LMFDB - Embedded newform 728.2.i.a.701.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(701,728)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("728.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			701.2
Character	$\chi$	$=$	728.701
Dual form			728.2.i.a.701.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40496 + 0.161540i) q^{2} -2.58827i q^{3} +(1.94781 - 0.453913i) q^{4} -1.51724 q^{5} +(0.418108 + 3.63640i) q^{6} -1.00000i q^{7} +(-2.66326 + 0.952378i) q^{8} -3.69913 q^{9} +(2.13165 - 0.245094i) q^{10} -1.15039 q^{11} +(-1.17485 - 5.04145i) q^{12} +(3.39762 - 1.20671i) q^{13} +(0.161540 + 1.40496i) q^{14} +3.92702i q^{15} +(3.58793 - 1.76827i) q^{16} +0.0878473 q^{17} +(5.19711 - 0.597556i) q^{18} -8.25567 q^{19} +(-2.95529 + 0.688694i) q^{20} -2.58827 q^{21} +(1.61625 - 0.185834i) q^{22} -6.48403 q^{23} +(2.46501 + 6.89324i) q^{24} -2.69799 q^{25} +(-4.57858 + 2.24423i) q^{26} +1.80953i q^{27} +(-0.453913 - 1.94781i) q^{28} +2.75060i q^{29} +(-0.634370 - 5.51729i) q^{30} -5.46650i q^{31} +(-4.75524 + 3.06394i) q^{32} +2.97752i q^{33} +(-0.123422 + 0.0141908i) q^{34} +1.51724i q^{35} +(-7.20519 + 1.67908i) q^{36} +8.75613 q^{37} +(11.5989 - 1.33362i) q^{38} +(-3.12330 - 8.79396i) q^{39} +(4.04080 - 1.44498i) q^{40} +0.221622i q^{41} +(3.63640 - 0.418108i) q^{42} +11.3062i q^{43} +(-2.24075 + 0.522179i) q^{44} +5.61245 q^{45} +(9.10979 - 1.04743i) q^{46} +4.58078i q^{47} +(-4.57676 - 9.28651i) q^{48} -1.00000 q^{49} +(3.79056 - 0.435833i) q^{50} -0.227372i q^{51} +(6.07018 - 3.89268i) q^{52} +10.8067i q^{53} +(-0.292311 - 2.54231i) q^{54} +1.74542 q^{55} +(0.952378 + 2.66326i) q^{56} +21.3679i q^{57} +(-0.444331 - 3.86447i) q^{58} -3.96379 q^{59} +(1.78252 + 7.64908i) q^{60} -11.0547i q^{61} +(0.883058 + 7.68021i) q^{62} +3.69913i q^{63} +(6.18595 - 5.07287i) q^{64} +(-5.15500 + 1.83087i) q^{65} +(-0.480989 - 4.18329i) q^{66} -4.63551 q^{67} +(0.171110 - 0.0398751i) q^{68} +16.7824i q^{69} +(-0.245094 - 2.13165i) q^{70} -9.36899i q^{71} +(9.85175 - 3.52297i) q^{72} +10.4110i q^{73} +(-12.3020 + 1.41446i) q^{74} +6.98312i q^{75} +(-16.0805 + 3.74736i) q^{76} +1.15039i q^{77} +(5.80867 + 11.8506i) q^{78} +7.68869 q^{79} +(-5.44373 + 2.68289i) q^{80} -6.41384 q^{81} +(-0.0358007 - 0.311369i) q^{82} -5.19464 q^{83} +(-5.04145 + 1.17485i) q^{84} -0.133285 q^{85} +(-1.82640 - 15.8847i) q^{86} +7.11928 q^{87} +(3.06380 - 1.09561i) q^{88} +1.08552i q^{89} +(-7.88526 + 0.906635i) q^{90} +(-1.20671 - 3.39762i) q^{91} +(-12.6297 + 2.94319i) q^{92} -14.1488 q^{93} +(-0.739978 - 6.43580i) q^{94} +12.5258 q^{95} +(7.93030 + 12.3078i) q^{96} -10.4826i q^{97} +(1.40496 - 0.161540i) q^{98} +4.25545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 84 q^{9} + 8 q^{10} - 20 q^{12} - 8 q^{16} + 8 q^{17} - 12 q^{22} - 24 q^{23} + 92 q^{25} - 40 q^{30} + 44 q^{36} + 20 q^{38} - 24 q^{39} - 28 q^{40} - 72 q^{48} - 84 q^{49} - 44 q^{52} + 32 q^{55}+ \cdots - 16 q^{95}+O(q^{100}) $ 84 * q - 84 * q^9 + 8 * q^10 - 20 * q^12 - 8 * q^16 + 8 * q^17 - 12 * q^22 - 24 * q^23 + 92 * q^25 - 40 * q^30 + 44 * q^36 + 20 * q^38 - 24 * q^39 - 28 * q^40 - 72 * q^48 - 84 * q^49 - 44 * q^52 + 32 * q^55 - 40 * q^62 + 72 * q^64 - 24 * q^65 - 60 * q^66 - 92 * q^68 + 28 * q^74 + 12 * q^78 - 40 * q^79 + 84 * q^81 + 24 * q^82 - 48 * q^87 - 108 * q^88 + 20 * q^90 + 60 * q^92 + 36 * q^94 - 16 * q^95

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 $

$2$	−1.40496	+	0.161540i	−0.993455	+	0.114226i
$2$	−1.40496	+	0.161540i	−0.993455	+	0.114226i
$3$		−	2.58827i		−	1.49434i	−0.664635	−	0.747168i	$-0.731413\pi$
$3$		−	2.58827i		−	1.49434i	0.664635	−	0.747168i	$-0.268587\pi$
$4$	1.94781	−	0.453913i	0.973905	−	0.226957i
$5$	−1.51724			−0.678529			−0.339265	−	0.940691i	$-0.610178\pi$
$5$	−1.51724			−0.678529			−0.339265	+	0.940691i	$0.610178\pi$
$6$	0.418108	+	3.63640i	0.170692	+	1.48456i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.66326	+	0.952378i	−0.941606	+	0.336716i
$9$	−3.69913			−1.23304
$10$	2.13165	−	0.245094i	0.674088	−	0.0775056i
$11$	−1.15039			−0.346857			−0.173428	−	0.984847i	$-0.555484\pi$
$11$	−1.15039			−0.346857			−0.173428	+	0.984847i	$0.555484\pi$
$12$	−1.17485	−	5.04145i	−0.339150	−	1.45534i
$13$	3.39762	−	1.20671i	0.942331	−	0.334682i
$13$	3.39762	−	1.20671i	0.942331	−	0.334682i
$14$	0.161540	+	1.40496i	0.0431734	+	0.375491i
$15$			3.92702i			1.01395i
$16$	3.58793	−	1.76827i	0.896981	−	0.442068i
$17$	0.0878473			0.0213061			0.0106531	−	0.999943i	$-0.496609\pi$
$17$	0.0878473			0.0213061			0.0106531	+	0.999943i	$0.496609\pi$
$18$	5.19711	−	0.597556i	1.22497	−	0.140845i
$19$	−8.25567			−1.89398			−0.946990	−	0.321262i	$-0.895893\pi$
$19$	−8.25567			−1.89398			−0.946990	+	0.321262i	$0.895893\pi$
$20$	−2.95529	+	0.688694i	−0.660823	+	0.153997i
$21$	−2.58827			−0.564806
$22$	1.61625	−	0.185834i	0.344586	−	0.0396200i
$23$	−6.48403			−1.35201			−0.676007	−	0.736895i	$-0.736291\pi$
$23$	−6.48403			−1.35201			−0.676007	+	0.736895i	$0.736291\pi$
$24$	2.46501	+	6.89324i	0.503168	+	1.40708i
$25$	−2.69799			−0.539598
$26$	−4.57858	+	2.24423i	−0.897934	+	0.440130i
$27$			1.80953i			0.348243i
$28$	−0.453913	−	1.94781i	−0.0857815	−	0.368101i
$29$			2.75060i			0.510773i	0.966839	+	0.255387i	$0.0822027\pi$
$29$			2.75060i			0.510773i	−0.966839	+	0.255387i	$0.917797\pi$
$30$	−0.634370	−	5.51729i	−0.115820	−	1.00731i
$31$		−	5.46650i		−	0.981813i	−0.871212	−	0.490907i	$-0.836666\pi$
$31$		−	5.46650i		−	0.981813i	0.871212	−	0.490907i	$-0.163334\pi$
$32$	−4.75524	+	3.06394i	−0.840615	+	0.541633i
$33$			2.97752i			0.518321i
$34$	−0.123422	+	0.0141908i	−0.0211667	+	0.00243371i
$35$			1.51724i			0.256460i
$36$	−7.20519	+	1.67908i	−1.20087	+	0.279847i
$37$	8.75613			1.43950			0.719750	−	0.694234i	$-0.244256\pi$
$37$	8.75613			1.43950			0.719750	+	0.694234i	$0.244256\pi$
$38$	11.5989	−	1.33362i	1.88158	−	0.216342i
$39$	−3.12330	−	8.79396i	−0.500128	−	1.40816i
$40$	4.04080	−	1.44498i	0.638907	−	0.228472i
$41$			0.221622i			0.0346115i	0.999850	+	0.0173057i	$0.00550886\pi$
$41$			0.221622i			0.0346115i	−0.999850	+	0.0173057i	$0.994491\pi$
$42$	3.63640	−	0.418108i	0.561109	−	0.0645155i
$43$			11.3062i			1.72417i	0.506760	+	0.862087i	$0.330843\pi$
$43$			11.3062i			1.72417i	−0.506760	+	0.862087i	$0.669157\pi$
$44$	−2.24075	+	0.522179i	−0.337805	+	0.0787214i
$45$	5.61245			0.836655
$46$	9.10979	−	1.04743i	1.34317	−	0.154435i
$47$			4.58078i			0.668175i	0.942542	+	0.334088i	$0.108428\pi$
$47$			4.58078i			0.668175i	−0.942542	+	0.334088i	$0.891572\pi$
$48$	−4.57676	−	9.28651i	−0.660599	−	1.34039i
$49$	−1.00000			−0.142857
$50$	3.79056	−	0.435833i	0.536066	−	0.0616361i
$51$		−	0.227372i		−	0.0318385i
$52$	6.07018	−	3.89268i	0.841782	−	0.539817i
$53$			10.8067i			1.48441i	0.670171	+	0.742207i	$0.266221\pi$
$53$			10.8067i			1.48441i	−0.670171	+	0.742207i	$0.733779\pi$
$54$	−0.292311	−	2.54231i	−0.0397784	−	0.345964i
$55$	1.74542			0.235352
$56$	0.952378	+	2.66326i	0.127267	+	0.355894i
$57$			21.3679i			2.83025i
$58$	−0.444331	−	3.86447i	−0.0583435	−	0.507430i
$59$	−3.96379			−0.516041			−0.258021	−	0.966139i	$-0.583070\pi$
$59$	−3.96379			−0.516041			−0.258021	+	0.966139i	$0.583070\pi$
$60$	1.78252	+	7.64908i	0.230123	+	0.987492i
$61$		−	11.0547i		−	1.41541i	−0.706509	−	0.707704i	$-0.749731\pi$
$61$		−	11.0547i		−	1.41541i	0.706509	−	0.707704i	$-0.250269\pi$
$62$	0.883058	+	7.68021i	0.112149	+	0.975387i
$63$			3.69913i			0.466046i
$64$	6.18595	−	5.07287i	0.773244	−	0.634108i
$65$	−5.15500	+	1.83087i	−0.639399	+	0.227092i
$66$	−0.480989	−	4.18329i	−0.0592057	−	0.514928i
$67$	−4.63551			−0.566317			−0.283159	−	0.959073i	$-0.591382\pi$
$67$	−4.63551			−0.566317			−0.283159	+	0.959073i	$0.591382\pi$
$68$	0.171110	−	0.0398751i	0.0207501	−	0.00483556i
$69$			16.7824i			2.02037i
$70$	−0.245094	−	2.13165i	−0.0292944	−	0.254781i
$71$		−	9.36899i		−	1.11190i	−0.831217	−	0.555948i	$-0.812356\pi$
$71$		−	9.36899i		−	1.11190i	0.831217	−	0.555948i	$-0.187644\pi$
$72$	9.85175	−	3.52297i	1.16104	−	0.415185i
$73$			10.4110i			1.21851i	0.792974	+	0.609255i	$0.208532\pi$
$73$			10.4110i			1.21851i	−0.792974	+	0.609255i	$0.791468\pi$
$74$	−12.3020	+	1.41446i	−1.43008	+	0.164428i
$75$			6.98312i			0.806341i
$76$	−16.0805	+	3.74736i	−1.84456	+	0.429852i
$77$			1.15039i			0.131099i
$78$	5.80867	+	11.8506i	0.657703	+	1.34182i
$79$	7.68869			0.865045			0.432523	−	0.901623i	$-0.357624\pi$
$79$	7.68869			0.865045			0.432523	+	0.901623i	$0.357624\pi$
$80$	−5.44373	+	2.68289i	−0.608628	+	0.299956i
$81$	−6.41384			−0.712649
$82$	−0.0358007	−	0.311369i	−0.00395353	−	0.0343849i
$83$	−5.19464			−0.570186			−0.285093	−	0.958500i	$-0.592024\pi$
$83$	−5.19464			−0.570186			−0.285093	+	0.958500i	$0.592024\pi$
$84$	−5.04145	+	1.17485i	−0.550067	+	0.128187i
$85$	−0.133285			−0.0144568
$86$	−1.82640	−	15.8847i	−0.196945	−	1.71289i
$87$	7.11928			0.763267
$88$	3.06380	−	1.09561i	0.326602	−	0.116792i
$89$			1.08552i			0.115064i	0.998344	+	0.0575322i	$0.0183232\pi$
$89$			1.08552i			0.115064i	−0.998344	+	0.0575322i	$0.981677\pi$
$90$	−7.88526	+	0.906635i	−0.831179	+	0.0955677i
$91$	−1.20671	−	3.39762i	−0.126498	−	0.356168i
$92$	−12.6297	+	2.94319i	−1.31673	+	0.306849i
$93$	−14.1488			−1.46716
$94$	−0.739978	−	6.43580i	−0.0763229	−	0.663802i
$95$	12.5258			1.28512
$96$	7.93030	+	12.3078i	0.809383	+	1.25616i
$97$		−	10.4826i		−	1.06434i	−0.846636	−	0.532172i	$-0.821376\pi$
$97$		−	10.4826i		−	1.06434i	0.846636	−	0.532172i	$-0.178624\pi$
$98$	1.40496	−	0.161540i	0.141922	−	0.0163180i
$99$	4.25545			0.427689
$100$	−5.25517	+	1.22465i	−0.525517	+	0.122465i
$101$			3.46200i			0.344482i	0.985055	+	0.172241i	$0.0551007\pi$
$101$			3.46200i			0.344482i	−0.985055	+	0.172241i	$0.944899\pi$
$102$	0.0367297	+	0.319448i	0.00363678	+	0.0316301i
$103$	5.66902			0.558586			0.279293	−	0.960206i	$-0.409900\pi$
$103$	5.66902			0.558586			0.279293	+	0.960206i	$0.409900\pi$
$104$	−7.89952	+	6.44962i	−0.774612	+	0.632437i
$105$	3.92702			0.383237
$106$	−1.74571	−	15.1829i	−0.169559	−	1.47470i
$107$		−	17.3294i		−	1.67530i	−0.546208	−	0.837650i	$-0.683929\pi$
$107$		−	17.3294i		−	1.67530i	0.546208	−	0.837650i	$-0.316071\pi$
$108$	0.821368	+	3.52461i	0.0790362	+	0.339156i
$109$	−11.0393			−1.05737			−0.528685	−	0.848818i	$-0.677315\pi$
$109$	−11.0393			−1.05737			−0.528685	+	0.848818i	$0.677315\pi$
$110$	−2.45224	+	0.281955i	−0.233812	+	0.0268833i
$111$		−	22.6632i		−	2.15110i
$112$	−1.76827	−	3.58793i	−0.167086	−	0.339027i
$113$	−7.22371			−0.679550			−0.339775	−	0.940507i	$-0.610351\pi$
$113$	−7.22371			−0.679550			−0.339775	+	0.940507i	$0.610351\pi$
$114$	−3.45177	−	30.0210i	−0.323287	−	2.81172i
$115$	9.83782			0.917381
$116$	1.24853	+	5.35764i	0.115923	+	0.497444i
$117$	−12.5682	+	4.46379i	−1.16193	+	0.412677i
$118$	5.56895	−	0.640310i	0.512664	−	0.0589453i
$119$		−	0.0878473i		−	0.00805295i
$120$	−3.74000	−	10.4587i	−0.341414	−	0.954743i
$121$	−9.67660			−0.879691
$122$	1.78577	+	15.5314i	0.161676	+	1.40614i
$123$	0.573616			0.0517212
$124$	−2.48132	−	10.6477i	−0.222829	−	0.956193i
$125$	11.6797			1.04466
$126$	−0.597556	−	5.19711i	−0.0532346	−	0.462996i
$127$	−10.8980			−0.967043			−0.483521	−	0.875333i	$-0.660642\pi$
$127$	−10.8980			−0.967043			−0.483521	+	0.875333i	$0.660642\pi$
$128$	−7.87153	+	8.12644i	−0.695752	+	0.718283i
$129$	29.2634			2.57650
$130$	6.94680	−	3.40503i	0.609274	−	0.298641i
$131$			11.3300i			0.989908i	0.868919	+	0.494954i	$0.164815\pi$
$131$			11.3300i			0.989908i	−0.868919	+	0.494954i	$0.835185\pi$
$132$	1.35154	+	5.79965i	0.117636	+	0.504795i
$133$			8.25567i			0.715857i
$134$	6.51269	−	0.748819i	0.562611	−	0.0646881i
$135$		−	2.74548i		−	0.236293i
$136$	−0.233961	+	0.0836638i	−0.0200620	+	0.00717412i
$137$		−	5.25241i		−	0.448744i	−0.974504	−	0.224372i	$-0.927967\pi$
$137$		−	5.25241i		−	0.448744i	0.974504	−	0.224372i	$-0.0720331\pi$
$138$	−2.71103	−	23.5786i	−0.230778	−	2.00714i
$139$			6.66621i			0.565421i	0.959205	+	0.282710i	$0.0912335\pi$
$139$			6.66621i			0.565421i	−0.959205	+	0.282710i	$0.908766\pi$
$140$	0.688694	+	2.95529i	0.0582053	+	0.249768i
$141$	11.8563			0.998479
$142$	1.51347	+	13.1630i	0.127007	+	1.10462i
$143$	−3.90860	+	1.38820i	−0.326854	+	0.116087i
$144$	−13.2722	+	6.54107i	−1.10602	+	0.545089i
$145$		−	4.17331i		−	0.346574i
$146$	−1.68179	−	14.6270i	−0.139186	−	1.21054i
$147$			2.58827i			0.213477i
$148$	17.0553	−	3.97453i	1.40194	−	0.326704i
$149$	−17.9670			−1.47192			−0.735959	−	0.677027i	$-0.763268\pi$
$149$	−17.9670			−1.47192			−0.735959	+	0.677027i	$0.763268\pi$
$150$	−1.12805	−	9.81099i	−0.0921051	−	0.801064i
$151$		−	0.785249i		−	0.0639027i	−0.999489	−	0.0319513i	$-0.989828\pi$
$151$		−	0.785249i		−	0.0639027i	0.999489	−	0.0319513i	$-0.0101722\pi$
$152$	21.9870	−	7.86252i	1.78338	−	0.637734i
$153$	−0.324958			−0.0262713
$154$	−0.185834	−	1.61625i	−0.0149750	−	0.130241i
$155$			8.29398i			0.666189i
$156$	−10.0753	−	15.7112i	−0.806668	−	1.25791i
$157$			11.0014i			0.878004i	0.898486	+	0.439002i	$0.144668\pi$
$157$			11.0014i			0.878004i	−0.898486	+	0.439002i	$0.855332\pi$
$158$	−10.8023	+	1.24203i	−0.859383	+	0.0988106i
$159$	27.9706			2.21821
$160$	7.21482	−	4.64873i	0.570382	−	0.367514i
$161$			6.48403i			0.511014i
$162$	9.01118	−	1.03609i	0.707985	−	0.0814030i
$163$	−9.28282			−0.727087			−0.363543	−	0.931577i	$-0.618433\pi$
$163$	−9.28282			−0.727087			−0.363543	+	0.931577i	$0.618433\pi$
$164$	0.100597	+	0.431677i	0.00785530	+	0.0337083i
$165$		−	4.51761i		−	0.351696i
$166$	7.29824	−	0.839141i	0.566454	−	0.0651300i
$167$		−	9.91186i		−	0.767002i	−0.923540	−	0.383501i	$-0.874718\pi$
$167$		−	9.91186i		−	0.767002i	0.923540	−	0.383501i	$-0.125282\pi$
$168$	6.89324	−	2.46501i	0.531825	−	0.190179i
$169$	10.0877	−	8.19992i	0.775976	−	0.630763i
$170$	0.187260	−	0.0215309i	0.0143622	−	0.00165134i
$171$	30.5388			2.33536
$172$	5.13202	+	22.0223i	0.391313	+	1.67918i
$173$		−	22.0729i		−	1.67817i	−0.543999	−	0.839086i	$-0.683090\pi$
$173$		−	22.0729i		−	1.67817i	0.543999	−	0.839086i	$-0.316910\pi$
$174$	−10.0023	+	1.15005i	−0.758271	+	0.0871849i
$175$			2.69799i			0.203949i
$176$	−4.12752	+	2.03421i	−0.311124	+	0.153334i
$177$			10.2593i			0.771139i
$178$	−0.175354	−	1.52510i	−0.0131433	−	0.114311i
$179$		−	20.2249i		−	1.51168i	−0.654756	−	0.755841i	$-0.727228\pi$
$179$		−	20.2249i		−	1.51168i	0.654756	−	0.755841i	$-0.272772\pi$
$180$	10.9320	−	2.54757i	0.814822	−	0.189884i
$181$		−	19.1349i		−	1.42229i	−0.703048	−	0.711143i	$-0.748178\pi$
$181$		−	19.1349i		−	1.42229i	0.703048	−	0.711143i	$-0.251822\pi$
$182$	2.24423	+	4.57858i	0.166354	+	0.339387i
$183$	−28.6125			−2.11510
$184$	17.2687	−	6.17525i	1.27307	−	0.455245i
$185$	−13.2851			−0.976743
$186$	19.8784	−	2.28559i	1.45756	−	0.167588i
$187$	−0.101059			−0.00739016
$188$	2.07928	+	8.92248i	0.151647	+	0.650739i
$189$	1.80953			0.131624
$190$	−17.5982	+	2.02342i	−1.27671	+	0.146794i
$191$	−1.20317			−0.0870584			−0.0435292	−	0.999052i	$-0.513860\pi$
$191$	−1.20317			−0.0870584			−0.0435292	+	0.999052i	$0.513860\pi$
$192$	−13.1299	−	16.0109i	−0.947571	−	1.15549i
$193$		−	16.6104i		−	1.19564i	−0.801630	−	0.597820i	$-0.796034\pi$
$193$		−	16.6104i		−	1.19564i	0.801630	−	0.597820i	$-0.203966\pi$
$194$	1.69335	+	14.7276i	0.121576	+	1.05738i
$195$	4.73878	+	13.3425i	0.339351	+	0.955478i
$196$	−1.94781	+	0.453913i	−0.139129	+	0.0324224i
$197$	12.3136			0.877306			0.438653	−	0.898656i	$-0.355456\pi$
$197$	12.3136			0.877306			0.438653	+	0.898656i	$0.355456\pi$
$198$	−5.97872	+	0.687425i	−0.424889	+	0.0488532i
$199$	−3.59829			−0.255076			−0.127538	−	0.991834i	$-0.540707\pi$
$199$	−3.59829			−0.255076			−0.127538	+	0.991834i	$0.540707\pi$
$200$	7.18546	−	2.56951i	0.508089	−	0.181692i
$201$			11.9979i			0.846269i
$202$	−0.559251	−	4.86396i	−0.0393487	−	0.342227i
$203$	2.75060			0.193054
$204$	−0.103207	−	0.442878i	−0.00722596	−	0.0310077i
$205$		−	0.336252i		−	0.0234849i
$206$	−7.96474	+	0.915774i	−0.554930	+	0.0638050i
$207$	23.9853			1.66709
$208$	10.0566	−	10.3375i	0.697301	−	0.716778i
$209$	9.49727			0.656940
$210$	−5.51729	+	0.634370i	−0.380729	+	0.0437757i
$211$		−	13.3979i		−	0.922352i	−0.887309	−	0.461176i	$-0.847428\pi$
$211$		−	13.3979i		−	0.922352i	0.887309	−	0.461176i	$-0.152572\pi$
$212$	4.90530	+	21.0494i	0.336898	+	1.44568i
$213$	−24.2495			−1.66155
$214$	2.79939	+	24.3471i	0.191363	+	1.66433i
$215$		−	17.1541i		−	1.16990i
$216$	−1.72335	−	4.81925i	−0.117259	−	0.327908i
$217$	−5.46650			−0.371091
$218$	15.5097	−	1.78328i	1.05045	−	0.120779i
$219$	26.9463			1.82087
$220$	3.39974	−	0.792269i	0.229211	−	0.0534148i
$221$	0.298472	−	0.106007i	0.0200774	−	0.00713078i
$222$	3.66101	+	31.8408i	0.245711	+	2.13702i
$223$		−	15.4009i		−	1.03132i	−0.856793	−	0.515660i	$-0.827547\pi$
$223$		−	15.4009i		−	1.03132i	0.856793	−	0.515660i	$-0.172453\pi$
$224$	3.06394	+	4.75524i	0.204718	+	0.317723i
$225$	9.98021			0.665347
$226$	10.1490	−	1.16692i	0.675102	−	0.0776222i
$227$	18.4841			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$227$	18.4841			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$228$	9.69917	+	41.6206i	0.642343	+	2.75639i
$229$	9.79269			0.647119			0.323560	−	0.946208i	$-0.395120\pi$
$229$	9.79269			0.647119			0.323560	+	0.946208i	$0.395120\pi$
$230$	−13.8217	+	1.58920i	−0.911377	+	0.104789i
$231$	2.97752			0.195907
$232$	−2.61961	−	7.32557i	−0.171986	−	0.480947i
$233$	−13.8891			−0.909903			−0.454952	−	0.890516i	$-0.650343\pi$
$233$	−13.8891			−0.909903			−0.454952	+	0.890516i	$0.650343\pi$
$234$	16.9368	−	8.30170i	1.10719	−	0.542699i
$235$		−	6.95013i		−	0.453376i
$236$	−7.72071	+	1.79922i	−0.502575	+	0.117119i
$237$		−	19.9004i		−	1.29267i
$238$	0.0141908	+	0.123422i	0.000919856	+	0.00800024i
$239$			3.54335i			0.229200i	0.993412	+	0.114600i	$0.0365587\pi$
$239$			3.54335i			0.229200i	−0.993412	+	0.114600i	$0.963441\pi$
$240$	6.94404	+	14.0898i	0.448236	+	0.909495i
$241$			2.53135i			0.163059i	0.996671	+	0.0815293i	$0.0259804\pi$
$241$			2.53135i			0.163059i	−0.996671	+	0.0815293i	$0.974020\pi$
$242$	13.5952	−	1.56316i	0.873933	−	0.100483i
$243$			22.0293i			1.41318i
$244$	−5.01787	−	21.5324i	−0.321236	−	1.37847i
$245$	1.51724			0.0969327
$246$	−0.805906	+	0.0926618i	−0.0513827	+	0.00590790i
$247$	−28.0497	+	9.96223i	−1.78476	+	0.633882i
$248$	5.20618	+	14.5587i	0.330593	+	0.924481i
$249$			13.4451i			0.852049i
$250$	−16.4094	+	1.88673i	−1.03782	+	0.119328i
$251$		−	28.4225i		−	1.79401i	−0.442019	−	0.897006i	$-0.645738\pi$
$251$		−	28.4225i		−	1.79401i	0.442019	−	0.897006i	$-0.354262\pi$
$252$	1.67908	+	7.20519i	0.105772	+	0.453885i
$253$	7.45919			0.468955
$254$	15.3113	−	1.76046i	0.960713	−	0.110461i
$255$			0.344978i			0.0216034i
$256$	9.74642	−	12.6889i	0.609151	−	0.793054i
$257$	1.65015			0.102934			0.0514668	−	0.998675i	$-0.483610\pi$
$257$	1.65015			0.102934			0.0514668	+	0.998675i	$0.483610\pi$
$258$	−41.1138	+	4.72720i	−2.55963	+	0.294303i
$259$		−	8.75613i		−	0.544080i
$260$	−9.20990	+	5.90611i	−0.571174	+	0.366282i
$261$		−	10.1748i		−	0.629805i
$262$	−1.83025	−	15.9182i	−0.113073	−	0.983429i
$263$	−13.6929			−0.844338			−0.422169	−	0.906517i	$-0.638731\pi$
$263$	−13.6929			−0.844338			−0.422169	+	0.906517i	$0.638731\pi$
$264$	−2.83573	−	7.92993i	−0.174527	−	0.488054i
$265$		−	16.3963i		−	1.00722i
$266$	−1.33362	−	11.5989i	−0.0817695	−	0.711172i
$267$	2.80960			0.171945
$268$	−9.02909	+	2.10412i	−0.551539	+	0.128529i
$269$		−	12.0078i		−	0.732128i	−0.930590	−	0.366064i	$-0.880705\pi$
$269$		−	12.0078i		−	0.732128i	0.930590	−	0.366064i	$-0.119295\pi$
$270$	0.443505	+	3.85728i	0.0269908	+	0.234747i
$271$		−	3.02364i		−	0.183673i	−0.995774	−	0.0918365i	$-0.970726\pi$
$271$		−	3.02364i		−	0.183673i	0.995774	−	0.0918365i	$-0.0292737\pi$
$272$	0.315190	−	0.155338i	0.0191112	−	0.00941876i
$273$	−8.79396	+	3.12330i	−0.532234	+	0.189031i
$274$	0.848474	+	7.37942i	0.0512582	+	0.445807i
$275$	3.10375			0.187163
$276$	7.61776	+	32.6889i	0.458535	+	1.96764i
$277$			22.1000i			1.32786i	0.747794	+	0.663931i	$0.231113\pi$
$277$			22.1000i			1.32786i	−0.747794	+	0.663931i	$0.768887\pi$
$278$	−1.07686	−	9.36574i	−0.0645857	−	0.561720i
$279$			20.2213i			1.21062i
$280$	−1.44498	−	4.04080i	−0.0863543	−	0.241484i
$281$			25.7594i			1.53668i	0.640044	+	0.768339i	$0.278916\pi$
$281$			25.7594i			1.53668i	−0.640044	+	0.768339i	$0.721084\pi$
$282$	−16.6576	+	1.91526i	−0.991943	+	0.114052i
$283$			1.31917i			0.0784165i	0.999231	+	0.0392083i	$0.0124836\pi$
$283$			1.31917i			0.0784165i	−0.999231	+	0.0392083i	$0.987516\pi$
$284$	−4.25271	−	18.2490i	−0.252352	−	1.08288i
$285$		−	32.4201i		−	1.92040i
$286$	5.26717	−	2.58175i	0.311454	−	0.152662i
$287$	0.221622			0.0130819
$288$	17.5902	−	11.3339i	1.03651	−	0.667857i
$289$	−16.9923			−0.999546
$290$	0.674156	+	5.86332i	0.0395878	+	0.344306i
$291$	−27.1317			−1.59049
$292$	4.72567	+	20.2786i	0.276549	+	1.18671i
$293$	−3.67811			−0.214878			−0.107439	−	0.994212i	$-0.534265\pi$
$293$	−3.67811			−0.214878			−0.107439	+	0.994212i	$0.534265\pi$
$294$	−0.418108	−	3.63640i	−0.0243846	−	0.212079i
$295$	6.01401			0.350149
$296$	−23.3199	+	8.33915i	−1.35544	+	0.484703i
$297$		−	2.08167i		−	0.120791i
$298$	25.2429	−	2.90239i	1.46228	−	0.168131i
$299$	−22.0303	+	7.82437i	−1.27405	+	0.452495i
$300$	3.16973	+	13.6018i	0.183005	+	0.785300i
$301$	11.3062			0.651677
$302$	0.126849	+	1.10324i	0.00729934	+	0.0634844i
$303$	8.96057			0.514772
$304$	−29.6207	+	14.5983i	−1.69887	+	0.837269i
$305$			16.7726i			0.960396i
$306$	0.456553	−	0.0524937i	0.0260994	−	0.00300087i
$307$	27.2095			1.55293			0.776463	−	0.630163i	$-0.217012\pi$
$307$	27.2095			1.55293			0.776463	+	0.630163i	$0.217012\pi$
$308$	0.522179	+	2.24075i	0.0297539	+	0.127678i
$309$		−	14.6729i		−	0.834715i
$310$	−1.33981	−	11.6527i	−0.0760961	−	0.661829i
$311$	−14.8834			−0.843960			−0.421980	−	0.906605i	$-0.638665\pi$
$311$	−14.8834			−0.843960			−0.421980	+	0.906605i	$0.638665\pi$
$312$	16.6933	+	20.4461i	0.945074	+	1.15753i
$313$	−11.4874			−0.649308			−0.324654	−	0.945833i	$-0.605248\pi$
$313$	−11.4874			−0.649308			−0.324654	+	0.945833i	$0.605248\pi$
$314$	−1.77716	−	15.4564i	−0.100291	−	0.872257i
$315$		−	5.61245i		−	0.316226i
$316$	14.9761	−	3.49000i	0.842472	−	0.196328i
$317$	−13.0995			−0.735743			−0.367872	−	0.929877i	$-0.619913\pi$
$317$	−13.0995			−0.735743			−0.367872	+	0.929877i	$0.619913\pi$
$318$	−39.2975	+	4.51837i	−2.20370	+	0.253378i
$319$		−	3.16427i		−	0.177165i
$320$	−9.38556	+	7.69674i	−0.524669	+	0.430261i
$321$	−44.8532			−2.50346
$322$	−1.04743	−	9.10979i	−0.0583710	−	0.507669i
$323$	−0.725239			−0.0403534
$324$	−12.4929	+	2.91133i	−0.694053	+	0.161740i
$325$	−9.16676	+	3.25570i	−0.508480	+	0.180594i
$326$	13.0420	−	1.49955i	0.722328	−	0.0830522i
$327$			28.5726i			1.58007i
$328$	−0.211067	−	0.590237i	−0.0116542	−	0.0325904i
$329$	4.58078			0.252546
$330$	0.729774	+	6.34705i	0.0401728	+	0.349394i
$331$	−21.5841			−1.18637			−0.593183	−	0.805067i	$-0.702129\pi$
$331$	−21.5841			−1.18637			−0.593183	+	0.805067i	$0.702129\pi$
$332$	−10.1182	+	2.35792i	−0.555307	+	0.129407i
$333$	−32.3900			−1.77496
$334$	1.60116	+	13.9257i	0.0876116	+	0.761982i
$335$	7.03317			0.384263
$336$	−9.28651	+	4.57676i	−0.506621	+	0.249683i
$337$	3.36280			0.183183			0.0915917	−	0.995797i	$-0.470805\pi$
$337$	3.36280			0.183183			0.0915917	+	0.995797i	$0.470805\pi$
$338$	−12.8481	+	13.1501i	−0.698847	+	0.715271i
$339$			18.6969i			1.01548i
$340$	−0.259614	+	0.0604999i	−0.0140796	+	0.00328107i
$341$			6.28863i			0.340548i
$342$	−42.9057	+	4.93323i	−2.32007	+	0.266759i
$343$			1.00000i			0.0539949i
$344$	−10.7677	−	30.1113i	−0.580558	−	1.62349i
$345$		−	25.4629i		−	1.37088i
$346$	3.56566	+	31.0115i	0.191691	+	1.66719i
$347$		−	10.4226i		−	0.559513i	−0.960071	−	0.279756i	$-0.909746\pi$
$347$		−	10.4226i		−	0.559513i	0.960071	−	0.279756i	$-0.0902537\pi$
$348$	13.8670	−	3.23154i	0.743349	−	0.173228i
$349$	5.88538			0.315037			0.157519	−	0.987516i	$-0.449651\pi$
$349$	5.88538			0.315037			0.157519	+	0.987516i	$0.449651\pi$
$350$	−0.435833	−	3.79056i	−0.0232963	−	0.202614i
$351$	2.18358	+	6.14809i	0.116551	+	0.328161i
$352$	5.47039	−	3.52474i	0.291573	−	0.187869i
$353$			18.2921i			0.973592i	0.873516	+	0.486796i	$0.161834\pi$
$353$			18.2921i			0.973592i	−0.873516	+	0.486796i	$0.838166\pi$
$354$	−1.65729	−	14.4139i	−0.0880841	−	0.766092i
$355$			14.2150i			0.754453i
$356$	0.492730	+	2.11438i	0.0261146	+	0.112062i
$357$	−0.227372			−0.0120338
$358$	3.26713	+	28.4151i	0.172673	+	1.50179i
$359$		−	10.4332i		−	0.550644i	−0.961352	−	0.275322i	$-0.911216\pi$
$359$		−	10.4332i		−	0.550644i	0.961352	−	0.275322i	$-0.0887845\pi$
$360$	−14.9474	+	5.34517i	−0.787800	+	0.281715i
$361$	49.1561			2.58716
$362$	3.09105	+	26.8837i	0.162462	+	1.41298i
$363$			25.0456i			1.31455i
$364$	−3.89268	−	6.07018i	−0.204032	−	0.318164i
$365$		−	15.7959i		−	0.826795i
$366$	40.1993	−	4.62206i	2.10125	−	0.241599i
$367$	10.6000			0.553316			0.276658	−	0.960968i	$-0.410773\pi$
$367$	10.6000			0.553316			0.276658	+	0.960968i	$0.410773\pi$
$368$	−23.2642	+	11.4655i	−1.21273	+	0.597683i
$369$		−	0.819806i		−	0.0426774i
$370$	18.6650	−	2.14608i	0.970350	−	0.111569i
$371$	10.8067			0.561056
$372$	−27.5591	+	6.42232i	−1.42887	+	0.332982i
$373$			21.9283i			1.13540i	0.823235	+	0.567701i	$0.192167\pi$
$373$			21.9283i			1.13540i	−0.823235	+	0.567701i	$0.807833\pi$
$374$	0.141984	−	0.0163251i	0.00734179	−	0.000844149i
$375$		−	30.2301i		−	1.56108i
$376$	−4.36263	−	12.1998i	−0.224986	−	0.629158i
$377$	3.31918	+	9.34549i	0.170947	+	0.481317i
$378$	−2.54231	+	0.292311i	−0.130762	+	0.0150348i
$379$	−10.9073			−0.560268			−0.280134	−	0.959961i	$-0.590379\pi$
$379$	−10.9073			−0.560268			−0.280134	+	0.959961i	$0.590379\pi$
$380$	24.3979	−	5.68563i	1.25159	−	0.291667i
$381$			28.2070i			1.44509i
$382$	1.69040	−	0.194360i	0.0864886	−	0.00994432i
$383$			11.6452i			0.595040i	0.954716	+	0.297520i	$0.0961594\pi$
$383$			11.6452i			0.595040i	−0.954716	+	0.297520i	$0.903841\pi$
$384$	21.0334	+	20.3736i	1.07336	+	1.03969i
$385$		−	1.74542i		−	0.0889548i
$386$	2.68324	+	23.3369i	0.136573	+	1.18781i
$387$		−	41.8229i		−	2.12598i
$388$	−4.75818	−	20.4181i	−0.241560	−	1.03657i
$389$		−	13.1587i		−	0.667172i	−0.942720	−	0.333586i	$-0.891741\pi$
$389$		−	13.1587i		−	0.667172i	0.942720	−	0.333586i	$-0.108259\pi$
$390$	−8.81314	−	17.9802i	−0.446271	−	0.910461i
$391$	−0.569605			−0.0288062
$392$	2.66326	−	0.952378i	0.134515	−	0.0481023i
$393$	29.3251			1.47926
$394$	−17.3001	+	1.98913i	−0.871564	+	0.100211i
$395$	−11.6656			−0.586958
$396$	8.28881	−	1.93160i	0.416528	−	0.0970668i
$397$	2.01211			0.100985			0.0504925	−	0.998724i	$-0.483921\pi$
$397$	2.01211			0.100985			0.0504925	+	0.998724i	$0.483921\pi$
$398$	5.05544	−	0.581267i	0.253407	−	0.0291363i
$399$	21.3679			1.06973
$400$	−9.68019	+	4.77079i	−0.484010	+	0.238539i
$401$			3.32731i			0.166158i	0.996543	+	0.0830789i	$0.0264753\pi$
$401$			3.32731i			0.166158i	−0.996543	+	0.0830789i	$0.973525\pi$
$402$	−1.93814	−	16.8566i	−0.0966659	−	0.840730i
$403$	−6.59651	−	18.5731i	−0.328595	−	0.925193i
$404$	1.57145	+	6.74331i	0.0781824	+	0.335492i
$405$	9.73132			0.483553
$406$	−3.86447	+	0.444331i	−0.191790	+	0.0220518i
$407$	−10.0730			−0.499300
$408$	0.216544	+	0.605553i	0.0107205	+	0.0299793i
$409$		−	35.5960i		−	1.76011i	−0.474872	−	0.880055i	$-0.657506\pi$
$409$		−	35.5960i		−	1.76011i	0.474872	−	0.880055i	$-0.342494\pi$
$410$	0.0543182	+	0.472420i	0.00268258	+	0.0233312i
$411$	−13.5947			−0.670575
$412$	11.0422	−	2.57325i	0.544009	−	0.126775i
$413$			3.96379i			0.195045i
$414$	−33.6983	+	3.87458i	−1.65618	+	0.190425i
$415$	7.88150			0.386888
$416$	−12.4592	+	16.1483i	−0.610862	+	0.791737i
$417$	17.2539			0.844929
$418$	−13.3433	+	1.53419i	−0.652640	+	0.0750396i
$419$			1.09920i			0.0536992i	0.999639	+	0.0268496i	$0.00854753\pi$
$419$			1.09920i			0.0536992i	−0.999639	+	0.0268496i	$0.991452\pi$
$420$	7.64908	−	1.78252i	0.373237	−	0.0869783i
$421$	9.75651			0.475503			0.237752	−	0.971326i	$-0.423590\pi$
$421$	9.75651			0.475503			0.237752	+	0.971326i	$0.423590\pi$
$422$	2.16430	+	18.8235i	0.105357	+	0.916315i
$423$		−	16.9449i		−	0.823888i
$424$	−10.2921	−	28.7811i	−0.499827	−	1.39773i
$425$	−0.237011			−0.0114967
$426$	34.0695	−	3.91726i	1.65067	−	0.189792i
$427$	−11.0547			−0.534974
$428$	−7.86606	−	33.7544i	−0.380220	−	1.63158i
$429$	3.59302	+	10.1165i	0.173473	+	0.488430i
$430$	2.77108	+	24.1008i	0.133633	+	1.16225i
$431$			6.44866i			0.310621i	0.987866	+	0.155310i	$0.0496378\pi$
$431$			6.44866i			0.310621i	−0.987866	+	0.155310i	$0.950362\pi$
$432$	3.19974	+	6.49244i	0.153947	+	0.312368i
$433$	−25.7879			−1.23929			−0.619643	−	0.784884i	$-0.712723\pi$
$433$	−25.7879			−1.23929			−0.619643	+	0.784884i	$0.712723\pi$
$434$	7.68021	−	0.883058i	0.368662	−	0.0423882i
$435$	−10.8016			−0.517899
$436$	−21.5024	+	5.01087i	−1.02978	+	0.239977i
$437$	53.5301			2.56069
$438$	−37.8585	+	4.35291i	−1.80895	+	0.207990i
$439$	−20.8825			−0.996668			−0.498334	−	0.866985i	$-0.666055\pi$
$439$	−20.8825			−0.996668			−0.498334	+	0.866985i	$0.666055\pi$
$440$	−4.64851	+	1.66230i	−0.221609	+	0.0792470i
$441$	3.69913			0.176149
$442$	−0.402216	+	0.197150i	−0.0191315	+	0.00937746i
$443$		−	1.97890i		−	0.0940205i	−0.998894	−	0.0470103i	$-0.985031\pi$
$443$		−	1.97890i		−	0.0940205i	0.998894	−	0.0470103i	$-0.0149694\pi$
$444$	−10.2871	−	44.1436i	−0.488206	−	2.09496i
$445$		−	1.64698i		−	0.0780745i
$446$	2.48786	+	21.6376i	0.117803	+	1.02457i
$447$			46.5035i			2.19954i
$448$	−5.07287	−	6.18595i	−0.239670	−	0.292259i
$449$		−	23.3403i		−	1.10150i	−0.834671	−	0.550749i	$-0.814342\pi$
$449$		−	23.3403i		−	1.10150i	0.834671	−	0.550749i	$-0.185658\pi$
$450$	−14.0218	+	1.61220i	−0.660992	+	0.0759999i
$451$		−	0.254952i		−	0.0120052i
$452$	−14.0704	+	3.27894i	−0.661817	+	0.154228i
$453$	−2.03243			−0.0954921
$454$	−25.9694	+	2.98592i	−1.21880	+	0.140136i
$455$	1.83087	+	5.15500i	0.0858326	+	0.241670i
$456$	−20.3503	−	56.9083i	−0.952990	−	2.66498i
$457$			12.8179i			0.599595i	0.954003	+	0.299798i	$0.0969191\pi$
$457$			12.8179i			0.599595i	−0.954003	+	0.299798i	$0.903081\pi$
$458$	−13.7583	+	1.58191i	−0.642884	+	0.0739178i
$459$			0.158962i			0.00741971i
$460$	19.1622	−	4.46552i	0.893442	−	0.208206i
$461$	30.2775			1.41016			0.705081	−	0.709127i	$-0.250911\pi$
$461$	30.2775			1.41016			0.705081	+	0.709127i	$0.250911\pi$
$462$	−4.18329	+	0.480989i	−0.194624	+	0.0223776i
$463$			0.839207i			0.0390013i	0.999810	+	0.0195006i	$0.00620764\pi$
$463$			0.839207i			0.0390013i	−0.999810	+	0.0195006i	$0.993792\pi$
$464$	4.86381	+	9.86894i	0.225797	+	0.458154i
$465$	21.4670			0.995510
$466$	19.5136	−	2.24364i	0.903948	−	0.103935i
$467$		−	31.5327i		−	1.45916i	−0.683895	−	0.729581i	$-0.739715\pi$
$467$		−	31.5327i		−	1.45916i	0.683895	−	0.729581i	$-0.260285\pi$
$468$	−22.4544	+	14.3995i	−1.03795	+	0.665617i
$469$			4.63551i			0.214048i
$470$	1.12272	+	9.76463i	0.0517873	+	0.450409i
$471$	28.4744			1.31203
$472$	10.5566	−	3.77502i	0.485908	−	0.173760i
$473$		−	13.0065i		−	0.598041i
$474$	3.21471	+	27.9592i	0.147656	+	1.28421i
$475$	22.2737			1.02199
$476$	−0.0398751	−	0.171110i	−0.00182767	−	0.00784281i
$477$		−	39.9753i		−	1.83035i
$478$	−0.572392	−	4.97825i	−0.0261806	−	0.227700i
$479$			37.3603i			1.70704i	0.521062	+	0.853519i	$0.325536\pi$
$479$			37.3603i			1.70704i	−0.521062	+	0.853519i	$0.674464\pi$
$480$	−12.0321	−	18.6739i	−0.549190	−	0.852342i
$481$	29.7500	−	10.5661i	1.35649	−	0.481775i
$482$	−0.408914	−	3.55644i	−0.0186255	−	0.161991i
$483$	16.7824			0.763626
$484$	−18.8482	+	4.39234i	−0.856735	+	0.199652i
$485$			15.9046i			0.722189i
$486$	−3.55861	−	30.9502i	−0.161422	−	1.40393i
$487$			38.6285i			1.75042i	0.483741	+	0.875211i	$0.339278\pi$
$487$			38.6285i			1.75042i	−0.483741	+	0.875211i	$0.660722\pi$
$488$	10.5282	+	29.4416i	0.476591	+	1.33276i
$489$			24.0264i			1.08651i
$490$	−2.13165	+	0.245094i	−0.0962983	+	0.0110722i
$491$		−	34.4399i		−	1.55425i	−0.629346	−	0.777125i	$-0.716677\pi$
$491$		−	34.4399i		−	1.55425i	0.629346	−	0.777125i	$-0.283323\pi$
$492$	1.11729	−	0.260372i	0.0503715	−	0.0117385i
$493$			0.241633i			0.0108826i
$494$	37.7993	−	18.5277i	1.70067	−	0.833598i
$495$	−6.45653			−0.290199
$496$	−9.66627	−	19.6134i	−0.434029	−	0.880668i
$497$	−9.36899			−0.420257
$498$	−2.17192	−	18.8898i	−0.0973261	−	0.846472i
$499$	−4.62862			−0.207205			−0.103603	−	0.994619i	$-0.533037\pi$
$499$	−4.62862			−0.207205			−0.103603	+	0.994619i	$0.533037\pi$
$500$	22.7498	−	5.30156i	1.01740	−	0.237093i
$501$	−25.6545			−1.14616
$502$	4.59137	+	39.9324i	0.204923	+	1.78227i
$503$	32.9666			1.46991			0.734954	−	0.678117i	$-0.237204\pi$
$503$	32.9666			1.46991			0.734954	+	0.678117i	$0.237204\pi$
$504$	−3.52297	−	9.85175i	−0.156925	−	0.438832i
$505$		−	5.25267i		−	0.233741i
$506$	−10.4798	+	1.20496i	−0.465886	+	0.0535668i
$507$	−21.2236	−	26.1096i	−0.942572	−	1.15957i
$508$	−21.2273	+	4.94676i	−0.941808	+	0.219477i
$509$	4.90267			0.217307			0.108654	−	0.994080i	$-0.465346\pi$
$509$	4.90267			0.217307			0.108654	+	0.994080i	$0.465346\pi$
$510$	−0.0557277	−	0.484679i	−0.00246766	−	0.0214620i
$511$	10.4110			0.460554
$512$	−11.6435	+	19.4017i	−0.514577	+	0.857444i
$513$		−	14.9389i		−	0.659566i
$514$	−2.31839	+	0.266565i	−0.102260	+	0.0117577i
$515$	−8.60126			−0.379017
$516$	56.9995	−	13.2830i	2.50926	−	0.584753i
$517$		−	5.26970i		−	0.231761i
$518$	1.41446	+	12.3020i	0.0621480	+	0.540519i
$519$	−57.1306			−2.50775
$520$	11.9854	−	9.78560i	0.525597	−	0.429127i
$521$	6.67667			0.292510			0.146255	−	0.989247i	$-0.453278\pi$
$521$	6.67667			0.292510			0.146255	+	0.989247i	$0.453278\pi$
$522$	1.64364	+	14.2952i	0.0719400	+	0.625682i
$523$			19.5635i			0.855451i	0.903909	+	0.427726i	$0.140685\pi$
$523$			19.5635i			0.855451i	−0.903909	+	0.427726i	$0.859315\pi$
$524$	5.14285	+	22.0687i	0.224666	+	0.964077i
$525$	6.98312			0.304768
$526$	19.2379	−	2.21194i	0.838812	−	0.0964453i
$527$		−	0.480218i		−	0.0209186i
$528$	5.26508	+	10.6831i	0.229133	+	0.464924i
$529$	19.0427			0.827944
$530$	2.64866	+	23.0361i	0.115050	+	1.00063i
$531$	14.6626			0.636301
$532$	3.74736	+	16.0805i	0.162469	+	0.697177i
$533$	0.267434	+	0.752986i	0.0115838	+	0.0326155i
$534$	−3.94737	+	0.453863i	−0.170820	+	0.0196406i
$535$			26.2929i			1.13674i
$536$	12.3456	−	4.41475i	0.533248	−	0.190688i
$537$	−52.3475			−2.25896
$538$	1.93974	+	16.8704i	0.0836280	+	0.727336i
$539$	1.15039			0.0495509
$540$	−1.24621	−	5.34767i	−0.0536283	−	0.230127i
$541$	37.0198			1.59160			0.795802	−	0.605557i	$-0.207050\pi$
$541$	37.0198			1.59160			0.795802	+	0.605557i	$0.207050\pi$
$542$	0.488439	+	4.24809i	0.0209802	+	0.182471i
$543$	−49.5262			−2.12537
$544$	−0.417735	+	0.269159i	−0.0179102	+	0.0115401i
$545$	16.7492			0.717457
$546$	11.8506	−	5.80867i	0.507159	−	0.248588i
$547$			44.1142i			1.88619i	0.332526	+	0.943094i	$0.392099\pi$
$547$			44.1142i			1.88619i	−0.332526	+	0.943094i	$0.607901\pi$
$548$	−2.38414	−	10.2307i	−0.101845	−	0.437034i
$549$			40.8927i			1.74526i
$550$	−4.36064	+	0.501379i	−0.185938	+	0.0213789i
$551$		−	22.7080i		−	0.967394i
$552$	−15.9832	−	44.6960i	−0.680290	−	1.90239i
$553$		−	7.68869i		−	0.326956i
$554$	−3.57004	−	31.0496i	−0.151676	−	1.31917i
$555$			34.3855i			1.45958i
$556$	3.02588	+	12.9845i	0.128326	+	0.550666i
$557$	12.6022			0.533972			0.266986	−	0.963700i	$-0.413972\pi$
$557$	12.6022			0.533972			0.266986	+	0.963700i	$0.413972\pi$
$558$	−3.26655	−	28.4100i	−0.138284	−	1.20269i
$559$	13.6433	+	38.4141i	0.577051	+	1.62474i
$560$	2.68289	+	5.44373i	0.113373	+	0.230040i
$561$			0.261568i			0.0110434i
$562$	−4.16117	−	36.1909i	−0.175528	−	1.52662i
$563$		−	4.78407i		−	0.201625i	−0.994905	−	0.100812i	$-0.967856\pi$
$563$		−	4.78407i		−	0.201625i	0.994905	−	0.100812i	$-0.0321442\pi$
$564$	23.0938	−	5.38172i	0.972423	−	0.226611i
$565$	10.9601			0.461094
$566$	−0.213099	−	1.85338i	−0.00895720	−	0.0779033i
$567$			6.41384i			0.269356i
$568$	8.92282	+	24.9521i	0.374393	+	1.04697i
$569$	28.1257			1.17909			0.589545	−	0.807736i	$-0.299307\pi$
$569$	28.1257			1.17909			0.589545	+	0.807736i	$0.299307\pi$
$570$	5.23715	+	45.5489i	0.219360	+	1.90783i
$571$		−	9.67429i		−	0.404856i	−0.979297	−	0.202428i	$-0.935117\pi$
$571$		−	9.67429i		−	0.404856i	0.979297	−	0.202428i	$-0.0648833\pi$
$572$	−6.98309	+	4.47811i	−0.291978	+	0.187239i
$573$			3.11413i			0.130095i
$574$	−0.311369	+	0.0358007i	−0.0129963	+	0.00149429i
$575$	17.4939			0.729545
$576$	−22.8826	+	18.7652i	−0.953443	+	0.781882i
$577$			5.85466i			0.243732i	0.992547	+	0.121866i	$0.0388879\pi$
$577$			5.85466i			0.243732i	−0.992547	+	0.121866i	$0.961112\pi$
$578$	23.8734	−	2.74493i	0.993004	−	0.114174i
$579$	−42.9921			−1.78669
$580$	−1.89432	−	8.12881i	−0.0786574	−	0.337531i
$581$			5.19464i			0.215510i
$582$	38.1189	−	4.38285i	1.58008	−	0.181675i
$583$		−	12.4320i		−	0.514879i
$584$	−9.91517	−	27.7271i	−0.410293	−	1.14736i
$585$	19.0690	−	6.77262i	0.788406	−	0.280014i
$586$	5.16759	−	0.594162i	0.213471	−	0.0245446i
$587$	−42.1940			−1.74153			−0.870766	−	0.491698i	$-0.836376\pi$
$587$	−42.1940			−1.74153			−0.870766	+	0.491698i	$0.836376\pi$
$588$	1.17485	+	5.04145i	0.0484499	+	0.207906i
$589$			45.1297i			1.85954i
$590$	−8.44942	+	0.971502i	−0.347857	+	0.0399961i
$591$		−	31.8708i		−	1.31099i
$592$	31.4164	−	15.4832i	1.29120	−	0.636357i
$593$		−	19.0752i		−	0.783325i	−0.920109	−	0.391663i	$-0.871900\pi$
$593$		−	19.0752i		−	0.783325i	0.920109	−	0.391663i	$-0.128100\pi$
$594$	0.336272	+	2.92465i	0.0137974	+	0.120000i
$595$			0.133285i			0.00546416i
$596$	−34.9964	+	8.15548i	−1.43351	+	0.334061i
$597$			9.31334i			0.381169i
$598$	29.6877	−	14.5517i	1.21402	−	0.595063i
$599$	−3.43267			−0.140255			−0.0701275	−	0.997538i	$-0.522341\pi$
$599$	−3.43267			−0.140255			−0.0701275	+	0.997538i	$0.522341\pi$
$600$	−6.65057	−	18.5979i	−0.271508	−	0.759256i
$601$	−38.6990			−1.57857			−0.789283	−	0.614029i	$-0.789548\pi$
$601$	−38.6990			−1.57857			−0.789283	+	0.614029i	$0.789548\pi$
$602$	−15.8847	+	1.82640i	−0.647411	+	0.0744384i
$603$	17.1473			0.698293
$604$	−0.356435	−	1.52952i	−0.0145031	−	0.0622351i
$605$	14.6817			0.596896
$606$	−12.5892	+	1.44749i	−0.511402	+	0.0588003i
$607$	17.5335			0.711664			0.355832	−	0.934550i	$-0.384197\pi$
$607$	17.5335			0.711664			0.355832	+	0.934550i	$0.384197\pi$
$608$	39.2577	−	25.2949i	1.59211	−	1.02584i
$609$		−	7.11928i		−	0.288488i
$610$	−2.70944	−	23.5648i	−0.109702	−	0.954110i
$611$	5.52769	+	15.5638i	0.223626	+	0.629642i
$612$	−0.632957	+	0.147503i	−0.0255858	+	0.00596245i
$613$	−17.9396			−0.724574			−0.362287	−	0.932067i	$-0.618004\pi$
$613$	−17.9396			−0.724574			−0.362287	+	0.932067i	$0.618004\pi$
$614$	−38.2281	+	4.39541i	−1.54276	+	0.177384i
$615$	−0.870311			−0.0350943
$616$	−1.09561	−	3.06380i	−0.0441433	−	0.123444i
$617$		−	11.0038i		−	0.442995i	−0.975161	−	0.221498i	$-0.928906\pi$
$617$		−	11.0038i		−	0.442995i	0.975161	−	0.221498i	$-0.0710945\pi$
$618$	2.37027	+	20.6149i	0.0953461	+	0.829252i
$619$	−43.6123			−1.75293			−0.876464	−	0.481467i	$-0.840104\pi$
$619$	−43.6123			−1.75293			−0.876464	+	0.481467i	$0.840104\pi$
$620$	3.76475	+	16.1551i	0.151196	+	0.648805i
$621$		−	11.7330i		−	0.470830i
$622$	20.9105	−	2.40426i	0.838436	−	0.0964022i
$623$	1.08552			0.0434902
$624$	−26.7563	−	26.0292i	−1.07111	−	1.04200i
$625$	−4.23089			−0.169236
$626$	16.1393	−	1.85568i	0.645058	−	0.0741678i
$627$		−	24.5815i		−	0.981689i
$628$	4.99366	+	21.4285i	0.199269	+	0.855092i
$629$	0.769203			0.0306701
$630$	0.906635	+	7.88526i	0.0361212	+	0.314156i
$631$		−	31.3565i		−	1.24828i	−0.781312	−	0.624141i	$-0.785449\pi$
$631$		−	31.3565i		−	1.24828i	0.781312	−	0.624141i	$-0.214551\pi$
$632$	−20.4770	+	7.32254i	−0.814532	+	0.291275i
$633$	−34.6774			−1.37830
$634$	18.4043	−	2.11610i	0.730928	−	0.0840410i
$635$	16.5349			0.656167
$636$	54.4814	−	12.6962i	2.16033	−	0.503439i
$637$	−3.39762	+	1.20671i	−0.134619	+	0.0478117i
$638$	0.511155	+	4.44566i	0.0202368	+	0.176005i
$639$			34.6571i			1.37101i
$640$	11.9430	−	12.3297i	0.472088	−	0.487376i
$641$	−3.14378			−0.124172			−0.0620859	−	0.998071i	$-0.519775\pi$
$641$	−3.14378			−0.124172			−0.0620859	+	0.998071i	$0.519775\pi$
$642$	63.0168	−	7.24558i	2.48708	−	0.285960i
$643$	23.9503			0.944508			0.472254	−	0.881462i	$-0.343440\pi$
$643$	23.9503			0.944508			0.472254	+	0.881462i	$0.343440\pi$
$644$	2.94319	+	12.6297i	0.115978	+	0.497679i
$645$	−44.3995			−1.74823
$646$	1.01893	−	0.117155i	0.0400892	−	0.00460940i
$647$	34.8065			1.36838			0.684192	−	0.729302i	$-0.260155\pi$
$647$	34.8065			1.36838			0.684192	+	0.729302i	$0.260155\pi$
$648$	17.0818	−	6.10840i	0.671035	−	0.239961i
$649$	4.55991			0.178992
$650$	12.3530	−	6.05492i	0.484523	−	0.237494i
$651$			14.1488i			0.554534i
$652$	−18.0812	+	4.21360i	−0.708113	+	0.165017i
$653$		−	23.9093i		−	0.935643i	−0.883823	−	0.467822i	$-0.845039\pi$
$653$		−	23.9093i		−	0.935643i	0.883823	−	0.467822i	$-0.154961\pi$
$654$	−4.61561	−	40.1433i	−0.180485	−	1.56973i
$655$		−	17.1903i		−	0.671682i
$656$	0.391887	+	0.795162i	0.0153006	+	0.0310458i
$657$		−	38.5115i		−	1.50248i
$658$	−6.43580	+	0.739978i	−0.250894	+	0.0288474i
$659$			9.71979i			0.378629i	0.981916	+	0.189315i	$0.0606266\pi$
$659$			9.71979i			0.378629i	−0.981916	+	0.189315i	$0.939373\pi$
$660$	−2.05060	−	8.79945i	−0.0798196	−	0.342518i
$661$	−3.10662			−0.120834			−0.0604168	−	0.998173i	$-0.519243\pi$
$661$	−3.10662			−0.120834			−0.0604168	+	0.998173i	$0.519243\pi$
$662$	30.3247	−	3.48669i	1.17860	−	0.135514i
$663$	−0.274373	−	0.772526i	−0.0106558	−	0.0300024i
$664$	13.8347	−	4.94726i	0.536890	−	0.191991i
$665$		−	12.5258i		−	0.485730i
$666$	45.5066	−	5.23228i	1.76335	−	0.202747i
$667$		−	17.8350i		−	0.690573i
$668$	−4.49912	−	19.3064i	−0.174076	−	0.746987i
$669$	−39.8616			−1.54114
$670$	−9.88130	+	1.13614i	−0.381748	+	0.0438928i
$671$			12.7172i			0.490944i
$672$	12.3078	−	7.93030i	0.474784	−	0.305918i
$673$	29.1531			1.12377			0.561884	−	0.827216i	$-0.310077\pi$
$673$	29.1531			1.12377			0.561884	+	0.827216i	$0.310077\pi$
$674$	−4.72459	+	0.543226i	−0.181984	+	0.0209243i
$675$		−	4.88208i		−	0.187912i
$676$	15.9268	−	20.5508i	0.612571	−	0.790416i
$677$		−	33.3416i		−	1.28142i	−0.767782	−	0.640711i	$-0.778640\pi$
$677$		−	33.3416i		−	1.28142i	0.767782	−	0.640711i	$-0.221360\pi$
$678$	−3.02029	−	26.2683i	−0.115994	−	1.00883i
$679$	−10.4826			−0.402284
$680$	0.354974	−	0.126938i	0.0136126	−	0.00486785i
$681$		−	47.8418i		−	1.83330i
$682$	−1.01586	−	8.83525i	−0.0388995	−	0.338319i
$683$	41.2913			1.57997			0.789984	−	0.613128i	$-0.210089\pi$
$683$	41.2913			1.57997			0.789984	+	0.613128i	$0.210089\pi$
$684$	59.4837	−	13.8620i	2.27442	−	0.530025i
$685$			7.96916i			0.304486i
$686$	−0.161540	−	1.40496i	−0.00616762	−	0.0536415i
$687$		−	25.3461i		−	0.967014i
$688$	19.9924	+	40.5657i	0.762203	+	1.54655i
$689$	13.0406	+	36.7171i	0.496807	+	1.39881i
$690$	4.11327	+	35.7743i	0.156590	+	1.36190i
$691$	−6.17715			−0.234990			−0.117495	−	0.993073i	$-0.537486\pi$
$691$	−6.17715			−0.234990			−0.117495	+	0.993073i	$0.537486\pi$
$692$	−10.0192	−	42.9938i	−0.380872	−	1.63438i
$693$		−	4.25545i		−	0.161651i
$694$	1.68366	+	14.6433i	0.0639109	+	0.555851i
$695$		−	10.1142i		−	0.383654i
$696$	−18.9605	+	6.78024i	−0.718697	+	0.257004i
$697$			0.0194689i			0.000737436i
$698$	−8.26871	+	0.950724i	−0.312975	+	0.0359854i
$699$			35.9486i			1.35970i
$700$	1.22465	+	5.25517i	0.0462876	+	0.198627i
$701$			37.6124i			1.42060i	0.703898	+	0.710301i	$0.251441\pi$
$701$			37.6124i			1.42060i	−0.703898	+	0.710301i	$0.748559\pi$
$702$	−4.06100	−	8.28506i	−0.153272	−	0.312700i
$703$	−72.2878			−2.72638
$704$	−7.11628	+	5.83579i	−0.268205	+	0.219945i
$705$	−17.9888			−0.677497
$706$	−2.95491	−	25.6997i	−0.111209	−	0.967220i
$707$	3.46200			0.130202
$708$	4.65685	+	19.9832i	0.175015	+	0.751016i
$709$	16.2893			0.611758			0.305879	−	0.952070i	$-0.401050\pi$
$709$	16.2893			0.611758			0.305879	+	0.952070i	$0.401050\pi$
$710$	−2.29629	−	19.9715i	−0.0861781	−	0.749515i
$711$	−28.4414			−1.06664
$712$	−1.03382	−	2.89101i	−0.0387441	−	0.108345i
$713$			35.4450i			1.32743i
$714$	0.319448	−	0.0367297i	0.0119551	−	0.00137457i
$715$	5.93028	−	2.10622i	0.221780	−	0.0787682i
$716$	−9.18036	−	39.3943i	−0.343086	−	1.47223i
$717$	9.17113			0.342502
$718$	1.68538	+	14.6582i	0.0628978	+	0.547040i
$719$	−12.6463			−0.471627			−0.235813	−	0.971798i	$-0.575775\pi$
$719$	−12.6463			−0.471627			−0.235813	+	0.971798i	$0.575775\pi$
$720$	20.1371	−	9.92435i	0.750464	−	0.369859i
$721$		−	5.66902i		−	0.211126i
$722$	−69.0622	+	7.94067i	−2.57023	+	0.295521i
$723$	6.55181			0.243665
$724$	−8.68558	−	37.2711i	−0.322797	−	1.38517i
$725$		−	7.42109i		−	0.275612i
$726$	−4.04587	−	35.1880i	−0.150156	−	1.30595i
$727$	−31.4098			−1.16492			−0.582462	−	0.812858i	$-0.697911\pi$
$727$	−31.4098			−1.16492			−0.582462	+	0.812858i	$0.697911\pi$
$728$	6.44962	+	7.89952i	0.239039	+	0.292776i
$729$	37.7762			1.39912
$730$	2.55167	+	22.1926i	0.0944415	+	0.821384i
$731$			0.993217i			0.0367355i
$732$	−55.7317	+	12.9876i	−2.05990	+	0.480035i
$733$	7.05081			0.260428			0.130214	−	0.991486i	$-0.458434\pi$
$733$	7.05081			0.260428			0.130214	+	0.991486i	$0.458434\pi$
$734$	−14.8926	+	1.71232i	−0.549694	+	0.0632030i
$735$		−	3.92702i		−	0.144850i
$736$	30.8331	−	19.8667i	1.13652	−	0.732296i
$737$	5.33266			0.196431
$738$	0.132431	+	1.15179i	0.00487487	+	0.0423981i
$739$	−23.2829			−0.856475			−0.428237	−	0.903666i	$-0.640865\pi$
$739$	−23.2829			−0.856475			−0.428237	+	0.903666i	$0.640865\pi$
$740$	−25.8769	+	6.03030i	−0.951254	+	0.221678i
$741$	25.7849	+	72.6000i	0.947233	+	2.66703i
$742$	−15.1829	+	1.74571i	−0.557384	+	0.0640871i
$743$		−	41.5984i		−	1.52610i	−0.646341	−	0.763049i	$-0.723702\pi$
$743$		−	41.5984i		−	1.52610i	0.646341	−	0.763049i	$-0.276298\pi$
$744$	37.6819	−	13.4750i	1.38149	−	0.494017i
$745$	27.2603			0.998739
$746$	−3.54229	−	30.8083i	−0.129692	−	1.12797i
$747$	19.2156			0.703063
$748$	−0.196844	+	0.0458720i	−0.00719732	+	0.00167725i
$749$	−17.3294			−0.633204
$750$	4.88337	+	42.4720i	0.178316	+	1.55086i
$751$	10.7904			0.393748			0.196874	−	0.980429i	$-0.436921\pi$
$751$	10.7904			0.393748			0.196874	+	0.980429i	$0.436921\pi$
$752$	8.10007	+	16.4355i	0.295379	+	0.599341i
$753$	−73.5650			−2.68086
$754$	−6.17298	−	12.5938i	−0.224807	−	0.458640i
$755$			1.19141i			0.0433598i
$756$	3.52461	−	0.821368i	0.128189	−	0.0298729i
$757$			6.37976i			0.231876i	0.993256	+	0.115938i	$0.0369874\pi$
$757$			6.37976i			0.231876i	−0.993256	+	0.115938i	$0.963013\pi$
$758$	15.3242	−	1.76196i	0.556601	−	0.0639972i
$759$		−	19.3064i		−	0.700777i
$760$	−33.3595	+	11.9293i	−1.21008	+	0.432721i
$761$		−	21.0373i		−	0.762603i	−0.924451	−	0.381301i	$-0.875476\pi$
$761$		−	21.0373i		−	0.762603i	0.924451	−	0.381301i	$-0.124524\pi$
$762$	−4.55655	−	39.6296i	−0.165067	−	1.43563i
$763$			11.0393i			0.399649i
$764$	−2.34355	+	0.546135i	−0.0847866	+	0.0197585i
$765$	0.493039			0.0178259
$766$	−1.88116	−	16.3609i	−0.0679690	−	0.591145i
$767$	−13.4675	+	4.78316i	−0.486282	+	0.172710i
$768$	−32.8422	−	25.2263i	−1.18509	−	0.910277i
$769$		−	7.90032i		−	0.284893i	−0.989803	−	0.142446i	$-0.954503\pi$
$769$		−	7.90032i		−	0.284893i	0.989803	−	0.142446i	$-0.0454969\pi$
$770$	0.281955	+	2.45224i	0.0101609	+	0.0883726i
$771$		−	4.27103i		−	0.153817i
$772$	−7.53967	−	32.3538i	−0.271359	−	1.16444i
$773$	−26.2770			−0.945119			−0.472560	−	0.881299i	$-0.656670\pi$
$773$	−26.2770			−0.945119			−0.472560	+	0.881299i	$0.656670\pi$
$774$	6.75607	+	58.7595i	0.242842	+	2.11206i
$775$			14.7486i			0.529785i
$776$	9.98337	+	27.9179i	0.358382	+	1.00219i
$777$	−22.6632			−0.813038
$778$	2.12565	+	18.4874i	0.0762083	+	0.662805i
$779$		−	1.82963i		−	0.0655535i
$780$	15.2866	+	23.8377i	0.547348	+	0.853526i
$781$			10.7780i			0.385668i
$782$	0.800271	−	0.0920140i	0.0286176	−	0.00329041i
$783$	−4.97728			−0.177873
$784$	−3.58793	+	1.76827i	−0.128140	+	0.0631526i
$785$		−	16.6917i		−	0.595751i
$786$	−41.2005	+	4.73718i	−1.46957	+	0.168969i
$787$	−11.3359			−0.404080			−0.202040	−	0.979377i	$-0.564757\pi$
$787$	−11.3359			−0.404080			−0.202040	+	0.979377i	$0.564757\pi$
$788$	23.9845	−	5.58930i	0.854413	−	0.199111i
$789$			35.4408i			1.26173i
$790$	16.3896	−	1.88445i	0.583117	−	0.0670459i
$791$			7.22371i			0.256846i
$792$	−11.3334	+	4.05280i	−0.402714	+	0.144010i
$793$	−13.3399	−	37.5597i	−0.473712	−	1.33378i
$794$	−2.82693	+	0.325037i	−0.100324	+	0.0115351i
$795$	−42.4381			−1.50512
$796$	−7.00879	+	1.63331i	−0.248420	+	0.0578912i
$797$		−	33.0929i		−	1.17221i	−0.810235	−	0.586105i	$-0.800661\pi$
$797$		−	33.0929i		−	1.17221i	0.810235	−	0.586105i	$-0.199339\pi$
$798$	−30.0210	+	3.45177i	−1.06273	+	0.122191i
$799$			0.402409i			0.0142362i
$800$	12.8296	−	8.26649i	0.453594	−	0.292264i
$801$		−	4.01546i		−	0.141879i
$802$	−0.537493	−	4.67472i	−0.0189795	−	0.165070i
$803$		−	11.9767i		−	0.422648i
$804$	5.44602	+	23.3697i	0.192066	+	0.824185i
$805$		−	9.83782i		−	0.346738i
$806$	12.2681	+	25.0288i	0.432126	+	0.881603i
$807$	−31.0794			−1.09405
$808$	−3.29713	−	9.22021i	−0.115993	−	0.324366i
$809$	−36.5501			−1.28503			−0.642516	−	0.766272i	$-0.722109\pi$
$809$	−36.5501			−1.28503			−0.642516	+	0.766272i	$0.722109\pi$
$810$	−13.6721	+	1.57200i	−0.480388	+	0.0552343i
$811$	−2.27406			−0.0798529			−0.0399265	−	0.999203i	$-0.512712\pi$
$811$	−2.27406			−0.0798529			−0.0399265	+	0.999203i	$0.512712\pi$
$812$	5.35764	−	1.24853i	0.188016	−	0.0438149i
$813$	−7.82599			−0.274469
$814$	14.1521	−	1.62719i	0.496032	−	0.0570330i
$815$	14.0842			0.493350
$816$	−0.402057	−	0.815795i	−0.0140748	−	0.0285585i
$817$		−	93.3400i		−	3.26555i
$818$	5.75018	+	50.0109i	0.201050	+	1.74859i
$819$	4.46379	+	12.5682i	0.155977	+	0.439170i
$820$	−0.152629	−	0.654956i	−0.00533005	−	0.0228720i
$821$	−28.9611			−1.01075			−0.505375	−	0.862900i	$-0.668646\pi$
$821$	−28.9611			−1.01075			−0.505375	+	0.862900i	$0.668646\pi$
$822$	19.0999	−	2.19608i	0.666186	−	0.0765970i
$823$	18.0668			0.629768			0.314884	−	0.949130i	$-0.398034\pi$
$823$	18.0668			0.629768			0.314884	+	0.949130i	$0.398034\pi$
$824$	−15.0981	+	5.39905i	−0.525968	+	0.188085i
$825$		−	8.03333i		−	0.279685i
$826$	−0.640310	−	5.56895i	−0.0222792	−	0.193769i
$827$	50.9766			1.77263			0.886315	−	0.463083i	$-0.153257\pi$
$827$	50.9766			1.77263			0.886315	+	0.463083i	$0.153257\pi$
$828$	46.7187	−	10.8872i	1.62359	−	0.378357i
$829$		−	42.8967i		−	1.48987i	−0.667140	−	0.744933i	$-0.732482\pi$
$829$		−	42.8967i		−	1.48987i	0.667140	−	0.744933i	$-0.267518\pi$
$830$	−11.0732	+	1.27318i	−0.384355	+	0.0441926i
$831$	57.2008			1.98427
$832$	14.8960	−	24.7004i	0.516427	−	0.856331i
$833$	−0.0878473			−0.00304373
$834$	−24.2410	+	2.78720i	−0.839399	+	0.0965128i
$835$			15.0386i			0.520434i
$836$	18.4989	−	4.31094i	0.639797	−	0.149097i
$837$	9.89178			0.341910
$838$	−0.177564	−	1.54432i	−0.00613385	−	0.0533478i
$839$			46.5281i			1.60633i	0.595758	+	0.803164i	$0.296852\pi$
$839$			46.5281i			1.60633i	−0.595758	+	0.803164i	$0.703148\pi$
$840$	−10.4587	+	3.74000i	−0.360859	+	0.129042i
$841$	21.4342			0.739111
$842$	−13.7075	+	1.57607i	−0.472391	+	0.0543148i
$843$	66.6722			2.29631
$844$	−6.08150	−	26.0966i	−0.209334	−	0.898283i
$845$	−15.3054	+	12.4412i	−0.526522	+	0.427991i
$846$	2.73727	+	23.8068i	0.0941094	+	0.818496i
$847$			9.67660i			0.332492i
$848$	19.1092	+	38.7736i	0.656212	+	1.33149i
$849$	3.41436			0.117181
$850$	0.332991	−	0.0382868i	0.0114215	−	0.00131323i
$851$	−56.7751			−1.94622
$852$	−47.2333	+	11.0072i	−1.61819	+	0.377099i
$853$	−34.8932			−1.19472			−0.597360	−	0.801973i	$-0.703784\pi$
$853$	−34.8932			−1.19472			−0.597360	+	0.801973i	$0.703784\pi$
$854$	15.5314	−	1.78577i	0.531473	−	0.0611079i
$855$	−46.3346			−1.58461
$856$	16.5042	+	46.1529i	0.564101	+	1.57747i
$857$	3.09683			0.105786			0.0528928	−	0.998600i	$-0.483156\pi$
$857$	3.09683			0.105786			0.0528928	+	0.998600i	$0.483156\pi$
$858$	−6.68226	−	13.6328i	−0.228129	−	0.465418i
$859$			32.0784i			1.09450i	0.836969	+	0.547251i	$0.184326\pi$
$859$			32.0784i			1.09450i	−0.836969	+	0.547251i	$0.815674\pi$
$860$	−7.78649	−	33.4130i	−0.265517	−	1.13937i
$861$		−	0.573616i		−	0.0195488i
$862$	−1.04172	−	9.06009i	−0.0354810	−	0.308588i
$863$			4.04153i			0.137575i	0.997631	+	0.0687876i	$0.0219131\pi$
$863$			4.04153i			0.137575i	−0.997631	+	0.0687876i	$0.978087\pi$
$864$	−5.54428	−	8.60472i	−0.188620	−	0.292739i
$865$			33.4898i			1.13869i
$866$	36.2309	−	4.16577i	1.23117	−	0.141559i
$867$			43.9806i			1.49366i
$868$	−10.6477	+	2.48132i	−0.361407	+	0.0842215i
$869$	−8.84502			−0.300047
$870$	15.1758	−	1.74490i	0.514509	−	0.0591575i
$871$	−15.7497	+	5.59373i	−0.533658	+	0.189536i
$872$	29.4005	−	10.5136i	0.995627	−	0.356034i
$873$			38.7764i			1.31238i
$874$	−75.2074	+	8.64724i	−2.54393	+	0.292497i
$875$		−	11.6797i		−	0.394845i
$876$	52.4864	−	12.2313i	1.77335	−	0.413257i
$877$	−6.27681			−0.211953			−0.105976	−	0.994369i	$-0.533797\pi$
$877$	−6.27681			−0.211953			−0.105976	+	0.994369i	$0.533797\pi$
$878$	29.3390	−	3.37336i	0.990145	−	0.113845i
$879$			9.51994i			0.321100i
$880$	6.26243	−	3.08638i	0.211107	−	0.104042i
$881$	5.41652			0.182487			0.0912437	−	0.995829i	$-0.470916\pi$
$881$	5.41652			0.182487			0.0912437	+	0.995829i	$0.470916\pi$
$882$	−5.19711	+	0.597556i	−0.174996	+	0.0201208i
$883$			16.4099i			0.552236i	0.961124	+	0.276118i	$0.0890480\pi$
$883$			16.4099i			0.552236i	−0.961124	+	0.276118i	$0.910952\pi$
$884$	0.533249	−	0.341961i	0.0179351	−	0.0115014i
$885$		−	15.5659i		−	0.523241i
$886$	0.319672	+	2.78027i	0.0107396	+	0.0934052i
$887$	39.5735			1.32875			0.664374	−	0.747400i	$-0.268698\pi$
$887$	39.5735			1.32875			0.664374	+	0.747400i	$0.268698\pi$
$888$	21.5839	+	60.3581i	0.724310	+	2.02549i
$889$			10.8980i			0.365508i
$890$	0.266054	+	2.31394i	0.00891814	+	0.0775635i
$891$	7.37844			0.247187
$892$	−6.99067	−	29.9980i	−0.234065	−	1.00441i
$893$		−	37.8174i		−	1.26551i
$894$	−7.51217	−	65.3354i	−0.251245	−	2.18514i
$895$			30.6860i			1.02572i
$896$	8.12644	+	7.87153i	0.271485	+	0.262969i
$897$	20.2516	+	57.0203i	0.676180	+	1.90385i
$898$	3.77039	+	32.7921i	0.125820	+	1.09429i
$899$	15.0362			0.501484
$900$	19.4395	−	4.53015i	0.647985	−	0.151005i
$901$			0.949340i			0.0316271i
$902$	0.0411849	+	0.358196i	0.00137131	+	0.0119266i
$903$		−	29.2634i		−	0.973824i
$904$	19.2387	−	6.87970i	0.639868	−	0.228816i
$905$			29.0322i			0.965062i
$906$	2.85548	−	0.328319i	0.0948671	−	0.0109077i
$907$			54.8552i			1.82144i	0.413026	+	0.910719i	$0.364472\pi$
$907$			54.8552i			1.82144i	−0.413026	+	0.910719i	$0.635528\pi$
$908$	36.0035	−	8.39018i	1.19482	−	0.278438i
$909$		−	12.8064i		−	0.424760i
$910$	−3.40503	−	6.94680i	−0.112876	−	0.230284i
$911$	−19.6423			−0.650778			−0.325389	−	0.945580i	$-0.605495\pi$
$911$	−19.6423			−0.650778			−0.325389	+	0.945580i	$0.605495\pi$
$912$	37.7843	+	76.6664i	1.25116	+	2.53868i
$913$	5.97588			0.197773
$914$	−2.07060	−	18.0086i	−0.0684893	−	0.595671i
$915$	43.4120			1.43515
$916$	19.0743	−	4.44503i	0.630232	−	0.146868i
$917$	11.3300			0.374150
$918$	−0.0256787	−	0.223335i	−0.000847524	−	0.00737115i
$919$	50.8099			1.67606			0.838032	−	0.545621i	$-0.183706\pi$
$919$	50.8099			1.67606			0.838032	+	0.545621i	$0.183706\pi$
$920$	−26.2007	+	9.36932i	−0.863812	+	0.308897i
$921$		−	70.4253i		−	2.32059i
$922$	−42.5385	+	4.89102i	−1.40093	+	0.161077i
$923$	−11.3057	−	31.8323i	−0.372132	−	1.04777i
$924$	5.79965	−	1.35154i	0.190795	−	0.0444623i
$925$	−23.6240			−0.776751
$926$	−0.135565	−	1.17905i	−0.00445496	−	0.0387460i
$927$	−20.9704			−0.688760
$928$	−8.42767	−	13.0797i	−0.276652	−	0.429363i
$929$		−	22.2352i		−	0.729515i	−0.931103	−	0.364757i	$-0.881152\pi$
$929$		−	22.2352i		−	0.729515i	0.931103	−	0.364757i	$-0.118848\pi$
$930$	−30.1603	+	3.46778i	−0.988995	+	0.113713i
$931$	8.25567			0.270569
$932$	−27.0533	+	6.30443i	−0.886159	+	0.206509i
$933$			38.5222i			1.26116i
$934$	5.09380	+	44.3022i	0.166674	+	1.44961i
$935$	0.153330			0.00501444
$936$	29.2213	−	23.8580i	0.955129	−	0.779822i
$937$	32.6708			1.06731			0.533653	−	0.845703i	$-0.320819\pi$
$937$	32.6708			1.06731			0.533653	+	0.845703i	$0.320819\pi$
$938$	−0.748819	−	6.51269i	−0.0244498	−	0.212647i
$939$			29.7325i			0.970285i
$940$	−3.15476	−	13.5375i	−0.102897	−	0.441545i
$941$	29.1551			0.950428			0.475214	−	0.879870i	$-0.342371\pi$
$941$	29.1551			0.950428			0.475214	+	0.879870i	$0.342371\pi$
$942$	−40.0054	+	4.59976i	−1.30345	+	0.149868i
$943$		−	1.43700i		−	0.0467952i
$944$	−14.2218	+	7.00906i	−0.462879	+	0.228126i
$945$	−2.74548			−0.0893105
$946$	2.10107	+	18.2736i	0.0683118	+	0.594127i
$947$	−46.5705			−1.51334			−0.756668	−	0.653799i	$-0.773174\pi$
$947$	−46.5705			−1.51334			−0.756668	+	0.653799i	$0.773174\pi$
$948$	−9.03305	−	38.7622i	−0.293380	−	1.25894i
$949$	12.5631	+	35.3725i	0.407814	+	1.14824i
$950$	−31.2936	+	3.59810i	−1.01530	+	0.116738i
$951$			33.9051i			1.09945i
$952$	0.0836638	+	0.233961i	0.00271156	+	0.00758271i
$953$	2.59239			0.0839758			0.0419879	−	0.999118i	$-0.486631\pi$
$953$	2.59239			0.0839758			0.0419879	+	0.999118i	$0.486631\pi$
$954$	6.45761	+	56.1636i	0.209073	+	1.81837i
$955$	1.82550			0.0590716
$956$	1.60837	+	6.90177i	0.0520185	+	0.223219i
$957$	−8.18997			−0.264744
$958$	−6.03519	−	52.4897i	−0.194988	−	1.69586i
$959$	−5.25241			−0.169609
$960$	19.9212	+	24.2923i	0.642955	+	0.784032i
$961$	1.11733			0.0360429
$962$	−40.0907	+	19.6508i	−1.29258	+	0.633567i
$963$			64.1038i			2.06571i
$964$	1.14901	+	4.93059i	0.0370072	+	0.158804i
$965$			25.2019i			0.811277i
$966$	−23.5786	+	2.71103i	−0.758628	+	0.0872259i
$967$			39.6322i			1.27449i	0.770663	+	0.637243i	$0.219925\pi$
$967$			39.6322i			1.27449i	−0.770663	+	0.637243i	$0.780075\pi$
$968$	25.7713	−	9.21577i	0.828322	−	0.296206i
$969$			1.87711i			0.0603015i
$970$	−2.56922	−	22.3452i	−0.0824927	−	0.717462i
$971$			28.8005i			0.924252i	0.886814	+	0.462126i	$0.152913\pi$
$971$			28.8005i			0.924252i	−0.886814	+	0.462126i	$0.847087\pi$
$972$	9.99940	+	42.9089i	0.320731	+	1.37630i
$973$	6.66621			0.213709
$974$	−6.24004	−	54.2713i	−0.199944	−	1.73897i
$975$	8.42663	+	23.7260i	0.269868	+	0.759840i
$976$	−19.5477	−	39.6634i	−0.625707	−	1.26960i
$977$			46.4373i			1.48566i	0.669480	+	0.742830i	$0.266517\pi$
$977$			46.4373i			1.48566i	−0.669480	+	0.742830i	$0.733483\pi$
$978$	−3.88123	−	33.7561i	−0.124108	−	1.07940i
$979$		−	1.24877i		−	0.0399108i
$980$	2.95529	−	0.688694i	0.0944033	−	0.0219995i
$981$	40.8357			1.30378
$982$	5.56341	+	48.3866i	0.177536	+	1.54408i
$983$			46.2252i			1.47436i	0.675699	+	0.737178i	$0.263842\pi$
$983$			46.2252i			1.47436i	−0.675699	+	0.737178i	$0.736158\pi$
$984$	−1.52769	+	0.546299i	−0.0487010	+	0.0174154i
$985$	−18.6826			−0.595278
$986$	−0.0390333	−	0.339484i	−0.00124307	−	0.0108114i
$987$		−	11.8563i		−	0.377389i
$988$	−50.1134	+	32.1366i	−1.59432	+	1.02240i
$989$		−	73.3096i		−	2.33111i
$990$	9.07114	−	1.04299i	0.288300	−	0.0331483i
$991$	10.6490			0.338277			0.169139	−	0.985592i	$-0.445901\pi$
$991$	10.6490			0.338277			0.169139	+	0.985592i	$0.445901\pi$
$992$	16.7490	+	25.9945i	0.531783	+	0.825327i
$993$			55.8653i			1.77283i
$994$	13.1630	−	1.51347i	0.417506	−	0.0480042i
$995$	5.45946			0.173077
$996$	6.10291	+	26.1885i	0.193378	+	0.829815i
$997$		−	50.3193i		−	1.59363i	−0.604225	−	0.796814i	$-0.706517\pi$
$997$		−	50.3193i		−	1.59363i	0.604225	−	0.796814i	$-0.293483\pi$
$998$	6.50301	−	0.747706i	0.205849	−	0.0236682i
$999$			15.8445i			0.501296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.i.a.701.2	yes	84
4.3	odd	2		2912.2.i.a.337.66		84
8.3	odd	2		2912.2.i.a.337.19		84
8.5	even	2	inner	728.2.i.a.701.84	yes	84
13.12	even	2	inner	728.2.i.a.701.83	yes	84
52.51	odd	2		2912.2.i.a.337.20		84
104.51	odd	2		2912.2.i.a.337.65		84
104.77	even	2	inner	728.2.i.a.701.1	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.i.a.701.1	✓	84	104.77	even	2	inner
728.2.i.a.701.2	yes	84	1.1	even	1	trivial
728.2.i.a.701.83	yes	84	13.12	even	2	inner
728.2.i.a.701.84	yes	84	8.5	even	2	inner
2912.2.i.a.337.19		84	8.3	odd	2
2912.2.i.a.337.20		84	52.51	odd	2
2912.2.i.a.337.65		84	104.51	odd	2
2912.2.i.a.337.66		84	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.40496 + 0.161540i) q^{2} -2.58827i q^{3} +(1.94781 - 0.453913i) q^{4} -1.51724 q^{5} +(0.418108 + 3.63640i) q^{6} -1.00000i q^{7} +(-2.66326 + 0.952378i) q^{8} -3.69913 q^{9} +(2.13165 - 0.245094i) q^{10} -1.15039 q^{11} +(-1.17485 - 5.04145i) q^{12} +(3.39762 - 1.20671i) q^{13} +(0.161540 + 1.40496i) q^{14} +3.92702i q^{15} +(3.58793 - 1.76827i) q^{16} +0.0878473 q^{17} +(5.19711 - 0.597556i) q^{18} -8.25567 q^{19} +(-2.95529 + 0.688694i) q^{20} -2.58827 q^{21} +(1.61625 - 0.185834i) q^{22} -6.48403 q^{23} +(2.46501 + 6.89324i) q^{24} -2.69799 q^{25} +(-4.57858 + 2.24423i) q^{26} +1.80953i q^{27} +(-0.453913 - 1.94781i) q^{28} +2.75060i q^{29} +(-0.634370 - 5.51729i) q^{30} -5.46650i q^{31} +(-4.75524 + 3.06394i) q^{32} +2.97752i q^{33} +(-0.123422 + 0.0141908i) q^{34} +1.51724i q^{35} +(-7.20519 + 1.67908i) q^{36} +8.75613 q^{37} +(11.5989 - 1.33362i) q^{38} +(-3.12330 - 8.79396i) q^{39} +(4.04080 - 1.44498i) q^{40} +0.221622i q^{41} +(3.63640 - 0.418108i) q^{42} +11.3062i q^{43} +(-2.24075 + 0.522179i) q^{44} +5.61245 q^{45} +(9.10979 - 1.04743i) q^{46} +4.58078i q^{47} +(-4.57676 - 9.28651i) q^{48} -1.00000 q^{49} +(3.79056 - 0.435833i) q^{50} -0.227372i q^{51} +(6.07018 - 3.89268i) q^{52} +10.8067i q^{53} +(-0.292311 - 2.54231i) q^{54} +1.74542 q^{55} +(0.952378 + 2.66326i) q^{56} +21.3679i q^{57} +(-0.444331 - 3.86447i) q^{58} -3.96379 q^{59} +(1.78252 + 7.64908i) q^{60} -11.0547i q^{61} +(0.883058 + 7.68021i) q^{62} +3.69913i q^{63} +(6.18595 - 5.07287i) q^{64} +(-5.15500 + 1.83087i) q^{65} +(-0.480989 - 4.18329i) q^{66} -4.63551 q^{67} +(0.171110 - 0.0398751i) q^{68} +16.7824i q^{69} +(-0.245094 - 2.13165i) q^{70} -9.36899i q^{71} +(9.85175 - 3.52297i) q^{72} +10.4110i q^{73} +(-12.3020 + 1.41446i) q^{74} +6.98312i q^{75} +(-16.0805 + 3.74736i) q^{76} +1.15039i q^{77} +(5.80867 + 11.8506i) q^{78} +7.68869 q^{79} +(-5.44373 + 2.68289i) q^{80} -6.41384 q^{81} +(-0.0358007 - 0.311369i) q^{82} -5.19464 q^{83} +(-5.04145 + 1.17485i) q^{84} -0.133285 q^{85} +(-1.82640 - 15.8847i) q^{86} +7.11928 q^{87} +(3.06380 - 1.09561i) q^{88} +1.08552i q^{89} +(-7.88526 + 0.906635i) q^{90} +(-1.20671 - 3.39762i) q^{91} +(-12.6297 + 2.94319i) q^{92} -14.1488 q^{93} +(-0.739978 - 6.43580i) q^{94} +12.5258 q^{95} +(7.93030 + 12.3078i) q^{96} -10.4826i q^{97} +(1.40496 - 0.161540i) q^{98} +4.25545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 84 q^{9} + 8 q^{10} - 20 q^{12} - 8 q^{16} + 8 q^{17} - 12 q^{22} - 24 q^{23} + 92 q^{25} - 40 q^{30} + 44 q^{36} + 20 q^{38} - 24 q^{39} - 28 q^{40} - 72 q^{48} - 84 q^{49} - 44 q^{52} + 32 q^{55}+ \cdots - 16 q^{95}+O(q^{100}) \) 84 * q - 84 * q^9 + 8 * q^10 - 20 * q^12 - 8 * q^16 + 8 * q^17 - 12 * q^22 - 24 * q^23 + 92 * q^25 - 40 * q^30 + 44 * q^36 + 20 * q^38 - 24 * q^39 - 28 * q^40 - 72 * q^48 - 84 * q^49 - 44 * q^52 + 32 * q^55 - 40 * q^62 + 72 * q^64 - 24 * q^65 - 60 * q^66 - 92 * q^68 + 28 * q^74 + 12 * q^78 - 40 * q^79 + 84 * q^81 + 24 * q^82 - 48 * q^87 - 108 * q^88 + 20 * q^90 + 60 * q^92 + 36 * q^94 - 16 * q^95

Introduction

L-functions

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