LMFDB - Embedded newform 728.2.c.b.365.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(365,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.365"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			365.19
Character	$\chi$	$=$	728.365
Dual form			728.2.c.b.365.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.242210 - 1.39332i) q^{2} +1.67830i q^{3} +(-1.88267 - 0.674950i) q^{4} +0.0254406i q^{5} +(2.33840 + 0.406500i) q^{6} +1.00000 q^{7} +(-1.39642 + 2.45968i) q^{8} +0.183319 q^{9} +(0.0354469 + 0.00616197i) q^{10} -3.21140i q^{11} +(1.13277 - 3.15968i) q^{12} -1.00000i q^{13} +(0.242210 - 1.39332i) q^{14} -0.0426969 q^{15} +(3.08889 + 2.54141i) q^{16} -0.473318 q^{17} +(0.0444017 - 0.255422i) q^{18} +3.69649i q^{19} +(0.0171712 - 0.0478963i) q^{20} +1.67830i q^{21} +(-4.47451 - 0.777832i) q^{22} +8.57943 q^{23} +(-4.12807 - 2.34361i) q^{24} +4.99935 q^{25} +(-1.39332 - 0.242210i) q^{26} +5.34256i q^{27} +(-1.88267 - 0.674950i) q^{28} -0.111981i q^{29} +(-0.0103416 + 0.0594904i) q^{30} +10.1148 q^{31} +(4.28915 - 3.68825i) q^{32} +5.38969 q^{33} +(-0.114642 + 0.659482i) q^{34} +0.0254406i q^{35} +(-0.345130 - 0.123731i) q^{36} +3.46435i q^{37} +(5.15038 + 0.895325i) q^{38} +1.67830 q^{39} +(-0.0625758 - 0.0355258i) q^{40} -5.45411 q^{41} +(2.33840 + 0.406500i) q^{42} -3.24219i q^{43} +(-2.16754 + 6.04601i) q^{44} +0.00466376i q^{45} +(2.07802 - 11.9539i) q^{46} -2.96799 q^{47} +(-4.26525 + 5.18407i) q^{48} +1.00000 q^{49} +(1.21089 - 6.96569i) q^{50} -0.794368i q^{51} +(-0.674950 + 1.88267i) q^{52} -13.1311i q^{53} +(7.44388 + 1.29402i) q^{54} +0.0817001 q^{55} +(-1.39642 + 2.45968i) q^{56} -6.20380 q^{57} +(-0.156025 - 0.0271229i) q^{58} +7.78767i q^{59} +(0.0803842 + 0.0288183i) q^{60} -6.75418i q^{61} +(2.44990 - 14.0931i) q^{62} +0.183319 q^{63} +(-4.10002 - 6.86948i) q^{64} +0.0254406 q^{65} +(1.30543 - 7.50955i) q^{66} +0.435241i q^{67} +(0.891101 + 0.319466i) q^{68} +14.3988i q^{69} +(0.0354469 + 0.00616197i) q^{70} +13.7539 q^{71} +(-0.255991 + 0.450906i) q^{72} -5.15501 q^{73} +(4.82695 + 0.839099i) q^{74} +8.39040i q^{75} +(2.49494 - 6.95926i) q^{76} -3.21140i q^{77} +(0.406500 - 2.33840i) q^{78} -9.86060 q^{79} +(-0.0646552 + 0.0785832i) q^{80} -8.41644 q^{81} +(-1.32104 + 7.59930i) q^{82} +12.9619i q^{83} +(1.13277 - 3.15968i) q^{84} -0.0120415i q^{85} +(-4.51740 - 0.785289i) q^{86} +0.187937 q^{87} +(7.89902 + 4.48447i) q^{88} -0.369066 q^{89} +(0.00649810 + 0.00112961i) q^{90} -1.00000i q^{91} +(-16.1522 - 5.79069i) q^{92} +16.9756i q^{93} +(-0.718876 + 4.13535i) q^{94} -0.0940410 q^{95} +(6.18997 + 7.19848i) q^{96} -10.3643 q^{97} +(0.242210 - 1.39332i) q^{98} -0.588712i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{4} + 14 q^{6} + 38 q^{7} - 6 q^{8} - 46 q^{9} - 4 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 4 q^{18} - 24 q^{20} + 10 q^{22} + 12 q^{23} + 10 q^{24} - 50 q^{25} + 8 q^{28} + 4 q^{30} + 16 q^{31}+ \cdots + 82 q^{96}+O(q^{100}) $ 38 * q + 8 * q^4 + 14 * q^6 + 38 * q^7 - 6 * q^8 - 46 * q^9 - 4 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 4 * q^18 - 24 * q^20 + 10 * q^22 + 12 * q^23 + 10 * q^24 - 50 * q^25 + 8 * q^28 + 4 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 - 4 * q^34 - 38 * q^36 - 28 * q^38 + 8 * q^39 + 4 * q^40 + 8 * q^41 + 14 * q^42 - 40 * q^44 - 16 * q^46 + 4 * q^48 + 38 * q^49 + 24 * q^50 - 4 * q^52 - 14 * q^54 - 6 * q^56 + 8 * q^57 - 24 * q^58 + 44 * q^60 - 12 * q^62 - 46 * q^63 + 32 * q^64 + 20 * q^65 - 76 * q^66 - 52 * q^68 + 42 * q^72 + 50 * q^74 - 28 * q^76 - 12 * q^79 - 16 * q^80 + 62 * q^81 - 4 * q^84 + 44 * q^86 - 56 * q^87 - 6 * q^88 + 48 * q^90 + 2 * q^92 - 48 * q^94 + 82 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.242210	−	1.39332i	0.171268	−	0.985224i
$2$	0.242210	−	1.39332i	0.171268	−	0.985224i
$3$			1.67830i			0.968965i	0.874801	+	0.484483i	$0.160992\pi$
$3$			1.67830i			0.968965i	−0.874801	+	0.484483i	$0.839008\pi$
$4$	−1.88267	−	0.674950i	−0.941335	−	0.337475i
$5$			0.0254406i			0.0113774i	0.999984	+	0.00568870i	$0.00181078\pi$
$5$			0.0254406i			0.0113774i	−0.999984	+	0.00568870i	$0.998189\pi$
$6$	2.33840	+	0.406500i	0.954648	+	0.165953i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.39642	+	2.45968i	−0.493709	+	0.869627i
$9$	0.183319			0.0611065
$10$	0.0354469	+	0.00616197i	0.0112093	+	0.00194858i
$11$		−	3.21140i		−	0.968275i	−0.874992	−	0.484137i	$-0.839134\pi$
$11$		−	3.21140i		−	0.968275i	0.874992	−	0.484137i	$-0.160866\pi$
$12$	1.13277	−	3.15968i	0.327001	−	0.912120i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	0.242210	−	1.39332i	0.0647332	−	0.372380i
$15$	−0.0426969			−0.0110243
$16$	3.08889	+	2.54141i	0.772221	+	0.635353i
$17$	−0.473318			−0.114796			−0.0573982	−	0.998351i	$-0.518280\pi$
$17$	−0.473318			−0.114796			−0.0573982	+	0.998351i	$0.518280\pi$
$18$	0.0444017	−	0.255422i	0.0104656	−	0.0602036i
$19$			3.69649i			0.848032i	0.905655	+	0.424016i	$0.139380\pi$
$19$			3.69649i			0.848032i	−0.905655	+	0.424016i	$0.860620\pi$
$20$	0.0171712	−	0.0478963i	0.00383959	−	0.0107099i
$21$			1.67830i			0.366234i
$22$	−4.47451	−	0.777832i	−0.953968	−	0.165834i
$23$	8.57943			1.78894			0.894468	−	0.447132i	$-0.147555\pi$
$23$	8.57943			1.78894			0.894468	+	0.447132i	$0.147555\pi$
$24$	−4.12807	−	2.34361i	−0.842638	−	0.478387i
$25$	4.99935			0.999871
$26$	−1.39332	−	0.242210i	−0.273252	−	0.0475012i
$27$			5.34256i			1.02818i
$28$	−1.88267	−	0.674950i	−0.355791	−	0.127554i
$29$		−	0.111981i		−	0.0207944i	−0.999946	−	0.0103972i	$-0.996690\pi$
$29$		−	0.111981i		−	0.0207944i	0.999946	−	0.0103972i	$-0.00330958\pi$
$30$	−0.0103416	+	0.0594904i	−0.00188811	+	0.0108614i
$31$	10.1148			1.81667			0.908335	−	0.418244i	$-0.137354\pi$
$31$	10.1148			1.81667			0.908335	+	0.418244i	$0.137354\pi$
$32$	4.28915	−	3.68825i	0.758223	−	0.651996i
$33$	5.38969			0.938224
$34$	−0.114642	+	0.659482i	−0.0196610	+	0.113100i
$35$			0.0254406i			0.00430025i
$36$	−0.345130	−	0.123731i	−0.0575216	−	0.0206219i
$37$			3.46435i			0.569536i	0.958596	+	0.284768i	$0.0919166\pi$
$37$			3.46435i			0.569536i	−0.958596	+	0.284768i	$0.908083\pi$
$38$	5.15038	+	0.895325i	0.835502	+	0.145241i
$39$	1.67830			0.268743
$40$	−0.0625758	−	0.0355258i	−0.00989410	−	0.00561712i
$41$	−5.45411			−0.851788			−0.425894	−	0.904773i	$-0.640040\pi$
$41$	−5.45411			−0.851788			−0.425894	+	0.904773i	$0.640040\pi$
$42$	2.33840	+	0.406500i	0.360823	+	0.0627242i
$43$		−	3.24219i		−	0.494429i	−0.968961	−	0.247215i	$-0.920485\pi$
$43$		−	3.24219i		−	0.494429i	0.968961	−	0.247215i	$-0.0795152\pi$
$44$	−2.16754	+	6.04601i	−0.326768	+	0.911470i
$45$			0.00466376i			0.000695233i
$46$	2.07802	−	11.9539i	0.306387	−	1.76250i
$47$	−2.96799			−0.432926			−0.216463	−	0.976291i	$-0.569452\pi$
$47$	−2.96799			−0.432926			−0.216463	+	0.976291i	$0.569452\pi$
$48$	−4.26525	+	5.18407i	−0.615635	+	0.748256i
$49$	1.00000			0.142857
$50$	1.21089	−	6.96569i	0.171246	−	0.985097i
$51$		−	0.794368i		−	0.111234i
$52$	−0.674950	+	1.88267i	−0.0935987	+	0.261079i
$53$		−	13.1311i		−	1.80369i	−0.432057	−	0.901846i	$-0.642212\pi$
$53$		−	13.1311i		−	1.80369i	0.432057	−	0.901846i	$-0.357788\pi$
$54$	7.44388	+	1.29402i	1.01298	+	0.176094i
$55$	0.0817001			0.0110164
$56$	−1.39642	+	2.45968i	−0.186604	+	0.328688i
$57$	−6.20380			−0.821714
$58$	−0.156025	−	0.0271229i	−0.0204871	−	0.00356141i
$59$			7.78767i			1.01387i	0.861985	+	0.506934i	$0.169221\pi$
$59$			7.78767i			1.01387i	−0.861985	+	0.506934i	$0.830779\pi$
$60$	0.0803842	+	0.0288183i	0.0103776	+	0.00372043i
$61$		−	6.75418i		−	0.864784i	−0.901686	−	0.432392i	$-0.857670\pi$
$61$		−	6.75418i		−	0.864784i	0.901686	−	0.432392i	$-0.142330\pi$
$62$	2.44990	−	14.0931i	0.311137	−	1.78983i
$63$	0.183319			0.0230961
$64$	−4.10002	−	6.86948i	−0.512503	−	0.858685i
$65$	0.0254406			0.00315552
$66$	1.30543	−	7.50955i	0.160688	−	0.924362i
$67$			0.435241i			0.0531732i	0.999647	+	0.0265866i	$0.00846377\pi$
$67$			0.435241i			0.0531732i	−0.999647	+	0.0265866i	$0.991536\pi$
$68$	0.891101	+	0.319466i	0.108062	+	0.0387409i
$69$			14.3988i			1.73342i
$70$	0.0354469	+	0.00616197i	0.00423671	+	0.000736496i
$71$	13.7539			1.63229			0.816144	−	0.577849i	$-0.196108\pi$
$71$	13.7539			1.63229			0.816144	+	0.577849i	$0.196108\pi$
$72$	−0.255991	+	0.450906i	−0.0301688	+	0.0531398i
$73$	−5.15501			−0.603349			−0.301674	−	0.953411i	$-0.597546\pi$
$73$	−5.15501			−0.603349			−0.301674	+	0.953411i	$0.597546\pi$
$74$	4.82695	+	0.839099i	0.561121	+	0.0975433i
$75$			8.39040i			0.968840i
$76$	2.49494	−	6.95926i	0.286190	−	0.798282i
$77$		−	3.21140i		−	0.365973i
$78$	0.406500	−	2.33840i	0.0460270	−	0.264772i
$79$	−9.86060			−1.10940			−0.554702	−	0.832049i	$-0.687168\pi$
$79$	−9.86060			−1.10940			−0.554702	+	0.832049i	$0.687168\pi$
$80$	−0.0646552	+	0.0785832i	−0.00722867	+	0.00878587i
$81$	−8.41644			−0.935160
$82$	−1.32104	+	7.59930i	−0.145884	+	0.839203i
$83$			12.9619i			1.42276i	0.702810	+	0.711378i	$0.251928\pi$
$83$			12.9619i			1.42276i	−0.702810	+	0.711378i	$0.748072\pi$
$84$	1.13277	−	3.15968i	0.123595	−	0.344749i
$85$		−	0.0120415i		−	0.00130608i
$86$	−4.51740	−	0.785289i	−0.487124	−	0.0846799i
$87$	0.187937			0.0201490
$88$	7.89902	+	4.48447i	0.842038	+	0.478046i
$89$	−0.369066			−0.0391210			−0.0195605	−	0.999809i	$-0.506227\pi$
$89$	−0.369066			−0.0391210			−0.0195605	+	0.999809i	$0.506227\pi$
$90$	0.00649810	+	0.00112961i	0.000684960	+	0.000119071i
$91$		−	1.00000i		−	0.104828i
$92$	−16.1522	−	5.79069i	−1.68399	−	0.603721i
$93$			16.9756i			1.76029i
$94$	−0.718876	+	4.13535i	−0.0741464	+	0.426529i
$95$	−0.0940410			−0.00964840
$96$	6.18997	+	7.19848i	0.631761	+	0.734691i
$97$	−10.3643			−1.05234			−0.526169	−	0.850380i	$-0.676372\pi$
$97$	−10.3643			−1.05234			−0.526169	+	0.850380i	$0.676372\pi$
$98$	0.242210	−	1.39332i	0.0244669	−	0.140746i
$99$		−	0.588712i		−	0.0591678i
$100$	−9.41213	−	3.37431i	−0.941213	−	0.337431i
$101$		−	2.45098i		−	0.243881i	−0.992537	−	0.121941i	$-0.961088\pi$
$101$		−	2.45098i		−	0.243881i	0.992537	−	0.121941i	$-0.0389117\pi$
$102$	−1.10681	−	0.192403i	−0.109590	−	0.0190508i
$103$	15.4665			1.52396			0.761980	−	0.647601i	$-0.224228\pi$
$103$	15.4665			1.52396			0.761980	+	0.647601i	$0.224228\pi$
$104$	2.45968	+	1.39642i	0.241191	+	0.136930i
$105$	−0.0426969			−0.00416680
$106$	−18.2958	−	3.18047i	−1.77704	−	0.308915i
$107$		−	9.14887i		−	0.884454i	−0.896903	−	0.442227i	$-0.854189\pi$
$107$		−	9.14887i		−	0.884454i	0.896903	−	0.442227i	$-0.145811\pi$
$108$	3.60596	−	10.0583i	0.346983	−	0.967857i
$109$			10.9192i			1.04587i	0.852372	+	0.522936i	$0.175163\pi$
$109$			10.9192i			1.04587i	−0.852372	+	0.522936i	$0.824837\pi$
$110$	0.0197886	−	0.113834i	0.00188676	−	0.0108537i
$111$	−5.81421			−0.551861
$112$	3.08889	+	2.54141i	0.291872	+	0.240141i
$113$	−16.9502			−1.59454			−0.797271	−	0.603622i	$-0.793724\pi$
$113$	−16.9502			−1.59454			−0.797271	+	0.603622i	$0.793724\pi$
$114$	−1.50262	+	8.64387i	−0.140733	+	0.809573i
$115$			0.218266i			0.0203534i
$116$	−0.0755816	+	0.210823i	−0.00701757	+	0.0195744i
$117$		−	0.183319i		−	0.0169479i
$118$	10.8507	+	1.88625i	0.998888	+	0.173643i
$119$	−0.473318			−0.0433890
$120$	0.0596229	−	0.105021i	0.00544280	−	0.00958703i
$121$	0.686889			0.0624445
$122$	−9.41072	−	1.63593i	−0.852006	−	0.148110i
$123$		−	9.15361i		−	0.825353i
$124$	−19.0428	−	6.82697i	−1.71009	−	0.613080i
$125$			0.254390i			0.0227533i
$126$	0.0444017	−	0.255422i	0.00395562	−	0.0227548i
$127$	−14.1685			−1.25725			−0.628625	−	0.777709i	$-0.716382\pi$
$127$	−14.1685			−1.25725			−0.628625	+	0.777709i	$0.716382\pi$
$128$	−10.5644	+	4.04878i	−0.933773	+	0.357865i
$129$	5.44135			0.479085
$130$	0.00616197	−	0.0354469i	0.000540440	−	0.00310890i
$131$		−	4.22954i		−	0.369537i	−0.982782	−	0.184768i	$-0.940847\pi$
$131$		−	4.22954i		−	0.369537i	0.982782	−	0.184768i	$-0.0591535\pi$
$132$	−10.1470	−	3.63777i	−0.883183	−	0.316627i
$133$			3.69649i			0.320526i
$134$	0.606429	+	0.105420i	0.0523875	+	0.00910686i
$135$	−0.135918			−0.0116980
$136$	0.660950	−	1.16421i	0.0566760	−	0.0998301i
$137$	−20.6399			−1.76339			−0.881693	−	0.471824i	$-0.843596\pi$
$137$	−20.6399			−1.76339			−0.881693	+	0.471824i	$0.843596\pi$
$138$	20.0622	+	3.48754i	1.70780	+	0.296879i
$139$		−	10.1855i		−	0.863925i	−0.901892	−	0.431962i	$-0.857821\pi$
$139$		−	10.1855i		−	0.863925i	0.901892	−	0.431962i	$-0.142179\pi$
$140$	0.0171712	−	0.0478963i	0.00145123	−	0.00404798i
$141$		−	4.98117i		−	0.419490i
$142$	3.33133	−	19.1636i	0.279559	−	1.60817i
$143$	−3.21140			−0.268551
$144$	0.566253	+	0.465890i	0.0471877	+	0.0388242i
$145$	0.00284887			0.000236586
$146$	−1.24859	+	7.18257i	−0.103334	+	0.594434i
$147$			1.67830i			0.138424i
$148$	2.33826	−	6.52223i	0.192204	−	0.536124i
$149$		−	0.613709i		−	0.0502770i	−0.999684	−	0.0251385i	$-0.991997\pi$
$149$		−	0.613709i		−	0.0502770i	0.999684	−	0.0251385i	$-0.00800267\pi$
$150$	11.6905	+	2.03223i	0.954525	+	0.165931i
$151$	3.27672			0.266656			0.133328	−	0.991072i	$-0.457434\pi$
$151$	3.27672			0.266656			0.133328	+	0.991072i	$0.457434\pi$
$152$	−9.09217	−	5.16185i	−0.737472	−	0.418681i
$153$	−0.0867683			−0.00701480
$154$	−4.47451	−	0.777832i	−0.360566	−	0.0626795i
$155$			0.257327i			0.0206690i
$156$	−3.15968	−	1.13277i	−0.252977	−	0.0906939i
$157$			16.0154i			1.27817i	0.769135	+	0.639086i	$0.220687\pi$
$157$			16.0154i			1.27817i	−0.769135	+	0.639086i	$0.779313\pi$
$158$	−2.38833	+	13.7389i	−0.190005	+	1.09301i
$159$	22.0378			1.74772
$160$	0.0938313	+	0.109119i	0.00741802	+	0.00862660i
$161$	8.57943			0.676154
$162$	−2.03854	+	11.7268i	−0.160163	+	0.921342i
$163$			18.4365i			1.44406i	0.691861	+	0.722031i	$0.256791\pi$
$163$			18.4365i			1.44406i	−0.691861	+	0.722031i	$0.743209\pi$
$164$	10.2683	+	3.68125i	0.801818	+	0.287457i
$165$			0.137117i			0.0106746i
$166$	18.0601	+	3.13950i	1.40173	+	0.243672i
$167$	−3.65572			−0.282888			−0.141444	−	0.989946i	$-0.545175\pi$
$167$	−3.65572			−0.282888			−0.141444	+	0.989946i	$0.545175\pi$
$168$	−4.12807	−	2.34361i	−0.318487	−	0.180813i
$169$	−1.00000			−0.0769231
$170$	−0.0167776	−	0.00291657i	−0.00128679	−	0.000223691i
$171$			0.677638i			0.0518203i
$172$	−2.18831	+	6.10397i	−0.166857	+	0.465423i
$173$		−	22.4379i		−	1.70592i	−0.521973	−	0.852962i	$-0.674804\pi$
$173$		−	22.4379i		−	1.70592i	0.521973	−	0.852962i	$-0.325196\pi$
$174$	0.0455202	−	0.261857i	0.00345088	−	0.0198513i
$175$	4.99935			0.377916
$176$	8.16150	−	9.91966i	0.615197	−	0.747722i
$177$	−13.0700			−0.982403
$178$	−0.0893914	+	0.514227i	−0.00670017	+	0.0385429i
$179$		−	21.6521i		−	1.61836i	−0.587563	−	0.809179i	$-0.699912\pi$
$179$		−	21.6521i		−	1.61836i	0.587563	−	0.809179i	$-0.300088\pi$
$180$	0.00314780	−	0.00878032i	0.000234623	−	0.000654446i
$181$			17.0547i			1.26766i	0.773471	+	0.633831i	$0.218519\pi$
$181$			17.0547i			1.26766i	−0.773471	+	0.633831i	$0.781481\pi$
$182$	−1.39332	−	0.242210i	−0.103280	−	0.0179538i
$183$	11.3355			0.837946
$184$	−11.9805	+	21.1026i	−0.883214	+	1.55571i
$185$	−0.0881354			−0.00647984
$186$	23.6524	+	4.11166i	1.73428	+	0.301481i
$187$			1.52001i			0.111154i
$188$	5.58775	+	2.00324i	0.407528	+	0.146102i
$189$			5.34256i			0.388614i
$190$	−0.0227776	+	0.131029i	−0.00165246	+	0.00950584i
$191$	−17.6395			−1.27635			−0.638174	−	0.769893i	$-0.720310\pi$
$191$	−17.6395			−1.27635			−0.638174	+	0.769893i	$0.720310\pi$
$192$	11.5290	−	6.88106i	0.832036	−	0.496597i
$193$	7.72383			0.555973			0.277987	−	0.960585i	$-0.410333\pi$
$193$	7.72383			0.555973			0.277987	+	0.960585i	$0.410333\pi$
$194$	−2.51034	+	14.4408i	−0.180232	+	1.03679i
$195$			0.0426969i			0.00305759i
$196$	−1.88267	−	0.674950i	−0.134476	−	0.0482107i
$197$			6.32271i			0.450474i	0.974304	+	0.225237i	$0.0723157\pi$
$197$			6.32271i			0.450474i	−0.974304	+	0.225237i	$0.927684\pi$
$198$	−0.820263	−	0.142592i	−0.0582936	−	0.0101336i
$199$	2.46570			0.174789			0.0873943	−	0.996174i	$-0.472146\pi$
$199$	2.46570			0.174789			0.0873943	+	0.996174i	$0.472146\pi$
$200$	−6.98120	+	12.2968i	−0.493645	+	0.869515i
$201$	−0.730464			−0.0515230
$202$	−3.41499	−	0.593650i	−0.240278	−	0.0417690i
$203$		−	0.111981i		−	0.00785953i
$204$	−0.536158	+	1.49553i	−0.0375386	+	0.104708i
$205$		−	0.138756i		−	0.00969114i
$206$	3.74613	−	21.5497i	0.261005	−	1.50144i
$207$	1.57278			0.109316
$208$	2.54141	−	3.08889i	0.176215	−	0.214176i
$209$	11.8709			0.821128
$210$	−0.0103416	+	0.0594904i	−0.000713639	+	0.00410523i
$211$			9.46999i			0.651941i	0.945380	+	0.325971i	$0.105691\pi$
$211$			9.46999i			0.651941i	−0.945380	+	0.325971i	$0.894309\pi$
$212$	−8.86282	+	24.7215i	−0.608701	+	1.69788i
$213$			23.0831i			1.58163i
$214$	−12.7473	−	2.21594i	−0.871386	−	0.151479i
$215$	0.0824833			0.00562532
$216$	−13.1410	−	7.46045i	−0.894129	−	0.507619i
$217$	10.1148			0.686636
$218$	15.2140	+	2.64474i	1.03042	+	0.179124i
$219$		−	8.65164i		−	0.584624i
$220$	−0.153814	−	0.0551435i	−0.0103702	−	0.00371777i
$221$			0.473318i			0.0318388i
$222$	−1.40826	+	8.10105i	−0.0945161	+	0.543707i
$223$	−15.0991			−1.01111			−0.505556	−	0.862794i	$-0.668713\pi$
$223$	−15.0991			−1.01111			−0.505556	+	0.862794i	$0.668713\pi$
$224$	4.28915	−	3.68825i	0.286581	−	0.246431i
$225$	0.916478			0.0610985
$226$	−4.10550	+	23.6170i	−0.273094	+	1.57098i
$227$		−	29.9838i		−	1.99009i	−0.0994043	−	0.995047i	$-0.531694\pi$
$227$		−	29.9838i		−	1.99009i	0.0994043	−	0.995047i	$-0.468306\pi$
$228$	11.6797	+	4.18726i	0.773508	+	0.277308i
$229$			4.28268i			0.283007i	0.989938	+	0.141504i	$0.0451937\pi$
$229$			4.28268i			0.283007i	−0.989938	+	0.141504i	$0.954806\pi$
$230$	0.304114	+	0.0528662i	0.0200527	+	0.00348589i
$231$	5.38969			0.354615
$232$	0.275437	+	0.156373i	0.0180833	+	0.0102664i
$233$	14.3460			0.939837			0.469918	−	0.882710i	$-0.344283\pi$
$233$	14.3460			0.939837			0.469918	+	0.882710i	$0.344283\pi$
$234$	−0.255422	−	0.0444017i	−0.0166975	−	0.00290263i
$235$		−	0.0755076i		−	0.00492557i
$236$	5.25629	−	14.6616i	0.342155	−	0.954389i
$237$		−	16.5490i		−	1.07497i
$238$	−0.114642	+	0.659482i	−0.00743114	+	0.0427479i
$239$	24.2083			1.56591			0.782953	−	0.622080i	$-0.213712\pi$
$239$	24.2083			1.56591			0.782953	+	0.622080i	$0.213712\pi$
$240$	−0.131886	−	0.108511i	−0.00851320	−	0.00700433i
$241$	−17.3212			−1.11576			−0.557878	−	0.829923i	$-0.688384\pi$
$241$	−17.3212			−1.11576			−0.557878	+	0.829923i	$0.688384\pi$
$242$	0.166371	−	0.957055i	0.0106947	−	0.0615218i
$243$			1.90239i			0.122038i
$244$	−4.55873	+	12.7159i	−0.291843	+	0.814051i
$245$			0.0254406i			0.00162534i
$246$	−12.7539	−	2.21709i	−0.813158	−	0.141357i
$247$	3.69649			0.235202
$248$	−14.1245	+	24.8791i	−0.896906	+	1.57983i
$249$	−21.7539			−1.37860
$250$	0.354446	+	0.0616157i	0.0224171	+	0.00389692i
$251$			17.7576i			1.12085i	0.828205	+	0.560425i	$0.189362\pi$
$251$			17.7576i			1.12085i	−0.828205	+	0.560425i	$0.810638\pi$
$252$	−0.345130	−	0.123731i	−0.0217411	−	0.00779434i
$253$		−	27.5520i		−	1.73218i
$254$	−3.43174	+	19.7412i	−0.215327	+	1.23867i
$255$	0.0202092			0.00126555
$256$	3.08243	+	15.7003i	0.192652	+	0.981267i
$257$	1.93207			0.120519			0.0602596	−	0.998183i	$-0.480807\pi$
$257$	1.93207			0.120519			0.0602596	+	0.998183i	$0.480807\pi$
$258$	1.31795	−	7.58154i	0.0820519	−	0.472006i
$259$			3.46435i			0.215264i
$260$	−0.0478963	−	0.0171712i	−0.00297040	−	0.00106491i
$261$		−	0.0205283i		−	0.00127067i
$262$	−5.89309	−	1.02443i	−0.364076	−	0.0632898i
$263$	−8.88251			−0.547719			−0.273859	−	0.961770i	$-0.588300\pi$
$263$	−8.88251			−0.547719			−0.273859	+	0.961770i	$0.588300\pi$
$264$	−7.52627	+	13.2569i	−0.463210	+	0.815905i
$265$	0.334063			0.0205213
$266$	5.15038	+	0.895325i	0.315790	+	0.0548959i
$267$		−	0.619403i		−	0.0379068i
$268$	0.293766	−	0.819415i	0.0179446	−	0.0500538i
$269$		−	14.9431i		−	0.911096i	−0.890211	−	0.455548i	$-0.849443\pi$
$269$		−	14.9431i		−	0.911096i	0.890211	−	0.455548i	$-0.150557\pi$
$270$	−0.0329206	+	0.189377i	−0.00200349	+	0.0115251i
$271$	−11.2237			−0.681793			−0.340897	−	0.940101i	$-0.610731\pi$
$271$	−11.2237			−0.681793			−0.340897	+	0.940101i	$0.610731\pi$
$272$	−1.46202	−	1.20290i	−0.0886483	−	0.0729363i
$273$	1.67830			0.101575
$274$	−4.99918	+	28.7579i	−0.302011	+	1.73733i
$275$		−	16.0549i		−	0.968149i
$276$	9.71849	−	27.1082i	0.584984	−	1.63172i
$277$		−	4.26984i		−	0.256550i	−0.991739	−	0.128275i	$-0.959056\pi$
$277$		−	4.26984i		−	0.256550i	0.991739	−	0.128275i	$-0.0409440\pi$
$278$	−14.1917	−	2.46703i	−0.851160	−	0.147963i
$279$	1.85424			0.111010
$280$	−0.0625758	−	0.0355258i	−0.00373962	−	0.00212307i
$281$	−3.39952			−0.202798			−0.101399	−	0.994846i	$-0.532332\pi$
$281$	−3.39952			−0.202798			−0.101399	+	0.994846i	$0.532332\pi$
$282$	−6.94035	−	1.20649i	−0.413292	−	0.0718453i
$283$			5.78761i			0.344038i	0.985094	+	0.172019i	$0.0550290\pi$
$283$			5.78761i			0.344038i	−0.985094	+	0.172019i	$0.944971\pi$
$284$	−25.8940	−	9.28319i	−1.53653	−	0.550856i
$285$		−	0.157829i		−	0.00934897i
$286$	−0.777832	+	4.47451i	−0.0459942	+	0.264583i
$287$	−5.45411			−0.321946
$288$	0.786285	−	0.676127i	0.0463323	−	0.0398412i
$289$	−16.7760			−0.986822
$290$	0.000690023	−	0.00396938i	4.05196e−5	−	0.000233090i
$291$		−	17.3944i		−	1.01968i
$292$	9.70519	+	3.47938i	0.567953	+	0.203615i
$293$		−	2.35823i		−	0.137769i	−0.997625	−	0.0688845i	$-0.978056\pi$
$293$		−	2.35823i		−	0.137769i	0.997625	−	0.0688845i	$-0.0219440\pi$
$294$	2.33840	+	0.406500i	0.136378	+	0.0237075i
$295$	−0.198123			−0.0115352
$296$	−8.52119	−	4.83769i	−0.495284	−	0.281185i
$297$	17.1571			0.995556
$298$	−0.855091	−	0.148646i	−0.0495341	−	0.00861083i
$299$		−	8.57943i		−	0.496161i
$300$	5.66310	−	15.7963i	0.326959	−	0.912002i
$301$		−	3.24219i		−	0.186877i
$302$	0.793652	−	4.56551i	0.0456696	−	0.262716i
$303$	4.11347			0.236312
$304$	−9.39431	+	11.4180i	−0.538800	+	0.654869i
$305$	0.171831			0.00983899
$306$	−0.0210161	+	0.120896i	−0.00120141	+	0.00691116i
$307$			24.2868i			1.38612i	0.720879	+	0.693061i	$0.243738\pi$
$307$			24.2868i			1.38612i	−0.720879	+	0.693061i	$0.756262\pi$
$308$	−2.16754	+	6.04601i	−0.123507	+	0.344503i
$309$			25.9574i			1.47666i
$310$	0.358538	+	0.0623270i	0.0203636	+	0.00353993i
$311$	32.8787			1.86438			0.932191	−	0.361966i	$-0.117894\pi$
$311$	32.8787			1.86438			0.932191	+	0.361966i	$0.117894\pi$
$312$	−2.34361	+	4.12807i	−0.132681	+	0.233706i
$313$	19.9027			1.12497			0.562483	−	0.826809i	$-0.309846\pi$
$313$	19.9027			1.12497			0.562483	+	0.826809i	$0.309846\pi$
$314$	22.3146	+	3.87909i	1.25929	+	0.218910i
$315$			0.00466376i			0.000262773i
$316$	18.5642	+	6.65541i	1.04432	+	0.374396i
$317$		−	1.54451i		−	0.0867486i	−0.999059	−	0.0433743i	$-0.986189\pi$
$317$		−	1.54451i		−	0.0867486i	0.999059	−	0.0433743i	$-0.0138108\pi$
$318$	5.33778	−	30.7057i	0.299328	−	1.72189i
$319$	−0.359616			−0.0201346
$320$	0.174764	−	0.104307i	0.00976961	−	0.00583095i
$321$	15.3545			0.857005
$322$	2.07802	−	11.9539i	0.115804	−	0.666164i
$323$		−	1.74961i		−	0.0973511i
$324$	15.8454	+	5.68067i	0.880298	+	0.315593i
$325$		−	4.99935i		−	0.277314i
$326$	25.6880	+	4.46551i	1.42272	+	0.247321i
$327$	−18.3257			−1.01341
$328$	7.61622	−	13.4153i	0.420536	−	0.740738i
$329$	−2.96799			−0.163631
$330$	0.191048	+	0.0332111i	0.0105168	+	0.00182821i
$331$		−	25.2516i		−	1.38795i	−0.719998	−	0.693977i	$-0.755857\pi$
$331$		−	25.2516i		−	1.38795i	0.719998	−	0.693977i	$-0.244143\pi$
$332$	8.74864	−	24.4030i	0.480144	−	1.33929i
$333$			0.635083i			0.0348023i
$334$	−0.885451	+	5.09358i	−0.0484497	+	0.278709i
$335$	−0.0110728			−0.000604973
$336$	−4.26525	+	5.18407i	−0.232688	+	0.282814i
$337$	−23.9779			−1.30616			−0.653079	−	0.757290i	$-0.726523\pi$
$337$	−23.9779			−1.30616			−0.653079	+	0.757290i	$0.726523\pi$
$338$	−0.242210	+	1.39332i	−0.0131745	+	0.0757865i
$339$		−	28.4475i		−	1.54506i
$340$	−0.00812741	+	0.0226702i	−0.000440771	+	0.00122946i
$341$		−	32.4827i		−	1.75903i
$342$	0.944165	+	0.164130i	0.0510546	+	0.00887515i
$343$	1.00000			0.0539949
$344$	7.97474	+	4.52746i	0.429969	+	0.244104i
$345$	−0.366316			−0.0197218
$346$	−31.2632	−	5.43468i	−1.68072	−	0.292170i
$347$		−	11.1925i		−	0.600843i	−0.953807	−	0.300421i	$-0.902873\pi$
$347$		−	11.1925i		−	0.600843i	0.953807	−	0.300421i	$-0.0971273\pi$
$348$	−0.353824	−	0.126848i	−0.0189670	−	0.00679978i
$349$		−	1.36047i		−	0.0728244i	−0.999337	−	0.0364122i	$-0.988407\pi$
$349$		−	1.36047i		−	0.0728244i	0.999337	−	0.0364122i	$-0.0115929\pi$
$350$	1.21089	−	6.96569i	0.0647248	−	0.372332i
$351$	5.34256			0.285164
$352$	−11.8444	−	13.7742i	−0.631311	−	0.734168i
$353$	4.61895			0.245842			0.122921	−	0.992416i	$-0.460774\pi$
$353$	4.61895			0.245842			0.122921	+	0.992416i	$0.460774\pi$
$354$	−3.16568	+	18.2107i	−0.168254	+	0.967888i
$355$			0.349908i			0.0185712i
$356$	0.694830	+	0.249101i	0.0368259	+	0.0132023i
$357$		−	0.794368i		−	0.0420424i
$358$	−30.1683	−	5.24436i	−1.59445	−	0.277173i
$359$	−9.92596			−0.523872			−0.261936	−	0.965085i	$-0.584361\pi$
$359$	−9.92596			−0.523872			−0.261936	+	0.965085i	$0.584361\pi$
$360$	−0.0114713	−	0.00651257i	−0.000604593	−	0.000343243i
$361$	5.33598			0.280841
$362$	23.7626	+	4.13080i	1.24893	+	0.217110i
$363$			1.15280i			0.0605065i
$364$	−0.674950	+	1.88267i	−0.0353770	+	0.0986787i
$365$		−	0.131147i		−	0.00686454i
$366$	2.74557	−	15.7940i	0.143513	−	0.825564i
$367$	2.48590			0.129763			0.0648815	−	0.997893i	$-0.479333\pi$
$367$	2.48590			0.129763			0.0648815	+	0.997893i	$0.479333\pi$
$368$	26.5009	+	21.8039i	1.38145	+	1.13661i
$369$	−0.999843			−0.0520498
$370$	−0.0213472	+	0.122801i	−0.00110979	+	0.00638410i
$371$		−	13.1311i		−	0.681732i
$372$	11.4577	−	31.9595i	0.594053	−	1.65702i
$373$		−	11.9080i		−	0.616574i	−0.951293	−	0.308287i	$-0.900244\pi$
$373$		−	11.9080i		−	0.616574i	0.951293	−	0.308287i	$-0.0997557\pi$
$374$	2.11786	+	0.368162i	0.109512	+	0.0190372i
$375$	−0.426942			−0.0220472
$376$	4.14456	−	7.30030i	0.213739	−	0.376484i
$377$	−0.111981			−0.00576732
$378$	7.44388	+	1.29402i	0.382872	+	0.0665571i
$379$			20.1421i			1.03463i	0.855795	+	0.517315i	$0.173069\pi$
$379$			20.1421i			1.03463i	−0.855795	+	0.517315i	$0.826931\pi$
$380$	0.177048	+	0.0634730i	0.00908238	+	0.00325609i
$381$		−	23.7789i		−	1.21823i
$382$	−4.27245	+	24.5774i	−0.218597	+	1.25749i
$383$	−31.3164			−1.60019			−0.800096	−	0.599873i	$-0.795218\pi$
$383$	−31.3164			−1.60019			−0.800096	+	0.599873i	$0.795218\pi$
$384$	−6.79506	−	17.7303i	−0.346759	−	0.904794i
$385$	0.0817001			0.00416383
$386$	1.87078	−	10.7617i	0.0952204	−	0.547759i
$387$		−	0.594356i		−	0.0302128i
$388$	19.5126	+	6.99540i	0.990603	+	0.355138i
$389$		−	20.7175i		−	1.05042i	−0.850973	−	0.525209i	$-0.823987\pi$
$389$		−	20.7175i		−	1.05042i	0.850973	−	0.525209i	$-0.176013\pi$
$390$	0.0594904	+	0.0103416i	0.00301241	+	0.000523668i
$391$	−4.06080			−0.205363
$392$	−1.39642	+	2.45968i	−0.0705299	+	0.124232i
$393$	7.09842			0.358068
$394$	8.80954	+	1.53142i	0.443818	+	0.0771518i
$395$		−	0.250860i		−	0.0126221i
$396$	−0.397351	+	1.10835i	−0.0199677	+	0.0556967i
$397$		−	26.2541i		−	1.31766i	−0.752294	−	0.658828i	$-0.771053\pi$
$397$		−	26.2541i		−	1.31766i	0.752294	−	0.658828i	$-0.228947\pi$
$398$	0.597215	−	3.43550i	0.0299357	−	0.172206i
$399$	−6.20380			−0.310579
$400$	15.4424	+	12.7054i	0.772121	+	0.635271i
$401$	3.65950			0.182747			0.0913735	−	0.995817i	$-0.470874\pi$
$401$	3.65950			0.182747			0.0913735	+	0.995817i	$0.470874\pi$
$402$	−0.176925	+	1.01777i	−0.00882423	+	0.0507617i
$403$		−	10.1148i		−	0.503853i
$404$	−1.65429	+	4.61438i	−0.0823038	+	0.229574i
$405$		−	0.214120i		−	0.0106397i
$406$	−0.156025	−	0.0271229i	−0.00774340	−	0.00134609i
$407$	11.1254			0.551467
$408$	1.95389	+	1.10927i	0.0967319	+	0.0549171i
$409$	−20.5818			−1.01770			−0.508851	−	0.860855i	$-0.669930\pi$
$409$	−20.5818			−1.01770			−0.508851	+	0.860855i	$0.669930\pi$
$410$	−0.193331	−	0.0336080i	−0.00954794	−	0.00165978i
$411$		−	34.6399i		−	1.70866i
$412$	−29.1183	−	10.4391i	−1.43456	−	0.514298i
$413$			7.78767i			0.383206i
$414$	0.380941	−	2.19138i	0.0187222	−	0.107700i
$415$	−0.329759			−0.0161873
$416$	−3.68825	−	4.28915i	−0.180831	−	0.210293i
$417$	17.0943			0.837113
$418$	2.87525	−	16.5400i	0.140633	−	0.808996i
$419$		−	14.9371i		−	0.729727i	−0.931061	−	0.364863i	$-0.881116\pi$
$419$		−	14.9371i		−	0.729727i	0.931061	−	0.364863i	$-0.118884\pi$
$420$	0.0803842	+	0.0288183i	0.00392235	+	0.00140619i
$421$			8.76725i			0.427290i	0.976911	+	0.213645i	$0.0685336\pi$
$421$			8.76725i			0.427290i	−0.976911	+	0.213645i	$0.931466\pi$
$422$	13.1947	+	2.29372i	0.642309	+	0.111657i
$423$	−0.544090			−0.0264546
$424$	32.2982	+	18.3365i	1.56854	+	0.890499i
$425$	−2.36628			−0.114782
$426$	32.1621	+	5.59095i	1.55826	+	0.270883i
$427$		−	6.75418i		−	0.326858i
$428$	−6.17502	+	17.2243i	−0.298481	+	0.832567i
$429$		−	5.38969i		−	0.260217i
$430$	0.0199783	−	0.114926i	0.000963437	−	0.00554220i
$431$	10.7638			0.518474			0.259237	−	0.965814i	$-0.416529\pi$
$431$	10.7638			0.518474			0.259237	+	0.965814i	$0.416529\pi$
$432$	−13.5776	+	16.5025i	−0.653255	+	0.793979i
$433$	10.0405			0.482518			0.241259	−	0.970461i	$-0.422440\pi$
$433$	10.0405			0.482518			0.241259	+	0.970461i	$0.422440\pi$
$434$	2.44990	−	14.0931i	0.117599	−	0.676491i
$435$			0.00478125i			0.000229243i
$436$	7.36993	−	20.5573i	0.352956	−	0.984516i
$437$			31.7138i			1.51708i
$438$	−12.0545	−	2.09551i	−0.575986	−	0.100127i
$439$	−26.4204			−1.26098			−0.630489	−	0.776198i	$-0.717146\pi$
$439$	−26.4204			−1.26098			−0.630489	+	0.776198i	$0.717146\pi$
$440$	−0.114088	+	0.200956i	−0.00543892	+	0.00958020i
$441$	0.183319			0.00872949
$442$	0.659482	+	0.114642i	0.0313684	+	0.00545297i
$443$			34.4318i			1.63590i	0.575286	+	0.817952i	$0.304891\pi$
$443$			34.4318i			1.63590i	−0.575286	+	0.817952i	$0.695109\pi$
$444$	10.9462	+	3.92430i	0.519486	+	0.186239i
$445$		−	0.00938928i		−	0.000445095i
$446$	−3.65715	+	21.0379i	−0.173171	+	0.996173i
$447$	1.02999			0.0487166
$448$	−4.10002	−	6.86948i	−0.193708	−	0.324553i
$449$	3.82597			0.180559			0.0902794	−	0.995916i	$-0.471224\pi$
$449$	3.82597			0.180559			0.0902794	+	0.995916i	$0.471224\pi$
$450$	0.221980	−	1.27695i	0.0104642	−	0.0601958i
$451$			17.5153i			0.824765i
$452$	31.9116	+	11.4405i	1.50100	+	0.538118i
$453$			5.49931i			0.258380i
$454$	−41.7770	−	7.26236i	−1.96069	−	0.340839i
$455$	0.0254406			0.00119268
$456$	8.66311	−	15.2594i	0.405688	−	0.714585i
$457$	7.56905			0.354065			0.177033	−	0.984205i	$-0.443350\pi$
$457$	7.56905			0.354065			0.177033	+	0.984205i	$0.443350\pi$
$458$	5.96713	+	1.03731i	0.278826	+	0.0484701i
$459$		−	2.52873i		−	0.118031i
$460$	0.147319	−	0.410923i	0.00686877	−	0.0191594i
$461$			10.7042i			0.498546i	0.968433	+	0.249273i	$0.0801917\pi$
$461$			10.7042i			0.498546i	−0.968433	+	0.249273i	$0.919808\pi$
$462$	1.30543	−	7.50955i	0.0607343	−	0.349376i
$463$	−0.485129			−0.0225459			−0.0112729	−	0.999936i	$-0.503588\pi$
$463$	−0.485129			−0.0225459			−0.0112729	+	0.999936i	$0.503588\pi$
$464$	0.284590	−	0.345897i	0.0132118	−	0.0160578i
$465$	−0.431871			−0.0200275
$466$	3.47474	−	19.9885i	0.160964	−	0.925950i
$467$			20.7652i			0.960901i	0.877022	+	0.480450i	$0.159527\pi$
$467$			20.7652i			0.960901i	−0.877022	+	0.480450i	$0.840473\pi$
$468$	−0.123731	+	0.345130i	−0.00571948	+	0.0159536i
$469$			0.435241i			0.0200976i
$470$	−0.105206	−	0.0182887i	−0.00485279	−	0.000843593i
$471$	−26.8787			−1.23850
$472$	−19.1552	−	10.8749i	−0.881687	−	0.500556i
$473$	−10.4120			−0.478743
$474$	−23.0580	−	4.00833i	−1.05909	−	0.184109i
$475$			18.4800i			0.847923i
$476$	0.891101	+	0.319466i	0.0408435	+	0.0146427i
$477$		−	2.40718i		−	0.110217i
$478$	5.86349	−	33.7299i	0.268190	−	1.54277i
$479$	9.52657			0.435280			0.217640	−	0.976029i	$-0.430164\pi$
$479$	9.52657			0.435280			0.217640	+	0.976029i	$0.430164\pi$
$480$	−0.183134	+	0.157477i	−0.00835888	+	0.00718780i
$481$	3.46435			0.157961
$482$	−4.19536	+	24.1339i	−0.191093	+	1.09927i
$483$			14.3988i			0.655170i
$484$	−1.29319	−	0.463616i	−0.0587811	−	0.0210734i
$485$		−	0.263675i		−	0.0119729i
$486$	2.65063	+	0.460776i	0.120235	+	0.0209012i
$487$	−13.6932			−0.620496			−0.310248	−	0.950656i	$-0.600412\pi$
$487$	−13.6932			−0.620496			−0.310248	+	0.950656i	$0.600412\pi$
$488$	16.6131	+	9.43167i	0.752040	+	0.426952i
$489$	−30.9420			−1.39925
$490$	0.0354469	+	0.00616197i	0.00160133	+	0.000278369i
$491$			12.7290i			0.574454i	0.957863	+	0.287227i	$0.0927333\pi$
$491$			12.7290i			0.574454i	−0.957863	+	0.287227i	$0.907267\pi$
$492$	−6.17823	+	17.2332i	−0.278536	+	0.776934i
$493$			0.0530026i			0.00238712i
$494$	0.895325	−	5.15038i	0.0402826	−	0.231727i
$495$	0.0149772			0.000673176
$496$	31.2434	+	25.7059i	1.40287	+	1.15423i
$497$	13.7539			0.616947
$498$	−5.26901	+	30.3102i	−0.236110	+	1.35823i
$499$			12.5821i			0.563252i	0.959524	+	0.281626i	$0.0908737\pi$
$499$			12.5821i			0.563252i	−0.959524	+	0.281626i	$0.909126\pi$
$500$	0.171700	−	0.478932i	0.00767868	−	0.0214185i
$501$		−	6.13539i		−	0.274109i
$502$	24.7420	+	4.30106i	1.10429	+	0.191966i
$503$	5.10421			0.227586			0.113793	−	0.993505i	$-0.463700\pi$
$503$	5.10421			0.227586			0.113793	+	0.993505i	$0.463700\pi$
$504$	−0.255991	+	0.450906i	−0.0114027	+	0.0200850i
$505$	0.0623544			0.00277473
$506$	−38.3887	−	6.67336i	−1.70659	−	0.296667i
$507$		−	1.67830i		−	0.0745358i
$508$	26.6746	+	9.56302i	1.18349	+	0.424290i
$509$		−	37.8248i		−	1.67655i	−0.545244	−	0.838277i	$-0.683563\pi$
$509$		−	37.8248i		−	1.67655i	0.545244	−	0.838277i	$-0.316437\pi$
$510$	0.00489487	−	0.0281579i	0.000216748	−	0.00124685i
$511$	−5.15501			−0.228044
$512$	22.6221	−	0.492050i	0.999764	−	0.0217458i
$513$	−19.7487			−0.871926
$514$	0.467965	−	2.69199i	0.0206411	−	0.118738i
$515$			0.393478i			0.0173387i
$516$	−10.2443	−	3.67264i	−0.450979	−	0.161679i
$517$			9.53142i			0.419191i
$518$	4.82695	+	0.839099i	0.212084	+	0.0368679i
$519$	37.6575			1.65298
$520$	−0.0355258	+	0.0625758i	−0.00155791	+	0.00274413i
$521$	14.1160			0.618431			0.309216	−	0.950992i	$-0.399934\pi$
$521$	14.1160			0.618431			0.309216	+	0.950992i	$0.399934\pi$
$522$	−0.0286024	−	0.00497215i	−0.00125189	−	0.000217625i
$523$			37.7582i			1.65105i	0.564364	+	0.825526i	$0.309121\pi$
$523$			37.7582i			1.65105i	−0.564364	+	0.825526i	$0.690879\pi$
$524$	−2.85473	+	7.96282i	−0.124709	+	0.347858i
$525$			8.39040i			0.366187i
$526$	−2.15143	+	12.3762i	−0.0938067	+	0.539626i
$527$	−4.78751			−0.208547
$528$	16.6481	+	13.6974i	0.724517	+	0.596104i
$529$	50.6067			2.20029
$530$	0.0809132	−	0.465456i	0.00351465	−	0.0202181i
$531$			1.42763i			0.0619539i
$532$	2.49494	−	6.95926i	0.108170	−	0.301722i
$533$			5.45411i			0.236244i
$534$	−0.863025	−	0.150025i	−0.0373468	−	0.00649223i
$535$	0.232753			0.0100628
$536$	−1.07055	−	0.607779i	−0.0462408	−	0.0262521i
$537$	36.3387			1.56813
$538$	−20.8205	−	3.61936i	−0.897634	−	0.156042i
$539$		−	3.21140i		−	0.138325i
$540$	0.255889	+	0.0917378i	0.0110117	+	0.00394777i
$541$		−	15.8058i		−	0.679543i	−0.940508	−	0.339771i	$-0.889650\pi$
$541$		−	15.8058i		−	0.679543i	0.940508	−	0.339771i	$-0.110350\pi$
$542$	−2.71849	+	15.6382i	−0.116769	+	0.671719i
$543$	−28.6228			−1.22832
$544$	−2.03013	+	1.74571i	−0.0870412	+	0.0748468i
$545$	−0.277792			−0.0118993
$546$	0.406500	−	2.33840i	0.0173966	−	0.100074i
$547$			44.2018i			1.88993i	0.327165	+	0.944967i	$0.393907\pi$
$547$			44.2018i			1.88993i	−0.327165	+	0.944967i	$0.606093\pi$
$548$	38.8581	+	13.9309i	1.65994	+	0.595098i
$549$		−	1.23817i		−	0.0528439i
$550$	−22.3696	−	3.88866i	−0.953844	−	0.165813i
$551$	0.413937			0.0176343
$552$	−35.4165	−	20.1068i	−1.50743	−	0.855803i
$553$	−9.86060			−0.419315
$554$	−5.94924	−	1.03420i	−0.252759	−	0.0439387i
$555$		−	0.147917i		−	0.00627874i
$556$	−6.87472	+	19.1760i	−0.291553	+	0.813242i
$557$			5.80491i			0.245962i	0.992409	+	0.122981i	$0.0392454\pi$
$557$			5.80491i			0.245962i	−0.992409	+	0.122981i	$0.960755\pi$
$558$	0.449114	−	2.58354i	0.0190125	−	0.109370i
$559$	−3.24219			−0.137130
$560$	−0.0646552	+	0.0785832i	−0.00273218	+	0.00332075i
$561$	−2.55104			−0.107705
$562$	−0.823397	+	4.73661i	−0.0347329	+	0.199802i
$563$			19.2053i			0.809406i	0.914448	+	0.404703i	$0.132625\pi$
$563$			19.2053i			0.809406i	−0.914448	+	0.404703i	$0.867375\pi$
$564$	−3.36204	+	9.37790i	−0.141567	+	0.394881i
$565$		−	0.431224i		−	0.0181417i
$566$	8.06399	+	1.40182i	0.338955	+	0.0589227i
$567$	−8.41644			−0.353457
$568$	−19.2062	+	33.8302i	−0.805875	+	1.41948i
$569$	−6.60326			−0.276823			−0.138411	−	0.990375i	$-0.544200\pi$
$569$	−6.60326			−0.276823			−0.138411	+	0.990375i	$0.544200\pi$
$570$	−0.219906	−	0.0382276i	−0.00921083	−	0.00160118i
$571$		−	31.1734i		−	1.30457i	−0.757975	−	0.652284i	$-0.773811\pi$
$571$		−	31.1734i		−	1.30457i	0.757975	−	0.652284i	$-0.226189\pi$
$572$	6.04601	+	2.16754i	0.252796	+	0.0906292i
$573$		−	29.6043i		−	1.23674i
$574$	−1.32104	+	7.59930i	−0.0551390	+	0.317189i
$575$	42.8916			1.78870
$576$	−0.751614	−	1.25931i	−0.0313172	−	0.0524712i
$577$	35.2397			1.46705			0.733524	−	0.679664i	$-0.237874\pi$
$577$	35.2397			1.46705			0.733524	+	0.679664i	$0.237874\pi$
$578$	−4.06330	+	23.3743i	−0.169011	+	0.972241i
$579$			12.9629i			0.538719i
$580$	−0.00536348	−	0.00192284i	−0.000222706	−	7.98417e-5i
$581$			12.9619i			0.537751i
$582$	−24.2360	−	4.21310i	−1.00461	−	0.174638i
$583$	−42.1692			−1.74647
$584$	7.19856	−	12.6797i	0.297879	−	0.524688i
$585$	0.00466376			0.000192823
$586$	−3.28576	−	0.571185i	−0.135733	−	0.0235954i
$587$		−	19.0104i		−	0.784644i	−0.919828	−	0.392322i	$-0.871672\pi$
$587$		−	19.0104i		−	0.784644i	0.919828	−	0.392322i	$-0.128328\pi$
$588$	1.13277	−	3.15968i	0.0467145	−	0.130303i
$589$			37.3892i			1.54059i
$590$	−0.0479874	+	0.276049i	−0.00197561	+	0.0113647i
$591$	−10.6114			−0.436494
$592$	−8.80436	+	10.7010i	−0.361857	+	0.439808i
$593$	−36.6864			−1.50653			−0.753264	−	0.657718i	$-0.771522\pi$
$593$	−36.6864			−1.50653			−0.753264	+	0.657718i	$0.771522\pi$
$594$	4.15561	−	23.9053i	0.170507	−	0.980846i
$595$		−	0.0120415i		−	0.000493654i
$596$	−0.414222	+	1.15541i	−0.0169672	+	0.0473274i
$597$			4.13817i			0.169364i
$598$	−11.9539	−	2.07802i	−0.488830	−	0.0849766i
$599$	21.1337			0.863501			0.431750	−	0.901993i	$-0.357896\pi$
$599$	21.1337			0.863501			0.431750	+	0.901993i	$0.357896\pi$
$600$	−20.6377	−	11.7165i	−0.842529	−	0.478325i
$601$	31.5295			1.28612			0.643058	−	0.765817i	$-0.277665\pi$
$601$	31.5295			1.28612			0.643058	+	0.765817i	$0.277665\pi$
$602$	−4.51740	−	0.785289i	−0.184115	−	0.0320060i
$603$			0.0797881i			0.00324922i
$604$	−6.16898	−	2.21162i	−0.251012	−	0.0899895i
$605$			0.0174749i			0.000710456i
$606$	0.996320	−	5.73136i	0.0404728	−	0.232821i
$607$	−19.4145			−0.788010			−0.394005	−	0.919108i	$-0.628911\pi$
$607$	−19.4145			−0.788010			−0.394005	+	0.919108i	$0.628911\pi$
$608$	13.6336	+	15.8548i	0.552914	+	0.642997i
$609$	0.187937			0.00761561
$610$	0.0416190	−	0.239415i	0.00168510	−	0.00969362i
$611$			2.96799i			0.120072i
$612$	0.163356	+	0.0585642i	0.00660328	+	0.00236732i
$613$			2.22681i			0.0899399i	0.998988	+	0.0449700i	$0.0143192\pi$
$613$			2.22681i			0.0899399i	−0.998988	+	0.0449700i	$0.985681\pi$
$614$	33.8392	+	5.88250i	1.36564	+	0.237398i
$615$	0.232874			0.00939037
$616$	7.89902	+	4.48447i	0.318260	+	0.180684i
$617$	−18.2019			−0.732781			−0.366391	−	0.930461i	$-0.619407\pi$
$617$	−18.2019			−0.732781			−0.366391	+	0.930461i	$0.619407\pi$
$618$	36.1669	+	6.28712i	1.45485	+	0.252905i
$619$			19.2357i			0.773148i	0.922258	+	0.386574i	$0.126342\pi$
$619$			19.2357i			0.773148i	−0.922258	+	0.386574i	$0.873658\pi$
$620$	0.173683	−	0.484461i	0.00697526	−	0.0194564i
$621$			45.8361i			1.83934i
$622$	7.96354	−	45.8105i	0.319309	−	1.83684i
$623$	−0.369066			−0.0147863
$624$	5.18407	+	4.26525i	0.207529	+	0.170747i
$625$	24.9903			0.999612
$626$	4.82062	−	27.7308i	0.192671	−	1.10834i
$627$			19.9229i			0.795645i
$628$	10.8096	−	30.1518i	0.431351	−	1.20319i
$629$		−	1.63974i		−	0.0653807i
$630$	0.00649810	+	0.00112961i	0.000258891	+	4.50046e-5i
$631$	−14.0857			−0.560742			−0.280371	−	0.959892i	$-0.590458\pi$
$631$	−14.0857			−0.560742			−0.280371	+	0.959892i	$0.590458\pi$
$632$	13.7695	−	24.2539i	0.547723	−	0.964768i
$633$	−15.8935			−0.631708
$634$	−2.15200	−	0.374096i	−0.0854668	−	0.0148573i
$635$		−	0.360455i		−	0.0143042i
$636$	−41.4900	−	14.8744i	−1.64518	−	0.589810i
$637$		−	1.00000i		−	0.0396214i
$638$	−0.0871025	+	0.501060i	−0.00344842	+	0.0198371i
$639$	2.52136			0.0997433
$640$	−0.103004	−	0.268766i	−0.00407157	−	0.0106239i
$641$	−8.12462			−0.320903			−0.160452	−	0.987044i	$-0.551295\pi$
$641$	−8.12462			−0.320903			−0.160452	+	0.987044i	$0.551295\pi$
$642$	3.71901	−	21.3937i	0.146778	−	0.844343i
$643$			37.7361i			1.48817i	0.668087	+	0.744083i	$0.267113\pi$
$643$			37.7361i			1.48817i	−0.668087	+	0.744083i	$0.732887\pi$
$644$	−16.1522	−	5.79069i	−0.636487	−	0.228185i
$645$			0.138432i			0.00545074i
$646$	−2.43777	−	0.423773i	−0.0959127	−	0.0166731i
$647$	−1.19852			−0.0471188			−0.0235594	−	0.999722i	$-0.507500\pi$
$647$	−1.19852			−0.0471188			−0.0235594	+	0.999722i	$0.507500\pi$
$648$	11.7529	−	20.7017i	0.461697	−	0.813240i
$649$	25.0093			0.981703
$650$	−6.96569	−	1.21089i	−0.273217	−	0.0474950i
$651$			16.9756i			0.665327i
$652$	12.4437	−	34.7099i	0.487334	−	1.35934i
$653$		−	27.8915i		−	1.09148i	−0.837956	−	0.545738i	$-0.816249\pi$
$653$		−	27.8915i		−	1.09148i	0.837956	−	0.545738i	$-0.183751\pi$
$654$	−4.43866	+	25.5335i	−0.173565	+	0.998440i
$655$	0.107602			0.00420436
$656$	−16.8471	−	13.8611i	−0.657769	−	0.541187i
$657$	−0.945014			−0.0368685
$658$	−0.718876	+	4.13535i	−0.0280247	+	0.161213i
$659$		−	29.0688i		−	1.13236i	−0.824282	−	0.566179i	$-0.808421\pi$
$659$		−	29.0688i		−	1.13236i	0.824282	−	0.566179i	$-0.191579\pi$
$660$	0.0925472	−	0.258146i	0.00360239	−	0.0100483i
$661$			31.5724i			1.22803i	0.789296	+	0.614013i	$0.210446\pi$
$661$			31.5724i			1.22803i	−0.789296	+	0.614013i	$0.789554\pi$
$662$	−35.1835	−	6.11618i	−1.36745	−	0.237712i
$663$	−0.794368			−0.0308507
$664$	−31.8821	−	18.1003i	−1.23727	−	0.702427i
$665$	−0.0940410			−0.00364675
$666$	0.884873	+	0.153823i	0.0342881	+	0.00596053i
$667$		−	0.960734i		−	0.0371998i
$668$	6.88252	+	2.46743i	0.266293	+	0.0954677i
$669$		−	25.3408i		−	0.979733i
$670$	−0.00268194	+	0.0154280i	−0.000103612	+	0.000596034i
$671$	−21.6904			−0.837348
$672$	6.18997	+	7.19848i	0.238783	+	0.277687i
$673$	−27.2491			−1.05037			−0.525187	−	0.850987i	$-0.676005\pi$
$673$	−27.2491			−1.05037			−0.525187	+	0.850987i	$0.676005\pi$
$674$	−5.80767	+	33.4088i	−0.223703	+	1.28686i
$675$			26.7093i			1.02804i
$676$	1.88267	+	0.674950i	0.0724103	+	0.0259596i
$677$			2.48444i			0.0954849i	0.998860	+	0.0477425i	$0.0152027\pi$
$677$			2.48444i			0.0954849i	−0.998860	+	0.0477425i	$0.984797\pi$
$678$	−39.6364	−	6.89025i	−1.52223	−	0.264619i
$679$	−10.3643			−0.397747
$680$	0.0296182	+	0.0168150i	0.00113581	+	0.000644826i
$681$	50.3217			1.92833
$682$	−45.2587	−	7.86761i	−1.73304	−	0.301266i
$683$			0.0289502i			0.00110775i	1.00000		0.000553875i	$0.000176304\pi$
$683$			0.0289502i			0.00110775i	−1.00000		0.000553875i	$0.999824\pi$
$684$	0.457371	−	1.27577i	0.0174880	−	0.0487802i
$685$		−	0.525092i		−	0.0200627i
$686$	0.242210	−	1.39332i	0.00924760	−	0.0531971i
$687$	−7.18761			−0.274224
$688$	8.23974	−	10.0147i	0.314137	−	0.381809i
$689$	−13.1311			−0.500254
$690$	−0.0887251	+	0.510394i	−0.00337771	+	0.0194304i
$691$		−	44.9205i		−	1.70885i	−0.519571	−	0.854427i	$-0.673908\pi$
$691$		−	44.9205i		−	1.70885i	0.519571	−	0.854427i	$-0.326092\pi$
$692$	−15.1445	+	42.2432i	−0.575706	+	1.60584i
$693$		−	0.588712i		−	0.0223633i
$694$	−15.5947	−	2.71092i	−0.591965	−	0.102905i
$695$	0.259126			0.00982922
$696$	−0.262440	+	0.462265i	−0.00994775	+	0.0175221i
$697$	2.58153			0.0977823
$698$	−1.89557	−	0.329519i	−0.0717483	−	0.0124725i
$699$			24.0768i			0.910669i
$700$	−9.41213	−	3.37431i	−0.355745	−	0.127537i
$701$		−	5.95075i		−	0.224757i	−0.993665	−	0.112378i	$-0.964153\pi$
$701$		−	5.95075i		−	0.224757i	0.993665	−	0.112378i	$-0.0358469\pi$
$702$	1.29402	−	7.44388i	0.0488396	−	0.280951i
$703$	−12.8059			−0.482985
$704$	−22.0607	+	13.1668i	−0.831443	+	0.496244i
$705$	0.126724			0.00477271
$706$	1.11875	−	6.43567i	0.0421049	−	0.242209i
$707$		−	2.45098i		−	0.0921784i
$708$	24.6065	+	8.82161i	0.924770	+	0.331536i
$709$		−	16.9951i		−	0.638263i	−0.947710	−	0.319131i	$-0.896609\pi$
$709$		−	16.9951i		−	0.638263i	0.947710	−	0.319131i	$-0.103391\pi$
$710$	0.487533	+	0.0847511i	0.0182968	+	0.00318065i
$711$	−1.80764			−0.0677918
$712$	0.515372	−	0.907784i	0.0193144	−	0.0340206i
$713$	86.7791			3.24990
$714$	−1.10681	−	0.192403i	−0.0414212	−	0.00720052i
$715$		−	0.0817001i		−	0.00305541i
$716$	−14.6141	+	40.7638i	−0.546155	+	1.52342i
$717$			40.6288i			1.51731i
$718$	−2.40416	+	13.8300i	−0.0897225	+	0.516132i
$719$	−36.9721			−1.37883			−0.689413	−	0.724369i	$-0.742131\pi$
$719$	−36.9721			−1.37883			−0.689413	+	0.724369i	$0.742131\pi$
$720$	−0.0118525	+	0.0144058i	−0.000441718	+	0.000536873i
$721$	15.4665			0.576003
$722$	1.29242	−	7.43471i	0.0480991	−	0.276691i
$723$		−	29.0701i		−	1.08113i
$724$	11.5110	−	32.1083i	0.427804	−	1.19329i
$725$		−	0.559833i		−	0.0207917i
$726$	1.60622	+	0.279220i	0.0596125	+	0.0103628i
$727$	−29.1839			−1.08237			−0.541185	−	0.840904i	$-0.682024\pi$
$727$	−29.1839			−1.08237			−0.541185	+	0.840904i	$0.682024\pi$
$728$	2.45968	+	1.39642i	0.0911617	+	0.0517548i
$729$	−28.4421			−1.05341
$730$	−0.182729	−	0.0317650i	−0.00676311	−	0.00117568i
$731$			1.53459i			0.0567587i
$732$	−21.3410	−	7.65090i	−0.788787	−	0.282786i
$733$		−	18.7002i		−	0.690707i	−0.938473	−	0.345354i	$-0.887759\pi$
$733$		−	18.7002i		−	0.690707i	0.938473	−	0.345354i	$-0.112241\pi$
$734$	0.602109	−	3.46365i	0.0222243	−	0.127846i
$735$	−0.0426969			−0.00157490
$736$	36.7985	−	31.6431i	1.35641	−	1.16638i
$737$	1.39774			0.0514862
$738$	−0.242172	+	1.39310i	−0.00891446	+	0.0512807i
$739$		−	50.7654i		−	1.86743i	−0.358011	−	0.933717i	$-0.616545\pi$
$739$		−	50.7654i		−	1.86743i	0.358011	−	0.933717i	$-0.383455\pi$
$740$	0.165930	+	0.0594869i	0.00609970	+	0.00218678i
$741$			6.20380i			0.227902i
$742$	−18.2958	−	3.18047i	−0.671659	−	0.116759i
$743$	−5.84406			−0.214398			−0.107199	−	0.994238i	$-0.534188\pi$
$743$	−5.84406			−0.214398			−0.107199	+	0.994238i	$0.534188\pi$
$744$	−41.7545	−	23.7051i	−1.53080	−	0.869071i
$745$	0.0156131			0.000572021
$746$	−16.5917	−	2.88424i	−0.607464	−	0.105599i
$747$			2.37617i			0.0869395i
$748$	1.02593	−	2.86168i	0.0375118	−	0.104634i
$749$		−	9.14887i		−	0.334292i
$750$	−0.103409	+	0.594866i	−0.00377598	+	0.0217214i
$751$	−53.4369			−1.94994			−0.974971	−	0.222333i	$-0.928633\pi$
$751$	−53.4369			−1.94994			−0.974971	+	0.222333i	$0.928633\pi$
$752$	−9.16779	−	7.54289i	−0.334315	−	0.275061i
$753$	−29.8025			−1.08606
$754$	−0.0271229	+	0.156025i	−0.000987757	+	0.00568210i
$755$			0.0833618i			0.00303385i
$756$	3.60596	−	10.0583i	0.131147	−	0.365816i
$757$			16.6601i			0.605520i	0.953067	+	0.302760i	$0.0979081\pi$
$757$			16.6601i			0.605520i	−0.953067	+	0.302760i	$0.902092\pi$
$758$	28.0644	+	4.87861i	1.01934	+	0.177199i
$759$	46.2405			1.67842
$760$	0.131321	−	0.231311i	0.00476350	−	0.00839051i
$761$	−15.7023			−0.569208			−0.284604	−	0.958645i	$-0.591862\pi$
$761$	−15.7023			−0.569208			−0.284604	+	0.958645i	$0.591862\pi$
$762$	−33.1316	−	5.75948i	−1.20023	−	0.208644i
$763$			10.9192i			0.395303i
$764$	33.2093	+	11.9058i	1.20147	+	0.430735i
$765$		−	0.00220744i		−	7.98102e-5i
$766$	−7.58512	+	43.6336i	−0.274062	+	1.57655i
$767$	7.78767			0.281196
$768$	−26.3497	+	5.17323i	−0.950814	+	0.186673i
$769$	25.6291			0.924210			0.462105	−	0.886825i	$-0.347094\pi$
$769$	25.6291			0.924210			0.462105	+	0.886825i	$0.347094\pi$
$770$	0.0197886	−	0.113834i	0.000713130	−	0.00410230i
$771$			3.24258i			0.116779i
$772$	−14.5414	−	5.21320i	−0.523357	−	0.187627i
$773$			14.3154i			0.514889i	0.966293	+	0.257445i	$0.0828805\pi$
$773$			14.3154i			0.514889i	−0.966293	+	0.257445i	$0.917120\pi$
$774$	−0.828127	−	0.143959i	−0.0297664	−	0.00517449i
$775$	50.5674			1.81643
$776$	14.4730	−	25.4929i	0.519549	−	0.915142i
$777$	−5.81421			−0.208584
$778$	−28.8660	−	5.01797i	−1.03490	−	0.179903i
$779$		−	20.1610i		−	0.722344i
$780$	0.0288183	−	0.0803842i	0.00103186	−	0.00287822i
$781$		−	44.1693i		−	1.58050i
$782$	−0.983564	+	5.65798i	−0.0351722	+	0.202329i
$783$	0.598265			0.0213802
$784$	3.08889	+	2.54141i	0.110317	+	0.0907648i
$785$	−0.407443			−0.0145423
$786$	1.71931	−	9.89036i	0.0613256	−	0.352777i
$787$			43.8734i			1.56392i	0.623330	+	0.781959i	$0.285779\pi$
$787$			43.8734i			1.56392i	−0.623330	+	0.781959i	$0.714221\pi$
$788$	4.26751	−	11.9036i	0.152024	−	0.424047i
$789$		−	14.9075i		−	0.530720i
$790$	−0.349528	−	0.0607607i	−0.0124356	−	0.00216177i
$791$	−16.9502			−0.602680
$792$	1.44804	+	0.822090i	0.0514539	+	0.0292117i
$793$	−6.75418			−0.239848
$794$	−36.5803	−	6.35899i	−1.29819	−	0.225672i
$795$			0.560657i			0.0198845i
$796$	−4.64209	−	1.66422i	−0.164535	−	0.0589868i
$797$			22.6850i			0.803545i	0.915739	+	0.401773i	$0.131606\pi$
$797$			22.6850i			0.803545i	−0.915739	+	0.401773i	$0.868394\pi$
$798$	−1.50262	+	8.64387i	−0.0531922	+	0.305990i
$799$	1.40480			0.0496984
$800$	21.4430	−	18.4388i	0.758124	−	0.651911i
$801$	−0.0676570			−0.00239054
$802$	0.886367	−	5.09885i	0.0312987	−	0.180047i
$803$			16.5548i			0.584207i
$804$	1.37522	+	0.493026i	0.0485003	+	0.0173877i
$805$			0.218266i			0.00769288i
$806$	−14.0931	−	2.44990i	−0.496409	−	0.0862940i
$807$	25.0789			0.882820
$808$	6.02861	+	3.42259i	0.212086	+	0.120406i
$809$	−16.2297			−0.570606			−0.285303	−	0.958437i	$-0.592094\pi$
$809$	−16.2297			−0.570606			−0.285303	+	0.958437i	$0.592094\pi$
$810$	−0.298337	−	0.0518618i	−0.0104825	−	0.00182224i
$811$		−	38.2364i		−	1.34266i	−0.741157	−	0.671331i	$-0.765723\pi$
$811$		−	38.2364i		−	1.34266i	0.741157	−	0.671331i	$-0.234277\pi$
$812$	−0.0755816	+	0.210823i	−0.00265239	+	0.00739845i
$813$		−	18.8368i		−	0.660634i
$814$	2.69469	−	15.5013i	0.0944487	−	0.543319i
$815$	−0.469037			−0.0164297
$816$	2.01882	−	2.45371i	0.0706727	−	0.0858971i
$817$	11.9847			0.419292
$818$	−4.98510	+	28.6769i	−0.174300	+	1.00267i
$819$		−	0.183319i		−	0.00640570i
$820$	−0.0936533	+	0.261232i	−0.00327051	+	0.00912260i
$821$			47.4481i			1.65595i	0.560766	+	0.827974i	$0.310507\pi$
$821$			47.4481i			1.65595i	−0.560766	+	0.827974i	$0.689493\pi$
$822$	−48.2644	−	8.39011i	−1.68341	−	0.292639i
$823$	37.4132			1.30414			0.652072	−	0.758157i	$-0.273900\pi$
$823$	37.4132			1.30414			0.652072	+	0.758157i	$0.273900\pi$
$824$	−21.5977	+	38.0426i	−0.752392	+	1.32528i
$825$	26.9450			0.938103
$826$	10.8507	+	1.88625i	0.377544	+	0.0656310i
$827$		−	1.68923i		−	0.0587402i	−0.999569	−	0.0293701i	$-0.990650\pi$
$827$		−	1.68923i		−	0.0587402i	0.999569	−	0.0293701i	$-0.00935013\pi$
$828$	−2.96102	−	1.06154i	−0.102902	−	0.0368912i
$829$		−	14.1339i		−	0.490892i	−0.969410	−	0.245446i	$-0.921066\pi$
$829$		−	14.1339i		−	0.490892i	0.969410	−	0.245446i	$-0.0789344\pi$
$830$	−0.0798709	+	0.459460i	−0.00277236	+	0.0159481i
$831$	7.16605			0.248588
$832$	−6.86948	+	4.10002i	−0.238157	+	0.142143i
$833$	−0.473318			−0.0163995
$834$	4.14041	−	23.8178i	0.143371	−	0.824744i
$835$		−	0.0930039i		−	0.00321853i
$836$	−22.3490	−	8.01227i	−0.772956	−	0.277110i
$837$			54.0388i			1.86785i
$838$	−20.8122	−	3.61792i	−0.718945	−	0.124979i
$839$	−3.03087			−0.104637			−0.0523187	−	0.998630i	$-0.516661\pi$
$839$	−3.03087			−0.104637			−0.0523187	+	0.998630i	$0.516661\pi$
$840$	0.0596229	−	0.105021i	0.00205718	−	0.00362356i
$841$	28.9875			0.999568
$842$	12.2156	+	2.12351i	0.420976	+	0.0731811i
$843$		−	5.70541i		−	0.196505i
$844$	6.39177	−	17.8289i	0.220014	−	0.613695i
$845$		−	0.0254406i		−	0.000875185i
$846$	−0.131784	+	0.758091i	−0.00453082	+	0.0260637i
$847$	0.686889			0.0236018
$848$	33.3715	−	40.5604i	1.14598	−	1.39285i
$849$	−9.71334			−0.333361
$850$	−0.573136	+	3.29698i	−0.0196584	+	0.113086i
$851$			29.7222i			1.01886i
$852$	15.5800	−	43.4579i	0.533760	−	1.48884i
$853$			20.1050i			0.688381i	0.938900	+	0.344191i	$0.111847\pi$
$853$			20.1050i			0.688381i	−0.938900	+	0.344191i	$0.888153\pi$
$854$	−9.41072	−	1.63593i	−0.322028	−	0.0559802i
$855$	−0.0172395			−0.000589580
$856$	22.5033	+	12.7757i	0.769145	+	0.436663i
$857$	−49.1410			−1.67862			−0.839312	−	0.543650i	$-0.817042\pi$
$857$	−49.1410			−1.67862			−0.839312	+	0.543650i	$0.817042\pi$
$858$	−7.50955	−	1.30543i	−0.256372	−	0.0445668i
$859$		−	0.0725355i		−	0.00247488i	−0.999999	−	0.00123744i	$-0.999606\pi$
$859$		−	0.0725355i		−	0.00247488i	0.999999	−	0.00123744i	$-0.000393889\pi$
$860$	−0.155289	−	0.0556721i	−0.00529531	−	0.00189840i
$861$		−	9.15361i		−	0.311954i
$862$	2.60710	−	14.9974i	0.0887981	−	0.510814i
$863$	30.5044			1.03838			0.519192	−	0.854658i	$-0.326233\pi$
$863$	30.5044			1.03838			0.519192	+	0.854658i	$0.326233\pi$
$864$	19.7047	+	22.9150i	0.670366	+	0.779586i
$865$	0.570835			0.0194090
$866$	2.43192	−	13.9897i	0.0826399	−	0.475389i
$867$		−	28.1551i		−	0.956196i
$868$	−19.0428	−	6.82697i	−0.646355	−	0.231723i
$869$			31.6664i			1.07421i
$870$	0.00666180	+	0.00115806i	0.000225856	+	3.92620e-5i
$871$	0.435241			0.0147476
$872$	−26.8578	−	15.2478i	−0.909519	−	0.516356i
$873$	−1.89998			−0.0643047
$874$	44.1874	+	7.68138i	1.49466	+	0.259826i
$875$			0.254390i			0.00859995i
$876$	−5.83942	+	16.2882i	−0.197296	+	0.550327i
$877$			20.3212i			0.686198i	0.939299	+	0.343099i	$0.111477\pi$
$877$			20.3212i			0.686198i	−0.939299	+	0.343099i	$0.888523\pi$
$878$	−6.39928	+	36.8120i	−0.215965	+	1.24235i
$879$	3.95780			0.133493
$880$	0.252362	+	0.207634i	0.00850714	+	0.00699934i
$881$	−25.7497			−0.867530			−0.433765	−	0.901026i	$-0.642815\pi$
$881$	−25.7497			−0.867530			−0.433765	+	0.901026i	$0.642815\pi$
$882$	0.0444017	−	0.255422i	0.00149508	−	0.00860051i
$883$		−	43.1211i		−	1.45114i	−0.688147	−	0.725571i	$-0.741576\pi$
$883$		−	43.1211i		−	1.45114i	0.688147	−	0.725571i	$-0.258424\pi$
$884$	0.319466	−	0.891101i	0.0107448	−	0.0299710i
$885$		−	0.332510i		−	0.0111772i
$886$	47.9744	+	8.33971i	1.61173	+	0.280178i
$887$	−43.8945			−1.47383			−0.736916	−	0.675984i	$-0.763719\pi$
$887$	−43.8945			−1.47383			−0.736916	+	0.675984i	$0.763719\pi$
$888$	8.11908	−	14.3011i	0.272459	−	0.479913i
$889$	−14.1685			−0.475196
$890$	−0.0130823	−	0.00227417i	−0.000438518	−	7.62305e-5i
$891$			27.0286i			0.905491i
$892$	28.4267	+	10.1912i	0.951795	+	0.341225i
$893$		−	10.9711i		−	0.367135i
$894$	0.249472	−	1.43510i	0.00834360	−	0.0479968i
$895$	0.550844			0.0184127
$896$	−10.5644	+	4.04878i	−0.352933	+	0.135260i
$897$	14.3988			0.480763
$898$	0.926687	−	5.33080i	0.0309240	−	0.177891i
$899$		−	1.13266i		−	0.0377765i
$900$	−1.72543	−	0.618577i	−0.0575142	−	0.0206192i
$901$			6.21517i			0.207057i
$902$	24.4044	+	4.24238i	0.812579	+	0.141256i
$903$	5.44135			0.181077
$904$	23.6696	−	41.6920i	0.787239	−	1.38666i
$905$	−0.433881			−0.0144227
$906$	7.66228	+	1.33198i	0.254562	+	0.0442522i
$907$			10.8586i			0.360555i	0.983616	+	0.180278i	$0.0576996\pi$
$907$			10.8586i			0.360555i	−0.983616	+	0.180278i	$0.942300\pi$
$908$	−20.2376	+	56.4496i	−0.671607	+	1.87334i
$909$		−	0.449311i		−	0.0149027i
$910$	0.00616197	−	0.0354469i	0.000204267	−	0.00117505i
$911$	−21.8057			−0.722454			−0.361227	−	0.932478i	$-0.617642\pi$
$911$	−21.8057			−0.722454			−0.361227	+	0.932478i	$0.617642\pi$
$912$	−19.1628	−	15.7664i	−0.634545	−	0.522079i
$913$	41.6259			1.37762
$914$	1.83330	−	10.5461i	0.0606401	−	0.348834i
$915$			0.288383i			0.00953364i
$916$	2.89059	−	8.06287i	0.0955079	−	0.266405i
$917$		−	4.22954i		−	0.139672i
$918$	−3.52332	−	0.612482i	−0.116287	−	0.0202149i
$919$	2.98773			0.0985560			0.0492780	−	0.998785i	$-0.484308\pi$
$919$	2.98773			0.0985560			0.0492780	+	0.998785i	$0.484308\pi$
$920$	−0.536865	−	0.304791i	−0.0176999	−	0.0100487i
$921$	−40.7605			−1.34310
$922$	14.9144	+	2.59267i	0.491180	+	0.0853850i
$923$		−	13.7539i		−	0.452715i
$924$	−10.1470	−	3.63777i	−0.333812	−	0.119674i
$925$			17.3195i			0.569462i
$926$	−0.117503	+	0.675940i	−0.00386139	+	0.0222128i
$927$	2.83531			0.0931238
$928$	−0.413014	−	0.480304i	−0.0135578	−	0.0157668i
$929$	19.5957			0.642913			0.321456	−	0.946924i	$-0.395828\pi$
$929$	19.5957			0.642913			0.321456	+	0.946924i	$0.395828\pi$
$930$	−0.104603	+	0.601733i	−0.00343007	+	0.0197316i
$931$			3.69649i			0.121147i
$932$	−27.0087	−	9.68282i	−0.884701	−	0.317171i
$933$			55.1803i			1.80652i
$934$	28.9326	+	5.02954i	0.946703	+	0.164572i
$935$	−0.0386701			−0.00126465
$936$	0.450906	+	0.255991i	0.0147383	+	0.00836732i
$937$	21.4830			0.701818			0.350909	−	0.936409i	$-0.385873\pi$
$937$	21.4830			0.701818			0.350909	+	0.936409i	$0.385873\pi$
$938$	0.606429	+	0.105420i	0.0198006	+	0.00344207i
$939$			33.4026i			1.09005i
$940$	−0.0509638	+	0.142156i	−0.00166226	+	0.00463661i
$941$		−	6.60152i		−	0.215204i	−0.994194	−	0.107602i	$-0.965683\pi$
$941$		−	6.60152i		−	0.215204i	0.994194	−	0.107602i	$-0.0343171\pi$
$942$	−6.51027	+	37.4505i	−0.212116	+	1.22020i
$943$	−46.7931			−1.52379
$944$	−19.7917	+	24.0552i	−0.644165	+	0.782931i
$945$	−0.135918			−0.00442141
$946$	−2.52188	+	14.5072i	−0.0819934	+	0.471669i
$947$		−	3.95598i		−	0.128552i	−0.997932	−	0.0642760i	$-0.979526\pi$
$947$		−	3.95598i		−	0.128552i	0.997932	−	0.0642760i	$-0.0204738\pi$
$948$	−11.1698	+	31.1563i	−0.362777	+	1.01191i
$949$			5.15501i			0.167339i
$950$	25.7486	+	4.47604i	0.835394	+	0.145222i
$951$	2.59215			0.0840564
$952$	0.660950	−	1.16421i	0.0214215	−	0.0377322i
$953$	−24.4978			−0.793562			−0.396781	−	0.917913i	$-0.629873\pi$
$953$	−24.4978			−0.793562			−0.396781	+	0.917913i	$0.629873\pi$
$954$	−3.35397	−	0.583042i	−0.108589	−	0.0188767i
$955$		−	0.448759i		−	0.0145215i
$956$	−45.5763	−	16.3394i	−1.47404	−	0.528454i
$957$		−	0.603543i		−	0.0195098i
$958$	2.30743	−	13.2735i	0.0745496	−	0.428849i
$959$	−20.6399			−0.666497
$960$	0.175058	+	0.293306i	0.00564999	+	0.00946641i
$961$	71.3089			2.30029
$962$	0.839099	−	4.82695i	0.0270537	−	0.155627i
$963$		−	1.67716i		−	0.0540459i
$964$	32.6101	+	11.6909i	1.05030	+	0.376540i
$965$			0.196499i			0.00632553i
$966$	20.0622	+	3.48754i	0.645489	+	0.112210i
$967$	−13.3675			−0.429870			−0.214935	−	0.976628i	$-0.568954\pi$
$967$	−13.3675			−0.429870			−0.214935	+	0.976628i	$0.568954\pi$
$968$	−0.959186	+	1.68953i	−0.0308294	+	0.0543034i
$969$	2.93637			0.0943298
$970$	−0.367383	−	0.0638647i	−0.0117960	−	0.00205057i
$971$		−	25.6105i		−	0.821880i	−0.911662	−	0.410940i	$-0.865201\pi$
$971$		−	25.6105i		−	0.821880i	0.911662	−	0.410940i	$-0.134799\pi$
$972$	1.28402	−	3.58156i	0.0411848	−	0.114879i
$973$		−	10.1855i		−	0.326533i
$974$	−3.31661	+	19.0789i	−0.106271	+	0.611328i
$975$	8.39040			0.268708
$976$	17.1652	−	20.8629i	0.549443	−	0.667805i
$977$	10.8736			0.347878			0.173939	−	0.984756i	$-0.444350\pi$
$977$	10.8736			0.347878			0.173939	+	0.984756i	$0.444350\pi$
$978$	−7.49444	+	43.1120i	−0.239646	+	1.37857i
$979$			1.18522i			0.0378798i
$980$	0.0171712	−	0.0478963i	0.000548512	−	0.00152999i
$981$			2.00171i			0.0639095i
$982$	17.7356	+	3.08309i	0.565966	+	0.0983855i
$983$	−40.8856			−1.30405			−0.652024	−	0.758198i	$-0.726080\pi$
$983$	−40.8856			−1.30405			−0.652024	+	0.758198i	$0.726080\pi$
$984$	22.5149	+	12.7823i	0.717750	+	0.407484i
$985$	−0.160854			−0.00512523
$986$	0.0738495	+	0.0128377i	0.00235185	+	0.000408837i
$987$		−	4.98117i		−	0.158552i
$988$	−6.95926	−	2.49494i	−0.221404	−	0.0793747i
$989$		−	27.8161i		−	0.884502i
$990$	0.00362763	−	0.0208680i	0.000115293	−	0.000663229i
$991$	−20.0515			−0.636958			−0.318479	−	0.947930i	$-0.603172\pi$
$991$	−20.0515			−0.636958			−0.318479	+	0.947930i	$0.603172\pi$
$992$	43.3839	−	37.3058i	1.37744	−	1.18446i
$993$	42.3797			1.34488
$994$	3.33133	−	19.1636i	0.105663	−	0.607831i
$995$			0.0627289i			0.00198864i
$996$	40.9555	+	14.6828i	1.29772	+	0.465243i
$997$		−	9.20059i		−	0.291386i	−0.989330	−	0.145693i	$-0.953459\pi$
$997$		−	9.20059i		−	0.291386i	0.989330	−	0.145693i	$-0.0465411\pi$
$998$	17.5308	+	3.04750i	0.554929	+	0.0964670i
$999$	−18.5085			−0.585583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.b.365.19	✓	38
4.3	odd	2		2912.2.c.b.1457.11		38
8.3	odd	2		2912.2.c.b.1457.28		38
8.5	even	2	inner	728.2.c.b.365.20	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.b.365.19	✓	38	1.1	even	1	trivial
728.2.c.b.365.20	yes	38	8.5	even	2	inner
2912.2.c.b.1457.11		38	4.3	odd	2
2912.2.c.b.1457.28		38	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.242210 - 1.39332i) q^{2} +1.67830i q^{3} +(-1.88267 - 0.674950i) q^{4} +0.0254406i q^{5} +(2.33840 + 0.406500i) q^{6} +1.00000 q^{7} +(-1.39642 + 2.45968i) q^{8} +0.183319 q^{9} +(0.0354469 + 0.00616197i) q^{10} -3.21140i q^{11} +(1.13277 - 3.15968i) q^{12} -1.00000i q^{13} +(0.242210 - 1.39332i) q^{14} -0.0426969 q^{15} +(3.08889 + 2.54141i) q^{16} -0.473318 q^{17} +(0.0444017 - 0.255422i) q^{18} +3.69649i q^{19} +(0.0171712 - 0.0478963i) q^{20} +1.67830i q^{21} +(-4.47451 - 0.777832i) q^{22} +8.57943 q^{23} +(-4.12807 - 2.34361i) q^{24} +4.99935 q^{25} +(-1.39332 - 0.242210i) q^{26} +5.34256i q^{27} +(-1.88267 - 0.674950i) q^{28} -0.111981i q^{29} +(-0.0103416 + 0.0594904i) q^{30} +10.1148 q^{31} +(4.28915 - 3.68825i) q^{32} +5.38969 q^{33} +(-0.114642 + 0.659482i) q^{34} +0.0254406i q^{35} +(-0.345130 - 0.123731i) q^{36} +3.46435i q^{37} +(5.15038 + 0.895325i) q^{38} +1.67830 q^{39} +(-0.0625758 - 0.0355258i) q^{40} -5.45411 q^{41} +(2.33840 + 0.406500i) q^{42} -3.24219i q^{43} +(-2.16754 + 6.04601i) q^{44} +0.00466376i q^{45} +(2.07802 - 11.9539i) q^{46} -2.96799 q^{47} +(-4.26525 + 5.18407i) q^{48} +1.00000 q^{49} +(1.21089 - 6.96569i) q^{50} -0.794368i q^{51} +(-0.674950 + 1.88267i) q^{52} -13.1311i q^{53} +(7.44388 + 1.29402i) q^{54} +0.0817001 q^{55} +(-1.39642 + 2.45968i) q^{56} -6.20380 q^{57} +(-0.156025 - 0.0271229i) q^{58} +7.78767i q^{59} +(0.0803842 + 0.0288183i) q^{60} -6.75418i q^{61} +(2.44990 - 14.0931i) q^{62} +0.183319 q^{63} +(-4.10002 - 6.86948i) q^{64} +0.0254406 q^{65} +(1.30543 - 7.50955i) q^{66} +0.435241i q^{67} +(0.891101 + 0.319466i) q^{68} +14.3988i q^{69} +(0.0354469 + 0.00616197i) q^{70} +13.7539 q^{71} +(-0.255991 + 0.450906i) q^{72} -5.15501 q^{73} +(4.82695 + 0.839099i) q^{74} +8.39040i q^{75} +(2.49494 - 6.95926i) q^{76} -3.21140i q^{77} +(0.406500 - 2.33840i) q^{78} -9.86060 q^{79} +(-0.0646552 + 0.0785832i) q^{80} -8.41644 q^{81} +(-1.32104 + 7.59930i) q^{82} +12.9619i q^{83} +(1.13277 - 3.15968i) q^{84} -0.0120415i q^{85} +(-4.51740 - 0.785289i) q^{86} +0.187937 q^{87} +(7.89902 + 4.48447i) q^{88} -0.369066 q^{89} +(0.00649810 + 0.00112961i) q^{90} -1.00000i q^{91} +(-16.1522 - 5.79069i) q^{92} +16.9756i q^{93} +(-0.718876 + 4.13535i) q^{94} -0.0940410 q^{95} +(6.18997 + 7.19848i) q^{96} -10.3643 q^{97} +(0.242210 - 1.39332i) q^{98} -0.588712i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{4} + 14 q^{6} + 38 q^{7} - 6 q^{8} - 46 q^{9} - 4 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 4 q^{18} - 24 q^{20} + 10 q^{22} + 12 q^{23} + 10 q^{24} - 50 q^{25} + 8 q^{28} + 4 q^{30} + 16 q^{31}+ \cdots + 82 q^{96}+O(q^{100}) \) 38 * q + 8 * q^4 + 14 * q^6 + 38 * q^7 - 6 * q^8 - 46 * q^9 - 4 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 4 * q^18 - 24 * q^20 + 10 * q^22 + 12 * q^23 + 10 * q^24 - 50 * q^25 + 8 * q^28 + 4 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 - 4 * q^34 - 38 * q^36 - 28 * q^38 + 8 * q^39 + 4 * q^40 + 8 * q^41 + 14 * q^42 - 40 * q^44 - 16 * q^46 + 4 * q^48 + 38 * q^49 + 24 * q^50 - 4 * q^52 - 14 * q^54 - 6 * q^56 + 8 * q^57 - 24 * q^58 + 44 * q^60 - 12 * q^62 - 46 * q^63 + 32 * q^64 + 20 * q^65 - 76 * q^66 - 52 * q^68 + 42 * q^72 + 50 * q^74 - 28 * q^76 - 12 * q^79 - 16 * q^80 + 62 * q^81 - 4 * q^84 + 44 * q^86 - 56 * q^87 - 6 * q^88 + 48 * q^90 + 2 * q^92 - 48 * q^94 + 82 * q^96

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