LMFDB - Embedded newform 2790.2.d.j.559.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2790,2,Mod(559,2790)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2790.559"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2790, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2790.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-6,4,0,0,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$22.2782621639$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.11669056.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 7x^{4} + 8x^{3} - x^{2} + 54x + 58 $ x^6 - 2x^5 + 7x^4 + 8x^3 - x^2 + 54x + 58
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 930)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.4
Root			$1.60509 - 2.15264i$ of defining polynomial
Character	$\chi$	$=$	2790.559
Dual form			2790.2.d.j.559.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.605092 + 2.15264i) q^{5} -2.00000i q^{7} -1.00000i q^{8} +(-2.15264 - 0.605092i) q^{10} -5.21018 q^{11} +0.789816i q^{13} +2.00000 q^{14} +1.00000 q^{16} -0.115086i q^{17} -0.115086 q^{19} +(0.605092 - 2.15264i) q^{20} -5.21018i q^{22} +4.42037i q^{23} +(-4.26773 - 2.60509i) q^{25} -0.789816 q^{26} +2.00000i q^{28} +4.42037 q^{29} -1.00000 q^{31} +1.00000i q^{32} +0.115086 q^{34} +(4.30528 + 1.21018i) q^{35} -6.61056i q^{37} -0.115086i q^{38} +(2.15264 + 0.605092i) q^{40} -2.00000 q^{41} -8.61056i q^{43} +5.21018 q^{44} -4.42037 q^{46} +0.115086i q^{47} +3.00000 q^{49} +(2.60509 - 4.26773i) q^{50} -0.789816i q^{52} +0.190196i q^{53} +(3.15264 - 11.2157i) q^{55} -2.00000 q^{56} +4.42037i q^{58} -4.19020 q^{59} +12.4955 q^{61} -1.00000i q^{62} -1.00000 q^{64} +(-1.70019 - 0.477911i) q^{65} -5.82075i q^{67} +0.115086i q^{68} +(-1.21018 + 4.30528i) q^{70} +13.8207 q^{71} -10.8407i q^{73} +6.61056 q^{74} +0.115086 q^{76} +10.4204i q^{77} -2.30528 q^{79} +(-0.605092 + 2.15264i) q^{80} -2.00000i q^{82} -15.1460i q^{83} +(0.247739 + 0.0696377i) q^{85} +8.61056 q^{86} +5.21018i q^{88} -2.23017 q^{89} +1.57963 q^{91} -4.42037i q^{92} -0.115086 q^{94} +(0.0696377 - 0.247739i) q^{95} +9.21018i q^{97} +3.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 4 q^{5} - 16 q^{11} + 12 q^{14} + 6 q^{16} + 4 q^{19} - 4 q^{20} - 8 q^{25} - 20 q^{26} - 4 q^{29} - 6 q^{31} - 4 q^{34} - 12 q^{41} + 16 q^{44} + 4 q^{46} + 18 q^{49} + 8 q^{50} + 6 q^{55}+ \cdots + 28 q^{95}+O(q^{100}) $ 6 * q - 6 * q^4 + 4 * q^5 - 16 * q^11 + 12 * q^14 + 6 * q^16 + 4 * q^19 - 4 * q^20 - 8 * q^25 - 20 * q^26 - 4 * q^29 - 6 * q^31 - 4 * q^34 - 12 * q^41 + 16 * q^44 + 4 * q^46 + 18 * q^49 + 8 * q^50 + 6 * q^55 - 12 * q^56 - 4 * q^59 + 28 * q^61 - 6 * q^64 + 8 * q^65 + 8 * q^70 + 16 * q^71 - 12 * q^74 - 4 * q^76 + 12 * q^79 + 4 * q^80 - 22 * q^85 - 4 * q^89 + 40 * q^91 + 4 * q^94 + 28 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2790\mathbb{Z}\right)^\times$.

$n$	$1117$	$1801$	$2171$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.605092	+	2.15264i	−0.270605	+	0.962690i
$5$	−0.605092	+	2.15264i	−0.270605	+	0.962690i
$6$		0			0
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−2.15264	−	0.605092i	−0.680725	−	0.191347i
$11$	−5.21018			−1.57093			−0.785465	−	0.618906i	$-0.787576\pi$
$11$	−5.21018			−1.57093			−0.785465	+	0.618906i	$0.787576\pi$
$12$		0			0
$13$			0.789816i			0.219056i	0.993984	+	0.109528i	$0.0349339\pi$
$13$			0.789816i			0.219056i	−0.993984	+	0.109528i	$0.965066\pi$
$14$	2.00000			0.534522
$15$		0			0
$16$	1.00000			0.250000
$17$		−	0.115086i		−	0.0279125i	−0.999903	−	0.0139562i	$-0.995557\pi$
$17$		−	0.115086i		−	0.0279125i	0.999903	−	0.0139562i	$-0.00444255\pi$
$18$		0			0
$19$	−0.115086			−0.0264026			−0.0132013	−	0.999913i	$-0.504202\pi$
$19$	−0.115086			−0.0264026			−0.0132013	+	0.999913i	$0.504202\pi$
$20$	0.605092	−	2.15264i	0.135303	−	0.481345i
$21$		0			0
$22$		−	5.21018i		−	1.11081i
$23$			4.42037i			0.921710i	0.887475	+	0.460855i	$0.152457\pi$
$23$			4.42037i			0.921710i	−0.887475	+	0.460855i	$0.847543\pi$
$24$		0			0
$25$	−4.26773	−	2.60509i	−0.853545	−	0.521018i
$26$	−0.789816			−0.154896
$27$		0			0
$28$			2.00000i			0.377964i
$29$	4.42037			0.820842			0.410421	−	0.911896i	$-0.365382\pi$
$29$	4.42037			0.820842			0.410421	+	0.911896i	$0.365382\pi$
$30$		0			0
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$			1.00000i			0.176777i
$33$		0			0
$34$	0.115086			0.0197371
$35$	4.30528	+	1.21018i	0.727726	+	0.204558i
$36$		0			0
$37$		−	6.61056i		−	1.08677i	−0.839484	−	0.543385i	$-0.817142\pi$
$37$		−	6.61056i		−	1.08677i	0.839484	−	0.543385i	$-0.182858\pi$
$38$		−	0.115086i		−	0.0186694i
$39$		0			0
$40$	2.15264	+	0.605092i	0.340362	+	0.0956735i
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$		−	8.61056i		−	1.31310i	−0.754283	−	0.656549i	$-0.772015\pi$
$43$		−	8.61056i		−	1.31310i	0.754283	−	0.656549i	$-0.227985\pi$
$44$	5.21018			0.785465
$45$		0			0
$46$	−4.42037			−0.651748
$47$			0.115086i			0.0167870i	0.999965	+	0.00839352i	$0.00267177\pi$
$47$			0.115086i			0.0167870i	−0.999965	+	0.00839352i	$0.997328\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$	2.60509	−	4.26773i	0.368416	−	0.603548i
$51$		0			0
$52$		−	0.789816i		−	0.109528i
$53$			0.190196i			0.0261254i	0.999915	+	0.0130627i	$0.00415811\pi$
$53$			0.190196i			0.0261254i	−0.999915	+	0.0130627i	$0.995842\pi$
$54$		0			0
$55$	3.15264	−	11.2157i	0.425102	−	1.51232i
$56$	−2.00000			−0.267261
$57$		0			0
$58$			4.42037i			0.580423i
$59$	−4.19020			−0.545517			−0.272759	−	0.962083i	$-0.587936\pi$
$59$	−4.19020			−0.545517			−0.272759	+	0.962083i	$0.587936\pi$
$60$		0			0
$61$	12.4955			1.59988			0.799941	−	0.600079i	$-0.204864\pi$
$61$	12.4955			1.59988			0.799941	+	0.600079i	$0.204864\pi$
$62$		−	1.00000i		−	0.127000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.70019	−	0.477911i	−0.210883	−	0.0592776i
$66$		0			0
$67$		−	5.82075i		−	0.711118i	−0.934654	−	0.355559i	$-0.884291\pi$
$67$		−	5.82075i		−	0.711118i	0.934654	−	0.355559i	$-0.115709\pi$
$68$			0.115086i			0.0139562i
$69$		0			0
$70$	−1.21018	+	4.30528i	−0.144645	+	0.514580i
$71$	13.8207			1.64022			0.820111	−	0.572205i	$-0.193912\pi$
$71$	13.8207			1.64022			0.820111	+	0.572205i	$0.193912\pi$
$72$		0			0
$73$		−	10.8407i		−	1.26881i	−0.773000	−	0.634406i	$-0.781245\pi$
$73$		−	10.8407i		−	1.26881i	0.773000	−	0.634406i	$-0.218755\pi$
$74$	6.61056			0.768462
$75$		0			0
$76$	0.115086			0.0132013
$77$			10.4204i			1.18751i
$78$		0			0
$79$	−2.30528			−0.259365			−0.129682	−	0.991556i	$-0.541396\pi$
$79$	−2.30528			−0.259365			−0.129682	+	0.991556i	$0.541396\pi$
$80$	−0.605092	+	2.15264i	−0.0676513	+	0.240673i
$81$		0			0
$82$		−	2.00000i		−	0.220863i
$83$		−	15.1460i		−	1.66249i	−0.555905	−	0.831246i	$-0.687628\pi$
$83$		−	15.1460i		−	1.66249i	0.555905	−	0.831246i	$-0.312372\pi$
$84$		0			0
$85$	0.247739	+	0.0696377i	0.0268711	+	0.00755327i
$86$	8.61056			0.928501
$87$		0			0
$88$			5.21018i			0.555407i
$89$	−2.23017			−0.236398			−0.118199	−	0.992990i	$-0.537712\pi$
$89$	−2.23017			−0.236398			−0.118199	+	0.992990i	$0.537712\pi$
$90$		0			0
$91$	1.57963			0.165590
$92$		−	4.42037i		−	0.460855i
$93$		0			0
$94$	−0.115086			−0.0118702
$95$	0.0696377	−	0.247739i	0.00714468	−	0.0254175i
$96$		0			0
$97$			9.21018i			0.935153i	0.883953	+	0.467576i	$0.154873\pi$
$97$			9.21018i			0.935153i	−0.883953	+	0.467576i	$0.845127\pi$
$98$			3.00000i			0.303046i
$99$		0			0
$100$	4.26773	+	2.60509i	0.426773	+	0.260509i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	0.789816			0.0774478
$105$		0			0
$106$	−0.190196			−0.0184735
$107$		−	3.03093i		−	0.293011i	−0.989210	−	0.146506i	$-0.953197\pi$
$107$		−	3.03093i		−	0.293011i	0.989210	−	0.146506i	$-0.0468027\pi$
$108$		0			0
$109$	8.19020			0.784479			0.392239	−	0.919863i	$-0.371701\pi$
$109$	8.19020			0.784479			0.392239	+	0.919863i	$0.371701\pi$
$110$	11.2157	+	3.15264i	1.06937	+	0.300593i
$111$		0			0
$112$		−	2.00000i		−	0.188982i
$113$		−	10.3804i		−	0.976505i	−0.872702	−	0.488253i	$-0.837634\pi$
$113$		−	10.3804i		−	0.976505i	0.872702	−	0.488253i	$-0.162366\pi$
$114$		0			0
$115$	−9.51547	−	2.67473i	−0.887322	−	0.249420i
$116$	−4.42037			−0.410421
$117$		0			0
$118$		−	4.19020i		−	0.385739i
$119$	−0.230172			−0.0210999
$120$		0			0
$121$	16.1460			1.46782
$122$			12.4955i			1.13129i
$123$		0			0
$124$	1.00000			0.0898027
$125$	8.19020	−	7.61056i	0.732553	−	0.680710i
$126$		0			0
$127$			10.4204i			0.924658i	0.886708	+	0.462329i	$0.152986\pi$
$127$			10.4204i			0.924658i	−0.886708	+	0.462329i	$0.847014\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	0.477911	−	1.70019i	0.0419156	−	0.149117i
$131$	0.190196			0.0166175			0.00830875	−	0.999965i	$-0.497355\pi$
$131$	0.190196			0.0166175			0.00830875	+	0.999965i	$0.497355\pi$
$132$		0			0
$133$			0.230172i			0.0199585i
$134$	5.82075			0.502836
$135$		0			0
$136$	−0.115086			−0.00986855
$137$		−	21.4513i		−	1.83271i	−0.400369	−	0.916354i	$-0.631118\pi$
$137$		−	21.4513i		−	1.83271i	0.400369	−	0.916354i	$-0.368882\pi$
$138$		0			0
$139$	−16.4204			−1.39276			−0.696379	−	0.717674i	$-0.745207\pi$
$139$	−16.4204			−1.39276			−0.696379	+	0.717674i	$0.745207\pi$
$140$	−4.30528	−	1.21018i	−0.363863	−	0.102279i
$141$		0			0
$142$			13.8207i			1.15981i
$143$		−	4.11509i		−	0.344121i
$144$		0			0
$145$	−2.67473	+	9.51547i	−0.222124	+	0.790216i
$146$	10.8407			0.897186
$147$		0			0
$148$			6.61056i			0.543385i
$149$	−3.63055			−0.297426			−0.148713	−	0.988880i	$-0.547513\pi$
$149$	−3.63055			−0.297426			−0.148713	+	0.988880i	$0.547513\pi$
$150$		0			0
$151$	−15.7566			−1.28225			−0.641126	−	0.767435i	$-0.721533\pi$
$151$	−15.7566			−1.28225			−0.641126	+	0.767435i	$0.721533\pi$
$152$			0.115086i			0.00933472i
$153$		0			0
$154$	−10.4204			−0.839697
$155$	0.605092	−	2.15264i	0.0486022	−	0.172904i
$156$		0			0
$157$			3.96002i			0.316044i	0.987436	+	0.158022i	$0.0505117\pi$
$157$			3.96002i			0.316044i	−0.987436	+	0.158022i	$0.949488\pi$
$158$		−	2.30528i		−	0.183398i
$159$		0			0
$160$	−2.15264	−	0.605092i	−0.170181	−	0.0478367i
$161$	8.84074			0.696748
$162$		0			0
$163$			9.82075i			0.769220i	0.923079	+	0.384610i	$0.125664\pi$
$163$			9.82075i			0.769220i	−0.923079	+	0.384610i	$0.874336\pi$
$164$	2.00000			0.156174
$165$		0			0
$166$	15.1460			1.17556
$167$			2.00000i			0.154765i	0.997001	+	0.0773823i	$0.0246562\pi$
$167$			2.00000i			0.154765i	−0.997001	+	0.0773823i	$0.975344\pi$
$168$		0			0
$169$	12.3762			0.952015
$170$	−0.0696377	+	0.247739i	−0.00534097	+	0.0190007i
$171$		0			0
$172$			8.61056i			0.656549i
$173$			0.535454i			0.0407098i	0.999793	+	0.0203549i	$0.00647962\pi$
$173$			0.535454i			0.0407098i	−0.999793	+	0.0203549i	$0.993520\pi$
$174$		0			0
$175$	−5.21018	+	8.53545i	−0.393853	+	0.645220i
$176$	−5.21018			−0.392732
$177$		0			0
$178$		−	2.23017i		−	0.167158i
$179$	10.4313			0.779673			0.389836	−	0.920884i	$-0.372532\pi$
$179$	10.4313			0.779673			0.389836	+	0.920884i	$0.372532\pi$
$180$		0			0
$181$	17.4513			1.29714			0.648572	−	0.761153i	$-0.275366\pi$
$181$	17.4513			1.29714			0.648572	+	0.761153i	$0.275366\pi$
$182$			1.57963i			0.117090i
$183$		0			0
$184$	4.42037			0.325874
$185$	14.2302	+	4.00000i	1.04622	+	0.294086i
$186$		0			0
$187$			0.599620i			0.0438485i
$188$		−	0.115086i		−	0.00839352i
$189$		0			0
$190$	0.247739	+	0.0696377i	0.0179729	+	0.00505205i
$191$	−19.2611			−1.39368			−0.696842	−	0.717224i	$-0.745412\pi$
$191$	−19.2611			−1.39368			−0.696842	+	0.717224i	$0.745412\pi$
$192$		0			0
$193$			14.4313i			1.03879i	0.854535	+	0.519394i	$0.173842\pi$
$193$			14.4313i			1.03879i	−0.854535	+	0.519394i	$0.826158\pi$
$194$	−9.21018			−0.661253
$195$		0			0
$196$	−3.00000			−0.214286
$197$			10.3804i			0.739572i	0.929117	+	0.369786i	$0.120569\pi$
$197$			10.3804i			0.739572i	−0.929117	+	0.369786i	$0.879431\pi$
$198$		0			0
$199$	−14.5355			−1.03039			−0.515196	−	0.857073i	$-0.672281\pi$
$199$	−14.5355			−1.03039			−0.515196	+	0.857073i	$0.672281\pi$
$200$	−2.60509	+	4.26773i	−0.184208	+	0.301774i
$201$		0			0
$202$		0			0
$203$		−	8.84074i		−	0.620498i
$204$		0			0
$205$	1.21018	−	4.30528i	0.0845229	−	0.300694i
$206$	6.00000			0.418040
$207$		0			0
$208$			0.789816i			0.0547639i
$209$	0.599620			0.0414766
$210$		0			0
$211$	24.8407			1.71011			0.855053	−	0.518540i	$-0.173524\pi$
$211$	24.8407			1.71011			0.855053	+	0.518540i	$0.173524\pi$
$212$		−	0.190196i		−	0.0130627i
$213$		0			0
$214$	3.03093			0.207190
$215$	18.5355	+	5.21018i	1.26411	+	0.355332i
$216$		0			0
$217$			2.00000i			0.135769i
$218$			8.19020i			0.554710i
$219$		0			0
$220$	−3.15264	+	11.2157i	−0.212551	+	0.756159i
$221$	0.0908968			0.00611438
$222$		0			0
$223$		−	19.6306i		−	1.31456i	−0.753647	−	0.657280i	$-0.771707\pi$
$223$		−	19.6306i		−	1.31456i	0.753647	−	0.657280i	$-0.228293\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	10.3804			0.690493
$227$		−	6.42037i		−	0.426135i	−0.977038	−	0.213067i	$-0.931655\pi$
$227$		−	6.42037i		−	0.426135i	0.977038	−	0.213067i	$-0.0683454\pi$
$228$		0			0
$229$	29.7166			1.96373			0.981864	−	0.189585i	$-0.0607142\pi$
$229$	29.7166			1.96373			0.981864	+	0.189585i	$0.0607142\pi$
$230$	2.67473	−	9.51547i	0.176366	−	0.627431i
$231$		0			0
$232$		−	4.42037i		−	0.290211i
$233$		−	5.38944i		−	0.353074i	−0.984294	−	0.176537i	$-0.943511\pi$
$233$		−	5.38944i		−	0.353074i	0.984294	−	0.176537i	$-0.0564895\pi$
$234$		0			0
$235$	−0.247739	−	0.0696377i	−0.0161607	−	0.00454266i
$236$	4.19020			0.272759
$237$		0			0
$238$		−	0.230172i		−	0.0149198i
$239$	7.03093			0.454793			0.227397	−	0.973802i	$-0.426979\pi$
$239$	7.03093			0.454793			0.227397	+	0.973802i	$0.426979\pi$
$240$		0			0
$241$	−0.190196			−0.0122516			−0.00612580	−	0.999981i	$-0.501950\pi$
$241$	−0.190196			−0.0122516			−0.00612580	+	0.999981i	$0.501950\pi$
$242$			16.1460i			1.03791i
$243$		0			0
$244$	−12.4955			−0.799941
$245$	−1.81528	+	6.45792i	−0.115974	+	0.412582i
$246$		0			0
$247$		−	0.0908968i		−	0.00578363i
$248$			1.00000i			0.0635001i
$249$		0			0
$250$	7.61056	+	8.19020i	0.481334	+	0.517993i
$251$	−14.4204			−0.910206			−0.455103	−	0.890439i	$-0.650397\pi$
$251$	−14.4204			−0.910206			−0.455103	+	0.890439i	$0.650397\pi$
$252$		0			0
$253$		−	23.0309i		−	1.44794i
$254$	−10.4204			−0.653832
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	1.76983i		−	0.110399i	−0.998475	−	0.0551994i	$-0.982421\pi$
$257$		−	1.76983i		−	0.110399i	0.998475	−	0.0551994i	$-0.0175795\pi$
$258$		0			0
$259$	−13.2211			−0.821521
$260$	1.70019	+	0.477911i	0.105441	+	0.0296388i
$261$		0			0
$262$			0.190196i			0.0117504i
$263$		−	14.2302i		−	0.877470i	−0.898616	−	0.438735i	$-0.855427\pi$
$263$		−	14.2302i		−	0.877470i	0.898616	−	0.438735i	$-0.144573\pi$
$264$		0			0
$265$	−0.409424	−	0.115086i	−0.0251507	−	0.00706968i
$266$	−0.230172			−0.0141128
$267$		0			0
$268$			5.82075i			0.355559i
$269$	−1.15926			−0.0706815			−0.0353408	−	0.999375i	$-0.511252\pi$
$269$	−1.15926			−0.0706815			−0.0353408	+	0.999375i	$0.511252\pi$
$270$		0			0
$271$	22.6857			1.37806			0.689028	−	0.724734i	$-0.258038\pi$
$271$	22.6857			1.37806			0.689028	+	0.724734i	$0.258038\pi$
$272$		−	0.115086i		−	0.00697812i
$273$		0			0
$274$	21.4513			1.29592
$275$	22.2356	+	13.5730i	1.34086	+	0.818483i
$276$		0			0
$277$			9.63055i			0.578644i	0.957232	+	0.289322i	$0.0934298\pi$
$277$			9.63055i			0.578644i	−0.957232	+	0.289322i	$0.906570\pi$
$278$		−	16.4204i		−	0.984828i
$279$		0			0
$280$	1.21018	−	4.30528i	0.0723223	−	0.257290i
$281$	−10.8407			−0.646704			−0.323352	−	0.946279i	$-0.604810\pi$
$281$	−10.8407			−0.646704			−0.323352	+	0.946279i	$0.604810\pi$
$282$		0			0
$283$		−	19.7808i		−	1.17584i	−0.808917	−	0.587922i	$-0.799946\pi$
$283$		−	19.7808i		−	1.17584i	0.808917	−	0.587922i	$-0.200054\pi$
$284$	−13.8207			−0.820111
$285$		0			0
$286$	4.11509			0.243330
$287$			4.00000i			0.236113i
$288$		0			0
$289$	16.9868			0.999221
$290$	−9.51547	−	2.67473i	−0.558767	−	0.157066i
$291$		0			0
$292$			10.8407i			0.634406i
$293$		−	31.2211i		−	1.82396i	−0.410237	−	0.911979i	$-0.634554\pi$
$293$		−	31.2211i		−	1.82396i	0.410237	−	0.911979i	$-0.365446\pi$
$294$		0			0
$295$	2.53545	−	9.01999i	0.147620	−	0.525164i
$296$	−6.61056			−0.384231
$297$		0			0
$298$		−	3.63055i		−	0.210312i
$299$	−3.49128			−0.201906
$300$		0			0
$301$	−17.2211			−0.992609
$302$		−	15.7566i		−	0.906689i
$303$		0			0
$304$	−0.115086			−0.00660064
$305$	−7.56091	+	26.8983i	−0.432937	+	1.54019i
$306$		0			0
$307$			13.5796i			0.775031i	0.921863	+	0.387515i	$0.126667\pi$
$307$			13.5796i			0.775031i	−0.921863	+	0.387515i	$0.873333\pi$
$308$		−	10.4204i		−	0.593756i
$309$		0			0
$310$	2.15264	+	0.605092i	0.122262	+	0.0343669i
$311$	−18.2811			−1.03663			−0.518313	−	0.855191i	$-0.673440\pi$
$311$	−18.2811			−1.03663			−0.518313	+	0.855191i	$0.673440\pi$
$312$		0			0
$313$		−	14.4603i		−	0.817347i	−0.912681	−	0.408673i	$-0.865991\pi$
$313$		−	14.4603i		−	0.817347i	0.912681	−	0.408673i	$-0.134009\pi$
$314$	−3.96002			−0.223477
$315$		0			0
$316$	2.30528			0.129682
$317$		−	3.46455i		−	0.194588i	−0.995256	−	0.0972941i	$-0.968981\pi$
$317$		−	3.46455i		−	0.194588i	0.995256	−	0.0972941i	$-0.0310188\pi$
$318$		0			0
$319$	−23.0309			−1.28948
$320$	0.605092	−	2.15264i	0.0338257	−	0.120336i
$321$		0			0
$322$			8.84074i			0.492675i
$323$			0.0132448i			0.000736961i
$324$		0			0
$325$	2.05754	−	3.37072i	0.114132	−	0.186974i
$326$	−9.82075			−0.543921
$327$		0			0
$328$			2.00000i			0.110432i
$329$	0.230172			0.0126898
$330$		0			0
$331$	−20.8008			−1.14331			−0.571657	−	0.820493i	$-0.693699\pi$
$331$	−20.8008			−1.14331			−0.571657	+	0.820493i	$0.693699\pi$
$332$			15.1460i			0.831246i
$333$		0			0
$334$	−2.00000			−0.109435
$335$	12.5300	+	3.52209i	0.684586	+	0.192432i
$336$		0			0
$337$			23.0709i			1.25675i	0.777910	+	0.628376i	$0.216280\pi$
$337$			23.0709i			1.25675i	−0.777910	+	0.628376i	$0.783720\pi$
$338$			12.3762i			0.673176i
$339$		0			0
$340$	−0.247739	−	0.0696377i	−0.0134355	−	0.00377663i
$341$	5.21018			0.282147
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$	−8.61056			−0.464251
$345$		0			0
$346$	−0.535454			−0.0287862
$347$		−	31.9868i		−	1.71714i	−0.512697	−	0.858569i	$-0.671354\pi$
$347$		−	31.9868i		−	1.71714i	0.512697	−	0.858569i	$-0.328646\pi$
$348$		0			0
$349$	−23.4513			−1.25532			−0.627660	−	0.778488i	$-0.715987\pi$
$349$	−23.4513			−1.25532			−0.627660	+	0.778488i	$0.715987\pi$
$350$	−8.53545	−	5.21018i	−0.456239	−	0.278496i
$351$		0			0
$352$		−	5.21018i		−	0.277704i
$353$		−	3.88491i		−	0.206773i	−0.994641	−	0.103387i	$-0.967032\pi$
$353$		−	3.88491i		−	0.206773i	0.994641	−	0.103387i	$-0.0329679\pi$
$354$		0			0
$355$	−8.36283	+	29.7511i	−0.443853	+	1.57903i
$356$	2.23017			0.118199
$357$		0			0
$358$			10.4313i			0.551312i
$359$	−21.3604			−1.12736			−0.563680	−	0.825994i	$-0.690615\pi$
$359$	−21.3604			−1.12736			−0.563680	+	0.825994i	$0.690615\pi$
$360$		0			0
$361$	−18.9868			−0.999303
$362$			17.4513i			0.917220i
$363$		0			0
$364$	−1.57963			−0.0827952
$365$	23.3362	+	6.55964i	1.22147	+	0.343347i
$366$		0			0
$367$			20.4713i			1.06859i	0.845297	+	0.534296i	$0.179423\pi$
$367$			20.4713i			1.06859i	−0.845297	+	0.534296i	$0.820577\pi$
$368$			4.42037i			0.230428i
$369$		0			0
$370$	−4.00000	+	14.2302i	−0.207950	+	0.739791i
$371$	0.380392			0.0197490
$372$		0			0
$373$		−	9.76983i		−	0.505863i	−0.967484	−	0.252931i	$-0.918605\pi$
$373$		−	9.76983i		−	0.505863i	0.967484	−	0.252931i	$-0.0813946\pi$
$374$	−0.599620			−0.0310056
$375$		0			0
$376$	0.115086			0.00593511
$377$			3.49128i			0.179810i
$378$		0			0
$379$	−3.65474			−0.187731			−0.0938657	−	0.995585i	$-0.529922\pi$
$379$	−3.65474			−0.187731			−0.0938657	+	0.995585i	$0.529922\pi$
$380$	−0.0696377	+	0.247739i	−0.00357234	+	0.0127087i
$381$		0			0
$382$		−	19.2611i		−	0.985484i
$383$			25.4913i			1.30254i	0.758845	+	0.651272i	$0.225764\pi$
$383$			25.4913i			1.30254i	−0.758845	+	0.651272i	$0.774236\pi$
$384$		0			0
$385$	−22.4313	−	6.30528i	−1.14321	−	0.321347i
$386$	−14.4313			−0.734534
$387$		0			0
$388$		−	9.21018i		−	0.467576i
$389$	4.65054			0.235792			0.117896	−	0.993026i	$-0.462385\pi$
$389$	4.65054			0.235792			0.117896	+	0.993026i	$0.462385\pi$
$390$		0			0
$391$	0.508723			0.0257272
$392$		−	3.00000i		−	0.151523i
$393$		0			0
$394$	−10.3804			−0.522957
$395$	1.39491	−	4.96245i	0.0701854	−	0.249688i
$396$		0			0
$397$		−	26.7124i		−	1.34066i	−0.742064	−	0.670329i	$-0.766153\pi$
$397$		−	26.7124i		−	1.34066i	0.742064	−	0.670329i	$-0.233847\pi$
$398$		−	14.5355i		−	0.728596i
$399$		0			0
$400$	−4.26773	−	2.60509i	−0.213386	−	0.130255i
$401$	−16.0509			−0.801545			−0.400772	−	0.916178i	$-0.631258\pi$
$401$	−16.0509			−0.801545			−0.400772	+	0.916178i	$0.631258\pi$
$402$		0			0
$403$		−	0.789816i		−	0.0393435i
$404$		0			0
$405$		0			0
$406$	8.84074			0.438758
$407$			34.4423i			1.70724i
$408$		0			0
$409$	−9.87167			−0.488123			−0.244061	−	0.969760i	$-0.578480\pi$
$409$	−9.87167			−0.488123			−0.244061	+	0.969760i	$0.578480\pi$
$410$	4.30528	+	1.21018i	0.212623	+	0.0597667i
$411$		0			0
$412$			6.00000i			0.295599i
$413$			8.38039i			0.412372i
$414$		0			0
$415$	32.6039	+	9.16474i	1.60046	+	0.449879i
$416$	−0.789816			−0.0387239
$417$		0			0
$418$			0.599620i			0.0293284i
$419$	−0.420368			−0.0205363			−0.0102682	−	0.999947i	$-0.503269\pi$
$419$	−0.420368			−0.0205363			−0.0102682	+	0.999947i	$0.503269\pi$
$420$		0			0
$421$	−39.2211			−1.91152			−0.955760	−	0.294146i	$-0.904965\pi$
$421$	−39.2211			−1.91152			−0.955760	+	0.294146i	$0.904965\pi$
$422$			24.8407i			1.20923i
$423$		0			0
$424$	0.190196			0.00923674
$425$	−0.299810	+	0.491156i	−0.0145429	+	0.0238246i
$426$		0			0
$427$		−	24.9910i		−	1.20940i
$428$			3.03093i			0.146506i
$429$		0			0
$430$	−5.21018	+	18.5355i	−0.251257	+	0.893859i
$431$	6.88071			0.331432			0.165716	−	0.986173i	$-0.447006\pi$
$431$	6.88071			0.331432			0.165716	+	0.986173i	$0.447006\pi$
$432$		0			0
$433$		−	1.38944i		−	0.0667720i	−0.999443	−	0.0333860i	$-0.989371\pi$
$433$		−	1.38944i		−	0.0667720i	0.999443	−	0.0333860i	$-0.0106291\pi$
$434$	−2.00000			−0.0960031
$435$		0			0
$436$	−8.19020			−0.392239
$437$		−	0.508723i		−	0.0243355i
$438$		0			0
$439$	−19.8717			−0.948423			−0.474212	−	0.880411i	$-0.657267\pi$
$439$	−19.8717			−0.948423			−0.474212	+	0.880411i	$0.657267\pi$
$440$	−11.2157	−	3.15264i	−0.534685	−	0.150296i
$441$		0			0
$442$			0.0908968i			0.00432352i
$443$		−	8.61056i		−	0.409100i	−0.978856	−	0.204550i	$-0.934427\pi$
$443$		−	8.61056i		−	0.409100i	0.978856	−	0.204550i	$-0.0655731\pi$
$444$		0			0
$445$	1.34946	−	4.80076i	0.0639705	−	0.227578i
$446$	19.6306			0.929534
$447$		0			0
$448$			2.00000i			0.0944911i
$449$	−10.3694			−0.489364			−0.244682	−	0.969603i	$-0.578684\pi$
$449$	−10.3694			−0.489364			−0.244682	+	0.969603i	$0.578684\pi$
$450$		0			0
$451$	10.4204			0.490676
$452$			10.3804i			0.488253i
$453$		0			0
$454$	6.42037			0.301323
$455$	−0.955823	+	3.40038i	−0.0448097	+	0.159412i
$456$		0			0
$457$			21.4913i			1.00532i	0.864484	+	0.502660i	$0.167645\pi$
$457$			21.4913i			1.00532i	−0.864484	+	0.502660i	$0.832355\pi$
$458$			29.7166i			1.38857i
$459$		0			0
$460$	9.51547	+	2.67473i	0.443661	+	0.124710i
$461$	−3.34946			−0.156000			−0.0779999	−	0.996953i	$-0.524853\pi$
$461$	−3.34946			−0.156000			−0.0779999	+	0.996953i	$0.524853\pi$
$462$		0			0
$463$		−	28.0109i		−	1.30178i	−0.759172	−	0.650889i	$-0.774396\pi$
$463$		−	28.0109i		−	1.30178i	0.759172	−	0.650889i	$-0.225604\pi$
$464$	4.42037			0.205210
$465$		0			0
$466$	5.38944			0.249661
$467$		−	37.6815i		−	1.74369i	−0.489781	−	0.871845i	$-0.662923\pi$
$467$		−	37.6815i		−	1.74369i	0.489781	−	0.871845i	$-0.337077\pi$
$468$		0			0
$469$	−11.6415			−0.537554
$470$	0.0696377	−	0.247739i	0.00321215	−	0.0114274i
$471$		0			0
$472$			4.19020i			0.192869i
$473$			44.8626i			2.06279i
$474$		0			0
$475$	0.491156	+	0.299810i	0.0225358	+	0.0137562i
$476$	0.230172			0.0105499
$477$		0			0
$478$			7.03093i			0.321587i
$479$	−10.2811			−0.469755			−0.234878	−	0.972025i	$-0.575469\pi$
$479$	−10.2811			−0.469755			−0.234878	+	0.972025i	$0.575469\pi$
$480$		0			0
$481$	5.22113			0.238063
$482$		−	0.190196i		−	0.00866319i
$483$		0			0
$484$	−16.1460			−0.733910
$485$	−19.8262	−	5.57301i	−0.900262	−	0.253057i
$486$		0			0
$487$			32.9316i			1.49227i	0.665792	+	0.746137i	$0.268094\pi$
$487$			32.9316i			1.49227i	−0.665792	+	0.746137i	$0.731906\pi$
$488$		−	12.4955i		−	0.565644i
$489$		0			0
$490$	−6.45792	−	1.81528i	−0.291739	−	0.0820058i
$491$	41.7034			1.88205			0.941023	−	0.338342i	$-0.109866\pi$
$491$	41.7034			1.88205			0.941023	+	0.338342i	$0.109866\pi$
$492$		0			0
$493$		−	0.508723i		−	0.0229117i
$494$	0.0908968			0.00408964
$495$		0			0
$496$	−1.00000			−0.0449013
$497$		−	27.6415i		−	1.23989i
$498$		0			0
$499$	−22.2302			−0.995159			−0.497580	−	0.867418i	$-0.665778\pi$
$499$	−22.2302			−0.995159			−0.497580	+	0.867418i	$0.665778\pi$
$500$	−8.19020	+	7.61056i	−0.366277	+	0.340355i
$501$		0			0
$502$		−	14.4204i		−	0.643613i
$503$			12.3453i			0.550448i	0.961380	+	0.275224i	$0.0887520\pi$
$503$			12.3453i			0.550448i	−0.961380	+	0.275224i	$0.911248\pi$
$504$		0			0
$505$		0			0
$506$	23.0309			1.02385
$507$		0			0
$508$		−	10.4204i		−	0.462329i
$509$	30.9910			1.37365			0.686825	−	0.726823i	$-0.259004\pi$
$509$	30.9910			1.37365			0.686825	+	0.726823i	$0.259004\pi$
$510$		0			0
$511$	−21.6815			−0.959132
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	1.76983			0.0780638
$515$	12.9158	+	3.63055i	0.569140	+	0.159981i
$516$		0			0
$517$		−	0.599620i		−	0.0263713i
$518$		−	13.2211i		−	0.580903i
$519$		0			0
$520$	−0.477911	+	1.70019i	−0.0209578	+	0.0745583i
$521$	−28.8008			−1.26178			−0.630892	−	0.775871i	$-0.717311\pi$
$521$	−28.8008			−1.26178			−0.630892	+	0.775871i	$0.717311\pi$
$522$		0			0
$523$		−	27.7698i		−	1.21429i	−0.794591	−	0.607145i	$-0.792315\pi$
$523$		−	27.7698i		−	1.21429i	0.794591	−	0.607145i	$-0.207685\pi$
$524$	−0.190196			−0.00830875
$525$		0			0
$526$	14.2302			0.620465
$527$			0.115086i			0.00501323i
$528$		0			0
$529$	3.46034			0.150450
$530$	0.115086	−	0.409424i	0.00499902	−	0.0177842i
$531$		0			0
$532$		−	0.230172i		−	0.00997923i
$533$		−	1.57963i		−	0.0684214i
$534$		0			0
$535$	6.52451	+	1.83399i	0.282079	+	0.0792904i
$536$	−5.82075			−0.251418
$537$		0			0
$538$		−	1.15926i		−	0.0499794i
$539$	−15.6306			−0.673256
$540$		0			0
$541$	34.9426			1.50230			0.751149	−	0.660132i	$-0.229500\pi$
$541$	34.9426			1.50230			0.751149	+	0.660132i	$0.229500\pi$
$542$			22.6857i			0.974433i
$543$		0			0
$544$	0.115086			0.00493428
$545$	−4.95582	+	17.6306i	−0.212284	+	0.755210i
$546$		0			0
$547$			23.6415i			1.01084i	0.862874	+	0.505419i	$0.168662\pi$
$547$			23.6415i			1.01084i	−0.862874	+	0.505419i	$0.831338\pi$
$548$			21.4513i			0.916354i
$549$		0			0
$550$	−13.5730	+	22.2356i	−0.578755	+	0.948131i
$551$	−0.508723			−0.0216723
$552$		0			0
$553$			4.61056i			0.196061i
$554$	−9.63055			−0.409163
$555$		0			0
$556$	16.4204			0.696379
$557$			22.9910i			0.974158i	0.873358	+	0.487079i	$0.161938\pi$
$557$			22.9910i			0.974158i	−0.873358	+	0.487079i	$0.838062\pi$
$558$		0			0
$559$	6.80076			0.287642
$560$	4.30528	+	1.21018i	0.181931	+	0.0511396i
$561$		0			0
$562$		−	10.8407i		−	0.457289i
$563$		−	7.87167i		−	0.331751i	−0.986147	−	0.165876i	$-0.946955\pi$
$563$		−	7.87167i		−	0.331751i	0.986147	−	0.165876i	$-0.0530450\pi$
$564$		0			0
$565$	22.3453	+	6.28109i	0.940072	+	0.264248i
$566$	19.7808			0.831448
$567$		0			0
$568$		−	13.8207i		−	0.579906i
$569$	−40.6724			−1.70508			−0.852538	−	0.522664i	$-0.824938\pi$
$569$	−40.6724			−1.70508			−0.852538	+	0.522664i	$0.824938\pi$
$570$		0			0
$571$	14.2302			0.595514			0.297757	−	0.954642i	$-0.403761\pi$
$571$	14.2302			0.595514			0.297757	+	0.954642i	$0.403761\pi$
$572$			4.11509i			0.172060i
$573$		0			0
$574$	−4.00000			−0.166957
$575$	11.5155	−	18.8649i	0.480228	−	0.786722i
$576$		0			0
$577$		−	7.63055i		−	0.317664i	−0.987306	−	0.158832i	$-0.949227\pi$
$577$		−	7.63055i		−	0.317664i	0.987306	−	0.158832i	$-0.0507728\pi$
$578$			16.9868i			0.706556i
$579$		0			0
$580$	2.67473	−	9.51547i	0.111062	−	0.395108i
$581$	−30.2920			−1.25673
$582$		0			0
$583$		−	0.990956i		−	0.0410412i
$584$	−10.8407			−0.448593
$585$		0			0
$586$	31.2211			1.28973
$587$		−	17.8449i		−	0.736539i	−0.929719	−	0.368270i	$-0.879950\pi$
$587$		−	17.8449i		−	0.736539i	0.929719	−	0.368270i	$-0.120050\pi$
$588$		0			0
$589$	0.115086			0.00474204
$590$	9.01999	+	2.53545i	0.371347	+	0.104383i
$591$		0			0
$592$		−	6.61056i		−	0.271693i
$593$			47.4732i			1.94949i	0.223320	+	0.974745i	$0.428310\pi$
$593$			47.4732i			1.94949i	−0.223320	+	0.974745i	$0.571690\pi$
$594$		0			0
$595$	0.139275	−	0.495478i	0.00570973	−	0.0203126i
$596$	3.63055			0.148713
$597$		0			0
$598$		−	3.49128i		−	0.142769i
$599$	41.4622			1.69410			0.847051	−	0.531512i	$-0.178376\pi$
$599$	41.4622			1.69410			0.847051	+	0.531512i	$0.178376\pi$
$600$		0			0
$601$	−8.77887			−0.358098			−0.179049	−	0.983840i	$-0.557302\pi$
$601$	−8.77887			−0.358098			−0.179049	+	0.983840i	$0.557302\pi$
$602$		−	17.2211i		−	0.701881i
$603$		0			0
$604$	15.7566			0.641126
$605$	−9.76983	+	34.7566i	−0.397200	+	1.41306i
$606$		0			0
$607$		−	32.0619i		−	1.30135i	−0.759356	−	0.650675i	$-0.774486\pi$
$607$		−	32.0619i		−	1.30135i	0.759356	−	0.650675i	$-0.225514\pi$
$608$		−	0.115086i		−	0.00466736i
$609$		0			0
$610$	−26.8983	−	7.56091i	−1.08908	−	0.306132i
$611$	−0.0908968			−0.00367729
$612$		0			0
$613$		−	23.2321i		−	0.938335i	−0.883109	−	0.469167i	$-0.844554\pi$
$613$		−	23.2321i		−	0.938335i	0.883109	−	0.469167i	$-0.155446\pi$
$614$	−13.5796			−0.548029
$615$		0			0
$616$	10.4204			0.419849
$617$		−	13.6196i		−	0.548305i	−0.961686	−	0.274152i	$-0.911603\pi$
$617$		−	13.6196i		−	0.548305i	0.961686	−	0.274152i	$-0.0883973\pi$
$618$		0			0
$619$	−25.3894			−1.02049			−0.510244	−	0.860030i	$-0.670445\pi$
$619$	−25.3894			−1.02049			−0.510244	+	0.860030i	$0.670445\pi$
$620$	−0.605092	+	2.15264i	−0.0243011	+	0.0864521i
$621$		0			0
$622$		−	18.2811i		−	0.733005i
$623$			4.46034i			0.178700i
$624$		0			0
$625$	11.4270	+	22.2356i	0.457080	+	0.889426i
$626$	14.4603			0.577952
$627$		0			0
$628$		−	3.96002i		−	0.158022i
$629$	−0.760784			−0.0303345
$630$		0			0
$631$	−28.3804			−1.12981			−0.564903	−	0.825157i	$-0.691086\pi$
$631$	−28.3804			−1.12981			−0.564903	+	0.825157i	$0.691086\pi$
$632$			2.30528i			0.0916992i
$633$		0			0
$634$	3.46455			0.137595
$635$	−22.4313	−	6.30528i	−0.890159	−	0.250217i
$636$		0			0
$637$			2.36945i			0.0938809i
$638$		−	23.0309i		−	0.911803i
$639$		0			0
$640$	2.15264	+	0.605092i	0.0850906	+	0.0239184i
$641$	−3.59058			−0.141819			−0.0709096	−	0.997483i	$-0.522590\pi$
$641$	−3.59058			−0.141819			−0.0709096	+	0.997483i	$0.522590\pi$
$642$		0			0
$643$		−	38.6505i		−	1.52423i	−0.647443	−	0.762114i	$-0.724161\pi$
$643$		−	38.6505i		−	1.52423i	0.647443	−	0.762114i	$-0.275839\pi$
$644$	−8.84074			−0.348374
$645$		0			0
$646$	−0.0132448			−0.000521110
$647$			32.9026i			1.29353i	0.762687	+	0.646767i	$0.223880\pi$
$647$			32.9026i			1.29353i	−0.762687	+	0.646767i	$0.776120\pi$
$648$		0			0
$649$	21.8317			0.856969
$650$	3.37072	+	2.05754i	0.132210	+	0.0807035i
$651$		0			0
$652$		−	9.82075i		−	0.384610i
$653$		−	25.5264i		−	0.998926i	−0.866335	−	0.499463i	$-0.833531\pi$
$653$		−	25.5264i		−	0.998926i	0.866335	−	0.499463i	$-0.166469\pi$
$654$		0			0
$655$	−0.115086	+	0.409424i	−0.00449679	+	0.0159975i
$656$	−2.00000			−0.0780869
$657$		0			0
$658$			0.230172i			0.00897305i
$659$	6.84074			0.266477			0.133239	−	0.991084i	$-0.457462\pi$
$659$	6.84074			0.266477			0.133239	+	0.991084i	$0.457462\pi$
$660$		0			0
$661$	−21.2611			−0.826961			−0.413481	−	0.910513i	$-0.635687\pi$
$661$	−21.2611			−0.826961			−0.413481	+	0.910513i	$0.635687\pi$
$662$		−	20.8008i		−	0.808445i
$663$		0			0
$664$	−15.1460			−0.587780
$665$	−0.495478	−	0.139275i	−0.0192138	−	0.00540087i
$666$		0			0
$667$			19.5397i			0.756578i
$668$		−	2.00000i		−	0.0773823i
$669$		0			0
$670$	−3.52209	+	12.5300i	−0.136070	+	0.484075i
$671$	−65.1037			−2.51330
$672$		0			0
$673$			39.7034i			1.53045i	0.643762	+	0.765226i	$0.277373\pi$
$673$			39.7034i			1.53045i	−0.643762	+	0.765226i	$0.722627\pi$
$674$	−23.0709			−0.888658
$675$		0			0
$676$	−12.3762			−0.476007
$677$		−	3.45130i		−	0.132644i	−0.997798	−	0.0663221i	$-0.978874\pi$
$677$		−	3.45130i		−	0.132644i	0.997798	−	0.0663221i	$-0.0211265\pi$
$678$		0			0
$679$	18.4204			0.706909
$680$	0.0696377	−	0.247739i	0.00267048	−	0.00950036i
$681$		0			0
$682$			5.21018i			0.199508i
$683$			20.4603i			0.782893i	0.920201	+	0.391447i	$0.128025\pi$
$683$			20.4603i			0.782893i	−0.920201	+	0.391447i	$0.871975\pi$
$684$		0			0
$685$	46.1770	+	12.9800i	1.76433	+	0.495941i
$686$	20.0000			0.763604
$687$		0			0
$688$		−	8.61056i		−	0.328275i
$689$	−0.150220			−0.00572292
$690$		0			0
$691$	−9.94678			−0.378393			−0.189197	−	0.981939i	$-0.560588\pi$
$691$	−9.94678			−0.378393			−0.189197	+	0.981939i	$0.560588\pi$
$692$		−	0.535454i		−	0.0203549i
$693$		0			0
$694$	31.9868			1.21420
$695$	9.93583	−	35.3472i	0.376888	−	1.34079i
$696$		0			0
$697$			0.230172i			0.00871839i
$698$		−	23.4513i		−	0.887645i
$699$		0			0
$700$	5.21018	−	8.53545i	0.196926	−	0.322610i
$701$	14.7898			0.558604			0.279302	−	0.960203i	$-0.409897\pi$
$701$	14.7898			0.558604			0.279302	+	0.960203i	$0.409897\pi$
$702$		0			0
$703$			0.760784i			0.0286935i
$704$	5.21018			0.196366
$705$		0			0
$706$	3.88491			0.146211
$707$		0			0
$708$		0			0
$709$	10.4336			0.391843			0.195921	−	0.980620i	$-0.437230\pi$
$709$	10.4336			0.391843			0.195921	+	0.980620i	$0.437230\pi$
$710$	−29.7511	−	8.36283i	−1.11654	−	0.313851i
$711$		0			0
$712$			2.23017i			0.0835792i
$713$		−	4.42037i		−	0.165544i
$714$		0			0
$715$	8.85830	+	2.49001i	0.331282	+	0.0931209i
$716$	−10.4313			−0.389836
$717$		0			0
$718$		−	21.3604i		−	0.797163i
$719$	−20.3320			−0.758256			−0.379128	−	0.925344i	$-0.623776\pi$
$719$	−20.3320			−0.758256			−0.379128	+	0.925344i	$0.623776\pi$
$720$		0			0
$721$	−12.0000			−0.446903
$722$		−	18.9868i		−	0.706614i
$723$		0			0
$724$	−17.4513			−0.648572
$725$	−18.8649	−	11.5155i	−0.700626	−	0.427674i
$726$		0			0
$727$			37.5132i			1.39129i	0.718387	+	0.695643i	$0.244881\pi$
$727$			37.5132i			1.39129i	−0.718387	+	0.695643i	$0.755119\pi$
$728$		−	1.57963i		−	0.0585450i
$729$		0			0
$730$	−6.55964	+	23.3362i	−0.242783	+	0.863712i
$731$	−0.990956			−0.0366518
$732$		0			0
$733$			28.6505i			1.05823i	0.848550	+	0.529116i	$0.177476\pi$
$733$			28.6505i			1.05823i	−0.848550	+	0.529116i	$0.822524\pi$
$734$	−20.4713			−0.755609
$735$		0			0
$736$	−4.42037			−0.162937
$737$			30.3272i			1.11712i
$738$		0			0
$739$	−21.6415			−0.796095			−0.398048	−	0.917365i	$-0.630312\pi$
$739$	−21.6415			−0.796095			−0.398048	+	0.917365i	$0.630312\pi$
$740$	−14.2302	−	4.00000i	−0.523112	−	0.147043i
$741$		0			0
$742$			0.380392i			0.0139646i
$743$			5.76983i			0.211674i	0.994383	+	0.105837i	$0.0337522\pi$
$743$			5.76983i			0.211674i	−0.994383	+	0.105837i	$0.966248\pi$
$744$		0			0
$745$	2.19682	−	7.81528i	0.0804852	−	0.286330i
$746$	9.76983			0.357699
$747$		0			0
$748$		−	0.599620i		−	0.0219243i
$749$	−6.06187			−0.221496
$750$		0			0
$751$	−31.7698			−1.15930			−0.579649	−	0.814866i	$-0.696810\pi$
$751$	−31.7698			−1.15930			−0.579649	+	0.814866i	$0.696810\pi$
$752$			0.115086i			0.00419676i
$753$		0			0
$754$	−3.49128			−0.127145
$755$	9.53418	−	33.9183i	0.346984	−	1.23441i
$756$		0			0
$757$		−	14.6905i		−	0.533936i	−0.963705	−	0.266968i	$-0.913978\pi$
$757$		−	14.6905i		−	0.533936i	0.963705	−	0.266968i	$-0.0860218\pi$
$758$		−	3.65474i		−	0.132746i
$759$		0			0
$760$	−0.247739	−	0.0696377i	−0.00898644	−	0.00252602i
$761$	−44.1528			−1.60054			−0.800268	−	0.599642i	$-0.795310\pi$
$761$	−44.1528			−1.60054			−0.800268	+	0.599642i	$0.795310\pi$
$762$		0			0
$763$		−	16.3804i		−	0.593010i
$764$	19.2611			0.696842
$765$		0			0
$766$	−25.4913			−0.921037
$767$		−	3.30948i		−	0.119499i
$768$		0			0
$769$	−2.07995			−0.0750050			−0.0375025	−	0.999297i	$-0.511940\pi$
$769$	−2.07995			−0.0750050			−0.0375025	+	0.999297i	$0.511940\pi$
$770$	6.30528	−	22.4313i	0.227227	−	0.808368i
$771$		0			0
$772$		−	14.4313i		−	0.519394i
$773$		−	30.1502i		−	1.08443i	−0.840240	−	0.542214i	$-0.817586\pi$
$773$		−	30.1502i		−	1.08443i	0.840240	−	0.542214i	$-0.182414\pi$
$774$		0			0
$775$	4.26773	+	2.60509i	0.153301	+	0.0935777i
$776$	9.21018			0.330626
$777$		0			0
$778$			4.65054i			0.166730i
$779$	0.230172			0.00824678
$780$		0			0
$781$	−72.0086			−2.57667
$782$			0.508723i			0.0181919i
$783$		0			0
$784$	3.00000			0.107143
$785$	−8.52451	−	2.39618i	−0.304253	−	0.0855233i
$786$		0			0
$787$		−	15.8717i		−	0.565764i	−0.959155	−	0.282882i	$-0.908710\pi$
$787$		−	15.8717i		−	0.565764i	0.959155	−	0.282882i	$-0.0912905\pi$
$788$		−	10.3804i		−	0.369786i
$789$		0			0
$790$	4.96245	+	1.39491i	0.176556	+	0.0496286i
$791$	−20.7608			−0.738169
$792$		0			0
$793$			9.86913i			0.350463i
$794$	26.7124			0.947988
$795$		0			0
$796$	14.5355			0.515196
$797$		−	25.6415i		−	0.908268i	−0.890933	−	0.454134i	$-0.849949\pi$
$797$		−	25.6415i		−	0.908268i	0.890933	−	0.454134i	$-0.150051\pi$
$798$		0			0
$799$	0.0132448			0.000468568
$800$	2.60509	−	4.26773i	0.0921039	−	0.150887i
$801$		0			0
$802$		−	16.0509i		−	0.566778i
$803$			56.4822i			1.99321i
$804$		0			0
$805$	−5.34946	+	19.0309i	−0.188544	+	0.670752i
$806$	0.789816			0.0278201
$807$		0			0
$808$		0			0
$809$	−37.7324			−1.32660			−0.663300	−	0.748353i	$-0.730845\pi$
$809$	−37.7324			−1.32660			−0.663300	+	0.748353i	$0.730845\pi$
$810$		0			0
$811$	9.22113			0.323798			0.161899	−	0.986807i	$-0.448238\pi$
$811$	9.22113			0.323798			0.161899	+	0.986807i	$0.448238\pi$
$812$			8.84074i			0.310249i
$813$		0			0
$814$	−34.4423			−1.20720
$815$	−21.1405	−	5.94246i	−0.740521	−	0.208155i
$816$		0			0
$817$			0.990956i			0.0346692i
$818$		−	9.87167i		−	0.345155i
$819$		0			0
$820$	−1.21018	+	4.30528i	−0.0422615	+	0.150347i
$821$	26.3804			0.920682			0.460341	−	0.887742i	$-0.347727\pi$
$821$	26.3804			0.920682			0.460341	+	0.887742i	$0.347727\pi$
$822$		0			0
$823$		−	24.0109i		−	0.836969i	−0.908224	−	0.418484i	$-0.862561\pi$
$823$		−	24.0109i		−	0.836969i	0.908224	−	0.418484i	$-0.137439\pi$
$824$	−6.00000			−0.209020
$825$		0			0
$826$	−8.38039			−0.291591
$827$		−	7.52641i		−	0.261719i	−0.991401	−	0.130859i	$-0.958226\pi$
$827$		−	7.52641i		−	0.261719i	0.991401	−	0.130859i	$-0.0417737\pi$
$828$		0			0
$829$	−7.30948			−0.253869			−0.126934	−	0.991911i	$-0.540514\pi$
$829$	−7.30948			−0.253869			−0.126934	+	0.991911i	$0.540514\pi$
$830$	−9.16474	+	32.6039i	−0.318113	+	1.13170i
$831$		0			0
$832$		−	0.789816i		−	0.0273819i
$833$		−	0.345258i		−	0.0119625i
$834$		0			0
$835$	−4.30528	−	1.21018i	−0.148990	−	0.0418801i
$836$	−0.599620			−0.0207383
$837$		0			0
$838$		−	0.420368i		−	0.0145214i
$839$	−45.2430			−1.56196			−0.780981	−	0.624555i	$-0.785281\pi$
$839$	−45.2430			−1.56196			−0.780981	+	0.624555i	$0.785281\pi$
$840$		0			0
$841$	−9.46034			−0.326219
$842$		−	39.2211i		−	1.35165i
$843$		0			0
$844$	−24.8407			−0.855053
$845$	−7.48873	+	26.6415i	−0.257620	+	0.916495i
$846$		0			0
$847$		−	32.2920i		−	1.10957i
$848$			0.190196i			0.00653136i
$849$		0			0
$850$	−0.491156	−	0.299810i	−0.0168465	−	0.0102834i
$851$	29.2211			1.00169
$852$		0			0
$853$		−	9.11088i		−	0.311951i	−0.987761	−	0.155975i	$-0.950148\pi$
$853$		−	9.11088i		−	0.311951i	0.987761	−	0.155975i	$-0.0498521\pi$
$854$	24.9910			0.855173
$855$		0			0
$856$	−3.03093			−0.103595
$857$		−	6.99096i		−	0.238807i	−0.992846	−	0.119403i	$-0.961902\pi$
$857$		−	6.99096i		−	0.238807i	0.992846	−	0.119403i	$-0.0380981\pi$
$858$		0			0
$859$	17.6196			0.601173			0.300587	−	0.953755i	$-0.402818\pi$
$859$	17.6196			0.601173			0.300587	+	0.953755i	$0.402818\pi$
$860$	−18.5355	−	5.21018i	−0.632054	−	0.177666i
$861$		0			0
$862$			6.88071i			0.234358i
$863$		−	45.8717i		−	1.56149i	−0.624850	−	0.780745i	$-0.714840\pi$
$863$		−	45.8717i		−	1.56149i	0.624850	−	0.780745i	$-0.285160\pi$
$864$		0			0
$865$	−1.15264	−	0.323999i	−0.0391910	−	0.0110163i
$866$	1.38944			0.0472149
$867$		0			0
$868$		−	2.00000i		−	0.0678844i
$869$	12.0109			0.407443
$870$		0			0
$871$	4.59732			0.155774
$872$		−	8.19020i		−	0.277355i
$873$		0			0
$874$	0.508723			0.0172078
$875$	−15.2211	−	16.3804i	−0.514568	−	0.553758i
$876$		0			0
$877$		−	48.4204i		−	1.63504i	−0.575900	−	0.817520i	$-0.695348\pi$
$877$		−	48.4204i		−	1.63504i	0.575900	−	0.817520i	$-0.304652\pi$
$878$		−	19.8717i		−	0.670636i
$879$		0			0
$880$	3.15264	−	11.2157i	0.106276	−	0.378080i
$881$	34.7717			1.17149			0.585745	−	0.810496i	$-0.300802\pi$
$881$	34.7717			1.17149			0.585745	+	0.810496i	$0.300802\pi$
$882$		0			0
$883$		−	35.7214i		−	1.20212i	−0.799203	−	0.601061i	$-0.794745\pi$
$883$		−	35.7214i		−	1.20212i	0.799203	−	0.601061i	$-0.205255\pi$
$884$	−0.0908968			−0.00305719
$885$		0			0
$886$	8.61056			0.289278
$887$			24.7608i			0.831386i	0.909505	+	0.415693i	$0.136461\pi$
$887$			24.7608i			0.831386i	−0.909505	+	0.415693i	$0.863539\pi$
$888$		0			0
$889$	20.8407			0.698976
$890$	4.80076	+	1.34946i	0.160922	+	0.0452340i
$891$		0			0
$892$			19.6306i			0.657280i
$893$		−	0.0132448i		−	0.000443221i
$894$		0			0
$895$	−6.31190	+	22.4549i	−0.210984	+	0.750584i
$896$	−2.00000			−0.0668153
$897$		0			0
$898$		−	10.3694i		−	0.346033i
$899$	−4.42037			−0.147428
$900$		0			0
$901$	0.0218889			0.000729226
$902$			10.4204i			0.346960i
$903$		0			0
$904$	−10.3804			−0.345247
$905$	−10.5596	+	37.5664i	−0.351014	+	1.24875i
$906$		0			0
$907$		−	20.5197i		−	0.681344i	−0.940182	−	0.340672i	$-0.889345\pi$
$907$		−	20.5197i		−	0.681344i	0.940182	−	0.340672i	$-0.110655\pi$
$908$			6.42037i			0.213067i
$909$		0			0
$910$	−3.40038	−	0.955823i	−0.112722	−	0.0316852i
$911$	27.1593			0.899827			0.449913	−	0.893072i	$-0.351455\pi$
$911$	27.1593			0.899827			0.449913	+	0.893072i	$0.351455\pi$
$912$		0			0
$913$			78.9135i			2.61166i
$914$	−21.4913			−0.710868
$915$		0			0
$916$	−29.7166			−0.981864
$917$		−	0.380392i		−	0.0125617i
$918$		0			0
$919$	37.5531			1.23876			0.619382	−	0.785090i	$-0.287383\pi$
$919$	37.5531			1.23876			0.619382	+	0.785090i	$0.287383\pi$
$920$	−2.67473	+	9.51547i	−0.0881832	+	0.313716i
$921$		0			0
$922$		−	3.34946i		−	0.110309i
$923$			10.9158i			0.359299i
$924$		0			0
$925$	−17.2211	+	28.2121i	−0.566227	+	0.927608i
$926$	28.0109			0.920497
$927$		0			0
$928$			4.42037i			0.145106i
$929$	28.2121			0.925608			0.462804	−	0.886461i	$-0.346843\pi$
$929$	28.2121			0.925608			0.462804	+	0.886461i	$0.346843\pi$
$930$		0			0
$931$	−0.345258			−0.0113154
$932$			5.38944i			0.176537i
$933$		0			0
$934$	37.6815			1.23298
$935$	−1.29077	−	0.362825i	−0.0422126	−	0.0118657i
$936$		0			0
$937$			54.0728i			1.76648i	0.468920	+	0.883241i	$0.344643\pi$
$937$			54.0728i			1.76648i	−0.468920	+	0.883241i	$0.655357\pi$
$938$		−	11.6415i		−	0.380108i
$939$		0			0
$940$	0.247739	+	0.0696377i	0.00808036	+	0.00227133i
$941$	−27.9600			−0.911471			−0.455735	−	0.890115i	$-0.650624\pi$
$941$	−27.9600			−0.911471			−0.455735	+	0.890115i	$0.650624\pi$
$942$		0			0
$943$		−	8.84074i		−	0.287894i
$944$	−4.19020			−0.136379
$945$		0			0
$946$	−44.8626			−1.45861
$947$		−	6.68567i		−	0.217255i	−0.994083	−	0.108628i	$-0.965354\pi$
$947$		−	6.68567i		−	0.217255i	0.994083	−	0.108628i	$-0.0346456\pi$
$948$		0			0
$949$	8.56219			0.277940
$950$	−0.299810	+	0.491156i	−0.00972712	+	0.0159352i
$951$		0			0
$952$			0.230172i			0.00745992i
$953$		−	33.3362i		−	1.07987i	−0.841708	−	0.539933i	$-0.818450\pi$
$953$		−	33.3362i		−	1.07987i	0.841708	−	0.539933i	$-0.181550\pi$
$954$		0			0
$955$	11.6547	−	41.4622i	0.377139	−	1.34169i
$956$	−7.03093			−0.227397
$957$		0			0
$958$		−	10.2811i		−	0.332167i
$959$	−42.9026			−1.38540
$960$		0			0
$961$	1.00000			0.0322581
$962$			5.22113i			0.168336i
$963$		0			0
$964$	0.190196			0.00612580
$965$	−31.0654	−	8.73227i	−1.00003	−	0.281102i
$966$		0			0
$967$		−	40.1128i		−	1.28994i	−0.764208	−	0.644970i	$-0.776870\pi$
$967$		−	40.1128i		−	1.28994i	0.764208	−	0.644970i	$-0.223130\pi$
$968$		−	16.1460i		−	0.518953i
$969$		0			0
$970$	5.57301	−	19.8262i	0.178939	−	0.636582i
$971$	53.1547			1.70581			0.852907	−	0.522063i	$-0.174837\pi$
$971$	53.1547			1.70581			0.852907	+	0.522063i	$0.174837\pi$
$972$		0			0
$973$			32.8407i			1.05283i
$974$	−32.9316			−1.05520
$975$		0			0
$976$	12.4955			0.399971
$977$			37.2830i			1.19279i	0.802692	+	0.596394i	$0.203401\pi$
$977$			37.2830i			1.19279i	−0.802692	+	0.596394i	$0.796599\pi$
$978$		0			0
$979$	11.6196			0.371364
$980$	1.81528	−	6.45792i	0.0579869	−	0.206291i
$981$		0			0
$982$			41.7034i			1.33081i
$983$		−	45.6415i		−	1.45574i	−0.685716	−	0.727869i	$-0.740511\pi$
$983$		−	45.6415i		−	1.45574i	0.685716	−	0.727869i	$-0.259489\pi$
$984$		0			0
$985$	−22.3453	−	6.28109i	−0.711979	−	0.200132i
$986$	0.508723			0.0162010
$987$		0			0
$988$			0.0908968i			0.00289181i
$989$	38.0619			1.21030
$990$		0			0
$991$	58.9026			1.87110			0.935551	−	0.353191i	$-0.114903\pi$
$991$	58.9026			1.87110			0.935551	+	0.353191i	$0.114903\pi$
$992$		−	1.00000i		−	0.0317500i
$993$		0			0
$994$	27.6415			0.876735
$995$	8.79529	−	31.2896i	0.278829	−	0.991948i
$996$		0			0
$997$		−	4.11024i		−	0.130173i	−0.997880	−	0.0650864i	$-0.979268\pi$
$997$		−	4.11024i		−	0.130173i	0.997880	−	0.0650864i	$-0.0207323\pi$
$998$		−	22.2302i		−	0.703684i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2790.2.d.j.559.4		6
3.2	odd	2		930.2.d.i.559.3	✓	6
5.4	even	2	inner	2790.2.d.j.559.1		6
15.2	even	4		4650.2.a.cp.1.3		3
15.8	even	4		4650.2.a.ci.1.3		3
15.14	odd	2		930.2.d.i.559.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.i.559.3	✓	6	3.2	odd	2
930.2.d.i.559.6	yes	6	15.14	odd	2
2790.2.d.j.559.1		6	5.4	even	2	inner
2790.2.d.j.559.4		6	1.1	even	1	trivial
4650.2.a.ci.1.3		3	15.8	even	4
4650.2.a.cp.1.3		3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.605092 + 2.15264i) q^{5} -2.00000i q^{7} -1.00000i q^{8} +(-2.15264 - 0.605092i) q^{10} -5.21018 q^{11} +0.789816i q^{13} +2.00000 q^{14} +1.00000 q^{16} -0.115086i q^{17} -0.115086 q^{19} +(0.605092 - 2.15264i) q^{20} -5.21018i q^{22} +4.42037i q^{23} +(-4.26773 - 2.60509i) q^{25} -0.789816 q^{26} +2.00000i q^{28} +4.42037 q^{29} -1.00000 q^{31} +1.00000i q^{32} +0.115086 q^{34} +(4.30528 + 1.21018i) q^{35} -6.61056i q^{37} -0.115086i q^{38} +(2.15264 + 0.605092i) q^{40} -2.00000 q^{41} -8.61056i q^{43} +5.21018 q^{44} -4.42037 q^{46} +0.115086i q^{47} +3.00000 q^{49} +(2.60509 - 4.26773i) q^{50} -0.789816i q^{52} +0.190196i q^{53} +(3.15264 - 11.2157i) q^{55} -2.00000 q^{56} +4.42037i q^{58} -4.19020 q^{59} +12.4955 q^{61} -1.00000i q^{62} -1.00000 q^{64} +(-1.70019 - 0.477911i) q^{65} -5.82075i q^{67} +0.115086i q^{68} +(-1.21018 + 4.30528i) q^{70} +13.8207 q^{71} -10.8407i q^{73} +6.61056 q^{74} +0.115086 q^{76} +10.4204i q^{77} -2.30528 q^{79} +(-0.605092 + 2.15264i) q^{80} -2.00000i q^{82} -15.1460i q^{83} +(0.247739 + 0.0696377i) q^{85} +8.61056 q^{86} +5.21018i q^{88} -2.23017 q^{89} +1.57963 q^{91} -4.42037i q^{92} -0.115086 q^{94} +(0.0696377 - 0.247739i) q^{95} +9.21018i q^{97} +3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 4 q^{5} - 16 q^{11} + 12 q^{14} + 6 q^{16} + 4 q^{19} - 4 q^{20} - 8 q^{25} - 20 q^{26} - 4 q^{29} - 6 q^{31} - 4 q^{34} - 12 q^{41} + 16 q^{44} + 4 q^{46} + 18 q^{49} + 8 q^{50} + 6 q^{55}+ \cdots + 28 q^{95}+O(q^{100}) \) 6 * q - 6 * q^4 + 4 * q^5 - 16 * q^11 + 12 * q^14 + 6 * q^16 + 4 * q^19 - 4 * q^20 - 8 * q^25 - 20 * q^26 - 4 * q^29 - 6 * q^31 - 4 * q^34 - 12 * q^41 + 16 * q^44 + 4 * q^46 + 18 * q^49 + 8 * q^50 + 6 * q^55 - 12 * q^56 - 4 * q^59 + 28 * q^61 - 6 * q^64 + 8 * q^65 + 8 * q^70 + 16 * q^71 - 12 * q^74 - 4 * q^76 + 12 * q^79 + 4 * q^80 - 22 * q^85 - 4 * q^89 + 40 * q^91 + 4 * q^94 + 28 * q^95

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