LMFDB - Embedded newform 855.2.b.d.854.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(854,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.854"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-56,0,0,0,0,0,0,0,0,0,0,0,8,0,0,32,0,0,0,0,0,-8,0,0,0, 0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(29)] == traces)

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			854.14
Character	$\chi$	$=$	855.854
Dual form			855.2.b.d.854.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.53119i q^{2} -0.344558 q^{4} +(-0.586990 + 2.15765i) q^{5} +4.30101i q^{7} +2.53480i q^{8} +(-3.30378 - 0.898797i) q^{10} -0.183502i q^{11} +5.46922 q^{13} -6.58568 q^{14} -4.57040 q^{16} -5.69781 q^{17} +(2.39593 - 3.64136i) q^{19} +(0.202252 - 0.743434i) q^{20} +0.280977 q^{22} +2.02354 q^{23} +(-4.31088 - 2.53304i) q^{25} +8.37443i q^{26} -1.48195i q^{28} +8.36004 q^{29} -6.92686i q^{31} -1.92856i q^{32} -8.72445i q^{34} +(-9.28006 - 2.52465i) q^{35} +2.44641 q^{37} +(5.57563 + 3.66864i) q^{38} +(-5.46922 - 1.48791i) q^{40} -11.7353 q^{41} +7.66418i q^{43} +0.0632269i q^{44} +3.09843i q^{46} -0.384738 q^{47} -11.4987 q^{49} +(3.87857 - 6.60080i) q^{50} -1.88446 q^{52} +1.00361i q^{53} +(0.395932 + 0.107714i) q^{55} -10.9022 q^{56} +12.8008i q^{58} +2.60748 q^{59} +9.55005 q^{61} +10.6064 q^{62} -6.18780 q^{64} +(-3.21038 + 11.8006i) q^{65} -13.6658 q^{67} +1.96322 q^{68} +(3.86573 - 14.2096i) q^{70} +7.18858 q^{71} -4.69475i q^{73} +3.74594i q^{74} +(-0.825537 + 1.25466i) q^{76} +0.789242 q^{77} +9.31356i q^{79} +(2.68278 - 9.86130i) q^{80} -17.9691i q^{82} +11.2235 q^{83} +(3.34456 - 12.2939i) q^{85} -11.7353 q^{86} +0.465141 q^{88} -0.668196 q^{89} +23.5231i q^{91} -0.697224 q^{92} -0.589109i q^{94} +(6.45038 + 7.30702i) q^{95} -2.55766 q^{97} -17.6067i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 56 q^{4} + 8 q^{16} + 32 q^{19} - 8 q^{25} - 104 q^{49} - 16 q^{55} - 16 q^{61} - 72 q^{64} - 112 q^{76} + 128 q^{85}+O(q^{100}) $ 24 * q - 56 * q^4 + 8 * q^16 + 32 * q^19 - 8 * q^25 - 104 * q^49 - 16 * q^55 - 16 * q^61 - 72 * q^64 - 112 * q^76 + 128 * q^85

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$			1.53119i			1.08272i	0.840791	+	0.541359i	$0.182090\pi$
$2$			1.53119i			1.08272i	−0.840791	+	0.541359i	$0.817910\pi$
$3$		0			0
$3$		0			0
$4$	−0.344558			−0.172279
$5$	−0.586990	+	2.15765i	−0.262510	+	0.964929i
$5$	−0.586990	+	2.15765i	−0.262510	+	0.964929i
$6$		0			0
$7$			4.30101i			1.62563i	0.582523	+	0.812814i	$0.302066\pi$
$7$			4.30101i			1.62563i	−0.582523	+	0.812814i	$0.697934\pi$
$8$			2.53480i			0.896189i
$9$		0			0
$10$	−3.30378	−	0.898797i	−1.04475	−	0.284224i
$11$		−	0.183502i		−	0.0553278i	−0.999617	−	0.0276639i	$-0.991193\pi$
$11$		−	0.183502i		−	0.0553278i	0.999617	−	0.0276639i	$-0.00880682\pi$
$12$		0			0
$13$	5.46922			1.51689			0.758444	−	0.651739i	$-0.225960\pi$
$13$	5.46922			1.51689			0.758444	+	0.651739i	$0.225960\pi$
$14$	−6.58568			−1.76010
$15$		0			0
$16$	−4.57040			−1.14260
$17$	−5.69781			−1.38192			−0.690961	−	0.722892i	$-0.742812\pi$
$17$	−5.69781			−1.38192			−0.690961	+	0.722892i	$0.742812\pi$
$18$		0			0
$19$	2.39593	−	3.64136i	0.549664	−	0.835386i
$19$	2.39593	−	3.64136i	0.549664	−	0.835386i
$20$	0.202252	−	0.743434i	0.0452249	−	0.166237i
$21$		0			0
$22$	0.280977			0.0599045
$23$	2.02354			0.421936			0.210968	−	0.977493i	$-0.432338\pi$
$23$	2.02354			0.421936			0.210968	+	0.977493i	$0.432338\pi$
$24$		0			0
$25$	−4.31088	−	2.53304i	−0.862177	−	0.506607i
$26$			8.37443i			1.64236i
$27$		0			0
$28$		−	1.48195i		−	0.280061i
$29$	8.36004			1.55242			0.776210	−	0.630474i	$-0.217140\pi$
$29$	8.36004			1.55242			0.776210	+	0.630474i	$0.217140\pi$
$30$		0			0
$31$		−	6.92686i		−	1.24410i	−0.782977	−	0.622050i	$-0.786300\pi$
$31$		−	6.92686i		−	1.24410i	0.782977	−	0.622050i	$-0.213700\pi$
$32$		−	1.92856i		−	0.340924i
$33$		0			0
$34$		−	8.72445i		−	1.49623i
$35$	−9.28006	−	2.52465i	−1.56862	−	0.426744i
$36$		0			0
$37$	2.44641			0.402188			0.201094	−	0.979572i	$-0.435550\pi$
$37$	2.44641			0.402188			0.201094	+	0.979572i	$0.435550\pi$
$38$	5.57563	+	3.66864i	0.904487	+	0.595132i
$39$		0			0
$40$	−5.46922	−	1.48791i	−0.864759	−	0.235259i
$41$	−11.7353			−1.83275			−0.916377	−	0.400317i	$-0.868900\pi$
$41$	−11.7353			−1.83275			−0.916377	+	0.400317i	$0.868900\pi$
$42$		0			0
$43$			7.66418i			1.16878i	0.811474	+	0.584388i	$0.198665\pi$
$43$			7.66418i			1.16878i	−0.811474	+	0.584388i	$0.801335\pi$
$44$			0.0632269i			0.00953181i
$45$		0			0
$46$			3.09843i			0.456838i
$47$	−0.384738			−0.0561199			−0.0280599	−	0.999606i	$-0.508933\pi$
$47$	−0.384738			−0.0561199			−0.0280599	+	0.999606i	$0.508933\pi$
$48$		0			0
$49$	−11.4987			−1.64267
$50$	3.87857	−	6.60080i	0.548513	−	0.933495i
$51$		0			0
$52$	−1.88446			−0.261328
$53$			1.00361i			0.137856i	0.997622	+	0.0689282i	$0.0219579\pi$
$53$			1.00361i			0.137856i	−0.997622	+	0.0689282i	$0.978042\pi$
$54$		0			0
$55$	0.395932	+	0.107714i	0.0533874	+	0.0145241i
$56$	−10.9022			−1.45687
$57$		0			0
$58$			12.8008i			1.68083i
$59$	2.60748			0.339465			0.169733	−	0.985490i	$-0.445710\pi$
$59$	2.60748			0.339465			0.169733	+	0.985490i	$0.445710\pi$
$60$		0			0
$61$	9.55005			1.22276			0.611380	−	0.791337i	$-0.290615\pi$
$61$	9.55005			1.22276			0.611380	+	0.791337i	$0.290615\pi$
$62$	10.6064			1.34701
$63$		0			0
$64$	−6.18780			−0.773474
$65$	−3.21038	+	11.8006i	−0.398198	+	1.46369i
$66$		0			0
$67$	−13.6658			−1.66955			−0.834773	−	0.550595i	$-0.814401\pi$
$67$	−13.6658			−1.66955			−0.834773	+	0.550595i	$0.814401\pi$
$68$	1.96322			0.238076
$69$		0			0
$70$	3.86573	−	14.2096i	0.462043	−	1.69837i
$71$	7.18858			0.853127			0.426564	−	0.904458i	$-0.359724\pi$
$71$	7.18858			0.853127			0.426564	+	0.904458i	$0.359724\pi$
$72$		0			0
$73$		−	4.69475i		−	0.549479i	−0.961519	−	0.274739i	$-0.911408\pi$
$73$		−	4.69475i		−	0.549479i	0.961519	−	0.274739i	$-0.0885916\pi$
$74$			3.74594i			0.435456i
$75$		0			0
$76$	−0.825537	+	1.25466i	−0.0946955	+	0.143919i
$77$	0.789242			0.0899425
$78$		0			0
$79$			9.31356i			1.04786i	0.851762	+	0.523929i	$0.175534\pi$
$79$			9.31356i			1.04786i	−0.851762	+	0.523929i	$0.824466\pi$
$80$	2.68278	−	9.86130i	0.299944	−	1.10253i
$81$		0			0
$82$		−	17.9691i		−	1.98436i
$83$	11.2235			1.23194			0.615971	−	0.787769i	$-0.288764\pi$
$83$	11.2235			1.23194			0.615971	+	0.787769i	$0.288764\pi$
$84$		0			0
$85$	3.34456	−	12.2939i	0.362768	−	1.33346i
$86$	−11.7353			−1.26545
$87$		0			0
$88$	0.465141			0.0495842
$89$	−0.668196			−0.0708286			−0.0354143	−	0.999373i	$-0.511275\pi$
$89$	−0.668196			−0.0708286			−0.0354143	+	0.999373i	$0.511275\pi$
$90$		0			0
$91$			23.5231i			2.46590i
$92$	−0.697224			−0.0726907
$93$		0			0
$94$		−	0.589109i		−	0.0607620i
$95$	6.45038	+	7.30702i	0.661795	+	0.749684i
$96$		0			0
$97$	−2.55766			−0.259691			−0.129846	−	0.991534i	$-0.541448\pi$
$97$	−2.55766			−0.259691			−0.129846	+	0.991534i	$0.541448\pi$
$98$		−	17.6067i		−	1.77855i
$99$		0			0
$100$	1.48535	+	0.872777i	0.148535	+	0.0872777i
$101$			10.5321i			1.04798i	0.851724	+	0.523991i	$0.175557\pi$
$101$			10.5321i			1.04798i	−0.851724	+	0.523991i	$0.824443\pi$
$102$		0			0
$103$	0.857365			0.0844787			0.0422394	−	0.999108i	$-0.486551\pi$
$103$	0.857365			0.0844787			0.0422394	+	0.999108i	$0.486551\pi$
$104$			13.8634i			1.35942i
$105$		0			0
$106$	−1.53672			−0.149260
$107$		−	8.94714i		−	0.864952i	−0.901645	−	0.432476i	$-0.857640\pi$
$107$		−	8.94714i		−	0.864952i	0.901645	−	0.432476i	$-0.142360\pi$
$108$		0			0
$109$		−	7.28272i		−	0.697558i	−0.937205	−	0.348779i	$-0.886596\pi$
$109$		−	7.28272i		−	0.697558i	0.937205	−	0.348779i	$-0.113404\pi$
$110$	−0.164931	+	0.606249i	−0.0157255	+	0.0578036i
$111$		0			0
$112$		−	19.6573i		−	1.85744i
$113$		−	13.0131i		−	1.22417i	−0.790791	−	0.612086i	$-0.790330\pi$
$113$		−	13.0131i		−	1.22417i	0.790791	−	0.612086i	$-0.209670\pi$
$114$		0			0
$115$	−1.18780	+	4.36608i	−0.110763	+	0.407139i
$116$	−2.88051			−0.267449
$117$		0			0
$118$			3.99256i			0.367545i
$119$		−	24.5063i		−	2.24649i
$120$		0			0
$121$	10.9663			0.996939
$122$			14.6230i			1.32390i
$123$		0			0
$124$			2.38670i			0.214332i
$125$	7.99585	−	7.81450i	0.715170	−	0.698950i
$126$		0			0
$127$	9.63036			0.854556			0.427278	−	0.904120i	$-0.359473\pi$
$127$	9.63036			0.854556			0.427278	+	0.904120i	$0.359473\pi$
$128$		−	13.3318i		−	1.17838i
$129$		0			0
$130$	−18.0691	−	4.91571i	−1.58476	−	0.431136i
$131$		−	4.93845i		−	0.431475i	−0.976451	−	0.215737i	$-0.930784\pi$
$131$		−	4.93845i		−	0.431475i	0.976451	−	0.215737i	$-0.0692155\pi$
$132$		0			0
$133$	15.6615	+	10.3049i	1.35803	+	0.893550i
$134$		−	20.9250i		−	1.80765i
$135$		0			0
$136$		−	14.4428i		−	1.23846i
$137$	−11.2433			−0.960579			−0.480289	−	0.877110i	$-0.659468\pi$
$137$	−11.2433			−0.960579			−0.480289	+	0.877110i	$0.659468\pi$
$138$		0			0
$139$	17.9327			1.52103			0.760514	−	0.649322i	$-0.224947\pi$
$139$	17.9327			1.52103			0.760514	+	0.649322i	$0.224947\pi$
$140$	3.19752	+	0.869888i	0.270239	+	0.0735189i
$141$		0			0
$142$			11.0071i			0.923696i
$143$		−	1.00361i		−	0.0839261i
$144$		0			0
$145$	−4.90726	+	18.0380i	−0.407526	+	1.49798i
$146$	7.18858			0.594931
$147$		0			0
$148$	−0.842930			−0.0692884
$149$			5.90358i			0.483640i	0.970321	+	0.241820i	$0.0777444\pi$
$149$			5.90358i			0.483640i	−0.970321	+	0.241820i	$0.922256\pi$
$150$		0			0
$151$			5.98189i			0.486799i	0.969926	+	0.243400i	$0.0782626\pi$
$151$			5.98189i			0.486799i	−0.969926	+	0.243400i	$0.921737\pi$
$152$	9.23014	+	6.07322i	0.748663	+	0.492603i
$153$		0			0
$154$			1.20848i			0.0973824i
$155$	14.9457	+	4.06600i	1.20047	+	0.326589i
$156$		0			0
$157$			12.0784i			0.963964i	0.876181	+	0.481982i	$0.160083\pi$
$157$			12.0784i			0.963964i	−0.876181	+	0.481982i	$0.839917\pi$
$158$	−14.2609			−1.13453
$159$		0			0
$160$	4.16114	+	1.13204i	0.328967	+	0.0894959i
$161$			8.70324i			0.685912i
$162$		0			0
$163$			7.62153i			0.596964i	0.954415	+	0.298482i	$0.0964803\pi$
$163$			7.62153i			0.596964i	−0.954415	+	0.298482i	$0.903520\pi$
$164$	4.04350			0.315745
$165$		0			0
$166$			17.1854i			1.33385i
$167$			11.8006i			0.913161i	0.889682	+	0.456580i	$0.150926\pi$
$167$			11.8006i			0.913161i	−0.889682	+	0.456580i	$0.849074\pi$
$168$		0			0
$169$	16.9123			1.30095
$170$	18.8243	+	5.12117i	1.44376	+	0.392776i
$171$		0			0
$172$		−	2.64075i		−	0.201355i
$173$		−	11.9580i		−	0.909147i	−0.890709	−	0.454574i	$-0.849792\pi$
$173$		−	11.9580i		−	0.909147i	0.890709	−	0.454574i	$-0.150208\pi$
$174$		0			0
$175$	10.8946	−	18.5412i	0.823555	−	1.40158i
$176$			0.838675i			0.0632175i
$177$		0			0
$178$		−	1.02314i		−	0.0766874i
$179$	20.8632			1.55939			0.779695	−	0.626160i	$-0.215374\pi$
$179$	20.8632			1.55939			0.779695	+	0.626160i	$0.215374\pi$
$180$		0			0
$181$			7.28272i			0.541320i	0.962675	+	0.270660i	$0.0872420\pi$
$181$			7.28272i			0.541320i	−0.962675	+	0.270660i	$0.912758\pi$
$182$	−36.0185			−2.66987
$183$		0			0
$184$			5.12927i			0.378135i
$185$	−1.43602	+	5.27850i	−0.105578	+	0.388083i
$186$		0			0
$187$			1.04556i			0.0764587i
$188$	0.132565			0.00966826
$189$		0			0
$190$	−11.1885	+	9.87680i	−0.811697	+	0.716538i
$191$			5.57104i			0.403106i	0.979478	+	0.201553i	$0.0645989\pi$
$191$			5.57104i			0.403106i	−0.979478	+	0.201553i	$0.935401\pi$
$192$		0			0
$193$	−17.8270			−1.28321			−0.641606	−	0.767034i	$-0.721732\pi$
$193$	−17.8270			−1.28321			−0.641606	+	0.767034i	$0.721732\pi$
$194$		−	3.91628i		−	0.281172i
$195$		0			0
$196$	3.96196			0.282997
$197$	5.45346			0.388543			0.194271	−	0.980948i	$-0.437766\pi$
$197$	5.45346			0.388543			0.194271	+	0.980948i	$0.437766\pi$
$198$		0			0
$199$	−14.2055			−1.00700			−0.503500	−	0.863995i	$-0.667955\pi$
$199$	−14.2055			−1.00700			−0.503500	+	0.863995i	$0.667955\pi$
$200$	6.42075	−	10.9273i	0.454016	−	0.772673i
$201$		0			0
$202$	−16.1267			−1.13467
$203$			35.9566i			2.52366i
$204$		0			0
$205$	6.88853	−	25.3207i	0.481116	−	1.76848i
$206$			1.31279i			0.0914666i
$207$		0			0
$208$	−24.9965			−1.73319
$209$	−0.668196	−	0.439657i	−0.0462201	−	0.0304117i
$210$		0			0
$211$			17.6822i			1.21729i	0.793443	+	0.608645i	$0.208287\pi$
$211$			17.6822i			1.21729i	−0.793443	+	0.608645i	$0.791713\pi$
$212$		−	0.345801i		−	0.0237497i
$213$		0			0
$214$	13.6998			0.936500
$215$	−16.5366	−	4.49880i	−1.12779	−	0.306815i
$216$		0			0
$217$	29.7925			2.02245
$218$	11.1513			0.755259
$219$		0			0
$220$	−0.136421	−	0.0371136i	−0.00919752	−	0.00250220i
$221$	−31.1625			−2.09622
$222$		0			0
$223$	12.3577			0.827536			0.413768	−	0.910382i	$-0.364212\pi$
$223$	12.3577			0.827536			0.413768	+	0.910382i	$0.364212\pi$
$224$	8.29474			0.554215
$225$		0			0
$226$	19.9256			1.32543
$227$		−	21.1451i		−	1.40345i	−0.712447	−	0.701726i	$-0.752413\pi$
$227$		−	21.1451i		−	1.40345i	0.712447	−	0.701726i	$-0.247587\pi$
$228$		0			0
$229$	−19.7422			−1.30460			−0.652301	−	0.757960i	$-0.726196\pi$
$229$	−19.7422			−1.30460			−0.652301	+	0.757960i	$0.726196\pi$
$230$	−6.68531	−	1.81875i	−0.440816	−	0.119925i
$231$		0			0
$232$			21.1911i			1.39126i
$233$	−15.7473			−1.03164			−0.515821	−	0.856696i	$-0.672513\pi$
$233$	−15.7473			−1.03164			−0.515821	+	0.856696i	$0.672513\pi$
$234$		0			0
$235$	0.225838	−	0.830130i	0.0147320	−	0.0541517i
$236$	−0.898428			−0.0584827
$237$		0			0
$238$	37.5240			2.43232
$239$			4.76438i			0.308182i	0.988057	+	0.154091i	$0.0492449\pi$
$239$			4.76438i			0.308182i	−0.988057	+	0.154091i	$0.950755\pi$
$240$		0			0
$241$			24.8240i			1.59905i	0.600631	+	0.799527i	$0.294916\pi$
$241$			24.8240i			1.59905i	−0.600631	+	0.799527i	$0.705084\pi$
$242$			16.7916i			1.07940i
$243$		0			0
$244$	−3.29054			−0.210655
$245$	6.74961	−	24.8101i	0.431217	−	1.58506i
$246$		0			0
$247$	13.1039	−	19.9154i	0.833779	−	1.26719i
$248$	17.5582			1.11495
$249$		0			0
$250$	11.9655	+	12.2432i	0.756766	+	0.774328i
$251$		−	17.0526i		−	1.07635i	−0.842832	−	0.538177i	$-0.819113\pi$
$251$		−	17.0526i		−	1.07635i	0.842832	−	0.538177i	$-0.180887\pi$
$252$		0			0
$253$		−	0.371322i		−	0.0233448i
$254$			14.7460i			0.925244i
$255$		0			0
$256$	8.03804			0.502378
$257$		−	2.21611i		−	0.138237i	−0.997608	−	0.0691185i	$-0.977981\pi$
$257$		−	2.21611i		−	0.138237i	0.997608	−	0.0691185i	$-0.0220187\pi$
$258$		0			0
$259$			10.5220i			0.653808i
$260$	1.10616	−	4.06600i	0.0686011	−	0.252163i
$261$		0			0
$262$	7.56174			0.467166
$263$	−15.0579			−0.928513			−0.464256	−	0.885701i	$-0.653678\pi$
$263$	−15.0579			−0.928513			−0.464256	+	0.885701i	$0.653678\pi$
$264$		0			0
$265$	−2.16544	−	0.589109i	−0.133022	−	0.0361887i
$266$	−15.7788	+	23.9809i	−0.967463	+	1.47036i
$267$		0			0
$268$	4.70866			0.287627
$269$	14.3428			0.874498			0.437249	−	0.899341i	$-0.355953\pi$
$269$	14.3428			0.874498			0.437249	+	0.899341i	$0.355953\pi$
$270$		0			0
$271$	30.2055			1.83485			0.917427	−	0.397905i	$-0.130263\pi$
$271$	30.2055			1.83485			0.917427	+	0.397905i	$0.130263\pi$
$272$	26.0412			1.57898
$273$		0			0
$274$		−	17.2157i		−	1.04004i
$275$	−0.464816	+	0.791054i	−0.0280295	+	0.0477024i
$276$		0			0
$277$			15.1129i			0.908048i	0.890990	+	0.454024i	$0.150012\pi$
$277$			15.1129i			0.908048i	−0.890990	+	0.454024i	$0.849988\pi$
$278$			27.4584i			1.64684i
$279$		0			0
$280$	6.39950	−	23.5231i	0.382443	−	1.40578i
$281$	11.9999			0.715854			0.357927	−	0.933750i	$-0.383484\pi$
$281$	11.9999			0.715854			0.357927	+	0.933750i	$0.383484\pi$
$282$		0			0
$283$		−	9.28179i		−	0.551745i	−0.961194	−	0.275872i	$-0.911033\pi$
$283$		−	9.28179i		−	0.551745i	0.961194	−	0.275872i	$-0.0889668\pi$
$284$	−2.47688			−0.146976
$285$		0			0
$286$	1.53672			0.0908683
$287$		−	50.4738i		−	2.97938i
$288$		0			0
$289$	15.4650			0.909706
$290$	−27.6197	−	7.51397i	−1.62189	−	0.441236i
$291$		0			0
$292$			1.61761i			0.0946636i
$293$		−	10.9855i		−	0.641780i	−0.947116	−	0.320890i	$-0.896018\pi$
$293$		−	10.9855i		−	0.641780i	0.947116	−	0.320890i	$-0.103982\pi$
$294$		0			0
$295$	−1.53057	+	5.62603i	−0.0891130	+	0.327560i
$296$			6.20118i			0.360436i
$297$		0			0
$298$	−9.03954			−0.523646
$299$	11.0671			0.640030
$300$		0			0
$301$	−32.9637			−1.90000
$302$	−9.15944			−0.527066
$303$		0			0
$304$	−10.9504	+	16.6425i	−0.628046	+	0.954511i
$305$	−5.60579	+	20.6057i	−0.320987	+	1.17988i
$306$		0			0
$307$	−16.3932			−0.935610			−0.467805	−	0.883832i	$-0.654955\pi$
$307$	−16.3932			−0.935610			−0.467805	+	0.883832i	$0.654955\pi$
$308$	−0.271939			−0.0154952
$309$		0			0
$310$	−6.22584	+	22.8848i	−0.353604	+	1.29977i
$311$			16.1069i			0.913336i	0.889637	+	0.456668i	$0.150957\pi$
$311$			16.1069i			0.913336i	−0.889637	+	0.456668i	$0.849043\pi$
$312$		0			0
$313$		−	16.4872i		−	0.931909i	−0.884809	−	0.465955i	$-0.845711\pi$
$313$		−	16.4872i		−	0.931909i	0.884809	−	0.465955i	$-0.154289\pi$
$314$	−18.4944			−1.04370
$315$		0			0
$316$		−	3.20906i		−	0.180524i
$317$			27.4272i			1.54047i	0.637762	+	0.770234i	$0.279860\pi$
$317$			27.4272i			1.54047i	−0.637762	+	0.770234i	$0.720140\pi$
$318$		0			0
$319$		−	1.53408i		−	0.0858920i
$320$	3.63218	−	13.3511i	0.203045	−	0.746348i
$321$		0			0
$322$	−13.3264			−0.742649
$323$	−13.6516	+	20.7478i	−0.759593	+	1.15444i
$324$		0			0
$325$	−23.5772	−	13.8537i	−1.30783	−	0.768466i
$326$	−11.6700			−0.646344
$327$		0			0
$328$		−	29.7468i		−	1.64249i
$329$		−	1.65476i		−	0.0912300i
$330$		0			0
$331$		−	23.5231i		−	1.29295i	−0.762936	−	0.646474i	$-0.776243\pi$
$331$		−	23.5231i		−	1.29295i	0.762936	−	0.646474i	$-0.223757\pi$
$332$	−3.86715			−0.212237
$333$		0			0
$334$	−18.0691			−0.988696
$335$	8.02170	−	29.4860i	0.438273	−	1.61099i
$336$		0			0
$337$	−10.2508			−0.558396			−0.279198	−	0.960234i	$-0.590069\pi$
$337$	−10.2508			−0.558396			−0.279198	+	0.960234i	$0.590069\pi$
$338$			25.8960i			1.40856i
$339$		0			0
$340$	−1.15239	+	4.23594i	−0.0624973	+	0.229726i
$341$	−1.27109			−0.0688334
$342$		0			0
$343$		−	19.3489i		−	1.04474i
$344$	−19.4272			−1.04744
$345$		0			0
$346$	18.3100			0.984350
$347$	31.6668			1.69996			0.849981	−	0.526813i	$-0.176613\pi$
$347$	31.6668			1.69996			0.849981	+	0.526813i	$0.176613\pi$
$348$		0			0
$349$	−11.3242			−0.606171			−0.303086	−	0.952963i	$-0.598017\pi$
$349$	−11.3242			−0.606171			−0.303086	+	0.952963i	$0.598017\pi$
$350$	28.3901	+	16.6818i	1.51752	+	0.891678i
$351$		0			0
$352$	−0.353893			−0.0188626
$353$	17.5702			0.935166			0.467583	−	0.883949i	$-0.345125\pi$
$353$	17.5702			0.935166			0.467583	+	0.883949i	$0.345125\pi$
$354$		0			0
$355$	−4.21963	+	15.5104i	−0.223954	+	0.823207i
$356$	0.230232			0.0122023
$357$		0			0
$358$			31.9456i			1.68838i
$359$		−	8.27301i		−	0.436633i	−0.975878	−	0.218316i	$-0.929943\pi$
$359$		−	8.27301i		−	0.436633i	0.975878	−	0.218316i	$-0.0700565\pi$
$360$		0			0
$361$	−7.51902	−	17.4489i	−0.395738	−	0.918363i
$362$	−11.1513			−0.586098
$363$		0			0
$364$		−	8.10508i		−	0.424822i
$365$	10.1296	+	2.75577i	0.530208	+	0.144244i
$366$		0			0
$367$		−	3.81644i		−	0.199217i	−0.995027	−	0.0996083i	$-0.968241\pi$
$367$		−	3.81644i		−	0.199217i	0.995027	−	0.0996083i	$-0.0317590\pi$
$368$	−9.24836			−0.482104
$369$		0			0
$370$	−8.08241	−	2.19883i	−0.420184	−	0.114312i
$371$	−4.31654			−0.224103
$372$		0			0
$373$	−25.8538			−1.33866			−0.669331	−	0.742965i	$-0.733419\pi$
$373$	−25.8538			−1.33866			−0.669331	+	0.742965i	$0.733419\pi$
$374$	−1.60095			−0.0827832
$375$		0			0
$376$		−	0.975237i		−	0.0502940i
$377$	45.7228			2.35485
$378$		0			0
$379$		−	0.122615i		−	0.00629831i	−0.999995	−	0.00314916i	$-0.998998\pi$
$379$		−	0.122615i		−	0.00629831i	0.999995	−	0.00314916i	$-0.00100241\pi$
$380$	−2.22253	−	2.51769i	−0.114013	−	0.129155i
$381$		0			0
$382$	−8.53035			−0.436451
$383$		−	15.4693i		−	0.790443i	−0.918586	−	0.395222i	$-0.870668\pi$
$383$		−	15.4693i		−	0.790443i	0.918586	−	0.395222i	$-0.129332\pi$
$384$		0			0
$385$	−0.463278	+	1.70291i	−0.0236108	+	0.0867882i
$386$		−	27.2966i		−	1.38936i
$387$		0			0
$388$	0.881262			0.0447393
$389$		−	26.3064i		−	1.33379i	−0.745153	−	0.666894i	$-0.767624\pi$
$389$		−	26.3064i		−	1.33379i	0.745153	−	0.666894i	$-0.232376\pi$
$390$		0			0
$391$	−11.5297			−0.583083
$392$		−	29.1469i		−	1.47214i
$393$		0			0
$394$			8.35031i			0.420682i
$395$	−20.0954	−	5.46697i	−1.01111	−	0.275073i
$396$		0			0
$397$			18.8474i			0.945924i	0.881083	+	0.472962i	$0.156815\pi$
$397$			18.8474i			0.945924i	−0.881083	+	0.472962i	$0.843185\pi$
$398$		−	21.7514i		−	1.09030i
$399$		0			0
$400$	19.7024	+	11.5770i	0.985122	+	0.578849i
$401$	−0.0996293			−0.00497525			−0.00248763	−	0.999997i	$-0.500792\pi$
$401$	−0.0996293			−0.00497525			−0.00248763	+	0.999997i	$0.500792\pi$
$402$		0			0
$403$		−	37.8845i		−	1.88716i
$404$		−	3.62891i		−	0.180545i
$405$		0			0
$406$	−55.0566			−2.73241
$407$		−	0.448921i		−	0.0222522i
$408$		0			0
$409$		−	21.3697i		−	1.05666i	−0.849038	−	0.528332i	$-0.822818\pi$
$409$		−	21.3697i		−	1.05666i	0.849038	−	0.528332i	$-0.177182\pi$
$410$	38.7710	+	10.5477i	1.91476	+	0.520913i
$411$		0			0
$412$	−0.295412			−0.0145539
$413$			11.2148i			0.551844i
$414$		0			0
$415$	−6.58810	+	24.2164i	−0.323397	+	1.18874i
$416$		−	10.5477i		−	0.517143i
$417$		0			0
$418$	0.673201	−	1.02314i	0.0329273	−	0.0500433i
$419$		−	7.88716i		−	0.385313i	−0.981266	−	0.192656i	$-0.938290\pi$
$419$		−	7.88716i		−	0.385313i	0.981266	−	0.192656i	$-0.0617103\pi$
$420$		0			0
$421$		−	3.11671i		−	0.151899i	−0.997112	−	0.0759495i	$-0.975801\pi$
$421$		−	3.11671i		−	0.151899i	0.997112	−	0.0759495i	$-0.0241988\pi$
$422$	−27.0748			−1.31798
$423$		0			0
$424$	−2.54396			−0.123545
$425$	24.5626	+	14.4328i	1.19146	+	0.700091i
$426$		0			0
$427$			41.0749i			1.98775i
$428$			3.08280i			0.149013i
$429$		0			0
$430$	6.88853	−	25.3207i	0.332195	−	1.22107i
$431$	−1.33639			−0.0643717			−0.0321859	−	0.999482i	$-0.510247\pi$
$431$	−1.33639			−0.0643717			−0.0321859	+	0.999482i	$0.510247\pi$
$432$		0			0
$433$	−2.85307			−0.137110			−0.0685550	−	0.997647i	$-0.521839\pi$
$433$	−2.85307			−0.137110			−0.0685550	+	0.997647i	$0.521839\pi$
$434$			45.6181i			2.18974i
$435$		0			0
$436$			2.50932i			0.120175i
$437$	4.84825	−	7.36842i	0.231923	−	0.352479i
$438$		0			0
$439$		−	13.8537i		−	0.661202i	−0.943771	−	0.330601i	$-0.892749\pi$
$439$		−	13.8537i		−	0.661202i	0.943771	−	0.330601i	$-0.107251\pi$
$440$	−0.273033	+	1.00361i	−0.0130163	+	0.0478452i
$441$		0			0
$442$		−	47.7159i		−	2.26961i
$443$	25.3321			1.20356			0.601781	−	0.798661i	$-0.294458\pi$
$443$	25.3321			1.20356			0.601781	+	0.798661i	$0.294458\pi$
$444$		0			0
$445$	0.392224	−	1.44173i	0.0185932	−	0.0683446i
$446$			18.9221i			0.895988i
$447$		0			0
$448$		−	26.6138i		−	1.25738i
$449$	0.403636			0.0190487			0.00952437	−	0.999955i	$-0.496968\pi$
$449$	0.403636			0.0190487			0.00952437	+	0.999955i	$0.496968\pi$
$450$		0			0
$451$			2.15346i			0.101402i
$452$			4.48377i			0.210899i
$453$		0			0
$454$	32.3773			1.51954
$455$	−50.7547	−	13.8079i	−2.37941	−	0.647322i
$456$		0			0
$457$		−	25.1914i		−	1.17840i	−0.807987	−	0.589201i	$-0.799443\pi$
$457$		−	25.1914i		−	1.17840i	0.807987	−	0.589201i	$-0.200557\pi$
$458$		−	30.2292i		−	1.41252i
$459$		0			0
$460$	0.409264	−	1.50436i	0.0190820	−	0.0701414i
$461$			9.60888i			0.447530i	0.974643	+	0.223765i	$0.0718348\pi$
$461$			9.60888i			0.447530i	−0.974643	+	0.223765i	$0.928165\pi$
$462$		0			0
$463$		−	2.49592i		−	0.115995i	−0.998317	−	0.0579977i	$-0.981528\pi$
$463$		−	2.49592i		−	0.115995i	0.998317	−	0.0579977i	$-0.0184716\pi$
$464$	−38.2087			−1.77379
$465$		0			0
$466$		−	24.1123i		−	1.11698i
$467$	−1.18592			−0.0548779			−0.0274389	−	0.999623i	$-0.508735\pi$
$467$	−1.18592			−0.0548779			−0.0274389	+	0.999623i	$0.508735\pi$
$468$		0			0
$469$		−	58.7768i		−	2.71406i
$470$	1.27109	+	0.345801i	0.0586310	+	0.0159506i
$471$		0			0
$472$			6.60946i			0.304225i
$473$	1.40639			0.0646658
$474$		0			0
$475$	−19.5523	+	9.62851i	−0.897120	+	0.441786i
$476$			8.44384i			0.387023i
$477$		0			0
$478$	−7.29519			−0.333674
$479$		−	7.97866i		−	0.364554i	−0.983247	−	0.182277i	$-0.941653\pi$
$479$		−	7.97866i		−	0.364554i	0.983247	−	0.182277i	$-0.0583468\pi$
$480$		0			0
$481$	13.3800			0.610074
$482$	−38.0103			−1.73132
$483$		0			0
$484$	−3.77853			−0.171751
$485$	1.50132	−	5.51853i	0.0681715	−	0.250584i
$486$		0			0
$487$	12.8085			0.580406			0.290203	−	0.956965i	$-0.406277\pi$
$487$	12.8085			0.580406			0.290203	+	0.956965i	$0.406277\pi$
$488$			24.2075i			1.09582i
$489$		0			0
$490$	37.9891	+	10.3350i	1.71617	+	0.466887i
$491$			21.9529i			0.990721i	0.868688	+	0.495360i	$0.164964\pi$
$491$			21.9529i			0.990721i	−0.868688	+	0.495360i	$0.835036\pi$
$492$		0			0
$493$	−47.6339			−2.14532
$494$	30.4943	+	20.0646i	1.37201	+	0.902748i
$495$		0			0
$496$			31.6585i			1.42151i
$497$			30.9181i			1.38687i
$498$		0			0
$499$	−27.5837			−1.23482			−0.617409	−	0.786643i	$-0.711817\pi$
$499$	−27.5837			−1.23482			−0.617409	+	0.786643i	$0.711817\pi$
$500$	−2.75503	+	2.69255i	−0.123209	+	0.120414i
$501$		0			0
$502$	26.1109			1.16539
$503$	−4.18746			−0.186710			−0.0933548	−	0.995633i	$-0.529759\pi$
$503$	−4.18746			−0.186710			−0.0933548	+	0.995633i	$0.529759\pi$
$504$		0			0
$505$	−22.7245	−	6.18223i	−1.01123	−	0.275106i
$506$	0.568566			0.0252759
$507$		0			0
$508$	−3.31821			−0.147222
$509$	−15.8132			−0.700907			−0.350453	−	0.936580i	$-0.613972\pi$
$509$	−15.8132			−0.700907			−0.350453	+	0.936580i	$0.613972\pi$
$510$		0			0
$511$	20.1922			0.893249
$512$		−	14.3559i		−	0.634445i
$513$		0			0
$514$	3.39329			0.149672
$515$	−0.503265	+	1.84989i	−0.0221765	+	0.0815160i
$516$		0			0
$517$			0.0706001i			0.00310499i
$518$	−16.1113			−0.707890
$519$		0			0
$520$	−29.9123	−	8.13768i	−1.31174	−	0.356861i
$521$	−39.0193			−1.70947			−0.854733	−	0.519067i	$-0.826279\pi$
$521$	−39.0193			−1.70947			−0.854733	+	0.519067i	$0.826279\pi$
$522$		0			0
$523$	15.0851			0.659627			0.329814	−	0.944046i	$-0.393014\pi$
$523$	15.0851			0.659627			0.329814	+	0.944046i	$0.393014\pi$
$524$			1.70158i			0.0743340i
$525$		0			0
$526$		−	23.0567i		−	1.00532i
$527$			39.4679i			1.71925i
$528$		0			0
$529$	−18.9053			−0.821970
$530$	0.902041	−	3.31571i	0.0391822	−	0.144025i
$531$		0			0
$532$	−5.39630	−	3.55064i	−0.233959	−	0.153940i
$533$	−64.1831			−2.78008
$534$		0			0
$535$	19.3048	+	5.25188i	0.834618	+	0.227059i
$536$		−	34.6402i		−	1.49623i
$537$		0			0
$538$			21.9617i			0.946835i
$539$			2.11003i			0.0908853i
$540$		0			0
$541$	−20.0761			−0.863138			−0.431569	−	0.902080i	$-0.642040\pi$
$541$	−20.0761			−0.863138			−0.431569	+	0.902080i	$0.642040\pi$
$542$			46.2505i			1.98663i
$543$		0			0
$544$			10.9885i			0.471130i
$545$	15.7135	+	4.27489i	0.673094	+	0.183116i
$546$		0			0
$547$	9.17965			0.392494			0.196247	−	0.980555i	$-0.437125\pi$
$547$	9.17965			0.392494			0.196247	+	0.980555i	$0.437125\pi$
$548$	3.87396			0.165487
$549$		0			0
$550$	−1.21126	−	0.711724i	−0.0516482	−	0.0303480i
$551$	20.0301	−	30.4419i	0.853310	−	1.29687i
$552$		0			0
$553$	−40.0577			−1.70343
$554$	−23.1408			−0.983160
$555$		0			0
$556$	−6.17883			−0.262041
$557$	33.9108			1.43685			0.718423	−	0.695606i	$-0.244864\pi$
$557$	33.9108			1.43685			0.718423	+	0.695606i	$0.244864\pi$
$558$		0			0
$559$			41.9170i			1.77290i
$560$	42.4135	+	11.5387i	1.79230	+	0.487597i
$561$		0			0
$562$			18.3742i			0.775069i
$563$		−	16.8702i		−	0.710996i	−0.934677	−	0.355498i	$-0.884311\pi$
$563$		−	16.8702i		−	0.710996i	0.934677	−	0.355498i	$-0.115689\pi$
$564$		0			0
$565$	28.0778	+	7.63858i	1.18124	+	0.321358i
$566$	14.2122			0.597384
$567$		0			0
$568$			18.2216i			0.764563i
$569$	8.36004			0.350471			0.175236	−	0.984527i	$-0.443931\pi$
$569$	8.36004			0.350471			0.175236	+	0.984527i	$0.443931\pi$
$570$		0			0
$571$	6.56776			0.274852			0.137426	−	0.990512i	$-0.456117\pi$
$571$	6.56776			0.274852			0.137426	+	0.990512i	$0.456117\pi$
$572$			0.345801i			0.0144587i
$573$		0			0
$574$	77.2853			3.22582
$575$	−8.72323	−	5.12569i	−0.363784	−	0.213756i
$576$		0			0
$577$			30.6141i			1.27448i	0.770666	+	0.637240i	$0.219924\pi$
$577$			30.6141i			1.27448i	−0.770666	+	0.637240i	$0.780076\pi$
$578$			23.6799i			0.984956i
$579$		0			0
$580$	1.69083	−	6.21514i	0.0702081	−	0.258069i
$581$			48.2725i			2.00268i
$582$		0			0
$583$	0.184164			0.00762730
$584$	11.9003			0.492437
$585$		0			0
$586$	16.8209			0.694867
$587$	−2.23618			−0.0922969			−0.0461485	−	0.998935i	$-0.514695\pi$
$587$	−2.23618			−0.0922969			−0.0461485	+	0.998935i	$0.514695\pi$
$588$		0			0
$589$	−25.2232	−	16.5963i	−1.03930	−	0.683838i
$590$	−8.61454	−	2.34360i	−0.354655	−	0.0964843i
$591$		0			0
$592$	−11.1811			−0.459539
$593$	6.02223			0.247303			0.123652	−	0.992326i	$-0.460539\pi$
$593$	6.02223			0.247303			0.123652	+	0.992326i	$0.460539\pi$
$594$		0			0
$595$	52.8760	+	14.3850i	2.16770	+	0.589726i
$596$		−	2.03412i		−	0.0833210i
$597$		0			0
$598$			16.9460i			0.692972i
$599$	9.53150			0.389447			0.194723	−	0.980858i	$-0.437619\pi$
$599$	9.53150			0.389447			0.194723	+	0.980858i	$0.437619\pi$
$600$		0			0
$601$		−	3.68754i		−	0.150418i	−0.997168	−	0.0752089i	$-0.976038\pi$
$601$		−	3.68754i		−	0.150418i	0.997168	−	0.0752089i	$-0.0239624\pi$
$602$		−	50.4738i		−	2.05716i
$603$		0			0
$604$		−	2.06111i		−	0.0838652i
$605$	−6.43713	+	23.6615i	−0.261706	+	0.961975i
$606$		0			0
$607$	43.6425			1.77139			0.885697	−	0.464264i	$-0.153681\pi$
$607$	43.6425			1.77139			0.885697	+	0.464264i	$0.153681\pi$
$608$	−7.02257	−	4.62069i	−0.284803	−	0.187394i
$609$		0			0
$610$	−31.5513	−	8.58356i	−1.27747	−	0.347538i
$611$	−2.10422			−0.0851275
$612$		0			0
$613$			15.8298i			0.639360i	0.947526	+	0.319680i	$0.103575\pi$
$613$			15.8298i			0.639360i	−0.947526	+	0.319680i	$0.896425\pi$
$614$		−	25.1012i		−	1.01300i
$615$		0			0
$616$			2.00058i			0.0806055i
$617$	−41.0586			−1.65296			−0.826479	−	0.562967i	$-0.809660\pi$
$617$	−41.0586			−1.65296			−0.826479	+	0.562967i	$0.809660\pi$
$618$		0			0
$619$	5.57040			0.223893			0.111947	−	0.993714i	$-0.464291\pi$
$619$	5.57040			0.223893			0.111947	+	0.993714i	$0.464291\pi$
$620$	−5.14966	−	1.40097i	−0.206815	−	0.0562644i
$621$		0			0
$622$	−24.6627			−0.988885
$623$		−	2.87392i		−	0.115141i
$624$		0			0
$625$	12.1675	+	21.8393i	0.486698	+	0.873570i
$626$	25.2450			1.00899
$627$		0			0
$628$		−	4.16172i		−	0.166071i
$629$	−13.9392			−0.555792
$630$		0			0
$631$	0.116081			0.00462110			0.00231055	−	0.999997i	$-0.499265\pi$
$631$	0.116081			0.00462110			0.00231055	+	0.999997i	$0.499265\pi$
$632$	−23.6081			−0.939078
$633$		0			0
$634$	−41.9965			−1.66789
$635$	−5.65293	+	20.7789i	−0.224330	+	0.824586i
$636$		0			0
$637$	−62.8888			−2.49174
$638$	2.34898			0.0929969
$639$		0			0
$640$	28.7654	+	7.82566i	1.13705	+	0.309336i
$641$	−20.7636			−0.820112			−0.410056	−	0.912060i	$-0.634491\pi$
$641$	−20.7636			−0.820112			−0.410056	+	0.912060i	$0.634491\pi$
$642$		0			0
$643$		−	4.54220i		−	0.179127i	−0.995981	−	0.0895634i	$-0.971453\pi$
$643$		−	4.54220i		−	0.179127i	0.995981	−	0.0895634i	$-0.0285472\pi$
$644$		−	2.99877i		−	0.118168i
$645$		0			0
$646$	−31.7689	−	20.9032i	−1.24993	−	0.822425i
$647$	35.6822			1.40281			0.701405	−	0.712763i	$-0.252556\pi$
$647$	35.6822			1.40281			0.701405	+	0.712763i	$0.252556\pi$
$648$		0			0
$649$		−	0.478477i		−	0.0187819i
$650$	21.2127	−	36.1012i	0.832032	−	1.41601i
$651$		0			0
$652$		−	2.62606i		−	0.102844i
$653$	−25.9809			−1.01671			−0.508356	−	0.861147i	$-0.669747\pi$
$653$	−25.9809			−1.01671			−0.508356	+	0.861147i	$0.669747\pi$
$654$		0			0
$655$	10.6554	+	2.89882i	0.416343	+	0.113266i
$656$	53.6352			2.09410
$657$		0			0
$658$	2.53376			0.0987764
$659$	32.3683			1.26089			0.630445	−	0.776234i	$-0.282872\pi$
$659$	32.3683			1.26089			0.630445	+	0.776234i	$0.282872\pi$
$660$		0			0
$661$		−	40.7085i		−	1.58338i	−0.610924	−	0.791689i	$-0.709202\pi$
$661$		−	40.7085i		−	1.58338i	0.610924	−	0.791689i	$-0.290798\pi$
$662$	36.0185			1.39990
$663$		0			0
$664$			28.4494i			1.10405i
$665$	−31.4276	+	27.7432i	−1.21871	+	1.07583i
$666$		0			0
$667$	16.9168			0.655022
$668$		−	4.06600i		−	0.157318i
$669$		0			0
$670$	45.1488	+	12.2828i	1.74425	+	0.474526i
$671$		−	1.75245i		−	0.0676526i
$672$		0			0
$673$	−11.3307			−0.436765			−0.218382	−	0.975863i	$-0.570078\pi$
$673$	−11.3307			−0.436765			−0.218382	+	0.975863i	$0.570078\pi$
$674$		−	15.6960i		−	0.604586i
$675$		0			0
$676$	−5.82727			−0.224126
$677$		−	3.40819i		−	0.130987i	−0.997853	−	0.0654937i	$-0.979138\pi$
$677$		−	3.40819i		−	0.130987i	0.997853	−	0.0654937i	$-0.0208622\pi$
$678$		0			0
$679$		−	11.0005i		−	0.422161i
$680$	31.1625	+	8.47780i	1.19503	+	0.325109i
$681$		0			0
$682$		−	1.94629i		−	0.0745272i
$683$			3.45975i			0.132384i	0.997807	+	0.0661918i	$0.0210849\pi$
$683$			3.45975i			0.132384i	−0.997807	+	0.0661918i	$0.978915\pi$
$684$		0			0
$685$	6.59970	−	24.2590i	0.252162	−	0.926890i
$686$	29.6269			1.13116
$687$		0			0
$688$		−	35.0283i		−	1.33544i
$689$			5.48896i			0.209113i
$690$		0			0
$691$	9.46765			0.360166			0.180083	−	0.983651i	$-0.442363\pi$
$691$	9.46765			0.360166			0.180083	+	0.983651i	$0.442363\pi$
$692$			4.12021i			0.156627i
$693$		0			0
$694$			48.4880i			1.84058i
$695$	−10.5263	+	38.6923i	−0.399285	+	1.46768i
$696$		0			0
$697$	66.8657			2.53272
$698$		−	17.3396i		−	0.656313i
$699$		0			0
$700$	−3.75382	+	6.38850i	−0.141881	+	0.241462i
$701$		−	28.9193i		−	1.09227i	−0.837698	−	0.546134i	$-0.816099\pi$
$701$		−	28.9193i		−	1.09227i	0.837698	−	0.546134i	$-0.183901\pi$
$702$		0			0
$703$	5.86144	−	8.90827i	0.221068	−	0.335982i
$704$			1.13547i			0.0427947i
$705$		0			0
$706$			26.9034i			1.01252i
$707$	−45.2986			−1.70363
$708$		0			0
$709$	−26.2125			−0.984431			−0.492216	−	0.870473i	$-0.663813\pi$
$709$	−26.2125			−0.984431			−0.492216	+	0.870473i	$0.663813\pi$
$710$	−23.7495	−	6.46107i	−0.891302	−	0.242480i
$711$		0			0
$712$		−	1.69375i		−	0.0634758i
$713$		−	14.0167i		−	0.524931i
$714$		0			0
$715$	2.16544	+	0.589109i	0.0809827	+	0.0220314i
$716$	−7.18858			−0.268650
$717$		0			0
$718$	12.6676			0.472750
$719$			52.8689i			1.97168i	0.167692	+	0.985839i	$0.446369\pi$
$719$			52.8689i			1.97168i	−0.167692	+	0.985839i	$0.553631\pi$
$720$		0			0
$721$			3.68754i			0.137331i
$722$	26.7177	−	11.5131i	0.994329	−	0.428473i
$723$		0			0
$724$		−	2.50932i		−	0.0932580i
$725$	−36.0392	−	21.1763i	−1.33846	−	0.786467i
$726$		0			0
$727$		−	38.9525i		−	1.44467i	−0.691545	−	0.722333i	$-0.743070\pi$
$727$		−	38.9525i		−	1.44467i	0.691545	−	0.722333i	$-0.256930\pi$
$728$	−59.6266			−2.20991
$729$		0			0
$730$	−4.21963	+	15.5104i	−0.156175	+	0.574066i
$731$		−	43.6690i		−	1.61516i
$732$		0			0
$733$			17.0592i			0.630096i	0.949076	+	0.315048i	$0.102021\pi$
$733$			17.0592i			0.630096i	−0.949076	+	0.315048i	$0.897979\pi$
$734$	5.84371			0.215695
$735$		0			0
$736$		−	3.90250i		−	0.143848i
$737$			2.50770i			0.0923723i
$738$		0			0
$739$	12.5324			0.461010			0.230505	−	0.973071i	$-0.425962\pi$
$739$	12.5324			0.461010			0.230505	+	0.973071i	$0.425962\pi$
$740$	0.494792	−	1.81875i	0.0181889	−	0.0668584i
$741$		0			0
$742$		−	6.60946i		−	0.242641i
$743$			23.4439i			0.860075i	0.902811	+	0.430038i	$0.141500\pi$
$743$			23.4439i			0.860075i	−0.902811	+	0.430038i	$0.858500\pi$
$744$		0			0
$745$	−12.7379	−	3.46535i	−0.466679	−	0.126960i
$746$		−	39.5873i		−	1.44939i
$747$		0			0
$748$		−	0.360255i		−	0.0131722i
$749$	38.4817			1.40609
$750$		0			0
$751$			8.95770i			0.326871i	0.986554	+	0.163436i	$0.0522576\pi$
$751$			8.95770i			0.326871i	−0.986554	+	0.163436i	$0.947742\pi$
$752$	1.75841			0.0641225
$753$		0			0
$754$			70.0106i			2.54964i
$755$	−12.9068	−	3.51131i	−0.469727	−	0.127790i
$756$		0			0
$757$			3.69403i			0.134262i	0.997744	+	0.0671309i	$0.0213845\pi$
$757$			3.69403i			0.134262i	−0.997744	+	0.0671309i	$0.978615\pi$
$758$	0.187747			0.00681930
$759$		0			0
$760$	−18.5219	+	16.3505i	−0.671859	+	0.593094i
$761$		−	21.5264i		−	0.780332i	−0.920745	−	0.390166i	$-0.872418\pi$
$761$		−	21.5264i		−	0.780332i	0.920745	−	0.390166i	$-0.127582\pi$
$762$		0			0
$763$	31.3231			1.13397
$764$		−	1.91954i		−	0.0694467i
$765$		0			0
$766$	23.6865			0.855827
$767$	14.2609			0.514930
$768$		0			0
$769$	−2.04068			−0.0735889			−0.0367944	−	0.999323i	$-0.511715\pi$
$769$	−2.04068			−0.0735889			−0.0367944	+	0.999323i	$0.511715\pi$
$770$	−2.60748	−	0.709368i	−0.0939671	−	0.0255639i
$771$		0			0
$772$	6.14242			0.221070
$773$		−	7.76578i		−	0.279316i	−0.990200	−	0.139658i	$-0.955400\pi$
$773$		−	7.76578i		−	0.279316i	0.990200	−	0.139658i	$-0.0446003\pi$
$774$		0			0
$775$	−17.5460	+	29.8609i	−0.630270	+	1.07264i
$776$		−	6.48317i		−	0.232732i
$777$		0			0
$778$	40.2802			1.44412
$779$	−28.1171	+	42.7326i	−1.00740	+	1.53106i
$780$		0			0
$781$		−	1.31912i		−	0.0472017i
$782$		−	17.6542i		−	0.631314i
$783$		0			0
$784$	52.5535			1.87691
$785$	−26.0610	−	7.08992i	−0.930157	−	0.253050i
$786$		0			0
$787$	−18.5146			−0.659974			−0.329987	−	0.943985i	$-0.607044\pi$
$787$	−18.5146			−0.659974			−0.329987	+	0.943985i	$0.607044\pi$
$788$	−1.87903			−0.0669377
$789$		0			0
$790$	8.37100	−	30.7699i	0.297827	−	1.09475i
$791$	55.9696			1.99005
$792$		0			0
$793$	52.2313			1.85479
$794$	−28.8591			−1.02417
$795$		0			0
$796$	4.89461			0.173485
$797$		−	7.76578i		−	0.275078i	−0.990496	−	0.137539i	$-0.956081\pi$
$797$		−	7.76578i		−	0.275078i	0.990496	−	0.137539i	$-0.0439193\pi$
$798$		0			0
$799$	2.19216			0.0775532
$800$	−4.88510	+	8.31378i	−0.172714	+	0.293937i
$801$		0			0
$802$		−	0.152552i		−	0.00538680i
$803$	−0.861494			−0.0304015
$804$		0			0
$805$	−18.7785	−	5.10872i	−0.661856	−	0.180059i
$806$	58.0085			2.04326
$807$		0			0
$808$	−26.6968			−0.939189
$809$		−	20.5769i		−	0.723445i	−0.932286	−	0.361722i	$-0.882189\pi$
$809$		−	20.5769i		−	0.723445i	0.932286	−	0.361722i	$-0.117811\pi$
$810$		0			0
$811$		−	29.1309i		−	1.02292i	−0.859306	−	0.511462i	$-0.829104\pi$
$811$		−	29.1309i		−	1.02292i	0.859306	−	0.511462i	$-0.170896\pi$
$812$		−	12.3891i		−	0.434773i
$813$		0			0
$814$	0.687385			0.0240928
$815$	−16.4446	−	4.47376i	−0.576028	−	0.156709i
$816$		0			0
$817$	27.9080	+	18.3628i	0.976378	+	0.642434i
$818$	32.7212			1.14407
$819$		0			0
$820$	−2.37350	+	8.72445i	−0.0828861	+	0.304671i
$821$			5.21346i			0.181951i	0.995853	+	0.0909756i	$0.0289985\pi$
$821$			5.21346i			0.181951i	−0.995853	+	0.0909756i	$0.971001\pi$
$822$		0			0
$823$			0.920958i			0.0321026i	0.999871	+	0.0160513i	$0.00510950\pi$
$823$			0.920958i			0.0321026i	−0.999871	+	0.0160513i	$0.994890\pi$
$824$			2.17325i			0.0757089i
$825$		0			0
$826$	−17.1720			−0.597492
$827$		−	4.24374i		−	0.147569i	−0.997274	−	0.0737847i	$-0.976492\pi$
$827$		−	4.24374i		−	0.147569i	0.997274	−	0.0737847i	$-0.0235078\pi$
$828$		0			0
$829$		−	50.1630i		−	1.74223i	−0.491076	−	0.871116i	$-0.663396\pi$
$829$		−	50.1630i		−	1.74223i	0.491076	−	0.871116i	$-0.336604\pi$
$830$	−37.0800	−	10.0877i	−1.28707	−	0.350148i
$831$		0			0
$832$	−33.8424			−1.17327
$833$	65.5173			2.27004
$834$		0			0
$835$	−25.4616	−	6.92686i	−0.881136	−	0.239714i
$836$	0.230232	+	0.151487i	0.00796274	+	0.00523930i
$837$		0			0
$838$	12.0768			0.417185
$839$	0.767825			0.0265083			0.0132541	−	0.999912i	$-0.495781\pi$
$839$	0.767825			0.0265083			0.0132541	+	0.999912i	$0.495781\pi$
$840$		0			0
$841$	40.8902			1.41001
$842$	4.77229			0.164464
$843$		0			0
$844$		−	6.09252i		−	0.209713i
$845$	−9.92736	+	36.4908i	−0.341512	+	1.25532i
$846$		0			0
$847$			47.1663i			1.62065i
$848$		−	4.58689i		−	0.157515i
$849$		0			0
$850$	−22.0994	+	37.6101i	−0.758002	+	1.29002i
$851$	4.95040			0.169698
$852$		0			0
$853$		−	38.4028i		−	1.31489i	−0.753504	−	0.657444i	$-0.771638\pi$
$853$		−	38.4028i		−	1.31489i	0.753504	−	0.657444i	$-0.228362\pi$
$854$	−62.8936			−2.15218
$855$		0			0
$856$	22.6792			0.775161
$857$		−	17.3707i		−	0.593373i	−0.954975	−	0.296686i	$-0.904118\pi$
$857$		−	17.3707i		−	0.593373i	0.954975	−	0.296686i	$-0.0958816\pi$
$858$		0			0
$859$	43.6731			1.49011			0.745054	−	0.667004i	$-0.232424\pi$
$859$	43.6731			1.49011			0.745054	+	0.667004i	$0.232424\pi$
$860$	5.69781	+	1.55009i	0.194294	+	0.0528578i
$861$		0			0
$862$		−	2.04628i		−	0.0696964i
$863$			29.9661i			1.02006i	0.860157	+	0.510029i	$0.170365\pi$
$863$			29.9661i			1.02006i	−0.860157	+	0.510029i	$0.829635\pi$
$864$		0			0
$865$	25.8011	+	7.01921i	0.877263	+	0.238660i
$866$		−	4.36861i		−	0.148451i
$867$		0			0
$868$	−10.2652			−0.348425
$869$	1.70905			0.0579757
$870$		0			0
$871$	−74.7413			−2.53251
$872$	18.4603			0.625144
$873$		0			0
$874$	11.2825	+	7.42362i	0.381636	+	0.251108i
$875$	33.6102	+	34.3902i	1.13623	+	1.16260i
$876$		0			0
$877$	−14.3151			−0.483387			−0.241694	−	0.970353i	$-0.577703\pi$
$877$	−14.3151			−0.483387			−0.241694	+	0.970353i	$0.577703\pi$
$878$	21.2127			0.715895
$879$		0			0
$880$	−1.80957	−	0.492294i	−0.0610004	−	0.0165952i
$881$			16.7238i			0.563440i	0.959497	+	0.281720i	$0.0909050\pi$
$881$			16.7238i			0.563440i	−0.959497	+	0.281720i	$0.909095\pi$
$882$		0			0
$883$			3.92750i			0.132171i	0.997814	+	0.0660854i	$0.0210510\pi$
$883$			3.92750i			0.132171i	−0.997814	+	0.0660854i	$0.978949\pi$
$884$	10.7373			0.361134
$885$		0			0
$886$			38.7883i			1.30312i
$887$			27.0814i			0.909306i	0.890669	+	0.454653i	$0.150237\pi$
$887$			27.0814i			0.909306i	−0.890669	+	0.454653i	$0.849763\pi$
$888$		0			0
$889$			41.4203i			1.38919i
$890$	2.20757	+	0.600572i	0.0739979	+	0.0201312i
$891$		0			0
$892$	−4.25796			−0.142567
$893$	−0.921807	+	1.40097i	−0.0308471	+	0.0468817i
$894$		0			0
$895$	−12.2465	+	45.0154i	−0.409355	+	1.50470i
$896$	57.3403			1.91561
$897$		0			0
$898$			0.618045i			0.0206244i
$899$		−	57.9088i		−	1.93137i
$900$		0			0
$901$		−	5.71838i		−	0.190507i
$902$	−3.29736			−0.109790
$903$		0			0
$904$	32.9858			1.09709
$905$	−15.7135	−	4.27489i	−0.522336	−	0.142102i
$906$		0			0
$907$	−39.6511			−1.31659			−0.658296	−	0.752759i	$-0.728722\pi$
$907$	−39.6511			−1.31659			−0.658296	+	0.752759i	$0.728722\pi$
$908$			7.28572i			0.241785i
$909$		0			0
$910$	21.1425	−	77.7153i	0.700868	−	2.57624i
$911$	10.8026			0.357906			0.178953	−	0.983858i	$-0.442729\pi$
$911$	10.8026			0.357906			0.178953	+	0.983858i	$0.442729\pi$
$912$		0			0
$913$		−	2.05953i		−	0.0681606i
$914$	38.5729			1.27588
$915$		0			0
$916$	6.80233			0.224755
$917$	21.2403			0.701418
$918$		0			0
$919$	19.7085			0.650125			0.325062	−	0.945693i	$-0.394615\pi$
$919$	19.7085			0.650125			0.325062	+	0.945693i	$0.394615\pi$
$920$	−11.0671	−	3.01083i	−0.364873	−	0.0992641i
$921$		0			0
$922$	−14.7131			−0.484549
$923$	39.3159			1.29410
$924$		0			0
$925$	−10.5462	−	6.19685i	−0.346757	−	0.203751i
$926$	3.82174			0.125590
$927$		0			0
$928$		−	16.1228i		−	0.529257i
$929$		−	43.0176i		−	1.41136i	−0.708531	−	0.705680i	$-0.750642\pi$
$929$		−	43.0176i		−	1.41136i	0.708531	−	0.705680i	$-0.249358\pi$
$930$		0			0
$931$	−27.5501	+	41.8708i	−0.902917	+	1.37226i
$932$	5.42587			0.177730
$933$		0			0
$934$		−	1.81588i		−	0.0594173i
$935$	−2.25594	−	0.613732i	−0.0737772	−	0.0200712i
$936$		0			0
$937$		−	37.7397i		−	1.23290i	−0.787394	−	0.616450i	$-0.788570\pi$
$937$		−	37.7397i		−	1.23290i	0.787394	−	0.616450i	$-0.211430\pi$
$938$	89.9988			2.93856
$939$		0			0
$940$	−0.0778141	+	0.286027i	−0.00253802	+	0.00932919i
$941$	−29.2232			−0.952651			−0.476325	−	0.879269i	$-0.658032\pi$
$941$	−29.2232			−0.952651			−0.476325	+	0.879269i	$0.658032\pi$
$942$		0			0
$943$	−23.7469			−0.773305
$944$	−11.9172			−0.387873
$945$		0			0
$946$			2.15346i			0.0700149i
$947$	−58.3211			−1.89518			−0.947590	−	0.319490i	$-0.896489\pi$
$947$	−58.3211			−1.89518			−0.947590	+	0.319490i	$0.896489\pi$
$948$		0			0
$949$		−	25.6766i		−	0.833498i
$950$	−14.7431	−	29.9384i	−0.478330	−	0.971329i
$951$		0			0
$952$	62.1187			2.01328
$953$			15.4381i			0.500090i	0.968234	+	0.250045i	$0.0804454\pi$
$953$			15.4381i			0.500090i	−0.968234	+	0.250045i	$0.919555\pi$
$954$		0			0
$955$	−12.0203	−	3.27015i	−0.388969	−	0.105819i
$956$		−	1.64160i		−	0.0530932i
$957$		0			0
$958$	12.2169			0.394710
$959$		−	48.3575i		−	1.56154i
$960$		0			0
$961$	−16.9814			−0.547787
$962$			20.4873i			0.660538i
$963$		0			0
$964$		−	8.55329i		−	0.275483i
$965$	10.4643	−	38.4643i	0.336856	−	1.23821i
$966$		0			0
$967$		−	2.05181i		−	0.0659817i	−0.999456	−	0.0329909i	$-0.989497\pi$
$967$		−	2.05181i		−	0.0659817i	0.999456	−	0.0329909i	$-0.0105032\pi$
$968$			27.7975i			0.893445i
$969$		0			0
$970$	8.44995	+	2.29882i	0.271311	+	0.0738106i
$971$	−15.4490			−0.495782			−0.247891	−	0.968788i	$-0.579737\pi$
$971$	−15.4490			−0.495782			−0.247891	+	0.968788i	$0.579737\pi$
$972$		0			0
$973$			77.1285i			2.47263i
$974$			19.6122i			0.628417i
$975$		0			0
$976$	−43.6475			−1.39712
$977$		−	54.0909i		−	1.73052i	−0.501322	−	0.865261i	$-0.667153\pi$
$977$		−	54.0909i		−	1.73052i	0.501322	−	0.865261i	$-0.332847\pi$
$978$		0			0
$979$			0.122615i			0.00391879i
$980$	−2.32563	+	8.54851i	−0.0742896	+	0.273072i
$981$		0			0
$982$	−33.6142			−1.07267
$983$		−	23.8929i		−	0.762064i	−0.924562	−	0.381032i	$-0.875569\pi$
$983$		−	23.8929i		−	0.762064i	0.924562	−	0.381032i	$-0.124431\pi$
$984$		0			0
$985$	−3.20113	+	11.7666i	−0.101996	+	0.374916i
$986$		−	72.9368i		−	2.32278i
$987$		0			0
$988$	−4.51504	+	6.86200i	−0.143642	+	0.218309i
$989$			15.5087i			0.493149i
$990$		0			0
$991$		−	12.3014i		−	0.390765i	−0.980727	−	0.195383i	$-0.937405\pi$
$991$		−	12.3014i		−	0.390765i	0.980727	−	0.195383i	$-0.0625949\pi$
$992$	−13.3588			−0.424144
$993$		0			0
$994$	−47.3417			−1.50159
$995$	8.33849	−	30.6505i	0.264348	−	0.971685i
$996$		0			0
$997$		−	52.7136i		−	1.66946i	−0.550663	−	0.834728i	$-0.685625\pi$
$997$		−	52.7136i		−	1.66946i	0.550663	−	0.834728i	$-0.314375\pi$
$998$		−	42.2361i		−	1.33696i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.b.d.854.14	yes	24
3.2	odd	2	inner	855.2.b.d.854.11	yes	24
5.4	even	2	inner	855.2.b.d.854.12	yes	24
15.14	odd	2	inner	855.2.b.d.854.13	yes	24
19.18	odd	2	inner	855.2.b.d.854.10	yes	24
57.56	even	2	inner	855.2.b.d.854.15	yes	24
95.94	odd	2	inner	855.2.b.d.854.16	yes	24
285.284	even	2	inner	855.2.b.d.854.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.b.d.854.9	✓	24	285.284	even	2	inner
855.2.b.d.854.10	yes	24	19.18	odd	2	inner
855.2.b.d.854.11	yes	24	3.2	odd	2	inner
855.2.b.d.854.12	yes	24	5.4	even	2	inner
855.2.b.d.854.13	yes	24	15.14	odd	2	inner
855.2.b.d.854.14	yes	24	1.1	even	1	trivial
855.2.b.d.854.15	yes	24	57.56	even	2	inner
855.2.b.d.854.16	yes	24	95.94	odd	2	inner

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.53119i q^{2} -0.344558 q^{4} +(-0.586990 + 2.15765i) q^{5} +4.30101i q^{7} +2.53480i q^{8} +(-3.30378 - 0.898797i) q^{10} -0.183502i q^{11} +5.46922 q^{13} -6.58568 q^{14} -4.57040 q^{16} -5.69781 q^{17} +(2.39593 - 3.64136i) q^{19} +(0.202252 - 0.743434i) q^{20} +0.280977 q^{22} +2.02354 q^{23} +(-4.31088 - 2.53304i) q^{25} +8.37443i q^{26} -1.48195i q^{28} +8.36004 q^{29} -6.92686i q^{31} -1.92856i q^{32} -8.72445i q^{34} +(-9.28006 - 2.52465i) q^{35} +2.44641 q^{37} +(5.57563 + 3.66864i) q^{38} +(-5.46922 - 1.48791i) q^{40} -11.7353 q^{41} +7.66418i q^{43} +0.0632269i q^{44} +3.09843i q^{46} -0.384738 q^{47} -11.4987 q^{49} +(3.87857 - 6.60080i) q^{50} -1.88446 q^{52} +1.00361i q^{53} +(0.395932 + 0.107714i) q^{55} -10.9022 q^{56} +12.8008i q^{58} +2.60748 q^{59} +9.55005 q^{61} +10.6064 q^{62} -6.18780 q^{64} +(-3.21038 + 11.8006i) q^{65} -13.6658 q^{67} +1.96322 q^{68} +(3.86573 - 14.2096i) q^{70} +7.18858 q^{71} -4.69475i q^{73} +3.74594i q^{74} +(-0.825537 + 1.25466i) q^{76} +0.789242 q^{77} +9.31356i q^{79} +(2.68278 - 9.86130i) q^{80} -17.9691i q^{82} +11.2235 q^{83} +(3.34456 - 12.2939i) q^{85} -11.7353 q^{86} +0.465141 q^{88} -0.668196 q^{89} +23.5231i q^{91} -0.697224 q^{92} -0.589109i q^{94} +(6.45038 + 7.30702i) q^{95} -2.55766 q^{97} -17.6067i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 56 q^{4} + 8 q^{16} + 32 q^{19} - 8 q^{25} - 104 q^{49} - 16 q^{55} - 16 q^{61} - 72 q^{64} - 112 q^{76} + 128 q^{85}+O(q^{100}) \) 24 * q - 56 * q^4 + 8 * q^16 + 32 * q^19 - 8 * q^25 - 104 * q^49 - 16 * q^55 - 16 * q^61 - 72 * q^64 - 112 * q^76 + 128 * q^85

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