LMFDB - Embedded newform 275.3.d.c.274.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(274,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.274"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,56] 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} - 54 x^{13} + 51 x^{12} - 118 x^{11} + 770 x^{10} - 1222 x^{9} + \cdots + 256 $ x^16 - 8x^15 + 32x^14 - 54x^13 + 51x^12 - 118x^11 + 770x^10 - 1222x^9 + 749x^8 + 724x^7 + 3920x^6 - 5016x^5 + 2916x^4 + 7088x^3 + 5408x^2 + 1664*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{22} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.13
Root			$-1.07977 - 1.07977i$ of defining polynomial
Character	$\chi$	$=$	275.274
Dual form			275.3.d.c.274.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.15955 q^{2} -3.03112i q^{3} +5.98274 q^{4} -9.57697i q^{6} +5.67155 q^{7} +6.26455 q^{8} -0.187686 q^{9} +(10.8573 - 1.76614i) q^{11} -18.1344i q^{12} -17.2349 q^{13} +17.9195 q^{14} -4.13780 q^{16} -3.43437 q^{17} -0.593004 q^{18} -18.5738i q^{19} -17.1911i q^{21} +(34.3041 - 5.58019i) q^{22} +15.7918i q^{23} -18.9886i q^{24} -54.4546 q^{26} -26.7112i q^{27} +33.9314 q^{28} +52.6031i q^{29} +27.5484 q^{31} -38.1318 q^{32} +(-5.35337 - 32.9097i) q^{33} -10.8510 q^{34} -1.12288 q^{36} +40.1425i q^{37} -58.6848i q^{38} +52.2411i q^{39} +74.8398i q^{41} -54.3162i q^{42} -9.72983 q^{43} +(64.9563 - 10.5663i) q^{44} +49.8949i q^{46} -18.2212i q^{47} +12.5422i q^{48} -16.8335 q^{49} +10.4100i q^{51} -103.112 q^{52} -75.2040i q^{53} -84.3952i q^{54} +35.5297 q^{56} -56.2994 q^{57} +166.202i q^{58} -1.75672 q^{59} +48.5900i q^{61} +87.0404 q^{62} -1.06447 q^{63} -103.928 q^{64} +(-16.9142 - 103.980i) q^{66} +35.4901i q^{67} -20.5469 q^{68} +47.8668 q^{69} +110.499 q^{71} -1.17577 q^{72} +50.7154 q^{73} +126.832i q^{74} -111.122i q^{76} +(61.5777 - 10.0167i) q^{77} +165.058i q^{78} +12.7481i q^{79} -82.6540 q^{81} +236.460i q^{82} -112.062 q^{83} -102.850i q^{84} -30.7419 q^{86} +159.446 q^{87} +(68.0161 - 11.0640i) q^{88} -66.3600 q^{89} -97.7488 q^{91} +94.4781i q^{92} -83.5024i q^{93} -57.5709i q^{94} +115.582i q^{96} -65.1302i q^{97} -53.1863 q^{98} +(-2.03776 + 0.331479i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 56 q^{4} + 8 q^{9} + 16 q^{11} + 176 q^{16} - 200 q^{26} + 72 q^{31} - 160 q^{34} - 432 q^{36} - 24 q^{44} - 344 q^{49} - 160 q^{56} + 32 q^{59} + 1176 q^{64} + 360 q^{66} - 16 q^{69} + 552 q^{71}+ \cdots + 368 q^{99}+O(q^{100}) $ 16 * q + 56 * q^4 + 8 * q^9 + 16 * q^11 + 176 * q^16 - 200 * q^26 + 72 * q^31 - 160 * q^34 - 432 * q^36 - 24 * q^44 - 344 * q^49 - 160 * q^56 + 32 * q^59 + 1176 * q^64 + 360 * q^66 - 16 * q^69 + 552 * q^71 - 640 * q^81 + 840 * q^86 - 888 * q^89 - 80 * q^91 + 368 * 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 $

$2$	3.15955			1.57977			0.789887	−	0.613253i	$-0.210139\pi$
$2$	3.15955			1.57977			0.789887	+	0.613253i	$0.210139\pi$
$3$		−	3.03112i		−	1.01037i	−0.863010	−	0.505187i	$-0.831424\pi$
$3$		−	3.03112i		−	1.01037i	0.863010	−	0.505187i	$-0.168576\pi$
$4$	5.98274			1.49568
$5$		0			0
$5$		0			0
$6$		−	9.57697i		−	1.59616i
$7$	5.67155			0.810221			0.405111	−	0.914268i	$-0.367233\pi$
$7$	5.67155			0.810221			0.405111	+	0.914268i	$0.367233\pi$
$8$	6.26455			0.783069
$9$	−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
$12$		−	18.1344i		−	1.51120i
$13$	−17.2349			−1.32576			−0.662882	−	0.748724i	$-0.730667\pi$
$13$	−17.2349			−1.32576			−0.662882	+	0.748724i	$0.730667\pi$
$14$	17.9195			1.27997
$15$		0			0
$16$	−4.13780			−0.258612
$17$	−3.43437			−0.202022			−0.101011	−	0.994885i	$-0.532208\pi$
$17$	−3.43437			−0.202022			−0.101011	+	0.994885i	$0.532208\pi$
$18$	−0.593004			−0.0329446
$19$		−	18.5738i		−	0.977569i	−0.872405	−	0.488784i	$-0.837441\pi$
$19$		−	18.5738i		−	0.977569i	0.872405	−	0.488784i	$-0.162559\pi$
$20$		0			0
$21$		−	17.1911i		−	0.818626i
$22$	34.3041	−	5.58019i	1.55928	−	0.253645i
$23$			15.7918i			0.686599i	0.939226	+	0.343300i	$0.111545\pi$
$23$			15.7918i			0.686599i	−0.939226	+	0.343300i	$0.888455\pi$
$24$		−	18.9886i		−	0.791192i
$25$		0			0
$26$	−54.4546			−2.09441
$27$		−	26.7112i		−	0.989303i
$28$	33.9314			1.21184
$29$			52.6031i			1.81390i	0.421238	+	0.906950i	$0.361596\pi$
$29$			52.6031i			1.81390i	−0.421238	+	0.906950i	$0.638404\pi$
$30$		0			0
$31$	27.5484			0.888657			0.444328	−	0.895864i	$-0.353442\pi$
$31$	27.5484			0.888657			0.444328	+	0.895864i	$0.353442\pi$
$32$	−38.1318			−1.19162
$33$	−5.35337	−	32.9097i	−0.162223	−	0.997265i
$34$	−10.8510			−0.319148
$35$		0			0
$36$	−1.12288			−0.0311910
$37$			40.1425i			1.08493i	0.840077	+	0.542467i	$0.182510\pi$
$37$			40.1425i			1.08493i	−0.840077	+	0.542467i	$0.817490\pi$
$38$		−	58.6848i		−	1.54434i
$39$			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	$0.634009\pi$
$42$		−	54.3162i		−	1.29324i
$43$	−9.72983			−0.226275			−0.113138	−	0.993579i	$-0.536090\pi$
$43$	−9.72983			−0.226275			−0.113138	+	0.993579i	$0.536090\pi$
$44$	64.9563	−	10.5663i	1.47628	−	0.240144i
$45$		0			0
$46$			49.8949i			1.08467i
$47$		−	18.2212i		−	0.387686i	−0.981033	−	0.193843i	$-0.937905\pi$
$47$		−	18.2212i		−	0.387686i	0.981033	−	0.193843i	$-0.0620952\pi$
$48$			12.5422i			0.261295i
$49$	−16.8335			−0.343541
$50$		0			0
$51$			10.4100i			0.204117i
$52$	−103.112			−1.98292
$53$		−	75.2040i		−	1.41894i	−0.704734	−	0.709471i	$-0.748934\pi$
$53$		−	75.2040i		−	1.41894i	0.704734	−	0.709471i	$-0.251066\pi$
$54$		−	84.3952i		−	1.56287i
$55$		0			0
$56$	35.5297			0.634459
$57$	−56.2994			−0.987709
$58$			166.202i			2.86555i
$59$	−1.75672			−0.0297750			−0.0148875	−	0.999889i	$-0.504739\pi$
$59$	−1.75672			−0.0297750			−0.0148875	+	0.999889i	$0.504739\pi$
$60$		0			0
$61$			48.5900i			0.796557i	0.917265	+	0.398278i	$0.130392\pi$
$61$			48.5900i			0.796557i	−0.917265	+	0.398278i	$0.869608\pi$
$62$	87.0404			1.40388
$63$	−1.06447			−0.0168964
$64$	−103.928			−1.62387
$65$		0			0
$66$	−16.9142	−	103.980i	−0.256276	−	1.57545i
$67$			35.4901i			0.529702i	0.964289	+	0.264851i	$0.0853228\pi$
$67$			35.4901i			0.529702i	−0.964289	+	0.264851i	$0.914677\pi$
$68$	−20.5469			−0.302161
$69$	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	$0.216154\pi$
$72$	−1.17577			−0.0163301
$73$	50.7154			0.694732			0.347366	−	0.937730i	$-0.387076\pi$
$73$	50.7154			0.694732			0.347366	+	0.937730i	$0.387076\pi$
$74$			126.832i			1.71395i
$75$		0			0
$76$		−	111.122i		−	1.46213i
$77$	61.5777	−	10.0167i	0.799710	−	0.130087i
$78$			165.058i			2.11613i
$79$			12.7481i			0.161368i	0.996740	+	0.0806842i	$0.0257105\pi$
$79$			12.7481i			0.161368i	−0.996740	+	0.0806842i	$0.974289\pi$
$80$		0			0
$81$	−82.6540			−1.02042
$82$			236.460i			2.88366i
$83$	−112.062			−1.35015			−0.675075	−	0.737749i	$-0.735889\pi$
$83$	−112.062			−1.35015			−0.675075	+	0.737749i	$0.735889\pi$
$84$		−	102.850i		−	1.22441i
$85$		0			0
$86$	−30.7419			−0.357463
$87$	159.446			1.83272
$88$	68.0161	−	11.0640i	0.772910	−	0.125728i
$89$	−66.3600			−0.745618			−0.372809	−	0.927908i	$-0.621605\pi$
$89$	−66.3600			−0.745618			−0.372809	+	0.927908i	$0.621605\pi$
$90$		0			0
$91$	−97.7488			−1.07416
$92$			94.4781i			1.02694i
$93$		−	83.5024i		−	0.897875i
$94$		−	57.5709i		−	0.612456i
$95$		0			0
$96$			115.582i			1.20398i
$97$		−	65.1302i		−	0.671445i	−0.941961	−	0.335723i	$-0.891020\pi$
$97$		−	65.1302i		−	0.671445i	0.941961	−	0.335723i	$-0.108980\pi$
$98$	−53.1863			−0.542717
$99$	−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	$-0.324354\pi$
$102$			32.8908i			0.322459i
$103$			28.3278i			0.275027i	0.990500	+	0.137514i	$0.0439111\pi$
$103$			28.3278i			0.275027i	−0.990500	+	0.137514i	$0.956089\pi$
$104$	−107.969			−1.03816
$105$		0			0
$106$		−	237.610i		−	2.24161i
$107$	−63.2464			−0.591088			−0.295544	−	0.955329i	$-0.595501\pi$
$107$	−63.2464			−0.591088			−0.295544	+	0.955329i	$0.595501\pi$
$108$		−	159.806i		−	1.47968i
$109$		−	128.641i		−	1.18020i	−0.807331	−	0.590098i	$-0.799089\pi$
$109$		−	128.641i		−	1.18020i	0.807331	−	0.590098i	$-0.200911\pi$
$110$		0			0
$111$	121.677			1.09619
$112$	−23.4677			−0.209533
$113$		−	35.4694i		−	0.313889i	−0.987607	−	0.156944i	$-0.949836\pi$
$113$		−	35.4694i		−	0.313889i	0.987607	−	0.156944i	$-0.0501643\pi$
$114$	−177.881			−1.56036
$115$		0			0
$116$			314.711i			2.71302i
$117$	3.23476			0.0276475
$118$	−5.55045			−0.0470377
$119$	−19.4782			−0.163682
$120$		0			0
$121$	114.762	−	38.3509i	0.948442	−	0.316949i
$122$			153.522i			1.25838i
$123$	226.848			1.84430
$124$	164.815			1.32915
$125$		0			0
$126$	−3.36325			−0.0266925
$127$	−210.686			−1.65895			−0.829473	−	0.558547i	$-0.811359\pi$
$127$	−210.686			−1.65895			−0.829473	+	0.558547i	$0.811359\pi$
$128$	−175.838			−1.37374
$129$			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	$-0.167684\pi$
$132$	−32.0278	−	196.890i	−0.242635	−	1.49159i
$133$		−	105.342i		−	0.792047i
$134$			112.133i			0.836810i
$135$		0			0
$136$	−21.5148			−0.158197
$137$		−	167.934i		−	1.22580i	−0.790162	−	0.612898i	$-0.790004\pi$
$137$		−	167.934i		−	1.22580i	0.790162	−	0.612898i	$-0.209996\pi$
$138$	151.237			1.09592
$139$		−	90.6142i		−	0.651901i	−0.945387	−	0.325950i	$-0.894316\pi$
$139$		−	90.6142i		−	0.651901i	0.945387	−	0.325950i	$-0.105684\pi$
$140$		0			0
$141$	−55.2308			−0.391708
$142$	349.125			2.45863
$143$	−187.125	+	30.4392i	−1.30856	+	0.212862i
$144$	0.776608			0.00539311
$145$		0			0
$146$	160.238			1.09752
$147$			51.0244i			0.347105i
$148$			240.162i			1.62272i
$149$			72.8977i			0.489246i	0.969618	+	0.244623i	$0.0786642\pi$
$149$			72.8977i			0.489246i	−0.969618	+	0.244623i	$0.921336\pi$
$150$		0			0
$151$			237.180i			1.57073i	0.619035	+	0.785364i	$0.287524\pi$
$151$			237.180i			1.57073i	−0.619035	+	0.785364i	$0.712476\pi$
$152$		−	116.357i		−	0.765504i
$153$	0.644584			0.00421296
$154$	194.558	−	31.6483i	1.26336	−	0.205509i
$155$		0			0
$156$			312.545i			2.00349i
$157$		−	105.915i		−	0.674620i	−0.941394	−	0.337310i	$-0.890483\pi$
$157$		−	105.915i		−	0.674620i	0.941394	−	0.337310i	$-0.109517\pi$
$158$			40.2783i			0.254926i
$159$	−227.952			−1.43366
$160$		0			0
$161$			89.5639i			0.556297i
$162$	−261.149			−1.61203
$163$			143.233i			0.878730i	0.898309	+	0.439365i	$0.144797\pi$
$163$			143.233i			0.878730i	−0.898309	+	0.439365i	$0.855203\pi$
$164$			447.747i			2.73016i
$165$		0			0
$166$	−354.067			−2.13293
$167$	35.5974			0.213158			0.106579	−	0.994304i	$-0.466010\pi$
$167$	35.5974			0.213158			0.106579	+	0.994304i	$0.466010\pi$
$168$		−	107.695i		−	0.641041i
$169$	128.043			0.757650
$170$		0			0
$171$			3.48605i			0.0203862i
$172$	−58.2110			−0.338436
$173$	196.047			1.13322			0.566609	−	0.823987i	$-0.308255\pi$
$173$	196.047			1.13322			0.566609	+	0.823987i	$0.308255\pi$
$174$	503.778			2.89528
$175$		0			0
$176$	−44.9253	+	7.30791i	−0.255257	+	0.0415222i
$177$			5.32484i			0.0300838i
$178$	−209.668			−1.17791
$179$	65.1824			0.364148			0.182074	−	0.983285i	$-0.441719\pi$
$179$	65.1824			0.364148			0.182074	+	0.983285i	$0.441719\pi$
$180$		0			0
$181$	−157.016			−0.867493			−0.433746	−	0.901035i	$-0.642809\pi$
$181$	−157.016			−0.867493			−0.433746	+	0.901035i	$0.642809\pi$
$182$	−308.842			−1.69693
$183$	147.282			0.804820
$184$			98.9285i			0.537655i
$185$		0			0
$186$		−	263.830i		−	1.41844i
$187$	−37.2879	+	6.06556i	−0.199401	+	0.0324361i
$188$		−	109.013i		−	0.579856i
$189$		−	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	$0.360627\pi$
$192$			315.018i			1.64072i
$193$	0.742915			0.00384930			0.00192465	−	0.999998i	$-0.499387\pi$
$193$	0.742915			0.00384930			0.00192465	+	0.999998i	$0.499387\pi$
$194$		−	205.782i		−	1.06073i
$195$		0			0
$196$	−100.711			−0.513829
$197$	43.0945			0.218754			0.109377	−	0.994000i	$-0.465114\pi$
$197$	43.0945			0.218754			0.109377	+	0.994000i	$0.465114\pi$
$198$	−6.43841	+	1.04732i	−0.0325172	+	0.00528952i
$199$	201.933			1.01474			0.507370	−	0.861729i	$-0.330618\pi$
$199$	201.933			1.01474			0.507370	+	0.861729i	$0.330618\pi$
$200$		0			0
$201$	107.575			0.535197
$202$		−	543.501i		−	2.69060i
$203$			298.341i			1.46966i
$204$			62.2802i			0.305295i
$205$		0			0
$206$			89.5031i			0.434481i
$207$		−	2.96390i		−	0.0143184i
$208$	71.3147			0.342859
$209$	−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	$0.959559\pi$
$212$		−	449.926i		−	2.12229i
$213$		−	334.934i		−	1.57246i
$214$	−199.830			−0.933785
$215$		0			0
$216$		−	167.334i		−	0.774693i
$217$	156.242			0.720009
$218$		−	406.449i		−	1.86444i
$219$		−	153.725i		−	0.701939i
$220$		0			0
$221$	59.1911			0.267833
$222$	384.444			1.73173
$223$		−	282.600i		−	1.26726i	−0.773635	−	0.633632i	$-0.781563\pi$
$223$		−	282.600i		−	1.26726i	0.773635	−	0.633632i	$-0.218437\pi$
$224$	−216.266			−0.965475
$225$		0			0
$226$		−	112.067i		−	0.495873i
$227$	111.251			0.490092			0.245046	−	0.969511i	$-0.421197\pi$
$227$	111.251			0.490092			0.245046	+	0.969511i	$0.421197\pi$
$228$	−336.825			−1.47730
$229$	53.3814			0.233107			0.116553	−	0.993184i	$-0.462815\pi$
$229$	53.3814			0.233107			0.116553	+	0.993184i	$0.462815\pi$
$230$		0			0
$231$	−30.3619	−	186.649i	−0.131437	−	0.808006i
$232$			329.535i			1.42041i
$233$	−42.7082			−0.183297			−0.0916485	−	0.995791i	$-0.529214\pi$
$233$	−42.7082			−0.183297			−0.0916485	+	0.995791i	$0.529214\pi$
$234$	10.2204			0.0436768
$235$		0			0
$236$	−10.5100			−0.0445340
$237$	38.6411			0.163042
$238$	−61.5423			−0.258581
$239$		−	216.974i		−	0.907840i	−0.891042	−	0.453920i	$-0.850025\pi$
$239$		−	216.974i		−	0.907840i	0.891042	−	0.453920i	$-0.149975\pi$
$240$		0			0
$241$		−	155.081i		−	0.643488i	−0.946827	−	0.321744i	$-0.895731\pi$
$241$		−	155.081i		−	0.643488i	0.946827	−	0.321744i	$-0.104269\pi$
$242$	362.594	−	121.171i	1.49832	−	0.500708i
$243$			10.1334i			0.0417013i
$244$			290.701i			1.19140i
$245$		0			0
$246$	716.738			2.91357
$247$			320.118i			1.29603i
$248$	172.578			0.695880
$249$			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	$0.574576\pi$
$252$	−6.36846			−0.0252717
$253$	27.8904	+	171.456i	0.110239	+	0.677692i
$254$	−665.673			−2.62076
$255$		0			0
$256$	−139.857			−0.546317
$257$			85.7024i			0.333472i	0.986002	+	0.166736i	$0.0533228\pi$
$257$			85.7024i			0.333472i	−0.986002	+	0.166736i	$0.946677\pi$
$258$			93.1822i			0.361171i
$259$			227.670i			0.879037i
$260$		0			0
$261$		−	9.87288i		−	0.0378271i
$262$		−	416.189i		−	1.58851i
$263$	398.864			1.51659			0.758296	−	0.651911i	$-0.226032\pi$
$263$	398.864			1.51659			0.758296	+	0.651911i	$0.226032\pi$
$264$	−33.5365	−	206.165i	−0.127032	−	0.780928i
$265$		0			0
$266$		−	332.834i		−	1.25125i
$267$			201.145i			0.753353i
$268$			212.328i			0.792268i
$269$	237.209			0.881819			0.440910	−	0.897552i	$-0.354656\pi$
$269$	237.209			0.881819			0.440910	+	0.897552i	$0.354656\pi$
$270$		0			0
$271$		−	34.0378i		−	0.125601i	−0.998026	−	0.0628003i	$-0.979997\pi$
$271$		−	34.0378i		−	0.125601i	0.998026	−	0.0628003i	$-0.0200031\pi$
$272$	14.2107			0.0522453
$273$			296.288i			1.08530i
$274$		−	530.595i		−	1.93648i
$275$		0			0
$276$	286.374			1.03759
$277$	−202.654			−0.731604			−0.365802	−	0.930693i	$-0.619205\pi$
$277$	−202.654			−0.731604			−0.365802	+	0.930693i	$0.619205\pi$
$278$		−	286.300i		−	1.02986i
$279$	−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	$-0.0574982\pi$
$282$	−174.504			−0.618809
$283$	162.113			0.572836			0.286418	−	0.958105i	$-0.407535\pi$
$283$	162.113			0.572836			0.286418	+	0.958105i	$0.407535\pi$
$284$	661.084			2.32776
$285$		0			0
$286$	−591.229	+	96.1741i	−2.06723	+	0.336273i
$287$			424.458i			1.47895i
$288$	7.15681			0.0248500
$289$	−277.205			−0.959187
$290$		0			0
$291$	−197.417			−0.678410
$292$	303.417			1.03910
$293$	−372.772			−1.27226			−0.636130	−	0.771582i	$-0.719466\pi$
$293$	−372.772			−1.27226			−0.636130	+	0.771582i	$0.719466\pi$
$294$			161.214i			0.548347i
$295$		0			0
$296$			251.475i			0.849578i
$297$	−47.1756	−	290.011i	−0.158840	−	0.976468i
$298$			230.324i			0.772898i
$299$		−	272.170i		−	0.910268i
$300$		0			0
$301$	−55.1832			−0.183333
$302$			749.381i			2.48139i
$303$	−521.409			−1.72082
$304$			76.8547i			0.252811i
$305$		0			0
$306$	2.03659			0.00665553
$307$	−445.994			−1.45275			−0.726374	−	0.687300i	$-0.758796\pi$
$307$	−445.994			−1.45275			−0.726374	+	0.687300i	$0.758796\pi$
$308$	368.403	−	59.9274i	1.19611	−	0.194570i
$309$	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	$0.631226\pi$
$312$			327.267i			1.04893i
$313$			463.222i			1.47994i	0.672638	+	0.739971i	$0.265161\pi$
$313$			463.222i			1.47994i	−0.672638	+	0.739971i	$0.734839\pi$
$314$		−	334.644i		−	1.06575i
$315$		0			0
$316$			76.2686i			0.241356i
$317$		−	167.548i		−	0.528542i	−0.964448	−	0.264271i	$-0.914869\pi$
$317$		−	167.548i		−	0.528542i	0.964448	−	0.264271i	$-0.0851313\pi$
$318$	−720.226			−2.26486
$319$	92.9042	+	571.127i	0.291236	+	1.79037i
$320$		0			0
$321$			191.707i			0.597220i
$322$			282.981i			0.878824i
$323$			63.7893i			0.197490i
$324$	−494.497			−1.52623
$325$		0			0
$326$			452.551i			1.38819i
$327$	−389.928			−1.19244
$328$			468.838i			1.42938i
$329$		−	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	$0.495682\pi$
$332$	−670.440			−2.01940
$333$		−	7.53420i		−	0.0226252i
$334$	112.472			0.336742
$335$		0			0
$336$			71.1335i			0.211707i
$337$	263.901			0.783090			0.391545	−	0.920159i	$-0.371941\pi$
$337$	263.901			0.783090			0.391545	+	0.920159i	$0.371941\pi$
$338$	404.557			1.19692
$339$	−107.512			−0.317145
$340$		0			0
$341$	299.101	−	48.6541i	0.877128	−	0.142681i
$342$			11.0143i			0.0322056i
$343$	−373.378			−1.08857
$344$	−60.9530			−0.177189
$345$		0			0
$346$	619.419			1.79023
$347$	611.749			1.76297			0.881483	−	0.472216i	$-0.156546\pi$
$347$	611.749			1.76297			0.881483	+	0.472216i	$0.156546\pi$
$348$	953.925			2.74117
$349$			282.223i			0.808662i	0.914613	+	0.404331i	$0.132496\pi$
$349$			282.223i			0.808662i	−0.914613	+	0.404331i	$0.867504\pi$
$350$		0			0
$351$			460.365i			1.31158i
$352$	−414.008	+	67.3459i	−1.17616	+	0.191324i
$353$		−	173.629i		−	0.491868i	−0.969287	−	0.245934i	$-0.920905\pi$
$353$		−	173.629i		−	0.491868i	0.969287	−	0.245934i	$-0.0790946\pi$
$354$			16.8241i			0.0475256i
$355$		0			0
$356$	−397.015			−1.11521
$357$			59.0407i			0.165380i
$358$	205.947			0.575271
$359$			285.384i			0.794941i	0.917615	+	0.397471i	$0.130112\pi$
$359$			285.384i			0.794941i	−0.917615	+	0.397471i	$0.869888\pi$
$360$		0			0
$361$	16.0139			0.0443597
$362$	−496.100			−1.37044
$363$	−116.246	−	347.856i	−0.320237	−	0.958281i
$364$	−584.805			−1.60661
$365$		0			0
$366$	465.344			1.27143
$367$			324.275i			0.883582i	0.897118	+	0.441791i	$0.145657\pi$
$367$			324.275i			0.883582i	−0.897118	+	0.441791i	$0.854343\pi$
$368$		−	65.3432i		−	0.177563i
$369$		−	14.0464i		−	0.0380661i
$370$		0			0
$371$		−	426.523i		−	1.14966i
$372$		−	499.573i		−	1.34294i
$373$	128.367			0.344148			0.172074	−	0.985084i	$-0.444953\pi$
$373$	128.367			0.344148			0.172074	+	0.985084i	$0.444953\pi$
$374$	−117.813	+	19.1644i	−0.315008	+	0.0512418i
$375$		0			0
$376$		−	114.148i		−	0.303585i
$377$		−	906.611i		−	2.40480i
$378$		−	478.652i		−	1.26627i
$379$	−684.510			−1.80610			−0.903048	−	0.429540i	$-0.858676\pi$
$379$	−684.510			−1.80610			−0.903048	+	0.429540i	$0.858676\pi$
$380$		0			0
$381$			638.615i			1.67615i
$382$	511.742			1.33964
$383$			338.766i			0.884506i	0.896890	+	0.442253i	$0.145821\pi$
$383$			338.766i			0.884506i	−0.896890	+	0.442253i	$0.854179\pi$
$384$			532.987i			1.38799i
$385$		0			0
$386$	2.34727			0.00608102
$387$	1.82616			0.00471875
$388$		−	389.657i		−	1.00427i
$389$	552.950			1.42146			0.710732	−	0.703463i	$-0.248364\pi$
$389$	552.950			1.42146			0.710732	+	0.703463i	$0.248364\pi$
$390$		0			0
$391$		−	54.2348i		−	0.138708i
$392$	−105.454			−0.269017
$393$	−399.272			−1.01596
$394$	136.159			0.345581
$395$		0			0
$396$	−12.1914	+	1.98315i	−0.0307864	+	0.00500796i
$397$		−	111.881i		−	0.281815i	−0.990023	−	0.140908i	$-0.954998\pi$
$397$		−	111.881i		−	0.281815i	0.990023	−	0.140908i	$-0.0450020\pi$
$398$	638.017			1.60306
$399$	−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	$0.615630\pi$
$402$	339.887			0.845490
$403$	−474.794			−1.17815
$404$		−	1029.14i		−	2.54738i
$405$		0			0
$406$			942.623i			2.32173i
$407$	70.8972	+	435.839i	0.174195	+	1.07086i
$408$			65.2139i			0.159838i
$409$		−	122.119i		−	0.298580i	−0.988793	−	0.149290i	$-0.952301\pi$
$409$		−	122.119i		−	0.298580i	0.988793	−	0.149290i	$-0.0476989\pi$
$410$		0			0
$411$	−509.028			−1.23851
$412$			169.478i			0.411354i
$413$	−9.96334			−0.0241243
$414$		−	9.36458i		−	0.0226198i
$415$		0			0
$416$	657.199			1.57980
$417$	−274.663			−0.658663
$418$	−103.645	−	637.158i	−0.247955	−	1.52430i
$419$	−407.625			−0.972852			−0.486426	−	0.873722i	$-0.661700\pi$
$419$	−407.625			−0.972852			−0.486426	+	0.873722i	$0.661700\pi$
$420$		0			0
$421$	−348.212			−0.827107			−0.413554	−	0.910480i	$-0.635713\pi$
$421$	−348.212			−0.827107			−0.413554	+	0.910480i	$0.635713\pi$
$422$			168.943i			0.400338i
$423$			3.41988i			0.00808481i
$424$		−	471.119i		−	1.11113i
$425$		0			0
$426$		−	1058.24i		−	2.48413i
$427$			275.580i			0.645387i
$428$	−378.387			−0.884081
$429$	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	$-0.176393\pi$
$432$			110.525i			0.255846i
$433$			760.149i			1.75554i	0.479081	+	0.877771i	$0.340970\pi$
$433$			760.149i			1.75554i	−0.479081	+	0.877771i	$0.659030\pi$
$434$	493.654			1.13745
$435$		0			0
$436$		−	769.628i		−	1.76520i
$437$	293.313			0.671198
$438$		−	485.700i		−	1.10890i
$439$		−	343.308i		−	0.782023i	−0.920386	−	0.391011i	$-0.872125\pi$
$439$		−	343.308i		−	0.782023i	0.920386	−	0.391011i	$-0.127875\pi$
$440$		0			0
$441$	3.15942			0.00716422
$442$	187.017			0.423115
$443$			47.4703i			0.107156i	0.998564	+	0.0535782i	$0.0170626\pi$
$443$			47.4703i			0.107156i	−0.998564	+	0.0535782i	$0.982937\pi$
$444$	727.961			1.63955
$445$		0			0
$446$		−	892.887i		−	2.00199i
$447$	220.962			0.494321
$448$	−589.433			−1.31570
$449$	339.087			0.755205			0.377602	−	0.925968i	$-0.376749\pi$
$449$	339.087			0.755205			0.377602	+	0.925968i	$0.376749\pi$
$450$		0			0
$451$	132.177	+	812.557i	0.293076	+	1.80168i
$452$		−	212.204i		−	0.469478i
$453$	718.921			1.58702
$454$	351.503			0.774235
$455$		0			0
$456$	−352.691			−0.773445
$457$	−276.791			−0.605669			−0.302835	−	0.953043i	$-0.597933\pi$
$457$	−276.791			−0.605669			−0.302835	+	0.953043i	$0.597933\pi$
$458$	168.661			0.368256
$459$			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	$-0.0544321\pi$
$462$	−95.9298	−	589.727i	−0.207640	−	1.27647i
$463$			407.669i			0.880494i	0.897877	+	0.440247i	$0.145109\pi$
$463$			407.669i			0.880494i	−0.897877	+	0.440247i	$0.854891\pi$
$464$		−	217.661i		−	0.469097i
$465$		0			0
$466$	−134.939			−0.289568
$467$		−	749.076i		−	1.60402i	−0.597313	−	0.802008i	$-0.703765\pi$
$467$		−	749.076i		−	1.60402i	0.597313	−	0.802008i	$-0.296235\pi$
$468$	19.3527			0.0413520
$469$			201.284i			0.429176i
$470$		0			0
$471$	−321.042			−0.681618
$472$	−11.0051			−0.0233159
$473$	−105.640	+	17.1842i	−0.223340	+	0.0363302i
$474$	122.088			0.257570
$475$		0			0
$476$	−116.533			−0.244817
$477$			14.1147i			0.0295907i
$478$		−	685.539i		−	1.43418i
$479$		−	11.2596i		−	0.0235064i	−0.999931	−	0.0117532i	$-0.996259\pi$
$479$		−	11.2596i		−	0.0235064i	0.999931	−	0.0117532i	$-0.00374124\pi$
$480$		0			0
$481$		−	691.854i		−	1.43837i
$482$		−	489.984i		−	1.01657i
$483$	271.479			0.562068
$484$	686.588	−	229.443i	1.41857	−	0.474056i
$485$		0			0
$486$			32.0170i			0.0658786i
$487$			734.846i			1.50892i	0.656344	+	0.754462i	$0.272102\pi$
$487$			734.846i			1.50892i	−0.656344	+	0.754462i	$0.727898\pi$
$488$			304.394i			0.623759i
$489$	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	$-0.115086\pi$
$492$	1357.17			2.75848
$493$		−	180.658i		−	0.366447i
$494$			1011.43i			2.04743i
$495$		0			0
$496$	−113.990			−0.229818
$497$	626.698			1.26096
$498$			1073.22i			2.15506i
$499$	−875.439			−1.75439			−0.877193	−	0.480138i	$-0.840587\pi$
$499$	−875.439			−1.75439			−0.877193	+	0.480138i	$0.840587\pi$
$500$		0			0
$501$		−	107.900i		−	0.215369i
$502$	−368.211			−0.733488
$503$	505.554			1.00508			0.502539	−	0.864554i	$-0.332399\pi$
$503$	505.554			1.00508			0.502539	+	0.864554i	$0.332399\pi$
$504$	−6.66844			−0.0132310
$505$		0			0
$506$	88.1211	+	541.723i	0.174152	+	1.07060i
$507$		−	388.113i		−	0.765509i
$508$	−1260.48			−2.48126
$509$	778.269			1.52902			0.764508	−	0.644614i	$-0.222982\pi$
$509$	778.269			1.52902			0.764508	+	0.644614i	$0.222982\pi$
$510$		0			0
$511$	287.635			0.562887
$512$	261.468			0.510679
$513$	−496.128			−0.967111
$514$			270.781i			0.526811i
$515$		0			0
$516$			176.445i			0.341947i
$517$	−32.1812	−	197.833i	−0.0622460	−	0.382656i
$518$			719.336i			1.38868i
$519$		−	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	$0.584610\pi$
$522$		−	31.1938i		−	0.0597583i
$523$	628.316			1.20137			0.600685	−	0.799486i	$-0.294895\pi$
$523$	628.316			1.20137			0.600685	+	0.799486i	$0.294895\pi$
$524$		−	788.071i		−	1.50395i
$525$		0			0
$526$	1260.23			2.39587
$527$	−94.6112			−0.179528
$528$	22.1512	+	136.174i	0.0419529	+	0.257905i
$529$	279.620			0.528582
$530$		0			0
$531$	0.329713			0.000620928
$532$		−	630.235i		−	1.18465i
$533$		−	1289.86i		−	2.42000i
$534$			635.528i			1.19013i
$535$		0			0
$536$			222.329i			0.414794i
$537$		−	197.576i		−	0.367925i
$538$	749.474			1.39307
$539$	−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	$0.832433\pi$
$542$		−	107.544i		−	0.198421i
$543$			475.935i			0.876492i
$544$	130.959			0.240733
$545$		0			0
$546$			936.137i			1.71454i
$547$	421.038			0.769722			0.384861	−	0.922975i	$-0.374249\pi$
$547$	421.038			0.769722			0.384861	+	0.922975i	$0.374249\pi$
$548$		−	1004.71i		−	1.83340i
$549$		−	9.11967i		−	0.0166114i
$550$		0			0
$551$	977.040			1.77321
$552$	299.864			0.543232
$553$			72.3016i			0.130744i
$554$	−640.296			−1.15577
$555$		0			0
$556$		−	542.121i		−	0.975038i
$557$	−940.508			−1.68852			−0.844262	−	0.535930i	$-0.819961\pi$
$557$	−940.508			−1.68852			−0.844262	+	0.535930i	$0.819961\pi$
$558$	−16.3363			−0.0292765
$559$	167.693			0.299987
$560$		0			0
$561$	18.3854	+	113.024i	0.0327726	+	0.201469i
$562$		−	319.008i		−	0.567629i
$563$	−285.806			−0.507649			−0.253824	−	0.967250i	$-0.581688\pi$
$563$	−285.806			−0.507649			−0.253824	+	0.967250i	$0.581688\pi$
$564$	−330.431			−0.585871
$565$		0			0
$566$	512.203			0.904952
$567$	−468.776			−0.826765
$568$	692.224			1.21870
$569$		−	307.137i		−	0.539783i	−0.962891	−	0.269892i	$-0.913012\pi$
$569$		−	307.137i		−	0.539783i	0.962891	−	0.269892i	$-0.0869879\pi$
$570$		0			0
$571$		−	390.713i		−	0.684261i	−0.939652	−	0.342130i	$-0.888852\pi$
$571$		−	390.713i		−	0.684261i	0.939652	−	0.342130i	$-0.111148\pi$
$572$	−1119.52	+	182.110i	−1.95720	+	0.318374i
$573$		−	490.941i		−	0.856791i
$574$			1341.09i			2.33640i
$575$		0			0
$576$	19.5059			0.0338643
$577$			119.491i			0.207090i	0.994625	+	0.103545i	$0.0330186\pi$
$577$			119.491i			0.207090i	−0.994625	+	0.103545i	$0.966981\pi$
$578$	−875.843			−1.51530
$579$		−	2.25186i		−	0.00388923i
$580$		0			0
$581$	−635.568			−1.09392
$582$	−623.749			−1.07173
$583$	−132.820	−	816.511i	−0.227822	−	1.40053i
$584$	317.710			0.544023
$585$		0			0
$586$	−1177.79			−2.00988
$587$			340.259i			0.579658i	0.957078	+	0.289829i	$0.0935984\pi$
$587$			340.259i			0.579658i	−0.957078	+	0.289829i	$0.906402\pi$
$588$			305.266i			0.519159i
$589$		−	511.678i		−	0.868723i
$590$		0			0
$591$		−	130.625i		−	0.221023i
$592$		−	166.102i		−	0.280577i
$593$	752.004			1.26813			0.634067	−	0.773278i	$-0.281384\pi$
$593$	752.004			1.26813			0.634067	+	0.773278i	$0.281384\pi$
$594$	−149.053	−	916.303i	−0.250932	−	1.54260i
$595$		0			0
$596$			436.128i			0.731758i
$597$		−	612.083i		−	1.02527i
$598$		−	859.935i		−	1.43802i
$599$	−274.841			−0.458833			−0.229416	−	0.973328i	$-0.573682\pi$
$599$	−274.841			−0.458833			−0.229416	+	0.973328i	$0.573682\pi$
$600$		0			0
$601$			397.025i			0.660608i	0.943875	+	0.330304i	$0.107151\pi$
$601$			397.025i			0.660608i	−0.943875	+	0.330304i	$0.892849\pi$
$602$	−174.354			−0.289625
$603$		−	6.66100i		−	0.0110464i
$604$			1418.98i			2.34931i
$605$		0			0
$606$	−1647.42			−2.71851
$607$	351.597			0.579238			0.289619	−	0.957142i	$-0.406471\pi$
$607$	351.597			0.579238			0.289619	+	0.957142i	$0.406471\pi$
$608$			708.252i			1.16489i
$609$	904.308			1.48491
$610$		0			0
$611$			314.042i			0.513980i
$612$	3.85637			0.00630127
$613$	−547.965			−0.893907			−0.446953	−	0.894557i	$-0.647491\pi$
$613$	−547.965			−0.893907			−0.446953	+	0.894557i	$0.647491\pi$
$614$	−1409.14			−2.29501
$615$		0			0
$616$	385.757	−	62.7503i	0.626228	−	0.101867i
$617$			1124.68i			1.82282i	0.411505	+	0.911408i	$0.365003\pi$
$617$			1124.68i			1.82282i	−0.411505	+	0.911408i	$0.634997\pi$
$618$	271.295			0.438988
$619$	−82.7193			−0.133634			−0.0668169	−	0.997765i	$-0.521284\pi$
$619$	−82.7193			−0.133634			−0.0668169	+	0.997765i	$0.521284\pi$
$620$		0			0
$621$	421.817			0.679254
$622$	−787.429			−1.26596
$623$	−376.364			−0.604116
$624$		−	216.163i		−	0.346416i
$625$		0			0
$626$			1463.57i			2.33797i
$627$	−611.259	+	99.4324i	−0.974895	+	0.158584i
$628$		−	633.663i		−	1.00902i
$629$		−	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	$0.418949\pi$
$632$			79.8612i			0.126363i
$633$	162.076			0.256043
$634$		−	529.375i		−	0.834976i
$635$		0			0
$636$	−1363.78			−2.14431
$637$	290.125			0.455454
$638$	293.535	+	1804.50i	0.460086	+	2.82838i
$639$	−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	$0.390549\pi$
$642$			605.709i			0.943472i
$643$			229.511i			0.356937i	0.983946	+	0.178469i	$0.0571143\pi$
$643$			229.511i			0.356937i	−0.983946	+	0.178469i	$0.942886\pi$
$644$			535.837i			0.832045i
$645$		0			0
$646$			201.545i			0.311989i
$647$			768.342i			1.18755i	0.804633	+	0.593773i	$0.202362\pi$
$647$			768.342i			1.18755i	−0.804633	+	0.593773i	$0.797638\pi$
$648$	−517.790			−0.799059
$649$	−19.0733	+	3.10261i	−0.0293887	+	0.00478060i
$650$		0			0
$651$		−	473.588i		−	0.727478i
$652$			856.926i			1.31430i
$653$			624.977i			0.957085i	0.878064	+	0.478543i	$0.158835\pi$
$653$			624.977i			0.957085i	−0.878064	+	0.478543i	$0.841165\pi$
$654$	−1231.99			−1.88378
$655$		0			0
$656$		−	309.672i		−	0.472061i
$657$	−9.51859			−0.0144880
$658$		−	326.516i		−	0.496225i
$659$		−	1104.04i		−	1.67533i	−0.546185	−	0.837665i	$-0.683920\pi$
$659$		−	1104.04i		−	1.67533i	0.546185	−	0.837665i	$-0.316080\pi$
$660$		0			0
$661$	246.985			0.373653			0.186827	−	0.982393i	$-0.440180\pi$
$661$	246.985			0.373653			0.186827	+	0.982393i	$0.440180\pi$
$662$	28.3729			0.0428594
$663$		−	179.415i		−	0.270611i
$664$	−702.021			−1.05726
$665$		0			0
$666$		−	23.8047i		−	0.0357427i
$667$	−830.697			−1.24542
$668$	212.970			0.318817
$669$	−856.594			−1.28041
$670$		0			0
$671$	85.8165	+	527.555i	0.127893	+	0.786223i
$672$			655.529i			0.975490i
$673$	715.709			1.06346			0.531730	−	0.846914i	$-0.321542\pi$
$673$	715.709			1.06346			0.531730	+	0.846914i	$0.321542\pi$
$674$	833.808			1.23710
$675$		0			0
$676$	766.047			1.13321
$677$	946.798			1.39852			0.699260	−	0.714867i	$-0.253513\pi$
$677$	946.798			1.39852			0.699260	+	0.714867i	$0.253513\pi$
$678$	−339.689			−0.501017
$679$		−	369.389i		−	0.544019i
$680$		0			0
$681$		−	337.215i		−	0.495176i
$682$	945.023	−	153.725i	1.38566	−	0.225403i
$683$			67.4542i			0.0987616i	0.998780	+	0.0493808i	$0.0157248\pi$
$683$			67.4542i			0.0987616i	−0.998780	+	0.0493808i	$0.984275\pi$
$684$			20.8561i			0.0304914i
$685$		0			0
$686$	−1179.71			−1.71969
$687$		−	161.805i		−	0.235525i
$688$	40.2601			0.0585176
$689$			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	$0.592597\pi$
$692$	1172.90			1.69494
$693$	−11.5573	+	1.88000i	−0.0166772	+	0.00271284i
$694$	1932.85			2.78509
$695$		0			0
$696$	998.860			1.43514
$697$		−	257.027i		−	0.368762i
$698$			891.697i			1.27750i
$699$			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	$-0.217218\pi$
$702$			1454.55i			2.07200i
$703$	745.600			1.06060
$704$	−1128.38	+	183.551i	−1.60281	+	0.260726i
$705$		0			0
$706$		−	548.590i		−	0.777040i
$707$		−	975.613i		−	1.37993i
$708$			31.8571i			0.0449959i
$709$	902.302			1.27264			0.636320	−	0.771425i	$-0.280456\pi$
$709$	902.302			1.27264			0.636320	+	0.771425i	$0.280456\pi$
$710$		0			0
$711$		−	2.39265i		−	0.00336518i
$712$	−415.716			−0.583871
$713$			435.038i			0.610151i
$714$			186.542i			0.261263i
$715$		0			0
$716$	389.969			0.544650
$717$	−657.673			−0.917257
$718$			901.684i			1.25583i
$719$	−1021.01			−1.42004			−0.710021	−	0.704180i	$-0.751315\pi$
$719$	−1021.01			−1.42004			−0.710021	+	0.704180i	$0.751315\pi$
$720$		0			0
$721$			160.663i			0.222833i
$722$	50.5966			0.0700784
$723$	−470.068			−0.650163
$724$	−939.387			−1.29750
$725$		0			0
$726$	−367.285	−	1099.07i	−0.505902	−	1.51387i
$727$		−	637.169i		−	0.876436i	−0.898869	−	0.438218i	$-0.855610\pi$
$727$		−	637.169i		−	0.876436i	0.898869	−	0.438218i	$-0.144390\pi$
$728$	−612.352			−0.841143
$729$	−713.170			−0.978285
$730$		0			0
$731$	33.4158			0.0457125
$732$	881.150			1.20376
$733$	−261.937			−0.357349			−0.178674	−	0.983908i	$-0.557181\pi$
$733$	−261.937			−0.357349			−0.178674	+	0.983908i	$0.557181\pi$
$734$			1024.56i			1.39586i
$735$		0			0
$736$		−	602.169i		−	0.818164i
$737$	62.6803	+	385.326i	0.0850478	+	0.522830i
$738$		−	44.3802i		−	0.0601358i
$739$			734.865i			0.994404i	0.867635	+	0.497202i	$0.165639\pi$
$739$			734.865i			0.994404i	−0.867635	+	0.497202i	$0.834361\pi$
$740$		0			0
$741$	970.317			1.30947
$742$		−	1347.62i		−	1.81620i
$743$	−161.161			−0.216905			−0.108453	−	0.994102i	$-0.534590\pi$
$743$	−161.161			−0.216905			−0.108453	+	0.994102i	$0.534590\pi$
$744$		−	523.105i		−	0.703098i
$745$		0			0
$746$	405.583			0.543676
$747$	21.0326			0.0281561
$748$	−223.084	+	36.2886i	−0.298241	+	0.0485142i
$749$	−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	$0.225117\pi$
$752$			75.3958i			0.100260i
$753$			353.244i			0.469116i
$754$		−	2864.48i		−	3.79904i
$755$		0			0
$756$		−	906.348i		−	1.19887i
$757$		−	119.677i		−	0.158094i	−0.996871	−	0.0790469i	$-0.974812\pi$
$757$		−	119.677i		−	0.158094i	0.996871	−	0.0790469i	$-0.0251877\pi$
$758$	−2162.74			−2.85322
$759$	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	$-0.0329523\pi$
$762$			2017.73i			2.64794i
$763$		−	729.596i		−	0.956221i
$764$	969.006			1.26833
$765$		0			0
$766$			1070.35i			1.39732i
$767$	30.2770			0.0394746
$768$			423.924i			0.551984i
$769$		−	1498.58i		−	1.94874i	−0.224947	−	0.974371i	$-0.572221\pi$
$769$		−	1498.58i		−	1.94874i	0.224947	−	0.974371i	$-0.427779\pi$
$770$		0			0
$771$	259.774			0.336931
$772$	4.44466			0.00575734
$773$		−	1528.87i		−	1.97784i	−0.148450	−	0.988920i	$-0.547428\pi$
$773$		−	1528.87i		−	1.97784i	0.148450	−	0.988920i	$-0.452572\pi$
$774$	5.76982			0.00745455
$775$		0			0
$776$		−	408.012i		−	0.525788i
$777$	690.096			0.888155
$778$	1747.07			2.24559
$779$	1390.06			1.78441
$780$		0			0
$781$	1199.72	−	195.155i	1.53613	−	0.249879i
$782$		−	171.357i		−	0.219127i
$783$	1405.09			1.79450
$784$	69.6537			0.0888440
$785$		0			0
$786$	−1261.52			−1.60498
$787$	930.613			1.18248			0.591241	−	0.806495i	$-0.298638\pi$
$787$	930.613			1.18248			0.591241	+	0.806495i	$0.298638\pi$
$788$	257.823			0.327187
$789$		−	1209.00i		−	1.53232i
$790$		0			0
$791$		−	201.167i		−	0.254319i
$792$	−12.7657	+	2.07657i	−0.0161183	+	0.00262193i
$793$		−	837.445i		−	1.05605i
$794$		−	353.492i		−	0.445204i
$795$		0			0
$796$	1208.11			1.51773
$797$			332.628i			0.417350i	0.977985	+	0.208675i	$0.0669151\pi$
$797$			332.628i			0.417350i	−0.977985	+	0.208675i	$0.933085\pi$
$798$	−1008.86			−1.26423
$799$			62.5784i			0.0783210i
$800$		0			0
$801$	12.4549			0.0155491
$802$	−900.383			−1.12267
$803$	550.632	−	89.5703i	0.685719	−	0.111545i
$804$	643.591			0.800486
$805$		0			0
$806$	−1500.13			−1.86121
$807$		−	719.010i		−	0.890966i
$808$		−	1077.62i		−	1.33369i
$809$			870.764i			1.07635i	0.842834	+	0.538173i	$0.180885\pi$
$809$			870.764i			1.07635i	−0.842834	+	0.538173i	$0.819115\pi$
$810$		0			0
$811$			1369.14i			1.68821i	0.536180	+	0.844103i	$0.319867\pi$
$811$			1369.14i			1.68821i	−0.536180	+	0.844103i	$0.680133\pi$
$812$			1784.90i			2.19815i
$813$	−103.173			−0.126904
$814$	224.003	+	1377.05i	0.275188	+	1.69171i
$815$		0			0
$816$		−	43.0744i		−	0.0527873i
$817$			180.720i			0.221199i
$818$		−	385.842i		−	0.471689i
$819$	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	$-0.153061\pi$
$822$	−1608.30			−1.95657
$823$			252.673i			0.307015i	0.988148	+	0.153507i	$0.0490569\pi$
$823$			252.673i			0.307015i	−0.988148	+	0.153507i	$0.950943\pi$
$824$			177.461i			0.215366i
$825$		0			0
$826$	−31.4797			−0.0381110
$827$	−172.995			−0.209184			−0.104592	−	0.994515i	$-0.533354\pi$
$827$	−172.995			−0.209184			−0.104592	+	0.994515i	$0.533354\pi$
$828$		−	17.7322i		−	0.0214157i
$829$	−1145.40			−1.38167			−0.690834	−	0.723013i	$-0.742756\pi$
$829$	−1145.40			−1.38167			−0.690834	+	0.723013i	$0.742756\pi$
$830$		0			0
$831$			614.270i			0.739193i
$832$	1791.19			2.15287
$833$	57.8125			0.0694027
$834$	−867.809			−1.04054
$835$		0			0
$836$	−196.257	−	1206.49i	−0.234757	−	1.44317i
$837$		−	735.849i		−	0.879151i
$838$	−1287.91			−1.53689
$839$	41.7126			0.0497170			0.0248585	−	0.999691i	$-0.492086\pi$
$839$	41.7126			0.0497170			0.0248585	+	0.999691i	$0.492086\pi$
$840$		0			0
$841$	−1926.09			−2.29023
$842$	−1100.19			−1.30664
$843$	−306.041			−0.363038
$844$			319.900i			0.379029i
$845$		0			0
$846$			10.8053i			0.0127722i
$847$	650.876	−	217.509i	0.768448	−	0.256799i
$848$			311.179i			0.366956i
$849$		−	491.383i		−	0.578778i
$850$		0			0
$851$	−633.922			−0.744915
$852$		−	2003.82i		−	2.35191i
$853$	725.094			0.850052			0.425026	−	0.905181i	$-0.360265\pi$
$853$	725.094			0.850052			0.425026	+	0.905181i	$0.360265\pi$
$854$			870.709i			1.01957i
$855$		0			0
$856$	−396.211			−0.462863
$857$	302.221			0.352650			0.176325	−	0.984332i	$-0.443579\pi$
$857$	302.221			0.352650			0.176325	+	0.984332i	$0.443579\pi$
$858$	291.515	+	1792.09i	0.339761	+	2.08868i
$859$	207.101			0.241096			0.120548	−	0.992708i	$-0.461535\pi$
$859$	207.101			0.241096			0.120548	+	0.992708i	$0.461535\pi$
$860$		0			0
$861$	1286.58			1.49429
$862$		−	1433.19i		−	1.66263i
$863$			482.444i			0.559032i	0.960141	+	0.279516i	$0.0901739\pi$
$863$			482.444i			0.559032i	−0.960141	+	0.279516i	$0.909826\pi$
$864$			1018.54i			1.17887i
$865$		0			0
$866$			2401.73i			2.77336i
$867$			840.242i			0.969137i
$868$	934.755			1.07691
$869$	22.5149	+	138.410i	0.0259090	+	0.159275i
$870$		0			0
$871$		−	611.669i		−	0.702260i
$872$		−	805.881i		−	0.924176i
$873$			12.2240i			0.0140023i
$874$	926.738			1.06034
$875$		0			0
$876$		−	919.694i		−	1.04988i
$877$	−377.864			−0.430860			−0.215430	−	0.976519i	$-0.569115\pi$
$877$	−377.864			−0.430860			−0.215430	+	0.976519i	$0.569115\pi$
$878$		−	1084.70i		−	1.23542i
$879$			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	$0.810784\pi$
$882$	9.98233			0.0113178
$883$		−	353.252i		−	0.400059i	−0.979790	−	0.200029i	$-0.935896\pi$
$883$		−	353.252i		−	0.400059i	0.979790	−	0.200029i	$-0.0641037\pi$
$884$	354.125			0.400594
$885$		0			0
$886$			149.985i			0.169283i
$887$	174.064			0.196239			0.0981194	−	0.995175i	$-0.468717\pi$
$887$	174.064			0.196239			0.0981194	+	0.995175i	$0.468717\pi$
$888$	762.251			0.858391
$889$	−1194.92			−1.34411
$890$		0			0
$891$	−897.398	+	145.978i	−1.00718	+	0.163836i
$892$		−	1690.72i		−	1.89543i
$893$	−338.438			−0.378990
$894$	698.138			0.780915
$895$		0			0
$896$	−997.275			−1.11303
$897$	−824.981			−0.919711
$898$	1071.36			1.19305
$899$			1449.13i			1.61193i
$900$		0			0
$901$			258.278i			0.286657i
$902$	417.620	+	2567.31i	0.462993	+	2.84624i
$903$			167.267i			0.185235i
$904$		−	222.200i		−	0.245797i
$905$		0			0
$906$	2271.46			2.50713
$907$			1341.78i			1.47936i	0.672960	+	0.739679i	$0.265023\pi$
$907$			1341.78i			1.47936i	−0.672960	+	0.739679i	$0.734977\pi$
$908$	665.586			0.733024
$909$			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	$0.485696\pi$
$912$	232.956			0.255434
$913$	−1216.70	+	197.918i	−1.33263	+	0.216777i
$914$	−874.534			−0.956821
$915$		0			0
$916$	319.367			0.348654
$917$		−	747.080i		−	0.814700i
$918$			289.844i			0.315734i
$919$			146.259i			0.159150i	0.996829	+	0.0795752i	$0.0253564\pi$
$919$			146.259i			0.159150i	−0.996829	+	0.0795752i	$0.974644\pi$
$920$		0			0
$921$			1351.86i			1.46782i
$922$		−	495.726i		−	0.537664i
$923$	−1904.44			−2.06331
$924$	−181.647	−	1116.67i	−0.196588	−	1.20852i
$925$		0			0
$926$			1288.05i			1.39098i
$927$		−	5.31674i		−	0.00573543i
$928$		−	2005.85i		−	2.16148i
$929$	624.735			0.672481			0.336240	−	0.941776i	$-0.390845\pi$
$929$	624.735			0.672481			0.336240	+	0.941776i	$0.390845\pi$
$930$		0			0
$931$			312.662i			0.335835i
$932$	−255.512			−0.274154
$933$			755.422i			0.809670i
$934$		−	2366.74i		−	2.53398i
$935$		0			0
$936$	20.2643			0.0216499
$937$	−1737.04			−1.85383			−0.926915	−	0.375273i	$-0.877549\pi$
$937$	−1737.04			−1.85383			−0.926915	+	0.375273i	$0.877549\pi$
$938$			635.965i			0.678001i
$939$	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	$0.776683\pi$
$942$	−1014.35			−1.07680
$943$	−1181.85			−1.25329
$944$	7.26897			0.00770018
$945$		0			0
$946$	−333.773	+	54.2943i	−0.352826	+	0.0573935i
$947$		−	1465.25i		−	1.54725i	−0.633641	−	0.773627i	$-0.718440\pi$
$947$		−	1465.25i		−	1.54725i	0.633641	−	0.773627i	$-0.281560\pi$
$948$	231.179			0.243860
$949$	−874.077			−0.921051
$950$		0			0
$951$	−507.857			−0.534025
$952$	−122.022			−0.128175
$953$	464.526			0.487435			0.243717	−	0.969846i	$-0.421633\pi$
$953$	464.526			0.487435			0.243717	+	0.969846i	$0.421633\pi$
$954$			44.5962i			0.0467465i
$955$		0			0
$956$		−	1298.10i		−	1.35784i
$957$	1731.15	−	281.604i	1.80894	−	0.294257i
$958$		−	35.5751i		−	0.0371348i
$959$		−	952.446i		−	0.993166i
$960$		0			0
$961$	−202.088			−0.210289
$962$		−	2185.95i		−	2.27229i
$963$	11.8705			0.0123266
$964$		−	927.807i		−	0.962455i
$965$		0			0
$966$	857.750			0.887940
$967$	−667.349			−0.690123			−0.345062	−	0.938580i	$-0.612142\pi$
$967$	−667.349			−0.690123			−0.345062	+	0.938580i	$0.612142\pi$
$968$	718.930	−	240.251i	0.742696	−	0.248193i
$969$	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	$0.331501\pi$
$972$			60.6256i			0.0623720i
$973$		−	513.923i		−	0.528184i
$974$			2321.78i			2.38376i
$975$		0			0
$976$		−	201.056i		−	0.206000i
$977$		−	342.678i		−	0.350745i	−0.984502	−	0.175372i	$-0.943887\pi$
$977$		−	342.678i		−	0.350745i	0.984502	−	0.175372i	$-0.0561129\pi$
$978$	1371.74			1.40259
$979$	−720.490	+	117.201i	−0.735945	+	0.119715i
$980$		0			0
$981$			24.1442i			0.0246118i
$982$		−	1097.50i		−	1.11762i
$983$		−	447.215i		−	0.454949i	−0.973784	−	0.227475i	$-0.926953\pi$
$983$		−	447.215i		−	0.454949i	0.973784	−	0.227475i	$-0.0730469\pi$
$984$	1421.10			1.44421
$985$		0			0
$986$		−	570.799i		−	0.578903i
$987$	−313.244			−0.317370
$988$			1915.18i			1.93844i
$989$		−	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	$0.478152\pi$
$992$	−1050.47			−1.05894
$993$		−	27.2196i		−	0.0274115i
$994$	1980.08			1.99203
$995$		0			0
$996$			2032.19i			2.04035i
$997$	303.075			0.303987			0.151993	−	0.988381i	$-0.451431\pi$
$997$	303.075			0.303987			0.151993	+	0.988381i	$0.451431\pi$
$998$	−2765.99			−2.77153
$999$	1072.25			1.07333

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.c.a.21.2	✓	8	55.32	even	4
55.3.c.a.21.7	yes	8	5.2	odd	4
275.3.c.f.76.2		8	5.3	odd	4
275.3.c.f.76.7		8	55.43	even	4
275.3.d.c.274.3		16	11.10	odd	2	inner
275.3.d.c.274.4		16	5.4	even	2	inner
275.3.d.c.274.13		16	1.1	even	1	trivial
275.3.d.c.274.14		16	55.54	odd	2	inner
495.3.b.a.406.2		8	15.2	even	4
495.3.b.a.406.7		8	165.32	odd	4
880.3.j.a.241.7		8	20.7	even	4
880.3.j.a.241.8		8	220.87	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.15955 q^{2} -3.03112i q^{3} +5.98274 q^{4} -9.57697i q^{6} +5.67155 q^{7} +6.26455 q^{8} -0.187686 q^{9} +(10.8573 - 1.76614i) q^{11} -18.1344i q^{12} -17.2349 q^{13} +17.9195 q^{14} -4.13780 q^{16} -3.43437 q^{17} -0.593004 q^{18} -18.5738i q^{19} -17.1911i q^{21} +(34.3041 - 5.58019i) q^{22} +15.7918i q^{23} -18.9886i q^{24} -54.4546 q^{26} -26.7112i q^{27} +33.9314 q^{28} +52.6031i q^{29} +27.5484 q^{31} -38.1318 q^{32} +(-5.35337 - 32.9097i) q^{33} -10.8510 q^{34} -1.12288 q^{36} +40.1425i q^{37} -58.6848i q^{38} +52.2411i q^{39} +74.8398i q^{41} -54.3162i q^{42} -9.72983 q^{43} +(64.9563 - 10.5663i) q^{44} +49.8949i q^{46} -18.2212i q^{47} +12.5422i q^{48} -16.8335 q^{49} +10.4100i q^{51} -103.112 q^{52} -75.2040i q^{53} -84.3952i q^{54} +35.5297 q^{56} -56.2994 q^{57} +166.202i q^{58} -1.75672 q^{59} +48.5900i q^{61} +87.0404 q^{62} -1.06447 q^{63} -103.928 q^{64} +(-16.9142 - 103.980i) q^{66} +35.4901i q^{67} -20.5469 q^{68} +47.8668 q^{69} +110.499 q^{71} -1.17577 q^{72} +50.7154 q^{73} +126.832i q^{74} -111.122i q^{76} +(61.5777 - 10.0167i) q^{77} +165.058i q^{78} +12.7481i q^{79} -82.6540 q^{81} +236.460i q^{82} -112.062 q^{83} -102.850i q^{84} -30.7419 q^{86} +159.446 q^{87} +(68.0161 - 11.0640i) q^{88} -66.3600 q^{89} -97.7488 q^{91} +94.4781i q^{92} -83.5024i q^{93} -57.5709i q^{94} +115.582i q^{96} -65.1302i q^{97} -53.1863 q^{98} +(-2.03776 + 0.331479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 56 q^{4} + 8 q^{9} + 16 q^{11} + 176 q^{16} - 200 q^{26} + 72 q^{31} - 160 q^{34} - 432 q^{36} - 24 q^{44} - 344 q^{49} - 160 q^{56} + 32 q^{59} + 1176 q^{64} + 360 q^{66} - 16 q^{69} + 552 q^{71}+ \cdots + 368 q^{99}+O(q^{100}) \) 16 * q + 56 * q^4 + 8 * q^9 + 16 * q^11 + 176 * q^16 - 200 * q^26 + 72 * q^31 - 160 * q^34 - 432 * q^36 - 24 * q^44 - 344 * q^49 - 160 * q^56 + 32 * q^59 + 1176 * q^64 + 360 * q^66 - 16 * q^69 + 552 * q^71 - 640 * q^81 + 840 * q^86 - 888 * q^89 - 80 * q^91 + 368 * q^99

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