LMFDB - Embedded newform 975.2.n.q.749.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(749,975)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			749.11
Character	$\chi$	$=$	975.749
Dual form			975.2.n.q.824.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.260415 + 0.260415i) q^{2} +(-1.26244 - 1.18585i) q^{3} -1.86437i q^{4} +(-0.0199472 - 0.637571i) q^{6} +(2.54331 + 2.54331i) q^{7} +(1.00634 - 1.00634i) q^{8} +(0.187534 + 2.99413i) q^{9} +O(q^{10})$	\(q+(0.260415 + 0.260415i) q^{2} +(-1.26244 - 1.18585i) q^{3} -1.86437i q^{4} +(-0.0199472 - 0.637571i) q^{6} +(2.54331 + 2.54331i) q^{7} +(1.00634 - 1.00634i) q^{8} +(0.187534 + 2.99413i) q^{9} +(0.348374 + 0.348374i) q^{11} +(-2.21086 + 2.35366i) q^{12} +(3.58949 + 0.339913i) q^{13} +1.32463i q^{14} -3.20461 q^{16} +5.28437i q^{17} +(-0.730879 + 0.828552i) q^{18} +(3.44898 + 3.44898i) q^{19} +(-0.194812 - 6.22677i) q^{21} +0.181443i q^{22} +9.38135i q^{23} +(-2.46381 + 0.0770834i) 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} +(-0.0266847 - 0.852920i) q^{33} +(-1.37613 + 1.37613i) q^{34} +(5.58217 - 0.349633i) q^{36} +(1.76399 + 1.76399i) q^{37} +1.79633i q^{38} +(-4.12845 - 4.68571i) 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} +(1.90523 - 0.179291i) 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} -1.54361i q^{62} +(-7.13805 + 8.09197i) q^{63} +4.92631i q^{64} +(0.215164 - 0.229062i) q^{66} +(1.34019 - 1.34019i) q^{67} +9.85202 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} +1.77204i q^{77} +(0.145118 - 2.29534i) q^{78} -2.66096 q^{79} +(-8.92966 + 1.12300i) q^{81} -1.15384 q^{82} +(-7.35570 - 7.35570i) q^{83} +(-11.6090 + 0.363202i) 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} +(0.227017 + 7.25614i) q^{93} +1.28645 q^{94} +(0.218090 + 6.97078i) q^{96} +(-10.4901 + 10.4901i) q^{97} +(-1.54604 + 1.54604i) q^{98} +(-0.977745 + 1.10841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 40 * q + 12 * q^6 - 16 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.260415	+	0.260415i	0.184141	+	0.184141i	0.793157	−	0.609017i	$-0.208436\pi$
$2$	0.260415	+	0.260415i	0.184141	+	0.184141i	−0.609017	+	0.793157i	$0.708436\pi$
$3$	−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
$6$	−0.0199472	−	0.637571i	−0.00814341	−	0.260287i
$7$	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	0.757673	−	0.652634i	$-0.226336\pi$
$11$	0.348374	+	0.348374i	0.105039	+	0.105039i	−0.652634	+	0.757673i	$0.726336\pi$
$12$	−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	$0.221407\pi$
$17$			5.28437i			1.28165i	−0.767688	+	0.640824i	$0.778593\pi$
$18$	−0.730879	+	0.828552i	−0.172270	+	0.195292i
$19$	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
$21$	−0.194812	−	6.22677i	−0.0425115	−	1.35879i
$22$			0.181443i			0.0386838i
$23$			9.38135i			1.95615i	0.208262	+	0.978073i	$0.433219\pi$
$23$			9.38135i			1.95615i	−0.208262	+	0.978073i	$0.566781\pi$
$24$	−2.46381	+	0.0770834i	−0.502923	+	0.0157346i
$25$		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	$-0.782158\pi$
$29$		−	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	$-0.184261\pi$
$37$	1.76399	+	1.76399i	0.289998	+	0.289998i	−0.547082	+	0.837079i	$0.684261\pi$
$38$			1.79633i			0.291403i
$39$	−4.12845	−	4.68571i	−0.661081	−	0.750314i
$40$		0			0
$41$	−2.21539	+	2.21539i	−0.345986	+	0.345986i	−0.858612	−	0.512626i	$-0.828673\pi$
$41$	−2.21539	+	2.21539i	−0.345986	+	0.345986i	0.512626	+	0.858612i	$0.328673\pi$
$42$	1.57081	−	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	−0.503632	−	0.863918i	$-0.668003\pi$
$47$	2.47000	−	2.47000i	0.360286	−	0.360286i	0.863918	+	0.503632i	$0.168003\pi$
$48$	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	$-0.341644\pi$
$53$	6.94843			0.954441			0.477220	+	0.878784i	$0.341644\pi$
$54$	1.90523	−	0.179291i	0.259269	−	0.0243984i
$55$		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	$0.574045\pi$
$62$		−	1.54361i		−	0.196039i
$63$	−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	−0.620486	−	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	$-0.311295\pi$
$71$	11.6961	−	11.6961i	1.38807	−	1.38807i	0.829361	−	0.558713i	$-0.188705\pi$
$72$	3.20183	+	2.82439i	0.377339	+	0.332857i
$73$	−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
$78$	0.145118	−	2.29534i	0.0164314	−	0.259896i
$79$	−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	0.176846	−	0.984239i	$-0.443411\pi$
$83$	−7.35570	−	7.35570i	−0.807393	−	0.807393i	−0.984239	+	0.176846i	$0.943411\pi$
$84$	−11.6090	+	0.363202i	−1.26664	+	0.0396286i
$85$		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	0.829136	−	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
$92$	17.4903			1.82349
$93$	0.227017	+	7.25614i	0.0235406	+	0.752426i
$94$	1.28645			0.132687
$95$		0			0
$96$	0.218090	+	6.97078i	0.0222587	+	0.711452i
$97$	−10.4901	+	10.4901i	−1.06511	+	1.06511i	−0.0673840	+	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
$99$	−0.977745	+	1.10841i	−0.0982670	+	0.111399i
$100$		0			0
$101$	2.56854			0.255579			0.127790	−	0.991801i	$-0.459212\pi$
$101$	2.56854			0.255579			0.127790	+	0.991801i	$0.459212\pi$
$102$	3.36916	−	0.105409i	0.333597	−	0.0104370i
$103$	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	$-0.640842\pi$
$107$	−8.85806			−0.856341			−0.428171	+	0.903698i	$0.640842\pi$
$108$	−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
$111$	−0.135118	−	4.31875i	−0.0128248	−	0.409918i
$112$	−8.15031	−	8.15031i	−0.770132	−	0.770132i
$113$	−11.4219			−1.07448			−0.537239	−	0.843430i	$-0.680533\pi$
$113$	−11.4219			−1.07448			−0.537239	+	0.843430i	$0.680533\pi$
$114$	2.13017	−	2.26776i	0.199509	−	0.212396i
$115$		0			0
$116$	−12.6942			−1.17863
$117$	−0.344594	+	10.8112i	−0.0318577	+	0.999492i
$118$			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
$123$	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
$127$	2.64759			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	$-0.928184\pi$
$131$		−	5.12086i		−	0.447412i	0.974657	−	0.223706i	$-0.0718155\pi$
$132$	−1.59016	+	0.0497501i	−0.138405	+	0.00433019i
$133$			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	−0.965505	−	0.260385i	$-0.916151\pi$
$137$	−8.25322	+	8.25322i	−0.705120	+	0.705120i	0.260385	+	0.965505i	$0.416151\pi$
$138$	5.98127	−	0.187132i	0.509160	−	0.0159297i
$139$	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
$141$	−6.04728	+	0.189197i	−0.509273	+	0.0159332i
$142$	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	−0.740080	−	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	$0.378026\pi$
$152$	6.94167			0.563044
$153$	−15.8221	+	0.991000i	−1.27914	+	0.0801176i
$154$	−0.461466	+	0.461466i	−0.0371860	+	0.0371860i
$155$		0			0
$156$	−8.73589	+	7.69696i	−0.699431	+	0.616250i
$157$			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
$162$	−2.61786	−	2.03297i	−0.205679	−	0.159725i
$163$	−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	−0.784354	−	0.620314i	$-0.787005\pi$
$167$	−2.11987	+	2.11987i	−0.164040	+	0.164040i	0.620314	+	0.784354i	$0.287005\pi$
$168$	−6.46228	−	6.07018i	−0.498576	−	0.468325i
$169$	12.7689	+	2.44023i	0.982224	+	0.187710i
$170$		0			0
$171$	−9.67989	+	10.9735i	−0.740240	+	0.839164i
$172$		−	10.0996i		−	0.770087i
$173$		−	21.2987i		−	1.61931i	−0.586906	−	0.809655i	$-0.699654\pi$
$173$		−	21.2987i		−	1.61931i	0.586906	−	0.809655i	$-0.300346\pi$
$174$	−4.34112	+	0.135817i	−0.329099	+	0.0102963i
$175$		0			0
$176$	−1.11640	−	1.11640i	−0.0841518	−	0.0841518i
$177$	−0.0190556	−	0.609074i	−0.00143231	−	0.0457808i
$178$			1.32708i			0.0994692i
$179$	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	$0.731435\pi$
$182$	−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
$189$	18.6072	−	1.75102i	1.35348	−	0.127368i
$190$		0			0
$191$		−	13.9497i		−	1.00937i	−0.863304	−	0.504684i	$-0.831609\pi$
$191$		−	13.9497i		−	1.00937i	0.863304	−	0.504684i	$-0.168391\pi$
$192$	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	0.561859	−	0.827233i	$-0.310086\pi$
$197$	−3.72469	−	3.72469i	−0.265373	−	0.265373i	−0.827233	+	0.561859i	$0.810086\pi$
$198$	−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
$201$	−3.28119	+	0.102656i	−0.231437	+	0.00724080i
$202$	0.668886	+	0.668886i	0.0470626	+	0.0470626i
$203$	17.3170	−	17.3170i	1.21542	−	1.21542i
$204$	−12.4376	−	11.6830i	−0.870808	−	0.817973i
$205$		0			0
$206$	3.96921	+	3.96921i	0.276548	+	0.276548i
$207$	−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
$213$	−28.6355	+	0.895898i	−1.96207	+	0.0613859i
$214$	−2.30677	−	2.30677i	−0.157687	−	0.157687i
$215$		0			0
$216$	−0.692846	−	7.36251i	−0.0471422	−	0.500956i
$217$		−	15.0755i		−	1.02339i
$218$			4.16289i			0.281947i
$219$	0.496762	+	15.8780i	0.0335681	+	1.07293i
$220$		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	0.916177	−	0.400775i	$-0.131259\pi$
$227$	7.76531	+	7.76531i	0.515402	+	0.515402i	−0.400775	+	0.916177i	$0.631259\pi$
$228$	−15.7429	+	0.492537i	−1.04260	+	0.0326191i
$229$	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	$0.103318\pi$
$233$			9.73604i			0.637829i	−0.947783	+	0.318915i	$0.896682\pi$
$234$	−2.90512	+	2.72565i	−0.189914	+	0.178181i
$235$		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	$-0.485716\pi$
$239$	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
$243$	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
$249$	0.563431	+	18.0089i	0.0357060	+	1.14127i
$250$		0			0
$251$	4.33610			0.273692			0.136846	−	0.990592i	$-0.456303\pi$
$251$	4.33610			0.273692			0.136846	+	0.990592i	$0.456303\pi$
$252$	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
$257$		−	4.95572i		−	0.309129i	−0.987983	−	0.154565i	$-0.950602\pi$
$257$		−	4.95572i		−	0.309129i	0.987983	−	0.154565i	$-0.0493975\pi$
$258$	−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
$263$	−21.5950			−1.33160			−0.665801	−	0.746129i	$-0.731910\pi$
$263$	−21.5950			−1.33160			−0.665801	+	0.746129i	$0.731910\pi$
$264$	−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	$0.289275\pi$
$272$		−	16.9343i		−	1.02680i
$273$	1.41728	−	22.4172i	0.0857779	−	1.35675i
$274$	−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
$279$	8.31807	−	9.42968i	0.497990	−	0.564540i
$280$		0			0
$281$	−14.6864	−	14.6864i	−0.876116	−	0.876116i	0.117015	−	0.993130i	$-0.462668\pi$
$281$	−14.6864	−	14.6864i	−0.876116	−	0.876116i	−0.993130	+	0.117015i	$0.962668\pi$
$282$	−1.62407	−	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
$288$	7.99095	−	9.05885i	0.470871	−	0.533798i
$289$	−10.9246			−0.642623
$290$		0			0
$291$	25.6829	−	0.803522i	1.50556	−	0.0471033i
$292$	−12.0910	+	12.0910i	−0.707574	+	0.707574i
$293$	15.8408	−	15.8408i	0.925429	−	0.925429i	−0.0719771	−	0.997406i	$-0.522931\pi$
$293$	15.8408	−	15.8408i	0.925429	−	0.925429i	0.997406	+	0.0719771i	$0.0229308\pi$
$294$	3.78517	−	0.118424i	0.220756	−	0.00690662i
$295$		0			0
$296$	3.55033			0.206359
$297$	2.54875	−	0.239849i	0.147894	−	0.0139175i
$298$	−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
$306$	−4.37838	−	3.86224i	−0.250295	−	0.220789i
$307$	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	$-0.355000\pi$
$311$	15.5168			0.879877			0.439938	+	0.898028i	$0.355000\pi$
$312$	−8.87003	−	0.560791i	−0.502166	−	0.0317486i
$313$			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	$-0.988153\pi$
$317$	−18.4547	−	18.4547i	−1.03652	−	1.03652i	−0.0372111	−	0.999307i	$-0.511847\pi$
$318$	−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
$322$	−12.4268			−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
$327$	−0.612233	−	19.5687i	−0.0338566	−	1.08215i
$328$			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
$333$	−4.95080	+	5.61242i	−0.271302	+	0.307559i
$334$	−1.10409			−0.0604131
$335$		0			0
$336$	0.624297	+	19.9543i	0.0340582	+	1.08860i
$337$	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	$-0.394300\pi$
$347$	12.1453			0.651991			0.325996	+	0.945371i	$0.394300\pi$
$348$	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
$351$	13.2554	−	13.2399i	0.707522	−	0.706692i
$352$		−	1.98378i		−	0.105736i
$353$	7.05913	+	7.05913i	0.375720	+	0.375720i	0.869555	−	0.493836i	$-0.164406\pi$
$353$	7.05913	+	7.05913i	0.375720	+	0.375720i	−0.493836	+	0.869555i	$0.664406\pi$
$354$	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
$363$	−12.7565	+	13.5805i	−0.669541	+	0.712789i
$364$	18.6319	−	15.4084i	0.976579	−	0.807621i
$365$		0			0
$366$	0.0718286	+	2.29585i	0.00375454	+	0.120006i
$367$			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
$369$	−7.04863	−	6.21771i	−0.366937	−	0.323681i
$370$		0			0
$371$	17.6720	+	17.6720i	0.917486	+	0.917486i
$372$	13.5281	−	0.423244i	0.701400	−	0.0219442i
$373$		−	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	$0.108453\pi$
$383$	24.9851	+	24.9851i	1.27668	+	1.27668i	0.334161	+	0.942516i	$0.391547\pi$
$384$	17.0824	−	0.534446i	0.871734	−	0.0272733i
$385$		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	$-0.456587\pi$
$389$	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
$393$	−6.07256	+	6.46481i	−0.306320	+	0.326106i
$394$		−	1.93993i		−	0.0977322i
$395$		0			0
$396$	2.06648	+	1.82288i	0.103845	+	0.0916030i
$397$	−2.52951	−	2.52951i	−0.126952	−	0.126952i	0.640776	−	0.767728i	$-0.278613\pi$
$397$	−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	0.371219	−	0.928545i	$-0.378940\pi$
$401$	−11.1604	−	11.1604i	−0.557326	−	0.557326i	−0.928545	+	0.371219i	$0.878940\pi$
$402$	−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
$408$	−0.407337	−	13.0197i	−0.0201662	−	0.644570i
$409$	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
$411$	20.2063	−	0.632179i	0.996703	−	0.0311831i
$412$		−	28.4165i		−	1.39998i
$413$			1.26542i			0.0622674i
$414$	−7.77294	−	6.85663i	−0.382019	−	0.336985i
$415$		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	$0.0487877\pi$
$419$			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
$428$			16.5147i			0.798268i
$429$	0.194134	−	3.07062i	0.00937290	−	0.148251i
$430$		0			0
$431$	3.03234	−	3.03234i	0.146063	−	0.146063i	−0.630294	−	0.776357i	$-0.717066\pi$
$431$	3.03234	−	3.03234i	0.146063	−	0.146063i	0.776357	+	0.630294i	$0.217066\pi$
$432$	−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	$-0.455282\pi$
$443$	5.89439			0.280051			0.140026	+	0.990148i	$0.455282\pi$
$444$	−8.05175	+	0.251909i	−0.382119	+	0.0119551i
$445$		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
$452$			21.2946i			1.00161i
$453$	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	−0.825604	−	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	−0.961982	−	0.273113i	$-0.911947\pi$
$461$	−14.7907	+	14.7907i	−0.688870	+	0.688870i	0.273113	+	0.961982i	$0.411947\pi$
$462$	1.12980	−	0.0353473i	0.0525632	−	0.00164451i
$463$	−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	$0.0691141\pi$
$467$			9.31080i			0.430853i	−0.976520	+	0.215426i	$0.930886\pi$
$468$	20.1560	+	0.642450i	0.931711	+	0.0296972i
$469$	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
$474$	0.0530788	+	1.69655i	0.00243799	+	0.0779253i
$475$		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	0.0292411	−	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
$482$	−3.31229			−0.150870
$483$	58.4155	−	1.82760i	2.65800	−	0.0831588i
$484$	−20.0555			−0.911614
$485$		0			0
$486$	0.894116	+	5.67089i	0.0405579	+	0.257237i
$487$	11.9347	−	11.9347i	0.540814	−	0.540814i	−0.382954	−	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
$489$	0.529675	+	16.9299i	0.0239527	+	0.765599i
$490$		0			0
$491$	−8.47582			−0.382508			−0.191254	−	0.981541i	$-0.561255\pi$
$491$	−8.47582			−0.382508			−0.191254	+	0.981541i	$0.561255\pi$
$492$	−0.316372	−	10.1122i	−0.0142632	−	0.455892i
$493$	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
$501$	5.19005	−	0.162377i	0.231875	−	0.00725449i
$502$	1.12918	+	1.12918i	0.0503979	+	0.0503979i
$503$	−20.4948			−0.913820			−0.456910	−	0.889513i	$-0.651044\pi$
$503$	−20.4948			−0.913820			−0.456910	+	0.889513i	$0.651044\pi$
$504$	0.959960	+	15.3265i	0.0427600	+	0.682699i
$505$		0			0
$506$	−1.70218			−0.0756712
$507$	−13.2263	−	18.2226i	−0.587401	−	0.809296i
$508$		−	4.93608i		−	0.219003i
$509$	−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
$517$	1.72096			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	$-0.962509\pi$
$521$		−	5.36438i		−	0.235018i	0.993072	−	0.117509i	$-0.0374909\pi$
$522$	5.64148	+	4.97644i	0.246921	+	0.217813i
$523$			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
$528$	0.0855139	+	2.73327i	0.00372152	+	0.118950i
$529$	−65.0097			−2.82651
$530$		0			0
$531$	−0.698211	+	0.791519i	−0.0302998	+	0.0343490i
$532$	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
$546$	6.20684	−	5.46867i	0.265628	−	0.234038i
$547$		−	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
$552$	−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	$-0.619538\pi$
$557$	13.2999	−	13.2999i	0.563537	−	0.563537i	0.930310	+	0.366773i	$0.119538\pi$
$558$	4.62177	−	0.289479i	0.195655	−	0.0122546i
$559$	19.4449	+	1.84137i	0.822431	+	0.0778815i
$560$		0			0
$561$	4.50715	−	0.141012i	0.190292	−	0.00595352i
$562$		−	7.64909i		−	0.322657i
$563$			21.9634i			0.925647i	0.886451	+	0.462823i	$0.153164\pi$
$563$			21.9634i			0.925647i	−0.886451	+	0.462823i	$0.846836\pi$
$564$	0.352732	+	11.2744i	0.0148527	+	0.474736i
$565$		0			0
$566$	1.97765	+	1.97765i	0.0831270	+	0.0831270i
$567$	−25.5671	−	19.8548i	−1.07372	−	0.833821i
$568$		−	23.5405i		−	0.987737i
$569$	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	$-0.213160\pi$
$572$	2.55214	−	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
$579$	−0.0395919	−	1.26547i	−0.00164538	−	0.0525913i
$580$		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	0.869802	−	0.493401i	$-0.164247\pi$
$587$	9.11946	+	9.11946i	0.376400	+	0.376400i	−0.493401	+	0.869802i	$0.664247\pi$
$588$	−13.9734	−	13.1255i	−0.576252	−	0.541288i
$589$		−	20.4438i		−	0.842374i
$590$		0			0
$591$	0.285304	+	9.11914i	0.0117358	+	0.375111i
$592$	−5.65288	−	5.65288i	−0.232332	−	0.232332i
$593$	−6.63125	+	6.63125i	−0.272313	+	0.272313i	−0.830031	−	0.557718i	$-0.811677\pi$
$593$	−6.63125	+	6.63125i	−0.272313	+	0.272313i	0.557718	+	0.830031i	$0.311677\pi$
$594$	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	$-0.696041\pi$
$599$		−	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	$0.361785\pi$
$602$			7.17574i			0.292461i
$603$	4.26405	+	3.76139i	0.173646	+	0.153176i
$604$	12.6826	+	12.6826i	0.516049	+	0.516049i
$605$		0			0
$606$	−0.0512353	−	1.63763i	−0.00208129	−	0.0665241i
$607$			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
$609$	−42.3971	+	1.32645i	−1.71802	+	0.0537503i
$610$		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	0.547894	−	0.836548i	$-0.315430\pi$
$617$	−7.17003	−	7.17003i	−0.288654	−	0.288654i	−0.836548	+	0.547894i	$0.815430\pi$
$618$	−0.304033	−	9.71779i	−0.0122300	−	0.390907i
$619$	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
$624$	13.2301	+	15.0159i	0.529626	+	0.601116i
$625$		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
$639$	37.2132	+	32.8263i	1.47213	+	1.29859i
$640$		0			0
$641$	25.8774			1.02210			0.511048	−	0.859552i	$-0.329258\pi$
$641$	25.8774			1.02210			0.511048	+	0.859552i	$0.329258\pi$
$642$	0.176694	+	5.64764i	0.00697354	+	0.222895i
$643$	−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	$-0.943747\pi$
$647$		−	8.94367i		−	0.351612i	0.984425	−	0.175806i	$-0.0562531\pi$
$648$	−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
$653$	−29.3417			−1.14823			−0.574115	−	0.818775i	$-0.694654\pi$
$653$	−29.3417			−1.14823			−0.574115	+	0.818775i	$0.694654\pi$
$654$	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	$0.369383\pi$
$662$		−	7.81973i		−	0.303922i
$663$	24.7610	−	21.8163i	0.961639	−	0.847274i
$664$	−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
$669$	−11.4979	+	0.359725i	−0.444533	+	0.0139078i
$670$		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	$-0.655375\pi$
$677$	−24.4044			−0.937939			−0.468970	+	0.883214i	$0.655375\pi$
$678$	0.227834	+	7.28225i	0.00874993	+	0.279673i
$679$	−53.3593			−2.04774
$680$		0			0
$681$	−0.594807	−	19.0117i	−0.0227930	−	0.728532i
$682$	0.537753	−	0.537753i	0.0205916	−	0.0205916i
$683$	24.2961	−	24.2961i	0.929666	−	0.929666i	−0.0680180	−	0.997684i	$-0.521668\pi$
$683$	24.2961	−	24.2961i	0.929666	−	0.929666i	0.997684	+	0.0680180i	$0.0216675\pi$
$684$	20.4586	+	18.0469i	0.782256	+	0.690040i
$685$		0			0
$686$	1.40827			0.0537679
$687$	−13.5163	+	0.422874i	−0.515679	+	0.0161337i
$688$	−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
$696$	0.524849	+	16.7757i	0.0198943	+	0.635881i
$697$	−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	$-0.625221\pi$
$701$	−20.2981			−0.766648			−0.383324	+	0.923614i	$0.625221\pi$
$702$	6.89976	+	0.00405037i	0.260415	+	0.000152871i
$703$			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
$708$	−1.13554	+	0.0355267i	−0.0426761	+	0.00133518i
$709$	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
$717$	−39.5094	+	1.23610i	−1.47551	+	0.0461631i
$718$			9.37268i			0.349785i
$719$	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
$726$	−6.85852	+	0.214578i	−0.254544	+	0.00796372i
$727$	−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
$741$	1.92197	−	30.3998i	0.0706055	−	1.11677i
$742$			9.20411i			0.337893i
$743$	7.55046	+	7.55046i	0.276999	+	0.276999i	0.831910	−	0.554911i	$-0.187248\pi$
$743$	7.55046	+	7.55046i	0.276999	+	0.276999i	−0.554911	+	0.831910i	$0.687248\pi$
$744$	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
$753$	−5.47409	−	5.14195i	−0.199487	−	0.187383i
$754$	6.96732	−	5.76190i	0.253735	−	0.209836i
$755$		0			0
$756$	−3.26456	−	34.6907i	−0.118731	−	1.26169i
$757$		−	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
$759$	8.00154	−	0.250338i	0.290438	−	0.00908670i
$760$		0			0
$761$	30.6519	+	30.6519i	1.11113	+	1.11113i	0.992998	+	0.118133i	$0.0376908\pi$
$761$	30.6519	+	30.6519i	1.11113	+	1.11113i	0.118133	+	0.992998i	$0.462309\pi$
$762$	−0.0528120	−	1.68803i	−0.00191318	−	0.0611507i
$763$			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	0.0253530	−	0.999679i	$-0.491929\pi$
$773$	−27.0891	−	27.0891i	−0.974326	−	0.974326i	−0.999679	+	0.0253530i	$0.991929\pi$
$774$	−3.95929	+	4.48841i	−0.142314	+	0.161332i
$775$		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
$786$	−3.26491	+	0.102147i	−0.116456	+	0.00364346i
$787$	−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	$0.175469\pi$
$797$			29.5724i			1.04751i	−0.851870	+	0.523754i	$0.824531\pi$
$798$	11.1853	−	0.349947i	0.395956	−	0.0123880i
$799$	13.0524	+	13.0524i	0.461760	+	0.461760i
$800$		0			0
$801$	−7.15128	+	8.10696i	−0.252678	+	0.286445i
$802$		−	5.81269i		−	0.205253i
$803$		−	4.51863i		−	0.159459i
$804$	0.191389	+	6.11734i	0.00674976	+	0.215742i
$805$		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	$-0.607540\pi$
$809$		−	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
$818$			6.50562i			0.227464i
$819$	−28.3726	+	26.6197i	−0.991417	+	0.930169i
$820$		0			0
$821$	−33.6801	+	33.6801i	−1.17544	+	1.17544i	−0.194553	+	0.980892i	$0.562326\pi$
$821$	−33.6801	+	33.6801i	−1.17544	+	1.17544i	−0.980892	+	0.194553i	$0.937674\pi$
$822$	5.42664	+	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	$-0.483670\pi$
$827$	30.1945	−	30.1945i	1.04996	−	1.04996i	0.998684	−	0.0512796i	$-0.0163300\pi$
$828$	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
$834$	−0.0103180	−	0.329792i	−0.000357282	−	0.0114198i
$835$		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
$842$		−	12.9775i		−	0.447233i
$843$	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
$848$	−22.2670			−0.764652
$849$	−9.58732	−	9.00562i	−0.329036	−	0.309072i
$850$		0			0
$851$	−16.5486	+	16.5486i	−0.567278	+	0.567278i
$852$	1.67028	+	53.3871i	0.0572230	+	1.82901i
$853$	−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	$-0.923872\pi$
$857$		−	13.8696i		−	0.473777i	0.971537	−	0.236889i	$-0.0761277\pi$
$858$	0.850190	−	0.749079i	0.0290250	−	0.0255731i
$859$	−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	0.950962	−	0.309308i	$-0.100097\pi$
$863$	18.8498	+	18.8498i	0.641654	+	0.641654i	−0.309308	+	0.950962i	$0.600097\pi$
$864$	−20.8305	+	1.96025i	−0.708670	+	0.0666890i
$865$		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
$873$	−33.3761	−	29.4416i	−1.12961	−	0.996447i
$874$	−16.8520			−0.570026
$875$		0			0
$876$	29.6024	−	0.926148i	1.00017	−	0.0312916i
$877$	−37.6363	+	37.6363i	−1.27089	+	1.27089i	−0.325265	+	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
$879$	−38.7829	+	1.21337i	−1.30811	+	0.0409260i
$880$		0			0
$881$	−48.6517			−1.63912			−0.819559	−	0.572995i	$-0.805781\pi$
$881$	−48.6517			−1.63912			−0.819559	+	0.572995i	$0.805781\pi$
$882$	−4.91900	−	4.33913i	−0.165631	−	0.146106i
$883$	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	$-0.318206\pi$
$887$	32.1996			1.08116			0.540578	+	0.841294i	$0.318206\pi$
$888$	−4.48210	−	4.21015i	−0.150409	−	0.141283i
$889$	6.73364	+	6.73364i	0.225839	+	0.225839i
$890$		0			0
$891$	−3.50208	−	2.71963i	−0.117324	−	0.0911111i
$892$	−8.75559	−	8.75559i	−0.293159	−	0.293159i
$893$	17.0379			0.570153
$894$	0.542256	+	0.509355i	0.0181358	+	0.0170354i
$895$		0			0
$896$	−35.4908			−1.18566
$897$	43.9583	−	38.7304i	1.46772	−	1.29317i
$898$		−	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
$903$	−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
$907$	−52.9829			−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	$0.0871617\pi$
$911$			16.3239i			0.540835i	−0.962743	+	0.270417i	$0.912838\pi$
$912$	0.846607	+	27.0600i	0.0280340	+	0.896047i
$913$		−	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
$918$	0.947440	+	10.0680i	0.0312702	+	0.332292i
$919$	−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
$921$	−1.50760	−	48.1874i	−0.0496772	−	1.58783i
$922$	−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	−0.296807	−	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
$932$	18.1516			0.594575
$933$	−19.5891	−	18.4005i	−0.641318	−	0.602407i
$934$	−2.42467	+	2.42467i	−0.0793376	+	0.0793376i
$935$		0			0
$936$	10.5329	+	11.2265i	0.344279	+	0.366948i
$937$		−	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	$-0.487709\pi$
$941$	31.8370	−	31.8370i	1.03786	−	1.03786i	0.999255	−	0.0386033i	$-0.0122909\pi$
$942$	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	−0.246523	+	0.969137i	$0.579288\pi$
$947$	−37.4100	+	37.4100i	−1.21566	+	1.21566i	−0.969137	+	0.246523i	$0.920712\pi$
$948$	5.88301	−	6.26301i	0.191071	−	0.203413i
$949$	−21.0746	−	25.4835i	−0.684109	−	0.827228i
$950$		0			0
$951$	1.41359	+	45.1825i	0.0458388	+	1.46514i
$952$			27.0500i			0.876694i
$953$		−	17.7294i		−	0.574311i	−0.957884	−	0.287156i	$-0.907290\pi$
$953$		−	17.7294i		−	0.574311i	0.957884	−	0.287156i	$-0.0927097\pi$
$954$	−5.07847	+	5.75714i	−0.164421	+	0.186394i
$955$		0			0
$956$	−30.0863	−	30.0863i	−0.973062	−	0.973062i
$957$	−5.80740	+	0.181692i	−0.187727	+	0.00587326i
$958$		−	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
$969$	44.6218	−	1.39605i	1.43346	−	0.0448476i
$970$		0			0
$971$			45.7568i			1.46841i	0.678930	+	0.734203i	$0.262444\pi$
$971$			45.7568i			1.46841i	−0.678930	+	0.734203i	$0.737556\pi$
$972$	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	0.630707	−	0.776021i	$-0.282765\pi$
$977$	−4.54207	−	4.54207i	−0.145314	−	0.145314i	−0.776021	+	0.630707i	$0.782765\pi$
$978$	−4.27087	+	4.54674i	−0.136567	+	0.145389i
$979$			1.77533i			0.0567397i
$980$		0			0
$981$	−22.4326	+	25.4305i	−0.716218	+	0.811932i
$982$	−2.20723	−	2.20723i	−0.0704354	−	0.0704354i
$983$	−22.8720	+	22.8720i	−0.729505	+	0.729505i	−0.970521	−	0.241016i	$-0.922519\pi$
$983$	−22.8720	+	22.8720i	−0.729505	+	0.729505i	0.241016	+	0.970521i	$0.422519\pi$
$984$	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
$993$	1.15004	+	36.7586i	0.0364954	+	1.16650i
$994$	15.4930	+	15.4930i	0.491409	+	0.491409i
$995$		0			0
$996$	33.5752	−	1.05044i	1.06387	−	0.0332846i
$997$			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
$999$	12.9056	−	1.21447i	0.408314	−	0.0384242i

Twists

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

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

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

\(f(q)\)	\(=\)	\(q+(0.260415 + 0.260415i) q^{2} +(-1.26244 - 1.18585i) q^{3} -1.86437i q^{4} +(-0.0199472 - 0.637571i) q^{6} +(2.54331 + 2.54331i) q^{7} +(1.00634 - 1.00634i) q^{8} +(0.187534 + 2.99413i) q^{9} +O(q^{10})\)	\(q+(0.260415 + 0.260415i) q^{2} +(-1.26244 - 1.18585i) q^{3} -1.86437i q^{4} +(-0.0199472 - 0.637571i) q^{6} +(2.54331 + 2.54331i) q^{7} +(1.00634 - 1.00634i) q^{8} +(0.187534 + 2.99413i) q^{9} +(0.348374 + 0.348374i) q^{11} +(-2.21086 + 2.35366i) q^{12} +(3.58949 + 0.339913i) q^{13} +1.32463i q^{14} -3.20461 q^{16} +5.28437i q^{17} +(-0.730879 + 0.828552i) q^{18} +(3.44898 + 3.44898i) q^{19} +(-0.194812 - 6.22677i) q^{21} +0.181443i q^{22} +9.38135i q^{23} +(-2.46381 + 0.0770834i) 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} +(-0.0266847 - 0.852920i) q^{33} +(-1.37613 + 1.37613i) q^{34} +(5.58217 - 0.349633i) q^{36} +(1.76399 + 1.76399i) q^{37} +1.79633i q^{38} +(-4.12845 - 4.68571i) 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} +(1.90523 - 0.179291i) 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} -1.54361i q^{62} +(-7.13805 + 8.09197i) q^{63} +4.92631i q^{64} +(0.215164 - 0.229062i) q^{66} +(1.34019 - 1.34019i) q^{67} +9.85202 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} +1.77204i q^{77} +(0.145118 - 2.29534i) q^{78} -2.66096 q^{79} +(-8.92966 + 1.12300i) q^{81} -1.15384 q^{82} +(-7.35570 - 7.35570i) q^{83} +(-11.6090 + 0.363202i) 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} +(0.227017 + 7.25614i) q^{93} +1.28645 q^{94} +(0.218090 + 6.97078i) q^{96} +(-10.4901 + 10.4901i) q^{97} +(-1.54604 + 1.54604i) q^{98} +(-0.977745 + 1.10841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 40 * q + 12 * q^6 - 16 * q^7	\( 40 q + 12 q^{6} - 16 q^{7} - 24 q^{12} + 24 q^{13} - 64 q^{16} + 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} + 32 q^{28} + 32 q^{31} + 4 q^{33} + 16 q^{34} + 32 q^{37} + 8 q^{39} - 32 q^{43} - 40 q^{46} - 8 q^{52} + 32 q^{54} + 36 q^{57} + 24 q^{58} + 8 q^{61} - 8 q^{63} - 48 q^{66} + 32 q^{67} + 132 q^{72} + 64 q^{73} + 16 q^{76} - 108 q^{78} - 40 q^{79} + 72 q^{81} - 128 q^{82} - 124 q^{84} - 80 q^{88} + 8 q^{91} - 108 q^{93} + 32 q^{94} - 76 q^{96} - 24 q^{97} + 20 q^{99}+O(q^{100}) \) 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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