LMFDB - Embedded newform 486.2.g.b.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [486,2,Mod(19,486)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("486.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [90] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 162)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	486.73
Dual form			486.2.g.b.253.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.893633 + 0.448799i) q^{2} +(0.597159 - 0.802123i) q^{4} +(-0.891212 + 2.97686i) q^{5} +(0.275210 - 0.638009i) q^{7} +(-0.173648 + 0.984808i) q^{8} +(-0.539594 - 3.06019i) q^{10} +(-5.37847 - 1.27472i) q^{11} +(-2.73022 + 1.79570i) q^{13} +(0.0404011 + 0.693660i) q^{14} +(-0.286803 - 0.957990i) q^{16} +(4.35745 + 1.58598i) q^{17} +(-2.23534 + 0.813599i) q^{19} +(1.85561 + 2.49252i) q^{20} +(5.37847 - 1.27472i) q^{22} +(-2.79341 - 6.47585i) q^{23} +(-3.88998 - 2.55848i) q^{25} +(1.63391 - 2.83001i) q^{26} +(-0.347418 - 0.601745i) q^{28} +(-0.0802101 + 1.37715i) q^{29} +(-3.53161 - 0.412786i) q^{31} +(0.686242 + 0.727374i) q^{32} +(-4.60574 + 0.538334i) q^{34} +(1.65399 + 1.38786i) q^{35} +(-0.935772 + 0.785206i) q^{37} +(1.63243 - 1.73028i) q^{38} +(-2.77687 - 1.39460i) q^{40} +(-10.1420 - 5.09352i) q^{41} +(-6.37841 + 6.76072i) q^{43} +(-4.23428 + 3.55299i) q^{44} +(5.40264 + 4.53335i) q^{46} +(-10.4074 + 1.21645i) q^{47} +(4.47238 + 4.74044i) q^{49} +(4.62445 + 0.540521i) q^{50} +(-0.190007 + 3.26229i) q^{52} +(2.11764 + 3.66786i) q^{53} +(8.58802 - 14.8749i) q^{55} +(0.580527 + 0.381818i) q^{56} +(-0.546388 - 1.26667i) q^{58} +(5.60397 - 1.32817i) q^{59} +(1.03387 + 1.38873i) q^{61} +(3.34122 - 1.21611i) q^{62} +(-0.939693 - 0.342020i) q^{64} +(-2.91232 - 9.72783i) q^{65} +(-0.0594932 - 1.02146i) q^{67} +(3.87424 - 2.54813i) q^{68} +(-2.10093 - 0.497930i) q^{70} +(2.04677 + 11.6078i) q^{71} +(1.49312 - 8.46788i) q^{73} +(0.483836 - 1.12166i) q^{74} +(-0.682248 + 2.27887i) q^{76} +(-2.29349 + 3.08070i) q^{77} +(-7.86088 + 3.94788i) q^{79} +3.10740 q^{80} +11.3492 q^{82} +(8.11371 - 4.07486i) q^{83} +(-8.60465 + 11.5580i) q^{85} +(2.66575 - 8.90423i) q^{86} +(2.18932 - 5.07541i) q^{88} +(0.642803 - 3.64552i) q^{89} +(0.394285 + 2.23610i) q^{91} +(-6.86253 - 1.62645i) q^{92} +(8.75447 - 5.75790i) q^{94} +(-0.429800 - 7.37939i) q^{95} +(0.260981 + 0.871736i) q^{97} +(-6.12417 - 2.22901i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 18 q^{13} + 9 q^{20} - 27 q^{23} - 18 q^{25} + 27 q^{26} - 18 q^{28} + 27 q^{29} + 54 q^{31} + 27 q^{35} + 18 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}) $ 90 * q - 18 * q^13 + 9 * q^20 - 27 * q^23 - 18 * q^25 + 27 * q^26 - 18 * q^28 + 27 * q^29 + 54 * q^31 + 27 * q^35 + 18 * 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 + 45 * q^59 - 9 * q^65 + 81 * q^67 - 36 * q^68 - 72 * q^70 - 72 * q^71 - 36 * q^73 - 45 * q^74 - 18 * q^76 - 144 * q^77 - 99 * q^79 - 18 * q^80 + 72 * q^82 - 45 * q^83 - 117 * q^85 - 72 * q^86 - 18 * q^88 - 45 * q^89 - 63 * q^91 - 36 * q^92 - 72 * q^94 - 45 * q^95 + 117 * 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
$5$	−0.891212	+	2.97686i	−0.398562	+	1.33129i	0.489675	+	0.871905i	$0.337116\pi$
$5$	−0.891212	+	2.97686i	−0.398562	+	1.33129i	−0.888237	+	0.459385i	$0.848070\pi$
$6$		0			0
$7$	0.275210	−	0.638009i	0.104020	−	0.241145i	−0.858256	−	0.513223i	$-0.828452\pi$
$7$	0.275210	−	0.638009i	0.104020	−	0.241145i	0.962275	+	0.272078i	$0.0877108\pi$
$8$	−0.173648	+	0.984808i	−0.0613939	+	0.348182i
$9$		0			0
$10$	−0.539594	−	3.06019i	−0.170635	−	0.967717i
$11$	−5.37847	−	1.27472i	−1.62167	−	0.384343i	−0.683345	−	0.730096i	$-0.739475\pi$
$11$	−5.37847	−	1.27472i	−1.62167	−	0.384343i	−0.938325	+	0.345753i	$0.887623\pi$
$12$		0			0
$13$	−2.73022	+	1.79570i	−0.757227	+	0.498036i	−0.868461	−	0.495758i	$-0.834890\pi$
$13$	−2.73022	+	1.79570i	−0.757227	+	0.498036i	0.111233	+	0.993794i	$0.464520\pi$
$14$	0.0404011	+	0.693660i	0.0107976	+	0.185388i
$15$		0			0
$16$	−0.286803	−	0.957990i	−0.0717008	−	0.239497i
$17$	4.35745	+	1.58598i	1.05684	+	0.384657i	0.811239	−	0.584715i	$-0.198794\pi$
$17$	4.35745	+	1.58598i	1.05684	+	0.384657i	0.245597	+	0.969372i	$0.421016\pi$
$18$		0			0
$19$	−2.23534	+	0.813599i	−0.512823	+	0.186652i	−0.585453	−	0.810707i	$-0.699083\pi$
$19$	−2.23534	+	0.813599i	−0.512823	+	0.186652i	0.0726295	+	0.997359i	$0.476861\pi$
$20$	1.85561	+	2.49252i	0.414927	+	0.557344i
$21$		0			0
$22$	5.37847	−	1.27472i	1.14669	−	0.271771i
$23$	−2.79341	−	6.47585i	−0.582466	−	1.35031i	−0.913558	−	0.406709i	$-0.866676\pi$
$23$	−2.79341	−	6.47585i	−0.582466	−	1.35031i	0.331092	−	0.943598i	$-0.392583\pi$
$24$		0			0
$25$	−3.88998	−	2.55848i	−0.777995	−	0.511695i
$26$	1.63391	−	2.83001i	0.320436	−	0.555011i
$27$		0			0
$28$	−0.347418	−	0.601745i	−0.0656558	−	0.113719i
$29$	−0.0802101	+	1.37715i	−0.0148946	+	0.255731i	0.982638	+	0.185532i	$0.0594007\pi$
$29$	−0.0802101	+	1.37715i	−0.0148946	+	0.255731i	−0.997533	+	0.0701997i	$0.977636\pi$
$30$		0			0
$31$	−3.53161	−	0.412786i	−0.634296	−	0.0741386i	−0.207133	−	0.978313i	$-0.566413\pi$
$31$	−3.53161	−	0.412786i	−0.634296	−	0.0741386i	−0.427164	+	0.904174i	$0.640487\pi$
$32$	0.686242	+	0.727374i	0.121312	+	0.128583i
$33$		0			0
$34$	−4.60574	+	0.538334i	−0.789879	+	0.0923236i
$35$	1.65399	+	1.38786i	0.279576	+	0.234592i
$36$		0			0
$37$	−0.935772	+	0.785206i	−0.153840	+	0.129087i	−0.716459	−	0.697629i	$-0.754238\pi$
$37$	−0.935772	+	0.785206i	−0.153840	+	0.129087i	0.562619	+	0.826716i	$0.309794\pi$
$38$	1.63243	−	1.73028i	0.264816	−	0.280688i
$39$		0			0
$40$	−2.77687	−	1.39460i	−0.439062	−	0.220505i
$41$	−10.1420	−	5.09352i	−1.58392	−	0.795474i	−0.584052	−	0.811716i	$-0.698534\pi$
$41$	−10.1420	−	5.09352i	−1.58392	−	0.795474i	−0.999868	+	0.0162419i	$0.994830\pi$
$42$		0			0
$43$	−6.37841	+	6.76072i	−0.972699	+	1.03100i	0.0268093	+	0.999641i	$0.491465\pi$
$43$	−6.37841	+	6.76072i	−0.972699	+	1.03100i	−0.999508	+	0.0313600i	$0.990016\pi$
$44$	−4.23428	+	3.55299i	−0.638342	+	0.535633i
$45$		0			0
$46$	5.40264	+	4.53335i	0.796575	+	0.668406i
$47$	−10.4074	+	1.21645i	−1.51808	+	0.177438i	−0.833916	−	0.551892i	$-0.813906\pi$
$47$	−10.4074	+	1.21645i	−1.51808	+	0.177438i	−0.684162	+	0.729330i	$0.739832\pi$
$48$		0			0
$49$	4.47238	+	4.74044i	0.638911	+	0.677206i
$50$	4.62445	+	0.540521i	0.653996	+	0.0764412i
$51$		0			0
$52$	−0.190007	+	3.26229i	−0.0263492	+	0.452398i
$53$	2.11764	+	3.66786i	0.290880	+	0.503819i	0.974018	−	0.226470i	$-0.0727185\pi$
$53$	2.11764	+	3.66786i	0.290880	+	0.503819i	−0.683138	+	0.730289i	$0.739385\pi$
$54$		0			0
$55$	8.58802	−	14.8749i	1.15801	−	2.00573i
$56$	0.580527	+	0.381818i	0.0775762	+	0.0510226i
$57$		0			0
$58$	−0.546388	−	1.26667i	−0.0717442	−	0.166322i
$59$	5.60397	−	1.32817i	0.729575	−	0.172913i	0.150991	−	0.988535i	$-0.451754\pi$
$59$	5.60397	−	1.32817i	0.729575	−	0.172913i	0.578584	+	0.815623i	$0.303605\pi$
$60$		0			0
$61$	1.03387	+	1.38873i	0.132374	+	0.177809i	0.863368	−	0.504575i	$-0.168351\pi$
$61$	1.03387	+	1.38873i	0.132374	+	0.177809i	−0.730994	+	0.682384i	$0.760943\pi$
$62$	3.34122	−	1.21611i	0.424336	−	0.154446i
$63$		0			0
$64$	−0.939693	−	0.342020i	−0.117462	−	0.0427525i
$65$	−2.91232	−	9.72783i	−0.361229	−	1.20659i
$66$		0			0
$67$	−0.0594932	−	1.02146i	−0.00726825	−	0.124791i	−0.999990	−	0.00436439i	$-0.998611\pi$
$67$	−0.0594932	−	1.02146i	−0.00726825	−	0.124791i	0.992722	−	0.120427i	$-0.0384263\pi$
$68$	3.87424	−	2.54813i	0.469821	−	0.309006i
$69$		0			0
$70$	−2.10093	−	0.497930i	−0.251109	−	0.0595140i
$71$	2.04677	+	11.6078i	0.242907	+	1.37759i	0.825304	+	0.564688i	$0.191004\pi$
$71$	2.04677	+	11.6078i	0.242907	+	1.37759i	−0.582397	+	0.812904i	$0.697885\pi$
$72$		0			0
$73$	1.49312	−	8.46788i	0.174756	−	0.991090i	−0.763669	−	0.645608i	$-0.776604\pi$
$73$	1.49312	−	8.46788i	0.174756	−	0.991090i	0.938425	−	0.345482i	$-0.112285\pi$
$74$	0.483836	−	1.12166i	0.0562448	−	0.130390i
$75$		0			0
$76$	−0.682248	+	2.27887i	−0.0782593	+	0.261404i
$77$	−2.29349	+	3.08070i	−0.261368	+	0.351078i
$78$		0			0
$79$	−7.86088	+	3.94788i	−0.884418	+	0.444171i	−0.832207	−	0.554465i	$-0.812923\pi$
$79$	−7.86088	+	3.94788i	−0.884418	+	0.444171i	−0.0522107	+	0.998636i	$0.516627\pi$
$80$	3.10740			0.347418
$81$		0			0
$82$	11.3492			1.25331
$83$	8.11371	−	4.07486i	0.890596	−	0.447274i	0.0561870	−	0.998420i	$-0.482106\pi$
$83$	8.11371	−	4.07486i	0.890596	−	0.447274i	0.834409	+	0.551146i	$0.185809\pi$
$84$		0			0
$85$	−8.60465	+	11.5580i	−0.933305	+	1.25365i
$86$	2.66575	−	8.90423i	0.287455	−	0.960168i
$87$		0			0
$88$	2.18932	−	5.07541i	0.233382	−	0.541040i
$89$	0.642803	−	3.64552i	0.0681370	−	0.386424i	−0.931600	−	0.363485i	$-0.881587\pi$
$89$	0.642803	−	3.64552i	0.0681370	−	0.386424i	0.999737	−	0.0229387i	$-0.00730225\pi$
$90$		0			0
$91$	0.394285	+	2.23610i	0.0413323	+	0.234407i
$92$	−6.86253	−	1.62645i	−0.715469	−	0.169569i
$93$		0			0
$94$	8.75447	−	5.75790i	0.902954	−	0.593882i
$95$	−0.429800	−	7.37939i	−0.0440966	−	0.757109i
$96$		0			0
$97$	0.260981	+	0.871736i	0.0264986	+	0.0885113i	0.970216	−	0.242241i	$-0.0778826\pi$
$97$	0.260981	+	0.871736i	0.0264986	+	0.0885113i	−0.943717	+	0.330753i	$0.892697\pi$
$98$	−6.12417	−	2.22901i	−0.618634	−	0.225165i
$99$		0			0
$100$	−4.37515	+	1.59242i	−0.437515	+	0.159242i
$101$	11.7954	+	15.8440i	1.17368	+	1.57653i	0.735294	+	0.677748i	$0.237044\pi$
$101$	11.7954	+	15.8440i	1.17368	+	1.57653i	0.438391	+	0.898785i	$0.355549\pi$
$102$		0			0
$103$	5.78007	−	1.36990i	0.569527	−	0.134980i	0.0642442	−	0.997934i	$-0.479536\pi$
$103$	5.78007	−	1.36990i	0.569527	−	0.134980i	0.505283	+	0.862954i	$0.331388\pi$
$104$	−1.29432	−	3.00056i	−0.126918	−	0.294229i
$105$		0			0
$106$	−3.53852	−	2.32732i	−0.343692	−	0.226050i
$107$	1.62313	−	2.81135i	0.156914	−	0.271783i	−0.776840	−	0.629698i	$-0.783179\pi$
$107$	1.62313	−	2.81135i	0.156914	−	0.271783i	0.933754	+	0.357914i	$0.116512\pi$
$108$		0			0
$109$	4.22282	+	7.31415i	0.404473	+	0.700568i	0.994260	−	0.106991i	$-0.0341215\pi$
$109$	4.22282	+	7.31415i	0.404473	+	0.700568i	−0.589787	+	0.807559i	$0.700788\pi$
$110$	−0.998698	+	17.1470i	−0.0952221	+	1.63490i
$111$		0			0
$112$	−0.690137	−	0.0806655i	−0.0652119	−	0.00762217i
$113$	7.98089	+	8.45925i	0.750779	+	0.795779i	0.984287	−	0.176576i	$-0.0565020\pi$
$113$	7.98089	+	8.45925i	0.750779	+	0.795779i	−0.233508	+	0.972355i	$0.575020\pi$
$114$		0			0
$115$	21.7672	−	2.54422i	2.02980	−	0.237250i
$116$	1.05675	+	0.886718i	0.0981168	+	0.0823297i
$117$		0			0
$118$	−4.41181	+	3.70195i	−0.406140	+	0.340792i
$119$	2.21109	−	2.34361i	0.202690	−	0.214839i
$120$		0			0
$121$	17.4731	+	8.77531i	1.58846	+	0.797755i
$122$	−1.54717	−	0.777016i	−0.140074	−	0.0703478i
$123$		0			0
$124$	−2.44004	+	2.58629i	−0.219122	+	0.232256i
$125$	−0.819020	+	0.687239i	−0.0732553	+	0.0614685i
$126$		0			0
$127$	−7.51805	−	6.30840i	−0.667119	−	0.559780i	0.245092	−	0.969500i	$-0.421182\pi$
$127$	−7.51805	−	6.30840i	−0.667119	−	0.559780i	−0.912211	+	0.409720i	$0.865626\pi$
$128$	0.993238	−	0.116093i	0.0877907	−	0.0102613i
$129$		0			0
$130$	6.96838	+	7.38606i	0.611168	+	0.647800i
$131$	18.3590	+	2.14586i	1.60403	+	0.187484i	0.870499	−	0.492169i	$-0.163796\pi$
$131$	18.3590	+	2.14586i	1.60403	+	0.187484i	0.733533	+	0.679654i	$0.237870\pi$
$132$		0			0
$133$	−0.0961063	+	1.65008i	−0.00833347	+	0.143080i
$134$	0.511595	+	0.886109i	0.0441951	+	0.0765481i
$135$		0			0
$136$	−2.31855	+	4.01585i	−0.198814	+	0.344356i
$137$	−12.2593	−	8.06304i	−1.04738	−	0.688872i	−0.0955257	−	0.995427i	$-0.530453\pi$
$137$	−12.2593	−	8.06304i	−1.04738	−	0.688872i	−0.951853	+	0.306555i	$0.900824\pi$
$138$		0			0
$139$	5.07402	+	11.7629i	0.430373	+	0.997716i	0.986070	+	0.166331i	$0.0531921\pi$
$139$	5.07402	+	11.7629i	0.430373	+	0.997716i	−0.555697	+	0.831385i	$0.687549\pi$
$140$	2.10093	−	0.497930i	0.177561	−	0.0420828i
$141$		0			0
$142$	−7.03863	−	9.45452i	−0.590669	−	0.793406i
$143$	16.9734	−	6.17782i	1.41939	−	0.516616i
$144$		0			0
$145$	−4.02811	−	1.46611i	−0.334516	−	0.121754i
$146$	2.46608	+	8.23728i	0.204094	+	0.681722i
$147$		0			0
$148$	0.0710276	+	1.21950i	0.00583843	+	0.100242i
$149$	−14.8005	+	9.73443i	−1.21250	+	0.797476i	−0.984363	−	0.176153i	$-0.943635\pi$
$149$	−14.8005	+	9.73443i	−1.21250	+	0.797476i	−0.228140	+	0.973628i	$0.573264\pi$
$150$		0			0
$151$	15.3504	+	3.63812i	1.24920	+	0.296066i	0.801434	−	0.598084i	$-0.204071\pi$
$151$	15.3504	+	3.63812i	1.24920	+	0.296066i	0.447768	+	0.894150i	$0.352219\pi$
$152$	−0.413075	−	2.34266i	−0.0335048	−	0.190015i
$153$		0			0
$154$	0.666927	−	3.78233i	0.0537425	−	0.304789i
$155$	4.37622	−	10.1452i	0.351507	−	0.814884i
$156$		0			0
$157$	0.902664	−	3.01511i	0.0720404	−	0.240632i	−0.914384	−	0.404848i	$-0.867324\pi$
$157$	0.902664	−	3.01511i	0.0720404	−	0.240632i	0.986424	+	0.164216i	$0.0525096\pi$
$158$	5.25293	−	7.05591i	0.417901	−	0.561338i
$159$		0			0
$160$	−2.77687	+	1.39460i	−0.219531	+	0.110253i
$161$	−4.90043			−0.386208
$162$		0			0
$163$	−10.6732			−0.835986			−0.417993	−	0.908450i	$-0.637266\pi$
$163$	−10.6732			−0.835986			−0.417993	+	0.908450i	$0.637266\pi$
$164$	−10.1420	+	5.09352i	−0.791960	+	0.397737i
$165$		0			0
$166$	−5.42188	+	7.28285i	−0.420820	+	0.565259i
$167$	0.546468	−	1.82533i	0.0422870	−	0.141248i	−0.934239	−	0.356647i	$-0.883920\pi$
$167$	0.546468	−	1.82533i	0.0422870	−	0.141248i	0.976526	+	0.215399i	$0.0691051\pi$
$168$		0			0
$169$	−0.919445	+	2.13151i	−0.0707265	+	0.163963i
$170$	2.50215	−	14.1904i	0.191906	−	1.08835i
$171$		0			0
$172$	1.61401	+	9.15350i	0.123067	+	0.697948i
$173$	−1.41829	−	0.336142i	−0.107831	−	0.0255564i	0.176346	−	0.984328i	$-0.443572\pi$
$173$	−1.41829	−	0.336142i	−0.107831	−	0.0255564i	−0.284177	+	0.958772i	$0.591720\pi$
$174$		0			0
$175$	−2.70289	+	1.77772i	−0.204320	+	0.134383i
$176$	0.321393	+	5.51811i	0.0242259	+	0.415943i
$177$		0			0
$178$	1.06168	+	3.54624i	0.0795759	+	0.265802i
$179$	−3.40456	−	1.23916i	−0.254469	−	0.0926191i	0.211636	−	0.977349i	$-0.432121\pi$
$179$	−3.40456	−	1.23916i	−0.254469	−	0.0926191i	−0.466105	+	0.884729i	$0.654343\pi$
$180$		0			0
$181$	−20.8444	+	7.58675i	−1.54935	+	0.563919i	−0.968266	−	0.249922i	$-0.919595\pi$
$181$	−20.8444	+	7.58675i	−1.54935	+	0.563919i	−0.581088	+	0.813841i	$0.697373\pi$
$182$	−1.35591	−	1.82130i	−0.100506	−	0.135004i
$183$		0			0
$184$	6.86253	−	1.62645i	0.505913	−	0.119904i
$185$	−1.50347	−	3.48544i	−0.110538	−	0.256255i
$186$		0			0
$187$	−21.4147	−	14.0847i	−1.56600	−	1.02997i
$188$	−5.23914	+	9.07445i	−0.382103	+	0.661822i
$189$		0			0
$190$	3.69595	+	6.40157i	0.268132	+	0.464418i
$191$	−0.340269	+	5.84219i	−0.0246210	+	0.422726i	0.963366	+	0.268190i	$0.0864254\pi$
$191$	−0.340269	+	5.84219i	−0.0246210	+	0.422726i	−0.987987	+	0.154536i	$0.950612\pi$
$192$		0			0
$193$	−14.3530	−	1.67762i	−1.03315	−	0.120758i	−0.417418	−	0.908714i	$-0.637065\pi$
$193$	−14.3530	−	1.67762i	−1.03315	−	0.120758i	−0.615731	+	0.787957i	$0.711139\pi$
$194$	−0.624455	−	0.661884i	−0.0448333	−	0.0475205i
$195$		0			0
$196$	6.47314	−	0.756601i	0.462367	−	0.0540429i
$197$	3.66493	+	3.07525i	0.261116	+	0.219102i	0.763941	−	0.645286i	$-0.223262\pi$
$197$	3.66493	+	3.07525i	0.261116	+	0.219102i	−0.502825	+	0.864388i	$0.667706\pi$
$198$		0			0
$199$	11.9225	−	10.0042i	0.845166	−	0.709178i	−0.113554	−	0.993532i	$-0.536223\pi$
$199$	11.9225	−	10.0042i	0.845166	−	0.709178i	0.958719	+	0.284354i	$0.0917790\pi$
$200$	3.19509	−	3.38660i	0.225927	−	0.239469i
$201$		0			0
$202$	−17.6515	−	8.86492i	−1.24196	−	0.623733i
$203$	0.856563	+	0.430182i	0.0601189	+	0.0301929i
$204$		0			0
$205$	24.2014	−	25.6520i	1.69030	−	1.79161i
$206$	−4.55045	+	3.81828i	−0.317045	+	0.266032i
$207$		0			0
$208$	2.50329	+	2.10051i	0.173572	+	0.145644i
$209$	13.0598	−	1.52648i	0.903368	−	0.105589i
$210$		0			0
$211$	−10.1033	−	10.7089i	−0.695542	−	0.737231i	0.279282	−	0.960209i	$-0.409904\pi$
$211$	−10.1033	−	10.7089i	−0.695542	−	0.737231i	−0.974824	+	0.222978i	$0.928422\pi$
$212$	4.20664	+	0.491686i	0.288913	+	0.0337691i
$213$		0			0
$214$	−0.188754	+	3.24077i	−0.0129029	+	0.221535i
$215$	−14.4412	−	25.0129i	−0.984880	−	1.70586i
$216$		0			0
$217$	−1.23530	+	2.13960i	−0.0838575	+	0.145245i
$218$	−7.05624	−	4.64096i	−0.477909	−	0.314325i
$219$		0			0
$220$	−6.80308	−	15.7713i	−0.458664	−	1.06330i
$221$	−14.7447	+	3.49457i	−0.991838	+	0.235070i
$222$		0			0
$223$	6.19591	+	8.32255i	0.414909	+	0.557319i	0.959618	−	0.281306i	$-0.0907675\pi$
$223$	6.19591	+	8.32255i	0.414909	+	0.557319i	−0.544710	+	0.838625i	$0.683360\pi$
$224$	0.652932	−	0.237648i	0.0436259	−	0.0158785i
$225$		0			0
$226$	−10.9285	−	3.97765i	−0.726952	−	0.264589i
$227$	−2.85714	−	9.54350i	−0.189635	−	0.633424i	−0.998940	−	0.0460357i	$-0.985341\pi$
$227$	−2.85714	−	9.54350i	−0.189635	−	0.633424i	0.809305	−	0.587389i	$-0.199844\pi$
$228$		0			0
$229$	−1.21402	−	20.8439i	−0.0802247	−	1.37740i	−0.762821	−	0.646609i	$-0.776186\pi$
$229$	−1.21402	−	20.8439i	−0.0802247	−	1.37740i	0.682597	−	0.730795i	$-0.260851\pi$
$230$	−18.3100	+	12.0427i	−1.20733	+	0.794072i
$231$		0			0
$232$	−1.34230	−	0.318132i	−0.0881266	−	0.0208864i
$233$	2.00393	+	11.3648i	0.131282	+	0.744535i	0.977377	+	0.211504i	$0.0678361\pi$
$233$	2.00393	+	11.3648i	0.131282	+	0.744535i	−0.846095	+	0.533031i	$0.821053\pi$
$234$		0			0
$235$	5.65402	−	32.0655i	0.368827	−	2.09172i
$236$	2.28111	−	5.28820i	0.148488	−	0.344233i
$237$		0			0
$238$	−0.924086	+	3.08666i	−0.0598996	+	0.200079i
$239$	−1.72538	+	2.31759i	−0.111606	+	0.149913i	−0.854416	−	0.519589i	$-0.826085\pi$
$239$	−1.72538	+	2.31759i	−0.111606	+	0.149913i	0.742810	+	0.669502i	$0.233492\pi$
$240$		0			0
$241$	0.0473887	−	0.0237995i	0.00305257	−	0.00153306i	−0.447272	−	0.894398i	$-0.647604\pi$
$241$	0.0473887	−	0.0237995i	0.00305257	−	0.00153306i	0.450325	+	0.892865i	$0.351308\pi$
$242$	−19.5529			−1.25691
$243$		0			0
$244$	1.73132			0.110837
$245$	−18.0975	+	9.08888i	−1.15620	+	0.580667i
$246$		0			0
$247$	4.64201	−	6.23530i	0.295364	−	0.396743i
$248$	1.01977	−	3.40628i	0.0647557	−	0.216299i
$249$		0			0
$250$	0.423470	−	0.981715i	0.0267826	−	0.0620891i
$251$	−1.45888	+	8.27374i	−0.0920839	+	0.522234i	0.903518	+	0.428550i	$0.140975\pi$
$251$	−1.45888	+	8.27374i	−0.0920839	+	0.522234i	−0.995602	+	0.0936838i	$0.970136\pi$
$252$		0			0
$253$	6.76936	+	38.3910i	0.425586	+	2.41362i
$254$	9.54958	+	2.26329i	0.599194	+	0.142012i
$255$		0			0
$256$	−0.835488	+	0.549509i	−0.0522180	+	0.0343443i
$257$	−0.825207	−	14.1683i	−0.0514750	−	0.883792i	−0.920917	−	0.389758i	$-0.872559\pi$
$257$	−0.825207	−	14.1683i	−0.0514750	−	0.883792i	0.869442	−	0.494034i	$-0.164478\pi$
$258$		0			0
$259$	0.243434	+	0.813128i	0.0151263	+	0.0505253i
$260$	−9.54203	−	3.47302i	−0.591772	−	0.215387i
$261$		0			0
$262$	−17.3693	+	6.32189i	−1.07308	+	0.390568i
$263$	14.3710	+	19.3035i	0.886151	+	1.19031i	0.980843	+	0.194801i	$0.0624060\pi$
$263$	14.3710	+	19.3035i	0.886151	+	1.19031i	−0.0946919	+	0.995507i	$0.530187\pi$
$264$		0			0
$265$	−12.8060	+	3.03507i	−0.786664	+	0.186443i
$266$	−0.654671	−	1.51770i	−0.0401405	−	0.0930561i
$267$		0			0
$268$	−0.854863	−	0.562252i	−0.0522191	−	0.0343450i
$269$	−4.00049	+	6.92906i	−0.243914	+	0.422472i	−0.961826	−	0.273662i	$-0.911765\pi$
$269$	−4.00049	+	6.92906i	−0.243914	+	0.422472i	0.717911	+	0.696134i	$0.245098\pi$
$270$		0			0
$271$	1.88940	+	3.27253i	0.114773	+	0.198792i	0.917689	−	0.397300i	$-0.130053\pi$
$271$	1.88940	+	3.27253i	0.114773	+	0.198792i	−0.802916	+	0.596092i	$0.796719\pi$
$272$	0.269623	−	4.62925i	0.0163483	−	0.280690i
$273$		0			0
$274$	14.5740	+	1.70345i	0.880445	+	0.102909i
$275$	17.6608	+	18.7193i	1.06498	+	1.12882i
$276$		0			0
$277$	−9.30469	+	1.08756i	−0.559064	+	0.0653453i	−0.390933	−	0.920419i	$-0.627847\pi$
$277$	−9.30469	+	1.08756i	−0.559064	+	0.0653453i	−0.168132	+	0.985765i	$0.553773\pi$
$278$	−9.81349	−	8.23449i	−0.588574	−	0.493872i
$279$		0			0
$280$	−1.65399	+	1.38786i	−0.0988449	+	0.0829407i
$281$	5.32890	−	5.64830i	0.317895	−	0.336949i	−0.548646	−	0.836055i	$-0.684856\pi$
$281$	5.32890	−	5.64830i	0.317895	−	0.336949i	0.866541	+	0.499105i	$0.166338\pi$
$282$		0			0
$283$	−17.1311	−	8.60354i	−1.01834	−	0.511427i	−0.140344	−	0.990103i	$-0.544821\pi$
$283$	−17.1311	−	8.60354i	−1.01834	−	0.511427i	−0.877992	+	0.478676i	$0.841117\pi$
$284$	10.5331	+	5.28994i	0.625026	+	0.313900i
$285$		0			0
$286$	−12.3954	+	13.1384i	−0.732956	+	0.776888i
$287$	−6.04091	+	5.06892i	−0.356584	+	0.299209i
$288$		0			0
$289$	3.44925	+	2.89427i	0.202897	+	0.170251i
$290$	4.25764	−	0.497647i	0.250017	−	0.0292228i
$291$		0			0
$292$	−5.90065	−	6.25433i	−0.345310	−	0.366007i
$293$	−17.5250	−	2.04838i	−1.02382	−	0.119668i	−0.412425	−	0.910991i	$-0.635318\pi$
$293$	−17.5250	−	2.04838i	−1.02382	−	0.119668i	−0.611398	+	0.791324i	$0.709392\pi$
$294$		0			0
$295$	−1.04057	+	17.8659i	−0.0605844	+	1.04019i
$296$	−0.610782	−	1.05790i	−0.0355010	−	0.0614895i
$297$		0			0
$298$	8.85739	−	15.3415i	0.513095	−	0.888706i
$299$	19.2553	+	12.6644i	1.11356	+	0.732401i
$300$		0			0
$301$	2.55800	+	5.93011i	0.147441	+	0.341806i
$302$	−15.3504	+	3.63812i	−0.883319	+	0.209350i
$303$		0			0
$304$	1.42052	+	1.90809i	0.0814726	+	0.109437i
$305$	−5.05546	+	1.84004i	−0.289475	+	0.105360i
$306$		0			0
$307$	−12.9189	−	4.70209i	−0.737320	−	0.268363i	−0.0540601	−	0.998538i	$-0.517216\pi$
$307$	−12.9189	−	4.70209i	−0.737320	−	0.268363i	−0.683260	+	0.730175i	$0.739438\pi$
$308$	1.10152	+	3.67933i	0.0627649	+	0.209649i
$309$		0			0
$310$	0.642433	+	11.0301i	0.0364877	+	0.626470i
$311$	−14.9898	+	9.85896i	−0.849995	+	0.559050i	−0.898100	−	0.439792i	$-0.855052\pi$
$311$	−14.9898	+	9.85896i	−0.849995	+	0.559050i	0.0481050	+	0.998842i	$0.484682\pi$
$312$		0			0
$313$	4.64166	+	1.10009i	0.262362	+	0.0621810i	0.359692	−	0.933071i	$-0.382882\pi$
$313$	4.64166	+	1.10009i	0.262362	+	0.0621810i	−0.0973294	+	0.995252i	$0.531030\pi$
$314$	0.546528	+	3.09951i	0.0308423	+	0.174916i
$315$		0			0
$316$	−1.52750	+	8.66290i	−0.0859288	+	0.487326i
$317$	1.95397	−	4.52981i	0.109746	−	0.254420i	−0.854489	−	0.519470i	$-0.826129\pi$
$317$	1.95397	−	4.52981i	0.109746	−	0.254420i	0.964235	+	0.265050i	$0.0853886\pi$
$318$		0			0
$319$	2.18690	−	7.30474i	0.122443	−	0.408987i
$320$	1.85561	−	2.49252i	0.103732	−	0.139336i
$321$		0			0
$322$	4.37918	−	2.19931i	0.244042	−	0.122563i
$323$	−11.0307			−0.613767
$324$		0			0
$325$	15.2147			0.843962
$326$	9.53788	−	4.79010i	0.528254	−	0.265299i
$327$		0			0
$328$	6.77729	−	9.10348i	0.374213	−	0.502655i
$329$	−2.08812	+	6.97481i	−0.115122	+	0.384534i
$330$		0			0
$331$	8.20945	−	19.0316i	0.451232	−	1.04607i	−0.529071	−	0.848577i	$-0.677460\pi$
$331$	8.20945	−	19.0316i	0.451232	−	1.04607i	0.980304	−	0.197497i	$-0.0632812\pi$
$332$	1.57663	−	8.94153i	0.0865290	−	0.490730i
$333$		0			0
$334$	0.330865	+	1.87643i	0.0181041	+	0.102674i
$335$	3.09376	+	0.733234i	0.169030	+	0.0400609i
$336$		0			0
$337$	23.4132	−	15.3991i	1.27540	−	0.838843i	0.282670	−	0.959217i	$-0.408780\pi$
$337$	23.4132	−	15.3991i	1.27540	−	0.838843i	0.992729	+	0.120374i	$0.0384095\pi$
$338$	−0.134975	−	2.31744i	−0.00734169	−	0.126052i
$339$		0			0
$340$	4.13264	+	13.8040i	0.224124	+	0.748626i
$341$	18.4685	+	6.72198i	1.00012	+	0.364016i
$342$		0			0
$343$	8.82581	−	3.21233i	0.476549	−	0.173450i
$344$	−5.55041	−	7.45550i	−0.299258	−	0.401973i
$345$		0			0
$346$	1.41829	−	0.336142i	0.0762480	−	0.0180711i
$347$	−4.31805	−	10.0104i	−0.231805	−	0.537384i	0.762121	−	0.647435i	$-0.224158\pi$
$347$	−4.31805	−	10.0104i	−0.231805	−	0.537384i	−0.993926	+	0.110050i	$0.964899\pi$
$348$		0			0
$349$	13.5397	+	8.90522i	0.724765	+	0.476685i	0.857512	−	0.514465i	$-0.172009\pi$
$349$	13.5397	+	8.90522i	0.724765	+	0.476685i	−0.132747	+	0.991150i	$0.542380\pi$
$350$	1.61755	−	2.80169i	0.0864619	−	0.149756i
$351$		0			0
$352$	−2.76373	−	4.78692i	−0.147307	−	0.255144i
$353$	1.59059	−	27.3094i	0.0846586	−	1.45353i	−0.642090	−	0.766629i	$-0.721933\pi$
$353$	1.59059	−	27.3094i	0.0846586	−	1.45353i	0.726749	−	0.686903i	$-0.241030\pi$
$354$		0			0
$355$	−36.3789	−	4.25208i	−1.93079	−	0.225677i
$356$	−2.54030	−	2.69256i	−0.134636	−	0.142705i
$357$		0			0
$358$	3.59856	−	0.420611i	0.190190	−	0.0222300i
$359$	4.66035	+	3.91050i	0.245964	+	0.206388i	0.757432	−	0.652914i	$-0.226454\pi$
$359$	4.66035	+	3.91050i	0.245964	+	0.206388i	−0.511468	+	0.859302i	$0.670898\pi$
$360$		0			0
$361$	−10.2200	+	8.57562i	−0.537896	+	0.451348i
$362$	15.2223	−	16.1347i	0.800068	−	0.848023i
$363$		0			0
$364$	2.02908	+	1.01904i	0.106353	+	0.0534123i
$365$	23.8770	+	11.9915i	1.24978	+	0.627662i
$366$		0			0
$367$	−12.3462	+	13.0862i	−0.644468	+	0.683096i	−0.964431	−	0.264334i	$-0.914848\pi$
$367$	−12.3462	+	13.0862i	−0.644468	+	0.683096i	0.319963	+	0.947430i	$0.396329\pi$
$368$	−5.40264	+	4.53335i	−0.281632	+	0.236317i
$369$		0			0
$370$	2.90782	+	2.43995i	0.151170	+	0.126847i
$371$	2.92293	−	0.341641i	0.151751	−	0.0177371i
$372$		0			0
$373$	16.3827	+	17.3646i	0.848262	+	0.899106i	0.995948	−	0.0899288i	$-0.0286639\pi$
$373$	16.3827	+	17.3646i	0.848262	+	0.899106i	−0.147686	+	0.989034i	$0.547182\pi$
$374$	25.4581	+	2.97562i	1.31641	+	0.153866i
$375$		0			0
$376$	0.609257	−	10.4605i	0.0314200	−	0.539461i
$377$	−2.25396	−	3.90397i	−0.116085	−	0.201065i
$378$		0			0
$379$	−11.8242	+	20.4801i	−0.607367	+	1.05199i	0.384305	+	0.923206i	$0.374441\pi$
$379$	−11.8242	+	20.4801i	−0.607367	+	1.05199i	−0.991673	+	0.128785i	$0.958892\pi$
$380$	−6.17584	−	4.06191i	−0.316814	−	0.208372i
$381$		0			0
$382$	−2.31789	−	5.37348i	−0.118594	−	0.274931i
$383$	13.8773	−	3.28898i	0.709097	−	0.168059i	0.139787	−	0.990182i	$-0.455358\pi$
$383$	13.8773	−	3.28898i	0.709097	−	0.168059i	0.569311	+	0.822123i	$0.307210\pi$
$384$		0			0
$385$	−7.12681	−	9.57296i	−0.363216	−	0.487883i
$386$	13.5792	−	4.94242i	0.691163	−	0.251563i
$387$		0			0
$388$	0.855086	+	0.311226i	0.0434104	+	0.0158001i
$389$	−10.2329	−	34.1803i	−0.518829	−	1.73301i	−0.667964	−	0.744193i	$-0.732834\pi$
$389$	−10.2329	−	34.1803i	−0.518829	−	1.73301i	0.149135	−	0.988817i	$-0.452351\pi$
$390$		0			0
$391$	−1.90156	−	32.6485i	−0.0961658	−	1.65110i
$392$	−5.44504	+	3.58126i	−0.275016	+	0.180881i
$393$		0			0
$394$	−4.65527	−	1.10332i	−0.234529	−	0.0555845i
$395$	−4.74656	−	26.9191i	−0.238826	−	1.35445i
$396$		0			0
$397$	4.23676	−	24.0278i	0.212637	−	1.20592i	−0.672324	−	0.740257i	$-0.734704\pi$
$397$	4.23676	−	24.0278i	0.212637	−	1.20592i	0.884961	−	0.465666i	$-0.154185\pi$
$398$	−6.16449	+	14.2909i	−0.308998	+	0.716338i
$399$		0			0
$400$	−1.33534	+	4.46033i	−0.0667668	+	0.223017i
$401$	−23.3072	+	31.3070i	−1.16391	+	1.56340i	−0.402093	+	0.915599i	$0.631717\pi$
$401$	−23.3072	+	31.3070i	−1.16391	+	1.56340i	−0.761812	+	0.647798i	$0.775690\pi$
$402$		0			0
$403$	10.3833	−	5.21470i	0.517230	−	0.259763i
$404$	19.7525			0.982725
$405$		0			0
$406$	−0.958518			−0.0475705
$407$	6.03394	−	3.03036i	0.299091	−	0.150209i
$408$		0			0
$409$	−10.6428	+	14.2958i	−0.526254	+	0.706882i	−0.983183	−	0.182621i	$-0.941542\pi$
$409$	−10.6428	+	14.2958i	−0.526254	+	0.706882i	0.456929	+	0.889503i	$0.348949\pi$
$410$	−10.1146	+	33.7850i	−0.499523	+	1.66852i
$411$		0			0
$412$	2.35279	−	5.45437i	0.115914	−	0.268718i
$413$	0.694889	−	3.94091i	0.0341933	−	0.193920i
$414$		0			0
$415$	4.89923	+	27.7849i	0.240494	+	1.36391i
$416$	−3.17973	−	0.753611i	−0.155899	−	0.0369488i
$417$		0			0
$418$	−10.9856	+	7.22536i	−0.537324	+	0.353404i
$419$	0.463457	+	7.95725i	0.0226414	+	0.388737i	0.990524	+	0.137336i	$0.0438542\pi$
$419$	0.463457	+	7.95725i	0.0226414	+	0.388737i	−0.967883	+	0.251401i	$0.919109\pi$
$420$		0			0
$421$	8.16468	+	27.2719i	0.397922	+	1.32915i	0.888948	+	0.458008i	$0.151437\pi$
$421$	8.16468	+	27.2719i	0.397922	+	1.32915i	−0.491026	+	0.871145i	$0.663378\pi$
$422$	13.8348	+	5.03546i	0.673468	+	0.245122i
$423$		0			0
$424$	−3.97986	+	1.44855i	−0.193279	+	0.0703479i
$425$	−12.8927	−	17.3179i	−0.625386	−	0.840039i
$426$		0			0
$427$	1.17056	−	0.277427i	0.0566473	−	0.0134257i
$428$	−1.28578	−	2.98077i	−0.0621505	−	0.144081i
$429$		0			0
$430$	24.1309	+	15.8711i	1.16369	+	0.765373i
$431$	13.7252	−	23.7728i	0.661122	−	1.14510i	−0.319200	−	0.947688i	$-0.603414\pi$
$431$	13.7252	−	23.7728i	0.661122	−	1.14510i	0.980321	−	0.197409i	$-0.0632526\pi$
$432$		0			0
$433$	1.90681	+	3.30270i	0.0916356	+	0.158717i	0.908199	−	0.418538i	$-0.137457\pi$
$433$	1.90681	+	3.30270i	0.0916356	+	0.158717i	−0.816564	+	0.577255i	$0.804124\pi$
$434$	0.143652	−	2.46642i	0.00689553	−	0.118392i
$435$		0			0
$436$	8.38854	+	0.980480i	0.401738	+	0.0469565i
$437$	11.5130	+	12.2030i	0.550740	+	0.583750i
$438$		0			0
$439$	−5.47284	+	0.639683i	−0.261204	+	0.0305304i	−0.245687	−	0.969349i	$-0.579014\pi$
$439$	−5.47284	+	0.639683i	−0.261204	+	0.0305304i	−0.0155172	+	0.999880i	$0.504939\pi$
$440$	13.1576	+	11.0405i	0.627265	+	0.526337i
$441$		0			0
$442$	11.6080	−	9.74029i	0.552137	−	0.463298i
$443$	−17.7115	+	18.7731i	−0.841499	+	0.891937i	−0.995366	−	0.0961548i	$-0.969346\pi$
$443$	−17.7115	+	18.7731i	−0.841499	+	0.891937i	0.153868	+	0.988091i	$0.450827\pi$
$444$		0			0
$445$	10.2793	+	5.16246i	0.487286	+	0.244724i
$446$	−9.27202	−	4.65658i	−0.439043	−	0.220496i
$447$		0			0
$448$	−0.476825	+	0.505405i	−0.0225279	+	0.0238781i
$449$	7.95557	−	6.67552i	0.375447	−	0.315037i	−0.435465	−	0.900206i	$-0.643416\pi$
$449$	7.95557	−	6.67552i	0.375447	−	0.315037i	0.810912	+	0.585168i	$0.198972\pi$
$450$		0			0
$451$	48.0558	+	40.3236i	2.26286	+	1.89877i
$452$	11.5512	−	1.35014i	0.543324	−	0.0635054i
$453$		0			0
$454$	6.83635	+	7.24610i	0.320846	+	0.340076i
$455$	−7.00794	−	0.819111i	−0.328537	−	0.0384005i
$456$		0			0
$457$	2.03404	−	34.9231i	0.0951485	−	1.63364i	−0.526384	−	0.850247i	$-0.676452\pi$
$457$	2.03404	−	34.9231i	0.0951485	−	1.63364i	0.621532	−	0.783389i	$-0.286511\pi$
$458$	10.4396	+	18.0819i	0.487811	+	0.844914i
$459$		0			0
$460$	10.9577	−	18.9793i	0.510905	−	0.884913i
$461$	13.1697	+	8.66185i	0.613374	+	0.403423i	0.817836	−	0.575452i	$-0.195174\pi$
$461$	13.1697	+	8.66185i	0.613374	+	0.403423i	−0.204461	+	0.978875i	$0.565544\pi$
$462$		0			0
$463$	1.50290	+	3.48411i	0.0698456	+	0.161920i	0.949563	−	0.313577i	$-0.101527\pi$
$463$	1.50290	+	3.48411i	0.0698456	+	0.161920i	−0.879717	+	0.475497i	$0.842268\pi$
$464$	1.34230	−	0.318132i	0.0623149	−	0.0147689i
$465$		0			0
$466$	−6.89131	−	9.25663i	−0.319234	−	0.428805i
$467$	−37.6811	+	13.7148i	−1.74367	+	0.634645i	−0.999446	−	0.0332831i	$-0.989404\pi$
$467$	−37.6811	+	13.7148i	−1.74367	+	0.634645i	−0.744226	+	0.667928i	$0.767181\pi$
$468$		0			0
$469$	−0.668073	−	0.243159i	−0.0308488	−	0.0112280i
$470$	9.33836	+	31.1923i	0.430747	+	1.43879i
$471$		0			0
$472$	0.334869	+	5.74947i	0.0154136	+	0.264641i
$473$	42.9241	−	28.2317i	1.97365	−	1.29809i
$474$		0			0
$475$	10.7770	+	2.55420i	0.494483	+	0.117195i
$476$	−0.559498	−	3.17307i	−0.0256446	−	0.145438i
$477$		0			0
$478$	0.501726	−	2.84543i	0.0229484	−	0.130147i
$479$	−8.98549	+	20.8307i	−0.410558	+	0.951780i	0.579992	+	0.814622i	$0.303056\pi$
$479$	−8.98549	+	20.8307i	−0.410558	+	0.951780i	−0.990549	+	0.137157i	$0.956203\pi$
$480$		0			0
$481$	1.14487	−	3.82415i	0.0522018	−	0.174366i
$482$	−0.0316669	+	0.0425360i	−0.00144239	+	0.00193746i
$483$		0			0
$484$	17.4731	−	8.77531i	0.794231	−	0.398878i
$485$	−2.82762			−0.128396
$486$		0			0
$487$	−27.0825			−1.22723			−0.613613	−	0.789607i	$-0.710285\pi$
$487$	−27.0825			−1.22723			−0.613613	+	0.789607i	$0.710285\pi$
$488$	−1.54717	+	0.777016i	−0.0700369	+	0.0351739i
$489$		0			0
$490$	12.0934	−	16.2442i	0.546324	−	0.733840i
$491$	2.03944	−	6.81222i	0.0920388	−	0.307431i	−0.899557	−	0.436803i	$-0.856111\pi$
$491$	2.03944	−	6.81222i	0.0920388	−	0.307431i	0.991596	+	0.129372i	$0.0412960\pi$
$492$		0			0
$493$	−2.53365	+	5.87367i	−0.114110	+	0.264537i
$494$	−1.34985	+	7.65540i	−0.0607328	+	0.344433i
$495$		0			0
$496$	0.617433	+	3.50164i	0.0277236	+	0.157228i
$497$	7.96918	+	1.88873i	0.357466	+	0.0847211i
$498$		0			0
$499$	−24.8765	+	16.3615i	−1.11362	+	0.732442i	−0.966498	−	0.256676i	$-0.917373\pi$
$499$	−24.8765	+	16.3615i	−1.11362	+	0.732442i	−0.147127	+	0.989118i	$0.547002\pi$
$500$	0.0621658	+	1.06735i	0.00278014	+	0.0477331i
$501$		0			0
$502$	−2.40954	−	8.04843i	−0.107543	−	0.359219i
$503$	−0.405417	−	0.147560i	−0.0180767	−	0.00657936i	0.332966	−	0.942939i	$-0.391951\pi$
$503$	−0.405417	−	0.147560i	−0.0180767	−	0.00657936i	−0.351043	+	0.936359i	$0.614173\pi$
$504$		0			0
$505$	−57.6774	+	20.9928i	−2.56661	+	0.934169i
$506$	−23.2792	−	31.2693i	−1.03488	−	1.39009i
$507$		0			0
$508$	−9.54958	+	2.26329i	−0.423694	+	0.100417i
$509$	−8.75229	−	20.2901i	−0.387939	−	0.899343i	−0.994542	−	0.104338i	$-0.966728\pi$
$509$	−8.75229	−	20.2901i	−0.387939	−	0.899343i	0.606603	−	0.795005i	$-0.292532\pi$
$510$		0			0
$511$	−4.99166	−	3.28307i	−0.220818	−	0.145234i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$		0			0
$514$	7.09614	+	12.2909i	0.312997	+	0.542127i
$515$	−1.07327	+	18.4273i	−0.0472939	+	0.812004i
$516$		0			0
$517$	57.5266	+	6.72390i	2.53002	+	0.295717i
$518$	−0.582472	−	0.617384i	−0.0255924	−	0.0271263i
$519$		0			0
$520$	10.0858	−	1.17886i	0.442290	−	0.0516963i
$521$	−0.934191	−	0.783879i	−0.0409276	−	0.0343424i	0.622094	−	0.782942i	$-0.286282\pi$
$521$	−0.934191	−	0.783879i	−0.0409276	−	0.0343424i	−0.663022	+	0.748600i	$0.730726\pi$
$522$		0			0
$523$	7.65711	−	6.42508i	0.334822	−	0.280949i	−0.459839	−	0.888002i	$-0.652093\pi$
$523$	7.65711	−	6.42508i	0.334822	−	0.280949i	0.794661	+	0.607053i	$0.207648\pi$
$524$	12.6845	−	13.4448i	0.554124	−	0.587337i
$525$		0			0
$526$	−21.5058	−	10.8006i	−0.937696	−	0.470929i
$527$	−14.7341	−	7.39977i	−0.641829	−	0.322339i
$528$		0			0
$529$	−18.3499	+	19.4498i	−0.797822	+	0.845642i
$530$	10.0817	−	8.45954i	0.437921	−	0.367459i
$531$		0			0
$532$	1.26618	+	1.06245i	0.0548958	+	0.0460630i
$533$	36.8364	−	4.30556i	1.59556	−	0.186495i
$534$		0			0
$535$	6.92243	+	7.33734i	0.299283	+	0.317221i
$536$	1.01627	+	0.118785i	0.0438962	+	0.00513074i
$537$		0			0
$538$	0.465216	−	7.98745i	0.0200569	−	0.344363i
$539$	−18.0118	−	31.1974i	−0.775823	−	1.34377i
$540$		0			0
$541$	−1.46755	+	2.54188i	−0.0630951	+	0.109284i	−0.895847	−	0.444362i	$-0.853430\pi$
$541$	−1.46755	+	2.54188i	−0.0630951	+	0.109284i	0.832752	+	0.553646i	$0.186764\pi$
$542$	−3.15714	−	2.07648i	−0.135611	−	0.0891925i
$543$		0			0
$544$	1.83666	+	4.25786i	0.0787462	+	0.182554i
$545$	−25.5366	+	6.05228i	−1.09387	+	0.259251i
$546$		0			0
$547$	9.40820	+	12.6374i	0.402266	+	0.540336i	0.956388	−	0.292099i	$-0.0943535\pi$
$547$	9.40820	+	12.6374i	0.402266	+	0.540336i	−0.554123	+	0.832435i	$0.686946\pi$
$548$	−13.7883	+	5.01852i	−0.589006	+	0.214380i
$549$		0			0
$550$	−24.1835	−	8.80206i	−1.03119	−	0.375321i
$551$	−0.941154	−	3.14367i	−0.0400945	−	0.133925i
$552$		0			0
$553$	0.355390	+	6.10181i	0.0151127	+	0.259475i
$554$	7.82687	−	5.14782i	0.332532	−	0.218710i
$555$		0			0
$556$	12.4653	+	2.95433i	0.528646	+	0.125291i
$557$	2.45674	+	13.9329i	0.104095	+	0.590354i	0.991578	+	0.129512i	$0.0413412\pi$
$557$	2.45674	+	13.9329i	0.104095	+	0.590354i	−0.887482	+	0.460841i	$0.847548\pi$
$558$		0			0
$559$	5.27429	−	29.9120i	0.223079	−	1.26514i
$560$	0.855189	−	1.98255i	0.0361383	−	0.0837780i
$561$		0			0
$562$	−2.22712	+	7.43911i	−0.0939455	+	0.313800i
$563$	14.2152	−	19.0944i	0.599101	−	0.804732i	−0.394354	−	0.918959i	$-0.629032\pi$
$563$	14.2152	−	19.0944i	0.599101	−	0.804732i	0.993455	+	0.114226i	$0.0364390\pi$
$564$		0			0
$565$	−32.2946	+	16.2190i	−1.35865	+	0.682338i
$566$	19.1701			0.805781
$567$		0			0
$568$	−11.7869			−0.494566
$569$	1.76778	−	0.887811i	0.0741091	−	0.0372190i	−0.411359	−	0.911474i	$-0.634946\pi$
$569$	1.76778	−	0.887811i	0.0741091	−	0.0372190i	0.485468	+	0.874255i	$0.338649\pi$
$570$		0			0
$571$	5.08064	−	6.82448i	0.212618	−	0.285596i	−0.683001	−	0.730417i	$-0.739326\pi$
$571$	5.08064	−	6.82448i	0.212618	−	0.285596i	0.895619	+	0.444822i	$0.146733\pi$
$572$	5.18046	−	17.3039i	0.216606	−	0.723513i
$573$		0			0
$574$	3.12342	−	7.24091i	0.130369	−	0.302230i
$575$	−5.70202	+	32.3378i	−0.237791	+	1.34858i
$576$		0			0
$577$	−6.90467	−	39.1583i	−0.287445	−	1.63018i	−0.696418	−	0.717636i	$-0.745224\pi$
$577$	−6.90467	−	39.1583i	−0.287445	−	1.63018i	0.408973	−	0.912546i	$-0.365887\pi$
$578$	−4.38131	−	1.03839i	−0.182239	−	0.0431913i
$579$		0			0
$580$	−3.58142	+	2.35554i	−0.148710	+	0.0978084i
$581$	−0.366821	−	6.29807i	−0.0152183	−	0.261288i
$582$		0			0
$583$	−6.71417	−	22.4269i	−0.278072	−	0.928826i
$584$	8.07995	+	2.94086i	0.334351	+	0.121694i
$585$		0			0
$586$	16.5802	−	6.03472i	0.684924	−	0.249292i
$587$	−6.53316	−	8.77555i	−0.269652	−	0.362206i	0.646585	−	0.762842i	$-0.276197\pi$
$587$	−6.53316	−	8.77555i	−0.269652	−	0.362206i	−0.916237	+	0.400636i	$0.868789\pi$
$588$		0			0
$589$	8.23021	−	1.95060i	0.339120	−	0.0803729i
$590$	−7.08832	−	16.4326i	−0.291821	−	0.676518i
$591$		0			0
$592$	1.02060	+	0.671260i	0.0419465	+	0.0275886i
$593$	6.95035	−	12.0384i	0.285417	−	0.494356i	−0.687293	−	0.726380i	$-0.741201\pi$
$593$	6.95035	−	12.0384i	0.285417	−	0.494356i	0.972710	+	0.232024i	$0.0745347\pi$
$594$		0			0
$595$	5.00605	+	8.67074i	0.205228	+	0.355466i
$596$	−1.03002	+	17.6848i	−0.0421914	+	0.724398i
$597$		0			0
$598$	−22.8909	−	2.67556i	−0.936079	−	0.109412i
$599$	−8.55657	−	9.06943i	−0.349612	−	0.370567i	0.528573	−	0.848888i	$-0.322727\pi$
$599$	−8.55657	−	9.06943i	−0.349612	−	0.370567i	−0.878185	+	0.478321i	$0.841246\pi$
$600$		0			0
$601$	−33.8011	+	3.95078i	−1.37877	+	0.161156i	−0.772962	−	0.634452i	$-0.781226\pi$
$601$	−33.8011	+	3.95078i	−1.37877	+	0.161156i	−0.605813	+	0.795607i	$0.707152\pi$
$602$	−4.94734	−	4.15131i	−0.201638	−	0.169195i
$603$		0			0
$604$	12.0849	−	10.1404i	0.491726	−	0.412607i
$605$	−41.6951	+	44.1942i	−1.69515	+	1.79675i
$606$		0			0
$607$	−0.126803	−	0.0636828i	−0.00514677	−	0.00258481i	0.446224	−	0.894921i	$-0.352768\pi$
$607$	−0.126803	−	0.0636828i	−0.00514677	−	0.00258481i	−0.451371	+	0.892337i	$0.649065\pi$
$608$	−2.12578	−	1.06760i	−0.0862116	−	0.0432971i
$609$		0			0
$610$	3.69192	−	3.91321i	0.149481	−	0.158441i
$611$	26.2302	−	22.0097i	1.06116	−	0.890419i
$612$		0			0
$613$	5.46537	+	4.58599i	0.220744	+	0.185226i	0.746453	−	0.665438i	$-0.231755\pi$
$613$	5.46537	+	4.58599i	0.220744	+	0.185226i	−0.525709	+	0.850665i	$0.676200\pi$
$614$	13.6550	−	1.59605i	0.551073	−	0.0644111i
$615$		0			0
$616$	−2.63563	−	2.79361i	−0.106193	−	0.112558i
$617$	12.3620	+	1.44491i	0.497674	+	0.0581698i	0.361228	−	0.932478i	$-0.382358\pi$
$617$	12.3620	+	1.44491i	0.497674	+	0.0581698i	0.136447	+	0.990647i	$0.456432\pi$
$618$		0			0
$619$	−0.942223	+	16.1773i	−0.0378711	+	0.650222i	0.924951	+	0.380086i	$0.124106\pi$
$619$	−0.942223	+	16.1773i	−0.0378711	+	0.650222i	−0.962822	+	0.270136i	$0.912931\pi$
$620$	−5.52442	−	9.56858i	−0.221866	−	0.384283i
$621$		0			0
$622$	8.97070	−	15.5377i	0.359692	−	0.623005i
$623$	−2.14897	−	1.41340i	−0.0860966	−	0.0566266i
$624$		0			0
$625$	−10.5365	−	24.4263i	−0.421460	−	0.977054i
$626$	−4.64166	+	1.10009i	−0.185518	+	0.0439686i
$627$		0			0
$628$	−1.87945	−	2.52454i	−0.0749984	−	0.100740i
$629$	−5.32290	+	1.93738i	−0.212238	+	0.0772482i
$630$		0			0
$631$	30.2871	+	11.0236i	1.20571	+	0.438843i	0.865214	−	0.501402i	$-0.167182\pi$
$631$	30.2871	+	11.0236i	1.20571	+	0.438843i	0.340497	+	0.940246i	$0.389405\pi$
$632$	−2.52288	−	8.42700i	−0.100355	−	0.335208i
$633$		0			0
$634$	0.286844	+	4.92493i	0.0113920	+	0.195594i
$635$	25.4794	−	16.7580i	1.01112	−	0.665023i
$636$		0			0
$637$	−20.7230	−	4.91143i	−0.821074	−	0.194598i
$638$	1.32408	+	7.50923i	0.0524208	+	0.297293i
$639$		0			0
$640$	−0.539594	+	3.06019i	−0.0213293	+	0.120965i
$641$	−2.93257	+	6.79846i	−0.115829	+	0.268523i	−0.966262	−	0.257561i	$-0.917081\pi$
$641$	−2.93257	+	6.79846i	−0.115829	+	0.268523i	0.850432	+	0.526084i	$0.176340\pi$
$642$		0			0
$643$	−2.09220	+	6.98845i	−0.0825085	+	0.275597i	−0.989281	−	0.146022i	$-0.953353\pi$
$643$	−2.09220	+	6.98845i	−0.0825085	+	0.275597i	0.906773	+	0.421619i	$0.138538\pi$
$644$	−2.92633	+	3.93074i	−0.115314	+	0.154893i
$645$		0			0
$646$	9.85743	−	4.95059i	0.387835	−	0.194778i
$647$	−25.8659			−1.01689			−0.508446	−	0.861094i	$-0.669780\pi$
$647$	−25.8659			−1.01689			−0.508446	+	0.861094i	$0.669780\pi$
$648$		0			0
$649$	−31.8339			−1.24959
$650$	−13.5964	+	6.82836i	−0.533294	+	0.267830i
$651$		0			0
$652$	−6.37357	+	8.56119i	−0.249608	+	0.335282i
$653$	−0.658203	+	2.19855i	−0.0257575	+	0.0860360i	−0.969902	−	0.243496i	$-0.921706\pi$
$653$	−0.658203	+	2.19855i	−0.0257575	+	0.0860360i	0.944144	+	0.329532i	$0.106891\pi$
$654$		0			0
$655$	−22.7497	+	52.7397i	−0.888903	+	2.06071i
$656$	−1.97077	+	11.1768i	−0.0769457	+	0.436381i
$657$		0			0
$658$	−1.26428	−	7.17007i	−0.0492866	−	0.279518i
$659$	32.6804	+	7.74540i	1.27305	+	0.301718i	0.810952	−	0.585113i	$-0.198950\pi$
$659$	32.6804	+	7.74540i	1.27305	+	0.301718i	0.462095	+	0.886830i	$0.347098\pi$
$660$		0			0
$661$	15.0448	−	9.89512i	0.585175	−	0.384875i	−0.222124	−	0.975018i	$-0.571299\pi$
$661$	15.0448	−	9.89512i	0.585175	−	0.384875i	0.807299	+	0.590143i	$0.200929\pi$
$662$	1.20515	+	20.6917i	0.0468396	+	0.804206i
$663$		0			0
$664$	2.60402	+	8.69804i	0.101056	+	0.337549i
$665$	−4.82640	−	1.75667i	−0.187160	−	0.0681206i
$666$		0			0
$667$	9.14230	−	3.32753i	0.353991	−	0.128842i
$668$	−1.13781	−	1.52835i	−0.0440232	−	0.0591335i
$669$		0			0
$670$	−3.09376	+	0.733234i	−0.119522	+	0.0283273i
$671$	−3.79041	−	8.78717i	−0.146327	−	0.339225i
$672$		0			0
$673$	7.51146	+	4.94036i	0.289545	+	0.190437i	0.685969	−	0.727631i	$-0.259378\pi$
$673$	7.51146	+	4.94036i	0.289545	+	0.190437i	−0.396424	+	0.918068i	$0.629749\pi$
$674$	−14.0117	+	24.2690i	−0.539710	+	0.934806i
$675$		0			0
$676$	1.16068	+	2.01036i	0.0446416	+	0.0773215i
$677$	1.07919	−	18.5289i	0.0414765	−	0.712124i	−0.911913	−	0.410383i	$-0.865395\pi$
$677$	1.07919	−	18.5289i	0.0414765	−	0.712124i	0.953390	−	0.301741i	$-0.0975679\pi$
$678$		0			0
$679$	0.628000	+	0.0734027i	0.0241004	+	0.00281694i
$680$	−9.88827	−	10.4810i	−0.379198	−	0.401926i
$681$		0			0
$682$	−19.5209	+	2.28166i	−0.747493	+	0.0873694i
$683$	−6.63544	−	5.56779i	−0.253898	−	0.213046i	0.506951	−	0.861975i	$-0.330773\pi$
$683$	−6.63544	−	5.56779i	−0.253898	−	0.213046i	−0.760849	+	0.648929i	$0.775217\pi$
$684$		0			0
$685$	34.9281	−	29.3082i	1.33453	−	1.11981i
$686$	−6.44534	+	6.83166i	−0.246084	+	0.260834i
$687$		0			0
$688$	8.30605	+	4.17146i	0.316665	+	0.159035i
$689$	−12.3680	−	6.21144i	−0.471183	−	0.236637i
$690$		0			0
$691$	25.2925	−	26.8085i	0.962172	−	1.01984i	−0.0376168	−	0.999292i	$-0.511977\pi$
$691$	25.2925	−	26.8085i	0.962172	−	1.01984i	0.999789	−	0.0205505i	$-0.00654189\pi$
$692$	−1.11657	+	0.936917i	−0.0424458	+	0.0356162i
$693$		0			0
$694$	8.35139	+	7.00765i	0.317015	+	0.266007i
$695$	−39.5385	+	4.62139i	−1.49978	+	0.175299i
$696$		0			0
$697$	−36.1152	−	38.2798i	−1.36796	−	1.44995i
$698$	−16.0962	−	1.88138i	−0.609250	−	0.0712111i
$699$		0			0
$700$	−0.188105	+	3.22964i	−0.00710969	+	0.122069i
$701$	18.8835	+	32.7071i	0.713218	+	1.23533i	0.963643	+	0.267194i	$0.0860965\pi$
$701$	18.8835	+	32.7071i	0.713218	+	1.23533i	−0.250425	+	0.968136i	$0.580570\pi$
$702$		0			0
$703$	1.45293	−	2.51655i	0.0547983	−	0.0949134i
$704$	4.61813	+	3.03739i	0.174052	+	0.114476i
$705$		0			0
$706$	10.8350	+	25.1184i	0.407782	+	0.945344i
$707$	13.3548	−	3.16515i	0.502259	−	0.119038i
$708$		0			0
$709$	−9.95354	−	13.3699i	−0.373813	−	0.502118i	0.574914	−	0.818214i	$-0.305035\pi$
$709$	−9.95354	−	13.3699i	−0.373813	−	0.502118i	−0.948727	+	0.316096i	$0.897628\pi$
$710$	34.4177	−	12.5270i	1.29167	−	0.470130i
$711$		0			0
$712$	3.47851	+	1.26608i	0.130363	+	0.0474482i
$713$	7.19209	+	24.0233i	0.269346	+	0.899678i
$714$		0			0
$715$	3.26356	+	56.0332i	0.122050	+	2.09552i
$716$	−3.02702	+	1.99090i	−0.113125	+	0.0744035i
$717$		0			0
$718$	−5.91967	−	1.40299i	−0.220920	−	0.0523590i
$719$	0.219237	+	1.24336i	0.00817617	+	0.0463694i	0.988623	−	0.150415i	$-0.0480611\pi$
$719$	0.219237	+	1.24336i	0.00817617	+	0.0463694i	−0.980447	+	0.196785i	$0.936950\pi$
$720$		0			0
$721$	0.716725	−	4.06475i	0.0266922	−	0.151379i
$722$	5.28422	−	12.2502i	0.196658	−	0.455905i
$723$		0			0
$724$	−6.36192	+	21.2503i	−0.236439	+	0.789761i
$725$	3.83543	−	5.15188i	0.142444	−	0.191336i
$726$		0			0
$727$	5.85101	−	2.93849i	0.217002	−	0.108982i	−0.336978	−	0.941513i	$-0.609405\pi$
$727$	5.85101	−	2.93849i	0.217002	−	0.108982i	0.553980	+	0.832530i	$0.313108\pi$
$728$	−2.27060			−0.0841539
$729$		0			0
$730$	−26.7190			−0.988915
$731$	−38.5160	+	19.3434i	−1.42456	+	0.715443i
$732$		0			0
$733$	4.97694	−	6.68519i	0.183827	−	0.246923i	−0.700651	−	0.713504i	$-0.747107\pi$
$733$	4.97694	−	6.68519i	0.183827	−	0.246923i	0.884478	+	0.466581i	$0.154514\pi$
$734$	5.15990	−	17.2353i	0.190455	−	0.636166i
$735$		0			0
$736$	2.79341	−	6.47585i	0.102966	−	0.238703i
$737$	−0.982093	+	5.56972i	−0.0361759	+	0.205163i
$738$		0			0
$739$	2.08267	+	11.8114i	0.0766121	+	0.434489i	0.998853	+	0.0478740i	$0.0152446\pi$
$739$	2.08267	+	11.8114i	0.0766121	+	0.434489i	−0.922241	+	0.386615i	$0.873644\pi$
$740$	−3.69357	−	0.875391i	−0.135778	−	0.0321800i
$741$		0			0
$742$	−2.45869	+	1.61711i	−0.0902615	+	0.0593659i
$743$	1.67970	+	28.8393i	0.0616222	+	1.05801i	0.877435	+	0.479696i	$0.159253\pi$
$743$	1.67970	+	28.8393i	0.0616222	+	1.05801i	−0.815813	+	0.578316i	$0.803710\pi$
$744$		0			0
$745$	−15.7876	−	52.7344i	−0.578414	−	1.93204i
$746$	−22.4333	−	8.16506i	−0.821342	−	0.298944i
$747$		0			0
$748$	−24.0856	+	8.76645i	−0.880658	+	0.320533i
$749$	−1.34696	−	1.80929i	−0.0492170	−	0.0661099i
$750$		0			0
$751$	−6.59190	+	1.56231i	−0.240542	+	0.0570094i	−0.349118	−	0.937079i	$-0.613519\pi$
$751$	−6.59190	+	1.56231i	−0.240542	+	0.0570094i	0.108577	+	0.994088i	$0.465371\pi$
$752$	4.15023	+	9.62132i	0.151343	+	0.350853i
$753$		0			0
$754$	3.76631	+	2.47714i	0.137161	+	0.0902122i
$755$	−24.5107	+	42.4537i	−0.892034	+	1.54505i
$756$		0			0
$757$	−10.9210	−	18.9158i	−0.396932	−	0.687506i	0.596414	−	0.802677i	$-0.296592\pi$
$757$	−10.9210	−	18.9158i	−0.396932	−	0.687506i	−0.993346	+	0.115171i	$0.963258\pi$
$758$	1.37503	−	23.6084i	0.0499433	−	0.857494i
$759$		0			0
$760$	7.34191	+	0.858146i	0.266319	+	0.0311282i
$761$	−16.0381	−	16.9994i	−0.581381	−	0.616228i	0.368201	−	0.929746i	$-0.379974\pi$
$761$	−16.0381	−	16.9994i	−0.581381	−	0.616228i	−0.949582	+	0.313518i	$0.898492\pi$
$762$		0			0
$763$	5.82866	−	0.681273i	0.211012	−	0.0246637i
$764$	4.48296	+	3.76165i	0.162188	+	0.136092i
$765$		0			0
$766$	−10.9251	+	9.16727i	−0.394741	+	0.331227i
$767$	−12.9151	+	13.6892i	−0.466338	+	0.494289i
$768$		0			0
$769$	34.6714	+	17.4126i	1.25028	+	0.627915i	0.945846	−	0.324617i	$-0.105235\pi$
$769$	34.6714	+	17.4126i	1.25028	+	0.627915i	0.304437	+	0.952532i	$0.401532\pi$
$770$	10.6651	+	5.35621i	0.384343	+	0.193024i
$771$		0			0
$772$	−9.91666	+	10.5110i	−0.356908	+	0.378301i
$773$	−32.0265	+	26.8735i	−1.15191	+	0.966571i	−0.999763	−	0.0217863i	$-0.993065\pi$
$773$	−32.0265	+	26.8735i	−1.15191	+	0.966571i	−0.152152	+	0.988357i	$0.548620\pi$
$774$		0			0
$775$	12.6818	+	10.6413i	0.455543	+	0.382246i
$776$	−0.903811	+	0.105640i	−0.0324449	+	0.00379227i
$777$		0			0
$778$	24.4846	+	25.9521i	0.877814	+	0.930428i
$779$	26.8150	+	3.13423i	0.960748	+	0.112295i
$780$		0			0
$781$	3.78822	−	65.0413i	0.135553	−	2.32736i
$782$	16.3519	+	28.3223i	0.584742	+	1.01280i
$783$		0			0
$784$	3.25860	−	5.64406i	0.116379	−	0.201574i
$785$	8.17107	+	5.37420i	0.291638	+	0.191813i
$786$		0			0
$787$	13.6882	+	31.7327i	0.487930	+	1.13115i	0.967323	+	0.253549i	$0.0815977\pi$
$787$	13.6882	+	31.7327i	0.487930	+	1.13115i	−0.479393	+	0.877601i	$0.659143\pi$
$788$	4.65527	−	1.10332i	0.165837	−	0.0393041i
$789$		0			0
$790$	16.3230	+	21.9255i	0.580745	+	0.780076i
$791$	7.59350	−	2.76381i	0.269994	−	0.0982698i
$792$		0			0
$793$	−5.31645	−	1.93503i	−0.188793	−	0.0687149i
$794$	6.99757	+	23.3735i	0.248335	+	0.829495i
$795$		0			0
$796$	−0.904952	−	15.5374i	−0.0320752	−	0.550709i
$797$	−2.47748	+	1.62946i	−0.0877569	+	0.0577186i	−0.592629	−	0.805476i	$-0.701910\pi$
$797$	−2.47748	+	1.62946i	−0.0877569	+	0.0577186i	0.504872	+	0.863194i	$0.331540\pi$
$798$		0			0
$799$	−47.2791	−	11.2053i	−1.67261	−	0.396417i
$800$	−0.808494	−	4.58520i	−0.0285846	−	0.162111i
$801$		0			0
$802$	6.77751	−	38.4372i	0.239322	−	1.35726i
$803$	−18.8249	+	43.6409i	−0.664315	+	1.54005i
$804$		0			0
$805$	4.36732	−	14.5879i	0.153928	−	0.514155i
$806$	−6.93853	+	9.32006i	−0.244399	+	0.328285i
$807$		0			0
$808$	−17.6515	+	8.86492i	−0.620978	+	0.311867i
$809$	49.0772			1.72546			0.862731	−	0.505663i	$-0.168752\pi$
$809$	49.0772			1.72546			0.862731	+	0.505663i	$0.168752\pi$
$810$		0			0
$811$	−19.4023			−0.681307			−0.340654	−	0.940189i	$-0.610648\pi$
$811$	−19.4023			−0.681307			−0.340654	+	0.940189i	$0.610648\pi$
$812$	0.856563	−	0.430182i	0.0300595	−	0.0150964i
$813$		0			0
$814$	−4.03210	+	5.41605i	−0.141325	+	0.189833i
$815$	9.51205	−	31.7725i	0.333193	−	1.11294i
$816$		0			0
$817$	8.75743	−	20.3020i	0.306384	−	0.710277i
$818$	3.09484	−	17.5517i	0.108208	−	0.613681i
$819$		0			0
$820$	−6.12398	−	34.7308i	−0.213859	−	1.21285i
$821$	−0.0542400	−	0.0128551i	−0.00189299	−	0.000448646i	0.229669	−	0.973269i	$-0.426236\pi$
$821$	−0.0542400	−	0.0128551i	−0.00189299	−	0.000448646i	−0.231562	+	0.972820i	$0.574384\pi$
$822$		0			0
$823$	24.4081	−	16.0535i	0.850813	−	0.559588i	−0.0475370	−	0.998869i	$-0.515137\pi$
$823$	24.4081	−	16.0535i	0.850813	−	0.559588i	0.898350	+	0.439281i	$0.144767\pi$
$824$	0.345391	+	5.93014i	0.0120323	+	0.206586i
$825$		0			0
$826$	1.14770	+	3.83359i	0.0399337	+	0.133388i
$827$	−39.4672	−	14.3649i	−1.37241	−	0.499516i	−0.452541	−	0.891744i	$-0.649482\pi$
$827$	−39.4672	−	14.3649i	−1.37241	−	0.499516i	−0.919868	+	0.392227i	$0.871705\pi$
$828$		0			0
$829$	−11.8020	+	4.29559i	−0.409902	+	0.149192i	−0.538737	−	0.842474i	$-0.681098\pi$
$829$	−11.8020	+	4.29559i	−0.409902	+	0.149192i	0.128835	+	0.991666i	$0.458876\pi$
$830$	−16.8480	−	22.6307i	−0.584801	−	0.785524i
$831$		0			0
$832$	3.17973	−	0.753611i	0.110237	−	0.0261268i
$833$	11.9699	+	27.7493i	0.414732	+	0.961457i
$834$		0			0
$835$	4.94673	+	3.25351i	0.171189	+	0.112592i
$836$	6.57437	−	11.3872i	0.227380	−	0.393833i
$837$		0			0
$838$	−3.98537	−	6.90286i	−0.137672	−	0.238455i
$839$	2.36536	−	40.6117i	0.0816613	−	1.40207i	−0.669922	−	0.742432i	$-0.733672\pi$
$839$	2.36536	−	40.6117i	0.0816613	−	1.40207i	0.751583	−	0.659638i	$-0.229291\pi$
$840$		0			0
$841$	26.9138	+	3.14577i	0.928062	+	0.108475i
$842$	−19.5358	−	20.7068i	−0.673250	−	0.713603i
$843$		0			0
$844$	−14.6232	+	1.70920i	−0.503350	+	0.0588331i
$845$	−5.52579	−	4.63669i	−0.190093	−	0.159507i
$846$		0			0
$847$	10.4075	−	8.73293i	0.357606	−	0.300067i
$848$	2.90643	−	3.08063i	0.0998071	−	0.105789i
$849$		0			0
$850$	19.2935	+	9.68958i	0.661763	+	0.332350i
$851$	7.69886	+	3.86651i	0.263914	+	0.132542i
$852$		0			0
$853$	17.4593	−	18.5058i	0.597795	−	0.633625i	−0.355856	−	0.934541i	$-0.615811\pi$
$853$	17.4593	−	18.5058i	0.597795	−	0.633625i	0.953651	+	0.300916i	$0.0972922\pi$
$854$	−0.921540	+	0.773264i	−0.0315344	+	0.0264605i
$855$		0			0
$856$	2.48678	+	2.08666i	0.0849965	+	0.0713206i
$857$	−45.3387	+	5.29934i	−1.54874	+	0.181022i	−0.847071	−	0.531480i	$-0.821636\pi$
$857$	−45.3387	+	5.29934i	−1.54874	+	0.181022i	−0.701670	+	0.712502i	$0.747562\pi$
$858$		0			0
$859$	−11.0934	−	11.7583i	−0.378501	−	0.401188i	0.509916	−	0.860224i	$-0.329676\pi$
$859$	−11.0934	−	11.7583i	−0.378501	−	0.401188i	−0.888418	+	0.459036i	$0.848195\pi$
$860$	−28.6871	−	3.35304i	−0.978221	−	0.114338i
$861$		0			0
$862$	−1.59610	+	27.4040i	−0.0543635	+	0.933385i
$863$	20.5808	+	35.6470i	0.700578	+	1.21344i	0.968264	+	0.249931i	$0.0804079\pi$
$863$	20.5808	+	35.6470i	0.700578	+	1.21344i	−0.267685	+	0.963506i	$0.586259\pi$
$864$		0			0
$865$	2.26465	−	3.92248i	0.0770003	−	0.133368i
$866$	−3.18624	−	2.09562i	−0.108273	−	0.0712121i
$867$		0			0
$868$	0.978553	+	2.26854i	0.0332143	+	0.0769993i
$869$	47.3120	−	11.2131i	1.60495	−	0.380380i
$870$		0			0
$871$	1.99666	+	2.68198i	0.0676542	+	0.0908754i
$872$	−7.93631	+	2.88858i	−0.268758	+	0.0978197i
$873$		0			0
$874$	−15.7651	−	5.73802i	−0.533262	−	0.194091i
$875$	0.213062	+	0.711677i	0.00720282	+	0.0240591i
$876$		0			0
$877$	1.27082	+	21.8191i	0.0429125	+	0.736778i	0.949308	+	0.314348i	$0.101786\pi$
$877$	1.27082	+	21.8191i	0.0429125	+	0.736778i	−0.906395	+	0.422430i	$0.861177\pi$
$878$	4.60362	−	3.02785i	0.155365	−	0.102185i
$879$		0			0
$880$	−16.7131	−	3.96107i	−0.563397	−	0.133528i
$881$	−9.44504	−	53.5655i	−0.318212	−	1.80467i	−0.553619	−	0.832770i	$-0.686753\pi$
$881$	−9.44504	−	53.5655i	−0.318212	−	1.80467i	0.235407	−	0.971897i	$-0.424358\pi$
$882$		0			0
$883$	7.67767	−	43.5423i	0.258374	−	1.46531i	−0.528886	−	0.848693i	$-0.677390\pi$
$883$	7.67767	−	43.5423i	0.258374	−	1.46531i	0.787260	−	0.616621i	$-0.211499\pi$
$884$	−6.00187	+	13.9139i	−0.201865	+	0.467975i
$885$		0			0
$886$	7.40223	−	24.7252i	0.248683	−	0.830658i
$887$	−12.8442	+	17.2527i	−0.431265	+	0.579290i	−0.963635	−	0.267222i	$-0.913894\pi$
$887$	−12.8442	+	17.2527i	−0.431265	+	0.579290i	0.532370	+	0.846512i	$0.321302\pi$
$888$		0			0
$889$	−6.09386	+	3.06045i	−0.204382	+	0.102644i
$890$	−11.5028			−0.385576
$891$		0			0
$892$	10.3756			0.347402
$893$	22.2745	−	11.1867i	0.745386	−	0.374347i
$894$		0			0
$895$	6.72299	−	9.03054i	0.224725	−	0.301858i
$896$	0.199281	−	0.665645i	0.00665752	−	0.0222376i
$897$		0			0
$898$	−4.11339	+	9.53592i	−0.137266	+	0.318218i
$899$	0.851742	−	4.83047i	0.0284072	−	0.161105i
$900$		0			0
$901$	3.41035	+	19.3410i	0.113615	+	0.644344i
$902$	−61.0415	−	14.4671i	−2.03246	−	0.481702i
$903$		0			0
$904$	−9.71660	+	6.39071i	−0.323169	+	0.212552i
$905$	−4.00786	−	68.8123i	−0.133226	−	2.28740i
$906$		0			0
$907$	0.0159538	+	0.0532895i	0.000529738	+	0.00176945i	0.958254	−	0.285918i	$-0.0922986\pi$
$907$	0.0159538	+	0.0532895i	0.000529738	+	0.00176945i	−0.957724	+	0.287688i	$0.907113\pi$
$908$	−9.36123	−	3.40721i	−0.310663	−	0.113072i
$909$		0			0
$910$	6.63014	−	2.41318i	0.219787	−	0.0799960i
$911$	5.46199	+	7.33672i	0.180964	+	0.243076i	0.883344	−	0.468726i	$-0.155287\pi$
$911$	5.46199	+	7.33672i	0.180964	+	0.243076i	−0.702380	+	0.711802i	$0.747879\pi$
$912$		0			0
$913$	−48.8337	+	11.5738i	−1.61616	+	0.383037i
$914$	13.8558	+	32.1213i	0.458309	+	1.06248i
$915$		0			0
$916$	−17.4443	−	11.4733i	−0.576377	−	0.379089i
$917$	6.42166	−	11.1226i	0.212062	−	0.367302i
$918$		0			0
$919$	1.08222	+	1.87445i	0.0356990	+	0.0618325i	0.883323	−	0.468765i	$-0.155301\pi$
$919$	1.08222	+	1.87445i	0.0356990	+	0.0618325i	−0.847624	+	0.530598i	$0.821968\pi$
$920$	−1.27427	+	21.8783i	−0.0420113	+	0.721306i
$921$		0			0
$922$	−15.6563	−	1.82996i	−0.515613	−	0.0602665i
$923$	−26.4322	−	28.0165i	−0.870027	−	0.922175i
$924$		0			0
$925$	5.64906	−	0.660280i	0.185740	−	0.0217099i
$926$	−2.90671	−	2.43902i	−0.0955203	−	0.0801510i
$927$		0			0
$928$	−1.05675	+	0.886718i	−0.0346895	+	0.0291080i
$929$	−1.40707	+	1.49140i	−0.0461643	+	0.0489313i	−0.750044	−	0.661388i	$-0.769968\pi$
$929$	−1.40707	+	1.49140i	−0.0461643	+	0.0489313i	0.703880	+	0.710319i	$0.251449\pi$
$930$		0			0
$931$	−13.8541	−	6.95780i	−0.454050	−	0.228033i
$932$	10.3127	+	5.17921i	0.337803	+	0.169651i
$933$		0			0
$934$	27.5178	−	29.1672i	0.900412	−	0.954380i
$935$	61.0131	−	51.1961i	1.99534	−	1.67429i
$936$		0			0
$937$	34.7783	+	29.1825i	1.13616	+	0.953350i	0.999306	−	0.0372415i	$-0.0118571\pi$
$937$	34.7783	+	29.1825i	1.13616	+	0.953350i	0.136852	+	0.990592i	$0.456302\pi$
$938$	0.706142	−	0.0825361i	0.0230563	−	0.00269490i
$939$		0			0
$940$	−22.3441	−	23.6834i	−0.728786	−	0.772468i
$941$	−3.74125	−	0.437289i	−0.121961	−	0.0142552i	0.0548933	−	0.998492i	$-0.482518\pi$
$941$	−3.74125	−	0.437289i	−0.121961	−	0.0142552i	−0.176855	+	0.984237i	$0.556592\pi$
$942$		0			0
$943$	−4.65403	+	79.9066i	−0.151556	+	2.60212i
$944$	−2.87961	−	4.98763i	−0.0937232	−	0.162333i
$945$		0			0
$946$	−25.6881	+	44.4930i	−0.835191	+	1.44659i
$947$	13.4364	+	8.83729i	0.436626	+	0.287173i	0.748731	−	0.662874i	$-0.230664\pi$
$947$	13.4364	+	8.83729i	0.436626	+	0.287173i	−0.312105	+	0.950048i	$0.601034\pi$
$948$		0			0
$949$	11.1292	+	25.8004i	0.361269	+	0.837515i
$950$	−10.7770	+	2.55420i	−0.349652	+	0.0828691i
$951$		0			0
$952$	1.92406	+	2.58446i	0.0623591	+	0.0837628i
$953$	22.6638	−	8.24893i	0.734151	−	0.267209i	0.0522302	−	0.998635i	$-0.483367\pi$
$953$	22.6638	−	8.24893i	0.734151	−	0.267209i	0.681921	+	0.731426i	$0.261145\pi$
$954$		0			0
$955$	−17.0881	−	6.21956i	−0.552958	−	0.201260i
$956$	0.828667	+	2.76794i	0.0268010	+	0.0895216i
$957$		0			0
$958$	−1.31908	−	22.6477i	−0.0426175	−	0.731714i
$959$	−8.51817	+	5.60249i	−0.275066	+	0.180914i
$960$		0			0
$961$	−17.8625	−	4.23349i	−0.576209	−	0.136564i
$962$	0.693177	+	3.93120i	0.0223489	+	0.126747i
$963$		0			0
$964$	0.00920844	−	0.0522236i	0.000296584	−	0.00168201i
$965$	17.7856	−	41.2316i	0.572538	−	1.32729i
$966$		0			0
$967$	−5.39397	+	18.0171i	−0.173458	+	0.579392i	0.826408	+	0.563071i	$0.190380\pi$
$967$	−5.39397	+	18.0171i	−0.173458	+	0.579392i	−0.999867	+	0.0163204i	$0.994805\pi$
$968$	−11.6762	+	15.6838i	−0.375286	+	0.504097i
$969$		0			0
$970$	2.52685	−	1.26903i	0.0811324	−	0.0407462i
$971$	29.0121			0.931043			0.465522	−	0.885036i	$-0.345867\pi$
$971$	29.0121			0.931043			0.465522	+	0.885036i	$0.345867\pi$
$972$		0			0
$973$	8.90126			0.285361
$974$	24.2018	−	12.1546i	0.775477	−	0.389459i
$975$		0			0
$976$	1.03387	−	1.38873i	0.0330935	−	0.0444523i
$977$	−0.146593	+	0.489655i	−0.00468993	+	0.0156655i	−0.960302	−	0.278961i	$-0.910010\pi$
$977$	−0.146593	+	0.489655i	−0.00468993	+	0.0156655i	0.955613	+	0.294626i	$0.0951952\pi$
$978$		0			0
$979$	−8.10432	+	18.7879i	−0.259015	+	0.600464i
$980$	−3.51665	+	19.9439i	−0.112335	+	0.637084i
$981$		0			0
$982$	1.23480	+	7.00292i	0.0394042	+	0.223472i
$983$	34.0298	+	8.06522i	1.08538	+	0.257241i	0.734109	−	0.679032i	$-0.237600\pi$
$983$	34.0298	+	8.06522i	1.08538	+	0.257241i	0.351275	+	0.936272i	$0.385748\pi$
$984$		0			0
$985$	−12.4208	+	8.16929i	−0.395760	+	0.260295i
$986$	−0.371942	−	6.38600i	−0.0118451	−	0.203372i
$987$		0			0
$988$	−2.22946	−	7.44693i	−0.0709287	−	0.236918i
$989$	61.5989	+	22.4202i	1.95873	+	0.712920i
$990$		0			0
$991$	−7.26164	+	2.64302i	−0.230674	+	0.0839583i	−0.454771	−	0.890608i	$-0.650279\pi$
$991$	−7.26164	+	2.64302i	−0.230674	+	0.0839583i	0.224097	+	0.974567i	$0.428057\pi$
$992$	−2.12329	−	2.85207i	−0.0674145	−	0.0905534i
$993$		0			0
$994$	−7.96918	+	1.88873i	−0.252767	+	0.0599069i
$995$	19.1555	+	44.4075i	0.607271	+	1.40781i
$996$		0			0
$997$	2.97274	+	1.95520i	0.0941476	+	0.0619218i	0.595710	−	0.803200i	$-0.296871\pi$
$997$	2.97274	+	1.95520i	0.0941476	+	0.0619218i	−0.501562	+	0.865122i	$0.667241\pi$
$998$	14.8874	−	25.7857i	0.471252	−	0.816233i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.g.b.73.1		90
3.2	odd	2		162.2.g.b.25.1	yes	90
81.13	even	27	inner	486.2.g.b.253.1		90
81.68	odd	54		162.2.g.b.13.1	✓	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.13.1	✓	90	81.68	odd	54
162.2.g.b.25.1	yes	90	3.2	odd	2
486.2.g.b.73.1		90	1.1	even	1	trivial
486.2.g.b.253.1		90	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.893633 + 0.448799i) q^{2} +(0.597159 - 0.802123i) q^{4} +(-0.891212 + 2.97686i) q^{5} +(0.275210 - 0.638009i) q^{7} +(-0.173648 + 0.984808i) q^{8} +(-0.539594 - 3.06019i) q^{10} +(-5.37847 - 1.27472i) q^{11} +(-2.73022 + 1.79570i) q^{13} +(0.0404011 + 0.693660i) q^{14} +(-0.286803 - 0.957990i) q^{16} +(4.35745 + 1.58598i) q^{17} +(-2.23534 + 0.813599i) q^{19} +(1.85561 + 2.49252i) q^{20} +(5.37847 - 1.27472i) q^{22} +(-2.79341 - 6.47585i) q^{23} +(-3.88998 - 2.55848i) q^{25} +(1.63391 - 2.83001i) q^{26} +(-0.347418 - 0.601745i) q^{28} +(-0.0802101 + 1.37715i) q^{29} +(-3.53161 - 0.412786i) q^{31} +(0.686242 + 0.727374i) q^{32} +(-4.60574 + 0.538334i) q^{34} +(1.65399 + 1.38786i) q^{35} +(-0.935772 + 0.785206i) q^{37} +(1.63243 - 1.73028i) q^{38} +(-2.77687 - 1.39460i) q^{40} +(-10.1420 - 5.09352i) q^{41} +(-6.37841 + 6.76072i) q^{43} +(-4.23428 + 3.55299i) q^{44} +(5.40264 + 4.53335i) q^{46} +(-10.4074 + 1.21645i) q^{47} +(4.47238 + 4.74044i) q^{49} +(4.62445 + 0.540521i) q^{50} +(-0.190007 + 3.26229i) q^{52} +(2.11764 + 3.66786i) q^{53} +(8.58802 - 14.8749i) q^{55} +(0.580527 + 0.381818i) q^{56} +(-0.546388 - 1.26667i) q^{58} +(5.60397 - 1.32817i) q^{59} +(1.03387 + 1.38873i) q^{61} +(3.34122 - 1.21611i) q^{62} +(-0.939693 - 0.342020i) q^{64} +(-2.91232 - 9.72783i) q^{65} +(-0.0594932 - 1.02146i) q^{67} +(3.87424 - 2.54813i) q^{68} +(-2.10093 - 0.497930i) q^{70} +(2.04677 + 11.6078i) q^{71} +(1.49312 - 8.46788i) q^{73} +(0.483836 - 1.12166i) q^{74} +(-0.682248 + 2.27887i) q^{76} +(-2.29349 + 3.08070i) q^{77} +(-7.86088 + 3.94788i) q^{79} +3.10740 q^{80} +11.3492 q^{82} +(8.11371 - 4.07486i) q^{83} +(-8.60465 + 11.5580i) q^{85} +(2.66575 - 8.90423i) q^{86} +(2.18932 - 5.07541i) q^{88} +(0.642803 - 3.64552i) q^{89} +(0.394285 + 2.23610i) q^{91} +(-6.86253 - 1.62645i) q^{92} +(8.75447 - 5.75790i) q^{94} +(-0.429800 - 7.37939i) q^{95} +(0.260981 + 0.871736i) q^{97} +(-6.12417 - 2.22901i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 18 q^{13} + 9 q^{20} - 27 q^{23} - 18 q^{25} + 27 q^{26} - 18 q^{28} + 27 q^{29} + 54 q^{31} + 27 q^{35} + 18 q^{38} + 9 q^{41} - 36 q^{43} + 18 q^{46} + 27 q^{47} + 36 q^{52} + 27 q^{53} - 54 q^{55}+ \cdots - 36 q^{98}+O(q^{100}) \) 90 * q - 18 * q^13 + 9 * q^20 - 27 * q^23 - 18 * q^25 + 27 * q^26 - 18 * q^28 + 27 * q^29 + 54 * q^31 + 27 * q^35 + 18 * 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 + 45 * q^59 - 9 * q^65 + 81 * q^67 - 36 * q^68 - 72 * q^70 - 72 * q^71 - 36 * q^73 - 45 * q^74 - 18 * q^76 - 144 * q^77 - 99 * q^79 - 18 * q^80 + 72 * q^82 - 45 * q^83 - 117 * q^85 - 72 * q^86 - 18 * q^88 - 45 * q^89 - 63 * q^91 - 36 * q^92 - 72 * q^94 - 45 * q^95 + 117 * q^97 - 36 * q^98

Introduction

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