LMFDB - Embedded newform 975.2.o.p.476.11

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)

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")

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);

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			476.11
Character	$\chi$	$=$	975.476
Dual form			975.2.o.p.551.11

$q$-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} +(-0.637571 - 0.0199472i) 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} +(0.730879 + 0.828552i) q^{18} +(-3.44898 - 3.44898i) q^{19} +(6.22677 + 0.194812i) q^{21} -0.181443 q^{22} -9.38135 q^{23} +(0.0770834 - 2.46381i) 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} +(-0.0266847 + 0.852920i) q^{33} +(1.37613 - 1.37613i) q^{34} +(-5.58217 - 0.349633i) q^{36} +(-1.76399 + 1.76399i) q^{37} -1.79633 q^{38} +(-4.93462 + 3.82747i) 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} +(0.179291 - 1.90523i) q^{54} -5.11886 q^{56} +(-0.264184 + 8.44410i) q^{57} +(-1.77312 - 1.77312i) q^{58} +(0.248775 + 0.248775i) q^{59} -3.60093 q^{61} -1.54361 q^{62} +(-7.13805 - 8.09197i) 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} +(-3.20183 + 2.82439i) q^{72} +(-6.48532 + 6.48532i) q^{73} +0.918735i q^{74} +(6.43016 - 6.43016i) q^{76} +1.77204 q^{77} +(-0.288319 + 2.28178i) q^{78} +2.66096 q^{79} +(-8.92966 - 1.12300i) q^{81} -1.15384i q^{82} +(7.35570 - 7.35570i) q^{83} +(-0.363202 + 11.6090i) 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} +(-0.227017 + 7.25614i) q^{93} -1.28645 q^{94} +(6.97078 + 0.218090i) q^{96} +(-10.4901 - 10.4901i) q^{97} +(-1.54604 - 1.54604i) q^{98} +(1.10841 - 0.977745i) 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	−0.609017	−	0.793157i	$-0.708436\pi$
$2$	0.260415	−	0.260415i	0.184141	−	0.184141i	0.793157	+	0.609017i	$0.208436\pi$
$3$	−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
$6$	−0.637571	−	0.0199472i	−0.260287	−	0.00814341i
$7$	−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	0.652634	−	0.757673i	$-0.273664\pi$
$11$	−0.348374	−	0.348374i	−0.105039	−	0.105039i	−0.757673	+	0.652634i	$0.773664\pi$
$12$	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	$-0.278593\pi$
$17$	5.28437			1.28165			0.640824	+	0.767688i	$0.278593\pi$
$18$	0.730879	+	0.828552i	0.172270	+	0.195292i
$19$	−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
$21$	6.22677	+	0.194812i	1.35879	+	0.0425115i
$22$	−0.181443			−0.0386838
$23$	−9.38135			−1.95615			−0.978073	−	0.208262i	$-0.933219\pi$
$23$	−9.38135			−1.95615			−0.978073	+	0.208262i	$0.933219\pi$
$24$	0.0770834	−	2.46381i	0.0157346	−	0.502923i
$25$		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	$-0.782158\pi$
$29$		−	6.80884i		−	1.26437i	0.774817	−	0.632185i	$-0.217842\pi$
$30$		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
$33$	−0.0266847	+	0.852920i	−0.00464521	+	0.148474i
$34$	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
$39$	−4.93462	+	3.82747i	−0.790172	+	0.612885i
$40$		0			0
$41$	2.21539	−	2.21539i	0.345986	−	0.345986i	−0.512626	−	0.858612i	$-0.671327\pi$
$41$	2.21539	−	2.21539i	0.345986	−	0.345986i	0.858612	+	0.512626i	$0.171327\pi$
$42$	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	0.503632	−	0.863918i	$-0.331997\pi$
$47$	−2.47000	−	2.47000i	−0.360286	−	0.360286i	−0.863918	+	0.503632i	$0.831997\pi$
$48$	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	$0.158356\pi$
$53$			6.94843i			0.954441i	−0.878784	+	0.477220i	$0.841644\pi$
$54$	0.179291	−	1.90523i	0.0243984	−	0.259269i
$55$		0			0
$56$	−5.11886			−0.684036
$57$	−0.264184	+	8.44410i	−0.0349921	+	1.11845i
$58$	−1.77312	−	1.77312i	−0.232822	−	0.232822i
$59$	0.248775	+	0.248775i	0.0323877	+	0.0323877i	0.723115	−	0.690727i	$-0.242710\pi$
$59$	0.248775	+	0.248775i	0.0323877	+	0.0323877i	−0.690727	+	0.723115i	$0.742710\pi$
$60$		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
$63$	−7.13805	−	8.09197i	−0.899310	−	1.01949i
$64$		−	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	$0.688705\pi$
$71$	−11.6961	+	11.6961i	−1.38807	+	1.38807i	−0.829361	+	0.558713i	$0.811295\pi$
$72$	−3.20183	+	2.82439i	−0.377339	+	0.332857i
$73$	−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
$78$	−0.288319	+	2.28178i	−0.0326457	+	0.258360i
$79$	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	−0.176846	−	0.984239i	$-0.556589\pi$
$83$	7.35570	−	7.35570i	0.807393	−	0.807393i	0.984239	+	0.176846i	$0.0565894\pi$
$84$	−0.363202	+	11.6090i	−0.0396286	+	1.26664i
$85$		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	0.829136	−	0.559046i	$-0.188833\pi$
$89$	2.54802	+	2.54802i	0.270090	+	0.270090i	−0.559046	+	0.829136i	$0.688833\pi$
$90$		0			0
$91$	8.26469	+	9.99370i	0.866375	+	1.04762i
$92$		−	17.4903i		−	1.82349i
$93$	−0.227017	+	7.25614i	−0.0235406	+	0.752426i
$94$	−1.28645			−0.132687
$95$		0			0
$96$	6.97078	+	0.218090i	0.711452	+	0.0222587i
$97$	−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
$99$	1.10841	−	0.977745i	0.111399	−	0.0982670i
$100$		0			0
$101$	−2.56854			−0.255579			−0.127790	−	0.991801i	$-0.540788\pi$
$101$	−2.56854			−0.255579			−0.127790	+	0.991801i	$0.540788\pi$
$102$	−3.36916	−	0.105409i	−0.333597	−	0.0104370i
$103$		−	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	$0.140842\pi$
$107$			8.85806i			0.856341i	−0.903698	+	0.428171i	$0.859158\pi$
$108$	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
$111$	4.31875	+	0.135118i	0.409918	+	0.0128248i
$112$	8.15031	−	8.15031i	0.770132	−	0.770132i
$113$		−	11.4219i		−	1.07448i	−0.843430	−	0.537239i	$-0.819467\pi$
$113$		−	11.4219i		−	1.07448i	0.843430	−	0.537239i	$-0.180533\pi$
$114$	2.13017	+	2.26776i	0.199509	+	0.212396i
$115$		0			0
$116$	12.6942			1.17863
$117$	10.6837	+	1.69090i	0.987706	+	0.156324i
$118$	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
$123$	−5.42392	−	0.169694i	−0.489058	−	0.0153008i
$124$	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	$0.0718155\pi$
$131$			5.12086i			0.447412i	−0.974657	+	0.223706i	$0.928184\pi$
$132$	−1.59016	−	0.0497501i	−0.138405	−	0.00433019i
$133$	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	0.965505	−	0.260385i	$-0.0838494\pi$
$137$	8.25322	+	8.25322i	0.705120	+	0.705120i	−0.260385	+	0.965505i	$0.583849\pi$
$138$	5.98127	+	0.187132i	0.509160	+	0.0159297i
$139$	−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
$141$	−0.189197	+	6.04728i	−0.0159332	+	0.509273i
$142$			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	−0.740080	−	0.672518i	$-0.765213\pi$
$149$	−0.824702	+	0.824702i	−0.0675622	+	0.0675622i	0.672518	+	0.740080i	$0.265213\pi$
$150$		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
$156$	−7.13581	−	9.19995i	−0.571322	−	0.736586i
$157$	−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
$162$	−2.61786	+	2.03297i	−0.205679	+	0.159725i
$163$	−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	0.784354	−	0.620314i	$-0.212995\pi$
$167$	2.11987	+	2.11987i	0.164040	+	0.164040i	−0.620314	+	0.784354i	$0.712995\pi$
$168$	6.07018	+	6.46228i	0.468325	+	0.498576i
$169$	−12.7689	−	2.44023i	−0.982224	−	0.187710i
$170$		0			0
$171$	10.9735	−	9.67989i	0.839164	−	0.740240i
$172$	10.0996			0.770087
$173$	21.2987			1.61931			0.809655	−	0.586906i	$-0.199654\pi$
$173$	21.2987			1.61931			0.809655	+	0.586906i	$0.199654\pi$
$174$	−0.135817	+	4.34112i	−0.0102963	+	0.329099i
$175$		0			0
$176$	1.11640	+	1.11640i	0.0841518	+	0.0841518i
$177$	0.0190556	−	0.609074i	0.00143231	−	0.0457808i
$178$	1.32708			0.0994692
$179$	2.77071			0.207093			0.103546	−	0.994625i	$-0.466981\pi$
$179$	2.77071			0.207093			0.103546	+	0.994625i	$0.466981\pi$
$180$		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
$189$	−1.75102	+	18.6072i	−0.127368	+	1.35348i
$190$		0			0
$191$			13.9497i			1.00937i	0.863304	+	0.504684i	$0.168391\pi$
$191$			13.9497i			1.00937i	−0.863304	+	0.504684i	$0.831609\pi$
$192$	−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	−0.827233	−	0.561859i	$-0.810086\pi$
$197$	−3.72469	+	3.72469i	−0.265373	+	0.265373i	0.561859	+	0.827233i	$0.310086\pi$
$198$	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
$201$	0.102656	−	3.28119i	0.00724080	−	0.231437i
$202$	−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
$213$	28.6355	+	0.895898i	1.96207	+	0.0613859i
$214$	2.30677	+	2.30677i	0.157687	+	0.157687i
$215$		0			0
$216$	7.36251	+	0.692846i	0.500956	+	0.0471422i
$217$	15.0755			1.02339
$218$	−4.16289			−0.281947
$219$	15.8780	+	0.496762i	1.07293	+	0.0335681i
$220$		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	−0.400775	−	0.916177i	$-0.631259\pi$
$227$	7.76531	−	7.76531i	0.515402	−	0.515402i	0.916177	+	0.400775i	$0.131259\pi$
$228$	−15.7429	−	0.492537i	−1.04260	−	0.0326191i
$229$	−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	$-0.603318\pi$
$233$	−9.73604			−0.637829			−0.318915	+	0.947783i	$0.603318\pi$
$234$	3.22252	−	2.34185i	0.210663	−	0.153091i
$235$		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	$-0.485716\pi$
$239$	16.1376	−	16.1376i	1.04385	−	1.04385i	0.998993	−	0.0448582i	$-0.0142836\pi$
$240$		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
$249$	−18.0089	−	0.563431i	−1.14127	−	0.0357060i
$250$		0			0
$251$	−4.33610			−0.273692			−0.136846	−	0.990592i	$-0.543697\pi$
$251$	−4.33610			−0.273692			−0.136846	+	0.990592i	$0.543697\pi$
$252$	15.0864	−	13.3080i	0.950354	−	0.838323i
$253$	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	$-0.549398\pi$
$257$	−4.95572			−0.309129			−0.154565	+	0.987983i	$0.549398\pi$
$258$	−0.108057	+	3.45383i	−0.00672736	+	0.215026i
$259$		−	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	$-0.768090\pi$
$263$		−	21.5950i		−	1.33160i	0.746129	−	0.665801i	$-0.231910\pi$
$264$	−0.885180	+	0.831472i	−0.0544790	+	0.0511736i
$265$		0			0
$266$	4.56862	−	4.56862i	0.280120	−	0.280120i
$267$	0.195173	−	6.23830i	0.0119444	−	0.381778i
$268$	−2.49862	+	2.49862i	−0.152627	+	0.152627i
$269$		−	4.12228i		−	0.251340i	−0.992072	−	0.125670i	$-0.959892\pi$
$269$		−	4.12228i		−	0.251340i	0.992072	−	0.125670i	$-0.0401080\pi$
$270$		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
$273$	2.81584	−	22.2847i	0.170422	−	1.34873i
$274$	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
$279$	9.42968	−	8.31807i	0.564540	−	0.497990i
$280$		0			0
$281$	14.6864	+	14.6864i	0.876116	+	0.876116i	0.993130	−	0.117015i	$-0.0373324\pi$
$281$	14.6864	+	14.6864i	0.876116	+	0.876116i	−0.117015	+	0.993130i	$0.537332\pi$
$282$	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
$288$	−7.99095	−	9.05885i	−0.470871	−	0.533798i
$289$	10.9246			0.642623
$290$		0			0
$291$	−0.803522	+	25.6829i	−0.0471033	+	1.50556i
$292$	−12.0910	−	12.0910i	−0.707574	−	0.707574i
$293$	15.8408	+	15.8408i	0.925429	+	0.925429i	0.997406	−	0.0719771i	$-0.0229308\pi$
$293$	15.8408	+	15.8408i	0.925429	+	0.925429i	−0.0719771	+	0.997406i	$0.522931\pi$
$294$	−0.118424	+	3.78517i	−0.00690662	+	0.220756i
$295$		0			0
$296$	−3.55033			−0.206359
$297$	−2.54875	−	0.239849i	−0.147894	−	0.0139175i
$298$			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
$306$	3.86224	+	4.37838i	0.220789	+	0.250295i
$307$	−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	$-0.645000\pi$
$311$	−15.5168			−0.879877			−0.439938	+	0.898028i	$0.645000\pi$
$312$	−8.81762	−	1.11417i	−0.499200	−	0.0630776i
$313$	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	$0.511847\pi$
$317$	−18.4547	+	18.4547i	−1.03652	+	1.03652i	−0.999307	+	0.0372111i	$0.988153\pi$
$318$	0.138602	−	4.43012i	0.00777241	−	0.248429i
$319$	−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
$327$	−0.612233	+	19.5687i	−0.0338566	+	1.08215i
$328$	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
$333$	−4.95080	−	5.61242i	−0.271302	−	0.307559i
$334$	1.10409			0.0604131
$335$		0			0
$336$	−19.9543	−	0.624297i	−1.08860	−	0.0340582i
$337$			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	$-0.894300\pi$
$347$		−	12.1453i		−	0.651991i	0.945371	−	0.325996i	$-0.105700\pi$
$348$	−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
$351$	−10.5345	−	15.4927i	−0.562292	−	0.826939i
$352$	1.98378			0.105736
$353$	−7.05913	+	7.05913i	−0.375720	+	0.375720i	−0.869555	−	0.493836i	$-0.835594\pi$
$353$	−7.05913	+	7.05913i	−0.375720	+	0.375720i	0.493836	+	0.869555i	$0.335594\pi$
$354$	−0.153649	−	0.163574i	−0.00816637	−	0.00869386i
$355$		0			0
$356$	−4.75045	+	4.75045i	−0.251774	+	0.251774i
$357$	32.9046	+	1.02946i	1.74149	+	0.0544848i
$358$	0.721534	−	0.721534i	0.0381343	−	0.0381343i
$359$	17.9957	+	17.9957i	0.949776	+	0.949776i	0.998798	−	0.0490218i	$-0.0156104\pi$
$359$	17.9957	+	17.9957i	0.949776	+	0.949776i	−0.0490218	+	0.998798i	$0.515610\pi$
$360$		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
$366$	2.29585	+	0.0718286i	0.120006	+	0.00375454i
$367$	−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
$369$	6.21771	+	7.04863i	0.323681	+	0.366937i
$370$		0			0
$371$	−17.6720	−	17.6720i	−0.917486	−	0.917486i
$372$	−13.5281	−	0.423244i	−0.701400	−	0.0219442i
$373$	−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	$0.608453\pi$
$383$	−24.9851	+	24.9851i	−1.27668	+	1.27668i	−0.942516	+	0.334161i	$0.891547\pi$
$384$	−0.534446	+	17.0824i	−0.0272733	+	0.871734i
$385$		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	$-0.456587\pi$
$389$	5.36318			0.271924			0.135962	+	0.990714i	$0.456587\pi$
$390$		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
$396$	1.82288	+	2.06648i	0.0916030	+	0.103845i
$397$	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	0.928545	−	0.371219i	$-0.121060\pi$
$401$	11.1604	+	11.1604i	0.557326	+	0.557326i	−0.371219	+	0.928545i	$0.621060\pi$
$402$	−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
$408$	0.407337	−	13.0197i	0.0201662	−	0.644570i
$409$	−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
$411$	0.632179	−	20.2063i	0.0311831	−	0.996703i
$412$	28.4165			1.39998
$413$	−1.26542			−0.0622674
$414$	−6.85663	−	7.77294i	−0.336985	−	0.382019i
$415$		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	$0.0487877\pi$
$419$			6.25022i			0.305343i	−0.988277	+	0.152672i	$0.951212\pi$
$420$		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
$423$	7.85871	−	6.93229i	0.382104	−	0.337060i
$424$	−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
$429$	3.05248	+	0.385703i	0.147375	+	0.0186219i
$430$		0			0
$431$	−3.03234	+	3.03234i	−0.146063	+	0.146063i	−0.776357	−	0.630294i	$-0.782934\pi$
$431$	−3.03234	+	3.03234i	−0.146063	+	0.146063i	0.630294	+	0.776357i	$0.282934\pi$
$432$	−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	$0.0447185\pi$
$443$			5.89439i			0.280051i	−0.990148	+	0.140026i	$0.955282\pi$
$444$	−0.251909	+	8.05175i	−0.0119551	+	0.382119i
$445$		0			0
$446$	−2.44596			−0.115819
$447$	2.01911	+	0.0631704i	0.0955006	+	0.00298786i
$448$	12.5291	+	12.5291i	0.591946	+	0.591946i
$449$	−15.1945	−	15.1945i	−0.717073	−	0.717073i	0.250932	−	0.968005i	$-0.419263\pi$
$449$	−15.1945	−	15.1945i	−0.717073	−	0.717073i	−0.968005	+	0.250932i	$0.919263\pi$
$450$		0			0
$451$	−1.54357			−0.0726837
$452$	21.2946			1.00161
$453$	16.6549	+	0.521068i	0.782514	+	0.0244819i
$454$		−	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	−0.273113	−	0.961982i	$-0.588053\pi$
$461$	14.7907	−	14.7907i	0.688870	−	0.688870i	0.961982	+	0.273113i	$0.0880531\pi$
$462$	−1.12980	−	0.0353473i	−0.0525632	−	0.00164451i
$463$	−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	$-0.430886\pi$
$467$	9.31080			0.430853			0.215426	+	0.976520i	$0.430886\pi$
$468$	−3.15246	+	19.9183i	−0.145722	+	0.920724i
$469$	−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
$474$	−1.69655	−	0.0530788i	−0.0779253	−	0.00243799i
$475$		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	0.0292411	−	0.999572i	$-0.490691\pi$
$479$	−21.2367	−	21.2367i	−0.970331	−	0.970331i	−0.999572	+	0.0292411i	$0.990691\pi$
$480$		0			0
$481$	5.73221	+	6.93142i	0.261366	+	0.316045i
$482$			3.31229i			0.150870i
$483$	−58.4155	−	1.82760i	−2.65800	−	0.0831588i
$484$	20.0555			0.911614
$485$		0			0
$486$	5.67089	+	0.894116i	0.257237	+	0.0405579i
$487$	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
$489$	16.9299	+	0.529675i	0.765599	+	0.0239527i
$490$		0			0
$491$	8.47582			0.382508			0.191254	−	0.981541i	$-0.438745\pi$
$491$	8.47582			0.382508			0.191254	+	0.981541i	$0.438745\pi$
$492$	0.316372	−	10.1122i	0.0142632	−	0.455892i
$493$		−	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
$501$	0.162377	−	5.19005i	0.00725449	−	0.231875i
$502$	−1.12918	+	1.12918i	−0.0503979	+	0.0503979i
$503$		−	20.4948i		−	0.913820i	−0.889513	−	0.456910i	$-0.848956\pi$
$503$		−	20.4948i		−	0.913820i	0.889513	−	0.456910i	$-0.151044\pi$
$504$	0.959960	−	15.3265i	0.0427600	−	0.682699i
$505$		0			0
$506$	1.70218			0.0756712
$507$	12.0613	+	19.0138i	0.535662	+	0.844432i
$508$	−4.93608			−0.219003
$509$	−25.6979	+	25.6979i	−1.13904	+	1.13904i	−0.150415	+	0.988623i	$0.548061\pi$
$509$	−25.6979	+	25.6979i	−1.13904	+	1.13904i	−0.988623	+	0.150415i	$0.951939\pi$
$510$		0			0
$511$		−	32.9884i		−	1.45932i
$512$	15.5740	−	15.5740i	0.688280	−	0.688280i
$513$	−25.2332	−	2.37456i	−1.11407	−	0.104839i
$514$	−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	$0.0374909\pi$
$521$			5.36438i			0.235018i	−0.993072	+	0.117509i	$0.962509\pi$
$522$	5.64148	−	4.97644i	0.246921	−	0.217813i
$523$	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
$528$	0.0855139	−	2.73327i	0.00372152	−	0.118950i
$529$	65.0097			2.82651
$530$		0			0
$531$	−0.791519	+	0.698211i	−0.0343490	+	0.0302998i
$532$			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
$546$	−5.06998	−	6.53655i	−0.216975	−	0.279739i
$547$	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
$552$	−0.723146	+	23.1138i	−0.0307791	+	0.983791i
$553$	−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	0.366773	−	0.930310i	$-0.380462\pi$
$557$	−13.2999	−	13.2999i	−0.563537	−	0.563537i	−0.930310	+	0.366773i	$0.880462\pi$
$558$	0.289479	−	4.62177i	0.0122546	−	0.195655i
$559$	−19.4449	−	1.84137i	−0.822431	−	0.0778815i
$560$		0			0
$561$	−0.141012	+	4.50715i	−0.00595352	+	0.190292i
$562$	7.64909			0.322657
$563$	−21.9634			−0.925647			−0.462823	−	0.886451i	$-0.653164\pi$
$563$	−21.9634			−0.925647			−0.462823	+	0.886451i	$0.653164\pi$
$564$	−11.2744	−	0.352732i	−0.474736	−	0.0148527i
$565$		0			0
$566$	−1.97765	−	1.97765i	−0.0831270	−	0.0831270i
$567$	25.5671	−	19.8548i	1.07372	−	0.833821i
$568$	−23.5405			−0.987737
$569$	18.1666			0.761585			0.380792	−	0.924661i	$-0.375651\pi$
$569$	18.1666			0.761585			0.380792	+	0.924661i	$0.375651\pi$
$570$		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
$579$	−1.26547	−	0.0395919i	−0.0525913	−	0.00164538i
$580$		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	−0.493401	−	0.869802i	$-0.664247\pi$
$587$	9.11946	−	9.11946i	0.376400	−	0.376400i	0.869802	+	0.493401i	$0.164247\pi$
$588$	−13.1255	−	13.9734i	−0.541288	−	0.576252i
$589$			20.4438i			0.842374i
$590$		0			0
$591$	9.11914	+	0.285304i	0.375111	+	0.0117358i
$592$	5.65288	−	5.65288i	0.232332	−	0.232332i
$593$	−6.63125	−	6.63125i	−0.272313	−	0.272313i	0.557718	−	0.830031i	$-0.311677\pi$
$593$	−6.63125	−	6.63125i	−0.272313	−	0.272313i	−0.830031	+	0.557718i	$0.811677\pi$
$594$	−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	$-0.696041\pi$
$599$		−	39.9553i		−	1.63253i	0.577679	−	0.816264i	$-0.303959\pi$
$600$		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
$603$	−4.26405	+	3.76139i	−0.173646	+	0.153176i
$604$	−12.6826	−	12.6826i	−0.516049	−	0.516049i
$605$		0			0
$606$	1.63763	+	0.0512353i	0.0665241	+	0.00208129i
$607$	−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
$609$	1.32645	−	42.3971i	0.0537503	−	1.71802i
$610$		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	−0.836548	−	0.547894i	$-0.815430\pi$
$617$	−7.17003	+	7.17003i	−0.288654	+	0.288654i	0.547894	+	0.836548i	$0.315430\pi$
$618$	−0.304033	+	9.71779i	−0.0122300	+	0.390907i
$619$	−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
$624$	15.8135	−	12.2655i	0.633048	−	0.491014i
$625$		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
$639$	−32.8263	−	37.2132i	−1.29859	−	1.47213i
$640$		0			0
$641$	−25.8774			−1.02210			−0.511048	−	0.859552i	$-0.670742\pi$
$641$	−25.8774			−1.02210			−0.511048	+	0.859552i	$0.670742\pi$
$642$	0.176694	−	5.64764i	0.00697354	−	0.222895i
$643$	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	$-0.556253\pi$
$647$	−8.94367			−0.351612			−0.175806	+	0.984425i	$0.556253\pi$
$648$	−7.85614	−	10.1164i	−0.308618	−	0.397409i
$649$		−	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	$-0.805346\pi$
$653$		−	29.3417i		−	1.14823i	0.818775	−	0.574115i	$-0.194654\pi$
$654$	4.93655	+	5.25542i	0.193034	+	0.205503i
$655$		0			0
$656$	−7.09945	+	7.09945i	−0.277187	+	0.277187i
$657$	−18.2017	−	20.6341i	−0.710116	−	0.805014i
$658$	3.27183	−	3.27183i	0.127549	−	0.127549i
$659$		−	20.2846i		−	0.790175i	−0.918644	−	0.395087i	$-0.870714\pi$
$659$		−	20.2846i		−	0.790175i	0.918644	−	0.395087i	$-0.129286\pi$
$660$		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
$663$	−26.0764	+	20.2258i	−1.01272	+	0.785504i
$664$	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
$669$	−0.359725	+	11.4979i	−0.0139078	+	0.444533i
$670$		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	$0.155375\pi$
$677$			24.4044i			0.937939i	−0.883214	+	0.468970i	$0.844625\pi$
$678$	−0.227834	+	7.28225i	−0.00874993	+	0.279673i
$679$	53.3593			2.04774
$680$		0			0
$681$	−19.0117	−	0.594807i	−0.728532	−	0.0227930i
$682$	0.537753	+	0.537753i	0.0205916	+	0.0205916i
$683$	24.2961	+	24.2961i	0.929666	+	0.929666i	0.997684	−	0.0680180i	$-0.0216675\pi$
$683$	24.2961	+	24.2961i	0.929666	+	0.929666i	−0.0680180	+	0.997684i	$0.521668\pi$
$684$	18.0469	+	20.4586i	0.690040	+	0.782256i
$685$		0			0
$686$	−1.40827			−0.0537679
$687$	13.5163	+	0.422874i	0.515679	+	0.0161337i
$688$			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
$696$	−16.7757	−	0.524849i	−0.635881	−	0.0198943i
$697$	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	$-0.374779\pi$
$701$	20.2981			0.766648			0.383324	+	0.923614i	$0.374779\pi$
$702$	−6.77787	−	1.29118i	−0.255814	−	0.0487323i
$703$	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
$708$	1.13554	+	0.0355267i	0.0426761	+	0.00133518i
$709$	−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
$717$	−39.5094	−	1.23610i	−1.47551	−	0.0461631i
$718$	9.37268			0.349785
$719$	44.3697			1.65471			0.827355	−	0.561679i	$-0.189844\pi$
$719$	44.3697			1.65471			0.827355	+	0.561679i	$0.189844\pi$
$720$		0			0
$721$	38.7649	+	38.7649i	1.44368	+	1.44368i
$722$	1.24761	+	1.24761i	0.0464314	+	0.0464314i
$723$	15.5703	+	0.487135i	0.579064	+	0.0181168i
$724$	−37.4794			−1.39291
$725$		0			0
$726$	−0.214578	+	6.85852i	−0.00796372	+	0.254544i
$727$		−	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
$741$	30.2202	+	3.81855i	1.11017	+	0.140278i
$742$	−9.20411			−0.337893
$743$	−7.55046	+	7.55046i	−0.276999	+	0.276999i	−0.831910	−	0.554911i	$-0.812752\pi$
$743$	−7.55046	+	7.55046i	−0.276999	+	0.276999i	0.554911	+	0.831910i	$0.312752\pi$
$744$	−7.53058	+	7.07367i	−0.276085	+	0.259333i
$745$		0			0
$746$	−3.37880	+	3.37880i	−0.123707	+	0.123707i
$747$	20.6445	+	23.4034i	0.755342	+	0.856285i
$748$	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
$756$	−34.6907	−	3.26456i	−1.26169	−	0.118731i
$757$	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
$759$	0.250338	−	8.00154i	0.00908670	−	0.290438i
$760$		0			0
$761$	−30.6519	−	30.6519i	−1.11113	−	1.11113i	−0.992998	−	0.118133i	$-0.962309\pi$
$761$	−30.6519	−	30.6519i	−1.11113	−	1.11113i	−0.118133	−	0.992998i	$-0.537691\pi$
$762$	0.0528120	−	1.68803i	0.00191318	−	0.0611507i
$763$	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	−0.0253530	−	0.999679i	$-0.508071\pi$
$773$	27.0891	−	27.0891i	0.974326	−	0.974326i	0.999679	+	0.0253530i	$0.00807098\pi$
$774$	4.48841	−	3.95929i	0.161332	−	0.142314i
$775$		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
$786$	0.102147	−	3.26491i	0.00364346	−	0.116456i
$787$	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	$-0.324531\pi$
$797$	29.5724			1.04751			0.523754	+	0.851870i	$0.324531\pi$
$798$	−11.1853	−	0.349947i	−0.395956	−	0.0123880i
$799$	−13.0524	−	13.0524i	−0.461760	−	0.461760i
$800$		0			0
$801$	−8.10696	+	7.15128i	−0.286445	+	0.252678i
$802$	5.81269			0.205253
$803$	4.51863			0.159459
$804$	6.11734	+	0.191389i	0.215742	+	0.00674976i
$805$		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	$-0.607540\pi$
$809$		−	53.6701i		−	1.88694i	0.331455	−	0.943471i	$-0.392460\pi$
$810$		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
$813$	7.01491	+	0.219470i	0.246024	+	0.00769717i
$814$	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
$819$	−31.4724	+	22.8714i	−1.09973	+	0.799192i
$820$		0			0
$821$	33.6801	−	33.6801i	1.17544	−	1.17544i	0.194553	−	0.980892i	$-0.437674\pi$
$821$	33.6801	−	33.6801i	1.17544	−	1.17544i	0.980892	−	0.194553i	$-0.0623255\pi$
$822$	−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	$-0.983670\pi$
$827$	−30.1945	−	30.1945i	−1.04996	−	1.04996i	−0.0512796	−	0.998684i	$-0.516330\pi$
$828$	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
$834$	0.329792	+	0.0103180i	0.0114198	+	0.000357282i
$835$		0			0
$836$	−4.48020			−0.154951
$837$	−21.6833	−	2.04049i	−0.749483	−	0.0705298i
$838$	1.62765	+	1.62765i	0.0562262	+	0.0562262i
$839$	−3.70208	−	3.70208i	−0.127810	−	0.127810i	0.640308	−	0.768118i	$-0.278807\pi$
$839$	−3.70208	−	3.70208i	−0.127810	−	0.127810i	−0.768118	+	0.640308i	$0.778807\pi$
$840$		0			0
$841$	−17.3603			−0.598632
$842$	−12.9775			−0.447233
$843$	1.12495	−	35.9565i	0.0387452	−	1.23841i
$844$			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
$852$	−1.67028	+	53.3871i	−0.0572230	+	1.82901i
$853$	−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	$-0.576128\pi$
$857$	−13.8696			−0.473777			−0.236889	+	0.971537i	$0.576128\pi$
$858$	0.895353	−	0.694468i	0.0305669	−	0.0237087i
$859$	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	−0.950962	−	0.309308i	$-0.899903\pi$
$863$	−18.8498	+	18.8498i	−0.641654	+	0.641654i	0.309308	+	0.950962i	$0.399903\pi$
$864$	−1.96025	+	20.8305i	−0.0666890	+	0.708670i
$865$		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
$873$	33.3761	−	29.4416i	1.12961	−	0.996447i
$874$	16.8520			0.570026
$875$		0			0
$876$	−0.926148	+	29.6024i	−0.0312916	+	1.00017i
$877$	−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
$879$	1.21337	−	38.7829i	0.0409260	−	1.30811i
$880$		0			0
$881$	48.6517			1.63912			0.819559	−	0.572995i	$-0.194219\pi$
$881$	48.6517			1.63912			0.819559	+	0.572995i	$0.194219\pi$
$882$	4.91900	−	4.33913i	0.165631	−	0.146106i
$883$		−	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	$-0.818206\pi$
$887$		−	32.1996i		−	1.08116i	0.841294	−	0.540578i	$-0.181794\pi$
$888$	4.21015	+	4.48210i	0.141283	+	0.150409i
$889$	−6.73364	−	6.73364i	−0.225839	−	0.225839i
$890$		0			0
$891$	2.71963	+	3.50208i	0.0911111	+	0.117324i
$892$	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
$897$	46.2934	−	35.9068i	1.54569	−	1.19889i
$898$	−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
$903$	1.05533	−	33.7314i	0.0351192	−	1.12251i
$904$	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	$-0.912838\pi$
$911$		−	16.3239i		−	0.540835i	0.962743	−	0.270417i	$-0.0871617\pi$
$912$	0.846607	−	27.0600i	0.0280340	−	0.896047i
$913$	−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
$918$	0.947440	−	10.0680i	0.0312702	−	0.332292i
$919$	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
$921$	48.1874	+	1.50760i	1.58783	+	0.0496772i
$922$		−	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	−0.296807	−	0.954938i	$-0.595922\pi$
$929$	20.0595	−	20.0595i	0.658131	−	0.658131i	0.954938	+	0.296807i	$0.0959217\pi$
$930$		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
$936$	9.04977	+	12.4530i	0.295801	+	0.407039i
$937$	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	$0.512291\pi$
$941$	−31.8370	+	31.8370i	−1.03786	+	1.03786i	−0.999255	+	0.0386033i	$0.987709\pi$
$942$	5.35982	+	0.167689i	0.174632	+	0.00546359i
$943$	−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	$0.0792881\pi$
$947$	37.4100	+	37.4100i	1.21566	+	1.21566i	0.246523	+	0.969137i	$0.420712\pi$
$948$	6.26301	−	5.88301i	0.203413	−	0.191071i
$949$	21.0746	+	25.4835i	0.684109	+	0.827228i
$950$		0			0
$951$	45.1825	+	1.41359i	1.46514	+	0.0458388i
$952$	−27.0500			−0.876694
$953$	17.7294			0.574311			0.287156	−	0.957884i	$-0.407290\pi$
$953$	17.7294			0.574311			0.287156	+	0.957884i	$0.407290\pi$
$954$	−5.75714	+	5.07847i	−0.186394	+	0.164421i
$955$		0			0
$956$	30.0863	+	30.0863i	0.973062	+	0.973062i
$957$	5.80740	+	0.181692i	0.187727	+	0.00587326i
$958$	−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
$969$	−1.39605	+	44.6218i	−0.0448476	+	1.43346i
$970$		0			0
$971$		−	45.7568i		−	1.46841i	−0.678930	−	0.734203i	$-0.737556\pi$
$971$		−	45.7568i		−	1.46841i	0.678930	−	0.734203i	$-0.262444\pi$
$972$	−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	−0.776021	−	0.630707i	$-0.782765\pi$
$977$	−4.54207	+	4.54207i	−0.145314	+	0.145314i	0.630707	+	0.776021i	$0.282765\pi$
$978$	4.54674	−	4.27087i	0.145389	−	0.136567i
$979$		−	1.77533i		−	0.0567397i
$980$		0			0
$981$	25.4305	−	22.4326i	0.811932	−	0.716218i
$982$	2.20723	−	2.20723i	0.0704354	−	0.0704354i
$983$	−22.8720	−	22.8720i	−0.729505	−	0.729505i	0.241016	−	0.970521i	$-0.422519\pi$
$983$	−22.8720	−	22.8720i	−0.729505	−	0.729505i	−0.970521	+	0.241016i	$0.922519\pi$
$984$	−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
$993$	−1.15004	+	36.7586i	−0.0364954	+	1.16650i
$994$	−15.4930	−	15.4930i	−0.491409	−	0.491409i
$995$		0			0
$996$	1.05044	−	33.5752i	0.0332846	−	1.06387i
$997$	−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
$999$	−1.21447	+	12.9056i	−0.0384242	+	0.408314i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.10	✓	40	5.4	even	2
195.2.o.a.86.11	yes	40	15.14	odd	2
195.2.o.a.161.10	yes	40	195.44	even	4
195.2.o.a.161.11	yes	40	65.44	odd	4
975.2.n.q.749.10		40	5.3	odd	4
975.2.n.q.749.11		40	15.8	even	4
975.2.n.q.824.10		40	195.122	odd	4
975.2.n.q.824.11		40	65.57	even	4
975.2.n.r.749.10		40	15.2	even	4
975.2.n.r.749.11		40	5.2	odd	4
975.2.n.r.824.10		40	65.18	even	4
975.2.n.r.824.11		40	195.83	odd	4
975.2.o.p.476.10		40	3.2	odd	2	inner
975.2.o.p.476.11		40	1.1	even	1	trivial
975.2.o.p.551.10		40	13.5	odd	4	inner
975.2.o.p.551.11		40	39.5	even	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} +(-0.637571 - 0.0199472i) 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} +(0.730879 + 0.828552i) q^{18} +(-3.44898 - 3.44898i) q^{19} +(6.22677 + 0.194812i) q^{21} -0.181443 q^{22} -9.38135 q^{23} +(0.0770834 - 2.46381i) 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} +(-0.0266847 + 0.852920i) q^{33} +(1.37613 - 1.37613i) q^{34} +(-5.58217 - 0.349633i) q^{36} +(-1.76399 + 1.76399i) q^{37} -1.79633 q^{38} +(-4.93462 + 3.82747i) 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} +(0.179291 - 1.90523i) q^{54} -5.11886 q^{56} +(-0.264184 + 8.44410i) q^{57} +(-1.77312 - 1.77312i) q^{58} +(0.248775 + 0.248775i) q^{59} -3.60093 q^{61} -1.54361 q^{62} +(-7.13805 - 8.09197i) 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} +(-3.20183 + 2.82439i) q^{72} +(-6.48532 + 6.48532i) q^{73} +0.918735i q^{74} +(6.43016 - 6.43016i) q^{76} +1.77204 q^{77} +(-0.288319 + 2.28178i) q^{78} +2.66096 q^{79} +(-8.92966 - 1.12300i) q^{81} -1.15384i q^{82} +(7.35570 - 7.35570i) q^{83} +(-0.363202 + 11.6090i) 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} +(-0.227017 + 7.25614i) q^{93} -1.28645 q^{94} +(6.97078 + 0.218090i) q^{96} +(-10.4901 - 10.4901i) q^{97} +(-1.54604 - 1.54604i) q^{98} +(1.10841 - 0.977745i) 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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