LMFDB - Embedded newform 680.2.l.a.101.8

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)

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);

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")

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			101.8
Character	$\chi$	$=$	680.101
Dual form			680.2.l.a.101.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26408 + 0.634112i) q^{2} -1.91553 q^{3} +(1.19580 - 1.60314i) q^{4} +1.00000 q^{5} +(2.42138 - 1.21466i) q^{6} +3.32813i q^{7} +(-0.495023 + 2.78477i) q^{8} +0.669252 q^{9} +(-1.26408 + 0.634112i) q^{10} +5.61990 q^{11} +(-2.29060 + 3.07086i) q^{12} -3.09895i q^{13} +(-2.11041 - 4.20702i) q^{14} -1.91553 q^{15} +(-1.14011 - 3.83408i) q^{16} +(-3.99001 + 1.03913i) q^{17} +(-0.845988 + 0.424380i) q^{18} +0.142902i q^{19} +(1.19580 - 1.60314i) q^{20} -6.37512i q^{21} +(-7.10401 + 3.56365i) q^{22} -1.97327i q^{23} +(0.948232 - 5.33431i) q^{24} +1.00000 q^{25} +(1.96508 + 3.91733i) q^{26} +4.46462 q^{27} +(5.33545 + 3.97979i) q^{28} +1.39629 q^{29} +(2.42138 - 1.21466i) q^{30} +5.08219i q^{31} +(3.87242 + 4.12363i) q^{32} -10.7651 q^{33} +(4.38478 - 3.84366i) q^{34} +3.32813i q^{35} +(0.800293 - 1.07290i) q^{36} +1.12245 q^{37} +(-0.0906161 - 0.180640i) q^{38} +5.93613i q^{39} +(-0.495023 + 2.78477i) q^{40} +4.91265i q^{41} +(4.04254 + 8.05867i) q^{42} +10.2306i q^{43} +(6.72030 - 9.00948i) q^{44} +0.669252 q^{45} +(1.25128 + 2.49438i) q^{46} +5.17052 q^{47} +(2.18391 + 7.34429i) q^{48} -4.07643 q^{49} +(-1.26408 + 0.634112i) q^{50} +(7.64299 - 1.99048i) q^{51} +(-4.96805 - 3.70574i) q^{52} +0.833534i q^{53} +(-5.64364 + 2.83107i) q^{54} +5.61990 q^{55} +(-9.26807 - 1.64750i) q^{56} -0.273734i q^{57} +(-1.76502 + 0.885402i) q^{58} -1.78441i q^{59} +(-2.29060 + 3.07086i) q^{60} -10.0513 q^{61} +(-3.22268 - 6.42430i) q^{62} +2.22735i q^{63} +(-7.50990 - 2.75705i) q^{64} -3.09895i q^{65} +(13.6079 - 6.82627i) q^{66} +13.2391i q^{67} +(-3.10541 + 7.63914i) q^{68} +3.77986i q^{69} +(-2.11041 - 4.20702i) q^{70} +13.0517i q^{71} +(-0.331295 + 1.86371i) q^{72} +8.46816i q^{73} +(-1.41887 + 0.711760i) q^{74} -1.91553 q^{75} +(0.229092 + 0.170883i) q^{76} +18.7037i q^{77} +(-3.76417 - 7.50375i) q^{78} +13.5702i q^{79} +(-1.14011 - 3.83408i) q^{80} -10.5599 q^{81} +(-3.11517 - 6.20999i) q^{82} -17.4618i q^{83} +(-10.2202 - 7.62340i) q^{84} +(-3.99001 + 1.03913i) q^{85} +(-6.48736 - 12.9323i) q^{86} -2.67463 q^{87} +(-2.78198 + 15.6501i) q^{88} +12.8756 q^{89} +(-0.845988 + 0.424380i) q^{90} +10.3137 q^{91} +(-3.16343 - 2.35965i) q^{92} -9.73508i q^{93} +(-6.53596 + 3.27869i) q^{94} +0.142902i q^{95} +(-7.41774 - 7.89894i) q^{96} +4.67407i q^{97} +(5.15293 - 2.58491i) q^{98} +3.76113 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 $

$2$	−1.26408	+	0.634112i	−0.893841	+	0.448385i
$2$	−1.26408	+	0.634112i	−0.893841	+	0.448385i
$3$	−1.91553			−1.10593			−0.552966	−	0.833204i	$-0.686504\pi$
$3$	−1.91553			−1.10593			−0.552966	+	0.833204i	$0.686504\pi$
$4$	1.19580	−	1.60314i	0.597902	−	0.801569i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	2.42138	−	1.21466i	0.988526	−	0.495883i
$7$			3.32813i			1.25791i	0.777440	+	0.628957i	$0.216518\pi$
$7$			3.32813i			1.25791i	−0.777440	+	0.628957i	$0.783482\pi$
$8$	−0.495023	+	2.78477i	−0.175017	+	0.984565i
$9$	0.669252			0.223084
$10$	−1.26408	+	0.634112i	−0.399738	+	0.200524i
$11$	5.61990			1.69446			0.847232	−	0.531223i	$-0.178268\pi$
$11$	5.61990			1.69446			0.847232	+	0.531223i	$0.178268\pi$
$12$	−2.29060	+	3.07086i	−0.661238	+	0.886481i
$13$		−	3.09895i		−	0.859495i	−0.902949	−	0.429747i	$-0.858603\pi$
$13$		−	3.09895i		−	0.859495i	0.902949	−	0.429747i	$-0.141397\pi$
$14$	−2.11041	−	4.20702i	−0.564030	−	1.12437i
$15$	−1.91553			−0.494587
$16$	−1.14011	−	3.83408i	−0.285027	−	0.958520i
$17$	−3.99001	+	1.03913i	−0.967721	+	0.252025i
$17$	−3.99001	+	1.03913i	−0.967721	+	0.252025i
$18$	−0.845988	+	0.424380i	−0.199401	+	0.100027i
$19$			0.142902i			0.0327841i	0.999866	+	0.0163920i	$0.00521798\pi$
$19$			0.142902i			0.0327841i	−0.999866	+	0.0163920i	$0.994782\pi$
$20$	1.19580	−	1.60314i	0.267390	−	0.358473i
$21$		−	6.37512i		−	1.39117i
$22$	−7.10401	+	3.56365i	−1.51458	+	0.759772i
$23$		−	1.97327i		−	0.411456i	−0.978609	−	0.205728i	$-0.934044\pi$
$23$		−	1.97327i		−	0.411456i	0.978609	−	0.205728i	$-0.0659562\pi$
$24$	0.948232	−	5.33431i	0.193557	−	1.08886i
$25$	1.00000			0.200000
$26$	1.96508	+	3.91733i	0.385384	+	0.768251i
$27$	4.46462			0.859216
$28$	5.33545	+	3.97979i	1.00830	+	0.752109i
$29$	1.39629			0.259284			0.129642	−	0.991561i	$-0.458617\pi$
$29$	1.39629			0.259284			0.129642	+	0.991561i	$0.458617\pi$
$30$	2.42138	−	1.21466i	0.442082	−	0.221766i
$31$			5.08219i			0.912788i	0.889778	+	0.456394i	$0.150859\pi$
$31$			5.08219i			0.912788i	−0.889778	+	0.456394i	$0.849141\pi$
$32$	3.87242	+	4.12363i	0.684554	+	0.728962i
$33$	−10.7651			−1.87396
$34$	4.38478	−	3.84366i	0.751984	−	0.659182i
$35$			3.32813i			0.562556i
$36$	0.800293	−	1.07290i	0.133382	−	0.178817i
$37$	1.12245			0.184530			0.0922650	−	0.995734i	$-0.470589\pi$
$37$	1.12245			0.184530			0.0922650	+	0.995734i	$0.470589\pi$
$38$	−0.0906161	−	0.180640i	−0.0146999	−	0.0293037i
$39$			5.93613i			0.950542i
$40$	−0.495023	+	2.78477i	−0.0782701	+	0.440311i
$41$			4.91265i			0.767227i	0.923494	+	0.383614i	$0.125321\pi$
$41$			4.91265i			0.767227i	−0.923494	+	0.383614i	$0.874679\pi$
$42$	4.04254	+	8.05867i	0.623778	+	1.24348i
$43$			10.2306i			1.56016i	0.625683	+	0.780078i	$0.284820\pi$
$43$			10.2306i			1.56016i	−0.625683	+	0.780078i	$0.715180\pi$
$44$	6.72030	−	9.00948i	1.01312	−	1.35823i
$45$	0.669252			0.0997661
$46$	1.25128	+	2.49438i	0.184491	+	0.367776i
$47$	5.17052			0.754198			0.377099	−	0.926173i	$-0.376922\pi$
$47$	5.17052			0.754198			0.377099	+	0.926173i	$0.376922\pi$
$48$	2.18391	+	7.34429i	0.315220	+	1.06006i
$49$	−4.07643			−0.582347
$50$	−1.26408	+	0.634112i	−0.178768	+	0.0896770i
$51$	7.64299	−	1.99048i	1.07023	−	0.278722i
$52$	−4.96805	−	3.70574i	−0.688945	−	0.513893i
$53$			0.833534i			0.114495i	0.998360	+	0.0572474i	$0.0182324\pi$
$53$			0.833534i			0.114495i	−0.998360	+	0.0572474i	$0.981768\pi$
$54$	−5.64364	+	2.83107i	−0.768002	+	0.385259i
$55$	5.61990			0.757787
$56$	−9.26807	−	1.64750i	−1.23850	−	0.220157i
$57$		−	0.273734i		−	0.0362569i
$58$	−1.76502	+	0.885402i	−0.231758	+	0.116259i
$59$		−	1.78441i		−	0.232310i	−0.993231	−	0.116155i	$-0.962943\pi$
$59$		−	1.78441i		−	0.232310i	0.993231	−	0.116155i	$-0.0370569\pi$
$60$	−2.29060	+	3.07086i	−0.295715	+	0.396446i
$61$	−10.0513			−1.28694			−0.643472	−	0.765470i	$-0.722507\pi$
$61$	−10.0513			−1.28694			−0.643472	+	0.765470i	$0.722507\pi$
$62$	−3.22268	−	6.42430i	−0.409281	−	0.815887i
$63$			2.22735i			0.280620i
$64$	−7.50990	−	2.75705i	−0.938738	−	0.344632i
$65$		−	3.09895i		−	0.384378i
$66$	13.6079	−	6.82627i	1.67502	−	0.840256i
$67$			13.2391i			1.61741i	0.588216	+	0.808704i	$0.299830\pi$
$67$			13.2391i			1.61741i	−0.588216	+	0.808704i	$0.700170\pi$
$68$	−3.10541	+	7.63914i	−0.376586	+	0.926382i
$69$			3.77986i			0.455042i
$70$	−2.11041	−	4.20702i	−0.252242	−	0.502835i
$71$			13.0517i			1.54895i	0.632605	+	0.774475i	$0.281986\pi$
$71$			13.0517i			1.54895i	−0.632605	+	0.774475i	$0.718014\pi$
$72$	−0.331295	+	1.86371i	−0.0390435	+	0.219641i
$73$			8.46816i			0.991123i	0.868573	+	0.495561i	$0.165038\pi$
$73$			8.46816i			0.991123i	−0.868573	+	0.495561i	$0.834962\pi$
$74$	−1.41887	+	0.711760i	−0.164940	+	0.0827404i
$75$	−1.91553			−0.221186
$76$	0.229092	+	0.170883i	0.0262787	+	0.0196016i
$77$			18.7037i			2.13149i
$78$	−3.76417	−	7.50375i	−0.426209	−	0.849633i
$79$			13.5702i			1.52676i	0.645947	+	0.763382i	$0.276463\pi$
$79$			13.5702i			1.52676i	−0.645947	+	0.763382i	$0.723537\pi$
$80$	−1.14011	−	3.83408i	−0.127468	−	0.428663i
$81$	−10.5599			−1.17332
$82$	−3.11517	−	6.20999i	−0.344013	−	0.685779i
$83$		−	17.4618i		−	1.91668i	−0.285624	−	0.958342i	$-0.592201\pi$
$83$		−	17.4618i		−	1.91668i	0.285624	−	0.958342i	$-0.407799\pi$
$84$	−10.2202	−	7.62340i	−1.11512	−	0.831781i
$85$	−3.99001	+	1.03913i	−0.432778	+	0.112709i
$86$	−6.48736	−	12.9323i	−0.699550	−	1.39453i
$87$	−2.67463			−0.286750
$88$	−2.78198	+	15.6501i	−0.296560	+	1.66831i
$89$	12.8756			1.36481			0.682407	−	0.730972i	$-0.260933\pi$
$89$	12.8756			1.36481			0.682407	+	0.730972i	$0.260933\pi$
$90$	−0.845988	+	0.424380i	−0.0891750	+	0.0447336i
$91$	10.3137			1.08117
$92$	−3.16343	−	2.35965i	−0.329810	−	0.246010i
$93$		−	9.73508i		−	1.00948i
$94$	−6.53596	+	3.27869i	−0.674133	+	0.338171i
$95$			0.142902i			0.0146615i
$96$	−7.41774	−	7.89894i	−0.757070	−	0.806182i
$97$			4.67407i			0.474580i	0.971439	+	0.237290i	$0.0762591\pi$
$97$			4.67407i			0.474580i	−0.971439	+	0.237290i	$0.923741\pi$
$98$	5.15293	−	2.58491i	0.520525	−	0.261115i
$99$	3.76113			0.378007
$100$	1.19580	−	1.60314i	0.119580	−	0.160314i
$101$		−	8.33556i		−	0.829419i	−0.909954	−	0.414710i	$-0.863883\pi$
$101$		−	8.33556i		−	0.829419i	0.909954	−	0.414710i	$-0.136117\pi$
$102$	−8.39918	+	7.36264i	−0.831642	+	0.729010i
$103$	5.81347			0.572818			0.286409	−	0.958107i	$-0.407538\pi$
$103$	5.81347			0.572818			0.286409	+	0.958107i	$0.407538\pi$
$104$	8.62987	+	1.53405i	0.846229	+	0.150426i
$105$		−	6.37512i		−	0.622148i
$106$	−0.528554	−	1.05366i	−0.0513377	−	0.102340i
$107$	1.24668			0.120521			0.0602604	−	0.998183i	$-0.480807\pi$
$107$	1.24668			0.120521			0.0602604	+	0.998183i	$0.480807\pi$
$108$	5.33880	−	7.15740i	0.513727	−	0.688721i
$109$	−5.08744			−0.487288			−0.243644	−	0.969865i	$-0.578343\pi$
$109$	−5.08744			−0.487288			−0.243644	+	0.969865i	$0.578343\pi$
$110$	−7.10401	+	3.56365i	−0.677341	+	0.339780i
$111$	−2.15009			−0.204077
$112$	12.7603	−	3.79442i	1.20573	−	0.358539i
$113$		−	2.08980i		−	0.196592i	−0.995157	−	0.0982959i	$-0.968661\pi$
$113$		−	2.08980i		−	0.196592i	0.995157	−	0.0982959i	$-0.0313392\pi$
$114$	0.173578	+	0.346022i	0.0162571	+	0.0324079i
$115$		−	1.97327i		−	0.184009i
$116$	1.66968	−	2.23844i	0.155026	−	0.207834i
$117$		−	2.07398i		−	0.191739i
$118$	1.13151	+	2.25563i	0.104164	+	0.207648i
$119$	−3.45834	−	13.2793i	−0.317026	−	1.21731i
$120$	0.948232	−	5.33431i	0.0865613	−	0.486954i
$121$	20.5833			1.87121
$122$	12.7057	−	6.37368i	1.15032	−	0.577046i
$123$		−	9.41033i		−	0.848501i
$124$	8.14745	+	6.07730i	0.731663	+	0.545758i
$125$	1.00000			0.0894427
$126$	−1.41239	−	2.81556i	−0.125826	−	0.250830i
$127$	−11.6290			−1.03191			−0.515954	−	0.856616i	$-0.672562\pi$
$127$	−11.6290			−1.03191			−0.515954	+	0.856616i	$0.672562\pi$
$128$	11.2414	−	1.27698i	0.993610	−	0.112870i
$129$		−	19.5971i		−	1.72542i
$130$	1.96508	+	3.91733i	0.172349	+	0.343572i
$131$	13.3354			1.16512			0.582558	−	0.812789i	$-0.302052\pi$
$131$	13.3354			1.16512			0.582558	+	0.812789i	$0.302052\pi$
$132$	−12.8729	+	17.2579i	−1.12044	+	1.50211i
$133$	−0.475597			−0.0412395
$134$	−8.39504	−	16.7352i	−0.725221	−	1.44570i
$135$	4.46462			0.384253
$136$	−0.918578	−	11.6257i	−0.0787674	−	0.996893i
$137$	17.1243			1.46303			0.731514	−	0.681826i	$-0.238814\pi$
$137$	17.1243			1.46303			0.731514	+	0.681826i	$0.238814\pi$
$138$	−2.39686	−	4.77805i	−0.204034	−	0.406735i
$139$	−5.78874			−0.490994			−0.245497	−	0.969397i	$-0.578951\pi$
$139$	−5.78874			−0.490994			−0.245497	+	0.969397i	$0.578951\pi$
$140$	5.33545	+	3.97979i	0.450928	+	0.336353i
$141$	−9.90429			−0.834091
$142$	−8.27623	−	16.4984i	−0.694526	−	1.38451i
$143$		−	17.4158i		−	1.45638i
$144$	−0.763019	−	2.56596i	−0.0635849	−	0.213830i
$145$	1.39629			0.115955
$146$	−5.36976	−	10.7044i	−0.444404	−	0.885906i
$147$	7.80851			0.644035
$148$	1.34223	−	1.79945i	0.110331	−	0.147914i
$149$		−	1.85859i		−	0.152262i	−0.997098	−	0.0761308i	$-0.975743\pi$
$149$		−	1.85859i		−	0.152262i	0.997098	−	0.0761308i	$-0.0242566\pi$
$150$	2.42138	−	1.21466i	0.197705	−	0.0991766i
$151$	−20.4111			−1.66103			−0.830515	−	0.556997i	$-0.811954\pi$
$151$	−20.4111			−1.66103			−0.830515	+	0.556997i	$0.811954\pi$
$152$	−0.397951	−	0.0707400i	−0.0322780	−	0.00573777i
$153$	−2.67032	+	0.695437i	−0.215883	+	0.0562227i
$154$	−11.8603	−	23.6430i	−0.955728	−	1.90521i
$155$			5.08219i			0.408211i
$156$	9.51644	+	7.09845i	0.761925	+	0.568331i
$157$			12.9192i			1.03106i	0.856870	+	0.515532i	$0.172406\pi$
$157$			12.9192i			1.03106i	−0.856870	+	0.515532i	$0.827594\pi$
$158$	−8.60501	−	17.1538i	−0.684578	−	1.36468i
$159$		−	1.59666i		−	0.126623i
$160$	3.87242	+	4.12363i	0.306142	+	0.326002i
$161$	6.56730			0.517576
$162$	13.3485	−	6.69613i	1.04876	−	0.526098i
$163$	16.1460			1.26465			0.632325	−	0.774704i	$-0.282101\pi$
$163$	16.1460			1.26465			0.632325	+	0.774704i	$0.282101\pi$
$164$	7.87566	+	5.87457i	0.614986	+	0.458727i
$165$	−10.7651			−0.838060
$166$	11.0727	+	22.0732i	0.859412	+	1.71321i
$167$		−	8.04236i		−	0.622337i	−0.950355	−	0.311168i	$-0.899280\pi$
$167$		−	8.04236i		−	0.622337i	0.950355	−	0.311168i	$-0.100720\pi$
$168$	17.7533	+	3.15584i	1.36969	+	0.243478i
$169$	3.39650			0.261269
$170$	4.38478	−	3.84366i	0.336297	−	0.294795i
$171$			0.0956376i			0.00731359i
$172$	16.4011	+	12.2338i	1.25057	+	0.932820i
$173$	−13.1004			−0.996003			−0.498002	−	0.867176i	$-0.665933\pi$
$173$	−13.1004			−0.996003			−0.498002	+	0.867176i	$0.665933\pi$
$174$	3.38095	−	1.69601i	0.256309	−	0.128574i
$175$			3.32813i			0.251583i
$176$	−6.40729	−	21.5471i	−0.482968	−	1.62418i
$177$			3.41808i			0.256919i
$178$	−16.2758	+	8.16460i	−1.21993	+	0.611962i
$179$			21.1603i			1.58159i	0.612080	+	0.790796i	$0.290333\pi$
$179$			21.1603i			1.58159i	−0.612080	+	0.790796i	$0.709667\pi$
$180$	0.800293	−	1.07290i	0.0596503	−	0.0799695i
$181$	1.42312			0.105780			0.0528898	−	0.998600i	$-0.483157\pi$
$181$	1.42312			0.105780			0.0528898	+	0.998600i	$0.483157\pi$
$182$	−13.0374	+	6.54004i	−0.966394	+	0.484780i
$183$	19.2536			1.42327
$184$	5.49512	+	0.976817i	0.405105	+	0.0720119i
$185$	1.12245			0.0825243
$186$	6.17313	+	12.3059i	0.452636	+	0.902315i
$187$	−22.4235	+	5.83978i	−1.63977	+	0.427047i
$188$	6.18293	−	8.28907i	0.450937	−	0.604542i
$189$			14.8588i			1.08082i
$190$	−0.0906161	−	0.180640i	−0.00657399	−	0.0131050i
$191$	−18.7557			−1.35712			−0.678558	−	0.734547i	$-0.737395\pi$
$191$	−18.7557			−1.35712			−0.678558	+	0.734547i	$0.737395\pi$
$192$	14.3854	+	5.28122i	1.03818	+	0.381139i
$193$		−	21.7003i		−	1.56202i	−0.624517	−	0.781011i	$-0.714704\pi$
$193$		−	21.7003i		−	1.56202i	0.624517	−	0.781011i	$-0.285296\pi$
$194$	−2.96388	−	5.90840i	−0.212794	−	0.424198i
$195$			5.93613i			0.425095i
$196$	−4.87461	+	6.53508i	−0.348186	+	0.466791i
$197$	0.446645			0.0318222			0.0159111	−	0.999873i	$-0.494935\pi$
$197$	0.446645			0.0318222			0.0159111	+	0.999873i	$0.494935\pi$
$198$	−4.75437	+	2.38498i	−0.337878	+	0.169493i
$199$			0.799910i			0.0567041i	0.999598	+	0.0283520i	$0.00902595\pi$
$199$			0.799910i			0.0567041i	−0.999598	+	0.0283520i	$0.990974\pi$
$200$	−0.495023	+	2.78477i	−0.0350034	+	0.196913i
$201$		−	25.3598i		−	1.78874i
$202$	5.28568	+	10.5368i	0.371899	+	0.741369i
$203$			4.64702i			0.326157i
$204$	5.94850	−	14.6330i	0.416479	−	1.02451i
$205$			4.91265i			0.343115i
$206$	−7.34870	+	3.68639i	−0.512008	+	0.256843i
$207$		−	1.32062i		−	0.0917892i
$208$	−11.8816	+	3.53314i	−0.823842	+	0.244979i
$209$			0.803097i			0.0555514i
$210$	4.04254	+	8.05867i	0.278962	+	0.556101i
$211$	2.54524			0.175222			0.0876109	−	0.996155i	$-0.472077\pi$
$211$	2.54524			0.175222			0.0876109	+	0.996155i	$0.472077\pi$
$212$	1.33627	+	0.996743i	0.0917755	+	0.0684566i
$213$		−	25.0009i		−	1.71303i
$214$	−1.57590	+	0.790533i	−0.107726	+	0.0540397i
$215$			10.2306i			0.697723i
$216$	−2.21009	+	12.4329i	−0.150378	+	0.845954i
$217$	−16.9142			−1.14821
$218$	6.43094	−	3.22601i	0.435558	−	0.218493i
$219$		−	16.2210i		−	1.09611i
$220$	6.72030	−	9.00948i	0.453082	−	0.607419i
$221$	3.22020	+	12.3649i	0.216614	+	0.831751i
$222$	2.71789	−	1.36340i	0.182413	−	0.0915052i
$223$	−26.0537			−1.74469			−0.872343	−	0.488895i	$-0.837400\pi$
$223$	−26.0537			−1.74469			−0.872343	+	0.488895i	$0.837400\pi$
$224$	−13.7240	+	12.8879i	−0.916971	+	0.861110i
$225$	0.669252			0.0446168
$226$	1.32517	+	2.64168i	0.0881489	+	0.175722i
$227$	−8.59371			−0.570385			−0.285192	−	0.958470i	$-0.592057\pi$
$227$	−8.59371			−0.570385			−0.285192	+	0.958470i	$0.592057\pi$
$228$	−0.438833	−	0.327332i	−0.0290624	−	0.0216781i
$229$		−	14.1378i		−	0.934255i	−0.884190	−	0.467127i	$-0.845289\pi$
$229$		−	14.1378i		−	0.934255i	0.884190	−	0.467127i	$-0.154711\pi$
$230$	1.25128	+	2.49438i	0.0825067	+	0.164474i
$231$		−	35.8276i		−	2.35728i
$232$	−0.691194	+	3.88834i	−0.0453791	+	0.255282i
$233$		−	15.4659i		−	1.01320i	−0.862180	−	0.506602i	$-0.830901\pi$
$233$		−	15.4659i		−	1.01320i	0.862180	−	0.506602i	$-0.169099\pi$
$234$	1.31513	+	2.62168i	0.0859730	+	0.171384i
$235$	5.17052			0.337288
$236$	−2.86065	−	2.13380i	−0.186212	−	0.138899i
$237$		−	25.9941i		−	1.68850i
$238$	12.7922	+	14.5931i	0.829194	+	0.945931i
$239$	23.9446			1.54885			0.774423	−	0.632668i	$-0.218040\pi$
$239$	23.9446			1.54885			0.774423	+	0.632668i	$0.218040\pi$
$240$	2.18391	+	7.34429i	0.140971	+	0.474072i
$241$			17.4933i			1.12684i	0.826171	+	0.563420i	$0.190515\pi$
$241$			17.4933i			1.12684i	−0.826171	+	0.563420i	$0.809485\pi$
$242$	−26.0189	+	13.0521i	−1.67256	+	0.839021i
$243$	6.83386			0.438393
$244$	−12.0194	+	16.1137i	−0.769466	+	1.03157i
$245$	−4.07643			−0.260433
$246$	5.96720	+	11.8954i	0.380455	+	0.758424i
$247$	0.442848			0.0281777
$248$	−14.1527	−	2.51580i	−0.898700	−	0.159754i
$249$			33.4486i			2.11972i
$250$	−1.26408	+	0.634112i	−0.0799475	+	0.0401048i
$251$		−	20.8823i		−	1.31808i	−0.752107	−	0.659041i	$-0.770962\pi$
$251$		−	20.8823i		−	1.31808i	0.752107	−	0.659041i	$-0.229038\pi$
$252$	3.57076	+	2.66348i	0.224937	+	0.167783i
$253$		−	11.0896i		−	0.697197i
$254$	14.7000	−	7.37410i	0.922361	−	0.462692i
$255$	7.64299	−	1.99048i	0.478623	−	0.124648i
$256$	−13.4003	+	8.74252i	−0.837519	+	0.546408i
$257$	−0.525927			−0.0328064			−0.0164032	−	0.999865i	$-0.505222\pi$
$257$	−0.525927			−0.0328064			−0.0164032	+	0.999865i	$0.505222\pi$
$258$	12.4267	+	24.7723i	0.773654	+	1.54225i
$259$			3.73566i			0.232123i
$260$	−4.96805	−	3.70574i	−0.308105	−	0.229820i
$261$	0.934467			0.0578420
$262$	−16.8570	+	8.45612i	−1.04143	+	0.522421i
$263$	−0.500325			−0.0308513			−0.0154257	−	0.999881i	$-0.504910\pi$
$263$	−0.500325			−0.0308513			−0.0154257	+	0.999881i	$0.504910\pi$
$264$	5.32897	−	29.9783i	0.327975	−	1.84504i
$265$			0.833534i			0.0512036i
$266$	0.601194	−	0.301582i	0.0368615	−	0.0184912i
$267$	−24.6637			−1.50939
$268$	21.2240	+	15.8313i	1.29646	+	0.967051i
$269$	27.3003			1.66453			0.832265	−	0.554377i	$-0.187044\pi$
$269$	27.3003			1.66453			0.832265	+	0.554377i	$0.187044\pi$
$270$	−5.64364	+	2.83107i	−0.343461	+	0.172293i
$271$	5.56998			0.338352			0.169176	−	0.985586i	$-0.445889\pi$
$271$	5.56998			0.338352			0.169176	+	0.985586i	$0.445889\pi$
$272$	8.53314	+	14.1133i	0.517397	+	0.855745i
$273$	−19.7562			−1.19570
$274$	−21.6465	+	10.8587i	−1.30771	+	0.656000i
$275$	5.61990			0.338893
$276$	6.05964	+	4.51997i	0.364748	+	0.272070i
$277$	−2.77924			−0.166989			−0.0834943	−	0.996508i	$-0.526608\pi$
$277$	−2.77924			−0.166989			−0.0834943	+	0.996508i	$0.526608\pi$
$278$	7.31744	−	3.67071i	0.438871	−	0.220154i
$279$			3.40126i			0.203628i
$280$	−9.26807	−	1.64750i	−0.553873	−	0.0984570i
$281$	−5.79372			−0.345624			−0.172812	−	0.984955i	$-0.555285\pi$
$281$	−5.79372			−0.345624			−0.172812	+	0.984955i	$0.555285\pi$
$282$	12.5198	−	6.28043i	0.745545	−	0.373994i
$283$	2.69243			0.160049			0.0800243	−	0.996793i	$-0.474500\pi$
$283$	2.69243			0.160049			0.0800243	+	0.996793i	$0.474500\pi$
$284$	20.9237	+	15.6072i	1.24159	+	0.926120i
$285$		−	0.273734i		−	0.0162146i
$286$	11.0436	+	22.0150i	0.653020	+	1.30177i
$287$	−16.3499			−0.965106
$288$	2.59163	+	2.75975i	0.152713	+	0.162620i
$289$	14.8404	−	8.29226i	0.872967	−	0.487780i
$290$	−1.76502	+	0.885402i	−0.103646	+	0.0519926i
$291$		−	8.95331i		−	0.524852i
$292$	13.5756	+	10.1263i	0.794453	+	0.592594i
$293$		−	9.70877i		−	0.567192i	−0.958944	−	0.283596i	$-0.908472\pi$
$293$		−	9.70877i		−	0.567192i	0.958944	−	0.283596i	$-0.0915275\pi$
$294$	−9.87060	+	4.95147i	−0.575665	+	0.288776i
$295$		−	1.78441i		−	0.103892i
$296$	−0.555640	+	3.12577i	−0.0322959	+	0.181682i
$297$	25.0907			1.45591
$298$	1.17855	+	2.34941i	0.0682718	+	0.136098i
$299$	−6.11508			−0.353644
$300$	−2.29060	+	3.07086i	−0.132248	+	0.177296i
$301$	−34.0488			−1.96254
$302$	25.8013	−	12.9429i	1.48470	−	0.744781i
$303$			15.9670i			0.917281i
$304$	0.547899	−	0.162924i	0.0314242	−	0.00934434i
$305$	−10.0513			−0.575538
$306$	2.93452	−	2.57237i	0.167755	−	0.147053i
$307$		−	31.9245i		−	1.82203i	−0.412373	−	0.911015i	$-0.635300\pi$
$307$		−	31.9245i		−	1.82203i	0.412373	−	0.911015i	$-0.364700\pi$
$308$	29.9847	+	22.3660i	1.70854	+	1.27442i
$309$	−11.1359			−0.633497
$310$	−3.22268	−	6.42430i	−0.183036	−	0.364876i
$311$			26.8685i			1.52357i	0.647829	+	0.761786i	$0.275677\pi$
$311$			26.8685i			1.52357i	−0.647829	+	0.761786i	$0.724323\pi$
$312$	−16.5308	−	2.93852i	−0.935871	−	0.166361i
$313$		−	28.2676i		−	1.59778i	−0.601478	−	0.798890i	$-0.705421\pi$
$313$		−	28.2676i		−	1.59778i	0.601478	−	0.798890i	$-0.294579\pi$
$314$	−8.19221	−	16.3309i	−0.462313	−	0.921606i
$315$			2.22735i			0.125497i
$316$	21.7549	+	16.2273i	1.22381	+	0.912855i
$317$	−8.09179			−0.454480			−0.227240	−	0.973839i	$-0.572970\pi$
$317$	−8.09179			−0.454480			−0.227240	+	0.973839i	$0.572970\pi$
$318$	1.01246	+	2.01831i	0.0567760	+	0.113181i
$319$	7.84699			0.439347
$320$	−7.50990	−	2.75705i	−0.419816	−	0.154124i
$321$	−2.38804			−0.133288
$322$	−8.30161	+	4.16441i	−0.462630	+	0.232073i
$323$	−0.148494	−	0.570183i	−0.00826241	−	0.0317258i
$324$	−12.6275	+	16.9289i	−0.701529	+	0.940495i
$325$		−	3.09895i		−	0.171899i
$326$	−20.4098	+	10.2383i	−1.13039	+	0.567050i
$327$	9.74514			0.538907
$328$	−13.6806	−	2.43188i	−0.755385	−	0.134278i
$329$			17.2082i			0.948716i
$330$	13.6079	−	6.82627i	0.749092	−	0.375774i
$331$		−	4.22596i		−	0.232280i	−0.993233	−	0.116140i	$-0.962948\pi$
$331$		−	4.22596i		−	0.232280i	0.993233	−	0.116140i	$-0.0370521\pi$
$332$	−27.9937	−	20.8809i	−1.53635	−	1.14599i
$333$	0.751203			0.0411656
$334$	5.09976	+	10.1662i	0.279046	+	0.556270i
$335$			13.2391i			0.723327i
$336$	−24.4427	+	7.26832i	−1.33346	+	0.396520i
$337$			18.0632i			0.983963i	0.870606	+	0.491981i	$0.163727\pi$
$337$			18.0632i			0.983963i	−0.870606	+	0.491981i	$0.836273\pi$
$338$	−4.29345	+	2.15376i	−0.233533	+	0.117149i
$339$			4.00307i			0.217417i
$340$	−3.10541	+	7.63914i	−0.168415	+	0.414290i
$341$			28.5614i			1.54669i
$342$	−0.0606450	−	0.120894i	−0.00327931	−	0.00653719i
$343$			9.73002i			0.525372i
$344$	−28.4899	−	5.06440i	−1.53607	−	0.273054i
$345$			3.77986i			0.203501i
$346$	16.5599	−	8.30711i	0.890268	−	0.446593i
$347$	13.9650			0.749679			0.374840	−	0.927090i	$-0.377698\pi$
$347$	13.9650			0.749679			0.374840	+	0.927090i	$0.377698\pi$
$348$	−3.19833	+	4.28780i	−0.171448	+	0.229850i
$349$		−	1.83664i		−	0.0983129i	−0.998791	−	0.0491565i	$-0.984347\pi$
$349$		−	1.83664i		−	0.0983129i	0.998791	−	0.0491565i	$-0.0156533\pi$
$350$	−2.11041	−	4.20702i	−0.112806	−	0.224875i
$351$		−	13.8356i		−	0.738491i
$352$	21.7626	+	23.1744i	1.15995	+	1.23520i
$353$	−21.1687			−1.12669			−0.563347	−	0.826220i	$-0.690487\pi$
$353$	−21.1687			−1.12669			−0.563347	+	0.826220i	$0.690487\pi$
$354$	−2.16745	−	4.32073i	−0.115199	−	0.229644i
$355$			13.0517i			0.692711i
$356$	15.3967	−	20.6414i	0.816025	−	1.09399i
$357$	6.62456	+	25.4368i	0.350609	+	1.34626i
$358$	−13.4180	−	26.7483i	−0.709162	−	1.41369i
$359$	−19.4778			−1.02800			−0.513999	−	0.857791i	$-0.671836\pi$
$359$	−19.4778			−1.02800			−0.513999	+	0.857791i	$0.671836\pi$
$360$	−0.331295	+	1.86371i	−0.0174608	+	0.0982263i
$361$	18.9796			0.998925
$362$	−1.79894	+	0.902416i	−0.0945500	+	0.0474299i
$363$	−39.4279			−2.06943
$364$	12.3332	−	16.5343i	0.646433	−	0.866633i
$365$			8.46816i			0.443244i
$366$	−24.3382	+	12.2090i	−1.27218	+	0.638173i
$367$		−	20.8474i		−	1.08823i	−0.839012	−	0.544113i	$-0.816866\pi$
$367$		−	20.8474i		−	1.08823i	0.839012	−	0.544113i	$-0.183134\pi$
$368$	−7.56568	+	2.24974i	−0.394389	+	0.117276i
$369$			3.28780i			0.171156i
$370$	−1.41887	+	0.711760i	−0.0737636	+	0.0370027i
$371$	−2.77411			−0.144024
$372$	−15.6067	−	11.6412i	−0.809169	−	0.603570i
$373$		−	11.3307i		−	0.586683i	−0.956008	−	0.293342i	$-0.905233\pi$
$373$		−	11.3307i		−	0.586683i	0.956008	−	0.293342i	$-0.0947673\pi$
$374$	24.6420	−	21.6010i	1.27421	−	1.11696i
$375$	−1.91553			−0.0989175
$376$	−2.55953	+	14.3987i	−0.131998	+	0.742558i
$377$		−	4.32702i		−	0.222853i
$378$	−9.42215	−	18.7827i	−0.484623	−	0.966080i
$379$	18.1526			0.932434			0.466217	−	0.884670i	$-0.345617\pi$
$379$	18.1526			0.932434			0.466217	+	0.884670i	$0.345617\pi$
$380$	0.229092	+	0.170883i	0.0117522	+	0.00876612i
$381$	22.2757			1.14122
$382$	23.7087	−	11.8932i	1.21304	−	0.608510i
$383$	26.1354			1.33546			0.667729	−	0.744405i	$-0.267267\pi$
$383$	26.1354			1.33546			0.667729	+	0.744405i	$0.267267\pi$
$384$	−21.5332	+	2.44609i	−1.09886	+	0.124827i
$385$			18.7037i			0.953231i
$386$	13.7604	+	27.4310i	0.700387	+	1.39620i
$387$			6.84686i			0.348045i
$388$	7.49318	+	5.58927i	0.380408	+	0.283752i
$389$			20.6458i			1.04678i	0.852092	+	0.523392i	$0.175334\pi$
$389$			20.6458i			1.04678i	−0.852092	+	0.523392i	$0.824666\pi$
$390$	−3.76417	−	7.50375i	−0.190606	−	0.379967i
$391$	2.05048	+	7.87339i	0.103697	+	0.398174i
$392$	2.01793	−	11.3519i	0.101921	−	0.573358i
$393$	−25.5443			−1.28854
$394$	−0.564596	+	0.283223i	−0.0284439	+	0.0142686i
$395$			13.5702i			0.682790i
$396$	4.49757	−	6.02961i	0.226011	−	0.302999i
$397$	24.4324			1.22623			0.613113	−	0.789995i	$-0.289917\pi$
$397$	24.4324			1.22623			0.613113	+	0.789995i	$0.289917\pi$
$398$	−0.507232	−	1.01115i	−0.0254253	−	0.0506844i
$399$	0.911020			0.0456081
$400$	−1.14011	−	3.83408i	−0.0570054	−	0.191704i
$401$		−	38.3454i		−	1.91488i	−0.288634	−	0.957439i	$-0.593201\pi$
$401$		−	38.3454i		−	1.91488i	0.288634	−	0.957439i	$-0.406799\pi$
$402$	16.0809	+	32.0568i	0.802045	+	1.59885i
$403$	15.7495			0.784537
$404$	−13.3631	−	9.96769i	−0.664837	−	0.495911i
$405$	−10.5599			−0.524724
$406$	−2.94673	−	5.87421i	−0.146244	−	0.291532i
$407$	6.30807			0.312679
$408$	1.75956	+	22.2693i	0.0871113	+	1.10250i
$409$	1.92082			0.0949784			0.0474892	−	0.998872i	$-0.484878\pi$
$409$	1.92082			0.0949784			0.0474892	+	0.998872i	$0.484878\pi$
$410$	−3.11517	−	6.20999i	−0.153847	−	0.306690i
$411$	−32.8021			−1.61801
$412$	6.95177	−	9.31979i	0.342489	−	0.459153i
$413$	5.93873			0.292226
$414$	0.837419	+	1.66937i	0.0411569	+	0.0820449i
$415$		−	17.4618i		−	0.857167i
$416$	12.7789	−	12.0005i	0.626539	−	0.588371i
$417$	11.0885			0.543006
$418$	−0.509254	−	1.01518i	−0.0249084	−	0.0496541i
$419$	−14.8975			−0.727790			−0.363895	−	0.931440i	$-0.618553\pi$
$419$	−14.8975			−0.727790			−0.363895	+	0.931440i	$0.618553\pi$
$420$	−10.2202	−	7.62340i	−0.498695	−	0.371984i
$421$			4.71333i			0.229714i	0.993382	+	0.114857i	$0.0366409\pi$
$421$			4.71333i			0.229714i	−0.993382	+	0.114857i	$0.963359\pi$
$422$	−3.21740	+	1.61397i	−0.156620	+	0.0785669i
$423$	3.46038			0.168249
$424$	−2.32120	−	0.412619i	−0.112728	−	0.0200386i
$425$	−3.99001	+	1.03913i	−0.193544	+	0.0504050i
$426$	15.8534	+	31.6031i	0.768098	+	1.53118i
$427$		−	33.4522i		−	1.61886i
$428$	1.49078	−	1.99860i	0.0720596	−	0.0966057i
$429$			33.3605i			1.61066i
$430$	−6.48736	−	12.9323i	−0.312848	−	0.623653i
$431$			4.42066i			0.212935i	0.994316	+	0.106468i	$0.0339541\pi$
$431$			4.42066i			0.212935i	−0.994316	+	0.106468i	$0.966046\pi$
$432$	−5.09014	−	17.1177i	−0.244900	−	0.823575i
$433$	3.43928			0.165281			0.0826407	−	0.996579i	$-0.473665\pi$
$433$	3.43928			0.165281			0.0826407	+	0.996579i	$0.473665\pi$
$434$	21.3809	−	10.7255i	1.02632	−	0.514840i
$435$	−2.67463			−0.128239
$436$	−6.08358	+	8.15587i	−0.291351	+	0.390595i
$437$	0.281985			0.0134892
$438$	10.2859	+	20.5047i	0.491481	+	0.979751i
$439$		−	17.2783i		−	0.824647i	−0.911037	−	0.412324i	$-0.864717\pi$
$439$		−	17.2783i		−	0.824647i	0.911037	−	0.412324i	$-0.135283\pi$
$440$	−2.78198	+	15.6501i	−0.132626	+	0.746091i
$441$	−2.72815			−0.129912
$442$	−11.9113	−	13.5882i	−0.566563	−	0.646326i
$443$			22.4135i			1.06490i	0.846462	+	0.532450i	$0.178728\pi$
$443$			22.4135i			1.06490i	−0.846462	+	0.532450i	$0.821272\pi$
$444$	−2.57108	+	3.44689i	−0.122018	+	0.163582i
$445$	12.8756			0.610364
$446$	32.9340	−	16.5210i	1.55947	−	0.782291i
$447$			3.56018i			0.168391i
$448$	9.17583	−	24.9939i	0.433517	−	1.18085i
$449$			13.2570i			0.625637i	0.949813	+	0.312818i	$0.101273\pi$
$449$			13.2570i			0.625637i	−0.949813	+	0.312818i	$0.898727\pi$
$450$	−0.845988	+	0.424380i	−0.0398803	+	0.0200055i
$451$			27.6086i			1.30004i
$452$	−3.35024	−	2.49899i	−0.157582	−	0.117543i
$453$	39.0980			1.83698
$454$	10.8632	−	5.44938i	0.509833	−	0.255752i
$455$	10.3137			0.483514
$456$	0.762286	+	0.135505i	0.0356973	+	0.00634558i
$457$	20.2149			0.945612			0.472806	−	0.881167i	$-0.343241\pi$
$457$	20.2149			0.945612			0.472806	+	0.881167i	$0.343241\pi$
$458$	8.96498	+	17.8714i	0.418906	+	0.835075i
$459$	−17.8139	+	4.63930i	−0.831481	+	0.216544i
$460$	−3.16343	−	2.35965i	−0.147496	−	0.110019i
$461$		−	41.2453i		−	1.92099i	−0.278303	−	0.960493i	$-0.589772\pi$
$461$		−	41.2453i		−	1.92099i	0.278303	−	0.960493i	$-0.410228\pi$
$462$	22.7187	+	45.2889i	1.05697	+	2.10703i
$463$	30.7003			1.42676			0.713381	−	0.700776i	$-0.247163\pi$
$463$	30.7003			1.42676			0.713381	+	0.700776i	$0.247163\pi$
$464$	−1.59192	−	5.35347i	−0.0739028	−	0.248529i
$465$		−	9.73508i		−	0.451454i
$466$	9.80712	+	19.5502i	0.454306	+	0.905644i
$467$			5.56967i			0.257733i	0.991662	+	0.128867i	$0.0411339\pi$
$467$			5.56967i			0.257733i	−0.991662	+	0.128867i	$0.958866\pi$
$468$	−3.32487	−	2.48007i	−0.153692	−	0.114641i
$469$	−44.0612			−2.03456
$470$	−6.53596	+	3.27869i	−0.301481	+	0.151235i
$471$		−	24.7471i		−	1.14029i
$472$	4.96916	+	0.883323i	0.228724	+	0.0406582i
$473$			57.4951i			2.64363i
$474$	16.4832	+	32.8586i	0.757096	+	1.50925i
$475$			0.142902i			0.00655681i
$476$	−25.4240	−	10.3352i	−1.16531	−	0.473713i
$477$			0.557844i			0.0255419i
$478$	−30.2679	+	15.1836i	−1.38442	+	0.694480i
$479$		−	30.9129i		−	1.41244i	−0.707990	−	0.706222i	$-0.750398\pi$
$479$		−	30.9129i		−	1.41244i	0.707990	−	0.706222i	$-0.249602\pi$
$480$	−7.41774	−	7.89894i	−0.338572	−	0.360535i
$481$		−	3.47842i		−	0.158602i
$482$	−11.0927	−	22.1129i	−0.505258	−	1.00722i
$483$	−12.5799			−0.572403
$484$	24.6136	−	32.9978i	1.11880	−	1.49990i
$485$			4.67407i			0.212238i
$486$	−8.63856	+	4.33344i	−0.391853	+	0.196569i
$487$			32.4017i			1.46826i	0.679009	+	0.734130i	$0.262410\pi$
$487$			32.4017i			1.46826i	−0.679009	+	0.734130i	$0.737590\pi$
$488$	4.97565	−	27.9907i	0.225237	−	1.26708i
$489$	−30.9281			−1.39861
$490$	5.15293	−	2.58491i	0.232786	−	0.116774i
$491$		−	1.76749i		−	0.0797656i	−0.999204	−	0.0398828i	$-0.987302\pi$
$491$		−	1.76749i		−	0.0797656i	0.999204	−	0.0398828i	$-0.0126985\pi$
$492$	−15.0861	−	11.2529i	−0.680132	−	0.507320i
$493$	−5.57120	+	1.45092i	−0.250914	+	0.0653460i
$494$	−0.559795	+	0.280815i	−0.0251864	+	0.0126345i
$495$	3.76113			0.169050
$496$	19.4855	−	5.79424i	0.874925	−	0.260169i
$497$	−43.4376			−1.94844
$498$	−21.2102	−	42.2818i	−0.950451	−	1.89469i
$499$	18.9122			0.846628			0.423314	−	0.905983i	$-0.360867\pi$
$499$	18.9122			0.846628			0.423314	+	0.905983i	$0.360867\pi$
$500$	1.19580	−	1.60314i	0.0534780	−	0.0716945i
$501$			15.4054i			0.688262i
$502$	13.2418	+	26.3970i	0.591008	+	1.17816i
$503$			39.0914i			1.74300i	0.490396	+	0.871499i	$0.336852\pi$
$503$			39.0914i			1.74300i	−0.490396	+	0.871499i	$0.663148\pi$
$504$	−6.20267	−	1.10259i	−0.276289	−	0.0491134i
$505$		−	8.33556i		−	0.370928i
$506$	7.03205	+	14.0182i	0.312613	+	0.623183i
$507$	−6.50609			−0.288946
$508$	−13.9060	+	18.6429i	−0.616980	+	0.827146i
$509$		−	12.6510i		−	0.560748i	−0.959891	−	0.280374i	$-0.909542\pi$
$509$		−	12.6510i		−	0.560748i	0.959891	−	0.280374i	$-0.0904584\pi$
$510$	−8.39918	+	7.36264i	−0.371922	+	0.326023i
$511$	−28.1831			−1.24675
$512$	11.3953	−	19.5486i	0.503608	−	0.863932i
$513$			0.638004i			0.0281686i
$514$	0.664814	−	0.333497i	0.0293237	−	0.0147099i
$515$	5.81347			0.256172
$516$	−31.4168	−	23.4342i	−1.38305	−	1.03163i
$517$	29.0578			1.27796
$518$	−2.36883	−	4.72218i	−0.104080	−	0.207481i
$519$	25.0942			1.10151
$520$	8.62987	+	1.53405i	0.378445	+	0.0672727i
$521$			35.0878i			1.53722i	0.639716	+	0.768611i	$0.279052\pi$
$521$			35.0878i			1.53722i	−0.639716	+	0.768611i	$0.720948\pi$
$522$	−1.18124	+	0.592557i	−0.0517016	+	0.0259355i
$523$			4.89316i			0.213963i	0.994261	+	0.106982i	$0.0341186\pi$
$523$			4.89316i			0.213963i	−0.994261	+	0.106982i	$0.965881\pi$
$524$	15.9465	−	21.3784i	0.696625	−	0.933922i
$525$		−	6.37512i		−	0.278233i
$526$	0.632451	−	0.317262i	0.0275762	−	0.0138333i
$527$	−5.28104	−	20.2780i	−0.230046	−	0.883324i
$528$	12.2733	+	41.2742i	0.534129	+	1.79623i
$529$	19.1062			0.830704
$530$	−0.528554	−	1.05366i	−0.0229589	−	0.0457679i
$531$		−	1.19422i		−	0.0518246i
$532$	−0.568721	+	0.762448i	−0.0246572	+	0.0330563i
$533$	15.2241			0.659428
$534$	31.1769	−	15.6395i	1.34915	−	0.676788i
$535$	1.24668			0.0538985
$536$	−36.8677	−	6.55364i	−1.59244	−	0.283074i
$537$		−	40.5331i		−	1.74913i
$538$	−34.5098	+	17.3115i	−1.48783	+	0.746351i
$539$	−22.9091			−0.986765
$540$	5.33880	−	7.15740i	0.229746	−	0.308005i
$541$	−40.0292			−1.72099			−0.860494	−	0.509460i	$-0.829845\pi$
$541$	−40.0292			−1.72099			−0.860494	+	0.509460i	$0.829845\pi$
$542$	−7.04091	+	3.53199i	−0.302433	+	0.151712i
$543$	−2.72602			−0.116985
$544$	−19.7360	−	12.4294i	−0.846174	−	0.532907i
$545$	−5.08744			−0.217922
$546$	24.9734	−	12.5276i	1.06876	−	0.536134i
$547$	28.3432			1.21187			0.605933	−	0.795516i	$-0.292800\pi$
$547$	28.3432			1.21187			0.605933	+	0.795516i	$0.292800\pi$
$548$	20.4773	−	27.4526i	0.874747	−	1.17272i
$549$	−6.72688			−0.287096
$550$	−7.10401	+	3.56365i	−0.302916	+	0.151954i
$551$			0.199533i			0.00850038i
$552$	−10.5261	−	1.87112i	−0.448019	−	0.0796402i
$553$	−45.1633			−1.92054
$554$	3.51319	−	1.76235i	0.149261	−	0.0748752i
$555$	−2.15009			−0.0912662
$556$	−6.92219	+	9.28015i	−0.293566	+	0.393566i
$557$		−	45.1187i		−	1.91174i	−0.293792	−	0.955869i	$-0.594917\pi$
$557$		−	45.1187i		−	1.91174i	0.293792	−	0.955869i	$-0.405083\pi$
$558$	−2.15678	−	4.29947i	−0.0913039	−	0.182011i
$559$	31.7042			1.34095
$560$	12.7603	−	3.79442i	0.539221	−	0.160344i
$561$	42.9528	−	11.1863i	1.81347	−	0.472285i
$562$	7.32374	−	3.67387i	0.308933	−	0.154973i
$563$		−	9.81887i		−	0.413816i	−0.978360	−	0.206908i	$-0.933660\pi$
$563$		−	9.81887i		−	0.413816i	0.978360	−	0.206908i	$-0.0663401\pi$
$564$	−11.8436	+	15.8779i	−0.498705	+	0.668582i
$565$		−	2.08980i		−	0.0879186i
$566$	−3.40346	+	1.70730i	−0.143058	+	0.0717634i
$567$		−	35.1445i		−	1.47593i
$568$	−36.3459	−	6.46089i	−1.52504	−	0.271093i
$569$	28.1252			1.17907			0.589534	−	0.807744i	$-0.299311\pi$
$569$	28.1252			1.17907			0.589534	+	0.807744i	$0.299311\pi$
$570$	0.173578	+	0.346022i	0.00727038	+	0.0144933i
$571$	−40.6467			−1.70101			−0.850506	−	0.525966i	$-0.823704\pi$
$571$	−40.6467			−1.70101			−0.850506	+	0.525966i	$0.823704\pi$
$572$	−27.9199	−	20.8259i	−1.16739	−	0.870774i
$573$	35.9271			1.50088
$574$	20.6676	−	10.3677i	0.862651	−	0.432739i
$575$		−	1.97327i		−	0.0822912i
$576$	−5.02601	−	1.84516i	−0.209417	−	0.0768818i
$577$	14.5879			0.607304			0.303652	−	0.952783i	$-0.401794\pi$
$577$	14.5879			0.607304			0.303652	+	0.952783i	$0.401794\pi$
$578$	−13.5013	+	19.8926i	−0.561580	+	0.827423i
$579$			41.5676i			1.72749i
$580$	1.66968	−	2.23844i	0.0693299	−	0.0929462i
$581$	58.1151			2.41102
$582$	5.67740	+	11.3177i	0.235336	+	0.469134i
$583$			4.68438i			0.194007i
$584$	−23.5819	−	4.19194i	−0.975825	−	0.173464i
$585$		−	2.07398i		−	0.0857484i
$586$	6.15645	+	12.2727i	0.254321	+	0.506980i
$587$		−	11.3901i		−	0.470121i	−0.971981	−	0.235061i	$-0.924471\pi$
$587$		−	11.3901i		−	0.470121i	0.971981	−	0.235061i	$-0.0755288\pi$
$588$	9.33745	−	12.5181i	0.385070	−	0.516239i
$589$	−0.726257			−0.0299249
$590$	1.13151	+	2.25563i	0.0465837	+	0.0928630i
$591$	−0.855562			−0.0351931
$592$	−1.27972	−	4.30357i	−0.0525960	−	0.176876i
$593$	−30.7174			−1.26141			−0.630705	−	0.776022i	$-0.717234\pi$
$593$	−30.7174			−1.26141			−0.630705	+	0.776022i	$0.717234\pi$
$594$	−31.7167	+	15.9103i	−1.30135	+	0.652808i
$595$	−3.45834	−	13.2793i	−0.141778	−	0.544397i
$596$	−2.97958	−	2.22251i	−0.122048	−	0.0910375i
$597$		−	1.53225i		−	0.0627108i
$598$	7.72996	−	3.87765i	0.316101	−	0.158569i
$599$	−5.53876			−0.226308			−0.113154	−	0.993577i	$-0.536095\pi$
$599$	−5.53876			−0.226308			−0.113154	+	0.993577i	$0.536095\pi$
$600$	0.948232	−	5.33431i	0.0387114	−	0.217772i
$601$			11.1252i			0.453807i	0.973917	+	0.226903i	$0.0728601\pi$
$601$			11.1252i			0.453807i	−0.973917	+	0.226903i	$0.927140\pi$
$602$	43.0405	−	21.5908i	1.75420	−	0.879974i
$603$			8.86026i			0.360818i
$604$	−24.4076	+	32.7218i	−0.993133	+	1.33143i
$605$	20.5833			0.836829
$606$	−10.1249	−	20.1836i	−0.411295	−	0.819903i
$607$		−	22.3277i		−	0.906252i	−0.891446	−	0.453126i	$-0.850309\pi$
$607$		−	22.3277i		−	0.906252i	0.891446	−	0.453126i	$-0.149691\pi$
$608$	−0.589277	+	0.553379i	−0.0238983	+	0.0224425i
$609$		−	8.90150i		−	0.360707i
$610$	12.7057	−	6.37368i	0.514440	−	0.258063i
$611$		−	16.0232i		−	0.648229i
$612$	−2.07830	+	5.11250i	−0.0840103	+	0.206661i
$613$			12.3546i			0.498999i	0.968375	+	0.249499i	$0.0802661\pi$
$613$			12.3546i			0.498999i	−0.968375	+	0.249499i	$0.919734\pi$
$614$	20.2437	+	40.3552i	0.816971	+	1.62860i
$615$		−	9.41033i		−	0.379461i
$616$	−52.0856	−	9.25879i	−2.09859	−	0.373047i
$617$		−	13.7285i		−	0.552690i	−0.961059	−	0.276345i	$-0.910877\pi$
$617$		−	13.7285i		−	0.552690i	0.961059	−	0.276345i	$-0.0891232\pi$
$618$	14.0766	−	7.06139i	0.566246	−	0.284051i
$619$	−19.8519			−0.797914			−0.398957	−	0.916970i	$-0.630628\pi$
$619$	−19.8519			−0.797914			−0.398957	+	0.916970i	$0.630628\pi$
$620$	8.14745	+	6.07730i	0.327210	+	0.244070i
$621$		−	8.80991i		−	0.353529i
$622$	−17.0376	−	33.9639i	−0.683146	−	1.36183i
$623$			42.8517i			1.71682i
$624$	22.7596	−	6.76783i	0.911113	−	0.270930i
$625$	1.00000			0.0400000
$626$	17.9248	+	35.7326i	0.716420	+	1.42816i
$627$		−	1.53836i		−	0.0614360i
$628$	20.7112	+	15.4488i	0.826469	+	0.616475i
$629$	−4.47860	+	1.16637i	−0.178573	+	0.0465062i
$630$	−1.41239	−	2.81556i	−0.0562710	−	0.112174i
$631$	−19.5862			−0.779714			−0.389857	−	0.920875i	$-0.627476\pi$
$631$	−19.5862			−0.779714			−0.389857	+	0.920875i	$0.627476\pi$
$632$	−37.7898	−	6.71755i	−1.50320	−	0.267210i
$633$	−4.87549			−0.193783
$634$	10.2287	−	5.13110i	0.406233	−	0.203782i
$635$	−11.6290			−0.461483
$636$	−2.55967	−	1.90929i	−0.101497	−	0.0757083i
$637$			12.6326i			0.500524i
$638$	−9.91923	+	4.97587i	−0.392706	+	0.196997i
$639$			8.73486i			0.345546i
$640$	11.2414	−	1.27698i	0.444356	−	0.0504771i
$641$			14.9074i			0.588805i	0.955681	+	0.294403i	$0.0951207\pi$
$641$			14.9074i			0.588805i	−0.955681	+	0.294403i	$0.904879\pi$
$642$	3.01868	−	1.51429i	0.119138	−	0.0597642i
$643$	13.4958			0.532224			0.266112	−	0.963942i	$-0.414261\pi$
$643$	13.4958			0.532224			0.266112	+	0.963942i	$0.414261\pi$
$644$	7.85321	−	10.5283i	0.309460	−	0.414873i
$645$		−	19.5971i		−	0.771633i
$646$	0.549268	+	0.626596i	0.0216107	+	0.0246531i
$647$	17.3061			0.680372			0.340186	−	0.940358i	$-0.389510\pi$
$647$	17.3061			0.680372			0.340186	+	0.940358i	$0.389510\pi$
$648$	5.22738	−	29.4068i	0.205351	−	1.15521i
$649$		−	10.0282i		−	0.393641i
$650$	1.96508	+	3.91733i	0.0770769	+	0.153650i
$651$	32.3996			1.26984
$652$	19.3074	−	25.8842i	0.756136	−	1.01370i
$653$	29.3539			1.14871			0.574354	−	0.818607i	$-0.305253\pi$
$653$	29.3539			1.14871			0.574354	+	0.818607i	$0.305253\pi$
$654$	−12.3187	+	6.17951i	−0.481697	+	0.241638i
$655$	13.3354			0.521056
$656$	18.8355	−	5.60095i	0.735402	−	0.218680i
$657$			5.66733i			0.221103i
$658$	−10.9119	−	21.7525i	−0.425390	−	0.848001i
$659$		−	16.0983i		−	0.627101i	−0.949572	−	0.313550i	$-0.898482\pi$
$659$		−	16.0983i		−	0.627101i	0.949572	−	0.313550i	$-0.101518\pi$
$660$	−12.8729	+	17.2579i	−0.501078	+	0.671764i
$661$			15.2351i			0.592576i	0.955099	+	0.296288i	$0.0957489\pi$
$661$			15.2351i			0.592576i	−0.955099	+	0.296288i	$0.904251\pi$
$662$	2.67973	+	5.34196i	0.104151	+	0.207621i
$663$	−6.16839	−	23.6853i	−0.239560	−	0.919859i
$664$	48.6272	+	8.64401i	1.88710	+	0.335453i
$665$	−0.475597			−0.0184429
$666$	−0.949581	+	0.476347i	−0.0367955	+	0.0184581i
$667$		−	2.75525i		−	0.106684i
$668$	−12.8930	−	9.61709i	−0.498846	−	0.372096i
$669$	49.9066			1.92950
$670$	−8.39504	−	16.7352i	−0.324329	−	0.646539i
$671$	−56.4876			−2.18068
$672$	26.2887	−	24.6872i	1.01411	−	0.952329i
$673$		−	5.31067i		−	0.204711i	−0.994748	−	0.102356i	$-0.967362\pi$
$673$		−	5.31067i		−	0.204711i	0.994748	−	0.102356i	$-0.0326380\pi$
$674$	−11.4541	−	22.8333i	−0.441194	−	0.879506i
$675$	4.46462			0.171843
$676$	4.06154	−	5.44506i	0.156213	−	0.209425i
$677$	2.26823			0.0871750			0.0435875	−	0.999050i	$-0.486121\pi$
$677$	2.26823			0.0871750			0.0435875	+	0.999050i	$0.486121\pi$
$678$	−2.53840	−	5.06021i	−0.0974866	−	0.194336i
$679$	−15.5559			−0.596980
$680$	−0.918578	−	11.6257i	−0.0352258	−	0.445824i
$681$	16.4615			0.630806
$682$	−18.1111	−	36.1039i	−0.693511	−	1.38249i
$683$	−51.1235			−1.95619			−0.978093	−	0.208168i	$-0.933250\pi$
$683$	−51.1235			−1.95619			−0.978093	+	0.208168i	$0.933250\pi$
$684$	0.153320	+	0.114364i	0.00586235	+	0.00437281i
$685$	17.1243			0.654286
$686$	−6.16993	−	12.2995i	−0.235569	−	0.469599i
$687$			27.0814i			1.03322i
$688$	39.2250	−	11.6640i	1.49544	−	0.444686i
$689$	2.58308			0.0984076
$690$	−2.39686	−	4.77805i	−0.0912468	−	0.181897i
$691$	28.1607			1.07128			0.535641	−	0.844446i	$-0.320070\pi$
$691$	28.1607			1.07128			0.535641	+	0.844446i	$0.320070\pi$
$692$	−15.6655	+	21.0017i	−0.595512	+	0.798366i
$693$			12.5175i			0.475501i
$694$	−17.6529	+	8.85536i	−0.670094	+	0.336145i
$695$	−5.78874			−0.219579
$696$	1.32400	−	7.44822i	0.0501862	−	0.282324i
$697$	−5.10486	−	19.6016i	−0.193361	−	0.742462i
$698$	1.16463	+	2.32166i	0.0440820	+	0.0878761i
$699$			29.6254i			1.12053i
$700$	5.33545	+	3.97979i	0.201661	+	0.150422i
$701$		−	26.9833i		−	1.01914i	−0.860428	−	0.509572i	$-0.829804\pi$
$701$		−	26.9833i		−	1.01914i	0.860428	−	0.509572i	$-0.170196\pi$
$702$	8.77334	+	17.4894i	0.331128	+	0.660094i
$703$			0.160401i			0.00604964i
$704$	−42.2049	−	15.4944i	−1.59066	−	0.583966i
$705$	−9.90429			−0.373017
$706$	26.7589	−	13.4233i	1.00709	−	0.505193i
$707$	27.7418			1.04334
$708$	5.47966	+	4.08735i	0.205938	+	0.153612i
$709$	−7.08750			−0.266177			−0.133088	−	0.991104i	$-0.542489\pi$
$709$	−7.08750			−0.266177			−0.133088	+	0.991104i	$0.542489\pi$
$710$	−8.27623	−	16.4984i	−0.310601	−	0.619173i
$711$			9.08186i			0.340596i
$712$	−6.37374	+	35.8557i	−0.238866	+	1.34375i
$713$	10.0285			0.375572
$714$	−24.5038	−	27.9535i	−0.917031	−	1.04613i
$715$		−	17.4158i		−	0.651314i
$716$	33.9228	+	25.3035i	1.26776	+	0.945637i
$717$	−45.8666			−1.71292
$718$	24.6215	−	12.3511i	0.918866	−	0.460939i
$719$		−	14.5272i		−	0.541773i	−0.962611	−	0.270886i	$-0.912683\pi$
$719$		−	14.5272i		−	0.541773i	0.962611	−	0.270886i	$-0.0873168\pi$
$720$	−0.763019	−	2.56596i	−0.0284360	−	0.0956278i
$721$			19.3480i			0.720555i
$722$	−23.9917	+	12.0352i	−0.892880	+	0.447903i
$723$		−	33.5088i		−	1.24621i
$724$	1.70177	−	2.28146i	0.0632458	−	0.0847896i
$725$	1.39629			0.0518568
$726$	49.8400	−	25.0017i	1.84974	−	0.927900i
$727$	−41.7933			−1.55003			−0.775014	−	0.631944i	$-0.782257\pi$
$727$	−41.7933			−1.55003			−0.775014	+	0.631944i	$0.782257\pi$
$728$	−5.10553	+	28.7213i	−0.189223	+	1.06448i
$729$	18.5891			0.688485
$730$	−5.36976	−	10.7044i	−0.198744	−	0.396189i
$731$	−10.6309	−	40.8203i	−0.393198	−	1.50979i
$732$	23.0236	−	30.8663i	0.850976	−	1.14085i
$733$		−	17.6138i		−	0.650581i	−0.945614	−	0.325290i	$-0.894538\pi$
$733$		−	17.6138i		−	0.650581i	0.945614	−	0.325290i	$-0.105462\pi$
$734$	13.2196	+	26.3528i	0.487944	+	0.972700i
$735$	7.80851			0.288021
$736$	8.13705	−	7.64135i	0.299936	−	0.281664i
$737$			74.4021i			2.74064i
$738$	−2.08483	−	4.15605i	−0.0767438	−	0.152986i
$739$		−	28.9662i		−	1.06554i	−0.846261	−	0.532769i	$-0.821152\pi$
$739$		−	28.9662i		−	1.06554i	0.846261	−	0.532769i	$-0.178848\pi$
$740$	1.34223	−	1.79945i	0.0493414	−	0.0661489i
$741$	−0.848288			−0.0311626
$742$	3.50670	−	1.75910i	0.128735	−	0.0645784i
$743$		−	12.1438i		−	0.445511i	−0.974874	−	0.222756i	$-0.928495\pi$
$743$		−	12.1438i		−	0.445511i	0.974874	−	0.222756i	$-0.0715052\pi$
$744$	27.1100	+	4.81909i	0.993900	+	0.176677i
$745$		−	1.85859i		−	0.0680934i
$746$	7.18495	+	14.3230i	0.263060	+	0.524401i
$747$		−	11.6863i		−	0.427581i
$748$	−17.4521	+	42.9312i	−0.638112	+	1.56972i
$749$			4.14910i			0.151605i
$750$	2.42138	−	1.21466i	0.0884165	−	0.0443531i
$751$		−	31.9240i		−	1.16493i	−0.812858	−	0.582463i	$-0.802089\pi$
$751$		−	31.9240i		−	1.16493i	0.812858	−	0.582463i	$-0.197911\pi$
$752$	−5.89495	−	19.8242i	−0.214967	−	0.722914i
$753$			40.0007i			1.45771i
$754$	2.74382	+	5.46971i	0.0999240	+	0.199195i
$755$	−20.4111			−0.742835
$756$	23.8207	+	17.7682i	0.866352	+	0.646224i
$757$		−	47.0366i		−	1.70957i	−0.518979	−	0.854787i	$-0.673688\pi$
$757$		−	47.0366i		−	1.70957i	0.518979	−	0.854787i	$-0.326312\pi$
$758$	−22.9463	+	11.5108i	−0.833447	+	0.418089i
$759$			21.2424i			0.771052i
$760$	−0.397951	−	0.0707400i	−0.0144352	−	0.00256601i
$761$	4.54400			0.164720			0.0823600	−	0.996603i	$-0.473754\pi$
$761$	4.54400			0.164720			0.0823600	+	0.996603i	$0.473754\pi$
$762$	−28.1583	+	14.1253i	−1.02007	+	0.511705i
$763$		−	16.9316i		−	0.612967i
$764$	−22.4281	+	30.0680i	−0.811422	+	1.08782i
$765$	−2.67032	+	0.695437i	−0.0965457	+	0.0251436i
$766$	−33.0373	+	16.5728i	−1.19369	+	0.598799i
$767$	−5.52979			−0.199669
$768$	25.6687	−	16.7466i	0.926239	−	0.604289i
$769$	−32.6478			−1.17731			−0.588654	−	0.808385i	$-0.700342\pi$
$769$	−32.6478			−1.17731			−0.588654	+	0.808385i	$0.700342\pi$
$770$	−11.8603	−	23.6430i	−0.427414	−	0.852036i
$771$	1.00743			0.0362816
$772$	−34.7886	−	25.9493i	−1.25207	−	0.933936i
$773$			35.7216i			1.28482i	0.766362	+	0.642409i	$0.222065\pi$
$773$			35.7216i			1.28482i	−0.766362	+	0.642409i	$0.777935\pi$
$774$	−4.34168	−	8.65499i	−0.156058	−	0.311097i
$775$			5.08219i			0.182558i
$776$	−13.0162	−	2.31377i	−0.467255	−	0.0830596i
$777$		−	7.15577i		−	0.256712i
$778$	−13.0918	−	26.0980i	−0.469362	−	0.935658i
$779$	−0.702030			−0.0251528
$780$	9.51644	+	7.09845i	0.340743	+	0.254165i
$781$			73.3491i			2.62464i
$782$	−7.58458	−	8.65237i	−0.271224	−	0.309408i
$783$	6.23388			0.222781
$784$	4.64756	+	15.6293i	0.165984	+	0.558191i
$785$			12.9192i			0.461106i
$786$	32.2901	−	16.1979i	1.15175	−	0.577761i
$787$	−17.0668			−0.608367			−0.304183	−	0.952613i	$-0.598384\pi$
$787$	−17.0668			−0.608367			−0.304183	+	0.952613i	$0.598384\pi$
$788$	0.534100	−	0.716034i	0.0190265	−	0.0255077i
$789$	0.958387			0.0341195
$790$	−8.60501	−	17.1538i	−0.306153	−	0.610305i
$791$	6.95512			0.247296
$792$	−1.86185	+	10.4739i	−0.0661578	+	0.372173i
$793$			31.1486i			1.10612i
$794$	−30.8845	+	15.4929i	−1.09605	+	0.549821i
$795$		−	1.59666i		−	0.0566277i
$796$	1.28237	+	0.956535i	0.0454523	+	0.0339035i
$797$			17.1921i			0.608977i	0.952516	+	0.304488i	$0.0984855\pi$
$797$			17.1921i			0.608977i	−0.952516	+	0.304488i	$0.901515\pi$
$798$	−1.15160	+	0.577689i	−0.0407663	+	0.0204500i
$799$	−20.6305	+	5.37283i	−0.729853	+	0.190077i
$800$	3.87242	+	4.12363i	0.136911	+	0.145792i
$801$	8.61704			0.304468
$802$	24.3153	+	48.4717i	0.858603	+	1.71160i
$803$			47.5902i			1.67942i
$804$	−40.6553	−	30.3253i	−1.43380	−	1.06949i
$805$	6.56730			0.231467
$806$	−19.9086	+	9.98692i	−0.701251	+	0.351774i
$807$	−52.2946			−1.84086
$808$	23.2126	+	4.12630i	0.816618	+	0.145163i
$809$			9.72475i			0.341904i	0.985279	+	0.170952i	$0.0546843\pi$
$809$			9.72475i			0.341904i	−0.985279	+	0.170952i	$0.945316\pi$
$810$	13.3485	−	6.69613i	0.469019	−	0.235278i
$811$	27.5068			0.965894			0.482947	−	0.875649i	$-0.339566\pi$
$811$	27.5068			0.965894			0.482947	+	0.875649i	$0.339566\pi$
$812$	7.44981	+	5.55692i	0.261437	+	0.195010i
$813$	−10.6695			−0.374194
$814$	−7.97391	+	4.00002i	−0.279485	+	0.140201i
$815$	16.1460			0.565568
$816$	−16.3455	−	27.0345i	−0.572206	−	0.946395i
$817$	−1.46198			−0.0511482
$818$	−2.42807	+	1.21802i	−0.0848956	+	0.0425869i
$819$	6.90246			0.241192
$820$	7.87566	+	5.87457i	0.275030	+	0.205149i
$821$	26.8453			0.936909			0.468455	−	0.883488i	$-0.344811\pi$
$821$	26.8453			0.936909			0.468455	+	0.883488i	$0.344811\pi$
$822$	41.4645	−	20.8002i	1.44624	−	0.725491i
$823$		−	39.3390i		−	1.37127i	−0.727945	−	0.685635i	$-0.759525\pi$
$823$		−	39.3390i		−	1.37127i	0.727945	−	0.685635i	$-0.240475\pi$
$824$	−2.87780	+	16.1892i	−0.100253	+	0.563977i
$825$	−10.7651			−0.374792
$826$	−7.50704	+	3.76582i	−0.261203	+	0.131030i
$827$	27.5464			0.957884			0.478942	−	0.877847i	$-0.341020\pi$
$827$	27.5464			0.957884			0.478942	+	0.877847i	$0.341020\pi$
$828$	−2.11713	−	1.57920i	−0.0735754	−	0.0548809i
$829$			9.24546i			0.321108i	0.987027	+	0.160554i	$0.0513281\pi$
$829$			9.24546i			0.321108i	−0.987027	+	0.160554i	$0.948672\pi$
$830$	11.0727	+	22.0732i	0.384341	+	0.766170i
$831$	5.32372			0.184678
$832$	−8.54398	+	23.2728i	−0.296209	+	0.806840i
$833$	16.2650	−	4.23592i	0.563549	−	0.146766i
$834$	−14.0168	+	7.03135i	−0.485361	+	0.243476i
$835$		−	8.04236i		−	0.278317i
$836$	1.28748	+	0.960347i	0.0445283	+	0.0332143i
$837$			22.6900i			0.784282i
$838$	18.8316	−	9.44668i	0.650528	−	0.326330i
$839$		−	9.90610i		−	0.341997i	−0.985271	−	0.170998i	$-0.945301\pi$
$839$		−	9.90610i		−	0.341997i	0.985271	−	0.170998i	$-0.0546993\pi$
$840$	17.7533	+	3.15584i	0.612546	+	0.108887i
$841$	−27.0504			−0.932772
$842$	−2.98878	−	5.95803i	−0.103000	−	0.205327i
$843$	11.0980			0.382237
$844$	3.04361	−	4.08038i	0.104765	−	0.140452i
$845$	3.39650			0.116843
$846$	−4.37420	+	2.19427i	−0.150388	+	0.0754405i
$847$			68.5037i			2.35382i
$848$	3.19584	−	0.950319i	0.109745	−	0.0326341i
$849$	−5.15743			−0.177003
$850$	4.38478	−	3.84366i	0.150397	−	0.131836i
$851$		−	2.21490i		−	0.0759259i
$852$	−40.0799	−	29.8961i	−1.37311	−	1.02422i
$853$	−34.4721			−1.18030			−0.590151	−	0.807293i	$-0.700932\pi$
$853$	−34.4721			−1.18030			−0.590151	+	0.807293i	$0.700932\pi$
$854$	21.2124	+	42.2862i	0.725874	+	1.44701i
$855$			0.0956376i			0.00327074i
$856$	−0.617134	+	3.47171i	−0.0210932	+	0.118661i
$857$			36.4740i			1.24593i	0.782251	+	0.622963i	$0.214071\pi$
$857$			36.4740i			1.24593i	−0.782251	+	0.622963i	$0.785929\pi$
$858$	−21.1543	−	42.1703i	−0.722195	−	1.43967i
$859$		−	26.3038i		−	0.897475i	−0.893664	−	0.448738i	$-0.851874\pi$
$859$		−	26.3038i		−	0.897475i	0.893664	−	0.448738i	$-0.148126\pi$
$860$	16.4011	+	12.2338i	0.559273	+	0.417170i
$861$	31.3188			1.06734
$862$	−2.80319	−	5.58807i	−0.0954771	−	0.190330i
$863$	11.9283			0.406044			0.203022	−	0.979174i	$-0.434924\pi$
$863$	11.9283			0.406044			0.203022	+	0.979174i	$0.434924\pi$
$864$	17.2889	+	18.4104i	0.588180	+	0.626336i
$865$	−13.1004			−0.445426
$866$	−4.34753	+	2.18089i	−0.147735	+	0.0741097i
$867$	−28.4273	+	15.8841i	−0.965441	+	0.539451i
$868$	−20.2260	+	27.1158i	−0.686516	+	0.920369i
$869$			76.2630i			2.58705i
$870$	3.38095	−	1.69601i	0.114625	−	0.0575002i
$871$	41.0272			1.39015
$872$	2.51840	−	14.1674i	0.0852839	−	0.479767i
$873$			3.12813i			0.105871i
$874$	−0.356453	+	0.178810i	−0.0120572	+	0.00604835i
$875$			3.32813i			0.112511i
$876$	−26.0045	−	19.3971i	−0.878611	−	0.655368i
$877$	−42.4524			−1.43352			−0.716759	−	0.697321i	$-0.754375\pi$
$877$	−42.4524			−1.43352			−0.716759	+	0.697321i	$0.754375\pi$
$878$	10.9564	+	21.8411i	0.369759	+	0.737103i
$879$			18.5974i			0.627276i
$880$	−6.40729	−	21.5471i	−0.215990	−	0.726354i
$881$		−	12.5082i		−	0.421413i	−0.977549	−	0.210707i	$-0.932423\pi$
$881$		−	12.5082i		−	0.421413i	0.977549	−	0.210707i	$-0.0675765\pi$
$882$	3.44861	−	1.72996i	0.116121	−	0.0582506i
$883$			54.1517i			1.82235i	0.412021	+	0.911174i	$0.364823\pi$
$883$			54.1517i			1.82235i	−0.412021	+	0.911174i	$0.635177\pi$
$884$	23.6733	+	9.62352i	0.796220	+	0.323674i
$885$			3.41808i			0.114898i
$886$	−14.2127	−	28.3325i	−0.477485	−	0.951850i
$887$			10.2928i			0.345597i	0.984957	+	0.172798i	$0.0552809\pi$
$887$			10.2928i			0.345597i	−0.984957	+	0.172798i	$0.944719\pi$
$888$	1.06434	−	5.98751i	0.0357171	−	0.200928i
$889$		−	38.7028i		−	1.29805i
$890$	−16.2758	+	8.16460i	−0.545568	+	0.273678i
$891$	−59.3453			−1.98814
$892$	−31.1551	+	41.7677i	−1.04315	+	1.39849i
$893$			0.738880i			0.0247257i
$894$	−2.25755	−	4.50036i	−0.0755039	−	0.150515i
$895$			21.1603i			0.707310i
$896$	4.24995	+	37.4128i	0.141981	+	1.24988i
$897$	11.7136			0.391106
$898$	−8.40643	−	16.7579i	−0.280526	−	0.559219i
$899$			7.09619i			0.236671i
$900$	0.800293	−	1.07290i	0.0266764	−	0.0357634i
$901$	−0.866147	−	3.32581i	−0.0288555	−	0.110799i
$902$	−17.5070	−	34.8995i	−0.582918	−	1.16203i
$903$	65.2215			2.17043
$904$	5.81962	+	1.03450i	0.193558	+	0.0344070i
$905$	1.42312			0.0473060
$906$	−49.4231	+	24.7925i	−1.64197	+	0.823676i
$907$	−25.5730			−0.849139			−0.424570	−	0.905395i	$-0.639575\pi$
$907$	−25.5730			−0.849139			−0.424570	+	0.905395i	$0.639575\pi$
$908$	−10.2764	+	13.7769i	−0.341034	+	0.457203i
$909$		−	5.57859i		−	0.185030i
$910$	−13.0374	+	6.54004i	−0.432184	+	0.216800i
$911$		−	54.8104i		−	1.81595i	−0.419024	−	0.907975i	$-0.637628\pi$
$911$		−	54.8104i		−	1.81595i	0.419024	−	0.907975i	$-0.362372\pi$
$912$	−1.04952	+	0.312086i	−0.0347530	+	0.0103342i
$913$		−	98.1337i		−	3.24775i
$914$	−25.5532	+	12.8185i	−0.845226	+	0.423998i
$915$	19.2536			0.636506
$916$	−22.6649	−	16.9061i	−0.748870	−	0.558593i
$917$			44.3818i			1.46562i
$918$	19.5764	−	17.1605i	0.646116	−	0.566379i
$919$	−49.1629			−1.62173			−0.810867	−	0.585230i	$-0.801004\pi$
$919$	−49.1629			−1.62173			−0.810867	+	0.585230i	$0.801004\pi$
$920$	5.49512	+	0.976817i	0.181169	+	0.0322047i
$921$			61.1524i			2.01504i
$922$	26.1542	+	52.1375i	0.861341	+	1.71706i
$923$	40.4465			1.33131
$924$	−57.4365	−	42.8427i	−1.88952	−	1.40942i
$925$	1.12245			0.0369060
$926$	−38.8076	+	19.4674i	−1.27530	+	0.639739i
$927$	3.89067			0.127786
$928$	5.40701	+	5.75777i	0.177494	+	0.189008i
$929$			4.73083i			0.155213i	0.996984	+	0.0776067i	$0.0247278\pi$
$929$			4.73083i			0.155213i	−0.996984	+	0.0776067i	$0.975272\pi$
$930$	6.17313	+	12.3059i	0.202425	+	0.403528i
$931$		−	0.582531i		−	0.0190917i
$932$	−24.7940	−	18.4942i	−0.812154	−	0.605797i
$933$		−	51.4673i		−	1.68497i
$934$	−3.53179	−	7.04051i	−0.115564	−	0.230373i
$935$	−22.4235	+	5.83978i	−0.733326	+	0.190981i
$936$	5.77556	+	1.02667i	0.188780	+	0.0335577i
$937$	25.4046			0.829933			0.414966	−	0.909837i	$-0.363793\pi$
$937$	25.4046			0.829933			0.414966	+	0.909837i	$0.363793\pi$
$938$	55.6970	−	27.9398i	1.81857	−	0.912266i
$939$			54.1474i			1.76703i
$940$	6.18293	−	8.28907i	0.201665	−	0.270360i
$941$	−24.7856			−0.807988			−0.403994	−	0.914762i	$-0.632378\pi$
$941$	−24.7856			−0.807988			−0.403994	+	0.914762i	$0.632378\pi$
$942$	15.6924	+	31.2823i	0.511287	+	1.01923i
$943$	9.69401			0.315680
$944$	−6.84155	+	2.03441i	−0.222674	+	0.0662146i
$945$			14.8588i			0.483357i
$946$	−36.4583	−	72.6785i	−1.18536	−	2.36298i
$947$	17.4224			0.566154			0.283077	−	0.959097i	$-0.408645\pi$
$947$	17.4224			0.566154			0.283077	+	0.959097i	$0.408645\pi$
$948$	−41.6721	−	31.0838i	−1.35345	−	1.00955i
$949$	26.2424			0.851865
$950$	−0.0906161	−	0.180640i	−0.00293998	−	0.00586074i
$951$	15.5001			0.502624
$952$	38.6917	−	3.05714i	1.25401	−	0.0990826i
$953$	37.0229			1.19929			0.599644	−	0.800267i	$-0.295309\pi$
$953$	37.0229			1.19929			0.599644	+	0.800267i	$0.295309\pi$
$954$	−0.353736	−	0.705160i	−0.0114526	−	0.0228304i
$955$	−18.7557			−0.606920
$956$	28.6330	−	38.3865i	0.926058	−	1.24151i
$957$	−15.0311			−0.485888
$958$	19.6022	+	39.0764i	0.633319	+	1.26250i
$959$			56.9919i			1.84036i
$960$	14.3854	+	5.28122i	0.464288	+	0.170451i
$961$	5.17135			0.166818
$962$	2.20571	+	4.39701i	0.0711150	+	0.141765i
$963$	0.834340			0.0268862
$964$	28.0441	+	20.9185i	0.903240	+	0.673740i
$965$		−	21.7003i		−	0.698558i
$966$	15.9020	−	7.97704i	0.511637	−	0.256657i
$967$	43.1977			1.38915			0.694573	−	0.719423i	$-0.255593\pi$
$967$	43.1977			1.38915			0.694573	+	0.719423i	$0.255593\pi$
$968$	−10.1892	+	57.3197i	−0.327493	+	1.84233i
$969$	0.284444	+	1.09220i	0.00913765	+	0.0350866i
$970$	−2.96388	−	5.90840i	−0.0951645	−	0.189707i
$971$		−	15.7513i		−	0.505482i	−0.967534	−	0.252741i	$-0.918668\pi$
$971$		−	15.7513i		−	0.505482i	0.967534	−	0.252741i	$-0.0813321\pi$
$972$	8.17196	−	10.9556i	0.262116	−	0.351402i
$973$		−	19.2657i		−	0.617628i
$974$	−20.5463	−	40.9584i	−0.658346	−	1.31239i
$975$			5.93613i			0.190108i
$976$	11.4596	+	38.5376i	0.366813	+	1.23356i
$977$	20.3273			0.650326			0.325163	−	0.945658i	$-0.394581\pi$
$977$	20.3273			0.650326			0.325163	+	0.945658i	$0.394581\pi$
$978$	39.0956	−	19.6119i	1.25014	−	0.627118i
$979$	72.3598			2.31263
$980$	−4.87461	+	6.53508i	−0.155714	+	0.208755i
$981$	−3.40478			−0.108706
$982$	1.12079	+	2.23425i	0.0357657	+	0.0712977i
$983$		−	10.3559i		−	0.330303i	−0.986268	−	0.165152i	$-0.947189\pi$
$983$		−	10.3559i		−	0.330303i	0.986268	−	0.165152i	$-0.0528113\pi$
$984$	26.2056	+	4.65833i	0.835404	+	0.148502i
$985$	0.446645			0.0142313
$986$	6.12241	−	5.36684i	0.194977	−	0.170915i
$987$		−	32.9627i		−	1.04921i
$988$	0.529559	−	0.709946i	0.0168475	−	0.0225864i
$989$	20.1878			0.641935
$990$	−4.75437	+	2.38498i	−0.151104	+	0.0757995i
$991$			55.8294i			1.77348i	0.462268	+	0.886740i	$0.347036\pi$
$991$			55.8294i			1.77348i	−0.462268	+	0.886740i	$0.652964\pi$
$992$	−20.9571	+	19.6804i	−0.665388	+	0.624853i
$993$			8.09495i			0.256886i
$994$	54.9087	−	27.5443i	1.74160	−	0.873653i
$995$			0.799910i			0.0253588i
$996$	53.6228	+	39.9980i	1.69910	+	1.26738i
$997$	−14.3259			−0.453706			−0.226853	−	0.973929i	$-0.572844\pi$
$997$	−14.3259			−0.453706			−0.226853	+	0.973929i	$0.572844\pi$
$998$	−23.9066	+	11.9925i	−0.756750	+	0.379615i
$999$	5.01132			0.158551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.l.a.101.8	yes	36
4.3	odd	2		2720.2.l.b.2481.28		36
8.3	odd	2		2720.2.l.a.2481.10		36
8.5	even	2		680.2.l.b.101.7	yes	36
17.16	even	2		680.2.l.b.101.8	yes	36
68.67	odd	2		2720.2.l.a.2481.9		36
136.67	odd	2		2720.2.l.b.2481.27		36
136.101	even	2	inner	680.2.l.a.101.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.l.a.101.7	✓	36	136.101	even	2	inner
680.2.l.a.101.8	yes	36	1.1	even	1	trivial
680.2.l.b.101.7	yes	36	8.5	even	2
680.2.l.b.101.8	yes	36	17.16	even	2
2720.2.l.a.2481.9		36	68.67	odd	2
2720.2.l.a.2481.10		36	8.3	odd	2
2720.2.l.b.2481.27		36	136.67	odd	2
2720.2.l.b.2481.28		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+(-1.26408 + 0.634112i) q^{2} -1.91553 q^{3} +(1.19580 - 1.60314i) q^{4} +1.00000 q^{5} +(2.42138 - 1.21466i) q^{6} +3.32813i q^{7} +(-0.495023 + 2.78477i) q^{8} +0.669252 q^{9} +(-1.26408 + 0.634112i) q^{10} +5.61990 q^{11} +(-2.29060 + 3.07086i) q^{12} -3.09895i q^{13} +(-2.11041 - 4.20702i) q^{14} -1.91553 q^{15} +(-1.14011 - 3.83408i) q^{16} +(-3.99001 + 1.03913i) q^{17} +(-0.845988 + 0.424380i) q^{18} +0.142902i q^{19} +(1.19580 - 1.60314i) q^{20} -6.37512i q^{21} +(-7.10401 + 3.56365i) q^{22} -1.97327i q^{23} +(0.948232 - 5.33431i) q^{24} +1.00000 q^{25} +(1.96508 + 3.91733i) q^{26} +4.46462 q^{27} +(5.33545 + 3.97979i) q^{28} +1.39629 q^{29} +(2.42138 - 1.21466i) q^{30} +5.08219i q^{31} +(3.87242 + 4.12363i) q^{32} -10.7651 q^{33} +(4.38478 - 3.84366i) q^{34} +3.32813i q^{35} +(0.800293 - 1.07290i) q^{36} +1.12245 q^{37} +(-0.0906161 - 0.180640i) q^{38} +5.93613i q^{39} +(-0.495023 + 2.78477i) q^{40} +4.91265i q^{41} +(4.04254 + 8.05867i) q^{42} +10.2306i q^{43} +(6.72030 - 9.00948i) q^{44} +0.669252 q^{45} +(1.25128 + 2.49438i) q^{46} +5.17052 q^{47} +(2.18391 + 7.34429i) q^{48} -4.07643 q^{49} +(-1.26408 + 0.634112i) q^{50} +(7.64299 - 1.99048i) q^{51} +(-4.96805 - 3.70574i) q^{52} +0.833534i q^{53} +(-5.64364 + 2.83107i) q^{54} +5.61990 q^{55} +(-9.26807 - 1.64750i) q^{56} -0.273734i q^{57} +(-1.76502 + 0.885402i) q^{58} -1.78441i q^{59} +(-2.29060 + 3.07086i) q^{60} -10.0513 q^{61} +(-3.22268 - 6.42430i) q^{62} +2.22735i q^{63} +(-7.50990 - 2.75705i) q^{64} -3.09895i q^{65} +(13.6079 - 6.82627i) q^{66} +13.2391i q^{67} +(-3.10541 + 7.63914i) q^{68} +3.77986i q^{69} +(-2.11041 - 4.20702i) q^{70} +13.0517i q^{71} +(-0.331295 + 1.86371i) q^{72} +8.46816i q^{73} +(-1.41887 + 0.711760i) q^{74} -1.91553 q^{75} +(0.229092 + 0.170883i) q^{76} +18.7037i q^{77} +(-3.76417 - 7.50375i) q^{78} +13.5702i q^{79} +(-1.14011 - 3.83408i) q^{80} -10.5599 q^{81} +(-3.11517 - 6.20999i) q^{82} -17.4618i q^{83} +(-10.2202 - 7.62340i) q^{84} +(-3.99001 + 1.03913i) q^{85} +(-6.48736 - 12.9323i) q^{86} -2.67463 q^{87} +(-2.78198 + 15.6501i) q^{88} +12.8756 q^{89} +(-0.845988 + 0.424380i) q^{90} +10.3137 q^{91} +(-3.16343 - 2.35965i) q^{92} -9.73508i q^{93} +(-6.53596 + 3.27869i) q^{94} +0.142902i q^{95} +(-7.41774 - 7.89894i) q^{96} +4.67407i q^{97} +(5.15293 - 2.58491i) q^{98} +3.76113 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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