LMFDB - Embedded newform 243.2.g.a.10.5

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			10.5
Character	$\chi$	$=$	243.10
Dual form			243.2.g.a.73.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.698417 + 0.350758i) q^{2} +(-0.829563 - 1.11430i) q^{4} +(-0.424677 - 1.41852i) q^{5} +(-1.50560 - 3.49038i) q^{7} +(-0.459961 - 2.60857i) q^{8} +(0.200956 - 1.13968i) q^{10} +(-4.91819 + 1.16563i) q^{11} +(3.75323 + 2.46854i) q^{13} +(0.172741 - 2.96584i) q^{14} +(-0.203113 + 0.678443i) q^{16} +(4.30582 - 1.56719i) q^{17} +(4.19524 + 1.52694i) q^{19} +(-1.22836 + 1.64997i) q^{20} +(-3.84380 - 0.910998i) q^{22} +(1.36843 - 3.17237i) q^{23} +(2.34559 - 1.54272i) q^{25} +(1.75546 + 3.04054i) q^{26} +(-2.64032 + 4.57318i) q^{28} +(0.0379650 + 0.651834i) q^{29} +(-0.653701 + 0.0764066i) q^{31} +(-4.01527 + 4.25594i) q^{32} +(3.55696 + 0.415749i) q^{34} +(-4.31178 + 3.61801i) q^{35} +(0.766165 + 0.642889i) q^{37} +(2.39444 + 2.53796i) q^{38} +(-3.50497 + 1.76026i) q^{40} +(0.610184 - 0.306446i) q^{41} +(-5.75968 - 6.10490i) q^{43} +(5.37881 + 4.51336i) q^{44} +(2.06847 - 1.73565i) q^{46} +(7.88112 + 0.921171i) q^{47} +(-5.11223 + 5.41864i) q^{49} +(2.17932 - 0.254726i) q^{50} +(-0.362857 - 6.23001i) q^{52} +(2.07469 - 3.59347i) q^{53} +(3.74212 + 6.48154i) q^{55} +(-8.41238 + 5.53291i) q^{56} +(-0.202121 + 0.468568i) q^{58} +(-5.12792 - 1.21534i) q^{59} +(-4.05529 + 5.44719i) q^{61} +(-0.483356 - 0.175927i) q^{62} +(-2.96617 + 1.07960i) q^{64} +(1.90776 - 6.37236i) q^{65} +(-0.308237 + 5.29223i) q^{67} +(-5.31826 - 3.49787i) q^{68} +(-4.28047 + 1.01449i) q^{70} +(1.06500 - 6.03991i) q^{71} +(-0.764322 - 4.33469i) q^{73} +(0.309604 + 0.717743i) q^{74} +(-1.77875 - 5.94144i) q^{76} +(11.4734 + 15.4114i) q^{77} +(10.0467 + 5.04564i) q^{79} +1.04864 q^{80} +0.533651 q^{82} +(-1.44915 - 0.727793i) q^{83} +(-4.05167 - 5.44234i) q^{85} +(-1.88131 - 6.28402i) q^{86} +(5.30281 + 12.2933i) q^{88} +(0.181087 + 1.02699i) q^{89} +(2.96526 - 16.8168i) q^{91} +(-4.67016 + 1.10685i) q^{92} +(5.18120 + 3.40773i) q^{94} +(0.384377 - 6.59950i) q^{95} +(-1.43062 + 4.77859i) q^{97} +(-5.47110 + 1.99132i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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 $

$2$	0.698417	+	0.350758i	0.493855	+	0.248023i	0.678253	−	0.734828i	$-0.262737\pi$
$2$	0.698417	+	0.350758i	0.493855	+	0.248023i	−0.184398	+	0.982852i	$0.559034\pi$
$3$		0			0
$3$		0			0
$4$	−0.829563	−	1.11430i	−0.414781	−	0.557148i
$5$	−0.424677	−	1.41852i	−0.189921	−	0.634382i	−0.998915	−	0.0465645i	$-0.985173\pi$
$5$	−0.424677	−	1.41852i	−0.189921	−	0.634382i	0.808994	−	0.587817i	$-0.200013\pi$
$6$		0			0
$7$	−1.50560	−	3.49038i	−0.569065	−	1.31924i	−0.923299	−	0.384083i	$-0.874518\pi$
$7$	−1.50560	−	3.49038i	−0.569065	−	1.31924i	0.354234	−	0.935157i	$-0.384742\pi$
$8$	−0.459961	−	2.60857i	−0.162621	−	0.922268i
$9$		0			0
$10$	0.200956	−	1.13968i	0.0635478	−	0.360398i
$11$	−4.91819	+	1.16563i	−1.48289	+	0.351452i	−0.890791	−	0.454413i	$-0.849849\pi$
$11$	−4.91819	+	1.16563i	−1.48289	+	0.351452i	−0.592100	+	0.805865i	$0.701701\pi$
$12$		0			0
$13$	3.75323	+	2.46854i	1.04096	+	0.684649i	0.950332	−	0.311237i	$-0.100743\pi$
$13$	3.75323	+	2.46854i	1.04096	+	0.684649i	0.0906250	+	0.995885i	$0.471114\pi$
$14$	0.172741	−	2.96584i	0.0461669	−	0.792655i
$15$		0			0
$16$	−0.203113	+	0.678443i	−0.0507782	+	0.169611i
$17$	4.30582	−	1.56719i	1.04431	−	0.380099i	0.237800	−	0.971314i	$-0.423574\pi$
$17$	4.30582	−	1.56719i	1.04431	−	0.380099i	0.806514	+	0.591215i	$0.201352\pi$
$18$		0			0
$19$	4.19524	+	1.52694i	0.962455	+	0.350305i	0.774995	−	0.631967i	$-0.217752\pi$
$19$	4.19524	+	1.52694i	0.962455	+	0.350305i	0.187460	+	0.982272i	$0.439975\pi$
$20$	−1.22836	+	1.64997i	−0.274669	+	0.368944i
$21$		0			0
$22$	−3.84380	−	0.910998i	−0.819502	−	0.194225i
$23$	1.36843	−	3.17237i	0.285337	−	0.661486i	−0.713912	−	0.700235i	$-0.753078\pi$
$23$	1.36843	−	3.17237i	0.285337	−	0.661486i	0.999249	+	0.0387500i	$0.0123376\pi$
$24$		0			0
$25$	2.34559	−	1.54272i	0.469118	−	0.308544i
$26$	1.75546	+	3.04054i	0.344273	+	0.596299i
$27$		0			0
$28$	−2.64032	+	4.57318i	−0.498974	+	0.864249i
$29$	0.0379650	+	0.651834i	0.00704993	+	0.121043i	0.999997	+	0.00248341i	$0.000790494\pi$
$29$	0.0379650	+	0.651834i	0.00704993	+	0.121043i	−0.992947	+	0.118559i	$0.962172\pi$
$30$		0			0
$31$	−0.653701	+	0.0764066i	−0.117408	+	0.0137230i	−0.174594	−	0.984641i	$-0.555861\pi$
$31$	−0.653701	+	0.0764066i	−0.117408	+	0.0137230i	0.0571859	+	0.998364i	$0.481787\pi$
$32$	−4.01527	+	4.25594i	−0.709807	+	0.752351i
$33$		0			0
$34$	3.55696	+	0.415749i	0.610013	+	0.0713003i
$35$	−4.31178	+	3.61801i	−0.728824	+	0.611556i
$36$		0			0
$37$	0.766165	+	0.642889i	0.125957	+	0.105690i	0.703590	−	0.710606i	$-0.251579\pi$
$37$	0.766165	+	0.642889i	0.125957	+	0.105690i	−0.577633	+	0.816296i	$0.696024\pi$
$38$	2.39444	+	2.53796i	0.388429	+	0.411711i
$39$		0			0
$40$	−3.50497	+	1.76026i	−0.554185	+	0.278322i
$41$	0.610184	−	0.306446i	0.0952947	−	0.0478588i	−0.400513	−	0.916291i	$-0.631168\pi$
$41$	0.610184	−	0.306446i	0.0952947	−	0.0478588i	0.495808	+	0.868432i	$0.334872\pi$
$42$		0			0
$43$	−5.75968	−	6.10490i	−0.878343	−	0.930989i	0.119745	−	0.992805i	$-0.461792\pi$
$43$	−5.75968	−	6.10490i	−0.878343	−	0.930989i	−0.998088	+	0.0618156i	$0.980311\pi$
$44$	5.37881	+	4.51336i	0.810886	+	0.680414i
$45$		0			0
$46$	2.06847	−	1.73565i	0.304979	−	0.255908i
$47$	7.88112	+	0.921171i	1.14958	+	0.134367i	0.669468	−	0.742841i	$-0.266522\pi$
$47$	7.88112	+	0.921171i	1.14958	+	0.134367i	0.480111	+	0.877207i	$0.340596\pi$
$48$		0			0
$49$	−5.11223	+	5.41864i	−0.730318	+	0.774092i
$50$	2.17932	−	0.254726i	0.308202	−	0.0360237i
$51$		0			0
$52$	−0.362857	−	6.23001i	−0.0503192	−	0.863947i
$53$	2.07469	−	3.59347i	0.284981	−	0.493601i	−0.687624	−	0.726067i	$-0.741346\pi$
$53$	2.07469	−	3.59347i	0.284981	−	0.493601i	0.972605	+	0.232466i	$0.0746794\pi$
$54$		0			0
$55$	3.74212	+	6.48154i	0.504587	+	0.873971i
$56$	−8.41238	+	5.53291i	−1.12415	+	0.739366i
$57$		0			0
$58$	−0.202121	+	0.468568i	−0.0265397	+	0.0615261i
$59$	−5.12792	−	1.21534i	−0.667598	−	0.158224i	−0.117177	−	0.993111i	$-0.537385\pi$
$59$	−5.12792	−	1.21534i	−0.667598	−	0.158224i	−0.550421	+	0.834887i	$0.685533\pi$
$60$		0			0
$61$	−4.05529	+	5.44719i	−0.519226	+	0.697442i	−0.981967	−	0.189052i	$-0.939459\pi$
$61$	−4.05529	+	5.44719i	−0.519226	+	0.697442i	0.462741	+	0.886494i	$0.346866\pi$
$62$	−0.483356	−	0.175927i	−0.0613862	−	0.0223428i
$63$		0			0
$64$	−2.96617	+	1.07960i	−0.370771	+	0.134950i
$65$	1.90776	−	6.37236i	0.236628	−	0.790394i
$66$		0			0
$67$	−0.308237	+	5.29223i	−0.0376572	+	0.646549i	0.925689	+	0.378286i	$0.123487\pi$
$67$	−0.308237	+	5.29223i	−0.0376572	+	0.646549i	−0.963346	+	0.268263i	$0.913551\pi$
$68$	−5.31826	−	3.49787i	−0.644933	−	0.424179i
$69$		0			0
$70$	−4.28047	+	1.01449i	−0.511614	+	0.121255i
$71$	1.06500	−	6.03991i	0.126392	−	0.716805i	−0.854079	−	0.520143i	$-0.825879\pi$
$71$	1.06500	−	6.03991i	0.126392	−	0.716805i	0.980471	−	0.196662i	$-0.0630103\pi$
$72$		0			0
$73$	−0.764322	−	4.33469i	−0.0894571	−	0.507337i	−0.996306	−	0.0858796i	$-0.972630\pi$
$73$	−0.764322	−	4.33469i	−0.0894571	−	0.507337i	0.906848	−	0.421457i	$-0.138481\pi$
$74$	0.309604	+	0.717743i	0.0359907	+	0.0834359i
$75$		0			0
$76$	−1.77875	−	5.94144i	−0.204037	−	0.681530i
$77$	11.4734	+	15.4114i	1.30751	+	1.75629i
$78$		0			0
$79$	10.0467	+	5.04564i	1.13034	+	0.567679i	0.912814	−	0.408375i	$-0.133904\pi$
$79$	10.0467	+	5.04564i	1.13034	+	0.567679i	0.217528	+	0.976054i	$0.430201\pi$
$80$	1.04864			0.117242
$81$		0			0
$82$	0.533651			0.0589319
$83$	−1.44915	−	0.727793i	−0.159065	−	0.0798857i	0.367486	−	0.930029i	$-0.380219\pi$
$83$	−1.44915	−	0.727793i	−0.159065	−	0.0798857i	−0.526551	+	0.850144i	$0.676515\pi$
$84$		0			0
$85$	−4.05167	−	5.44234i	−0.439465	−	0.590305i
$86$	−1.88131	−	6.28402i	−0.202867	−	0.677623i
$87$		0			0
$88$	5.30281	+	12.2933i	0.565281	+	1.31047i
$89$	0.181087	+	1.02699i	0.0191952	+	0.108861i	0.992900	−	0.118952i	$-0.0379535\pi$
$89$	0.181087	+	1.02699i	0.0191952	+	0.108861i	−0.973705	+	0.227813i	$0.926842\pi$
$90$		0			0
$91$	2.96526	−	16.8168i	0.310844	−	1.76288i
$92$	−4.67016	+	1.10685i	−0.486898	+	0.115397i
$93$		0			0
$94$	5.18120	+	3.40773i	0.534400	+	0.351480i
$95$	0.384377	−	6.59950i	0.0394362	−	0.677094i
$96$		0			0
$97$	−1.43062	+	4.77859i	−0.145257	+	0.485192i	−0.999392	−	0.0348588i	$-0.988902\pi$
$97$	−1.43062	+	4.77859i	−0.145257	+	0.485192i	0.854135	+	0.520051i	$0.174087\pi$
$98$	−5.47110	+	1.99132i	−0.552664	+	0.201153i
$99$		0			0
$100$	−3.66486	−	1.33390i	−0.366486	−	0.133390i
$101$	5.71510	−	7.67671i	0.568673	−	0.763861i	−0.421022	−	0.907050i	$-0.638328\pi$
$101$	5.71510	−	7.67671i	0.568673	−	0.763861i	0.989695	+	0.143190i	$0.0457359\pi$
$102$		0			0
$103$	3.16740	+	0.750687i	0.312093	+	0.0739673i	0.383677	−	0.923467i	$-0.374657\pi$
$103$	3.16740	+	0.750687i	0.312093	+	0.0739673i	−0.0715847	+	0.997435i	$0.522806\pi$
$104$	4.71300	−	10.9260i	0.462148	−	1.07138i
$105$		0			0
$106$	2.70944	−	1.78203i	0.263164	−	0.173086i
$107$	8.40680	+	14.5610i	0.812716	+	1.40767i	0.910956	+	0.412503i	$0.135345\pi$
$107$	8.40680	+	14.5610i	0.812716	+	1.40767i	−0.0982402	+	0.995163i	$0.531321\pi$
$108$		0			0
$109$	−3.81772	+	6.61249i	−0.365671	+	0.633361i	−0.988884	−	0.148691i	$-0.952494\pi$
$109$	−3.81772	+	6.61249i	−0.365671	+	0.633361i	0.623212	+	0.782053i	$0.285827\pi$
$110$	0.340106	+	5.83939i	0.0324278	+	0.556764i
$111$		0			0
$112$	2.67383	−	0.312526i	0.252653	−	0.0295310i
$113$	−6.87571	+	7.28783i	−0.646812	+	0.685581i	−0.964941	−	0.262466i	$-0.915464\pi$
$113$	−6.87571	+	7.28783i	−0.646812	+	0.685581i	0.318129	+	0.948048i	$0.396946\pi$
$114$		0			0
$115$	−5.08122	−	0.593909i	−0.473826	−	0.0553823i
$116$	0.694842	−	0.583042i	0.0645144	−	0.0541340i
$117$		0			0
$118$	−3.15514	−	2.64747i	−0.290454	−	0.243720i
$119$	−11.9529	−	12.6694i	−1.09572	−	1.16140i
$120$		0			0
$121$	13.0000	−	6.52883i	1.18182	−	0.593530i
$122$	−4.74293	+	2.38199i	−0.429404	+	0.215655i
$123$		0			0
$124$	0.627425	+	0.665032i	0.0563444	+	0.0597216i
$125$	−8.85601	−	7.43107i	−0.792105	−	0.664655i
$126$		0			0
$127$	2.97665	−	2.49770i	0.264135	−	0.221635i	−0.501096	−	0.865392i	$-0.667070\pi$
$127$	2.97665	−	2.49770i	0.264135	−	0.221635i	0.765230	+	0.643757i	$0.222625\pi$
$128$	9.17279	+	1.07215i	0.810768	+	0.0947651i
$129$		0			0
$130$	3.56757	−	3.78140i	0.312896	−	0.331651i
$131$	−16.5366	+	1.93285i	−1.44481	+	0.168874i	−0.802080	−	0.597217i	$-0.796273\pi$
$131$	−16.5366	+	1.93285i	−1.44481	+	0.168874i	−0.642732	+	0.766091i	$0.722199\pi$
$132$		0			0
$133$	−0.986757	−	16.9420i	−0.0855627	−	1.46905i
$134$	−2.07157	+	3.58807i	−0.178956	+	0.309962i
$135$		0			0
$136$	−6.06863	−	10.5112i	−0.520380	−	0.901325i
$137$	7.74989	−	5.09718i	0.662118	−	0.435482i	−0.173470	−	0.984839i	$-0.555498\pi$
$137$	7.74989	−	5.09718i	0.662118	−	0.435482i	0.835587	+	0.549358i	$0.185127\pi$
$138$		0			0
$139$	6.30605	−	14.6191i	0.534872	−	1.23997i	−0.409866	−	0.912146i	$-0.634424\pi$
$139$	6.30605	−	14.6191i	0.534872	−	1.23997i	0.944738	−	0.327827i	$-0.106316\pi$
$140$	7.60843	+	1.80323i	0.643030	+	0.152401i
$141$		0			0
$142$	2.86236	−	3.84482i	0.240204	−	0.322650i
$143$	−21.3365	−	7.76585i	−1.78425	−	0.649413i
$144$		0			0
$145$	0.908517	−	0.330673i	0.0754483	−	0.0274609i
$146$	0.986611	−	3.29551i	0.0816525	−	0.272738i
$147$		0			0
$148$	0.0807865	−	1.38705i	0.00664061	−	0.114015i
$149$	19.5018	+	12.8265i	1.59765	+	1.05079i	0.959823	+	0.280607i	$0.0905356\pi$
$149$	19.5018	+	12.8265i	1.59765	+	1.05079i	0.637824	+	0.770182i	$0.279835\pi$
$150$		0			0
$151$	−2.26923	+	0.537818i	−0.184667	+	0.0437670i	−0.321909	−	0.946771i	$-0.604324\pi$
$151$	−2.26923	+	0.537818i	−0.184667	+	0.0437670i	0.137242	+	0.990538i	$0.456176\pi$
$152$	2.05349	−	11.6459i	0.166560	−	0.944608i
$153$		0			0
$154$	2.60751	+	14.7879i	0.210119	+	1.19165i
$155$	0.385996	+	0.894840i	0.0310040	+	0.0718752i
$156$		0			0
$157$	5.64522	+	18.8563i	0.450538	+	1.50490i	0.818196	+	0.574939i	$0.194974\pi$
$157$	5.64522	+	18.8563i	0.450538	+	1.50490i	−0.367658	+	0.929961i	$0.619840\pi$
$158$	5.24698	+	7.04792i	0.417428	+	0.560702i
$159$		0			0
$160$	7.74233	+	3.88835i	0.612085	+	0.307401i
$161$	−13.1331			−1.03503
$162$		0			0
$163$	−17.6622			−1.38341			−0.691707	−	0.722179i	$-0.743141\pi$
$163$	−17.6622			−1.38341			−0.691707	+	0.722179i	$0.743141\pi$
$164$	−0.847657	−	0.425709i	−0.0661909	−	0.0332423i
$165$		0			0
$166$	−0.756835	−	1.01661i	−0.0587418	−	0.0789039i
$167$	0.972303	+	3.24772i	0.0752391	+	0.251316i	0.987332	−	0.158667i	$-0.0507197\pi$
$167$	0.972303	+	3.24772i	0.0752391	+	0.251316i	−0.912093	+	0.409983i	$0.865535\pi$
$168$		0			0
$169$	2.84400	+	6.59313i	0.218769	+	0.507164i
$170$	−0.920811	−	5.22218i	−0.0706230	−	0.400523i
$171$		0			0
$172$	−2.02465	+	11.4824i	−0.154378	+	0.875524i
$173$	18.1755	−	4.30767i	1.38186	−	0.327506i	0.528545	−	0.848906i	$-0.322738\pi$
$173$	18.1755	−	4.30767i	1.38186	−	0.327506i	0.853313	+	0.521399i	$0.174590\pi$
$174$		0			0
$175$	−8.91620	−	5.86428i	−0.674002	−	0.443298i
$176$	0.208131	−	3.57347i	0.0156885	−	0.269360i
$177$		0			0
$178$	−0.233753	+	0.780788i	−0.0175205	+	0.0585225i
$179$	11.1678	−	4.06476i	0.834723	−	0.303814i	0.110927	−	0.993829i	$-0.464618\pi$
$179$	11.1678	−	4.06476i	0.834723	−	0.303814i	0.723796	+	0.690014i	$0.242396\pi$
$180$		0			0
$181$	14.8329	+	5.39873i	1.10252	+	0.401284i	0.828244	−	0.560367i	$-0.189340\pi$
$181$	14.8329	+	5.39873i	1.10252	+	0.401284i	0.274275	+	0.961651i	$0.411562\pi$
$182$	7.96962	−	10.7051i	0.590748	−	0.793512i
$183$		0			0
$184$	−8.90477	−	2.11047i	−0.656469	−	0.155586i
$185$	0.586578	−	1.35984i	0.0431261	−	0.0999775i
$186$		0			0
$187$	−19.3501	+	12.7267i	−1.41502	+	0.930672i
$188$	−5.51142	−	9.54607i	−0.401962	−	0.696219i
$189$		0			0
$190$	2.58328	−	4.47437i	0.187411	−	0.324605i
$191$	0.335299	+	5.75686i	0.0242614	+	0.416552i	0.988471	+	0.151410i	$0.0483815\pi$
$191$	0.335299	+	5.75686i	0.0242614	+	0.416552i	−0.964210	+	0.265141i	$0.914581\pi$
$192$		0			0
$193$	−0.174569	+	0.0204042i	−0.0125657	+	0.00146872i	−0.122373	−	0.992484i	$-0.539051\pi$
$193$	−0.174569	+	0.0204042i	−0.0125657	+	0.00146872i	0.109808	+	0.993953i	$0.464976\pi$
$194$	−2.67529	+	2.83565i	−0.192075	+	0.203588i
$195$		0			0
$196$	10.2789	+	1.20143i	0.734206	+	0.0858164i
$197$	−8.59155	+	7.20917i	−0.612123	+	0.513632i	−0.895316	−	0.445431i	$-0.853050\pi$
$197$	−8.59155	+	7.20917i	−0.612123	+	0.513632i	0.283194	+	0.959063i	$0.408606\pi$
$198$		0			0
$199$	−15.6873	−	13.1632i	−1.11204	−	0.933114i	−0.113866	−	0.993496i	$-0.536324\pi$
$199$	−15.6873	−	13.1632i	−1.11204	−	0.933114i	−0.998175	+	0.0603824i	$0.980768\pi$
$200$	−5.10316	−	5.40904i	−0.360848	−	0.382477i
$201$		0			0
$202$	6.68418	−	3.35692i	0.470298	−	0.236192i
$203$	2.21799	−	1.11392i	0.155672	−	0.0781816i
$204$		0			0
$205$	−0.693831	−	0.735418i	−0.0484593	−	0.0513638i
$206$	1.94885	+	1.63528i	0.135783	+	0.113935i
$207$		0			0
$208$	−2.43709	+	2.04496i	−0.168982	+	0.141792i
$209$	−22.4129	−	2.61969i	−1.55033	−	0.181208i
$210$		0			0
$211$	−0.817579	+	0.866583i	−0.0562844	+	0.0596580i	−0.754904	−	0.655835i	$-0.772317\pi$
$211$	−0.817579	+	0.866583i	−0.0562844	+	0.0596580i	0.698620	+	0.715493i	$0.253798\pi$
$212$	−5.72528	+	0.669189i	−0.393214	+	0.0459601i
$213$		0			0
$214$	0.764060	+	13.1184i	0.0522301	+	0.896756i
$215$	−6.21393	+	10.7628i	−0.423786	+	0.734019i
$216$		0			0
$217$	1.25090	+	2.16663i	0.0849168	+	0.147080i
$218$	−4.98574	+	3.27918i	−0.337677	+	0.222094i
$219$		0			0
$220$	4.11803	−	9.54667i	0.277638	−	0.643636i
$221$	20.0294	+	4.74705i	1.34732	+	0.319321i
$222$		0			0
$223$	−8.89760	+	11.9515i	−0.595827	+	0.800335i	−0.993088	−	0.117371i	$-0.962553\pi$
$223$	−8.89760	+	11.9515i	−0.595827	+	0.800335i	0.397261	+	0.917706i	$0.369961\pi$
$224$	20.9003	+	7.60707i	1.39646	+	0.508269i
$225$		0			0
$226$	−7.35838	+	2.67823i	−0.489472	+	0.178153i
$227$	−7.05501	+	23.5654i	−0.468258	+	1.56409i	0.319179	+	0.947694i	$0.396593\pi$
$227$	−7.05501	+	23.5654i	−0.468258	+	1.56409i	−0.787437	+	0.616395i	$0.788592\pi$
$228$		0			0
$229$	−0.0887860	+	1.52440i	−0.00586714	+	0.100735i	−0.999970	−	0.00770332i	$-0.997548\pi$
$229$	−0.0887860	+	1.52440i	−0.00586714	+	0.100735i	0.994103	+	0.108438i	$0.0345850\pi$
$230$	−3.34049	−	2.19707i	−0.220265	−	0.144871i
$231$		0			0
$232$	1.68289	−	0.398853i	0.110487	−	0.0261860i
$233$	−2.44148	+	13.8463i	−0.159946	+	0.907101i	0.794177	+	0.607687i	$0.207902\pi$
$233$	−2.44148	+	13.8463i	−0.159946	+	0.907101i	−0.954123	+	0.299414i	$0.903209\pi$
$234$		0			0
$235$	−2.04023	−	11.5707i	−0.133090	−	0.754791i
$236$	2.89968	+	6.72222i	0.188753	+	0.437579i
$237$		0			0
$238$	−3.90425	−	13.0411i	−0.253075	−	0.845329i
$239$	13.6853	+	18.3826i	0.885229	+	1.18907i	0.981066	+	0.193672i	$0.0620396\pi$
$239$	13.6853	+	18.3826i	0.885229	+	1.18907i	−0.0958376	+	0.995397i	$0.530553\pi$
$240$		0			0
$241$	−6.31686	−	3.17245i	−0.406905	−	0.204355i	0.233561	−	0.972342i	$-0.424962\pi$
$241$	−6.31686	−	3.17245i	−0.406905	−	0.204355i	−0.640465	+	0.767987i	$0.721259\pi$
$242$	11.3694			0.730855
$243$		0			0
$244$	9.43390			0.603943
$245$	9.85750	+	4.95062i	0.629773	+	0.316284i
$246$		0			0
$247$	11.9764	+	16.0871i	0.762039	+	1.02360i
$248$	0.499989	+	1.67008i	0.0317493	+	0.106050i
$249$		0			0
$250$	−3.57867	−	8.29630i	−0.226335	−	0.524704i
$251$	−0.0115419	−	0.0654574i	−0.000728518	−	0.00413163i	0.984441	−	0.175714i	$-0.0562233\pi$
$251$	−0.0115419	−	0.0654574i	−0.000728518	−	0.00413163i	−0.985170	+	0.171582i	$0.945112\pi$
$252$		0			0
$253$	−3.03237	+	17.1974i	−0.190644	+	1.08119i
$254$	2.95503	−	0.700355i	0.185415	−	0.0439442i
$255$		0			0
$256$	11.3048	+	7.43532i	0.706553	+	0.464707i
$257$	1.12474	−	19.3110i	0.0701591	−	1.20459i	−0.761075	−	0.648663i	$-0.775328\pi$
$257$	1.12474	−	19.3110i	0.0701591	−	1.20459i	0.831235	−	0.555922i	$-0.187635\pi$
$258$		0			0
$259$	1.09039	−	3.64214i	0.0677533	−	0.226312i
$260$	−8.68330	+	3.16046i	−0.538515	+	0.196003i
$261$		0			0
$262$	−12.2274	−	4.45042i	−0.755413	−	0.274948i
$263$	−8.99328	+	12.0801i	−0.554549	+	0.744889i	−0.987688	−	0.156439i	$-0.949999\pi$
$263$	−8.99328	+	12.0801i	−0.554549	+	0.744889i	0.433139	+	0.901327i	$0.357406\pi$
$264$		0			0
$265$	−5.97849	−	1.41693i	−0.367256	−	0.0870412i
$266$	5.25336	−	12.1787i	0.322104	−	0.746722i
$267$		0			0
$268$	6.15281	−	4.04677i	0.375843	−	0.247196i
$269$	−5.86823	−	10.1641i	−0.357792	−	0.619715i	0.629799	−	0.776758i	$-0.283137\pi$
$269$	−5.86823	−	10.1641i	−0.357792	−	0.619715i	−0.987592	+	0.157043i	$0.949804\pi$
$270$		0			0
$271$	1.44013	−	2.49438i	0.0874817	−	0.151523i	−0.818964	−	0.573844i	$-0.805451\pi$
$271$	1.44013	−	2.49438i	0.0874817	−	0.151523i	0.906446	+	0.422322i	$0.138785\pi$
$272$	0.188683	+	3.23957i	0.0114406	+	0.196428i
$273$		0			0
$274$	7.20053	−	0.841621i	0.435000	−	0.0508442i
$275$	−9.73782	+	10.3215i	−0.587213	+	0.622409i
$276$		0			0
$277$	2.28547	+	0.267133i	0.137320	+	0.0160504i	0.184475	−	0.982837i	$-0.440941\pi$
$277$	2.28547	+	0.267133i	0.137320	+	0.0160504i	−0.0471550	+	0.998888i	$0.515015\pi$
$278$	9.53200	−	7.99830i	0.571692	−	0.479706i
$279$		0			0
$280$	11.4211	+	9.58343i	0.682540	+	0.572719i
$281$	4.35455	+	4.61556i	0.259771	+	0.275341i	0.844112	−	0.536167i	$-0.180128\pi$
$281$	4.35455	+	4.61556i	0.259771	+	0.275341i	−0.584341	+	0.811508i	$0.698647\pi$
$282$		0			0
$283$	−13.1201	+	6.58917i	−0.779910	+	0.391686i	−0.793770	−	0.608218i	$-0.791885\pi$
$283$	−13.1201	+	6.58917i	−0.779910	+	0.391686i	0.0138596	+	0.999904i	$0.495588\pi$
$284$	−7.61373	+	3.82376i	−0.451792	+	0.226898i
$285$		0			0
$286$	−12.1778	−	12.9077i	−0.720090	−	0.763251i
$287$	−1.98831	−	1.66839i	−0.117366	−	0.0984819i
$288$		0			0
$289$	3.06122	−	2.56867i	0.180072	−	0.151098i
$290$	0.750510	+	0.0877220i	0.0440715	+	0.00515121i
$291$		0			0
$292$	−4.19607	+	4.44757i	−0.245556	+	0.260275i
$293$	−25.1838	+	2.94357i	−1.47125	+	0.171965i	−0.813631	−	0.581382i	$-0.802512\pi$
$293$	−25.1838	+	2.94357i	−1.47125	+	0.171965i	−0.657623	+	0.753347i	$0.728438\pi$
$294$		0			0
$295$	0.453727	+	7.79019i	0.0264170	+	0.453562i
$296$	1.32461	−	2.29430i	0.0769916	−	0.133353i
$297$		0			0
$298$	9.12136	+	15.7987i	0.528386	+	0.915191i
$299$	12.9671	−	8.52862i	0.749909	−	0.493223i
$300$		0			0
$301$	−12.6366	+	29.2950i	−0.728364	+	1.68854i
$302$	−1.77351	−	0.420330i	−0.102054	−	0.0241873i
$303$		0			0
$304$	−1.88805	+	2.53609i	−0.108287	+	0.145455i
$305$	9.44914	+	3.43921i	0.541056	+	0.196928i
$306$		0			0
$307$	11.4486	−	4.16694i	0.653405	−	0.237820i	0.00601852	−	0.999982i	$-0.498084\pi$
$307$	11.4486	−	4.16694i	0.653405	−	0.237820i	0.647386	+	0.762162i	$0.275862\pi$
$308$	7.65498	−	25.5694i	0.436183	−	1.45695i
$309$		0			0
$310$	−0.0442860	+	0.760362i	−0.00251528	+	0.0431857i
$311$	−21.0005	−	13.8123i	−1.19083	−	0.783221i	−0.209927	−	0.977717i	$-0.567323\pi$
$311$	−21.0005	−	13.8123i	−1.19083	−	0.783221i	−0.980903	+	0.194496i	$0.937693\pi$
$312$		0			0
$313$	28.7660	−	6.81767i	1.62595	−	0.385358i	0.686254	−	0.727362i	$-0.259254\pi$
$313$	28.7660	−	6.81767i	1.62595	−	0.385358i	0.939698	+	0.342005i	$0.111106\pi$
$314$	−2.67130	+	15.1497i	−0.150750	+	0.854947i
$315$		0			0
$316$	−2.71203	−	15.3807i	−0.152563	−	0.865230i
$317$	−1.69844	−	3.93743i	−0.0953940	−	0.221148i	0.863837	−	0.503771i	$-0.168055\pi$
$317$	−1.69844	−	3.93743i	−0.0953940	−	0.221148i	−0.959231	+	0.282623i	$0.908795\pi$
$318$		0			0
$319$	−0.946519	−	3.16159i	−0.0529949	−	0.177015i
$320$	2.79109	+	3.74909i	0.156027	+	0.209580i
$321$		0			0
$322$	−9.17238	−	4.60654i	−0.511157	−	0.256712i
$323$	20.4570			1.13826
$324$		0			0
$325$	12.6118			0.699576
$326$	−12.3356	−	6.19517i	−0.683206	−	0.343119i
$327$		0			0
$328$	−1.08005	−	1.45075i	−0.0596355	−	0.0801044i
$329$	−8.65060	−	28.8950i	−0.476923	−	1.59303i
$330$		0			0
$331$	−11.0234	−	25.5552i	−0.605903	−	1.40464i	−0.894447	−	0.447174i	$-0.852431\pi$
$331$	−11.0234	−	25.5552i	−0.605903	−	1.40464i	0.288545	−	0.957466i	$-0.406829\pi$
$332$	0.391188	+	2.21854i	0.0214692	+	0.121758i
$333$		0			0
$334$	−0.460091	+	2.60930i	−0.0251750	+	0.142775i
$335$	7.63804	−	1.81025i	0.417311	−	0.0989044i
$336$		0			0
$337$	−22.4760	−	14.7827i	−1.22435	−	0.805267i	−0.238214	−	0.971213i	$-0.576562\pi$
$337$	−22.4760	−	14.7827i	−1.22435	−	0.805267i	−0.986135	+	0.165946i	$0.946932\pi$
$338$	−0.326297	+	5.60231i	−0.0177482	+	0.304725i
$339$		0			0
$340$	−2.70326	+	9.02952i	−0.146605	+	0.489695i
$341$	3.12596	−	1.13776i	0.169280	−	0.0616130i
$342$		0			0
$343$	1.60598	+	0.584529i	0.0867148	+	0.0315616i
$344$	−13.2758	+	17.8325i	−0.715785	+	0.961466i
$345$		0			0
$346$	14.2050	+	3.36665i	0.763667	+	0.180992i
$347$	12.0799	−	28.0044i	0.648485	−	1.50336i	−0.203109	−	0.979156i	$-0.565105\pi$
$347$	12.0799	−	28.0044i	0.648485	−	1.50336i	0.851594	−	0.524201i	$-0.175636\pi$
$348$		0			0
$349$	6.66329	−	4.38252i	0.356678	−	0.234591i	−0.358506	−	0.933528i	$-0.616714\pi$
$349$	6.66329	−	4.38252i	0.356678	−	0.234591i	0.715183	+	0.698937i	$0.246343\pi$
$350$	−4.17028	−	7.22314i	−0.222911	−	0.386093i
$351$		0			0
$352$	14.7870	−	25.6119i	0.788151	−	1.36512i
$353$	−1.26931	−	21.7932i	−0.0675587	−	1.15994i	−0.846340	−	0.532643i	$-0.821199\pi$
$353$	−1.26931	−	21.7932i	−0.0675587	−	1.15994i	0.778782	−	0.627295i	$-0.215838\pi$
$354$		0			0
$355$	−9.02001	+	1.05429i	−0.478733	+	0.0559558i
$356$	0.994153	−	1.05374i	0.0526900	−	0.0558481i
$357$		0			0
$358$	9.22555	+	1.07831i	0.487585	+	0.0569906i
$359$	13.2606	−	11.1269i	0.699866	−	0.587258i	−0.221869	−	0.975076i	$-0.571216\pi$
$359$	13.2606	−	11.1269i	0.699866	−	0.587258i	0.921736	+	0.387819i	$0.126771\pi$
$360$		0			0
$361$	0.713665	+	0.598836i	0.0375613	+	0.0315177i
$362$	8.46589	+	8.97332i	0.444957	+	0.471627i
$363$		0			0
$364$	−21.1988	+	10.6464i	−1.11112	+	0.558024i
$365$	−5.82425	+	2.92505i	−0.304855	+	0.153104i
$366$		0			0
$367$	16.4058	+	17.3891i	0.856376	+	0.907705i	0.996598	−	0.0824149i	$-0.0262633\pi$
$367$	16.4058	+	17.3891i	0.856376	+	0.907705i	−0.140222	+	0.990120i	$0.544782\pi$
$368$	1.87433	+	1.57275i	0.0977062	+	0.0819853i
$369$		0			0
$370$	0.886651	−	0.743989i	0.0460948	−	0.0386781i
$371$	−15.6663	−	1.83112i	−0.813351	−	0.0950671i
$372$		0			0
$373$	7.91296	−	8.38725i	0.409718	−	0.434275i	−0.489348	−	0.872088i	$-0.662765\pi$
$373$	7.91296	−	8.38725i	0.409718	−	0.434275i	0.899066	+	0.437813i	$0.144247\pi$
$374$	−17.9784	+	2.10138i	−0.929642	+	0.108660i
$375$		0			0
$376$	−1.22207	−	20.9821i	−0.0630235	−	1.08207i
$377$	−1.46658	+	2.54020i	−0.0755329	+	0.130827i
$378$		0			0
$379$	−10.3656	−	17.9537i	−0.532443	−	0.922218i	−0.999282	−	0.0378763i	$-0.987941\pi$
$379$	−10.3656	−	17.9537i	−0.532443	−	0.922218i	0.466839	−	0.884342i	$-0.345393\pi$
$380$	−7.67266	+	5.04638i	−0.393599	+	0.258874i
$381$		0			0
$382$	−1.78509	+	4.13829i	−0.0913329	+	0.211734i
$383$	15.4278	+	3.65646i	0.788324	+	0.186836i	0.605010	−	0.796218i	$-0.293169\pi$
$383$	15.4278	+	3.65646i	0.788324	+	0.186836i	0.183314	+	0.983054i	$0.441317\pi$
$384$		0			0
$385$	16.9889	−	22.8200i	0.865834	−	1.16302i
$386$	−0.129079	−	0.0469808i	−0.00656994	−	0.00239126i
$387$		0			0
$388$	6.51155	−	2.37001i	0.330574	−	0.120319i
$389$	−8.17648	+	27.3114i	−0.414564	+	1.38474i	0.454811	+	0.890588i	$0.349707\pi$
$389$	−8.17648	+	27.3114i	−0.414564	+	1.38474i	−0.869375	+	0.494153i	$0.835478\pi$
$390$		0			0
$391$	0.920492	−	15.8042i	0.0465513	−	0.799255i
$392$	16.4863	+	10.8432i	0.832685	+	0.547665i
$393$		0			0
$394$	−8.52915	+	2.02145i	−0.429693	+	0.101839i
$395$	2.89074	−	16.3942i	0.145449	−	0.824882i
$396$		0			0
$397$	5.49087	+	31.1403i	0.275579	+	1.56289i	0.737117	+	0.675765i	$0.236187\pi$
$397$	5.49087	+	31.1403i	0.275579	+	1.56289i	−0.461538	+	0.887120i	$0.652702\pi$
$398$	−6.33916	−	14.6958i	−0.317753	−	0.736635i
$399$		0			0
$400$	0.570228	+	1.90470i	0.0285114	+	0.0952348i
$401$	−10.1802	−	13.6744i	−0.508376	−	0.682867i	0.471639	−	0.881792i	$-0.343663\pi$
$401$	−10.1802	−	13.6744i	−0.508376	−	0.682867i	−0.980015	+	0.198924i	$0.936255\pi$
$402$		0			0
$403$	−2.64210	−	1.32691i	−0.131612	−	0.0660982i
$404$	−13.2952			−0.661458
$405$		0			0
$406$	1.93980			0.0962705
$407$	−4.51752	−	2.26878i	−0.223925	−	0.112459i
$408$		0			0
$409$	−14.2344	−	19.1202i	−0.703848	−	0.945432i	0.296105	−	0.955155i	$-0.404312\pi$
$409$	−14.2344	−	19.1202i	−0.703848	−	0.945432i	−0.999953	+	0.00972374i	$0.996905\pi$
$410$	−0.226629	−	0.756995i	−0.0111924	−	0.0373853i
$411$		0			0
$412$	−1.79107	−	4.15216i	−0.0882395	−	0.204562i
$413$	3.47862	+	19.7282i	0.171172	+	0.970762i
$414$		0			0
$415$	−0.416966	+	2.36473i	−0.0204681	+	0.116080i
$416$	−25.5762	+	6.06166i	−1.25397	+	0.297197i
$417$		0			0
$418$	−14.7346	−	9.69113i	−0.720695	−	0.474009i
$419$	−0.914980	+	15.7096i	−0.0446997	+	0.767464i	0.899262	+	0.437410i	$0.144104\pi$
$419$	−0.914980	+	15.7096i	−0.0446997	+	0.767464i	−0.943962	+	0.330054i	$0.892933\pi$
$420$		0			0
$421$	6.75647	−	22.5682i	0.329290	−	1.09991i	−0.619763	−	0.784789i	$-0.712771\pi$
$421$	6.75647	−	22.5682i	0.329290	−	1.09991i	0.949053	−	0.315116i	$-0.102044\pi$
$422$	−0.874971	+	0.318464i	−0.0425929	+	0.0155026i
$423$		0			0
$424$	−10.3281	−	3.75912i	−0.501577	−	0.182559i
$425$	7.68195	−	10.3186i	0.372629	−	0.500528i
$426$		0			0
$427$	25.1184	+	5.95318i	1.21557	+	0.288094i
$428$	9.25130	−	21.4469i	0.447179	−	1.03668i
$429$		0			0
$430$	−8.11506	+	5.33736i	−0.391343	+	0.257390i
$431$	−0.705848	−	1.22256i	−0.0339995	−	0.0588888i	0.848525	−	0.529155i	$-0.177491\pi$
$431$	−0.705848	−	1.22256i	−0.0339995	−	0.0588888i	−0.882524	+	0.470267i	$0.844158\pi$
$432$		0			0
$433$	−6.50524	+	11.2674i	−0.312622	+	0.541477i	−0.978929	−	0.204200i	$-0.934541\pi$
$433$	−6.50524	+	11.2674i	−0.312622	+	0.541477i	0.666307	+	0.745677i	$0.267874\pi$
$434$	0.113689	+	1.95197i	0.00545727	+	0.0936977i
$435$		0			0
$436$	10.5353	−	1.23140i	0.504550	−	0.0589734i
$437$	10.5849	−	11.2194i	0.506346	−	0.536695i
$438$		0			0
$439$	−20.5982	−	2.40758i	−0.983097	−	0.114908i	−0.390669	−	0.920531i	$-0.627756\pi$
$439$	−20.5982	−	2.40758i	−0.983097	−	0.114908i	−0.592428	+	0.805624i	$0.701830\pi$
$440$	15.1863	−	12.7428i	0.723979	−	0.607490i
$441$		0			0
$442$	12.3238	+	10.3409i	0.586182	+	0.491865i
$443$	23.3099	+	24.7070i	1.10749	+	1.17387i	0.983373	+	0.181599i	$0.0581272\pi$
$443$	23.3099	+	24.7070i	1.10749	+	1.17387i	0.124113	+	0.992268i	$0.460391\pi$
$444$		0			0
$445$	1.37991	−	0.693016i	0.0654140	−	0.0328521i
$446$	−10.4063	+	5.22626i	−0.492754	+	0.247470i
$447$		0			0
$448$	8.23407	+	8.72761i	0.389023	+	0.412341i
$449$	−0.919709	−	0.771727i	−0.0434038	−	0.0364201i	0.620828	−	0.783947i	$-0.286797\pi$
$449$	−0.919709	−	0.771727i	−0.0434038	−	0.0364201i	−0.664231	+	0.747527i	$0.731241\pi$
$450$		0			0
$451$	−2.64380	+	2.21841i	−0.124492	+	0.104461i
$452$	13.8246	+	1.61587i	0.650256	+	0.0760040i
$453$		0			0
$454$	−13.1931	+	13.9839i	−0.619182	+	0.656295i
$455$	−25.1143	+	2.93544i	−1.17738	+	0.137615i
$456$		0			0
$457$	1.86373	+	31.9990i	0.0871815	+	1.49685i	0.704257	+	0.709945i	$0.251280\pi$
$457$	1.86373	+	31.9990i	0.0871815	+	1.49685i	−0.617076	+	0.786904i	$0.711683\pi$
$458$	−0.596704	+	1.03352i	−0.0278821	+	0.0482933i
$459$		0			0
$460$	3.55340	+	6.15466i	0.165678	+	0.286963i
$461$	0.281296	−	0.185011i	0.0131013	−	0.00861684i	−0.542941	−	0.839771i	$-0.682689\pi$
$461$	0.281296	−	0.185011i	0.0131013	−	0.00861684i	0.556043	+	0.831154i	$0.312319\pi$
$462$		0			0
$463$	−1.16952	+	2.71124i	−0.0543520	+	0.126002i	−0.943228	−	0.332145i	$-0.892228\pi$
$463$	−1.16952	+	2.71124i	−0.0543520	+	0.126002i	0.888876	+	0.458147i	$0.151487\pi$
$464$	−0.449944	−	0.106639i	−0.0208881	−	0.00495057i
$465$		0			0
$466$	−6.56187	+	8.81412i	−0.303973	+	0.408306i
$467$	3.55605	+	1.29430i	0.164554	+	0.0598929i	0.422984	−	0.906137i	$-0.360983\pi$
$467$	3.55605	+	1.29430i	0.164554	+	0.0598929i	−0.258429	+	0.966030i	$0.583205\pi$
$468$		0			0
$469$	18.9360	−	6.89213i	0.874382	−	0.318249i
$470$	2.63359	−	8.79682i	0.121479	−	0.405767i
$471$		0			0
$472$	−0.811652	+	13.9355i	−0.0373593	+	0.641435i
$473$	35.4433	+	23.3114i	1.62968	+	1.07186i
$474$		0			0
$475$	12.1960	−	2.89050i	0.559589	−	0.132625i
$476$	−4.20172	+	23.8292i	−0.192586	+	1.09221i
$477$		0			0
$478$	3.11022	+	17.6389i	0.142258	+	0.806785i
$479$	1.25429	+	2.90777i	0.0573100	+	0.132859i	0.944465	−	0.328612i	$-0.106581\pi$
$479$	1.25429	+	2.90777i	0.0573100	+	0.132859i	−0.887155	+	0.461472i	$0.847322\pi$
$480$		0			0
$481$	1.28860	+	4.30421i	0.0587549	+	0.196255i
$482$	−3.29904	−	4.43138i	−0.150267	−	0.201844i
$483$		0			0
$484$	−18.0593	−	9.06974i	−0.820879	−	0.412261i
$485$	7.38607			0.335384
$486$		0			0
$487$	1.22501			0.0555106			0.0277553	−	0.999615i	$-0.491164\pi$
$487$	1.22501			0.0555106			0.0277553	+	0.999615i	$0.491164\pi$
$488$	16.0746	+	8.07299i	0.727665	+	0.365447i
$489$		0			0
$490$	5.14817	+	6.91520i	0.232571	+	0.312397i
$491$	−11.6292	−	38.8443i	−0.524819	−	1.75302i	−0.649032	−	0.760761i	$-0.724826\pi$
$491$	−11.6292	−	38.8443i	−0.524819	−	1.75302i	0.124213	−	0.992256i	$-0.460359\pi$
$492$		0			0
$493$	1.18502	+	2.74718i	0.0533705	+	0.123727i
$494$	2.72183	+	15.4363i	0.122461	+	0.694512i
$495$		0			0
$496$	0.0809373	−	0.459018i	0.00363419	−	0.0206105i
$497$	−22.6850	+	5.37646i	−1.01756	+	0.241167i
$498$		0			0
$499$	34.3817	+	22.6132i	1.53914	+	1.01231i	0.983506	+	0.180876i	$0.0578934\pi$
$499$	34.3817	+	22.6132i	1.53914	+	1.01231i	0.555630	+	0.831429i	$0.312477\pi$
$500$	−0.933801	+	16.0328i	−0.0417609	+	0.717006i
$501$		0			0
$502$	0.0148986	−	0.0497649i	0.000664959	−	0.00222112i
$503$	−9.54144	+	3.47280i	−0.425432	+	0.154845i	−0.545858	−	0.837878i	$-0.683796\pi$
$503$	−9.54144	+	3.47280i	−0.425432	+	0.154845i	0.120426	+	0.992722i	$0.461574\pi$
$504$		0			0
$505$	−13.3166	−	4.84686i	−0.592582	−	0.215682i
$506$	−8.15000	+	10.9473i	−0.362311	+	0.486669i
$507$		0			0
$508$	−5.25250	−	1.24486i	−0.233042	−	0.0552319i
$509$	−9.60383	+	22.2642i	−0.425682	+	0.986842i	0.561534	+	0.827454i	$0.310211\pi$
$509$	−9.60383	+	22.2642i	−0.425682	+	0.986842i	−0.987216	+	0.159388i	$0.949048\pi$
$510$		0			0
$511$	−13.9789	+	9.19409i	−0.618392	+	0.406723i
$512$	−3.94773	−	6.83768i	−0.174467	−	0.302186i
$513$		0			0
$514$	7.55901	−	13.0926i	0.333414	−	0.577490i
$515$	−0.280256	−	4.81181i	−0.0123496	−	0.212034i
$516$		0			0
$517$	−39.8346	+	4.65600i	−1.75192	+	0.204771i
$518$	2.03905	−	2.16127i	0.0895909	−	0.0949608i
$519$		0			0
$520$	−17.5002	−	2.04548i	−0.767435	−	0.0897003i
$521$	4.86477	−	4.08202i	0.213129	−	0.178837i	−0.529973	−	0.848014i	$-0.677798\pi$
$521$	4.86477	−	4.08202i	0.213129	−	0.178837i	0.743102	+	0.669178i	$0.233354\pi$
$522$		0			0
$523$	21.5335	+	18.0688i	0.941595	+	0.790092i	0.977862	−	0.209250i	$-0.0671024\pi$
$523$	21.5335	+	18.0688i	0.941595	+	0.790092i	−0.0362674	+	0.999342i	$0.511547\pi$
$524$	15.8719	+	16.8233i	0.693369	+	0.734928i
$525$		0			0
$526$	−10.5182	+	5.28246i	−0.458617	+	0.230326i
$527$	−2.69497	+	1.35347i	−0.117395	+	0.0589579i
$528$		0			0
$529$	7.59220	+	8.04726i	0.330096	+	0.349881i
$530$	−3.67848	−	3.08661i	−0.159783	−	0.134074i
$531$		0			0
$532$	−18.0598	+	15.1540i	−0.782991	+	0.657008i
$533$	3.04663	+	0.356100i	0.131964	+	0.0154244i
$534$		0			0
$535$	17.0849	−	18.1089i	0.738645	−	0.782918i
$536$	13.9469	−	1.63016i	0.602415	−	0.0704122i
$537$		0			0
$538$	−0.533340	−	9.15709i	−0.0229939	−	0.394790i
$539$	18.8268	−	32.6089i	0.810926	−	1.40457i
$540$		0			0
$541$	−1.34390	−	2.32771i	−0.0577788	−	0.100076i	0.835689	−	0.549203i	$-0.185068\pi$
$541$	−1.34390	−	2.32771i	−0.0577788	−	0.100076i	−0.893468	+	0.449127i	$0.851735\pi$
$542$	1.88074	−	1.23698i	0.0807845	−	0.0531328i
$543$		0			0
$544$	−10.6192	+	24.6180i	−0.455293	+	1.05549i
$545$	11.0012	+	2.60734i	0.471242	+	0.111686i
$546$		0			0
$547$	19.5913	−	26.3156i	0.837662	−	1.12518i	−0.152918	−	0.988239i	$-0.548867\pi$
$547$	19.5913	−	26.3156i	0.837662	−	1.12518i	0.990580	−	0.136937i	$-0.0437257\pi$
$548$	−12.1088	−	4.40724i	−0.517262	−	0.188268i
$549$		0			0
$550$	−10.4214	+	3.79308i	−0.444370	+	0.161737i
$551$	−0.836042	+	2.79257i	−0.0356166	+	0.118968i
$552$		0			0
$553$	2.48487	−	42.6635i	0.105667	−	1.81424i
$554$	1.50251	+	0.988215i	0.0638355	+	0.0419852i
$555$		0			0
$556$	−21.5212	+	5.10062i	−0.912703	+	0.216315i
$557$	−1.71906	+	9.74928i	−0.0728390	+	0.413090i	0.926485	+	0.376331i	$0.122815\pi$
$557$	−1.71906	+	9.74928i	−0.0728390	+	0.413090i	−0.999324	+	0.0367591i	$0.988297\pi$
$558$		0			0
$559$	−6.54721	−	37.1311i	−0.276917	−	1.57048i
$560$	−1.57884	−	3.66016i	−0.0667182	−	0.154670i
$561$		0			0
$562$	1.42235	+	4.75098i	0.0599982	+	0.200408i
$563$	4.20131	+	5.64334i	0.177064	+	0.237838i	0.881791	−	0.471640i	$-0.156338\pi$
$563$	4.20131	+	5.64334i	0.177064	+	0.237838i	−0.704727	+	0.709479i	$0.748930\pi$
$564$		0			0
$565$	13.2579	+	6.65836i	0.557764	+	0.280119i
$566$	−11.4745			−0.482310
$567$		0			0
$568$	−16.2454			−0.681640
$569$	−3.51923	−	1.76742i	−0.147534	−	0.0740943i	0.373501	−	0.927630i	$-0.378157\pi$
$569$	−3.51923	−	1.76742i	−0.147534	−	0.0740943i	−0.521034	+	0.853536i	$0.674454\pi$
$570$		0			0
$571$	15.2678	+	20.5083i	0.638939	+	0.858244i	0.997154	−	0.0753955i	$-0.0240219\pi$
$571$	15.2678	+	20.5083i	0.638939	+	0.858244i	−0.358215	+	0.933639i	$0.616615\pi$
$572$	9.04650	+	30.2174i	0.378253	+	1.26345i
$573$		0			0
$574$	−0.803467	−	1.86265i	−0.0335361	−	0.0777453i
$575$	−1.68431	−	9.55219i	−0.0702405	−	0.398354i
$576$		0			0
$577$	0.816045	−	4.62802i	0.0339724	−	0.192667i	−0.963099	−	0.269149i	$-0.913258\pi$
$577$	0.816045	−	4.62802i	0.0339724	−	0.192667i	0.997071	+	0.0764818i	$0.0243687\pi$
$578$	3.03899	−	0.720254i	0.126405	−	0.0299586i
$579$		0			0
$580$	−1.12214	−	0.738043i	−0.0465943	−	0.0306456i
$581$	−0.358422	+	6.15387i	−0.0148699	+	0.255306i
$582$		0			0
$583$	−6.01507	+	20.0917i	−0.249119	+	0.832114i
$584$	−10.9558	+	3.98757i	−0.453353	+	0.165007i
$585$		0			0
$586$	−18.6213	−	6.77759i	−0.769238	−	0.279980i
$587$	−16.5849	+	22.2775i	−0.684534	+	0.919489i	−0.999562	−	0.0295936i	$-0.990579\pi$
$587$	−16.5849	+	22.2775i	−0.684534	+	0.919489i	0.315028	+	0.949082i	$0.397986\pi$
$588$		0			0
$589$	−2.85910	−	0.677620i	−0.117807	−	0.0279208i
$590$	−2.41558	+	5.59994i	−0.0994479	+	0.230546i
$591$		0			0
$592$	−0.591781	+	0.389221i	−0.0243221	+	0.0159969i
$593$	−7.16631	−	12.4124i	−0.294285	−	0.509717i	0.680533	−	0.732717i	$-0.261748\pi$
$593$	−7.16631	−	12.4124i	−0.294285	−	0.509717i	−0.974818	+	0.223000i	$0.928415\pi$
$594$		0			0
$595$	−12.8956	+	22.3359i	−0.528669	+	0.915682i
$596$	−1.88540	−	32.3711i	−0.0772291	−	1.32597i
$597$		0			0
$598$	12.0479	−	1.40820i	0.492677	−	0.0575857i
$599$	18.8738	−	20.0050i	0.771161	−	0.817383i	−0.216120	−	0.976367i	$-0.569340\pi$
$599$	18.8738	−	20.0050i	0.771161	−	0.817383i	0.987281	+	0.158983i	$0.0508217\pi$
$600$		0			0
$601$	−18.6234	−	2.17676i	−0.759665	−	0.0887921i	−0.272564	−	0.962138i	$-0.587872\pi$
$601$	−18.6234	−	2.17676i	−0.759665	−	0.0887921i	−0.487101	+	0.873346i	$0.661946\pi$
$602$	−19.1011	+	16.0277i	−0.778503	+	0.653242i
$603$		0			0
$604$	2.48176	+	2.08244i	0.100981	+	0.0847333i
$605$	−14.7821	−	15.6681i	−0.600976	−	0.636998i
$606$		0			0
$607$	23.5997	−	11.8522i	0.957881	−	0.481066i	0.100041	−	0.994983i	$-0.468103\pi$
$607$	23.5997	−	11.8522i	0.957881	−	0.481066i	0.857840	+	0.513918i	$0.171806\pi$
$608$	−23.3436	+	11.7236i	−0.946709	+	0.475455i
$609$		0			0
$610$	5.39311	+	5.71636i	0.218361	+	0.231449i
$611$	27.3057	+	22.9122i	1.10467	+	0.926928i
$612$		0			0
$613$	−26.7821	+	22.4728i	−1.08172	+	0.907670i	−0.996062	−	0.0886553i	$-0.971743\pi$
$613$	−26.7821	+	22.4728i	−1.08172	+	0.907670i	−0.0856560	+	0.996325i	$0.527299\pi$
$614$	9.45747	+	1.10542i	0.381672	+	0.0446111i
$615$		0			0
$616$	34.9243	−	37.0176i	1.40714	−	1.49148i
$617$	−7.10306	+	0.830228i	−0.285958	+	0.0334237i	−0.257863	−	0.966182i	$-0.583018\pi$
$617$	−7.10306	+	0.830228i	−0.285958	+	0.0334237i	−0.0280954	+	0.999605i	$0.508944\pi$
$618$		0			0
$619$	1.09438	+	18.7898i	0.0439868	+	0.755224i	0.946130	+	0.323787i	$0.104956\pi$
$619$	1.09438	+	18.7898i	0.0439868	+	0.755224i	−0.902143	+	0.431437i	$0.858007\pi$
$620$	0.676908	−	1.17244i	0.0271853	−	0.0470863i
$621$		0			0
$622$	−9.82235	−	17.0128i	−0.393841	−	0.682152i
$623$	3.31196	−	2.17831i	0.132691	−	0.0872721i
$624$		0			0
$625$	−1.22031	+	2.82901i	−0.0488126	+	0.113160i
$626$	22.4820	+	5.32834i	0.898562	+	0.212963i
$627$		0			0
$628$	16.3285	−	21.9330i	0.651578	−	0.875221i
$629$	4.30649	+	1.56744i	0.171711	+	0.0624978i
$630$		0			0
$631$	−22.0642	+	8.03070i	−0.878361	+	0.319697i	−0.741548	−	0.670900i	$-0.765908\pi$
$631$	−22.0642	+	8.03070i	−0.878361	+	0.319697i	−0.136813	+	0.990597i	$0.543686\pi$
$632$	8.54081	−	28.5283i	0.339735	−	1.13479i
$633$		0			0
$634$	0.194865	−	3.34571i	0.00773909	−	0.132875i
$635$	−4.80716	−	3.16172i	−0.190766	−	0.125469i
$636$		0			0
$637$	−32.5634	+	7.71768i	−1.29021	+	0.305786i
$638$	0.447890	−	2.54011i	0.0177321	−	0.100564i
$639$		0			0
$640$	−2.37461	−	13.4671i	−0.0938648	−	0.532334i
$641$	1.72652	+	4.00251i	0.0681933	+	0.158090i	0.948904	−	0.315565i	$-0.102194\pi$
$641$	1.72652	+	4.00251i	0.0681933	+	0.158090i	−0.880711	+	0.473654i	$0.842935\pi$
$642$		0			0
$643$	−5.45270	−	18.2133i	−0.215034	−	0.718262i	−0.995643	−	0.0932433i	$-0.970277\pi$
$643$	−5.45270	−	18.2133i	−0.215034	−	0.718262i	0.780610	−	0.625019i	$-0.214909\pi$
$644$	10.8947	+	14.6342i	0.429312	+	0.576667i
$645$		0			0
$646$	14.2875	+	7.17544i	0.562133	+	0.282314i
$647$	20.6268			0.810924			0.405462	−	0.914112i	$-0.367111\pi$
$647$	20.6268			0.810924			0.405462	+	0.914112i	$0.367111\pi$
$648$		0			0
$649$	26.6367			1.04558
$650$	8.80828	+	4.42368i	0.345489	+	0.173511i
$651$		0			0
$652$	14.6519	+	19.6810i	0.573814	+	0.770766i
$653$	1.71817	+	5.73909i	0.0672372	+	0.224588i	0.985004	−	0.172532i	$-0.0551949\pi$
$653$	1.71817	+	5.73909i	0.0672372	+	0.224588i	−0.917767	+	0.397120i	$0.870010\pi$
$654$		0			0
$655$	9.76452	+	22.6367i	0.381531	+	0.884489i
$656$	0.0839701	+	0.476218i	0.00327848	+	0.0185932i
$657$		0			0
$658$	4.09344	−	23.2150i	0.159579	−	0.905016i
$659$	37.7920	−	8.95688i	1.47217	−	0.348910i	0.585256	−	0.810848i	$-0.300994\pi$
$659$	37.7920	−	8.95688i	1.47217	−	0.348910i	0.886912	+	0.461938i	$0.152846\pi$
$660$		0			0
$661$	−25.8965	−	17.0324i	−1.00726	−	0.662483i	−0.0651777	−	0.997874i	$-0.520761\pi$
$661$	−25.8965	−	17.0324i	−1.00726	−	0.662483i	−0.942079	+	0.335390i	$0.891132\pi$
$662$	1.26474	−	21.7147i	0.0491555	−	0.843967i
$663$		0			0
$664$	−1.23194	+	4.11497i	−0.0478086	+	0.159692i
$665$	−23.6135	+	8.59460i	−0.915691	+	0.333284i
$666$		0			0
$667$	2.11981	+	0.771549i	0.0820795	+	0.0298745i
$668$	2.81233	−	3.77762i	0.108812	−	0.146160i
$669$		0			0
$670$	5.96949	+	1.41480i	0.230622	+	0.0546583i
$671$	13.5952	−	31.5173i	0.524839	−	1.21671i
$672$		0			0
$673$	32.2411	−	21.2053i	1.24280	−	0.817405i	0.254085	−	0.967182i	$-0.418226\pi$
$673$	32.2411	−	21.2053i	1.24280	−	0.817405i	0.988720	+	0.149777i	$0.0478554\pi$
$674$	−10.5125	−	18.2082i	−0.404926	−	0.701352i
$675$		0			0
$676$	4.98742	−	8.63847i	0.191824	−	0.332249i
$677$	0.231922	+	3.98194i	0.00891348	+	0.153039i	0.999828	+	0.0185455i	$0.00590355\pi$
$677$	0.231922	+	3.98194i	0.00891348	+	0.153039i	−0.990915	+	0.134493i	$0.957059\pi$
$678$		0			0
$679$	18.8330	−	2.20127i	0.722745	−	0.0844768i
$680$	−12.3331	+	13.0723i	−0.472953	+	0.501301i
$681$		0			0
$682$	2.58230	+	0.301828i	0.0988815	+	0.0115576i
$683$	−32.2624	+	27.0713i	−1.23449	+	1.03586i	−0.236551	+	0.971619i	$0.576017\pi$
$683$	−32.2624	+	27.0713i	−1.23449	+	1.03586i	−0.997935	+	0.0642370i	$0.979539\pi$
$684$		0			0
$685$	−10.5217	−	8.82872i	−0.402012	−	0.337328i
$686$	0.916615	+	0.971555i	0.0349965	+	0.0370941i
$687$		0			0
$688$	5.31170	−	2.66763i	0.202506	−	0.101703i
$689$	16.6574	−	8.36566i	0.634597	−	0.318706i
$690$		0			0
$691$	5.86779	+	6.21949i	0.223221	+	0.236601i	0.829300	−	0.558804i	$-0.188740\pi$
$691$	5.86779	+	6.21949i	0.223221	+	0.236601i	−0.606078	+	0.795405i	$0.707258\pi$
$692$	−19.8777	−	16.6794i	−0.755638	−	0.634056i
$693$		0			0
$694$	18.2596	−	15.3216i	0.693125	−	0.581601i
$695$	−23.4155	−	2.73688i	−0.888200	−	0.103816i
$696$		0			0
$697$	2.14708	−	2.27577i	0.0813265	−	0.0862011i
$698$	6.19096	−	0.723619i	0.234331	−	0.0273894i
$699$		0			0
$700$	0.862006	+	14.8001i	0.0325808	+	0.559390i
$701$	0.440975	−	0.763791i	0.0166554	−	0.0288480i	−0.857578	−	0.514355i	$-0.828032\pi$
$701$	0.440975	−	0.763791i	0.0166554	−	0.0288480i	0.874233	+	0.485507i	$0.161365\pi$
$702$		0			0
$703$	2.23259	+	3.86697i	0.0842039	+	0.145845i
$704$	13.3298	−	8.76713i	0.502385	−	0.330424i
$705$		0			0
$706$	6.75765	−	15.6660i	0.254327	−	0.589597i
$707$	−35.3993	−	8.38979i	−1.33133	−	0.315530i
$708$		0			0
$709$	−24.0259	+	32.2724i	−0.902312	+	1.21202i	0.0743501	+	0.997232i	$0.476312\pi$
$709$	−24.0259	+	32.2724i	−0.902312	+	1.21202i	−0.976662	+	0.214783i	$0.931096\pi$
$710$	−6.66953	−	2.42751i	−0.250303	−	0.0911028i
$711$		0			0
$712$	2.59569	−	0.944754i	0.0972777	−	0.0354062i
$713$	−0.652152	+	2.17834i	−0.0244233	+	0.0815795i
$714$		0			0
$715$	−1.95489	+	33.5642i	−0.0731089	+	1.25523i
$716$	−13.7938	−	9.07230i	−0.515497	−	0.339048i
$717$		0			0
$718$	13.1643	−	3.11999i	0.491286	−	0.116437i
$719$	2.39151	−	13.5629i	0.0891883	−	0.505812i	−0.907186	−	0.420730i	$-0.861774\pi$
$719$	2.39151	−	13.5629i	0.0891883	−	0.505812i	0.996374	−	0.0850815i	$-0.0271151\pi$
$720$		0			0
$721$	−2.14866	−	12.1857i	−0.0800203	−	0.453817i
$722$	0.288389	+	0.668561i	0.0107327	+	0.0248813i
$723$		0			0
$724$	−6.28902	−	21.0068i	−0.233730	−	0.780712i
$725$	1.09465	+	1.47037i	0.0406542	+	0.0546080i
$726$		0			0
$727$	−11.1569	−	5.60321i	−0.413787	−	0.207812i	0.229712	−	0.973259i	$-0.426222\pi$
$727$	−11.1569	−	5.60321i	−0.413787	−	0.207812i	−0.643499	+	0.765447i	$0.722518\pi$
$728$	−45.2317			−1.67640
$729$		0			0
$730$	−5.09374			−0.188528
$731$	−34.3677	−	17.2601i	−1.27113	−	0.638388i
$732$		0			0
$733$	−16.0474	−	21.5554i	−0.592725	−	0.796168i	0.400007	−	0.916512i	$-0.369008\pi$
$733$	−16.0474	−	21.5554i	−0.592725	−	0.796168i	−0.992732	+	0.120344i	$0.961600\pi$
$734$	5.35871	+	17.8993i	0.197793	+	0.660676i
$735$		0			0
$736$	8.00682	+	18.5619i	0.295135	+	0.684200i
$737$	−4.65283	−	26.3875i	−0.171389	−	0.971996i
$738$		0			0
$739$	−4.23374	+	24.0107i	−0.155740	+	0.883248i	0.802365	+	0.596833i	$0.203575\pi$
$739$	−4.23374	+	24.0107i	−0.155740	+	0.883248i	−0.958106	+	0.286415i	$0.907536\pi$
$740$	−2.00187	+	0.474451i	−0.0735901	+	0.0174412i
$741$		0			0
$742$	−10.2993	−	6.77395i	−0.378099	−	0.248680i
$743$	−2.09728	+	36.0090i	−0.0769418	+	1.32104i	0.710082	+	0.704118i	$0.248658\pi$
$743$	−2.09728	+	36.0090i	−0.0769418	+	1.32104i	−0.787024	+	0.616922i	$0.788379\pi$
$744$		0			0
$745$	9.91272	−	33.1108i	0.363174	−	1.21308i
$746$	8.46844	−	3.08226i	0.310052	−	0.112850i
$747$		0			0
$748$	30.2335	+	11.0041i	1.10544	+	0.402349i
$749$	38.1661	−	51.2660i	1.39456	−	1.87322i
$750$		0			0
$751$	−2.27344	−	0.538814i	−0.0829588	−	0.0196616i	0.188927	−	0.981991i	$-0.439499\pi$
$751$	−2.27344	−	0.538814i	−0.0829588	−	0.0196616i	−0.271886	+	0.962330i	$0.587647\pi$
$752$	−2.22572	+	5.15979i	−0.0811635	+	0.188158i
$753$		0			0
$754$	−1.91528	+	1.25970i	−0.0697505	+	0.0458756i
$755$	1.72660	+	2.99055i	0.0628372	+	0.108837i
$756$		0			0
$757$	8.08646	−	14.0062i	0.293907	−	0.509063i	−0.680823	−	0.732448i	$-0.738378\pi$
$757$	8.08646	−	14.0062i	0.293907	−	0.509063i	0.974730	+	0.223386i	$0.0717109\pi$
$758$	−0.942084	−	16.1750i	−0.0342180	−	0.587501i
$759$		0			0
$760$	−17.3920	+	2.03284i	−0.630875	+	0.0737387i
$761$	−31.1257	+	32.9914i	−1.12831	+	1.19594i	−0.150020	+	0.988683i	$0.547934\pi$
$761$	−31.1257	+	32.9914i	−1.12831	+	1.19594i	−0.978287	+	0.207253i	$0.933548\pi$
$762$		0			0
$763$	28.8281	+	3.36952i	1.04365	+	0.121985i
$764$	6.13669	−	5.14929i	0.222018	−	0.186295i
$765$		0			0
$766$	9.49250	+	7.96515i	0.342978	+	0.287793i
$767$	−16.2461	−	17.2199i	−0.586614	−	0.621774i
$768$		0			0
$769$	16.4123	−	8.24257i	0.591843	−	0.297235i	−0.127557	−	0.991831i	$-0.540713\pi$
$769$	16.4123	−	8.24257i	0.591843	−	0.297235i	0.719399	+	0.694597i	$0.244417\pi$
$770$	19.8696	−	9.97891i	0.716052	−	0.359615i
$771$		0			0
$772$	0.167552	+	0.177595i	0.00603033	+	0.00639178i
$773$	−22.5821	−	18.9486i	−0.812222	−	0.681536i	0.138915	−	0.990304i	$-0.455639\pi$
$773$	−22.5821	−	18.9486i	−0.812222	−	0.681536i	−0.951137	+	0.308769i	$0.900083\pi$
$774$		0			0
$775$	−1.41544	+	1.18769i	−0.0508441	+	0.0426633i
$776$	13.1233	+	1.53389i	0.471099	+	0.0550636i
$777$		0			0
$778$	−15.2903	+	16.2067i	−0.548183	+	0.581040i
$779$	3.02780	−	0.353899i	0.108482	−	0.0126797i
$780$		0			0
$781$	1.80245	+	30.9468i	0.0644967	+	1.10736i
$782$	6.18635	−	10.7151i	0.221224	−	0.383170i
$783$		0			0
$784$	−2.63788	−	4.56895i	−0.0942102	−	0.163177i
$785$	24.3507	−	16.0157i	0.869114	−	0.571626i
$786$		0			0
$787$	12.6971	−	29.4351i	0.452601	−	1.04925i	−0.527284	−	0.849689i	$-0.676790\pi$
$787$	12.6971	−	29.4351i	0.452601	−	1.04925i	0.979886	−	0.199559i	$-0.0639510\pi$
$788$	15.1604	+	3.59307i	0.540066	+	0.127998i
$789$		0			0
$790$	7.76935	−	10.4360i	0.276421	−	0.371298i
$791$	35.7894	+	13.0263i	1.27252	+	0.463161i
$792$		0			0
$793$	−28.6670	+	10.4339i	−1.01799	+	0.370520i
$794$	−7.08779	+	23.6749i	−0.251536	+	0.840189i
$795$		0			0
$796$	−1.65411	+	28.4000i	−0.0586283	+	1.00661i
$797$	9.84741	+	6.47674i	0.348813	+	0.229418i	0.711810	−	0.702373i	$-0.247876\pi$
$797$	9.84741	+	6.47674i	0.348813	+	0.229418i	−0.362996	+	0.931791i	$0.618246\pi$
$798$		0			0
$799$	35.3783	−	8.38481i	1.25159	−	0.296633i
$800$	−2.85246	+	16.1771i	−0.100850	+	0.571948i
$801$		0			0
$802$	−2.31363	−	13.1212i	−0.0816970	−	0.463327i
$803$	8.81174	+	20.4279i	0.310960	+	0.720885i
$804$		0			0
$805$	5.57733	+	18.6296i	0.196575	+	0.656606i
$806$	−1.37986	−	1.85347i	−0.0486035	−	0.0652859i
$807$		0			0
$808$	−22.6539	−	11.3772i	−0.796962	−	0.400249i
$809$	−21.4155			−0.752929			−0.376464	−	0.926431i	$-0.622860\pi$
$809$	−21.4155			−0.752929			−0.376464	+	0.926431i	$0.622860\pi$
$810$		0			0
$811$	1.73790			0.0610258			0.0305129	−	0.999534i	$-0.490286\pi$
$811$	1.73790			0.0610258			0.0305129	+	0.999534i	$0.490286\pi$
$812$	−3.08119	−	1.54743i	−0.108129	−	0.0543043i
$813$		0			0
$814$	−2.35932	−	3.16911i	−0.0826940	−	0.111077i
$815$	7.50075	+	25.0542i	0.262740	+	0.877612i
$816$		0			0
$817$	−14.8414	−	34.4063i	−0.519235	−	1.20372i
$818$	−3.23502	−	18.3467i	−0.113110	−	0.641477i
$819$		0			0
$820$	−0.243897	+	1.38321i	−0.00851725	+	0.0483037i
$821$	8.67839	−	2.05682i	0.302878	−	0.0717834i	−0.0763667	−	0.997080i	$-0.524332\pi$
$821$	8.67839	−	2.05682i	0.302878	−	0.0717834i	0.379245	+	0.925296i	$0.376184\pi$
$822$		0			0
$823$	−1.54747	−	1.01779i	−0.0539414	−	0.0354778i	0.522252	−	0.852791i	$-0.325092\pi$
$823$	−1.54747	−	1.01779i	−0.0539414	−	0.0354778i	−0.576193	+	0.817313i	$0.695462\pi$
$824$	0.501339	−	8.60765i	0.0174650	−	0.299862i
$825$		0			0
$826$	−4.49031	+	14.9987i	−0.156238	+	0.521870i
$827$	19.7686	−	7.19517i	0.687420	−	0.250200i	0.0253900	−	0.999678i	$-0.491917\pi$
$827$	19.7686	−	7.19517i	0.687420	−	0.250200i	0.662030	+	0.749477i	$0.269695\pi$
$828$		0			0
$829$	−5.33030	−	1.94007i	−0.185129	−	0.0673814i	0.247792	−	0.968813i	$-0.420295\pi$
$829$	−5.33030	−	1.94007i	−0.185129	−	0.0673814i	−0.432921	+	0.901432i	$0.642517\pi$
$830$	−1.12067	+	1.50531i	−0.0388989	+	0.0522502i
$831$		0			0
$832$	−13.7977	−	3.27012i	−0.478350	−	0.113371i
$833$	−13.5203	+	31.3435i	−0.468450	+	1.08599i
$834$		0			0
$835$	4.19404	−	2.75846i	0.145141	−	0.0954606i
$836$	15.6738	+	27.1478i	0.542089	+	0.938925i
$837$		0			0
$838$	−6.14931	+	10.6509i	−0.212424	+	0.367930i
$839$	1.39131	+	23.8879i	0.0480334	+	0.824701i	0.933184	+	0.359398i	$0.117018\pi$
$839$	1.39131	+	23.8879i	0.0480334	+	0.824701i	−0.885151	+	0.465304i	$0.845945\pi$
$840$		0			0
$841$	28.3805	−	3.31720i	0.978637	−	0.114386i
$842$	12.6348	−	13.3921i	0.435424	−	0.461522i
$843$		0			0
$844$	1.64386	+	0.192140i	0.0565841	+	0.00661373i
$845$	8.14471	−	6.83422i	0.280186	−	0.235104i
$846$		0			0
$847$	−42.3609	−	35.5450i	−1.45554	−	1.22134i
$848$	2.01657	+	2.13744i	0.0692494	+	0.0734000i
$849$		0			0
$850$	8.98455	−	4.51221i	0.308168	−	0.154768i
$851$	3.08792	−	1.55081i	0.105853	−	0.0531612i
$852$		0			0
$853$	−4.63443	−	4.91221i	−0.158680	−	0.168191i	0.643156	−	0.765735i	$-0.277625\pi$
$853$	−4.63443	−	4.91221i	−0.158680	−	0.168191i	−0.801836	+	0.597544i	$0.796143\pi$
$854$	15.4550	+	12.9683i	0.528860	+	0.443766i
$855$		0			0
$856$	34.1166	−	28.6272i	1.16608	−	0.978457i
$857$	−18.7289	−	2.18910i	−0.639768	−	0.0747782i	−0.209977	−	0.977706i	$-0.567339\pi$
$857$	−18.7289	−	2.18910i	−0.639768	−	0.0747782i	−0.429791	+	0.902928i	$0.641413\pi$
$858$		0			0
$859$	−22.2456	+	23.5790i	−0.759010	+	0.804503i	−0.985530	−	0.169503i	$-0.945784\pi$
$859$	−22.2456	+	23.5790i	−0.759010	+	0.804503i	0.226520	+	0.974007i	$0.427265\pi$
$860$	17.1478	−	2.00429i	0.584736	−	0.0683458i
$861$		0			0
$862$	−0.0641516	−	1.10144i	−0.00218501	−	0.0375152i
$863$	−23.6121	+	40.8973i	−0.803765	+	1.39216i	0.113357	+	0.993554i	$0.463840\pi$
$863$	−23.6121	+	40.8973i	−0.803765	+	1.39216i	−0.917122	+	0.398607i	$0.869494\pi$
$864$		0			0
$865$	−13.8292	−	23.9529i	−0.470208	−	0.814424i
$866$	−8.49550	+	5.58758i	−0.288689	+	0.189874i
$867$		0			0
$868$	1.37656	−	3.19123i	0.0467235	−	0.108317i
$869$	−55.2930	−	13.1047i	−1.87569	−	0.444546i
$870$		0			0
$871$	−14.2209	+	19.1020i	−0.481858	+	0.647248i
$872$	19.0051	+	6.91730i	0.643595	+	0.234249i
$873$		0			0
$874$	11.3280	−	4.12304i	0.383174	−	0.139464i
$875$	−12.6036	+	42.0991i	−0.426081	+	1.42321i
$876$		0			0
$877$	−0.327452	+	5.62213i	−0.0110573	+	0.189846i	0.988256	+	0.152804i	$0.0488304\pi$
$877$	−0.327452	+	5.62213i	−0.0110573	+	0.189846i	−0.999314	+	0.0370415i	$0.988207\pi$
$878$	−13.5416	−	8.90647i	−0.457008	−	0.300579i
$879$		0			0
$880$	−5.15743	+	1.22233i	−0.173857	+	0.0412048i
$881$	0.984686	−	5.58443i	0.0331749	−	0.188144i	−0.963717	−	0.266926i	$-0.913992\pi$
$881$	0.984686	−	5.58443i	0.0331749	−	0.188144i	0.996892	+	0.0787820i	$0.0251031\pi$
$882$		0			0
$883$	5.95650	+	33.7810i	0.200452	+	1.13682i	0.904437	+	0.426606i	$0.140291\pi$
$883$	5.95650	+	33.7810i	0.200452	+	1.13682i	−0.703985	+	0.710215i	$0.748598\pi$
$884$	−11.3260	−	26.2566i	−0.380934	−	0.883105i
$885$		0			0
$886$	7.61382	+	25.4319i	0.255791	+	0.854403i
$887$	−16.0539	−	21.5641i	−0.539037	−	0.724053i	0.446260	−	0.894904i	$-0.352756\pi$
$887$	−16.0539	−	21.5641i	−0.539037	−	0.724053i	−0.985297	+	0.170851i	$0.945348\pi$
$888$		0			0
$889$	−13.1996	−	6.62908i	−0.442700	−	0.222332i
$890$	1.20683			0.0404531
$891$		0			0
$892$	20.6987			0.693043
$893$	31.6566	+	15.8986i	1.05935	+	0.532025i
$894$		0			0
$895$	−10.5087	−	14.1156i	−0.351266	−	0.471832i
$896$	−10.0684	−	33.6307i	−0.336361	−	1.12352i
$897$		0			0
$898$	−0.371650	−	0.861583i	−0.0124021	−	0.0287514i
$899$	−0.0746222	−	0.423204i	−0.00248879	−	0.0141146i
$900$		0			0
$901$	3.30159	−	18.7243i	0.109992	−	0.623796i
$902$	−2.62460	+	0.622041i	−0.0873896	+	0.0207117i
$903$		0			0
$904$	22.1733	+	14.5836i	0.737475	+	0.485045i
$905$	1.35902	−	23.3335i	0.0451753	−	0.775631i
$906$		0			0
$907$	−8.72987	+	29.1598i	−0.289871	+	0.968235i	0.681729	+	0.731605i	$0.261228\pi$
$907$	−8.72987	+	29.1598i	−0.289871	+	0.968235i	−0.971600	+	0.236631i	$0.923957\pi$
$908$	32.1114	−	11.6876i	1.06565	−	0.387866i
$909$		0			0
$910$	−18.5699	−	6.75888i	−0.615585	−	0.224055i
$911$	−8.39961	+	11.2826i	−0.278291	+	0.373810i	−0.919189	−	0.393816i	$-0.871155\pi$
$911$	−8.39961	+	11.2826i	−0.278291	+	0.373810i	0.640898	+	0.767626i	$0.278562\pi$
$912$		0			0
$913$	7.97556	+	1.89024i	0.263953	+	0.0625579i
$914$	−9.92224	+	23.0023i	−0.328199	+	0.760850i
$915$		0			0
$916$	1.77228	−	1.16565i	0.0585578	−	0.0385141i
$917$	31.6440	+	54.8090i	1.04498	+	1.80995i
$918$		0			0
$919$	−14.5007	+	25.1160i	−0.478335	+	0.828501i	−0.999691	−	0.0248384i	$-0.992093\pi$
$919$	−14.5007	+	25.1160i	−0.478335	+	0.828501i	0.521356	+	0.853339i	$0.325426\pi$
$920$	0.787909	+	13.5279i	0.0259766	+	0.446001i
$921$		0			0
$922$	0.261356	−	0.0305482i	0.00860731	−	0.00100605i
$923$	18.9069	−	20.0402i	0.622329	−	0.659630i
$924$		0			0
$925$	2.78891	+	0.325976i	0.0916986	+	0.0107180i
$926$	−1.76780	+	1.48336i	−0.0580935	+	0.0487462i
$927$		0			0
$928$	−2.92661	−	2.45572i	−0.0960706	−	0.0806128i
$929$	−30.5782	−	32.4109i	−1.00324	−	1.06337i	−0.997989	−	0.0633825i	$-0.979811\pi$
$929$	−30.5782	−	32.4109i	−1.00324	−	1.06337i	−0.00524738	−	0.999986i	$-0.501670\pi$
$930$		0			0
$931$	−29.7210	+	14.9264i	−0.974066	+	0.489194i
$932$	17.4542	−	8.76584i	0.571732	−	0.287135i
$933$		0			0
$934$	2.02962	+	2.15127i	0.0664112	+	0.0703918i
$935$	26.2707	+	22.0437i	0.859143	+	0.720907i
$936$		0			0
$937$	−15.7744	+	13.2363i	−0.515326	+	0.432409i	−0.862999	−	0.505206i	$-0.831416\pi$
$937$	−15.7744	+	13.2363i	−0.515326	+	0.432409i	0.347673	+	0.937616i	$0.386972\pi$
$938$	15.6427	+	1.82837i	0.510752	+	0.0596983i
$939$		0			0
$940$	−11.2007	+	11.8721i	−0.365327	+	0.387224i
$941$	56.3981	−	6.59199i	1.83852	−	0.214893i	0.875298	−	0.483584i	$-0.160665\pi$
$941$	56.3981	−	6.59199i	1.83852	−	0.214893i	0.963226	+	0.268691i	$0.0865912\pi$
$942$		0			0
$943$	−0.137168	−	2.35508i	−0.00446680	−	0.0766920i
$944$	1.86608	−	3.23215i	0.0607359	−	0.105198i
$945$		0			0
$946$	16.5775	+	28.7131i	0.538982	+	0.933544i
$947$	−13.1803	+	8.66883i	−0.428303	+	0.281699i	−0.745302	−	0.666727i	$-0.767695\pi$
$947$	−13.1803	+	8.66883i	−0.428303	+	0.281699i	0.317000	+	0.948426i	$0.397325\pi$
$948$		0			0
$949$	7.83165	−	18.1558i	0.254226	−	0.589363i
$950$	9.53173	+	2.25906i	0.309250	+	0.0732936i
$951$		0			0
$952$	−27.5510	+	37.0075i	−0.892934	+	1.19942i
$953$	−47.3933	−	17.2497i	−1.53522	−	0.558774i	−0.570326	−	0.821418i	$-0.693183\pi$
$953$	−47.3933	−	17.2497i	−1.53522	−	0.558774i	−0.964893	+	0.262645i	$0.915405\pi$
$954$		0			0
$955$	8.02382	−	2.92043i	0.259645	−	0.0945030i
$956$	9.13079	−	30.4990i	0.295311	−	0.986407i
$957$		0			0
$958$	−0.143907	+	2.47079i	−0.00464942	+	0.0798275i
$959$	−29.4594	−	19.3757i	−0.951293	−	0.625675i
$960$		0			0
$961$	−29.7429	+	7.04920i	−0.959449	+	0.227393i
$962$	−0.609760	+	3.45812i	−0.0196594	+	0.111494i
$963$		0			0
$964$	1.70519	+	9.67059i	0.0549203	+	0.311469i
$965$	0.103079	+	0.238964i	0.00331824	+	0.00769253i
$966$		0			0
$967$	−6.27933	−	20.9744i	−0.201930	−	0.674492i	−0.997630	−	0.0688018i	$-0.978082\pi$
$967$	−6.27933	−	20.9744i	−0.201930	−	0.674492i	0.795701	−	0.605690i	$-0.207103\pi$
$968$	−23.0104	−	30.9083i	−0.739581	−	0.993430i
$969$		0			0
$970$	5.15856	+	2.59072i	0.165631	+	0.0831832i
$971$	21.3313			0.684555			0.342277	−	0.939599i	$-0.388802\pi$
$971$	21.3313			0.684555			0.342277	+	0.939599i	$0.388802\pi$
$972$		0			0
$973$	−60.5205			−1.94020
$974$	0.855569	+	0.429683i	0.0274142	+	0.0137679i
$975$		0			0
$976$	−2.87193	−	3.85768i	−0.0919283	−	0.123481i
$977$	2.05675	+	6.87002i	0.0658012	+	0.219791i	0.984566	−	0.175014i	$-0.0559971\pi$
$977$	2.05675	+	6.87002i	0.0658012	+	0.219791i	−0.918765	+	0.394806i	$0.870812\pi$
$978$		0			0
$979$	−2.08772	−	4.83988i	−0.0667238	−	0.154683i
$980$	−2.66095	−	15.0910i	−0.0850011	−	0.482065i
$981$		0			0
$982$	5.50290	−	31.2085i	0.175605	−	0.995904i
$983$	40.2972	−	9.55061i	1.28528	−	0.304617i	0.469477	−	0.882945i	$-0.344443\pi$
$983$	40.2972	−	9.55061i	1.28528	−	0.304617i	0.815805	+	0.578328i	$0.196295\pi$
$984$		0			0
$985$	13.8750	+	9.12572i	0.442094	+	0.290770i
$986$	−0.135959	+	2.33433i	−0.00432983	+	0.0743403i
$987$		0			0
$988$	7.99060	−	26.6905i	0.254215	−	0.849137i
$989$	−27.2487	+	9.91773i	−0.866460	+	0.315365i
$990$		0			0
$991$	51.2878	+	18.6672i	1.62921	+	0.592984i	0.985105	−	0.171953i	$-0.0550079\pi$
$991$	51.2878	+	18.6672i	1.62921	+	0.592984i	0.644105	+	0.764937i	$0.277230\pi$
$992$	2.29960	−	3.08890i	0.0730125	−	0.0980728i
$993$		0			0
$994$	−17.7295	−	4.20196i	−0.562344	−	0.133278i
$995$	−12.0102	+	27.8428i	−0.380750	+	0.882677i
$996$		0			0
$997$	22.1506	−	14.5687i	0.701516	−	0.461395i	−0.147979	−	0.988990i	$-0.547277\pi$
$997$	22.1506	−	14.5687i	0.701516	−	0.461395i	0.849495	+	0.527596i	$0.176906\pi$
$998$	16.0810	+	27.8531i	0.509035	+	0.881674i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.10.5		144
3.2	odd	2		81.2.g.a.13.4	✓	144
9.2	odd	6		729.2.g.d.514.5		144
9.4	even	3		729.2.g.b.28.4		144
9.5	odd	6		729.2.g.c.28.5		144
9.7	even	3		729.2.g.a.514.4		144
81.2	odd	54		729.2.g.c.703.5		144
81.5	odd	54		6561.2.a.c.1.30		72
81.25	even	27	inner	243.2.g.a.73.5		144
81.29	odd	54		729.2.g.d.217.5		144
81.52	even	27		729.2.g.a.217.4		144
81.56	odd	54		81.2.g.a.25.4	yes	144
81.76	even	27		6561.2.a.d.1.43		72
81.79	even	27		729.2.g.b.703.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.4	✓	144	3.2	odd	2
81.2.g.a.25.4	yes	144	81.56	odd	54
243.2.g.a.10.5		144	1.1	even	1	trivial
243.2.g.a.73.5		144	81.25	even	27	inner
729.2.g.a.217.4		144	81.52	even	27
729.2.g.a.514.4		144	9.7	even	3
729.2.g.b.28.4		144	9.4	even	3
729.2.g.b.703.4		144	81.79	even	27
729.2.g.c.28.5		144	9.5	odd	6
729.2.g.c.703.5		144	81.2	odd	54
729.2.g.d.217.5		144	81.29	odd	54
729.2.g.d.514.5		144	9.2	odd	6
6561.2.a.c.1.30		72	81.5	odd	54
6561.2.a.d.1.43		72	81.76	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)

\(f(q)\)	\(=\)	\(q+(0.698417 + 0.350758i) q^{2} +(-0.829563 - 1.11430i) q^{4} +(-0.424677 - 1.41852i) q^{5} +(-1.50560 - 3.49038i) q^{7} +(-0.459961 - 2.60857i) q^{8} +(0.200956 - 1.13968i) q^{10} +(-4.91819 + 1.16563i) q^{11} +(3.75323 + 2.46854i) q^{13} +(0.172741 - 2.96584i) q^{14} +(-0.203113 + 0.678443i) q^{16} +(4.30582 - 1.56719i) q^{17} +(4.19524 + 1.52694i) q^{19} +(-1.22836 + 1.64997i) q^{20} +(-3.84380 - 0.910998i) q^{22} +(1.36843 - 3.17237i) q^{23} +(2.34559 - 1.54272i) q^{25} +(1.75546 + 3.04054i) q^{26} +(-2.64032 + 4.57318i) q^{28} +(0.0379650 + 0.651834i) q^{29} +(-0.653701 + 0.0764066i) q^{31} +(-4.01527 + 4.25594i) q^{32} +(3.55696 + 0.415749i) q^{34} +(-4.31178 + 3.61801i) q^{35} +(0.766165 + 0.642889i) q^{37} +(2.39444 + 2.53796i) q^{38} +(-3.50497 + 1.76026i) q^{40} +(0.610184 - 0.306446i) q^{41} +(-5.75968 - 6.10490i) q^{43} +(5.37881 + 4.51336i) q^{44} +(2.06847 - 1.73565i) q^{46} +(7.88112 + 0.921171i) q^{47} +(-5.11223 + 5.41864i) q^{49} +(2.17932 - 0.254726i) q^{50} +(-0.362857 - 6.23001i) q^{52} +(2.07469 - 3.59347i) q^{53} +(3.74212 + 6.48154i) q^{55} +(-8.41238 + 5.53291i) q^{56} +(-0.202121 + 0.468568i) q^{58} +(-5.12792 - 1.21534i) q^{59} +(-4.05529 + 5.44719i) q^{61} +(-0.483356 - 0.175927i) q^{62} +(-2.96617 + 1.07960i) q^{64} +(1.90776 - 6.37236i) q^{65} +(-0.308237 + 5.29223i) q^{67} +(-5.31826 - 3.49787i) q^{68} +(-4.28047 + 1.01449i) q^{70} +(1.06500 - 6.03991i) q^{71} +(-0.764322 - 4.33469i) q^{73} +(0.309604 + 0.717743i) q^{74} +(-1.77875 - 5.94144i) q^{76} +(11.4734 + 15.4114i) q^{77} +(10.0467 + 5.04564i) q^{79} +1.04864 q^{80} +0.533651 q^{82} +(-1.44915 - 0.727793i) q^{83} +(-4.05167 - 5.44234i) q^{85} +(-1.88131 - 6.28402i) q^{86} +(5.30281 + 12.2933i) q^{88} +(0.181087 + 1.02699i) q^{89} +(2.96526 - 16.8168i) q^{91} +(-4.67016 + 1.10685i) q^{92} +(5.18120 + 3.40773i) q^{94} +(0.384377 - 6.59950i) q^{95} +(-1.43062 + 4.77859i) q^{97} +(-5.47110 + 1.99132i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 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

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