LMFDB - Embedded newform 495.2.c.e.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(199,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("495.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.4
Root			$1.45161 - 1.45161i$ of defining polynomial
Character	$\chi$	$=$	495.199
Dual form			495.2.c.e.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.311108i q^{2} +1.90321 q^{4} +(-0.311108 + 2.21432i) q^{5} +0.903212i q^{7} +1.21432i q^{8} +(-0.688892 - 0.0967881i) q^{10} -1.00000 q^{11} +2.90321i q^{13} -0.280996 q^{14} +3.42864 q^{16} +2.28100i q^{17} -2.42864 q^{19} +(-0.592104 + 4.21432i) q^{20} -0.311108i q^{22} -4.00000i q^{23} +(-4.80642 - 1.37778i) q^{25} -0.903212 q^{26} +1.71900i q^{28} +7.05086 q^{29} -2.62222 q^{31} +3.49532i q^{32} -0.709636 q^{34} +(-2.00000 - 0.280996i) q^{35} -5.80642i q^{37} -0.755569i q^{38} +(-2.68889 - 0.377784i) q^{40} +10.6637 q^{41} +10.7096i q^{43} -1.90321 q^{44} +1.24443 q^{46} +0.949145i q^{47} +6.18421 q^{49} +(0.428639 - 1.49532i) q^{50} +5.52543i q^{52} -0.815792i q^{53} +(0.311108 - 2.21432i) q^{55} -1.09679 q^{56} +2.19358i q^{58} -1.67307 q^{59} -7.24443 q^{61} -0.815792i q^{62} +5.76986 q^{64} +(-6.42864 - 0.903212i) q^{65} -12.8573i q^{67} +4.34122i q^{68} +(0.0874201 - 0.622216i) q^{70} -9.28592 q^{71} -5.65878i q^{73} +1.80642 q^{74} -4.62222 q^{76} -0.903212i q^{77} +16.5303 q^{79} +(-1.06668 + 7.59210i) q^{80} +3.31756i q^{82} -7.76049i q^{83} +(-5.05086 - 0.709636i) q^{85} -3.33185 q^{86} -1.21432i q^{88} +6.13335 q^{89} -2.62222 q^{91} -7.61285i q^{92} -0.295286 q^{94} +(0.755569 - 5.37778i) q^{95} +12.4701i q^{97} +1.92396i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} - 2 q^{5} - 4 q^{10} - 6 q^{11} + 12 q^{14} - 6 q^{16} + 12 q^{19} + 10 q^{20} - 2 q^{25} + 8 q^{26} + 16 q^{29} - 16 q^{31} + 36 q^{34} - 12 q^{35} - 16 q^{40} - 16 q^{41} + 2 q^{44} + 8 q^{46}+ \cdots + 4 q^{95}+O(q^{100}) $ 6 * q - 2 * q^4 - 2 * q^5 - 4 * q^10 - 6 * q^11 + 12 * q^14 - 6 * q^16 + 12 * q^19 + 10 * q^20 - 2 * q^25 + 8 * q^26 + 16 * q^29 - 16 * q^31 + 36 * q^34 - 12 * q^35 - 16 * q^40 - 16 * q^41 + 2 * q^44 + 8 * q^46 + 10 * q^49 - 24 * q^50 + 2 * q^55 - 20 * q^56 + 16 * q^59 - 44 * q^61 + 22 * q^64 - 12 * q^65 - 40 * q^70 + 24 * q^71 - 16 * q^74 - 28 * q^76 + 20 * q^79 - 6 * q^80 - 4 * q^85 + 20 * q^86 + 36 * q^89 - 16 * q^91 + 24 * q^94 + 4 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			0.311108i			0.219986i	0.993932	+	0.109993i	$0.0350829\pi$
$2$			0.311108i			0.219986i	−0.993932	+	0.109993i	$0.964917\pi$
$3$		0			0
$3$		0			0
$4$	1.90321			0.951606
$5$	−0.311108	+	2.21432i	−0.139132	+	0.990274i
$5$	−0.311108	+	2.21432i	−0.139132	+	0.990274i
$6$		0			0
$7$			0.903212i			0.341382i	0.985325	+	0.170691i	$0.0546000\pi$
$7$			0.903212i			0.341382i	−0.985325	+	0.170691i	$0.945400\pi$
$8$			1.21432i			0.429327i
$9$		0			0
$10$	−0.688892	−	0.0967881i	−0.217847	−	0.0306071i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		0			0
$13$			2.90321i			0.805206i	0.915375	+	0.402603i	$0.131894\pi$
$13$			2.90321i			0.805206i	−0.915375	+	0.402603i	$0.868106\pi$
$14$	−0.280996			−0.0750994
$15$		0			0
$16$	3.42864			0.857160
$17$			2.28100i			0.553223i	0.960982	+	0.276611i	$0.0892115\pi$
$17$			2.28100i			0.553223i	−0.960982	+	0.276611i	$0.910789\pi$
$18$		0			0
$19$	−2.42864			−0.557168			−0.278584	−	0.960412i	$-0.589865\pi$
$19$	−2.42864			−0.557168			−0.278584	+	0.960412i	$0.589865\pi$
$20$	−0.592104	+	4.21432i	−0.132399	+	0.942351i
$21$		0			0
$22$		−	0.311108i		−	0.0663284i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$	−4.80642	−	1.37778i	−0.961285	−	0.275557i
$26$	−0.903212			−0.177134
$27$		0			0
$28$			1.71900i			0.324861i
$29$	7.05086			1.30931			0.654655	−	0.755927i	$-0.272814\pi$
$29$	7.05086			1.30931			0.654655	+	0.755927i	$0.272814\pi$
$30$		0			0
$31$	−2.62222			−0.470964			−0.235482	−	0.971879i	$-0.575667\pi$
$31$	−2.62222			−0.470964			−0.235482	+	0.971879i	$0.575667\pi$
$32$			3.49532i			0.617890i
$33$		0			0
$34$	−0.709636			−0.121702
$35$	−2.00000	−	0.280996i	−0.338062	−	0.0474970i
$36$		0			0
$37$		−	5.80642i		−	0.954570i	−0.878749	−	0.477285i	$-0.841621\pi$
$37$		−	5.80642i		−	0.954570i	0.878749	−	0.477285i	$-0.158379\pi$
$38$		−	0.755569i		−	0.122569i
$39$		0			0
$40$	−2.68889	−	0.377784i	−0.425151	−	0.0597330i
$41$	10.6637			1.66539			0.832695	−	0.553731i	$-0.186797\pi$
$41$	10.6637			1.66539			0.832695	+	0.553731i	$0.186797\pi$
$42$		0			0
$43$			10.7096i			1.63320i	0.577201	+	0.816602i	$0.304145\pi$
$43$			10.7096i			1.63320i	−0.577201	+	0.816602i	$0.695855\pi$
$44$	−1.90321			−0.286920
$45$		0			0
$46$	1.24443			0.183481
$47$			0.949145i			0.138447i	0.997601	+	0.0692235i	$0.0220522\pi$
$47$			0.949145i			0.138447i	−0.997601	+	0.0692235i	$0.977948\pi$
$48$		0			0
$49$	6.18421			0.883458
$50$	0.428639	−	1.49532i	0.0606188	−	0.211470i
$51$		0			0
$52$			5.52543i			0.766239i
$53$		−	0.815792i		−	0.112058i	−0.998429	−	0.0560288i	$-0.982156\pi$
$53$		−	0.815792i		−	0.112058i	0.998429	−	0.0560288i	$-0.0178439\pi$
$54$		0			0
$55$	0.311108	−	2.21432i	0.0419498	−	0.298579i
$56$	−1.09679			−0.146564
$57$		0			0
$58$			2.19358i			0.288031i
$59$	−1.67307			−0.217815			−0.108908	−	0.994052i	$-0.534735\pi$
$59$	−1.67307			−0.217815			−0.108908	+	0.994052i	$0.534735\pi$
$60$		0			0
$61$	−7.24443			−0.927554			−0.463777	−	0.885952i	$-0.653506\pi$
$61$	−7.24443			−0.927554			−0.463777	+	0.885952i	$0.653506\pi$
$62$		−	0.815792i		−	0.103606i
$63$		0			0
$64$	5.76986			0.721232
$65$	−6.42864	−	0.903212i	−0.797375	−	0.112030i
$66$		0			0
$67$		−	12.8573i		−	1.57077i	−0.619010	−	0.785383i	$-0.712466\pi$
$67$		−	12.8573i		−	1.57077i	0.619010	−	0.785383i	$-0.287534\pi$
$68$			4.34122i			0.526450i
$69$		0			0
$70$	0.0874201	−	0.622216i	0.0104487	−	0.0743690i
$71$	−9.28592			−1.10204			−0.551018	−	0.834493i	$-0.685760\pi$
$71$	−9.28592			−1.10204			−0.551018	+	0.834493i	$0.685760\pi$
$72$		0			0
$73$		−	5.65878i		−	0.662310i	−0.943576	−	0.331155i	$-0.892562\pi$
$73$		−	5.65878i		−	0.662310i	0.943576	−	0.331155i	$-0.107438\pi$
$74$	1.80642			0.209993
$75$		0			0
$76$	−4.62222			−0.530204
$77$		−	0.903212i		−	0.102931i
$78$		0			0
$79$	16.5303			1.85981			0.929905	−	0.367800i	$-0.119889\pi$
$79$	16.5303			1.85981			0.929905	+	0.367800i	$0.119889\pi$
$80$	−1.06668	+	7.59210i	−0.119258	+	0.848823i
$81$		0			0
$82$			3.31756i			0.366363i
$83$		−	7.76049i		−	0.851825i	−0.904764	−	0.425912i	$-0.859953\pi$
$83$		−	7.76049i		−	0.851825i	0.904764	−	0.425912i	$-0.140047\pi$
$84$		0			0
$85$	−5.05086	−	0.709636i	−0.547842	−	0.0769708i
$86$	−3.33185			−0.359283
$87$		0			0
$88$		−	1.21432i		−	0.129447i
$89$	6.13335			0.650134			0.325067	−	0.945691i	$-0.394613\pi$
$89$	6.13335			0.650134			0.325067	+	0.945691i	$0.394613\pi$
$90$		0			0
$91$	−2.62222			−0.274883
$92$		−	7.61285i		−	0.793694i
$93$		0			0
$94$	−0.295286			−0.0304565
$95$	0.755569	−	5.37778i	0.0775197	−	0.551749i
$96$		0			0
$97$			12.4701i			1.26615i	0.774091	+	0.633075i	$0.218207\pi$
$97$			12.4701i			1.26615i	−0.774091	+	0.633075i	$0.781793\pi$
$98$			1.92396i			0.194349i
$99$		0			0
$100$	−9.14764	−	2.62222i	−0.914764	−	0.262222i
$101$	−16.1748			−1.60946			−0.804728	−	0.593643i	$-0.797689\pi$
$101$	−16.1748			−1.60946			−0.804728	+	0.593643i	$0.797689\pi$
$102$		0			0
$103$		−	17.1526i		−	1.69009i	−0.534693	−	0.845046i	$-0.679573\pi$
$103$		−	17.1526i		−	1.69009i	0.534693	−	0.845046i	$-0.320427\pi$
$104$	−3.52543			−0.345697
$105$		0			0
$106$	0.253799			0.0246512
$107$		−	13.5669i		−	1.31156i	−0.754951	−	0.655782i	$-0.772339\pi$
$107$		−	13.5669i		−	1.31156i	0.754951	−	0.655782i	$-0.227661\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	0.688892	+	0.0967881i	0.0656833	+	0.00922838i
$111$		0			0
$112$			3.09679i			0.292619i
$113$		−	14.2351i		−	1.33912i	−0.742757	−	0.669561i	$-0.766482\pi$
$113$		−	14.2351i		−	1.33912i	0.742757	−	0.669561i	$-0.233518\pi$
$114$		0			0
$115$	8.85728	+	1.24443i	0.825946	+	0.116044i
$116$	13.4193			1.24595
$117$		0			0
$118$		−	0.520505i		−	0.0479164i
$119$	−2.06022			−0.188860
$120$		0			0
$121$	1.00000			0.0909091
$122$		−	2.25380i		−	0.204049i
$123$		0			0
$124$	−4.99063			−0.448172
$125$	4.54617	−	10.2143i	0.406622	−	0.913597i
$126$		0			0
$127$		−	11.0049i		−	0.976529i	−0.872696	−	0.488264i	$-0.837630\pi$
$127$		−	11.0049i		−	0.976529i	0.872696	−	0.488264i	$-0.162370\pi$
$128$			8.78568i			0.776552i
$129$		0			0
$130$	0.280996	−	2.00000i	0.0246450	−	0.175412i
$131$	−1.24443			−0.108726			−0.0543632	−	0.998521i	$-0.517313\pi$
$131$	−1.24443			−0.108726			−0.0543632	+	0.998521i	$0.517313\pi$
$132$		0			0
$133$		−	2.19358i		−	0.190207i
$134$	4.00000			0.345547
$135$		0			0
$136$	−2.76986			−0.237513
$137$		−	4.42864i		−	0.378364i	−0.981942	−	0.189182i	$-0.939416\pi$
$137$		−	4.42864i		−	0.378364i	0.981942	−	0.189182i	$-0.0605836\pi$
$138$		0			0
$139$	−0.917502			−0.0778215			−0.0389108	−	0.999243i	$-0.512389\pi$
$139$	−0.917502			−0.0778215			−0.0389108	+	0.999243i	$0.512389\pi$
$140$	−3.80642	−	0.534795i	−0.321702	−	0.0451985i
$141$		0			0
$142$		−	2.88892i		−	0.242433i
$143$		−	2.90321i		−	0.242779i
$144$		0			0
$145$	−2.19358	+	15.6128i	−0.182167	+	1.29658i
$146$	1.76049			0.145699
$147$		0			0
$148$		−	11.0509i		−	0.908375i
$149$	2.19358			0.179705			0.0898524	−	0.995955i	$-0.471360\pi$
$149$	2.19358			0.179705			0.0898524	+	0.995955i	$0.471360\pi$
$150$		0			0
$151$	−10.4286			−0.848671			−0.424335	−	0.905505i	$-0.639492\pi$
$151$	−10.4286			−0.848671			−0.424335	+	0.905505i	$0.639492\pi$
$152$		−	2.94914i		−	0.239207i
$153$		0			0
$154$	0.280996			0.0226433
$155$	0.815792	−	5.80642i	0.0655260	−	0.466383i
$156$		0			0
$157$		−	5.80642i		−	0.463403i	−0.972787	−	0.231702i	$-0.925571\pi$
$157$		−	5.80642i		−	0.463403i	0.972787	−	0.231702i	$-0.0744293\pi$
$158$			5.14272i			0.409133i
$159$		0			0
$160$	−7.73975	−	1.08742i	−0.611881	−	0.0859681i
$161$	3.61285			0.284732
$162$		0			0
$163$			11.0509i			0.865570i	0.901497	+	0.432785i	$0.142469\pi$
$163$			11.0509i			0.865570i	−0.901497	+	0.432785i	$0.857531\pi$
$164$	20.2953			1.58480
$165$		0			0
$166$	2.41435			0.187390
$167$			13.9541i			1.07980i	0.841730	+	0.539899i	$0.181538\pi$
$167$			13.9541i			1.07980i	−0.841730	+	0.539899i	$0.818462\pi$
$168$		0			0
$169$	4.57136			0.351643
$170$	0.220773	−	1.57136i	0.0169325	−	0.120518i
$171$		0			0
$172$			20.3827i			1.55417i
$173$			18.8430i			1.43261i	0.697789	+	0.716303i	$0.254167\pi$
$173$			18.8430i			1.43261i	−0.697789	+	0.716303i	$0.745833\pi$
$174$		0			0
$175$	1.24443	−	4.34122i	0.0940702	−	0.328165i
$176$	−3.42864			−0.258443
$177$		0			0
$178$			1.90813i			0.143021i
$179$	4.85728			0.363050			0.181525	−	0.983386i	$-0.441897\pi$
$179$	4.85728			0.363050			0.181525	+	0.983386i	$0.441897\pi$
$180$		0			0
$181$	−16.7971			−1.24852			−0.624258	−	0.781219i	$-0.714598\pi$
$181$	−16.7971			−1.24852			−0.624258	+	0.781219i	$0.714598\pi$
$182$		−	0.815792i		−	0.0604705i
$183$		0			0
$184$	4.85728			0.358083
$185$	12.8573	+	1.80642i	0.945286	+	0.132811i
$186$		0			0
$187$		−	2.28100i		−	0.166803i
$188$			1.80642i			0.131747i
$189$		0			0
$190$	1.67307	+	0.235063i	0.121377	+	0.0170533i
$191$	−16.8573			−1.21975			−0.609875	−	0.792498i	$-0.708780\pi$
$191$	−16.8573			−1.21975			−0.609875	+	0.792498i	$0.708780\pi$
$192$		0			0
$193$		−	24.6178i		−	1.77203i	−0.463661	−	0.886013i	$-0.653464\pi$
$193$		−	24.6178i		−	1.77203i	0.463661	−	0.886013i	$-0.346536\pi$
$194$	−3.87955			−0.278536
$195$		0			0
$196$	11.7699			0.840704
$197$			14.8716i			1.05956i	0.848137	+	0.529778i	$0.177725\pi$
$197$			14.8716i			1.05956i	−0.848137	+	0.529778i	$0.822275\pi$
$198$		0			0
$199$	11.2257			0.795768			0.397884	−	0.917436i	$-0.369745\pi$
$199$	11.2257			0.795768			0.397884	+	0.917436i	$0.369745\pi$
$200$	1.67307	−	5.83654i	0.118304	−	0.412705i
$201$		0			0
$202$		−	5.03212i		−	0.354059i
$203$			6.36842i			0.446975i
$204$		0			0
$205$	−3.31756	+	23.6128i	−0.231709	+	1.64919i
$206$	5.33630			0.371797
$207$		0			0
$208$			9.95407i			0.690190i
$209$	2.42864			0.167993
$210$		0			0
$211$	−11.9398			−0.821968			−0.410984	−	0.911643i	$-0.634815\pi$
$211$	−11.9398			−0.821968			−0.410984	+	0.911643i	$0.634815\pi$
$212$		−	1.55262i		−	0.106635i
$213$		0			0
$214$	4.22077			0.288526
$215$	−23.7146	−	3.33185i	−1.61732	−	0.227230i
$216$		0			0
$217$		−	2.36842i		−	0.160779i
$218$			3.11108i			0.210709i
$219$		0			0
$220$	0.592104	−	4.21432i	0.0399197	−	0.284129i
$221$	−6.62222			−0.445458
$222$		0			0
$223$			21.8064i			1.46027i	0.683305	+	0.730133i	$0.260542\pi$
$223$			21.8064i			1.46027i	−0.683305	+	0.730133i	$0.739458\pi$
$224$	−3.15701			−0.210937
$225$		0			0
$226$	4.42864			0.294589
$227$			3.19850i			0.212292i	0.994351	+	0.106146i	$0.0338511\pi$
$227$			3.19850i			0.212292i	−0.994351	+	0.106146i	$0.966149\pi$
$228$		0			0
$229$	−7.12399			−0.470766			−0.235383	−	0.971903i	$-0.575634\pi$
$229$	−7.12399			−0.470766			−0.235383	+	0.971903i	$0.575634\pi$
$230$	−0.387152	+	2.75557i	−0.0255281	+	0.181697i
$231$		0			0
$232$			8.56199i			0.562122i
$233$			19.5254i			1.27915i	0.768727	+	0.639577i	$0.220890\pi$
$233$			19.5254i			1.27915i	−0.768727	+	0.639577i	$0.779110\pi$
$234$		0			0
$235$	−2.10171	−	0.295286i	−0.137100	−	0.0192624i
$236$	−3.18421			−0.207274
$237$		0			0
$238$		−	0.640951i		−	0.0415467i
$239$	−21.9813			−1.42185			−0.710925	−	0.703268i	$-0.751723\pi$
$239$	−21.9813			−1.42185			−0.710925	+	0.703268i	$0.751723\pi$
$240$		0			0
$241$	5.34614			0.344375			0.172188	−	0.985064i	$-0.444916\pi$
$241$	5.34614			0.344375			0.172188	+	0.985064i	$0.444916\pi$
$242$			0.311108i			0.0199988i
$243$		0			0
$244$	−13.7877			−0.882666
$245$	−1.92396	+	13.6938i	−0.122917	+	0.874866i
$246$		0			0
$247$		−	7.05086i		−	0.448635i
$248$		−	3.18421i		−	0.202197i
$249$		0			0
$250$	3.17775	+	1.41435i	0.200979	+	0.0894513i
$251$	23.7748			1.50065			0.750325	−	0.661069i	$-0.229897\pi$
$251$	23.7748			1.50065			0.750325	+	0.661069i	$0.229897\pi$
$252$		0			0
$253$			4.00000i			0.251478i
$254$	3.42372			0.214823
$255$		0			0
$256$	8.80642			0.550401
$257$		−	8.13335i		−	0.507345i	−0.967290	−	0.253672i	$-0.918362\pi$
$257$		−	8.13335i		−	0.507345i	0.967290	−	0.253672i	$-0.0816385\pi$
$258$		0			0
$259$	5.24443			0.325873
$260$	−12.2351	−	1.71900i	−0.758786	−	0.106608i
$261$		0			0
$262$		−	0.387152i		−	0.0239183i
$263$		−	22.9032i		−	1.41227i	−0.708076	−	0.706136i	$-0.750437\pi$
$263$		−	22.9032i		−	1.41227i	0.708076	−	0.706136i	$-0.249563\pi$
$264$		0			0
$265$	1.80642	+	0.253799i	0.110968	+	0.0155908i
$266$	0.682439			0.0418430
$267$		0			0
$268$		−	24.4701i		−	1.49475i
$269$	11.8350			0.721593			0.360796	−	0.932645i	$-0.382505\pi$
$269$	11.8350			0.721593			0.360796	+	0.932645i	$0.382505\pi$
$270$		0			0
$271$	14.8988			0.905036			0.452518	−	0.891755i	$-0.350526\pi$
$271$	14.8988			0.905036			0.452518	+	0.891755i	$0.350526\pi$
$272$			7.82071i			0.474200i
$273$		0			0
$274$	1.37778			0.0832350
$275$	4.80642	+	1.37778i	0.289838	+	0.0830835i
$276$		0			0
$277$			27.6686i			1.66245i	0.555939	+	0.831223i	$0.312359\pi$
$277$			27.6686i			1.66245i	−0.555939	+	0.831223i	$0.687641\pi$
$278$		−	0.285442i		−	0.0171197i
$279$		0			0
$280$	0.341219	−	2.42864i	0.0203918	−	0.145139i
$281$	−9.80642			−0.585002			−0.292501	−	0.956265i	$-0.594488\pi$
$281$	−9.80642			−0.585002			−0.292501	+	0.956265i	$0.594488\pi$
$282$		0			0
$283$		−	19.0049i		−	1.12973i	−0.825185	−	0.564863i	$-0.808929\pi$
$283$		−	19.0049i		−	1.12973i	0.825185	−	0.564863i	$-0.191071\pi$
$284$	−17.6731			−1.04870
$285$		0			0
$286$	0.903212			0.0534080
$287$			9.63158i			0.568534i
$288$		0			0
$289$	11.7971			0.693944
$290$	−4.85728	−	0.682439i	−0.285229	−	0.0400742i
$291$		0			0
$292$		−	10.7699i		−	0.630258i
$293$			30.7511i			1.79650i	0.439485	+	0.898250i	$0.355161\pi$
$293$			30.7511i			1.79650i	−0.439485	+	0.898250i	$0.644839\pi$
$294$		0			0
$295$	0.520505	−	3.70471i	0.0303050	−	0.215697i
$296$	7.05086			0.409823
$297$		0			0
$298$			0.682439i			0.0395326i
$299$	11.6128			0.671588
$300$		0			0
$301$	−9.67307			−0.557547
$302$		−	3.24443i		−	0.186696i
$303$		0			0
$304$	−8.32693			−0.477582
$305$	2.25380	−	16.0415i	0.129052	−	0.918533i
$306$		0			0
$307$			13.4938i			0.770131i	0.922889	+	0.385065i	$0.125821\pi$
$307$			13.4938i			0.770131i	−0.922889	+	0.385065i	$0.874179\pi$
$308$		−	1.71900i		−	0.0979493i
$309$		0			0
$310$	1.80642	+	0.253799i	0.102598	+	0.0144148i
$311$	17.5526			0.995318			0.497659	−	0.867373i	$-0.334193\pi$
$311$	17.5526			0.995318			0.497659	+	0.867373i	$0.334193\pi$
$312$		0			0
$313$			14.3970i			0.813766i	0.913480	+	0.406883i	$0.133384\pi$
$313$			14.3970i			0.813766i	−0.913480	+	0.406883i	$0.866616\pi$
$314$	1.80642			0.101942
$315$		0			0
$316$	31.4608			1.76981
$317$			29.4608i			1.65468i	0.561701	+	0.827341i	$0.310147\pi$
$317$			29.4608i			1.65468i	−0.561701	+	0.827341i	$0.689853\pi$
$318$		0			0
$319$	−7.05086			−0.394772
$320$	−1.79505	+	12.7763i	−0.100346	+	0.714218i
$321$		0			0
$322$			1.12399i			0.0626372i
$323$		−	5.53972i		−	0.308238i
$324$		0			0
$325$	4.00000	−	13.9541i	0.221880	−	0.774032i
$326$	−3.43801			−0.190414
$327$		0			0
$328$			12.9491i			0.714997i
$329$	−0.857279			−0.0472633
$330$		0			0
$331$	−2.62222			−0.144130			−0.0720650	−	0.997400i	$-0.522959\pi$
$331$	−2.62222			−0.144130			−0.0720650	+	0.997400i	$0.522959\pi$
$332$		−	14.7699i		−	0.810601i
$333$		0			0
$334$	−4.34122			−0.237541
$335$	28.4701	+	4.00000i	1.55549	+	0.218543i
$336$		0			0
$337$			5.00492i			0.272635i	0.990665	+	0.136318i	$0.0435268\pi$
$337$			5.00492i			0.272635i	−0.990665	+	0.136318i	$0.956473\pi$
$338$			1.42219i			0.0773567i
$339$		0			0
$340$	−9.61285	−	1.35059i	−0.521330	−	0.0732459i
$341$	2.62222			0.142001
$342$		0			0
$343$			11.9081i			0.642979i
$344$	−13.0049			−0.701178
$345$		0			0
$346$	−5.86220			−0.315154
$347$		−	22.8113i		−	1.22458i	−0.790634	−	0.612289i	$-0.790249\pi$
$347$		−	22.8113i		−	1.22458i	0.790634	−	0.612289i	$-0.209751\pi$
$348$		0			0
$349$	−21.2257			−1.13619			−0.568093	−	0.822965i	$-0.692319\pi$
$349$	−21.2257			−1.13619			−0.568093	+	0.822965i	$0.692319\pi$
$350$	1.35059	+	0.387152i	0.0721919	+	0.0206942i
$351$		0			0
$352$		−	3.49532i		−	0.186301i
$353$		−	7.18421i		−	0.382377i	−0.981553	−	0.191188i	$-0.938766\pi$
$353$		−	7.18421i		−	0.382377i	0.981553	−	0.191188i	$-0.0612341\pi$
$354$		0			0
$355$	2.88892	−	20.5620i	0.153328	−	1.09132i
$356$	11.6731			0.618672
$357$		0			0
$358$			1.51114i			0.0798661i
$359$	−14.1017			−0.744260			−0.372130	−	0.928181i	$-0.621372\pi$
$359$	−14.1017			−0.744260			−0.372130	+	0.928181i	$0.621372\pi$
$360$		0			0
$361$	−13.1017			−0.689564
$362$		−	5.22570i		−	0.274656i
$363$		0			0
$364$	−4.99063			−0.261580
$365$	12.5303	+	1.76049i	0.655868	+	0.0921483i
$366$		0			0
$367$			3.90813i			0.204003i	0.994784	+	0.102001i	$0.0325246\pi$
$367$			3.90813i			0.204003i	−0.994784	+	0.102001i	$0.967475\pi$
$368$		−	13.7146i		−	0.714921i
$369$		0			0
$370$	−0.561993	+	4.00000i	−0.0292166	+	0.207950i
$371$	0.736833			0.0382545
$372$		0			0
$373$			12.9763i			0.671890i	0.941882	+	0.335945i	$0.109056\pi$
$373$			12.9763i			0.671890i	−0.941882	+	0.335945i	$0.890944\pi$
$374$	0.709636			0.0366944
$375$		0			0
$376$	−1.15257			−0.0594390
$377$			20.4701i			1.05427i
$378$		0			0
$379$	−36.0830			−1.85346			−0.926729	−	0.375731i	$-0.877392\pi$
$379$	−36.0830			−1.85346			−0.926729	+	0.375731i	$0.877392\pi$
$380$	1.43801	−	10.2351i	0.0737682	−	0.525048i
$381$		0			0
$382$		−	5.24443i		−	0.268328i
$383$		−	20.2953i		−	1.03704i	−0.855065	−	0.518520i	$-0.826483\pi$
$383$		−	20.2953i		−	1.03704i	0.855065	−	0.518520i	$-0.173517\pi$
$384$		0			0
$385$	2.00000	+	0.280996i	0.101929	+	0.0143209i
$386$	7.65878			0.389822
$387$		0			0
$388$			23.7333i			1.20488i
$389$	30.4701			1.54490			0.772448	−	0.635078i	$-0.219032\pi$
$389$	30.4701			1.54490			0.772448	+	0.635078i	$0.219032\pi$
$390$		0			0
$391$	9.12399			0.461420
$392$			7.50961i			0.379292i
$393$		0			0
$394$	−4.62666			−0.233088
$395$	−5.14272	+	36.6035i	−0.258758	+	1.84172i
$396$		0			0
$397$		−	4.97773i		−	0.249825i	−0.992168	−	0.124912i	$-0.960135\pi$
$397$		−	4.97773i		−	0.249825i	0.992168	−	0.124912i	$-0.0398650\pi$
$398$			3.49240i			0.175058i
$399$		0			0
$400$	−16.4795	−	4.72393i	−0.823975	−	0.236196i
$401$	1.86665			0.0932159			0.0466079	−	0.998913i	$-0.485159\pi$
$401$	1.86665			0.0932159			0.0466079	+	0.998913i	$0.485159\pi$
$402$		0			0
$403$		−	7.61285i		−	0.379223i
$404$	−30.7841			−1.53157
$405$		0			0
$406$	−1.98126			−0.0983285
$407$			5.80642i			0.287814i
$408$		0			0
$409$	3.63158			0.179570			0.0897851	−	0.995961i	$-0.471382\pi$
$409$	3.63158			0.179570			0.0897851	+	0.995961i	$0.471382\pi$
$410$	−7.34614	−	1.03212i	−0.362800	−	0.0509727i
$411$		0			0
$412$		−	32.6450i		−	1.60830i
$413$		−	1.51114i		−	0.0743582i
$414$		0			0
$415$	17.1842	+	2.41435i	0.843540	+	0.118516i
$416$	−10.1476			−0.497529
$417$		0			0
$418$			0.755569i			0.0369561i
$419$	4.85728			0.237294			0.118647	−	0.992937i	$-0.462144\pi$
$419$	4.85728			0.237294			0.118647	+	0.992937i	$0.462144\pi$
$420$		0			0
$421$	22.6321			1.10302			0.551510	−	0.834169i	$-0.314052\pi$
$421$	22.6321			1.10302			0.551510	+	0.834169i	$0.314052\pi$
$422$		−	3.71456i		−	0.180822i
$423$		0			0
$424$	0.990632			0.0481093
$425$	3.14272	−	10.9634i	0.152444	−	0.531805i
$426$		0			0
$427$		−	6.54326i		−	0.316650i
$428$		−	25.8207i		−	1.24809i
$429$		0			0
$430$	1.03657	−	7.37778i	0.0499876	−	0.355788i
$431$	−1.24443			−0.0599421			−0.0299711	−	0.999551i	$-0.509542\pi$
$431$	−1.24443			−0.0599421			−0.0299711	+	0.999551i	$0.509542\pi$
$432$		0			0
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$	0.736833			0.0353691
$435$		0			0
$436$	19.0321			0.911473
$437$			9.71456i			0.464710i
$438$		0			0
$439$	2.42864			0.115913			0.0579563	−	0.998319i	$-0.481542\pi$
$439$	2.42864			0.115913			0.0579563	+	0.998319i	$0.481542\pi$
$440$	2.68889	+	0.377784i	0.128188	+	0.0180102i
$441$		0			0
$442$		−	2.06022i		−	0.0979948i
$443$		−	31.0509i		−	1.47527i	−0.675199	−	0.737635i	$-0.735942\pi$
$443$		−	31.0509i		−	1.47527i	0.675199	−	0.737635i	$-0.264058\pi$
$444$		0			0
$445$	−1.90813	+	13.5812i	−0.0904542	+	0.643811i
$446$	−6.78415			−0.321239
$447$		0			0
$448$			5.21141i			0.246216i
$449$	−37.3590			−1.76308			−0.881541	−	0.472107i	$-0.843494\pi$
$449$	−37.3590			−1.76308			−0.881541	+	0.472107i	$0.843494\pi$
$450$		0			0
$451$	−10.6637			−0.502134
$452$		−	27.0923i		−	1.27432i
$453$		0			0
$454$	−0.995078			−0.0467013
$455$	0.815792	−	5.80642i	0.0382449	−	0.272209i
$456$		0			0
$457$		−	8.73822i		−	0.408757i	−0.978892	−	0.204378i	$-0.934483\pi$
$457$		−	8.73822i		−	0.408757i	0.978892	−	0.204378i	$-0.0655172\pi$
$458$		−	2.21633i		−	0.103562i
$459$		0			0
$460$	16.8573	+	2.36842i	0.785975	+	0.110428i
$461$	−31.7877			−1.48050			−0.740250	−	0.672332i	$-0.765293\pi$
$461$	−31.7877			−1.48050			−0.740250	+	0.672332i	$0.765293\pi$
$462$		0			0
$463$			12.0919i			0.561957i	0.959714	+	0.280978i	$0.0906589\pi$
$463$			12.0919i			0.561957i	−0.959714	+	0.280978i	$0.909341\pi$
$464$	24.1748			1.12229
$465$		0			0
$466$	−6.07451			−0.281396
$467$		−	15.3461i		−	0.710135i	−0.934841	−	0.355067i	$-0.884458\pi$
$467$		−	15.3461i		−	0.710135i	0.934841	−	0.355067i	$-0.115542\pi$
$468$		0			0
$469$	11.6128			0.536231
$470$	0.0918659	−	0.653858i	0.00423746	−	0.0301602i
$471$		0			0
$472$		−	2.03164i		−	0.0935139i
$473$		−	10.7096i		−	0.492430i
$474$		0			0
$475$	11.6731	+	3.34614i	0.535597	+	0.153532i
$476$	−3.92104			−0.179721
$477$		0			0
$478$		−	6.83854i		−	0.312788i
$479$	5.89829			0.269500			0.134750	−	0.990880i	$-0.456977\pi$
$479$	5.89829			0.269500			0.134750	+	0.990880i	$0.456977\pi$
$480$		0			0
$481$	16.8573			0.768626
$482$			1.66323i			0.0757579i
$483$		0			0
$484$	1.90321			0.0865096
$485$	−27.6128	−	3.87955i	−1.25383	−	0.176161i
$486$		0			0
$487$		−	31.3461i		−	1.42043i	−0.703985	−	0.710215i	$-0.748598\pi$
$487$		−	31.3461i		−	1.42043i	0.703985	−	0.710215i	$-0.251402\pi$
$488$		−	8.79706i		−	0.398224i
$489$		0			0
$490$	−4.26025	−	0.598558i	−0.192459	−	0.0270401i
$491$	8.00000			0.361035			0.180517	−	0.983572i	$-0.442223\pi$
$491$	8.00000			0.361035			0.180517	+	0.983572i	$0.442223\pi$
$492$		0			0
$493$			16.0830i			0.724341i
$494$	2.19358			0.0986937
$495$		0			0
$496$	−8.99063			−0.403691
$497$		−	8.38715i		−	0.376215i
$498$		0			0
$499$	−15.1427			−0.677881			−0.338941	−	0.940808i	$-0.610069\pi$
$499$	−15.1427			−0.677881			−0.338941	+	0.940808i	$0.610069\pi$
$500$	8.65233	−	19.4400i	0.386944	−	0.869384i
$501$		0			0
$502$			7.39652i			0.330123i
$503$		−	26.0370i		−	1.16093i	−0.814284	−	0.580467i	$-0.802870\pi$
$503$		−	26.0370i		−	1.16093i	0.814284	−	0.580467i	$-0.197130\pi$
$504$		0			0
$505$	5.03212	−	35.8163i	0.223926	−	1.59380i
$506$	−1.24443			−0.0553217
$507$		0			0
$508$		−	20.9447i		−	0.929271i
$509$	−24.5718			−1.08913			−0.544564	−	0.838719i	$-0.683305\pi$
$509$	−24.5718			−1.08913			−0.544564	+	0.838719i	$0.683305\pi$
$510$		0			0
$511$	5.11108			0.226101
$512$			20.3111i			0.897633i
$513$		0			0
$514$	2.53035			0.111609
$515$	37.9813	+	5.33630i	1.67365	+	0.235145i
$516$		0			0
$517$		−	0.949145i		−	0.0417433i
$518$			1.63158i			0.0716877i
$519$		0			0
$520$	1.09679	−	7.80642i	0.0480973	−	0.342334i
$521$	4.88892			0.214188			0.107094	−	0.994249i	$-0.465845\pi$
$521$	4.88892			0.214188			0.107094	+	0.994249i	$0.465845\pi$
$522$		0			0
$523$		−	4.22077i		−	0.184562i	−0.995733	−	0.0922808i	$-0.970584\pi$
$523$		−	4.22077i		−	0.184562i	0.995733	−	0.0922808i	$-0.0294157\pi$
$524$	−2.36842			−0.103465
$525$		0			0
$526$	7.12537			0.310681
$527$		−	5.98126i		−	0.260548i
$528$		0			0
$529$	7.00000			0.304348
$530$	−0.0789589	+	0.561993i	−0.00342976	+	0.0244114i
$531$		0			0
$532$		−	4.17484i		−	0.181002i
$533$			30.9590i			1.34098i
$534$		0			0
$535$	30.0415	+	4.22077i	1.29881	+	0.182480i
$536$	15.6128			0.674372
$537$		0			0
$538$			3.68196i			0.158741i
$539$	−6.18421			−0.266373
$540$		0			0
$541$	−13.6128			−0.585262			−0.292631	−	0.956225i	$-0.594531\pi$
$541$	−13.6128			−0.585262			−0.292631	+	0.956225i	$0.594531\pi$
$542$			4.63512i			0.199096i
$543$		0			0
$544$	−7.97280			−0.341831
$545$	−3.11108	+	22.1432i	−0.133264	+	0.948510i
$546$		0			0
$547$			7.48394i			0.319990i	0.987118	+	0.159995i	$0.0511478\pi$
$547$			7.48394i			0.319990i	−0.987118	+	0.159995i	$0.948852\pi$
$548$		−	8.42864i		−	0.360054i
$549$		0			0
$550$	−0.428639	+	1.49532i	−0.0182772	+	0.0637605i
$551$	−17.1240			−0.729506
$552$		0			0
$553$			14.9304i			0.634906i
$554$	−8.60793			−0.365716
$555$		0			0
$556$	−1.74620			−0.0740554
$557$		−	32.2908i		−	1.36821i	−0.729385	−	0.684103i	$-0.760194\pi$
$557$		−	32.2908i		−	1.36821i	0.729385	−	0.684103i	$-0.239806\pi$
$558$		0			0
$559$	−31.0923			−1.31507
$560$	−6.85728	−	0.963435i	−0.289773	−	0.0407126i
$561$		0			0
$562$		−	3.05086i		−	0.128693i
$563$			7.49378i			0.315825i	0.987453	+	0.157913i	$0.0504765\pi$
$563$			7.49378i			0.315825i	−0.987453	+	0.157913i	$0.949524\pi$
$564$		0			0
$565$	31.5210	+	4.42864i	1.32610	+	0.186314i
$566$	5.91258			0.248524
$567$		0			0
$568$		−	11.2761i		−	0.473134i
$569$	−12.9491			−0.542856			−0.271428	−	0.962459i	$-0.587496\pi$
$569$	−12.9491			−0.542856			−0.271428	+	0.962459i	$0.587496\pi$
$570$		0			0
$571$	−15.2859			−0.639696			−0.319848	−	0.947469i	$-0.603632\pi$
$571$	−15.2859			−0.639696			−0.319848	+	0.947469i	$0.603632\pi$
$572$		−	5.52543i		−	0.231030i
$573$		0			0
$574$	−2.99646			−0.125070
$575$	−5.51114	+	19.2257i	−0.229830	+	0.801767i
$576$		0			0
$577$			28.4415i			1.18404i	0.805924	+	0.592019i	$0.201669\pi$
$577$			28.4415i			1.18404i	−0.805924	+	0.592019i	$0.798331\pi$
$578$			3.67016i			0.152658i
$579$		0			0
$580$	−4.17484	+	29.7146i	−0.173351	+	1.23383i
$581$	7.00937			0.290798
$582$		0			0
$583$			0.815792i			0.0337866i
$584$	6.87157			0.284348
$585$		0			0
$586$	−9.56691			−0.395206
$587$			8.47013i			0.349600i	0.984604	+	0.174800i	$0.0559278\pi$
$587$			8.47013i			0.349600i	−0.984604	+	0.174800i	$0.944072\pi$
$588$		0			0
$589$	6.36842			0.262406
$590$	1.15257	+	0.161933i	0.0474504	+	0.00666669i
$591$		0			0
$592$		−	19.9081i		−	0.818219i
$593$			26.5763i			1.09136i	0.837995	+	0.545679i	$0.183728\pi$
$593$			26.5763i			1.09136i	−0.837995	+	0.545679i	$0.816272\pi$
$594$		0			0
$595$	0.640951	−	4.56199i	0.0262764	−	0.187023i
$596$	4.17484			0.171008
$597$		0			0
$598$			3.61285i			0.147740i
$599$	−8.77430			−0.358508			−0.179254	−	0.983803i	$-0.557368\pi$
$599$	−8.77430			−0.358508			−0.179254	+	0.983803i	$0.557368\pi$
$600$		0			0
$601$	−41.8163			−1.70572			−0.852861	−	0.522139i	$-0.825134\pi$
$601$	−41.8163			−1.70572			−0.852861	+	0.522139i	$0.825134\pi$
$602$		−	3.00937i		−	0.122653i
$603$		0			0
$604$	−19.8479			−0.807600
$605$	−0.311108	+	2.21432i	−0.0126483	+	0.0900249i
$606$		0			0
$607$			29.9353i			1.21504i	0.794305	+	0.607519i	$0.207835\pi$
$607$			29.9353i			1.21504i	−0.794305	+	0.607519i	$0.792165\pi$
$608$		−	8.48886i		−	0.344269i
$609$		0			0
$610$	4.99063	+	0.701175i	0.202065	+	0.0283897i
$611$	−2.75557			−0.111478
$612$		0			0
$613$		−	26.1289i		−	1.05534i	−0.849450	−	0.527668i	$-0.823066\pi$
$613$		−	26.1289i		−	1.05534i	0.849450	−	0.527668i	$-0.176934\pi$
$614$	−4.19802			−0.169418
$615$		0			0
$616$	1.09679			0.0441909
$617$			3.66323i			0.147476i	0.997278	+	0.0737380i	$0.0234928\pi$
$617$			3.66323i			0.147476i	−0.997278	+	0.0737380i	$0.976507\pi$
$618$		0			0
$619$	−43.2958			−1.74020			−0.870102	−	0.492872i	$-0.835947\pi$
$619$	−43.2958			−1.74020			−0.870102	+	0.492872i	$0.835947\pi$
$620$	1.55262	−	11.0509i	0.0623549	−	0.443813i
$621$		0			0
$622$			5.46076i			0.218956i
$623$			5.53972i			0.221944i
$624$		0			0
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$	−4.47902			−0.179018
$627$		0			0
$628$		−	11.0509i		−	0.440977i
$629$	13.2444			0.528090
$630$		0			0
$631$	8.97773			0.357398			0.178699	−	0.983904i	$-0.442811\pi$
$631$	8.97773			0.357398			0.178699	+	0.983904i	$0.442811\pi$
$632$			20.0731i			0.798466i
$633$		0			0
$634$	−9.16547			−0.364007
$635$	24.3684	+	3.42372i	0.967031	+	0.135866i
$636$		0			0
$637$			17.9541i			0.711366i
$638$		−	2.19358i		−	0.0868445i
$639$		0			0
$640$	−19.4543	−	2.73329i	−0.768999	−	0.108043i
$641$	−9.21279			−0.363883			−0.181942	−	0.983309i	$-0.558238\pi$
$641$	−9.21279			−0.363883			−0.181942	+	0.983309i	$0.558238\pi$
$642$		0			0
$643$			16.3783i			0.645896i	0.946417	+	0.322948i	$0.104674\pi$
$643$			16.3783i			0.645896i	−0.946417	+	0.322948i	$0.895326\pi$
$644$	6.87601			0.270953
$645$		0			0
$646$	1.72345			0.0678082
$647$		−	9.80642i		−	0.385530i	−0.981245	−	0.192765i	$-0.938254\pi$
$647$		−	9.80642i		−	0.385530i	0.981245	−	0.192765i	$-0.0617456\pi$
$648$		0			0
$649$	1.67307			0.0656738
$650$	4.34122	+	1.24443i	0.170277	+	0.0488106i
$651$		0			0
$652$			21.0321i			0.823681i
$653$			33.0736i			1.29427i	0.762375	+	0.647135i	$0.224033\pi$
$653$			33.0736i			1.29427i	−0.762375	+	0.647135i	$0.775967\pi$
$654$		0			0
$655$	0.387152	−	2.75557i	0.0151273	−	0.107669i
$656$	36.5620			1.42751
$657$		0			0
$658$		−	0.266706i		−	0.0103973i
$659$	34.1017			1.32841			0.664207	−	0.747549i	$-0.268769\pi$
$659$	34.1017			1.32841			0.664207	+	0.747549i	$0.268769\pi$
$660$		0			0
$661$	−5.40943			−0.210402			−0.105201	−	0.994451i	$-0.533549\pi$
$661$	−5.40943			−0.210402			−0.105201	+	0.994451i	$0.533549\pi$
$662$		−	0.815792i		−	0.0317066i
$663$		0			0
$664$	9.42372			0.365711
$665$	4.85728	+	0.682439i	0.188357	+	0.0264638i
$666$		0			0
$667$		−	28.2034i		−	1.09204i
$668$			26.5575i			1.02754i
$669$		0			0
$670$	−1.24443	+	8.85728i	−0.0480766	+	0.342187i
$671$	7.24443			0.279668
$672$		0			0
$673$		−	24.1476i		−	0.930823i	−0.885094	−	0.465412i	$-0.845906\pi$
$673$		−	24.1476i		−	0.930823i	0.885094	−	0.465412i	$-0.154094\pi$
$674$	−1.55707			−0.0599761
$675$		0			0
$676$	8.70027			0.334626
$677$		−	26.2810i		−	1.01006i	−0.863102	−	0.505030i	$-0.831481\pi$
$677$		−	26.2810i		−	1.01006i	0.863102	−	0.505030i	$-0.168519\pi$
$678$		0			0
$679$	−11.2632			−0.432241
$680$	0.861725	−	6.13335i	0.0330456	−	0.235203i
$681$		0			0
$682$			0.815792i			0.0312383i
$683$			15.3176i			0.586110i	0.956096	+	0.293055i	$0.0946719\pi$
$683$			15.3176i			0.586110i	−0.956096	+	0.293055i	$0.905328\pi$
$684$		0			0
$685$	9.80642	+	1.37778i	0.374684	+	0.0526424i
$686$	−3.70471			−0.141447
$687$		0			0
$688$			36.7195i			1.39992i
$689$	2.36842			0.0902295
$690$		0			0
$691$	15.0223			0.571474			0.285737	−	0.958308i	$-0.407762\pi$
$691$	15.0223			0.571474			0.285737	+	0.958308i	$0.407762\pi$
$692$			35.8622i			1.36328i
$693$		0			0
$694$	7.09679			0.269390
$695$	0.285442	−	2.03164i	0.0108274	−	0.0770646i
$696$		0			0
$697$			24.3239i			0.921332i
$698$		−	6.60348i		−	0.249945i
$699$		0			0
$700$	2.36842	−	8.26226i	0.0895177	−	0.312284i
$701$	19.9081			0.751920			0.375960	−	0.926636i	$-0.377313\pi$
$701$	19.9081			0.751920			0.375960	+	0.926636i	$0.377313\pi$
$702$		0			0
$703$			14.1017i			0.531856i
$704$	−5.76986			−0.217460
$705$		0			0
$706$	2.23506			0.0841177
$707$		−	14.6093i		−	0.549440i
$708$		0			0
$709$	13.5081			0.507306			0.253653	−	0.967295i	$-0.418368\pi$
$709$	13.5081			0.507306			0.253653	+	0.967295i	$0.418368\pi$
$710$	6.39700	+	0.898766i	0.240075	+	0.0337301i
$711$		0			0
$712$			7.44785i			0.279120i
$713$			10.4889i			0.392811i
$714$		0			0
$715$	6.42864	+	0.903212i	0.240417	+	0.0337782i
$716$	9.24443			0.345481
$717$		0			0
$718$		−	4.38715i		−	0.163727i
$719$	−16.0830			−0.599794			−0.299897	−	0.953972i	$-0.596952\pi$
$719$	−16.0830			−0.599794			−0.299897	+	0.953972i	$0.596952\pi$
$720$		0			0
$721$	15.4924			0.576967
$722$		−	4.07604i		−	0.151695i
$723$		0			0
$724$	−31.9684			−1.18809
$725$	−33.8894	−	9.71456i	−1.25862	−	0.360790i
$726$		0			0
$727$		−	23.6128i		−	0.875752i	−0.899035	−	0.437876i	$-0.855731\pi$
$727$		−	23.6128i		−	0.875752i	0.899035	−	0.437876i	$-0.144269\pi$
$728$		−	3.18421i		−	0.118015i
$729$		0			0
$730$	−0.547702	+	3.89829i	−0.0202714	+	0.144282i
$731$	−24.4286			−0.903526
$732$		0			0
$733$		−	30.0459i		−	1.10977i	−0.831926	−	0.554886i	$-0.812762\pi$
$733$		−	30.0459i		−	1.10977i	0.831926	−	0.554886i	$-0.187238\pi$
$734$	−1.21585			−0.0448779
$735$		0			0
$736$	13.9813			0.515356
$737$			12.8573i			0.473604i
$738$		0			0
$739$	24.4099			0.897933			0.448966	−	0.893549i	$-0.351792\pi$
$739$	24.4099			0.897933			0.448966	+	0.893549i	$0.351792\pi$
$740$	24.4701	+	3.43801i	0.899540	+	0.126384i
$741$		0			0
$742$			0.229234i			0.00841546i
$743$			33.1798i			1.21725i	0.793459	+	0.608624i	$0.208278\pi$
$743$			33.1798i			1.21725i	−0.793459	+	0.608624i	$0.791722\pi$
$744$		0			0
$745$	−0.682439	+	4.85728i	−0.0250026	+	0.177957i
$746$	−4.03704			−0.147807
$747$		0			0
$748$		−	4.34122i		−	0.158731i
$749$	12.2538			0.447744
$750$		0			0
$751$	−22.5718			−0.823658			−0.411829	−	0.911261i	$-0.635110\pi$
$751$	−22.5718			−0.823658			−0.411829	+	0.911261i	$0.635110\pi$
$752$			3.25428i			0.118671i
$753$		0			0
$754$	−6.36842			−0.231924
$755$	3.24443	−	23.0923i	0.118077	−	0.840416i
$756$		0			0
$757$			4.94914i			0.179880i	0.995947	+	0.0899399i	$0.0286675\pi$
$757$			4.94914i			0.179880i	−0.995947	+	0.0899399i	$0.971333\pi$
$758$		−	11.2257i		−	0.407736i
$759$		0			0
$760$	6.53035	+	0.917502i	0.236881	+	0.0332813i
$761$	−14.6637			−0.531559			−0.265779	−	0.964034i	$-0.585629\pi$
$761$	−14.6637			−0.531559			−0.265779	+	0.964034i	$0.585629\pi$
$762$		0			0
$763$			9.03212i			0.326985i
$764$	−32.0830			−1.16072
$765$		0			0
$766$	6.31402			0.228135
$767$		−	4.85728i		−	0.175386i
$768$		0			0
$769$	44.5718			1.60730			0.803651	−	0.595101i	$-0.202888\pi$
$769$	44.5718			1.60730			0.803651	+	0.595101i	$0.202888\pi$
$770$	−0.0874201	+	0.622216i	−0.00315040	+	0.0224231i
$771$		0			0
$772$		−	46.8528i		−	1.68627i
$773$			17.3145i			0.622759i	0.950286	+	0.311380i	$0.100791\pi$
$773$			17.3145i			0.622759i	−0.950286	+	0.311380i	$0.899209\pi$
$774$		0			0
$775$	12.6035	+	3.61285i	0.452730	+	0.129777i
$776$	−15.1427			−0.543592
$777$		0			0
$778$			9.47949i			0.339856i
$779$	−25.8983			−0.927903
$780$		0			0
$781$	9.28592			0.332276
$782$			2.83854i			0.101506i
$783$		0			0
$784$	21.2034			0.757265
$785$	12.8573	+	1.80642i	0.458896	+	0.0644740i
$786$		0			0
$787$			36.5161i			1.30166i	0.759225	+	0.650828i	$0.225578\pi$
$787$			36.5161i			1.30166i	−0.759225	+	0.650828i	$0.774422\pi$
$788$			28.3037i			1.00828i
$789$		0			0
$790$	−11.3876	−	1.59994i	−0.405154	−	0.0569233i
$791$	12.8573			0.457152
$792$		0			0
$793$		−	21.0321i		−	0.746872i
$794$	1.54861			0.0549581
$795$		0			0
$796$	21.3649			0.757258
$797$			14.3180i			0.507171i	0.967313	+	0.253585i	$0.0816099\pi$
$797$			14.3180i			0.507171i	−0.967313	+	0.253585i	$0.918390\pi$
$798$		0			0
$799$	−2.16500			−0.0765921
$800$	4.81579	−	16.8000i	0.170264	−	0.593969i
$801$		0			0
$802$			0.580728i			0.0205062i
$803$			5.65878i			0.199694i
$804$		0			0
$805$	−1.12399	+	8.00000i	−0.0396153	+	0.281963i
$806$	2.36842			0.0834239
$807$		0			0
$808$		−	19.6414i		−	0.690983i
$809$	32.0544			1.12697			0.563486	−	0.826125i	$-0.309460\pi$
$809$	32.0544			1.12697			0.563486	+	0.826125i	$0.309460\pi$
$810$		0			0
$811$	−8.44738			−0.296627			−0.148314	−	0.988940i	$-0.547385\pi$
$811$	−8.44738			−0.296627			−0.148314	+	0.988940i	$0.547385\pi$
$812$			12.1204i			0.425344i
$813$		0			0
$814$	−1.80642			−0.0633151
$815$	−24.4701	−	3.43801i	−0.857151	−	0.120428i
$816$		0			0
$817$		−	26.0098i		−	0.909969i
$818$			1.12981i			0.0395030i
$819$		0			0
$820$	−6.31402	+	44.9403i	−0.220495	+	1.56938i
$821$	−17.2159			−0.600837			−0.300419	−	0.953807i	$-0.597126\pi$
$821$	−17.2159			−0.600837			−0.300419	+	0.953807i	$0.597126\pi$
$822$		0			0
$823$		−	12.7654i		−	0.444974i	−0.974936	−	0.222487i	$-0.928582\pi$
$823$		−	12.7654i		−	0.444974i	0.974936	−	0.222487i	$-0.0714175\pi$
$824$	20.8287			0.725602
$825$		0			0
$826$	0.470127			0.0163578
$827$		−	8.70964i		−	0.302864i	−0.988468	−	0.151432i	$-0.951612\pi$
$827$		−	8.70964i		−	0.302864i	0.988468	−	0.151432i	$-0.0483884\pi$
$828$		0			0
$829$	8.32693			0.289206			0.144603	−	0.989490i	$-0.453809\pi$
$829$	8.32693			0.289206			0.144603	+	0.989490i	$0.453809\pi$
$830$	−0.751123	+	5.34614i	−0.0260719	+	0.185567i
$831$		0			0
$832$			16.7511i			0.580741i
$833$			14.1062i			0.488749i
$834$		0			0
$835$	−30.8988	−	4.34122i	−1.06930	−	0.150234i
$836$	4.62222			0.159863
$837$		0			0
$838$			1.51114i			0.0522014i
$839$	12.8988			0.445315			0.222657	−	0.974897i	$-0.428527\pi$
$839$	12.8988			0.445315			0.222657	+	0.974897i	$0.428527\pi$
$840$		0			0
$841$	20.7146			0.714295
$842$			7.04101i			0.242649i
$843$		0			0
$844$	−22.7239			−0.782190
$845$	−1.42219	+	10.1225i	−0.0489247	+	0.348223i
$846$		0			0
$847$			0.903212i			0.0310347i
$848$		−	2.79706i		−	0.0960513i
$849$		0			0
$850$	3.41081	+	0.977725i	0.116990	+	0.0335357i
$851$	−23.2257			−0.796167
$852$		0			0
$853$			19.6686i			0.673441i	0.941605	+	0.336720i	$0.109318\pi$
$853$			19.6686i			0.673441i	−0.941605	+	0.336720i	$0.890682\pi$
$854$	2.03566			0.0696588
$855$		0			0
$856$	16.4746			0.563089
$857$		−	31.8207i		−	1.08697i	−0.839417	−	0.543487i	$-0.817104\pi$
$857$		−	31.8207i		−	1.08697i	0.839417	−	0.543487i	$-0.182896\pi$
$858$		0			0
$859$	−27.8292			−0.949519			−0.474760	−	0.880116i	$-0.657465\pi$
$859$	−27.8292			−0.949519			−0.474760	+	0.880116i	$0.657465\pi$
$860$	−45.1338	−	6.34122i	−1.53905	−	0.216234i
$861$		0			0
$862$		−	0.387152i		−	0.0131865i
$863$		−	4.82870i		−	0.164371i	−0.996617	−	0.0821854i	$-0.973810\pi$
$863$		−	4.82870i		−	0.164371i	0.996617	−	0.0821854i	$-0.0261900\pi$
$864$		0			0
$865$	−41.7244	−	5.86220i	−1.41867	−	0.199321i
$866$	4.97773			0.169150
$867$		0			0
$868$		−	4.50760i		−	0.152998i
$869$	−16.5303			−0.560754
$870$		0			0
$871$	37.3274			1.26479
$872$			12.1432i			0.411221i
$873$		0			0
$874$	−3.02227			−0.102230
$875$	9.22570	+	4.10616i	0.311885	+	0.138813i
$876$		0			0
$877$			21.9826i			0.742301i	0.928573	+	0.371151i	$0.121037\pi$
$877$			21.9826i			0.742301i	−0.928573	+	0.371151i	$0.878963\pi$
$878$			0.755569i			0.0254992i
$879$		0			0
$880$	1.06668	−	7.59210i	0.0359577	−	0.255930i
$881$	12.1017			0.407717			0.203858	−	0.979000i	$-0.434652\pi$
$881$	12.1017			0.407717			0.203858	+	0.979000i	$0.434652\pi$
$882$		0			0
$883$		−	8.73683i		−	0.294018i	−0.989135	−	0.147009i	$-0.953035\pi$
$883$		−	8.73683i		−	0.294018i	0.989135	−	0.147009i	$-0.0469646\pi$
$884$	−12.6035			−0.423901
$885$		0			0
$886$	9.66016			0.324540
$887$			19.8524i			0.666577i	0.942825	+	0.333288i	$0.108158\pi$
$887$			19.8524i			0.666577i	−0.942825	+	0.333288i	$0.891842\pi$
$888$		0			0
$889$	9.93978			0.333369
$890$	−4.22522	−	0.593635i	−0.141630	−	0.0198987i
$891$		0			0
$892$			41.5022i			1.38960i
$893$		−	2.30513i		−	0.0771383i
$894$		0			0
$895$	−1.51114	+	10.7556i	−0.0505118	+	0.359519i
$896$	−7.93533			−0.265101
$897$		0			0
$898$		−	11.6227i		−	0.387854i
$899$	−18.4889			−0.616638
$900$		0			0
$901$	1.86082			0.0619928
$902$		−	3.31756i		−	0.110463i
$903$		0			0
$904$	17.2859			0.574921
$905$	5.22570	−	37.1941i	0.173708	−	1.23637i
$906$		0			0
$907$			32.8287i			1.09006i	0.838417	+	0.545030i	$0.183482\pi$
$907$			32.8287i			1.09006i	−0.838417	+	0.545030i	$0.816518\pi$
$908$			6.08742i			0.202018i
$909$		0			0
$910$	1.80642	+	0.253799i	0.0598824	+	0.00841336i
$911$	16.3497			0.541689			0.270845	−	0.962623i	$-0.412697\pi$
$911$	16.3497			0.541689			0.270845	+	0.962623i	$0.412697\pi$
$912$		0			0
$913$			7.76049i			0.256835i
$914$	2.71853			0.0899209
$915$		0			0
$916$	−13.5585			−0.447984
$917$		−	1.12399i		−	0.0371173i
$918$		0			0
$919$	−20.0228			−0.660490			−0.330245	−	0.943895i	$-0.607131\pi$
$919$	−20.0228			−0.660490			−0.330245	+	0.943895i	$0.607131\pi$
$920$	−1.51114	+	10.7556i	−0.0498207	+	0.354601i
$921$		0			0
$922$		−	9.88940i		−	0.325690i
$923$		−	26.9590i		−	0.887366i
$924$		0			0
$925$	−8.00000	+	27.9081i	−0.263038	+	0.917614i
$926$	−3.76187			−0.123623
$927$		0			0
$928$			24.6450i			0.809011i
$929$	−43.5308			−1.42820			−0.714100	−	0.700044i	$-0.753164\pi$
$929$	−43.5308			−1.42820			−0.714100	+	0.700044i	$0.753164\pi$
$930$		0			0
$931$	−15.0192			−0.492235
$932$			37.1610i			1.21725i
$933$		0			0
$934$	4.77430			0.156220
$935$	5.05086	+	0.709636i	0.165181	+	0.0232076i
$936$		0			0
$937$		−	43.4563i		−	1.41966i	−0.704375	−	0.709828i	$-0.748773\pi$
$937$		−	43.4563i		−	1.41966i	0.704375	−	0.709828i	$-0.251227\pi$
$938$			3.61285i			0.117964i
$939$		0			0
$940$	−4.00000	−	0.561993i	−0.130466	−	0.0183302i
$941$	23.7244			0.773393			0.386697	−	0.922207i	$-0.373616\pi$
$941$	23.7244			0.773393			0.386697	+	0.922207i	$0.373616\pi$
$942$		0			0
$943$		−	42.6548i		−	1.38903i
$944$	−5.73636			−0.186703
$945$		0			0
$946$	3.33185			0.108328
$947$			11.7047i			0.380352i	0.981750	+	0.190176i	$0.0609059\pi$
$947$			11.7047i			0.380352i	−0.981750	+	0.190176i	$0.939094\pi$
$948$		0			0
$949$	16.4286			0.533296
$950$	−1.04101	+	3.63158i	−0.0337748	+	0.117824i
$951$		0			0
$952$		−	2.50177i		−	0.0810828i
$953$		−	46.1258i		−	1.49416i	−0.664733	−	0.747081i	$-0.731455\pi$
$953$		−	46.1258i		−	1.49416i	0.664733	−	0.747081i	$-0.268545\pi$
$954$		0			0
$955$	5.24443	−	37.3274i	0.169706	−	1.20789i
$956$	−41.8350			−1.35304
$957$		0			0
$958$			1.83500i			0.0592863i
$959$	4.00000			0.129167
$960$		0			0
$961$	−24.1240			−0.778193
$962$			5.24443i			0.169087i
$963$		0			0
$964$	10.1748			0.327710
$965$	54.5116	+	7.65878i	1.75479	+	0.246545i
$966$		0			0
$967$		−	17.0495i		−	0.548274i	−0.961691	−	0.274137i	$-0.911608\pi$
$967$		−	17.0495i		−	0.548274i	0.961691	−	0.274137i	$-0.0883922\pi$
$968$			1.21432i			0.0390297i
$969$		0			0
$970$	1.20696	−	8.59057i	0.0387531	−	0.275827i
$971$	58.1847			1.86724			0.933618	−	0.358271i	$-0.116634\pi$
$971$	58.1847			1.86724			0.933618	+	0.358271i	$0.116634\pi$
$972$		0			0
$973$		−	0.828699i		−	0.0265669i
$974$	9.75203			0.312475
$975$		0			0
$976$	−24.8385			−0.795062
$977$		−	51.7373i		−	1.65522i	−0.561301	−	0.827612i	$-0.689699\pi$
$977$		−	51.7373i		−	1.65522i	0.561301	−	0.827612i	$-0.310301\pi$
$978$		0			0
$979$	−6.13335			−0.196023
$980$	−3.66170	+	26.0622i	−0.116969	+	0.832527i
$981$		0			0
$982$			2.48886i			0.0794228i
$983$			26.3970i			0.841933i	0.907076	+	0.420967i	$0.138309\pi$
$983$			26.3970i			0.841933i	−0.907076	+	0.420967i	$0.861691\pi$
$984$		0			0
$985$	−32.9304	−	4.62666i	−1.04925	−	0.147418i
$986$	−5.00354			−0.159345
$987$		0			0
$988$		−	13.4193i		−	0.426924i
$989$	42.8385			1.36219
$990$		0			0
$991$	−23.0923			−0.733552			−0.366776	−	0.930309i	$-0.619539\pi$
$991$	−23.0923			−0.733552			−0.366776	+	0.930309i	$0.619539\pi$
$992$		−	9.16547i		−	0.291004i
$993$		0			0
$994$	2.60931			0.0827622
$995$	−3.49240	+	24.8573i	−0.110717	+	0.788029i
$996$		0			0
$997$		−	12.9131i		−	0.408961i	−0.978871	−	0.204480i	$-0.934450\pi$
$997$		−	12.9131i		−	0.408961i	0.978871	−	0.204480i	$-0.0655504\pi$
$998$		−	4.71102i		−	0.149125i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.c.e.199.4		6
3.2	odd	2		165.2.c.b.34.3	✓	6
5.2	odd	4		2475.2.a.ba.1.2		3
5.3	odd	4		2475.2.a.bc.1.2		3
5.4	even	2	inner	495.2.c.e.199.3		6
12.11	even	2		2640.2.d.h.529.2		6
15.2	even	4		825.2.a.l.1.2		3
15.8	even	4		825.2.a.j.1.2		3
15.14	odd	2		165.2.c.b.34.4	yes	6
33.32	even	2		1815.2.c.e.364.4		6
60.59	even	2		2640.2.d.h.529.5		6
165.32	odd	4		9075.2.a.cg.1.2		3
165.98	odd	4		9075.2.a.ch.1.2		3
165.164	even	2		1815.2.c.e.364.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.c.b.34.3	✓	6	3.2	odd	2
165.2.c.b.34.4	yes	6	15.14	odd	2
495.2.c.e.199.3		6	5.4	even	2	inner
495.2.c.e.199.4		6	1.1	even	1	trivial
825.2.a.j.1.2		3	15.8	even	4
825.2.a.l.1.2		3	15.2	even	4
1815.2.c.e.364.3		6	165.164	even	2
1815.2.c.e.364.4		6	33.32	even	2
2475.2.a.ba.1.2		3	5.2	odd	4
2475.2.a.bc.1.2		3	5.3	odd	4
2640.2.d.h.529.2		6	12.11	even	2
2640.2.d.h.529.5		6	60.59	even	2
9075.2.a.cg.1.2		3	165.32	odd	4
9075.2.a.ch.1.2		3	165.98	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.311108i q^{2} +1.90321 q^{4} +(-0.311108 + 2.21432i) q^{5} +0.903212i q^{7} +1.21432i q^{8} +(-0.688892 - 0.0967881i) q^{10} -1.00000 q^{11} +2.90321i q^{13} -0.280996 q^{14} +3.42864 q^{16} +2.28100i q^{17} -2.42864 q^{19} +(-0.592104 + 4.21432i) q^{20} -0.311108i q^{22} -4.00000i q^{23} +(-4.80642 - 1.37778i) q^{25} -0.903212 q^{26} +1.71900i q^{28} +7.05086 q^{29} -2.62222 q^{31} +3.49532i q^{32} -0.709636 q^{34} +(-2.00000 - 0.280996i) q^{35} -5.80642i q^{37} -0.755569i q^{38} +(-2.68889 - 0.377784i) q^{40} +10.6637 q^{41} +10.7096i q^{43} -1.90321 q^{44} +1.24443 q^{46} +0.949145i q^{47} +6.18421 q^{49} +(0.428639 - 1.49532i) q^{50} +5.52543i q^{52} -0.815792i q^{53} +(0.311108 - 2.21432i) q^{55} -1.09679 q^{56} +2.19358i q^{58} -1.67307 q^{59} -7.24443 q^{61} -0.815792i q^{62} +5.76986 q^{64} +(-6.42864 - 0.903212i) q^{65} -12.8573i q^{67} +4.34122i q^{68} +(0.0874201 - 0.622216i) q^{70} -9.28592 q^{71} -5.65878i q^{73} +1.80642 q^{74} -4.62222 q^{76} -0.903212i q^{77} +16.5303 q^{79} +(-1.06668 + 7.59210i) q^{80} +3.31756i q^{82} -7.76049i q^{83} +(-5.05086 - 0.709636i) q^{85} -3.33185 q^{86} -1.21432i q^{88} +6.13335 q^{89} -2.62222 q^{91} -7.61285i q^{92} -0.295286 q^{94} +(0.755569 - 5.37778i) q^{95} +12.4701i q^{97} +1.92396i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} - 2 q^{5} - 4 q^{10} - 6 q^{11} + 12 q^{14} - 6 q^{16} + 12 q^{19} + 10 q^{20} - 2 q^{25} + 8 q^{26} + 16 q^{29} - 16 q^{31} + 36 q^{34} - 12 q^{35} - 16 q^{40} - 16 q^{41} + 2 q^{44} + 8 q^{46}+ \cdots + 4 q^{95}+O(q^{100}) \) 6 * q - 2 * q^4 - 2 * q^5 - 4 * q^10 - 6 * q^11 + 12 * q^14 - 6 * q^16 + 12 * q^19 + 10 * q^20 - 2 * q^25 + 8 * q^26 + 16 * q^29 - 16 * q^31 + 36 * q^34 - 12 * q^35 - 16 * q^40 - 16 * q^41 + 2 * q^44 + 8 * q^46 + 10 * q^49 - 24 * q^50 + 2 * q^55 - 20 * q^56 + 16 * q^59 - 44 * q^61 + 22 * q^64 - 12 * q^65 - 40 * q^70 + 24 * q^71 - 16 * q^74 - 28 * q^76 + 20 * q^79 - 6 * q^80 - 4 * q^85 + 20 * q^86 + 36 * q^89 - 16 * q^91 + 24 * q^94 + 4 * q^95

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