LMFDB - Embedded newform 690.2.h.b.689.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(689,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.h (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			689.5
Character	$\chi$	$=$	690.689
Dual form			690.2.h.b.689.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.44698 - 0.951967i) q^{3} +1.00000 q^{4} +(-1.42959 - 1.71938i) q^{5} +(-1.44698 - 0.951967i) q^{6} +4.73682 q^{7} +1.00000 q^{8} +(1.18752 + 2.75496i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.44698 - 0.951967i) q^{3} +1.00000 q^{4} +(-1.42959 - 1.71938i) q^{5} +(-1.44698 - 0.951967i) q^{6} +4.73682 q^{7} +1.00000 q^{8} +(1.18752 + 2.75496i) q^{9} +(-1.42959 - 1.71938i) q^{10} +0.109553 q^{11} +(-1.44698 - 0.951967i) q^{12} +2.46994i q^{13} +4.73682 q^{14} +(0.431808 + 3.84884i) q^{15} +1.00000 q^{16} -3.72035i q^{17} +(1.18752 + 2.75496i) q^{18} -6.76462i q^{19} +(-1.42959 - 1.71938i) q^{20} +(-6.85409 - 4.50929i) q^{21} +0.109553 q^{22} +(4.67990 - 1.04813i) q^{23} +(-1.44698 - 0.951967i) q^{24} +(-0.912517 + 4.91603i) q^{25} +2.46994i q^{26} +(0.904315 - 5.11686i) q^{27} +4.73682 q^{28} -7.05802i q^{29} +(0.431808 + 3.84884i) q^{30} -9.34339 q^{31} +1.00000 q^{32} +(-0.158521 - 0.104291i) q^{33} -3.72035i q^{34} +(-6.77173 - 8.14437i) q^{35} +(1.18752 + 2.75496i) q^{36} +1.34148 q^{37} -6.76462i q^{38} +(2.35130 - 3.57395i) q^{39} +(-1.42959 - 1.71938i) q^{40} +7.38300i q^{41} +(-6.85409 - 4.50929i) q^{42} -2.31465 q^{43} +0.109553 q^{44} +(3.03915 - 5.98027i) q^{45} +(4.67990 - 1.04813i) q^{46} +5.53476 q^{47} +(-1.44698 - 0.951967i) q^{48} +15.4374 q^{49} +(-0.912517 + 4.91603i) q^{50} +(-3.54165 + 5.38329i) q^{51} +2.46994i q^{52} -3.77179i q^{53} +(0.904315 - 5.11686i) q^{54} +(-0.156616 - 0.188362i) q^{55} +4.73682 q^{56} +(-6.43970 + 9.78829i) q^{57} -7.05802i q^{58} +4.18459i q^{59} +(0.431808 + 3.84884i) q^{60} -7.57377i q^{61} -9.34339 q^{62} +(5.62505 + 13.0497i) q^{63} +1.00000 q^{64} +(4.24675 - 3.53101i) q^{65} +(-0.158521 - 0.104291i) q^{66} +5.95975 q^{67} -3.72035i q^{68} +(-7.76951 - 2.93848i) q^{69} +(-6.77173 - 8.14437i) q^{70} +9.66771i q^{71} +(1.18752 + 2.75496i) q^{72} -9.28694i q^{73} +1.34148 q^{74} +(6.00029 - 6.24472i) q^{75} -6.76462i q^{76} +0.518931 q^{77} +(2.35130 - 3.57395i) q^{78} +12.3843i q^{79} +(-1.42959 - 1.71938i) q^{80} +(-6.17961 + 6.54312i) q^{81} +7.38300i q^{82} +16.6139i q^{83} +(-6.85409 - 4.50929i) q^{84} +(-6.39669 + 5.31860i) q^{85} -2.31465 q^{86} +(-6.71900 + 10.2128i) q^{87} +0.109553 q^{88} -10.2277 q^{89} +(3.03915 - 5.98027i) q^{90} +11.6996i q^{91} +(4.67990 - 1.04813i) q^{92} +(13.5197 + 8.89460i) q^{93} +5.53476 q^{94} +(-11.6309 + 9.67067i) q^{95} +(-1.44698 - 0.951967i) q^{96} +9.94453 q^{97} +15.4374 q^{98} +(0.130096 + 0.301813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} - 2 q^{3} + 24 q^{4} - 2 q^{6} + 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 - 2 * q^3 + 24 * q^4 - 2 * q^6 + 24 * q^8 + 6 * q^9	$ 24 q + 24 q^{2} - 2 q^{3} + 24 q^{4} - 2 q^{6} + 24 q^{8} + 6 q^{9} - 2 q^{12} + 24 q^{16} + 6 q^{18} + 4 q^{23} - 2 q^{24} + 12 q^{25} - 2 q^{27} - 28 q^{31} + 24 q^{32} - 8 q^{35} + 6 q^{36} + 4 q^{46} - 16 q^{47} - 2 q^{48} - 4 q^{49} + 12 q^{50} - 2 q^{54} + 4 q^{55} - 28 q^{62} + 24 q^{64} - 8 q^{69} - 8 q^{70} + 6 q^{72} - 6 q^{75} - 8 q^{77} + 14 q^{81} - 44 q^{85} - 28 q^{87} + 4 q^{92} + 4 q^{93} - 16 q^{94} - 4 q^{95} - 2 q^{96} - 4 q^{98}+O(q^{100}) $ 24 * q + 24 * q^2 - 2 * q^3 + 24 * q^4 - 2 * q^6 + 24 * q^8 + 6 * q^9 - 2 * q^12 + 24 * q^16 + 6 * q^18 + 4 * q^23 - 2 * q^24 + 12 * q^25 - 2 * q^27 - 28 * q^31 + 24 * q^32 - 8 * q^35 + 6 * q^36 + 4 * q^46 - 16 * q^47 - 2 * q^48 - 4 * q^49 + 12 * q^50 - 2 * q^54 + 4 * q^55 - 28 * q^62 + 24 * q^64 - 8 * q^69 - 8 * q^70 + 6 * q^72 - 6 * q^75 - 8 * q^77 + 14 * q^81 - 44 * q^85 - 28 * q^87 + 4 * q^92 + 4 * q^93 - 16 * q^94 - 4 * q^95 - 2 * q^96 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.44698	−	0.951967i	−0.835416	−	0.549618i
$3$	−1.44698	−	0.951967i	−0.835416	−	0.549618i
$4$	1.00000			0.500000
$5$	−1.42959	−	1.71938i	−0.639334	−	0.768929i
$5$	−1.42959	−	1.71938i	−0.639334	−	0.768929i
$6$	−1.44698	−	0.951967i	−0.590728	−	0.388639i
$7$	4.73682			1.79035			0.895174	−	0.445717i	$-0.147051\pi$
$7$	4.73682			1.79035			0.895174	+	0.445717i	$0.147051\pi$
$8$	1.00000			0.353553
$9$	1.18752	+	2.75496i	0.395839	+	0.918320i
$10$	−1.42959	−	1.71938i	−0.452078	−	0.543715i
$11$	0.109553			0.0330314			0.0165157	−	0.999864i	$-0.494743\pi$
$11$	0.109553			0.0330314			0.0165157	+	0.999864i	$0.494743\pi$
$12$	−1.44698	−	0.951967i	−0.417708	−	0.274809i
$13$			2.46994i			0.685037i	0.939511	+	0.342518i	$0.111280\pi$
$13$			2.46994i			0.685037i	−0.939511	+	0.342518i	$0.888720\pi$
$14$	4.73682			1.26597
$15$	0.431808	+	3.84884i	0.111492	+	0.993765i
$16$	1.00000			0.250000
$17$		−	3.72035i		−	0.902318i	−0.892443	−	0.451159i	$-0.851011\pi$
$17$		−	3.72035i		−	0.902318i	0.892443	−	0.451159i	$-0.148989\pi$
$18$	1.18752	+	2.75496i	0.279900	+	0.649350i
$19$		−	6.76462i		−	1.55191i	−0.630788	−	0.775955i	$-0.717268\pi$
$19$		−	6.76462i		−	1.55191i	0.630788	−	0.775955i	$-0.282732\pi$
$20$	−1.42959	−	1.71938i	−0.319667	−	0.384464i
$21$	−6.85409	−	4.50929i	−1.49568	−	0.984008i
$22$	0.109553			0.0233567
$23$	4.67990	−	1.04813i	0.975826	−	0.218551i
$23$	4.67990	−	1.04813i	0.975826	−	0.218551i
$24$	−1.44698	−	0.951967i	−0.295364	−	0.194319i
$25$	−0.912517	+	4.91603i	−0.182503	+	0.983205i
$26$			2.46994i			0.484394i
$27$	0.904315	−	5.11686i	0.174035	−	0.984739i
$28$	4.73682			0.895174
$29$		−	7.05802i		−	1.31064i	−0.755351	−	0.655320i	$-0.772534\pi$
$29$		−	7.05802i		−	1.31064i	0.755351	−	0.655320i	$-0.227466\pi$
$30$	0.431808	+	3.84884i	0.0788370	+	0.702698i
$31$	−9.34339			−1.67812			−0.839061	−	0.544038i	$-0.816895\pi$
$31$	−9.34339			−1.67812			−0.839061	+	0.544038i	$0.816895\pi$
$32$	1.00000			0.176777
$33$	−0.158521	−	0.104291i	−0.0275949	−	0.0181547i
$34$		−	3.72035i		−	0.638035i
$35$	−6.77173	−	8.14437i	−1.14463	−	1.37665i
$36$	1.18752	+	2.75496i	0.197920	+	0.459160i
$37$	1.34148			0.220538			0.110269	−	0.993902i	$-0.464829\pi$
$37$	1.34148			0.220538			0.110269	+	0.993902i	$0.464829\pi$
$38$		−	6.76462i		−	1.09737i
$39$	2.35130	−	3.57395i	0.376509	−	0.572291i
$40$	−1.42959	−	1.71938i	−0.226039	−	0.271857i
$41$			7.38300i			1.15303i	0.817086	+	0.576516i	$0.195588\pi$
$41$			7.38300i			1.15303i	−0.817086	+	0.576516i	$0.804412\pi$
$42$	−6.85409	−	4.50929i	−1.05761	−	0.695799i
$43$	−2.31465			−0.352980			−0.176490	−	0.984302i	$-0.556474\pi$
$43$	−2.31465			−0.352980			−0.176490	+	0.984302i	$0.556474\pi$
$44$	0.109553			0.0165157
$45$	3.03915	−	5.98027i	0.453049	−	0.891485i
$46$	4.67990	−	1.04813i	0.690013	−	0.154539i
$47$	5.53476			0.807327			0.403664	−	0.914907i	$-0.367737\pi$
$47$	5.53476			0.807327			0.403664	+	0.914907i	$0.367737\pi$
$48$	−1.44698	−	0.951967i	−0.208854	−	0.137405i
$49$	15.4374			2.20535
$50$	−0.912517	+	4.91603i	−0.129049	+	0.695231i
$51$	−3.54165	+	5.38329i	−0.495931	+	0.753811i
$52$			2.46994i			0.342518i
$53$		−	3.77179i		−	0.518096i	−0.965864	−	0.259048i	$-0.916591\pi$
$53$		−	3.77179i		−	0.518096i	0.965864	−	0.259048i	$-0.0834087\pi$
$54$	0.904315	−	5.11686i	0.123062	−	0.696316i
$55$	−0.156616	−	0.188362i	−0.0211181	−	0.0253988i
$56$	4.73682			0.632984
$57$	−6.43970	+	9.78829i	−0.852959	+	1.29649i
$58$		−	7.05802i		−	0.926763i
$59$			4.18459i			0.544788i	0.962186	+	0.272394i	$0.0878154\pi$
$59$			4.18459i			0.544788i	−0.962186	+	0.272394i	$0.912185\pi$
$60$	0.431808	+	3.84884i	0.0557462	+	0.496883i
$61$		−	7.57377i		−	0.969722i	−0.874591	−	0.484861i	$-0.838870\pi$
$61$		−	7.57377i		−	0.969722i	0.874591	−	0.484861i	$-0.161130\pi$
$62$	−9.34339			−1.18661
$63$	5.62505	+	13.0497i	0.708690	+	1.64411i
$64$	1.00000			0.125000
$65$	4.24675	−	3.53101i	0.526745	−	0.437967i
$66$	−0.158521	−	0.104291i	−0.0195126	−	0.0128373i
$67$	5.95975			0.728099			0.364050	−	0.931380i	$-0.381394\pi$
$67$	5.95975			0.728099			0.364050	+	0.931380i	$0.381394\pi$
$68$		−	3.72035i		−	0.451159i
$69$	−7.76951	−	2.93848i	−0.935340	−	0.353751i
$70$	−6.77173	−	8.14437i	−0.809376	−	0.973439i
$71$			9.66771i			1.14735i	0.819084	+	0.573673i	$0.194482\pi$
$71$			9.66771i			1.14735i	−0.819084	+	0.573673i	$0.805518\pi$
$72$	1.18752	+	2.75496i	0.139950	+	0.324675i
$73$		−	9.28694i		−	1.08695i	−0.839424	−	0.543477i	$-0.817108\pi$
$73$		−	9.28694i		−	1.08695i	0.839424	−	0.543477i	$-0.182892\pi$
$74$	1.34148			0.155944
$75$	6.00029	−	6.24472i	0.692854	−	0.721078i
$76$		−	6.76462i		−	0.775955i
$77$	0.518931			0.0591377
$78$	2.35130	−	3.57395i	0.266232	−	0.404671i
$79$			12.3843i			1.39334i	0.717389	+	0.696672i	$0.245337\pi$
$79$			12.3843i			1.39334i	−0.717389	+	0.696672i	$0.754663\pi$
$80$	−1.42959	−	1.71938i	−0.159834	−	0.192232i
$81$	−6.17961	+	6.54312i	−0.686623	+	0.727014i
$82$			7.38300i			0.815316i
$83$			16.6139i			1.82362i	0.410616	+	0.911808i	$0.365314\pi$
$83$			16.6139i			1.82362i	−0.410616	+	0.911808i	$0.634686\pi$
$84$	−6.85409	−	4.50929i	−0.747842	−	0.492004i
$85$	−6.39669	+	5.31860i	−0.693819	+	0.576883i
$86$	−2.31465			−0.249595
$87$	−6.71900	+	10.2128i	−0.720352	+	1.09493i
$88$	0.109553			0.0116784
$89$	−10.2277			−1.08413			−0.542067	−	0.840335i	$-0.682358\pi$
$89$	−10.2277			−1.08413			−0.542067	+	0.840335i	$0.682358\pi$
$90$	3.03915	−	5.98027i	0.320354	−	0.630375i
$91$			11.6996i			1.22645i
$92$	4.67990	−	1.04813i	0.487913	−	0.109275i
$93$	13.5197	+	8.89460i	1.40193	+	0.922327i
$94$	5.53476			0.570867
$95$	−11.6309	+	9.67067i	−1.19331	+	0.992190i
$96$	−1.44698	−	0.951967i	−0.147682	−	0.0971597i
$97$	9.94453			1.00971			0.504857	−	0.863203i	$-0.331545\pi$
$97$	9.94453			1.00971			0.504857	+	0.863203i	$0.331545\pi$
$98$	15.4374			1.55941
$99$	0.130096	+	0.301813i	0.0130751	+	0.0303334i
$100$	−0.912517	+	4.91603i	−0.0912517	+	0.491603i
$101$		−	8.68562i		−	0.864251i	−0.901813	−	0.432126i	$-0.857764\pi$
$101$		−	8.68562i		−	0.864251i	0.901813	−	0.432126i	$-0.142236\pi$
$102$	−3.54165	+	5.38329i	−0.350676	+	0.533025i
$103$	−3.27739			−0.322931			−0.161465	−	0.986878i	$-0.551622\pi$
$103$	−3.27739			−0.322931			−0.161465	+	0.986878i	$0.551622\pi$
$104$			2.46994i			0.242197i
$105$	2.04540	+	18.2312i	0.199610	+	1.77919i
$106$		−	3.77179i		−	0.366349i
$107$			1.42323i			0.137589i	0.997631	+	0.0687945i	$0.0219153\pi$
$107$			1.42323i			0.137589i	−0.997631	+	0.0687945i	$0.978085\pi$
$108$	0.904315	−	5.11686i	0.0870177	−	0.492370i
$109$			18.7318i			1.79418i	0.441849	+	0.897090i	$0.354323\pi$
$109$			18.7318i			1.79418i	−0.441849	+	0.897090i	$0.645677\pi$
$110$	−0.156616	−	0.188362i	−0.0149327	−	0.0179597i
$111$	−1.94110	−	1.27704i	−0.184241	−	0.121212i
$112$	4.73682			0.447587
$113$		−	3.47135i		−	0.326557i	−0.986580	−	0.163278i	$-0.947793\pi$
$113$		−	3.47135i		−	0.326557i	0.986580	−	0.163278i	$-0.0522069\pi$
$114$	−6.43970	+	9.78829i	−0.603133	+	0.916757i
$115$	−8.49249	−	6.54810i	−0.791929	−	0.610614i
$116$		−	7.05802i		−	0.655320i
$117$	−6.80457	+	2.93309i	−0.629083	+	0.271164i
$118$			4.18459i			0.385223i
$119$		−	17.6226i		−	1.61546i
$120$	0.431808	+	3.84884i	0.0394185	+	0.351349i
$121$	−10.9880			−0.998909
$122$		−	7.57377i		−	0.685697i
$123$	7.02838	−	10.6831i	0.633727	−	0.963261i
$124$	−9.34339			−0.839061
$125$	9.75703	−	5.45897i	0.872696	−	0.488265i
$126$	5.62505	+	13.0497i	0.501119	+	1.16256i
$127$		−	3.36092i		−	0.298234i	−0.988820	−	0.149117i	$-0.952357\pi$
$127$		−	3.36092i		−	0.298234i	0.988820	−	0.149117i	$-0.0476431\pi$
$128$	1.00000			0.0883883
$129$	3.34925	+	2.20347i	0.294885	+	0.194005i
$130$	4.24675	−	3.53101i	0.372465	−	0.309690i
$131$			13.6399i			1.19173i	0.803086	+	0.595863i	$0.203190\pi$
$131$			13.6399i			1.19173i	−0.803086	+	0.595863i	$0.796810\pi$
$132$	−0.158521	−	0.104291i	−0.0137975	−	0.00907733i
$133$		−	32.0428i		−	2.77846i
$134$	5.95975			0.514844
$135$	−10.0906	+	5.76017i	−0.868461	+	0.495757i
$136$		−	3.72035i		−	0.319018i
$137$			0.102320i			0.00874176i	0.999990	+	0.00437088i	$0.00139130\pi$
$137$			0.102320i			0.00874176i	−0.999990	+	0.00437088i	$0.998609\pi$
$138$	−7.76951	−	2.93848i	−0.661385	−	0.250140i
$139$	1.57186			0.133323			0.0666617	−	0.997776i	$-0.478765\pi$
$139$	1.57186			0.133323			0.0666617	+	0.997776i	$0.478765\pi$
$140$	−6.77173	−	8.14437i	−0.572315	−	0.688325i
$141$	−8.00870	−	5.26891i	−0.674454	−	0.443722i
$142$			9.66771i			0.811296i
$143$			0.270588i			0.0226277i
$144$	1.18752	+	2.75496i	0.0989598	+	0.229580i
$145$	−12.1354	+	10.0901i	−1.00779	+	0.837937i
$146$		−	9.28694i		−	0.768592i
$147$	−22.3377	−	14.6959i	−1.84238	−	1.21210i
$148$	1.34148			0.110269
$149$	10.9226			0.894817			0.447408	−	0.894330i	$-0.352347\pi$
$149$	10.9226			0.894817			0.447408	+	0.894330i	$0.352347\pi$
$150$	6.00029	−	6.24472i	0.489922	−	0.509879i
$151$	6.42872			0.523162			0.261581	−	0.965182i	$-0.415756\pi$
$151$	6.42872			0.523162			0.261581	+	0.965182i	$0.415756\pi$
$152$		−	6.76462i		−	0.548683i
$153$	10.2494	−	4.41798i	0.828617	−	0.357173i
$154$	0.518931			0.0418166
$155$	13.3573	+	16.0648i	1.07288	+	1.29036i
$156$	2.35130	−	3.57395i	0.188254	−	0.286145i
$157$	−24.1285			−1.92567			−0.962834	−	0.270095i	$-0.912945\pi$
$157$	−24.1285			−1.92567			−0.962834	+	0.270095i	$0.912945\pi$
$158$			12.3843i			0.985244i
$159$	−3.59062	+	5.45772i	−0.284755	+	0.432825i
$160$	−1.42959	−	1.71938i	−0.113019	−	0.135929i
$161$	22.1678	−	4.96481i	1.74707	−	0.391281i
$162$	−6.17961	+	6.54312i	−0.485516	+	0.514076i
$163$			15.4395i			1.20932i	0.796485	+	0.604659i	$0.206690\pi$
$163$			15.4395i			1.20932i	−0.796485	+	0.604659i	$0.793310\pi$
$164$			7.38300i			0.576516i
$165$	0.0473058	+	0.421650i	0.00368275	+	0.0328254i
$166$			16.6139i			1.28949i
$167$	4.86290			0.376302			0.188151	−	0.982140i	$-0.439751\pi$
$167$	4.86290			0.376302			0.188151	+	0.982140i	$0.439751\pi$
$168$	−6.85409	−	4.50929i	−0.528804	−	0.347899i
$169$	6.89942			0.530725
$170$	−6.39669	+	5.31860i	−0.490604	+	0.407918i
$171$	18.6363	−	8.03310i	1.42515	−	0.614307i
$172$	−2.31465			−0.176490
$173$	17.0492			1.29623			0.648114	−	0.761543i	$-0.275558\pi$
$173$	17.0492			1.29623			0.648114	+	0.761543i	$0.275558\pi$
$174$	−6.71900	+	10.2128i	−0.509366	+	0.774232i
$175$	−4.32242	+	23.2863i	−0.326745	+	1.76028i
$176$	0.109553			0.00825785
$177$	3.98360	−	6.05503i	0.299425	−	0.455124i
$178$	−10.2277			−0.766598
$179$			8.37101i			0.625679i	0.949806	+	0.312839i	$0.101280\pi$
$179$			8.37101i			0.625679i	−0.949806	+	0.312839i	$0.898720\pi$
$180$	3.03915	−	5.98027i	0.226525	−	0.445743i
$181$			3.91727i			0.291169i	0.989346	+	0.145584i	$0.0465062\pi$
$181$			3.91727i			0.291169i	−0.989346	+	0.145584i	$0.953494\pi$
$182$			11.6996i			0.867234i
$183$	−7.20998	+	10.9591i	−0.532977	+	0.810121i
$184$	4.67990	−	1.04813i	0.345006	−	0.0772693i
$185$	−1.91777	−	2.30651i	−0.140997	−	0.169578i
$186$	13.5197	+	8.89460i	0.991314	+	0.652183i
$187$		−	0.407575i		−	0.0298048i
$188$	5.53476			0.403664
$189$	4.28357	−	24.2376i	0.311584	−	1.76303i
$190$	−11.6309	+	9.67067i	−0.843797	+	0.701584i
$191$	−10.0632			−0.728147			−0.364073	−	0.931370i	$-0.618614\pi$
$191$	−10.0632			−0.728147			−0.364073	+	0.931370i	$0.618614\pi$
$192$	−1.44698	−	0.951967i	−0.104427	−	0.0687023i
$193$		−	1.36921i		−	0.0985576i	−0.998785	−	0.0492788i	$-0.984308\pi$
$193$		−	1.36921i		−	0.0985576i	0.998785	−	0.0492788i	$-0.0156923\pi$
$194$	9.94453			0.713976
$195$	−9.50638	+	1.06654i	−0.680766	+	0.0763764i
$196$	15.4374			1.10267
$197$	3.46037			0.246541			0.123271	−	0.992373i	$-0.460662\pi$
$197$	3.46037			0.246541			0.123271	+	0.992373i	$0.460662\pi$
$198$	0.130096	+	0.301813i	0.00924550	+	0.0214489i
$199$		−	2.84735i		−	0.201843i	−0.994894	−	0.100922i	$-0.967821\pi$
$199$		−	2.84735i		−	0.201843i	0.994894	−	0.100922i	$-0.0321791\pi$
$200$	−0.912517	+	4.91603i	−0.0645247	+	0.347616i
$201$	−8.62365	−	5.67348i	−0.608265	−	0.400177i
$202$		−	8.68562i		−	0.611118i
$203$		−	33.4325i		−	2.34650i
$204$	−3.54165	+	5.38329i	−0.247965	+	0.376906i
$205$	12.6942	−	10.5547i	0.886599	−	0.737173i
$206$	−3.27739			−0.228347
$207$	8.44502	+	11.6482i	0.586969	+	0.809609i
$208$			2.46994i			0.171259i
$209$		−	0.741083i		−	0.0512618i
$210$	2.04540	+	18.2312i	0.141146	+	1.25807i
$211$	−11.9262			−0.821033			−0.410517	−	0.911853i	$-0.634652\pi$
$211$	−11.9262			−0.821033			−0.410517	+	0.911853i	$0.634652\pi$
$212$		−	3.77179i		−	0.259048i
$213$	9.20334	−	13.9890i	0.630603	−	0.958511i
$214$			1.42323i			0.0972901i
$215$	3.30901	+	3.97975i	0.225672	+	0.271417i
$216$	0.904315	−	5.11686i	0.0615308	−	0.348158i
$217$	−44.2579			−3.00442
$218$			18.7318i			1.26868i
$219$	−8.84086	+	13.4380i	−0.597410	+	0.908058i
$220$	−0.156616	−	0.188362i	−0.0105590	−	0.0126994i
$221$	9.18903			0.618121
$222$	−1.94110	−	1.27704i	−0.130278	−	0.0857095i
$223$			18.5236i			1.24043i	0.784432	+	0.620215i	$0.212955\pi$
$223$			18.5236i			1.24043i	−0.784432	+	0.620215i	$0.787045\pi$
$224$	4.73682			0.316492
$225$	−14.6271	+	3.32392i	−0.975139	+	0.221595i
$226$		−	3.47135i		−	0.230910i
$227$		−	15.3110i		−	1.01623i	−0.861290	−	0.508115i	$-0.830343\pi$
$227$		−	15.3110i		−	1.01623i	0.861290	−	0.508115i	$-0.169657\pi$
$228$	−6.43970	+	9.78829i	−0.426479	+	0.648245i
$229$		−	5.31624i		−	0.351307i	−0.984452	−	0.175654i	$-0.943796\pi$
$229$		−	5.31624i		−	0.351307i	0.984452	−	0.175654i	$-0.0562038\pi$
$230$	−8.49249	−	6.54810i	−0.559978	−	0.431769i
$231$	−0.750884	−	0.494005i	−0.0494045	−	0.0325032i
$232$		−	7.05802i		−	0.463381i
$233$	8.00870			0.524667			0.262334	−	0.964977i	$-0.415508\pi$
$233$	8.00870			0.524667			0.262334	+	0.964977i	$0.415508\pi$
$234$	−6.80457	+	2.93309i	−0.444829	+	0.191742i
$235$	−7.91246	−	9.51634i	−0.516152	−	0.620777i
$236$			4.18459i			0.272394i
$237$	11.7895	−	17.9199i	0.765808	−	1.16402i
$238$		−	17.6226i		−	1.14231i
$239$			1.30708i			0.0845482i	0.999106	+	0.0422741i	$0.0134603\pi$
$239$			1.30708i			0.0845482i	−0.999106	+	0.0422741i	$0.986540\pi$
$240$	0.431808	+	3.84884i	0.0278731	+	0.248441i
$241$			9.16266i			0.590219i	0.955463	+	0.295109i	$0.0953561\pi$
$241$			9.16266i			0.590219i	−0.955463	+	0.295109i	$0.904644\pi$
$242$	−10.9880			−0.706335
$243$	15.1706	−	3.58500i	0.973196	−	0.229978i
$244$		−	7.57377i		−	0.484861i
$245$	−22.0693	−	26.5427i	−1.40995	−	1.69575i
$246$	7.02838	−	10.6831i	0.448113	−	0.681128i
$247$	16.7082			1.06312
$248$	−9.34339			−0.593306
$249$	15.8159	−	24.0401i	1.00229	−	1.52348i
$250$	9.75703	−	5.45897i	0.617089	−	0.345255i
$251$	−24.8840			−1.57067			−0.785333	−	0.619073i	$-0.787508\pi$
$251$	−24.8840			−1.57067			−0.785333	+	0.619073i	$0.787508\pi$
$252$	5.62505	+	13.0497i	0.354345	+	0.822056i
$253$	0.512695	−	0.114826i	0.0322329	−	0.00721903i
$254$		−	3.36092i		−	0.210883i
$255$	14.3190	−	1.60648i	0.896693	−	0.100602i
$256$	1.00000			0.0625000
$257$	−18.7650			−1.17053			−0.585264	−	0.810843i	$-0.699009\pi$
$257$	−18.7650			−1.17053			−0.585264	+	0.810843i	$0.699009\pi$
$258$	3.34925	+	2.20347i	0.208515	+	0.137182i
$259$	6.35434			0.394839
$260$	4.24675	−	3.53101i	0.263372	−	0.218984i
$261$	19.4445	−	8.38151i	1.20359	−	0.518803i
$262$			13.6399i			0.842677i
$263$			9.31348i			0.574294i	0.957887	+	0.287147i	$0.0927068\pi$
$263$			9.31348i			0.574294i	−0.957887	+	0.287147i	$0.907293\pi$
$264$	−0.158521	−	0.104291i	−0.00975628	−	0.00641864i
$265$	−6.48514	+	5.39214i	−0.398379	+	0.331236i
$266$		−	32.0428i		−	1.96467i
$267$	14.7993	+	9.73643i	0.905702	+	0.595860i
$268$	5.95975			0.364050
$269$			14.0040i			0.853841i	0.904289	+	0.426921i	$0.140402\pi$
$269$			14.0040i			0.853841i	−0.904289	+	0.426921i	$0.859598\pi$
$270$	−10.0906	+	5.76017i	−0.614095	+	0.350553i
$271$	19.5682			1.18868			0.594340	−	0.804214i	$-0.297413\pi$
$271$	19.5682			1.18868			0.594340	+	0.804214i	$0.297413\pi$
$272$		−	3.72035i		−	0.225580i
$273$	11.1377	−	16.9292i	0.674082	−	1.02460i
$274$			0.102320i			0.00618136i
$275$	−0.0999687	+	0.538564i	−0.00602834	+	0.0324766i
$276$	−7.76951	−	2.93848i	−0.467670	−	0.176876i
$277$		−	12.1168i		−	0.728026i	−0.931394	−	0.364013i	$-0.881406\pi$
$277$		−	12.1168i		−	0.728026i	0.931394	−	0.364013i	$-0.118594\pi$
$278$	1.57186			0.0942739
$279$	−11.0954	−	25.7407i	−0.664266	−	1.54105i
$280$	−6.77173	−	8.14437i	−0.404688	−	0.486719i
$281$	0.997575			0.0595103			0.0297552	−	0.999557i	$-0.490527\pi$
$281$	0.997575			0.0595103			0.0297552	+	0.999557i	$0.490527\pi$
$282$	−8.00870	−	5.26891i	−0.476911	−	0.313759i
$283$	−8.27225			−0.491734			−0.245867	−	0.969304i	$-0.579073\pi$
$283$	−8.27225			−0.491734			−0.245867	+	0.969304i	$0.579073\pi$
$284$			9.66771i			0.573673i
$285$	26.0359	−	2.92102i	1.54223	−	0.173026i
$286$			0.270588i			0.0160002i
$287$			34.9719i			2.06433i
$288$	1.18752	+	2.75496i	0.0699751	+	0.162338i
$289$	3.15896			0.185821
$290$	−12.1354	+	10.0901i	−0.712615	+	0.592511i
$291$	−14.3896	−	9.46687i	−0.843531	−	0.554958i
$292$		−	9.28694i		−	0.543477i
$293$		−	5.35051i		−	0.312580i	−0.987711	−	0.156290i	$-0.950047\pi$
$293$		−	5.35051i		−	0.312580i	0.987711	−	0.156290i	$-0.0499535\pi$
$294$	−22.3377	−	14.6959i	−1.30276	−	0.857083i
$295$	7.19490	−	5.98227i	0.418903	−	0.348301i
$296$	1.34148			0.0779718
$297$	0.0990701	−	0.560565i	0.00574863	−	0.0325273i
$298$	10.9226			0.632731
$299$	2.58882	+	11.5590i	0.149715	+	0.668476i
$300$	6.00029	−	6.24472i	0.346427	−	0.360539i
$301$	−10.9641			−0.631958
$302$	6.42872			0.369931
$303$	−8.26842	+	12.5679i	−0.475008	+	0.722009i
$304$		−	6.76462i		−	0.387978i
$305$	−13.0222	+	10.8274i	−0.745648	+	0.619977i
$306$	10.2494	−	4.41798i	0.585921	−	0.252559i
$307$			23.6777i			1.35136i	0.737197	+	0.675678i	$0.236149\pi$
$307$			23.6777i			1.35136i	−0.737197	+	0.675678i	$0.763851\pi$
$308$	0.518931			0.0295688
$309$	4.74232	+	3.11997i	0.269781	+	0.177489i
$310$	13.3573	+	16.0648i	0.758641	+	0.912420i
$311$		−	12.8720i		−	0.729906i	−0.931026	−	0.364953i	$-0.881085\pi$
$311$		−	12.8720i		−	0.729906i	0.931026	−	0.364953i	$-0.118915\pi$
$312$	2.35130	−	3.57395i	0.133116	−	0.202335i
$313$	4.59243			0.259579			0.129790	−	0.991542i	$-0.458570\pi$
$313$	4.59243			0.259579			0.129790	+	0.991542i	$0.458570\pi$
$314$	−24.1285			−1.36165
$315$	14.3959	−	28.3274i	0.811116	−	1.59607i
$316$			12.3843i			0.696672i
$317$	3.67077			0.206171			0.103085	−	0.994673i	$-0.467129\pi$
$317$	3.67077			0.206171			0.103085	+	0.994673i	$0.467129\pi$
$318$	−3.59062	+	5.45772i	−0.201352	+	0.306054i
$319$		−	0.773225i		−	0.0432923i
$320$	−1.42959	−	1.71938i	−0.0799168	−	0.0961161i
$321$	1.35487	−	2.05939i	0.0756215	−	0.114944i
$322$	22.1678	−	4.96481i	1.23536	−	0.276678i
$323$	−25.1668			−1.40032
$324$	−6.17961	+	6.54312i	−0.343311	+	0.363507i
$325$	−12.1423	−	2.25386i	−0.673532	−	0.125022i
$326$			15.4395i			0.855116i
$327$	17.8320	−	27.1046i	0.986114	−	1.49889i
$328$			7.38300i			0.407658i
$329$	26.2171			1.44540
$330$	0.0473058	+	0.421650i	0.00260410	+	0.0232111i
$331$	−20.9486			−1.15144			−0.575721	−	0.817646i	$-0.695278\pi$
$331$	−20.9486			−1.15144			−0.575721	+	0.817646i	$0.695278\pi$
$332$			16.6139i			0.911808i
$333$	1.59303	+	3.69572i	0.0872974	+	0.202524i
$334$	4.86290			0.266086
$335$	−8.52003	−	10.2471i	−0.465499	−	0.559856i
$336$	−6.85409	−	4.50929i	−0.373921	−	0.246002i
$337$	−8.58764			−0.467799			−0.233899	−	0.972261i	$-0.575149\pi$
$337$	−8.58764			−0.467799			−0.233899	+	0.972261i	$0.575149\pi$
$338$	6.89942			0.375279
$339$	−3.30461	+	5.02298i	−0.179482	+	0.272811i
$340$	−6.39669	+	5.31860i	−0.346909	+	0.288442i
$341$	−1.02359			−0.0554307
$342$	18.6363	−	8.03310i	1.00773	−	0.434381i
$343$	39.9665			2.15799
$344$	−2.31465			−0.124797
$345$	6.05490	+	17.5596i	0.325985	+	0.945375i
$346$	17.0492			0.916572
$347$	29.9351			1.60700			0.803499	−	0.595305i	$-0.202969\pi$
$347$	29.9351			1.60700			0.803499	+	0.595305i	$0.202969\pi$
$348$	−6.71900	+	10.2128i	−0.360176	+	0.547465i
$349$	22.4642			1.20248			0.601240	−	0.799068i	$-0.294673\pi$
$349$	22.4642			1.20248			0.601240	+	0.799068i	$0.294673\pi$
$350$	−4.32242	+	23.2863i	−0.231043	+	1.24471i
$351$	12.6383	+	2.23360i	0.674583	+	0.119221i
$352$	0.109553			0.00583918
$353$	−13.4442			−0.715563			−0.357782	−	0.933805i	$-0.616467\pi$
$353$	−13.4442			−0.715563			−0.357782	+	0.933805i	$0.616467\pi$
$354$	3.98360	−	6.05503i	0.211726	−	0.321821i
$355$	16.6224	−	13.8209i	0.882228	−	0.733538i
$356$	−10.2277			−0.542067
$357$	−16.7762	+	25.4996i	−0.887889	+	1.34958i
$358$			8.37101i			0.442422i
$359$	−32.7887			−1.73052			−0.865260	−	0.501323i	$-0.832847\pi$
$359$	−32.7887			−1.73052			−0.865260	+	0.501323i	$0.832847\pi$
$360$	3.03915	−	5.98027i	0.160177	−	0.315188i
$361$	−26.7601			−1.40843
$362$			3.91727i			0.205887i
$363$	15.8994	+	10.4602i	0.834504	+	0.549019i
$364$			11.6996i			0.613227i
$365$	−15.9678	+	13.2766i	−0.835790	+	0.694927i
$366$	−7.20998	+	10.9591i	−0.376872	+	0.572842i
$367$	0.619262			0.0323252			0.0161626	−	0.999869i	$-0.494855\pi$
$367$	0.619262			0.0323252			0.0161626	+	0.999869i	$0.494855\pi$
$368$	4.67990	−	1.04813i	0.243956	−	0.0546376i
$369$	−20.3399	+	8.76744i	−1.05885	+	0.456415i
$370$	−1.91777	−	2.30651i	−0.0997002	−	0.119910i
$371$		−	17.8663i		−	0.927571i
$372$	13.5197	+	8.89460i	0.700965	+	0.461163i
$373$	−33.9726			−1.75904			−0.879518	−	0.475866i	$-0.842135\pi$
$373$	−33.9726			−1.75904			−0.879518	+	0.475866i	$0.842135\pi$
$374$		−	0.407575i		−	0.0210752i
$375$	−19.3150	−	1.38935i	−0.997423	−	0.0717456i
$376$	5.53476			0.285433
$377$	17.4328			0.897837
$378$	4.28357	−	24.2376i	0.220323	−	1.24665i
$379$			6.22071i			0.319537i	0.987155	+	0.159768i	$0.0510747\pi$
$379$			6.22071i			0.319537i	−0.987155	+	0.159768i	$0.948925\pi$
$380$	−11.6309	+	9.67067i	−0.596654	+	0.496095i
$381$	−3.19949	+	4.86320i	−0.163915	+	0.249149i
$382$	−10.0632			−0.514877
$383$		−	0.328653i		−	0.0167934i	−0.999965	−	0.00839669i	$-0.997327\pi$
$383$		−	0.328653i		−	0.0167934i	0.999965	−	0.00839669i	$-0.00267278\pi$
$384$	−1.44698	−	0.951967i	−0.0738410	−	0.0485799i
$385$	−0.741861	−	0.892238i	−0.0378087	−	0.0454727i
$386$		−	1.36921i		−	0.0696908i
$387$	−2.74868	−	6.37676i	−0.139723	−	0.324149i
$388$	9.94453			0.504857
$389$	−28.8039			−1.46042			−0.730208	−	0.683225i	$-0.760577\pi$
$389$	−28.8039			−1.46042			−0.730208	+	0.683225i	$0.760577\pi$
$390$	−9.50638	+	1.06654i	−0.481374	+	0.0540063i
$391$	−3.89942	−	17.4109i	−0.197202	−	0.880505i
$392$	15.4374			0.779707
$393$	12.9848	−	19.7367i	0.654994	−	0.995586i
$394$	3.46037			0.174331
$395$	21.2933	−	17.7046i	1.07138	−	0.890813i
$396$	0.130096	+	0.301813i	0.00653756	+	0.0151667i
$397$			25.5527i			1.28245i	0.767352	+	0.641226i	$0.221574\pi$
$397$			25.5527i			1.28245i	−0.767352	+	0.641226i	$0.778426\pi$
$398$		−	2.84735i		−	0.142725i
$399$	−30.5037	+	46.3653i	−1.52709	+	2.32117i
$400$	−0.912517	+	4.91603i	−0.0456258	+	0.245801i
$401$	16.8426			0.841080			0.420540	−	0.907274i	$-0.361841\pi$
$401$	16.8426			0.841080			0.420540	+	0.907274i	$0.361841\pi$
$402$	−8.62365	−	5.67348i	−0.430109	−	0.282968i
$403$		−	23.0776i		−	1.14958i
$404$		−	8.68562i		−	0.432126i
$405$	20.0844	+	1.27106i	0.998003	+	0.0631594i
$406$		−	33.4325i		−	1.65923i
$407$	0.146963			0.00728466
$408$	−3.54165	+	5.38329i	−0.175338	+	0.266512i
$409$	1.73082			0.0855838			0.0427919	−	0.999084i	$-0.486375\pi$
$409$	1.73082			0.0855838			0.0427919	+	0.999084i	$0.486375\pi$
$410$	12.6942	−	10.5547i	0.626920	−	0.521260i
$411$	0.0974049	−	0.148055i	0.00480463	−	0.00730300i
$412$	−3.27739			−0.161465
$413$			19.8216i			0.975359i
$414$	8.44502	+	11.6482i	0.415050	+	0.572480i
$415$	28.5656	−	23.7512i	1.40223	−	1.16590i
$416$			2.46994i			0.121099i
$417$	−2.27445	−	1.49636i	−0.111381	−	0.0732770i
$418$		−	0.741083i		−	0.0362475i
$419$	0.0603174			0.00294670			0.00147335	−	0.999999i	$-0.499531\pi$
$419$	0.0603174			0.00294670			0.00147335	+	0.999999i	$0.499531\pi$
$420$	2.04540	+	18.2312i	0.0998051	+	0.889593i
$421$		−	16.7804i		−	0.817829i	−0.912573	−	0.408914i	$-0.865908\pi$
$421$		−	16.7804i		−	0.817829i	0.912573	−	0.408914i	$-0.134092\pi$
$422$	−11.9262			−0.580558
$423$	6.57262	+	15.2480i	0.319572	+	0.741385i
$424$		−	3.77179i		−	0.183174i
$425$	18.2894	+	3.39489i	0.887164	+	0.164676i
$426$	9.20334	−	13.9890i	0.445903	−	0.677770i
$427$		−	35.8756i		−	1.73614i
$428$			1.42323i			0.0687945i
$429$	0.257591	−	0.391536i	0.0124366	−	0.0189035i
$430$	3.30901	+	3.97975i	0.159575	+	0.191921i
$431$	−4.36493			−0.210251			−0.105126	−	0.994459i	$-0.533524\pi$
$431$	−4.36493			−0.210251			−0.105126	+	0.994459i	$0.533524\pi$
$432$	0.904315	−	5.11686i	0.0435089	−	0.246185i
$433$	29.9206			1.43789			0.718947	−	0.695065i	$-0.244625\pi$
$433$	29.9206			1.43789			0.718947	+	0.695065i	$0.244625\pi$
$434$	−44.2579			−2.12445
$435$	27.1651	−	3.04771i	1.30247	−	0.146126i
$436$			18.7318i			0.897090i
$437$	−7.09021	−	31.6577i	−0.339171	−	1.51439i
$438$	−8.84086	+	13.4380i	−0.422433	+	0.642094i
$439$	−16.9861			−0.810702			−0.405351	−	0.914161i	$-0.632851\pi$
$439$	−16.9861			−0.810702			−0.405351	+	0.914161i	$0.632851\pi$
$440$	−0.156616	−	0.188362i	−0.00746637	−	0.00897983i
$441$	18.3322	+	42.5295i	0.872962	+	2.02521i
$442$	9.18903			0.437078
$443$	−24.5257			−1.16525			−0.582626	−	0.812740i	$-0.697975\pi$
$443$	−24.5257			−1.16525			−0.582626	+	0.812740i	$0.697975\pi$
$444$	−1.94110	−	1.27704i	−0.0921203	−	0.0606058i
$445$	14.6215	+	17.5853i	0.693124	+	0.833622i
$446$			18.5236i			0.877117i
$447$	−15.8049	−	10.3980i	−0.747544	−	0.491808i
$448$	4.73682			0.223793
$449$		−	16.0667i		−	0.758233i	−0.925349	−	0.379117i	$-0.876228\pi$
$449$		−	16.0667i		−	0.758233i	0.925349	−	0.379117i	$-0.123772\pi$
$450$	−14.6271	+	3.32392i	−0.689527	+	0.156691i
$451$			0.808828i			0.0380862i
$452$		−	3.47135i		−	0.163278i
$453$	−9.30225	−	6.11993i	−0.437058	−	0.287540i
$454$		−	15.3110i		−	0.718582i
$455$	20.1161	−	16.7257i	0.943056	−	0.784114i
$456$	−6.43970	+	9.78829i	−0.301566	+	0.458379i
$457$	13.2071			0.617802			0.308901	−	0.951094i	$-0.400039\pi$
$457$	13.2071			0.617802			0.308901	+	0.951094i	$0.400039\pi$
$458$		−	5.31624i		−	0.248412i
$459$	−19.0365	−	3.36437i	−0.888549	−	0.157035i
$460$	−8.49249	−	6.54810i	−0.395964	−	0.305307i
$461$			25.4941i			1.18738i	0.804695	+	0.593689i	$0.202329\pi$
$461$			25.4941i			1.18738i	−0.804695	+	0.593689i	$0.797671\pi$
$462$	−0.750884	−	0.494005i	−0.0349343	−	0.0229832i
$463$		−	20.0822i		−	0.933298i	−0.884443	−	0.466649i	$-0.845461\pi$
$463$		−	20.0822i		−	0.933298i	0.884443	−	0.466649i	$-0.154539\pi$
$464$		−	7.05802i		−	0.327660i
$465$	−4.03455	−	35.9612i	−0.187098	−	1.66766i
$466$	8.00870			0.370996
$467$		−	14.7644i		−	0.683215i	−0.939843	−	0.341607i	$-0.889029\pi$
$467$		−	14.7644i		−	0.683215i	0.939843	−	0.341607i	$-0.110971\pi$
$468$	−6.80457	+	2.93309i	−0.314541	+	0.135582i
$469$	28.2302			1.30355
$470$	−7.91246	−	9.51634i	−0.364975	−	0.438956i
$471$	34.9136	+	22.9696i	1.60873	+	1.05838i
$472$			4.18459i			0.192612i
$473$	−0.253576			−0.0116594
$474$	11.7895	−	17.9199i	0.541508	−	0.823088i
$475$	33.2551	+	6.17283i	1.52585	+	0.283229i
$476$		−	17.6226i		−	0.807732i
$477$	10.3911	−	4.47907i	0.475778	−	0.205082i
$478$			1.30708i			0.0597846i
$479$	0.527998			0.0241248			0.0120624	−	0.999927i	$-0.496160\pi$
$479$	0.527998			0.0241248			0.0120624	+	0.999927i	$0.496160\pi$
$480$	0.431808	+	3.84884i	0.0197093	+	0.175675i
$481$			3.31336i			0.151076i
$482$			9.16266i			0.417348i
$483$	−36.8028	−	13.9190i	−1.67458	−	0.633338i
$484$	−10.9880			−0.499454
$485$	−14.2167	−	17.0984i	−0.645545	−	0.776398i
$486$	15.1706	−	3.58500i	0.688153	−	0.162619i
$487$		−	15.1423i		−	0.686164i	−0.939306	−	0.343082i	$-0.888529\pi$
$487$		−	15.1423i		−	0.686164i	0.939306	−	0.343082i	$-0.111471\pi$
$488$		−	7.57377i		−	0.342849i
$489$	14.6979	−	22.3407i	0.664663	−	1.01028i
$490$	−22.0693	−	26.5427i	−0.996987	−	1.19908i
$491$		−	23.0745i		−	1.04134i	−0.853759	−	0.520668i	$-0.825683\pi$
$491$		−	23.0745i		−	1.04134i	0.853759	−	0.520668i	$-0.174317\pi$
$492$	7.02838	−	10.6831i	0.316864	−	0.481630i
$493$	−26.2583			−1.18262
$494$	16.7082			0.751736
$495$	0.332947	−	0.655154i	0.0149648	−	0.0294470i
$496$	−9.34339			−0.419530
$497$			45.7942i			2.05415i
$498$	15.8159	−	24.0401i	0.708728	−	1.07726i
$499$	2.99246			0.133961			0.0669805	−	0.997754i	$-0.478663\pi$
$499$	2.99246			0.133961			0.0669805	+	0.997754i	$0.478663\pi$
$500$	9.75703	−	5.45897i	0.436348	−	0.244132i
$501$	−7.03652	−	4.62932i	−0.314369	−	0.206823i
$502$	−24.8840			−1.11063
$503$			35.8449i			1.59825i	0.601167	+	0.799123i	$0.294703\pi$
$503$			35.8449i			1.59825i	−0.601167	+	0.799123i	$0.705297\pi$
$504$	5.62505	+	13.0497i	0.250560	+	0.581281i
$505$	−14.9339	+	12.4169i	−0.664548	+	0.552545i
$506$	0.512695	−	0.114826i	0.0227921	−	0.00510462i
$507$	−9.98334	−	6.56802i	−0.443376	−	0.291696i
$508$		−	3.36092i		−	0.149117i
$509$		−	15.8139i		−	0.700937i	−0.936575	−	0.350468i	$-0.886022\pi$
$509$		−	15.8139i		−	0.700937i	0.936575	−	0.350468i	$-0.113978\pi$
$510$	14.3190	−	1.60648i	0.634058	−	0.0711361i
$511$		−	43.9905i		−	1.94603i
$512$	1.00000			0.0441942
$513$	−34.6136	−	6.11735i	−1.52823	−	0.270087i
$514$	−18.7650			−0.827688
$515$	4.68534	+	5.63507i	0.206461	+	0.248311i
$516$	3.34925	+	2.20347i	0.147443	+	0.0970023i
$517$	0.606348			0.0266671
$518$	6.35434			0.279193
$519$	−24.6699	−	16.2303i	−1.08289	−	0.712431i
$520$	4.24675	−	3.53101i	0.186232	−	0.154845i
$521$	21.4453			0.939538			0.469769	−	0.882789i	$-0.344337\pi$
$521$	21.4453			0.939538			0.469769	+	0.882789i	$0.344337\pi$
$522$	19.4445	−	8.38151i	0.851065	−	0.366849i
$523$	−21.4978			−0.940033			−0.470017	−	0.882658i	$-0.655752\pi$
$523$	−21.4978			−0.940033			−0.470017	+	0.882658i	$0.655752\pi$
$524$			13.6399i			0.595863i
$525$	28.4223	−	29.5801i	1.24045	−	1.29098i
$526$			9.31348i			0.406087i
$527$			34.7607i			1.51420i
$528$	−0.158521	−	0.104291i	−0.00689873	−	0.00453866i
$529$	20.8028	−	9.81029i	0.904471	−	0.426534i
$530$	−6.48514	+	5.39214i	−0.281696	+	0.234219i
$531$	−11.5284	+	4.96928i	−0.500289	+	0.215648i
$532$		−	32.0428i		−	1.38923i
$533$	−18.2355			−0.789869
$534$	14.7993	+	9.73643i	0.640428	+	0.421336i
$535$	2.44707	−	2.03464i	0.105796	−	0.0879654i
$536$	5.95975			0.257422
$537$	7.96893	−	12.1127i	0.343885	−	0.522702i
$538$			14.0040i			0.603757i
$539$	1.69121			0.0728456
$540$	−10.0906	+	5.76017i	−0.434231	+	0.247878i
$541$	−28.9815			−1.24601			−0.623005	−	0.782218i	$-0.714088\pi$
$541$	−28.9815			−1.24601			−0.623005	+	0.782218i	$0.714088\pi$
$542$	19.5682			0.840524
$543$	3.72911	−	5.66822i	0.160032	−	0.243247i
$544$		−	3.72035i		−	0.159509i
$545$	32.2070	−	26.7789i	1.37960	−	1.14708i
$546$	11.1377	−	16.9292i	0.476648	−	0.724501i
$547$			31.1585i			1.33224i	0.745844	+	0.666121i	$0.232046\pi$
$547$			31.1585i			1.33224i	−0.745844	+	0.666121i	$0.767954\pi$
$548$			0.102320i			0.00437088i
$549$	20.8654	−	8.99399i	0.890515	−	0.383854i
$550$	−0.0999687	+	0.538564i	−0.00426268	+	0.0229644i
$551$	−47.7448			−2.03400
$552$	−7.76951	−	2.93848i	−0.330692	−	0.125070i
$553$			58.6622i			2.49457i
$554$		−	12.1168i		−	0.514792i
$555$	0.579261	+	5.16313i	0.0245883	+	0.219163i
$556$	1.57186			0.0666617
$557$		−	33.0466i		−	1.40023i	−0.714030	−	0.700115i	$-0.753132\pi$
$557$		−	33.0466i		−	1.40023i	0.714030	−	0.700115i	$-0.246868\pi$
$558$	−11.0954	−	25.7407i	−0.469707	−	1.08969i
$559$		−	5.71703i		−	0.241805i
$560$	−6.77173	−	8.14437i	−0.286158	−	0.344163i
$561$	−0.387998	+	0.589754i	−0.0163813	+	0.0248994i
$562$	0.997575			0.0420801
$563$		−	22.9282i		−	0.966310i	−0.875535	−	0.483155i	$-0.839491\pi$
$563$		−	22.9282i		−	0.966310i	0.875535	−	0.483155i	$-0.160509\pi$
$564$	−8.00870	−	5.26891i	−0.337227	−	0.221861i
$565$	−5.96855	+	4.96262i	−0.251099	+	0.208779i
$566$	−8.27225			−0.347709
$567$	−29.2717	+	30.9936i	−1.22929	+	1.30161i
$568$			9.66771i			0.405648i
$569$	7.12332			0.298625			0.149312	−	0.988790i	$-0.452294\pi$
$569$	7.12332			0.298625			0.149312	+	0.988790i	$0.452294\pi$
$570$	26.0359	−	2.92102i	1.09052	−	0.122348i
$571$		−	15.0075i		−	0.628044i	−0.949416	−	0.314022i	$-0.898323\pi$
$571$		−	15.0075i		−	0.628044i	0.949416	−	0.314022i	$-0.101677\pi$
$572$			0.270588i			0.0113139i
$573$	14.5613	+	9.57982i	0.608305	+	0.400203i
$574$			34.9719i			1.45970i
$575$	0.882158	+	23.9629i	0.0367886	+	0.999323i
$576$	1.18752	+	2.75496i	0.0494799	+	0.114790i
$577$		−	32.3173i		−	1.34539i	−0.739922	−	0.672693i	$-0.765138\pi$
$577$		−	32.3173i		−	1.34539i	0.739922	−	0.672693i	$-0.234862\pi$
$578$	3.15896			0.131396
$579$	−1.30344	+	1.98122i	−0.0541691	+	0.0823366i
$580$	−12.1354	+	10.0901i	−0.503895	+	0.418969i
$581$			78.6972i			3.26491i
$582$	−14.3896	−	9.46687i	−0.596467	−	0.392414i
$583$		−	0.413210i		−	0.0171134i
$584$		−	9.28694i		−	0.384296i
$585$	14.7709	+	7.50650i	0.610700	+	0.310355i
$586$		−	5.35051i		−	0.221028i
$587$	−9.64803			−0.398217			−0.199108	−	0.979977i	$-0.563805\pi$
$587$	−9.64803			−0.398217			−0.199108	+	0.979977i	$0.563805\pi$
$588$	−22.3377	−	14.6959i	−0.921190	−	0.606049i
$589$			63.2045i			2.60429i
$590$	7.19490	−	5.98227i	0.296209	−	0.246286i
$591$	−5.00710	−	3.29416i	−0.205964	−	0.135504i
$592$	1.34148			0.0551344
$593$	12.6479			0.519385			0.259693	−	0.965691i	$-0.416379\pi$
$593$	12.6479			0.519385			0.259693	+	0.965691i	$0.416379\pi$
$594$	0.0990701	−	0.560565i	0.00406490	−	0.0230003i
$595$	−30.3000	+	25.1932i	−1.24218	+	1.03282i
$596$	10.9226			0.447408
$597$	−2.71058	+	4.12007i	−0.110937	+	0.168623i
$598$	2.58882	+	11.5590i	0.105865	+	0.472684i
$599$			24.2565i			0.991094i	0.868581	+	0.495547i	$0.165032\pi$
$599$			24.2565i			0.991094i	−0.868581	+	0.495547i	$0.834968\pi$
$600$	6.00029	−	6.24472i	0.244961	−	0.254940i
$601$	3.91095			0.159531			0.0797655	−	0.996814i	$-0.474583\pi$
$601$	3.91095			0.159531			0.0797655	+	0.996814i	$0.474583\pi$
$602$	−10.9641			−0.446862
$603$	7.07730	+	16.4189i	0.288210	+	0.668628i
$604$	6.42872			0.261581
$605$	15.7084	+	18.8925i	0.638637	+	0.768090i
$606$	−8.26842	+	12.5679i	−0.335882	+	0.510537i
$607$			31.9532i			1.29694i	0.761241	+	0.648469i	$0.224590\pi$
$607$			31.9532i			1.29694i	−0.761241	+	0.648469i	$0.775410\pi$
$608$		−	6.76462i		−	0.274342i
$609$	−31.8267	+	48.3763i	−1.28968	+	1.96031i
$610$	−13.0222	+	10.8274i	−0.527252	+	0.438390i
$611$			13.6705i			0.553049i
$612$	10.2494	−	4.41798i	0.414308	−	0.178586i
$613$	−6.81990			−0.275453			−0.137727	−	0.990470i	$-0.543980\pi$
$613$	−6.81990			−0.275453			−0.137727	+	0.990470i	$0.543980\pi$
$614$			23.6777i			0.955553i
$615$	−28.4160	+	3.18804i	−1.14584	+	0.128554i
$616$	0.518931			0.0209083
$617$			7.46733i			0.300623i	0.988639	+	0.150312i	$0.0480277\pi$
$617$			7.46733i			0.300623i	−0.988639	+	0.150312i	$0.951972\pi$
$618$	4.74232	+	3.11997i	0.190764	+	0.125503i
$619$		−	41.5273i		−	1.66912i	−0.550915	−	0.834561i	$-0.685721\pi$
$619$		−	41.5273i		−	1.66912i	0.550915	−	0.834561i	$-0.314279\pi$
$620$	13.3573	+	16.0648i	0.536440	+	0.645178i
$621$	−1.13104	−	24.8942i	−0.0453871	−	0.998969i
$622$		−	12.8720i		−	0.516122i
$623$	−48.4467			−1.94098
$624$	2.35130	−	3.57395i	0.0941272	−	0.143073i
$625$	−23.3346	−	8.97191i	−0.933385	−	0.358877i
$626$	4.59243			0.183550
$627$	−0.705486	+	1.07233i	−0.0281744	+	0.0428249i
$628$	−24.1285			−0.962834
$629$		−	4.99077i		−	0.198995i
$630$	14.3959	−	28.3274i	0.573545	−	1.12859i
$631$			36.9311i			1.47020i	0.677956	+	0.735102i	$0.262866\pi$
$631$			36.9311i			1.47020i	−0.677956	+	0.735102i	$0.737134\pi$
$632$			12.3843i			0.492622i
$633$	17.2570	+	11.3533i	0.685904	+	0.451255i
$634$	3.67077			0.145785
$635$	−5.77870	+	4.80476i	−0.229321	+	0.190671i
$636$	−3.59062	+	5.45772i	−0.142377	+	0.216413i
$637$			38.1294i			1.51074i
$638$		−	0.773225i		−	0.0306123i
$639$	−26.6342	+	11.4806i	−1.05363	+	0.454164i
$640$	−1.42959	−	1.71938i	−0.0565097	−	0.0679644i
$641$	−23.5864			−0.931606			−0.465803	−	0.884888i	$-0.654235\pi$
$641$	−23.5864			−0.931606			−0.465803	+	0.884888i	$0.654235\pi$
$642$	1.35487	−	2.05939i	0.0534725	−	0.0812777i
$643$	25.9305			1.02260			0.511299	−	0.859403i	$-0.329164\pi$
$643$	25.9305			1.02260			0.511299	+	0.859403i	$0.329164\pi$
$644$	22.1678	−	4.96481i	0.873534	−	0.195641i
$645$	−0.999484	−	8.90870i	−0.0393546	−	0.350780i
$646$	−25.1668			−0.990174
$647$	5.05526			0.198743			0.0993713	−	0.995050i	$-0.468317\pi$
$647$	5.05526			0.198743			0.0993713	+	0.995050i	$0.468317\pi$
$648$	−6.17961	+	6.54312i	−0.242758	+	0.257038i
$649$			0.458433i			0.0179951i
$650$	−12.1423	−	2.25386i	−0.476259	−	0.0884036i
$651$	64.0404	+	42.1321i	2.50994	+	1.65129i
$652$			15.4395i			0.604659i
$653$	−9.19815			−0.359952			−0.179976	−	0.983671i	$-0.557602\pi$
$653$	−9.19815			−0.359952			−0.179976	+	0.983671i	$0.557602\pi$
$654$	17.8320	−	27.1046i	0.697288	−	1.05987i
$655$	23.4522	−	19.4996i	0.916352	−	0.761911i
$656$			7.38300i			0.288258i
$657$	25.5851	−	11.0284i	0.998171	−	0.430259i
$658$	26.2171			1.02205
$659$	40.3687			1.57254			0.786270	−	0.617883i	$-0.212009\pi$
$659$	40.3687			1.57254			0.786270	+	0.617883i	$0.212009\pi$
$660$	0.0473058	+	0.421650i	0.00184137	+	0.0164127i
$661$			16.6400i			0.647220i	0.946191	+	0.323610i	$0.104897\pi$
$661$			16.6400i			0.647220i	−0.946191	+	0.323610i	$0.895103\pi$
$662$	−20.9486			−0.814192
$663$	−13.2964	−	8.74766i	−0.516388	−	0.339731i
$664$			16.6139i			0.644746i
$665$	−55.0936	+	45.8082i	−2.13644	+	1.77636i
$666$	1.59303	+	3.69572i	0.0617286	+	0.143206i
$667$	−7.39773	−	33.0308i	−0.286441	−	1.27896i
$668$	4.86290			0.188151
$669$	17.6338	−	26.8033i	0.681764	−	1.03628i
$670$	−8.52003	−	10.2471i	−0.329157	−	0.395878i
$671$		−	0.829727i		−	0.0320313i
$672$	−6.85409	−	4.50929i	−0.264402	−	0.173950i
$673$		−	32.2214i		−	1.24204i	−0.783793	−	0.621022i	$-0.786718\pi$
$673$		−	32.2214i		−	1.24204i	0.783793	−	0.621022i	$-0.213282\pi$
$674$	−8.58764			−0.330784
$675$	24.3294	+	9.11485i	0.936439	+	0.350831i
$676$	6.89942			0.265362
$677$			23.6610i			0.909366i	0.890653	+	0.454683i	$0.150247\pi$
$677$			23.6610i			0.909366i	−0.890653	+	0.454683i	$0.849753\pi$
$678$	−3.30461	+	5.02298i	−0.126913	+	0.192906i
$679$	47.1054			1.80774
$680$	−6.39669	+	5.31860i	−0.245302	+	0.203959i
$681$	−14.5756	+	22.1548i	−0.558538	+	0.848974i
$682$	−1.02359			−0.0391954
$683$	2.38670			0.0913245			0.0456622	−	0.998957i	$-0.485460\pi$
$683$	2.38670			0.0913245			0.0456622	+	0.998957i	$0.485460\pi$
$684$	18.6363	−	8.03310i	0.712575	−	0.307153i
$685$	0.175926	−	0.146276i	0.00672179	−	0.00558890i
$686$	39.9665			1.52593
$687$	−5.06089	+	7.69251i	−0.193085	+	0.293487i
$688$	−2.31465			−0.0882451
$689$	9.31608			0.354915
$690$	6.05490	+	17.5596i	0.230506	+	0.668481i
$691$	12.4301			0.472862			0.236431	−	0.971648i	$-0.424022\pi$
$691$	12.4301			0.472862			0.236431	+	0.971648i	$0.424022\pi$
$692$	17.0492			0.648114
$693$	0.616239	+	1.42963i	0.0234090	+	0.0543073i
$694$	29.9351			1.13632
$695$	−2.24712	−	2.70262i	−0.0852383	−	0.102516i
$696$	−6.71900	+	10.2128i	−0.254683	+	0.387116i
$697$	27.4674			1.04040
$698$	22.4642			0.850282
$699$	−11.5884	−	7.62402i	−0.438315	−	0.288367i
$700$	−4.32242	+	23.2863i	−0.163372	+	0.880140i
$701$	−40.2008			−1.51836			−0.759181	−	0.650879i	$-0.774400\pi$
$701$	−40.2008			−1.51836			−0.759181	+	0.650879i	$0.774400\pi$
$702$	12.6383	+	2.23360i	0.477002	+	0.0843017i
$703$		−	9.07459i		−	0.342255i
$704$	0.109553			0.00412892
$705$	2.38995	+	21.3024i	0.0900109	+	0.802294i
$706$	−13.4442			−0.505980
$707$		−	41.1422i		−	1.54731i
$708$	3.98360	−	6.05503i	0.149713	−	0.227562i
$709$			4.06296i			0.152588i	0.997085	+	0.0762938i	$0.0243087\pi$
$709$			4.06296i			0.152588i	−0.997085	+	0.0762938i	$0.975691\pi$
$710$	16.6224	−	13.8209i	0.623829	−	0.518690i
$711$	−34.1183	+	14.7066i	−1.27954	+	0.551540i
$712$	−10.2277			−0.383299
$713$	−43.7261	+	9.79310i	−1.63755	+	0.366754i
$714$	−16.7762	+	25.4996i	−0.627832	+	0.954300i
$715$	0.465243	−	0.386831i	0.0173991	−	0.0144667i
$716$			8.37101i			0.312839i
$717$	1.24430	−	1.89133i	0.0464693	−	0.0706329i
$718$	−32.7887			−1.22366
$719$		−	27.4547i		−	1.02389i	−0.859019	−	0.511944i	$-0.828925\pi$
$719$		−	27.4547i		−	1.02389i	0.859019	−	0.511944i	$-0.171075\pi$
$720$	3.03915	−	5.98027i	0.113262	−	0.222871i
$721$	−15.5244			−0.578158
$722$	−26.7601			−0.995908
$723$	8.72255	−	13.2582i	0.324395	−	0.493078i
$724$			3.91727i			0.145584i
$725$	34.6974	+	6.44056i	1.28863	+	0.239196i
$726$	15.8994	+	10.4602i	0.590084	+	0.388215i
$727$	39.9198			1.48054			0.740272	−	0.672308i	$-0.234697\pi$
$727$	39.9198			1.48054			0.740272	+	0.672308i	$0.234697\pi$
$728$			11.6996i			0.433617i
$729$	−25.3644	−	9.25449i	−0.939423	−	0.342759i
$730$	−15.9678	+	13.2766i	−0.590993	+	0.491388i
$731$			8.61131i			0.318501i
$732$	−7.20998	+	10.9591i	−0.266489	+	0.405061i
$733$	−30.5739			−1.12927			−0.564636	−	0.825340i	$-0.690984\pi$
$733$	−30.5739			−1.12927			−0.564636	+	0.825340i	$0.690984\pi$
$734$	0.619262			0.0228574
$735$	6.66600	+	59.4161i	0.245879	+	2.19160i
$736$	4.67990	−	1.04813i	0.172503	−	0.0386346i
$737$	0.652906			0.0240501
$738$	−20.3399	+	8.76744i	−0.748721	+	0.322734i
$739$	14.6803			0.540022			0.270011	−	0.962857i	$-0.412973\pi$
$739$	14.6803			0.540022			0.270011	+	0.962857i	$0.412973\pi$
$740$	−1.91777	−	2.30651i	−0.0704987	−	0.0847889i
$741$	−24.1764	−	15.9056i	−0.888144	−	0.584308i
$742$		−	17.8663i		−	0.655892i
$743$			11.9149i			0.437115i	0.975824	+	0.218557i	$0.0701351\pi$
$743$			11.9149i			0.437115i	−0.975824	+	0.218557i	$0.929865\pi$
$744$	13.5197	+	8.89460i	0.495657	+	0.326092i
$745$	−15.6149	−	18.7801i	−0.572087	−	0.688050i
$746$	−33.9726			−1.24383
$747$	−45.7707	+	19.7293i	−1.67466	+	0.721859i
$748$		−	0.407575i		−	0.0149024i
$749$			6.74159i			0.246332i
$750$	−19.3150	−	1.38935i	−0.705285	−	0.0507318i
$751$			47.3378i			1.72738i	0.504024	+	0.863690i	$0.331852\pi$
$751$			47.3378i			1.72738i	−0.504024	+	0.863690i	$0.668148\pi$
$752$	5.53476			0.201832
$753$	36.0068	+	23.6888i	1.31216	+	0.863267i
$754$	17.4328			0.634867
$755$	−9.19047	−	11.0534i	−0.334475	−	0.402274i
$756$	4.28357	−	24.2376i	0.155792	−	0.881513i
$757$	48.7061			1.77025			0.885126	−	0.465352i	$-0.154072\pi$
$757$	48.7061			1.77025			0.885126	+	0.465352i	$0.154072\pi$
$758$			6.22071i			0.225947i
$759$	−0.851171	−	0.321918i	−0.0308956	−	0.0116849i
$760$	−11.6309	+	9.67067i	−0.421898	+	0.350792i
$761$		−	44.5378i		−	1.61450i	−0.590213	−	0.807248i	$-0.700956\pi$
$761$		−	44.5378i		−	1.61450i	0.590213	−	0.807248i	$-0.299044\pi$
$762$	−3.19949	+	4.86320i	−0.115905	+	0.176175i
$763$			88.7290i			3.21220i
$764$	−10.0632			−0.364073
$765$	−22.2487	−	11.3067i	−0.804404	−	0.408795i
$766$		−	0.328653i		−	0.0118747i
$767$	−10.3357			−0.373200
$768$	−1.44698	−	0.951967i	−0.0522135	−	0.0343512i
$769$		−	2.64729i		−	0.0954636i	−0.998860	−	0.0477318i	$-0.984801\pi$
$769$		−	2.64729i		−	0.0954636i	0.998860	−	0.0477318i	$-0.0151993\pi$
$770$	−0.741861	−	0.892238i	−0.0267348	−	0.0321540i
$771$	27.1526	+	17.8636i	0.977877	+	0.643343i
$772$		−	1.36921i		−	0.0492788i
$773$			42.9774i			1.54579i	0.634533	+	0.772896i	$0.281192\pi$
$773$			42.9774i			1.54579i	−0.634533	+	0.772896i	$0.718808\pi$
$774$	−2.74868	−	6.37676i	−0.0987994	−	0.229208i
$775$	8.52600	−	45.9323i	0.306263	−	1.64994i
$776$	9.94453			0.356988
$777$	−9.19461	−	6.04912i	−0.329855	−	0.217011i
$778$	−28.8039			−1.03267
$779$	49.9432			1.78940
$780$	−9.50638	+	1.06654i	−0.340383	+	0.0381882i
$781$			1.05912i			0.0378984i
$782$	−3.89942	−	17.4109i	−0.139443	−	0.622611i
$783$	−36.1148	−	6.38267i	−1.29064	−	0.228098i
$784$	15.4374			0.551336
$785$	34.4940	+	41.4861i	1.23115	+	1.48070i
$786$	12.9848	−	19.7367i	0.463151	−	0.703986i
$787$	23.4951			0.837510			0.418755	−	0.908099i	$-0.362467\pi$
$787$	23.4951			0.837510			0.418755	+	0.908099i	$0.362467\pi$
$788$	3.46037			0.123271
$789$	8.86613	−	13.4764i	0.315643	−	0.479774i
$790$	21.2933	−	17.7046i	0.757582	−	0.629900i
$791$		−	16.4431i		−	0.584650i
$792$	0.130096	+	0.301813i	0.00462275	+	0.0107245i
$793$	18.7067			0.664295
$794$			25.5527i			0.906831i
$795$	14.5170	−	1.62869i	0.514865	−	0.0577637i
$796$		−	2.84735i		−	0.100922i
$797$		−	22.3667i		−	0.792268i	−0.918193	−	0.396134i	$-0.870352\pi$
$797$		−	22.3667i		−	0.792268i	0.918193	−	0.396134i	$-0.129648\pi$
$798$	−30.5037	+	46.3653i	−1.07982	+	1.64131i
$799$		−	20.5913i		−	0.728466i
$800$	−0.912517	+	4.91603i	−0.0322623	+	0.173808i
$801$	−12.1456	−	28.1769i	−0.429142	−	0.995581i
$802$	16.8426			0.594733
$803$		−	1.01741i		−	0.0359036i
$804$	−8.62365	−	5.67348i	−0.304133	−	0.200088i
$805$	−40.2273	−	31.0172i	−1.41783	−	1.09321i
$806$		−	23.0776i		−	0.812872i
$807$	13.3314	−	20.2636i	0.469287	−	0.713312i
$808$		−	8.68562i		−	0.305559i
$809$		−	49.1755i		−	1.72892i	−0.502702	−	0.864460i	$-0.667661\pi$
$809$		−	49.1755i		−	1.72892i	0.502702	−	0.864460i	$-0.332339\pi$
$810$	20.0844	+	1.27106i	0.705695	+	0.0446604i
$811$	−42.2987			−1.48531			−0.742654	−	0.669675i	$-0.766433\pi$
$811$	−42.2987			−1.48531			−0.742654	+	0.669675i	$0.766433\pi$
$812$		−	33.4325i		−	1.17325i
$813$	−28.3148	−	18.6282i	−0.993043	−	0.653321i
$814$	0.146963			0.00515104
$815$	26.5464	−	22.0723i	0.929879	−	0.773158i
$816$	−3.54165	+	5.38329i	−0.123983	+	0.188453i
$817$			15.6577i			0.547794i
$818$	1.73082			0.0605169
$819$	−32.2320	+	13.8935i	−1.12628	+	0.485478i
$820$	12.6942	−	10.5547i	0.443300	−	0.368586i
$821$		−	0.358202i		−	0.0125013i	−0.999980	−	0.00625067i	$-0.998010\pi$
$821$		−	0.358202i		−	0.0125013i	0.999980	−	0.00625067i	$-0.00198966\pi$
$822$	0.0974049	−	0.148055i	0.00339739	−	0.00516400i
$823$		−	3.19924i		−	0.111519i	−0.998444	−	0.0557593i	$-0.982242\pi$
$823$		−	3.19924i		−	0.111519i	0.998444	−	0.0557593i	$-0.0177579\pi$
$824$	−3.27739			−0.114173
$825$	0.657348	−	0.684126i	0.0228859	−	0.0238182i
$826$			19.8216i			0.689683i
$827$			40.6080i			1.41208i	0.708173	+	0.706039i	$0.249520\pi$
$827$			40.6080i			1.41208i	−0.708173	+	0.706039i	$0.750480\pi$
$828$	8.44502	+	11.6482i	0.293485	+	0.404805i
$829$	−16.9961			−0.590298			−0.295149	−	0.955451i	$-0.595369\pi$
$829$	−16.9961			−0.590298			−0.295149	+	0.955451i	$0.595369\pi$
$830$	28.5656	−	23.7512i	0.991527	−	0.824416i
$831$	−11.5348	+	17.5327i	−0.400136	+	0.608204i
$832$			2.46994i			0.0856296i
$833$		−	57.4327i		−	1.98992i
$834$	−2.27445	−	1.49636i	−0.0787579	−	0.0518147i
$835$	−6.95197	−	8.36115i	−0.240583	−	0.289350i
$836$		−	0.741083i		−	0.0256309i
$837$	−8.44936	+	47.8088i	−0.292053	+	1.65251i
$838$	0.0603174			0.00208363
$839$	−19.0943			−0.659209			−0.329605	−	0.944119i	$-0.606915\pi$
$839$	−19.0943			−0.659209			−0.329605	+	0.944119i	$0.606915\pi$
$840$	2.04540	+	18.2312i	0.0705729	+	0.629037i
$841$	−20.8156			−0.717779
$842$		−	16.7804i		−	0.578292i
$843$	−1.44347	−	0.949658i	−0.0497159	−	0.0327080i
$844$	−11.9262			−0.410517
$845$	−9.86338	−	11.8627i	−0.339310	−	0.408090i
$846$	6.57262	+	15.2480i	0.225971	+	0.524238i
$847$	−52.0481			−1.78839
$848$		−	3.77179i		−	0.129524i
$849$	11.9698	+	7.87491i	0.410803	+	0.270266i
$850$	18.2894	+	3.39489i	0.627320	+	0.116444i
$851$	6.27798	−	1.40605i	0.215206	−	0.0481986i
$852$	9.20334	−	13.9890i	0.315301	−	0.479256i
$853$			3.50621i			0.120050i	0.998197	+	0.0600251i	$0.0191181\pi$
$853$			3.50621i			0.120050i	−0.998197	+	0.0600251i	$0.980882\pi$
$854$		−	35.8756i		−	1.22764i
$855$	−40.4542	−	20.5587i	−1.38351	−	0.703092i
$856$			1.42323i			0.0486451i
$857$	26.4700			0.904198			0.452099	−	0.891968i	$-0.350675\pi$
$857$	26.4700			0.904198			0.452099	+	0.891968i	$0.350675\pi$
$858$	0.257591	−	0.391536i	0.00879401	−	0.0133668i
$859$	14.5773			0.497372			0.248686	−	0.968584i	$-0.420001\pi$
$859$	14.5773			0.497372			0.248686	+	0.968584i	$0.420001\pi$
$860$	3.30901	+	3.97975i	0.112836	+	0.135708i
$861$	33.2921	−	50.6038i	1.13459	−	1.72457i
$862$	−4.36493			−0.148670
$863$	−11.1724			−0.380312			−0.190156	−	0.981754i	$-0.560899\pi$
$863$	−11.1724			−0.380312			−0.190156	+	0.981754i	$0.560899\pi$
$864$	0.904315	−	5.11686i	0.0307654	−	0.174079i
$865$	−24.3735	−	29.3140i	−0.828723	−	0.996707i
$866$	29.9206			1.01674
$867$	−4.57097	−	3.00723i	−0.155238	−	0.102131i
$868$	−44.2579			−1.50221
$869$			1.35674i			0.0460241i
$870$	27.1651	−	3.04771i	0.920985	−	0.103327i
$871$			14.7202i			0.498775i
$872$			18.7318i			0.634338i
$873$	11.8093	+	27.3968i	0.399684	+	0.927241i
$874$	−7.09021	−	31.6577i	−0.239830	−	1.07084i
$875$	46.2173	−	25.8581i	1.56243	−	0.874164i
$876$	−8.84086	+	13.4380i	−0.298705	+	0.454029i
$877$			16.8838i			0.570124i	0.958509	+	0.285062i	$0.0920143\pi$
$877$			16.8838i			0.570124i	−0.958509	+	0.285062i	$0.907986\pi$
$878$	−16.9861			−0.573253
$879$	−5.09351	+	7.74210i	−0.171800	+	0.261135i
$880$	−0.156616	−	0.188362i	−0.00527952	−	0.00634970i
$881$	−20.1111			−0.677559			−0.338780	−	0.940866i	$-0.610014\pi$
$881$	−20.1111			−0.677559			−0.338780	+	0.940866i	$0.610014\pi$
$882$	18.3322	+	42.5295i	0.617277	+	1.43204i
$883$			1.20645i			0.0406003i	0.999794	+	0.0203002i	$0.00646219\pi$
$883$			1.20645i			0.0406003i	−0.999794	+	0.0203002i	$0.993538\pi$
$884$	9.18903			0.309061
$885$	−16.1058	+	1.80694i	−0.541391	+	0.0607397i
$886$	−24.5257			−0.823958
$887$	−19.2753			−0.647200			−0.323600	−	0.946194i	$-0.604893\pi$
$887$	−19.2753			−0.647200			−0.323600	+	0.946194i	$0.604893\pi$
$888$	−1.94110	−	1.27704i	−0.0651389	−	0.0428548i
$889$		−	15.9201i		−	0.533942i
$890$	14.6215	+	17.5853i	0.490112	+	0.589459i
$891$	−0.676993	+	0.716817i	−0.0226801	+	0.0240143i
$892$			18.5236i			0.620215i
$893$		−	37.4405i		−	1.25290i
$894$	−15.8049	−	10.3980i	−0.528593	−	0.347761i
$895$	14.3929	−	11.9672i	0.481103	−	0.400018i
$896$	4.73682			0.158246
$897$	7.25785	−	19.1902i	0.242333	−	0.640742i
$898$		−	16.0667i		−	0.536152i
$899$			65.9458i			2.19941i
$900$	−14.6271	+	3.32392i	−0.487569	+	0.110797i
$901$	−14.0324			−0.467487
$902$			0.808828i			0.0269310i
$903$	15.8648	+	10.4374i	0.527947	+	0.347336i
$904$		−	3.47135i		−	0.115455i
$905$	6.73527	−	5.60011i	0.223888	−	0.186154i
$906$	−9.30225	−	6.11993i	−0.309047	−	0.203321i
$907$	−16.5189			−0.548502			−0.274251	−	0.961658i	$-0.588430\pi$
$907$	−16.5189			−0.548502			−0.274251	+	0.961658i	$0.588430\pi$
$908$		−	15.3110i		−	0.508115i
$909$	23.9285	−	10.3143i	0.793659	−	0.342104i
$910$	20.1161	−	16.7257i	0.666841	−	0.554452i
$911$	−1.38119			−0.0457608			−0.0228804	−	0.999738i	$-0.507284\pi$
$911$	−1.38119			−0.0457608			−0.0228804	+	0.999738i	$0.507284\pi$
$912$	−6.43970	+	9.78829i	−0.213240	+	0.324123i
$913$			1.82010i			0.0602366i
$914$	13.2071			0.436852
$915$	29.1502	−	3.27042i	0.963676	−	0.108117i
$916$		−	5.31624i		−	0.175654i
$917$			64.6098i			2.13360i
$918$	−19.0365	−	3.36437i	−0.628299	−	0.111041i
$919$			8.35624i			0.275647i	0.990457	+	0.137823i	$0.0440107\pi$
$919$			8.35624i			0.275647i	−0.990457	+	0.137823i	$0.955989\pi$
$920$	−8.49249	−	6.54810i	−0.279989	−	0.215885i
$921$	22.5404	−	34.2612i	0.742730	−	1.12894i
$922$			25.4941i			0.839603i
$923$	−23.8786			−0.785974
$924$	−0.750884	−	0.494005i	−0.0247023	−	0.0162516i
$925$	−1.22412	+	6.59474i	−0.0402489	+	0.216834i
$926$		−	20.0822i		−	0.659941i
$927$	−3.89196	−	9.02907i	−0.127829	−	0.296554i
$928$		−	7.05802i		−	0.231691i
$929$			3.75617i			0.123236i	0.998100	+	0.0616180i	$0.0196261\pi$
$929$			3.75617i			0.123236i	−0.998100	+	0.0616180i	$0.980374\pi$
$930$	−4.03455	−	35.9612i	−0.132298	−	1.17921i
$931$		−	104.428i		−	3.42250i
$932$	8.00870			0.262334
$933$	−12.2538	+	18.6256i	−0.401170	+	0.609775i
$934$		−	14.7644i		−	0.483106i
$935$	−0.700775	+	0.582667i	−0.0229178	+	0.0190552i
$936$	−6.80457	+	2.93309i	−0.222414	+	0.0958711i
$937$	8.00163			0.261402			0.130701	−	0.991422i	$-0.458277\pi$
$937$	8.00163			0.261402			0.130701	+	0.991422i	$0.458277\pi$
$938$	28.2302			0.921750
$939$	−6.64517	−	4.37184i	−0.216857	−	0.142670i
$940$	−7.91246	−	9.51634i	−0.258076	−	0.310389i
$941$	43.2565			1.41012			0.705060	−	0.709148i	$-0.250920\pi$
$941$	43.2565			1.41012			0.705060	+	0.709148i	$0.250920\pi$
$942$	34.9136	+	22.9696i	1.13755	+	0.748389i
$943$	7.73836	+	34.5517i	0.251996	+	1.12516i
$944$			4.18459i			0.136197i
$945$	−47.7974	+	27.2849i	−1.55485	+	0.887577i
$946$	−0.253576			−0.00824446
$947$	43.5718			1.41589			0.707947	−	0.706266i	$-0.249622\pi$
$947$	43.5718			1.41589			0.707947	+	0.706266i	$0.249622\pi$
$948$	11.7895	−	17.9199i	0.382904	−	0.582011i
$949$	22.9381			0.744603
$950$	33.2551	+	6.17283i	1.07894	+	0.200273i
$951$	−5.31153	−	3.49445i	−0.172238	−	0.113315i
$952$		−	17.6226i		−	0.571153i
$953$		−	29.1349i		−	0.943773i	−0.881659	−	0.471887i	$-0.843573\pi$
$953$		−	29.1349i		−	0.943773i	0.881659	−	0.471887i	$-0.156427\pi$
$954$	10.3911	−	4.47907i	0.336426	−	0.145015i
$955$	14.3863	+	17.3024i	0.465529	+	0.559893i
$956$			1.30708i			0.0422741i
$957$	−0.736084	+	1.11884i	−0.0237942	+	0.0361670i
$958$	0.527998			0.0170588
$959$			0.484669i			0.0156508i
$960$	0.431808	+	3.84884i	0.0139365	+	0.124221i
$961$	56.2989			1.81609
$962$			3.31336i			0.106827i
$963$	−3.92095	+	1.69011i	−0.126351	+	0.0544631i
$964$			9.16266i			0.295109i
$965$	−2.35418	+	1.95741i	−0.0757838	+	0.0630113i
$966$	−36.8028	−	13.9190i	−1.18411	−	0.447837i
$967$		−	13.1496i		−	0.422863i	−0.977393	−	0.211432i	$-0.932187\pi$
$967$		−	13.1496i		−	0.422863i	0.977393	−	0.211432i	$-0.0678126\pi$
$968$	−10.9880			−0.353168
$969$	36.4159	+	23.9580i	1.16985	+	0.769640i
$970$	−14.2167	−	17.0984i	−0.456469	−	0.548997i
$971$	54.4195			1.74641			0.873203	−	0.487358i	$-0.162039\pi$
$971$	54.4195			1.74641			0.873203	+	0.487358i	$0.162039\pi$
$972$	15.1706	−	3.58500i	0.486598	−	0.114989i
$973$	7.44561			0.238695
$974$		−	15.1423i		−	0.485191i
$975$	15.4240	+	14.8203i	0.493965	+	0.474630i
$976$		−	7.57377i		−	0.242431i
$977$		−	59.8495i		−	1.91476i	−0.288837	−	0.957378i	$-0.593269\pi$
$977$		−	59.8495i		−	1.91476i	0.288837	−	0.957378i	$-0.406731\pi$
$978$	14.6979	−	22.3407i	0.469988	−	0.714378i
$979$	−1.12047			−0.0358104
$980$	−22.0693	−	26.5427i	−0.704977	−	0.847877i
$981$	−51.6053	+	22.2443i	−1.64763	+	0.710206i
$982$		−	23.0745i		−	0.736336i
$983$		−	50.9264i		−	1.62430i	−0.583448	−	0.812150i	$-0.698297\pi$
$983$		−	50.9264i		−	1.62430i	0.583448	−	0.812150i	$-0.301703\pi$
$984$	7.02838	−	10.6831i	0.224056	−	0.340564i
$985$	−4.94693	−	5.94968i	−0.157622	−	0.189573i
$986$	−26.2583			−0.836235
$987$	−37.9357	−	24.9578i	−1.20751	−	0.794417i
$988$	16.7082			0.531558
$989$	−10.8323	+	2.42605i	−0.344447	+	0.0771441i
$990$	0.332947	−	0.655154i	0.0105817	−	0.0208222i
$991$	31.4399			0.998722			0.499361	−	0.866394i	$-0.333568\pi$
$991$	31.4399			0.998722			0.499361	+	0.866394i	$0.333568\pi$
$992$	−9.34339			−0.296653
$993$	30.3123	+	19.9424i	0.961932	+	0.632854i
$994$			45.7942i			1.45250i
$995$	−4.89567	+	4.07056i	−0.155203	+	0.129045i
$996$	15.8159	−	24.0401i	0.501147	−	0.761739i
$997$		−	55.3486i		−	1.75291i	−0.481487	−	0.876453i	$-0.659903\pi$
$997$		−	55.3486i		−	1.75291i	0.481487	−	0.876453i	$-0.340097\pi$
$998$	2.99246			0.0947248
$999$	1.21312	−	6.86415i	0.0383814	−	0.217172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.h.b.689.5	yes	24
3.2	odd	2		690.2.h.a.689.18	yes	24
5.4	even	2		690.2.h.a.689.19	yes	24
15.14	odd	2	inner	690.2.h.b.689.8	yes	24
23.22	odd	2	inner	690.2.h.b.689.6	yes	24
69.68	even	2		690.2.h.a.689.17	✓	24
115.114	odd	2		690.2.h.a.689.20	yes	24
345.344	even	2	inner	690.2.h.b.689.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.h.a.689.17	✓	24	69.68	even	2
690.2.h.a.689.18	yes	24	3.2	odd	2
690.2.h.a.689.19	yes	24	5.4	even	2
690.2.h.a.689.20	yes	24	115.114	odd	2
690.2.h.b.689.5	yes	24	1.1	even	1	trivial
690.2.h.b.689.6	yes	24	23.22	odd	2	inner
690.2.h.b.689.7	yes	24	345.344	even	2	inner
690.2.h.b.689.8	yes	24	15.14	odd	2	inner

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.44698 - 0.951967i) q^{3} +1.00000 q^{4} +(-1.42959 - 1.71938i) q^{5} +(-1.44698 - 0.951967i) q^{6} +4.73682 q^{7} +1.00000 q^{8} +(1.18752 + 2.75496i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.44698 - 0.951967i) q^{3} +1.00000 q^{4} +(-1.42959 - 1.71938i) q^{5} +(-1.44698 - 0.951967i) q^{6} +4.73682 q^{7} +1.00000 q^{8} +(1.18752 + 2.75496i) q^{9} +(-1.42959 - 1.71938i) q^{10} +0.109553 q^{11} +(-1.44698 - 0.951967i) q^{12} +2.46994i q^{13} +4.73682 q^{14} +(0.431808 + 3.84884i) q^{15} +1.00000 q^{16} -3.72035i q^{17} +(1.18752 + 2.75496i) q^{18} -6.76462i q^{19} +(-1.42959 - 1.71938i) q^{20} +(-6.85409 - 4.50929i) q^{21} +0.109553 q^{22} +(4.67990 - 1.04813i) q^{23} +(-1.44698 - 0.951967i) q^{24} +(-0.912517 + 4.91603i) q^{25} +2.46994i q^{26} +(0.904315 - 5.11686i) q^{27} +4.73682 q^{28} -7.05802i q^{29} +(0.431808 + 3.84884i) q^{30} -9.34339 q^{31} +1.00000 q^{32} +(-0.158521 - 0.104291i) q^{33} -3.72035i q^{34} +(-6.77173 - 8.14437i) q^{35} +(1.18752 + 2.75496i) q^{36} +1.34148 q^{37} -6.76462i q^{38} +(2.35130 - 3.57395i) q^{39} +(-1.42959 - 1.71938i) q^{40} +7.38300i q^{41} +(-6.85409 - 4.50929i) q^{42} -2.31465 q^{43} +0.109553 q^{44} +(3.03915 - 5.98027i) q^{45} +(4.67990 - 1.04813i) q^{46} +5.53476 q^{47} +(-1.44698 - 0.951967i) q^{48} +15.4374 q^{49} +(-0.912517 + 4.91603i) q^{50} +(-3.54165 + 5.38329i) q^{51} +2.46994i q^{52} -3.77179i q^{53} +(0.904315 - 5.11686i) q^{54} +(-0.156616 - 0.188362i) q^{55} +4.73682 q^{56} +(-6.43970 + 9.78829i) q^{57} -7.05802i q^{58} +4.18459i q^{59} +(0.431808 + 3.84884i) q^{60} -7.57377i q^{61} -9.34339 q^{62} +(5.62505 + 13.0497i) q^{63} +1.00000 q^{64} +(4.24675 - 3.53101i) q^{65} +(-0.158521 - 0.104291i) q^{66} +5.95975 q^{67} -3.72035i q^{68} +(-7.76951 - 2.93848i) q^{69} +(-6.77173 - 8.14437i) q^{70} +9.66771i q^{71} +(1.18752 + 2.75496i) q^{72} -9.28694i q^{73} +1.34148 q^{74} +(6.00029 - 6.24472i) q^{75} -6.76462i q^{76} +0.518931 q^{77} +(2.35130 - 3.57395i) q^{78} +12.3843i q^{79} +(-1.42959 - 1.71938i) q^{80} +(-6.17961 + 6.54312i) q^{81} +7.38300i q^{82} +16.6139i q^{83} +(-6.85409 - 4.50929i) q^{84} +(-6.39669 + 5.31860i) q^{85} -2.31465 q^{86} +(-6.71900 + 10.2128i) q^{87} +0.109553 q^{88} -10.2277 q^{89} +(3.03915 - 5.98027i) q^{90} +11.6996i q^{91} +(4.67990 - 1.04813i) q^{92} +(13.5197 + 8.89460i) q^{93} +5.53476 q^{94} +(-11.6309 + 9.67067i) q^{95} +(-1.44698 - 0.951967i) q^{96} +9.94453 q^{97} +15.4374 q^{98} +(0.130096 + 0.301813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} - 2 q^{3} + 24 q^{4} - 2 q^{6} + 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 - 2 * q^3 + 24 * q^4 - 2 * q^6 + 24 * q^8 + 6 * q^9	\( 24 q + 24 q^{2} - 2 q^{3} + 24 q^{4} - 2 q^{6} + 24 q^{8} + 6 q^{9} - 2 q^{12} + 24 q^{16} + 6 q^{18} + 4 q^{23} - 2 q^{24} + 12 q^{25} - 2 q^{27} - 28 q^{31} + 24 q^{32} - 8 q^{35} + 6 q^{36} + 4 q^{46} - 16 q^{47} - 2 q^{48} - 4 q^{49} + 12 q^{50} - 2 q^{54} + 4 q^{55} - 28 q^{62} + 24 q^{64} - 8 q^{69} - 8 q^{70} + 6 q^{72} - 6 q^{75} - 8 q^{77} + 14 q^{81} - 44 q^{85} - 28 q^{87} + 4 q^{92} + 4 q^{93} - 16 q^{94} - 4 q^{95} - 2 q^{96} - 4 q^{98}+O(q^{100}) \) 24 * q + 24 * q^2 - 2 * q^3 + 24 * q^4 - 2 * q^6 + 24 * q^8 + 6 * q^9 - 2 * q^12 + 24 * q^16 + 6 * q^18 + 4 * q^23 - 2 * q^24 + 12 * q^25 - 2 * q^27 - 28 * q^31 + 24 * q^32 - 8 * q^35 + 6 * q^36 + 4 * q^46 - 16 * q^47 - 2 * q^48 - 4 * q^49 + 12 * q^50 - 2 * q^54 + 4 * q^55 - 28 * q^62 + 24 * q^64 - 8 * q^69 - 8 * q^70 + 6 * q^72 - 6 * q^75 - 8 * q^77 + 14 * q^81 - 44 * q^85 - 28 * q^87 + 4 * q^92 + 4 * q^93 - 16 * q^94 - 4 * q^95 - 2 * q^96 - 4 * q^98

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