LMFDB - Embedded newform 297.2.t.a.35.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] 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("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			35.4
Character	$\chi$	$=$	297.35
Dual form			297.2.t.a.17.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.148911 - 0.165382i) q^{2} +(0.203880 - 1.93979i) q^{4} +(-0.397470 - 0.357884i) q^{5} +(-1.30165 - 2.92356i) q^{7} +(-0.711251 + 0.516754i) q^{8} +0.119027i q^{10} +(-3.12205 + 1.11928i) q^{11} +(0.183129 + 0.861553i) q^{13} +(-0.289675 + 0.650620i) q^{14} +(-3.62433 - 0.770375i) q^{16} +(-1.83995 - 5.66278i) q^{17} +(2.50028 + 3.44134i) q^{19} +(-0.775255 + 0.698043i) q^{20} +(0.650017 + 0.349660i) q^{22} +(3.19429 - 1.84423i) q^{23} +(-0.492741 - 4.68811i) q^{25} +(0.115216 - 0.158581i) q^{26} +(-5.93647 + 1.92887i) q^{28} +(2.17094 - 0.966564i) q^{29} +(7.08615 - 1.50621i) q^{31} +(1.29145 + 2.23686i) q^{32} +(-0.662535 + 1.14754i) q^{34} +(-0.528926 + 1.62787i) q^{35} +(-0.636941 - 0.462765i) q^{37} +(0.196818 - 0.925955i) q^{38} +(0.467639 + 0.0491508i) q^{40} +(-9.17098 - 4.08318i) q^{41} +(3.73912 + 2.15878i) q^{43} +(1.53464 + 6.28432i) q^{44} +(-0.780668 - 0.253654i) q^{46} +(1.89502 - 0.199174i) q^{47} +(-2.16898 + 2.40889i) q^{49} +(-0.701957 + 0.779602i) q^{50} +(1.70857 - 0.179578i) q^{52} +(9.64245 + 3.13302i) q^{53} +(1.64149 + 0.672452i) q^{55} +(2.43656 + 1.40675i) q^{56} +(-0.483129 - 0.215103i) q^{58} +(11.0642 + 1.16290i) q^{59} +(-0.383703 + 1.80518i) q^{61} +(-1.30431 - 0.947634i) q^{62} +(-2.11237 + 6.50122i) q^{64} +(0.235548 - 0.407980i) q^{65} +(-0.337099 - 0.583872i) q^{67} +(-11.3597 + 2.41458i) q^{68} +(0.347983 - 0.154932i) q^{70} +(-4.21053 + 1.36808i) q^{71} +(0.0544863 - 0.0749940i) q^{73} +(0.0183144 + 0.174250i) q^{74} +(7.18523 - 4.14840i) q^{76} +(7.33610 + 7.67059i) q^{77} +(-11.5129 + 10.3663i) q^{79} +(1.16486 + 1.60329i) q^{80} +(0.690373 + 2.12475i) q^{82} +(13.9274 + 2.96037i) q^{83} +(-1.29529 + 2.90927i) q^{85} +(-0.199771 - 0.939851i) q^{86} +(1.64217 - 2.40942i) q^{88} -4.58327i q^{89} +(2.28043 - 1.65683i) q^{91} +(-2.92616 - 6.57226i) q^{92} +(-0.315129 - 0.283743i) q^{94} +(0.237813 - 2.26264i) q^{95} +(6.55256 + 7.27736i) q^{97} +0.721373 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.148911	−	0.165382i	−0.105296	−	0.116943i	0.688193	−	0.725528i	$-0.258404\pi$
$2$	−0.148911	−	0.165382i	−0.105296	−	0.116943i	−0.793489	+	0.608585i	$0.791738\pi$
$3$		0			0
$3$		0			0
$4$	0.203880	−	1.93979i	0.101940	−	0.969895i
$5$	−0.397470	−	0.357884i	−0.177754	−	0.160051i	0.575451	−	0.817836i	$-0.304827\pi$
$5$	−0.397470	−	0.357884i	−0.177754	−	0.160051i	−0.753205	+	0.657786i	$0.771493\pi$
$6$		0			0
$7$	−1.30165	−	2.92356i	−0.491978	−	1.10500i	−0.973525	−	0.228581i	$-0.926592\pi$
$7$	−1.30165	−	2.92356i	−0.491978	−	1.10500i	0.481547	−	0.876420i	$-0.340075\pi$
$8$	−0.711251	+	0.516754i	−0.251465	+	0.182700i
$9$		0			0
$10$			0.119027i			0.0376398i
$11$	−3.12205	+	1.11928i	−0.941334	+	0.337475i
$11$	−3.12205	+	1.11928i	−0.941334	+	0.337475i
$12$		0			0
$13$	0.183129	+	0.861553i	0.0507908	+	0.238952i	0.996219	−	0.0868790i	$-0.0276894\pi$
$13$	0.183129	+	0.861553i	0.0507908	+	0.238952i	−0.945428	+	0.325831i	$0.894356\pi$
$14$	−0.289675	+	0.650620i	−0.0774188	+	0.173885i
$15$		0			0
$16$	−3.62433	−	0.770375i	−0.906082	−	0.192594i
$17$	−1.83995	−	5.66278i	−0.446253	−	1.37342i	−0.881104	−	0.472923i	$-0.843199\pi$
$17$	−1.83995	−	5.66278i	−0.446253	−	1.37342i	0.434851	−	0.900502i	$-0.356801\pi$
$18$		0			0
$19$	2.50028	+	3.44134i	0.573604	+	0.789497i	0.992976	−	0.118317i	$-0.0377498\pi$
$19$	2.50028	+	3.44134i	0.573604	+	0.789497i	−0.419372	+	0.907814i	$0.637750\pi$
$20$	−0.775255	+	0.698043i	−0.173352	+	0.156087i
$21$		0			0
$22$	0.650017	+	0.349660i	0.138584	+	0.0745477i
$23$	3.19429	−	1.84423i	0.666056	−	0.384548i	−0.128524	−	0.991706i	$-0.541024\pi$
$23$	3.19429	−	1.84423i	0.666056	−	0.384548i	0.794581	+	0.607159i	$0.207691\pi$
$24$		0			0
$25$	−0.492741	−	4.68811i	−0.0985481	−	0.937623i
$26$	0.115216	−	0.158581i	0.0225957	−	0.0311003i
$27$		0			0
$28$	−5.93647	+	1.92887i	−1.12189	+	0.364523i
$29$	2.17094	−	0.966564i	0.403133	−	0.179486i	−0.195146	−	0.980774i	$-0.562518\pi$
$29$	2.17094	−	0.966564i	0.403133	−	0.179486i	0.598279	+	0.801288i	$0.295851\pi$
$30$		0			0
$31$	7.08615	−	1.50621i	1.27271	−	0.270523i	0.478458	−	0.878111i	$-0.341196\pi$
$31$	7.08615	−	1.50621i	1.27271	−	0.270523i	0.794253	+	0.607588i	$0.207863\pi$
$32$	1.29145	+	2.23686i	0.228298	+	0.395424i
$33$		0			0
$34$	−0.662535	+	1.14754i	−0.113624	+	0.196802i
$35$	−0.528926	+	1.62787i	−0.0894048	+	0.275160i
$36$		0			0
$37$	−0.636941	−	0.462765i	−0.104713	−	0.0760781i	0.534197	−	0.845360i	$-0.320614\pi$
$37$	−0.636941	−	0.462765i	−0.104713	−	0.0760781i	−0.638909	+	0.769282i	$0.720614\pi$
$38$	0.196818	−	0.925955i	0.0319281	−	0.150210i
$39$		0			0
$40$	0.467639	+	0.0491508i	0.0739402	+	0.00777143i
$41$	−9.17098	−	4.08318i	−1.43227	−	0.637686i	−0.463599	−	0.886045i	$-0.653442\pi$
$41$	−9.17098	−	4.08318i	−1.43227	−	0.637686i	−0.968668	+	0.248359i	$0.920109\pi$
$42$		0			0
$43$	3.73912	+	2.15878i	0.570210	+	0.329211i	0.757233	−	0.653144i	$-0.226551\pi$
$43$	3.73912	+	2.15878i	0.570210	+	0.329211i	−0.187023	+	0.982356i	$0.559884\pi$
$44$	1.53464	+	6.28432i	0.231356	+	0.947397i
$45$		0			0
$46$	−0.780668	−	0.253654i	−0.115103	−	0.0373993i
$47$	1.89502	−	0.199174i	0.276417	−	0.0290526i	0.0346943	−	0.999398i	$-0.488954\pi$
$47$	1.89502	−	0.199174i	0.276417	−	0.0290526i	0.241723	+	0.970345i	$0.422288\pi$
$48$		0			0
$49$	−2.16898	+	2.40889i	−0.309854	+	0.344127i
$50$	−0.701957	+	0.779602i	−0.0992717	+	0.110252i
$51$		0			0
$52$	1.70857	−	0.179578i	0.236936	−	0.0249029i
$53$	9.64245	+	3.13302i	1.32449	+	0.430353i	0.884035	−	0.467420i	$-0.154817\pi$
$53$	9.64245	+	3.13302i	1.32449	+	0.430353i	0.440457	+	0.897774i	$0.354817\pi$
$54$		0			0
$55$	1.64149	+	0.672452i	0.221339	+	0.0906734i
$56$	2.43656	+	1.40675i	0.325599	+	0.187985i
$57$		0			0
$58$	−0.483129	−	0.215103i	−0.0634380	−	0.0282444i
$59$	11.0642	+	1.16290i	1.44044	+	0.151396i	0.792302	−	0.610129i	$-0.208883\pi$
$59$	11.0642	+	1.16290i	1.44044	+	0.151396i	0.648135	+	0.761525i	$0.275549\pi$
$60$		0			0
$61$	−0.383703	+	1.80518i	−0.0491282	+	0.231130i	−0.995861	−	0.0908905i	$-0.971029\pi$
$61$	−0.383703	+	1.80518i	−0.0491282	+	0.231130i	0.946733	+	0.322020i	$0.104362\pi$
$62$	−1.30431	−	0.947634i	−0.165647	−	0.120350i
$63$		0			0
$64$	−2.11237	+	6.50122i	−0.264047	+	0.812653i
$65$	0.235548	−	0.407980i	0.0292161	−	0.0506037i
$66$		0			0
$67$	−0.337099	−	0.583872i	−0.0411832	−	0.0713314i	0.844699	−	0.535241i	$-0.179779\pi$
$67$	−0.337099	−	0.583872i	−0.0411832	−	0.0713314i	−0.885882	+	0.463910i	$0.846446\pi$
$68$	−11.3597	+	2.41458i	−1.37757	+	0.292811i
$69$		0			0
$70$	0.347983	−	0.154932i	0.0415920	−	0.0185179i
$71$	−4.21053	+	1.36808i	−0.499698	+	0.162362i	−0.548012	−	0.836470i	$-0.684615\pi$
$71$	−4.21053	+	1.36808i	−0.499698	+	0.162362i	0.0483139	+	0.998832i	$0.484615\pi$
$72$		0			0
$73$	0.0544863	−	0.0749940i	0.00637714	−	0.00877738i	−0.805817	−	0.592165i	$-0.798273\pi$
$73$	0.0544863	−	0.0749940i	0.00637714	−	0.00877738i	0.812194	+	0.583388i	$0.198273\pi$
$74$	0.0183144	+	0.174250i	0.00212900	+	0.0202561i
$75$		0			0
$76$	7.18523	−	4.14840i	0.824203	−	0.475854i
$77$	7.33610	+	7.67059i	0.836026	+	0.874145i
$78$		0			0
$79$	−11.5129	+	10.3663i	−1.29531	+	1.16630i	−0.319519	+	0.947580i	$0.603521\pi$
$79$	−11.5129	+	10.3663i	−1.29531	+	1.16630i	−0.975788	+	0.218719i	$0.929812\pi$
$80$	1.16486	+	1.60329i	0.130235	+	0.179253i
$81$		0			0
$82$	0.690373	+	2.12475i	0.0762390	+	0.234639i
$83$	13.9274	+	2.96037i	1.52873	+	0.324943i	0.894099	−	0.447869i	$-0.147817\pi$
$83$	13.9274	+	2.96037i	1.52873	+	0.324943i	0.634635	+	0.772812i	$0.281150\pi$
$84$		0			0
$85$	−1.29529	+	2.90927i	−0.140494	+	0.315555i
$86$	−0.199771	−	0.939851i	−0.0215419	−	0.101347i
$87$		0			0
$88$	1.64217	−	2.40942i	0.175056	−	0.256845i
$89$		−	4.58327i		−	0.485826i	−0.970048	−	0.242913i	$-0.921897\pi$
$89$		−	4.58327i		−	0.485826i	0.970048	−	0.242913i	$-0.0781029\pi$
$90$		0			0
$91$	2.28043	−	1.65683i	0.239054	−	0.173683i
$92$	−2.92616	−	6.57226i	−0.305073	−	0.685205i
$93$		0			0
$94$	−0.315129	−	0.283743i	−0.0325031	−	0.0292659i
$95$	0.237813	−	2.26264i	0.0243991	−	0.232142i
$96$		0			0
$97$	6.55256	+	7.27736i	0.665312	+	0.738904i	0.977458	−	0.211130i	$-0.0677144\pi$
$97$	6.55256	+	7.27736i	0.665312	+	0.738904i	−0.312146	+	0.950034i	$0.601048\pi$
$98$	0.721373			0.0728696
$99$		0			0
$100$	−9.19441			−0.919441
$101$	−7.15791	−	7.94967i	−0.712239	−	0.791022i	0.273035	−	0.962004i	$-0.411973\pi$
$101$	−7.15791	−	7.94967i	−0.712239	−	0.791022i	−0.985274	+	0.170983i	$0.945306\pi$
$102$		0			0
$103$	0.392106	−	3.73064i	0.0386354	−	0.367591i	−0.958073	−	0.286523i	$-0.907500\pi$
$103$	0.392106	−	3.73064i	0.0386354	−	0.367591i	0.996709	−	0.0810676i	$-0.0258330\pi$
$104$	−0.575461	−	0.518148i	−0.0564286	−	0.0508085i
$105$		0			0
$106$	−0.917719	−	2.06123i	−0.0891368	−	0.200205i
$107$	−0.664192	+	0.482564i	−0.0642098	+	0.0466512i	−0.619427	−	0.785054i	$-0.712635\pi$
$107$	−0.664192	+	0.482564i	−0.0642098	+	0.0466512i	0.555217	+	0.831705i	$0.312635\pi$
$108$		0			0
$109$		−	0.344350i		−	0.0329828i	−0.999864	−	0.0164914i	$-0.994750\pi$
$109$		−	0.344350i		−	0.0329828i	0.999864	−	0.0164914i	$-0.00524961\pi$
$110$	−0.133225	−	0.371610i	−0.0127025	−	0.0354316i
$111$		0			0
$112$	2.46538	+	11.5987i	0.232956	+	1.09597i
$113$	5.95347	−	13.3717i	0.560056	−	1.25791i	−0.382531	−	0.923943i	$-0.624947\pi$
$113$	5.95347	−	13.3717i	0.560056	−	1.25791i	0.942586	−	0.333963i	$-0.108386\pi$
$114$		0			0
$115$	−1.92966	−	0.410161i	−0.179941	−	0.0382477i
$116$	−1.43232	−	4.40823i	−0.132988	−	0.409294i
$117$		0			0
$118$	−1.45526	−	2.00299i	−0.133967	−	0.184390i
$119$	−14.1605	+	12.7502i	−1.29809	+	1.16880i
$120$		0			0
$121$	8.49443	−	6.98889i	0.772221	−	0.635354i
$122$	0.355683	−	0.205354i	0.0322020	−	0.0185918i
$123$		0			0
$124$	−1.47700	−	14.0527i	−0.132639	−	1.26197i
$125$	−3.05383	+	4.20324i	−0.273143	+	0.375949i
$126$		0			0
$127$	13.3595	−	4.34077i	1.18546	−	0.385181i	0.351070	−	0.936349i	$-0.385818\pi$
$127$	13.3595	−	4.34077i	1.18546	−	0.385181i	0.834394	+	0.551168i	$0.185818\pi$
$128$	6.10894	−	2.71987i	0.539959	−	0.240405i
$129$		0			0
$130$	−0.102548	+	0.0217973i	−0.00899409	+	0.00191175i
$131$	−1.07963	−	1.86997i	−0.0943274	−	0.163380i	0.815000	−	0.579461i	$-0.196737\pi$
$131$	−1.07963	−	1.86997i	−0.0943274	−	0.163380i	−0.909328	+	0.416081i	$0.863403\pi$
$132$		0			0
$133$	6.80646	−	11.7891i	0.590195	−	1.02225i
$134$	−0.0463645	+	0.142695i	−0.00400528	+	0.0123270i
$135$		0			0
$136$	4.23492	+	3.07685i	0.363142	+	0.263838i
$137$	0.150225	−	0.706754i	0.0128346	−	0.0603821i	−0.971264	−	0.238004i	$-0.923507\pi$
$137$	0.150225	−	0.706754i	0.0128346	−	0.0603821i	0.984099	+	0.177622i	$0.0568403\pi$
$138$		0			0
$139$	−18.0949	−	1.90185i	−1.53479	−	0.161313i	−0.700907	−	0.713252i	$-0.747221\pi$
$139$	−18.0949	−	1.90185i	−1.53479	−	0.161313i	−0.833884	+	0.551939i	$0.813888\pi$
$140$	3.04988	+	1.35789i	0.257762	+	0.114763i
$141$		0			0
$142$	0.853251	+	0.492625i	0.0716033	+	0.0413402i
$143$	−1.53606	−	2.48484i	−0.128451	−	0.207793i
$144$		0			0
$145$	−1.20880	−	0.392763i	−0.100385	−	0.0326172i
$146$	−0.0205163	+	0.00215635i	−0.00169794	+	0.000178461i
$147$		0			0
$148$	−1.02753	+	1.14118i	−0.0844621	+	0.0938047i
$149$	−15.2390	+	16.9247i	−1.24843	+	1.38652i	−0.356533	+	0.934283i	$0.616041\pi$
$149$	−15.2390	+	16.9247i	−1.24843	+	1.38652i	−0.891897	+	0.452239i	$0.850625\pi$
$150$		0			0
$151$	−11.3594	+	1.19392i	−0.924412	+	0.0971596i	−0.554760	−	0.832011i	$-0.687190\pi$
$151$	−11.3594	+	1.19392i	−0.924412	+	0.0971596i	−0.369652	+	0.929170i	$0.620523\pi$
$152$	−3.55665	−	1.15563i	−0.288482	−	0.0937336i
$153$		0			0
$154$	0.176155	−	2.35550i	0.0141949	−	0.189811i
$155$	−3.35558	−	1.93735i	−0.269527	−	0.155611i
$156$		0			0
$157$	−18.1548	−	8.08304i	−1.44891	−	0.645097i	−0.476671	−	0.879082i	$-0.658157\pi$
$157$	−18.1548	−	8.08304i	−1.44891	−	0.645097i	−0.972240	+	0.233985i	$0.924823\pi$
$158$	3.42880	+	0.360382i	0.272781	+	0.0286704i
$159$		0			0
$160$	0.287222	−	1.35127i	0.0227069	−	0.106828i
$161$	−9.54956	−	6.93816i	−0.752611	−	0.546804i
$162$		0			0
$163$	3.18523	−	9.80313i	0.249486	−	0.767840i	−0.745380	−	0.666640i	$-0.767732\pi$
$163$	3.18523	−	9.80313i	0.249486	−	0.767840i	0.994866	−	0.101200i	$-0.0322683\pi$
$164$	−9.79030	+	16.9573i	−0.764494	+	1.32414i
$165$		0			0
$166$	−1.58435	−	2.74418i	−0.122970	−	0.212990i
$167$	−11.5938	+	2.46433i	−0.897153	+	0.190696i	−0.633336	−	0.773877i	$-0.718315\pi$
$167$	−11.5938	+	2.46433i	−0.897153	+	0.190696i	−0.263817	+	0.964573i	$0.584982\pi$
$168$		0			0
$169$	11.1674	−	4.97203i	0.859027	−	0.382464i
$170$	0.674025	−	0.219004i	0.0516954	−	0.0167969i
$171$		0			0
$172$	4.94991	−	6.81297i	0.377427	−	0.519484i
$173$	−1.65458	−	15.7423i	−0.125796	−	1.19687i	−0.857223	−	0.514946i	$-0.827812\pi$
$173$	−1.65458	−	15.7423i	−0.125796	−	1.19687i	0.731427	−	0.681920i	$-0.238855\pi$
$174$		0			0
$175$	−13.0646	+	7.54285i	−0.987590	+	0.570186i
$176$	12.1776	−	1.65148i	0.917922	−	0.124485i
$177$		0			0
$178$	−0.757992	+	0.682499i	−0.0568139	+	0.0511555i
$179$	−4.11815	−	5.66815i	−0.307805	−	0.423658i	0.626890	−	0.779108i	$-0.284328\pi$
$179$	−4.11815	−	5.66815i	−0.307805	−	0.423658i	−0.934695	+	0.355450i	$0.884328\pi$
$180$		0			0
$181$	−3.74044	−	11.5119i	−0.278025	−	0.855673i	−0.988403	−	0.151853i	$-0.951476\pi$
$181$	−3.74044	−	11.5119i	−0.278025	−	0.855673i	0.710378	−	0.703820i	$-0.248524\pi$
$182$	−0.613591	−	0.130423i	−0.0454824	−	0.00966758i
$183$		0			0
$184$	−1.31893	+	2.96237i	−0.0972330	+	0.218389i
$185$	0.0875491	+	0.411886i	0.00643674	+	0.0302825i
$186$		0			0
$187$	12.0826	+	15.6201i	0.883570	+	1.14225i
$188$		−	3.71654i		−	0.271057i
$189$		0			0
$190$	−0.409614	+	0.297602i	−0.0297165	+	0.0215903i
$191$	8.25925	+	18.5506i	0.597618	+	1.34227i	0.918600	+	0.395187i	$0.129320\pi$
$191$	8.25925	+	18.5506i	0.597618	+	1.34227i	−0.320982	+	0.947085i	$0.604013\pi$
$192$		0			0
$193$	4.22233	+	3.80181i	0.303930	+	0.273660i	0.806956	−	0.590611i	$-0.201113\pi$
$193$	4.22233	+	3.80181i	0.303930	+	0.273660i	−0.503026	+	0.864271i	$0.667780\pi$
$194$	0.227798	−	2.16736i	0.0163550	−	0.155607i
$195$		0			0
$196$	4.23053	+	4.69848i	0.302181	+	0.335606i
$197$	16.4596			1.17270			0.586350	−	0.810058i	$-0.300564\pi$
$197$	16.4596			1.17270			0.586350	+	0.810058i	$0.300564\pi$
$198$		0			0
$199$	13.9772			0.990818			0.495409	−	0.868660i	$-0.335018\pi$
$199$	13.9772			0.990818			0.495409	+	0.868660i	$0.335018\pi$
$200$	2.77306	+	3.07980i	0.196085	+	0.217775i
$201$		0			0
$202$	−0.248843	+	2.36759i	−0.0175086	+	0.166583i
$203$	−5.65161	−	5.08873i	−0.396665	−	0.357159i
$204$		0			0
$205$	2.18389	+	4.90509i	0.152529	+	0.342586i
$206$	−0.675371	+	0.490686i	−0.0470554	+	0.0341877i
$207$		0			0
$208$		−	3.26363i		−	0.226292i
$209$	−11.6578	−	7.94554i	−0.806389	−	0.549604i
$210$		0			0
$211$	2.23574	+	10.5183i	0.153915	+	0.724112i	0.985631	+	0.168911i	$0.0540252\pi$
$211$	2.23574	+	10.5183i	0.153915	+	0.724112i	−0.831716	+	0.555201i	$0.812641\pi$
$212$	8.04330	−	18.0656i	0.552416	−	1.24075i
$213$		0			0
$214$	0.178713	+	0.0379866i	0.0122166	+	0.00259671i
$215$	−0.713596	−	2.19622i	−0.0486668	−	0.149781i
$216$		0			0
$217$	−13.6272	−	18.7562i	−0.925074	−	1.27325i
$218$	−0.0569495	+	0.0512775i	−0.00385711	+	0.00347295i
$219$		0			0
$220$	1.63908	−	3.04705i	0.110507	−	0.205432i
$221$	4.54183	−	2.62223i	0.305517	−	0.176390i
$222$		0			0
$223$	1.71464	+	16.3137i	0.114821	+	1.09245i	0.888503	+	0.458871i	$0.151746\pi$
$223$	1.71464	+	16.3137i	0.114821	+	1.09245i	−0.773682	+	0.633574i	$0.781587\pi$
$224$	4.85856	−	6.68724i	0.324626	−	0.446810i
$225$		0			0
$226$	−3.09798	+	1.00660i	−0.206075	+	0.0669578i
$227$	13.8406	−	6.16224i	0.918634	−	0.409002i	0.107729	−	0.994180i	$-0.465642\pi$
$227$	13.8406	−	6.16224i	0.918634	−	0.409002i	0.810905	+	0.585178i	$0.198975\pi$
$228$		0			0
$229$	−6.93316	+	1.47369i	−0.458156	+	0.0973841i	−0.431208	−	0.902253i	$-0.641912\pi$
$229$	−6.93316	+	1.47369i	−0.458156	+	0.0973841i	−0.0269485	+	0.999637i	$0.508579\pi$
$230$	0.219513	+	0.380208i	0.0144743	+	0.0250702i
$231$		0			0
$232$	−1.04461	+	1.80931i	−0.0685817	+	0.118787i
$233$	−6.69692	+	20.6110i	−0.438730	+	1.35027i	0.450486	+	0.892784i	$0.351251\pi$
$233$	−6.69692	+	20.6110i	−0.438730	+	1.35027i	−0.889216	+	0.457488i	$0.848749\pi$
$234$		0			0
$235$	−0.824495	−	0.599031i	−0.0537841	−	0.0390764i
$236$	4.51154	−	21.2251i	0.293676	−	1.38164i
$237$		0			0
$238$	4.21730	+	0.443256i	0.273367	+	0.0287320i
$239$	16.9181	+	7.53244i	1.09434	+	0.487233i	0.872880	−	0.487936i	$-0.162250\pi$
$239$	16.9181	+	7.53244i	1.09434	+	0.487233i	0.221463	+	0.975169i	$0.428917\pi$
$240$		0			0
$241$	9.56117	+	5.52014i	0.615889	+	0.355584i	0.775267	−	0.631634i	$-0.217615\pi$
$241$	9.56117	+	5.52014i	0.615889	+	0.355584i	−0.159378	+	0.987218i	$0.550949\pi$
$242$	−2.42075	−	0.364106i	−0.155612	−	0.0234056i
$243$		0			0
$244$	3.42344	+	1.11234i	0.219164	+	0.0712106i
$245$	1.72421	−	0.181221i	0.110156	−	0.0115778i
$246$		0			0
$247$	−2.50702	+	2.78433i	−0.159518	+	0.177163i
$248$	−4.26169	+	4.73309i	−0.270618	+	0.300551i
$249$		0			0
$250$	1.14989	−	0.120858i	0.0727255	−	0.00764375i
$251$	18.6948	+	6.07431i	1.18001	+	0.383407i	0.832369	−	0.554223i	$-0.186984\pi$
$251$	18.6948	+	6.07431i	1.18001	+	0.383407i	0.347636	+	0.937629i	$0.386984\pi$
$252$		0			0
$253$	−7.90855	+	9.33308i	−0.497206	+	0.586766i
$254$	−2.70726	−	1.56304i	−0.169869	−	0.0980738i
$255$		0			0
$256$	11.1301	+	4.95544i	0.695631	+	0.309715i
$257$	−26.1815	−	2.75179i	−1.63316	−	0.171652i	−0.756913	−	0.653516i	$-0.773293\pi$
$257$	−26.1815	−	2.75179i	−1.63316	−	0.171652i	−0.876246	+	0.481864i	$0.839960\pi$
$258$		0			0
$259$	−0.523844	+	2.46449i	−0.0325501	+	0.153136i
$260$	−0.743373	−	0.540092i	−0.0461020	−	0.0334951i
$261$		0			0
$262$	−0.148491	+	0.457010i	−0.00917384	+	0.0282342i
$263$	−1.31836	+	2.28347i	−0.0812936	+	0.140805i	−0.903806	−	0.427943i	$-0.859238\pi$
$263$	−1.31836	+	2.28347i	−0.0812936	+	0.140805i	0.822512	+	0.568747i	$0.192572\pi$
$264$		0			0
$265$	−2.71133	−	4.69616i	−0.166556	−	0.288483i
$266$	−2.96327	+	0.629863i	−0.181690	+	0.0386194i
$267$		0			0
$268$	−1.20132	+	0.534861i	−0.0733821	+	0.0326718i
$269$	−3.48174	+	1.13129i	−0.212285	+	0.0689757i	−0.413229	−	0.910627i	$-0.635599\pi$
$269$	−3.48174	+	1.13129i	−0.212285	+	0.0689757i	0.200944	+	0.979603i	$0.435599\pi$
$270$		0			0
$271$	−6.37358	+	8.77249i	−0.387168	+	0.532891i	−0.957466	−	0.288547i	$-0.906828\pi$
$271$	−6.37358	+	8.77249i	−0.387168	+	0.532891i	0.570298	+	0.821438i	$0.306828\pi$
$272$	2.30611	+	21.9412i	0.139829	+	1.33038i
$273$		0			0
$274$	−0.139255	+	0.0803988i	−0.00841269	+	0.00485707i
$275$	6.78567	+	14.0850i	0.409191	+	0.849359i
$276$		0			0
$277$	−0.148105	+	0.133354i	−0.00889876	+	0.00801248i	−0.673568	−	0.739125i	$-0.735239\pi$
$277$	−0.148105	+	0.133354i	−0.00889876	+	0.00801248i	0.664669	+	0.747138i	$0.268572\pi$
$278$	2.38000	+	3.27579i	0.142743	+	0.196469i
$279$		0			0
$280$	−0.465007	−	1.43115i	−0.0277895	−	0.0855273i
$281$	7.46681	+	1.58712i	0.445433	+	0.0946797i	0.425167	−	0.905115i	$-0.360215\pi$
$281$	7.46681	+	1.58712i	0.445433	+	0.0946797i	0.0202659	+	0.999795i	$0.493549\pi$
$282$		0			0
$283$	0.229559	−	0.515598i	0.0136459	−	0.0306491i	−0.906594	−	0.422004i	$-0.861327\pi$
$283$	0.229559	−	0.515598i	0.0136459	−	0.0306491i	0.920240	+	0.391355i	$0.127993\pi$
$284$	1.79535	+	8.44647i	0.106535	+	0.501206i
$285$		0			0
$286$	−0.182214	+	0.624057i	−0.0107745	+	0.0369012i
$287$			32.1268i			1.89638i
$288$		0			0
$289$	−14.9283	+	10.8461i	−0.878137	+	0.638004i
$290$	0.115048	+	0.258401i	0.00675583	+	0.0151738i
$291$		0			0
$292$	−0.134364	−	0.120982i	−0.00786305	−	0.00707992i
$293$	0.534278	−	5.08332i	0.0312129	−	0.296971i	−0.967768	−	0.251842i	$-0.918964\pi$
$293$	0.534278	−	5.08332i	0.0312129	−	0.296971i	0.998981	−	0.0451285i	$-0.0143697\pi$
$294$		0			0
$295$	−3.98151	−	4.42192i	−0.231813	−	0.257454i
$296$	0.692160			0.0402310
$297$		0			0
$298$	5.06830			0.293599
$299$	2.17387	+	2.41432i	0.125718	+	0.139624i
$300$		0			0
$301$	1.44429	−	13.7415i	0.0832475	−	0.792048i
$302$	1.88899	+	1.70085i	0.108699	+	0.0978730i
$303$		0			0
$304$	−6.41071	−	14.3987i	−0.367680	−	0.825822i
$305$	0.798556	−	0.580185i	0.0457252	−	0.0332213i
$306$		0			0
$307$		−	2.87711i		−	0.164205i	−0.996624	−	0.0821026i	$-0.973836\pi$
$307$		−	2.87711i		−	0.164205i	0.996624	−	0.0821026i	$-0.0261635\pi$
$308$	16.3750	−	12.6666i	0.933053	−	0.721747i
$309$		0			0
$310$	0.179280	+	0.843446i	0.0101824	+	0.0479045i
$311$	−1.10271	+	2.47674i	−0.0625292	+	0.140443i	−0.942107	−	0.335312i	$-0.891158\pi$
$311$	−1.10271	+	2.47674i	−0.0625292	+	0.140443i	0.879578	+	0.475755i	$0.157825\pi$
$312$		0			0
$313$	10.9007	+	2.31701i	0.616144	+	0.130965i	0.505402	−	0.862884i	$-0.331344\pi$
$313$	10.9007	+	2.31701i	0.616144	+	0.130965i	0.110742	+	0.993849i	$0.464677\pi$
$314$	1.36666	+	4.20614i	0.0771249	+	0.237366i
$315$		0			0
$316$	17.7612	+	24.4462i	0.999144	+	1.37520i
$317$	−4.64579	+	4.18309i	−0.260933	+	0.234946i	−0.789205	−	0.614130i	$-0.789507\pi$
$317$	−4.64579	+	4.18309i	−0.260933	+	0.234946i	0.528271	+	0.849076i	$0.322840\pi$
$318$		0			0
$319$	−5.69593	+	5.44755i	−0.318911	+	0.305004i
$320$	3.16629	−	1.82806i	0.177001	−	0.102191i
$321$		0			0
$322$	0.274585	+	2.61250i	0.0153020	+	0.145589i
$323$	14.8872	−	20.4904i	0.828343	−	1.14012i
$324$		0			0
$325$	3.94882	−	1.28305i	0.219041	−	0.0711708i
$326$	−2.09558	+	0.933013i	−0.116063	+	0.0516748i
$327$		0			0
$328$	8.63287	−	1.83497i	0.476670	−	0.101319i
$329$	−3.04895	−	5.28094i	−0.168094	−	0.291148i
$330$		0			0
$331$	−1.55234	+	2.68873i	−0.0853242	+	0.147786i	−0.905529	−	0.424284i	$-0.860526\pi$
$331$	−1.55234	+	2.68873i	−0.0853242	+	0.147786i	0.820205	+	0.572070i	$0.193859\pi$
$332$	8.58202	−	26.4127i	0.470999	−	1.44959i
$333$		0			0
$334$	2.13400	+	1.55044i	0.116767	+	0.0848363i
$335$	−0.0749717	+	0.352714i	−0.00409614	+	0.0192708i
$336$		0			0
$337$	13.3023	+	1.39813i	0.724622	+	0.0761608i	0.459656	−	0.888097i	$-0.347973\pi$
$337$	13.3023	+	1.39813i	0.724622	+	0.0761608i	0.264966	+	0.964258i	$0.414639\pi$
$338$	−2.48523	−	1.10649i	−0.135179	−	0.0601854i
$339$		0			0
$340$	5.37929	+	3.10574i	0.291733	+	0.168432i
$341$	−20.4375	+	12.6338i	−1.10675	+	0.684161i
$342$		0			0
$343$	−11.4394	−	3.71689i	−0.617671	−	0.200693i
$344$	−3.77501	+	0.396769i	−0.203535	+	0.0213924i
$345$		0			0
$346$	−2.35712	+	2.61784i	−0.126719	+	0.140736i
$347$	1.88487	−	2.09336i	0.101185	−	0.112377i	−0.690425	−	0.723404i	$-0.742576\pi$
$347$	1.88487	−	2.09336i	0.101185	−	0.112377i	0.791610	+	0.611027i	$0.209243\pi$
$348$		0			0
$349$	−26.7592	+	2.81251i	−1.43239	+	0.150550i	−0.788719	−	0.614754i	$-0.789255\pi$
$349$	−26.7592	+	2.81251i	−1.43239	+	0.150550i	−0.643669	+	0.765304i	$0.722589\pi$
$350$	3.19291	+	1.03744i	0.170668	+	0.0554535i
$351$		0			0
$352$	−6.53564	−	5.53809i	−0.348351	−	0.295181i
$353$	1.73418	+	1.00123i	0.0923011	+	0.0532901i	0.545440	−	0.838150i	$-0.316363\pi$
$353$	1.73418	+	1.00123i	0.0923011	+	0.0532901i	−0.453139	+	0.891440i	$0.649696\pi$
$354$		0			0
$355$	2.16318	+	0.963108i	0.114809	+	0.0511165i
$356$	−8.89058	−	0.934437i	−0.471200	−	0.0495251i
$357$		0			0
$358$	−0.324174	+	1.52512i	−0.0171331	+	0.0806051i
$359$	−2.02249	−	1.46942i	−0.106743	−	0.0775532i	0.533133	−	0.846031i	$-0.321014\pi$
$359$	−2.02249	−	1.46942i	−0.106743	−	0.0775532i	−0.639876	+	0.768478i	$0.721014\pi$
$360$		0			0
$361$	0.279902	−	0.861450i	0.0147317	−	0.0453395i
$362$	−1.34687	+	2.33285i	−0.0707901	+	0.122612i
$363$		0			0
$364$	−2.74897	−	4.76135i	−0.144085	−	0.249562i
$365$	−0.0484958	+	0.0103081i	−0.00253839	+	0.000539551i
$366$		0			0
$367$	−12.1115	+	5.39240i	−0.632217	+	0.281481i	−0.697719	−	0.716371i	$-0.745802\pi$
$367$	−12.1115	+	5.39240i	−0.632217	+	0.281481i	0.0655024	+	0.997852i	$0.479135\pi$
$368$	−12.9979	+	4.22328i	−0.677563	+	0.220154i
$369$		0			0
$370$	0.0550817	−	0.0758135i	0.00286356	−	0.00394135i
$371$	−3.39154	−	32.2683i	−0.176080	−	1.67529i
$372$		0			0
$373$	27.5050	−	15.8800i	1.42416	−	0.822238i	0.427507	−	0.904012i	$-0.359392\pi$
$373$	27.5050	−	15.8800i	1.42416	−	0.822238i	0.996651	+	0.0817746i	$0.0260588\pi$
$374$	0.784048	−	4.32426i	0.0405421	−	0.223602i
$375$		0			0
$376$	−1.24491	+	1.12092i	−0.0642013	+	0.0578071i
$377$	1.23031	+	1.69337i	0.0633641	+	0.0872131i
$378$		0			0
$379$	7.34658	+	22.6104i	0.377368	+	1.16142i	0.941867	+	0.335986i	$0.109070\pi$
$379$	7.34658	+	22.6104i	0.377368	+	1.16142i	−0.564498	+	0.825434i	$0.690930\pi$
$380$	−4.34056	−	0.922614i	−0.222666	−	0.0473291i
$381$		0			0
$382$	1.83805	−	4.12832i	0.0940426	−	0.211223i
$383$	−3.70805	−	17.4450i	−0.189472	−	0.891397i	−0.965440	−	0.260625i	$-0.916071\pi$
$383$	−3.70805	−	17.4450i	−0.189472	−	0.891397i	0.775968	−	0.630772i	$-0.217262\pi$
$384$		0			0
$385$	−0.170702	−	5.67430i	−0.00869976	−	0.289189i
$386$		−	1.26443i		−	0.0643578i
$387$		0			0
$388$	15.4525	−	11.2269i	0.784481	−	0.569959i
$389$	10.0542	+	22.5821i	0.509769	+	1.14496i	0.966806	+	0.255512i	$0.0822440\pi$
$389$	10.0542	+	22.5821i	0.509769	+	1.14496i	−0.457037	+	0.889448i	$0.651089\pi$
$390$		0			0
$391$	−16.3208	−	14.6953i	−0.825377	−	0.743173i
$392$	0.297881	−	2.83415i	0.0150453	−	0.143146i
$393$		0			0
$394$	−2.45102	−	2.72213i	−0.123480	−	0.137139i
$395$	8.28598			0.416913
$396$		0			0
$397$	−4.07143			−0.204339			−0.102170	−	0.994767i	$-0.532578\pi$
$397$	−4.07143			−0.204339			−0.102170	+	0.994767i	$0.532578\pi$
$398$	−2.08136	−	2.31158i	−0.104329	−	0.115869i
$399$		0			0
$400$	−1.82575	+	17.3709i	−0.0912875	+	0.868543i
$401$	18.8206	+	16.9462i	0.939857	+	0.846251i	0.988292	−	0.152575i	$-0.0487565\pi$
$401$	18.8206	+	16.9462i	0.939857	+	0.846251i	−0.0484344	+	0.998826i	$0.515423\pi$
$402$		0			0
$403$	2.59536	+	5.82926i	0.129284	+	0.290376i
$404$	−16.8800	+	12.2641i	−0.839813	+	0.610160i
$405$		0			0
$406$			1.69245i			0.0839946i
$407$	2.50653	+	0.731862i	0.124244	+	0.0362771i
$408$		0			0
$409$	−1.86286	−	8.76406i	−0.0921124	−	0.433355i	−0.999903	−	0.0139310i	$-0.995565\pi$
$409$	−1.86286	−	8.76406i	−0.0921124	−	0.433355i	0.907791	−	0.419424i	$-0.137768\pi$
$410$	0.486011	−	1.09160i	0.0240024	−	0.0539102i
$411$		0			0
$412$	−7.15672	−	1.52121i	−0.352586	−	0.0749445i
$413$	−11.0020	−	33.8605i	−0.541371	−	1.66617i
$414$		0			0
$415$	−4.47627	−	6.16106i	−0.219732	−	0.302435i
$416$	−1.69067	+	1.52229i	−0.0828919	+	0.0746362i
$417$		0			0
$418$	0.421926	+	3.11118i	0.0206371	+	0.152173i
$419$	2.71746	−	1.56893i	0.132757	−	0.0766471i	−0.432151	−	0.901801i	$-0.642245\pi$
$419$	2.71746	−	1.56893i	0.132757	−	0.0766471i	0.564908	+	0.825154i	$0.308912\pi$
$420$		0			0
$421$	−3.00840	−	28.6230i	−0.146620	−	1.39500i	−0.782230	−	0.622990i	$-0.785918\pi$
$421$	−3.00840	−	28.6230i	−0.146620	−	1.39500i	0.635609	−	0.772011i	$-0.280749\pi$
$422$	1.40662	−	1.93605i	0.0684732	−	0.0942453i
$423$		0			0
$424$	−8.47720	+	2.75441i	−0.411689	+	0.133766i
$425$	−25.6411	+	11.4162i	−1.24378	+	0.553765i
$426$		0			0
$427$	5.77700	−	1.22794i	0.279569	−	0.0594242i
$428$	0.800656	+	1.38678i	0.0387012	+	0.0670324i
$429$		0			0
$430$	−0.256954	+	0.445058i	−0.0123914	+	0.0214626i
$431$	8.71998	−	26.8373i	0.420027	−	1.29271i	−0.487650	−	0.873039i	$-0.662146\pi$
$431$	8.71998	−	26.8373i	0.420027	−	1.29271i	0.907677	−	0.419670i	$-0.137854\pi$
$432$		0			0
$433$	0.815921	+	0.592801i	0.0392107	+	0.0284882i	0.607218	−	0.794535i	$-0.292285\pi$
$433$	0.815921	+	0.592801i	0.0392107	+	0.0284882i	−0.568007	+	0.823024i	$0.692285\pi$
$434$	−1.07271	+	5.04670i	−0.0514917	+	0.242249i
$435$		0			0
$436$	−0.667967	−	0.0702062i	−0.0319898	−	0.00336227i
$437$	14.3332	+	6.38157i	0.685652	+	0.305272i
$438$		0			0
$439$	−30.7703	−	17.7652i	−1.46859	−	0.847888i	−0.469205	−	0.883089i	$-0.655459\pi$
$439$	−30.7703	−	17.7652i	−1.46859	−	0.847888i	−0.999380	+	0.0352012i	$0.988793\pi$
$440$	−1.51501	+	0.369967i	−0.0722251	+	0.0176375i
$441$		0			0
$442$	−1.11000	−	0.360661i	−0.0527973	−	0.0171549i
$443$	−18.7712	+	1.97294i	−0.891849	+	0.0937371i	−0.539356	−	0.842078i	$-0.681332\pi$
$443$	−18.7712	+	1.97294i	−0.891849	+	0.0937371i	−0.352492	+	0.935815i	$0.614666\pi$
$444$		0			0
$445$	−1.64028	+	1.82171i	−0.0777566	+	0.0863575i
$446$	2.44267	−	2.71286i	0.115664	−	0.128458i
$447$		0			0
$448$	21.7563	−	2.28668i	1.02789	−	0.108035i
$449$	−3.71574	−	1.20732i	−0.175356	−	0.0569768i	0.220023	−	0.975495i	$-0.429387\pi$
$449$	−3.71574	−	1.20732i	−0.175356	−	0.0569768i	−0.395379	+	0.918518i	$0.629387\pi$
$450$		0			0
$451$	33.2025	+	2.48303i	1.56345	+	0.116922i
$452$	−24.7245	−	14.2747i	−1.16294	−	0.671426i
$453$		0			0
$454$	−3.08015	−	1.37137i	−0.144558	−	0.0643615i
$455$	−1.49936	−	0.157589i	−0.0702909	−	0.00738787i
$456$		0			0
$457$	5.69308	−	26.7839i	0.266311	−	1.25290i	−0.618067	−	0.786125i	$-0.712084\pi$
$457$	5.69308	−	26.7839i	0.266311	−	1.25290i	0.884378	−	0.466771i	$-0.154583\pi$
$458$	1.27615	+	0.927174i	0.0596304	+	0.0433240i
$459$		0			0
$460$	−1.18904	+	3.65950i	−0.0554395	+	0.170625i
$461$	2.42545	−	4.20100i	0.112964	−	0.195660i	−0.804000	−	0.594629i	$-0.797299\pi$
$461$	2.42545	−	4.20100i	0.112964	−	0.195660i	0.916964	+	0.398970i	$0.130632\pi$
$462$		0			0
$463$	16.3454	+	28.3111i	0.759637	+	1.31573i	0.943036	+	0.332691i	$0.107956\pi$
$463$	16.3454	+	28.3111i	0.759637	+	1.31573i	−0.183400	+	0.983038i	$0.558710\pi$
$464$	−8.61281	+	1.83071i	−0.399840	+	0.0849886i
$465$		0			0
$466$	4.40594	−	1.96165i	0.204101	−	0.0908718i
$467$	−23.1944	+	7.53631i	−1.07331	+	0.348739i	−0.791775	−	0.610813i	$-0.790843\pi$
$467$	−23.1944	+	7.53631i	−1.07331	+	0.348739i	−0.281533	+	0.959552i	$0.590843\pi$
$468$		0			0
$469$	−1.26820	+	1.74553i	−0.0585600	+	0.0806009i
$470$	0.0237072	+	0.225559i	0.00109353	+	0.0104043i
$471$		0			0
$472$	−8.47035	+	4.89036i	−0.389880	+	0.225097i
$473$	−14.0900	−	2.55471i	−0.647859	−	0.117466i
$474$		0			0
$475$	14.9014	−	13.4173i	0.683723	−	0.615627i
$476$	21.8456	+	30.0678i	1.00129	+	1.37816i
$477$		0			0
$478$	−1.27356	−	3.91962i	−0.0582514	−	0.179279i
$479$	22.8097	+	4.84835i	1.04220	+	0.221527i	0.697052	−	0.717021i	$-0.254495\pi$
$479$	22.8097	+	4.84835i	1.04220	+	0.221527i	0.345150	+	0.938548i	$0.387828\pi$
$480$		0			0
$481$	0.282054	−	0.633504i	0.0128606	−	0.0288853i
$482$	−0.510828	−	2.40326i	−0.0232676	−	0.109465i
$483$		0			0
$484$	−11.8251	−	17.9023i	−0.537506	−	0.813741i
$485$		−	5.23759i		−	0.237827i
$486$		0			0
$487$	−4.01884	+	2.91986i	−0.182111	+	0.132311i	−0.675106	−	0.737721i	$-0.735902\pi$
$487$	−4.01884	+	2.91986i	−0.182111	+	0.132311i	0.492995	+	0.870032i	$0.335902\pi$
$488$	−0.659926	−	1.48222i	−0.0298734	−	0.0670968i
$489$		0			0
$490$	−0.286724	−	0.258168i	−0.0129529	−	0.0116628i
$491$	−1.81851	+	17.3020i	−0.0820682	+	0.780827i	0.873652	+	0.486551i	$0.161745\pi$
$491$	−1.81851	+	17.3020i	−0.0820682	+	0.780827i	−0.955720	+	0.294276i	$0.904921\pi$
$492$		0			0
$493$	−9.46785	−	10.5151i	−0.426410	−	0.473577i
$494$	0.833803			0.0375146
$495$		0			0
$496$	−26.8429			−1.20528
$497$	9.48032	+	10.5290i	0.425250	+	0.472288i
$498$		0			0
$499$	1.12880	−	10.7398i	0.0505321	−	0.480781i	−0.939766	−	0.341819i	$-0.888957\pi$
$499$	1.12880	−	10.7398i	0.0505321	−	0.480781i	0.990298	−	0.138961i	$-0.0443764\pi$
$500$	7.53078	+	6.78075i	0.336787	+	0.303244i
$501$		0			0
$502$	−1.77928	−	3.99632i	−0.0794130	−	0.178365i
$503$	−22.5838	+	16.4081i	−1.00696	+	0.731599i	−0.963569	−	0.267459i	$-0.913816\pi$
$503$	−22.5838	+	16.4081i	−1.00696	+	0.731599i	−0.0433908	+	0.999058i	$0.513816\pi$
$504$		0			0
$505$			5.72146i			0.254602i
$506$	2.72120	−	0.0818625i	0.120972	−	0.00363923i
$507$		0			0
$508$	−5.69644	−	26.7996i	−0.252738	−	1.18904i
$509$	−12.2879	+	27.5991i	−0.544652	+	1.22331i	0.406234	+	0.913769i	$0.366842\pi$
$509$	−12.2879	+	27.5991i	−0.544652	+	1.22331i	−0.950886	+	0.309540i	$0.899825\pi$
$510$		0			0
$511$	−0.290171	−	0.0616778i	−0.0128364	−	0.00272847i
$512$	−4.97068	−	15.2982i	−0.219675	−	0.676091i
$513$		0			0
$514$	3.44362	+	4.73974i	0.151892	+	0.209061i
$515$	−1.49099	+	1.34249i	−0.0657007	+	0.0591572i
$516$		0			0
$517$	−5.69342	+	2.74289i	−0.250396	+	0.120632i
$518$	0.485590	−	0.280355i	0.0213356	−	0.0123181i
$519$		0			0
$520$	0.0432921	+	0.411896i	0.00189848	+	0.0180629i
$521$	1.84317	−	2.53691i	0.0807507	−	0.111144i	−0.766731	−	0.641969i	$-0.778118\pi$
$521$	1.84317	−	2.53691i	0.0807507	−	0.111144i	0.847481	+	0.530825i	$0.178118\pi$
$522$		0			0
$523$	−9.10633	+	2.95883i	−0.398192	+	0.129380i	−0.501266	−	0.865293i	$-0.667132\pi$
$523$	−9.10633	+	2.95883i	−0.398192	+	0.129380i	0.103074	+	0.994674i	$0.467132\pi$
$524$	−3.84746	+	1.71300i	−0.168077	+	0.0748327i
$525$		0			0
$526$	0.573963	−	0.122000i	0.0250260	−	0.00531944i
$527$	−21.5675	−	37.3559i	−0.939493	−	1.62725i
$528$		0			0
$529$	−4.69766	+	8.13658i	−0.204246	+	0.353764i
$530$	−0.372915	+	1.14772i	−0.0161984	+	0.0498536i
$531$		0			0
$532$	−21.4807	−	15.6067i	−0.931308	−	0.676635i
$533$	1.83841	−	8.64904i	0.0796303	−	0.374631i
$534$		0			0
$535$	0.436698	+	0.0458988i	0.0188801	+	0.00198438i
$536$	0.541480	+	0.241082i	0.0233884	+	0.0104132i
$537$		0			0
$538$	0.705564	+	0.407357i	0.0304190	+	0.0175624i
$539$	4.07544	−	9.94838i	0.175542	−	0.428507i
$540$		0			0
$541$	12.3285	+	4.00578i	0.530045	+	0.172222i	0.561799	−	0.827274i	$-0.310109\pi$
$541$	12.3285	+	4.00578i	0.530045	+	0.172222i	−0.0317543	+	0.999496i	$0.510109\pi$
$542$	2.39991	−	0.252241i	0.103085	−	0.0108347i
$543$		0			0
$544$	10.2906	−	11.4289i	0.441207	−	0.490010i
$545$	−0.123237	+	0.136869i	−0.00527891	+	0.00586282i
$546$		0			0
$547$	38.1211	−	4.00669i	1.62994	−	0.171314i	0.755062	−	0.655653i	$-0.227607\pi$
$547$	38.1211	−	4.00669i	1.62994	−	0.171314i	0.874880	+	0.484340i	$0.160940\pi$
$548$	−1.34033	−	0.435498i	−0.0572559	−	0.0186036i
$549$		0			0
$550$	1.31895	−	3.21964i	0.0562404	−	0.137286i
$551$	8.75423	+	5.05426i	0.372943	+	0.215319i
$552$		0			0
$553$	45.2923	+	20.1654i	1.92602	+	0.857521i
$554$	0.0441089	+	0.00463603i	0.00187401	+	0.000196966i
$555$		0			0
$556$	−7.37839	+	34.7126i	−0.312913	+	1.47214i
$557$	20.0026	+	14.5328i	0.847538	+	0.615773i	0.924466	−	0.381264i	$-0.124511\pi$
$557$	20.0026	+	14.5328i	0.847538	+	0.615773i	−0.0769278	+	0.997037i	$0.524511\pi$
$558$		0			0
$559$	−1.17516	+	3.61678i	−0.0497042	+	0.152974i
$560$	3.17107	−	5.49245i	0.134002	−	0.232099i
$561$		0			0
$562$	−0.849409	−	1.47122i	−0.0358301	−	0.0620596i
$563$	30.7670	−	6.53972i	1.29667	−	0.275616i	0.492657	−	0.870223i	$-0.336026\pi$
$563$	30.7670	−	6.53972i	1.29667	−	0.275616i	0.804017	+	0.594607i	$0.202692\pi$
$564$		0			0
$565$	−7.15185	+	3.18421i	−0.300881	+	0.133961i
$566$	−0.119455	+	0.0388131i	−0.00502105	+	0.00163144i
$567$		0			0
$568$	2.28778	−	3.14886i	0.0959931	−	0.132123i
$569$	−2.39430	−	22.7803i	−0.100374	−	0.954998i	−0.922580	−	0.385807i	$-0.873923\pi$
$569$	−2.39430	−	22.7803i	−0.100374	−	0.954998i	0.822205	−	0.569191i	$-0.192744\pi$
$570$		0			0
$571$	−14.2974	+	8.25459i	−0.598326	+	0.345444i	−0.768383	−	0.639990i	$-0.778938\pi$
$571$	−14.2974	+	8.25459i	−0.598326	+	0.345444i	0.170057	+	0.985434i	$0.445605\pi$
$572$	−5.13324	+	2.47301i	−0.214632	+	0.103402i
$573$		0			0
$574$	5.31320	−	4.78403i	0.221769	−	0.199682i
$575$	−10.2199	−	14.0665i	−0.426199	−	0.586613i
$576$		0			0
$577$	3.22929	+	9.93872i	0.134437	+	0.413754i	0.995502	−	0.0947405i	$-0.0302021\pi$
$577$	3.22929	+	9.93872i	0.134437	+	0.413754i	−0.861065	+	0.508495i	$0.830202\pi$
$578$	4.01674	+	0.853785i	0.167074	+	0.0355128i
$579$		0			0
$580$	−1.00833	+	2.26474i	−0.0418686	+	0.0940383i
$581$	−9.47386	−	44.5710i	−0.393042	−	1.84912i
$582$		0			0
$583$	−33.6110	+	1.01113i	−1.39202	+	0.0418766i
$584$			0.0814955i			0.00337231i
$585$		0			0
$586$	−0.920251	+	0.668602i	−0.0380152	+	0.0276197i
$587$	−9.74504	−	21.8877i	−0.402221	−	0.903403i	−0.995170	−	0.0981633i	$-0.968703\pi$
$587$	−9.74504	−	21.8877i	−0.402221	−	0.903403i	0.592949	−	0.805240i	$-0.297963\pi$
$588$		0			0
$589$	22.9007	+	20.6199i	0.943608	+	0.849629i
$590$	−0.138416	+	1.31694i	−0.00569851	+	0.0542177i
$591$		0			0
$592$	1.95198	+	2.16790i	0.0802260	+	0.0891000i
$593$	34.0556			1.39850			0.699248	−	0.714880i	$-0.253519\pi$
$593$	34.0556			1.39850			0.699248	+	0.714880i	$0.253519\pi$
$594$		0			0
$595$	10.1914			0.417808
$596$	29.7233	+	33.0111i	1.21751	+	1.35219i
$597$		0			0
$598$	0.0755740	−	0.719038i	0.00309045	−	0.0294037i
$599$	28.6823	+	25.8256i	1.17193	+	1.05521i	0.997509	+	0.0705342i	$0.0224704\pi$
$599$	28.6823	+	25.8256i	1.17193	+	1.05521i	0.174416	+	0.984672i	$0.444196\pi$
$600$		0			0
$601$	5.99885	+	13.4736i	0.244698	+	0.549601i	0.993584	−	0.113098i	$-0.0360774\pi$
$601$	5.99885	+	13.4736i	0.244698	+	0.549601i	−0.748886	+	0.662699i	$0.769411\pi$
$602$	−2.48767	+	1.80740i	−0.101390	+	0.0736642i
$603$		0			0
$604$			22.2782i			0.906486i
$605$	−5.87750	−	0.262142i	−0.238954	−	0.0106576i
$606$		0			0
$607$	−3.39430	−	15.9689i	−0.137770	−	0.648159i	−0.991786	−	0.127911i	$-0.959173\pi$
$607$	−3.39430	−	15.9689i	−0.137770	−	0.648159i	0.854015	−	0.520248i	$-0.174160\pi$
$608$	−4.46880	+	10.0371i	−0.181234	+	0.407058i
$609$		0			0
$610$	−0.214866	−	0.0456712i	−0.00869968	−	0.00184917i
$611$	0.518632	+	1.59618i	0.0209816	+	0.0645747i
$612$		0			0
$613$	9.77045	+	13.4479i	0.394625	+	0.543155i	0.959385	−	0.282101i	$-0.0910312\pi$
$613$	9.77045	+	13.4479i	0.394625	+	0.543155i	−0.564760	+	0.825255i	$0.691031\pi$
$614$	−0.475823	+	0.428433i	−0.0192026	+	0.0172901i
$615$		0			0
$616$	−9.18161	−	1.66475i	−0.369938	−	0.0670748i
$617$	25.5162	−	14.7318i	1.02724	−	0.593080i	0.111051	−	0.993815i	$-0.464578\pi$
$617$	25.5162	−	14.7318i	1.02724	−	0.593080i	0.916194	+	0.400735i	$0.131245\pi$
$618$		0			0
$619$	4.61802	+	43.9375i	0.185614	+	1.76600i	0.550394	+	0.834905i	$0.314477\pi$
$619$	4.61802	+	43.9375i	0.185614	+	1.76600i	−0.364780	+	0.931094i	$0.618856\pi$
$620$	−4.44218	+	6.11413i	−0.178402	+	0.245550i
$621$		0			0
$622$	0.573815	−	0.186444i	0.0230079	−	0.00747571i
$623$	−13.3994	+	5.96582i	−0.536838	+	0.239015i
$624$		0			0
$625$	−20.3366	+	4.32267i	−0.813462	+	0.172907i
$626$	−1.24004	−	2.14781i	−0.0495620	−	0.0858438i
$627$		0			0
$628$	−19.3808	+	33.5685i	−0.773378	+	1.33953i
$629$	−1.44860	+	4.45832i	−0.0577593	+	0.177765i
$630$		0			0
$631$	9.62953	+	6.99627i	0.383346	+	0.278517i	0.762723	−	0.646725i	$-0.223862\pi$
$631$	9.62953	+	6.99627i	0.383346	+	0.278517i	−0.379378	+	0.925242i	$0.623862\pi$
$632$	2.83176	−	13.3224i	0.112641	−	0.529936i
$633$		0			0
$634$	1.38362	+	0.145424i	0.0549505	+	0.00577553i
$635$	−6.86350	−	3.05583i	−0.272370	−	0.121267i
$636$		0			0
$637$	−2.47259	−	1.42755i	−0.0979676	−	0.0565616i
$638$	1.74912	+	0.130807i	0.0692481	+	0.00517869i
$639$		0			0
$640$	−3.40152	−	1.10522i	−0.134457	−	0.0436877i
$641$	0.424548	−	0.0446218i	0.0167686	−	0.00176245i	−0.0961404	−	0.995368i	$-0.530650\pi$
$641$	0.424548	−	0.0446218i	0.0167686	−	0.00176245i	0.112909	+	0.993605i	$0.463983\pi$
$642$		0			0
$643$	19.7755	−	21.9629i	0.779870	−	0.866133i	−0.213983	−	0.976837i	$-0.568644\pi$
$643$	19.7755	−	21.9629i	0.779870	−	0.866133i	0.993853	+	0.110704i	$0.0353105\pi$
$644$	−15.4055	+	17.1096i	−0.607063	+	0.674212i
$645$		0			0
$646$	−5.60561	+	0.589174i	−0.220550	+	0.0231807i
$647$	12.2213	+	3.97095i	0.480470	+	0.156114i	0.539231	−	0.842158i	$-0.318715\pi$
$647$	12.2213	+	3.97095i	0.480470	+	0.156114i	−0.0587611	+	0.998272i	$0.518715\pi$
$648$		0			0
$649$	−35.8446	+	8.75331i	−1.40703	+	0.343597i
$650$	−0.800217	−	0.462005i	−0.0313871	−	0.0181213i
$651$		0			0
$652$	−18.3666	−	8.17734i	−0.719292	−	0.320249i
$653$	−10.4284	−	1.09606i	−0.408093	−	0.0428923i	−0.101742	−	0.994811i	$-0.532442\pi$
$653$	−10.4284	−	1.09606i	−0.408093	−	0.0428923i	−0.306351	+	0.951919i	$0.599108\pi$
$654$		0			0
$655$	−0.240112	+	1.12964i	−0.00938194	+	0.0441386i
$656$	30.0931	+	21.8639i	1.17494	+	0.853642i
$657$		0			0
$658$	−0.419352	+	1.29063i	−0.0163480	+	0.0503141i
$659$	−10.1911	+	17.6516i	−0.396990	+	0.687607i	−0.993353	−	0.115108i	$-0.963279\pi$
$659$	−10.1911	+	17.6516i	−0.396990	+	0.687607i	0.596363	+	0.802715i	$0.296612\pi$
$660$		0			0
$661$	−2.66875	−	4.62241i	−0.103802	−	0.179791i	0.809446	−	0.587194i	$-0.199768\pi$
$661$	−2.66875	−	4.62241i	−0.103802	−	0.179791i	−0.913248	+	0.407403i	$0.866434\pi$
$662$	0.675828	−	0.143652i	0.0262668	−	0.00558318i
$663$		0			0
$664$	−11.4357	+	5.09149i	−0.443790	+	0.197588i
$665$	−6.92451	+	2.24991i	−0.268521	+	0.0872477i
$666$		0			0
$667$	5.15205	−	7.09119i	0.199488	−	0.274572i
$668$	2.41655	+	22.9919i	0.0934990	+	0.889584i
$669$		0			0
$670$	0.0694968	−	0.0401240i	0.00268490	−	0.00155013i
$671$	−0.822560	−	6.06535i	−0.0317546	−	0.234150i
$672$		0			0
$673$	22.3581	−	20.1313i	0.861840	−	0.776005i	−0.114231	−	0.993454i	$-0.536440\pi$
$673$	22.3581	−	20.1313i	0.861840	−	0.776005i	0.976072	+	0.217450i	$0.0697738\pi$
$674$	−1.74963	−	2.40816i	−0.0673933	−	0.0927589i
$675$		0			0
$676$	−7.36788	−	22.6760i	−0.283380	−	0.872154i
$677$	26.3994	+	5.61137i	1.01461	+	0.215662i	0.685069	−	0.728478i	$-0.259772\pi$
$677$	26.3994	+	5.61137i	1.01461	+	0.215662i	0.329543	+	0.944141i	$0.393105\pi$
$678$		0			0
$679$	12.7466	−	28.6294i	0.489170	−	1.09869i
$680$	−0.582101	−	2.73857i	−0.0223225	−	0.105019i
$681$		0			0
$682$	5.13278	+	1.49868i	0.196544	+	0.0573874i
$683$			19.1623i			0.733224i	0.930374	+	0.366612i	$0.119482\pi$
$683$			19.1623i			0.733224i	−0.930374	+	0.366612i	$0.880518\pi$
$684$		0			0
$685$	−0.312646	+	0.227151i	−0.0119456	+	0.00867898i
$686$	1.08875	+	2.44537i	0.0415685	+	0.0933645i
$687$		0			0
$688$	−11.8887	−	10.7047i	−0.453253	−	0.408111i
$689$	−0.933454	+	8.88122i	−0.0355618	+	0.338348i
$690$		0			0
$691$	−4.07683	−	4.52777i	−0.155090	−	0.172245i	0.660593	−	0.750744i	$-0.270305\pi$
$691$	−4.07683	−	4.52777i	−0.155090	−	0.172245i	−0.815683	+	0.578500i	$0.803638\pi$
$692$	−30.8741			−1.17366
$693$		0			0
$694$	−0.626882			−0.0237961
$695$	6.51155	+	7.23181i	0.246997	+	0.274318i
$696$		0			0
$697$	−6.24803	+	59.4461i	−0.236661	+	2.25168i
$698$	4.44988	+	4.00669i	0.168430	+	0.151655i
$699$		0			0
$700$	11.9679	+	26.8804i	0.452345	+	1.01598i
$701$	20.3206	−	14.7638i	0.767499	−	0.557621i	−0.133702	−	0.991022i	$-0.542687\pi$
$701$	20.3206	−	14.7638i	0.767499	−	0.557621i	0.901201	+	0.433401i	$0.142687\pi$
$702$		0			0
$703$		−	3.34897i		−	0.126309i
$704$	−0.681732	−	22.6615i	−0.0256937	−	0.854087i
$705$		0			0
$706$	−0.0926527	−	0.435897i	−0.00348703	−	0.0164052i
$707$	−13.9242	+	31.2743i	−0.523674	+	1.17619i
$708$		0			0
$709$	−5.60465	−	1.19131i	−0.210487	−	0.0447404i	0.101461	−	0.994840i	$-0.467648\pi$
$709$	−5.60465	−	1.19131i	−0.210487	−	0.0447404i	−0.311948	+	0.950099i	$0.600982\pi$
$710$	−0.162840	−	0.501168i	−0.00611126	−	0.0188085i
$711$		0			0
$712$	2.36842	+	3.25985i	0.0887603	+	0.122168i
$713$	19.8575	−	17.8797i	0.743668	−	0.669601i
$714$		0			0
$715$	−0.278748	+	1.53738i	−0.0104246	+	0.0574948i
$716$	−11.8346	+	6.83273i	−0.442281	+	0.255351i
$717$		0			0
$718$	0.0581538	+	0.553297i	0.00217028	+	0.0206489i
$719$	−6.16104	+	8.47994i	−0.229768	+	0.316248i	−0.908298	−	0.418325i	$-0.862617\pi$
$719$	−6.16104	+	8.47994i	−0.229768	+	0.316248i	0.678530	+	0.734573i	$0.262617\pi$
$720$		0			0
$721$	−11.4171	+	3.70965i	−0.425196	+	0.138155i
$722$	−0.184149	+	0.0819884i	−0.00685332	+	0.00305129i
$723$		0			0
$724$	−23.0933	+	4.90863i	−0.858255	+	0.182428i
$725$	−5.60107	−	9.70134i	−0.208019	−	0.360299i
$726$		0			0
$727$	17.0164	−	29.4732i	0.631102	−	1.09310i	−0.356225	−	0.934400i	$-0.615936\pi$
$727$	17.0164	−	29.4732i	0.631102	−	1.09310i	0.987327	−	0.158700i	$-0.0507304\pi$
$728$	−0.765784	+	2.35684i	−0.0283818	+	0.0873503i
$729$		0			0
$730$	0.00892634	+	0.00648536i	0.000330379	+	0.000240034i
$731$	5.34491	−	25.1458i	0.197689	−	0.930052i
$732$		0			0
$733$	29.4641	+	3.09680i	1.08828	+	0.114383i	0.631636	−	0.775265i	$-0.282384\pi$
$733$	29.4641	+	3.09680i	1.08828	+	0.114383i	0.456646	+	0.889648i	$0.349051\pi$
$734$	2.69535	+	1.20005i	0.0994871	+	0.0442945i
$735$		0			0
$736$	8.25054	+	4.76345i	0.304119	+	0.175583i
$737$	1.70596	+	1.44557i	0.0628397	+	0.0532484i
$738$		0			0
$739$	25.4725	+	8.27651i	0.937020	+	0.304456i	0.737430	−	0.675423i	$-0.236039\pi$
$739$	25.4725	+	8.27651i	0.937020	+	0.304456i	0.199590	+	0.979880i	$0.436039\pi$
$740$	0.816822	−	0.0858515i	0.0300270	−	0.00315596i
$741$		0			0
$742$	−4.83158	+	5.36601i	−0.177373	+	0.196992i
$743$	−16.5430	+	18.3729i	−0.606904	+	0.674035i	−0.965784	−	0.259348i	$-0.916492\pi$
$743$	−16.5430	+	18.3729i	−0.606904	+	0.674035i	0.358880	+	0.933384i	$0.383159\pi$
$744$		0			0
$745$	12.1141	−	1.27325i	0.443827	−	0.0466481i
$746$	−6.72208	−	2.18414i	−0.246113	−	0.0799669i
$747$		0			0
$748$	32.7631	−	20.2531i	1.19794	−	0.740528i
$749$	2.27535	+	1.31367i	0.0831394	+	0.0480006i
$750$		0			0
$751$	−6.74831	−	3.00454i	−0.246249	−	0.109637i	0.279901	−	0.960029i	$-0.409698\pi$
$751$	−6.74831	−	3.00454i	−0.246249	−	0.109637i	−0.526150	+	0.850392i	$0.676365\pi$
$752$	−7.02161	−	0.738001i	−0.256052	−	0.0269121i
$753$		0			0
$754$	0.0968478	−	0.455633i	0.00352699	−	0.0165932i
$755$	4.94229	+	3.59079i	0.179868	+	0.130682i
$756$		0			0
$757$	0.0920305	−	0.283241i	0.00334491	−	0.0102946i	−0.949370	−	0.314160i	$-0.898277\pi$
$757$	0.0920305	−	0.283241i	0.00334491	−	0.0102946i	0.952715	+	0.303865i	$0.0982772\pi$
$758$	2.64538	−	4.58194i	0.0960846	−	0.166423i
$759$		0			0
$760$	1.00008	+	1.73219i	0.0362768	+	0.0628333i
$761$	24.8141	−	5.27440i	0.899511	−	0.191197i	0.265126	−	0.964214i	$-0.414587\pi$
$761$	24.8141	−	5.27440i	0.899511	−	0.191197i	0.634386	+	0.773017i	$0.281253\pi$
$762$		0			0
$763$	−1.00673	+	0.448224i	−0.0364460	+	0.0162268i
$764$	37.6681	−	12.2391i	1.36278	−	0.442795i
$765$		0			0
$766$	−2.33292	+	3.21099i	−0.0842920	+	0.116018i
$767$	1.02428	+	9.74536i	0.0369846	+	0.351885i
$768$		0			0
$769$	−9.05193	+	5.22613i	−0.326421	+	0.188459i	−0.654251	−	0.756278i	$-0.727016\pi$
$769$	−9.05193	+	5.22613i	−0.326421	+	0.188459i	0.327830	+	0.944737i	$0.393683\pi$
$770$	−0.913010	+	0.873197i	−0.0329026	+	0.0314678i
$771$		0			0
$772$	8.23555	−	7.41532i	0.296404	−	0.266883i
$773$	−5.51171	−	7.58622i	−0.198243	−	0.272857i	0.698309	−	0.715796i	$-0.253936\pi$
$773$	−5.51171	−	7.58622i	−0.198243	−	0.272857i	−0.896552	+	0.442939i	$0.853936\pi$
$774$		0			0
$775$	−10.5529	−	32.4785i	−0.379072	−	1.16666i
$776$	−8.42112	−	1.78996i	−0.302301	−	0.0642560i
$777$		0			0
$778$	2.23750	−	5.02552i	0.0802184	−	0.180174i
$779$	−8.87840	−	41.7696i	−0.318102	−	1.49655i
$780$		0			0
$781$	11.6142	−	8.98399i	0.415590	−	0.321472i
$782$			4.88746i			0.174775i
$783$		0			0
$784$	9.71683	−	7.05969i	0.347030	−	0.252132i
$785$	4.32321	+	9.71008i	0.154302	+	0.346568i
$786$		0			0
$787$	6.51938	+	5.87007i	0.232391	+	0.209246i	0.777096	−	0.629382i	$-0.216692\pi$
$787$	6.51938	+	5.87007i	0.232391	+	0.209246i	−0.544705	+	0.838627i	$0.683359\pi$
$788$	3.35579	−	31.9282i	0.119545	−	1.13739i
$789$		0			0
$790$	−1.23387	−	1.37035i	−0.0438992	−	0.0487550i
$791$	−46.8423			−1.66552
$792$		0			0
$793$	−1.62553			−0.0577242
$794$	0.606280	+	0.673343i	0.0215161	+	0.0238960i
$795$		0			0
$796$	2.84967	−	27.1128i	0.101004	−	0.960989i
$797$	16.2068	+	14.5926i	0.574073	+	0.516897i	0.904240	−	0.427025i	$-0.140438\pi$
$797$	16.2068	+	14.5926i	0.574073	+	0.516897i	−0.330167	+	0.943923i	$0.607105\pi$
$798$		0			0
$799$	−4.61462	−	10.3646i	−0.163253	−	0.366673i
$800$	9.85029	−	7.15665i	0.348260	−	0.253026i
$801$		0			0
$802$		−	5.63607i		−	0.199017i
$803$	−0.0861700	+	0.295120i	−0.00304087	+	0.0104146i
$804$		0			0
$805$	1.31261	+	6.17535i	0.0462634	+	0.217652i
$806$	0.577581	−	1.29727i	0.0203444	−	0.0456943i
$807$		0			0
$808$	9.19909	+	1.95533i	0.323623	+	0.0687882i
$809$	2.71969	+	8.37033i	0.0956190	+	0.294285i	0.987415	−	0.158154i	$-0.0505541\pi$
$809$	2.71969	+	8.37033i	0.0956190	+	0.294285i	−0.891795	+	0.452439i	$0.850554\pi$
$810$		0			0
$811$	−24.6647	−	33.9480i	−0.866094	−	1.19208i	−0.980082	−	0.198594i	$-0.936363\pi$
$811$	−24.6647	−	33.9480i	−0.866094	−	1.19208i	0.113988	−	0.993482i	$-0.463637\pi$
$812$	−11.0233	+	9.92544i	−0.386843	+	0.348315i
$813$		0			0
$814$	−0.252212	−	0.523518i	−0.00884004	−	0.0183493i
$815$	−4.77442	+	2.75651i	−0.167240	+	0.0965563i
$816$		0			0
$817$	1.91974	+	18.2651i	0.0671633	+	0.639016i
$818$	−1.17202	+	1.61315i	−0.0409787	+	0.0564024i
$819$		0			0
$820$	9.96009	−	3.23623i	0.347822	−	0.113014i
$821$	−31.8328	+	14.1729i	−1.11097	+	0.494637i	−0.878392	−	0.477940i	$-0.841384\pi$
$821$	−31.8328	+	14.1729i	−1.11097	+	0.494637i	−0.232580	+	0.972577i	$0.574717\pi$
$822$		0			0
$823$	−14.2424	+	3.02732i	−0.496459	+	0.105526i	−0.449335	−	0.893363i	$-0.648339\pi$
$823$	−14.2424	+	3.02732i	−0.496459	+	0.105526i	−0.0471242	+	0.998889i	$0.515006\pi$
$824$	1.64894	+	2.85604i	0.0574435	+	0.0994950i
$825$		0			0
$826$	−3.96162	+	6.86173i	−0.137842	+	0.238750i
$827$	14.8117	−	45.5858i	0.515054	−	1.58517i	−0.268131	−	0.963383i	$-0.586406\pi$
$827$	14.8117	−	45.5858i	0.515054	−	1.58517i	0.783184	−	0.621790i	$-0.213594\pi$
$828$		0			0
$829$	10.6108	+	7.70918i	0.368527	+	0.267751i	0.756600	−	0.653878i	$-0.226859\pi$
$829$	10.6108	+	7.70918i	0.368527	+	0.267751i	−0.388073	+	0.921629i	$0.626859\pi$
$830$	−0.352365	+	1.65775i	−0.0122308	+	0.0575412i
$831$		0			0
$832$	−5.98798	−	0.629362i	−0.207596	−	0.0218192i
$833$	17.6318	+	7.85019i	0.610906	+	0.271993i
$834$		0			0
$835$	5.49012	+	3.16972i	0.189994	+	0.109693i
$836$	−17.7895	+	20.9938i	−0.615261	+	0.726085i
$837$		0			0
$838$	−0.664133	−	0.215790i	−0.0229421	−	0.00745434i
$839$	−27.7651	+	2.91823i	−0.958559	+	0.100749i	−0.570869	−	0.821041i	$-0.693394\pi$
$839$	−27.7651	+	2.91823i	−0.958559	+	0.100749i	−0.387690	+	0.921790i	$0.626727\pi$
$840$		0			0
$841$	−15.6261	+	17.3545i	−0.538830	+	0.598431i
$842$	−4.28576	+	4.75982i	−0.147697	+	0.164034i
$843$		0			0
$844$	20.8592	−	2.19239i	0.718003	−	0.0754651i
$845$	−6.21810	−	2.02038i	−0.213909	−	0.0695033i
$846$		0			0
$847$	−31.4892	−	15.7368i	−1.08198	−	0.540725i
$848$	−32.5338	−	18.7834i	−1.11721	−	0.645024i
$849$		0			0
$850$	5.70628	+	2.54060i	0.195724	+	0.0871418i
$851$	−2.88802	−	0.303543i	−0.0990001	−	0.0104053i
$852$		0			0
$853$	0.697099	−	3.27959i	0.0238682	−	0.112291i	−0.964601	−	0.263714i	$-0.915052\pi$
$853$	0.697099	−	3.27959i	0.0238682	−	0.112291i	0.988469	+	0.151423i	$0.0483857\pi$
$854$	−1.06334	−	0.772561i	−0.0363867	−	0.0264365i
$855$		0			0
$856$	0.223040	−	0.686447i	0.00762336	−	0.0234623i
$857$	−5.78843	+	10.0259i	−0.197729	+	0.342477i	−0.947792	−	0.318890i	$-0.896690\pi$
$857$	−5.78843	+	10.0259i	−0.197729	+	0.342477i	0.750063	+	0.661367i	$0.230023\pi$
$858$		0			0
$859$	−17.2606	−	29.8962i	−0.588923	−	1.02005i	−0.994374	−	0.105928i	$-0.966219\pi$
$859$	−17.2606	−	29.8962i	−0.588923	−	1.02005i	0.405450	−	0.914117i	$-0.367115\pi$
$860$	−4.40570	+	0.936459i	−0.150233	+	0.0319330i
$861$		0			0
$862$	−5.73692	+	2.55424i	−0.195400	+	0.0869979i
$863$	−23.6801	+	7.69412i	−0.806079	+	0.261911i	−0.682936	−	0.730478i	$-0.739297\pi$
$863$	−23.6801	+	7.69412i	−0.806079	+	0.261911i	−0.123143	+	0.992389i	$0.539297\pi$
$864$		0			0
$865$	−4.97627	+	6.84925i	−0.169198	+	0.232882i
$866$	−0.0234607	−	0.223214i	−0.000797227	−	0.00758511i
$867$		0			0
$868$	−39.1614	+	22.6098i	−1.32922	+	0.767428i
$869$	24.3412	−	45.2503i	0.825720	−	1.53501i
$870$		0			0
$871$	0.441304	−	0.397352i	0.0149530	−	0.0134638i
$872$	0.177944	+	0.244919i	0.00602596	+	0.00829402i
$873$		0			0
$874$	−1.07898	−	3.32075i	−0.0364970	−	0.112326i
$875$	16.2634	+	3.45690i	0.549804	+	0.116865i
$876$		0			0
$877$	−16.5596	+	37.1936i	−0.559179	+	1.25594i	0.383902	+	0.923374i	$0.374580\pi$
$877$	−16.5596	+	37.1936i	−0.559179	+	1.25594i	−0.943081	+	0.332563i	$0.892086\pi$
$878$	1.64398	+	7.73430i	0.0554815	+	0.261020i
$879$		0			0
$880$	−5.43128	−	3.70175i	−0.183088	−	0.124786i
$881$		−	15.5331i		−	0.523323i	−0.965160	−	0.261661i	$-0.915730\pi$
$881$		−	15.5331i		−	0.523323i	0.965160	−	0.261661i	$-0.0842703\pi$
$882$		0			0
$883$	−11.1691	+	8.11482i	−0.375870	+	0.273086i	−0.759641	−	0.650343i	$-0.774625\pi$
$883$	−11.1691	+	8.11482i	−0.375870	+	0.273086i	0.383771	+	0.923428i	$0.374625\pi$
$884$	−4.16058	−	9.34482i	−0.139936	−	0.314300i
$885$		0			0
$886$	3.12153	+	2.81064i	0.104870	+	0.0944253i
$887$	−3.28428	+	31.2478i	−0.110275	+	1.04920i	0.789770	+	0.613403i	$0.210200\pi$
$887$	−3.28428	+	31.2478i	−0.110275	+	1.04920i	−0.900046	+	0.435796i	$0.856467\pi$
$888$		0			0
$889$	−30.0799	−	33.4071i	−1.00885	−	1.12044i
$890$	0.545534			0.0182864
$891$		0			0
$892$	31.9947			1.07126
$893$	5.42350	+	6.02341i	0.181491	+	0.201566i
$894$		0			0
$895$	−0.391696	+	3.72674i	−0.0130930	+	0.124571i
$896$	−15.9034	−	14.3195i	−0.531296	−	0.478381i
$897$		0			0
$898$	0.353645	+	0.794300i	0.0118013	+	0.0265061i
$899$	13.9278	−	10.1191i	0.464516	−	0.337491i
$900$		0			0
$901$		−	60.3676i		−	2.01114i
$902$	−4.53357	−	5.86086i	−0.150951	−	0.195145i
$903$		0			0
$904$	2.67548	+	12.5871i	0.0889850	+	0.418641i
$905$	−2.63321	+	5.91428i	−0.0875308	+	0.196597i
$906$		0			0
$907$	45.3069	+	9.63029i	1.50439	+	0.319768i	0.885103	−	0.465395i	$-0.154088\pi$
$907$	45.3069	+	9.63029i	1.50439	+	0.319768i	0.619289	+	0.785163i	$0.287421\pi$
$908$	−9.13162	−	28.1042i	−0.303044	−	0.932672i
$909$		0			0
$910$	0.197208	+	0.271434i	0.00653738	+	0.00899794i
$911$	−14.4923	+	13.0489i	−0.480151	+	0.432330i	−0.873328	−	0.487133i	$-0.838043\pi$
$911$	−14.4923	+	13.0489i	−0.480151	+	0.432330i	0.393176	+	0.919463i	$0.371376\pi$
$912$		0			0
$913$	−46.7957	+	6.34625i	−1.54871	+	0.210030i
$914$	−5.27734	+	3.04687i	−0.174559	+	0.100782i
$915$		0			0
$916$	1.44511	+	13.7493i	0.0477479	+	0.454290i
$917$	−4.06166	+	5.59040i	−0.134128	+	0.184611i
$918$		0			0
$919$	51.8032	−	16.8319i	1.70883	−	0.555232i	0.718691	−	0.695329i	$-0.244742\pi$
$919$	51.8032	−	16.8319i	1.70883	−	0.555232i	0.990138	+	0.140097i	$0.0447415\pi$
$920$	1.58442	−	0.705430i	0.0522368	−	0.0232573i
$921$		0			0
$922$	−1.05595	+	0.224448i	−0.0347757	+	0.00739181i
$923$	−1.94975	−	3.37706i	−0.0641767	−	0.111157i
$924$		0			0
$925$	−1.85565	+	3.21408i	−0.0610133	+	0.105678i
$926$	2.24815	−	6.91908i	0.0738787	−	0.227375i
$927$		0			0
$928$	4.96572	+	3.60781i	0.163008	+	0.118432i
$929$	−3.27981	+	15.4303i	−0.107607	+	0.506251i	0.891025	+	0.453955i	$0.149987\pi$
$929$	−3.27981	+	15.4303i	−0.107607	+	0.506251i	−0.998632	+	0.0522962i	$0.983346\pi$
$930$		0			0
$931$	−13.7129	−	1.44128i	−0.449421	−	0.0472361i
$932$	38.6156	+	17.1928i	1.26490	+	0.563169i
$933$		0			0
$934$	4.70027	+	2.71370i	0.153798	+	0.0887950i
$935$	0.787682	−	10.5327i	0.0257600	−	0.344456i
$936$		0			0
$937$	−26.3765	−	8.57025i	−0.861683	−	0.279978i	−0.155352	−	0.987859i	$-0.549651\pi$
$937$	−26.3765	−	8.57025i	−0.861683	−	0.279978i	−0.706331	+	0.707882i	$0.749651\pi$
$938$	0.477528	−	0.0501902i	0.0155918	−	0.00163877i
$939$		0			0
$940$	−1.33009	+	1.47722i	−0.0433828	+	0.0481815i
$941$	6.20656	−	6.89308i	0.202328	−	0.224708i	−0.633438	−	0.773793i	$-0.718357\pi$
$941$	6.20656	−	6.89308i	0.202328	−	0.224708i	0.835766	+	0.549085i	$0.185024\pi$
$942$		0			0
$943$	−36.8251	+	3.87048i	−1.19919	+	0.126040i
$944$	−39.2045	−	12.7383i	−1.27600	−	0.414596i
$945$		0			0
$946$	1.67565	+	2.71066i	0.0544801	+	0.0881313i
$947$	−4.44675	−	2.56733i	−0.144500	−	0.0834270i	0.426007	−	0.904720i	$-0.359920\pi$
$947$	−4.44675	−	2.56733i	−0.144500	−	0.0834270i	−0.570507	+	0.821293i	$0.693253\pi$
$948$		0			0
$949$	0.0745893	+	0.0332093i	0.00242127	+	0.00107802i
$950$	−4.43796	−	0.466449i	−0.143987	−	0.0151336i
$951$		0			0
$952$	3.48296	−	16.3860i	0.112883	−	0.531074i
$953$	−33.1526	−	24.0868i	−1.07392	−	0.780248i	−0.0973068	−	0.995254i	$-0.531023\pi$
$953$	−33.1526	−	24.0868i	−1.07392	−	0.780248i	−0.976613	+	0.215006i	$0.931023\pi$
$954$		0			0
$955$	3.35615	−	10.3292i	0.108602	−	0.334244i
$956$	18.0606	−	31.2819i	0.584122	−	1.01173i
$957$		0			0
$958$	−2.59478	−	4.49429i	−0.0838336	−	0.145204i
$959$	−2.26178	+	0.480756i	−0.0730366	+	0.0155244i
$960$		0			0
$961$	19.6250	−	8.73759i	0.633063	−	0.281858i
$962$	−0.146771	+	0.0476889i	−0.00473210	+	0.00153755i
$963$		0			0
$964$	12.6572	−	17.4212i	0.407663	−	0.561099i
$965$	−0.317647	−	3.02221i	−0.0102254	−	0.0972883i
$966$		0			0
$967$	13.7225	−	7.92268i	0.441285	−	0.254776i	−0.262857	−	0.964835i	$-0.584665\pi$
$967$	13.7225	−	7.92268i	0.441285	−	0.254776i	0.704143	+	0.710059i	$0.251332\pi$
$968$	−2.43013	+	9.36038i	−0.0781074	+	0.300854i
$969$		0			0
$970$	−0.866205	+	0.779935i	−0.0278122	+	0.0250422i
$971$	1.51662	+	2.08745i	0.0486708	+	0.0669896i	0.832659	−	0.553786i	$-0.186818\pi$
$971$	1.51662	+	2.08745i	0.0486708	+	0.0669896i	−0.783988	+	0.620776i	$0.786818\pi$
$972$		0			0
$973$	17.9931	+	55.3771i	0.576833	+	1.77531i
$974$	1.08134	+	0.229846i	0.0346484	+	0.00736475i
$975$		0			0
$976$	2.78133	−	6.24698i	0.0890283	−	0.199961i
$977$	6.37823	+	30.0072i	0.204058	+	0.960015i	0.954300	+	0.298852i	$0.0966037\pi$
$977$	6.37823	+	30.0072i	0.204058	+	0.960015i	−0.750242	+	0.661163i	$0.770063\pi$
$978$		0			0
$979$	5.12995	+	14.3092i	0.163954	+	0.457324i
$980$		−	3.38155i		−	0.108020i
$981$		0			0
$982$	3.13224	−	2.27570i	0.0999537	−	0.0726206i
$983$	−14.3155	−	32.1531i	−0.456593	−	1.02553i	−0.984365	−	0.176139i	$-0.943639\pi$
$983$	−14.3155	−	32.1531i	−0.456593	−	1.02553i	0.527772	−	0.849386i	$-0.323028\pi$
$984$		0			0
$985$	−6.54221	−	5.89063i	−0.208452	−	0.187691i
$986$	−0.329148	+	3.13163i	−0.0104822	+	0.0997314i
$987$		0			0
$988$	4.88988	+	5.43077i	0.155568	+	0.172776i
$989$	15.9251			0.506390
$990$		0			0
$991$	−2.21717			−0.0704307			−0.0352154	−	0.999380i	$-0.511212\pi$
$991$	−2.21717			−0.0704307			−0.0352154	+	0.999380i	$0.511212\pi$
$992$	12.5206	+	13.9055i	0.397529	+	0.441500i
$993$		0			0
$994$	0.329581	−	3.13575i	0.0104537	−	0.0994601i
$995$	−5.55552	−	5.00222i	−0.176122	−	0.158581i
$996$		0			0
$997$	13.9619	+	31.3590i	0.442178	+	0.993149i	0.987887	+	0.155174i	$0.0495939\pi$
$997$	13.9619	+	31.3590i	0.442178	+	0.993149i	−0.545709	+	0.837975i	$0.683739\pi$
$998$	−1.94427	+	1.41259i	−0.0615447	+	0.0447149i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.35.4		80
3.2	odd	2		99.2.p.a.2.7	✓	80
9.2	odd	6		891.2.k.a.728.12		80
9.4	even	3		99.2.p.a.68.7	yes	80
9.5	odd	6	inner	297.2.t.a.233.4		80
9.7	even	3		891.2.k.a.728.9		80
11.6	odd	10	inner	297.2.t.a.116.4		80
33.17	even	10		99.2.p.a.83.7	yes	80
99.50	even	30	inner	297.2.t.a.17.4		80
99.61	odd	30		891.2.k.a.809.12		80
99.83	even	30		891.2.k.a.809.9		80
99.94	odd	30		99.2.p.a.50.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.7	✓	80	3.2	odd	2
99.2.p.a.50.7	yes	80	99.94	odd	30
99.2.p.a.68.7	yes	80	9.4	even	3
99.2.p.a.83.7	yes	80	33.17	even	10
297.2.t.a.17.4		80	99.50	even	30	inner
297.2.t.a.35.4		80	1.1	even	1	trivial
297.2.t.a.116.4		80	11.6	odd	10	inner
297.2.t.a.233.4		80	9.5	odd	6	inner
891.2.k.a.728.9		80	9.7	even	3
891.2.k.a.728.12		80	9.2	odd	6
891.2.k.a.809.9		80	99.83	even	30
891.2.k.a.809.12		80	99.61	odd	30

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.148911 - 0.165382i) q^{2} +(0.203880 - 1.93979i) q^{4} +(-0.397470 - 0.357884i) q^{5} +(-1.30165 - 2.92356i) q^{7} +(-0.711251 + 0.516754i) q^{8} +0.119027i q^{10} +(-3.12205 + 1.11928i) q^{11} +(0.183129 + 0.861553i) q^{13} +(-0.289675 + 0.650620i) q^{14} +(-3.62433 - 0.770375i) q^{16} +(-1.83995 - 5.66278i) q^{17} +(2.50028 + 3.44134i) q^{19} +(-0.775255 + 0.698043i) q^{20} +(0.650017 + 0.349660i) q^{22} +(3.19429 - 1.84423i) q^{23} +(-0.492741 - 4.68811i) q^{25} +(0.115216 - 0.158581i) q^{26} +(-5.93647 + 1.92887i) q^{28} +(2.17094 - 0.966564i) q^{29} +(7.08615 - 1.50621i) q^{31} +(1.29145 + 2.23686i) q^{32} +(-0.662535 + 1.14754i) q^{34} +(-0.528926 + 1.62787i) q^{35} +(-0.636941 - 0.462765i) q^{37} +(0.196818 - 0.925955i) q^{38} +(0.467639 + 0.0491508i) q^{40} +(-9.17098 - 4.08318i) q^{41} +(3.73912 + 2.15878i) q^{43} +(1.53464 + 6.28432i) q^{44} +(-0.780668 - 0.253654i) q^{46} +(1.89502 - 0.199174i) q^{47} +(-2.16898 + 2.40889i) q^{49} +(-0.701957 + 0.779602i) q^{50} +(1.70857 - 0.179578i) q^{52} +(9.64245 + 3.13302i) q^{53} +(1.64149 + 0.672452i) q^{55} +(2.43656 + 1.40675i) q^{56} +(-0.483129 - 0.215103i) q^{58} +(11.0642 + 1.16290i) q^{59} +(-0.383703 + 1.80518i) q^{61} +(-1.30431 - 0.947634i) q^{62} +(-2.11237 + 6.50122i) q^{64} +(0.235548 - 0.407980i) q^{65} +(-0.337099 - 0.583872i) q^{67} +(-11.3597 + 2.41458i) q^{68} +(0.347983 - 0.154932i) q^{70} +(-4.21053 + 1.36808i) q^{71} +(0.0544863 - 0.0749940i) q^{73} +(0.0183144 + 0.174250i) q^{74} +(7.18523 - 4.14840i) q^{76} +(7.33610 + 7.67059i) q^{77} +(-11.5129 + 10.3663i) q^{79} +(1.16486 + 1.60329i) q^{80} +(0.690373 + 2.12475i) q^{82} +(13.9274 + 2.96037i) q^{83} +(-1.29529 + 2.90927i) q^{85} +(-0.199771 - 0.939851i) q^{86} +(1.64217 - 2.40942i) q^{88} -4.58327i q^{89} +(2.28043 - 1.65683i) q^{91} +(-2.92616 - 6.57226i) q^{92} +(-0.315129 - 0.283743i) q^{94} +(0.237813 - 2.26264i) q^{95} +(6.55256 + 7.27736i) q^{97} +0.721373 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

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