LMFDB - Embedded newform 728.2.c.a.365.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(365,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.365"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [34] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			365.6
Character	$\chi$	$=$	728.365
Dual form			728.2.c.a.365.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14018 + 0.836660i) q^{2} -2.38465i q^{3} +(0.600001 - 1.90788i) q^{4} -1.59665i q^{5} +(1.99514 + 2.71892i) q^{6} -1.00000 q^{7} +(0.912139 + 2.67731i) q^{8} -2.68654 q^{9} +(1.33585 + 1.82046i) q^{10} -4.18960i q^{11} +(-4.54962 - 1.43079i) q^{12} -1.00000i q^{13} +(1.14018 - 0.836660i) q^{14} -3.80744 q^{15} +(-3.28000 - 2.28946i) q^{16} +0.570087 q^{17} +(3.06313 - 2.24772i) q^{18} -2.53707i q^{19} +(-3.04621 - 0.957990i) q^{20} +2.38465i q^{21} +(3.50527 + 4.77688i) q^{22} +0.0190668 q^{23} +(6.38445 - 2.17513i) q^{24} +2.45072 q^{25} +(0.836660 + 1.14018i) q^{26} -0.747485i q^{27} +(-0.600001 + 1.90788i) q^{28} +0.742125i q^{29} +(4.34115 - 3.18553i) q^{30} -3.88210 q^{31} +(5.65527 - 0.133860i) q^{32} -9.99073 q^{33} +(-0.649999 + 0.476969i) q^{34} +1.59665i q^{35} +(-1.61193 + 5.12560i) q^{36} +1.77977i q^{37} +(2.12266 + 2.89270i) q^{38} -2.38465 q^{39} +(4.27473 - 1.45636i) q^{40} -8.08770 q^{41} +(-1.99514 - 2.71892i) q^{42} +11.7998i q^{43} +(-7.99326 - 2.51377i) q^{44} +4.28946i q^{45} +(-0.0217395 + 0.0159524i) q^{46} -5.33750 q^{47} +(-5.45955 + 7.82164i) q^{48} +1.00000 q^{49} +(-2.79425 + 2.05042i) q^{50} -1.35946i q^{51} +(-1.90788 - 0.600001i) q^{52} +4.60925i q^{53} +(0.625390 + 0.852264i) q^{54} -6.68932 q^{55} +(-0.912139 - 2.67731i) q^{56} -6.05001 q^{57} +(-0.620906 - 0.846153i) q^{58} -7.12700i q^{59} +(-2.28447 + 7.26414i) q^{60} +10.6962i q^{61} +(4.42627 - 3.24799i) q^{62} +2.68654 q^{63} +(-6.33601 + 4.88416i) q^{64} -1.59665 q^{65} +(11.3912 - 8.35884i) q^{66} -8.45532i q^{67} +(0.342052 - 1.08766i) q^{68} -0.0454676i q^{69} +(-1.33585 - 1.82046i) q^{70} -0.425314 q^{71} +(-2.45050 - 7.19272i) q^{72} +8.18795 q^{73} +(-1.48906 - 2.02925i) q^{74} -5.84409i q^{75} +(-4.84042 - 1.52224i) q^{76} +4.18960i q^{77} +(2.71892 - 1.99514i) q^{78} +1.30570 q^{79} +(-3.65546 + 5.23700i) q^{80} -9.84212 q^{81} +(9.22140 - 6.76665i) q^{82} -11.3255i q^{83} +(4.54962 + 1.43079i) q^{84} -0.910228i q^{85} +(-9.87244 - 13.4539i) q^{86} +1.76971 q^{87} +(11.2169 - 3.82150i) q^{88} -1.64900 q^{89} +(-3.58882 - 4.89074i) q^{90} +1.00000i q^{91} +(0.0114401 - 0.0363771i) q^{92} +9.25743i q^{93} +(6.08569 - 4.46567i) q^{94} -4.05081 q^{95} +(-0.319209 - 13.4858i) q^{96} -4.79975 q^{97} +(-1.14018 + 0.836660i) q^{98} +11.2556i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 2 q^{2} - 2 q^{4} - 6 q^{6} - 34 q^{7} + 8 q^{8} - 26 q^{9} - 4 q^{12} - 2 q^{14} - 8 q^{15} - 6 q^{16} - 20 q^{17} + 14 q^{18} - 4 q^{20} - 10 q^{22} - 20 q^{23} + 10 q^{24} - 22 q^{25} + 2 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) $ 34 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 - 34 * q^7 + 8 * q^8 - 26 * q^9 - 4 * q^12 - 2 * q^14 - 8 * q^15 - 6 * q^16 - 20 * q^17 + 14 * q^18 - 4 * q^20 - 10 * q^22 - 20 * q^23 + 10 * q^24 - 22 * q^25 + 2 * q^28 - 60 * q^30 + 16 * q^31 + 12 * q^32 - 8 * q^33 + 28 * q^34 - 4 * q^36 - 28 * q^38 + 8 * q^39 + 64 * q^40 + 8 * q^41 + 6 * q^42 + 24 * q^44 + 16 * q^46 + 24 * q^48 + 34 * q^49 + 10 * q^50 - 4 * q^52 - 18 * q^54 - 32 * q^55 - 8 * q^56 + 8 * q^57 + 44 * q^58 - 24 * q^60 + 60 * q^62 + 26 * q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 12 * q^68 + 64 * q^71 - 92 * q^72 - 22 * q^74 + 4 * q^76 + 20 * q^79 - 56 * q^80 - 6 * q^81 - 20 * q^82 + 4 * q^84 - 12 * q^86 - 56 * q^87 - 34 * q^88 - 4 * q^90 - 54 * q^92 + 12 * q^94 + 42 * q^96 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−1.14018	+	0.836660i	−0.806226	+	0.591608i
$2$	−1.14018	+	0.836660i	−0.806226	+	0.591608i
$3$		−	2.38465i		−	1.37678i	−0.725342	−	0.688388i	$-0.758318\pi$
$3$		−	2.38465i		−	1.37678i	0.725342	−	0.688388i	$-0.241682\pi$
$4$	0.600001	−	1.90788i	0.300000	−	0.953939i
$5$		−	1.59665i		−	0.714043i	−0.934096	−	0.357021i	$-0.883792\pi$
$5$		−	1.59665i		−	0.714043i	0.934096	−	0.357021i	$-0.116208\pi$
$6$	1.99514	+	2.71892i	0.814512	+	1.10999i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.912139	+	2.67731i	0.322490	+	0.946573i
$9$	−2.68654			−0.895514
$10$	1.33585	+	1.82046i	0.422433	+	0.575680i
$11$		−	4.18960i		−	1.26321i	−0.775289	−	0.631607i	$-0.782396\pi$
$11$		−	4.18960i		−	1.26321i	0.775289	−	0.631607i	$-0.217604\pi$
$12$	−4.54962	−	1.43079i	−1.31336	−	0.413034i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	1.14018	−	0.836660i	0.304725	−	0.223607i
$15$	−3.80744			−0.983077
$16$	−3.28000	−	2.28946i	−0.820000	−	0.572364i
$17$	0.570087			0.138266			0.0691332	−	0.997607i	$-0.477977\pi$
$17$	0.570087			0.138266			0.0691332	+	0.997607i	$0.477977\pi$
$18$	3.06313	−	2.24772i	0.721987	−	0.529793i
$19$		−	2.53707i		−	0.582043i	−0.956716	−	0.291022i	$-0.906005\pi$
$19$		−	2.53707i		−	0.582043i	0.956716	−	0.291022i	$-0.0939952\pi$
$20$	−3.04621	−	0.957990i	−0.681153	−	0.214213i
$21$			2.38465i			0.520373i
$22$	3.50527	+	4.77688i	0.747327	+	1.01844i
$23$	0.0190668			0.00397570			0.00198785	−	0.999998i	$-0.499367\pi$
$23$	0.0190668			0.00397570			0.00198785	+	0.999998i	$0.499367\pi$
$24$	6.38445	−	2.17513i	1.30322	−	0.443996i
$25$	2.45072			0.490143
$26$	0.836660	+	1.14018i	0.164082	+	0.223607i
$27$		−	0.747485i		−	0.143854i
$28$	−0.600001	+	1.90788i	−0.113389	+	0.360555i
$29$			0.742125i			0.137809i	0.997623	+	0.0689046i	$0.0219504\pi$
$29$			0.742125i			0.137809i	−0.997623	+	0.0689046i	$0.978050\pi$
$30$	4.34115	−	3.18553i	0.792582	−	0.581596i
$31$	−3.88210			−0.697245			−0.348623	−	0.937263i	$-0.613350\pi$
$31$	−3.88210			−0.697245			−0.348623	+	0.937263i	$0.613350\pi$
$32$	5.65527	−	0.133860i	0.999720	−	0.0236634i
$33$	−9.99073			−1.73916
$34$	−0.649999	+	0.476969i	−0.111474	+	0.0817995i
$35$			1.59665i			0.269883i
$36$	−1.61193	+	5.12560i	−0.268655	+	0.854266i
$37$			1.77977i			0.292593i	0.989241	+	0.146296i	$0.0467353\pi$
$37$			1.77977i			0.292593i	−0.989241	+	0.146296i	$0.953265\pi$
$38$	2.12266	+	2.89270i	0.344341	+	0.469259i
$39$	−2.38465			−0.381849
$40$	4.27473	−	1.45636i	0.675893	−	0.230271i
$41$	−8.08770			−1.26309			−0.631543	−	0.775341i	$-0.717578\pi$
$41$	−8.08770			−1.26309			−0.631543	+	0.775341i	$0.717578\pi$
$42$	−1.99514	−	2.71892i	−0.307857	−	0.419538i
$43$			11.7998i			1.79946i	0.436450	+	0.899729i	$0.356236\pi$
$43$			11.7998i			1.79946i	−0.436450	+	0.899729i	$0.643764\pi$
$44$	−7.99326	−	2.51377i	−1.20503	−	0.378964i
$45$			4.28946i			0.639435i
$46$	−0.0217395	+	0.0159524i	−0.00320531	+	0.00235206i
$47$	−5.33750			−0.778555			−0.389277	−	0.921121i	$-0.627275\pi$
$47$	−5.33750			−0.778555			−0.389277	+	0.921121i	$0.627275\pi$
$48$	−5.45955	+	7.82164i	−0.788018	+	1.12896i
$49$	1.00000			0.142857
$50$	−2.79425	+	2.05042i	−0.395166	+	0.289972i
$51$		−	1.35946i		−	0.190362i
$52$	−1.90788	−	0.600001i	−0.264575	−	0.0832051i
$53$			4.60925i			0.633130i	0.948571	+	0.316565i	$0.102530\pi$
$53$			4.60925i			0.633130i	−0.948571	+	0.316565i	$0.897470\pi$
$54$	0.625390	+	0.852264i	0.0851049	+	0.115978i
$55$	−6.68932			−0.901988
$56$	−0.912139	−	2.67731i	−0.121890	−	0.357771i
$57$	−6.05001			−0.801344
$58$	−0.620906	−	0.846153i	−0.0815290	−	0.111105i
$59$		−	7.12700i		−	0.927857i	−0.885873	−	0.463928i	$-0.846439\pi$
$59$		−	7.12700i		−	0.927857i	0.885873	−	0.463928i	$-0.153561\pi$
$60$	−2.28447	+	7.26414i	−0.294924	+	0.937796i
$61$			10.6962i			1.36950i	0.728777	+	0.684751i	$0.240089\pi$
$61$			10.6962i			1.36950i	−0.728777	+	0.684751i	$0.759911\pi$
$62$	4.42627	−	3.24799i	0.562137	−	0.412496i
$63$	2.68654			0.338473
$64$	−6.33601	+	4.88416i	−0.792001	+	0.610520i
$65$	−1.59665			−0.198040
$66$	11.3912	−	8.35884i	1.40216	−	1.02890i
$67$		−	8.45532i		−	1.03298i	−0.856293	−	0.516491i	$-0.827238\pi$
$67$		−	8.45532i		−	1.03298i	0.856293	−	0.516491i	$-0.172762\pi$
$68$	0.342052	−	1.08766i	0.0414800	−	0.131898i
$69$		−	0.0454676i		−	0.00547365i
$70$	−1.33585	−	1.82046i	−0.159665	−	0.217586i
$71$	−0.425314			−0.0504754			−0.0252377	−	0.999681i	$-0.508034\pi$
$71$	−0.425314			−0.0504754			−0.0252377	+	0.999681i	$0.508034\pi$
$72$	−2.45050	−	7.19272i	−0.288794	−	0.847670i
$73$	8.18795			0.958327			0.479164	−	0.877726i	$-0.340940\pi$
$73$	8.18795			0.958327			0.479164	+	0.877726i	$0.340940\pi$
$74$	−1.48906	−	2.02925i	−0.173100	−	0.235896i
$75$		−	5.84409i		−	0.674818i
$76$	−4.84042	−	1.52224i	−0.555234	−	0.174613i
$77$			4.18960i			0.477450i
$78$	2.71892	−	1.99514i	0.307857	−	0.225905i
$79$	1.30570			0.146902			0.0734512	−	0.997299i	$-0.476599\pi$
$79$	1.30570			0.146902			0.0734512	+	0.997299i	$0.476599\pi$
$80$	−3.65546	+	5.23700i	−0.408692	+	0.585515i
$81$	−9.84212			−1.09357
$82$	9.22140	−	6.76665i	1.01833	−	0.747252i
$83$		−	11.3255i		−	1.24313i	−0.783361	−	0.621567i	$-0.786496\pi$
$83$		−	11.3255i		−	1.24313i	0.783361	−	0.621567i	$-0.213504\pi$
$84$	4.54962	+	1.43079i	0.496404	+	0.156112i
$85$		−	0.910228i		−	0.0987281i
$86$	−9.87244	−	13.4539i	−1.06457	−	1.45077i
$87$	1.76971			0.189733
$88$	11.2169	−	3.82150i	1.19572	−	0.407373i
$89$	−1.64900			−0.174794			−0.0873970	−	0.996174i	$-0.527855\pi$
$89$	−1.64900			−0.174794			−0.0873970	+	0.996174i	$0.527855\pi$
$90$	−3.58882	−	4.89074i	−0.378295	−	0.515529i
$91$			1.00000i			0.104828i
$92$	0.0114401	−	0.0363771i	0.00119271	−	0.00379258i
$93$			9.25743i			0.959951i
$94$	6.08569	−	4.46567i	0.627691	−	0.460599i
$95$	−4.05081			−0.415604
$96$	−0.319209	−	13.4858i	−0.0325792	−	1.37639i
$97$	−4.79975			−0.487341			−0.243670	−	0.969858i	$-0.578352\pi$
$97$	−4.79975			−0.487341			−0.243670	+	0.969858i	$0.578352\pi$
$98$	−1.14018	+	0.836660i	−0.115175	+	0.0845154i
$99$			11.2556i			1.13123i
$100$	1.47043	−	4.67567i	0.147043	−	0.467567i
$101$		−	7.48152i		−	0.744439i	−0.928145	−	0.372220i	$-0.878597\pi$
$101$		−	7.48152i		−	0.744439i	0.928145	−	0.372220i	$-0.121403\pi$
$102$	1.13740	+	1.55002i	0.112620	+	0.153475i
$103$	11.8173			1.16439			0.582197	−	0.813048i	$-0.302193\pi$
$103$	11.8173			1.16439			0.582197	+	0.813048i	$0.302193\pi$
$104$	2.67731	−	0.912139i	0.262532	−	0.0894426i
$105$	3.80744			0.371568
$106$	−3.85638	−	5.25536i	−0.374565	−	0.510446i
$107$		−	16.5805i		−	1.60289i	−0.598066	−	0.801447i	$-0.704064\pi$
$107$		−	16.5805i		−	1.60289i	0.598066	−	0.801447i	$-0.295936\pi$
$108$	−1.42611	−	0.448491i	−0.137227	−	0.0431561i
$109$			11.9418i			1.14381i	0.820318	+	0.571907i	$0.193796\pi$
$109$			11.9418i			1.14381i	−0.820318	+	0.571907i	$0.806204\pi$
$110$	7.62700	−	5.59669i	0.727206	−	0.533623i
$111$	4.24413			0.402835
$112$	3.28000	+	2.28946i	0.309931	+	0.216333i
$113$	5.32589			0.501017			0.250509	−	0.968114i	$-0.419402\pi$
$113$	5.32589			0.501017			0.250509	+	0.968114i	$0.419402\pi$
$114$	6.89808	−	5.06180i	0.646064	−	0.474081i
$115$		−	0.0304429i		−	0.00283882i
$116$	1.41588	+	0.445276i	0.131462	+	0.0413428i
$117$			2.68654i			0.248371i
$118$	5.96288	+	8.12603i	0.548927	+	0.748062i
$119$	−0.570087			−0.0522598
$120$	−3.47292	−	10.1937i	−0.317032	−	0.930554i
$121$	−6.55279			−0.595708
$122$	−8.94905	−	12.1955i	−0.810209	−	1.10413i
$123$			19.2863i			1.73899i
$124$	−2.32926	+	7.40657i	−0.209174	+	0.665129i
$125$		−	11.8962i		−	1.06403i
$126$	−3.06313	+	2.24772i	−0.272885	+	0.200243i
$127$	15.1726			1.34635			0.673176	−	0.739483i	$-0.264930\pi$
$127$	15.1726			1.34635			0.673176	+	0.739483i	$0.264930\pi$
$128$	3.13778	−	10.8699i	0.277343	−	0.960771i
$129$	28.1384			2.47745
$130$	1.82046	−	1.33585i	0.159665	−	0.117162i
$131$		−	1.62340i		−	0.141837i	−0.997482	−	0.0709184i	$-0.977407\pi$
$131$		−	1.62340i		−	0.141837i	0.997482	−	0.0709184i	$-0.0225930\pi$
$132$	−5.99444	+	19.0611i	−0.521749	+	1.65906i
$133$			2.53707i			0.219992i
$134$	7.07423	+	9.64055i	0.611120	+	0.832817i
$135$	−1.19347			−0.102718
$136$	0.519998	+	1.52630i	0.0445895	+	0.130879i
$137$	−9.53449			−0.814587			−0.407293	−	0.913297i	$-0.633527\pi$
$137$	−9.53449			−0.814587			−0.407293	+	0.913297i	$0.633527\pi$
$138$	0.0380409	+	0.0518410i	0.00323826	+	0.00441300i
$139$		−	12.2351i		−	1.03776i	−0.854846	−	0.518882i	$-0.826348\pi$
$139$		−	12.2351i		−	1.03776i	0.854846	−	0.518882i	$-0.173652\pi$
$140$	3.04621	+	0.957990i	0.257452	+	0.0809649i
$141$			12.7281i			1.07190i
$142$	0.484932	−	0.355843i	0.0406946	−	0.0298617i
$143$	−4.18960			−0.350352
$144$	8.81186	+	6.15072i	0.734321	+	0.512560i
$145$	1.18491			0.0984017
$146$	−9.33570	+	6.85053i	−0.772628	+	0.566954i
$147$		−	2.38465i		−	0.196682i
$148$	3.39559	+	1.06786i	0.279116	+	0.0877780i
$149$			1.97177i			0.161534i	0.996733	+	0.0807669i	$0.0257369\pi$
$149$			1.97177i			0.161534i	−0.996733	+	0.0807669i	$0.974263\pi$
$150$	4.88952	+	6.66329i	0.399227	+	0.544055i
$151$	−16.5785			−1.34914			−0.674571	−	0.738210i	$-0.735672\pi$
$151$	−16.5785			−1.34914			−0.674571	+	0.738210i	$0.735672\pi$
$152$	6.79253	−	2.31416i	0.550947	−	0.187703i
$153$	−1.53156			−0.123819
$154$	−3.50527	−	4.77688i	−0.282463	−	0.384932i
$155$			6.19834i			0.497863i
$156$	−1.43079	+	4.54962i	−0.114555	+	0.364261i
$157$			7.21761i			0.576028i	0.957626	+	0.288014i	$0.0929950\pi$
$157$			7.21761i			0.576028i	−0.957626	+	0.288014i	$0.907005\pi$
$158$	−1.48872	+	1.09242i	−0.118436	+	0.0869086i
$159$	10.9914			0.871678
$160$	−0.213728	−	9.02948i	−0.0168967	−	0.713843i
$161$	−0.0190668			−0.00150267
$162$	11.2217	−	8.23450i	0.881663	−	0.646964i
$163$			20.8322i			1.63170i	0.578260	+	0.815852i	$0.303732\pi$
$163$			20.8322i			1.63170i	−0.578260	+	0.815852i	$0.696268\pi$
$164$	−4.85263	+	15.4303i	−0.378926	+	1.20491i
$165$			15.9517i			1.24184i
$166$	9.47559	+	12.9131i	0.735448	+	1.00225i
$167$	16.5728			1.28245			0.641223	−	0.767355i	$-0.278428\pi$
$167$	16.5728			1.28245			0.641223	+	0.767355i	$0.278428\pi$
$168$	−6.38445	+	2.17513i	−0.492571	+	0.167815i
$169$	−1.00000			−0.0769231
$170$	0.761551	+	1.03782i	0.0584083	+	0.0795971i
$171$			6.81594i			0.521228i
$172$	22.5126	+	7.07991i	1.71657	+	0.539838i
$173$		−	3.48473i		−	0.264939i	−0.991187	−	0.132469i	$-0.957709\pi$
$173$		−	3.48473i		−	0.264939i	0.991187	−	0.132469i	$-0.0422906\pi$
$174$	−2.01778	+	1.48064i	−0.152967	+	0.112247i
$175$	−2.45072			−0.185257
$176$	−9.59192	+	13.7419i	−0.723018	+	1.03583i
$177$	−16.9954			−1.27745
$178$	1.88015	−	1.37965i	0.140923	−	0.103409i
$179$		−	22.1527i		−	1.65577i	−0.560900	−	0.827884i	$-0.689545\pi$
$179$		−	22.1527i		−	1.65577i	0.560900	−	0.827884i	$-0.310455\pi$
$180$	8.18377	+	2.57368i	0.609982	+	0.191831i
$181$		−	16.9513i		−	1.25998i	−0.776604	−	0.629989i	$-0.783059\pi$
$181$		−	16.9513i		−	1.25998i	0.776604	−	0.629989i	$-0.216941\pi$
$182$	−0.836660	−	1.14018i	−0.0620174	−	0.0845154i
$183$	25.5066			1.88550
$184$	0.0173916	+	0.0510478i	0.00128212	+	0.00376329i
$185$	2.84167			0.208924
$186$	−7.74532	−	10.5551i	−0.567914	−	0.773937i
$187$		−	2.38844i		−	0.174660i
$188$	−3.20251	+	10.1833i	−0.233567	+	0.742694i
$189$			0.747485i			0.0543715i
$190$	4.61863	−	3.38915i	0.335071	−	0.245874i
$191$	−21.6345			−1.56542			−0.782708	−	0.622389i	$-0.786162\pi$
$191$	−21.6345			−1.56542			−0.782708	+	0.622389i	$0.786162\pi$
$192$	11.6470	+	15.1091i	0.840550	+	1.09041i
$193$	16.1797			1.16464			0.582319	−	0.812960i	$-0.302145\pi$
$193$	16.1797			1.16464			0.582319	+	0.812960i	$0.302145\pi$
$194$	5.47256	−	4.01576i	0.392907	−	0.288315i
$195$			3.80744i			0.272657i
$196$	0.600001	−	1.90788i	0.0428572	−	0.136277i
$197$		−	15.2317i		−	1.08521i	−0.839987	−	0.542607i	$-0.817437\pi$
$197$		−	15.2317i		−	1.08521i	0.839987	−	0.542607i	$-0.182563\pi$
$198$	−9.41707	−	12.8333i	−0.669242	−	0.912023i
$199$	6.21008			0.440221			0.220110	−	0.975475i	$-0.429358\pi$
$199$	6.21008			0.440221			0.220110	+	0.975475i	$0.429358\pi$
$200$	2.23539	+	6.56133i	0.158066	+	0.463956i
$201$	−20.1630			−1.42219
$202$	6.25949	+	8.53025i	0.440416	+	0.600186i
$203$		−	0.742125i		−	0.0520870i
$204$	−2.59368	−	0.815675i	−0.181594	−	0.0571086i
$205$			12.9132i			0.901898i
$206$	−13.4738	+	9.88706i	−0.938764	+	0.688864i
$207$	−0.0512237			−0.00356030
$208$	−2.28946	+	3.28000i	−0.158745	+	0.227427i
$209$	−10.6293			−0.735245
$210$	−4.34115	+	3.18553i	−0.299568	+	0.219823i
$211$			5.94685i			0.409398i	0.978825	+	0.204699i	$0.0656215\pi$
$211$			5.94685i			0.409398i	−0.978825	+	0.204699i	$0.934378\pi$
$212$	8.79390	+	2.76556i	0.603967	+	0.189939i
$213$			1.01422i			0.0694934i
$214$	13.8722	+	18.9046i	0.948284	+	1.29229i
$215$	18.8402			1.28489
$216$	2.00125	−	0.681810i	0.136168	−	0.0463913i
$217$	3.88210			0.263534
$218$	−9.99120	−	13.6157i	−0.676690	−	0.922173i
$219$		−	19.5254i		−	1.31940i
$220$	−4.01360	+	12.7624i	−0.270597	+	0.860442i
$221$		−	0.570087i		−	0.0383482i
$222$	−4.83905	+	3.55089i	−0.324776	+	0.238320i
$223$	9.96356			0.667209			0.333605	−	0.942713i	$-0.391735\pi$
$223$	9.96356			0.667209			0.333605	+	0.942713i	$0.391735\pi$
$224$	−5.65527	+	0.133860i	−0.377859	+	0.00894391i
$225$	−6.58395			−0.438930
$226$	−6.07244	+	4.45595i	−0.403933	+	0.296406i
$227$			10.4441i			0.693198i	0.938013	+	0.346599i	$0.112663\pi$
$227$			10.4441i			0.693198i	−0.938013	+	0.346599i	$0.887337\pi$
$228$	−3.63001	+	11.5427i	−0.240403	+	0.764433i
$229$		−	26.5939i		−	1.75737i	−0.477398	−	0.878687i	$-0.658420\pi$
$229$		−	26.5939i		−	1.75737i	0.477398	−	0.878687i	$-0.341580\pi$
$230$	0.0254704	+	0.0347103i	0.00167947	+	0.00228873i
$231$	9.99073			0.657342
$232$	−1.98690	+	0.676921i	−0.130446	+	0.0444421i
$233$	14.4199			0.944676			0.472338	−	0.881417i	$-0.343410\pi$
$233$	14.4199			0.944676			0.472338	+	0.881417i	$0.343410\pi$
$234$	−2.24772	−	3.06313i	−0.146938	−	0.200243i
$235$			8.52211i			0.555921i
$236$	−13.5975	−	4.27621i	−0.885119	−	0.278357i
$237$		−	3.11363i		−	0.202252i
$238$	0.649999	−	0.476969i	0.0421332	−	0.0309173i
$239$	1.16899			0.0756154			0.0378077	−	0.999285i	$-0.487963\pi$
$239$	1.16899			0.0756154			0.0378077	+	0.999285i	$0.487963\pi$
$240$	12.4884	+	8.71697i	0.806123	+	0.562678i
$241$	17.6819			1.13899			0.569495	−	0.821995i	$-0.307139\pi$
$241$	17.6819			1.13899			0.569495	+	0.821995i	$0.307139\pi$
$242$	7.47133	−	5.48245i	0.480275	−	0.352425i
$243$			21.2275i			1.36175i
$244$	20.4070	+	6.41770i	1.30642	+	0.410851i
$245$		−	1.59665i		−	0.102006i
$246$	−16.1361	−	21.9898i	−1.02880	−	1.40202i
$247$	−2.53707			−0.161430
$248$	−3.54101	−	10.3936i	−0.224854	−	0.659993i
$249$	−27.0073			−1.71152
$250$	9.95305	+	13.5637i	0.629486	+	0.857845i
$251$		−	15.3853i		−	0.971109i	−0.874206	−	0.485554i	$-0.838618\pi$
$251$		−	15.3853i		−	0.971109i	0.874206	−	0.485554i	$-0.161382\pi$
$252$	1.61193	−	5.12560i	0.101542	−	0.322882i
$253$		−	0.0798823i		−	0.00502216i
$254$	−17.2994	+	12.6943i	−1.08546	+	0.796512i
$255$	−2.17057			−0.135927
$256$	5.51678	+	15.0188i	0.344799	+	0.938677i
$257$	−3.88506			−0.242343			−0.121172	−	0.992632i	$-0.538665\pi$
$257$	−3.88506			−0.242343			−0.121172	+	0.992632i	$0.538665\pi$
$258$	−32.0828	+	23.5423i	−1.99739	+	1.46568i
$259$		−	1.77977i		−	0.110590i
$260$	−0.957990	+	3.04621i	−0.0594120	+	0.188918i
$261$		−	1.99375i		−	0.123410i
$262$	1.35823	+	1.85096i	0.0839117	+	0.114352i
$263$	21.8664			1.34834			0.674169	−	0.738577i	$-0.264502\pi$
$263$	21.8664			1.34834			0.674169	+	0.738577i	$0.264502\pi$
$264$	−9.11293	−	26.7483i	−0.560862	−	1.64624i
$265$	7.35936			0.452082
$266$	−2.12266	−	2.89270i	−0.130149	−	0.177363i
$267$			3.93229i			0.240652i
$268$	−16.1317	−	5.07320i	−0.985402	−	0.309895i
$269$			28.9652i			1.76604i	0.469338	+	0.883019i	$0.344493\pi$
$269$			28.9652i			1.76604i	−0.469338	+	0.883019i	$0.655507\pi$
$270$	1.36077	−	0.998528i	0.0828135	−	0.0607685i
$271$	16.7574			1.01794			0.508971	−	0.860784i	$-0.330026\pi$
$271$	16.7574			1.01794			0.508971	+	0.860784i	$0.330026\pi$
$272$	−1.86988	−	1.30519i	−0.113378	−	0.0791387i
$273$	2.38465			0.144325
$274$	10.8710	−	7.97713i	0.656741	−	0.481916i
$275$		−	10.2675i		−	0.619155i
$276$	−0.0867466	−	0.0272806i	−0.00522153	−	0.00164210i
$277$		−	19.3546i		−	1.16290i	−0.813581	−	0.581451i	$-0.802485\pi$
$277$		−	19.3546i		−	1.16290i	0.813581	−	0.581451i	$-0.197515\pi$
$278$	10.2366	+	13.9501i	0.613950	+	0.836673i
$279$	10.4294			0.624393
$280$	−4.27473	+	1.45636i	−0.255464	+	0.0870344i
$281$	2.77097			0.165302			0.0826510	−	0.996579i	$-0.473661\pi$
$281$	2.77097			0.165302			0.0826510	+	0.996579i	$0.473661\pi$
$282$	−10.6491	−	14.5122i	−0.634142	−	0.864190i
$283$		−	27.6707i		−	1.64485i	−0.568873	−	0.822426i	$-0.692620\pi$
$283$		−	27.6707i		−	1.64485i	0.568873	−	0.822426i	$-0.307380\pi$
$284$	−0.255188	+	0.811447i	−0.0151427	+	0.0481505i
$285$			9.65974i			0.572194i
$286$	4.77688	−	3.50527i	0.282463	−	0.207271i
$287$	8.08770			0.477402
$288$	−15.1931	+	0.359621i	−0.895264	+	0.0211909i
$289$	−16.6750			−0.980882
$290$	−1.35101	+	0.991369i	−0.0793340	+	0.0582152i
$291$			11.4457i			0.670960i
$292$	4.91278	−	15.6216i	0.287499	−	0.914186i
$293$		−	4.72248i		−	0.275890i	−0.990440	−	0.137945i	$-0.955950\pi$
$293$		−	4.72248i		−	0.275890i	0.990440	−	0.137945i	$-0.0440498\pi$
$294$	1.99514	+	2.71892i	0.116359	+	0.158570i
$295$	−11.3793			−0.662529
$296$	−4.76501	+	1.62340i	−0.276960	+	0.0943582i
$297$	−3.13167			−0.181718
$298$	−1.64970	−	2.24817i	−0.0955647	−	0.130233i
$299$		−	0.0190668i		−	0.00110266i
$300$	−11.1498	−	3.50646i	−0.643735	−	0.202446i
$301$		−	11.7998i		−	0.680131i
$302$	18.9024	−	13.8706i	1.08771	−	0.798163i
$303$	−17.8408			−1.02493
$304$	−5.80851	+	8.32158i	−0.333141	+	0.477275i
$305$	17.0780			0.977883
$306$	1.74625	−	1.28140i	0.0998265	−	0.0732526i
$307$		−	20.2156i		−	1.15376i	−0.816827	−	0.576882i	$-0.804269\pi$
$307$		−	20.2156i		−	1.15376i	0.816827	−	0.576882i	$-0.195731\pi$
$308$	7.99326	+	2.51377i	0.455458	+	0.143235i
$309$		−	28.1801i		−	1.60311i
$310$	−5.18590	−	7.06720i	−0.294539	−	0.401390i
$311$	33.4197			1.89505			0.947527	−	0.319675i	$-0.103574\pi$
$311$	33.4197			1.89505			0.947527	+	0.319675i	$0.103574\pi$
$312$	−2.17513	−	6.38445i	−0.123142	−	0.361448i
$313$	−29.8694			−1.68832			−0.844159	−	0.536093i	$-0.819900\pi$
$313$	−29.8694			−1.68832			−0.844159	+	0.536093i	$0.819900\pi$
$314$	−6.03869	−	8.22934i	−0.340783	−	0.464409i
$315$		−	4.28946i		−	0.241684i
$316$	0.783419	−	2.49111i	0.0440708	−	0.140136i
$317$		−	2.84875i		−	0.160002i	−0.996795	−	0.0800009i	$-0.974508\pi$
$317$		−	2.84875i		−	0.160002i	0.996795	−	0.0800009i	$-0.0254923\pi$
$318$	−12.5322	+	9.19610i	−0.702770	+	0.515692i
$319$	3.10921			0.174082
$320$	7.79829	+	10.1164i	0.435937	+	0.565522i
$321$	−39.5385			−2.20683
$322$	0.0217395	−	0.0159524i	0.00121149	−	0.000888993i
$323$		−	1.44635i		−	0.0804770i
$324$	−5.90528	+	18.7776i	−0.328071	+	1.04320i
$325$		−	2.45072i		−	0.135941i
$326$	−17.4295	−	23.7524i	−0.965329	−	1.31552i
$327$	28.4769			1.57478
$328$	−7.37710	−	21.6533i	−0.407332	−	1.19560i
$329$	5.33750			0.294266
$330$	−13.3461	−	18.1877i	−0.734680	−	1.00120i
$331$			17.6436i			0.969778i	0.874576	+	0.484889i	$0.161140\pi$
$331$			17.6436i			0.969778i	−0.874576	+	0.484889i	$0.838860\pi$
$332$	−21.6077	−	6.79531i	−1.18587	−	0.372941i
$333$		−	4.78144i		−	0.262021i
$334$	−18.8960	+	13.8658i	−1.03394	+	0.758705i
$335$	−13.5002			−0.737593
$336$	5.45955	−	7.82164i	0.297843	−	0.426705i
$337$	21.7156			1.18292			0.591462	−	0.806333i	$-0.298551\pi$
$337$	21.7156			1.18292			0.591462	+	0.806333i	$0.298551\pi$
$338$	1.14018	−	0.836660i	0.0620174	−	0.0455083i
$339$		−	12.7004i		−	0.689789i
$340$	−1.73660	−	0.546137i	−0.0941806	−	0.0296185i
$341$			16.2644i			0.880769i
$342$	−5.70263	−	7.77137i	−0.308363	−	0.420228i
$343$	−1.00000			−0.0539949
$344$	−31.5918	+	10.7631i	−1.70332	+	0.580307i
$345$	−0.0725957			−0.00390842
$346$	2.91553	+	3.97320i	0.156740	+	0.213601i
$347$		−	1.68632i		−	0.0905264i	−0.998975	−	0.0452632i	$-0.985587\pi$
$347$		−	1.68632i		−	0.0905264i	0.998975	−	0.0452632i	$-0.0144127\pi$
$348$	1.06183	−	3.37639i	0.0569198	−	0.180993i
$349$		−	5.49984i		−	0.294400i	−0.989107	−	0.147200i	$-0.952974\pi$
$349$		−	5.49984i		−	0.294400i	0.989107	−	0.147200i	$-0.0470260\pi$
$350$	2.79425	−	2.05042i	0.149359	−	0.109599i
$351$	−0.747485			−0.0398978
$352$	−0.560821	−	23.6933i	−0.0298919	−	1.26286i
$353$	5.12477			0.272764			0.136382	−	0.990656i	$-0.456453\pi$
$353$	5.12477			0.272764			0.136382	+	0.990656i	$0.456453\pi$
$354$	19.3777	−	14.2194i	1.02991	−	0.755750i
$355$			0.679076i			0.0360416i
$356$	−0.989403	+	3.14610i	−0.0524382	+	0.166743i
$357$			1.35946i			0.0719500i
$358$	18.5342	+	25.2579i	0.979565	+	1.33492i
$359$	−28.3506			−1.49629			−0.748144	−	0.663537i	$-0.769055\pi$
$359$	−28.3506			−1.49629			−0.748144	+	0.663537i	$0.769055\pi$
$360$	−11.4842	+	3.91259i	−0.605272	+	0.206211i
$361$	12.5633			0.661225
$362$	14.1825	+	19.3274i	0.745413	+	1.01583i
$363$			15.6261i			0.820157i
$364$	1.90788	+	0.600001i	0.100000	+	0.0314486i
$365$		−	13.0733i		−	0.684287i
$366$	−29.0820	+	21.3403i	−1.52014	+	1.11548i
$367$	−24.8090			−1.29502			−0.647509	−	0.762058i	$-0.724189\pi$
$367$	−24.8090			−1.29502			−0.647509	+	0.762058i	$0.724189\pi$
$368$	−0.0625390	−	0.0436526i	−0.00326007	−	0.00227555i
$369$	21.7279			1.13111
$370$	−3.24000	+	2.37751i	−0.168440	+	0.123601i
$371$		−	4.60925i		−	0.239301i
$372$	17.6620	+	5.55446i	0.915735	+	0.287986i
$373$			34.3736i			1.77980i	0.456159	+	0.889898i	$0.349225\pi$
$373$			34.3736i			1.77980i	−0.456159	+	0.889898i	$0.650775\pi$
$374$	1.99831	+	2.72324i	0.103330	+	0.140815i
$375$	−28.3682			−1.46493
$376$	−4.86854	−	14.2902i	−0.251076	−	0.736959i
$377$	0.742125			0.0382214
$378$	−0.625390	−	0.852264i	−0.0321666	−	0.0438357i
$379$			3.46978i			0.178231i	0.996021	+	0.0891153i	$0.0284039\pi$
$379$			3.46978i			0.178231i	−0.996021	+	0.0891153i	$0.971596\pi$
$380$	−2.43049	+	7.72844i	−0.124681	+	0.396461i
$381$		−	36.1813i		−	1.85362i
$382$	24.6671	−	18.1007i	1.26208	−	0.926113i
$383$	−30.3382			−1.55021			−0.775104	−	0.631834i	$-0.782302\pi$
$383$	−30.3382			−1.55021			−0.775104	+	0.631834i	$0.782302\pi$
$384$	−25.9208	−	7.48249i	−1.32277	−	0.381839i
$385$	6.68932			0.340919
$386$	−18.4477	+	13.5369i	−0.938962	+	0.689010i
$387$		−	31.7007i		−	1.61144i
$388$	−2.87985	+	9.15734i	−0.146202	+	0.464893i
$389$		−	6.57349i		−	0.333289i	−0.986017	−	0.166645i	$-0.946707\pi$
$389$		−	6.57349i		−	0.333289i	0.986017	−	0.166645i	$-0.0532933\pi$
$390$	−3.18553	−	4.34115i	−0.161306	−	0.219823i
$391$	0.0108697			0.000549706
$392$	0.912139	+	2.67731i	0.0460700	+	0.135225i
$393$	−3.87123			−0.195278
$394$	12.7438	+	17.3668i	0.642021	+	0.874928i
$395$		−	2.08474i		−	0.104895i
$396$	21.4742	+	6.75334i	1.07912	+	0.339368i
$397$		−	17.5876i		−	0.882698i	−0.897336	−	0.441349i	$-0.854500\pi$
$397$		−	17.5876i		−	0.882698i	0.897336	−	0.441349i	$-0.145500\pi$
$398$	−7.08058	+	5.19572i	−0.354917	+	0.260438i
$399$	6.05001			0.302880
$400$	−8.03834	−	5.61081i	−0.401917	−	0.280540i
$401$	13.1238			0.655370			0.327685	−	0.944787i	$-0.393732\pi$
$401$	13.1238			0.655370			0.327685	+	0.944787i	$0.393732\pi$
$402$	22.9893	−	16.8695i	1.14660	−	0.841376i
$403$			3.88210i			0.193381i
$404$	−14.2738	−	4.48892i	−0.710150	−	0.223332i
$405$			15.7144i			0.780855i
$406$	0.620906	+	0.846153i	0.0308151	+	0.0419939i
$407$	7.45654			0.369607
$408$	3.63969	−	1.24001i	0.180191	−	0.0613898i
$409$	−8.55038			−0.422789			−0.211394	−	0.977401i	$-0.567800\pi$
$409$	−8.55038			−0.422789			−0.211394	+	0.977401i	$0.567800\pi$
$410$	−10.8040	−	14.7233i	−0.533570	−	0.727133i
$411$			22.7364i			1.12150i
$412$	7.09039	−	22.5460i	0.349318	−	1.11076i
$413$			7.12700i			0.350697i
$414$	0.0584041	−	0.0428568i	0.00287040	−	0.00210630i
$415$	−18.0828			−0.887651
$416$	−0.133860	−	5.65527i	−0.00656304	−	0.277272i
$417$	−29.1763			−1.42877
$418$	12.1193	−	8.89312i	0.592774	−	0.434977i
$419$			0.544846i			0.0266175i	0.999911	+	0.0133087i	$0.00423643\pi$
$419$			0.544846i			0.0266175i	−0.999911	+	0.0133087i	$0.995764\pi$
$420$	2.28447	−	7.26414i	0.111471	−	0.354454i
$421$		−	34.7806i		−	1.69510i	−0.530715	−	0.847550i	$-0.678077\pi$
$421$		−	34.7806i		−	1.69510i	0.530715	−	0.847550i	$-0.321923\pi$
$422$	−4.97549	−	6.78045i	−0.242203	−	0.330067i
$423$	14.3394			0.697207
$424$	−12.3404	+	4.20428i	−0.599304	+	0.204178i
$425$	1.39712			0.0677703
$426$	−0.848560	−	1.15639i	−0.0411128	−	0.0560274i
$427$		−	10.6962i		−	0.517623i
$428$	−31.6335	−	9.94829i	−1.52906	−	0.480869i
$429$			9.99073i			0.482357i
$430$	−21.4811	+	15.7628i	−1.03591	+	0.760150i
$431$	−40.6679			−1.95890			−0.979451	−	0.201682i	$-0.935359\pi$
$431$	−40.6679			−1.95890			−0.979451	+	0.201682i	$0.935359\pi$
$432$	−1.71133	+	2.45175i	−0.0823366	+	0.117960i
$433$	39.7133			1.90850			0.954251	−	0.299008i	$-0.0966556\pi$
$433$	39.7133			1.90850			0.954251	+	0.299008i	$0.0966556\pi$
$434$	−4.42627	+	3.24799i	−0.212468	+	0.155909i
$435$		−	2.82560i		−	0.135477i
$436$	22.7835	+	7.16507i	1.09113	+	0.343145i
$437$		−	0.0483737i		−	0.00231403i
$438$	16.3361	+	22.2624i	0.780569	+	1.06374i
$439$	−14.2217			−0.678766			−0.339383	−	0.940648i	$-0.610218\pi$
$439$	−14.2217			−0.678766			−0.339383	+	0.940648i	$0.610218\pi$
$440$	−6.10159	−	17.9094i	−0.290882	−	0.853798i
$441$	−2.68654			−0.127931
$442$	0.476969	+	0.649999i	0.0226871	+	0.0309173i
$443$		−	19.4745i		−	0.925262i	−0.886551	−	0.462631i	$-0.846906\pi$
$443$		−	19.4745i		−	0.925262i	0.886551	−	0.462631i	$-0.153094\pi$
$444$	2.54648	−	8.09728i	0.120851	−	0.384280i
$445$			2.63288i			0.124810i
$446$	−11.3602	+	8.33611i	−0.537921	+	0.394726i
$447$	4.70198			0.222396
$448$	6.33601	−	4.88416i	0.299348	−	0.230755i
$449$	13.7969			0.651114			0.325557	−	0.945522i	$-0.394448\pi$
$449$	13.7969			0.651114			0.325557	+	0.945522i	$0.394448\pi$
$450$	7.50686	−	5.50853i	0.353877	−	0.259675i
$451$			33.8843i			1.59555i
$452$	3.19553	−	10.1611i	0.150305	−	0.477940i
$453$			39.5340i			1.85747i
$454$	−8.73814	−	11.9081i	−0.410101	−	0.558874i
$455$	1.59665			0.0748520
$456$	−5.51845	−	16.1978i	−0.258425	−	0.758530i
$457$	41.3406			1.93383			0.966915	−	0.255100i	$-0.0821084\pi$
$457$	41.3406			1.93383			0.966915	+	0.255100i	$0.0821084\pi$
$458$	22.2500	+	30.3217i	1.03968	+	1.41684i
$459$		−	0.426131i		−	0.0198901i
$460$	−0.0580814	−	0.0182658i	−0.00270806	−	0.000851647i
$461$			3.00550i			0.139980i	0.997548	+	0.0699900i	$0.0222967\pi$
$461$			3.00550i			0.139980i	−0.997548	+	0.0699900i	$0.977703\pi$
$462$	−11.3912	+	8.35884i	−0.529966	+	0.388889i
$463$	−33.4122			−1.55280			−0.776399	−	0.630241i	$-0.782956\pi$
$463$	−33.4122			−1.55280			−0.776399	+	0.630241i	$0.782956\pi$
$464$	1.69906	−	2.43417i	0.0788771	−	0.113003i
$465$	14.7809			0.685446
$466$	−16.4412	+	12.0645i	−0.761622	+	0.558878i
$467$			35.0509i			1.62196i	0.585071	+	0.810982i	$0.301066\pi$
$467$			35.0509i			1.62196i	−0.585071	+	0.810982i	$0.698934\pi$
$468$	5.12560	+	1.61193i	0.236931	+	0.0745114i
$469$			8.45532i			0.390431i
$470$	−7.13011	−	9.71670i	−0.328887	−	0.448198i
$471$	17.2115			0.793062
$472$	19.0812	−	6.50082i	0.878284	−	0.299224i
$473$	49.4366			2.27310
$474$	2.60505	+	3.55008i	0.119654	+	0.163061i
$475$		−	6.21763i		−	0.285285i
$476$	−0.342052	+	1.08766i	−0.0156779	+	0.0498526i
$477$		−	12.3830i		−	0.566977i
$478$	−1.33285	+	0.978043i	−0.0609631	+	0.0447346i
$479$	16.9518			0.774550			0.387275	−	0.921964i	$-0.373416\pi$
$479$	16.9518			0.774550			0.387275	+	0.921964i	$0.373416\pi$
$480$	−21.5321	+	0.509665i	−0.982802	+	0.0232629i
$481$	1.77977			0.0811507
$482$	−20.1604	+	14.7937i	−0.918283	+	0.673835i
$483$			0.0454676i			0.00206885i
$484$	−3.93168	+	12.5019i	−0.178713	+	0.568269i
$485$			7.66351i			0.347982i
$486$	−17.7602	−	24.2031i	−0.805620	−	1.09787i
$487$	−5.22200			−0.236631			−0.118316	−	0.992976i	$-0.537749\pi$
$487$	−5.22200			−0.236631			−0.118316	+	0.992976i	$0.537749\pi$
$488$	−28.6370	+	9.75638i	−1.29633	+	0.441651i
$489$	49.6775			2.24649
$490$	1.33585	+	1.82046i	0.0603476	+	0.0822400i
$491$		−	9.41493i		−	0.424890i	−0.977173	−	0.212445i	$-0.931857\pi$
$491$		−	9.41493i		−	0.424890i	0.977173	−	0.212445i	$-0.0681426\pi$
$492$	36.7959	+	11.5718i	1.65889	+	0.521697i
$493$			0.423076i			0.0190544i
$494$	2.89270	−	2.12266i	0.130149	−	0.0955031i
$495$	17.9712			0.807743
$496$	12.7333	+	8.88789i	0.571741	+	0.399078i
$497$	0.425314			0.0190779
$498$	30.7931	−	22.5959i	1.37987	−	1.01255i
$499$			26.2053i			1.17311i	0.809910	+	0.586555i	$0.199516\pi$
$499$			26.2053i			1.17311i	−0.809910	+	0.586555i	$0.800484\pi$
$500$	−22.6964	−	7.13771i	−1.01502	−	0.319208i
$501$		−	39.5204i		−	1.76564i
$502$	12.8722	+	17.5419i	0.574516	+	0.782933i
$503$	16.3145			0.727427			0.363713	−	0.931511i	$-0.381509\pi$
$503$	16.3145			0.727427			0.363713	+	0.931511i	$0.381509\pi$
$504$	2.45050	+	7.19272i	0.109154	+	0.320389i
$505$	−11.9454			−0.531561
$506$	0.0668343	+	0.0910798i	0.00297115	+	0.00404899i
$507$			2.38465i			0.105906i
$508$	9.10357	−	28.9475i	0.403906	−	1.28434i
$509$			28.9494i			1.28316i	0.767056	+	0.641580i	$0.221721\pi$
$509$			28.9494i			1.28316i	−0.767056	+	0.641580i	$0.778279\pi$
$510$	2.47483	−	1.81603i	0.109587	−	0.0804152i
$511$	−8.18795			−0.362214
$512$	−18.8557	−	12.5084i	−0.833314	−	0.552800i
$513$	−1.89642			−0.0837290
$514$	4.42965	−	3.25047i	0.195384	−	0.143372i
$515$		−	18.8681i		−	0.831426i
$516$	16.8831	−	53.6847i	0.743236	−	2.36334i
$517$			22.3620i			0.983481i
$518$	1.48906	+	2.02925i	0.0654257	+	0.0891603i
$519$	−8.30985			−0.364762
$520$	−1.45636	−	4.27473i	−0.0638658	−	0.187459i
$521$	4.82104			0.211213			0.105607	−	0.994408i	$-0.466322\pi$
$521$	4.82104			0.211213			0.105607	+	0.994408i	$0.466322\pi$
$522$	1.66809	+	2.27323i	0.0730104	+	0.0994964i
$523$			41.0621i			1.79552i	0.440483	+	0.897761i	$0.354807\pi$
$523$			41.0621i			1.79552i	−0.440483	+	0.897761i	$0.645193\pi$
$524$	−3.09724	−	0.974038i	−0.135304	−	0.0425511i
$525$			5.84409i			0.255057i
$526$	−24.9315	+	18.2947i	−1.08706	+	0.797687i
$527$	−2.21313			−0.0964055
$528$	32.7696	+	22.8733i	1.42611	+	0.995434i
$529$	−22.9996			−0.999984
$530$	−8.39096	+	6.15728i	−0.364480	+	0.267455i
$531$			19.1470i			0.830909i
$532$	4.84042	+	1.52224i	0.209859	+	0.0659976i
$533$			8.08770i			0.350317i
$534$	−3.28999	−	4.48350i	−0.142372	−	0.194020i
$535$	−26.4732			−1.14453
$536$	22.6375	−	7.71243i	0.977793	−	0.333126i
$537$	−52.8263			−2.27962
$538$	−24.2340	−	33.0254i	−1.04480	−	1.42383i
$539$		−	4.18960i		−	0.180459i
$540$	−0.716083	+	2.27700i	−0.0308153	+	0.0979863i
$541$		−	21.6909i		−	0.932563i	−0.884636	−	0.466281i	$-0.845593\pi$
$541$		−	21.6909i		−	0.932563i	0.884636	−	0.466281i	$-0.154407\pi$
$542$	−19.1064	+	14.0203i	−0.820691	+	0.602222i
$543$	−40.4228			−1.73471
$544$	3.22399	−	0.0763119i	0.138228	−	0.00327185i
$545$	19.0668			0.816732
$546$	−2.71892	+	1.99514i	−0.116359	+	0.0853840i
$547$			1.00864i			0.0431261i	0.999767	+	0.0215631i	$0.00686427\pi$
$547$			1.00864i			0.0431261i	−0.999767	+	0.0215631i	$0.993136\pi$
$548$	−5.72070	+	18.1906i	−0.244376	+	0.777066i
$549$		−	28.7357i		−	1.22641i
$550$	8.59043	+	11.7068i	0.366297	+	0.499179i
$551$	1.88282			0.0802110
$552$	0.121731	−	0.0414727i	0.00518121	−	0.00176520i
$553$	−1.30570			−0.0555239
$554$	16.1932	+	22.0676i	0.687982	+	0.937562i
$555$		−	6.77638i		−	0.287641i
$556$	−23.3430	−	7.34105i	−0.989964	−	0.311330i
$557$			36.2601i			1.53639i	0.640215	+	0.768196i	$0.278845\pi$
$557$			36.2601i			1.53639i	−0.640215	+	0.768196i	$0.721155\pi$
$558$	−11.8914	+	8.72587i	−0.503402	+	0.369396i
$559$	11.7998			0.499080
$560$	3.65546	−	5.23700i	0.154471	−	0.221304i
$561$	−5.69558			−0.240468
$562$	−3.15939	+	2.31836i	−0.133271	+	0.0977940i
$563$			6.62119i			0.279050i	0.990219	+	0.139525i	$0.0445576\pi$
$563$			6.62119i			0.279050i	−0.990219	+	0.139525i	$0.955442\pi$
$564$	24.2836	+	7.63685i	1.02252	+	0.321569i
$565$		−	8.50356i		−	0.357748i
$566$	23.1509	+	31.5494i	0.973107	+	1.32612i
$567$	9.84212			0.413330
$568$	−0.387945	−	1.13870i	−0.0162778	−	0.0477787i
$569$	−7.93150			−0.332506			−0.166253	−	0.986083i	$-0.553167\pi$
$569$	−7.93150			−0.332506			−0.166253	+	0.986083i	$0.553167\pi$
$570$	−8.08192	−	11.0138i	−0.338514	−	0.461317i
$571$			12.5240i			0.524113i	0.965053	+	0.262056i	$0.0844006\pi$
$571$			12.5240i			0.524113i	−0.965053	+	0.262056i	$0.915599\pi$
$572$	−2.51377	+	7.99326i	−0.105106	+	0.334215i
$573$			51.5906i			2.15523i
$574$	−9.22140	+	6.76665i	−0.384894	+	0.282435i
$575$	0.0467273			0.00194866
$576$	17.0220	−	13.1215i	0.709248	−	0.546730i
$577$	0.359975			0.0149860			0.00749298	−	0.999972i	$-0.497615\pi$
$577$	0.359975			0.0149860			0.00749298	+	0.999972i	$0.497615\pi$
$578$	19.0124	−	13.9513i	0.790813	−	0.580298i
$579$		−	38.5828i		−	1.60345i
$580$	0.710949	−	2.26067i	0.0295205	−	0.0938692i
$581$			11.3255i			0.469861i
$582$	−9.57617	−	13.0501i	−0.396945	−	0.540945i
$583$	19.3110			0.799778
$584$	7.46855	+	21.9217i	0.309051	+	0.907127i
$585$	4.28946			0.177347
$586$	3.95111	+	5.38446i	0.163219	+	0.222430i
$587$			5.69179i			0.234925i	0.993077	+	0.117463i	$0.0374760\pi$
$587$			5.69179i			0.234925i	−0.993077	+	0.117463i	$0.962524\pi$
$588$	−4.54962	−	1.43079i	−0.187623	−	0.0590048i
$589$			9.84914i			0.405827i
$590$	12.9744	−	9.52061i	0.534148	−	0.391958i
$591$	−36.3222			−1.49410
$592$	4.07471	−	5.83765i	0.167470	−	0.239926i
$593$	7.86945			0.323160			0.161580	−	0.986860i	$-0.448341\pi$
$593$	7.86945			0.323160			0.161580	+	0.986860i	$0.448341\pi$
$594$	3.57065	−	2.62014i	0.146505	−	0.107506i
$595$			0.910228i			0.0373157i
$596$	3.76190	+	1.18306i	0.154093	+	0.0484602i
$597$		−	14.8088i		−	0.606085i
$598$	0.0159524	+	0.0217395i	0.000652343	+	0.000888994i
$599$	−19.6972			−0.804804			−0.402402	−	0.915463i	$-0.631825\pi$
$599$	−19.6972			−0.804804			−0.402402	+	0.915463i	$0.631825\pi$
$600$	15.6465	−	5.33062i	0.638764	−	0.217622i
$601$	−12.1355			−0.495018			−0.247509	−	0.968886i	$-0.579612\pi$
$601$	−12.1355			−0.495018			−0.247509	+	0.968886i	$0.579612\pi$
$602$	9.87244	+	13.4539i	0.402371	+	0.548339i
$603$			22.7156i			0.925050i
$604$	−9.94714	+	31.6298i	−0.404743	+	1.28700i
$605$			10.4625i			0.425361i
$606$	20.3416	−	14.9267i	0.826323	−	0.606355i
$607$	−4.16567			−0.169080			−0.0845398	−	0.996420i	$-0.526942\pi$
$607$	−4.16567			−0.169080			−0.0845398	+	0.996420i	$0.526942\pi$
$608$	−0.339613	−	14.3478i	−0.0137731	−	0.581880i
$609$	−1.76971			−0.0717122
$610$	−19.4719	+	14.2885i	−0.788395	+	0.578524i
$611$			5.33750i			0.215932i
$612$	−0.918939	+	2.92203i	−0.0371459	+	0.118116i
$613$			10.8143i			0.436785i	0.975861	+	0.218392i	$0.0700813\pi$
$613$			10.8143i			0.436785i	−0.975861	+	0.218392i	$0.929919\pi$
$614$	16.9136	+	23.0493i	0.682576	+	0.930195i
$615$	30.7934			1.24171
$616$	−11.2169	+	3.82150i	−0.451941	+	0.153973i
$617$	39.6347			1.59563			0.797817	−	0.602899i	$-0.205988\pi$
$617$	39.6347			1.59563			0.797817	+	0.602899i	$0.205988\pi$
$618$	23.5772	+	32.1303i	0.948412	+	1.29247i
$619$			29.0915i			1.16928i	0.811291	+	0.584642i	$0.198765\pi$
$619$			29.0915i			1.16928i	−0.811291	+	0.584642i	$0.801235\pi$
$620$	11.8257	+	3.71901i	0.474931	+	0.149359i
$621$		−	0.0142521i		−	0.000571918i
$622$	−38.1043	+	27.9609i	−1.52784	+	1.12113i
$623$	1.64900			0.0660659
$624$	7.82164	+	5.45955i	0.313116	+	0.218557i
$625$	−6.74042			−0.269617
$626$	34.0563	−	24.9905i	1.36117	−	0.998822i
$627$			25.3472i			1.01227i
$628$	13.7703	+	4.33057i	0.549496	+	0.172809i
$629$			1.01462i			0.0404557i
$630$	3.58882	+	4.89074i	0.142982	+	0.194852i
$631$	−8.48512			−0.337787			−0.168894	−	0.985634i	$-0.554019\pi$
$631$	−8.48512			−0.337787			−0.168894	+	0.985634i	$0.554019\pi$
$632$	1.19098	+	3.49576i	0.0473745	+	0.139054i
$633$	14.1811			0.563650
$634$	2.38344	+	3.24808i	0.0946583	+	0.128998i
$635$		−	24.2253i		−	0.961352i
$636$	6.59488	−	20.9703i	0.261504	−	0.831528i
$637$		−	1.00000i		−	0.0396214i
$638$	−3.54505	+	2.60135i	−0.140350	+	0.102989i
$639$	1.14262			0.0452015
$640$	−17.3554	−	5.00993i	−0.686031	−	0.198035i
$641$	7.62094			0.301009			0.150504	−	0.988609i	$-0.451910\pi$
$641$	7.62094			0.301009			0.150504	+	0.988609i	$0.451910\pi$
$642$	45.0809	−	33.0803i	1.77920	−	1.30558i
$643$			6.34543i			0.250239i	0.992142	+	0.125120i	$0.0399314\pi$
$643$			6.34543i			0.250239i	−0.992142	+	0.125120i	$0.960069\pi$
$644$	−0.0114401	+	0.0363771i	−0.000450803	+	0.00143346i
$645$		−	44.9272i		−	1.76901i
$646$	1.21010	+	1.64909i	0.0476108	+	0.0648827i
$647$	−8.51589			−0.334794			−0.167397	−	0.985890i	$-0.553536\pi$
$647$	−8.51589			−0.334794			−0.167397	+	0.985890i	$0.553536\pi$
$648$	−8.97738	−	26.3504i	−0.352665	−	1.03514i
$649$	−29.8593			−1.17208
$650$	2.05042	+	2.79425i	0.0804239	+	0.109599i
$651$		−	9.25743i		−	0.362827i
$652$	39.7453	+	12.4993i	1.55655	+	0.489512i
$653$		−	13.5010i		−	0.528334i	−0.964477	−	0.264167i	$-0.914903\pi$
$653$		−	13.5010i		−	0.528334i	0.964477	−	0.264167i	$-0.0850971\pi$
$654$	−32.4687	+	23.8255i	−1.26963	+	0.931651i
$655$	−2.59199			−0.101277
$656$	26.5276	+	18.5164i	1.03573	+	0.722945i
$657$	−21.9973			−0.858196
$658$	−6.08569	+	4.46567i	−0.237245	+	0.174090i
$659$		−	17.4197i		−	0.678574i	−0.940683	−	0.339287i	$-0.889814\pi$
$659$		−	17.4197i		−	0.678574i	0.940683	−	0.339287i	$-0.110186\pi$
$660$	30.4339	+	9.57102i	1.18464	+	0.372551i
$661$		−	13.2692i		−	0.516112i	−0.966130	−	0.258056i	$-0.916918\pi$
$661$		−	13.2692i		−	0.516112i	0.966130	−	0.258056i	$-0.0830819\pi$
$662$	−14.7617	−	20.1168i	−0.573728	−	0.781860i
$663$	−1.35946			−0.0527969
$664$	30.3219	−	10.3304i	1.17672	−	0.400898i
$665$	4.05081			0.157083
$666$	4.00044	+	5.45168i	0.155014	+	0.211248i
$667$			0.0141499i			0.000547888i
$668$	9.94372	−	31.6190i	0.384734	−	1.22337i
$669$		−	23.7596i		−	0.918598i
$670$	15.3926	−	11.2951i	0.594667	−	0.436366i
$671$	44.8127			1.72997
$672$	0.319209	+	13.4858i	0.0123138	+	0.520227i
$673$	−2.84846			−0.109800			−0.0549001	−	0.998492i	$-0.517484\pi$
$673$	−2.84846			−0.109800			−0.0549001	+	0.998492i	$0.517484\pi$
$674$	−24.7596	+	18.1686i	−0.953704	+	0.699827i
$675$		−	1.83187i		−	0.0705088i
$676$	−0.600001	+	1.90788i	−0.0230770	+	0.0733799i
$677$		−	10.2692i		−	0.394677i	−0.980335	−	0.197338i	$-0.936770\pi$
$677$		−	10.2692i		−	0.394677i	0.980335	−	0.197338i	$-0.0632297\pi$
$678$	10.6259	+	14.4806i	0.408084	+	0.556126i
$679$	4.79975			0.184198
$680$	2.43696	−	0.830254i	0.0934533	−	0.0318388i
$681$	24.9054			0.954379
$682$	−13.6078	−	18.5443i	−0.521070	−	0.710099i
$683$			32.8742i			1.25790i	0.777447	+	0.628949i	$0.216515\pi$
$683$			32.8742i			1.25790i	−0.777447	+	0.628949i	$0.783485\pi$
$684$	13.0040	+	4.08957i	0.497220	+	0.156369i
$685$			15.2232i			0.581650i
$686$	1.14018	−	0.836660i	0.0435321	−	0.0319438i
$687$	−63.4171			−2.41951
$688$	27.0152	−	38.7034i	1.02994	−	1.47555i
$689$	4.60925			0.175599
$690$	0.0827718	−	0.0607379i	0.00315107	−	0.00231225i
$691$		−	27.5365i		−	1.04754i	−0.851860	−	0.523769i	$-0.824526\pi$
$691$		−	27.5365i		−	1.04754i	0.851860	−	0.523769i	$-0.175474\pi$
$692$	−6.64844	−	2.09084i	−0.252736	−	0.0794818i
$693$		−	11.2556i		−	0.427563i
$694$	1.41088	+	1.92270i	0.0535562	+	0.0729848i
$695$	−19.5351			−0.741008
$696$	1.61422	+	4.73806i	0.0611868	+	0.179596i
$697$	−4.61069			−0.174642
$698$	4.60149	+	6.27078i	0.174169	+	0.237353i
$699$		−	34.3863i		−	1.30061i
$700$	−1.47043	+	4.67567i	−0.0555771	+	0.176724i
$701$		−	12.0330i		−	0.454480i	−0.973839	−	0.227240i	$-0.927030\pi$
$701$		−	12.0330i		−	0.454480i	0.973839	−	0.227240i	$-0.0729701\pi$
$702$	0.852264	−	0.625390i	0.0321666	−	0.0236038i
$703$	4.51541			0.170302
$704$	20.4627	+	26.5454i	0.771217	+	1.00047i
$705$	20.3222			0.765379
$706$	−5.84314	+	4.28769i	−0.219910	+	0.161369i
$707$			7.48152i			0.281372i
$708$	−10.1972	+	32.4251i	−0.383236	+	1.21861i
$709$		−	13.3957i		−	0.503085i	−0.967846	−	0.251543i	$-0.919062\pi$
$709$		−	13.3957i		−	0.503085i	0.967846	−	0.251543i	$-0.0809379\pi$
$710$	−0.568156	−	0.774266i	−0.0213225	−	0.0290577i
$711$	−3.50781			−0.131553
$712$	−1.50412	−	4.41489i	−0.0563692	−	0.165455i
$713$	−0.0740191			−0.00277204
$714$	−1.13740	−	1.55002i	−0.0425662	−	0.0580080i
$715$			6.68932i			0.250167i
$716$	−42.2646	−	13.2916i	−1.57950	−	0.496731i
$717$		−	2.78762i		−	0.104105i
$718$	32.3247	−	23.7198i	1.20635	−	0.885215i
$719$	19.5596			0.729452			0.364726	−	0.931115i	$-0.381163\pi$
$719$	19.5596			0.729452			0.364726	+	0.931115i	$0.381163\pi$
$720$	9.82054	−	14.0694i	0.365990	−	0.524337i
$721$	−11.8173			−0.440099
$722$	−14.3243	+	10.5112i	−0.533097	+	0.391186i
$723$		−	42.1650i		−	1.56813i
$724$	−32.3410	−	10.1708i	−1.20194	−	0.377994i
$725$			1.81874i			0.0675462i
$726$	−13.0737	−	17.8165i	−0.485211	−	0.661232i
$727$	−1.11125			−0.0412139			−0.0206069	−	0.999788i	$-0.506560\pi$
$727$	−1.11125			−0.0412139			−0.0206069	+	0.999788i	$0.506560\pi$
$728$	−2.67731	+	0.912139i	−0.0992278	+	0.0338061i
$729$	21.0938			0.781252
$730$	10.9379	+	14.9058i	0.404829	+	0.551690i
$731$			6.72693i			0.248804i
$732$	15.3040	−	48.6634i	0.565651	−	1.79865i
$733$		−	9.82787i		−	0.363001i	−0.983391	−	0.181500i	$-0.941905\pi$
$733$		−	9.82787i		−	0.363001i	0.983391	−	0.181500i	$-0.0580954\pi$
$734$	28.2866	−	20.7567i	1.04408	−	0.766143i
$735$	−3.80744			−0.140440
$736$	0.107828	−	0.00255228i	0.00397459	−	9.40784e-5i
$737$	−35.4245			−1.30488
$738$	−24.7737	+	18.1789i	−0.911932	+	0.669175i
$739$		−	14.9997i		−	0.551773i	−0.961190	−	0.275887i	$-0.911029\pi$
$739$		−	14.9997i		−	0.551773i	0.961190	−	0.275887i	$-0.0889714\pi$
$740$	1.70500	−	5.42156i	0.0626772	−	0.199301i
$741$			6.05001i			0.222253i
$742$	3.85638	+	5.25536i	0.141572	+	0.192930i
$743$	−9.74460			−0.357495			−0.178747	−	0.983895i	$-0.557204\pi$
$743$	−9.74460			−0.357495			−0.178747	+	0.983895i	$0.557204\pi$
$744$	−24.7850	+	8.44406i	−0.908663	+	0.309574i
$745$	3.14823			0.115342
$746$	−28.7590	−	39.1919i	−1.05294	−	1.43492i
$747$			30.4264i			1.11325i
$748$	−4.55685	−	1.43306i	−0.166615	−	0.0523980i
$749$			16.5805i			0.605837i
$750$	32.3447	−	23.7345i	1.18106	−	0.866662i
$751$	−8.70157			−0.317525			−0.158762	−	0.987317i	$-0.550750\pi$
$751$	−8.70157			−0.317525			−0.158762	+	0.987317i	$0.550750\pi$
$752$	17.5070	+	12.2200i	0.638415	+	0.445617i
$753$	−36.6884			−1.33700
$754$	−0.846153	+	0.620906i	−0.0308151	+	0.0226121i
$755$			26.4701i			0.963345i
$756$	1.42611	+	0.448491i	0.0518671	+	0.0163115i
$757$		−	15.2448i		−	0.554082i	−0.960858	−	0.277041i	$-0.910646\pi$
$757$		−	15.2448i		−	0.554082i	0.960858	−	0.277041i	$-0.0893539\pi$
$758$	−2.90302	−	3.95616i	−0.105443	−	0.143694i
$759$	−0.190491			−0.00691439
$760$	−3.69490	−	10.8453i	−0.134028	−	0.393399i
$761$	−43.2546			−1.56798			−0.783990	−	0.620774i	$-0.786819\pi$
$761$	−43.2546			−1.56798			−0.783990	+	0.620774i	$0.786819\pi$
$762$	30.2715	+	41.2531i	1.09662	+	1.49444i
$763$		−	11.9418i		−	0.432321i
$764$	−12.9807	+	41.2760i	−0.469625	+	1.49331i
$765$			2.44537i			0.0884124i
$766$	34.5908	−	25.3827i	1.24982	−	0.917115i
$767$	−7.12700			−0.257341
$768$	35.8146	−	13.1556i	1.29235	−	0.474711i
$769$	39.5036			1.42454			0.712269	−	0.701907i	$-0.247668\pi$
$769$	39.5036			1.42454			0.712269	+	0.701907i	$0.247668\pi$
$770$	−7.62700	+	5.59669i	−0.274858	+	0.201691i
$771$			9.26450i			0.333653i
$772$	9.70782	−	30.8689i	0.349392	−	1.11099i
$773$		−	42.8504i		−	1.54122i	−0.637306	−	0.770611i	$-0.719951\pi$
$773$		−	42.8504i		−	1.54122i	0.637306	−	0.770611i	$-0.280049\pi$
$774$	26.5227	+	36.1444i	0.953340	+	1.29918i
$775$	−9.51391			−0.341750
$776$	−4.37804	−	12.8504i	−0.157162	−	0.461304i
$777$	−4.24413			−0.152257
$778$	5.49978	+	7.49494i	0.197177	+	0.268707i
$779$			20.5190i			0.735171i
$780$	7.26414	+	2.28447i	0.260098	+	0.0817971i
$781$			1.78190i			0.0637612i
$782$	−0.0123934	+	0.00909426i	−0.000443187	+	0.000325210i
$783$	0.554727			0.0198243
$784$	−3.28000	−	2.28946i	−0.117143	−	0.0817663i
$785$	11.5240			0.411309
$786$	4.41388	−	3.23890i	0.157438	−	0.115528i
$787$			21.9628i			0.782891i	0.920201	+	0.391446i	$0.128025\pi$
$787$			21.9628i			0.782891i	−0.920201	+	0.391446i	$0.871975\pi$
$788$	−29.0602	−	9.13903i	−1.03523	−	0.325565i
$789$		−	52.1436i		−	1.85636i
$790$	1.74422	+	2.37697i	0.0620564	+	0.0845687i
$791$	−5.32589			−0.189367
$792$	−30.1346	+	10.2666i	−1.07079	+	0.364809i
$793$	10.6962			0.379832
$794$	14.7149	+	20.0530i	0.522211	+	0.711654i
$795$		−	17.5495i		−	0.622416i
$796$	3.72605	−	11.8481i	0.132066	−	0.419944i
$797$			43.1481i			1.52838i	0.644990	+	0.764191i	$0.276862\pi$
$797$			43.1481i			1.52838i	−0.644990	+	0.764191i	$0.723138\pi$
$798$	−6.89808	+	5.06180i	−0.244189	+	0.179186i
$799$	−3.04284			−0.107648
$800$	13.8595	−	0.328053i	0.490006	−	0.0115984i
$801$	4.43012			0.156530
$802$	−14.9634	+	10.9801i	−0.528376	+	0.387722i
$803$		−	34.3043i		−	1.21057i
$804$	−12.0978	+	38.4685i	−0.426656	+	1.35668i
$805$			0.0304429i			0.00107297i
$806$	−3.24799	−	4.42627i	−0.114406	−	0.155909i
$807$	69.0717			2.43144
$808$	20.0304	−	6.82419i	0.704666	−	0.240074i
$809$	17.1306			0.602280			0.301140	−	0.953580i	$-0.402633\pi$
$809$	17.1306			0.602280			0.301140	+	0.953580i	$0.402633\pi$
$810$	−13.1476	−	17.9172i	−0.461960	−	0.629545i
$811$		−	13.1707i		−	0.462486i	−0.972896	−	0.231243i	$-0.925721\pi$
$811$		−	13.1707i		−	0.462486i	0.972896	−	0.231243i	$-0.0742793\pi$
$812$	−1.41588	−	0.445276i	−0.0496878	−	0.0156261i
$813$		−	39.9606i		−	1.40148i
$814$	−8.50177	+	6.23859i	−0.297987	+	0.218662i
$815$	33.2617			1.16511
$816$	−3.11242	+	4.45901i	−0.108956	+	0.156097i
$817$	29.9370			1.04736
$818$	9.74893	−	7.15376i	0.340863	−	0.250125i
$819$		−	2.68654i		−	0.0938754i
$820$	24.6368	+	7.74793i	0.860355	+	0.270570i
$821$		−	9.58055i		−	0.334364i	−0.985926	−	0.167182i	$-0.946533\pi$
$821$		−	9.58055i		−	0.334364i	0.985926	−	0.167182i	$-0.0534667\pi$
$822$	−19.0226	−	25.9235i	−0.663490	−	0.904185i
$823$	−36.0229			−1.25568			−0.627839	−	0.778343i	$-0.716060\pi$
$823$	−36.0229			−1.25568			−0.627839	+	0.778343i	$0.716060\pi$
$824$	10.7790	+	31.6386i	0.375505	+	1.10218i
$825$	−24.4844			−0.852439
$826$	−5.96288	−	8.12603i	−0.207475	−	0.282741i
$827$			20.6959i			0.719668i	0.933016	+	0.359834i	$0.117167\pi$
$827$			20.6959i			0.719668i	−0.933016	+	0.359834i	$0.882833\pi$
$828$	−0.0307343	+	0.0977287i	−0.00106809	+	0.00339631i
$829$		−	6.63330i		−	0.230384i	−0.993343	−	0.115192i	$-0.963252\pi$
$829$		−	6.63330i		−	0.230384i	0.993343	−	0.115192i	$-0.0367483\pi$
$830$	20.6176	−	15.1292i	0.715647	−	0.525141i
$831$	−46.1538			−1.60106
$832$	4.88416	+	6.33601i	0.169328	+	0.219661i
$833$	0.570087			0.0197523
$834$	33.2661	−	24.4106i	1.15191	−	0.845272i
$835$		−	26.4610i		−	0.915721i
$836$	−6.37760	+	20.2794i	−0.220574	+	0.701379i
$837$			2.90181i			0.100301i
$838$	−0.455851	−	0.621220i	−0.0157471	−	0.0214597i
$839$	−2.63463			−0.0909576			−0.0454788	−	0.998965i	$-0.514481\pi$
$839$	−2.63463			−0.0909576			−0.0454788	+	0.998965i	$0.514481\pi$
$840$	3.47292	+	10.1937i	0.119827	+	0.351717i
$841$	28.4493			0.981009
$842$	29.0995	+	39.6559i	1.00283	+	1.36663i
$843$		−	6.60778i		−	0.227584i
$844$	11.3459	+	3.56811i	0.390541	+	0.122820i
$845$			1.59665i			0.0549264i
$846$	−16.3495	+	11.9972i	−0.562106	+	0.412473i
$847$	6.55279			0.225156
$848$	10.5527	−	15.1183i	0.362381	−	0.519166i
$849$	−65.9848			−2.26459
$850$	−1.59296	+	1.16891i	−0.0546382	+	0.0400934i
$851$			0.0339345i			0.00116326i
$852$	1.93501	+	0.608535i	0.0662925	+	0.0208481i
$853$		−	17.6477i		−	0.604247i	−0.953269	−	0.302123i	$-0.902305\pi$
$853$		−	17.6477i		−	0.604247i	0.953269	−	0.302123i	$-0.0976955\pi$
$854$	8.94905	+	12.1955i	0.306230	+	0.417321i
$855$	10.8827			0.372179
$856$	44.3911	−	15.1237i	1.51726	−	0.516917i
$857$	5.05243			0.172588			0.0862939	−	0.996270i	$-0.472498\pi$
$857$	5.05243			0.172588			0.0862939	+	0.996270i	$0.472498\pi$
$858$	−8.35884	−	11.3912i	−0.285366	−	0.388889i
$859$		−	39.4750i		−	1.34687i	−0.739247	−	0.673434i	$-0.764818\pi$
$859$		−	39.4750i		−	1.34687i	0.739247	−	0.673434i	$-0.235182\pi$
$860$	11.3041	−	35.9448i	0.385467	−	1.22571i
$861$		−	19.2863i		−	0.657276i
$862$	46.3685	−	34.0252i	1.57932	−	1.15890i
$863$	2.70602			0.0921141			0.0460571	−	0.998939i	$-0.485334\pi$
$863$	2.70602			0.0921141			0.0460571	+	0.998939i	$0.485334\pi$
$864$	−0.100058	−	4.22723i	−0.00340406	−	0.143813i
$865$	−5.56388			−0.189178
$866$	−45.2802	+	33.2266i	−1.53868	+	1.12908i
$867$			39.7640i			1.35046i
$868$	2.32926	−	7.40657i	0.0790602	−	0.251395i
$869$		−	5.47035i		−	0.185569i
$870$	2.36407	+	3.22168i	0.0801493	+	0.109225i
$871$	−8.45532			−0.286498
$872$	−31.9719	+	10.8926i	−1.08270	+	0.368868i
$873$	12.8947			0.436421
$874$	0.0404724	+	0.0551546i	0.00136900	+	0.00186563i
$875$			11.8962i			0.402164i
$876$	−37.2520	−	11.7152i	−1.25863	−	0.395821i
$877$			39.6508i			1.33891i	0.742852	+	0.669456i	$0.233473\pi$
$877$			39.6508i			1.33891i	−0.742852	+	0.669456i	$0.766527\pi$
$878$	16.2153	−	11.8987i	0.547239	−	0.401563i
$879$	−11.2614			−0.379839
$880$	21.9410	+	15.3149i	0.739630	+	0.516266i
$881$	−43.1406			−1.45344			−0.726721	−	0.686932i	$-0.758957\pi$
$881$	−43.1406			−1.45344			−0.726721	+	0.686932i	$0.758957\pi$
$882$	3.06313	−	2.24772i	0.103141	−	0.0756848i
$883$			56.2653i			1.89348i	0.322001	+	0.946739i	$0.395644\pi$
$883$			56.2653i			1.89348i	−0.322001	+	0.946739i	$0.604356\pi$
$884$	−1.08766	−	0.342052i	−0.0365818	−	0.0115045i
$885$			27.1357i			0.912155i
$886$	16.2935	+	22.2044i	0.547392	+	0.745970i
$887$	11.6364			0.390712			0.195356	−	0.980732i	$-0.437414\pi$
$887$	11.6364			0.390712			0.195356	+	0.980732i	$0.437414\pi$
$888$	3.87124	+	11.3629i	0.129910	+	0.381313i
$889$	−15.1726			−0.508873
$890$	−2.20282	−	3.00194i	−0.0738387	−	0.100625i
$891$			41.2346i			1.38141i
$892$	5.97814	−	19.0093i	0.200163	−	0.636477i
$893$			13.5416i			0.453153i
$894$	−5.36108	+	3.93396i	−0.179301	+	0.131571i
$895$	−35.3700			−1.18229
$896$	−3.13778	+	10.8699i	−0.104826	+	0.363137i
$897$	−0.0454676			−0.00151812
$898$	−15.7308	+	11.5433i	−0.524945	+	0.385204i
$899$		−	2.88100i		−	0.0960868i
$900$	−3.95038	+	12.5614i	−0.131679	+	0.418713i
$901$			2.62768i			0.0875406i
$902$	−28.3496	−	38.6340i	−0.943938	−	1.28637i
$903$	−28.1384			−0.936388
$904$	4.85795	+	14.2591i	0.161573	+	0.474249i
$905$	−27.0652			−0.899678
$906$	−33.0765	−	45.0757i	−1.09889	−	1.49754i
$907$			36.5641i			1.21409i	0.794667	+	0.607046i	$0.207645\pi$
$907$			36.5641i			1.21409i	−0.794667	+	0.607046i	$0.792355\pi$
$908$	19.9260	+	6.26645i	0.661268	+	0.207960i
$909$			20.0994i			0.666656i
$910$	−1.82046	+	1.33585i	−0.0603476	+	0.0442830i
$911$	40.3066			1.33542			0.667709	−	0.744423i	$-0.267275\pi$
$911$	40.3066			1.33542			0.667709	+	0.744423i	$0.267275\pi$
$912$	19.8440	+	13.8512i	0.657102	+	0.458661i
$913$	−47.4494			−1.57034
$914$	−47.1355	+	34.5880i	−1.55910	+	1.14407i
$915$		−	40.7250i		−	1.34633i
$916$	−50.7379	−	15.9564i	−1.67643	−	0.527213i
$917$			1.62340i			0.0536092i
$918$	0.356527	+	0.485864i	0.0117671	+	0.0160359i
$919$	34.0077			1.12181			0.560905	−	0.827880i	$-0.310453\pi$
$919$	34.0077			1.12181			0.560905	+	0.827880i	$0.310453\pi$
$920$	0.0815053	−	0.0277682i	0.00268715	−	0.000915490i
$921$	−48.2070			−1.58848
$922$	−2.51458	−	3.42680i	−0.0828133	−	0.112856i
$923$			0.425314i			0.0139994i
$924$	5.99444	−	19.0611i	0.197203	−	0.627064i
$925$			4.36172i			0.143412i
$926$	38.0958	−	27.9547i	1.25191	−	0.918648i
$927$	−31.7477			−1.04273
$928$	0.0993411	+	4.19692i	0.00326103	+	0.137771i
$929$	−23.9803			−0.786769			−0.393385	−	0.919374i	$-0.628696\pi$
$929$	−23.9803			−0.786769			−0.393385	+	0.919374i	$0.628696\pi$
$930$	−16.8528	+	12.3665i	−0.552624	+	0.405515i
$931$		−	2.53707i		−	0.0831491i
$932$	8.65192	−	27.5113i	0.283403	−	0.901163i
$933$		−	79.6941i		−	2.60907i
$934$	−29.3257	−	39.9642i	−0.959566	−	1.30767i
$935$	−3.81349			−0.124715
$936$	−7.19272	+	2.45050i	−0.235101	+	0.0800971i
$937$	−33.4215			−1.09183			−0.545917	−	0.837840i	$-0.683818\pi$
$937$	−33.4215			−1.09183			−0.545917	+	0.837840i	$0.683818\pi$
$938$	−7.07423	−	9.64055i	−0.230982	−	0.314775i
$939$			71.2280i			2.32444i
$940$	16.2592	+	5.11327i	0.530315	+	0.166777i
$941$		−	24.8842i		−	0.811201i	−0.914050	−	0.405600i	$-0.867062\pi$
$941$		−	24.8842i		−	0.811201i	0.914050	−	0.405600i	$-0.132938\pi$
$942$	−19.6241	+	14.4001i	−0.639387	+	0.469182i
$943$	−0.154206			−0.00502165
$944$	−16.3170	+	23.3766i	−0.531072	+	0.760842i
$945$	1.19347			0.0388236
$946$	−56.3664	+	41.3616i	−1.83263	+	1.34478i
$947$			40.0196i			1.30046i	0.759737	+	0.650231i	$0.225328\pi$
$947$			40.0196i			1.30046i	−0.759737	+	0.650231i	$0.774672\pi$
$948$	−5.94042	−	1.86818i	−0.192936	−	0.0606756i
$949$		−	8.18795i		−	0.265792i
$950$	5.20204	+	7.08919i	0.168777	+	0.230004i
$951$	−6.79327			−0.220287
$952$	−0.519998	−	1.52630i	−0.0168532	−	0.0494677i
$953$	45.4900			1.47356			0.736782	−	0.676130i	$-0.236344\pi$
$953$	45.4900			1.47356			0.736782	+	0.676130i	$0.236344\pi$
$954$	10.3603	+	14.1187i	0.335428	+	0.457111i
$955$			34.5427i			1.11777i
$956$	0.701392	−	2.23028i	0.0226846	−	0.0721325i
$957$		−	7.41437i		−	0.239673i
$958$	−19.3281	+	14.1829i	−0.624462	+	0.458230i
$959$	9.53449			0.307885
$960$	24.1240	−	18.5962i	0.778598	−	0.600189i
$961$	−15.9293			−0.513849
$962$	−2.02925	+	1.48906i	−0.0654258	+	0.0480094i
$963$			44.5441i			1.43541i
$964$	10.6091	−	33.7349i	0.341697	−	1.08653i
$965$		−	25.8333i		−	0.831602i
$966$	−0.0380409	−	0.0518410i	−0.00122395	−	0.00166796i
$967$	−60.9357			−1.95956			−0.979779	−	0.200081i	$-0.935879\pi$
$967$	−60.9357			−1.95956			−0.979779	+	0.200081i	$0.935879\pi$
$968$	−5.97705	−	17.5439i	−0.192110	−	0.563881i
$969$	−3.44903			−0.110799
$970$	−6.41175	−	8.73775i	−0.205869	−	0.280552i
$971$		−	40.4125i		−	1.29690i	−0.761257	−	0.648450i	$-0.775418\pi$
$971$		−	40.4125i		−	1.29690i	0.761257	−	0.648450i	$-0.224582\pi$
$972$	40.4995	+	12.7365i	1.29902	+	0.408524i
$973$			12.2351i			0.392238i
$974$	5.95399	−	4.36903i	0.190778	−	0.139993i
$975$	−5.84409			−0.187161
$976$	24.4884	−	35.0834i	0.783854	−	1.12299i
$977$	−19.0379			−0.609076			−0.304538	−	0.952500i	$-0.598502\pi$
$977$	−19.0379			−0.609076			−0.304538	+	0.952500i	$0.598502\pi$
$978$	−56.6410	+	41.5631i	−1.81118	+	1.32904i
$979$			6.90867i			0.220802i
$980$	−3.04621	−	0.957990i	−0.0973076	−	0.0306019i
$981$		−	32.0821i		−	1.02430i
$982$	7.87709	+	10.7347i	0.251368	+	0.342557i
$983$	29.8442			0.951883			0.475942	−	0.879477i	$-0.342107\pi$
$983$	29.8442			0.951883			0.475942	+	0.879477i	$0.342107\pi$
$984$	−51.6355	+	17.5918i	−1.64608	+	0.560806i
$985$	−24.3197			−0.774889
$986$	−0.353971	−	0.482381i	−0.0112727	−	0.0153621i
$987$		−	12.7281i		−	0.405139i
$988$	−1.52224	+	4.84042i	−0.0484290	+	0.153994i
$989$			0.224985i			0.00715410i
$990$	−20.4903	+	15.0357i	−0.651224	+	0.477867i
$991$	49.4336			1.57031			0.785154	−	0.619300i	$-0.212584\pi$
$991$	49.4336			1.57031			0.785154	+	0.619300i	$0.212584\pi$
$992$	−21.9543	+	0.519658i	−0.697050	+	0.0164992i
$993$	42.0737			1.33517
$994$	−0.484932	+	0.355843i	−0.0153811	+	0.0112866i
$995$		−	9.91530i		−	0.314336i
$996$	−16.2044	+	51.5267i	−0.513456	+	1.63269i
$997$			9.50971i			0.301176i	0.988597	+	0.150588i	$0.0481166\pi$
$997$			9.50971i			0.301176i	−0.988597	+	0.150588i	$0.951883\pi$
$998$	−21.9249	−	29.8786i	−0.694021	−	0.945791i
$999$	1.33035			0.0420905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.a.365.6	yes	34
4.3	odd	2		2912.2.c.a.1457.29		34
8.3	odd	2		2912.2.c.a.1457.6		34
8.5	even	2	inner	728.2.c.a.365.5	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.a.365.5	✓	34	8.5	even	2	inner
728.2.c.a.365.6	yes	34	1.1	even	1	trivial
2912.2.c.a.1457.6		34	8.3	odd	2
2912.2.c.a.1457.29		34	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14018 + 0.836660i) q^{2} -2.38465i q^{3} +(0.600001 - 1.90788i) q^{4} -1.59665i q^{5} +(1.99514 + 2.71892i) q^{6} -1.00000 q^{7} +(0.912139 + 2.67731i) q^{8} -2.68654 q^{9} +(1.33585 + 1.82046i) q^{10} -4.18960i q^{11} +(-4.54962 - 1.43079i) q^{12} -1.00000i q^{13} +(1.14018 - 0.836660i) q^{14} -3.80744 q^{15} +(-3.28000 - 2.28946i) q^{16} +0.570087 q^{17} +(3.06313 - 2.24772i) q^{18} -2.53707i q^{19} +(-3.04621 - 0.957990i) q^{20} +2.38465i q^{21} +(3.50527 + 4.77688i) q^{22} +0.0190668 q^{23} +(6.38445 - 2.17513i) q^{24} +2.45072 q^{25} +(0.836660 + 1.14018i) q^{26} -0.747485i q^{27} +(-0.600001 + 1.90788i) q^{28} +0.742125i q^{29} +(4.34115 - 3.18553i) q^{30} -3.88210 q^{31} +(5.65527 - 0.133860i) q^{32} -9.99073 q^{33} +(-0.649999 + 0.476969i) q^{34} +1.59665i q^{35} +(-1.61193 + 5.12560i) q^{36} +1.77977i q^{37} +(2.12266 + 2.89270i) q^{38} -2.38465 q^{39} +(4.27473 - 1.45636i) q^{40} -8.08770 q^{41} +(-1.99514 - 2.71892i) q^{42} +11.7998i q^{43} +(-7.99326 - 2.51377i) q^{44} +4.28946i q^{45} +(-0.0217395 + 0.0159524i) q^{46} -5.33750 q^{47} +(-5.45955 + 7.82164i) q^{48} +1.00000 q^{49} +(-2.79425 + 2.05042i) q^{50} -1.35946i q^{51} +(-1.90788 - 0.600001i) q^{52} +4.60925i q^{53} +(0.625390 + 0.852264i) q^{54} -6.68932 q^{55} +(-0.912139 - 2.67731i) q^{56} -6.05001 q^{57} +(-0.620906 - 0.846153i) q^{58} -7.12700i q^{59} +(-2.28447 + 7.26414i) q^{60} +10.6962i q^{61} +(4.42627 - 3.24799i) q^{62} +2.68654 q^{63} +(-6.33601 + 4.88416i) q^{64} -1.59665 q^{65} +(11.3912 - 8.35884i) q^{66} -8.45532i q^{67} +(0.342052 - 1.08766i) q^{68} -0.0454676i q^{69} +(-1.33585 - 1.82046i) q^{70} -0.425314 q^{71} +(-2.45050 - 7.19272i) q^{72} +8.18795 q^{73} +(-1.48906 - 2.02925i) q^{74} -5.84409i q^{75} +(-4.84042 - 1.52224i) q^{76} +4.18960i q^{77} +(2.71892 - 1.99514i) q^{78} +1.30570 q^{79} +(-3.65546 + 5.23700i) q^{80} -9.84212 q^{81} +(9.22140 - 6.76665i) q^{82} -11.3255i q^{83} +(4.54962 + 1.43079i) q^{84} -0.910228i q^{85} +(-9.87244 - 13.4539i) q^{86} +1.76971 q^{87} +(11.2169 - 3.82150i) q^{88} -1.64900 q^{89} +(-3.58882 - 4.89074i) q^{90} +1.00000i q^{91} +(0.0114401 - 0.0363771i) q^{92} +9.25743i q^{93} +(6.08569 - 4.46567i) q^{94} -4.05081 q^{95} +(-0.319209 - 13.4858i) q^{96} -4.79975 q^{97} +(-1.14018 + 0.836660i) q^{98} +11.2556i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 2 q^{2} - 2 q^{4} - 6 q^{6} - 34 q^{7} + 8 q^{8} - 26 q^{9} - 4 q^{12} - 2 q^{14} - 8 q^{15} - 6 q^{16} - 20 q^{17} + 14 q^{18} - 4 q^{20} - 10 q^{22} - 20 q^{23} + 10 q^{24} - 22 q^{25} + 2 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) \) 34 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 - 34 * q^7 + 8 * q^8 - 26 * q^9 - 4 * q^12 - 2 * q^14 - 8 * q^15 - 6 * q^16 - 20 * q^17 + 14 * q^18 - 4 * q^20 - 10 * q^22 - 20 * q^23 + 10 * q^24 - 22 * q^25 + 2 * q^28 - 60 * q^30 + 16 * q^31 + 12 * q^32 - 8 * q^33 + 28 * q^34 - 4 * q^36 - 28 * q^38 + 8 * q^39 + 64 * q^40 + 8 * q^41 + 6 * q^42 + 24 * q^44 + 16 * q^46 + 24 * q^48 + 34 * q^49 + 10 * q^50 - 4 * q^52 - 18 * q^54 - 32 * q^55 - 8 * q^56 + 8 * q^57 + 44 * q^58 - 24 * q^60 + 60 * q^62 + 26 * q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 12 * q^68 + 64 * q^71 - 92 * q^72 - 22 * q^74 + 4 * q^76 + 20 * q^79 - 56 * q^80 - 6 * q^81 - 20 * q^82 + 4 * q^84 - 12 * q^86 - 56 * q^87 - 34 * q^88 - 4 * q^90 - 54 * q^92 + 12 * q^94 + 42 * q^96 + 2 * q^98

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