LMFDB - Embedded newform 680.2.l.b.101.21

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			101.21
Character	$\chi$	$=$	680.101
Dual form			680.2.l.b.101.22

$q$-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} +(5.67539 - 1.33787i) 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} +(0.813685 - 8.20597i) 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 + 12 * 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 + 16 * 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	$-0.762953\pi$
$3$	−2.54711			−1.47058			−0.735288	+	0.677755i	$0.762953\pi$
$4$	−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	$-0.613643\pi$
$11$	−2.31821			−0.698967			−0.349484	+	0.936942i	$0.613643\pi$
$12$	4.02228	+	3.12609i	1.16113	+	0.902424i
$13$			0.495577i			0.137448i	0.997636	+	0.0687241i	$0.0218928\pi$
$13$			0.495577i			0.137448i	−0.997636	+	0.0687241i	$0.978107\pi$
$14$	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	$-0.904462\pi$
$19$		−	2.57745i		−	0.591308i	0.955295	−	0.295654i	$-0.0955376\pi$
$20$	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	$-0.280281\pi$
$29$	6.85794			1.27349			0.636743	+	0.771076i	$0.280281\pi$
$30$	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
$34$	5.67539	−	1.33787i	0.973322	−	0.229443i
$35$		−	0.654431i		−	0.110619i
$36$	−5.50774	−	4.28058i	−0.917957	−	0.713430i
$37$	3.06408			0.503732			0.251866	−	0.967762i	$-0.418956\pi$
$37$	3.06408			0.503732			0.251866	+	0.967762i	$0.418956\pi$
$38$	−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	$0.0874335\pi$
$43$			3.55727i			0.542479i	−0.962512	+	0.271239i	$0.912566\pi$
$44$	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	$0.197871\pi$
$53$			8.47932i			1.16472i	−0.812930	+	0.582362i	$0.802129\pi$
$54$	−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	$0.00896933\pi$
$59$			0.432821i			0.0563485i	−0.999603	+	0.0281743i	$0.991031\pi$
$60$	−4.02228	−	3.12609i	−0.519274	−	0.403576i
$61$	3.55435			0.455089			0.227544	−	0.973768i	$-0.426930\pi$
$61$	3.55435			0.455089			0.227544	+	0.973768i	$0.426930\pi$
$62$	−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	$0.177461\pi$
$67$			8.66134i			1.05815i	−0.848575	+	0.529076i	$0.822539\pi$
$68$	0.813685	−	8.20597i	0.0986738	−	0.995120i
$69$		−	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	$0.317794\pi$
$83$			15.3164i			1.68119i	−0.541665	+	0.840595i	$0.682206\pi$
$84$	−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	$0.126114\pi$
$101$			7.75678i			0.771828i	−0.922535	+	0.385914i	$0.873886\pi$
$102$	−14.4559	+	3.40770i	−1.43134	+	0.337413i
$103$	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	$-0.315442\pi$
$107$	11.3343			1.09572			0.547862	+	0.836569i	$0.315442\pi$
$108$	1.96201	+	1.52486i	0.188794	+	0.146730i
$109$	2.73908			0.262357			0.131178	−	0.991359i	$-0.458124\pi$
$109$	2.73908			0.262357			0.131178	+	0.991359i	$0.458124\pi$
$110$	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	$-0.482545\pi$
$131$	1.25462			0.109617			0.0548084	+	0.998497i	$0.482545\pi$
$132$	−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
$136$	−10.6043	−	4.85275i	−0.909310	−	0.416120i
$137$	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	$-0.574812\pi$
$139$	−5.49102			−0.465742			−0.232871	+	0.972508i	$0.574812\pi$
$140$	−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	$-0.947704\pi$
$149$		−	3.99288i		−	0.327109i	0.986534	−	0.163555i	$-0.0522960\pi$
$150$	−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	$-0.632769\pi$
$157$		−	22.9114i		−	1.82853i	0.405116	−	0.914265i	$-0.367231\pi$
$158$	−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	$-0.282445\pi$
$163$	16.1246			1.26297			0.631487	+	0.775387i	$0.282445\pi$
$164$	−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
$170$	−5.67539	+	1.33787i	−0.435283	+	0.102610i
$171$		−	8.98960i		−	0.687452i
$172$	4.36586	−	5.61747i	0.332894	−	0.428328i
$173$	−21.3027			−1.61961			−0.809806	−	0.586697i	$-0.800428\pi$
$173$	−21.3027			−1.61961			−0.809806	+	0.586697i	$0.800428\pi$
$174$	−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	$0.141075\pi$
$179$			11.4748i			0.857667i	−0.903384	+	0.428833i	$0.858925\pi$
$180$	5.50774	+	4.28058i	0.410523	+	0.319056i
$181$	−8.44241			−0.627519			−0.313760	−	0.949502i	$-0.601589\pi$
$181$	−8.44241			−0.627519			−0.313760	+	0.949502i	$0.601589\pi$
$182$	−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	$-0.592496\pi$
$197$	−8.04276			−0.573023			−0.286512	+	0.958077i	$0.592496\pi$
$198$	−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
$204$	−2.07255	+	20.9015i	−0.145107	+	1.46340i
$205$			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	$-0.229443\pi$
$211$	21.8256			1.50254			0.751268	+	0.659998i	$0.229443\pi$
$212$	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	$-0.432271\pi$
$227$	6.36332			0.422348			0.211174	+	0.977448i	$0.432271\pi$
$228$	8.05735	−	10.3672i	0.533611	−	0.686587i
$229$		−	6.95553i		−	0.459634i	−0.973234	−	0.229817i	$-0.926187\pi$
$229$		−	6.95553i		−	0.459634i	0.973234	−	0.229817i	$-0.0738128\pi$
$230$	−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
$238$	0.875543	+	3.71416i	0.0567531	+	0.240753i
$239$	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	$0.233806\pi$
$251$			21.2370i			1.34047i	−0.742151	+	0.670233i	$0.766194\pi$
$252$	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	$-0.741620\pi$
$269$	−22.5763			−1.37650			−0.688249	+	0.725474i	$0.741620\pi$
$270$	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	$0.429391\pi$
$272$	−11.3562	+	11.9598i	−0.688569	+	0.725171i
$273$	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	$-0.346352\pi$
$277$	15.4507			0.928342			0.464171	+	0.885746i	$0.346352\pi$
$278$	−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	$-0.278839\pi$
$283$	21.5407			1.28046			0.640230	+	0.768183i	$0.278839\pi$
$284$	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	$-0.786564\pi$
$293$		−	21.2734i		−	1.24280i	0.783492	−	0.621401i	$-0.213436\pi$
$294$	−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
$306$	19.7946	−	4.66620i	1.13158	−	0.266749i
$307$		−	24.5694i		−	1.40225i	−0.713037	−	0.701126i	$-0.752681\pi$
$307$		−	24.5694i		−	1.40225i	0.713037	−	0.701126i	$-0.247319\pi$
$308$	−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	$-0.469501\pi$
$317$	3.40672			0.191341			0.0956704	+	0.995413i	$0.469501\pi$
$318$	−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	$-0.842754\pi$
$331$		−	17.2530i		−	0.948310i	0.880441	−	0.474155i	$-0.157246\pi$
$332$	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
$340$	−0.813685	+	8.20597i	−0.0441283	+	0.445031i
$341$			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	$-0.552306\pi$
$347$	−6.09457			−0.327174			−0.163587	+	0.986529i	$0.552306\pi$
$348$	27.5845	+	21.4385i	1.47869	+	1.14923i
$349$		−	34.5283i		−	1.84826i	−0.382080	−	0.924129i	$-0.624792\pi$
$349$		−	34.5283i		−	1.84826i	0.382080	−	0.924129i	$-0.375208\pi$
$350$	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	$-0.732610\pi$
$373$		−	28.7637i		−	1.48933i	0.667439	−	0.744664i	$-0.267390\pi$
$374$	−13.1568	+	3.10147i	−0.680320	+	0.160373i
$375$	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	$-0.522903\pi$
$379$	−2.79911			−0.143780			−0.0718902	+	0.997413i	$0.522903\pi$
$380$	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	$0.365264\pi$
$389$			35.9648i			1.82349i	−0.410758	+	0.911744i	$0.634736\pi$
$390$	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	$-0.315063\pi$
$397$	21.8718			1.09772			0.548858	+	0.835916i	$0.315063\pi$
$398$	−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
$408$	27.0103	+	12.3605i	1.33721	+	0.611936i
$409$	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	$-0.475492\pi$
$419$	3.14894			0.153836			0.0769180	+	0.997037i	$0.475492\pi$
$420$	2.04581	−	2.63230i	0.0998253	−	0.128443i
$421$			13.3377i			0.650042i	0.945707	+	0.325021i	$0.105371\pi$
$421$			13.3377i			0.650042i	−0.945707	+	0.325021i	$0.894629\pi$
$422$	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
$442$	0.663017	+	2.81259i	0.0315365	+	0.133781i
$443$			6.08646i			0.289176i	0.989492	+	0.144588i	$0.0461857\pi$
$443$			6.08646i			0.289176i	−0.989492	+	0.144588i	$0.953814\pi$
$444$	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	$0.293380\pi$
$461$			34.2083i			1.59324i	−0.604481	+	0.796619i	$0.706620\pi$
$462$	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	$-0.801381\pi$
$467$		−	25.2523i		−	1.16854i	0.811560	−	0.584269i	$-0.198619\pi$
$468$	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
$476$	5.37024	+	0.532501i	0.246145	+	0.0244071i
$477$			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	$0.179827\pi$
$491$			23.7259i			1.07074i	−0.844619	+	0.535368i	$0.820173\pi$
$492$	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	$-0.474812\pi$
$499$	3.53161			0.158097			0.0790483	+	0.996871i	$0.474812\pi$
$500$	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	$-0.925887\pi$
$509$		−	10.4113i		−	0.461472i	0.973016	−	0.230736i	$-0.0741134\pi$
$510$	14.4559	−	3.40770i	0.640117	−	0.150896i
$511$	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	$0.239924\pi$
$523$			31.3021i			1.36875i	−0.729132	+	0.684373i	$0.760076\pi$
$524$	−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	$-0.414222\pi$
$541$	12.3847			0.532461			0.266231	+	0.963909i	$0.414222\pi$
$542$	3.32279	−	9.69014i	0.142726	−	0.416227i
$543$	21.5038			0.922815
$544$	10.7899	+	20.6779i	0.462615	+	0.886559i
$545$	−2.73908			−0.117329
$546$	0.378941	−	1.10509i	0.0162172	−	0.0472935i
$547$	7.06558			0.302102			0.151051	−	0.988526i	$-0.451734\pi$
$547$	7.06558			0.302102			0.151051	+	0.988526i	$0.451734\pi$
$548$	−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	$-0.951615\pi$
$557$		−	7.14741i		−	0.302845i	0.988469	−	0.151423i	$-0.0483855\pi$
$558$	−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	$-0.671484\pi$
$563$		−	40.7336i		−	1.71672i	0.513049	−	0.858359i	$-0.328516\pi$
$564$	−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	$-0.587596\pi$
$571$	−12.9863			−0.543460			−0.271730	+	0.962374i	$0.587596\pi$
$572$	−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	$0.825692\pi$
$578$	17.1346	+	16.8643i	0.712707	+	0.701462i
$579$		−	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	$0.255347\pi$
$587$			34.8343i			1.43777i	−0.695131	+	0.718884i	$0.744653\pi$
$588$	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
$612$	2.83796	−	28.6207i	0.114718	−	1.15692i
$613$		−	17.7388i		−	0.716462i	−0.933633	−	0.358231i	$-0.883380\pi$
$613$		−	17.7388i		−	0.716462i	0.933633	−	0.358231i	$-0.116620\pi$
$614$	−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	$-0.682902\pi$
$619$	−27.0444			−1.08700			−0.543502	+	0.839408i	$0.682902\pi$
$620$	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	$-0.336499\pi$
$643$	24.9194			0.982725			0.491363	+	0.870955i	$0.336499\pi$
$644$	0.194548	+	0.151202i	0.00766627	+	0.00595818i
$645$			9.06077i			0.356768i
$646$	−3.44830	−	14.6281i	−0.135671	−	0.575534i
$647$	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	$-0.865939\pi$
$653$	−46.6416			−1.82523			−0.912613	+	0.408825i	$0.865939\pi$
$654$	−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	$0.192651\pi$
$659$			29.2111i			1.13790i	−0.822371	+	0.568952i	$0.807349\pi$
$660$	9.32449	+	7.24694i	0.362955	+	0.282087i
$661$			6.88515i			0.267801i	0.990995	+	0.133901i	$0.0427503\pi$
$661$			6.88515i			0.267801i	−0.990995	+	0.133901i	$0.957250\pi$
$662$	−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	$-0.769004\pi$
$677$	−38.9268			−1.49608			−0.748039	+	0.663655i	$0.769004\pi$
$678$	−47.6637	−	16.3441i	−1.83051	−	0.627691i
$679$	−7.62847			−0.292754
$680$	10.6043	+	4.85275i	0.406656	+	0.186095i
$681$	−16.2081			−0.621096
$682$	12.3107	+	4.22138i	0.471400	+	0.161645i
$683$	−8.48371			−0.324620			−0.162310	−	0.986740i	$-0.551894\pi$
$683$	−8.48371			−0.324620			−0.162310	+	0.986740i	$0.551894\pi$
$684$	−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	$-0.843844\pi$
$691$	−46.3733			−1.76412			−0.882061	+	0.471136i	$0.843844\pi$
$692$	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	$-0.935279\pi$
$701$		−	10.6927i		−	0.403858i	0.979400	−	0.201929i	$-0.0647210\pi$
$702$	−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	$-0.697418\pi$
$709$	−30.9514			−1.16240			−0.581202	+	0.813759i	$0.697418\pi$
$710$	−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
$714$	−2.23011	−	9.46037i	−0.0834597	−	0.354046i
$715$			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	$0.149451\pi$
$733$			24.4994i			0.904905i	−0.891788	+	0.452453i	$0.850549\pi$
$734$	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	$-0.949144\pi$
$739$		−	8.64956i		−	0.318179i	0.987264	−	0.159090i	$-0.0508559\pi$
$740$	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
$748$	−1.88629	+	19.0232i	−0.0689697	+	0.695556i
$749$			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	$-0.991883\pi$
$757$		−	1.40306i		−	0.0509950i	0.999675	−	0.0254975i	$-0.00811699\pi$
$758$	−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	$0.0924836\pi$
$773$			15.9297i			0.572951i	−0.958088	+	0.286475i	$0.907516\pi$
$774$	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
$782$	0.251856	+	1.06840i	0.00900637	+	0.0382060i
$783$	−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	$-0.227814\pi$
$787$	42.3403			1.50927			0.754634	+	0.656146i	$0.227814\pi$
$788$	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	$-0.829474\pi$
$797$		−	28.8219i		−	1.02092i	0.859900	−	0.510462i	$-0.170526\pi$
$798$	−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	$-0.596944\pi$
$811$	−17.0795			−0.599744			−0.299872	+	0.953979i	$0.596944\pi$
$812$	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
$816$	28.9255	−	30.4630i	1.01259	−	1.06642i
$817$	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	$-0.586340\pi$
$821$	−15.3541			−0.535861			−0.267930	+	0.963438i	$0.586340\pi$
$822$	−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	$-0.291478\pi$
$827$	35.0401			1.21846			0.609232	+	0.792992i	$0.291478\pi$
$828$	0.805828	−	1.03684i	0.0280044	−	0.0360328i
$829$		−	24.1097i		−	0.837366i	−0.908132	−	0.418683i	$-0.862492\pi$
$829$		−	24.1097i		−	0.837366i	0.908132	−	0.418683i	$-0.137508\pi$
$830$	−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
$850$	5.67539	−	1.33787i	0.194664	−	0.0458885i
$851$			0.576819i			0.0197731i
$852$	−30.4102	+	39.1282i	−1.04184	+	1.34051i
$853$	−17.7132			−0.606490			−0.303245	−	0.952913i	$-0.598070\pi$
$853$	−17.7132			−0.606490			−0.303245	+	0.952913i	$0.598070\pi$
$854$	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	$0.398782\pi$
$859$			55.6788i			1.89974i	−0.312652	+	0.949868i	$0.601218\pi$
$860$	−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	$-0.638569\pi$
$877$	−24.9771			−0.843417			−0.421708	+	0.906732i	$0.638569\pi$
$878$	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	$0.187022\pi$
$883$			32.9436i			1.10864i	−0.832304	+	0.554320i	$0.812978\pi$
$884$	4.06669	+	0.403243i	0.136777	+	0.0135625i
$885$			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	$-0.471515\pi$
$907$	5.38304			0.178741			0.0893704	+	0.995998i	$0.471515\pi$
$908$	−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
$918$	−7.05136	+	1.66223i	−0.232729	+	0.0548616i
$919$	−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	$-0.267816\pi$
$941$	40.8872			1.33288			0.666442	+	0.745557i	$0.267816\pi$
$942$	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	$-0.281975\pi$
$947$	38.9364			1.26526			0.632632	+	0.774452i	$0.281975\pi$
$948$	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
$952$	3.17579	−	6.93977i	0.102928	−	0.224919i
$953$	−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	$-0.869390\pi$
$971$		−	24.8605i		−	0.797812i	0.916992	−	0.398906i	$-0.130610\pi$
$972$	−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
$986$	38.9215	−	9.17502i	1.23951	−	0.292192i
$987$			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	$-0.211861\pi$
$997$	49.6717			1.57312			0.786559	+	0.617515i	$0.211861\pi$
$998$	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.b.101.21	yes	36
4.3	odd	2		2720.2.l.a.2481.32		36
8.3	odd	2		2720.2.l.b.2481.6		36
8.5	even	2		680.2.l.a.101.22	yes	36
17.16	even	2		680.2.l.a.101.21	✓	36
68.67	odd	2		2720.2.l.b.2481.5		36
136.67	odd	2		2720.2.l.a.2481.31		36
136.101	even	2	inner	680.2.l.b.101.22	yes	36

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
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} +(5.67539 - 1.33787i) 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} +(0.813685 - 8.20597i) 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 + 12 * 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 + 16 * 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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