LMFDB - Embedded newform 1665.2.c.e.334.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1665,2,Mod(334,1665)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1665.334"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1665, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1665 = 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1665.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0,-22,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.2950919365$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 28x^{16} + 306x^{14} + 1684x^{12} + 5049x^{10} + 8280x^{8} + 7004x^{6} + 2672x^{4} + 368x^{2} + 16 $ x^18 + 28x^16 + 306x^14 + 1684x^12 + 5049x^10 + 8280x^8 + 7004x^6 + 2672x^4 + 368x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			334.11
Root			$-0.296889i$ of defining polynomial
Character	$\chi$	$=$	1665.334
Dual form			1665.2.c.e.334.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.703111i q^{2} +1.50564 q^{4} +(2.08504 + 0.807843i) q^{5} -0.501390i q^{7} +2.46485i q^{8} +(-0.568003 + 1.46601i) q^{10} +1.80401 q^{11} +1.63218i q^{13} +0.352533 q^{14} +1.27821 q^{16} +1.92844i q^{17} +0.869173 q^{19} +(3.13931 + 1.21632i) q^{20} +1.26842i q^{22} -4.86522i q^{23} +(3.69478 + 3.36877i) q^{25} -1.14761 q^{26} -0.754910i q^{28} -3.15000 q^{29} +2.39134 q^{31} +5.82842i q^{32} -1.35591 q^{34} +(0.405044 - 1.04542i) q^{35} +1.00000i q^{37} +0.611125i q^{38} +(-1.99121 + 5.13931i) q^{40} -8.24040 q^{41} +11.6931i q^{43} +2.71619 q^{44} +3.42079 q^{46} -1.43311i q^{47} +6.74861 q^{49} +(-2.36862 + 2.59784i) q^{50} +2.45747i q^{52} -10.7692i q^{53} +(3.76144 + 1.45736i) q^{55} +1.23585 q^{56} -2.21480i q^{58} +8.71701 q^{59} -7.84555 q^{61} +1.68138i q^{62} -1.54161 q^{64} +(-1.31855 + 3.40317i) q^{65} -11.8599i q^{67} +2.90353i q^{68} +(0.735044 + 0.284791i) q^{70} +6.06069 q^{71} -5.56086i q^{73} -0.703111 q^{74} +1.30866 q^{76} -0.904514i q^{77} -7.44924 q^{79} +(2.66511 + 1.03259i) q^{80} -5.79391i q^{82} +4.70795i q^{83} +(-1.55788 + 4.02088i) q^{85} -8.22154 q^{86} +4.44662i q^{88} +5.16332 q^{89} +0.818361 q^{91} -7.32524i q^{92} +1.00764 q^{94} +(1.81226 + 0.702156i) q^{95} +6.48639i q^{97} +4.74502i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 22 q^{4} - 2 q^{5} + 6 q^{10} - 8 q^{14} + 22 q^{16} + 8 q^{19} + 4 q^{20} - 18 q^{25} + 12 q^{26} - 4 q^{29} - 12 q^{31} - 12 q^{34} + 2 q^{35} - 6 q^{40} - 4 q^{41} + 8 q^{44} + 32 q^{46} + 14 q^{49}+ \cdots + 44 q^{95}+O(q^{100}) $ 18 * q - 22 * q^4 - 2 * q^5 + 6 * q^10 - 8 * q^14 + 22 * q^16 + 8 * q^19 + 4 * q^20 - 18 * q^25 + 12 * q^26 - 4 * q^29 - 12 * q^31 - 12 * q^34 + 2 * q^35 - 6 * q^40 - 4 * q^41 + 8 * q^44 + 32 * q^46 + 14 * q^49 - 8 * q^50 - 34 * q^55 + 48 * q^56 + 20 * q^59 + 16 * q^61 - 30 * q^64 - 20 * q^65 + 40 * q^70 - 16 * q^71 - 10 * q^74 - 96 * q^76 + 52 * q^79 - 36 * q^80 - 8 * q^85 + 32 * q^86 - 16 * q^89 - 36 * q^91 + 52 * q^94 + 44 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1665\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			0.703111i			0.497174i	0.968610	+	0.248587i	$0.0799662\pi$
$2$			0.703111i			0.497174i	−0.968610	+	0.248587i	$0.920034\pi$
$3$		0			0
$3$		0			0
$4$	1.50564			0.752818
$5$	2.08504	+	0.807843i	0.932458	+	0.361279i
$5$	2.08504	+	0.807843i	0.932458	+	0.361279i
$6$		0			0
$7$		−	0.501390i		−	0.189508i	−0.995501	−	0.0947538i	$-0.969794\pi$
$7$		−	0.501390i		−	0.189508i	0.995501	−	0.0947538i	$-0.0302064\pi$
$8$			2.46485i			0.871456i
$9$		0			0
$10$	−0.568003	+	1.46601i	−0.179618	+	0.463594i
$11$	1.80401			0.543931			0.271965	−	0.962307i	$-0.412326\pi$
$11$	1.80401			0.543931			0.271965	+	0.962307i	$0.412326\pi$
$12$		0			0
$13$			1.63218i			0.452686i	0.974048	+	0.226343i	$0.0726771\pi$
$13$			1.63218i			0.452686i	−0.974048	+	0.226343i	$0.927323\pi$
$14$	0.352533			0.0942183
$15$		0			0
$16$	1.27821			0.319552
$17$			1.92844i			0.467717i	0.972271	+	0.233858i	$0.0751352\pi$
$17$			1.92844i			0.467717i	−0.972271	+	0.233858i	$0.924865\pi$
$18$		0			0
$19$	0.869173			0.199402			0.0997010	−	0.995017i	$-0.468211\pi$
$19$	0.869173			0.199402			0.0997010	+	0.995017i	$0.468211\pi$
$20$	3.13931	+	1.21632i	0.701971	+	0.271977i
$21$		0			0
$22$			1.26842i			0.270428i
$23$		−	4.86522i		−	1.01447i	−0.861808	−	0.507234i	$-0.830668\pi$
$23$		−	4.86522i		−	1.01447i	0.861808	−	0.507234i	$-0.169332\pi$
$24$		0			0
$25$	3.69478	+	3.36877i	0.738956	+	0.673754i
$26$	−1.14761			−0.225064
$27$		0			0
$28$		−	0.754910i		−	0.142665i
$29$	−3.15000			−0.584940			−0.292470	−	0.956275i	$-0.594477\pi$
$29$	−3.15000			−0.584940			−0.292470	+	0.956275i	$0.594477\pi$
$30$		0			0
$31$	2.39134			0.429498			0.214749	−	0.976669i	$-0.431107\pi$
$31$	2.39134			0.429498			0.214749	+	0.976669i	$0.431107\pi$
$32$			5.82842i			1.03033i
$33$		0			0
$34$	−1.35591			−0.232537
$35$	0.405044	−	1.04542i	0.0684650	−	0.176708i
$36$		0			0
$37$			1.00000i			0.164399i
$37$			1.00000i			0.164399i
$38$			0.611125i			0.0991375i
$39$		0			0
$40$	−1.99121	+	5.13931i	−0.314838	+	0.812596i
$41$	−8.24040			−1.28693			−0.643467	−	0.765474i	$-0.722505\pi$
$41$	−8.24040			−1.28693			−0.643467	+	0.765474i	$0.722505\pi$
$42$		0			0
$43$			11.6931i			1.78318i	0.452844	+	0.891590i	$0.350410\pi$
$43$			11.6931i			1.78318i	−0.452844	+	0.891590i	$0.649590\pi$
$44$	2.71619			0.409481
$45$		0			0
$46$	3.42079			0.504368
$47$		−	1.43311i		−	0.209041i	−0.994523	−	0.104521i	$-0.966669\pi$
$47$		−	1.43311i		−	0.209041i	0.994523	−	0.104521i	$-0.0333308\pi$
$48$		0			0
$49$	6.74861			0.964087
$50$	−2.36862	+	2.59784i	−0.334973	+	0.367390i
$51$		0			0
$52$			2.45747i			0.340790i
$53$		−	10.7692i		−	1.47927i	−0.673010	−	0.739633i	$-0.734999\pi$
$53$		−	10.7692i		−	1.47927i	0.673010	−	0.739633i	$-0.265001\pi$
$54$		0			0
$55$	3.76144	+	1.45736i	0.507192	+	0.196510i
$56$	1.23585			0.165148
$57$		0			0
$58$		−	2.21480i		−	0.290817i
$59$	8.71701			1.13486			0.567429	−	0.823422i	$-0.307938\pi$
$59$	8.71701			1.13486			0.567429	+	0.823422i	$0.307938\pi$
$60$		0			0
$61$	−7.84555			−1.00452			−0.502260	−	0.864717i	$-0.667498\pi$
$61$	−7.84555			−1.00452			−0.502260	+	0.864717i	$0.667498\pi$
$62$			1.68138i			0.213535i
$63$		0			0
$64$	−1.54161			−0.192701
$65$	−1.31855	+	3.40317i	−0.163546	+	0.422111i
$66$		0			0
$67$		−	11.8599i		−	1.44891i	−0.689321	−	0.724456i	$-0.742091\pi$
$67$		−	11.8599i		−	1.44891i	0.689321	−	0.724456i	$-0.257909\pi$
$68$			2.90353i			0.352105i
$69$		0			0
$70$	0.735044	+	0.284791i	0.0878546	+	0.0340390i
$71$	6.06069			0.719272			0.359636	−	0.933093i	$-0.382901\pi$
$71$	6.06069			0.719272			0.359636	+	0.933093i	$0.382901\pi$
$72$		0			0
$73$		−	5.56086i		−	0.650849i	−0.945568	−	0.325424i	$-0.894493\pi$
$73$		−	5.56086i		−	0.650849i	0.945568	−	0.325424i	$-0.105507\pi$
$74$	−0.703111			−0.0817350
$75$		0			0
$76$	1.30866			0.150113
$77$		−	0.904514i		−	0.103079i
$78$		0			0
$79$	−7.44924			−0.838105			−0.419052	−	0.907962i	$-0.637638\pi$
$79$	−7.44924			−0.838105			−0.419052	+	0.907962i	$0.637638\pi$
$80$	2.66511	+	1.03259i	0.297969	+	0.115447i
$81$		0			0
$82$		−	5.79391i		−	0.639830i
$83$			4.70795i			0.516765i	0.966043	+	0.258382i	$0.0831894\pi$
$83$			4.70795i			0.516765i	−0.966043	+	0.258382i	$0.916811\pi$
$84$		0			0
$85$	−1.55788	+	4.02088i	−0.168976	+	0.436126i
$86$	−8.22154			−0.886551
$87$		0			0
$88$			4.44662i			0.474012i
$89$	5.16332			0.547311			0.273656	−	0.961828i	$-0.411767\pi$
$89$	5.16332			0.547311			0.273656	+	0.961828i	$0.411767\pi$
$90$		0			0
$91$	0.818361			0.0857875
$92$		−	7.32524i		−	0.763709i
$93$		0			0
$94$	1.00764			0.103930
$95$	1.81226	+	0.702156i	0.185934	+	0.0720396i
$96$		0			0
$97$			6.48639i			0.658593i	0.944227	+	0.329297i	$0.106812\pi$
$97$			6.48639i			0.658593i	−0.944227	+	0.329297i	$0.893188\pi$
$98$			4.74502i			0.479319i
$99$		0			0
$100$	5.56299	+	5.07214i	0.556299	+	0.507214i
$101$	−2.50611			−0.249367			−0.124684	−	0.992197i	$-0.539792\pi$
$101$	−2.50611			−0.249367			−0.124684	+	0.992197i	$0.539792\pi$
$102$		0			0
$103$		−	6.40079i		−	0.630688i	−0.948977	−	0.315344i	$-0.897880\pi$
$103$		−	6.40079i		−	0.630688i	0.948977	−	0.315344i	$-0.102120\pi$
$104$	−4.02309			−0.394496
$105$		0			0
$106$	7.57195			0.735453
$107$			11.6711i			1.12829i	0.825675	+	0.564146i	$0.190794\pi$
$107$			11.6711i			1.12829i	−0.825675	+	0.564146i	$0.809206\pi$
$108$		0			0
$109$	−7.93573			−0.760105			−0.380053	−	0.924965i	$-0.624094\pi$
$109$	−7.93573			−0.760105			−0.380053	+	0.924965i	$0.624094\pi$
$110$	−1.02469	+	2.64471i	−0.0977000	+	0.252163i
$111$		0			0
$112$		−	0.640881i		−	0.0605575i
$113$		−	16.2261i		−	1.52643i	−0.646146	−	0.763213i	$-0.723620\pi$
$113$		−	16.2261i		−	1.52643i	0.646146	−	0.763213i	$-0.276380\pi$
$114$		0			0
$115$	3.93033	−	10.1442i	0.366506	−	0.945949i
$116$	−4.74275			−0.440353
$117$		0			0
$118$			6.12902i			0.564222i
$119$	0.966903			0.0886358
$120$		0			0
$121$	−7.74553			−0.704139
$122$		−	5.51629i		−	0.499421i
$123$		0			0
$124$	3.60049			0.323333
$125$	4.98232	+	10.0088i	0.445632	+	0.895216i
$126$		0			0
$127$			9.56408i			0.848675i	0.905504	+	0.424337i	$0.139493\pi$
$127$			9.56408i			0.848675i	−0.905504	+	0.424337i	$0.860507\pi$
$128$			10.5729i			0.934523i
$129$		0			0
$130$	−2.39280	−	0.927086i	−0.209863	−	0.0813108i
$131$	20.2974			1.77340			0.886698	−	0.462350i	$-0.152994\pi$
$131$	20.2974			1.77340			0.886698	+	0.462350i	$0.152994\pi$
$132$		0			0
$133$		−	0.435795i		−	0.0377882i
$134$	8.33879			0.720362
$135$		0			0
$136$	−4.75333			−0.407594
$137$		−	11.0879i		−	0.947300i	−0.880713	−	0.473650i	$-0.842936\pi$
$137$		−	11.0879i		−	0.947300i	0.880713	−	0.473650i	$-0.157064\pi$
$138$		0			0
$139$	−14.1716			−1.20202			−0.601009	−	0.799242i	$-0.705235\pi$
$139$	−14.1716			−1.20202			−0.601009	+	0.799242i	$0.705235\pi$
$140$	0.609849	−	1.57402i	0.0515417	−	0.133029i
$141$		0			0
$142$			4.26134i			0.357603i
$143$			2.94448i			0.246230i
$144$		0			0
$145$	−6.56787	−	2.54471i	−0.545432	−	0.211326i
$146$	3.90990			0.323585
$147$		0			0
$148$			1.50564i			0.123762i
$149$	−17.5785			−1.44008			−0.720042	−	0.693930i	$-0.755878\pi$
$149$	−17.5785			−1.44008			−0.720042	+	0.693930i	$0.755878\pi$
$150$		0			0
$151$	10.4870			0.853422			0.426711	−	0.904388i	$-0.359672\pi$
$151$	10.4870			0.853422			0.426711	+	0.904388i	$0.359672\pi$
$152$			2.14238i			0.173770i
$153$		0			0
$154$	0.635974			0.0512482
$155$	4.98604	+	1.93183i	0.400488	+	0.155168i
$156$		0			0
$157$			14.1135i			1.12638i	0.826328	+	0.563189i	$0.190426\pi$
$157$			14.1135i			1.12638i	−0.826328	+	0.563189i	$0.809574\pi$
$158$		−	5.23764i		−	0.416684i
$159$		0			0
$160$	−4.70845	+	12.1525i	−0.372236	+	0.960739i
$161$	−2.43937			−0.192249
$162$		0			0
$163$			0.261155i			0.0204553i	0.999948	+	0.0102276i	$0.00325561\pi$
$163$			0.261155i			0.0204553i	−0.999948	+	0.0102276i	$0.996744\pi$
$164$	−12.4070			−0.968826
$165$		0			0
$166$	−3.31021			−0.256922
$167$			11.7929i			0.912560i	0.889836	+	0.456280i	$0.150818\pi$
$167$			11.7929i			0.912560i	−0.889836	+	0.456280i	$0.849182\pi$
$168$		0			0
$169$	10.3360			0.795075
$170$	−2.82713	−	1.09536i	−0.216831	−	0.0840105i
$171$		0			0
$172$			17.6055i			1.34241i
$173$		−	13.5257i		−	1.02834i	−0.857688	−	0.514170i	$-0.828100\pi$
$173$		−	13.5257i		−	1.02834i	0.857688	−	0.514170i	$-0.171900\pi$
$174$		0			0
$175$	1.68907	−	1.85252i	0.127681	−	0.140038i
$176$	2.30591			0.173814
$177$		0			0
$178$			3.63039i			0.272109i
$179$	0.443280			0.0331323			0.0165661	−	0.999863i	$-0.494727\pi$
$179$	0.443280			0.0331323			0.0165661	+	0.999863i	$0.494727\pi$
$180$		0			0
$181$	11.4380			0.850182			0.425091	−	0.905151i	$-0.360242\pi$
$181$	11.4380			0.850182			0.425091	+	0.905151i	$0.360242\pi$
$182$			0.575398i			0.0426513i
$183$		0			0
$184$	11.9920			0.884064
$185$	−0.807843	+	2.08504i	−0.0593938	+	0.153295i
$186$		0			0
$187$			3.47894i			0.254405i
$188$		−	2.15775i		−	0.157370i
$189$		0			0
$190$	−0.493693	+	1.27422i	−0.0358163	+	0.0924416i
$191$	−10.1652			−0.735531			−0.367765	−	0.929919i	$-0.619877\pi$
$191$	−10.1652			−0.735531			−0.367765	+	0.929919i	$0.619877\pi$
$192$		0			0
$193$		−	8.94479i		−	0.643860i	−0.946763	−	0.321930i	$-0.895668\pi$
$193$		−	8.94479i		−	0.643860i	0.946763	−	0.321930i	$-0.104332\pi$
$194$	−4.56065			−0.327436
$195$		0			0
$196$	10.1609			0.725782
$197$		−	8.65157i		−	0.616399i	−0.951322	−	0.308199i	$-0.900274\pi$
$197$		−	8.65157i		−	0.616399i	0.951322	−	0.308199i	$-0.0997264\pi$
$198$		0			0
$199$	−10.2145			−0.724084			−0.362042	−	0.932162i	$-0.617920\pi$
$199$	−10.2145			−0.724084			−0.362042	+	0.932162i	$0.617920\pi$
$200$	−8.30351	+	9.10707i	−0.587147	+	0.643967i
$201$		0			0
$202$		−	1.76207i		−	0.123979i
$203$			1.57938i			0.110851i
$204$		0			0
$205$	−17.1816	−	6.65695i	−1.20001	−	0.464941i
$206$	4.50046			0.313562
$207$		0			0
$208$			2.08627i			0.144657i
$209$	1.56800			0.108461
$210$		0			0
$211$	13.6414			0.939113			0.469557	−	0.882902i	$-0.344414\pi$
$211$	13.6414			0.939113			0.469557	+	0.882902i	$0.344414\pi$
$212$		−	16.2145i		−	1.11362i
$213$		0			0
$214$	−8.20611			−0.560958
$215$	−9.44619	+	24.3806i	−0.644225	+	1.66274i
$216$		0			0
$217$		−	1.19899i		−	0.0813930i
$218$		−	5.57970i		−	0.377905i
$219$		0			0
$220$	5.66336	+	2.19425i	0.381823	+	0.147937i
$221$	−3.14758			−0.211729
$222$		0			0
$223$		−	6.66288i		−	0.446180i	−0.974798	−	0.223090i	$-0.928386\pi$
$223$		−	6.66288i		−	0.446180i	0.974798	−	0.223090i	$-0.0716143\pi$
$224$	2.92231			0.195255
$225$		0			0
$226$	11.4088			0.758900
$227$			5.71859i			0.379556i	0.981827	+	0.189778i	$0.0607768\pi$
$227$			5.71859i			0.379556i	−0.981827	+	0.189778i	$0.939223\pi$
$228$		0			0
$229$	−29.9549			−1.97948			−0.989738	−	0.142895i	$-0.954359\pi$
$229$	−29.9549			−1.97948			−0.989738	+	0.142895i	$0.954359\pi$
$230$	7.13248	+	2.76346i	0.470302	+	0.182217i
$231$		0			0
$232$		−	7.76427i		−	0.509750i
$233$			25.4277i			1.66583i	0.553404	+	0.832913i	$0.313329\pi$
$233$			25.4277i			1.66583i	−0.553404	+	0.832913i	$0.686671\pi$
$234$		0			0
$235$	1.15773	−	2.98810i	0.0755221	−	0.194922i
$236$	13.1246			0.854341
$237$		0			0
$238$			0.679840i			0.0440675i
$239$	−10.9704			−0.709615			−0.354808	−	0.934939i	$-0.615454\pi$
$239$	−10.9704			−0.709615			−0.354808	+	0.934939i	$0.615454\pi$
$240$		0			0
$241$	23.8516			1.53642			0.768208	−	0.640200i	$-0.221149\pi$
$241$	23.8516			1.53642			0.768208	+	0.640200i	$0.221149\pi$
$242$		−	5.44597i		−	0.350080i
$243$		0			0
$244$	−11.8125			−0.756220
$245$	14.0711	+	5.45182i	0.898970	+	0.348304i
$246$		0			0
$247$			1.41865i			0.0902666i
$248$			5.89430i			0.374288i
$249$		0			0
$250$	−7.03731	+	3.50312i	−0.445079	+	0.221557i
$251$	−18.9886			−1.19855			−0.599275	−	0.800543i	$-0.704545\pi$
$251$	−18.9886			−1.19855			−0.599275	+	0.800543i	$0.704545\pi$
$252$		0			0
$253$		−	8.77692i		−	0.551800i
$254$	−6.72461			−0.421939
$255$		0			0
$256$	−10.5172			−0.657322
$257$			5.12928i			0.319956i	0.987121	+	0.159978i	$0.0511423\pi$
$257$			5.12928i			0.319956i	−0.987121	+	0.159978i	$0.948858\pi$
$258$		0			0
$259$	0.501390			0.0311549
$260$	−1.98525	+	5.12393i	−0.123120	+	0.317773i
$261$		0			0
$262$			14.2713i			0.881687i
$263$		−	27.1591i		−	1.67470i	−0.546666	−	0.837351i	$-0.684103\pi$
$263$		−	27.1591i		−	1.67470i	0.546666	−	0.837351i	$-0.315897\pi$
$264$		0			0
$265$	8.69984	−	22.4542i	0.534427	−	1.37935i
$266$	0.306412			0.0187873
$267$		0			0
$268$		−	17.8566i		−	1.09077i
$269$	19.0743			1.16298			0.581492	−	0.813552i	$-0.302469\pi$
$269$	19.0743			1.16298			0.581492	+	0.813552i	$0.302469\pi$
$270$		0			0
$271$	−18.0630			−1.09725			−0.548626	−	0.836068i	$-0.684849\pi$
$271$	−18.0630			−1.09725			−0.548626	+	0.836068i	$0.684849\pi$
$272$			2.46495i			0.149460i
$273$		0			0
$274$	7.79600			0.470973
$275$	6.66543	+	6.07731i	0.401941	+	0.366475i
$276$		0			0
$277$		−	22.9367i		−	1.37813i	−0.724698	−	0.689067i	$-0.758021\pi$
$277$		−	22.9367i		−	1.37813i	0.724698	−	0.689067i	$-0.241979\pi$
$278$		−	9.96420i		−	0.597613i
$279$		0			0
$280$	2.57680	+	0.998374i	0.153993	+	0.0596642i
$281$	−14.1793			−0.845869			−0.422934	−	0.906160i	$-0.639000\pi$
$281$	−14.1793			−0.845869			−0.422934	+	0.906160i	$0.639000\pi$
$282$		0			0
$283$		−	8.55472i		−	0.508525i	−0.967135	−	0.254263i	$-0.918167\pi$
$283$		−	8.55472i		−	0.508525i	0.967135	−	0.254263i	$-0.0818327\pi$
$284$	9.12519			0.541480
$285$		0			0
$286$	−2.07030			−0.122419
$287$			4.13165i			0.243884i
$288$		0			0
$289$	13.2811			0.781241
$290$	1.78921	−	4.61794i	0.105066	−	0.271175i
$291$		0			0
$292$		−	8.37262i		−	0.489971i
$293$		−	26.2220i		−	1.53191i	−0.642896	−	0.765953i	$-0.722267\pi$
$293$		−	26.2220i		−	1.53191i	0.642896	−	0.765953i	$-0.277733\pi$
$294$		0			0
$295$	18.1753	+	7.04198i	1.05821	+	0.410000i
$296$	−2.46485			−0.143266
$297$		0			0
$298$		−	12.3596i		−	0.715973i
$299$	7.94093			0.459236
$300$		0			0
$301$	5.86280			0.337926
$302$			7.37354i			0.424300i
$303$		0			0
$304$	1.11098			0.0637193
$305$	−16.3583	−	6.33797i	−0.936672	−	0.362911i
$306$		0			0
$307$		−	20.8170i		−	1.18809i	−0.804431	−	0.594046i	$-0.797530\pi$
$307$		−	20.8170i		−	1.18809i	0.804431	−	0.594046i	$-0.202470\pi$
$308$		−	1.36187i		−	0.0775997i
$309$		0			0
$310$	−1.35829	+	3.50574i	−0.0771457	+	0.199113i
$311$	−15.9789			−0.906078			−0.453039	−	0.891491i	$-0.649660\pi$
$311$	−15.9789			−0.906078			−0.453039	+	0.891491i	$0.649660\pi$
$312$		0			0
$313$		−	4.27429i		−	0.241597i	−0.992677	−	0.120799i	$-0.961454\pi$
$313$		−	4.27429i		−	0.241597i	0.992677	−	0.120799i	$-0.0385455\pi$
$314$	−9.92333			−0.560006
$315$		0			0
$316$	−11.2158			−0.630940
$317$		−	6.19424i		−	0.347903i	−0.984754	−	0.173952i	$-0.944346\pi$
$317$		−	6.19424i		−	0.347903i	0.984754	−	0.173952i	$-0.0556537\pi$
$318$		0			0
$319$	−5.68264			−0.318167
$320$	−3.21432	−	1.24538i	−0.179686	−	0.0696188i
$321$		0			0
$322$		−	1.71515i		−	0.0955815i
$323$			1.67615i			0.0932636i
$324$		0			0
$325$	−5.49845	+	6.03056i	−0.304999	+	0.334515i
$326$	−0.183621			−0.0101698
$327$		0			0
$328$		−	20.3113i		−	1.12151i
$329$	−0.718549			−0.0396149
$330$		0			0
$331$	−32.0400			−1.76108			−0.880540	−	0.473972i	$-0.842820\pi$
$331$	−32.0400			−1.76108			−0.880540	+	0.473972i	$0.842820\pi$
$332$			7.08846i			0.389030i
$333$		0			0
$334$	−8.29169			−0.453701
$335$	9.58090	−	24.7283i	0.523461	−	1.35105i
$336$		0			0
$337$		−	12.5183i		−	0.681917i	−0.940078	−	0.340959i	$-0.889248\pi$
$337$		−	12.5183i		−	0.681917i	0.940078	−	0.340959i	$-0.110752\pi$
$338$			7.26733i			0.395291i
$339$		0			0
$340$	−2.34560	+	6.05398i	−0.127208	+	0.328323i
$341$	4.31401			0.233617
$342$		0			0
$343$		−	6.89341i		−	0.372209i
$344$	−28.8217			−1.55396
$345$		0			0
$346$	9.51007			0.511264
$347$			3.30472i			0.177407i	0.996058	+	0.0887033i	$0.0282723\pi$
$347$			3.30472i			0.177407i	−0.996058	+	0.0887033i	$0.971728\pi$
$348$		0			0
$349$	4.45130			0.238273			0.119136	−	0.992878i	$-0.461987\pi$
$349$	4.45130			0.238273			0.119136	+	0.992878i	$0.461987\pi$
$350$	1.30253	+	1.18760i	0.0696231	+	0.0634800i
$351$		0			0
$352$			10.5146i			0.560428i
$353$		−	31.9145i		−	1.69864i	−0.527879	−	0.849319i	$-0.677013\pi$
$353$		−	31.9145i		−	1.69864i	0.527879	−	0.849319i	$-0.322987\pi$
$354$		0			0
$355$	12.6368	+	4.89609i	0.670691	+	0.259857i
$356$	7.77408			0.412026
$357$		0			0
$358$			0.311675i			0.0164725i
$359$	31.8986			1.68354			0.841771	−	0.539835i	$-0.181513\pi$
$359$	31.8986			1.68354			0.841771	+	0.539835i	$0.181513\pi$
$360$		0			0
$361$	−18.2445			−0.960239
$362$			8.04220i			0.422689i
$363$		0			0
$364$	1.23215			0.0645823
$365$	4.49230	−	11.5946i	0.235138	−	0.606889i
$366$		0			0
$367$			22.7089i			1.18540i	0.805425	+	0.592698i	$0.201937\pi$
$367$			22.7089i			1.18540i	−0.805425	+	0.592698i	$0.798063\pi$
$368$		−	6.21876i		−	0.324175i
$369$		0			0
$370$	−1.46601	−	0.568003i	−0.0762144	−	0.0295291i
$371$	−5.39958			−0.280332
$372$		0			0
$373$		−	28.7105i		−	1.48657i	−0.668973	−	0.743287i	$-0.733266\pi$
$373$		−	28.7105i		−	1.48657i	0.668973	−	0.743287i	$-0.266734\pi$
$374$	−2.44608			−0.126484
$375$		0			0
$376$	3.53241			0.182170
$377$		−	5.14138i		−	0.264794i
$378$		0			0
$379$	−30.3515			−1.55905			−0.779526	−	0.626370i	$-0.784540\pi$
$379$	−30.3515			−1.55905			−0.779526	+	0.626370i	$0.784540\pi$
$380$	2.72860	+	1.05719i	0.139974	+	0.0542327i
$381$		0			0
$382$		−	7.14729i		−	0.365687i
$383$		−	35.4366i		−	1.81073i	−0.424639	−	0.905363i	$-0.639599\pi$
$383$		−	35.4366i		−	1.81073i	0.424639	−	0.905363i	$-0.360401\pi$
$384$		0			0
$385$	0.730706	−	1.88595i	0.0372402	−	0.0961168i
$386$	6.28918			0.320111
$387$		0			0
$388$			9.76614i			0.495801i
$389$	−17.2794			−0.876102			−0.438051	−	0.898950i	$-0.644331\pi$
$389$	−17.2794			−0.876102			−0.438051	+	0.898950i	$0.644331\pi$
$390$		0			0
$391$	9.38230			0.474483
$392$			16.6343i			0.840159i
$393$		0			0
$394$	6.08301			0.306458
$395$	−15.5320	−	6.01782i	−0.781498	−	0.302789i
$396$		0			0
$397$			4.68683i			0.235225i	0.993060	+	0.117613i	$0.0375241\pi$
$397$			4.68683i			0.235225i	−0.993060	+	0.117613i	$0.962476\pi$
$398$		−	7.18190i		−	0.359996i
$399$		0			0
$400$	4.72270	+	4.30599i	0.236135	+	0.215299i
$401$	22.3427			1.11574			0.557871	−	0.829928i	$-0.311618\pi$
$401$	22.3427			1.11574			0.557871	+	0.829928i	$0.311618\pi$
$402$		0			0
$403$			3.90311i			0.194428i
$404$	−3.77329			−0.187728
$405$		0			0
$406$	−1.11048			−0.0551121
$407$			1.80401i			0.0894216i
$408$		0			0
$409$	5.17691			0.255982			0.127991	−	0.991775i	$-0.459147\pi$
$409$	5.17691			0.255982			0.127991	+	0.991775i	$0.459147\pi$
$410$	4.68057	−	12.0805i	0.231157	−	0.596615i
$411$		0			0
$412$		−	9.63725i		−	0.474793i
$413$		−	4.37062i		−	0.215064i
$414$		0			0
$415$	−3.80329	+	9.81626i	−0.186696	+	0.481861i
$416$	−9.51306			−0.466416
$417$		0			0
$418$			1.10248i			0.0539239i
$419$	−15.8651			−0.775063			−0.387531	−	0.921857i	$-0.626672\pi$
$419$	−15.8651			−0.775063			−0.387531	+	0.921857i	$0.626672\pi$
$420$		0			0
$421$	6.46992			0.315325			0.157662	−	0.987493i	$-0.449604\pi$
$421$	6.46992			0.315325			0.157662	+	0.987493i	$0.449604\pi$
$422$			9.59142i			0.466903i
$423$		0			0
$424$	26.5445			1.28912
$425$	−6.49649	+	7.12518i	−0.315126	+	0.345622i
$426$		0			0
$427$			3.93368i			0.190364i
$428$			17.5725i			0.849398i
$429$		0			0
$430$	−17.1422	−	6.64171i	−0.826672	−	0.320292i
$431$	24.9727			1.20289			0.601445	−	0.798914i	$-0.294592\pi$
$431$	24.9727			1.20289			0.601445	+	0.798914i	$0.294592\pi$
$432$		0			0
$433$		−	38.7308i		−	1.86128i	−0.365934	−	0.930641i	$-0.619250\pi$
$433$		−	38.7308i		−	1.86128i	0.365934	−	0.930641i	$-0.380750\pi$
$434$	0.843026			0.0404665
$435$		0			0
$436$	−11.9483			−0.572220
$437$		−	4.22872i		−	0.202287i
$438$		0			0
$439$	32.8425			1.56749			0.783743	−	0.621085i	$-0.213308\pi$
$439$	32.8425			1.56749			0.783743	+	0.621085i	$0.213308\pi$
$440$	−3.59217	+	9.27138i	−0.171250	+	0.441996i
$441$		0			0
$442$		−	2.21310i		−	0.105266i
$443$		−	24.4262i		−	1.16052i	−0.814430	−	0.580262i	$-0.802950\pi$
$443$		−	24.4262i		−	1.16052i	0.814430	−	0.580262i	$-0.197050\pi$
$444$		0			0
$445$	10.7657	+	4.17116i	0.510345	+	0.197732i
$446$	4.68475			0.221829
$447$		0			0
$448$			0.772947i			0.0365183i
$449$	−23.8188			−1.12408			−0.562040	−	0.827110i	$-0.689983\pi$
$449$	−23.8188			−1.12408			−0.562040	+	0.827110i	$0.689983\pi$
$450$		0			0
$451$	−14.8658			−0.700003
$452$		−	24.4307i		−	1.14912i
$453$		0			0
$454$	−4.02080			−0.188706
$455$	1.70631	+	0.661107i	0.0799932	+	0.0309932i
$456$		0			0
$457$		−	35.0439i		−	1.63928i	−0.572876	−	0.819642i	$-0.694172\pi$
$457$		−	35.0439i		−	1.63928i	0.572876	−	0.819642i	$-0.305828\pi$
$458$		−	21.0616i		−	0.984145i
$459$		0			0
$460$	5.91765	−	15.2734i	0.275912	−	0.712127i
$461$	−7.94572			−0.370069			−0.185035	−	0.982732i	$-0.559240\pi$
$461$	−7.94572			−0.370069			−0.185035	+	0.982732i	$0.559240\pi$
$462$		0			0
$463$			23.9463i			1.11288i	0.830888	+	0.556440i	$0.187833\pi$
$463$			23.9463i			1.11288i	−0.830888	+	0.556440i	$0.812167\pi$
$464$	−4.02635			−0.186919
$465$		0			0
$466$	−17.8785			−0.828206
$467$			42.2147i			1.95346i	0.214464	+	0.976732i	$0.431200\pi$
$467$			42.2147i			1.95346i	−0.214464	+	0.976732i	$0.568800\pi$
$468$		0			0
$469$	−5.94641			−0.274580
$470$	2.10096	+	0.814013i	0.0969103	+	0.0375476i
$471$		0			0
$472$			21.4861i			0.988979i
$473$			21.0945i			0.969926i
$474$		0			0
$475$	3.21140	+	2.92804i	0.147349	+	0.134348i
$476$	1.45580			0.0667266
$477$		0			0
$478$		−	7.71340i		−	0.352803i
$479$	34.3187			1.56806			0.784031	−	0.620721i	$-0.213160\pi$
$479$	34.3187			1.56806			0.784031	+	0.620721i	$0.213160\pi$
$480$		0			0
$481$	−1.63218			−0.0744212
$482$			16.7703i			0.763867i
$483$		0			0
$484$	−11.6619			−0.530089
$485$	−5.23999	+	13.5244i	−0.237936	+	0.614110i
$486$		0			0
$487$			3.03995i			0.137753i	0.997625	+	0.0688766i	$0.0219415\pi$
$487$			3.03995i			0.137753i	−0.997625	+	0.0688766i	$0.978059\pi$
$488$		−	19.3381i		−	0.875394i
$489$		0			0
$490$	−3.83323	+	9.89355i	−0.173168	+	0.446945i
$491$	11.4565			0.517023			0.258511	−	0.966008i	$-0.416768\pi$
$491$	11.4565			0.517023			0.258511	+	0.966008i	$0.416768\pi$
$492$		0			0
$493$		−	6.07460i		−	0.273586i
$494$	−0.997468			−0.0448782
$495$		0			0
$496$	3.05663			0.137247
$497$		−	3.03877i		−	0.136307i
$498$		0			0
$499$	39.9114			1.78668			0.893340	−	0.449381i	$-0.148355\pi$
$499$	39.9114			1.78668			0.893340	+	0.449381i	$0.148355\pi$
$500$	7.50156	+	15.0696i	0.335480	+	0.673934i
$501$		0			0
$502$		−	13.3511i		−	0.595889i
$503$			14.8201i			0.660794i	0.943842	+	0.330397i	$0.107183\pi$
$503$			14.8201i			0.660794i	−0.943842	+	0.330397i	$0.892817\pi$
$504$		0			0
$505$	−5.22534	−	2.02455i	−0.232525	−	0.0900911i
$506$	6.17115			0.274341
$507$		0			0
$508$			14.4000i			0.638897i
$509$	−22.3612			−0.991145			−0.495572	−	0.868567i	$-0.665042\pi$
$509$	−22.3612			−0.991145			−0.495572	+	0.868567i	$0.665042\pi$
$510$		0			0
$511$	−2.78816			−0.123341
$512$			13.7511i			0.607719i
$513$		0			0
$514$	−3.60645			−0.159074
$515$	5.17083	−	13.3459i	0.227854	−	0.588090i
$516$		0			0
$517$		−	2.58536i		−	0.113704i
$518$			0.352533i			0.0154894i
$519$		0			0
$520$	−8.38830	−	3.25003i	−0.367851	−	0.142523i
$521$	2.48042			0.108669			0.0543346	−	0.998523i	$-0.482696\pi$
$521$	2.48042			0.108669			0.0543346	+	0.998523i	$0.482696\pi$
$522$		0			0
$523$		−	0.452507i		−	0.0197867i	−0.999951	−	0.00989336i	$-0.996851\pi$
$523$		−	0.452507i		−	0.0197867i	0.999951	−	0.00989336i	$-0.00314921\pi$
$524$	30.5605			1.33504
$525$		0			0
$526$	19.0958			0.832618
$527$			4.61157i			0.200883i
$528$		0			0
$529$	−0.670348			−0.0291455
$530$	15.7878	+	6.11695i	0.685779	+	0.265703i
$531$		0			0
$532$		−	0.656148i		−	0.0284476i
$533$		−	13.4498i		−	0.582577i
$534$		0			0
$535$	−9.42845	+	24.3348i	−0.407628	+	1.05208i
$536$	29.2328			1.26266
$537$		0			0
$538$			13.4114i			0.578205i
$539$	12.1746			0.524396
$540$		0			0
$541$	−16.4102			−0.705531			−0.352765	−	0.935712i	$-0.614759\pi$
$541$	−16.4102			−0.705531			−0.352765	+	0.935712i	$0.614759\pi$
$542$		−	12.7003i		−	0.545525i
$543$		0			0
$544$	−11.2398			−0.481902
$545$	−16.5463	−	6.41083i	−0.708766	−	0.274610i
$546$		0			0
$547$		−	8.18537i		−	0.349981i	−0.984570	−	0.174991i	$-0.944010\pi$
$547$		−	8.18537i		−	0.349981i	0.984570	−	0.174991i	$-0.0559895\pi$
$548$		−	16.6943i		−	0.713144i
$549$		0			0
$550$	−4.27302	+	4.68654i	−0.182202	+	0.199835i
$551$	−2.73789			−0.116638
$552$		0			0
$553$			3.73497i			0.158827i
$554$	16.1271			0.685173
$555$		0			0
$556$	−21.3372			−0.904901
$557$			25.8788i			1.09652i	0.836309	+	0.548259i	$0.184709\pi$
$557$			25.8788i			1.09652i	−0.836309	+	0.548259i	$0.815291\pi$
$558$		0			0
$559$	−19.0853			−0.807221
$560$	0.517731	−	1.33626i	0.0218781	−	0.0564674i
$561$		0			0
$562$		−	9.96965i		−	0.420544i
$563$		−	24.4404i		−	1.03004i	−0.857178	−	0.515021i	$-0.827784\pi$
$563$		−	24.4404i		−	1.03004i	0.857178	−	0.515021i	$-0.172216\pi$
$564$		0			0
$565$	13.1082	−	33.8321i	0.551465	−	1.42333i
$566$	6.01491			0.252826
$567$		0			0
$568$			14.9387i			0.626814i
$569$	5.31751			0.222922			0.111461	−	0.993769i	$-0.464447\pi$
$569$	5.31751			0.222922			0.111461	+	0.993769i	$0.464447\pi$
$570$		0			0
$571$	−13.2022			−0.552496			−0.276248	−	0.961086i	$-0.589091\pi$
$571$	−13.2022			−0.552496			−0.276248	+	0.961086i	$0.589091\pi$
$572$			4.43332i			0.185366i
$573$		0			0
$574$	−2.90501			−0.121253
$575$	16.3898	−	17.9759i	0.683502	−	0.749647i
$576$		0			0
$577$			41.4001i			1.72351i	0.507325	+	0.861755i	$0.330635\pi$
$577$			41.4001i			1.72351i	−0.507325	+	0.861755i	$0.669365\pi$
$578$			9.33808i			0.388413i
$579$		0			0
$580$	−9.88882	−	3.83140i	−0.410611	−	0.159090i
$581$	2.36052			0.0979308
$582$		0			0
$583$		−	19.4278i		−	0.804618i
$584$	13.7067			0.567186
$585$		0			0
$586$	18.4370			0.761625
$587$			11.4771i			0.473712i	0.971545	+	0.236856i	$0.0761169\pi$
$587$			11.4771i			0.473712i	−0.971545	+	0.236856i	$0.923883\pi$
$588$		0			0
$589$	2.07849			0.0856426
$590$	−4.95129	+	12.7793i	−0.203841	+	0.526114i
$591$		0			0
$592$			1.27821i			0.0525340i
$593$			11.1191i			0.456608i	0.973590	+	0.228304i	$0.0733180\pi$
$593$			11.1191i			0.456608i	−0.973590	+	0.228304i	$0.926682\pi$
$594$		0			0
$595$	2.01603	+	0.781106i	0.0826492	+	0.0320222i
$596$	−26.4668			−1.08412
$597$		0			0
$598$			5.58335i			0.228320i
$599$	7.25813			0.296559			0.148280	−	0.988945i	$-0.452626\pi$
$599$	7.25813			0.296559			0.148280	+	0.988945i	$0.452626\pi$
$600$		0			0
$601$	−14.6121			−0.596040			−0.298020	−	0.954560i	$-0.596326\pi$
$601$	−14.6121			−0.596040			−0.298020	+	0.954560i	$0.596326\pi$
$602$			4.12220i			0.168008i
$603$		0			0
$604$	15.7896			0.642471
$605$	−16.1497	−	6.25718i	−0.656580	−	0.254390i
$606$		0			0
$607$		−	26.3898i		−	1.07113i	−0.844495	−	0.535564i	$-0.820099\pi$
$607$		−	26.3898i		−	1.07113i	0.844495	−	0.535564i	$-0.179901\pi$
$608$			5.06591i			0.205450i
$609$		0			0
$610$	4.45630	−	11.5017i	0.180430	−	0.465689i
$611$	2.33911			0.0946301
$612$		0			0
$613$		−	40.8554i		−	1.65013i	−0.565035	−	0.825067i	$-0.691137\pi$
$613$		−	40.8554i		−	1.65013i	0.565035	−	0.825067i	$-0.308863\pi$
$614$	14.6367			0.590689
$615$		0			0
$616$	2.22949			0.0898288
$617$			28.2802i			1.13852i	0.822158	+	0.569260i	$0.192770\pi$
$617$			28.2802i			1.13852i	−0.822158	+	0.569260i	$0.807230\pi$
$618$		0			0
$619$	7.17028			0.288198			0.144099	−	0.989563i	$-0.453972\pi$
$619$	7.17028			0.288198			0.144099	+	0.989563i	$0.453972\pi$
$620$	7.50716	+	2.90863i	0.301495	+	0.116813i
$621$		0			0
$622$		−	11.2349i		−	0.450479i
$623$		−	2.58884i		−	0.103720i
$624$		0			0
$625$	2.30277	+	24.8937i	0.0921110	+	0.995749i
$626$	3.00530			0.120116
$627$		0			0
$628$			21.2497i			0.847957i
$629$	−1.92844			−0.0768921
$630$		0			0
$631$	−7.70444			−0.306709			−0.153354	−	0.988171i	$-0.549008\pi$
$631$	−7.70444			−0.306709			−0.153354	+	0.988171i	$0.549008\pi$
$632$		−	18.3613i		−	0.730372i
$633$		0			0
$634$	4.35524			0.172969
$635$	−7.72628	+	19.9415i	−0.306608	+	0.791354i
$636$		0			0
$637$			11.0150i			0.436429i
$638$		−	3.99553i		−	0.158184i
$639$		0			0
$640$	−8.54126	+	22.0450i	−0.337623	+	0.871403i
$641$	−24.3375			−0.961274			−0.480637	−	0.876920i	$-0.659595\pi$
$641$	−24.3375			−0.961274			−0.480637	+	0.876920i	$0.659595\pi$
$642$		0			0
$643$			27.8512i			1.09834i	0.835710	+	0.549171i	$0.185057\pi$
$643$			27.8512i			1.09834i	−0.835710	+	0.549171i	$0.814943\pi$
$644$	−3.67280			−0.144729
$645$		0			0
$646$	−1.17852			−0.0463683
$647$			24.6280i			0.968228i	0.875005	+	0.484114i	$0.160858\pi$
$647$			24.6280i			0.968228i	−0.875005	+	0.484114i	$0.839142\pi$
$648$		0			0
$649$	15.7256			0.617284
$650$	−4.24015	−	3.86602i	−0.166312	−	0.151638i
$651$		0			0
$652$			0.393205i			0.0153991i
$653$			27.8960i			1.09165i	0.837898	+	0.545827i	$0.183784\pi$
$653$			27.8960i			1.09165i	−0.837898	+	0.545827i	$0.816216\pi$
$654$		0			0
$655$	42.3210	+	16.3971i	1.65362	+	0.640690i
$656$	−10.5329			−0.411242
$657$		0			0
$658$		−	0.505219i		−	0.0196955i
$659$	−18.3903			−0.716384			−0.358192	−	0.933648i	$-0.616607\pi$
$659$	−18.3903			−0.716384			−0.358192	+	0.933648i	$0.616607\pi$
$660$		0			0
$661$	2.05323			0.0798614			0.0399307	−	0.999202i	$-0.487286\pi$
$661$	2.05323			0.0798614			0.0399307	+	0.999202i	$0.487286\pi$
$662$		−	22.5277i		−	0.875564i
$663$		0			0
$664$	−11.6044			−0.450338
$665$	0.352054	−	0.908649i	0.0136521	−	0.0352359i
$666$		0			0
$667$			15.3254i			0.593403i
$668$			17.7558i			0.686991i
$669$		0			0
$670$	17.3867	+	6.73643i	0.671707	+	0.260251i
$671$	−14.1535			−0.546389
$672$		0			0
$673$			16.8287i			0.648698i	0.945938	+	0.324349i	$0.105145\pi$
$673$			16.8287i			0.648698i	−0.945938	+	0.324349i	$0.894855\pi$
$674$	8.80178			0.339032
$675$		0			0
$676$	15.5622			0.598546
$677$		−	20.8182i		−	0.800108i	−0.916491	−	0.400054i	$-0.868991\pi$
$677$		−	20.8182i		−	0.800108i	0.916491	−	0.400054i	$-0.131009\pi$
$678$		0			0
$679$	3.25221			0.124808
$680$	−9.91087	−	3.83994i	−0.380065	−	0.147255i
$681$		0			0
$682$			3.03323i			0.116148i
$683$		−	6.40527i		−	0.245091i	−0.992463	−	0.122545i	$-0.960894\pi$
$683$		−	6.40527i		−	0.245091i	0.992463	−	0.122545i	$-0.0391057\pi$
$684$		0			0
$685$	8.95726	−	23.1186i	0.342239	−	0.883318i
$686$	4.84683			0.185053
$687$		0			0
$688$			14.9462i			0.569819i
$689$	17.5774			0.669644
$690$		0			0
$691$	−0.406659			−0.0154700			−0.00773502	−	0.999970i	$-0.502462\pi$
$691$	−0.406659			−0.0154700			−0.00773502	+	0.999970i	$0.502462\pi$
$692$		−	20.3648i		−	0.774153i
$693$		0			0
$694$	−2.32358			−0.0882020
$695$	−29.5483	−	11.4484i	−1.12083	−	0.434263i
$696$		0			0
$697$		−	15.8911i		−	0.601920i
$698$			3.12976i			0.118463i
$699$		0			0
$700$	2.54312	−	2.78923i	0.0961209	−	0.105423i
$701$	−2.39744			−0.0905501			−0.0452750	−	0.998975i	$-0.514416\pi$
$701$	−2.39744			−0.0905501			−0.0452750	+	0.998975i	$0.514416\pi$
$702$		0			0
$703$			0.869173i			0.0327815i
$704$	−2.78108			−0.104816
$705$		0			0
$706$	22.4394			0.844520
$707$			1.25654i			0.0472570i
$708$		0			0
$709$	−22.0154			−0.826804			−0.413402	−	0.910549i	$-0.635660\pi$
$709$	−22.0154			−0.826804			−0.413402	+	0.910549i	$0.635660\pi$
$710$	−3.44249	+	8.88506i	−0.129194	+	0.333450i
$711$		0			0
$712$			12.7268i			0.476958i
$713$		−	11.6344i		−	0.435712i
$714$		0			0
$715$	−2.37868	+	6.13936i	−0.0889576	+	0.229599i
$716$	0.667418			0.0249426
$717$		0			0
$718$			22.4282i			0.837014i
$719$	−9.29180			−0.346526			−0.173263	−	0.984876i	$-0.555431\pi$
$719$	−9.29180			−0.346526			−0.173263	+	0.984876i	$0.555431\pi$
$720$		0			0
$721$	−3.20929			−0.119520
$722$		−	12.8279i		−	0.477406i
$723$		0			0
$724$	17.2215			0.640032
$725$	−11.6385	−	10.6116i	−0.432245	−	0.394106i
$726$		0			0
$727$			29.4352i			1.09169i	0.837886	+	0.545846i	$0.183792\pi$
$727$			29.4352i			1.09169i	−0.837886	+	0.545846i	$0.816208\pi$
$728$			2.01714i			0.0747600i
$729$		0			0
$730$	8.15229	+	3.15858i	0.301730	+	0.116904i
$731$	−22.5495			−0.834023
$732$		0			0
$733$		−	3.71935i		−	0.137377i	−0.997638	−	0.0686887i	$-0.978118\pi$
$733$		−	3.71935i		−	0.137377i	0.997638	−	0.0686887i	$-0.0218815\pi$
$734$	−15.9669			−0.589349
$735$		0			0
$736$	28.3565			1.04524
$737$		−	21.3953i		−	0.788107i
$738$		0			0
$739$	−20.2734			−0.745768			−0.372884	−	0.927878i	$-0.621631\pi$
$739$	−20.2734			−0.745768			−0.372884	+	0.927878i	$0.621631\pi$
$740$	−1.21632	+	3.13931i	−0.0447127	+	0.115403i
$741$		0			0
$742$		−	3.79650i		−	0.139374i
$743$		−	1.11337i		−	0.0408457i	−0.999791	−	0.0204229i	$-0.993499\pi$
$743$		−	1.11337i		−	0.0408457i	0.999791	−	0.0204229i	$-0.00650125\pi$
$744$		0			0
$745$	−36.6518	−	14.2006i	−1.34282	−	0.520271i
$746$	20.1867			0.739086
$747$		0			0
$748$			5.23802i			0.191521i
$749$	5.85179			0.213820
$750$		0			0
$751$	−37.9213			−1.38377			−0.691885	−	0.722008i	$-0.743219\pi$
$751$	−37.9213			−1.38377			−0.691885	+	0.722008i	$0.743219\pi$
$752$		−	1.83182i		−	0.0667995i
$753$		0			0
$754$	3.61496			0.131649
$755$	21.8659	+	8.47187i	0.795780	+	0.308323i
$756$		0			0
$757$			41.8794i			1.52213i	0.648674	+	0.761066i	$0.275324\pi$
$757$			41.8794i			1.52213i	−0.648674	+	0.761066i	$0.724676\pi$
$758$		−	21.3405i		−	0.775121i
$759$		0			0
$760$	−1.73071	+	4.46695i	−0.0627794	+	0.162033i
$761$	12.6827			0.459749			0.229875	−	0.973220i	$-0.426168\pi$
$761$	12.6827			0.459749			0.229875	+	0.973220i	$0.426168\pi$
$762$		0			0
$763$			3.97889i			0.144046i
$764$	−15.3051			−0.553721
$765$		0			0
$766$	24.9159			0.900247
$767$			14.2278i			0.513735i
$768$		0			0
$769$	−34.0483			−1.22781			−0.613907	−	0.789378i	$-0.710403\pi$
$769$	−34.0483			−1.22781			−0.613907	+	0.789378i	$0.710403\pi$
$770$	1.32603	+	0.513767i	0.0477868	+	0.0185149i
$771$		0			0
$772$		−	13.4676i		−	0.484709i
$773$			20.6092i			0.741261i	0.928780	+	0.370630i	$0.120858\pi$
$773$			20.6092i			0.741261i	−0.928780	+	0.370630i	$0.879142\pi$
$774$		0			0
$775$	8.83548	+	8.05588i	0.317380	+	0.289376i
$776$	−15.9880			−0.573935
$777$		0			0
$778$		−	12.1494i		−	0.435576i
$779$	−7.16233			−0.256617
$780$		0			0
$781$	10.9336			0.391234
$782$			6.59680i			0.235901i
$783$		0			0
$784$	8.62613			0.308076
$785$	−11.4015	+	29.4271i	−0.406936	+	1.05030i
$786$		0			0
$787$			49.1315i			1.75135i	0.482903	+	0.875674i	$0.339583\pi$
$787$			49.1315i			1.75135i	−0.482903	+	0.875674i	$0.660417\pi$
$788$		−	13.0261i		−	0.464036i
$789$		0			0
$790$	4.23119	−	10.9207i	0.150539	−	0.388541i
$791$	−8.13562			−0.289269
$792$		0			0
$793$		−	12.8054i		−	0.454732i
$794$	−3.29536			−0.116948
$795$		0			0
$796$	−15.3793			−0.545103
$797$			1.87847i			0.0665389i	0.999446	+	0.0332694i	$0.0105919\pi$
$797$			1.87847i			0.0665389i	−0.999446	+	0.0332694i	$0.989408\pi$
$798$		0			0
$799$	2.76368			0.0977720
$800$	−19.6346	+	21.5347i	−0.694188	+	0.761368i
$801$		0			0
$802$			15.7094i			0.554718i
$803$		−	10.0319i		−	0.354017i
$804$		0			0
$805$	−5.08618	−	1.97063i	−0.179264	−	0.0694556i
$806$	−2.74432			−0.0966645
$807$		0			0
$808$		−	6.17719i		−	0.217313i
$809$	−15.4989			−0.544912			−0.272456	−	0.962168i	$-0.587836\pi$
$809$	−15.4989			−0.544912			−0.272456	+	0.962168i	$0.587836\pi$
$810$		0			0
$811$	6.06459			0.212956			0.106478	−	0.994315i	$-0.466043\pi$
$811$	6.06459			0.212956			0.106478	+	0.994315i	$0.466043\pi$
$812$			2.37797i			0.0834503i
$813$		0			0
$814$	−1.26842			−0.0444582
$815$	−0.210973	+	0.544519i	−0.00739005	+	0.0190737i
$816$		0			0
$817$			10.1633i			0.355570i
$818$			3.63994i			0.127267i
$819$		0			0
$820$	−25.8691	−	10.0229i	−0.903390	−	0.350016i
$821$	3.79024			0.132280			0.0661402	−	0.997810i	$-0.478932\pi$
$821$	3.79024			0.132280			0.0661402	+	0.997810i	$0.478932\pi$
$822$		0			0
$823$			2.64216i			0.0920999i	0.998939	+	0.0460499i	$0.0146633\pi$
$823$			2.64216i			0.0920999i	−0.998939	+	0.0460499i	$0.985337\pi$
$824$	15.7770			0.549617
$825$		0			0
$826$	3.07303			0.106924
$827$			21.8953i			0.761376i	0.924704	+	0.380688i	$0.124313\pi$
$827$			21.8953i			0.761376i	−0.924704	+	0.380688i	$0.875687\pi$
$828$		0			0
$829$	−7.03307			−0.244269			−0.122134	−	0.992514i	$-0.538974\pi$
$829$	−7.03307			−0.244269			−0.122134	+	0.992514i	$0.538974\pi$
$830$	−6.90192	−	2.67413i	−0.239569	−	0.0928204i
$831$		0			0
$832$		−	2.51619i		−	0.0872332i
$833$			13.0143i			0.450919i
$834$		0			0
$835$	−9.52679	+	24.5886i	−0.329688	+	0.850923i
$836$	2.36084			0.0816512
$837$		0			0
$838$		−	11.1549i		−	0.385341i
$839$	−49.4466			−1.70709			−0.853544	−	0.521021i	$-0.825551\pi$
$839$	−49.4466			−1.70709			−0.853544	+	0.521021i	$0.825551\pi$
$840$		0			0
$841$	−19.0775			−0.657845
$842$			4.54907i			0.156771i
$843$		0			0
$844$	20.5390			0.706981
$845$	21.5509	+	8.34985i	0.741374	+	0.287244i
$846$		0			0
$847$			3.88353i			0.133440i
$848$		−	13.7653i		−	0.472703i
$849$		0			0
$850$	−5.00979	−	4.56775i	−0.171834	−	0.156673i
$851$	4.86522			0.166778
$852$		0			0
$853$			2.94665i			0.100891i	0.998727	+	0.0504457i	$0.0160642\pi$
$853$			2.94665i			0.100891i	−0.998727	+	0.0504457i	$0.983936\pi$
$854$	−2.76581			−0.0946441
$855$		0			0
$856$	−28.7676			−0.983257
$857$		−	27.7795i		−	0.948929i	−0.880275	−	0.474465i	$-0.842642\pi$
$857$		−	27.7795i		−	0.948929i	0.880275	−	0.474465i	$-0.157358\pi$
$858$		0			0
$859$	50.2134			1.71326			0.856629	−	0.515933i	$-0.172555\pi$
$859$	50.2134			1.71326			0.856629	+	0.515933i	$0.172555\pi$
$860$	−14.2225	+	36.7082i	−0.484984	+	1.25174i
$861$		0			0
$862$			17.5585i			0.598046i
$863$			1.11827i			0.0380663i	0.999819	+	0.0190331i	$0.00605880\pi$
$863$			1.11827i			0.0380663i	−0.999819	+	0.0190331i	$0.993941\pi$
$864$		0			0
$865$	10.9267	−	28.2016i	0.371517	−	0.958884i
$866$	27.2320			0.925382
$867$		0			0
$868$		−	1.80525i		−	0.0612741i
$869$	−13.4385			−0.455871
$870$		0			0
$871$	19.3575			0.655903
$872$		−	19.5604i		−	0.662398i
$873$		0			0
$874$	2.97326			0.100572
$875$	5.01832	−	2.49808i	0.169650	−	0.0844507i
$876$		0			0
$877$		−	23.0843i		−	0.779502i	−0.920920	−	0.389751i	$-0.872561\pi$
$877$		−	23.0843i		−	0.779502i	0.920920	−	0.389751i	$-0.127439\pi$
$878$			23.0919i			0.779314i
$879$		0			0
$880$	4.80790	+	1.86281i	0.162074	+	0.0627953i
$881$	10.1304			0.341301			0.170650	−	0.985332i	$-0.445413\pi$
$881$	10.1304			0.341301			0.170650	+	0.985332i	$0.445413\pi$
$882$		0			0
$883$			0.620421i			0.0208788i	0.999946	+	0.0104394i	$0.00332303\pi$
$883$			0.620421i			0.0208788i	−0.999946	+	0.0104394i	$0.996677\pi$
$884$	−4.73910			−0.159393
$885$		0			0
$886$	17.1743			0.576983
$887$			0.762728i			0.0256099i	0.999918	+	0.0128049i	$0.00407605\pi$
$887$			0.762728i			0.0256099i	−0.999918	+	0.0128049i	$0.995924\pi$
$888$		0			0
$889$	4.79533			0.160830
$890$	−2.93279	+	7.56950i	−0.0983072	+	0.253730i
$891$		0			0
$892$		−	10.0319i		−	0.335892i
$893$		−	1.24562i		−	0.0416832i
$894$		0			0
$895$	0.924256	+	0.358101i	0.0308945	+	0.0119700i
$896$	5.30116			0.177099
$897$		0			0
$898$		−	16.7473i		−	0.558864i
$899$	−7.53272			−0.251230
$900$		0			0
$901$	20.7678			0.691877
$902$		−	10.4523i		−	0.348023i
$903$		0			0
$904$	39.9950			1.33021
$905$	23.8487	+	9.24013i	0.792759	+	0.307152i
$906$		0			0
$907$		−	44.6062i		−	1.48112i	−0.671988	−	0.740562i	$-0.734559\pi$
$907$		−	44.6062i		−	1.48112i	0.671988	−	0.740562i	$-0.265441\pi$
$908$			8.61011i			0.285737i
$909$		0			0
$910$	−0.464832	+	1.19973i	−0.0154090	+	0.0397706i
$911$	−21.5382			−0.713591			−0.356796	−	0.934182i	$-0.616131\pi$
$911$	−21.5382			−0.713591			−0.356796	+	0.934182i	$0.616131\pi$
$912$		0			0
$913$			8.49321i			0.281084i
$914$	24.6397			0.815010
$915$		0			0
$916$	−45.1012			−1.49018
$917$		−	10.1769i		−	0.336072i
$918$		0			0
$919$	32.1570			1.06076			0.530380	−	0.847760i	$-0.322049\pi$
$919$	32.1570			1.06076			0.530380	+	0.847760i	$0.322049\pi$
$920$	25.0039	+	9.68768i	0.824353	+	0.319393i
$921$		0			0
$922$		−	5.58672i		−	0.183989i
$923$			9.89217i			0.325605i
$924$		0			0
$925$	−3.36877	+	3.69478i	−0.110764	+	0.121484i
$926$	−16.8369			−0.553295
$927$		0			0
$928$		−	18.3595i		−	0.602681i
$929$	53.7540			1.76361			0.881805	−	0.471614i	$-0.156328\pi$
$929$	53.7540			1.76361			0.881805	+	0.471614i	$0.156328\pi$
$930$		0			0
$931$	5.86571			0.192241
$932$			38.2849i			1.25406i
$933$		0			0
$934$	−29.6816			−0.971212
$935$	−2.81044	+	7.25373i	−0.0919112	+	0.237222i
$936$		0			0
$937$			32.7426i			1.06965i	0.844961	+	0.534827i	$0.179623\pi$
$937$			32.7426i			1.06965i	−0.844961	+	0.534827i	$0.820377\pi$
$938$		−	4.18098i		−	0.136514i
$939$		0			0
$940$	1.74312	−	4.49899i	0.0568543	−	0.146741i
$941$	7.12766			0.232355			0.116178	−	0.993228i	$-0.462936\pi$
$941$	7.12766			0.232355			0.116178	+	0.993228i	$0.462936\pi$
$942$		0			0
$943$			40.0913i			1.30555i
$944$	11.1422			0.362646
$945$		0			0
$946$	−14.8318			−0.482222
$947$		−	14.6389i		−	0.475702i	−0.971302	−	0.237851i	$-0.923557\pi$
$947$		−	14.6389i		−	0.475702i	0.971302	−	0.237851i	$-0.0764429\pi$
$948$		0			0
$949$	9.07634			0.294630
$950$	−2.05874	+	2.25797i	−0.0667943	+	0.0732582i
$951$		0			0
$952$			2.38327i			0.0772422i
$953$			51.2467i			1.66004i	0.557731	+	0.830021i	$0.311672\pi$
$953$			51.2467i			1.66004i	−0.557731	+	0.830021i	$0.688328\pi$
$954$		0			0
$955$	−21.1949	−	8.21192i	−0.685852	−	0.265732i
$956$	−16.5174			−0.534211
$957$		0			0
$958$			24.1299i			0.779601i
$959$	−5.55934			−0.179521
$960$		0			0
$961$	−25.2815			−0.815532
$962$		−	1.14761i		−	0.0370003i
$963$		0			0
$964$	35.9118			1.15664
$965$	7.22599	−	18.6502i	0.232613	−	0.600372i
$966$		0			0
$967$			12.5599i			0.403899i	0.979396	+	0.201949i	$0.0647277\pi$
$967$			12.5599i			0.403899i	−0.979396	+	0.201949i	$0.935272\pi$
$968$		−	19.0916i		−	0.613627i
$969$		0			0
$970$	−9.50914	−	3.68429i	−0.305320	−	0.118295i
$971$	5.56513			0.178594			0.0892968	−	0.996005i	$-0.471538\pi$
$971$	5.56513			0.178594			0.0892968	+	0.996005i	$0.471538\pi$
$972$		0			0
$973$			7.10549i			0.227792i
$974$	−2.13742			−0.0684874
$975$		0			0
$976$	−10.0282			−0.320996
$977$		−	25.6883i		−	0.821843i	−0.911671	−	0.410922i	$-0.865207\pi$
$977$		−	25.6883i		−	0.821843i	0.911671	−	0.410922i	$-0.134793\pi$
$978$		0			0
$979$	9.31471			0.297699
$980$	21.1860	+	8.20845i	0.676761	+	0.262209i
$981$		0			0
$982$			8.05516i			0.257050i
$983$			21.5725i			0.688057i	0.938959	+	0.344028i	$0.111792\pi$
$983$			21.5725i			0.688057i	−0.938959	+	0.344028i	$0.888208\pi$
$984$		0			0
$985$	6.98911	−	18.0389i	0.222692	−	0.574766i
$986$	4.27112			0.136020
$987$		0			0
$988$			2.13597i			0.0679543i
$989$	56.8894			1.80898
$990$		0			0
$991$	9.15527			0.290827			0.145413	−	0.989371i	$-0.453549\pi$
$991$	9.15527			0.290827			0.145413	+	0.989371i	$0.453549\pi$
$992$			13.9377i			0.442524i
$993$		0			0
$994$	2.13659			0.0677686
$995$	−21.2976	−	8.25169i	−0.675178	−	0.261596i
$996$		0			0
$997$		−	21.1522i		−	0.669896i	−0.942237	−	0.334948i	$-0.891281\pi$
$997$		−	21.1522i		−	0.669896i	0.942237	−	0.334948i	$-0.108719\pi$
$998$			28.0621i			0.888292i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1665.2.c.e.334.11		18
3.2	odd	2		185.2.b.a.149.8	✓	18
5.2	odd	4		8325.2.a.cq.1.5		9
5.3	odd	4		8325.2.a.cr.1.5		9
5.4	even	2	inner	1665.2.c.e.334.8		18
15.2	even	4		925.2.a.m.1.5		9
15.8	even	4		925.2.a.l.1.5		9
15.14	odd	2		185.2.b.a.149.11	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.b.a.149.8	✓	18	3.2	odd	2
185.2.b.a.149.11	yes	18	15.14	odd	2
925.2.a.l.1.5		9	15.8	even	4
925.2.a.m.1.5		9	15.2	even	4
1665.2.c.e.334.8		18	5.4	even	2	inner
1665.2.c.e.334.11		18	1.1	even	1	trivial
8325.2.a.cq.1.5		9	5.2	odd	4
8325.2.a.cr.1.5		9	5.3	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:	\( N \)	\(=\)	\( 1665 = 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1665.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.703111i q^{2} +1.50564 q^{4} +(2.08504 + 0.807843i) q^{5} -0.501390i q^{7} +2.46485i q^{8} +(-0.568003 + 1.46601i) q^{10} +1.80401 q^{11} +1.63218i q^{13} +0.352533 q^{14} +1.27821 q^{16} +1.92844i q^{17} +0.869173 q^{19} +(3.13931 + 1.21632i) q^{20} +1.26842i q^{22} -4.86522i q^{23} +(3.69478 + 3.36877i) q^{25} -1.14761 q^{26} -0.754910i q^{28} -3.15000 q^{29} +2.39134 q^{31} +5.82842i q^{32} -1.35591 q^{34} +(0.405044 - 1.04542i) q^{35} +1.00000i q^{37} +0.611125i q^{38} +(-1.99121 + 5.13931i) q^{40} -8.24040 q^{41} +11.6931i q^{43} +2.71619 q^{44} +3.42079 q^{46} -1.43311i q^{47} +6.74861 q^{49} +(-2.36862 + 2.59784i) q^{50} +2.45747i q^{52} -10.7692i q^{53} +(3.76144 + 1.45736i) q^{55} +1.23585 q^{56} -2.21480i q^{58} +8.71701 q^{59} -7.84555 q^{61} +1.68138i q^{62} -1.54161 q^{64} +(-1.31855 + 3.40317i) q^{65} -11.8599i q^{67} +2.90353i q^{68} +(0.735044 + 0.284791i) q^{70} +6.06069 q^{71} -5.56086i q^{73} -0.703111 q^{74} +1.30866 q^{76} -0.904514i q^{77} -7.44924 q^{79} +(2.66511 + 1.03259i) q^{80} -5.79391i q^{82} +4.70795i q^{83} +(-1.55788 + 4.02088i) q^{85} -8.22154 q^{86} +4.44662i q^{88} +5.16332 q^{89} +0.818361 q^{91} -7.32524i q^{92} +1.00764 q^{94} +(1.81226 + 0.702156i) q^{95} +6.48639i q^{97} +4.74502i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 22 q^{4} - 2 q^{5} + 6 q^{10} - 8 q^{14} + 22 q^{16} + 8 q^{19} + 4 q^{20} - 18 q^{25} + 12 q^{26} - 4 q^{29} - 12 q^{31} - 12 q^{34} + 2 q^{35} - 6 q^{40} - 4 q^{41} + 8 q^{44} + 32 q^{46} + 14 q^{49}+ \cdots + 44 q^{95}+O(q^{100}) \) 18 * q - 22 * q^4 - 2 * q^5 + 6 * q^10 - 8 * q^14 + 22 * q^16 + 8 * q^19 + 4 * q^20 - 18 * q^25 + 12 * q^26 - 4 * q^29 - 12 * q^31 - 12 * q^34 + 2 * q^35 - 6 * q^40 - 4 * q^41 + 8 * q^44 + 32 * q^46 + 14 * q^49 - 8 * q^50 - 34 * q^55 + 48 * q^56 + 20 * q^59 + 16 * q^61 - 30 * q^64 - 20 * q^65 + 40 * q^70 - 16 * q^71 - 10 * q^74 - 96 * q^76 + 52 * q^79 - 36 * q^80 - 8 * q^85 + 32 * q^86 - 16 * q^89 - 36 * q^91 + 52 * q^94 + 44 * q^95

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