LMFDB - Embedded newform 738.2.ba.a.71.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(17,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,-4,0,4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$3$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			71.3
Character	$\chi$	$=$	738.71
Dual form			738.2.ba.a.395.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.156434 + 0.987688i) q^{2} +(-0.951057 + 0.309017i) q^{4} +(1.67738 + 0.854668i) q^{5} +(0.674403 + 2.80909i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.581745 + 1.79043i) q^{10} +(1.59129 + 1.35909i) q^{11} +(5.08494 - 3.11606i) q^{13} +(-2.66901 + 1.10554i) q^{14} +(0.809017 - 0.587785i) q^{16} +(0.285386 + 3.62618i) q^{17} +(-5.16527 - 3.16528i) q^{19} +(-1.85939 - 0.294498i) q^{20} +(-1.09342 + 1.78430i) q^{22} +(1.05753 + 0.768342i) q^{23} +(-0.855780 - 1.17788i) q^{25} +(3.87315 + 4.53488i) q^{26} +(-1.50945 - 2.46320i) q^{28} +(-0.591330 + 7.51356i) q^{29} +(-4.80088 - 1.55990i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.53689 + 0.849132i) q^{34} +(-1.26961 + 5.28831i) q^{35} +(2.34600 + 7.22026i) q^{37} +(2.31828 - 5.59683i) q^{38} -1.88257i q^{40} +(6.19363 + 1.62449i) q^{41} +(-1.47841 + 0.234157i) q^{43} +(-1.93338 - 0.800833i) q^{44} +(-0.593448 + 1.16471i) q^{46} +(4.08701 + 0.981203i) q^{47} +(-1.19914 + 0.610990i) q^{49} +(1.02950 - 1.02950i) q^{50} +(-3.87315 + 4.53488i) q^{52} +(-8.29549 - 0.652869i) q^{53} +(1.50762 + 3.63972i) q^{55} +(2.19675 - 1.87620i) q^{56} +(-7.51356 + 0.591330i) q^{58} +(2.18312 - 3.00481i) q^{59} +(-0.525895 + 3.32037i) q^{61} +(0.789672 - 4.98579i) q^{62} +(-0.587785 + 0.809017i) q^{64} +(11.1926 - 0.880875i) q^{65} +(8.89050 - 7.59320i) q^{67} +(-1.39197 - 3.36051i) q^{68} +(-5.42181 - 0.426706i) q^{70} +(-7.87266 + 9.21770i) q^{71} +(7.26357 - 7.26357i) q^{73} +(-6.76437 + 3.44662i) q^{74} +(5.89059 + 1.41420i) q^{76} +(-2.74463 + 5.38664i) q^{77} +(-15.7432 - 6.52104i) q^{79} +(1.85939 - 0.294498i) q^{80} +(-0.635595 + 6.37150i) q^{82} +5.06215i q^{83} +(-2.62048 + 6.32639i) q^{85} +(-0.462548 - 1.42358i) q^{86} +(0.488526 - 2.03486i) q^{88} +(-7.06697 + 1.69663i) q^{89} +(12.1826 + 12.1826i) q^{91} +(-1.24320 - 0.403941i) q^{92} +(-0.329774 + 4.19018i) q^{94} +(-5.95885 - 9.72397i) q^{95} +(-6.99036 - 8.18466i) q^{97} +(-0.791054 - 1.08879i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{17} - 4 q^{19} + 16 q^{20} + 20 q^{22} - 40 q^{25} - 20 q^{26} - 4 q^{28} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) $ 48 * q - 4 * q^5 + 4 * q^7 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^17 - 4 * q^19 + 16 * q^20 + 20 * q^22 - 40 * q^25 - 20 * q^26 - 4 * q^28 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 52 * q^35 - 24 * q^37 + 16 * q^38 + 12 * q^41 - 20 * q^44 + 16 * q^46 - 8 * q^47 - 48 * q^49 - 16 * q^50 + 20 * q^52 + 64 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^58 + 20 * q^59 - 60 * q^61 - 36 * q^62 + 128 * q^65 - 12 * q^67 - 8 * q^68 + 8 * q^70 - 40 * q^71 + 8 * q^73 + 8 * q^74 + 12 * q^76 - 44 * q^77 + 36 * q^79 - 16 * q^80 + 68 * q^82 + 104 * q^85 - 16 * q^86 + 8 * q^88 - 60 * q^89 + 56 * q^91 - 12 * q^94 - 28 * q^95 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{23}{40}\right)$

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 $

$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$3$		0			0
$3$		0			0
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	1.67738	+	0.854668i	0.750147	+	0.382219i	0.786880	−	0.617106i	$-0.211695\pi$
$5$	1.67738	+	0.854668i	0.750147	+	0.382219i	−0.0367329	+	0.999325i	$0.511695\pi$
$6$		0			0
$7$	0.674403	+	2.80909i	0.254901	+	1.06174i	0.942117	+	0.335284i	$0.108832\pi$
$7$	0.674403	+	2.80909i	0.254901	+	1.06174i	−0.687216	+	0.726453i	$0.741168\pi$
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$		0			0
$10$	−0.581745	+	1.79043i	−0.183964	+	0.566183i
$11$	1.59129	+	1.35909i	0.479791	+	0.409780i	0.856177	−	0.516683i	$-0.172833\pi$
$11$	1.59129	+	1.35909i	0.479791	+	0.409780i	−0.376386	+	0.926463i	$0.622833\pi$
$12$		0			0
$13$	5.08494	−	3.11606i	1.41031	−	0.864239i	0.411424	−	0.911444i	$-0.365031\pi$
$13$	5.08494	−	3.11606i	1.41031	−	0.864239i	0.998885	+	0.0472050i	$0.0150314\pi$
$14$	−2.66901	+	1.10554i	−0.713322	+	0.295468i
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	0.285386	+	3.62618i	0.0692164	+	0.879477i	0.929300	+	0.369325i	$0.120411\pi$
$17$	0.285386	+	3.62618i	0.0692164	+	0.879477i	−0.860084	+	0.510152i	$0.829589\pi$
$18$		0			0
$19$	−5.16527	−	3.16528i	−1.18499	−	0.726165i	−0.216763	−	0.976224i	$-0.569550\pi$
$19$	−5.16527	−	3.16528i	−1.18499	−	0.726165i	−0.968231	+	0.250059i	$0.919550\pi$
$20$	−1.85939	−	0.294498i	−0.415772	−	0.0658519i
$21$		0			0
$22$	−1.09342	+	1.78430i	−0.233118	+	0.380414i
$23$	1.05753	+	0.768342i	0.220511	+	0.160210i	0.692557	−	0.721364i	$-0.256484\pi$
$23$	1.05753	+	0.768342i	0.220511	+	0.160210i	−0.472046	+	0.881574i	$0.656484\pi$
$24$		0			0
$25$	−0.855780	−	1.17788i	−0.171156	−	0.235576i
$26$	3.87315	+	4.53488i	0.759588	+	0.889363i
$27$		0			0
$28$	−1.50945	−	2.46320i	−0.285260	−	0.465502i
$29$	−0.591330	+	7.51356i	−0.109807	+	1.39523i	0.657259	+	0.753665i	$0.271716\pi$
$29$	−0.591330	+	7.51356i	−0.109807	+	1.39523i	−0.767066	+	0.641568i	$0.778284\pi$
$30$		0			0
$31$	−4.80088	−	1.55990i	−0.862263	−	0.280166i	−0.155689	−	0.987806i	$-0.549760\pi$
$31$	−4.80088	−	1.55990i	−0.862263	−	0.280166i	−0.706573	+	0.707640i	$0.749760\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−3.53689	+	0.849132i	−0.606571	+	0.145625i
$35$	−1.26961	+	5.28831i	−0.214603	+	0.893887i
$36$		0			0
$37$	2.34600	+	7.22026i	0.385681	+	1.18700i	0.935985	+	0.352039i	$0.114512\pi$
$37$	2.34600	+	7.22026i	0.385681	+	1.18700i	−0.550305	+	0.834964i	$0.685488\pi$
$38$	2.31828	−	5.59683i	0.376075	−	0.907926i
$39$		0			0
$40$		−	1.88257i		−	0.297660i
$41$	6.19363	+	1.62449i	0.967282	+	0.253703i
$41$	6.19363	+	1.62449i	0.967282	+	0.253703i
$42$		0			0
$43$	−1.47841	+	0.234157i	−0.225455	+	0.0357086i	−0.268140	−	0.963380i	$-0.586409\pi$
$43$	−1.47841	+	0.234157i	−0.225455	+	0.0357086i	0.0426846	+	0.999089i	$0.486409\pi$
$44$	−1.93338	−	0.800833i	−0.291468	−	0.120730i
$45$		0			0
$46$	−0.593448	+	1.16471i	−0.0874991	+	0.171727i
$47$	4.08701	+	0.981203i	0.596151	+	0.143123i	0.520282	−	0.853995i	$-0.325827\pi$
$47$	4.08701	+	0.981203i	0.596151	+	0.143123i	0.0758692	+	0.997118i	$0.475827\pi$
$48$		0			0
$49$	−1.19914	+	0.610990i	−0.171305	+	0.0872843i
$50$	1.02950	−	1.02950i	0.145594	−	0.145594i
$51$		0			0
$52$	−3.87315	+	4.53488i	−0.537110	+	0.628875i
$53$	−8.29549	−	0.652869i	−1.13947	−	0.0896785i	−0.505353	−	0.862913i	$-0.668638\pi$
$53$	−8.29549	−	0.652869i	−1.13947	−	0.0896785i	−0.634120	+	0.773234i	$0.718638\pi$
$54$		0			0
$55$	1.50762	+	3.63972i	0.203288	+	0.490780i
$56$	2.19675	−	1.87620i	0.293553	−	0.250718i
$57$		0			0
$58$	−7.51356	+	0.591330i	−0.986579	+	0.0776454i
$59$	2.18312	−	3.00481i	0.284218	−	0.391192i	−0.642907	−	0.765944i	$-0.722272\pi$
$59$	2.18312	−	3.00481i	0.284218	−	0.391192i	0.927125	+	0.374751i	$0.122272\pi$
$60$		0			0
$61$	−0.525895	+	3.32037i	−0.0673340	+	0.425130i	0.930877	+	0.365334i	$0.119045\pi$
$61$	−0.525895	+	3.32037i	−0.0673340	+	0.425130i	−0.998211	+	0.0597964i	$0.980955\pi$
$62$	0.789672	−	4.98579i	0.100288	−	0.633196i
$63$		0			0
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	11.1926	−	0.880875i	1.38827	−	0.109259i
$66$		0			0
$67$	8.89050	−	7.59320i	1.08615	−	0.927657i	0.0884905	−	0.996077i	$-0.471796\pi$
$67$	8.89050	−	7.59320i	1.08615	−	0.927657i	0.997657	+	0.0684197i	$0.0217957\pi$
$68$	−1.39197	−	3.36051i	−0.168801	−	0.407522i
$69$		0			0
$70$	−5.42181	−	0.426706i	−0.648030	−	0.0510011i
$71$	−7.87266	+	9.21770i	−0.934313	+	1.09394i	0.0610866	+	0.998132i	$0.480543\pi$
$71$	−7.87266	+	9.21770i	−0.934313	+	1.09394i	−0.995400	+	0.0958078i	$0.969457\pi$
$72$		0			0
$73$	7.26357	−	7.26357i	0.850137	−	0.850137i	−0.140013	−	0.990150i	$-0.544714\pi$
$73$	7.26357	−	7.26357i	0.850137	−	0.850137i	0.990150	+	0.140013i	$0.0447144\pi$
$74$	−6.76437	+	3.44662i	−0.786342	+	0.400661i
$75$		0			0
$76$	5.89059	+	1.41420i	0.675697	+	0.162220i
$77$	−2.74463	+	5.38664i	−0.312780	+	0.613865i
$78$		0			0
$79$	−15.7432	−	6.52104i	−1.77125	−	0.733675i	−0.994605	−	0.103733i	$-0.966921\pi$
$79$	−15.7432	−	6.52104i	−1.77125	−	0.733675i	−0.776643	−	0.629942i	$-0.783079\pi$
$80$	1.85939	−	0.294498i	0.207886	−	0.0329259i
$81$		0			0
$82$	−0.635595	+	6.37150i	−0.0701897	+	0.703615i
$83$			5.06215i			0.555643i	0.960633	+	0.277821i	$0.0896124\pi$
$83$			5.06215i			0.555643i	−0.960633	+	0.277821i	$0.910388\pi$
$84$		0			0
$85$	−2.62048	+	6.32639i	−0.284230	+	0.686193i
$86$	−0.462548	−	1.42358i	−0.0498778	−	0.153508i
$87$		0			0
$88$	0.488526	−	2.03486i	0.0520771	−	0.216917i
$89$	−7.06697	+	1.69663i	−0.749098	+	0.179842i	−0.589981	−	0.807417i	$-0.700865\pi$
$89$	−7.06697	+	1.69663i	−0.749098	+	0.179842i	−0.159117	+	0.987260i	$0.550865\pi$
$90$		0			0
$91$	12.1826	+	12.1826i	1.27708	+	1.27708i
$92$	−1.24320	−	0.403941i	−0.129613	−	0.0421138i
$93$		0			0
$94$	−0.329774	+	4.19018i	−0.0340136	+	0.432184i
$95$	−5.95885	−	9.72397i	−0.611366	−	0.997658i
$96$		0			0
$97$	−6.99036	−	8.18466i	−0.709764	−	0.831026i	0.281959	−	0.959427i	$-0.409016\pi$
$97$	−6.99036	−	8.18466i	−0.709764	−	0.831026i	−0.991722	+	0.128400i	$0.959016\pi$
$98$	−0.791054	−	1.08879i	−0.0799085	−	0.109985i
$99$		0			0
$100$	1.17788	+	0.855780i	0.117788	+	0.0855780i
$101$	8.52284	−	13.9080i	0.848055	−	1.38390i	−0.0741704	−	0.997246i	$-0.523631\pi$
$101$	8.52284	−	13.9080i	0.848055	−	1.38390i	0.922225	−	0.386654i	$-0.126369\pi$
$102$		0			0
$103$	−5.84924	−	0.926429i	−0.576343	−	0.0912838i	−0.138544	−	0.990356i	$-0.544242\pi$
$103$	−5.84924	−	0.926429i	−0.576343	−	0.0912838i	−0.437800	+	0.899073i	$0.644242\pi$
$104$	−5.08494	−	3.11606i	−0.498620	−	0.305555i
$105$		0			0
$106$	−0.652869	−	8.29549i	−0.0634123	−	0.805729i
$107$	6.18045	−	4.49036i	0.597487	−	0.434100i	−0.247499	−	0.968888i	$-0.579609\pi$
$107$	6.18045	−	4.49036i	0.597487	−	0.434100i	0.844986	+	0.534788i	$0.179609\pi$
$108$		0			0
$109$	16.3177	−	6.75901i	1.56295	−	0.647396i	0.577353	−	0.816494i	$-0.304086\pi$
$109$	16.3177	−	6.75901i	1.56295	−	0.647396i	0.985599	+	0.169098i	$0.0540855\pi$
$110$	−3.35907	+	2.05844i	−0.320275	+	0.196265i
$111$		0			0
$112$	2.19675	+	1.87620i	0.207573	+	0.177284i
$113$	3.61579	−	11.1283i	0.340145	−	1.04686i	−0.623986	−	0.781435i	$-0.714488\pi$
$113$	3.61579	−	11.1283i	0.340145	−	1.04686i	0.964132	−	0.265424i	$-0.0855121\pi$
$114$		0			0
$115$	1.11721	+	2.19264i	0.104180	+	0.204465i
$116$	−1.75943	−	7.32855i	−0.163359	−	0.680439i
$117$		0			0
$118$	3.30933	+	1.68619i	0.304648	+	0.155226i
$119$	−9.99380	+	3.24718i	−0.916130	+	0.297669i
$120$		0			0
$121$	−1.03571	−	6.53918i	−0.0941550	−	0.594471i
$122$	−3.36176			−0.304360
$123$		0			0
$124$	5.04794			0.453318
$125$	−1.90126	−	12.0041i	−0.170054	−	1.07368i
$126$		0			0
$127$	3.08839	−	1.00348i	0.274051	−	0.0890444i	−0.168768	−	0.985656i	$-0.553979\pi$
$127$	3.08839	−	1.00348i	0.274051	−	0.0890444i	0.442818	+	0.896611i	$0.353979\pi$
$128$	−0.891007	−	0.453990i	−0.0787546	−	0.0401275i
$129$		0			0
$130$	2.62093	+	10.9170i	0.229871	+	0.957482i
$131$	−6.01360	−	11.8023i	−0.525410	−	1.03118i	−0.989384	−	0.145327i	$-0.953577\pi$
$131$	−6.01360	−	11.8023i	−0.525410	−	1.03118i	0.463973	−	0.885849i	$-0.346423\pi$
$132$		0			0
$133$	5.40809	−	16.6444i	0.468941	−	1.44325i
$134$	8.89050	+	7.59320i	0.768022	+	0.655953i
$135$		0			0
$136$	3.10139	−	1.90053i	0.265942	−	0.162969i
$137$	0.963044	−	0.398906i	0.0822784	−	0.0340808i	−0.341165	−	0.940004i	$-0.610821\pi$
$137$	0.963044	−	0.398906i	0.0822784	−	0.0340808i	0.423443	+	0.905923i	$0.360821\pi$
$138$		0			0
$139$	0.405607	−	0.294691i	0.0344031	−	0.0249953i	−0.570451	−	0.821332i	$-0.693231\pi$
$139$	0.405607	−	0.294691i	0.0344031	−	0.0249953i	0.604854	+	0.796336i	$0.293231\pi$
$140$	−0.426706	−	5.42181i	−0.0360632	−	0.458227i
$141$		0			0
$142$	−10.3358	−	6.33377i	−0.867359	−	0.531518i
$143$	12.3266	+	1.95234i	1.03080	+	0.163263i
$144$		0			0
$145$	−7.41348	+	12.0977i	−0.615656	+	1.00466i
$146$	8.31042	+	6.03787i	0.687775	+	0.499698i
$147$		0			0
$148$	−4.46237	−	6.14192i	−0.366804	−	0.504863i
$149$	10.0789	+	11.8009i	0.825694	+	0.966764i	0.999839	−	0.0179563i	$-0.00571596\pi$
$149$	10.0789	+	11.8009i	0.825694	+	0.966764i	−0.174144	+	0.984720i	$0.555716\pi$
$150$		0			0
$151$	3.01388	+	4.91821i	0.245266	+	0.400238i	0.951456	−	0.307784i	$-0.0995876\pi$
$151$	3.01388	+	4.91821i	0.245266	+	0.400238i	−0.706190	+	0.708022i	$0.749588\pi$
$152$	−0.475303	+	6.03929i	−0.0385521	+	0.489851i
$153$		0			0
$154$	−5.74968	−	1.86818i	−0.463322	−	0.150542i
$155$	−6.71970	−	6.71970i	−0.539739	−	0.539739i
$156$		0			0
$157$	6.79860	−	1.63220i	0.542587	−	0.130264i	0.0471183	−	0.998889i	$-0.484996\pi$
$157$	6.79860	−	1.63220i	0.542587	−	0.130264i	0.495469	+	0.868626i	$0.334996\pi$
$158$	3.97798	−	16.5695i	0.316471	−	1.31820i
$159$		0			0
$160$	0.581745	+	1.79043i	0.0459910	+	0.141546i
$161$	−1.44514	+	3.48888i	−0.113893	+	0.274962i
$162$		0			0
$163$			14.1254i			1.10639i	0.833053	+	0.553194i	$0.186591\pi$
$163$			14.1254i			1.10639i	−0.833053	+	0.553194i	$0.813409\pi$
$164$	−6.39249	+	0.368953i	−0.499169	+	0.0288104i
$165$		0			0
$166$	−4.99982	+	0.791894i	−0.388062	+	0.0614629i
$167$	0.549996	+	0.227816i	0.0425599	+	0.0176289i	0.403862	−	0.914820i	$-0.367668\pi$
$167$	0.549996	+	0.227816i	0.0425599	+	0.0176289i	−0.361302	+	0.932449i	$0.617668\pi$
$168$		0			0
$169$	10.2450	−	20.1069i	0.788074	−	1.54668i
$170$	−6.65843	−	1.59855i	−0.510678	−	0.122603i
$171$		0			0
$172$	1.33369	−	0.679550i	0.101693	−	0.0518152i
$173$	3.35951	−	3.35951i	0.255419	−	0.255419i	−0.567769	−	0.823188i	$-0.692193\pi$
$173$	3.35951	−	3.35951i	0.255419	−	0.255419i	0.823188	+	0.567769i	$0.192193\pi$
$174$		0			0
$175$	2.73163	−	3.19833i	0.206492	−	0.241771i
$176$	2.08623	+	0.164190i	0.157255	+	0.0123763i
$177$		0			0
$178$	−2.78126	−	6.71455i	−0.208464	−	0.503277i
$179$	8.18798	−	6.99320i	0.611998	−	0.522696i	−0.288543	−	0.957467i	$-0.593171\pi$
$179$	8.18798	−	6.99320i	0.611998	−	0.522696i	0.900541	+	0.434771i	$0.143171\pi$
$180$		0			0
$181$	8.14318	−	0.640882i	0.605278	−	0.0476364i	0.227882	−	0.973689i	$-0.426820\pi$
$181$	8.14318	−	0.640882i	0.605278	−	0.0476364i	0.377395	+	0.926052i	$0.376820\pi$
$182$	−10.1268	+	13.9384i	−0.750651	+	1.03318i
$183$		0			0
$184$	0.204488	−	1.29109i	0.0150751	−	0.0951803i
$185$	−2.23578	+	14.1162i	−0.164378	+	1.03784i
$186$		0			0
$187$	−4.47416	+	6.15815i	−0.327183	+	0.450328i
$188$	−4.19018	+	0.329774i	−0.305600	+	0.0240513i
$189$		0			0
$190$	8.67208	−	7.40665i	0.629139	−	0.537335i
$191$	−1.70395	−	4.11370i	−0.123294	−	0.297657i	0.850167	−	0.526514i	$-0.176501\pi$
$191$	−1.70395	−	4.11370i	−0.123294	−	0.297657i	−0.973460	+	0.228857i	$0.926501\pi$
$192$		0			0
$193$	4.92622	+	0.387702i	0.354597	+	0.0279074i	0.254507	−	0.967071i	$-0.418087\pi$
$193$	4.92622	+	0.387702i	0.354597	+	0.0279074i	0.100090	+	0.994978i	$0.468087\pi$
$194$	6.99036	−	8.18466i	0.501879	−	0.587624i
$195$		0			0
$196$	0.951639	−	0.951639i	0.0679742	−	0.0679742i
$197$	−13.1332	+	6.69169i	−0.935701	+	0.476763i	−0.854220	−	0.519911i	$-0.825965\pi$
$197$	−13.1332	+	6.69169i	−0.935701	+	0.476763i	−0.0814808	+	0.996675i	$0.525965\pi$
$198$		0			0
$199$	18.6638	+	4.48077i	1.32304	+	0.317633i	0.832616	−	0.553851i	$-0.186842\pi$
$199$	18.6638	+	4.48077i	1.32304	+	0.317633i	0.490423	+	0.871485i	$0.336842\pi$
$200$	−0.660983	+	1.29725i	−0.0467385	+	0.0917295i
$201$		0			0
$202$	15.0701	+	6.24222i	1.06033	+	0.439201i
$203$	−21.5051	+	3.40607i	−1.50936	+	0.239059i
$204$		0			0
$205$	9.00067	+	8.01838i	0.628634	+	0.560028i
$206$		−	5.92216i		−	0.412616i
$207$		0			0
$208$	2.28223	−	5.50980i	0.158244	−	0.382036i
$209$	−3.91753	−	12.0569i	−0.270981	−	0.833994i
$210$		0			0
$211$	−4.90461	+	20.4292i	−0.337647	+	1.40640i	0.502750	+	0.864432i	$0.332321\pi$
$211$	−4.90461	+	20.4292i	−0.337647	+	1.40640i	−0.840398	+	0.541970i	$0.817679\pi$
$212$	8.09123	−	1.94253i	0.555708	−	0.133414i
$213$		0			0
$214$	5.40191	+	5.40191i	0.369267	+	0.369267i
$215$	−2.67998	−	0.870778i	−0.182773	−	0.0593866i
$216$		0			0
$217$	1.14417	−	14.5381i	0.0776716	−	0.986911i
$218$	9.22845	+	15.0595i	0.625030	+	1.01996i
$219$		0			0
$220$	−2.55857	−	2.99570i	−0.172499	−	0.201970i
$221$	12.7506	+	17.5496i	0.857695	+	1.18052i
$222$		0			0
$223$	7.71219	+	5.60323i	0.516446	+	0.375220i	0.815263	−	0.579090i	$-0.196592\pi$
$223$	7.71219	+	5.60323i	0.516446	+	0.375220i	−0.298817	+	0.954310i	$0.596592\pi$
$224$	−1.50945	+	2.46320i	−0.100855	+	0.164580i
$225$		0			0
$226$	11.5569	+	1.83043i	0.768753	+	0.121759i
$227$	−22.3933	−	13.7226i	−1.48629	−	0.910802i	−0.999301	−	0.0373966i	$-0.988094\pi$
$227$	−22.3933	−	13.7226i	−1.48629	−	0.910802i	−0.486994	−	0.873406i	$-0.661906\pi$
$228$		0			0
$229$	−0.409881	−	5.20803i	−0.0270857	−	0.344156i	−0.995497	−	0.0947966i	$-0.969780\pi$
$229$	−0.409881	−	5.20803i	−0.0270857	−	0.344156i	0.968411	−	0.249359i	$-0.0802201\pi$
$230$	−1.99088	+	1.44646i	−0.131274	+	0.0953765i
$231$		0			0
$232$	6.96309	−	2.88421i	0.457149	−	0.189357i
$233$	14.0283	−	8.59654i	0.919023	−	0.563178i	0.0193841	−	0.999812i	$-0.493829\pi$
$233$	14.0283	−	8.59654i	0.919023	−	0.563178i	0.899639	+	0.436634i	$0.143829\pi$
$234$		0			0
$235$	6.01686	+	5.13888i	0.392497	+	0.335224i
$236$	−1.14773	+	3.53236i	−0.0747111	+	0.229937i
$237$		0			0
$238$	−4.77058	−	9.36279i	−0.309231	−	0.606900i
$239$	−3.98951	−	16.6175i	−0.258060	−	1.07490i	−0.939371	−	0.342903i	$-0.888590\pi$
$239$	−3.98951	−	16.6175i	−0.258060	−	1.07490i	0.681311	−	0.731994i	$-0.261410\pi$
$240$		0			0
$241$	3.73242	+	1.90176i	0.240426	+	0.122503i	0.570053	−	0.821608i	$-0.306923\pi$
$241$	3.73242	+	1.90176i	0.240426	+	0.122503i	−0.329626	+	0.944111i	$0.606923\pi$
$242$	6.29666	−	2.04591i	0.404764	−	0.131516i
$243$		0			0
$244$	−0.525895	−	3.32037i	−0.0336670	−	0.212565i
$245$	−2.53360			−0.161866
$246$		0			0
$247$	−36.1283			−2.29879
$248$	0.789672	+	4.98579i	0.0501442	+	0.316598i
$249$		0			0
$250$	11.5589	−	3.75571i	0.731049	−	0.237532i
$251$	−11.6555	−	5.93879i	−0.735690	−	0.374853i	0.0456505	−	0.998957i	$-0.485464\pi$
$251$	−11.6555	−	5.93879i	−0.735690	−	0.374853i	−0.781341	+	0.624105i	$0.785464\pi$
$252$		0			0
$253$	0.638592	+	2.65993i	0.0401480	+	0.167228i
$254$	1.47426	+	2.89339i	0.0925031	+	0.181548i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.03707	+	3.44798i	0.251826	+	0.215079i	0.766395	−	0.642369i	$-0.222048\pi$
$257$	4.03707	+	3.44798i	0.251826	+	0.215079i	−0.514570	+	0.857448i	$0.672048\pi$
$258$		0			0
$259$	−18.7002	+	11.4595i	−1.16198	+	0.712059i
$260$	−10.3726	+	4.29646i	−0.643279	+	0.266455i
$261$		0			0
$262$	10.7163	−	7.78585i	0.662056	−	0.481012i
$263$	−0.735198	−	9.34158i	−0.0453343	−	0.576027i	−0.977074	−	0.212900i	$-0.931709\pi$
$263$	−0.735198	−	9.34158i	−0.0453343	−	0.576027i	0.931740	−	0.363127i	$-0.118291\pi$
$264$		0			0
$265$	−13.3567	−	8.18500i	−0.820496	−	0.502800i
$266$	17.2855	+	2.73775i	1.05984	+	0.167862i
$267$		0			0
$268$	−6.10894	+	9.96888i	−0.373163	+	0.608946i
$269$	8.23110	+	5.98024i	0.501859	+	0.364622i	0.809727	−	0.586807i	$-0.199615\pi$
$269$	8.23110	+	5.98024i	0.501859	+	0.364622i	−0.307868	+	0.951429i	$0.599615\pi$
$270$		0			0
$271$	−5.25654	−	7.23501i	−0.319312	−	0.439496i	0.618945	−	0.785435i	$-0.287560\pi$
$271$	−5.25654	−	7.23501i	−0.319312	−	0.439496i	−0.938257	+	0.345939i	$0.887560\pi$
$272$	2.36230	+	2.76589i	0.143235	+	0.167707i
$273$		0			0
$274$	0.544648	+	0.888785i	0.0329034	+	0.0536935i
$275$	0.239050	−	3.03742i	0.0144153	−	0.183163i
$276$		0			0
$277$	−19.0093	−	6.17651i	−1.14216	−	0.371110i	−0.323975	−	0.946066i	$-0.605019\pi$
$277$	−19.0093	−	6.17651i	−1.14216	−	0.371110i	−0.818185	+	0.574955i	$0.805019\pi$
$278$	0.354513	+	0.354513i	0.0212623	+	0.0212623i
$279$		0			0
$280$	5.28831	−	1.26961i	0.316037	−	0.0758737i
$281$	−0.708656	+	2.95177i	−0.0422749	+	0.176088i	−0.989513	−	0.144443i	$-0.953861\pi$
$281$	−0.708656	+	2.95177i	−0.0422749	+	0.176088i	0.947238	+	0.320530i	$0.103861\pi$
$282$		0			0
$283$	−7.89572	−	24.3005i	−0.469352	−	1.44452i	−0.853426	−	0.521214i	$-0.825480\pi$
$283$	−7.89572	−	24.3005i	−0.469352	−	1.44452i	0.384075	−	0.923302i	$-0.374520\pi$
$284$	4.63892	−	11.1993i	0.275269	−	0.664559i
$285$		0			0
$286$			12.4802i			0.737972i
$287$	−0.386344	+	18.4940i	−0.0228051	+	1.09167i
$288$		0			0
$289$	3.72298	−	0.589663i	0.218999	−	0.0346860i
$290$	−13.1085	−	5.42971i	−0.769757	−	0.318844i
$291$		0			0
$292$	−4.66350	+	9.15264i	−0.272911	+	0.535618i
$293$	−3.70333	−	0.889091i	−0.216351	−	0.0519413i	0.123821	−	0.992305i	$-0.460485\pi$
$293$	−3.70333	−	0.889091i	−0.216351	−	0.0519413i	−0.340172	+	0.940363i	$0.610485\pi$
$294$		0			0
$295$	6.23003	−	3.17436i	0.362727	−	0.184818i
$296$	5.36823	−	5.36823i	0.312022	−	0.312022i
$297$		0			0
$298$	−10.0789	+	11.8009i	−0.583854	+	0.683605i
$299$	7.77169	+	0.611645i	0.449448	+	0.0353724i
$300$		0			0
$301$	−1.65481	−	3.99507i	−0.0953818	−	0.230272i
$302$	−4.38618	+	3.74615i	−0.252396	+	0.215567i
$303$		0			0
$304$	−6.03929	+	0.475303i	−0.346377	+	0.0272605i
$305$	−3.71994	+	5.12006i	−0.213003	+	0.293174i
$306$		0			0
$307$	0.267664	−	1.68996i	0.0152764	−	0.0964513i	−0.978872	−	0.204474i	$-0.934452\pi$
$307$	0.267664	−	1.68996i	0.0152764	−	0.0964513i	0.994148	+	0.108022i	$0.0344518\pi$
$308$	0.945735	−	5.97114i	0.0538883	−	0.340237i
$309$		0			0
$310$	5.58577	−	7.68816i	0.317251	−	0.436658i
$311$	27.2162	−	2.14196i	1.54329	−	0.121459i	0.721968	−	0.691927i	$-0.243238\pi$
$311$	27.2162	−	2.14196i	1.54329	−	0.121459i	0.821320	+	0.570467i	$0.193238\pi$
$312$		0			0
$313$	−18.9008	+	16.1428i	−1.06833	+	0.912444i	−0.996384	−	0.0849647i	$-0.972922\pi$
$313$	−18.9008	+	16.1428i	−1.06833	+	0.912444i	−0.0719502	+	0.997408i	$0.522922\pi$
$314$	2.67564	+	6.45956i	0.150995	+	0.364534i
$315$		0			0
$316$	16.9878	+	1.33697i	0.955637	+	0.0752103i
$317$	−17.1317	+	20.0587i	−0.962214	+	1.12661i	0.0296829	+	0.999559i	$0.490550\pi$
$317$	−17.1317	+	20.0587i	−0.962214	+	1.12661i	−0.991897	+	0.127048i	$0.959450\pi$
$318$		0			0
$319$	−11.1526	+	11.1526i	−0.624423	+	0.624423i
$320$	−1.67738	+	0.854668i	−0.0937684	+	0.0477774i
$321$		0			0
$322$	−3.67199	−	0.881568i	−0.204632	−	0.0491279i
$323$	10.0038	−	19.6335i	0.556625	−	1.09244i
$324$		0			0
$325$	−8.02193	−	3.32279i	−0.444977	−	0.184315i
$326$	−13.9515	+	2.20970i	−0.772702	+	0.122384i
$327$		0			0
$328$	−1.36442	−	6.25607i	−0.0753372	−	0.345433i
$329$			12.1425i			0.669438i
$330$		0			0
$331$	−9.73822	+	23.5102i	−0.535261	+	1.29223i	0.392737	+	0.919651i	$0.371528\pi$
$331$	−9.73822	+	23.5102i	−0.535261	+	1.29223i	−0.927998	+	0.372584i	$0.878472\pi$
$332$	−1.56429	−	4.81439i	−0.0858516	−	0.264224i
$333$		0			0
$334$	−0.138973	+	0.578862i	−0.00760424	+	0.0316739i
$335$	21.4024	−	5.13826i	1.16934	−	0.280733i
$336$		0			0
$337$	9.48589	+	9.48589i	0.516729	+	0.516729i	0.916580	−	0.399851i	$-0.130938\pi$
$337$	9.48589	+	9.48589i	0.516729	+	0.516729i	−0.399851	+	0.916580i	$0.630938\pi$
$338$	21.4620	+	6.97342i	1.16738	+	0.379304i
$339$		0			0
$340$	0.537259	−	6.82652i	0.0291370	−	0.370220i
$341$	−5.51953	−	9.00705i	−0.298899	−	0.487759i
$342$		0			0
$343$	10.6084	+	12.4208i	0.572798	+	0.670660i
$344$	0.879819	+	1.21097i	0.0474367	+	0.0652909i
$345$		0			0
$346$	3.84369	+	2.79260i	0.206638	+	0.150131i
$347$	7.10868	−	11.6003i	0.381614	−	0.622737i	−0.602947	−	0.797781i	$-0.706007\pi$
$347$	7.10868	−	11.6003i	0.381614	−	0.622737i	0.984561	+	0.175044i	$0.0560068\pi$
$348$		0			0
$349$	−21.2575	−	3.36686i	−1.13789	−	0.180224i	−0.441071	−	0.897472i	$-0.645401\pi$
$349$	−21.2575	−	3.36686i	−1.13789	−	0.180224i	−0.696818	+	0.717248i	$0.745401\pi$
$350$	3.58628	+	2.19767i	0.191694	+	0.117471i
$351$		0			0
$352$	0.164190	+	2.08623i	0.00875134	+	0.111196i
$353$	−4.92112	+	3.57541i	−0.261925	+	0.190300i	−0.710995	−	0.703197i	$-0.751755\pi$
$353$	−4.92112	+	3.57541i	−0.261925	+	0.190300i	0.449070	+	0.893496i	$0.351755\pi$
$354$		0			0
$355$	−21.0835	+	8.73308i	−1.11900	+	0.463504i
$356$	6.19680	−	3.79741i	0.328430	−	0.201262i
$357$		0			0
$358$	8.18798	+	6.99320i	0.432748	+	0.369602i
$359$	−9.51098	+	29.2718i	−0.501970	+	1.54491i	0.303835	+	0.952725i	$0.401733\pi$
$359$	−9.51098	+	29.2718i	−0.501970	+	1.54491i	−0.805805	+	0.592181i	$0.798267\pi$
$360$		0			0
$361$	8.03517	+	15.7699i	0.422904	+	0.829996i
$362$	1.90687	+	7.94267i	0.100223	+	0.417457i
$363$		0			0
$364$	−15.3510	−	7.82171i	−0.804609	−	0.409969i
$365$	18.3917	−	5.97583i	0.962666	−	0.312789i
$366$		0			0
$367$	−4.91804	−	31.0513i	−0.256720	−	1.62086i	−0.692920	−	0.721015i	$-0.743676\pi$
$367$	−4.91804	−	31.0513i	−0.256720	−	1.62086i	0.436200	−	0.899850i	$-0.356324\pi$
$368$	1.30718			0.0681416
$369$		0			0
$370$	−14.2921			−0.743012
$371$	−3.76054	−	23.7431i	−0.195237	−	1.23268i
$372$		0			0
$373$	0.283136	−	0.0919965i	0.0146602	−	0.00476340i	−0.301678	−	0.953410i	$-0.597547\pi$
$373$	0.283136	−	0.0919965i	0.0146602	−	0.00476340i	0.316338	+	0.948647i	$0.397547\pi$
$374$	−6.78224	−	3.45573i	−0.350701	−	0.178691i
$375$		0			0
$376$	−0.981203	−	4.08701i	−0.0506017	−	0.210771i
$377$	20.4058	+	40.0487i	1.05095	+	2.06261i
$378$		0			0
$379$	1.57642	−	4.85173i	0.0809755	−	0.249217i	−0.902370	−	0.430962i	$-0.858174\pi$
$379$	1.57642	−	4.85173i	0.0809755	−	0.249217i	0.983346	+	0.181745i	$0.0581744\pi$
$380$	8.67208	+	7.40665i	0.444868	+	0.379953i
$381$		0			0
$382$	3.79650	−	2.32650i	0.194246	−	0.119034i
$383$	−1.33710	+	0.553847i	−0.0683229	+	0.0283003i	−0.416583	−	0.909098i	$-0.636773\pi$
$383$	−1.33710	+	0.553847i	−0.0683229	+	0.0283003i	0.348260	+	0.937398i	$0.386773\pi$
$384$		0			0
$385$	−9.20758	+	6.68969i	−0.469261	+	0.340938i
$386$	0.387702	+	4.92622i	0.0197335	+	0.250738i
$387$		0			0
$388$	9.17743	+	5.62394i	0.465913	+	0.285512i
$389$	−3.68106	−	0.583022i	−0.186637	−	0.0295604i	0.0624162	−	0.998050i	$-0.480119\pi$
$389$	−3.68106	−	0.583022i	−0.186637	−	0.0295604i	−0.249053	+	0.968490i	$0.580119\pi$
$390$		0			0
$391$	−2.48434	+	4.05407i	−0.125638	+	0.205023i
$392$	1.08879	+	0.791054i	0.0549923	+	0.0399543i
$393$		0			0
$394$	−8.66379	−	11.9247i	−0.436475	−	0.600757i
$395$	−20.8340	−	24.3935i	−1.04827	−	1.22737i
$396$		0			0
$397$	−6.33172	−	10.3324i	−0.317780	−	0.518570i	0.653370	−	0.757039i	$-0.273355\pi$
$397$	−6.33172	−	10.3324i	−0.317780	−	0.518570i	−0.971150	+	0.238469i	$0.923355\pi$
$398$	−1.50595	+	19.1349i	−0.0754865	+	0.959147i
$399$		0			0
$400$	−1.38468	−	0.449910i	−0.0692340	−	0.0224955i
$401$	−27.7177	−	27.7177i	−1.38415	−	1.38415i	−0.837093	−	0.547061i	$-0.815747\pi$
$401$	−27.7177	−	27.7177i	−1.38415	−	1.38415i	−0.547061	−	0.837093i	$-0.684253\pi$
$402$		0			0
$403$	−29.2729	+	7.02781i	−1.45819	+	0.350080i
$404$	−3.80789	+	15.8610i	−0.189450	+	0.789115i
$405$		0			0
$406$	−6.72827	−	20.7075i	−0.333919	−	1.02770i
$407$	−6.07979	+	14.6779i	−0.301364	+	0.727557i
$408$		0			0
$409$			0.420045i			0.0207699i	0.999946	+	0.0103849i	$0.00330569\pi$
$409$			0.420045i			0.0207699i	−0.999946	+	0.0103849i	$0.996694\pi$
$410$	−6.51165	+	10.1442i	−0.321587	+	0.500987i
$411$		0			0
$412$	5.84924	−	0.926429i	0.288172	−	0.0456419i
$413$	9.91308	+	4.10613i	0.487791	+	0.202050i
$414$		0			0
$415$	−4.32645	+	8.49115i	−0.212377	+	0.416814i
$416$	5.79898	+	1.39221i	0.284319	+	0.0682588i
$417$		0			0
$418$	11.2956	−	5.75541i	0.552487	−	0.281506i
$419$	−23.5931	+	23.5931i	−1.15260	+	1.15260i	−0.166566	+	0.986030i	$0.553268\pi$
$419$	−23.5931	+	23.5931i	−1.15260	+	1.15260i	−0.986030	+	0.166566i	$0.946732\pi$
$420$		0			0
$421$	10.1738	−	11.9120i	0.495842	−	0.580557i	−0.454899	−	0.890543i	$-0.650325\pi$
$421$	10.1738	−	11.9120i	0.495842	−	0.580557i	0.950741	+	0.309987i	$0.100325\pi$
$422$	−20.9449	−	1.64840i	−1.01958	−	0.0802428i
$423$		0			0
$424$	3.18436	+	7.68773i	0.154646	+	0.373349i
$425$	4.02697	−	3.43936i	0.195337	−	0.166833i
$426$		0			0
$427$	−9.68190	+	0.761982i	−0.468540	+	0.0368749i
$428$	−4.49036	+	6.18045i	−0.217050	+	0.298743i
$429$		0			0
$430$	0.440816	−	2.78320i	0.0212580	−	0.134218i
$431$	−4.16195	+	26.2775i	−0.200474	+	1.26574i	0.658052	+	0.752972i	$0.271381\pi$
$431$	−4.16195	+	26.2775i	−0.200474	+	1.26574i	−0.858526	+	0.512770i	$0.828619\pi$
$432$		0			0
$433$	−22.9032	+	31.5236i	−1.10066	+	1.51493i	−0.266149	+	0.963932i	$0.585751\pi$
$433$	−22.9032	+	31.5236i	−1.10066	+	1.51493i	−0.834509	+	0.550994i	$0.814249\pi$
$434$	14.5381	−	1.14417i	0.697851	−	0.0549221i
$435$		0			0
$436$	−13.4304	+	11.4707i	−0.643200	+	0.549345i
$437$	−3.03042	−	7.31608i	−0.144965	−	0.349976i
$438$		0			0
$439$	14.0124	+	1.10280i	0.668777	+	0.0526339i	0.408302	−	0.912847i	$-0.366121\pi$
$439$	14.0124	+	1.10280i	0.668777	+	0.0526339i	0.260474	+	0.965481i	$0.416121\pi$
$440$	2.55857	−	2.99570i	0.121975	−	0.142814i
$441$		0			0
$442$	−15.3389	+	15.3389i	−0.729599	+	0.729599i
$443$	0.410929	−	0.209379i	0.0195238	−	0.00994787i	−0.444201	−	0.895927i	$-0.646513\pi$
$443$	0.410929	−	0.209379i	0.0195238	−	0.00994787i	0.463725	+	0.885979i	$0.346513\pi$
$444$		0			0
$445$	−13.3041	−	3.19402i	−0.630673	−	0.151411i
$446$	−4.32779	+	8.49377i	−0.204927	+	0.402192i
$447$		0			0
$448$	−2.66901	−	1.10554i	−0.126099	−	0.0522318i
$449$	9.63514	−	1.52606i	0.454710	−	0.0720191i	0.0751216	−	0.997174i	$-0.476065\pi$
$449$	9.63514	−	1.52606i	0.454710	−	0.0720191i	0.379589	+	0.925155i	$0.376065\pi$
$450$		0			0
$451$	7.64800	+	11.0027i	0.360130	+	0.518097i
$452$			11.7010i			0.550367i
$453$		0			0
$454$	10.0506	−	24.2643i	0.471698	−	1.13878i
$455$	10.0228	+	30.8469i	0.469875	+	1.44613i
$456$		0			0
$457$	2.32467	−	9.68295i	0.108744	−	0.452949i	−0.891256	−	0.453500i	$-0.850175\pi$
$457$	2.32467	−	9.68295i	0.108744	−	0.452949i	1.00000		0.000550579i	$0.000175255\pi$
$458$	5.07979	−	1.21955i	0.237363	−	0.0569858i
$459$		0			0
$460$	−1.74009	−	1.74009i	−0.0811321	−	0.0811321i
$461$	24.3349	+	7.90689i	1.13339	+	0.368261i	0.814863	−	0.579653i	$-0.196812\pi$
$461$	24.3349	+	7.90689i	1.13339	+	0.368261i	0.318527	+	0.947914i	$0.396812\pi$
$462$		0			0
$463$	2.89148	−	36.7397i	0.134378	−	1.70744i	−0.447598	−	0.894235i	$-0.647720\pi$
$463$	2.89148	−	36.7397i	0.134378	−	1.70744i	0.581977	−	0.813206i	$-0.302280\pi$
$464$	3.93796	+	6.42617i	0.182815	+	0.298328i
$465$		0			0
$466$	10.6852	+	12.5108i	0.494983	+	0.579551i
$467$	−1.13834	−	1.56679i	−0.0526761	−	0.0725025i	0.781866	−	0.623446i	$-0.214268\pi$
$467$	−1.13834	−	1.56679i	−0.0526761	−	0.0725025i	−0.834542	+	0.550944i	$0.814268\pi$
$468$		0			0
$469$	27.3258	+	19.8533i	1.26179	+	0.916742i
$470$	−4.13437	+	6.74668i	−0.190704	+	0.311201i
$471$		0			0
$472$	−3.66842	−	0.581020i	−0.168853	−	0.0267436i
$473$	−2.67081	−	1.63667i	−0.122804	−	0.0752543i
$474$		0			0
$475$	0.692012	+	8.79285i	0.0317517	+	0.403444i
$476$	8.50124	−	6.17651i	0.389654	−	0.283100i
$477$		0			0
$478$	15.7888	−	6.53995i	0.722164	−	0.299130i
$479$	17.1209	−	10.4917i	0.782272	−	0.479377i	−0.0731420	−	0.997322i	$-0.523303\pi$
$479$	17.1209	−	10.4917i	0.782272	−	0.479377i	0.855414	+	0.517944i	$0.173303\pi$
$480$		0			0
$481$	34.4280	+	29.4043i	1.56978	+	1.34072i
$482$	−1.29447	+	3.98397i	−0.0589615	+	0.181465i
$483$		0			0
$484$	3.00573	+	5.89908i	0.136624	+	0.268140i
$485$	−4.73033	−	19.7032i	−0.214793	−	0.894677i
$486$		0			0
$487$	−12.0463	−	6.13790i	−0.545870	−	0.278135i	0.159231	−	0.987241i	$-0.449098\pi$
$487$	−12.0463	−	6.13790i	−0.545870	−	0.278135i	−0.705101	+	0.709107i	$0.749098\pi$
$488$	3.19723	−	1.03884i	0.144732	−	0.0470261i
$489$		0			0
$490$	−0.396342	−	2.50241i	−0.0179049	−	0.113047i
$491$	−26.5420			−1.19782			−0.598911	−	0.800816i	$-0.704400\pi$
$491$	−26.5420			−1.19782			−0.598911	+	0.800816i	$0.704400\pi$
$492$		0			0
$493$	−27.4143			−1.23468
$494$	−5.65171	−	35.6835i	−0.254282	−	1.60548i
$495$		0			0
$496$	−4.80088	+	1.55990i	−0.215566	+	0.0700415i
$497$	−31.2027	−	15.8986i	−1.39963	−	0.713149i
$498$		0			0
$499$	8.22321	+	34.2521i	0.368121	+	1.53334i	0.782161	+	0.623077i	$0.214118\pi$
$499$	8.22321	+	34.2521i	0.368121	+	1.53334i	−0.414039	+	0.910259i	$0.635882\pi$
$500$	5.51768	+	10.8291i	0.246758	+	0.484290i
$501$		0			0
$502$	4.04235	−	12.4411i	0.180419	−	0.555272i
$503$	29.2953	+	25.0206i	1.30621	+	1.11561i	0.985725	+	0.168361i	$0.0538473\pi$
$503$	29.2953	+	25.0206i	1.30621	+	1.11561i	0.320489	+	0.947252i	$0.396153\pi$
$504$		0			0
$505$	26.1828	−	16.0448i	1.16512	−	0.713985i
$506$	−2.52728	+	1.04683i	−0.112351	+	0.0465375i
$507$		0			0
$508$	−2.62714	+	1.90873i	−0.116561	+	0.0846863i
$509$	3.25458	+	41.3534i	0.144257	+	1.83296i	0.464445	+	0.885602i	$0.346254\pi$
$509$	3.25458	+	41.3534i	0.144257	+	1.83296i	−0.320188	+	0.947354i	$0.603746\pi$
$510$		0			0
$511$	25.3026	+	15.5055i	1.11932	+	0.685922i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$		0			0
$514$	−2.77400	+	4.52675i	−0.122356	+	0.199666i
$515$	−9.01962	−	6.55313i	−0.397452	−	0.288766i
$516$		0			0
$517$	5.17005	+	7.11597i	0.227379	+	0.312960i
$518$	−14.2438	−	16.6773i	−0.625836	−	0.732760i
$519$		0			0
$520$	−5.86619	−	9.57275i	−0.257249	−	0.419793i
$521$	2.41917	−	30.7384i	0.105986	−	1.34668i	−0.682167	−	0.731196i	$-0.738962\pi$
$521$	2.41917	−	30.7384i	0.105986	−	1.34668i	0.788153	−	0.615479i	$-0.211038\pi$
$522$		0			0
$523$	−19.0536	−	6.19090i	−0.833157	−	0.270709i	−0.138783	−	0.990323i	$-0.544319\pi$
$523$	−19.0536	−	6.19090i	−0.833157	−	0.270709i	−0.694375	+	0.719614i	$0.744319\pi$
$524$	9.36640	+	9.36640i	0.409173	+	0.409173i
$525$		0			0
$526$	9.11156	−	2.18749i	0.397283	−	0.0953792i
$527$	4.28637	−	17.8540i	0.186717	−	0.777733i
$528$		0			0
$529$	−6.57937	−	20.2492i	−0.286059	−	0.880400i
$530$	5.99478	−	14.4727i	0.260397	−	0.628653i
$531$		0			0
$532$			17.5009i			0.758762i
$533$	36.5563	−	11.0393i	1.58343	−	0.478163i
$534$		0			0
$535$	14.2047	−	2.24981i	0.614124	−	0.0972677i
$536$	−10.8018	−	4.47425i	−0.466566	−	0.193258i
$537$		0			0
$538$	−4.61899	+	9.06528i	−0.199139	+	0.390832i
$539$	−2.73855	−	0.657469i	−0.117958	−	0.0283192i
$540$		0			0
$541$	19.3093	−	9.83858i	0.830172	−	0.422994i	0.0133690	−	0.999911i	$-0.495744\pi$
$541$	19.3093	−	9.83858i	0.830172	−	0.422994i	0.816803	+	0.576917i	$0.195744\pi$
$542$	6.32363	−	6.32363i	0.271623	−	0.271623i
$543$		0			0
$544$	−2.36230	+	2.76589i	−0.101283	+	0.118587i
$545$	33.1477	+	2.60878i	1.41989	+	0.111748i
$546$		0			0
$547$	−2.29531	−	5.54136i	−0.0981402	−	0.236931i	0.867183	−	0.497990i	$-0.165928\pi$
$547$	−2.29531	−	5.54136i	−0.0981402	−	0.236931i	−0.965323	+	0.261059i	$0.915928\pi$
$548$	−0.792641	+	0.676979i	−0.0338599	+	0.0289191i
$549$		0			0
$550$	3.03742	−	0.239050i	0.129516	−	0.0101931i
$551$	26.8369	−	36.9378i	1.14329	−	1.57360i
$552$		0			0
$553$	7.70095	−	48.6219i	0.327478	−	2.06761i
$554$	3.12675	−	19.7415i	0.132843	−	0.838737i
$555$		0			0
$556$	−0.294691	+	0.405607i	−0.0124977	+	0.0172016i
$557$	−24.2343	+	1.90728i	−1.02684	+	0.0808139i	−0.580673	−	0.814137i	$-0.697211\pi$
$557$	−24.2343	+	1.90728i	−1.02684	+	0.0808139i	−0.446165	+	0.894951i	$0.647211\pi$
$558$		0			0
$559$	−6.78798	+	5.79748i	−0.287101	+	0.245207i
$560$	2.08125	+	5.02459i	0.0879490	+	0.212328i
$561$		0			0
$562$	−3.02628	−	0.238174i	−0.127656	−	0.0100467i
$563$	−17.7676	+	20.8032i	−0.748817	+	0.876752i	−0.995733	−	0.0922852i	$-0.970583\pi$
$563$	−17.7676	+	20.8032i	−0.748817	+	0.876752i	0.246916	+	0.969037i	$0.420583\pi$
$564$		0			0
$565$	15.5760	−	15.5760i	0.655289	−	0.655289i
$566$	22.7662	−	11.5999i	0.956934	−	0.487582i
$567$		0			0
$568$	11.7871	+	2.82984i	0.494578	+	0.118738i
$569$	−10.7377	+	21.0740i	−0.450149	+	0.883467i	0.548724	+	0.836003i	$0.315114\pi$
$569$	−10.7377	+	21.0740i	−0.450149	+	0.883467i	−0.998873	+	0.0474634i	$0.984886\pi$
$570$		0			0
$571$	28.2666	+	11.7084i	1.18292	+	0.489981i	0.885443	−	0.464748i	$-0.153855\pi$
$571$	28.2666	+	11.7084i	1.18292	+	0.489981i	0.297476	+	0.954729i	$0.403855\pi$
$572$	−12.3266	+	1.95234i	−0.515400	+	0.0816314i
$573$		0			0
$574$	−18.3268	+	2.51152i	−0.764945	+	0.104829i
$575$		−	1.90318i		−	0.0793680i
$576$		0			0
$577$	7.49072	−	18.0842i	0.311843	−	0.752855i	−0.687794	−	0.725906i	$-0.741421\pi$
$577$	7.49072	−	18.0842i	0.311843	−	0.752855i	0.999637	−	0.0269492i	$-0.00857923\pi$
$578$	1.16481	+	3.58490i	0.0484495	+	0.149112i
$579$		0			0
$580$	3.31225	−	13.7965i	0.137534	−	0.572868i
$581$	−14.2200	+	3.41393i	−0.589947	+	0.141634i
$582$		0			0
$583$	−12.3132	−	12.3132i	−0.509960	−	0.509960i
$584$	−9.76948	−	3.17430i	−0.404264	−	0.131353i
$585$		0			0
$586$	0.298816	−	3.79682i	0.0123440	−	0.156845i
$587$	19.4113	+	31.6764i	0.801191	+	1.30742i	0.948003	+	0.318260i	$0.103098\pi$
$587$	19.4113	+	31.6764i	0.801191	+	1.30742i	−0.146813	+	0.989164i	$0.546902\pi$
$588$		0			0
$589$	19.8603	+	23.2534i	0.818329	+	0.958140i
$590$	4.10987	+	5.65675i	0.169201	+	0.232885i
$591$		0			0
$592$	6.14192	+	4.46237i	0.252431	+	0.183402i
$593$	−5.94434	+	9.70028i	−0.244105	+	0.398343i	−0.951104	−	0.308872i	$-0.900049\pi$
$593$	−5.94434	+	9.70028i	−0.244105	+	0.398343i	0.706999	+	0.707215i	$0.250049\pi$
$594$		0			0
$595$	−19.5387	−	3.09462i	−0.801007	−	0.126867i
$596$	−13.2323	−	8.10874i	−0.542014	−	0.332147i
$597$		0			0
$598$	0.611645	+	7.77169i	0.0250120	+	0.317808i
$599$	−21.3344	+	15.5003i	−0.871700	+	0.633327i	−0.931043	−	0.364911i	$-0.881100\pi$
$599$	−21.3344	+	15.5003i	−0.871700	+	0.633327i	0.0593427	+	0.998238i	$0.481100\pi$
$600$		0			0
$601$	17.3931	−	7.20448i	0.709481	−	0.293877i	0.00139136	−	0.999999i	$-0.499557\pi$
$601$	17.3931	−	7.20448i	0.709481	−	0.293877i	0.708090	+	0.706122i	$0.249557\pi$
$602$	3.68701	−	2.25941i	0.150272	−	0.0920865i
$603$		0			0
$604$	−4.38618	−	3.74615i	−0.178471	−	0.152429i
$605$	3.85156	−	11.8539i	0.156588	−	0.481929i
$606$		0			0
$607$	−10.9176	−	21.4270i	−0.443131	−	0.869694i	−0.999255	−	0.0385945i	$-0.987712\pi$
$607$	−10.9176	−	21.4270i	−0.443131	−	0.869694i	0.556124	−	0.831100i	$-0.312288\pi$
$608$	−1.41420	−	5.89059i	−0.0573536	−	0.238895i
$609$		0			0
$610$	−5.63895	−	2.87319i	−0.228314	−	0.116332i
$611$	23.8397	−	7.74598i	0.964450	−	0.313369i
$612$		0			0
$613$	4.22334	+	26.6651i	0.170579	+	1.07699i	0.913269	+	0.407357i	$0.133550\pi$
$613$	4.22334	+	26.6651i	0.170579	+	1.07699i	−0.742690	+	0.669636i	$0.766450\pi$
$614$	1.71103			0.0690515
$615$		0			0
$616$	6.04557			0.243583
$617$	−0.910820	−	5.75069i	−0.0366682	−	0.231514i	0.962547	−	0.271113i	$-0.0873919\pi$
$617$	−0.910820	−	5.75069i	−0.0366682	−	0.231514i	−0.999216	+	0.0395993i	$0.987392\pi$
$618$		0			0
$619$	−20.3098	+	6.59904i	−0.816318	+	0.265238i	−0.687271	−	0.726401i	$-0.741192\pi$
$619$	−20.3098	+	6.59904i	−0.816318	+	0.265238i	−0.129047	+	0.991639i	$0.541192\pi$
$620$	8.46731	+	4.31431i	0.340055	+	0.173267i
$621$		0			0
$622$	6.37314	+	26.5460i	0.255540	+	1.06440i
$623$	−9.53198	−	18.7076i	−0.381891	−	0.749503i
$624$		0			0
$625$	4.82083	−	14.8370i	0.192833	−	0.593480i
$626$	−18.9008	−	16.1428i	−0.755426	−	0.645195i
$627$		0			0
$628$	−5.96147	+	3.65320i	−0.237889	+	0.145778i
$629$	−25.5124	+	10.5676i	−1.01725	+	0.421357i
$630$		0			0
$631$	26.5259	−	19.2722i	1.05598	−	0.767214i	0.0826397	−	0.996579i	$-0.473665\pi$
$631$	26.5259	−	19.2722i	1.05598	−	0.767214i	0.973340	+	0.229365i	$0.0736649\pi$
$632$	1.33697	+	16.9878i	0.0531817	+	0.675738i
$633$		0			0
$634$	−22.4917	−	13.7829i	−0.893260	−	0.547390i
$635$	6.03805	+	0.956333i	0.239613	+	0.0379509i
$636$		0			0
$637$	−4.19366	+	6.84343i	−0.166159	+	0.271146i
$638$	−12.7599	−	9.27060i	−0.505169	−	0.367027i
$639$		0			0
$640$	−1.10655	−	1.52303i	−0.0437400	−	0.0602030i
$641$	−8.81906	−	10.3258i	−0.348332	−	0.407844i	0.558386	−	0.829581i	$-0.311421\pi$
$641$	−8.81906	−	10.3258i	−0.348332	−	0.407844i	−0.906718	+	0.421737i	$0.861421\pi$
$642$		0			0
$643$	−15.2237	−	24.8428i	−0.600363	−	0.979703i	−0.998064	−	0.0621884i	$-0.980192\pi$
$643$	−15.2237	−	24.8428i	−0.600363	−	0.979703i	0.397701	−	0.917515i	$-0.369808\pi$
$644$	0.296288	−	3.76469i	0.0116754	−	0.148350i
$645$		0			0
$646$	20.9567	+	6.80925i	0.824531	+	0.267906i
$647$	−6.77333	−	6.77333i	−0.266287	−	0.266287i	0.561315	−	0.827602i	$-0.310296\pi$
$647$	−6.77333	−	6.77333i	−0.266287	−	0.266287i	−0.827602	+	0.561315i	$0.810296\pi$
$648$		0			0
$649$	7.55776	−	1.81446i	0.296668	−	0.0712237i
$650$	2.02698	−	8.44297i	0.0795046	−	0.331160i
$651$		0			0
$652$	−4.36499	−	13.4341i	−0.170946	−	0.526118i
$653$	5.45644	−	13.1730i	0.213527	−	0.515500i	−0.780433	−	0.625239i	$-0.785001\pi$
$653$	5.45644	−	13.1730i	0.213527	−	0.515500i	0.993960	+	0.109739i	$0.0350015\pi$
$654$		0			0
$655$		−	24.9366i		−	0.974355i
$656$	5.96560	−	2.32628i	0.232918	−	0.0908260i
$657$		0			0
$658$	−11.9930	+	1.89951i	−0.467536	+	0.0740505i
$659$	−35.4734	−	14.6936i	−1.38185	−	0.572381i	−0.436874	−	0.899523i	$-0.643914\pi$
$659$	−35.4734	−	14.6936i	−1.38185	−	0.572381i	−0.944975	+	0.327142i	$0.893914\pi$
$660$		0			0
$661$	−10.0938	+	19.8101i	−0.392602	+	0.770524i	−0.999710	−	0.0240952i	$-0.992330\pi$
$661$	−10.0938	+	19.8101i	−0.392602	+	0.770524i	0.607108	+	0.794619i	$0.292330\pi$
$662$	−24.7441	−	5.94053i	−0.961707	−	0.230885i
$663$		0			0
$664$	4.51041	−	2.29817i	0.175038	−	0.0891862i
$665$	23.2968	−	23.2968i	0.903413	−	0.903413i
$666$		0			0
$667$	−6.39834	+	7.49149i	−0.247745	+	0.290072i
$668$	−0.593476	−	0.0467076i	−0.0229623	−	0.00180717i
$669$		0			0
$670$	8.42308	+	20.3351i	0.325412	+	0.785614i
$671$	−5.34952	+	4.56892i	−0.206516	+	0.176381i
$672$		0			0
$673$	20.8878	−	1.64391i	0.805167	−	0.0633680i	0.330807	−	0.943699i	$-0.392679\pi$
$673$	20.8878	−	1.64391i	0.805167	−	0.0633680i	0.474361	+	0.880331i	$0.342679\pi$
$674$	−7.88518	+	10.8530i	−0.303726	+	0.418043i
$675$		0			0
$676$	−3.53017	+	22.2886i	−0.135776	+	0.857255i
$677$	5.48492	−	34.6304i	0.210802	−	1.33095i	−0.624440	−	0.781073i	$-0.714673\pi$
$677$	5.48492	−	34.6304i	0.210802	−	1.33095i	0.835243	−	0.549882i	$-0.185327\pi$
$678$		0			0
$679$	18.2771	−	25.1563i	0.701413	−	0.965412i
$680$	6.82652	−	0.537259i	0.261785	−	0.0206029i
$681$		0			0
$682$	8.03271	−	6.86058i	0.307588	−	0.262705i
$683$	10.3695	+	25.0342i	0.396777	+	0.957905i	0.988425	+	0.151709i	$0.0484776\pi$
$683$	10.3695	+	25.0342i	0.396777	+	0.957905i	−0.591648	+	0.806196i	$0.701522\pi$
$684$		0			0
$685$	1.95632	+	0.153966i	0.0747473	+	0.00588274i
$686$	−10.6084	+	12.4208i	−0.405029	+	0.474228i
$687$		0			0
$688$	−1.05842	+	1.05842i	−0.0403520	+	0.0403520i
$689$	−44.2165	+	22.5294i	−1.68451	+	0.858303i
$690$		0			0
$691$	34.8611	+	8.36941i	1.32618	+	0.318387i	0.833835	−	0.552014i	$-0.186141\pi$
$691$	34.8611	+	8.36941i	1.32618	+	0.318387i	0.492343	+	0.870401i	$0.336141\pi$
$692$	−2.15694	+	4.23323i	−0.0819944	+	0.160923i
$693$		0			0
$694$	12.5695	+	5.20647i	0.477133	+	0.197635i
$695$	0.932219	−	0.147649i	0.0353611	−	0.00560065i
$696$		0			0
$697$	−4.12312	+	22.9228i	−0.156174	+	0.868263i
$698$		−	21.5225i		−	0.814638i
$699$		0			0
$700$	−1.60960	+	3.88591i	−0.0608371	+	0.146874i
$701$	−14.0207	−	43.1512i	−0.529553	−	1.62980i	−0.755132	−	0.655573i	$-0.772427\pi$
$701$	−14.0207	−	43.1512i	−0.529553	−	1.62980i	0.225579	−	0.974225i	$-0.427573\pi$
$702$		0			0
$703$	10.7364	−	44.7203i	0.404931	−	1.68666i
$704$	−2.03486	+	0.488526i	−0.0766916	+	0.0184120i
$705$		0			0
$706$	−4.30122	−	4.30122i	−0.161879	−	0.161879i
$707$	44.8167	+	14.5618i	1.68551	+	0.547654i
$708$		0			0
$709$	3.46281	−	43.9991i	0.130048	−	1.65242i	−0.492846	−	0.870117i	$-0.664043\pi$
$709$	3.46281	−	43.9991i	0.130048	−	1.65242i	0.622894	−	0.782306i	$-0.285957\pi$
$710$	−11.9238	−	19.4578i	−0.447490	−	0.730238i
$711$		0			0
$712$	4.72005	+	5.52646i	0.176891	+	0.207113i
$713$	−3.87854	−	5.33836i	−0.145253	−	0.199923i
$714$		0			0
$715$	19.0078	+	13.8100i	0.710850	+	0.516463i
$716$	−5.62622	+	9.18115i	−0.210262	+	0.343116i
$717$		0			0
$718$	−30.3992	−	4.81477i	−1.13449	−	0.179685i
$719$	−23.7252	−	14.5388i	−0.884799	−	0.542205i	0.00426385	−	0.999991i	$-0.498643\pi$
$719$	−23.7252	−	14.5388i	−0.884799	−	0.542205i	−0.889063	+	0.457785i	$0.848643\pi$
$720$		0			0
$721$	−1.34233	−	17.0559i	−0.0499908	−	0.635193i
$722$	−14.3188	+	10.4032i	−0.532890	+	0.387167i
$723$		0			0
$724$	−7.54658	+	3.12590i	−0.280466	+	0.116173i
$725$	9.35612	−	5.73344i	0.347478	−	0.212935i
$726$		0			0
$727$	28.1414	+	24.0350i	1.04371	+	0.891409i	0.994220	−	0.107366i	$-0.0342417\pi$
$727$	28.1414	+	24.0350i	1.04371	+	0.891409i	0.0494858	+	0.998775i	$0.484242\pi$
$728$	5.32399	−	16.3856i	0.197320	−	0.607289i
$729$		0			0
$730$	8.77936	+	17.2305i	0.324939	+	0.637728i
$731$	−1.27101	−	5.29415i	−0.0470101	−	0.195811i
$732$		0			0
$733$	−5.49846	−	2.80161i	−0.203090	−	0.103480i	0.349487	−	0.936941i	$-0.386356\pi$
$733$	−5.49846	−	2.80161i	−0.203090	−	0.103480i	−0.552578	+	0.833461i	$0.686356\pi$
$734$	29.8996	−	9.71498i	1.10362	−	0.358587i
$735$		0			0
$736$	0.204488	+	1.29109i	0.00753754	+	0.0475901i
$737$	24.4671			0.901258
$738$		0			0
$739$	−33.9185			−1.24771			−0.623857	−	0.781539i	$-0.714435\pi$
$739$	−33.9185			−1.24771			−0.623857	+	0.781539i	$0.714435\pi$
$740$	−2.23578	−	14.1162i	−0.0821890	−	0.518921i
$741$		0			0
$742$	22.8625	−	7.42848i	0.839309	−	0.272708i
$743$	−32.1371	−	16.3747i	−1.17900	−	0.600729i	−0.249074	−	0.968484i	$-0.580126\pi$
$743$	−32.1371	−	16.3747i	−1.17900	−	0.600729i	−0.929922	+	0.367756i	$0.880126\pi$
$744$		0			0
$745$	6.82031	+	28.4086i	0.249877	+	1.04081i
$746$	0.135156	+	0.265259i	0.00494842	+	0.00971181i
$747$		0			0
$748$	2.35220	−	7.23934i	0.0860051	−	0.264696i
$749$	16.7820	+	14.3331i	0.613200	+	0.523722i
$750$		0			0
$751$	−22.7431	+	13.9370i	−0.829906	+	0.508567i	−0.871401	−	0.490572i	$-0.836788\pi$
$751$	−22.7431	+	13.9370i	−0.829906	+	0.508567i	0.0414948	+	0.999139i	$0.486788\pi$
$752$	3.88319	−	1.60847i	0.141606	−	0.0586549i
$753$		0			0
$754$	−36.3634	+	26.4196i	−1.32428	+	0.962144i
$755$	0.851991	+	10.8256i	0.0310071	+	0.393983i
$756$		0			0
$757$	−15.6982	−	9.61985i	−0.570560	−	0.349639i	0.207105	−	0.978319i	$-0.433596\pi$
$757$	−15.6982	−	9.61985i	−0.570560	−	0.349639i	−0.777665	+	0.628679i	$0.783596\pi$
$758$	5.03861	+	0.798037i	0.183011	+	0.0289860i
$759$		0			0
$760$	−5.95885	+	9.72397i	−0.216150	+	0.352725i
$761$	40.4597	+	29.3957i	1.46666	+	1.06559i	0.981564	+	0.191136i	$0.0612170\pi$
$761$	40.4597	+	29.3957i	1.46666	+	1.06559i	0.485101	+	0.874458i	$0.338783\pi$
$762$		0			0
$763$	29.9914	+	41.2796i	1.08576	+	1.49442i
$764$	2.89176	+	3.38581i	0.104620	+	0.122494i
$765$		0			0
$766$	−0.756197	−	1.23400i	−0.0273225	−	0.0445863i
$767$	1.73789	−	22.0820i	0.0627516	−	0.797335i
$768$		0			0
$769$	6.11380	+	1.98649i	0.220469	+	0.0716347i	0.417169	−	0.908829i	$-0.363022\pi$
$769$	6.11380	+	1.98649i	0.220469	+	0.0716347i	−0.196700	+	0.980464i	$0.563022\pi$
$770$	−8.04772	−	8.04772i	−0.290020	−	0.290020i
$771$		0			0
$772$	−4.80492	+	1.15356i	−0.172933	+	0.0415175i
$773$	−10.0122	+	41.7037i	−0.360113	+	1.49998i	0.438829	+	0.898570i	$0.355393\pi$
$773$	−10.0122	+	41.7037i	−0.360113	+	1.49998i	−0.798942	+	0.601408i	$0.794607\pi$
$774$		0			0
$775$	2.27112	+	6.98978i	0.0815810	+	0.251080i
$776$	−4.11903	+	9.94422i	−0.147865	+	0.356977i
$777$		0			0
$778$		−	3.72694i		−	0.133617i
$779$	−26.8498	−	27.9955i	−0.961993	−	1.00304i
$780$		0			0
$781$	−25.0553	+	3.96837i	−0.896549	+	0.141999i
$782$	−4.39280	−	1.81956i	−0.157086	−	0.0650672i
$783$		0			0
$784$	−0.610990	+	1.19914i	−0.0218211	+	0.0428263i
$785$	12.7988	+	3.07273i	0.456810	+	0.109670i
$786$		0			0
$787$	19.2466	−	9.80663i	0.686067	−	0.349569i	−0.0759625	−	0.997111i	$-0.524203\pi$
$787$	19.2466	−	9.80663i	0.686067	−	0.349569i	0.762030	+	0.647542i	$0.224203\pi$
$788$	10.4226	−	10.4226i	0.371288	−	0.371288i
$789$		0			0
$790$	20.8340	−	24.3935i	0.741240	−	0.867881i
$791$	33.6988	+	2.65216i	1.19819	+	0.0942998i
$792$		0			0
$793$	7.67232	+	18.5226i	0.272452	+	0.657758i
$794$	9.21472	−	7.87012i	0.327018	−	0.279300i
$795$		0			0
$796$	−19.1349	+	1.50595i	−0.678219	+	0.0533770i
$797$	−32.1492	+	44.2496i	−1.13878	+	1.56740i	−0.368591	+	0.929592i	$0.620160\pi$
$797$	−32.1492	+	44.2496i	−1.13878	+	1.56740i	−0.770193	+	0.637811i	$0.779840\pi$
$798$		0			0
$799$	−2.39164	+	15.1002i	−0.0846102	+	0.534208i
$800$	0.227759	−	1.43801i	0.00805250	−	0.0508415i
$801$		0			0
$802$	23.0404	−	31.7124i	0.813585	−	1.11980i
$803$	21.4302	−	1.68660i	0.756257	−	0.0595187i
$804$		0			0
$805$	−5.40588	+	4.61706i	−0.190532	+	0.162730i
$806$	−11.5206	−	27.8131i	−0.405795	−	0.979676i
$807$		0			0
$808$	−16.2614	−	1.27980i	−0.572075	−	0.0450233i
$809$	14.7980	−	17.3262i	0.520270	−	0.609158i	−0.436607	−	0.899653i	$-0.643820\pi$
$809$	14.7980	−	17.3262i	0.520270	−	0.609158i	0.956877	+	0.290495i	$0.0938198\pi$
$810$		0			0
$811$	7.57901	−	7.57901i	0.266135	−	0.266135i	−0.561406	−	0.827541i	$-0.689739\pi$
$811$	7.57901	−	7.57901i	0.266135	−	0.266135i	0.827541	+	0.561406i	$0.189739\pi$
$812$	19.4000	−	9.88480i	0.680807	−	0.346889i
$813$		0			0
$814$	−15.4483	−	3.70881i	−0.541462	−	0.129994i
$815$	−12.0725	+	23.6937i	−0.422882	+	0.829953i
$816$		0			0
$817$	8.37755	+	3.47009i	0.293093	+	0.121403i
$818$	−0.414874	+	0.0657095i	−0.0145057	+	0.00229748i
$819$		0			0
$820$	−11.0380	−	4.84458i	−0.385462	−	0.169180i
$821$		−	11.3070i		−	0.394617i	−0.980341	−	0.197308i	$-0.936780\pi$
$821$		−	11.3070i		−	0.394617i	0.980341	−	0.197308i	$-0.0632200\pi$
$822$		0			0
$823$	−0.748891	+	1.80798i	−0.0261047	+	0.0630223i	−0.936394	−	0.350950i	$-0.885859\pi$
$823$	−0.748891	+	1.80798i	−0.0261047	+	0.0630223i	0.910290	+	0.413972i	$0.135859\pi$
$824$	1.83005	+	5.63231i	0.0637527	+	0.196211i
$825$		0			0
$826$	−2.50483	+	10.4334i	−0.0871543	+	0.363024i
$827$	−55.1747	+	13.2463i	−1.91861	+	0.460618i	−0.921166	+	0.389169i	$0.872762\pi$
$827$	−55.1747	+	13.2463i	−1.91861	+	0.460618i	−0.997444	+	0.0714485i	$0.977238\pi$
$828$		0			0
$829$	−0.640579	−	0.640579i	−0.0222482	−	0.0222482i	0.695895	−	0.718143i	$-0.255008\pi$
$829$	−0.640579	−	0.640579i	−0.0222482	−	0.0222482i	−0.718143	+	0.695895i	$0.755008\pi$
$830$	−9.06341	−	2.94488i	−0.314596	−	0.102218i
$831$		0			0
$832$	−0.467911	+	5.94538i	−0.0162219	+	0.206119i
$833$	−2.55778	−	4.17391i	−0.0886217	−	0.144617i
$834$		0			0
$835$	0.727845	+	0.852197i	0.0251881	+	0.0294915i
$836$	7.45158	+	10.2562i	0.257718	+	0.354719i
$837$		0			0
$838$	−26.9934	−	19.6118i	−0.932470	−	0.677479i
$839$	12.7860	−	20.8648i	0.441421	−	0.720333i	−0.552126	−	0.833761i	$-0.686183\pi$
$839$	12.7860	−	20.8648i	0.441421	−	0.720333i	0.993546	+	0.113428i	$0.0361831\pi$
$840$		0			0
$841$	−27.4610	−	4.34939i	−0.946930	−	0.149979i
$842$	13.3569	+	8.18512i	0.460309	+	0.282078i
$843$		0			0
$844$	−1.64840	−	20.9449i	−0.0567402	−	0.720953i
$845$	34.3694	−	24.9708i	1.18234	−	0.859022i
$846$		0			0
$847$	17.6707	−	7.31944i	0.607172	−	0.251499i
$848$	−7.09494	+	4.34778i	−0.243641	+	0.149304i
$849$		0			0
$850$	4.02697	+	3.43936i	0.138124	+	0.117969i
$851$	−3.06665	+	9.43819i	−0.105124	+	0.323537i
$852$		0			0
$853$	−2.53385	−	4.97295i	−0.0867572	−	0.170271i	0.843551	−	0.537049i	$-0.180461\pi$
$853$	−2.53385	−	4.97295i	−0.0867572	−	0.170271i	−0.930308	+	0.366778i	$0.880461\pi$
$854$	−2.26718	−	9.44350i	−0.0775814	−	0.323150i
$855$		0			0
$856$	−6.80681	−	3.46824i	−0.232652	−	0.118542i
$857$	−2.37551	+	0.771850i	−0.0811459	+	0.0263659i	−0.349309	−	0.937008i	$-0.613584\pi$
$857$	−2.37551	+	0.771850i	−0.0811459	+	0.0263659i	0.268163	+	0.963374i	$0.413584\pi$
$858$		0			0
$859$	4.41181	+	27.8551i	0.150529	+	0.950402i	0.941124	+	0.338062i	$0.109772\pi$
$859$	4.41181	+	27.8551i	0.150529	+	0.950402i	−0.790595	+	0.612340i	$0.790228\pi$
$860$	2.81790			0.0960895
$861$		0			0
$862$	−26.6050			−0.906171
$863$	0.765136	+	4.83088i	0.0260455	+	0.164445i	0.997283	−	0.0736689i	$-0.0234708\pi$
$863$	0.765136	+	4.83088i	0.0260455	+	0.164445i	−0.971237	+	0.238114i	$0.923471\pi$
$864$		0			0
$865$	8.50644	−	2.76391i	0.289227	−	0.0939757i
$866$	−34.7183	−	17.6899i	−1.17978	−	0.601126i
$867$		0			0
$868$	3.40435	+	14.1801i	0.115551	+	0.481305i
$869$	−16.1893	−	31.7732i	−0.549183	−	1.07783i
$870$		0			0
$871$	21.5468	−	66.3143i	0.730086	−	2.24697i
$872$	−13.4304	−	11.4707i	−0.454811	−	0.388445i
$873$		0			0
$874$	6.75194	−	4.13760i	0.228388	−	0.139956i
$875$	32.4384	−	13.4364i	1.09662	−	0.454235i
$876$		0			0
$877$	−44.6276	+	32.4238i	−1.50697	+	1.09487i	−0.539465	+	0.842008i	$0.681373\pi$
$877$	−44.6276	+	32.4238i	−1.50697	+	1.09487i	−0.967501	+	0.252867i	$0.918627\pi$
$878$	1.10280	+	14.0124i	0.0372178	+	0.472896i
$879$		0			0
$880$	3.35907	+	2.05844i	0.113234	+	0.0693900i
$881$	−48.4552	−	7.67455i	−1.63250	−	0.258562i	−0.728168	−	0.685399i	$-0.759628\pi$
$881$	−48.4552	−	7.67455i	−1.63250	−	0.258562i	−0.904329	+	0.426837i	$0.859628\pi$
$882$		0			0
$883$	5.85765	−	9.55881i	0.197125	−	0.321680i	−0.738770	−	0.673958i	$-0.764593\pi$
$883$	5.85765	−	9.55881i	0.197125	−	0.321680i	0.935895	+	0.352278i	$0.114593\pi$
$884$	−17.5496	−	12.7506i	−0.590258	−	0.428847i
$885$		0			0
$886$	0.271084	+	0.373115i	0.00910725	+	0.0125351i
$887$	−19.5055	−	22.8380i	−0.654929	−	0.766824i	0.329203	−	0.944259i	$-0.393220\pi$
$887$	−19.5055	−	22.8380i	−0.654929	−	0.766824i	−0.984132	+	0.177436i	$0.943220\pi$
$888$		0			0
$889$	4.90169	+	7.99883i	0.164397	+	0.268272i
$890$	1.07348	−	13.6399i	0.0359833	−	0.457211i
$891$		0			0
$892$	−9.06622	−	2.94579i	−0.303559	−	0.0986324i
$893$	−18.0047	−	18.0047i	−0.602504	−	0.602504i
$894$		0			0
$895$	19.7112	−	4.73224i	0.658873	−	0.158181i
$896$	0.674403	−	2.80909i	0.0225302	−	0.0938452i
$897$		0			0
$898$	3.01454	+	9.27779i	0.100596	+	0.309604i
$899$	14.5593	−	35.1493i	0.485580	−	1.17229i
$900$		0			0
$901$		−	30.2672i		−	1.00835i
$902$	−9.67083	+	9.27505i	−0.322003	+	0.308825i
$903$		0			0
$904$	−11.5569	+	1.83043i	−0.384377	+	0.0608793i
$905$	14.2069	+	5.88471i	0.472255	+	0.195614i
$906$		0			0
$907$	−4.91226	+	9.64085i	−0.163109	+	0.320119i	−0.958067	−	0.286546i	$-0.907493\pi$
$907$	−4.91226	+	9.64085i	−0.163109	+	0.320119i	0.794958	+	0.606665i	$0.207493\pi$
$908$	25.5378	+	6.13108i	0.847501	+	0.203467i
$909$		0			0
$910$	−28.8992	+	14.7249i	−0.958000	+	0.488126i
$911$	15.3684	−	15.3684i	0.509179	−	0.509179i	−0.405096	−	0.914274i	$-0.632762\pi$
$911$	15.3684	−	15.3684i	0.509179	−	0.509179i	0.914274	+	0.405096i	$0.132762\pi$
$912$		0			0
$913$	−6.87989	+	8.05532i	−0.227691	+	0.266592i
$914$	9.92740	+	0.781303i	0.328369	+	0.0258432i
$915$		0			0
$916$	1.99919	+	4.82647i	0.0660550	+	0.159471i
$917$	29.0983	−	24.8523i	0.960910	−	0.820695i
$918$		0			0
$919$	53.1819	−	4.18550i	1.75431	−	0.138067i	0.839869	−	0.542790i	$-0.182632\pi$
$919$	53.1819	−	4.18550i	1.75431	−	0.138067i	0.914439	+	0.404723i	$0.132632\pi$
$920$	1.44646	−	1.99088i	0.0476882	−	0.0656372i
$921$		0			0
$922$	−4.00273	+	25.2722i	−0.131823	+	0.832296i
$923$	−11.3092	+	71.4032i	−0.372245	+	2.35026i
$924$		0			0
$925$	6.49693	−	8.94226i	0.213618	−	0.294020i
$926$	36.7397	−	2.89148i	1.20734	−	0.0950199i
$927$		0			0
$928$	−5.73102	+	4.89476i	−0.188130	+	0.160678i
$929$	15.5113	+	37.4477i	0.508910	+	1.22862i	0.944512	+	0.328478i	$0.106536\pi$
$929$	15.5113	+	37.4477i	0.508910	+	1.22862i	−0.435601	+	0.900140i	$0.643464\pi$
$930$		0			0
$931$	8.12781	+	0.639673i	0.266378	+	0.0209644i
$932$	−10.6852	+	12.5108i	−0.350006	+	0.409804i
$933$		0			0
$934$	1.36943	−	1.36943i	0.0448090	−	0.0448090i
$935$	−12.7680	+	6.50564i	−0.417559	+	0.212757i
$936$		0			0
$937$	−28.0654	−	6.73790i	−0.916856	−	0.220118i	−0.252555	−	0.967583i	$-0.581271\pi$
$937$	−28.0654	−	6.73790i	−0.916856	−	0.220118i	−0.664301	+	0.747465i	$0.731271\pi$
$938$	−15.3342	+	30.0951i	−0.500680	+	0.982640i
$939$		0			0
$940$	−7.31037	−	3.02806i	−0.238438	−	0.0987643i
$941$	12.8563	−	2.03624i	0.419105	−	0.0663797i	0.0566792	−	0.998392i	$-0.481949\pi$
$941$	12.8563	−	2.03624i	0.419105	−	0.0663797i	0.362425	+	0.932013i	$0.381949\pi$
$942$		0			0
$943$	5.30180	+	6.47678i	0.172650	+	0.210913i
$944$		−	3.71414i		−	0.120885i
$945$		0			0
$946$	1.19872	−	2.89396i	0.0389737	−	0.0940907i
$947$	5.79610	+	17.8386i	0.188348	+	0.579676i	0.999990	−	0.00447957i	$-0.00142590\pi$
$947$	5.79610	+	17.8386i	0.188348	+	0.579676i	−0.811642	+	0.584155i	$0.801426\pi$
$948$		0			0
$949$	14.3011	−	59.5686i	0.464235	−	1.93368i
$950$	−8.57634	+	2.05900i	−0.278253	+	0.0668027i
$951$		0			0
$952$	7.43035	+	7.43035i	0.240819	+	0.240819i
$953$	−31.2324	−	10.1480i	−1.01172	−	0.328727i	−0.244179	−	0.969730i	$-0.578518\pi$
$953$	−31.2324	−	10.1480i	−1.01172	−	0.328727i	−0.767538	+	0.641003i	$0.778518\pi$
$954$		0			0
$955$	0.657675	−	8.35655i	0.0212819	−	0.270412i
$956$	8.92934	+	14.5714i	0.288796	+	0.471272i
$957$		0			0
$958$	13.0408	+	15.2688i	0.421329	+	0.493313i
$959$	1.77004	+	2.43626i	0.0571577	+	0.0786708i
$960$		0			0
$961$	−4.46440	−	3.24358i	−0.144013	−	0.104632i
$962$	−23.6566	+	38.6040i	−0.762719	+	1.24464i
$963$		0			0
$964$	−4.13742	−	0.655303i	−0.133257	−	0.0211059i
$965$	7.93178	+	4.86060i	0.255333	+	0.156468i
$966$		0			0
$967$	−1.31096	−	16.6573i	−0.0421576	−	0.535663i	−0.981345	−	0.192257i	$-0.938419\pi$
$967$	−1.31096	−	16.6573i	−0.0421576	−	0.535663i	0.939187	−	0.343406i	$-0.111581\pi$
$968$	−5.35626	+	3.89155i	−0.172157	+	0.125079i
$969$		0			0
$970$	18.7207	−	7.75435i	0.601084	−	0.248977i
$971$	−10.0788	+	6.17631i	−0.323445	+	0.198207i	−0.674736	−	0.738059i	$-0.735743\pi$
$971$	−10.0788	+	6.17631i	−0.323445	+	0.198207i	0.351291	+	0.936266i	$0.385743\pi$
$972$		0			0
$973$	1.10136	+	0.940646i	0.0353078	+	0.0301557i
$974$	4.17787	−	12.8582i	0.133868	−	0.412002i
$975$		0			0
$976$	1.52621	+	2.99535i	0.0488527	+	0.0958789i
$977$	−5.68128	−	23.6642i	−0.181760	−	0.757086i	−0.986541	−	0.163514i	$-0.947717\pi$
$977$	−5.68128	−	23.6642i	−0.181760	−	0.757086i	0.804781	−	0.593572i	$-0.202283\pi$
$978$		0			0
$979$	−13.5514	−	6.90480i	−0.433106	−	0.220678i
$980$	2.40960	−	0.782925i	0.0769717	−	0.0250096i
$981$		0			0
$982$	−4.15208	−	26.2152i	−0.132498	−	0.836560i
$983$	38.9601			1.24263			0.621317	−	0.783559i	$-0.286598\pi$
$983$	38.9601			1.24263			0.621317	+	0.783559i	$0.286598\pi$
$984$		0			0
$985$	−27.7485			−0.884141
$986$	−4.28854	−	27.0768i	−0.136575	−	0.862299i
$987$		0			0
$988$	34.3600	−	11.1643i	1.09314	−	0.355182i
$989$	−1.74338	−	0.888295i	−0.0554362	−	0.0282461i
$990$		0			0
$991$	7.32970	+	30.5304i	0.232835	+	0.969830i	0.959247	+	0.282569i	$0.0911867\pi$
$991$	7.32970	+	30.5304i	0.232835	+	0.969830i	−0.726411	+	0.687260i	$0.758813\pi$
$992$	−2.29172	−	4.49775i	−0.0727621	−	0.142804i
$993$		0			0
$994$	10.8217	−	33.3057i	0.343242	−	1.05639i
$995$	27.4766	+	23.4673i	0.871068	+	0.743962i
$996$		0			0
$997$	−13.5618	+	8.31066i	−0.429505	+	0.263201i	−0.720407	−	0.693552i	$-0.756045\pi$
$997$	−13.5618	+	8.31066i	−0.429505	+	0.263201i	0.290901	+	0.956753i	$0.406045\pi$
$998$	−32.5440	+	13.4802i	−1.03016	+	0.426708i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.ba.a.71.3	✓	48
3.2	odd	2		738.2.ba.b.71.1	yes	48
41.26	odd	40		738.2.ba.b.395.1	yes	48
123.26	even	40	inner	738.2.ba.a.395.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.a.71.3	✓	48	1.1	even	1	trivial
738.2.ba.a.395.3	yes	48	123.26	even	40	inner
738.2.ba.b.71.1	yes	48	3.2	odd	2
738.2.ba.b.395.1	yes	48	41.26	odd	40

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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 + 0.987688i) q^{2} +(-0.951057 + 0.309017i) q^{4} +(1.67738 + 0.854668i) q^{5} +(0.674403 + 2.80909i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.581745 + 1.79043i) q^{10} +(1.59129 + 1.35909i) q^{11} +(5.08494 - 3.11606i) q^{13} +(-2.66901 + 1.10554i) q^{14} +(0.809017 - 0.587785i) q^{16} +(0.285386 + 3.62618i) q^{17} +(-5.16527 - 3.16528i) q^{19} +(-1.85939 - 0.294498i) q^{20} +(-1.09342 + 1.78430i) q^{22} +(1.05753 + 0.768342i) q^{23} +(-0.855780 - 1.17788i) q^{25} +(3.87315 + 4.53488i) q^{26} +(-1.50945 - 2.46320i) q^{28} +(-0.591330 + 7.51356i) q^{29} +(-4.80088 - 1.55990i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.53689 + 0.849132i) q^{34} +(-1.26961 + 5.28831i) q^{35} +(2.34600 + 7.22026i) q^{37} +(2.31828 - 5.59683i) q^{38} -1.88257i q^{40} +(6.19363 + 1.62449i) q^{41} +(-1.47841 + 0.234157i) q^{43} +(-1.93338 - 0.800833i) q^{44} +(-0.593448 + 1.16471i) q^{46} +(4.08701 + 0.981203i) q^{47} +(-1.19914 + 0.610990i) q^{49} +(1.02950 - 1.02950i) q^{50} +(-3.87315 + 4.53488i) q^{52} +(-8.29549 - 0.652869i) q^{53} +(1.50762 + 3.63972i) q^{55} +(2.19675 - 1.87620i) q^{56} +(-7.51356 + 0.591330i) q^{58} +(2.18312 - 3.00481i) q^{59} +(-0.525895 + 3.32037i) q^{61} +(0.789672 - 4.98579i) q^{62} +(-0.587785 + 0.809017i) q^{64} +(11.1926 - 0.880875i) q^{65} +(8.89050 - 7.59320i) q^{67} +(-1.39197 - 3.36051i) q^{68} +(-5.42181 - 0.426706i) q^{70} +(-7.87266 + 9.21770i) q^{71} +(7.26357 - 7.26357i) q^{73} +(-6.76437 + 3.44662i) q^{74} +(5.89059 + 1.41420i) q^{76} +(-2.74463 + 5.38664i) q^{77} +(-15.7432 - 6.52104i) q^{79} +(1.85939 - 0.294498i) q^{80} +(-0.635595 + 6.37150i) q^{82} +5.06215i q^{83} +(-2.62048 + 6.32639i) q^{85} +(-0.462548 - 1.42358i) q^{86} +(0.488526 - 2.03486i) q^{88} +(-7.06697 + 1.69663i) q^{89} +(12.1826 + 12.1826i) q^{91} +(-1.24320 - 0.403941i) q^{92} +(-0.329774 + 4.19018i) q^{94} +(-5.95885 - 9.72397i) q^{95} +(-6.99036 - 8.18466i) q^{97} +(-0.791054 - 1.08879i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{17} - 4 q^{19} + 16 q^{20} + 20 q^{22} - 40 q^{25} - 20 q^{26} - 4 q^{28} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) \) 48 * q - 4 * q^5 + 4 * q^7 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^17 - 4 * q^19 + 16 * q^20 + 20 * q^22 - 40 * q^25 - 20 * q^26 - 4 * q^28 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 52 * q^35 - 24 * q^37 + 16 * q^38 + 12 * q^41 - 20 * q^44 + 16 * q^46 - 8 * q^47 - 48 * q^49 - 16 * q^50 + 20 * q^52 + 64 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^58 + 20 * q^59 - 60 * q^61 - 36 * q^62 + 128 * q^65 - 12 * q^67 - 8 * q^68 + 8 * q^70 - 40 * q^71 + 8 * q^73 + 8 * q^74 + 12 * q^76 - 44 * q^77 + 36 * q^79 - 16 * q^80 + 68 * q^82 + 104 * q^85 - 16 * q^86 + 8 * q^88 - 60 * q^89 + 56 * q^91 - 12 * q^94 - 28 * q^95 + 16 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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