$606$	−6.92820	−	4.89898i	−0.281439	−	0.199007i
$607$		−	21.2132i		−	0.861017i	−0.902586	−	0.430509i	$-0.858334\pi$
$607$		−	21.2132i		−	0.861017i	0.902586	−	0.430509i	$-0.141666\pi$
$608$	21.8038			0.884263
$609$	−7.46410	+	32.1851i	−0.302461	+	1.30421i
$610$	−5.41154			−0.219107
$611$			37.4631i			1.51559i
$612$	2.19615	+	6.21166i	0.0887742	+	0.251091i
$613$	23.0000			0.928961			0.464481	−	0.885583i	$-0.346241\pi$
$613$	23.0000			0.928961			0.464481	+	0.885583i	$0.346241\pi$
$614$	6.46410			0.260870
$615$	1.73205	−	2.44949i	0.0698430	−	0.0987730i
$616$	2.00000	+	4.89898i	0.0805823	+	0.197386i
$617$		−	5.10205i		−	0.205401i	−0.994712	−	0.102700i	$-0.967252\pi$
$617$		−	5.10205i		−	0.205401i	0.994712	−	0.102700i	$-0.0327483\pi$
$618$	−5.53590	+	7.82894i	−0.222686	+	0.314926i
$619$		−	23.5983i		−	0.948497i	−0.880391	−	0.474248i	$-0.842720\pi$
$619$		−	23.5983i		−	0.948497i	0.880391	−	0.474248i	$-0.157280\pi$
$620$			1.96902i			0.0790776i
$621$	10.1962	−	36.0488i	0.409158	−	1.44659i
$622$			4.65874i			0.186799i
$623$	−2.53590	−	6.21166i	−0.101599	−	0.248865i
$624$	−20.1962	−	14.2808i	−0.808493	−	0.571691i
$625$	−11.0000			−0.440000
$626$	−7.39230			−0.295456
$627$	−4.39230	+	6.21166i	−0.175412	+	0.248070i
$628$			6.51626i			0.260027i
$629$	4.05256			0.161586
$630$	4.73205	+	5.31508i	0.188529	+	0.211758i
$631$	−42.7846			−1.70323			−0.851614	−	0.524169i	$-0.824376\pi$
$631$	−42.7846			−1.70323			−0.851614	+	0.524169i	$0.824376\pi$
$632$		−	22.0082i		−	0.875441i
$633$	23.9282	−	33.8396i	0.951061	−	1.34500i
$634$	−13.1051			−0.520471
$635$	−21.7128			−0.861647
$636$	−16.7321	−	11.8313i	−0.663469	−	0.469143i
$637$	28.3923	+	28.9778i	1.12494	+	1.14814i
$638$			3.86370i			0.152965i
$639$	26.6410	−	9.41902i	1.05390	−	0.372611i
$640$			19.8362i			0.784093i
$641$		−	24.5221i		−	0.968565i	−0.874912	−	0.484282i	$-0.839081\pi$
$641$		−	24.5221i		−	0.968565i	0.874912	−	0.484282i	$-0.160919\pi$
$642$	2.85641	−	4.03957i	0.112733	−	0.159429i
$643$			5.07484i			0.200132i	0.994981	+	0.100066i	$0.0319055\pi$
$643$			5.07484i			0.200132i	−0.994981	+	0.100066i	$0.968095\pi$
$644$	−30.5885	+	12.4877i	−1.20535	+	0.492084i
$645$	16.0526	−	22.7017i	0.632069	−	0.893880i
$646$	−2.78461			−0.109559
$647$	−28.0526			−1.10286			−0.551430	−	0.834221i	$-0.685918\pi$
$647$	−28.0526			−1.10286			−0.551430	+	0.834221i	$0.685918\pi$
$648$	−10.9282	−	13.5230i	−0.429300	−	0.531232i
$649$		−	12.0716i		−	0.473851i
$650$	−6.00000			−0.235339
$651$	−0.679492	+	2.92996i	−0.0266314	+	0.114834i
$652$	13.2679			0.519613
$653$		−	3.48477i		−	0.136369i	−0.997673	−	0.0681847i	$-0.978279\pi$
$653$		−	3.48477i		−	0.136369i	0.997673	−	0.0681847i	$-0.0217207\pi$
$654$	7.46410	+	5.27792i	0.291869	+	0.206383i
$655$	12.5885			0.491872
$656$	2.46410			0.0962070
$657$	−25.8564	+	9.14162i	−1.00875	+	0.356649i
$658$	8.19615	−	3.34607i	0.319519	−	0.130443i
$659$		−	13.9391i		−	0.542989i	−0.962440	−	0.271494i	$-0.912482\pi$
$659$		−	13.9391i		−	0.542989i	0.962440	−	0.271494i	$-0.0875178\pi$
$660$	−4.39230	−	3.10583i	−0.170970	−	0.120894i
$661$		−	25.4558i		−	0.990118i	−0.868859	−	0.495059i	$-0.835147\pi$
$661$		−	25.4558i		−	0.990118i	0.868859	−	0.495059i	$-0.164853\pi$
$662$		−	7.86611i		−	0.305725i
$663$	10.3923	+	7.34847i	0.403604	+	0.285391i
$664$		−	26.7685i		−	1.03882i
$665$	18.0000	−	7.34847i	0.698010	−	0.284961i
$666$	−4.67949	+	1.65445i	−0.181327	+	0.0641086i
$667$	−51.9808			−2.01270
$668$	29.7846			1.15240
$669$	26.1962	+	18.5235i	1.01280	+	0.716159i
$670$		−	0.896575i		−	0.0346377i
$671$	6.24871			0.241229
$672$	−5.32051	+	22.9420i	−0.205243	+	0.885006i
$673$	−38.3013			−1.47641			−0.738203	−	0.674579i	$-0.764325\pi$
$673$	−38.3013			−1.47641			−0.738203	+	0.674579i	$0.764325\pi$
$674$			11.2493i			0.433308i
$675$	10.0000	+	2.82843i	0.384900	+	0.108866i
$676$	−35.6603			−1.37155
$677$	25.8564			0.993742			0.496871	−	0.867824i	$-0.334482\pi$
$677$	25.8564			0.993742			0.496871	+	0.867824i	$0.334482\pi$
$678$	−2.92820	+	4.14110i	−0.112457	+	0.159038i
$679$	12.5885	−	5.13922i	0.483101	−	0.197225i
$680$		−	4.24264i		−	0.162698i
$681$	−14.3205	+	20.2523i	−0.548763	+	0.776068i
$682$			0.351731i			0.0134685i
$683$			14.1421i			0.541134i	0.962701	+	0.270567i	$0.0872111\pi$
$683$			14.1421i			0.541134i	−0.962701	+	0.270567i	$0.912789\pi$
$684$	−20.7846	+	7.34847i	−0.794719	+	0.280976i
$685$		−	22.2856i		−	0.851491i
$686$	3.80385	−	8.79985i	0.145232	−	0.335980i
$687$	23.6603	+	16.7303i	0.902695	+	0.638302i
$688$	22.8372			0.870659
$689$	−39.5885			−1.50820
$690$	−6.46410	+	9.14162i	−0.246084	+	0.348016i
$691$			25.8076i			0.981766i	0.871225	+	0.490883i	$0.163326\pi$
$691$			25.8076i			0.981766i	−0.871225	+	0.490883i	$0.836674\pi$
$692$	−31.9808			−1.21573
$693$	−5.46410	−	6.13733i	−0.207564	−	0.233138i
$694$	2.73205			0.103707
$695$		−	23.5983i		−	0.895135i
$696$	−13.9282	+	19.6975i	−0.527947	+	0.746630i
$697$	−1.26795			−0.0480270
$698$	2.87564			0.108845
$699$	−38.3923	−	27.1475i	−1.45213	−	1.02681i
$700$	−3.46410	−	8.48528i	−0.130931	−	0.320713i
$701$			33.2576i			1.25612i	0.778164	+	0.628061i	$0.216151\pi$
$701$			33.2576i			1.25612i	−0.778164	+	0.628061i	$0.783849\pi$
$702$	−15.0000	−	4.24264i	−0.566139	−	0.160128i
$703$			13.5601i			0.511430i
$704$		−	2.34795i		−	0.0884918i
$705$	−11.1962	+	15.8338i	−0.421671	+	0.596334i
$706$			3.58630i			0.134972i
$707$	−9.46410	−	23.1822i	−0.355934	−	0.871857i
$708$	20.1962	−	28.5617i	0.759018	−	1.07341i
$709$	−11.8564			−0.445277			−0.222638	−	0.974901i	$-0.571467\pi$
$709$	−11.8564			−0.445277			−0.222638	+	0.974901i	$0.571467\pi$
$710$	−8.44486			−0.316930
$711$	11.3923	+	32.2223i	0.427245	+	1.20843i
$712$		−	4.89898i		−	0.183597i
$713$	−4.73205			−0.177217
$714$	0.679492	−	2.92996i	0.0254293	−	0.109651i
$715$	−10.3923			−0.388650
$716$		−	6.86800i		−	0.256669i
$717$	−18.5359	−	13.1069i	−0.692236	−	0.489485i
$718$	3.53590			0.131959
$719$	30.2487			1.12809			0.564043	−	0.825745i	$-0.309245\pi$
$719$	30.2487			1.12809			0.564043	+	0.825745i	$0.309245\pi$
$720$	−4.26795	−	12.0716i	−0.159057	−	0.449881i
$721$	−26.1962	+	10.6945i	−0.975596	+	0.398285i
$722$			0.517638i			0.0192645i
$723$	21.4641	+	15.1774i	0.798259	+	0.564454i
$724$			33.6365i			1.25009i
$725$		−	14.4195i		−	0.535528i
$726$	7.26795	+	5.13922i	0.269739	+	0.190734i
$727$			20.0764i			0.744592i	0.928114	+	0.372296i	$0.121429\pi$
$727$			20.0764i			0.744592i	−0.928114	+	0.372296i	$0.878571\pi$
$728$	11.1962	+	27.4249i	0.414957	+	1.01643i
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	8.19615			0.303353
$731$	−11.7513			−0.434637
$732$	14.7846	+	10.4543i	0.546455	+	0.386402i
$733$			2.27362i			0.0839782i	0.999118	+	0.0419891i	$0.0133695\pi$
$733$			2.27362i			0.0839782i	−0.999118	+	0.0419891i	$0.986631\pi$
$734$	1.14359			0.0422108
$735$	3.33975	+	20.7327i	0.123188	+	0.764738i
$736$	−37.0526			−1.36578
$737$			1.03528i			0.0381349i
$738$	1.46410	−	0.517638i	0.0538943	−	0.0190545i
$739$	−12.1962			−0.448643			−0.224321	−	0.974515i	$-0.572017\pi$
$739$	−12.1962			−0.448643			−0.224321	+	0.974515i	$0.572017\pi$
$740$	−9.58846			−0.352479
$741$	−24.5885	+	34.7733i	−0.903280	+	1.27743i
$742$	3.53590	+	8.66115i	0.129807	+	0.317961i
$743$			31.7690i			1.16549i	0.812654	+	0.582746i	$0.198022\pi$
$743$			31.7690i			1.16549i	−0.812654	+	0.582746i	$0.801978\pi$
$744$	−1.26795	+	1.79315i	−0.0464853	+	0.0657401i
$745$		−	6.86800i		−	0.251624i
$746$		−	8.69831i		−	0.318468i
$747$	13.8564	+	39.1918i	0.506979	+	1.43395i
$748$			2.27362i			0.0831319i
$749$	13.5167	−	5.51815i	0.493888	−	0.201629i
$750$	−8.87564	−	6.27603i	−0.324093	−	0.229168i
$751$	52.5692			1.91828			0.959139	−	0.282935i	$-0.0913081\pi$
$751$	52.5692			1.91828			0.959139	+	0.282935i	$0.0913081\pi$
$752$	−15.9282			−0.580842
$753$	24.0000	−	33.9411i	0.874609	−	1.23688i
$754$			21.6293i			0.787693i
$755$	−18.9282			−0.688868
$756$	−2.66025	−	23.6627i	−0.0967525	−	0.860604i
$757$	21.1769			0.769688			0.384844	−	0.922982i	$-0.374255\pi$
$757$	21.1769			0.769688			0.384844	+	0.922982i	$0.374255\pi$
$758$			6.11012i			0.221930i
$759$	7.46410	−	10.5558i	0.270930	−	0.383152i
$760$	14.1962			0.514949
$761$	14.6603			0.531434			0.265717	−	0.964051i	$-0.414391\pi$
$761$	14.6603			0.531434			0.265717	+	0.964051i	$0.414391\pi$
$762$	−9.17691	−	6.48906i	−0.332445	−	0.235074i
$763$	10.1962	+	24.9754i	0.369126	+	0.904169i
$764$		−	23.0064i		−	0.832341i
$765$	2.19615	+	6.21166i	0.0794021	+	0.224583i
$766$			6.93237i			0.250477i
$767$		−	67.5776i		−	2.44009i
$768$	−1.39230	+	1.96902i	−0.0502405	+	0.0710508i
$769$			45.5322i			1.64193i	0.570975	+	0.820967i	$0.306565\pi$
$769$			45.5322i			1.64193i	−0.570975	+	0.820967i	$0.693435\pi$
$770$	0.928203	+	2.27362i	0.0334501	+	0.0819357i
$771$	−19.8564	+	28.0812i	−0.715111	+	1.01132i
$772$	17.6603			0.635606
$773$	−7.60770			−0.273630			−0.136815	−	0.990597i	$-0.543687\pi$
$773$	−7.60770			−0.273630			−0.136815	+	0.990597i	$0.543687\pi$
$774$	13.5692	−	4.79744i	0.487736	−	0.172441i
$775$		−	1.31268i		−	0.0471528i
$776$	9.92820			0.356402
$777$	−14.2679	−	3.30890i	−0.511860	−	0.118706i
$778$	10.8372			0.388531
$779$		−	4.24264i		−	0.152008i
$780$	−24.5885	−	17.3867i	−0.880408	−	0.622542i
$781$	9.75129			0.348929
$782$	4.73205			0.169218
$783$	10.1962	−	36.0488i	0.364381	−	1.28828i
$784$	−12.3205	+	12.0716i	−0.440018	+	0.431128i
$785$			6.51626i			0.232575i
$786$	5.32051	+	3.76217i	0.189776	+	0.134192i
$787$			36.3262i			1.29489i	0.762112	+	0.647445i	$0.224163\pi$
$787$			36.3262i			1.29489i	−0.762112	+	0.647445i	$0.775837\pi$
$788$			38.3596i			1.36651i
$789$	−5.85641	−	4.14110i	−0.208494	−	0.147427i
$790$		−	10.2141i		−	0.363400i
$791$	−13.8564	+	5.65685i	−0.492677	+	0.201135i
$792$	−2.00000	−	5.65685i	−0.0710669	−	0.201008i
$793$	34.9808			1.24220
$794$	7.01924			0.249103
$795$	−16.7321	−	11.8313i	−0.593425	−	0.419615i
$796$		−	9.62209i		−	0.341046i
$797$	−43.8564			−1.55347			−0.776737	−	0.629825i	$-0.783126\pi$
$797$	−43.8564			−1.55347			−0.776737	+	0.629825i	$0.783126\pi$
$798$	9.80385	+	2.27362i	0.347052	+	0.0804854i
$799$	8.19615			0.289959
$800$		−	10.2784i		−	0.363397i
$801$	2.53590	+	7.17260i	0.0896016	+	0.253431i
$802$	11.6077			0.409882
$803$	−9.46410			−0.333981
$804$	−1.73205	+	2.44949i	−0.0610847	+	0.0863868i
$805$	−30.5885	+	12.4877i	−1.07810	+	0.440133i
$806$			1.96902i			0.0693556i
$807$	−10.8564	+	15.3533i	−0.382164	+	0.540461i
$808$		−	18.2832i		−	0.643202i
$809$		−	54.1562i		−	1.90403i	−0.306049	−	0.952016i	$-0.599007\pi$
$809$		−	54.1562i		−	1.90403i	0.306049	−	0.952016i	$-0.400993\pi$
$810$	−5.07180	−	6.27603i	−0.178205	−	0.220517i
$811$		−	0.416102i		−	0.0146113i	−0.999973	−	0.00730566i	$-0.997675\pi$
$811$		−	0.416102i		−	0.0146113i	0.999973	−	0.00730566i	$-0.00232548\pi$
$812$	−30.5885	+	12.4877i	−1.07344	+	0.438232i
$813$	−28.0526	−	19.8362i	−0.983846	−	0.695684i
$814$	−1.71281			−0.0600341
$815$	13.2679			0.464756
$816$	−3.12436	+	4.41851i	−0.109374	+	0.154679i
$817$		−	39.3206i		−	1.37565i
$818$	0.679492			0.0237579
$819$	−30.5885	−	34.3572i	−1.06885	−	1.20054i
$820$	3.00000			0.104765
$821$			36.6680i			1.27972i	0.768490	+	0.639861i	$0.221008\pi$
$821$			36.6680i			1.27972i	−0.768490	+	0.639861i	$0.778992\pi$
$822$	6.66025	−	9.41902i	0.232303	−	0.328526i
$823$	−2.39230			−0.0833905			−0.0416953	−	0.999130i	$-0.513276\pi$
$823$	−2.39230			−0.0833905			−0.0416953	+	0.999130i	$0.513276\pi$
$824$	−20.6603			−0.719734
$825$	2.92820	+	2.07055i	0.101947	+	0.0720874i
$826$	−14.7846	+	6.03579i	−0.514422	+	0.210012i
$827$			6.48906i			0.225647i	0.993615	+	0.112823i	$0.0359894\pi$
$827$			6.48906i			0.225647i	−0.993615	+	0.112823i	$0.964011\pi$
$828$	35.3205	−	12.4877i	1.22747	−	0.433977i
$829$		−	4.89898i		−	0.170149i	−0.996375	−	0.0850743i	$-0.972887\pi$
$829$		−	4.89898i		−	0.170149i	0.996375	−	0.0850743i	$-0.0271128\pi$
$830$		−	12.4233i		−	0.431220i
$831$	−18.0718	+	25.5574i	−0.626904	+	0.886576i
$832$		−	13.1440i		−	0.455687i
$833$	6.33975	−	6.21166i	0.219659	−	0.215221i
$834$	7.05256	−	9.97382i	0.244210	−	0.345365i
$835$	29.7846			1.03074
$836$	−7.60770			−0.263118
$837$	0.928203	−	3.28169i	0.0320834	−	0.113432i
$838$			18.1074i			0.625509i
$839$	10.2679			0.354489			0.177244	−	0.984167i	$-0.443282\pi$
$839$	10.2679			0.354489			0.177244	+	0.984167i	$0.443282\pi$
$840$	−3.46410	+	14.9372i	−0.119523	+	0.515382i
$841$	−22.9808			−0.792440
$842$			13.7632i			0.474311i
$843$	6.73205	+	4.76028i	0.231864	+	0.163953i
$844$	41.4449			1.42659
$845$	−35.6603			−1.22675
$846$	−9.46410	+	3.34607i	−0.325383	+	0.115040i
$847$	9.92820	+	24.3190i	0.341137	+	0.835612i
$848$		−	16.8319i		−	0.578009i
$849$	−12.2487	−	8.66115i	−0.420375	−	0.297250i
$850$			1.31268i			0.0450245i
$851$		−	23.0435i		−	0.789922i
$852$	23.0718	+	16.3142i	0.790427	+	0.558916i
$853$		−	20.5569i		−	0.703854i	−0.936028	−	0.351927i	$-0.885527\pi$
$853$		−	20.5569i		−	0.703854i	0.936028	−	0.351927i	$-0.114473\pi$
$854$	−3.12436	−	7.65308i	−0.106913	−	0.261883i
$855$	−20.7846	+	7.34847i	−0.710819	+	0.251312i
$856$	10.6603			0.364360
$857$	−50.9090			−1.73902			−0.869509	−	0.493918i	$-0.835564\pi$
$857$	−50.9090			−1.73902			−0.869509	+	0.493918i	$0.835564\pi$
$858$	−4.39230	−	3.10583i	−0.149951	−	0.106031i
$859$			5.13922i			0.175348i	0.996149	+	0.0876739i	$0.0279433\pi$
$859$			5.13922i			0.175348i	−0.996149	+	0.0876739i	$0.972057\pi$
$860$	27.8038			0.948103
$861$	4.46410	+	1.03528i	0.152136	+	0.0352821i
$862$	−15.9474			−0.543172
$863$			36.9083i			1.25637i	0.778063	+	0.628186i	$0.216202\pi$
$863$			36.9083i			1.25637i	−0.778063	+	0.628186i	$0.783798\pi$
$864$	7.26795	−	25.6961i	0.247261	−	0.874198i
$865$	−31.9808			−1.08738
$866$	−11.0718			−0.376235
$867$	−15.3923	+	21.7680i	−0.522750	+	0.739280i
$868$	−2.78461	+	1.13681i	−0.0945158	+	0.0385859i
$869$			11.7942i			0.400090i
$870$	−6.46410	+	9.14162i	−0.219154	+	0.309930i
$871$			5.79555i			0.196375i
$872$			19.6975i			0.667040i
$873$	−14.5359	+	5.13922i	−0.491966	+	0.173936i
$874$			15.8338i			0.535585i
$875$	−12.1244	−	29.6985i	−0.409878	−	1.00399i
$876$	−22.3923	−	15.8338i	−0.756566	−	0.534973i
$877$	−23.8564			−0.805574			−0.402787	−	0.915294i	$-0.631958\pi$
$877$	−23.8564			−0.805574			−0.402787	+	0.915294i	$0.631958\pi$
$878$	15.1244			0.510422
$879$	−20.1962	+	28.5617i	−0.681199	+	0.963361i
$880$		−	4.41851i		−	0.148948i
$881$	48.3731			1.62973			0.814865	−	0.579651i	$-0.196811\pi$
$881$	48.3731			1.62973			0.814865	+	0.579651i	$0.196811\pi$
$882$	−4.78461	+	9.76079i	−0.161106	+	0.328663i
$883$	46.2295			1.55575			0.777873	−	0.628422i	$-0.216299\pi$
$883$	46.2295			1.55575			0.777873	+	0.628422i	$0.216299\pi$
$884$			12.7279i			0.428086i
$885$	20.1962	−	28.5617i	0.678886	−	0.960090i
$886$	8.05256			0.270531
$887$	−30.1244			−1.01148			−0.505738	−	0.862687i	$-0.668780\pi$
$887$	−30.1244			−1.01148			−0.505738	+	0.862687i	$0.668780\pi$
$888$	−8.73205	−	6.17449i	−0.293028	−	0.207202i
$889$	−12.5359	−	30.7066i	−0.420441	−	1.02986i
$890$		−	2.27362i		−	0.0762121i
$891$	5.85641	+	7.24693i	0.196197	+	0.242781i
$892$			32.0836i			1.07424i
$893$			27.4249i			0.917738i
$894$	2.05256	−	2.90276i	0.0686478	−	0.0970827i
$895$		−	6.86800i		−	0.229572i
$896$	−28.0526	+	11.4524i	−0.937170	+	0.382598i
$897$	41.7846	−	59.0924i	1.39515	−	1.97304i
$898$	−15.5167			−0.517798
$899$	−4.73205			−0.157823
$900$	3.46410	+	9.79796i	0.115470	+	0.326599i
$901$			8.66115i			0.288545i
$902$	0.535898			0.0178435
$903$	41.3731	+	9.59489i	1.37681	+	0.319298i
$904$	−10.9282			−0.363467
$905$			33.6365i			1.11812i
$906$	−8.00000	−	5.65685i	−0.265782	−	0.187936i
$907$	1.07180			0.0355884			0.0177942	−	0.999842i	$-0.494336\pi$
$907$	1.07180			0.0355884			0.0177942	+	0.999842i	$0.494336\pi$
$908$	−24.8038			−0.823145
$909$	9.46410	+	26.7685i	0.313904	+	0.887856i
$910$	5.19615	+	12.7279i	0.172251	+	0.421927i
$911$		−	22.6002i		−	0.748778i	−0.927272	−	0.374389i	$-0.877852\pi$
$911$		−	22.6002i		−	0.748778i	0.927272	−	0.374389i	$-0.122148\pi$
$912$	−14.7846	−	10.4543i	−0.489567	−	0.346176i
$913$			14.3452i			0.474757i
$914$		−	0.406144i		−	0.0134340i
$915$	14.7846	+	10.4543i	0.488764	+	0.345608i
$916$			28.9778i			0.957453i
$917$	7.26795	+	17.8028i	0.240009	+	0.587899i
$918$	−0.928203	+	3.28169i	−0.0306353	+	0.108312i
$919$	45.0526			1.48615			0.743073	−	0.669210i	$-0.233367\pi$
$919$	45.0526			1.48615			0.743073	+	0.669210i	$0.233367\pi$
$920$	−24.1244			−0.795356
$921$	−17.6603	−	12.4877i	−0.581925	−	0.411483i
$922$			12.6636i			0.417052i
$923$	54.5885			1.79680
$924$	1.85641	−	8.00481i	0.0610713	−	0.263339i
$925$	6.39230			0.210178
$926$			9.28032i			0.304970i
$927$	30.2487	−	10.6945i	0.993498	−	0.351255i
$928$	−37.0526			−1.21631
$929$	−15.1244			−0.496214			−0.248107	−	0.968733i	$-0.579808\pi$
$929$	−15.1244			−0.496214			−0.248107	+	0.968733i	$0.579808\pi$
$930$	−0.588457	+	0.832204i	−0.0192963	+	0.0272891i
$931$	20.7846	+	21.2132i	0.681188	+	0.695235i
$932$		−	47.0208i		−	1.54022i
$933$	9.00000	−	12.7279i	0.294647	−	0.416693i
$934$		−	1.96902i		−	0.0644282i
$935$			2.27362i			0.0743555i
$936$	−11.1962	−	31.6675i	−0.365958	−	1.03508i
$937$		−	3.41044i		−	0.111414i	−0.998447	−	0.0557071i	$-0.982259\pi$
$937$		−	3.41044i		−	0.111414i	0.998447	−	0.0557071i	$-0.0177413\pi$
$938$	1.26795	−	0.517638i	0.0414000	−	0.0169015i
$939$	20.1962	+	14.2808i	0.659077	+	0.466037i
$940$	−19.3923			−0.632507
$941$	−39.9282			−1.30162			−0.650811	−	0.759240i	$-0.725571\pi$
$941$	−39.9282			−1.30162			−0.650811	+	0.759240i	$0.725571\pi$
$942$	−1.94744	+	2.75410i	−0.0634511	+	0.0897334i
$943$			7.20977i			0.234782i
$944$	28.7321			0.935149
$945$	−2.66025	−	23.6627i	−0.0865381	−	0.769747i
$946$	4.96668			0.161481
$947$		−	31.8062i		−	1.03356i	−0.856117	−	0.516781i	$-0.827130\pi$
$947$		−	31.8062i		−	1.03356i	0.856117	−	0.516781i	$-0.172870\pi$
$948$	−19.7321	+	27.9053i	−0.640867	+	0.906323i
$949$	−52.9808			−1.71983
$950$	−4.39230			−0.142505
$951$	35.8038	+	25.3171i	1.16102	+	0.820965i
$952$	6.00000	−	2.44949i	0.194461	−	0.0793884i
$953$			0.582009i			0.0188531i	0.999956	+	0.00942657i	$0.00300061\pi$
$953$			0.582009i			0.0188531i	−0.999956	+	0.00942657i	$0.996999\pi$
$954$	−3.53590	−	10.0010i	−0.114479	−	0.323795i
$955$		−	23.0064i		−	0.744468i
$956$		−	22.7017i		−	0.734227i
$957$	7.46410	−	10.5558i	0.241280	−	0.341222i
$958$		−	8.83701i		−	0.285511i
$959$	31.5167	−	12.8666i	1.01773	−	0.415485i
$960$	3.92820	−	5.55532i	0.126782	−	0.179297i
$961$	30.5692			0.986104
$962$	−9.58846			−0.309144
$963$	−15.6077	+	5.51815i	−0.502951	+	0.177820i
$964$			26.2880i			0.846681i
$965$	17.6603			0.568504
$966$	−16.6603	−	3.86370i	−0.536035	−	0.124313i
$967$	47.5885			1.53034			0.765171	−	0.643827i	$-0.222654\pi$
$967$	47.5885			1.53034			0.765171	+	0.643827i	$0.222654\pi$
$968$			19.1798i			0.616463i
$969$	7.60770	+	5.37945i	0.244394	+	0.172813i
$970$	4.60770			0.147944
$971$	27.0000			0.866471			0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000			0.866471			0.433236	+	0.901281i	$0.357372\pi$
$972$	1.73205	+	26.9444i	0.0555556	+	0.864242i
$973$	33.3731	−	13.6245i	1.06989	−	0.436781i
$974$			1.86748i			0.0598379i
$975$	16.3923	+	11.5911i	0.524974	+	0.371213i
$976$			14.8728i			0.476067i
$977$			38.4612i			1.23048i	0.788339	+	0.615241i	$0.210941\pi$
$977$			38.4612i			1.23048i	−0.788339	+	0.615241i	$0.789059\pi$
$978$	5.60770	+	3.96524i	0.179314	+	0.126794i
$979$			2.62536i			0.0839067i
$980$	−15.0000	+	14.6969i	−0.479157	+	0.469476i
$981$	−10.1962	−	28.8391i	−0.325538	−	0.920761i
$982$	20.4833			0.653650
$983$	−16.9808			−0.541602			−0.270801	−	0.962635i	$-0.587289\pi$
$983$	−16.9808			−0.541602			−0.270801	+	0.962635i	$0.587289\pi$
$984$	2.73205	+	1.93185i	0.0870946	+	0.0615852i
$985$			38.3596i			1.22224i
$986$	4.73205			0.150699
$987$	−28.8564	−	6.69213i	−0.918510	−	0.213013i
$988$	−42.5885			−1.35492
$989$			66.8198i			2.12475i
$990$	−0.928203	−	2.62536i	−0.0295002	−	0.0834393i
$991$	−15.8756			−0.504306			−0.252153	−	0.967687i	$-0.581139\pi$
$991$	−15.8756			−0.504306			−0.252153	+	0.967687i	$0.581139\pi$
$992$	−3.37307			−0.107095
$993$	−15.1962	+	21.4906i	−0.482235	+	0.681984i
$994$	−4.87564	−	11.9428i	−0.154646	−	0.378804i
$995$		−	9.62209i		−	0.305041i
$996$	−24.0000	+	33.9411i	−0.760469	+	1.07547i
$997$		−	28.8019i		−	0.912166i	−0.889937	−	0.456083i	$-0.849252\pi$
$997$		−	28.8019i		−	0.912166i	0.889937	−	0.456083i	$-0.150748\pi$
$998$			21.1117i			0.668278i
$999$	15.9808	+	4.52004i	0.505609	+	0.143008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.d.b.83.3	yes	4
3.2	odd	2		861.2.d.a.83.2	✓	4
7.6	odd	2		861.2.d.a.83.3	yes	4
21.20	even	2	inner	861.2.d.b.83.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.d.a.83.2	✓	4	3.2	odd	2
861.2.d.a.83.3	yes	4	7.6	odd	2
861.2.d.b.83.2	yes	4	21.20	even	2	inner
861.2.d.b.83.3	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.517638i q^{2} +(1.00000 - 1.41421i) q^{3} +1.73205 q^{4} +1.73205 q^{5} +(0.732051 + 0.517638i) q^{6} +(1.00000 + 2.44949i) q^{7} +1.93185i q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+0.517638i q^{2} +(1.00000 - 1.41421i) q^{3} +1.73205 q^{4} +1.73205 q^{5} +(0.732051 + 0.517638i) q^{6} +(1.00000 + 2.44949i) q^{7} +1.93185i q^{8} +(-1.00000 - 2.82843i) q^{9} +0.896575i q^{10} -1.03528i q^{11} +(1.73205 - 2.44949i) q^{12} -5.79555i q^{13} +(-1.26795 + 0.517638i) q^{14} +(1.73205 - 2.44949i) q^{15} +2.46410 q^{16} -1.26795 q^{17} +(1.46410 - 0.517638i) q^{18} -4.24264i q^{19} +3.00000 q^{20} +(4.46410 + 1.03528i) q^{21} +0.535898 q^{22} +7.20977i q^{23} +(2.73205 + 1.93185i) q^{24} -2.00000 q^{25} +3.00000 q^{26} +(-5.00000 - 1.41421i) q^{27} +(1.73205 + 4.24264i) q^{28} +7.20977i q^{29} +(1.26795 + 0.896575i) q^{30} +0.656339i q^{31} +5.13922i q^{32} +(-1.46410 - 1.03528i) q^{33} -0.656339i q^{34} +(1.73205 + 4.24264i) q^{35} +(-1.73205 - 4.89898i) q^{36} -3.19615 q^{37} +2.19615 q^{38} +(-8.19615 - 5.79555i) q^{39} +3.34607i q^{40} +1.00000 q^{41} +(-0.535898 + 2.31079i) q^{42} +9.26795 q^{43} -1.79315i q^{44} +(-1.73205 - 4.89898i) q^{45} -3.73205 q^{46} -6.46410 q^{47} +(2.46410 - 3.48477i) q^{48} +(-5.00000 + 4.89898i) q^{49} -1.03528i q^{50} +(-1.26795 + 1.79315i) q^{51} -10.0382i q^{52} -6.83083i q^{53} +(0.732051 - 2.58819i) q^{54} -1.79315i q^{55} +(-4.73205 + 1.93185i) q^{56} +(-6.00000 - 4.24264i) q^{57} -3.73205 q^{58} +11.6603 q^{59} +(3.00000 - 4.24264i) q^{60} +6.03579i q^{61} -0.339746 q^{62} +(5.92820 - 5.27792i) q^{63} +2.26795 q^{64} -10.0382i q^{65} +(0.535898 - 0.757875i) q^{66} -1.00000 q^{67} -2.19615 q^{68} +(10.1962 + 7.20977i) q^{69} +(-2.19615 + 0.896575i) q^{70} +9.41902i q^{71} +(5.46410 - 1.93185i) q^{72} -9.14162i q^{73} -1.65445i q^{74} +(-2.00000 + 2.82843i) q^{75} -7.34847i q^{76} +(2.53590 - 1.03528i) q^{77} +(3.00000 - 4.24264i) q^{78} -11.3923 q^{79} +4.26795 q^{80} +(-7.00000 + 5.65685i) q^{81} +0.517638i q^{82} -13.8564 q^{83} +(7.73205 + 1.79315i) q^{84} -2.19615 q^{85} +4.79744i q^{86} +(10.1962 + 7.20977i) q^{87} +2.00000 q^{88} -2.53590 q^{89} +(2.53590 - 0.896575i) q^{90} +(14.1962 - 5.79555i) q^{91} +12.4877i q^{92} +(0.928203 + 0.656339i) q^{93} -3.34607i q^{94} -7.34847i q^{95} +(7.26795 + 5.13922i) q^{96} -5.13922i q^{97} +(-2.53590 - 2.58819i) q^{98} +(-2.92820 + 1.03528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 - 4 * q^9	\( 4 q + 4 q^{3} - 4 q^{6} + 4 q^{7} - 4 q^{9} - 12 q^{14} - 4 q^{16} - 12 q^{17} - 8 q^{18} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 4 q^{24} - 8 q^{25} + 12 q^{26} - 20 q^{27} + 12 q^{30} + 8 q^{33} + 8 q^{37} - 12 q^{38} - 12 q^{39} + 4 q^{41} - 16 q^{42} + 44 q^{43} - 8 q^{46} - 12 q^{47} - 4 q^{48} - 20 q^{49} - 12 q^{51} - 4 q^{54} - 12 q^{56} - 24 q^{57} - 8 q^{58} + 12 q^{59} + 12 q^{60} - 36 q^{62} - 4 q^{63} + 16 q^{64} + 16 q^{66} - 4 q^{67} + 12 q^{68} + 20 q^{69} + 12 q^{70} + 8 q^{72} - 8 q^{75} + 24 q^{77} + 12 q^{78} - 4 q^{79} + 24 q^{80} - 28 q^{81} + 24 q^{84} + 12 q^{85} + 20 q^{87} + 8 q^{88} - 24 q^{89} + 24 q^{90} + 36 q^{91} - 24 q^{93} + 36 q^{96} - 24 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^6 + 4 * q^7 - 4 * q^9 - 12 * q^14 - 4 * q^16 - 12 * q^17 - 8 * q^18 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 4 * q^24 - 8 * q^25 + 12 * q^26 - 20 * q^27 + 12 * q^30 + 8 * q^33 + 8 * q^37 - 12 * q^38 - 12 * q^39 + 4 * q^41 - 16 * q^42 + 44 * q^43 - 8 * q^46 - 12 * q^47 - 4 * q^48 - 20 * q^49 - 12 * q^51 - 4 * q^54 - 12 * q^56 - 24 * q^57 - 8 * q^58 + 12 * q^59 + 12 * q^60 - 36 * q^62 - 4 * q^63 + 16 * q^64 + 16 * q^66 - 4 * q^67 + 12 * q^68 + 20 * q^69 + 12 * q^70 + 8 * q^72 - 8 * q^75 + 24 * q^77 + 12 * q^78 - 4 * q^79 + 24 * q^80 - 28 * q^81 + 24 * q^84 + 12 * q^85 + 20 * q^87 + 8 * q^88 - 24 * q^89 + 24 * q^90 + 36 * q^91 - 24 * q^93 + 36 * q^96 - 24 * q^98 + 16 * q^99

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