LMFDB - Embedded newform 552.2.n.b.91.13

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			91.13
Character	$\chi$	$=$	552.91
Dual form			552.2.n.b.91.15

$q$-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} +(0.868398 - 6.72651i) 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} +(-8.74851 - 3.93237i) 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	$-0.564607\pi$
$5$	−0.901487			−0.403157			−0.201579	+	0.979472i	$0.564607\pi$
$6$	−0.409868	+	1.35352i	−0.167328	+	0.552571i
$7$	−1.56211			−0.590423			−0.295211	−	0.955432i	$-0.595390\pi$
$7$	−1.56211			−0.590423			−0.295211	+	0.955432i	$0.595390\pi$
$8$	−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	$0.188051\pi$
$11$			3.69478i			1.11402i	−0.830506	+	0.557010i	$0.811949\pi$
$12$	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	$0.0182695\pi$
$17$			0.473035i			0.114728i	−0.998353	+	0.0573639i	$0.981730\pi$
$18$	0.409868	−	1.35352i	0.0966069	−	0.319027i
$19$			7.66256i			1.75791i	0.476904	+	0.878955i	$0.341759\pi$
$19$			7.66256i			1.75791i	−0.476904	+	0.878955i	$0.658241\pi$
$20$	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	$-0.658743\pi$
$37$	−5.81865			−0.956580			−0.478290	+	0.878202i	$0.658743\pi$
$38$	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	$0.181018\pi$
$43$			7.06267i			1.07705i	−0.842610	+	0.538524i	$0.818982\pi$
$44$	4.09947	−	6.14818i	0.618018	−	0.926873i
$45$	−0.901487			−0.134386
$46$	0.868398	−	6.72651i	0.128038	−	0.991769i
$47$		−	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	$-0.396747\pi$
$53$	4.64065			0.637442			0.318721	+	0.947849i	$0.396747\pi$
$54$	−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	$-0.778797\pi$
$61$	−11.9981			−1.53620			−0.768098	+	0.640332i	$0.778797\pi$
$62$	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	$0.106061\pi$
$67$			5.35433i			0.654135i	−0.945001	+	0.327068i	$0.893939\pi$
$68$	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	$-0.850230\pi$
$79$	−15.8447			−1.78267			−0.891335	+	0.453345i	$0.850230\pi$
$80$	−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	$0.131881\pi$
$83$			7.33508i			0.805129i	−0.915392	+	0.402565i	$0.868119\pi$
$84$	−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	$-0.916135\pi$
$89$		−	4.91384i		−	0.520866i	0.965492	−	0.260433i	$-0.0838653\pi$
$90$	−0.369491	+	1.22018i	−0.0389478	+	0.128618i
$91$			3.69537i			0.387380i
$92$	−8.74851	−	3.93237i	−0.912095	−	0.409978i
$93$		−	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	$-0.723691\pi$
$97$		−	15.0308i		−	1.52614i	0.646314	−	0.763071i	$-0.276309\pi$
$98$	−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	$-0.560317\pi$
$103$	−3.82331			−0.376722			−0.188361	+	0.982100i	$0.560317\pi$
$104$	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	$-0.863952\pi$
$107$		−	8.57550i		−	0.829024i	0.910044	−	0.414512i	$-0.136048\pi$
$108$	1.66402	+	1.10953i	0.160120	+	0.106764i
$109$	−15.2790			−1.46346			−0.731732	−	0.681592i	$-0.761288\pi$
$109$	−15.2790			−1.46346			−0.731732	+	0.681592i	$0.761288\pi$
$110$	−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	$0.0893542\pi$
$113$			5.89000i			0.554085i	−0.960858	+	0.277042i	$0.910646\pi$
$114$	−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	$0.0431994\pi$
$137$			3.16726i			0.270597i	−0.990805	+	0.135299i	$0.956801\pi$
$138$	−0.868398	+	6.72651i	−0.0739230	+	0.572598i
$139$	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	$-0.456291\pi$
$149$	3.34176			0.273767			0.136884	+	0.990587i	$0.456291\pi$
$150$	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	$-0.562404\pi$
$157$	−4.88151			−0.389587			−0.194793	+	0.980844i	$0.562404\pi$
$158$	−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	$-0.302225\pi$
$181$	15.6631			1.16423			0.582115	+	0.813106i	$0.302225\pi$
$182$	5.00174	+	1.51462i	0.370754	+	0.112271i
$183$	11.9981			0.886924
$184$	−8.90827	+	10.2295i	−0.656727	+	0.754129i
$185$	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	$-0.624709\pi$
$191$	−10.5542			−0.763677			−0.381839	+	0.924229i	$0.624709\pi$
$192$	−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	$-0.405857\pi$
$199$	8.22327			0.582932			0.291466	+	0.956581i	$0.405857\pi$
$200$	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	$-0.710050\pi$
$227$		−	23.8069i		−	1.58012i	0.613030	−	0.790059i	$-0.289950\pi$
$228$	−8.50182	+	12.7506i	−0.563047	+	0.844430i
$229$	10.4208			0.688628			0.344314	−	0.938854i	$-0.388111\pi$
$229$	10.4208			0.688628			0.344314	+	0.938854i	$0.388111\pi$
$230$	−0.782850	+	6.06386i	−0.0516196	+	0.399839i
$231$			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	$-0.931365\pi$
$241$		−	6.64297i		−	0.427911i	0.976843	−	0.213956i	$-0.0686348\pi$
$242$	−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	$-0.854223\pi$
$251$		−	14.0093i		−	0.884259i	0.896951	−	0.442130i	$-0.145777\pi$
$252$	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	$-0.373166\pi$
$263$	12.5846			0.775999			0.388000	+	0.921660i	$0.373166\pi$
$264$	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
$276$	8.74851	+	3.93237i	0.526598	+	0.236701i
$277$			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	$0.213998\pi$
$281$			20.8795i			1.24557i	−0.782395	+	0.622783i	$0.786002\pi$
$282$	5.79040	+	1.75343i	0.344813	+	0.104415i
$283$			11.8930i			0.706966i	0.935441	+	0.353483i	$0.115003\pi$
$283$			11.8930i			0.706966i	−0.935441	+	0.353483i	$0.884997\pi$
$284$	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	$-0.176897\pi$
$293$	29.0826			1.69902			0.849512	+	0.527570i	$0.176897\pi$
$294$	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	$-0.954847\pi$
$313$		−	5.00245i		−	0.282755i	0.989956	−	0.141378i	$-0.0451532\pi$
$314$	−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
$322$	−1.35654	+	10.5076i	−0.0755967	+	0.585563i
$323$	−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	$0.138966\pi$
$337$			15.5246i			0.845678i	−0.906205	+	0.422839i	$0.861034\pi$
$338$	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	$-0.448706\pi$
$359$	6.08015			0.320898			0.160449	+	0.987044i	$0.448706\pi$
$360$	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	$-0.693225\pi$
$367$	−21.8559			−1.14087			−0.570433	+	0.821344i	$0.693225\pi$
$368$	10.1946	+	16.2502i	0.531429	+	0.847103i
$369$	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	$-0.444532\pi$
$373$	6.69692			0.346754			0.173377	+	0.984856i	$0.444532\pi$
$374$	−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	$0.234820\pi$
$379$			26.1881i			1.34519i	−0.740011	+	0.672595i	$0.765180\pi$
$380$	−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	$-0.571181\pi$
$383$	−8.67994			−0.443524			−0.221762	+	0.975101i	$0.571181\pi$
$384$	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	$-0.745750\pi$
$389$	−27.5178			−1.39521			−0.697604	+	0.716484i	$0.745750\pi$
$390$	−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	$0.242509\pi$
$401$			27.6454i			1.38054i	−0.723550	+	0.690272i	$0.757491\pi$
$402$	−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
$414$	0.868398	−	6.72651i	0.0426795	−	0.330590i
$415$		−	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	$-0.960262\pi$
$419$		−	5.09760i		−	0.249034i	0.992217	−	0.124517i	$-0.0397381\pi$
$420$	2.34331	+	1.56246i	0.114342	+	0.0762404i
$421$	−19.3072			−0.940977			−0.470489	−	0.882406i	$-0.655922\pi$
$421$	−19.3072			−0.940977			−0.470489	+	0.882406i	$0.655922\pi$
$422$	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	$-0.875217\pi$
$431$	−38.3713			−1.84828			−0.924140	+	0.382054i	$0.875217\pi$
$432$	−1.53790	−	3.69254i	−0.0739921	−	0.177658i
$433$			4.61645i			0.221853i	0.993829	+	0.110926i	$0.0353817\pi$
$433$			4.61645i			0.221853i	−0.993829	+	0.110926i	$0.964618\pi$
$434$	−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	$0.135839\pi$
$457$			17.6970i			0.827829i	−0.910316	+	0.413915i	$0.864161\pi$
$458$	4.27117	−	14.1048i	0.199579	−	0.659073i
$459$		−	0.473035i		−	0.0220794i
$460$	7.88667	+	3.54498i	0.367718	+	0.165286i
$461$			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	$-0.647886\pi$
$467$		−	38.6391i		−	1.78800i	0.448063	−	0.894002i	$-0.352114\pi$
$468$	−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	$-0.830819\pi$
$479$	−37.7337			−1.72410			−0.862049	+	0.506826i	$0.830819\pi$
$480$	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	$-0.284798\pi$
$503$	28.0677			1.25148			0.625738	+	0.780033i	$0.284798\pi$
$504$	3.41133	−	2.80792i	0.151953	−	0.125074i
$505$		−	1.33207i		−	0.0592762i
$506$	24.8530	+	3.20855i	1.10485	+	0.142637i
$507$	−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	$0.0979287\pi$
$521$			13.8241i			0.605644i	−0.953047	+	0.302822i	$0.902071\pi$
$522$	5.81205	+	1.75999i	0.254386	+	0.0770326i
$523$			8.04855i			0.351939i	0.984396	+	0.175969i	$0.0563060\pi$
$523$			8.04855i			0.351939i	−0.984396	+	0.175969i	$0.943694\pi$
$524$	−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
$552$	8.90827	−	10.2295i	0.379161	−	0.435396i
$553$	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	$-0.629079\pi$
$557$	−18.6206			−0.788980			−0.394490	+	0.918900i	$0.629079\pi$
$558$	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	$-0.976534\pi$
$563$		−	3.49532i		−	0.147310i	0.997284	−	0.0736551i	$-0.0234664\pi$
$564$	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	$0.151760\pi$
$569$			21.8934i			0.917819i	−0.888483	+	0.458909i	$0.848240\pi$
$570$	9.34968	+	2.83125i	0.391615	+	0.118588i
$571$		−	28.9265i		−	1.21053i	−0.796022	−	0.605267i	$-0.793066\pi$
$571$		−	28.9265i		−	1.21053i	0.796022	−	0.605267i	$-0.206934\pi$
$572$	−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
$598$	−15.9124	−	2.05430i	−0.650706	−	0.0840067i
$599$			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	$-0.366006\pi$
$613$	20.2345			0.817262			0.408631	+	0.912700i	$0.366006\pi$
$614$	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	$0.0458149\pi$
$617$			7.12572i			0.286871i	−0.989660	+	0.143435i	$0.954185\pi$
$618$	1.56705	−	5.17491i	0.0630361	−	0.208165i
$619$		−	41.0670i		−	1.65062i	−0.564679	−	0.825311i	$-0.691000\pi$
$619$		−	41.0670i		−	1.65062i	0.564679	−	0.825311i	$-0.309000\pi$
$620$	−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	$-0.427024\pi$
$631$	11.4174			0.454518			0.227259	+	0.973834i	$0.427024\pi$
$632$	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	$0.327010\pi$
$641$			43.3405i			1.71185i	−0.517103	+	0.855923i	$0.672990\pi$
$642$	11.6071	+	3.51483i	0.458095	+	0.138719i
$643$		−	26.6168i		−	1.04966i	−0.851206	−	0.524832i	$-0.824128\pi$
$643$		−	26.6168i		−	1.04966i	0.851206	−	0.524832i	$-0.175872\pi$
$644$	13.6661	+	6.14281i	0.538522	+	0.242061i
$645$			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	$0.184888\pi$
$659$			28.1729i			1.09746i	−0.836000	+	0.548730i	$0.815112\pi$
$660$	3.69562	−	5.54250i	0.143852	−	0.215742i
$661$	6.71763			0.261285			0.130643	−	0.991430i	$-0.458296\pi$
$661$	6.71763			0.261285			0.130643	+	0.991430i	$0.458296\pi$
$662$	−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	$-0.938283\pi$
$677$	−51.0634			−1.96252			−0.981262	+	0.192678i	$0.938283\pi$
$678$	−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
$690$	0.782850	−	6.06386i	0.0298026	−	0.230847i
$691$	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	$-0.533203\pi$
$701$	−5.51359			−0.208246			−0.104123	+	0.994564i	$0.533203\pi$
$702$	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	$-0.349025\pi$
$709$	24.3221			0.913437			0.456719	+	0.889611i	$0.349025\pi$
$710$	−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	$-0.358439\pi$
$727$	23.1995			0.860420			0.430210	+	0.902729i	$0.358439\pi$
$728$	−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	$-0.496670\pi$
$733$	0.566445			0.0209221			0.0104611	+	0.999945i	$0.496670\pi$
$734$	−8.95802	+	29.5823i	−0.330647	+	1.09190i
$735$	−4.11061			−0.151622
$736$	26.1734	−	7.13807i	0.964765	−	0.263113i
$737$	−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	$-0.256516\pi$
$743$	37.7515			1.38497			0.692485	+	0.721433i	$0.256516\pi$
$744$	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	$-0.601248\pi$
$751$	−17.1412			−0.625490			−0.312745	+	0.949837i	$0.601248\pi$
$752$	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	$-0.296447\pi$
$757$	32.8391			1.19356			0.596779	+	0.802406i	$0.296447\pi$
$758$	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	$-0.969272\pi$
$769$		−	5.34560i		−	0.192767i	0.995344	−	0.0963837i	$-0.0307276\pi$
$770$	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	$-0.430795\pi$
$773$	11.9945			0.431413			0.215707	+	0.976458i	$0.430795\pi$
$774$	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
$782$	3.18187	+	0.410782i	0.113783	+	0.0146896i
$783$		−	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	$0.0815104\pi$
$787$			14.2110i			0.506566i	−0.967392	+	0.253283i	$0.918490\pi$
$788$	−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	$-0.132838\pi$
$797$	51.6166			1.82835			0.914177	+	0.405315i	$0.132838\pi$
$798$	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	$0.349455\pi$
$827$			51.2016i			1.78046i	−0.455515	+	0.890228i	$0.650545\pi$
$828$	−8.74851	−	3.93237i	−0.304032	−	0.136659i
$829$			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	$-0.330743\pi$
$839$	29.3728			1.01406			0.507031	+	0.861928i	$0.330743\pi$
$840$	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
$874$	51.5422	+	6.65415i	1.74344	+	0.225080i
$875$	−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	$0.198378\pi$
$881$			34.6478i			1.16731i	−0.812001	+	0.583656i	$0.801622\pi$
$882$	−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	$0.0417956\pi$
$907$			7.88616i			0.261856i	−0.991392	+	0.130928i	$0.958204\pi$
$908$	−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	$-0.625093\pi$
$911$	−23.1173			−0.765909			−0.382954	+	0.923767i	$0.625093\pi$
$912$	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	$-0.263820\pi$
$919$	40.9707			1.35150			0.675749	+	0.737132i	$0.263820\pi$
$920$	8.03069	−	9.22176i	0.264764	−	0.304032i
$921$	−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	$-0.810998\pi$
$937$		−	34.2523i		−	1.11897i	0.828839	−	0.559487i	$-0.189002\pi$
$938$	−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	$-0.492560\pi$
$941$	1.43382			0.0467413			0.0233706	+	0.999727i	$0.492560\pi$
$942$	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	$-0.612171\pi$
$953$		−	57.9473i		−	1.87710i	0.345146	−	0.938549i	$-0.387829\pi$
$954$	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
$966$	1.35654	−	10.5076i	0.0436458	−	0.338075i
$967$		−	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	$0.0109694\pi$
$971$			2.14726i			0.0689089i	−0.999406	+	0.0344545i	$0.989031\pi$
$972$	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	$-0.787970\pi$
$977$		−	38.6295i		−	1.23587i	0.786231	−	0.617933i	$-0.212030\pi$
$978$	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	$-0.366610\pi$
$983$	25.5149			0.813799			0.406899	+	0.913473i	$0.366610\pi$
$984$	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.91.13	✓	24
4.3	odd	2		2208.2.n.b.367.11		24
8.3	odd	2	inner	552.2.n.b.91.16	yes	24
8.5	even	2		2208.2.n.b.367.13		24
23.22	odd	2	inner	552.2.n.b.91.14	yes	24
92.91	even	2		2208.2.n.b.367.14		24
184.45	odd	2		2208.2.n.b.367.12		24
184.91	even	2	inner	552.2.n.b.91.15	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.b.91.13	✓	24	1.1	even	1	trivial
552.2.n.b.91.14	yes	24	23.22	odd	2	inner
552.2.n.b.91.15	yes	24	184.91	even	2	inner
552.2.n.b.91.16	yes	24	8.3	odd	2	inner
2208.2.n.b.367.11		24	4.3	odd	2
2208.2.n.b.367.12		24	184.45	odd	2
2208.2.n.b.367.13		24	8.5	even	2
2208.2.n.b.367.14		24	92.91	even	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} +(0.868398 - 6.72651i) 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} +(-8.74851 - 3.93237i) 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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