LMFDB - Embedded newform 728.2.c.a.365.10

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			365.10
Character	$\chi$	$=$	728.365
Dual form			728.2.c.a.365.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.720007 + 1.21721i) q^{2} +2.66332i q^{3} +(-0.963179 - 1.75279i) q^{4} +2.77422i q^{5} +(-3.24180 - 1.91761i) q^{6} -1.00000 q^{7} +(2.82701 + 0.0896372i) q^{8} -4.09325 q^{9} +(-3.37680 - 1.99746i) q^{10} +2.30522i q^{11} +(4.66824 - 2.56525i) q^{12} -1.00000i q^{13} +(0.720007 - 1.21721i) q^{14} -7.38863 q^{15} +(-2.14457 + 3.37651i) q^{16} -6.69704 q^{17} +(2.94717 - 4.98233i) q^{18} -2.40379i q^{19} +(4.86264 - 2.67207i) q^{20} -2.66332i q^{21} +(-2.80592 - 1.65977i) q^{22} +5.02802 q^{23} +(-0.238732 + 7.52921i) q^{24} -2.69630 q^{25} +(1.21721 + 0.720007i) q^{26} -2.91168i q^{27} +(0.963179 + 1.75279i) q^{28} +4.22120i q^{29} +(5.31986 - 8.99348i) q^{30} -6.52105 q^{31} +(-2.56580 - 5.04150i) q^{32} -6.13952 q^{33} +(4.82192 - 8.15168i) q^{34} -2.77422i q^{35} +(3.94254 + 7.17463i) q^{36} -7.64478i q^{37} +(2.92591 + 1.73075i) q^{38} +2.66332 q^{39} +(-0.248673 + 7.84274i) q^{40} -1.66987 q^{41} +(3.24180 + 1.91761i) q^{42} +4.89973i q^{43} +(4.04057 - 2.22034i) q^{44} -11.3556i q^{45} +(-3.62021 + 6.12013i) q^{46} +13.5343 q^{47} +(-8.99271 - 5.71167i) q^{48} +1.00000 q^{49} +(1.94135 - 3.28195i) q^{50} -17.8363i q^{51} +(-1.75279 + 0.963179i) q^{52} -0.579570i q^{53} +(3.54412 + 2.09643i) q^{54} -6.39518 q^{55} +(-2.82701 - 0.0896372i) q^{56} +6.40205 q^{57} +(-5.13807 - 3.03929i) q^{58} +10.2153i q^{59} +(7.11657 + 12.9507i) q^{60} +7.92093i q^{61} +(4.69520 - 7.93746i) q^{62} +4.09325 q^{63} +(7.98393 + 0.506810i) q^{64} +2.77422 q^{65} +(4.42050 - 7.47306i) q^{66} -6.80101i q^{67} +(6.45045 + 11.7385i) q^{68} +13.3912i q^{69} +(3.37680 + 1.99746i) q^{70} +7.75298 q^{71} +(-11.5717 - 0.366908i) q^{72} -5.71664 q^{73} +(9.30527 + 5.50430i) q^{74} -7.18109i q^{75} +(-4.21335 + 2.31528i) q^{76} -2.30522i q^{77} +(-1.91761 + 3.24180i) q^{78} +12.0537 q^{79} +(-9.36718 - 5.94951i) q^{80} -4.52503 q^{81} +(1.20232 - 2.03258i) q^{82} -0.262559i q^{83} +(-4.66824 + 2.56525i) q^{84} -18.5791i q^{85} +(-5.96397 - 3.52784i) q^{86} -11.2424 q^{87} +(-0.206633 + 6.51686i) q^{88} -14.0431 q^{89} +(13.8221 + 8.17611i) q^{90} +1.00000i q^{91} +(-4.84288 - 8.81308i) q^{92} -17.3676i q^{93} +(-9.74482 + 16.4741i) q^{94} +6.66864 q^{95} +(13.4271 - 6.83353i) q^{96} -15.9382 q^{97} +(-0.720007 + 1.21721i) q^{98} -9.43584i 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 $

$2$	−0.720007	+	1.21721i	−0.509122	+	0.860694i
$2$	−0.720007	+	1.21721i	−0.509122	+	0.860694i
$3$			2.66332i			1.53767i	0.639449	+	0.768833i	$0.279162\pi$
$3$			2.66332i			1.53767i	−0.639449	+	0.768833i	$0.720838\pi$
$4$	−0.963179	−	1.75279i	−0.481590	−	0.876397i
$5$			2.77422i			1.24067i	0.784337	+	0.620334i	$0.213003\pi$
$5$			2.77422i			1.24067i	−0.784337	+	0.620334i	$0.786997\pi$
$6$	−3.24180	−	1.91761i	−1.32346	−	0.782860i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.82701	+	0.0896372i	0.999498	+	0.0316915i
$9$	−4.09325			−1.36442
$10$	−3.37680	−	1.99746i	−1.06784	−	0.631652i
$11$			2.30522i			0.695049i	0.937671	+	0.347524i	$0.112978\pi$
$11$			2.30522i			0.695049i	−0.937671	+	0.347524i	$0.887022\pi$
$12$	4.66824	−	2.56525i	1.34761	−	0.740524i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	0.720007	−	1.21721i	0.192430	−	0.325312i
$15$	−7.38863			−1.90773
$16$	−2.14457	+	3.37651i	−0.536143	+	0.844127i
$17$	−6.69704			−1.62427			−0.812135	−	0.583469i	$-0.801695\pi$
$17$	−6.69704			−1.62427			−0.812135	+	0.583469i	$0.801695\pi$
$18$	2.94717	−	4.98233i	0.694655	−	1.17435i
$19$		−	2.40379i		−	0.551467i	−0.961234	−	0.275734i	$-0.911079\pi$
$19$		−	2.40379i		−	0.551467i	0.961234	−	0.275734i	$-0.0889208\pi$
$20$	4.86264	−	2.67207i	1.08732	−	0.597493i
$21$		−	2.66332i		−	0.581183i
$22$	−2.80592	−	1.65977i	−0.598225	−	0.353865i
$23$	5.02802			1.04841			0.524207	−	0.851591i	$-0.324362\pi$
$23$	5.02802			1.04841			0.524207	+	0.851591i	$0.324362\pi$
$24$	−0.238732	+	7.52921i	−0.0487310	+	1.53689i
$25$	−2.69630			−0.539259
$26$	1.21721	+	0.720007i	0.238714	+	0.141205i
$27$		−	2.91168i		−	0.560354i
$28$	0.963179	+	1.75279i	0.182024	+	0.331247i
$29$			4.22120i			0.783857i	0.919996	+	0.391929i	$0.128192\pi$
$29$			4.22120i			0.783857i	−0.919996	+	0.391929i	$0.871808\pi$
$30$	5.31986	−	8.99348i	0.971270	−	1.64198i
$31$	−6.52105			−1.17122			−0.585608	−	0.810595i	$-0.699144\pi$
$31$	−6.52105			−1.17122			−0.585608	+	0.810595i	$0.699144\pi$
$32$	−2.56580	−	5.04150i	−0.453573	−	0.891219i
$33$	−6.13952			−1.06875
$34$	4.82192	−	8.15168i	0.826952	−	1.39800i
$35$		−	2.77422i		−	0.468929i
$36$	3.94254	+	7.17463i	0.657090	+	1.19577i
$37$		−	7.64478i		−	1.25679i	−0.777893	−	0.628397i	$-0.783711\pi$
$37$		−	7.64478i		−	1.25679i	0.777893	−	0.628397i	$-0.216289\pi$
$38$	2.92591	+	1.73075i	0.474645	+	0.280764i
$39$	2.66332			0.426472
$40$	−0.248673	+	7.84274i	−0.0393187	+	1.24005i
$41$	−1.66987			−0.260790			−0.130395	−	0.991462i	$-0.541625\pi$
$41$	−1.66987			−0.260790			−0.130395	+	0.991462i	$0.541625\pi$
$42$	3.24180	+	1.91761i	0.500221	+	0.295893i
$43$			4.89973i			0.747201i	0.927590	+	0.373601i	$0.121877\pi$
$43$			4.89973i			0.747201i	−0.927590	+	0.373601i	$0.878123\pi$
$44$	4.04057	−	2.22034i	0.609139	−	0.334728i
$45$		−	11.3556i		−	1.69279i
$46$	−3.62021	+	6.12013i	−0.533771	+	0.902364i
$47$	13.5343			1.97419			0.987093	−	0.160148i	$-0.0511970\pi$
$47$	13.5343			1.97419			0.987093	+	0.160148i	$0.0511970\pi$
$48$	−8.99271	−	5.71167i	−1.29799	−	0.824409i
$49$	1.00000			0.142857
$50$	1.94135	−	3.28195i	0.274549	−	0.464137i
$51$		−	17.8363i		−	2.49759i
$52$	−1.75279	+	0.963179i	−0.243069	+	0.133569i
$53$		−	0.579570i		−	0.0796101i	−0.999207	−	0.0398050i	$-0.987326\pi$
$53$		−	0.579570i		−	0.0796101i	0.999207	−	0.0398050i	$-0.0126737\pi$
$54$	3.54412	+	2.09643i	0.482293	+	0.285288i
$55$	−6.39518			−0.862325
$56$	−2.82701	−	0.0896372i	−0.377775	−	0.0119783i
$57$	6.40205			0.847973
$58$	−5.13807	−	3.03929i	−0.674661	−	0.399079i
$59$			10.2153i			1.32992i	0.746880	+	0.664959i	$0.231551\pi$
$59$			10.2153i			1.32992i	−0.746880	+	0.664959i	$0.768449\pi$
$60$	7.11657	+	12.9507i	0.918745	+	1.67193i
$61$			7.92093i			1.01417i	0.861896	+	0.507086i	$0.169277\pi$
$61$			7.92093i			1.01417i	−0.861896	+	0.507086i	$0.830723\pi$
$62$	4.69520	−	7.93746i	0.596291	−	1.00806i
$63$	4.09325			0.515702
$64$	7.98393	+	0.506810i	0.997991	+	0.0633512i
$65$	2.77422			0.344100
$66$	4.42050	−	7.47306i	0.544126	−	0.919870i
$67$		−	6.80101i		−	0.830876i	−0.909621	−	0.415438i	$-0.863628\pi$
$67$		−	6.80101i		−	0.830876i	0.909621	−	0.415438i	$-0.136372\pi$
$68$	6.45045	+	11.7385i	0.782232	+	1.42351i
$69$			13.3912i			1.61211i
$70$	3.37680	+	1.99746i	0.403604	+	0.238742i
$71$	7.75298			0.920110			0.460055	−	0.887890i	$-0.347830\pi$
$71$	7.75298			0.920110			0.460055	+	0.887890i	$0.347830\pi$
$72$	−11.5717	−	0.366908i	−1.36373	−	0.0432405i
$73$	−5.71664			−0.669082			−0.334541	−	0.942381i	$-0.608581\pi$
$73$	−5.71664			−0.669082			−0.334541	+	0.942381i	$0.608581\pi$
$74$	9.30527	+	5.50430i	1.08172	+	0.639862i
$75$		−	7.18109i		−	0.829201i
$76$	−4.21335	+	2.31528i	−0.483304	+	0.265581i
$77$		−	2.30522i		−	0.262704i
$78$	−1.91761	+	3.24180i	−0.217126	+	0.367062i
$79$	12.0537			1.35615			0.678076	−	0.734992i	$-0.262814\pi$
$79$	12.0537			1.35615			0.678076	+	0.734992i	$0.262814\pi$
$80$	−9.36718	−	5.94951i	−1.04728	−	0.665176i
$81$	−4.52503			−0.502781
$82$	1.20232	−	2.03258i	0.132774	−	0.224461i
$83$		−	0.262559i		−	0.0288196i	−0.999896	−	0.0144098i	$-0.995413\pi$
$83$		−	0.262559i		−	0.0288196i	0.999896	−	0.0144098i	$-0.00458695\pi$
$84$	−4.66824	+	2.56525i	−0.509347	+	0.279892i
$85$		−	18.5791i		−	2.01518i
$86$	−5.96397	−	3.52784i	−0.643112	−	0.380417i
$87$	−11.2424			−1.20531
$88$	−0.206633	+	6.51686i	−0.0220272	+	0.694700i
$89$	−14.0431			−1.48857			−0.744283	−	0.667865i	$-0.767208\pi$
$89$	−14.0431			−1.48857			−0.744283	+	0.667865i	$0.767208\pi$
$90$	13.8221	+	8.17611i	1.45698	+	0.861837i
$91$			1.00000i			0.104828i
$92$	−4.84288	−	8.81308i	−0.504905	−	0.918827i
$93$		−	17.3676i		−	1.80094i
$94$	−9.74482	+	16.4741i	−1.00510	+	1.69917i
$95$	6.66864			0.684188
$96$	13.4271	−	6.83353i	1.37040	−	0.697444i
$97$	−15.9382			−1.61828			−0.809142	−	0.587613i	$-0.800068\pi$
$97$	−15.9382			−1.61828			−0.809142	+	0.587613i	$0.800068\pi$
$98$	−0.720007	+	1.21721i	−0.0727317	+	0.122956i
$99$		−	9.43584i		−	0.948337i
$100$	2.59702	+	4.72605i	0.259702	+	0.472605i
$101$		−	11.8085i		−	1.17499i	−0.809229	−	0.587494i	$-0.800115\pi$
$101$		−	11.8085i		−	1.17499i	0.809229	−	0.587494i	$-0.199885\pi$
$102$	21.7105	+	12.8423i	2.14966	+	1.27158i
$103$	−2.80041			−0.275933			−0.137966	−	0.990437i	$-0.544057\pi$
$103$	−2.80041			−0.275933			−0.137966	+	0.990437i	$0.544057\pi$
$104$	0.0896372	−	2.82701i	0.00878965	−	0.277211i
$105$	7.38863			0.721056
$106$	0.705456	+	0.417295i	0.0685200	+	0.0405313i
$107$			2.80406i			0.271079i	0.990772	+	0.135539i	$0.0432767\pi$
$107$			2.80406i			0.271079i	−0.990772	+	0.135539i	$0.956723\pi$
$108$	−5.10358	+	2.80447i	−0.491092	+	0.269860i
$109$			9.23050i			0.884122i	0.896985	+	0.442061i	$0.145753\pi$
$109$			9.23050i			0.884122i	−0.896985	+	0.442061i	$0.854247\pi$
$110$	4.60457	−	7.78424i	0.439029	−	0.742198i
$111$	20.3605			1.93253
$112$	2.14457	−	3.37651i	0.202643	−	0.319050i
$113$	7.99544			0.752148			0.376074	−	0.926590i	$-0.377274\pi$
$113$	7.99544			0.752148			0.376074	+	0.926590i	$0.377274\pi$
$114$	−4.60952	+	7.79262i	−0.431722	+	0.729845i
$115$			13.9488i			1.30074i
$116$	7.39889	−	4.06577i	0.686970	−	0.377497i
$117$			4.09325i			0.378422i
$118$	−12.4341	−	7.35508i	−1.14465	−	0.677090i
$119$	6.69704			0.613917
$120$	−20.8877	−	0.662296i	−1.90678	−	0.0604590i
$121$	5.68598			0.516907
$122$	−9.64140	−	5.70313i	−0.872891	−	0.516337i
$123$		−	4.44740i		−	0.401008i
$124$	6.28094	+	11.4301i	0.564045	+	1.02645i
$125$			6.39098i			0.571627i
$126$	−2.94717	+	4.98233i	−0.262555	+	0.443861i
$127$	−9.95073			−0.882985			−0.441492	−	0.897265i	$-0.645551\pi$
$127$	−9.95073			−0.882985			−0.441492	+	0.897265i	$0.645551\pi$
$128$	−6.36538	+	9.35318i	−0.562625	+	0.826712i
$129$	−13.0495			−1.14895
$130$	−1.99746	+	3.37680i	−0.175189	+	0.296165i
$131$			0.170370i			0.0148853i	0.999972	+	0.00744265i	$0.00236909\pi$
$131$			0.170370i			0.0148853i	−0.999972	+	0.00744265i	$0.997631\pi$
$132$	5.91346	+	10.7613i	0.514700	+	0.936652i
$133$			2.40379i			0.208435i
$134$	8.27823	+	4.89678i	0.715130	+	0.423017i
$135$	8.07765			0.695213
$136$	−18.9326	−	0.600304i	−1.62346	−	0.0514756i
$137$	−21.3225			−1.82170			−0.910852	−	0.412734i	$-0.864574\pi$
$137$	−21.3225			−1.82170			−0.910852	+	0.412734i	$0.864574\pi$
$138$	−16.2999	−	9.64177i	−1.38754	−	0.820762i
$139$			2.75623i			0.233781i	0.993145	+	0.116890i	$0.0372926\pi$
$139$			2.75623i			0.233781i	−0.993145	+	0.116890i	$0.962707\pi$
$140$	−4.86264	+	2.67207i	−0.410968	+	0.225831i
$141$			36.0462i			3.03564i
$142$	−5.58220	+	9.43698i	−0.468448	+	0.791933i
$143$	2.30522			0.192772
$144$	8.77828	−	13.8209i	0.731523	−	1.15174i
$145$	−11.7105			−0.972507
$146$	4.11602	−	6.95833i	0.340644	−	0.575875i
$147$			2.66332i			0.219667i
$148$	−13.3997	+	7.36329i	−1.10145	+	0.605259i
$149$		−	4.75728i		−	0.389732i	−0.980830	−	0.194866i	$-0.937573\pi$
$149$		−	4.75728i		−	0.389732i	0.980830	−	0.194866i	$-0.0624271\pi$
$150$	8.74086	+	5.17044i	0.713688	+	0.422164i
$151$	−6.72897			−0.547596			−0.273798	−	0.961787i	$-0.588280\pi$
$151$	−6.72897			−0.547596			−0.273798	+	0.961787i	$0.588280\pi$
$152$	0.215469	−	6.79553i	0.0174768	−	0.551190i
$153$	27.4127			2.21618
$154$	2.80592	+	1.65977i	0.226108	+	0.133748i
$155$		−	18.0908i		−	1.45309i
$156$	−2.56525	−	4.66824i	−0.205384	−	0.373759i
$157$			7.37175i			0.588330i	0.955755	+	0.294165i	$0.0950415\pi$
$157$			7.37175i			0.588330i	−0.955755	+	0.294165i	$0.904958\pi$
$158$	−8.67878	+	14.6719i	−0.690446	+	1.16723i
$159$	1.54358			0.122414
$160$	13.9862	−	7.11809i	1.10571	−	0.562734i
$161$	−5.02802			−0.396263
$162$	3.25805	−	5.50789i	0.255977	−	0.432741i
$163$			10.1735i			0.796853i	0.917200	+	0.398426i	$0.130444\pi$
$163$			10.1735i			0.796853i	−0.917200	+	0.398426i	$0.869556\pi$
$164$	1.60839	+	2.92694i	0.125594	+	0.228556i
$165$		−	17.0324i		−	1.32597i
$166$	0.319589	+	0.189045i	0.0248049	+	0.0146727i
$167$	−20.1675			−1.56061			−0.780303	−	0.625401i	$-0.784935\pi$
$167$	−20.1675			−1.56061			−0.780303	+	0.625401i	$0.784935\pi$
$168$	0.238732	−	7.52921i	0.0184186	−	0.580891i
$169$	−1.00000			−0.0769231
$170$	22.6145	+	13.3771i	1.73446	+	1.02597i
$171$			9.83932i			0.752432i
$172$	8.58821	−	4.71931i	0.654845	−	0.359844i
$173$			5.41669i			0.411823i	0.978571	+	0.205911i	$0.0660159\pi$
$173$			5.41669i			0.411823i	−0.978571	+	0.205911i	$0.933984\pi$
$174$	8.09460	−	13.6843i	0.613650	−	1.03740i
$175$	2.69630			0.203821
$176$	−7.78358	−	4.94370i	−0.586710	−	0.372646i
$177$	−27.2065			−2.04497
$178$	10.1111	−	17.0933i	0.757861	−	1.28120i
$179$			6.79698i			0.508030i	0.967200	+	0.254015i	$0.0817513\pi$
$179$			6.79698i			0.508030i	−0.967200	+	0.254015i	$0.918249\pi$
$180$	−19.9040	+	10.9375i	−1.48356	+	0.815231i
$181$			14.9174i			1.10880i	0.832249	+	0.554402i	$0.187053\pi$
$181$			14.9174i			1.10880i	−0.832249	+	0.554402i	$0.812947\pi$
$182$	−1.21721	−	0.720007i	−0.0902253	−	0.0533705i
$183$	−21.0959			−1.55946
$184$	14.2142	+	0.450698i	1.04789	+	0.0332259i
$185$	21.2083			1.55927
$186$	21.1400	+	12.5048i	1.55006	+	0.916897i
$187$		−	15.4381i		−	1.12895i
$188$	−13.0360	−	23.7229i	−0.950747	−	1.73017i
$189$			2.91168i			0.211794i
$190$	−4.80147	+	8.11711i	−0.348335	+	0.588877i
$191$	−13.5542			−0.980744			−0.490372	−	0.871513i	$-0.663139\pi$
$191$	−13.5542			−0.980744			−0.490372	+	0.871513i	$0.663139\pi$
$192$	−1.34980	+	21.2637i	−0.0974131	+	1.53458i
$193$	−4.61365			−0.332098			−0.166049	−	0.986118i	$-0.553101\pi$
$193$	−4.61365			−0.332098			−0.166049	+	0.986118i	$0.553101\pi$
$194$	11.4757	−	19.4001i	0.823904	−	1.39285i
$195$			7.38863i			0.529110i
$196$	−0.963179	−	1.75279i	−0.0687985	−	0.125200i
$197$		−	5.21055i		−	0.371236i	−0.982622	−	0.185618i	$-0.940571\pi$
$197$		−	5.21055i		−	0.371236i	0.982622	−	0.185618i	$-0.0594287\pi$
$198$	11.4854	+	6.79387i	0.816228	+	0.482819i
$199$	23.8017			1.68726			0.843629	−	0.536927i	$-0.180415\pi$
$199$	23.8017			1.68726			0.843629	+	0.536927i	$0.180415\pi$
$200$	−7.62244	−	0.241688i	−0.538988	−	0.0170899i
$201$	18.1133			1.27761
$202$	14.3733	+	8.50219i	1.01130	+	0.598212i
$203$		−	4.22120i		−	0.296270i
$204$	−31.2634	+	17.1796i	−2.18888	+	1.20281i
$205$		−	4.63259i		−	0.323554i
$206$	2.01632	−	3.40867i	0.140483	−	0.237494i
$207$	−20.5810			−1.43048
$208$	3.37651	+	2.14457i	0.234119	+	0.148699i
$209$	5.54125			0.383297
$210$	−5.31986	+	8.99348i	−0.367105	+	0.620609i
$211$			9.64867i			0.664242i	0.943237	+	0.332121i	$0.107764\pi$
$211$			9.64867i			0.664242i	−0.943237	+	0.332121i	$0.892236\pi$
$212$	−1.01587	+	0.558230i	−0.0697700	+	0.0383394i
$213$			20.6487i			1.41482i
$214$	−3.41312	−	2.01894i	−0.233316	−	0.138012i
$215$	−13.5929			−0.927029
$216$	0.260995	−	8.23135i	0.0177585	−	0.560072i
$217$	6.52105			0.442678
$218$	−11.2354	−	6.64603i	−0.760959	−	0.450126i
$219$		−	15.2252i		−	1.02883i
$220$	6.15970	+	11.2094i	0.415287	+	0.755739i
$221$			6.69704i			0.450492i
$222$	−14.6597	+	24.7829i	−0.983894	+	1.66332i
$223$	−1.12765			−0.0755129			−0.0377565	−	0.999287i	$-0.512021\pi$
$223$	−1.12765			−0.0755129			−0.0377565	+	0.999287i	$0.512021\pi$
$224$	2.56580	+	5.04150i	0.171435	+	0.336849i
$225$	11.0366			0.735775
$226$	−5.75678	+	9.73210i	−0.382935	+	0.647370i
$227$			28.0410i			1.86115i	0.366103	+	0.930574i	$0.380692\pi$
$227$			28.0410i			1.86115i	−0.366103	+	0.930574i	$0.619308\pi$
$228$	−6.16632	−	11.2215i	−0.408375	−	0.743161i
$229$			19.7757i			1.30682i	0.757006	+	0.653408i	$0.226662\pi$
$229$			19.7757i			1.30682i	−0.757006	+	0.653408i	$0.773338\pi$
$230$	−16.9786	−	10.0433i	−1.11954	−	0.662233i
$231$	6.13952			0.403951
$232$	−0.378376	+	11.9334i	−0.0248416	+	0.783463i
$233$	−26.7490			−1.75239			−0.876194	−	0.481958i	$-0.839926\pi$
$233$	−26.7490			−1.75239			−0.876194	+	0.481958i	$0.839926\pi$
$234$	−4.98233	−	2.94717i	−0.325705	−	0.192663i
$235$			37.5472i			2.44931i
$236$	17.9053	−	9.83915i	1.16554	−	0.640474i
$237$			32.1029i			2.08531i
$238$	−4.82192	+	8.15168i	−0.312559	+	0.528395i
$239$	19.6982			1.27417			0.637086	−	0.770793i	$-0.280140\pi$
$239$	19.6982			1.27417			0.637086	+	0.770793i	$0.280140\pi$
$240$	15.8454	−	24.9478i	1.02282	−	1.61037i
$241$	8.31281			0.535475			0.267738	−	0.963492i	$-0.413724\pi$
$241$	8.31281			0.535475			0.267738	+	0.963492i	$0.413724\pi$
$242$	−4.09395	+	6.92101i	−0.263169	+	0.444899i
$243$		−	20.7866i		−	1.33346i
$244$	13.8838	−	7.62927i	0.888816	−	0.488414i
$245$			2.77422i			0.177238i
$246$	5.41340	+	3.20216i	0.345146	+	0.204162i
$247$	−2.40379			−0.152949
$248$	−18.4351	−	0.584529i	−1.17063	−	0.0371176i
$249$	0.699279			0.0443150
$250$	−7.77914	−	4.60155i	−0.491996	−	0.291028i
$251$		−	24.2860i		−	1.53292i	−0.642292	−	0.766460i	$-0.722016\pi$
$251$		−	24.2860i		−	1.53292i	0.642292	−	0.766460i	$-0.277984\pi$
$252$	−3.94254	−	7.17463i	−0.248357	−	0.451959i
$253$			11.5907i			0.728699i
$254$	7.16460	−	12.1121i	0.449547	−	0.759980i
$255$	49.4819			3.09868
$256$	−6.80162	−	14.4823i	−0.425101	−	0.905146i
$257$	11.7809			0.734871			0.367436	−	0.930049i	$-0.380236\pi$
$257$	11.7809			0.734871			0.367436	+	0.930049i	$0.380236\pi$
$258$	9.39575	−	15.8840i	0.584954	−	0.988892i
$259$			7.64478i			0.475024i
$260$	−2.67207	−	4.86264i	−0.165715	−	0.301568i
$261$		−	17.2784i		−	1.06951i
$262$	−0.207375	−	0.122668i	−0.0128117	−	0.00757843i
$263$	16.2221			1.00029			0.500147	−	0.865940i	$-0.333279\pi$
$263$	16.2221			1.00029			0.500147	+	0.865940i	$0.333279\pi$
$264$	−17.3565	−	0.550329i	−1.06822	−	0.0338704i
$265$	1.60786			0.0987698
$266$	−2.92591	−	1.73075i	−0.179399	−	0.106119i
$267$		−	37.4012i		−	2.28892i
$268$	−11.9208	+	6.55060i	−0.728177	+	0.400141i
$269$			26.4552i			1.61300i	0.591233	+	0.806501i	$0.298641\pi$
$269$			26.4552i			1.61300i	−0.591233	+	0.806501i	$0.701359\pi$
$270$	−5.81597	+	9.83216i	−0.353948	+	0.598366i
$271$	−21.9987			−1.33633			−0.668164	−	0.744014i	$-0.732920\pi$
$271$	−21.9987			−1.33633			−0.668164	+	0.744014i	$0.732920\pi$
$272$	14.3623	−	22.6126i	0.870842	−	1.37109i
$273$	−2.66332			−0.161191
$274$	15.3523	−	25.9539i	0.927469	−	1.56793i
$275$		−	6.21554i		−	0.374811i
$276$	23.4720	−	12.8981i	1.41285	−	0.776376i
$277$			8.68422i			0.521784i	0.965368	+	0.260892i	$0.0840167\pi$
$277$			8.68422i			0.521784i	−0.965368	+	0.260892i	$0.915983\pi$
$278$	−3.35490	−	1.98451i	−0.201214	−	0.119023i
$279$	26.6923			1.59803
$280$	0.248673	−	7.84274i	0.0148611	−	0.468693i
$281$	33.4194			1.99363			0.996817	−	0.0797253i	$-0.0254043\pi$
$281$	33.4194			1.99363			0.996817	+	0.0797253i	$0.0254043\pi$
$282$	−43.8757	−	25.9535i	−2.61276	−	1.54551i
$283$		−	23.1585i		−	1.37663i	−0.725412	−	0.688314i	$-0.758351\pi$
$283$		−	23.1585i		−	1.37663i	0.725412	−	0.688314i	$-0.241649\pi$
$284$	−7.46751	−	13.5894i	−0.443115	−	0.806382i
$285$			17.7607i			1.05205i
$286$	−1.65977	+	2.80592i	−0.0981444	+	0.165918i
$287$	1.66987			0.0985695
$288$	10.5025	+	20.6361i	0.618864	+	1.21600i
$289$	27.8504			1.63826
$290$	8.43167	−	14.2541i	0.495125	−	0.837031i
$291$		−	42.4486i		−	2.48838i
$292$	5.50615	+	10.0201i	0.322223	+	0.586381i
$293$		−	20.2527i		−	1.18318i	−0.806241	−	0.591588i	$-0.798501\pi$
$293$		−	20.2527i		−	1.18318i	0.806241	−	0.591588i	$-0.201499\pi$
$294$	−3.24180	−	1.91761i	−0.189066	−	0.111837i
$295$	−28.3395			−1.64999
$296$	0.685257	−	21.6118i	0.0398297	−	1.25616i
$297$	6.71206			0.389473
$298$	5.79059	+	3.42528i	0.335440	+	0.198421i
$299$		−	5.02802i		−	0.290778i
$300$	−12.5870	+	6.91667i	−0.726709	+	0.399334i
$301$		−	4.89973i		−	0.282416i
$302$	4.84491	−	8.19054i	0.278793	−	0.471313i
$303$	31.4497			1.80674
$304$	8.11642	+	5.15510i	0.465508	+	0.295665i
$305$	−21.9744			−1.25825
$306$	−19.7373	+	33.3669i	−1.12831	+	1.90746i
$307$		−	11.4584i		−	0.653968i	−0.945030	−	0.326984i	$-0.893968\pi$
$307$		−	11.4584i		−	0.653968i	0.945030	−	0.326984i	$-0.106032\pi$
$308$	−4.04057	+	2.22034i	−0.230233	+	0.126515i
$309$		−	7.45838i		−	0.424292i
$310$	22.0203	+	13.0255i	1.25067	+	0.739800i
$311$	7.17869			0.407066			0.203533	−	0.979068i	$-0.434758\pi$
$311$	7.17869			0.407066			0.203533	+	0.979068i	$0.434758\pi$
$312$	7.52921	+	0.238732i	0.426258	+	0.0135156i
$313$	28.1120			1.58898			0.794492	−	0.607275i	$-0.207737\pi$
$313$	28.1120			1.58898			0.794492	+	0.607275i	$0.207737\pi$
$314$	−8.97294	−	5.30772i	−0.506372	−	0.299532i
$315$			11.3556i			0.639815i
$316$	−11.6099	−	21.1277i	−0.653108	−	1.18853i
$317$		−	15.6537i		−	0.879198i	−0.898194	−	0.439599i	$-0.855120\pi$
$317$		−	15.6537i		−	0.879198i	0.898194	−	0.439599i	$-0.144880\pi$
$318$	−1.11139	+	1.87885i	−0.0623235	+	0.105361i
$319$	−9.73078			−0.544819
$320$	−1.40600	+	22.1492i	−0.0785979	+	1.23818i
$321$	−7.46810			−0.416829
$322$	3.62021	−	6.12013i	0.201746	−	0.341062i
$323$			16.0983i			0.895732i
$324$	4.35841	+	7.93144i	0.242134	+	0.440636i
$325$			2.69630i			0.149564i
$326$	−12.3833	−	7.32502i	−0.685847	−	0.405695i
$327$	−24.5838			−1.35948
$328$	−4.72074	−	0.149683i	−0.260659	−	0.00826484i
$329$	−13.5343			−0.746172
$330$	20.7319	+	12.2634i	1.14125	+	0.675080i
$331$		−	17.1765i		−	0.944106i	−0.881570	−	0.472053i	$-0.843513\pi$
$331$		−	17.1765i		−	0.944106i	0.881570	−	0.472053i	$-0.156487\pi$
$332$	−0.460212	+	0.252892i	−0.0252574	+	0.0138792i
$333$			31.2920i			1.71479i
$334$	14.5207	−	24.5480i	0.794539	−	1.34321i
$335$	18.8675			1.03084
$336$	8.99271	+	5.71167i	0.490593	+	0.311597i
$337$	−24.0567			−1.31045			−0.655227	−	0.755432i	$-0.727427\pi$
$337$	−24.0567			−1.31045			−0.655227	+	0.755432i	$0.727427\pi$
$338$	0.720007	−	1.21721i	0.0391632	−	0.0662073i
$339$			21.2944i			1.15655i
$340$	−32.5653	+	17.8950i	−1.76610	+	0.970491i
$341$		−	15.0324i		−	0.814052i
$342$	−11.9765	−	7.08438i	−0.647614	−	0.383080i
$343$	−1.00000			−0.0539949
$344$	−0.439198	+	13.8516i	−0.0236800	+	0.746826i
$345$	−37.1502			−2.00010
$346$	−6.59322	−	3.90005i	−0.354454	−	0.209668i
$347$			10.0923i			0.541785i	0.962610	+	0.270893i	$0.0873189\pi$
$347$			10.0923i			0.541785i	−0.962610	+	0.270893i	$0.912681\pi$
$348$	10.8284	+	19.7056i	0.580465	+	1.05633i
$349$		−	22.2058i		−	1.18865i	−0.804225	−	0.594325i	$-0.797419\pi$
$349$		−	22.2058i		−	1.18865i	0.804225	−	0.594325i	$-0.202581\pi$
$350$	−1.94135	+	3.28195i	−0.103770	+	0.175427i
$351$	−2.91168			−0.155414
$352$	11.6217	−	5.91472i	0.619441	−	0.315256i
$353$	2.84719			0.151540			0.0757702	−	0.997125i	$-0.475858\pi$
$353$	2.84719			0.151540			0.0757702	+	0.997125i	$0.475858\pi$
$354$	19.5889	−	33.1160i	1.04114	−	1.76009i
$355$			21.5085i			1.14155i
$356$	13.5260	+	24.6147i	0.716878	+	1.30457i
$357$			17.8363i			0.943999i
$358$	−8.27332	−	4.89388i	−0.437259	−	0.258649i
$359$	−5.38588			−0.284256			−0.142128	−	0.989848i	$-0.545394\pi$
$359$	−5.38588			−0.284256			−0.142128	+	0.989848i	$0.545394\pi$
$360$	1.01788	−	32.1023i	0.0536472	−	1.69194i
$361$	13.2218			0.695884
$362$	−18.1576	−	10.7407i	−0.954341	−	0.564516i
$363$			15.1436i			0.794831i
$364$	1.75279	−	0.963179i	0.0918714	−	0.0504843i
$365$		−	15.8592i		−	0.830109i
$366$	15.1892	−	25.6781i	0.793954	−	1.34222i
$367$	27.3949			1.43000			0.715001	−	0.699123i	$-0.246426\pi$
$367$	27.3949			1.43000			0.715001	+	0.699123i	$0.246426\pi$
$368$	−10.7830	+	16.9772i	−0.562100	+	0.884995i
$369$	6.83521			0.355827
$370$	−15.2701	+	25.8149i	−0.793856	+	1.34205i
$371$			0.579570i			0.0300898i
$372$	−30.4419	+	16.7281i	−1.57834	+	0.867313i
$373$			1.81294i			0.0938703i	0.998898	+	0.0469351i	$0.0149454\pi$
$373$			1.81294i			0.0938703i	−0.998898	+	0.0469351i	$0.985055\pi$
$374$	18.7914	+	11.1156i	0.971679	+	0.574772i
$375$	−17.0212			−0.878971
$376$	38.2617	+	1.21318i	1.97319	+	0.0625650i
$377$	4.22120			0.217403
$378$	−3.54412	−	2.09643i	−0.182290	−	0.107829i
$379$			14.4281i			0.741122i	0.928808	+	0.370561i	$0.120835\pi$
$379$			14.4281i			0.741122i	−0.928808	+	0.370561i	$0.879165\pi$
$380$	−6.42310	−	11.6888i	−0.329498	−	0.599620i
$381$		−	26.5019i		−	1.35774i
$382$	9.75909	−	16.4982i	0.499319	−	0.844121i
$383$	20.0617			1.02510			0.512552	−	0.858656i	$-0.328700\pi$
$383$	20.0617			1.02510			0.512552	+	0.858656i	$0.328700\pi$
$384$	−24.9105	−	16.9530i	−1.27121	−	0.865130i
$385$	6.39518			0.325928
$386$	3.32186	−	5.61576i	0.169078	−	0.285835i
$387$		−	20.0558i		−	1.01950i
$388$	15.3514	+	27.9365i	0.779349	+	1.41826i
$389$		−	20.5109i		−	1.03994i	−0.854183	−	0.519972i	$-0.825942\pi$
$389$		−	20.5109i		−	1.03994i	0.854183	−	0.519972i	$-0.174058\pi$
$390$	−8.99348	−	5.31986i	−0.455402	−	0.269382i
$391$	−33.6729			−1.70291
$392$	2.82701	+	0.0896372i	0.142785	+	0.00452736i
$393$	−0.453749			−0.0228886
$394$	6.34231	+	3.75163i	0.319521	+	0.189005i
$395$			33.4397i			1.68253i
$396$	−16.5391	+	9.08840i	−0.831120	+	0.456709i
$397$		−	0.791932i		−	0.0397459i	−0.999803	−	0.0198730i	$-0.993674\pi$
$397$		−	0.791932i		−	0.0397459i	0.999803	−	0.0198730i	$-0.00632618\pi$
$398$	−17.1374	+	28.9716i	−0.859020	+	1.45221i
$399$	−6.40205			−0.320504
$400$	5.78240	−	9.10406i	0.289120	−	0.455203i
$401$	22.0537			1.10131			0.550656	−	0.834732i	$-0.314378\pi$
$401$	22.0537			1.10131			0.550656	+	0.834732i	$0.314378\pi$
$402$	−13.0417	+	22.0476i	−0.650460	+	1.09963i
$403$			6.52105i			0.324837i
$404$	−20.6978	+	11.3737i	−1.02976	+	0.565862i
$405$		−	12.5534i		−	0.623785i
$406$	5.13807	+	3.03929i	0.254998	+	0.150838i
$407$	17.6229			0.873533
$408$	1.59880	−	50.4234i	0.0791524	−	2.49633i
$409$	−22.6362			−1.11929			−0.559645	−	0.828732i	$-0.689063\pi$
$409$	−22.6362			−1.11929			−0.559645	+	0.828732i	$0.689063\pi$
$410$	5.63882	+	3.33550i	0.278481	+	0.164729i
$411$		−	56.7885i		−	2.80117i
$412$	2.69730	+	4.90854i	0.132886	+	0.241826i
$413$		−	10.2153i		−	0.502661i
$414$	14.8184	−	25.0513i	0.728287	−	1.23120i
$415$	0.728397			0.0357556
$416$	−5.04150	+	2.56580i	−0.247180	+	0.125799i
$417$	−7.34072			−0.359477
$418$	−3.98974	+	6.74485i	−0.195145	+	0.329901i
$419$			29.3054i			1.43166i	0.698274	+	0.715831i	$0.253952\pi$
$419$			29.3054i			1.43166i	−0.698274	+	0.715831i	$0.746048\pi$
$420$	−7.11657	−	12.9507i	−0.347253	−	0.631931i
$421$		−	12.9130i		−	0.629342i	−0.949201	−	0.314671i	$-0.898106\pi$
$421$		−	12.9130i		−	0.629342i	0.949201	−	0.314671i	$-0.101894\pi$
$422$	−11.7444	−	6.94711i	−0.571709	−	0.338180i
$423$	−55.3995			−2.69362
$424$	0.0519511	−	1.63845i	0.00252297	−	0.0795701i
$425$	18.0572			0.875903
$426$	−25.1337	−	14.8672i	−1.21773	−	0.720317i
$427$		−	7.92093i		−	0.383321i
$428$	4.91494	−	2.70081i	0.237573	−	0.130549i
$429$			6.13952i			0.296419i
$430$	9.78700	−	16.5454i	0.471971	−	0.797889i
$431$	−11.6196			−0.559695			−0.279847	−	0.960044i	$-0.590284\pi$
$431$	−11.6196			−0.559695			−0.279847	+	0.960044i	$0.590284\pi$
$432$	9.83132	+	6.24431i	0.473010	+	0.300430i
$433$	11.7701			0.565634			0.282817	−	0.959174i	$-0.408731\pi$
$433$	11.7701			0.565634			0.282817	+	0.959174i	$0.408731\pi$
$434$	−4.69520	+	7.93746i	−0.225377	+	0.381010i
$435$		−	31.1889i		−	1.49539i
$436$	16.1792	−	8.89063i	0.774842	−	0.425784i
$437$		−	12.0863i		−	0.578166i
$438$	18.5322	+	10.9623i	0.885504	+	0.523798i
$439$	0.365184			0.0174293			0.00871464	−	0.999962i	$-0.497226\pi$
$439$	0.365184			0.0174293			0.00871464	+	0.999962i	$0.497226\pi$
$440$	−18.0792	−	0.573246i	−0.861892	−	0.0273284i
$441$	−4.09325			−0.194917
$442$	−8.15168	−	4.82192i	−0.387736	−	0.229355i
$443$			36.1653i			1.71826i	0.511755	+	0.859132i	$0.328996\pi$
$443$			36.1653i			1.71826i	−0.511755	+	0.859132i	$0.671004\pi$
$444$	−19.6108	−	35.6877i	−0.930686	−	1.69366i
$445$		−	38.9586i		−	1.84682i
$446$	0.811915	−	1.37258i	0.0384453	−	0.0649935i
$447$	12.6701			0.599277
$448$	−7.98393	−	0.506810i	−0.377205	−	0.0239445i
$449$	21.4503			1.01230			0.506152	−	0.862444i	$-0.331067\pi$
$449$	21.4503			1.01230			0.506152	+	0.862444i	$0.331067\pi$
$450$	−7.94645	+	13.4338i	−0.374599	+	0.633277i
$451$		−	3.84942i		−	0.181262i
$452$	−7.70105	−	14.0144i	−0.362227	−	0.659180i
$453$		−	17.9214i		−	0.842020i
$454$	−34.1317	−	20.1897i	−1.60188	−	0.947552i
$455$	−2.77422			−0.130057
$456$	18.0986	+	0.573862i	0.847547	+	0.0268736i
$457$	2.80295			0.131116			0.0655582	−	0.997849i	$-0.479117\pi$
$457$	2.80295			0.131116			0.0655582	+	0.997849i	$0.479117\pi$
$458$	−24.0711	−	14.2387i	−1.12477	−	0.665329i
$459$			19.4997i			0.910166i
$460$	24.4494	−	13.4352i	1.13996	−	0.626421i
$461$			19.6840i			0.916774i	0.888753	+	0.458387i	$0.151573\pi$
$461$			19.6840i			0.916774i	−0.888753	+	0.458387i	$0.848427\pi$
$462$	−4.42050	+	7.47306i	−0.205660	+	0.347678i
$463$	10.9945			0.510959			0.255479	−	0.966815i	$-0.417767\pi$
$463$	10.9945			0.510959			0.255479	+	0.966815i	$0.417767\pi$
$464$	−14.2529	−	9.05267i	−0.661675	−	0.420259i
$465$	48.1816			2.23437
$466$	19.2595	−	32.5591i	0.892180	−	1.50827i
$467$			26.1563i			1.21037i	0.796086	+	0.605184i	$0.206901\pi$
$467$			26.1563i			1.21037i	−0.796086	+	0.605184i	$0.793099\pi$
$468$	7.17463	−	3.94254i	0.331647	−	0.182244i
$469$			6.80101i			0.314042i
$470$	−45.7027	−	27.0343i	−2.10811	−	1.24700i
$471$	−19.6333			−0.904655
$472$	−0.915670	+	28.8787i	−0.0421471	+	1.32925i
$473$	−11.2949			−0.519341
$474$	−39.0758	−	23.1143i	−1.79481	−	1.06168i
$475$			6.48133i			0.297384i
$476$	−6.45045	−	11.7385i	−0.295656	−	0.538035i
$477$			2.37233i			0.108621i
$478$	−14.1829	+	23.9768i	−0.648709	+	1.09667i
$479$	1.13276			0.0517574			0.0258787	−	0.999665i	$-0.491762\pi$
$479$	1.13276			0.0517574			0.0258787	+	0.999665i	$0.491762\pi$
$480$	18.9577	+	37.2497i	0.865298	+	1.70021i
$481$	−7.64478			−0.348572
$482$	−5.98528	+	10.1184i	−0.272622	+	0.460881i
$483$		−	13.3912i		−	0.609321i
$484$	−5.47662	−	9.96635i	−0.248937	−	0.453016i
$485$		−	44.2162i		−	2.00775i
$486$	25.3016	+	14.9665i	1.14770	+	0.678896i
$487$	−19.1216			−0.866482			−0.433241	−	0.901278i	$-0.642630\pi$
$487$	−19.1216			−0.866482			−0.433241	+	0.901278i	$0.642630\pi$
$488$	−0.710010	+	22.3925i	−0.0321406	+	1.01366i
$489$	−27.0953			−1.22529
$490$	−3.37680	−	1.99746i	−0.152548	−	0.0902360i
$491$			41.9448i			1.89294i	0.322788	+	0.946471i	$0.395380\pi$
$491$			41.9448i			1.89294i	−0.322788	+	0.946471i	$0.604620\pi$
$492$	−7.79537	+	4.28364i	−0.351443	+	0.193121i
$493$		−	28.2695i		−	1.27320i
$494$	1.73075	−	2.92591i	0.0778700	−	0.131643i
$495$	26.1771			1.17657
$496$	13.9849	−	22.0184i	0.627939	−	0.988655i
$497$	−7.75298			−0.347769
$498$	−0.503486	+	0.851166i	−0.0225617	+	0.0381417i
$499$			34.0302i			1.52340i	0.647928	+	0.761702i	$0.275636\pi$
$499$			34.0302i			1.52340i	−0.647928	+	0.761702i	$0.724364\pi$
$500$	11.2021	−	6.15566i	0.500972	−	0.275290i
$501$		−	53.7124i		−	2.39969i
$502$	29.5611	+	17.4861i	1.31938	+	0.780444i
$503$	35.5484			1.58502			0.792512	−	0.609856i	$-0.208773\pi$
$503$	35.5484			1.58502			0.792512	+	0.609856i	$0.208773\pi$
$504$	11.5717	+	0.366908i	0.515443	+	0.0163434i
$505$	32.7593			1.45777
$506$	−14.1082	−	8.34537i	−0.627187	−	0.370997i
$507$		−	2.66332i		−	0.118282i
$508$	9.58434	+	17.4416i	0.425236	+	0.773845i
$509$			40.4806i			1.79427i	0.441755	+	0.897136i	$0.354356\pi$
$509$			40.4806i			1.79427i	−0.441755	+	0.897136i	$0.645644\pi$
$510$	−35.6273	+	60.2297i	−1.57761	+	2.66701i
$511$	5.71664			0.252889
$512$	22.5252	+	2.14841i	0.995482	+	0.0949473i
$513$	−6.99907			−0.309017
$514$	−8.48232	+	14.3398i	−0.374139	+	0.632499i
$515$		−	7.76895i		−	0.342341i
$516$	12.5690	+	22.8731i	0.553321	+	1.00693i
$517$			31.1996i			1.37216i
$518$	−9.30527	−	5.50430i	−0.408850	−	0.241845i
$519$	−14.4263			−0.633246
$520$	7.84274	+	0.248673i	0.343927	+	0.0109050i
$521$	23.0145			1.00828			0.504142	−	0.863621i	$-0.331809\pi$
$521$	23.0145			1.00828			0.504142	+	0.863621i	$0.331809\pi$
$522$	21.0314	+	12.4406i	0.920520	+	0.544510i
$523$		−	2.66001i		−	0.116314i	−0.998307	−	0.0581570i	$-0.981478\pi$
$523$		−	2.66001i		−	0.116314i	0.998307	−	0.0581570i	$-0.0185224\pi$
$524$	0.298623	−	0.164097i	0.0130454	−	0.00716860i
$525$			7.18109i			0.313408i
$526$	−11.6800	+	19.7456i	−0.509272	+	0.860948i
$527$	43.6717			1.90237
$528$	13.1666	−	20.7301i	0.573005	−	0.902164i
$529$	2.28098			0.0991731
$530$	−1.15767	+	1.95709i	−0.0502859	+	0.0850106i
$531$		−	41.8138i		−	1.81456i
$532$	4.21335	−	2.31528i	0.182672	−	0.100380i
$533$			1.66987i			0.0723302i
$534$	45.5250	+	26.9291i	1.97006	+	1.16534i
$535$	−7.77908			−0.336319
$536$	0.609624	−	19.2265i	0.0263317	−	0.830459i
$537$	−18.1025			−0.781181
$538$	−32.2014	−	19.0479i	−1.38830	−	0.821214i
$539$			2.30522i			0.0992927i
$540$	−7.78022	−	14.1585i	−0.334808	−	0.609283i
$541$		−	8.51106i		−	0.365919i	−0.983120	−	0.182959i	$-0.941432\pi$
$541$		−	8.51106i		−	0.365919i	0.983120	−	0.182959i	$-0.0585677\pi$
$542$	15.8393	−	26.7770i	0.680354	−	1.15017i
$543$	−39.7298			−1.70497
$544$	17.1833	+	33.7631i	0.736726	+	1.44758i
$545$	−25.6074			−1.09690
$546$	1.91761	−	3.24180i	0.0820660	−	0.138736i
$547$			8.16036i			0.348912i	0.984665	+	0.174456i	$0.0558166\pi$
$547$			8.16036i			0.348912i	−0.984665	+	0.174456i	$0.944183\pi$
$548$	20.5374	+	37.3739i	0.877313	+	1.59653i
$549$		−	32.4224i		−	1.38375i
$550$	7.56559	+	4.47524i	0.322598	+	0.190825i
$551$	10.1469			0.432271
$552$	−1.20035	+	37.8570i	−0.0510903	+	1.61130i
$553$	−12.0537			−0.512577
$554$	−10.5705	−	6.25270i	−0.449097	−	0.265652i
$555$			56.4844i			2.39763i
$556$	4.83111	−	2.65475i	0.204885	−	0.112586i
$557$		−	30.1130i		−	1.27593i	−0.770066	−	0.637964i	$-0.779777\pi$
$557$		−	30.1130i		−	1.27593i	0.770066	−	0.637964i	$-0.220223\pi$
$558$	−19.2187	+	32.4900i	−0.813591	+	1.37541i
$559$	4.89973			0.207236
$560$	9.36718	+	5.94951i	0.395835	+	0.251413i
$561$	41.1166			1.73594
$562$	−24.0622	+	40.6783i	−1.01500	+	1.71591i
$563$		−	20.3344i		−	0.856993i	−0.903543	−	0.428497i	$-0.859043\pi$
$563$		−	20.3344i		−	0.856993i	0.903543	−	0.428497i	$-0.140957\pi$
$564$	63.1816	−	34.7190i	2.66043	−	1.46193i
$565$			22.1811i			0.933167i
$566$	28.1886	+	16.6743i	1.18486	+	0.700872i
$567$	4.52503			0.190033
$568$	21.9177	+	0.694956i	0.919648	+	0.0291597i
$569$	41.3117			1.73188			0.865939	−	0.500150i	$-0.166722\pi$
$569$	41.3117			1.73188			0.865939	+	0.500150i	$0.166722\pi$
$570$	−21.6184	−	12.7878i	−0.905496	−	0.535623i
$571$			40.7491i			1.70530i	0.522483	+	0.852649i	$0.325006\pi$
$571$			40.7491i			1.70530i	−0.522483	+	0.852649i	$0.674994\pi$
$572$	−2.22034	−	4.04057i	−0.0928369	−	0.168945i
$573$		−	36.0990i		−	1.50806i
$574$	−1.20232	+	2.03258i	−0.0501839	+	0.0848382i
$575$	−13.5570			−0.565367
$576$	−32.6803	−	2.07450i	−1.36168	−	0.0864376i
$577$	18.2569			0.760043			0.380021	−	0.924978i	$-0.375917\pi$
$577$	18.2569			0.760043			0.380021	+	0.924978i	$0.375917\pi$
$578$	−20.0525	+	33.8996i	−0.834072	+	1.41004i
$579$		−	12.2876i		−	0.510656i
$580$	11.2793	+	20.5262i	0.468349	+	0.852302i
$581$			0.262559i			0.0108928i
$582$	51.6687	+	30.5633i	2.14174	+	1.26689i
$583$	1.33603			0.0553329
$584$	−16.1610	−	0.512424i	−0.668746	−	0.0212042i
$585$	−11.3556			−0.469496
$586$	24.6517	+	14.5821i	1.01835	+	0.602381i
$587$		−	32.8881i		−	1.35744i	−0.734399	−	0.678718i	$-0.762536\pi$
$587$		−	32.8881i		−	1.35744i	0.734399	−	0.678718i	$-0.237464\pi$
$588$	4.66824	−	2.56525i	0.192515	−	0.105789i
$589$			15.6752i			0.645887i
$590$	20.4046	−	34.4949i	0.840045	−	1.42013i
$591$	13.8773			0.570837
$592$	25.8127	+	16.3948i	1.06089	+	0.673821i
$593$	−46.0425			−1.89074			−0.945369	−	0.326001i	$-0.894299\pi$
$593$	−46.0425			−1.89074			−0.945369	+	0.326001i	$0.894299\pi$
$594$	−4.83273	+	8.16996i	−0.198289	+	0.335217i
$595$			18.5791i			0.761667i
$596$	−8.33853	+	4.58211i	−0.341560	+	0.187691i
$597$			63.3915i			2.59444i
$598$	6.12013	+	3.62021i	0.250271	+	0.148041i
$599$	−2.58321			−0.105547			−0.0527735	−	0.998607i	$-0.516806\pi$
$599$	−2.58321			−0.105547			−0.0527735	+	0.998607i	$0.516806\pi$
$600$	0.643693	−	20.3010i	0.0262786	−	0.828784i
$601$	5.32403			0.217172			0.108586	−	0.994087i	$-0.465368\pi$
$601$	5.32403			0.217172			0.108586	+	0.994087i	$0.465368\pi$
$602$	5.96397	+	3.52784i	0.243073	+	0.143784i
$603$			27.8383i			1.13366i
$604$	6.48120	+	11.7945i	0.263716	+	0.479911i
$605$			15.7742i			0.641311i
$606$	−22.6440	+	38.2808i	−0.919850	+	1.55505i
$607$	−12.7131			−0.516010			−0.258005	−	0.966144i	$-0.583065\pi$
$607$	−12.7131			−0.516010			−0.258005	+	0.966144i	$0.583065\pi$
$608$	−12.1187	+	6.16764i	−0.491478	+	0.250131i
$609$	11.2424			0.455565
$610$	15.8217	−	26.7474i	0.640603	−	1.08297i
$611$		−	13.5343i		−	0.547541i
$612$	−26.4033	−	48.0488i	−1.06729	−	1.94226i
$613$		−	25.9763i		−	1.04917i	−0.851357	−	0.524587i	$-0.824220\pi$
$613$		−	25.9763i		−	1.04917i	0.851357	−	0.524587i	$-0.175780\pi$
$614$	13.9473	+	8.25017i	0.562867	+	0.332950i
$615$	12.3381			0.497519
$616$	0.206633	−	6.51686i	0.00832548	−	0.262572i
$617$	12.9002			0.519343			0.259671	−	0.965697i	$-0.416386\pi$
$617$	12.9002			0.519343			0.259671	+	0.965697i	$0.416386\pi$
$618$	9.07838	+	5.37009i	0.365186	+	0.216017i
$619$		−	8.88577i		−	0.357149i	−0.983926	−	0.178575i	$-0.942851\pi$
$619$		−	8.88577i		−	0.357149i	0.983926	−	0.178575i	$-0.0571486\pi$
$620$	−31.7095	+	17.4247i	−1.27348	+	0.699793i
$621$		−	14.6400i		−	0.587483i
$622$	−5.16871	+	8.73794i	−0.207246	+	0.350360i
$623$	14.0431			0.562625
$624$	−5.71167	+	8.99271i	−0.228650	+	0.359997i
$625$	−31.2115			−1.24846
$626$	−20.2408	+	34.2181i	−0.808986	+	1.36763i
$627$			14.7581i			0.589382i
$628$	12.9212	−	7.10032i	0.515611	−	0.283334i
$629$			51.1974i			2.04137i
$630$	−13.8221	−	8.17611i	−0.550685	−	0.325744i
$631$	17.0995			0.680719			0.340359	−	0.940295i	$-0.389451\pi$
$631$	17.0995			0.680719			0.340359	+	0.940295i	$0.389451\pi$
$632$	34.0760	+	1.08046i	1.35547	+	0.0429785i
$633$	−25.6975			−1.02138
$634$	19.0538	+	11.2708i	0.756721	+	0.447619i
$635$		−	27.6055i		−	1.09549i
$636$	−1.48674	−	2.70558i	−0.0589532	−	0.107283i
$637$		−	1.00000i		−	0.0396214i
$638$	7.00623	−	11.8444i	0.277379	−	0.468922i
$639$	−31.7349			−1.25541
$640$	−25.9478	−	17.6590i	−1.02568	−	0.698032i
$641$	−5.85739			−0.231353			−0.115677	−	0.993287i	$-0.536904\pi$
$641$	−5.85739			−0.231353			−0.115677	+	0.993287i	$0.536904\pi$
$642$	5.37709	−	9.09021i	0.212217	−	0.358762i
$643$			45.2251i			1.78350i	0.452526	+	0.891751i	$0.350523\pi$
$643$			45.2251i			1.78350i	−0.452526	+	0.891751i	$0.649477\pi$
$644$	4.84288	+	8.81308i	0.190836	+	0.347284i
$645$		−	36.2022i		−	1.42546i
$646$	−19.5949	−	11.5909i	−0.770952	−	0.456037i
$647$	−26.6756			−1.04873			−0.524364	−	0.851494i	$-0.675697\pi$
$647$	−26.6756			−1.04873			−0.524364	+	0.851494i	$0.675697\pi$
$648$	−12.7923	−	0.405611i	−0.502529	−	0.0159339i
$649$	−23.5484			−0.924357
$650$	−3.28195	−	1.94135i	−0.128729	−	0.0761461i
$651$			17.3676i			0.680691i
$652$	17.8321	−	9.79893i	0.698359	−	0.383756i
$653$		−	0.320551i		−	0.0125441i	−0.999980	−	0.00627206i	$-0.998004\pi$
$653$		−	0.320551i		−	0.0125441i	0.999980	−	0.00627206i	$-0.00199647\pi$
$654$	17.7005	−	29.9235i	0.692144	−	1.17010i
$655$	−0.472644			−0.0184677
$656$	3.58116	−	5.63834i	0.139821	−	0.220140i
$657$	23.3997			0.912908
$658$	9.74482	−	16.4741i	0.379893	−	0.642226i
$659$			18.9811i			0.739398i	0.929151	+	0.369699i	$0.120539\pi$
$659$			18.9811i			0.739398i	−0.929151	+	0.369699i	$0.879461\pi$
$660$	−29.8542	+	16.4052i	−1.16207	+	0.638573i
$661$		−	32.3812i		−	1.25948i	−0.776804	−	0.629742i	$-0.783161\pi$
$661$		−	32.3812i		−	1.25948i	0.776804	−	0.629742i	$-0.216839\pi$
$662$	20.9073	+	12.3672i	0.812587	+	0.480665i
$663$	−17.8363			−0.692706
$664$	0.0235351	−	0.742257i	0.000913338	−	0.0288052i
$665$	−6.66864			−0.258599
$666$	−38.0888	−	22.5305i	−1.47591	−	0.873039i
$667$			21.2243i			0.821807i
$668$	19.4249	+	35.3494i	0.751572	+	1.36771i
$669$		−	3.00328i		−	0.116114i
$670$	−13.5847	+	22.9656i	−0.524824	+	0.887240i
$671$	−18.2595			−0.704898
$672$	−13.4271	+	6.83353i	−0.517962	+	0.263609i
$673$	−1.03242			−0.0397970			−0.0198985	−	0.999802i	$-0.506334\pi$
$673$	−1.03242			−0.0397970			−0.0198985	+	0.999802i	$0.506334\pi$
$674$	17.3210	−	29.2820i	0.667181	−	1.12790i
$675$			7.85076i			0.302176i
$676$	0.963179	+	1.75279i	0.0370454	+	0.0674151i
$677$		−	5.19777i		−	0.199767i	−0.994999	−	0.0998833i	$-0.968153\pi$
$677$		−	5.19777i		−	0.199767i	0.994999	−	0.0998833i	$-0.0318470\pi$
$678$	−25.9197	−	15.3321i	−0.995439	−	0.588827i
$679$	15.9382			0.611654
$680$	1.66538	−	52.5231i	0.0638642	−	2.01417i
$681$	−74.6821			−2.86183
$682$	18.2976	+	10.8235i	0.700650	+	0.414452i
$683$		−	4.36371i		−	0.166973i	−0.996509	−	0.0834865i	$-0.973394\pi$
$683$		−	4.36371i		−	0.166973i	0.996509	−	0.0834865i	$-0.0266055\pi$
$684$	17.2463	−	9.47703i	0.659429	−	0.362363i
$685$		−	59.1533i		−	2.26013i
$686$	0.720007	−	1.21721i	0.0274900	−	0.0464731i
$687$	−52.6690			−2.00945
$688$	−16.5440	−	10.5078i	−0.630733	−	0.400607i
$689$	−0.579570			−0.0220799
$690$	26.7484	−	45.2194i	1.01829	−	1.72147i
$691$			5.66095i			0.215353i	0.994186	+	0.107676i	$0.0343410\pi$
$691$			5.66095i			0.215353i	−0.994186	+	0.107676i	$0.965659\pi$
$692$	9.49433	−	5.21724i	0.360920	−	0.198330i
$693$			9.43584i			0.358438i
$694$	−12.2845	−	7.26656i	−0.466312	−	0.275835i
$695$	−7.64639			−0.290044
$696$	−31.7823	−	1.00774i	−1.20471	−	0.0381981i
$697$	11.1832			0.423594
$698$	27.0290	+	15.9883i	1.02306	+	0.605167i
$699$		−	71.2412i		−	2.69459i
$700$	−2.59702	−	4.72605i	−0.0981580	−	0.178628i
$701$			13.3890i			0.505695i	0.967506	+	0.252848i	$0.0813671\pi$
$701$			13.3890i			0.505695i	−0.967506	+	0.252848i	$0.918633\pi$
$702$	2.09643	−	3.54412i	0.0791248	−	0.133764i
$703$	−18.3764			−0.693081
$704$	−1.16831	+	18.4047i	−0.0440322	+	0.693653i
$705$	−100.000			−3.76622
$706$	−2.04999	+	3.46561i	−0.0771526	+	0.130430i
$707$			11.8085i			0.444103i
$708$	26.2048	+	47.6875i	0.984836	+	1.79220i
$709$			27.4963i			1.03265i	0.856394	+	0.516323i	$0.172699\pi$
$709$			27.4963i			1.03265i	−0.856394	+	0.516323i	$0.827301\pi$
$710$	−26.1802	−	15.4863i	−0.982527	−	0.581189i
$711$	−49.3390			−1.85036
$712$	−39.6999	−	1.25878i	−1.48782	−	0.0471749i
$713$	−32.7880			−1.22792
$714$	−21.7105	−	12.8423i	−0.812495	−	0.480611i
$715$			6.39518i			0.239166i
$716$	11.9137	−	6.54671i	0.445236	−	0.244662i
$717$			52.4626i			1.95925i
$718$	3.87787	−	6.55572i	0.144721	−	0.244657i
$719$	−5.61384			−0.209361			−0.104681	−	0.994506i	$-0.533382\pi$
$719$	−5.61384			−0.209361			−0.104681	+	0.994506i	$0.533382\pi$
$720$	38.3422	+	24.3529i	1.42893	+	0.907578i
$721$	2.80041			0.104293
$722$	−9.51979	+	16.0936i	−0.354290	+	0.598943i
$723$			22.1396i			0.823382i
$724$	26.1472	−	14.3681i	0.971752	−	0.533988i
$725$		−	11.3816i		−	0.422702i
$726$	−18.4328	−	10.9035i	−0.684107	−	0.404666i
$727$	41.5030			1.53926			0.769630	−	0.638490i	$-0.220441\pi$
$727$	41.5030			1.53926			0.769630	+	0.638490i	$0.220441\pi$
$728$	−0.0896372	+	2.82701i	−0.00332218	+	0.104776i
$729$	41.7863			1.54764
$730$	19.3039	+	11.4188i	0.714470	+	0.422627i
$731$		−	32.8137i		−	1.21366i
$732$	20.3192	+	36.9768i	0.751018	+	1.36670i
$733$		−	15.7818i		−	0.582913i	−0.956584	−	0.291456i	$-0.905860\pi$
$733$		−	15.7818i		−	0.582913i	0.956584	−	0.291456i	$-0.0941398\pi$
$734$	−19.7245	+	33.3452i	−0.728046	+	1.23079i
$735$	−7.38863			−0.272534
$736$	−12.9009	−	25.3487i	−0.475533	−	0.934367i
$737$	15.6778			0.577499
$738$	−4.92140	+	8.31986i	−0.181159	+	0.306258i
$739$		−	35.4864i		−	1.30539i	−0.757622	−	0.652694i	$-0.773639\pi$
$739$		−	35.4864i		−	1.30539i	0.757622	−	0.652694i	$-0.226361\pi$
$740$	−20.4274	−	37.1738i	−0.750926	−	1.36654i
$741$		−	6.40205i		−	0.235185i
$742$	−0.705456	−	0.417295i	−0.0258981	−	0.0153194i
$743$	43.4551			1.59421			0.797107	−	0.603838i	$-0.206363\pi$
$743$	43.4551			1.59421			0.797107	+	0.603838i	$0.206363\pi$
$744$	1.55678	−	49.0984i	0.0570745	−	1.80003i
$745$	13.1977			0.483528
$746$	−2.20672	−	1.30533i	−0.0807936	−	0.0477914i
$747$			1.07472i			0.0393220i
$748$	−27.0598	+	14.8697i	−0.989406	+	0.543689i
$749$		−	2.80406i		−	0.102458i
$750$	12.2554	−	20.7183i	0.447504	−	0.756526i
$751$	0.732227			0.0267193			0.0133597	−	0.999911i	$-0.495747\pi$
$751$	0.732227			0.0267193			0.0133597	+	0.999911i	$0.495747\pi$
$752$	−29.0254	+	45.6988i	−1.05845	+	1.66646i
$753$	64.6814			2.35712
$754$	−3.03929	+	5.13807i	−0.110685	+	0.187117i
$755$		−	18.6676i		−	0.679385i
$756$	5.10358	−	2.80447i	0.185615	−	0.101998i
$757$		−	14.3837i		−	0.522785i	−0.965233	−	0.261393i	$-0.915818\pi$
$757$		−	14.3837i		−	0.522785i	0.965233	−	0.261393i	$-0.0841817\pi$
$758$	−17.5620	−	10.3883i	−0.637880	−	0.377322i
$759$	−30.8696			−1.12050
$760$	18.8523	+	0.597758i	0.683845	+	0.0216830i
$761$	1.97792			0.0716996			0.0358498	−	0.999357i	$-0.488586\pi$
$761$	1.97792			0.0716996			0.0358498	+	0.999357i	$0.488586\pi$
$762$	32.2583	+	19.0816i	1.16860	+	0.691253i
$763$		−	9.23050i		−	0.334167i
$764$	13.0551	+	23.7576i	0.472316	+	0.859521i
$765$			76.0488i			2.74955i
$766$	−14.4446	+	24.4192i	−0.521903	+	0.882301i
$767$	10.2153			0.368853
$768$	38.5710	−	18.1149i	1.39181	−	0.653664i
$769$	−14.1082			−0.508754			−0.254377	−	0.967105i	$-0.581870\pi$
$769$	−14.1082			−0.508754			−0.254377	+	0.967105i	$0.581870\pi$
$770$	−4.60457	+	7.78424i	−0.165937	+	0.280525i
$771$			31.3762i			1.12999i
$772$	4.44377	+	8.08678i	0.159935	+	0.291050i
$773$			39.4071i			1.41737i	0.705523	+	0.708687i	$0.250712\pi$
$773$			39.4071i			1.41737i	−0.705523	+	0.708687i	$0.749288\pi$
$774$	24.4121	+	14.4403i	0.877474	+	0.519047i
$775$	17.5827			0.631588
$776$	−45.0575	−	1.42866i	−1.61747	−	0.0512859i
$777$	−20.3605			−0.730428
$778$	24.9660	+	14.7680i	0.895074	+	0.529459i
$779$			4.01402i			0.143817i
$780$	12.9507	−	7.11657i	0.463711	−	0.254814i
$781$			17.8723i			0.639521i
$782$	24.2447	−	40.9868i	0.866989	−	1.46568i
$783$	12.2908			0.439237
$784$	−2.14457	+	3.37651i	−0.0765919	+	0.120590i
$785$	−20.4509			−0.729923
$786$	0.326703	−	0.552306i	0.0116531	−	0.0197001i
$787$		−	10.4800i		−	0.373571i	−0.982401	−	0.186786i	$-0.940193\pi$
$787$		−	10.4800i		−	0.373571i	0.982401	−	0.186786i	$-0.0598070\pi$
$788$	−9.13302	+	5.01869i	−0.325350	+	0.178783i
$789$			43.2045i			1.53812i
$790$	−40.7030	−	24.0768i	−1.44815	−	0.856615i
$791$	−7.99544			−0.284285
$792$	0.845802	−	26.6752i	0.0300543	−	0.947861i
$793$	7.92093			0.281280
$794$	0.963945	+	0.570197i	0.0342091	+	0.0202355i
$795$			4.28223i			0.151875i
$796$	−22.9253	−	41.7195i	−0.812566	−	1.47871i
$797$			31.7295i			1.12392i	0.827166	+	0.561958i	$0.189952\pi$
$797$			31.7295i			1.12392i	−0.827166	+	0.561958i	$0.810048\pi$
$798$	4.60952	−	7.79262i	0.163175	−	0.275856i
$799$	−90.6400			−3.20661
$800$	6.91815	+	13.5934i	0.244594	+	0.480598i
$801$	57.4820			2.03103
$802$	−15.8789	+	26.8439i	−0.560702	+	0.947893i
$803$		−	13.1781i		−	0.465045i
$804$	−17.4463	−	31.7488i	−0.615284	−	1.11969i
$805$		−	13.9488i		−	0.491632i
$806$	−7.93746	−	4.69520i	−0.279585	−	0.165381i
$807$	−70.4585			−2.48026
$808$	1.05848	−	33.3826i	0.0372371	−	1.17440i
$809$	17.7495			0.624039			0.312019	−	0.950076i	$-0.398995\pi$
$809$	17.7495			0.624039			0.312019	+	0.950076i	$0.398995\pi$
$810$	15.2801	+	9.03856i	0.536888	+	0.317583i
$811$			12.0825i			0.424273i	0.977240	+	0.212136i	$0.0680421\pi$
$811$			12.0825i			0.424273i	−0.977240	+	0.212136i	$0.931958\pi$
$812$	−7.39889	+	4.06577i	−0.259650	+	0.142681i
$813$		−	58.5896i		−	2.05483i
$814$	−12.6886	+	21.4507i	−0.444735	+	0.751845i
$815$	−28.2236			−0.988630
$816$	60.2246	+	38.2513i	2.10828	+	1.33906i
$817$	11.7779			0.412057
$818$	16.2983	−	27.5530i	0.569855	−	0.963367i
$819$		−	4.09325i		−	0.143030i
$820$	−8.11998	+	4.46202i	−0.283562	+	0.155820i
$821$		−	14.5237i		−	0.506882i	−0.967351	−	0.253441i	$-0.918438\pi$
$821$		−	14.5237i		−	0.506882i	0.967351	−	0.253441i	$-0.0815623\pi$
$822$	69.1233	+	40.8882i	2.41095	+	1.42614i
$823$	−32.1613			−1.12107			−0.560536	−	0.828130i	$-0.689405\pi$
$823$	−32.1613			−1.12107			−0.560536	+	0.828130i	$0.689405\pi$
$824$	−7.91678	−	0.251021i	−0.275794	−	0.00874473i
$825$	16.5540			0.576335
$826$	12.4341	+	7.35508i	0.432638	+	0.255916i
$827$		−	27.0041i		−	0.939026i	−0.882925	−	0.469513i	$-0.844429\pi$
$827$		−	27.0041i		−	0.939026i	0.882925	−	0.469513i	$-0.155571\pi$
$828$	19.8232	+	36.0742i	0.688902	+	1.25366i
$829$			32.8357i			1.14043i	0.821496	+	0.570215i	$0.193140\pi$
$829$			32.8357i			1.14043i	−0.821496	+	0.570215i	$0.806860\pi$
$830$	−0.524451	+	0.886609i	−0.0182040	+	0.0307747i
$831$	−23.1288			−0.802330
$832$	0.506810	−	7.98393i	0.0175705	−	0.276793i
$833$	−6.69704			−0.232039
$834$	5.28537	−	8.93516i	0.183017	−	0.309399i
$835$		−	55.9490i		−	1.93620i
$836$	−5.33722	−	9.71268i	−0.184592	−	0.335920i
$837$			18.9872i			0.656295i
$838$	−35.6707	−	21.1001i	−1.23222	−	0.728890i
$839$	28.8041			0.994429			0.497215	−	0.867628i	$-0.334356\pi$
$839$	28.8041			0.994429			0.497215	+	0.867628i	$0.334356\pi$
$840$	20.8877	+	0.662296i	0.720694	+	0.0228514i
$841$	11.1815			0.385568
$842$	15.7178	+	9.29746i	0.541671	+	0.320412i
$843$			89.0064i			3.06554i
$844$	16.9121	−	9.29339i	0.582139	−	0.319892i
$845$		−	2.77422i		−	0.0954361i
$846$	39.8880	−	67.4326i	1.37138	−	2.31838i
$847$	−5.68598			−0.195373
$848$	1.95692	+	1.24293i	0.0672010	+	0.0426824i
$849$	61.6784			2.11680
$850$	−13.0013	+	21.9793i	−0.445941	+	0.753885i
$851$		−	38.4381i		−	1.31764i
$852$	36.1928	−	19.8883i	1.23995	−	0.681364i
$853$		−	34.6783i		−	1.18736i	−0.804700	−	0.593681i	$-0.797674\pi$
$853$		−	34.6783i		−	1.18736i	0.804700	−	0.593681i	$-0.202326\pi$
$854$	9.64140	+	5.70313i	0.329922	+	0.195157i
$855$	−27.2964			−0.933519
$856$	−0.251348	+	7.92710i	−0.00859090	+	0.270943i
$857$	3.12688			0.106812			0.0534062	−	0.998573i	$-0.482992\pi$
$857$	3.12688			0.106812			0.0534062	+	0.998573i	$0.482992\pi$
$858$	−7.47306	−	4.42050i	−0.255126	−	0.150913i
$859$			36.7898i			1.25525i	0.778515	+	0.627626i	$0.215973\pi$
$859$			36.7898i			1.25525i	−0.778515	+	0.627626i	$0.784027\pi$
$860$	13.0924	+	23.8256i	0.446448	+	0.812446i
$861$			4.44740i			0.151567i
$862$	8.36617	−	14.1434i	0.284953	−	0.481726i
$863$	16.4365			0.559506			0.279753	−	0.960072i	$-0.409747\pi$
$863$	16.4365			0.559506			0.279753	+	0.960072i	$0.409747\pi$
$864$	−14.6792	+	7.47079i	−0.499398	+	0.254161i
$865$	−15.0271			−0.510936
$866$	−8.47454	+	14.3266i	−0.287977	+	0.486838i
$867$			74.1743i			2.51909i
$868$	−6.28094	−	11.4301i	−0.213189	−	0.387961i
$869$			27.7865i			0.942591i
$870$	37.9633	+	22.4562i	1.28707	+	0.761337i
$871$	−6.80101			−0.230444
$872$	−0.827396	+	26.0947i	−0.0280192	+	0.883678i
$873$	65.2393			2.20802
$874$	14.7115	+	8.70223i	0.497624	+	0.294357i
$875$		−	6.39098i		−	0.216055i
$876$	−26.6867	+	14.6646i	−0.901659	+	0.495471i
$877$		−	10.0167i		−	0.338240i	−0.985595	−	0.169120i	$-0.945908\pi$
$877$		−	10.0167i		−	0.338240i	0.985595	−	0.169120i	$-0.0540925\pi$
$878$	−0.262935	+	0.444504i	−0.00887363	+	0.0150013i
$879$	53.9394			1.81933
$880$	13.7149	−	21.5934i	0.462330	−	0.727912i
$881$	20.3551			0.685779			0.342890	−	0.939376i	$-0.388594\pi$
$881$	20.3551			0.685779			0.342890	+	0.939376i	$0.388594\pi$
$882$	2.94717	−	4.98233i	0.0992365	−	0.167764i
$883$		−	16.8609i		−	0.567415i	−0.958911	−	0.283707i	$-0.908436\pi$
$883$		−	16.8609i		−	0.567415i	0.958911	−	0.283707i	$-0.0915644\pi$
$884$	11.7385	−	6.45045i	0.394810	−	0.216952i
$885$		−	75.4769i		−	2.53713i
$886$	−44.0206	−	26.0392i	−1.47890	−	0.874806i
$887$	3.98272			0.133727			0.0668633	−	0.997762i	$-0.478701\pi$
$887$	3.98272			0.133727			0.0668633	+	0.997762i	$0.478701\pi$
$888$	57.5592	+	1.82506i	1.93156	+	0.0612449i
$889$	9.95073			0.333737
$890$	47.4207	+	28.0505i	1.58954	+	0.940255i
$891$		−	10.4312i		−	0.349457i
$892$	1.08613	+	1.97653i	0.0363662	+	0.0661793i
$893$		−	32.5337i		−	1.08870i
$894$	−9.12260	+	15.4222i	−0.305105	+	0.515795i
$895$	−18.8563			−0.630297
$896$	6.36538	−	9.35318i	0.212652	−	0.312468i
$897$	13.3912			0.447119
$898$	−15.4444	+	26.1095i	−0.515386	+	0.871284i
$899$		−	27.5267i		−	0.918065i
$900$	−10.6302	−	19.3449i	−0.354342	−	0.644831i
$901$			3.88141i			0.129308i
$902$	4.68553	+	2.77161i	0.156011	+	0.0922845i
$903$	13.0495			0.434261
$904$	22.6032	+	0.716689i	0.751770	+	0.0238367i
$905$	−41.3842			−1.37566
$906$	21.8140	+	12.9035i	0.724722	+	0.428691i
$907$		−	16.0034i		−	0.531385i	−0.964058	−	0.265692i	$-0.914399\pi$
$907$		−	16.0034i		−	0.531385i	0.964058	−	0.265692i	$-0.0856005\pi$
$908$	49.1501	−	27.0085i	1.63110	−	0.896310i
$909$			48.3351i			1.60317i
$910$	1.99746	−	3.37680i	0.0662151	−	0.111940i
$911$	5.85697			0.194050			0.0970250	−	0.995282i	$-0.469067\pi$
$911$	5.85697			0.194050			0.0970250	+	0.995282i	$0.469067\pi$
$912$	−13.7297	+	21.6166i	−0.454635	+	0.715797i
$913$	0.605256			0.0200310
$914$	−2.01814	+	3.41176i	−0.0667542	+	0.112851i
$915$		−	58.5248i		−	1.93477i
$916$	34.6628	−	19.0476i	1.14529	−	0.629349i
$917$		−	0.170370i		−	0.00562611i
$918$	−23.7351	−	14.0399i	−0.783375	−	0.463386i
$919$	−34.9195			−1.15189			−0.575943	−	0.817490i	$-0.695365\pi$
$919$	−34.9195			−1.15189			−0.575943	+	0.817490i	$0.695365\pi$
$920$	−1.25033	+	39.4334i	−0.0412223	+	1.30008i
$921$	30.5175			1.00559
$922$	−23.9594	−	14.1726i	−0.789062	−	0.466750i
$923$		−	7.75298i		−	0.255193i
$924$	−5.91346	−	10.7613i	−0.194538	−	0.354021i
$925$			20.6126i			0.677738i
$926$	−7.91614	+	13.3826i	−0.260140	+	0.439779i
$927$	11.4628			0.376487
$928$	21.2812	−	10.8307i	0.698588	−	0.355537i
$929$	−43.0245			−1.41159			−0.705794	−	0.708417i	$-0.749410\pi$
$929$	−43.0245			−1.41159			−0.705794	+	0.708417i	$0.749410\pi$
$930$	−34.6911	+	58.6469i	−1.13757	+	1.92311i
$931$		−	2.40379i		−	0.0787810i
$932$	25.7641	+	46.8856i	0.843932	+	1.53579i
$933$			19.1191i			0.625932i
$934$	−31.8376	−	18.8327i	−1.04176	−	0.616225i
$935$	42.8287			1.40065
$936$	−0.366908	+	11.5717i	−0.0119928	+	0.378231i
$937$	−0.552460			−0.0180481			−0.00902404	−	0.999959i	$-0.502872\pi$
$937$	−0.552460			−0.0180481			−0.00902404	+	0.999959i	$0.502872\pi$
$938$	−8.27823	−	4.89678i	−0.270294	−	0.159886i
$939$			74.8711i			2.44333i
$940$	65.8126	−	36.1647i	2.14657	−	1.17956i
$941$			54.7997i			1.78642i	0.449641	+	0.893210i	$0.351552\pi$
$941$			54.7997i			1.78642i	−0.449641	+	0.893210i	$0.648448\pi$
$942$	14.1361	−	23.8978i	0.460580	−	0.778632i
$943$	−8.39615			−0.273416
$944$	−34.4920	−	21.9074i	−1.12262	−	0.713026i
$945$	−8.07765			−0.262766
$946$	8.13243	−	13.7482i	0.264408	−	0.446994i
$947$		−	33.7873i		−	1.09794i	−0.835843	−	0.548969i	$-0.815020\pi$
$947$		−	33.7873i		−	1.09794i	0.835843	−	0.548969i	$-0.184980\pi$
$948$	56.2698	−	30.9209i	1.82756	−	1.00426i
$949$			5.71664i			0.185570i
$950$	−7.88911	−	4.66660i	−0.255956	−	0.151405i
$951$	41.6907			1.35191
$952$	18.9326	+	0.600304i	0.613608	+	0.0194560i
$953$	15.2367			0.493565			0.246782	−	0.969071i	$-0.420627\pi$
$953$	15.2367			0.493565			0.246782	+	0.969071i	$0.420627\pi$
$954$	−2.88761	−	1.70809i	−0.0934899	−	0.0553016i
$955$		−	37.6022i		−	1.21678i
$956$	−18.9729	−	34.5269i	−0.613628	−	1.11668i
$957$		−	25.9161i		−	0.837750i
$958$	−0.815599	+	1.37881i	−0.0263508	+	0.0445473i
$959$	21.3225			0.688539
$960$	−58.9903	−	3.74463i	−1.90390	−	0.120857i
$961$	11.5241			0.371745
$962$	5.50430	−	9.30527i	0.177466	−	0.300014i
$963$		−	11.4777i		−	0.369865i
$964$	−8.00673	−	14.5706i	−0.257879	−	0.469289i
$965$		−	12.7993i		−	0.412023i
$966$	16.2999	+	9.64177i	0.524439	+	0.310219i
$967$	−14.5570			−0.468121			−0.234060	−	0.972222i	$-0.575201\pi$
$967$	−14.5570			−0.468121			−0.234060	+	0.972222i	$0.575201\pi$
$968$	16.0743	+	0.509675i	0.516648	+	0.0163816i
$969$	−42.8748			−1.37734
$970$	53.8202	+	31.8360i	1.72806	+	1.02219i
$971$			11.6461i			0.373742i	0.982384	+	0.186871i	$0.0598346\pi$
$971$			11.6461i			0.373742i	−0.982384	+	0.186871i	$0.940165\pi$
$972$	−36.4347	+	20.0213i	−1.16864	+	0.642182i
$973$		−	2.75623i		−	0.0883608i
$974$	13.7677	−	23.2749i	0.441145	−	0.745777i
$975$	−7.18109			−0.229979
$976$	−26.7451	−	16.9870i	−0.856089	−	0.543741i
$977$	58.9341			1.88547			0.942734	−	0.333545i	$-0.108245\pi$
$977$	58.9341			1.88547			0.942734	+	0.333545i	$0.108245\pi$
$978$	19.5088	−	32.9806i	0.623824	−	1.05460i
$979$		−	32.3724i		−	1.03463i
$980$	4.86264	−	2.67207i	0.155331	−	0.0853562i
$981$		−	37.7828i		−	1.20631i
$982$	−51.0555	−	30.2006i	−1.62925	−	0.963739i
$983$	−58.3762			−1.86191			−0.930957	−	0.365130i	$-0.881025\pi$
$983$	−58.3762			−1.86191			−0.930957	+	0.365130i	$0.881025\pi$
$984$	0.398652	−	12.5728i	0.0127086	−	0.400807i
$985$	14.4552			0.460581
$986$	34.4098	+	20.3543i	1.09583	+	0.648212i
$987$		−	36.0462i		−	1.14736i
$988$	2.31528	+	4.21335i	0.0736589	+	0.134044i
$989$			24.6359i			0.783377i
$990$	−18.8477	+	31.8629i	−0.599019	+	1.01267i
$991$	−4.43349			−0.140834			−0.0704172	−	0.997518i	$-0.522433\pi$
$991$	−4.43349			−0.140834			−0.0704172	+	0.997518i	$0.522433\pi$
$992$	16.7317	+	32.8758i	0.531232	+	1.04381i
$993$	45.7465			1.45172
$994$	5.58220	−	9.43698i	0.177057	−	0.299323i
$995$			66.0312i			2.09333i
$996$	−0.673531	−	1.22569i	−0.0213416	−	0.0388375i
$997$		−	19.9632i		−	0.632241i	−0.948719	−	0.316121i	$-0.897620\pi$
$997$		−	19.9632i		−	0.632241i	0.948719	−	0.316121i	$-0.102380\pi$
$998$	−41.4218	−	24.5020i	−1.31118	−	0.775598i
$999$	−22.2592			−0.704249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.a.365.10	yes	34
4.3	odd	2		2912.2.c.a.1457.5		34
8.3	odd	2		2912.2.c.a.1457.30		34
8.5	even	2	inner	728.2.c.a.365.9	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.a.365.9	✓	34	8.5	even	2	inner
728.2.c.a.365.10	yes	34	1.1	even	1	trivial
2912.2.c.a.1457.5		34	4.3	odd	2
2912.2.c.a.1457.30		34	8.3	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+(-0.720007 + 1.21721i) q^{2} +2.66332i q^{3} +(-0.963179 - 1.75279i) q^{4} +2.77422i q^{5} +(-3.24180 - 1.91761i) q^{6} -1.00000 q^{7} +(2.82701 + 0.0896372i) q^{8} -4.09325 q^{9} +(-3.37680 - 1.99746i) q^{10} +2.30522i q^{11} +(4.66824 - 2.56525i) q^{12} -1.00000i q^{13} +(0.720007 - 1.21721i) q^{14} -7.38863 q^{15} +(-2.14457 + 3.37651i) q^{16} -6.69704 q^{17} +(2.94717 - 4.98233i) q^{18} -2.40379i q^{19} +(4.86264 - 2.67207i) q^{20} -2.66332i q^{21} +(-2.80592 - 1.65977i) q^{22} +5.02802 q^{23} +(-0.238732 + 7.52921i) q^{24} -2.69630 q^{25} +(1.21721 + 0.720007i) q^{26} -2.91168i q^{27} +(0.963179 + 1.75279i) q^{28} +4.22120i q^{29} +(5.31986 - 8.99348i) q^{30} -6.52105 q^{31} +(-2.56580 - 5.04150i) q^{32} -6.13952 q^{33} +(4.82192 - 8.15168i) q^{34} -2.77422i q^{35} +(3.94254 + 7.17463i) q^{36} -7.64478i q^{37} +(2.92591 + 1.73075i) q^{38} +2.66332 q^{39} +(-0.248673 + 7.84274i) q^{40} -1.66987 q^{41} +(3.24180 + 1.91761i) q^{42} +4.89973i q^{43} +(4.04057 - 2.22034i) q^{44} -11.3556i q^{45} +(-3.62021 + 6.12013i) q^{46} +13.5343 q^{47} +(-8.99271 - 5.71167i) q^{48} +1.00000 q^{49} +(1.94135 - 3.28195i) q^{50} -17.8363i q^{51} +(-1.75279 + 0.963179i) q^{52} -0.579570i q^{53} +(3.54412 + 2.09643i) q^{54} -6.39518 q^{55} +(-2.82701 - 0.0896372i) q^{56} +6.40205 q^{57} +(-5.13807 - 3.03929i) q^{58} +10.2153i q^{59} +(7.11657 + 12.9507i) q^{60} +7.92093i q^{61} +(4.69520 - 7.93746i) q^{62} +4.09325 q^{63} +(7.98393 + 0.506810i) q^{64} +2.77422 q^{65} +(4.42050 - 7.47306i) q^{66} -6.80101i q^{67} +(6.45045 + 11.7385i) q^{68} +13.3912i q^{69} +(3.37680 + 1.99746i) q^{70} +7.75298 q^{71} +(-11.5717 - 0.366908i) q^{72} -5.71664 q^{73} +(9.30527 + 5.50430i) q^{74} -7.18109i q^{75} +(-4.21335 + 2.31528i) q^{76} -2.30522i q^{77} +(-1.91761 + 3.24180i) q^{78} +12.0537 q^{79} +(-9.36718 - 5.94951i) q^{80} -4.52503 q^{81} +(1.20232 - 2.03258i) q^{82} -0.262559i q^{83} +(-4.66824 + 2.56525i) q^{84} -18.5791i q^{85} +(-5.96397 - 3.52784i) q^{86} -11.2424 q^{87} +(-0.206633 + 6.51686i) q^{88} -14.0431 q^{89} +(13.8221 + 8.17611i) q^{90} +1.00000i q^{91} +(-4.84288 - 8.81308i) q^{92} -17.3676i q^{93} +(-9.74482 + 16.4741i) q^{94} +6.66864 q^{95} +(13.4271 - 6.83353i) q^{96} -15.9382 q^{97} +(-0.720007 + 1.21721i) q^{98} -9.43584i 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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