LMFDB - Embedded newform 728.2.c.b.365.14

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 = [38] 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:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			365.14
Character	$\chi$	$=$	728.365
Dual form			728.2.c.b.365.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.716045 + 1.21954i) q^{2} -0.472093i q^{3} +(-0.974560 - 1.74649i) q^{4} -4.35100i q^{5} +(0.575736 + 0.338039i) q^{6} +1.00000 q^{7} +(2.82775 + 0.0620491i) q^{8} +2.77713 q^{9} +(5.30622 + 3.11551i) q^{10} -5.41704i q^{11} +(-0.824505 + 0.460083i) q^{12} +1.00000i q^{13} +(-0.716045 + 1.21954i) q^{14} -2.05407 q^{15} +(-2.10046 + 3.40412i) q^{16} -6.30026 q^{17} +(-1.98855 + 3.38682i) q^{18} +2.90969i q^{19} +(-7.59898 + 4.24031i) q^{20} -0.472093i q^{21} +(6.60630 + 3.87884i) q^{22} +1.16816 q^{23} +(0.0292929 - 1.33496i) q^{24} -13.9312 q^{25} +(-1.21954 - 0.716045i) q^{26} -2.72734i q^{27} +(-0.974560 - 1.74649i) q^{28} -0.400654i q^{29} +(1.47081 - 2.50503i) q^{30} +8.74485 q^{31} +(-2.64744 - 4.99911i) q^{32} -2.55734 q^{33} +(4.51127 - 7.68343i) q^{34} -4.35100i q^{35} +(-2.70648 - 4.85023i) q^{36} -0.159884i q^{37} +(-3.54849 - 2.08347i) q^{38} +0.472093 q^{39} +(0.269975 - 12.3035i) q^{40} -0.297993 q^{41} +(0.575736 + 0.338039i) q^{42} +3.74805i q^{43} +(-9.46082 + 5.27924i) q^{44} -12.0833i q^{45} +(-0.836453 + 1.42462i) q^{46} -3.08775 q^{47} +(1.60706 + 0.991613i) q^{48} +1.00000 q^{49} +(9.97533 - 16.9896i) q^{50} +2.97431i q^{51} +(1.74649 - 0.974560i) q^{52} -2.19197i q^{53} +(3.32610 + 1.95290i) q^{54} -23.5695 q^{55} +(2.82775 + 0.0620491i) q^{56} +1.37364 q^{57} +(0.488614 + 0.286886i) q^{58} +3.99383i q^{59} +(2.00182 + 3.58742i) q^{60} +3.08877i q^{61} +(-6.26170 + 10.6647i) q^{62} +2.77713 q^{63} +(7.99230 + 0.350918i) q^{64} +4.35100 q^{65} +(1.83117 - 3.11879i) q^{66} -13.4949i q^{67} +(6.13998 + 11.0033i) q^{68} -0.551479i q^{69} +(5.30622 + 3.11551i) q^{70} +12.0190 q^{71} +(7.85302 + 0.172318i) q^{72} -14.9363 q^{73} +(0.194985 + 0.114484i) q^{74} +6.57680i q^{75} +(5.08175 - 2.83567i) q^{76} -5.41704i q^{77} +(-0.338039 + 0.575736i) q^{78} +10.8497 q^{79} +(14.8113 + 9.13911i) q^{80} +7.04383 q^{81} +(0.213376 - 0.363414i) q^{82} +2.84395i q^{83} +(-0.824505 + 0.460083i) q^{84} +27.4124i q^{85} +(-4.57090 - 2.68377i) q^{86} -0.189146 q^{87} +(0.336122 - 15.3180i) q^{88} -12.0820 q^{89} +(14.7360 + 8.65216i) q^{90} +1.00000i q^{91} +(-1.13844 - 2.04018i) q^{92} -4.12838i q^{93} +(2.21096 - 3.76563i) q^{94} +12.6600 q^{95} +(-2.36004 + 1.24984i) q^{96} +4.12596 q^{97} +(-0.716045 + 1.21954i) q^{98} -15.0438i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{4} + 14 q^{6} + 38 q^{7} - 6 q^{8} - 46 q^{9} - 4 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 4 q^{18} - 24 q^{20} + 10 q^{22} + 12 q^{23} + 10 q^{24} - 50 q^{25} + 8 q^{28} + 4 q^{30} + 16 q^{31}+ \cdots + 82 q^{96}+O(q^{100}) $ 38 * q + 8 * q^4 + 14 * q^6 + 38 * q^7 - 6 * q^8 - 46 * q^9 - 4 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 4 * q^18 - 24 * q^20 + 10 * q^22 + 12 * q^23 + 10 * q^24 - 50 * q^25 + 8 * q^28 + 4 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 - 4 * q^34 - 38 * q^36 - 28 * q^38 + 8 * q^39 + 4 * q^40 + 8 * q^41 + 14 * q^42 - 40 * q^44 - 16 * q^46 + 4 * q^48 + 38 * q^49 + 24 * q^50 - 4 * q^52 - 14 * q^54 - 6 * q^56 + 8 * q^57 - 24 * q^58 + 44 * q^60 - 12 * q^62 - 46 * q^63 + 32 * q^64 + 20 * q^65 - 76 * q^66 - 52 * q^68 + 42 * q^72 + 50 * q^74 - 28 * q^76 - 12 * q^79 - 16 * q^80 + 62 * q^81 - 4 * q^84 + 44 * q^86 - 56 * q^87 - 6 * q^88 + 48 * q^90 + 2 * q^92 - 48 * q^94 + 82 * q^96

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 $

$2$	−0.716045	+	1.21954i	−0.506320	+	0.862346i
$2$	−0.716045	+	1.21954i	−0.506320	+	0.862346i
$3$		−	0.472093i		−	0.272563i	−0.990670	−	0.136281i	$-0.956485\pi$
$3$		−	0.472093i		−	0.272563i	0.990670	−	0.136281i	$-0.0435151\pi$
$4$	−0.974560	−	1.74649i	−0.487280	−	0.873246i
$5$		−	4.35100i		−	1.94582i	−0.231175	−	0.972912i	$-0.574257\pi$
$5$		−	4.35100i		−	1.94582i	0.231175	−	0.972912i	$-0.425743\pi$
$6$	0.575736	+	0.338039i	0.235043	+	0.138004i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.82775	+	0.0620491i	0.999759	+	0.0219377i
$9$	2.77713			0.925710
$10$	5.30622	+	3.11551i	1.67797	+	0.985210i
$11$		−	5.41704i		−	1.63330i	−0.577133	−	0.816650i	$-0.695829\pi$
$11$		−	5.41704i		−	1.63330i	0.577133	−	0.816650i	$-0.304171\pi$
$12$	−0.824505	+	0.460083i	−0.238014	+	0.132814i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−0.716045	+	1.21954i	−0.191371	+	0.325936i
$15$	−2.05407			−0.530359
$16$	−2.10046	+	3.40412i	−0.525116	+	0.851031i
$17$	−6.30026			−1.52804			−0.764019	−	0.645194i	$-0.776777\pi$
$17$	−6.30026			−1.52804			−0.764019	+	0.645194i	$0.776777\pi$
$18$	−1.98855	+	3.38682i	−0.468705	+	0.798282i
$19$			2.90969i			0.667529i	0.942657	+	0.333764i	$0.108319\pi$
$19$			2.90969i			0.667529i	−0.942657	+	0.333764i	$0.891681\pi$
$20$	−7.59898	+	4.24031i	−1.69918	+	0.948162i
$21$		−	0.472093i		−	0.103019i
$22$	6.60630	+	3.87884i	1.40847	+	0.826972i
$23$	1.16816			0.243578			0.121789	−	0.992556i	$-0.461137\pi$
$23$	1.16816			0.243578			0.121789	+	0.992556i	$0.461137\pi$
$24$	0.0292929	−	1.33496i	0.00597939	−	0.272497i
$25$	−13.9312			−2.78623
$26$	−1.21954	−	0.716045i	−0.239172	−	0.140428i
$27$		−	2.72734i		−	0.524877i
$28$	−0.974560	−	1.74649i	−0.184175	−	0.330056i
$29$		−	0.400654i		−	0.0743996i	−0.999308	−	0.0371998i	$-0.988156\pi$
$29$		−	0.400654i		−	0.0743996i	0.999308	−	0.0371998i	$-0.0118438\pi$
$30$	1.47081	−	2.50503i	0.268531	−	0.457353i
$31$	8.74485			1.57062			0.785310	−	0.619102i	$-0.212503\pi$
$31$	8.74485			1.57062			0.785310	+	0.619102i	$0.212503\pi$
$32$	−2.64744	−	4.99911i	−0.468006	−	0.883725i
$33$	−2.55734			−0.445177
$34$	4.51127	−	7.68343i	0.773676	−	1.31770i
$35$		−	4.35100i		−	0.735453i
$36$	−2.70648	−	4.85023i	−0.451080	−	0.808372i
$37$		−	0.159884i		−	0.0262848i	−0.999914	−	0.0131424i	$-0.995817\pi$
$37$		−	0.159884i		−	0.0262848i	0.999914	−	0.0131424i	$-0.00418348\pi$
$38$	−3.54849	−	2.08347i	−0.575640	−	0.337983i
$39$	0.472093			0.0755953
$40$	0.269975	−	12.3035i	0.0426868	−	1.94536i
$41$	−0.297993			−0.0465386			−0.0232693	−	0.999729i	$-0.507408\pi$
$41$	−0.297993			−0.0465386			−0.0232693	+	0.999729i	$0.507408\pi$
$42$	0.575736	+	0.338039i	0.0888380	+	0.0521606i
$43$			3.74805i			0.571573i	0.958293	+	0.285786i	$0.0922548\pi$
$43$			3.74805i			0.571573i	−0.958293	+	0.285786i	$0.907745\pi$
$44$	−9.46082	+	5.27924i	−1.42627	+	0.795875i
$45$		−	12.0833i		−	1.80127i
$46$	−0.836453	+	1.42462i	−0.123328	+	0.210048i
$47$	−3.08775			−0.450394			−0.225197	−	0.974313i	$-0.572303\pi$
$47$	−3.08775			−0.450394			−0.225197	+	0.974313i	$0.572303\pi$
$48$	1.60706	+	0.991613i	0.231959	+	0.143127i
$49$	1.00000			0.142857
$50$	9.97533	−	16.9896i	1.41073	−	2.40270i
$51$			2.97431i			0.416486i
$52$	1.74649	−	0.974560i	0.242195	−	0.135147i
$53$		−	2.19197i		−	0.301090i	−0.988603	−	0.150545i	$-0.951897\pi$
$53$		−	2.19197i		−	0.301090i	0.988603	−	0.150545i	$-0.0481028\pi$
$54$	3.32610	+	1.95290i	0.452625	+	0.265756i
$55$	−23.5695			−3.17811
$56$	2.82775	+	0.0620491i	0.377874	+	0.00829166i
$57$	1.37364			0.181943
$58$	0.488614	+	0.286886i	0.0641582	+	0.0376700i
$59$			3.99383i			0.519953i	0.965615	+	0.259976i	$0.0837147\pi$
$59$			3.99383i			0.519953i	−0.965615	+	0.259976i	$0.916285\pi$
$60$	2.00182	+	3.58742i	0.258434	+	0.463134i
$61$			3.08877i			0.395476i	0.980255	+	0.197738i	$0.0633595\pi$
$61$			3.08877i			0.395476i	−0.980255	+	0.197738i	$0.936640\pi$
$62$	−6.26170	+	10.6647i	−0.795236	+	1.35442i
$63$	2.77713			0.349885
$64$	7.99230	+	0.350918i	0.999037	+	0.0438648i
$65$	4.35100			0.539675
$66$	1.83117	−	3.11879i	0.225402	−	0.383896i
$67$		−	13.4949i		−	1.64866i	−0.566108	−	0.824331i	$-0.691551\pi$
$67$		−	13.4949i		−	1.64866i	0.566108	−	0.824331i	$-0.308449\pi$
$68$	6.13998	+	11.0033i	0.744582	+	1.33435i
$69$		−	0.551479i		−	0.0663902i
$70$	5.30622	+	3.11551i	0.634214	+	0.372374i
$71$	12.0190			1.42639			0.713194	−	0.700966i	$-0.247248\pi$
$71$	12.0190			1.42639			0.713194	+	0.700966i	$0.247248\pi$
$72$	7.85302	+	0.172318i	0.925487	+	0.0203079i
$73$	−14.9363			−1.74817			−0.874083	−	0.485777i	$-0.838537\pi$
$73$	−14.9363			−1.74817			−0.874083	+	0.485777i	$0.838537\pi$
$74$	0.194985	+	0.114484i	0.0226666	+	0.0133085i
$75$			6.57680i			0.759423i
$76$	5.08175	−	2.83567i	0.582916	−	0.325274i
$77$		−	5.41704i		−	0.617329i
$78$	−0.338039	+	0.575736i	−0.0382754	+	0.0651893i
$79$	10.8497			1.22069			0.610344	−	0.792136i	$-0.291031\pi$
$79$	10.8497			1.22069			0.610344	+	0.792136i	$0.291031\pi$
$80$	14.8113	+	9.13911i	1.65596	+	1.02178i
$81$	7.04383			0.782648
$82$	0.213376	−	0.363414i	0.0235634	−	0.0401324i
$83$			2.84395i			0.312164i	0.987744	+	0.156082i	$0.0498864\pi$
$83$			2.84395i			0.312164i	−0.987744	+	0.156082i	$0.950114\pi$
$84$	−0.824505	+	0.460083i	−0.0899609	+	0.0501991i
$85$			27.4124i			2.97329i
$86$	−4.57090	−	2.68377i	−0.492893	−	0.289399i
$87$	−0.189146			−0.0202786
$88$	0.336122	−	15.3180i	0.0358308	−	1.63291i
$89$	−12.0820			−1.28069			−0.640344	−	0.768089i	$-0.721208\pi$
$89$	−12.0820			−1.28069			−0.640344	+	0.768089i	$0.721208\pi$
$90$	14.7360	+	8.65216i	1.55332	+	0.912018i
$91$			1.00000i			0.104828i
$92$	−1.13844	−	2.04018i	−0.118691	−	0.212703i
$93$		−	4.12838i		−	0.428093i
$94$	2.21096	−	3.76563i	0.228044	−	0.388396i
$95$	12.6600			1.29889
$96$	−2.36004	+	1.24984i	−0.240871	+	0.127561i
$97$	4.12596			0.418928			0.209464	−	0.977816i	$-0.432828\pi$
$97$	4.12596			0.418928			0.209464	+	0.977816i	$0.432828\pi$
$98$	−0.716045	+	1.21954i	−0.0723314	+	0.123192i
$99$		−	15.0438i		−	1.51196i
$100$	13.5768	+	24.3307i	1.35768	+	2.43307i
$101$		−	12.4823i		−	1.24203i	−0.783798	−	0.621016i	$-0.786720\pi$
$101$		−	12.4823i		−	1.24203i	0.783798	−	0.621016i	$-0.213280\pi$
$102$	−3.62729	−	2.12974i	−0.359155	−	0.210875i
$103$	−6.86512			−0.676441			−0.338220	−	0.941067i	$-0.609825\pi$
$103$	−6.86512			−0.676441			−0.338220	+	0.941067i	$0.609825\pi$
$104$	−0.0620491	+	2.82775i	−0.00608441	+	0.277283i
$105$	−2.05407			−0.200457
$106$	2.67319	+	1.56955i	0.259643	+	0.152448i
$107$		−	11.9949i		−	1.15959i	−0.814761	−	0.579797i	$-0.803132\pi$
$107$		−	11.9949i		−	1.15959i	0.814761	−	0.579797i	$-0.196868\pi$
$108$	−4.76327	+	2.65796i	−0.458346	+	0.255762i
$109$			8.48497i			0.812713i	0.913715	+	0.406357i	$0.133201\pi$
$109$			8.48497i			0.812713i	−0.913715	+	0.406357i	$0.866799\pi$
$110$	16.8768	−	28.7440i	1.60914	−	2.74063i
$111$	−0.0754802			−0.00716426
$112$	−2.10046	+	3.40412i	−0.198475	+	0.321659i
$113$	4.48473			0.421888			0.210944	−	0.977498i	$-0.432346\pi$
$113$	4.48473			0.421888			0.210944	+	0.977498i	$0.432346\pi$
$114$	−0.983589	+	1.67521i	−0.0921216	+	0.156898i
$115$		−	5.08265i		−	0.473960i
$116$	−0.699739	+	0.390462i	−0.0649691	+	0.0362535i
$117$			2.77713i			0.256746i
$118$	−4.87064	−	2.85976i	−0.448379	−	0.263262i
$119$	−6.30026			−0.577544
$120$	−5.80840	−	0.127453i	−0.530232	−	0.0116348i
$121$	−18.3443			−1.66767
$122$	−3.76688	−	2.21169i	−0.341037	−	0.200237i
$123$			0.140680i			0.0126847i
$124$	−8.52238	−	15.2728i	−0.765332	−	1.37154i
$125$			38.8595i			3.47570i
$126$	−1.98855	+	3.38682i	−0.177154	+	0.301722i
$127$	−12.3978			−1.10013			−0.550064	−	0.835123i	$-0.685397\pi$
$127$	−12.3978			−1.10013			−0.550064	+	0.835123i	$0.685397\pi$
$128$	−6.15080	+	9.49566i	−0.543659	+	0.839306i
$129$	1.76943			0.155789
$130$	−3.11551	+	5.30622i	−0.273248	+	0.465386i
$131$		−	9.57331i		−	0.836424i	−0.908349	−	0.418212i	$-0.862657\pi$
$131$		−	9.57331i		−	0.836424i	0.908349	−	0.418212i	$-0.137343\pi$
$132$	2.49229	+	4.46638i	0.216926	+	0.388749i
$133$			2.90969i			0.252302i
$134$	16.4576	+	9.66294i	1.42172	+	0.834751i
$135$	−11.8666			−1.02132
$136$	−17.8155	−	0.390925i	−1.52767	−	0.0335216i
$137$	18.9891			1.62235			0.811173	−	0.584806i	$-0.198830\pi$
$137$	18.9891			1.62235			0.811173	+	0.584806i	$0.198830\pi$
$138$	0.672551	+	0.394883i	0.0572513	+	0.0336147i
$139$			3.06890i			0.260300i	0.991494	+	0.130150i	$0.0415459\pi$
$139$			3.06890i			0.260300i	−0.991494	+	0.130150i	$0.958454\pi$
$140$	−7.59898	+	4.24031i	−0.642231	+	0.358371i
$141$			1.45770i			0.122761i
$142$	−8.60611	+	14.6576i	−0.722209	+	1.23004i
$143$	5.41704			0.452996
$144$	−5.83326	+	9.45369i	−0.486105	+	0.787807i
$145$	−1.74324			−0.144769
$146$	10.6951	−	18.2155i	0.885131	−	1.50752i
$147$		−	0.472093i		−	0.0389375i
$148$	−0.279237	+	0.155817i	−0.0229531	+	0.0128081i
$149$			21.2507i			1.74092i	0.492238	+	0.870461i	$0.336179\pi$
$149$			21.2507i			1.74092i	−0.492238	+	0.870461i	$0.663821\pi$
$150$	−8.02068	−	4.70928i	−0.654885	−	0.384511i
$151$	20.7829			1.69129			0.845644	−	0.533748i	$-0.179217\pi$
$151$	20.7829			1.69129			0.845644	+	0.533748i	$0.179217\pi$
$152$	−0.180544	+	8.22786i	−0.0146440	+	0.667368i
$153$	−17.4966			−1.41452
$154$	6.60630	+	3.87884i	0.532351	+	0.312566i
$155$		−	38.0488i		−	3.05615i
$156$	−0.460083	−	0.824505i	−0.0368361	−	0.0660133i
$157$		−	22.4296i		−	1.79007i	−0.445992	−	0.895037i	$-0.647149\pi$
$157$		−	22.4296i		−	1.79007i	0.445992	−	0.895037i	$-0.352851\pi$
$158$	−7.76888	+	13.2317i	−0.618059	+	1.05266i
$159$	−1.03481			−0.0820658
$160$	−21.7511	+	11.5190i	−1.71957	+	0.910658i
$161$	1.16816			0.0920637
$162$	−5.04370	+	8.59024i	−0.396270	+	0.674913i
$163$			4.96229i			0.388676i	0.980935	+	0.194338i	$0.0622559\pi$
$163$			4.96229i			0.388676i	−0.980935	+	0.194338i	$0.937744\pi$
$164$	0.290412	+	0.520442i	0.0226774	+	0.0406397i
$165$			11.1270i			0.866236i
$166$	−3.46832	−	2.03640i	−0.269193	−	0.158055i
$167$	14.1209			1.09271			0.546354	−	0.837554i	$-0.316015\pi$
$167$	14.1209			1.09271			0.546354	+	0.837554i	$0.316015\pi$
$168$	0.0292929	−	1.33496i	0.00226000	−	0.102994i
$169$	−1.00000			−0.0769231
$170$	−33.4306	−	19.6285i	−2.56401	−	1.50544i
$171$			8.08058i			0.617938i
$172$	6.54594	−	3.65270i	0.499123	−	0.278516i
$173$			12.3799i			0.941225i	0.882340	+	0.470613i	$0.155967\pi$
$173$			12.3799i			0.941225i	−0.882340	+	0.470613i	$0.844033\pi$
$174$	0.135437	−	0.230671i	0.0102674	−	0.0174871i
$175$	−13.9312			−1.05310
$176$	18.4403	+	11.3783i	1.38999	+	0.857672i
$177$	1.88546			0.141720
$178$	8.65124	−	14.7345i	0.648438	−	1.10440i
$179$		−	2.72223i		−	0.203469i	−0.994812	−	0.101735i	$-0.967561\pi$
$179$		−	2.72223i		−	0.203469i	0.994812	−	0.101735i	$-0.0324393\pi$
$180$	−21.1033	+	11.7759i	−1.57295	+	0.877722i
$181$		−	8.86877i		−	0.659210i	−0.944119	−	0.329605i	$-0.893084\pi$
$181$		−	8.86877i		−	0.659210i	0.944119	−	0.329605i	$-0.106916\pi$
$182$	−1.21954	−	0.716045i	−0.0903984	−	0.0530768i
$183$	1.45818			0.107792
$184$	3.30325	+	0.0724831i	0.243519	+	0.00534353i
$185$	−0.695656			−0.0511456
$186$	5.03472	+	2.95610i	0.369164	+	0.216752i
$187$			34.1288i			2.49574i
$188$	3.00920	+	5.39272i	0.219468	+	0.393305i
$189$		−	2.72734i		−	0.198385i
$190$	−9.06516	+	15.4394i	−0.657656	+	1.12010i
$191$	12.7496			0.922526			0.461263	−	0.887264i	$-0.347397\pi$
$191$	12.7496			0.922526			0.461263	+	0.887264i	$0.347397\pi$
$192$	0.165666	−	3.77310i	0.0119559	−	0.272300i
$193$	6.80859			0.490093			0.245047	−	0.969511i	$-0.421197\pi$
$193$	6.80859			0.490093			0.245047	+	0.969511i	$0.421197\pi$
$194$	−2.95437	+	5.03178i	−0.212112	+	0.361261i
$195$		−	2.05407i		−	0.147095i
$196$	−0.974560	−	1.74649i	−0.0696115	−	0.124749i
$197$		−	14.9703i		−	1.06659i	−0.845929	−	0.533295i	$-0.820954\pi$
$197$		−	14.9703i		−	1.06659i	0.845929	−	0.533295i	$-0.179046\pi$
$198$	18.3466	+	10.7720i	1.30383	+	0.765536i
$199$	3.95895			0.280643			0.140321	−	0.990106i	$-0.455186\pi$
$199$	3.95895			0.280643			0.140321	+	0.990106i	$0.455186\pi$
$200$	−39.3938	−	0.864416i	−2.78556	−	0.0611234i
$201$	−6.37083			−0.449364
$202$	15.2226	+	8.93786i	1.07106	+	0.628865i
$203$		−	0.400654i		−	0.0281204i
$204$	5.19460	−	2.89864i	0.363695	−	0.202945i
$205$			1.29656i			0.0905560i
$206$	4.91573	−	8.37230i	0.342495	−	0.583326i
$207$	3.24412			0.225482
$208$	−3.40412	−	2.10046i	−0.236033	−	0.145641i
$209$	15.7619			1.09027
$210$	1.47081	−	2.50503i	0.101495	−	0.172863i
$211$			14.8313i			1.02103i	0.859870	+	0.510514i	$0.170545\pi$
$211$			14.8313i			1.02103i	−0.859870	+	0.510514i	$0.829455\pi$
$212$	−3.82825	+	2.13620i	−0.262925	+	0.146715i
$213$		−	5.67406i		−	0.388780i
$214$	14.6283	+	8.58890i	0.999970	+	0.587125i
$215$	16.3078			1.11218
$216$	0.169229	−	7.71222i	0.0115146	−	0.524750i
$217$	8.74485			0.593639
$218$	−10.3478	−	6.07562i	−0.700840	−	0.411493i
$219$			7.05133i			0.476485i
$220$	22.9699	+	41.1640i	1.54863	+	2.77527i
$221$		−	6.30026i		−	0.423801i
$222$	0.0540472	−	0.0920512i	0.00362741	−	0.00617807i
$223$	−7.89772			−0.528871			−0.264435	−	0.964403i	$-0.585186\pi$
$223$	−7.89772			−0.528871			−0.264435	+	0.964403i	$0.585186\pi$
$224$	−2.64744	−	4.99911i	−0.176890	−	0.334017i
$225$	−38.6886			−2.57924
$226$	−3.21126	+	5.46931i	−0.213610	+	0.363813i
$227$		−	1.72809i		−	0.114697i	−0.998354	−	0.0573486i	$-0.981735\pi$
$227$		−	1.72809i		−	0.114697i	0.998354	−	0.0573486i	$-0.0182647\pi$
$228$	−1.33870	−	2.39906i	−0.0886574	−	0.158881i
$229$			7.57367i			0.500482i	0.968184	+	0.250241i	$0.0805098\pi$
$229$			7.57367i			0.500482i	−0.968184	+	0.250241i	$0.919490\pi$
$230$	6.19850	+	3.63940i	0.408717	+	0.239975i
$231$	−2.55734			−0.168261
$232$	0.0248602	−	1.13295i	0.00163215	−	0.0743817i
$233$	−18.9238			−1.23974			−0.619869	−	0.784705i	$-0.712814\pi$
$233$	−18.9238			−1.23974			−0.619869	+	0.784705i	$0.712814\pi$
$234$	−3.38682	−	1.98855i	−0.221403	−	0.129995i
$235$			13.4348i			0.876388i
$236$	6.97519	−	3.89223i	0.454046	−	0.253363i
$237$		−	5.12207i		−	0.332714i
$238$	4.51127	−	7.68343i	0.292422	−	0.498042i
$239$	8.20643			0.530830			0.265415	−	0.964134i	$-0.414491\pi$
$239$	8.20643			0.530830			0.265415	+	0.964134i	$0.414491\pi$
$240$	4.31450	−	6.99232i	0.278500	−	0.451352i
$241$	2.28939			0.147473			0.0737364	−	0.997278i	$-0.476508\pi$
$241$	2.28939			0.147473			0.0737364	+	0.997278i	$0.476508\pi$
$242$	13.1354	−	22.3717i	0.844373	−	1.43811i
$243$		−	11.5074i		−	0.738197i
$244$	5.39450	−	3.01019i	0.345348	−	0.192708i
$245$		−	4.35100i		−	0.277975i
$246$	−0.171565	−	0.100733i	−0.0109386	−	0.00642251i
$247$	−2.90969			−0.185139
$248$	24.7282	+	0.542610i	1.57024	+	0.0344557i
$249$	1.34261			0.0850843
$250$	−47.3907	−	27.8251i	−2.99725	−	1.75981i
$251$		−	17.3722i		−	1.09652i	−0.836307	−	0.548261i	$-0.815290\pi$
$251$		−	17.3722i		−	1.09652i	0.836307	−	0.548261i	$-0.184710\pi$
$252$	−2.70648	−	4.85023i	−0.170492	−	0.305536i
$253$		−	6.32796i		−	0.397835i
$254$	8.87738	−	15.1196i	0.557017	−	0.948690i
$255$	12.9412			0.810409
$256$	−7.17610	−	14.3005i	−0.448507	−	0.893780i
$257$	22.3274			1.39274			0.696371	−	0.717682i	$-0.254797\pi$
$257$	22.3274			1.39274			0.696371	+	0.717682i	$0.254797\pi$
$258$	−1.26699	+	2.15789i	−0.0788793	+	0.134344i
$259$		−	0.159884i		−	0.00993473i
$260$	−4.24031	−	7.59898i	−0.262973	−	0.471269i
$261$		−	1.11267i		−	0.0688724i
$262$	11.6750	+	6.85492i	0.721287	+	0.423498i
$263$	−4.59398			−0.283277			−0.141638	−	0.989918i	$-0.545237\pi$
$263$	−4.59398			−0.283277			−0.141638	+	0.989918i	$0.545237\pi$
$264$	−7.23152	−	0.158681i	−0.445069	−	0.00976613i
$265$	−9.53723			−0.585868
$266$	−3.54849	−	2.08347i	−0.217572	−	0.127746i
$267$			5.70381i			0.349068i
$268$	−23.5687	+	13.1516i	−1.43969	+	0.803361i
$269$			13.6099i			0.829811i	0.909864	+	0.414906i	$0.136185\pi$
$269$			13.6099i			0.829811i	−0.909864	+	0.414906i	$0.863815\pi$
$270$	8.49704	−	14.4719i	0.517114	−	0.880729i
$271$	5.67078			0.344475			0.172238	−	0.985055i	$-0.444900\pi$
$271$	5.67078			0.344475			0.172238	+	0.985055i	$0.444900\pi$
$272$	13.2335	−	21.4469i	0.802397	−	1.30041i
$273$	0.472093			0.0285723
$274$	−13.5970	+	23.1580i	−0.821426	+	1.39902i
$275$			75.4657i			4.55075i
$276$	−0.963152	+	0.537449i	−0.0579750	+	0.0323506i
$277$			8.84466i			0.531424i	0.964052	+	0.265712i	$0.0856070\pi$
$277$			8.84466i			0.531424i	−0.964052	+	0.265712i	$0.914393\pi$
$278$	−3.74264	−	2.19747i	−0.224469	−	0.131795i
$279$	24.2856			1.45394
$280$	0.269975	−	12.3035i	0.0161341	−	0.735276i
$281$	−7.44480			−0.444120			−0.222060	−	0.975033i	$-0.571278\pi$
$281$	−7.44480			−0.444120			−0.222060	+	0.975033i	$0.571278\pi$
$282$	−1.77773	−	1.04378i	−0.105862	−	0.0621562i
$283$			20.0551i			1.19215i	0.802928	+	0.596076i	$0.203274\pi$
$283$			20.0551i			1.19215i	−0.802928	+	0.596076i	$0.796726\pi$
$284$	−11.7132	−	20.9910i	−0.695051	−	1.24559i
$285$		−	5.97671i		−	0.354030i
$286$	−3.87884	+	6.60630i	−0.229361	+	0.390639i
$287$	−0.297993			−0.0175899
$288$	−7.35229	−	13.8832i	−0.433238	−	0.818073i
$289$	22.6933			1.33490
$290$	1.24824	−	2.12596i	0.0732992	−	0.124841i
$291$		−	1.94784i		−	0.114184i
$292$	14.5564	+	26.0862i	0.851847	+	1.52658i
$293$		−	10.5540i		−	0.616571i	−0.951294	−	0.308286i	$-0.900245\pi$
$293$		−	10.5540i		−	0.616571i	0.951294	−	0.308286i	$-0.0997553\pi$
$294$	0.575736	+	0.338039i	0.0335776	+	0.0197148i
$295$	17.3771			1.01174
$296$	0.00992067	−	0.452112i	0.000576627	−	0.0262785i
$297$	−14.7741			−0.857281
$298$	−25.9160	−	15.2164i	−1.50128	−	0.881463i
$299$			1.16816i			0.0675563i
$300$	11.4863	−	6.40949i	0.663163	−	0.370052i
$301$			3.74805i			0.216034i
$302$	−14.8815	+	25.3456i	−0.856332	+	1.45847i
$303$	−5.89278			−0.338532
$304$	−9.90494	−	6.11170i	−0.568087	−	0.350530i
$305$	13.4392			0.769527
$306$	12.5284	−	21.3379i	0.716199	−	1.21980i
$307$			30.5275i			1.74230i	0.491019	+	0.871149i	$0.336625\pi$
$307$			30.5275i			1.74230i	−0.491019	+	0.871149i	$0.663375\pi$
$308$	−9.46082	+	5.27924i	−0.539080	+	0.300812i
$309$			3.24097i			0.184373i
$310$	46.4021	+	27.2446i	2.63546	+	1.54739i
$311$	−6.79005			−0.385028			−0.192514	−	0.981294i	$-0.561664\pi$
$311$	−6.79005			−0.385028			−0.192514	+	0.981294i	$0.561664\pi$
$312$	1.33496	+	0.0292929i	0.0755771	+	0.00165838i
$313$	13.1789			0.744916			0.372458	−	0.928049i	$-0.378515\pi$
$313$	13.1789			0.744916			0.372458	+	0.928049i	$0.378515\pi$
$314$	27.3538	+	16.0606i	1.54366	+	0.906350i
$315$		−	12.0833i		−	0.680815i
$316$	−10.5737	−	18.9489i	−0.594817	−	1.06596i
$317$		−	0.546150i		−	0.0306748i	−0.999882	−	0.0153374i	$-0.995118\pi$
$317$		−	0.546150i		−	0.0306748i	0.999882	−	0.0153374i	$-0.00488224\pi$
$318$	0.740971	−	1.26199i	0.0415516	−	0.0707691i
$319$	−2.17036			−0.121517
$320$	1.52684	−	34.7745i	0.0853531	−	1.94395i
$321$	−5.66271			−0.316062
$322$	−0.836453	+	1.42462i	−0.0466137	+	0.0793908i
$323$		−	18.3318i		−	1.02001i
$324$	−6.86464	−	12.3020i	−0.381369	−	0.683444i
$325$		−	13.9312i		−	0.772762i
$326$	−6.05171	−	3.55322i	−0.335173	−	0.196795i
$327$	4.00569			0.221515
$328$	−0.842648	−	0.0184902i	−0.0465274	−	0.00102095i
$329$	−3.08775			−0.170233
$330$	−13.5698	−	7.96743i	−0.746995	−	0.438592i
$331$		−	7.11055i		−	0.390831i	−0.980721	−	0.195416i	$-0.937394\pi$
$331$		−	7.11055i		−	0.390831i	0.980721	−	0.195416i	$-0.0626056\pi$
$332$	4.96694	−	2.77160i	0.272596	−	0.152111i
$333$		−	0.444019i		−	0.0243321i
$334$	−10.1112	+	17.2210i	−0.553260	+	0.942293i
$335$	−58.7162			−3.20801
$336$	1.60706	+	0.991613i	0.0876724	+	0.0540969i
$337$	26.3087			1.43313			0.716563	−	0.697522i	$-0.245714\pi$
$337$	26.3087			1.43313			0.716563	+	0.697522i	$0.245714\pi$
$338$	0.716045	−	1.21954i	0.0389477	−	0.0663343i
$339$		−	2.11721i		−	0.114991i
$340$	47.8755	−	26.7150i	2.59641	−	1.44883i
$341$		−	47.3712i		−	2.56529i
$342$	−9.85460	−	5.78606i	−0.532876	−	0.312874i
$343$	1.00000			0.0539949
$344$	−0.232563	+	10.5985i	−0.0125390	+	0.571435i
$345$	−2.39948			−0.129184
$346$	−15.0978	−	8.86455i	−0.811662	−	0.476561i
$347$			1.49493i			0.0802522i	0.999195	+	0.0401261i	$0.0127760\pi$
$347$			1.49493i			0.0802522i	−0.999195	+	0.0401261i	$0.987224\pi$
$348$	0.184334	+	0.330342i	0.00988134	+	0.0177082i
$349$		−	18.6568i		−	0.998676i	−0.866407	−	0.499338i	$-0.833577\pi$
$349$		−	18.6568i		−	0.998676i	0.866407	−	0.499338i	$-0.166423\pi$
$350$	9.97533	−	16.9896i	0.533204	−	0.908134i
$351$	2.72734			0.145575
$352$	−27.0804	+	14.3413i	−1.44339	+	0.764394i
$353$	−10.9878			−0.584819			−0.292410	−	0.956293i	$-0.594457\pi$
$353$	−10.9878			−0.584819			−0.292410	+	0.956293i	$0.594457\pi$
$354$	−1.35007	+	2.29939i	−0.0717555	+	0.122211i
$355$		−	52.2945i		−	2.77550i
$356$	11.7746	+	21.1011i	0.624054	+	1.11835i
$357$			2.97431i			0.157417i
$358$	3.31988	+	1.94924i	0.175461	+	0.103021i
$359$	21.7824			1.14963			0.574816	−	0.818283i	$-0.305074\pi$
$359$	21.7824			1.14963			0.574816	+	0.818283i	$0.305074\pi$
$360$	0.749756	−	34.1684i	0.0395156	−	1.80083i
$361$	10.5337			0.554406
$362$	10.8158	+	6.35043i	0.568467	+	0.333771i
$363$			8.66023i			0.454544i
$364$	1.74649	−	0.974560i	0.0915410	−	0.0510808i
$365$			64.9879i			3.40162i
$366$	−1.04412	+	1.77831i	−0.0545772	+	0.0929540i
$367$	4.69959			0.245317			0.122658	−	0.992449i	$-0.460858\pi$
$367$	4.69959			0.245317			0.122658	+	0.992449i	$0.460858\pi$
$368$	−2.45367	+	3.97655i	−0.127907	+	0.207292i
$369$	−0.827564			−0.0430813
$370$	0.498121	−	0.848381i	0.0258961	−	0.0441052i
$371$		−	2.19197i		−	0.113801i
$372$	−7.21017	+	4.02335i	−0.373830	+	0.208601i
$373$		−	21.5919i		−	1.11798i	−0.829173	−	0.558992i	$-0.811188\pi$
$373$		−	21.5919i		−	1.11798i	0.829173	−	0.558992i	$-0.188812\pi$
$374$	−41.6214	−	24.4377i	−2.15219	−	1.26364i
$375$	18.3453			0.947345
$376$	−8.73137	−	0.191592i	−0.450286	−	0.00988060i
$377$	0.400654			0.0206347
$378$	3.32610	+	1.95290i	0.171076	+	0.100446i
$379$		−	9.62845i		−	0.494580i	−0.968941	−	0.247290i	$-0.920460\pi$
$379$		−	9.62845i		−	0.494580i	0.968941	−	0.247290i	$-0.0795401\pi$
$380$	−12.3380	−	22.1107i	−0.632925	−	1.13425i
$381$			5.85291i			0.299854i
$382$	−9.12925	+	15.5486i	−0.467093	+	0.795536i
$383$	22.1615			1.13240			0.566200	−	0.824268i	$-0.308413\pi$
$383$	22.1615			1.13240			0.566200	+	0.824268i	$0.308413\pi$
$384$	4.48283	+	2.90375i	0.228764	+	0.148181i
$385$	−23.5695			−1.20121
$386$	−4.87525	+	8.30336i	−0.248144	+	0.422630i
$387$			10.4088i			0.529110i
$388$	−4.02100	−	7.20596i	−0.204135	−	0.365827i
$389$			3.73770i			0.189509i	0.995501	+	0.0947544i	$0.0302066\pi$
$389$			3.73770i			0.189509i	−0.995501	+	0.0947544i	$0.969793\pi$
$390$	2.50503	+	1.47081i	0.126847	+	0.0744772i
$391$	−7.35970			−0.372196
$392$	2.82775	+	0.0620491i	0.142823	+	0.00313395i
$393$	−4.51949			−0.227978
$394$	18.2569	+	10.7194i	0.919769	+	0.540036i
$395$		−	47.2071i		−	2.37524i
$396$	−26.2739	+	14.6611i	−1.32031	+	0.736749i
$397$		−	1.99523i		−	0.100138i	−0.998746	−	0.0500689i	$-0.984056\pi$
$397$		−	1.99523i		−	0.100138i	0.998746	−	0.0500689i	$-0.0159441\pi$
$398$	−2.83479	+	4.82810i	−0.142095	+	0.242011i
$399$	1.37364			0.0687682
$400$	29.2619	−	47.4234i	1.46310	−	2.37117i
$401$	21.5512			1.07622			0.538108	−	0.842876i	$-0.319139\pi$
$401$	21.5512			1.07622			0.538108	+	0.842876i	$0.319139\pi$
$402$	4.56180	−	7.76949i	0.227522	−	0.387507i
$403$			8.74485i			0.435612i
$404$	−21.8002	+	12.1647i	−1.08460	+	0.605218i
$405$		−	30.6477i		−	1.52290i
$406$	0.488614	+	0.286886i	0.0242495	+	0.0142379i
$407$	−0.866100			−0.0429310
$408$	−0.184553	+	8.41058i	−0.00913673	+	0.416386i
$409$	2.57866			0.127507			0.0637533	−	0.997966i	$-0.479693\pi$
$409$	2.57866			0.127507			0.0637533	+	0.997966i	$0.479693\pi$
$410$	−1.58121	−	0.928398i	−0.0780906	−	0.0458503i
$411$		−	8.96460i		−	0.442191i
$412$	6.69048	+	11.9899i	0.329616	+	0.590699i
$413$			3.99383i			0.196524i
$414$	−2.32294	+	3.95634i	−0.114166	+	0.194444i
$415$	12.3740			0.607417
$416$	4.99911	−	2.64744i	0.245101	−	0.129802i
$417$	1.44880			0.0709482
$418$	−11.2862	+	19.2223i	−0.552028	+	0.940193i
$419$		−	19.4601i		−	0.950687i	−0.879800	−	0.475344i	$-0.842324\pi$
$419$		−	19.4601i		−	0.950687i	0.879800	−	0.475344i	$-0.157676\pi$
$420$	2.00182	+	3.58742i	0.0976787	+	0.175048i
$421$		−	29.1474i		−	1.42056i	−0.703921	−	0.710278i	$-0.748569\pi$
$421$		−	29.1474i		−	1.42056i	0.703921	−	0.710278i	$-0.251431\pi$
$422$	−18.0874	−	10.6199i	−0.880479	−	0.516967i
$423$	−8.57507			−0.416934
$424$	0.136009	−	6.19832i	0.00660520	−	0.301017i
$425$	87.7700			4.25747
$426$	6.91975	+	4.06288i	0.335263	+	0.196847i
$427$			3.08877i			0.149476i
$428$	−20.9490	+	11.6898i	−1.01261	+	0.565047i
$429$		−	2.55734i		−	0.123470i
$430$	−11.6771	+	19.8880i	−0.563119	+	0.959084i
$431$	−2.14758			−0.103445			−0.0517227	−	0.998661i	$-0.516471\pi$
$431$	−2.14758			−0.103445			−0.0517227	+	0.998661i	$0.516471\pi$
$432$	9.28420	+	5.72868i	0.446686	+	0.275621i
$433$	5.29651			0.254534			0.127267	−	0.991869i	$-0.459380\pi$
$433$	5.29651			0.254534			0.127267	+	0.991869i	$0.459380\pi$
$434$	−6.26170	+	10.6647i	−0.300571	+	0.511922i
$435$			0.822973i			0.0394585i
$436$	14.8189	−	8.26912i	0.709698	−	0.396019i
$437$			3.39898i			0.162595i
$438$	−8.59939	−	5.04907i	−0.410895	−	0.241254i
$439$	10.7736			0.514195			0.257097	−	0.966386i	$-0.417234\pi$
$439$	10.7736			0.514195			0.257097	+	0.966386i	$0.417234\pi$
$440$	−66.6486	−	1.46247i	−3.17735	−	0.0697204i
$441$	2.77713			0.132244
$442$	7.68343	+	4.51127i	0.365463	+	0.214579i
$443$			17.6054i			0.836456i	0.908342	+	0.418228i	$0.137349\pi$
$443$			17.6054i			0.836456i	−0.908342	+	0.418228i	$0.862651\pi$
$444$	0.0735600	+	0.131825i	0.00349100	+	0.00625616i
$445$			52.5686i			2.49199i
$446$	5.65512	−	9.63160i	0.267778	−	0.456069i
$447$	10.0323			0.474510
$448$	7.99230	+	0.350918i	0.377601	+	0.0165793i
$449$	−3.03371			−0.143170			−0.0715848	−	0.997435i	$-0.522806\pi$
$449$	−3.03371			−0.143170			−0.0715848	+	0.997435i	$0.522806\pi$
$450$	27.7028	−	47.1824i	1.30592	−	2.22420i
$451$			1.61424i			0.0760115i
$452$	−4.37064	−	7.83253i	−0.205577	−	0.368411i
$453$		−	9.81144i		−	0.460982i
$454$	2.10748	+	1.23739i	0.0989087	+	0.0580735i
$455$	4.35100			0.203978
$456$	3.88431	+	0.0852333i	0.181900	+	0.00399141i
$457$	12.3629			0.578314			0.289157	−	0.957282i	$-0.406625\pi$
$457$	12.3629			0.578314			0.289157	+	0.957282i	$0.406625\pi$
$458$	−9.23640	−	5.42308i	−0.431588	−	0.253404i
$459$			17.1829i			0.802031i
$460$	−8.87680	+	4.95335i	−0.413883	+	0.230951i
$461$			12.3695i			0.576105i	0.957615	+	0.288053i	$0.0930078\pi$
$461$			12.3695i			0.576105i	−0.957615	+	0.288053i	$0.906992\pi$
$462$	1.83117	−	3.11879i	0.0851939	−	0.145099i
$463$	−10.5401			−0.489842			−0.244921	−	0.969543i	$-0.578762\pi$
$463$	−10.5401			−0.489842			−0.244921	+	0.969543i	$0.578762\pi$
$464$	1.36388	+	0.841560i	0.0633164	+	0.0390684i
$465$	−17.9625			−0.832993
$466$	13.5503	−	23.0783i	0.627704	−	1.06908i
$467$		−	24.0562i		−	1.11319i	−0.830785	−	0.556593i	$-0.812108\pi$
$467$		−	24.0562i		−	1.11319i	0.830785	−	0.556593i	$-0.187892\pi$
$468$	4.85023	−	2.70648i	0.224202	−	0.125107i
$469$		−	13.4949i		−	0.623136i
$470$	−16.3843	−	9.61990i	−0.755750	−	0.443733i
$471$	−10.5888			−0.487907
$472$	−0.247814	+	11.2935i	−0.0114065	+	0.519827i
$473$	20.3034			0.933549
$474$	6.24657	+	3.66763i	0.286915	+	0.168460i
$475$		−	40.5354i		−	1.85989i
$476$	6.13998	+	11.0033i	0.281426	+	0.504338i
$477$		−	6.08737i		−	0.278722i
$478$	−5.87617	+	10.0081i	−0.268770	+	0.457759i
$479$	27.9128			1.27537			0.637684	−	0.770298i	$-0.279893\pi$
$479$	27.9128			1.27537			0.637684	+	0.770298i	$0.279893\pi$
$480$	5.43804	+	10.2685i	0.248211	+	0.468692i
$481$	0.159884			0.00729010
$482$	−1.63931	+	2.79201i	−0.0746685	+	0.127173i
$483$		−	0.551479i		−	0.0250931i
$484$	17.8777	+	32.0382i	0.812622	+	1.45628i
$485$		−	17.9520i		−	0.815160i
$486$	14.0337	+	8.23978i	0.636581	+	0.373764i
$487$	16.7547			0.759228			0.379614	−	0.925145i	$-0.376057\pi$
$487$	16.7547			0.759228			0.379614	+	0.925145i	$0.376057\pi$
$488$	−0.191655	+	8.73424i	−0.00867582	+	0.395381i
$489$	2.34266			0.105939
$490$	5.30622	+	3.11551i	0.239710	+	0.140744i
$491$			20.4381i			0.922358i	0.887307	+	0.461179i	$0.152573\pi$
$491$			20.4381i			0.922358i	−0.887307	+	0.461179i	$0.847427\pi$
$492$	0.245697	−	0.137101i	0.0110769	−	0.00618100i
$493$			2.52423i			0.113685i
$494$	2.08347	−	3.54849i	0.0937396	−	0.159654i
$495$	−65.4556			−2.94201
$496$	−18.3682	+	29.7685i	−0.824758	+	1.33665i
$497$	12.0190			0.539124
$498$	−0.961367	+	1.63737i	−0.0430799	+	0.0733721i
$499$		−	7.68749i		−	0.344140i	−0.985085	−	0.172070i	$-0.944955\pi$
$499$		−	7.68749i		−	0.344140i	0.985085	−	0.172070i	$-0.0550454\pi$
$500$	67.8677	−	37.8709i	3.03514	−	1.69364i
$501$		−	6.66637i		−	0.297832i
$502$	21.1861	+	12.4392i	0.945581	+	0.555191i
$503$	−8.82850			−0.393643			−0.196822	−	0.980439i	$-0.563062\pi$
$503$	−8.82850			−0.393643			−0.196822	+	0.980439i	$0.563062\pi$
$504$	7.85302	+	0.172318i	0.349801	+	0.00767567i
$505$	−54.3103			−2.41678
$506$	7.71721	+	4.53110i	0.343072	+	0.201432i
$507$			0.472093i			0.0209664i
$508$	12.0824	+	21.6527i	0.536071	+	0.960682i
$509$			32.5689i			1.44359i	0.692107	+	0.721795i	$0.256683\pi$
$509$			32.5689i			1.44359i	−0.692107	+	0.721795i	$0.743317\pi$
$510$	−9.26647	+	15.7823i	−0.410326	+	0.698853i
$511$	−14.9363			−0.660745
$512$	22.5784	+	1.48822i	0.997835	+	0.0657708i
$513$	7.93571			0.350370
$514$	−15.9874	+	27.2291i	−0.705173	+	1.20103i
$515$			29.8701i			1.31624i
$516$	−1.72441	−	3.09029i	−0.0759131	−	0.136042i
$517$			16.7265i			0.735629i
$518$	0.194985	+	0.114484i	0.00856717	+	0.00503015i
$519$	5.84445			0.256543
$520$	12.3035	+	0.269975i	0.539545	+	0.0118392i
$521$	−45.4292			−1.99029			−0.995145	−	0.0984169i	$-0.968622\pi$
$521$	−45.4292			−1.99029			−0.995145	+	0.0984169i	$0.968622\pi$
$522$	1.35694	+	0.796720i	0.0593919	+	0.0348715i
$523$			30.9751i			1.35445i	0.735778	+	0.677223i	$0.236817\pi$
$523$			30.9751i			1.35445i	−0.735778	+	0.677223i	$0.763183\pi$
$524$	−16.7197	+	9.32977i	−0.730404	+	0.407573i
$525$			6.57680i			0.287035i
$526$	3.28949	−	5.60254i	0.143429	−	0.244282i
$527$	−55.0948			−2.39997
$528$	5.37161	−	8.70552i	0.233769	−	0.378859i
$529$	−21.6354			−0.940670
$530$	6.82908	−	11.6310i	0.296636	−	0.505220i
$531$			11.0914i			0.481325i
$532$	5.08175	−	2.83567i	0.220322	−	0.122942i
$533$		−	0.297993i		−	0.0129075i
$534$	−6.95603	−	4.08418i	−0.301017	−	0.176740i
$535$	−52.1899			−2.25636
$536$	0.837345	−	38.1601i	0.0361678	−	1.64827i
$537$	−1.28515			−0.0554582
$538$	−16.5978	−	9.74530i	−0.715584	−	0.420150i
$539$		−	5.41704i		−	0.233329i
$540$	11.5648	+	20.7250i	0.497668	+	0.891861i
$541$		−	6.42309i		−	0.276150i	−0.990422	−	0.138075i	$-0.955908\pi$
$541$		−	6.42309i		−	0.276150i	0.990422	−	0.138075i	$-0.0440915\pi$
$542$	−4.06053	+	6.91574i	−0.174415	+	0.297057i
$543$	−4.18688			−0.179676
$544$	16.6796	+	31.4957i	0.715131	+	1.35037i
$545$	36.9181			1.58140
$546$	−0.338039	+	0.575736i	−0.0144667	+	0.0246392i
$547$			20.2300i			0.864973i	0.901640	+	0.432487i	$0.142364\pi$
$547$			20.2300i			0.864973i	−0.901640	+	0.432487i	$0.857636\pi$
$548$	−18.5060	−	33.1642i	−0.790537	−	1.41671i
$549$			8.57790i			0.366096i
$550$	−92.0335	−	54.0368i	−3.92432	−	2.30414i
$551$	1.16578			0.0496639
$552$	0.0342187	−	1.55944i	0.00145645	−	0.0663742i
$553$	10.8497			0.461377
$554$	−10.7864	−	6.33317i	−0.458271	−	0.269070i
$555$			0.328414i			0.0139404i
$556$	5.35980	−	2.99082i	0.227306	−	0.126839i
$557$		−	16.0202i		−	0.678797i	−0.940643	−	0.339398i	$-0.889777\pi$
$557$		−	16.0202i		−	0.678797i	0.940643	−	0.339398i	$-0.110223\pi$
$558$	−17.3895	+	29.6172i	−0.736158	+	1.25380i
$559$	−3.74805			−0.158526
$560$	14.8113	+	9.13911i	0.625893	+	0.386198i
$561$	16.1119			0.680247
$562$	5.33081	−	9.07924i	0.224867	−	0.382985i
$563$		−	22.9794i		−	0.968466i	−0.874939	−	0.484233i	$-0.839099\pi$
$563$		−	22.9794i		−	0.968466i	0.874939	−	0.484233i	$-0.160901\pi$
$564$	2.54586	−	1.42062i	0.107200	−	0.0598189i
$565$		−	19.5130i		−	0.820919i
$566$	−24.4580	−	14.3604i	−1.02805	−	0.603611i
$567$	7.04383			0.295813
$568$	33.9866	+	0.745766i	1.42605	+	0.0312916i
$569$	−14.7944			−0.620214			−0.310107	−	0.950702i	$-0.600365\pi$
$569$	−14.7944			−0.620214			−0.310107	+	0.950702i	$0.600365\pi$
$570$	7.28885	+	4.27959i	0.305296	+	0.179252i
$571$		−	20.6522i		−	0.864270i	−0.901809	−	0.432135i	$-0.857760\pi$
$571$		−	20.6522i		−	0.864270i	0.901809	−	0.432135i	$-0.142240\pi$
$572$	−5.27924	−	9.46082i	−0.220736	−	0.395577i
$573$		−	6.01897i		−	0.251446i
$574$	0.213376	−	0.363414i	0.00890614	−	0.0151686i
$575$	−16.2738			−0.678664
$576$	22.1956	+	0.974545i	0.924819	+	0.0406060i
$577$	−21.2585			−0.885004			−0.442502	−	0.896768i	$-0.645909\pi$
$577$	−21.2585			−0.885004			−0.442502	+	0.896768i	$0.645909\pi$
$578$	−16.2494	+	27.6754i	−0.675886	+	1.15114i
$579$		−	3.21429i		−	0.133581i
$580$	1.69890	+	3.04456i	0.0705429	+	0.126419i
$581$			2.84395i			0.117987i
$582$	2.37547	+	1.39474i	0.0984662	+	0.0578137i
$583$	−11.8740			−0.491770
$584$	−42.2362	−	0.926786i	−1.74774	−	0.0383507i
$585$	12.0833			0.499582
$586$	12.8710	+	7.55714i	0.531698	+	0.312182i
$587$			31.7469i			1.31033i	0.755484	+	0.655167i	$0.227402\pi$
$587$			31.7469i			1.31033i	−0.755484	+	0.655167i	$0.772598\pi$
$588$	−0.824505	+	0.460083i	−0.0340020	+	0.0189735i
$589$			25.4448i			1.04843i
$590$	−12.4428	+	21.1921i	−0.512262	+	0.872467i
$591$	−7.06737			−0.290713
$592$	0.544266	+	0.335831i	0.0223692	+	0.0138026i
$593$	20.3172			0.834327			0.417163	−	0.908832i	$-0.363024\pi$
$593$	20.3172			0.834327			0.417163	+	0.908832i	$0.363024\pi$
$594$	10.5789	−	18.0176i	0.434058	−	0.739272i
$595$			27.4124i			1.12380i
$596$	37.1141	−	20.7100i	1.52025	−	0.848316i
$597$		−	1.86899i		−	0.0764927i
$598$	−1.42462	−	0.836453i	−0.0582569	−	0.0342051i
$599$	−38.4170			−1.56968			−0.784838	−	0.619701i	$-0.787254\pi$
$599$	−38.4170			−1.56968			−0.784838	+	0.619701i	$0.787254\pi$
$600$	−0.408084	+	18.5975i	−0.0166600	+	0.759241i
$601$	1.51894			0.0619589			0.0309795	−	0.999520i	$-0.490137\pi$
$601$	1.51894			0.0619589			0.0309795	+	0.999520i	$0.490137\pi$
$602$	−4.57090	−	2.68377i	−0.186296	−	0.109382i
$603$		−	37.4770i		−	1.52618i
$604$	−20.2542	−	36.2971i	−0.824131	−	1.47691i
$605$			79.8162i			3.24499i
$606$	4.21950	−	7.18649i	0.171405	−	0.291931i
$607$	0.377734			0.0153317			0.00766587	−	0.999971i	$-0.497560\pi$
$607$	0.377734			0.0153317			0.00766587	+	0.999971i	$0.497560\pi$
$608$	14.5458	−	7.70323i	0.589912	−	0.312407i
$609$	−0.189146			−0.00766458
$610$	−9.62307	+	16.3897i	−0.389627	+	0.663598i
$611$		−	3.08775i		−	0.124917i
$612$	17.0515	+	30.5577i	0.689267	+	1.23522i
$613$			8.90194i			0.359546i	0.983708	+	0.179773i	$0.0575363\pi$
$613$			8.90194i			0.359546i	−0.983708	+	0.179773i	$0.942464\pi$
$614$	−37.2296	−	21.8591i	−1.50246	−	0.882160i
$615$	0.612098			0.0246822
$616$	0.336122	−	15.3180i	0.0135428	−	0.617181i
$617$	−34.3539			−1.38304			−0.691518	−	0.722359i	$-0.743058\pi$
$617$	−34.3539			−1.38304			−0.691518	+	0.722359i	$0.743058\pi$
$618$	−3.95250	−	2.32068i	−0.158993	−	0.0933515i
$619$		−	21.8310i		−	0.877462i	−0.898618	−	0.438731i	$-0.855428\pi$
$619$		−	21.8310i		−	0.877462i	0.898618	−	0.438731i	$-0.144572\pi$
$620$	−66.4519	+	37.0808i	−2.66877	+	1.48920i
$621$		−	3.18596i		−	0.127848i
$622$	4.86198	−	8.28075i	0.194948	−	0.332028i
$623$	−12.0820			−0.484054
$624$	−0.991613	+	1.60706i	−0.0396963	+	0.0643339i
$625$	99.4215			3.97686
$626$	−9.43669	+	16.0722i	−0.377166	+	0.642375i
$627$		−	7.44108i		−	0.297168i
$628$	−39.1730	+	21.8590i	−1.56317	+	0.872268i
$629$			1.00731i			0.0401642i
$630$	14.7360	+	8.65216i	0.587098	+	0.344710i
$631$	6.11176			0.243305			0.121653	−	0.992573i	$-0.461181\pi$
$631$	6.11176			0.243305			0.121653	+	0.992573i	$0.461181\pi$
$632$	30.6802	+	0.673215i	1.22039	+	0.0267790i
$633$	7.00174			0.278294
$634$	0.666052	+	0.391068i	0.0264523	+	0.0155313i
$635$			53.9428i			2.14066i
$636$	1.00849	+	1.80729i	0.0399891	+	0.0716636i
$637$			1.00000i			0.0396214i
$638$	1.55407	−	2.64684i	0.0615264	−	0.104790i
$639$	33.3782			1.32042
$640$	41.3156	+	26.7621i	1.63314	+	1.05787i
$641$	−31.4315			−1.24147			−0.620735	−	0.784021i	$-0.713166\pi$
$641$	−31.4315			−1.24147			−0.620735	+	0.784021i	$0.713166\pi$
$642$	4.05476	−	6.90591i	0.160028	−	0.272555i
$643$			39.7488i			1.56754i	0.621051	+	0.783770i	$0.286706\pi$
$643$			39.7488i			1.56754i	−0.621051	+	0.783770i	$0.713294\pi$
$644$	−1.13844	−	2.04018i	−0.0448608	−	0.0803943i
$645$		−	7.69877i		−	0.303139i
$646$	22.3564	+	13.1264i	0.879600	+	0.516451i
$647$	−35.5007			−1.39568			−0.697838	−	0.716256i	$-0.745854\pi$
$647$	−35.5007			−1.39568			−0.697838	+	0.716256i	$0.745854\pi$
$648$	19.9182	+	0.437063i	0.782459	+	0.0171695i
$649$	21.6348			0.849238
$650$	16.9896	+	9.97533i	0.666388	+	0.391265i
$651$		−	4.12838i		−	0.161804i
$652$	8.66659	−	4.83605i	0.339410	−	0.189394i
$653$			32.5153i			1.27242i	0.771514	+	0.636212i	$0.219500\pi$
$653$			32.5153i			1.27242i	−0.771514	+	0.636212i	$0.780500\pi$
$654$	−2.86825	+	4.88511i	−0.112158	+	0.191023i
$655$	−41.6534			−1.62753
$656$	0.625923	−	1.01440i	0.0244382	−	0.0396058i
$657$	−41.4801			−1.61829
$658$	2.21096	−	3.76563i	0.0861924	−	0.146800i
$659$			0.733823i			0.0285857i	0.999898	+	0.0142928i	$0.00454971\pi$
$659$			0.733823i			0.0285857i	−0.999898	+	0.0142928i	$0.995450\pi$
$660$	19.4332	−	10.8439i	0.756436	−	0.422099i
$661$			1.48742i			0.0578538i	0.999582	+	0.0289269i	$0.00920900\pi$
$661$			1.48742i			0.0578538i	−0.999582	+	0.0289269i	$0.990791\pi$
$662$	8.67161	+	5.09147i	0.337032	+	0.197886i
$663$	−2.97431			−0.115512
$664$	−0.176465	+	8.04197i	−0.00684815	+	0.312089i
$665$	12.6600			0.490936
$666$	0.541500	+	0.317938i	0.0209827	+	0.0123198i
$667$		−	0.468027i		−	0.0181221i
$668$	−13.7617	−	24.6620i	−0.532455	−	0.954203i
$669$			3.72846i			0.144150i
$670$	42.0434	−	71.6068i	1.62428	−	2.76641i
$671$	16.7320			0.645931
$672$	−2.36004	+	1.24984i	−0.0910405	+	0.0482135i
$673$	−18.8007			−0.724715			−0.362358	−	0.932039i	$-0.618028\pi$
$673$	−18.8007			−0.724715			−0.362358	+	0.932039i	$0.618028\pi$
$674$	−18.8382	+	32.0846i	−0.725621	+	1.23585i
$675$			37.9950i			1.46243i
$676$	0.974560	+	1.74649i	0.0374831	+	0.0671727i
$677$		−	20.9488i		−	0.805127i	−0.915392	−	0.402563i	$-0.868119\pi$
$677$		−	20.9488i		−	0.805127i	0.915392	−	0.402563i	$-0.131881\pi$
$678$	2.58202	+	1.51601i	0.0991618	+	0.0582221i
$679$	4.12596			0.158340
$680$	−1.70091	+	77.5153i	−0.0652271	+	2.97258i
$681$	−0.815818			−0.0312622
$682$	57.7711	+	33.9199i	2.21217	+	1.29886i
$683$			18.0106i			0.689158i	0.938757	+	0.344579i	$0.111978\pi$
$683$			18.0106i			0.689158i	−0.938757	+	0.344579i	$0.888022\pi$
$684$	14.1127	−	7.87502i	0.539611	−	0.301109i
$685$		−	82.6214i		−	3.15680i
$686$	−0.716045	+	1.21954i	−0.0273387	+	0.0465623i
$687$	3.57547			0.136413
$688$	−12.7588	−	7.87265i	−0.486426	−	0.300142i
$689$	2.19197			0.0835072
$690$	1.71814	−	2.92627i	0.0654083	−	0.111401i
$691$		−	28.0918i		−	1.06866i	−0.845275	−	0.534332i	$-0.820563\pi$
$691$		−	28.0918i		−	1.06866i	0.845275	−	0.534332i	$-0.179437\pi$
$692$	21.6214	−	12.0649i	0.821921	−	0.458641i
$693$		−	15.0438i		−	0.571468i
$694$	−1.82313	−	1.07044i	−0.0692051	−	0.0406333i
$695$	13.3528			0.506499
$696$	−0.534857	−	0.0117363i	−0.0202737	−	0.000444864i
$697$	1.87743			0.0711128
$698$	22.7528	+	13.3591i	0.861204	+	0.505650i
$699$			8.93378i			0.337907i
$700$	13.5768	+	24.3307i	0.513153	+	0.919612i
$701$		−	37.4275i		−	1.41362i	−0.707406	−	0.706808i	$-0.750135\pi$
$701$		−	37.4275i		−	1.41362i	0.707406	−	0.706808i	$-0.249865\pi$
$702$	−1.95290	+	3.32610i	−0.0737073	+	0.125536i
$703$	0.465214			0.0175459
$704$	1.90094	−	43.2946i	0.0716443	−	1.63173i
$705$	6.34246			0.238871
$706$	7.86772	−	13.4000i	0.296106	−	0.504316i
$707$		−	12.4823i		−	0.469444i
$708$	−1.83749	−	3.29294i	−0.0690572	−	0.123756i
$709$		−	20.2798i		−	0.761625i	−0.924652	−	0.380813i	$-0.875644\pi$
$709$		−	20.2798i		−	0.761625i	0.924652	−	0.380813i	$-0.124356\pi$
$710$	63.7752	+	37.4452i	2.39344	+	1.40529i
$711$	30.1310			1.13000
$712$	−34.1648	−	0.749676i	−1.28038	−	0.0280953i
$713$	10.2154			0.382568
$714$	−3.62729	−	2.12974i	−0.135748	−	0.0797033i
$715$		−	23.5695i		−	0.881450i
$716$	−4.75436	+	2.65298i	−0.177679	+	0.0991466i
$717$		−	3.87419i		−	0.144684i
$718$	−15.5972	+	26.5645i	−0.582081	+	0.991380i
$719$	28.1784			1.05088			0.525439	−	0.850831i	$-0.323901\pi$
$719$	28.1784			1.05088			0.525439	+	0.850831i	$0.323901\pi$
$720$	41.1330	+	25.3805i	1.53293	+	0.945875i
$721$	−6.86512			−0.255671
$722$	−7.54260	+	12.8463i	−0.280707	+	0.478089i
$723$		−	1.08081i		−	0.0401956i
$724$	−15.4892	+	8.64315i	−0.575652	+	0.321220i
$725$			5.58158i			0.207295i
$726$	−10.5615	−	6.20111i	−0.391974	−	0.230145i
$727$	−33.5453			−1.24413			−0.622063	−	0.782967i	$-0.713705\pi$
$727$	−33.5453			−1.24413			−0.622063	+	0.782967i	$0.713705\pi$
$728$	−0.0620491	+	2.82775i	−0.00229969	+	0.104803i
$729$	15.6990			0.581443
$730$	−79.2554	−	46.5343i	−2.93338	−	1.72231i
$731$		−	23.6137i		−	0.873384i
$732$	−1.42109	−	2.54670i	−0.0525249	−	0.0941289i
$733$		−	18.3299i		−	0.677029i	−0.940961	−	0.338514i	$-0.890076\pi$
$733$		−	18.3299i		−	0.677029i	0.940961	−	0.338514i	$-0.109924\pi$
$734$	−3.36512	+	5.73135i	−0.124209	+	0.211548i
$735$	−2.05407			−0.0757656
$736$	−3.09263	−	5.83974i	−0.113996	−	0.215256i
$737$	−73.1023			−2.69276
$738$	0.592573	−	1.00925i	0.0218129	−	0.0371509i
$739$			24.5294i			0.902329i	0.892441	+	0.451165i	$0.148991\pi$
$739$			24.5294i			0.902329i	−0.892441	+	0.451165i	$0.851009\pi$
$740$	0.677959	+	1.21496i	0.0249223	+	0.0446627i
$741$			1.37364i			0.0504620i
$742$	2.67319	+	1.56955i	0.0981360	+	0.0576198i
$743$	30.2539			1.10991			0.554953	−	0.831882i	$-0.312736\pi$
$743$	30.2539			1.10991			0.554953	+	0.831882i	$0.312736\pi$
$744$	0.256162	−	11.6740i	0.00939135	−	0.427990i
$745$	92.4615			3.38753
$746$	26.3322	+	15.4607i	0.964089	+	0.566058i
$747$			7.89802i			0.288973i
$748$	59.6056	−	33.2606i	2.17940	−	1.21613i
$749$		−	11.9949i		−	0.438285i
$750$	−13.1360	+	22.3728i	−0.479660	+	0.816939i
$751$	−8.36978			−0.305418			−0.152709	−	0.988271i	$-0.548800\pi$
$751$	−8.36978			−0.305418			−0.152709	+	0.988271i	$0.548800\pi$
$752$	6.48570	−	10.5111i	0.236509	−	0.383299i
$753$	−8.20127			−0.298871
$754$	−0.286886	+	0.488614i	−0.0104478	+	0.0177943i
$755$		−	90.4262i		−	3.29095i
$756$	−4.76327	+	2.65796i	−0.173239	+	0.0966690i
$757$			36.9792i			1.34403i	0.740537	+	0.672016i	$0.234571\pi$
$757$			36.9792i			1.34403i	−0.740537	+	0.672016i	$0.765429\pi$
$758$	11.7423	+	6.89440i	0.426499	+	0.250416i
$759$	−2.98738			−0.108435
$760$	35.7994	+	0.785544i	1.29858	+	0.0284947i
$761$	38.2877			1.38793			0.693963	−	0.720011i	$-0.255863\pi$
$761$	38.2877			1.38793			0.693963	+	0.720011i	$0.255863\pi$
$762$	−7.13787	−	4.19095i	−0.258578	−	0.151822i
$763$			8.48497i			0.307177i
$764$	−12.4252	−	22.2670i	−0.449529	−	0.805592i
$765$			76.1278i			2.75241i
$766$	−15.8686	+	27.0269i	−0.573357	+	0.976521i
$767$	−3.99383			−0.144209
$768$	−6.75115	+	3.38778i	−0.243611	+	0.122246i
$769$	31.9613			1.15255			0.576276	−	0.817255i	$-0.304505\pi$
$769$	31.9613			1.15255			0.576276	+	0.817255i	$0.304505\pi$
$770$	16.8768	−	28.7440i	0.608199	−	1.03586i
$771$		−	10.5406i		−	0.379610i
$772$	−6.63538	−	11.8911i	−0.238813	−	0.427972i
$773$			19.8905i			0.715410i	0.933835	+	0.357705i	$0.116441\pi$
$773$			19.8905i			0.715410i	−0.933835	+	0.357705i	$0.883559\pi$
$774$	−12.6940	−	7.45318i	−0.456276	−	0.267899i
$775$	−121.826			−4.37611
$776$	11.6672	+	0.256012i	0.418827	+	0.00919030i
$777$	−0.0754802			−0.00270784
$778$	−4.55827	−	2.67636i	−0.163422	−	0.0959521i
$779$		−	0.867066i		−	0.0310659i
$780$	−3.58742	+	2.00182i	−0.128450	+	0.0716766i
$781$		−	65.1072i		−	2.32972i
$782$	5.26987	−	8.97545i	0.188450	−	0.320962i
$783$	−1.09272			−0.0390506
$784$	−2.10046	+	3.40412i	−0.0750166	+	0.121576i
$785$	−97.5909			−3.48317
$786$	3.23615	−	5.51170i	0.115430	−	0.196596i
$787$			19.5677i			0.697512i	0.937214	+	0.348756i	$0.113396\pi$
$787$			19.5677i			0.697512i	−0.937214	+	0.348756i	$0.886604\pi$
$788$	−26.1455	+	14.5895i	−0.931395	+	0.519728i
$789$			2.16878i			0.0772107i
$790$	57.5709	+	33.8024i	2.04828	+	1.20263i
$791$	4.48473			0.159458
$792$	0.933455	−	42.5401i	0.0331689	−	1.51160i
$793$	−3.08877			−0.109685
$794$	2.43326	+	1.42867i	0.0863533	+	0.0507017i
$795$			4.50246i			0.159686i
$796$	−3.85824	−	6.91427i	−0.136752	−	0.245070i
$797$			17.4036i			0.616467i	0.951311	+	0.308234i	$0.0997378\pi$
$797$			17.4036i			0.616467i	−0.951311	+	0.308234i	$0.900262\pi$
$798$	−0.983589	+	1.67521i	−0.0348187	+	0.0593019i
$799$	19.4536			0.688219
$800$	36.8819	+	69.6434i	1.30397	+	2.46226i
$801$	−33.5532			−1.18554
$802$	−15.4316	+	26.2826i	−0.544909	+	0.928070i
$803$			80.9108i			2.85528i
$804$	6.20876	+	11.1266i	0.218966	+	0.392405i
$805$		−	5.08265i		−	0.179140i
$806$	−10.6647	−	6.26170i	−0.375648	−	0.220559i
$807$	6.42514			0.226176
$808$	0.774513	−	35.2967i	0.0272473	−	1.24173i
$809$	−11.1003			−0.390264			−0.195132	−	0.980777i	$-0.562514\pi$
$809$	−11.1003			−0.390264			−0.195132	+	0.980777i	$0.562514\pi$
$810$	37.3761	+	21.9451i	1.31326	+	0.771072i
$811$			25.3764i			0.891087i	0.895260	+	0.445544i	$0.146990\pi$
$811$			25.3764i			0.891087i	−0.895260	+	0.445544i	$0.853010\pi$
$812$	−0.699739	+	0.390462i	−0.0245560	+	0.0137025i
$813$		−	2.67713i		−	0.0938911i
$814$	0.620166	−	1.05624i	0.0217368	−	0.0370213i
$815$	21.5909			0.756296
$816$	−10.1249	−	6.24742i	−0.354442	−	0.218703i
$817$	−10.9057			−0.381541
$818$	−1.84644	+	3.14478i	−0.0645592	+	0.109955i
$819$			2.77713i			0.0970407i
$820$	2.26444	−	1.26358i	0.0790776	−	0.0441262i
$821$		−	12.7401i		−	0.444631i	−0.974975	−	0.222316i	$-0.928638\pi$
$821$		−	12.7401i		−	0.444631i	0.974975	−	0.222316i	$-0.0713615\pi$
$822$	10.9327	+	6.41905i	0.381322	+	0.223890i
$823$	10.7265			0.373903			0.186952	−	0.982369i	$-0.440139\pi$
$823$	10.7265			0.373903			0.186952	+	0.982369i	$0.440139\pi$
$824$	−19.4128	−	0.425975i	−0.676278	−	0.0148395i
$825$	35.6268			1.24037
$826$	−4.87064	−	2.85976i	−0.169471	−	0.0995038i
$827$			31.1260i			1.08236i	0.840907	+	0.541179i	$0.182022\pi$
$827$			31.1260i			1.08236i	−0.840907	+	0.541179i	$0.817978\pi$
$828$	−3.16160	−	5.66584i	−0.109873	−	0.196901i
$829$		−	34.4962i		−	1.19810i	−0.800711	−	0.599050i	$-0.795545\pi$
$829$		−	34.4962i		−	1.19810i	0.800711	−	0.599050i	$-0.204455\pi$
$830$	−8.86035	+	15.0906i	−0.307547	+	0.523803i
$831$	4.17550			0.144846
$832$	−0.350918	+	7.99230i	−0.0121659	+	0.277083i
$833$	−6.30026			−0.218291
$834$	−1.03741	+	1.76687i	−0.0359225	+	0.0611818i
$835$		−	61.4400i		−	2.12622i
$836$	−15.3609	−	27.5280i	−0.531269	−	0.952077i
$837$		−	23.8502i		−	0.824382i
$838$	23.7324	+	13.9343i	0.819821	+	0.481352i
$839$	−31.7211			−1.09513			−0.547566	−	0.836762i	$-0.684446\pi$
$839$	−31.7211			−1.09513			−0.547566	+	0.836762i	$0.684446\pi$
$840$	−5.80840	−	0.127453i	−0.200409	−	0.00439756i
$841$	28.8395			0.994465
$842$	35.5464	+	20.8708i	1.22501	+	0.719256i
$843$			3.51464i			0.121050i
$844$	25.9027	−	14.4540i	0.891608	−	0.497527i
$845$			4.35100i			0.149679i
$846$	6.14013	−	10.4577i	0.211102	−	0.359541i
$847$	−18.3443			−0.630319
$848$	7.46172	+	4.60414i	0.256237	+	0.158107i
$849$	9.46787			0.324936
$850$	−62.8472	+	107.039i	−2.15564	+	3.67141i
$851$		−	0.186770i		−	0.00640240i
$852$	−9.90970	+	5.52972i	−0.339501	+	0.189445i
$853$		−	19.2111i		−	0.657775i	−0.944369	−	0.328887i	$-0.893326\pi$
$853$		−	19.2111i		−	0.657775i	0.944369	−	0.328887i	$-0.106674\pi$
$854$	−3.76688	−	2.21169i	−0.128900	−	0.0756826i
$855$	35.1586			1.20240
$856$	0.744274	−	33.9186i	0.0254388	−	1.15931i
$857$	−2.34960			−0.0802610			−0.0401305	−	0.999194i	$-0.512777\pi$
$857$	−2.34960			−0.0802610			−0.0401305	+	0.999194i	$0.512777\pi$
$858$	3.11879	+	1.83117i	0.106474	+	0.0625152i
$859$		−	19.8276i		−	0.676510i	−0.941054	−	0.338255i	$-0.890163\pi$
$859$		−	19.8276i		−	0.676510i	0.941054	−	0.338255i	$-0.109837\pi$
$860$	−15.8929	−	28.4814i	−0.541943	−	0.971206i
$861$			0.140680i			0.00479436i
$862$	1.53777	−	2.61907i	0.0523765	−	0.0892058i
$863$	−9.18962			−0.312818			−0.156409	−	0.987692i	$-0.549992\pi$
$863$	−9.18962			−0.312818			−0.156409	+	0.987692i	$0.549992\pi$
$864$	−13.6343	+	7.22047i	−0.463847	+	0.245645i
$865$	53.8648			1.83146
$866$	−3.79253	+	6.45931i	−0.128876	+	0.219496i
$867$		−	10.7133i		−	0.363844i
$868$	−8.52238	−	15.2728i	−0.289268	−	0.518392i
$869$		−	58.7733i		−	1.99375i
$870$	−1.00365	−	0.589285i	−0.0340269	−	0.0199786i
$871$	13.4949			0.457257
$872$	−0.526485	+	23.9934i	−0.0178290	+	0.812518i
$873$	11.4583			0.387806
$874$	−4.14519	−	2.43382i	−0.140213	−	0.0823251i
$875$			38.8595i			1.31369i
$876$	12.3151	−	6.87195i	0.416088	−	0.232182i
$877$		−	18.3706i		−	0.620332i	−0.950682	−	0.310166i	$-0.899615\pi$
$877$		−	18.3706i		−	0.620332i	0.950682	−	0.310166i	$-0.100385\pi$
$878$	−7.71436	+	13.1388i	−0.260347	+	0.443414i
$879$	−4.98247			−0.168054
$880$	49.5069	−	80.2336i	1.66888	−	2.70467i
$881$	−4.99860			−0.168407			−0.0842035	−	0.996449i	$-0.526835\pi$
$881$	−4.99860			−0.168407			−0.0842035	+	0.996449i	$0.526835\pi$
$882$	−1.98855	+	3.38682i	−0.0669579	+	0.114040i
$883$			33.9889i			1.14382i	0.820317	+	0.571908i	$0.193797\pi$
$883$			33.9889i			1.14382i	−0.820317	+	0.571908i	$0.806203\pi$
$884$	−11.0033	+	6.13998i	−0.370083	+	0.206510i
$885$		−	8.20362i		−	0.275762i
$886$	−21.4705	−	12.6062i	−0.721314	−	0.423514i
$887$	−15.9377			−0.535134			−0.267567	−	0.963539i	$-0.586220\pi$
$887$	−15.9377			−0.535134			−0.267567	+	0.963539i	$0.586220\pi$
$888$	−0.213439	−	0.00468348i	−0.00716254	−	0.000157167i
$889$	−12.3978			−0.415809
$890$	−64.1096	−	37.6415i	−2.14896	−	1.26175i
$891$		−	38.1567i		−	1.27830i
$892$	7.69681	+	13.7933i	0.257708	+	0.461834i
$893$		−	8.98439i		−	0.300651i
$894$	−7.18355	+	12.2348i	−0.240254	+	0.409192i
$895$	−11.8444			−0.395916
$896$	−6.15080	+	9.49566i	−0.205484	+	0.317228i
$897$	0.551479			0.0184133
$898$	2.17227	−	3.69973i	0.0724896	−	0.123462i
$899$		−	3.50366i		−	0.116854i
$900$	37.7044	+	67.5694i	1.25681	+	2.25231i
$901$			13.8100i			0.460076i
$902$	−1.96863	−	1.15587i	−0.0655482	−	0.0384862i
$903$	1.76943			0.0588829
$904$	12.6817	+	0.278273i	0.421786	+	0.00925523i
$905$	−38.5880			−1.28271
$906$	11.9655	+	7.02543i	0.397526	+	0.233404i
$907$			33.7784i			1.12159i	0.827954	+	0.560796i	$0.189505\pi$
$907$			33.7784i			1.12159i	−0.827954	+	0.560796i	$0.810495\pi$
$908$	−3.01809	+	1.68413i	−0.100159	+	0.0558897i
$909$		−	34.6649i		−	1.14976i
$910$	−3.11551	+	5.30622i	−0.103278	+	0.175899i
$911$	−4.38521			−0.145288			−0.0726442	−	0.997358i	$-0.523144\pi$
$911$	−4.38521			−0.145288			−0.0726442	+	0.997358i	$0.523144\pi$
$912$	−2.88529	+	4.67605i	−0.0955414	+	0.154839i
$913$	15.4058			0.509858
$914$	−8.85242	+	15.0771i	−0.292812	+	0.498707i
$915$		−	6.34455i		−	0.209744i
$916$	13.2273	−	7.38100i	0.437044	−	0.243875i
$917$		−	9.57331i		−	0.316139i
$918$	−20.9553	−	12.3038i	−0.691628	−	0.406084i
$919$	−48.7802			−1.60911			−0.804555	−	0.593878i	$-0.797596\pi$
$919$	−48.7802			−1.60911			−0.804555	+	0.593878i	$0.797596\pi$
$920$	0.315374	−	14.3724i	0.0103976	−	0.473845i
$921$	14.4118			0.474886
$922$	−15.0851	−	8.85712i	−0.496802	−	0.291694i
$923$			12.0190i			0.395609i
$924$	2.49229	+	4.46638i	0.0819902	+	0.146933i
$925$			2.22737i			0.0732356i
$926$	7.54721	−	12.8541i	0.248017	−	0.422413i
$927$	−19.0653			−0.626188
$928$	−2.00291	+	1.06071i	−0.0657488	+	0.0348195i
$929$	−51.9099			−1.70311			−0.851554	−	0.524267i	$-0.824339\pi$
$929$	−51.9099			−1.70311			−0.851554	+	0.524267i	$0.824339\pi$
$930$	12.8620	−	21.9061i	0.421761	−	0.718328i
$931$			2.90969i			0.0953612i
$932$	18.4424	+	33.0502i	0.604100	+	1.08260i
$933$			3.20553i			0.104944i
$934$	29.3375	+	17.2253i	0.959951	+	0.563628i
$935$	148.494			4.85628
$936$	−0.172318	+	7.85302i	−0.00563240	+	0.256684i
$937$	−37.1826			−1.21470			−0.607351	−	0.794434i	$-0.707768\pi$
$937$	−37.1826			−1.21470			−0.607351	+	0.794434i	$0.707768\pi$
$938$	16.4576	+	9.66294i	0.537358	+	0.315506i
$939$		−	6.22166i		−	0.203036i
$940$	23.4637	−	13.0930i	0.765302	−	0.427047i
$941$		−	11.2287i		−	0.366044i	−0.983109	−	0.183022i	$-0.941412\pi$
$941$		−	11.2287i		−	0.366044i	0.983109	−	0.183022i	$-0.0585880\pi$
$942$	7.58207	−	12.9135i	0.247037	−	0.420745i
$943$	−0.348102			−0.0113358
$944$	−13.5955	−	8.38890i	−0.442496	−	0.273035i
$945$	−11.8666			−0.386022
$946$	−14.5381	+	24.7608i	−0.472675	+	0.805042i
$947$		−	54.3921i		−	1.76751i	−0.467955	−	0.883753i	$-0.655009\pi$
$947$		−	54.3921i		−	1.76751i	0.467955	−	0.883753i	$-0.344991\pi$
$948$	−8.94565	+	4.99177i	−0.290541	+	0.162125i
$949$		−	14.9363i		−	0.484854i
$950$	49.4345	+	29.0251i	1.60387	+	0.941700i
$951$	−0.257833			−0.00836081
$952$	−17.8155	−	0.390925i	−0.577405	−	0.0126700i
$953$	25.8510			0.837397			0.418698	−	0.908125i	$-0.362486\pi$
$953$	25.8510			0.837397			0.418698	+	0.908125i	$0.362486\pi$
$954$	7.42380	+	4.35883i	0.240354	+	0.141122i
$955$		−	55.4733i		−	1.79507i
$956$	−7.99766	−	14.3325i	−0.258663	−	0.463545i
$957$			1.02461i			0.0331210i
$958$	−19.9868	+	34.0408i	−0.645744	+	1.09981i
$959$	18.9891			0.613189
$960$	−16.4168	−	0.720811i	−0.529849	−	0.0232641i
$961$	45.4723			1.46685
$962$	−0.114484	+	0.194985i	−0.00369112	+	0.00628658i
$963$		−	33.3115i		−	1.07345i
$964$	−2.23115	−	3.99841i	−0.0718606	−	0.128780i
$965$		−	29.6242i		−	0.953635i
$966$	0.672551	+	0.394883i	0.0216390	+	0.0127052i
$967$	53.4063			1.71743			0.858715	−	0.512454i	$-0.171263\pi$
$967$	53.4063			1.71743			0.858715	+	0.512454i	$0.171263\pi$
$968$	−51.8732	−	1.13825i	−1.66727	−	0.0365847i
$969$	−8.65431			−0.278016
$970$	21.8933	+	12.8545i	0.702950	+	0.412732i
$971$			54.3422i			1.74393i	0.489572	+	0.871963i	$0.337153\pi$
$971$			54.3422i			1.74393i	−0.489572	+	0.871963i	$0.662847\pi$
$972$	−20.0975	+	11.2146i	−0.644628	+	0.359709i
$973$			3.06890i			0.0983843i
$974$	−11.9971	+	20.4330i	−0.384412	+	0.654717i
$975$	−6.57680			−0.210626
$976$	−10.5145	−	6.48784i	−0.336562	−	0.207671i
$977$	−40.8656			−1.30741			−0.653703	−	0.756751i	$-0.726785\pi$
$977$	−40.8656			−1.30741			−0.653703	+	0.756751i	$0.726785\pi$
$978$	−1.67745	+	2.85697i	−0.0536389	+	0.0913558i
$979$			65.4486i			2.09175i
$980$	−7.59898	+	4.24031i	−0.242740	+	0.135452i
$981$			23.5639i			0.752336i
$982$	−24.9251	−	14.6346i	−0.795392	−	0.467008i
$983$	−3.87342			−0.123543			−0.0617715	−	0.998090i	$-0.519675\pi$
$983$	−3.87342			−0.123543			−0.0617715	+	0.998090i	$0.519675\pi$
$984$	−0.00872907	+	0.397808i	−0.000278273	+	0.0126816i
$985$	−65.1357			−2.07540
$986$	−3.07840	−	1.80746i	−0.0980361	−	0.0575612i
$987$			1.45770i			0.0463992i
$988$	2.83567	+	5.08175i	0.0902146	+	0.161672i
$989$			4.37832i			0.139222i
$990$	46.8691	−	79.8258i	1.48960	−	2.53703i
$991$	44.9706			1.42854			0.714269	−	0.699871i	$-0.246759\pi$
$991$	44.9706			1.42854			0.714269	+	0.699871i	$0.246759\pi$
$992$	−23.1515	−	43.7164i	−0.735060	−	1.38800i
$993$	−3.35684			−0.106526
$994$	−8.60611	+	14.6576i	−0.272969	+	0.464911i
$995$		−	17.2254i		−	0.546081i
$996$	−1.30845	−	2.34485i	−0.0414599	−	0.0742995i
$997$			11.0142i			0.348824i	0.984673	+	0.174412i	$0.0558024\pi$
$997$			11.0142i			0.348824i	−0.984673	+	0.174412i	$0.944198\pi$
$998$	9.37521	+	5.50459i	0.296767	+	0.174245i
$999$	−0.436059			−0.0137963

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.b.365.14	yes	38
4.3	odd	2		2912.2.c.b.1457.22		38
8.3	odd	2		2912.2.c.b.1457.17		38
8.5	even	2	inner	728.2.c.b.365.13	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.b.365.13	✓	38	8.5	even	2	inner
728.2.c.b.365.14	yes	38	1.1	even	1	trivial
2912.2.c.b.1457.17		38	8.3	odd	2
2912.2.c.b.1457.22		38	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+(-0.716045 + 1.21954i) q^{2} -0.472093i q^{3} +(-0.974560 - 1.74649i) q^{4} -4.35100i q^{5} +(0.575736 + 0.338039i) q^{6} +1.00000 q^{7} +(2.82775 + 0.0620491i) q^{8} +2.77713 q^{9} +(5.30622 + 3.11551i) q^{10} -5.41704i q^{11} +(-0.824505 + 0.460083i) q^{12} +1.00000i q^{13} +(-0.716045 + 1.21954i) q^{14} -2.05407 q^{15} +(-2.10046 + 3.40412i) q^{16} -6.30026 q^{17} +(-1.98855 + 3.38682i) q^{18} +2.90969i q^{19} +(-7.59898 + 4.24031i) q^{20} -0.472093i q^{21} +(6.60630 + 3.87884i) q^{22} +1.16816 q^{23} +(0.0292929 - 1.33496i) q^{24} -13.9312 q^{25} +(-1.21954 - 0.716045i) q^{26} -2.72734i q^{27} +(-0.974560 - 1.74649i) q^{28} -0.400654i q^{29} +(1.47081 - 2.50503i) q^{30} +8.74485 q^{31} +(-2.64744 - 4.99911i) q^{32} -2.55734 q^{33} +(4.51127 - 7.68343i) q^{34} -4.35100i q^{35} +(-2.70648 - 4.85023i) q^{36} -0.159884i q^{37} +(-3.54849 - 2.08347i) q^{38} +0.472093 q^{39} +(0.269975 - 12.3035i) q^{40} -0.297993 q^{41} +(0.575736 + 0.338039i) q^{42} +3.74805i q^{43} +(-9.46082 + 5.27924i) q^{44} -12.0833i q^{45} +(-0.836453 + 1.42462i) q^{46} -3.08775 q^{47} +(1.60706 + 0.991613i) q^{48} +1.00000 q^{49} +(9.97533 - 16.9896i) q^{50} +2.97431i q^{51} +(1.74649 - 0.974560i) q^{52} -2.19197i q^{53} +(3.32610 + 1.95290i) q^{54} -23.5695 q^{55} +(2.82775 + 0.0620491i) q^{56} +1.37364 q^{57} +(0.488614 + 0.286886i) q^{58} +3.99383i q^{59} +(2.00182 + 3.58742i) q^{60} +3.08877i q^{61} +(-6.26170 + 10.6647i) q^{62} +2.77713 q^{63} +(7.99230 + 0.350918i) q^{64} +4.35100 q^{65} +(1.83117 - 3.11879i) q^{66} -13.4949i q^{67} +(6.13998 + 11.0033i) q^{68} -0.551479i q^{69} +(5.30622 + 3.11551i) q^{70} +12.0190 q^{71} +(7.85302 + 0.172318i) q^{72} -14.9363 q^{73} +(0.194985 + 0.114484i) q^{74} +6.57680i q^{75} +(5.08175 - 2.83567i) q^{76} -5.41704i q^{77} +(-0.338039 + 0.575736i) q^{78} +10.8497 q^{79} +(14.8113 + 9.13911i) q^{80} +7.04383 q^{81} +(0.213376 - 0.363414i) q^{82} +2.84395i q^{83} +(-0.824505 + 0.460083i) q^{84} +27.4124i q^{85} +(-4.57090 - 2.68377i) q^{86} -0.189146 q^{87} +(0.336122 - 15.3180i) q^{88} -12.0820 q^{89} +(14.7360 + 8.65216i) q^{90} +1.00000i q^{91} +(-1.13844 - 2.04018i) q^{92} -4.12838i q^{93} +(2.21096 - 3.76563i) q^{94} +12.6600 q^{95} +(-2.36004 + 1.24984i) q^{96} +4.12596 q^{97} +(-0.716045 + 1.21954i) q^{98} -15.0438i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{4} + 14 q^{6} + 38 q^{7} - 6 q^{8} - 46 q^{9} - 4 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 4 q^{18} - 24 q^{20} + 10 q^{22} + 12 q^{23} + 10 q^{24} - 50 q^{25} + 8 q^{28} + 4 q^{30} + 16 q^{31}+ \cdots + 82 q^{96}+O(q^{100}) \) 38 * q + 8 * q^4 + 14 * q^6 + 38 * q^7 - 6 * q^8 - 46 * q^9 - 4 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 4 * q^18 - 24 * q^20 + 10 * q^22 + 12 * q^23 + 10 * q^24 - 50 * q^25 + 8 * q^28 + 4 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 - 4 * q^34 - 38 * q^36 - 28 * q^38 + 8 * q^39 + 4 * q^40 + 8 * q^41 + 14 * q^42 - 40 * q^44 - 16 * q^46 + 4 * q^48 + 38 * q^49 + 24 * q^50 - 4 * q^52 - 14 * q^54 - 6 * q^56 + 8 * q^57 - 24 * q^58 + 44 * q^60 - 12 * q^62 - 46 * q^63 + 32 * q^64 + 20 * q^65 - 76 * q^66 - 52 * q^68 + 42 * q^72 + 50 * q^74 - 28 * q^76 - 12 * q^79 - 16 * q^80 + 62 * q^81 - 4 * q^84 + 44 * q^86 - 56 * q^87 - 6 * q^88 + 48 * q^90 + 2 * q^92 - 48 * q^94 + 82 * q^96

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