LMFDB - Embedded newform 441.2.bb.c.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	441.109
Dual form			441.2.bb.c.352.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615612 + 0.571205i) q^{2} +(-0.0967566 + 1.29113i) q^{4} +(0.568152 - 1.44763i) q^{5} +(1.56778 - 2.13121i) q^{7} +(-1.72514 - 2.16325i) q^{8} +O(q^{10})$	\(q+(-0.615612 + 0.571205i) q^{2} +(-0.0967566 + 1.29113i) q^{4} +(0.568152 - 1.44763i) q^{5} +(1.56778 - 2.13121i) q^{7} +(-1.72514 - 2.16325i) q^{8} +(0.477130 + 1.21571i) q^{10} +(1.88719 + 0.582120i) q^{11} +(-0.828434 - 3.62961i) q^{13} +(0.252214 + 2.20752i) q^{14} +(-0.262894 - 0.0396249i) q^{16} +(3.40886 - 2.32412i) q^{17} +(-1.88493 - 3.26480i) q^{19} +(1.81410 + 0.873624i) q^{20} +(-1.49428 + 0.719609i) q^{22} +(2.44141 + 1.66453i) q^{23} +(1.89243 + 1.75592i) q^{25} +(2.58324 + 1.76123i) q^{26} +(2.59997 + 2.23041i) q^{28} +(-1.94616 - 0.937220i) q^{29} +(0.421689 - 0.730388i) q^{31} +(4.75673 - 3.24308i) q^{32} +(-0.770987 + 3.37792i) q^{34} +(-2.19446 - 3.48041i) q^{35} +(0.772823 + 10.3126i) q^{37} +(3.02525 + 0.933168i) q^{38} +(-4.11173 + 1.26830i) q^{40} +(6.50119 + 8.15223i) q^{41} +(4.94257 - 6.19778i) q^{43} +(-0.934188 + 2.38027i) q^{44} +(-2.45375 + 0.369843i) q^{46} +(1.22264 - 1.13444i) q^{47} +(-2.08413 - 6.68254i) q^{49} -2.16799 q^{50} +(4.76644 - 0.718425i) q^{52} +(0.368379 - 4.91568i) q^{53} +(1.91490 - 2.40121i) q^{55} +(-7.31499 + 0.285127i) q^{56} +(1.73342 - 0.534690i) q^{58} +(-2.99661 - 7.63524i) q^{59} +(-0.197327 - 2.63314i) q^{61} +(0.157604 + 0.690506i) q^{62} +(-0.957515 + 4.19515i) q^{64} +(-5.72500 - 0.862905i) q^{65} +(-2.13080 + 3.69065i) q^{67} +(2.67091 + 4.62615i) q^{68} +(3.33897 + 0.889097i) q^{70} +(-13.2041 + 6.35877i) q^{71} +(-3.45312 - 3.20403i) q^{73} +(-6.36637 - 5.90712i) q^{74} +(4.39765 - 2.11780i) q^{76} +(4.19931 - 3.10936i) q^{77} +(7.12262 + 12.3367i) q^{79} +(-0.206726 + 0.358060i) q^{80} +(-8.65880 - 1.30510i) q^{82} +(0.636629 - 2.78925i) q^{83} +(-1.42771 - 6.25522i) q^{85} +(0.497498 + 6.63865i) q^{86} +(-1.99638 - 5.08670i) q^{88} +(-16.3237 + 5.03519i) q^{89} +(-9.03427 - 3.92486i) q^{91} +(-2.38534 + 2.99112i) q^{92} +(-0.104672 + 1.39675i) q^{94} +(-5.79714 + 0.873778i) q^{95} +5.74864 q^{97} +(5.10012 + 2.92339i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$1$

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 $

$2$	−0.615612	+	0.571205i	−0.435304	+	0.403903i	−0.867152	−	0.498043i	$-0.834052\pi$
$2$	−0.615612	+	0.571205i	−0.435304	+	0.403903i	0.431849	+	0.901946i	$0.357862\pi$
$3$		0			0
$3$		0			0
$4$	−0.0967566	+	1.29113i	−0.0483783	+	0.645563i
$5$	0.568152	−	1.44763i	0.254085	−	0.647399i	−0.745737	−	0.666240i	$-0.767903\pi$
$5$	0.568152	−	1.44763i	0.254085	−	0.647399i	0.999822	+	0.0188414i	$0.00599776\pi$
$6$		0			0
$7$	1.56778	−	2.13121i	0.592565	−	0.805522i
$7$	1.56778	−	2.13121i	0.592565	−	0.805522i
$8$	−1.72514	−	2.16325i	−0.609928	−	0.764826i
$9$		0			0
$10$	0.477130	+	1.21571i	0.150882	+	0.384441i
$11$	1.88719	+	0.582120i	0.569008	+	0.175516i	0.565892	−	0.824479i	$-0.308532\pi$
$11$	1.88719	+	0.582120i	0.569008	+	0.175516i	0.00311601	+	0.999995i	$0.499008\pi$
$12$		0			0
$13$	−0.828434	−	3.62961i	−0.229766	−	1.00667i	−0.949831	−	0.312765i	$-0.898745\pi$
$13$	−0.828434	−	3.62961i	−0.229766	−	1.00667i	0.720064	−	0.693907i	$-0.244112\pi$
$14$	0.252214	+	2.20752i	0.0674069	+	0.589985i
$15$		0			0
$16$	−0.262894	−	0.0396249i	−0.0657235	−	0.00990622i
$17$	3.40886	−	2.32412i	0.826771	−	0.563683i	−0.0743595	−	0.997232i	$-0.523691\pi$
$17$	3.40886	−	2.32412i	0.826771	−	0.563683i	0.901130	+	0.433549i	$0.142739\pi$
$18$		0			0
$19$	−1.88493	−	3.26480i	−0.432433	−	0.748996i	0.564649	−	0.825331i	$-0.309011\pi$
$19$	−1.88493	−	3.26480i	−0.432433	−	0.748996i	−0.997082	+	0.0763350i	$0.975678\pi$
$20$	1.81410	+	0.873624i	0.405645	+	0.195348i
$21$		0			0
$22$	−1.49428	+	0.719609i	−0.318582	+	0.153421i
$23$	2.44141	+	1.66453i	0.509070	+	0.347078i	0.790458	−	0.612516i	$-0.209842\pi$
$23$	2.44141	+	1.66453i	0.509070	+	0.347078i	−0.281388	+	0.959594i	$0.590795\pi$
$24$		0			0
$25$	1.89243	+	1.75592i	0.378486	+	0.351184i
$26$	2.58324	+	1.76123i	0.506616	+	0.345405i
$27$		0			0
$28$	2.59997	+	2.23041i	0.491348	+	0.421508i
$29$	−1.94616	−	0.937220i	−0.361393	−	0.174037i	0.244372	−	0.969682i	$-0.421418\pi$
$29$	−1.94616	−	0.937220i	−0.361393	−	0.174037i	−0.605764	+	0.795644i	$0.707133\pi$
$30$		0			0
$31$	0.421689	−	0.730388i	0.0757377	−	0.131181i	−0.825669	−	0.564155i	$-0.809202\pi$
$31$	0.421689	−	0.730388i	0.0757377	−	0.131181i	0.901407	+	0.432973i	$0.142536\pi$
$32$	4.75673	−	3.24308i	0.840878	−	0.573301i
$33$		0			0
$34$	−0.770987	+	3.37792i	−0.132223	+	0.579308i
$35$	−2.19446	−	3.48041i	−0.370932	−	0.588298i
$36$		0			0
$37$	0.772823	+	10.3126i	0.127051	+	1.69538i	0.588726	+	0.808332i	$0.299630\pi$
$37$	0.772823	+	10.3126i	0.127051	+	1.69538i	−0.461675	+	0.887049i	$0.652751\pi$
$38$	3.02525	+	0.933168i	0.490761	+	0.151380i
$39$		0			0
$40$	−4.11173	+	1.26830i	−0.650121	+	0.200536i
$41$	6.50119	+	8.15223i	1.01532	+	1.27316i	0.961555	+	0.274611i	$0.0885491\pi$
$41$	6.50119	+	8.15223i	1.01532	+	1.27316i	0.0537598	+	0.998554i	$0.482879\pi$
$42$		0			0
$43$	4.94257	−	6.19778i	0.753734	−	0.945153i	−0.245975	−	0.969276i	$-0.579108\pi$
$43$	4.94257	−	6.19778i	0.753734	−	0.945153i	0.999709	+	0.0241232i	$0.00767941\pi$
$44$	−0.934188	+	2.38027i	−0.140834	+	0.358839i
$45$		0			0
$46$	−2.45375	+	0.369843i	−0.361786	+	0.0545304i
$47$	1.22264	−	1.13444i	0.178340	−	0.165476i	−0.585952	−	0.810346i	$-0.699279\pi$
$47$	1.22264	−	1.13444i	0.178340	−	0.165476i	0.764292	+	0.644870i	$0.223089\pi$
$48$		0			0
$49$	−2.08413	−	6.68254i	−0.297733	−	0.954649i
$50$	−2.16799			−0.306600
$51$		0			0
$52$	4.76644	−	0.718425i	0.660986	−	0.0996276i
$53$	0.368379	−	4.91568i	0.0506008	−	0.675221i	−0.913014	−	0.407927i	$-0.866252\pi$
$53$	0.368379	−	4.91568i	0.0506008	−	0.675221i	0.963615	−	0.267293i	$-0.0861293\pi$
$54$		0			0
$55$	1.91490	−	2.40121i	0.258205	−	0.323779i
$56$	−7.31499	+	0.285127i	−0.977507	+	0.0381018i
$57$		0			0
$58$	1.73342	−	0.534690i	0.227610	−	0.0702083i
$59$	−2.99661	−	7.63524i	−0.390126	−	0.994024i	−0.982149	−	0.188103i	$-0.939766\pi$
$59$	−2.99661	−	7.63524i	−0.390126	−	0.994024i	0.592024	−	0.805921i	$-0.298329\pi$
$60$		0			0
$61$	−0.197327	−	2.63314i	−0.0252651	−	0.337139i	−0.995485	−	0.0949150i	$-0.969742\pi$
$61$	−0.197327	−	2.63314i	−0.0252651	−	0.337139i	0.970220	−	0.242224i	$-0.0778770\pi$
$62$	0.157604	+	0.690506i	0.0200157	+	0.0876944i
$63$		0			0
$64$	−0.957515	+	4.19515i	−0.119689	+	0.524394i
$65$	−5.72500	−	0.862905i	−0.710099	−	0.107030i
$66$		0			0
$67$	−2.13080	+	3.69065i	−0.260318	+	0.450884i	−0.966326	−	0.257319i	$-0.917161\pi$
$67$	−2.13080	+	3.69065i	−0.260318	+	0.450884i	0.706008	+	0.708204i	$0.250494\pi$
$68$	2.67091	+	4.62615i	0.323895	+	0.561003i
$69$		0			0
$70$	3.33897	+	0.889097i	0.399083	+	0.106267i
$71$	−13.2041	+	6.35877i	−1.56704	+	0.754647i	−0.997721	−	0.0674700i	$-0.978507\pi$
$71$	−13.2041	+	6.35877i	−1.56704	+	0.754647i	−0.569319	+	0.822117i	$0.692793\pi$
$72$		0			0
$73$	−3.45312	−	3.20403i	−0.404157	−	0.375003i	0.451740	−	0.892150i	$-0.350804\pi$
$73$	−3.45312	−	3.20403i	−0.404157	−	0.375003i	−0.855897	+	0.517147i	$0.826994\pi$
$74$	−6.36637	−	5.90712i	−0.740075	−	0.686689i
$75$		0			0
$76$	4.39765	−	2.11780i	0.504445	−	0.242928i
$77$	4.19931	−	3.10936i	0.478556	−	0.354344i
$78$		0			0
$79$	7.12262	+	12.3367i	0.801357	+	1.38799i	0.918723	+	0.394902i	$0.129222\pi$
$79$	7.12262	+	12.3367i	0.801357	+	1.38799i	−0.117366	+	0.993089i	$0.537445\pi$
$80$	−0.206726	+	0.358060i	−0.0231127	+	0.0400323i
$81$		0			0
$82$	−8.65880	−	1.30510i	−0.956205	−	0.144125i
$83$	0.636629	−	2.78925i	0.0698791	−	0.306160i	−0.927895	−	0.372841i	$-0.878384\pi$
$83$	0.636629	−	2.78925i	0.0698791	−	0.306160i	0.997774	+	0.0666807i	$0.0212409\pi$
$84$		0			0
$85$	−1.42771	−	6.25522i	−0.154857	−	0.678474i
$86$	0.497498	+	6.63865i	0.0536466	+	0.715864i
$87$		0			0
$88$	−1.99638	−	5.08670i	−0.212815	−	0.542244i
$89$	−16.3237	+	5.03519i	−1.73031	+	0.533729i	−0.990309	−	0.138879i	$-0.955650\pi$
$89$	−16.3237	+	5.03519i	−1.73031	+	0.533729i	−0.739999	+	0.672608i	$0.765174\pi$
$90$		0			0
$91$	−9.03427	−	3.92486i	−0.947049	−	0.411437i
$92$	−2.38534	+	2.99112i	−0.248689	+	0.311846i
$93$		0			0
$94$	−0.104672	+	1.39675i	−0.0107961	+	0.144064i
$95$	−5.79714	+	0.873778i	−0.594774	+	0.0896478i
$96$		0			0
$97$	5.74864			0.583686			0.291843	−	0.956466i	$-0.405732\pi$
$97$	5.74864			0.583686			0.291843	+	0.956466i	$0.405732\pi$
$98$	5.10012	+	2.92339i	0.515190	+	0.295307i
$99$		0			0
$100$	−2.45022	+	2.27347i	−0.245022	+	0.227347i
$101$	15.2483	−	2.29831i	1.51726	−	0.228690i	0.663034	−	0.748589i	$-0.269268\pi$
$101$	15.2483	−	2.29831i	1.51726	−	0.228690i	0.854228	+	0.519899i	$0.174030\pi$
$102$		0			0
$103$	−3.76936	+	9.60418i	−0.371406	+	0.946328i	0.615946	+	0.787788i	$0.288774\pi$
$103$	−3.76936	+	9.60418i	−0.371406	+	0.946328i	−0.987353	+	0.158540i	$0.949321\pi$
$104$	−6.42260	+	8.05369i	−0.629788	+	0.789729i
$105$		0			0
$106$	2.58108	+	3.23657i	0.250697	+	0.314364i
$107$	−14.2127	+	4.38405i	−1.37400	+	0.423822i	−0.891875	−	0.452283i	$-0.850610\pi$
$107$	−14.2127	+	4.38405i	−1.37400	+	0.423822i	−0.482122	+	0.876104i	$0.660134\pi$
$108$		0			0
$109$	−11.4918	−	3.54475i	−1.10071	−	0.339525i	−0.309397	−	0.950933i	$-0.600127\pi$
$109$	−11.4918	−	3.54475i	−1.10071	−	0.339525i	−0.791316	+	0.611408i	$0.790604\pi$
$110$	0.192746	+	2.57201i	0.0183776	+	0.245232i
$111$		0			0
$112$	−0.496609	+	0.498160i	−0.0469251	+	0.0470717i
$113$	2.11863	−	9.28234i	0.199304	−	0.873209i	−0.772048	−	0.635565i	$-0.780767\pi$
$113$	2.11863	−	9.28234i	0.199304	−	0.873209i	0.971352	−	0.237645i	$-0.0763755\pi$
$114$		0			0
$115$	3.79671	−	2.58855i	0.354045	−	0.241384i
$116$	1.39837	−	2.42205i	0.129836	−	0.224882i
$117$		0			0
$118$	6.20604	+	2.98867i	0.571312	+	0.275129i
$119$	0.391148	−	10.9087i	0.0358564	−	1.00000i
$120$		0			0
$121$	−5.86602	−	3.99938i	−0.533275	−	0.363580i
$122$	1.62554	+	1.50828i	0.147169	+	0.136553i
$123$		0			0
$124$	0.902222	+	0.615124i	0.0810219	+	0.0552398i
$125$	10.6227	−	5.11563i	0.950124	−	0.457556i
$126$		0			0
$127$	−2.42017	−	1.16549i	−0.214755	−	0.103421i	0.323414	−	0.946258i	$-0.395169\pi$
$127$	−2.42017	−	1.16549i	−0.214755	−	0.103421i	−0.538169	+	0.842837i	$0.680884\pi$
$128$	3.95025	+	6.84204i	0.349156	+	0.604757i
$129$		0			0
$130$	4.01727	−	2.73893i	0.352338	−	0.240220i
$131$	−17.9781	−	2.70977i	−1.57076	−	0.236754i	−0.694822	−	0.719182i	$-0.744517\pi$
$131$	−17.9781	−	2.70977i	−1.57076	−	0.236754i	−0.875936	+	0.482428i	$0.839755\pi$
$132$		0			0
$133$	−9.91314	−	1.10130i	−0.859578	−	0.0954944i
$134$	−0.796371	−	3.48913i	−0.0687959	−	0.301415i
$135$		0			0
$136$	−10.9084	−	3.36481i	−0.935390	−	0.288530i
$137$	3.70090	+	9.42974i	0.316189	+	0.805637i	0.997299	+	0.0734553i	$0.0234026\pi$
$137$	3.70090	+	9.42974i	0.316189	+	0.805637i	−0.681109	+	0.732182i	$0.738502\pi$
$138$		0			0
$139$	7.34333	+	9.20824i	0.622853	+	0.781033i	0.988743	−	0.149625i	$-0.0478068\pi$
$139$	7.34333	+	9.20824i	0.622853	+	0.781033i	−0.365890	+	0.930658i	$0.619235\pi$
$140$	4.70599	−	2.49658i	0.397728	−	0.210999i
$141$		0			0
$142$	4.49646	−	11.4568i	0.377334	−	0.961432i
$143$	0.549457	−	7.33199i	0.0459479	−	0.613132i
$144$		0			0
$145$	−2.46246	+	2.28483i	−0.204496	+	0.189745i
$146$	3.95594			0.327396
$147$		0			0
$148$	−13.3897			−1.10062
$149$	11.4118	−	10.5886i	0.934895	−	0.867456i	−0.0564944	−	0.998403i	$-0.517992\pi$
$149$	11.4118	−	10.5886i	0.934895	−	0.867456i	0.991389	+	0.130947i	$0.0418018\pi$
$150$		0			0
$151$	0.677882	−	9.04571i	0.0551653	−	0.736129i	−0.899210	−	0.437518i	$-0.855858\pi$
$151$	0.677882	−	9.04571i	0.0551653	−	0.736129i	0.954375	−	0.298611i	$-0.0965234\pi$
$152$	−3.81082	+	9.70982i	−0.309098	+	0.787570i
$153$		0			0
$154$	−0.809069	+	4.31283i	−0.0651966	+	0.347537i
$155$	−0.817746	−	1.02542i	−0.0656829	−	0.0823638i
$156$		0			0
$157$	7.93645	+	20.2218i	0.633398	+	1.61387i	0.780790	+	0.624793i	$0.214817\pi$
$157$	7.93645	+	20.2218i	0.633398	+	1.61387i	−0.147392	+	0.989078i	$0.547088\pi$
$158$	−11.4316	−	3.52617i	−0.909447	−	0.280527i
$159$		0			0
$160$	−1.99223	−	8.72853i	−0.157500	−	0.690051i
$161$	7.37506	−	2.59356i	0.581236	−	0.204401i
$162$		0			0
$163$	−22.1163	−	3.33349i	−1.73228	−	0.261099i	−0.794234	−	0.607612i	$-0.792127\pi$
$163$	−22.1163	−	3.33349i	−1.73228	−	0.261099i	−0.938045	+	0.346513i	$0.887366\pi$
$164$	−11.1546	+	7.60508i	−0.871028	+	0.593857i
$165$		0			0
$166$	1.20132	+	2.08074i	0.0932403	+	0.161497i
$167$	8.08364	+	3.89288i	0.625531	+	0.301240i	0.719667	−	0.694320i	$-0.244295\pi$
$167$	8.08364	+	3.89288i	0.625531	+	0.301240i	−0.0941360	+	0.995559i	$0.530009\pi$
$168$		0			0
$169$	−0.775155	+	0.373295i	−0.0596273	+	0.0287150i
$170$	4.45193	+	3.03527i	0.341447	+	0.232795i
$171$		0			0
$172$	7.52390	+	6.98116i	0.573692	+	0.532308i
$173$	5.56390	+	3.79340i	0.423016	+	0.288407i	0.756058	−	0.654505i	$-0.227123\pi$
$173$	5.56390	+	3.79340i	0.423016	+	0.288407i	−0.333042	+	0.942912i	$0.608075\pi$
$174$		0			0
$175$	6.70915	−	1.28028i	0.507164	−	0.0967797i
$176$	−0.473063	−	0.227815i	−0.0356585	−	0.0171722i
$177$		0			0
$178$	7.17294	−	12.4239i	0.537634	−	0.931210i
$179$	1.32150	−	0.900985i	0.0987737	−	0.0673428i	−0.512926	−	0.858433i	$-0.671438\pi$
$179$	1.32150	−	0.900985i	0.0987737	−	0.0673428i	0.611700	+	0.791090i	$0.290486\pi$
$180$		0			0
$181$	−4.10323	+	17.9774i	−0.304991	+	1.33625i	0.557499	+	0.830178i	$0.311761\pi$
$181$	−4.10323	+	17.9774i	−0.304991	+	1.33625i	−0.862490	+	0.506075i	$0.831096\pi$
$182$	7.80350	−	2.74422i	0.578434	−	0.203415i
$183$		0			0
$184$	−0.610979	−	8.15294i	−0.0450419	−	0.601043i
$185$	15.3679	+	4.74037i	1.12987	+	0.348519i
$186$		0			0
$187$	7.78607	−	2.40169i	0.569374	−	0.175629i
$188$	1.34641	+	1.68835i	0.0981971	+	0.123135i
$189$		0			0
$190$	3.06968	−	3.84926i	0.222698	−	0.279255i
$191$	−1.49470	+	3.80842i	−0.108152	+	0.275568i	−0.974696	−	0.223533i	$-0.928241\pi$
$191$	−1.49470	+	3.80842i	−0.108152	+	0.275568i	0.866544	+	0.499101i	$0.166336\pi$
$192$		0			0
$193$	16.3389	−	2.46269i	1.17610	−	0.177269i	0.468227	−	0.883608i	$-0.344893\pi$
$193$	16.3389	−	2.46269i	1.17610	−	0.177269i	0.707873	+	0.706339i	$0.249655\pi$
$194$	−3.53893	+	3.28365i	−0.254080	+	0.235752i
$195$		0			0
$196$	8.82966	−	2.04430i	0.630690	−	0.146021i
$197$	11.1608			0.795175			0.397587	−	0.917564i	$-0.369848\pi$
$197$	11.1608			0.795175			0.397587	+	0.917564i	$0.369848\pi$
$198$		0			0
$199$	7.12386	−	1.07375i	0.504997	−	0.0761160i	0.108397	−	0.994108i	$-0.465428\pi$
$199$	7.12386	−	1.07375i	0.504997	−	0.0761160i	0.396600	+	0.917992i	$0.370190\pi$
$200$	0.533796	−	7.12301i	0.0377451	−	0.503673i
$201$		0			0
$202$	−8.07423	+	10.1248i	−0.568101	+	0.712376i
$203$	−5.04856	+	2.67832i	−0.354340	+	0.187981i
$204$		0			0
$205$	15.4951	−	4.77959i	1.08222	−	0.333821i
$206$	−3.16549	−	8.06553i	−0.220550	−	0.561952i
$207$		0			0
$208$	0.0739676	+	0.987029i	0.00512873	+	0.0684381i
$209$	−1.65671	−	7.25854i	−0.114597	−	0.502083i
$210$		0			0
$211$	0.553514	−	2.42510i	0.0381055	−	0.166951i	−0.952295	−	0.305179i	$-0.901284\pi$
$211$	0.553514	−	2.42510i	0.0381055	−	0.166951i	0.990400	+	0.138228i	$0.0441408\pi$
$212$	6.31112	+	0.951249i	0.433450	+	0.0653320i
$213$		0			0
$214$	6.24534	−	10.8172i	0.426923	−	0.739452i
$215$	−6.16395	−	10.6763i	−0.420378	−	0.728116i
$216$		0			0
$217$	−0.895495	−	2.04380i	−0.0607901	−	0.138742i
$218$	9.09926	−	4.38197i	0.616279	−	0.296785i
$219$		0			0
$220$	2.91499	+	2.70471i	0.196528	+	0.182352i
$221$	−11.2597	−	10.4475i	−0.757408	−	0.702772i
$222$		0			0
$223$	−1.24604	+	0.600062i	−0.0834411	+	0.0401831i	−0.475139	−	0.879911i	$-0.657602\pi$
$223$	−1.24604	+	0.600062i	−0.0834411	+	0.0401831i	0.391698	+	0.920094i	$0.371888\pi$
$224$	0.545807	−	15.2220i	0.0364683	−	1.01706i
$225$		0			0
$226$	3.99786	+	6.92450i	0.265934	+	0.460611i
$227$	−6.72599	+	11.6497i	−0.446419	+	0.773221i	−0.998150	−	0.0608014i	$-0.980634\pi$
$227$	−6.72599	+	11.6497i	−0.446419	+	0.773221i	0.551731	+	0.834022i	$0.313968\pi$
$228$		0			0
$229$	22.9583	+	3.46040i	1.51712	+	0.228670i	0.854171	−	0.519991i	$-0.174065\pi$
$229$	22.9583	+	3.46040i	1.51712	+	0.228670i	0.662953	+	0.748661i	$0.269303\pi$
$230$	−0.858708	+	3.76224i	−0.0566215	+	0.248075i
$231$		0			0
$232$	1.32995	+	5.82687i	0.0873152	+	0.382553i
$233$	1.84558	+	24.6275i	0.120908	+	1.61340i	0.646669	+	0.762771i	$0.276161\pi$
$233$	1.84558	+	24.6275i	0.120908	+	1.61340i	−0.525761	+	0.850632i	$0.676219\pi$
$234$		0			0
$235$	−0.947607	−	2.41446i	−0.0618151	−	0.157502i
$236$	10.1480	−	3.13024i	0.660579	−	0.203762i
$237$		0			0
$238$	5.99032	+	6.93897i	0.388295	+	0.449787i
$239$	2.37269	−	2.97526i	0.153476	−	0.192453i	−0.699149	−	0.714976i	$-0.746438\pi$
$239$	2.37269	−	2.97526i	0.153476	−	0.192453i	0.852625	+	0.522523i	$0.175009\pi$
$240$		0			0
$241$	0.933186	−	12.4525i	0.0601118	−	0.802137i	−0.882939	−	0.469488i	$-0.844439\pi$
$241$	0.933186	−	12.4525i	0.0601118	−	0.802137i	0.943051	−	0.332649i	$-0.107942\pi$
$242$	5.89566	−	0.888628i	0.378987	−	0.0571232i
$243$		0			0
$244$	3.41881			0.218867
$245$	−10.8579	−	0.779656i	−0.693688	−	0.0498104i
$246$		0			0
$247$	−10.2884	+	9.54624i	−0.654635	+	0.607412i
$248$	−2.30749	+	0.347798i	−0.146526	+	0.0220852i
$249$		0			0
$250$	−3.61740	+	9.21699i	−0.228785	+	0.582933i
$251$	−2.94025	+	3.68696i	−0.185587	+	0.232719i	−0.865918	−	0.500186i	$-0.833265\pi$
$251$	−2.94025	+	3.68696i	−0.185587	+	0.232719i	0.680331	+	0.732905i	$0.261836\pi$
$252$		0			0
$253$	3.63845	+	4.56247i	0.228747	+	0.286840i
$254$	2.15562	−	0.664921i	0.135256	−	0.0417208i
$255$		0			0
$256$	−14.5638	−	4.49232i	−0.910235	−	0.280770i
$257$	0.382042	+	5.09800i	0.0238312	+	0.318005i	0.996361	+	0.0852283i	$0.0271620\pi$
$257$	0.382042	+	5.09800i	0.0238312	+	0.318005i	−0.972530	+	0.232776i	$0.925219\pi$
$258$		0			0
$259$	23.1900	+	14.5208i	1.44095	+	0.902281i
$260$	1.66805	−	7.30821i	0.103448	−	0.453236i
$261$		0			0
$262$	12.6154	−	8.60103i	0.779382	−	0.531374i
$263$	−10.9785	+	19.0154i	−0.676966	+	1.17254i	0.298924	+	0.954277i	$0.403372\pi$
$263$	−10.9785	+	19.0154i	−0.676966	+	1.17254i	−0.975890	+	0.218263i	$0.929961\pi$
$264$		0			0
$265$	−6.90678	−	3.32613i	−0.424280	−	0.204323i
$266$	6.73171	−	4.98446i	0.412748	−	0.305617i
$267$		0			0
$268$	−4.55892	−	3.10822i	−0.278481	−	0.189865i
$269$	19.9467	+	18.5079i	1.21617	+	1.12844i	0.987940	+	0.154838i	$0.0494856\pi$
$269$	19.9467	+	18.5079i	1.21617	+	1.12844i	0.228234	+	0.973606i	$0.426705\pi$
$270$		0			0
$271$	2.05651	+	1.40211i	0.124924	+	0.0851720i	0.624170	−	0.781288i	$-0.285437\pi$
$271$	2.05651	+	1.40211i	0.124924	+	0.0851720i	−0.499246	+	0.866460i	$0.666390\pi$
$272$	−0.988263	+	0.475922i	−0.0599222	+	0.0288570i
$273$		0			0
$274$	−7.66463	−	3.69109i	−0.463037	−	0.222987i
$275$	2.54921	+	4.41536i	0.153723	+	0.266256i
$276$		0			0
$277$	−2.92681	+	1.99546i	−0.175855	+	0.119896i	−0.648049	−	0.761599i	$-0.724415\pi$
$277$	−2.92681	+	1.99546i	−0.175855	+	0.119896i	0.472194	+	0.881495i	$0.343462\pi$
$278$	−9.78043	−	1.47416i	−0.586591	−	0.0884144i
$279$		0			0
$280$	−3.74327	+	10.7514i	−0.223703	+	0.642518i
$281$	2.54829	+	11.1648i	0.152018	+	0.666034i	0.992297	+	0.123880i	$0.0395339\pi$
$281$	2.54829	+	11.1648i	0.152018	+	0.666034i	−0.840279	+	0.542154i	$0.817609\pi$
$282$		0			0
$283$	−26.3880	−	8.13963i	−1.56860	−	0.483850i	−0.615920	−	0.787809i	$-0.711215\pi$
$283$	−26.3880	−	8.13963i	−1.56860	−	0.483850i	−0.952685	+	0.303959i	$0.901692\pi$
$284$	−6.93239	−	17.6634i	−0.411362	−	1.04813i
$285$		0			0
$286$	3.84982	+	4.82752i	0.227644	+	0.285457i
$287$	27.5666	−	1.07450i	1.62720	−	0.0634259i
$288$		0			0
$289$	0.00799793	−	0.0203784i	0.000470467	−	0.00119873i
$290$	0.210816	−	2.81314i	0.0123795	−	0.165193i
$291$		0			0
$292$	4.47092	−	4.14840i	0.261641	−	0.242767i
$293$	9.10545			0.531946			0.265973	−	0.963981i	$-0.414307\pi$
$293$	9.10545			0.531946			0.265973	+	0.963981i	$0.414307\pi$
$294$		0			0
$295$	−12.7555			−0.742655
$296$	20.9756	−	19.4625i	1.21918	−	1.13123i
$297$		0			0
$298$	−0.976988	+	13.0370i	−0.0565954	+	0.755213i
$299$	4.01903	−	10.2403i	0.232427	−	0.592213i
$300$		0			0
$301$	−5.45993	−	20.2504i	−0.314705	−	1.16721i
$302$	4.74964	+	5.95586i	0.273311	+	0.342721i
$303$		0			0
$304$	0.366170	+	0.932986i	0.0210013	+	0.0535104i
$305$	−3.92392	−	1.21037i	−0.224683	−	0.0693056i
$306$		0			0
$307$	−1.86877	−	8.18761i	−0.106656	−	0.467292i	−0.999845	−	0.0176095i	$-0.994394\pi$
$307$	−1.86877	−	8.18761i	−0.106656	−	0.467292i	0.893189	−	0.449682i	$-0.148463\pi$
$308$	3.60826	+	5.72270i	0.205600	+	0.326081i
$309$		0			0
$310$	1.08914	+	0.164161i	0.0618590	+	0.00932374i
$311$	−10.1115	+	6.89392i	−0.573372	+	0.390918i	−0.815009	−	0.579448i	$-0.803268\pi$
$311$	−10.1115	+	6.89392i	−0.573372	+	0.390918i	0.241637	+	0.970367i	$0.422316\pi$
$312$		0			0
$313$	−8.82627	−	15.2876i	−0.498890	−	0.864104i	0.501109	−	0.865384i	$-0.332926\pi$
$313$	−8.82627	−	15.2876i	−0.498890	−	0.864104i	−0.999999	+	0.00128070i	$0.999592\pi$
$314$	−16.4365	−	7.91542i	−0.927567	−	0.446693i
$315$		0			0
$316$	−16.6174	+	8.00254i	−0.934804	+	0.450178i
$317$	7.07629	+	4.82453i	0.397444	+	0.270973i	0.745506	−	0.666499i	$-0.232208\pi$
$317$	7.07629	+	4.82453i	0.397444	+	0.270973i	−0.348062	+	0.937471i	$0.613160\pi$
$318$		0			0
$319$	−3.12719	−	2.90161i	−0.175089	−	0.162459i
$320$	5.52900	+	3.76961i	0.309080	+	0.210728i
$321$		0			0
$322$	−3.05873	+	5.80930i	−0.170456	+	0.323739i
$323$	−14.0133	−	6.74843i	−0.779719	−	0.375493i
$324$		0			0
$325$	4.80554	−	8.32344i	0.266563	−	0.461701i
$326$	15.5191	−	10.5808i	0.859526	−	0.586015i
$327$		0			0
$328$	6.41991	−	28.1275i	0.354480	−	1.55308i
$329$	−0.500910	−	4.38426i	−0.0276161	−	0.241712i
$330$		0			0
$331$	−1.07459	−	14.3394i	−0.0590649	−	0.788166i	−0.945564	−	0.325436i	$-0.894489\pi$
$331$	−1.07459	−	14.3394i	−0.0590649	−	0.788166i	0.886499	−	0.462730i	$-0.153130\pi$
$332$	3.53968	+	1.09185i	0.194265	+	0.0599229i
$333$		0			0
$334$	−7.20001	+	2.22091i	−0.393967	+	0.121523i
$335$	4.13207	+	5.18145i	0.225759	+	0.283093i
$336$		0			0
$337$	−10.5880	+	13.2769i	−0.576765	+	0.723240i	−0.981557	−	0.191168i	$-0.938772\pi$
$337$	−10.5880	+	13.2769i	−0.576765	+	0.723240i	0.404792	+	0.914409i	$0.367344\pi$
$338$	0.263967	−	0.672577i	0.0143579	−	0.0365834i
$339$		0			0
$340$	8.21442	−	1.23812i	0.445490	−	0.0671467i
$341$	1.22098	−	1.13290i	0.0661197	−	0.0613502i
$342$		0			0
$343$	−17.5094	−	6.03504i	−0.945418	−	0.325861i
$344$	−21.9340			−1.18260
$345$		0			0
$346$	−5.59202	+	0.842861i	−0.300629	+	0.0453125i
$347$	−0.753056	+	10.0488i	−0.0404261	+	0.539449i	0.939820	+	0.341669i	$0.110992\pi$
$347$	−0.753056	+	10.0488i	−0.0404261	+	0.539449i	−0.980246	+	0.197780i	$0.936627\pi$
$348$		0			0
$349$	−11.5611	+	14.4972i	−0.618852	+	0.776015i	−0.988182	−	0.153283i	$-0.951016\pi$
$349$	−11.5611	+	14.4972i	−0.618852	+	0.776015i	0.369331	+	0.929298i	$0.379587\pi$
$350$	−3.39893	+	4.62045i	−0.181681	+	0.246973i
$351$		0			0
$352$	10.8647	−	3.35131i	0.579090	−	0.178626i
$353$	−3.68758	−	9.39580i	−0.196270	−	0.500088i	0.798528	−	0.601958i	$-0.205613\pi$
$353$	−3.68758	−	9.39580i	−0.196270	−	0.500088i	−0.994798	+	0.101870i	$0.967517\pi$
$354$		0			0
$355$	1.70318	+	22.7274i	0.0903955	+	1.20624i
$356$	−4.92165	−	21.5631i	−0.260847	−	1.14284i
$357$		0			0
$358$	−0.298886	+	1.30951i	−0.0157966	+	0.0692095i
$359$	−32.9820	−	4.97124i	−1.74072	−	0.262372i	−0.799625	−	0.600500i	$-0.794968\pi$
$359$	−32.9820	−	4.97124i	−1.74072	−	0.262372i	−0.941100	+	0.338128i	$0.890206\pi$
$360$		0			0
$361$	2.39406	−	4.14664i	0.126003	−	0.218244i
$362$	−7.74280	−	13.4109i	−0.406952	−	0.704862i
$363$		0			0
$364$	5.94161	−	11.2846i	0.311425	−	0.591475i
$365$	−6.60014	+	3.17846i	−0.345467	+	0.166368i
$366$		0			0
$367$	12.8909	+	11.9610i	0.672898	+	0.624358i	0.940750	−	0.339102i	$-0.110123\pi$
$367$	12.8909	+	11.9610i	0.672898	+	0.624358i	−0.267851	+	0.963460i	$0.586314\pi$
$368$	−0.575876	−	0.534335i	−0.0300196	−	0.0278542i
$369$		0			0
$370$	−12.1684	+	5.85998i	−0.632604	+	0.304646i
$371$	−9.89882	−	8.49180i	−0.513921	−	0.440872i
$372$		0			0
$373$	7.69839	+	13.3340i	0.398607	+	0.690408i	0.993554	−	0.113357i	$-0.0361603\pi$
$373$	7.69839	+	13.3340i	0.398607	+	0.690408i	−0.594947	+	0.803765i	$0.702827\pi$
$374$	−3.42135	+	5.92595i	−0.176914	+	0.306424i
$375$		0			0
$376$	−4.56331	−	0.687809i	−0.235335	−	0.0354710i
$377$	−1.78948	+	7.84022i	−0.0921628	+	0.403792i
$378$		0			0
$379$	−1.76360	−	7.72682i	−0.0905899	−	0.396900i	0.909222	−	0.416312i	$-0.136678\pi$
$379$	−1.76360	−	7.72682i	−0.0905899	−	0.396900i	−0.999812	+	0.0194121i	$0.993821\pi$
$380$	−0.567247	−	7.56939i	−0.0290992	−	0.388301i
$381$		0			0
$382$	−1.25524	−	3.19829i	−0.0642234	−	0.163639i
$383$	20.5400	−	6.33575i	1.04955	−	0.323742i	0.278443	−	0.960453i	$-0.410182\pi$
$383$	20.5400	−	6.33575i	1.04955	−	0.323742i	0.771103	+	0.636711i	$0.219706\pi$
$384$		0			0
$385$	−2.11534	−	7.84563i	−0.107808	−	0.399850i
$386$	−8.65173	+	10.8489i	−0.440361	+	0.552196i
$387$		0			0
$388$	−0.556218	+	7.42222i	−0.0282377	+	0.376806i
$389$	−9.44730	+	1.42395i	−0.478997	+	0.0721972i	−0.384103	−	0.923290i	$-0.625489\pi$
$389$	−9.44730	+	1.42395i	−0.478997	+	0.0721972i	−0.0948940	+	0.995487i	$0.530251\pi$
$390$		0			0
$391$	12.1910			0.616526
$392$	−10.8606	+	16.0368i	−0.548545	+	0.809982i
$393$		0			0
$394$	−6.87073	+	6.37511i	−0.346142	+	0.321173i
$395$	21.9057	−	3.30176i	1.10220	−	0.166129i
$396$		0			0
$397$	6.96208	−	17.7391i	0.349417	−	0.890300i	−0.642829	−	0.766010i	$-0.722239\pi$
$397$	6.96208	−	17.7391i	0.349417	−	0.890300i	0.992246	−	0.124290i	$-0.0396654\pi$
$398$	−3.77220	+	4.73019i	−0.189083	+	0.237103i
$399$		0			0
$400$	−0.427930	−	0.536608i	−0.0213965	−	0.0268304i
$401$	−30.9027	+	9.53221i	−1.54321	+	0.476016i	−0.945479	−	0.325684i	$-0.894405\pi$
$401$	−30.9027	+	9.53221i	−1.54321	+	0.476016i	−0.597727	+	0.801700i	$0.703929\pi$
$402$		0			0
$403$	−3.00036	−	0.925489i	−0.149459	−	0.0461019i
$404$	1.49204	+	19.9099i	0.0742316	+	0.990552i
$405$		0			0
$406$	1.57809	−	4.53257i	0.0783192	−	0.224948i
$407$	−4.54471	+	19.9117i	−0.225273	+	0.986985i
$408$		0			0
$409$	−11.6265	+	7.92678i	−0.574891	+	0.391954i	−0.815577	−	0.578649i	$-0.803580\pi$
$409$	−11.6265	+	7.92678i	−0.574891	+	0.391954i	0.240685	+	0.970603i	$0.422628\pi$
$410$	−6.80882	+	11.7932i	−0.336264	+	0.582426i
$411$		0			0
$412$	−12.0355	−	5.79599i	−0.592947	−	0.285548i
$413$	−20.9703	−	5.58397i	−1.03188	−	0.274769i
$414$		0			0
$415$	−3.67610	−	2.50632i	−0.180453	−	0.123030i
$416$	−15.7117	−	14.5784i	−0.770332	−	0.714763i
$417$		0			0
$418$	5.16600	+	3.52212i	0.252677	+	0.172273i
$419$	−0.877545	+	0.422604i	−0.0428709	+	0.0206455i	−0.455196	−	0.890391i	$-0.650431\pi$
$419$	−0.877545	+	0.422604i	−0.0428709	+	0.0206455i	0.412325	+	0.911037i	$0.364717\pi$
$420$		0			0
$421$	14.9287	+	7.18927i	0.727579	+	0.350384i	0.760731	−	0.649067i	$-0.224840\pi$
$421$	14.9287	+	7.18927i	0.727579	+	0.350384i	−0.0331525	+	0.999450i	$0.510555\pi$
$422$	1.04448	+	1.80909i	0.0508445	+	0.0880652i
$423$		0			0
$424$	−11.2694	+	7.68333i	−0.547289	+	0.373136i
$425$	10.5320	+	1.58744i	0.510877	+	0.0770023i
$426$		0			0
$427$	−5.92115	−	3.70764i	−0.286545	−	0.179425i
$428$	−4.28518	−	18.7746i	−0.207132	−	0.907505i
$429$		0			0
$430$	9.89295	+	3.05157i	0.477080	+	0.147160i
$431$	11.3514	+	28.9228i	0.546777	+	1.39316i	0.890883	+	0.454233i	$0.150087\pi$
$431$	11.3514	+	28.9228i	0.546777	+	1.39316i	−0.344106	+	0.938931i	$0.611818\pi$
$432$		0			0
$433$	5.99900	+	7.52251i	0.288294	+	0.361509i	0.904797	−	0.425844i	$-0.140023\pi$
$433$	5.99900	+	7.52251i	0.288294	+	0.361509i	−0.616503	+	0.787352i	$0.711451\pi$
$434$	1.71870	+	0.746676i	0.0825004	+	0.0358416i
$435$		0			0
$436$	5.68862	−	14.4944i	0.272436	−	0.694154i
$437$	0.832448	−	11.1082i	0.0398214	−	0.531379i
$438$		0			0
$439$	−5.85274	+	5.43055i	−0.279336	+	0.259186i	−0.807381	−	0.590030i	$-0.799116\pi$
$439$	−5.85274	+	5.43055i	−0.279336	+	0.259186i	0.528045	+	0.849216i	$0.322925\pi$
$440$	−8.49790			−0.405121
$441$		0			0
$442$	12.8992			0.613554
$443$	19.6223	−	18.2068i	0.932283	−	0.865032i	−0.0588014	−	0.998270i	$-0.518728\pi$
$443$	19.6223	−	18.2068i	0.932283	−	0.865032i	0.991084	+	0.133238i	$0.0425374\pi$
$444$		0			0
$445$	−1.98525	+	26.4914i	−0.0941101	+	1.25581i
$446$	0.424320	−	1.08115i	0.0200921	−	0.0511940i
$447$		0			0
$448$	7.43958	+	8.61774i	0.351487	+	0.407150i
$449$	13.3900	+	16.7905i	0.631912	+	0.792392i	0.989966	−	0.141309i	$-0.0451310\pi$
$449$	13.3900	+	16.7905i	0.631912	+	0.792392i	−0.358054	+	0.933701i	$0.616560\pi$
$450$		0			0
$451$	7.52338	+	19.1692i	0.354262	+	0.902645i
$452$	11.7797	+	3.63355i	0.554070	+	0.170908i
$453$		0			0
$454$	−2.51379	−	11.0136i	−0.117978	−	0.516896i
$455$	−10.8146	+	10.8483i	−0.506995	+	0.508578i
$456$		0			0
$457$	22.9968	+	3.46621i	1.07575	+	0.162142i	0.662937	−	0.748675i	$-0.269310\pi$
$457$	22.9968	+	3.46621i	1.07575	+	0.162142i	0.412808	+	0.910818i	$0.364548\pi$
$458$	−16.1100	+	10.9836i	−0.752770	+	0.513230i
$459$		0			0
$460$	2.97479	+	5.15249i	0.138701	+	0.240236i
$461$	−33.7233	−	16.2403i	−1.57065	−	0.756386i	−0.572663	−	0.819791i	$-0.694090\pi$
$461$	−33.7233	−	16.2403i	−1.57065	−	0.756386i	−0.997988	+	0.0634052i	$0.979804\pi$
$462$		0			0
$463$	1.58111	−	0.761424i	0.0734806	−	0.0353864i	−0.396783	−	0.917913i	$-0.629873\pi$
$463$	1.58111	−	0.761424i	0.0734806	−	0.0353864i	0.470263	+	0.882526i	$0.344159\pi$
$464$	0.474496	+	0.323506i	0.0220279	+	0.0150184i
$465$		0			0
$466$	−15.2035	−	14.1068i	−0.704289	−	0.653485i
$467$	13.6874	+	9.33192i	0.633378	+	0.431830i	0.836987	−	0.547222i	$-0.184315\pi$
$467$	13.6874	+	9.33192i	0.633378	+	0.431830i	−0.203609	+	0.979052i	$0.565267\pi$
$468$		0			0
$469$	4.52493	+	10.3273i	0.208942	+	0.476870i
$470$	1.96251	+	0.945095i	0.0905239	+	0.0435940i
$471$		0			0
$472$	−11.3474	+	19.6543i	−0.522307	+	0.904662i
$473$	12.9354	−	8.81920i	0.594770	−	0.405507i
$474$		0			0
$475$	2.16562	−	9.48819i	0.0993653	−	0.435348i
$476$	14.0467	+	1.56051i	0.643829	+	0.0715259i
$477$		0			0
$478$	0.238825	+	3.18689i	0.0109236	+	0.145765i
$479$	−24.2816	−	7.48988i	−1.10945	−	0.342221i	−0.314723	−	0.949183i	$-0.601912\pi$
$479$	−24.2816	−	7.48988i	−1.10945	−	0.342221i	−0.794731	+	0.606962i	$0.792388\pi$
$480$		0			0
$481$	36.7905	−	11.3484i	1.67750	−	0.517441i
$482$	6.53845	+	8.19896i	0.297818	+	0.373452i
$483$		0			0
$484$	5.73129	−	7.18681i	0.260513	−	0.326673i
$485$	3.26610	−	8.32189i	0.148306	−	0.377878i
$486$		0			0
$487$	11.7884	−	1.77681i	0.534183	−	0.0805151i	0.123589	−	0.992333i	$-0.460560\pi$
$487$	11.7884	−	1.77681i	0.534183	−	0.0805151i	0.410594	+	0.911818i	$0.365321\pi$
$488$	−5.35574	+	4.96940i	−0.242443	+	0.224954i
$489$		0			0
$490$	7.12962	−	5.72214i	0.322084	−	0.258500i
$491$	−2.54465			−0.114838			−0.0574191	−	0.998350i	$-0.518287\pi$
$491$	−2.54465			−0.114838			−0.0574191	+	0.998350i	$0.518287\pi$
$492$		0			0
$493$	−8.81240	+	1.32826i	−0.396891	+	0.0598216i
$494$	0.880807	−	11.7536i	0.0396294	−	0.528818i
$495$		0			0
$496$	−0.139801	+	0.175305i	−0.00627726	+	0.00787143i
$497$	−7.14927	+	38.1099i	−0.320689	+	1.70946i
$498$		0			0
$499$	−31.2286	+	9.63275i	−1.39798	+	0.431221i	−0.899971	−	0.435949i	$-0.856413\pi$
$499$	−31.2286	+	9.63275i	−1.39798	+	0.431221i	−0.498012	+	0.867170i	$0.665937\pi$
$500$	5.57711	+	14.2102i	0.249416	+	0.635501i
$501$		0			0
$502$	−0.295954	−	3.94923i	−0.0132091	−	0.176263i
$503$	1.75120	+	7.67250i	0.0780821	+	0.342100i	0.998846	−	0.0480193i	$-0.0152909\pi$
$503$	1.75120	+	7.67250i	0.0780821	+	0.342100i	−0.920764	+	0.390119i	$0.872434\pi$
$504$		0			0
$505$	5.33625	−	23.3796i	0.237460	−	1.04038i
$506$	−4.84598	−	0.730413i	−0.215430	−	0.0324708i
$507$		0			0
$508$	1.73896	−	3.01198i	0.0771541	−	0.133635i
$509$	−6.85394	−	11.8714i	−0.303795	−	0.526189i	0.673197	−	0.739463i	$-0.264921\pi$
$509$	−6.85394	−	11.8714i	−0.303795	−	0.526189i	−0.976992	+	0.213274i	$0.931587\pi$
$510$		0			0
$511$	−12.2422	+	2.33612i	−0.541563	+	0.103344i
$512$	−2.70456	+	1.30245i	−0.119526	+	0.0575606i
$513$		0			0
$514$	−3.14719	−	2.92017i	−0.138817	−	0.128803i
$515$	11.7617	+	10.9133i	0.518283	+	0.480896i
$516$		0			0
$517$	2.96773	−	1.42918i	0.130521	−	0.0628554i
$518$	−22.5704	+	4.30700i	−0.991686	+	0.189239i
$519$		0			0
$520$	8.00973	+	13.8733i	0.351250	+	0.608383i
$521$	10.4713	−	18.1368i	0.458756	−	0.794589i	−0.540140	−	0.841575i	$-0.681629\pi$
$521$	10.4713	−	18.1368i	0.458756	−	0.794589i	0.998896	+	0.0469869i	$0.0149619\pi$
$522$		0			0
$523$	−31.2960	−	4.71711i	−1.36848	−	0.206265i	−0.576640	−	0.816998i	$-0.695637\pi$
$523$	−31.2960	−	4.71711i	−1.36848	−	0.206265i	−0.791836	+	0.610734i	$0.790875\pi$
$524$	5.23816	−	22.9499i	0.228830	−	1.00257i
$525$		0			0
$526$	−4.10316	−	17.9771i	−0.178906	−	0.783839i
$527$	−0.260029	−	3.46985i	−0.0113271	−	0.151149i
$528$		0			0
$529$	−5.21299	−	13.2825i	−0.226652	−	0.577500i
$530$	6.15180	−	1.89758i	0.267217	−	0.0824256i
$531$		0			0
$532$	2.38107	−	12.6926i	0.103233	−	0.550292i
$533$	24.2036	−	30.3504i	1.04837	−	1.31462i
$534$		0			0
$535$	−1.72852	+	23.0655i	−0.0747306	+	0.997211i
$536$	11.6597	−	1.75742i	0.503624	−	0.0759090i
$537$		0			0
$538$	−22.8512			−0.985186
$539$	−0.0431009	−	13.8244i	−0.00185649	−	0.595460i
$540$		0			0
$541$	15.5052	−	14.3867i	0.666620	−	0.618533i	−0.272486	−	0.962160i	$-0.587846\pi$
$541$	15.5052	−	14.3867i	0.666620	−	0.618533i	0.939106	+	0.343626i	$0.111655\pi$
$542$	−2.06691	+	0.311536i	−0.0887812	+	0.0133816i
$543$		0			0
$544$	8.67771	−	22.1104i	0.372054	−	0.947977i
$545$	−11.6606	+	14.6219i	−0.499483	+	0.626332i
$546$		0			0
$547$	26.8397	+	33.6560i	1.14758	+	1.43903i	0.879671	+	0.475583i	$0.157763\pi$
$547$	26.8397	+	33.6560i	1.14758	+	1.43903i	0.267914	+	0.963443i	$0.413666\pi$
$548$	−12.5331	+	3.86594i	−0.535386	+	0.165145i
$549$		0			0
$550$	−4.09140	−	1.26203i	−0.174458	−	0.0538132i
$551$	0.608541	+	8.12041i	0.0259247	+	0.345941i
$552$		0			0
$553$	37.4589	+	4.16148i	1.59291	+	0.176964i
$554$	0.661960	−	2.90024i	0.0281240	−	0.123219i
$555$		0			0
$556$	−12.5995	+	8.59021i	−0.534339	+	0.364306i
$557$	14.3910	−	24.9260i	0.609767	−	1.05615i	−0.381512	−	0.924364i	$-0.624597\pi$
$557$	14.3910	−	24.9260i	0.609767	−	1.05615i	0.991279	−	0.131783i	$-0.0420702\pi$
$558$		0			0
$559$	−26.5901	−	12.8051i	−1.12464	−	0.541599i
$560$	0.439001	+	1.00194i	0.0185512	+	0.0423395i
$561$		0			0
$562$	−7.94613	−	5.41758i	−0.335187	−	0.228527i
$563$	−10.9502	−	10.1603i	−0.461495	−	0.428205i	0.414849	−	0.909890i	$-0.363834\pi$
$563$	−10.9502	−	10.1603i	−0.461495	−	0.428205i	−0.876344	+	0.481685i	$0.840025\pi$
$564$		0			0
$565$	−12.2337	−	8.34078i	−0.514675	−	0.350899i
$566$	20.8942	−	10.0621i	0.878248	−	0.422942i
$567$		0			0
$568$	36.5346	+	17.5941i	1.53296	+	0.738233i
$569$	−15.8714	−	27.4901i	−0.665365	−	1.15245i	−0.979186	−	0.202964i	$-0.934942\pi$
$569$	−15.8714	−	27.4901i	−0.665365	−	1.15245i	0.313821	−	0.949482i	$-0.398391\pi$
$570$		0			0
$571$	−19.3732	+	13.2084i	−0.810743	+	0.552755i	−0.896233	−	0.443584i	$-0.853707\pi$
$571$	−19.3732	+	13.2084i	−0.810743	+	0.552755i	0.0854898	+	0.996339i	$0.472754\pi$
$572$	9.41337	+	1.41884i	0.393593	+	0.0593245i
$573$		0			0
$574$	−16.3566	+	16.4076i	−0.682709	+	0.684841i
$575$	1.69743	+	7.43693i	0.0707877	+	0.310141i
$576$		0			0
$577$	−29.8886	−	9.21941i	−1.24428	−	0.383809i	−0.398414	−	0.917206i	$-0.630439\pi$
$577$	−29.8886	−	9.21941i	−1.24428	−	0.383809i	−0.845865	+	0.533397i	$0.820915\pi$
$578$	0.00671661	+	0.0171137i	0.000279374	+	0.000711834i
$579$		0			0
$580$	−2.71174	−	3.40042i	−0.112599	−	0.141195i
$581$	−4.94639	−	5.72972i	−0.205211	−	0.237709i
$582$		0			0
$583$	3.55672	−	9.06236i	0.147304	−	0.375325i
$584$	−0.974018	+	12.9974i	−0.0403052	+	0.537835i
$585$		0			0
$586$	−5.60542	+	5.20107i	−0.231558	+	0.214854i
$587$	11.4659			0.473249			0.236624	−	0.971601i	$-0.423959\pi$
$587$	11.4659			0.473249			0.236624	+	0.971601i	$0.423959\pi$
$588$		0			0
$589$	−3.17942			−0.131006
$590$	7.85245	−	7.28601i	0.323280	−	0.299960i
$591$		0			0
$592$	0.205465	−	2.74174i	0.00844457	−	0.112685i
$593$	14.6960	−	37.4448i	0.603492	−	1.53767i	−0.223056	−	0.974806i	$-0.571603\pi$
$593$	14.6960	−	37.4448i	0.603492	−	1.53767i	0.826548	−	0.562866i	$-0.190301\pi$
$594$		0			0
$595$	−15.5695	−	6.76405i	−0.638289	−	0.277299i
$596$	12.5671	+	15.7587i	0.514769	+	0.645500i
$597$		0			0
$598$	3.37516	+	8.59976i	0.138020	+	0.351670i
$599$	37.5322	+	11.5772i	1.53352	+	0.473030i	0.942664	−	0.333744i	$-0.108312\pi$
$599$	37.5322	+	11.5772i	1.53352	+	0.473030i	0.590860	+	0.806774i	$0.298788\pi$
$600$		0			0
$601$	3.03965	+	13.3176i	0.123990	+	0.543235i	0.998322	+	0.0579072i	$0.0184427\pi$
$601$	3.03965	+	13.3176i	0.123990	+	0.543235i	−0.874332	+	0.485328i	$0.838700\pi$
$602$	14.9283	+	9.34767i	0.608433	+	0.380982i
$603$		0			0
$604$	11.6136	+	1.75046i	0.472549	+	0.0712254i
$605$	−9.12241	+	6.21956i	−0.370879	+	0.252861i
$606$		0			0
$607$	−0.983647	−	1.70373i	−0.0399250	−	0.0691521i	0.845372	−	0.534177i	$-0.179379\pi$
$607$	−0.983647	−	1.70373i	−0.0399250	−	0.0691521i	−0.885297	+	0.465025i	$0.846045\pi$
$608$	−19.5541	−	9.41676i	−0.793024	−	0.381900i
$609$		0			0
$610$	3.10698	−	1.49624i	0.125798	−	0.0605812i
$611$	−5.13046	−	3.49789i	−0.207556	−	0.141509i
$612$		0			0
$613$	23.3975	+	21.7098i	0.945018	+	0.876849i	0.992527	−	0.122022i	$-0.0389379\pi$
$613$	23.3975	+	21.7098i	0.945018	+	0.876849i	−0.0475092	+	0.998871i	$0.515128\pi$
$614$	5.82724	+	3.97294i	0.235168	+	0.160335i
$615$		0			0
$616$	−13.9707	−	3.72011i	−0.562897	−	0.149888i
$617$	27.3475	+	13.1699i	1.10097	+	0.530199i	0.893963	−	0.448141i	$-0.147914\pi$
$617$	27.3475	+	13.1699i	1.10097	+	0.530199i	0.207006	+	0.978340i	$0.433628\pi$
$618$		0			0
$619$	6.39508	−	11.0766i	0.257040	−	0.445206i	−0.708408	−	0.705803i	$-0.750586\pi$
$619$	6.39508	−	11.0766i	0.257040	−	0.445206i	0.965448	+	0.260597i	$0.0839195\pi$
$620$	1.40307	−	0.956597i	0.0563487	−	0.0384179i
$621$		0			0
$622$	2.28694	−	10.0197i	0.0916979	−	0.401755i
$623$	−14.8609	+	42.6833i	−0.595389	+	1.71007i
$624$		0			0
$625$	−0.405603	−	5.41240i	−0.0162241	−	0.216496i
$626$	14.1659	+	4.36960i	0.566183	+	0.174644i
$627$		0			0
$628$	−26.8767	+	8.29038i	−1.07250	+	0.330822i
$629$	26.6022	+	33.3581i	1.06070	+	1.33007i
$630$		0			0
$631$	7.37543	−	9.24849i	0.293611	−	0.368177i	−0.613044	−	0.790048i	$-0.710055\pi$
$631$	7.37543	−	9.24849i	0.293611	−	0.368177i	0.906655	+	0.421872i	$0.138627\pi$
$632$	14.4000	−	36.6906i	0.572801	−	1.45947i
$633$		0			0
$634$	−7.11205	+	1.07197i	−0.282456	+	0.0425733i
$635$	−3.06222	+	2.84133i	−0.121521	+	0.112755i
$636$		0			0
$637$	−22.5285	+	13.1006i	−0.892610	+	0.519066i
$638$	3.58255			0.141834
$639$		0			0
$640$	12.1491	−	1.83118i	0.480234	−	0.0723837i
$641$	−1.39350	+	18.5950i	−0.0550400	+	0.734458i	0.899604	+	0.436707i	$0.143855\pi$
$641$	−1.39350	+	18.5950i	−0.0550400	+	0.734458i	−0.954644	+	0.297751i	$0.903764\pi$
$642$		0			0
$643$	28.5454	−	35.7948i	1.12572	−	1.41161i	0.226558	−	0.973998i	$-0.427253\pi$
$643$	28.5454	−	35.7948i	1.12572	−	1.41161i	0.899164	−	0.437612i	$-0.144176\pi$
$644$	2.63503	+	9.77308i	0.103835	+	0.385113i
$645$		0			0
$646$	12.4815	−	3.85002i	0.491077	−	0.151477i
$647$	−4.81750	−	12.2748i	−0.189395	−	0.482572i	0.804361	−	0.594140i	$-0.202508\pi$
$647$	−4.81750	−	12.2748i	−0.189395	−	0.482572i	−0.993757	+	0.111569i	$0.964412\pi$
$648$		0			0
$649$	−1.21054	−	16.1535i	−0.0475178	−	0.634081i
$650$	1.79604	+	7.86896i	0.0704464	+	0.308646i
$651$		0			0
$652$	6.44385	−	28.2323i	0.252361	−	1.10566i
$653$	−18.5750	−	2.79974i	−0.726897	−	0.109562i	−0.224839	−	0.974396i	$-0.572186\pi$
$653$	−18.5750	−	2.79974i	−0.726897	−	0.109562i	−0.502058	+	0.864834i	$0.667424\pi$
$654$		0			0
$655$	−14.1371	+	24.4861i	−0.552381	+	0.956751i
$656$	−1.38609	−	2.40078i	−0.0541178	−	0.0937348i
$657$		0			0
$658$	2.81268	+	2.41288i	0.109650	+	0.0940639i
$659$	20.8237	−	10.0282i	0.811175	−	0.390641i	0.0181538	−	0.999835i	$-0.494221\pi$
$659$	20.8237	−	10.0282i	0.811175	−	0.390641i	0.793021	+	0.609194i	$0.208507\pi$
$660$		0			0
$661$	2.34575	+	2.17653i	0.0912390	+	0.0846574i	0.724474	−	0.689302i	$-0.242083\pi$
$661$	2.34575	+	2.17653i	0.0912390	+	0.0846574i	−0.633235	+	0.773960i	$0.718273\pi$
$662$	8.85227	+	8.21371i	0.344053	+	0.319235i
$663$		0			0
$664$	−7.13214	+	3.43466i	−0.276781	+	0.133290i
$665$	−7.22644	+	13.7248i	−0.280229	+	0.532226i
$666$		0			0
$667$	−3.19135	−	5.52758i	−0.123570	−	0.214029i
$668$	−5.80834	+	10.0603i	−0.224731	+	0.389246i
$669$		0			0
$670$	−5.50342	−	0.829507i	−0.212616	−	0.0320466i
$671$	1.16041	−	5.08410i	0.0447972	−	0.196269i
$672$		0			0
$673$	8.58427	+	37.6101i	0.330899	+	1.44976i	0.817393	+	0.576080i	$0.195418\pi$
$673$	8.58427	+	37.6101i	0.330899	+	1.44976i	−0.486494	+	0.873684i	$0.661725\pi$
$674$	−1.06574	−	14.2213i	−0.0410509	−	0.547786i
$675$		0			0
$676$	−0.406970	−	1.03694i	−0.0156527	−	0.0398824i
$677$	29.7041	−	9.16251i	1.14162	−	0.352144i	0.334423	−	0.942423i	$-0.391458\pi$
$677$	29.7041	−	9.16251i	1.14162	−	0.352144i	0.807199	+	0.590279i	$0.200982\pi$
$678$		0			0
$679$	9.01260	−	12.2516i	0.345872	−	0.470172i
$680$	−11.0686	+	13.8796i	−0.424463	+	0.532259i
$681$		0			0
$682$	−0.104530	+	1.39486i	−0.00400267	+	0.0534119i
$683$	−24.5906	+	3.70644i	−0.940935	+	0.141823i	−0.601560	−	0.798828i	$-0.705454\pi$
$683$	−24.5906	+	3.70644i	−0.940935	+	0.141823i	−0.339375	+	0.940651i	$0.610216\pi$
$684$		0			0
$685$	15.7534			0.601908
$686$	14.2262	−	6.28620i	0.543160	−	0.240008i
$687$		0			0
$688$	−1.54496	+	1.43351i	−0.0589010	+	0.0546521i
$689$	−18.1472	+	2.73525i	−0.691352	+	0.104205i
$690$		0			0
$691$	6.31090	−	16.0799i	0.240078	−	0.611709i	−0.759153	−	0.650912i	$-0.774387\pi$
$691$	6.31090	−	16.0799i	0.240078	−	0.611709i	0.999231	+	0.0392032i	$0.0124820\pi$
$692$	−5.43611	+	6.81666i	−0.206650	+	0.259131i
$693$		0			0
$694$	−5.27635	−	6.61633i	−0.200287	−	0.251152i
$695$	17.5022	−	5.39872i	0.663897	−	0.204785i
$696$		0			0
$697$	41.1085	+	12.6803i	1.55709	+	0.480300i
$698$	−1.16369	−	15.5284i	−0.0440464	−	0.587758i
$699$		0			0
$700$	1.00384	+	8.78623i	0.0379417	+	0.332088i
$701$	0.845137	−	3.70279i	0.0319204	−	0.139852i	−0.956457	−	0.291874i	$-0.905721\pi$
$701$	0.845137	−	3.70279i	0.0319204	−	0.139852i	0.988377	+	0.152022i	$0.0485784\pi$
$702$		0			0
$703$	32.2118	−	21.9617i	1.21489	−	0.828300i
$704$	−4.24909	+	7.35964i	−0.160144	+	0.277377i
$705$		0			0
$706$	7.63705	+	3.67781i	0.287424	+	0.138416i
$707$	19.0078	−	36.1006i	0.714861	−	1.35770i
$708$		0			0
$709$	−10.6425	−	7.25595i	−0.399688	−	0.272503i	0.346750	−	0.937958i	$-0.387285\pi$
$709$	−10.6425	−	7.25595i	−0.399688	−	0.272503i	−0.746438	+	0.665455i	$0.768238\pi$
$710$	−14.0305	−	13.0184i	−0.526555	−	0.488572i
$711$		0			0
$712$	39.0530	+	26.6259i	1.46357	+	0.997848i
$713$	2.24527	−	1.08126i	0.0840860	−	0.0404937i
$714$		0			0
$715$	−10.3018	−	4.96110i	−0.385266	−	0.185534i
$716$	1.03542	+	1.79340i	0.0386955	+	0.0670226i
$717$		0			0
$718$	23.1437	−	15.7791i	0.863716	−	0.588872i
$719$	−1.98391	−	0.299027i	−0.0739874	−	0.0111518i	0.111944	−	0.993714i	$-0.464292\pi$
$719$	−1.98391	−	0.299027i	−0.0739874	−	0.0111518i	−0.185932	+	0.982563i	$0.559530\pi$
$720$		0			0
$721$	14.5590	+	23.0906i	0.542206	+	0.859937i
$722$	0.894765	+	3.92022i	0.0332997	+	0.145895i
$723$		0			0
$724$	−22.8141	−	7.03723i	−0.847881	−	0.261537i
$725$	−2.03729	−	5.19092i	−0.0756629	−	0.192786i
$726$		0			0
$727$	0.721824	+	0.905139i	0.0267710	+	0.0335698i	0.795037	−	0.606561i	$-0.207452\pi$
$727$	0.721824	+	0.905139i	0.0267710	+	0.0335698i	−0.768266	+	0.640131i	$0.778880\pi$
$728$	7.09489	+	26.3143i	0.262954	+	0.975275i
$729$		0			0
$730$	2.24757	−	5.72673i	0.0831865	−	0.211956i
$731$	2.44412	−	32.6145i	0.0903991	−	1.20629i
$732$		0			0
$733$	−13.0295	+	12.0896i	−0.481257	+	0.446541i	−0.883112	−	0.469162i	$-0.844556\pi$
$733$	−13.0295	+	12.0896i	−0.481257	+	0.446541i	0.401855	+	0.915703i	$0.368365\pi$
$734$	−14.7680			−0.545095
$735$		0			0
$736$	17.0113			0.627046
$737$	−6.16961	+	5.72456i	−0.227260	+	0.210867i
$738$		0			0
$739$	0.928510	−	12.3901i	0.0341558	−	0.455778i	−0.953737	−	0.300641i	$-0.902799\pi$
$739$	0.928510	−	12.3901i	0.0341558	−	0.455778i	0.987893	−	0.155136i	$-0.0495816\pi$
$740$	−7.60736	+	19.3832i	−0.279652	+	0.712542i
$741$		0			0
$742$	10.9444	−	0.426596i	0.401781	−	0.0156608i
$743$	−17.9412	−	22.4975i	−0.658198	−	0.825354i	0.334948	−	0.942237i	$-0.391281\pi$
$743$	−17.9412	−	22.4975i	−0.658198	−	0.825354i	−0.993146	+	0.116883i	$0.962710\pi$
$744$		0			0
$745$	−8.84476	−	22.5361i	−0.324047	−	0.825658i
$746$	−12.3557	−	3.81122i	−0.452373	−	0.139539i
$747$		0			0
$748$	2.34753	+	10.2852i	0.0858341	+	0.376064i
$749$	−12.9391	+	37.1636i	−0.472784	+	1.35793i
$750$		0			0
$751$	−37.6333	−	5.67231i	−1.37326	−	0.206985i	−0.579378	−	0.815059i	$-0.696704\pi$
$751$	−37.6333	−	5.67231i	−1.37326	−	0.206985i	−0.793881	+	0.608074i	$0.791943\pi$
$752$	−0.366377	+	0.249791i	−0.0133604	+	0.00910896i
$753$		0			0
$754$	−3.37674	−	5.84869i	−0.122974	−	0.212997i
$755$	−12.7097	−	6.12066i	−0.462553	−	0.222754i
$756$		0			0
$757$	4.08887	−	1.96910i	0.148613	−	0.0715681i	−0.358099	−	0.933684i	$-0.616575\pi$
$757$	4.08887	−	1.96910i	0.148613	−	0.0715681i	0.506712	+	0.862115i	$0.330861\pi$
$758$	5.49929	+	3.74935i	0.199743	+	0.136183i
$759$		0			0
$760$	11.8911	+	11.0333i	0.431335	+	0.400220i
$761$	9.54330	+	6.50651i	0.345944	+	0.235861i	0.723810	−	0.690000i	$-0.242389\pi$
$761$	9.54330	+	6.50651i	0.345944	+	0.235861i	−0.377865	+	0.925861i	$0.623342\pi$
$762$		0			0
$763$	−25.5712	+	18.9340i	−0.925739	+	0.685458i
$764$	−4.77253	−	2.29833i	−0.172664	−	0.0831507i
$765$		0			0
$766$	−9.02567	+	15.6329i	−0.326111	+	0.564840i
$767$	−25.2304	+	17.2018i	−0.911018	+	0.621122i
$768$		0			0
$769$	−1.66942	+	7.31422i	−0.0602009	+	0.263757i	−0.996068	−	0.0885969i	$-0.971762\pi$
$769$	−1.66942	+	7.31422i	−0.0602009	+	0.263757i	0.935867	+	0.352354i	$0.114619\pi$
$770$	5.78369	+	3.62157i	0.208430	+	0.130512i
$771$		0			0
$772$	1.59875	+	21.3339i	0.0575404	+	0.767823i
$773$	−13.2902	−	4.09949i	−0.478016	−	0.147448i	0.0463783	−	0.998924i	$-0.485232\pi$
$773$	−13.2902	−	4.09949i	−0.478016	−	0.147448i	−0.524394	+	0.851476i	$0.675708\pi$
$774$		0			0
$775$	2.08052	−	0.641755i	0.0747344	−	0.0230525i
$776$	−9.91720	−	12.4358i	−0.356007	−	0.446418i
$777$		0			0
$778$	5.00251	−	6.27294i	0.179349	−	0.224896i
$779$	14.3611	−	36.5915i	0.514540	−	1.31103i
$780$		0			0
$781$	−28.6202	+	4.31380i	−1.02411	+	0.154360i
$782$	−7.50494	+	6.96356i	−0.268376	+	0.249017i
$783$		0			0
$784$	0.283110	+	1.83938i	0.0101111	+	0.0656923i
$785$	33.7827			1.20576
$786$		0			0
$787$	10.0787	−	1.51913i	0.359268	−	0.0541510i	0.0330718	−	0.999453i	$-0.489471\pi$
$787$	10.0787	−	1.51913i	0.359268	−	0.0541510i	0.326196	+	0.945302i	$0.394233\pi$
$788$	−1.07988	+	14.4100i	−0.0384692	+	0.513336i
$789$		0			0
$790$	−11.5995	+	14.5453i	−0.412690	+	0.517497i
$791$	−16.4611	−	19.0679i	−0.585289	−	0.677978i
$792$		0			0
$793$	−9.39380	+	2.89760i	−0.333584	+	0.102897i
$794$	5.84671	+	14.8972i	0.207492	+	0.528681i
$795$		0			0
$796$	0.697065	+	9.30169i	0.0247068	+	0.329690i
$797$	−9.94651	−	43.5785i	−0.352324	−	1.54363i	−0.771801	−	0.635865i	$-0.780644\pi$
$797$	−9.94651	−	43.5785i	−0.352324	−	1.54363i	0.419477	−	0.907766i	$-0.362213\pi$
$798$		0			0
$799$	1.53122	−	6.70872i	0.0541708	−	0.237338i
$800$	14.6964	+	2.21512i	0.519595	+	0.0783163i
$801$		0			0
$802$	13.5792	−	23.5199i	0.479499	−	0.830516i
$803$	−4.65155	−	8.05672i	−0.164150	−	0.284316i
$804$		0			0
$805$	0.435651	−	12.1499i	0.0153547	−	0.428227i
$806$	2.37570	−	1.14408i	0.0836806	−	0.0402984i
$807$		0			0
$808$	−31.2772	−	29.0210i	−1.10033	−	1.02096i
$809$	−11.1385	−	10.3350i	−0.391608	−	0.363359i	0.459656	−	0.888097i	$-0.347973\pi$
$809$	−11.1385	−	10.3350i	−0.391608	−	0.363359i	−0.851264	+	0.524738i	$0.824163\pi$
$810$		0			0
$811$	33.3462	−	16.0587i	1.17094	−	0.563896i	0.255682	−	0.966761i	$-0.417700\pi$
$811$	33.3462	−	16.0587i	1.17094	−	0.563896i	0.915259	+	0.402865i	$0.131986\pi$
$812$	−2.96957	−	6.77748i	−0.104211	−	0.237843i
$813$		0			0
$814$	−8.57586	−	14.8538i	−0.300584	−	0.520626i
$815$	−17.3910	+	30.1222i	−0.609182	+	1.05513i
$816$		0			0
$817$	−29.5509	−	4.45408i	−1.03386	−	0.155829i
$818$	2.62957	−	11.5209i	0.0919408	−	0.402819i
$819$		0			0
$820$	4.67181	+	20.4685i	0.163147	+	0.714793i
$821$	2.80605	+	37.4441i	0.0979318	+	1.30681i	0.802277	+	0.596951i	$0.203621\pi$
$821$	2.80605	+	37.4441i	0.0979318	+	1.30681i	−0.704346	+	0.709857i	$0.748759\pi$
$822$		0			0
$823$	18.7334	+	47.7319i	0.653005	+	1.66383i	0.744167	+	0.667993i	$0.232847\pi$
$823$	18.7334	+	47.7319i	0.653005	+	1.66383i	−0.0911622	+	0.995836i	$0.529058\pi$
$824$	27.2790	−	8.41445i	0.950308	−	0.293131i
$825$		0			0
$826$	16.0992	−	8.54080i	0.560162	−	0.297173i
$827$	27.0513	−	33.9212i	0.940664	−	1.17956i	−0.0429148	−	0.999079i	$-0.513664\pi$
$827$	27.0513	−	33.9212i	0.940664	−	1.17956i	0.983579	−	0.180477i	$-0.0577642\pi$
$828$		0			0
$829$	3.29360	−	43.9500i	0.114391	−	1.52645i	−0.584603	−	0.811320i	$-0.698750\pi$
$829$	3.29360	−	43.9500i	0.114391	−	1.52645i	0.698994	−	0.715128i	$-0.253631\pi$
$830$	3.69467	−	0.556882i	0.128244	−	0.0193297i
$831$		0			0
$832$	16.0200			0.555393
$833$	−22.6356	−	17.9361i	−0.784276	−	0.621449i
$834$		0			0
$835$	10.2282	−	9.49036i	0.353960	−	0.328427i
$836$	9.53199	−	1.43672i	0.329671	−	0.0496899i
$837$		0			0
$838$	0.298834	−	0.761418i	0.0103231	−	0.0263027i
$839$	−15.6386	+	19.6102i	−0.539905	+	0.677019i	−0.974702	−	0.223509i	$-0.928249\pi$
$839$	−15.6386	+	19.6102i	−0.539905	+	0.677019i	0.434797	+	0.900529i	$0.356820\pi$
$840$		0			0
$841$	−15.1721	−	19.0252i	−0.523174	−	0.656040i
$842$	−13.2968	+	4.10152i	−0.458239	+	0.141348i
$843$		0			0
$844$	3.07756	+	0.949301i	0.105934	+	0.0326763i
$845$	0.0999863	+	1.33422i	0.00343963	+	0.0458987i
$846$		0			0
$847$	−17.7202	+	6.23158i	−0.608872	+	0.214120i
$848$	−0.291628	+	1.27771i	−0.0100146	+	0.0438766i
$849$		0			0
$850$	−7.39038	+	5.03868i	−0.253488	+	0.172825i
$851$	−15.2788	+	26.4637i	−0.523752	+	0.907165i
$852$		0			0
$853$	−19.1929	−	9.24280i	−0.657151	−	0.316467i	0.0754259	−	0.997151i	$-0.475968\pi$
$853$	−19.1929	−	9.24280i	−0.657151	−	0.316467i	−0.732577	+	0.680684i	$0.761683\pi$
$854$	5.76296	−	1.09972i	0.197204	−	0.0376316i
$855$		0			0
$856$	34.0027	+	23.1827i	1.16219	+	0.792367i
$857$	11.5022	+	10.6724i	0.392906	+	0.364564i	0.851746	−	0.523955i	$-0.175544\pi$
$857$	11.5022	+	10.6724i	0.392906	+	0.364564i	−0.458839	+	0.888519i	$0.651735\pi$
$858$		0			0
$859$	14.9195	+	10.1720i	0.509047	+	0.347062i	0.790449	−	0.612527i	$-0.209847\pi$
$859$	14.9195	+	10.1720i	0.509047	+	0.347062i	−0.281402	+	0.959590i	$0.590799\pi$
$860$	14.3808	−	6.92544i	0.490382	−	0.236156i
$861$		0			0
$862$	−23.5089	−	11.3213i	−0.800717	−	0.385605i
$863$	19.5951	+	33.9397i	0.667026	+	1.15532i	0.978732	+	0.205144i	$0.0657662\pi$
$863$	19.5951	+	33.9397i	0.667026	+	1.15532i	−0.311706	+	0.950179i	$0.600900\pi$
$864$		0			0
$865$	8.65258	−	5.89923i	0.294197	−	0.200580i
$866$	−7.98995	−	1.20429i	−0.271510	−	0.0409235i
$867$		0			0
$868$	2.72545	−	0.958446i	0.0925076	−	0.0325318i
$869$	6.26024	+	27.4279i	0.212364	+	0.930429i
$870$		0			0
$871$	15.1608	+	4.67650i	0.513705	+	0.158457i
$872$	12.1567	+	30.9748i	0.411679	+	1.04894i
$873$		0			0
$874$	5.83262	+	7.31387i	0.197291	+	0.247395i
$875$	5.75159	−	30.6594i	0.194439	−	1.03648i
$876$		0			0
$877$	−12.2633	+	31.2463i	−0.414102	+	1.05511i	0.559897	+	0.828562i	$0.310841\pi$
$877$	−12.2633	+	31.2463i	−0.414102	+	1.05511i	−0.973999	+	0.226552i	$0.927255\pi$
$878$	0.501063	−	6.68622i	0.0169101	−	0.225649i
$879$		0			0
$880$	−0.598564	+	0.555386i	−0.0201776	+	0.0187221i
$881$	−4.10302			−0.138234			−0.0691171	−	0.997609i	$-0.522018\pi$
$881$	−4.10302			−0.138234			−0.0691171	+	0.997609i	$0.522018\pi$
$882$		0			0
$883$	8.81326			0.296590			0.148295	−	0.988943i	$-0.452622\pi$
$883$	8.81326			0.296590			0.148295	+	0.988943i	$0.452622\pi$
$884$	14.5784	−	13.5268i	0.490326	−	0.454956i
$885$		0			0
$886$	−1.67990	+	22.4167i	−0.0564373	+	0.753103i
$887$	15.6292	−	39.8226i	0.524778	−	1.33711i	−0.385345	−	0.922773i	$-0.625917\pi$
$887$	15.6292	−	39.8226i	0.524778	−	1.33711i	0.910122	−	0.414339i	$-0.135987\pi$
$888$		0			0
$889$	−6.27820	+	3.33066i	−0.210564	+	0.111707i
$890$	−13.9099	−	17.4424i	−0.466259	−	0.584671i
$891$		0			0
$892$	−0.654193	−	1.66686i	−0.0219040	−	0.0558105i
$893$	−6.00832	−	1.85332i	−0.201061	−	0.0620190i
$894$		0			0
$895$	−0.553477	−	2.42494i	−0.0185007	−	0.0810568i
$896$	20.7750	+	2.30799i	0.694043	+	0.0771044i
$897$		0			0
$898$	−17.8338	−	2.68802i	−0.595123	−	0.0897003i
$899$	−1.50521	+	1.02623i	−0.0502015	+	0.0342268i
$900$		0			0
$901$	−10.1689	−	17.6130i	−0.338775	−	0.586775i
$902$	−15.5810	−	7.50344i	−0.518792	−	0.249837i
$903$		0			0
$904$	−23.7350	+	11.4302i	−0.789415	+	0.380162i
$905$	23.6934	+	16.1539i	0.787595	+	0.536973i
$906$		0			0
$907$	−20.6259	−	19.1380i	−0.684871	−	0.635467i	0.258963	−	0.965887i	$-0.416619\pi$
$907$	−20.6259	−	19.1380i	−0.684871	−	0.635467i	−0.943834	+	0.330420i	$0.892810\pi$
$908$	−14.3905	−	9.81129i	−0.477566	−	0.325599i
$909$		0			0
$910$	0.460959	−	12.8557i	0.0152807	−	0.426162i
$911$	44.8307	+	21.5893i	1.48531	+	0.715286i	0.988309	−	0.152465i	$-0.0487211\pi$
$911$	44.8307	+	21.5893i	1.48531	+	0.715286i	0.496999	+	0.867751i	$0.334435\pi$
$912$		0			0
$913$	2.82511	−	4.89324i	0.0934977	−	0.161943i
$914$	−16.1370	+	11.0020i	−0.533765	+	0.363915i
$915$		0			0
$916$	−6.68918	+	29.3072i	−0.221017	+	0.968337i
$917$	−33.9609	+	34.0669i	−1.12149	+	1.12499i
$918$		0			0
$919$	−1.99544	−	26.6273i	−0.0658236	−	0.878355i	−0.928199	−	0.372085i	$-0.878643\pi$
$919$	−1.99544	−	26.6273i	−0.0658236	−	0.878355i	0.862375	−	0.506270i	$-0.168976\pi$
$920$	−12.1496	−	3.74764i	−0.400559	−	0.123556i
$921$		0			0
$922$	30.0370	−	9.26519i	0.989216	−	0.305133i
$923$	34.0186	+	42.6579i	1.11973	+	1.40410i
$924$		0			0
$925$	−16.6456	+	20.8729i	−0.547303	+	0.686296i
$926$	−0.538424	+	1.37188i	−0.0176937	+	0.0450828i
$927$		0			0
$928$	−12.2968	+	1.85345i	−0.403663	+	0.0608424i
$929$	−11.8656	+	11.0096i	−0.389296	+	0.361214i	−0.850404	−	0.526130i	$-0.823643\pi$
$929$	−11.8656	+	11.0096i	−0.389296	+	0.361214i	0.461108	+	0.887344i	$0.347452\pi$
$930$		0			0
$931$	−17.8887	+	19.4004i	−0.586279	+	0.635823i
$932$	−31.9758			−1.04740
$933$		0			0
$934$	−13.7566	+	2.07347i	−0.450129	+	0.0678460i
$935$	0.946927	−	12.6359i	0.0309678	−	0.413237i
$936$		0			0
$937$	−12.9598	+	16.2511i	−0.423379	+	0.530900i	−0.947078	−	0.321003i	$-0.895980\pi$
$937$	−12.9598	+	16.2511i	−0.423379	+	0.530900i	0.523699	+	0.851903i	$0.324552\pi$
$938$	−8.68460	−	3.77295i	−0.283562	−	0.123191i
$939$		0			0
$940$	3.20906	−	0.989865i	0.104668	−	0.0322858i
$941$	−1.43081	−	3.64565i	−0.0466431	−	0.118845i	0.905654	−	0.424018i	$-0.139381\pi$
$941$	−1.43081	−	3.64565i	−0.0466431	−	0.118845i	−0.952297	+	0.305174i	$0.901286\pi$
$942$		0			0
$943$	2.30247	+	30.7244i	0.0749789	+	1.00052i
$944$	0.485246	+	2.12600i	0.0157934	+	0.0691954i
$945$		0			0
$946$	−2.92562	+	12.8180i	−0.0951200	+	0.416748i
$947$	−50.6784	−	7.63854i	−1.64683	−	0.248219i	−0.740889	−	0.671628i	$-0.765595\pi$
$947$	−50.6784	−	7.63854i	−1.64683	−	0.248219i	−0.905939	+	0.423409i	$0.860833\pi$
$948$		0			0
$949$	−8.76868	+	15.1878i	−0.284643	+	0.493017i
$950$	4.08652	+	7.07805i	0.132584	+	0.229642i
$951$		0			0
$952$	−24.2731	+	17.9729i	−0.786697	+	0.582505i
$953$	16.6190	−	8.00331i	0.538344	−	0.259253i	−0.144896	−	0.989447i	$-0.546285\pi$
$953$	16.6190	−	8.00331i	0.538344	−	0.259253i	0.683240	+	0.730194i	$0.260570\pi$
$954$		0			0
$955$	4.66396	+	4.32753i	0.150922	+	0.140035i
$956$	3.61186	+	3.35132i	0.116816	+	0.108389i
$957$		0			0
$958$	19.2263	−	9.25889i	0.621173	−	0.299141i
$959$	25.8990	+	6.89636i	0.836321	+	0.222695i
$960$		0			0
$961$	15.1444	+	26.2308i	0.488528	+	0.846155i
$962$	−16.1664	+	28.0011i	−0.521227	+	0.902791i
$963$		0			0
$964$	15.9875	+	2.40972i	0.514922	+	0.0776120i
$965$	5.71792	−	25.0518i	0.184066	−	0.806448i
$966$		0			0
$967$	−4.88443	−	21.4001i	−0.157073	−	0.688181i	−0.990724	−	0.135890i	$-0.956611\pi$
$967$	−4.88443	−	21.4001i	−0.157073	−	0.688181i	0.833651	−	0.552291i	$-0.186246\pi$
$968$	1.46801	+	19.5892i	0.0471835	+	0.629620i
$969$		0			0
$970$	2.74285	+	6.98867i	0.0880676	+	0.224393i
$971$	−38.1611	+	11.7711i	−1.22465	+	0.377754i	−0.838612	−	0.544729i	$-0.816632\pi$
$971$	−38.1611	+	11.7711i	−1.22465	+	0.377754i	−0.386037	+	0.922483i	$0.626156\pi$
$972$		0			0
$973$	31.1374	−	1.21369i	0.998220	−	0.0389091i
$974$	−6.24215	+	7.82741i	−0.200011	+	0.250806i
$975$		0			0
$976$	−0.0524620	+	0.700056i	−0.00167927	+	0.0224083i
$977$	23.9392	−	3.60825i	0.765882	−	0.115438i	0.245529	−	0.969389i	$-0.421038\pi$
$977$	23.9392	−	3.60825i	0.765882	−	0.115438i	0.520353	+	0.853951i	$0.325800\pi$
$978$		0			0
$979$	−33.7369			−1.07824
$980$	2.05721	−	13.9435i	0.0657152	−	0.445410i
$981$		0			0
$982$	1.56651	−	1.45351i	0.0499895	−	0.0463835i
$983$	−51.8632	+	7.81712i	−1.65418	+	0.249328i	−0.908776	−	0.417285i	$-0.862982\pi$
$983$	−51.8632	+	7.81712i	−1.65418	+	0.249328i	−0.745404	+	0.666613i	$0.767744\pi$
$984$		0			0
$985$	6.34104	−	16.1567i	0.202042	−	0.514795i
$986$	4.66632	−	5.85138i	0.148606	−	0.186346i
$987$		0			0
$988$	−11.3299	−	14.2073i	−0.360453	−	0.451994i
$989$	22.3832	−	6.90431i	0.711746	−	0.219544i
$990$		0			0
$991$	−0.259667	−	0.0800967i	−0.00824860	−	0.00254436i	0.290628	−	0.956836i	$-0.406136\pi$
$991$	−0.259667	−	0.0800967i	−0.00824860	−	0.00254436i	−0.298877	+	0.954292i	$0.596612\pi$
$992$	−0.362845	−	4.84183i	−0.0115203	−	0.153728i
$993$		0			0
$994$	−17.3674	−	27.5446i	−0.550860	−	0.873662i
$995$	2.49305	−	10.9227i	0.0790348	−	0.346274i
$996$		0			0
$997$	−0.829292	+	0.565402i	−0.0262639	+	0.0179065i	−0.576381	−	0.817181i	$-0.695536\pi$
$997$	−0.829292	+	0.565402i	−0.0262639	+	0.0179065i	0.550117	+	0.835088i	$0.314583\pi$
$998$	13.7224	−	23.7680i	0.434376	−	0.752361i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.109.2		48
3.2	odd	2		147.2.m.a.109.3	yes	48
49.9	even	21	inner	441.2.bb.c.352.2		48
147.95	odd	42		7203.2.a.i.1.10		24
147.101	even	42		7203.2.a.k.1.10		24
147.107	odd	42		147.2.m.a.58.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.58.3	✓	48	147.107	odd	42
147.2.m.a.109.3	yes	48	3.2	odd	2
441.2.bb.c.109.2		48	1.1	even	1	trivial
441.2.bb.c.352.2		48	49.9	even	21	inner
7203.2.a.i.1.10		24	147.95	odd	42
7203.2.a.k.1.10		24	147.101	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615612 + 0.571205i) q^{2} +(-0.0967566 + 1.29113i) q^{4} +(0.568152 - 1.44763i) q^{5} +(1.56778 - 2.13121i) q^{7} +(-1.72514 - 2.16325i) q^{8} +O(q^{10})\)	\(q+(-0.615612 + 0.571205i) q^{2} +(-0.0967566 + 1.29113i) q^{4} +(0.568152 - 1.44763i) q^{5} +(1.56778 - 2.13121i) q^{7} +(-1.72514 - 2.16325i) q^{8} +(0.477130 + 1.21571i) q^{10} +(1.88719 + 0.582120i) q^{11} +(-0.828434 - 3.62961i) q^{13} +(0.252214 + 2.20752i) q^{14} +(-0.262894 - 0.0396249i) q^{16} +(3.40886 - 2.32412i) q^{17} +(-1.88493 - 3.26480i) q^{19} +(1.81410 + 0.873624i) q^{20} +(-1.49428 + 0.719609i) q^{22} +(2.44141 + 1.66453i) q^{23} +(1.89243 + 1.75592i) q^{25} +(2.58324 + 1.76123i) q^{26} +(2.59997 + 2.23041i) q^{28} +(-1.94616 - 0.937220i) q^{29} +(0.421689 - 0.730388i) q^{31} +(4.75673 - 3.24308i) q^{32} +(-0.770987 + 3.37792i) q^{34} +(-2.19446 - 3.48041i) q^{35} +(0.772823 + 10.3126i) q^{37} +(3.02525 + 0.933168i) q^{38} +(-4.11173 + 1.26830i) q^{40} +(6.50119 + 8.15223i) q^{41} +(4.94257 - 6.19778i) q^{43} +(-0.934188 + 2.38027i) q^{44} +(-2.45375 + 0.369843i) q^{46} +(1.22264 - 1.13444i) q^{47} +(-2.08413 - 6.68254i) q^{49} -2.16799 q^{50} +(4.76644 - 0.718425i) q^{52} +(0.368379 - 4.91568i) q^{53} +(1.91490 - 2.40121i) q^{55} +(-7.31499 + 0.285127i) q^{56} +(1.73342 - 0.534690i) q^{58} +(-2.99661 - 7.63524i) q^{59} +(-0.197327 - 2.63314i) q^{61} +(0.157604 + 0.690506i) q^{62} +(-0.957515 + 4.19515i) q^{64} +(-5.72500 - 0.862905i) q^{65} +(-2.13080 + 3.69065i) q^{67} +(2.67091 + 4.62615i) q^{68} +(3.33897 + 0.889097i) q^{70} +(-13.2041 + 6.35877i) q^{71} +(-3.45312 - 3.20403i) q^{73} +(-6.36637 - 5.90712i) q^{74} +(4.39765 - 2.11780i) q^{76} +(4.19931 - 3.10936i) q^{77} +(7.12262 + 12.3367i) q^{79} +(-0.206726 + 0.358060i) q^{80} +(-8.65880 - 1.30510i) q^{82} +(0.636629 - 2.78925i) q^{83} +(-1.42771 - 6.25522i) q^{85} +(0.497498 + 6.63865i) q^{86} +(-1.99638 - 5.08670i) q^{88} +(-16.3237 + 5.03519i) q^{89} +(-9.03427 - 3.92486i) q^{91} +(-2.38534 + 2.99112i) q^{92} +(-0.104672 + 1.39675i) q^{94} +(-5.79714 + 0.873778i) q^{95} +5.74864 q^{97} +(5.10012 + 2.92339i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

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