LMFDB - Embedded newform 945.2.d.c.379.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(379,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, 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("945.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.d (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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.5
Root			$0.228425 + 1.39564i$ of defining polynomial
Character	$\chi$	$=$	945.379
Dual form			945.2.d.c.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.456850i q^{2} +1.79129 q^{4} +(-0.456850 + 2.18890i) q^{5} -1.00000i q^{7} +1.73205i q^{8} +O(q^{10})$	\(q+0.456850i q^{2} +1.79129 q^{4} +(-0.456850 + 2.18890i) q^{5} -1.00000i q^{7} +1.73205i q^{8} +(-1.00000 - 0.208712i) q^{10} +1.73205 q^{11} -0.208712i q^{13} +0.456850 q^{14} +2.79129 q^{16} +3.00725i q^{17} +2.20871 q^{19} +(-0.818350 + 3.92095i) q^{20} +0.791288i q^{22} +3.10260i q^{23} +(-4.58258 - 2.00000i) q^{25} +0.0953502 q^{26} -1.79129i q^{28} +5.65300 q^{29} +0.582576 q^{31} +4.73930i q^{32} -1.37386 q^{34} +(2.18890 + 0.456850i) q^{35} +8.16515i q^{37} +1.00905i q^{38} +(-3.79129 - 0.791288i) q^{40} -6.47135 q^{41} +1.00000i q^{43} +3.10260 q^{44} -1.41742 q^{46} -1.73205i q^{47} -1.00000 q^{49} +(0.913701 - 2.09355i) q^{50} -0.373864i q^{52} -1.37055i q^{53} +(-0.791288 + 3.79129i) q^{55} +1.73205 q^{56} +2.58258i q^{58} -13.0381 q^{59} +0.208712 q^{61} +0.266150i q^{62} +3.41742 q^{64} +(0.456850 + 0.0953502i) q^{65} -12.3739i q^{67} +5.38685i q^{68} +(-0.208712 + 1.00000i) q^{70} +14.4086 q^{71} -4.58258i q^{73} -3.73025 q^{74} +3.95644 q^{76} -1.73205i q^{77} +10.3739 q^{79} +(-1.27520 + 6.10985i) q^{80} -2.95644i q^{82} +6.83285i q^{83} +(-6.58258 - 1.37386i) q^{85} -0.456850 q^{86} +3.00000i q^{88} +8.66025 q^{89} -0.208712 q^{91} +5.55765i q^{92} +0.791288 q^{94} +(-1.00905 + 4.83465i) q^{95} +12.3739i q^{97} -0.456850i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4}+O(q^{10}) $ 8 * q - 4 * q^4	$ 8 q - 4 q^{4} - 8 q^{10} + 4 q^{16} + 36 q^{19} - 32 q^{31} + 44 q^{34} - 12 q^{40} - 48 q^{46} - 8 q^{49} + 12 q^{55} + 20 q^{61} + 64 q^{64} - 20 q^{70} - 60 q^{76} + 28 q^{79} - 16 q^{85} - 20 q^{91} - 12 q^{94}+O(q^{100}) $ 8 * q - 4 * q^4 - 8 * q^10 + 4 * q^16 + 36 * q^19 - 32 * q^31 + 44 * q^34 - 12 * q^40 - 48 * q^46 - 8 * q^49 + 12 * q^55 + 20 * q^61 + 64 * q^64 - 20 * q^70 - 60 * q^76 + 28 * q^79 - 16 * q^85 - 20 * q^91 - 12 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			0.456850i			0.323042i	0.986869	+	0.161521i	$0.0516399\pi$
$2$			0.456850i			0.323042i	−0.986869	+	0.161521i	$0.948360\pi$
$3$		0			0
$3$		0			0
$4$	1.79129			0.895644
$5$	−0.456850	+	2.18890i	−0.204310	+	0.978906i
$5$	−0.456850	+	2.18890i	−0.204310	+	0.978906i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			1.73205i			0.612372i
$9$		0			0
$10$	−1.00000	−	0.208712i	−0.316228	−	0.0660006i
$11$	1.73205			0.522233			0.261116	−	0.965307i	$-0.415909\pi$
$11$	1.73205			0.522233			0.261116	+	0.965307i	$0.415909\pi$
$12$		0			0
$13$		−	0.208712i		−	0.0578863i	−0.999581	−	0.0289432i	$-0.990786\pi$
$13$		−	0.208712i		−	0.0578863i	0.999581	−	0.0289432i	$-0.00921418\pi$
$14$	0.456850			0.122098
$15$		0			0
$16$	2.79129			0.697822
$17$			3.00725i			0.729366i	0.931132	+	0.364683i	$0.118823\pi$
$17$			3.00725i			0.729366i	−0.931132	+	0.364683i	$0.881177\pi$
$18$		0			0
$19$	2.20871			0.506713			0.253357	−	0.967373i	$-0.418465\pi$
$19$	2.20871			0.506713			0.253357	+	0.967373i	$0.418465\pi$
$20$	−0.818350	+	3.92095i	−0.182989	+	0.876751i
$21$		0			0
$22$			0.791288i			0.168703i
$23$			3.10260i			0.646937i	0.946239	+	0.323469i	$0.104849\pi$
$23$			3.10260i			0.646937i	−0.946239	+	0.323469i	$0.895151\pi$
$24$		0			0
$25$	−4.58258	−	2.00000i	−0.916515	−	0.400000i
$26$	0.0953502			0.0186997
$27$		0			0
$28$		−	1.79129i		−	0.338522i
$29$	5.65300			1.04974			0.524868	−	0.851184i	$-0.324115\pi$
$29$	5.65300			1.04974			0.524868	+	0.851184i	$0.324115\pi$
$30$		0			0
$31$	0.582576			0.104634			0.0523168	−	0.998631i	$-0.483339\pi$
$31$	0.582576			0.104634			0.0523168	+	0.998631i	$0.483339\pi$
$32$			4.73930i			0.837798i
$33$		0			0
$34$	−1.37386			−0.235616
$35$	2.18890	+	0.456850i	0.369992	+	0.0772218i
$36$		0			0
$37$			8.16515i			1.34234i	0.741302	+	0.671171i	$0.234209\pi$
$37$			8.16515i			1.34234i	−0.741302	+	0.671171i	$0.765791\pi$
$38$			1.00905i			0.163690i
$39$		0			0
$40$	−3.79129	−	0.791288i	−0.599455	−	0.125114i
$41$	−6.47135			−1.01066			−0.505328	−	0.862927i	$-0.668628\pi$
$41$	−6.47135			−1.01066			−0.505328	+	0.862927i	$0.668628\pi$
$42$		0			0
$43$			1.00000i			0.152499i	0.997089	+	0.0762493i	$0.0242945\pi$
$43$			1.00000i			0.152499i	−0.997089	+	0.0762493i	$0.975706\pi$
$44$	3.10260			0.467735
$45$		0			0
$46$	−1.41742			−0.208988
$47$		−	1.73205i		−	0.252646i	−0.991989	−	0.126323i	$-0.959682\pi$
$47$		−	1.73205i		−	0.252646i	0.991989	−	0.126323i	$-0.0403175\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	0.913701	−	2.09355i	0.129217	−	0.296073i
$51$		0			0
$52$		−	0.373864i		−	0.0518455i
$53$		−	1.37055i		−	0.188260i	−0.995560	−	0.0941298i	$-0.969993\pi$
$53$		−	1.37055i		−	0.188260i	0.995560	−	0.0941298i	$-0.0300069\pi$
$54$		0			0
$55$	−0.791288	+	3.79129i	−0.106697	+	0.511217i
$56$	1.73205			0.231455
$57$		0			0
$58$			2.58258i			0.339109i
$59$	−13.0381			−1.69741			−0.848705	−	0.528866i	$-0.822617\pi$
$59$	−13.0381			−1.69741			−0.848705	+	0.528866i	$0.822617\pi$
$60$		0			0
$61$	0.208712			0.0267229			0.0133614	−	0.999911i	$-0.495747\pi$
$61$	0.208712			0.0267229			0.0133614	+	0.999911i	$0.495747\pi$
$62$			0.266150i			0.0338011i
$63$		0			0
$64$	3.41742			0.427178
$65$	0.456850	+	0.0953502i	0.0566653	+	0.0118267i
$66$		0			0
$67$		−	12.3739i		−	1.51171i	−0.654740	−	0.755854i	$-0.727222\pi$
$67$		−	12.3739i		−	1.51171i	0.654740	−	0.755854i	$-0.272778\pi$
$68$			5.38685i			0.653252i
$69$		0			0
$70$	−0.208712	+	1.00000i	−0.0249459	+	0.119523i
$71$	14.4086			1.70999			0.854994	−	0.518639i	$-0.173561\pi$
$71$	14.4086			1.70999			0.854994	+	0.518639i	$0.173561\pi$
$72$		0			0
$73$		−	4.58258i		−	0.536350i	−0.963370	−	0.268175i	$-0.913579\pi$
$73$		−	4.58258i		−	0.536350i	0.963370	−	0.268175i	$-0.0864205\pi$
$74$	−3.73025			−0.433633
$75$		0			0
$76$	3.95644			0.453835
$77$		−	1.73205i		−	0.197386i
$78$		0			0
$79$	10.3739			1.16715			0.583575	−	0.812059i	$-0.301653\pi$
$79$	10.3739			1.16715			0.583575	+	0.812059i	$0.301653\pi$
$80$	−1.27520	+	6.10985i	−0.142572	+	0.683102i
$81$		0			0
$82$		−	2.95644i		−	0.326484i
$83$			6.83285i			0.750003i	0.927024	+	0.375002i	$0.122358\pi$
$83$			6.83285i			0.750003i	−0.927024	+	0.375002i	$0.877642\pi$
$84$		0			0
$85$	−6.58258	−	1.37386i	−0.713981	−	0.149016i
$86$	−0.456850			−0.0492634
$87$		0			0
$88$			3.00000i			0.319801i
$89$	8.66025			0.917985			0.458993	−	0.888440i	$-0.348210\pi$
$89$	8.66025			0.917985			0.458993	+	0.888440i	$0.348210\pi$
$90$		0			0
$91$	−0.208712			−0.0218790
$92$			5.55765i			0.579425i
$93$		0			0
$94$	0.791288			0.0816151
$95$	−1.00905	+	4.83465i	−0.103526	+	0.496025i
$96$		0			0
$97$			12.3739i			1.25638i	0.778062	+	0.628188i	$0.216203\pi$
$97$			12.3739i			1.25638i	−0.778062	+	0.628188i	$0.783797\pi$
$98$		−	0.456850i		−	0.0461488i
$99$		0			0
$100$	−8.20871	−	3.58258i	−0.820871	−	0.358258i
$101$	−15.8745			−1.57957			−0.789786	−	0.613382i	$-0.789809\pi$
$101$	−15.8745			−1.57957			−0.789786	+	0.613382i	$0.789809\pi$
$102$		0			0
$103$			3.37386i			0.332437i	0.986089	+	0.166218i	$0.0531556\pi$
$103$			3.37386i			0.332437i	−0.986089	+	0.166218i	$0.946844\pi$
$104$	0.361500			0.0354480
$105$		0			0
$106$	0.626136			0.0608157
$107$		−	7.02355i		−	0.678993i	−0.940607	−	0.339496i	$-0.889743\pi$
$107$		−	7.02355i		−	0.678993i	0.940607	−	0.339496i	$-0.110257\pi$
$108$		0			0
$109$	4.79129			0.458922			0.229461	−	0.973318i	$-0.426304\pi$
$109$	4.79129			0.458922			0.229461	+	0.973318i	$0.426304\pi$
$110$	−1.73205	−	0.361500i	−0.165145	−	0.0344677i
$111$		0			0
$112$		−	2.79129i		−	0.263752i
$113$		−	6.56670i		−	0.617743i	−0.951104	−	0.308872i	$-0.900049\pi$
$113$		−	6.56670i		−	0.617743i	0.951104	−	0.308872i	$-0.0999514\pi$
$114$		0			0
$115$	−6.79129	−	1.41742i	−0.633291	−	0.132175i
$116$	10.1262			0.940190
$117$		0			0
$118$		−	5.95644i		−	0.548335i
$119$	3.00725			0.275674
$120$		0			0
$121$	−8.00000			−0.727273
$122$			0.0953502i			0.00863260i
$123$		0			0
$124$	1.04356			0.0937145
$125$	6.47135	−	9.11710i	0.578815	−	0.815459i
$126$		0			0
$127$		−	1.62614i		−	0.144296i	−0.997394	−	0.0721481i	$-0.977015\pi$
$127$		−	1.62614i		−	0.144296i	0.997394	−	0.0721481i	$-0.0229854\pi$
$128$			11.0399i			0.975795i
$129$		0			0
$130$	−0.0435608	+	0.208712i	−0.00382053	+	0.0183053i
$131$	−6.66205			−0.582066			−0.291033	−	0.956713i	$-0.593999\pi$
$131$	−6.66205			−0.582066			−0.291033	+	0.956713i	$0.593999\pi$
$132$		0			0
$133$		−	2.20871i		−	0.191520i
$134$	5.65300			0.488345
$135$		0			0
$136$	−5.20871			−0.446643
$137$		−	15.8745i		−	1.35625i	−0.734946	−	0.678125i	$-0.762793\pi$
$137$		−	15.8745i		−	1.35625i	0.734946	−	0.678125i	$-0.237207\pi$
$138$		0			0
$139$	20.5826			1.74579			0.872896	−	0.487907i	$-0.162239\pi$
$139$	20.5826			1.74579			0.872896	+	0.487907i	$0.162239\pi$
$140$	3.92095	+	0.818350i	0.331381	+	0.0691632i
$141$		0			0
$142$			6.58258i			0.552397i
$143$		−	0.361500i		−	0.0302302i
$144$		0			0
$145$	−2.58258	+	12.3739i	−0.214471	+	1.02759i
$146$	2.09355			0.173264
$147$		0			0
$148$			14.6261i			1.20226i
$149$	−15.4177			−1.26306			−0.631532	−	0.775350i	$-0.717574\pi$
$149$	−15.4177			−1.26306			−0.631532	+	0.775350i	$0.717574\pi$
$150$		0			0
$151$	−3.83485			−0.312076			−0.156038	−	0.987751i	$-0.549872\pi$
$151$	−3.83485			−0.312076			−0.156038	+	0.987751i	$0.549872\pi$
$152$			3.82560i			0.310297i
$153$		0			0
$154$	0.791288			0.0637638
$155$	−0.266150	+	1.27520i	−0.0213777	+	0.102427i
$156$		0			0
$157$		−	16.7477i		−	1.33661i	−0.743886	−	0.668307i	$-0.767019\pi$
$157$		−	16.7477i		−	1.33661i	0.743886	−	0.668307i	$-0.232981\pi$
$158$			4.73930i			0.377039i
$159$		0			0
$160$	−10.3739	−	2.16515i	−0.820126	−	0.171170i
$161$	3.10260			0.244519
$162$		0			0
$163$		−	14.7477i		−	1.15513i	−0.816344	−	0.577566i	$-0.804003\pi$
$163$		−	14.7477i		−	1.15513i	0.816344	−	0.577566i	$-0.195997\pi$
$164$	−11.5921			−0.905187
$165$		0			0
$166$	−3.12159			−0.242282
$167$		−	11.4014i		−	0.882263i	−0.897442	−	0.441132i	$-0.854577\pi$
$167$		−	11.4014i		−	0.882263i	0.897442	−	0.441132i	$-0.145423\pi$
$168$		0			0
$169$	12.9564			0.996649
$170$	0.627650	−	3.00725i	0.0481386	−	0.230646i
$171$		0			0
$172$			1.79129i			0.136584i
$173$		−	21.0707i		−	1.60197i	−0.598683	−	0.800986i	$-0.704309\pi$
$173$		−	21.0707i		−	1.60197i	0.598683	−	0.800986i	$-0.295691\pi$
$174$		0			0
$175$	−2.00000	+	4.58258i	−0.151186	+	0.346410i
$176$	4.83465			0.364426
$177$		0			0
$178$			3.95644i			0.296548i
$179$	16.6929			1.24768			0.623841	−	0.781551i	$-0.285571\pi$
$179$	16.6929			1.24768			0.623841	+	0.781551i	$0.285571\pi$
$180$		0			0
$181$	−15.3303			−1.13949			−0.569746	−	0.821821i	$-0.692959\pi$
$181$	−15.3303			−1.13949			−0.569746	+	0.821821i	$0.692959\pi$
$182$		−	0.0953502i		−	0.00706783i
$183$		0			0
$184$	−5.37386			−0.396166
$185$	−17.8727	−	3.73025i	−1.31403	−	0.274254i
$186$		0			0
$187$			5.20871i			0.380899i
$188$		−	3.10260i		−	0.226280i
$189$		0			0
$190$	−2.20871	−	0.460985i	−0.160237	−	0.0334434i
$191$	−13.4949			−0.976457			−0.488229	−	0.872716i	$-0.662357\pi$
$191$	−13.4949			−0.976457			−0.488229	+	0.872716i	$0.662357\pi$
$192$		0			0
$193$			11.9564i			0.860643i	0.902676	+	0.430322i	$0.141600\pi$
$193$			11.9564i			0.860643i	−0.902676	+	0.430322i	$0.858400\pi$
$194$	−5.65300			−0.405862
$195$		0			0
$196$	−1.79129			−0.127949
$197$		−	26.1715i		−	1.86464i	−0.361635	−	0.932320i	$-0.617781\pi$
$197$		−	26.1715i		−	1.86464i	0.361635	−	0.932320i	$-0.382219\pi$
$198$		0			0
$199$	22.7913			1.61563			0.807816	−	0.589435i	$-0.200650\pi$
$199$	22.7913			1.61563			0.807816	+	0.589435i	$0.200650\pi$
$200$	3.46410	−	7.93725i	0.244949	−	0.561249i
$201$		0			0
$202$		−	7.25227i		−	0.510268i
$203$		−	5.65300i		−	0.396763i
$204$		0			0
$205$	2.95644	−	14.1652i	0.206487	−	0.989337i
$206$	−1.54135			−0.107391
$207$		0			0
$208$		−	0.582576i		−	0.0403944i
$209$	3.82560			0.264622
$210$		0			0
$211$	−19.1652			−1.31938			−0.659692	−	0.751536i	$-0.729313\pi$
$211$	−19.1652			−1.31938			−0.659692	+	0.751536i	$0.729313\pi$
$212$		−	2.45505i		−	0.168614i
$213$		0			0
$214$	3.20871			0.219343
$215$	−2.18890	−	0.456850i	−0.149282	−	0.0311569i
$216$		0			0
$217$		−	0.582576i		−	0.0395478i
$218$			2.18890i			0.148251i
$219$		0			0
$220$	−1.41742	+	6.79129i	−0.0955627	+	0.457869i
$221$	0.627650			0.0422203
$222$		0			0
$223$		−	9.00000i		−	0.602685i	−0.953516	−	0.301342i	$-0.902565\pi$
$223$		−	9.00000i		−	0.602685i	0.953516	−	0.301342i	$-0.0974347\pi$
$224$	4.73930			0.316658
$225$		0			0
$226$	3.00000			0.199557
$227$		−	6.47135i		−	0.429519i	−0.976667	−	0.214759i	$-0.931103\pi$
$227$		−	6.47135i		−	0.429519i	0.976667	−	0.214759i	$-0.0688967\pi$
$228$		0			0
$229$	19.0000			1.25556			0.627778	−	0.778393i	$-0.283965\pi$
$229$	19.0000			1.25556			0.627778	+	0.778393i	$0.283965\pi$
$230$	0.647551	−	3.10260i	0.0426982	−	0.204579i
$231$		0			0
$232$			9.79129i			0.642830i
$233$		−	20.6138i		−	1.35046i	−0.737609	−	0.675228i	$-0.764045\pi$
$233$		−	20.6138i		−	1.35046i	0.737609	−	0.675228i	$-0.235955\pi$
$234$		0			0
$235$	3.79129	+	0.791288i	0.247316	+	0.0516179i
$236$	−23.3549			−1.52028
$237$		0			0
$238$			1.37386i			0.0890543i
$239$	−1.73205			−0.112037			−0.0560185	−	0.998430i	$-0.517841\pi$
$239$	−1.73205			−0.112037			−0.0560185	+	0.998430i	$0.517841\pi$
$240$		0			0
$241$	−10.3739			−0.668239			−0.334120	−	0.942531i	$-0.608439\pi$
$241$	−10.3739			−0.668239			−0.334120	+	0.942531i	$0.608439\pi$
$242$		−	3.65480i		−	0.234940i
$243$		0			0
$244$	0.373864			0.0239342
$245$	0.456850	−	2.18890i	0.0291871	−	0.139844i
$246$		0			0
$247$		−	0.460985i		−	0.0293318i
$248$			1.00905i			0.0640748i
$249$		0			0
$250$	4.16515	+	2.95644i	0.263427	+	0.186982i
$251$	15.8745			1.00199			0.500995	−	0.865450i	$-0.332967\pi$
$251$	15.8745			1.00199			0.500995	+	0.865450i	$0.332967\pi$
$252$		0			0
$253$			5.37386i			0.337852i
$254$	0.742901			0.0466137
$255$		0			0
$256$	1.79129			0.111955
$257$		−	1.82740i		−	0.113990i	−0.998374	−	0.0569951i	$-0.981848\pi$
$257$		−	1.82740i		−	0.113990i	0.998374	−	0.0569951i	$-0.0181519\pi$
$258$		0			0
$259$	8.16515			0.507358
$260$	0.818350	+	0.170800i	0.0507519	+	0.0105925i
$261$		0			0
$262$		−	3.04356i		−	0.188032i
$263$		−	22.1552i		−	1.36615i	−0.730350	−	0.683073i	$-0.760643\pi$
$263$		−	22.1552i		−	1.36615i	0.730350	−	0.683073i	$-0.239357\pi$
$264$		0			0
$265$	3.00000	+	0.626136i	0.184289	+	0.0384633i
$266$	1.00905			0.0618689
$267$		0			0
$268$		−	22.1652i		−	1.35395i
$269$	−24.7255			−1.50754			−0.753769	−	0.657139i	$-0.771766\pi$
$269$	−24.7255			−1.50754			−0.753769	+	0.657139i	$0.771766\pi$
$270$		0			0
$271$	−7.20871			−0.437898			−0.218949	−	0.975736i	$-0.570263\pi$
$271$	−7.20871			−0.437898			−0.218949	+	0.975736i	$0.570263\pi$
$272$			8.39410i			0.508967i
$273$		0			0
$274$	7.25227			0.438126
$275$	−7.93725	−	3.46410i	−0.478634	−	0.208893i
$276$		0			0
$277$			1.20871i			0.0726245i	0.999340	+	0.0363122i	$0.0115611\pi$
$277$			1.20871i			0.0726245i	−0.999340	+	0.0363122i	$0.988439\pi$
$278$			9.40315i			0.563964i
$279$		0			0
$280$	−0.791288	+	3.79129i	−0.0472885	+	0.226573i
$281$	27.2560			1.62595			0.812977	−	0.582296i	$-0.197845\pi$
$281$	27.2560			1.62595			0.812977	+	0.582296i	$0.197845\pi$
$282$		0			0
$283$			24.3739i			1.44888i	0.689340	+	0.724438i	$0.257901\pi$
$283$			24.3739i			1.44888i	−0.689340	+	0.724438i	$0.742099\pi$
$284$	25.8100			1.53154
$285$		0			0
$286$	0.165151			0.00976561
$287$			6.47135i			0.381992i
$288$		0			0
$289$	7.95644			0.468026
$290$	−5.65300	−	1.17985i	−0.331956	−	0.0692832i
$291$		0			0
$292$		−	8.20871i		−	0.480379i
$293$		−	17.3205i		−	1.01187i	−0.862570	−	0.505937i	$-0.831147\pi$
$293$		−	17.3205i		−	1.01187i	0.862570	−	0.505937i	$-0.168853\pi$
$294$		0			0
$295$	5.95644	−	28.5390i	0.346797	−	1.66161i
$296$	−14.1425			−0.822014
$297$		0			0
$298$		−	7.04356i		−	0.408023i
$299$	0.647551			0.0374488
$300$		0			0
$301$	1.00000			0.0576390
$302$		−	1.75195i		−	0.100813i
$303$		0			0
$304$	6.16515			0.353596
$305$	−0.0953502	+	0.456850i	−0.00545974	+	0.0261592i
$306$		0			0
$307$			23.5826i			1.34593i	0.739675	+	0.672964i	$0.234979\pi$
$307$			23.5826i			1.34593i	−0.739675	+	0.672964i	$0.765021\pi$
$308$		−	3.10260i		−	0.176787i
$309$		0			0
$310$	−0.582576	−	0.121591i	−0.0330881	−	0.00690588i
$311$	−16.9590			−0.961657			−0.480829	−	0.876815i	$-0.659664\pi$
$311$	−16.9590			−0.961657			−0.480829	+	0.876815i	$0.659664\pi$
$312$		0			0
$313$		−	7.41742i		−	0.419258i	−0.977781	−	0.209629i	$-0.932774\pi$
$313$		−	7.41742i		−	0.419258i	0.977781	−	0.209629i	$-0.0672256\pi$
$314$	7.65120			0.431782
$315$		0			0
$316$	18.5826			1.04535
$317$			25.2578i			1.41862i	0.704898	+	0.709309i	$0.250993\pi$
$317$			25.2578i			1.41862i	−0.704898	+	0.709309i	$0.749007\pi$
$318$		0			0
$319$	9.79129			0.548207
$320$	−1.56125	+	7.48040i	−0.0872766	+	0.418167i
$321$		0			0
$322$			1.41742i			0.0789900i
$323$			6.64215i			0.369579i
$324$		0			0
$325$	−0.417424	+	0.956439i	−0.0231545	+	0.0530537i
$326$	6.73750			0.373156
$327$		0			0
$328$		−	11.2087i		−	0.618898i
$329$	−1.73205			−0.0954911
$330$		0			0
$331$	−23.3739			−1.28474			−0.642372	−	0.766393i	$-0.722050\pi$
$331$	−23.3739			−1.28474			−0.642372	+	0.766393i	$0.722050\pi$
$332$			12.2396i			0.671736i
$333$		0			0
$334$	5.20871			0.285008
$335$	27.0852	+	5.65300i	1.47982	+	0.308857i
$336$		0			0
$337$		−	17.7042i		−	0.964407i	−0.876059	−	0.482204i	$-0.839837\pi$
$337$		−	17.7042i		−	0.964407i	0.876059	−	0.482204i	$-0.160163\pi$
$338$			5.91915i			0.321959i
$339$		0			0
$340$	−11.7913	−	2.46099i	−0.639472	−	0.133466i
$341$	1.00905			0.0546432
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−1.73205			−0.0933859
$345$		0			0
$346$	9.62614			0.517504
$347$			22.0797i			1.18530i	0.805460	+	0.592650i	$0.201918\pi$
$347$			22.0797i			1.18530i	−0.805460	+	0.592650i	$0.798082\pi$
$348$		0			0
$349$	−5.74773			−0.307669			−0.153834	−	0.988097i	$-0.549162\pi$
$349$	−5.74773			−0.307669			−0.153834	+	0.988097i	$0.549162\pi$
$350$	−2.09355	−	0.913701i	−0.111905	−	0.0488393i
$351$		0			0
$352$			8.20871i			0.437526i
$353$		−	1.46590i		−	0.0780220i	−0.999239	−	0.0390110i	$-0.987579\pi$
$353$		−	1.46590i		−	0.0780220i	0.999239	−	0.0390110i	$-0.0124207\pi$
$354$		0			0
$355$	−6.58258	+	31.5390i	−0.349367	+	1.67392i
$356$	15.5130			0.822188
$357$		0			0
$358$			7.62614i			0.403054i
$359$	−25.4485			−1.34312			−0.671559	−	0.740951i	$-0.734375\pi$
$359$	−25.4485			−1.34312			−0.671559	+	0.740951i	$0.734375\pi$
$360$		0			0
$361$	−14.1216			−0.743242
$362$		−	7.00365i		−	0.368104i
$363$		0			0
$364$	−0.373864			−0.0195958
$365$	10.0308	+	2.09355i	0.525036	+	0.109581i
$366$		0			0
$367$		−	3.95644i		−	0.206524i	−0.994654	−	0.103262i	$-0.967072\pi$
$367$		−	3.95644i		−	0.206524i	0.994654	−	0.103262i	$-0.0329281\pi$
$368$			8.66025i			0.451447i
$369$		0			0
$370$	1.70417	−	8.16515i	0.0885954	−	0.424486i
$371$	−1.37055			−0.0711554
$372$		0			0
$373$		−	12.9564i		−	0.670859i	−0.942065	−	0.335429i	$-0.891119\pi$
$373$		−	12.9564i		−	0.670859i	0.942065	−	0.335429i	$-0.108881\pi$
$374$	−2.37960			−0.123046
$375$		0			0
$376$	3.00000			0.154713
$377$		−	1.17985i		−	0.0607654i
$378$		0			0
$379$	−3.58258			−0.184025			−0.0920123	−	0.995758i	$-0.529330\pi$
$379$	−3.58258			−0.184025			−0.0920123	+	0.995758i	$0.529330\pi$
$380$	−1.80750	+	8.66025i	−0.0927228	+	0.444262i
$381$		0			0
$382$		−	6.16515i		−	0.315437i
$383$			15.3978i			0.786789i	0.919370	+	0.393394i	$0.128699\pi$
$383$			15.3978i			0.786789i	−0.919370	+	0.393394i	$0.871301\pi$
$384$		0			0
$385$	3.79129	+	0.791288i	0.193222	+	0.0403278i
$386$	−5.46230			−0.278024
$387$		0			0
$388$			22.1652i			1.12527i
$389$	24.3640			1.23530			0.617651	−	0.786452i	$-0.288084\pi$
$389$	24.3640			1.23530			0.617651	+	0.786452i	$0.288084\pi$
$390$		0			0
$391$	−9.33030			−0.471854
$392$		−	1.73205i		−	0.0874818i
$393$		0			0
$394$	11.9564			0.602357
$395$	−4.73930	+	22.7074i	−0.238460	+	1.14253i
$396$		0			0
$397$			6.83485i			0.343031i	0.985181	+	0.171516i	$0.0548664\pi$
$397$			6.83485i			0.343031i	−0.985181	+	0.171516i	$0.945134\pi$
$398$			10.4122i			0.521917i
$399$		0			0
$400$	−12.7913	−	5.58258i	−0.639564	−	0.279129i
$401$	−19.7001			−0.983777			−0.491888	−	0.870658i	$-0.663693\pi$
$401$	−19.7001			−0.983777			−0.491888	+	0.870658i	$0.663693\pi$
$402$		0			0
$403$		−	0.121591i		−	0.00605686i
$404$	−28.4358			−1.41473
$405$		0			0
$406$	2.58258			0.128171
$407$			14.1425i			0.701016i
$408$		0			0
$409$	−17.1652			−0.848762			−0.424381	−	0.905484i	$-0.639508\pi$
$409$	−17.1652			−0.848762			−0.424381	+	0.905484i	$0.639508\pi$
$410$	6.47135	+	1.35065i	0.319597	+	0.0667038i
$411$		0			0
$412$			6.04356i			0.297745i
$413$			13.0381i			0.641561i
$414$		0			0
$415$	−14.9564	−	3.12159i	−0.734183	−	0.153233i
$416$	0.989150			0.0484971
$417$		0			0
$418$			1.74773i			0.0854841i
$419$	22.5167			1.10001			0.550005	−	0.835161i	$-0.314626\pi$
$419$	22.5167			1.10001			0.550005	+	0.835161i	$0.314626\pi$
$420$		0			0
$421$	−20.2087			−0.984912			−0.492456	−	0.870337i	$-0.663901\pi$
$421$	−20.2087			−0.984912			−0.492456	+	0.870337i	$0.663901\pi$
$422$		−	8.75560i		−	0.426216i
$423$		0			0
$424$	2.37386			0.115285
$425$	6.01450	−	13.7810i	0.291746	−	0.668475i
$426$		0			0
$427$		−	0.208712i		−	0.0101003i
$428$		−	12.5812i		−	0.608136i
$429$		0			0
$430$	0.208712	−	1.00000i	0.0100650	−	0.0482243i
$431$	−1.17985			−0.0568314			−0.0284157	−	0.999596i	$-0.509046\pi$
$431$	−1.17985			−0.0568314			−0.0284157	+	0.999596i	$0.509046\pi$
$432$		0			0
$433$		−	13.5390i		−	0.650644i	−0.945603	−	0.325322i	$-0.894527\pi$
$433$		−	13.5390i		−	0.650644i	0.945603	−	0.325322i	$-0.105473\pi$
$434$	0.266150			0.0127756
$435$		0			0
$436$	8.58258			0.411031
$437$			6.85275i			0.327812i
$438$		0			0
$439$	3.33030			0.158947			0.0794733	−	0.996837i	$-0.474676\pi$
$439$	3.33030			0.158947			0.0794733	+	0.996837i	$0.474676\pi$
$440$	−6.56670	−	1.37055i	−0.313055	−	0.0653384i
$441$		0			0
$442$			0.286742i			0.0136389i
$443$			40.6754i			1.93255i	0.257517	+	0.966274i	$0.417096\pi$
$443$			40.6754i			1.93255i	−0.257517	+	0.966274i	$0.582904\pi$
$444$		0			0
$445$	−3.95644	+	18.9564i	−0.187553	+	0.898621i
$446$	4.11165			0.194692
$447$		0			0
$448$		−	3.41742i		−	0.161458i
$449$	3.27340			0.154481			0.0772407	−	0.997012i	$-0.475389\pi$
$449$	3.27340			0.154481			0.0772407	+	0.997012i	$0.475389\pi$
$450$		0			0
$451$	−11.2087			−0.527798
$452$		−	11.7629i		−	0.553278i
$453$		0			0
$454$	2.95644			0.138753
$455$	0.0953502	−	0.456850i	0.00447009	−	0.0214175i
$456$		0			0
$457$			39.8693i			1.86501i	0.361160	+	0.932504i	$0.382381\pi$
$457$			39.8693i			1.86501i	−0.361160	+	0.932504i	$0.617619\pi$
$458$			8.68015i			0.405597i
$459$		0			0
$460$	−12.1652	−	2.53901i	−0.567203	−	0.118382i
$461$	22.4412			1.04519			0.522596	−	0.852581i	$-0.324964\pi$
$461$	22.4412			1.04519			0.522596	+	0.852581i	$0.324964\pi$
$462$		0			0
$463$			24.6261i			1.14447i	0.820088	+	0.572237i	$0.193924\pi$
$463$			24.6261i			1.14447i	−0.820088	+	0.572237i	$0.806076\pi$
$464$	15.7792			0.732529
$465$		0			0
$466$	9.41742			0.436254
$467$			32.4720i			1.50263i	0.659946	+	0.751313i	$0.270579\pi$
$467$			32.4720i			1.50263i	−0.659946	+	0.751313i	$0.729421\pi$
$468$		0			0
$469$	−12.3739			−0.571372
$470$	−0.361500	+	1.73205i	−0.0166748	+	0.0798935i
$471$		0			0
$472$		−	22.5826i		−	1.03945i
$473$			1.73205i			0.0796398i
$474$		0			0
$475$	−10.1216	−	4.41742i	−0.464410	−	0.202685i
$476$	5.38685			0.246906
$477$		0			0
$478$		−	0.791288i		−	0.0361927i
$479$	−24.8963			−1.13754			−0.568770	−	0.822497i	$-0.692580\pi$
$479$	−24.8963			−1.13754			−0.568770	+	0.822497i	$0.692580\pi$
$480$		0			0
$481$	1.70417			0.0777033
$482$		−	4.73930i		−	0.215869i
$483$		0			0
$484$	−14.3303			−0.651377
$485$	−27.0852	−	5.65300i	−1.22987	−	0.256690i
$486$		0			0
$487$		−	13.9129i		−	0.630453i	−0.949017	−	0.315226i	$-0.897920\pi$
$487$		−	13.9129i		−	0.630453i	0.949017	−	0.315226i	$-0.102080\pi$
$488$			0.361500i			0.0163643i
$489$		0			0
$490$	1.00000	+	0.208712i	0.0451754	+	0.00942865i
$491$	20.8999			0.943198			0.471599	−	0.881813i	$-0.343677\pi$
$491$	20.8999			0.943198			0.471599	+	0.881813i	$0.343677\pi$
$492$		0			0
$493$			17.0000i			0.765641i
$494$	0.210601			0.00947539
$495$		0			0
$496$	1.62614			0.0730157
$497$		−	14.4086i		−	0.646314i
$498$		0			0
$499$	1.83485			0.0821391			0.0410696	−	0.999156i	$-0.486923\pi$
$499$	1.83485			0.0821391			0.0410696	+	0.999156i	$0.486923\pi$
$500$	11.5921	−	16.3314i	0.518413	−	0.730361i
$501$		0			0
$502$			7.25227i			0.323685i
$503$		−	9.30780i		−	0.415014i	−0.978233	−	0.207507i	$-0.933465\pi$
$503$		−	9.30780i		−	0.415014i	0.978233	−	0.207507i	$-0.0665351\pi$
$504$		0			0
$505$	7.25227	−	34.7477i	0.322722	−	1.54625i
$506$	−2.45505			−0.109140
$507$		0			0
$508$		−	2.91288i		−	0.129238i
$509$	6.49125			0.287720			0.143860	−	0.989598i	$-0.454049\pi$
$509$	6.49125			0.287720			0.143860	+	0.989598i	$0.454049\pi$
$510$		0			0
$511$	−4.58258			−0.202721
$512$			22.8981i			1.01196i
$513$		0			0
$514$	0.834849			0.0368236
$515$	−7.38505	−	1.54135i	−0.325424	−	0.0679200i
$516$		0			0
$517$		−	3.00000i		−	0.131940i
$518$			3.73025i			0.163898i
$519$		0			0
$520$	−0.165151	+	0.791288i	−0.00724237	+	0.0347003i
$521$	−19.9663			−0.874738			−0.437369	−	0.899282i	$-0.644090\pi$
$521$	−19.9663			−0.874738			−0.437369	+	0.899282i	$0.644090\pi$
$522$		0			0
$523$		−	32.9564i		−	1.44108i	−0.693411	−	0.720542i	$-0.743893\pi$
$523$		−	32.9564i		−	1.44108i	0.693411	−	0.720542i	$-0.256107\pi$
$524$	−11.9337			−0.521324
$525$		0			0
$526$	10.1216			0.441322
$527$			1.75195i			0.0763162i
$528$		0			0
$529$	13.3739			0.581472
$530$	−0.286051	+	1.37055i	−0.0124252	+	0.0595329i
$531$		0			0
$532$		−	3.95644i		−	0.171533i
$533$			1.35065i			0.0585031i
$534$		0			0
$535$	15.3739	+	3.20871i	0.664670	+	0.138725i
$536$	21.4322			0.925728
$537$		0			0
$538$		−	11.2958i		−	0.486998i
$539$	−1.73205			−0.0746047
$540$		0			0
$541$	14.7042			0.632181			0.316091	−	0.948729i	$-0.397630\pi$
$541$	14.7042			0.632181			0.316091	+	0.948729i	$0.397630\pi$
$542$		−	3.29330i		−	0.141459i
$543$		0			0
$544$	−14.2523			−0.611061
$545$	−2.18890	+	10.4877i	−0.0937622	+	0.449242i
$546$		0			0
$547$			0.582576i			0.0249091i	0.999922	+	0.0124546i	$0.00396451\pi$
$547$			0.582576i			0.0249091i	−0.999922	+	0.0124546i	$0.996035\pi$
$548$		−	28.4358i		−	1.21472i
$549$		0			0
$550$	1.58258	−	3.62614i	0.0674813	−	0.154619i
$551$	12.4859			0.531915
$552$		0			0
$553$		−	10.3739i		−	0.441142i
$554$	−0.552200			−0.0234607
$555$		0			0
$556$	36.8693			1.56361
$557$			10.4122i			0.441179i	0.975367	+	0.220590i	$0.0707982\pi$
$557$			10.4122i			0.441179i	−0.975367	+	0.220590i	$0.929202\pi$
$558$		0			0
$559$	0.208712			0.00882758
$560$	6.10985	+	1.27520i	0.258188	+	0.0538871i
$561$		0			0
$562$			12.4519i			0.525251i
$563$			28.3604i			1.19525i	0.801777	+	0.597623i	$0.203888\pi$
$563$			28.3604i			1.19525i	−0.801777	+	0.597623i	$0.796112\pi$
$564$		0			0
$565$	14.3739	+	3.00000i	0.604713	+	0.126211i
$566$	−11.1352			−0.468048
$567$		0			0
$568$			24.9564i			1.04715i
$569$	21.0707			0.883328			0.441664	−	0.897181i	$-0.354388\pi$
$569$	21.0707			0.883328			0.441664	+	0.897181i	$0.354388\pi$
$570$		0			0
$571$	−6.79129			−0.284207			−0.142103	−	0.989852i	$-0.545387\pi$
$571$	−6.79129			−0.284207			−0.142103	+	0.989852i	$0.545387\pi$
$572$		−	0.647551i		−	0.0270755i
$573$		0			0
$574$	−2.95644			−0.123399
$575$	6.20520	−	14.2179i	0.258775	−	0.592928i
$576$		0			0
$577$		−	19.3303i		−	0.804731i	−0.915479	−	0.402366i	$-0.868188\pi$
$577$		−	19.3303i		−	0.804731i	0.915479	−	0.402366i	$-0.131812\pi$
$578$			3.63490i			0.151192i
$579$		0			0
$580$	−4.62614	+	22.1652i	−0.192090	+	0.920358i
$581$	6.83285			0.283475
$582$		0			0
$583$		−	2.37386i		−	0.0983154i
$584$	7.93725			0.328446
$585$		0			0
$586$	7.91288			0.326878
$587$			36.2976i			1.49816i	0.662478	+	0.749082i	$0.269505\pi$
$587$			36.2976i			1.49816i	−0.662478	+	0.749082i	$0.730495\pi$
$588$		0			0
$589$	1.28674			0.0530193
$590$	13.0381	+	2.72120i	0.536768	+	0.112030i
$591$		0			0
$592$			22.7913i			0.936716i
$593$			9.57395i			0.393155i	0.980488	+	0.196578i	$0.0629828\pi$
$593$			9.57395i			0.393155i	−0.980488	+	0.196578i	$0.937017\pi$
$594$		0			0
$595$	−1.37386	+	6.58258i	−0.0563229	+	0.269859i
$596$	−27.6175			−1.13126
$597$		0			0
$598$			0.295834i			0.0120975i
$599$	13.5148			0.552200			0.276100	−	0.961129i	$-0.410958\pi$
$599$	13.5148			0.552200			0.276100	+	0.961129i	$0.410958\pi$
$600$		0			0
$601$	47.6170			1.94234			0.971170	−	0.238388i	$-0.0766191\pi$
$601$	47.6170			1.94234			0.971170	+	0.238388i	$0.0766191\pi$
$602$			0.456850i			0.0186198i
$603$		0			0
$604$	−6.86932			−0.279509
$605$	3.65480	−	17.5112i	0.148589	−	0.711932i
$606$		0			0
$607$		−	48.1652i		−	1.95496i	−0.211021	−	0.977482i	$-0.567679\pi$
$607$		−	48.1652i		−	1.95496i	0.211021	−	0.977482i	$-0.432321\pi$
$608$			10.4678i			0.424523i
$609$		0			0
$610$	−0.208712	−	0.0435608i	−0.00845051	−	0.00176372i
$611$	−0.361500			−0.0146247
$612$		0			0
$613$			23.3303i			0.942302i	0.882053	+	0.471151i	$0.156161\pi$
$613$			23.3303i			0.942302i	−0.882053	+	0.471151i	$0.843839\pi$
$614$	−10.7737			−0.434791
$615$		0			0
$616$	3.00000			0.120873
$617$			13.3996i			0.539446i	0.962938	+	0.269723i	$0.0869321\pi$
$617$			13.3996i			0.539446i	−0.962938	+	0.269723i	$0.913068\pi$
$618$		0			0
$619$	−10.4955			−0.421848			−0.210924	−	0.977502i	$-0.567647\pi$
$619$	−10.4955			−0.421848			−0.210924	+	0.977502i	$0.567647\pi$
$620$	−0.476751	+	2.28425i	−0.0191468	+	0.0917377i
$621$		0			0
$622$		−	7.74773i		−	0.310656i
$623$		−	8.66025i		−	0.346966i
$624$		0			0
$625$	17.0000	+	18.3303i	0.680000	+	0.733212i
$626$	3.38865			0.135438
$627$		0			0
$628$		−	30.0000i		−	1.19713i
$629$	−24.5547			−0.979059
$630$		0			0
$631$	27.0780			1.07796			0.538980	−	0.842319i	$-0.318810\pi$
$631$	27.0780			1.07796			0.538980	+	0.842319i	$0.318810\pi$
$632$			17.9681i			0.714731i
$633$		0			0
$634$	−11.5390			−0.458273
$635$	3.55945	+	0.742901i	0.141253	+	0.0294811i
$636$		0			0
$637$			0.208712i			0.00826948i
$638$			4.47315i			0.177094i
$639$		0			0
$640$	−24.1652	−	5.04356i	−0.955211	−	0.199364i
$641$	−24.2686			−0.958553			−0.479276	−	0.877664i	$-0.659101\pi$
$641$	−24.2686			−0.958553			−0.479276	+	0.877664i	$0.659101\pi$
$642$		0			0
$643$		−	0.208712i		−	0.00823080i	−0.999992	−	0.00411540i	$-0.998690\pi$
$643$		−	0.208712i		−	0.00823080i	0.999992	−	0.00411540i	$-0.00130998\pi$
$644$	5.55765			0.219002
$645$		0			0
$646$	−3.03447			−0.119390
$647$			30.6446i			1.20476i	0.798208	+	0.602382i	$0.205782\pi$
$647$			30.6446i			1.20476i	−0.798208	+	0.602382i	$0.794218\pi$
$648$		0			0
$649$	−22.5826			−0.886444
$650$	−0.436950	−	0.190700i	−0.0171386	−	0.00747989i
$651$		0			0
$652$		−	26.4174i		−	1.03459i
$653$		−	21.5275i		−	0.842437i	−0.906959	−	0.421218i	$-0.861603\pi$
$653$		−	21.5275i		−	0.842437i	0.906959	−	0.421218i	$-0.138397\pi$
$654$		0			0
$655$	3.04356	−	14.5826i	0.118922	−	0.569788i
$656$	−18.0634			−0.705258
$657$		0			0
$658$		−	0.791288i		−	0.0308476i
$659$	19.3386			0.753325			0.376663	−	0.926351i	$-0.377072\pi$
$659$	19.3386			0.753325			0.376663	+	0.926351i	$0.377072\pi$
$660$		0			0
$661$	−14.5390			−0.565502			−0.282751	−	0.959193i	$-0.591247\pi$
$661$	−14.5390			−0.565502			−0.282751	+	0.959193i	$0.591247\pi$
$662$		−	10.6784i		−	0.415026i
$663$		0			0
$664$	−11.8348			−0.459281
$665$	4.83465	+	1.00905i	0.187480	+	0.0391293i
$666$		0			0
$667$			17.5390i			0.679113i
$668$		−	20.4231i		−	0.790194i
$669$		0			0
$670$	−2.58258	+	12.3739i	−0.0997736	+	0.478044i
$671$	0.361500			0.0139556
$672$		0			0
$673$			37.9129i			1.46143i	0.682680	+	0.730717i	$0.260814\pi$
$673$			37.9129i			1.46143i	−0.682680	+	0.730717i	$0.739186\pi$
$674$	8.08815			0.311544
$675$		0			0
$676$	23.2087			0.892643
$677$		−	25.4485i		−	0.978064i	−0.872266	−	0.489032i	$-0.837350\pi$
$677$		−	25.4485i		−	0.978064i	0.872266	−	0.489032i	$-0.162650\pi$
$678$		0			0
$679$	12.3739			0.474865
$680$	2.37960	−	11.4014i	0.0912536	−	0.437222i
$681$		0			0
$682$			0.460985i			0.0176520i
$683$			39.5710i			1.51414i	0.653332	+	0.757071i	$0.273371\pi$
$683$			39.5710i			1.51414i	−0.653332	+	0.757071i	$0.726629\pi$
$684$		0			0
$685$	34.7477	+	7.25227i	1.32764	+	0.277095i
$686$	−0.456850			−0.0174426
$687$		0			0
$688$			2.79129i			0.106417i
$689$	−0.286051			−0.0108977
$690$		0			0
$691$	−29.3303			−1.11578			−0.557889	−	0.829916i	$-0.688388\pi$
$691$	−29.3303			−1.11578			−0.557889	+	0.829916i	$0.688388\pi$
$692$		−	37.7436i		−	1.43480i
$693$		0			0
$694$	−10.0871			−0.382902
$695$	−9.40315	+	45.0532i	−0.356682	+	1.70897i
$696$		0			0
$697$		−	19.4610i		−	0.737137i
$698$		−	2.62585i		−	0.0993899i
$699$		0			0
$700$	−3.58258	+	8.20871i	−0.135409	+	0.310260i
$701$	−12.3151			−0.465133			−0.232567	−	0.972580i	$-0.574712\pi$
$701$	−12.3151			−0.465133			−0.232567	+	0.972580i	$0.574712\pi$
$702$		0			0
$703$			18.0345i			0.680183i
$704$	5.91915			0.223086
$705$		0			0
$706$	0.669697			0.0252044
$707$			15.8745i			0.597022i
$708$		0			0
$709$	−29.4955			−1.10773			−0.553863	−	0.832608i	$-0.686847\pi$
$709$	−29.4955			−1.10773			−0.553863	+	0.832608i	$0.686847\pi$
$710$	−14.4086	−	3.00725i	−0.540745	−	0.112860i
$711$		0			0
$712$			15.0000i			0.562149i
$713$			1.80750i			0.0676914i
$714$		0			0
$715$	0.791288	+	0.165151i	0.0295925	+	0.00617631i
$716$	29.9017			1.11748
$717$		0			0
$718$		−	11.6261i		−	0.433884i
$719$	33.1196			1.23515			0.617576	−	0.786511i	$-0.288115\pi$
$719$	33.1196			1.23515			0.617576	+	0.786511i	$0.288115\pi$
$720$		0			0
$721$	3.37386			0.125649
$722$		−	6.45145i		−	0.240098i
$723$		0			0
$724$	−27.4610			−1.02058
$725$	−25.9053	−	11.3060i	−0.962099	−	0.419894i
$726$		0			0
$727$			42.4519i			1.57445i	0.616664	+	0.787227i	$0.288484\pi$
$727$			42.4519i			1.57445i	−0.616664	+	0.787227i	$0.711516\pi$
$728$		−	0.361500i		−	0.0133981i
$729$		0			0
$730$	−0.956439	+	4.58258i	−0.0353994	+	0.169609i
$731$	−3.00725			−0.111227
$732$		0			0
$733$		−	40.7913i		−	1.50666i	−0.657642	−	0.753330i	$-0.728446\pi$
$733$		−	40.7913i		−	1.50666i	0.657642	−	0.753330i	$-0.271554\pi$
$734$	1.80750			0.0667161
$735$		0			0
$736$	−14.7042			−0.542003
$737$		−	21.4322i		−	0.789464i
$738$		0			0
$739$	−31.4955			−1.15858			−0.579290	−	0.815122i	$-0.696670\pi$
$739$	−31.4955			−1.15858			−0.579290	+	0.815122i	$0.696670\pi$
$740$	−32.0152	−	6.68195i	−1.17690	−	0.245634i
$741$		0			0
$742$		−	0.626136i		−	0.0229862i
$743$		−	0.989150i		−	0.0362884i	−0.999835	−	0.0181442i	$-0.994224\pi$
$743$		−	0.989150i		−	0.0362884i	0.999835	−	0.0181442i	$-0.00577579\pi$
$744$		0			0
$745$	7.04356	−	33.7477i	0.258056	−	1.23642i
$746$	5.91915			0.216716
$747$		0			0
$748$			9.33030i			0.341150i
$749$	−7.02355			−0.256635
$750$		0			0
$751$	36.6606			1.33776			0.668882	−	0.743368i	$-0.266773\pi$
$751$	36.6606			1.33776			0.668882	+	0.743368i	$0.266773\pi$
$752$		−	4.83465i		−	0.176302i
$753$		0			0
$754$	0.539015			0.0196298
$755$	1.75195	−	8.39410i	0.0637600	−	0.305493i
$756$		0			0
$757$		−	1.62614i		−	0.0591029i	−0.999563	−	0.0295515i	$-0.990592\pi$
$757$		−	1.62614i		−	0.0591029i	0.999563	−	0.0295515i	$-0.00940789\pi$
$758$		−	1.63670i		−	0.0594476i
$759$		0			0
$760$	−8.37386	−	1.74773i	−0.303752	−	0.0633967i
$761$	30.6247			1.11015			0.555073	−	0.831802i	$-0.312691\pi$
$761$	30.6247			1.11015			0.555073	+	0.831802i	$0.312691\pi$
$762$		0			0
$763$		−	4.79129i		−	0.173456i
$764$	−24.1733			−0.874558
$765$		0			0
$766$	−7.03447			−0.254166
$767$			2.72120i			0.0982569i
$768$		0			0
$769$	−19.7477			−0.712121			−0.356061	−	0.934463i	$-0.615880\pi$
$769$	−19.7477			−0.712121			−0.356061	+	0.934463i	$0.615880\pi$
$770$	−0.361500	+	1.73205i	−0.0130276	+	0.0624188i
$771$		0			0
$772$			21.4174i			0.770830i
$773$			5.84370i			0.210183i	0.994463	+	0.105092i	$0.0335136\pi$
$773$			5.84370i			0.210183i	−0.994463	+	0.105092i	$0.966486\pi$
$774$		0			0
$775$	−2.66970	−	1.16515i	−0.0958984	−	0.0418535i
$776$	−21.4322			−0.769370
$777$		0			0
$778$			11.1307i			0.399054i
$779$	−14.2934			−0.512113
$780$		0			0
$781$	24.9564			0.893012
$782$		−	4.26255i		−	0.152429i
$783$		0			0
$784$	−2.79129			−0.0996889
$785$	36.6591	+	7.65120i	1.30842	+	0.273083i
$786$		0			0
$787$		−	7.16515i		−	0.255410i	−0.991812	−	0.127705i	$-0.959239\pi$
$787$		−	7.16515i		−	0.255410i	0.991812	−	0.127705i	$-0.0407611\pi$
$788$		−	46.8806i		−	1.67005i
$789$		0			0
$790$	−10.3739	−	2.16515i	−0.369086	−	0.0770326i
$791$	−6.56670			−0.233485
$792$		0			0
$793$		−	0.0435608i		−	0.00154689i
$794$	−3.12250			−0.110813
$795$		0			0
$796$	40.8258			1.44703
$797$			5.36695i			0.190107i	0.995472	+	0.0950536i	$0.0303022\pi$
$797$			5.36695i			0.190107i	−0.995472	+	0.0950536i	$0.969698\pi$
$798$		0			0
$799$	5.20871			0.184271
$800$	9.47860	−	21.7182i	0.335119	−	0.767855i
$801$		0			0
$802$		−	9.00000i		−	0.317801i
$803$		−	7.93725i		−	0.280100i
$804$		0			0
$805$	−1.41742	+	6.79129i	−0.0499576	+	0.239361i
$806$	0.0555487			0.00195662
$807$		0			0
$808$		−	27.4955i		−	0.967287i
$809$	−31.4630			−1.10618			−0.553089	−	0.833122i	$-0.686551\pi$
$809$	−31.4630			−1.10618			−0.553089	+	0.833122i	$0.686551\pi$
$810$		0			0
$811$	−34.8693			−1.22443			−0.612214	−	0.790692i	$-0.709721\pi$
$811$	−34.8693			−1.22443			−0.612214	+	0.790692i	$0.709721\pi$
$812$		−	10.1262i		−	0.355358i
$813$		0			0
$814$	−6.46099			−0.226457
$815$	32.2813	+	6.73750i	1.13077	+	0.236004i
$816$		0			0
$817$			2.20871i			0.0772731i
$818$		−	7.84190i		−	0.274186i
$819$		0			0
$820$	5.29583	−	25.3739i	0.184939	−	0.886094i
$821$	37.8589			1.32128			0.660642	−	0.750701i	$-0.270284\pi$
$821$	37.8589			1.32128			0.660642	+	0.750701i	$0.270284\pi$
$822$		0			0
$823$			19.0000i			0.662298i	0.943578	+	0.331149i	$0.107436\pi$
$823$			19.0000i			0.662298i	−0.943578	+	0.331149i	$0.892564\pi$
$824$	−5.84370			−0.203575
$825$		0			0
$826$	−5.95644			−0.207251
$827$		−	14.1425i		−	0.491781i	−0.969298	−	0.245891i	$-0.920920\pi$
$827$		−	14.1425i		−	0.491781i	0.969298	−	0.245891i	$-0.0790804\pi$
$828$		0			0
$829$	40.9129			1.42096			0.710482	−	0.703716i	$-0.248477\pi$
$829$	40.9129			1.42096			0.710482	+	0.703716i	$0.248477\pi$
$830$	1.42610	−	6.83285i	0.0495006	−	0.237172i
$831$		0			0
$832$		−	0.713258i		−	0.0247278i
$833$		−	3.00725i		−	0.104195i
$834$		0			0
$835$	24.9564	+	5.20871i	0.863653	+	0.180255i
$836$	6.85275			0.237007
$837$		0			0
$838$			10.2867i			0.355350i
$839$	−11.7629			−0.406099			−0.203049	−	0.979168i	$-0.565085\pi$
$839$	−11.7629			−0.406099			−0.203049	+	0.979168i	$0.565085\pi$
$840$		0			0
$841$	2.95644			0.101946
$842$		−	9.23236i		−	0.318168i
$843$		0			0
$844$	−34.3303			−1.18170
$845$	−5.91915	+	28.3604i	−0.203625	+	0.975626i
$846$		0			0
$847$			8.00000i			0.274883i
$848$		−	3.82560i		−	0.131372i
$849$		0			0
$850$	6.29583	+	2.74773i	0.215945	+	0.0942463i
$851$	−25.3332			−0.868411
$852$		0			0
$853$		−	45.6606i		−	1.56339i	−0.623661	−	0.781695i	$-0.714356\pi$
$853$		−	45.6606i		−	1.56339i	0.623661	−	0.781695i	$-0.285644\pi$
$854$	0.0953502			0.00326282
$855$		0			0
$856$	12.1652			0.415796
$857$		−	58.4528i		−	1.99671i	−0.0573449	−	0.998354i	$-0.518263\pi$
$857$		−	58.4528i		−	1.99671i	0.0573449	−	0.998354i	$-0.481737\pi$
$858$		0			0
$859$	−11.5826			−0.395192			−0.197596	−	0.980284i	$-0.563313\pi$
$859$	−11.5826			−0.395192			−0.197596	+	0.980284i	$0.563313\pi$
$860$	−3.92095	−	0.818350i	−0.133703	−	0.0279055i
$861$		0			0
$862$		−	0.539015i		−	0.0183589i
$863$		−	34.6410i		−	1.17919i	−0.807698	−	0.589597i	$-0.799287\pi$
$863$		−	34.6410i		−	1.17919i	0.807698	−	0.589597i	$-0.200713\pi$
$864$		0			0
$865$	46.1216	+	9.62614i	1.56818	+	0.327298i
$866$	6.18530			0.210185
$867$		0			0
$868$		−	1.04356i		−	0.0354208i
$869$	17.9681			0.609525
$870$		0			0
$871$	−2.58258			−0.0875072
$872$			8.29875i			0.281031i
$873$		0			0
$874$	−3.13068			−0.105897
$875$	−9.11710	−	6.47135i	−0.308214	−	0.218772i
$876$		0			0
$877$		−	16.4955i		−	0.557012i	−0.960435	−	0.278506i	$-0.910161\pi$
$877$		−	16.4955i		−	0.557012i	0.960435	−	0.278506i	$-0.0898392\pi$
$878$			1.52145i			0.0513464i
$879$		0			0
$880$	−2.20871	+	10.5826i	−0.0744557	+	0.356739i
$881$	−25.8854			−0.872102			−0.436051	−	0.899922i	$-0.643623\pi$
$881$	−25.8854			−0.872102			−0.436051	+	0.899922i	$0.643623\pi$
$882$		0			0
$883$			45.6606i			1.53660i	0.640089	+	0.768301i	$0.278898\pi$
$883$			45.6606i			1.53660i	−0.640089	+	0.768301i	$0.721102\pi$
$884$	1.12430			0.0378144
$885$		0			0
$886$	−18.5826			−0.624294
$887$		−	31.9397i		−	1.07243i	−0.844081	−	0.536215i	$-0.819853\pi$
$887$		−	31.9397i		−	1.07243i	0.844081	−	0.536215i	$-0.180147\pi$
$888$		0			0
$889$	−1.62614			−0.0545389
$890$	−8.66025	−	1.80750i	−0.290292	−	0.0605875i
$891$		0			0
$892$		−	16.1216i		−	0.539791i
$893$		−	3.82560i		−	0.128019i
$894$		0			0
$895$	−7.62614	+	36.5390i	−0.254914	+	1.22136i
$896$	11.0399			0.368816
$897$		0			0
$898$			1.49545i			0.0499040i
$899$	3.29330			0.109838
$900$		0			0
$901$	4.12159			0.137310
$902$		−	5.12070i		−	0.170501i
$903$		0			0
$904$	11.3739			0.378289
$905$	7.00365	−	33.5565i	0.232809	−	1.11546i
$906$		0			0
$907$		−	13.3739i		−	0.444072i	−0.975038	−	0.222036i	$-0.928730\pi$
$907$		−	13.3739i		−	0.444072i	0.975038	−	0.222036i	$-0.0712702\pi$
$908$		−	11.5921i		−	0.384696i
$909$		0			0
$910$	0.208712	+	0.0435608i	0.00691874	+	0.00144403i
$911$	−22.2306			−0.736533			−0.368266	−	0.929720i	$-0.620049\pi$
$911$	−22.2306			−0.736533			−0.368266	+	0.929720i	$0.620049\pi$
$912$		0			0
$913$			11.8348i			0.391676i
$914$	−18.2143			−0.602476
$915$		0			0
$916$	34.0345			1.12453
$917$			6.66205i			0.220000i
$918$		0			0
$919$	8.79129			0.289998			0.144999	−	0.989432i	$-0.453682\pi$
$919$	8.79129			0.289998			0.144999	+	0.989432i	$0.453682\pi$
$920$	2.45505	−	11.7629i	0.0809406	−	0.387810i
$921$		0			0
$922$			10.2523i			0.337641i
$923$		−	3.00725i		−	0.0989849i
$924$		0			0
$925$	16.3303	−	37.4174i	0.536937	−	1.23028i
$926$	−11.2505			−0.369713
$927$		0			0
$928$			26.7913i			0.879467i
$929$	40.5801			1.33139			0.665694	−	0.746224i	$-0.268135\pi$
$929$	40.5801			1.33139			0.665694	+	0.746224i	$0.268135\pi$
$930$		0			0
$931$	−2.20871			−0.0723876
$932$		−	36.9253i		−	1.20953i
$933$		0			0
$934$	−14.8348			−0.485411
$935$	−11.4014	−	2.37960i	−0.372864	−	0.0778213i
$936$		0			0
$937$			8.33030i			0.272139i	0.990699	+	0.136070i	$0.0434471\pi$
$937$			8.33030i			0.272139i	−0.990699	+	0.136070i	$0.956553\pi$
$938$		−	5.65300i		−	0.184577i
$939$		0			0
$940$	6.79129	+	1.41742i	0.221507	+	0.0462313i
$941$	−3.75015			−0.122251			−0.0611257	−	0.998130i	$-0.519469\pi$
$941$	−3.75015			−0.122251			−0.0611257	+	0.998130i	$0.519469\pi$
$942$		0			0
$943$		−	20.0780i		−	0.653831i
$944$	−36.3930			−1.18449
$945$		0			0
$946$	−0.791288			−0.0257270
$947$			33.8426i			1.09974i	0.835252	+	0.549868i	$0.185322\pi$
$947$			33.8426i			1.09974i	−0.835252	+	0.549868i	$0.814678\pi$
$948$		0			0
$949$	−0.956439			−0.0310473
$950$	2.01810	−	4.62405i	0.0654759	−	0.150024i
$951$		0			0
$952$			5.20871i			0.168815i
$953$		−	52.2476i		−	1.69246i	−0.532814	−	0.846232i	$-0.678865\pi$
$953$		−	52.2476i		−	1.69246i	0.532814	−	0.846232i	$-0.321135\pi$
$954$		0			0
$955$	6.16515	−	29.5390i	0.199500	−	0.955860i
$956$	−3.10260			−0.100345
$957$		0			0
$958$		−	11.3739i		−	0.367473i
$959$	−15.8745			−0.512615
$960$		0			0
$961$	−30.6606			−0.989052
$962$			0.778549i			0.0251014i
$963$		0			0
$964$	−18.5826			−0.598504
$965$	−26.1715	−	5.46230i	−0.842489	−	0.175838i
$966$		0			0
$967$		−	25.8348i		−	0.830793i	−0.909641	−	0.415396i	$-0.863643\pi$
$967$		−	25.8348i		−	0.830793i	0.909641	−	0.415396i	$-0.136357\pi$
$968$		−	13.8564i		−	0.445362i
$969$		0			0
$970$	2.58258	−	12.3739i	0.0829215	−	0.397301i
$971$	30.6446			0.983432			0.491716	−	0.870755i	$-0.336370\pi$
$971$	30.6446			0.983432			0.491716	+	0.870755i	$0.336370\pi$
$972$		0			0
$973$		−	20.5826i		−	0.659847i
$974$	6.35610			0.203663
$975$		0			0
$976$	0.582576			0.0186478
$977$		−	25.6947i		−	0.822047i	−0.911625	−	0.411023i	$-0.865171\pi$
$977$		−	25.6947i		−	0.822047i	0.911625	−	0.411023i	$-0.134829\pi$
$978$		0			0
$979$	15.0000			0.479402
$980$	0.818350	−	3.92095i	0.0261412	−	0.125250i
$981$		0			0
$982$			9.54811i			0.304692i
$983$		−	45.9669i		−	1.46612i	−0.680166	−	0.733059i	$-0.738092\pi$
$983$		−	45.9669i		−	1.46612i	0.680166	−	0.733059i	$-0.261908\pi$
$984$		0			0
$985$	57.2867	+	11.9564i	1.82531	+	0.380964i
$986$	−7.76645			−0.247334
$987$		0			0
$988$		−	0.825757i		−	0.0262708i
$989$	−3.10260			−0.0986570
$990$		0			0
$991$	−22.0780			−0.701332			−0.350666	−	0.936501i	$-0.614045\pi$
$991$	−22.0780			−0.701332			−0.350666	+	0.936501i	$0.614045\pi$
$992$			2.76100i			0.0876619i
$993$		0			0
$994$	6.58258			0.208787
$995$	−10.4122	+	49.8879i	−0.330089	+	1.58155i
$996$		0			0
$997$			49.2432i			1.55955i	0.626062	+	0.779774i	$0.284666\pi$
$997$			49.2432i			1.55955i	−0.626062	+	0.779774i	$0.715334\pi$
$998$			0.838251i			0.0265344i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.d.c.379.5	yes	8
3.2	odd	2	inner	945.2.d.c.379.4	yes	8
5.2	odd	4		4725.2.a.bs.1.2		4
5.3	odd	4		4725.2.a.br.1.3		4
5.4	even	2	inner	945.2.d.c.379.3	✓	8
15.2	even	4		4725.2.a.bs.1.3		4
15.8	even	4		4725.2.a.br.1.2		4
15.14	odd	2	inner	945.2.d.c.379.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.d.c.379.3	✓	8	5.4	even	2	inner
945.2.d.c.379.4	yes	8	3.2	odd	2	inner
945.2.d.c.379.5	yes	8	1.1	even	1	trivial
945.2.d.c.379.6	yes	8	15.14	odd	2	inner
4725.2.a.br.1.2		4	15.8	even	4
4725.2.a.br.1.3		4	5.3	odd	4
4725.2.a.bs.1.2		4	5.2	odd	4
4725.2.a.bs.1.3		4	15.2	even	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.456850i q^{2} +1.79129 q^{4} +(-0.456850 + 2.18890i) q^{5} -1.00000i q^{7} +1.73205i q^{8} +O(q^{10})\)	\(q+0.456850i q^{2} +1.79129 q^{4} +(-0.456850 + 2.18890i) q^{5} -1.00000i q^{7} +1.73205i q^{8} +(-1.00000 - 0.208712i) q^{10} +1.73205 q^{11} -0.208712i q^{13} +0.456850 q^{14} +2.79129 q^{16} +3.00725i q^{17} +2.20871 q^{19} +(-0.818350 + 3.92095i) q^{20} +0.791288i q^{22} +3.10260i q^{23} +(-4.58258 - 2.00000i) q^{25} +0.0953502 q^{26} -1.79129i q^{28} +5.65300 q^{29} +0.582576 q^{31} +4.73930i q^{32} -1.37386 q^{34} +(2.18890 + 0.456850i) q^{35} +8.16515i q^{37} +1.00905i q^{38} +(-3.79129 - 0.791288i) q^{40} -6.47135 q^{41} +1.00000i q^{43} +3.10260 q^{44} -1.41742 q^{46} -1.73205i q^{47} -1.00000 q^{49} +(0.913701 - 2.09355i) q^{50} -0.373864i q^{52} -1.37055i q^{53} +(-0.791288 + 3.79129i) q^{55} +1.73205 q^{56} +2.58258i q^{58} -13.0381 q^{59} +0.208712 q^{61} +0.266150i q^{62} +3.41742 q^{64} +(0.456850 + 0.0953502i) q^{65} -12.3739i q^{67} +5.38685i q^{68} +(-0.208712 + 1.00000i) q^{70} +14.4086 q^{71} -4.58258i q^{73} -3.73025 q^{74} +3.95644 q^{76} -1.73205i q^{77} +10.3739 q^{79} +(-1.27520 + 6.10985i) q^{80} -2.95644i q^{82} +6.83285i q^{83} +(-6.58258 - 1.37386i) q^{85} -0.456850 q^{86} +3.00000i q^{88} +8.66025 q^{89} -0.208712 q^{91} +5.55765i q^{92} +0.791288 q^{94} +(-1.00905 + 4.83465i) q^{95} +12.3739i q^{97} -0.456850i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4}+O(q^{10}) \) 8 * q - 4 * q^4	\( 8 q - 4 q^{4} - 8 q^{10} + 4 q^{16} + 36 q^{19} - 32 q^{31} + 44 q^{34} - 12 q^{40} - 48 q^{46} - 8 q^{49} + 12 q^{55} + 20 q^{61} + 64 q^{64} - 20 q^{70} - 60 q^{76} + 28 q^{79} - 16 q^{85} - 20 q^{91} - 12 q^{94}+O(q^{100}) \) 8 * q - 4 * q^4 - 8 * q^10 + 4 * q^16 + 36 * q^19 - 32 * q^31 + 44 * q^34 - 12 * q^40 - 48 * q^46 - 8 * q^49 + 12 * q^55 + 20 * q^61 + 64 * q^64 - 20 * q^70 - 60 * q^76 + 28 * q^79 - 16 * q^85 - 20 * q^91 - 12 * q^94

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