LMFDB - Embedded newform 243.2.g.a.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(10,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("243.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	243.37
Dual form			243.2.g.a.46.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.395901 - 1.32240i) q^{2} +(0.0789711 + 0.0519401i) q^{4} +(-1.59916 + 3.70727i) q^{5} +(0.206731 + 3.54944i) q^{7} +(2.21483 - 1.85846i) q^{8} +(4.26939 + 3.58244i) q^{10} +(-0.0970299 + 0.130334i) q^{11} +(-0.239595 + 0.253956i) q^{13} +(4.77563 + 1.13184i) q^{14} +(-1.50590 - 3.49108i) q^{16} +(0.388085 - 2.20094i) q^{17} +(-0.215481 - 1.22205i) q^{19} +(-0.318844 + 0.209707i) q^{20} +(0.133939 + 0.179912i) q^{22} +(0.176164 - 3.02462i) q^{23} +(-7.75535 - 8.22019i) q^{25} +(0.240975 + 0.417381i) q^{26} +(-0.168033 + 0.291041i) q^{28} +(6.91689 - 1.63933i) q^{29} +(-0.773247 + 0.388339i) q^{31} +(0.530624 - 0.0620210i) q^{32} +(-2.75688 - 1.38456i) q^{34} +(-13.4893 - 4.90972i) q^{35} +(4.23271 - 1.54058i) q^{37} +(-1.70135 - 0.198860i) q^{38} +(3.34796 + 11.1830i) q^{40} +(2.02741 + 6.77201i) q^{41} +(9.37262 + 1.09550i) q^{43} +(-0.0144321 + 0.00525286i) q^{44} +(-3.93001 - 1.43041i) q^{46} +(-3.90796 - 1.96265i) q^{47} +(-5.60313 + 0.654911i) q^{49} +(-13.9407 + 7.00129i) q^{50} +(-0.0321115 + 0.00761057i) q^{52} +(-2.32646 + 4.02955i) q^{53} +(-0.328016 - 0.568141i) q^{55} +(7.05439 + 7.47721i) q^{56} +(0.570547 - 9.79591i) q^{58} +(-3.02485 - 4.06308i) q^{59} +(7.71017 - 5.07106i) q^{61} +(0.207411 + 1.17629i) q^{62} +(1.44849 - 8.21478i) q^{64} +(-0.558332 - 1.29436i) q^{65} +(-12.6466 - 2.99731i) q^{67} +(0.144965 - 0.153654i) q^{68} +(-11.8331 + 15.8945i) q^{70} +(1.23797 + 1.03878i) q^{71} +(-8.94621 + 7.50676i) q^{73} +(-0.361531 - 6.20725i) q^{74} +(0.0464569 - 0.107699i) q^{76} +(-0.482671 - 0.317458i) q^{77} +(2.06871 - 6.90998i) q^{79} +15.3506 q^{80} +9.75795 q^{82} +(-0.659082 + 2.20149i) q^{83} +(7.53888 + 4.95840i) q^{85} +(5.15932 - 11.9606i) q^{86} +(0.0273158 + 0.468994i) q^{88} +(-8.92827 + 7.49171i) q^{89} +(-0.950932 - 0.797927i) q^{91} +(0.171011 - 0.229707i) q^{92} +(-4.14257 + 4.39087i) q^{94} +(4.87508 + 1.15541i) q^{95} +(-1.66422 - 3.85810i) q^{97} +(-1.35223 + 7.66885i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{16}{27}\right)$

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 $

$2$	0.395901	−	1.32240i	0.279944	−	0.935078i	−0.696181	−	0.717867i	$-0.745119\pi$
$2$	0.395901	−	1.32240i	0.279944	−	0.935078i	0.976125	−	0.217211i	$-0.0696961\pi$
$3$		0			0
$3$		0			0
$4$	0.0789711	+	0.0519401i	0.0394856	+	0.0259701i
$5$	−1.59916	+	3.70727i	−0.715167	+	1.65794i	0.0372929	+	0.999304i	$0.488127\pi$
$5$	−1.59916	+	3.70727i	−0.715167	+	1.65794i	−0.752460	+	0.658638i	$0.771133\pi$
$6$		0			0
$7$	0.206731	+	3.54944i	0.0781371	+	1.34156i	0.778441	+	0.627718i	$0.216011\pi$
$7$	0.206731	+	3.54944i	0.0781371	+	1.34156i	−0.700304	+	0.713845i	$0.746952\pi$
$8$	2.21483	−	1.85846i	0.783061	−	0.657066i
$9$		0			0
$10$	4.26939	+	3.58244i	1.35010	+	1.13287i
$11$	−0.0970299	+	0.130334i	−0.0292556	+	0.0392971i	−0.816510	−	0.577331i	$-0.804094\pi$
$11$	−0.0970299	+	0.130334i	−0.0292556	+	0.0392971i	0.787255	+	0.616628i	$0.211502\pi$
$12$		0			0
$13$	−0.239595	+	0.253956i	−0.0664516	+	0.0704346i	−0.759746	−	0.650220i	$-0.774677\pi$
$13$	−0.239595	+	0.253956i	−0.0664516	+	0.0704346i	0.693295	+	0.720654i	$0.256158\pi$
$14$	4.77563	+	1.13184i	1.27634	+	0.302498i
$15$		0			0
$16$	−1.50590	−	3.49108i	−0.376476	−	0.872770i
$17$	0.388085	−	2.20094i	0.0941245	−	0.533807i	−0.900888	−	0.434053i	$-0.857083\pi$
$17$	0.388085	−	2.20094i	0.0941245	−	0.533807i	0.995012	−	0.0997542i	$-0.0318057\pi$
$18$		0			0
$19$	−0.215481	−	1.22205i	−0.0494348	−	0.280358i	0.950063	−	0.312059i	$-0.101019\pi$
$19$	−0.215481	−	1.22205i	−0.0494348	−	0.280358i	−0.999497	+	0.0317008i	$0.989908\pi$
$20$	−0.318844	+	0.209707i	−0.0712956	+	0.0468919i
$21$		0			0
$22$	0.133939	+	0.179912i	0.0285559	+	0.0383573i
$23$	0.176164	−	3.02462i	0.0367327	−	0.630676i	−0.928830	−	0.370506i	$-0.879184\pi$
$23$	0.176164	−	3.02462i	0.0367327	−	0.630676i	0.965563	−	0.260170i	$-0.0837787\pi$
$24$		0			0
$25$	−7.75535	−	8.22019i	−1.55107	−	1.64404i
$26$	0.240975	+	0.417381i	0.0472591	+	0.0818552i
$27$		0			0
$28$	−0.168033	+	0.291041i	−0.0317552	+	0.0550016i
$29$	6.91689	−	1.63933i	1.28443	−	0.304417i	0.468965	−	0.883217i	$-0.344627\pi$
$29$	6.91689	−	1.63933i	1.28443	−	0.304417i	0.815469	+	0.578800i	$0.196479\pi$
$30$		0			0
$31$	−0.773247	+	0.388339i	−0.138879	+	0.0697478i	−0.516882	−	0.856057i	$-0.672907\pi$
$31$	−0.773247	+	0.388339i	−0.138879	+	0.0697478i	0.378003	+	0.925805i	$0.376611\pi$
$32$	0.530624	−	0.0620210i	0.0938019	−	0.0109639i
$33$		0			0
$34$	−2.75688	−	1.38456i	−0.472801	−	0.237450i
$35$	−13.4893	−	4.90972i	−2.28012	−	0.829894i
$36$		0			0
$37$	4.23271	−	1.54058i	0.695853	−	0.253270i	0.0302136	−	0.999543i	$-0.490381\pi$
$37$	4.23271	−	1.54058i	0.695853	−	0.253270i	0.665639	+	0.746274i	$0.268159\pi$
$38$	−1.70135	−	0.198860i	−0.275996	−	0.0322593i
$39$		0			0
$40$	3.34796	+	11.1830i	0.529359	+	1.76818i
$41$	2.02741	+	6.77201i	0.316628	+	1.05761i	0.957131	+	0.289655i	$0.0935405\pi$
$41$	2.02741	+	6.77201i	0.316628	+	1.05761i	−0.640504	+	0.767955i	$0.721274\pi$
$42$		0			0
$43$	9.37262	+	1.09550i	1.42931	+	0.167063i	0.795279	−	0.606244i	$-0.207324\pi$
$43$	9.37262	+	1.09550i	1.42931	+	0.167063i	0.634033	+	0.773306i	$0.281398\pi$
$44$	−0.0144321	+	0.00525286i	−0.00217572	+	0.000791898i
$45$		0			0
$46$	−3.93001	−	1.43041i	−0.579448	−	0.210902i
$47$	−3.90796	−	1.96265i	−0.570034	−	0.286282i	0.140343	−	0.990103i	$-0.455179\pi$
$47$	−3.90796	−	1.96265i	−0.570034	−	0.286282i	−0.710377	+	0.703821i	$0.751476\pi$
$48$		0			0
$49$	−5.60313	+	0.654911i	−0.800447	+	0.0935588i
$50$	−13.9407	+	7.00129i	−1.97152	+	0.990132i
$51$		0			0
$52$	−0.0321115	+	0.00761057i	−0.00445307	+	0.00105540i
$53$	−2.32646	+	4.02955i	−0.319564	+	0.553502i	−0.980397	−	0.197031i	$-0.936870\pi$
$53$	−2.32646	+	4.02955i	−0.319564	+	0.553502i	0.660833	+	0.750533i	$0.270203\pi$
$54$		0			0
$55$	−0.328016	−	0.568141i	−0.0442297	−	0.0766081i
$56$	7.05439	+	7.47721i	0.942682	+	0.999185i
$57$		0			0
$58$	0.570547	−	9.79591i	0.0749165	−	1.28627i
$59$	−3.02485	−	4.06308i	−0.393802	−	0.528968i	0.560364	−	0.828247i	$-0.310661\pi$
$59$	−3.02485	−	4.06308i	−0.393802	−	0.528968i	−0.954166	+	0.299279i	$0.903254\pi$
$60$		0			0
$61$	7.71017	−	5.07106i	0.987186	−	0.649282i	0.0502327	−	0.998738i	$-0.484004\pi$
$61$	7.71017	−	5.07106i	0.987186	−	0.649282i	0.936953	+	0.349455i	$0.113633\pi$
$62$	0.207411	+	1.17629i	0.0263412	+	0.149388i
$63$		0			0
$64$	1.44849	−	8.21478i	0.181061	−	1.02685i
$65$	−0.558332	−	1.29436i	−0.0692526	−	0.160545i
$66$		0			0
$67$	−12.6466	−	2.99731i	−1.54503	−	0.366179i	−0.632295	−	0.774728i	$-0.717887\pi$
$67$	−12.6466	−	2.99731i	−1.54503	−	0.366179i	−0.912737	+	0.408548i	$0.866035\pi$
$68$	0.144965	−	0.153654i	0.0175795	−	0.0186332i
$69$		0			0
$70$	−11.8331	+	15.8945i	−1.41432	+	1.89976i
$71$	1.23797	+	1.03878i	0.146921	+	0.123281i	0.713286	−	0.700874i	$-0.247206\pi$
$71$	1.23797	+	1.03878i	0.146921	+	0.123281i	−0.566365	+	0.824155i	$0.691651\pi$
$72$		0			0
$73$	−8.94621	+	7.50676i	−1.04707	+	0.878600i	−0.992783	−	0.119925i	$-0.961734\pi$
$73$	−8.94621	+	7.50676i	−1.04707	+	0.878600i	−0.0542914	+	0.998525i	$0.517290\pi$
$74$	−0.361531	−	6.20725i	−0.0420271	−	0.721578i
$75$		0			0
$76$	0.0464569	−	0.107699i	0.00532897	−	0.0123539i
$77$	−0.482671	−	0.317458i	−0.0550055	−	0.0361777i
$78$		0			0
$79$	2.06871	−	6.90998i	0.232748	−	0.777434i	−0.759207	−	0.650849i	$-0.774413\pi$
$79$	2.06871	−	6.90998i	0.232748	−	0.777434i	0.991956	−	0.126585i	$-0.0404017\pi$
$80$	15.3506			1.71625
$81$		0			0
$82$	9.75795			1.07759
$83$	−0.659082	+	2.20149i	−0.0723437	+	0.241645i	−0.986512	−	0.163691i	$-0.947660\pi$
$83$	−0.659082	+	2.20149i	−0.0723437	+	0.241645i	0.914168	+	0.405335i	$0.132845\pi$
$84$		0			0
$85$	7.53888	+	4.95840i	0.817706	+	0.537814i
$86$	5.15932	−	11.9606i	0.556344	−	1.28975i
$87$		0			0
$88$	0.0273158	+	0.468994i	0.00291187	+	0.0499949i
$89$	−8.92827	+	7.49171i	−0.946395	+	0.794119i	−0.978687	−	0.205359i	$-0.934164\pi$
$89$	−8.92827	+	7.49171i	−0.946395	+	0.794119i	0.0322920	+	0.999478i	$0.489719\pi$
$90$		0			0
$91$	−0.950932	−	0.797927i	−0.0996848	−	0.0836455i
$92$	0.171011	−	0.229707i	0.0178291	−	0.0239486i
$93$		0			0
$94$	−4.14257	+	4.39087i	−0.427273	+	0.452883i
$95$	4.87508	+	1.15541i	0.500172	+	0.118543i
$96$		0			0
$97$	−1.66422	−	3.85810i	−0.168976	−	0.391730i	0.812595	−	0.582829i	$-0.198054\pi$
$97$	−1.66422	−	3.85810i	−0.168976	−	0.391730i	−0.981571	+	0.191099i	$0.938795\pi$
$98$	−1.35223	+	7.66885i	−0.136595	+	0.774671i
$99$		0			0
$100$	−0.185491	−	1.05197i	−0.0185491	−	0.105197i
$101$	−1.39966	+	0.920574i	−0.139272	+	0.0916005i	−0.617233	−	0.786780i	$-0.711746\pi$
$101$	−1.39966	+	0.920574i	−0.139272	+	0.0916005i	0.477961	+	0.878381i	$0.341376\pi$
$102$		0			0
$103$	2.00543	+	2.69376i	0.197601	+	0.265424i	0.889869	−	0.456217i	$-0.150796\pi$
$103$	2.00543	+	2.69376i	0.197601	+	0.265424i	−0.692268	+	0.721641i	$0.743388\pi$
$104$	−0.0586946	+	1.00775i	−0.00575548	+	0.0988177i
$105$		0			0
$106$	4.40763	+	4.67182i	0.428107	+	0.453767i
$107$	−5.90368	−	10.2255i	−0.570730	−	0.988534i	−0.996491	−	0.0836983i	$-0.973327\pi$
$107$	−5.90368	−	10.2255i	−0.570730	−	0.988534i	0.425761	−	0.904836i	$-0.360007\pi$
$108$		0			0
$109$	5.03157	−	8.71493i	0.481937	−	0.834739i	−0.517848	−	0.855472i	$-0.673267\pi$
$109$	5.03157	−	8.71493i	0.481937	−	0.834739i	0.999785	+	0.0207336i	$0.00660019\pi$
$110$	−0.881172	+	0.208842i	−0.0840164	+	0.0199123i
$111$		0			0
$112$	12.0801	−	6.06684i	1.14146	−	0.573262i
$113$	3.87592	−	0.453029i	0.364615	−	0.0426174i	0.0681871	−	0.997673i	$-0.478279\pi$
$113$	3.87592	−	0.453029i	0.364615	−	0.0426174i	0.296428	+	0.955055i	$0.404204\pi$
$114$		0			0
$115$	10.9314	+	5.48994i	1.01935	+	0.511939i
$116$	0.631382	+	0.229804i	0.0586223	+	0.0213368i
$117$		0			0
$118$	−6.57056	+	2.39149i	−0.604869	+	0.220154i
$119$	7.89234	+	0.922482i	0.723490	+	0.0845638i
$120$		0			0
$121$	3.14726	+	10.5126i	0.286115	+	0.955690i
$122$	−3.65351	−	12.2036i	−0.330773	−	1.10486i
$123$		0			0
$124$	−0.0812345	−	0.00949496i	−0.00729508	−	0.000852672i
$125$	23.9066	−	8.70129i	2.13827	−	0.778267i
$126$		0			0
$127$	−8.01819	−	2.91838i	−0.711499	−	0.258965i	−0.0391867	−	0.999232i	$-0.512477\pi$
$127$	−8.01819	−	2.91838i	−0.711499	−	0.258965i	−0.672313	+	0.740267i	$0.734699\pi$
$128$	−9.33494	−	4.68818i	−0.825100	−	0.414381i
$129$		0			0
$130$	−1.93270	+	0.225901i	−0.169509	+	0.0198128i
$131$	14.4538	−	7.25896i	1.26283	−	0.634218i	0.313827	−	0.949480i	$-0.398389\pi$
$131$	14.4538	−	7.25896i	1.26283	−	0.634218i	0.949005	+	0.315262i	$0.102092\pi$
$132$		0			0
$133$	4.29306	−	1.01747i	0.372256	−	0.0882262i
$134$	−8.97045	+	15.5373i	−0.774929	+	1.34222i
$135$		0			0
$136$	−3.23083	−	5.59596i	−0.277041	−	0.479849i
$137$	−2.34600	−	2.48662i	−0.200432	−	0.212446i	0.619359	−	0.785108i	$-0.287392\pi$
$137$	−2.34600	−	2.48662i	−0.200432	−	0.212446i	−0.819792	+	0.572662i	$0.805911\pi$
$138$		0			0
$139$	0.655687	−	11.2577i	0.0556147	−	0.954867i	−0.848935	−	0.528498i	$-0.822755\pi$
$139$	0.655687	−	11.2577i	0.0556147	−	0.954867i	0.904549	−	0.426369i	$-0.140208\pi$
$140$	−0.810257	−	1.08836i	−0.0684792	−	0.0919835i
$141$		0			0
$142$	1.86380	−	1.22584i	0.156407	−	0.102870i
$143$	−0.00985114	−	0.0558686i	−0.000823793	−	0.00467196i
$144$		0			0
$145$	−4.98377	+	28.2644i	−0.413879	+	2.34723i
$146$	6.38513	+	14.8024i	0.528437	+	1.22505i
$147$		0			0
$148$	0.414279	+	0.0981860i	0.0340536	+	0.00807084i
$149$	−0.410178	+	0.434764i	−0.0336031	+	0.0356172i	−0.743957	−	0.668227i	$-0.767053\pi$
$149$	−0.410178	+	0.434764i	−0.0336031	+	0.0356172i	0.710354	+	0.703845i	$0.248535\pi$
$150$		0			0
$151$	1.00156	−	1.34533i	0.0815058	−	0.109481i	−0.759500	−	0.650507i	$-0.774556\pi$
$151$	1.00156	−	1.34533i	0.0815058	−	0.109481i	0.841006	+	0.541026i	$0.181964\pi$
$152$	−2.74840	−	2.30618i	−0.222925	−	0.187056i
$153$		0			0
$154$	−0.610896	+	0.512603i	−0.0492274	+	0.0413067i
$155$	−0.203133	−	3.48765i	−0.0163160	−	0.280135i
$156$		0			0
$157$	3.61313	−	8.37618i	0.288359	−	0.668492i	−0.711040	−	0.703152i	$-0.751776\pi$
$157$	3.61313	−	8.37618i	0.288359	−	0.668492i	0.999399	+	0.0346599i	$0.0110348\pi$
$158$	−8.31876	−	5.47133i	−0.661805	−	0.435276i
$159$		0			0
$160$	−0.618624	+	2.06635i	−0.0489065	+	0.163359i
$161$	10.7721			0.848962
$162$		0			0
$163$	−21.8751			−1.71339			−0.856697	−	0.515821i	$-0.827487\pi$
$163$	−21.8751			−1.71339			−0.856697	+	0.515821i	$0.827487\pi$
$164$	−0.191632	+	0.640097i	−0.0149640	+	0.0499831i
$165$		0			0
$166$	2.65032	+	1.74314i	0.205704	+	0.135294i
$167$	2.06311	−	4.78282i	0.159648	−	0.370106i	−0.819551	−	0.573006i	$-0.805777\pi$
$167$	2.06311	−	4.78282i	0.159648	−	0.370106i	0.979199	+	0.202900i	$0.0650366\pi$
$168$		0			0
$169$	0.748795	+	12.8563i	0.0575996	+	0.988947i
$170$	9.54163	−	8.00638i	0.731810	−	0.614061i
$171$		0			0
$172$	0.683266	+	0.573328i	0.0520985	+	0.0437159i
$173$	−12.4570	+	16.7326i	−0.947087	+	1.27216i	0.0151331	+	0.999885i	$0.495183\pi$
$173$	−12.4570	+	16.7326i	−0.947087	+	1.27216i	−0.962220	+	0.272273i	$0.912225\pi$
$174$		0			0
$175$	27.5738	−	29.2265i	2.08438	−	2.20932i
$176$	0.601123	+	0.142469i	0.0453114	+	0.0107390i
$177$		0			0
$178$	6.37233	+	14.7727i	0.477626	+	1.10726i
$179$	0.709018	−	4.02104i	0.0529945	−	0.300547i	−0.946778	−	0.321888i	$-0.895683\pi$
$179$	0.709018	−	4.02104i	0.0529945	−	0.300547i	0.999772	+	0.0213413i	$0.00679365\pi$
$180$		0			0
$181$	2.85517	+	16.1925i	0.212223	+	1.20358i	0.885661	+	0.464333i	$0.153706\pi$
$181$	2.85517	+	16.1925i	0.212223	+	1.20358i	−0.673437	+	0.739244i	$0.735183\pi$
$182$	−1.43165	+	0.941613i	−0.106121	+	0.0697970i
$183$		0			0
$184$	−5.23097	−	7.02641i	−0.385632	−	0.517994i
$185$	−1.05743	+	18.1554i	−0.0777441	+	1.33481i
$186$		0			0
$187$	0.249201	+	0.264138i	0.0182234	+	0.0193157i
$188$	−0.206675	−	0.357972i	−0.0150734	−	0.0261078i
$189$		0			0
$190$	3.45797	−	5.98937i	0.250867	−	0.434515i
$191$	0.00405677		0.000961473i	0.000293538		6.95698e-5i	−0.230469	−	0.973080i	$-0.574026\pi$
$191$	0.00405677		0.000961473i	0.000293538		6.95698e-5i	0.230763	+	0.973010i	$0.425878\pi$
$192$		0			0
$193$	−18.7551	+	9.41917i	−1.35002	+	0.678007i	−0.969116	−	0.246607i	$-0.920684\pi$
$193$	−18.7551	+	9.41917i	−1.35002	+	0.678007i	−0.380907	+	0.924613i	$0.624388\pi$
$194$	−5.76081	+	0.673342i	−0.413602	+	0.0483432i
$195$		0			0
$196$	−0.476501	−	0.239308i	−0.0340358	−	0.0170934i
$197$	9.14507	+	3.32853i	0.651559	+	0.237148i	0.646588	−	0.762839i	$-0.276195\pi$
$197$	9.14507	+	3.32853i	0.651559	+	0.237148i	0.00497138	+	0.999988i	$0.498418\pi$
$198$		0			0
$199$	22.6674	−	8.25026i	1.60685	−	0.584846i	0.626036	−	0.779794i	$-0.284676\pi$
$199$	22.6674	−	8.25026i	1.60685	−	0.584846i	0.980814	+	0.194948i	$0.0624539\pi$
$200$	−32.4537	−	3.79329i	−2.29482	−	0.268226i
$201$		0			0
$202$	0.663239	+	2.21537i	0.0466653	+	0.155873i
$203$	7.24866	+	24.2122i	0.508756	+	1.69936i
$204$		0			0
$205$	−28.3478	−	3.31339i	−1.97990	−	0.231417i
$206$	4.35618	−	1.58552i	0.303509	−	0.110468i
$207$		0			0
$208$	1.24739	+	0.454011i	0.0864907	+	0.0314800i
$209$	0.180183	+	0.0904913i	0.0124635	+	0.00625942i
$210$		0			0
$211$	−14.9458	+	1.74691i	−1.02891	+	0.120262i	−0.613762	−	0.789491i	$-0.710345\pi$
$211$	−14.9458	+	1.74691i	−1.02891	+	0.120262i	−0.415149	+	0.909753i	$0.636271\pi$
$212$	−0.393019	+	0.197382i	−0.0269926	+	0.0135562i
$213$		0			0
$214$	−15.8594	+	3.75876i	−1.08413	+	0.256943i
$215$	−19.0497	+	32.9950i	−1.29918	+	2.25024i
$216$		0			0
$217$	−1.53824	−	2.66431i	−0.104423	−	0.180865i
$218$	−9.53262	−	10.1040i	−0.645631	−	0.684329i
$219$		0			0
$220$	0.00360549	−	0.0619039i	0.000243082	−	0.00417356i
$221$	0.465958	+	0.625890i	0.0313437	+	0.0421019i
$222$		0			0
$223$	−7.95827	+	5.23424i	−0.532925	+	0.350511i	−0.787275	−	0.616602i	$-0.788509\pi$
$223$	−7.95827	+	5.23424i	−0.532925	+	0.350511i	0.254350	+	0.967112i	$0.418139\pi$
$224$	0.329837	+	1.87060i	0.0220381	+	0.124984i
$225$		0			0
$226$	0.935391	−	5.30486i	0.0622213	−	0.352874i
$227$	−4.85191	−	11.2480i	−0.322033	−	0.746556i	−0.999935	−	0.0114038i	$-0.996370\pi$
$227$	−4.85191	−	11.2480i	−0.322033	−	0.746556i	0.677902	−	0.735152i	$-0.262889\pi$
$228$		0			0
$229$	3.63295	+	0.861025i	0.240072	+	0.0568981i	0.348890	−	0.937164i	$-0.386559\pi$
$229$	3.63295	+	0.861025i	0.240072	+	0.0568981i	−0.108818	+	0.994062i	$0.534707\pi$
$230$	11.5876	−	12.2822i	0.764065	−	0.809862i
$231$		0			0
$232$	12.2731	−	16.4856i	0.805769	−	1.08234i
$233$	−15.7065	−	13.1793i	−1.02896	−	0.863404i	−0.0382373	−	0.999269i	$-0.512174\pi$
$233$	−15.7065	−	13.1793i	−1.02896	−	0.863404i	−0.990727	+	0.135865i	$0.956619\pi$
$234$		0			0
$235$	13.5255	−	11.3493i	0.882308	−	0.740344i
$236$	−0.0278390	−	0.477977i	−0.00181216	−	0.0311136i
$237$		0			0
$238$	4.34447	−	10.0716i	0.281610	−	0.652846i
$239$	−10.8213	−	7.11728i	−0.699972	−	0.460379i	0.148986	−	0.988839i	$-0.452399\pi$
$239$	−10.8213	−	7.11728i	−0.699972	−	0.460379i	−0.848958	+	0.528461i	$0.822769\pi$
$240$		0			0
$241$	−3.47782	+	11.6167i	−0.224026	+	0.748299i	0.769892	+	0.638174i	$0.220310\pi$
$241$	−3.47782	+	11.6167i	−0.224026	+	0.748299i	−0.993918	+	0.110124i	$0.964875\pi$
$242$	15.1479			0.973741
$243$		0			0
$244$	0.872272			0.0558415
$245$	6.53237	−	21.8196i	0.417338	−	1.39400i
$246$		0			0
$247$	0.361976	+	0.238075i	0.0230320	+	0.0151484i
$248$	−0.990897	+	2.29716i	−0.0629220	+	0.145870i
$249$		0			0
$250$	−2.04195	−	35.0589i	−0.129144	−	2.21732i
$251$	21.7457	−	18.2468i	1.37257	−	1.15173i	0.400705	−	0.916207i	$-0.368765\pi$
$251$	21.7457	−	18.2468i	1.37257	−	1.15173i	0.971869	−	0.235520i	$-0.0756794\pi$
$252$		0			0
$253$	0.377117	+	0.316438i	0.0237091	+	0.0198943i
$254$	−7.03368	+	9.44787i	−0.441332	+	0.592812i
$255$		0			0
$256$	1.55321	−	1.64631i	0.0970756	−	0.102894i
$257$	−26.7471	−	6.33917i	−1.66844	−	0.395426i	−0.715503	−	0.698610i	$-0.753802\pi$
$257$	−26.7471	−	6.33917i	−1.66844	−	0.395426i	−0.952932	+	0.303183i	$0.901951\pi$
$258$		0			0
$259$	6.34323	+	14.7053i	0.394149	+	0.913740i
$260$	0.0231371	−	0.131217i	0.00143490	−	0.00813772i
$261$		0			0
$262$	−3.87699	−	21.9875i	−0.239521	−	1.35839i
$263$	3.87982	−	2.55179i	0.239240	−	0.157350i	−0.424228	−	0.905555i	$-0.639454\pi$
$263$	3.87982	−	2.55179i	0.239240	−	0.157350i	0.663468	+	0.748205i	$0.269084\pi$
$264$		0			0
$265$	−11.2183	−	15.0687i	−0.689132	−	0.925666i
$266$	0.354118	−	6.07997i	0.0217123	−	0.372787i
$267$		0			0
$268$	−0.843038	−	0.893568i	−0.0514967	−	0.0545834i
$269$	−2.50768	−	4.34343i	−0.152896	−	0.264824i	0.779395	−	0.626533i	$-0.215527\pi$
$269$	−2.50768	−	4.34343i	−0.152896	−	0.264824i	−0.932291	+	0.361709i	$0.882193\pi$
$270$		0			0
$271$	−8.04356	+	13.9319i	−0.488612	+	0.846300i	−0.999914	−	0.0131007i	$-0.995830\pi$
$271$	−8.04356	+	13.9319i	−0.488612	+	0.846300i	0.511303	+	0.859401i	$0.329163\pi$
$272$	−8.26808	+	1.95957i	−0.501326	+	0.118816i
$273$		0			0
$274$	−4.21708	+	2.11790i	−0.254763	+	0.127947i
$275$	1.82387	−	0.213180i	0.109983	−	0.0128552i
$276$		0			0
$277$	8.79442	+	4.41672i	0.528405	+	0.265375i	0.692939	−	0.720996i	$-0.256316\pi$
$277$	8.79442	+	4.41672i	0.528405	+	0.265375i	−0.164534	+	0.986371i	$0.552612\pi$
$278$	−14.6276	−	5.32402i	−0.877306	−	0.319313i
$279$		0			0
$280$	−39.0012	+	14.1953i	−2.33077	+	0.848329i
$281$	21.5953	+	2.52413i	1.28827	+	0.150577i	0.732503	−	0.680763i	$-0.238352\pi$
$281$	21.5953	+	2.52413i	1.28827	+	0.150577i	0.555764	+	0.831340i	$0.312426\pi$
$282$		0			0
$283$	1.37756	+	4.60137i	0.0818874	+	0.273523i	0.989121	−	0.147104i	$-0.0469953\pi$
$283$	1.37756	+	4.60137i	0.0818874	+	0.273523i	−0.907234	+	0.420627i	$0.861810\pi$
$284$	0.0438097	+	0.146334i	0.00259963	+	0.00868335i
$285$		0			0
$286$	−0.0777807	−	0.00909126i	−0.00459927	−	0.000537577i
$287$	−23.6177	+	8.59614i	−1.39411	+	0.507414i
$288$		0			0
$289$	11.2812	+	4.10604i	0.663602	+	0.241532i
$290$	35.4037	+	17.7804i	2.07898	+	1.04410i
$291$		0			0
$292$	−1.09639	+	0.128150i	−0.0641616	+	0.00749941i
$293$	5.04906	−	2.53574i	0.294969	−	0.148139i	−0.295160	−	0.955448i	$-0.595373\pi$
$293$	5.04906	−	2.53574i	0.294969	−	0.148139i	0.590130	+	0.807309i	$0.299077\pi$
$294$		0			0
$295$	19.9002	−	4.71643i	1.15863	−	0.274601i
$296$	6.51162	−	11.2785i	0.378480	−	0.655547i
$297$		0			0
$298$	0.412542	+	0.714543i	0.0238979	+	0.0413924i
$299$	0.725910	+	0.769420i	0.0419805	+	0.0444967i
$300$		0			0
$301$	−1.95081	+	33.4941i	−0.112443	+	1.93057i
$302$	−1.38254	−	1.85708i	−0.0795565	−	0.106863i
$303$		0			0
$304$	−3.94179	+	2.59256i	−0.226077	+	0.148693i
$305$	6.46999	+	36.6931i	0.370470	+	2.10104i
$306$		0			0
$307$	1.38619	−	7.86146i	0.0791139	−	0.448677i	−0.919358	−	0.393421i	$-0.871291\pi$
$307$	1.38619	−	7.86146i	0.0791139	−	0.448677i	0.998472	−	0.0552559i	$-0.0175975\pi$
$308$	−0.0216283	−	0.0501400i	−0.00123239	−	0.00285699i
$309$		0			0
$310$	−4.69249	−	1.11214i	−0.266516	−	0.0631654i
$311$	−14.1673	+	15.0165i	−0.803354	+	0.851506i	−0.991429	−	0.130649i	$-0.958294\pi$
$311$	−14.1673	+	15.0165i	−0.803354	+	0.851506i	0.188074	+	0.982155i	$0.439775\pi$
$312$		0			0
$313$	11.6045	−	15.5876i	0.655928	−	0.881064i	−0.342359	−	0.939569i	$-0.611226\pi$
$313$	11.6045	−	15.5876i	0.655928	−	0.881064i	0.998287	+	0.0585052i	$0.0186334\pi$
$314$	−9.64622	−	8.09414i	−0.544367	−	0.456779i
$315$		0			0
$316$	0.522274	−	0.438240i	0.0293802	−	0.0246529i
$317$	1.69124	+	29.0374i	0.0949894	+	1.63090i	0.623391	+	0.781910i	$0.285754\pi$
$317$	1.69124	+	29.0374i	0.0949894	+	1.63090i	−0.528402	+	0.848994i	$0.677209\pi$
$318$		0			0
$319$	−0.457485	+	1.06057i	−0.0256142	+	0.0593805i
$320$	28.1381	+	18.5067i	1.57296	+	1.03456i
$321$		0			0
$322$	4.26469	−	14.2450i	0.237662	−	0.793845i
$323$	−2.77330			−0.154310
$324$		0			0
$325$	3.94570			0.218868
$326$	−8.66038	+	28.9277i	−0.479654	+	1.60216i
$327$		0			0
$328$	17.0759	+	11.2310i	0.942859	+	0.620128i
$329$	6.15841	−	14.2768i	0.339524	−	0.787106i
$330$		0			0
$331$	−0.178574	−	3.06600i	−0.00981533	−	0.168523i	−0.999653	−	0.0263240i	$-0.991620\pi$
$331$	−0.178574	−	3.06600i	−0.00981533	−	0.168523i	0.989838	−	0.142199i	$-0.0454172\pi$
$332$	−0.166394	+	0.139621i	−0.00913206	+	0.00766271i
$333$		0			0
$334$	−5.50801	−	4.62177i	−0.301385	−	0.252892i
$335$	31.3358	−	42.0913i	1.71206	−	2.29970i
$336$		0			0
$337$	−19.0790	+	20.2226i	−1.03930	+	1.10159i	−0.0445753	+	0.999006i	$0.514193\pi$
$337$	−19.0790	+	20.2226i	−1.03930	+	1.10159i	−0.994724	+	0.102587i	$0.967288\pi$
$338$	17.2976	+	4.09962i	0.940867	+	0.222990i
$339$		0			0
$340$	0.337814	+	0.783140i	0.0183205	+	0.0424718i
$341$	0.0244144	−	0.138461i	0.00132211	−	0.00749807i
$342$		0			0
$343$	0.838878	+	4.75751i	0.0452951	+	0.256882i
$344$	22.7947	−	14.9923i	1.22901	−	0.808333i
$345$		0			0
$346$	17.1955	+	23.0976i	0.924436	+	1.24173i
$347$	−0.203769	+	3.49857i	−0.0109389	+	0.187813i	0.988412	+	0.151794i	$0.0485049\pi$
$347$	−0.203769	+	3.49857i	−0.0109389	+	0.187813i	−0.999351	+	0.0360195i	$0.988532\pi$
$348$		0			0
$349$	7.85075	+	8.32131i	0.420241	+	0.445430i	0.902559	−	0.430567i	$-0.141686\pi$
$349$	7.85075	+	8.32131i	0.420241	+	0.445430i	−0.482318	+	0.875996i	$0.660205\pi$
$350$	−27.7327	−	48.0344i	−1.48237	−	2.56755i
$351$		0			0
$352$	−0.0434029	+	0.0751761i	−0.00231338	+	0.00400690i
$353$	1.78513	−	0.423083i	0.0950127	−	0.0225184i	−0.182835	−	0.983144i	$-0.558527\pi$
$353$	1.78513	−	0.423083i	0.0950127	−	0.0225184i	0.277847	+	0.960625i	$0.410379\pi$
$354$		0			0
$355$	−5.83078	+	2.92833i	−0.309466	+	0.155419i
$356$	−1.09420	+	0.127893i	−0.0579922	+	0.00677832i
$357$		0			0
$358$	−5.03672	−	2.52954i	−0.266199	−	0.133690i
$359$	−18.9025	−	6.87995i	−0.997636	−	0.363110i	−0.208964	−	0.977923i	$-0.567009\pi$
$359$	−18.9025	−	6.87995i	−0.997636	−	0.363110i	−0.788673	+	0.614814i	$0.789231\pi$
$360$		0			0
$361$	16.4072	−	5.97172i	0.863536	−	0.314301i
$362$	22.5433	+	2.63493i	1.18485	+	0.138489i
$363$		0			0
$364$	−0.0336518	−	0.112405i	−0.00176383	−	0.00589161i
$365$	−13.5232	−	45.1705i	−0.707835	−	2.36433i
$366$		0			0
$367$	−26.2319	−	3.06607i	−1.36929	−	0.160048i	−0.600542	−	0.799594i	$-0.705048\pi$
$367$	−26.2319	−	3.06607i	−1.36929	−	0.160048i	−0.768753	+	0.639546i	$0.779122\pi$
$368$	−10.8245	+	3.93978i	−0.564264	+	0.205375i
$369$		0			0
$370$	23.5901	+	8.58610i	1.22639	+	0.446370i
$371$	−14.7836	−	7.42461i	−0.767527	−	0.385467i
$372$		0			0
$373$	29.4383	−	3.44084i	1.52426	−	0.178160i	0.687682	−	0.726012i	$-0.258628\pi$
$373$	29.4383	−	3.44084i	1.52426	−	0.178160i	0.836575	+	0.547852i	$0.184554\pi$
$374$	0.447955	−	0.224971i	0.0231632	−	0.0116330i
$375$		0			0
$376$	−12.3030	+	2.91586i	−0.634478	+	0.150374i
$377$	−1.24093	+	2.14936i	−0.0639113	+	0.110698i
$378$		0			0
$379$	5.75292	+	9.96436i	0.295508	+	0.511835i	0.975103	−	0.221753i	$-0.0711778\pi$
$379$	5.75292	+	9.96436i	0.295508	+	0.511835i	−0.679595	+	0.733587i	$0.737844\pi$
$380$	0.324978	+	0.344456i	0.0166710	+	0.0176702i
$381$		0			0
$382$	0.000334627	−	0.00574533i	1.71210e−5	−	0.000293956i
$383$	17.1767	+	23.0723i	0.877689	+	1.17894i	0.982835	+	0.184485i	$0.0590616\pi$
$383$	17.1767	+	23.0723i	0.877689	+	1.17894i	−0.105146	+	0.994457i	$0.533531\pi$
$384$		0			0
$385$	1.94877	−	1.28173i	0.0993186	−	0.0653229i
$386$	5.03075	+	28.5308i	0.256059	+	1.45218i
$387$		0			0
$388$	0.0689646	−	0.391118i	0.00350115	−	0.0198560i
$389$	4.53722	+	10.5185i	0.230046	+	0.533307i	0.993668	−	0.112357i	$-0.0358400\pi$
$389$	4.53722	+	10.5185i	0.230046	+	0.533307i	−0.763622	+	0.645664i	$0.776581\pi$
$390$		0			0
$391$	−6.58864	−	1.56154i	−0.333202	−	0.0789703i
$392$	−11.1929	+	11.8637i	−0.565324	+	0.599209i
$393$		0			0
$394$	8.02219	−	10.7757i	0.404152	−	0.542871i
$395$	22.3090	+	18.7195i	1.12249	+	0.941878i
$396$		0			0
$397$	8.38197	−	7.03331i	0.420679	−	0.352992i	−0.407742	−	0.913097i	$-0.633684\pi$
$397$	8.38197	−	7.03331i	0.420679	−	0.352992i	0.828421	+	0.560105i	$0.189239\pi$
$398$	−1.93611	−	33.2417i	−0.0970482	−	1.66625i
$399$		0			0
$400$	−17.0185	+	39.4533i	−0.850926	+	1.97267i
$401$	0.290388	+	0.190991i	0.0145013	+	0.00953765i	0.556739	−	0.830688i	$-0.312052\pi$
$401$	0.290388	+	0.190991i	0.0145013	+	0.00953765i	−0.542238	+	0.840225i	$0.682423\pi$
$402$		0			0
$403$	0.0866450	−	0.289414i	0.00431609	−	0.0144168i
$404$	−0.158348			−0.00787810
$405$		0			0
$406$	34.8880			1.73146
$407$	−0.209910	+	0.701147i	−0.0104048	+	0.0347546i
$408$		0			0
$409$	−22.2252	−	14.6178i	−1.09897	−	0.722802i	−0.135539	−	0.990772i	$-0.543277\pi$
$409$	−22.2252	−	14.6178i	−1.09897	−	0.722802i	−0.963427	+	0.267970i	$0.913647\pi$
$410$	−15.6045	+	36.1754i	−0.770653	+	1.78658i
$411$		0			0
$412$	0.0184568	+	0.316891i	0.000909303	+	0.0156121i
$413$	13.7963	−	11.5765i	0.678873	−	0.569642i
$414$		0			0
$415$	−7.10754	−	5.96393i	−0.348895	−	0.292758i
$416$	−0.111384	+	0.149615i	−0.00546105	+	0.00733547i
$417$		0			0
$418$	0.191000	−	0.202449i	0.00934213	−	0.00990208i
$419$	−12.4465	−	2.94986i	−0.608049	−	0.144110i	−0.0849545	−	0.996385i	$-0.527074\pi$
$419$	−12.4465	−	2.94986i	−0.608049	−	0.144110i	−0.523095	+	0.852275i	$0.675223\pi$
$420$		0			0
$421$	−4.30731	−	9.98546i	−0.209925	−	0.486662i	0.780425	−	0.625250i	$-0.215003\pi$
$421$	−4.30731	−	9.98546i	−0.209925	−	0.486662i	−0.990350	+	0.138588i	$0.955744\pi$
$422$	−3.60693	+	20.4559i	−0.175583	+	0.995779i
$423$		0			0
$424$	2.33606	+	13.2484i	0.113449	+	0.643401i
$425$	−21.1019	+	13.8789i	−1.02359	+	0.673227i
$426$		0			0
$427$	19.5934	+	26.3184i	0.948189	+	1.27364i
$428$	0.0648921	−	1.11416i	0.00313668	−	0.0538547i
$429$		0			0
$430$	36.0908	+	38.2540i	1.74045	+	1.84477i
$431$	−1.22970	−	2.12989i	−0.0592323	−	0.102593i	0.834889	−	0.550419i	$-0.185532\pi$
$431$	−1.22970	−	2.12989i	−0.0592323	−	0.102593i	−0.894121	+	0.447825i	$0.852199\pi$
$432$		0			0
$433$	6.44336	−	11.1602i	0.309648	−	0.536326i	−0.668637	−	0.743589i	$-0.733122\pi$
$433$	6.44336	−	11.1602i	0.309648	−	0.536326i	0.978285	+	0.207263i	$0.0664554\pi$
$434$	−4.13228	+	0.979368i	−0.198356	+	0.0470112i
$435$		0			0
$436$	0.850003	−	0.426887i	0.0407077	−	0.0204442i
$437$	−3.73421	+	0.436466i	−0.178631	+	0.0208790i
$438$		0			0
$439$	−24.6343	−	12.3718i	−1.17573	−	0.590473i	−0.249847	−	0.968285i	$-0.580380\pi$
$439$	−24.6343	−	12.3718i	−1.17573	−	0.590473i	−0.925882	+	0.377812i	$0.876677\pi$
$440$	−1.78237	−	0.648730i	−0.0849712	−	0.0309270i
$441$		0			0
$442$	1.01215	−	0.368393i	0.0481431	−	0.0175227i
$443$	5.69485	+	0.665633i	0.270571	+	0.0316252i	0.250296	−	0.968169i	$-0.419472\pi$
$443$	5.69485	+	0.665633i	0.270571	+	0.0316252i	0.0202743	+	0.999794i	$0.493546\pi$
$444$		0			0
$445$	−13.4961	−	45.0800i	−0.639775	−	2.13700i
$446$	3.77107	+	12.5963i	0.178565	+	0.596450i
$447$		0			0
$448$	29.4573	+	3.44307i	1.39173	+	0.162670i
$449$	32.3537	−	11.7758i	1.52687	−	0.555734i	0.564015	−	0.825764i	$-0.309256\pi$
$449$	32.3537	−	11.7758i	1.52687	−	0.555734i	0.962852	+	0.270030i	$0.0870338\pi$
$450$		0			0
$451$	−1.07934	−	0.392848i	−0.0508242	−	0.0184985i
$452$	0.329616	+	0.165539i	0.0155038	+	0.00778631i
$453$		0			0
$454$	−16.7952	+	1.96308i	−0.788239	+	0.0921319i
$455$	4.47883	−	2.24935i	0.209971	−	0.105451i
$456$		0			0
$457$	−7.38263	+	1.74972i	−0.345345	+	0.0818483i	−0.399628	−	0.916677i	$-0.630861\pi$
$457$	−7.38263	+	1.74972i	−0.345345	+	0.0818483i	0.0542832	+	0.998526i	$0.482713\pi$
$458$	2.57691	−	4.46333i	0.120411	−	0.208558i
$459$		0			0
$460$	0.578114	+	1.00132i	0.0269547	+	0.0466869i
$461$	−1.26349	−	1.33922i	−0.0588467	−	0.0623738i	0.697281	−	0.716797i	$-0.254393\pi$
$461$	−1.26349	−	1.33922i	−0.0588467	−	0.0623738i	−0.756128	+	0.654424i	$0.772911\pi$
$462$		0			0
$463$	1.30847	−	22.4655i	0.0608096	−	1.04406i	−0.820538	−	0.571592i	$-0.806326\pi$
$463$	1.30847	−	22.4655i	0.0608096	−	1.04406i	0.881347	−	0.472469i	$-0.156637\pi$
$464$	−16.1392	−	21.6787i	−0.749245	−	1.00641i
$465$		0			0
$466$	−23.6465	+	15.5525i	−1.09540	+	0.720458i
$467$	−6.84563	−	38.8235i	−0.316778	−	1.79654i	−0.562071	−	0.827089i	$-0.689995\pi$
$467$	−6.84563	−	38.8235i	−0.316778	−	1.79654i	0.245292	−	0.969449i	$-0.421116\pi$
$468$		0			0
$469$	8.02431	−	45.5081i	0.370528	−	2.10137i
$470$	−9.65350	−	22.3793i	−0.445283	−	1.03228i
$471$		0			0
$472$	−14.2506	−	3.37746i	−0.655938	−	0.155460i
$473$	−1.05221	+	1.11527i	−0.0483805	+	0.0512803i
$474$		0			0
$475$	−8.37438	+	11.2487i	−0.384243	+	0.516128i
$476$	0.575353	+	0.482779i	0.0263713	+	0.0221281i
$477$		0			0
$478$	−13.6960	+	11.4923i	−0.626443	+	0.525648i
$479$	−0.153461	−	2.63482i	−0.00701182	−	0.120388i	−0.999998	−	0.00215507i	$-0.999314\pi$
$479$	−0.153461	−	2.63482i	−0.00701182	−	0.120388i	0.992986	−	0.118233i	$-0.0377230\pi$
$480$		0			0
$481$	−0.622896	+	1.44403i	−0.0284016	+	0.0658423i
$482$	13.9851	+	9.19813i	0.637003	+	0.418963i
$483$		0			0
$484$	−0.297482	+	0.993660i	−0.0135219	+	0.0451664i
$485$	16.9644			0.770312
$486$		0			0
$487$	−25.0040			−1.13304			−0.566519	−	0.824048i	$-0.691710\pi$
$487$	−25.0040			−1.13304			−0.566519	+	0.824048i	$0.691710\pi$
$488$	7.65234	−	25.5606i	0.346405	−	1.15707i
$489$		0			0
$490$	−26.2681	−	17.2768i	−1.18667	−	0.780486i
$491$	−11.9246	+	27.6444i	−0.538151	+	1.24757i	0.404727	+	0.914437i	$0.367366\pi$
$491$	−11.9246	+	27.6444i	−0.538151	+	1.24757i	−0.942878	+	0.333137i	$0.891893\pi$
$492$		0			0
$493$	−0.923732	−	15.8599i	−0.0416028	−	0.714293i
$494$	0.458137	−	0.384423i	0.0206126	−	0.0172960i
$495$		0			0
$496$	2.52016	+	2.11466i	0.113158	+	0.0949512i
$497$	−3.43118	+	4.60887i	−0.153909	+	0.206736i
$498$		0			0
$499$	3.86891	−	4.10081i	0.173196	−	0.183577i	−0.634961	−	0.772544i	$-0.718984\pi$
$499$	3.86891	−	4.10081i	0.173196	−	0.183577i	0.808157	+	0.588967i	$0.200465\pi$
$500$	2.33988	+	0.554561i	0.104642	+	0.0248007i
$501$		0			0
$502$	−15.5204	−	35.9804i	−0.692711	−	1.60588i
$503$	−2.01083	+	11.4040i	−0.0896587	+	0.508479i	0.906595	+	0.422002i	$0.138672\pi$
$503$	−2.01083	+	11.4040i	−0.0896587	+	0.508479i	−0.996254	+	0.0864779i	$0.972439\pi$
$504$		0			0
$505$	−1.17453	−	6.66108i	−0.0522659	−	0.296414i
$506$	0.567759	−	0.373421i	0.0252400	−	0.0166006i
$507$		0			0
$508$	−0.481624	−	0.646934i	−0.0213686	−	0.0287030i
$509$	2.08525	−	35.8024i	0.0924273	−	1.58691i	−0.559628	−	0.828744i	$-0.689056\pi$
$509$	2.08525	−	35.8024i	0.0924273	−	1.58691i	0.652056	−	0.758171i	$-0.273907\pi$
$510$		0			0
$511$	−28.4943	−	30.2022i	−1.26051	−	1.33606i
$512$	−12.0082	−	20.7988i	−0.530693	−	0.919188i
$513$		0			0
$514$	−18.9721	+	32.8606i	−0.836823	+	1.44942i
$515$	−13.1935	+	3.12692i	−0.581375	+	0.137789i
$516$		0			0
$517$	0.634988	−	0.318903i	0.0279267	−	0.0140253i
$518$	21.9575	−	2.56647i	0.964758	−	0.112764i
$519$		0			0
$520$	−3.64213	−	1.82915i	−0.159718	−	0.0802134i
$521$	−8.36834	−	3.04583i	−0.366624	−	0.133440i	0.152137	−	0.988359i	$-0.451384\pi$
$521$	−8.36834	−	3.04583i	−0.366624	−	0.133440i	−0.518761	+	0.854919i	$0.673607\pi$
$522$		0			0
$523$	−15.1809	+	5.52540i	−0.663815	+	0.241609i	−0.651883	−	0.758320i	$-0.726021\pi$
$523$	−15.1809	+	5.52540i	−0.663815	+	0.241609i	−0.0119324	+	0.999929i	$0.503798\pi$
$524$	1.51846	+	0.177483i	0.0663343	+	0.00775337i
$525$		0			0
$526$	−1.83847	−	6.14093i	−0.0801612	−	0.267757i
$527$	0.554626	+	1.85258i	0.0241599	+	0.0806997i
$528$		0			0
$529$	13.7272	+	1.60448i	0.596835	+	0.0697600i
$530$	−24.3682	+	8.86931i	−1.05849	+	0.385258i
$531$		0			0
$532$	0.391876	+	0.142631i	0.0169900	+	0.00618384i
$533$	−2.20554	−	1.10767i	−0.0955327	−	0.0479783i
$534$		0			0
$535$	47.3496	−	5.53437i	2.04710	−	0.239272i
$536$	−33.5805	+	16.8648i	−1.45046	+	0.728448i
$537$		0			0
$538$	−6.73655	+	1.59659i	−0.290433	+	0.0688339i
$539$	0.458314	−	0.793823i	0.0197410	−	0.0341924i
$540$		0			0
$541$	4.75257	+	8.23170i	0.204329	+	0.353908i	0.949919	−	0.312497i	$-0.101165\pi$
$541$	4.75257	+	8.23170i	0.204329	+	0.353908i	−0.745590	+	0.666405i	$0.767832\pi$
$542$	15.2390	+	16.1524i	0.654573	+	0.693807i
$543$		0			0
$544$	0.0694227	−	1.19194i	0.00297647	−	0.0511041i
$545$	24.2623	+	32.5900i	1.03928	+	1.39600i
$546$		0			0
$547$	−4.43310	+	2.91569i	−0.189545	+	0.124666i	−0.640735	−	0.767762i	$-0.721370\pi$
$547$	−4.43310	+	2.91569i	−0.189545	+	0.124666i	0.451189	+	0.892428i	$0.351000\pi$
$548$	−0.0561112	−	0.318222i	−0.00239695	−	0.0135938i
$549$		0			0
$550$	0.440162	−	2.49628i	0.0187686	−	0.106442i
$551$	−3.49381	−	8.09957i	−0.148841	−	0.345053i
$552$		0			0
$553$	24.9542	+	5.91427i	1.06116	+	0.251500i
$554$	9.32239	−	9.88115i	0.396070	−	0.419810i
$555$		0			0
$556$	0.636507	−	0.854978i	0.0269939	−	0.0362591i
$557$	−25.1867	−	21.1341i	−1.06719	−	0.895481i	−0.0723978	−	0.997376i	$-0.523065\pi$
$557$	−25.1867	−	21.1341i	−1.06719	−	0.895481i	−0.994795	+	0.101895i	$0.967510\pi$
$558$		0			0
$559$	−2.52384	+	2.11775i	−0.106747	+	0.0895714i
$560$	3.17344	+	54.4859i	0.134103	+	2.30245i
$561$		0			0
$562$	11.8875	−	27.5583i	0.501444	−	1.16248i
$563$	10.6668	+	7.01570i	0.449554	+	0.295676i	0.754026	−	0.656845i	$-0.228109\pi$
$563$	10.6668	+	7.01570i	0.449554	+	0.295676i	−0.304471	+	0.952521i	$0.598480\pi$
$564$		0			0
$565$	−4.51871	+	15.0935i	−0.190104	+	0.634990i
$566$	6.63022			0.278689
$567$		0			0
$568$	4.67245			0.196052
$569$	−12.3260	+	41.1716i	−0.516732	+	1.72600i	0.157533	+	0.987514i	$0.449646\pi$
$569$	−12.3260	+	41.1716i	−0.516732	+	1.72600i	−0.674265	+	0.738490i	$0.735539\pi$
$570$		0			0
$571$	3.17924	+	2.09102i	0.133047	+	0.0875064i	0.614288	−	0.789082i	$-0.289443\pi$
$571$	3.17924	+	2.09102i	0.133047	+	0.0875064i	−0.481241	+	0.876588i	$0.659814\pi$
$572$	0.00212386	−	0.00492367i	8.88032e−5	−	0.000205869i
$573$		0			0
$574$	2.01728	+	34.6353i	0.0841994	+	1.44565i
$575$	−26.2291	+	22.0088i	−1.09383	+	0.917832i
$576$		0			0
$577$	11.5311	+	9.67573i	0.480045	+	0.402806i	0.850443	−	0.526067i	$-0.176334\pi$
$577$	11.5311	+	9.67573i	0.480045	+	0.402806i	−0.370397	+	0.928873i	$0.620779\pi$
$578$	9.89607	−	13.2927i	0.411622	−	0.552905i
$579$		0			0
$580$	−1.86163	+	1.97321i	−0.0772999	+	0.0819331i
$581$	−7.95031	−	1.88426i	−0.329834	−	0.0781722i
$582$		0			0
$583$	−0.299450	−	0.694204i	−0.0124020	−	0.0287510i
$584$	−5.86330	+	33.2524i	−0.242625	+	1.37599i
$585$		0			0
$586$	−1.35433	−	7.68078i	−0.0559468	−	0.317290i
$587$	−31.8562	+	20.9522i	−1.31485	+	0.864789i	−0.996533	−	0.0831959i	$-0.973487\pi$
$587$	−31.8562	+	20.9522i	−1.31485	+	0.864789i	−0.318315	+	0.947985i	$0.603117\pi$
$588$		0			0
$589$	0.641192	+	0.861270i	0.0264198	+	0.0354880i
$590$	1.64149	−	28.1832i	0.0675789	−	1.16028i
$591$		0			0
$592$	−11.7523	−	12.4568i	−0.483018	−	0.511969i
$593$	−5.81375	−	10.0697i	−0.238742	−	0.413513i	0.721612	−	0.692298i	$-0.243402\pi$
$593$	−5.81375	−	10.0697i	−0.238742	−	0.413513i	−0.960354	+	0.278785i	$0.910068\pi$
$594$		0			0
$595$	−16.0410	+	27.7839i	−0.657618	+	1.13903i
$596$	−0.0549739	+	0.0130291i	−0.00225182	+	0.000533691i
$597$		0			0
$598$	1.30487	−	0.655330i	0.0533601	−	0.0267984i
$599$	−40.1027	+	4.68733i	−1.63855	+	0.191519i	−0.884909	−	0.465765i	$-0.845779\pi$
$599$	−40.1027	+	4.68733i	−1.63855	+	0.191519i	−0.753643	+	0.657284i	$0.771705\pi$
$600$		0			0
$601$	−17.6188	−	8.84850i	−0.718686	−	0.360938i	0.0515724	−	0.998669i	$-0.483577\pi$
$601$	−17.6188	−	8.84850i	−0.718686	−	0.360938i	−0.770259	+	0.637731i	$0.779873\pi$
$602$	43.5202	+	15.8401i	1.77375	+	0.645593i
$603$		0			0
$604$	0.148971	−	0.0542210i	0.00606154	−	0.00220622i
$605$	−44.0060	−	5.14357i	−1.78910	−	0.209116i
$606$		0			0
$607$	−0.527406	−	1.76166i	−0.0214068	−	0.0715036i	0.946619	−	0.322355i	$-0.104475\pi$
$607$	−0.527406	−	1.76166i	−0.0214068	−	0.0715036i	−0.968026	+	0.250852i	$0.919289\pi$
$608$	−0.190133	−	0.635087i	−0.00771089	−	0.0257562i
$609$		0			0
$610$	51.0845	+	5.97092i	2.06835	+	0.241755i
$611$	1.43475	−	0.522207i	0.0580438	−	0.0211262i
$612$		0			0
$613$	−33.2921	−	12.1173i	−1.34465	−	0.489414i	−0.433379	−	0.901212i	$-0.642679\pi$
$613$	−33.2921	−	12.1173i	−1.34465	−	0.489414i	−0.911275	+	0.411797i	$0.864901\pi$
$614$	−9.84720	−	4.94545i	−0.397401	−	0.199582i
$615$		0			0
$616$	−1.65902	+	0.193912i	−0.0668438	+	0.00781292i
$617$	33.1709	−	16.6591i	1.33541	−	0.670668i	0.369424	−	0.929261i	$-0.379555\pi$
$617$	33.1709	−	16.6591i	1.33541	−	0.670668i	0.965986	+	0.258593i	$0.0832587\pi$
$618$		0			0
$619$	33.0588	−	7.83508i	1.32875	−	0.314918i	0.495879	−	0.868392i	$-0.334846\pi$
$619$	33.0588	−	7.83508i	1.32875	−	0.314918i	0.832867	+	0.553473i	$0.186698\pi$
$620$	0.165108	−	0.285975i	0.00663088	−	0.0114850i
$621$		0			0
$622$	14.2489	+	24.6799i	0.571330	+	0.989573i
$623$	−28.4371	−	30.1416i	−1.13931	−	1.20760i
$624$		0			0
$625$	−2.68693	+	46.1327i	−0.107477	+	1.84531i
$626$	−16.0188	−	21.5170i	−0.640240	−	0.859992i
$627$		0			0
$628$	0.720392	−	0.473810i	0.0287468	−	0.0189071i
$629$	−1.74807	−	9.91382i	−0.0697003	−	0.395290i
$630$		0			0
$631$	−1.91892	+	10.8828i	−0.0763912	+	0.433236i	0.922493	+	0.386013i	$0.126148\pi$
$631$	−1.91892	+	10.8828i	−0.0763912	+	0.433236i	−0.998884	+	0.0472226i	$0.984963\pi$
$632$	−8.26011	−	19.1491i	−0.328569	−	0.761710i
$633$		0			0
$634$	39.0687	+	9.25944i	1.55161	+	0.367739i
$635$	23.6416	−	25.0587i	0.938189	−	0.994422i
$636$		0			0
$637$	1.17616	−	1.57986i	0.0466012	−	0.0625963i
$638$	1.22138	+	1.02486i	0.0483548	+	0.0405745i
$639$		0			0
$640$	32.3085	−	27.1100i	1.27710	−	1.07162i
$641$	0.945542	+	16.2343i	0.0373467	+	0.641217i	0.964099	+	0.265544i	$0.0855515\pi$
$641$	0.945542	+	16.2343i	0.0373467	+	0.641217i	−0.926752	+	0.375673i	$0.877411\pi$
$642$		0			0
$643$	5.65337	−	13.1060i	0.222947	−	0.516849i	−0.769627	−	0.638494i	$-0.779558\pi$
$643$	5.65337	−	13.1060i	0.222947	−	0.516849i	0.992574	+	0.121645i	$0.0388169\pi$
$644$	0.850686	+	0.559505i	0.0335217	+	0.0220476i
$645$		0			0
$646$	−1.09795	+	3.66741i	−0.0431982	+	0.144292i
$647$	40.7899			1.60362			0.801808	−	0.597582i	$-0.203872\pi$
$647$	40.7899			1.60362			0.801808	+	0.597582i	$0.203872\pi$
$648$		0			0
$649$	0.823057			0.0323078
$650$	1.56211	−	5.21780i	0.0612708	−	0.204659i
$651$		0			0
$652$	−1.72750	−	1.13620i	−0.0676543	−	0.0444969i
$653$	−1.01933	+	2.36308i	−0.0398896	+	0.0924745i	−0.936996	−	0.349340i	$-0.886406\pi$
$653$	−1.01933	+	2.36308i	−0.0398896	+	0.0924745i	0.897106	+	0.441815i	$0.145665\pi$
$654$		0			0
$655$	3.79702	+	65.1923i	0.148362	+	2.54727i
$656$	20.5885	−	17.2758i	0.803847	−	0.674508i
$657$		0			0
$658$	−16.4415	−	13.7961i	−0.640957	−	0.537827i
$659$	5.12688	−	6.88660i	0.199715	−	0.268264i	−0.690971	−	0.722882i	$-0.742817\pi$
$659$	5.12688	−	6.88660i	0.199715	−	0.268264i	0.890686	+	0.454618i	$0.150224\pi$
$660$		0			0
$661$	−25.4540	+	26.9797i	−0.990046	+	1.04939i	0.00873230	+	0.999962i	$0.497220\pi$
$661$	−25.4540	+	26.9797i	−0.990046	+	1.04939i	−0.998778	+	0.0494251i	$0.984261\pi$
$662$	−4.12518	−	0.977686i	−0.160330	−	0.0379988i
$663$		0			0
$664$	2.63163	+	6.10081i	0.102127	+	0.236757i
$665$	−3.09324	+	17.5427i	−0.119951	+	0.680275i
$666$		0			0
$667$	−3.73985	−	21.2097i	−0.144807	−	0.821244i
$668$	0.411346	−	0.270546i	0.0159155	−	0.0104678i
$669$		0			0
$670$	−43.2557	−	58.1025i	−1.67111	−	2.24470i
$671$	−0.0871868	+	1.49694i	−0.00336581	+	0.0577887i
$672$		0			0
$673$	−15.2211	−	16.1335i	−0.586731	−	0.621899i	0.364193	−	0.931324i	$-0.381345\pi$
$673$	−15.2211	−	16.1335i	−0.586731	−	0.621899i	−0.950924	+	0.309425i	$0.899863\pi$
$674$	19.1889	+	33.2362i	0.739130	+	1.28021i
$675$		0			0
$676$	−0.608625	+	1.05417i	−0.0234087	+	0.0405450i
$677$	−4.21498	+	0.998968i	−0.161995	+	0.0383935i	−0.310813	−	0.950471i	$-0.600601\pi$
$677$	−4.21498	+	0.998968i	−0.161995	+	0.0383935i	0.148818	+	0.988865i	$0.452453\pi$
$678$		0			0
$679$	13.3500	−	6.70464i	0.512327	−	0.257300i
$680$	25.9124	−	3.02872i	0.993694	−	0.116146i
$681$		0			0
$682$	−0.173435	−	0.0871022i	−0.00664116	−	0.00333532i
$683$	38.0275	+	13.8409i	1.45508	+	0.529607i	0.944006	−	0.329928i	$-0.107024\pi$
$683$	38.0275	+	13.8409i	1.45508	+	0.529607i	0.511077	+	0.859535i	$0.329247\pi$
$684$		0			0
$685$	12.9702	−	4.72076i	0.495566	−	0.180371i
$686$	6.62345	+	0.774170i	0.252884	+	0.0295579i
$687$		0			0
$688$	−10.2898	−	34.3703i	−0.392295	−	1.31036i
$689$	−0.465919	−	1.55628i	−0.0177501	−	0.0592895i
$690$		0			0
$691$	23.1530	+	2.70620i	0.880782	+	0.102949i	0.544448	−	0.838794i	$-0.316739\pi$
$691$	23.1530	+	2.70620i	0.880782	+	0.102949i	0.336333	+	0.941743i	$0.390813\pi$
$692$	−1.85284	+	0.674377i	−0.0704343	+	0.0256360i
$693$		0			0
$694$	4.54584	+	1.65455i	0.172558	+	0.0628058i
$695$	40.6869	+	20.4337i	1.54334	+	0.775095i
$696$		0			0
$697$	15.6916	−	1.83408i	0.594362	−	0.0694709i
$698$	14.1122	−	7.08742i	0.534155	−	0.268263i
$699$		0			0
$700$	3.69556	−	0.875864i	0.139679	−	0.0331046i
$701$	5.97599	−	10.3507i	0.225710	−	0.390941i	−0.730822	−	0.682568i	$-0.760863\pi$
$701$	5.97599	−	10.3507i	0.225710	−	0.390941i	0.956532	+	0.291627i	$0.0941964\pi$
$702$		0			0
$703$	−2.79474	−	4.84063i	−0.105406	−	0.182568i
$704$	0.930116	+	0.985866i	0.0350551	+	0.0371562i
$705$		0			0
$706$	0.147248	−	2.52815i	0.00554175	−	0.0951481i
$707$	−3.55688	−	4.77772i	−0.133770	−	0.179684i
$708$		0			0
$709$	11.9412	−	7.85386i	0.448462	−	0.294958i	−0.305118	−	0.952315i	$-0.598696\pi$
$709$	11.9412	−	7.85386i	0.448462	−	0.294958i	0.753580	+	0.657357i	$0.228325\pi$
$710$	1.56401	+	8.86995i	0.0586963	+	0.332883i
$711$		0			0
$712$	−5.85154	+	33.1857i	−0.219296	+	1.24369i
$713$	1.03836	+	2.40719i	0.0388868	+	0.0901498i
$714$		0			0
$715$	0.222874	+	0.0528220i	0.00833500	+	0.00197543i
$716$	0.264845	−	0.280720i	0.00989773	−	0.0104910i
$717$		0			0
$718$	−16.5816	+	22.2729i	−0.618818	+	0.831217i
$719$	10.2202	+	8.57578i	0.381150	+	0.319823i	0.813154	−	0.582049i	$-0.197749\pi$
$719$	10.2202	+	8.57578i	0.381150	+	0.319823i	−0.432004	+	0.901872i	$0.642193\pi$
$720$		0			0
$721$	−9.14676	+	7.67504i	−0.340643	+	0.285833i
$722$	−1.40140	−	24.0611i	−0.0521546	−	0.895460i
$723$		0			0
$724$	−0.615563	+	1.42704i	−0.0228772	+	0.0530354i
$725$	−67.1185	−	44.1445i	−2.49272	−	1.63949i
$726$		0			0
$727$	−11.8237	+	39.4940i	−0.438518	+	1.46475i	0.398292	+	0.917259i	$0.369603\pi$
$727$	−11.8237	+	39.4940i	−0.438518	+	1.46475i	−0.836810	+	0.547493i	$0.815582\pi$
$728$	−3.58907			−0.133020
$729$		0			0
$730$	−65.0874			−2.40899
$731$	6.04852	−	20.2034i	0.223712	−	0.747252i
$732$		0			0
$733$	−9.70117	−	6.38056i	−0.358321	−	0.235671i	0.357566	−	0.933888i	$-0.383607\pi$
$733$	−9.70117	−	6.38056i	−0.358321	−	0.235671i	−0.715887	+	0.698217i	$0.753977\pi$
$734$	−14.4398	+	33.4752i	−0.532983	+	1.23559i
$735$		0			0
$736$	−0.0941131	−	1.61586i	−0.00346905	−	0.0595614i
$737$	1.61775	−	1.35745i	0.0595907	−	0.0500025i
$738$		0			0
$739$	−27.7185	−	23.2586i	−1.01964	−	0.855581i	−0.0300588	−	0.999548i	$-0.509569\pi$
$739$	−27.7185	−	23.2586i	−1.01964	−	0.855581i	−0.989582	+	0.143968i	$0.954014\pi$
$740$	−1.02650	+	1.37883i	−0.0377350	+	0.0506869i
$741$		0			0
$742$	−15.6711	+	16.6104i	−0.575306	+	0.609789i
$743$	49.2204	+	11.6654i	1.80572	+	0.427964i	0.988857	−	0.148868i	$-0.0475630\pi$
$743$	49.2204	+	11.6654i	1.80572	+	0.427964i	0.816863	+	0.576832i	$0.195711\pi$
$744$		0			0
$745$	−0.955846	−	2.21590i	−0.0350195	−	0.0811843i
$746$	7.10447	−	40.2914i	0.260113	−	1.47517i
$747$		0			0
$748$	0.00596034	+	0.0338028i	0.000217932	+	0.00123595i
$749$	35.0743	−	23.0687i	1.28159	−	0.842912i
$750$		0			0
$751$	24.1007	+	32.3729i	0.879447	+	1.18130i	0.982432	+	0.186620i	$0.0597532\pi$
$751$	24.1007	+	32.3729i	0.879447	+	1.18130i	−0.102985	+	0.994683i	$0.532839\pi$
$752$	−0.966755	+	16.5985i	−0.0352539	+	0.605287i
$753$		0			0
$754$	2.35103	+	2.49194i	0.0856193	+	0.0907512i
$755$	3.38584	+	5.86446i	0.123224	+	0.213429i
$756$		0			0
$757$	23.2499	−	40.2700i	0.845032	−	1.46364i	−0.0405607	−	0.999177i	$-0.512914\pi$
$757$	23.2499	−	40.2700i	0.845032	−	1.46364i	0.885593	−	0.464462i	$-0.153752\pi$
$758$	15.4544	−	3.66277i	0.561331	−	0.133038i
$759$		0			0
$760$	12.9448	−	6.50111i	0.469556	−	0.235820i
$761$	−6.68417	+	0.781268i	−0.242301	+	0.0283209i	−0.236377	−	0.971662i	$-0.575960\pi$
$761$	−6.68417	+	0.781268i	−0.242301	+	0.0283209i	−0.00592448	+	0.999982i	$0.501886\pi$
$762$		0			0
$763$	31.9733	+	16.0576i	1.15751	+	0.581324i
$764$	0.000370307	0	0.000134781i	1.33972e−5	0	4.87620e-6i
$765$		0			0
$766$	37.3111	−	13.5801i	1.34811	−	0.490671i
$767$	1.75658	+	0.205315i	0.0634264	+	0.00741348i
$768$		0			0
$769$	−7.51325	−	25.0960i	−0.270935	−	0.904985i	−0.979857	−	0.199699i	$-0.936004\pi$
$769$	−7.51325	−	25.0960i	−0.270935	−	0.904985i	0.708923	−	0.705286i	$-0.249182\pi$
$770$	−0.923437	−	3.08449i	−0.0332783	−	0.111157i
$771$		0			0
$772$	−1.97034	−	0.230300i	−0.0709143	−	0.00828869i
$773$	−15.5434	+	5.65735i	−0.559059	+	0.203481i	−0.606067	−	0.795414i	$-0.707254\pi$
$773$	−15.5434	+	5.65735i	−0.559059	+	0.203481i	0.0470079	+	0.998895i	$0.485031\pi$
$774$		0			0
$775$	9.18902	+	3.34453i	0.330079	+	0.120139i
$776$	−10.8561	−	5.45214i	−0.389711	−	0.195720i
$777$		0			0
$778$	15.7059	−	1.83576i	0.563084	−	0.0658151i
$779$	7.83889	−	3.93684i	0.280857	−	0.141052i
$780$		0			0
$781$	−0.255509	+	0.0605568i	−0.00914284	+	0.00216689i
$782$	−4.67342	+	8.09460i	−0.167121	+	0.289462i
$783$		0			0
$784$	10.7241	+	18.5747i	0.383004	+	0.663383i
$785$	25.2748	+	26.7897i	0.902096	+	0.956166i
$786$		0			0
$787$	0.782826	−	13.4406i	0.0279047	−	0.479106i	−0.955188	−	0.295999i	$-0.904348\pi$
$787$	0.782826	−	13.4406i	0.0279047	−	0.479106i	0.983093	−	0.183107i	$-0.0586154\pi$
$788$	0.549312	+	0.737854i	0.0195684	+	0.0262850i
$789$		0			0
$790$	33.5868	−	22.0904i	1.19496	−	0.785940i
$791$	2.40927	+	13.6637i	0.0856640	+	0.485824i
$792$		0			0
$793$	−0.559492	+	3.17304i	−0.0198682	+	0.112678i
$794$	−5.98242	−	13.8688i	−0.212308	−	0.492186i
$795$		0			0
$796$	2.21859	+	0.525815i	0.0786358	+	0.0186370i
$797$	−0.340406	+	0.360810i	−0.0120578	+	0.0127805i	−0.733374	−	0.679825i	$-0.762056\pi$
$797$	−0.340406	+	0.360810i	−0.0120578	+	0.0127805i	0.721317	+	0.692605i	$0.243537\pi$
$798$		0			0
$799$	−5.83630	+	7.83951i	−0.206473	+	0.277342i
$800$	−4.62500	−	3.88083i	−0.163518	−	0.137208i
$801$		0			0
$802$	0.367532	−	0.308396i	0.0129780	−	0.0108898i
$803$	−0.110335	−	1.89437i	−0.00389363	−	0.0668510i
$804$		0			0
$805$	−17.2264	+	39.9352i	−0.607149	+	1.40753i
$806$	−0.348419	−	0.229159i	−0.0122725	−	0.00807177i
$807$		0			0
$808$	−1.38917	+	4.64014i	−0.0488708	+	0.163240i
$809$	−20.5900			−0.723906			−0.361953	−	0.932196i	$-0.617890\pi$
$809$	−20.5900			−0.723906			−0.361953	+	0.932196i	$0.617890\pi$
$810$		0			0
$811$	27.9946			0.983022			0.491511	−	0.870871i	$-0.336445\pi$
$811$	27.9946			0.983022			0.491511	+	0.870871i	$0.336445\pi$
$812$	−0.685150	+	2.28856i	−0.0240440	+	0.0803127i
$813$		0			0
$814$	0.844094	+	0.555169i	0.0295855	+	0.0194587i
$815$	34.9819	−	81.0971i	1.22536	−	2.84071i
$816$		0			0
$817$	−0.680860	−	11.6899i	−0.0238203	−	0.408978i
$818$	−28.1295	+	23.6035i	−0.983525	+	0.825275i
$819$		0			0
$820$	−2.06656	−	1.73405i	−0.0721675	−	0.0605557i
$821$	−26.4698	+	35.5551i	−0.923803	+	1.24088i	0.0464821	+	0.998919i	$0.485199\pi$
$821$	−26.4698	+	35.5551i	−0.923803	+	1.24088i	−0.970285	+	0.241964i	$0.922208\pi$
$822$		0			0
$823$	9.56078	−	10.1338i	0.333268	−	0.353243i	−0.538970	−	0.842325i	$-0.681186\pi$
$823$	9.56078	−	10.1338i	0.333268	−	0.353243i	0.872238	+	0.489082i	$0.162668\pi$
$824$	9.44795	+	2.23920i	0.329135	+	0.0780064i
$825$		0			0
$826$	−9.84678	−	22.8274i	−0.342613	−	0.794267i
$827$	1.96973	−	11.1709i	0.0684943	−	0.388451i	−0.931218	−	0.364463i	$-0.881253\pi$
$827$	1.96973	−	11.1709i	0.0684943	−	0.388451i	0.999712	−	0.0239878i	$-0.00763628\pi$
$828$		0			0
$829$	6.55402	+	37.1697i	0.227630	+	1.29096i	0.857592	+	0.514330i	$0.171959\pi$
$829$	6.55402	+	37.1697i	0.227630	+	1.29096i	−0.629962	+	0.776626i	$0.716929\pi$
$830$	−10.7006	+	7.03788i	−0.371423	+	0.244289i
$831$		0			0
$832$	1.73914	+	2.33607i	0.0602938	+	0.0809886i
$833$	−0.733069	+	12.5863i	−0.0253993	+	0.436090i
$834$		0			0
$835$	14.4320	+	15.2970i	0.499439	+	0.529374i
$836$	0.00952913	+	0.0165049i	0.000329572	+	0.000570835i
$837$		0			0
$838$	−8.82846	+	15.2913i	−0.304974	+	0.528231i
$839$	−27.7309	+	6.57235i	−0.957378	+	0.226903i	−0.679469	−	0.733705i	$-0.737790\pi$
$839$	−27.7309	+	6.57235i	−0.957378	+	0.226903i	−0.277909	+	0.960607i	$0.589641\pi$
$840$		0			0
$841$	19.2406	−	9.66300i	0.663470	−	0.333207i
$842$	−14.9100	+	1.74273i	−0.513834	+	0.0600586i
$843$		0			0
$844$	−1.27102	−	0.638331i	−0.0437503	−	0.0219723i
$845$	−48.8593	−	17.7833i	−1.68081	−	0.611765i
$846$		0			0
$847$	−36.6632	+	13.3443i	−1.25976	+	0.458516i
$848$	17.5709	+	2.05375i	0.603388	+	0.0705260i
$849$		0			0
$850$	9.99925	+	33.3998i	0.342971	+	1.14560i
$851$	−3.91401	−	13.0737i	−0.134171	−	0.448161i
$852$		0			0
$853$	28.2542	+	3.30244i	0.967405	+	0.113073i	0.585099	−	0.810962i	$-0.301056\pi$
$853$	28.2542	+	3.30244i	0.967405	+	0.113073i	0.382306	+	0.924036i	$0.375130\pi$
$854$	42.5605	−	15.4908i	1.45639	−	0.530083i
$855$		0			0
$856$	−32.0793	−	11.6759i	−1.09645	−	0.399075i
$857$	−14.5454	−	7.30499i	−0.496862	−	0.249534i	0.182677	−	0.983173i	$-0.441524\pi$
$857$	−14.5454	−	7.30499i	−0.496862	−	0.249534i	−0.679539	+	0.733639i	$0.737820\pi$
$858$		0			0
$859$	−56.3897	+	6.59101i	−1.92399	+	0.224882i	−0.990884	−	0.134716i	$-0.956988\pi$
$859$	−56.3897	+	6.59101i	−1.92399	+	0.224882i	−0.933107	+	0.359598i	$0.882914\pi$
$860$	−3.21814	+	1.61621i	−0.109738	+	0.0551123i
$861$		0			0
$862$	−3.30341	+	0.782922i	−0.112515	+	0.0266664i
$863$	−3.57676	+	6.19512i	−0.121754	+	0.210884i	−0.920460	−	0.390838i	$-0.872185\pi$
$863$	−3.57676	+	6.19512i	−0.121754	+	0.210884i	0.798705	+	0.601722i	$0.205519\pi$
$864$		0			0
$865$	−42.1117	−	72.9396i	−1.43184	−	2.48002i
$866$	−12.2073	−	12.9390i	−0.414823	−	0.439686i
$867$		0			0
$868$	0.0169081	−	0.290300i	0.000573897	−	0.00985343i
$869$	0.699877	+	0.940098i	0.0237417	+	0.0318907i
$870$		0			0
$871$	3.79125	−	2.49354i	0.128462	−	0.0844905i
$872$	−5.05231	−	28.6531i	−0.171093	−	0.970316i
$873$		0			0
$874$	−0.901191	+	5.11091i	−0.0304833	+	0.172879i
$875$	35.8270	+	83.0562i	1.21117	+	2.80781i
$876$		0			0
$877$	18.0369	+	4.27483i	0.609063	+	0.144351i	0.523562	−	0.851987i	$-0.324603\pi$
$877$	18.0369	+	4.27483i	0.609063	+	0.144351i	0.0855009	+	0.996338i	$0.472751\pi$
$878$	−26.1132	+	27.6783i	−0.881277	+	0.934099i
$879$		0			0
$880$	−1.48946	+	2.00070i	−0.0502098	+	0.0674435i
$881$	35.8699	+	30.0984i	1.20849	+	1.01404i	0.999346	+	0.0361571i	$0.0115117\pi$
$881$	35.8699	+	30.0984i	1.20849	+	1.01404i	0.209142	+	0.977885i	$0.432933\pi$
$882$		0			0
$883$	−35.2742	+	29.5986i	−1.18707	+	0.996071i	−0.187166	+	0.982328i	$0.559930\pi$
$883$	−35.2742	+	29.5986i	−1.18707	+	0.996071i	−0.999906	+	0.0137426i	$0.995625\pi$
$884$	0.00428841	+	0.0736292i	0.000144235	+	0.00247642i
$885$		0			0
$886$	3.13483	−	7.26735i	0.105317	−	0.244151i
$887$	3.06993	+	2.01912i	0.103078	+	0.0677955i	0.600001	−	0.799999i	$-0.295167\pi$
$887$	3.06993	+	2.01912i	0.103078	+	0.0677955i	−0.496923	+	0.867794i	$0.665537\pi$
$888$		0			0
$889$	8.70102	−	29.0634i	0.291823	−	0.974756i
$890$	−64.9569			−2.17736
$891$		0			0
$892$	−0.900341			−0.0301456
$893$	−1.55637	+	5.19865i	−0.0520820	+	0.173966i
$894$		0			0
$895$	13.7733	+	9.05882i	0.460389	+	0.302803i
$896$	14.7106	−	34.1030i	0.491447	−	1.13930i
$897$		0			0
$898$	−2.76345	−	47.4466i	−0.0922175	−	1.58331i
$899$	−4.71185	+	3.95371i	−0.157149	+	0.131864i
$900$		0			0
$901$	7.96595	+	6.68422i	0.265384	+	0.222684i
$902$	−0.946813	+	1.27179i	−0.0315254	+	0.0423460i
$903$		0			0
$904$	7.74256	−	8.20664i	0.257514	−	0.272949i
$905$	−64.5958	−	15.3095i	−2.14724	−	0.508905i
$906$		0			0
$907$	5.38773	+	12.4902i	0.178897	+	0.414729i	0.983943	−	0.178483i	$-0.0571189\pi$
$907$	5.38773	+	12.4902i	0.178897	+	0.414729i	−0.805046	+	0.593212i	$0.797860\pi$
$908$	0.201061	−	1.14028i	0.00667246	−	0.0378414i
$909$		0			0
$910$	−1.20137	−	6.81332i	−0.0398251	−	0.225859i
$911$	−3.78604	+	2.49012i	−0.125437	+	0.0825013i	−0.610677	−	0.791880i	$-0.709103\pi$
$911$	−3.78604	+	2.49012i	−0.125437	+	0.0825013i	0.485240	+	0.874381i	$0.338732\pi$
$912$		0			0
$913$	−0.222978	−	0.299511i	−0.00737948	−	0.00991236i
$914$	−0.608964	+	10.4555i	−0.0201427	+	0.345838i
$915$		0			0
$916$	0.242176	+	0.256692i	0.00800173	+	0.00848134i
$917$	28.7533	+	49.8022i	0.949517	+	1.64461i
$918$		0			0
$919$	12.4131	−	21.5002i	0.409472	−	0.709226i	−0.585359	−	0.810775i	$-0.699046\pi$
$919$	12.4131	−	21.5002i	0.409472	−	0.709226i	0.994831	+	0.101548i	$0.0323796\pi$
$920$	34.4140	−	8.15626i	1.13460	−	0.268904i
$921$		0			0
$922$	−2.27121	+	1.14064i	−0.0747982	+	0.0375650i
$923$	−0.560417	+	0.0655034i	−0.0184464	+	0.00215607i
$924$		0			0
$925$	−45.4900	−	22.8459i	−1.49570	−	0.751169i
$926$	−29.1904	−	10.6244i	−0.959255	−	0.349140i
$927$		0			0
$928$	3.56859	−	1.29886i	0.117145	−	0.0426372i
$929$	12.8422	+	1.50104i	0.421338	+	0.0492474i	0.324121	−	0.946016i	$-0.394932\pi$
$929$	12.8422	+	1.50104i	0.421338	+	0.0492474i	0.0972176	+	0.995263i	$0.469006\pi$
$930$		0			0
$931$	2.00771	+	6.70620i	0.0657999	+	0.219787i
$932$	−0.555823	−	1.85658i	−0.0182066	−	0.0608142i
$933$		0			0
$934$	−54.0504	−	6.31759i	−1.76858	−	0.206718i
$935$	−1.37774	+	0.501458i	−0.0450570	+	0.0163994i
$936$		0			0
$937$	54.1109	+	19.6948i	1.76773	+	0.643400i	0.999997	+	0.00262511i	$0.000835598\pi$
$937$	54.1109	+	19.6948i	1.76773	+	0.643400i	0.767729	+	0.640774i	$0.221387\pi$
$938$	−57.0031	−	28.6280i	−1.86122	−	0.934738i
$939$		0			0
$940$	1.65761	−	0.193747i	0.0540652	−	0.00631932i
$941$	14.7478	−	7.40660i	0.480763	−	0.241448i	−0.191876	−	0.981419i	$-0.561457\pi$
$941$	14.7478	−	7.40660i	0.480763	−	0.241448i	0.672639	+	0.739971i	$0.265161\pi$
$942$		0			0
$943$	20.8399	−	4.93914i	0.678640	−	0.160841i
$944$	−9.62940	+	16.6786i	−0.313410	+	0.542842i
$945$		0			0
$946$	1.05827	+	1.83297i	0.0344073	+	0.0595951i
$947$	12.4502	+	13.1964i	0.404576	+	0.428825i	0.897342	−	0.441337i	$-0.145496\pi$
$947$	12.4502	+	13.1964i	0.404576	+	0.428825i	−0.492766	+	0.870162i	$0.664014\pi$
$948$		0			0
$949$	0.237081	−	4.07052i	0.00769597	−	0.132135i
$950$	11.5599	+	15.5277i	0.375053	+	0.503784i
$951$		0			0
$952$	19.1946	−	12.6245i	0.622101	−	0.409162i
$953$	4.36891	+	24.7773i	0.141523	+	0.802616i	0.970094	+	0.242732i	$0.0780434\pi$
$953$	4.36891	+	24.7773i	0.141523	+	0.802616i	−0.828571	+	0.559885i	$0.810845\pi$
$954$		0			0
$955$	−0.00292299	+	0.0165771i	−9.45859e−5	+	0.000536423i
$956$	−0.484898	−	1.12412i	−0.0156827	−	0.0363566i
$957$		0			0
$958$	−3.54505	−	0.840192i	−0.114535	−	0.0271454i
$959$	8.34110	−	8.84105i	0.269348	−	0.285492i
$960$		0			0
$961$	−18.0648	+	24.2653i	−0.582736	+	0.782750i
$962$	1.66299	+	1.39541i	0.0536168	+	0.0449899i
$963$		0			0
$964$	−0.878021	+	0.736747i	−0.0282791	+	0.0237290i
$965$	−4.92699	−	84.5931i	−0.158605	−	2.72315i
$966$		0			0
$967$	−18.7139	+	43.3837i	−0.601798	+	1.39513i	0.296200	+	0.955126i	$0.404281\pi$
$967$	−18.7139	+	43.3837i	−0.601798	+	1.39513i	−0.897998	+	0.439999i	$0.854979\pi$
$968$	26.5079	+	17.4345i	0.851997	+	0.560368i
$969$		0			0
$970$	6.71620	−	22.4337i	0.215644	−	0.720302i
$971$	−40.3149			−1.29377			−0.646883	−	0.762589i	$-0.723928\pi$
$971$	−40.3149			−1.29377			−0.646883	+	0.762589i	$0.723928\pi$
$972$		0			0
$973$	40.0942			1.28536
$974$	−9.89909	+	33.0653i	−0.317187	+	1.05948i
$975$		0			0
$976$	−29.3142	−	19.2803i	−0.938326	−	0.617147i
$977$	1.09500	−	2.53851i	0.0350323	−	0.0812140i	−0.899802	−	0.436299i	$-0.856289\pi$
$977$	1.09500	−	2.53851i	0.0350323	−	0.0812140i	0.934834	+	0.355085i	$0.115548\pi$
$978$		0			0
$979$	−0.110113	−	1.89058i	−0.00351924	−	0.0604230i
$980$	1.64918	−	1.38383i	0.0526812	−	0.0442048i
$981$		0			0
$982$	31.8360	+	26.7136i	1.01593	+	0.852464i
$983$	−1.00359	+	1.34805i	−0.0320094	+	0.0429961i	−0.817840	−	0.575446i	$-0.804828\pi$
$983$	−1.00359	+	1.34805i	−0.0320094	+	0.0429961i	0.785830	+	0.618442i	$0.212236\pi$
$984$		0			0
$985$	−26.9642	+	28.5804i	−0.859152	+	0.910648i
$986$	−21.3388	−	5.05739i	−0.679566	−	0.161060i
$987$		0			0
$988$	0.0162200	+	0.0376021i	0.000516026	+	0.00119628i
$989$	4.96459	−	28.1556i	0.157865	−	0.895296i
$990$		0			0
$991$	−1.27536	−	7.23291i	−0.0405130	−	0.229761i	0.957828	−	0.287343i	$-0.0927720\pi$
$991$	−1.27536	−	7.23291i	−0.0405130	−	0.229761i	−0.998341	+	0.0575822i	$0.981661\pi$
$992$	−0.386218	+	0.254020i	−0.0122624	+	0.00806513i
$993$		0			0
$994$	4.73636	+	6.36204i	0.150228	+	0.201792i
$995$	−5.66287	+	97.2278i	−0.179525	+	3.08233i
$996$		0			0
$997$	13.2174	+	14.0096i	0.418598	+	0.443688i	0.902017	−	0.431701i	$-0.142086\pi$
$997$	13.2174	+	14.0096i	0.418598	+	0.443688i	−0.483418	+	0.875389i	$0.660605\pi$
$998$	−3.89120	−	6.73976i	−0.123174	−	0.213344i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.37.6		144
3.2	odd	2		81.2.g.a.49.3	yes	144
9.2	odd	6		729.2.g.d.595.6		144
9.4	even	3		729.2.g.b.109.6		144
9.5	odd	6		729.2.g.c.109.3		144
9.7	even	3		729.2.g.a.595.3		144
81.11	odd	54		729.2.g.d.136.6		144
81.16	even	27		729.2.g.b.622.6		144
81.23	odd	54		6561.2.a.c.1.54		72
81.38	odd	54		81.2.g.a.43.3	✓	144
81.43	even	27	inner	243.2.g.a.46.6		144
81.58	even	27		6561.2.a.d.1.19		72
81.65	odd	54		729.2.g.c.622.3		144
81.70	even	27		729.2.g.a.136.3		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.43.3	✓	144	81.38	odd	54
81.2.g.a.49.3	yes	144	3.2	odd	2
243.2.g.a.37.6		144	1.1	even	1	trivial
243.2.g.a.46.6		144	81.43	even	27	inner
729.2.g.a.136.3		144	81.70	even	27
729.2.g.a.595.3		144	9.7	even	3
729.2.g.b.109.6		144	9.4	even	3
729.2.g.b.622.6		144	81.16	even	27
729.2.g.c.109.3		144	9.5	odd	6
729.2.g.c.622.3		144	81.65	odd	54
729.2.g.d.136.6		144	81.11	odd	54
729.2.g.d.595.6		144	9.2	odd	6
6561.2.a.c.1.54		72	81.23	odd	54
6561.2.a.d.1.19		72	81.58	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.395901 - 1.32240i) q^{2} +(0.0789711 + 0.0519401i) q^{4} +(-1.59916 + 3.70727i) q^{5} +(0.206731 + 3.54944i) q^{7} +(2.21483 - 1.85846i) q^{8} +(4.26939 + 3.58244i) q^{10} +(-0.0970299 + 0.130334i) q^{11} +(-0.239595 + 0.253956i) q^{13} +(4.77563 + 1.13184i) q^{14} +(-1.50590 - 3.49108i) q^{16} +(0.388085 - 2.20094i) q^{17} +(-0.215481 - 1.22205i) q^{19} +(-0.318844 + 0.209707i) q^{20} +(0.133939 + 0.179912i) q^{22} +(0.176164 - 3.02462i) q^{23} +(-7.75535 - 8.22019i) q^{25} +(0.240975 + 0.417381i) q^{26} +(-0.168033 + 0.291041i) q^{28} +(6.91689 - 1.63933i) q^{29} +(-0.773247 + 0.388339i) q^{31} +(0.530624 - 0.0620210i) q^{32} +(-2.75688 - 1.38456i) q^{34} +(-13.4893 - 4.90972i) q^{35} +(4.23271 - 1.54058i) q^{37} +(-1.70135 - 0.198860i) q^{38} +(3.34796 + 11.1830i) q^{40} +(2.02741 + 6.77201i) q^{41} +(9.37262 + 1.09550i) q^{43} +(-0.0144321 + 0.00525286i) q^{44} +(-3.93001 - 1.43041i) q^{46} +(-3.90796 - 1.96265i) q^{47} +(-5.60313 + 0.654911i) q^{49} +(-13.9407 + 7.00129i) q^{50} +(-0.0321115 + 0.00761057i) q^{52} +(-2.32646 + 4.02955i) q^{53} +(-0.328016 - 0.568141i) q^{55} +(7.05439 + 7.47721i) q^{56} +(0.570547 - 9.79591i) q^{58} +(-3.02485 - 4.06308i) q^{59} +(7.71017 - 5.07106i) q^{61} +(0.207411 + 1.17629i) q^{62} +(1.44849 - 8.21478i) q^{64} +(-0.558332 - 1.29436i) q^{65} +(-12.6466 - 2.99731i) q^{67} +(0.144965 - 0.153654i) q^{68} +(-11.8331 + 15.8945i) q^{70} +(1.23797 + 1.03878i) q^{71} +(-8.94621 + 7.50676i) q^{73} +(-0.361531 - 6.20725i) q^{74} +(0.0464569 - 0.107699i) q^{76} +(-0.482671 - 0.317458i) q^{77} +(2.06871 - 6.90998i) q^{79} +15.3506 q^{80} +9.75795 q^{82} +(-0.659082 + 2.20149i) q^{83} +(7.53888 + 4.95840i) q^{85} +(5.15932 - 11.9606i) q^{86} +(0.0273158 + 0.468994i) q^{88} +(-8.92827 + 7.49171i) q^{89} +(-0.950932 - 0.797927i) q^{91} +(0.171011 - 0.229707i) q^{92} +(-4.14257 + 4.39087i) q^{94} +(4.87508 + 1.15541i) q^{95} +(-1.66422 - 3.85810i) q^{97} +(-1.35223 + 7.66885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

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