LMFDB - Embedded newform 975.2.o.p.476.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(476,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.476"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.o (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,12,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			476.10
Character	$\chi$	$=$	975.476
Dual form			975.2.o.p.551.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.260415 + 0.260415i) q^{2} +(-1.18585 + 1.26244i) q^{3} +1.86437i q^{4} +(-0.0199472 - 0.637571i) q^{6} +(-2.54331 + 2.54331i) q^{7} +(-1.00634 - 1.00634i) q^{8} +(-0.187534 - 2.99413i) q^{9} +(0.348374 + 0.348374i) q^{11} +(-2.35366 - 2.21086i) q^{12} +(0.339913 - 3.58949i) q^{13} -1.32463i q^{14} -3.20461 q^{16} -5.28437 q^{17} +(0.828552 + 0.730879i) q^{18} +(-3.44898 - 3.44898i) q^{19} +(-0.194812 - 6.22677i) q^{21} -0.181443 q^{22} +9.38135 q^{23} +(2.46381 - 0.0770834i) q^{24} +(0.846238 + 1.02327i) q^{26} +(4.00231 + 3.31383i) q^{27} +(-4.74167 - 4.74167i) q^{28} +6.80884i q^{29} +(-2.96376 - 2.96376i) q^{31} +(2.84720 - 2.84720i) q^{32} +(-0.852920 + 0.0266847i) q^{33} +(1.37613 - 1.37613i) q^{34} +(5.58217 - 0.349633i) q^{36} +(-1.76399 + 1.76399i) q^{37} +1.79633 q^{38} +(4.12845 + 4.68571i) q^{39} +(-2.21539 + 2.21539i) q^{41} +(1.67227 + 1.57081i) q^{42} -5.41717i q^{43} +(-0.649497 + 0.649497i) q^{44} +(-2.44304 + 2.44304i) q^{46} +(2.47000 + 2.47000i) q^{47} +(3.80017 - 4.04564i) q^{48} -5.93686i q^{49} +(6.26646 - 6.67123i) q^{51} +(6.69214 + 0.633724i) q^{52} -6.94843i q^{53} +(-1.90523 + 0.179291i) q^{54} +5.11886 q^{56} +(8.44410 - 0.264184i) q^{57} +(-1.77312 - 1.77312i) q^{58} +(-0.248775 - 0.248775i) q^{59} -3.60093 q^{61} +1.54361 q^{62} +(8.09197 + 7.13805i) q^{63} -4.92631i q^{64} +(0.215164 - 0.229062i) q^{66} +(1.34019 + 1.34019i) q^{67} -9.85202i q^{68} +(-11.1248 + 11.8434i) q^{69} +(11.6961 - 11.6961i) q^{71} +(-2.82439 + 3.20183i) q^{72} +(-6.48532 + 6.48532i) q^{73} -0.918735i q^{74} +(6.43016 - 6.43016i) q^{76} -1.77204 q^{77} +(-2.29534 - 0.145118i) q^{78} +2.66096 q^{79} +(-8.92966 + 1.12300i) q^{81} -1.15384i q^{82} +(-7.35570 + 7.35570i) q^{83} +(11.6090 - 0.363202i) q^{84} +(1.41071 + 1.41071i) q^{86} +(-8.59579 - 8.07424i) q^{87} -0.701163i q^{88} +(-2.54802 - 2.54802i) q^{89} +(8.26469 + 9.99370i) q^{91} +17.4903i q^{92} +(7.25614 - 0.227017i) q^{93} -1.28645 q^{94} +(0.218090 + 6.97078i) q^{96} +(-10.4901 - 10.4901i) q^{97} +(1.54604 + 1.54604i) q^{98} +(0.977745 - 1.10841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} + 16 q^{7} - 64 q^{16} - 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} + 24 q^{27} - 32 q^{28} + 32 q^{31} + 4 q^{33} - 16 q^{34} - 32 q^{37} - 8 q^{39} - 8 q^{42} - 40 q^{46} - 8 q^{48} - 32 q^{54}+ \cdots - 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 + 16 * q^7 - 64 * q^16 - 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 + 24 * q^27 - 32 * q^28 + 32 * q^31 + 4 * q^33 - 16 * q^34 - 32 * q^37 - 8 * q^39 - 8 * q^42 - 40 * q^46 - 8 * q^48 - 32 * q^54 + 36 * q^57 - 24 * q^58 + 8 * q^61 - 8 * q^63 - 48 * q^66 + 32 * q^67 - 132 * q^72 + 64 * q^73 + 16 * q^76 + 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 16 * q^87 + 8 * q^91 + 108 * q^93 - 32 * q^94 - 76 * q^96 - 24 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.260415	+	0.260415i	−0.184141	+	0.184141i	−0.793157	−	0.609017i	$-0.791564\pi$
$2$	−0.260415	+	0.260415i	−0.184141	+	0.184141i	0.609017	+	0.793157i	$0.291564\pi$
$3$	−1.18585	+	1.26244i	−0.684649	+	0.728873i
$3$	−1.18585	+	1.26244i	−0.684649	+	0.728873i
$4$			1.86437i			0.932184i
$5$		0			0
$5$		0			0
$6$	−0.0199472	−	0.637571i	−0.00814341	−	0.260287i
$7$	−2.54331	+	2.54331i	−0.961281	+	0.961281i	−0.999278	−	0.0379967i	$-0.987902\pi$
$7$	−2.54331	+	2.54331i	−0.961281	+	0.961281i	0.0379967	+	0.999278i	$0.487902\pi$
$8$	−1.00634	−	1.00634i	−0.355794	−	0.355794i
$9$	−0.187534	−	2.99413i	−0.0625113	−	0.998044i
$10$		0			0
$11$	0.348374	+	0.348374i	0.105039	+	0.105039i	0.757673	−	0.652634i	$-0.226336\pi$
$11$	0.348374	+	0.348374i	0.105039	+	0.105039i	−0.652634	+	0.757673i	$0.726336\pi$
$12$	−2.35366	−	2.21086i	−0.679444	−	0.638219i
$13$	0.339913	−	3.58949i	0.0942750	−	0.995546i
$13$	0.339913	−	3.58949i	0.0942750	−	0.995546i
$14$		−	1.32463i		−	0.354022i
$15$		0			0
$16$	−3.20461			−0.801152
$17$	−5.28437			−1.28165			−0.640824	−	0.767688i	$-0.721407\pi$
$17$	−5.28437			−1.28165			−0.640824	+	0.767688i	$0.721407\pi$
$18$	0.828552	+	0.730879i	0.195292	+	0.172270i
$19$	−3.44898	−	3.44898i	−0.791249	−	0.791249i	0.190448	−	0.981697i	$-0.439006\pi$
$19$	−3.44898	−	3.44898i	−0.791249	−	0.791249i	−0.981697	+	0.190448i	$0.939006\pi$
$20$		0			0
$21$	−0.194812	−	6.22677i	−0.0425115	−	1.35879i
$22$	−0.181443			−0.0386838
$23$	9.38135			1.95615			0.978073	−	0.208262i	$-0.0667807\pi$
$23$	9.38135			1.95615			0.978073	+	0.208262i	$0.0667807\pi$
$24$	2.46381	−	0.0770834i	0.502923	−	0.0157346i
$25$		0			0
$26$	0.846238	+	1.02327i	0.165961	+	0.200681i
$27$	4.00231	+	3.31383i	0.770246	+	0.637747i
$28$	−4.74167	−	4.74167i	−0.896091	−	0.896091i
$29$			6.80884i			1.26437i	0.774817	+	0.632185i	$0.217842\pi$
$29$			6.80884i			1.26437i	−0.774817	+	0.632185i	$0.782158\pi$
$30$		0			0
$31$	−2.96376	−	2.96376i	−0.532306	−	0.532306i	0.388952	−	0.921258i	$-0.372837\pi$
$31$	−2.96376	−	2.96376i	−0.532306	−	0.532306i	−0.921258	+	0.388952i	$0.872837\pi$
$32$	2.84720	−	2.84720i	0.503319	−	0.503319i
$33$	−0.852920	+	0.0266847i	−0.148474	+	0.00464521i
$34$	1.37613	−	1.37613i	0.236004	−	0.236004i
$35$		0			0
$36$	5.58217	−	0.349633i	0.930361	−	0.0582721i
$37$	−1.76399	+	1.76399i	−0.289998	+	0.289998i	−0.837079	−	0.547082i	$-0.815739\pi$
$37$	−1.76399	+	1.76399i	−0.289998	+	0.289998i	0.547082	+	0.837079i	$0.315739\pi$
$38$	1.79633			0.291403
$39$	4.12845	+	4.68571i	0.661081	+	0.750314i
$40$		0			0
$41$	−2.21539	+	2.21539i	−0.345986	+	0.345986i	−0.858612	−	0.512626i	$-0.828673\pi$
$41$	−2.21539	+	2.21539i	−0.345986	+	0.345986i	0.512626	+	0.858612i	$0.328673\pi$
$42$	1.67227	+	1.57081i	0.258037	+	0.242381i
$43$		−	5.41717i		−	0.826110i	−0.910706	−	0.413055i	$-0.864462\pi$
$43$		−	5.41717i		−	0.826110i	0.910706	−	0.413055i	$-0.135538\pi$
$44$	−0.649497	+	0.649497i	−0.0979153	+	0.0979153i
$45$		0			0
$46$	−2.44304	+	2.44304i	−0.360207	+	0.360207i
$47$	2.47000	+	2.47000i	0.360286	+	0.360286i	0.863918	−	0.503632i	$-0.168003\pi$
$47$	2.47000	+	2.47000i	0.360286	+	0.360286i	−0.503632	+	0.863918i	$0.668003\pi$
$48$	3.80017	−	4.04564i	0.548508	−	0.583938i
$49$		−	5.93686i		−	0.848123i
$50$		0			0
$51$	6.26646	−	6.67123i	0.877480	−	0.934159i
$52$	6.69214	+	0.633724i	0.928032	+	0.0878817i
$53$		−	6.94843i		−	0.954441i	−0.878784	−	0.477220i	$-0.841644\pi$
$53$		−	6.94843i		−	0.954441i	0.878784	−	0.477220i	$-0.158356\pi$
$54$	−1.90523	+	0.179291i	−0.259269	+	0.0243984i
$55$		0			0
$56$	5.11886			0.684036
$57$	8.44410	−	0.264184i	1.11845	−	0.0349921i
$58$	−1.77312	−	1.77312i	−0.232822	−	0.232822i
$59$	−0.248775	−	0.248775i	−0.0323877	−	0.0323877i	0.690727	−	0.723115i	$-0.257290\pi$
$59$	−0.248775	−	0.248775i	−0.0323877	−	0.0323877i	−0.723115	+	0.690727i	$0.757290\pi$
$60$		0			0
$61$	−3.60093			−0.461052			−0.230526	−	0.973066i	$-0.574045\pi$
$61$	−3.60093			−0.461052			−0.230526	+	0.973066i	$0.574045\pi$
$62$	1.54361			0.196039
$63$	8.09197	+	7.13805i	1.01949	+	0.899310i
$64$		−	4.92631i		−	0.615789i
$65$		0			0
$66$	0.215164	−	0.229062i	0.0264848	−	0.0281956i
$67$	1.34019	+	1.34019i	0.163731	+	0.163731i	0.784217	−	0.620486i	$-0.213065\pi$
$67$	1.34019	+	1.34019i	0.163731	+	0.163731i	−0.620486	+	0.784217i	$0.713065\pi$
$68$		−	9.85202i		−	1.19473i
$69$	−11.1248	+	11.8434i	−1.33927	+	1.42578i
$70$		0			0
$71$	11.6961	−	11.6961i	1.38807	−	1.38807i	0.558713	−	0.829361i	$-0.311295\pi$
$71$	11.6961	−	11.6961i	1.38807	−	1.38807i	0.829361	−	0.558713i	$-0.188705\pi$
$72$	−2.82439	+	3.20183i	−0.332857	+	0.377339i
$73$	−6.48532	+	6.48532i	−0.759050	+	0.759050i	−0.976149	−	0.217100i	$-0.930340\pi$
$73$	−6.48532	+	6.48532i	−0.759050	+	0.759050i	0.217100	+	0.976149i	$0.430340\pi$
$74$		−	0.918735i		−	0.106801i
$75$		0			0
$76$	6.43016	−	6.43016i	0.737590	−	0.737590i
$77$	−1.77204			−0.201943
$78$	−2.29534	−	0.145118i	−0.259896	−	0.0164314i
$79$	2.66096			0.299382			0.149691	−	0.988733i	$-0.452172\pi$
$79$	2.66096			0.299382			0.149691	+	0.988733i	$0.452172\pi$
$80$		0			0
$81$	−8.92966	+	1.12300i	−0.992185	+	0.124778i
$82$		−	1.15384i		−	0.127420i
$83$	−7.35570	+	7.35570i	−0.807393	+	0.807393i	−0.984239	−	0.176846i	$-0.943411\pi$
$83$	−7.35570	+	7.35570i	−0.807393	+	0.807393i	0.176846	+	0.984239i	$0.443411\pi$
$84$	11.6090	−	0.363202i	1.26664	−	0.0396286i
$85$		0			0
$86$	1.41071	+	1.41071i	0.152121	+	0.152121i
$87$	−8.59579	−	8.07424i	−0.921565	−	0.865650i
$88$		−	0.701163i		−	0.0747442i
$89$	−2.54802	−	2.54802i	−0.270090	−	0.270090i	0.559046	−	0.829136i	$-0.311167\pi$
$89$	−2.54802	−	2.54802i	−0.270090	−	0.270090i	−0.829136	+	0.559046i	$0.811167\pi$
$90$		0			0
$91$	8.26469	+	9.99370i	0.866375	+	1.04762i
$92$			17.4903i			1.82349i
$93$	7.25614	−	0.227017i	0.752426	−	0.0235406i
$94$	−1.28645			−0.132687
$95$		0			0
$96$	0.218090	+	6.97078i	0.0222587	+	0.711452i
$97$	−10.4901	−	10.4901i	−1.06511	−	1.06511i	−0.997727	−	0.0673840i	$-0.978535\pi$
$97$	−10.4901	−	10.4901i	−1.06511	−	1.06511i	−0.0673840	−	0.997727i	$-0.521465\pi$
$98$	1.54604	+	1.54604i	0.156174	+	0.156174i
$99$	0.977745	−	1.10841i	0.0982670	−	0.111399i
$100$		0			0
$101$	2.56854			0.255579			0.127790	−	0.991801i	$-0.459212\pi$
$101$	2.56854			0.255579			0.127790	+	0.991801i	$0.459212\pi$
$102$	0.105409	+	3.36916i	0.0104370	+	0.333597i
$103$		−	15.2419i		−	1.50183i	−0.660400	−	0.750914i	$-0.729613\pi$
$103$		−	15.2419i		−	1.50183i	0.660400	−	0.750914i	$-0.270387\pi$
$104$	−3.95431	+	3.27017i	−0.387752	+	0.320667i
$105$		0			0
$106$	1.80947	+	1.80947i	0.175752	+	0.175752i
$107$		−	8.85806i		−	0.856341i	−0.903698	−	0.428171i	$-0.859158\pi$
$107$		−	8.85806i		−	0.856341i	0.903698	−	0.428171i	$-0.140842\pi$
$108$	−6.17820	+	7.46179i	−0.594498	+	0.718011i
$109$	−7.99281	−	7.99281i	−0.765573	−	0.765573i	0.211751	−	0.977324i	$-0.432083\pi$
$109$	−7.99281	−	7.99281i	−0.765573	−	0.765573i	−0.977324	+	0.211751i	$0.932083\pi$
$110$		0			0
$111$	−0.135118	−	4.31875i	−0.0128248	−	0.409918i
$112$	8.15031	−	8.15031i	0.770132	−	0.770132i
$113$			11.4219i			1.07448i	0.843430	+	0.537239i	$0.180533\pi$
$113$			11.4219i			1.07448i	−0.843430	+	0.537239i	$0.819467\pi$
$114$	−2.13017	+	2.26776i	−0.199509	+	0.212396i
$115$		0			0
$116$	−12.6942			−1.17863
$117$	−10.8112	−	0.344594i	−0.999492	−	0.0318577i
$118$	0.129569			0.0119278
$119$	13.4398	−	13.4398i	1.23202	−	1.23202i
$120$		0			0
$121$		−	10.7573i		−	0.977934i
$122$	0.937735	−	0.937735i	0.0848986	−	0.0848986i
$123$	−0.169694	−	5.42392i	−0.0153008	−	0.489058i
$124$	5.52553	−	5.52553i	0.496207	−	0.496207i
$125$		0			0
$126$	−3.96612	+	0.248413i	−0.353330	+	0.0221304i
$127$			2.64759i			0.234936i	0.993077	+	0.117468i	$0.0374777\pi$
$127$			2.64759i			0.234936i	−0.993077	+	0.117468i	$0.962522\pi$
$128$	6.97729	+	6.97729i	0.616711	+	0.616711i
$129$	6.83887	+	6.42393i	0.602129	+	0.565595i
$130$		0			0
$131$		−	5.12086i		−	0.447412i	−0.974657	−	0.223706i	$-0.928184\pi$
$131$		−	5.12086i		−	0.447412i	0.974657	−	0.223706i	$-0.0718155\pi$
$132$	−0.0497501	−	1.59016i	−0.00433019	−	0.138405i
$133$	17.5436			1.52123
$134$	−0.698012			−0.0602991
$135$		0			0
$136$	5.31786	+	5.31786i	0.456003	+	0.456003i
$137$	−8.25322	−	8.25322i	−0.705120	−	0.705120i	0.260385	−	0.965505i	$-0.416151\pi$
$137$	−8.25322	−	8.25322i	−0.705120	−	0.705120i	−0.965505	+	0.260385i	$0.916151\pi$
$138$	−0.187132	−	5.98127i	−0.0159297	−	0.509160i
$139$	−0.517263			−0.0438737			−0.0219369	−	0.999759i	$-0.506983\pi$
$139$	−0.517263			−0.0438737			−0.0219369	+	0.999759i	$0.506983\pi$
$140$		0			0
$141$	−6.04728	+	0.189197i	−0.509273	+	0.0159332i
$142$			6.09168i			0.511202i
$143$	1.36890	−	1.13207i	0.114473	−	0.0946682i
$144$	0.600973	+	9.59502i	0.0500811	+	0.799585i
$145$		0			0
$146$		−	3.37774i		−	0.279544i
$147$	7.49496	+	7.04021i	0.618174	+	0.580666i
$148$	−3.28872	−	3.28872i	−0.270331	−	0.270331i
$149$	0.824702	−	0.824702i	0.0675622	−	0.0675622i	−0.672518	−	0.740080i	$-0.734787\pi$
$149$	0.824702	−	0.824702i	0.0675622	−	0.0675622i	0.740080	+	0.672518i	$0.234787\pi$
$150$		0			0
$151$	−6.80265	+	6.80265i	−0.553591	+	0.553591i	−0.927475	−	0.373884i	$-0.878026\pi$
$151$	−6.80265	+	6.80265i	−0.553591	+	0.553591i	0.373884	+	0.927475i	$0.378026\pi$
$152$			6.94167i			0.563044i
$153$	0.991000	+	15.8221i	0.0801176	+	1.27914i
$154$	0.461466	−	0.461466i	0.0371860	−	0.0371860i
$155$		0			0
$156$	−8.73589	+	7.69696i	−0.699431	+	0.616250i
$157$	−8.40663			−0.670922			−0.335461	−	0.942054i	$-0.608892\pi$
$157$	−8.40663			−0.670922			−0.335461	+	0.942054i	$0.608892\pi$
$158$	−0.692954	+	0.692954i	−0.0551284	+	0.0551284i
$159$	8.77202	+	8.23978i	0.695666	+	0.653457i
$160$		0			0
$161$	−23.8597	+	23.8597i	−1.88041	+	1.88041i
$162$	2.03297	−	2.61786i	0.159725	−	0.205679i
$163$	−6.91500	+	6.91500i	−0.541625	+	0.541625i	−0.924005	−	0.382380i	$-0.875104\pi$
$163$	−6.91500	+	6.91500i	−0.541625	+	0.541625i	0.382380	+	0.924005i	$0.375104\pi$
$164$	−4.13030	−	4.13030i	−0.322522	−	0.322522i
$165$		0			0
$166$		−	3.83106i		−	0.297348i
$167$	−2.11987	−	2.11987i	−0.164040	−	0.164040i	0.620314	−	0.784354i	$-0.287005\pi$
$167$	−2.11987	−	2.11987i	−0.164040	−	0.164040i	−0.784354	+	0.620314i	$0.787005\pi$
$168$	−6.07018	+	6.46228i	−0.468325	+	0.498576i
$169$	−12.7689	−	2.44023i	−0.982224	−	0.187710i
$170$		0			0
$171$	−9.67989	+	10.9735i	−0.740240	+	0.839164i
$172$	10.0996			0.770087
$173$	−21.2987			−1.61931			−0.809655	−	0.586906i	$-0.800346\pi$
$173$	−21.2987			−1.61931			−0.809655	+	0.586906i	$0.800346\pi$
$174$	4.34112	−	0.135817i	0.329099	−	0.0102963i
$175$		0			0
$176$	−1.11640	−	1.11640i	−0.0841518	−	0.0841518i
$177$	0.609074	−	0.0190556i	0.0457808	−	0.00143231i
$178$	1.32708			0.0994692
$179$	−2.77071			−0.207093			−0.103546	−	0.994625i	$-0.533019\pi$
$179$	−2.77071			−0.207093			−0.103546	+	0.994625i	$0.533019\pi$
$180$		0			0
$181$			20.1030i			1.49425i	0.664686	+	0.747123i	$0.268565\pi$
$181$			20.1030i			1.49425i	−0.664686	+	0.747123i	$0.731435\pi$
$182$	−4.75475	−	0.450260i	−0.352446	−	0.0333755i
$183$	4.27015	−	4.54598i	0.315659	−	0.336048i
$184$	−9.44081	−	9.44081i	−0.695985	−	0.695985i
$185$		0			0
$186$	−1.83049	+	1.94872i	−0.134218	+	0.142887i
$187$	−1.84094	−	1.84094i	−0.134623	−	0.134623i
$188$	−4.60499	+	4.60499i	−0.335853	+	0.335853i
$189$	−18.6072	+	1.75102i	−1.35348	+	0.127368i
$190$		0			0
$191$		−	13.9497i		−	1.00937i	−0.863304	−	0.504684i	$-0.831609\pi$
$191$		−	13.9497i		−	1.00937i	0.863304	−	0.504684i	$-0.168391\pi$
$192$	6.21919	+	5.84185i	0.448832	+	0.421599i
$193$	0.516880	−	0.516880i	0.0372058	−	0.0372058i	−0.688259	−	0.725465i	$-0.741625\pi$
$193$	0.516880	−	0.516880i	0.0372058	−	0.0372058i	0.725465	+	0.688259i	$0.241625\pi$
$194$	5.46356			0.392261
$195$		0			0
$196$	11.0685			0.790607
$197$	3.72469	−	3.72469i	0.265373	−	0.265373i	−0.561859	−	0.827233i	$-0.689914\pi$
$197$	3.72469	−	3.72469i	0.265373	−	0.265373i	0.827233	+	0.561859i	$0.189914\pi$
$198$	0.0340268	+	0.543265i	0.00241818	+	0.0386081i
$199$			14.3661i			1.01839i	0.860652	+	0.509193i	$0.170056\pi$
$199$			14.3661i			1.01839i	−0.860652	+	0.509193i	$0.829944\pi$
$200$		0			0
$201$	−3.28119	+	0.102656i	−0.231437	+	0.00724080i
$202$	−0.668886	+	0.668886i	−0.0470626	+	0.0470626i
$203$	−17.3170	−	17.3170i	−1.21542	−	1.21542i
$204$	12.4376	+	11.6830i	0.870808	+	0.817973i
$205$		0			0
$206$	3.96921	+	3.96921i	0.276548	+	0.276548i
$207$	−1.75932	−	28.0890i	−0.122281	−	1.95232i
$208$	−1.08929	+	11.5029i	−0.0755286	+	0.797584i
$209$		−	2.40306i		−	0.166223i
$210$		0			0
$211$	9.49226			0.653474			0.326737	−	0.945115i	$-0.394051\pi$
$211$	9.49226			0.653474			0.326737	+	0.945115i	$0.394051\pi$
$212$	12.9544			0.889715
$213$	0.895898	+	28.6355i	0.0613859	+	1.96207i
$214$	2.30677	+	2.30677i	0.157687	+	0.157687i
$215$		0			0
$216$	−0.692846	−	7.36251i	−0.0471422	−	0.500956i
$217$	15.0755			1.02339
$218$	4.16289			0.281947
$219$	−0.496762	−	15.8780i	−0.0335681	−	1.07293i
$220$		0			0
$221$	−1.79623	+	18.9682i	−0.120827	+	1.27594i
$222$	1.15985	+	1.08948i	0.0778442	+	0.0731211i
$223$	−4.69628	−	4.69628i	−0.314486	−	0.314486i	0.532159	−	0.846645i	$-0.321381\pi$
$223$	−4.69628	−	4.69628i	−0.314486	−	0.314486i	−0.846645	+	0.532159i	$0.821381\pi$
$224$			14.4826i			0.967662i
$225$		0			0
$226$	−2.97442	−	2.97442i	−0.197855	−	0.197855i
$227$	−7.76531	+	7.76531i	−0.515402	+	0.515402i	−0.916177	−	0.400775i	$-0.868741\pi$
$227$	−7.76531	+	7.76531i	−0.515402	+	0.515402i	0.400775	+	0.916177i	$0.368741\pi$
$228$	0.492537	+	15.7429i	0.0326191	+	1.04260i
$229$	−5.52070	+	5.52070i	−0.364818	+	0.364818i	−0.865583	−	0.500765i	$-0.833052\pi$
$229$	−5.52070	+	5.52070i	−0.364818	+	0.364818i	0.500765	+	0.865583i	$0.333052\pi$
$230$		0			0
$231$	2.10137	−	2.23711i	0.138260	−	0.147191i
$232$	6.85200	−	6.85200i	0.449856	−	0.449856i
$233$	9.73604			0.637829			0.318915	−	0.947783i	$-0.396682\pi$
$233$	9.73604			0.637829			0.318915	+	0.947783i	$0.396682\pi$
$234$	2.90512	−	2.72565i	0.189914	−	0.178181i
$235$		0			0
$236$	0.463808	−	0.463808i	0.0301913	−	0.0301913i
$237$	−3.15550	+	3.35932i	−0.204971	+	0.218211i
$238$			6.99984i			0.453732i
$239$	−16.1376	+	16.1376i	−1.04385	+	1.04385i	−0.0448582	+	0.998993i	$0.514284\pi$
$239$	−16.1376	+	16.1376i	−1.04385	+	1.04385i	−0.998993	+	0.0448582i	$0.985716\pi$
$240$		0			0
$241$	−6.35964	+	6.35964i	−0.409660	+	0.409660i	−0.881620	−	0.471960i	$-0.843547\pi$
$241$	−6.35964	+	6.35964i	−0.409660	+	0.409660i	0.471960	+	0.881620i	$0.343547\pi$
$242$	2.80135	+	2.80135i	0.180078	+	0.180078i
$243$	9.17148	−	12.6049i	0.588351	−	0.808606i
$244$		−	6.71346i		−	0.429786i
$245$		0			0
$246$	1.45666	+	1.36828i	0.0928731	+	0.0872381i
$247$	−13.5524	+	11.2077i	−0.862320	+	0.713130i
$248$			5.96508i			0.378783i
$249$	−0.563431	−	18.0089i	−0.0357060	−	1.14127i
$250$		0			0
$251$	4.33610			0.273692			0.136846	−	0.990592i	$-0.456303\pi$
$251$	4.33610			0.273692			0.136846	+	0.990592i	$0.456303\pi$
$252$	−13.3080	+	15.0864i	−0.838323	+	0.950354i
$253$	3.26821	+	3.26821i	0.205471	+	0.205471i
$254$	−0.689471	−	0.689471i	−0.0432612	−	0.0432612i
$255$		0			0
$256$	6.21864			0.388665
$257$	4.95572			0.309129			0.154565	−	0.987983i	$-0.450602\pi$
$257$	4.95572			0.309129			0.154565	+	0.987983i	$0.450602\pi$
$258$	−3.45383	+	0.108057i	−0.215026	+	0.00672736i
$259$		−	8.97273i		−	0.557538i
$260$		0			0
$261$	20.3866	−	1.27689i	1.26190	−	0.0790375i
$262$	1.33355	+	1.33355i	0.0823868	+	0.0823868i
$263$			21.5950i			1.33160i	0.746129	+	0.665801i	$0.231910\pi$
$263$			21.5950i			1.33160i	−0.746129	+	0.665801i	$0.768090\pi$
$264$	0.885180	+	0.831472i	0.0544790	+	0.0511736i
$265$		0			0
$266$	−4.56862	+	4.56862i	−0.280120	+	0.280120i
$267$	6.23830	−	0.195173i	0.381778	−	0.0119444i
$268$	−2.49862	+	2.49862i	−0.152627	+	0.152627i
$269$			4.12228i			0.251340i	0.992072	+	0.125670i	$0.0401080\pi$
$269$			4.12228i			0.251340i	−0.992072	+	0.125670i	$0.959892\pi$
$270$		0			0
$271$	−2.86523	+	2.86523i	−0.174050	+	0.174050i	−0.788756	−	0.614706i	$-0.789275\pi$
$271$	−2.86523	+	2.86523i	−0.174050	+	0.174050i	0.614706	+	0.788756i	$0.289275\pi$
$272$	16.9343			1.02680
$273$	−22.4172	−	1.41728i	−1.35675	−	0.0857779i
$274$	4.29852			0.259683
$275$		0			0
$276$	−22.0805	−	20.7408i	−1.32909	−	1.24845i
$277$		−	13.8782i		−	0.833857i	−0.908939	−	0.416929i	$-0.863106\pi$
$277$		−	13.8782i		−	0.833857i	0.908939	−	0.416929i	$-0.136894\pi$
$278$	0.134703	−	0.134703i	0.00807894	−	0.00807894i
$279$	−8.31807	+	9.42968i	−0.497990	+	0.564540i
$280$		0			0
$281$	−14.6864	−	14.6864i	−0.876116	−	0.876116i	0.117015	−	0.993130i	$-0.462668\pi$
$281$	−14.6864	−	14.6864i	−0.876116	−	0.876116i	−0.993130	+	0.117015i	$0.962668\pi$
$282$	1.52553	−	1.62407i	0.0908439	−	0.0967119i
$283$		−	7.59425i		−	0.451431i	−0.974193	−	0.225716i	$-0.927528\pi$
$283$		−	7.59425i		−	0.451431i	0.974193	−	0.225716i	$-0.0724720\pi$
$284$	21.8059	+	21.8059i	1.29394	+	1.29394i
$285$		0			0
$286$	−0.0616749	+	0.651289i	−0.00364692	+	0.0385115i
$287$		−	11.2688i		−	0.665179i
$288$	−9.05885	−	7.99095i	−0.533798	−	0.470871i
$289$	10.9246			0.642623
$290$		0			0
$291$	25.6829	−	0.803522i	1.50556	−	0.0471033i
$292$	−12.0910	−	12.0910i	−0.707574	−	0.707574i
$293$	−15.8408	−	15.8408i	−0.925429	−	0.925429i	0.0719771	−	0.997406i	$-0.477069\pi$
$293$	−15.8408	−	15.8408i	−0.925429	−	0.925429i	−0.997406	+	0.0719771i	$0.977069\pi$
$294$	−3.78517	+	0.118424i	−0.220756	+	0.00690662i
$295$		0			0
$296$	3.55033			0.206359
$297$	0.239849	+	2.54875i	0.0139175	+	0.147894i
$298$			0.429529i			0.0248819i
$299$	3.18885	−	33.6743i	0.184416	−	1.94743i
$300$		0			0
$301$	13.7775	+	13.7775i	0.794124	+	0.794124i
$302$		−	3.54302i		−	0.203878i
$303$	−3.04590	+	3.24264i	−0.174982	+	0.186285i
$304$	11.0526	+	11.0526i	0.633911	+	0.633911i
$305$		0			0
$306$	−4.37838	−	3.86224i	−0.250295	−	0.220789i
$307$	−19.6820	+	19.6820i	−1.12331	+	1.12331i	−0.132074	+	0.991240i	$0.542164\pi$
$307$	−19.6820	+	19.6820i	−1.12331	+	1.12331i	−0.991240	+	0.132074i	$0.957836\pi$
$308$		−	3.30374i		−	0.188248i
$309$	19.2421	+	18.0746i	1.09464	+	1.02823i
$310$		0			0
$311$	15.5168			0.879877			0.439938	−	0.898028i	$-0.355000\pi$
$311$	15.5168			0.879877			0.439938	+	0.898028i	$0.355000\pi$
$312$	0.560791	−	8.87003i	0.0317486	−	0.502166i
$313$	3.72939			0.210797			0.105399	−	0.994430i	$-0.466388\pi$
$313$	3.72939			0.210797			0.105399	+	0.994430i	$0.466388\pi$
$314$	2.18921	−	2.18921i	0.123544	−	0.123544i
$315$		0			0
$316$			4.96102i			0.279079i
$317$	18.4547	−	18.4547i	1.03652	−	1.03652i	0.0372111	−	0.999307i	$-0.488153\pi$
$317$	18.4547	−	18.4547i	1.03652	−	1.03652i	0.999307	−	0.0372111i	$-0.0118474\pi$
$318$	−4.43012	+	0.138602i	−0.248429	+	0.00777241i
$319$	−2.37202	+	2.37202i	−0.132808	+	0.132808i
$320$		0			0
$321$	11.1828	+	10.5043i	0.624164	+	0.586293i
$322$		−	12.4268i		−	0.692519i
$323$	18.2257	+	18.2257i	1.01410	+	1.01410i
$324$	−2.09369	−	16.6482i	−0.116316	−	0.924899i
$325$		0			0
$326$		−	3.60154i		−	0.199471i
$327$	19.5687	−	0.612233i	1.08215	−	0.0338566i
$328$	4.45886			0.246199
$329$	−12.5639			−0.692673
$330$		0			0
$331$	−15.0140	−	15.0140i	−0.825244	−	0.825244i	0.161611	−	0.986855i	$-0.448331\pi$
$331$	−15.0140	−	15.0140i	−0.825244	−	0.825244i	−0.986855	+	0.161611i	$0.948331\pi$
$332$	−13.7137	−	13.7137i	−0.752639	−	0.752639i
$333$	5.61242	+	4.95080i	0.307559	+	0.271302i
$334$	1.10409			0.0604131
$335$		0			0
$336$	0.624297	+	19.9543i	0.0340582	+	1.08860i
$337$			18.0210i			0.981666i	0.871254	+	0.490833i	$0.163308\pi$
$337$			18.0210i			0.981666i	−0.871254	+	0.490833i	$0.836692\pi$
$338$	3.96068	−	2.68974i	0.215433	−	0.146303i
$339$	−14.4195	−	13.5446i	−0.783158	−	0.735641i
$340$		0			0
$341$		−	2.06499i		−	0.111825i
$342$	−0.336873	−	5.37844i	−0.0182160	−	0.290833i
$343$	−2.70390	−	2.70390i	−0.145997	−	0.145997i
$344$	−5.45150	+	5.45150i	−0.293925	+	0.293925i
$345$		0			0
$346$	5.54649	−	5.54649i	0.298181	−	0.298181i
$347$			12.1453i			0.651991i	0.945371	+	0.325996i	$0.105700\pi$
$347$			12.1453i			0.651991i	−0.945371	+	0.325996i	$0.894300\pi$
$348$	15.0534	−	16.0257i	0.806945	−	0.859069i
$349$	22.2952	−	22.2952i	1.19343	−	1.19343i	0.217337	−	0.976097i	$-0.430263\pi$
$349$	22.2952	−	22.2952i	1.19343	−	1.19343i	0.976097	−	0.217337i	$-0.0697371\pi$
$350$		0			0
$351$	13.2554	−	13.2399i	0.707522	−	0.706692i
$352$	1.98378			0.105736
$353$	7.05913	−	7.05913i	0.375720	−	0.375720i	−0.493836	−	0.869555i	$-0.664406\pi$
$353$	7.05913	−	7.05913i	0.375720	−	0.375720i	0.869555	+	0.493836i	$0.164406\pi$
$354$	−0.153649	+	0.163574i	−0.00816637	+	0.00869386i
$355$		0			0
$356$	4.75045	−	4.75045i	0.251774	−	0.251774i
$357$	1.02946	+	32.9046i	0.0544848	+	1.74149i
$358$	0.721534	−	0.721534i	0.0381343	−	0.0381343i
$359$	−17.9957	−	17.9957i	−0.949776	−	0.949776i	0.0490218	−	0.998798i	$-0.484390\pi$
$359$	−17.9957	−	17.9957i	−0.949776	−	0.949776i	−0.998798	+	0.0490218i	$0.984390\pi$
$360$		0			0
$361$			4.79088i			0.252151i
$362$	−5.23512	−	5.23512i	−0.275152	−	0.275152i
$363$	13.5805	+	12.7565i	0.712789	+	0.669541i
$364$	−18.6319	+	15.4084i	−0.976579	+	0.807621i
$365$		0			0
$366$	0.0718286	+	2.29585i	0.00375454	+	0.120006i
$367$	−17.4749			−0.912181			−0.456090	−	0.889933i	$-0.650751\pi$
$367$	−17.4749			−0.912181			−0.456090	+	0.889933i	$0.650751\pi$
$368$	−30.0635			−1.56717
$369$	7.04863	+	6.21771i	0.366937	+	0.323681i
$370$		0			0
$371$	17.6720	+	17.6720i	0.917486	+	0.917486i
$372$	0.423244	+	13.5281i	0.0219442	+	0.701400i
$373$	−12.9747			−0.671805			−0.335903	−	0.941897i	$-0.609041\pi$
$373$	−12.9747			−0.671805			−0.335903	+	0.941897i	$0.609041\pi$
$374$	0.958813			0.0495790
$375$		0			0
$376$		−	4.97131i		−	0.256376i
$377$	24.4403	+	2.31442i	1.25874	+	0.119199i
$378$	4.38960	−	5.30159i	0.225777	−	0.272684i
$379$	−4.51436	−	4.51436i	−0.231887	−	0.231887i	0.581593	−	0.813480i	$-0.302430\pi$
$379$	−4.51436	−	4.51436i	−0.231887	−	0.231887i	−0.813480	+	0.581593i	$0.802430\pi$
$380$		0			0
$381$	−3.34244	−	3.13964i	−0.171238	−	0.160848i
$382$	3.63271	+	3.63271i	0.185866	+	0.185866i
$383$	24.9851	−	24.9851i	1.27668	−	1.27668i	0.334161	−	0.942516i	$-0.391547\pi$
$383$	24.9851	−	24.9851i	1.27668	−	1.27668i	0.942516	−	0.334161i	$-0.108453\pi$
$384$	−17.0824	+	0.534446i	−0.871734	+	0.0272733i
$385$		0			0
$386$			0.269206i			0.0137022i
$387$	−16.2197	+	1.01590i	−0.824494	+	0.0516412i
$388$	19.5575	−	19.5575i	0.992880	−	0.992880i
$389$	−5.36318			−0.271924			−0.135962	−	0.990714i	$-0.543413\pi$
$389$	−5.36318			−0.271924			−0.135962	+	0.990714i	$0.543413\pi$
$390$		0			0
$391$	−49.5745			−2.50709
$392$	−5.97449	+	5.97449i	−0.301757	+	0.301757i
$393$	6.46481	+	6.07256i	0.326106	+	0.306320i
$394$			1.93993i			0.0977322i
$395$		0			0
$396$	2.06648	+	1.82288i	0.103845	+	0.0916030i
$397$	2.52951	−	2.52951i	0.126952	−	0.126952i	−0.640776	−	0.767728i	$-0.721387\pi$
$397$	2.52951	−	2.52951i	0.126952	−	0.126952i	0.767728	+	0.640776i	$0.221387\pi$
$398$	−3.74114	−	3.74114i	−0.187527	−	0.187527i
$399$	−20.8041	+	22.1479i	−1.04151	+	1.10878i
$400$		0			0
$401$	−11.1604	−	11.1604i	−0.557326	−	0.557326i	0.371219	−	0.928545i	$-0.378940\pi$
$401$	−11.1604	−	11.1604i	−0.557326	−	0.557326i	−0.928545	+	0.371219i	$0.878940\pi$
$402$	0.827736	−	0.881202i	0.0412837	−	0.0439504i
$403$	−11.6458	+	9.63096i	−0.580119	+	0.479752i
$404$			4.78871i			0.238247i
$405$		0			0
$406$	9.01920			0.447615
$407$	−1.22905			−0.0609219
$408$	−13.0197	+	0.407337i	−0.644570	+	0.0201662i
$409$	−12.4909	−	12.4909i	−0.617634	−	0.617634i	0.327290	−	0.944924i	$-0.393865\pi$
$409$	−12.4909	−	12.4909i	−0.617634	−	0.617634i	−0.944924	+	0.327290i	$0.893865\pi$
$410$		0			0
$411$	20.2063	−	0.632179i	0.996703	−	0.0311831i
$412$	28.4165			1.39998
$413$	1.26542			0.0622674
$414$	7.77294	+	6.85663i	0.382019	+	0.336985i
$415$		0			0
$416$	−9.25221	−	11.1878i	−0.453627	−	0.548528i
$417$	0.613395	−	0.653016i	0.0300381	−	0.0319784i
$418$	0.625793	+	0.625793i	0.0306085	+	0.0306085i
$419$		−	6.25022i		−	0.305343i	−0.988277	−	0.152672i	$-0.951212\pi$
$419$		−	6.25022i		−	0.305343i	0.988277	−	0.152672i	$-0.0487877\pi$
$420$		0			0
$421$	−24.9169	−	24.9169i	−1.21438	−	1.21438i	−0.969573	−	0.244803i	$-0.921277\pi$
$421$	−24.9169	−	24.9169i	−1.21438	−	1.21438i	−0.244803	−	0.969573i	$-0.578723\pi$
$422$	−2.47192	+	2.47192i	−0.120331	+	0.120331i
$423$	6.93229	−	7.85871i	0.337060	−	0.382104i
$424$	−6.99247	+	6.99247i	−0.339585	+	0.339585i
$425$		0			0
$426$	−7.69041	−	7.22380i	−0.372602	−	0.349994i
$427$	9.15829	−	9.15829i	0.443201	−	0.443201i
$428$	16.5147			0.798268
$429$	−0.194134	+	3.07062i	−0.00937290	+	0.148251i
$430$		0			0
$431$	3.03234	−	3.03234i	0.146063	−	0.146063i	−0.630294	−	0.776357i	$-0.717066\pi$
$431$	3.03234	−	3.03234i	0.146063	−	0.146063i	0.776357	+	0.630294i	$0.217066\pi$
$432$	−12.8258	−	10.6195i	−0.617084	−	0.510932i
$433$			30.0237i			1.44285i	0.692493	+	0.721424i	$0.256512\pi$
$433$			30.0237i			1.44285i	−0.692493	+	0.721424i	$0.743488\pi$
$434$	−3.92588	+	3.92588i	−0.188448	+	0.188448i
$435$		0			0
$436$	14.9016	−	14.9016i	0.713655	−	0.713655i
$437$	−32.3560	−	32.3560i	−1.54780	−	1.54780i
$438$	4.26422	+	4.00549i	0.203752	+	0.191390i
$439$			13.8417i			0.660629i	0.943871	+	0.330314i	$0.107155\pi$
$439$			13.8417i			0.660629i	−0.943871	+	0.330314i	$0.892845\pi$
$440$		0			0
$441$	−17.7757	+	1.11336i	−0.846464	+	0.0530173i
$442$	−4.47184	−	5.40736i	−0.212704	−	0.257202i
$443$		−	5.89439i		−	0.280051i	−0.990148	−	0.140026i	$-0.955282\pi$
$443$		−	5.89439i		−	0.280051i	0.990148	−	0.140026i	$-0.0447185\pi$
$444$	8.05175	−	0.251909i	0.382119	−	0.0119551i
$445$		0			0
$446$	2.44596			0.115819
$447$	0.0631704	+	2.01911i	0.00298786	+	0.0955006i
$448$	12.5291	+	12.5291i	0.591946	+	0.591946i
$449$	15.1945	+	15.1945i	0.717073	+	0.717073i	0.968005	−	0.250932i	$-0.0807369\pi$
$449$	15.1945	+	15.1945i	0.717073	+	0.717073i	−0.250932	+	0.968005i	$0.580737\pi$
$450$		0			0
$451$	−1.54357			−0.0726837
$452$	−21.2946			−1.00161
$453$	−0.521068	−	16.6549i	−0.0244819	−	0.782514i
$454$		−	4.04440i		−	0.189813i
$455$		0			0
$456$	−8.76348	−	8.23176i	−0.410387	−	0.385487i
$457$	−5.58713	−	5.58713i	−0.261355	−	0.261355i	0.564250	−	0.825604i	$-0.309166\pi$
$457$	−5.58713	−	5.58713i	−0.261355	−	0.261355i	−0.825604	+	0.564250i	$0.809166\pi$
$458$		−	2.87534i		−	0.134356i
$459$	−21.1497	−	17.5115i	−0.987184	−	0.817368i
$460$		0			0
$461$	−14.7907	+	14.7907i	−0.688870	+	0.688870i	−0.961982	−	0.273113i	$-0.911947\pi$
$461$	−14.7907	+	14.7907i	−0.688870	+	0.688870i	0.273113	+	0.961982i	$0.411947\pi$
$462$	0.0353473	+	1.12980i	0.00164451	+	0.0525632i
$463$	−8.79012	+	8.79012i	−0.408512	+	0.408512i	−0.881219	−	0.472708i	$-0.843277\pi$
$463$	−8.79012	+	8.79012i	−0.408512	+	0.408512i	0.472708	+	0.881219i	$0.343277\pi$
$464$		−	21.8197i		−	1.01295i
$465$		0			0
$466$	−2.53541	+	2.53541i	−0.117450	+	0.117450i
$467$	−9.31080			−0.430853			−0.215426	−	0.976520i	$-0.569114\pi$
$467$	−9.31080			−0.430853			−0.215426	+	0.976520i	$0.569114\pi$
$468$	0.642450	−	20.1560i	0.0296972	−	0.931711i
$469$	−6.81706			−0.314783
$470$		0			0
$471$	9.96897	−	10.6129i	0.459346	−	0.489017i
$472$			0.500703i			0.0230467i
$473$	1.88720	−	1.88720i	0.0867734	−	0.0867734i
$474$	−0.0530788	−	1.69655i	−0.00243799	−	0.0779253i
$475$		0			0
$476$	25.0567	+	25.0567i	1.14847	+	1.14847i
$477$	−20.8045	+	1.30307i	−0.952574	+	0.0596634i
$478$		−	8.40491i		−	0.384432i
$479$	21.2367	+	21.2367i	0.970331	+	0.970331i	0.999572	−	0.0292411i	$-0.00930906\pi$
$479$	21.2367	+	21.2367i	0.970331	+	0.970331i	−0.0292411	+	0.999572i	$0.509309\pi$
$480$		0			0
$481$	5.73221	+	6.93142i	0.261366	+	0.316045i
$482$		−	3.31229i		−	0.150870i
$483$	−1.82760	−	58.4155i	−0.0831588	−	2.65800i
$484$	20.0555			0.911614
$485$		0			0
$486$	0.894116	+	5.67089i	0.0405579	+	0.257237i
$487$	11.9347	+	11.9347i	0.540814	+	0.540814i	0.923768	−	0.382954i	$-0.125093\pi$
$487$	11.9347	+	11.9347i	0.540814	+	0.540814i	−0.382954	+	0.923768i	$0.625093\pi$
$488$	3.62375	+	3.62375i	0.164040	+	0.164040i
$489$	−0.529675	−	16.9299i	−0.0239527	−	0.765599i
$490$		0			0
$491$	−8.47582			−0.382508			−0.191254	−	0.981541i	$-0.561255\pi$
$491$	−8.47582			−0.382508			−0.191254	+	0.981541i	$0.561255\pi$
$492$	10.1122	−	0.316372i	0.455892	−	0.0142632i
$493$		−	35.9805i		−	1.62048i
$494$	0.610596	−	6.44790i	0.0274720	−	0.290105i
$495$		0			0
$496$	9.49767	+	9.49767i	0.426458	+	0.426458i
$497$			59.4937i			2.66866i
$498$	4.83650	+	4.54305i	0.216729	+	0.203579i
$499$	25.0163	+	25.0163i	1.11988	+	1.11988i	0.991758	+	0.128124i	$0.0408957\pi$
$499$	25.0163	+	25.0163i	1.11988	+	1.11988i	0.128124	+	0.991758i	$0.459104\pi$
$500$		0			0
$501$	5.19005	−	0.162377i	0.231875	−	0.00725449i
$502$	−1.12918	+	1.12918i	−0.0503979	+	0.0503979i
$503$			20.4948i			0.913820i	0.889513	+	0.456910i	$0.151044\pi$
$503$			20.4948i			0.913820i	−0.889513	+	0.456910i	$0.848956\pi$
$504$	−0.959960	−	15.3265i	−0.0427600	−	0.682699i
$505$		0			0
$506$	−1.70218			−0.0756712
$507$	18.2226	−	13.2263i	0.809296	−	0.587401i
$508$	−4.93608			−0.219003
$509$	25.6979	−	25.6979i	1.13904	−	1.13904i	0.150415	−	0.988623i	$-0.451939\pi$
$509$	25.6979	−	25.6979i	1.13904	−	1.13904i	0.988623	−	0.150415i	$-0.0480609\pi$
$510$		0			0
$511$		−	32.9884i		−	1.45932i
$512$	−15.5740	+	15.5740i	−0.688280	+	0.688280i
$513$	−2.37456	−	25.2332i	−0.104839	−	1.11407i
$514$	−1.29054	+	1.29054i	−0.0569234	+	0.0569234i
$515$		0			0
$516$	−11.9766	+	12.7502i	−0.527239	+	0.561295i
$517$			1.72096i			0.0756879i
$518$	2.33663	+	2.33663i	0.102666	+	0.102666i
$519$	25.2570	−	26.8884i	1.10866	−	1.18027i
$520$		0			0
$521$		−	5.36438i		−	0.235018i	−0.993072	−	0.117509i	$-0.962509\pi$
$521$		−	5.36438i		−	0.235018i	0.993072	−	0.117509i	$-0.0374909\pi$
$522$	−4.97644	+	5.64148i	−0.217813	+	0.246921i
$523$	18.4316			0.805960			0.402980	−	0.915209i	$-0.367974\pi$
$523$	18.4316			0.805960			0.402980	+	0.915209i	$0.367974\pi$
$524$	9.54718			0.417070
$525$		0			0
$526$	−5.62365	−	5.62365i	−0.245203	−	0.245203i
$527$	15.6616	+	15.6616i	0.682230	+	0.682230i
$528$	2.73327	−	0.0855139i	0.118950	−	0.00372152i
$529$	65.0097			2.82651
$530$		0			0
$531$	−0.698211	+	0.791519i	−0.0302998	+	0.0343490i
$532$			32.7078i			1.41806i
$533$	7.19908	+	8.70516i	0.311827	+	0.377062i
$534$	−1.57372	+	1.67537i	−0.0681015	+	0.0725004i
$535$		0			0
$536$		−	2.69738i		−	0.116509i
$537$	3.28564	−	3.49787i	0.141786	−	0.150944i
$538$	−1.07350	−	1.07350i	−0.0462820	−	0.0462820i
$539$	2.06824	−	2.06824i	0.0890856	−	0.0890856i
$540$		0			0
$541$	−19.8497	+	19.8497i	−0.853407	+	0.853407i	−0.990551	−	0.137144i	$-0.956208\pi$
$541$	−19.8497	+	19.8497i	−0.853407	+	0.853407i	0.137144	+	0.990551i	$0.456208\pi$
$542$		−	1.49229i		−	0.0640995i
$543$	−25.3790	−	23.8391i	−1.08912	−	1.02303i
$544$	−15.0457	+	15.0457i	−0.645078	+	0.645078i
$545$		0			0
$546$	6.20684	−	5.46867i	0.265628	−	0.234038i
$547$	9.53713			0.407778			0.203889	−	0.978994i	$-0.434642\pi$
$547$	9.53713			0.407778			0.203889	+	0.978994i	$0.434642\pi$
$548$	15.3870	−	15.3870i	0.657302	−	0.657302i
$549$	0.675297	+	10.7817i	0.0288210	+	0.460150i
$550$		0			0
$551$	23.4835	−	23.4835i	1.00043	−	1.00043i
$552$	23.1138	−	0.723146i	0.983791	−	0.0307791i
$553$	−6.76766	+	6.76766i	−0.287790	+	0.287790i
$554$	3.61407	+	3.61407i	0.153547	+	0.153547i
$555$		0			0
$556$		−	0.964369i		−	0.0408984i
$557$	13.2999	+	13.2999i	0.563537	+	0.563537i	0.930310	−	0.366773i	$-0.119538\pi$
$557$	13.2999	+	13.2999i	0.563537	+	0.563537i	−0.366773	+	0.930310i	$0.619538\pi$
$558$	−0.289479	−	4.62177i	−0.0122546	−	0.195655i
$559$	−19.4449	−	1.84137i	−0.822431	−	0.0778815i
$560$		0			0
$561$	4.50715	−	0.141012i	0.190292	−	0.00595352i
$562$	7.64909			0.322657
$563$	21.9634			0.925647			0.462823	−	0.886451i	$-0.346836\pi$
$563$	21.9634			0.925647			0.462823	+	0.886451i	$0.346836\pi$
$564$	−0.352732	−	11.2744i	−0.0148527	−	0.474736i
$565$		0			0
$566$	1.97765	+	1.97765i	0.0831270	+	0.0831270i
$567$	19.8548	−	25.5671i	0.833821	−	1.07372i
$568$	−23.5405			−0.987737
$569$	−18.1666			−0.761585			−0.380792	−	0.924661i	$-0.624349\pi$
$569$	−18.1666			−0.761585			−0.380792	+	0.924661i	$0.624349\pi$
$570$		0			0
$571$		−	29.6650i		−	1.24144i	−0.784032	−	0.620720i	$-0.786840\pi$
$571$		−	29.6650i		−	1.24144i	0.784032	−	0.620720i	$-0.213160\pi$
$572$	2.11059	+	2.55214i	0.0882482	+	0.106710i
$573$	17.6108	+	16.5422i	0.735700	+	0.691062i
$574$	2.93457	+	2.93457i	0.122487	+	0.122487i
$575$		0			0
$576$	−14.7500	+	0.923850i	−0.614584	+	0.0384938i
$577$	−11.2277	−	11.2277i	−0.467414	−	0.467414i	0.433662	−	0.901076i	$-0.357221\pi$
$577$	−11.2277	−	11.2277i	−0.467414	−	0.467414i	−0.901076	+	0.433662i	$0.857221\pi$
$578$	−2.84492	+	2.84492i	−0.118333	+	0.118333i
$579$	0.0395919	+	1.26547i	0.00164538	+	0.0525913i
$580$		0			0
$581$		−	37.4156i		−	1.55226i
$582$	−6.47895	+	6.89745i	−0.268561	+	0.285908i
$583$	2.42065	−	2.42065i	0.100253	−	0.100253i
$584$	13.0529			0.540131
$585$		0			0
$586$	8.25035			0.340819
$587$	−9.11946	+	9.11946i	−0.376400	+	0.376400i	−0.869802	−	0.493401i	$-0.835753\pi$
$587$	−9.11946	+	9.11946i	−0.376400	+	0.376400i	0.493401	+	0.869802i	$0.335753\pi$
$588$	−13.1255	+	13.9734i	−0.541288	+	0.576252i
$589$			20.4438i			0.842374i
$590$		0			0
$591$	0.285304	+	9.11914i	0.0117358	+	0.375111i
$592$	5.65288	−	5.65288i	0.232332	−	0.232332i
$593$	6.63125	+	6.63125i	0.272313	+	0.272313i	0.830031	−	0.557718i	$-0.188323\pi$
$593$	6.63125	+	6.63125i	0.272313	+	0.272313i	−0.557718	+	0.830031i	$0.688323\pi$
$594$	−0.726192	−	0.601272i	−0.0297960	−	0.0246705i
$595$		0			0
$596$	1.53755	+	1.53755i	0.0629804	+	0.0629804i
$597$	−18.1364	−	17.0360i	−0.742274	−	0.697237i
$598$	7.93885	+	9.59969i	0.324644	+	0.392561i
$599$			39.9553i			1.63253i	0.577679	+	0.816264i	$0.303959\pi$
$599$			39.9553i			1.63253i	−0.577679	+	0.816264i	$0.696041\pi$
$600$		0			0
$601$	20.6271			0.841398			0.420699	−	0.907200i	$-0.361785\pi$
$601$	20.6271			0.841398			0.420699	+	0.907200i	$0.361785\pi$
$602$	−7.17574			−0.292461
$603$	3.76139	−	4.26405i	0.153176	−	0.173646i
$604$	−12.6826	−	12.6826i	−0.516049	−	0.516049i
$605$		0			0
$606$	−0.0512353	−	1.63763i	−0.00208129	−	0.0665241i
$607$	−1.59959			−0.0649252			−0.0324626	−	0.999473i	$-0.510335\pi$
$607$	−1.59959			−0.0649252			−0.0324626	+	0.999473i	$0.510335\pi$
$608$	−19.6399			−0.796502
$609$	42.3971	−	1.32645i	1.71802	−	0.0537503i
$610$		0			0
$611$	9.70563	−	8.02646i	0.392648	−	0.324716i
$612$	−29.4983	+	1.84759i	−1.19240	+	0.0746843i
$613$	−10.4572	−	10.4572i	−0.422362	−	0.422362i	0.463654	−	0.886016i	$-0.346538\pi$
$613$	−10.4572	−	10.4572i	−0.422362	−	0.422362i	−0.886016	+	0.463654i	$0.846538\pi$
$614$		−	10.2510i		−	0.413696i
$615$		0			0
$616$	1.78328	+	1.78328i	0.0718502	+	0.0718502i
$617$	7.17003	−	7.17003i	0.288654	−	0.288654i	−0.547894	−	0.836548i	$-0.684570\pi$
$617$	7.17003	−	7.17003i	0.288654	−	0.288654i	0.836548	+	0.547894i	$0.184570\pi$
$618$	−9.71779	+	0.304033i	−0.390907	+	0.0122300i
$619$	−34.7195	+	34.7195i	−1.39550	+	1.39550i	−0.583085	+	0.812411i	$0.698154\pi$
$619$	−34.7195	+	34.7195i	−1.39550	+	1.39550i	−0.812411	+	0.583085i	$0.801846\pi$
$620$		0			0
$621$	37.5471	+	31.0882i	1.50671	+	1.24753i
$622$	−4.04080	+	4.04080i	−0.162021	+	0.162021i
$623$	12.9608			0.519265
$624$	−13.2301	−	15.0159i	−0.529626	−	0.601116i
$625$		0			0
$626$	−0.971187	+	0.971187i	−0.0388164	+	0.0388164i
$627$	3.03374	+	2.84967i	0.121156	+	0.113805i
$628$		−	15.6730i		−	0.625423i
$629$	9.32156	−	9.32156i	0.371675	−	0.371675i
$630$		0			0
$631$	15.2658	−	15.2658i	0.607723	−	0.607723i	−0.334627	−	0.942351i	$-0.608610\pi$
$631$	15.2658	−	15.2658i	0.607723	−	0.607723i	0.942351	+	0.334627i	$0.108610\pi$
$632$	−2.67783	−	2.67783i	−0.106518	−	0.106518i
$633$	−11.2564	+	11.9835i	−0.447400	+	0.476300i
$634$			9.61174i			0.381731i
$635$		0			0
$636$	−15.3620	+	16.3543i	−0.609142	+	0.648489i
$637$	−21.3103	−	2.01802i	−0.844345	−	0.0799568i
$638$		−	1.23542i		−	0.0489106i
$639$	−37.2132	−	32.8263i	−1.47213	−	1.29859i
$640$		0			0
$641$	25.8774			1.02210			0.511048	−	0.859552i	$-0.329258\pi$
$641$	25.8774			1.02210			0.511048	+	0.859552i	$0.329258\pi$
$642$	−5.64764	+	0.176694i	−0.222895	+	0.00697354i
$643$	5.93694	+	5.93694i	0.234130	+	0.234130i	0.814414	−	0.580284i	$-0.197058\pi$
$643$	5.93694	+	5.93694i	0.234130	+	0.234130i	−0.580284	+	0.814414i	$0.697058\pi$
$644$	−44.4832	−	44.4832i	−1.75289	−	1.75289i
$645$		0			0
$646$	−9.49246			−0.373476
$647$	8.94367			0.351612			0.175806	−	0.984425i	$-0.443747\pi$
$647$	8.94367			0.351612			0.175806	+	0.984425i	$0.443747\pi$
$648$	10.1164	+	7.85614i	0.397409	+	0.308618i
$649$		−	0.173333i		−	0.00680392i
$650$		0			0
$651$	−17.8772	+	19.0320i	−0.700664	+	0.745922i
$652$	−12.8921	−	12.8921i	−0.504894	−	0.504894i
$653$			29.3417i			1.14823i	0.818775	+	0.574115i	$0.194654\pi$
$653$			29.3417i			1.14823i	−0.818775	+	0.574115i	$0.805346\pi$
$654$	−4.93655	+	5.25542i	−0.193034	+	0.205503i
$655$		0			0
$656$	7.09945	−	7.09945i	0.277187	−	0.277187i
$657$	20.6341	+	18.2017i	0.805014	+	0.710116i
$658$	3.27183	−	3.27183i	0.127549	−	0.127549i
$659$			20.2846i			0.790175i	0.918644	+	0.395087i	$0.129286\pi$
$659$			20.2846i			0.790175i	−0.918644	+	0.395087i	$0.870714\pi$
$660$		0			0
$661$	−13.3192	+	13.3192i	−0.518055	+	0.518055i	−0.916983	−	0.398927i	$-0.869383\pi$
$661$	−13.3192	+	13.3192i	−0.518055	+	0.518055i	0.398927	+	0.916983i	$0.369383\pi$
$662$	7.81973			0.303922
$663$	−21.8163	−	24.7610i	−0.847274	−	0.961639i
$664$	14.8046			0.574531
$665$		0			0
$666$	−2.75082	+	0.172294i	−0.106592	+	0.00667626i
$667$			63.8761i			2.47329i
$668$	3.95221	−	3.95221i	0.152916	−	0.152916i
$669$	11.4979	−	0.359725i	0.444533	−	0.0139078i
$670$		0			0
$671$	−1.25447	−	1.25447i	−0.0484283	−	0.0484283i
$672$	−18.2835	−	17.1742i	−0.705303	−	0.662509i
$673$			26.5074i			1.02179i	0.859644	+	0.510893i	$0.170685\pi$
$673$			26.5074i			1.02179i	−0.859644	+	0.510893i	$0.829315\pi$
$674$	−4.69293	−	4.69293i	−0.180765	−	0.180765i
$675$		0			0
$676$	4.54949	−	23.8060i	0.174981	−	0.915614i
$677$		−	24.4044i		−	0.937939i	−0.883214	−	0.468970i	$-0.844625\pi$
$677$		−	24.4044i		−	0.937939i	0.883214	−	0.468970i	$-0.155375\pi$
$678$	7.28225	−	0.227834i	0.279673	−	0.00874993i
$679$	53.3593			2.04774
$680$		0			0
$681$	−0.594807	−	19.0117i	−0.0227930	−	0.728532i
$682$	0.537753	+	0.537753i	0.0205916	+	0.0205916i
$683$	−24.2961	−	24.2961i	−0.929666	−	0.929666i	0.0680180	−	0.997684i	$-0.478332\pi$
$683$	−24.2961	−	24.2961i	−0.929666	−	0.929666i	−0.997684	+	0.0680180i	$0.978332\pi$
$684$	−20.4586	−	18.0469i	−0.782256	−	0.690040i
$685$		0			0
$686$	1.40827			0.0537679
$687$	−0.422874	−	13.5163i	−0.0161337	−	0.515679i
$688$			17.3599i			0.661839i
$689$	−24.9414	−	2.36187i	−0.950190	−	0.0899799i
$690$		0			0
$691$	−20.5928	−	20.5928i	−0.783388	−	0.783388i	0.197013	−	0.980401i	$-0.436876\pi$
$691$	−20.5928	−	20.5928i	−0.783388	−	0.783388i	−0.980401	+	0.197013i	$0.936876\pi$
$692$		−	39.7086i		−	1.50950i
$693$	0.332319	+	5.30574i	0.0126237	+	0.201548i
$694$	−3.16280	−	3.16280i	−0.120058	−	0.120058i
$695$		0			0
$696$	0.524849	+	16.7757i	0.0198943	+	0.635881i
$697$	11.7069	−	11.7069i	0.443432	−	0.443432i
$698$			11.6120i			0.439520i
$699$	−11.5455	+	12.2912i	−0.436689	+	0.464897i
$700$		0			0
$701$	−20.2981			−0.766648			−0.383324	−	0.923614i	$-0.625221\pi$
$701$	−20.2981			−0.766648			−0.383324	+	0.923614i	$0.625221\pi$
$702$	−0.00405037	+	6.89976i	−0.000152871	+	0.260415i
$703$	12.1679			0.458921
$704$	1.71620	−	1.71620i	0.0646816	−	0.0646816i
$705$		0			0
$706$			3.67660i			0.138371i
$707$	−6.53260	+	6.53260i	−0.245684	+	0.245684i
$708$	0.0355267	+	1.13554i	0.00133518	+	0.0426761i
$709$	−24.9325	+	24.9325i	−0.936361	+	0.936361i	−0.998093	−	0.0617322i	$-0.980338\pi$
$709$	−24.9325	+	24.9325i	−0.936361	+	0.936361i	0.0617322	+	0.998093i	$0.480338\pi$
$710$		0			0
$711$	−0.499021	−	7.96728i	−0.0187148	−	0.298796i
$712$			5.12834i			0.192193i
$713$	−27.8040	−	27.8040i	−1.04127	−	1.04127i
$714$	−8.83691	−	8.30074i	−0.330713	−	0.310647i
$715$		0			0
$716$		−	5.16563i		−	0.193049i
$717$	−1.23610	−	39.5094i	−0.0461631	−	1.47551i
$718$	9.37268			0.349785
$719$	−44.3697			−1.65471			−0.827355	−	0.561679i	$-0.810156\pi$
$719$	−44.3697			−1.65471			−0.827355	+	0.561679i	$0.810156\pi$
$720$		0			0
$721$	38.7649	+	38.7649i	1.44368	+	1.44368i
$722$	−1.24761	−	1.24761i	−0.0464314	−	0.0464314i
$723$	−0.487135	−	15.5703i	−0.0181168	−	0.579064i
$724$	−37.4794			−1.39291
$725$		0			0
$726$	−6.85852	+	0.214578i	−0.254544	+	0.00796372i
$727$		−	19.3095i		−	0.716150i	−0.933693	−	0.358075i	$-0.883433\pi$
$727$		−	19.3095i		−	0.716150i	0.933693	−	0.358075i	$-0.116567\pi$
$728$	1.73997	−	18.3741i	0.0644875	−	0.680990i
$729$	5.03704	+	26.5260i	0.186557	+	0.982444i
$730$		0			0
$731$			28.6263i			1.05878i
$732$	8.47538	+	7.96114i	0.313259	+	0.294252i
$733$	8.23013	+	8.23013i	0.303987	+	0.303987i	0.842571	−	0.538585i	$-0.181041\pi$
$733$	8.23013	+	8.23013i	0.303987	+	0.303987i	−0.538585	+	0.842571i	$0.681041\pi$
$734$	4.55071	−	4.55071i	0.167970	−	0.167970i
$735$		0			0
$736$	26.7106	−	26.7106i	0.984565	−	0.984565i
$737$			0.933777i			0.0343961i
$738$	−3.45475	+	0.216384i	−0.127171	+	0.00796521i
$739$	−11.8446	+	11.8446i	−0.435710	+	0.435710i	−0.890565	−	0.454855i	$-0.849691\pi$
$739$	−11.8446	+	11.8446i	−0.435710	+	0.435710i	0.454855	+	0.890565i	$0.349691\pi$
$740$		0			0
$741$	1.92197	−	30.3998i	0.0706055	−	1.11677i
$742$	−9.20411			−0.337893
$743$	7.55046	−	7.55046i	0.276999	−	0.276999i	−0.554911	−	0.831910i	$-0.687248\pi$
$743$	7.55046	−	7.55046i	0.276999	−	0.276999i	0.831910	+	0.554911i	$0.187248\pi$
$744$	−7.53058	−	7.07367i	−0.276085	−	0.259333i
$745$		0			0
$746$	3.37880	−	3.37880i	0.123707	−	0.123707i
$747$	23.4034	+	20.6445i	0.856285	+	0.755342i
$748$	3.43218	−	3.43218i	0.125493	−	0.125493i
$749$	22.5288	+	22.5288i	0.823185	+	0.823185i
$750$		0			0
$751$		−	0.869234i		−	0.0317188i	−0.999874	−	0.0158594i	$-0.994952\pi$
$751$		−	0.869234i		−	0.0317188i	0.999874	−	0.0158594i	$-0.00504841\pi$
$752$	−7.91537	−	7.91537i	−0.288644	−	0.288644i
$753$	−5.14195	+	5.47409i	−0.187383	+	0.199487i
$754$	−6.96732	+	5.76190i	−0.253735	+	0.209836i
$755$		0			0
$756$	−3.26456	−	34.6907i	−0.118731	−	1.26169i
$757$	32.3586			1.17609			0.588046	−	0.808828i	$-0.299897\pi$
$757$	32.3586			1.17609			0.588046	+	0.808828i	$0.299897\pi$
$758$	2.35121			0.0853998
$759$	−8.00154	+	0.250338i	−0.290438	+	0.00908670i
$760$		0			0
$761$	30.6519	+	30.6519i	1.11113	+	1.11113i	0.992998	+	0.118133i	$0.0376908\pi$
$761$	30.6519	+	30.6519i	1.11113	+	1.11113i	0.118133	+	0.992998i	$0.462309\pi$
$762$	1.68803	−	0.0528120i	0.0611507	−	0.00191318i
$763$	40.6564			1.47186
$764$	26.0074			0.940916
$765$		0			0
$766$			13.0129i			0.470177i
$767$	−0.977538	+	0.808414i	−0.0352968	+	0.0291901i
$768$	−7.37436	+	7.85069i	−0.266099	+	0.283287i
$769$	−10.9540	−	10.9540i	−0.395013	−	0.395013i	0.481457	−	0.876470i	$-0.340108\pi$
$769$	−10.9540	−	10.9540i	−0.395013	−	0.395013i	−0.876470	+	0.481457i	$0.840108\pi$
$770$		0			0
$771$	−5.87673	+	6.25633i	−0.211645	+	0.225316i
$772$	0.963655	+	0.963655i	0.0346827	+	0.0346827i
$773$	−27.0891	+	27.0891i	−0.974326	+	0.974326i	−0.999679	−	0.0253530i	$-0.991929\pi$
$773$	−27.0891	+	27.0891i	−0.974326	+	0.974326i	0.0253530	+	0.999679i	$0.491929\pi$
$774$	3.95929	−	4.48841i	0.142314	−	0.161332i
$775$		0			0
$776$			21.1132i			0.757921i
$777$	11.3276	+	10.6403i	0.406375	+	0.381718i
$778$	1.39665	−	1.39665i	0.0500723	−	0.0500723i
$779$	15.2816			0.547522
$780$		0			0
$781$	8.14924			0.291603
$782$	12.9099	−	12.9099i	0.461658	−	0.461658i
$783$	−22.5634	+	27.2511i	−0.806349	+	0.973876i
$784$			19.0253i			0.679475i
$785$		0			0
$786$	−3.26491	+	0.102147i	−0.116456	+	0.00364346i
$787$	36.5342	−	36.5342i	1.30230	−	1.30230i	0.375468	−	0.926836i	$-0.377482\pi$
$787$	36.5342	−	36.5342i	1.30230	−	1.30230i	0.926836	−	0.375468i	$-0.122518\pi$
$788$	6.94420	+	6.94420i	0.247377	+	0.247377i
$789$	−27.2625	−	25.6083i	−0.970569	−	0.911681i
$790$		0			0
$791$	−29.0494	−	29.0494i	−1.03288	−	1.03288i
$792$	−2.09938	+	0.131492i	−0.0745980	+	0.00467236i
$793$	−1.22401	+	12.9255i	−0.0434657	+	0.458999i
$794$			1.31744i			0.0467543i
$795$		0			0
$796$	−26.7837			−0.949324
$797$	−29.5724			−1.04751			−0.523754	−	0.851870i	$-0.675469\pi$
$797$	−29.5724			−1.04751			−0.523754	+	0.851870i	$0.675469\pi$
$798$	−0.349947	−	11.1853i	−0.0123880	−	0.395956i
$799$	−13.0524	−	13.0524i	−0.461760	−	0.461760i
$800$		0			0
$801$	−7.15128	+	8.10696i	−0.252678	+	0.286445i
$802$	5.81269			0.205253
$803$	−4.51863			−0.159459
$804$	−0.191389	−	6.11734i	−0.00674976	−	0.215742i
$805$		0			0
$806$	0.524694	−	5.54078i	0.0184815	−	0.195166i
$807$	−5.20415	−	4.88840i	−0.183195	−	0.172080i
$808$	−2.58482	−	2.58482i	−0.0909337	−	0.0909337i
$809$			53.6701i			1.88694i	0.331455	+	0.943471i	$0.392460\pi$
$809$			53.6701i			1.88694i	−0.331455	+	0.943471i	$0.607540\pi$
$810$		0			0
$811$	22.4475	+	22.4475i	0.788238	+	0.788238i	0.981205	−	0.192967i	$-0.0618110\pi$
$811$	22.4475	+	22.4475i	0.788238	+	0.788238i	−0.192967	+	0.981205i	$0.561811\pi$
$812$	32.2853	−	32.2853i	1.13299	−	1.13299i
$813$	−0.219470	−	7.01491i	−0.00769717	−	0.246024i
$814$	0.320063	−	0.320063i	0.0112182	−	0.0112182i
$815$		0			0
$816$	−20.0815	+	21.3787i	−0.702994	+	0.748403i
$817$	−18.6837	+	18.6837i	−0.653659	+	0.653659i
$818$	6.50562			0.227464
$819$	28.3726	−	26.6197i	0.991417	−	0.930169i
$820$		0			0
$821$	−33.6801	+	33.6801i	−1.17544	+	1.17544i	−0.194553	+	0.980892i	$0.562326\pi$
$821$	−33.6801	+	33.6801i	−1.17544	+	1.17544i	−0.980892	+	0.194553i	$0.937674\pi$
$822$	−5.09738	+	5.42664i	−0.177792	+	0.189276i
$823$			43.9680i			1.53263i	0.642467	+	0.766313i	$0.277911\pi$
$823$			43.9680i			1.53263i	−0.642467	+	0.766313i	$0.722089\pi$
$824$	−15.3385	+	15.3385i	−0.534342	+	0.534342i
$825$		0			0
$826$	−0.329535	+	0.329535i	−0.0114660	+	0.0114660i
$827$	30.1945	+	30.1945i	1.04996	+	1.04996i	0.998684	+	0.0512796i	$0.0163300\pi$
$827$	30.1945	+	30.1945i	1.04996	+	1.04996i	0.0512796	+	0.998684i	$0.483670\pi$
$828$	52.3682	−	3.28002i	1.81992	−	0.113989i
$829$		−	34.9574i		−	1.21412i	−0.794656	−	0.607060i	$-0.792349\pi$
$829$		−	34.9574i		−	1.21412i	0.794656	−	0.607060i	$-0.207651\pi$
$830$		0			0
$831$	17.5204	+	16.4574i	0.607776	+	0.570900i
$832$	−17.6829	−	1.67452i	−0.613046	−	0.0580535i
$833$			31.3726i			1.08700i
$834$	0.0103180	+	0.329792i	0.000357282	+	0.0114198i
$835$		0			0
$836$	4.48020			0.154951
$837$	−2.04049	−	21.6833i	−0.0705298	−	0.749483i
$838$	1.62765	+	1.62765i	0.0562262	+	0.0562262i
$839$	3.70208	+	3.70208i	0.127810	+	0.127810i	0.768118	−	0.640308i	$-0.221193\pi$
$839$	3.70208	+	3.70208i	0.127810	+	0.127810i	−0.640308	+	0.768118i	$0.721193\pi$
$840$		0			0
$841$	−17.3603			−0.598632
$842$	12.9775			0.447233
$843$	35.9565	−	1.12495i	1.23841	−	0.0387452i
$844$			17.6971i			0.609158i
$845$		0			0
$846$	0.241253	+	3.85179i	0.00829444	+	0.132427i
$847$	27.3591	+	27.3591i	0.940069	+	0.940069i
$848$			22.2670i			0.764652i
$849$	9.58732	+	9.00562i	0.329036	+	0.309072i
$850$		0			0
$851$	−16.5486	+	16.5486i	−0.567278	+	0.567278i
$852$	−53.3871	+	1.67028i	−1.82901	+	0.0572230i
$853$	−19.6790	+	19.6790i	−0.673797	+	0.673797i	−0.958589	−	0.284792i	$-0.908075\pi$
$853$	−19.6790	+	19.6790i	−0.673797	+	0.673797i	0.284792	+	0.958589i	$0.408075\pi$
$854$			4.76990i			0.163223i
$855$		0			0
$856$	−8.91420	+	8.91420i	−0.304681	+	0.304681i
$857$	13.8696			0.473777			0.236889	−	0.971537i	$-0.423872\pi$
$857$	13.8696			0.473777			0.236889	+	0.971537i	$0.423872\pi$
$858$	−0.749079	−	0.850190i	−0.0255731	−	0.0290250i
$859$	47.5429			1.62214			0.811072	−	0.584946i	$-0.198884\pi$
$859$	47.5429			1.62214			0.811072	+	0.584946i	$0.198884\pi$
$860$		0			0
$861$	14.2263	+	13.3631i	0.484831	+	0.455414i
$862$			1.57933i			0.0537922i
$863$	18.8498	−	18.8498i	0.641654	−	0.641654i	−0.309308	−	0.950962i	$-0.600097\pi$
$863$	18.8498	−	18.8498i	0.641654	−	0.641654i	0.950962	+	0.309308i	$0.100097\pi$
$864$	20.8305	−	1.96025i	0.708670	−	0.0666890i
$865$		0			0
$866$	−7.81862	−	7.81862i	−0.265687	−	0.265687i
$867$	−12.9549	+	13.7917i	−0.439972	+	0.468391i
$868$			28.1063i			0.953990i
$869$	0.927010	+	0.927010i	0.0314466	+	0.0314466i
$870$		0			0
$871$	5.26617	−	4.35507i	0.178437	−	0.147566i
$872$			16.0869i			0.544773i
$873$	−29.4416	+	33.3761i	−0.996447	+	1.12961i
$874$	16.8520			0.570026
$875$		0			0
$876$	29.6024	−	0.926148i	1.00017	−	0.0312916i
$877$	−37.6363	−	37.6363i	−1.27089	−	1.27089i	−0.945623	−	0.325265i	$-0.894546\pi$
$877$	−37.6363	−	37.6363i	−1.27089	−	1.27089i	−0.325265	−	0.945623i	$-0.605454\pi$
$878$	−3.60458	−	3.60458i	−0.121649	−	0.121649i
$879$	38.7829	−	1.21337i	1.30811	−	0.0409260i
$880$		0			0
$881$	−48.6517			−1.63912			−0.819559	−	0.572995i	$-0.805781\pi$
$881$	−48.6517			−1.63912			−0.819559	+	0.572995i	$0.805781\pi$
$882$	4.33913	−	4.91900i	0.146106	−	0.165631i
$883$		−	27.2665i		−	0.917592i	−0.888542	−	0.458796i	$-0.848281\pi$
$883$		−	27.2665i		−	0.917592i	0.888542	−	0.458796i	$-0.151719\pi$
$884$	−35.3638	−	3.34883i	−1.18941	−	0.112633i
$885$		0			0
$886$	1.53499	+	1.53499i	0.0515689	+	0.0515689i
$887$			32.1996i			1.08116i	0.841294	+	0.540578i	$0.181794\pi$
$887$			32.1996i			1.08116i	−0.841294	+	0.540578i	$0.818206\pi$
$888$	−4.21015	+	4.48210i	−0.141283	+	0.150409i
$889$	−6.73364	−	6.73364i	−0.225839	−	0.225839i
$890$		0			0
$891$	−3.50208	−	2.71963i	−0.117324	−	0.0911111i
$892$	8.75559	−	8.75559i	0.293159	−	0.293159i
$893$		−	17.0379i		−	0.570153i
$894$	−0.542256	−	0.509355i	−0.0181358	−	0.0170354i
$895$		0			0
$896$	−35.4908			−1.18566
$897$	38.7304	+	43.9583i	1.29317	+	1.46772i
$898$	−7.91374			−0.264085
$899$	20.1797	−	20.1797i	0.673032	−	0.673032i
$900$		0			0
$901$			36.7181i			1.22326i
$902$	0.401967	−	0.401967i	0.0133840	−	0.0133840i
$903$	−33.7314	+	1.05533i	−1.12251	+	0.0351192i
$904$	11.4943	−	11.4943i	0.382293	−	0.382293i
$905$		0			0
$906$	4.47286	+	4.20147i	0.148601	+	0.139585i
$907$		−	52.9829i		−	1.75927i	−0.475651	−	0.879634i	$-0.657787\pi$
$907$		−	52.9829i		−	1.75927i	0.475651	−	0.879634i	$-0.342213\pi$
$908$	−14.4774	−	14.4774i	−0.480449	−	0.480449i
$909$	−0.481689	−	7.69056i	−0.0159766	−	0.255080i
$910$		0			0
$911$			16.3239i			0.540835i	0.962743	+	0.270417i	$0.0871617\pi$
$911$			16.3239i			0.540835i	−0.962743	+	0.270417i	$0.912838\pi$
$912$	−27.0600	+	0.846607i	−0.896047	+	0.0280340i
$913$	−5.12506			−0.169615
$914$	2.90994			0.0962522
$915$		0			0
$916$	−10.2926	−	10.2926i	−0.340078	−	0.340078i
$917$	13.0239	+	13.0239i	0.430089	+	0.430089i
$918$	10.0680	−	0.947440i	0.332292	−	0.0312702i
$919$	46.3976			1.53051			0.765257	−	0.643725i	$-0.222612\pi$
$919$	46.3976			1.53051			0.765257	+	0.643725i	$0.222612\pi$
$920$		0			0
$921$	−1.50760	−	48.1874i	−0.0496772	−	1.58783i
$922$		−	7.70340i		−	0.253698i
$923$	−38.0075	−	45.9588i	−1.25103	−	1.51275i
$924$	4.17079	+	3.91773i	0.137209	+	0.128884i
$925$		0			0
$926$		−	4.57815i		−	0.150447i
$927$	−45.6363	+	2.85837i	−1.49889	+	0.0938813i
$928$	19.3861	+	19.3861i	0.636382	+	0.636382i
$929$	−20.0595	+	20.0595i	−0.658131	+	0.658131i	−0.954938	−	0.296807i	$-0.904078\pi$
$929$	−20.0595	+	20.0595i	−0.658131	+	0.658131i	0.296807	+	0.954938i	$0.404078\pi$
$930$		0			0
$931$	−20.4761	+	20.4761i	−0.671077	+	0.671077i
$932$			18.1516i			0.594575i
$933$	−18.4005	+	19.5891i	−0.602407	+	0.641318i
$934$	2.42467	−	2.42467i	0.0793376	−	0.0793376i
$935$		0			0
$936$	10.5329	+	11.2265i	0.344279	+	0.366948i
$937$	23.7901			0.777188			0.388594	−	0.921409i	$-0.372961\pi$
$937$	23.7901			0.777188			0.388594	+	0.921409i	$0.372961\pi$
$938$	1.77526	−	1.77526i	0.0579644	−	0.0579644i
$939$	−4.42248	+	4.70815i	−0.144322	+	0.153645i
$940$		0			0
$941$	31.8370	−	31.8370i	1.03786	−	1.03786i	0.0386033	−	0.999255i	$-0.487709\pi$
$941$	31.8370	−	31.8370i	1.03786	−	1.03786i	0.999255	−	0.0386033i	$-0.0122909\pi$
$942$	0.167689	+	5.35982i	0.00546359	+	0.174632i
$943$	−20.7833	+	20.7833i	−0.676798	+	0.676798i
$944$	0.797226	+	0.797226i	0.0259475	+	0.0259475i
$945$		0			0
$946$			0.982907i			0.0319571i
$947$	−37.4100	−	37.4100i	−1.21566	−	1.21566i	−0.969137	−	0.246523i	$-0.920712\pi$
$947$	−37.4100	−	37.4100i	−1.21566	−	1.21566i	−0.246523	−	0.969137i	$-0.579288\pi$
$948$	−6.26301	−	5.88301i	−0.203413	−	0.191071i
$949$	21.0746	+	25.4835i	0.684109	+	0.827228i
$950$		0			0
$951$	1.41359	+	45.1825i	0.0458388	+	1.46514i
$952$	−27.0500			−0.876694
$953$	−17.7294			−0.574311			−0.287156	−	0.957884i	$-0.592710\pi$
$953$	−17.7294			−0.574311			−0.287156	+	0.957884i	$0.592710\pi$
$954$	5.07847	−	5.75714i	0.164421	−	0.186394i
$955$		0			0
$956$	−30.0863	−	30.0863i	−0.973062	−	0.973062i
$957$	−0.181692	−	5.80740i	−0.00587326	−	0.187727i
$958$	−11.0607			−0.357355
$959$	41.9810			1.35564
$960$		0			0
$961$		−	13.4323i		−	0.433300i
$962$	−3.29779	−	0.312290i	−0.106325	−	0.0100686i
$963$	−26.5222	+	1.66119i	−0.854666	+	0.0535310i
$964$	−11.8567	−	11.8567i	−0.381879	−	0.381879i
$965$		0			0
$966$	15.6882	+	14.7363i	0.504759	+	0.474133i
$967$	1.98285	+	1.98285i	0.0637640	+	0.0637640i	0.738270	−	0.674506i	$-0.235643\pi$
$967$	1.98285	+	1.98285i	0.0637640	+	0.0637640i	−0.674506	+	0.738270i	$0.735643\pi$
$968$	−10.8254	+	10.8254i	−0.347943	+	0.347943i
$969$	−44.6218	+	1.39605i	−1.43346	+	0.0448476i
$970$		0			0
$971$			45.7568i			1.46841i	0.678930	+	0.734203i	$0.262444\pi$
$971$			45.7568i			1.46841i	−0.678930	+	0.734203i	$0.737556\pi$
$972$	23.5002	+	17.0990i	0.753770	+	0.548451i
$973$	1.31556	−	1.31556i	0.0421750	−	0.0421750i
$974$	−6.21595			−0.199172
$975$		0			0
$976$	11.5396			0.369373
$977$	4.54207	−	4.54207i	0.145314	−	0.145314i	−0.630707	−	0.776021i	$-0.717235\pi$
$977$	4.54207	−	4.54207i	0.145314	−	0.145314i	0.776021	+	0.630707i	$0.217235\pi$
$978$	4.54674	+	4.27087i	0.145389	+	0.136567i
$979$		−	1.77533i		−	0.0567397i
$980$		0			0
$981$	−22.4326	+	25.4305i	−0.716218	+	0.811932i
$982$	2.20723	−	2.20723i	0.0704354	−	0.0704354i
$983$	22.8720	+	22.8720i	0.729505	+	0.729505i	0.970521	−	0.241016i	$-0.0774808\pi$
$983$	22.8720	+	22.8720i	0.729505	+	0.729505i	−0.241016	+	0.970521i	$0.577481\pi$
$984$	−5.28752	+	5.62906i	−0.168560	+	0.179448i
$985$		0			0
$986$	9.36984	+	9.36984i	0.298396	+	0.298396i
$987$	14.8989	−	15.8613i	0.474238	−	0.504870i
$988$	−20.8953	−	25.2667i	−0.664769	−	0.803842i
$989$		−	50.8203i		−	1.61599i
$990$		0			0
$991$	−13.1807			−0.418700			−0.209350	−	0.977841i	$-0.567135\pi$
$991$	−13.1807			−0.418700			−0.209350	+	0.977841i	$0.567135\pi$
$992$	−16.8768			−0.535840
$993$	36.7586	−	1.15004i	1.16650	−	0.0364954i
$994$	−15.4930	−	15.4930i	−0.491409	−	0.491409i
$995$		0			0
$996$	33.5752	−	1.05044i	1.06387	−	0.0332846i
$997$	−9.27082			−0.293610			−0.146805	−	0.989165i	$-0.546899\pi$
$997$	−9.27082			−0.293610			−0.146805	+	0.989165i	$0.546899\pi$
$998$	−13.0292			−0.412432
$999$	−12.9056	+	1.21447i	−0.408314	+	0.0384242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.o.p.476.10		40
3.2	odd	2	inner	975.2.o.p.476.11		40
5.2	odd	4		975.2.n.r.749.10		40
5.3	odd	4		975.2.n.q.749.11		40
5.4	even	2		195.2.o.a.86.11	yes	40
13.5	odd	4	inner	975.2.o.p.551.11		40
15.2	even	4		975.2.n.r.749.11		40
15.8	even	4		975.2.n.q.749.10		40
15.14	odd	2		195.2.o.a.86.10	✓	40
39.5	even	4	inner	975.2.o.p.551.10		40
65.18	even	4		975.2.n.r.824.11		40
65.44	odd	4		195.2.o.a.161.10	yes	40
65.57	even	4		975.2.n.q.824.10		40
195.44	even	4		195.2.o.a.161.11	yes	40
195.83	odd	4		975.2.n.r.824.10		40
195.122	odd	4		975.2.n.q.824.11		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.10	✓	40	15.14	odd	2
195.2.o.a.86.11	yes	40	5.4	even	2
195.2.o.a.161.10	yes	40	65.44	odd	4
195.2.o.a.161.11	yes	40	195.44	even	4
975.2.n.q.749.10		40	15.8	even	4
975.2.n.q.749.11		40	5.3	odd	4
975.2.n.q.824.10		40	65.57	even	4
975.2.n.q.824.11		40	195.122	odd	4
975.2.n.r.749.10		40	5.2	odd	4
975.2.n.r.749.11		40	15.2	even	4
975.2.n.r.824.10		40	195.83	odd	4
975.2.n.r.824.11		40	65.18	even	4
975.2.o.p.476.10		40	1.1	even	1	trivial
975.2.o.p.476.11		40	3.2	odd	2	inner
975.2.o.p.551.10		40	39.5	even	4	inner
975.2.o.p.551.11		40	13.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.260415 + 0.260415i) q^{2} +(-1.18585 + 1.26244i) q^{3} +1.86437i q^{4} +(-0.0199472 - 0.637571i) q^{6} +(-2.54331 + 2.54331i) q^{7} +(-1.00634 - 1.00634i) q^{8} +(-0.187534 - 2.99413i) q^{9} +(0.348374 + 0.348374i) q^{11} +(-2.35366 - 2.21086i) q^{12} +(0.339913 - 3.58949i) q^{13} -1.32463i q^{14} -3.20461 q^{16} -5.28437 q^{17} +(0.828552 + 0.730879i) q^{18} +(-3.44898 - 3.44898i) q^{19} +(-0.194812 - 6.22677i) q^{21} -0.181443 q^{22} +9.38135 q^{23} +(2.46381 - 0.0770834i) q^{24} +(0.846238 + 1.02327i) q^{26} +(4.00231 + 3.31383i) q^{27} +(-4.74167 - 4.74167i) q^{28} +6.80884i q^{29} +(-2.96376 - 2.96376i) q^{31} +(2.84720 - 2.84720i) q^{32} +(-0.852920 + 0.0266847i) q^{33} +(1.37613 - 1.37613i) q^{34} +(5.58217 - 0.349633i) q^{36} +(-1.76399 + 1.76399i) q^{37} +1.79633 q^{38} +(4.12845 + 4.68571i) q^{39} +(-2.21539 + 2.21539i) q^{41} +(1.67227 + 1.57081i) q^{42} -5.41717i q^{43} +(-0.649497 + 0.649497i) q^{44} +(-2.44304 + 2.44304i) q^{46} +(2.47000 + 2.47000i) q^{47} +(3.80017 - 4.04564i) q^{48} -5.93686i q^{49} +(6.26646 - 6.67123i) q^{51} +(6.69214 + 0.633724i) q^{52} -6.94843i q^{53} +(-1.90523 + 0.179291i) q^{54} +5.11886 q^{56} +(8.44410 - 0.264184i) q^{57} +(-1.77312 - 1.77312i) q^{58} +(-0.248775 - 0.248775i) q^{59} -3.60093 q^{61} +1.54361 q^{62} +(8.09197 + 7.13805i) q^{63} -4.92631i q^{64} +(0.215164 - 0.229062i) q^{66} +(1.34019 + 1.34019i) q^{67} -9.85202i q^{68} +(-11.1248 + 11.8434i) q^{69} +(11.6961 - 11.6961i) q^{71} +(-2.82439 + 3.20183i) q^{72} +(-6.48532 + 6.48532i) q^{73} -0.918735i q^{74} +(6.43016 - 6.43016i) q^{76} -1.77204 q^{77} +(-2.29534 - 0.145118i) q^{78} +2.66096 q^{79} +(-8.92966 + 1.12300i) q^{81} -1.15384i q^{82} +(-7.35570 + 7.35570i) q^{83} +(11.6090 - 0.363202i) q^{84} +(1.41071 + 1.41071i) q^{86} +(-8.59579 - 8.07424i) q^{87} -0.701163i q^{88} +(-2.54802 - 2.54802i) q^{89} +(8.26469 + 9.99370i) q^{91} +17.4903i q^{92} +(7.25614 - 0.227017i) q^{93} -1.28645 q^{94} +(0.218090 + 6.97078i) q^{96} +(-10.4901 - 10.4901i) q^{97} +(1.54604 + 1.54604i) q^{98} +(0.977745 - 1.10841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} + 16 q^{7} - 64 q^{16} - 4 q^{18} - 16 q^{19} - 12 q^{21} + 8 q^{24} + 24 q^{27} - 32 q^{28} + 32 q^{31} + 4 q^{33} - 16 q^{34} - 32 q^{37} - 8 q^{39} - 8 q^{42} - 40 q^{46} - 8 q^{48} - 32 q^{54}+ \cdots - 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 + 16 * q^7 - 64 * q^16 - 4 * q^18 - 16 * q^19 - 12 * q^21 + 8 * q^24 + 24 * q^27 - 32 * q^28 + 32 * q^31 + 4 * q^33 - 16 * q^34 - 32 * q^37 - 8 * q^39 - 8 * q^42 - 40 * q^46 - 8 * q^48 - 32 * q^54 + 36 * q^57 - 24 * q^58 + 8 * q^61 - 8 * q^63 - 48 * q^66 + 32 * q^67 - 132 * q^72 + 64 * q^73 + 16 * q^76 + 12 * q^78 + 40 * q^79 + 72 * q^81 + 124 * q^84 - 16 * q^87 + 8 * q^91 + 108 * q^93 - 32 * q^94 - 76 * q^96 - 24 * q^97 - 20 * q^99

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