LMFDB - Embedded newform 975.2.n.q.749.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(749,975)] 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, 2, 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("975.749"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.n (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,12,-16,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == 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			749.10
Character	$\chi$	$=$	975.749
Dual form			975.2.n.q.824.10

$q$-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} +(1.26244 - 1.18585i) 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} +(-2.21086 - 2.35366i) q^{12} +(3.58949 + 0.339913i) q^{13} -1.32463i q^{14} -3.20461 q^{16} -5.28437i q^{17} +(-0.828552 + 0.730879i) q^{18} +(3.44898 + 3.44898i) q^{19} +(6.22677 + 0.194812i) q^{21} +0.181443i q^{22} -9.38135i q^{23} +(-0.0770834 + 2.46381i) q^{24} +(-0.846238 - 1.02327i) q^{26} +(-3.31383 - 4.00231i) 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} -1.79633i q^{38} +(4.93462 - 3.82747i) q^{39} +(2.21539 - 2.21539i) q^{41} +(-1.57081 - 1.67227i) q^{42} +5.41717 q^{43} +(-0.649497 + 0.649497i) q^{44} +(-2.44304 + 2.44304i) q^{46} +(-2.47000 + 2.47000i) q^{47} +(-4.04564 + 3.80017i) q^{48} +5.93686i q^{49} +(-6.26646 - 6.67123i) q^{51} +(0.633724 - 6.69214i) q^{52} -6.94843 q^{53} +(-0.179291 + 1.90523i) 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} +1.54361i q^{62} +(8.09197 - 7.13805i) q^{63} +4.92631i q^{64} +(0.215164 + 0.229062i) q^{66} +(1.34019 - 1.34019i) q^{67} -9.85202 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} -1.77204i q^{77} +(-2.28178 - 0.288319i) q^{78} -2.66096 q^{79} +(-8.92966 - 1.12300i) q^{81} -1.15384 q^{82} +(7.35570 + 7.35570i) q^{83} +(0.363202 - 11.6090i) q^{84} +(-1.41071 - 1.41071i) q^{86} +(8.07424 + 8.59579i) q^{87} +0.701163 q^{88} +(-2.54802 - 2.54802i) q^{89} +(8.26469 + 9.99370i) q^{91} -17.4903 q^{92} +(-7.25614 - 0.227017i) 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} - 24 q^{12} + 24 q^{13} - 64 q^{16} + 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} + 32 q^{28} + 32 q^{31} + 4 q^{33} + 16 q^{34} + 32 q^{37} + 8 q^{39} - 32 q^{43} - 40 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 - 16 * q^7 - 24 * q^12 + 24 * q^13 - 64 * q^16 + 4 * q^18 + 16 * q^19 - 12 * q^21 - 8 * q^24 + 32 * q^28 + 32 * q^31 + 4 * q^33 + 16 * q^34 + 32 * q^37 + 8 * q^39 - 32 * q^43 - 40 * q^46 - 8 * q^52 + 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 - 108 * q^78 - 40 * q^79 + 72 * q^81 - 128 * q^82 - 124 * q^84 - 80 * q^88 + 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	$-0.291564\pi$
$2$	−0.260415	−	0.260415i	−0.184141	−	0.184141i	−0.793157	+	0.609017i	$0.791564\pi$
$3$	1.26244	−	1.18585i	0.728873	−	0.684649i
$3$	1.26244	−	1.18585i	0.728873	−	0.684649i
$4$		−	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	$-0.0120976\pi$
$7$	2.54331	+	2.54331i	0.961281	+	0.961281i	−0.0379967	+	0.999278i	$0.512098\pi$
$8$	−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	$0.773664\pi$
$12$	−2.21086	−	2.35366i	−0.638219	−	0.679444i
$13$	3.58949	+	0.339913i	0.995546	+	0.0942750i
$13$	3.58949	+	0.339913i	0.995546	+	0.0942750i
$14$		−	1.32463i		−	0.354022i
$15$		0			0
$16$	−3.20461			−0.801152
$17$		−	5.28437i		−	1.28165i	−0.767688	−	0.640824i	$-0.778593\pi$
$17$		−	5.28437i		−	1.28165i	0.767688	−	0.640824i	$-0.221407\pi$
$18$	−0.828552	+	0.730879i	−0.195292	+	0.172270i
$19$	3.44898	+	3.44898i	0.791249	+	0.791249i	0.981697	−	0.190448i	$-0.0609940\pi$
$19$	3.44898	+	3.44898i	0.791249	+	0.791249i	−0.190448	+	0.981697i	$0.560994\pi$
$20$		0			0
$21$	6.22677	+	0.194812i	1.35879	+	0.0425115i
$22$			0.181443i			0.0386838i
$23$		−	9.38135i		−	1.95615i	−0.208262	−	0.978073i	$-0.566781\pi$
$23$		−	9.38135i		−	1.95615i	0.208262	−	0.978073i	$-0.433219\pi$
$24$	−0.0770834	+	2.46381i	−0.0157346	+	0.502923i
$25$		0			0
$26$	−0.846238	−	1.02327i	−0.165961	−	0.200681i
$27$	−3.31383	−	4.00231i	−0.637747	−	0.770246i
$28$	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	$-0.184261\pi$
$37$	1.76399	+	1.76399i	0.289998	+	0.289998i	−0.547082	+	0.837079i	$0.684261\pi$
$38$		−	1.79633i		−	0.291403i
$39$	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	$0.171327\pi$
$42$	−1.57081	−	1.67227i	−0.242381	−	0.258037i
$43$	5.41717			0.826110			0.413055	−	0.910706i	$-0.364462\pi$
$43$	5.41717			0.826110			0.413055	+	0.910706i	$0.364462\pi$
$44$	−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	$-0.831997\pi$
$47$	−2.47000	+	2.47000i	−0.360286	+	0.360286i	0.503632	+	0.863918i	$0.331997\pi$
$48$	−4.04564	+	3.80017i	−0.583938	+	0.548508i
$49$			5.93686i			0.848123i
$50$		0			0
$51$	−6.26646	−	6.67123i	−0.877480	−	0.934159i
$52$	0.633724	−	6.69214i	0.0878817	−	0.928032i
$53$	−6.94843			−0.954441			−0.477220	−	0.878784i	$-0.658356\pi$
$53$	−6.94843			−0.954441			−0.477220	+	0.878784i	$0.658356\pi$
$54$	−0.179291	+	1.90523i	−0.0243984	+	0.259269i
$55$		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	$0.574045\pi$
$62$			1.54361i			0.196039i
$63$	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	−0.620486	−	0.784217i	$-0.713065\pi$
$67$	1.34019	−	1.34019i	0.163731	−	0.163731i	0.784217	+	0.620486i	$0.213065\pi$
$68$	−9.85202			−1.19473
$69$	−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	$0.811295\pi$
$72$	2.82439	+	3.20183i	0.332857	+	0.377339i
$73$	−6.48532	−	6.48532i	−0.759050	−	0.759050i	0.217100	−	0.976149i	$-0.430340\pi$
$73$	−6.48532	−	6.48532i	−0.759050	−	0.759050i	−0.976149	+	0.217100i	$0.930340\pi$
$74$		−	0.918735i		−	0.106801i
$75$		0			0
$76$	6.43016	−	6.43016i	0.737590	−	0.737590i
$77$		−	1.77204i		−	0.201943i
$78$	−2.28178	−	0.288319i	−0.258360	−	0.0326457i
$79$	−2.66096			−0.299382			−0.149691	−	0.988733i	$-0.547828\pi$
$79$	−2.66096			−0.299382			−0.149691	+	0.988733i	$0.547828\pi$
$80$		0			0
$81$	−8.92966	−	1.12300i	−0.992185	−	0.124778i
$82$	−1.15384			−0.127420
$83$	7.35570	+	7.35570i	0.807393	+	0.807393i	0.984239	−	0.176846i	$-0.0565894\pi$
$83$	7.35570	+	7.35570i	0.807393	+	0.807393i	−0.176846	+	0.984239i	$0.556589\pi$
$84$	0.363202	−	11.6090i	0.0396286	−	1.26664i
$85$		0			0
$86$	−1.41071	−	1.41071i	−0.152121	−	0.152121i
$87$	8.07424	+	8.59579i	0.865650	+	0.921565i
$88$	0.701163			0.0747442
$89$	−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
$92$	−17.4903			−1.82349
$93$	−7.25614	−	0.227017i	−0.752426	−	0.0235406i
$94$	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	−0.0673840	+	0.997727i	$0.521465\pi$
$97$	−10.4901	+	10.4901i	−1.06511	+	1.06511i	−0.997727	+	0.0673840i	$0.978535\pi$
$98$	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	$0.540788\pi$
$102$	−0.105409	+	3.36916i	−0.0104370	+	0.333597i
$103$	15.2419			1.50183			0.750914	−	0.660400i	$-0.229613\pi$
$103$	15.2419			1.50183			0.750914	+	0.660400i	$0.229613\pi$
$104$	−3.95431	+	3.27017i	−0.387752	+	0.320667i
$105$		0			0
$106$	1.80947	+	1.80947i	0.175752	+	0.175752i
$107$	8.85806			0.856341			0.428171	−	0.903698i	$-0.359158\pi$
$107$	8.85806			0.856341			0.428171	+	0.903698i	$0.359158\pi$
$108$	−7.46179	+	6.17820i	−0.718011	+	0.594498i
$109$	7.99281	+	7.99281i	0.765573	+	0.765573i	0.977324	−	0.211751i	$-0.0679166\pi$
$109$	7.99281	+	7.99281i	0.765573	+	0.765573i	−0.211751	+	0.977324i	$0.567917\pi$
$110$		0			0
$111$	4.31875	+	0.135118i	0.409918	+	0.0128248i
$112$	−8.15031	−	8.15031i	−0.770132	−	0.770132i
$113$	11.4219			1.07448			0.537239	−	0.843430i	$-0.319467\pi$
$113$	11.4219			1.07448			0.537239	+	0.843430i	$0.319467\pi$
$114$	−2.13017	−	2.26776i	−0.199509	−	0.212396i
$115$		0			0
$116$	12.6942			1.17863
$117$	1.69090	−	10.6837i	0.156324	−	0.987706i
$118$			0.129569i			0.0119278i
$119$	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
$127$	2.64759			0.234936			0.117468	−	0.993077i	$-0.462522\pi$
$127$	2.64759			0.234936			0.117468	+	0.993077i	$0.462522\pi$
$128$	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	$0.928184\pi$
$132$	−0.0497501	+	1.59016i	−0.00433019	+	0.138405i
$133$			17.5436i			1.52123i
$134$	−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	$-0.583849\pi$
$137$	8.25322	−	8.25322i	0.705120	−	0.705120i	0.965505	+	0.260385i	$0.0838494\pi$
$138$	−0.187132	+	5.98127i	−0.0159297	+	0.509160i
$139$	0.517263			0.0438737			0.0219369	−	0.999759i	$-0.493017\pi$
$139$	0.517263			0.0438737			0.0219369	+	0.999759i	$0.493017\pi$
$140$		0			0
$141$	−0.189197	+	6.04728i	−0.0159332	+	0.509273i
$142$	6.09168			0.511202
$143$	−1.13207	−	1.36890i	−0.0946682	−	0.114473i
$144$	−0.600973	+	9.59502i	−0.0500811	+	0.799585i
$145$		0			0
$146$			3.37774i			0.279544i
$147$	7.04021	+	7.49496i	0.580666	+	0.618174i
$148$	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	$0.378026\pi$
$152$	−6.94167			−0.563044
$153$	−15.8221	−	0.991000i	−1.27914	−	0.0801176i
$154$	−0.461466	+	0.461466i	−0.0371860	+	0.0371860i
$155$		0			0
$156$	−7.13581	−	9.19995i	−0.571322	−	0.736586i
$157$			8.40663i			0.670922i	0.942054	+	0.335461i	$0.108892\pi$
$157$			8.40663i			0.670922i	−0.942054	+	0.335461i	$0.891108\pi$
$158$	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	0.382380	−	0.924005i	$-0.375104\pi$
$163$	−6.91500	−	6.91500i	−0.541625	−	0.541625i	−0.924005	+	0.382380i	$0.875104\pi$
$164$	−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	$-0.712995\pi$
$167$	2.11987	−	2.11987i	0.164040	−	0.164040i	0.784354	+	0.620314i	$0.212995\pi$
$168$	−6.46228	+	6.07018i	−0.498576	+	0.468325i
$169$	12.7689	+	2.44023i	0.982224	+	0.187710i
$170$		0			0
$171$	10.9735	−	9.67989i	0.839164	−	0.740240i
$172$		−	10.0996i		−	0.770087i
$173$			21.2987i			1.61931i	0.586906	+	0.809655i	$0.300346\pi$
$173$			21.2987i			1.61931i	−0.586906	+	0.809655i	$0.699654\pi$
$174$	0.135817	−	4.34112i	0.0102963	−	0.329099i
$175$		0			0
$176$	1.11640	+	1.11640i	0.0841518	+	0.0841518i
$177$	−0.609074	−	0.0190556i	−0.0457808	−	0.00143231i
$178$			1.32708i			0.0994692i
$179$	−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	$0.731435\pi$
$182$	0.450260	−	4.75475i	0.0333755	−	0.352446i
$183$	−4.54598	+	4.27015i	−0.336048	+	0.315659i
$184$	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	$0.831609\pi$
$192$	5.84185	+	6.21919i	0.421599	+	0.448832i
$193$	0.516880	+	0.516880i	0.0372058	+	0.0372058i	0.725465	−	0.688259i	$-0.241625\pi$
$193$	0.516880	+	0.516880i	0.0372058	+	0.0372058i	−0.688259	+	0.725465i	$0.741625\pi$
$194$	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	$-0.189914\pi$
$197$	3.72469	+	3.72469i	0.265373	+	0.265373i	−0.561859	+	0.827233i	$0.689914\pi$
$198$	0.543265	+	0.0340268i	0.0386081	+	0.00241818i
$199$		−	14.3661i		−	1.01839i	−0.860652	−	0.509193i	$-0.829944\pi$
$199$		−	14.3661i		−	1.01839i	0.860652	−	0.509193i	$-0.170056\pi$
$200$		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
$207$	−28.0890	−	1.75932i	−1.95232	−	0.122281i
$208$	−11.5029	−	1.08929i	−0.797584	−	0.0755286i
$209$		−	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	$0.394051\pi$
$212$			12.9544i			0.889715i
$213$	−0.895898	+	28.6355i	−0.0613859	+	1.96207i
$214$	−2.30677	−	2.30677i	−0.157687	−	0.157687i
$215$		0			0
$216$	7.36251	+	0.692846i	0.500956	+	0.0471422i
$217$		−	15.0755i		−	1.02339i
$218$		−	4.16289i		−	0.281947i
$219$	−15.8780	−	0.496762i	−1.07293	−	0.0335681i
$220$		0			0
$221$	1.79623	−	18.9682i	0.120827	−	1.27594i
$222$	−1.08948	−	1.15985i	−0.0731211	−	0.0778442i
$223$	4.69628	−	4.69628i	0.314486	−	0.314486i	−0.532159	−	0.846645i	$-0.678619\pi$
$223$	4.69628	−	4.69628i	0.314486	−	0.314486i	0.846645	+	0.532159i	$0.178619\pi$
$224$			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	$-0.368741\pi$
$227$	−7.76531	−	7.76531i	−0.515402	−	0.515402i	−0.916177	+	0.400775i	$0.868741\pi$
$228$	0.492537	−	15.7429i	0.0326191	−	1.04260i
$229$	5.52070	−	5.52070i	0.364818	−	0.364818i	−0.500765	−	0.865583i	$-0.666948\pi$
$229$	5.52070	−	5.52070i	0.364818	−	0.364818i	0.865583	+	0.500765i	$0.166948\pi$
$230$		0			0
$231$	−2.10137	−	2.23711i	−0.138260	−	0.147191i
$232$	−6.85200	−	6.85200i	−0.449856	−	0.449856i
$233$		−	9.73604i		−	0.637829i	−0.947783	−	0.318915i	$-0.896682\pi$
$233$		−	9.73604i		−	0.637829i	0.947783	−	0.318915i	$-0.103318\pi$
$234$	−3.22252	+	2.34185i	−0.210663	+	0.153091i
$235$		0			0
$236$	−0.463808	+	0.463808i	−0.0301913	+	0.0301913i
$237$	−3.35932	+	3.15550i	−0.218211	+	0.204971i
$238$	−6.99984			−0.453732
$239$	−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
$243$	−12.6049	+	9.17148i	−0.808606	+	0.588351i
$244$			6.71346i			0.429786i
$245$		0			0
$246$	−1.45666	+	1.36828i	−0.0928731	+	0.0872381i
$247$	11.2077	+	13.5524i	0.713130	+	0.862320i
$248$	5.96508			0.378783
$249$	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	$0.543697\pi$
$252$	−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
$257$			4.95572i			0.309129i	0.987983	+	0.154565i	$0.0493975\pi$
$257$			4.95572i			0.309129i	−0.987983	+	0.154565i	$0.950602\pi$
$258$	−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
$263$	21.5950			1.33160			0.665801	−	0.746129i	$-0.268090\pi$
$263$	21.5950			1.33160			0.665801	+	0.746129i	$0.268090\pi$
$264$	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	$0.289275\pi$
$272$			16.9343i			1.02680i
$273$	22.2847	+	2.81584i	1.34873	+	0.170422i
$274$	−4.29852			−0.259683
$275$		0			0
$276$	−22.0805	+	20.7408i	−1.32909	+	1.24845i
$277$	−13.8782			−0.833857			−0.416929	−	0.908939i	$-0.636894\pi$
$277$	−13.8782			−0.833857			−0.416929	+	0.908939i	$0.636894\pi$
$278$	−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	$0.537332\pi$
$282$	1.62407	−	1.52553i	0.0967119	−	0.0908439i
$283$	7.59425			0.451431			0.225716	−	0.974193i	$-0.427528\pi$
$283$	7.59425			0.451431			0.225716	+	0.974193i	$0.427528\pi$
$284$	21.8059	+	21.8059i	1.29394	+	1.29394i
$285$		0			0
$286$	−0.0616749	+	0.651289i	−0.00364692	+	0.0385115i
$287$	11.2688			0.665179
$288$	9.05885	−	7.99095i	0.533798	−	0.470871i
$289$	−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	$-0.977069\pi$
$293$	−15.8408	+	15.8408i	−0.925429	+	0.925429i	0.0719771	+	0.997406i	$0.477069\pi$
$294$	0.118424	−	3.78517i	0.00690662	−	0.220756i
$295$		0			0
$296$	−3.55033			−0.206359
$297$	−0.239849	+	2.54875i	−0.0139175	+	0.147894i
$298$	−0.429529			−0.0248819
$299$	3.18885	−	33.6743i	0.184416	−	1.94743i
$300$		0			0
$301$	13.7775	+	13.7775i	0.794124	+	0.794124i
$302$	3.54302			0.203878
$303$	−3.24264	+	3.04590i	−0.186285	+	0.174982i
$304$	−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	0.991240	+	0.132074i	$0.0421636\pi$
$307$	19.6820	+	19.6820i	1.12331	+	1.12331i	0.132074	+	0.991240i	$0.457836\pi$
$308$	−3.30374			−0.188248
$309$	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	$0.645000\pi$
$312$	−1.11417	+	8.81762i	−0.0630776	+	0.499200i
$313$			3.72939i			0.210797i	0.994430	+	0.105399i	$0.0336119\pi$
$313$			3.72939i			0.210797i	−0.994430	+	0.105399i	$0.966388\pi$
$314$	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	0.999307	+	0.0372111i	$0.0118474\pi$
$317$	18.4547	+	18.4547i	1.03652	+	1.03652i	0.0372111	+	0.999307i	$0.488153\pi$
$318$	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
$322$	−12.4268			−0.692519
$323$	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
$328$			4.45886i			0.246199i
$329$	−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
$336$	−19.9543	−	0.624297i	−1.08860	−	0.0340582i
$337$	18.0210			0.981666			0.490833	−	0.871254i	$-0.336692\pi$
$337$	18.0210			0.981666			0.490833	+	0.871254i	$0.336692\pi$
$338$	−2.68974	−	3.96068i	−0.146303	−	0.215433i
$339$	14.4195	−	13.5446i	0.783158	−	0.735641i
$340$		0			0
$341$			2.06499i			0.111825i
$342$	−5.37844	−	0.336873i	−0.290833	−	0.0182160i
$343$	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
$347$	−12.1453			−0.651991			−0.325996	−	0.945371i	$-0.605700\pi$
$347$	−12.1453			−0.651991			−0.325996	+	0.945371i	$0.605700\pi$
$348$	16.0257	−	15.0534i	0.859069	−	0.806945i
$349$	−22.2952	+	22.2952i	−1.19343	+	1.19343i	−0.217337	+	0.976097i	$0.569737\pi$
$349$	−22.2952	+	22.2952i	−1.19343	+	1.19343i	−0.976097	+	0.217337i	$0.930263\pi$
$350$		0			0
$351$	−10.5345	−	15.4927i	−0.562292	−	0.826939i
$352$		−	1.98378i		−	0.105736i
$353$	−7.05913	−	7.05913i	−0.375720	−	0.375720i	0.493836	−	0.869555i	$-0.335594\pi$
$353$	−7.05913	−	7.05913i	−0.375720	−	0.375720i	−0.869555	+	0.493836i	$0.835594\pi$
$354$	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
$363$	−12.7565	−	13.5805i	−0.669541	−	0.712789i
$364$	18.6319	−	15.4084i	0.976579	−	0.807621i
$365$		0			0
$366$	2.29585	+	0.0718286i	0.120006	+	0.00375454i
$367$			17.4749i			0.912181i	0.889933	+	0.456090i	$0.150751\pi$
$367$			17.4749i			0.912181i	−0.889933	+	0.456090i	$0.849249\pi$
$368$			30.0635i			1.56717i
$369$	−6.21771	−	7.04863i	−0.323681	−	0.366937i
$370$		0			0
$371$	−17.6720	−	17.6720i	−0.917486	−	0.917486i
$372$	−0.423244	+	13.5281i	−0.0219442	+	0.701400i
$373$		−	12.9747i		−	0.671805i	−0.941897	−	0.335903i	$-0.890959\pi$
$373$		−	12.9747i		−	0.671805i	0.941897	−	0.335903i	$-0.109041\pi$
$374$	0.958813			0.0495790
$375$		0			0
$376$		−	4.97131i		−	0.256376i
$377$	−2.31442	+	24.4403i	−0.119199	+	1.25874i
$378$	−5.30159	+	4.38960i	−0.272684	+	0.225777i
$379$	4.51436	+	4.51436i	0.231887	+	0.231887i	0.813480	−	0.581593i	$-0.197570\pi$
$379$	4.51436	+	4.51436i	0.231887	+	0.231887i	−0.581593	+	0.813480i	$0.697570\pi$
$380$		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	−0.942516	−	0.334161i	$-0.891547\pi$
$383$	−24.9851	−	24.9851i	−1.27668	−	1.27668i	−0.334161	−	0.942516i	$-0.608453\pi$
$384$	0.534446	−	17.0824i	0.0272733	−	0.871734i
$385$		0			0
$386$		−	0.269206i		−	0.0137022i
$387$	1.01590	−	16.2197i	0.0516412	−	0.824494i
$388$	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
$393$	6.07256	+	6.46481i	0.306320	+	0.326106i
$394$		−	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	$-0.278613\pi$
$397$	−2.52951	−	2.52951i	−0.126952	−	0.126952i	−0.767728	+	0.640776i	$0.778613\pi$
$398$	−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	$0.621060\pi$
$402$	−0.881202	+	0.827736i	−0.0439504	+	0.0412837i
$403$	−9.63096	−	11.6458i	−0.479752	−	0.580119i
$404$			4.78871i			0.238247i
$405$		0			0
$406$	9.01920			0.447615
$407$		−	1.22905i		−	0.0609219i
$408$	13.0197	+	0.407337i	0.644570	+	0.0201662i
$409$	12.4909	+	12.4909i	0.617634	+	0.617634i	0.944924	−	0.327290i	$-0.106135\pi$
$409$	12.4909	+	12.4909i	0.617634	+	0.617634i	−0.327290	+	0.944924i	$0.606135\pi$
$410$		0			0
$411$	0.632179	−	20.2063i	0.0311831	−	0.996703i
$412$		−	28.4165i		−	1.39998i
$413$		−	1.26542i		−	0.0622674i
$414$	6.85663	+	7.77294i	0.336985	+	0.382019i
$415$		0			0
$416$	9.25221	+	11.1878i	0.453627	+	0.548528i
$417$	0.653016	−	0.613395i	0.0319784	−	0.0300381i
$418$	−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
$428$		−	16.5147i		−	0.798268i
$429$	−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	$0.282934\pi$
$432$	10.6195	+	12.8258i	0.510932	+	0.617084i
$433$	−30.0237			−1.44285			−0.721424	−	0.692493i	$-0.756512\pi$
$433$	−30.0237			−1.44285			−0.721424	+	0.692493i	$0.756512\pi$
$434$	−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
$438$	4.00549	+	4.26422i	0.191390	+	0.203752i
$439$		−	13.8417i		−	0.660629i	−0.943871	−	0.330314i	$-0.892845\pi$
$439$		−	13.8417i		−	0.660629i	0.943871	−	0.330314i	$-0.107155\pi$
$440$		0			0
$441$	17.7757	+	1.11336i	0.846464	+	0.0530173i
$442$	−5.40736	+	4.47184i	−0.257202	+	0.212704i
$443$	−5.89439			−0.280051			−0.140026	−	0.990148i	$-0.544718\pi$
$443$	−5.89439			−0.280051			−0.140026	+	0.990148i	$0.544718\pi$
$444$	0.251909	−	8.05175i	0.0119551	−	0.382119i
$445$		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
$452$		−	21.2946i		−	1.00161i
$453$	−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	−0.825604	−	0.564250i	$-0.809166\pi$
$457$	−5.58713	+	5.58713i	−0.261355	+	0.261355i	0.564250	+	0.825604i	$0.309166\pi$
$458$	−2.87534			−0.134356
$459$	−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	$0.0880531\pi$
$462$	−0.0353473	+	1.12980i	−0.00164451	+	0.0525632i
$463$	−8.79012	−	8.79012i	−0.408512	−	0.408512i	0.472708	−	0.881219i	$-0.343277\pi$
$463$	−8.79012	−	8.79012i	−0.408512	−	0.408512i	−0.881219	+	0.472708i	$0.843277\pi$
$464$		−	21.8197i		−	1.01295i
$465$		0			0
$466$	−2.53541	+	2.53541i	−0.117450	+	0.117450i
$467$		−	9.31080i		−	0.430853i	−0.976520	−	0.215426i	$-0.930886\pi$
$467$		−	9.31080i		−	0.430853i	0.976520	−	0.215426i	$-0.0691141\pi$
$468$	−19.9183	−	3.15246i	−0.920724	−	0.145722i
$469$	6.81706			0.314783
$470$		0			0
$471$	9.96897	+	10.6129i	0.459346	+	0.489017i
$472$	0.500703			0.0230467
$473$	−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
$477$	−1.30307	+	20.8045i	−0.0596634	+	0.952574i
$478$	8.40491			0.384432
$479$	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
$482$	3.31229			0.150870
$483$	1.82760	−	58.4155i	0.0831588	−	2.65800i
$484$	−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	−0.382954	−	0.923768i	$-0.625093\pi$
$487$	11.9347	−	11.9347i	0.540814	−	0.540814i	0.923768	+	0.382954i	$0.125093\pi$
$488$	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	$0.438745\pi$
$492$	−10.1122	−	0.316372i	−0.455892	−	0.0142632i
$493$	35.9805			1.62048
$494$	0.610596	−	6.44790i	0.0274720	−	0.290105i
$495$		0			0
$496$	9.49767	+	9.49767i	0.426458	+	0.426458i
$497$	−59.4937			−2.66866
$498$	−4.54305	−	4.83650i	−0.203579	−	0.216729i
$499$	−25.0163	−	25.0163i	−1.11988	−	1.11988i	−0.991758	−	0.128124i	$-0.959104\pi$
$499$	−25.0163	−	25.0163i	−1.11988	−	1.11988i	−0.128124	−	0.991758i	$-0.540896\pi$
$500$		0			0
$501$	0.162377	−	5.19005i	0.00725449	−	0.231875i
$502$	1.12918	+	1.12918i	0.0503979	+	0.0503979i
$503$	20.4948			0.913820			0.456910	−	0.889513i	$-0.348956\pi$
$503$	20.4948			0.913820			0.456910	+	0.889513i	$0.348956\pi$
$504$	−0.959960	+	15.3265i	−0.0427600	+	0.682699i
$505$		0			0
$506$	1.70218			0.0756712
$507$	19.0138	−	12.0613i	0.844432	−	0.535662i
$508$		−	4.93608i		−	0.219003i
$509$	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
$517$	1.72096			0.0756879
$518$	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	$0.962509\pi$
$522$	−4.97644	−	5.64148i	−0.217813	−	0.246921i
$523$			18.4316i			0.805960i	0.915209	+	0.402980i	$0.132026\pi$
$523$			18.4316i			0.805960i	−0.915209	+	0.402980i	$0.867974\pi$
$524$	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
$531$	−0.791519	+	0.698211i	−0.0343490	+	0.0302998i
$532$	32.7078			1.41806
$533$	8.70516	−	7.19908i	0.377062	−	0.311827i
$534$	1.57372	+	1.67537i	0.0681015	+	0.0725004i
$535$		0			0
$536$			2.69738i			0.116509i
$537$	−3.49787	+	3.28564i	−0.150944	+	0.141786i
$538$	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	$0.456208\pi$
$542$	1.49229			0.0640995
$543$	23.8391	+	25.3790i	1.02303	+	1.08912i
$544$	15.0457	−	15.0457i	0.645078	−	0.645078i
$545$		0			0
$546$	−5.06998	−	6.53655i	−0.216975	−	0.279739i
$547$		−	9.53713i		−	0.407778i	−0.978994	−	0.203889i	$-0.934642\pi$
$547$		−	9.53713i		−	0.407778i	0.978994	−	0.203889i	$-0.0653582\pi$
$548$	−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	$-0.880462\pi$
$557$	−13.2999	+	13.2999i	−0.563537	+	0.563537i	0.366773	+	0.930310i	$0.380462\pi$
$558$	4.62177	+	0.289479i	0.195655	+	0.0122546i
$559$	19.4449	+	1.84137i	0.822431	+	0.0778815i
$560$		0			0
$561$	−0.141012	+	4.50715i	−0.00595352	+	0.190292i
$562$		−	7.64909i		−	0.322657i
$563$		−	21.9634i		−	0.925647i	−0.886451	−	0.462823i	$-0.846836\pi$
$563$		−	21.9634i		−	0.925647i	0.886451	−	0.462823i	$-0.153164\pi$
$564$	11.2744	+	0.352732i	0.474736	+	0.0148527i
$565$		0			0
$566$	−1.97765	−	1.97765i	−0.0831270	−	0.0831270i
$567$	−19.8548	−	25.5671i	−0.833821	−	1.07372i
$568$		−	23.5405i		−	0.987737i
$569$	−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	$-0.213160\pi$
$572$	−2.55214	+	2.11059i	−0.106710	+	0.0882482i
$573$	16.5422	+	17.6108i	0.691062	+	0.735700i
$574$	−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	−0.901076	−	0.433662i	$-0.857221\pi$
$577$	−11.2277	+	11.2277i	−0.467414	+	0.467414i	0.433662	+	0.901076i	$0.357221\pi$
$578$	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
$582$	6.89745	−	6.47895i	0.285908	−	0.268561i
$583$	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	$-0.335753\pi$
$587$	−9.11946	−	9.11946i	−0.376400	−	0.376400i	−0.869802	+	0.493401i	$0.835753\pi$
$588$	13.9734	−	13.1255i	0.576252	−	0.541288i
$589$		−	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	$-0.688323\pi$
$593$	6.63125	−	6.63125i	0.272313	−	0.272313i	0.830031	+	0.557718i	$0.188323\pi$
$594$	0.726192	−	0.601272i	0.0297960	−	0.0246705i
$595$		0			0
$596$	−1.53755	−	1.53755i	−0.0629804	−	0.0629804i
$597$	−17.0360	−	18.1364i	−0.697237	−	0.742274i
$598$	−9.59969	+	7.93885i	−0.392561	+	0.324644i
$599$			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	$0.361785\pi$
$602$		−	7.17574i		−	0.292461i
$603$	−3.76139	−	4.26405i	−0.153176	−	0.173646i
$604$	12.6826	+	12.6826i	0.516049	+	0.516049i
$605$		0			0
$606$	1.63763	+	0.0512353i	0.0665241	+	0.00208129i
$607$			1.59959i			0.0649252i	0.999473	+	0.0324626i	$0.0103350\pi$
$607$			1.59959i			0.0649252i	−0.999473	+	0.0324626i	$0.989665\pi$
$608$			19.6399i			0.796502i
$609$	−1.32645	+	42.3971i	−0.0537503	+	1.71802i
$610$		0			0
$611$	−9.70563	+	8.02646i	−0.392648	+	0.324716i
$612$	−1.84759	+	29.4983i	−0.0746843	+	1.19240i
$613$	10.4572	−	10.4572i	0.422362	−	0.422362i	−0.463654	−	0.886016i	$-0.653462\pi$
$613$	10.4572	−	10.4572i	0.422362	−	0.422362i	0.886016	+	0.463654i	$0.153462\pi$
$614$		−	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	$-0.184570\pi$
$617$	7.17003	+	7.17003i	0.288654	+	0.288654i	−0.547894	+	0.836548i	$0.684570\pi$
$618$	−9.71779	−	0.304033i	−0.390907	−	0.0122300i
$619$	34.7195	−	34.7195i	1.39550	−	1.39550i	0.583085	−	0.812411i	$-0.301846\pi$
$619$	34.7195	−	34.7195i	1.39550	−	1.39550i	0.812411	−	0.583085i	$-0.198154\pi$
$620$		0			0
$621$	−37.5471	+	31.0882i	−1.50671	+	1.24753i
$622$	4.04080	+	4.04080i	0.162021	+	0.162021i
$623$		−	12.9608i		−	0.519265i
$624$	−15.8135	+	12.2655i	−0.633048	+	0.491014i
$625$		0			0
$626$	0.971187	−	0.971187i	0.0388164	−	0.0388164i
$627$	−2.84967	−	3.03374i	−0.113805	−	0.121156i
$628$	15.6730			0.625423
$629$	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
$633$	11.9835	−	11.2564i	0.476300	−	0.447400i
$634$		−	9.61174i		−	0.381731i
$635$		0			0
$636$	15.3620	+	16.3543i	0.609142	+	0.648489i
$637$	−2.01802	+	21.3103i	−0.0799568	+	0.844345i
$638$	−1.23542			−0.0489106
$639$	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	$0.670742\pi$
$642$	−5.64764	−	0.176694i	−0.222895	−	0.00697354i
$643$	−5.93694	+	5.93694i	−0.234130	+	0.234130i	−0.814414	−	0.580284i	$-0.802942\pi$
$643$	−5.93694	+	5.93694i	−0.234130	+	0.234130i	0.580284	+	0.814414i	$0.302942\pi$
$644$	−44.4832	−	44.4832i	−1.75289	−	1.75289i
$645$		0			0
$646$	−9.49246			−0.373476
$647$			8.94367i			0.351612i	0.984425	+	0.175806i	$0.0562531\pi$
$647$			8.94367i			0.351612i	−0.984425	+	0.175806i	$0.943747\pi$
$648$	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
$653$	29.3417			1.14823			0.574115	−	0.818775i	$-0.305346\pi$
$653$	29.3417			1.14823			0.574115	+	0.818775i	$0.305346\pi$
$654$	−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	$0.369383\pi$
$662$			7.81973i			0.303922i
$663$	−20.2258	−	26.0764i	−0.785504	−	1.01272i
$664$	−14.8046			−0.574531
$665$		0			0
$666$	−2.75082	−	0.172294i	−0.106592	−	0.00667626i
$667$	63.8761			2.47329
$668$	−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
$672$	17.1742	+	18.2835i	0.662509	+	0.705303i
$673$	−26.5074			−1.02179			−0.510893	−	0.859644i	$-0.670685\pi$
$673$	−26.5074			−1.02179			−0.510893	+	0.859644i	$0.670685\pi$
$674$	−4.69293	−	4.69293i	−0.180765	−	0.180765i
$675$		0			0
$676$	4.54949	−	23.8060i	0.174981	−	0.915614i
$677$	24.4044			0.937939			0.468970	−	0.883214i	$-0.344625\pi$
$677$	24.4044			0.937939			0.468970	+	0.883214i	$0.344625\pi$
$678$	−7.28225	−	0.227834i	−0.279673	−	0.00874993i
$679$	−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	$-0.978332\pi$
$683$	−24.2961	+	24.2961i	−0.929666	+	0.929666i	0.0680180	+	0.997684i	$0.478332\pi$
$684$	−18.0469	−	20.4586i	−0.690040	−	0.782256i
$685$		0			0
$686$	−1.40827			−0.0537679
$687$	0.422874	−	13.5163i	0.0161337	−	0.515679i
$688$	−17.3599			−0.661839
$689$	−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	$0.936876\pi$
$692$	39.7086			1.50950
$693$	−5.30574	−	0.332319i	−0.201548	−	0.0126237i
$694$	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
$698$	11.6120			0.439520
$699$	−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	$0.374779\pi$
$702$	−1.29118	+	6.77787i	−0.0487323	+	0.255814i
$703$			12.1679i			0.458921i
$704$	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	−0.0617322	−	0.998093i	$-0.519662\pi$
$709$	24.9325	−	24.9325i	0.936361	−	0.936361i	0.998093	+	0.0617322i	$0.0196625\pi$
$710$		0			0
$711$	−0.499021	+	7.96728i	−0.0187148	+	0.298796i
$712$	5.12834			0.192193
$713$	−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
$718$			9.37268i			0.349785i
$719$	−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
$726$	−0.214578	+	6.85852i	−0.00796372	+	0.254544i
$727$	−19.3095			−0.716150			−0.358075	−	0.933693i	$-0.616567\pi$
$727$	−19.3095			−0.716150			−0.358075	+	0.933693i	$0.616567\pi$
$728$	−18.3741	−	1.73997i	−0.680990	−	0.0644875i
$729$	−5.03704	+	26.5260i	−0.186557	+	0.982444i
$730$		0			0
$731$		−	28.6263i		−	1.05878i
$732$	7.96114	+	8.47538i	0.294252	+	0.313259i
$733$	−8.23013	+	8.23013i	−0.303987	+	0.303987i	−0.842571	−	0.538585i	$-0.818959\pi$
$733$	−8.23013	+	8.23013i	−0.303987	+	0.303987i	0.538585	+	0.842571i	$0.318959\pi$
$734$	4.55071	−	4.55071i	0.167970	−	0.167970i
$735$		0			0
$736$	26.7106	−	26.7106i	0.984565	−	0.984565i
$737$	−0.933777			−0.0343961
$738$	−0.216384	+	3.45475i	−0.00796521	+	0.127171i
$739$	11.8446	−	11.8446i	0.435710	−	0.435710i	−0.454855	−	0.890565i	$-0.650309\pi$
$739$	11.8446	−	11.8446i	0.435710	−	0.435710i	0.890565	+	0.454855i	$0.150309\pi$
$740$		0			0
$741$	30.2202	+	3.81855i	1.11017	+	0.140278i
$742$			9.20411i			0.337893i
$743$	−7.55046	−	7.55046i	−0.276999	−	0.276999i	0.554911	−	0.831910i	$-0.312752\pi$
$743$	−7.55046	−	7.55046i	−0.276999	−	0.276999i	−0.831910	+	0.554911i	$0.812752\pi$
$744$	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
$753$	−5.47409	+	5.14195i	−0.199487	+	0.187383i
$754$	6.96732	−	5.76190i	0.253735	−	0.209836i
$755$		0			0
$756$	−34.6907	−	3.26456i	−1.26169	−	0.118731i
$757$		−	32.3586i		−	1.17609i	−0.808828	−	0.588046i	$-0.799897\pi$
$757$		−	32.3586i		−	1.17609i	0.808828	−	0.588046i	$-0.200103\pi$
$758$		−	2.35121i		−	0.0853998i
$759$	−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	$-0.537691\pi$
$762$	−1.68803	−	0.0528120i	−0.0611507	−	0.00191318i
$763$			40.6564i			1.47186i
$764$	26.0074			0.940916
$765$		0			0
$766$			13.0129i			0.470177i
$767$	−0.808414	−	0.977538i	−0.0291901	−	0.0352968i
$768$	7.85069	−	7.37436i	0.283287	−	0.266099i
$769$	10.9540	+	10.9540i	0.395013	+	0.395013i	0.876470	−	0.481457i	$-0.159892\pi$
$769$	10.9540	+	10.9540i	0.395013	+	0.395013i	−0.481457	+	0.876470i	$0.659892\pi$
$770$		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	$-0.00807098\pi$
$773$	27.0891	+	27.0891i	0.974326	+	0.974326i	−0.0253530	+	0.999679i	$0.508071\pi$
$774$	−4.48841	+	3.95929i	−0.161332	+	0.142314i
$775$		0			0
$776$		−	21.1132i		−	0.757921i
$777$	10.6403	+	11.3276i	0.381718	+	0.406375i
$778$	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
$783$	27.2511	−	22.5634i	0.973876	−	0.806349i
$784$		−	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	−0.926836	−	0.375468i	$-0.877482\pi$
$787$	−36.5342	−	36.5342i	−1.30230	−	1.30230i	−0.375468	−	0.926836i	$-0.622518\pi$
$788$	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
$792$	0.131492	−	2.09938i	0.00467236	−	0.0745980i
$793$	−12.9255	−	1.22401i	−0.458999	−	0.0434657i
$794$			1.31744i			0.0467543i
$795$		0			0
$796$	−26.7837			−0.949324
$797$		−	29.5724i		−	1.04751i	−0.851870	−	0.523754i	$-0.824531\pi$
$797$		−	29.5724i		−	1.04751i	0.851870	−	0.523754i	$-0.175469\pi$
$798$	0.349947	−	11.1853i	0.0123880	−	0.395956i
$799$	13.0524	+	13.0524i	0.461760	+	0.461760i
$800$		0			0
$801$	−8.10696	+	7.15128i	−0.286445	+	0.252678i
$802$		−	5.81269i		−	0.205253i
$803$			4.51863i			0.159459i
$804$	−6.11734	−	0.191389i	−0.215742	−	0.00674976i
$805$		0			0
$806$	−0.524694	+	5.54078i	−0.0184815	+	0.195166i
$807$	4.88840	+	5.20415i	0.172080	+	0.183195i
$808$	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
$818$		−	6.50562i		−	0.227464i
$819$	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	$-0.0623255\pi$
$822$	−5.42664	+	5.09738i	−0.189276	+	0.177792i
$823$	−43.9680			−1.53263			−0.766313	−	0.642467i	$-0.777911\pi$
$823$	−43.9680			−1.53263			−0.766313	+	0.642467i	$0.777911\pi$
$824$	−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	−0.0512796	+	0.998684i	$0.516330\pi$
$827$	−30.1945	+	30.1945i	−1.04996	+	1.04996i	−0.998684	+	0.0512796i	$0.983670\pi$
$828$	−3.28002	+	52.3682i	−0.113989	+	1.81992i
$829$			34.9574i			1.21412i	0.794656	+	0.607060i	$0.207651\pi$
$829$			34.9574i			1.21412i	−0.794656	+	0.607060i	$0.792349\pi$
$830$		0			0
$831$	−17.5204	+	16.4574i	−0.607776	+	0.570900i
$832$	−1.67452	+	17.6829i	−0.0580535	+	0.613046i
$833$	31.3726			1.08700
$834$	−0.329792	−	0.0103180i	−0.0114198	−	0.000357282i
$835$		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
$842$			12.9775i			0.447233i
$843$	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
$848$	22.2670			0.764652
$849$	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	0.284792	−	0.958589i	$-0.408075\pi$
$853$	−19.6790	−	19.6790i	−0.673797	−	0.673797i	−0.958589	+	0.284792i	$0.908075\pi$
$854$			4.76990i			0.163223i
$855$		0			0
$856$	−8.91420	+	8.91420i	−0.304681	+	0.304681i
$857$			13.8696i			0.473777i	0.971537	+	0.236889i	$0.0761277\pi$
$857$			13.8696i			0.473777i	−0.971537	+	0.236889i	$0.923872\pi$
$858$	0.694468	+	0.895353i	0.0237087	+	0.0305669i
$859$	−47.5429			−1.62214			−0.811072	−	0.584946i	$-0.801116\pi$
$859$	−47.5429			−1.62214			−0.811072	+	0.584946i	$0.801116\pi$
$860$		0			0
$861$	14.2263	−	13.3631i	0.484831	−	0.455414i
$862$	1.57933			0.0537922
$863$	−18.8498	−	18.8498i	−0.641654	−	0.641654i	0.309308	−	0.950962i	$-0.399903\pi$
$863$	−18.8498	−	18.8498i	−0.641654	−	0.641654i	−0.950962	+	0.309308i	$0.899903\pi$
$864$	1.96025	−	20.8305i	0.0666890	−	0.708670i
$865$		0			0
$866$	7.81862	+	7.81862i	0.265687	+	0.265687i
$867$	−13.7917	+	12.9549i	−0.468391	+	0.439972i
$868$	−28.1063			−0.953990
$869$	0.927010	+	0.927010i	0.0314466	+	0.0314466i
$870$		0			0
$871$	5.26617	−	4.35507i	0.178437	−	0.147566i
$872$	−16.0869			−0.544773
$873$	29.4416	+	33.3761i	0.996447	+	1.12961i
$874$	−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	−0.325265	+	0.945623i	$0.605454\pi$
$877$	−37.6363	+	37.6363i	−1.27089	+	1.27089i	−0.945623	+	0.325265i	$0.894546\pi$
$878$	−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	$0.194219\pi$
$882$	−4.33913	−	4.91900i	−0.146106	−	0.165631i
$883$	27.2665			0.917592			0.458796	−	0.888542i	$-0.348281\pi$
$883$	27.2665			0.917592			0.458796	+	0.888542i	$0.348281\pi$
$884$	−35.3638	−	3.34883i	−1.18941	−	0.112633i
$885$		0			0
$886$	1.53499	+	1.53499i	0.0515689	+	0.0515689i
$887$	−32.1996			−1.08116			−0.540578	−	0.841294i	$-0.681794\pi$
$887$	−32.1996			−1.08116			−0.540578	+	0.841294i	$0.681794\pi$
$888$	−4.48210	+	4.21015i	−0.150409	+	0.141283i
$889$	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
$893$	−17.0379			−0.570153
$894$	−0.542256	+	0.509355i	−0.0181358	+	0.0170354i
$895$		0			0
$896$	35.4908			1.18566
$897$	−35.9068	−	46.2934i	−1.19889	−	1.54569i
$898$		−	7.91374i		−	0.264085i
$899$	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
$907$	−52.9829			−1.75927			−0.879634	−	0.475651i	$-0.842213\pi$
$907$	−52.9829			−1.75927			−0.879634	+	0.475651i	$0.842213\pi$
$908$	−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	$-0.0871617\pi$
$912$	−27.0600	−	0.846607i	−0.896047	−	0.0280340i
$913$		−	5.12506i		−	0.169615i
$914$	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	$-0.777388\pi$
$919$	−46.3976			−1.53051			−0.765257	+	0.643725i	$0.777388\pi$
$920$		0			0
$921$	48.1874	+	1.50760i	1.58783	+	0.0496772i
$922$	−7.70340			−0.253698
$923$	−45.9588	+	38.0075i	−1.51275	+	1.25103i
$924$	−4.17079	+	3.91773i	−0.137209	+	0.128884i
$925$		0			0
$926$			4.57815i			0.150447i
$927$	2.85837	−	45.6363i	0.0938813	−	1.49889i
$928$	−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
$932$	−18.1516			−0.594575
$933$	−19.5891	+	18.4005i	−0.641318	+	0.602407i
$934$	−2.42467	+	2.42467i	−0.0793376	+	0.0793376i
$935$		0			0
$936$	9.04977	+	12.4530i	0.295801	+	0.407039i
$937$		−	23.7901i		−	0.777188i	−0.921409	−	0.388594i	$-0.872961\pi$
$937$		−	23.7901i		−	0.777188i	0.921409	−	0.388594i	$-0.127039\pi$
$938$	−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	$0.987709\pi$
$942$	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	0.246523	−	0.969137i	$-0.420712\pi$
$947$	37.4100	−	37.4100i	1.21566	−	1.21566i	0.969137	−	0.246523i	$-0.0792881\pi$
$948$	5.88301	+	6.26301i	0.191071	+	0.203413i
$949$	−21.0746	−	25.4835i	−0.684109	−	0.827228i
$950$		0			0
$951$	45.1825	+	1.41359i	1.46514	+	0.0458388i
$952$			27.0500i			0.876694i
$953$			17.7294i			0.574311i	0.957884	+	0.287156i	$0.0927097\pi$
$953$			17.7294i			0.574311i	−0.957884	+	0.287156i	$0.907290\pi$
$954$	5.75714	−	5.07847i	0.186394	−	0.164421i
$955$		0			0
$956$	30.0863	+	30.0863i	0.973062	+	0.973062i
$957$	0.181692	−	5.80740i	0.00587326	−	0.187727i
$958$		−	11.0607i		−	0.357355i
$959$	41.9810			1.35564
$960$		0			0
$961$		−	13.4323i		−	0.433300i
$962$	0.312290	−	3.29779i	0.0100686	−	0.106325i
$963$	1.66119	−	26.5222i	0.0535310	−	0.854666i
$964$	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	−0.674506	−	0.738270i	$-0.735643\pi$
$967$	1.98285	−	1.98285i	0.0637640	−	0.0637640i	0.738270	+	0.674506i	$0.235643\pi$
$968$	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	$-0.262444\pi$
$972$	17.0990	+	23.5002i	0.548451	+	0.753770i
$973$	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	$-0.217235\pi$
$977$	4.54207	+	4.54207i	0.145314	+	0.145314i	−0.630707	+	0.776021i	$0.717235\pi$
$978$	4.27087	+	4.54674i	0.136567	+	0.145389i
$979$			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	$-0.577481\pi$
$983$	22.8720	−	22.8720i	0.729505	−	0.729505i	0.970521	+	0.241016i	$0.0774808\pi$
$984$	5.28752	+	5.62906i	0.168560	+	0.179448i
$985$		0			0
$986$	−9.36984	−	9.36984i	−0.298396	−	0.298396i
$987$	−15.8613	+	14.8989i	−0.504870	+	0.474238i
$988$	25.2667	−	20.8953i	0.803842	−	0.664769i
$989$		−	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	$0.567135\pi$
$992$		−	16.8768i		−	0.535840i
$993$	−36.7586	−	1.15004i	−1.16650	−	0.0364954i
$994$	15.4930	+	15.4930i	0.491409	+	0.491409i
$995$		0			0
$996$	1.05044	−	33.5752i	0.0332846	−	1.06387i
$997$			9.27082i			0.293610i	0.989165	+	0.146805i	$0.0468989\pi$
$997$			9.27082i			0.293610i	−0.989165	+	0.146805i	$0.953101\pi$
$998$			13.0292i			0.412432i
$999$	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.n.q.749.10		40
3.2	odd	2	inner	975.2.n.q.749.11		40
5.2	odd	4		975.2.o.p.476.11		40
5.3	odd	4		195.2.o.a.86.10	✓	40
5.4	even	2		975.2.n.r.749.11		40
13.5	odd	4		975.2.n.r.824.10		40
15.2	even	4		975.2.o.p.476.10		40
15.8	even	4		195.2.o.a.86.11	yes	40
15.14	odd	2		975.2.n.r.749.10		40
39.5	even	4		975.2.n.r.824.11		40
65.18	even	4		195.2.o.a.161.11	yes	40
65.44	odd	4	inner	975.2.n.q.824.11		40
65.57	even	4		975.2.o.p.551.10		40
195.44	even	4	inner	975.2.n.q.824.10		40
195.83	odd	4		195.2.o.a.161.10	yes	40
195.122	odd	4		975.2.o.p.551.11		40

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

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.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.260415 - 0.260415i) q^{2} +(1.26244 - 1.18585i) 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} +(-2.21086 - 2.35366i) q^{12} +(3.58949 + 0.339913i) q^{13} -1.32463i q^{14} -3.20461 q^{16} -5.28437i q^{17} +(-0.828552 + 0.730879i) q^{18} +(3.44898 + 3.44898i) q^{19} +(6.22677 + 0.194812i) q^{21} +0.181443i q^{22} -9.38135i q^{23} +(-0.0770834 + 2.46381i) q^{24} +(-0.846238 - 1.02327i) q^{26} +(-3.31383 - 4.00231i) 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} -1.79633i q^{38} +(4.93462 - 3.82747i) q^{39} +(2.21539 - 2.21539i) q^{41} +(-1.57081 - 1.67227i) q^{42} +5.41717 q^{43} +(-0.649497 + 0.649497i) q^{44} +(-2.44304 + 2.44304i) q^{46} +(-2.47000 + 2.47000i) q^{47} +(-4.04564 + 3.80017i) q^{48} +5.93686i q^{49} +(-6.26646 - 6.67123i) q^{51} +(0.633724 - 6.69214i) q^{52} -6.94843 q^{53} +(-0.179291 + 1.90523i) 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} +1.54361i q^{62} +(8.09197 - 7.13805i) q^{63} +4.92631i q^{64} +(0.215164 + 0.229062i) q^{66} +(1.34019 - 1.34019i) q^{67} -9.85202 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} -1.77204i q^{77} +(-2.28178 - 0.288319i) q^{78} -2.66096 q^{79} +(-8.92966 - 1.12300i) q^{81} -1.15384 q^{82} +(7.35570 + 7.35570i) q^{83} +(0.363202 - 11.6090i) q^{84} +(-1.41071 - 1.41071i) q^{86} +(8.07424 + 8.59579i) q^{87} +0.701163 q^{88} +(-2.54802 - 2.54802i) q^{89} +(8.26469 + 9.99370i) q^{91} -17.4903 q^{92} +(-7.25614 - 0.227017i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} - 16 q^{7} - 24 q^{12} + 24 q^{13} - 64 q^{16} + 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} + 32 q^{28} + 32 q^{31} + 4 q^{33} + 16 q^{34} + 32 q^{37} + 8 q^{39} - 32 q^{43} - 40 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 - 16 * q^7 - 24 * q^12 + 24 * q^13 - 64 * q^16 + 4 * q^18 + 16 * q^19 - 12 * q^21 - 8 * q^24 + 32 * q^28 + 32 * q^31 + 4 * q^33 + 16 * q^34 + 32 * q^37 + 8 * q^39 - 32 * q^43 - 40 * q^46 - 8 * q^52 + 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 - 108 * q^78 - 40 * q^79 + 72 * q^81 - 128 * q^82 - 124 * q^84 - 80 * q^88 + 8 * q^91 - 108 * q^93 + 32 * q^94 - 76 * q^96 - 24 * q^97 + 20 * q^99

Introduction

L-functions

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