LMFDB - Embedded newform 680.2.l.a.101.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(101,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.22
Character	$\chi$	$=$	680.101
Dual form			680.2.l.a.101.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.458720 + 1.33775i) q^{2} +2.54711 q^{3} +(-1.57915 + 1.22731i) q^{4} +1.00000 q^{5} +(1.16841 + 3.40740i) q^{6} +0.654431i q^{7} +(-2.36622 - 1.54952i) q^{8} +3.48778 q^{9} +(0.458720 + 1.33775i) q^{10} +2.31821 q^{11} +(-4.02228 + 3.12609i) q^{12} -0.495577i q^{13} +(-0.875466 + 0.300201i) q^{14} +2.54711 q^{15} +(0.987437 - 3.87621i) q^{16} +(2.19658 + 3.48928i) q^{17} +(1.59992 + 4.66578i) q^{18} +2.57745i q^{19} +(-1.57915 + 1.22731i) q^{20} +1.66691i q^{21} +(1.06341 + 3.10119i) q^{22} +0.188252i q^{23} +(-6.02703 - 3.94680i) q^{24} +1.00000 q^{25} +(0.662958 - 0.227331i) q^{26} +1.24244 q^{27} +(-0.803188 - 1.03345i) q^{28} -6.85794 q^{29} +(1.16841 + 3.40740i) q^{30} -3.96966i q^{31} +(5.63835 - 0.457151i) q^{32} +5.90475 q^{33} +(-3.66017 + 4.53907i) q^{34} +0.654431i q^{35} +(-5.50774 + 4.28058i) q^{36} -3.06408 q^{37} +(-3.44799 + 1.18233i) q^{38} -1.26229i q^{39} +(-2.36622 - 1.54952i) q^{40} -3.21537i q^{41} +(-2.22991 + 0.764646i) q^{42} -3.55727i q^{43} +(-3.66081 + 2.84516i) q^{44} +3.48778 q^{45} +(-0.251834 + 0.0863550i) q^{46} -3.43065 q^{47} +(2.51511 - 9.87313i) q^{48} +6.57172 q^{49} +(0.458720 + 1.33775i) q^{50} +(5.59493 + 8.88758i) q^{51} +(0.608224 + 0.782590i) q^{52} -8.47932i q^{53} +(0.569934 + 1.66208i) q^{54} +2.31821 q^{55} +(1.01405 - 1.54853i) q^{56} +6.56507i q^{57} +(-3.14588 - 9.17420i) q^{58} -0.432821i q^{59} +(-4.02228 + 3.12609i) q^{60} -3.55435 q^{61} +(5.31041 - 1.82096i) q^{62} +2.28252i q^{63} +(3.19798 + 7.33300i) q^{64} -0.495577i q^{65} +(2.70863 + 7.89908i) q^{66} -8.66134i q^{67} +(-7.75114 - 2.81422i) q^{68} +0.479499i q^{69} +(-0.875466 + 0.300201i) q^{70} +9.72787i q^{71} +(-8.25286 - 5.40439i) q^{72} -3.67345i q^{73} +(-1.40556 - 4.09897i) q^{74} +2.54711 q^{75} +(-3.16333 - 4.07019i) q^{76} +1.51711i q^{77} +(1.68863 - 0.579038i) q^{78} -4.08394i q^{79} +(0.987437 - 3.87621i) q^{80} -7.29871 q^{81} +(4.30136 - 1.47495i) q^{82} -15.3164i q^{83} +(-2.04581 - 2.63230i) q^{84} +(2.19658 + 3.48928i) q^{85} +(4.75874 - 1.63179i) q^{86} -17.4679 q^{87} +(-5.48540 - 3.59211i) q^{88} +8.98386 q^{89} +(1.59992 + 4.66578i) q^{90} +0.324321 q^{91} +(-0.231043 - 0.297278i) q^{92} -10.1112i q^{93} +(-1.57371 - 4.58935i) q^{94} +2.57745i q^{95} +(14.3615 - 1.16442i) q^{96} +11.6566i q^{97} +(3.01458 + 8.79132i) q^{98} +8.08543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3} + 2 q^{4} + 36 q^{5} + 36 q^{9} - 8 q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} + 2 q^{20} + 26 q^{24} + 36 q^{25} + 6 q^{26} - 16 q^{27} + 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) $ 36 * q - 4 * q^3 + 2 * q^4 + 36 * q^5 + 36 * q^9 - 8 * q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 + 2 * q^20 + 26 * q^24 + 36 * q^25 + 6 * q^26 - 16 * q^27 + 14 * q^28 - 10 * q^32 - 8 * q^33 - 24 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 + 6 * q^44 + 36 * q^45 + 24 * q^46 + 20 * q^47 - 4 * q^48 - 36 * q^49 + 6 * q^52 - 56 * q^54 - 8 * q^55 + 20 * q^56 - 18 * q^58 - 2 * q^60 - 24 * q^62 + 14 * q^64 - 16 * q^66 - 40 * q^68 + 2 * q^70 - 54 * q^72 + 6 * q^74 - 4 * q^75 + 2 * q^76 - 14 * q^78 + 6 * q^80 + 44 * q^81 + 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 - 58 * q^88 - 10 * q^90 - 56 * q^91 - 12 * q^92 + 14 * q^94 - 24 * q^96 + 10 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	0.458720	+	1.33775i	0.324364	+	0.945932i
$2$	0.458720	+	1.33775i	0.324364	+	0.945932i
$3$	2.54711			1.47058			0.735288	−	0.677755i	$-0.237047\pi$
$3$	2.54711			1.47058			0.735288	+	0.677755i	$0.237047\pi$
$4$	−1.57915	+	1.22731i	−0.789576	+	0.613653i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.16841	+	3.40740i	0.477003	+	1.39107i
$7$			0.654431i			0.247352i	0.992323	+	0.123676i	$0.0394683\pi$
$7$			0.654431i			0.247352i	−0.992323	+	0.123676i	$0.960532\pi$
$8$	−2.36622	−	1.54952i	−0.836585	−	0.547838i
$9$	3.48778			1.16259
$10$	0.458720	+	1.33775i	0.145060	+	0.423034i
$11$	2.31821			0.698967			0.349484	−	0.936942i	$-0.386357\pi$
$11$	2.31821			0.698967			0.349484	+	0.936942i	$0.386357\pi$
$12$	−4.02228	+	3.12609i	−1.16113	+	0.902424i
$13$		−	0.495577i		−	0.137448i	−0.997636	−	0.0687241i	$-0.978107\pi$
$13$		−	0.495577i		−	0.137448i	0.997636	−	0.0687241i	$-0.0218928\pi$
$14$	−0.875466	+	0.300201i	−0.233978	+	0.0802321i
$15$	2.54711			0.657662
$16$	0.987437	−	3.87621i	0.246859	−	0.969051i
$17$	2.19658	+	3.48928i	0.532748	+	0.846274i
$17$	2.19658	+	3.48928i	0.532748	+	0.846274i
$18$	1.59992	+	4.66578i	0.377104	+	1.09974i
$19$			2.57745i			0.591308i	0.955295	+	0.295654i	$0.0955376\pi$
$19$			2.57745i			0.591308i	−0.955295	+	0.295654i	$0.904462\pi$
$20$	−1.57915	+	1.22731i	−0.353109	+	0.274434i
$21$			1.66691i			0.363750i
$22$	1.06341	+	3.10119i	0.226720	+	0.661176i
$23$			0.188252i			0.0392532i	0.999807	+	0.0196266i	$0.00624775\pi$
$23$			0.188252i			0.0392532i	−0.999807	+	0.0196266i	$0.993752\pi$
$24$	−6.02703	−	3.94680i	−1.23026	−	0.805637i
$25$	1.00000			0.200000
$26$	0.662958	−	0.227331i	0.130017	−	0.0445833i
$27$	1.24244			0.239108
$28$	−0.803188	−	1.03345i	−0.151788	−	0.195303i
$29$	−6.85794			−1.27349			−0.636743	−	0.771076i	$-0.719719\pi$
$29$	−6.85794			−1.27349			−0.636743	+	0.771076i	$0.719719\pi$
$30$	1.16841	+	3.40740i	0.213322	+	0.622103i
$31$		−	3.96966i		−	0.712972i	−0.934301	−	0.356486i	$-0.883975\pi$
$31$		−	3.96966i		−	0.712972i	0.934301	−	0.356486i	$-0.116025\pi$
$32$	5.63835	−	0.457151i	0.996729	−	0.0808137i
$33$	5.90475			1.02789
$34$	−3.66017	+	4.53907i	−0.627713	+	0.778445i
$35$			0.654431i			0.110619i
$36$	−5.50774	+	4.28058i	−0.917957	+	0.713430i
$37$	−3.06408			−0.503732			−0.251866	−	0.967762i	$-0.581044\pi$
$37$	−3.06408			−0.503732			−0.251866	+	0.967762i	$0.581044\pi$
$38$	−3.44799	+	1.18233i	−0.559338	+	0.191799i
$39$		−	1.26229i		−	0.202128i
$40$	−2.36622	−	1.54952i	−0.374132	−	0.245000i
$41$		−	3.21537i		−	0.502156i	−0.967967	−	0.251078i	$-0.919215\pi$
$41$		−	3.21537i		−	0.502156i	0.967967	−	0.251078i	$-0.0807851\pi$
$42$	−2.22991	+	0.764646i	−0.344083	+	0.117987i
$43$		−	3.55727i		−	0.542479i	−0.962512	−	0.271239i	$-0.912566\pi$
$43$		−	3.55727i		−	0.542479i	0.962512	−	0.271239i	$-0.0874335\pi$
$44$	−3.66081	+	2.84516i	−0.551888	+	0.428924i
$45$	3.48778			0.519928
$46$	−0.251834	+	0.0863550i	−0.0371309	+	0.0127324i
$47$	−3.43065			−0.500411			−0.250206	−	0.968193i	$-0.580498\pi$
$47$	−3.43065			−0.500411			−0.250206	+	0.968193i	$0.580498\pi$
$48$	2.51511	−	9.87313i	0.363025	−	1.42506i
$49$	6.57172			0.938817
$50$	0.458720	+	1.33775i	0.0648729	+	0.189186i
$51$	5.59493	+	8.88758i	0.783447	+	1.24451i
$52$	0.608224	+	0.782590i	0.0843456	+	0.108526i
$53$		−	8.47932i		−	1.16472i	−0.812930	−	0.582362i	$-0.802129\pi$
$53$		−	8.47932i		−	1.16472i	0.812930	−	0.582362i	$-0.197871\pi$
$54$	0.569934	+	1.66208i	0.0775582	+	0.226180i
$55$	2.31821			0.312588
$56$	1.01405	−	1.54853i	0.135509	−	0.206931i
$57$			6.56507i			0.869564i
$58$	−3.14588	−	9.17420i	−0.413074	−	1.20463i
$59$		−	0.432821i		−	0.0563485i	−0.999603	−	0.0281743i	$-0.991031\pi$
$59$		−	0.432821i		−	0.0563485i	0.999603	−	0.0281743i	$-0.00896933\pi$
$60$	−4.02228	+	3.12609i	−0.519274	+	0.403576i
$61$	−3.55435			−0.455089			−0.227544	−	0.973768i	$-0.573070\pi$
$61$	−3.55435			−0.455089			−0.227544	+	0.973768i	$0.573070\pi$
$62$	5.31041	−	1.82096i	0.674423	−	0.231263i
$63$			2.28252i			0.287570i
$64$	3.19798	+	7.33300i	0.399748	+	0.916625i
$65$		−	0.495577i		−	0.0614687i
$66$	2.70863	+	7.89908i	0.333409	+	0.972310i
$67$		−	8.66134i		−	1.05815i	−0.848575	−	0.529076i	$-0.822539\pi$
$67$		−	8.66134i		−	1.05815i	0.848575	−	0.529076i	$-0.177461\pi$
$68$	−7.75114	−	2.81422i	−0.939964	−	0.341274i
$69$			0.479499i			0.0577249i
$70$	−0.875466	+	0.300201i	−0.104638	+	0.0358809i
$71$			9.72787i			1.15449i	0.816573	+	0.577243i	$0.195871\pi$
$71$			9.72787i			1.15449i	−0.816573	+	0.577243i	$0.804129\pi$
$72$	−8.25286	−	5.40439i	−0.972609	−	0.636913i
$73$		−	3.67345i		−	0.429945i	−0.976620	−	0.214973i	$-0.931034\pi$
$73$		−	3.67345i		−	0.429945i	0.976620	−	0.214973i	$-0.0689662\pi$
$74$	−1.40556	−	4.09897i	−0.163393	−	0.476496i
$75$	2.54711			0.294115
$76$	−3.16333	−	4.07019i	−0.362858	−	0.466883i
$77$			1.51711i			0.172891i
$78$	1.68863	−	0.579038i	0.191199	−	0.0655631i
$79$		−	4.08394i		−	0.459480i	−0.973252	−	0.229740i	$-0.926212\pi$
$79$		−	4.08394i		−	0.459480i	0.973252	−	0.229740i	$-0.0737875\pi$
$80$	0.987437	−	3.87621i	0.110399	−	0.433373i
$81$	−7.29871			−0.810968
$82$	4.30136	−	1.47495i	0.475006	−	0.162881i
$83$		−	15.3164i		−	1.68119i	−0.541665	−	0.840595i	$-0.682206\pi$
$83$		−	15.3164i		−	1.68119i	0.541665	−	0.840595i	$-0.317794\pi$
$84$	−2.04581	−	2.63230i	−0.223216	−	0.287208i
$85$	2.19658	+	3.48928i	0.238252	+	0.378465i
$86$	4.75874	−	1.63179i	0.513148	−	0.175961i
$87$	−17.4679			−1.87276
$88$	−5.48540	−	3.59211i	−0.584745	−	0.382921i
$89$	8.98386			0.952287			0.476144	−	0.879368i	$-0.342034\pi$
$89$	8.98386			0.952287			0.476144	+	0.879368i	$0.342034\pi$
$90$	1.59992	+	4.66578i	0.168646	+	0.491817i
$91$	0.324321			0.0339981
$92$	−0.231043	−	0.297278i	−0.0240879	−	0.0309934i
$93$		−	10.1112i		−	1.04848i
$94$	−1.57371	−	4.58935i	−0.162316	−	0.473355i
$95$			2.57745i			0.264441i
$96$	14.3615	−	1.16442i	1.46577	−	0.118843i
$97$			11.6566i			1.18355i	0.806102	+	0.591776i	$0.201573\pi$
$97$			11.6566i			1.18355i	−0.806102	+	0.591776i	$0.798427\pi$
$98$	3.01458	+	8.79132i	0.304519	+	0.888057i
$99$	8.08543			0.812616
$100$	−1.57915	+	1.22731i	−0.157915	+	0.122731i
$101$		−	7.75678i		−	0.771828i	−0.922535	−	0.385914i	$-0.873886\pi$
$101$		−	7.75678i		−	0.771828i	0.922535	−	0.385914i	$-0.126114\pi$
$102$	−9.32285	+	11.5615i	−0.923100	+	1.14476i
$103$	5.75307			0.566866			0.283433	−	0.958992i	$-0.408527\pi$
$103$	5.75307			0.566866			0.283433	+	0.958992i	$0.408527\pi$
$104$	−0.767905	+	1.17264i	−0.0752993	+	0.114987i
$105$			1.66691i			0.162674i
$106$	11.3432	−	3.88964i	1.10175	−	0.377795i
$107$	−11.3343			−1.09572			−0.547862	−	0.836569i	$-0.684558\pi$
$107$	−11.3343			−1.09572			−0.547862	+	0.836569i	$0.684558\pi$
$108$	−1.96201	+	1.52486i	−0.188794	+	0.146730i
$109$	−2.73908			−0.262357			−0.131178	−	0.991359i	$-0.541876\pi$
$109$	−2.73908			−0.262357			−0.131178	+	0.991359i	$0.541876\pi$
$110$	1.06341	+	3.10119i	0.101392	+	0.295687i
$111$	−7.80456			−0.740776
$112$	2.53671	+	0.646209i	0.239697	+	0.0610610i
$113$			13.9883i			1.31591i	0.753059	+	0.657953i	$0.228577\pi$
$113$			13.9883i			1.31591i	−0.753059	+	0.657953i	$0.771423\pi$
$114$	−8.78242	+	3.01153i	−0.822549	+	0.282056i
$115$			0.188252i			0.0175546i
$116$	10.8297	−	8.41679i	1.00551	−	0.781479i
$117$		−	1.72846i		−	0.159797i
$118$	0.579007	−	0.198544i	0.0533019	−	0.0182775i
$119$	−2.28349	+	1.43751i	−0.209327	+	0.131776i
$120$	−6.02703	−	3.94680i	−0.550190	−	0.360292i
$121$	−5.62589			−0.511445
$122$	−1.63046	−	4.75484i	−0.147614	−	0.430483i
$123$		−	8.18990i		−	0.738459i
$124$	4.87199	+	6.26869i	0.437518	+	0.562945i
$125$	1.00000			0.0894427
$126$	−3.05344	+	1.04704i	−0.272022	+	0.0932774i
$127$	−16.7241			−1.48403			−0.742013	−	0.670385i	$-0.766129\pi$
$127$	−16.7241			−1.48403			−0.742013	+	0.670385i	$0.766129\pi$
$128$	−8.34274	+	7.64190i	−0.737401	+	0.675455i
$129$		−	9.06077i		−	0.797757i
$130$	0.662958	−	0.227331i	0.0581452	−	0.0199383i
$131$	−1.25462			−0.109617			−0.0548084	−	0.998497i	$-0.517455\pi$
$131$	−1.25462			−0.109617			−0.0548084	+	0.998497i	$0.517455\pi$
$132$	−9.32449	+	7.24694i	−0.811593	+	0.630765i
$133$	−1.68677			−0.146261
$134$	11.5867	−	3.97313i	1.00094	−	0.343227i
$135$	1.24244			0.106932
$136$	0.209118	−	11.6600i	0.0179317	−	0.999839i
$137$	15.8578			1.35483			0.677413	−	0.735603i	$-0.263101\pi$
$137$	15.8578			1.35483			0.677413	+	0.735603i	$0.263101\pi$
$138$	−0.641450	+	0.219956i	−0.0546038	+	0.0187239i
$139$	5.49102			0.465742			0.232871	−	0.972508i	$-0.425188\pi$
$139$	5.49102			0.465742			0.232871	+	0.972508i	$0.425188\pi$
$140$	−0.803188	−	1.03345i	−0.0678818	−	0.0873421i
$141$	−8.73824			−0.735893
$142$	−13.0135	+	4.46237i	−1.09206	+	0.374474i
$143$		−	1.14885i		−	0.0960718i
$144$	3.44397	−	13.5194i	0.286997	−	1.12661i
$145$	−6.85794			−0.569521
$146$	4.91416	−	1.68509i	0.406699	−	0.139459i
$147$	16.7389			1.38060
$148$	4.83865	−	3.76057i	0.397734	−	0.309117i
$149$			3.99288i			0.327109i	0.986534	+	0.163555i	$0.0522960\pi$
$149$			3.99288i			0.327109i	−0.986534	+	0.163555i	$0.947704\pi$
$150$	1.16841	+	3.40740i	0.0954005	+	0.278213i
$151$	−6.42385			−0.522765			−0.261383	−	0.965235i	$-0.584178\pi$
$151$	−6.42385			−0.522765			−0.261383	+	0.965235i	$0.584178\pi$
$152$	3.99381	−	6.09882i	0.323941	−	0.494680i
$153$	7.66119	+	12.1698i	0.619370	+	0.983874i
$154$	−2.02952	+	0.695930i	−0.163543	+	0.0560796i
$155$		−	3.96966i		−	0.318851i
$156$	1.54922	+	1.99335i	0.124037	+	0.159595i
$157$			22.9114i			1.82853i	0.405116	+	0.914265i	$0.367231\pi$
$157$			22.9114i			1.82853i	−0.405116	+	0.914265i	$0.632769\pi$
$158$	5.46330	−	1.87339i	0.434637	−	0.149039i
$159$		−	21.5978i		−	1.71282i
$160$	5.63835	−	0.457151i	0.445751	−	0.0361410i
$161$	−0.123198			−0.00970936
$162$	−3.34807	−	9.76385i	−0.263049	−	0.767121i
$163$	−16.1246			−1.26297			−0.631487	−	0.775387i	$-0.717555\pi$
$163$	−16.1246			−1.26297			−0.631487	+	0.775387i	$0.717555\pi$
$164$	3.94624	+	5.07755i	0.308150	+	0.396490i
$165$	5.90475			0.459684
$166$	20.4895	−	7.02593i	1.59029	−	0.545318i
$167$		−	13.2324i		−	1.02395i	−0.859000	−	0.511976i	$-0.828914\pi$
$167$		−	13.2324i		−	1.02395i	0.859000	−	0.511976i	$-0.171086\pi$
$168$	2.58291	−	3.94427i	0.199276	−	0.304307i
$169$	12.7544			0.981108
$170$	−3.66017	+	4.53907i	−0.280722	+	0.348131i
$171$			8.98960i			0.687452i
$172$	4.36586	+	5.61747i	0.332894	+	0.428328i
$173$	21.3027			1.61961			0.809806	−	0.586697i	$-0.199572\pi$
$173$	21.3027			1.61961			0.809806	+	0.586697i	$0.199572\pi$
$174$	−8.01290	−	23.3677i	−0.607456	−	1.77150i
$175$			0.654431i			0.0494704i
$176$	2.28909	−	8.98587i	0.172546	−	0.677335i
$177$		−	1.10244i		−	0.0828648i
$178$	4.12108	+	12.0182i	0.308888	+	0.900799i
$179$		−	11.4748i		−	0.857667i	−0.903384	−	0.428833i	$-0.858925\pi$
$179$		−	11.4748i		−	0.857667i	0.903384	−	0.428833i	$-0.141075\pi$
$180$	−5.50774	+	4.28058i	−0.410523	+	0.319056i
$181$	8.44241			0.627519			0.313760	−	0.949502i	$-0.398411\pi$
$181$	8.44241			0.627519			0.313760	+	0.949502i	$0.398411\pi$
$182$	0.148773	+	0.433860i	0.0110278	+	0.0321599i
$183$	−9.05334			−0.669242
$184$	0.291700	−	0.445445i	0.0215044	−	0.0328387i
$185$	−3.06408			−0.225276
$186$	13.5262	−	4.63820i	0.991791	−	0.340089i
$187$	5.09213	+	8.08888i	0.372374	+	0.591518i
$188$	5.41751	−	4.21045i	0.395112	−	0.307079i
$189$			0.813094i			0.0591439i
$190$	−3.44799	+	1.18233i	−0.250143	+	0.0857753i
$191$	26.7666			1.93676			0.968382	−	0.249473i	$-0.0802575\pi$
$191$	26.7666			1.93676			0.968382	+	0.249473i	$0.0802575\pi$
$192$	8.14562	+	18.6780i	0.587860	+	1.34797i
$193$			19.5588i			1.40788i	0.710261	+	0.703938i	$0.248577\pi$
$193$			19.5588i			1.40788i	−0.710261	+	0.703938i	$0.751423\pi$
$194$	−15.5937	+	5.34714i	−1.11956	+	0.383902i
$195$		−	1.26229i		−	0.0903944i
$196$	−10.3777	+	8.06552i	−0.741267	+	0.576108i
$197$	8.04276			0.573023			0.286512	−	0.958077i	$-0.407504\pi$
$197$	8.04276			0.573023			0.286512	+	0.958077i	$0.407504\pi$
$198$	3.70895	+	10.8163i	0.263584	+	0.768680i
$199$		−	23.3064i		−	1.65215i	−0.563561	−	0.826075i	$-0.690569\pi$
$199$		−	23.3064i		−	1.65215i	0.563561	−	0.826075i	$-0.309431\pi$
$200$	−2.36622	−	1.54952i	−0.167317	−	0.109568i
$201$		−	22.0614i		−	1.55609i
$202$	10.3766	−	3.55819i	0.730097	−	0.250353i
$203$		−	4.48805i		−	0.314999i
$204$	−19.7430	−	7.16814i	−1.38229	−	0.501870i
$205$		−	3.21537i		−	0.224571i
$206$	2.63905	+	7.69616i	0.183871	+	0.536217i
$207$			0.656582i			0.0456356i
$208$	−1.92096	−	0.489350i	−0.133194	−	0.0339303i
$209$			5.97509i			0.413305i
$210$	−2.22991	+	0.764646i	−0.153878	+	0.0527656i
$211$	−21.8256			−1.50254			−0.751268	−	0.659998i	$-0.770557\pi$
$211$	−21.8256			−1.50254			−0.751268	+	0.659998i	$0.770557\pi$
$212$	10.4067	+	13.3901i	0.714737	+	0.919638i
$213$			24.7780i			1.69776i
$214$	−5.19925	−	15.1624i	−0.355414	−	1.03648i
$215$		−	3.55727i		−	0.242604i
$216$	−2.93989	−	1.92519i	−0.200034	−	0.130993i
$217$	2.59787			0.176355
$218$	−1.25647	−	3.66421i	−0.0850992	−	0.248172i
$219$		−	9.35670i		−	0.632267i
$220$	−3.66081	+	2.84516i	−0.246812	+	0.191821i
$221$	1.72920	−	1.08857i	0.116319	−	0.0732253i
$222$	−3.58011	−	10.4406i	−0.240281	−	0.700724i
$223$	−14.9113			−0.998536			−0.499268	−	0.866448i	$-0.666398\pi$
$223$	−14.9113			−0.998536			−0.499268	+	0.866448i	$0.666398\pi$
$224$	0.299174	+	3.68991i	0.0199894	+	0.246543i
$225$	3.48778			0.232519
$226$	−18.7128	+	6.41671i	−1.24476	+	0.426833i
$227$	−6.36332			−0.422348			−0.211174	−	0.977448i	$-0.567729\pi$
$227$	−6.36332			−0.422348			−0.211174	+	0.977448i	$0.567729\pi$
$228$	−8.05735	−	10.3672i	−0.533611	−	0.686587i
$229$			6.95553i			0.459634i	0.973234	+	0.229817i	$0.0738128\pi$
$229$			6.95553i			0.459634i	−0.973234	+	0.229817i	$0.926187\pi$
$230$	−0.251834	+	0.0863550i	−0.0166054	+	0.00569408i
$231$			3.86425i			0.254249i
$232$	16.2274	+	10.6265i	1.06538	+	0.697664i
$233$			4.82255i			0.315936i	0.987444	+	0.157968i	$0.0504942\pi$
$233$			4.82255i			0.315936i	−0.987444	+	0.157968i	$0.949506\pi$
$234$	2.31225	−	0.792882i	0.151157	−	0.0518323i
$235$	−3.43065			−0.223791
$236$	0.531204	+	0.683490i	0.0345785	+	0.0444914i
$237$		−	10.4023i		−	0.675700i
$238$	−2.97051	−	2.39533i	−0.192550	−	0.155266i
$239$	2.02631			0.131071			0.0655355	−	0.997850i	$-0.479124\pi$
$239$	2.02631			0.131071			0.0655355	+	0.997850i	$0.479124\pi$
$240$	2.51511	−	9.87313i	0.162350	−	0.637308i
$241$			5.62463i			0.362315i	0.983454	+	0.181157i	$0.0579843\pi$
$241$			5.62463i			0.362315i	−0.983454	+	0.181157i	$0.942016\pi$
$242$	−2.58071	−	7.52604i	−0.165894	−	0.483792i
$243$	−22.3180			−1.43170
$244$	5.61286	−	4.36228i	0.359327	−	0.279267i
$245$	6.57172			0.419852
$246$	10.9560	−	3.75688i	0.698532	−	0.239530i
$247$	1.27733			0.0812743
$248$	−6.15106	+	9.39308i	−0.390593	+	0.596461i
$249$		−	39.0125i		−	2.47232i
$250$	0.458720	+	1.33775i	0.0290120	+	0.0846068i
$251$		−	21.2370i		−	1.34047i	−0.742151	−	0.670233i	$-0.766194\pi$
$251$		−	21.2370i		−	1.34047i	0.742151	−	0.670233i	$-0.233806\pi$
$252$	−2.80135	−	3.60444i	−0.176468	−	0.227058i
$253$			0.436408i			0.0274367i
$254$	−7.67170	−	22.3727i	−0.481365	−	1.40379i
$255$	5.59493	+	8.88758i	0.350368	+	0.556562i
$256$	−14.0499	−	7.65501i	−0.878121	−	0.478438i
$257$	−3.56840			−0.222591			−0.111295	−	0.993787i	$-0.535500\pi$
$257$	−3.56840			−0.222591			−0.111295	+	0.993787i	$0.535500\pi$
$258$	12.1211	−	4.15636i	0.754624	−	0.258764i
$259$		−	2.00523i		−	0.124599i
$260$	0.608224	+	0.782590i	0.0377205	+	0.0485342i
$261$	−23.9190			−1.48055
$262$	−0.575520	−	1.67837i	−0.0355558	−	0.103690i
$263$	1.31194			0.0808976			0.0404488	−	0.999182i	$-0.487121\pi$
$263$	1.31194			0.0808976			0.0404488	+	0.999182i	$0.487121\pi$
$264$	−13.9719	−	9.14952i	−0.859913	−	0.563114i
$265$		−	8.47932i		−	0.520880i
$266$	−0.773754	−	2.25647i	−0.0474419	−	0.138353i
$267$	22.8829			1.40041
$268$	10.6301	+	13.6776i	0.649338	+	0.835490i
$269$	22.5763			1.37650			0.688249	−	0.725474i	$-0.258380\pi$
$269$	22.5763			1.37650			0.688249	+	0.725474i	$0.258380\pi$
$270$	0.569934	+	1.66208i	0.0346851	+	0.101151i
$271$	7.24361			0.440018			0.220009	−	0.975498i	$-0.429391\pi$
$271$	7.24361			0.440018			0.220009	+	0.975498i	$0.429391\pi$
$272$	15.6941	−	5.06895i	0.951597	−	0.307350i
$273$	0.826082			0.0499967
$274$	7.27432	+	21.2138i	0.439457	+	1.28157i
$275$	2.31821			0.139793
$276$	−0.588492	−	0.757201i	−0.0354231	−	0.0455782i
$277$	−15.4507			−0.928342			−0.464171	−	0.885746i	$-0.653648\pi$
$277$	−15.4507			−0.928342			−0.464171	+	0.885746i	$0.653648\pi$
$278$	2.51884	+	7.34561i	0.151070	+	0.440560i
$279$		−	13.8453i		−	0.828897i
$280$	1.01405	−	1.54853i	0.0606013	−	0.0925422i
$281$	−19.5260			−1.16482			−0.582412	−	0.812894i	$-0.697891\pi$
$281$	−19.5260			−1.16482			−0.582412	+	0.812894i	$0.697891\pi$
$282$	−4.00841	−	11.6896i	−0.238697	−	0.696105i
$283$	−21.5407			−1.28046			−0.640230	−	0.768183i	$-0.721161\pi$
$283$	−21.5407			−1.28046			−0.640230	+	0.768183i	$0.721161\pi$
$284$	−11.9391	−	15.3618i	−0.708454	−	0.911553i
$285$			6.56507i			0.388881i
$286$	1.53688	−	0.527002i	0.0908774	−	0.0311623i
$287$	2.10424			0.124209
$288$	19.6654	−	1.59445i	1.15879	−	0.0939536i
$289$	−7.35010	+	15.3289i	−0.432359	+	0.901702i
$290$	−3.14588	−	9.17420i	−0.184732	−	0.538728i
$291$			29.6908i			1.74050i
$292$	4.50845	+	5.80094i	0.263837	+	0.339474i
$293$			21.2734i			1.24280i	0.783492	+	0.621401i	$0.213436\pi$
$293$			21.2734i			1.24280i	−0.783492	+	0.621401i	$0.786564\pi$
$294$	7.67848	+	22.3925i	0.447818	+	1.30596i
$295$		−	0.432821i		−	0.0251998i
$296$	7.25028	+	4.74785i	0.421414	+	0.275963i
$297$	2.88025			0.167129
$298$	−5.34148	+	1.83162i	−0.309423	+	0.106103i
$299$	0.0932932			0.00539529
$300$	−4.02228	+	3.12609i	−0.232226	+	0.180485i
$301$	2.32799			0.134183
$302$	−2.94675	−	8.59350i	−0.169566	−	0.494501i
$303$		−	19.7574i		−	1.13503i
$304$	9.99074	+	2.54507i	0.573008	+	0.145970i
$305$	−3.55435			−0.203522
$306$	−12.7659	+	15.8313i	−0.729776	+	0.905016i
$307$			24.5694i			1.40225i	0.713037	+	0.701126i	$0.247319\pi$
$307$			24.5694i			1.40225i	−0.713037	+	0.701126i	$0.752681\pi$
$308$	−1.86196	−	2.39575i	−0.106095	−	0.136510i
$309$	14.6537			0.833620
$310$	5.31041	−	1.82096i	0.301611	−	0.103424i
$311$			31.0746i			1.76208i	0.473044	+	0.881039i	$0.343155\pi$
$311$			31.0746i			1.76208i	−0.473044	+	0.881039i	$0.656845\pi$
$312$	−1.95594	+	2.98685i	−0.110733	+	0.169097i
$313$		−	15.7952i		−	0.892798i	−0.894834	−	0.446399i	$-0.852706\pi$
$313$		−	15.7952i		−	0.892798i	0.894834	−	0.446399i	$-0.147294\pi$
$314$	−30.6498	+	10.5099i	−1.72967	+	0.593110i
$315$			2.28252i			0.128605i
$316$	5.01225	+	6.44916i	0.281961	+	0.362794i
$317$	−3.40672			−0.191341			−0.0956704	−	0.995413i	$-0.530499\pi$
$317$	−3.40672			−0.191341			−0.0956704	+	0.995413i	$0.530499\pi$
$318$	28.8924	−	9.90734i	1.62021	−	0.555576i
$319$	−15.8982			−0.890126
$320$	3.19798	+	7.33300i	0.178773	+	0.409927i
$321$	−28.8696			−1.61135
$322$	−0.0565134	−	0.164808i	−0.00314937	−	0.00918439i
$323$	−8.99345	+	5.66158i	−0.500409	+	0.315018i
$324$	11.5258	−	8.95776i	0.640320	−	0.497653i
$325$		−	0.495577i		−	0.0274896i
$326$	−7.39667	−	21.5706i	−0.409664	−	1.19469i
$327$	−6.97676			−0.385816
$328$	−4.98227	+	7.60826i	−0.275100	+	0.420096i
$329$		−	2.24512i		−	0.123778i
$330$	2.70863	+	7.89908i	0.149105	+	0.434830i
$331$			17.2530i			0.948310i	0.880441	+	0.474155i	$0.157246\pi$
$331$			17.2530i			0.948310i	−0.880441	+	0.474155i	$0.842754\pi$
$332$	18.7979	+	24.1869i	1.03167	+	1.32743i
$333$	−10.6869			−0.585636
$334$	17.7016	−	6.06996i	0.968589	−	0.332133i
$335$		−	8.66134i		−	0.473220i
$336$	6.46129	+	1.64597i	0.352492	+	0.0897949i
$337$			13.8486i			0.754383i	0.926135	+	0.377192i	$0.123110\pi$
$337$			13.8486i			0.754383i	−0.926135	+	0.377192i	$0.876890\pi$
$338$	5.85071	+	17.0622i	0.318236	+	0.928062i
$339$			35.6297i			1.93514i
$340$	−7.75114	−	2.81422i	−0.420365	−	0.152623i
$341$		−	9.20251i		−	0.498344i
$342$	−12.0258	+	4.12371i	−0.650283	+	0.222985i
$343$			8.88176i			0.479570i
$344$	−5.51206	+	8.41728i	−0.297190	+	0.453829i
$345$			0.479499i			0.0258154i
$346$	9.77198	+	28.4977i	0.525345	+	1.53204i
$347$	6.09457			0.327174			0.163587	−	0.986529i	$-0.447694\pi$
$347$	6.09457			0.327174			0.163587	+	0.986529i	$0.447694\pi$
$348$	27.5845	−	21.4385i	1.47869	−	1.14923i
$349$			34.5283i			1.84826i	0.382080	+	0.924129i	$0.375208\pi$
$349$			34.5283i			1.84826i	−0.382080	+	0.924129i	$0.624792\pi$
$350$	−0.875466	+	0.300201i	−0.0467956	+	0.0160464i
$351$		−	0.615726i		−	0.0328650i
$352$	13.0709	−	1.05977i	0.696681	−	0.0564861i
$353$	−33.5676			−1.78662			−0.893312	−	0.449437i	$-0.851625\pi$
$353$	−33.5676			−1.78662			−0.893312	+	0.449437i	$0.851625\pi$
$354$	1.47480	−	0.505714i	0.0783845	−	0.0268784i
$355$			9.72787i			0.516302i
$356$	−14.1869	+	11.0260i	−0.751903	+	0.584374i
$357$	−5.81631	+	3.66150i	−0.307832	+	0.193787i
$358$	15.3504	−	5.26372i	0.811295	−	0.278196i
$359$	9.02404			0.476271			0.238135	−	0.971232i	$-0.423464\pi$
$359$	9.02404			0.476271			0.238135	+	0.971232i	$0.423464\pi$
$360$	−8.25286	−	5.40439i	−0.434964	−	0.284836i
$361$	12.3567			0.650354
$362$	3.87271	+	11.2938i	0.203545	+	0.593591i
$363$	−14.3298			−0.752118
$364$	−0.512152	+	0.398041i	−0.0268440	+	0.0208630i
$365$		−	3.67345i		−	0.192277i
$366$	−4.15295	−	12.1111i	−0.217078	−	0.633058i
$367$			35.2634i			1.84073i	0.391055	+	0.920367i	$0.372110\pi$
$367$			35.2634i			1.84073i	−0.391055	+	0.920367i	$0.627890\pi$
$368$	0.729703	+	0.185887i	0.0380384	+	0.00969002i
$369$		−	11.2145i		−	0.583804i
$370$	−1.40556	−	4.09897i	−0.0730714	−	0.213096i
$371$	5.54913			0.288097
$372$	12.4095	+	15.9671i	0.643403	+	0.827854i
$373$			28.7637i			1.48933i	0.667439	+	0.744664i	$0.267390\pi$
$373$			28.7637i			1.48933i	−0.667439	+	0.744664i	$0.732610\pi$
$374$	−8.48504	+	10.5225i	−0.438751	+	0.544108i
$375$	2.54711			0.131532
$376$	8.11766	+	5.31585i	0.418636	+	0.274144i
$377$			3.39863i			0.175038i
$378$	−1.08772	+	0.372983i	−0.0559461	+	0.0191842i
$379$	2.79911			0.143780			0.0718902	−	0.997413i	$-0.477097\pi$
$379$	2.79911			0.143780			0.0718902	+	0.997413i	$0.477097\pi$
$380$	−3.16333	−	4.07019i	−0.162275	−	0.208796i
$381$	−42.5982			−2.18237
$382$	12.2784	+	35.8070i	0.628217	+	1.83205i
$383$	4.68600			0.239444			0.119722	−	0.992807i	$-0.461800\pi$
$383$	4.68600			0.239444			0.119722	+	0.992807i	$0.461800\pi$
$384$	−21.2499	+	19.4648i	−1.08441	+	0.993308i
$385$			1.51711i			0.0773191i
$386$	−26.1648	+	8.97204i	−1.33176	+	0.456665i
$387$		−	12.4070i		−	0.630683i
$388$	−14.3063	−	18.4076i	−0.726291	−	0.934504i
$389$		−	35.9648i		−	1.82349i	−0.410758	−	0.911744i	$-0.634736\pi$
$389$		−	35.9648i		−	1.82349i	0.410758	−	0.911744i	$-0.365264\pi$
$390$	1.68863	−	0.579038i	0.0855070	−	0.0293207i
$391$	−0.656863	+	0.413510i	−0.0332190	+	0.0209121i
$392$	−15.5501	−	10.1830i	−0.785400	−	0.514319i
$393$	−3.19566			−0.161200
$394$	3.68938	+	10.7592i	0.185868	+	0.542041i
$395$		−	4.08394i		−	0.205486i
$396$	−12.7681	+	9.92330i	−0.641622	+	0.498665i
$397$	−21.8718			−1.09772			−0.548858	−	0.835916i	$-0.684937\pi$
$397$	−21.8718			−1.09772			−0.548858	+	0.835916i	$0.684937\pi$
$398$	31.1782	−	10.6911i	1.56282	−	0.535898i
$399$	−4.29638			−0.215088
$400$	0.987437	−	3.87621i	0.0493718	−	0.193810i
$401$		−	3.78040i		−	0.188784i	−0.995535	−	0.0943922i	$-0.969909\pi$
$401$		−	3.78040i		−	0.188784i	0.995535	−	0.0943922i	$-0.0300908\pi$
$402$	29.5127	−	10.1200i	1.47196	−	0.504741i
$403$	−1.96727			−0.0979967
$404$	9.51994	+	12.2491i	0.473635	+	0.609417i
$405$	−7.29871			−0.362676
$406$	6.00389	−	2.05876i	0.297968	−	0.102174i
$407$	−7.10319			−0.352092
$408$	0.532647	−	29.6994i	0.0263700	−	1.47034i
$409$	23.7023			1.17200			0.586001	−	0.810311i	$-0.300702\pi$
$409$	23.7023			1.17200			0.586001	+	0.810311i	$0.300702\pi$
$410$	4.30136	−	1.47495i	0.212429	−	0.0728428i
$411$	40.3917			1.99238
$412$	−9.08496	+	7.06078i	−0.447584	+	0.347859i
$413$	0.283252			0.0139379
$414$	−0.878343	+	0.301188i	−0.0431682	+	0.0148026i
$415$		−	15.3164i		−	0.751851i
$416$	−0.226553	−	2.79424i	−0.0111077	−	0.136999i
$417$	13.9862			0.684909
$418$	−7.99317	+	2.74089i	−0.390959	+	0.134061i
$419$	−3.14894			−0.153836			−0.0769180	−	0.997037i	$-0.524508\pi$
$419$	−3.14894			−0.153836			−0.0769180	+	0.997037i	$0.524508\pi$
$420$	−2.04581	−	2.63230i	−0.0998253	−	0.128443i
$421$		−	13.3377i		−	0.650042i	−0.945707	−	0.325021i	$-0.894629\pi$
$421$		−	13.3377i		−	0.650042i	0.945707	−	0.325021i	$-0.105371\pi$
$422$	−10.0118	−	29.1972i	−0.487369	−	1.42130i
$423$	−11.9654			−0.581775
$424$	−13.1389	+	20.0639i	−0.638080	+	0.974390i
$425$	2.19658	+	3.48928i	0.106550	+	0.169255i
$426$	−33.1467	+	11.3662i	−1.60596	+	0.550692i
$427$		−	2.32608i		−	0.112567i
$428$	17.8985	−	13.9106i	0.865157	−	0.672394i
$429$		−	2.92626i		−	0.141281i
$430$	4.75874	−	1.63179i	0.229487	−	0.0786921i
$431$		−	7.13978i		−	0.343911i	−0.985105	−	0.171955i	$-0.944991\pi$
$431$		−	7.13978i		−	0.343911i	0.985105	−	0.171955i	$-0.0550085\pi$
$432$	1.22683	−	4.81596i	0.0590261	−	0.231708i
$433$	−12.0593			−0.579534			−0.289767	−	0.957097i	$-0.593578\pi$
$433$	−12.0593			−0.579534			−0.289767	+	0.957097i	$0.593578\pi$
$434$	1.19170	+	3.47530i	0.0572032	+	0.166820i
$435$	−17.4679			−0.837523
$436$	4.32543	−	3.36170i	0.207150	−	0.160996i
$437$	−0.485211			−0.0232108
$438$	12.5169	−	4.29211i	0.598082	−	0.205085i
$439$			16.9899i			0.810885i	0.914121	+	0.405443i	$0.132883\pi$
$439$			16.9899i			0.810885i	−0.914121	+	0.405443i	$0.867117\pi$
$440$	−5.48540	−	3.59211i	−0.261506	−	0.171247i
$441$	22.9207			1.09146
$442$	2.24946	+	1.81389i	0.106996	+	0.0862781i
$443$		−	6.08646i		−	0.289176i	−0.989492	−	0.144588i	$-0.953814\pi$
$443$		−	6.08646i		−	0.289176i	0.989492	−	0.144588i	$-0.0461857\pi$
$444$	12.3246	−	9.57859i	0.584899	−	0.454580i
$445$	8.98386			0.425876
$446$	−6.84013	−	19.9476i	−0.323890	−	0.944548i
$447$			10.1703i			0.481039i
$448$	−4.79895	+	2.09286i	−0.226729	+	0.0988783i
$449$			15.7621i			0.743859i	0.928261	+	0.371929i	$0.121304\pi$
$449$			15.7621i			0.743859i	−0.928261	+	0.371929i	$0.878696\pi$
$450$	1.59992	+	4.66578i	0.0754209	+	0.219947i
$451$		−	7.45391i		−	0.350991i
$452$	−17.1679	−	22.0896i	−0.807510	−	1.03901i
$453$	−16.3623			−0.768766
$454$	−2.91898	−	8.51253i	−0.136995	−	0.399513i
$455$	0.324321			0.0152044
$456$	10.1727	−	15.5344i	0.476380	−	0.727464i
$457$	7.72090			0.361169			0.180584	−	0.983560i	$-0.442201\pi$
$457$	7.72090			0.361169			0.180584	+	0.983560i	$0.442201\pi$
$458$	−9.30476	+	3.19064i	−0.434783	+	0.149089i
$459$	2.72912	+	4.33523i	0.127385	+	0.202351i
$460$	−0.231043	−	0.297278i	−0.0107724	−	0.0138607i
$461$		−	34.2083i		−	1.59324i	−0.604481	−	0.796619i	$-0.706620\pi$
$461$		−	34.2083i		−	1.59324i	0.604481	−	0.796619i	$-0.293380\pi$
$462$	−5.16941	+	1.77261i	−0.240502	+	0.0824694i
$463$	2.77955			0.129177			0.0645883	−	0.997912i	$-0.479427\pi$
$463$	2.77955			0.129177			0.0645883	+	0.997912i	$0.479427\pi$
$464$	−6.77178	+	26.5828i	−0.314372	+	1.23407i
$465$		−	10.1112i		−	0.468894i
$466$	−6.45137	+	2.21220i	−0.298854	+	0.102478i
$467$			25.2523i			1.16854i	0.811560	+	0.584269i	$0.198619\pi$
$467$			25.2523i			1.16854i	−0.811560	+	0.584269i	$0.801381\pi$
$468$	2.12136	+	2.72951i	0.0980597	+	0.126171i
$469$	5.66825			0.261736
$470$	−1.57371	−	4.58935i	−0.0725897	−	0.211691i
$471$			58.3580i			2.68899i
$472$	−0.670665	+	1.02415i	−0.0308698	+	0.0471403i
$473$		−	8.24651i		−	0.379175i
$474$	13.9156	−	4.77173i	0.639166	−	0.219173i
$475$			2.57745i			0.118262i
$476$	1.84171	−	5.07259i	0.0844148	−	0.232502i
$477$		−	29.5740i		−	1.35410i
$478$	0.929509	+	2.71069i	0.0425147	+	0.123984i
$479$			16.9072i			0.772511i	0.922392	+	0.386255i	$0.126232\pi$
$479$			16.9072i			0.772511i	−0.922392	+	0.386255i	$0.873768\pi$
$480$	14.3615	−	1.16442i	0.655511	−	0.0531481i
$481$			1.51849i			0.0692370i
$482$	−7.52436	+	2.58013i	−0.342725	+	0.117522i
$483$	−0.313799			−0.0142784
$484$	8.88413	−	6.90469i	0.403824	−	0.313850i
$485$			11.6566i			0.529301i
$486$	−10.2377	−	29.8559i	−0.464392	−	1.35429i
$487$		−	29.1269i		−	1.31987i	−0.751324	−	0.659933i	$-0.770585\pi$
$487$		−	29.1269i		−	1.31987i	0.751324	−	0.659933i	$-0.229415\pi$
$488$	8.41038	+	5.50754i	0.380720	+	0.249315i
$489$	−41.0711			−1.85730
$490$	3.01458	+	8.79132i	0.136185	+	0.397151i
$491$		−	23.7259i		−	1.07074i	−0.844619	−	0.535368i	$-0.820173\pi$
$491$		−	23.7259i		−	1.07074i	0.844619	−	0.535368i	$-0.179827\pi$
$492$	10.0515	+	12.9331i	0.453158	+	0.583069i
$493$	−15.0640	−	23.9292i	−0.678448	−	1.07772i
$494$	0.585935	+	1.70874i	0.0263625	+	0.0768800i
$495$	8.08543			0.363413
$496$	−15.3872	−	3.91979i	−0.690906	−	0.176004i
$497$	−6.36622			−0.285564
$498$	52.1890	−	17.8958i	2.33864	−	0.801932i
$499$	−3.53161			−0.158097			−0.0790483	−	0.996871i	$-0.525188\pi$
$499$	−3.53161			−0.158097			−0.0790483	+	0.996871i	$0.525188\pi$
$500$	−1.57915	+	1.22731i	−0.0706218	+	0.0548868i
$501$		−	33.7043i		−	1.50580i
$502$	28.4098	−	9.74183i	1.26799	−	0.434799i
$503$			27.6635i			1.23346i	0.787177	+	0.616728i	$0.211542\pi$
$503$			27.6635i			1.23346i	−0.787177	+	0.616728i	$0.788458\pi$
$504$	3.53680	−	5.40093i	0.157542	−	0.240577i
$505$		−	7.75678i		−	0.345172i
$506$	−0.583805	+	0.200189i	−0.0259533	+	0.00889950i
$507$	32.4869			1.44279
$508$	26.4099	−	20.5256i	1.17175	−	0.910678i
$509$			10.4113i			0.461472i	0.973016	+	0.230736i	$0.0741134\pi$
$509$			10.4113i			0.461472i	−0.973016	+	0.230736i	$0.925887\pi$
$510$	−9.32285	+	11.5615i	−0.412823	+	0.511953i
$511$	2.40402			0.106348
$512$	3.79550	−	22.3068i	0.167739	−	0.985831i
$513$			3.20234i			0.141387i
$514$	−1.63690	−	4.77363i	−0.0722005	−	0.210556i
$515$	5.75307			0.253510
$516$	11.1203	+	14.3083i	0.489546	+	0.629889i
$517$	−7.95297			−0.349771
$518$	2.68250	−	0.919840i	0.117862	−	0.0404154i
$519$	54.2603			2.38176
$520$	−0.767905	+	1.17264i	−0.0336749	+	0.0514238i
$521$		−	13.3749i		−	0.585965i	−0.956118	−	0.292983i	$-0.905352\pi$
$521$		−	13.3749i		−	0.585965i	0.956118	−	0.292983i	$-0.0946478\pi$
$522$	−10.9721	−	31.9977i	−0.480237	−	1.40050i
$523$		−	31.3021i		−	1.36875i	−0.729132	−	0.684373i	$-0.760076\pi$
$523$		−	31.3021i		−	1.36875i	0.729132	−	0.684373i	$-0.239924\pi$
$524$	1.98124	−	1.53980i	0.0865507	−	0.0672667i
$525$			1.66691i			0.0727499i
$526$	0.601813	+	1.75505i	0.0262403	+	0.0765237i
$527$	13.8512	−	8.71966i	0.603369	−	0.379834i
$528$	5.83057	−	22.8880i	0.253743	−	0.996073i
$529$	22.9646			0.998459
$530$	11.3432	−	3.88964i	0.492718	−	0.168955i
$531$		−	1.50959i		−	0.0655105i
$532$	2.66366	−	2.07018i	0.115484	−	0.0897537i
$533$	−1.59346			−0.0690204
$534$	10.4969	+	30.6116i	0.454243	+	1.32469i
$535$	−11.3343			−0.490023
$536$	−13.4209	+	20.4946i	−0.579695	+	0.885233i
$537$		−	29.2276i		−	1.26126i
$538$	10.3562	+	30.2014i	0.446487	+	1.30207i
$539$	15.2346			0.656203
$540$	−1.96201	+	1.52486i	−0.0844313	+	0.0656195i
$541$	−12.3847			−0.532461			−0.266231	−	0.963909i	$-0.585778\pi$
$541$	−12.3847			−0.532461			−0.266231	+	0.963909i	$0.585778\pi$
$542$	3.32279	+	9.69014i	0.142726	+	0.416227i
$543$	21.5038			0.922815
$544$	13.9802	+	18.6696i	0.599396	+	0.800452i
$545$	−2.73908			−0.117329
$546$	0.378941	+	1.10509i	0.0162172	+	0.0472935i
$547$	−7.06558			−0.302102			−0.151051	−	0.988526i	$-0.548266\pi$
$547$	−7.06558			−0.302102			−0.151051	+	0.988526i	$0.548266\pi$
$548$	−25.0419	+	19.4624i	−1.06974	+	0.831394i
$549$	−12.3968			−0.529084
$550$	1.06341	+	3.10119i	0.0453440	+	0.132235i
$551$		−	17.6760i		−	0.753023i
$552$	0.742993	−	1.13460i	0.0316239	−	0.0482918i
$553$	2.67266			0.113653
$554$	−7.08754	−	20.6692i	−0.301121	−	0.878148i
$555$	−7.80456			−0.331285
$556$	−8.67114	+	6.73916i	−0.367738	+	0.285804i
$557$			7.14741i			0.302845i	0.988469	+	0.151423i	$0.0483855\pi$
$557$			7.14741i			0.302845i	−0.988469	+	0.151423i	$0.951615\pi$
$558$	18.5216	−	6.35113i	0.784081	−	0.268865i
$559$	−1.76290			−0.0745627
$560$	2.53671	+	0.646209i	0.107196	+	0.0273073i
$561$	12.9702	+	20.6033i	0.547604	+	0.869872i
$562$	−8.95698	−	26.1209i	−0.377827	−	1.10184i
$563$			40.7336i			1.71672i	0.513049	+	0.858359i	$0.328516\pi$
$563$			40.7336i			1.71672i	−0.513049	+	0.858359i	$0.671484\pi$
$564$	13.7990	−	10.7245i	0.581043	−	0.451583i
$565$			13.9883i			0.588491i
$566$	−9.88114	−	28.8160i	−0.415335	−	1.21123i
$567$		−	4.77651i		−	0.200594i
$568$	15.0735	−	23.0183i	0.632471	−	0.965825i
$569$	13.5629			0.568587			0.284293	−	0.958737i	$-0.408241\pi$
$569$	13.5629			0.568587			0.284293	+	0.958737i	$0.408241\pi$
$570$	−8.78242	+	3.01153i	−0.367855	+	0.126139i
$571$	12.9863			0.543460			0.271730	−	0.962374i	$-0.412404\pi$
$571$	12.9863			0.543460			0.271730	+	0.962374i	$0.412404\pi$
$572$	1.40999	+	1.81421i	0.0589548	+	0.0758560i
$573$	68.1776			2.84816
$574$	0.965256	+	2.81494i	0.0402890	+	0.117493i
$575$			0.188252i			0.00785065i
$576$	11.1539	+	25.5759i	0.464745	+	1.06566i
$577$	−41.0167			−1.70755			−0.853773	−	0.520645i	$-0.825692\pi$
$577$	−41.0167			−1.70755			−0.853773	+	0.520645i	$0.825692\pi$
$578$	−23.8779	−	2.80090i	−0.993190	−	0.116502i
$579$			49.8186i			2.07039i
$580$	10.8297	−	8.41679i	0.449679	−	0.349488i
$581$	10.0235			0.415845
$582$	−39.7189	+	13.6198i	−1.64640	+	0.564558i
$583$		−	19.6569i		−	0.814104i
$584$	−5.69209	+	8.69220i	−0.235540	+	0.359686i
$585$		−	1.72846i		−	0.0714632i
$586$	−28.4584	+	9.75852i	−1.17561	+	0.403121i
$587$		−	34.8343i		−	1.43777i	−0.695131	−	0.718884i	$-0.744653\pi$
$587$		−	34.8343i		−	1.43777i	0.695131	−	0.718884i	$-0.255347\pi$
$588$	−26.4333	+	20.5438i	−1.09009	+	0.847211i
$589$	10.2316			0.421586
$590$	0.579007	−	0.198544i	0.0238373	−	0.00817393i
$591$	20.4858			0.842674
$592$	−3.02558	+	11.8770i	−0.124351	+	0.488142i
$593$	−17.2670			−0.709072			−0.354536	−	0.935042i	$-0.615361\pi$
$593$	−17.2670			−0.709072			−0.354536	+	0.935042i	$0.615361\pi$
$594$	1.32123	+	3.85305i	0.0542107	+	0.158093i
$595$	−2.28349	+	1.43751i	−0.0936140	+	0.0589321i
$596$	−4.90049	−	6.30536i	−0.200732	−	0.258278i
$597$		−	59.3641i		−	2.42961i
$598$	0.0427955	+	0.124803i	0.00175004	+	0.00510358i
$599$	14.3306			0.585531			0.292766	−	0.956184i	$-0.405424\pi$
$599$	14.3306			0.585531			0.292766	+	0.956184i	$0.405424\pi$
$600$	−6.02703	−	3.94680i	−0.246052	−	0.161127i
$601$		−	1.65416i		−	0.0674746i	−0.999431	−	0.0337373i	$-0.989259\pi$
$601$		−	1.65416i		−	0.0674746i	0.999431	−	0.0337373i	$-0.0107409\pi$
$602$	1.06790	+	3.11427i	0.0435242	+	0.126928i
$603$		−	30.2089i		−	1.23020i
$604$	10.1442	−	7.88403i	0.412763	−	0.320797i
$605$	−5.62589			−0.228725
$606$	26.4304	−	9.06312i	1.07366	−	0.368164i
$607$			15.0062i			0.609082i	0.952499	+	0.304541i	$0.0985031\pi$
$607$			15.0062i			0.609082i	−0.952499	+	0.304541i	$0.901497\pi$
$608$	1.17829	+	14.5326i	0.0477858	+	0.589374i
$609$		−	11.4316i		−	0.463230i
$610$	−1.63046	−	4.75484i	−0.0660152	−	0.192518i
$611$			1.70015i			0.0687806i
$612$	−27.0343	−	9.81540i	−1.09280	−	0.396764i
$613$			17.7388i			0.716462i	0.933633	+	0.358231i	$0.116620\pi$
$613$			17.7388i			0.716462i	−0.933633	+	0.358231i	$0.883380\pi$
$614$	−32.8678	+	11.2705i	−1.32644	+	0.454841i
$615$		−	8.18990i		−	0.330249i
$616$	2.35079	−	3.58982i	0.0947161	−	0.144638i
$617$		−	43.1029i		−	1.73526i	−0.497211	−	0.867629i	$-0.665643\pi$
$617$		−	43.1029i		−	1.73526i	0.497211	−	0.867629i	$-0.334357\pi$
$618$	6.72196	+	19.6030i	0.270397	+	0.788548i
$619$	27.0444			1.08700			0.543502	−	0.839408i	$-0.317098\pi$
$619$	27.0444			1.08700			0.543502	+	0.839408i	$0.317098\pi$
$620$	4.87199	+	6.26869i	0.195664	+	0.251757i
$621$			0.233892i			0.00938577i
$622$	−41.5700	+	14.2545i	−1.66681	+	0.571555i
$623$			5.87932i			0.235550i
$624$	−4.89289	−	1.24643i	−0.195873	−	0.0498972i
$625$	1.00000			0.0400000
$626$	21.1301	−	7.24559i	0.844527	−	0.289592i
$627$			15.2192i			0.607797i
$628$	−28.1193	−	36.1806i	−1.12208	−	1.44376i
$629$	−6.73049	−	10.6914i	−0.268362	−	0.426295i
$630$	−3.05344	+	1.04704i	−0.121652	+	0.0417149i
$631$	−20.9950			−0.835796			−0.417898	−	0.908494i	$-0.637233\pi$
$631$	−20.9950			−0.835796			−0.417898	+	0.908494i	$0.637233\pi$
$632$	−6.32815	+	9.66350i	−0.251720	+	0.384394i
$633$	−55.5922			−2.20959
$634$	−1.56273	−	4.55735i	−0.0620641	−	0.180995i
$635$	−16.7241			−0.663677
$636$	26.5071	+	34.1062i	1.05108	+	1.35240i
$637$		−	3.25679i		−	0.129039i
$638$	−7.29281	−	21.2678i	−0.288725	−	0.841999i
$639$			33.9287i			1.34220i
$640$	−8.34274	+	7.64190i	−0.329776	+	0.302073i
$641$			11.0768i			0.437509i	0.975780	+	0.218755i	$0.0701994\pi$
$641$			11.0768i			0.437509i	−0.975780	+	0.218755i	$0.929801\pi$
$642$	−13.2431	−	38.6203i	−0.522663	−	1.52422i
$643$	−24.9194			−0.982725			−0.491363	−	0.870955i	$-0.663501\pi$
$643$	−24.9194			−0.982725			−0.491363	+	0.870955i	$0.663501\pi$
$644$	0.194548	−	0.151202i	0.00766627	−	0.00595818i
$645$		−	9.06077i		−	0.356768i
$646$	−11.6993	−	9.43391i	−0.460301	−	0.371172i
$647$	38.2146			1.50237			0.751185	−	0.660092i	$-0.229483\pi$
$647$	38.2146			1.50237			0.751185	+	0.660092i	$0.229483\pi$
$648$	17.2703	+	11.3095i	0.678443	+	0.444279i
$649$		−	1.00337i		−	0.0393858i
$650$	0.662958	−	0.227331i	0.0260033	−	0.00891666i
$651$	6.61707			0.259343
$652$	25.4631	−	19.7898i	0.997213	−	0.775028i
$653$	46.6416			1.82523			0.912613	−	0.408825i	$-0.134061\pi$
$653$	46.6416			1.82523			0.912613	+	0.408825i	$0.134061\pi$
$654$	−3.20038	−	9.33316i	−0.125145	−	0.364955i
$655$	−1.25462			−0.0490221
$656$	−12.4634	−	3.17497i	−0.486615	−	0.123962i
$657$		−	12.8122i		−	0.499852i
$658$	3.00341	−	1.02988i	0.117085	−	0.0401490i
$659$		−	29.2111i		−	1.13790i	−0.822371	−	0.568952i	$-0.807349\pi$
$659$		−	29.2111i		−	1.13790i	0.822371	−	0.568952i	$-0.192651\pi$
$660$	−9.32449	+	7.24694i	−0.362955	+	0.282087i
$661$		−	6.88515i		−	0.267801i	−0.990995	−	0.133901i	$-0.957250\pi$
$661$		−	6.88515i		−	0.267801i	0.990995	−	0.133901i	$-0.0427503\pi$
$662$	−23.0802	+	7.91430i	−0.897037	+	0.307598i
$663$	4.40448	−	2.77272i	0.171056	−	0.107683i
$664$	−23.7330	+	36.2419i	−0.921019	+	1.40646i
$665$	−1.68677			−0.0654100
$666$	−4.90228	−	14.2963i	−0.189959	−	0.553972i
$667$		−	1.29102i		−	0.0499885i
$668$	16.2402	+	20.8959i	0.628351	+	0.808487i
$669$	−37.9808			−1.46842
$670$	11.5867	−	3.97313i	0.447634	−	0.153496i
$671$	−8.23975			−0.318092
$672$	0.762030	+	9.39863i	0.0293960	+	0.362560i
$673$			39.7685i			1.53296i	0.642267	+	0.766481i	$0.277994\pi$
$673$			39.7685i			1.53296i	−0.642267	+	0.766481i	$0.722006\pi$
$674$	−18.5260	+	6.35265i	−0.713595	+	0.244695i
$675$	1.24244			0.0478217
$676$	−20.1411	+	15.6536i	−0.774659	+	0.602060i
$677$	38.9268			1.49608			0.748039	−	0.663655i	$-0.230996\pi$
$677$	38.9268			1.49608			0.748039	+	0.663655i	$0.230996\pi$
$678$	−47.6637	+	16.3441i	−1.83051	+	0.627691i
$679$	−7.62847			−0.292754
$680$	0.209118	−	11.6600i	0.00801931	−	0.447142i
$681$	−16.2081			−0.621096
$682$	12.3107	−	4.22138i	0.471400	−	0.161645i
$683$	8.48371			0.324620			0.162310	−	0.986740i	$-0.448106\pi$
$683$	8.48371			0.324620			0.162310	+	0.986740i	$0.448106\pi$
$684$	−11.0330	−	14.1959i	−0.421857	−	0.542795i
$685$	15.8578			0.605897
$686$	−11.8816	+	4.07424i	−0.453641	+	0.155555i
$687$			17.7165i			0.675927i
$688$	−13.7887	−	3.51258i	−0.525690	−	0.133916i
$689$	−4.20215			−0.160089
$690$	−0.641450	+	0.219956i	−0.0244196	+	0.00837358i
$691$	46.3733			1.76412			0.882061	−	0.471136i	$-0.156156\pi$
$691$	46.3733			1.76412			0.882061	+	0.471136i	$0.156156\pi$
$692$	−33.6402	+	26.1449i	−1.27881	+	0.993881i
$693$			5.29136i			0.201002i
$694$	2.79570	+	8.15301i	0.106123	+	0.309484i
$695$	5.49102			0.208286
$696$	41.3330	+	27.0669i	1.56672	+	1.02597i
$697$	11.2193	−	7.06280i	0.424961	−	0.267523i
$698$	−46.1903	+	15.8388i	−1.74833	+	0.599509i
$699$			12.2836i			0.464608i
$700$	−0.803188	−	1.03345i	−0.0303576	−	0.0390606i
$701$			10.6927i			0.403858i	0.979400	+	0.201929i	$0.0647210\pi$
$701$			10.6927i			0.403858i	−0.979400	+	0.201929i	$0.935279\pi$
$702$	0.823687	−	0.282446i	0.0310881	−	0.0106602i
$703$		−	7.89752i		−	0.297861i
$704$	7.41360	+	16.9995i	0.279411	+	0.640691i
$705$	−8.73824			−0.329101
$706$	−15.3982	−	44.9051i	−0.579517	−	1.69003i
$707$	5.07628			0.190913
$708$	1.35304	+	1.74093i	0.0508503	+	0.0654280i
$709$	30.9514			1.16240			0.581202	−	0.813759i	$-0.302582\pi$
$709$	30.9514			1.16240			0.581202	+	0.813759i	$0.302582\pi$
$710$	−13.0135	+	4.46237i	−0.488386	+	0.167470i
$711$		−	14.2439i		−	0.534189i
$712$	−21.2578	−	13.9207i	−0.796669	−	0.521699i
$713$	0.747296			0.0279865
$714$	−7.56623	−	6.10117i	−0.283159	−	0.228330i
$715$		−	1.14885i		−	0.0429646i
$716$	14.0831	+	18.1204i	0.526310	+	0.677193i
$717$	5.16123			0.192750
$718$	4.13951	+	12.0719i	0.154485	+	0.450520i
$719$			4.18798i			0.156185i	0.996946	+	0.0780927i	$0.0248830\pi$
$719$			4.18798i			0.156185i	−0.996946	+	0.0780927i	$0.975117\pi$
$720$	3.44397	−	13.5194i	0.128349	−	0.503837i
$721$			3.76499i			0.140215i
$722$	5.66829	+	16.5302i	0.210952	+	0.615191i
$723$			14.3266i			0.532811i
$724$	−13.3318	+	10.3614i	−0.495474	+	0.385079i
$725$	−6.85794			−0.254697
$726$	−6.57336	−	19.1697i	−0.243960	−	0.711453i
$727$	26.6170			0.987169			0.493584	−	0.869698i	$-0.335686\pi$
$727$	26.6170			0.987169			0.493584	+	0.869698i	$0.335686\pi$
$728$	−0.767414	−	0.502541i	−0.0284423	−	0.0186254i
$729$	−34.9503			−1.29445
$730$	4.91416	−	1.68509i	0.181881	−	0.0623679i
$731$	12.4123	−	7.81382i	0.459086	−	0.289005i
$732$	14.2966	−	11.1112i	0.528417	−	0.410683i
$733$		−	24.4994i		−	0.904905i	−0.891788	−	0.452453i	$-0.850549\pi$
$733$		−	24.4994i		−	0.904905i	0.891788	−	0.452453i	$-0.149451\pi$
$734$	−47.1736	+	16.1760i	−1.74121	+	0.597069i
$735$	16.7389			0.617424
$736$	0.0860596	+	1.06143i	0.00317220	+	0.0391248i
$737$		−	20.0788i		−	0.739613i
$738$	15.0022	−	5.14432i	0.552239	−	0.189365i
$739$			8.64956i			0.318179i	0.987264	+	0.159090i	$0.0508559\pi$
$739$			8.64956i			0.318179i	−0.987264	+	0.159090i	$0.949144\pi$
$740$	4.83865	−	3.76057i	0.177872	−	0.138241i
$741$	3.25349			0.119520
$742$	2.54550	+	7.42335i	0.0934482	+	0.272520i
$743$			29.2437i			1.07285i	0.843949	+	0.536424i	$0.180225\pi$
$743$			29.2437i			1.07285i	−0.843949	+	0.536424i	$0.819775\pi$
$744$	−15.6674	+	23.9252i	−0.574397	+	0.877142i
$745$			3.99288i			0.146288i
$746$	−38.4787	+	13.1945i	−1.40880	+	0.483085i
$747$		−	53.4202i		−	1.95454i
$748$	−17.9688	−	6.52396i	−0.657004	−	0.238540i
$749$		−	7.41749i		−	0.271029i
$750$	1.16841	+	3.40740i	0.0426644	+	0.124421i
$751$		−	11.4840i		−	0.419057i	−0.977802	−	0.209529i	$-0.932807\pi$
$751$		−	11.4840i		−	0.419057i	0.977802	−	0.209529i	$-0.0671930\pi$
$752$	−3.38754	+	13.2979i	−0.123531	+	0.484924i
$753$		−	54.0930i		−	1.97126i
$754$	−4.54652	+	1.55902i	−0.165575	+	0.0567762i
$755$	−6.42385			−0.233788
$756$	−0.997915	−	1.28400i	−0.0362938	−	0.0466985i
$757$			1.40306i			0.0509950i	0.999675	+	0.0254975i	$0.00811699\pi$
$757$			1.40306i			0.0509950i	−0.999675	+	0.0254975i	$0.991883\pi$
$758$	1.28401	+	3.74450i	0.0466372	+	0.136007i
$759$			1.11158i			0.0403478i
$760$	3.99381	−	6.09882i	0.144871	−	0.221227i
$761$	29.1306			1.05598			0.527991	−	0.849250i	$-0.322945\pi$
$761$	29.1306			1.05598			0.527991	+	0.849250i	$0.322945\pi$
$762$	−19.5407	−	56.9858i	−0.707884	−	2.06438i
$763$		−	1.79254i		−	0.0648944i
$764$	−42.2685	+	32.8508i	−1.52922	+	1.18850i
$765$	7.66119	+	12.1698i	0.276991	+	0.440002i
$766$	2.14957	+	6.26870i	0.0776670	+	0.226497i
$767$	−0.214496			−0.00774500
$768$	−35.7868	−	19.4982i	−1.29134	−	0.703580i
$769$	16.7407			0.603685			0.301842	−	0.953358i	$-0.402398\pi$
$769$	16.7407			0.603685			0.301842	+	0.953358i	$0.402398\pi$
$770$	−2.02952	+	0.695930i	−0.0731387	+	0.0250796i
$771$	−9.08912			−0.327337
$772$	−24.0047	−	30.8864i	−0.863948	−	1.11162i
$773$		−	15.9297i		−	0.572951i	−0.958088	−	0.286475i	$-0.907516\pi$
$773$		−	15.9297i		−	0.572951i	0.958088	−	0.286475i	$-0.0924836\pi$
$774$	16.5975	−	5.69134i	0.596583	−	0.204571i
$775$		−	3.96966i		−	0.142594i
$776$	18.0622	−	27.5822i	0.648395	−	0.990142i
$777$		−	5.10755i		−	0.183232i
$778$	48.1119	−	16.4978i	1.72490	−	0.591475i
$779$	8.28746			0.296929
$780$	1.54922	+	1.99335i	0.0554708	+	0.0713732i
$781$			22.5513i			0.806948i
$782$	−0.854489	−	0.689033i	−0.0305565	−	0.0246398i
$783$	−8.52059			−0.304501
$784$	6.48916	−	25.4733i	0.231756	−	0.909762i
$785$			22.9114i			0.817744i
$786$	−1.46592	−	4.27500i	−0.0522875	−	0.152484i
$787$	−42.3403			−1.50927			−0.754634	−	0.656146i	$-0.772186\pi$
$787$	−42.3403			−1.50927			−0.754634	+	0.656146i	$0.772186\pi$
$788$	−12.7007	+	9.87094i	−0.452445	+	0.351638i
$789$	3.34166			0.118966
$790$	5.46330	−	1.87339i	0.194375	−	0.0666522i
$791$	−9.15436			−0.325492
$792$	−19.1319	−	12.5285i	−0.679822	−	0.445182i
$793$			1.76146i			0.0625511i
$794$	−10.0330	−	29.2590i	−0.356060	−	1.03836i
$795$		−	21.5978i		−	0.765994i
$796$	28.6041	+	36.8044i	1.01385	+	1.30450i
$797$			28.8219i			1.02092i	0.859900	+	0.510462i	$0.170526\pi$
$797$			28.8219i			1.02092i	−0.859900	+	0.510462i	$0.829474\pi$
$798$	−1.97084	−	5.74749i	−0.0697670	−	0.203459i
$799$	−7.53568	−	11.9705i	−0.266593	−	0.423485i
$800$	5.63835	−	0.457151i	0.199346	−	0.0161627i
$801$	31.3338			1.10712
$802$	5.05724	−	1.73415i	0.178577	−	0.0612349i
$803$		−	8.51585i		−	0.300518i
$804$	27.0761	+	34.8383i	0.954901	+	1.22865i
$805$	−0.123198			−0.00434216
$806$	−0.902427	−	2.63172i	−0.0317866	−	0.0926982i
$807$	57.5043			2.02425
$808$	−12.0193	+	18.3542i	−0.422836	+	0.645699i
$809$			17.6944i			0.622103i	0.950393	+	0.311052i	$0.100681\pi$
$809$			17.6944i			0.622103i	−0.950393	+	0.311052i	$0.899319\pi$
$810$	−3.34807	−	9.76385i	−0.117639	−	0.343067i
$811$	17.0795			0.599744			0.299872	−	0.953979i	$-0.403056\pi$
$811$	17.0795			0.599744			0.299872	+	0.953979i	$0.403056\pi$
$812$	5.50821	+	7.08731i	0.193300	+	0.248716i
$813$	18.4503			0.647080
$814$	−3.25838	−	9.50229i	−0.114206	−	0.333055i
$815$	−16.1246			−0.564819
$816$	39.9747	−	12.9112i	1.39940	−	0.451982i
$817$	9.16870			0.320772
$818$	10.8727	+	31.7077i	0.380155	+	1.10863i
$819$	1.13116			0.0395260
$820$	3.94624	+	5.07755i	0.137809	+	0.177316i
$821$	15.3541			0.535861			0.267930	−	0.963438i	$-0.413660\pi$
$821$	15.3541			0.535861			0.267930	+	0.963438i	$0.413660\pi$
$822$	18.5285	+	54.0340i	0.646256	+	1.88465i
$823$		−	33.9882i		−	1.18475i	−0.805661	−	0.592377i	$-0.798189\pi$
$823$		−	33.9882i		−	1.18475i	0.805661	−	0.592377i	$-0.201811\pi$
$824$	−13.6130	−	8.91448i	−0.474232	−	0.310551i
$825$	5.90475			0.205577
$826$	0.129933	+	0.378920i	0.00452096	+	0.0131843i
$827$	−35.0401			−1.21846			−0.609232	−	0.792992i	$-0.708522\pi$
$827$	−35.0401			−1.21846			−0.609232	+	0.792992i	$0.708522\pi$
$828$	−0.805828	−	1.03684i	−0.0280044	−	0.0360328i
$829$			24.1097i			0.837366i	0.908132	+	0.418683i	$0.137508\pi$
$829$			24.1097i			0.837366i	−0.908132	+	0.418683i	$0.862492\pi$
$830$	20.4895	−	7.02593i	0.711200	−	0.243874i
$831$	−39.3546			−1.36520
$832$	3.63406	−	1.58484i	0.125989	−	0.0549446i
$833$	14.4353	+	22.9305i	0.500153	+	0.794496i
$834$	6.41577	+	18.7101i	0.222160	+	0.647877i
$835$		−	13.2324i		−	0.457925i
$836$	−7.33326	−	9.43556i	−0.253626	−	0.326336i
$837$		−	4.93208i		−	0.170477i
$838$	−1.44448	−	4.21250i	−0.0498989	−	0.145518i
$839$		−	23.0802i		−	0.796818i	−0.917208	−	0.398409i	$-0.869562\pi$
$839$		−	23.0802i		−	0.796818i	0.917208	−	0.398409i	$-0.130438\pi$
$840$	2.58291	−	3.94427i	0.0891188	−	0.136090i
$841$	18.0313			0.621768
$842$	17.8426	−	6.11830i	0.614895	−	0.210850i
$843$	−49.7350			−1.71296
$844$	34.4659	−	26.7867i	1.18637	−	0.922036i
$845$	12.7544			0.438765
$846$	−5.48875	−	16.0067i	−0.188707	−	0.550320i
$847$		−	3.68176i		−	0.126507i
$848$	−32.8676	−	8.37279i	−1.12868	−	0.287523i
$849$	−54.8665			−1.88301
$850$	−3.66017	+	4.53907i	−0.125543	+	0.155689i
$851$		−	0.576819i		−	0.0197731i
$852$	−30.4102	−	39.1282i	−1.04184	−	1.34051i
$853$	17.7132			0.606490			0.303245	−	0.952913i	$-0.401930\pi$
$853$	17.7132			0.606490			0.303245	+	0.952913i	$0.401930\pi$
$854$	3.11172	−	1.06702i	0.106481	−	0.0365127i
$855$			8.98960i			0.307438i
$856$	26.8193	+	17.5626i	0.916666	+	0.600279i
$857$			21.2303i			0.725214i	0.931942	+	0.362607i	$0.118113\pi$
$857$			21.2303i			0.725214i	−0.931942	+	0.362607i	$0.881887\pi$
$858$	3.91460	−	1.34233i	0.133642	−	0.0458265i
$859$		−	55.6788i		−	1.89974i	−0.312652	−	0.949868i	$-0.601218\pi$
$859$		−	55.6788i		−	1.89974i	0.312652	−	0.949868i	$-0.398782\pi$
$860$	4.36586	+	5.61747i	0.148875	+	0.191554i
$861$	5.35973			0.182659
$862$	9.55124	−	3.27516i	0.325316	−	0.111552i
$863$	30.0014			1.02126			0.510630	−	0.859801i	$-0.329412\pi$
$863$	30.0014			1.02126			0.510630	+	0.859801i	$0.329412\pi$
$864$	7.00533	−	0.567984i	0.238326	−	0.0193232i
$865$	21.3027			0.724313
$866$	−5.53186	−	16.1324i	−0.187980	−	0.548200i
$867$	−18.7215	+	39.0445i	−0.635816	+	1.32602i
$868$	−4.10243	+	3.18838i	−0.139245	+	0.108221i
$869$		−	9.46745i		−	0.321161i
$870$	−8.01290	−	23.3677i	−0.271663	−	0.792240i
$871$	−4.29236			−0.145441
$872$	6.48127	+	4.24426i	0.219484	+	0.143729i
$873$			40.6559i			1.37599i
$874$	−0.222576	−	0.649091i	−0.00752875	−	0.0219558i
$875$			0.654431i			0.0221238i
$876$	11.4835	+	14.7756i	0.387993	+	0.499223i
$877$	24.9771			0.843417			0.421708	−	0.906732i	$-0.361431\pi$
$877$	24.9771			0.843417			0.421708	+	0.906732i	$0.361431\pi$
$878$	−22.7283	+	7.79363i	−0.767042	+	0.263022i
$879$			54.1856i			1.82764i
$880$	2.28909	−	8.98587i	0.0771651	−	0.302914i
$881$		−	51.0071i		−	1.71847i	−0.511580	−	0.859236i	$-0.670939\pi$
$881$		−	51.0071i		−	1.71847i	0.511580	−	0.859236i	$-0.329061\pi$
$882$	10.5142	+	30.6622i	0.354032	+	1.03245i
$883$		−	32.9436i		−	1.10864i	−0.832304	−	0.554320i	$-0.812978\pi$
$883$		−	32.9436i		−	1.10864i	0.832304	−	0.554320i	$-0.187022\pi$
$884$	−1.39466	+	3.84128i	−0.0469076	+	0.129196i
$885$		−	1.10244i		−	0.0370583i
$886$	8.14216	−	2.79198i	0.273541	−	0.0937985i
$887$		−	36.3257i		−	1.21970i	−0.792518	−	0.609848i	$-0.791230\pi$
$887$		−	36.3257i		−	1.21970i	0.792518	−	0.609848i	$-0.208770\pi$
$888$	18.4673	+	12.0933i	0.619722	+	0.405825i
$889$		−	10.9448i		−	0.367077i
$890$	4.12108	+	12.0182i	0.138139	+	0.402850i
$891$	−16.9200			−0.566840
$892$	23.5472	−	18.3008i	0.788420	−	0.612755i
$893$		−	8.84233i		−	0.295897i
$894$	−13.6053	+	4.66533i	−0.455031	+	0.156032i
$895$		−	11.4748i		−	0.383560i
$896$	−5.00110	−	5.45975i	−0.167075	−	0.182398i
$897$	0.237628			0.00793418
$898$	−21.0857	+	7.23039i	−0.703640	+	0.241281i
$899$			27.2237i			0.907960i
$900$	−5.50774	+	4.28058i	−0.183591	+	0.142686i
$901$	29.5867	−	18.6255i	0.985675	−	0.620505i
$902$	9.97146	−	3.41926i	0.332013	−	0.113849i
$903$	5.92965			0.197326
$904$	21.6751	−	33.0993i	0.720903	−	1.10087i
$905$	8.44241			0.280635
$906$	−7.50571	−	21.8886i	−0.249360	−	0.727201i
$907$	−5.38304			−0.178741			−0.0893704	−	0.995998i	$-0.528485\pi$
$907$	−5.38304			−0.178741			−0.0893704	+	0.995998i	$0.528485\pi$
$908$	10.0486	−	7.80975i	0.333476	−	0.259176i
$909$		−	27.0540i		−	0.897323i
$910$	0.148773	+	0.433860i	0.00493176	+	0.0143823i
$911$		−	22.7399i		−	0.753405i	−0.926334	−	0.376703i	$-0.877058\pi$
$911$		−	22.7399i		−	0.753405i	0.926334	−	0.376703i	$-0.122942\pi$
$912$	25.4475	+	6.48259i	0.842652	+	0.214660i
$913$		−	35.5066i		−	1.17510i
$914$	3.54174	+	10.3286i	0.117150	+	0.341641i
$915$	−9.05334			−0.299294
$916$	−8.53656	−	10.9838i	−0.282056	−	0.362916i
$917$		−	0.821063i		−	0.0271139i
$918$	−4.54755	+	5.63954i	−0.150091	+	0.186133i
$919$	−20.0866			−0.662595			−0.331298	−	0.943526i	$-0.607486\pi$
$919$	−20.0866			−0.662595			−0.331298	+	0.943526i	$0.607486\pi$
$920$	0.291700	−	0.445445i	0.00961706	−	0.0146859i
$921$			62.5811i			2.06212i
$922$	45.7621	−	15.6920i	1.50710	−	0.516790i
$923$	4.82090			0.158682
$924$	−4.74262	−	6.10224i	−0.156021	−	0.200749i
$925$	−3.06408			−0.100746
$926$	1.27504	+	3.71834i	0.0419003	+	0.122192i
$927$	20.0655			0.659036
$928$	−38.6675	+	3.13511i	−1.26932	+	0.102915i
$929$		−	32.7749i		−	1.07531i	−0.843165	−	0.537654i	$-0.819311\pi$
$929$		−	32.7749i		−	1.07531i	0.843165	−	0.537654i	$-0.180689\pi$
$930$	13.5262	−	4.63820i	0.443542	−	0.152093i
$931$			16.9383i			0.555130i
$932$	−5.91875	−	7.61554i	−0.193875	−	0.249455i
$933$			79.1504i			2.59127i
$934$	−33.7813	+	11.5838i	−1.10536	+	0.379032i
$935$	5.09213	+	8.08888i	0.166531	+	0.264535i
$936$	−2.67829	+	4.08993i	−0.0875426	+	0.133683i
$937$	−16.6829			−0.545008			−0.272504	−	0.962155i	$-0.587852\pi$
$937$	−16.6829			−0.545008			−0.272504	+	0.962155i	$0.587852\pi$
$938$	2.60014	+	7.58271i	0.0848977	+	0.247584i
$939$		−	40.2322i		−	1.31293i
$940$	5.41751	−	4.21045i	0.176700	−	0.137330i
$941$	−40.8872			−1.33288			−0.666442	−	0.745557i	$-0.732184\pi$
$941$	−40.8872			−1.33288			−0.666442	+	0.745557i	$0.732184\pi$
$942$	−78.0684	+	26.7700i	−2.54361	+	0.872214i
$943$	0.605299			0.0197112
$944$	−1.67770	−	0.427384i	−0.0546046	−	0.0139101i
$945$			0.813094i			0.0264499i
$946$	11.0318	−	3.78284i	0.358674	−	0.122991i
$947$	−38.9364			−1.26526			−0.632632	−	0.774452i	$-0.718025\pi$
$947$	−38.9364			−1.26526			−0.632632	+	0.774452i	$0.718025\pi$
$948$	12.7668	+	16.4268i	0.414645	+	0.533516i
$949$	−1.82048			−0.0590952
$950$	−3.44799	+	1.18233i	−0.111868	+	0.0383599i
$951$	−8.67731			−0.281381
$952$	7.63069	+	0.136853i	0.247312	+	0.00443544i
$953$	−9.09398			−0.294583			−0.147292	−	0.989093i	$-0.547056\pi$
$953$	−9.09398			−0.294583			−0.147292	+	0.989093i	$0.547056\pi$
$954$	39.5627	−	13.5662i	1.28089	−	0.439222i
$955$	26.7666			0.866147
$956$	−3.19985	+	2.48690i	−0.103490	+	0.0804321i
$957$	−40.4944			−1.30900
$958$	−22.6176	+	7.75569i	−0.730743	+	0.250575i
$959$			10.3779i			0.335119i
$960$	8.14562	+	18.6780i	0.262899	+	0.602829i
$961$	15.2418			0.491671
$962$	−2.03136	+	0.696561i	−0.0654935	+	0.0224580i
$963$	−39.5314			−1.27388
$964$	−6.90315	−	8.88215i	−0.222336	−	0.286075i
$965$			19.5588i			0.629622i
$966$	−0.143946	−	0.419785i	−0.00463139	−	0.0135064i
$967$	−12.8681			−0.413809			−0.206905	−	0.978361i	$-0.566339\pi$
$967$	−12.8681			−0.413809			−0.206905	+	0.978361i	$0.566339\pi$
$968$	13.3121	+	8.71742i	0.427867	+	0.280189i
$969$	−22.9073	+	14.4207i	−0.735889	+	0.463259i
$970$	−15.5937	+	5.34714i	−0.500683	+	0.171686i
$971$			24.8605i			0.797812i	0.916992	+	0.398906i	$0.130610\pi$
$971$			24.8605i			0.797812i	−0.916992	+	0.398906i	$0.869390\pi$
$972$	35.2435	−	27.3910i	1.13043	−	0.878567i
$973$			3.59349i			0.115202i
$974$	38.9645	−	13.3611i	1.24850	−	0.428117i
$975$		−	1.26229i		−	0.0404256i
$976$	−3.50970	+	13.7774i	−0.112343	+	0.441004i
$977$	−4.01155			−0.128341			−0.0641704	−	0.997939i	$-0.520440\pi$
$977$	−4.01155			−0.128341			−0.0641704	+	0.997939i	$0.520440\pi$
$978$	−18.8401	−	54.9429i	−0.602442	−	1.75688i
$979$	20.8265			0.665618
$980$	−10.3777	+	8.06552i	−0.331505	+	0.257643i
$981$	−9.55334			−0.305015
$982$	31.7394	−	10.8836i	1.01284	−	0.347309i
$983$			47.3479i			1.51016i	0.655631	+	0.755081i	$0.272403\pi$
$983$			47.3479i			1.51016i	−0.655631	+	0.755081i	$0.727597\pi$
$984$	−12.6904	+	19.3791i	−0.404556	+	0.617783i
$985$	8.04276			0.256264
$986$	25.1012	−	31.1287i	0.799384	−	0.991339i
$987$		−	5.71858i		−	0.182024i
$988$	−2.01709	+	1.56767i	−0.0641722	+	0.0498742i
$989$	0.669663			0.0212940
$990$	3.70895	+	10.8163i	0.117878	+	0.343764i
$991$			4.27944i			0.135941i	0.997687	+	0.0679704i	$0.0216524\pi$
$991$			4.27944i			0.135941i	−0.997687	+	0.0679704i	$0.978348\pi$
$992$	−1.81473	−	22.3823i	−0.0576179	−	0.710640i
$993$			43.9453i			1.39456i
$994$	−2.92032	−	8.51641i	−0.0926268	−	0.270124i
$995$		−	23.3064i		−	0.738864i
$996$	47.8803	+	61.6066i	1.51715	+	1.95208i
$997$	−49.6717			−1.57312			−0.786559	−	0.617515i	$-0.788139\pi$
$997$	−49.6717			−1.57312			−0.786559	+	0.617515i	$0.788139\pi$
$998$	−1.62002	−	4.72442i	−0.0512809	−	0.149549i
$999$	−3.80695			−0.120446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.l.a.101.22	yes	36
4.3	odd	2		2720.2.l.b.2481.6		36
8.3	odd	2		2720.2.l.a.2481.32		36
8.5	even	2		680.2.l.b.101.21	yes	36
17.16	even	2		680.2.l.b.101.22	yes	36
68.67	odd	2		2720.2.l.a.2481.31		36
136.67	odd	2		2720.2.l.b.2481.5		36
136.101	even	2	inner	680.2.l.a.101.21	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.l.a.101.21	✓	36	136.101	even	2	inner
680.2.l.a.101.22	yes	36	1.1	even	1	trivial
680.2.l.b.101.21	yes	36	8.5	even	2
680.2.l.b.101.22	yes	36	17.16	even	2
2720.2.l.a.2481.31		36	68.67	odd	2
2720.2.l.a.2481.32		36	8.3	odd	2
2720.2.l.b.2481.5		36	136.67	odd	2
2720.2.l.b.2481.6		36	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.458720 + 1.33775i) q^{2} +2.54711 q^{3} +(-1.57915 + 1.22731i) q^{4} +1.00000 q^{5} +(1.16841 + 3.40740i) q^{6} +0.654431i q^{7} +(-2.36622 - 1.54952i) q^{8} +3.48778 q^{9} +(0.458720 + 1.33775i) q^{10} +2.31821 q^{11} +(-4.02228 + 3.12609i) q^{12} -0.495577i q^{13} +(-0.875466 + 0.300201i) q^{14} +2.54711 q^{15} +(0.987437 - 3.87621i) q^{16} +(2.19658 + 3.48928i) q^{17} +(1.59992 + 4.66578i) q^{18} +2.57745i q^{19} +(-1.57915 + 1.22731i) q^{20} +1.66691i q^{21} +(1.06341 + 3.10119i) q^{22} +0.188252i q^{23} +(-6.02703 - 3.94680i) q^{24} +1.00000 q^{25} +(0.662958 - 0.227331i) q^{26} +1.24244 q^{27} +(-0.803188 - 1.03345i) q^{28} -6.85794 q^{29} +(1.16841 + 3.40740i) q^{30} -3.96966i q^{31} +(5.63835 - 0.457151i) q^{32} +5.90475 q^{33} +(-3.66017 + 4.53907i) q^{34} +0.654431i q^{35} +(-5.50774 + 4.28058i) q^{36} -3.06408 q^{37} +(-3.44799 + 1.18233i) q^{38} -1.26229i q^{39} +(-2.36622 - 1.54952i) q^{40} -3.21537i q^{41} +(-2.22991 + 0.764646i) q^{42} -3.55727i q^{43} +(-3.66081 + 2.84516i) q^{44} +3.48778 q^{45} +(-0.251834 + 0.0863550i) q^{46} -3.43065 q^{47} +(2.51511 - 9.87313i) q^{48} +6.57172 q^{49} +(0.458720 + 1.33775i) q^{50} +(5.59493 + 8.88758i) q^{51} +(0.608224 + 0.782590i) q^{52} -8.47932i q^{53} +(0.569934 + 1.66208i) q^{54} +2.31821 q^{55} +(1.01405 - 1.54853i) q^{56} +6.56507i q^{57} +(-3.14588 - 9.17420i) q^{58} -0.432821i q^{59} +(-4.02228 + 3.12609i) q^{60} -3.55435 q^{61} +(5.31041 - 1.82096i) q^{62} +2.28252i q^{63} +(3.19798 + 7.33300i) q^{64} -0.495577i q^{65} +(2.70863 + 7.89908i) q^{66} -8.66134i q^{67} +(-7.75114 - 2.81422i) q^{68} +0.479499i q^{69} +(-0.875466 + 0.300201i) q^{70} +9.72787i q^{71} +(-8.25286 - 5.40439i) q^{72} -3.67345i q^{73} +(-1.40556 - 4.09897i) q^{74} +2.54711 q^{75} +(-3.16333 - 4.07019i) q^{76} +1.51711i q^{77} +(1.68863 - 0.579038i) q^{78} -4.08394i q^{79} +(0.987437 - 3.87621i) q^{80} -7.29871 q^{81} +(4.30136 - 1.47495i) q^{82} -15.3164i q^{83} +(-2.04581 - 2.63230i) q^{84} +(2.19658 + 3.48928i) q^{85} +(4.75874 - 1.63179i) q^{86} -17.4679 q^{87} +(-5.48540 - 3.59211i) q^{88} +8.98386 q^{89} +(1.59992 + 4.66578i) q^{90} +0.324321 q^{91} +(-0.231043 - 0.297278i) q^{92} -10.1112i q^{93} +(-1.57371 - 4.58935i) q^{94} +2.57745i q^{95} +(14.3615 - 1.16442i) q^{96} +11.6566i q^{97} +(3.01458 + 8.79132i) q^{98} +8.08543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3} + 2 q^{4} + 36 q^{5} + 36 q^{9} - 8 q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} + 2 q^{20} + 26 q^{24} + 36 q^{25} + 6 q^{26} - 16 q^{27} + 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) \) 36 * q - 4 * q^3 + 2 * q^4 + 36 * q^5 + 36 * q^9 - 8 * q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 + 2 * q^20 + 26 * q^24 + 36 * q^25 + 6 * q^26 - 16 * q^27 + 14 * q^28 - 10 * q^32 - 8 * q^33 - 24 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 + 6 * q^44 + 36 * q^45 + 24 * q^46 + 20 * q^47 - 4 * q^48 - 36 * q^49 + 6 * q^52 - 56 * q^54 - 8 * q^55 + 20 * q^56 - 18 * q^58 - 2 * q^60 - 24 * q^62 + 14 * q^64 - 16 * q^66 - 40 * q^68 + 2 * q^70 - 54 * q^72 + 6 * q^74 - 4 * q^75 + 2 * q^76 - 14 * q^78 + 6 * q^80 + 44 * q^81 + 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 - 58 * q^88 - 10 * q^90 - 56 * q^91 - 12 * q^92 + 14 * q^94 - 24 * q^96 + 10 * q^98 - 40 * q^99

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