LMFDB - Embedded newform 648.2.t.a.397.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(37,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("648.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, 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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			397.26
Character	$\chi$	$=$	648.397
Dual form			648.2.t.a.253.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.938269 + 1.05814i) q^{2} +(-0.239304 + 1.98563i) q^{4} +(1.55117 + 1.84861i) q^{5} +(-1.49685 + 0.544810i) q^{7} +(-2.32560 + 1.60984i) q^{8} +O(q^{10})$	\(q+(0.938269 + 1.05814i) q^{2} +(-0.239304 + 1.98563i) q^{4} +(1.55117 + 1.84861i) q^{5} +(-1.49685 + 0.544810i) q^{7} +(-2.32560 + 1.60984i) q^{8} +(-0.500669 + 3.37584i) q^{10} +(-0.102391 + 0.122025i) q^{11} +(-3.39140 + 0.597995i) q^{13} +(-1.98093 - 1.07270i) q^{14} +(-3.88547 - 0.950339i) q^{16} +(1.43581 + 2.48690i) q^{17} +(3.75621 + 2.16865i) q^{19} +(-4.04186 + 2.63767i) q^{20} +(-0.225190 + 0.00614850i) q^{22} +(-2.14748 - 0.781619i) q^{23} +(-0.142997 + 0.810974i) q^{25} +(-3.81480 - 3.02748i) q^{26} +(-0.723589 - 3.10257i) q^{28} +(8.60509 + 1.51731i) q^{29} +(-6.69129 - 2.43543i) q^{31} +(-2.64002 - 5.00303i) q^{32} +(-1.28430 + 3.85267i) q^{34} +(-3.32901 - 1.92201i) q^{35} +(5.14590 - 2.97099i) q^{37} +(1.22961 + 6.00935i) q^{38} +(-6.58336 - 1.80200i) q^{40} +(1.74706 + 9.90807i) q^{41} +(7.59829 - 9.05529i) q^{43} +(-0.217795 - 0.232513i) q^{44} +(-1.18785 - 3.00570i) q^{46} +(-3.66367 + 1.33347i) q^{47} +(-3.41856 + 2.86851i) q^{49} +(-0.992290 + 0.609602i) q^{50} +(-0.375823 - 6.87717i) q^{52} +9.80805i q^{53} -0.384404 q^{55} +(2.60402 - 3.67670i) q^{56} +(6.46837 + 10.5290i) q^{58} +(1.72220 + 2.05244i) q^{59} +(0.492702 + 1.35369i) q^{61} +(-3.70121 - 9.36539i) q^{62} +(2.81683 - 7.48769i) q^{64} +(-6.36609 - 5.34178i) q^{65} +(-0.225321 + 0.0397302i) q^{67} +(-5.28167 + 2.25587i) q^{68} +(-1.08976 - 5.32591i) q^{70} +(-2.82317 - 4.88987i) q^{71} +(7.14574 - 12.3768i) q^{73} +(7.97195 + 2.65748i) q^{74} +(-5.20501 + 6.93948i) q^{76} +(0.0867843 - 0.238438i) q^{77} +(-2.18269 + 12.3786i) q^{79} +(-4.27021 - 8.65685i) q^{80} +(-8.84487 + 11.1451i) q^{82} +(11.1079 + 1.95862i) q^{83} +(-2.37013 + 6.51187i) q^{85} +(16.7110 - 0.456270i) q^{86} +(0.0416802 - 0.448616i) q^{88} +(3.73417 - 6.46777i) q^{89} +(4.75063 - 2.74278i) q^{91} +(2.06591 - 4.07706i) q^{92} +(-4.84850 - 2.62551i) q^{94} +(1.81753 + 10.3077i) q^{95} +(5.17680 + 4.34385i) q^{97} +(-6.24280 - 0.925866i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40} + 24 q^{41} - 21 q^{44} - 3 q^{46} + 12 q^{47} - 12 q^{49} + 99 q^{50} - 33 q^{52} - 24 q^{55} - 99 q^{56} + 21 q^{58} + 36 q^{62} - 3 q^{64} + 12 q^{65} - 75 q^{68} + 9 q^{70} + 90 q^{71} - 6 q^{73} - 9 q^{74} - 18 q^{76} - 12 q^{79} - 78 q^{80} - 12 q^{82} + 30 q^{86} - 30 q^{88} + 6 q^{89} - 111 q^{92} - 33 q^{94} + 42 q^{95} - 12 q^{97} - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.938269	+	1.05814i	0.663456	+	0.748215i
$2$	0.938269	+	1.05814i	0.663456	+	0.748215i
$3$		0			0
$3$		0			0
$4$	−0.239304	+	1.98563i	−0.119652	+	0.992816i
$5$	1.55117	+	1.84861i	0.693704	+	0.826724i	0.991798	−	0.127812i	$-0.0407956\pi$
$5$	1.55117	+	1.84861i	0.693704	+	0.826724i	−0.298095	+	0.954536i	$0.596351\pi$
$6$		0			0
$7$	−1.49685	+	0.544810i	−0.565757	+	0.205919i	−0.609034	−	0.793144i	$-0.708443\pi$
$7$	−1.49685	+	0.544810i	−0.565757	+	0.205919i	0.0432765	+	0.999063i	$0.486220\pi$
$8$	−2.32560	+	1.60984i	−0.822224	+	0.569164i
$9$		0			0
$10$	−0.500669	+	3.37584i	−0.158325	+	1.06753i
$11$	−0.102391	+	0.122025i	−0.0308722	+	0.0367920i	−0.781260	−	0.624206i	$-0.785423\pi$
$11$	−0.102391	+	0.122025i	−0.0308722	+	0.0367920i	0.750387	+	0.660998i	$0.229867\pi$
$12$		0			0
$13$	−3.39140	+	0.597995i	−0.940604	+	0.165854i	−0.622869	−	0.782326i	$-0.714033\pi$
$13$	−3.39140	+	0.597995i	−0.940604	+	0.165854i	−0.317735	+	0.948180i	$0.602922\pi$
$14$	−1.98093	−	1.07270i	−0.529427	−	0.286690i
$15$		0			0
$16$	−3.88547	−	0.950339i	−0.971367	−	0.237585i
$17$	1.43581	+	2.48690i	0.348236	+	0.603163i	0.985936	−	0.167122i	$-0.0534474\pi$
$17$	1.43581	+	2.48690i	0.348236	+	0.603163i	−0.637700	+	0.770285i	$0.720114\pi$
$18$		0			0
$19$	3.75621	+	2.16865i	0.861733	+	0.497522i	0.864592	−	0.502474i	$-0.167577\pi$
$19$	3.75621	+	2.16865i	0.861733	+	0.497522i	−0.00285908	+	0.999996i	$0.500910\pi$
$20$	−4.04186	+	2.63767i	−0.903788	+	0.589801i
$21$		0			0
$22$	−0.225190	+	0.00614850i	−0.0480107	+	0.00131087i
$23$	−2.14748	−	0.781619i	−0.447781	−	0.162979i	0.108280	−	0.994120i	$-0.465466\pi$
$23$	−2.14748	−	0.781619i	−0.447781	−	0.162979i	−0.556061	+	0.831142i	$0.687688\pi$
$24$		0			0
$25$	−0.142997	+	0.810974i	−0.0285993	+	0.162195i
$26$	−3.81480	−	3.02748i	−0.748144	−	0.593737i
$27$		0			0
$28$	−0.723589	−	3.10257i	−0.136746	−	0.586331i
$29$	8.60509	+	1.51731i	1.59793	+	0.281757i	0.900486	−	0.434886i	$-0.143211\pi$
$29$	8.60509	+	1.51731i	1.59793	+	0.281757i	0.697440	+	0.716643i	$0.254322\pi$
$30$		0			0
$31$	−6.69129	−	2.43543i	−1.20179	−	0.437416i	−0.337942	−	0.941167i	$-0.609731\pi$
$31$	−6.69129	−	2.43543i	−1.20179	−	0.437416i	−0.863849	+	0.503751i	$0.831953\pi$
$32$	−2.64002	−	5.00303i	−0.466695	−	0.884418i
$33$		0			0
$34$	−1.28430	+	3.85267i	−0.220256	+	0.660727i
$35$	−3.32901	−	1.92201i	−0.562706	−	0.324878i
$36$		0			0
$37$	5.14590	−	2.97099i	0.845981	−	0.488427i	−0.0133118	−	0.999911i	$-0.504237\pi$
$37$	5.14590	−	2.97099i	0.845981	−	0.488427i	0.859293	+	0.511484i	$0.170904\pi$
$38$	1.22961	+	6.00935i	0.199469	+	0.974846i
$39$		0			0
$40$	−6.58336	−	1.80200i	−1.04092	−	0.284921i
$41$	1.74706	+	9.90807i	0.272845	+	1.54738i	0.745725	+	0.666254i	$0.232103\pi$
$41$	1.74706	+	9.90807i	0.272845	+	1.54738i	−0.472880	+	0.881127i	$0.656786\pi$
$42$		0			0
$43$	7.59829	−	9.05529i	1.15873	−	1.38092i	0.247567	−	0.968871i	$-0.420369\pi$
$43$	7.59829	−	9.05529i	1.15873	−	1.38092i	0.911162	−	0.412048i	$-0.135187\pi$
$44$	−0.217795	−	0.232513i	−0.0328338	−	0.0350526i
$45$		0			0
$46$	−1.18785	−	3.00570i	−0.175140	−	0.443166i
$47$	−3.66367	+	1.33347i	−0.534402	+	0.194506i	−0.595103	−	0.803650i	$-0.702889\pi$
$47$	−3.66367	+	1.33347i	−0.534402	+	0.194506i	0.0607009	+	0.998156i	$0.480666\pi$
$48$		0			0
$49$	−3.41856	+	2.86851i	−0.488366	+	0.409788i
$50$	−0.992290	+	0.609602i	−0.140331	+	0.0862107i
$51$		0			0
$52$	−0.375823	−	6.87717i	−0.0521173	−	0.953691i
$53$			9.80805i			1.34724i	0.739078	+	0.673620i	$0.235262\pi$
$53$			9.80805i			1.34724i	−0.739078	+	0.673620i	$0.764738\pi$
$54$		0			0
$55$	−0.384404			−0.0518330
$56$	2.60402	−	3.67670i	0.347977	−	0.491320i
$57$		0			0
$58$	6.46837	+	10.5290i	0.849338	+	1.38253i
$59$	1.72220	+	2.05244i	0.224212	+	0.267205i	0.866410	−	0.499334i	$-0.166422\pi$
$59$	1.72220	+	2.05244i	0.224212	+	0.267205i	−0.642198	+	0.766539i	$0.721977\pi$
$60$		0			0
$61$	0.492702	+	1.35369i	0.0630841	+	0.173322i	0.967230	−	0.253902i	$-0.0817139\pi$
$61$	0.492702	+	1.35369i	0.0630841	+	0.173322i	−0.904146	+	0.427224i	$0.859492\pi$
$62$	−3.70121	−	9.36539i	−0.470054	−	1.18941i
$63$		0			0
$64$	2.81683	−	7.48769i	0.352104	−	0.935961i
$65$	−6.36609	−	5.34178i	−0.789616	−	0.662566i
$66$		0			0
$67$	−0.225321	+	0.0397302i	−0.0275273	+	0.00485381i	−0.187395	−	0.982285i	$-0.560004\pi$
$67$	−0.225321	+	0.0397302i	−0.0275273	+	0.00485381i	0.159868	+	0.987138i	$0.448893\pi$
$68$	−5.28167	+	2.25587i	−0.640497	+	0.273565i
$69$		0			0
$70$	−1.08976	−	5.32591i	−0.130252	−	0.636568i
$71$	−2.82317	−	4.88987i	−0.335048	−	0.580320i	0.648446	−	0.761261i	$-0.275419\pi$
$71$	−2.82317	−	4.88987i	−0.335048	−	0.580320i	−0.983494	+	0.180940i	$0.942086\pi$
$72$		0			0
$73$	7.14574	−	12.3768i	0.836346	−	1.44859i	−0.0565836	−	0.998398i	$-0.518021\pi$
$73$	7.14574	−	12.3768i	0.836346	−	1.44859i	0.892930	−	0.450196i	$-0.148646\pi$
$74$	7.97195	+	2.65748i	0.926720	+	0.308926i
$75$		0			0
$76$	−5.20501	+	6.93948i	−0.597056	+	0.796013i
$77$	0.0867843	−	0.238438i	0.00988999	−	0.0271725i
$78$		0			0
$79$	−2.18269	+	12.3786i	−0.245572	+	1.39271i	0.573590	+	0.819143i	$0.305550\pi$
$79$	−2.18269	+	12.3786i	−0.245572	+	1.39271i	−0.819161	+	0.573563i	$0.805561\pi$
$80$	−4.27021	−	8.65685i	−0.477424	−	0.967865i
$81$		0			0
$82$	−8.84487	+	11.1451i	−0.976753	+	1.23077i
$83$	11.1079	+	1.95862i	1.21925	+	0.214987i	0.746003	−	0.665942i	$-0.231970\pi$
$83$	11.1079	+	1.95862i	1.21925	+	0.214987i	0.473248	+	0.880929i	$0.343081\pi$
$84$		0			0
$85$	−2.37013	+	6.51187i	−0.257076	+	0.706311i
$86$	16.7110	−	0.456270i	1.80199	−	0.0492008i
$87$		0			0
$88$	0.0416802	−	0.448616i	0.00444313	−	0.0478226i
$89$	3.73417	−	6.46777i	0.395821	−	0.685582i	−0.597385	−	0.801955i	$-0.703793\pi$
$89$	3.73417	−	6.46777i	0.395821	−	0.685582i	0.993206	+	0.116373i	$0.0371268\pi$
$90$		0			0
$91$	4.75063	−	2.74278i	0.498001	−	0.287521i
$92$	2.06591	−	4.07706i	0.215386	−	0.425063i
$93$		0			0
$94$	−4.84850	−	2.62551i	−0.500085	−	0.270801i
$95$	1.81753	+	10.3077i	0.186474	+	1.05755i
$96$		0			0
$97$	5.17680	+	4.34385i	0.525624	+	0.441051i	0.866587	−	0.499026i	$-0.166309\pi$
$97$	5.17680	+	4.34385i	0.525624	+	0.441051i	−0.340963	+	0.940077i	$0.610753\pi$
$98$	−6.24280	−	0.925866i	−0.630618	−	0.0935266i
$99$		0			0
$100$	−1.57608	−	0.478008i	−0.157608	−	0.0478008i
$101$	0.582767	+	1.60114i	0.0579875	+	0.159319i	0.965304	−	0.261129i	$-0.0840949\pi$
$101$	0.582767	+	1.60114i	0.0579875	+	0.159319i	−0.907316	+	0.420449i	$0.861873\pi$
$102$		0			0
$103$	9.82235	−	8.24193i	0.967825	−	0.812102i	−0.0143832	−	0.999897i	$-0.504578\pi$
$103$	9.82235	−	8.24193i	0.967825	−	0.812102i	0.982208	+	0.187795i	$0.0601340\pi$
$104$	6.92435	−	6.85030i	0.678989	−	0.671727i
$105$		0			0
$106$	−10.3783	+	9.20259i	−1.00803	+	0.893835i
$107$		−	15.7558i		−	1.52317i	−0.648065	−	0.761585i	$-0.724421\pi$
$107$		−	15.7558i		−	1.52317i	0.648065	−	0.761585i	$-0.275579\pi$
$108$		0			0
$109$			4.23854i			0.405978i	0.979181	+	0.202989i	$0.0650656\pi$
$109$			4.23854i			0.405978i	−0.979181	+	0.202989i	$0.934934\pi$
$110$	−0.360674	−	0.406752i	−0.0343889	−	0.0387822i
$111$		0			0
$112$	6.33373	−	0.694324i	0.598481	−	0.0656074i
$113$	5.72871	−	4.80696i	0.538912	−	0.452201i	−0.332254	−	0.943190i	$-0.607809\pi$
$113$	5.72871	−	4.80696i	0.538912	−	0.452201i	0.871166	+	0.490989i	$0.163365\pi$
$114$		0			0
$115$	−1.88620	−	5.18228i	−0.175889	−	0.483250i
$116$	−5.07205	+	16.7234i	−0.470928	+	1.55273i
$117$		0			0
$118$	−0.555873	+	3.74807i	−0.0511723	+	0.345037i
$119$	−3.50409	−	2.94028i	−0.321220	−	0.269535i
$120$		0			0
$121$	1.90572	+	10.8079i	0.173248	+	0.982536i
$122$	−0.970099	+	1.79147i	−0.0878287	+	0.162192i
$123$		0			0
$124$	6.43712	−	12.7036i	0.578071	−	1.14082i
$125$	8.72843	−	5.03936i	0.780695	−	0.450734i
$126$		0			0
$127$	6.92735	−	11.9985i	0.614703	−	1.06470i	−0.375734	−	0.926728i	$-0.622609\pi$
$127$	6.92735	−	11.9985i	0.614703	−	1.06470i	0.990437	−	0.137969i	$-0.0440574\pi$
$128$	10.5659	−	4.04487i	0.933906	−	0.357520i
$129$		0			0
$130$	−0.320768	−	11.7482i	−0.0281332	−	1.03039i
$131$	−1.76657	+	4.85361i	−0.154346	+	0.424061i	−0.992632	−	0.121169i	$-0.961336\pi$
$131$	−1.76657	+	4.85361i	−0.154346	+	0.424061i	0.838286	+	0.545231i	$0.183558\pi$
$132$		0			0
$133$	−6.80399	−	1.19973i	−0.589981	−	0.104030i
$134$	−0.253452	−	0.201143i	−0.0218949	−	0.0173761i
$135$		0			0
$136$	−7.34265	−	3.47211i	−0.629627	−	0.297731i
$137$	3.27446	−	18.5704i	0.279756	−	1.58658i	−0.443680	−	0.896185i	$-0.646327\pi$
$137$	3.27446	−	18.5704i	0.279756	−	1.58658i	0.723436	−	0.690391i	$-0.242562\pi$
$138$		0			0
$139$	5.53623	−	15.2107i	0.469577	−	1.29015i	−0.448512	−	0.893777i	$-0.648046\pi$
$139$	5.53623	−	15.2107i	0.469577	−	1.29015i	0.918089	−	0.396375i	$-0.129732\pi$
$140$	4.61304	−	6.15025i	0.389873	−	0.519791i
$141$		0			0
$142$	2.52526	−	7.57530i	0.211915	−	0.635705i
$143$	0.274279	−	0.475066i	0.0229364	−	0.0397270i
$144$		0			0
$145$	10.5430	+	18.2611i	0.875551	+	1.51650i
$146$	19.8010	−	4.05159i	1.63874	−	0.335312i
$147$		0			0
$148$	4.66785	+	10.9288i	0.383695	+	0.898345i
$149$	−12.7731	+	2.25224i	−1.04641	+	0.184511i	−0.670321	−	0.742071i	$-0.733843\pi$
$149$	−12.7731	+	2.25224i	−1.04641	+	0.184511i	−0.376092	+	0.926582i	$0.622732\pi$
$150$		0			0
$151$	2.57721	+	2.16253i	0.209730	+	0.175985i	0.741602	−	0.670841i	$-0.234067\pi$
$151$	2.57721	+	2.16253i	0.209730	+	0.175985i	−0.531871	+	0.846825i	$0.678511\pi$
$152$	−12.2266	+	1.00349i	−0.991709	+	0.0813935i
$153$		0			0
$154$	0.333727	−	0.131889i	0.0268925	−	0.0106279i
$155$	−5.87716	−	16.1474i	−0.472065	−	1.29699i
$156$		0			0
$157$	0.320529	+	0.381992i	0.0255810	+	0.0304863i	0.778683	−	0.627417i	$-0.215888\pi$
$157$	0.320529	+	0.381992i	0.0255810	+	0.0304863i	−0.753102	+	0.657903i	$0.771443\pi$
$158$	−15.1462	+	9.30491i	−1.20497	+	0.740259i
$159$		0			0
$160$	5.15352	−	12.6409i	0.407422	−	0.999352i
$161$	3.64030			0.286896
$162$		0			0
$163$			11.3041i			0.885405i	0.896669	+	0.442703i	$0.145980\pi$
$163$			11.3041i			0.885405i	−0.896669	+	0.442703i	$0.854020\pi$
$164$	−20.0919	+	1.09798i	−1.56891	+	0.0857377i
$165$		0			0
$166$	8.34971	+	13.5914i	0.648063	+	1.05490i
$167$	−10.0898	+	8.46632i	−0.780770	+	0.655144i	−0.943442	−	0.331536i	$-0.892433\pi$
$167$	−10.0898	+	8.46632i	−0.780770	+	0.655144i	0.162673	+	0.986680i	$0.447989\pi$
$168$		0			0
$169$	−1.07204	+	0.390189i	−0.0824644	+	0.0300146i
$170$	−9.11426	+	3.60197i	−0.699032	+	0.276258i
$171$		0			0
$172$	16.1622	+	17.2544i	1.23235	+	1.31563i
$173$	−10.5281	+	12.5470i	−0.800440	+	0.953928i	−0.999661	−	0.0260269i	$-0.991714\pi$
$173$	−10.5281	+	12.5470i	−0.800440	+	0.953928i	0.199221	+	0.979955i	$0.436159\pi$
$174$		0			0
$175$	−0.227782	−	1.29182i	−0.0172187	−	0.0976521i
$176$	0.513804	−	0.376819i	0.0387294	−	0.0284038i
$177$		0			0
$178$	10.3474	−	2.11725i	0.775572	−	0.158694i
$179$	−5.13398	+	2.96410i	−0.383731	+	0.221547i	−0.679441	−	0.733731i	$-0.737777\pi$
$179$	−5.13398	+	2.96410i	−0.383731	+	0.221547i	0.295709	+	0.955278i	$0.404444\pi$
$180$		0			0
$181$	−1.50802	−	0.870656i	−0.112090	−	0.0647154i	0.442907	−	0.896568i	$-0.353947\pi$
$181$	−1.50802	−	0.870656i	−0.112090	−	0.0647154i	−0.554997	+	0.831852i	$0.687281\pi$
$182$	7.35960	+	2.45335i	0.545529	+	0.181854i
$183$		0			0
$184$	6.25246	−	1.63937i	0.460938	−	0.120856i
$185$	13.4744	+	4.90427i	0.990655	+	0.360569i
$186$		0			0
$187$	−0.450481	−	0.0794319i	−0.0329424	−	0.00580863i
$188$	−1.77105	−	7.59381i	−0.129167	−	0.553836i
$189$		0			0
$190$	−9.20163	+	11.5946i	−0.667556	+	0.841160i
$191$	−1.88621	+	10.6972i	−0.136481	+	0.774023i	0.837336	+	0.546689i	$0.184112\pi$
$191$	−1.88621	+	10.6972i	−0.136481	+	0.774023i	−0.973817	+	0.227334i	$0.926999\pi$
$192$		0			0
$193$	−13.6021	−	4.95075i	−0.979100	−	0.356363i	−0.197609	−	0.980281i	$-0.563318\pi$
$193$	−13.6021	−	4.95075i	−0.979100	−	0.356363i	−0.781490	+	0.623918i	$0.785540\pi$
$194$	0.260844	+	9.55346i	0.0187275	+	0.685898i
$195$		0			0
$196$	−4.87774	−	7.47445i	−0.348410	−	0.533889i
$197$	7.36911	+	4.25456i	0.525027	+	0.303125i	0.738989	−	0.673717i	$-0.235303\pi$
$197$	7.36911	+	4.25456i	0.525027	+	0.303125i	−0.213962	+	0.976842i	$0.568637\pi$
$198$		0			0
$199$	−6.17939	−	10.7030i	−0.438045	−	0.758716i	0.559494	−	0.828835i	$-0.310996\pi$
$199$	−6.17939	−	10.7030i	−0.438045	−	0.758716i	−0.997539	+	0.0701183i	$0.977662\pi$
$200$	−0.972986	−	2.11620i	−0.0688005	−	0.149638i
$201$		0			0
$202$	−1.14743	+	2.11895i	−0.0807330	+	0.149089i
$203$	−13.7072	+	2.41695i	−0.962057	+	0.169637i
$204$		0			0
$205$	−15.6062	+	18.5987i	−1.08998	+	1.29899i
$206$	17.9371	+	2.66024i	1.24974	+	0.185348i
$207$		0			0
$208$	13.7455	+	0.899487i	0.953076	+	0.0623682i
$209$	−0.649234	+	0.236302i	−0.0449084	+	0.0163453i
$210$		0			0
$211$	−1.13641	−	1.35433i	−0.0782339	−	0.0932356i	0.725508	−	0.688214i	$-0.241605\pi$
$211$	−1.13641	−	1.35433i	−0.0782339	−	0.0932356i	−0.803742	+	0.594978i	$0.797161\pi$
$212$	−19.4752	−	2.34711i	−1.33756	−	0.161200i
$213$		0			0
$214$	16.6718	−	14.7832i	1.13966	−	1.01056i
$215$	28.5259			1.94545
$216$		0			0
$217$	11.3427			0.769994
$218$	−4.48495	+	3.97689i	−0.303759	+	0.269349i
$219$		0			0
$220$	0.0919893	−	0.763285i	0.00620192	−	0.0514606i
$221$	−6.35657	−	7.57546i	−0.427589	−	0.509581i
$222$		0			0
$223$	−2.82725	+	1.02903i	−0.189327	+	0.0689092i	−0.434944	−	0.900458i	$-0.643232\pi$
$223$	−2.82725	+	1.02903i	−0.189327	+	0.0689092i	0.245617	+	0.969367i	$0.421009\pi$
$224$	6.67743	+	6.05048i	0.446154	+	0.404265i
$225$		0			0
$226$	10.4615	+	1.55154i	0.695888	+	0.103207i
$227$	3.65533	−	4.35626i	0.242613	−	0.289135i	−0.630973	−	0.775805i	$-0.717344\pi$
$227$	3.65533	−	4.35626i	0.242613	−	0.289135i	0.873586	+	0.486670i	$0.161789\pi$
$228$		0			0
$229$	21.4459	−	3.78149i	1.41718	−	0.249888i	0.587998	−	0.808862i	$-0.299916\pi$
$229$	21.4459	−	3.78149i	1.41718	−	0.249888i	0.829185	+	0.558974i	$0.188805\pi$
$230$	3.71380	−	6.85822i	0.244881	−	0.452218i
$231$		0			0
$232$	−22.4546	+	10.3242i	−1.47422	+	0.677815i
$233$	11.7482	+	20.3485i	0.769650	+	1.33307i	0.937753	+	0.347303i	$0.112903\pi$
$233$	11.7482	+	20.3485i	0.769650	+	1.33307i	−0.168103	+	0.985769i	$0.553764\pi$
$234$		0			0
$235$	−8.14804	−	4.70427i	−0.531520	−	0.306873i
$236$	−4.48752	+	2.92850i	−0.292113	+	0.190629i
$237$		0			0
$238$	−0.176561	−	6.46658i	−0.0114447	−	0.419166i
$239$	−21.9880	−	8.00297i	−1.42228	−	0.517669i	−0.487574	−	0.873082i	$-0.662118\pi$
$239$	−21.9880	−	8.00297i	−1.42228	−	0.517669i	−0.934710	+	0.355413i	$0.884340\pi$
$240$		0			0
$241$	0.682320	−	3.86963i	0.0439521	−	0.249265i	−0.954913	−	0.296884i	$-0.904052\pi$
$241$	0.682320	−	3.86963i	0.0439521	−	0.249265i	0.998866	+	0.0476196i	$0.0151635\pi$
$242$	−9.64814	+	12.1572i	−0.620206	+	0.781496i
$243$		0			0
$244$	−2.80583	+	0.654382i	−0.179625	+	0.0418925i
$245$	−10.6055	−	1.87004i	−0.677562	−	0.119472i
$246$		0			0
$247$	−14.0356	−	5.10855i	−0.893066	−	0.325049i
$248$	19.4819	−	5.10807i	1.23710	−	0.324363i
$249$		0			0
$250$	13.5219	+	4.50759i	0.855203	+	0.285085i
$251$	0.431970	+	0.249398i	0.0272657	+	0.0157419i	0.513571	−	0.858047i	$-0.328322\pi$
$251$	0.431970	+	0.249398i	0.0272657	+	0.0157419i	−0.486305	+	0.873789i	$0.661656\pi$
$252$		0			0
$253$	0.315261	−	0.182016i	0.0198203	−	0.0114433i
$254$	19.1958	−	3.92776i	1.20445	−	0.246449i
$255$		0			0
$256$	14.1937	+	7.38502i	0.887107	+	0.461564i
$257$	−0.156179	−	0.885735i	−0.00974218	−	0.0552506i	0.979549	−	0.201205i	$-0.0644858\pi$
$257$	−0.156179	−	0.885735i	−0.00974218	−	0.0552506i	−0.989291	+	0.145955i	$0.953375\pi$
$258$		0			0
$259$	−6.08403	+	7.25067i	−0.378043	+	0.450535i
$260$	12.1302	−	11.3624i	0.752285	−	0.704666i
$261$		0			0
$262$	−6.79329	+	2.68472i	−0.419691	+	0.165862i
$263$	9.42004	−	3.42861i	0.580864	−	0.211417i	−0.0348423	−	0.999393i	$-0.511093\pi$
$263$	9.42004	−	3.42861i	0.580864	−	0.211417i	0.615707	+	0.787976i	$0.288871\pi$
$264$		0			0
$265$	−18.1313	+	15.2139i	−1.11380	+	0.934585i
$266$	−5.11450	−	8.32522i	−0.313590	−	0.510452i
$267$		0			0
$268$	−0.0249693	−	0.456912i	−0.00152524	−	0.0279104i
$269$		−	1.04059i		−	0.0634460i	−0.999497	−	0.0317230i	$-0.989901\pi$
$269$		−	1.04059i		−	0.0634460i	0.999497	−	0.0317230i	$-0.0100994\pi$
$270$		0			0
$271$	−30.0408			−1.82485			−0.912423	−	0.409248i	$-0.865791\pi$
$271$	−30.0408			−1.82485			−0.912423	+	0.409248i	$0.865791\pi$
$272$	−3.21541	−	11.0273i	−0.194963	−	0.668628i
$273$		0			0
$274$	22.7223	−	13.9592i	1.37271	−	0.843306i
$275$	−0.0843178	−	0.100486i	−0.00508456	−	0.00605954i
$276$		0			0
$277$	−6.71914	−	18.4607i	−0.403714	−	1.10920i	−0.960437	−	0.278497i	$-0.910164\pi$
$277$	−6.71914	−	18.4607i	−0.403714	−	1.10920i	0.556723	−	0.830698i	$-0.312059\pi$
$278$	21.2894	−	8.41361i	1.27686	−	0.504615i
$279$		0			0
$280$	10.8361	−	0.889360i	0.647579	−	0.0531494i
$281$	−21.2698	−	17.8475i	−1.26885	−	1.06469i	−0.994681	−	0.103008i	$-0.967153\pi$
$281$	−21.2698	−	17.8475i	−1.26885	−	1.06469i	−0.274167	−	0.961682i	$-0.588402\pi$
$282$		0			0
$283$	−24.5768	+	4.33356i	−1.46094	+	0.257603i	−0.846934	−	0.531698i	$-0.821554\pi$
$283$	−24.5768	+	4.33356i	−1.46094	+	0.257603i	−0.614007	+	0.789301i	$0.710443\pi$
$284$	10.3851	−	4.43560i	0.616240	−	0.263205i
$285$		0			0
$286$	0.760032	−	0.155515i	0.0449417	−	0.00919577i
$287$	−8.01310	−	13.8791i	−0.472999	−	0.819258i
$288$		0			0
$289$	4.37687	−	7.58097i	0.257463	−	0.445939i
$290$	−9.43050	+	28.2897i	−0.553778	+	1.66123i
$291$		0			0
$292$	22.8657	+	17.1506i	1.33812	+	1.00366i
$293$	2.79279	−	7.67312i	0.163156	−	0.448268i	−0.830993	−	0.556283i	$-0.812227\pi$
$293$	2.79279	−	7.67312i	0.163156	−	0.448268i	0.994149	+	0.108015i	$0.0344493\pi$
$294$		0			0
$295$	−1.12274	+	6.36736i	−0.0653683	+	0.370722i
$296$	−7.18449	+	15.1934i	−0.417590	+	0.883099i
$297$		0			0
$298$	−14.3678	−	11.4025i	−0.832303	−	0.660527i
$299$	7.75036	+	1.36660i	0.448215	+	0.0790324i
$300$		0			0
$301$	−6.44011	+	17.6941i	−0.371202	+	1.01987i
$302$	0.129858	+	4.75607i	0.00747248	+	0.273681i
$303$		0			0
$304$	−12.5337	−	11.9959i	−0.718855	−	0.688011i
$305$	−1.73818	+	3.01061i	−0.0995278	+	0.172387i
$306$		0			0
$307$	−16.1236	+	9.30896i	−0.920222	+	0.531290i	−0.883706	−	0.468043i	$-0.844959\pi$
$307$	−16.1236	+	9.30896i	−0.920222	+	0.531290i	−0.0365160	+	0.999333i	$0.511626\pi$
$308$	0.452682	+	0.229381i	0.0257940	+	0.0130702i
$309$		0			0
$310$	11.5717	−	21.3694i	0.657231	−	1.21370i
$311$	0.851609	+	4.82971i	0.0482903	+	0.273868i	0.999386	−	0.0350274i	$-0.0111518\pi$
$311$	0.851609	+	4.82971i	0.0482903	+	0.273868i	−0.951096	+	0.308895i	$0.900041\pi$
$312$		0			0
$313$	−7.88890	−	6.61958i	−0.445907	−	0.374161i	0.392007	−	0.919962i	$-0.371781\pi$
$313$	−7.88890	−	6.61958i	−0.445907	−	0.374161i	−0.837914	+	0.545802i	$0.816225\pi$
$314$	−0.103457	+	0.697574i	−0.00583840	+	0.0393664i
$315$		0			0
$316$	−24.0571	−	7.29627i	−1.35332	−	0.410447i
$317$	−7.72259	−	21.2177i	−0.433744	−	1.19170i	−0.943497	−	0.331381i	$-0.892485\pi$
$317$	−7.72259	−	21.2177i	−0.433744	−	1.19170i	0.509753	−	0.860321i	$-0.329737\pi$
$318$		0			0
$319$	−1.06624	+	0.894680i	−0.0596979	+	0.0500925i
$320$	18.2112	−	6.40744i	1.01804	−	0.358187i
$321$		0			0
$322$	3.41558	+	3.85193i	0.190343	+	0.214660i
$323$			12.4551i			0.693020i
$324$		0			0
$325$		−	2.83585i		−	0.157304i
$326$	−11.9613	+	10.6063i	−0.662474	+	0.587427i
$327$		0			0
$328$	−20.0134	−	20.2297i	−1.10505	−	1.11700i
$329$	4.75749	−	3.99201i	0.262289	−	0.220087i
$330$		0			0
$331$	8.06296	+	22.1528i	0.443180	+	1.21763i	0.937389	+	0.348284i	$0.113236\pi$
$331$	8.06296	+	22.1528i	0.443180	+	1.21763i	−0.494209	+	0.869343i	$0.664542\pi$
$332$	−6.54727	+	21.5875i	−0.359328	+	1.18477i
$333$		0			0
$334$	−18.4254	−	2.73266i	−1.00819	−	0.149525i
$335$	−0.422957	−	0.354903i	−0.0231086	−	0.0193904i
$336$		0			0
$337$	−5.70981	−	32.3820i	−0.311033	−	1.76396i	−0.593649	−	0.804724i	$-0.702313\pi$
$337$	−5.70981	−	32.3820i	−0.311033	−	1.76396i	0.282615	−	0.959233i	$-0.408798\pi$
$338$	−1.41873	−	0.768258i	−0.0771688	−	0.0417877i
$339$		0			0
$340$	−12.3630	−	6.26451i	−0.670477	−	0.339741i
$341$	0.982316	−	0.567140i	0.0531954	−	0.0307124i
$342$		0			0
$343$	9.12950	−	15.8128i	0.492947	−	0.853809i
$344$	−3.09302	+	33.2910i	−0.166764	+	1.79493i
$345$		0			0
$346$	−23.1546	+	0.632204i	−1.24480	+	0.0339875i
$347$	0.288638	−	0.793027i	0.0154949	−	0.0425719i	−0.931704	−	0.363218i	$-0.881678\pi$
$347$	0.288638	−	0.793027i	0.0154949	−	0.0425719i	0.947199	+	0.320646i	$0.103900\pi$
$348$		0			0
$349$	−13.8072	−	2.43459i	−0.739085	−	0.130321i	−0.208583	−	0.978005i	$-0.566885\pi$
$349$	−13.8072	−	2.43459i	−0.739085	−	0.130321i	−0.530501	+	0.847684i	$0.677996\pi$
$350$	1.15320	−	1.45309i	0.0616409	−	0.0776711i
$351$		0			0
$352$	0.880812	+	0.190117i	0.0469475	+	0.0101333i
$353$	−4.09441	+	23.2205i	−0.217923	+	1.23590i	0.657838	+	0.753159i	$0.271471\pi$
$353$	−4.09441	+	23.2205i	−0.217923	+	1.23590i	−0.875761	+	0.482744i	$0.839640\pi$
$354$		0			0
$355$	4.66025	−	12.8039i	0.247341	−	0.679562i
$356$	11.9490	+	8.96244i	0.633296	+	0.475008i
$357$		0			0
$358$	−7.95347	−	2.65132i	−0.420354	−	0.140127i
$359$	13.4957	−	23.3753i	0.712277	−	1.23370i	−0.251724	−	0.967799i	$-0.580997\pi$
$359$	13.4957	−	23.3753i	0.712277	−	1.23370i	0.964001	−	0.265900i	$-0.0856692\pi$
$360$		0			0
$361$	−0.0939335	−	0.162698i	−0.00494387	−	0.00856303i
$362$	−0.493656	−	2.41260i	−0.0259460	−	0.126804i
$363$		0			0
$364$	4.30930	+	10.0894i	0.225869	+	0.528826i
$365$	33.9641	−	5.98879i	1.77776	−	0.313468i
$366$		0			0
$367$	22.3181	+	18.7271i	1.16500	+	0.977547i	0.999962	−	0.00874090i	$-0.00278235\pi$
$367$	22.3181	+	18.7271i	1.16500	+	0.977547i	0.165033	+	0.986288i	$0.447227\pi$
$368$	7.60116	+	5.07779i	0.396238	+	0.264698i
$369$		0			0
$370$	7.45319	+	18.8592i	0.387473	+	0.980444i
$371$	−5.34353	−	14.6812i	−0.277422	−	0.762211i
$372$		0			0
$373$	0.738799	+	0.880467i	0.0382536	+	0.0455888i	0.784832	−	0.619709i	$-0.212749\pi$
$373$	0.738799	+	0.880467i	0.0382536	+	0.0455888i	−0.746578	+	0.665297i	$0.768305\pi$
$374$	−0.338622	−	0.551198i	−0.0175097	−	0.0285018i
$375$		0			0
$376$	6.37357	−	8.99904i	0.328692	−	0.464090i
$377$	−30.0906			−1.54975
$378$		0			0
$379$			16.9124i			0.868731i	0.900737	+	0.434365i	$0.143027\pi$
$379$			16.9124i			0.868731i	−0.900737	+	0.434365i	$0.856973\pi$
$380$	−20.9022	+	1.14226i	−1.07226	+	0.0585969i
$381$		0			0
$382$	−13.0889	+	8.04099i	−0.669685	+	0.411413i
$383$	−15.4572	+	12.9701i	−0.789826	+	0.662743i	−0.945702	−	0.325034i	$-0.894624\pi$
$383$	−15.4572	+	12.9701i	−0.789826	+	0.662743i	0.155876	+	0.987777i	$0.450180\pi$
$384$		0			0
$385$	0.575396	−	0.209427i	0.0293249	−	0.0106734i
$386$	−7.52384	−	19.0380i	−0.382953	−	0.969008i
$387$		0			0
$388$	−9.86412	+	9.23972i	−0.500775	+	0.469076i
$389$	−18.7454	+	22.3399i	−0.950428	+	1.13268i	0.0406204	+	0.999175i	$0.487067\pi$
$389$	−18.7454	+	22.3399i	−0.950428	+	1.13268i	−0.991049	+	0.133502i	$0.957378\pi$
$390$		0			0
$391$	−1.13957	−	6.46284i	−0.0576307	−	0.326840i
$392$	3.33236	−	12.1743i	0.168309	−	0.614897i
$393$		0			0
$394$	2.41230	+	11.7894i	0.121530	+	0.593943i
$395$	−26.2690	+	15.1664i	−1.32174	+	0.763105i
$396$		0			0
$397$	−10.3158	−	5.95584i	−0.517736	−	0.298915i	0.218272	−	0.975888i	$-0.429958\pi$
$397$	−10.3158	−	5.95584i	−0.517736	−	0.298915i	−0.736008	+	0.676973i	$0.763291\pi$
$398$	5.52732	−	16.5809i	0.277059	−	0.831127i
$399$		0			0
$400$	1.32631	−	3.01512i	0.0663155	−	0.150756i
$401$	−2.23681	−	0.814132i	−0.111701	−	0.0406558i	0.285565	−	0.958359i	$-0.407819\pi$
$401$	−2.23681	−	0.814132i	−0.111701	−	0.0406558i	−0.397266	+	0.917704i	$0.630041\pi$
$402$		0			0
$403$	24.1492	+	4.25815i	1.20296	+	0.212114i
$404$	−3.31873	+	0.774002i	−0.165113	+	0.0385080i
$405$		0			0
$406$	−15.4185	−	12.2363i	−0.765207	−	0.607279i
$407$	−0.164360	+	0.932134i	−0.00814705	+	0.0462042i
$408$		0			0
$409$	12.0885	+	4.39986i	0.597739	+	0.217559i	0.623130	−	0.782119i	$-0.285861\pi$
$409$	12.0885	+	4.39986i	0.597739	+	0.217559i	−0.0253911	+	0.999678i	$0.508083\pi$
$410$	−34.3228	+	0.937135i	−1.69508	+	0.0462818i
$411$		0			0
$412$	14.0149	+	21.4759i	0.690465	+	1.05804i
$413$	−3.69607	−	2.13393i	−0.181872	−	0.105004i
$414$		0			0
$415$	13.6095	+	23.5724i	0.668064	+	1.15712i
$416$	11.9451	+	15.3885i	0.585659	+	0.754484i
$417$		0			0
$418$	−0.859195	−	0.465263i	−0.0420246	−	0.0227568i
$419$	7.38244	−	1.30172i	0.360656	−	0.0635933i	0.00961568	−	0.999954i	$-0.496939\pi$
$419$	7.38244	−	1.30172i	0.360656	−	0.0635933i	0.351040	+	0.936360i	$0.385828\pi$
$420$		0			0
$421$	5.15270	−	6.14075i	0.251127	−	0.299282i	−0.625723	−	0.780045i	$-0.715196\pi$
$421$	5.15270	−	6.14075i	0.251127	−	0.299282i	0.876850	+	0.480763i	$0.159640\pi$
$422$	0.366799	−	2.47320i	0.0178555	−	0.120394i
$423$		0			0
$424$	−15.7894	−	22.8096i	−0.766801	−	1.10773i
$425$	−2.22213	+	0.808790i	−0.107789	+	0.0392321i
$426$		0			0
$427$	−1.47501	−	1.75784i	−0.0713805	−	0.0850680i
$428$	31.2852	+	3.77042i	1.51223	+	0.182250i
$429$		0			0
$430$	26.7650	+	30.1843i	1.29072	+	1.45562i
$431$	4.63698			0.223356			0.111678	−	0.993744i	$-0.464378\pi$
$431$	4.63698			0.223356			0.111678	+	0.993744i	$0.464378\pi$
$432$		0			0
$433$	−0.0678381			−0.00326009			−0.00163005	−	0.999999i	$-0.500519\pi$
$433$	−0.0678381			−0.00326009			−0.00163005	+	0.999999i	$0.500519\pi$
$434$	10.6425	+	12.0021i	0.510858	+	0.576122i
$435$		0			0
$436$	−8.41618	−	1.01430i	−0.403062	−	0.0485761i
$437$	−6.37133	−	7.59305i	−0.304782	−	0.363225i
$438$		0			0
$439$	12.9530	−	4.71449i	0.618211	−	0.225010i	−0.0138813	−	0.999904i	$-0.504419\pi$
$439$	12.9530	−	4.71449i	0.618211	−	0.225010i	0.632092	+	0.774893i	$0.282196\pi$
$440$	0.893970	−	0.618829i	0.0426183	−	0.0295015i
$441$		0			0
$442$	2.05170	−	13.8339i	0.0975895	−	0.658013i
$443$	−8.58044	+	10.2258i	−0.407669	+	0.485841i	−0.930342	−	0.366692i	$-0.880490\pi$
$443$	−8.58044	+	10.2258i	−0.407669	+	0.485841i	0.522673	+	0.852533i	$0.324935\pi$
$444$		0			0
$445$	17.7487	−	3.12957i	0.841369	−	0.148356i
$446$	−3.74158	−	2.02610i	−0.177169	−	0.0959388i
$447$		0			0
$448$	−0.137014	+	12.7426i	−0.00647332	+	0.602031i
$449$	−6.26480	−	10.8509i	−0.295654	−	0.512088i	0.679483	−	0.733692i	$-0.262204\pi$
$449$	−6.26480	−	10.8509i	−0.295654	−	0.512088i	−0.975137	+	0.221604i	$0.928871\pi$
$450$		0			0
$451$	−1.38792	−	0.801316i	−0.0653546	−	0.0377325i
$452$	8.17395	+	12.5254i	0.384470	+	0.589147i
$453$		0			0
$454$	8.03919	−	0.219499i	0.377298	−	0.0103016i
$455$	12.4393	+	4.52755i	0.583166	+	0.212255i
$456$		0			0
$457$	3.14504	−	17.8364i	0.147119	−	0.834352i	−0.818523	−	0.574474i	$-0.805207\pi$
$457$	3.14504	−	17.8364i	0.147119	−	0.834352i	0.965642	−	0.259878i	$-0.0836822\pi$
$458$	24.1233	+	19.1446i	1.12721	+	0.894569i
$459$		0			0
$460$	10.7415	−	2.50515i	0.500824	−	0.116803i
$461$	6.87340	+	1.21197i	0.320126	+	0.0564469i	0.331402	−	0.943490i	$-0.392478\pi$
$461$	6.87340	+	1.21197i	0.320126	+	0.0564469i	−0.0112760	+	0.999936i	$0.503589\pi$
$462$		0			0
$463$	26.8210	+	9.76206i	1.24648	+	0.453681i	0.879210	−	0.476434i	$-0.158071\pi$
$463$	26.8210	+	9.76206i	1.24648	+	0.453681i	0.367269	+	0.930115i	$0.380293\pi$
$464$	−31.9928	−	14.0732i	−1.48523	−	0.653332i
$465$		0			0
$466$	−10.5085	+	31.5235i	−0.486796	+	1.46030i
$467$	0.471619	+	0.272289i	0.0218239	+	0.0126000i	0.510872	−	0.859657i	$-0.329323\pi$
$467$	0.471619	+	0.272289i	0.0218239	+	0.0126000i	−0.489048	+	0.872257i	$0.662656\pi$
$468$		0			0
$469$	0.315627	−	0.182227i	0.0145743	−	0.00841448i
$470$	−2.66729	−	13.0356i	−0.123033	−	0.601288i
$471$		0			0
$472$	−7.30926	−	2.00069i	−0.336436	−	0.0920891i
$473$	0.326975	+	1.85437i	0.0150343	+	0.0852640i
$474$		0			0
$475$	−2.29584	+	2.73608i	−0.105340	+	0.125540i
$476$	6.67686	−	6.25422i	0.306033	−	0.286662i
$477$		0			0
$478$	−12.1624	−	30.7752i	−0.556295	−	1.40762i
$479$	−7.93244	+	2.88717i	−0.362442	+	0.131918i	−0.516821	−	0.856094i	$-0.672885\pi$
$479$	−7.93244	+	2.88717i	−0.362442	+	0.131918i	0.154379	+	0.988012i	$0.450662\pi$
$480$		0			0
$481$	−15.6752	+	13.1530i	−0.714725	+	0.599726i
$482$	4.73479	−	2.90877i	0.215664	−	0.132491i
$483$		0			0
$484$	−21.9166	+	1.19769i	−0.996207	+	0.0544406i
$485$			16.3079i			0.740505i
$486$		0			0
$487$	−15.0013			−0.679775			−0.339888	−	0.940466i	$-0.610389\pi$
$487$	−15.0013			−0.679775			−0.339888	+	0.940466i	$0.610389\pi$
$488$	−3.32505	−	2.35497i	−0.150518	−	0.106604i
$489$		0			0
$490$	−7.97207	−	12.9767i	−0.360142	−	0.586227i
$491$	9.43399	+	11.2430i	0.425750	+	0.507389i	0.935691	−	0.352820i	$-0.114777\pi$
$491$	9.43399	+	11.2430i	0.425750	+	0.507389i	−0.509941	+	0.860209i	$0.670333\pi$
$492$		0			0
$493$	8.58191	+	23.5786i	0.386510	+	1.06193i
$494$	−7.76365	−	19.6448i	−0.349303	−	0.883861i
$495$		0			0
$496$	23.6843	+	15.8218i	1.06346	+	0.710419i
$497$	6.88991	+	5.78132i	0.309055	+	0.259328i
$498$		0			0
$499$	−17.0588	+	3.00792i	−0.763655	+	0.134653i	−0.541892	−	0.840448i	$-0.682292\pi$
$499$	−17.0588	+	3.00792i	−0.763655	+	0.134653i	−0.221762	+	0.975101i	$0.571181\pi$
$500$	7.91757	+	18.5374i	0.354084	+	0.829017i
$501$		0			0
$502$	0.141407	+	0.691086i	0.00631131	+	0.0308447i
$503$	2.40445	+	4.16463i	0.107209	+	0.185692i	0.914639	−	0.404272i	$-0.132475\pi$
$503$	2.40445	+	4.16463i	0.107209	+	0.185692i	−0.807429	+	0.589964i	$0.799142\pi$
$504$		0			0
$505$	−2.05591	+	3.56095i	−0.0914870	+	0.158460i
$506$	0.488397	+	0.162809i	0.0217119	+	0.00723775i
$507$		0			0
$508$	22.1669	+	16.6265i	0.983497	+	0.737680i
$509$	10.1785	−	27.9653i	0.451155	−	1.23954i	−0.480757	−	0.876854i	$-0.659638\pi$
$509$	10.1785	−	27.9653i	0.451155	−	1.23954i	0.931912	−	0.362685i	$-0.118140\pi$
$510$		0			0
$511$	−3.95313	+	22.4193i	−0.174876	+	0.991772i
$512$	5.50316	+	21.9480i	0.243208	+	0.969974i
$513$		0			0
$514$	0.790690	−	0.996316i	0.0348759	−	0.0439456i
$515$	30.4722	+	5.37308i	1.34277	+	0.236766i
$516$		0			0
$517$	0.212412	−	0.583597i	0.00934187	−	0.0256666i
$518$	−13.3807	+	0.365340i	−0.587912	+	0.0160521i
$519$		0			0
$520$	23.4044	+	2.17446i	1.02635	+	0.0953566i
$521$	−15.3931	+	26.6615i	−0.674382	+	1.16806i	0.302267	+	0.953223i	$0.402256\pi$
$521$	−15.3931	+	26.6615i	−0.674382	+	1.16806i	−0.976649	+	0.214840i	$0.931077\pi$
$522$		0			0
$523$	20.1716	−	11.6461i	0.882042	−	0.509247i	0.0107111	−	0.999943i	$-0.496590\pi$
$523$	20.1716	−	11.6461i	0.882042	−	0.509247i	0.871331	+	0.490695i	$0.163257\pi$
$524$	−9.21473	−	4.66924i	−0.402547	−	0.203977i
$525$		0			0
$526$	12.4665	+	6.75072i	0.543564	+	0.294345i
$527$	−3.55077	−	20.1374i	−0.154674	−	0.877200i
$528$		0			0
$529$	−13.6183	−	11.4271i	−0.592099	−	0.496830i
$530$	−33.1104	−	4.91059i	−1.43823	−	0.213302i
$531$		0			0
$532$	4.01044	−	13.2231i	0.173875	−	0.573295i
$533$	−11.8499	−	32.5574i	−0.513278	−	1.41022i
$534$		0			0
$535$	29.1263	−	24.4399i	1.25924	−	1.05663i
$536$	0.460047	−	0.455127i	0.0198710	−	0.0196585i
$537$		0			0
$538$	1.10109	−	0.976354i	0.0474712	−	0.0420936i
$539$		−	0.710862i		−	0.0306190i
$540$		0			0
$541$		−	29.0030i		−	1.24694i	−0.781848	−	0.623469i	$-0.785723\pi$
$541$		−	29.0030i		−	1.24694i	0.781848	−	0.623469i	$-0.214277\pi$
$542$	−28.1863	−	31.7872i	−1.21071	−	1.36538i
$543$		0			0
$544$	8.65146	−	13.7489i	0.370928	−	0.589479i
$545$	−7.83541	+	6.57469i	−0.335632	+	0.281629i
$546$		0			0
$547$	−3.84045	−	10.5516i	−0.164206	−	0.451152i	0.830113	−	0.557596i	$-0.188276\pi$
$547$	−3.84045	−	10.5516i	−0.164206	−	0.451152i	−0.994319	+	0.106443i	$0.966054\pi$
$548$	36.0904	+	10.9458i	1.54171	+	0.467583i
$549$		0			0
$550$	0.0272152	−	0.183503i	0.00116046	−	0.00782458i
$551$	29.0320	+	24.3607i	1.23681	+	1.03780i
$552$		0			0
$553$	−3.47684	−	19.7182i	−0.147850	−	0.838501i
$554$	13.2296	−	24.4309i	0.562070	−	1.03797i
$555$		0			0
$556$	28.8779	+	14.6329i	1.22470	+	0.620573i
$557$	2.53413	−	1.46308i	0.107374	−	0.0619927i	−0.445351	−	0.895356i	$-0.646921\pi$
$557$	2.53413	−	1.46308i	0.107374	−	0.0619927i	0.552726	+	0.833363i	$0.313588\pi$
$558$		0			0
$559$	−20.3538	+	35.2538i	−0.860874	+	1.49108i
$560$	11.1082	+	10.6316i	0.469408	+	0.449266i
$561$		0			0
$562$	−1.07172	−	39.2520i	−0.0452078	−	1.65575i
$563$	−2.96778	+	8.15390i	−0.125077	+	0.343646i	−0.986389	−	0.164431i	$-0.947421\pi$
$563$	−2.96778	+	8.15390i	−0.125077	+	0.343646i	0.861312	+	0.508077i	$0.169643\pi$
$564$		0			0
$565$	17.7724	+	3.13375i	0.747690	+	0.131838i
$566$	−27.6452	−	21.9396i	−1.16201	−	0.922190i
$567$		0			0
$568$	14.4375	+	6.82703i	0.605782	+	0.286456i
$569$	1.80356	−	10.2285i	0.0756093	−	0.428802i	−0.923381	−	0.383884i	$-0.874586\pi$
$569$	1.80356	−	10.2285i	0.0756093	−	0.428802i	0.998991	−	0.0449179i	$-0.0143026\pi$
$570$		0			0
$571$	−1.71537	+	4.71295i	−0.0717862	+	0.197231i	−0.970397	−	0.241516i	$-0.922355\pi$
$571$	−1.71537	+	4.71295i	−0.0717862	+	0.197231i	0.898611	+	0.438747i	$0.144578\pi$
$572$	0.877670	+	0.658303i	0.0366972	+	0.0275250i
$573$		0			0
$574$	7.16754	−	21.5013i	0.299167	−	0.897446i
$575$	0.940956	−	1.62978i	0.0392406	−	0.0679667i
$576$		0			0
$577$	4.43057	+	7.67398i	0.184447	+	0.319472i	0.943390	−	0.331685i	$-0.107617\pi$
$577$	4.43057	+	7.67398i	0.184447	+	0.319472i	−0.758943	+	0.651157i	$0.774284\pi$
$578$	12.1284	−	2.48166i	0.504474	−	0.103223i
$579$		0			0
$580$	−38.7827	+	16.5646i	−1.61037	+	0.687809i
$581$	−17.6940	+	3.11993i	−0.734070	+	0.129436i
$582$		0			0
$583$	−1.19683	−	1.00426i	−0.0495677	−	0.0415922i
$584$	3.30651	+	40.2870i	0.136824	+	1.66709i
$585$		0			0
$586$	10.7396	−	4.24430i	0.443648	−	0.175330i
$587$	−0.553940	−	1.52194i	−0.0228636	−	0.0628171i	0.927736	−	0.373238i	$-0.121752\pi$
$587$	−0.553940	−	1.52194i	−0.0228636	−	0.0628171i	−0.950599	+	0.310420i	$0.899530\pi$
$588$		0			0
$589$	−19.8523	−	23.6590i	−0.817999	−	0.974854i
$590$	−7.79097	+	4.78629i	−0.320749	+	0.197048i
$591$		0			0
$592$	−22.8177	+	6.65333i	−0.937801	+	0.273450i
$593$	16.7535			0.687984			0.343992	−	0.938973i	$-0.388221\pi$
$593$	16.7535			0.687984			0.343992	+	0.938973i	$0.388221\pi$
$594$		0			0
$595$		−	11.0386i		−	0.452538i
$596$	−1.41547	−	25.9016i	−0.0579799	−	1.06097i
$597$		0			0
$598$	5.82588	+	9.48317i	0.238238	+	0.387796i
$599$	31.3875	−	26.3372i	1.28246	−	1.07611i	0.289557	−	0.957161i	$-0.406492\pi$
$599$	31.3875	−	26.3372i	1.28246	−	1.07611i	0.992900	−	0.118949i	$-0.0379524\pi$
$600$		0			0
$601$	−8.03176	+	2.92332i	−0.327622	+	0.119245i	−0.500594	−	0.865682i	$-0.666885\pi$
$601$	−8.03176	+	2.92332i	−0.327622	+	0.119245i	0.172972	+	0.984927i	$0.444663\pi$
$602$	−24.7653	+	9.78727i	−1.00936	+	0.398899i
$603$		0			0
$604$	−4.91073	+	4.59988i	−0.199815	+	0.187167i
$605$	−17.0235	+	20.2878i	−0.692103	+	0.824817i
$606$		0			0
$607$	4.22098	+	23.9383i	0.171324	+	0.971627i	0.942302	+	0.334765i	$0.108657\pi$
$607$	4.22098	+	23.9383i	0.171324	+	0.971627i	−0.770978	+	0.636862i	$0.780232\pi$
$608$	0.933321	−	24.5177i	0.0378511	−	0.994324i
$609$		0			0
$610$	−4.81652	+	0.985535i	−0.195015	+	0.0399031i
$611$	11.6276	−	6.71318i	0.470401	−	0.271586i
$612$		0			0
$613$	−14.3628	−	8.29237i	−0.580108	−	0.334926i	0.181068	−	0.983471i	$-0.442045\pi$
$613$	−14.3628	−	8.29237i	−0.580108	−	0.334926i	−0.761176	+	0.648545i	$0.775378\pi$
$614$	−24.9784	−	8.32665i	−1.00805	−	0.336036i
$615$		0			0
$616$	0.182021	+	0.694220i	0.00733385	+	0.0279709i
$617$	17.6023	+	6.40672i	0.708642	+	0.257925i	0.671096	−	0.741370i	$-0.265824\pi$
$617$	17.6023	+	6.40672i	0.708642	+	0.257925i	0.0375461	+	0.999295i	$0.488046\pi$
$618$		0			0
$619$	4.87939	+	0.860368i	0.196119	+	0.0345811i	0.270845	−	0.962623i	$-0.412697\pi$
$619$	4.87939	+	0.860368i	0.196119	+	0.0345811i	−0.0747256	+	0.997204i	$0.523808\pi$
$620$	33.4691	−	7.80575i	1.34415	−	0.313486i
$621$		0			0
$622$	−4.31146	+	5.43269i	−0.172874	+	0.217831i
$623$	−2.06579	+	11.7157i	−0.0827643	+	0.469380i
$624$		0			0
$625$	26.7242	+	9.72681i	1.06897	+	0.389072i
$626$	−0.397499	−	14.5585i	−0.0158872	−	0.581874i
$627$		0			0
$628$	−0.835199	+	0.545041i	−0.0333281	+	0.0217495i
$629$	14.7771	+	8.53157i	0.589202	+	0.340176i
$630$		0			0
$631$	−2.46788	−	4.27449i	−0.0982447	−	0.170165i	0.812713	−	0.582664i	$-0.197989\pi$
$631$	−2.46788	−	4.27449i	−0.0982447	−	0.170165i	−0.910958	+	0.412499i	$0.864656\pi$
$632$	−14.8516	−	32.3015i	−0.590764	−	1.28489i
$633$		0			0
$634$	15.2053	−	28.0794i	0.603879	−	1.11518i
$635$	32.9261	−	5.80576i	1.30663	−	0.230394i
$636$		0			0
$637$	9.87834	−	11.7725i	0.391394	−	0.466445i
$638$	−1.94711	−	0.288775i	−0.0770869	−	0.0114327i
$639$		0			0
$640$	23.8669	+	13.2580i	0.943424	+	0.524069i
$641$	−1.74409	+	0.634798i	−0.0688875	+	0.0250730i	−0.376234	−	0.926525i	$-0.622781\pi$
$641$	−1.74409	+	0.634798i	−0.0688875	+	0.0250730i	0.307347	+	0.951598i	$0.400559\pi$
$642$		0			0
$643$	21.2761	+	25.3559i	0.839048	+	0.999938i	0.999916	+	0.0129623i	$0.00412614\pi$
$643$	21.2761	+	25.3559i	0.839048	+	0.999938i	−0.160868	+	0.986976i	$0.551429\pi$
$644$	−0.871137	+	7.22829i	−0.0343276	+	0.284835i
$645$		0			0
$646$	−13.1792	+	11.6862i	−0.518528	+	0.459789i
$647$	−8.85391			−0.348083			−0.174042	−	0.984738i	$-0.555683\pi$
$647$	−8.85391			−0.348083			−0.174042	+	0.984738i	$0.555683\pi$
$648$		0			0
$649$	−0.426789			−0.0167529
$650$	3.00071	−	2.66079i	0.117698	−	0.104365i
$651$		0			0
$652$	−22.4458	−	2.70511i	−0.879044	−	0.105940i
$653$	−6.38975	−	7.61501i	−0.250050	−	0.297998i	0.626389	−	0.779511i	$-0.284532\pi$
$653$	−6.38975	−	7.61501i	−0.250050	−	0.297998i	−0.876439	+	0.481512i	$0.840088\pi$
$654$		0			0
$655$	−11.7127	+	4.26306i	−0.457652	+	0.166572i
$656$	2.62788	−	40.1578i	0.102601	−	1.56790i
$657$		0			0
$658$	8.68790	+	1.28850i	0.338690	+	0.0502308i
$659$	−27.1973	+	32.4125i	−1.05946	+	1.26261i	−0.0958197	+	0.995399i	$0.530547\pi$
$659$	−27.1973	+	32.4125i	−1.05946	+	1.26261i	−0.963637	+	0.267213i	$0.913897\pi$
$660$		0			0
$661$	49.7307	−	8.76886i	1.93430	−	0.341069i	0.934414	−	0.356189i	$-0.115924\pi$
$661$	49.7307	−	8.76886i	1.93430	−	0.341069i	0.999886	+	0.0151198i	$0.00481297\pi$
$662$	−15.8754	+	29.3170i	−0.617017	+	1.13944i
$663$		0			0
$664$	−28.9856	+	13.3270i	−1.12486	+	0.517187i
$665$	−8.33631	−	14.4389i	−0.323268	−	0.559917i
$666$		0			0
$667$	−17.2933	−	9.98430i	−0.669600	−	0.386594i
$668$	−14.3965	−	22.0606i	−0.557016	−	0.853550i
$669$		0			0
$670$	−0.0213115	−	0.780540i	−0.000823337	−	0.0301549i
$671$	−0.215633	−	0.0784840i	−0.00832442	−	0.00302984i
$672$		0			0
$673$	2.52619	−	14.3267i	0.0973775	−	0.552255i	−0.896615	−	0.442810i	$-0.853981\pi$
$673$	2.52619	−	14.3267i	0.0973775	−	0.552255i	0.993993	−	0.109445i	$-0.0349074\pi$
$674$	28.9072	−	36.4247i	1.11346	−	1.40303i
$675$		0			0
$676$	−0.518230	−	2.22204i	−0.0199319	−	0.0854632i
$677$	39.3485	+	6.93820i	1.51229	+	0.266657i	0.867396	−	0.497619i	$-0.165792\pi$
$677$	39.3485	+	6.93820i	1.51229	+	0.266657i	0.644890	+	0.764276i	$0.276903\pi$
$678$		0			0
$679$	−10.1155	−	3.68173i	−0.388197	−	0.141292i
$680$	−4.97110	−	18.9595i	−0.190633	−	0.727064i
$681$		0			0
$682$	1.52179	+	0.507294i	0.0582723	+	0.0194253i
$683$	16.3031	+	9.41260i	0.623821	+	0.360163i	0.778355	−	0.627824i	$-0.216054\pi$
$683$	16.3031	+	9.41260i	0.623821	+	0.360163i	−0.154534	+	0.987987i	$0.549388\pi$
$684$		0			0
$685$	39.4087	−	22.7526i	1.50573	−	0.869333i
$686$	25.2980	−	5.17636i	0.965881	−	0.197634i
$687$		0			0
$688$	−38.1285	+	27.9631i	−1.45364	+	1.06608i
$689$	−5.86516	−	33.2630i	−0.223445	−	1.26722i
$690$		0			0
$691$	7.33473	−	8.74119i	0.279026	−	0.332531i	−0.608270	−	0.793730i	$-0.708136\pi$
$691$	7.33473	−	8.74119i	0.279026	−	0.332531i	0.887297	+	0.461199i	$0.152581\pi$
$692$	−22.3942	−	23.9076i	−0.851300	−	0.908829i
$693$		0			0
$694$	1.10995	−	0.438654i	0.0421331	−	0.0166511i
$695$	36.7062	−	13.3600i	1.39235	−	0.506773i
$696$		0			0
$697$	−22.1320	+	18.5709i	−0.838307	+	0.703423i
$698$	−10.3788	−	16.8942i	−0.392842	−	0.639456i
$699$		0			0
$700$	2.61958	−	0.143155i	0.0990108	−	0.00541073i
$701$		−	29.8398i		−	1.12704i	−0.826104	−	0.563518i	$-0.809448\pi$
$701$		−	29.8398i		−	1.12704i	0.826104	−	0.563518i	$-0.190552\pi$
$702$		0			0
$703$	25.7721			0.972013
$704$	0.625269	+	1.11040i	0.0235657	+	0.0418498i
$705$		0			0
$706$	−28.4121	+	17.4547i	−1.06930	+	0.656915i
$707$	−1.74463	−	2.07917i	−0.0656137	−	0.0781954i
$708$		0			0
$709$	0.897749	+	2.46655i	0.0337157	+	0.0926331i	0.955408	−	0.295288i	$-0.0954156\pi$
$709$	0.897749	+	2.46655i	0.0337157	+	0.0926331i	−0.921693	+	0.387921i	$0.873193\pi$
$710$	17.9209	−	7.08235i	0.672559	−	0.265796i
$711$		0			0
$712$	1.72789	+	21.0528i	0.0647554	+	0.788989i
$713$	12.4658	+	10.4601i	0.466849	+	0.391733i
$714$		0			0
$715$	1.30367	−	0.229871i	0.0487543	−	0.00859670i
$716$	−4.65704	−	10.9035i	−0.174042	−	0.407483i
$717$		0			0
$718$	37.3968	−	7.65198i	1.39564	−	0.285569i
$719$	6.54404	+	11.3346i	0.244051	+	0.422709i	0.961864	−	0.273526i	$-0.0881901\pi$
$719$	6.54404	+	11.3346i	0.244051	+	0.422709i	−0.717813	+	0.696236i	$0.754857\pi$
$720$		0			0
$721$	−10.2123	+	17.6883i	−0.380327	+	0.658746i
$722$	0.0840213	−	0.252049i	0.00312695	−	0.00938027i
$723$		0			0
$724$	2.08968	−	2.78602i	0.0776623	−	0.103542i
$725$	−2.46100	+	6.76154i	−0.0913992	+	0.251117i
$726$		0			0
$727$	6.97054	−	39.5319i	0.258523	−	1.46616i	−0.528342	−	0.849031i	$-0.677186\pi$
$727$	6.97054	−	39.5319i	0.258523	−	1.46616i	0.786865	−	0.617125i	$-0.211703\pi$
$728$	−6.63263	+	14.0263i	−0.245822	+	0.519851i
$729$		0			0
$730$	38.2044	+	30.3196i	1.41401	+	1.12218i
$731$	33.4294	+	5.89450i	1.23643	+	0.218016i
$732$		0			0
$733$	−0.696450	+	1.91348i	−0.0257240	+	0.0706760i	−0.951890	−	0.306440i	$-0.900862\pi$
$733$	−0.696450	+	1.91348i	−0.0257240	+	0.0706760i	0.926166	+	0.377116i	$0.123084\pi$
$734$	1.12454	+	41.1866i	0.0415077	+	1.52023i
$735$		0			0
$736$	1.75894	+	12.8074i	0.0648354	+	0.472087i
$737$	0.0182229	−	0.0315629i	0.000671248	−	0.00116264i
$738$		0			0
$739$	−30.6990	+	17.7241i	−1.12928	+	0.651990i	−0.943754	−	0.330649i	$-0.892732\pi$
$739$	−30.6990	+	17.7241i	−1.12928	+	0.651990i	−0.185526	+	0.982639i	$0.559399\pi$
$740$	−12.9625	+	25.5815i	−0.476512	+	0.940395i
$741$		0			0
$742$	10.5211	−	19.4291i	0.386240	−	0.713265i
$743$	−9.22773	−	52.3330i	−0.338532	−	1.91991i	−0.389106	−	0.921193i	$-0.627216\pi$
$743$	−9.22773	−	52.3330i	−0.338532	−	1.91991i	0.0505739	−	0.998720i	$-0.483895\pi$
$744$		0			0
$745$	−23.9767	−	20.1189i	−0.878440	−	0.737099i
$746$	−0.238461	+	1.60786i	−0.00873069	+	0.0588681i
$747$		0			0
$748$	0.265524	−	0.875480i	0.00970853	−	0.0320107i
$749$	8.58392	+	23.5841i	0.313649	+	0.861745i
$750$		0			0
$751$	6.58894	−	5.52878i	0.240434	−	0.201748i	−0.514606	−	0.857427i	$-0.672062\pi$
$751$	6.58894	−	5.52878i	0.240434	−	0.201748i	0.755040	+	0.655679i	$0.227617\pi$
$752$	15.5023	−	1.69942i	0.565312	−	0.0619713i
$753$		0			0
$754$	−28.2331	−	31.8400i	−1.02819	−	1.15954i
$755$			8.11871i			0.295470i
$756$		0			0
$757$		−	21.7216i		−	0.789484i	−0.918792	−	0.394742i	$-0.870834\pi$
$757$		−	21.7216i		−	0.789484i	0.918792	−	0.394742i	$-0.129166\pi$
$758$	−17.8956	+	15.8684i	−0.649998	+	0.576365i
$759$		0			0
$760$	−20.8206	−	21.0457i	−0.755242	−	0.763407i
$761$	0.341041	−	0.286168i	0.0123627	−	0.0103736i	−0.636585	−	0.771206i	$-0.719654\pi$
$761$	0.341041	−	0.286168i	0.0123627	−	0.0103736i	0.648948	+	0.760833i	$0.275209\pi$
$762$		0			0
$763$	−2.30920	−	6.34447i	−0.0835986	−	0.229685i
$764$	−20.7893	−	6.30519i	−0.752132	−	0.228114i
$765$		0			0
$766$	−28.2272	−	4.18636i	−1.01989	−	0.151259i
$767$	−7.06802	−	5.93077i	−0.255211	−	0.214148i
$768$		0			0
$769$	3.22004	+	18.2618i	0.116118	+	0.658536i	0.986191	+	0.165614i	$0.0529604\pi$
$769$	3.22004	+	18.2618i	0.116118	+	0.658536i	−0.870073	+	0.492923i	$0.835928\pi$
$770$	0.761478	+	0.412349i	0.0274418	+	0.0148600i
$771$		0			0
$772$	13.0854	−	25.8240i	0.470954	−	0.929426i
$773$	1.50501	−	0.868919i	0.0541315	−	0.0312528i	−0.472690	−	0.881229i	$-0.656717\pi$
$773$	1.50501	−	0.868919i	0.0541315	−	0.0312528i	0.526822	+	0.849976i	$0.323384\pi$
$774$		0			0
$775$	2.93190	−	5.07821i	0.105317	−	0.182415i
$776$	−19.0321	−	1.76824i	−0.683211	−	0.0634761i
$777$		0			0
$778$	−41.2268	+	1.12564i	−1.47805	+	0.0403562i
$779$	−14.9248	+	41.0055i	−0.534736	+	1.46918i
$780$		0			0
$781$	0.885756	+	0.156183i	0.0316948	+	0.00558865i
$782$	5.76934	−	7.26970i	0.206311	−	0.259964i
$783$		0			0
$784$	16.0088	−	7.89672i	0.571742	−	0.282026i
$785$	−0.208959	+	1.18507i	−0.00745808	+	0.0422969i
$786$		0			0
$787$	12.6576	−	34.7764i	0.451193	−	1.23964i	−0.480692	−	0.876890i	$-0.659614\pi$
$787$	12.6576	−	34.7764i	0.451193	−	1.23964i	0.931885	−	0.362754i	$-0.118163\pi$
$788$	−10.2114	+	13.6142i	−0.363767	+	0.484986i
$789$		0			0
$790$	−40.6955	−	13.5660i	−1.44788	−	0.482657i
$791$	−5.95616	+	10.3164i	−0.211777	+	0.366808i
$792$		0			0
$793$	−2.48045	−	4.29626i	−0.0880833	−	0.152565i
$794$	−3.37692	−	16.5037i	−0.119842	−	0.585695i
$795$		0			0
$796$	22.7310	−	9.70871i	0.805679	−	0.344116i
$797$	11.7114	−	2.06503i	0.414837	−	0.0731470i	0.0376658	−	0.999290i	$-0.488008\pi$
$797$	11.7114	−	2.06503i	0.414837	−	0.0731470i	0.377172	+	0.926143i	$0.376897\pi$
$798$		0			0
$799$	−8.57656	−	7.19659i	−0.303417	−	0.254597i
$800$	4.43484	−	1.42558i	0.156795	−	0.0504017i
$801$		0			0
$802$	−1.23727	−	3.13072i	−0.0436894	−	0.110550i
$803$	0.778620	+	2.13924i	0.0274769	+	0.0754922i
$804$		0			0
$805$	5.64671	+	6.72949i	0.199021	+	0.237183i
$806$	18.1527	+	29.5484i	0.639402	+	1.04080i
$807$		0			0
$808$	−3.93286	−	2.78545i	−0.138358	−	0.0979917i
$809$	−13.6067			−0.478385			−0.239192	−	0.970972i	$-0.576883\pi$
$809$	−13.6067			−0.478385			−0.239192	+	0.970972i	$0.576883\pi$
$810$		0			0
$811$			23.1998i			0.814656i	0.913282	+	0.407328i	$0.133539\pi$
$811$			23.1998i			0.814656i	−0.913282	+	0.407328i	$0.866461\pi$
$812$	−1.51899	−	27.7958i	−0.0533059	−	0.975443i
$813$		0			0
$814$	−1.14054	+	0.700677i	−0.0399759	+	0.0245587i
$815$	−20.8969	+	17.5346i	−0.731985	+	0.614209i
$816$		0			0
$817$	48.1785	−	17.5355i	1.68555	−	0.613491i
$818$	6.68662	+	16.9195i	0.233792	+	0.591578i
$819$		0			0
$820$	−33.1956	−	35.4389i	−1.15924	−	1.23758i
$821$	18.9516	−	22.5856i	0.661414	−	0.788243i	−0.326174	−	0.945310i	$-0.605759\pi$
$821$	18.9516	−	22.5856i	0.661414	−	0.788243i	0.987588	+	0.157067i	$0.0502039\pi$
$822$		0			0
$823$	2.95142	+	16.7383i	0.102880	+	0.583462i	0.992046	+	0.125877i	$0.0401744\pi$
$823$	2.95142	+	16.7383i	0.102880	+	0.583462i	−0.889166	+	0.457585i	$0.848715\pi$
$824$	−9.57467	+	34.9799i	−0.333549	+	1.21858i
$825$		0			0
$826$	−1.20992	−	5.91315i	−0.0420986	−	0.205745i
$827$	44.0488	−	25.4316i	1.53173	−	0.884343i	0.532444	−	0.846465i	$-0.321274\pi$
$827$	44.0488	−	25.4316i	1.53173	−	0.884343i	0.999282	−	0.0378772i	$-0.0120596\pi$
$828$		0			0
$829$	41.8595	+	24.1676i	1.45384	+	0.839374i	0.998696	−	0.0510440i	$-0.0162549\pi$
$829$	41.8595	+	24.1676i	1.45384	+	0.839374i	0.455143	+	0.890418i	$0.349588\pi$
$830$	−12.1734	+	36.5179i	−0.422544	+	1.26755i
$831$		0			0
$832$	−5.07539	+	27.0782i	−0.175957	+	0.938766i
$833$	−12.0421	−	4.38298i	−0.417235	−	0.151861i
$834$		0			0
$835$	−31.3019	−	5.51936i	−1.08325	−	0.191005i
$836$	−0.313844	−	1.34569i	−0.0108545	−	0.0465416i
$837$		0			0
$838$	8.30411	+	6.59026i	0.286861	+	0.227657i
$839$	−4.93028	+	27.9610i	−0.170212	+	0.965321i	0.773314	+	0.634023i	$0.218598\pi$
$839$	−4.93028	+	27.9610i	−0.170212	+	0.965321i	−0.943526	+	0.331298i	$0.892514\pi$
$840$		0			0
$841$	44.4943	+	16.1946i	1.53429	+	0.558434i
$842$	11.3324	−	0.309414i	0.390539	−	0.0106631i
$843$		0			0
$844$	2.96114	−	1.93240i	0.101927	−	0.0665161i
$845$	−2.38422	−	1.37653i	−0.0820196	−	0.0473540i
$846$		0			0
$847$	−8.74084	−	15.1396i	−0.300339	−	0.520202i
$848$	9.32097	−	38.1089i	0.320084	−	1.30866i
$849$		0			0
$850$	−2.94077	−	1.59246i	−0.100867	−	0.0546208i
$851$	−13.3729	+	2.35800i	−0.458417	+	0.0808313i
$852$		0			0
$853$	17.3921	−	20.7271i	0.595495	−	0.709684i	−0.381157	−	0.924510i	$-0.624474\pi$
$853$	17.3921	−	20.7271i	0.595495	−	0.709684i	0.976652	+	0.214827i	$0.0689186\pi$
$854$	0.476086	−	3.21009i	0.0162913	−	0.109847i
$855$		0			0
$856$	25.3643	+	36.6417i	0.866934	+	1.25239i
$857$	−1.73329	+	0.630867i	−0.0592082	+	0.0215500i	−0.371454	−	0.928451i	$-0.621141\pi$
$857$	−1.73329	+	0.630867i	−0.0592082	+	0.0215500i	0.312246	+	0.950001i	$0.398919\pi$
$858$		0			0
$859$	11.6792	+	13.9187i	0.398489	+	0.474901i	0.927559	−	0.373678i	$-0.121903\pi$
$859$	11.6792	+	13.9187i	0.398489	+	0.474901i	−0.529070	+	0.848578i	$0.677459\pi$
$860$	−6.82637	+	56.6420i	−0.232777	+	1.93148i
$861$		0			0
$862$	4.35074	+	4.90656i	0.148187	+	0.167118i
$863$	−49.6695			−1.69077			−0.845385	−	0.534157i	$-0.820629\pi$
$863$	−49.6695			−1.69077			−0.845385	+	0.534157i	$0.820629\pi$
$864$		0			0
$865$	−39.5254			−1.34390
$866$	−0.0636504	−	0.0717820i	−0.00216293	−	0.00243925i
$867$		0			0
$868$	−2.71436	+	22.5225i	−0.0921313	+	0.764463i
$869$	−1.28702	−	1.53381i	−0.0436592	−	0.0520310i
$870$		0			0
$871$	0.740394	−	0.269482i	0.0250873	−	0.00913103i
$872$	−6.82337	−	9.85715i	−0.231068	−	0.333805i
$873$		0			0
$874$	2.05647	−	13.8661i	0.0695610	−	0.469026i
$875$	−10.3197	+	12.2985i	−0.348869	+	0.415766i
$876$		0			0
$877$	−22.9919	+	4.05410i	−0.776382	+	0.136897i	−0.547779	−	0.836623i	$-0.684527\pi$
$877$	−22.9919	+	4.05410i	−0.776382	+	0.136897i	−0.228603	+	0.973520i	$0.573416\pi$
$878$	17.1419	+	9.28253i	0.578512	+	0.313270i
$879$		0			0
$880$	1.49359	+	0.365314i	0.0503489	+	0.0123147i
$881$	15.9640	+	27.6505i	0.537842	+	0.931569i	0.999020	+	0.0442614i	$0.0140935\pi$
$881$	15.9640	+	27.6505i	0.537842	+	0.931569i	−0.461178	+	0.887307i	$0.652573\pi$
$882$		0			0
$883$	40.1101	+	23.1576i	1.34981	+	0.779315i	0.988223	−	0.153023i	$-0.0489007\pi$
$883$	40.1101	+	23.1576i	1.34981	+	0.779315i	0.361590	+	0.932337i	$0.382234\pi$
$884$	16.5632	−	10.8090i	0.557082	−	0.363545i
$885$		0			0
$886$	−18.8710	+	0.515247i	−0.633984	+	0.0173101i
$887$	32.0649	+	11.6707i	1.07663	+	0.391863i	0.818654	−	0.574288i	$-0.194721\pi$
$887$	32.0649	+	11.6707i	1.07663	+	0.391863i	0.257980	+	0.966150i	$0.416943\pi$
$888$		0			0
$889$	−3.83231	+	21.7341i	−0.128532	+	0.728939i
$890$	19.9646	+	15.8442i	0.669214	+	0.531097i
$891$		0			0
$892$	−1.36671	−	5.86013i	−0.0457609	−	0.196212i
$893$	−16.6533	−	2.93643i	−0.557283	−	0.0982640i
$894$		0			0
$895$	−13.4431	−	4.89290i	−0.449354	−	0.163552i
$896$	−13.6120	+	11.8110i	−0.454744	+	0.394578i
$897$		0			0
$898$	5.60372	−	16.8101i	0.186998	−	0.560961i
$899$	−53.8839	−	31.1099i	−1.79713	−	1.03757i
$900$		0			0
$901$	−24.3917	+	14.0825i	−0.812605	+	0.469158i
$902$	−0.454340	−	2.22046i	−0.0151279	−	0.0739332i
$903$		0			0
$904$	−5.58425	+	20.4014i	−0.185730	+	0.678539i
$905$	−0.729690	−	4.13828i	−0.0242557	−	0.137561i
$906$		0			0
$907$	−0.685743	+	0.817237i	−0.0227697	+	0.0271359i	−0.777309	−	0.629119i	$-0.783416\pi$
$907$	−0.685743	+	0.817237i	−0.0227697	+	0.0271359i	0.754539	+	0.656255i	$0.227860\pi$
$908$	7.77518	+	8.30061i	0.258029	+	0.275466i
$909$		0			0
$910$	6.88068	+	17.4106i	0.228092	+	0.577155i
$911$	−2.39685	+	0.872383i	−0.0794113	+	0.0289033i	−0.381420	−	0.924402i	$-0.624565\pi$
$911$	−2.39685	+	0.872383i	−0.0794113	+	0.0289033i	0.302009	+	0.953305i	$0.402343\pi$
$912$		0			0
$913$	−1.37636	+	1.15490i	−0.0455508	+	0.0382216i
$914$	21.8242	−	13.4075i	0.721881	−	0.443479i
$915$		0			0
$916$	2.37656	+	43.4885i	0.0785237	+	1.43690i
$917$		−	8.22758i		−	0.271699i
$918$		0			0
$919$	3.85703			0.127232			0.0636159	−	0.997974i	$-0.479737\pi$
$919$	3.85703			0.127232			0.0636159	+	0.997974i	$0.479737\pi$
$920$	12.7292	+	9.01544i	0.419669	+	0.297230i
$921$		0			0
$922$	5.16667	+	8.41015i	0.170155	+	0.276973i
$923$	12.4986	+	14.8952i	0.411396	+	0.490283i
$924$		0			0
$925$	1.67355	+	4.59804i	0.0550259	+	0.151182i
$926$	14.8357	+	37.5397i	0.487533	+	1.23363i
$927$		0			0
$928$	−15.1265	−	47.0572i	−0.496552	−	1.54473i
$929$	−23.6191	−	19.8188i	−0.774919	−	0.650234i	0.167045	−	0.985949i	$-0.446578\pi$
$929$	−23.6191	−	19.8188i	−0.774919	−	0.650234i	−0.941964	+	0.335715i	$0.891022\pi$
$930$		0			0
$931$	−19.0616	+	3.36108i	−0.624719	+	0.110155i
$932$	−43.2160	+	18.4581i	−1.41559	+	0.604616i
$933$		0			0
$934$	0.154386	+	0.754517i	0.00505167	+	0.0246886i
$935$	−0.551933	−	0.955975i	−0.0180501	−	0.0312637i
$936$		0			0
$937$	3.69048	−	6.39210i	0.120563	−	0.208821i	−0.799427	−	0.600763i	$-0.794863\pi$
$937$	3.69048	−	6.39210i	0.120563	−	0.208821i	0.919990	+	0.391942i	$0.128197\pi$
$938$	0.488964	+	0.162998i	0.0159653	+	0.00532208i
$939$		0			0
$940$	11.2908	−	15.0533i	0.368266	−	0.490983i
$941$	−13.1119	+	36.0246i	−0.427435	+	1.17437i	0.519929	+	0.854209i	$0.325958\pi$
$941$	−13.1119	+	36.0246i	−0.427435	+	1.17437i	−0.947364	+	0.320158i	$0.896264\pi$
$942$		0			0
$943$	3.99256	−	22.6429i	0.130016	−	0.737355i
$944$	−4.74105	−	9.61137i	−0.154308	−	0.312823i
$945$		0			0
$946$	−1.65538	+	2.08588i	−0.0538212	+	0.0678178i
$947$	−21.8272	−	3.84873i	−0.709289	−	0.125067i	−0.192647	−	0.981268i	$-0.561707\pi$
$947$	−21.8272	−	3.84873i	−0.709289	−	0.125067i	−0.516642	+	0.856201i	$0.672818\pi$
$948$		0			0
$949$	−16.8328	+	46.2477i	−0.546416	+	1.50126i
$950$	−5.04926	+	0.137863i	−0.163820	+	0.00447287i
$951$		0			0
$952$	12.8825	+	1.19689i	0.417524	+	0.0387915i
$953$	−22.3908	+	38.7819i	−0.725308	+	1.25627i	0.233540	+	0.972347i	$0.424969\pi$
$953$	−22.3908	+	38.7819i	−0.725308	+	1.25627i	−0.958847	+	0.283922i	$0.908364\pi$
$954$		0			0
$955$	−22.7008	+	13.1063i	−0.734580	+	0.424110i
$956$	21.1528	−	41.7449i	0.684129	−	1.35013i
$957$		0			0
$958$	−10.4978	−	5.68466i	−0.339168	−	0.183663i
$959$	5.21595	+	29.5811i	0.168432	+	0.955224i
$960$		0			0
$961$	15.0947	+	12.6659i	0.486925	+	0.408579i
$962$	−28.6252	−	4.24538i	−0.922913	−	0.136877i
$963$		0			0
$964$	7.52038	+	2.28085i	0.242215	+	0.0734614i
$965$	−11.9471	−	32.8244i	−0.384591	−	1.05666i
$966$		0			0
$967$	32.4852	−	27.2583i	1.04465	−	0.876567i	0.0521310	−	0.998640i	$-0.483399\pi$
$967$	32.4852	−	27.2583i	1.04465	−	0.876567i	0.992521	+	0.122073i	$0.0389542\pi$
$968$	−21.8309	−	22.0669i	−0.701673	−	0.709258i
$969$		0			0
$970$	−17.2560	+	15.3012i	−0.554057	+	0.491293i
$971$		−	9.33492i		−	0.299572i	−0.988718	−	0.149786i	$-0.952142\pi$
$971$		−	9.33492i		−	0.299572i	0.988718	−	0.149786i	$-0.0478584\pi$
$972$		0			0
$973$			25.7843i			0.826608i
$974$	−14.0753	−	15.8735i	−0.451001	−	0.508618i
$975$		0			0
$976$	−0.627916	−	5.72795i	−0.0200991	−	0.183347i
$977$	−0.274142	+	0.230032i	−0.00877057	+	0.00735938i	−0.647162	−	0.762352i	$-0.724044\pi$
$977$	−0.274142	+	0.230032i	−0.00877057	+	0.00735938i	0.638392	+	0.769712i	$0.279600\pi$
$978$		0			0
$979$	0.406885	+	1.11791i	0.0130041	+	0.0357285i
$980$	6.25115	−	20.6112i	0.199686	−	0.658399i
$981$		0			0
$982$	−3.04500	+	20.5314i	−0.0971698	+	0.655183i
$983$	6.53130	+	5.48041i	0.208316	+	0.174798i	0.740976	−	0.671531i	$-0.234363\pi$
$983$	6.53130	+	5.48041i	0.208316	+	0.174798i	−0.532660	+	0.846329i	$0.678808\pi$
$984$		0			0
$985$	3.56571	+	20.2221i	0.113613	+	0.644331i
$986$	−16.8972	+	31.2039i	−0.538118	+	0.993734i
$987$		0			0
$988$	13.5025	−	26.6471i	0.429571	−	0.847757i
$989$	−23.3950	+	13.5071i	−0.743917	+	0.429501i
$990$		0			0
$991$	−25.9790	+	44.9969i	−0.825249	+	1.42937i	0.0764798	+	0.997071i	$0.475632\pi$
$991$	−25.9790	+	44.9969i	−0.825249	+	1.42937i	−0.901729	+	0.432302i	$0.857701\pi$
$992$	5.48065	+	39.9063i	0.174011	+	1.26703i
$993$		0			0
$994$	0.347162	+	12.7149i	0.0110113	+	0.403292i
$995$	10.2004	−	28.0255i	0.323375	−	0.888467i
$996$		0			0
$997$	−44.7921	−	7.89805i	−1.41858	−	0.250134i	−0.588824	−	0.808262i	$-0.700409\pi$
$997$	−44.7921	−	7.89805i	−1.41858	−	0.250134i	−0.829755	+	0.558128i	$0.811520\pi$
$998$	−19.1885	−	15.2282i	−0.607401	−	0.482042i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.397.26		204
3.2	odd	2		216.2.t.a.133.9	yes	204
8.5	even	2	inner	648.2.t.a.397.4		204
12.11	even	2		864.2.bf.a.241.18		204
24.5	odd	2		216.2.t.a.133.31	yes	204
24.11	even	2		864.2.bf.a.241.17		204
27.13	even	9	inner	648.2.t.a.253.4		204
27.14	odd	18		216.2.t.a.13.31	yes	204
108.95	even	18		864.2.bf.a.337.17		204
216.13	even	18	inner	648.2.t.a.253.26		204
216.149	odd	18		216.2.t.a.13.9	✓	204
216.203	even	18		864.2.bf.a.337.18		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.9	✓	204	216.149	odd	18
216.2.t.a.13.31	yes	204	27.14	odd	18
216.2.t.a.133.9	yes	204	3.2	odd	2
216.2.t.a.133.31	yes	204	24.5	odd	2
648.2.t.a.253.4		204	27.13	even	9	inner
648.2.t.a.253.26		204	216.13	even	18	inner
648.2.t.a.397.4		204	8.5	even	2	inner
648.2.t.a.397.26		204	1.1	even	1	trivial
864.2.bf.a.241.17		204	24.11	even	2
864.2.bf.a.241.18		204	12.11	even	2
864.2.bf.a.337.17		204	108.95	even	18
864.2.bf.a.337.18		204	216.203	even	18

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.938269 + 1.05814i) q^{2} +(-0.239304 + 1.98563i) q^{4} +(1.55117 + 1.84861i) q^{5} +(-1.49685 + 0.544810i) q^{7} +(-2.32560 + 1.60984i) q^{8} +O(q^{10})\)	\(q+(0.938269 + 1.05814i) q^{2} +(-0.239304 + 1.98563i) q^{4} +(1.55117 + 1.84861i) q^{5} +(-1.49685 + 0.544810i) q^{7} +(-2.32560 + 1.60984i) q^{8} +(-0.500669 + 3.37584i) q^{10} +(-0.102391 + 0.122025i) q^{11} +(-3.39140 + 0.597995i) q^{13} +(-1.98093 - 1.07270i) q^{14} +(-3.88547 - 0.950339i) q^{16} +(1.43581 + 2.48690i) q^{17} +(3.75621 + 2.16865i) q^{19} +(-4.04186 + 2.63767i) q^{20} +(-0.225190 + 0.00614850i) q^{22} +(-2.14748 - 0.781619i) q^{23} +(-0.142997 + 0.810974i) q^{25} +(-3.81480 - 3.02748i) q^{26} +(-0.723589 - 3.10257i) q^{28} +(8.60509 + 1.51731i) q^{29} +(-6.69129 - 2.43543i) q^{31} +(-2.64002 - 5.00303i) q^{32} +(-1.28430 + 3.85267i) q^{34} +(-3.32901 - 1.92201i) q^{35} +(5.14590 - 2.97099i) q^{37} +(1.22961 + 6.00935i) q^{38} +(-6.58336 - 1.80200i) q^{40} +(1.74706 + 9.90807i) q^{41} +(7.59829 - 9.05529i) q^{43} +(-0.217795 - 0.232513i) q^{44} +(-1.18785 - 3.00570i) q^{46} +(-3.66367 + 1.33347i) q^{47} +(-3.41856 + 2.86851i) q^{49} +(-0.992290 + 0.609602i) q^{50} +(-0.375823 - 6.87717i) q^{52} +9.80805i q^{53} -0.384404 q^{55} +(2.60402 - 3.67670i) q^{56} +(6.46837 + 10.5290i) q^{58} +(1.72220 + 2.05244i) q^{59} +(0.492702 + 1.35369i) q^{61} +(-3.70121 - 9.36539i) q^{62} +(2.81683 - 7.48769i) q^{64} +(-6.36609 - 5.34178i) q^{65} +(-0.225321 + 0.0397302i) q^{67} +(-5.28167 + 2.25587i) q^{68} +(-1.08976 - 5.32591i) q^{70} +(-2.82317 - 4.88987i) q^{71} +(7.14574 - 12.3768i) q^{73} +(7.97195 + 2.65748i) q^{74} +(-5.20501 + 6.93948i) q^{76} +(0.0867843 - 0.238438i) q^{77} +(-2.18269 + 12.3786i) q^{79} +(-4.27021 - 8.65685i) q^{80} +(-8.84487 + 11.1451i) q^{82} +(11.1079 + 1.95862i) q^{83} +(-2.37013 + 6.51187i) q^{85} +(16.7110 - 0.456270i) q^{86} +(0.0416802 - 0.448616i) q^{88} +(3.73417 - 6.46777i) q^{89} +(4.75063 - 2.74278i) q^{91} +(2.06591 - 4.07706i) q^{92} +(-4.84850 - 2.62551i) q^{94} +(1.81753 + 10.3077i) q^{95} +(5.17680 + 4.34385i) q^{97} +(-6.24280 - 0.925866i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40} + 24 q^{41} - 21 q^{44} - 3 q^{46} + 12 q^{47} - 12 q^{49} + 99 q^{50} - 33 q^{52} - 24 q^{55} - 99 q^{56} + 21 q^{58} + 36 q^{62} - 3 q^{64} + 12 q^{65} - 75 q^{68} + 9 q^{70} + 90 q^{71} - 6 q^{73} - 9 q^{74} - 18 q^{76} - 12 q^{79} - 78 q^{80} - 12 q^{82} + 30 q^{86} - 30 q^{88} + 6 q^{89} - 111 q^{92} - 33 q^{94} + 42 q^{95} - 12 q^{97} - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

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