LMFDB - Embedded newform 275.3.c.f.76.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(76,275)] 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("275.76"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-8,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 30x^{6} + 280x^{4} + 890x^{2} + 895 $ x^8 + 30x^6 + 280x^4 + 890*x^2 + 895
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.2
Root			$-3.15955i$ of defining polynomial
Character	$\chi$	$=$	275.76
Dual form			275.3.c.f.76.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.15955i q^{2} +3.03112 q^{3} -5.98274 q^{4} -9.57697i q^{6} -5.67155i q^{7} +6.26455i q^{8} +0.187686 q^{9} +(10.8573 - 1.76614i) q^{11} -18.1344 q^{12} -17.2349i q^{13} -17.9195 q^{14} -4.13780 q^{16} +3.43437i q^{17} -0.593004i q^{18} +18.5738i q^{19} -17.1911i q^{21} +(-5.58019 - 34.3041i) q^{22} -15.7918 q^{23} +18.9886i q^{24} -54.4546 q^{26} -26.7112 q^{27} +33.9314i q^{28} -52.6031i q^{29} +27.5484 q^{31} +38.1318i q^{32} +(32.9097 - 5.35337i) q^{33} +10.8510 q^{34} -1.12288 q^{36} +40.1425 q^{37} +58.6848 q^{38} -52.2411i q^{39} +74.8398i q^{41} -54.3162 q^{42} -9.72983i q^{43} +(-64.9563 + 10.5663i) q^{44} +49.8949i q^{46} -18.2212 q^{47} -12.5422 q^{48} +16.8335 q^{49} +10.4100i q^{51} +103.112i q^{52} +75.2040 q^{53} +84.3952i q^{54} +35.5297 q^{56} +56.2994i q^{57} -166.202 q^{58} +1.75672 q^{59} +48.5900i q^{61} -87.0404i q^{62} -1.06447i q^{63} +103.928 q^{64} +(-16.9142 - 103.980i) q^{66} +35.4901 q^{67} -20.5469i q^{68} -47.8668 q^{69} +110.499 q^{71} +1.17577i q^{72} +50.7154i q^{73} -126.832i q^{74} -111.122i q^{76} +(-10.0167 - 61.5777i) q^{77} -165.058 q^{78} -12.7481i q^{79} -82.6540 q^{81} +236.460 q^{82} -112.062i q^{83} +102.850i q^{84} -30.7419 q^{86} -159.446i q^{87} +(11.0640 + 68.0161i) q^{88} +66.3600 q^{89} -97.7488 q^{91} +94.4781 q^{92} +83.5024 q^{93} +57.5709i q^{94} +115.582i q^{96} -65.1302 q^{97} -53.1863i q^{98} +(2.03776 - 0.331479i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} - 28 q^{4} - 4 q^{9} + 8 q^{11} + 48 q^{12} + 88 q^{16} - 80 q^{22} - 8 q^{23} - 100 q^{26} + 16 q^{27} + 36 q^{31} + 152 q^{33} + 80 q^{34} - 216 q^{36} + 88 q^{37} + 160 q^{38} - 280 q^{42}+ \cdots - 184 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 - 28 * q^4 - 4 * q^9 + 8 * q^11 + 48 * q^12 + 88 * q^16 - 80 * q^22 - 8 * q^23 - 100 * q^26 + 16 * q^27 + 36 * q^31 + 152 * q^33 + 80 * q^34 - 216 * q^36 + 88 * q^37 + 160 * q^38 - 280 * q^42 + 12 * q^44 + 8 * q^47 - 488 * q^48 + 172 * q^49 + 152 * q^53 - 80 * q^56 - 160 * q^58 - 16 * q^59 - 588 * q^64 + 180 * q^66 + 88 * q^67 + 8 * q^69 + 276 * q^71 - 160 * q^77 - 160 * q^78 - 320 * q^81 + 520 * q^82 + 420 * q^86 + 520 * q^88 + 444 * q^89 - 40 * q^91 + 368 * q^92 + 104 * q^93 - 312 * q^97 - 184 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	3.15955i		−	1.57977i	−0.613253	−	0.789887i	$-0.710139\pi$
$2$		−	3.15955i		−	1.57977i	0.613253	−	0.789887i	$-0.289861\pi$
$3$	3.03112			1.01037			0.505187	−	0.863010i	$-0.331424\pi$
$3$	3.03112			1.01037			0.505187	+	0.863010i	$0.331424\pi$
$4$	−5.98274			−1.49568
$5$		0			0
$5$		0			0
$6$		−	9.57697i		−	1.59616i
$7$		−	5.67155i		−	0.810221i	−0.914268	−	0.405111i	$-0.867233\pi$
$7$		−	5.67155i		−	0.810221i	0.914268	−	0.405111i	$-0.132767\pi$
$8$			6.26455i			0.783069i
$9$	0.187686			0.0208540
$10$		0			0
$11$	10.8573	−	1.76614i	0.987026	−	0.160558i
$11$	10.8573	−	1.76614i	0.987026	−	0.160558i
$12$	−18.1344			−1.51120
$13$		−	17.2349i		−	1.32576i	−0.748724	−	0.662882i	$-0.769333\pi$
$13$		−	17.2349i		−	1.32576i	0.748724	−	0.662882i	$-0.230667\pi$
$14$	−17.9195			−1.27997
$15$		0			0
$16$	−4.13780			−0.258612
$17$			3.43437i			0.202022i	0.994885	+	0.101011i	$0.0322077\pi$
$17$			3.43437i			0.202022i	−0.994885	+	0.101011i	$0.967792\pi$
$18$		−	0.593004i		−	0.0329446i
$19$			18.5738i			0.977569i	0.872405	+	0.488784i	$0.162559\pi$
$19$			18.5738i			0.977569i	−0.872405	+	0.488784i	$0.837441\pi$
$20$		0			0
$21$		−	17.1911i		−	0.818626i
$22$	−5.58019	−	34.3041i	−0.253645	−	1.55928i
$23$	−15.7918			−0.686599			−0.343300	−	0.939226i	$-0.611545\pi$
$23$	−15.7918			−0.686599			−0.343300	+	0.939226i	$0.611545\pi$
$24$			18.9886i			0.791192i
$25$		0			0
$26$	−54.4546			−2.09441
$27$	−26.7112			−0.989303
$28$			33.9314i			1.21184i
$29$		−	52.6031i		−	1.81390i	−0.421238	−	0.906950i	$-0.638404\pi$
$29$		−	52.6031i		−	1.81390i	0.421238	−	0.906950i	$-0.361596\pi$
$30$		0			0
$31$	27.5484			0.888657			0.444328	−	0.895864i	$-0.353442\pi$
$31$	27.5484			0.888657			0.444328	+	0.895864i	$0.353442\pi$
$32$			38.1318i			1.19162i
$33$	32.9097	−	5.35337i	0.997265	−	0.162223i
$34$	10.8510			0.319148
$35$		0			0
$36$	−1.12288			−0.0311910
$37$	40.1425			1.08493			0.542467	−	0.840077i	$-0.317490\pi$
$37$	40.1425			1.08493			0.542467	+	0.840077i	$0.317490\pi$
$38$	58.6848			1.54434
$39$		−	52.2411i		−	1.33952i
$40$		0			0
$41$			74.8398i			1.82536i	0.408675	+	0.912680i	$0.365991\pi$
$41$			74.8398i			1.82536i	−0.408675	+	0.912680i	$0.634009\pi$
$42$	−54.3162			−1.29324
$43$		−	9.72983i		−	0.226275i	−0.993579	−	0.113138i	$-0.963910\pi$
$43$		−	9.72983i		−	0.226275i	0.993579	−	0.113138i	$-0.0360901\pi$
$44$	−64.9563	+	10.5663i	−1.47628	+	0.240144i
$45$		0			0
$46$			49.8949i			1.08467i
$47$	−18.2212			−0.387686			−0.193843	−	0.981033i	$-0.562095\pi$
$47$	−18.2212			−0.387686			−0.193843	+	0.981033i	$0.562095\pi$
$48$	−12.5422			−0.261295
$49$	16.8335			0.343541
$50$		0			0
$51$			10.4100i			0.204117i
$52$			103.112i			1.98292i
$53$	75.2040			1.41894			0.709471	−	0.704734i	$-0.248934\pi$
$53$	75.2040			1.41894			0.709471	+	0.704734i	$0.248934\pi$
$54$			84.3952i			1.56287i
$55$		0			0
$56$	35.5297			0.634459
$57$			56.2994i			0.987709i
$58$	−166.202			−2.86555
$59$	1.75672			0.0297750			0.0148875	−	0.999889i	$-0.495261\pi$
$59$	1.75672			0.0297750			0.0148875	+	0.999889i	$0.495261\pi$
$60$		0			0
$61$			48.5900i			0.796557i	0.917265	+	0.398278i	$0.130392\pi$
$61$			48.5900i			0.796557i	−0.917265	+	0.398278i	$0.869608\pi$
$62$		−	87.0404i		−	1.40388i
$63$		−	1.06447i		−	0.0168964i
$64$	103.928			1.62387
$65$		0			0
$66$	−16.9142	−	103.980i	−0.256276	−	1.57545i
$67$	35.4901			0.529702			0.264851	−	0.964289i	$-0.414677\pi$
$67$	35.4901			0.529702			0.264851	+	0.964289i	$0.414677\pi$
$68$		−	20.5469i		−	0.302161i
$69$	−47.8668			−0.693721
$70$		0			0
$71$	110.499			1.55632			0.778159	−	0.628067i	$-0.216154\pi$
$71$	110.499			1.55632			0.778159	+	0.628067i	$0.216154\pi$
$72$			1.17577i			0.0163301i
$73$			50.7154i			0.694732i	0.937730	+	0.347366i	$0.112924\pi$
$73$			50.7154i			0.694732i	−0.937730	+	0.347366i	$0.887076\pi$
$74$		−	126.832i		−	1.71395i
$75$		0			0
$76$		−	111.122i		−	1.46213i
$77$	−10.0167	−	61.5777i	−0.130087	−	0.799710i
$78$	−165.058			−2.11613
$79$		−	12.7481i		−	0.161368i	−0.996740	−	0.0806842i	$-0.974289\pi$
$79$		−	12.7481i		−	0.161368i	0.996740	−	0.0806842i	$-0.0257105\pi$
$80$		0			0
$81$	−82.6540			−1.02042
$82$	236.460			2.88366
$83$		−	112.062i		−	1.35015i	−0.737749	−	0.675075i	$-0.764111\pi$
$83$		−	112.062i		−	1.35015i	0.737749	−	0.675075i	$-0.235889\pi$
$84$			102.850i			1.22441i
$85$		0			0
$86$	−30.7419			−0.357463
$87$		−	159.446i		−	1.83272i
$88$	11.0640	+	68.0161i	0.125728	+	0.772910i
$89$	66.3600			0.745618			0.372809	−	0.927908i	$-0.378395\pi$
$89$	66.3600			0.745618			0.372809	+	0.927908i	$0.378395\pi$
$90$		0			0
$91$	−97.7488			−1.07416
$92$	94.4781			1.02694
$93$	83.5024			0.897875
$94$			57.5709i			0.612456i
$95$		0			0
$96$			115.582i			1.20398i
$97$	−65.1302			−0.671445			−0.335723	−	0.941961i	$-0.608980\pi$
$97$	−65.1302			−0.671445			−0.335723	+	0.941961i	$0.608980\pi$
$98$		−	53.1863i		−	0.542717i
$99$	2.03776	−	0.331479i	0.0205835	−	0.00334828i
$100$		0			0
$101$		−	172.019i		−	1.70316i	−0.524229	−	0.851578i	$-0.675646\pi$
$101$		−	172.019i		−	1.70316i	0.524229	−	0.851578i	$-0.324354\pi$
$102$	32.8908			0.322459
$103$	−28.3278			−0.275027			−0.137514	−	0.990500i	$-0.543911\pi$
$103$	−28.3278			−0.275027			−0.137514	+	0.990500i	$0.543911\pi$
$104$	107.969			1.03816
$105$		0			0
$106$		−	237.610i		−	2.24161i
$107$			63.2464i			0.591088i	0.955329	+	0.295544i	$0.0955009\pi$
$107$			63.2464i			0.591088i	−0.955329	+	0.295544i	$0.904499\pi$
$108$	159.806			1.47968
$109$			128.641i			1.18020i	0.807331	+	0.590098i	$0.200911\pi$
$109$			128.641i			1.18020i	−0.807331	+	0.590098i	$0.799089\pi$
$110$		0			0
$111$	121.677			1.09619
$112$			23.4677i			0.209533i
$113$	35.4694			0.313889			0.156944	−	0.987607i	$-0.449836\pi$
$113$	35.4694			0.313889			0.156944	+	0.987607i	$0.449836\pi$
$114$	177.881			1.56036
$115$		0			0
$116$			314.711i			2.71302i
$117$		−	3.23476i		−	0.0276475i
$118$		−	5.55045i		−	0.0470377i
$119$	19.4782			0.163682
$120$		0			0
$121$	114.762	−	38.3509i	0.948442	−	0.316949i
$122$	153.522			1.25838
$123$			226.848i			1.84430i
$124$	−164.815			−1.32915
$125$		0			0
$126$	−3.36325			−0.0266925
$127$			210.686i			1.65895i	0.558547	+	0.829473i	$0.311359\pi$
$127$			210.686i			1.65895i	−0.558547	+	0.829473i	$0.688641\pi$
$128$		−	175.838i		−	1.37374i
$129$		−	29.4923i		−	0.228622i
$130$		0			0
$131$		−	131.724i		−	1.00553i	−0.864424	−	0.502764i	$-0.832316\pi$
$131$		−	131.724i		−	1.00553i	0.864424	−	0.502764i	$-0.167684\pi$
$132$	−196.890	+	32.0278i	−1.49159	+	0.242635i
$133$	105.342			0.792047
$134$		−	112.133i		−	0.836810i
$135$		0			0
$136$	−21.5148			−0.158197
$137$	−167.934			−1.22580			−0.612898	−	0.790162i	$-0.709996\pi$
$137$	−167.934			−1.22580			−0.612898	+	0.790162i	$0.709996\pi$
$138$			151.237i			1.09592i
$139$			90.6142i			0.651901i	0.945387	+	0.325950i	$0.105684\pi$
$139$			90.6142i			0.651901i	−0.945387	+	0.325950i	$0.894316\pi$
$140$		0			0
$141$	−55.2308			−0.391708
$142$		−	349.125i		−	2.45863i
$143$	−30.4392	−	187.125i	−0.212862	−	1.30856i
$144$	−0.776608			−0.00539311
$145$		0			0
$146$	160.238			1.09752
$147$	51.0244			0.347105
$148$	−240.162			−1.62272
$149$		−	72.8977i		−	0.489246i	−0.969618	−	0.244623i	$-0.921336\pi$
$149$		−	72.8977i		−	0.489246i	0.969618	−	0.244623i	$-0.0786642\pi$
$150$		0			0
$151$			237.180i			1.57073i	0.619035	+	0.785364i	$0.287524\pi$
$151$			237.180i			1.57073i	−0.619035	+	0.785364i	$0.712476\pi$
$152$	−116.357			−0.765504
$153$			0.644584i			0.00421296i
$154$	−194.558	+	31.6483i	−1.26336	+	0.205509i
$155$		0			0
$156$			312.545i			2.00349i
$157$	−105.915			−0.674620			−0.337310	−	0.941394i	$-0.609517\pi$
$157$	−105.915			−0.674620			−0.337310	+	0.941394i	$0.609517\pi$
$158$	−40.2783			−0.254926
$159$	227.952			1.43366
$160$		0			0
$161$			89.5639i			0.556297i
$162$			261.149i			1.61203i
$163$	−143.233			−0.878730			−0.439365	−	0.898309i	$-0.644797\pi$
$163$	−143.233			−0.878730			−0.439365	+	0.898309i	$0.644797\pi$
$164$		−	447.747i		−	2.73016i
$165$		0			0
$166$	−354.067			−2.13293
$167$		−	35.5974i		−	0.213158i	−0.994304	−	0.106579i	$-0.966010\pi$
$167$		−	35.5974i		−	0.213158i	0.994304	−	0.106579i	$-0.0339897\pi$
$168$	107.695			0.641041
$169$	−128.043			−0.757650
$170$		0			0
$171$			3.48605i			0.0203862i
$172$			58.2110i			0.338436i
$173$			196.047i			1.13322i	0.823987	+	0.566609i	$0.191745\pi$
$173$			196.047i			1.13322i	−0.823987	+	0.566609i	$0.808255\pi$
$174$	−503.778			−2.89528
$175$		0			0
$176$	−44.9253	+	7.30791i	−0.255257	+	0.0415222i
$177$	5.32484			0.0300838
$178$		−	209.668i		−	1.17791i
$179$	−65.1824			−0.364148			−0.182074	−	0.983285i	$-0.558281\pi$
$179$	−65.1824			−0.364148			−0.182074	+	0.983285i	$0.558281\pi$
$180$		0			0
$181$	−157.016			−0.867493			−0.433746	−	0.901035i	$-0.642809\pi$
$181$	−157.016			−0.867493			−0.433746	+	0.901035i	$0.642809\pi$
$182$			308.842i			1.69693i
$183$			147.282i			0.804820i
$184$		−	98.9285i		−	0.537655i
$185$		0			0
$186$		−	263.830i		−	1.41844i
$187$	6.06556	+	37.2879i	0.0324361	+	0.199401i
$188$	109.013			0.579856
$189$			151.494i			0.801554i
$190$		0			0
$191$	161.967			0.847995			0.423997	−	0.905663i	$-0.360627\pi$
$191$	161.967			0.847995			0.423997	+	0.905663i	$0.360627\pi$
$192$	315.018			1.64072
$193$			0.742915i			0.00384930i	0.999998	+	0.00192465i	$0.000612635\pi$
$193$			0.742915i			0.00384930i	−0.999998	+	0.00192465i	$0.999387\pi$
$194$			205.782i			1.06073i
$195$		0			0
$196$	−100.711			−0.513829
$197$		−	43.0945i		−	0.218754i	−0.994000	−	0.109377i	$-0.965114\pi$
$197$		−	43.0945i		−	0.218754i	0.994000	−	0.109377i	$-0.0348855\pi$
$198$	−1.04732	−	6.43841i	−0.00528952	−	0.0325172i
$199$	−201.933			−1.01474			−0.507370	−	0.861729i	$-0.669382\pi$
$199$	−201.933			−1.01474			−0.507370	+	0.861729i	$0.669382\pi$
$200$		0			0
$201$	107.575			0.535197
$202$	−543.501			−2.69060
$203$	−298.341			−1.46966
$204$		−	62.2802i		−	0.305295i
$205$		0			0
$206$			89.5031i			0.434481i
$207$	−2.96390			−0.0143184
$208$			71.3147i			0.342859i
$209$	32.8038	+	201.661i	0.156956	+	0.964886i
$210$		0			0
$211$			53.4705i			0.253415i	0.991940	+	0.126707i	$0.0404409\pi$
$211$			53.4705i			0.253415i	−0.991940	+	0.126707i	$0.959559\pi$
$212$	−449.926			−2.12229
$213$	334.934			1.57246
$214$	199.830			0.933785
$215$		0			0
$216$		−	167.334i		−	0.774693i
$217$		−	156.242i		−	0.720009i
$218$	406.449			1.86444
$219$			153.725i			0.701939i
$220$		0			0
$221$	59.1911			0.267833
$222$		−	384.444i		−	1.73173i
$223$	282.600			1.26726			0.633632	−	0.773635i	$-0.281563\pi$
$223$	282.600			1.26726			0.633632	+	0.773635i	$0.281563\pi$
$224$	216.266			0.965475
$225$		0			0
$226$		−	112.067i		−	0.495873i
$227$		−	111.251i		−	0.490092i	−0.969511	−	0.245046i	$-0.921197\pi$
$227$		−	111.251i		−	0.490092i	0.969511	−	0.245046i	$-0.0788031\pi$
$228$		−	336.825i		−	1.47730i
$229$	−53.3814			−0.233107			−0.116553	−	0.993184i	$-0.537185\pi$
$229$	−53.3814			−0.233107			−0.116553	+	0.993184i	$0.537185\pi$
$230$		0			0
$231$	−30.3619	−	186.649i	−0.131437	−	0.808006i
$232$	329.535			1.42041
$233$		−	42.7082i		−	0.183297i	−0.995791	−	0.0916485i	$-0.970786\pi$
$233$		−	42.7082i		−	0.183297i	0.995791	−	0.0916485i	$-0.0292136\pi$
$234$	−10.2204			−0.0436768
$235$		0			0
$236$	−10.5100			−0.0445340
$237$		−	38.6411i		−	0.163042i
$238$		−	61.5423i		−	0.258581i
$239$			216.974i			0.907840i	0.891042	+	0.453920i	$0.149975\pi$
$239$			216.974i			0.907840i	−0.891042	+	0.453920i	$0.850025\pi$
$240$		0			0
$241$		−	155.081i		−	0.643488i	−0.946827	−	0.321744i	$-0.895731\pi$
$241$		−	155.081i		−	0.643488i	0.946827	−	0.321744i	$-0.104269\pi$
$242$	−121.171	−	362.594i	−0.500708	−	1.49832i
$243$	−10.1334			−0.0417013
$244$		−	290.701i		−	1.19140i
$245$		0			0
$246$	716.738			2.91357
$247$	320.118			1.29603
$248$			172.578i			0.695880i
$249$		−	339.675i		−	1.36416i
$250$		0			0
$251$	−116.539			−0.464300			−0.232150	−	0.972680i	$-0.574576\pi$
$251$	−116.539			−0.464300			−0.232150	+	0.972680i	$0.574576\pi$
$252$			6.36846i			0.0252717i
$253$	−171.456	+	27.8904i	−0.677692	+	0.110239i
$254$	665.673			2.62076
$255$		0			0
$256$	−139.857			−0.546317
$257$	85.7024			0.333472			0.166736	−	0.986002i	$-0.446677\pi$
$257$	85.7024			0.333472			0.166736	+	0.986002i	$0.446677\pi$
$258$	−93.1822			−0.361171
$259$		−	227.670i		−	0.879037i
$260$		0			0
$261$		−	9.87288i		−	0.0378271i
$262$	−416.189			−1.58851
$263$			398.864i			1.51659i	0.651911	+	0.758296i	$0.273968\pi$
$263$			398.864i			1.51659i	−0.651911	+	0.758296i	$0.726032\pi$
$264$	33.5365	+	206.165i	0.127032	+	0.780928i
$265$		0			0
$266$		−	332.834i		−	1.25125i
$267$	201.145			0.753353
$268$	−212.328			−0.792268
$269$	−237.209			−0.881819			−0.440910	−	0.897552i	$-0.645344\pi$
$269$	−237.209			−0.881819			−0.440910	+	0.897552i	$0.645344\pi$
$270$		0			0
$271$		−	34.0378i		−	0.125601i	−0.998026	−	0.0628003i	$-0.979997\pi$
$271$		−	34.0378i		−	0.125601i	0.998026	−	0.0628003i	$-0.0200031\pi$
$272$		−	14.2107i		−	0.0522453i
$273$	−296.288			−1.08530
$274$			530.595i			1.93648i
$275$		0			0
$276$	286.374			1.03759
$277$			202.654i			0.731604i	0.930693	+	0.365802i	$0.119205\pi$
$277$			202.654i			0.731604i	−0.930693	+	0.365802i	$0.880795\pi$
$278$	286.300			1.02986
$279$	5.17045			0.0185321
$280$		0			0
$281$		−	100.966i		−	0.359311i	−0.983730	−	0.179655i	$-0.942502\pi$
$281$		−	100.966i		−	0.359311i	0.983730	−	0.179655i	$-0.0574982\pi$
$282$			174.504i			0.618809i
$283$			162.113i			0.572836i	0.958105	+	0.286418i	$0.0924646\pi$
$283$			162.113i			0.572836i	−0.958105	+	0.286418i	$0.907535\pi$
$284$	−661.084			−2.32776
$285$		0			0
$286$	−591.229	+	96.1741i	−2.06723	+	0.336273i
$287$	424.458			1.47895
$288$			7.15681i			0.0248500i
$289$	277.205			0.959187
$290$		0			0
$291$	−197.417			−0.678410
$292$		−	303.417i		−	1.03910i
$293$		−	372.772i		−	1.27226i	−0.771582	−	0.636130i	$-0.780534\pi$
$293$		−	372.772i		−	1.27226i	0.771582	−	0.636130i	$-0.219466\pi$
$294$		−	161.214i		−	0.548347i
$295$		0			0
$296$			251.475i			0.849578i
$297$	−290.011	+	47.1756i	−0.976468	+	0.158840i
$298$	−230.324			−0.772898
$299$			272.170i			0.910268i
$300$		0			0
$301$	−55.1832			−0.183333
$302$	749.381			2.48139
$303$		−	521.409i		−	1.72082i
$304$		−	76.8547i		−	0.252811i
$305$		0			0
$306$	2.03659			0.00665553
$307$			445.994i			1.45275i	0.687300	+	0.726374i	$0.258796\pi$
$307$			445.994i			1.45275i	−0.687300	+	0.726374i	$0.741204\pi$
$308$	59.9274	+	368.403i	0.194570	+	1.19611i
$309$	−85.8650			−0.277880
$310$		0			0
$311$	−249.222			−0.801357			−0.400679	−	0.916219i	$-0.631226\pi$
$311$	−249.222			−0.801357			−0.400679	+	0.916219i	$0.631226\pi$
$312$	327.267			1.04893
$313$	−463.222			−1.47994			−0.739971	−	0.672638i	$-0.765161\pi$
$313$	−463.222			−1.47994			−0.739971	+	0.672638i	$0.765161\pi$
$314$			334.644i			1.06575i
$315$		0			0
$316$			76.2686i			0.241356i
$317$	−167.548			−0.528542			−0.264271	−	0.964448i	$-0.585131\pi$
$317$	−167.548			−0.528542			−0.264271	+	0.964448i	$0.585131\pi$
$318$		−	720.226i		−	2.26486i
$319$	−92.9042	−	571.127i	−0.291236	−	1.79037i
$320$		0			0
$321$			191.707i			0.597220i
$322$	282.981			0.878824
$323$	−63.7893			−0.197490
$324$	494.497			1.52623
$325$		0			0
$326$			452.551i			1.38819i
$327$			389.928i			1.19244i
$328$	−468.838			−1.42938
$329$			103.343i			0.314112i
$330$		0			0
$331$	8.98005			0.0271301			0.0135650	−	0.999908i	$-0.495682\pi$
$331$	8.98005			0.0271301			0.0135650	+	0.999908i	$0.495682\pi$
$332$			670.440i			2.01940i
$333$	7.53420			0.0226252
$334$	−112.472			−0.336742
$335$		0			0
$336$			71.1335i			0.211707i
$337$		−	263.901i		−	0.783090i	−0.920159	−	0.391545i	$-0.871941\pi$
$337$		−	263.901i		−	0.783090i	0.920159	−	0.391545i	$-0.128059\pi$
$338$			404.557i			1.19692i
$339$	107.512			0.317145
$340$		0			0
$341$	299.101	−	48.6541i	0.877128	−	0.142681i
$342$	11.0143			0.0322056
$343$		−	373.378i		−	1.08857i
$344$	60.9530			0.177189
$345$		0			0
$346$	619.419			1.79023
$347$		−	611.749i		−	1.76297i	−0.472216	−	0.881483i	$-0.656546\pi$
$347$		−	611.749i		−	1.76297i	0.472216	−	0.881483i	$-0.343454\pi$
$348$			953.925i			2.74117i
$349$		−	282.223i		−	0.808662i	−0.914613	−	0.404331i	$-0.867504\pi$
$349$		−	282.223i		−	0.808662i	0.914613	−	0.404331i	$-0.132496\pi$
$350$		0			0
$351$			460.365i			1.31158i
$352$	67.3459	+	414.008i	0.191324	+	1.17616i
$353$	173.629			0.491868			0.245934	−	0.969287i	$-0.420905\pi$
$353$	173.629			0.491868			0.245934	+	0.969287i	$0.420905\pi$
$354$		−	16.8241i		−	0.0475256i
$355$		0			0
$356$	−397.015			−1.11521
$357$	59.0407			0.165380
$358$			205.947i			0.575271i
$359$		−	285.384i		−	0.794941i	−0.917615	−	0.397471i	$-0.869888\pi$
$359$		−	285.384i		−	0.794941i	0.917615	−	0.397471i	$-0.130112\pi$
$360$		0			0
$361$	16.0139			0.0443597
$362$			496.100i			1.37044i
$363$	347.856	−	116.246i	0.958281	−	0.320237i
$364$	584.805			1.60661
$365$		0			0
$366$	465.344			1.27143
$367$	324.275			0.883582			0.441791	−	0.897118i	$-0.354343\pi$
$367$	324.275			0.883582			0.441791	+	0.897118i	$0.354343\pi$
$368$	65.3432			0.177563
$369$			14.0464i			0.0380661i
$370$		0			0
$371$		−	426.523i		−	1.14966i
$372$	−499.573			−1.34294
$373$			128.367i			0.344148i	0.985084	+	0.172074i	$0.0550469\pi$
$373$			128.367i			0.344148i	−0.985084	+	0.172074i	$0.944953\pi$
$374$	117.813	−	19.1644i	0.315008	−	0.0512418i
$375$		0			0
$376$		−	114.148i		−	0.303585i
$377$	−906.611			−2.40480
$378$	478.652			1.26627
$379$	684.510			1.80610			0.903048	−	0.429540i	$-0.141324\pi$
$379$	684.510			1.80610			0.903048	+	0.429540i	$0.141324\pi$
$380$		0			0
$381$			638.615i			1.67615i
$382$		−	511.742i		−	1.33964i
$383$	−338.766			−0.884506			−0.442253	−	0.896890i	$-0.645821\pi$
$383$	−338.766			−0.884506			−0.442253	+	0.896890i	$0.645821\pi$
$384$		−	532.987i		−	1.38799i
$385$		0			0
$386$	2.34727			0.00608102
$387$		−	1.82616i		−	0.00471875i
$388$	389.657			1.00427
$389$	−552.950			−1.42146			−0.710732	−	0.703463i	$-0.751636\pi$
$389$	−552.950			−1.42146			−0.710732	+	0.703463i	$0.751636\pi$
$390$		0			0
$391$		−	54.2348i		−	0.138708i
$392$			105.454i			0.269017i
$393$		−	399.272i		−	1.01596i
$394$	−136.159			−0.345581
$395$		0			0
$396$	−12.1914	+	1.98315i	−0.0307864	+	0.00500796i
$397$	−111.881			−0.281815			−0.140908	−	0.990023i	$-0.545002\pi$
$397$	−111.881			−0.281815			−0.140908	+	0.990023i	$0.545002\pi$
$398$			638.017i			1.60306i
$399$	319.305			0.800263
$400$		0			0
$401$	−284.972			−0.710654			−0.355327	−	0.934742i	$-0.615630\pi$
$401$	−284.972			−0.710654			−0.355327	+	0.934742i	$0.615630\pi$
$402$		−	339.887i		−	0.845490i
$403$		−	474.794i		−	1.17815i
$404$			1029.14i			2.54738i
$405$		0			0
$406$			942.623i			2.32173i
$407$	435.839	−	70.8972i	1.07086	−	0.174195i
$408$	−65.2139			−0.159838
$409$			122.119i			0.298580i	0.988793	+	0.149290i	$0.0476989\pi$
$409$			122.119i			0.298580i	−0.988793	+	0.149290i	$0.952301\pi$
$410$		0			0
$411$	−509.028			−1.23851
$412$	169.478			0.411354
$413$		−	9.96334i		−	0.0241243i
$414$			9.36458i			0.0226198i
$415$		0			0
$416$	657.199			1.57980
$417$			274.663i			0.658663i
$418$	637.158	−	103.645i	1.52430	−	0.247955i
$419$	407.625			0.972852			0.486426	−	0.873722i	$-0.338300\pi$
$419$	407.625			0.972852			0.486426	+	0.873722i	$0.338300\pi$
$420$		0			0
$421$	−348.212			−0.827107			−0.413554	−	0.910480i	$-0.635713\pi$
$421$	−348.212			−0.827107			−0.413554	+	0.910480i	$0.635713\pi$
$422$	168.943			0.400338
$423$	−3.41988			−0.00808481
$424$			471.119i			1.11113i
$425$		0			0
$426$		−	1058.24i		−	2.48413i
$427$	275.580			0.645387
$428$		−	378.387i		−	0.884081i
$429$	−92.2649	−	567.197i	−0.215070	−	1.32214i
$430$		0			0
$431$		−	453.606i		−	1.05245i	−0.850346	−	0.526225i	$-0.823607\pi$
$431$		−	453.606i		−	1.05245i	0.850346	−	0.526225i	$-0.176393\pi$
$432$	110.525			0.255846
$433$	−760.149			−1.75554			−0.877771	−	0.479081i	$-0.840970\pi$
$433$	−760.149			−1.75554			−0.877771	+	0.479081i	$0.840970\pi$
$434$	−493.654			−1.13745
$435$		0			0
$436$		−	769.628i		−	1.76520i
$437$		−	293.313i		−	0.671198i
$438$	485.700			1.10890
$439$			343.308i			0.782023i	0.920386	+	0.391011i	$0.127875\pi$
$439$			343.308i			0.782023i	−0.920386	+	0.391011i	$0.872125\pi$
$440$		0			0
$441$	3.15942			0.00716422
$442$		−	187.017i		−	0.423115i
$443$	−47.4703			−0.107156			−0.0535782	−	0.998564i	$-0.517063\pi$
$443$	−47.4703			−0.107156			−0.0535782	+	0.998564i	$0.517063\pi$
$444$	−727.961			−1.63955
$445$		0			0
$446$		−	892.887i		−	2.00199i
$447$		−	220.962i		−	0.494321i
$448$		−	589.433i		−	1.31570i
$449$	−339.087			−0.755205			−0.377602	−	0.925968i	$-0.623251\pi$
$449$	−339.087			−0.755205			−0.377602	+	0.925968i	$0.623251\pi$
$450$		0			0
$451$	132.177	+	812.557i	0.293076	+	1.80168i
$452$	−212.204			−0.469478
$453$			718.921i			1.58702i
$454$	−351.503			−0.774235
$455$		0			0
$456$	−352.691			−0.773445
$457$			276.791i			0.605669i	0.953043	+	0.302835i	$0.0979330\pi$
$457$			276.791i			0.605669i	−0.953043	+	0.302835i	$0.902067\pi$
$458$			168.661i			0.368256i
$459$		−	91.7360i		−	0.199861i
$460$		0			0
$461$		−	156.898i		−	0.340342i	−0.985415	−	0.170171i	$-0.945568\pi$
$461$		−	156.898i		−	0.340342i	0.985415	−	0.170171i	$-0.0544321\pi$
$462$	−589.727	+	95.9298i	−1.27647	+	0.207640i
$463$	−407.669			−0.880494			−0.440247	−	0.897877i	$-0.645109\pi$
$463$	−407.669			−0.880494			−0.440247	+	0.897877i	$0.645109\pi$
$464$			217.661i			0.469097i
$465$		0			0
$466$	−134.939			−0.289568
$467$	−749.076			−1.60402			−0.802008	−	0.597313i	$-0.796235\pi$
$467$	−749.076			−1.60402			−0.802008	+	0.597313i	$0.796235\pi$
$468$			19.3527i			0.0413520i
$469$		−	201.284i		−	0.429176i
$470$		0			0
$471$	−321.042			−0.681618
$472$			11.0051i			0.0233159i
$473$	−17.1842	−	105.640i	−0.0363302	−	0.223340i
$474$	−122.088			−0.257570
$475$		0			0
$476$	−116.533			−0.244817
$477$	14.1147			0.0295907
$478$	685.539			1.43418
$479$			11.2596i			0.0235064i	0.999931	+	0.0117532i	$0.00374124\pi$
$479$			11.2596i			0.0235064i	−0.999931	+	0.0117532i	$0.996259\pi$
$480$		0			0
$481$		−	691.854i		−	1.43837i
$482$	−489.984			−1.01657
$483$			271.479i			0.562068i
$484$	−686.588	+	229.443i	−1.41857	+	0.474056i
$485$		0			0
$486$			32.0170i			0.0658786i
$487$	734.846			1.50892			0.754462	−	0.656344i	$-0.227898\pi$
$487$	734.846			1.50892			0.754462	+	0.656344i	$0.227898\pi$
$488$	−304.394			−0.623759
$489$	−434.156			−0.887845
$490$		0			0
$491$		−	347.360i		−	0.707455i	−0.935349	−	0.353727i	$-0.884914\pi$
$491$		−	347.360i		−	0.707455i	0.935349	−	0.353727i	$-0.115086\pi$
$492$		−	1357.17i		−	2.75848i
$493$	180.658			0.366447
$494$		−	1011.43i		−	2.04743i
$495$		0			0
$496$	−113.990			−0.229818
$497$		−	626.698i		−	1.26096i
$498$	−1073.22			−2.15506
$499$	875.439			1.75439			0.877193	−	0.480138i	$-0.159413\pi$
$499$	875.439			1.75439			0.877193	+	0.480138i	$0.159413\pi$
$500$		0			0
$501$		−	107.900i		−	0.215369i
$502$			368.211i			0.733488i
$503$			505.554i			1.00508i	0.864554	+	0.502539i	$0.167601\pi$
$503$			505.554i			1.00508i	−0.864554	+	0.502539i	$0.832399\pi$
$504$	6.66844			0.0132310
$505$		0			0
$506$	88.1211	+	541.723i	0.174152	+	1.07060i
$507$	−388.113			−0.765509
$508$		−	1260.48i		−	2.48126i
$509$	−778.269			−1.52902			−0.764508	−	0.644614i	$-0.777018\pi$
$509$	−778.269			−1.52902			−0.764508	+	0.644614i	$0.777018\pi$
$510$		0			0
$511$	287.635			0.562887
$512$		−	261.468i		−	0.510679i
$513$		−	496.128i		−	0.967111i
$514$		−	270.781i		−	0.526811i
$515$		0			0
$516$			176.445i			0.341947i
$517$	−197.833	+	32.1812i	−0.382656	+	0.0622460i
$518$	−719.336			−1.38868
$519$			594.241i			1.14497i
$520$		0			0
$521$	−273.723			−0.525380			−0.262690	−	0.964880i	$-0.584610\pi$
$521$	−273.723			−0.525380			−0.262690	+	0.964880i	$0.584610\pi$
$522$	−31.1938			−0.0597583
$523$			628.316i			1.20137i	0.799486	+	0.600685i	$0.205105\pi$
$523$			628.316i			1.20137i	−0.799486	+	0.600685i	$0.794895\pi$
$524$			788.071i			1.50395i
$525$		0			0
$526$	1260.23			2.39587
$527$			94.6112i			0.179528i
$528$	−136.174	+	22.1512i	−0.257905	+	0.0419529i
$529$	−279.620			−0.528582
$530$		0			0
$531$	0.329713			0.000620928
$532$	−630.235			−1.18465
$533$	1289.86			2.42000
$534$		−	635.528i		−	1.19013i
$535$		0			0
$536$			222.329i			0.414794i
$537$	−197.576			−0.367925
$538$			749.474i			1.39307i
$539$	182.766	−	29.7303i	0.339084	−	0.0551582i
$540$		0			0
$541$			543.648i			1.00490i	0.864608	+	0.502448i	$0.167567\pi$
$541$			543.648i			1.00490i	−0.864608	+	0.502448i	$0.832433\pi$
$542$	−107.544			−0.198421
$543$	−475.935			−0.876492
$544$	−130.959			−0.240733
$545$		0			0
$546$			936.137i			1.71454i
$547$		−	421.038i		−	0.769722i	−0.922975	−	0.384861i	$-0.874249\pi$
$547$		−	421.038i		−	0.769722i	0.922975	−	0.384861i	$-0.125751\pi$
$548$	1004.71			1.83340
$549$			9.11967i			0.0166114i
$550$		0			0
$551$	977.040			1.77321
$552$		−	299.864i		−	0.543232i
$553$	−72.3016			−0.130744
$554$	640.296			1.15577
$555$		0			0
$556$		−	542.121i		−	0.975038i
$557$			940.508i			1.68852i	0.535930	+	0.844262i	$0.319961\pi$
$557$			940.508i			1.68852i	−0.535930	+	0.844262i	$0.680039\pi$
$558$		−	16.3363i		−	0.0292765i
$559$	−167.693			−0.299987
$560$		0			0
$561$	18.3854	+	113.024i	0.0327726	+	0.201469i
$562$	−319.008			−0.567629
$563$		−	285.806i		−	0.507649i	−0.967250	−	0.253824i	$-0.918312\pi$
$563$		−	285.806i		−	0.507649i	0.967250	−	0.253824i	$-0.0816885\pi$
$564$	330.431			0.585871
$565$		0			0
$566$	512.203			0.904952
$567$			468.776i			0.826765i
$568$			692.224i			1.21870i
$569$			307.137i			0.539783i	0.962891	+	0.269892i	$0.0869879\pi$
$569$			307.137i			0.539783i	−0.962891	+	0.269892i	$0.913012\pi$
$570$		0			0
$571$		−	390.713i		−	0.684261i	−0.939652	−	0.342130i	$-0.888852\pi$
$571$		−	390.713i		−	0.684261i	0.939652	−	0.342130i	$-0.111148\pi$
$572$	182.110	+	1119.52i	0.318374	+	1.95720i
$573$	490.941			0.856791
$574$		−	1341.09i		−	2.33640i
$575$		0			0
$576$	19.5059			0.0338643
$577$	119.491			0.207090			0.103545	−	0.994625i	$-0.466981\pi$
$577$	119.491			0.207090			0.103545	+	0.994625i	$0.466981\pi$
$578$		−	875.843i		−	1.51530i
$579$			2.25186i			0.00388923i
$580$		0			0
$581$	−635.568			−1.09392
$582$			623.749i			1.07173i
$583$	816.511	−	132.820i	1.40053	−	0.227822i
$584$	−317.710			−0.544023
$585$		0			0
$586$	−1177.79			−2.00988
$587$	340.259			0.579658			0.289829	−	0.957078i	$-0.406402\pi$
$587$	340.259			0.579658			0.289829	+	0.957078i	$0.406402\pi$
$588$	−305.266			−0.519159
$589$			511.678i			0.868723i
$590$		0			0
$591$		−	130.625i		−	0.221023i
$592$	−166.102			−0.280577
$593$			752.004i			1.26813i	0.773278	+	0.634067i	$0.218616\pi$
$593$			752.004i			1.26813i	−0.773278	+	0.634067i	$0.781384\pi$
$594$	149.053	+	916.303i	0.250932	+	1.54260i
$595$		0			0
$596$			436.128i			0.731758i
$597$	−612.083			−1.02527
$598$	859.935			1.43802
$599$	274.841			0.458833			0.229416	−	0.973328i	$-0.426318\pi$
$599$	274.841			0.458833			0.229416	+	0.973328i	$0.426318\pi$
$600$		0			0
$601$			397.025i			0.660608i	0.943875	+	0.330304i	$0.107151\pi$
$601$			397.025i			0.660608i	−0.943875	+	0.330304i	$0.892849\pi$
$602$			174.354i			0.289625i
$603$	6.66100			0.0110464
$604$		−	1418.98i		−	2.34931i
$605$		0			0
$606$	−1647.42			−2.71851
$607$		−	351.597i		−	0.579238i	−0.957142	−	0.289619i	$-0.906471\pi$
$607$		−	351.597i		−	0.579238i	0.957142	−	0.289619i	$-0.0935286\pi$
$608$	−708.252			−1.16489
$609$	−904.308			−1.48491
$610$		0			0
$611$			314.042i			0.513980i
$612$		−	3.85637i		−	0.00630127i
$613$		−	547.965i		−	0.893907i	−0.894557	−	0.446953i	$-0.852509\pi$
$613$		−	547.965i		−	0.893907i	0.894557	−	0.446953i	$-0.147491\pi$
$614$	1409.14			2.29501
$615$		0			0
$616$	385.757	−	62.7503i	0.626228	−	0.101867i
$617$	1124.68			1.82282			0.911408	−	0.411505i	$-0.134997\pi$
$617$	1124.68			1.82282			0.911408	+	0.411505i	$0.134997\pi$
$618$			271.295i			0.438988i
$619$	82.7193			0.133634			0.0668169	−	0.997765i	$-0.478716\pi$
$619$	82.7193			0.133634			0.0668169	+	0.997765i	$0.478716\pi$
$620$		0			0
$621$	421.817			0.679254
$622$			787.429i			1.26596i
$623$		−	376.364i		−	0.604116i
$624$			216.163i			0.346416i
$625$		0			0
$626$			1463.57i			2.33797i
$627$	99.4324	+	611.259i	0.158584	+	0.974895i
$628$	633.663			1.00902
$629$			137.864i			0.219180i
$630$		0			0
$631$	317.879			0.503771			0.251885	−	0.967757i	$-0.418949\pi$
$631$	317.879			0.503771			0.251885	+	0.967757i	$0.418949\pi$
$632$	79.8612			0.126363
$633$			162.076i			0.256043i
$634$			529.375i			0.834976i
$635$		0			0
$636$	−1363.78			−2.14431
$637$		−	290.125i		−	0.455454i
$638$	−1804.50	+	293.535i	−2.82838	+	0.460086i
$639$	20.7391			0.0324555
$640$		0			0
$641$	432.182			0.674230			0.337115	−	0.941463i	$-0.390549\pi$
$641$	432.182			0.674230			0.337115	+	0.941463i	$0.390549\pi$
$642$	605.709			0.943472
$643$	−229.511			−0.356937			−0.178469	−	0.983946i	$-0.557114\pi$
$643$	−229.511			−0.356937			−0.178469	+	0.983946i	$0.557114\pi$
$644$		−	535.837i		−	0.832045i
$645$		0			0
$646$			201.545i			0.311989i
$647$	768.342			1.18755			0.593773	−	0.804633i	$-0.297638\pi$
$647$	768.342			1.18755			0.593773	+	0.804633i	$0.297638\pi$
$648$		−	517.790i		−	0.799059i
$649$	19.0733	−	3.10261i	0.0293887	−	0.00478060i
$650$		0			0
$651$		−	473.588i		−	0.727478i
$652$	856.926			1.31430
$653$	−624.977			−0.957085			−0.478543	−	0.878064i	$-0.658835\pi$
$653$	−624.977			−0.957085			−0.478543	+	0.878064i	$0.658835\pi$
$654$	1231.99			1.88378
$655$		0			0
$656$		−	309.672i		−	0.472061i
$657$			9.51859i			0.0144880i
$658$	326.516			0.496225
$659$			1104.04i			1.67533i	0.546185	+	0.837665i	$0.316080\pi$
$659$			1104.04i			1.67533i	−0.546185	+	0.837665i	$0.683920\pi$
$660$		0			0
$661$	246.985			0.373653			0.186827	−	0.982393i	$-0.440180\pi$
$661$	246.985			0.373653			0.186827	+	0.982393i	$0.440180\pi$
$662$		−	28.3729i		−	0.0428594i
$663$	179.415			0.270611
$664$	702.021			1.05726
$665$		0			0
$666$		−	23.8047i		−	0.0357427i
$667$			830.697i			1.24542i
$668$			212.970i			0.318817i
$669$	856.594			1.28041
$670$		0			0
$671$	85.8165	+	527.555i	0.127893	+	0.786223i
$672$	655.529			0.975490
$673$			715.709i			1.06346i	0.846914	+	0.531730i	$0.178458\pi$
$673$			715.709i			1.06346i	−0.846914	+	0.531730i	$0.821542\pi$
$674$	−833.808			−1.23710
$675$		0			0
$676$	766.047			1.13321
$677$		−	946.798i		−	1.39852i	−0.714867	−	0.699260i	$-0.753513\pi$
$677$		−	946.798i		−	1.39852i	0.714867	−	0.699260i	$-0.246487\pi$
$678$		−	339.689i		−	0.501017i
$679$			369.389i			0.544019i
$680$		0			0
$681$		−	337.215i		−	0.495176i
$682$	−153.725	−	945.023i	−0.225403	−	1.38566i
$683$	−67.4542			−0.0987616			−0.0493808	−	0.998780i	$-0.515725\pi$
$683$	−67.4542			−0.0987616			−0.0493808	+	0.998780i	$0.515725\pi$
$684$		−	20.8561i		−	0.0304914i
$685$		0			0
$686$	−1179.71			−1.71969
$687$	−161.805			−0.235525
$688$			40.2601i			0.0585176i
$689$		−	1296.13i		−	1.88118i
$690$		0			0
$691$	−396.379			−0.573632			−0.286816	−	0.957986i	$-0.592597\pi$
$691$	−396.379			−0.573632			−0.286816	+	0.957986i	$0.592597\pi$
$692$		−	1172.90i		−	1.69494i
$693$	−1.88000	−	11.5573i	−0.00271284	−	0.0166772i
$694$	−1932.85			−2.78509
$695$		0			0
$696$	998.860			1.43514
$697$	−257.027			−0.368762
$698$	−891.697			−1.27750
$699$		−	129.454i		−	0.185198i
$700$		0			0
$701$		−	884.194i		−	1.26133i	−0.776054	−	0.630666i	$-0.782782\pi$
$701$		−	884.194i		−	1.26133i	0.776054	−	0.630666i	$-0.217218\pi$
$702$	1454.55			2.07200
$703$			745.600i			1.06060i
$704$	1128.38	−	183.551i	1.60281	−	0.260726i
$705$		0			0
$706$		−	548.590i		−	0.777040i
$707$	−975.613			−1.37993
$708$	−31.8571			−0.0449959
$709$	−902.302			−1.27264			−0.636320	−	0.771425i	$-0.719544\pi$
$709$	−902.302			−1.27264			−0.636320	+	0.771425i	$0.719544\pi$
$710$		0			0
$711$		−	2.39265i		−	0.00336518i
$712$			415.716i			0.583871i
$713$	−435.038			−0.610151
$714$		−	186.542i		−	0.261263i
$715$		0			0
$716$	389.969			0.544650
$717$			657.673i			0.917257i
$718$	−901.684			−1.25583
$719$	1021.01			1.42004			0.710021	−	0.704180i	$-0.248685\pi$
$719$	1021.01			1.42004			0.710021	+	0.704180i	$0.248685\pi$
$720$		0			0
$721$			160.663i			0.222833i
$722$		−	50.5966i		−	0.0700784i
$723$		−	470.068i		−	0.650163i
$724$	939.387			1.29750
$725$		0			0
$726$	−367.285	−	1099.07i	−0.505902	−	1.51387i
$727$	−637.169			−0.876436			−0.438218	−	0.898869i	$-0.644390\pi$
$727$	−637.169			−0.876436			−0.438218	+	0.898869i	$0.644390\pi$
$728$		−	612.352i		−	0.841143i
$729$	713.170			0.978285
$730$		0			0
$731$	33.4158			0.0457125
$732$		−	881.150i		−	1.20376i
$733$		−	261.937i		−	0.357349i	−0.983908	−	0.178674i	$-0.942819\pi$
$733$		−	261.937i		−	0.357349i	0.983908	−	0.178674i	$-0.0571809\pi$
$734$		−	1024.56i		−	1.39586i
$735$		0			0
$736$		−	602.169i		−	0.818164i
$737$	385.326	−	62.6803i	0.522830	−	0.0850478i
$738$	44.3802			0.0601358
$739$		−	734.865i		−	0.994404i	−0.867635	−	0.497202i	$-0.834361\pi$
$739$		−	734.865i		−	0.994404i	0.867635	−	0.497202i	$-0.165639\pi$
$740$		0			0
$741$	970.317			1.30947
$742$	−1347.62			−1.81620
$743$		−	161.161i		−	0.216905i	−0.994102	−	0.108453i	$-0.965410\pi$
$743$		−	161.161i		−	0.216905i	0.994102	−	0.108453i	$-0.0345896\pi$
$744$			523.105i			0.703098i
$745$		0			0
$746$	405.583			0.543676
$747$		−	21.0326i		−	0.0281561i
$748$	−36.2886	−	223.084i	−0.0485142	−	0.298241i
$749$	358.705			0.478912
$750$		0			0
$751$	1141.77			1.52033			0.760167	−	0.649728i	$-0.225117\pi$
$751$	1141.77			1.52033			0.760167	+	0.649728i	$0.225117\pi$
$752$	75.3958			0.100260
$753$	−353.244			−0.469116
$754$			2864.48i			3.79904i
$755$		0			0
$756$		−	906.348i		−	1.19887i
$757$	−119.677			−0.158094			−0.0790469	−	0.996871i	$-0.525188\pi$
$757$	−119.677			−0.158094			−0.0790469	+	0.996871i	$0.525188\pi$
$758$		−	2162.74i		−	2.85322i
$759$	−519.704	+	84.5392i	−0.684721	+	0.111382i
$760$		0			0
$761$		−	157.280i		−	0.206676i	−0.994646	−	0.103338i	$-0.967048\pi$
$761$		−	157.280i		−	0.206676i	0.994646	−	0.103338i	$-0.0329523\pi$
$762$	2017.73			2.64794
$763$	729.596			0.956221
$764$	−969.006			−1.26833
$765$		0			0
$766$			1070.35i			1.39732i
$767$		−	30.2770i		−	0.0394746i
$768$	−423.924			−0.551984
$769$			1498.58i			1.94874i	0.224947	+	0.974371i	$0.427779\pi$
$769$			1498.58i			1.94874i	−0.224947	+	0.974371i	$0.572221\pi$
$770$		0			0
$771$	259.774			0.336931
$772$		−	4.44466i		−	0.00575734i
$773$	1528.87			1.97784			0.988920	−	0.148450i	$-0.0474283\pi$
$773$	1528.87			1.97784			0.988920	+	0.148450i	$0.0474283\pi$
$774$	−5.76982			−0.00745455
$775$		0			0
$776$		−	408.012i		−	0.525788i
$777$		−	690.096i		−	0.888155i
$778$			1747.07i			2.24559i
$779$	−1390.06			−1.78441
$780$		0			0
$781$	1199.72	−	195.155i	1.53613	−	0.249879i
$782$	−171.357			−0.219127
$783$			1405.09i			1.79450i
$784$	−69.6537			−0.0888440
$785$		0			0
$786$	−1261.52			−1.60498
$787$		−	930.613i		−	1.18248i	−0.806495	−	0.591241i	$-0.798638\pi$
$787$		−	930.613i		−	1.18248i	0.806495	−	0.591241i	$-0.201362\pi$
$788$			257.823i			0.327187i
$789$			1209.00i			1.53232i
$790$		0			0
$791$		−	201.167i		−	0.254319i
$792$	2.07657	+	12.7657i	0.00262193	+	0.0161183i
$793$	837.445			1.05605
$794$			353.492i			0.445204i
$795$		0			0
$796$	1208.11			1.51773
$797$	332.628			0.417350			0.208675	−	0.977985i	$-0.433085\pi$
$797$	332.628			0.417350			0.208675	+	0.977985i	$0.433085\pi$
$798$		−	1008.86i		−	1.26423i
$799$		−	62.5784i		−	0.0783210i
$800$		0			0
$801$	12.4549			0.0155491
$802$			900.383i			1.12267i
$803$	89.5703	+	550.632i	0.111545	+	0.685719i
$804$	−643.591			−0.800486
$805$		0			0
$806$	−1500.13			−1.86121
$807$	−719.010			−0.890966
$808$	1077.62			1.33369
$809$		−	870.764i		−	1.07635i	−0.842834	−	0.538173i	$-0.819115\pi$
$809$		−	870.764i		−	1.07635i	0.842834	−	0.538173i	$-0.180885\pi$
$810$		0			0
$811$			1369.14i			1.68821i	0.536180	+	0.844103i	$0.319867\pi$
$811$			1369.14i			1.68821i	−0.536180	+	0.844103i	$0.680133\pi$
$812$	1784.90			2.19815
$813$		−	103.173i		−	0.126904i
$814$	−224.003	−	1377.05i	−0.275188	−	1.69171i
$815$		0			0
$816$		−	43.0744i		−	0.0527873i
$817$	180.720			0.221199
$818$	385.842			0.471689
$819$	−18.3461			−0.0224006
$820$		0			0
$821$		−	759.486i		−	0.925075i	−0.886600	−	0.462537i	$-0.846939\pi$
$821$		−	759.486i		−	0.925075i	0.886600	−	0.462537i	$-0.153061\pi$
$822$			1608.30i			1.95657i
$823$	−252.673			−0.307015			−0.153507	−	0.988148i	$-0.549057\pi$
$823$	−252.673			−0.307015			−0.153507	+	0.988148i	$0.549057\pi$
$824$		−	177.461i		−	0.215366i
$825$		0			0
$826$	−31.4797			−0.0381110
$827$			172.995i			0.209184i	0.994515	+	0.104592i	$0.0333536\pi$
$827$			172.995i			0.209184i	−0.994515	+	0.104592i	$0.966646\pi$
$828$	17.7322			0.0214157
$829$	1145.40			1.38167			0.690834	−	0.723013i	$-0.257244\pi$
$829$	1145.40			1.38167			0.690834	+	0.723013i	$0.257244\pi$
$830$		0			0
$831$			614.270i			0.739193i
$832$		−	1791.19i		−	2.15287i
$833$			57.8125i			0.0694027i
$834$	867.809			1.04054
$835$		0			0
$836$	−196.257	−	1206.49i	−0.234757	−	1.44317i
$837$	−735.849			−0.879151
$838$		−	1287.91i		−	1.53689i
$839$	−41.7126			−0.0497170			−0.0248585	−	0.999691i	$-0.507914\pi$
$839$	−41.7126			−0.0497170			−0.0248585	+	0.999691i	$0.507914\pi$
$840$		0			0
$841$	−1926.09			−2.29023
$842$			1100.19i			1.30664i
$843$		−	306.041i		−	0.363038i
$844$		−	319.900i		−	0.379029i
$845$		0			0
$846$			10.8053i			0.0127722i
$847$	−217.509	−	650.876i	−0.256799	−	0.768448i
$848$	−311.179			−0.366956
$849$			491.383i			0.578778i
$850$		0			0
$851$	−633.922			−0.744915
$852$	−2003.82			−2.35191
$853$			725.094i			0.850052i	0.905181	+	0.425026i	$0.139735\pi$
$853$			725.094i			0.850052i	−0.905181	+	0.425026i	$0.860265\pi$
$854$		−	870.709i		−	1.01957i
$855$		0			0
$856$	−396.211			−0.462863
$857$		−	302.221i		−	0.352650i	−0.984332	−	0.176325i	$-0.943579\pi$
$857$		−	302.221i		−	0.352650i	0.984332	−	0.176325i	$-0.0564210\pi$
$858$	−1792.09	+	291.515i	−2.08868	+	0.339761i
$859$	−207.101			−0.241096			−0.120548	−	0.992708i	$-0.538465\pi$
$859$	−207.101			−0.241096			−0.120548	+	0.992708i	$0.538465\pi$
$860$		0			0
$861$	1286.58			1.49429
$862$	−1433.19			−1.66263
$863$	−482.444			−0.559032			−0.279516	−	0.960141i	$-0.590174\pi$
$863$	−482.444			−0.559032			−0.279516	+	0.960141i	$0.590174\pi$
$864$		−	1018.54i		−	1.17887i
$865$		0			0
$866$			2401.73i			2.77336i
$867$	840.242			0.969137
$868$			934.755i			1.07691i
$869$	−22.5149	−	138.410i	−0.0259090	−	0.159275i
$870$		0			0
$871$		−	611.669i		−	0.702260i
$872$	−805.881			−0.924176
$873$	−12.2240			−0.0140023
$874$	−926.738			−1.06034
$875$		0			0
$876$		−	919.694i		−	1.04988i
$877$			377.864i			0.430860i	0.976519	+	0.215430i	$0.0691153\pi$
$877$			377.864i			0.430860i	−0.976519	+	0.215430i	$0.930885\pi$
$878$	1084.70			1.23542
$879$		−	1129.92i		−	1.28546i
$880$		0			0
$881$	−1459.75			−1.65693			−0.828463	−	0.560045i	$-0.810784\pi$
$881$	−1459.75			−1.65693			−0.828463	+	0.560045i	$0.810784\pi$
$882$		−	9.98233i		−	0.0113178i
$883$	353.252			0.400059			0.200029	−	0.979790i	$-0.435896\pi$
$883$	353.252			0.400059			0.200029	+	0.979790i	$0.435896\pi$
$884$	−354.125			−0.400594
$885$		0			0
$886$			149.985i			0.169283i
$887$		−	174.064i		−	0.196239i	−0.995175	−	0.0981194i	$-0.968717\pi$
$887$		−	174.064i		−	0.196239i	0.995175	−	0.0981194i	$-0.0312827\pi$
$888$			762.251i			0.858391i
$889$	1194.92			1.34411
$890$		0			0
$891$	−897.398	+	145.978i	−1.00718	+	0.163836i
$892$	−1690.72			−1.89543
$893$		−	338.438i		−	0.378990i
$894$	−698.138			−0.780915
$895$		0			0
$896$	−997.275			−1.11303
$897$			824.981i			0.919711i
$898$			1071.36i			1.19305i
$899$		−	1449.13i		−	1.61193i
$900$		0			0
$901$			258.278i			0.286657i
$902$	2567.31	−	417.620i	2.84624	−	0.462993i
$903$	−167.267			−0.185235
$904$			222.200i			0.245797i
$905$		0			0
$906$	2271.46			2.50713
$907$	1341.78			1.47936			0.739679	−	0.672960i	$-0.234977\pi$
$907$	1341.78			1.47936			0.739679	+	0.672960i	$0.234977\pi$
$908$			665.586i			0.733024i
$909$		−	32.2855i		−	0.0355176i
$910$		0			0
$911$	81.8460			0.0898419			0.0449210	−	0.998991i	$-0.485696\pi$
$911$	81.8460			0.0898419			0.0449210	+	0.998991i	$0.485696\pi$
$912$		−	232.956i		−	0.255434i
$913$	−197.918	−	1216.70i	−0.216777	−	1.33263i
$914$	874.534			0.956821
$915$		0			0
$916$	319.367			0.348654
$917$	−747.080			−0.814700
$918$	−289.844			−0.315734
$919$		−	146.259i		−	0.159150i	−0.996829	−	0.0795752i	$-0.974644\pi$
$919$		−	146.259i		−	0.159150i	0.996829	−	0.0795752i	$-0.0253564\pi$
$920$		0			0
$921$			1351.86i			1.46782i
$922$	−495.726			−0.537664
$923$		−	1904.44i		−	2.06331i
$924$	181.647	+	1116.67i	0.196588	+	1.20852i
$925$		0			0
$926$			1288.05i			1.39098i
$927$	−5.31674			−0.00573543
$928$	2005.85			2.16148
$929$	−624.735			−0.672481			−0.336240	−	0.941776i	$-0.609155\pi$
$929$	−624.735			−0.672481			−0.336240	+	0.941776i	$0.609155\pi$
$930$		0			0
$931$			312.662i			0.335835i
$932$			255.512i			0.274154i
$933$	−755.422			−0.809670
$934$			2366.74i			2.53398i
$935$		0			0
$936$	20.2643			0.0216499
$937$			1737.04i			1.85383i	0.375273	+	0.926915i	$0.377549\pi$
$937$			1737.04i			1.85383i	−0.375273	+	0.926915i	$0.622451\pi$
$938$	−635.965			−0.678001
$939$	−1404.08			−1.49529
$940$		0			0
$941$			1214.68i			1.29084i	0.763830	+	0.645418i	$0.223317\pi$
$941$			1214.68i			1.29084i	−0.763830	+	0.645418i	$0.776683\pi$
$942$			1014.35i			1.07680i
$943$		−	1181.85i		−	1.25329i
$944$	−7.26897			−0.00770018
$945$		0			0
$946$	−333.773	+	54.2943i	−0.352826	+	0.0573935i
$947$	−1465.25			−1.54725			−0.773627	−	0.633641i	$-0.781560\pi$
$947$	−1465.25			−1.54725			−0.773627	+	0.633641i	$0.781560\pi$
$948$			231.179i			0.243860i
$949$	874.077			0.921051
$950$		0			0
$951$	−507.857			−0.534025
$952$			122.022i			0.128175i
$953$			464.526i			0.487435i	0.969846	+	0.243717i	$0.0783670\pi$
$953$			464.526i			0.487435i	−0.969846	+	0.243717i	$0.921633\pi$
$954$		−	44.5962i		−	0.0467465i
$955$		0			0
$956$		−	1298.10i		−	1.35784i
$957$	−281.604	−	1731.15i	−0.294257	−	1.80894i
$958$	35.5751			0.0371348
$959$			952.446i			0.993166i
$960$		0			0
$961$	−202.088			−0.210289
$962$	−2185.95			−2.27229
$963$			11.8705i			0.0123266i
$964$			927.807i			0.962455i
$965$		0			0
$966$	857.750			0.887940
$967$			667.349i			0.690123i	0.938580	+	0.345062i	$0.112142\pi$
$967$			667.349i			0.690123i	−0.938580	+	0.345062i	$0.887858\pi$
$968$	240.251	+	718.930i	0.248193	+	0.742696i
$969$	−193.353			−0.199539
$970$		0			0
$971$	980.665			1.00995			0.504977	−	0.863133i	$-0.331501\pi$
$971$	980.665			1.00995			0.504977	+	0.863133i	$0.331501\pi$
$972$	60.6256			0.0623720
$973$	513.923			0.528184
$974$		−	2321.78i		−	2.38376i
$975$		0			0
$976$		−	201.056i		−	0.206000i
$977$	−342.678			−0.350745			−0.175372	−	0.984502i	$-0.556113\pi$
$977$	−342.678			−0.350745			−0.175372	+	0.984502i	$0.556113\pi$
$978$			1371.74i			1.40259i
$979$	720.490	−	117.201i	0.735945	−	0.119715i
$980$		0			0
$981$			24.1442i			0.0246118i
$982$	−1097.50			−1.11762
$983$	447.215			0.454949			0.227475	−	0.973784i	$-0.426953\pi$
$983$	447.215			0.454949			0.227475	+	0.973784i	$0.426953\pi$
$984$	−1421.10			−1.44421
$985$		0			0
$986$		−	570.799i		−	0.578903i
$987$			313.244i			0.317370i
$988$	−1915.18			−1.93844
$989$			153.651i			0.155360i
$990$		0			0
$991$	135.932			0.137166			0.0685831	−	0.997645i	$-0.478152\pi$
$991$	135.932			0.137166			0.0685831	+	0.997645i	$0.478152\pi$
$992$			1050.47i			1.05894i
$993$	27.2196			0.0274115
$994$	−1980.08			−1.99203
$995$		0			0
$996$			2032.19i			2.04035i
$997$		−	303.075i		−	0.303987i	−0.988381	−	0.151993i	$-0.951431\pi$
$997$		−	303.075i		−	0.303987i	0.988381	−	0.151993i	$-0.0485693\pi$
$998$		−	2765.99i		−	2.77153i
$999$	−1072.25			−1.07333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.c.f.76.2		8
5.2	odd	4		275.3.d.c.274.13		16
5.3	odd	4		275.3.d.c.274.4		16
5.4	even	2		55.3.c.a.21.7	yes	8
11.10	odd	2	inner	275.3.c.f.76.7		8
15.14	odd	2		495.3.b.a.406.2		8
20.19	odd	2		880.3.j.a.241.7		8
55.32	even	4		275.3.d.c.274.3		16
55.43	even	4		275.3.d.c.274.14		16
55.54	odd	2		55.3.c.a.21.2	✓	8
165.164	even	2		495.3.b.a.406.7		8
220.219	even	2		880.3.j.a.241.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.c.a.21.2	✓	8	55.54	odd	2
55.3.c.a.21.7	yes	8	5.4	even	2
275.3.c.f.76.2		8	1.1	even	1	trivial
275.3.c.f.76.7		8	11.10	odd	2	inner
275.3.d.c.274.3		16	55.32	even	4
275.3.d.c.274.4		16	5.3	odd	4
275.3.d.c.274.13		16	5.2	odd	4
275.3.d.c.274.14		16	55.43	even	4
495.3.b.a.406.2		8	15.14	odd	2
495.3.b.a.406.7		8	165.164	even	2
880.3.j.a.241.7		8	20.19	odd	2
880.3.j.a.241.8		8	220.219	even	2

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.15955i q^{2} +3.03112 q^{3} -5.98274 q^{4} -9.57697i q^{6} -5.67155i q^{7} +6.26455i q^{8} +0.187686 q^{9} +(10.8573 - 1.76614i) q^{11} -18.1344 q^{12} -17.2349i q^{13} -17.9195 q^{14} -4.13780 q^{16} +3.43437i q^{17} -0.593004i q^{18} +18.5738i q^{19} -17.1911i q^{21} +(-5.58019 - 34.3041i) q^{22} -15.7918 q^{23} +18.9886i q^{24} -54.4546 q^{26} -26.7112 q^{27} +33.9314i q^{28} -52.6031i q^{29} +27.5484 q^{31} +38.1318i q^{32} +(32.9097 - 5.35337i) q^{33} +10.8510 q^{34} -1.12288 q^{36} +40.1425 q^{37} +58.6848 q^{38} -52.2411i q^{39} +74.8398i q^{41} -54.3162 q^{42} -9.72983i q^{43} +(-64.9563 + 10.5663i) q^{44} +49.8949i q^{46} -18.2212 q^{47} -12.5422 q^{48} +16.8335 q^{49} +10.4100i q^{51} +103.112i q^{52} +75.2040 q^{53} +84.3952i q^{54} +35.5297 q^{56} +56.2994i q^{57} -166.202 q^{58} +1.75672 q^{59} +48.5900i q^{61} -87.0404i q^{62} -1.06447i q^{63} +103.928 q^{64} +(-16.9142 - 103.980i) q^{66} +35.4901 q^{67} -20.5469i q^{68} -47.8668 q^{69} +110.499 q^{71} +1.17577i q^{72} +50.7154i q^{73} -126.832i q^{74} -111.122i q^{76} +(-10.0167 - 61.5777i) q^{77} -165.058 q^{78} -12.7481i q^{79} -82.6540 q^{81} +236.460 q^{82} -112.062i q^{83} +102.850i q^{84} -30.7419 q^{86} -159.446i q^{87} +(11.0640 + 68.0161i) q^{88} +66.3600 q^{89} -97.7488 q^{91} +94.4781 q^{92} +83.5024 q^{93} +57.5709i q^{94} +115.582i q^{96} -65.1302 q^{97} -53.1863i q^{98} +(2.03776 - 0.331479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} - 28 q^{4} - 4 q^{9} + 8 q^{11} + 48 q^{12} + 88 q^{16} - 80 q^{22} - 8 q^{23} - 100 q^{26} + 16 q^{27} + 36 q^{31} + 152 q^{33} + 80 q^{34} - 216 q^{36} + 88 q^{37} + 160 q^{38} - 280 q^{42}+ \cdots - 184 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 - 28 * q^4 - 4 * q^9 + 8 * q^11 + 48 * q^12 + 88 * q^16 - 80 * q^22 - 8 * q^23 - 100 * q^26 + 16 * q^27 + 36 * q^31 + 152 * q^33 + 80 * q^34 - 216 * q^36 + 88 * q^37 + 160 * q^38 - 280 * q^42 + 12 * q^44 + 8 * q^47 - 488 * q^48 + 172 * q^49 + 152 * q^53 - 80 * q^56 - 160 * q^58 - 16 * q^59 - 588 * q^64 + 180 * q^66 + 88 * q^67 + 8 * q^69 + 276 * q^71 - 160 * q^77 - 160 * q^78 - 320 * q^81 + 520 * q^82 + 420 * q^86 + 520 * q^88 + 444 * q^89 - 40 * q^91 + 368 * q^92 + 104 * q^93 - 312 * q^97 - 184 * q^99

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