LMFDB - Embedded newform 387.2.y.c.154.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(10,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.y (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			154.3
Character	$\chi$	$=$	387.154
Dual form			387.2.y.c.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06783 + 0.514239i) q^{2} +(-0.371164 - 0.465425i) q^{4} +(-2.37710 + 2.20563i) q^{5} +(-1.38418 + 2.39748i) q^{7} +(-0.684463 - 2.99883i) q^{8} +O(q^{10})$	\(q+(1.06783 + 0.514239i) q^{2} +(-0.371164 - 0.465425i) q^{4} +(-2.37710 + 2.20563i) q^{5} +(-1.38418 + 2.39748i) q^{7} +(-0.684463 - 2.99883i) q^{8} +(-3.67256 + 1.13283i) q^{10} +(-3.47915 + 4.36271i) q^{11} +(1.57105 + 0.484606i) q^{13} +(-2.71095 + 1.84829i) q^{14} +(0.546293 - 2.39346i) q^{16} +(-0.555777 - 0.515686i) q^{17} +(-0.795961 + 2.02807i) q^{19} +(1.90885 + 0.287713i) q^{20} +(-5.95861 + 2.86951i) q^{22} +(-0.00139480 - 0.000210232i) q^{23} +(0.412168 - 5.50000i) q^{25} +(1.42841 + 1.32537i) q^{26} +(1.62960 - 0.245623i) q^{28} +(3.87133 - 2.63943i) q^{29} +(0.301429 + 4.02229i) q^{31} +(-2.02149 + 2.53487i) q^{32} +(-0.328289 - 0.836466i) q^{34} +(-1.99760 - 8.75205i) q^{35} +(-0.999506 - 1.73120i) q^{37} +(-1.89286 + 1.75632i) q^{38} +(8.24135 + 5.61886i) q^{40} +(-6.30781 - 3.03768i) q^{41} +(6.54912 + 0.330261i) q^{43} +3.32185 q^{44} +(-0.00138130 - 0.000941752i) q^{46} +(4.90255 + 6.14760i) q^{47} +(-0.331936 - 0.574929i) q^{49} +(3.26844 - 5.66111i) q^{50} +(-0.357571 - 0.911075i) q^{52} +(3.76860 - 1.16246i) q^{53} +(-1.35223 - 18.0443i) q^{55} +(8.13705 + 2.50995i) q^{56} +(5.49121 - 0.827667i) q^{58} +(0.811036 - 3.55338i) q^{59} +(-0.639001 + 8.52687i) q^{61} +(-1.74654 + 4.45012i) q^{62} +(-7.88592 + 3.79766i) q^{64} +(-4.80342 + 2.31320i) q^{65} +(3.43004 - 8.73959i) q^{67} +(-0.0337286 + 0.450076i) q^{68} +(2.36756 - 10.3729i) q^{70} +(-6.83052 + 1.02953i) q^{71} +(-10.6150 - 3.27429i) q^{73} +(-0.177053 - 2.36261i) q^{74} +(1.23935 - 0.382288i) q^{76} +(-5.64372 - 14.3800i) q^{77} +(-3.26980 + 5.66346i) q^{79} +(3.98050 + 6.89443i) q^{80} +(-5.17357 - 6.48745i) q^{82} +(4.71578 + 3.21516i) q^{83} +2.45855 q^{85} +(6.82350 + 3.72047i) q^{86} +(15.4644 + 7.44725i) q^{88} +(7.13427 + 4.86406i) q^{89} +(-3.33646 + 3.09578i) q^{91} +(0.000419851 + 0.000727204i) q^{92} +(2.07374 + 9.08566i) q^{94} +(-2.58110 - 6.57654i) q^{95} +(-11.0143 + 13.8115i) q^{97} +(-0.0587992 - 0.784620i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{4}{21}\right)$	$1$

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 $

$2$	1.06783	+	0.514239i	0.755069	+	0.363622i	0.771489	−	0.636243i	$-0.219513\pi$
$2$	1.06783	+	0.514239i	0.755069	+	0.363622i	−0.0164198	+	0.999865i	$0.505227\pi$
$3$		0			0
$3$		0			0
$4$	−0.371164	−	0.465425i	−0.185582	−	0.232712i
$5$	−2.37710	+	2.20563i	−1.06307	+	0.986388i	−0.999933	−	0.0116171i	$-0.996302\pi$
$5$	−2.37710	+	2.20563i	−1.06307	+	0.986388i	−0.0631405	+	0.998005i	$0.520112\pi$
$6$		0			0
$7$	−1.38418	+	2.39748i	−0.523173	+	0.906162i	0.476464	+	0.879194i	$0.341918\pi$
$7$	−1.38418	+	2.39748i	−0.523173	+	0.906162i	−0.999636	+	0.0269675i	$0.991415\pi$
$8$	−0.684463	−	2.99883i	−0.241994	−	1.06025i
$9$		0			0
$10$	−3.67256	+	1.13283i	−1.16137	+	0.358234i
$11$	−3.47915	+	4.36271i	−1.04900	+	1.31541i	−0.101787	+	0.994806i	$0.532456\pi$
$11$	−3.47915	+	4.36271i	−1.04900	+	1.31541i	−0.947215	+	0.320600i	$0.896115\pi$
$12$		0			0
$13$	1.57105	+	0.484606i	0.435732	+	0.134406i	0.504858	−	0.863202i	$-0.331545\pi$
$13$	1.57105	+	0.484606i	0.435732	+	0.134406i	−0.0691260	+	0.997608i	$0.522021\pi$
$14$	−2.71095	+	1.84829i	−0.724532	+	0.493977i
$15$		0			0
$16$	0.546293	−	2.39346i	0.136573	−	0.598366i
$17$	−0.555777	−	0.515686i	−0.134796	−	0.125072i	0.609894	−	0.792483i	$-0.291212\pi$
$17$	−0.555777	−	0.515686i	−0.134796	−	0.125072i	−0.744690	+	0.667411i	$0.767403\pi$
$18$		0			0
$19$	−0.795961	+	2.02807i	−0.182606	+	0.465272i	−0.992639	−	0.121112i	$-0.961354\pi$
$19$	−0.795961	+	2.02807i	−0.182606	+	0.465272i	0.810033	+	0.586384i	$0.199449\pi$
$20$	1.90885	+	0.287713i	0.426832	+	0.0643345i
$21$		0			0
$22$	−5.95861	+	2.86951i	−1.27038	+	0.611782i
$23$	−0.00139480		0.000210232i	−0.000290836		4.38364e-5i	0.148897	−	0.988853i	$-0.452428\pi$
$23$	−0.00139480		0.000210232i	−0.000290836		4.38364e-5i	−0.149188	+	0.988809i	$0.547666\pi$
$24$		0			0
$25$	0.412168	−	5.50000i	0.0824336	−	1.10000i
$26$	1.42841	+	1.32537i	0.280135	+	0.259927i
$27$		0			0
$28$	1.62960	−	0.245623i	0.307966	−	0.0464185i
$29$	3.87133	−	2.63943i	0.718888	−	0.490129i	−0.147777	−	0.989021i	$-0.547212\pi$
$29$	3.87133	−	2.63943i	0.718888	−	0.490129i	0.866665	+	0.498891i	$0.166259\pi$
$30$		0			0
$31$	0.301429	+	4.02229i	0.0541382	+	0.722424i	0.956553	+	0.291557i	$0.0941733\pi$
$31$	0.301429	+	4.02229i	0.0541382	+	0.722424i	−0.902415	+	0.430867i	$0.858208\pi$
$32$	−2.02149	+	2.53487i	−0.357352	+	0.448105i
$33$		0			0
$34$	−0.328289	−	0.836466i	−0.0563011	−	0.143453i
$35$	−1.99760	−	8.75205i	−0.337656	−	1.47937i
$36$		0			0
$37$	−0.999506	−	1.73120i	−0.164318	−	0.284607i	0.772095	−	0.635507i	$-0.219209\pi$
$37$	−0.999506	−	1.73120i	−0.164318	−	0.284607i	−0.936413	+	0.350900i	$0.885876\pi$
$38$	−1.89286	+	1.75632i	−0.307063	+	0.284913i
$39$		0			0
$40$	8.24135	+	5.61886i	1.30307	+	0.888419i
$41$	−6.30781	−	3.03768i	−0.985115	−	0.474406i	−0.129253	−	0.991612i	$-0.541258\pi$
$41$	−6.30781	−	3.03768i	−0.985115	−	0.474406i	−0.855861	+	0.517205i	$0.826972\pi$
$42$		0			0
$43$	6.54912	+	0.330261i	0.998731	+	0.0503643i
$43$	6.54912	+	0.330261i	0.998731	+	0.0503643i
$44$	3.32185			0.500787
$45$		0			0
$46$	−0.00138130		0.000941752i	−0.000203661		0.000138854i
$47$	4.90255	+	6.14760i	0.715110	+	0.896720i	0.998050	−	0.0624180i	$-0.0198812\pi$
$47$	4.90255	+	6.14760i	0.715110	+	0.896720i	−0.282940	+	0.959138i	$0.591310\pi$
$48$		0			0
$49$	−0.331936	−	0.574929i	−0.0474194	−	0.0821328i
$50$	3.26844	−	5.66111i	0.462227	−	0.800601i
$51$		0			0
$52$	−0.357571	−	0.911075i	−0.0495861	−	0.126343i
$53$	3.76860	−	1.16246i	0.517657	−	0.159676i	−0.0249081	−	0.999690i	$-0.507929\pi$
$53$	3.76860	−	1.16246i	0.517657	−	0.159676i	0.542565	+	0.840014i	$0.317453\pi$
$54$		0			0
$55$	−1.35223	−	18.0443i	−0.182335	−	2.43310i
$56$	8.13705	+	2.50995i	1.08736	+	0.335406i
$57$		0			0
$58$	5.49121	−	0.827667i	0.721032	−	0.108678i
$59$	0.811036	−	3.55338i	0.105588	−	0.462611i	−0.894297	−	0.447473i	$-0.852324\pi$
$59$	0.811036	−	3.55338i	0.105588	−	0.462611i	0.999885	−	0.0151380i	$-0.00481876\pi$
$60$		0			0
$61$	−0.639001	+	8.52687i	−0.0818157	+	1.09175i	0.793618	+	0.608416i	$0.208195\pi$
$61$	−0.639001	+	8.52687i	−0.0818157	+	1.09175i	−0.875434	+	0.483338i	$0.839424\pi$
$62$	−1.74654	+	4.45012i	−0.221811	+	0.565166i
$63$		0			0
$64$	−7.88592	+	3.79766i	−0.985740	+	0.474707i
$65$	−4.80342	+	2.31320i	−0.595791	+	0.286918i
$66$		0			0
$67$	3.43004	−	8.73959i	0.419046	−	1.06771i	−0.553054	−	0.833145i	$-0.686538\pi$
$67$	3.43004	−	8.73959i	0.419046	−	1.06771i	0.972100	−	0.234566i	$-0.0753670\pi$
$68$	−0.0337286	+	0.450076i	−0.00409019	+	0.0545798i
$69$		0			0
$70$	2.36756	−	10.3729i	0.282977	−	1.23980i
$71$	−6.83052	+	1.02953i	−0.810633	+	0.122183i	−0.541263	−	0.840853i	$-0.682054\pi$
$71$	−6.83052	+	1.02953i	−0.810633	+	0.122183i	−0.269370	+	0.963037i	$0.586816\pi$
$72$		0			0
$73$	−10.6150	−	3.27429i	−1.24239	−	0.383226i	−0.397220	−	0.917724i	$-0.630025\pi$
$73$	−10.6150	−	3.27429i	−1.24239	−	0.383226i	−0.845170	+	0.534497i	$0.820501\pi$
$74$	−0.177053	−	2.36261i	−0.0205820	−	0.274647i
$75$		0			0
$76$	1.23935	−	0.382288i	0.142163	−	0.0438515i
$77$	−5.64372	−	14.3800i	−0.643162	−	1.63875i
$78$		0			0
$79$	−3.26980	+	5.66346i	−0.367882	+	0.637190i	−0.989234	−	0.146342i	$-0.953250\pi$
$79$	−3.26980	+	5.66346i	−0.367882	+	0.637190i	0.621353	+	0.783531i	$0.286583\pi$
$80$	3.98050	+	6.89443i	0.445034	+	0.770821i
$81$		0			0
$82$	−5.17357	−	6.48745i	−0.571325	−	0.716419i
$83$	4.71578	+	3.21516i	0.517624	+	0.352910i	0.793782	−	0.608202i	$-0.208109\pi$
$83$	4.71578	+	3.21516i	0.517624	+	0.352910i	−0.276158	+	0.961112i	$0.589061\pi$
$84$		0			0
$85$	2.45855			0.266667
$86$	6.82350	+	3.72047i	0.735797	+	0.401189i
$87$		0			0
$88$	15.4644	+	7.44725i	1.64851	+	0.793880i
$89$	7.13427	+	4.86406i	0.756231	+	0.515590i	0.878986	−	0.476847i	$-0.158221\pi$
$89$	7.13427	+	4.86406i	0.756231	+	0.515590i	−0.122755	+	0.992437i	$0.539173\pi$
$90$		0			0
$91$	−3.33646	+	3.09578i	−0.349756	+	0.324526i
$92$	0.000419851	0	0.000727204i	4.37725e−5	0	7.58163e-5i
$93$		0			0
$94$	2.07374	+	9.08566i	0.213890	+	0.937115i
$95$	−2.58110	−	6.57654i	−0.264815	−	0.674739i
$96$		0			0
$97$	−11.0143	+	13.8115i	−1.11833	+	1.40234i	−0.213306	+	0.976986i	$0.568423\pi$
$97$	−11.0143	+	13.8115i	−1.11833	+	1.40234i	−0.905026	+	0.425357i	$0.860148\pi$
$98$	−0.0587992	−	0.784620i	−0.00593961	−	0.0792586i
$99$		0			0
$100$	−2.71282	+	1.84957i	−0.271282	+	0.184957i
$101$	9.98838	−	1.50551i	0.993881	−	0.149803i	0.368086	−	0.929792i	$-0.380013\pi$
$101$	9.98838	−	1.50551i	0.993881	−	0.149803i	0.625794	+	0.779988i	$0.284775\pi$
$102$		0			0
$103$	10.2237	+	9.48624i	1.00737	+	0.934707i	0.997869	−	0.0652474i	$-0.0207837\pi$
$103$	10.2237	+	9.48624i	1.00737	+	0.934707i	0.00950588	+	0.999955i	$0.496974\pi$
$104$	0.377922	−	5.04302i	0.0370583	−	0.494509i
$105$		0			0
$106$	4.62200	+	0.696655i	0.448929	+	0.0676651i
$107$	−6.73185	+	3.24189i	−0.650793	+	0.313405i	−0.729994	−	0.683453i	$-0.760477\pi$
$107$	−6.73185	+	3.24189i	−0.650793	+	0.313405i	0.0792013	+	0.996859i	$0.474763\pi$
$108$		0			0
$109$	7.53258	+	1.13535i	0.721490	+	0.108747i	0.499515	−	0.866305i	$-0.333512\pi$
$109$	7.53258	+	1.13535i	0.721490	+	0.108747i	0.221975	+	0.975052i	$0.428750\pi$
$110$	7.83514	−	19.9636i	0.747051	−	1.90346i
$111$		0			0
$112$	4.98211	+	4.62272i	0.470765	+	0.436806i
$113$	−1.43538	+	6.28879i	−0.135029	+	0.591600i	0.861456	+	0.507831i	$0.169553\pi$
$113$	−1.43538	+	6.28879i	−0.135029	+	0.591600i	−0.996485	+	0.0837684i	$0.973304\pi$
$114$		0			0
$115$	0.00377927	−	0.00257667i	0.000352419	−	0.000240275i
$116$	−2.66535	−	0.822152i	−0.247472	−	0.0763349i
$117$		0			0
$118$	2.69334	−	3.37734i	0.247942	−	0.310909i
$119$	2.00564	−	0.618659i	0.183857	−	0.0567124i
$120$		0			0
$121$	−4.48106	−	19.6328i	−0.407369	−	1.78480i
$122$	−5.06719	+	8.77664i	−0.458762	+	0.794599i
$123$		0			0
$124$	1.76019	−	1.63322i	0.158070	−	0.146668i
$125$	1.04209	+	1.30674i	0.0932077	+	0.116879i
$126$		0			0
$127$	−6.89399	−	3.31997i	−0.611743	−	0.294600i	0.102243	−	0.994759i	$-0.467398\pi$
$127$	−6.89399	−	3.31997i	−0.611743	−	0.294600i	−0.713986	+	0.700159i	$0.753112\pi$
$128$	−3.88928			−0.343767
$129$		0			0
$130$	−6.31877			−0.554193
$131$	15.7172	+	7.56902i	1.37322	+	0.661308i	0.967543	−	0.252708i	$-0.0813211\pi$
$131$	15.7172	+	7.56902i	1.37322	+	0.661308i	0.405678	+	0.914016i	$0.367035\pi$
$132$		0			0
$133$	−3.76051	−	4.71553i	−0.326077	−	0.408888i
$134$	8.15693	−	7.56853i	0.704652	−	0.653821i
$135$		0			0
$136$	−1.16605	+	2.01965i	−0.0999876	+	0.173184i
$137$	0.579094	+	2.53718i	0.0494753	+	0.216766i	0.993622	−	0.112759i	$-0.0359687\pi$
$137$	0.579094	+	2.53718i	0.0494753	+	0.216766i	−0.944147	+	0.329524i	$0.893112\pi$
$138$		0			0
$139$	7.59006	−	2.34122i	0.643780	−	0.198580i	0.0443616	−	0.999016i	$-0.485875\pi$
$139$	7.59006	−	2.34122i	0.643780	−	0.198580i	0.599419	+	0.800436i	$0.295398\pi$
$140$	−3.33199	+	4.17818i	−0.281604	+	0.353120i
$141$		0			0
$142$	−7.82325	−	2.41315i	−0.656512	−	0.202507i
$143$	−7.58012	+	5.16804i	−0.633881	+	0.432173i
$144$		0			0
$145$	−3.38095	+	14.8129i	−0.280773	+	1.23015i
$146$	−9.65121	−	8.95502i	−0.798740	−	0.741123i
$147$		0			0
$148$	−0.434761	+	1.10775i	−0.0357371	+	0.0910566i
$149$	−18.4553	−	2.78168i	−1.51191	−	0.227884i	−0.659880	−	0.751371i	$-0.729393\pi$
$149$	−18.4553	−	2.78168i	−1.51191	−	0.227884i	−0.852034	+	0.523487i	$0.824631\pi$
$150$		0			0
$151$	−8.42384	+	4.05671i	−0.685522	+	0.330130i	−0.744020	−	0.668158i	$-0.767083\pi$
$151$	−8.42384	+	4.05671i	−0.685522	+	0.330130i	0.0584978	+	0.998288i	$0.481369\pi$
$152$	6.62666	+	0.998808i	0.537493	+	0.0810140i
$153$		0			0
$154$	1.36822	−	18.2576i	0.110254	−	1.47124i
$155$	−9.58821	−	8.89656i	−0.770143	−	0.714589i
$156$		0			0
$157$	−1.46599	+	0.220962i	−0.116999	+	0.0176347i	−0.207280	−	0.978282i	$-0.566461\pi$
$157$	−1.46599	+	0.220962i	−0.116999	+	0.0176347i	0.0902820	+	0.995916i	$0.471223\pi$
$158$	−6.40396	+	4.36615i	−0.509472	+	0.347352i
$159$		0			0
$160$	−0.785689	−	10.4843i	−0.0621142	−	0.828856i
$161$	0.00243469	−	0.00305300i	0.000191880	−	0.000240610i
$162$		0			0
$163$	5.31184	+	13.5344i	0.416056	+	1.06009i	0.973258	+	0.229715i	$0.0737796\pi$
$163$	5.31184	+	13.5344i	0.416056	+	1.06009i	−0.557202	+	0.830377i	$0.688125\pi$
$164$	0.927419	+	4.06329i	0.0724193	+	0.317289i
$165$		0			0
$166$	3.38228	+	5.85828i	0.262516	+	0.454691i
$167$	5.81721	−	5.39758i	0.450149	−	0.417677i	−0.422244	−	0.906482i	$-0.638757\pi$
$167$	5.81721	−	5.39758i	0.450149	−	0.417677i	0.872393	+	0.488805i	$0.162567\pi$
$168$		0			0
$169$	−8.50774	−	5.80048i	−0.654441	−	0.446191i
$170$	2.62531	+	1.26428i	0.201352	+	0.0969661i
$171$		0			0
$172$	−2.27708	−	3.17070i	−0.173626	−	0.241764i
$173$	1.73137			0.131634			0.0658169	−	0.997832i	$-0.479035\pi$
$173$	1.73137			0.131634			0.0658169	+	0.997832i	$0.479035\pi$
$174$		0			0
$175$	12.6156	+	8.60118i	0.953651	+	0.650188i
$176$	8.54136	+	10.7105i	0.643829	+	0.807336i
$177$		0			0
$178$	5.11688	+	8.86270i	0.383527	+	0.664288i
$179$	−4.07203	+	7.05296i	−0.304358	+	0.527163i	−0.977118	−	0.212698i	$-0.931775\pi$
$179$	−4.07203	+	7.05296i	−0.304358	+	0.527163i	0.672761	+	0.739860i	$0.265108\pi$
$180$		0			0
$181$	−4.70194	−	11.9804i	−0.349493	−	0.890493i	−0.992231	−	0.124407i	$-0.960297\pi$
$181$	−4.70194	−	11.9804i	−0.349493	−	0.890493i	0.642739	−	0.766086i	$-0.277798\pi$
$182$	−5.15474	+	1.59003i	−0.382095	+	0.117861i
$183$		0			0
$184$	0.000324238		0.00432666i	2.39032e−5		0.000318966i
$185$	6.19431	+	1.91069i	0.455414	+	0.140477i
$186$		0			0
$187$	4.18342	−	0.630549i	0.305922	−	0.0461103i
$188$	1.04160	−	4.56353i	0.0759662	−	0.332830i
$189$		0			0
$190$	0.625740	−	8.34992i	0.0453959	−	0.605767i
$191$	5.39153	−	13.7374i	0.390118	−	0.994003i	−0.592034	−	0.805913i	$-0.701675\pi$
$191$	5.39153	−	13.7374i	0.390118	−	0.994003i	0.982152	−	0.188090i	$-0.0602298\pi$
$192$		0			0
$193$	−15.7520	+	7.58576i	−1.13385	+	0.546035i	−0.904145	−	0.427225i	$-0.859491\pi$
$193$	−15.7520	+	7.58576i	−1.13385	+	0.546035i	−0.229708	+	0.973260i	$0.573777\pi$
$194$	−18.8638	+	9.08431i	−1.35434	+	0.652216i
$195$		0			0
$196$	−0.144384	+	0.367884i	−0.0103131	+	0.0262774i
$197$	0.204205	−	2.72492i	0.0145490	−	0.194143i	−0.985193	−	0.171447i	$-0.945156\pi$
$197$	0.204205	−	2.72492i	0.0145490	−	0.194143i	0.999742	−	0.0226962i	$-0.00722505\pi$
$198$		0			0
$199$	0.867208	−	3.79949i	0.0614747	−	0.269338i	−0.934845	−	0.355057i	$-0.884461\pi$
$199$	0.867208	−	3.79949i	0.0614747	−	0.269338i	0.996319	+	0.0857186i	$0.0273186\pi$
$200$	−16.7757	+	2.52853i	−1.18622	+	0.178794i
$201$		0			0
$202$	11.4401	+	3.52879i	0.804920	+	0.248285i
$203$	0.969336	+	12.9349i	0.0680340	+	0.907851i
$204$		0			0
$205$	21.6943	−	6.69181i	1.51520	−	0.467376i
$206$	6.03900	+	15.3871i	0.420757	+	1.07207i
$207$		0			0
$208$	2.01814	−	3.49552i	0.139933	−	0.242371i
$209$	−6.07864	−	10.5285i	−0.420468	−	0.728272i
$210$		0			0
$211$	−6.26808	−	7.85992i	−0.431512	−	0.541099i	0.517772	−	0.855519i	$-0.326762\pi$
$211$	−6.26808	−	7.85992i	−0.431512	−	0.541099i	−0.949284	+	0.314419i	$0.898190\pi$
$212$	−1.93981	−	1.32254i	−0.133226	−	0.0908322i
$213$		0			0
$214$	−8.85557			−0.605355
$215$	−16.2964	+	13.6599i	−1.11140	+	0.931595i
$216$		0			0
$217$	−10.0606	−	4.84492i	−0.682957	−	0.328895i
$218$	7.45966	+	5.08591i	0.505232	+	0.344461i
$219$		0			0
$220$	−7.89637	+	7.32676i	−0.532373	+	0.493970i
$221$	−0.623252	−	1.07950i	−0.0419244	−	0.0726152i
$222$		0			0
$223$	3.33401	+	14.6072i	0.223262	+	0.978173i	0.955004	+	0.296592i	$0.0958501\pi$
$223$	3.33401	+	14.6072i	0.223262	+	0.978173i	−0.731743	+	0.681581i	$0.761293\pi$
$224$	−3.27917	−	8.35520i	−0.219099	−	0.558255i
$225$		0			0
$226$	−4.76668	+	5.97723i	−0.317075	+	0.397599i
$227$	0.663861	+	8.85861i	0.0440620	+	0.587966i	0.974916	+	0.222574i	$0.0714460\pi$
$227$	0.663861	+	8.85861i	0.0440620	+	0.587966i	−0.930854	+	0.365392i	$0.880935\pi$
$228$		0			0
$229$	16.7625	−	11.4285i	1.10770	−	0.755217i	0.135829	−	0.990732i	$-0.456630\pi$
$229$	16.7625	−	11.4285i	1.10770	−	0.755217i	0.971871	+	0.235515i	$0.0756778\pi$
$230$	0.00536064		0.000807986i	0.000353470		5.32770e-5i
$231$		0			0
$232$	−10.5650	−	9.80287i	−0.693625	−	0.643590i
$233$	−0.762419	+	10.1738i	−0.0499477	+	0.666506i	0.914897	+	0.403687i	$0.132271\pi$
$233$	−0.762419	+	10.1738i	−0.0499477	+	0.666506i	−0.964845	+	0.262819i	$0.915348\pi$
$234$		0			0
$235$	−25.2132	−	3.80028i	−1.64473	−	0.247903i
$236$	−1.95486	+	0.941410i	−0.127250	+	0.0612806i
$237$		0			0
$238$	2.45982	+	0.370759i	0.159447	+	0.0240327i
$239$	2.91886	−	7.43713i	0.188805	−	0.481068i	−0.804858	−	0.593468i	$-0.797759\pi$
$239$	2.91886	−	7.43713i	0.188805	−	0.481068i	0.993663	+	0.112400i	$0.0358538\pi$
$240$		0			0
$241$	6.16388	+	5.71925i	0.397051	+	0.368409i	0.853280	−	0.521453i	$-0.174610\pi$
$241$	6.16388	+	5.71925i	0.397051	+	0.368409i	−0.456229	+	0.889862i	$0.650800\pi$
$242$	5.31095	−	23.2688i	0.341401	−	1.49577i
$243$		0			0
$244$	4.20579	−	2.86746i	0.269248	−	0.183570i
$245$	2.05713	+	0.634540i	0.131425	+	0.0405392i
$246$		0			0
$247$	−2.23331	+	2.80049i	−0.142102	+	0.178191i
$248$	11.8558	−	3.65704i	0.752847	−	0.232223i
$249$		0			0
$250$	0.440799	+	1.93126i	0.0278786	+	0.122144i
$251$	−9.14704	+	15.8431i	−0.577356	+	1.00001i	0.418425	+	0.908251i	$0.362582\pi$
$251$	−9.14704	+	15.8431i	−0.577356	+	1.00001i	−0.995781	+	0.0917585i	$0.970751\pi$
$252$		0			0
$253$	0.00576989	−	0.00535367i	0.000362750	−	0.000336583i
$254$	−5.65434	−	7.09032i	−0.354785	−	0.444886i
$255$		0			0
$256$	11.6187	+	5.59529i	0.726172	+	0.349706i
$257$	−19.1765			−1.19620			−0.598098	−	0.801423i	$-0.704077\pi$
$257$	−19.1765			−1.19620			−0.598098	+	0.801423i	$0.704077\pi$
$258$		0			0
$259$	5.53401			0.343866
$260$	2.85948	+	1.37705i	0.177337	+	0.0854011i
$261$		0			0
$262$	12.8910	+	16.1648i	0.796410	+	0.998666i
$263$	−10.1950	+	9.45955i	−0.628649	+	0.583301i	−0.928796	−	0.370592i	$-0.879155\pi$
$263$	−10.1950	+	9.45955i	−0.628649	+	0.583301i	0.300147	+	0.953893i	$0.402964\pi$
$264$		0			0
$265$	−6.39440	+	11.0754i	−0.392805	+	0.680358i
$266$	−1.59067	−	6.96918i	−0.0975302	−	0.427308i
$267$		0			0
$268$	−5.34073	+	1.64740i	−0.326237	+	0.100631i
$269$	16.8908	−	21.1804i	1.02985	−	1.29139i	0.0740861	−	0.997252i	$-0.476396\pi$
$269$	16.8908	−	21.1804i	1.02985	−	1.29139i	0.955763	−	0.294138i	$-0.0950325\pi$
$270$		0			0
$271$	19.3810	+	5.97823i	1.17731	+	0.363152i	0.820842	−	0.571156i	$-0.193505\pi$
$271$	19.3810	+	5.97823i	1.17731	+	0.363152i	0.356467	+	0.934308i	$0.383981\pi$
$272$	−1.53789	+	1.04852i	−0.0932484	+	0.0635757i
$273$		0			0
$274$	−0.686342	+	3.00706i	−0.0414635	+	0.181663i
$275$	22.5609	+	20.9335i	1.36047	+	1.26234i
$276$		0			0
$277$	6.37801	−	16.2509i	0.383218	−	0.976423i	−0.600966	−	0.799274i	$-0.705217\pi$
$277$	6.37801	−	16.2509i	0.383218	−	0.976423i	0.984184	−	0.177149i	$-0.0566873\pi$
$278$	9.30883	+	1.40308i	0.558307	+	0.0841512i
$279$		0			0
$280$	−24.8786	+	11.9809i	−1.48678	+	0.715997i
$281$	15.2324	+	2.29591i	0.908688	+	0.136963i	0.586722	−	0.809789i	$-0.300418\pi$
$281$	15.2324	+	2.29591i	0.908688	+	0.136963i	0.321966	+	0.946751i	$0.395656\pi$
$282$		0			0
$283$	−1.21194	+	16.1722i	−0.0720423	+	0.961338i	0.837691	+	0.546144i	$0.183905\pi$
$283$	−1.21194	+	16.1722i	−0.0720423	+	0.961338i	−0.909733	+	0.415193i	$0.863714\pi$
$284$	3.01441	+	2.79696i	0.178872	+	0.165969i
$285$		0			0
$286$	−10.7519	+	1.62058i	−0.635772	+	0.0958272i
$287$	16.0140	−	10.9181i	0.945274	−	0.644477i
$288$		0			0
$289$	−1.22746	−	16.3793i	−0.0722032	−	0.963485i
$290$	−11.2277	+	14.0790i	−0.659310	+	0.826749i
$291$		0			0
$292$	2.41596	+	6.15577i	0.141384	+	0.360239i
$293$	−4.51144	−	19.7659i	−0.263561	−	1.15474i	−0.917357	−	0.398066i	$-0.869682\pi$
$293$	−4.51144	−	19.7659i	−0.263561	−	1.15474i	0.653796	−	0.756671i	$-0.273176\pi$
$294$		0			0
$295$	5.90953	+	10.2356i	0.344066	+	0.595940i
$296$	−4.50744	+	4.18229i	−0.261989	+	0.243091i
$297$		0			0
$298$	−18.2766	−	12.4608i	−1.05874	−	0.721833i
$299$	−0.00208942	−	0.00100621i	−0.000120835	−	5.81908e-5i
$300$		0			0
$301$	−9.85698	+	15.2442i	−0.568147	+	0.878663i
$302$	−11.0813			−0.637659
$303$		0			0
$304$	4.41930	+	3.01303i	0.253464	+	0.172809i
$305$	−17.2882	−	21.6787i	−0.989917	−	1.24132i
$306$		0			0
$307$	−4.14771	−	7.18404i	−0.236722	−	0.410015i	0.723050	−	0.690796i	$-0.242740\pi$
$307$	−4.14771	−	7.18404i	−0.236722	−	0.410015i	−0.959772	+	0.280781i	$0.909406\pi$
$308$	−4.59805	+	7.96405i	−0.261998	+	0.453794i
$309$		0			0
$310$	−5.66360	−	14.4306i	−0.321671	−	0.819605i
$311$	28.6492	−	8.83711i	1.62455	−	0.501107i	0.657021	−	0.753872i	$-0.271816\pi$
$311$	28.6492	−	8.83711i	1.62455	−	0.501107i	0.967528	+	0.252766i	$0.0813402\pi$
$312$		0			0
$313$	−0.488509	−	6.51870i	−0.0276122	−	0.368459i	−0.993844	−	0.110786i	$-0.964663\pi$
$313$	−0.488509	−	6.51870i	−0.0276122	−	0.368459i	0.966232	−	0.257673i	$-0.0829558\pi$
$314$	−1.67905	−	0.517918i	−0.0947543	−	0.0292278i
$315$		0			0
$316$	3.84955	−	0.580226i	0.216554	−	0.0326403i
$317$	−1.74389	+	7.64049i	−0.0979468	+	0.429133i	−0.999997	−	0.00249843i	$-0.999205\pi$
$317$	−1.74389	+	7.64049i	−0.0979468	+	0.429133i	0.902050	+	0.431631i	$0.142062\pi$
$318$		0			0
$319$	−1.95386	+	26.0724i	−0.109395	+	1.45978i
$320$	10.3694	−	26.4208i	0.579668	−	1.47697i
$321$		0			0
$322$	0.00416980	−	0.00200807i	0.000232374	−	0.000111905i
$323$	1.48823	−	0.716692i	0.0828071	−	0.0398778i
$324$		0			0
$325$	3.31287	−	8.44106i	0.183765	−	0.468226i
$326$	−1.28776	+	17.1839i	−0.0713223	+	0.951729i
$327$		0			0
$328$	−4.79203	+	20.9952i	−0.264595	+	1.15927i
$329$	−21.5248	+	3.24434i	−1.18670	+	0.178866i
$330$		0			0
$331$	−23.1834	−	7.15112i	−1.27427	−	0.393061i	−0.417463	−	0.908694i	$-0.637081\pi$
$331$	−23.1834	−	7.15112i	−1.27427	−	0.393061i	−0.856810	+	0.515633i	$0.827557\pi$
$332$	−0.253910	−	3.38819i	−0.0139351	−	0.185951i
$333$		0			0
$334$	8.98743	−	2.77225i	0.491770	−	0.151691i
$335$	11.1228	+	28.3403i	0.607701	+	1.54840i
$336$		0			0
$337$	16.5673	−	28.6953i	0.902476	−	1.56313i	0.0782058	−	0.996937i	$-0.475081\pi$
$337$	16.5673	−	28.6953i	0.902476	−	1.56313i	0.824270	−	0.566197i	$-0.191586\pi$
$338$	−6.10197	−	10.5689i	−0.331904	−	0.574874i
$339$		0			0
$340$	−0.912525	−	1.14427i	−0.0494886	−	0.0620568i
$341$	−18.5968	−	12.6791i	−1.00707	−	0.686611i
$342$		0			0
$343$	−17.5407			−0.947111
$344$	−3.49223	−	19.8657i	−0.188289	−	1.07109i
$345$		0			0
$346$	1.84881	+	0.890340i	0.0993926	+	0.0478650i
$347$	3.01977	+	2.05885i	0.162110	+	0.110525i	0.641658	−	0.766991i	$-0.278247\pi$
$347$	3.01977	+	2.05885i	0.162110	+	0.110525i	−0.479548	+	0.877516i	$0.659199\pi$
$348$		0			0
$349$	4.09206	−	3.79688i	0.219043	−	0.203242i	−0.563017	−	0.826445i	$-0.690359\pi$
$349$	4.09206	−	3.79688i	0.219043	−	0.203242i	0.782060	+	0.623203i	$0.214169\pi$
$350$	9.04825	+	15.6720i	0.483649	+	0.837705i
$351$		0			0
$352$	−4.02583	−	17.6383i	−0.214578	−	0.940126i
$353$	1.50000	+	3.82194i	0.0798369	+	0.203421i	0.965219	−	0.261443i	$-0.0841984\pi$
$353$	1.50000	+	3.82194i	0.0798369	+	0.203421i	−0.885382	+	0.464864i	$0.846103\pi$
$354$		0			0
$355$	13.9661	−	17.5129i	0.741242	−	0.929488i
$356$	−0.384128	−	5.12583i	−0.0203587	−	0.271668i
$357$		0			0
$358$	−7.97513	+	5.43735i	−0.421499	+	0.287373i
$359$	2.63409	−	0.397026i	0.139022	−	0.0209542i	−0.0791625	−	0.996862i	$-0.525225\pi$
$359$	2.63409	−	0.397026i	0.139022	−	0.0209542i	0.218185	+	0.975908i	$0.429986\pi$
$360$		0			0
$361$	10.4485	+	9.69475i	0.549919	+	0.510250i
$362$	1.13990	−	15.2109i	0.0599117	−	0.799466i
$363$		0			0
$364$	2.67923	+	0.403829i	0.140430	+	0.0211664i
$365$	32.4548	−	15.6294i	1.69876	−	0.818080i
$366$		0			0
$367$	2.72302	+	0.410430i	0.142141	+	0.0214243i	0.219727	−	0.975561i	$-0.429483\pi$
$367$	2.72302	+	0.410430i	0.142141	+	0.0214243i	−0.0775865	+	0.996986i	$0.524721\pi$
$368$	−0.00126515	+	0.00322355i	−6.59505e−5	+	0.000168039i
$369$		0			0
$370$	5.63191	+	5.22564i	0.292789	+	0.271668i
$371$	−2.42947	+	10.6442i	−0.126132	+	0.552619i
$372$		0			0
$373$	27.6542	−	18.8543i	1.43188	−	0.976241i	0.434751	−	0.900551i	$-0.356836\pi$
$373$	27.6542	−	18.8543i	1.43188	−	0.976241i	0.997131	−	0.0756903i	$-0.0241160\pi$
$374$	4.79143	+	1.47796i	0.247759	+	0.0764234i
$375$		0			0
$376$	15.0800	−	18.9097i	0.777691	−	0.975194i
$377$	7.36115	−	2.27061i	0.379118	−	0.116943i
$378$		0			0
$379$	3.61567	+	15.8413i	0.185725	+	0.813713i	0.978838	+	0.204638i	$0.0656018\pi$
$379$	3.61567	+	15.8413i	0.185725	+	0.813713i	−0.793113	+	0.609074i	$0.791541\pi$
$380$	−2.10287	+	3.64228i	−0.107875	+	0.186845i
$381$		0			0
$382$	12.8215	−	11.8967i	0.656007	−	0.608686i
$383$	21.5546	+	27.0287i	1.10139	+	1.38110i	0.917303	+	0.398191i	$0.130362\pi$
$383$	21.5546	+	27.0287i	1.10139	+	1.38110i	0.184088	+	0.982910i	$0.441067\pi$
$384$		0			0
$385$	45.1326	+	21.7347i	2.30017	+	1.10770i
$386$	−20.7213			−1.05469
$387$		0			0
$388$	10.5163			0.533884
$389$	16.7611	+	8.07174i	0.849823	+	0.409253i	0.807512	−	0.589851i	$-0.200814\pi$
$389$	16.7611	+	8.07174i	0.849823	+	0.409253i	0.0423114	+	0.999104i	$0.486528\pi$
$390$		0			0
$391$	0.000666784	0	0.000836120i	3.37207e−5	0	4.22844e-5i
$392$	−1.49692	+	1.38894i	−0.0756058	+	0.0701519i
$393$		0			0
$394$	1.61932	−	2.80474i	0.0815801	−	0.141301i
$395$	−4.71885	−	20.6746i	−0.237431	−	1.04025i
$396$		0			0
$397$	29.0394	−	8.95748i	1.45745	−	0.449563i	0.538057	−	0.842909i	$-0.319159\pi$
$397$	29.0394	−	8.95748i	1.45745	−	0.449563i	0.919391	+	0.393346i	$0.128682\pi$
$398$	2.87987	−	3.61125i	0.144355	−	0.181015i
$399$		0			0
$400$	−12.9389	−	3.99112i	−0.646945	−	0.199556i
$401$	31.2339	−	21.2949i	1.55975	−	1.06342i	0.593820	−	0.804598i	$-0.297619\pi$
$401$	31.2339	−	21.2949i	1.55975	−	1.06342i	0.965926	−	0.258819i	$-0.0833334\pi$
$402$		0			0
$403$	−1.47566	+	6.46531i	−0.0735081	+	0.322060i
$404$	−4.40802	−	4.09005i	−0.219307	−	0.203487i
$405$		0			0
$406$	−5.61654	+	14.3107i	−0.278744	+	0.710229i
$407$	11.0301	+	1.66252i	0.546743	+	0.0824083i
$408$		0			0
$409$	−3.84798	+	1.85309i	−0.190271	+	0.0916294i	−0.526593	−	0.850117i	$-0.676531\pi$
$409$	−3.84798	+	1.85309i	−0.190271	+	0.0916294i	0.336323	+	0.941747i	$0.390817\pi$
$410$	26.6070	+	4.01036i	1.31403	+	0.198058i
$411$		0			0
$412$	0.620450	−	8.27933i	0.0305674	−	0.407893i
$413$	7.39653	+	6.86298i	0.363960	+	0.337705i
$414$		0			0
$415$	−18.3014	+	2.75849i	−0.898378	+	0.135409i
$416$	−4.40428	+	3.00279i	−0.215937	+	0.147224i
$417$		0			0
$418$	−1.07677	−	14.3685i	−0.0526666	−	0.702787i
$419$	−7.59816	+	9.52780i	−0.371195	+	0.465463i	−0.931986	−	0.362494i	$-0.881925\pi$
$419$	−7.59816	+	9.52780i	−0.371195	+	0.465463i	0.560792	+	0.827957i	$0.310497\pi$
$420$		0			0
$421$	−3.62044	−	9.22474i	−0.176450	−	0.449586i	0.815099	−	0.579322i	$-0.196682\pi$
$421$	−3.62044	−	9.22474i	−0.176450	−	0.449586i	−0.991549	+	0.129735i	$0.958587\pi$
$422$	−2.65135	−	11.6163i	−0.129066	−	0.565475i
$423$		0			0
$424$	−6.06549	−	10.5057i	−0.294566	−	0.510204i
$425$	−3.06535	+	2.84423i	−0.148691	+	0.137965i
$426$		0			0
$427$	−19.5585	−	13.3348i	−0.946502	−	0.645314i
$428$	4.00748	+	1.92990i	0.193709	+	0.0932852i
$429$		0			0
$430$	−24.4262	+	6.20616i	−1.17793	+	0.299288i
$431$	20.4652			0.985772			0.492886	−	0.870094i	$-0.335942\pi$
$431$	20.4652			0.985772			0.492886	+	0.870094i	$0.335942\pi$
$432$		0			0
$433$	−1.14039	−	0.777507i	−0.0548038	−	0.0373646i	0.535608	−	0.844467i	$-0.320082\pi$
$433$	−1.14039	−	0.777507i	−0.0548038	−	0.0373646i	−0.590412	+	0.807102i	$0.701035\pi$
$434$	−8.25153	−	10.3471i	−0.396086	−	0.496676i
$435$		0			0
$436$	−2.26740	−	3.92725i	−0.108589	−	0.188081i
$437$	0.00153657	−	0.00266142i	7.35042e−5	−	0.000127313i
$438$		0			0
$439$	−3.75806	−	9.57538i	−0.179362	−	0.457008i	0.812711	−	0.582667i	$-0.197991\pi$
$439$	−3.75806	−	9.57538i	−0.179362	−	0.457008i	−0.992074	+	0.125659i	$0.959896\pi$
$440$	−53.1863	+	16.4058i	−2.53556	+	0.782116i
$441$		0			0
$442$	−0.110403	−	1.47322i	−0.00525133	−	0.0700742i
$443$	−5.22921	−	1.61300i	−0.248447	−	0.0766358i	0.168030	−	0.985782i	$-0.446259\pi$
$443$	−5.22921	−	1.61300i	−0.248447	−	0.0766358i	−0.416477	+	0.909146i	$0.636736\pi$
$444$		0			0
$445$	−27.6872	+	4.17318i	−1.31250	+	0.197828i
$446$	−3.95146	+	17.3125i	−0.187107	+	0.819770i
$447$		0			0
$448$	1.81076	−	24.1630i	0.0855506	−	1.14159i
$449$	−10.2240	+	26.0503i	−0.482499	+	1.22939i	0.457805	+	0.889053i	$0.348636\pi$
$449$	−10.2240	+	26.0503i	−0.482499	+	1.22939i	−0.940304	+	0.340335i	$0.889459\pi$
$450$		0			0
$451$	35.1983	−	16.9506i	1.65742	−	0.798173i
$452$	3.45972	−	1.66611i	0.162731	−	0.0783674i
$453$		0			0
$454$	−3.84655	+	9.80086i	−0.180528	+	0.459977i
$455$	1.10296	−	14.7180i	0.0517076	−	0.689990i
$456$		0			0
$457$	−8.19722	+	35.9144i	−0.383450	+	1.68000i	0.303131	+	0.952949i	$0.401968\pi$
$457$	−8.19722	+	35.9144i	−0.383450	+	1.68000i	−0.686581	+	0.727054i	$0.740889\pi$
$458$	23.7765	−	3.58373i	1.11100	−	0.167457i
$459$		0			0
$460$	−0.00260197		0.000802602i	−0.000121318		3.74215e-5i
$461$	−0.984869	−	13.1422i	−0.0458699	−	0.612092i	−0.972014	−	0.234922i	$-0.924516\pi$
$461$	−0.984869	−	13.1422i	−0.0458699	−	0.612092i	0.926144	−	0.377170i	$-0.123103\pi$
$462$		0			0
$463$	27.5468	−	8.49706i	1.28021	−	0.394892i	0.421253	−	0.906943i	$-0.361591\pi$
$463$	27.5468	−	8.49706i	1.28021	−	0.394892i	0.858955	+	0.512052i	$0.171114\pi$
$464$	−4.20250	−	10.7078i	−0.195096	−	0.497097i
$465$		0			0
$466$	−6.04589	+	10.4718i	−0.280070	+	0.485096i
$467$	−1.62410	−	2.81302i	−0.0751544	−	0.130171i	0.825999	−	0.563672i	$-0.190612\pi$
$467$	−1.62410	−	2.81302i	−0.0751544	−	0.130171i	−0.901153	+	0.433500i	$0.857278\pi$
$468$		0			0
$469$	16.2052	+	20.3207i	0.748286	+	0.938321i
$470$	−24.9691	−	17.0237i	−1.15174	−	0.785243i
$471$		0			0
$472$	−11.2111			−0.516033
$473$	−24.2262	+	27.4229i	−1.11392	+	1.26090i
$474$		0			0
$475$	10.8263	+	5.21369i	0.496747	+	0.239221i
$476$	−1.03236	−	0.703852i	−0.0473182	−	0.0322610i
$477$		0			0
$478$	6.94130	−	6.44058i	0.317488	−	0.294585i
$479$	−11.1630	−	19.3348i	−0.510049	−	0.883431i	−0.999932	−	0.0116426i	$-0.996294\pi$
$479$	−11.1630	−	19.3348i	−0.510049	−	0.883431i	0.489883	−	0.871788i	$-0.337039\pi$
$480$		0			0
$481$	−0.731330	−	3.20417i	−0.0333458	−	0.146097i
$482$	3.64091	+	9.27688i	0.165839	+	0.422550i
$483$		0			0
$484$	−7.47438	+	9.37258i	−0.339745	+	0.426026i
$485$	−4.28091	−	57.1247i	−0.194386	−	2.59390i
$486$		0			0
$487$	−11.1751	+	7.61906i	−0.506393	+	0.345253i	−0.789414	−	0.613861i	$-0.789616\pi$
$487$	−11.1751	+	7.61906i	−0.506393	+	0.345253i	0.283022	+	0.959114i	$0.408663\pi$
$488$	26.0080	−	3.92008i	1.17733	−	0.177454i
$489$		0			0
$490$	1.87035	+	1.73543i	0.0844940	+	0.0783989i
$491$	−0.751481	+	10.0278i	−0.0339139	+	0.452549i	0.954236	+	0.299055i	$0.0966715\pi$
$491$	−0.751481	+	10.0278i	−0.0339139	+	0.452549i	−0.988150	+	0.153494i	$0.950948\pi$
$492$		0			0
$493$	−3.51271	−	0.529456i	−0.158205	−	0.0238455i
$494$	−3.82492	+	1.84198i	−0.172091	+	0.0828747i
$495$		0			0
$496$	9.79187	+	1.47589i	0.439668	+	0.0662693i
$497$	6.98641	−	17.8011i	0.313383	−	0.798488i
$498$		0			0
$499$	−17.9853	−	16.6880i	−0.805135	−	0.747056i	0.165862	−	0.986149i	$-0.446959\pi$
$499$	−17.9853	−	16.6880i	−0.805135	−	0.747056i	−0.970997	+	0.239093i	$0.923150\pi$
$500$	0.221404	−	0.970033i	0.00990147	−	0.0433812i
$501$		0			0
$502$	−17.9146	+	12.2140i	−0.799569	+	0.545137i
$503$	18.7167	+	5.77333i	0.834535	+	0.257420i	0.682436	−	0.730945i	$-0.260921\pi$
$503$	18.7167	+	5.77333i	0.834535	+	0.257420i	0.152099	+	0.988365i	$0.451397\pi$
$504$		0			0
$505$	−20.4228	+	25.6094i	−0.908803	+	1.13960i
$506$	0.00891432	−	0.00274970i	0.000396290	−	0.000122239i
$507$		0			0
$508$	1.01360	+	4.44089i	0.0449714	+	0.197033i
$509$	−2.13596	+	3.69959i	−0.0946747	+	0.163981i	−0.909473	−	0.415763i	$-0.863514\pi$
$509$	−2.13596	+	3.69959i	−0.0946747	+	0.163981i	0.814798	+	0.579745i	$0.196848\pi$
$510$		0			0
$511$	22.5431	−	20.9170i	0.997250	−	0.925312i
$512$	14.3794	+	18.0312i	0.635484	+	0.796872i
$513$		0			0
$514$	−20.4772	−	9.86130i	−0.903210	−	0.434963i
$515$	−45.2260			−1.99290
$516$		0			0
$517$	−43.8769			−1.92970
$518$	5.90937	+	2.84580i	0.259643	+	0.125037i
$519$		0			0
$520$	10.2247	+	12.8213i	0.448382	+	0.562253i
$521$	−2.62150	+	2.43239i	−0.114850	+	0.106565i	−0.735507	−	0.677517i	$-0.763056\pi$
$521$	−2.62150	+	2.43239i	−0.114850	+	0.106565i	0.620658	+	0.784082i	$0.286866\pi$
$522$		0			0
$523$	−0.344694	+	0.597027i	−0.0150724	+	0.0261062i	−0.873463	−	0.486890i	$-0.838131\pi$
$523$	−0.344694	+	0.597027i	−0.0150724	+	0.0261062i	0.858391	+	0.512996i	$0.171465\pi$
$524$	−2.31086	−	10.1245i	−0.100950	−	0.442292i
$525$		0			0
$526$	−15.7509	+	4.85852i	−0.686774	+	0.211842i
$527$	1.90671	−	2.39094i	0.0830576	−	0.104151i
$528$		0			0
$529$	−21.9782	−	6.77937i	−0.955573	−	0.294755i
$530$	−12.5235	+	8.53840i	−0.543988	+	0.370885i
$531$		0			0
$532$	−0.798959	+	3.50047i	−0.0346393	+	0.151764i
$533$	−8.43783	−	7.82916i	−0.365483	−	0.339119i
$534$		0			0
$535$	8.85191	−	22.5543i	0.382701	−	0.975107i
$536$	−28.5563	−	4.30417i	−1.23344	−	0.185912i
$537$		0			0
$538$	28.9282	−	13.9311i	1.24718	−	0.600612i
$539$	3.66310	+	0.552124i	0.157781	+	0.0237817i
$540$		0			0
$541$	−2.98772	+	39.8684i	−0.128452	+	1.71408i	0.445579	+	0.895243i	$0.352998\pi$
$541$	−2.98772	+	39.8684i	−0.128452	+	1.71408i	−0.574031	+	0.818834i	$0.694621\pi$
$542$	17.6213	+	16.3502i	0.756899	+	0.702300i
$543$		0			0
$544$	2.43069	−	0.366368i	0.104215	−	0.0157079i
$545$	−20.4099	+	13.9152i	−0.874263	+	0.596063i
$546$		0			0
$547$	2.84068	+	37.9062i	0.121459	+	1.62075i	0.641853	+	0.766828i	$0.278166\pi$
$547$	2.84068	+	37.9062i	0.121459	+	1.62075i	−0.520394	+	0.853926i	$0.674215\pi$
$548$	0.965926	−	1.21123i	0.0412623	−	0.0517413i
$549$		0			0
$550$	13.3264	+	33.9551i	0.568239	+	1.44785i
$551$	2.27153	+	9.95222i	0.0967704	+	0.423979i
$552$		0			0
$553$	−9.05202	−	15.6786i	−0.384931	−	0.666720i
$554$	15.1675	−	14.0734i	0.644405	−	0.597920i
$555$		0			0
$556$	−3.90682	−	2.66362i	−0.165686	−	0.112963i
$557$	33.9643	+	16.3563i	1.43911	+	0.693040i	0.980667	−	0.195683i	$-0.0626922\pi$
$557$	33.9643	+	16.3563i	1.43911	+	0.693040i	0.458445	+	0.888723i	$0.348407\pi$
$558$		0			0
$559$	10.1290	+	3.69260i	0.428410	+	0.156180i
$560$	−22.0390			−0.931318
$561$		0			0
$562$	15.0849	+	10.2847i	0.636319	+	0.433835i
$563$	22.6446	+	28.3955i	0.954357	+	1.19673i	0.980391	+	0.197065i	$0.0631409\pi$
$563$	22.6446	+	28.3955i	0.954357	+	1.19673i	−0.0260336	+	0.999661i	$0.508288\pi$
$564$		0			0
$565$	−10.4587	−	18.1150i	−0.440001	−	0.762105i
$566$	−9.61052	+	16.6459i	−0.403960	+	0.699680i
$567$		0			0
$568$	7.76264	+	19.7789i	0.325713	+	0.829903i
$569$	−27.5039	+	8.48383i	−1.15302	+	0.355661i	−0.811580	−	0.584241i	$-0.801392\pi$
$569$	−27.5039	+	8.48383i	−1.15302	+	0.355661i	−0.341444	+	0.939902i	$0.610916\pi$
$570$		0			0
$571$	−1.35501	−	18.0813i	−0.0567052	−	0.756679i	−0.950998	−	0.309197i	$-0.899940\pi$
$571$	−1.35501	−	18.0813i	−0.0567052	−	0.756679i	0.894293	−	0.447482i	$-0.147679\pi$
$572$	5.21880	+	1.60979i	0.218209	+	0.0673085i
$573$		0			0
$574$	22.7147	−	3.42369i	0.948093	−	0.142902i
$575$	−0.00173117	+	0.00758474i	−7.21947e−5	+	0.000316306i
$576$		0			0
$577$	−0.994996	+	13.2773i	−0.0414222	+	0.552741i	0.937430	+	0.348173i	$0.113198\pi$
$577$	−0.994996	+	13.2773i	−0.0414222	+	0.552741i	−0.978852	+	0.204568i	$0.934421\pi$
$578$	7.11214	−	18.1214i	0.295826	−	0.753752i
$579$		0			0
$580$	8.14918	−	3.92444i	0.338376	−	0.162953i
$581$	−14.2358	+	6.85560i	−0.590600	+	0.284418i
$582$		0			0
$583$	−8.04004	+	20.4857i	−0.332984	+	0.848430i
$584$	−2.55347	+	34.0737i	−0.105663	+	1.40998i
$585$		0			0
$586$	5.34696	−	23.4266i	0.220881	−	0.967742i
$587$	−6.55180	+	0.987525i	−0.270422	+	0.0407595i	−0.282853	−	0.959163i	$-0.591281\pi$
$587$	−6.55180	+	0.987525i	−0.270422	+	0.0407595i	0.0124315	+	0.999923i	$0.496043\pi$
$588$		0			0
$589$	−8.39743	−	2.59026i	−0.346010	−	0.106730i
$590$	1.04682	+	13.9688i	0.0430967	+	0.575085i
$591$		0			0
$592$	−4.68958	+	1.44654i	−0.192740	+	0.0594526i
$593$	−1.57645	−	4.01673i	−0.0647371	−	0.164947i	0.894844	−	0.446378i	$-0.147286\pi$
$593$	−1.57645	−	4.01673i	−0.0647371	−	0.164947i	−0.959582	+	0.281431i	$0.909191\pi$
$594$		0			0
$595$	−3.40309	+	5.89433i	−0.139513	+	0.241644i
$596$	5.55526	+	9.62199i	0.227552	+	0.394132i
$597$		0			0
$598$	−0.00171371	−	0.00214893i	−7.00789e−5	−	8.78762e-5i
$599$	−18.5509	−	12.6478i	−0.757968	−	0.516774i	0.121581	−	0.992581i	$-0.461203\pi$
$599$	−18.5509	−	12.6478i	−0.757968	−	0.516774i	−0.879549	+	0.475808i	$0.842156\pi$
$600$		0			0
$601$	3.82446			0.156003			0.0780015	−	0.996953i	$-0.475146\pi$
$601$	3.82446			0.156003			0.0780015	+	0.996953i	$0.475146\pi$
$602$	−18.3647	+	11.2094i	−0.748491	+	0.456860i
$603$		0			0
$604$	5.01471	+	2.41496i	0.204046	+	0.0982633i
$605$	53.9546	+	36.7856i	2.19357	+	1.49555i
$606$		0			0
$607$	−17.0366	+	15.8077i	−0.691495	+	0.641613i	−0.945512	−	0.325586i	$-0.894438\pi$
$607$	−17.0366	+	15.8077i	−0.691495	+	0.641613i	0.254018	+	0.967200i	$0.418248\pi$
$608$	−3.53187	−	6.11738i	−0.143236	−	0.248093i
$609$		0			0
$610$	−7.31277	−	32.0393i	−0.296085	−	1.29723i
$611$	4.72300	+	12.0340i	0.191072	+	0.486844i
$612$		0			0
$613$	2.06228	−	2.58602i	0.0832947	−	0.104448i	−0.738438	−	0.674321i	$-0.764436\pi$
$613$	2.06228	−	2.58602i	0.0832947	−	0.104448i	0.821733	+	0.569873i	$0.193008\pi$
$614$	−0.734726	−	9.80423i	−0.0296511	−	0.395667i
$615$		0			0
$616$	−39.2602	+	26.7671i	−1.58184	+	1.07848i
$617$	−34.6142	+	5.21724i	−1.39351	+	0.210038i	−0.802514	−	0.596633i	$-0.796505\pi$
$617$	−34.6142	+	5.21724i	−1.39351	+	0.210038i	−0.591000	+	0.806672i	$0.701267\pi$
$618$		0			0
$619$	−13.1838	−	12.2328i	−0.529903	−	0.491678i	0.369239	−	0.929334i	$-0.379618\pi$
$619$	−13.1838	−	12.2328i	−0.529903	−	0.491678i	−0.899142	+	0.437656i	$0.855809\pi$
$620$	−0.581881	+	7.76467i	−0.0233689	+	0.311837i
$621$		0			0
$622$	35.1368	+	5.29603i	1.40886	+	0.212351i
$623$	−21.5366	+	10.3715i	−0.862847	+	0.415525i
$624$		0			0
$625$	21.9097	+	3.30236i	0.876390	+	0.132094i
$626$	2.83053	−	7.21207i	0.113131	−	0.288252i
$627$		0			0
$628$	0.646962	+	0.600293i	0.0258166	+	0.0239543i
$629$	−0.337250	+	1.47759i	−0.0134471	+	0.0589154i
$630$		0			0
$631$	20.8020	−	14.1826i	0.828114	−	0.564599i	−0.0734225	−	0.997301i	$-0.523392\pi$
$631$	20.8020	−	14.1826i	0.828114	−	0.564599i	0.901537	+	0.432702i	$0.142440\pi$
$632$	19.2218	+	5.92915i	0.764603	+	0.235849i
$633$		0			0
$634$	−5.79122	+	7.26196i	−0.229999	+	0.288409i
$635$	23.7104	−	7.31368i	0.940917	−	0.290235i
$636$		0			0
$637$	−0.242875	−	1.06410i	−0.00962304	−	0.0421613i
$638$	−15.4939	+	26.8361i	−0.613408	+	1.06245i
$639$		0			0
$640$	9.24522	−	8.57831i	0.365449	−	0.339088i
$641$	−22.6472	−	28.3987i	−0.894511	−	1.12168i	−0.991974	−	0.126442i	$-0.959644\pi$
$641$	−22.6472	−	28.3987i	−0.894511	−	1.12168i	0.0974634	−	0.995239i	$-0.468927\pi$
$642$		0			0
$643$	−2.99826	−	1.44389i	−0.118240	−	0.0569413i	0.373829	−	0.927498i	$-0.378045\pi$
$643$	−2.99826	−	1.44389i	−0.118240	−	0.0569413i	−0.492069	+	0.870556i	$0.663759\pi$
$644$	−0.00232461			−9.16024e−5
$645$		0			0
$646$	1.95772			0.0770255
$647$	−37.9436	−	18.2727i	−1.49172	−	0.718372i	−0.502464	−	0.864598i	$-0.667573\pi$
$647$	−37.9436	−	18.2727i	−1.49172	−	0.718372i	−0.989251	+	0.146226i	$0.953287\pi$
$648$		0			0
$649$	12.6807	+	15.9010i	0.497759	+	0.624171i
$650$	7.87830	−	7.31000i	0.309012	−	0.286722i
$651$		0			0
$652$	4.32766	−	7.49572i	0.169484	−	0.293555i
$653$	5.31138	+	23.2707i	0.207850	+	0.910652i	0.965994	+	0.258564i	$0.0832494\pi$
$653$	5.31138	+	23.2707i	0.207850	+	0.910652i	−0.758144	+	0.652088i	$0.773893\pi$
$654$		0			0
$655$	−54.0559	+	16.6740i	−2.11214	+	0.651509i
$656$	−10.7165	+	13.4381i	−0.418409	+	0.524668i
$657$		0			0
$658$	−24.6531	−	7.60448i	−0.961079	−	0.296454i
$659$	3.95025	−	2.69323i	0.153880	−	0.104913i	−0.483932	−	0.875105i	$-0.660792\pi$
$659$	3.95025	−	2.69323i	0.153880	−	0.104913i	0.637812	+	0.770192i	$0.279840\pi$
$660$		0			0
$661$	3.18440	−	13.9518i	0.123859	−	0.542662i	−0.874481	−	0.485060i	$-0.838798\pi$
$661$	3.18440	−	13.9518i	0.123859	−	0.542662i	0.998340	−	0.0576012i	$-0.0183452\pi$
$662$	−21.0785	−	19.5580i	−0.819238	−	0.760142i
$663$		0			0
$664$	6.41395	−	16.3425i	0.248910	−	0.634211i
$665$	19.3398	+	2.91501i	0.749966	+	0.113039i
$666$		0			0
$667$	−0.00595462	+	0.00286759i	−0.000230564	+	0.000111034i
$668$	−4.67130	−	0.704086i	−0.180738	−	0.0272419i
$669$		0			0
$670$	−2.69650	+	35.9824i	−0.104175	+	1.39012i
$671$	−34.9771	−	32.4540i	−1.35028	−	1.25287i
$672$		0			0
$673$	−22.9150	+	3.45387i	−0.883307	+	0.133137i	−0.575003	−	0.818151i	$-0.694999\pi$
$673$	−22.9150	+	3.45387i	−0.883307	+	0.133137i	−0.308303	+	0.951288i	$0.599761\pi$
$674$	32.4472	−	22.1222i	1.24982	−	0.852114i
$675$		0			0
$676$	0.458079	+	6.11264i	0.0176184	+	0.235101i
$677$	−8.82015	+	11.0601i	−0.338986	+	0.425075i	−0.921881	−	0.387472i	$-0.873348\pi$
$677$	−8.82015	+	11.0601i	−0.338986	+	0.425075i	0.582895	+	0.812547i	$0.301920\pi$
$678$		0			0
$679$	−17.8669	−	45.5241i	−0.685669	−	1.74706i
$680$	−1.68279	−	7.37278i	−0.0645320	−	0.282733i
$681$		0			0
$682$	−13.3381	−	23.1023i	−0.510743	−	0.884632i
$683$	34.9013	−	32.3837i	1.33546	−	1.23913i	0.387060	−	0.922054i	$-0.373491\pi$
$683$	34.9013	−	32.3837i	1.33546	−	1.23913i	0.948401	−	0.317073i	$-0.102700\pi$
$684$		0			0
$685$	−6.97264	−	4.75386i	−0.266411	−	0.181636i
$686$	−18.7305	−	9.02014i	−0.715134	−	0.344390i
$687$		0			0
$688$	4.36820	−	15.4947i	0.166536	−	0.590728i
$689$	6.48401			0.247021
$690$		0			0
$691$	34.1689	+	23.2959i	1.29985	+	0.886220i	0.997749	−	0.0670578i	$-0.0213612\pi$
$691$	34.1689	+	23.2959i	1.29985	+	0.886220i	0.302096	+	0.953277i	$0.402314\pi$
$692$	−0.642623	−	0.805824i	−0.0244289	−	0.0306328i
$693$		0			0
$694$	2.16586	+	3.75138i	0.0822149	+	0.142400i
$695$	−12.8785	+	22.3062i	−0.488509	+	0.846122i
$696$		0			0
$697$	1.93925	+	4.94112i	0.0734543	+	0.187158i
$698$	6.32213	−	1.95012i	0.239296	−	0.0738131i
$699$		0			0
$700$	−0.679258	−	9.06407i	−0.0256735	−	0.342590i
$701$	−45.7066	−	14.0986i	−1.72632	−	0.532498i	−0.736698	−	0.676222i	$-0.763616\pi$
$701$	−45.7066	−	14.0986i	−1.72632	−	0.532498i	−0.989618	+	0.143725i	$0.954092\pi$
$702$		0			0
$703$	4.30656	−	0.649110i	0.162425	−	0.0244816i
$704$	10.8682	−	47.6166i	0.409610	−	1.79462i
$705$		0			0
$706$	−0.363647	+	4.85253i	−0.0136860	+	0.182627i
$707$	−10.2163	+	26.0308i	−0.384225	+	0.978990i
$708$		0			0
$709$	−26.2688	+	12.6504i	−0.986547	+	0.475096i	−0.856352	−	0.516392i	$-0.827275\pi$
$709$	−26.2688	+	12.6504i	−0.986547	+	0.475096i	−0.130195	+	0.991488i	$0.541560\pi$
$710$	23.9192	−	11.5189i	0.897671	−	0.432296i
$711$		0			0
$712$	9.70335	−	24.7237i	0.363648	−	0.926561i
$713$	0.000425181	−	0.00567365i	1.59232e−5	−	0.000212480i
$714$		0			0
$715$	6.61995	−	29.0039i	0.247572	−	1.08468i
$716$	4.79401	−	0.722580i	0.179160	−	0.0270041i
$717$		0			0
$718$	3.01693	+	0.930599i	0.112591	+	0.0347296i
$719$	−0.145367	−	1.93979i	−0.00542127	−	0.0723418i	0.993837	−	0.110852i	$-0.0353579\pi$
$719$	−0.145367	−	1.93979i	−0.00542127	−	0.0723418i	−0.999258	+	0.0385100i	$0.987739\pi$
$720$		0			0
$721$	−36.8946	+	11.3805i	−1.37403	+	0.423831i
$722$	6.17174	+	15.7253i	0.229688	+	0.585236i
$723$		0			0
$724$	−3.83076	+	6.63507i	−0.142369	+	0.246591i
$725$	−12.9212	−	22.3802i	−0.479882	−	0.831180i
$726$		0			0
$727$	5.86302	+	7.35200i	0.217447	+	0.272670i	0.878576	−	0.477602i	$-0.158494\pi$
$727$	5.86302	+	7.35200i	0.217447	+	0.272670i	−0.661129	+	0.750272i	$0.729922\pi$
$728$	11.5674	+	7.88653i	0.428717	+	0.292294i
$729$		0			0
$730$	42.6934			1.58015
$731$	−3.46954	−	3.56084i	−0.128326	−	0.131702i
$732$		0			0
$733$	11.3172	+	5.45007i	0.418010	+	0.201303i	0.631053	−	0.775740i	$-0.282623\pi$
$733$	11.3172	+	5.45007i	0.418010	+	0.201303i	−0.213043	+	0.977043i	$0.568337\pi$
$734$	2.69666	+	1.83855i	0.0995356	+	0.0678622i
$735$		0			0
$736$	0.00335248	−	0.00311065i	0.000123574	−	0.000114660i
$737$	26.1947	+	45.3706i	0.964895	+	1.67125i
$738$		0			0
$739$	−9.29738	−	40.7345i	−0.342010	−	1.49844i	−0.794825	−	0.606838i	$-0.792437\pi$
$739$	−9.29738	−	40.7345i	−0.342010	−	1.49844i	0.452815	−	0.891604i	$-0.350420\pi$
$740$	−1.40982	−	3.59216i	−0.0518260	−	0.132050i
$741$		0			0
$742$	−8.06792	+	10.1169i	−0.296183	+	0.371401i
$743$	−0.118093	−	1.57585i	−0.00433243	−	0.0578122i	0.994619	−	0.103605i	$-0.0330377\pi$
$743$	−0.118093	−	1.57585i	−0.00433243	−	0.0578122i	−0.998951	+	0.0457926i	$0.985419\pi$
$744$		0			0
$745$	50.0054	−	34.0931i	1.83206	−	1.24908i
$746$	39.2256	−	5.91231i	1.43615	−	0.216465i
$747$		0			0
$748$	−1.84621	−	1.71303i	−0.0675040	−	0.0626345i
$749$	1.54577	−	20.6269i	0.0564812	−	0.753689i
$750$		0			0
$751$	−6.12248	−	0.922815i	−0.223412	−	0.0336740i	0.0363820	−	0.999338i	$-0.488417\pi$
$751$	−6.12248	−	0.922815i	−0.223412	−	0.0336740i	−0.259794	+	0.965664i	$0.583655\pi$
$752$	17.3923	−	8.37568i	0.634231	−	0.305430i
$753$		0			0
$754$	9.02808	+	1.36076i	0.328783	+	0.0495561i
$755$	11.0767	−	28.2231i	0.403124	−	1.02714i
$756$		0			0
$757$	4.19269	+	3.89025i	0.152386	+	0.141394i	0.752682	−	0.658385i	$-0.228760\pi$
$757$	4.19269	+	3.89025i	0.152386	+	0.141394i	−0.600296	+	0.799778i	$0.704950\pi$
$758$	−4.28529	+	18.7751i	−0.155649	+	0.681942i
$759$		0			0
$760$	−17.9553	+	12.2417i	−0.651305	+	0.444052i
$761$	−16.3236	−	5.03516i	−0.591729	−	0.182524i	−0.0155937	−	0.999878i	$-0.504964\pi$
$761$	−16.3236	−	5.03516i	−0.591729	−	0.182524i	−0.576136	+	0.817354i	$0.695440\pi$
$762$		0			0
$763$	−13.1485	+	16.4877i	−0.476006	+	0.596893i
$764$	−8.39487	+	2.58947i	−0.303716	+	0.0936838i
$765$		0			0
$766$	9.11747	+	39.9462i	0.329427	+	1.44332i
$767$	2.99617	−	5.18952i	0.108185	−	0.187383i
$768$		0			0
$769$	1.75024	−	1.62399i	0.0631153	−	0.0585624i	−0.647985	−	0.761653i	$-0.724388\pi$
$769$	1.75024	−	1.62399i	0.0631153	−	0.0585624i	0.711100	+	0.703091i	$0.248197\pi$
$770$	37.0170	+	46.4179i	1.33400	+	1.67279i
$771$		0			0
$772$	9.37717	+	4.51581i	0.337492	+	0.162527i
$773$	−1.76858			−0.0636114			−0.0318057	−	0.999494i	$-0.510126\pi$
$773$	−1.76858			−0.0636114			−0.0318057	+	0.999494i	$0.510126\pi$
$774$		0			0
$775$	22.2468			0.799130
$776$	48.9571	+	23.5765i	1.75746	+	0.846348i
$777$		0			0
$778$	13.7472	+	17.2385i	0.492862	+	0.618029i
$779$	11.1814	−	10.3748i	0.400616	−	0.371717i
$780$		0			0
$781$	19.2728	−	33.3815i	0.689635	−	1.19448i
$782$	0.000282045		0.00123572i	1.00859e−5		4.41892e-5i
$783$		0			0
$784$	−1.55741	+	0.480396i	−0.0556217	+	0.0171570i
$785$	2.99744	−	3.75867i	0.106983	−	0.134153i
$786$		0			0
$787$	31.5189	+	9.72230i	1.12353	+	0.346563i	0.800205	−	0.599726i	$-0.204724\pi$
$787$	31.5189	+	9.72230i	1.12353	+	0.346563i	0.323323	+	0.946289i	$0.395200\pi$
$788$	−1.34404	+	0.916351i	−0.0478794	+	0.0326437i
$789$		0			0
$790$	5.59278	−	24.5036i	0.198982	−	0.871798i
$791$	−13.0904	−	12.1461i	−0.465442	−	0.431867i
$792$		0			0
$793$	−5.13608	+	13.0865i	−0.182387	+	0.464716i
$794$	35.6154	+	5.36816i	1.26394	+	0.190509i
$795$		0			0
$796$	−2.09025	+	1.00661i	−0.0740870	+	0.0356784i
$797$	−22.3286	−	3.36550i	−0.790921	−	0.119212i	−0.258856	−	0.965916i	$-0.583346\pi$
$797$	−22.3286	−	3.36550i	−0.790921	−	0.119212i	−0.532065	+	0.846704i	$0.678584\pi$
$798$		0			0
$799$	0.445506	−	5.94487i	0.0157609	−	0.210314i
$800$	13.1086	+	12.1630i	0.463458	+	0.430026i
$801$		0			0
$802$	44.3031	−	6.67762i	1.56440	−	0.235795i
$803$	51.2158	−	34.9184i	1.80737	−	1.23224i
$804$		0			0
$805$	0.000946286		0.0126273i	3.33522e−5		0.000445054i
$806$	−4.90047	+	6.14499i	−0.172612	+	0.216448i
$807$		0			0
$808$	−11.3514	−	28.9230i	−0.399342	−	1.01751i
$809$	−2.39510	−	10.4936i	−0.0842072	−	0.368936i	0.915213	−	0.402969i	$-0.132022\pi$
$809$	−2.39510	−	10.4936i	−0.0842072	−	0.368936i	−0.999421	+	0.0340335i	$0.989165\pi$
$810$		0			0
$811$	−9.44394	−	16.3574i	−0.331621	−	0.574385i	0.651208	−	0.758899i	$-0.274262\pi$
$811$	−9.44394	−	16.3574i	−0.331621	−	0.574385i	−0.982830	+	0.184514i	$0.940929\pi$
$812$	5.66043	−	5.25211i	0.198642	−	0.184313i
$813$		0			0
$814$	10.9234	+	7.44742i	0.382863	+	0.261032i
$815$	−42.4786	−	20.4566i	−1.48796	−	0.716563i
$816$		0			0
$817$	−5.88263	+	13.0192i	−0.205807	+	0.455485i
$818$	−5.06192			−0.176986
$819$		0			0
$820$	−11.1667	−	7.61331i	−0.389957	−	0.265868i
$821$	29.5066	+	37.0001i	1.02979	+	1.29131i	0.955789	+	0.294053i	$0.0950041\pi$
$821$	29.5066	+	37.0001i	1.02979	+	1.29131i	0.0739969	+	0.997258i	$0.476424\pi$
$822$		0			0
$823$	−0.551677	−	0.955532i	−0.0192302	−	0.0333078i	0.856250	−	0.516561i	$-0.172788\pi$
$823$	−0.551677	−	0.955532i	−0.0192302	−	0.0333078i	−0.875480	+	0.483254i	$0.839455\pi$
$824$	21.4499	−	37.1522i	0.747241	−	1.29426i
$825$		0			0
$826$	4.36902	+	11.1321i	0.152018	+	0.387334i
$827$	−21.0646	+	6.49756i	−0.732487	+	0.225942i	−0.638490	−	0.769630i	$-0.720441\pi$
$827$	−21.0646	+	6.49756i	−0.732487	+	0.225942i	−0.0939973	+	0.995572i	$0.529965\pi$
$828$		0			0
$829$	−3.82921	−	51.0972i	−0.132994	−	1.77468i	−0.521518	−	0.853241i	$-0.674634\pi$
$829$	−3.82921	−	51.0972i	−0.132994	−	1.77468i	0.388524	−	0.921439i	$-0.372985\pi$
$830$	−20.9612	−	6.46568i	−0.727575	−	0.224427i
$831$		0			0
$832$	−14.2296	+	2.14476i	−0.493321	+	0.0743563i
$833$	−0.112001	+	0.490707i	−0.00388060	+	0.0170020i
$834$		0			0
$835$	−1.92304	+	25.6612i	−0.0665496	+	0.888043i
$836$	−2.64406	+	6.73695i	−0.0914467	+	0.233002i
$837$		0			0
$838$	−13.0131	+	6.26678i	−0.449530	+	0.216482i
$839$	−10.0756	+	4.85214i	−0.347847	+	0.167514i	−0.599646	−	0.800265i	$-0.704692\pi$
$839$	−10.0756	+	4.85214i	−0.347847	+	0.167514i	0.251799	+	0.967780i	$0.418978\pi$
$840$		0			0
$841$	−2.57428	+	6.55915i	−0.0887682	+	0.226178i
$842$	0.877709	−	11.7122i	0.0302479	−	0.403630i
$843$		0			0
$844$	−1.33172	+	5.83464i	−0.0458396	+	0.200837i
$845$	33.0175	−	4.97658i	1.13584	−	0.171200i
$846$		0			0
$847$	53.2718	+	16.4322i	1.83044	+	0.564616i
$848$	−0.723546	−	9.65505i	−0.0248467	−	0.331556i
$849$		0			0
$850$	−4.73588	+	1.46082i	−0.162439	+	0.0501059i
$851$	0.00103016	+	0.00262480i	3.53133e−5	+	8.99769e-5i
$852$		0			0
$853$	−10.4719	+	18.1379i	−0.358553	+	0.621031i	−0.987719	−	0.156239i	$-0.950063\pi$
$853$	−10.4719	+	18.1379i	−0.358553	+	0.621031i	0.629167	+	0.777270i	$0.283396\pi$
$854$	−14.0279	−	24.2970i	−0.480024	−	0.831425i
$855$		0			0
$856$	14.3296	+	17.9687i	0.489775	+	0.614159i
$857$	−6.50785	−	4.43698i	−0.222304	−	0.151564i	0.447047	−	0.894510i	$-0.352476\pi$
$857$	−6.50785	−	4.43698i	−0.222304	−	0.151564i	−0.669351	+	0.742946i	$0.733428\pi$
$858$		0			0
$859$	−42.8104			−1.46067			−0.730337	−	0.683087i	$-0.760637\pi$
$859$	−42.8104			−1.46067			−0.730337	+	0.683087i	$0.760637\pi$
$860$	12.4063	+	2.51468i	0.423050	+	0.0857499i
$861$		0			0
$862$	21.8533	+	10.5240i	0.744326	+	0.358448i
$863$	−0.563855	−	0.384430i	−0.0191939	−	0.0130861i	0.553685	−	0.832726i	$-0.313221\pi$
$863$	−0.563855	−	0.384430i	−0.0191939	−	0.0130861i	−0.572879	+	0.819640i	$0.694174\pi$
$864$		0			0
$865$	−4.11565	+	3.81877i	−0.139936	+	0.129842i
$866$	−0.817920	−	1.41668i	−0.0277941	−	0.0481407i
$867$		0			0
$868$	1.47918	+	6.48070i	0.0502066	+	0.219969i
$869$	−13.3319	−	33.9692i	−0.452255	−	1.15233i
$870$		0			0
$871$	9.62403	−	12.0682i	0.326098	−	0.408914i
$872$	−1.75104	−	23.3660i	−0.0592977	−	0.791273i
$873$		0			0
$874$	0.00300940	−	0.00205177i	0.000101794	−	6.94023e-5i
$875$	−4.57534	+	0.689622i	−0.154675	+	0.0233135i
$876$		0			0
$877$	−25.4736	−	23.6361i	−0.860183	−	0.798133i	0.120709	−	0.992688i	$-0.461483\pi$
$877$	−25.4736	−	23.6361i	−0.860183	−	0.798133i	−0.980892	+	0.194555i	$0.937674\pi$
$878$	0.911072	−	12.1574i	0.0307472	−	0.410293i
$879$		0			0
$880$	−43.9271	−	6.62095i	−1.48078	−	0.223192i
$881$	−3.50466	+	1.68776i	−0.118075	+	0.0568620i	−0.491989	−	0.870602i	$-0.663730\pi$
$881$	−3.50466	+	1.68776i	−0.118075	+	0.0568620i	0.373914	+	0.927463i	$0.378016\pi$
$882$		0			0
$883$	36.9489	+	5.56915i	1.24343	+	0.187417i	0.737613	−	0.675224i	$-0.235953\pi$
$883$	36.9489	+	5.56915i	1.24343	+	0.187417i	0.505817	+	0.862641i	$0.331191\pi$
$884$	−0.271099	+	0.690749i	−0.00911805	+	0.0232324i
$885$		0			0
$886$	−4.75443	−	4.41147i	−0.159728	−	0.148206i
$887$	−0.0666391	+	0.291965i	−0.00223752	+	0.00980322i	−0.976034	−	0.217617i	$-0.930172\pi$
$887$	−0.0666391	+	0.291965i	−0.00223752	+	0.00980322i	0.973797	+	0.227420i	$0.0730289\pi$
$888$		0			0
$889$	17.5021	−	11.9327i	0.587002	−	0.400211i
$890$	−31.7112	−	9.78161i	−1.06296	−	0.327880i
$891$		0			0
$892$	5.56110	−	6.97340i	0.186200	−	0.233487i
$893$	−16.3700	+	5.04948i	−0.547802	+	0.168975i
$894$		0			0
$895$	−5.87658	−	25.7470i	−0.196432	−	0.860627i
$896$	5.38348	−	9.32447i	0.179850	−	0.311509i
$897$		0			0
$898$	−24.3135	+	22.5596i	−0.811353	+	0.752825i
$899$	11.7835	+	14.7760i	0.393001	+	0.492807i
$900$		0			0
$901$	−2.69397	−	1.29735i	−0.0897490	−	0.0432209i
$902$	46.3024			1.54170
$903$		0			0
$904$	19.8415			0.659918
$905$	37.6012	+	18.1078i	1.24991	+	0.601924i
$906$		0			0
$907$	−19.3860	−	24.3092i	−0.643700	−	0.807175i	0.347760	−	0.937584i	$-0.386942\pi$
$907$	−19.3860	−	24.3092i	−0.643700	−	0.807175i	−0.991460	+	0.130409i	$0.958371\pi$
$908$	3.87661	−	3.59697i	0.128650	−	0.119370i
$909$		0			0
$910$	8.74634	−	15.1491i	0.289938	−	0.502188i
$911$	−6.55930	−	28.7382i	−0.217319	−	0.952139i	−0.959449	−	0.281882i	$-0.909041\pi$
$911$	−6.55930	−	28.7382i	−0.217319	−	0.952139i	0.742130	−	0.670256i	$-0.233816\pi$
$912$		0			0
$913$	−30.4337	+	9.38756i	−1.00721	+	0.310683i
$914$	−27.2218	+	34.1350i	−0.900417	+	1.12909i
$915$		0			0
$916$	−11.5408	−	3.55985i	−0.381317	−	0.117621i
$917$	−39.9021	+	27.2048i	−1.31768	+	0.898382i
$918$		0			0
$919$	−3.58384	+	15.7018i	−0.118220	+	0.517956i	0.880792	+	0.473504i	$0.157011\pi$
$919$	−3.58384	+	15.7018i	−0.118220	+	0.517956i	−0.999012	+	0.0444515i	$0.985846\pi$
$920$	−0.0103138	−	0.00956977i	−0.000340035	−	0.000315506i
$921$		0			0
$922$	5.70655	−	14.5400i	0.187935	−	0.478851i
$923$	−11.2300	−	1.69265i	−0.369641	−	0.0557144i
$924$		0			0
$925$	−9.93354	+	4.78374i	−0.326613	+	0.157288i
$926$	33.7848	+	5.09223i	1.11024	+	0.167341i
$927$		0			0
$928$	−1.13525	+	15.1489i	−0.0372664	+	0.497286i
$929$	16.5691	+	15.3739i	0.543616	+	0.504402i	0.903496	−	0.428597i	$-0.140992\pi$
$929$	16.5691	+	15.3739i	0.543616	+	0.504402i	−0.359880	+	0.932999i	$0.617182\pi$
$930$		0			0
$931$	1.43021	−	0.215569i	0.0468732	−	0.00706499i
$932$	5.01811	−	3.42129i	0.164374	−	0.112068i
$933$		0			0
$934$	−0.287694	−	3.83900i	−0.00941362	−	0.125616i
$935$	−8.55366	+	10.7260i	−0.279735	+	0.350776i
$936$		0			0
$937$	11.9474	+	30.4414i	0.390304	+	0.994478i	0.982095	+	0.188387i	$0.0603258\pi$
$937$	11.9474	+	30.4414i	0.390304	+	0.994478i	−0.591791	+	0.806091i	$0.701579\pi$
$938$	6.85468	+	30.0323i	0.223813	+	0.980590i
$939$		0			0
$940$	7.58948	+	13.1454i	0.247542	+	0.428755i
$941$	0.214487	−	0.199015i	0.00699209	−	0.00648771i	−0.676669	−	0.736287i	$-0.736577\pi$
$941$	0.214487	−	0.199015i	0.00699209	−	0.00648771i	0.683661	+	0.729800i	$0.260387\pi$
$942$		0			0
$943$	0.00815951	+	0.00556306i	0.000265710	+	0.000181158i
$944$	−8.06183	−	3.88237i	−0.262390	−	0.126360i
$945$		0			0
$946$	−39.9713	+	16.8249i	−1.29958	+	0.547024i
$947$	−13.5390			−0.439959			−0.219979	−	0.975504i	$-0.570599\pi$
$947$	−13.5390			−0.439959			−0.219979	+	0.975504i	$0.570599\pi$
$948$		0			0
$949$	−15.0900	−	10.2882i	−0.489841	−	0.333968i
$950$	8.87959	+	11.1347i	0.288092	+	0.361256i
$951$		0			0
$952$	−3.22804	−	5.59114i	−0.104622	−	0.181210i
$953$	6.90661	−	11.9626i	0.223727	−	0.387507i	−0.732210	−	0.681079i	$-0.761511\pi$
$953$	6.90661	−	11.9626i	0.223727	−	0.387507i	0.955937	+	0.293573i	$0.0948443\pi$
$954$		0			0
$955$	17.4834	+	44.5469i	0.565749	+	1.44151i
$956$	−4.54480	+	1.40188i	−0.146989	+	0.0453402i
$957$		0			0
$958$	−1.97741	−	26.3867i	−0.0638872	−	0.852516i
$959$	−6.88440	−	2.12356i	−0.222309	−	0.0685732i
$960$		0			0
$961$	14.5658	−	2.19544i	0.469865	−	0.0708207i
$962$	0.866773	−	3.79758i	0.0279459	−	0.122439i
$963$		0			0
$964$	0.374069	−	4.99160i	0.0120479	−	0.160769i
$965$	20.7127	−	52.7752i	0.666767	−	1.69889i
$966$		0			0
$967$	10.3525	−	4.98550i	0.332914	−	0.160323i	−0.259958	−	0.965620i	$-0.583709\pi$
$967$	10.3525	−	4.98550i	0.332914	−	0.160323i	0.592871	+	0.805297i	$0.297994\pi$
$968$	−55.8083	+	26.8759i	−1.79375	+	0.863823i
$969$		0			0
$970$	24.8045	−	63.2008i	0.796424	−	2.02926i
$971$	−3.68142	+	49.1251i	−0.118142	+	1.57650i	0.551729	+	0.834023i	$0.313968\pi$
$971$	−3.68142	+	49.1251i	−0.118142	+	1.57650i	−0.669872	+	0.742477i	$0.733651\pi$
$972$		0			0
$973$	−4.89301	+	21.4377i	−0.156863	+	0.687261i
$974$	−15.8511	+	2.38917i	−0.507903	+	0.0765540i
$975$		0			0
$976$	20.0597	+	6.18759i	0.642095	+	0.198060i
$977$	2.57239	+	34.3262i	0.0822982	+	1.09819i	0.873560	+	0.486716i	$0.161805\pi$
$977$	2.57239	+	34.3262i	0.0822982	+	1.09819i	−0.791262	+	0.611477i	$0.790576\pi$
$978$		0			0
$979$	−46.0416	+	14.2020i	−1.47150	+	0.453897i
$980$	−0.468201	−	1.19296i	−0.0149561	−	0.0381076i
$981$		0			0
$982$	−5.95915	+	10.3215i	−0.190164	+	0.329374i
$983$	23.3956	+	40.5224i	0.746205	+	1.29247i	0.949630	+	0.313375i	$0.101460\pi$
$983$	23.3956	+	40.5224i	0.746205	+	1.29247i	−0.203424	+	0.979091i	$0.565207\pi$
$984$		0			0
$985$	5.52476	+	6.92783i	0.176033	+	0.220739i
$986$	−3.47871	−	2.37174i	−0.110785	−	0.0755317i
$987$		0			0
$988$	2.13234			0.0678388
$989$	−0.00906527	−	0.00183748i	−0.000288259	−	5.84285e-5i
$990$		0			0
$991$	−21.0704	−	10.1470i	−0.669325	−	0.322330i	0.0681788	−	0.997673i	$-0.478281\pi$
$991$	−21.0704	−	10.1470i	−0.669325	−	0.322330i	−0.737503	+	0.675343i	$0.763995\pi$
$992$	−10.8053	−	7.36693i	−0.343069	−	0.233900i
$993$		0			0
$994$	16.6143	−	15.4158i	0.526974	−	0.488960i
$995$	6.31882	+	10.9445i	0.200320	+	0.346964i
$996$		0			0
$997$	11.0399	+	48.3689i	0.349637	+	1.53186i	0.778007	+	0.628255i	$0.216231\pi$
$997$	11.0399	+	48.3689i	0.349637	+	1.53186i	−0.428370	+	0.903603i	$0.640912\pi$
$998$	−10.6237	−	27.0686i	−0.336286	−	0.856843i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.154.3		36
3.2	odd	2		43.2.g.a.25.1	✓	36
12.11	even	2		688.2.bg.c.369.2		36
43.31	even	21	inner	387.2.y.c.289.3		36
129.17	odd	42		1849.2.a.n.1.14		18
129.26	even	42		1849.2.a.o.1.5		18
129.74	odd	42		43.2.g.a.31.1	yes	36
516.203	even	42		688.2.bg.c.289.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.25.1	✓	36	3.2	odd	2
43.2.g.a.31.1	yes	36	129.74	odd	42
387.2.y.c.154.3		36	1.1	even	1	trivial
387.2.y.c.289.3		36	43.31	even	21	inner
688.2.bg.c.289.2		36	516.203	even	42
688.2.bg.c.369.2		36	12.11	even	2
1849.2.a.n.1.14		18	129.17	odd	42
1849.2.a.o.1.5		18	129.26	even	42

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06783 + 0.514239i) q^{2} +(-0.371164 - 0.465425i) q^{4} +(-2.37710 + 2.20563i) q^{5} +(-1.38418 + 2.39748i) q^{7} +(-0.684463 - 2.99883i) q^{8} +O(q^{10})\)	\(q+(1.06783 + 0.514239i) q^{2} +(-0.371164 - 0.465425i) q^{4} +(-2.37710 + 2.20563i) q^{5} +(-1.38418 + 2.39748i) q^{7} +(-0.684463 - 2.99883i) q^{8} +(-3.67256 + 1.13283i) q^{10} +(-3.47915 + 4.36271i) q^{11} +(1.57105 + 0.484606i) q^{13} +(-2.71095 + 1.84829i) q^{14} +(0.546293 - 2.39346i) q^{16} +(-0.555777 - 0.515686i) q^{17} +(-0.795961 + 2.02807i) q^{19} +(1.90885 + 0.287713i) q^{20} +(-5.95861 + 2.86951i) q^{22} +(-0.00139480 - 0.000210232i) q^{23} +(0.412168 - 5.50000i) q^{25} +(1.42841 + 1.32537i) q^{26} +(1.62960 - 0.245623i) q^{28} +(3.87133 - 2.63943i) q^{29} +(0.301429 + 4.02229i) q^{31} +(-2.02149 + 2.53487i) q^{32} +(-0.328289 - 0.836466i) q^{34} +(-1.99760 - 8.75205i) q^{35} +(-0.999506 - 1.73120i) q^{37} +(-1.89286 + 1.75632i) q^{38} +(8.24135 + 5.61886i) q^{40} +(-6.30781 - 3.03768i) q^{41} +(6.54912 + 0.330261i) q^{43} +3.32185 q^{44} +(-0.00138130 - 0.000941752i) q^{46} +(4.90255 + 6.14760i) q^{47} +(-0.331936 - 0.574929i) q^{49} +(3.26844 - 5.66111i) q^{50} +(-0.357571 - 0.911075i) q^{52} +(3.76860 - 1.16246i) q^{53} +(-1.35223 - 18.0443i) q^{55} +(8.13705 + 2.50995i) q^{56} +(5.49121 - 0.827667i) q^{58} +(0.811036 - 3.55338i) q^{59} +(-0.639001 + 8.52687i) q^{61} +(-1.74654 + 4.45012i) q^{62} +(-7.88592 + 3.79766i) q^{64} +(-4.80342 + 2.31320i) q^{65} +(3.43004 - 8.73959i) q^{67} +(-0.0337286 + 0.450076i) q^{68} +(2.36756 - 10.3729i) q^{70} +(-6.83052 + 1.02953i) q^{71} +(-10.6150 - 3.27429i) q^{73} +(-0.177053 - 2.36261i) q^{74} +(1.23935 - 0.382288i) q^{76} +(-5.64372 - 14.3800i) q^{77} +(-3.26980 + 5.66346i) q^{79} +(3.98050 + 6.89443i) q^{80} +(-5.17357 - 6.48745i) q^{82} +(4.71578 + 3.21516i) q^{83} +2.45855 q^{85} +(6.82350 + 3.72047i) q^{86} +(15.4644 + 7.44725i) q^{88} +(7.13427 + 4.86406i) q^{89} +(-3.33646 + 3.09578i) q^{91} +(0.000419851 + 0.000727204i) q^{92} +(2.07374 + 9.08566i) q^{94} +(-2.58110 - 6.57654i) q^{95} +(-11.0143 + 13.8115i) q^{97} +(-0.0587992 - 0.784620i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

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