LMFDB - Embedded newform 486.2.g.a.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [486,2,Mod(19,486)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(486, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([52]))

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

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

chi := DirichletCharacter("486.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.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:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 162)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	486.73
Dual form			486.2.g.a.253.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.893633 - 0.448799i) q^{2} +(0.597159 - 0.802123i) q^{4} +(0.267154 - 0.892356i) q^{5} +(1.11188 - 2.57764i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-0.161751 - 0.917337i) q^{10} +(-4.46341 - 1.05785i) q^{11} +(1.47403 - 0.969483i) q^{13} +(-0.163226 - 2.80247i) q^{14} +(-0.286803 - 0.957990i) q^{16} +(-1.42569 - 0.518907i) q^{17} +(4.12421 - 1.50109i) q^{19} +(-0.556246 - 0.747168i) q^{20} +(-4.46341 + 1.05785i) q^{22} +(2.92223 + 6.77448i) q^{23} +(3.45251 + 2.27075i) q^{25} +(0.882135 - 1.52790i) q^{26} +(-1.40361 - 2.43113i) q^{28} +(0.418954 - 7.19315i) q^{29} +(-6.24778 - 0.730261i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-1.50693 + 0.176134i) q^{34} +(-2.00313 - 1.68082i) q^{35} +(-0.516723 + 0.433582i) q^{37} +(3.01184 - 3.19236i) q^{38} +(-0.832408 - 0.418051i) q^{40} +(8.46317 + 4.25037i) q^{41} +(3.77539 - 4.00168i) q^{43} +(-3.51389 + 2.94850i) q^{44} +(5.65178 + 4.74241i) q^{46} +(-5.01677 + 0.586377i) q^{47} +(-0.604237 - 0.640453i) q^{49} +(4.10439 + 0.479734i) q^{50} +(0.102583 - 1.76129i) q^{52} +(1.33883 + 2.31892i) q^{53} +(-2.13639 + 3.70034i) q^{55} +(-2.34540 - 1.54259i) q^{56} +(-2.85389 - 6.61606i) q^{58} +(-4.89941 + 1.16118i) q^{59} +(3.14866 + 4.22938i) q^{61} +(-5.91096 + 2.15141i) q^{62} +(-0.939693 - 0.342020i) q^{64} +(-0.471331 - 1.57436i) q^{65} +(0.832311 + 14.2902i) q^{67} +(-1.26759 + 0.833706i) q^{68} +(-2.54441 - 0.603036i) q^{70} +(0.0492509 + 0.279316i) q^{71} +(-2.01050 + 11.4021i) q^{73} +(-0.267169 + 0.619368i) q^{74} +(1.25875 - 4.20451i) q^{76} +(-7.68955 + 10.3289i) q^{77} +(3.17920 - 1.59665i) q^{79} -0.931488 q^{80} +9.47053 q^{82} +(9.56164 - 4.80204i) q^{83} +(-0.843927 + 1.13359i) q^{85} +(1.57786 - 5.27043i) q^{86} +(-1.81684 + 4.21191i) q^{88} +(-1.74720 + 9.90888i) q^{89} +(-0.860028 - 4.87746i) q^{91} +(7.17900 + 1.70145i) q^{92} +(-4.21999 + 2.77553i) q^{94} +(-0.237708 - 4.08128i) q^{95} +(-4.96298 - 16.5775i) q^{97} +(-0.827401 - 0.301149i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{13} + 9 q^{20} + 81 q^{23} + 18 q^{25} + 27 q^{26} + 18 q^{28} + 27 q^{29} - 54 q^{31} + 27 q^{35} - 9 q^{38} + 9 q^{41} + 36 q^{43} - 18 q^{46} + 27 q^{47} - 36 q^{52} + 27 q^{53} + 54 q^{55}+ \cdots - 36 q^{98}+O(q^{100}) $ 72 * q + 18 * q^13 + 9 * q^20 + 81 * q^23 + 18 * q^25 + 27 * q^26 + 18 * q^28 + 27 * q^29 - 54 * q^31 + 27 * q^35 - 9 * q^38 + 9 * q^41 + 36 * q^43 - 18 * q^46 + 27 * q^47 - 36 * q^52 + 27 * q^53 + 54 * q^55 + 9 * q^58 + 18 * q^59 - 9 * q^65 - 135 * q^67 + 18 * q^68 + 18 * q^70 - 72 * q^71 + 36 * q^73 - 99 * q^74 - 9 * q^76 - 144 * q^77 - 9 * q^79 - 18 * q^80 - 72 * q^82 - 99 * q^83 + 9 * q^85 - 72 * q^86 - 9 * q^88 - 126 * q^89 + 63 * q^91 - 36 * q^92 + 18 * q^94 - 45 * q^95 - 171 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$3$		0			0
$3$		0			0
$4$	0.597159	−	0.802123i	0.298579	−	0.401062i
$5$	0.267154	−	0.892356i	0.119475	−	0.399074i	−0.877241	−	0.480050i	$-0.840619\pi$
$5$	0.267154	−	0.892356i	0.119475	−	0.399074i	0.996716	+	0.0809762i	$0.0258038\pi$
$6$		0			0
$7$	1.11188	−	2.57764i	0.420253	−	0.974255i	−0.568223	−	0.822875i	$-0.692369\pi$
$7$	1.11188	−	2.57764i	0.420253	−	0.974255i	0.988476	−	0.151381i	$-0.0483719\pi$
$8$	0.173648	−	0.984808i	0.0613939	−	0.348182i
$9$		0			0
$10$	−0.161751	−	0.917337i	−0.0511502	−	0.290087i
$11$	−4.46341	−	1.05785i	−1.34577	−	0.318953i	−0.506299	−	0.862358i	$-0.668987\pi$
$11$	−4.46341	−	1.05785i	−1.34577	−	0.318953i	−0.839471	+	0.543405i	$0.817135\pi$
$12$		0			0
$13$	1.47403	−	0.969483i	0.408821	−	0.268886i	−0.328398	−	0.944539i	$-0.606509\pi$
$13$	1.47403	−	0.969483i	0.408821	−	0.268886i	0.737219	+	0.675653i	$0.236138\pi$
$14$	−0.163226	−	2.80247i	−0.0436239	−	0.748993i
$15$		0			0
$16$	−0.286803	−	0.957990i	−0.0717008	−	0.239497i
$17$	−1.42569	−	0.518907i	−0.345780	−	0.125854i	0.163292	−	0.986578i	$-0.447789\pi$
$17$	−1.42569	−	0.518907i	−0.345780	−	0.125854i	−0.509071	+	0.860724i	$0.670011\pi$
$18$		0			0
$19$	4.12421	−	1.50109i	0.946158	−	0.344373i	0.177563	−	0.984109i	$-0.443179\pi$
$19$	4.12421	−	1.50109i	0.946158	−	0.344373i	0.768595	+	0.639736i	$0.220956\pi$
$20$	−0.556246	−	0.747168i	−0.124380	−	0.167072i
$21$		0			0
$22$	−4.46341	+	1.05785i	−0.951603	+	0.225534i
$23$	2.92223	+	6.77448i	0.609326	+	1.41258i	0.891415	+	0.453189i	$0.149714\pi$
$23$	2.92223	+	6.77448i	0.609326	+	1.41258i	−0.282088	+	0.959388i	$0.591027\pi$
$24$		0			0
$25$	3.45251	+	2.27075i	0.690502	+	0.454151i
$26$	0.882135	−	1.52790i	0.173001	−	0.299646i
$27$		0			0
$28$	−1.40361	−	2.43113i	−0.265258	−	0.459440i
$29$	0.418954	−	7.19315i	0.0777977	−	1.33574i	−0.703107	−	0.711085i	$-0.748204\pi$
$29$	0.418954	−	7.19315i	0.0777977	−	1.33574i	0.780904	−	0.624651i	$-0.214759\pi$
$30$		0			0
$31$	−6.24778	−	0.730261i	−1.12213	−	0.131159i	−0.465271	−	0.885168i	$-0.654043\pi$
$31$	−6.24778	−	0.730261i	−1.12213	−	0.131159i	−0.656863	+	0.754010i	$0.728117\pi$
$32$	−0.686242	−	0.727374i	−0.121312	−	0.128583i
$33$		0			0
$34$	−1.50693	+	0.176134i	−0.258436	+	0.0302068i
$35$	−2.00313	−	1.68082i	−0.338590	−	0.284111i
$36$		0			0
$37$	−0.516723	+	0.433582i	−0.0849487	+	0.0712804i	−0.684273	−	0.729226i	$-0.739880\pi$
$37$	−0.516723	+	0.433582i	−0.0849487	+	0.0712804i	0.599324	+	0.800506i	$0.295436\pi$
$38$	3.01184	−	3.19236i	0.488585	−	0.517870i
$39$		0			0
$40$	−0.832408	−	0.418051i	−0.131615	−	0.0660997i
$41$	8.46317	+	4.25037i	1.32173	+	0.663796i	0.962963	−	0.269633i	$-0.0869025\pi$
$41$	8.46317	+	4.25037i	1.32173	+	0.663796i	0.358763	+	0.933429i	$0.383199\pi$
$42$		0			0
$43$	3.77539	−	4.00168i	0.575742	−	0.610251i	−0.372410	−	0.928068i	$-0.621468\pi$
$43$	3.77539	−	4.00168i	0.575742	−	0.610251i	0.948152	+	0.317817i	$0.102950\pi$
$44$	−3.51389	+	2.94850i	−0.529739	+	0.444504i
$45$		0			0
$46$	5.65178	+	4.74241i	0.833309	+	0.699230i
$47$	−5.01677	+	0.586377i	−0.731772	+	0.0855319i	−0.473815	−	0.880625i	$-0.657123\pi$
$47$	−5.01677	+	0.586377i	−0.731772	+	0.0855319i	−0.257957	+	0.966156i	$0.583049\pi$
$48$		0			0
$49$	−0.604237	−	0.640453i	−0.0863195	−	0.0914934i
$50$	4.10439	+	0.479734i	0.580448	+	0.0678447i
$51$		0			0
$52$	0.102583	−	1.76129i	0.0142257	−	0.244246i
$53$	1.33883	+	2.31892i	0.183903	+	0.318529i	0.943206	−	0.332208i	$-0.107794\pi$
$53$	1.33883	+	2.31892i	0.183903	+	0.318529i	−0.759304	+	0.650737i	$0.774460\pi$
$54$		0			0
$55$	−2.13639	+	3.70034i	−0.288071	+	0.498954i
$56$	−2.34540	−	1.54259i	−0.313417	−	0.206138i
$57$		0			0
$58$	−2.85389	−	6.61606i	−0.374734	−	0.868732i
$59$	−4.89941	+	1.16118i	−0.637849	+	0.151173i	−0.536802	−	0.843708i	$-0.680368\pi$
$59$	−4.89941	+	1.16118i	−0.637849	+	0.151173i	−0.101048	+	0.994882i	$0.532219\pi$
$60$		0			0
$61$	3.14866	+	4.22938i	0.403144	+	0.541517i	0.956616	−	0.291351i	$-0.0941048\pi$
$61$	3.14866	+	4.22938i	0.403144	+	0.541517i	−0.553472	+	0.832868i	$0.686697\pi$
$62$	−5.91096	+	2.15141i	−0.750693	+	0.273230i
$63$		0			0
$64$	−0.939693	−	0.342020i	−0.117462	−	0.0427525i
$65$	−0.471331	−	1.57436i	−0.0584615	−	0.195275i
$66$		0			0
$67$	0.832311	+	14.2902i	0.101683	+	1.74583i	0.535237	+	0.844702i	$0.320222\pi$
$67$	0.832311	+	14.2902i	0.101683	+	1.74583i	−0.433554	+	0.901127i	$0.642741\pi$
$68$	−1.26759	+	0.833706i	−0.153718	+	0.101102i
$69$		0			0
$70$	−2.54441	−	0.603036i	−0.304115	−	0.0720766i
$71$	0.0492509	+	0.279316i	0.00584501	+	0.0331487i	0.987591	−	0.157049i	$-0.0501981\pi$
$71$	0.0492509	+	0.279316i	0.00584501	+	0.0331487i	−0.981746	+	0.190198i	$0.939087\pi$
$72$		0			0
$73$	−2.01050	+	11.4021i	−0.235312	+	1.33452i	0.606645	+	0.794973i	$0.292515\pi$
$73$	−2.01050	+	11.4021i	−0.235312	+	1.33452i	−0.841957	+	0.539545i	$0.818596\pi$
$74$	−0.267169	+	0.619368i	−0.0310578	+	0.0720000i
$75$		0			0
$76$	1.25875	−	4.20451i	0.144388	−	0.482290i
$77$	−7.68955	+	10.3289i	−0.876305	+	1.17708i
$78$		0			0
$79$	3.17920	−	1.59665i	0.357687	−	0.179637i	−0.260876	−	0.965372i	$-0.584011\pi$
$79$	3.17920	−	1.59665i	0.357687	−	0.179637i	0.618563	+	0.785735i	$0.287715\pi$
$80$	−0.931488			−0.104144
$81$		0			0
$82$	9.47053			1.04584
$83$	9.56164	−	4.80204i	1.04953	−	0.527092i	0.161494	−	0.986874i	$-0.448369\pi$
$83$	9.56164	−	4.80204i	1.04953	−	0.527092i	0.888032	+	0.459782i	$0.152072\pi$
$84$		0			0
$85$	−0.843927	+	1.13359i	−0.0915368	+	0.122955i
$86$	1.57786	−	5.27043i	0.170145	−	0.568325i
$87$		0			0
$88$	−1.81684	+	4.21191i	−0.193676	+	0.448991i
$89$	−1.74720	+	9.90888i	−0.185203	+	1.05034i	0.740491	+	0.672066i	$0.234593\pi$
$89$	−1.74720	+	9.90888i	−0.185203	+	1.05034i	−0.925694	+	0.378273i	$0.876518\pi$
$90$		0			0
$91$	−0.860028	−	4.87746i	−0.0901554	−	0.511297i
$92$	7.17900	+	1.70145i	0.748463	+	0.177389i
$93$		0			0
$94$	−4.21999	+	2.77553i	−0.435259	+	0.286274i
$95$	−0.237708	−	4.08128i	−0.0243883	−	0.418731i
$96$		0			0
$97$	−4.96298	−	16.5775i	−0.503914	−	1.68319i	−0.709626	−	0.704579i	$-0.751136\pi$
$97$	−4.96298	−	16.5775i	−0.503914	−	1.68319i	0.205711	−	0.978613i	$-0.434049\pi$
$98$	−0.827401	−	0.301149i	−0.0835801	−	0.0304207i
$99$		0			0
$100$	3.88312	−	1.41334i	0.388312	−	0.141334i
$101$	3.77928	+	5.07645i	0.376052	+	0.505126i	0.949350	−	0.314222i	$-0.101743\pi$
$101$	3.77928	+	5.07645i	0.376052	+	0.505126i	−0.573298	+	0.819347i	$0.694336\pi$
$102$		0			0
$103$	−18.1237	+	4.29540i	−1.78578	+	0.423238i	−0.984548	−	0.175112i	$-0.943971\pi$
$103$	−18.1237	+	4.29540i	−1.78578	+	0.423238i	−0.801234	+	0.598350i	$0.795823\pi$
$104$	−0.698792	−	1.61998i	−0.0685222	−	0.158852i
$105$		0			0
$106$	2.23715	+	1.47140i	0.217292	+	0.142915i
$107$	0.530621	−	0.919062i	0.0512970	−	0.0888491i	−0.839237	−	0.543766i	$-0.816998\pi$
$107$	0.530621	−	0.919062i	0.0512970	−	0.0888491i	0.890534	+	0.454917i	$0.150331\pi$
$108$		0			0
$109$	6.12250	+	10.6045i	0.586429	+	1.01573i	0.994696	+	0.102863i	$0.0328002\pi$
$109$	6.12250	+	10.6045i	0.586429	+	1.01573i	−0.408266	+	0.912863i	$0.633866\pi$
$110$	−0.248441	+	4.26556i	−0.0236879	+	0.406705i
$111$		0			0
$112$	−2.78824	−	0.325899i	−0.263464	−	0.0307945i
$113$	4.67396	+	4.95410i	0.439689	+	0.466043i	0.908882	−	0.417052i	$-0.136937\pi$
$113$	4.67396	+	4.95410i	0.439689	+	0.466043i	−0.469194	+	0.883095i	$0.655455\pi$
$114$		0			0
$115$	6.82593	−	0.797837i	0.636521	−	0.0743987i
$116$	−5.51961	−	4.63151i	−0.512483	−	0.430025i
$117$		0			0
$118$	−3.85714	+	3.23652i	−0.355078	+	0.297946i
$119$	−2.92275	+	3.09794i	−0.267928	+	0.283987i
$120$		0			0
$121$	8.97305	+	4.50643i	0.815732	+	0.409676i
$122$	4.71189	+	2.36640i	0.426594	+	0.214244i
$123$		0			0
$124$	−4.31667	+	4.57541i	−0.387649	+	0.410884i
$125$	6.51648	−	5.46797i	0.582851	−	0.489070i
$126$		0			0
$127$	−6.52630	−	5.47622i	−0.579116	−	0.485936i	0.305541	−	0.952179i	$-0.401163\pi$
$127$	−6.52630	−	5.47622i	−0.579116	−	0.485936i	−0.884657	+	0.466243i	$0.845607\pi$
$128$	−0.993238	+	0.116093i	−0.0877907	+	0.0102613i
$129$		0			0
$130$	−1.12777	−	1.19536i	−0.0989117	−	0.104840i
$131$	15.8598	+	1.85375i	1.38568	+	0.161963i	0.776024	−	0.630703i	$-0.217234\pi$
$131$	15.8598	+	1.85375i	1.38568	+	0.161963i	0.609656	+	0.792666i	$0.291308\pi$
$132$		0			0
$133$	0.716379	−	12.2997i	0.0621179	−	1.06652i
$134$	7.15722	+	12.3967i	0.618290	+	1.07091i
$135$		0			0
$136$	−0.758592	+	1.31392i	−0.0650487	+	0.112668i
$137$	−8.99273	−	5.91461i	−0.768301	−	0.505319i	0.103828	−	0.994595i	$-0.466891\pi$
$137$	−8.99273	−	5.91461i	−0.768301	−	0.505319i	−0.872129	+	0.489276i	$0.837261\pi$
$138$		0			0
$139$	2.55292	+	5.91833i	0.216536	+	0.501986i	0.991514	−	0.130002i	$-0.0414984\pi$
$139$	2.55292	+	5.91833i	0.216536	+	0.501986i	−0.774978	+	0.631988i	$0.782239\pi$
$140$	−2.54441	+	0.603036i	−0.215042	+	0.0509659i
$141$		0			0
$142$	0.169369	+	0.227502i	0.0142131	+	0.0190916i
$143$	−7.60475	+	2.76790i	−0.635941	+	0.231464i
$144$		0			0
$145$	−6.30693	−	2.29553i	−0.523762	−	0.190634i
$146$	3.32061	+	11.0916i	0.274816	+	0.917949i
$147$		0			0
$148$	0.0392206	+	0.673392i	0.00322392	+	0.0553525i
$149$	0.0289210	−	0.0190217i	0.00236930	−	0.00155831i	−0.548324	−	0.836266i	$-0.684734\pi$
$149$	0.0289210	−	0.0190217i	0.00236930	−	0.00155831i	0.550693	+	0.834708i	$0.314363\pi$
$150$		0			0
$151$	−22.1823	−	5.25731i	−1.80517	−	0.427834i	−0.816429	−	0.577446i	$-0.804049\pi$
$151$	−22.1823	−	5.25731i	−1.80517	−	0.427834i	−0.988745	+	0.149613i	$0.952197\pi$
$152$	−0.762123	−	4.32221i	−0.0618163	−	0.350578i
$153$		0			0
$154$	−2.23605	+	12.6813i	−0.180186	+	1.02189i
$155$	−2.32077	+	5.38015i	−0.186409	+	0.432144i
$156$		0			0
$157$	2.53198	−	8.45740i	0.202074	−	0.674974i	−0.795538	−	0.605904i	$-0.792812\pi$
$157$	2.53198	−	8.45740i	0.202074	−	0.674974i	0.997612	−	0.0690700i	$-0.0220032\pi$
$158$	2.12446	−	2.85364i	0.169013	−	0.227023i
$159$		0			0
$160$	−0.832408	+	0.418051i	−0.0658076	+	0.0330498i
$161$	20.7113			1.63228
$162$		0			0
$163$	−21.2225			−1.66227			−0.831137	−	0.556067i	$-0.812310\pi$
$163$	−21.2225			−1.66227			−0.831137	+	0.556067i	$0.812310\pi$
$164$	8.46317	−	4.25037i	0.660863	−	0.331898i
$165$		0			0
$166$	6.38944	−	8.58251i	0.495917	−	0.666132i
$167$	4.59344	−	15.3431i	0.355451	−	1.18729i	−0.574159	−	0.818744i	$-0.694671\pi$
$167$	4.59344	−	15.3431i	0.355451	−	1.18729i	0.929610	−	0.368544i	$-0.120144\pi$
$168$		0			0
$169$	−3.91618	+	9.07872i	−0.301245	+	0.698363i
$170$	−0.245406	+	1.39177i	−0.0188218	+	0.106744i
$171$		0			0
$172$	−0.955334	−	5.41797i	−0.0728436	−	0.413116i
$173$	10.9871	+	2.60399i	0.835334	+	0.197978i	0.625957	−	0.779857i	$-0.284708\pi$
$173$	10.9871	+	2.60399i	0.835334	+	0.197978i	0.209376	+	0.977835i	$0.432857\pi$
$174$		0			0
$175$	9.69197	−	6.37451i	0.732644	−	0.481868i
$176$	0.266714	+	4.57930i	0.0201043	+	0.345177i
$177$		0			0
$178$	2.88574	+	9.63905i	0.216295	+	0.722477i
$179$	−18.7430	−	6.82191i	−1.40092	−	0.509893i	−0.472469	−	0.881347i	$-0.656637\pi$
$179$	−18.7430	−	6.82191i	−1.40092	−	0.509893i	−0.928451	+	0.371454i	$0.878859\pi$
$180$		0			0
$181$	19.9989	−	7.27900i	1.48651	−	0.541044i	0.533979	−	0.845498i	$-0.320696\pi$
$181$	19.9989	−	7.27900i	1.48651	−	0.541044i	0.952527	+	0.304454i	$0.0984739\pi$
$182$	−2.95755	−	3.97268i	−0.219228	−	0.294474i
$183$		0			0
$184$	7.17900	−	1.70145i	0.529243	−	0.125433i
$185$	0.248865	+	0.576933i	0.0182969	+	0.0424170i
$186$		0			0
$187$	5.81450	+	3.82426i	0.425198	+	0.279657i
$188$	−2.52546	+	4.37423i	−0.184188	+	0.319024i
$189$		0			0
$190$	−2.04410	−	3.54048i	−0.148294	−	0.256854i
$191$	1.03657	−	17.7972i	0.0750033	−	1.28776i	−0.725414	−	0.688313i	$-0.758351\pi$
$191$	1.03657	−	17.7972i	0.0750033	−	1.28776i	0.800417	−	0.599444i	$-0.204612\pi$
$192$		0			0
$193$	22.1969	+	2.59445i	1.59777	+	0.186753i	0.867866	−	0.496798i	$-0.165491\pi$
$193$	22.1969	+	2.59445i	1.59777	+	0.186753i	0.729904	+	0.683550i	$0.239565\pi$
$194$	−11.8751	−	12.5868i	−0.852579	−	0.903681i
$195$		0			0
$196$	−0.874548	+	0.102220i	−0.0624677	+	0.00730143i
$197$	3.12785	+	2.62458i	0.222850	+	0.186994i	0.747377	−	0.664401i	$-0.231313\pi$
$197$	3.12785	+	2.62458i	0.222850	+	0.186994i	−0.524526	+	0.851394i	$0.675758\pi$
$198$		0			0
$199$	−0.620215	+	0.520423i	−0.0439659	+	0.0368918i	−0.664506	−	0.747283i	$-0.731358\pi$
$199$	−0.620215	+	0.520423i	−0.0439659	+	0.0368918i	0.620540	+	0.784175i	$0.286913\pi$
$200$	2.83578	−	3.00575i	0.200520	−	0.212538i
$201$		0			0
$202$	5.65559	+	2.84035i	0.397926	+	0.199846i
$203$	−18.0755	−	9.07787i	−1.26865	−	0.637141i
$204$		0			0
$205$	6.05381	−	6.41666i	0.422816	−	0.448159i
$206$	−14.2682	+	11.9724i	−0.994111	+	0.834158i
$207$		0			0
$208$	−1.35151	−	1.13405i	−0.0937103	−	0.0786323i
$209$	−19.9960	+	2.33719i	−1.38315	+	0.161667i
$210$		0			0
$211$	−7.80319	−	8.27090i	−0.537194	−	0.569392i	0.400746	−	0.916189i	$-0.368751\pi$
$211$	−7.80319	−	8.27090i	−0.537194	−	0.569392i	−0.937940	+	0.346797i	$0.887269\pi$
$212$	2.65956	+	0.310858i	0.182659	+	0.0213498i
$213$		0			0
$214$	0.0617057	−	1.05945i	0.00421811	−	0.0724222i
$215$	−2.56231	−	4.43806i	−0.174748	−	0.302673i
$216$		0			0
$217$	−8.82916	+	15.2925i	−0.599362	+	1.03813i
$218$	10.2306	+	6.72874i	0.692900	+	0.455728i
$219$		0			0
$220$	1.69236	+	3.92334i	0.114099	+	0.264512i
$221$	−2.60457	+	0.617295i	−0.175202	+	0.0415237i
$222$		0			0
$223$	10.6088	+	14.2500i	0.710415	+	0.954252i	0.999996	−	0.00290107i	$-0.000923440\pi$
$223$	10.6088	+	14.2500i	0.710415	+	0.954252i	−0.289581	+	0.957153i	$0.593516\pi$
$224$	−2.63793	+	0.960127i	−0.176254	+	0.0641512i
$225$		0			0
$226$	6.40020	+	2.32948i	0.425735	+	0.154955i
$227$	−0.718661	−	2.40050i	−0.0476992	−	0.159327i	0.930822	−	0.365473i	$-0.119093\pi$
$227$	−0.718661	−	2.40050i	−0.0476992	−	0.159327i	−0.978521	+	0.206147i	$0.933908\pi$
$228$		0			0
$229$	−0.262629	−	4.50916i	−0.0173550	−	0.297974i	−0.995806	−	0.0914931i	$-0.970836\pi$
$229$	−0.262629	−	4.50916i	−0.0173550	−	0.297974i	0.978451	−	0.206480i	$-0.0662010\pi$
$230$	5.74181	−	3.77645i	0.378604	−	0.249011i
$231$		0			0
$232$	−7.01112	−	1.66167i	−0.460303	−	0.109094i
$233$	−2.12497	−	12.0513i	−0.139212	−	0.789508i	−0.971834	−	0.235667i	$-0.924273\pi$
$233$	−2.12497	−	12.0513i	−0.139212	−	0.789508i	0.832622	−	0.553841i	$-0.186839\pi$
$234$		0			0
$235$	−0.816993	+	4.63340i	−0.0532948	+	0.302250i
$236$	−1.99432	+	4.62334i	−0.129819	+	0.300954i
$237$		0			0
$238$	−1.22152	+	4.08015i	−0.0791791	+	0.264477i
$239$	−15.8275	+	21.2601i	−1.02380	+	1.37520i	−0.0988519	+	0.995102i	$0.531517\pi$
$239$	−15.8275	+	21.2601i	−1.02380	+	1.37520i	−0.924946	+	0.380098i	$0.875890\pi$
$240$		0			0
$241$	−4.87872	+	2.45019i	−0.314266	+	0.157830i	−0.598940	−	0.800794i	$-0.704411\pi$
$241$	−4.87872	+	2.45019i	−0.314266	+	0.157830i	0.284674	+	0.958625i	$0.408115\pi$
$242$	10.0411			0.645466
$243$		0			0
$244$	5.27273			0.337552
$245$	−0.732936	+	0.368094i	−0.0468256	+	0.0235167i
$246$		0			0
$247$	4.62391	−	6.21099i	0.294212	−	0.395196i
$248$	−1.80408	+	6.02605i	−0.114559	+	0.382655i
$249$		0			0
$250$	3.36931	−	7.81095i	0.213094	−	0.494008i
$251$	−0.521714	+	2.95878i	−0.0329303	+	0.186757i	−0.996836	−	0.0794874i	$-0.974672\pi$
$251$	−0.521714	+	2.95878i	−0.0329303	+	0.186757i	0.963906	+	0.266244i	$0.0857828\pi$
$252$		0			0
$253$	−5.87673	−	33.3286i	−0.369467	−	2.09535i
$254$	−8.28984	−	1.96473i	−0.520151	−	0.123278i
$255$		0			0
$256$	−0.835488	+	0.549509i	−0.0522180	+	0.0343443i
$257$	−0.761444	−	13.0735i	−0.0474975	−	0.815501i	−0.934989	−	0.354677i	$-0.884591\pi$
$257$	−0.761444	−	13.0735i	−0.0474975	−	0.815501i	0.887491	−	0.460824i	$-0.152446\pi$
$258$		0			0
$259$	0.543081	+	1.81402i	0.0337454	+	0.112717i
$260$	−1.54429	−	0.562075i	−0.0957727	−	0.0348584i
$261$		0			0
$262$	15.0048	−	5.46131i	0.927001	−	0.337401i
$263$	1.87795	+	2.52252i	0.115799	+	0.155545i	0.856244	−	0.516572i	$-0.172792\pi$
$263$	1.87795	+	2.52252i	0.115799	+	0.155545i	−0.740444	+	0.672118i	$0.765385\pi$
$264$		0			0
$265$	2.42698	−	0.575204i	0.149088	−	0.0353345i
$266$	−4.87994	−	11.3130i	−0.299208	−	0.693642i
$267$		0			0
$268$	11.9595	+	7.86592i	0.730545	+	0.480487i
$269$	10.1021	−	17.4974i	0.615938	−	1.06684i	−0.374282	−	0.927315i	$-0.622111\pi$
$269$	10.1021	−	17.4974i	0.615938	−	1.06684i	0.990219	−	0.139520i	$-0.0445560\pi$
$270$		0			0
$271$	−14.8899	−	25.7901i	−0.904500	−	1.56664i	−0.821587	−	0.570083i	$-0.806911\pi$
$271$	−14.8899	−	25.7901i	−0.904500	−	1.56664i	−0.0829129	−	0.996557i	$-0.526422\pi$
$272$	−0.0882164	+	1.51462i	−0.00534890	+	0.0918371i
$273$		0			0
$274$	−10.6907	−	1.24956i	−0.645847	−	0.0754887i
$275$	−13.0079	−	13.7875i	−0.784404	−	0.831420i
$276$		0			0
$277$	−4.36989	+	0.510767i	−0.262561	+	0.0306890i	−0.246355	−	0.969180i	$-0.579233\pi$
$277$	−4.36989	+	0.510767i	−0.262561	+	0.0306890i	−0.0162063	+	0.999869i	$0.505159\pi$
$278$	4.93751	+	4.14306i	0.296132	+	0.248484i
$279$		0			0
$280$	−2.00313	+	1.68082i	−0.119710	+	0.100448i
$281$	−19.4042	+	20.5672i	−1.15755	+	1.22694i	−0.187972	+	0.982174i	$0.560191\pi$
$281$	−19.4042	+	20.5672i	−1.15755	+	1.22694i	−0.969583	+	0.244762i	$0.921290\pi$
$282$		0			0
$283$	6.51124	+	3.27007i	0.387053	+	0.194385i	0.631675	−	0.775233i	$-0.282368\pi$
$283$	6.51124	+	3.27007i	0.387053	+	0.194385i	−0.244622	+	0.969618i	$0.578664\pi$
$284$	0.253456	+	0.127291i	0.0150399	+	0.00755331i
$285$		0			0
$286$	−5.55362	+	5.88650i	−0.328393	+	0.348076i
$287$	20.3660	−	17.0891i	1.20217	−	1.00874i
$288$		0			0
$289$	−11.2594	−	9.44779i	−0.662320	−	0.555752i
$290$	−6.66631	+	0.779180i	−0.391459	+	0.0457550i
$291$		0			0
$292$	7.94532	+	8.42155i	0.464965	+	0.492834i
$293$	0.386477	+	0.0451727i	0.0225782	+	0.00263902i	0.127375	−	0.991855i	$-0.459345\pi$
$293$	0.386477	+	0.0451727i	0.0225782	+	0.00263902i	−0.104796	+	0.994494i	$0.533419\pi$
$294$		0			0
$295$	−0.272709	+	4.68223i	−0.0158777	+	0.272610i
$296$	0.337267	+	0.584163i	0.0196032	+	0.0339538i
$297$		0			0
$298$	0.0173079	−	0.0299781i	0.00100262	−	0.00173658i
$299$	10.8752	+	7.15272i	0.628928	+	0.413652i
$300$		0			0
$301$	−6.11709	−	14.1810i	−0.352583	−	0.817380i
$302$	−22.1823	+	5.25731i	−1.27645	+	0.302524i
$303$		0			0
$304$	−2.62086	−	3.52043i	−0.150317	−	0.201910i
$305$	4.61529	−	1.67983i	0.264271	−	0.0961866i
$306$		0			0
$307$	15.8628	+	5.77360i	0.905340	+	0.329517i	0.752391	−	0.658717i	$-0.228901\pi$
$307$	15.8628	+	5.77360i	0.905340	+	0.329517i	0.152949	+	0.988234i	$0.451123\pi$
$308$	3.69313	+	12.3359i	0.210436	+	0.702905i
$309$		0			0
$310$	0.340691	+	5.84944i	0.0193499	+	0.332226i
$311$	20.9613	−	13.7865i	1.18861	−	0.781760i	0.208074	−	0.978113i	$-0.433280\pi$
$311$	20.9613	−	13.7865i	1.18861	−	0.781760i	0.980533	+	0.196353i	$0.0629100\pi$
$312$		0			0
$313$	9.15572	+	2.16994i	0.517512	+	0.122653i	0.481068	−	0.876683i	$-0.340249\pi$
$313$	9.15572	+	2.16994i	0.517512	+	0.122653i	0.0364435	+	0.999336i	$0.488397\pi$
$314$	−1.53301	−	8.69416i	−0.0865130	−	0.490640i
$315$		0			0
$316$	0.617772	−	3.50356i	0.0347524	−	0.197091i
$317$	5.32798	−	12.3516i	0.299249	−	0.693737i	−0.700554	−	0.713600i	$-0.747064\pi$
$317$	5.32798	−	12.3516i	0.299249	−	0.693737i	0.999803	+	0.0198626i	$0.00632287\pi$
$318$		0			0
$319$	−9.47923	+	31.6628i	−0.530735	+	1.77278i
$320$	−0.556246	+	0.747168i	−0.0310951	+	0.0417680i
$321$		0			0
$322$	18.5083	−	9.29523i	1.03143	−	0.518003i
$323$	−6.65875			−0.370503
$324$		0			0
$325$	7.29055			0.404407
$326$	−18.9651	+	9.52464i	−1.05038	+	0.527521i
$327$		0			0
$328$	5.65541	−	7.59653i	0.312268	−	0.419448i
$329$	−4.06661	+	13.5834i	−0.224199	+	0.748878i
$330$		0			0
$331$	−5.56619	+	12.9039i	−0.305946	+	0.709262i	−0.999943	−	0.0107163i	$-0.996589\pi$
$331$	−5.56619	+	12.9039i	−0.305946	+	0.709262i	0.693997	+	0.719978i	$0.255848\pi$
$332$	1.85799	−	10.5372i	0.101971	−	0.578303i
$333$		0			0
$334$	−2.78115	−	15.7727i	−0.152178	−	0.863042i
$335$	12.9743	+	3.07497i	0.708863	+	0.168004i
$336$		0			0
$337$	5.45623	−	3.58862i	0.297220	−	0.195485i	−0.392136	−	0.919907i	$-0.628264\pi$
$337$	5.45623	−	3.58862i	0.297220	−	0.195485i	0.689356	+	0.724423i	$0.257894\pi$
$338$	0.574898	+	9.87062i	0.0312703	+	0.536891i
$339$		0			0
$340$	0.405321	+	1.35387i	0.0219816	+	0.0734238i
$341$	27.1139	+	9.86866i	1.46830	+	0.534418i
$342$		0			0
$343$	16.1428	−	5.87549i	0.871629	−	0.317247i
$344$	−3.28530	−	4.41292i	−0.177131	−	0.237929i
$345$		0			0
$346$	10.9871	−	2.60399i	0.590670	−	0.139991i
$347$	−10.6690	−	24.7336i	−0.572744	−	1.32777i	−0.920705	−	0.390260i	$-0.872385\pi$
$347$	−10.6690	−	24.7336i	−0.572744	−	1.32777i	0.347961	−	0.937509i	$-0.386874\pi$
$348$		0			0
$349$	−21.0859	−	13.8684i	−1.12870	−	0.742359i	−0.159153	−	0.987254i	$-0.550876\pi$
$349$	−21.0859	−	13.8684i	−1.12870	−	0.742359i	−0.969550	+	0.244895i	$0.921247\pi$
$350$	5.80019	−	10.0462i	0.310033	−	0.536993i
$351$		0			0
$352$	2.29353	+	3.97251i	0.122245	+	0.211735i
$353$	0.0557860	−	0.957808i	0.00296919	−	0.0509790i	−0.996498	−	0.0836154i	$-0.973353\pi$
$353$	0.0557860	−	0.957808i	0.00296919	−	0.0509790i	0.999467	+	0.0326364i	$0.0103903\pi$
$354$		0			0
$355$	0.262407	+	0.0306710i	0.0139271	+	0.00162785i
$356$	6.90479	+	7.31865i	0.365953	+	0.387888i
$357$		0			0
$358$	−19.8111	+	2.31558i	−1.04705	+	0.122382i
$359$	12.5985	+	10.5714i	0.664925	+	0.557939i	0.911559	−	0.411170i	$-0.134880\pi$
$359$	12.5985	+	10.5714i	0.664925	+	0.557939i	−0.246633	+	0.969109i	$0.579324\pi$
$360$		0			0
$361$	0.200968	−	0.168633i	0.0105773	−	0.00887540i
$362$	14.6049	−	15.4802i	0.767614	−	0.813623i
$363$		0			0
$364$	−4.42590	−	2.22277i	−0.231980	−	0.116505i
$365$	9.63764	+	4.84020i	0.504457	+	0.253348i
$366$		0			0
$367$	−1.16969	+	1.23980i	−0.0610575	+	0.0647172i	−0.757182	−	0.653204i	$-0.773425\pi$
$367$	−1.16969	+	1.23980i	−0.0610575	+	0.0647172i	0.696125	+	0.717921i	$0.254906\pi$
$368$	5.65178	−	4.74241i	0.294619	−	0.247215i
$369$		0			0
$370$	0.481321	+	0.403876i	0.0250227	+	0.0209965i
$371$	7.46597	−	0.872647i	0.387614	−	0.0453056i
$372$		0			0
$373$	−9.80490	−	10.3926i	−0.507678	−	0.538108i	0.421944	−	0.906622i	$-0.361348\pi$
$373$	−9.80490	−	10.3926i	−0.507678	−	0.538108i	−0.929622	+	0.368514i	$0.879866\pi$
$374$	6.91235	+	0.807938i	0.357429	+	0.0417775i
$375$		0			0
$376$	−0.293685	+	5.04238i	−0.0151457	+	0.260041i
$377$	−6.35609	−	11.0091i	−0.327355	−	0.566996i
$378$		0			0
$379$	−12.0604	+	20.8893i	−0.619504	+	1.07301i	0.370073	+	0.929003i	$0.379333\pi$
$379$	−12.0604	+	20.8893i	−0.619504	+	1.07301i	−0.989576	+	0.144009i	$0.954001\pi$
$380$	−3.41564	−	2.24650i	−0.175219	−	0.115243i
$381$		0			0
$382$	−7.06104	−	16.3693i	−0.361274	−	0.837528i
$383$	−5.64393	+	1.33764i	−0.288391	+	0.0683500i	−0.372265	−	0.928126i	$-0.621419\pi$
$383$	−5.64393	+	1.33764i	−0.288391	+	0.0683500i	0.0838739	+	0.996476i	$0.473271\pi$
$384$		0			0
$385$	7.16272	+	9.62120i	0.365046	+	0.490342i
$386$	21.0003	−	7.64348i	1.06889	−	0.389043i
$387$		0			0
$388$	−16.2609	−	5.91848i	−0.825522	−	0.300465i
$389$	5.89390	+	19.6870i	0.298833	+	0.998170i	0.967131	+	0.254277i	$0.0818376\pi$
$389$	5.89390	+	19.6870i	0.298833	+	0.998170i	−0.668299	+	0.743893i	$0.732977\pi$
$390$		0			0
$391$	−0.650849	−	11.1747i	−0.0329149	−	0.565126i
$392$	−0.735648	+	0.483843i	−0.0371558	+	0.0244378i
$393$		0			0
$394$	3.97306	+	0.941633i	0.200160	+	0.0474388i
$395$	−0.575447	−	3.26352i	−0.0289539	−	0.164206i
$396$		0			0
$397$	−2.54727	+	14.4463i	−0.127844	+	0.725039i	0.851734	+	0.523974i	$0.175551\pi$
$397$	−2.54727	+	14.4463i	−0.127844	+	0.725039i	−0.979578	+	0.201065i	$0.935560\pi$
$398$	−0.320680	+	0.743419i	−0.0160742	+	0.0372642i
$399$		0			0
$400$	1.18517	−	3.95873i	0.0592583	−	0.197936i
$401$	−15.9451	+	21.4180i	−0.796262	+	1.06957i	0.199706	+	0.979856i	$0.436001\pi$
$401$	−15.9451	+	21.4180i	−0.796262	+	1.06957i	−0.995968	+	0.0897093i	$0.971406\pi$
$402$		0			0
$403$	−9.91737	+	4.98069i	−0.494019	+	0.248106i
$404$	6.32877			0.314868
$405$		0			0
$406$	−20.2270			−1.00385
$407$	2.76501	−	1.38864i	0.137056	−	0.0688323i
$408$		0			0
$409$	−5.81400	+	7.80956i	−0.287484	+	0.386158i	−0.922280	−	0.386521i	$-0.873677\pi$
$409$	−5.81400	+	7.80956i	−0.287484	+	0.386158i	0.634796	+	0.772679i	$0.281084\pi$
$410$	2.53009	−	8.45108i	0.124952	−	0.417369i
$411$		0			0
$412$	−7.37729	+	17.1025i	−0.363453	+	0.842579i
$413$	−2.45447	+	13.9200i	−0.120777	+	0.684959i
$414$		0			0
$415$	−1.73070	−	9.81527i	−0.0849565	−	0.481812i
$416$	−1.71671	−	0.406869i	−0.0841688	−	0.0199484i
$417$		0			0
$418$	−16.8201	+	11.0628i	−0.822698	+	0.541097i
$419$	−0.515542	−	8.85151i	−0.0251859	−	0.432425i	−0.987206	−	0.159448i	$-0.949029\pi$
$419$	−0.515542	−	8.85151i	−0.0251859	−	0.432425i	0.962021	−	0.272977i	$-0.0880083\pi$
$420$		0			0
$421$	3.31057	+	11.0581i	0.161347	+	0.538938i	0.999983	−	0.00575434i	$-0.00183167\pi$
$421$	3.31057	+	11.0581i	0.161347	+	0.538938i	−0.838636	+	0.544692i	$0.816646\pi$
$422$	−10.6852	−	3.88908i	−0.520145	−	0.189317i
$423$		0			0
$424$	2.51618	−	0.915814i	0.122196	−	0.0444759i
$425$	−3.74389	−	5.02891i	−0.181605	−	0.243938i
$426$		0			0
$427$	14.4028	−	3.41352i	0.696998	−	0.165192i
$428$	−0.420336	−	0.974449i	−0.0203177	−	0.0471018i
$429$		0			0
$430$	−4.28156	−	2.81603i	−0.206475	−	0.135801i
$431$	−13.5607	+	23.4878i	−0.653196	+	1.13137i	0.329147	+	0.944279i	$0.393239\pi$
$431$	−13.5607	+	23.4878i	−0.653196	+	1.13137i	−0.982343	+	0.187090i	$0.940094\pi$
$432$		0			0
$433$	0.933229	+	1.61640i	0.0448481	+	0.0776792i	0.887578	−	0.460657i	$-0.152386\pi$
$433$	0.933229	+	1.61640i	0.0448481	+	0.0776792i	−0.842730	+	0.538337i	$0.819053\pi$
$434$	−1.02674	+	17.6284i	−0.0492851	+	0.846192i
$435$		0			0
$436$	12.1622	+	1.42156i	0.582464	+	0.0680803i
$437$	22.2210	+	23.5528i	1.06297	+	1.12669i
$438$		0			0
$439$	5.43863	−	0.635684i	0.259571	−	0.0303396i	0.0146882	−	0.999892i	$-0.495324\pi$
$439$	5.43863	−	0.635684i	0.259571	−	0.0303396i	0.244883	+	0.969553i	$0.421250\pi$
$440$	3.27315	+	2.74650i	0.156041	+	0.130934i
$441$		0			0
$442$	−2.05049	+	1.72056i	−0.0975318	+	0.0818389i
$443$	−7.84510	+	8.31532i	−0.372732	+	0.395073i	−0.886403	−	0.462914i	$-0.846804\pi$
$443$	−7.84510	+	8.31532i	−0.372732	+	0.395073i	0.513671	+	0.857987i	$0.328285\pi$
$444$		0			0
$445$	8.37548	+	4.20632i	0.397036	+	0.199399i
$446$	15.8757	+	7.97309i	0.751737	+	0.377537i
$447$		0			0
$448$	−1.92643	+	2.04190i	−0.0910154	+	0.0964707i
$449$	0.447406	−	0.375418i	0.0211144	−	0.0177171i	−0.632169	−	0.774830i	$-0.717835\pi$
$449$	0.447406	−	0.375418i	0.0211144	−	0.0177171i	0.653284	+	0.757113i	$0.273391\pi$
$450$		0			0
$451$	−33.2784	−	27.9239i	−1.56702	−	1.31488i
$452$	6.76489	−	0.790703i	0.318194	−	0.0371915i
$453$		0			0
$454$	−1.71956	−	1.82263i	−0.0807029	−	0.0855401i
$455$	−4.58219	−	0.535581i	−0.214816	−	0.0251084i
$456$		0			0
$457$	−0.759073	+	13.0328i	−0.0355079	+	0.609648i	0.932878	+	0.360192i	$0.117289\pi$
$457$	−0.759073	+	13.0328i	−0.0355079	+	0.609648i	−0.968386	+	0.249456i	$0.919748\pi$
$458$	−2.25840	−	3.91166i	−0.105528	−	0.182780i
$459$		0			0
$460$	3.43620	−	5.95167i	0.160214	−	0.277498i
$461$	−9.75285	−	6.41455i	−0.454236	−	0.298756i	0.301698	−	0.953403i	$-0.402447\pi$
$461$	−9.75285	−	6.41455i	−0.454236	−	0.298756i	−0.755934	+	0.654648i	$0.772817\pi$
$462$		0			0
$463$	3.89577	+	9.03140i	0.181052	+	0.419725i	0.984438	−	0.175734i	$-0.0562297\pi$
$463$	3.89577	+	9.03140i	0.181052	+	0.419725i	−0.803386	+	0.595458i	$0.796970\pi$
$464$	−7.01112	+	1.66167i	−0.325483	+	0.0771409i
$465$		0			0
$466$	−7.30757	−	9.81577i	−0.338517	−	0.454707i
$467$	−16.7575	+	6.09922i	−0.775444	+	0.282238i	−0.699271	−	0.714856i	$-0.746492\pi$
$467$	−16.7575	+	6.09922i	−0.775444	+	0.282238i	−0.0761723	+	0.997095i	$0.524270\pi$
$468$		0			0
$469$	37.7605	+	13.7437i	1.74362	+	0.634624i
$470$	1.34937	+	4.50722i	0.0622420	+	0.207903i
$471$		0			0
$472$	0.292767	+	5.02662i	0.0134757	+	0.231369i
$473$	−21.0843	+	13.8674i	−0.969458	+	0.637622i
$474$		0			0
$475$	17.6475	+	4.18253i	0.809722	+	0.191908i
$476$	0.739580	+	4.19437i	0.0338986	+	0.192249i
$477$		0			0
$478$	−4.60250	+	26.1021i	−0.210513	+	1.19388i
$479$	−14.2659	+	33.0722i	−0.651827	+	1.51111i	0.195873	+	0.980629i	$0.437246\pi$
$479$	−14.2659	+	33.0722i	−0.651827	+	1.51111i	−0.847700	+	0.530476i	$0.822013\pi$
$480$		0			0
$481$	−0.341313	+	1.14006i	−0.0155625	+	0.0519825i
$482$	−3.26014	+	4.37913i	−0.148496	+	0.199464i
$483$		0			0
$484$	8.97305	−	4.50643i	0.407866	−	0.204838i
$485$	−16.1189			−0.731922
$486$		0			0
$487$	28.2800			1.28149			0.640744	−	0.767754i	$-0.278626\pi$
$487$	28.2800			1.28149			0.640744	+	0.767754i	$0.278626\pi$
$488$	4.71189	−	2.36640i	0.213297	−	0.107122i
$489$		0			0
$490$	−0.489775	+	0.657882i	−0.0221258	+	0.0297201i
$491$	1.26149	−	4.21368i	0.0569303	−	0.190161i	−0.924794	−	0.380467i	$-0.875763\pi$
$491$	1.26149	−	4.21368i	0.0569303	−	0.190161i	0.981725	+	0.190307i	$0.0609483\pi$
$492$		0			0
$493$	−4.32988	+	10.0378i	−0.195008	+	0.452079i
$494$	1.34459	−	7.62555i	0.0604960	−	0.343090i
$495$		0			0
$496$	1.09230	+	6.19475i	0.0490458	+	0.278152i
$497$	0.774737	+	0.183616i	0.0347517	+	0.00823630i
$498$		0			0
$499$	−13.2375	+	8.70642i	−0.592590	+	0.389753i	−0.810088	−	0.586308i	$-0.800581\pi$
$499$	−13.2375	+	8.70642i	−0.592590	+	0.389753i	0.217498	+	0.976061i	$0.430210\pi$
$500$	−0.494618	−	8.49226i	−0.0221200	−	0.379786i
$501$		0			0
$502$	0.861680	+	2.87821i	0.0384587	+	0.128461i
$503$	12.5996	+	4.58586i	0.561786	+	0.204473i	0.607275	−	0.794491i	$-0.292262\pi$
$503$	12.5996	+	4.58586i	0.561786	+	0.204473i	−0.0454892	+	0.998965i	$0.514485\pi$
$504$		0			0
$505$	5.53965	−	2.01627i	0.246511	−	0.0897227i
$506$	−20.2095	−	27.1460i	−0.898421	−	1.20679i
$507$		0			0
$508$	−8.28984	+	1.96473i	−0.367802	+	0.0871707i
$509$	5.98696	+	13.8793i	0.265367	+	0.615191i	0.997846	−	0.0655993i	$-0.0208959\pi$
$509$	5.98696	+	13.8793i	0.265367	+	0.615191i	−0.732479	+	0.680790i	$0.761637\pi$
$510$		0			0
$511$	27.1551	+	17.8602i	1.20127	+	0.790088i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$		0			0
$514$	−6.54782	−	11.3412i	−0.288812	−	0.500237i
$515$	−1.00879	+	17.3203i	−0.0444528	+	0.763225i
$516$		0			0
$517$	23.0122	+	2.68974i	1.01208	+	0.118295i
$518$	1.29944	+	1.37733i	0.0570943	+	0.0605164i
$519$		0			0
$520$	−1.63228	+	0.190787i	−0.0715804	+	0.00836655i
$521$	−1.94311	−	1.63047i	−0.0851294	−	0.0714321i	0.599230	−	0.800577i	$-0.295474\pi$
$521$	−1.94311	−	1.63047i	−0.0851294	−	0.0714321i	−0.684359	+	0.729145i	$0.739918\pi$
$522$		0			0
$523$	−14.0884	+	11.8216i	−0.616042	+	0.516921i	−0.896557	−	0.442929i	$-0.853939\pi$
$523$	−14.0884	+	11.8216i	−0.616042	+	0.516921i	0.280514	+	0.959850i	$0.409495\pi$
$524$	10.9578	−	11.6146i	0.478692	−	0.507384i
$525$		0			0
$526$	2.81030	+	1.41139i	0.122535	+	0.0615394i
$527$	8.52844	+	4.28314i	0.371505	+	0.186577i
$528$		0			0
$529$	−21.5707	+	22.8636i	−0.937854	+	0.994068i
$530$	1.91068	−	1.60325i	0.0829945	−	0.0696406i
$531$		0			0
$532$	−9.43812	−	7.91952i	−0.409194	−	0.343355i
$533$	16.5956	−	1.93975i	0.718835	−	0.0840198i
$534$		0			0
$535$	−0.678373	−	0.719033i	−0.0293286	−	0.0310865i
$536$	14.2177	+	1.66181i	0.614109	+	0.0717791i
$537$		0			0
$538$	1.17477	−	20.1701i	0.0506481	−	0.869594i
$539$	2.01945	+	3.49780i	0.0869841	+	0.150661i
$540$		0			0
$541$	−7.56562	+	13.1040i	−0.325271	+	0.563386i	−0.981567	−	0.191117i	$-0.938789\pi$
$541$	−7.56562	+	13.1040i	−0.325271	+	0.563386i	0.656296	+	0.754504i	$0.272122\pi$
$542$	−24.8807	−	16.3643i	−1.06872	−	0.702908i
$543$		0			0
$544$	0.600926	+	1.39310i	0.0257645	+	0.0597288i
$545$	11.0986	−	2.63042i	0.475413	−	0.112675i
$546$		0			0
$547$	−10.5461	−	14.1659i	−0.450920	−	0.605690i	0.517296	−	0.855806i	$-0.326939\pi$
$547$	−10.5461	−	14.1659i	−0.450920	−	0.605690i	−0.968216	+	0.250116i	$0.919531\pi$
$548$	−10.1143	+	3.68132i	−0.432063	+	0.157258i
$549$		0			0
$550$	−17.8121	−	6.48307i	−0.759510	−	0.276439i
$551$	−9.06971	−	30.2949i	−0.386383	−	1.29061i
$552$		0			0
$553$	−0.580693	−	9.97011i	−0.0246936	−	0.423972i
$554$	−3.67584	+	2.41764i	−0.156172	+	0.102716i
$555$		0			0
$556$	6.27172	+	1.48643i	0.265980	+	0.0630385i
$557$	−2.15648	−	12.2300i	−0.0913731	−	0.518203i	−0.995799	−	0.0915710i	$-0.970811\pi$
$557$	−2.15648	−	12.2300i	−0.0913731	−	0.518203i	0.904425	−	0.426632i	$-0.140300\pi$
$558$		0			0
$559$	1.68547	−	9.55877i	0.0712877	−	0.404293i
$560$	−1.03571	+	2.40104i	−0.0437666	+	0.101462i
$561$		0			0
$562$	−8.10964	+	27.0881i	−0.342085	+	1.14264i
$563$	15.6180	−	20.9785i	0.658218	−	0.884140i	−0.340201	−	0.940353i	$-0.610495\pi$
$563$	15.6180	−	20.9785i	0.658218	−	0.884140i	0.998419	+	0.0562125i	$0.0179024\pi$
$564$		0			0
$565$	5.66949	−	2.84732i	0.238517	−	0.119788i
$566$	7.28626			0.306264
$567$		0			0
$568$	0.283625			0.0119006
$569$	−13.1704	+	6.61443i	−0.552133	+	0.277291i	−0.702913	−	0.711276i	$-0.748118\pi$
$569$	−13.1704	+	6.61443i	−0.552133	+	0.277291i	0.150780	+	0.988567i	$0.451821\pi$
$570$		0			0
$571$	3.97285	−	5.33646i	0.166259	−	0.223324i	−0.711184	−	0.703006i	$-0.751841\pi$
$571$	3.97285	−	5.33646i	0.166259	−	0.223324i	0.877442	+	0.479682i	$0.159248\pi$
$572$	−2.32104	+	7.75283i	−0.0970477	+	0.324162i
$573$		0			0
$574$	10.5301	−	24.4116i	0.439519	−	1.01892i
$575$	−5.29415	+	30.0246i	−0.220781	+	1.25211i
$576$		0			0
$577$	5.41335	+	30.7007i	0.225361	+	1.27809i	0.861994	+	0.506918i	$0.169215\pi$
$577$	5.41335	+	30.7007i	0.225361	+	1.27809i	−0.636633	+	0.771167i	$0.719673\pi$
$578$	−14.3020	−	3.38963i	−0.594883	−	0.140990i
$579$		0			0
$580$	−5.60754	+	3.68813i	−0.232840	+	0.153141i
$581$	−1.74647	−	29.9858i	−0.0724558	−	1.24402i
$582$		0			0
$583$	−3.52269	−	11.7666i	−0.145895	−	0.487322i
$584$	10.8798	+	3.95992i	0.450209	+	0.163863i
$585$		0			0
$586$	0.365642	−	0.133083i	0.0151045	−	0.00549760i
$587$	25.5016	+	34.2546i	1.05256	+	1.41384i	0.905316	+	0.424739i	$0.139634\pi$
$587$	25.5016	+	34.2546i	1.05256	+	1.41384i	0.147248	+	0.989100i	$0.452958\pi$
$588$		0			0
$589$	−26.8633	+	6.36672i	−1.10688	+	0.262336i
$590$	1.85768	+	4.30659i	0.0764795	+	0.177299i
$591$		0			0
$592$	0.563564	+	0.370662i	0.0231624	+	0.0152341i
$593$	−6.95785	+	12.0513i	−0.285725	+	0.494890i	−0.972785	−	0.231711i	$-0.925568\pi$
$593$	−6.95785	+	12.0513i	−0.285725	+	0.494890i	0.687060	+	0.726601i	$0.258901\pi$
$594$		0			0
$595$	1.98364	+	3.43576i	0.0813212	+	0.140852i
$596$	0.00201273	−	0.0345572i	8.24445e−5	−	0.00141552i
$597$		0			0
$598$	12.9286	+	1.51113i	0.528688	+	0.0617947i
$599$	4.87779	+	5.17016i	0.199301	+	0.211247i	0.819314	−	0.573344i	$-0.194354\pi$
$599$	4.87779	+	5.17016i	0.199301	+	0.211247i	−0.620013	+	0.784591i	$0.712873\pi$
$600$		0			0
$601$	−22.4454	+	2.62349i	−0.915567	+	0.107014i	−0.560811	−	0.827944i	$-0.689510\pi$
$601$	−22.4454	+	2.62349i	−0.915567	+	0.107014i	−0.354757	+	0.934959i	$0.615436\pi$
$602$	−11.8309	−	9.92726i	−0.482190	−	0.404605i
$603$		0			0
$604$	−17.4634	+	14.6535i	−0.710575	+	0.596243i
$605$	6.41852	−	6.80324i	0.260950	−	0.276591i
$606$		0			0
$607$	−28.7677	−	14.4477i	−1.16765	−	0.586414i	−0.244043	−	0.969764i	$-0.578474\pi$
$607$	−28.7677	−	14.4477i	−1.16765	−	0.586414i	−0.923603	+	0.383350i	$0.874770\pi$
$608$	−3.92205	−	1.96973i	−0.159060	−	0.0798831i
$609$		0			0
$610$	3.37047	−	3.57249i	0.136466	−	0.144646i
$611$	−6.82638	+	5.72801i	−0.276166	+	0.231730i
$612$		0			0
$613$	−17.0259	−	14.2864i	−0.687670	−	0.577024i	0.230566	−	0.973057i	$-0.425942\pi$
$613$	−17.0259	−	14.2864i	−0.687670	−	0.577024i	−0.918236	+	0.396033i	$0.870387\pi$
$614$	16.7667	−	1.95975i	0.676650	−	0.0790891i
$615$		0			0
$616$	8.83666	+	9.36631i	0.356039	+	0.377379i
$617$	−33.2913	−	3.89120i	−1.34026	−	0.156654i	−0.584441	−	0.811437i	$-0.698686\pi$
$617$	−33.2913	−	3.89120i	−1.34026	−	0.156654i	−0.755817	+	0.654783i	$0.772760\pi$
$618$		0			0
$619$	0.202006	−	3.46831i	0.00811931	−	0.139403i	−0.991812	−	0.127704i	$-0.959239\pi$
$619$	0.202006	−	3.46831i	0.00811931	−	0.139403i	0.999932	−	0.0116986i	$-0.00372387\pi$
$620$	2.92968	+	5.07435i	0.117659	+	0.203791i
$621$		0			0
$622$	12.5444	−	21.7275i	0.502983	−	0.871192i
$623$	23.5988	+	15.5212i	0.945467	+	0.621843i
$624$		0			0
$625$	5.04519	+	11.6961i	0.201807	+	0.467842i
$626$	9.15572	−	2.16994i	0.365936	−	0.0867284i
$627$		0			0
$628$	−5.27188	−	7.08137i	−0.210371	−	0.282577i
$629$	0.961673	−	0.350020i	0.0383444	−	0.0139562i
$630$		0			0
$631$	38.5574	+	14.0337i	1.53494	+	0.558674i	0.964826	−	0.262888i	$-0.0846751\pi$
$631$	38.5574	+	14.0337i	1.53494	+	0.558674i	0.570118	+	0.821563i	$0.306897\pi$
$632$	−1.02033	−	3.40815i	−0.0405867	−	0.135569i
$633$		0			0
$634$	−0.782151	−	13.4290i	−0.0310632	−	0.533334i
$635$	−6.63026	+	4.36079i	−0.263114	+	0.173053i
$636$		0			0
$637$	−1.51157	−	0.358249i	−0.0598906	−	0.0141943i
$638$	5.73930	+	32.5492i	0.227221	+	1.28864i
$639$		0			0
$640$	−0.161751	+	0.917337i	−0.00639378	+	0.0362609i
$641$	9.47251	−	21.9598i	0.374142	−	0.867358i	−0.622277	−	0.782797i	$-0.713792\pi$
$641$	9.47251	−	21.9598i	0.374142	−	0.867358i	0.996418	−	0.0845606i	$-0.0269486\pi$
$642$		0			0
$643$	5.06218	−	16.9089i	0.199633	−	0.666821i	−0.798282	−	0.602284i	$-0.794258\pi$
$643$	5.06218	−	16.9089i	0.199633	−	0.666821i	0.997915	−	0.0645373i	$-0.0205572\pi$
$644$	12.3680	−	16.6130i	0.487366	−	0.654646i
$645$		0			0
$646$	−5.95048	+	2.98844i	−0.234118	+	0.117579i
$647$	−28.7326			−1.12959			−0.564797	−	0.825230i	$-0.691046\pi$
$647$	−28.7326			−1.12959			−0.564797	+	0.825230i	$0.691046\pi$
$648$		0			0
$649$	23.0965			0.906615
$650$	6.51507	−	3.27199i	0.255542	−	0.128338i
$651$		0			0
$652$	−12.6732	+	17.0231i	−0.496321	+	0.666675i
$653$	5.44267	−	18.1798i	0.212988	−	0.711430i	−0.783006	−	0.622014i	$-0.786315\pi$
$653$	5.44267	−	18.1798i	0.212988	−	0.711430i	0.995994	−	0.0894161i	$-0.0285001\pi$
$654$		0			0
$655$	5.89122	−	13.6574i	0.230189	−	0.533638i
$656$	1.64454	−	9.32665i	0.0642085	−	0.364145i
$657$		0			0
$658$	2.46217	+	13.9637i	0.0959854	+	0.544360i
$659$	28.0969	+	6.65909i	1.09450	+	0.259401i	0.737937	−	0.674870i	$-0.235800\pi$
$659$	28.0969	+	6.65909i	1.09450	+	0.259401i	0.356564	+	0.934271i	$0.383948\pi$
$660$		0			0
$661$	28.6512	−	18.8442i	1.11440	−	0.732955i	0.147746	−	0.989025i	$-0.452798\pi$
$661$	28.6512	−	18.8442i	1.11440	−	0.732955i	0.966658	+	0.256070i	$0.0824278\pi$
$662$	0.817122	+	14.0294i	0.0317583	+	0.545270i
$663$		0			0
$664$	−3.06872	−	10.2502i	−0.119089	−	0.397787i
$665$	−10.7844	−	3.92519i	−0.418200	−	0.152212i
$666$		0			0
$667$	49.9542	−	18.1818i	1.93423	−	0.704003i
$668$	−9.56408	−	12.8468i	−0.370045	−	0.497057i
$669$		0			0
$670$	12.9743	−	3.07497i	0.501242	−	0.118796i
$671$	−9.57971	−	22.2083i	−0.369821	−	0.857341i
$672$		0			0
$673$	−36.5808	−	24.0596i	−1.41009	−	0.927429i	−0.999881	−	0.0154368i	$-0.995086\pi$
$673$	−36.5808	−	24.0596i	−1.41009	−	0.927429i	−0.410207	−	0.911992i	$-0.634544\pi$
$674$	3.26530	−	5.65566i	0.125775	−	0.217848i
$675$		0			0
$676$	4.94367	+	8.56270i	0.190141	+	0.329334i
$677$	2.24011	−	38.4612i	0.0860945	−	1.47819i	−0.628042	−	0.778179i	$-0.716143\pi$
$677$	2.24011	−	38.4612i	0.0860945	−	1.47819i	0.714137	−	0.700006i	$-0.246819\pi$
$678$		0			0
$679$	−48.2491	−	5.63951i	−1.85163	−	0.216424i
$680$	0.969823	+	1.02795i	0.0371910	+	0.0394202i
$681$		0			0
$682$	28.6589	−	3.34975i	1.09741	−	0.128268i
$683$	−4.17850	−	3.50618i	−0.159886	−	0.134160i	0.559335	−	0.828942i	$-0.311057\pi$
$683$	−4.17850	−	3.50618i	−0.159886	−	0.134160i	−0.719221	+	0.694782i	$0.755501\pi$
$684$		0			0
$685$	−7.68038	+	6.44460i	−0.293452	+	0.246236i
$686$	11.7888	−	12.4954i	0.450099	−	0.477077i
$687$		0			0
$688$	−4.91637	−	2.46909i	−0.187435	−	0.0941332i
$689$	4.22163	+	2.12018i	0.160831	+	0.0807725i
$690$		0			0
$691$	17.2210	−	18.2532i	0.655117	−	0.694384i	−0.311605	−	0.950212i	$-0.600867\pi$
$691$	17.2210	−	18.2532i	0.655117	−	0.694384i	0.966722	+	0.255828i	$0.0823481\pi$
$692$	8.64976	−	7.25801i	0.328815	−	0.275908i
$693$		0			0
$694$	−20.6346	−	17.3145i	−0.783279	−	0.657250i
$695$	5.96327	−	0.697007i	0.226200	−	0.0264390i
$696$		0			0
$697$	−9.86028	−	10.4513i	−0.373485	−	0.395871i
$698$	−25.0672	−	2.92993i	−0.948807	−	0.110900i
$699$		0			0
$700$	0.674502	−	11.5807i	0.0254938	−	0.437711i
$701$	3.42730	+	5.93625i	0.129447	+	0.224209i	0.923463	−	0.383689i	$-0.125346\pi$
$701$	3.42730	+	5.93625i	0.129447	+	0.224209i	−0.794015	+	0.607898i	$0.792013\pi$
$702$		0			0
$703$	−1.48023	+	2.56383i	−0.0558278	+	0.0966966i
$704$	3.83243	+	2.52063i	0.144440	+	0.0949998i
$705$		0			0
$706$	−0.380011	−	0.880965i	−0.0143019	−	0.0331556i
$707$	17.2874	−	4.09718i	0.650158	−	0.154090i
$708$		0			0
$709$	−17.0943	−	22.9617i	−0.641991	−	0.862344i	0.355386	−	0.934720i	$-0.384349\pi$
$709$	−17.0943	−	22.9617i	−0.641991	−	0.862344i	−0.997377	+	0.0723754i	$0.976942\pi$
$710$	0.248260	−	0.0903594i	0.00931705	−	0.00339113i
$711$		0			0
$712$	9.45495	+	3.44132i	0.354339	+	0.128969i
$713$	−13.3103	−	44.4595i	−0.498474	−	1.66502i
$714$		0			0
$715$	0.438316	+	7.52560i	0.0163921	+	0.281442i
$716$	−16.6646	+	10.9605i	−0.622785	+	0.409612i
$717$		0			0
$718$	16.0029	+	3.79276i	0.597223	+	0.141545i
$719$	1.27419	+	7.22626i	0.0475191	+	0.269494i	0.999305	−	0.0372680i	$-0.0118655\pi$
$719$	1.27419	+	7.22626i	0.0475191	+	0.269494i	−0.951786	+	0.306762i	$0.900754\pi$
$720$		0			0
$721$	−9.07949	+	51.4924i	−0.338138	+	1.91768i
$722$	0.103910	−	0.240890i	0.00386712	−	0.00896500i
$723$		0			0
$724$	6.10386	−	20.3883i	0.226848	−	0.757725i
$725$	17.7803	−	23.8831i	0.660344	−	0.886996i
$726$		0			0
$727$	13.3751	−	6.71724i	0.496056	−	0.249129i	−0.183138	−	0.983087i	$-0.558626\pi$
$727$	13.3751	−	6.71724i	0.496056	−	0.249129i	0.679194	+	0.733958i	$0.262329\pi$
$728$	−4.95270			−0.183559
$729$		0			0
$730$	10.7848			0.399163
$731$	−7.45903	+	3.74607i	−0.275882	+	0.138553i
$732$		0			0
$733$	0.198111	−	0.266109i	0.00731738	−	0.00982895i	−0.798449	−	0.602062i	$-0.794346\pi$
$733$	0.198111	−	0.266109i	0.00731738	−	0.00982895i	0.805767	+	0.592233i	$0.201753\pi$
$734$	−0.488854	+	1.63289i	−0.0180439	+	0.0602709i
$735$		0			0
$736$	2.92223	−	6.77448i	0.107715	−	0.249711i
$737$	11.4019	−	64.6636i	0.419996	−	2.38192i
$738$		0			0
$739$	0.921946	+	5.22861i	0.0339143	+	0.192338i	0.997058	−	0.0766494i	$-0.0244222\pi$
$739$	0.921946	+	5.22861i	0.0339143	+	0.192338i	−0.963144	+	0.268987i	$0.913311\pi$
$740$	0.611383	+	0.144901i	0.0224749	+	0.00532665i
$741$		0			0
$742$	6.28019	−	4.13055i	0.230553	−	0.151637i
$743$	1.43288	+	24.6016i	0.0525673	+	0.902547i	0.916773	+	0.399408i	$0.130784\pi$
$743$	1.43288	+	24.6016i	0.0525673	+	0.902547i	−0.864206	+	0.503138i	$0.832179\pi$
$744$		0			0
$745$	−0.00924772	−	0.0308895i	−0.000338810	−	0.00113171i
$746$	−13.4262	−	4.88672i	−0.491567	−	0.178916i
$747$		0			0
$748$	6.53970	−	2.38026i	0.239115	−	0.0870308i
$749$	−1.77902	−	2.38964i	−0.0650040	−	0.0873155i
$750$		0			0
$751$	38.8862	−	9.21620i	1.41898	−	0.336304i	0.551665	−	0.834066i	$-0.313993\pi$
$751$	38.8862	−	9.21620i	1.41898	−	0.336304i	0.867314	+	0.497762i	$0.165845\pi$
$752$	2.00057	+	4.63784i	0.0729533	+	0.169125i
$753$		0			0
$754$	−10.6209	−	6.98546i	−0.386789	−	0.254395i
$755$	−10.6175	+	18.3900i	−0.386410	+	0.669282i
$756$		0			0
$757$	−1.35834	−	2.35271i	−0.0493695	−	0.0855105i	0.840285	−	0.542146i	$-0.182388\pi$
$757$	−1.35834	−	2.35271i	−0.0493695	−	0.0855105i	−0.889654	+	0.456635i	$0.849055\pi$
$758$	−1.40251	+	24.0801i	−0.0509413	+	0.874628i
$759$		0			0
$760$	−4.06055	−	0.474611i	−0.147292	−	0.0172159i
$761$	5.86783	+	6.21954i	0.212709	+	0.225458i	0.824939	−	0.565221i	$-0.191209\pi$
$761$	5.86783	+	6.21954i	0.212709	+	0.225458i	−0.612231	+	0.790679i	$0.709728\pi$
$762$		0			0
$763$	34.1420	−	3.99063i	1.23602	−	0.144471i
$764$	−13.6565	−	11.4592i	−0.494075	−	0.414579i
$765$		0			0
$766$	−4.44327	+	3.72835i	−0.160542	+	0.134711i
$767$	−6.09612	+	6.46151i	−0.220118	+	0.233312i
$768$		0			0
$769$	−11.2283	−	5.63904i	−0.404901	−	0.203349i	0.234680	−	0.972073i	$-0.424596\pi$
$769$	−11.2283	−	5.63904i	−0.404901	−	0.203349i	−0.639581	+	0.768724i	$0.720892\pi$
$770$	10.7188	+	5.38320i	0.386280	+	0.193997i
$771$		0			0
$772$	15.3362	−	16.2554i	0.551960	−	0.585044i
$773$	−39.4061	+	33.0656i	−1.41734	+	1.18929i	−0.464590	+	0.885526i	$0.653798\pi$
$773$	−39.4061	+	33.0656i	−1.41734	+	1.18929i	−0.952748	+	0.303761i	$0.901757\pi$
$774$		0			0
$775$	−19.9123	−	16.7084i	−0.715271	−	0.600183i
$776$	−17.1875	+	2.00893i	−0.616994	+	0.0721163i
$777$		0			0
$778$	14.1025	+	14.9478i	0.505599	+	0.535903i
$779$	41.2841	+	4.82541i	1.47915	+	0.172888i
$780$		0			0
$781$	0.0756466	−	1.29880i	0.00270685	−	0.0464748i
$782$	−5.59680	−	9.69393i	−0.200141	−	0.346654i
$783$		0			0
$784$	−0.440251	+	0.762537i	−0.0157232	+	0.0272334i
$785$	−6.87058	−	4.51885i	−0.245221	−	0.161285i
$786$		0			0
$787$	1.22244	+	2.83392i	0.0435751	+	0.101018i	0.938613	−	0.344971i	$-0.112111\pi$
$787$	1.22244	+	2.83392i	0.0435751	+	0.101018i	−0.895038	+	0.445989i	$0.852852\pi$
$788$	3.97306	−	0.941633i	0.141534	−	0.0335443i
$789$		0			0
$790$	−1.97891	−	2.65813i	−0.0704063	−	0.0945721i
$791$	17.9668	−	6.53937i	0.638825	−	0.232513i
$792$		0			0
$793$	8.74152	+	3.18165i	0.310420	+	0.112984i
$794$	4.20716	+	14.0529i	0.149307	+	0.498719i
$795$		0			0
$796$	0.0470760	+	0.808264i	0.00166857	+	0.0286482i
$797$	14.5827	−	9.59119i	0.516546	−	0.339738i	−0.264321	−	0.964435i	$-0.585148\pi$
$797$	14.5827	−	9.59119i	0.516546	−	0.339738i	0.780867	+	0.624697i	$0.214778\pi$
$798$		0			0
$799$	7.45662	+	1.76725i	0.263796	+	0.0625209i
$800$	−0.717572	−	4.06955i	−0.0253700	−	0.143880i
$801$		0			0
$802$	−4.63670	+	26.2960i	−0.163727	+	0.928544i
$803$	21.0354	−	48.7656i	0.742324	−	1.72090i
$804$		0			0
$805$	5.53311	−	18.4819i	0.195017	−	0.651401i
$806$	−6.62716	+	8.90181i	−0.233432	+	0.313553i
$807$		0			0
$808$	5.65559	−	2.84035i	0.198963	−	0.0999230i
$809$	−55.0128			−1.93415			−0.967074	−	0.254495i	$-0.918091\pi$
$809$	−55.0128			−1.93415			−0.967074	+	0.254495i	$0.918091\pi$
$810$		0			0
$811$	−0.195906			−0.00687919			−0.00343960	−	0.999994i	$-0.501095\pi$
$811$	−0.195906			−0.00687919			−0.00343960	+	0.999994i	$0.501095\pi$
$812$	−18.0755	+	9.07787i	−0.634326	+	0.318571i
$813$		0			0
$814$	1.84768	−	2.48187i	0.0647612	−	0.0869894i
$815$	−5.66967	+	18.9380i	−0.198600	+	0.663370i
$816$		0			0
$817$	9.56362	−	22.1710i	0.334589	−	0.775664i
$818$	−1.69066	+	9.58820i	−0.0591125	+	0.335244i
$819$		0			0
$820$	−1.53187	−	8.68766i	−0.0534952	−	0.303386i
$821$	−8.41661	−	1.99477i	−0.293742	−	0.0696181i	0.0811028	−	0.996706i	$-0.474156\pi$
$821$	−8.41661	−	1.99477i	−0.293742	−	0.0696181i	−0.374845	+	0.927088i	$0.622304\pi$
$822$		0			0
$823$	−29.5504	+	19.4356i	−1.03006	+	0.677482i	−0.947714	−	0.319122i	$-0.896612\pi$
$823$	−29.5504	+	19.4356i	−1.03006	+	0.677482i	−0.0823472	+	0.996604i	$0.526242\pi$
$824$	1.08299	+	18.5943i	0.0377278	+	0.647762i
$825$		0			0
$826$	4.05389	+	13.5409i	0.141053	+	0.471150i
$827$	−17.2621	−	6.28287i	−0.600261	−	0.218477i	0.0239758	−	0.999713i	$-0.492368\pi$
$827$	−17.2621	−	6.28287i	−0.600261	−	0.218477i	−0.624236	+	0.781236i	$0.714590\pi$
$828$		0			0
$829$	−25.5086	+	9.28437i	−0.885951	+	0.322460i	−0.744609	−	0.667501i	$-0.767364\pi$
$829$	−25.5086	+	9.28437i	−0.885951	+	0.322460i	−0.141342	+	0.989961i	$0.545142\pi$
$830$	−5.95169	−	7.99451i	−0.206586	−	0.277493i
$831$		0			0
$832$	−1.71671	+	0.406869i	−0.0595164	+	0.0141056i
$833$	0.529116	+	1.22663i	0.0183328	+	0.0425002i
$834$		0			0
$835$	−12.4644	−	8.19796i	−0.431348	−	0.283702i
$836$	−10.0660	+	17.4349i	−0.348141	+	0.602998i
$837$		0			0
$838$	−4.43326	−	7.67862i	−0.153144	−	0.265254i
$839$	0.691745	−	11.8768i	0.0238817	−	0.410033i	−0.965089	−	0.261922i	$-0.915644\pi$
$839$	0.691745	−	11.8768i	0.0238817	−	0.410033i	0.988971	−	0.148111i	$-0.0473193\pi$
$840$		0			0
$841$	−22.7620	−	2.66050i	−0.784898	−	0.0917414i
$842$	7.92129	+	8.39608i	0.272986	+	0.289348i
$843$		0			0
$844$	−11.2940	+	1.32008i	−0.388756	+	0.0454391i
$845$	7.05523	+	5.92004i	0.242707	+	0.203656i
$846$		0			0
$847$	21.5929	−	18.1186i	0.741942	−	0.622564i
$848$	1.83752	−	1.94766i	0.0631008	−	0.0668830i
$849$		0			0
$850$	−5.60263	−	2.81375i	−0.192169	−	0.0965108i
$851$	−4.44727	−	2.23350i	−0.152451	−	0.0765635i
$852$		0			0
$853$	20.9646	−	22.2211i	0.717813	−	0.760837i	−0.261056	−	0.965324i	$-0.584071\pi$
$853$	20.9646	−	22.2211i	0.717813	−	0.760837i	0.978869	+	0.204486i	$0.0655523\pi$
$854$	11.3388	−	9.51437i	0.388005	−	0.325575i
$855$		0			0
$856$	−0.812958	−	0.682153i	−0.0277863	−	0.0233155i
$857$	26.5253	−	3.10036i	0.906087	−	0.105906i	0.349731	−	0.936850i	$-0.386273\pi$
$857$	26.5253	−	3.10036i	0.906087	−	0.105906i	0.556356	+	0.830944i	$0.312199\pi$
$858$		0			0
$859$	12.8776	+	13.6495i	0.439379	+	0.465715i	0.908783	−	0.417269i	$-0.137013\pi$
$859$	12.8776	+	13.6495i	0.439379	+	0.465715i	−0.469404	+	0.882984i	$0.655531\pi$
$860$	−5.08998	−	0.594933i	−0.173567	−	0.0202870i
$861$		0			0
$862$	−1.57697	+	27.0755i	−0.0537118	+	0.922196i
$863$	−20.7662	−	35.9682i	−0.706891	−	1.22437i	−0.966005	−	0.258525i	$-0.916764\pi$
$863$	−20.7662	−	35.9682i	−0.706891	−	1.22437i	0.259113	−	0.965847i	$-0.416570\pi$
$864$		0			0
$865$	5.25893	−	9.10873i	0.178809	−	0.309706i
$866$	1.55940	+	1.02564i	0.0529907	+	0.0348525i
$867$		0			0
$868$	6.99410	+	16.2141i	0.237395	+	0.550344i
$869$	−15.8791	+	3.76341i	−0.538661	+	0.127665i
$870$		0			0
$871$	15.0810	+	20.2573i	0.510999	+	0.686391i
$872$	11.5065	−	4.18804i	0.389661	−	0.141825i
$873$		0			0
$874$	30.4279	+	11.0748i	1.02924	+	0.374612i
$875$	−6.84888	−	22.8769i	−0.231535	−	0.773379i
$876$		0			0
$877$	−2.80398	−	48.1425i	−0.0946838	−	1.62566i	−0.626935	−	0.779072i	$-0.715691\pi$
$877$	−2.80398	−	48.1425i	−0.0946838	−	1.62566i	0.532251	−	0.846587i	$-0.321346\pi$
$878$	4.57484	−	3.00892i	0.154393	−	0.101546i
$879$		0			0
$880$	4.15761	+	0.985373i	0.140153	+	0.0332169i
$881$	6.90826	+	39.1787i	0.232745	+	1.31996i	0.847310	+	0.531098i	$0.178220\pi$
$881$	6.90826	+	39.1787i	0.232745	+	1.31996i	−0.614565	+	0.788866i	$0.710669\pi$
$882$		0			0
$883$	0.0528584	−	0.299775i	0.00177883	−	0.0100882i	−0.983905	−	0.178690i	$-0.942814\pi$
$883$	0.0528584	−	0.299775i	0.00177883	−	0.0100882i	0.985684	+	0.168602i	$0.0539252\pi$
$884$	−1.06020	+	2.45781i	−0.0356582	+	0.0826651i
$885$		0			0
$886$	−3.27873	+	10.9517i	−0.110151	+	0.367930i
$887$	12.3866	−	16.6381i	0.415901	−	0.558652i	−0.543966	−	0.839107i	$-0.683078\pi$
$887$	12.3866	−	16.6381i	0.415901	−	0.558652i	0.959867	+	0.280455i	$0.0904854\pi$
$888$		0			0
$889$	−21.3722	+	10.7335i	−0.716800	+	0.359991i
$890$	9.37239			0.314163
$891$		0			0
$892$	17.7654			0.594829
$893$	−19.8100	+	9.94896i	−0.662917	+	0.332929i
$894$		0			0
$895$	−11.0948	+	14.9030i	−0.370860	+	0.498151i
$896$	−0.805121	+	2.68929i	−0.0268972	+	0.0898429i
$897$		0			0
$898$	0.231329	−	0.536281i	0.00771956	−	0.0178959i
$899$	−7.87041	+	44.6353i	−0.262493	+	1.48867i
$900$		0			0
$901$	−0.705447	−	4.00079i	−0.0235018	−	0.133286i
$902$	−42.2709	−	10.0184i	−1.40747	−	0.333576i
$903$		0			0
$904$	5.69046	−	3.74268i	0.189262	−	0.124480i
$905$	−1.15268	−	19.7907i	−0.0383164	−	0.657866i
$906$		0			0
$907$	−6.46164	−	21.5834i	−0.214555	−	0.716664i	−0.995727	−	0.0923479i	$-0.970563\pi$
$907$	−6.46164	−	21.5834i	−0.214555	−	0.716664i	0.781172	−	0.624316i	$-0.214622\pi$
$908$	−2.35465	−	0.857022i	−0.0781418	−	0.0284413i
$909$		0			0
$910$	−4.33516	+	1.57787i	−0.143709	+	0.0523059i
$911$	10.4625	+	14.0536i	0.346640	+	0.465618i	0.940915	−	0.338644i	$-0.109968\pi$
$911$	10.4625	+	14.0536i	0.346640	+	0.465618i	−0.594275	+	0.804262i	$0.702561\pi$
$912$		0			0
$913$	−47.7574	+	11.3187i	−1.58054	+	0.374594i
$914$	5.17077	+	11.9872i	0.171034	+	0.396501i
$915$		0			0
$916$	−3.77373	−	2.48202i	−0.124688	−	0.0820083i
$917$	22.4126	−	38.8197i	0.740129	−	1.28194i
$918$		0			0
$919$	6.84333	+	11.8530i	0.225741	+	0.390994i	0.956541	−	0.291597i	$-0.0941865\pi$
$919$	6.84333	+	11.8530i	0.225741	+	0.390994i	−0.730801	+	0.682591i	$0.760853\pi$
$920$	0.399595	−	6.86077i	0.0131742	−	0.226193i
$921$		0			0
$922$	−11.5943	−	1.35518i	−0.381838	−	0.0446305i
$923$	0.343389	+	0.363971i	0.0113028	+	0.0119803i
$924$		0			0
$925$	−2.76855	+	0.323597i	−0.0910293	+	0.0106398i
$926$	7.53467	+	6.32234i	0.247605	+	0.207765i
$927$		0			0
$928$	−5.51961	+	4.63151i	−0.181190	+	0.152037i
$929$	−24.0142	+	25.4536i	−0.787880	+	0.835104i	−0.989526	−	0.144354i	$-0.953890\pi$
$929$	−24.0142	+	25.4536i	−0.787880	+	0.835104i	0.201646	+	0.979459i	$0.435371\pi$
$930$		0			0
$931$	−3.45337	−	1.73435i	−0.113180	−	0.0568410i
$932$	−10.9356	−	5.49206i	−0.358207	−	0.179898i
$933$		0			0
$934$	−12.2377	+	12.9712i	−0.400430	+	0.424431i
$935$	4.96596	−	4.16694i	0.162404	−	0.136273i
$936$		0			0
$937$	16.4755	+	13.8246i	0.538230	+	0.451629i	0.870932	−	0.491403i	$-0.163516\pi$
$937$	16.4755	+	13.8246i	0.538230	+	0.451629i	−0.332702	+	0.943032i	$0.607960\pi$
$938$	39.9121	−	4.66506i	1.30318	−	0.152320i
$939$		0			0
$940$	3.22868	+	3.42220i	0.105308	+	0.111620i
$941$	−3.44570	−	0.402744i	−0.112326	−	0.0131291i	0.0597439	−	0.998214i	$-0.480972\pi$
$941$	−3.44570	−	0.402744i	−0.112326	−	0.0131291i	−0.172070	+	0.985085i	$0.555046\pi$
$942$		0			0
$943$	−4.06272	+	69.7542i	−0.132300	+	2.27151i
$944$	2.51757	+	4.36056i	0.0819399	+	0.141924i
$945$		0			0
$946$	−12.6180	+	21.8550i	−0.410245	+	0.710566i
$947$	43.1639	+	28.3894i	1.40264	+	0.922530i	0.999974	+	0.00718267i	$0.00228633\pi$
$947$	43.1639	+	28.3894i	1.40264	+	0.922530i	0.402665	+	0.915348i	$0.368084\pi$
$948$		0			0
$949$	8.09063	+	18.7562i	0.262633	+	0.608852i
$950$	17.6475	−	4.18253i	0.572560	−	0.135699i
$951$		0			0
$952$	2.54334	+	3.41630i	0.0824302	+	0.110723i
$953$	1.06059	−	0.386024i	0.0343559	−	0.0125045i	−0.324785	−	0.945788i	$-0.605292\pi$
$953$	1.06059	−	0.386024i	0.0343559	−	0.0125045i	0.359141	+	0.933283i	$0.383070\pi$
$954$		0			0
$955$	−15.6045	−	5.67956i	−0.504949	−	0.183786i
$956$	7.60165	+	25.3913i	0.245855	+	0.821212i
$957$		0			0
$958$	2.09425	+	35.9569i	0.0676622	+	1.16171i
$959$	−25.2446	+	16.6036i	−0.815191	+	0.536159i
$960$		0			0
$961$	8.33709	+	1.97593i	0.268938	+	0.0637395i
$962$	0.206652	+	1.17198i	0.00666272	+	0.0377861i
$963$		0			0
$964$	−0.948020	+	5.37649i	−0.0305337	+	0.173165i
$965$	8.24516	−	19.1144i	0.265421	−	0.615316i
$966$		0			0
$967$	3.58456	−	11.9733i	0.115272	−	0.385035i	−0.880810	−	0.473470i	$-0.843001\pi$
$967$	3.58456	−	11.9733i	0.115272	−	0.385035i	0.996082	+	0.0884350i	$0.0281866\pi$
$968$	5.99612	−	8.05419i	0.192723	−	0.258872i
$969$		0			0
$970$	−14.4044	+	7.23416i	−0.462497	+	0.232275i
$971$	−13.7306			−0.440635			−0.220318	−	0.975428i	$-0.570709\pi$
$971$	−13.7306			−0.440635			−0.220318	+	0.975428i	$0.570709\pi$
$972$		0			0
$973$	18.0939			0.580062
$974$	25.2719	−	12.6920i	0.809765	−	0.406679i
$975$		0			0
$976$	3.14866	−	4.22938i	0.100786	−	0.135379i
$977$	−1.36028	+	4.54365i	−0.0435192	+	0.145364i	−0.976988	−	0.213295i	$-0.931581\pi$
$977$	−1.36028	+	4.54365i	−0.0435192	+	0.145364i	0.933469	+	0.358659i	$0.116766\pi$
$978$		0			0
$979$	18.2806	−	42.3792i	0.584250	−	1.35444i
$980$	−0.142422	+	0.807716i	−0.00454951	+	0.0258015i
$981$		0			0
$982$	−0.763784	−	4.33163i	−0.0243733	−	0.138228i
$983$	−25.3644	−	6.01148i	−0.808999	−	0.191736i	−0.194754	−	0.980852i	$-0.562391\pi$
$983$	−25.3644	−	6.01148i	−0.808999	−	0.191736i	−0.614245	+	0.789116i	$0.710539\pi$
$984$		0			0
$985$	3.17768	−	2.08999i	0.101249	−	0.0665926i
$986$	0.635629	+	10.9133i	0.0202426	+	0.347551i
$987$		0			0
$988$	−2.22077	−	7.41789i	−0.0706521	−	0.235995i
$989$	38.1419	+	13.8825i	1.21284	+	0.441438i
$990$		0			0
$991$	−18.1061	+	6.59007i	−0.575158	+	0.209340i	−0.613189	−	0.789936i	$-0.710114\pi$
$991$	−18.1061	+	6.59007i	−0.575158	+	0.209340i	0.0380312	+	0.999277i	$0.487891\pi$
$992$	3.75631	+	5.04561i	0.119263	+	0.160198i
$993$		0			0
$994$	0.774737	−	0.183616i	0.0245732	−	0.00582395i
$995$	0.298709	+	0.692486i	0.00946972	+	0.0219533i
$996$		0			0
$997$	−20.9254	−	13.7628i	−0.662713	−	0.435873i	0.173088	−	0.984906i	$-0.444626\pi$
$997$	−20.9254	−	13.7628i	−0.662713	−	0.435873i	−0.835800	+	0.549033i	$0.814996\pi$
$998$	−7.92200	+	13.7213i	−0.250766	+	0.434340i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.g.a.73.3		72
3.2	odd	2		162.2.g.a.25.1	yes	72
81.13	even	27	inner	486.2.g.a.253.3		72
81.68	odd	54		162.2.g.a.13.1	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.13.1	✓	72	81.68	odd	54
162.2.g.a.25.1	yes	72	3.2	odd	2
486.2.g.a.73.3		72	1.1	even	1	trivial
486.2.g.a.253.3		72	81.13	even	27	inner

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:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.893633 - 0.448799i) q^{2} +(0.597159 - 0.802123i) q^{4} +(0.267154 - 0.892356i) q^{5} +(1.11188 - 2.57764i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-0.161751 - 0.917337i) q^{10} +(-4.46341 - 1.05785i) q^{11} +(1.47403 - 0.969483i) q^{13} +(-0.163226 - 2.80247i) q^{14} +(-0.286803 - 0.957990i) q^{16} +(-1.42569 - 0.518907i) q^{17} +(4.12421 - 1.50109i) q^{19} +(-0.556246 - 0.747168i) q^{20} +(-4.46341 + 1.05785i) q^{22} +(2.92223 + 6.77448i) q^{23} +(3.45251 + 2.27075i) q^{25} +(0.882135 - 1.52790i) q^{26} +(-1.40361 - 2.43113i) q^{28} +(0.418954 - 7.19315i) q^{29} +(-6.24778 - 0.730261i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-1.50693 + 0.176134i) q^{34} +(-2.00313 - 1.68082i) q^{35} +(-0.516723 + 0.433582i) q^{37} +(3.01184 - 3.19236i) q^{38} +(-0.832408 - 0.418051i) q^{40} +(8.46317 + 4.25037i) q^{41} +(3.77539 - 4.00168i) q^{43} +(-3.51389 + 2.94850i) q^{44} +(5.65178 + 4.74241i) q^{46} +(-5.01677 + 0.586377i) q^{47} +(-0.604237 - 0.640453i) q^{49} +(4.10439 + 0.479734i) q^{50} +(0.102583 - 1.76129i) q^{52} +(1.33883 + 2.31892i) q^{53} +(-2.13639 + 3.70034i) q^{55} +(-2.34540 - 1.54259i) q^{56} +(-2.85389 - 6.61606i) q^{58} +(-4.89941 + 1.16118i) q^{59} +(3.14866 + 4.22938i) q^{61} +(-5.91096 + 2.15141i) q^{62} +(-0.939693 - 0.342020i) q^{64} +(-0.471331 - 1.57436i) q^{65} +(0.832311 + 14.2902i) q^{67} +(-1.26759 + 0.833706i) q^{68} +(-2.54441 - 0.603036i) q^{70} +(0.0492509 + 0.279316i) q^{71} +(-2.01050 + 11.4021i) q^{73} +(-0.267169 + 0.619368i) q^{74} +(1.25875 - 4.20451i) q^{76} +(-7.68955 + 10.3289i) q^{77} +(3.17920 - 1.59665i) q^{79} -0.931488 q^{80} +9.47053 q^{82} +(9.56164 - 4.80204i) q^{83} +(-0.843927 + 1.13359i) q^{85} +(1.57786 - 5.27043i) q^{86} +(-1.81684 + 4.21191i) q^{88} +(-1.74720 + 9.90888i) q^{89} +(-0.860028 - 4.87746i) q^{91} +(7.17900 + 1.70145i) q^{92} +(-4.21999 + 2.77553i) q^{94} +(-0.237708 - 4.08128i) q^{95} +(-4.96298 - 16.5775i) q^{97} +(-0.827401 - 0.301149i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{13} + 9 q^{20} + 81 q^{23} + 18 q^{25} + 27 q^{26} + 18 q^{28} + 27 q^{29} - 54 q^{31} + 27 q^{35} - 9 q^{38} + 9 q^{41} + 36 q^{43} - 18 q^{46} + 27 q^{47} - 36 q^{52} + 27 q^{53} + 54 q^{55}+ \cdots - 36 q^{98}+O(q^{100}) \) 72 * q + 18 * q^13 + 9 * q^20 + 81 * q^23 + 18 * q^25 + 27 * q^26 + 18 * q^28 + 27 * q^29 - 54 * q^31 + 27 * q^35 - 9 * q^38 + 9 * q^41 + 36 * q^43 - 18 * q^46 + 27 * q^47 - 36 * q^52 + 27 * q^53 + 54 * q^55 + 9 * q^58 + 18 * q^59 - 9 * q^65 - 135 * q^67 + 18 * q^68 + 18 * q^70 - 72 * q^71 + 36 * q^73 - 99 * q^74 - 9 * q^76 - 144 * q^77 - 9 * q^79 - 18 * q^80 - 72 * q^82 - 99 * q^83 + 9 * q^85 - 72 * q^86 - 9 * q^88 - 126 * q^89 + 63 * q^91 - 36 * q^92 + 18 * q^94 - 45 * q^95 - 171 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more