LMFDB - Embedded newform 486.2.g.b.469.2

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:	$90$
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			469.2
Character	$\chi$	$=$	486.469
Dual form			486.2.g.b.343.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.597159 + 0.802123i) q^{2} +(-0.286803 - 0.957990i) q^{4} +(-1.23282 - 0.810835i) q^{5} +(0.694984 + 0.736640i) q^{7} +(0.939693 + 0.342020i) q^{8} +O(q^{10})$	\(q+(-0.597159 + 0.802123i) q^{2} +(-0.286803 - 0.957990i) q^{4} +(-1.23282 - 0.810835i) q^{5} +(0.694984 + 0.736640i) q^{7} +(0.939693 + 0.342020i) q^{8} +(1.38658 - 0.504672i) q^{10} +(-0.261194 - 0.131176i) q^{11} +(1.36323 - 3.16033i) q^{13} +(-1.00589 + 0.117572i) q^{14} +(-0.835488 + 0.549509i) q^{16} +(1.92630 + 1.61636i) q^{17} +(3.04721 - 2.55692i) q^{19} +(-0.423196 + 1.41357i) q^{20} +(0.261194 - 0.131176i) q^{22} +(3.54079 - 3.75302i) q^{23} +(-1.11802 - 2.59186i) q^{25} +(1.72091 + 2.98070i) q^{26} +(0.506370 - 0.877058i) q^{28} +(9.88356 + 1.15522i) q^{29} +(1.32136 + 0.313167i) q^{31} +(0.0581448 - 0.998308i) q^{32} +(-2.44683 + 0.579909i) q^{34} +(-0.259493 - 1.47166i) q^{35} +(1.03595 - 5.87515i) q^{37} +(0.231292 + 3.97112i) q^{38} +(-0.881145 - 1.18358i) q^{40} +(-2.84830 - 3.82593i) q^{41} +(0.689149 + 11.8322i) q^{43} +(-0.0507544 + 0.287843i) q^{44} +(0.895970 + 5.08130i) q^{46} +(2.71368 - 0.643154i) q^{47} +(0.347378 - 5.96425i) q^{49} +(2.74663 + 0.650962i) q^{50} +(-3.41855 - 0.399571i) q^{52} +(-1.31648 + 2.28021i) q^{53} +(0.215641 + 0.373501i) q^{55} +(0.401126 + 0.929914i) q^{56} +(-6.82868 + 7.23798i) q^{58} +(-0.159662 + 0.0801851i) q^{59} +(-2.93491 + 9.80328i) q^{61} +(-1.04026 + 0.872879i) q^{62} +(0.766044 + 0.642788i) q^{64} +(-4.24313 + 2.79075i) q^{65} +(8.02516 - 0.938006i) q^{67} +(0.995986 - 2.30896i) q^{68} +(1.33541 + 0.670668i) q^{70} +(-13.2365 + 4.81768i) q^{71} +(-1.12990 - 0.411250i) q^{73} +(4.09397 + 4.33936i) q^{74} +(-3.32345 - 2.18587i) q^{76} +(-0.0848957 - 0.283571i) q^{77} +(5.40569 - 7.26110i) q^{79} +1.47556 q^{80} +4.76975 q^{82} +(7.45078 - 10.0081i) q^{83} +(-1.06417 - 3.55459i) q^{85} +(-9.90244 - 6.51294i) q^{86} +(-0.200577 - 0.212599i) q^{88} +(-10.6875 - 3.88993i) q^{89} +(3.27545 - 1.19217i) q^{91} +(-4.61086 - 2.31566i) q^{92} +(-1.10461 + 2.56077i) q^{94} +(-5.82989 + 0.681416i) q^{95} +(-8.36554 + 5.50211i) q^{97} +(4.57662 + 3.84024i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q+O(q^{10}) $ 90 * 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} - 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$245$
$\chi(n)$	$e\left(\frac{19}{27}\right)$

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 $

$2$	−0.597159	+	0.802123i	−0.422255	+	0.567187i
$2$	−0.597159	+	0.802123i	−0.422255	+	0.567187i
$3$		0			0
$3$		0			0
$4$	−0.286803	−	0.957990i	−0.143402	−	0.478995i
$5$	−1.23282	−	0.810835i	−0.551332	−	0.362617i	0.243070	−	0.970009i	$-0.421845\pi$
$5$	−1.23282	−	0.810835i	−0.551332	−	0.362617i	−0.794402	+	0.607392i	$0.792216\pi$
$6$		0			0
$7$	0.694984	+	0.736640i	0.262679	+	0.278424i	0.845267	−	0.534344i	$-0.179441\pi$
$7$	0.694984	+	0.736640i	0.262679	+	0.278424i	−0.582588	+	0.812768i	$0.697960\pi$
$8$	0.939693	+	0.342020i	0.332232	+	0.120922i
$9$		0			0
$10$	1.38658	−	0.504672i	0.438474	−	0.159591i
$11$	−0.261194	−	0.131176i	−0.0787529	−	0.0395512i	0.408987	−	0.912540i	$-0.365882\pi$
$11$	−0.261194	−	0.131176i	−0.0787529	−	0.0395512i	−0.487740	+	0.872989i	$0.662178\pi$
$12$		0			0
$13$	1.36323	−	3.16033i	0.378093	−	0.876518i	−0.617830	−	0.786312i	$-0.711988\pi$
$13$	1.36323	−	3.16033i	0.378093	−	0.876518i	0.995923	−	0.0902067i	$-0.0287528\pi$
$14$	−1.00589	+	0.117572i	−0.268836	+	0.0314224i
$15$		0			0
$16$	−0.835488	+	0.549509i	−0.208872	+	0.137377i
$17$	1.92630	+	1.61636i	0.467197	+	0.392025i	0.845771	−	0.533546i	$-0.179141\pi$
$17$	1.92630	+	1.61636i	0.467197	+	0.392025i	−0.378574	+	0.925571i	$0.623585\pi$
$18$		0			0
$19$	3.04721	−	2.55692i	0.699079	−	0.586597i	−0.222433	−	0.974948i	$-0.571400\pi$
$19$	3.04721	−	2.55692i	0.699079	−	0.586597i	0.921511	+	0.388351i	$0.126955\pi$
$20$	−0.423196	+	1.41357i	−0.0946296	+	0.316085i
$21$		0			0
$22$	0.261194	−	0.131176i	0.0556867	−	0.0279669i
$23$	3.54079	−	3.75302i	0.738306	−	0.782558i	−0.244013	−	0.969772i	$-0.578464\pi$
$23$	3.54079	−	3.75302i	0.738306	−	0.782558i	0.982319	+	0.187213i	$0.0599456\pi$
$24$		0			0
$25$	−1.11802	−	2.59186i	−0.223604	−	0.518372i
$26$	1.72091	+	2.98070i	0.337498	+	0.584564i
$27$		0			0
$28$	0.506370	−	0.877058i	0.0956949	−	0.165748i
$29$	9.88356	+	1.15522i	1.83533	+	0.214519i	0.962083	−	0.272756i	$-0.0879353\pi$
$29$	9.88356	+	1.15522i	1.83533	+	0.214519i	0.873248	+	0.487276i	$0.162009\pi$
$30$		0			0
$31$	1.32136	+	0.313167i	0.237322	+	0.0562465i	0.347556	−	0.937659i	$-0.387012\pi$
$31$	1.32136	+	0.313167i	0.237322	+	0.0562465i	−0.110233	+	0.993906i	$0.535160\pi$
$32$	0.0581448	−	0.998308i	0.0102787	−	0.176478i
$33$		0			0
$34$	−2.44683	+	0.579909i	−0.419628	+	0.0994536i
$35$	−0.259493	−	1.47166i	−0.0438624	−	0.248756i
$36$		0			0
$37$	1.03595	−	5.87515i	0.170309	−	0.965869i	−0.773112	−	0.634270i	$-0.781301\pi$
$37$	1.03595	−	5.87515i	0.170309	−	0.965869i	0.943420	−	0.331599i	$-0.107588\pi$
$38$	0.231292	+	3.97112i	0.0375205	+	0.644201i
$39$		0			0
$40$	−0.881145	−	1.18358i	−0.139321	−	0.187141i
$41$	−2.84830	−	3.82593i	−0.444829	−	0.597510i	0.521996	−	0.852948i	$-0.325188\pi$
$41$	−2.84830	−	3.82593i	−0.444829	−	0.597510i	−0.966825	+	0.255438i	$0.917780\pi$
$42$		0			0
$43$	0.689149	+	11.8322i	0.105094	+	1.80440i	0.479929	+	0.877307i	$0.340662\pi$
$43$	0.689149	+	11.8322i	0.105094	+	1.80440i	−0.374835	+	0.927092i	$0.622300\pi$
$44$	−0.0507544	+	0.287843i	−0.00765152	+	0.0433939i
$45$		0			0
$46$	0.895970	+	5.08130i	0.132104	+	0.749196i
$47$	2.71368	−	0.643154i	0.395831	−	0.0938137i	−0.0278795	−	0.999611i	$-0.508875\pi$
$47$	2.71368	−	0.643154i	0.395831	−	0.0938137i	0.423711	+	0.905798i	$0.360727\pi$
$48$		0			0
$49$	0.347378	−	5.96425i	0.0496254	−	0.852036i
$50$	2.74663	+	0.650962i	0.388431	+	0.0920600i
$51$		0			0
$52$	−3.41855	−	0.399571i	−0.474067	−	0.0554105i
$53$	−1.31648	+	2.28021i	−0.180832	+	0.313210i	−0.942164	−	0.335152i	$-0.891212\pi$
$53$	−1.31648	+	2.28021i	−0.180832	+	0.313210i	0.761332	+	0.648362i	$0.224546\pi$
$54$		0			0
$55$	0.215641	+	0.373501i	0.0290770	+	0.0503629i
$56$	0.401126	+	0.929914i	0.0536027	+	0.124265i
$57$		0			0
$58$	−6.82868	+	7.23798i	−0.896650	+	0.950394i
$59$	−0.159662	+	0.0801851i	−0.0207862	+	0.0104392i	−0.459162	−	0.888353i	$-0.651850\pi$
$59$	−0.159662	+	0.0801851i	−0.0207862	+	0.0104392i	0.438376	+	0.898792i	$0.355554\pi$
$60$		0			0
$61$	−2.93491	+	9.80328i	−0.375776	+	1.25518i	0.535903	+	0.844279i	$0.319971\pi$
$61$	−2.93491	+	9.80328i	−0.375776	+	1.25518i	−0.911680	+	0.410901i	$0.865214\pi$
$62$	−1.04026	+	0.872879i	−0.132113	+	0.110856i
$63$		0			0
$64$	0.766044	+	0.642788i	0.0957556	+	0.0803485i
$65$	−4.24313	+	2.79075i	−0.526295	+	0.346150i
$66$		0			0
$67$	8.02516	−	0.938006i	0.980429	−	0.114596i	0.389247	−	0.921134i	$-0.372735\pi$
$67$	8.02516	−	0.938006i	0.980429	−	0.114596i	0.591182	+	0.806538i	$0.298661\pi$
$68$	0.995986	−	2.30896i	0.120781	−	0.280002i
$69$		0			0
$70$	1.33541	+	0.670668i	0.159612	+	0.0801602i
$71$	−13.2365	+	4.81768i	−1.57088	+	0.571754i	−0.973196	−	0.229977i	$-0.926135\pi$
$71$	−13.2365	+	4.81768i	−1.57088	+	0.571754i	−0.597685	+	0.801731i	$0.703913\pi$
$72$		0			0
$73$	−1.12990	−	0.411250i	−0.132245	−	0.0481332i	0.275050	−	0.961430i	$-0.411306\pi$
$73$	−1.12990	−	0.411250i	−0.132245	−	0.0481332i	−0.407295	+	0.913297i	$0.633528\pi$
$74$	4.09397	+	4.33936i	0.475914	+	0.504440i
$75$		0			0
$76$	−3.32345	−	2.18587i	−0.381226	−	0.250736i
$77$	−0.0848957	−	0.283571i	−0.00967476	−	0.0323159i
$78$		0			0
$79$	5.40569	−	7.26110i	0.608187	−	0.816937i	−0.386236	−	0.922400i	$-0.626225\pi$
$79$	5.40569	−	7.26110i	0.608187	−	0.816937i	0.994423	+	0.105463i	$0.0336323\pi$
$80$	1.47556			0.164973
$81$		0			0
$82$	4.76975			0.526731
$83$	7.45078	−	10.0081i	0.817830	−	1.09854i	−0.175642	−	0.984454i	$-0.556200\pi$
$83$	7.45078	−	10.0081i	0.817830	−	1.09854i	0.993471	−	0.114082i	$-0.0363926\pi$
$84$		0			0
$85$	−1.06417	−	3.55459i	−0.115426	−	0.385549i
$86$	−9.90244	−	6.51294i	−1.06781	−	0.702308i
$87$		0			0
$88$	−0.200577	−	0.212599i	−0.0213816	−	0.0226631i
$89$	−10.6875	−	3.88993i	−1.13287	−	0.412332i	−0.293537	−	0.955948i	$-0.594833\pi$
$89$	−10.6875	−	3.88993i	−1.13287	−	0.412332i	−0.839334	+	0.543616i	$0.817055\pi$
$90$		0			0
$91$	3.27545	−	1.19217i	0.343361	−	0.124973i
$92$	−4.61086	−	2.31566i	−0.480716	−	0.241424i
$93$		0			0
$94$	−1.10461	+	2.56077i	−0.113932	+	0.264124i
$95$	−5.82989	+	0.681416i	−0.598134	+	0.0699118i
$96$		0			0
$97$	−8.36554	+	5.50211i	−0.849392	+	0.558654i	−0.897915	−	0.440168i	$-0.854919\pi$
$97$	−8.36554	+	5.50211i	−0.849392	+	0.558654i	0.0485231	+	0.998822i	$0.484549\pi$
$98$	4.57662	+	3.84024i	0.462309	+	0.387923i
$99$		0			0
$100$	−2.16232	+	1.81440i	−0.216232	+	0.181440i
$101$	−1.75773	+	5.87122i	−0.174901	+	0.584209i	0.824920	+	0.565250i	$0.191220\pi$
$101$	−1.75773	+	5.87122i	−0.174901	+	0.584209i	−0.999820	+	0.0189587i	$0.993965\pi$
$102$		0			0
$103$	3.43637	−	1.72581i	0.338595	−	0.170049i	−0.271374	−	0.962474i	$-0.587478\pi$
$103$	3.43637	−	1.72581i	0.338595	−	0.170049i	0.609969	+	0.792425i	$0.291182\pi$
$104$	2.36192	−	2.50349i	0.231605	−	0.245487i
$105$		0			0
$106$	−1.04286	−	2.41762i	−0.101292	−	0.234820i
$107$	−5.61980	−	9.73378i	−0.543286	−	0.941000i	−0.998713	−	0.0507261i	$-0.983846\pi$
$107$	−5.61980	−	9.73378i	−0.543286	−	0.941000i	0.455426	−	0.890274i	$-0.349487\pi$
$108$		0			0
$109$	−4.65880	+	8.06927i	−0.446232	+	0.772896i	−0.998137	−	0.0610106i	$-0.980568\pi$
$109$	−4.65880	+	8.06927i	−0.446232	+	0.772896i	0.551905	+	0.833907i	$0.313901\pi$
$110$	−0.428366	−	0.0500688i	−0.0408431	−	0.00477387i
$111$		0			0
$112$	−0.985441	−	0.233554i	−0.0931154	−	0.0220688i
$113$	0.369387	−	6.34212i	0.0347490	−	0.596617i	−0.935322	−	0.353797i	$-0.884890\pi$
$113$	0.369387	−	6.34212i	0.0347490	−	0.596617i	0.970071	−	0.242820i	$-0.0780725\pi$
$114$		0			0
$115$	−7.40822	+	1.75578i	−0.690820	+	0.163727i
$116$	−1.72795	−	9.79967i	−0.160436	−	0.909877i
$117$		0			0
$118$	0.0310250	−	0.175952i	0.00285608	−	0.0161977i
$119$	0.148074	+	2.54234i	0.0135739	+	0.233056i
$120$		0			0
$121$	−6.51773	−	8.75483i	−0.592521	−	0.795894i
$122$	−6.11083	−	8.20827i	−0.553248	−	0.743142i
$123$		0			0
$124$	−0.0789583	−	1.35566i	−0.00709067	−	0.121742i
$125$	−2.00441	+	11.3675i	−0.179279	+	1.01674i
$126$		0			0
$127$	1.81665	+	10.3027i	0.161202	+	0.914220i	0.952895	+	0.303301i	$0.0980888\pi$
$127$	1.81665	+	10.3027i	0.161202	+	0.914220i	−0.791693	+	0.610919i	$0.790800\pi$
$128$	−0.973045	+	0.230616i	−0.0860058	+	0.0203838i
$129$		0			0
$130$	0.295296	−	5.07003i	0.0258991	−	0.444671i
$131$	12.9203	+	3.06218i	1.12886	+	0.267544i	0.752281	−	0.658843i	$-0.228954\pi$
$131$	12.9203	+	3.06218i	1.12886	+	0.267544i	0.376575	+	0.926386i	$0.377102\pi$
$132$		0			0
$133$	4.00129	+	0.467684i	0.346956	+	0.0405533i
$134$	−4.03989	+	6.99730i	−0.348994	+	0.604475i
$135$		0			0
$136$	1.25731	+	2.17772i	0.107813	+	0.186738i
$137$	−7.16269	−	16.6050i	−0.611950	−	1.41866i	−0.889046	−	0.457817i	$-0.848631\pi$
$137$	−7.16269	−	16.6050i	−0.611950	−	1.41866i	0.277096	−	0.960842i	$-0.410628\pi$
$138$		0			0
$139$	−14.1586	+	15.0072i	−1.20092	+	1.27290i	−0.248314	+	0.968680i	$0.579876\pi$
$139$	−14.1586	+	15.0072i	−1.20092	+	1.27290i	−0.952603	+	0.304218i	$0.901605\pi$
$140$	−1.33541	+	0.670668i	−0.112863	+	0.0566818i
$141$		0			0
$142$	4.03990	−	13.4942i	0.339021	−	1.13241i
$143$	−0.770629	+	0.646635i	−0.0644433	+	0.0540743i
$144$		0			0
$145$	−11.2479	−	9.43812i	−0.934088	−	0.783793i
$146$	1.00460	−	0.660737i	0.0831415	−	0.0546830i
$147$		0			0
$148$	−5.92545	+	0.692586i	−0.487069	+	0.0569302i
$149$	−5.84986	+	13.5615i	−0.479239	+	1.11100i	0.491503	+	0.870876i	$0.336448\pi$
$149$	−5.84986	+	13.5615i	−0.479239	+	1.11100i	−0.970742	+	0.240125i	$0.922811\pi$
$150$		0			0
$151$	0.0952090	+	0.0478158i	0.00774800	+	0.00389119i	0.452669	−	0.891679i	$-0.350472\pi$
$151$	0.0952090	+	0.0478158i	0.00774800	+	0.00389119i	−0.444921	+	0.895570i	$0.646768\pi$
$152$	3.73796	−	1.36051i	0.303189	−	0.110352i
$153$		0			0
$154$	0.278155	+	0.101240i	0.0224144	+	0.00815817i
$155$	−1.37506	−	1.45748i	−0.110448	−	0.117068i
$156$		0			0
$157$	−19.3773	−	12.7447i	−1.54648	−	1.01714i	−0.981371	−	0.192121i	$-0.938464\pi$
$157$	−19.3773	−	12.7447i	−1.54648	−	1.01714i	−0.565110	−	0.825016i	$-0.691166\pi$
$158$	2.59624	+	8.67205i	0.206546	+	0.689912i
$159$		0			0
$160$	−0.881145	+	1.18358i	−0.0696607	+	0.0935705i
$161$	5.22542			0.411821
$162$		0			0
$163$	12.3733			0.969151			0.484575	−	0.874750i	$-0.338974\pi$
$163$	12.3733			0.969151			0.484575	+	0.874750i	$0.338974\pi$
$164$	−2.84830	+	3.82593i	−0.222415	+	0.298755i
$165$		0			0
$166$	3.57846	+	11.9529i	0.277742	+	0.927724i
$167$	7.87067	+	5.17662i	0.609051	+	0.400579i	0.816233	−	0.577723i	$-0.196059\pi$
$167$	7.87067	+	5.17662i	0.609051	+	0.400579i	−0.207182	+	0.978302i	$0.566429\pi$
$168$		0			0
$169$	0.791849	+	0.839311i	0.0609115	+	0.0645624i
$170$	3.48670	+	1.26905i	0.267418	+	0.0973321i
$171$		0			0
$172$	11.1375	−	4.05372i	0.849227	−	0.309093i
$173$	−8.30471	−	4.17078i	−0.631395	−	0.317099i	0.104163	−	0.994560i	$-0.466784\pi$
$173$	−8.30471	−	4.17078i	−0.631395	−	0.317099i	−0.735558	+	0.677462i	$0.763080\pi$
$174$		0			0
$175$	1.13226	−	2.62488i	0.0855910	−	0.198422i
$176$	0.290307	−	0.0339320i	0.0218827	−	0.00255772i
$177$		0			0
$178$	9.50233	−	6.24978i	0.712229	−	0.468441i
$179$	7.25336	+	6.08629i	0.542141	+	0.454911i	0.872269	−	0.489025i	$-0.162647\pi$
$179$	7.25336	+	6.08629i	0.542141	+	0.454911i	−0.330128	+	0.943936i	$0.607092\pi$
$180$		0			0
$181$	−15.8413	+	13.2924i	−1.17747	+	0.988017i	−0.177480	+	0.984124i	$0.556794\pi$
$181$	−15.8413	+	13.2924i	−1.17747	+	0.988017i	−0.999992	+	0.00389225i	$0.998761\pi$
$182$	−0.999700	+	3.33923i	−0.0741027	+	0.247520i
$183$		0			0
$184$	4.61086	−	2.31566i	0.339917	−	0.170713i
$185$	−6.04092	+	6.40300i	−0.444137	+	0.470758i
$186$		0			0
$187$	−0.291110	−	0.674869i	−0.0212881	−	0.0493513i
$188$	−1.39443	−	2.41522i	−0.101699	−	0.176148i
$189$		0			0
$190$	2.93479	−	5.08320i	0.212912	−	0.368774i
$191$	24.7404	+	2.89174i	1.79015	+	0.209239i	0.945399	−	0.325914i	$-0.105672\pi$
$191$	24.7404	+	2.89174i	1.79015	+	0.209239i	0.844755	+	0.535153i	$0.179746\pi$
$192$		0			0
$193$	18.9072	+	4.48109i	1.36097	+	0.322556i	0.845328	−	0.534248i	$-0.179405\pi$
$193$	18.9072	+	4.48109i	1.36097	+	0.322556i	0.515643	+	0.856804i	$0.327553\pi$
$194$	0.582191	−	9.99583i	0.0417989	−	0.717659i
$195$		0			0
$196$	−5.81332	+	1.37778i	−0.415237	+	0.0984130i
$197$	−0.819992	−	4.65040i	−0.0584220	−	0.331328i	0.941563	−	0.336837i	$-0.109357\pi$
$197$	−0.819992	−	4.65040i	−0.0584220	−	0.331328i	−0.999985	+	0.00550983i	$0.998246\pi$
$198$		0			0
$199$	2.01799	−	11.4446i	0.143051	−	0.811285i	−0.825860	−	0.563876i	$-0.809310\pi$
$199$	2.01799	−	11.4446i	0.143051	−	0.811285i	0.968911	−	0.247409i	$-0.0795792\pi$
$200$	−0.164126	−	2.81794i	−0.0116055	−	0.199258i
$201$		0			0
$202$	−3.65980	−	4.91597i	−0.257503	−	0.345886i
$203$	6.01793	+	8.08349i	0.422376	+	0.567350i
$204$		0			0
$205$	0.409227	+	7.02616i	0.0285817	+	0.490729i
$206$	−0.667745	+	3.78697i	−0.0465240	+	0.263851i
$207$		0			0
$208$	0.597665	+	3.38953i	0.0414406	+	0.235022i
$209$	−1.13132	+	0.268128i	−0.0782550	+	0.0185468i
$210$		0			0
$211$	−1.07665	+	18.4853i	−0.0741195	+	1.27258i	0.732195	+	0.681095i	$0.238496\pi$
$211$	−1.07665	+	18.4853i	−0.0741195	+	1.27258i	−0.806315	+	0.591487i	$0.798541\pi$
$212$	2.56198	+	0.607201i	0.175958	+	0.0417027i
$213$		0			0
$214$	11.1636	+	1.30484i	0.763128	+	0.0891968i
$215$	8.74440	−	15.1458i	0.596363	−	1.03293i
$216$		0			0
$217$	0.687630	+	1.19101i	0.0466793	+	0.0808510i
$218$	−3.69051	−	8.55557i	−0.249953	−	0.579456i
$219$		0			0
$220$	0.295964	−	0.313703i	0.0199539	−	0.0211499i
$221$	7.73424	−	3.88428i	0.520261	−	0.261285i
$222$		0			0
$223$	−0.596094	+	1.99109i	−0.0399174	+	0.133333i	−0.975626	−	0.219441i	$-0.929577\pi$
$223$	−0.596094	+	1.99109i	−0.0399174	+	0.133333i	0.935708	+	0.352775i	$0.114762\pi$
$224$	0.775804	−	0.650976i	0.0518356	−	0.0434952i
$225$		0			0
$226$	4.86658	+	4.08355i	0.323720	+	0.271634i
$227$	7.78356	−	5.11933i	0.516613	−	0.339782i	−0.264281	−	0.964446i	$-0.585134\pi$
$227$	7.78356	−	5.11933i	0.516613	−	0.339782i	0.780894	+	0.624664i	$0.214764\pi$
$228$		0			0
$229$	24.3104	−	2.84147i	1.60647	−	0.187770i	0.734949	−	0.678122i	$-0.237206\pi$
$229$	24.3104	−	2.84147i	1.60647	−	0.187770i	0.871524	+	0.490352i	$0.163132\pi$
$230$	3.01553	−	6.99079i	0.198838	−	0.460959i
$231$		0			0
$232$	8.89240	+	4.46593i	0.583815	+	0.293203i
$233$	−12.4662	+	4.53733i	−0.816689	+	0.297250i	−0.716384	−	0.697706i	$-0.754204\pi$
$233$	−12.4662	+	4.53733i	−0.816689	+	0.297250i	−0.100305	+	0.994957i	$0.531982\pi$
$234$		0			0
$235$	−3.86696	−	1.40746i	−0.252253	−	0.0918125i
$236$	0.122608	+	0.129957i	0.00798110	+	0.00845948i
$237$		0			0
$238$	−2.12769	−	1.39940i	−0.137918	−	0.0907099i
$239$	6.15279	+	20.5518i	0.397991	+	1.32938i	0.888872	+	0.458156i	$0.151490\pi$
$239$	6.15279	+	20.5518i	0.397991	+	1.32938i	−0.490881	+	0.871227i	$0.663325\pi$
$240$		0			0
$241$	11.8121	−	15.8665i	0.760887	−	1.02205i	−0.237825	−	0.971308i	$-0.576435\pi$
$241$	11.8121	−	15.8665i	0.760887	−	1.02205i	0.998712	−	0.0507402i	$-0.0161581\pi$
$242$	10.9146			0.701615
$243$		0			0
$244$	10.2332			0.655112
$245$	−5.26428	+	7.07115i	−0.336322	+	0.451759i
$246$		0			0
$247$	−3.92664	−	13.1159i	−0.249846	−	0.834543i
$248$	1.13456	+	0.746211i	0.0720445	+	0.0473844i
$249$		0			0
$250$	−7.92122	−	8.39601i	−0.500982	−	0.531010i
$251$	0.508965	+	0.185248i	0.0321256	+	0.0116928i	0.358033	−	0.933709i	$-0.383448\pi$
$251$	0.508965	+	0.185248i	0.0321256	+	0.0116928i	−0.325907	+	0.945402i	$0.605670\pi$
$252$		0			0
$253$	−1.41714	+	0.515797i	−0.0890948	+	0.0324279i
$254$	−9.34889	−	4.69519i	−0.586602	−	0.294602i
$255$		0			0
$256$	0.396080	−	0.918216i	0.0247550	−	0.0573885i
$257$	−7.83901	+	0.916248i	−0.488984	+	0.0571540i	−0.357013	−	0.934100i	$-0.616205\pi$
$257$	−7.83901	+	0.916248i	−0.488984	+	0.0571540i	−0.131971	+	0.991254i	$0.542131\pi$
$258$		0			0
$259$	5.04784	−	3.32002i	0.313658	−	0.206296i
$260$	3.89045	+	3.26447i	0.241275	+	0.202454i
$261$		0			0
$262$	−10.1717	+	8.53510i	−0.628412	+	0.527300i
$263$	−2.50201	+	8.35730i	−0.154281	+	0.515333i	−0.999828	−	0.0185680i	$-0.994089\pi$
$263$	−2.50201	+	8.35730i	−0.154281	+	0.515333i	0.845547	+	0.533901i	$0.179274\pi$
$264$		0			0
$265$	3.47184	−	1.74363i	0.213274	−	0.107110i
$266$	−2.76454	+	2.93025i	−0.169505	+	0.179665i
$267$		0			0
$268$	−3.20024	−	7.41899i	−0.195486	−	0.453187i
$269$	10.4195	+	18.0470i	0.635286	+	1.10035i	0.986455	+	0.164035i	$0.0524510\pi$
$269$	10.4195	+	18.0470i	0.635286	+	1.10035i	−0.351169	+	0.936312i	$0.614216\pi$
$270$		0			0
$271$	−5.05259	+	8.75134i	−0.306923	+	0.531606i	−0.977688	−	0.210064i	$-0.932633\pi$
$271$	−5.05259	+	8.75134i	−0.306923	+	0.531606i	0.670765	+	0.741670i	$0.265966\pi$
$272$	−2.49761	−	0.291928i	−0.151440	−	0.0177008i
$273$		0			0
$274$	17.5965	+	4.17045i	1.06304	+	0.251946i
$275$	−0.0479713	+	0.823635i	−0.00289278	+	0.0496671i
$276$		0			0
$277$	13.6284	−	3.23000i	0.818853	−	0.194072i	0.200219	−	0.979751i	$-0.435835\pi$
$277$	13.6284	−	3.23000i	0.818853	−	0.194072i	0.618634	+	0.785680i	$0.287687\pi$
$278$	−3.58272	−	20.3186i	−0.214878	−	1.21863i
$279$		0			0
$280$	0.259493	−	1.47166i	0.0155077	−	0.0879484i
$281$	1.20751	+	20.7322i	0.0720343	+	1.23678i	0.819734	+	0.572744i	$0.194121\pi$
$281$	1.20751	+	20.7322i	0.0720343	+	1.23678i	−0.747700	+	0.664037i	$0.768842\pi$
$282$		0			0
$283$	14.4041	+	19.3480i	0.856233	+	1.15012i	0.987319	+	0.158750i	$0.0507463\pi$
$283$	14.4041	+	19.3480i	0.856233	+	1.15012i	−0.131086	+	0.991371i	$0.541846\pi$
$284$	8.41156	+	11.2987i	0.499134	+	0.670453i
$285$		0			0
$286$	−0.0584928	−	1.00428i	−0.00345875	−	0.0593845i
$287$	0.838810	−	4.75713i	0.0495134	−	0.280804i
$288$		0			0
$289$	−1.85400	−	10.5145i	−0.109059	−	0.618502i
$290$	14.2873	−	3.38616i	0.838980	−	0.198842i
$291$		0			0
$292$	−0.0699142	+	1.20038i	−0.00409142	+	0.0702469i
$293$	0.633850	+	0.150225i	0.0370299	+	0.00877625i	0.249089	−	0.968481i	$-0.419869\pi$
$293$	0.633850	+	0.150225i	0.0370299	+	0.00877625i	−0.212059	+	0.977257i	$0.568017\pi$
$294$		0			0
$295$	0.261850	+	0.0306059i	0.0152455	+	0.00178195i
$296$	2.98289	−	5.16652i	0.173377	−	0.300298i
$297$		0			0
$298$	−7.38470	−	12.7907i	−0.427784	−	0.740944i
$299$	−7.03386	−	16.3063i	−0.406779	−	0.943019i
$300$		0			0
$301$	−8.23715	+	8.73087i	−0.474782	+	0.503239i
$302$	−0.0952090	+	0.0478158i	−0.00547866	+	0.00275149i
$303$		0			0
$304$	−1.14086	+	3.81074i	−0.0654329	+	0.218561i
$305$	11.5670	−	9.70590i	0.662327	−	0.555758i
$306$		0			0
$307$	−22.7388	−	19.0801i	−1.29777	−	1.08896i	−0.990526	−	0.137328i	$-0.956149\pi$
$307$	−22.7388	−	19.0801i	−1.29777	−	1.08896i	−0.307245	−	0.951631i	$-0.599407\pi$
$308$	−0.247310	+	0.162658i	−0.0140918	+	0.00926832i
$309$		0			0
$310$	1.99021	−	0.232622i	0.113036	−	0.0132120i
$311$	−7.73217	+	17.9252i	−0.438451	+	1.01644i	0.545517	+	0.838100i	$0.316333\pi$
$311$	−7.73217	+	17.9252i	−0.438451	+	1.01644i	−0.983968	+	0.178344i	$0.942926\pi$
$312$		0			0
$313$	6.93327	+	3.48202i	0.391891	+	0.196815i	0.633823	−	0.773478i	$-0.281485\pi$
$313$	6.93327	+	3.48202i	0.391891	+	0.196815i	−0.241932	+	0.970293i	$0.577781\pi$
$314$	21.7942	−	7.93242i	1.22992	−	0.447653i
$315$		0			0
$316$	−8.50642	−	3.09609i	−0.478524	−	0.174168i
$317$	−6.35622	−	6.73720i	−0.357001	−	0.378399i	0.523835	−	0.851819i	$-0.324501\pi$
$317$	−6.35622	−	6.73720i	−0.357001	−	0.378399i	−0.880837	+	0.473420i	$0.843019\pi$
$318$		0			0
$319$	−2.42999	−	1.59823i	−0.136053	−	0.0894835i
$320$	−0.423196	−	1.41357i	−0.0236574	−	0.0790212i
$321$		0			0
$322$	−3.12040	+	4.19143i	−0.173893	+	0.233579i
$323$	10.0028			0.556568
$324$		0			0
$325$	−9.71526			−0.538906
$326$	−7.38881	+	9.92490i	−0.409229	+	0.549689i
$327$		0			0
$328$	−1.36798	−	4.56937i	−0.0755341	−	0.252301i
$329$	2.35974	+	1.55202i	0.130097	+	0.0855659i
$330$		0			0
$331$	−14.0917	−	14.9364i	−0.774552	−	0.820978i	0.213200	−	0.977009i	$-0.431611\pi$
$331$	−14.0917	−	14.9364i	−0.774552	−	0.820978i	−0.987752	+	0.156031i	$0.950130\pi$
$332$	−11.7246	−	4.26741i	−0.643471	−	0.234204i
$333$		0			0
$334$	−8.85233	+	3.22198i	−0.484378	+	0.176299i
$335$	−10.6541	−	5.35069i	−0.582096	−	0.292340i
$336$		0			0
$337$	−2.49237	+	5.77797i	−0.135768	+	0.314746i	−0.972514	−	0.232846i	$-0.925196\pi$
$337$	−2.49237	+	5.77797i	−0.135768	+	0.314746i	0.836745	+	0.547592i	$0.184455\pi$
$338$	−1.14609	+	0.133959i	−0.0623391	+	0.00728640i
$339$		0			0
$340$	−3.10005	+	2.03894i	−0.168124	+	0.110577i
$341$	−0.304050	−	0.255128i	−0.0164652	−	0.0138160i
$342$		0			0
$343$	10.0656	−	8.44600i	0.543489	−	0.456041i
$344$	−3.39927	+	11.3544i	−0.183277	+	0.612187i
$345$		0			0
$346$	8.30471	−	4.17078i	0.446464	−	0.224223i
$347$	7.40994	−	7.85408i	0.397786	−	0.421629i	−0.497260	−	0.867601i	$-0.665661\pi$
$347$	7.40994	−	7.85408i	0.397786	−	0.421629i	0.895047	+	0.445972i	$0.147142\pi$
$348$		0			0
$349$	−3.58166	−	8.30322i	−0.191722	−	0.444461i	0.795057	−	0.606535i	$-0.207441\pi$
$349$	−3.58166	−	8.30322i	−0.191722	−	0.444461i	−0.986779	+	0.162074i	$0.948182\pi$
$350$	1.42934	+	2.47568i	0.0764012	+	0.132331i
$351$		0			0
$352$	−0.146142	+	0.253125i	−0.00778937	+	0.0134916i
$353$	−10.3434	−	1.20897i	−0.550523	−	0.0643469i	−0.163716	−	0.986508i	$-0.552348\pi$
$353$	−10.3434	−	1.20897i	−0.550523	−	0.0643469i	−0.386807	+	0.922161i	$0.626422\pi$
$354$		0			0
$355$	20.2245	+	4.79329i	1.07340	+	0.254402i
$356$	−0.661304	+	11.3541i	−0.0350490	+	0.601769i
$357$		0			0
$358$	−9.21336	+	2.18361i	−0.486941	+	0.115407i
$359$	2.29332	+	13.0061i	0.121037	+	0.686435i	0.983583	+	0.180456i	$0.0577575\pi$
$359$	2.29332	+	13.0061i	0.121037	+	0.686435i	−0.862546	+	0.505979i	$0.831131\pi$
$360$		0			0
$361$	−0.551625	+	3.12842i	−0.0290329	+	0.164654i
$362$	−1.20239	−	20.6443i	−0.0631965	−	1.08504i
$363$		0			0
$364$	−2.08149	−	2.79593i	−0.109100	−	0.146547i
$365$	1.05950	+	1.42316i	0.0554569	+	0.0744915i
$366$		0			0
$367$	−0.773313	−	13.2773i	−0.0403666	−	0.693068i	−0.956417	−	0.292005i	$-0.905678\pi$
$367$	−0.773313	−	13.2773i	−0.0403666	−	0.693068i	0.916050	−	0.401063i	$-0.131359\pi$
$368$	−0.895970	+	5.08130i	−0.0467057	+	0.264881i
$369$		0			0
$370$	−1.52861	−	8.66916i	−0.0794685	−	0.450688i
$371$	−2.59462	+	0.614937i	−0.134706	+	0.0319259i
$372$		0			0
$373$	−1.04263	+	17.9013i	−0.0539855	+	0.926896i	0.857222	+	0.514948i	$0.172189\pi$
$373$	−1.04263	+	17.9013i	−0.0539855	+	0.926896i	−0.911207	+	0.411948i	$0.864848\pi$
$374$	0.715167	+	0.169498i	0.0369804	+	0.00876451i
$375$		0			0
$376$	2.77000	+	0.323766i	0.142852	+	0.0166970i
$377$	17.1245	−	29.6605i	0.881956	−	1.52759i
$378$		0			0
$379$	8.70708	+	15.0811i	0.447253	+	0.774665i	0.998206	−	0.0598715i	$-0.0190691\pi$
$379$	8.70708	+	15.0811i	0.447253	+	0.774665i	−0.550953	+	0.834536i	$0.685736\pi$
$380$	2.32482	+	5.38954i	0.119261	+	0.276478i
$381$		0			0
$382$	−17.0935	+	18.1180i	−0.874579	+	0.927000i
$383$	6.49080	−	3.25980i	0.331664	−	0.166568i	−0.275172	−	0.961395i	$-0.588735\pi$
$383$	6.49080	−	3.25980i	0.331664	−	0.166568i	0.606836	+	0.794827i	$0.292438\pi$
$384$		0			0
$385$	−0.125269	+	0.418427i	−0.00638430	+	0.0213250i
$386$	−14.8850	+	12.4900i	−0.757626	+	0.635724i
$387$		0			0
$388$	7.67022	+	6.43608i	0.389397	+	0.326743i
$389$	−24.6039	+	16.1822i	−1.24747	+	0.820473i	−0.989338	−	0.145638i	$-0.953477\pi$
$389$	−24.6039	+	16.1822i	−1.24747	+	0.820473i	−0.258130	+	0.966110i	$0.583106\pi$
$390$		0			0
$391$	12.8869	−	1.50626i	0.651717	−	0.0761748i
$392$	2.36632	−	5.48575i	0.119517	−	0.277072i
$393$		0			0
$394$	4.21986	+	2.11929i	0.212594	+	0.106769i
$395$	−12.5518	+	4.56847i	−0.631548	+	0.229865i
$396$		0			0
$397$	−15.0174	−	5.46590i	−0.753704	−	0.274326i	−0.0635405	−	0.997979i	$-0.520239\pi$
$397$	−15.0174	−	5.46590i	−0.753704	−	0.274326i	−0.690164	+	0.723653i	$0.742461\pi$
$398$	7.97491	+	8.45291i	0.399746	+	0.423706i
$399$		0			0
$400$	2.35834	+	1.55111i	0.117917	+	0.0775553i
$401$	−9.90488	−	33.0846i	−0.494626	−	1.65217i	−0.732422	−	0.680851i	$-0.761610\pi$
$401$	−9.90488	−	33.0846i	−0.494626	−	1.65217i	0.237796	−	0.971315i	$-0.423575\pi$
$402$		0			0
$403$	2.79103	−	3.74900i	0.139031	−	0.186751i
$404$	6.12869			0.304914
$405$		0			0
$406$	−10.0776			−0.500144
$407$	−1.04126	+	1.39866i	−0.0516136	+	0.0693291i
$408$		0			0
$409$	−7.51744	−	25.1100i	−0.371713	−	1.24161i	−0.915477	−	0.402370i	$-0.868186\pi$
$409$	−7.51744	−	25.1100i	−0.371713	−	1.24161i	0.543764	−	0.839238i	$-0.316999\pi$
$410$	−5.88022	−	3.86748i	−0.290404	−	0.191001i
$411$		0			0
$412$	−2.63887	−	2.79704i	−0.130008	−	0.137800i
$413$	−0.170030	−	0.0618858i	−0.00836663	−	0.00304520i
$414$		0			0
$415$	−17.3004	+	6.29683i	−0.849243	+	0.309099i
$416$	−3.07572	−	1.54468i	−0.150800	−	0.0757344i
$417$		0			0
$418$	0.460506	−	1.06757i	0.0225241	−	0.0522167i
$419$	−24.6224	+	2.87794i	−1.20288	+	0.140597i	−0.693830	−	0.720139i	$-0.744078\pi$
$419$	−24.6224	+	2.87794i	−1.20288	+	0.140597i	−0.509052	+	0.860736i	$0.670004\pi$
$420$		0			0
$421$	−5.86400	+	3.85682i	−0.285794	+	0.187970i	−0.684309	−	0.729192i	$-0.739896\pi$
$421$	−5.86400	+	3.85682i	−0.285794	+	0.187970i	0.398515	+	0.917162i	$0.369526\pi$
$422$	−14.1846	−	11.9023i	−0.690494	−	0.579394i
$423$		0			0
$424$	−2.01696	+	1.69243i	−0.0979522	+	0.0821917i
$425$	2.03574	−	6.79983i	0.0987477	−	0.329840i
$426$		0			0
$427$	−9.26120	+	4.65115i	−0.448181	+	0.225085i
$428$	−7.71308	+	8.17539i	−0.372826	+	0.395172i
$429$		0			0
$430$	6.92696	+	16.0585i	0.334048	+	0.774410i
$431$	−3.67191	−	6.35994i	−0.176870	−	0.306347i	0.763937	−	0.645291i	$-0.223264\pi$
$431$	−3.67191	−	6.35994i	−0.176870	−	0.306347i	−0.940807	+	0.338943i	$0.889930\pi$
$432$		0			0
$433$	5.89605	−	10.2123i	0.283346	−	0.490770i	−0.688860	−	0.724894i	$-0.741889\pi$
$433$	5.89605	−	10.2123i	0.283346	−	0.490770i	0.972207	+	0.234124i	$0.0752221\pi$
$434$	−1.36596	−	0.159658i	−0.0655682	−	0.00766382i
$435$		0			0
$436$	9.06644	+	2.14879i	0.434204	+	0.102908i
$437$	1.19339	−	20.4897i	0.0570877	−	0.980157i
$438$		0			0
$439$	−11.0238	+	2.61268i	−0.526136	+	0.124696i	−0.485096	−	0.874461i	$-0.661215\pi$
$439$	−11.0238	+	2.61268i	−0.526136	+	0.124696i	−0.0410400	+	0.999158i	$0.513067\pi$
$440$	0.0748914	+	0.424730i	0.00357031	+	0.0202482i
$441$		0			0
$442$	−1.50290	+	8.52334i	−0.0714855	+	0.405414i
$443$	−0.214947	−	3.69050i	−0.0102124	−	0.175341i	−0.999557	−	0.0297502i	$-0.990529\pi$
$443$	−0.214947	−	3.69050i	−0.0102124	−	0.175341i	0.989345	−	0.145591i	$-0.0465082\pi$
$444$		0			0
$445$	10.0216	+	13.4614i	0.475070	+	0.638130i
$446$	−1.24114	−	1.66714i	−0.0587696	−	0.0789413i
$447$		0			0
$448$	0.0588856	+	1.01103i	0.00278208	+	0.0477665i
$449$	2.13648	−	12.1166i	0.100827	−	0.571817i	−0.891979	−	0.452078i	$-0.850683\pi$
$449$	2.13648	−	12.1166i	0.100827	−	0.571817i	0.992805	−	0.119739i	$-0.0382059\pi$
$450$		0			0
$451$	0.242086	+	1.37294i	0.0113994	+	0.0646491i
$452$	−6.18163	+	1.46507i	−0.290759	+	0.0689112i
$453$		0			0
$454$	−0.541688	+	9.30042i	−0.0254227	+	0.436491i
$455$	−5.00468	−	1.18613i	−0.234623	−	0.0556067i
$456$		0			0
$457$	3.08603	+	0.360705i	0.144358	+	0.0168731i	0.187965	−	0.982176i	$-0.439811\pi$
$457$	3.08603	+	0.360705i	0.144358	+	0.0168731i	−0.0436068	+	0.999049i	$0.513885\pi$
$458$	−12.2379	+	21.1967i	−0.571841	+	0.990457i
$459$		0			0
$460$	3.80672	+	6.59343i	0.177489	+	0.307420i
$461$	4.34834	+	10.0806i	0.202522	+	0.469499i	0.988962	−	0.148167i	$-0.0473374\pi$
$461$	4.34834	+	10.0806i	0.202522	+	0.469499i	−0.786440	+	0.617667i	$0.788078\pi$
$462$		0			0
$463$	−15.2156	+	16.1276i	−0.707128	+	0.749512i	−0.976966	−	0.213394i	$-0.931548\pi$
$463$	−15.2156	+	16.1276i	−0.707128	+	0.749512i	0.269838	+	0.962906i	$0.413030\pi$
$464$	−8.89240	+	4.46593i	−0.412819	+	0.207326i
$465$		0			0
$466$	3.80481	−	12.7089i	0.176254	−	0.588730i
$467$	11.3543	−	9.52736i	0.525413	−	0.440873i	−0.341101	−	0.940027i	$-0.610800\pi$
$467$	11.3543	−	9.52736i	0.525413	−	0.440873i	0.866514	+	0.499153i	$0.166355\pi$
$468$		0			0
$469$	6.26833	+	5.25975i	0.289445	+	0.242873i
$470$	3.43814	−	2.26130i	0.158590	−	0.104306i
$471$		0			0
$472$	−0.177458	+	0.0207419i	−0.00816816	+	0.000954721i
$473$	1.37211	−	3.18091i	0.0630896	−	0.146258i
$474$		0			0
$475$	−10.0340	−	5.03927i	−0.460392	−	0.231217i
$476$	2.39306	−	0.871004i	0.109686	−	0.0399224i
$477$		0			0
$478$	−20.1592	−	7.33736i	−0.922062	−	0.335603i
$479$	−0.0945719	−	0.100240i	−0.00432110	−	0.00458010i	0.725209	−	0.688528i	$-0.241743\pi$
$479$	−0.0945719	−	0.100240i	−0.00432110	−	0.00458010i	−0.729531	+	0.683948i	$0.760261\pi$
$480$		0			0
$481$	−17.1552	−	11.2831i	−0.782210	−	0.514467i
$482$	5.67313	+	18.9496i	0.258404	+	0.863130i
$483$		0			0
$484$	−6.51773	+	8.75483i	−0.296260	+	0.397947i
$485$	14.7745			0.670874
$486$		0			0
$487$	16.2267			0.735304			0.367652	−	0.929964i	$-0.380162\pi$
$487$	16.2267			0.735304			0.367652	+	0.929964i	$0.380162\pi$
$488$	−6.11083	+	8.20827i	−0.276624	+	0.371571i
$489$		0			0
$490$	−2.52833	−	8.44520i	−0.114218	−	0.381515i
$491$	−13.8751	−	9.12579i	−0.626174	−	0.411841i	0.196380	−	0.980528i	$-0.437081\pi$
$491$	−13.8751	−	9.12579i	−0.626174	−	0.411841i	−0.822554	+	0.568687i	$0.807452\pi$
$492$		0			0
$493$	17.1715	+	18.2007i	0.773365	+	0.819719i
$494$	12.8654	+	4.68261i	0.578841	+	0.210681i
$495$		0			0
$496$	−1.27606	+	0.464449i	−0.0572970	+	0.0208544i
$497$	−12.7480	−	6.40231i	−0.571828	−	0.287183i
$498$		0			0
$499$	−4.81631	+	11.1655i	−0.215608	+	0.499835i	−0.991355	−	0.131209i	$-0.958114\pi$
$499$	−4.81631	+	11.1655i	−0.215608	+	0.499835i	0.775747	+	0.631044i	$0.217373\pi$
$500$	11.4649	−	1.34005i	0.512724	−	0.0599289i
$501$		0			0
$502$	−0.452525	+	0.297630i	−0.0201972	+	0.0132839i
$503$	−23.2557	−	19.5138i	−1.03692	−	0.870079i	−0.0452612	−	0.998975i	$-0.514412\pi$
$503$	−23.2557	−	19.5138i	−1.03692	−	0.870079i	−0.991658	+	0.128897i	$0.958856\pi$
$504$		0			0
$505$	6.92755	−	5.81291i	0.308272	−	0.258671i
$506$	0.432525	−	1.44473i	0.0192281	−	0.0642262i
$507$		0			0
$508$	9.34889	−	4.69519i	0.414790	−	0.208315i
$509$	1.02916	−	1.09085i	0.0456167	−	0.0483509i	−0.704163	−	0.710038i	$-0.748678\pi$
$509$	1.02916	−	1.09085i	0.0456167	−	0.0483509i	0.749780	+	0.661687i	$0.230159\pi$
$510$		0			0
$511$	−0.482319	−	1.11814i	−0.0213365	−	0.0494637i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$		0			0
$514$	3.94619	−	6.83499i	0.174059	−	0.301479i
$515$	−5.63575	−	0.658725i	−0.248341	−	0.0290269i
$516$		0			0
$517$	−0.793163	−	0.187983i	−0.0348833	−	0.00826749i
$518$	−0.351299	+	6.03157i	−0.0154352	+	0.265012i
$519$		0			0
$520$	−4.94173	+	1.17121i	−0.216709	+	0.0513610i
$521$	7.06081	+	40.0438i	0.309340	+	1.75435i	0.602339	+	0.798240i	$0.294235\pi$
$521$	7.06081	+	40.0438i	0.309340	+	1.75435i	−0.293000	+	0.956113i	$0.594653\pi$
$522$		0			0
$523$	0.0742445	−	0.421062i	0.00324649	−	0.0184117i	−0.983141	−	0.182846i	$-0.941469\pi$
$523$	0.0742445	−	0.421062i	0.00324649	−	0.0184117i	0.986388	+	0.164435i	$0.0525800\pi$
$524$	−0.772062	−	13.2558i	−0.0337277	−	0.579082i
$525$		0			0
$526$	−5.20948	−	6.99755i	−0.227144	−	0.305108i
$527$	2.03914	+	2.73904i	0.0888264	+	0.119315i
$528$		0			0
$529$	−0.210621	−	3.61622i	−0.00915742	−	0.157227i
$530$	−0.674639	+	3.82607i	−0.0293045	+	0.166194i
$531$		0			0
$532$	−0.699547	−	3.96733i	−0.0303292	−	0.172005i
$533$	−15.9741	+	3.78593i	−0.691915	+	0.163987i
$534$		0			0
$535$	−0.964317	+	16.5567i	−0.0416910	+	0.715808i
$536$	7.86200	+	1.86333i	0.339587	+	0.0804835i
$537$		0			0
$538$	−20.6980	−	2.41925i	−0.892355	−	0.104301i
$539$	−0.873102	+	1.51226i	−0.0376072	+	0.0651375i
$540$		0			0
$541$	14.2644	+	24.7067i	0.613275	+	1.06222i	0.990685	+	0.136177i	$0.0434814\pi$
$541$	14.2644	+	24.7067i	0.613275	+	1.06222i	−0.377410	+	0.926046i	$0.623185\pi$
$542$	−4.00246	−	9.27874i	−0.171920	−	0.398556i
$543$		0			0
$544$	1.72563	−	1.82906i	0.0739858	−	0.0784204i
$545$	12.2863	−	6.17041i	0.526287	−	0.264311i
$546$		0			0
$547$	−4.21852	+	14.0909i	−0.180371	+	0.602481i	0.819209	+	0.573495i	$0.194413\pi$
$547$	−4.21852	+	14.0909i	−0.180371	+	0.602481i	−0.999580	+	0.0289859i	$0.990772\pi$
$548$	−13.8531	+	11.6241i	−0.591776	+	0.496559i
$549$		0			0
$550$	−0.632010	−	0.530320i	−0.0269490	−	0.0226129i
$551$	33.0711	−	21.7512i	1.40888	−	0.926633i
$552$		0			0
$553$	9.10568	−	1.06430i	0.387213	−	0.0452587i
$554$	−5.54748	+	12.8605i	−0.235690	+	0.546390i
$555$		0			0
$556$	18.4375	+	9.25966i	0.781924	+	0.392697i
$557$	33.4429	−	12.1722i	1.41702	−	0.515753i	0.483838	−	0.875157i	$-0.339242\pi$
$557$	33.4429	−	12.1722i	1.41702	−	0.515753i	0.933182	+	0.359404i	$0.117020\pi$
$558$		0			0
$559$	38.3333	+	13.9522i	1.62132	+	0.590114i
$560$	1.02549	+	1.08696i	0.0433350	+	0.0459324i
$561$		0			0
$562$	−17.3509	−	11.4118i	−0.731902	−	0.481380i
$563$	−2.19211	−	7.32215i	−0.0923864	−	0.308592i	0.899289	−	0.437355i	$-0.144085\pi$
$563$	−2.19211	−	7.32215i	−0.0923864	−	0.308592i	−0.991675	+	0.128763i	$0.958899\pi$
$564$		0			0
$565$	−5.59780	+	7.51916i	−0.235501	+	0.316333i
$566$	−24.1210			−1.01388
$567$		0			0
$568$	−14.0860			−0.591034
$569$	−3.14062	+	4.21859i	−0.131662	+	0.176852i	−0.863065	−	0.505093i	$-0.831458\pi$
$569$	−3.14062	+	4.21859i	−0.131662	+	0.176852i	0.731403	+	0.681945i	$0.238866\pi$
$570$		0			0
$571$	−10.8128	−	36.1171i	−0.452500	−	1.51145i	−0.814994	−	0.579469i	$-0.803260\pi$
$571$	−10.8128	−	36.1171i	−0.452500	−	1.51145i	0.362495	−	0.931986i	$-0.381925\pi$
$572$	0.840488	+	0.552798i	0.0351426	+	0.0231136i
$573$		0			0
$574$	3.31490	+	3.51359i	0.138361	+	0.146654i
$575$	−13.6860	−	4.98129i	−0.570744	−	0.207734i
$576$		0			0
$577$	−18.5516	+	6.75224i	−0.772314	+	0.281099i	−0.697964	−	0.716133i	$-0.745910\pi$
$577$	−18.5516	+	6.75224i	−0.772314	+	0.281099i	−0.0743500	+	0.997232i	$0.523688\pi$
$578$	9.54108	+	4.79171i	0.396856	+	0.199309i
$579$		0			0
$580$	−5.81568	+	13.4823i	−0.241483	+	0.559821i
$581$	12.5506	−	1.46695i	0.520685	−	0.0608594i
$582$		0			0
$583$	0.642965	−	0.422885i	0.0266289	−	0.0175141i
$584$	−0.921103	−	0.772897i	−0.0381155	−	0.0319827i
$585$		0			0
$586$	−0.499008	+	0.418717i	−0.0206138	+	0.0172971i
$587$	−1.45939	+	4.87471i	−0.0602356	+	0.201201i	−0.982811	−	0.184617i	$-0.940896\pi$
$587$	−1.45939	+	4.87471i	−0.0602356	+	0.201201i	0.922575	+	0.385818i	$0.126081\pi$
$588$		0			0
$589$	4.82719	−	2.42431i	0.198901	−	0.0998918i
$590$	−0.180916	+	0.191760i	−0.00744819	+	0.00789462i
$591$		0			0
$592$	2.36293	+	5.47788i	0.0971157	+	0.225140i
$593$	5.37983	+	9.31815i	0.220923	+	0.382650i	0.955089	−	0.296320i	$-0.0957596\pi$
$593$	5.37983	+	9.31815i	0.220923	+	0.382650i	−0.734165	+	0.678971i	$0.762426\pi$
$594$		0			0
$595$	1.87887	−	3.25430i	0.0770261	−	0.133413i
$596$	14.6695	+	1.71462i	0.600887	+	0.0702337i
$597$		0			0
$598$	17.2800	+	4.09544i	0.706632	+	0.167475i
$599$	−1.42782	+	24.5147i	−0.0583390	+	1.00164i	0.834426	+	0.551120i	$0.185799\pi$
$599$	−1.42782	+	24.5147i	−0.0583390	+	1.00164i	−0.892765	+	0.450522i	$0.851238\pi$
$600$		0			0
$601$	24.8634	−	5.89272i	1.01420	−	0.240369i	0.310276	−	0.950647i	$-0.399579\pi$
$601$	24.8634	−	5.89272i	1.01420	−	0.240369i	0.703922	+	0.710277i	$0.251431\pi$
$602$	−2.08435	−	11.8209i	−0.0849517	−	0.481785i
$603$		0			0
$604$	0.0185007	−	0.104923i	0.000752785	−	0.00426925i
$605$	0.936431	+	16.0779i	0.0380713	+	0.653659i
$606$		0			0
$607$	−20.3020	−	27.2703i	−0.824033	−	1.10687i	−0.992630	−	0.121183i	$-0.961331\pi$
$607$	−20.3020	−	27.2703i	−0.824033	−	1.10687i	0.168597	−	0.985685i	$-0.446076\pi$
$608$	−2.37541	−	3.19073i	−0.0963356	−	0.129401i
$609$		0			0
$610$	0.877970	+	15.0742i	0.0355480	+	0.610335i
$611$	1.66680	−	9.45291i	0.0674316	−	0.382424i
$612$		0			0
$613$	−1.14418	−	6.48896i	−0.0462129	−	0.262086i	0.952944	−	0.303147i	$-0.0980374\pi$
$613$	−1.14418	−	6.48896i	−0.0462129	−	0.262086i	−0.999157	+	0.0410607i	$0.986926\pi$
$614$	28.8832	−	6.84545i	1.16563	−	0.276260i
$615$		0			0
$616$	0.0172113	−	0.295506i	0.000693461	−	0.0119063i
$617$	−34.6803	−	8.21937i	−1.39618	−	0.330900i	−0.537432	−	0.843307i	$-0.680606\pi$
$617$	−34.6803	−	8.21937i	−1.39618	−	0.330900i	−0.858743	+	0.512407i	$0.828754\pi$
$618$		0			0
$619$	3.37117	+	0.394034i	0.135499	+	0.0158376i	0.183572	−	0.983006i	$-0.441234\pi$
$619$	3.37117	+	0.394034i	0.135499	+	0.0158376i	−0.0480731	+	0.998844i	$0.515308\pi$
$620$	−1.00188	+	1.73530i	−0.0402364	+	0.0696915i
$621$		0			0
$622$	−9.76087	−	16.9063i	−0.391375	−	0.677882i
$623$	−4.56216	−	10.5763i	−0.182779	−	0.423729i
$624$		0			0
$625$	2.00296	−	2.12301i	0.0801184	−	0.0849205i
$626$	−6.93327	+	3.48202i	−0.277109	+	0.139169i
$627$		0			0
$628$	−6.65179	+	22.2185i	−0.265435	+	0.886615i
$629$	11.4919	−	9.64286i	0.458213	−	0.384486i
$630$		0			0
$631$	30.5244	+	25.6130i	1.21516	+	1.01964i	0.999064	+	0.0432637i	$0.0137756\pi$
$631$	30.5244	+	25.6130i	1.21516	+	1.01964i	0.216092	+	0.976373i	$0.430669\pi$
$632$	7.56313	−	4.97435i	0.300845	−	0.197869i
$633$		0			0
$634$	9.19974	−	1.07530i	0.365368	−	0.0427054i
$635$	6.11423	−	14.1744i	0.242636	−	0.562493i
$636$		0			0
$637$	−18.3755	−	9.22850i	−0.728062	−	0.365647i
$638$	2.73306	−	0.994753i	0.108203	−	0.0393827i
$639$		0			0
$640$	1.38658	+	0.504672i	0.0548092	+	0.0199489i
$641$	2.73470	+	2.89862i	0.108014	+	0.114488i	0.779125	−	0.626869i	$-0.215664\pi$
$641$	2.73470	+	2.89862i	0.108014	+	0.114488i	−0.671110	+	0.741357i	$0.734182\pi$
$642$		0			0
$643$	−2.33370	−	1.53490i	−0.0920322	−	0.0605305i	0.502659	−	0.864485i	$-0.332355\pi$
$643$	−2.33370	−	1.53490i	−0.0920322	−	0.0605305i	−0.594691	+	0.803954i	$0.702726\pi$
$644$	−1.49867	−	5.00589i	−0.0590557	−	0.197260i
$645$		0			0
$646$	−5.97323	+	8.02344i	−0.235014	+	0.315678i
$647$	−33.0307			−1.29857			−0.649286	−	0.760544i	$-0.724932\pi$
$647$	−33.0307			−1.29857			−0.649286	+	0.760544i	$0.724932\pi$
$648$		0			0
$649$	0.0522210			0.00204986
$650$	5.80155	−	7.79283i	0.227556	−	0.305660i
$651$		0			0
$652$	−3.54870	−	11.8535i	−0.138978	−	0.464218i
$653$	32.8991	+	21.6381i	1.28744	+	0.846763i	0.994018	−	0.109220i	$-0.0348353\pi$
$653$	32.8991	+	21.6381i	1.28744	+	0.846763i	0.293423	+	0.955983i	$0.405206\pi$
$654$		0			0
$655$	−13.4455	−	14.2514i	−0.525358	−	0.556847i
$656$	4.48210	+	1.63135i	0.174997	+	0.0636936i
$657$		0			0
$658$	−2.65405	+	0.965996i	−0.103466	+	0.0376585i
$659$	7.78382	+	3.90918i	0.303215	+	0.152280i	0.593901	−	0.804538i	$-0.297587\pi$
$659$	7.78382	+	3.90918i	0.303215	+	0.152280i	−0.290686	+	0.956818i	$0.593884\pi$
$660$		0			0
$661$	−9.21346	+	21.3592i	−0.358362	+	0.830777i	0.639704	+	0.768621i	$0.279057\pi$
$661$	−9.21346	+	21.3592i	−0.358362	+	0.830777i	−0.998066	+	0.0621557i	$0.980202\pi$
$662$	20.3958	−	2.38393i	0.792706	−	0.0926541i
$663$		0			0
$664$	10.4244	−	6.85626i	0.404546	−	0.266074i
$665$	−4.55364	−	3.82096i	−0.176583	−	0.148170i
$666$		0			0
$667$	39.3312	−	33.0028i	1.52291	−	1.27787i
$668$	2.70182	−	9.02469i	0.104536	−	0.349176i
$669$		0			0
$670$	10.6541	−	5.35069i	0.411604	−	0.206715i
$671$	2.05254	−	2.17556i	0.0792373	−	0.0839867i
$672$		0			0
$673$	0.0541399	+	0.125510i	0.00208694	+	0.00483807i	0.919256	−	0.393659i	$-0.128791\pi$
$673$	0.0541399	+	0.125510i	0.00208694	+	0.00483807i	−0.917169	+	0.398497i	$0.869532\pi$
$674$	−3.14630	−	5.44955i	−0.121191	−	0.209909i
$675$		0			0
$676$	0.576946	−	0.999300i	0.0221902	−	0.0384346i
$677$	36.1462	+	4.22489i	1.38921	+	0.162376i	0.777589	−	0.628773i	$-0.216443\pi$
$677$	36.1462	+	4.22489i	1.38921	+	0.162376i	0.611624	+	0.791149i	$0.290517\pi$
$678$		0			0
$679$	−9.86699	−	2.33852i	−0.378660	−	0.0897442i
$680$	0.215745	−	3.70419i	0.00827343	−	0.142049i
$681$		0			0
$682$	0.386210	−	0.0915334i	0.0147887	−	0.00350500i
$683$	8.32718	+	47.2258i	0.318631	+	1.80704i	0.551099	+	0.834440i	$0.314209\pi$
$683$	8.32718	+	47.2258i	0.318631	+	1.80704i	−0.232468	+	0.972604i	$0.574680\pi$
$684$		0			0
$685$	−4.63363	+	26.2786i	−0.177042	+	1.00406i
$686$	0.764002	+	13.1174i	0.0291698	+	0.500825i
$687$		0			0
$688$	−7.07770	−	9.50700i	−0.269835	−	0.362451i
$689$	5.41154	+	7.26896i	0.206163	+	0.276925i
$690$		0			0
$691$	−2.10628	−	36.1634i	−0.0801267	−	1.37572i	−0.763573	−	0.645722i	$-0.776557\pi$
$691$	−2.10628	−	36.1634i	−0.0801267	−	1.37572i	0.683446	−	0.730001i	$-0.260480\pi$
$692$	−1.61375	+	9.15202i	−0.0613455	+	0.347907i
$693$		0			0
$694$	1.87503	+	10.6338i	0.0711751	+	0.403654i
$695$	29.6233	−	7.02086i	1.12368	−	0.266316i
$696$		0			0
$697$	0.697393	−	11.9738i	0.0264156	−	0.453539i
$698$	8.79902	+	2.08541i	0.333048	+	0.0789338i
$699$		0			0
$700$	−2.83934	−	0.331872i	−0.107317	−	0.0125436i
$701$	−11.2890	+	19.5531i	−0.426379	+	0.738510i	−0.996548	−	0.0830175i	$-0.973544\pi$
$701$	−11.2890	+	19.5531i	−0.426379	+	0.738510i	0.570169	+	0.821527i	$0.306878\pi$
$702$		0			0
$703$	−11.8655	−	20.5517i	−0.447516	−	0.775121i
$704$	−0.115767	−	0.268379i	−0.00436315	−	0.0101149i
$705$		0			0
$706$	7.14638	−	7.57472i	0.268958	−	0.285078i
$707$	−5.54657	+	2.78559i	−0.208600	+	0.104763i
$708$		0			0
$709$	2.33458	−	7.79803i	0.0876768	−	0.292861i	−0.902894	−	0.429864i	$-0.858562\pi$
$709$	2.33458	−	7.79803i	0.0876768	−	0.292861i	0.990571	+	0.137003i	$0.0437468\pi$
$710$	−15.9220	+	13.3602i	−0.597543	+	0.501398i
$711$		0			0
$712$	−8.71252	−	7.31067i	−0.326516	−	0.273979i
$713$	5.85396	−	3.85021i	0.219233	−	0.144192i
$714$		0			0
$715$	1.47436	−	0.172328i	0.0551379	−	0.00644469i
$716$	3.75032	−	8.69421i	0.140156	−	0.324918i
$717$		0			0
$718$	−11.8020	−	5.92717i	−0.440445	−	0.221200i
$719$	−35.9377	+	13.0803i	−1.34025	+	0.487811i	−0.909891	−	0.414847i	$-0.863835\pi$
$719$	−35.9377	+	13.0803i	−1.34025	+	0.487811i	−0.430359	+	0.902658i	$0.641613\pi$
$720$		0			0
$721$	3.65952	+	1.33196i	0.136288	+	0.0496047i
$722$	−2.17997	−	2.31063i	−0.0811301	−	0.0859929i
$723$		0			0
$724$	17.2773	+	11.3635i	0.642106	+	0.422320i
$725$	−8.05584	−	26.9084i	−0.299186	−	0.999352i
$726$		0			0
$727$	−7.07018	+	9.49690i	−0.262219	+	0.352221i	−0.913661	−	0.406478i	$-0.866757\pi$
$727$	−7.07018	+	9.49690i	−0.262219	+	0.352221i	0.651442	+	0.758698i	$0.274164\pi$
$728$	3.48566			0.129187
$729$		0			0
$730$	−1.77424			−0.0656675
$731$	−17.7977	+	23.9064i	−0.658270	+	0.884210i
$732$		0			0
$733$	−14.6597	−	48.9667i	−0.541467	−	1.80863i	−0.586899	−	0.809660i	$-0.699652\pi$
$733$	−14.6597	−	48.9667i	−0.541467	−	1.80863i	0.0454318	−	0.998967i	$-0.485534\pi$
$734$	11.1118	+	7.30835i	0.410144	+	0.269756i
$735$		0			0
$736$	−3.54079	−	3.75302i	−0.130515	−	0.138338i
$737$	−2.21916	−	0.807710i	−0.0817440	−	0.0297524i
$738$		0			0
$739$	39.7127	−	14.4542i	1.46086	−	0.531708i	0.515255	−	0.857037i	$-0.327697\pi$
$739$	39.7127	−	14.4542i	1.46086	−	0.531708i	0.945601	+	0.325329i	$0.105475\pi$
$740$	7.86656	+	3.95073i	0.289180	+	0.145232i
$741$		0			0
$742$	1.05615	−	2.44842i	0.0387723	−	0.0898843i
$743$	19.8229	−	2.31697i	0.727232	−	0.0850012i	0.255582	−	0.966787i	$-0.417733\pi$
$743$	19.8229	−	2.31697i	0.727232	−	0.0850012i	0.471650	+	0.881786i	$0.343659\pi$
$744$		0			0
$745$	18.2079	−	11.9756i	0.667087	−	0.438750i
$746$	−13.7365	−	11.5263i	−0.502927	−	0.422006i
$747$		0			0
$748$	−0.563026	+	0.472435i	−0.0205863	+	0.0172739i
$749$	3.26462	−	10.9046i	0.119287	−	0.398445i
$750$		0			0
$751$	12.7486	−	6.40258i	0.465203	−	0.233634i	−0.200728	−	0.979647i	$-0.564331\pi$
$751$	12.7486	−	6.40258i	0.465203	−	0.233634i	0.665931	+	0.746013i	$0.268035\pi$
$752$	−1.91383	+	2.02854i	−0.0697902	+	0.0739733i
$753$		0			0
$754$	13.5653	+	31.4480i	0.494020	+	1.14527i
$755$	−0.0786044	−	0.136147i	−0.00286071	−	0.00495489i
$756$		0			0
$757$	12.8586	−	22.2718i	0.467354	−	0.809481i	−0.531950	−	0.846776i	$-0.678541\pi$
$757$	12.8586	−	22.2718i	0.467354	−	0.809481i	0.999304	+	0.0372945i	$0.0118740\pi$
$758$	−17.2964	−	2.02166i	−0.628234	−	0.0734300i
$759$		0			0
$760$	−5.71136	−	1.35362i	−0.207173	−	0.0491009i
$761$	1.46071	−	25.0794i	0.0529506	−	0.909127i	−0.862339	−	0.506331i	$-0.831001\pi$
$761$	1.46071	−	25.0794i	0.0529506	−	0.909127i	0.915290	−	0.402796i	$-0.131962\pi$
$762$		0			0
$763$	−9.18194	+	2.17616i	−0.332409	+	0.0787823i
$764$	−4.32538	−	24.5304i	−0.156487	−	0.887480i
$765$		0			0
$766$	−1.26127	+	7.15304i	−0.0455717	+	0.258450i
$767$	0.0357553	+	0.613895i	0.00129105	+	0.0221665i
$768$		0			0
$769$	−16.8641	−	22.6525i	−0.608136	−	0.816869i	0.386282	−	0.922381i	$-0.373759\pi$
$769$	−16.8641	−	22.6525i	−0.608136	−	0.816869i	−0.994418	+	0.105512i	$0.966352\pi$
$770$	−0.260825	−	0.350349i	−0.00939948	−	0.0126257i
$771$		0			0
$772$	−1.12981	−	19.3981i	−0.0406628	−	0.698153i
$773$	−2.38629	+	13.5333i	−0.0858288	+	0.486759i	0.911346	+	0.411641i	$0.135044\pi$
$773$	−2.38629	+	13.5333i	−0.0858288	+	0.486759i	−0.997175	+	0.0751178i	$0.976067\pi$
$774$		0			0
$775$	−0.665616	−	3.77489i	−0.0239096	−	0.135598i
$776$	−9.74287	+	2.30910i	−0.349749	+	0.0828920i
$777$		0			0
$778$	1.71228	−	29.3987i	0.0613883	−	1.05400i
$779$	−18.4619	−	4.37556i	−0.661468	−	0.156771i
$780$		0			0
$781$	4.08925	+	0.477965i	0.146325	+	0.0171029i
$782$	−6.48730	+	11.2363i	−0.231985	+	0.401810i
$783$		0			0
$784$	2.98718	+	5.17395i	0.106685	+	0.184784i
$785$	13.5549	+	31.4237i	0.483793	+	1.12156i
$786$		0			0
$787$	−20.0808	+	21.2844i	−0.715802	+	0.758706i	−0.978517	−	0.206168i	$-0.933901\pi$
$787$	−20.0808	+	21.2844i	−0.715802	+	0.758706i	0.262715	+	0.964874i	$0.415382\pi$
$788$	−4.21986	+	2.11929i	−0.150326	+	0.0754967i
$789$		0			0
$790$	3.83092	−	12.7962i	0.136298	−	0.455267i
$791$	4.92858	−	4.13557i	0.175240	−	0.147044i
$792$		0			0
$793$	26.9806	+	22.6394i	0.958111	+	0.803950i
$794$	13.3521	−	8.78183i	0.473849	−	0.311656i
$795$		0			0
$796$	−11.5426	+	1.34913i	−0.409115	+	0.0478187i
$797$	3.97697	−	9.21966i	0.140872	−	0.326577i	−0.833145	−	0.553055i	$-0.813462\pi$
$797$	3.97697	−	9.21966i	0.140872	−	0.326577i	0.974016	+	0.226478i	$0.0727211\pi$
$798$		0			0
$799$	6.26694	+	3.14738i	0.221709	+	0.111346i
$800$	−2.65248	+	0.965424i	−0.0937794	+	0.0341329i
$801$		0			0
$802$	32.4527	+	11.8118i	1.14594	+	0.417090i
$803$	0.241176	+	0.255632i	0.00851093	+	0.00902106i
$804$		0			0
$805$	−6.44197	−	4.23695i	−0.227050	−	0.149333i
$806$	1.34047	+	4.47750i	0.0472162	+	0.157713i
$807$		0			0
$808$	−3.65980	+	4.91597i	−0.128751	+	0.172943i
$809$	−37.5147			−1.31895			−0.659473	−	0.751728i	$-0.729221\pi$
$809$	−37.5147			−1.31895			−0.659473	+	0.751728i	$0.729221\pi$
$810$		0			0
$811$	−33.8326			−1.18802			−0.594012	−	0.804456i	$-0.702457\pi$
$811$	−33.8326			−1.18802			−0.594012	+	0.804456i	$0.702457\pi$
$812$	6.01793	−	8.08349i	0.211188	−	0.283675i
$813$		0			0
$814$	−0.500098	−	1.67044i	−0.0175284	−	0.0585491i
$815$	−15.2540	−	10.0327i	−0.534324	−	0.351430i
$816$		0			0
$817$	32.3540	+	34.2932i	1.13192	+	1.19977i
$818$	24.6304	+	8.96473i	0.861182	+	0.313445i
$819$		0			0
$820$	6.61362	−	2.40716i	0.230958	−	0.0840618i
$821$	49.8792	+	25.0503i	1.74080	+	0.874261i	0.972072	+	0.234682i	$0.0754050\pi$
$821$	49.8792	+	25.0503i	1.74080	+	0.874261i	0.768725	+	0.639579i	$0.220891\pi$
$822$		0			0
$823$	−6.48460	+	15.0330i	−0.226039	+	0.524017i	−0.993061	−	0.117604i	$-0.962479\pi$
$823$	−6.48460	+	15.0330i	−0.226039	+	0.524017i	0.767022	+	0.641621i	$0.221738\pi$
$824$	3.81939	−	0.446423i	0.133055	−	0.0155519i
$825$		0			0
$826$	0.151175	−	0.0994293i	0.00526005	−	0.00345959i
$827$	16.8499	+	14.1387i	0.585927	+	0.491651i	0.886888	−	0.461985i	$-0.152863\pi$
$827$	16.8499	+	14.1387i	0.585927	+	0.491651i	−0.300960	+	0.953637i	$0.597307\pi$
$828$		0			0
$829$	−17.8569	+	14.9837i	−0.620195	+	0.520405i	−0.897865	−	0.440271i	$-0.854882\pi$
$829$	−17.8569	+	14.9837i	−0.620195	+	0.520405i	0.277670	+	0.960677i	$0.410438\pi$
$830$	5.28025	−	17.6373i	0.183280	−	0.612198i
$831$		0			0
$832$	3.07572	−	1.54468i	0.106631	−	0.0535523i
$833$	10.3095	−	10.9275i	0.357204	−	0.378614i
$834$		0			0
$835$	−5.50570	−	12.7636i	−0.190533	−	0.441704i
$836$	0.581330	+	1.00689i	0.0201057	+	0.0348241i
$837$		0			0
$838$	12.3950	−	21.4688i	0.428178	−	0.741626i
$839$	−33.9198	−	3.96466i	−1.17104	−	0.136875i	−0.491745	−	0.870739i	$-0.663641\pi$
$839$	−33.9198	−	3.96466i	−1.17104	−	0.136875i	−0.679296	+	0.733864i	$0.737715\pi$
$840$		0			0
$841$	68.1319	+	16.1476i	2.34938	+	0.556813i
$842$	0.408099	−	7.00678i	0.0140640	−	0.241470i
$843$		0			0
$844$	18.0175	−	4.27023i	0.620189	−	0.146987i
$845$	−0.295661	−	1.67678i	−0.0101710	−	0.0576828i
$846$		0			0
$847$	1.91944	−	10.8857i	0.0659528	−	0.374037i
$848$	−0.153093	−	2.62850i	−0.00525722	−	0.0902631i
$849$		0			0
$850$	4.23864	+	5.69349i	0.145384	+	0.195285i
$851$	−18.3815	−	24.6906i	−0.630109	−	0.846383i
$852$		0			0
$853$	2.03057	+	34.8635i	0.0695253	+	1.19370i	0.835005	+	0.550243i	$0.185465\pi$
$853$	2.03057	+	34.8635i	0.0695253	+	1.19370i	−0.765479	+	0.643461i	$0.777498\pi$
$854$	1.79961	−	10.2061i	0.0615814	−	0.349245i
$855$		0			0
$856$	−1.95174	−	11.0688i	−0.0667089	−	0.378325i
$857$	−16.9001	+	4.00540i	−0.577297	+	0.136822i	−0.508884	−	0.860835i	$-0.669942\pi$
$857$	−16.9001	+	4.00540i	−0.577297	+	0.136822i	−0.0684129	+	0.997657i	$0.521794\pi$
$858$		0			0
$859$	−2.56080	+	43.9673i	−0.0873734	+	1.50014i	0.615109	+	0.788442i	$0.289112\pi$
$859$	−2.56080	+	43.9673i	−0.0873734	+	1.50014i	−0.702482	+	0.711702i	$0.747925\pi$
$860$	−17.0174	−	4.03320i	−0.580288	−	0.137531i
$861$		0			0
$862$	7.29417	+	0.852566i	0.248440	+	0.0290385i
$863$	−0.797525	+	1.38135i	−0.0271481	+	0.0470218i	−0.879280	−	0.476305i	$-0.841976\pi$
$863$	−0.797525	+	1.38135i	−0.0271481	+	0.0470218i	0.852132	+	0.523327i	$0.175309\pi$
$864$		0			0
$865$	6.85636	+	11.8756i	0.233123	+	0.403781i
$866$	4.67062	+	10.8277i	0.158714	+	0.367940i
$867$		0			0
$868$	0.943760	−	1.00033i	0.0320333	−	0.0339533i
$869$	−2.36442	+	1.18745i	−0.0802073	+	0.0402816i
$870$		0			0
$871$	7.97576	−	26.6409i	0.270248	−	0.902692i
$872$	−7.13769	+	5.98923i	−0.241713	+	0.202821i
$873$		0			0
$874$	15.7227	+	13.1929i	0.531827	+	0.446256i
$875$	−9.76682	+	6.42374i	−0.330179	+	0.217162i
$876$		0			0
$877$	−46.7884	+	5.46879i	−1.57993	+	0.184668i	−0.860337	−	0.509725i	$-0.829747\pi$
$877$	−46.7884	+	5.46879i	−1.57993	+	0.184668i	−0.719596	+	0.694393i	$0.755673\pi$
$878$	4.48725	−	10.4026i	0.151437	−	0.351071i
$879$		0			0
$880$	−0.385408	−	0.193559i	−0.0129921	−	0.00652488i
$881$	28.9882	−	10.5508i	0.976638	−	0.355467i	0.196106	−	0.980583i	$-0.437170\pi$
$881$	28.9882	−	10.5508i	0.976638	−	0.355467i	0.780532	+	0.625116i	$0.214948\pi$
$882$		0			0
$883$	38.2989	+	13.9397i	1.28886	+	0.469107i	0.893353	−	0.449356i	$-0.148347\pi$
$883$	38.2989	+	13.9397i	1.28886	+	0.469107i	0.395507	+	0.918463i	$0.370569\pi$
$884$	−5.93931	−	6.29530i	−0.199760	−	0.211734i
$885$		0			0
$886$	3.08859	+	2.03140i	0.103763	+	0.0682461i
$887$	−0.776268	−	2.59292i	−0.0260645	−	0.0870616i	0.943968	−	0.330038i	$-0.107062\pi$
$887$	−0.776268	−	2.59292i	−0.0260645	−	0.0870616i	−0.970032	+	0.242976i	$0.921876\pi$
$888$		0			0
$889$	−6.32687	+	8.49846i	−0.212196	+	0.285029i
$890$	−16.7822			−0.562539
$891$		0			0
$892$	2.07841			0.0695902
$893$	6.62467	−	8.89848i	0.221686	−	0.297776i
$894$		0			0
$895$	−4.00707	−	13.3846i	−0.133942	−	0.447396i
$896$	−0.846132	−	0.556509i	−0.0282673	−	0.0185917i
$897$		0			0
$898$	8.44317	+	8.94924i	0.281752	+	0.298640i
$899$	12.6979	+	4.62167i	0.423499	+	0.154141i
$900$		0			0
$901$	−6.22157	+	2.26447i	−0.207271	+	0.0754403i
$902$	−1.24583	−	0.625679i	−0.0414816	−	0.0208328i
$903$		0			0
$904$	2.51624	−	5.83331i	0.0836890	−	0.194013i
$905$	30.3073	−	3.54242i	1.00745	−	0.117754i
$906$		0			0
$907$	−21.2759	+	13.9934i	−0.706456	+	0.464643i	−0.851211	−	0.524824i	$-0.824131\pi$
$907$	−21.2759	+	13.9934i	−0.706456	+	0.464643i	0.144755	+	0.989468i	$0.453761\pi$
$908$	−7.13661	−	5.98833i	−0.236837	−	0.198730i
$909$		0			0
$910$	3.94001	−	3.30606i	0.130610	−	0.109595i
$911$	−4.39134	+	14.6681i	−0.145492	+	0.485976i	−0.999407	−	0.0344360i	$-0.989037\pi$
$911$	−4.39134	+	14.6681i	−0.145492	+	0.485976i	0.853915	+	0.520412i	$0.174222\pi$
$912$		0			0
$913$	−3.25893	+	1.63670i	−0.107855	+	0.0541667i
$914$	−2.13218	+	2.25998i	−0.0705262	+	0.0747534i
$915$		0			0
$916$	−9.69439	−	22.4741i	−0.320312	−	0.742566i
$917$	6.72371	+	11.6458i	0.222036	+	0.384578i
$918$		0			0
$919$	−27.4733	+	47.5851i	−0.906260	+	1.56969i	−0.0870420	+	0.996205i	$0.527741\pi$
$919$	−27.4733	+	47.5851i	−0.906260	+	1.56969i	−0.819218	+	0.573483i	$0.805592\pi$
$920$	−7.56196	−	0.883867i	−0.249311	−	0.0291402i
$921$		0			0
$922$	−10.6825	−	2.53180i	−0.351810	−	0.0833805i
$923$	−2.81894	+	48.3993i	−0.0927865	+	1.59308i
$924$		0			0
$925$	−16.3858	+	3.88350i	−0.538761	+	0.127689i
$926$	−3.85019	−	21.8355i	−0.126525	−	0.717559i
$927$		0			0
$928$	1.72795	−	9.79967i	0.0567226	−	0.321690i
$929$	−0.0571022	−	0.980406i	−0.00187346	−	0.0321661i	0.997242	−	0.0742203i	$-0.0236468\pi$
$929$	−0.0571022	−	0.980406i	−0.00187346	−	0.0321661i	−0.999115	+	0.0420542i	$0.986610\pi$
$930$		0			0
$931$	−14.1915	−	19.0626i	−0.465109	−	0.624750i
$932$	7.92207	+	10.6412i	0.259496	+	0.348563i
$933$		0			0
$934$	0.861819	+	14.7969i	0.0281996	+	0.484168i
$935$	−0.188323	+	1.06803i	−0.00615881	+	0.0349283i
$936$		0			0
$937$	−2.79599	−	15.8568i	−0.0913410	−	0.518021i	−0.995807	−	0.0914755i	$-0.970842\pi$
$937$	−2.79599	−	15.8568i	−0.0913410	−	0.518021i	0.904466	−	0.426545i	$-0.140269\pi$
$938$	−7.96216	+	1.88707i	−0.259974	+	0.0616149i
$939$		0			0
$940$	−0.239274	+	4.10817i	−0.00780425	+	0.133994i
$941$	−7.68558	−	1.82152i	−0.250543	−	0.0593797i	0.103425	−	0.994637i	$-0.467020\pi$
$941$	−7.68558	−	1.82152i	−0.250543	−	0.0593797i	−0.353968	+	0.935257i	$0.615168\pi$
$942$		0			0
$943$	−24.4440	−	2.85709i	−0.796006	−	0.0930398i
$944$	0.0893330	−	0.154729i	0.00290754	−	0.00503601i
$945$		0			0
$946$	1.73211	+	3.00011i	0.0563158	+	0.0975418i
$947$	9.40975	+	21.8143i	0.305776	+	0.708868i	0.999940	−	0.0109485i	$-0.00348509\pi$
$947$	9.40975	+	21.8143i	0.305776	+	0.708868i	−0.694164	+	0.719817i	$0.744226\pi$
$948$		0			0
$949$	−2.84000	+	3.01023i	−0.0921904	+	0.0977162i
$950$	10.0340	−	5.03927i	0.325546	−	0.163495i
$951$		0			0
$952$	−0.730386	+	2.43966i	−0.0236720	+	0.0790698i
$953$	6.59171	−	5.53110i	0.213526	−	0.179170i	−0.529751	−	0.848153i	$-0.677715\pi$
$953$	6.59171	−	5.53110i	0.213526	−	0.179170i	0.743277	+	0.668983i	$0.233270\pi$
$954$		0			0
$955$	−28.1557	−	23.6254i	−0.911096	−	0.764500i
$956$	17.9237	−	11.7886i	0.579695	−	0.381271i
$957$		0			0
$958$	0.136880	−	0.0159989i	0.00442238	−	0.000516902i
$959$	7.25394	−	16.8165i	0.234242	−	0.543034i
$960$		0			0
$961$	−26.0547	−	13.0852i	−0.840474	−	0.422102i
$962$	19.2948	−	7.02275i	0.622091	−	0.226423i
$963$		0			0
$964$	−18.5877	−	6.76535i	−0.598668	−	0.217897i
$965$	−19.6757	−	20.8550i	−0.633382	−	0.671346i
$966$		0			0
$967$	5.71212	+	3.75692i	0.183689	+	0.120814i	0.638023	−	0.770017i	$-0.279752\pi$
$967$	5.71212	+	3.75692i	0.183689	+	0.120814i	−0.454334	+	0.890831i	$0.650123\pi$
$968$	−3.13033	−	10.4560i	−0.100613	−	0.336070i
$969$		0			0
$970$	−8.82270	+	11.8509i	−0.283280	+	0.380511i
$971$	−11.1814			−0.358830			−0.179415	−	0.983774i	$-0.557420\pi$
$971$	−11.1814			−0.358830			−0.179415	+	0.983774i	$0.557420\pi$
$972$		0			0
$973$	−20.8949			−0.669861
$974$	−9.68994	+	13.0158i	−0.310486	+	0.417054i
$975$		0			0
$976$	−2.93491	−	9.80328i	−0.0939441	−	0.313795i
$977$	−22.1906	−	14.5950i	−0.709939	−	0.466934i	0.142477	−	0.989798i	$-0.454493\pi$
$977$	−22.1906	−	14.5950i	−0.709939	−	0.466934i	−0.852416	+	0.522864i	$0.824864\pi$
$978$		0			0
$979$	2.28124	+	2.41797i	0.0729087	+	0.0772787i
$980$	8.28390	+	3.01509i	0.264620	+	0.0963137i
$981$		0			0
$982$	15.6056	−	5.67999i	0.497996	−	0.181256i
$983$	49.4675	+	24.8435i	1.57777	+	0.792385i	0.999721	−	0.0236172i	$-0.00751829\pi$
$983$	49.4675	+	24.8435i	1.57777	+	0.792385i	0.578048	+	0.816003i	$0.303815\pi$
$984$		0			0
$985$	−2.75981	+	6.39797i	−0.0879350	+	0.203856i
$986$	−24.8533	+	2.90494i	−0.791491	+	0.0925120i
$987$		0			0
$988$	−11.4387	+	7.52335i	−0.363914	+	0.239350i
$989$	46.8467	+	39.3091i	1.48964	+	1.24996i
$990$		0			0
$991$	−23.5575	+	19.7671i	−0.748328	+	0.627922i	−0.935060	−	0.354489i	$-0.884655\pi$
$991$	−23.5575	+	19.7671i	−0.748328	+	0.627922i	0.186732	+	0.982411i	$0.440210\pi$
$992$	0.389467	−	1.30091i	0.0123656	−	0.0413040i
$993$		0			0
$994$	12.7480	−	6.40231i	0.404343	−	0.203069i
$995$	−11.7675	+	12.4728i	−0.373054	+	0.395414i
$996$		0			0
$997$	15.6677	+	36.3219i	0.496202	+	1.15033i	0.963858	+	0.266415i	$0.0858391\pi$
$997$	15.6677	+	36.3219i	0.496202	+	1.15033i	−0.467657	+	0.883910i	$0.654902\pi$
$998$	−6.07998	−	10.5308i	−0.192458	−	0.333348i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.g.b.469.2		90
3.2	odd	2		162.2.g.b.139.3	yes	90
81.7	even	27	inner	486.2.g.b.343.2		90
81.74	odd	54		162.2.g.b.7.3	✓	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.7.3	✓	90	81.74	odd	54
162.2.g.b.139.3	yes	90	3.2	odd	2
486.2.g.b.343.2		90	81.7	even	27	inner
486.2.g.b.469.2		90	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.597159 + 0.802123i) q^{2} +(-0.286803 - 0.957990i) q^{4} +(-1.23282 - 0.810835i) q^{5} +(0.694984 + 0.736640i) q^{7} +(0.939693 + 0.342020i) q^{8} +O(q^{10})\)	\(q+(-0.597159 + 0.802123i) q^{2} +(-0.286803 - 0.957990i) q^{4} +(-1.23282 - 0.810835i) q^{5} +(0.694984 + 0.736640i) q^{7} +(0.939693 + 0.342020i) q^{8} +(1.38658 - 0.504672i) q^{10} +(-0.261194 - 0.131176i) q^{11} +(1.36323 - 3.16033i) q^{13} +(-1.00589 + 0.117572i) q^{14} +(-0.835488 + 0.549509i) q^{16} +(1.92630 + 1.61636i) q^{17} +(3.04721 - 2.55692i) q^{19} +(-0.423196 + 1.41357i) q^{20} +(0.261194 - 0.131176i) q^{22} +(3.54079 - 3.75302i) q^{23} +(-1.11802 - 2.59186i) q^{25} +(1.72091 + 2.98070i) q^{26} +(0.506370 - 0.877058i) q^{28} +(9.88356 + 1.15522i) q^{29} +(1.32136 + 0.313167i) q^{31} +(0.0581448 - 0.998308i) q^{32} +(-2.44683 + 0.579909i) q^{34} +(-0.259493 - 1.47166i) q^{35} +(1.03595 - 5.87515i) q^{37} +(0.231292 + 3.97112i) q^{38} +(-0.881145 - 1.18358i) q^{40} +(-2.84830 - 3.82593i) q^{41} +(0.689149 + 11.8322i) q^{43} +(-0.0507544 + 0.287843i) q^{44} +(0.895970 + 5.08130i) q^{46} +(2.71368 - 0.643154i) q^{47} +(0.347378 - 5.96425i) q^{49} +(2.74663 + 0.650962i) q^{50} +(-3.41855 - 0.399571i) q^{52} +(-1.31648 + 2.28021i) q^{53} +(0.215641 + 0.373501i) q^{55} +(0.401126 + 0.929914i) q^{56} +(-6.82868 + 7.23798i) q^{58} +(-0.159662 + 0.0801851i) q^{59} +(-2.93491 + 9.80328i) q^{61} +(-1.04026 + 0.872879i) q^{62} +(0.766044 + 0.642788i) q^{64} +(-4.24313 + 2.79075i) q^{65} +(8.02516 - 0.938006i) q^{67} +(0.995986 - 2.30896i) q^{68} +(1.33541 + 0.670668i) q^{70} +(-13.2365 + 4.81768i) q^{71} +(-1.12990 - 0.411250i) q^{73} +(4.09397 + 4.33936i) q^{74} +(-3.32345 - 2.18587i) q^{76} +(-0.0848957 - 0.283571i) q^{77} +(5.40569 - 7.26110i) q^{79} +1.47556 q^{80} +4.76975 q^{82} +(7.45078 - 10.0081i) q^{83} +(-1.06417 - 3.55459i) q^{85} +(-9.90244 - 6.51294i) q^{86} +(-0.200577 - 0.212599i) q^{88} +(-10.6875 - 3.88993i) q^{89} +(3.27545 - 1.19217i) q^{91} +(-4.61086 - 2.31566i) q^{92} +(-1.10461 + 2.56077i) q^{94} +(-5.82989 + 0.681416i) q^{95} +(-8.36554 + 5.50211i) q^{97} +(4.57662 + 3.84024i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q+O(q^{10}) \) 90 * q	\( 90 q - 18 q^{13} + 9 q^{20} - 27 q^{23} - 18 q^{25} + 27 q^{26} - 18 q^{28} + 27 q^{29} + 54 q^{31} + 27 q^{35} + 18 q^{38} + 9 q^{41} - 36 q^{43} + 18 q^{46} + 27 q^{47} + 36 q^{52} + 27 q^{53} - 54 q^{55} - 9 q^{58} + 45 q^{59} - 9 q^{65} + 81 q^{67} - 36 q^{68} - 72 q^{70} - 72 q^{71} - 36 q^{73} - 45 q^{74} - 18 q^{76} - 144 q^{77} - 99 q^{79} - 18 q^{80} + 72 q^{82} - 45 q^{83} - 117 q^{85} - 72 q^{86} - 18 q^{88} - 45 q^{89} - 63 q^{91} - 36 q^{92} - 72 q^{94} - 45 q^{95} + 117 q^{97} - 36 q^{98}+O(q^{100}) \) 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

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