LMFDB - Embedded newform 504.2.bk.c.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.c.451.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.297109 + 1.38265i) q^{2} +(-1.82345 + 0.821596i) q^{4} +(1.44142 - 2.49662i) q^{5} +(2.63862 - 0.194181i) q^{7} +(-1.67775 - 2.27710i) q^{8} +O(q^{10})$	\(q+(0.297109 + 1.38265i) q^{2} +(-1.82345 + 0.821596i) q^{4} +(1.44142 - 2.49662i) q^{5} +(2.63862 - 0.194181i) q^{7} +(-1.67775 - 2.27710i) q^{8} +(3.88021 + 1.25122i) q^{10} +(-2.91340 - 5.04616i) q^{11} -1.04841 q^{13} +(1.05244 + 3.59059i) q^{14} +(2.64996 - 2.99628i) q^{16} +(5.91062 - 3.41250i) q^{17} +(-0.589961 - 0.340614i) q^{19} +(-0.577155 + 5.73673i) q^{20} +(6.11148 - 5.52748i) q^{22} +(-1.85937 - 1.07351i) q^{23} +(-1.65540 - 2.86723i) q^{25} +(-0.311491 - 1.44958i) q^{26} +(-4.65185 + 2.52196i) q^{28} +6.61515i q^{29} +(1.91558 + 3.31788i) q^{31} +(4.93014 + 2.77375i) q^{32} +(6.47439 + 7.15845i) q^{34} +(3.31857 - 6.86751i) q^{35} +(2.06185 + 1.19041i) q^{37} +(0.295668 - 0.916911i) q^{38} +(-8.10338 + 0.906428i) q^{40} +1.19919i q^{41} +1.34319 q^{43} +(9.45835 + 6.80779i) q^{44} +(0.931851 - 2.88980i) q^{46} +(-5.52670 + 9.57253i) q^{47} +(6.92459 - 1.02474i) q^{49} +(3.47255 - 3.14072i) q^{50} +(1.91172 - 0.861368i) q^{52} +(6.99615 - 4.03923i) q^{53} -16.7978 q^{55} +(-4.86909 - 5.68260i) q^{56} +(-9.14645 + 1.96542i) q^{58} +(-6.81625 + 3.93537i) q^{59} +(-1.63471 + 2.83140i) q^{61} +(-4.01834 + 3.63435i) q^{62} +(-2.37034 + 7.64078i) q^{64} +(-1.51120 + 2.61747i) q^{65} +(-6.65629 - 11.5290i) q^{67} +(-7.97404 + 11.0787i) q^{68} +(10.4813 + 2.54802i) q^{70} +1.08533i q^{71} +(4.88878 - 2.82254i) q^{73} +(-1.03333 + 3.20450i) q^{74} +(1.35561 + 0.136384i) q^{76} +(-8.66721 - 12.7491i) q^{77} +(10.9630 + 6.32946i) q^{79} +(-3.66086 - 10.9348i) q^{80} +(-1.65806 + 0.356289i) q^{82} -0.482042i q^{83} -19.6754i q^{85} +(0.399075 + 1.85717i) q^{86} +(-6.60265 + 15.1003i) q^{88} +(-10.7308 - 6.19543i) q^{89} +(-2.76635 + 0.203581i) q^{91} +(4.27246 + 0.429839i) q^{92} +(-14.8775 - 4.79742i) q^{94} +(-1.70077 + 0.981939i) q^{95} -3.63532i q^{97} +(3.47421 + 9.26984i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	0.297109	+	1.38265i	0.210088	+	0.977683i
$2$	0.297109	+	1.38265i	0.210088	+	0.977683i
$3$		0			0
$3$		0			0
$4$	−1.82345	+	0.821596i	−0.911726	+	0.410798i
$5$	1.44142	−	2.49662i	0.644624	−	1.11652i	−0.339765	−	0.940511i	$-0.610347\pi$
$5$	1.44142	−	2.49662i	0.644624	−	1.11652i	0.984388	−	0.176010i	$-0.0563193\pi$
$6$		0			0
$7$	2.63862	−	0.194181i	0.997303	−	0.0733933i
$7$	2.63862	−	0.194181i	0.997303	−	0.0733933i
$8$	−1.67775	−	2.27710i	−0.593172	−	0.805075i
$9$		0			0
$10$	3.88021	+	1.25122i	1.22703	+	0.395670i
$11$	−2.91340	−	5.04616i	−0.878423	−	1.52147i	−0.853071	−	0.521795i	$-0.825262\pi$
$11$	−2.91340	−	5.04616i	−0.878423	−	1.52147i	−0.0253527	−	0.999679i	$-0.508071\pi$
$12$		0			0
$13$	−1.04841			−0.290776			−0.145388	−	0.989375i	$-0.546443\pi$
$13$	−1.04841			−0.290776			−0.145388	+	0.989375i	$0.546443\pi$
$14$	1.05244	+	3.59059i	0.281276	+	0.959627i
$15$		0			0
$16$	2.64996	−	2.99628i	0.662490	−	0.749071i
$17$	5.91062	−	3.41250i	1.43354	−	0.827652i	0.436147	−	0.899875i	$-0.356343\pi$
$17$	5.91062	−	3.41250i	1.43354	−	0.827652i	0.997388	+	0.0722232i	$0.0230094\pi$
$18$		0			0
$19$	−0.589961	−	0.340614i	−0.135346	−	0.0781423i	0.430798	−	0.902448i	$-0.358232\pi$
$19$	−0.589961	−	0.340614i	−0.135346	−	0.0781423i	−0.566144	+	0.824306i	$0.691566\pi$
$20$	−0.577155	+	5.73673i	−0.129056	+	1.28277i
$21$		0			0
$22$	6.11148	−	5.52748i	1.30297	−	1.17846i
$23$	−1.85937	−	1.07351i	−0.387705	−	0.223841i	0.293460	−	0.955971i	$-0.405193\pi$
$23$	−1.85937	−	1.07351i	−0.387705	−	0.223841i	−0.681165	+	0.732130i	$0.738526\pi$
$24$		0			0
$25$	−1.65540	−	2.86723i	−0.331079	−	0.573446i
$26$	−0.311491	−	1.44958i	−0.0610885	−	0.284287i
$27$		0			0
$28$	−4.65185	+	2.52196i	−0.879118	+	0.476605i
$29$			6.61515i			1.22840i	0.789149	+	0.614201i	$0.210522\pi$
$29$			6.61515i			1.22840i	−0.789149	+	0.614201i	$0.789478\pi$
$30$		0			0
$31$	1.91558	+	3.31788i	0.344048	+	0.595909i	0.985180	−	0.171522i	$-0.0548684\pi$
$31$	1.91558	+	3.31788i	0.344048	+	0.595909i	−0.641132	+	0.767430i	$0.721535\pi$
$32$	4.93014	+	2.77375i	0.871534	+	0.490334i
$33$		0			0
$34$	6.47439	+	7.15845i	1.11035	+	1.22766i
$35$	3.31857	−	6.86751i	0.560940	−	1.16082i
$36$		0			0
$37$	2.06185	+	1.19041i	0.338966	+	0.195702i	0.659814	−	0.751429i	$-0.270635\pi$
$37$	2.06185	+	1.19041i	0.338966	+	0.195702i	−0.320849	+	0.947130i	$0.603968\pi$
$38$	0.295668	−	0.916911i	0.0479638	−	0.148743i
$39$		0			0
$40$	−8.10338	+	0.906428i	−1.28126	+	0.143319i
$41$			1.19919i			0.187281i	0.995606	+	0.0936407i	$0.0298505\pi$
$41$			1.19919i			0.187281i	−0.995606	+	0.0936407i	$0.970149\pi$
$42$		0			0
$43$	1.34319			0.204835			0.102418	−	0.994741i	$-0.467342\pi$
$43$	1.34319			0.204835			0.102418	+	0.994741i	$0.467342\pi$
$44$	9.45835	+	6.80779i	1.42590	+	1.02631i
$45$		0			0
$46$	0.931851	−	2.88980i	0.137394	−	0.426078i
$47$	−5.52670	+	9.57253i	−0.806152	+	1.39630i	0.109359	+	0.994002i	$0.465120\pi$
$47$	−5.52670	+	9.57253i	−0.806152	+	1.39630i	−0.915511	+	0.402294i	$0.868213\pi$
$48$		0			0
$49$	6.92459	−	1.02474i	0.989227	−	0.146391i
$50$	3.47255	−	3.14072i	0.491093	−	0.444165i
$51$		0			0
$52$	1.91172	−	0.861368i	0.265108	−	0.119450i
$53$	6.99615	−	4.03923i	0.960995	−	0.554830i	0.0645156	−	0.997917i	$-0.479450\pi$
$53$	6.99615	−	4.03923i	0.960995	−	0.554830i	0.896479	+	0.443086i	$0.146116\pi$
$54$		0			0
$55$	−16.7978			−2.26501
$56$	−4.86909	−	5.68260i	−0.650660	−	0.759369i
$57$		0			0
$58$	−9.14645	+	1.96542i	−1.20099	+	0.258072i
$59$	−6.81625	+	3.93537i	−0.887400	+	0.512341i	−0.873091	−	0.487557i	$-0.837888\pi$
$59$	−6.81625	+	3.93537i	−0.887400	+	0.512341i	−0.0143092	+	0.999898i	$0.504555\pi$
$60$		0			0
$61$	−1.63471	+	2.83140i	−0.209303	+	0.362524i	−0.951495	−	0.307663i	$-0.900453\pi$
$61$	−1.63471	+	2.83140i	−0.209303	+	0.362524i	0.742192	+	0.670187i	$0.233786\pi$
$62$	−4.01834	+	3.63435i	−0.510329	+	0.461563i
$63$		0			0
$64$	−2.37034	+	7.64078i	−0.296293	+	0.955097i
$65$	−1.51120	+	2.61747i	−0.187441	+	0.324658i
$66$		0			0
$67$	−6.65629	−	11.5290i	−0.813195	−	1.40850i	−0.910617	−	0.413252i	$-0.864393\pi$
$67$	−6.65629	−	11.5290i	−0.813195	−	1.40850i	0.0974214	−	0.995243i	$-0.468941\pi$
$68$	−7.97404	+	11.0787i	−0.966994	+	1.34349i
$69$		0			0
$70$	10.4813	+	2.54802i	1.25276	+	0.304547i
$71$			1.08533i			0.128805i	0.997924	+	0.0644027i	$0.0205142\pi$
$71$			1.08533i			0.128805i	−0.997924	+	0.0644027i	$0.979486\pi$
$72$		0			0
$73$	4.88878	−	2.82254i	0.572188	−	0.330353i	−0.185835	−	0.982581i	$-0.559499\pi$
$73$	4.88878	−	2.82254i	0.572188	−	0.330353i	0.758023	+	0.652228i	$0.226166\pi$
$74$	−1.03333	+	3.20450i	−0.120122	+	0.372515i
$75$		0			0
$76$	1.35561	+	0.136384i	0.155500	+	0.0156444i
$77$	−8.66721	−	12.7491i	−0.987720	−	1.45290i
$78$		0			0
$79$	10.9630	+	6.32946i	1.23343	+	0.712120i	0.967743	−	0.251939i	$-0.0810684\pi$
$79$	10.9630	+	6.32946i	1.23343	+	0.712120i	0.265686	+	0.964060i	$0.414402\pi$
$80$	−3.66086	−	10.9348i	−0.409296	−	1.22255i
$81$		0			0
$82$	−1.65806	+	0.356289i	−0.183102	+	0.0393455i
$83$		−	0.482042i		−	0.0529110i	−0.999650	−	0.0264555i	$-0.991578\pi$
$83$		−	0.482042i		−	0.0529110i	0.999650	−	0.0264555i	$-0.00842203\pi$
$84$		0			0
$85$		−	19.6754i		−	2.13410i
$86$	0.399075	+	1.85717i	0.0430333	+	0.200264i
$87$		0			0
$88$	−6.60265	+	15.1003i	−0.703845	+	1.60969i
$89$	−10.7308	−	6.19543i	−1.13746	−	0.656714i	−0.191661	−	0.981461i	$-0.561388\pi$
$89$	−10.7308	−	6.19543i	−1.13746	−	0.656714i	−0.945801	+	0.324747i	$0.894721\pi$
$90$		0			0
$91$	−2.76635	+	0.203581i	−0.289992	+	0.0213410i
$92$	4.27246	+	0.429839i	0.445434	+	0.0448138i
$93$		0			0
$94$	−14.8775	−	4.79742i	−1.53450	−	0.494816i
$95$	−1.70077	+	0.981939i	−0.174495	+	0.100745i
$96$		0			0
$97$		−	3.63532i		−	0.369111i	−0.982822	−	0.184556i	$-0.940915\pi$
$97$		−	3.63532i		−	0.369111i	0.982822	−	0.184556i	$-0.0590846\pi$
$98$	3.47421	+	9.26984i	0.350948	+	0.936395i
$99$		0			0
$100$	5.37424	+	3.86819i	0.537424	+	0.386819i
$101$	−1.25234	−	2.16911i	−0.124612	−	0.215835i	0.796969	−	0.604020i	$-0.206435\pi$
$101$	−1.25234	−	2.16911i	−0.124612	−	0.215835i	−0.921581	+	0.388185i	$0.873102\pi$
$102$		0			0
$103$	−2.31322	+	4.00661i	−0.227928	+	0.394783i	−0.957194	−	0.289447i	$-0.906529\pi$
$103$	−2.31322	+	4.00661i	−0.227928	+	0.394783i	0.729266	+	0.684231i	$0.239862\pi$
$104$	1.75896	+	2.38733i	0.172480	+	0.234097i
$105$		0			0
$106$	7.66346	+	8.47315i	0.744341	+	0.822985i
$107$	−3.03473	+	5.25631i	−0.293378	+	0.508146i	−0.974606	−	0.223925i	$-0.928113\pi$
$107$	−3.03473	+	5.25631i	−0.293378	+	0.508146i	0.681228	+	0.732071i	$0.261446\pi$
$108$		0			0
$109$	12.6132	−	7.28224i	1.20813	−	0.697513i	0.245777	−	0.969326i	$-0.420957\pi$
$109$	12.6132	−	7.28224i	1.20813	−	0.697513i	0.962350	+	0.271814i	$0.0876235\pi$
$110$	−4.99076	−	23.2255i	−0.475851	−	2.21446i
$111$		0			0
$112$	6.41041	−	8.42061i	0.605727	−	0.795673i
$113$	3.82875			0.360179			0.180089	−	0.983650i	$-0.442361\pi$
$113$	3.82875			0.360179			0.180089	+	0.983650i	$0.442361\pi$
$114$		0			0
$115$	−5.36027	+	3.09475i	−0.499847	+	0.288587i
$116$	−5.43498	−	12.0624i	−0.504625	−	1.11997i
$117$		0			0
$118$	−7.46641	−	8.25527i	−0.687339	−	0.759959i
$119$	14.9332	−	10.1520i	1.36893	−	0.930632i
$120$		0			0
$121$	−11.4758	+	19.8767i	−1.04326	+	1.80697i
$122$	−4.40053	−	1.41900i	−0.398405	−	0.128470i
$123$		0			0
$124$	−6.21892	−	4.47616i	−0.558476	−	0.401971i
$125$	4.86972			0.435561
$126$		0			0
$127$		−	0.550415i		−	0.0488415i	−0.999702	−	0.0244207i	$-0.992226\pi$
$127$		−	0.550415i		−	0.0488415i	0.999702	−	0.0244207i	$-0.00777413\pi$
$128$	−11.2688	−	1.00722i	−0.996029	−	0.0890263i
$129$		0			0
$130$	−4.06805	−	1.31179i	−0.356791	−	0.115051i
$131$	2.42818	+	1.40191i	0.212151	+	0.122486i	0.602311	−	0.798262i	$-0.294247\pi$
$131$	2.42818	+	1.40191i	0.212151	+	0.122486i	−0.390159	+	0.920747i	$0.627580\pi$
$132$		0			0
$133$	−1.62282	−	0.784192i	−0.140717	−	0.0679980i
$134$	13.9630	−	12.6287i	1.20622	−	1.09095i
$135$		0			0
$136$	−17.6871	−	7.73375i	−1.51666	−	0.663164i
$137$	6.38148	+	11.0530i	0.545206	+	0.944325i	0.998594	+	0.0530118i	$0.0168821\pi$
$137$	6.38148	+	11.0530i	0.545206	+	0.944325i	−0.453387	+	0.891314i	$0.649785\pi$
$138$		0			0
$139$			6.11761i			0.518889i	0.965758	+	0.259444i	$0.0835394\pi$
$139$			6.11761i			0.518889i	−0.965758	+	0.259444i	$0.916461\pi$
$140$	−0.408930	+	15.2491i	−0.0345609	+	1.28878i
$141$		0			0
$142$	−1.50064	+	0.322462i	−0.125931	+	0.0270604i
$143$	3.05443	+	5.29044i	0.255425	+	0.442408i
$144$		0			0
$145$	16.5155	+	9.53522i	1.37154	+	0.791857i
$146$	5.35508	+	5.92087i	0.443190	+	0.490015i
$147$		0			0
$148$	−4.73771	−	0.476647i	−0.389438	−	0.0391802i
$149$	1.75163	+	1.01130i	0.143499	+	0.0828491i	0.570030	−	0.821624i	$-0.306931\pi$
$149$	1.75163	+	1.01130i	0.143499	+	0.0828491i	−0.426532	+	0.904473i	$0.640265\pi$
$150$		0			0
$151$	−12.1833	+	7.03404i	−0.991464	+	0.572422i	−0.905712	−	0.423895i	$-0.860663\pi$
$151$	−12.1833	+	7.03404i	−0.991464	+	0.572422i	−0.0857523	+	0.996316i	$0.527329\pi$
$152$	0.214193	+	1.91486i	0.0173733	+	0.155316i
$153$		0			0
$154$	15.0525	−	15.7716i	1.21297	−	1.27091i
$155$	11.0446			0.887126
$156$		0			0
$157$	−2.61739	−	4.53344i	−0.208890	−	0.361808i	0.742475	−	0.669874i	$-0.233652\pi$
$157$	−2.61739	−	4.53344i	−0.208890	−	0.361808i	−0.951365	+	0.308065i	$0.900318\pi$
$158$	−5.49426	+	17.0385i	−0.437100	+	1.35551i
$159$		0			0
$160$	14.0314	−	8.31053i	1.10928	−	0.657005i
$161$	−5.11461	−	2.47152i	−0.403088	−	0.194783i
$162$		0			0
$163$	−0.488212	+	0.845609i	−0.0382397	+	0.0662332i	−0.884512	−	0.466518i	$-0.845508\pi$
$163$	−0.488212	+	0.845609i	−0.0382397	+	0.0662332i	0.846272	+	0.532751i	$0.178842\pi$
$164$	−0.985247	−	2.18666i	−0.0769349	−	0.170749i
$165$		0			0
$166$	0.666497	−	0.143219i	0.0517302	−	0.0111160i
$167$	−2.08267			−0.161162			−0.0805808	−	0.996748i	$-0.525678\pi$
$167$	−2.08267			−0.161162			−0.0805808	+	0.996748i	$0.525678\pi$
$168$		0			0
$169$	−11.9008			−0.915449
$170$	27.2042	−	5.84573i	2.08647	−	0.448347i
$171$		0			0
$172$	−2.44925	+	1.10356i	−0.186754	+	0.0841459i
$173$	−10.6732	+	18.4864i	−0.811465	+	1.40550i	0.100374	+	0.994950i	$0.467996\pi$
$173$	−10.6732	+	18.4864i	−0.811465	+	1.40550i	−0.911839	+	0.410548i	$0.865337\pi$
$174$		0			0
$175$	−4.92472	−	7.24408i	−0.372274	−	0.547601i
$176$	−22.8401	−	4.64274i	−1.72164	−	0.349960i
$177$		0			0
$178$	5.37791	−	16.6777i	0.403091	−	1.25004i
$179$	−3.47487	−	6.01865i	−0.259724	−	0.449855i	0.706444	−	0.707769i	$-0.250298\pi$
$179$	−3.47487	−	6.01865i	−0.259724	−	0.449855i	−0.966168	+	0.257914i	$0.916965\pi$
$180$		0			0
$181$	7.67619			0.570566			0.285283	−	0.958443i	$-0.407912\pi$
$181$	7.67619			0.570566			0.285283	+	0.958443i	$0.407912\pi$
$182$	−1.10339	−	3.76441i	−0.0817885	−	0.279037i
$183$		0			0
$184$	0.675066	+	6.03503i	0.0497665	+	0.444908i
$185$	5.94398	−	3.43176i	0.437010	−	0.252308i
$186$		0			0
$187$	−34.4400	−	19.8839i	−2.51850	−	1.45406i
$188$	2.21293	−	21.9958i	0.161394	−	1.60421i
$189$		0			0
$190$	−1.86299	−	2.05983i	−0.135156	−	0.149436i
$191$	−15.4238	−	8.90495i	−1.11603	−	0.644340i	−0.175645	−	0.984454i	$-0.556201\pi$
$191$	−15.4238	−	8.90495i	−1.11603	−	0.644340i	−0.940384	+	0.340114i	$0.889534\pi$
$192$		0			0
$193$	6.89797	+	11.9476i	0.496527	+	0.860010i	0.999992	−	0.00400574i	$-0.00127507\pi$
$193$	6.89797	+	11.9476i	0.496527	+	0.860010i	−0.503465	+	0.864016i	$0.667942\pi$
$194$	5.02639	−	1.08009i	0.360874	−	0.0775457i
$195$		0			0
$196$	−11.7847	+	7.55777i	−0.841767	+	0.539841i
$197$			1.13180i			0.0806374i	0.999187	+	0.0403187i	$0.0128373\pi$
$197$			1.13180i			0.0806374i	−0.999187	+	0.0403187i	$0.987163\pi$
$198$		0			0
$199$	4.26593	+	7.38881i	0.302404	+	0.523779i	0.976680	−	0.214701i	$-0.0688776\pi$
$199$	4.26593	+	7.38881i	0.302404	+	0.523779i	−0.674276	+	0.738479i	$0.735544\pi$
$200$	−3.75163	+	8.57998i	−0.265280	+	0.606696i
$201$		0			0
$202$	2.62705	−	2.37601i	0.184838	−	0.167175i
$203$	1.28453	+	17.4548i	0.0901566	+	1.22509i
$204$		0			0
$205$	2.99391	+	1.72853i	0.209104	+	0.120726i
$206$	−6.22703	−	2.00798i	−0.433858	−	0.139902i
$207$		0			0
$208$	−2.77824	+	3.14133i	−0.192636	+	0.217812i
$209$			3.96939i			0.274568i
$210$		0			0
$211$	21.2436			1.46247			0.731237	−	0.682124i	$-0.238944\pi$
$211$	21.2436			1.46247			0.731237	+	0.682124i	$0.238944\pi$
$212$	−9.43853	+	13.1133i	−0.648241	+	0.900628i
$213$		0			0
$214$	−8.16929	−	2.63428i	−0.558441	−	0.180076i
$215$	1.93611	−	3.35344i	0.132042	−	0.228703i
$216$		0			0
$217$	5.69874	+	8.38264i	0.386856	+	0.569051i
$218$	13.8163	+	15.2761i	0.935758	+	1.03463i
$219$		0			0
$220$	30.6299	−	13.8010i	2.06507	−	0.930462i
$221$	−6.19674	+	3.57769i	−0.416838	+	0.240662i
$222$		0			0
$223$	−3.12207			−0.209069			−0.104535	−	0.994521i	$-0.533335\pi$
$223$	−3.12207			−0.209069			−0.104535	+	0.994521i	$0.533335\pi$
$224$	13.5474	+	6.36152i	0.905171	+	0.425047i
$225$		0			0
$226$	1.13756	+	5.29383i	0.0756691	+	0.352140i
$227$	−4.52649	+	2.61337i	−0.300434	+	0.173456i	−0.642638	−	0.766170i	$-0.722160\pi$
$227$	−4.52649	+	2.61337i	−0.300434	+	0.173456i	0.342204	+	0.939626i	$0.388827\pi$
$228$		0			0
$229$	−14.2129	+	24.6175i	−0.939215	+	1.62677i	−0.172276	+	0.985049i	$0.555112\pi$
$229$	−14.2129	+	24.6175i	−0.939215	+	1.62677i	−0.766939	+	0.641720i	$0.778221\pi$
$230$	−5.87154	−	6.49190i	−0.387158	−	0.428063i
$231$		0			0
$232$	15.0633	−	11.0985i	0.988957	−	0.728655i
$233$	3.05971	−	5.29957i	0.200448	−	0.347186i	−0.748225	−	0.663445i	$-0.769094\pi$
$233$	3.05971	−	5.29957i	0.200448	−	0.347186i	0.948673	+	0.316259i	$0.102427\pi$
$234$		0			0
$235$	15.9326	+	27.5961i	1.03933	+	1.80017i
$236$	9.19583	−	12.7762i	0.598598	−	0.831657i
$237$		0			0
$238$	18.4735	+	17.6312i	1.19746	+	1.14286i
$239$			8.83528i			0.571507i	0.958303	+	0.285753i	$0.0922439\pi$
$239$			8.83528i			0.571507i	−0.958303	+	0.285753i	$0.907756\pi$
$240$		0			0
$241$	5.15757	−	2.97772i	0.332228	−	0.191812i	−0.324602	−	0.945851i	$-0.605230\pi$
$241$	5.15757	−	2.97772i	0.332228	−	0.191812i	0.656830	+	0.754039i	$0.271897\pi$
$242$	−30.8921	−	9.96151i	−1.98582	−	0.640350i
$243$		0			0
$244$	0.654550	−	6.50600i	0.0419032	−	0.416504i
$245$	7.42288	−	18.7651i	0.474231	−	1.19886i
$246$		0			0
$247$	0.618521	+	0.357103i	0.0393555	+	0.0227219i
$248$	4.34128	−	9.92851i	0.275672	−	0.630461i
$249$		0			0
$250$	1.44684	+	6.73313i	0.0915059	+	0.425840i
$251$			2.13955i			0.135047i	0.997718	+	0.0675235i	$0.0215098\pi$
$251$			2.13955i			0.135047i	−0.997718	+	0.0675235i	$0.978490\pi$
$252$		0			0
$253$			12.5102i			0.786510i
$254$	0.761033	−	0.163533i	0.0477514	−	0.0102610i
$255$		0			0
$256$	−1.95542	−	15.8801i	−0.122214	−	0.992504i
$257$	16.7030	+	9.64346i	1.04190	+	0.601543i	0.920372	−	0.391045i	$-0.127886\pi$
$257$	16.7030	+	9.64346i	1.04190	+	0.601543i	0.121531	+	0.992588i	$0.461220\pi$
$258$		0			0
$259$	5.67158	+	2.74066i	0.352415	+	0.170296i
$260$	0.605095	−	6.01444i	0.0375264	−	0.373000i
$261$		0			0
$262$	−1.21692	+	3.77385i	−0.0751817	+	0.233150i
$263$	21.0740	−	12.1671i	1.29948	−	0.750254i	0.319164	−	0.947699i	$-0.396598\pi$
$263$	21.0740	−	12.1671i	1.29948	−	0.750254i	0.980314	+	0.197446i	$0.0632646\pi$
$264$		0			0
$265$		−	23.2889i		−	1.43063i
$266$	0.602109	−	2.47679i	0.0369177	−	0.151862i
$267$		0			0
$268$	21.6096	+	15.5539i	1.32002	+	0.950103i
$269$	10.4505	+	18.1007i	0.637176	+	1.10362i	0.986050	+	0.166452i	$0.0532310\pi$
$269$	10.4505	+	18.1007i	0.637176	+	1.10362i	−0.348873	+	0.937170i	$0.613436\pi$
$270$		0			0
$271$	9.99697	−	17.3153i	0.607273	−	1.05183i	−0.384415	−	0.923160i	$-0.625597\pi$
$271$	9.99697	−	17.3153i	0.607273	−	1.05183i	0.991688	−	0.128667i	$-0.0410698\pi$
$272$	5.43810	−	26.7529i	0.329733	−	1.62213i
$273$		0			0
$274$	−13.3865	+	12.1073i	−0.808709	+	0.731430i
$275$	−9.64567	+	16.7068i	−0.581656	+	1.00746i
$276$		0			0
$277$	13.2433	−	7.64600i	0.795710	−	0.459404i	−0.0462586	−	0.998929i	$-0.514730\pi$
$277$	13.2433	−	7.64600i	0.795710	−	0.459404i	0.841969	+	0.539526i	$0.181396\pi$
$278$	−8.45852	+	1.81760i	−0.507309	+	0.109012i
$279$		0			0
$280$	−21.2057	+	3.96523i	−1.26728	+	0.236968i
$281$	−5.59802			−0.333950			−0.166975	−	0.985961i	$-0.553400\pi$
$281$	−5.59802			−0.333950			−0.166975	+	0.985961i	$0.553400\pi$
$282$		0			0
$283$	9.72911	−	5.61710i	0.578335	−	0.333902i	−0.182136	−	0.983273i	$-0.558301\pi$
$283$	9.72911	−	5.61710i	0.578335	−	0.333902i	0.760472	+	0.649371i	$0.224968\pi$
$284$	−0.891706	−	1.97905i	−0.0529130	−	0.117435i
$285$		0			0
$286$	−6.40733	+	5.79505i	−0.378874	+	0.342669i
$287$	0.232859	+	3.16419i	0.0137452	+	0.186776i
$288$		0			0
$289$	14.7903	−	25.6175i	0.870016	−	1.50691i
$290$	−8.27700	+	25.6682i	−0.486042	+	1.50729i
$291$		0			0
$292$	−6.59547	+	9.16336i	−0.385971	+	0.536245i
$293$	−17.7212			−1.03528			−0.517642	−	0.855598i	$-0.673190\pi$
$293$	−17.7212			−1.03528			−0.517642	+	0.855598i	$0.673190\pi$
$294$		0			0
$295$			22.6901i			1.32107i
$296$	−0.748579	−	6.69223i	−0.0435103	−	0.388978i
$297$		0			0
$298$	−0.877855	+	2.72236i	−0.0508528	+	0.157702i
$299$	1.94938	+	1.12547i	0.112735	+	0.0650878i
$300$		0			0
$301$	3.54417	−	0.260822i	0.204283	−	0.0150335i
$302$	−13.3454	−	14.7554i	−0.767941	−	0.849078i
$303$		0			0
$304$	−2.58395	+	0.865077i	−0.148200	+	0.0496156i
$305$	4.71262	+	8.16250i	0.269844	+	0.467383i
$306$		0			0
$307$			20.3724i			1.16271i	0.813649	+	0.581357i	$0.197478\pi$
$307$			20.3724i			1.16271i	−0.813649	+	0.581357i	$0.802522\pi$
$308$	26.2789	+	16.1265i	1.49738	+	0.918894i
$309$		0			0
$310$	3.28146	+	15.2709i	0.186374	+	0.867328i
$311$	14.4363	+	25.0045i	0.818610	+	1.41787i	0.906706	+	0.421762i	$0.138588\pi$
$311$	14.4363	+	25.0045i	0.818610	+	1.41787i	−0.0880964	+	0.996112i	$0.528078\pi$
$312$		0			0
$313$	−4.08718	−	2.35974i	−0.231021	−	0.133380i	0.380022	−	0.924978i	$-0.375916\pi$
$313$	−4.08718	−	2.35974i	−0.231021	−	0.133380i	−0.611043	+	0.791597i	$0.709250\pi$
$314$	5.49053	−	4.96586i	0.309848	−	0.280240i
$315$		0			0
$316$	−25.1907	−	2.53436i	−1.41709	−	0.142569i
$317$	22.0349	+	12.7218i	1.23760	+	0.714529i	0.968603	−	0.248612i	$-0.0799743\pi$
$317$	22.0349	+	12.7218i	1.23760	+	0.714529i	0.268998	+	0.963141i	$0.413308\pi$
$318$		0			0
$319$	33.3811	−	19.2726i	1.86898	−	1.07906i
$320$	15.6594	+	16.9314i	0.875389	+	0.946495i
$321$		0			0
$322$	1.89765	−	7.80603i	0.105752	−	0.435013i
$323$	−4.64938			−0.258699
$324$		0			0
$325$	1.73553	+	3.00603i	0.0962700	+	0.166745i
$326$	−1.31423	−	0.423790i	−0.0727887	−	0.0234716i
$327$		0			0
$328$	2.73066	−	2.01193i	0.150776	−	0.111090i
$329$	−12.7240	+	26.3314i	−0.701499	+	1.45170i
$330$		0			0
$331$	9.85929	−	17.0768i	0.541916	−	0.938625i	−0.456878	−	0.889529i	$-0.651033\pi$
$331$	9.85929	−	17.0768i	0.541916	−	0.938625i	0.998794	−	0.0490963i	$-0.0156341\pi$
$332$	0.396044	+	0.878981i	0.0217357	+	0.0482404i
$333$		0			0
$334$	−0.618778	−	2.87960i	−0.0338581	−	0.157565i
$335$	−38.3781			−2.09682
$336$		0			0
$337$	−24.7720			−1.34942			−0.674709	−	0.738084i	$-0.735731\pi$
$337$	−24.7720			−1.34942			−0.674709	+	0.738084i	$0.735731\pi$
$338$	−3.53584	−	16.4547i	−0.192325	−	0.895019i
$339$		0			0
$340$	16.1652	+	35.8772i	0.876683	+	1.94571i
$341$	11.1617	−	19.3326i	0.604440	−	1.04692i
$342$		0			0
$343$	18.0723	−	4.04850i	0.975815	−	0.218599i
$344$	−2.25354	−	3.05858i	−0.121503	−	0.164908i
$345$		0			0
$346$	−28.7314	−	9.26477i	−1.54461	−	0.498077i
$347$	−7.49413	−	12.9802i	−0.402306	−	0.696815i	0.591698	−	0.806160i	$-0.298458\pi$
$347$	−7.49413	−	12.9802i	−0.402306	−	0.696815i	−0.994004	+	0.109345i	$0.965125\pi$
$348$		0			0
$349$	−27.4546			−1.46961			−0.734806	−	0.678278i	$-0.762727\pi$
$349$	−27.4546			−1.46961			−0.734806	+	0.678278i	$0.762727\pi$
$350$	8.55286	−	8.96145i	0.457170	−	0.479010i
$351$		0			0
$352$	−0.366699	−	32.9593i	−0.0195451	−	1.75674i
$353$	−20.7884	+	12.0022i	−1.10645	+	0.638811i	−0.937908	−	0.346883i	$-0.887240\pi$
$353$	−20.7884	+	12.0022i	−1.10645	+	0.638811i	−0.168544	+	0.985694i	$0.553907\pi$
$354$		0			0
$355$	2.70966	+	1.56442i	0.143814	+	0.0830310i
$356$	24.6572	+	2.48069i	1.30683	+	0.131476i
$357$		0			0
$358$	7.28928	−	6.59273i	0.385251	−	0.348437i
$359$	−11.8249	−	6.82714i	−0.624097	−	0.360322i	0.154366	−	0.988014i	$-0.450667\pi$
$359$	−11.8249	−	6.82714i	−0.624097	−	0.360322i	−0.778462	+	0.627691i	$0.784000\pi$
$360$		0			0
$361$	−9.26796	−	16.0526i	−0.487788	−	0.844873i
$362$	2.28066	+	10.6135i	0.119869	+	0.557833i
$363$		0			0
$364$	4.87704	−	2.64404i	0.255627	−	0.138585i
$365$		−	16.2739i		−	0.851813i
$366$		0			0
$367$	−17.3424	−	30.0379i	−0.905264	−	1.56796i	−0.820562	−	0.571557i	$-0.806340\pi$
$367$	−17.3424	−	30.0379i	−0.905264	−	1.56796i	−0.0847016	−	0.996406i	$-0.526994\pi$
$368$	−8.14377	+	2.72644i	−0.424524	+	0.142126i
$369$		0			0
$370$	6.51094	+	7.19885i	0.338488	+	0.374251i
$371$	17.6758	−	12.0165i	0.917682	−	0.623865i
$372$		0			0
$373$	−5.26744	−	3.04116i	−0.272738	−	0.157465i	0.357393	−	0.933954i	$-0.383666\pi$
$373$	−5.26744	−	3.04116i	−0.272738	−	0.157465i	−0.630131	+	0.776489i	$0.716999\pi$
$374$	17.2601	−	53.5262i	0.892501	−	2.76778i
$375$		0			0
$376$	31.0700	−	3.47542i	1.60231	−	0.179231i
$377$		−	6.93538i		−	0.357190i
$378$		0			0
$379$	19.0628			0.979189			0.489594	−	0.871950i	$-0.337145\pi$
$379$	19.0628			0.979189			0.489594	+	0.871950i	$0.337145\pi$
$380$	2.29451	−	3.18786i	0.117706	−	0.163534i
$381$		0			0
$382$	7.72989	−	23.9715i	0.395496	−	1.22649i
$383$	−4.12501	+	7.14473i	−0.210778	+	0.365079i	−0.951958	−	0.306228i	$-0.900933\pi$
$383$	−4.12501	+	7.14473i	−0.210778	+	0.365079i	0.741180	+	0.671306i	$0.234267\pi$
$384$		0			0
$385$	−44.3228	+	3.26180i	−2.25890	+	0.166237i
$386$	−14.4700	+	13.0872i	−0.736502	+	0.666123i
$387$		0			0
$388$	2.98677	+	6.62884i	0.151630	+	0.336528i
$389$	16.9926	−	9.81070i	0.861560	−	0.497422i	−0.00297421	−	0.999996i	$-0.500947\pi$
$389$	16.9926	−	9.81070i	0.861560	−	0.497422i	0.864534	+	0.502574i	$0.167613\pi$
$390$		0			0
$391$	−14.6533			−0.741051
$392$	−13.9511	−	14.0487i	−0.704638	−	0.709567i
$393$		0			0
$394$	−1.56488	+	0.336268i	−0.0788378	+	0.0169409i
$395$	31.6045	−	18.2469i	1.59019	−	0.918099i
$396$		0			0
$397$	−15.6816	+	27.1613i	−0.787035	+	1.36318i	0.140741	+	0.990047i	$0.455052\pi$
$397$	−15.6816	+	27.1613i	−0.787035	+	1.36318i	−0.927776	+	0.373138i	$0.878282\pi$
$398$	−8.94870	+	8.09358i	−0.448558	+	0.405694i
$399$		0			0
$400$	−12.9778	−	2.63801i	−0.648889	−	0.131901i
$401$	17.4562	−	30.2350i	0.871722	−	1.50987i	0.0115069	−	0.999934i	$-0.496337\pi$
$401$	17.4562	−	30.2350i	0.871722	−	1.50987i	0.860215	−	0.509932i	$-0.170330\pi$
$402$		0			0
$403$	−2.00831	−	3.47849i	−0.100041	−	0.173276i
$404$	4.06571	+	2.92636i	0.202277	+	0.145592i
$405$		0			0
$406$	−23.7523	+	6.96205i	−1.17881	+	0.345521i
$407$		−	13.8725i		−	0.687636i
$408$		0			0
$409$	11.8182	−	6.82325i	0.584373	−	0.337388i	−0.178496	−	0.983941i	$-0.557123\pi$
$409$	11.8182	−	6.82325i	0.584373	−	0.337388i	0.762869	+	0.646553i	$0.223790\pi$
$410$	−1.50044	+	4.65310i	−0.0741017	+	0.229800i
$411$		0			0
$412$	0.926229	−	9.20640i	0.0456320	−	0.453567i
$413$	−17.2213	+	11.7075i	−0.847405	+	0.576088i
$414$		0			0
$415$	−1.20348	−	0.694827i	−0.0590763	−	0.0341077i
$416$	−5.16880	−	2.90802i	−0.253421	−	0.142578i
$417$		0			0
$418$	−5.48828	+	1.17934i	−0.268440	+	0.0576834i
$419$			4.22322i			0.206318i	0.994665	+	0.103159i	$0.0328950\pi$
$419$			4.22322i			0.206318i	−0.994665	+	0.103159i	$0.967105\pi$
$420$		0			0
$421$		−	11.6892i		−	0.569697i	−0.958573	−	0.284849i	$-0.908057\pi$
$421$		−	11.6892i		−	0.569697i	0.958573	−	0.284849i	$-0.0919433\pi$
$422$	6.31167	+	29.3726i	0.307247	+	1.42983i
$423$		0			0
$424$	−20.9355	−	9.15411i	−1.01672	−	0.444563i
$425$	−19.5688	−	11.2981i	−0.949228	−	0.548037i
$426$		0			0
$427$	−3.76357	+	7.78842i	−0.182132	+	0.376908i
$428$	1.21513	−	12.0779i	0.0587354	−	0.583810i
$429$		0			0
$430$	5.21188	+	1.68063i	0.251339	+	0.0810472i
$431$	29.7064	−	17.1510i	1.43091	−	0.826136i	0.433719	−	0.901048i	$-0.357201\pi$
$431$	29.7064	−	17.1510i	1.43091	−	0.826136i	0.997190	+	0.0749129i	$0.0238679\pi$
$432$		0			0
$433$			14.1884i			0.681853i	0.940090	+	0.340926i	$0.110741\pi$
$433$			14.1884i			0.681853i	−0.940090	+	0.340926i	$0.889259\pi$
$434$	−9.89713	+	10.3699i	−0.475077	+	0.497773i
$435$		0			0
$436$	−17.0165	+	23.6418i	−0.814945	+	1.13224i
$437$	0.731303	+	1.26665i	0.0349830	+	0.0605923i
$438$		0			0
$439$	14.0252	−	24.2923i	0.669386	−	1.15941i	−0.308691	−	0.951163i	$-0.599891\pi$
$439$	14.0252	−	24.2923i	0.669386	−	1.15941i	0.978076	−	0.208247i	$-0.0667759\pi$
$440$	28.1824	+	38.2501i	1.34354	+	1.82350i
$441$		0			0
$442$	−6.78781	−	7.50498i	−0.322863	−	0.356975i
$443$	5.51040	−	9.54430i	0.261807	−	0.453463i	−0.704915	−	0.709292i	$-0.749015\pi$
$443$	5.51040	−	9.54430i	0.261807	−	0.453463i	0.966722	+	0.255828i	$0.0823482\pi$
$444$		0			0
$445$	−30.9352	+	17.8605i	−1.46647	+	0.846667i
$446$	−0.927595	−	4.31674i	−0.0439229	−	0.204403i
$447$		0			0
$448$	−4.77073	+	20.6214i	−0.225396	+	0.974267i
$449$	−30.2270			−1.42650			−0.713250	−	0.700910i	$-0.752778\pi$
$449$	−30.2270			−1.42650			−0.713250	+	0.700910i	$0.752778\pi$
$450$		0			0
$451$	6.05128	−	3.49371i	0.284944	−	0.164512i
$452$	−6.98155	+	3.14569i	−0.328384	+	0.147961i
$453$		0			0
$454$	−4.95825	−	5.48211i	−0.232702	−	0.257288i
$455$	−3.47921	+	7.19996i	−0.163108	+	0.337539i
$456$		0			0
$457$	−12.7386	+	22.0639i	−0.595887	+	1.03211i	0.397534	+	0.917587i	$0.369866\pi$
$457$	−12.7386	+	22.0639i	−0.595887	+	1.03211i	−0.993421	+	0.114519i	$0.963467\pi$
$458$	−38.2602	−	12.3374i	−1.78778	−	0.576490i
$459$		0			0
$460$	7.23156	−	10.0471i	0.337173	−	0.468449i
$461$	−27.9292			−1.30079			−0.650395	−	0.759596i	$-0.725397\pi$
$461$	−27.9292			−1.30079			−0.650395	+	0.759596i	$0.725397\pi$
$462$		0			0
$463$			19.4232i			0.902674i	0.892354	+	0.451337i	$0.149053\pi$
$463$			19.4232i			0.902674i	−0.892354	+	0.451337i	$0.850947\pi$
$464$	19.8209	+	17.5299i	0.920160	+	0.813804i
$465$		0			0
$466$	8.23652	+	2.65596i	0.381550	+	0.123035i
$467$	1.30760	+	0.754943i	0.0605085	+	0.0349346i	0.529949	−	0.848029i	$-0.322211\pi$
$467$	1.30760	+	0.754943i	0.0605085	+	0.0349346i	−0.469441	+	0.882964i	$0.655544\pi$
$468$		0			0
$469$	−19.8021	−	29.1282i	−0.914376	−	1.34501i
$470$	−33.4221	+	30.2283i	−1.54165	+	1.39433i
$471$		0			0
$472$	20.3971	+	8.91873i	0.938855	+	0.410518i
$473$	−3.91326	−	6.77797i	−0.179932	−	0.311651i
$474$		0			0
$475$			2.25541i			0.103485i
$476$	−18.8892	+	30.7808i	−0.865784	+	1.41083i
$477$		0			0
$478$	−12.2161	+	2.62504i	−0.558752	+	0.120067i
$479$	−7.12030	−	12.3327i	−0.325335	−	0.563496i	0.656245	−	0.754548i	$-0.272144\pi$
$479$	−7.12030	−	12.3327i	−0.325335	−	0.563496i	−0.981580	+	0.191051i	$0.938810\pi$
$480$		0			0
$481$	−2.16166	−	1.24803i	−0.0985631	−	0.0569054i
$482$	5.64951	+	6.24641i	0.257328	+	0.284516i
$483$		0			0
$484$	4.59499	−	45.6727i	0.208863	−	2.07603i
$485$	−9.07601	−	5.24004i	−0.412120	−	0.237938i
$486$		0			0
$487$	−6.40076	+	3.69548i	−0.290046	+	0.167458i	−0.637963	−	0.770067i	$-0.720223\pi$
$487$	−6.40076	+	3.69548i	−0.290046	+	0.167458i	0.347916	+	0.937526i	$0.386889\pi$
$488$	9.19001	−	1.02798i	0.416012	−	0.0465343i
$489$		0			0
$490$	28.1510	+	4.68798i	1.27173	+	0.211781i
$491$	−14.0578			−0.634420			−0.317210	−	0.948355i	$-0.602746\pi$
$491$	−14.0578			−0.634420			−0.317210	+	0.948355i	$0.602746\pi$
$492$		0			0
$493$	22.5742	+	39.0996i	1.01669	+	1.76096i
$494$	−0.309981	+	0.961297i	−0.0139467	+	0.0432508i
$495$		0			0
$496$	15.0175	+	3.05263i	0.674306	+	0.137067i
$497$	0.210751	+	2.86378i	0.00945346	+	0.128458i
$498$		0			0
$499$	−13.4960	+	23.3757i	−0.604162	+	1.04644i	0.388021	+	0.921651i	$0.373159\pi$
$499$	−13.4960	+	23.3757i	−0.604162	+	1.04644i	−0.992183	+	0.124789i	$0.960175\pi$
$500$	−8.87970	+	4.00094i	−0.397112	+	0.178928i
$501$		0			0
$502$	−2.95825	+	0.635678i	−0.132033	+	0.0283717i
$503$	−3.15505			−0.140677			−0.0703384	−	0.997523i	$-0.522408\pi$
$503$	−3.15505			−0.140677			−0.0703384	+	0.997523i	$0.522408\pi$
$504$		0			0
$505$	−7.22059			−0.321312
$506$	−17.2973	+	3.71689i	−0.768957	+	0.165236i
$507$		0			0
$508$	0.452219	+	1.00366i	0.0200640	+	0.0445301i
$509$	−10.8815	+	18.8473i	−0.482315	+	0.835394i	−0.999794	−	0.0203019i	$-0.993537\pi$
$509$	−10.8815	+	18.8473i	−0.482315	+	0.835394i	0.517479	+	0.855696i	$0.326871\pi$
$510$		0			0
$511$	12.3515	−	8.39689i	0.546399	−	0.371457i
$512$	21.3756	−	7.42178i	0.944678	−	0.327999i
$513$		0			0
$514$	−8.37095	+	25.9595i	−0.369227	+	1.14503i
$515$	6.66865	+	11.5504i	0.293856	+	0.508973i
$516$		0			0
$517$	64.4060			2.83257
$518$	−2.10430	+	8.65609i	−0.0924577	+	0.380327i
$519$		0			0
$520$	8.49565	−	0.950307i	0.372559	−	0.0416737i
$521$	34.9828	−	20.1973i	1.53262	−	0.884860i	0.533383	−	0.845874i	$-0.320920\pi$
$521$	34.9828	−	20.1973i	1.53262	−	0.884860i	0.999240	−	0.0389867i	$-0.0124130\pi$
$522$		0			0
$523$	25.4468	+	14.6917i	1.11271	+	0.642424i	0.939530	−	0.342466i	$-0.111262\pi$
$523$	25.4468	+	14.6917i	1.11271	+	0.642424i	0.173181	+	0.984890i	$0.444595\pi$
$524$	−5.57949	−	0.561335i	−0.243741	−	0.0245221i
$525$		0			0
$526$	23.0841	+	25.5230i	1.00651	+	1.11286i
$527$	22.6445	+	13.0738i	0.986410	+	0.569504i
$528$		0			0
$529$	−9.19517	−	15.9265i	−0.399790	−	0.692457i
$530$	32.2005	−	6.91934i	1.39870	−	0.300557i
$531$		0			0
$532$	3.60343	+	0.0966319i	0.156228	+	0.00418952i
$533$		−	1.25724i		−	0.0544570i
$534$		0			0
$535$	8.74866	+	15.1531i	0.378237	+	0.655126i
$536$	−15.0852	+	34.4998i	−0.651580	+	1.49016i
$537$		0			0
$538$	−21.9221	+	19.8272i	−0.945129	+	0.854813i
$539$	−25.3451	−	31.9571i	−1.09169	−	1.37649i
$540$		0			0
$541$	−26.5848	−	15.3487i	−1.14297	−	0.659893i	−0.195805	−	0.980643i	$-0.562732\pi$
$541$	−26.5848	−	15.3487i	−1.14297	−	0.659893i	−0.947164	+	0.320749i	$0.896065\pi$
$542$	26.9112	+	8.67782i	1.15593	+	0.372744i
$543$		0			0
$544$	38.6056	−	0.429518i	1.65520	−	0.0184154i
$545$		−	41.9872i		−	1.79853i
$546$		0			0
$547$	−15.7691			−0.674240			−0.337120	−	0.941462i	$-0.609453\pi$
$547$	−15.7691			−0.674240			−0.337120	+	0.941462i	$0.609453\pi$
$548$	−20.7175	−	14.9117i	−0.885006	−	0.636997i
$549$		0			0
$550$	−25.9655	−	8.37287i	−1.10717	−	0.357020i
$551$	2.25322	−	3.90268i	0.0959902	−	0.166260i
$552$		0			0
$553$	30.1561	+	14.5722i	1.28237	+	0.619674i
$554$	14.5064	+	16.0391i	0.616320	+	0.681437i
$555$		0			0
$556$	−5.02620	−	11.1552i	−0.213158	−	0.473085i
$557$	−19.2427	+	11.1098i	−0.815340	+	0.470737i	−0.848807	−	0.528703i	$-0.822679\pi$
$557$	−19.2427	+	11.1098i	−0.815340	+	0.470737i	0.0334668	+	0.999440i	$0.489345\pi$
$558$		0			0
$559$	−1.40822			−0.0595612
$560$	−11.7829	−	28.1420i	−0.497920	−	1.18922i
$561$		0			0
$562$	−1.66322	−	7.74012i	−0.0701588	−	0.326497i
$563$	−20.7809	+	11.9978i	−0.875809	+	0.505648i	−0.869274	−	0.494330i	$-0.835413\pi$
$563$	−20.7809	+	11.9978i	−0.875809	+	0.505648i	−0.00653450	+	0.999979i	$0.502080\pi$
$564$		0			0
$565$	5.51885	−	9.55893i	0.232180	−	0.402147i
$566$	10.6571	+	11.7831i	0.447951	+	0.495280i
$567$		0			0
$568$	2.47141	−	1.82091i	0.103698	−	0.0764038i
$569$	0.631897	−	1.09448i	0.0264905	−	0.0458829i	−0.852476	−	0.522766i	$-0.824900\pi$
$569$	0.631897	−	1.09448i	0.0264905	−	0.0458829i	0.878967	+	0.476883i	$0.158233\pi$
$570$		0			0
$571$	−10.3555	−	17.9363i	−0.433365	−	0.750611i	0.563795	−	0.825915i	$-0.309341\pi$
$571$	−10.3555	−	17.9363i	−0.433365	−	0.750611i	−0.997161	+	0.0753037i	$0.976007\pi$
$572$	−9.91622	−	7.13735i	−0.414618	−	0.298428i
$573$		0			0
$574$	−4.30579	+	1.26207i	−0.179720	+	0.0526779i
$575$			7.10831i			0.296437i
$576$		0			0
$577$	−27.2402	+	15.7271i	−1.13402	+	0.654728i	−0.944943	−	0.327234i	$-0.893884\pi$
$577$	−27.2402	+	15.7271i	−1.13402	+	0.654728i	−0.189079	+	0.981962i	$0.560550\pi$
$578$	39.8144	+	12.8386i	1.65606	+	0.534016i
$579$		0			0
$580$	−37.9493	−	3.81797i	−1.57576	−	0.158533i
$581$	−0.0936032	−	1.27192i	−0.00388332	−	0.0527683i
$582$		0			0
$583$	−40.7652	−	23.5358i	−1.68832	−	0.974752i
$584$	−14.6293	−	6.39672i	−0.605365	−	0.264698i
$585$		0			0
$586$	−5.26512	−	24.5022i	−0.217500	−	1.01218i
$587$			5.93391i			0.244919i	0.992474	+	0.122459i	$0.0390781\pi$
$587$			5.93391i			0.244919i	−0.992474	+	0.122459i	$0.960922\pi$
$588$		0			0
$589$		−	2.60989i		−	0.107539i
$590$	−31.3725	+	6.74143i	−1.29159	+	0.277540i
$591$		0			0
$592$	9.03061	−	3.02334i	0.371156	−	0.124259i
$593$	13.6001	+	7.85199i	0.558487	+	0.322443i	0.752538	−	0.658549i	$-0.228829\pi$
$593$	13.6001	+	7.85199i	0.558487	+	0.322443i	−0.194051	+	0.980991i	$0.562163\pi$
$594$		0			0
$595$	−3.82058	−	51.9158i	−0.156628	−	2.12834i
$596$	−4.02489	−	0.404932i	−0.164866	−	0.0165867i
$597$		0			0
$598$	−0.976960	+	3.02970i	−0.0399509	+	0.123894i
$599$	15.0452	−	8.68632i	0.614728	−	0.354914i	−0.160085	−	0.987103i	$-0.551177\pi$
$599$	15.0452	−	8.68632i	0.614728	−	0.354914i	0.774814	+	0.632190i	$0.217844\pi$
$600$		0			0
$601$		−	43.6846i		−	1.78193i	−0.454069	−	0.890966i	$-0.650028\pi$
$601$		−	43.6846i		−	1.78193i	0.454069	−	0.890966i	$-0.349972\pi$
$602$	1.41363	+	4.82287i	0.0576153	+	0.196565i
$603$		0			0
$604$	16.4366	−	22.8360i	0.668794	−	0.929184i
$605$	33.0830	+	57.3014i	1.34501	+	2.32963i
$606$		0			0
$607$	−9.60046	+	16.6285i	−0.389671	+	0.674929i	−0.992405	−	0.123012i	$-0.960745\pi$
$607$	−9.60046	+	16.6285i	−0.389671	+	0.674929i	0.602734	+	0.797942i	$0.294078\pi$
$608$	−1.96382	−	3.31568i	−0.0796432	−	0.134469i
$609$		0			0
$610$	−9.88573	+	8.94106i	−0.400262	+	0.362013i
$611$	5.79424	−	10.0359i	0.234410	−	0.406010i
$612$		0			0
$613$	−14.8672	+	8.58358i	−0.600480	+	0.346688i	−0.769231	−	0.638971i	$-0.779360\pi$
$613$	−14.8672	+	8.58358i	−0.600480	+	0.346688i	0.168750	+	0.985659i	$0.446027\pi$
$614$	−28.1679	+	6.05282i	−1.13676	+	0.244272i
$615$		0			0
$616$	−14.4897	+	41.1259i	−0.583806	+	1.65701i
$617$	16.8150			0.676946			0.338473	−	0.940976i	$-0.390090\pi$
$617$	16.8150			0.676946			0.338473	+	0.940976i	$0.390090\pi$
$618$		0			0
$619$	−30.1572	+	17.4113i	−1.21212	+	0.699818i	−0.963221	−	0.268712i	$-0.913402\pi$
$619$	−30.1572	+	17.4113i	−1.21212	+	0.699818i	−0.248899	+	0.968529i	$0.580069\pi$
$620$	−20.1394	+	9.07422i	−0.808816	+	0.364430i
$621$		0			0
$622$	−30.2833	+	27.3895i	−1.21425	+	1.09822i
$623$	−29.5175	−	14.2636i	−1.18259	−	0.571461i
$624$		0			0
$625$	15.2963	−	26.4940i	0.611852	−	1.05976i
$626$	2.04836	−	6.35225i	0.0818688	−	0.253887i
$627$		0			0
$628$	8.49734	+	6.11609i	0.339081	+	0.244059i
$629$	16.2491			0.647892
$630$		0			0
$631$		−	11.8869i		−	0.473210i	−0.971606	−	0.236605i	$-0.923965\pi$
$631$		−	11.8869i		−	0.473210i	0.971606	−	0.236605i	$-0.0760346\pi$
$632$	−3.98024	−	35.5829i	−0.158325	−	1.41541i
$633$		0			0
$634$	−11.0431	+	34.2463i	−0.438578	+	1.36009i
$635$	−1.37418	−	0.793381i	−0.0545325	−	0.0314844i
$636$		0			0
$637$	−7.25980	+	1.07434i	−0.287644	+	0.0425670i
$638$	36.5651	+	40.4284i	1.44763	+	1.60057i
$639$		0			0
$640$	−18.7577	+	26.6820i	−0.741464	+	1.05470i
$641$	−18.4447	−	31.9472i	−0.728523	−	1.26184i	−0.957507	−	0.288409i	$-0.906874\pi$
$641$	−18.4447	−	31.9472i	−0.728523	−	1.26184i	0.228984	−	0.973430i	$-0.426460\pi$
$642$		0			0
$643$			10.0475i			0.396235i	0.980178	+	0.198117i	$0.0634827\pi$
$643$			10.0475i			0.396235i	−0.980178	+	0.198117i	$0.936517\pi$
$644$	11.3568	+	0.304552i	0.447522	+	0.0120010i
$645$		0			0
$646$	−1.38137	−	6.42848i	−0.0543494	−	0.252925i
$647$	−19.5824	−	33.9177i	−0.769862	−	1.33344i	−0.937637	−	0.347615i	$-0.886992\pi$
$647$	−19.5824	−	33.9177i	−0.769862	−	1.33344i	0.167775	−	0.985825i	$-0.446342\pi$
$648$		0			0
$649$	39.7169	+	22.9306i	1.55903	+	0.900104i
$650$	−3.64065	+	3.29276i	−0.142798	+	0.129153i
$651$		0			0
$652$	0.195484	−	1.94304i	0.00765573	−	0.0760954i
$653$	−35.9422	−	20.7512i	−1.40653	−	0.812058i	−0.411475	−	0.911421i	$-0.634986\pi$
$653$	−35.9422	−	20.7512i	−1.40653	−	0.812058i	−0.995051	+	0.0993632i	$0.968319\pi$
$654$		0			0
$655$	7.00008	−	4.04150i	0.273516	−	0.157914i
$656$	3.59310	+	3.17780i	0.140287	+	0.124072i
$657$		0			0
$658$	−40.1876	−	9.76963i	−1.56667	−	0.380860i
$659$	35.4347			1.38034			0.690170	−	0.723647i	$-0.257536\pi$
$659$	35.4347			1.38034			0.690170	+	0.723647i	$0.257536\pi$
$660$		0			0
$661$	11.8165	+	20.4668i	0.459610	+	0.796067i	0.998940	−	0.0460268i	$-0.0146560\pi$
$661$	11.8165	+	20.4668i	0.459610	+	0.796067i	−0.539330	+	0.842094i	$0.681323\pi$
$662$	26.5405	+	8.55830i	1.03153	+	0.332628i
$663$		0			0
$664$	−1.09766	+	0.808744i	−0.0425974	+	0.0313854i
$665$	−4.29700	+	2.92121i	−0.166630	+	0.113280i
$666$		0			0
$667$	7.10140	−	12.3000i	0.274967	−	0.476257i
$668$	3.79764	−	1.71111i	0.146935	−	0.0662049i
$669$		0			0
$670$	−11.4025	−	53.0636i	−0.440516	−	2.05002i
$671$	19.0503			0.735428
$672$		0			0
$673$	8.69720			0.335253			0.167626	−	0.985851i	$-0.446390\pi$
$673$	8.69720			0.335253			0.167626	+	0.985851i	$0.446390\pi$
$674$	−7.35999	−	34.2511i	−0.283496	−	1.31930i
$675$		0			0
$676$	21.7006	−	9.77768i	0.834639	−	0.376065i
$677$	5.45947	−	9.45608i	0.209825	−	0.363427i	−0.741835	−	0.670583i	$-0.766044\pi$
$677$	5.45947	−	9.45608i	0.209825	−	0.363427i	0.951659	+	0.307156i	$0.0993774\pi$
$678$		0			0
$679$	−0.705909	−	9.59223i	−0.0270903	−	0.368116i
$680$	−44.8028	+	33.0103i	−1.71811	+	1.26589i
$681$		0			0
$682$	30.0465	+	9.68885i	1.15054	+	0.371005i
$683$	18.2758	+	31.6547i	0.699305	+	1.21123i	0.968708	+	0.248204i	$0.0798405\pi$
$683$	18.2758	+	31.6547i	0.699305	+	1.21123i	−0.269402	+	0.963028i	$0.586826\pi$
$684$		0			0
$685$	36.7936			1.40581
$686$	10.9671	+	23.7849i	0.418727	+	0.908112i
$687$		0			0
$688$	3.55941	−	4.02459i	0.135701	−	0.153436i
$689$	−7.33482	+	4.23476i	−0.279434	+	0.161332i
$690$		0			0
$691$	−4.59821	−	2.65478i	−0.174924	−	0.100993i	0.409981	−	0.912094i	$-0.365535\pi$
$691$	−4.59821	−	2.65478i	−0.174924	−	0.100993i	−0.584906	+	0.811101i	$0.698869\pi$
$692$	4.27360	−	42.4782i	0.162458	−	1.61478i
$693$		0			0
$694$	15.7206	−	14.2183i	0.596744	−	0.539720i
$695$	15.2733	+	8.81806i	0.579350	+	0.334488i
$696$		0			0
$697$	4.09222	+	7.08793i	0.155004	+	0.268475i
$698$	−8.15700	−	37.9602i	−0.308747	−	1.43681i
$699$		0			0
$700$	14.9317	+	9.16311i	0.564365	+	0.346333i
$701$			6.16681i			0.232917i	0.993196	+	0.116459i	$0.0371542\pi$
$701$			6.16681i			0.232917i	−0.993196	+	0.116459i	$0.962846\pi$
$702$		0			0
$703$	−0.810940	−	1.40459i	−0.0305852	−	0.0529751i
$704$	45.4623	−	10.2995i	1.71343	−	0.388178i
$705$		0			0
$706$	−22.7712	−	25.1771i	−0.857006	−	0.947553i
$707$	−3.72564	−	5.48028i	−0.140117	−	0.206107i
$708$		0			0
$709$	−1.73062	−	0.999172i	−0.0649947	−	0.0375247i	0.467151	−	0.884178i	$-0.345281\pi$
$709$	−1.73062	−	0.999172i	−0.0649947	−	0.0375247i	−0.532145	+	0.846653i	$0.678614\pi$
$710$	−1.35799	+	4.21132i	−0.0509644	+	0.158048i
$711$		0			0
$712$	3.89595	+	34.8294i	0.146007	+	1.30529i
$713$		−	8.22554i		−	0.308049i
$714$		0			0
$715$	17.6109			0.658611
$716$	11.2812	+	8.11979i	0.421597	+	0.303451i
$717$		0			0
$718$	5.92626	−	18.3782i	0.221166	−	0.685868i
$719$	6.72446	−	11.6471i	0.250780	−	0.434364i	−0.712961	−	0.701204i	$-0.752646\pi$
$719$	6.72446	−	11.6471i	0.250780	−	0.434364i	0.963741	+	0.266840i	$0.0859795\pi$
$720$		0			0
$721$	−5.32569	+	11.0211i	−0.198339	+	0.410447i
$722$	19.4415	−	17.5837i	0.723539	−	0.654399i
$723$		0			0
$724$	−13.9972	+	6.30672i	−0.520201	+	0.234388i
$725$	18.9672	−	10.9507i	0.704423	−	0.406699i
$726$		0			0
$727$	19.6532			0.728897			0.364448	−	0.931224i	$-0.381258\pi$
$727$	19.6532			0.728897			0.364448	+	0.931224i	$0.381258\pi$
$728$	5.10480	+	5.95769i	0.189196	+	0.220807i
$729$		0			0
$730$	22.5011	−	4.83511i	0.832803	−	0.178955i
$731$	7.93911	−	4.58365i	0.293639	−	0.169532i
$732$		0			0
$733$	12.6139	−	21.8480i	0.465907	−	0.806974i	−0.533335	−	0.845904i	$-0.679062\pi$
$733$	12.6139	−	21.8480i	0.465907	−	0.806974i	0.999242	+	0.0389298i	$0.0123949\pi$
$734$	36.3793	−	32.9030i	1.34279	−	1.21447i
$735$		0			0
$736$	−6.18931	−	10.4500i	−0.228141	−	0.385190i
$737$	−38.7849	+	67.1774i	−1.42866	+	2.47451i
$738$		0			0
$739$	−3.35478	−	5.81064i	−0.123407	−	0.213748i	0.797702	−	0.603052i	$-0.206049\pi$
$739$	−3.35478	−	5.81064i	−0.123407	−	0.213748i	−0.921109	+	0.389304i	$0.872716\pi$
$740$	−8.01905	+	11.1412i	−0.294786	+	0.409559i
$741$		0			0
$742$	21.8662	+	20.8693i	0.802735	+	0.766135i
$743$			26.0661i			0.956273i	0.878286	+	0.478137i	$0.158688\pi$
$743$			26.0661i			0.956273i	−0.878286	+	0.478137i	$0.841312\pi$
$744$		0			0
$745$	5.04967	−	2.91543i	0.185005	−	0.106813i
$746$	2.63986	−	8.18660i	0.0966522	−	0.299733i
$747$		0			0
$748$	79.1363	+	7.96167i	2.89351	+	0.291107i
$749$	−6.98682	+	14.4587i	−0.255293	+	0.528308i
$750$		0			0
$751$	−4.94762	−	2.85651i	−0.180541	−	0.104236i	0.407006	−	0.913426i	$-0.366573\pi$
$751$	−4.94762	−	2.85651i	−0.180541	−	0.104236i	−0.587547	+	0.809190i	$0.699906\pi$
$752$	14.0365	+	41.9264i	0.511857	+	1.52890i
$753$		0			0
$754$	9.58922	−	2.06056i	0.349219	−	0.0750412i
$755$			40.5561i			1.47599i
$756$		0			0
$757$		−	4.75364i		−	0.172774i	−0.996262	−	0.0863869i	$-0.972468\pi$
$757$		−	4.75364i		−	0.172774i	0.996262	−	0.0863869i	$-0.0275321\pi$
$758$	5.66371	+	26.3572i	0.205715	+	0.957336i
$759$		0			0
$760$	5.08942	+	2.22537i	0.184613	+	0.0807227i
$761$	23.6671	+	13.6642i	0.857931	+	0.495327i	0.863319	−	0.504659i	$-0.168382\pi$
$761$	23.6671	+	13.6642i	0.857931	+	0.495327i	−0.00538774	+	0.999985i	$0.501715\pi$
$762$		0			0
$763$	31.8674	−	21.6643i	1.15368	−	0.784300i
$764$	35.4409	+	3.56560i	1.28221	+	0.128999i
$765$		0			0
$766$	−11.1043	−	3.58070i	−0.401213	−	0.129376i
$767$	7.14622	−	4.12587i	0.258035	−	0.148977i
$768$		0			0
$769$		−	22.7151i		−	0.819127i	−0.912282	−	0.409564i	$-0.865681\pi$
$769$		−	22.7151i		−	0.819127i	0.912282	−	0.409564i	$-0.134319\pi$
$770$	−17.6786	−	60.3140i	−0.637094	−	2.17356i
$771$		0			0
$772$	−22.3943	−	16.1186i	−0.805987	−	0.580121i
$773$	−9.05937	−	15.6913i	−0.325843	−	0.564376i	0.655840	−	0.754900i	$-0.272315\pi$
$773$	−9.05937	−	15.6913i	−0.325843	−	0.564376i	−0.981683	+	0.190524i	$0.938981\pi$
$774$		0			0
$775$	6.34209	−	10.9848i	0.227814	−	0.394586i
$776$	−8.27799	+	6.09915i	−0.297162	+	0.218947i
$777$		0			0
$778$	18.6134	+	20.5800i	0.667324	+	0.737830i
$779$	0.408460	−	0.707474i	0.0146346	−	0.0253479i
$780$		0			0
$781$	5.47676	−	3.16201i	0.195974	−	0.113146i
$782$	−4.35364	−	20.2605i	−0.155686	−	0.724513i
$783$		0			0
$784$	15.2795	−	23.4635i	0.545696	−	0.837983i
$785$	−15.0910			−0.538622
$786$		0			0
$787$	4.25358	−	2.45581i	0.151624	−	0.0875400i	−0.422269	−	0.906471i	$-0.638766\pi$
$787$	4.25358	−	2.45581i	0.151624	−	0.0875400i	0.573892	+	0.818931i	$0.305433\pi$
$788$	−0.929882	−	2.06378i	−0.0331257	−	0.0735192i
$789$		0			0
$790$	34.6190	+	38.2767i	1.23169	+	1.36182i
$791$	10.1026	−	0.743469i	0.359207	−	0.0264347i
$792$		0			0
$793$	1.71385	−	2.96847i	0.0608604	−	0.105413i
$794$	−42.2137	−	13.6123i	−1.49811	−	0.483082i
$795$		0			0
$796$	−13.8493	−	9.96827i	−0.490877	−	0.353316i
$797$	23.8384			0.844398			0.422199	−	0.906503i	$-0.361258\pi$
$797$	23.8384			0.844398			0.422199	+	0.906503i	$0.361258\pi$
$798$		0			0
$799$			75.4394i			2.66885i
$800$	−0.208358	−	18.7275i	−0.00736658	−	0.662118i
$801$		0			0
$802$	46.9909	+	15.1528i	1.65931	+	0.535063i
$803$	−28.4859	−	16.4464i	−1.00525	−	0.580379i
$804$		0			0
$805$	−13.5427	+	9.20672i	−0.477319	+	0.324494i
$806$	4.21286	−	3.81028i	0.148392	−	0.134211i
$807$		0			0
$808$	−2.83818	+	6.49091i	−0.0998467	+	0.228350i
$809$	−0.597915	−	1.03562i	−0.0210216	−	0.0364104i	0.855323	−	0.518095i	$-0.173359\pi$
$809$	−0.597915	−	1.03562i	−0.0210216	−	0.0364104i	−0.876345	+	0.481684i	$0.840025\pi$
$810$		0			0
$811$		−	6.44559i		−	0.226335i	−0.993576	−	0.113168i	$-0.963900\pi$
$811$		−	6.44559i		−	0.226335i	0.993576	−	0.113168i	$-0.0360997\pi$
$812$	−16.6831	−	30.7727i	−0.585462	−	1.07991i
$813$		0			0
$814$	19.1809	−	4.12165i	0.672290	−	0.144464i
$815$	1.40744	+	2.43776i	0.0493005	+	0.0853910i
$816$		0			0
$817$	−0.792433	−	0.457511i	−0.0277237	−	0.0160063i
$818$	12.9455	+	14.3132i	0.452628	+	0.500450i
$819$		0			0
$820$	−6.87941	−	0.692117i	−0.240239	−	0.0241698i
$821$	−1.87701	−	1.08369i	−0.0655079	−	0.0378210i	0.466888	−	0.884316i	$-0.345375\pi$
$821$	−1.87701	−	1.08369i	−0.0655079	−	0.0378210i	−0.532396	+	0.846495i	$0.678708\pi$
$822$		0			0
$823$	−5.19529	+	2.99950i	−0.181096	+	0.104556i	−0.587808	−	0.809001i	$-0.700009\pi$
$823$	−5.19529	+	2.99950i	−0.181096	+	0.104556i	0.406711	+	0.913557i	$0.366675\pi$
$824$	13.0044	−	1.45465i	0.453031	−	0.0506752i
$825$		0			0
$826$	−21.3040	−	20.3327i	−0.741261	−	0.707464i
$827$	−21.0143			−0.730738			−0.365369	−	0.930863i	$-0.619057\pi$
$827$	−21.0143			−0.730738			−0.365369	+	0.930863i	$0.619057\pi$
$828$		0			0
$829$	−6.59891	−	11.4296i	−0.229190	−	0.396968i	0.728379	−	0.685175i	$-0.240274\pi$
$829$	−6.59891	−	11.4296i	−0.229190	−	0.396968i	−0.957568	+	0.288207i	$0.906941\pi$
$830$	0.603140	−	1.87043i	0.0209353	−	0.0649234i
$831$		0			0
$832$	2.48509	−	8.01066i	0.0861549	−	0.277720i
$833$	37.4317	−	29.6870i	1.29693	−	1.02859i
$834$		0			0
$835$	−3.00200	+	5.19962i	−0.103889	+	0.179940i
$836$	−3.26123	−	7.23799i	−0.112792	−	0.250331i
$837$		0			0
$838$	−5.83924	+	1.25475i	−0.201713	+	0.0433448i
$839$	−33.8661			−1.16919			−0.584594	−	0.811326i	$-0.698746\pi$
$839$	−33.8661			−1.16919			−0.584594	+	0.811326i	$0.698746\pi$
$840$		0			0
$841$	−14.7602			−0.508973
$842$	16.1621	−	3.47297i	0.556983	−	0.119686i
$843$		0			0
$844$	−38.7368	+	17.4537i	−1.33338	+	0.600781i
$845$	−17.1541	+	29.7118i	−0.590120	+	1.02212i
$846$		0			0
$847$	−26.4206	+	54.6753i	−0.907822	+	1.87867i
$848$	6.43684	−	31.6662i	0.221042	−	1.08742i
$849$		0			0
$850$	9.80723	−	30.4137i	0.336385	−	1.04318i
$851$	−2.55582	−	4.42681i	−0.0876124	−	0.151749i
$852$		0			0
$853$	−50.0832			−1.71482			−0.857408	−	0.514638i	$-0.827926\pi$
$853$	−50.0832			−1.71482			−0.857408	+	0.514638i	$0.827926\pi$
$854$	−11.8869	−	2.88970i	−0.406760	−	0.0988836i
$855$		0			0
$856$	17.0606	−	1.90837i	0.583120	−	0.0652267i
$857$	−42.6628	+	24.6314i	−1.45734	+	0.841393i	−0.998880	−	0.0473246i	$-0.984930\pi$
$857$	−42.6628	+	24.6314i	−1.45734	+	0.841393i	−0.458455	+	0.888717i	$0.651597\pi$
$858$		0			0
$859$	−3.38667	−	1.95530i	−0.115552	−	0.0667139i	0.441110	−	0.897453i	$-0.354585\pi$
$859$	−3.38667	−	1.95530i	−0.115552	−	0.0667139i	−0.556662	+	0.830739i	$0.687918\pi$
$860$	−0.775232	+	7.70554i	−0.0264352	+	0.262757i
$861$		0			0
$862$	32.5399	+	35.9779i	1.10831	+	1.22541i
$863$	37.4230	+	21.6062i	1.27390	+	0.735484i	0.975719	−	0.219027i	$-0.0702883\pi$
$863$	37.4230	+	21.6062i	1.27390	+	0.735484i	0.298176	+	0.954511i	$0.403622\pi$
$864$		0			0
$865$	30.7690	+	53.2935i	1.04618	+	1.81203i
$866$	−19.6177	+	4.21551i	−0.666636	+	0.143249i
$867$		0			0
$868$	−17.2785	−	10.6033i	−0.586472	−	0.359899i
$869$		−	73.7611i		−	2.50217i
$870$		0			0
$871$	6.97851	+	12.0871i	0.236458	+	0.409557i
$872$	−37.7441	−	16.5038i	−1.27818	−	0.558888i
$873$		0			0
$874$	−1.53407	+	1.38747i	−0.0518905	+	0.0469319i
$875$	12.8493	−	0.945604i	0.434386	−	0.0319673i
$876$		0			0
$877$	18.3069	+	10.5695i	0.618182	+	0.356907i	0.776161	−	0.630535i	$-0.217165\pi$
$877$	18.3069	+	10.5695i	0.618182	+	0.356907i	−0.157979	+	0.987442i	$0.550498\pi$
$878$	37.7549	+	12.1745i	1.27416	+	0.410869i
$879$		0			0
$880$	−44.5134	+	50.3309i	−1.50055	+	1.69665i
$881$			49.1167i			1.65478i	0.561625	+	0.827392i	$0.310177\pi$
$881$			49.1167i			1.65478i	−0.561625	+	0.827392i	$0.689823\pi$
$882$		0			0
$883$	37.8457			1.27361			0.636804	−	0.771025i	$-0.280256\pi$
$883$	37.8457			1.27361			0.636804	+	0.771025i	$0.280256\pi$
$884$	8.36005	−	11.6150i	0.281179	−	0.390654i
$885$		0			0
$886$	14.8336	+	4.78328i	0.498346	+	0.160697i
$887$	8.97039	−	15.5372i	0.301196	−	0.521687i	−0.675211	−	0.737625i	$-0.735947\pi$
$887$	8.97039	−	15.5372i	0.301196	−	0.521687i	0.976407	+	0.215937i	$0.0692807\pi$
$888$		0			0
$889$	−0.106880	−	1.45233i	−0.00358464	−	0.0487097i
$890$	−33.8859	−	37.4662i	−1.13586	−	1.25587i
$891$		0			0
$892$	5.69295	−	2.56508i	0.190614	−	0.0858853i
$893$	6.52108	−	3.76495i	0.218220	−	0.125989i
$894$		0			0
$895$	−20.0350			−0.669697
$896$	−29.9296	−	0.469481i	−0.999877	−	0.0156843i
$897$		0			0
$898$	−8.98070	−	41.7934i	−0.299690	−	1.39466i
$899$	−21.9483	+	12.6718i	−0.732016	+	0.422629i
$900$		0			0
$901$	27.5677	−	47.7487i	0.918413	−	1.59074i
$902$	6.62848	+	7.32881i	0.220704	+	0.244023i
$903$		0			0
$904$	−6.42367	−	8.71844i	−0.213648	−	0.289971i
$905$	11.0646	−	19.1645i	0.367801	−	0.637049i
$906$		0			0
$907$	−11.0887	−	19.2062i	−0.368194	−	0.637730i	0.621089	−	0.783740i	$-0.286690\pi$
$907$	−11.0887	−	19.2062i	−0.368194	−	0.637730i	−0.989283	+	0.146009i	$0.953357\pi$
$908$	6.10671	−	8.48431i	0.202658	−	0.281562i
$909$		0			0
$910$	−10.9887	−	2.67137i	−0.364273	−	0.0885551i
$911$			35.2495i			1.16787i	0.811801	+	0.583934i	$0.198487\pi$
$911$			35.2495i			1.16787i	−0.811801	+	0.583934i	$0.801513\pi$
$912$		0			0
$913$	−2.43246	+	1.40438i	−0.0805027	+	0.0464783i
$914$	−34.2915	−	11.0577i	−1.13426	−	0.365756i
$915$		0			0
$916$	5.69094	−	56.5661i	0.188034	−	1.86900i
$917$	6.67927	+	3.22760i	0.220569	+	0.106585i
$918$		0			0
$919$	15.1837	+	8.76632i	0.500864	+	0.289174i	0.729070	−	0.684439i	$-0.239953\pi$
$919$	15.1837	+	8.76632i	0.500864	+	0.289174i	−0.228206	+	0.973613i	$0.573286\pi$
$920$	16.0402	+	7.01364i	0.528830	+	0.231233i
$921$		0			0
$922$	−8.29800	−	38.6163i	−0.273280	−	1.27176i
$923$		−	1.13787i		−	0.0374535i
$924$		0			0
$925$		−	7.88239i		−	0.259171i
$926$	−26.8556	+	5.77081i	−0.882529	+	0.189641i
$927$		0			0
$928$	−18.3488	+	32.6136i	−0.602328	+	1.07059i
$929$	44.9106	+	25.9292i	1.47347	+	0.850708i	0.999554	−	0.0298619i	$-0.00950676\pi$
$929$	44.9106	+	25.9292i	1.47347	+	0.850708i	0.473916	+	0.880570i	$0.342840\pi$
$930$		0			0
$931$	−4.43428	−	1.75406i	−0.145328	−	0.0574870i
$932$	−1.22513	+	12.1774i	−0.0401304	+	0.398882i
$933$		0			0
$934$	−0.655324	+	2.03225i	−0.0214428	+	0.0664974i
$935$	−99.2852	+	57.3223i	−3.24697	+	1.87464i
$936$		0			0
$937$			36.9665i			1.20764i	0.797120	+	0.603821i	$0.206356\pi$
$937$			36.9665i			1.20764i	−0.797120	+	0.603821i	$0.793644\pi$
$938$	34.3907	−	36.0337i	1.12290	−	1.17654i
$939$		0			0
$940$	−51.7252	−	37.2300i	−1.68709	−	1.21431i
$941$	−26.2751	−	45.5098i	−0.856544	−	1.48358i	−0.875206	−	0.483751i	$-0.839274\pi$
$941$	−26.2751	−	45.5098i	−0.856544	−	1.48358i	0.0186621	−	0.999826i	$-0.494059\pi$
$942$		0			0
$943$	1.28733	−	2.22973i	0.0419214	−	0.0726099i
$944$	−6.27133	+	30.8520i	−0.204114	+	1.00415i
$945$		0			0
$946$	8.20891	−	7.42448i	0.266895	−	0.241391i
$947$	13.4671	−	23.3256i	0.437621	−	0.757982i	−0.559885	−	0.828571i	$-0.689155\pi$
$947$	13.4671	−	23.3256i	0.437621	−	0.757982i	0.997505	+	0.0705889i	$0.0224879\pi$
$948$		0			0
$949$	−5.12543	+	2.95917i	−0.166379	+	0.0960588i
$950$	−3.11844	+	0.670102i	−0.101176	+	0.0217410i
$951$		0			0
$952$	−48.1712	−	16.9719i	−1.56124	−	0.550063i
$953$	31.5488			1.02196			0.510982	−	0.859591i	$-0.329282\pi$
$953$	31.5488			1.02196			0.510982	+	0.859591i	$0.329282\pi$
$954$		0			0
$955$	−44.4645	+	25.6716i	−1.43884	+	0.830713i
$956$	−7.25903	−	16.1107i	−0.234774	−	0.521058i
$957$		0			0
$958$	14.9364	−	13.5091i	0.482572	−	0.436458i
$959$	18.9846	+	27.9256i	0.613043	+	0.901764i
$960$		0			0
$961$	8.16112	−	14.1355i	0.263262	−	0.455983i
$962$	1.08335	−	3.35962i	0.0349286	−	0.108319i
$963$		0			0
$964$	−6.95810	+	9.66717i	−0.224105	+	0.311359i
$965$	39.7716			1.28029
$966$		0			0
$967$		−	60.7635i		−	1.95402i	−0.213187	−	0.977011i	$-0.568384\pi$
$967$		−	60.7635i		−	1.95402i	0.213187	−	0.977011i	$-0.431616\pi$
$968$	64.5146	−	7.21648i	2.07358	−	0.231946i
$969$		0			0
$970$	4.54859	−	14.1058i	0.146046	−	0.452911i
$971$	13.9382	+	8.04723i	0.447299	+	0.258248i	0.706689	−	0.707525i	$-0.250188\pi$
$971$	13.9382	+	8.04723i	0.447299	+	0.258248i	−0.259390	+	0.965773i	$0.583521\pi$
$972$		0			0
$973$	1.18792	+	16.1420i	0.0380830	+	0.517489i
$974$	−7.01129	−	7.75207i	−0.224656	−	0.248392i
$975$		0			0
$976$	4.15177	+	12.4012i	0.132895	+	0.396952i
$977$	−16.3583	−	28.3334i	−0.523349	−	0.906467i	−0.999631	−	0.0271741i	$-0.991349\pi$
$977$	−16.3583	−	28.3334i	−0.523349	−	0.906467i	0.476282	−	0.879293i	$-0.341984\pi$
$978$		0			0
$979$			72.1991i			2.30749i
$980$	1.88207	+	40.3159i	0.0601205	+	1.28784i
$981$		0			0
$982$	−4.17670	−	19.4371i	−0.133284	−	0.620261i
$983$	18.5785	+	32.1789i	0.592561	+	1.02635i	0.993886	+	0.110410i	$0.0352165\pi$
$983$	18.5785	+	32.1789i	0.592561	+	1.02635i	−0.401325	+	0.915936i	$0.631450\pi$
$984$		0			0
$985$	2.82567	+	1.63140i	0.0900333	+	0.0519808i
$986$	−47.3542	+	42.8291i	−1.50806	+	1.36396i
$987$		0			0
$988$	−1.42124	−	0.142987i	−0.0452156	−	0.00454901i
$989$	−2.49749	−	1.44193i	−0.0794156	−	0.0458506i
$990$		0			0
$991$	38.2912	−	22.1074i	1.21636	−	0.702266i	0.252223	−	0.967669i	$-0.418838\pi$
$991$	38.2912	−	22.1074i	1.21636	−	0.702266i	0.964137	+	0.265403i	$0.0855051\pi$
$992$	0.241107	+	21.6710i	0.00765514	+	0.688053i
$993$		0			0
$994$	−3.89699	+	1.14225i	−0.123605	+	0.0362299i
$995$	24.5960			0.779747
$996$		0			0
$997$	−13.3432	−	23.1110i	−0.422582	−	0.731934i	0.573609	−	0.819129i	$-0.305543\pi$
$997$	−13.3432	−	23.1110i	−0.422582	−	0.731934i	−0.996191	+	0.0871953i	$0.972210\pi$
$998$	−36.3302	−	11.7151i	−1.15001	−	0.370835i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.c.19.8		32
3.2	odd	2		168.2.t.a.19.9	✓	32
4.3	odd	2		2016.2.bs.c.271.14		32
7.3	odd	6	inner	504.2.bk.c.451.3		32
8.3	odd	2	inner	504.2.bk.c.19.3		32
8.5	even	2		2016.2.bs.c.271.3		32
12.11	even	2		672.2.bb.a.271.10		32
21.2	odd	6		1176.2.p.a.979.7		32
21.5	even	6		1176.2.p.a.979.8		32
21.17	even	6		168.2.t.a.115.14	yes	32
24.5	odd	2		672.2.bb.a.271.15		32
24.11	even	2		168.2.t.a.19.14	yes	32
28.3	even	6		2016.2.bs.c.1711.3		32
56.3	even	6	inner	504.2.bk.c.451.8		32
56.45	odd	6		2016.2.bs.c.1711.14		32
84.23	even	6		4704.2.p.a.3919.30		32
84.47	odd	6		4704.2.p.a.3919.25		32
84.59	odd	6		672.2.bb.a.367.15		32
168.5	even	6		4704.2.p.a.3919.29		32
168.59	odd	6		168.2.t.a.115.9	yes	32
168.101	even	6		672.2.bb.a.367.10		32
168.107	even	6		1176.2.p.a.979.6		32
168.131	odd	6		1176.2.p.a.979.5		32
168.149	odd	6		4704.2.p.a.3919.26		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.9	✓	32	3.2	odd	2
168.2.t.a.19.14	yes	32	24.11	even	2
168.2.t.a.115.9	yes	32	168.59	odd	6
168.2.t.a.115.14	yes	32	21.17	even	6
504.2.bk.c.19.3		32	8.3	odd	2	inner
504.2.bk.c.19.8		32	1.1	even	1	trivial
504.2.bk.c.451.3		32	7.3	odd	6	inner
504.2.bk.c.451.8		32	56.3	even	6	inner
672.2.bb.a.271.10		32	12.11	even	2
672.2.bb.a.271.15		32	24.5	odd	2
672.2.bb.a.367.10		32	168.101	even	6
672.2.bb.a.367.15		32	84.59	odd	6
1176.2.p.a.979.5		32	168.131	odd	6
1176.2.p.a.979.6		32	168.107	even	6
1176.2.p.a.979.7		32	21.2	odd	6
1176.2.p.a.979.8		32	21.5	even	6
2016.2.bs.c.271.3		32	8.5	even	2
2016.2.bs.c.271.14		32	4.3	odd	2
2016.2.bs.c.1711.3		32	28.3	even	6
2016.2.bs.c.1711.14		32	56.45	odd	6
4704.2.p.a.3919.25		32	84.47	odd	6
4704.2.p.a.3919.26		32	168.149	odd	6
4704.2.p.a.3919.29		32	168.5	even	6
4704.2.p.a.3919.30		32	84.23	even	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.297109 + 1.38265i) q^{2} +(-1.82345 + 0.821596i) q^{4} +(1.44142 - 2.49662i) q^{5} +(2.63862 - 0.194181i) q^{7} +(-1.67775 - 2.27710i) q^{8} +O(q^{10})\)	\(q+(0.297109 + 1.38265i) q^{2} +(-1.82345 + 0.821596i) q^{4} +(1.44142 - 2.49662i) q^{5} +(2.63862 - 0.194181i) q^{7} +(-1.67775 - 2.27710i) q^{8} +(3.88021 + 1.25122i) q^{10} +(-2.91340 - 5.04616i) q^{11} -1.04841 q^{13} +(1.05244 + 3.59059i) q^{14} +(2.64996 - 2.99628i) q^{16} +(5.91062 - 3.41250i) q^{17} +(-0.589961 - 0.340614i) q^{19} +(-0.577155 + 5.73673i) q^{20} +(6.11148 - 5.52748i) q^{22} +(-1.85937 - 1.07351i) q^{23} +(-1.65540 - 2.86723i) q^{25} +(-0.311491 - 1.44958i) q^{26} +(-4.65185 + 2.52196i) q^{28} +6.61515i q^{29} +(1.91558 + 3.31788i) q^{31} +(4.93014 + 2.77375i) q^{32} +(6.47439 + 7.15845i) q^{34} +(3.31857 - 6.86751i) q^{35} +(2.06185 + 1.19041i) q^{37} +(0.295668 - 0.916911i) q^{38} +(-8.10338 + 0.906428i) q^{40} +1.19919i q^{41} +1.34319 q^{43} +(9.45835 + 6.80779i) q^{44} +(0.931851 - 2.88980i) q^{46} +(-5.52670 + 9.57253i) q^{47} +(6.92459 - 1.02474i) q^{49} +(3.47255 - 3.14072i) q^{50} +(1.91172 - 0.861368i) q^{52} +(6.99615 - 4.03923i) q^{53} -16.7978 q^{55} +(-4.86909 - 5.68260i) q^{56} +(-9.14645 + 1.96542i) q^{58} +(-6.81625 + 3.93537i) q^{59} +(-1.63471 + 2.83140i) q^{61} +(-4.01834 + 3.63435i) q^{62} +(-2.37034 + 7.64078i) q^{64} +(-1.51120 + 2.61747i) q^{65} +(-6.65629 - 11.5290i) q^{67} +(-7.97404 + 11.0787i) q^{68} +(10.4813 + 2.54802i) q^{70} +1.08533i q^{71} +(4.88878 - 2.82254i) q^{73} +(-1.03333 + 3.20450i) q^{74} +(1.35561 + 0.136384i) q^{76} +(-8.66721 - 12.7491i) q^{77} +(10.9630 + 6.32946i) q^{79} +(-3.66086 - 10.9348i) q^{80} +(-1.65806 + 0.356289i) q^{82} -0.482042i q^{83} -19.6754i q^{85} +(0.399075 + 1.85717i) q^{86} +(-6.60265 + 15.1003i) q^{88} +(-10.7308 - 6.19543i) q^{89} +(-2.76635 + 0.203581i) q^{91} +(4.27246 + 0.429839i) q^{92} +(-14.8775 - 4.79742i) q^{94} +(-1.70077 + 0.981939i) q^{95} -3.63532i q^{97} +(3.47421 + 9.26984i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

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