LMFDB - Embedded newform 552.2.n.b.91.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(91,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("552.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.n (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.14
Character	$\chi$	$=$	552.91
Dual form			552.2.n.b.91.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.409868 - 1.35352i) q^{2} -1.00000 q^{3} +(-1.66402 - 1.10953i) q^{4} +0.901487 q^{5} +(-0.409868 + 1.35352i) q^{6} +1.56211 q^{7} +(-2.18379 + 1.79751i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.409868 - 1.35352i) q^{2} -1.00000 q^{3} +(-1.66402 - 1.10953i) q^{4} +0.901487 q^{5} +(-0.409868 + 1.35352i) q^{6} +1.56211 q^{7} +(-2.18379 + 1.79751i) q^{8} +1.00000 q^{9} +(0.369491 - 1.22018i) q^{10} -3.69478i q^{11} +(1.66402 + 1.10953i) q^{12} -2.36562i q^{13} +(0.640260 - 2.11434i) q^{14} -0.901487 q^{15} +(1.53790 + 3.69254i) q^{16} -0.473035i q^{17} +(0.409868 - 1.35352i) q^{18} -7.66256i q^{19} +(-1.50009 - 1.00022i) q^{20} -1.56211 q^{21} +(-5.00095 - 1.51438i) q^{22} +(-4.73018 - 0.790796i) q^{23} +(2.18379 - 1.79751i) q^{24} -4.18732 q^{25} +(-3.20191 - 0.969595i) q^{26} -1.00000 q^{27} +(-2.59938 - 1.73321i) q^{28} +4.29403i q^{29} +(-0.369491 + 1.22018i) q^{30} +1.83523i q^{31} +(5.62825 - 0.568111i) q^{32} +3.69478i q^{33} +(-0.640260 - 0.193882i) q^{34} +1.40822 q^{35} +(-1.66402 - 1.10953i) q^{36} +5.81865 q^{37} +(-10.3714 - 3.14064i) q^{38} +2.36562i q^{39} +(-1.96866 + 1.62043i) q^{40} +2.62473 q^{41} +(-0.640260 + 2.11434i) q^{42} -7.06267i q^{43} +(-4.09947 + 6.14818i) q^{44} +0.901487 q^{45} +(-3.00911 + 6.07826i) q^{46} -4.27804i q^{47} +(-1.53790 - 3.69254i) q^{48} -4.55981 q^{49} +(-1.71625 + 5.66761i) q^{50} +0.473035i q^{51} +(-2.62473 + 3.93644i) q^{52} -4.64065 q^{53} +(-0.409868 + 1.35352i) q^{54} -3.33080i q^{55} +(-3.41133 + 2.80792i) q^{56} +7.66256i q^{57} +(5.81205 + 1.75999i) q^{58} -7.81205 q^{59} +(1.50009 + 1.00022i) q^{60} +11.9981 q^{61} +(2.48402 + 0.752203i) q^{62} +1.56211 q^{63} +(1.53790 - 7.85079i) q^{64} -2.13258i q^{65} +(5.00095 + 1.51438i) q^{66} -5.35433i q^{67} +(-0.524845 + 0.787137i) q^{68} +(4.73018 + 0.790796i) q^{69} +(0.577186 - 1.90605i) q^{70} +6.95616i q^{71} +(-2.18379 + 1.79751i) q^{72} +11.2808 q^{73} +(2.38488 - 7.87564i) q^{74} +4.18732 q^{75} +(-8.50182 + 12.7506i) q^{76} -5.77167i q^{77} +(3.20191 + 0.969595i) q^{78} +15.8447 q^{79} +(1.38639 + 3.32878i) q^{80} +1.00000 q^{81} +(1.07579 - 3.55261i) q^{82} -7.33508i q^{83} +(2.59938 + 1.73321i) q^{84} -0.426435i q^{85} +(-9.55945 - 2.89477i) q^{86} -4.29403i q^{87} +(6.64142 + 8.06864i) q^{88} +4.91384i q^{89} +(0.369491 - 1.22018i) q^{90} -3.69537i q^{91} +(6.99369 + 6.56417i) q^{92} -1.83523i q^{93} +(-5.79040 - 1.75343i) q^{94} -6.90769i q^{95} +(-5.62825 + 0.568111i) q^{96} +15.0308i q^{97} +(-1.86892 + 6.17178i) q^{98} -3.69478i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9	$ 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81} - 40 q^{82} + 40 q^{92} - 48 q^{94}+O(q^{100}) $ 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9 - 4 * q^12 + 4 * q^16 + 24 * q^25 - 24 * q^27 + 4 * q^36 - 44 * q^46 - 4 * q^48 + 56 * q^49 - 40 * q^50 - 48 * q^58 - 40 * q^62 + 4 * q^64 + 32 * q^73 - 24 * q^75 + 24 * q^81 - 40 * q^82 + 40 * q^92 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	0.409868	−	1.35352i	0.289821	−	0.957081i
$2$	0.409868	−	1.35352i	0.289821	−	0.957081i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.66402	−	1.10953i	−0.832008	−	0.554764i
$5$	0.901487			0.403157			0.201579	−	0.979472i	$-0.435393\pi$
$5$	0.901487			0.403157			0.201579	+	0.979472i	$0.435393\pi$
$6$	−0.409868	+	1.35352i	−0.167328	+	0.552571i
$7$	1.56211			0.590423			0.295211	−	0.955432i	$-0.404610\pi$
$7$	1.56211			0.590423			0.295211	+	0.955432i	$0.404610\pi$
$8$	−2.18379	+	1.79751i	−0.772087	+	0.635517i
$9$	1.00000			0.333333
$10$	0.369491	−	1.22018i	0.116843	−	0.385854i
$11$		−	3.69478i		−	1.11402i	−0.830506	−	0.557010i	$-0.811949\pi$
$11$		−	3.69478i		−	1.11402i	0.830506	−	0.557010i	$-0.188051\pi$
$12$	1.66402	+	1.10953i	0.480360	+	0.320293i
$13$		−	2.36562i		−	0.656106i	−0.944659	−	0.328053i	$-0.893608\pi$
$13$		−	2.36562i		−	0.656106i	0.944659	−	0.328053i	$-0.106392\pi$
$14$	0.640260	−	2.11434i	0.171117	−	0.565082i
$15$	−0.901487			−0.232763
$16$	1.53790	+	3.69254i	0.384474	+	0.923136i
$17$		−	0.473035i		−	0.114728i	−0.998353	−	0.0573639i	$-0.981730\pi$
$17$		−	0.473035i		−	0.114728i	0.998353	−	0.0573639i	$-0.0182695\pi$
$18$	0.409868	−	1.35352i	0.0966069	−	0.319027i
$19$		−	7.66256i		−	1.75791i	−0.476904	−	0.878955i	$-0.658241\pi$
$19$		−	7.66256i		−	1.75791i	0.476904	−	0.878955i	$-0.341759\pi$
$20$	−1.50009	−	1.00022i	−0.335430	−	0.223657i
$21$	−1.56211			−0.340881
$22$	−5.00095	−	1.51438i	−1.06621	−	0.322866i
$23$	−4.73018	−	0.790796i	−0.986312	−	0.164892i
$23$	−4.73018	−	0.790796i	−0.986312	−	0.164892i
$24$	2.18379	−	1.79751i	0.445765	−	0.366916i
$25$	−4.18732			−0.837464
$26$	−3.20191	−	0.969595i	−0.627947	−	0.190153i
$27$	−1.00000			−0.192450
$28$	−2.59938	−	1.73321i	−0.491236	−	0.327545i
$29$			4.29403i			0.797382i	0.917085	+	0.398691i	$0.130535\pi$
$29$			4.29403i			0.797382i	−0.917085	+	0.398691i	$0.869465\pi$
$30$	−0.369491	+	1.22018i	−0.0674595	+	0.222773i
$31$			1.83523i			0.329617i	0.986326	+	0.164809i	$0.0527006\pi$
$31$			1.83523i			0.329617i	−0.986326	+	0.164809i	$0.947299\pi$
$32$	5.62825	−	0.568111i	0.994944	−	0.100429i
$33$			3.69478i			0.643179i
$34$	−0.640260	−	0.193882i	−0.109804	−	0.0332505i
$35$	1.40822			0.238033
$36$	−1.66402	−	1.10953i	−0.277336	−	0.184921i
$37$	5.81865			0.956580			0.478290	−	0.878202i	$-0.341257\pi$
$37$	5.81865			0.956580			0.478290	+	0.878202i	$0.341257\pi$
$38$	−10.3714	−	3.14064i	−1.68246	−	0.509479i
$39$			2.36562i			0.378803i
$40$	−1.96866	+	1.62043i	−0.311273	+	0.256213i
$41$	2.62473			0.409913			0.204957	−	0.978771i	$-0.434295\pi$
$41$	2.62473			0.409913			0.204957	+	0.978771i	$0.434295\pi$
$42$	−0.640260	+	2.11434i	−0.0987943	+	0.326250i
$43$		−	7.06267i		−	1.07705i	−0.842610	−	0.538524i	$-0.818982\pi$
$43$		−	7.06267i		−	1.07705i	0.842610	−	0.538524i	$-0.181018\pi$
$44$	−4.09947	+	6.14818i	−0.618018	+	0.926873i
$45$	0.901487			0.134386
$46$	−3.00911	+	6.07826i	−0.443669	+	0.896191i
$47$		−	4.27804i		−	0.624016i	−0.950079	−	0.312008i	$-0.898998\pi$
$47$		−	4.27804i		−	0.624016i	0.950079	−	0.312008i	$-0.101002\pi$
$48$	−1.53790	−	3.69254i	−0.221976	−	0.532973i
$49$	−4.55981			−0.651401
$50$	−1.71625	+	5.66761i	−0.242715	+	0.801521i
$51$			0.473035i			0.0662381i
$52$	−2.62473	+	3.93644i	−0.363984	+	0.545885i
$53$	−4.64065			−0.637442			−0.318721	−	0.947849i	$-0.603253\pi$
$53$	−4.64065			−0.637442			−0.318721	+	0.947849i	$0.603253\pi$
$54$	−0.409868	+	1.35352i	−0.0557760	+	0.184190i
$55$		−	3.33080i		−	0.449125i
$56$	−3.41133	+	2.80792i	−0.455858	+	0.375223i
$57$			7.66256i			1.01493i
$58$	5.81205	+	1.75999i	0.763159	+	0.231098i
$59$	−7.81205			−1.01704			−0.508521	−	0.861050i	$-0.669808\pi$
$59$	−7.81205			−1.01704			−0.508521	+	0.861050i	$0.669808\pi$
$60$	1.50009	+	1.00022i	0.193661	+	0.129128i
$61$	11.9981			1.53620			0.768098	−	0.640332i	$-0.221203\pi$
$61$	11.9981			1.53620			0.768098	+	0.640332i	$0.221203\pi$
$62$	2.48402	+	0.752203i	0.315470	+	0.0955299i
$63$	1.56211			0.196808
$64$	1.53790	−	7.85079i	0.192237	−	0.981349i
$65$		−	2.13258i		−	0.264514i
$66$	5.00095	+	1.51438i	0.615575	+	0.186407i
$67$		−	5.35433i		−	0.654135i	−0.945001	−	0.327068i	$-0.893939\pi$
$67$		−	5.35433i		−	0.654135i	0.945001	−	0.327068i	$-0.106061\pi$
$68$	−0.524845	+	0.787137i	−0.0636468	+	0.0954544i
$69$	4.73018	+	0.790796i	0.569447	+	0.0952006i
$70$	0.577186	−	1.90605i	0.0689870	−	0.227817i
$71$			6.95616i			0.825544i	0.910834	+	0.412772i	$0.135439\pi$
$71$			6.95616i			0.825544i	−0.910834	+	0.412772i	$0.864561\pi$
$72$	−2.18379	+	1.79751i	−0.257362	+	0.211839i
$73$	11.2808			1.32032			0.660158	−	0.751127i	$-0.270489\pi$
$73$	11.2808			1.32032			0.660158	+	0.751127i	$0.270489\pi$
$74$	2.38488	−	7.87564i	0.277237	−	0.915525i
$75$	4.18732			0.483510
$76$	−8.50182	+	12.7506i	−0.975225	+	1.46260i
$77$		−	5.77167i		−	0.657742i
$78$	3.20191	+	0.969595i	0.362545	+	0.109785i
$79$	15.8447			1.78267			0.891335	−	0.453345i	$-0.149770\pi$
$79$	15.8447			1.78267			0.891335	+	0.453345i	$0.149770\pi$
$80$	1.38639	+	3.32878i	0.155003	+	0.372169i
$81$	1.00000			0.111111
$82$	1.07579	−	3.55261i	0.118801	−	0.392320i
$83$		−	7.33508i		−	0.805129i	−0.915392	−	0.402565i	$-0.868119\pi$
$83$		−	7.33508i		−	0.805129i	0.915392	−	0.402565i	$-0.131881\pi$
$84$	2.59938	+	1.73321i	0.283615	+	0.189108i
$85$		−	0.426435i		−	0.0462533i
$86$	−9.55945	−	2.89477i	−1.03082	−	0.312151i
$87$		−	4.29403i		−	0.460369i
$88$	6.64142	+	8.06864i	0.707978	+	0.860120i
$89$			4.91384i			0.520866i	0.965492	+	0.260433i	$0.0838653\pi$
$89$			4.91384i			0.520866i	−0.965492	+	0.260433i	$0.916135\pi$
$90$	0.369491	−	1.22018i	0.0389478	−	0.128618i
$91$		−	3.69537i		−	0.387380i
$92$	6.99369	+	6.56417i	0.729143	+	0.684362i
$93$		−	1.83523i		−	0.190305i
$94$	−5.79040	−	1.75343i	−0.597234	−	0.180853i
$95$		−	6.90769i		−	0.708714i
$96$	−5.62825	+	0.568111i	−0.574431	+	0.0579826i
$97$			15.0308i			1.52614i	0.646314	+	0.763071i	$0.276309\pi$
$97$			15.0308i			1.52614i	−0.646314	+	0.763071i	$0.723691\pi$
$98$	−1.86892	+	6.17178i	−0.188790	+	0.623444i
$99$		−	3.69478i		−	0.371340i
$100$	6.96777	+	4.64595i	0.696777	+	0.464595i
$101$			1.47763i			0.147030i	0.997294	+	0.0735149i	$0.0234217\pi$
$101$			1.47763i			0.147030i	−0.997294	+	0.0735149i	$0.976578\pi$
$102$	0.640260	+	0.193882i	0.0633952	+	0.0191972i
$103$	3.82331			0.376722			0.188361	−	0.982100i	$-0.439683\pi$
$103$	3.82331			0.376722			0.188361	+	0.982100i	$0.439683\pi$
$104$	4.25224	+	5.16603i	0.416966	+	0.506571i
$105$	−1.40822			−0.137429
$106$	−1.90205	+	6.28119i	−0.184744	+	0.610083i
$107$			8.57550i			0.829024i	0.910044	+	0.414512i	$0.136048\pi$
$107$			8.57550i			0.829024i	−0.910044	+	0.414512i	$0.863952\pi$
$108$	1.66402	+	1.10953i	0.160120	+	0.106764i
$109$	15.2790			1.46346			0.731732	−	0.681592i	$-0.238712\pi$
$109$	15.2790			1.46346			0.731732	+	0.681592i	$0.238712\pi$
$110$	−4.50829	−	1.36519i	−0.429849	−	0.130166i
$111$	−5.81865			−0.552282
$112$	2.40237	+	5.76816i	0.227002	+	0.545040i
$113$		−	5.89000i		−	0.554085i	−0.960858	−	0.277042i	$-0.910646\pi$
$113$		−	5.89000i		−	0.554085i	0.960858	−	0.277042i	$-0.0893542\pi$
$114$	10.3714	+	3.14064i	0.971370	+	0.294148i
$115$	−4.26420	−	0.712892i	−0.397639	−	0.0664775i
$116$	4.76435	−	7.14534i	0.442359	−	0.663428i
$117$		−	2.36562i		−	0.218702i
$118$	−3.20191	+	10.5737i	−0.294760	+	0.973391i
$119$		−	0.738933i		−	0.0677379i
$120$	1.96866	−	1.62043i	0.179713	−	0.147925i
$121$	−2.65143			−0.241039
$122$	4.91764	−	16.2396i	0.445222	−	1.47026i
$123$	−2.62473			−0.236664
$124$	2.03624	−	3.05385i	0.182860	−	0.274244i
$125$	−8.28225			−0.740787
$126$	0.640260	−	2.11434i	0.0570389	−	0.188361i
$127$			18.7735i			1.66588i	0.553364	+	0.832939i	$0.313344\pi$
$127$			18.7735i			1.66588i	−0.553364	+	0.832939i	$0.686656\pi$
$128$	−9.99584	−	5.29936i	−0.883516	−	0.468402i
$129$			7.06267i			0.621834i
$130$	−2.88648	−	0.874077i	−0.253161	−	0.0766616i
$131$	6.40382			0.559505			0.279752	−	0.960072i	$-0.409748\pi$
$131$	6.40382			0.559505			0.279752	+	0.960072i	$0.409748\pi$
$132$	4.09947	−	6.14818i	0.356813	−	0.535130i
$133$		−	11.9698i		−	1.03791i
$134$	−7.24717	−	2.19457i	−0.626061	−	0.189582i
$135$	−0.901487			−0.0775876
$136$	0.850286	+	1.03301i	0.0729114	+	0.0885798i
$137$		−	3.16726i		−	0.270597i	−0.990805	−	0.135299i	$-0.956801\pi$
$137$		−	3.16726i		−	0.270597i	0.990805	−	0.135299i	$-0.0431994\pi$
$138$	3.00911	−	6.07826i	0.256152	−	0.517416i
$139$	4.84346			0.410817			0.205408	−	0.978676i	$-0.434148\pi$
$139$	4.84346			0.410817			0.205408	+	0.978676i	$0.434148\pi$
$140$	−2.34331	−	1.56246i	−0.198045	−	0.132052i
$141$			4.27804i			0.360276i
$142$	9.41528	+	2.85111i	0.790113	+	0.239260i
$143$	−8.74047			−0.730915
$144$	1.53790	+	3.69254i	0.128158	+	0.307712i
$145$			3.87102i			0.321470i
$146$	4.62364	−	15.2687i	0.382655	−	1.26365i
$147$	4.55981			0.376087
$148$	−9.68233	−	6.45596i	−0.795882	−	0.530676i
$149$	−3.34176			−0.273767			−0.136884	−	0.990587i	$-0.543709\pi$
$149$	−3.34176			−0.273767			−0.136884	+	0.990587i	$0.543709\pi$
$150$	1.71625	−	5.66761i	0.140131	−	0.462758i
$151$		−	17.3731i		−	1.41380i	−0.707314	−	0.706900i	$-0.750093\pi$
$151$		−	17.3731i		−	1.41380i	0.707314	−	0.706900i	$-0.249907\pi$
$152$	13.7735	+	16.7334i	1.11718	+	1.35726i
$153$		−	0.473035i		−	0.0382426i
$154$	−7.81205	−	2.36562i	−0.629513	−	0.190627i
$155$			1.65444i			0.132888i
$156$	2.62473	−	3.93644i	0.210146	−	0.315167i
$157$	4.88151			0.389587			0.194793	−	0.980844i	$-0.437596\pi$
$157$	4.88151			0.389587			0.194793	+	0.980844i	$0.437596\pi$
$158$	6.49425	−	21.4461i	0.516655	−	1.70616i
$159$	4.64065			0.368027
$160$	5.07380	−	0.512145i	0.401119	−	0.0404886i
$161$	−7.38908	−	1.23531i	−0.582341	−	0.0973561i
$162$	0.409868	−	1.35352i	0.0322023	−	0.106342i
$163$	−22.1556			−1.73536			−0.867680	−	0.497124i	$-0.834389\pi$
$163$	−22.1556			−1.73536			−0.867680	+	0.497124i	$0.834389\pi$
$164$	−4.36758	−	2.91221i	−0.341051	−	0.227405i
$165$			3.33080i			0.259302i
$166$	−9.92815	−	3.00642i	−0.770574	−	0.233343i
$167$			21.3490i			1.65203i	0.563645	+	0.826017i	$0.309399\pi$
$167$			21.3490i			1.65203i	−0.563645	+	0.826017i	$0.690601\pi$
$168$	3.41133	−	2.80792i	0.263190	−	0.216635i
$169$	7.40382			0.569525
$170$	−0.577186	−	0.174782i	−0.0442682	−	0.0134052i
$171$		−	7.66256i		−	0.585970i
$172$	−7.83623	+	11.7524i	−0.597507	+	0.896112i
$173$			16.6902i			1.26893i	0.772950	+	0.634467i	$0.218781\pi$
$173$			16.6902i			1.26893i	−0.772950	+	0.634467i	$0.781219\pi$
$174$	−5.81205	−	1.75999i	−0.440610	−	0.133424i
$175$	−6.54106			−0.494458
$176$	13.6432	−	5.68220i	1.02839	−	0.428312i
$177$	7.81205			0.587189
$178$	6.65097	+	2.01403i	0.498511	+	0.150958i
$179$	13.5240			1.01083			0.505416	−	0.862876i	$-0.331339\pi$
$179$	13.5240			1.01083			0.505416	+	0.862876i	$0.331339\pi$
$180$	−1.50009	−	1.00022i	−0.111810	−	0.0745524i
$181$	−15.6631			−1.16423			−0.582115	−	0.813106i	$-0.697775\pi$
$181$	−15.6631			−1.16423			−0.582115	+	0.813106i	$0.697775\pi$
$182$	−5.00174	−	1.51462i	−0.370754	−	0.112271i
$183$	−11.9981			−0.886924
$184$	11.7512	−	6.77563i	0.866310	−	0.499506i
$185$	5.24544			0.385652
$186$	−2.48402	−	0.752203i	−0.182137	−	0.0551542i
$187$	−1.74776			−0.127809
$188$	−4.74660	+	7.11872i	−0.346182	+	0.519186i
$189$	−1.56211			−0.113627
$190$	−9.34968	−	2.83125i	−0.678297	−	0.205400i
$191$	10.5542			0.763677			0.381839	−	0.924229i	$-0.375291\pi$
$191$	10.5542			0.763677			0.381839	+	0.924229i	$0.375291\pi$
$192$	−1.53790	+	7.85079i	−0.110988	+	0.566582i
$193$	0.464113			0.0334076			0.0167038	−	0.999860i	$-0.494683\pi$
$193$	0.464113			0.0334076			0.0167038	+	0.999860i	$0.494683\pi$
$194$	20.3444	+	6.16064i	1.46064	+	0.442308i
$195$			2.13258i			0.152717i
$196$	7.58759	+	5.05923i	0.541971	+	0.361374i
$197$		−	10.0657i		−	0.717151i	−0.933501	−	0.358576i	$-0.883262\pi$
$197$		−	10.0657i		−	0.717151i	0.933501	−	0.358576i	$-0.116738\pi$
$198$	−5.00095	−	1.51438i	−0.355402	−	0.107622i
$199$	−8.22327			−0.582932			−0.291466	−	0.956581i	$-0.594143\pi$
$199$	−8.22327			−0.582932			−0.291466	+	0.956581i	$0.594143\pi$
$200$	9.14424	−	7.52676i	0.646595	−	0.532223i
$201$			5.35433i			0.377665i
$202$	2.00000	+	0.605635i	0.140720	+	0.0426123i
$203$			6.70776i			0.470792i
$204$	0.524845	−	0.787137i	0.0367465	−	0.0551106i
$205$	2.36616			0.165259
$206$	1.56705	−	5.17491i	0.109182	−	0.360553i
$207$	−4.73018	−	0.790796i	−0.328771	−	0.0549641i
$208$	8.73517	−	3.63808i	0.605675	−	0.252256i
$209$	−28.3115			−1.95835
$210$	−0.577186	+	1.90605i	−0.0398296	+	0.131530i
$211$	16.1286			1.11034			0.555168	−	0.831738i	$-0.312654\pi$
$211$	16.1286			1.11034			0.555168	+	0.831738i	$0.312654\pi$
$212$	7.72211	+	5.14893i	0.530357	+	0.353630i
$213$		−	6.95616i		−	0.476628i
$214$	11.6071	+	3.51483i	0.793444	+	0.240269i
$215$		−	6.36691i		−	0.434220i
$216$	2.18379	−	1.79751i	0.148588	−	0.122305i
$217$			2.86683i			0.194613i
$218$	6.26239	−	20.6804i	0.424143	−	1.40065i
$219$	−11.2808			−0.762285
$220$	−3.69562	+	5.54250i	−0.249158	+	0.373676i
$221$	−1.11902			−0.0752736
$222$	−2.38488	+	7.87564i	−0.160063	+	0.528579i
$223$		−	6.77440i		−	0.453647i	−0.973936	−	0.226824i	$-0.927166\pi$
$223$		−	6.77440i		−	0.453647i	0.973936	−	0.226824i	$-0.0728341\pi$
$224$	8.79196	−	0.887453i	0.587438	−	0.0592954i
$225$	−4.18732			−0.279155
$226$	−7.97221	−	2.41413i	−0.530304	−	0.160585i
$227$			23.8069i			1.58012i	0.613030	+	0.790059i	$0.289950\pi$
$227$			23.8069i			1.58012i	−0.613030	+	0.790059i	$0.710050\pi$
$228$	8.50182	−	12.7506i	0.563047	−	0.844430i
$229$	−10.4208			−0.688628			−0.344314	−	0.938854i	$-0.611889\pi$
$229$	−10.4208			−0.688628			−0.344314	+	0.938854i	$0.611889\pi$
$230$	−2.71267	+	5.47947i	−0.178868	+	0.361306i
$231$			5.77167i			0.379748i
$232$	−7.71858	−	9.37728i	−0.506750	−	0.615648i
$233$	2.52840			0.165641			0.0828205	−	0.996564i	$-0.473607\pi$
$233$	2.52840			0.165641			0.0828205	+	0.996564i	$0.473607\pi$
$234$	−3.20191	−	0.969595i	−0.209316	−	0.0633844i
$235$		−	3.85660i		−	0.251577i
$236$	12.9994	+	8.66768i	0.846187	+	0.564218i
$237$	−15.8447			−1.02922
$238$	−1.00016	−	0.302865i	−0.0648306	−	0.0196318i
$239$		−	12.3970i		−	0.801895i	−0.916101	−	0.400948i	$-0.868681\pi$
$239$		−	12.3970i		−	0.801895i	0.916101	−	0.400948i	$-0.131319\pi$
$240$	−1.38639	−	3.32878i	−0.0894913	−	0.214872i
$241$			6.64297i			0.427911i	0.976843	+	0.213956i	$0.0686348\pi$
$241$			6.64297i			0.427911i	−0.976843	+	0.213956i	$0.931365\pi$
$242$	−1.08674	+	3.58876i	−0.0698583	+	0.230694i
$243$	−1.00000			−0.0641500
$244$	−19.9650	−	13.3122i	−1.27813	−	0.852227i
$245$	−4.11061			−0.262617
$246$	−1.07579	+	3.55261i	−0.0685900	+	0.226506i
$247$	−18.1267			−1.15338
$248$	−3.29885	−	4.00776i	−0.209477	−	0.254493i
$249$			7.33508i			0.464842i
$250$	−3.39463	+	11.2102i	−0.214695	+	0.708993i
$251$			14.0093i			0.884259i	0.896951	+	0.442130i	$0.145777\pi$
$251$			14.0093i			0.884259i	−0.896951	+	0.442130i	$0.854223\pi$
$252$	−2.59938	−	1.73321i	−0.163745	−	0.109182i
$253$	−2.92182	+	17.4770i	−0.183693	+	1.09877i
$254$	25.4102	+	7.69467i	1.59438	+	0.482806i
$255$			0.426435i			0.0267044i
$256$	−11.2698	+	11.3575i	−0.704359	+	0.709843i
$257$	17.0620			1.06430			0.532150	−	0.846650i	$-0.321384\pi$
$257$	17.0620			1.06430			0.532150	+	0.846650i	$0.321384\pi$
$258$	9.55945	+	2.89477i	0.595145	+	0.180220i
$259$	9.08938			0.564787
$260$	−2.36616	+	3.54865i	−0.146743	+	0.220078i
$261$			4.29403i			0.265794i
$262$	2.62473	−	8.66768i	0.162156	−	0.535491i
$263$	−12.5846			−0.775999			−0.388000	−	0.921660i	$-0.626834\pi$
$263$	−12.5846			−0.775999			−0.388000	+	0.921660i	$0.626834\pi$
$264$	−6.64142	−	8.06864i	−0.408751	−	0.496591i
$265$	−4.18348			−0.256989
$266$	−16.2013	−	4.90603i	−0.993364	−	0.300808i
$267$		−	4.91384i		−	0.300722i
$268$	−5.94078	+	8.90969i	−0.362891	+	0.544246i
$269$		−	5.33445i		−	0.325247i	−0.986688	−	0.162624i	$-0.948004\pi$
$269$		−	5.33445i		−	0.325247i	0.986688	−	0.162624i	$-0.0519956\pi$
$270$	−0.369491	+	1.22018i	−0.0224865	+	0.0742577i
$271$		−	5.16603i		−	0.313814i	−0.987613	−	0.156907i	$-0.949848\pi$
$271$		−	5.16603i		−	0.313814i	0.987613	−	0.156907i	$-0.0501523\pi$
$272$	1.74670	−	0.727478i	0.105909	−	0.0441098i
$273$			3.69537i			0.223654i
$274$	−4.28694	−	1.29816i	−0.258983	−	0.0784247i
$275$			15.4713i			0.932952i
$276$	−6.99369	−	6.56417i	−0.420971	−	0.395116i
$277$			26.4195i			1.58739i	0.608313	+	0.793697i	$0.291846\pi$
$277$			26.4195i			1.58739i	−0.608313	+	0.793697i	$0.708154\pi$
$278$	1.98518	−	6.55570i	0.119063	−	0.393185i
$279$			1.83523i			0.109872i
$280$	−3.07527	+	2.53130i	−0.183782	+	0.151274i
$281$		−	20.8795i		−	1.24557i	−0.782395	−	0.622783i	$-0.786002\pi$
$281$		−	20.8795i		−	1.24557i	0.782395	−	0.622783i	$-0.213998\pi$
$282$	5.79040	+	1.75343i	0.344813	+	0.104415i
$283$		−	11.8930i		−	0.706966i	−0.935441	−	0.353483i	$-0.884997\pi$
$283$		−	11.8930i		−	0.706966i	0.935441	−	0.353483i	$-0.115003\pi$
$284$	7.71805	−	11.5752i	0.457982	−	0.686859i
$285$			6.90769i			0.409176i
$286$	−3.58244	+	11.8304i	−0.211834	+	0.699545i
$287$	4.10011			0.242022
$288$	5.62825	−	0.568111i	0.331648	−	0.0334763i
$289$	16.7762			0.986838
$290$	5.23948	+	1.58661i	0.307673	+	0.0931688i
$291$		−	15.0308i		−	0.881119i
$292$	−18.7714	−	12.5163i	−1.09851	−	0.732464i
$293$	−29.0826			−1.69902			−0.849512	−	0.527570i	$-0.823103\pi$
$293$	−29.0826			−1.69902			−0.849512	+	0.527570i	$0.823103\pi$
$294$	1.86892	−	6.17178i	0.108998	−	0.359945i
$295$	−7.04246			−0.410028
$296$	−12.7067	+	10.4591i	−0.738563	+	0.607923i
$297$			3.69478i			0.214393i
$298$	−1.36968	+	4.52313i	−0.0793435	+	0.262018i
$299$	−1.87072	+	11.1898i	−0.108187	+	0.647125i
$300$	−6.96777	−	4.64595i	−0.402284	−	0.268234i
$301$		−	11.0327i		−	0.635913i
$302$	−23.5147	−	7.12067i	−1.35312	−	0.409748i
$303$		−	1.47763i		−	0.0848877i
$304$	28.2943	−	11.7842i	1.62279	−	0.675871i
$305$	10.8161			0.619329
$306$	−0.640260	−	0.193882i	−0.0366012	−	0.0110835i
$307$	0.564207			0.0322010			0.0161005	−	0.999870i	$-0.494875\pi$
$307$	0.564207			0.0322010			0.0161005	+	0.999870i	$0.494875\pi$
$308$	−6.40382	+	9.60414i	−0.364892	+	0.547247i
$309$	−3.82331			−0.217500
$310$	2.23931	+	0.678101i	0.127184	+	0.0385136i
$311$			22.4646i			1.27385i	0.770924	+	0.636927i	$0.219795\pi$
$311$			22.4646i			1.27385i	−0.770924	+	0.636927i	$0.780205\pi$
$312$	−4.25224	−	5.16603i	−0.240736	−	0.292469i
$313$			5.00245i			0.282755i	0.989956	+	0.141378i	$0.0451532\pi$
$313$			5.00245i			0.282755i	−0.989956	+	0.141378i	$0.954847\pi$
$314$	2.00078	−	6.60720i	0.112910	−	0.372866i
$315$	1.40822			0.0793444
$316$	−26.3659	−	17.5802i	−1.48320	−	0.988961i
$317$		−	19.1167i		−	1.07370i	−0.843678	−	0.536849i	$-0.819614\pi$
$317$		−	19.1167i		−	1.07370i	0.843678	−	0.536849i	$-0.180386\pi$
$318$	1.90205	−	6.28119i	0.106662	−	0.352232i
$319$	15.8655			0.888299
$320$	1.38639	−	7.07738i	0.0775017	−	0.395638i
$321$		−	8.57550i		−	0.478638i
$322$	−4.70056	+	9.49492i	−0.261952	+	0.529131i
$323$	−3.62465			−0.201681
$324$	−1.66402	−	1.10953i	−0.0924453	−	0.0616404i
$325$			9.90563i			0.549465i
$326$	−9.08087	+	29.9880i	−0.502943	+	1.66088i
$327$	−15.2790			−0.844932
$328$	−5.73185	+	4.71798i	−0.316489	+	0.260507i
$329$		−	6.68277i		−	0.368433i
$330$	4.50829	+	1.36519i	0.248173	+	0.0751512i
$331$	−9.65359			−0.530609			−0.265305	−	0.964165i	$-0.585473\pi$
$331$	−9.65359			−0.530609			−0.265305	+	0.964165i	$0.585473\pi$
$332$	−8.13847	+	12.2057i	−0.446657	+	0.669874i
$333$	5.81865			0.318860
$334$	28.8962	+	8.75028i	1.58113	+	0.478794i
$335$		−	4.82686i		−	0.263719i
$336$	−2.40237	−	5.76816i	−0.131060	−	0.314679i
$337$		−	15.5246i		−	0.845678i	−0.906205	−	0.422839i	$-0.861034\pi$
$337$		−	15.5246i		−	0.845678i	0.906205	−	0.422839i	$-0.138966\pi$
$338$	3.03459	−	10.0212i	0.165060	−	0.545081i
$339$			5.89000i			0.319901i
$340$	−0.473141	+	0.709594i	−0.0256597	+	0.0384831i
$341$	6.78078			0.367200
$342$	−10.3714	−	3.14064i	−0.560821	−	0.169826i
$343$	−18.0577			−0.975025
$344$	12.6952	+	15.4234i	0.684482	+	0.831575i
$345$	4.26420	+	0.712892i	0.229577	+	0.0383808i
$346$	22.5905	+	6.84080i	1.21447	+	0.367764i
$347$	−24.2199			−1.30019			−0.650095	−	0.759853i	$-0.725271\pi$
$347$	−24.2199			−1.30019			−0.650095	+	0.759853i	$0.725271\pi$
$348$	−4.76435	+	7.14534i	−0.255396	+	0.383030i
$349$		−	2.99062i		−	0.160084i	−0.996791	−	0.0800421i	$-0.974495\pi$
$349$		−	2.99062i		−	0.160084i	0.996791	−	0.0800421i	$-0.0255055\pi$
$350$	−2.68098	+	8.85344i	−0.143304	+	0.473236i
$351$			2.36562i			0.126268i
$352$	−2.09905	−	20.7952i	−0.111880	−	1.10839i
$353$	4.59122			0.244366			0.122183	−	0.992508i	$-0.461011\pi$
$353$	4.59122			0.244366			0.122183	+	0.992508i	$0.461011\pi$
$354$	3.20191	−	10.5737i	0.170180	−	0.561988i
$355$			6.27089i			0.332824i
$356$	5.45204	−	8.17671i	0.288958	−	0.433365i
$357$			0.738933i			0.0391085i
$358$	5.54306	−	18.3050i	0.292960	−	0.967447i
$359$	−6.08015			−0.320898			−0.160449	−	0.987044i	$-0.551294\pi$
$359$	−6.08015			−0.320898			−0.160449	+	0.987044i	$0.551294\pi$
$360$	−1.96866	+	1.62043i	−0.103758	+	0.0854044i
$361$	−39.7148			−2.09025
$362$	−6.41982	+	21.2003i	−0.337418	+	1.11426i
$363$	2.65143			0.139164
$364$	−4.10011	+	6.14915i	−0.214904	+	0.322303i
$365$	10.1695			0.532295
$366$	−4.91764	+	16.2396i	−0.257049	+	0.848858i
$367$	21.8559			1.14087			0.570433	−	0.821344i	$-0.306775\pi$
$367$	21.8559			1.14087			0.570433	+	0.821344i	$0.306775\pi$
$368$	−4.35449	−	18.6826i	−0.226993	−	0.973896i
$369$	2.62473			0.136638
$370$	2.14994	−	7.09979i	0.111770	−	0.369101i
$371$	−7.24921			−0.376360
$372$	−2.03624	+	3.05385i	−0.105574	+	0.158335i
$373$	−6.69692			−0.346754			−0.173377	−	0.984856i	$-0.555468\pi$
$373$	−6.69692			−0.346754			−0.173377	+	0.984856i	$0.555468\pi$
$374$	−0.716352	+	2.36562i	−0.0370417	+	0.122323i
$375$	8.28225			0.427694
$376$	7.68983	+	9.34235i	0.396573	+	0.481795i
$377$	10.1581			0.523167
$378$	−0.640260	+	2.11434i	−0.0329314	+	0.108750i
$379$		−	26.1881i		−	1.34519i	−0.740011	−	0.672595i	$-0.765180\pi$
$379$		−	26.1881i		−	1.34519i	0.740011	−	0.672595i	$-0.234820\pi$
$380$	−7.66428	+	11.4945i	−0.393169	+	0.589656i
$381$		−	18.7735i		−	0.961796i
$382$	4.32585	−	14.2853i	0.221329	−	0.730901i
$383$	8.67994			0.443524			0.221762	−	0.975101i	$-0.428819\pi$
$383$	8.67994			0.443524			0.221762	+	0.975101i	$0.428819\pi$
$384$	9.99584	+	5.29936i	0.510098	+	0.270432i
$385$		−	5.20308i		−	0.265174i
$386$	0.190225	−	0.628185i	0.00968222	−	0.0319738i
$387$		−	7.06267i		−	0.359016i
$388$	16.6770	−	25.0114i	0.846649	−	1.26976i
$389$	27.5178			1.39521			0.697604	−	0.716484i	$-0.254250\pi$
$389$	27.5178			1.39521			0.697604	+	0.716484i	$0.254250\pi$
$390$	2.88648	+	0.874077i	0.146163	+	0.0442606i
$391$	−0.374074	+	2.23754i	−0.0189177	+	0.113157i
$392$	9.95767	−	8.19631i	0.502938	−	0.413976i
$393$	−6.40382			−0.323030
$394$	−13.6241	−	4.12561i	−0.686372	−	0.207845i
$395$	14.2838			0.718696
$396$	−4.09947	+	6.14818i	−0.206006	+	0.308958i
$397$		−	33.4878i		−	1.68070i	−0.542042	−	0.840351i	$-0.682349\pi$
$397$		−	33.4878i		−	1.68070i	0.542042	−	0.840351i	$-0.317651\pi$
$398$	−3.37046	+	11.1303i	−0.168946	+	0.557913i
$399$			11.9698i			0.599238i
$400$	−6.43967	−	15.4619i	−0.321983	−	0.773093i
$401$		−	27.6454i		−	1.38054i	−0.723550	−	0.690272i	$-0.757491\pi$
$401$		−	27.6454i		−	1.38054i	0.723550	−	0.690272i	$-0.242509\pi$
$402$	7.24717	+	2.19457i	0.361456	+	0.109455i
$403$	4.34147			0.216264
$404$	1.63947	−	2.45880i	0.0815669	−	0.122330i
$405$	0.901487			0.0447952
$406$	9.07906	+	2.74930i	0.450586	+	0.136445i
$407$		−	21.4987i		−	1.06565i
$408$	−0.850286	−	1.03301i	−0.0420954	−	0.0511416i
$409$	−3.78504			−0.187158			−0.0935790	−	0.995612i	$-0.529831\pi$
$409$	−3.78504			−0.187158			−0.0935790	+	0.995612i	$0.529831\pi$
$410$	0.969813	−	3.20263i	0.0478956	−	0.158167i
$411$			3.16726i			0.156229i
$412$	−6.36204	−	4.24206i	−0.313435	−	0.208992i
$413$	−12.2033			−0.600485
$414$	−3.00911	+	6.07826i	−0.147890	+	0.298730i
$415$		−	6.61248i		−	0.324594i
$416$	−1.34394	−	13.3143i	−0.0658920	−	0.652789i
$417$	−4.84346			−0.237185
$418$	−11.6040	+	38.3201i	−0.567570	+	1.87430i
$419$			5.09760i			0.249034i	0.992217	+	0.124517i	$0.0397381\pi$
$419$			5.09760i			0.249034i	−0.992217	+	0.124517i	$0.960262\pi$
$420$	2.34331	+	1.56246i	0.114342	+	0.0762404i
$421$	19.3072			0.940977			0.470489	−	0.882406i	$-0.344078\pi$
$421$	19.3072			0.940977			0.470489	+	0.882406i	$0.344078\pi$
$422$	6.61059	−	21.8303i	0.321799	−	1.06268i
$423$		−	4.27804i		−	0.208005i
$424$	10.1342	−	8.34162i	0.492161	−	0.405105i
$425$			1.98075i			0.0960804i
$426$	−9.41528	−	2.85111i	−0.456172	−	0.138137i
$427$	18.7423			0.907005
$428$	9.51475	−	14.2698i	0.459913	−	0.689755i
$429$	8.74047			0.421994
$430$	−8.61772	−	2.60960i	−0.415583	−	0.125846i
$431$	38.3713			1.84828			0.924140	−	0.382054i	$-0.124783\pi$
$431$	38.3713			1.84828			0.924140	+	0.382054i	$0.124783\pi$
$432$	−1.53790	−	3.69254i	−0.0739921	−	0.177658i
$433$		−	4.61645i		−	0.221853i	−0.993829	−	0.110926i	$-0.964618\pi$
$433$		−	4.61645i		−	0.221853i	0.993829	−	0.110926i	$-0.0353817\pi$
$434$	3.88031	+	1.17503i	0.186261	+	0.0564030i
$435$		−	3.87102i		−	0.185601i
$436$	−25.4245	−	16.9525i	−1.21761	−	0.811877i
$437$	−6.05951	+	36.2453i	−0.289866	+	1.73385i
$438$	−4.62364	+	15.2687i	−0.220926	+	0.729568i
$439$			5.78060i			0.275893i	0.990440	+	0.137946i	$0.0440502\pi$
$439$			5.78060i			0.275893i	−0.990440	+	0.137946i	$0.955950\pi$
$440$	5.98716	+	7.27378i	0.285426	+	0.346764i
$441$	−4.55981			−0.217134
$442$	−0.458652	+	1.51462i	−0.0218158	+	0.0720429i
$443$	37.7822			1.79508			0.897542	−	0.440928i	$-0.145351\pi$
$443$	37.7822			1.79508			0.897542	+	0.440928i	$0.145351\pi$
$444$	9.68233	+	6.45596i	0.459503	+	0.306386i
$445$			4.42976i			0.209991i
$446$	−9.16926	−	2.77661i	−0.434177	−	0.131476i
$447$	3.34176			0.158060
$448$	2.40237	−	12.2638i	0.113501	−	0.579410i
$449$	−18.7113			−0.883042			−0.441521	−	0.897251i	$-0.645561\pi$
$449$	−18.7113			−0.883042			−0.441521	+	0.897251i	$0.645561\pi$
$450$	−1.71625	+	5.66761i	−0.0809048	+	0.267174i
$451$		−	9.69780i		−	0.456651i
$452$	−6.53512	+	9.80105i	−0.307386	+	0.461003i
$453$			17.3731i			0.816257i
$454$	32.2230	+	9.75769i	1.51230	+	0.457951i
$455$		−	3.33133i		−	0.156175i
$456$	−13.7735	−	16.7334i	−0.645005	−	0.783615i
$457$		−	17.6970i		−	0.827829i	−0.910316	−	0.413915i	$-0.864161\pi$
$457$		−	17.6970i		−	0.827829i	0.910316	−	0.413915i	$-0.135839\pi$
$458$	−4.27117	+	14.1048i	−0.199579	+	0.659073i
$459$			0.473035i			0.0220794i
$460$	6.30472	+	5.91751i	0.293959	+	0.275905i
$461$			4.75304i			0.221371i	0.993855	+	0.110686i	$0.0353047\pi$
$461$			4.75304i			0.221371i	−0.993855	+	0.110686i	$0.964695\pi$
$462$	7.81205	+	2.36562i	0.363449	+	0.110059i
$463$			10.7668i			0.500378i	0.968197	+	0.250189i	$0.0804927\pi$
$463$			10.7668i			0.500378i	−0.968197	+	0.250189i	$0.919507\pi$
$464$	−15.8559	+	6.60378i	−0.736092	+	0.306573i
$465$		−	1.65444i		−	0.0767227i
$466$	1.03631	−	3.42223i	0.0480062	−	0.158532i
$467$			38.6391i			1.78800i	0.448063	+	0.894002i	$0.352114\pi$
$467$			38.6391i			1.78800i	−0.448063	+	0.894002i	$0.647886\pi$
$468$	−2.62473	+	3.93644i	−0.121328	+	0.181962i
$469$		−	8.36406i		−	0.386216i
$470$	−5.21997	−	1.58070i	−0.240779	−	0.0729121i
$471$	−4.88151			−0.224928
$472$	17.0599	−	14.0423i	0.785245	−	0.646347i
$473$	−26.0951			−1.19985
$474$	−6.49425	+	21.4461i	−0.298291	+	0.985052i
$475$			32.0856i			1.47219i
$476$	−0.819866	+	1.22960i	−0.0375785	+	0.0563584i
$477$	−4.64065			−0.212481
$478$	−16.7796	−	5.08114i	−0.767479	−	0.232406i
$479$	37.7337			1.72410			0.862049	−	0.506826i	$-0.169181\pi$
$479$	37.7337			1.72410			0.862049	+	0.506826i	$0.169181\pi$
$480$	−5.07380	+	0.512145i	−0.231586	+	0.0233761i
$481$		−	13.7647i		−	0.627618i
$482$	8.99137	+	2.72274i	0.409545	+	0.124018i
$483$	7.38908	+	1.23531i	0.336215	+	0.0562086i
$484$	4.41203	+	2.94184i	0.200547	+	0.133720i
$485$			13.5500i			0.615275i
$486$	−0.409868	+	1.35352i	−0.0185920	+	0.0613968i
$487$			12.5644i			0.569347i	0.958625	+	0.284673i	$0.0918851\pi$
$487$			12.5644i			0.569347i	−0.958625	+	0.284673i	$0.908115\pi$
$488$	−26.2013	+	21.5667i	−1.18608	+	0.976279i
$489$	22.1556			1.00191
$490$	−1.68481	+	5.56378i	−0.0761119	+	0.251346i
$491$	24.1152			1.08830			0.544152	−	0.838987i	$-0.316851\pi$
$491$	24.1152			1.08830			0.544152	+	0.838987i	$0.316851\pi$
$492$	4.36758	+	2.91221i	0.196906	+	0.131292i
$493$	2.03123			0.0914818
$494$	−7.42957	+	24.5348i	−0.334272	+	1.10387i
$495$		−	3.33080i		−	0.149708i
$496$	−6.77667	+	2.82239i	−0.304281	+	0.126729i
$497$			10.8663i			0.487420i
$498$	9.92815	+	3.00642i	0.444891	+	0.134721i
$499$	−38.6256			−1.72912			−0.864560	−	0.502530i	$-0.832403\pi$
$499$	−38.6256			−1.72912			−0.864560	+	0.502530i	$0.832403\pi$
$500$	13.7818	+	9.18939i	0.616341	+	0.410962i
$501$		−	21.3490i		−	0.953802i
$502$	18.9618	+	5.74197i	0.846308	+	0.256277i
$503$	−28.0677			−1.25148			−0.625738	−	0.780033i	$-0.715202\pi$
$503$	−28.0677			−1.25148			−0.625738	+	0.780033i	$0.715202\pi$
$504$	−3.41133	+	2.80792i	−0.151953	+	0.125074i
$505$			1.33207i			0.0592762i
$506$	22.4579	+	11.1180i	0.998374	+	0.494256i
$507$	−7.40382			−0.328815
$508$	20.8297	−	31.2394i	0.924169	−	1.38602i
$509$		−	27.0543i		−	1.19916i	−0.800315	−	0.599580i	$-0.795334\pi$
$509$		−	27.0543i		−	1.19916i	0.800315	−	0.599580i	$-0.204666\pi$
$510$	0.577186	+	0.174782i	0.0255582	+	0.00773948i
$511$	17.6218			0.779545
$512$	10.7534	+	19.9089i	0.475240	+	0.879856i
$513$			7.66256i			0.338310i
$514$	6.99319	−	23.0938i	0.308457	−	1.01862i
$515$	3.44666			0.151878
$516$	7.83623	−	11.7524i	0.344971	−	0.517371i
$517$	−15.8064			−0.695166
$518$	3.72545	−	12.3026i	0.163687	−	0.540547i
$519$		−	16.6902i		−	0.732620i
$520$	3.83334	+	4.65711i	0.168103	+	0.204228i
$521$		−	13.8241i		−	0.605644i	−0.953047	−	0.302822i	$-0.902071\pi$
$521$		−	13.8241i		−	0.605644i	0.953047	−	0.302822i	$-0.0979287\pi$
$522$	5.81205	+	1.75999i	0.254386	+	0.0770326i
$523$		−	8.04855i		−	0.351939i	−0.984396	−	0.175969i	$-0.943694\pi$
$523$		−	8.04855i		−	0.351939i	0.984396	−	0.175969i	$-0.0563060\pi$
$524$	−10.6561	−	7.10522i	−0.465512	−	0.310393i
$525$	6.54106			0.285475
$526$	−5.15803	+	17.0335i	−0.224901	+	0.742694i
$527$	0.868128			0.0378162
$528$	−13.6432	+	5.68220i	−0.593742	+	0.247286i
$529$	21.7493	+	7.48122i	0.945621	+	0.325270i
$530$	−1.71468	+	5.66241i	−0.0744808	+	0.245960i
$531$	−7.81205			−0.339014
$532$	−13.2808	+	19.9179i	−0.575795	+	0.863550i
$533$		−	6.20911i		−	0.268947i
$534$	−6.65097	−	2.01403i	−0.287815	−	0.0871555i
$535$			7.73070i			0.334227i
$536$	9.62447	+	11.6927i	0.415714	+	0.505050i
$537$	−13.5240			−0.583604
$538$	−7.22027	−	2.18642i	−0.311288	−	0.0942634i
$539$			16.8475i			0.725674i
$540$	1.50009	+	1.00022i	0.0645535	+	0.0430428i
$541$			4.11616i			0.176968i	0.996078	+	0.0884838i	$0.0282022\pi$
$541$			4.11616i			0.176968i	−0.996078	+	0.0884838i	$0.971798\pi$
$542$	−6.99231	−	2.11739i	−0.300345	−	0.0909498i
$543$	15.6631			0.672169
$544$	−0.268736	−	2.66236i	−0.0115220	−	0.114148i
$545$	13.7738			0.590006
$546$	5.00174	+	1.51462i	0.214055	+	0.0648195i
$547$	−6.49890			−0.277873			−0.138936	−	0.990301i	$-0.544368\pi$
$547$	−6.49890			−0.277873			−0.138936	+	0.990301i	$0.544368\pi$
$548$	−3.51416	+	5.27037i	−0.150117	+	0.225139i
$549$	11.9981			0.512066
$550$	20.9406	+	6.34118i	0.892910	+	0.270389i
$551$	32.9033			1.40173
$552$	−11.7512	+	6.77563i	−0.500164	+	0.288390i
$553$	24.7512			1.05253
$554$	35.7592	+	10.8285i	1.51926	+	0.460060i
$555$	−5.24544			−0.222656
$556$	−8.05959	−	5.37395i	−0.341803	−	0.227906i
$557$	18.6206			0.788980			0.394490	−	0.918900i	$-0.370921\pi$
$557$	18.6206			0.788980			0.394490	+	0.918900i	$0.370921\pi$
$558$	2.48402	+	0.752203i	0.105157	+	0.0318433i
$559$	−16.7076			−0.706658
$560$	2.16570	+	5.19992i	0.0915176	+	0.219737i
$561$	1.74776			0.0737905
$562$	−28.2607	−	8.55784i	−1.19211	−	0.360991i
$563$			3.49532i			0.147310i	0.997284	+	0.0736551i	$0.0234664\pi$
$563$			3.49532i			0.147310i	−0.997284	+	0.0736551i	$0.976534\pi$
$564$	4.74660	−	7.11872i	0.199868	−	0.299752i
$565$		−	5.30976i		−	0.223383i
$566$	−16.0974	−	4.87457i	−0.676624	−	0.204893i
$567$	1.56211			0.0656025
$568$	−12.5038	−	15.1908i	−0.524647	−	0.637392i
$569$		−	21.8934i		−	0.917819i	−0.888483	−	0.458909i	$-0.848240\pi$
$569$		−	21.8934i		−	0.917819i	0.888483	−	0.458909i	$-0.151760\pi$
$570$	9.34968	+	2.83125i	0.391615	+	0.118588i
$571$			28.9265i			1.21053i	0.796022	+	0.605267i	$0.206934\pi$
$571$			28.9265i			1.21053i	−0.796022	+	0.605267i	$0.793066\pi$
$572$	14.5443	+	9.69780i	0.608127	+	0.405485i
$573$	−10.5542			−0.440909
$574$	1.68051	−	5.54957i	0.0701430	−	0.231635i
$575$	19.8068	+	3.31131i	0.826001	+	0.138091i
$576$	1.53790	−	7.85079i	0.0640790	−	0.327116i
$577$	−23.6246			−0.983507			−0.491753	−	0.870735i	$-0.663644\pi$
$577$	−23.6246			−0.983507			−0.491753	+	0.870735i	$0.663644\pi$
$578$	6.87605	−	22.7069i	0.286006	−	0.944483i
$579$	−0.464113			−0.0192879
$580$	4.29500	−	6.44143i	0.178340	−	0.267466i
$581$		−	11.4582i		−	0.475367i
$582$	−20.3444	−	6.16064i	−0.843302	−	0.255367i
$583$			17.1462i			0.710123i
$584$	−24.6349	+	20.2774i	−1.01940	+	0.839083i
$585$		−	2.13258i		−	0.0881713i
$586$	−11.9200	+	39.3638i	−0.492412	+	1.62610i
$587$	−29.1236			−1.20206			−0.601030	−	0.799226i	$-0.705243\pi$
$587$	−29.1236			−1.20206			−0.601030	+	0.799226i	$0.705243\pi$
$588$	−7.58759	−	5.05923i	−0.312907	−	0.208639i
$589$	14.0626			0.579438
$590$	−2.88648	+	9.53209i	−0.118835	+	0.392430i
$591$			10.0657i			0.414048i
$592$	8.94848	+	21.4856i	0.367780	+	0.883054i
$593$	−10.2451			−0.420717			−0.210359	−	0.977624i	$-0.567463\pi$
$593$	−10.2451			−0.420717			−0.210359	+	0.977624i	$0.567463\pi$
$594$	5.00095	+	1.51438i	0.205192	+	0.0621356i
$595$		−	0.666138i		−	0.0273090i
$596$	5.56074	+	3.70777i	0.227777	+	0.151876i
$597$	8.22327			0.336556
$598$	14.3789	+	7.11842i	0.587996	+	0.291094i
$599$			1.56887i			0.0641022i	0.999486	+	0.0320511i	$0.0102039\pi$
$599$			1.56887i			0.0641022i	−0.999486	+	0.0320511i	$0.989796\pi$
$600$	−9.14424	+	7.52676i	−0.373312	+	0.307279i
$601$	7.22050			0.294530			0.147265	−	0.989097i	$-0.452953\pi$
$601$	7.22050			0.294530			0.147265	+	0.989097i	$0.452953\pi$
$602$	−14.9329	−	4.52195i	−0.608621	−	0.184301i
$603$		−	5.35433i		−	0.218045i
$604$	−19.2759	+	28.9090i	−0.784325	+	1.17629i
$605$	−2.39023			−0.0971768
$606$	−2.00000	−	0.605635i	−0.0812444	−	0.0246022i
$607$		−	32.2388i		−	1.30853i	−0.756264	−	0.654266i	$-0.772978\pi$
$607$		−	32.2388i		−	1.30853i	0.756264	−	0.654266i	$-0.227022\pi$
$608$	−4.35318	−	43.1268i	−0.176545	−	1.74902i
$609$		−	6.70776i		−	0.271812i
$610$	4.43318	−	14.6398i	0.179494	−	0.592748i
$611$	−10.1202			−0.409421
$612$	−0.524845	+	0.787137i	−0.0212156	+	0.0318181i
$613$	−20.2345			−0.817262			−0.408631	−	0.912700i	$-0.633994\pi$
$613$	−20.2345			−0.817262			−0.408631	+	0.912700i	$0.633994\pi$
$614$	0.231251	−	0.763664i	0.00933252	−	0.0308190i
$615$	−2.36616			−0.0954126
$616$	10.3746	+	12.6041i	0.418006	+	0.507834i
$617$		−	7.12572i		−	0.286871i	−0.989660	−	0.143435i	$-0.954185\pi$
$617$		−	7.12572i		−	0.286871i	0.989660	−	0.143435i	$-0.0458149\pi$
$618$	−1.56705	+	5.17491i	−0.0630361	+	0.208165i
$619$			41.0670i			1.65062i	0.564679	+	0.825311i	$0.309000\pi$
$619$			41.0670i			1.65062i	−0.564679	+	0.825311i	$0.691000\pi$
$620$	1.83564	−	2.75301i	0.0737212	−	0.110563i
$621$	4.73018	+	0.790796i	0.189816	+	0.0317335i
$622$	30.4063	+	9.20755i	1.21918	+	0.369189i
$623$			7.67597i			0.307531i
$624$	−8.73517	+	3.63808i	−0.349687	+	0.145640i
$625$	13.4703			0.538811
$626$	6.77090	+	2.05035i	0.270620	+	0.0819483i
$627$	28.3115			1.13065
$628$	−8.12291	−	5.41617i	−0.324139	−	0.216129i
$629$		−	2.75242i		−	0.109746i
$630$	0.577186	−	1.90605i	0.0229957	−	0.0759390i
$631$	−11.4174			−0.454518			−0.227259	−	0.973834i	$-0.572976\pi$
$631$	−11.4174			−0.454518			−0.227259	+	0.973834i	$0.572976\pi$
$632$	−34.6016	+	28.4811i	−1.37638	+	1.13292i
$633$	−16.1286			−0.641053
$634$	−25.8747	−	7.83532i	−1.02762	−	0.311180i
$635$			16.9241i			0.671611i
$636$	−7.72211	−	5.14893i	−0.306201	−	0.204168i
$637$			10.7868i			0.427388i
$638$	6.50278	−	21.4743i	0.257448	−	0.850174i
$639$			6.95616i			0.275181i
$640$	−9.01112	−	4.77730i	−0.356196	−	0.188839i
$641$		−	43.3405i		−	1.71185i	−0.517103	−	0.855923i	$-0.672990\pi$
$641$		−	43.3405i		−	1.71185i	0.517103	−	0.855923i	$-0.327010\pi$
$642$	−11.6071	−	3.51483i	−0.458095	−	0.138719i
$643$			26.6168i			1.04966i	0.851206	+	0.524832i	$0.175872\pi$
$643$			26.6168i			1.04966i	−0.851206	+	0.524832i	$0.824128\pi$
$644$	10.9249	+	10.2540i	0.430502	+	0.404063i
$645$			6.36691i			0.250697i
$646$	−1.48563	+	4.90603i	−0.0584514	+	0.193025i
$647$		−	36.4289i		−	1.43217i	−0.698014	−	0.716084i	$-0.745933\pi$
$647$		−	36.4289i		−	1.43217i	0.698014	−	0.716084i	$-0.254067\pi$
$648$	−2.18379	+	1.79751i	−0.0857875	+	0.0706130i
$649$			28.8638i			1.13300i
$650$	13.4074	+	4.06000i	0.525883	+	0.159246i
$651$		−	2.86683i		−	0.112360i
$652$	36.8672	+	24.5822i	1.44383	+	0.962715i
$653$			39.6850i			1.55300i	0.630120	+	0.776498i	$0.283006\pi$
$653$			39.6850i			1.55300i	−0.630120	+	0.776498i	$0.716994\pi$
$654$	−6.26239	+	20.6804i	−0.244879	+	0.808668i
$655$	5.77296			0.225568
$656$	4.03656	+	9.69191i	0.157601	+	0.378406i
$657$	11.2808			0.440105
$658$	−9.04525	−	2.73906i	−0.352620	−	0.106780i
$659$		−	28.1729i		−	1.09746i	−0.836000	−	0.548730i	$-0.815112\pi$
$659$		−	28.1729i		−	1.09746i	0.836000	−	0.548730i	$-0.184888\pi$
$660$	3.69562	−	5.54250i	0.143852	−	0.215742i
$661$	−6.71763			−0.261285			−0.130643	−	0.991430i	$-0.541704\pi$
$661$	−6.71763			−0.261285			−0.130643	+	0.991430i	$0.541704\pi$
$662$	−3.95670	+	13.0663i	−0.153782	+	0.507836i
$663$	1.11902			0.0434592
$664$	13.1849	+	16.0183i	0.511673	+	0.621630i
$665$		−	10.7906i		−	0.418441i
$666$	2.38488	−	7.87564i	0.0924123	−	0.305175i
$667$	3.39570	−	20.3116i	0.131482	−	0.786467i
$668$	23.6873	−	35.5250i	0.916489	−	1.37451i
$669$			6.77440i			0.261913i
$670$	−6.53323	−	1.97838i	−0.252401	−	0.0764314i
$671$		−	44.3303i		−	1.71135i
$672$	−8.79196	+	0.887453i	−0.339157	+	0.0342342i
$673$	6.37456			0.245721			0.122861	−	0.992424i	$-0.460793\pi$
$673$	6.37456			0.245721			0.122861	+	0.992424i	$0.460793\pi$
$674$	−21.0128	−	6.36303i	−0.809382	−	0.245095i
$675$	4.18732			0.161170
$676$	−12.3201	−	8.21475i	−0.473849	−	0.315952i
$677$	51.0634			1.96252			0.981262	−	0.192678i	$-0.0617172\pi$
$677$	51.0634			1.96252			0.981262	+	0.192678i	$0.0617172\pi$
$678$	7.97221	+	2.41413i	0.306171	+	0.0927139i
$679$			23.4797i			0.901069i
$680$	0.766521	+	0.931244i	0.0293948	+	0.0357116i
$681$		−	23.8069i		−	0.912282i
$682$	2.77923	−	9.17790i	0.106422	−	0.351440i
$683$	−13.7454			−0.525955			−0.262977	−	0.964802i	$-0.584704\pi$
$683$	−13.7454			−0.525955			−0.262977	+	0.964802i	$0.584704\pi$
$684$	−8.50182	+	12.7506i	−0.325075	+	0.487532i
$685$		−	2.85524i		−	0.109093i
$686$	−7.40129	+	24.4414i	−0.282582	+	0.933177i
$687$	10.4208			0.397580
$688$	26.0792	−	10.8617i	0.994261	−	0.414097i
$689$			10.9780i			0.418229i
$690$	2.71267	−	5.47947i	0.103270	−	0.208600i
$691$	20.1619			0.766995			0.383497	−	0.923542i	$-0.374720\pi$
$691$	20.1619			0.766995			0.383497	+	0.923542i	$0.374720\pi$
$692$	18.5183	−	27.7728i	0.703959	−	1.05576i
$693$		−	5.77167i		−	0.219247i
$694$	−9.92696	+	32.7820i	−0.376822	+	1.24439i
$695$	4.36631			0.165624
$696$	7.71858	+	9.37728i	0.292572	+	0.355445i
$697$		−	1.24159i		−	0.0470284i
$698$	−4.04786	−	1.22576i	−0.153214	−	0.0463957i
$699$	−2.52840			−0.0956328
$700$	10.8844	+	7.25749i	0.411393	+	0.274307i
$701$	5.51359			0.208246			0.104123	−	0.994564i	$-0.466797\pi$
$701$	5.51359			0.208246			0.104123	+	0.994564i	$0.466797\pi$
$702$	3.20191	+	0.969595i	0.120848	+	0.0365950i
$703$		−	44.5857i		−	1.68158i
$704$	−29.0070	−	5.68220i	−1.09324	−	0.214156i
$705$			3.85660i			0.145248i
$706$	1.88179	−	6.21429i	0.0708223	−	0.233878i
$707$			2.30823i			0.0868098i
$708$	−12.9994	−	8.66768i	−0.488546	−	0.325751i
$709$	−24.3221			−0.913437			−0.456719	−	0.889611i	$-0.650975\pi$
$709$	−24.3221			−0.913437			−0.456719	+	0.889611i	$0.650975\pi$
$710$	8.48775	+	2.57024i	0.318540	+	0.0964594i
$711$	15.8447			0.594223
$712$	−8.83269	−	10.7308i	−0.331019	−	0.402154i
$713$	1.45129	−	8.68098i	0.0543513	−	0.325105i
$714$	1.00016	+	0.302865i	0.0374300	+	0.0113344i
$715$	−7.87942			−0.294674
$716$	−22.5041	−	15.0053i	−0.841019	−	0.560773i
$717$			12.3970i			0.462975i
$718$	−2.49206	+	8.22959i	−0.0930030	+	0.307125i
$719$			48.2017i			1.79762i	0.438338	+	0.898810i	$0.355567\pi$
$719$			48.2017i			1.79762i	−0.438338	+	0.898810i	$0.644433\pi$
$720$	1.38639	+	3.32878i	0.0516678	+	0.124056i
$721$	5.97243			0.222425
$722$	−16.2778	+	53.7546i	−0.605798	+	2.00054i
$723$		−	6.64297i		−	0.247055i
$724$	26.0637	+	17.3787i	0.968649	+	0.645873i
$725$		−	17.9805i		−	0.667779i
$726$	1.08674	−	3.58876i	0.0403327	−	0.133191i
$727$	−23.1995			−0.860420			−0.430210	−	0.902729i	$-0.641561\pi$
$727$	−23.1995			−0.860420			−0.430210	+	0.902729i	$0.641561\pi$
$728$	6.64247	+	8.06992i	0.246186	+	0.299091i
$729$	1.00000			0.0370370
$730$	4.16815	−	13.7646i	0.154270	−	0.509449i
$731$	−3.34089			−0.123567
$732$	19.9650	+	13.3122i	0.737927	+	0.492033i
$733$	−0.566445			−0.0209221			−0.0104611	−	0.999945i	$-0.503330\pi$
$733$	−0.566445			−0.0209221			−0.0104611	+	0.999945i	$0.503330\pi$
$734$	8.95802	−	29.5823i	0.330647	−	1.09190i
$735$	4.11061			0.151622
$736$	−27.0719	−	1.76353i	−0.997885	−	0.0650045i
$737$	−19.7831			−0.728720
$738$	1.07579	−	3.55261i	0.0396005	−	0.130773i
$739$	26.9657			0.991950			0.495975	−	0.868337i	$-0.334811\pi$
$739$	26.9657			0.991950			0.495975	+	0.868337i	$0.334811\pi$
$740$	−8.72849	−	5.81996i	−0.320866	−	0.213946i
$741$	18.1267			0.665902
$742$	−2.97122	+	9.81192i	−0.109077	+	0.360207i
$743$	−37.7515			−1.38497			−0.692485	−	0.721433i	$-0.743484\pi$
$743$	−37.7515			−1.38497			−0.692485	+	0.721433i	$0.743484\pi$
$744$	3.29885	+	4.00776i	0.120942	+	0.146932i
$745$	−3.01255			−0.110371
$746$	−2.74486	+	9.06440i	−0.100496	+	0.331871i
$747$		−	7.33508i		−	0.268376i
$748$	2.90830	+	1.93919i	0.106338	+	0.0709038i
$749$			13.3959i			0.489475i
$750$	3.39463	−	11.2102i	0.123954	−	0.409337i
$751$	17.1412			0.625490			0.312745	−	0.949837i	$-0.398752\pi$
$751$	17.1412			0.625490			0.312745	+	0.949837i	$0.398752\pi$
$752$	15.7968	−	6.57918i	0.576052	−	0.239918i
$753$		−	14.0093i		−	0.510527i
$754$	4.16347	−	13.7491i	0.151625	−	0.500713i
$755$		−	15.6616i		−	0.569983i
$756$	2.59938	+	1.73321i	0.0945385	+	0.0630361i
$757$	−32.8391			−1.19356			−0.596779	−	0.802406i	$-0.703553\pi$
$757$	−32.8391			−1.19356			−0.596779	+	0.802406i	$0.703553\pi$
$758$	−35.4460	−	10.7337i	−1.28746	−	0.389864i
$759$	2.92182	−	17.4770i	0.106055	−	0.634375i
$760$	12.4167	+	15.0850i	0.450400	+	0.547189i
$761$	−21.8078			−0.790532			−0.395266	−	0.918567i	$-0.629348\pi$
$761$	−21.8078			−0.790532			−0.395266	+	0.918567i	$0.629348\pi$
$762$	−25.4102	−	7.69467i	−0.920516	−	0.278748i
$763$	23.8675			0.864063
$764$	−17.5624	−	11.7102i	−0.635385	−	0.423660i
$765$		−	0.426435i		−	0.0154178i
$766$	3.55763	−	11.7484i	0.128543	−	0.424489i
$767$			18.4804i			0.667287i
$768$	11.2698	−	11.3575i	0.406662	−	0.409828i
$769$			5.34560i			0.192767i	0.995344	+	0.0963837i	$0.0307276\pi$
$769$			5.34560i			0.192767i	−0.995344	+	0.0963837i	$0.969272\pi$
$770$	−7.04246	−	2.13258i	−0.253793	−	0.0768528i
$771$	−17.0620			−0.614474
$772$	−0.772291	−	0.514946i	−0.0277954	−	0.0185333i
$773$	−11.9945			−0.431413			−0.215707	−	0.976458i	$-0.569205\pi$
$773$	−11.9945			−0.431413			−0.215707	+	0.976458i	$0.569205\pi$
$774$	−9.55945	−	2.89477i	−0.343607	−	0.104050i
$775$		−	7.68470i		−	0.276043i
$776$	−27.0180	−	32.8241i	−0.969889	−	1.17832i
$777$	−9.08938			−0.326080
$778$	11.2787	−	37.2458i	0.404360	−	1.33533i
$779$		−	20.1121i		−	0.720591i
$780$	2.36616	−	3.54865i	0.0847220	−	0.127062i
$781$	25.7015			0.919673
$782$	2.87523	+	1.42341i	0.102818	+	0.0509011i
$783$		−	4.29403i		−	0.153456i
$784$	−7.01251	−	16.8373i	−0.250447	−	0.601332i
$785$	4.40062			0.157065
$786$	−2.62473	+	8.66768i	−0.0936209	+	0.309166i
$787$		−	14.2110i		−	0.506566i	−0.967392	−	0.253283i	$-0.918490\pi$
$787$		−	14.2110i		−	0.506566i	0.967392	−	0.253283i	$-0.0815104\pi$
$788$	−11.1682	+	16.7495i	−0.397850	+	0.596676i
$789$	12.5846			0.448023
$790$	5.85448	−	19.3334i	0.208293	−	0.687850i
$791$		−	9.20084i		−	0.327144i
$792$	6.64142	+	8.06864i	0.235993	+	0.286707i
$793$		−	28.3829i		−	1.00791i
$794$	−45.3262	−	13.7256i	−1.60857	−	0.487102i
$795$	4.18348			0.148373
$796$	13.6836	+	9.12394i	0.485004	+	0.323390i
$797$	−51.6166			−1.82835			−0.914177	−	0.405315i	$-0.867162\pi$
$797$	−51.6166			−1.82835			−0.914177	+	0.405315i	$0.867162\pi$
$798$	16.2013	+	4.90603i	0.573519	+	0.173672i
$799$	−2.02366			−0.0715920
$800$	−23.5673	+	2.37886i	−0.833230	+	0.0841055i
$801$			4.91384i			0.173622i
$802$	−37.4185	−	11.3310i	−1.32129	−	0.400110i
$803$		−	41.6801i		−	1.47086i
$804$	5.94078	−	8.90969i	0.209515	−	0.314220i
$805$	−6.66115	−	1.11362i	−0.234775	−	0.0392498i
$806$	1.77943	−	5.87625i	0.0626777	−	0.206982i
$807$			5.33445i			0.187782i
$808$	−2.65606	−	3.22684i	−0.0934400	−	0.113520i
$809$	29.5286			1.03817			0.519084	−	0.854723i	$-0.326273\pi$
$809$	29.5286			1.03817			0.519084	+	0.854723i	$0.326273\pi$
$810$	0.369491	−	1.22018i	0.0129826	−	0.0428727i
$811$	28.3984			0.997203			0.498602	−	0.866831i	$-0.333847\pi$
$811$	28.3984			0.997203			0.498602	+	0.866831i	$0.333847\pi$
$812$	7.44245	−	11.1618i	0.261179	−	0.391703i
$813$			5.16603i			0.181181i
$814$	−29.0988	−	8.81163i	−1.01991	−	0.308847i
$815$	−19.9730			−0.699623
$816$	−1.74670	+	0.727478i	−0.0611468	+	0.0254668i
$817$	−54.1181			−1.89335
$818$	−1.55137	+	5.12311i	−0.0542423	+	0.179125i
$819$		−	3.69537i		−	0.129127i
$820$	−3.93732	−	2.62532i	−0.137497	−	0.0916800i
$821$			2.10263i			0.0733822i	0.999327	+	0.0366911i	$0.0116818\pi$
$821$			2.10263i			0.0733822i	−0.999327	+	0.0366911i	$0.988318\pi$
$822$	4.28694	+	1.29816i	0.149524	+	0.0452785i
$823$			46.6676i			1.62673i	0.581754	+	0.813365i	$0.302367\pi$
$823$			46.6676i			1.62673i	−0.581754	+	0.813365i	$0.697633\pi$
$824$	−8.34931	+	6.87244i	−0.290862	+	0.239413i
$825$		−	15.4713i		−	0.538640i
$826$	−5.00174	+	16.5174i	−0.174033	+	0.574712i
$827$		−	51.2016i		−	1.78046i	−0.455515	−	0.890228i	$-0.650545\pi$
$827$		−	51.2016i		−	1.78046i	0.455515	−	0.890228i	$-0.349455\pi$
$828$	6.99369	+	6.56417i	0.243048	+	0.228121i
$829$			47.1124i			1.63628i	0.575017	+	0.818141i	$0.304995\pi$
$829$			47.1124i			1.63628i	−0.575017	+	0.818141i	$0.695005\pi$
$830$	−8.95010	−	2.71025i	−0.310662	−	0.0940740i
$831$		−	26.4195i		−	0.916483i
$832$	−18.5720	−	3.63808i	−0.643869	−	0.126128i
$833$			2.15695i			0.0747338i
$834$	−1.98518	+	6.55570i	−0.0687412	+	0.227005i
$835$			19.2458i			0.666030i
$836$	47.1108	+	31.4124i	1.62936	+	1.08642i
$837$		−	1.83523i		−	0.0634348i
$838$	6.89969	+	2.08935i	0.238346	+	0.0721752i
$839$	−29.3728			−1.01406			−0.507031	−	0.861928i	$-0.669257\pi$
$839$	−29.3728			−1.01406			−0.507031	+	0.861928i	$0.669257\pi$
$840$	3.07527	−	2.53130i	0.106107	−	0.0873381i
$841$	10.5613			0.364182
$842$	7.91343	−	26.1327i	0.272715	−	0.900592i
$843$			20.8795i			0.719128i
$844$	−26.8382	−	17.8951i	−0.923809	−	0.615975i
$845$	6.67445			0.229608
$846$	−5.79040	−	1.75343i	−0.199078	−	0.0602843i
$847$	−4.14184			−0.142315
$848$	−7.13683	−	17.1358i	−0.245080	−	0.588445i
$849$			11.8930i			0.408167i
$850$	2.68098	+	0.811846i	0.0919567	+	0.0278461i
$851$	−27.5233	−	4.60136i	−0.943486	−	0.157733i
$852$	−7.71805	+	11.5752i	−0.264416	+	0.396558i
$853$		−	11.6850i		−	0.400086i	−0.979787	−	0.200043i	$-0.935892\pi$
$853$		−	11.6850i		−	0.400086i	0.979787	−	0.200043i	$-0.0641082\pi$
$854$	7.68190	−	25.3681i	0.262869	−	0.868078i
$855$		−	6.90769i		−	0.236238i
$856$	−15.4146	−	18.7271i	−0.526859	−	0.640079i
$857$	30.6664			1.04754			0.523772	−	0.851859i	$-0.324525\pi$
$857$	30.6664			1.04754			0.523772	+	0.851859i	$0.324525\pi$
$858$	3.58244	−	11.8304i	0.122303	−	0.403882i
$859$	−19.3065			−0.658731			−0.329365	−	0.944203i	$-0.606835\pi$
$859$	−19.3065			−0.658731			−0.329365	+	0.944203i	$0.606835\pi$
$860$	−7.06426	+	10.5946i	−0.240889	+	0.361274i
$861$	−4.10011			−0.139732
$862$	15.7272	−	51.9362i	0.535670	−	1.76895i
$863$			22.0488i			0.750550i	0.926913	+	0.375275i	$0.122452\pi$
$863$			22.0488i			0.750550i	−0.926913	+	0.375275i	$0.877548\pi$
$864$	−5.62825	+	0.568111i	−0.191477	+	0.0193275i
$865$			15.0460i			0.511580i
$866$	−6.24845	−	1.89214i	−0.212331	−	0.0642975i
$867$	−16.7762			−0.569751
$868$	3.18083	−	4.77046i	0.107965	−	0.161920i
$869$		−	58.5428i		−	1.98593i
$870$	−5.23948	−	1.58661i	−0.177635	−	0.0537910i
$871$	−12.6663			−0.429182
$872$	−33.3662	+	27.4642i	−1.12992	+	0.930056i
$873$			15.0308i			0.508714i
$874$	46.5750	+	23.0575i	1.57542	+	0.779930i
$875$	−12.9378			−0.437377
$876$	18.7714	+	12.5163i	0.634227	+	0.422888i
$877$		−	38.7191i		−	1.30745i	−0.756732	−	0.653725i	$-0.773205\pi$
$877$		−	38.7191i		−	1.30745i	0.756732	−	0.653725i	$-0.226795\pi$
$878$	7.82414	+	2.36928i	0.264052	+	0.0799595i
$879$	29.0826			0.980931
$880$	12.2991	−	5.12242i	0.414603	−	0.172677i
$881$		−	34.6478i		−	1.16731i	−0.812001	−	0.583656i	$-0.801622\pi$
$881$		−	34.6478i		−	1.16731i	0.812001	−	0.583656i	$-0.198378\pi$
$882$	−1.86892	+	6.17178i	−0.0629299	+	0.207815i
$883$	−38.6865			−1.30190			−0.650952	−	0.759119i	$-0.725630\pi$
$883$	−38.6865			−1.30190			−0.650952	+	0.759119i	$0.725630\pi$
$884$	1.86207	+	1.24159i	0.0626282	+	0.0417591i
$885$	7.04246			0.236730
$886$	15.4857	−	51.1388i	0.520253	−	1.71804i
$887$			16.9840i			0.570265i	0.958488	+	0.285133i	$0.0920377\pi$
$887$			16.9840i			0.570265i	−0.958488	+	0.285133i	$0.907962\pi$
$888$	12.7067	−	10.4591i	0.426410	−	0.350984i
$889$			29.3263i			0.983573i
$890$	5.99576	+	1.81562i	0.200978	+	0.0608597i
$891$		−	3.69478i		−	0.123780i
$892$	−7.51638	+	11.2727i	−0.251667	+	0.377438i
$893$	−32.7807			−1.09696
$894$	1.36968	−	4.52313i	0.0458090	−	0.151276i
$895$	12.1917			0.407524
$896$	−15.6146	−	8.27819i	−0.521648	−	0.276555i
$897$	1.87072	−	11.1898i	0.0624617	−	0.373618i
$898$	−7.66918	+	25.3261i	−0.255924	+	0.845142i
$899$	−7.88054			−0.262831
$900$	6.96777	+	4.64595i	0.232259	+	0.154865i
$901$			2.19519i			0.0731323i
$902$	−13.1261	−	3.97482i	−0.437052	−	0.132347i
$903$			11.0327i			0.367145i
$904$	10.5873	+	12.8625i	0.352130	+	0.427802i
$905$	−14.1201			−0.469368
$906$	23.5147	+	7.12067i	0.781224	+	0.236568i
$907$		−	7.88616i		−	0.261856i	−0.991392	−	0.130928i	$-0.958204\pi$
$907$		−	7.88616i		−	0.261856i	0.991392	−	0.130928i	$-0.0417956\pi$
$908$	26.4144	−	39.6150i	0.876593	−	1.31467i
$909$			1.47763i			0.0490100i
$910$	−4.50901	−	1.36541i	−0.149472	−	0.0452628i
$911$	23.1173			0.765909			0.382954	−	0.923767i	$-0.374907\pi$
$911$	23.1173			0.765909			0.382954	+	0.923767i	$0.374907\pi$
$912$	−28.2943	+	11.7842i	−0.936918	+	0.390214i
$913$	−27.1015			−0.896930
$914$	−23.9531	−	7.25343i	−0.792299	−	0.239922i
$915$	−10.8161			−0.357570
$916$	17.3404	+	11.5622i	0.572944	+	0.382026i
$917$	10.0035			0.330344
$918$	0.640260	+	0.193882i	0.0211317	+	0.00639906i
$919$	−40.9707			−1.35150			−0.675749	−	0.737132i	$-0.736180\pi$
$919$	−40.9707			−1.35150			−0.675749	+	0.737132i	$0.736180\pi$
$920$	10.5936	−	6.10815i	0.349259	−	0.201380i
$921$	−0.564207			−0.0185913
$922$	6.43332	+	1.94812i	0.211870	+	0.0641580i
$923$	16.4557			0.541645
$924$	6.40382	−	9.60414i	0.210670	−	0.315953i
$925$	−24.3646			−0.801102
$926$	14.5731	+	4.41299i	0.478902	+	0.145020i
$927$	3.82331			0.125574
$928$	2.43949	+	24.1679i	0.0800801	+	0.793351i
$929$	32.6873			1.07243			0.536217	−	0.844080i	$-0.319853\pi$
$929$	32.6873			1.07243			0.536217	+	0.844080i	$0.319853\pi$
$930$	−2.23931	−	0.678101i	−0.0734298	−	0.0222358i
$931$			34.9398i			1.14511i
$932$	−4.20730	−	2.80533i	−0.137815	−	0.0918916i
$933$		−	22.4646i		−	0.735459i
$934$	52.2987	+	15.8369i	1.71126	+	0.518201i
$935$	−1.57558			−0.0515271
$936$	4.25224	+	5.16603i	0.138989	+	0.168857i
$937$			34.2523i			1.11897i	0.828839	+	0.559487i	$0.189002\pi$
$937$			34.2523i			1.11897i	−0.828839	+	0.559487i	$0.810998\pi$
$938$	−11.3209	−	3.42816i	−0.369640	−	0.111934i
$939$		−	5.00245i		−	0.163249i
$940$	−4.27900	+	6.41744i	−0.139566	+	0.209314i
$941$	−1.43382			−0.0467413			−0.0233706	−	0.999727i	$-0.507440\pi$
$941$	−1.43382			−0.0467413			−0.0233706	+	0.999727i	$0.507440\pi$
$942$	−2.00078	+	6.60720i	−0.0651888	+	0.215274i
$943$	−12.4154	−	2.07562i	−0.404302	−	0.0675915i
$944$	−12.0141	−	28.8463i	−0.391026	−	0.938868i
$945$	−1.40822			−0.0458095
$946$	−10.6955	+	35.3201i	−0.347742	+	1.14836i
$947$	38.9980			1.26727			0.633633	−	0.773634i	$-0.281563\pi$
$947$	38.9980			1.26727			0.633633	+	0.773634i	$0.281563\pi$
$948$	26.3659	+	17.5802i	0.856323	+	0.570977i
$949$		−	26.6861i		−	0.866268i
$950$	43.4284	+	13.1509i	1.40900	+	0.426671i
$951$			19.1167i			0.619900i
$952$	1.32824	+	1.61368i	0.0430485	+	0.0522995i
$953$			57.9473i			1.87710i	0.345146	+	0.938549i	$0.387829\pi$
$953$			57.9473i			1.87710i	−0.345146	+	0.938549i	$0.612171\pi$
$954$	−1.90205	+	6.28119i	−0.0615813	+	0.203361i
$955$	9.51450			0.307882
$956$	−13.7548	+	20.6288i	−0.444863	+	0.667183i
$957$	−15.8655			−0.512860
$958$	15.4659	−	51.0732i	0.499679	−	1.65010i
$959$		−	4.94761i		−	0.159767i
$960$	−1.38639	+	7.07738i	−0.0447457	+	0.228422i
$961$	27.6319			0.891353
$962$	−18.6308	−	5.64173i	−0.600681	−	0.181897i
$963$			8.57550i			0.276341i
$964$	7.37055	−	11.0540i	0.237390	−	0.356025i
$965$	0.418392			0.0134685
$966$	4.70056	−	9.49492i	0.151238	−	0.305494i
$967$		−	8.58256i		−	0.275997i	−0.990432	−	0.137998i	$-0.955933\pi$
$967$		−	8.58256i		−	0.275997i	0.990432	−	0.137998i	$-0.0440668\pi$
$968$	5.79018	−	4.76599i	0.186103	−	0.153185i
$969$	3.62465			0.116441
$970$	18.3402	+	5.55373i	0.588868	+	0.178320i
$971$		−	2.14726i		−	0.0689089i	−0.999406	−	0.0344545i	$-0.989031\pi$
$971$		−	2.14726i		−	0.0689089i	0.999406	−	0.0344545i	$-0.0109694\pi$
$972$	1.66402	+	1.10953i	0.0533733	+	0.0355881i
$973$	7.56602			0.242555
$974$	17.0061	+	5.14975i	0.544911	+	0.165009i
$975$		−	9.90563i		−	0.317234i
$976$	18.4518	+	44.3034i	0.590628	+	1.41812i
$977$			38.6295i			1.23587i	0.786231	+	0.617933i	$0.212030\pi$
$977$			38.6295i			1.23587i	−0.786231	+	0.617933i	$0.787970\pi$
$978$	9.08087	−	29.9880i	0.290374	−	0.958909i
$979$	18.1556			0.580255
$980$	6.84011	+	4.56083i	0.218499	+	0.145690i
$981$	15.2790			0.487822
$982$	9.88407	−	32.6404i	0.315413	−	1.04160i
$983$	−25.5149			−0.813799			−0.406899	−	0.913473i	$-0.633390\pi$
$983$	−25.5149			−0.813799			−0.406899	+	0.913473i	$0.633390\pi$
$984$	5.73185	−	4.71798i	0.182725	−	0.150404i
$985$		−	9.07410i		−	0.289125i
$986$	0.832536	−	2.74930i	0.0265133	−	0.0875555i
$987$			6.68277i			0.212715i
$988$	30.1632	+	20.1121i	0.959618	+	0.639851i
$989$	−5.58513	+	33.4078i	−0.177597	+	1.06230i
$990$	−4.50829	−	1.36519i	−0.143283	−	0.0433886i
$991$			26.3998i			0.838616i	0.907844	+	0.419308i	$0.137727\pi$
$991$			26.3998i			0.838616i	−0.907844	+	0.419308i	$0.862273\pi$
$992$	1.04262	+	10.3291i	0.0331031	+	0.327951i
$993$	9.65359			0.306347
$994$	14.7077	+	4.45375i	0.466501	+	0.141264i
$995$	−7.41317			−0.235013
$996$	8.13847	−	12.2057i	0.257877	−	0.386752i
$997$			32.7755i			1.03801i	0.854771	+	0.519006i	$0.173698\pi$
$997$			32.7755i			1.03801i	−0.854771	+	0.519006i	$0.826302\pi$
$998$	−15.8314	+	52.2804i	−0.501135	+	1.65491i
$999$	−5.81865			−0.184094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.b.91.14	yes	24
4.3	odd	2		2208.2.n.b.367.14		24
8.3	odd	2	inner	552.2.n.b.91.15	yes	24
8.5	even	2		2208.2.n.b.367.12		24
23.22	odd	2	inner	552.2.n.b.91.13	✓	24
92.91	even	2		2208.2.n.b.367.11		24
184.45	odd	2		2208.2.n.b.367.13		24
184.91	even	2	inner	552.2.n.b.91.16	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.b.91.13	✓	24	23.22	odd	2	inner
552.2.n.b.91.14	yes	24	1.1	even	1	trivial
552.2.n.b.91.15	yes	24	8.3	odd	2	inner
552.2.n.b.91.16	yes	24	184.91	even	2	inner
2208.2.n.b.367.11		24	92.91	even	2
2208.2.n.b.367.12		24	8.5	even	2
2208.2.n.b.367.13		24	184.45	odd	2
2208.2.n.b.367.14		24	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.409868 - 1.35352i) q^{2} -1.00000 q^{3} +(-1.66402 - 1.10953i) q^{4} +0.901487 q^{5} +(-0.409868 + 1.35352i) q^{6} +1.56211 q^{7} +(-2.18379 + 1.79751i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.409868 - 1.35352i) q^{2} -1.00000 q^{3} +(-1.66402 - 1.10953i) q^{4} +0.901487 q^{5} +(-0.409868 + 1.35352i) q^{6} +1.56211 q^{7} +(-2.18379 + 1.79751i) q^{8} +1.00000 q^{9} +(0.369491 - 1.22018i) q^{10} -3.69478i q^{11} +(1.66402 + 1.10953i) q^{12} -2.36562i q^{13} +(0.640260 - 2.11434i) q^{14} -0.901487 q^{15} +(1.53790 + 3.69254i) q^{16} -0.473035i q^{17} +(0.409868 - 1.35352i) q^{18} -7.66256i q^{19} +(-1.50009 - 1.00022i) q^{20} -1.56211 q^{21} +(-5.00095 - 1.51438i) q^{22} +(-4.73018 - 0.790796i) q^{23} +(2.18379 - 1.79751i) q^{24} -4.18732 q^{25} +(-3.20191 - 0.969595i) q^{26} -1.00000 q^{27} +(-2.59938 - 1.73321i) q^{28} +4.29403i q^{29} +(-0.369491 + 1.22018i) q^{30} +1.83523i q^{31} +(5.62825 - 0.568111i) q^{32} +3.69478i q^{33} +(-0.640260 - 0.193882i) q^{34} +1.40822 q^{35} +(-1.66402 - 1.10953i) q^{36} +5.81865 q^{37} +(-10.3714 - 3.14064i) q^{38} +2.36562i q^{39} +(-1.96866 + 1.62043i) q^{40} +2.62473 q^{41} +(-0.640260 + 2.11434i) q^{42} -7.06267i q^{43} +(-4.09947 + 6.14818i) q^{44} +0.901487 q^{45} +(-3.00911 + 6.07826i) q^{46} -4.27804i q^{47} +(-1.53790 - 3.69254i) q^{48} -4.55981 q^{49} +(-1.71625 + 5.66761i) q^{50} +0.473035i q^{51} +(-2.62473 + 3.93644i) q^{52} -4.64065 q^{53} +(-0.409868 + 1.35352i) q^{54} -3.33080i q^{55} +(-3.41133 + 2.80792i) q^{56} +7.66256i q^{57} +(5.81205 + 1.75999i) q^{58} -7.81205 q^{59} +(1.50009 + 1.00022i) q^{60} +11.9981 q^{61} +(2.48402 + 0.752203i) q^{62} +1.56211 q^{63} +(1.53790 - 7.85079i) q^{64} -2.13258i q^{65} +(5.00095 + 1.51438i) q^{66} -5.35433i q^{67} +(-0.524845 + 0.787137i) q^{68} +(4.73018 + 0.790796i) q^{69} +(0.577186 - 1.90605i) q^{70} +6.95616i q^{71} +(-2.18379 + 1.79751i) q^{72} +11.2808 q^{73} +(2.38488 - 7.87564i) q^{74} +4.18732 q^{75} +(-8.50182 + 12.7506i) q^{76} -5.77167i q^{77} +(3.20191 + 0.969595i) q^{78} +15.8447 q^{79} +(1.38639 + 3.32878i) q^{80} +1.00000 q^{81} +(1.07579 - 3.55261i) q^{82} -7.33508i q^{83} +(2.59938 + 1.73321i) q^{84} -0.426435i q^{85} +(-9.55945 - 2.89477i) q^{86} -4.29403i q^{87} +(6.64142 + 8.06864i) q^{88} +4.91384i q^{89} +(0.369491 - 1.22018i) q^{90} -3.69537i q^{91} +(6.99369 + 6.56417i) q^{92} -1.83523i q^{93} +(-5.79040 - 1.75343i) q^{94} -6.90769i q^{95} +(-5.62825 + 0.568111i) q^{96} +15.0308i q^{97} +(-1.86892 + 6.17178i) q^{98} -3.69478i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9	\( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81} - 40 q^{82} + 40 q^{92} - 48 q^{94}+O(q^{100}) \) 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9 - 4 * q^12 + 4 * q^16 + 24 * q^25 - 24 * q^27 + 4 * q^36 - 44 * q^46 - 4 * q^48 + 56 * q^49 - 40 * q^50 - 48 * q^58 - 40 * q^62 + 4 * q^64 + 32 * q^73 - 24 * q^75 + 24 * q^81 - 40 * q^82 + 40 * q^92 - 48 * q^94

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