LMFDB - Embedded newform 648.2.v.b.35.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(35,648)]

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([9, 9, 13]))

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

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

chi := DirichletCharacter("648.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.v (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:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.6
Character	$\chi$	$=$	648.35
Dual form			648.2.v.b.611.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16920 + 0.795599i) q^{2} +(0.734044 - 1.86042i) q^{4} +(3.21529 + 1.17027i) q^{5} +(-2.85909 - 0.504135i) q^{7} +(0.621910 + 2.75921i) q^{8} +O(q^{10})$	\(q+(-1.16920 + 0.795599i) q^{2} +(0.734044 - 1.86042i) q^{4} +(3.21529 + 1.17027i) q^{5} +(-2.85909 - 0.504135i) q^{7} +(0.621910 + 2.75921i) q^{8} +(-4.69037 + 1.18981i) q^{10} +(0.927560 + 2.54845i) q^{11} +(1.60411 + 1.91170i) q^{13} +(3.74393 - 1.68526i) q^{14} +(-2.92236 - 2.73127i) q^{16} +(-4.30856 + 2.48755i) q^{17} +(-1.31569 + 2.27884i) q^{19} +(4.53736 - 5.12277i) q^{20} +(-3.11204 - 2.24167i) q^{22} +(-0.157970 - 0.895893i) q^{23} +(5.13833 + 4.31157i) q^{25} +(-3.39646 - 0.958928i) q^{26} +(-3.03660 + 4.94907i) q^{28} +(7.00248 + 5.87578i) q^{29} +(2.90502 - 0.512234i) q^{31} +(5.58981 + 0.868362i) q^{32} +(3.05847 - 6.33633i) q^{34} +(-8.60284 - 4.96685i) q^{35} +(9.78021 - 5.64661i) q^{37} +(-0.274743 - 3.71117i) q^{38} +(-1.22939 + 9.59946i) q^{40} +(3.04161 + 3.62485i) q^{41} +(-6.12779 + 2.23033i) q^{43} +(5.42207 + 0.145018i) q^{44} +(0.897470 + 0.921795i) q^{46} +(0.225833 - 1.28076i) q^{47} +(1.34241 + 0.488598i) q^{49} +(-9.43801 - 0.953026i) q^{50} +(4.73406 - 1.58105i) q^{52} -10.3399 q^{53} +9.27950i q^{55} +(-0.387086 - 8.20236i) q^{56} +(-12.8621 - 1.29878i) q^{58} +(-2.96267 + 8.13988i) q^{59} +(0.720351 + 0.127017i) q^{61} +(-2.98901 + 2.91014i) q^{62} +(-7.22645 + 3.43196i) q^{64} +(2.92046 + 8.02391i) q^{65} +(5.00144 - 4.19671i) q^{67} +(1.46523 + 9.84173i) q^{68} +(14.0100 - 1.03718i) q^{70} +(5.18176 + 8.97507i) q^{71} +(-7.34034 + 12.7138i) q^{73} +(-6.94256 + 14.3831i) q^{74} +(3.27383 + 4.12050i) q^{76} +(-1.36722 - 7.75387i) q^{77} +(5.64811 - 6.73115i) q^{79} +(-6.19991 - 12.2018i) q^{80} +(-6.44017 - 1.81826i) q^{82} +(-3.15228 + 3.75674i) q^{83} +(-16.7644 + 2.95601i) q^{85} +(5.39014 - 7.48296i) q^{86} +(-6.45484 + 4.14424i) q^{88} +(4.90094 + 2.82956i) q^{89} +(-3.62253 - 6.27441i) q^{91} +(-1.78270 - 0.363733i) q^{92} +(0.754930 + 1.67714i) q^{94} +(-6.89717 + 5.78741i) q^{95} +(-0.126739 + 0.0461291i) q^{97} +(-1.95827 + 0.496754i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−1.16920	+	0.795599i	−0.826747	+	0.562574i
$2$	−1.16920	+	0.795599i	−0.826747	+	0.562574i
$3$		0			0
$3$		0			0
$4$	0.734044	−	1.86042i	0.367022	−	0.930212i
$5$	3.21529	+	1.17027i	1.43792	+	0.523361i	0.939191	−	0.343396i	$-0.111577\pi$
$5$	3.21529	+	1.17027i	1.43792	+	0.523361i	0.498731	+	0.866757i	$0.333800\pi$
$6$		0			0
$7$	−2.85909	−	0.504135i	−1.08064	−	0.190545i	−0.395139	−	0.918621i	$-0.629304\pi$
$7$	−2.85909	−	0.504135i	−1.08064	−	0.190545i	−0.685496	+	0.728076i	$0.740415\pi$
$8$	0.621910	+	2.75921i	0.219879	+	0.975527i
$9$		0			0
$10$	−4.69037	+	1.18981i	−1.48323	+	0.376250i
$11$	0.927560	+	2.54845i	0.279670	+	0.768386i	0.997400	+	0.0720650i	$0.0229589\pi$
$11$	0.927560	+	2.54845i	0.279670	+	0.768386i	−0.717730	+	0.696321i	$0.754819\pi$
$12$		0			0
$13$	1.60411	+	1.91170i	0.444899	+	0.530210i	0.941159	−	0.337964i	$-0.109738\pi$
$13$	1.60411	+	1.91170i	0.444899	+	0.530210i	−0.496260	+	0.868174i	$0.665294\pi$
$14$	3.74393	−	1.68526i	1.00061	−	0.450404i
$15$		0			0
$16$	−2.92236	−	2.73127i	−0.730590	−	0.682817i
$17$	−4.30856	+	2.48755i	−1.04498	+	0.603319i	−0.921240	−	0.388995i	$-0.872822\pi$
$17$	−4.30856	+	2.48755i	−1.04498	+	0.603319i	−0.123740	+	0.992315i	$0.539489\pi$
$18$		0			0
$19$	−1.31569	+	2.27884i	−0.301839	+	0.522801i	−0.976553	−	0.215279i	$-0.930934\pi$
$19$	−1.31569	+	2.27884i	−0.301839	+	0.522801i	0.674713	+	0.738080i	$0.264267\pi$
$20$	4.53736	−	5.12277i	1.01458	−	1.14549i
$21$		0			0
$22$	−3.11204	−	2.24167i	−0.663490	−	0.477926i
$23$	−0.157970	−	0.895893i	−0.0329391	−	0.186807i	0.963899	−	0.266269i	$-0.0857909\pi$
$23$	−0.157970	−	0.895893i	−0.0329391	−	0.186807i	−0.996838	+	0.0794621i	$0.974680\pi$
$24$		0			0
$25$	5.13833	+	4.31157i	1.02767	+	0.862315i
$26$	−3.39646	−	0.958928i	−0.666101	−	0.188061i
$27$		0			0
$28$	−3.03660	+	4.94907i	−0.573864	+	0.935286i
$29$	7.00248	+	5.87578i	1.30033	+	1.09111i	0.990088	+	0.140447i	$0.0448540\pi$
$29$	7.00248	+	5.87578i	1.30033	+	1.09111i	0.310241	+	0.950658i	$0.399590\pi$
$30$		0			0
$31$	2.90502	−	0.512234i	0.521758	−	0.0920000i	0.0934343	−	0.995625i	$-0.470215\pi$
$31$	2.90502	−	0.512234i	0.521758	−	0.0920000i	0.428324	+	0.903625i	$0.359104\pi$
$32$	5.58981	+	0.868362i	0.988148	+	0.153506i
$33$		0			0
$34$	3.05847	−	6.33633i	0.524523	−	1.08667i
$35$	−8.60284	−	4.96685i	−1.45414	−	0.839551i
$36$		0			0
$37$	9.78021	−	5.64661i	1.60786	−	0.928296i	0.618008	−	0.786172i	$-0.287940\pi$
$37$	9.78021	−	5.64661i	1.60786	−	0.928296i	0.989849	−	0.142124i	$-0.0453932\pi$
$38$	−0.274743	−	3.71117i	−0.0445692	−	0.602031i
$39$		0			0
$40$	−1.22939	+	9.59946i	−0.194384	+	1.51781i
$41$	3.04161	+	3.62485i	0.475020	+	0.566106i	0.949342	−	0.314245i	$-0.101751\pi$
$41$	3.04161	+	3.62485i	0.475020	+	0.566106i	−0.474322	+	0.880351i	$0.657307\pi$
$42$		0			0
$43$	−6.12779	+	2.23033i	−0.934479	+	0.340123i	−0.763983	−	0.645236i	$-0.776759\pi$
$43$	−6.12779	+	2.23033i	−0.934479	+	0.340123i	−0.170496	+	0.985358i	$0.554537\pi$
$44$	5.42207	+	0.145018i	0.817407	+	0.0218624i
$45$		0			0
$46$	0.897470	+	0.921795i	0.132325	+	0.135911i
$47$	0.225833	−	1.28076i	0.0329411	−	0.186818i	−0.963897	−	0.266275i	$-0.914207\pi$
$47$	0.225833	−	1.28076i	0.0329411	−	0.186818i	0.996838	+	0.0794561i	$0.0253183\pi$
$48$		0			0
$49$	1.34241	+	0.488598i	0.191773	+	0.0697997i
$50$	−9.43801	−	0.953026i	−1.33474	−	0.134778i
$51$		0			0
$52$	4.73406	−	1.58105i	0.656496	−	0.219252i
$53$	−10.3399			−1.42029			−0.710146	−	0.704054i	$-0.751371\pi$
$53$	−10.3399			−1.42029			−0.710146	+	0.704054i	$0.751371\pi$
$54$		0			0
$55$			9.27950i			1.25125i
$56$	−0.387086	−	8.20236i	−0.0517266	−	1.09609i
$57$		0			0
$58$	−12.8621	−	1.29878i	−1.68887	−	0.170538i
$59$	−2.96267	+	8.13988i	−0.385707	+	1.05972i	0.583207	+	0.812324i	$0.301798\pi$
$59$	−2.96267	+	8.13988i	−0.385707	+	1.05972i	−0.968914	+	0.247398i	$0.920425\pi$
$60$		0			0
$61$	0.720351	+	0.127017i	0.0922315	+	0.0162629i	0.219573	−	0.975596i	$-0.429533\pi$
$61$	0.720351	+	0.127017i	0.0922315	+	0.0162629i	−0.127342	+	0.991859i	$0.540645\pi$
$62$	−2.98901	+	2.91014i	−0.379605	+	0.369588i
$63$		0			0
$64$	−7.22645	+	3.43196i	−0.903307	+	0.428995i
$65$	2.92046	+	8.02391i	0.362239	+	0.995243i
$66$		0			0
$67$	5.00144	−	4.19671i	0.611023	−	0.512709i	−0.283944	−	0.958841i	$-0.591643\pi$
$67$	5.00144	−	4.19671i	0.611023	−	0.512709i	0.894968	+	0.446131i	$0.147199\pi$
$68$	1.46523	+	9.84173i	0.177685	+	1.19348i
$69$		0			0
$70$	14.0100	−	1.03718i	1.67452	−	0.123967i
$71$	5.18176	+	8.97507i	0.614961	+	1.06514i	0.990391	+	0.138294i	$0.0441618\pi$
$71$	5.18176	+	8.97507i	0.614961	+	1.06514i	−0.375430	+	0.926851i	$0.622505\pi$
$72$		0			0
$73$	−7.34034	+	12.7138i	−0.859122	+	1.48804i	0.0136452	+	0.999907i	$0.495656\pi$
$73$	−7.34034	+	12.7138i	−0.859122	+	1.48804i	−0.872767	+	0.488136i	$0.837677\pi$
$74$	−6.94256	+	14.3831i	−0.807056	+	1.67200i
$75$		0			0
$76$	3.27383	+	4.12050i	0.375534	+	0.472654i
$77$	−1.36722	−	7.75387i	−0.155809	−	0.883635i
$78$		0			0
$79$	5.64811	−	6.73115i	0.635462	−	0.757314i	−0.348184	−	0.937426i	$-0.613202\pi$
$79$	5.64811	−	6.73115i	0.635462	−	0.757314i	0.983646	+	0.180112i	$0.0576461\pi$
$80$	−6.19991	−	12.2018i	−0.693171	−	1.36420i
$81$		0			0
$82$	−6.44017	−	1.81826i	−0.711197	−	0.200793i
$83$	−3.15228	+	3.75674i	−0.346007	+	0.412356i	−0.910781	−	0.412891i	$-0.864519\pi$
$83$	−3.15228	+	3.75674i	−0.346007	+	0.412356i	0.564773	+	0.825246i	$0.308964\pi$
$84$		0			0
$85$	−16.7644	+	2.95601i	−1.81835	+	0.320625i
$86$	5.39014	−	7.48296i	0.581234	−	0.806909i
$87$		0			0
$88$	−6.45484	+	4.14424i	−0.688088	+	0.441777i
$89$	4.90094	+	2.82956i	0.519499	+	0.299933i	0.736730	−	0.676187i	$-0.236369\pi$
$89$	4.90094	+	2.82956i	0.519499	+	0.299933i	−0.217231	+	0.976120i	$0.569702\pi$
$90$		0			0
$91$	−3.62253	−	6.27441i	−0.379745	−	0.657737i
$92$	−1.78270	−	0.363733i	−0.185859	−	0.0379218i
$93$		0			0
$94$	0.754930	+	1.67714i	0.0778651	+	0.172983i
$95$	−6.89717	+	5.78741i	−0.707635	+	0.593776i
$96$		0			0
$97$	−0.126739	+	0.0461291i	−0.0128684	+	0.00468370i	−0.348446	−	0.937329i	$-0.613291\pi$
$97$	−0.126739	+	0.0461291i	−0.0128684	+	0.00468370i	0.335578	+	0.942012i	$0.391068\pi$
$98$	−1.95827	+	0.496754i	−0.197815	+	0.0501798i
$99$		0			0
$100$	11.7931	−	6.39460i	1.17931	−	0.639460i
$101$	2.26461	−	12.8432i	0.225337	−	1.27795i	−0.636704	−	0.771109i	$-0.719702\pi$
$101$	2.26461	−	12.8432i	0.225337	−	1.27795i	0.862040	−	0.506840i	$-0.169186\pi$
$102$		0			0
$103$	0.422665	−	1.16126i	0.0416464	−	0.114423i	−0.917126	−	0.398597i	$-0.869497\pi$
$103$	0.422665	−	1.16126i	0.0416464	−	0.114423i	0.958773	+	0.284174i	$0.0917195\pi$
$104$	−4.27717	+	5.61497i	−0.419411	+	0.550593i
$105$		0			0
$106$	12.0894	−	8.22641i	1.17422	−	0.799019i
$107$		−	15.9792i		−	1.54476i	−0.635159	−	0.772382i	$-0.719065\pi$
$107$		−	15.9792i		−	1.54476i	0.635159	−	0.772382i	$-0.280935\pi$
$108$		0			0
$109$			2.38211i			0.228165i	0.993471	+	0.114082i	$0.0363927\pi$
$109$			2.38211i			0.228165i	−0.993471	+	0.114082i	$0.963607\pi$
$110$	−7.38276	−	10.8496i	−0.703919	−	1.03446i
$111$		0			0
$112$	6.97837	+	9.28221i	0.659394	+	0.877086i
$113$	3.24570	−	8.91748i	0.305330	−	0.838886i	−0.688221	−	0.725501i	$-0.741608\pi$
$113$	3.24570	−	8.91748i	0.305330	−	0.838886i	0.993551	−	0.113386i	$-0.0361695\pi$
$114$		0			0
$115$	0.540517	−	3.06542i	0.0504035	−	0.285852i
$116$	16.0716	−	8.71451i	1.49221	−	0.809122i
$117$		0			0
$118$	−3.01213	−	11.8742i	−0.277289	−	1.09311i
$119$	13.5726	−	4.94004i	1.24420	−	0.452853i
$120$		0			0
$121$	2.79226	−	2.34299i	0.253842	−	0.212999i
$122$	−0.943287	+	0.424602i	−0.0854012	+	0.0384417i
$123$		0			0
$124$	1.17944	−	5.78058i	0.105917	−	0.519112i
$125$	2.92143	+	5.06006i	0.261300	+	0.452586i
$126$		0			0
$127$	−3.94090	−	2.27528i	−0.349698	−	0.201898i	0.314854	−	0.949140i	$-0.398044\pi$
$127$	−3.94090	−	2.27528i	−0.349698	−	0.201898i	−0.664552	+	0.747242i	$0.731378\pi$
$128$	5.71868	−	9.76200i	0.505465	−	0.862847i
$129$		0			0
$130$	−9.79841	−	7.05801i	−0.859378	−	0.619028i
$131$	−1.53208	+	0.270147i	−0.133858	+	0.0236028i	−0.240176	−	0.970729i	$-0.577205\pi$
$131$	−1.53208	+	0.270147i	−0.133858	+	0.0236028i	0.106318	+	0.994332i	$0.466094\pi$
$132$		0			0
$133$	4.91051	−	5.85212i	0.425796	−	0.507443i
$134$	−2.50877	+	8.88592i	−0.216725	+	0.767627i
$135$		0			0
$136$	−9.54321	−	10.3412i	−0.818323	−	0.886749i
$137$	0.557261	−	0.664118i	0.0476101	−	0.0567394i	−0.741714	−	0.670716i	$-0.765987\pi$
$137$	0.557261	−	0.664118i	0.0476101	−	0.0567394i	0.789324	+	0.613977i	$0.210431\pi$
$138$		0			0
$139$	−2.63752	−	14.9581i	−0.223711	−	1.26873i	−0.865133	−	0.501542i	$-0.832766\pi$
$139$	−2.63752	−	14.9581i	−0.223711	−	1.26873i	0.641422	−	0.767188i	$-0.278345\pi$
$140$	−15.5553	+	12.3590i	−1.31466	+	1.04453i
$141$		0			0
$142$	−13.1991	−	6.37102i	−1.10764	−	0.534644i
$143$	−3.38397	+	5.86120i	−0.282981	+	0.490138i
$144$		0			0
$145$	15.6388	+	27.0871i	1.29873	+	2.24946i
$146$	−1.53282	−	20.7050i	−0.126857	−	1.71356i
$147$		0			0
$148$	−3.32598	−	22.3402i	−0.273394	−	1.83635i
$149$	6.54605	−	5.49279i	0.536273	−	0.449987i	−0.333988	−	0.942577i	$-0.608394\pi$
$149$	6.54605	−	5.49279i	0.536273	−	0.449987i	0.870261	+	0.492591i	$0.163950\pi$
$150$		0			0
$151$	3.59322	+	9.87229i	0.292412	+	0.803396i	0.995712	+	0.0925028i	$0.0294867\pi$
$151$	3.59322	+	9.87229i	0.292412	+	0.803396i	−0.703300	+	0.710893i	$0.748291\pi$
$152$	−7.10602	−	2.21302i	−0.576375	−	0.179500i
$153$		0			0
$154$	7.76752	+	7.97804i	0.625924	+	0.642889i
$155$	9.93995	+	1.75268i	0.798396	+	0.140779i
$156$		0			0
$157$	3.29479	−	9.05237i	0.262953	−	0.722458i	−0.736012	−	0.676969i	$-0.763293\pi$
$157$	3.29479	−	9.05237i	0.262953	−	0.722458i	0.998965	−	0.0454891i	$-0.0144846\pi$
$158$	−1.24845	+	12.3637i	−0.0993215	+	0.983601i
$159$		0			0
$160$	16.9566	+	9.33362i	1.34054	+	0.737887i
$161$			2.64108i			0.208146i
$162$		0			0
$163$	19.6202			1.53678			0.768388	−	0.639984i	$-0.221059\pi$
$163$	19.6202			1.53678			0.768388	+	0.639984i	$0.221059\pi$
$164$	8.97643	−	2.99789i	0.700942	−	0.234096i
$165$		0			0
$166$	0.696776	−	6.90032i	0.0540803	−	0.535568i
$167$	10.7043	+	3.89606i	0.828327	+	0.301486i	0.721172	−	0.692756i	$-0.243604\pi$
$167$	10.7043	+	3.89606i	0.828327	+	0.301486i	0.107155	+	0.994242i	$0.465826\pi$
$168$		0			0
$169$	1.17599	−	6.66936i	0.0904606	−	0.513028i
$170$	17.2491	−	16.7939i	1.32294	−	1.28803i
$171$		0			0
$172$	−0.348699	+	13.0375i	−0.0265881	+	0.994096i
$173$	−14.8832	+	5.41704i	−1.13155	+	0.411850i	−0.838854	−	0.544356i	$-0.816774\pi$
$173$	−14.8832	+	5.41704i	−1.13155	+	0.411850i	−0.292694	+	0.956206i	$0.594552\pi$
$174$		0			0
$175$	−12.5174	−	14.9176i	−0.946223	−	1.12767i
$176$	4.24983	−	9.98090i	0.320343	−	0.752338i
$177$		0			0
$178$	−7.98136	+	0.590872i	−0.598229	+	0.0442877i
$179$	−13.6572	+	7.88498i	−1.02079	+	0.589351i	−0.914331	−	0.404967i	$-0.867283\pi$
$179$	−13.6572	+	7.88498i	−1.02079	+	0.589351i	−0.106454	+	0.994318i	$0.533950\pi$
$180$		0			0
$181$	4.39147	+	2.53542i	0.326416	+	0.188456i	0.654249	−	0.756280i	$-0.272985\pi$
$181$	4.39147	+	2.53542i	0.326416	+	0.188456i	−0.327833	+	0.944736i	$0.606318\pi$
$182$	9.22738	+	4.45394i	0.683979	+	0.330148i
$183$		0			0
$184$	2.37371	−	0.993038i	0.174992	−	0.0732077i
$185$	38.0543	−	6.70999i	2.79780	−	0.493328i
$186$		0			0
$187$	−10.3358	−	8.67280i	−0.755832	−	0.634218i
$188$	−2.21699	−	1.36028i	−0.161691	−	0.0992087i
$189$		0			0
$190$	3.45969	−	12.2540i	0.250992	−	0.888999i
$191$	−19.1259	−	16.0486i	−1.38390	−	1.16123i	−0.967742	−	0.251944i	$-0.918930\pi$
$191$	−19.1259	−	16.0486i	−1.38390	−	1.16123i	−0.416163	−	0.909290i	$-0.636625\pi$
$192$		0			0
$193$	−1.63585	−	9.27734i	−0.117751	−	0.667798i	−0.985351	−	0.170536i	$-0.945450\pi$
$193$	−1.63585	−	9.27734i	−0.117751	−	0.667798i	0.867601	−	0.497262i	$-0.165661\pi$
$194$	0.111482	−	0.154767i	0.00800396	−	0.0111116i
$195$		0			0
$196$	1.89439	−	2.13880i	0.135313	−	0.152772i
$197$	−0.195281	+	0.338236i	−0.0139132	+	0.0240983i	−0.872898	−	0.487902i	$-0.837762\pi$
$197$	−0.195281	+	0.338236i	−0.0139132	+	0.0240983i	0.858985	+	0.512001i	$0.171096\pi$
$198$		0			0
$199$	6.27422	−	3.62242i	0.444768	−	0.256787i	−0.260850	−	0.965379i	$-0.584003\pi$
$199$	6.27422	−	3.62242i	0.444768	−	0.256787i	0.705618	+	0.708592i	$0.250670\pi$
$200$	−8.70095	+	16.8591i	−0.615250	+	1.19212i
$201$		0			0
$202$	7.57029	+	16.8180i	0.532643	+	1.18331i
$203$	−17.0586	−	20.3296i	−1.19728	−	1.42686i
$204$		0			0
$205$	5.53760	+	15.2144i	0.386763	+	1.06262i
$206$	0.429721	+	1.69402i	0.0299401	+	0.118028i
$207$		0			0
$208$	0.533585	−	9.96792i	0.0369975	−	0.691151i
$209$	−7.02788	−	1.23920i	−0.486128	−	0.0857176i
$210$		0			0
$211$	20.9809	+	7.63642i	1.44438	+	0.525713i	0.941017	−	0.338359i	$-0.109872\pi$
$211$	20.9809	+	7.63642i	1.44438	+	0.525713i	0.503368	+	0.864072i	$0.332094\pi$
$212$	−7.58993	+	19.2366i	−0.521279	+	1.32117i
$213$		0			0
$214$	12.7130	+	18.6828i	0.869043	+	1.27713i
$215$	−22.3127			−1.52171
$216$		0			0
$217$	−8.56397			−0.581360
$218$	−1.89520	−	2.78515i	−0.128359	−	0.188634i
$219$		0			0
$220$	17.2638	+	6.81156i	1.16393	+	0.459235i
$221$	−11.6668	−	4.24638i	−0.784797	−	0.285643i
$222$		0			0
$223$	−7.83765	−	1.38199i	−0.524848	−	0.0925448i	−0.0950544	−	0.995472i	$-0.530303\pi$
$223$	−7.83765	−	1.38199i	−0.524848	−	0.0925448i	−0.429793	+	0.902927i	$0.641414\pi$
$224$	−15.5440	−	5.30075i	−1.03858	−	0.354171i
$225$		0			0
$226$	3.29988	+	13.0086i	0.219505	+	0.865317i
$227$	2.95471	+	8.11801i	0.196111	+	0.538811i	0.998302	−	0.0582571i	$-0.0185543\pi$
$227$	2.95471	+	8.11801i	0.196111	+	0.538811i	−0.802190	+	0.597068i	$0.796332\pi$
$228$		0			0
$229$	−4.90565	−	5.84633i	−0.324175	−	0.386336i	0.579202	−	0.815184i	$-0.303364\pi$
$229$	−4.90565	−	5.84633i	−0.324175	−	0.386336i	−0.903377	+	0.428848i	$0.858920\pi$
$230$	1.80688	+	4.01412i	0.119142	+	0.264683i
$231$		0			0
$232$	−11.8576	+	22.9755i	−0.778489	+	1.50842i
$233$	6.15633	−	3.55436i	0.403315	−	0.232854i	−0.284599	−	0.958647i	$-0.591860\pi$
$233$	6.15633	−	3.55436i	0.403315	−	0.232854i	0.687913	+	0.725793i	$0.258527\pi$
$234$		0			0
$235$	2.22496	−	3.85374i	0.145140	−	0.251390i
$236$	12.9689	+	11.4869i	0.844203	+	0.747731i
$237$		0			0
$238$	−11.9388	+	16.5743i	−0.773878	+	1.07435i
$239$	−0.386367	−	2.19120i	−0.0249920	−	0.141737i	0.969759	−	0.244066i	$-0.0784815\pi$
$239$	−0.386367	−	2.19120i	−0.0249920	−	0.141737i	−0.994751	+	0.102330i	$0.967370\pi$
$240$		0			0
$241$	0.156407	+	0.131241i	0.0100750	+	0.00845397i	0.647811	−	0.761801i	$-0.275685\pi$
$241$	0.156407	+	0.131241i	0.0100750	+	0.00845397i	−0.637736	+	0.770255i	$0.720129\pi$
$242$	−1.40063	+	4.96094i	−0.0900358	+	0.318901i
$243$		0			0
$244$	0.765075	−	1.24692i	0.0489789	−	0.0798260i
$245$	3.74445	+	3.14197i	0.239224	+	0.200733i
$246$		0			0
$247$	−6.46696	+	1.14030i	−0.411483	+	0.0725555i
$248$	3.22003	+	7.69700i	0.204472	+	0.488760i
$249$		0			0
$250$	−7.44151	−	3.59192i	−0.470642	−	0.227173i
$251$	−11.4836	−	6.63004i	−0.724837	−	0.418485i	0.0916936	−	0.995787i	$-0.470772\pi$
$251$	−11.4836	−	6.63004i	−0.724837	−	0.418485i	−0.816530	+	0.577303i	$0.804105\pi$
$252$		0			0
$253$	2.13661	−	1.23357i	0.134328	−	0.0775541i
$254$	6.41790	−	0.475126i	0.402695	−	0.0298121i
$255$		0			0
$256$	1.08037	+	15.9635i	0.0675231	+	0.997718i
$257$	−14.5879	−	17.3851i	−0.909966	−	1.08446i	−0.996105	−	0.0881721i	$-0.971897\pi$
$257$	−14.5879	−	17.3851i	−0.909966	−	1.08446i	0.0861393	−	0.996283i	$-0.472547\pi$
$258$		0			0
$259$	−30.8092	+	11.2136i	−1.91439	+	0.696781i
$260$	17.0716	+	0.456597i	1.05874	+	0.0283170i
$261$		0			0
$262$	1.57637	−	1.53478i	0.0973887	−	0.0948188i
$263$	−3.05022	+	17.2987i	−0.188085	+	1.06668i	0.733843	+	0.679319i	$0.237725\pi$
$263$	−3.05022	+	17.2987i	−0.188085	+	1.06668i	−0.921927	+	0.387363i	$0.873386\pi$
$264$		0			0
$265$	−33.2457	−	12.1005i	−2.04227	−	0.743325i
$266$	−1.08541	+	10.7491i	−0.0665510	+	0.659069i
$267$		0			0
$268$	−4.13638	−	12.3854i	−0.252670	−	0.756557i
$269$	25.2404			1.53894			0.769468	−	0.638686i	$-0.220522\pi$
$269$	25.2404			1.53894			0.769468	+	0.638686i	$0.220522\pi$
$270$		0			0
$271$		−	28.2779i		−	1.71776i	−0.512175	−	0.858881i	$-0.671160\pi$
$271$		−	28.2779i		−	1.71776i	0.512175	−	0.858881i	$-0.328840\pi$
$272$	19.3853	+	4.49832i	1.17541	+	0.272751i
$273$		0			0
$274$	−0.123176	+	1.21984i	−0.00744136	+	0.0736933i
$275$	−6.22172	+	17.0940i	−0.375184	+	1.03081i
$276$		0			0
$277$	−10.7115	−	1.88873i	−0.643592	−	0.113483i	−0.157680	−	0.987490i	$-0.550401\pi$
$277$	−10.7115	−	1.88873i	−0.643592	−	0.113483i	−0.485912	+	0.874008i	$0.661512\pi$
$278$	14.9844	+	15.3906i	0.898707	+	0.923065i
$279$		0			0
$280$	8.35438	−	26.8260i	0.499270	−	1.60316i
$281$	−1.98862	−	5.46370i	−0.118631	−	0.325937i	0.866137	−	0.499806i	$-0.166595\pi$
$281$	−1.98862	−	5.46370i	−0.118631	−	0.325937i	−0.984769	+	0.173869i	$0.944373\pi$
$282$		0			0
$283$	6.97262	−	5.85072i	0.414479	−	0.347789i	−0.411579	−	0.911374i	$-0.635023\pi$
$283$	6.97262	−	5.85072i	0.414479	−	0.347789i	0.826058	+	0.563585i	$0.190578\pi$
$284$	20.5011	−	3.05218i	1.21651	−	0.181113i
$285$		0			0
$286$	−0.706643	−	9.54518i	−0.0417847	−	0.564418i
$287$	−6.86883	−	11.8972i	−0.405454	−	0.702267i
$288$		0			0
$289$	3.87581	−	6.71310i	0.227989	−	0.394888i
$290$	−39.8353	−	19.2280i	−2.33921	−	1.12911i
$291$		0			0
$292$	18.2650	+	22.9887i	1.06888	+	1.34531i
$293$	−0.704403	−	3.99487i	−0.0411517	−	0.233383i	0.957294	−	0.289116i	$-0.0933614\pi$
$293$	−0.704403	−	3.99487i	−0.0411517	−	0.233383i	−0.998446	+	0.0557335i	$0.982250\pi$
$294$		0			0
$295$	−19.0517	+	22.7049i	−1.10923	+	1.32193i
$296$	21.6626	+	23.4739i	1.25911	+	1.36440i
$297$		0			0
$298$	−3.28357	+	11.6302i	−0.190212	+	0.673719i
$299$	1.45928	−	1.73910i	0.0843922	−	0.100575i
$300$		0			0
$301$	18.6443	−	3.28749i	1.07464	−	0.189488i
$302$	−12.0556	−	8.68389i	−0.693720	−	0.499702i
$303$		0			0
$304$	10.0690	−	3.06609i	0.577498	−	0.175852i
$305$	2.16749	+	1.25140i	0.124110	+	0.0716551i
$306$		0			0
$307$	−16.8379	−	29.1641i	−0.960989	−	1.66448i	−0.720025	−	0.693948i	$-0.755870\pi$
$307$	−16.8379	−	29.1641i	−0.960989	−	1.66448i	−0.240964	−	0.970534i	$-0.577464\pi$
$308$	−15.4291	−	3.14808i	−0.879154	−	0.179378i
$309$		0			0
$310$	−13.0162	+	5.85899i	−0.739270	+	0.332768i
$311$	9.39589	−	7.88409i	0.532792	−	0.447066i	−0.336272	−	0.941765i	$-0.609166\pi$
$311$	9.39589	−	7.88409i	0.532792	−	0.447066i	0.869064	+	0.494699i	$0.164722\pi$
$312$		0			0
$313$	−5.01611	+	1.82572i	−0.283528	+	0.103196i	−0.479869	−	0.877340i	$-0.659316\pi$
$313$	−5.01611	+	1.82572i	−0.283528	+	0.103196i	0.196342	+	0.980535i	$0.437094\pi$
$314$	3.34980	+	13.2053i	0.189040	+	0.745221i
$315$		0			0
$316$	−8.37685	−	15.4488i	−0.471234	−	0.869065i
$317$	−0.00253246	+	0.0143623i	−0.000142237	+	0.000806666i	−0.984879	−	0.173245i	$-0.944575\pi$
$317$	−0.00253246	+	0.0143623i	−0.000142237	+	0.000806666i	0.984737	+	0.174051i	$0.0556859\pi$
$318$		0			0
$319$	−8.47891	+	23.2956i	−0.474728	+	1.30430i
$320$	−27.2515	+	2.57785i	−1.52340	+	0.144106i
$321$		0			0
$322$	−2.10124	−	3.08794i	−0.117098	−	0.172084i
$323$		−	13.0914i		−	0.728422i
$324$		0			0
$325$			16.7392i			0.928523i
$326$	−22.9399	+	15.6099i	−1.27053	+	0.864550i
$327$		0			0
$328$	−8.11010	+	10.6468i	−0.447805	+	0.587869i
$329$	−1.29136	+	3.54797i	−0.0711947	+	0.195606i
$330$		0			0
$331$	0.663118	−	3.76073i	0.0364482	−	0.206708i	−0.961145	−	0.276043i	$-0.910977\pi$
$331$	0.663118	−	3.76073i	0.0364482	−	0.206708i	0.997593	+	0.0693351i	$0.0220878\pi$
$332$	4.67522	+	8.62219i	0.256586	+	0.473204i
$333$		0			0
$334$	−15.6152	+	3.96110i	−0.854425	+	0.216742i
$335$	20.9924	−	7.64060i	1.14694	−	0.417450i
$336$		0			0
$337$	6.62429	−	5.55844i	0.360848	−	0.302787i	−0.444281	−	0.895888i	$-0.646541\pi$
$337$	6.62429	−	5.55844i	0.360848	−	0.302787i	0.805129	+	0.593100i	$0.202096\pi$
$338$	3.93118	+	8.73341i	0.213828	+	0.475035i
$339$		0			0
$340$	−6.80635	+	33.3587i	−0.369126	+	1.80913i
$341$	3.99999	+	6.92818i	0.216611	+	0.375182i
$342$		0			0
$343$	14.0079	+	8.08749i	0.756358	+	0.436684i
$344$	−9.96489	−	15.5208i	−0.537271	−	0.836824i
$345$		0			0
$346$	13.0916	−	18.1746i	0.703809	−	0.977075i
$347$	24.1858	−	4.26461i	1.29836	−	0.228936i	0.518602	−	0.855016i	$-0.326453\pi$
$347$	24.1858	−	4.26461i	1.29836	−	0.228936i	0.779759	+	0.626079i	$0.215341\pi$
$348$		0			0
$349$	−4.36508	+	5.20210i	−0.233658	+	0.278462i	−0.870114	−	0.492850i	$-0.835955\pi$
$349$	−4.36508	+	5.20210i	−0.233658	+	0.278462i	0.636457	+	0.771313i	$0.280399\pi$
$350$	26.5037	+	7.48282i	1.41668	+	0.399974i
$351$		0			0
$352$	2.97190	+	15.0508i	0.158403	+	0.802210i
$353$	−9.32471	+	11.1128i	−0.496304	+	0.591472i	−0.954809	−	0.297220i	$-0.903941\pi$
$353$	−9.32471	+	11.1128i	−0.496304	+	0.591472i	0.458505	+	0.888692i	$0.348385\pi$
$354$		0			0
$355$	6.15760	+	34.9215i	0.326812	+	1.85344i
$356$	8.86169	−	7.04081i	0.469669	−	0.373162i
$357$		0			0
$358$	9.69466	−	20.0847i	0.512379	−	1.06151i
$359$	1.61294	−	2.79370i	0.0851279	−	0.147446i	−0.820318	−	0.571908i	$-0.806203\pi$
$359$	1.61294	−	2.79370i	0.0851279	−	0.147446i	0.905446	+	0.424462i	$0.139537\pi$
$360$		0			0
$361$	6.03793	+	10.4580i	0.317786	+	0.550422i
$362$	−7.15167	+	0.529449i	−0.375884	+	0.0278272i
$363$		0			0
$364$	−14.3322	+	2.13376i	−0.751210	+	0.111839i
$365$	−38.4800	+	32.2885i	−2.01413	+	1.69006i
$366$		0			0
$367$	10.2734	+	28.2260i	0.536268	+	1.47338i	0.851492	+	0.524367i	$0.175698\pi$
$367$	10.2734	+	28.2260i	0.536268	+	1.47338i	−0.315224	+	0.949017i	$0.602080\pi$
$368$	−1.98528	+	3.04958i	−0.103490	+	0.158970i
$369$		0			0
$370$	−39.1545	+	38.1212i	−2.03554	+	1.98183i
$371$	29.5627	+	5.21270i	1.53482	+	0.270630i
$372$		0			0
$373$	−5.31103	+	14.5919i	−0.274995	+	0.755542i	0.722916	+	0.690936i	$0.242801\pi$
$373$	−5.31103	+	14.5919i	−0.274995	+	0.755542i	−0.997911	+	0.0646062i	$0.979421\pi$
$374$	18.9847	+	1.91703i	0.981676	+	0.0991271i
$375$		0			0
$376$	3.67434	−	0.173400i	0.189490	−	0.00894240i
$377$			22.8120i			1.17488i
$378$		0			0
$379$	−6.68763			−0.343521			−0.171760	−	0.985139i	$-0.554945\pi$
$379$	−6.68763			−0.343521			−0.171760	+	0.985139i	$0.554945\pi$
$380$	5.70422	+	17.0799i	0.292620	+	0.876179i
$381$		0			0
$382$	35.1302	+	3.54736i	1.79742	+	0.181499i
$383$	−6.52420	−	2.37461i	−0.333371	−	0.121337i	0.169911	−	0.985459i	$-0.445652\pi$
$383$	−6.52420	−	2.37461i	−0.333371	−	0.121337i	−0.503282	+	0.864122i	$0.667874\pi$
$384$		0			0
$385$	4.67812	−	26.5309i	0.238419	−	1.35214i
$386$	9.29367	+	9.54556i	0.473035	+	0.485856i
$387$		0			0
$388$	−0.00721202	+	0.269649i	−0.000366135	+	0.0136893i
$389$	1.33770	−	0.486883i	0.0678241	−	0.0246860i	−0.307885	−	0.951423i	$-0.599621\pi$
$389$	1.33770	−	0.486883i	0.0678241	−	0.0246860i	0.375709	+	0.926738i	$0.377399\pi$
$390$		0			0
$391$	2.90920	+	3.46705i	0.147125	+	0.175336i
$392$	−0.513283	+	4.00786i	−0.0259247	+	0.202427i
$393$		0			0
$394$	−0.0407787	−	0.550830i	−0.00205440	−	0.0277504i
$395$	26.0376	−	15.0328i	1.31009	−	0.756382i
$396$		0			0
$397$	−16.5544	−	9.55769i	−0.830842	−	0.479687i	0.0232990	−	0.999729i	$-0.492583\pi$
$397$	−16.5544	−	9.55769i	−0.830842	−	0.479687i	−0.854141	+	0.520042i	$0.825916\pi$
$398$	−4.45381	+	9.22709i	−0.223249	+	0.462512i
$399$		0			0
$400$	−3.24000	−	26.6341i	−0.162000	−	1.33171i
$401$	18.4212	−	3.24815i	0.919909	−	0.162205i	0.306409	−	0.951900i	$-0.400872\pi$
$401$	18.4212	−	3.24815i	0.919909	−	0.162205i	0.613500	+	0.789695i	$0.289761\pi$
$402$		0			0
$403$	5.63921	+	4.73186i	0.280909	+	0.235711i
$404$	−22.2315	−	13.6406i	−1.10606	−	0.678646i
$405$		0			0
$406$	36.1190	+	10.1975i	1.79256	+	0.506095i
$407$	23.4618	+	19.6868i	1.16296	+	0.975838i
$408$		0			0
$409$	−3.21877	−	18.2546i	−0.159158	−	0.902630i	−0.954885	−	0.296975i	$-0.904022\pi$
$409$	−3.21877	−	18.2546i	−0.159158	−	0.902630i	0.795727	−	0.605655i	$-0.207089\pi$
$410$	−18.5791	−	13.3830i	−0.917559	−	0.660938i
$411$		0			0
$412$	−1.85019	−	1.63875i	−0.0911521	−	0.0807356i
$413$	12.5742	−	21.7791i	0.618734	−	1.07168i
$414$		0			0
$415$	−14.5319	+	8.38999i	−0.713342	+	0.411848i
$416$	7.30660	+	12.0790i	0.358236	+	0.592221i
$417$		0			0
$418$	9.20288	−	4.14250i	0.450128	−	0.202616i
$419$	14.4375	+	17.2059i	0.705317	+	0.840564i	0.993117	−	0.117126i	$-0.0373682\pi$
$419$	14.4375	+	17.2059i	0.705317	+	0.840564i	−0.287800	+	0.957691i	$0.592924\pi$
$420$		0			0
$421$	−5.98056	−	16.4314i	−0.291475	−	0.800820i	−0.995851	−	0.0909935i	$-0.970996\pi$
$421$	−5.98056	−	16.4314i	−0.291475	−	0.800820i	0.704377	−	0.709826i	$-0.251226\pi$
$422$	−30.6063	+	7.76390i	−1.48989	+	0.377941i
$423$		0			0
$424$	−6.43048	−	28.5299i	−0.312292	−	1.38553i
$425$	−32.8641	−	5.79483i	−1.59414	−	0.281090i
$426$		0			0
$427$	−1.99552	−	0.726309i	−0.0965698	−	0.0351485i
$428$	−29.7280	−	11.7294i	−1.43696	−	0.566962i
$429$		0			0
$430$	26.0880	−	17.7520i	1.25807	−	0.856076i
$431$	13.1374			0.632807			0.316403	−	0.948625i	$-0.397525\pi$
$431$	13.1374			0.632807			0.316403	+	0.948625i	$0.397525\pi$
$432$		0			0
$433$	−22.6607			−1.08900			−0.544502	−	0.838759i	$-0.683281\pi$
$433$	−22.6607			−1.08900			−0.544502	+	0.838759i	$0.683281\pi$
$434$	10.0130	−	6.81349i	0.480638	−	0.327058i
$435$		0			0
$436$	4.43173	+	1.74857i	0.212241	+	0.0837414i
$437$	2.24943	+	0.818727i	0.107605	+	0.0391650i
$438$		0			0
$439$	14.8982	+	2.62696i	0.711053	+	0.125378i	0.517464	−	0.855705i	$-0.326876\pi$
$439$	14.8982	+	2.62696i	0.711053	+	0.125378i	0.193589	+	0.981083i	$0.437987\pi$
$440$	−25.6041	+	5.77102i	−1.22063	+	0.275122i
$441$		0			0
$442$	17.0193	−	4.31727i	0.809524	−	0.205352i
$443$	−1.36146	−	3.74057i	−0.0646848	−	0.177720i	0.903139	−	0.429347i	$-0.141256\pi$
$443$	−1.36146	−	3.74057i	−0.0646848	−	0.177720i	−0.967824	+	0.251628i	$0.919034\pi$
$444$		0			0
$445$	12.4466	+	14.8333i	0.590026	+	0.703165i
$446$	10.2633	−	4.61981i	0.485980	−	0.218754i
$447$		0			0
$448$	22.3913	−	6.16918i	1.05789	−	0.291467i
$449$	−22.3682	+	12.9143i	−1.05562	+	0.609464i	−0.924218	−	0.381865i	$-0.875282\pi$
$449$	−22.3682	+	12.9143i	−1.05562	+	0.609464i	−0.131404	+	0.991329i	$0.541948\pi$
$450$		0			0
$451$	−6.41647	+	11.1136i	−0.302140	+	0.523321i
$452$	−14.2078	−	12.5842i	−0.668280	−	0.591911i
$453$		0			0
$454$	−9.91333	−	7.14079i	−0.465255	−	0.335134i
$455$	−4.30474	−	24.4134i	−0.201809	−	1.14452i
$456$		0			0
$457$	2.14884	+	1.80309i	0.100518	+	0.0843449i	0.691662	−	0.722221i	$-0.256879\pi$
$457$	2.14884	+	1.80309i	0.100518	+	0.0843449i	−0.591143	+	0.806566i	$0.701323\pi$
$458$	10.3870	+	2.93258i	0.485353	+	0.137030i
$459$		0			0
$460$	−5.30623	−	3.25575i	−0.247404	−	0.151800i
$461$	11.5119	+	9.65964i	0.536163	+	0.449894i	0.870223	−	0.492657i	$-0.163974\pi$
$461$	11.5119	+	9.65964i	0.536163	+	0.449894i	−0.334060	+	0.942552i	$0.608419\pi$
$462$		0			0
$463$	21.5380	−	3.79772i	1.00095	−	0.176495i	0.350924	−	0.936404i	$-0.385868\pi$
$463$	21.5380	−	3.79772i	1.00095	−	0.176495i	0.650030	+	0.759909i	$0.274756\pi$
$464$	−4.41545	−	36.2968i	−0.204982	−	1.68504i
$465$		0			0
$466$	−4.37012	+	9.05372i	−0.202442	+	0.419405i
$467$	16.2109	+	9.35938i	0.750152	+	0.433100i	0.825749	−	0.564038i	$-0.190753\pi$
$467$	16.2109	+	9.35938i	0.750152	+	0.433100i	−0.0755968	+	0.997138i	$0.524086\pi$
$468$		0			0
$469$	−16.4153	+	9.47738i	−0.757988	+	0.437625i
$470$	0.464618	+	6.27595i	0.0214312	+	0.289488i
$471$		0			0
$472$	−24.3021	−	3.11235i	−1.11860	−	0.143258i
$473$	−11.3678	−	13.5476i	−0.522691	−	0.622919i
$474$		0			0
$475$	−16.5858	+	6.03674i	−0.761009	+	0.276985i
$476$	0.772346	−	28.8771i	0.0354004	−	1.32358i
$477$		0			0
$478$	2.19505	+	2.25455i	0.100399	+	0.103121i
$479$	−3.48398	+	19.7587i	−0.159187	+	0.902796i	0.795670	+	0.605731i	$0.207119\pi$
$479$	−3.48398	+	19.7587i	−0.159187	+	0.902796i	−0.954857	+	0.297065i	$0.903992\pi$
$480$		0			0
$481$	26.4831	+	9.63907i	1.20753	+	0.439504i
$482$	−0.287286	−	0.0290093i	−0.0130855	−	0.00132134i
$483$		0			0
$484$	−2.30931	−	6.91465i	−0.104969	−	0.314302i
$485$	−0.461485			−0.0209550
$486$		0			0
$487$		−	14.0996i		−	0.638916i	−0.947600	−	0.319458i	$-0.896499\pi$
$487$		−	14.0996i		−	0.638916i	0.947600	−	0.319458i	$-0.103501\pi$
$488$	0.0975267	+	2.06659i	0.00441482	+	0.0935502i
$489$		0			0
$490$	−6.87775	−	0.694497i	−0.310705	−	0.0313742i
$491$	−0.766879	+	2.10698i	−0.0346088	+	0.0950868i	−0.955794	−	0.294039i	$-0.905001\pi$
$491$	−0.766879	+	2.10698i	−0.0346088	+	0.0950868i	0.921185	+	0.389125i	$0.127223\pi$
$492$		0			0
$493$	−44.7869	−	7.89715i	−2.01710	−	0.355670i
$494$	6.65392	−	6.47834i	0.299374	−	0.291474i
$495$		0			0
$496$	−9.88858	−	6.43746i	−0.444010	−	0.289051i
$497$	−10.2905	−	28.2729i	−0.461591	−	1.26821i
$498$		0			0
$499$	−7.09602	+	5.95427i	−0.317661	+	0.266550i	−0.787650	−	0.616123i	$-0.788702\pi$
$499$	−7.09602	+	5.95427i	−0.317661	+	0.266550i	0.469989	+	0.882672i	$0.344258\pi$
$500$	11.5583	−	1.72079i	0.516904	−	0.0769561i
$501$		0			0
$502$	18.7014	−	1.38449i	0.834685	−	0.0617930i
$503$	−7.08381	−	12.2695i	−0.315852	−	0.547071i	0.663767	−	0.747940i	$-0.268957\pi$
$503$	−7.08381	−	12.2695i	−0.315852	−	0.547071i	−0.979618	+	0.200869i	$0.935624\pi$
$504$		0			0
$505$	22.3114	−	38.6445i	0.992844	−	1.71966i
$506$	−1.51669	+	3.14218i	−0.0674251	+	0.139687i
$507$		0			0
$508$	−7.12577	+	5.66159i	−0.316155	+	0.251192i
$509$	−7.28735	−	41.3286i	−0.323006	−	1.83186i	−0.523333	−	0.852129i	$-0.675311\pi$
$509$	−7.28735	−	41.3286i	−0.323006	−	1.83186i	0.200327	−	0.979729i	$-0.435800\pi$
$510$		0			0
$511$	27.3962	−	32.6495i	1.21194	−	1.44433i
$512$	−13.9637	−	17.8049i	−0.617114	−	0.786874i
$513$		0			0
$514$	30.8877	+	8.72056i	1.36240	+	0.384647i
$515$	2.71798	−	3.23916i	0.119769	−	0.142735i
$516$		0			0
$517$	3.47343	−	0.612460i	0.152761	−	0.0269359i
$518$	27.1005	−	37.6227i	1.19073	−	1.65305i
$519$		0			0
$520$	−20.3234	+	13.0483i	−0.891238	+	0.572207i
$521$	−4.99532	−	2.88405i	−0.218849	−	0.126353i	0.386568	−	0.922261i	$-0.373660\pi$
$521$	−4.99532	−	2.88405i	−0.218849	−	0.126353i	−0.605417	+	0.795908i	$0.706994\pi$
$522$		0			0
$523$	−3.83688	−	6.64566i	−0.167775	−	0.290595i	0.769862	−	0.638210i	$-0.220325\pi$
$523$	−3.83688	−	6.64566i	−0.167775	−	0.290595i	−0.937637	+	0.347615i	$0.886991\pi$
$524$	−0.622025	+	3.04862i	−0.0271733	+	0.133179i
$525$		0			0
$526$	−10.1965	−	22.6523i	−0.444589	−	0.987688i
$527$	−11.2423	+	9.43339i	−0.489721	+	0.410925i
$528$		0			0
$529$	20.8353	−	7.58341i	0.905881	−	0.329714i
$530$	48.4979	−	12.3025i	2.10662	−	0.534385i
$531$		0			0
$532$	−7.28290	−	13.4314i	−0.315754	−	0.582323i
$533$	−2.05056	+	11.6293i	−0.0888195	+	0.503720i
$534$		0			0
$535$	18.6999	−	51.3776i	0.808468	−	2.22125i
$536$	14.6900	+	11.1900i	0.634513	+	0.483336i
$537$		0			0
$538$	−29.5110	+	20.0813i	−1.27231	+	0.865764i
$539$			3.87427i			0.166877i
$540$		0			0
$541$		−	34.8844i		−	1.49980i	−0.661552	−	0.749899i	$-0.730102\pi$
$541$		−	34.8844i		−	1.49980i	0.661552	−	0.749899i	$-0.269898\pi$
$542$	22.4979	+	33.0625i	0.966367	+	1.42015i
$543$		0			0
$544$	−26.2441	+	10.1635i	−1.12521	+	0.435758i
$545$	−2.78771	+	7.65917i	−0.119412	+	0.328083i
$546$		0			0
$547$	−5.15974	+	29.2623i	−0.220614	+	1.25117i	0.650279	+	0.759695i	$0.274652\pi$
$547$	−5.15974	+	29.2623i	−0.220614	+	1.25117i	−0.870894	+	0.491471i	$0.836459\pi$
$548$	−0.826488	−	1.52423i	−0.0353058	−	0.0651121i
$549$		0			0
$550$	−6.32558	−	24.9363i	−0.269724	−	1.06329i
$551$	−22.6030	+	8.22683i	−0.962921	+	0.350475i
$552$		0			0
$553$	−19.5419	+	16.3976i	−0.831005	+	0.697296i
$554$	14.0265	−	6.31377i	0.595930	−	0.268246i
$555$		0			0
$556$	−29.7645	−	6.07300i	−1.26229	−	0.257553i
$557$	−8.65814	−	14.9963i	−0.366857	−	0.635415i	0.622215	−	0.782846i	$-0.286233\pi$
$557$	−8.65814	−	14.9963i	−0.366857	−	0.635415i	−0.989072	+	0.147431i	$0.952900\pi$
$558$		0			0
$559$	−14.0934	−	8.13680i	−0.596085	−	0.344150i
$560$	11.5748	+	38.0116i	0.489124	+	1.60628i
$561$		0			0
$562$	6.67201	+	4.80600i	0.281442	+	0.202729i
$563$	−19.0265	+	3.35488i	−0.801870	+	0.141391i	−0.559541	−	0.828803i	$-0.689022\pi$
$563$	−19.0265	+	3.35488i	−0.801870	+	0.141391i	−0.242329	+	0.970194i	$0.577911\pi$
$564$		0			0
$565$	20.8717	−	24.8739i	0.878080	−	1.04645i
$566$	−3.49753	+	12.3881i	−0.147012	+	0.520709i
$567$		0			0
$568$	−21.5415	+	19.8792i	−0.903861	+	0.834114i
$569$	−14.3568	+	17.1097i	−0.601867	+	0.717277i	−0.977840	−	0.209353i	$-0.932864\pi$
$569$	−14.3568	+	17.1097i	−0.601867	+	0.717277i	0.375973	+	0.926631i	$0.377309\pi$
$570$		0			0
$571$	6.51955	+	36.9742i	0.272835	+	1.54732i	0.745757	+	0.666218i	$0.232088\pi$
$571$	6.51955	+	36.9742i	0.272835	+	1.54732i	−0.472922	+	0.881104i	$0.656801\pi$
$572$	8.42034	+	10.5980i	0.352072	+	0.443124i
$573$		0			0
$574$	17.4964	+	8.44529i	0.730285	+	0.352500i
$575$	3.05101	−	5.28450i	0.127236	−	0.220379i
$576$		0			0
$577$	11.0922	+	19.2123i	0.461775	+	0.799817i	0.999050	−	0.0435901i	$-0.0138796\pi$
$577$	11.0922	+	19.2123i	0.461775	+	0.799817i	−0.537275	+	0.843407i	$0.680546\pi$
$578$	0.809351	+	10.9325i	0.0336646	+	0.454733i
$579$		0			0
$580$	61.8731	−	9.21160i	2.56914	−	0.382491i
$581$	10.9066	−	9.15169i	0.452480	−	0.379676i
$582$		0			0
$583$	−9.59086	−	26.3507i	−0.397213	−	1.09133i
$584$	−39.6452	−	12.3467i	−1.64053	−	0.510908i
$585$		0			0
$586$	4.00190	+	4.11037i	0.165317	+	0.169798i
$587$	8.52654	+	1.50346i	0.351928	+	0.0620544i	0.346818	−	0.937933i	$-0.387262\pi$
$587$	8.52654	+	1.50346i	0.351928	+	0.0620544i	0.00511024	+	0.999987i	$0.498373\pi$
$588$		0			0
$589$	−2.65481	+	7.29402i	−0.109389	+	0.300545i
$590$	4.21117	−	41.7041i	0.173371	−	1.71693i
$591$		0			0
$592$	−44.0037	−	10.2109i	−1.80854	−	0.419667i
$593$			19.4361i			0.798144i	0.916920	+	0.399072i	$0.130668\pi$
$593$			19.4361i			0.798144i	−0.916920	+	0.399072i	$0.869332\pi$
$594$		0			0
$595$	49.4212			2.02607
$596$	−5.41383	−	16.2104i	−0.221759	−	0.664003i
$597$		0			0
$598$	−0.322557	+	3.19435i	−0.0131903	+	0.130627i
$599$	6.17877	+	2.24889i	0.252458	+	0.0918871i	0.465149	−	0.885232i	$-0.346001\pi$
$599$	6.17877	+	2.24889i	0.252458	+	0.0918871i	−0.212691	+	0.977119i	$0.568223\pi$
$600$		0			0
$601$	−0.821185	+	4.65717i	−0.0334968	+	0.189970i	−0.996965	−	0.0778536i	$-0.975193\pi$
$601$	−0.821185	+	4.65717i	−0.0334968	+	0.189970i	0.963468	+	0.267824i	$0.0863044\pi$
$602$	−19.1833	+	18.6771i	−0.781855	+	0.761223i
$603$		0			0
$604$	21.0042	+	0.561779i	0.854650	+	0.0228585i
$605$	11.7199	−	4.26568i	0.476480	−	0.173425i
$606$		0			0
$607$	22.8132	+	27.1877i	0.925960	+	1.10352i	0.994381	+	0.105859i	$0.0337594\pi$
$607$	22.8132	+	27.1877i	0.925960	+	1.10352i	−0.0684212	+	0.997657i	$0.521796\pi$
$608$	−9.33329	+	11.5958i	−0.378515	+	0.470270i
$609$		0			0
$610$	−3.52984	+	0.261319i	−0.142919	+	0.0105805i
$611$	2.81069	−	1.62275i	0.113709	−	0.0656496i
$612$		0			0
$613$	35.0635	+	20.2439i	1.41620	+	0.817644i	0.995963	−	0.0897701i	$-0.0286132\pi$
$613$	35.0635	+	20.2439i	1.41620	+	0.817644i	0.420238	+	0.907414i	$0.361947\pi$
$614$	42.8897	+	20.7023i	1.73089	+	0.835479i
$615$		0			0
$616$	20.5442	−	8.59464i	0.827751	−	0.346288i
$617$	−10.1725	+	1.79368i	−0.409528	+	0.0722109i	−0.374617	−	0.927179i	$-0.622226\pi$
$617$	−10.1725	+	1.79368i	−0.409528	+	0.0722109i	−0.0349111	+	0.999390i	$0.511115\pi$
$618$		0			0
$619$	10.0980	+	8.47326i	0.405874	+	0.340569i	0.822759	−	0.568390i	$-0.192434\pi$
$619$	10.0980	+	8.47326i	0.405874	+	0.340569i	−0.416885	+	0.908959i	$0.636878\pi$
$620$	10.5571	−	17.2060i	0.423983	−	0.691009i
$621$		0			0
$622$	−4.71307	+	16.6934i	−0.188977	+	0.669345i
$623$	−12.5858	−	10.5607i	−0.504238	−	0.423106i
$624$		0			0
$625$	−2.35223	−	13.3402i	−0.0940891	−	0.533606i
$626$	4.41229	−	6.12544i	0.176350	−	0.244822i
$627$		0			0
$628$	−14.4227	−	12.7746i	−0.575530	−	0.509760i
$629$	−28.0924	+	48.6575i	−1.12012	+	1.94010i
$630$		0			0
$631$	−30.9490	+	17.8684i	−1.23206	+	0.711329i	−0.967459	−	0.253029i	$-0.918573\pi$
$631$	−30.9490	+	17.8684i	−1.23206	+	0.711329i	−0.264600	+	0.964358i	$0.585240\pi$
$632$	22.0853	+	11.3981i	0.878505	+	0.453393i
$633$		0			0
$634$	−0.00846568	−	0.0188072i	−0.000336215	−	0.000746928i
$635$	−10.0084	−	11.9276i	−0.397173	−	0.473332i
$636$		0			0
$637$	1.21932	+	3.35005i	0.0483112	+	0.132734i
$638$	−8.62045	−	33.9830i	−0.341287	−	1.34540i
$639$		0			0
$640$	29.8114	−	24.6953i	1.17840	−	0.976166i
$641$	−23.8743	−	4.20968i	−0.942977	−	0.166272i	−0.319035	−	0.947743i	$-0.603359\pi$
$641$	−23.8743	−	4.20968i	−0.942977	−	0.166272i	−0.623942	+	0.781471i	$0.714470\pi$
$642$		0			0
$643$	24.2825	+	8.83811i	0.957609	+	0.348541i	0.773096	−	0.634289i	$-0.218707\pi$
$643$	24.2825	+	8.83811i	0.957609	+	0.348541i	0.184513	+	0.982830i	$0.440929\pi$
$644$	4.91353	+	1.93867i	0.193620	+	0.0763943i
$645$		0			0
$646$	10.4155	+	15.3064i	0.409791	+	0.602221i
$647$	19.0593			0.749298			0.374649	−	0.927167i	$-0.377763\pi$
$647$	19.0593			0.749298			0.374649	+	0.927167i	$0.377763\pi$
$648$		0			0
$649$	−23.4921			−0.922146
$650$	−13.3177	−	19.5714i	−0.522362	−	0.767653i
$651$		0			0
$652$	14.4021	−	36.5020i	0.564031	−	1.42953i
$653$	37.3455	+	13.5927i	1.46144	+	0.531922i	0.945762	−	0.324860i	$-0.105317\pi$
$653$	37.3455	+	13.5927i	1.46144	+	0.531922i	0.515680	+	0.856781i	$0.327539\pi$
$654$		0			0
$655$	−5.24222	−	0.924345i	−0.204831	−	0.0361172i
$656$	1.01175	−	18.9006i	0.0395023	−	0.737943i
$657$		0			0
$658$	−1.31291	−	5.17568i	−0.0511827	−	0.201769i
$659$	8.73494	+	23.9990i	0.340265	+	0.934870i	0.985318	+	0.170732i	$0.0546132\pi$
$659$	8.73494	+	23.9990i	0.340265	+	0.934870i	−0.645053	+	0.764138i	$0.723165\pi$
$660$		0			0
$661$	−4.94246	−	5.89019i	−0.192239	−	0.229102i	0.661312	−	0.750111i	$-0.270000\pi$
$661$	−4.94246	−	5.89019i	−0.192239	−	0.229102i	−0.853551	+	0.521009i	$0.825556\pi$
$662$	2.21672	+	4.92461i	0.0861551	+	0.191400i
$663$		0			0
$664$	−12.3261	−	6.36143i	−0.478344	−	0.246872i
$665$	22.6373	−	13.0696i	0.877836	−	0.506819i
$666$		0			0
$667$	4.15789	−	7.20168i	0.160994	−	0.278850i
$668$	15.1058	−	17.0547i	0.584460	−	0.659868i
$669$		0			0
$670$	−18.4654	+	25.6349i	−0.713379	+	0.990362i
$671$	0.344471	+	1.95359i	0.0132982	+	0.0754176i
$672$		0			0
$673$	8.06476	+	6.76714i	0.310874	+	0.260854i	0.784853	−	0.619682i	$-0.212738\pi$
$673$	8.06476	+	6.76714i	0.310874	+	0.260854i	−0.473979	+	0.880536i	$0.657183\pi$
$674$	−3.32281	+	11.7692i	−0.127990	+	0.453332i
$675$		0			0
$676$	−11.5446	−	7.08344i	−0.444024	−	0.272440i
$677$	−27.3660	−	22.9628i	−1.05176	−	0.882533i	−0.0584838	−	0.998288i	$-0.518627\pi$
$677$	−27.3660	−	22.9628i	−1.05176	−	0.882533i	−0.993278	+	0.115756i	$0.963071\pi$
$678$		0			0
$679$	0.385613	−	0.0679940i	0.0147985	−	0.00260937i
$680$	−18.5822	−	44.4180i	−0.712595	−	1.70335i
$681$		0			0
$682$	−10.1888	−	4.91802i	−0.390150	−	0.188321i
$683$	−11.6024	−	6.69864i	−0.443953	−	0.256316i	0.261320	−	0.965252i	$-0.415842\pi$
$683$	−11.6024	−	6.69864i	−0.443953	−	0.256316i	−0.705273	+	0.708936i	$0.749176\pi$
$684$		0			0
$685$	2.56895	−	1.48319i	0.0981547	−	0.0566696i
$686$	−22.8125	+	1.68884i	−0.870984	+	0.0644802i
$687$		0			0
$688$	23.9992	+	10.2188i	0.914962	+	0.389588i
$689$	−16.5863	−	19.7668i	−0.631887	−	0.753054i
$690$		0			0
$691$	32.2794	−	11.7487i	1.22797	−	0.446943i	0.355066	−	0.934841i	$-0.384458\pi$
$691$	32.2794	−	11.7487i	1.22797	−	0.446943i	0.872901	+	0.487898i	$0.162236\pi$
$692$	−0.846922	+	31.6654i	−0.0321952	+	1.20374i
$693$		0			0
$694$	−24.8850	+	24.2284i	−0.944623	+	0.919696i
$695$	9.02463	−	51.1812i	0.342324	−	1.94142i
$696$		0			0
$697$	−22.1220	−	8.05173i	−0.837929	−	0.304981i
$698$	0.964853	−	9.55514i	0.0365202	−	0.361667i
$699$		0			0
$700$	−36.9414	+	12.3374i	−1.39625	+	0.466311i
$701$	−5.81942			−0.219796			−0.109898	−	0.993943i	$-0.535052\pi$
$701$	−5.81942			−0.219796			−0.109898	+	0.993943i	$0.535052\pi$
$702$		0			0
$703$			29.7167i			1.12079i
$704$	−15.4491	−	15.2329i	−0.582261	−	0.574112i
$705$		0			0
$706$	2.06112	−	20.4117i	0.0775714	−	0.768205i
$707$	−12.9494	+	35.5783i	−0.487014	+	1.33806i
$708$		0			0
$709$	43.2874	+	7.63273i	1.62569	+	0.286653i	0.910882	−	0.412666i	$-0.135402\pi$
$709$	43.2874	+	7.63273i	1.62569	+	0.286653i	0.714809	+	0.699320i	$0.246514\pi$
$710$	−34.9830	−	35.9311i	−1.31289	−	1.34847i
$711$		0			0
$712$	−4.75940	+	15.2825i	−0.178366	+	0.572734i
$713$	−0.917815	−	2.52167i	−0.0343724	−	0.0944375i
$714$		0			0
$715$	−17.7396	+	14.8853i	−0.663424	+	0.556679i
$716$	4.64444	+	31.1961i	0.173571	+	1.16585i
$717$		0			0
$718$	0.336817	+	4.54965i	0.0125699	+	0.169791i
$719$	13.4590	+	23.3117i	0.501938	+	0.869381i	0.999997	+	0.00223877i	$0.000712623\pi$
$719$	13.4590	+	23.3117i	0.501938	+	0.869381i	−0.498060	+	0.867143i	$0.665954\pi$
$720$		0			0
$721$	−1.79387	+	3.10708i	−0.0668073	+	0.115714i
$722$	−15.3799	−	7.42370i	−0.572381	−	0.276281i
$723$		0			0
$724$	7.94048	−	6.30889i	0.295106	−	0.234468i
$725$	10.6472	+	60.3835i	0.395428	+	2.24259i
$726$		0			0
$727$	−7.10391	+	8.46611i	−0.263470	+	0.313991i	−0.881519	−	0.472148i	$-0.843479\pi$
$727$	−7.10391	+	8.46611i	−0.263470	+	0.313991i	0.618050	+	0.786139i	$0.287923\pi$
$728$	15.0595	−	13.8975i	0.558143	−	0.515074i
$729$		0			0
$730$	19.3019	−	68.3663i	0.714397	−	2.53035i
$731$	20.8539	−	24.8527i	0.771309	−	0.919211i
$732$		0			0
$733$	5.25607	−	0.926787i	0.194137	−	0.0342316i	−0.0757339	−	0.997128i	$-0.524130\pi$
$733$	5.25607	−	0.926787i	0.194137	−	0.0342316i	0.269871	+	0.962896i	$0.413019\pi$
$734$	−34.4682	−	24.8282i	−1.27225	−	0.916426i
$735$		0			0
$736$	−0.105063	−	5.14505i	−0.00387269	−	0.189649i
$737$	15.3342	+	8.85322i	0.564844	+	0.326113i
$738$		0			0
$739$	7.72474	+	13.3796i	0.284159	+	0.492178i	0.972405	−	0.233299i	$-0.0749522\pi$
$739$	7.72474	+	13.3796i	0.284159	+	0.492178i	−0.688246	+	0.725478i	$0.741619\pi$
$740$	15.4501	−	75.7225i	0.567955	−	2.78361i
$741$		0			0
$742$	−38.7118	+	17.4254i	−1.42116	+	0.639706i
$743$	−21.9616	+	18.4280i	−0.805692	+	0.676056i	−0.949575	−	0.313539i	$-0.898485\pi$
$743$	−21.9616	+	18.4280i	−0.805692	+	0.676056i	0.143883	+	0.989595i	$0.454041\pi$
$744$		0			0
$745$	27.4755	−	10.0003i	1.00662	−	0.366381i
$746$	−5.39969	−	21.2863i	−0.197697	−	0.779347i
$747$		0			0
$748$	−23.7221	+	12.8628i	−0.867364	+	0.470312i
$749$	−8.05566	+	45.6859i	−0.294347	+	1.66933i
$750$		0			0
$751$	8.91474	−	24.4930i	0.325303	−	0.893764i	−0.663979	−	0.747751i	$-0.731134\pi$
$751$	8.91474	−	24.4930i	0.325303	−	0.893764i	0.989283	−	0.146013i	$-0.0466440\pi$
$752$	−4.15807	+	3.12604i	−0.151629	+	0.113995i
$753$		0			0
$754$	−18.1492	−	26.6718i	−0.660956	−	0.971328i
$755$			35.9473i			1.30826i
$756$		0			0
$757$			6.07158i			0.220675i	0.993894	+	0.110338i	$0.0351932\pi$
$757$			6.07158i			0.220675i	−0.993894	+	0.110338i	$0.964807\pi$
$758$	7.81916	−	5.32068i	0.284005	−	0.193256i
$759$		0			0
$760$	−20.2581	−	15.4315i	−0.734838	−	0.559758i
$761$	−7.74422	+	21.2771i	−0.280728	+	0.771293i	0.716549	+	0.697537i	$0.245721\pi$
$761$	−7.74422	+	21.2771i	−0.280728	+	0.771293i	−0.997276	+	0.0737560i	$0.976501\pi$
$762$		0			0
$763$	1.20090	−	6.81067i	0.0434757	−	0.246563i
$764$	−43.8964	+	23.8020i	−1.58812	+	0.861127i
$765$		0			0
$766$	9.51731	−	2.41425i	0.343874	−	0.0872306i
$767$	−20.3134	+	7.39349i	−0.733476	+	0.266963i
$768$		0			0
$769$	−11.2565	+	9.44536i	−0.405921	+	0.340608i	−0.822777	−	0.568364i	$-0.807576\pi$
$769$	−11.2565	+	9.44536i	−0.405921	+	0.340608i	0.416856	+	0.908973i	$0.363132\pi$
$770$	15.6384	+	34.7418i	0.563567	+	1.25201i
$771$		0			0
$772$	−18.4606	−	3.76661i	−0.664411	−	0.135563i
$773$	−9.84699	−	17.0555i	−0.354172	−	0.613443i	0.632804	−	0.774312i	$-0.281904\pi$
$773$	−9.84699	−	17.0555i	−0.354172	−	0.613443i	−0.986976	+	0.160869i	$0.948570\pi$
$774$		0			0
$775$	17.1355	+	9.89320i	0.615526	+	0.355374i
$776$	−0.206100	−	0.321010i	−0.00739856	−	0.0115236i
$777$		0			0
$778$	−1.17667	+	1.63354i	−0.0421857	+	0.0585651i
$779$	−12.2622	+	2.16216i	−0.439341	+	0.0774676i
$780$		0			0
$781$	−18.0661	+	21.5304i	−0.646456	+	0.770417i
$782$	−6.15982	−	1.73911i	−0.220275	−	0.0621904i
$783$		0			0
$784$	−2.58852	−	5.09434i	−0.0924471	−	0.181941i
$785$	21.1874	−	25.2502i	0.756212	−	0.901218i
$786$		0			0
$787$	−2.49296	−	14.1383i	−0.0888646	−	0.503976i	−0.996456	−	0.0841207i	$-0.973192\pi$
$787$	−2.49296	−	14.1383i	−0.0888646	−	0.503976i	0.907591	−	0.419855i	$-0.137919\pi$
$788$	0.485918	+	0.611585i	0.0173101	+	0.0217868i
$789$		0			0
$790$	−18.4830	+	38.2918i	−0.657595	+	1.36236i
$791$	−13.7754	+	23.8596i	−0.489796	+	0.848351i
$792$		0			0
$793$	0.912701	+	1.58084i	0.0324110	+	0.0561374i
$794$	26.9595	−	1.99585i	0.956755	−	0.0708300i
$795$		0			0
$796$	−2.13369	−	14.3317i	−0.0756267	−	0.507975i
$797$	16.5677	−	13.9019i	0.586857	−	0.492431i	−0.300334	−	0.953834i	$-0.597098\pi$
$797$	16.5677	−	13.9019i	0.586857	−	0.492431i	0.887191	+	0.461403i	$0.152654\pi$
$798$		0			0
$799$	2.21295	+	6.08002i	0.0782884	+	0.215096i
$800$	24.9783	+	28.5628i	0.883116	+	1.00985i
$801$		0			0
$802$	−18.9537	+	18.4536i	−0.669280	+	0.651619i
$803$	−39.2092	−	6.91364i	−1.38366	−	0.243977i
$804$		0			0
$805$	−3.09078	+	8.49184i	−0.108936	+	0.299298i
$806$	−10.3580	−	1.04592i	−0.364845	−	0.0368411i
$807$		0			0
$808$	36.8455	−	1.73881i	1.29622	−	0.0611713i
$809$		−	27.7706i		−	0.976363i	−0.872742	−	0.488182i	$-0.837660\pi$
$809$		−	27.7706i		−	0.976363i	0.872742	−	0.488182i	$-0.162340\pi$
$810$		0			0
$811$	−6.91746			−0.242905			−0.121452	−	0.992597i	$-0.538755\pi$
$811$	−6.91746			−0.242905			−0.121452	+	0.992597i	$0.538755\pi$
$812$	−50.3434	+	16.8134i	−1.76671	+	0.590033i
$813$		0			0
$814$	−43.0943	−	4.35155i	−1.51045	−	0.152522i
$815$	63.0848	+	22.9610i	2.20976	+	0.804288i
$816$		0			0
$817$	2.97969	−	16.8987i	0.104246	−	0.591209i
$818$	18.2867	+	18.7823i	0.639380	+	0.656709i
$819$		0			0
$820$	32.3702	+	0.865772i	1.13042	+	0.0302341i
$821$	−6.71754	+	2.44498i	−0.234444	+	0.0853305i	−0.456570	−	0.889687i	$-0.650922\pi$
$821$	−6.71754	+	2.44498i	−0.234444	+	0.0853305i	0.222127	+	0.975018i	$0.428700\pi$
$822$		0			0
$823$	1.29022	+	1.53762i	0.0449742	+	0.0535981i	0.788063	−	0.615595i	$-0.211084\pi$
$823$	1.29022	+	1.53762i	0.0449742	+	0.0535981i	−0.743088	+	0.669193i	$0.766640\pi$
$824$	3.46702	+	0.444019i	0.120779	+	0.0154681i
$825$		0			0
$826$	2.62575	+	35.4680i	0.0913615	+	1.23409i
$827$	22.7464	−	13.1326i	0.790969	−	0.456666i	−0.0493347	−	0.998782i	$-0.515710\pi$
$827$	22.7464	−	13.1326i	0.790969	−	0.456666i	0.840303	+	0.542116i	$0.182377\pi$
$828$		0			0
$829$	−36.0689	−	20.8244i	−1.25272	−	0.723260i	−0.281074	−	0.959686i	$-0.590691\pi$
$829$	−36.0689	−	20.8244i	−1.25272	−	0.723260i	−0.971649	+	0.236426i	$0.924024\pi$
$830$	10.3156	−	21.3711i	0.358059	−	0.741802i
$831$		0			0
$832$	−18.1529	−	8.30958i	−0.629338	−	0.288083i
$833$	−6.99928	+	1.23416i	−0.242511	+	0.0427611i
$834$		0			0
$835$	29.8581	+	25.0539i	1.03328	+	0.867027i
$836$	−7.46422	+	12.1652i	−0.258155	+	0.420742i
$837$		0			0
$838$	−30.5693	−	8.63066i	−1.05600	−	0.298141i
$839$	−17.8040	−	14.9393i	−0.614662	−	0.515762i	0.281459	−	0.959573i	$-0.409182\pi$
$839$	−17.8040	−	14.9393i	−0.614662	−	0.515762i	−0.896120	+	0.443811i	$0.853626\pi$
$840$		0			0
$841$	9.47417	+	53.7307i	0.326696	+	1.85278i
$842$	20.0653	+	14.4535i	0.691496	+	0.498100i
$843$		0			0
$844$	29.6079	−	33.4279i	1.01915	−	1.15064i
$845$	11.5861	−	20.0677i	0.398574	−	0.690350i
$846$		0			0
$847$	−9.16452	+	5.29114i	−0.314897	+	0.181806i
$848$	30.2169	+	28.2410i	1.03765	+	0.969799i
$849$		0			0
$850$	43.0350	−	19.3714i	1.47609	−	0.664432i
$851$	−6.60374	−	7.87003i	−0.226373	−	0.269781i
$852$		0			0
$853$	0.546744	+	1.50217i	0.0187202	+	0.0514332i	0.948701	−	0.316175i	$-0.102399\pi$
$853$	0.546744	+	1.50217i	0.0187202	+	0.0514332i	−0.929981	+	0.367609i	$0.880177\pi$
$854$	2.91100	−	0.738433i	0.0996125	−	0.0252687i
$855$		0			0
$856$	44.0898	−	9.93761i	1.50696	−	0.339660i
$857$	21.3303	+	3.76110i	0.728629	+	0.128477i	0.525644	−	0.850705i	$-0.323825\pi$
$857$	21.3303	+	3.76110i	0.728629	+	0.128477i	0.202985	+	0.979182i	$0.434936\pi$
$858$		0			0
$859$	−13.9293	−	5.06987i	−0.475263	−	0.172982i	0.0932719	−	0.995641i	$-0.470267\pi$
$859$	−13.9293	−	5.06987i	−0.475263	−	0.172982i	−0.568535	+	0.822659i	$0.692490\pi$
$860$	−16.3785	+	41.5111i	−0.558502	+	1.41552i
$861$		0			0
$862$	−15.3602	+	10.4521i	−0.523171	+	0.356000i
$863$	37.5749			1.27907			0.639533	−	0.768764i	$-0.279128\pi$
$863$	37.5749			1.27907			0.639533	+	0.768764i	$0.279128\pi$
$864$		0			0
$865$	−54.1932			−1.84262
$866$	26.4949	−	18.0289i	0.900332	−	0.612645i
$867$		0			0
$868$	−6.28633	+	15.9326i	−0.213372	+	0.540788i
$869$	22.3930	+	8.15037i	0.759629	+	0.276482i
$870$		0			0
$871$	16.0457	+	2.82929i	0.543688	+	0.0958668i
$872$	−6.57273	+	1.48146i	−0.222581	+	0.0501685i
$873$		0			0
$874$	−3.28141	+	0.832395i	−0.110995	+	0.0281562i
$875$	−5.80168	−	15.9400i	−0.196133	−	0.538870i
$876$		0			0
$877$	−25.3049	−	30.1572i	−0.854484	−	1.01833i	−0.999582	−	0.0289176i	$-0.990794\pi$
$877$	−25.3049	−	30.1572i	−0.854484	−	1.01833i	0.145097	−	0.989417i	$-0.453650\pi$
$878$	−19.5090	+	8.78158i	−0.658396	+	0.296364i
$879$		0			0
$880$	25.3448	−	27.1180i	0.854372	−	0.914148i
$881$	−22.6325	+	13.0669i	−0.762509	+	0.440235i	−0.830196	−	0.557472i	$-0.811772\pi$
$881$	−22.6325	+	13.0669i	−0.762509	+	0.440235i	0.0676867	+	0.997707i	$0.478438\pi$
$882$		0			0
$883$	−24.4508	+	42.3501i	−0.822837	+	1.42519i	0.0807251	+	0.996736i	$0.474276\pi$
$883$	−24.4508	+	42.3501i	−0.822837	+	1.42519i	−0.903562	+	0.428458i	$0.859057\pi$
$884$	−16.4641	+	18.5883i	−0.553746	+	0.625191i
$885$		0			0
$886$	4.56781	+	3.29029i	0.153459	+	0.110540i
$887$	2.89846	+	16.4380i	0.0973207	+	0.551933i	0.994011	+	0.109276i	$0.0348531\pi$
$887$	2.89846	+	16.4380i	0.0973207	+	0.551933i	−0.896691	+	0.442658i	$0.854036\pi$
$888$		0			0
$889$	10.1203	+	8.49198i	0.339425	+	0.284812i
$890$	−26.3539	−	7.44052i	−0.883384	−	0.249407i
$891$		0			0
$892$	−8.32427	+	13.5669i	−0.278717	+	0.454254i
$893$	2.62152	+	2.19972i	0.0877259	+	0.0736108i
$894$		0			0
$895$	−53.1394	+	9.36990i	−1.77625	+	0.313201i
$896$	−21.2716	+	25.0275i	−0.710635	+	0.836109i
$897$		0			0
$898$	15.8783	−	32.8955i	0.529864	−	1.09774i
$899$	23.3522	+	13.4824i	0.778838	+	0.449663i
$900$		0			0
$901$	44.5501	−	25.7210i	1.48418	−	0.856890i
$902$	−1.33989	−	18.0990i	−0.0446136	−	0.602630i
$903$		0			0
$904$	26.6237	+	3.40968i	0.885492	+	0.113404i
$905$	11.1527	+	13.2913i	0.370729	+	0.441818i
$906$		0			0
$907$	9.94085	−	3.61817i	0.330081	−	0.120140i	−0.171663	−	0.985156i	$-0.554914\pi$
$907$	9.94085	−	3.61817i	0.330081	−	0.120140i	0.501744	+	0.865016i	$0.332692\pi$
$908$	17.2718	+	0.461952i	0.573186	+	0.0153304i
$909$		0			0
$910$	24.4564	+	25.1192i	0.810721	+	0.832694i
$911$	10.2298	−	58.0158i	0.338927	−	1.92215i	−0.0454332	−	0.998967i	$-0.514467\pi$
$911$	10.2298	−	58.0158i	0.338927	−	1.92215i	0.384360	−	0.923183i	$-0.374422\pi$
$912$		0			0
$913$	−12.4978	−	4.54882i	−0.413616	−	0.150544i
$914$	−3.94695	−	0.398553i	−0.130554	−	0.0131830i
$915$		0			0
$916$	−14.4776	+	4.83513i	−0.478354	+	0.159757i
$917$	4.51655			0.149150
$918$		0			0
$919$		−	25.4259i		−	0.838724i	−0.907819	−	0.419362i	$-0.862254\pi$
$919$		−	25.4259i		−	0.838724i	0.907819	−	0.419362i	$-0.137746\pi$
$920$	8.79430	−	0.415021i	0.289939	−	0.0136828i
$921$		0			0
$922$	−21.1449	−	2.13516i	−0.696370	−	0.0703176i
$923$	−8.84554	+	24.3029i	−0.291155	+	0.799941i
$924$		0			0
$925$	74.5997	+	13.1539i	2.45282	+	0.432499i
$926$	−22.1607	+	21.5759i	−0.728244	+	0.709027i
$927$		0			0
$928$	34.0402	+	38.9252i	1.11743	+	1.27778i
$929$	1.65289	+	4.54128i	0.0542296	+	0.148995i	0.963850	−	0.266446i	$-0.0858495\pi$
$929$	1.65289	+	4.54128i	0.0542296	+	0.148995i	−0.909620	+	0.415441i	$0.863627\pi$
$930$		0			0
$931$	−2.87963	+	2.41630i	−0.0943760	+	0.0791909i
$932$	−2.09360	−	14.0624i	−0.0685782	−	0.460631i
$933$		0			0
$934$	−26.4001	+	1.95444i	−0.863837	+	0.0639511i
$935$	−23.0832	−	39.9813i	−0.754902	−	1.30753i
$936$		0			0
$937$	25.7048	−	44.5220i	0.839738	−	1.45447i	−0.0503753	−	0.998730i	$-0.516042\pi$
$937$	25.7048	−	44.5220i	0.839738	−	1.45447i	0.890114	−	0.455739i	$-0.150625\pi$
$938$	11.6525	−	24.1409i	0.380468	−	0.788229i
$939$		0			0
$940$	−5.53637	−	6.96817i	−0.180577	−	0.227277i
$941$	−6.83831	−	38.7820i	−0.222922	−	1.26426i	−0.866617	−	0.498973i	$-0.833711\pi$
$941$	−6.83831	−	38.7820i	−0.222922	−	1.26426i	0.643695	−	0.765282i	$-0.277401\pi$
$942$		0			0
$943$	2.76699	−	3.29758i	0.0901057	−	0.107384i
$944$	30.8902	−	15.6958i	1.00539	−	0.510855i
$945$		0			0
$946$	24.0696	+	6.79561i	0.782571	+	0.220944i
$947$	−18.2848	+	21.7910i	−0.594178	+	0.708113i	−0.976403	−	0.215956i	$-0.930713\pi$
$947$	−18.2848	+	21.7910i	−0.594178	+	0.708113i	0.382226	+	0.924069i	$0.375158\pi$
$948$		0			0
$949$	−36.0798	+	6.36183i	−1.17120	+	0.206514i
$950$	14.5893	−	20.2538i	0.473338	−	0.657120i
$951$		0			0
$952$	22.0716	+	34.3775i	0.715343	+	1.11418i
$953$	24.5811	+	14.1919i	0.796261	+	0.459722i	0.842162	−	0.539224i	$-0.181282\pi$
$953$	24.5811	+	14.1919i	0.796261	+	0.459722i	−0.0459008	+	0.998946i	$0.514616\pi$
$954$		0			0
$955$	−42.7143	−	73.9833i	−1.38220	−	2.39404i
$956$	−4.36017	−	0.889627i	−0.141018	−	0.0287726i
$957$		0			0
$958$	−11.6465	−	25.8736i	−0.376282	−	0.835939i
$959$	−1.92807	+	1.61784i	−0.0622605	+	0.0522428i
$960$		0			0
$961$	−20.9537	+	7.62652i	−0.675925	+	0.246017i
$962$	−38.6328	+	9.79998i	−1.24557	+	0.315964i
$963$		0			0
$964$	0.358973	−	0.194647i	0.0115618	−	0.00626914i
$965$	5.59727	−	31.7437i	0.180183	−	1.02187i
$966$		0			0
$967$	−14.1101	+	38.7671i	−0.453749	+	1.24667i	0.476317	+	0.879274i	$0.341972\pi$
$967$	−14.1101	+	38.7671i	−0.453749	+	1.24667i	−0.930066	+	0.367392i	$0.880251\pi$
$968$	8.20133	+	6.24731i	0.263601	+	0.200796i
$969$		0			0
$970$	0.539567	−	0.367157i	0.0173245	−	0.0117887i
$971$		−	5.59715i		−	0.179621i	−0.995959	−	0.0898105i	$-0.971374\pi$
$971$		−	5.59715i		−	0.179621i	0.995959	−	0.0898105i	$-0.0286261\pi$
$972$		0			0
$973$			44.0963i			1.41366i
$974$	11.2177	+	16.4853i	0.359437	+	0.528222i
$975$		0			0
$976$	−1.75821	−	2.33866i	−0.0562788	−	0.0748587i
$977$	−7.61083	+	20.9106i	−0.243492	+	0.668989i	0.756397	+	0.654112i	$0.226958\pi$
$977$	−7.61083	+	20.9106i	−0.243492	+	0.668989i	−0.999889	+	0.0148763i	$0.995265\pi$
$978$		0			0
$979$	−2.66507	+	15.1144i	−0.0851762	+	0.483058i
$980$	8.59398	−	4.65993i	0.274525	−	0.148856i
$981$		0			0
$982$	−0.779681	−	3.07361i	−0.0248806	−	0.0980827i
$983$	−43.7402	+	15.9201i	−1.39510	+	0.507774i	−0.926719	−	0.375755i	$-0.877383\pi$
$983$	−43.7402	+	15.9201i	−1.39510	+	0.507774i	−0.468378	+	0.883528i	$0.655161\pi$
$984$		0			0
$985$	−1.02371	+	0.858996i	−0.0326182	+	0.0273699i
$986$	58.6477	−	26.3991i	1.86772	−	0.840720i
$987$		0			0
$988$	−2.62559	+	12.8683i	−0.0835311	+	0.409396i
$989$	2.96615	+	5.13752i	0.0943180	+	0.163364i
$990$		0			0
$991$	38.1847	+	22.0460i	1.21298	+	0.700313i	0.963407	−	0.268044i	$-0.0863772\pi$
$991$	38.1847	+	22.0460i	1.21298	+	0.700313i	0.249571	+	0.968357i	$0.419711\pi$
$992$	16.6833	−	0.340679i	0.529696	−	0.0108166i
$993$		0			0
$994$	34.5255	+	24.8694i	1.09508	+	0.788811i
$995$	24.4127	−	4.30461i	0.773933	−	0.136465i
$996$		0			0
$997$	−13.4946	+	16.0822i	−0.427378	+	0.509330i	−0.936164	−	0.351563i	$-0.885650\pi$
$997$	−13.4946	+	16.0822i	−0.427378	+	0.509330i	0.508786	+	0.860893i	$0.330095\pi$
$998$	3.55943	−	12.6073i	0.112672	−	0.399077i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.35.6		192
3.2	odd	2		216.2.v.b.11.27	yes	192
8.3	odd	2	inner	648.2.v.b.35.12		192
12.11	even	2		864.2.bh.b.335.27		192
24.5	odd	2		864.2.bh.b.335.28		192
24.11	even	2		216.2.v.b.11.21	✓	192
27.5	odd	18	inner	648.2.v.b.611.12		192
27.22	even	9		216.2.v.b.59.21	yes	192
108.103	odd	18		864.2.bh.b.815.28		192
216.59	even	18	inner	648.2.v.b.611.6		192
216.157	even	18		864.2.bh.b.815.27		192
216.211	odd	18		216.2.v.b.59.27	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.21	✓	192	24.11	even	2
216.2.v.b.11.27	yes	192	3.2	odd	2
216.2.v.b.59.21	yes	192	27.22	even	9
216.2.v.b.59.27	yes	192	216.211	odd	18
648.2.v.b.35.6		192	1.1	even	1	trivial
648.2.v.b.35.12		192	8.3	odd	2	inner
648.2.v.b.611.6		192	216.59	even	18	inner
648.2.v.b.611.12		192	27.5	odd	18	inner
864.2.bh.b.335.27		192	12.11	even	2
864.2.bh.b.335.28		192	24.5	odd	2
864.2.bh.b.815.27		192	216.157	even	18
864.2.bh.b.815.28		192	108.103	odd	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.v (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.16920 + 0.795599i) q^{2} +(0.734044 - 1.86042i) q^{4} +(3.21529 + 1.17027i) q^{5} +(-2.85909 - 0.504135i) q^{7} +(0.621910 + 2.75921i) q^{8} +O(q^{10})\)	\(q+(-1.16920 + 0.795599i) q^{2} +(0.734044 - 1.86042i) q^{4} +(3.21529 + 1.17027i) q^{5} +(-2.85909 - 0.504135i) q^{7} +(0.621910 + 2.75921i) q^{8} +(-4.69037 + 1.18981i) q^{10} +(0.927560 + 2.54845i) q^{11} +(1.60411 + 1.91170i) q^{13} +(3.74393 - 1.68526i) q^{14} +(-2.92236 - 2.73127i) q^{16} +(-4.30856 + 2.48755i) q^{17} +(-1.31569 + 2.27884i) q^{19} +(4.53736 - 5.12277i) q^{20} +(-3.11204 - 2.24167i) q^{22} +(-0.157970 - 0.895893i) q^{23} +(5.13833 + 4.31157i) q^{25} +(-3.39646 - 0.958928i) q^{26} +(-3.03660 + 4.94907i) q^{28} +(7.00248 + 5.87578i) q^{29} +(2.90502 - 0.512234i) q^{31} +(5.58981 + 0.868362i) q^{32} +(3.05847 - 6.33633i) q^{34} +(-8.60284 - 4.96685i) q^{35} +(9.78021 - 5.64661i) q^{37} +(-0.274743 - 3.71117i) q^{38} +(-1.22939 + 9.59946i) q^{40} +(3.04161 + 3.62485i) q^{41} +(-6.12779 + 2.23033i) q^{43} +(5.42207 + 0.145018i) q^{44} +(0.897470 + 0.921795i) q^{46} +(0.225833 - 1.28076i) q^{47} +(1.34241 + 0.488598i) q^{49} +(-9.43801 - 0.953026i) q^{50} +(4.73406 - 1.58105i) q^{52} -10.3399 q^{53} +9.27950i q^{55} +(-0.387086 - 8.20236i) q^{56} +(-12.8621 - 1.29878i) q^{58} +(-2.96267 + 8.13988i) q^{59} +(0.720351 + 0.127017i) q^{61} +(-2.98901 + 2.91014i) q^{62} +(-7.22645 + 3.43196i) q^{64} +(2.92046 + 8.02391i) q^{65} +(5.00144 - 4.19671i) q^{67} +(1.46523 + 9.84173i) q^{68} +(14.0100 - 1.03718i) q^{70} +(5.18176 + 8.97507i) q^{71} +(-7.34034 + 12.7138i) q^{73} +(-6.94256 + 14.3831i) q^{74} +(3.27383 + 4.12050i) q^{76} +(-1.36722 - 7.75387i) q^{77} +(5.64811 - 6.73115i) q^{79} +(-6.19991 - 12.2018i) q^{80} +(-6.44017 - 1.81826i) q^{82} +(-3.15228 + 3.75674i) q^{83} +(-16.7644 + 2.95601i) q^{85} +(5.39014 - 7.48296i) q^{86} +(-6.45484 + 4.14424i) q^{88} +(4.90094 + 2.82956i) q^{89} +(-3.62253 - 6.27441i) q^{91} +(-1.78270 - 0.363733i) q^{92} +(0.754930 + 1.67714i) q^{94} +(-6.89717 + 5.78741i) q^{95} +(-0.126739 + 0.0461291i) q^{97} +(-1.95827 + 0.496754i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

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