LMFDB - Embedded newform 1305.2.c.h.784.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1305,2,Mod(784,1305)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1305, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1305.784"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-14,-3,0,0,0,0,-3,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.84345856.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 13x^{4} + 41x^{2} + 1 $ x^6 + 13x^4 + 41x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.3
Root			$-0.156785i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.h.784.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.156785i q^{2} +1.97542 q^{4} +(-1.28672 + 1.82876i) q^{5} -1.09364i q^{7} -0.623285i q^{8} +(0.286721 + 0.201738i) q^{10} +4.40198 q^{11} +3.97108i q^{13} -0.171466 q^{14} +3.85312 q^{16} +6.22138i q^{17} -6.97542 q^{19} +(-2.54181 + 3.61256i) q^{20} -0.690163i q^{22} +0.780070i q^{23} +(-1.68870 - 4.70620i) q^{25} +0.622605 q^{26} -2.16040i q^{28} -1.00000 q^{29} +6.40198 q^{31} -1.85068i q^{32} +0.975419 q^{34} +(2.00000 + 1.40721i) q^{35} +1.09364i q^{37} +1.09364i q^{38} +(1.13984 + 0.801994i) q^{40} -0.376593i q^{43} +8.69575 q^{44} +0.122303 q^{46} -4.75115i q^{47} +5.80395 q^{49} +(-0.737860 + 0.264762i) q^{50} +7.84455i q^{52} +11.2861i q^{53} +(-5.66412 + 8.05014i) q^{55} -0.681649 q^{56} +0.156785i q^{58} +10.0000 q^{59} -1.14688 q^{61} -1.00373i q^{62} +7.41607 q^{64} +(-7.26214 - 5.10967i) q^{65} +5.90782i q^{67} +12.2898i q^{68} +(0.220629 - 0.313570i) q^{70} -2.00000 q^{71} +8.72223i q^{73} +0.171466 q^{74} -13.7794 q^{76} -4.81418i q^{77} +5.54886 q^{79} +(-4.95789 + 7.04641i) q^{80} -6.22138i q^{83} +(-11.3774 - 8.00519i) q^{85} -0.0590441 q^{86} -2.74369i q^{88} -10.8040 q^{89} +4.34293 q^{91} +1.54096i q^{92} -0.744908 q^{94} +(8.97542 - 12.7563i) q^{95} +17.4176i q^{97} -0.909972i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 14 q^{4} - 3 q^{5} - 3 q^{10} + 10 q^{11} - 8 q^{14} + 42 q^{16} - 16 q^{19} - 13 q^{20} + 11 q^{25} + 46 q^{26} - 6 q^{29} + 22 q^{31} - 20 q^{34} + 12 q^{35} + 21 q^{40} - 2 q^{44} - 44 q^{46} + 2 q^{49}+ \cdots + 28 q^{95}+O(q^{100}) $ 6 * q - 14 * q^4 - 3 * q^5 - 3 * q^10 + 10 * q^11 - 8 * q^14 + 42 * q^16 - 16 * q^19 - 13 * q^20 + 11 * q^25 + 46 * q^26 - 6 * q^29 + 22 * q^31 - 20 * q^34 + 12 * q^35 + 21 * q^40 - 2 * q^44 - 44 * q^46 + 2 * q^49 - 35 * q^50 + 13 * q^55 - 16 * q^56 + 60 * q^59 + 12 * q^61 - 38 * q^64 - 13 * q^65 + 60 * q^70 - 12 * q^71 + 8 * q^74 - 24 * q^76 - 2 * q^79 + 55 * q^80 - 26 * q^85 + 30 * q^86 - 32 * q^89 + 40 * q^91 - 2 * q^94 + 28 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	0.156785i		−	0.110864i	−0.998462	−	0.0554318i	$-0.982346\pi$
$2$		−	0.156785i		−	0.110864i	0.998462	−	0.0554318i	$-0.0176535\pi$
$3$		0			0
$3$		0			0
$4$	1.97542			0.987709
$5$	−1.28672	+	1.82876i	−0.575439	+	0.817845i
$5$	−1.28672	+	1.82876i	−0.575439	+	0.817845i
$6$		0			0
$7$		−	1.09364i		−	0.413357i	−0.978409	−	0.206678i	$-0.933735\pi$
$7$		−	1.09364i		−	0.413357i	0.978409	−	0.206678i	$-0.0662654\pi$
$8$		−	0.623285i		−	0.220365i
$9$		0			0
$10$	0.286721	+	0.201738i	0.0906692	+	0.0637953i
$11$	4.40198			1.32725			0.663623	−	0.748067i	$-0.269018\pi$
$11$	4.40198			1.32725			0.663623	+	0.748067i	$0.269018\pi$
$12$		0			0
$13$			3.97108i			1.10138i	0.834710	+	0.550690i	$0.185635\pi$
$13$			3.97108i			1.10138i	−0.834710	+	0.550690i	$0.814365\pi$
$14$	−0.171466			−0.0458262
$15$		0			0
$16$	3.85312			0.963279
$17$			6.22138i			1.50891i	0.656353	+	0.754454i	$0.272098\pi$
$17$			6.22138i			1.50891i	−0.656353	+	0.754454i	$0.727902\pi$
$18$		0			0
$19$	−6.97542			−1.60027			−0.800135	−	0.599819i	$-0.795239\pi$
$19$	−6.97542			−1.60027			−0.800135	+	0.599819i	$0.795239\pi$
$20$	−2.54181	+	3.61256i	−0.568367	+	0.807793i
$21$		0			0
$22$		−	0.690163i		−	0.147143i
$23$			0.780070i			0.162656i	0.996687	+	0.0813279i	$0.0259161\pi$
$23$			0.780070i			0.162656i	−0.996687	+	0.0813279i	$0.974084\pi$
$24$		0			0
$25$	−1.68870	−	4.70620i	−0.337739	−	0.941240i
$26$	0.622605			0.122103
$27$		0			0
$28$		−	2.16040i		−	0.408276i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$		0			0
$31$	6.40198			1.14983			0.574914	−	0.818214i	$-0.305035\pi$
$31$	6.40198			1.14983			0.574914	+	0.818214i	$0.305035\pi$
$32$		−	1.85068i		−	0.327157i
$33$		0			0
$34$	0.975419			0.167283
$35$	2.00000	+	1.40721i	0.338062	+	0.237862i
$36$		0			0
$37$			1.09364i			0.179793i	0.995951	+	0.0898966i	$0.0286537\pi$
$37$			1.09364i			0.179793i	−0.995951	+	0.0898966i	$0.971346\pi$
$38$			1.09364i			0.177412i
$39$		0			0
$40$	1.13984	+	0.801994i	0.180224	+	0.126806i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$		−	0.376593i		−	0.0574299i	−0.999588	−	0.0287150i	$-0.990858\pi$
$43$		−	0.376593i		−	0.0574299i	0.999588	−	0.0287150i	$-0.00914152\pi$
$44$	8.69575			1.31093
$45$		0			0
$46$	0.122303			0.0180326
$47$		−	4.75115i		−	0.693027i	−0.938045	−	0.346513i	$-0.887366\pi$
$47$		−	4.75115i		−	0.693027i	0.938045	−	0.346513i	$-0.112634\pi$
$48$		0			0
$49$	5.80395			0.829136
$50$	−0.737860	+	0.264762i	−0.104349	+	0.0374430i
$51$		0			0
$52$			7.84455i			1.08784i
$53$			11.2861i			1.55027i	0.631798	+	0.775133i	$0.282317\pi$
$53$			11.2861i			1.55027i	−0.631798	+	0.775133i	$0.717683\pi$
$54$		0			0
$55$	−5.66412	+	8.05014i	−0.763749	+	1.08548i
$56$	−0.681649			−0.0910892
$57$		0			0
$58$			0.156785i			0.0205869i
$59$	10.0000			1.30189			0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000			1.30189			0.650945	+	0.759125i	$0.274373\pi$
$60$		0			0
$61$	−1.14688			−0.146844			−0.0734218	−	0.997301i	$-0.523392\pi$
$61$	−1.14688			−0.146844			−0.0734218	+	0.997301i	$0.523392\pi$
$62$		−	1.00373i		−	0.127474i
$63$		0			0
$64$	7.41607			0.927009
$65$	−7.26214	−	5.10967i	−0.900758	−	0.633777i
$66$		0			0
$67$			5.90782i			0.721754i	0.932613	+	0.360877i	$0.117523\pi$
$67$			5.90782i			0.721754i	−0.932613	+	0.360877i	$0.882477\pi$
$68$			12.2898i			1.49036i
$69$		0			0
$70$	0.220629	−	0.313570i	0.0263702	−	0.0374787i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$			8.72223i			1.02086i	0.859919	+	0.510430i	$0.170514\pi$
$73$			8.72223i			1.02086i	−0.859919	+	0.510430i	$0.829486\pi$
$74$	0.171466			0.0199325
$75$		0			0
$76$	−13.7794			−1.58060
$77$		−	4.81418i		−	0.548626i
$78$		0			0
$79$	5.54886			0.624296			0.312148	−	0.950034i	$-0.398952\pi$
$79$	5.54886			0.624296			0.312148	+	0.950034i	$0.398952\pi$
$80$	−4.95789	+	7.04641i	−0.554308	+	0.787812i
$81$		0			0
$82$		0			0
$83$		−	6.22138i		−	0.682886i	−0.939903	−	0.341443i	$-0.889084\pi$
$83$		−	6.22138i		−	0.682886i	0.939903	−	0.341443i	$-0.110916\pi$
$84$		0			0
$85$	−11.3774	−	8.00519i	−1.23405	−	0.868284i
$86$	−0.0590441			−0.00636689
$87$		0			0
$88$		−	2.74369i		−	0.292478i
$89$	−10.8040			−1.14522			−0.572608	−	0.819829i	$-0.694068\pi$
$89$	−10.8040			−1.14522			−0.572608	+	0.819829i	$0.694068\pi$
$90$		0			0
$91$	4.34293			0.455263
$92$			1.54096i			0.160657i
$93$		0			0
$94$	−0.744908			−0.0768314
$95$	8.97542	−	12.7563i	0.920859	−	1.30877i
$96$		0			0
$97$			17.4176i			1.76849i	0.467026	+	0.884244i	$0.345326\pi$
$97$			17.4176i			1.76849i	−0.467026	+	0.884244i	$0.654674\pi$
$98$		−	0.909972i		−	0.0919210i
$99$		0			0
$100$	−3.33588	−	9.29671i	−0.333588	−	0.929671i
$101$	12.7548			1.26915			0.634574	−	0.772862i	$-0.281175\pi$
$101$	12.7548			1.26915			0.634574	+	0.772862i	$0.281175\pi$
$102$		0			0
$103$		−	5.15463i		−	0.507901i	−0.967217	−	0.253950i	$-0.918270\pi$
$103$		−	5.15463i		−	0.507901i	0.967217	−	0.253950i	$-0.0817300\pi$
$104$	2.47512			0.242705
$105$		0			0
$106$	1.76949			0.171868
$107$		−	1.09364i		−	0.105726i	−0.998602	−	0.0528631i	$-0.983165\pi$
$107$		−	1.09364i		−	0.105726i	0.998602	−	0.0528631i	$-0.0168347\pi$
$108$		0			0
$109$	−15.3282			−1.46818			−0.734089	−	0.679053i	$-0.762391\pi$
$109$	−15.3282			−1.46818			−0.734089	+	0.679053i	$0.762391\pi$
$110$	1.26214	+	0.888047i	0.120340	+	0.0846720i
$111$		0			0
$112$		−	4.21392i		−	0.398178i
$113$		−	7.28814i		−	0.685611i	−0.939406	−	0.342805i	$-0.888623\pi$
$113$		−	7.28814i		−	0.685611i	0.939406	−	0.342805i	$-0.111377\pi$
$114$		0			0
$115$	−1.42656	−	1.00373i	−0.133027	−	0.0935985i
$116$	−1.97542			−0.183413
$117$		0			0
$118$		−	1.56785i		−	0.144332i
$119$	6.80395			0.623717
$120$		0			0
$121$	8.37739			0.761581
$122$			0.179814i			0.0162796i
$123$		0			0
$124$	12.6466			1.13570
$125$	10.7794	+	2.96735i	0.964136	+	0.265408i
$126$		0			0
$127$		−	17.7312i		−	1.57339i	−0.617345	−	0.786693i	$-0.711792\pi$
$127$		−	17.7312i		−	1.57339i	0.617345	−	0.786693i	$-0.288208\pi$
$128$		−	4.86409i		−	0.429929i
$129$		0			0
$130$	−0.801119	+	1.13859i	−0.0702628	+	0.0998612i
$131$	−7.31835			−0.639407			−0.319704	−	0.947518i	$-0.603583\pi$
$131$	−7.31835			−0.639407			−0.319704	+	0.947518i	$0.603583\pi$
$132$		0			0
$133$			7.62859i			0.661483i
$134$	0.926256			0.0800163
$135$		0			0
$136$	3.87770			0.332510
$137$			9.78899i			0.836330i	0.908371	+	0.418165i	$0.137327\pi$
$137$			9.78899i			0.836330i	−0.908371	+	0.418165i	$0.862673\pi$
$138$		0			0
$139$	2.75479			0.233658			0.116829	−	0.993152i	$-0.462727\pi$
$139$	2.75479			0.233658			0.116829	+	0.993152i	$0.462727\pi$
$140$	3.95084	+	2.77983i	0.333907	+	0.234938i
$141$		0			0
$142$			0.313570i			0.0263142i
$143$			17.4806i			1.46180i
$144$		0			0
$145$	1.28672	−	1.82876i	0.106856	−	0.151870i
$146$	1.36751			0.113176
$147$		0			0
$148$			2.16040i			0.177583i
$149$	−4.52428			−0.370643			−0.185322	−	0.982678i	$-0.559333\pi$
$149$	−4.52428			−0.370643			−0.185322	+	0.982678i	$0.559333\pi$
$150$		0			0
$151$	2.80395			0.228182			0.114091	−	0.993470i	$-0.463604\pi$
$151$	2.80395			0.228182			0.114091	+	0.993470i	$0.463604\pi$
$152$			4.34768i			0.352643i
$153$		0			0
$154$	−0.754790			−0.0608227
$155$	−8.23756	+	11.7077i	−0.661657	+	0.940381i
$156$		0			0
$157$			4.97481i			0.397033i	0.980098	+	0.198517i	$0.0636124\pi$
$157$			4.97481i			0.397033i	−0.980098	+	0.198517i	$0.936388\pi$
$158$		−	0.869977i		−	0.0692117i
$159$		0			0
$160$	3.38444	+	2.38131i	0.267564	+	0.188259i
$161$	0.853115			0.0672349
$162$		0			0
$163$		−	20.7615i		−	1.62617i	−0.582146	−	0.813084i	$-0.697787\pi$
$163$		−	20.7615i		−	1.62617i	0.582146	−	0.813084i	$-0.302213\pi$
$164$		0			0
$165$		0			0
$166$	−0.975419			−0.0757072
$167$		−	21.9182i		−	1.69608i	−0.529932	−	0.848040i	$-0.677783\pi$
$167$		−	21.9182i		−	1.69608i	0.529932	−	0.848040i	$-0.322217\pi$
$168$		0			0
$169$	−2.76949			−0.213038
$170$	−1.25509	+	1.78380i	−0.0962611	+	0.136811i
$171$		0			0
$172$		−	0.743929i		−	0.0567241i
$173$		−	3.25404i		−	0.247400i	−0.992320	−	0.123700i	$-0.960524\pi$
$173$		−	3.25404i		−	0.247400i	0.992320	−	0.123700i	$-0.0394760\pi$
$174$		0			0
$175$	−5.14688	+	1.84683i	−0.389068	+	0.139607i
$176$	16.9613			1.27851
$177$		0			0
$178$			1.69390i			0.126963i
$179$	−7.19605			−0.537858			−0.268929	−	0.963160i	$-0.586670\pi$
$179$	−7.19605			−0.537858			−0.268929	+	0.963160i	$0.586670\pi$
$180$		0			0
$181$	13.0345			0.968844			0.484422	−	0.874834i	$-0.339030\pi$
$181$	13.0345			0.968844			0.484422	+	0.874834i	$0.339030\pi$
$182$		−	0.680906i		−	0.0504721i
$183$		0			0
$184$	0.486206			0.0358436
$185$	−2.00000	−	1.40721i	−0.147043	−	0.103460i
$186$		0			0
$187$			27.3864i			2.00269i
$188$		−	9.38551i		−	0.684509i
$189$		0			0
$190$	−2.00000	−	1.40721i	−0.145095	−	0.102090i
$191$	10.1223			0.732424			0.366212	−	0.930531i	$-0.380654\pi$
$191$	10.1223			0.732424			0.366212	+	0.930531i	$0.380654\pi$
$192$		0			0
$193$		−	22.8589i		−	1.64542i	−0.568462	−	0.822710i	$-0.692461\pi$
$193$		−	22.8589i		−	1.64542i	0.568462	−	0.822710i	$-0.307539\pi$
$194$	2.73081			0.196061
$195$		0			0
$196$	11.4652			0.818945
$197$		−	22.0711i		−	1.57250i	−0.617907	−	0.786251i	$-0.712019\pi$
$197$		−	22.0711i		−	1.57250i	0.617907	−	0.786251i	$-0.287981\pi$
$198$		0			0
$199$	−5.19605			−0.368338			−0.184169	−	0.982895i	$-0.558959\pi$
$199$	−5.19605			−0.368338			−0.184169	+	0.982895i	$0.558959\pi$
$200$	−2.93330	+	1.05254i	−0.207416	+	0.0744258i
$201$		0			0
$202$		−	1.99976i		−	0.140702i
$203$			1.09364i			0.0767585i
$204$		0			0
$205$		0			0
$206$	−0.808167			−0.0563077
$207$		0			0
$208$			15.3010i			1.06094i
$209$	−30.7056			−2.12395
$210$		0			0
$211$	1.64719			0.113397			0.0566985	−	0.998391i	$-0.481943\pi$
$211$	1.64719			0.113397			0.0566985	+	0.998391i	$0.481943\pi$
$212$			22.2948i			1.53121i
$213$		0			0
$214$	−0.171466			−0.0117212
$215$	0.688697	+	0.484571i	0.0469688	+	0.0330474i
$216$		0			0
$217$		−	7.00145i		−	0.475290i
$218$			2.40323i			0.162768i
$219$		0			0
$220$	−11.1890	+	15.9024i	−0.754362	+	1.07214i
$221$	−24.7056			−1.66188
$222$		0			0
$223$		−	9.47542i		−	0.634521i	−0.948338	−	0.317261i	$-0.897237\pi$
$223$		−	9.47542i		−	0.634521i	0.948338	−	0.317261i	$-0.102763\pi$
$224$	−2.02398			−0.135233
$225$		0			0
$226$	−1.14267			−0.0760093
$227$		−	5.72800i		−	0.380181i	−0.981767	−	0.190090i	$-0.939122\pi$
$227$		−	5.72800i		−	0.380181i	0.981767	−	0.190090i	$-0.0608781\pi$
$228$		0			0
$229$	−15.1469			−1.00093			−0.500467	−	0.865756i	$-0.666838\pi$
$229$	−15.1469			−1.00093			−0.500467	+	0.865756i	$0.666838\pi$
$230$	−0.157370	+	0.223663i	−0.0103767	+	0.0147479i
$231$		0			0
$232$			0.623285i			0.0409207i
$233$		−	0.717046i		−	0.0469753i	−0.999724	−	0.0234876i	$-0.992523\pi$
$233$		−	0.717046i		−	0.0469753i	0.999724	−	0.0234876i	$-0.00747703\pi$
$234$		0			0
$235$	8.68870	+	6.11341i	0.566788	+	0.398795i
$236$	19.7542			1.28589
$237$		0			0
$238$		−	1.06676i		−	0.0691475i
$239$	−2.00000			−0.129369			−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000			−0.129369			−0.0646846	+	0.997906i	$0.520604\pi$
$240$		0			0
$241$	17.3282			1.11621			0.558105	−	0.829770i	$-0.311529\pi$
$241$	17.3282			1.11621			0.558105	+	0.829770i	$0.311529\pi$
$242$		−	1.31345i		−	0.0844316i
$243$		0			0
$244$	−2.26558			−0.145039
$245$	−7.46807	+	10.6140i	−0.477117	+	0.678104i
$246$		0			0
$247$		−	27.7000i		−	1.76251i
$248$		−	3.99026i		−	0.253382i
$249$		0			0
$250$	0.465235	−	1.69004i	0.0294241	−	0.106888i
$251$	−26.0099			−1.64173			−0.820865	−	0.571123i	$-0.806508\pi$
$251$	−26.0099			−1.64173			−0.820865	+	0.571123i	$0.806508\pi$
$252$		0			0
$253$			3.43385i			0.215884i
$254$	−2.77998			−0.174431
$255$		0			0
$256$	14.0695			0.879346
$257$		−	15.0335i		−	0.937766i	−0.883260	−	0.468883i	$-0.844657\pi$
$257$		−	15.0335i		−	0.937766i	0.883260	−	0.468883i	$-0.155343\pi$
$258$		0			0
$259$	1.19605			0.0743188
$260$	−14.3458	−	10.0937i	−0.889687	−	0.625988i
$261$		0			0
$262$			1.14741i			0.0708870i
$263$		−	12.0662i		−	0.744032i	−0.928226	−	0.372016i	$-0.878667\pi$
$263$		−	12.0662i		−	0.744032i	0.928226	−	0.372016i	$-0.121333\pi$
$264$		0			0
$265$	−20.6395	−	14.5221i	−1.26788	−	0.892084i
$266$	1.19605			0.0733344
$267$		0			0
$268$			11.6704i			0.712884i
$269$	−10.8531			−0.661726			−0.330863	−	0.943679i	$-0.607340\pi$
$269$	−10.8531			−0.661726			−0.330863	+	0.943679i	$0.607340\pi$
$270$		0			0
$271$	−12.7449			−0.774198			−0.387099	−	0.922038i	$-0.626523\pi$
$271$	−12.7449			−0.774198			−0.387099	+	0.922038i	$0.626523\pi$
$272$			23.9717i			1.45350i
$273$		0			0
$274$	1.53476			0.0927185
$275$	−7.43361	−	20.7166i	−0.448263	−	1.24926i
$276$		0			0
$277$		−	20.0714i		−	1.20597i	−0.797752	−	0.602986i	$-0.793978\pi$
$277$		−	20.0714i		−	1.20597i	0.797752	−	0.602986i	$-0.206022\pi$
$278$		−	0.431909i		−	0.0259042i
$279$		0			0
$280$	0.877093	−	1.24657i	0.0524163	−	0.0744968i
$281$	20.9361			1.24895			0.624473	−	0.781047i	$-0.285314\pi$
$281$	20.9361			1.24895			0.624473	+	0.781047i	$0.285314\pi$
$282$		0			0
$283$			16.9703i			1.00878i	0.863477	+	0.504389i	$0.168282\pi$
$283$			16.9703i			1.00878i	−0.863477	+	0.504389i	$0.831718\pi$
$284$	−3.95084			−0.234439
$285$		0			0
$286$	2.74069			0.162061
$287$		0			0
$288$		0			0
$289$	−21.7056			−1.27680
$290$	−0.286721	−	0.201738i	−0.0168368	−	0.0118465i
$291$		0			0
$292$			17.2301i			1.00831i
$293$			9.47542i			0.553560i	0.960933	+	0.276780i	$0.0892673\pi$
$293$			9.47542i			0.553560i	−0.960933	+	0.276780i	$0.910733\pi$
$294$		0			0
$295$	−12.8672	+	18.2876i	−0.749158	+	1.06474i
$296$	0.681649			0.0396201
$297$		0			0
$298$			0.709338i			0.0410909i
$299$	−3.09772			−0.179146
$300$		0			0
$301$	−0.411857			−0.0237391
$302$		−	0.439617i		−	0.0252971i
$303$		0			0
$304$	−26.8771			−1.54151
$305$	1.47572	−	2.09737i	0.0844995	−	0.120095i
$306$		0			0
$307$		−	19.3812i		−	1.10614i	−0.833134	−	0.553072i	$-0.813456\pi$
$307$		−	19.3812i		−	1.10614i	0.833134	−	0.553072i	$-0.186544\pi$
$308$		−	9.51001i		−	0.541883i
$309$		0			0
$310$	1.83558	+	1.29152i	0.104254	+	0.0733536i
$311$	9.26919			0.525607			0.262804	−	0.964849i	$-0.415353\pi$
$311$	9.26919			0.525607			0.262804	+	0.964849i	$0.415353\pi$
$312$		0			0
$313$		−	14.5324i		−	0.821422i	−0.911766	−	0.410711i	$-0.865281\pi$
$313$		−	14.5324i		−	0.821422i	0.911766	−	0.410711i	$-0.134719\pi$
$314$	0.779975			0.0440165
$315$		0			0
$316$	10.9613			0.616623
$317$		−	22.4116i		−	1.25876i	−0.777098	−	0.629380i	$-0.783309\pi$
$317$		−	22.4116i		−	1.25876i	0.777098	−	0.629380i	$-0.216691\pi$
$318$		0			0
$319$	−4.40198			−0.246463
$320$	−9.54242	+	13.5622i	−0.533437	+	0.758149i
$321$		0			0
$322$		−	0.133756i		−	0.00745390i
$323$		−	43.3968i		−	2.41466i
$324$		0			0
$325$	18.6887	−	6.70596i	1.03666	−	0.371979i
$326$	−3.25509			−0.180283
$327$		0			0
$328$		0			0
$329$	−5.19605			−0.286467
$330$		0			0
$331$	7.89179			0.433772			0.216886	−	0.976197i	$-0.430410\pi$
$331$	7.89179			0.433772			0.216886	+	0.976197i	$0.430410\pi$
$332$		−	12.2898i		−	0.674493i
$333$		0			0
$334$	−3.43644			−0.188034
$335$	−10.8040	−	7.60171i	−0.590283	−	0.415326i
$336$		0			0
$337$		−	33.4280i		−	1.82094i	−0.413579	−	0.910468i	$-0.635721\pi$
$337$		−	33.4280i		−	1.82094i	0.413579	−	0.910468i	$-0.364279\pi$
$338$			0.434214i			0.0236181i
$339$		0			0
$340$	−22.4751	−	15.8136i	−1.21888	−	0.857613i
$341$	28.1813			1.52611
$342$		0			0
$343$		−	14.0029i		−	0.756086i
$344$	−0.234725			−0.0126555
$345$		0			0
$346$	−0.510183			−0.0274276
$347$			31.1069i			1.66991i	0.550320	+	0.834954i	$0.314506\pi$
$347$			31.1069i			1.66991i	−0.550320	+	0.834954i	$0.685494\pi$
$348$		0			0
$349$	5.76949			0.308834			0.154417	−	0.988006i	$-0.450650\pi$
$349$	5.76949			0.308834			0.154417	+	0.988006i	$0.450650\pi$
$350$	0.289554	+	0.806953i	0.0154773	+	0.0431335i
$351$		0			0
$352$		−	8.14665i		−	0.434218i
$353$			13.5095i			0.719039i	0.933137	+	0.359520i	$0.117059\pi$
$353$			13.5095i			0.719039i	−0.933137	+	0.359520i	$0.882941\pi$
$354$		0			0
$355$	2.57344	−	3.65751i	0.136584	−	0.194121i
$356$	−21.3423			−1.13114
$357$		0			0
$358$			1.12823i			0.0596289i
$359$	−1.15677			−0.0610518			−0.0305259	−	0.999534i	$-0.509718\pi$
$359$	−1.15677			−0.0610518			−0.0305259	+	0.999534i	$0.509718\pi$
$360$		0			0
$361$	29.6565			1.56087
$362$		−	2.04361i		−	0.107410i
$363$		0			0
$364$	8.57911			0.449667
$365$	−15.9508	−	11.2231i	−0.834905	−	0.587443i
$366$		0			0
$367$			10.5959i			0.553104i	0.960999	+	0.276552i	$0.0891918\pi$
$367$			10.5959i			0.553104i	−0.960999	+	0.276552i	$0.910808\pi$
$368$			3.00570i			0.156683i
$369$		0			0
$370$	−0.220629	+	0.313570i	−0.0114700	+	0.0163017i
$371$	12.3429			0.640813
$372$		0			0
$373$		−	7.09907i		−	0.367576i	−0.982966	−	0.183788i	$-0.941164\pi$
$373$		−	7.09907i		−	0.367576i	0.982966	−	0.183788i	$-0.0588360\pi$
$374$	4.29377			0.222026
$375$		0			0
$376$	−2.96132			−0.152719
$377$		−	3.97108i		−	0.204521i
$378$		0			0
$379$	−18.1223			−0.930880			−0.465440	−	0.885079i	$-0.654104\pi$
$379$	−18.1223			−0.930880			−0.465440	+	0.885079i	$0.654104\pi$
$380$	17.7302	−	25.1991i	0.909540	−	1.29269i
$381$		0			0
$382$		−	1.58702i		−	0.0811992i
$383$			3.28092i			0.167647i	0.996481	+	0.0838236i	$0.0267132\pi$
$383$			3.28092i			0.167647i	−0.996481	+	0.0838236i	$0.973287\pi$
$384$		0			0
$385$	8.80395	+	6.19450i	0.448691	+	0.315701i
$386$	−3.58393			−0.182417
$387$		0			0
$388$			34.4070i			1.74675i
$389$	−12.0000			−0.608424			−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000			−0.608424			−0.304212	+	0.952604i	$0.598393\pi$
$390$		0			0
$391$	−4.85312			−0.245433
$392$		−	3.61752i		−	0.182712i
$393$		0			0
$394$	−3.46042			−0.174333
$395$	−7.13984	+	10.1475i	−0.359244	+	0.510577i
$396$		0			0
$397$			36.3054i			1.82212i	0.412278	+	0.911058i	$0.364733\pi$
$397$			36.3054i			1.82212i	−0.412278	+	0.911058i	$0.635267\pi$
$398$			0.814661i			0.0408353i
$399$		0			0
$400$	−6.50675	−	18.1335i	−0.325337	−	0.906676i
$401$	−26.0830			−1.30252			−0.651262	−	0.758853i	$-0.725760\pi$
$401$	−26.0830			−1.30252			−0.651262	+	0.758853i	$0.725760\pi$
$402$		0			0
$403$			25.4228i			1.26640i
$404$	25.1960			1.25355
$405$		0			0
$406$	0.171466			0.00850972
$407$			4.81418i			0.238630i
$408$		0			0
$409$	−13.0486			−0.645210			−0.322605	−	0.946534i	$-0.604558\pi$
$409$	−13.0486			−0.645210			−0.322605	+	0.946534i	$0.604558\pi$
$410$		0			0
$411$		0			0
$412$		−	10.1825i		−	0.501658i
$413$		−	10.9364i		−	0.538145i
$414$		0			0
$415$	11.3774	+	8.00519i	0.558494	+	0.392959i
$416$	7.34920			0.360324
$417$		0			0
$418$			4.81418i			0.235469i
$419$	35.8525			1.75151			0.875755	−	0.482756i	$-0.160364\pi$
$419$	35.8525			1.75151			0.875755	+	0.482756i	$0.160364\pi$
$420$		0			0
$421$	16.7056			0.814182			0.407091	−	0.913388i	$-0.366543\pi$
$421$	16.7056			0.814182			0.407091	+	0.913388i	$0.366543\pi$
$422$		−	0.258254i		−	0.0125716i
$423$		0			0
$424$	7.03446			0.341624
$425$	29.2791	−	10.5060i	1.42024	−	0.509618i
$426$		0			0
$427$			1.25428i			0.0606988i
$428$		−	2.16040i		−	0.104427i
$429$		0			0
$430$	0.0759733	−	0.107977i	0.00366376	−	0.00520713i
$431$	26.3135			1.26748			0.633739	−	0.773547i	$-0.281519\pi$
$431$	26.3135			1.26748			0.633739	+	0.773547i	$0.281519\pi$
$432$		0			0
$433$			10.7220i			0.515266i	0.966243	+	0.257633i	$0.0829425\pi$
$433$			10.7220i			0.515266i	−0.966243	+	0.257633i	$0.917057\pi$
$434$	−1.09772			−0.0526923
$435$		0			0
$436$	−30.2797			−1.45013
$437$		−	5.44131i		−	0.260293i
$438$		0			0
$439$	−29.5587			−1.41076			−0.705381	−	0.708828i	$-0.749224\pi$
$439$	−29.5587			−1.41076			−0.705381	+	0.708828i	$0.749224\pi$
$440$	5.01753	+	3.53036i	0.239202	+	0.168303i
$441$		0			0
$442$			3.87347i			0.184242i
$443$			3.40697i			0.161870i	0.996719	+	0.0809349i	$0.0257906\pi$
$443$			3.40697i			0.161870i	−0.996719	+	0.0809349i	$0.974209\pi$
$444$		0			0
$445$	13.9017	−	19.7578i	0.659003	−	0.936609i
$446$	−1.48560			−0.0703453
$447$		0			0
$448$		−	8.11051i		−	0.383186i
$449$	0.461020			0.0217569			0.0108784	−	0.999941i	$-0.496537\pi$
$449$	0.461020			0.0217569			0.0108784	+	0.999941i	$0.496537\pi$
$450$		0			0
$451$		0			0
$452$		−	14.3971i		−	0.677184i
$453$		0			0
$454$	−0.898063			−0.0421482
$455$	−5.58814	+	7.94216i	−0.261976	+	0.372334i
$456$		0			0
$457$		−	1.37262i		−	0.0642084i	−0.999485	−	0.0321042i	$-0.989779\pi$
$457$		−	1.37262i		−	0.0642084i	0.999485	−	0.0321042i	$-0.0102208\pi$
$458$			2.37480i			0.110967i
$459$		0			0
$460$	−2.81805	−	1.98279i	−0.131392	−	0.0924481i
$461$	−14.5875			−0.679409			−0.339705	−	0.940532i	$-0.610327\pi$
$461$	−14.5875			−0.679409			−0.339705	+	0.940532i	$0.610327\pi$
$462$		0			0
$463$		−	18.8517i		−	0.876112i	−0.898948	−	0.438056i	$-0.855667\pi$
$463$		−	18.8517i		−	0.876112i	0.898948	−	0.438056i	$-0.144333\pi$
$464$	−3.85312			−0.178876
$465$		0			0
$466$	−0.112422			−0.00520785
$467$			29.9580i			1.38629i	0.720798	+	0.693145i	$0.243775\pi$
$467$			29.9580i			1.38629i	−0.720798	+	0.693145i	$0.756225\pi$
$468$		0			0
$469$	6.46102			0.298342
$470$	0.958489	−	1.36226i	0.0442118	−	0.0628362i
$471$		0			0
$472$		−	6.23285i		−	0.286890i
$473$		−	1.65776i		−	0.0762237i
$474$		0			0
$475$	11.7794	+	32.8277i	0.540475	+	1.50624i
$476$	13.4407			0.616051
$477$		0			0
$478$			0.313570i			0.0143423i
$479$	−32.7647			−1.49706			−0.748528	−	0.663103i	$-0.769239\pi$
$479$	−32.7647			−1.49706			−0.748528	+	0.663103i	$0.769239\pi$
$480$		0			0
$481$	−4.34293			−0.198021
$482$		−	2.71680i		−	0.123747i
$483$		0			0
$484$	16.5489			0.752221
$485$	−31.8525	−	22.4116i	−1.44635	−	1.01766i
$486$		0			0
$487$			14.1098i			0.639375i	0.947523	+	0.319688i	$0.103578\pi$
$487$			14.1098i			0.639375i	−0.947523	+	0.319688i	$0.896422\pi$
$488$			0.714836i			0.0323591i
$489$		0			0
$490$	1.66412	+	1.17088i	0.0751771	+	0.0528949i
$491$	−4.10821			−0.185401			−0.0927004	−	0.995694i	$-0.529550\pi$
$491$	−4.10821			−0.185401			−0.0927004	+	0.995694i	$0.529550\pi$
$492$		0			0
$493$		−	6.22138i		−	0.280197i
$494$	−4.34293			−0.195398
$495$		0			0
$496$	24.6676			1.10761
$497$			2.18728i			0.0981129i
$498$		0			0
$499$	−30.0689			−1.34607			−0.673035	−	0.739611i	$-0.735010\pi$
$499$	−30.0689			−1.34607			−0.673035	+	0.739611i	$0.735010\pi$
$500$	21.2938	+	5.86176i	0.952286	+	0.262146i
$501$		0			0
$502$			4.07795i			0.182008i
$503$			14.8806i			0.663493i	0.943369	+	0.331746i	$0.107638\pi$
$503$			14.8806i			0.663493i	−0.943369	+	0.331746i	$0.892362\pi$
$504$		0			0
$505$	−16.4119	+	23.3254i	−0.730318	+	1.03797i
$506$	0.538375			0.0239337
$507$		0			0
$508$		−	35.0264i		−	1.55405i
$509$	1.93674			0.0858445			0.0429223	−	0.999078i	$-0.486333\pi$
$509$	1.93674			0.0858445			0.0429223	+	0.999078i	$0.486333\pi$
$510$		0			0
$511$	9.53898			0.421980
$512$		−	11.9341i		−	0.527416i
$513$		0			0
$514$	−2.35703			−0.103964
$515$	9.42656	+	6.63257i	0.415384	+	0.292266i
$516$		0			0
$517$		−	20.9145i		−	0.919817i
$518$		−	0.187522i		−	0.00823925i
$519$		0			0
$520$	−3.18478	+	4.52638i	−0.139662	+	0.198495i
$521$	4.23051			0.185342			0.0926710	−	0.995697i	$-0.470460\pi$
$521$	4.23051			0.185342			0.0926710	+	0.995697i	$0.470460\pi$
$522$		0			0
$523$		−	4.40144i		−	0.192462i	−0.995359	−	0.0962308i	$-0.969321\pi$
$523$		−	4.40144i		−	0.192462i	0.995359	−	0.0962308i	$-0.0306787\pi$
$524$	−14.4568			−0.631548
$525$		0			0
$526$	−1.89179			−0.0824861
$527$			39.8292i			1.73499i
$528$		0			0
$529$	22.3915			0.973543
$530$	−2.27684	+	3.23597i	−0.0988996	+	0.140561i
$531$		0			0
$532$			15.0697i			0.653353i
$533$		0			0
$534$		0			0
$535$	2.00000	+	1.40721i	0.0864675	+	0.0608390i
$536$	3.68225			0.159049
$537$		0			0
$538$			1.70160i			0.0733613i
$539$	25.5489			1.10047
$540$		0			0
$541$	−32.4119			−1.39349			−0.696747	−	0.717317i	$-0.745370\pi$
$541$	−32.4119			−1.39349			−0.696747	+	0.717317i	$0.745370\pi$
$542$			1.99821i			0.0858304i
$543$		0			0
$544$	11.5138			0.493650
$545$	19.7232	−	28.0316i	0.844847	−	1.20074i
$546$		0			0
$547$			12.9093i			0.551961i	0.961163	+	0.275980i	$0.0890024\pi$
$547$			12.9093i			0.551961i	−0.961163	+	0.275980i	$0.910998\pi$
$548$			19.3374i			0.826051i
$549$		0			0
$550$	−3.24804	+	1.16548i	−0.138497	+	0.0496961i
$551$	6.97542			0.297163
$552$		0			0
$553$		−	6.06845i		−	0.258057i
$554$	−3.14688			−0.133698
$555$		0			0
$556$	5.44186			0.230786
$557$			23.0195i			0.975369i	0.873020	+	0.487685i	$0.162158\pi$
$557$			23.0195i			0.975369i	−0.873020	+	0.487685i	$0.837842\pi$
$558$		0			0
$559$	1.49548			0.0632522
$560$	7.70623	+	5.42214i	0.325648	+	0.229127i
$561$		0			0
$562$		−	3.28247i		−	0.138463i
$563$			27.3234i			1.15154i	0.817611	+	0.575771i	$0.195298\pi$
$563$			27.3234i			1.15154i	−0.817611	+	0.575771i	$0.804702\pi$
$564$		0			0
$565$	13.3282	+	9.37781i	0.560723	+	0.394527i
$566$	2.66068			0.111837
$567$		0			0
$568$			1.24657i			0.0523049i
$569$	−0.803952			−0.0337034			−0.0168517	−	0.999858i	$-0.505364\pi$
$569$	−0.803952			−0.0337034			−0.0168517	+	0.999858i	$0.505364\pi$
$570$		0			0
$571$	43.4604			1.81876			0.909381	−	0.415964i	$-0.136556\pi$
$571$	43.4604			1.81876			0.909381	+	0.415964i	$0.136556\pi$
$572$			34.5315i			1.44384i
$573$		0			0
$574$		0			0
$575$	3.67116	−	1.31730i	0.153098	−	0.0549353i
$576$		0			0
$577$			1.27345i			0.0530146i	0.999649	+	0.0265073i	$0.00843852\pi$
$577$			1.27345i			0.0530146i	−0.999649	+	0.0265073i	$0.991561\pi$
$578$			3.40311i			0.141551i
$579$		0			0
$580$	2.54181	−	3.61256i	0.105543	−	0.150003i
$581$	−6.80395			−0.282276
$582$		0			0
$583$			49.6812i			2.05758i
$584$	5.43644			0.224961
$585$		0			0
$586$	1.48560			0.0613696
$587$			31.8678i			1.31533i	0.753312	+	0.657663i	$0.228455\pi$
$587$			31.8678i			1.31533i	−0.753312	+	0.657663i	$0.771545\pi$
$588$		0			0
$589$	−44.6565			−1.84004
$590$	2.86721	+	2.01738i	0.118041	+	0.0830543i
$591$		0			0
$592$			4.21392i			0.173191i
$593$		−	1.21043i		−	0.0497064i	−0.999691	−	0.0248532i	$-0.992088\pi$
$593$		−	1.21043i		−	0.0497064i	0.999691	−	0.0248532i	$-0.00791183\pi$
$594$		0			0
$595$	−8.75479	+	12.4428i	−0.358911	+	0.510104i
$596$	−8.93735			−0.366088
$597$		0			0
$598$			0.485676i			0.0198608i
$599$	24.2053			0.989003			0.494501	−	0.869177i	$-0.335351\pi$
$599$	24.2053			0.989003			0.494501	+	0.869177i	$0.335351\pi$
$600$		0			0
$601$	4.68586			0.191140			0.0955702	−	0.995423i	$-0.469533\pi$
$601$	4.68586			0.191140			0.0955702	+	0.995423i	$0.469533\pi$
$602$			0.0645730i			0.00263180i
$603$		0			0
$604$	5.53898			0.225378
$605$	−10.7794	+	15.3202i	−0.438244	+	0.622855i
$606$		0			0
$607$		−	0.502641i		−	0.0204016i	−0.999948	−	0.0102008i	$-0.996753\pi$
$607$		−	0.502641i		−	0.0204016i	0.999948	−	0.0102008i	$-0.00324707\pi$
$608$			12.9093i			0.523540i
$609$		0			0
$610$	−0.328836	−	0.231371i	−0.0133142	−	0.00936792i
$611$	18.8672			0.763286
$612$		0			0
$613$		−	22.9142i		−	0.925496i	−0.886490	−	0.462748i	$-0.846863\pi$
$613$		−	22.9142i		−	0.925496i	0.886490	−	0.462748i	$-0.153137\pi$
$614$	−3.03868			−0.122631
$615$		0			0
$616$	−3.00060			−0.120898
$617$			15.8574i			0.638397i	0.947688	+	0.319198i	$0.103414\pi$
$617$			15.8574i			0.638397i	−0.947688	+	0.319198i	$0.896586\pi$
$618$		0			0
$619$	35.4014			1.42290			0.711451	−	0.702736i	$-0.248039\pi$
$619$	35.4014			1.42290			0.711451	+	0.702736i	$0.248039\pi$
$620$	−16.2726	+	23.1275i	−0.653524	+	0.928823i
$621$		0			0
$622$		−	1.45327i		−	0.0582707i
$623$			11.8156i			0.473383i
$624$		0			0
$625$	−19.2966	+	15.8947i	−0.771864	+	0.635788i
$626$	−2.27846			−0.0910658
$627$		0			0
$628$			9.82734i			0.392154i
$629$	−6.80395			−0.271291
$630$		0			0
$631$	44.7056			1.77970			0.889851	−	0.456250i	$-0.150808\pi$
$631$	44.7056			1.77970			0.889851	+	0.456250i	$0.150808\pi$
$632$		−	3.45852i		−	0.137573i
$633$		0			0
$634$	−3.51379			−0.139551
$635$	32.4260	+	22.8150i	1.28678	+	0.905388i
$636$		0			0
$637$			23.0480i			0.913194i
$638$			0.690163i			0.0273238i
$639$		0			0
$640$	8.89523	+	6.25872i	0.351615	+	0.247398i
$641$	−10.0689			−0.397699			−0.198849	−	0.980030i	$-0.563720\pi$
$641$	−10.0689			−0.397699			−0.198849	+	0.980030i	$0.563720\pi$
$642$		0			0
$643$		−	13.9760i		−	0.551161i	−0.961278	−	0.275580i	$-0.911130\pi$
$643$		−	13.9760i		−	0.551161i	0.961278	−	0.275580i	$-0.0888700\pi$
$644$	1.68526			0.0664085
$645$		0			0
$646$	−6.80395			−0.267698
$647$		−	31.1607i		−	1.22505i	−0.790450	−	0.612527i	$-0.790153\pi$
$647$		−	31.1607i		−	1.22505i	0.790450	−	0.612527i	$-0.209847\pi$
$648$		0			0
$649$	44.0198			1.72793
$650$	−1.05139	−	2.93010i	−0.0412390	−	0.114928i
$651$		0			0
$652$		−	41.0127i		−	1.60618i
$653$		−	26.1129i		−	1.02188i	−0.859617	−	0.510939i	$-0.829298\pi$
$653$		−	26.1129i		−	1.02188i	0.859617	−	0.510939i	$-0.170702\pi$
$654$		0			0
$655$	9.41668	−	13.3835i	0.367940	−	0.522936i
$656$		0			0
$657$		0			0
$658$			0.814661i			0.0317588i
$659$	−28.5974			−1.11400			−0.556999	−	0.830513i	$-0.688047\pi$
$659$	−28.5974			−1.11400			−0.556999	+	0.830513i	$0.688047\pi$
$660$		0			0
$661$	−38.9994			−1.51690			−0.758450	−	0.651731i	$-0.774043\pi$
$661$	−38.9994			−1.51690			−0.758450	+	0.651731i	$0.774043\pi$
$662$		−	1.23731i		−	0.0480895i
$663$		0			0
$664$	−3.87770			−0.150484
$665$	−13.9508	−	9.81587i	−0.540990	−	0.380643i
$666$		0			0
$667$		−	0.780070i		−	0.0302044i
$668$		−	43.2976i		−	1.67523i
$669$		0			0
$670$	−1.19183	+	1.69390i	−0.0460445	+	0.0654409i
$671$	−5.04856			−0.194897
$672$		0			0
$673$			38.6725i			1.49072i	0.666665	+	0.745358i	$0.267721\pi$
$673$			38.6725i			1.49072i	−0.666665	+	0.745358i	$0.732279\pi$
$674$	−5.24100			−0.201876
$675$		0			0
$676$	−5.47090			−0.210419
$677$		−	28.4800i		−	1.09458i	−0.836944	−	0.547288i	$-0.815660\pi$
$677$		−	28.4800i		−	1.09458i	0.836944	−	0.547288i	$-0.184340\pi$
$678$		0			0
$679$	19.0486			0.731017
$680$	−4.98951	+	7.09136i	−0.191339	+	0.271941i
$681$		0			0
$682$		−	4.41841i		−	0.169190i
$683$			12.4159i			0.475081i	0.971378	+	0.237540i	$0.0763412\pi$
$683$			12.4159i			0.475081i	−0.971378	+	0.237540i	$0.923659\pi$
$684$		0			0
$685$	−17.9017	−	12.5957i	−0.683988	−	0.481257i
$686$	−2.19544			−0.0838224
$687$		0			0
$688$		−	1.45106i		−	0.0553211i
$689$	−44.8180			−1.70743
$690$		0			0
$691$	10.8040			0.411002			0.205501	−	0.978657i	$-0.434118\pi$
$691$	10.8040			0.411002			0.205501	+	0.978657i	$0.434118\pi$
$692$		−	6.42808i		−	0.244359i
$693$		0			0
$694$	4.87709			0.185132
$695$	−3.54465	+	5.03784i	−0.134456	+	0.191096i
$696$		0			0
$697$		0			0
$698$		−	0.904568i		−	0.0342384i
$699$		0			0
$700$	−10.1673	+	3.64825i	−0.384286	+	0.137891i
$701$	−8.47512			−0.320101			−0.160050	−	0.987109i	$-0.551166\pi$
$701$	−8.47512			−0.320101			−0.160050	+	0.987109i	$0.551166\pi$
$702$		0			0
$703$		−	7.62859i		−	0.287718i
$704$	32.6454			1.23037
$705$		0			0
$706$	2.11809			0.0797153
$707$		−	13.9491i		−	0.524612i
$708$		0			0
$709$	32.8180			1.23251			0.616254	−	0.787548i	$-0.288650\pi$
$709$	32.8180			1.23251			0.616254	+	0.787548i	$0.288650\pi$
$710$	−0.573442	−	0.403477i	−0.0215209	−	0.0151422i
$711$		0			0
$712$			6.73394i			0.252365i
$713$			4.99399i			0.187026i
$714$		0			0
$715$	−31.9678	−	22.4927i	−1.19553	−	0.841178i
$716$	−14.2152			−0.531247
$717$		0			0
$718$			0.181363i			0.00676842i
$719$	39.7542			1.48258			0.741290	−	0.671184i	$-0.234214\pi$
$719$	39.7542			1.48258			0.741290	+	0.671184i	$0.234214\pi$
$720$		0			0
$721$	−5.63731			−0.209944
$722$		−	4.64968i		−	0.173043i
$723$		0			0
$724$	25.7485			0.956936
$725$	1.68870	+	4.70620i	0.0627166	+	0.174784i
$726$		0			0
$727$		−	49.4844i		−	1.83527i	−0.397419	−	0.917637i	$-0.630094\pi$
$727$		−	49.4844i		−	1.83527i	0.397419	−	0.917637i	$-0.369906\pi$
$728$		−	2.70689i		−	0.100324i
$729$		0			0
$730$	−1.75961	+	2.50085i	−0.0651260	+	0.0925606i
$731$	2.34293			0.0866565
$732$		0			0
$733$		−	46.2381i		−	1.70784i	−0.520403	−	0.853921i	$-0.674218\pi$
$733$		−	46.2381i		−	1.70784i	0.520403	−	0.853921i	$-0.325782\pi$
$734$	1.66128			0.0613191
$735$		0			0
$736$	1.44366			0.0532140
$737$			26.0061i			0.957946i
$738$		0			0
$739$	−28.7155			−1.05632			−0.528159	−	0.849146i	$-0.677117\pi$
$739$	−28.7155			−1.05632			−0.528159	+	0.849146i	$0.677117\pi$
$740$	−3.95084	−	2.77983i	−0.145236	−	0.102188i
$741$		0			0
$742$		−	1.93518i		−	0.0710428i
$743$		−	27.0536i		−	0.992502i	−0.868179	−	0.496251i	$-0.834710\pi$
$743$		−	27.0536i		−	0.992502i	0.868179	−	0.496251i	$-0.165290\pi$
$744$		0			0
$745$	5.82149	−	8.27380i	0.213283	−	0.303129i
$746$	−1.11303			−0.0407508
$747$		0			0
$748$			54.0996i			1.97808i
$749$	−1.19605			−0.0437026
$750$		0			0
$751$	−26.8771			−0.980759			−0.490380	−	0.871509i	$-0.663142\pi$
$751$	−26.8771			−0.980759			−0.490380	+	0.871509i	$0.663142\pi$
$752$		−	18.3067i		−	0.667578i
$753$		0			0
$754$	−0.622605			−0.0226739
$755$	−3.60790	+	5.12775i	−0.131305	+	0.186618i
$756$		0			0
$757$			7.28814i			0.264892i	0.991190	+	0.132446i	$0.0422831\pi$
$757$			7.28814i			0.264892i	−0.991190	+	0.132446i	$0.957717\pi$
$758$			2.84130i			0.103201i
$759$		0			0
$760$	−7.95084	−	5.59425i	−0.288407	−	0.202925i
$761$	31.6079			1.14579			0.572893	−	0.819630i	$-0.305821\pi$
$761$	31.6079			1.14579			0.572893	+	0.819630i	$0.305821\pi$
$762$		0			0
$763$			16.7636i			0.606882i
$764$	19.9958			0.723422
$765$		0			0
$766$	0.514398			0.0185860
$767$			39.7108i			1.43387i
$768$		0			0
$769$	0.293769			0.0105936			0.00529679	−	0.999986i	$-0.498314\pi$
$769$	0.293769			0.0105936			0.00529679	+	0.999986i	$0.498314\pi$
$770$	0.971204	−	1.38033i	0.0349997	−	0.0497435i
$771$		0			0
$772$		−	45.1559i		−	1.62520i
$773$		−	28.4877i		−	1.02463i	−0.858797	−	0.512316i	$-0.828788\pi$
$773$		−	28.4877i		−	1.02463i	0.858797	−	0.512316i	$-0.171212\pi$
$774$		0			0
$775$	−10.8110	−	30.1290i	−0.388343	−	1.08226i
$776$	10.8561			0.389712
$777$		0			0
$778$			1.88142i			0.0674521i
$779$		0			0
$780$		0			0
$781$	−8.80395			−0.315030
$782$			0.760895i			0.0272095i
$783$		0			0
$784$	22.3633			0.798689
$785$	−9.09772	−	6.40120i	−0.324712	−	0.228469i
$786$		0			0
$787$			32.9883i			1.17591i	0.808895	+	0.587954i	$0.200066\pi$
$787$			32.9883i			1.17591i	−0.808895	+	0.587954i	$0.799934\pi$
$788$		−	43.5997i		−	1.55317i
$789$		0			0
$790$	1.59098	+	1.11942i	0.0566044	+	0.0398271i
$791$	−7.97060			−0.283402
$792$		0			0
$793$		−	4.55437i		−	0.161731i
$794$	5.69213			0.202006
$795$		0			0
$796$	−10.2644			−0.363811
$797$		−	30.9194i		−	1.09522i	−0.836733	−	0.547611i	$-0.815537\pi$
$797$		−	30.9194i		−	1.09522i	0.836733	−	0.547611i	$-0.184463\pi$
$798$		0			0
$799$	29.5587			1.04571
$800$	−8.70967	+	3.12524i	−0.307933	+	0.110494i
$801$		0			0
$802$			4.08942i			0.144402i
$803$			38.3951i			1.35493i
$804$		0			0
$805$	−1.09772	+	1.56014i	−0.0386896	+	0.0549877i
$806$	3.98590			0.140397
$807$		0			0
$808$		−	7.94987i		−	0.279675i
$809$	21.0977			0.741756			0.370878	−	0.928682i	$-0.379057\pi$
$809$	21.0977			0.741756			0.370878	+	0.928682i	$0.379057\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$			2.16040i			0.0758150i
$813$		0			0
$814$	0.754790			0.0264554
$815$	37.9678	+	26.7143i	1.32995	+	0.935761i
$816$		0			0
$817$			2.62690i			0.0919035i
$818$			2.04582i			0.0715303i
$819$		0			0
$820$		0			0
$821$	15.2791			0.533243			0.266622	−	0.963801i	$-0.414093\pi$
$821$	15.2791			0.533243			0.266622	+	0.963801i	$0.414093\pi$
$822$		0			0
$823$			7.78152i			0.271247i	0.990760	+	0.135623i	$0.0433037\pi$
$823$			7.78152i			0.271247i	−0.990760	+	0.135623i	$0.956696\pi$
$824$	−3.21280			−0.111923
$825$		0			0
$826$	−1.71466			−0.0596607
$827$			0.376593i			0.0130954i	0.999979	+	0.00654772i	$0.00208422\pi$
$827$			0.376593i			0.0130954i	−0.999979	+	0.00654772i	$0.997916\pi$
$828$		0			0
$829$	49.8723			1.73214			0.866068	−	0.499927i	$-0.166640\pi$
$829$	49.8723			1.73214			0.866068	+	0.499927i	$0.166640\pi$
$830$	1.25509	−	1.78380i	0.0435649	−	0.0619167i
$831$		0			0
$832$			29.4498i			1.02099i
$833$			36.1086i			1.25109i
$834$		0			0
$835$	40.0830	+	28.2026i	1.38713	+	0.975991i
$836$	−60.6565			−2.09785
$837$		0			0
$838$		−	5.62113i		−	0.194179i
$839$	−0.0590441			−0.00203843			−0.00101921	−	0.999999i	$-0.500324\pi$
$839$	−0.0590441			−0.00203843			−0.00101921	+	0.999999i	$0.500324\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$		−	2.61919i		−	0.0902632i
$843$		0			0
$844$	3.25388			0.112003
$845$	3.56356	−	5.06472i	0.122590	−	0.174232i
$846$		0			0
$847$		−	9.16185i		−	0.314805i
$848$			43.4867i			1.49334i
$849$		0			0
$850$	−1.64719	−	4.59051i	−0.0564980	−	0.157453i
$851$	−0.853115			−0.0292444
$852$		0			0
$853$		−	2.77983i		−	0.0951795i	−0.998867	−	0.0475897i	$-0.984846\pi$
$853$		−	2.77983i		−	0.0951795i	0.998867	−	0.0475897i	$-0.0151540\pi$
$854$	0.196652			0.00672929
$855$		0			0
$856$	−0.681649			−0.0232983
$857$		−	0.850802i		−	0.0290628i	−0.999894	−	0.0145314i	$-0.995374\pi$
$857$		−	0.850802i		−	0.0290628i	0.999894	−	0.0145314i	$-0.00462566\pi$
$858$		0			0
$859$	−7.35342			−0.250895			−0.125448	−	0.992100i	$-0.540037\pi$
$859$	−7.35342			−0.250895			−0.125448	+	0.992100i	$0.540037\pi$
$860$	1.36047	+	0.957230i	0.0463915	+	0.0326413i
$861$		0			0
$862$		−	4.12556i		−	0.140517i
$863$			42.6167i			1.45069i	0.688386	+	0.725345i	$0.258320\pi$
$863$			42.6167i			1.45069i	−0.688386	+	0.725345i	$0.741680\pi$
$864$		0			0
$865$	5.95084	+	4.18704i	0.202335	+	0.142364i
$866$	1.68105			0.0571242
$867$		0			0
$868$		−	13.8308i		−	0.469448i
$869$	24.4260			0.828594
$870$		0			0
$871$	−23.4604			−0.794926
$872$			9.55386i			0.323535i
$873$		0			0
$874$	−0.853115			−0.0288571
$875$	3.24521	−	11.7887i	0.109708	−	0.398532i
$876$		0			0
$877$			13.4196i			0.453148i	0.973994	+	0.226574i	$0.0727526\pi$
$877$			13.4196i			0.453148i	−0.973994	+	0.226574i	$0.927247\pi$
$878$			4.63436i			0.156402i
$879$		0			0
$880$	−21.8245	+	31.0181i	−0.735703	+	1.04562i
$881$	38.3135			1.29082			0.645408	−	0.763838i	$-0.276687\pi$
$881$	38.3135			1.29082			0.645408	+	0.763838i	$0.276687\pi$
$882$		0			0
$883$			31.5542i			1.06188i	0.847408	+	0.530942i	$0.178162\pi$
$883$			31.5542i			1.06188i	−0.847408	+	0.530942i	$0.821838\pi$
$884$	−48.8040			−1.64145
$885$		0			0
$886$	0.534161			0.0179455
$887$		−	23.3961i		−	0.785565i	−0.919631	−	0.392783i	$-0.871512\pi$
$887$		−	23.3961i		−	0.785565i	0.919631	−	0.392783i	$-0.128488\pi$
$888$		0			0
$889$	−19.3915			−0.650370
$890$	−3.09772	−	2.17957i	−0.103836	−	0.0730594i
$891$		0			0
$892$		−	18.7179i		−	0.626722i
$893$			33.1413i			1.10903i
$894$		0			0
$895$	9.25931	−	13.1598i	0.309504	−	0.439884i
$896$	−5.31956			−0.177714
$897$		0			0
$898$		−	0.0722810i		−	0.00241205i
$899$	−6.40198			−0.213518
$900$		0			0
$901$	−70.2152			−2.33921
$902$		0			0
$903$		0			0
$904$	−4.54259			−0.151084
$905$	−16.7717	+	23.8369i	−0.557511	+	0.792364i
$906$		0			0
$907$			32.4150i			1.07632i	0.842842	+	0.538161i	$0.180881\pi$
$907$			32.4150i			1.07632i	−0.842842	+	0.538161i	$0.819119\pi$
$908$		−	11.3152i		−	0.375508i
$909$		0			0
$910$	1.24521	+	0.876136i	0.0412783	+	0.0290436i
$911$	45.2749			1.50002			0.750011	−	0.661425i	$-0.230048\pi$
$911$	45.2749			1.50002			0.750011	+	0.661425i	$0.230048\pi$
$912$		0			0
$913$		−	27.3864i		−	0.906357i
$914$	−0.215206			−0.00711837
$915$		0			0
$916$	−29.9214			−0.988632
$917$			8.00364i			0.264303i
$918$		0			0
$919$	5.90167			0.194678			0.0973391	−	0.995251i	$-0.468967\pi$
$919$	5.90167			0.194678			0.0973391	+	0.995251i	$0.468967\pi$
$920$	−0.625612	+	0.889152i	−0.0206258	+	0.0293145i
$921$		0			0
$922$			2.28710i			0.0753218i
$923$		−	7.94216i		−	0.261419i
$924$		0			0
$925$	5.14688	−	1.84683i	0.169229	−	0.0607233i
$926$	−2.95566			−0.0971289
$927$		0			0
$928$			1.85068i			0.0607516i
$929$	−6.00000			−0.196854			−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000			−0.196854			−0.0984268	+	0.995144i	$0.531381\pi$
$930$		0			0
$931$	−40.4850			−1.32684
$932$		−	1.41647i		−	0.0463979i
$933$		0			0
$934$	4.69695			0.153689
$935$	−50.0830	−	35.2386i	−1.63789	−	1.15243i
$936$		0			0
$937$			43.0755i			1.40721i	0.710589	+	0.703607i	$0.248429\pi$
$937$			43.0755i			1.40721i	−0.710589	+	0.703607i	$0.751571\pi$
$938$		−	1.01299i		−	0.0330753i
$939$		0			0
$940$	17.1638	+	12.0765i	0.559822	+	0.393893i
$941$	−2.91637			−0.0950711			−0.0475355	−	0.998870i	$-0.515137\pi$
$941$	−2.91637			−0.0950711			−0.0475355	+	0.998870i	$0.515137\pi$
$942$		0			0
$943$		0			0
$944$	38.5312			1.25408
$945$		0			0
$946$	−0.259911			−0.00845043
$947$		−	0.556407i		−	0.0180808i	−0.999959	−	0.00904041i	$-0.997122\pi$
$947$		−	0.556407i		−	0.0180808i	0.999959	−	0.00904041i	$-0.00287769\pi$
$948$		0			0
$949$	−34.6367			−1.12435
$950$	5.14688	−	1.84683i	0.166987	−	0.0599190i
$951$		0			0
$952$		−	4.24080i		−	0.137445i
$953$		−	37.1661i		−	1.20393i	−0.798523	−	0.601964i	$-0.794385\pi$
$953$		−	37.1661i		−	1.20393i	0.798523	−	0.601964i	$-0.205615\pi$
$954$		0			0
$955$	−13.0246	+	18.5112i	−0.421466	+	0.599009i
$956$	−3.95084			−0.127779
$957$		0			0
$958$			5.13700i			0.165969i
$959$	10.7056			0.345703
$960$		0			0
$961$	9.98530			0.322106
$962$			0.680906i			0.0219533i
$963$		0			0
$964$	34.2305			1.10249
$965$	41.8033	+	29.4130i	1.34570	+	0.946839i
$966$		0			0
$967$		−	24.2754i		−	0.780643i	−0.920679	−	0.390322i	$-0.872364\pi$
$967$		−	24.2754i		−	0.780643i	0.920679	−	0.390322i	$-0.127636\pi$
$968$		−	5.22151i		−	0.167826i
$969$		0			0
$970$	−3.51379	+	4.99399i	−0.112821	+	0.160347i
$971$	17.1709			0.551039			0.275520	−	0.961295i	$-0.411150\pi$
$971$	17.1709			0.551039			0.275520	+	0.961295i	$0.411150\pi$
$972$		0			0
$973$		−	3.01275i		−	0.0965842i
$974$	2.21220			0.0708834
$975$		0			0
$976$	−4.41908			−0.141451
$977$			4.95785i			0.158616i	0.996850	+	0.0793078i	$0.0252710\pi$
$977$			4.95785i			0.158616i	−0.996850	+	0.0793078i	$0.974729\pi$
$978$		0			0
$979$	−47.5587			−1.51998
$980$	−14.7526	+	20.9671i	−0.471253	+	0.669770i
$981$		0			0
$982$			0.644104i			0.0205542i
$983$		−	11.5651i		−	0.368869i	−0.982845	−	0.184434i	$-0.940955\pi$
$983$		−	11.5651i		−	0.368869i	0.982845	−	0.184434i	$-0.0590453\pi$
$984$		0			0
$985$	40.3627	+	28.3994i	1.28606	+	0.904879i
$986$	−0.975419			−0.0310637
$987$		0			0
$988$		−	54.7190i		−	1.74084i
$989$	0.293769			0.00934132
$990$		0			0
$991$	−18.3429			−0.582682			−0.291341	−	0.956619i	$-0.594102\pi$
$991$	−18.3429			−0.582682			−0.291341	+	0.956619i	$0.594102\pi$
$992$		−	11.8480i		−	0.376175i
$993$		0			0
$994$	0.342932			0.0108771
$995$	6.68586	−	9.50230i	0.211956	−	0.301243i
$996$		0			0
$997$			32.2997i			1.02294i	0.859300	+	0.511471i	$0.170899\pi$
$997$			32.2997i			1.02294i	−0.859300	+	0.511471i	$0.829101\pi$
$998$			4.71435i			0.149230i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.h.784.3		6
3.2	odd	2		145.2.b.c.59.4	yes	6
5.2	odd	4		6525.2.a.bt.1.4		6
5.3	odd	4		6525.2.a.bt.1.3		6
5.4	even	2	inner	1305.2.c.h.784.4		6
12.11	even	2		2320.2.d.g.929.2		6
15.2	even	4		725.2.a.l.1.3		6
15.8	even	4		725.2.a.l.1.4		6
15.14	odd	2		145.2.b.c.59.3	✓	6
60.59	even	2		2320.2.d.g.929.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.b.c.59.3	✓	6	15.14	odd	2
145.2.b.c.59.4	yes	6	3.2	odd	2
725.2.a.l.1.3		6	15.2	even	4
725.2.a.l.1.4		6	15.8	even	4
1305.2.c.h.784.3		6	1.1	even	1	trivial
1305.2.c.h.784.4		6	5.4	even	2	inner
2320.2.d.g.929.2		6	12.11	even	2
2320.2.d.g.929.5		6	60.59	even	2
6525.2.a.bt.1.3		6	5.3	odd	4
6525.2.a.bt.1.4		6	5.2	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.156785i q^{2} +1.97542 q^{4} +(-1.28672 + 1.82876i) q^{5} -1.09364i q^{7} -0.623285i q^{8} +(0.286721 + 0.201738i) q^{10} +4.40198 q^{11} +3.97108i q^{13} -0.171466 q^{14} +3.85312 q^{16} +6.22138i q^{17} -6.97542 q^{19} +(-2.54181 + 3.61256i) q^{20} -0.690163i q^{22} +0.780070i q^{23} +(-1.68870 - 4.70620i) q^{25} +0.622605 q^{26} -2.16040i q^{28} -1.00000 q^{29} +6.40198 q^{31} -1.85068i q^{32} +0.975419 q^{34} +(2.00000 + 1.40721i) q^{35} +1.09364i q^{37} +1.09364i q^{38} +(1.13984 + 0.801994i) q^{40} -0.376593i q^{43} +8.69575 q^{44} +0.122303 q^{46} -4.75115i q^{47} +5.80395 q^{49} +(-0.737860 + 0.264762i) q^{50} +7.84455i q^{52} +11.2861i q^{53} +(-5.66412 + 8.05014i) q^{55} -0.681649 q^{56} +0.156785i q^{58} +10.0000 q^{59} -1.14688 q^{61} -1.00373i q^{62} +7.41607 q^{64} +(-7.26214 - 5.10967i) q^{65} +5.90782i q^{67} +12.2898i q^{68} +(0.220629 - 0.313570i) q^{70} -2.00000 q^{71} +8.72223i q^{73} +0.171466 q^{74} -13.7794 q^{76} -4.81418i q^{77} +5.54886 q^{79} +(-4.95789 + 7.04641i) q^{80} -6.22138i q^{83} +(-11.3774 - 8.00519i) q^{85} -0.0590441 q^{86} -2.74369i q^{88} -10.8040 q^{89} +4.34293 q^{91} +1.54096i q^{92} -0.744908 q^{94} +(8.97542 - 12.7563i) q^{95} +17.4176i q^{97} -0.909972i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 14 q^{4} - 3 q^{5} - 3 q^{10} + 10 q^{11} - 8 q^{14} + 42 q^{16} - 16 q^{19} - 13 q^{20} + 11 q^{25} + 46 q^{26} - 6 q^{29} + 22 q^{31} - 20 q^{34} + 12 q^{35} + 21 q^{40} - 2 q^{44} - 44 q^{46} + 2 q^{49}+ \cdots + 28 q^{95}+O(q^{100}) \) 6 * q - 14 * q^4 - 3 * q^5 - 3 * q^10 + 10 * q^11 - 8 * q^14 + 42 * q^16 - 16 * q^19 - 13 * q^20 + 11 * q^25 + 46 * q^26 - 6 * q^29 + 22 * q^31 - 20 * q^34 + 12 * q^35 + 21 * q^40 - 2 * q^44 - 44 * q^46 + 2 * q^49 - 35 * q^50 + 13 * q^55 - 16 * q^56 + 60 * q^59 + 12 * q^61 - 38 * q^64 - 13 * q^65 + 60 * q^70 - 12 * q^71 + 8 * q^74 - 24 * q^76 - 2 * q^79 + 55 * q^80 - 26 * q^85 + 30 * q^86 - 32 * q^89 + 40 * q^91 - 2 * q^94 + 28 * q^95

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