LMFDB - Embedded newform 275.3.d.c.274.11

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			274.11
Root			$-0.333846 + 0.333846i$ of defining polynomial
Character	$\chi$	$=$	275.274
Dual form			275.3.d.c.274.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.66769 q^{2} -2.79505i q^{3} -1.21881 q^{4} -4.66128i q^{6} -6.72266 q^{7} -8.70336 q^{8} +1.18769 q^{9} +(-6.62122 - 8.78404i) q^{11} +3.40663i q^{12} +2.91291 q^{13} -11.2113 q^{14} -9.63929 q^{16} -30.9615 q^{17} +1.98069 q^{18} -4.49991i q^{19} +18.7902i q^{21} +(-11.0422 - 14.6491i) q^{22} -13.0410i q^{23} +24.3263i q^{24} +4.85783 q^{26} -28.4751i q^{27} +8.19362 q^{28} +44.8359i q^{29} +26.1730 q^{31} +18.7381 q^{32} +(-24.5519 + 18.5067i) q^{33} -51.6342 q^{34} -1.44756 q^{36} -28.8149i q^{37} -7.50446i q^{38} -8.14172i q^{39} -24.6573i q^{41} +31.3362i q^{42} +2.28690 q^{43} +(8.06999 + 10.7060i) q^{44} -21.7484i q^{46} -2.33270i q^{47} +26.9423i q^{48} -3.80580 q^{49} +86.5390i q^{51} -3.55027 q^{52} -93.1057i q^{53} -47.4877i q^{54} +58.5097 q^{56} -12.5775 q^{57} +74.7724i q^{58} +108.616 q^{59} -54.7958i q^{61} +43.6485 q^{62} -7.98441 q^{63} +69.8065 q^{64} +(-40.9449 + 30.8634i) q^{66} +9.01793i q^{67} +37.7361 q^{68} -36.4504 q^{69} -1.24936 q^{71} -10.3369 q^{72} -24.1060 q^{73} -48.0543i q^{74} +5.48452i q^{76} +(44.5123 + 59.0522i) q^{77} -13.5779i q^{78} -108.479i q^{79} -68.9002 q^{81} -41.1207i q^{82} -8.27453 q^{83} -22.9016i q^{84} +3.81384 q^{86} +125.319 q^{87} +(57.6269 + 76.4507i) q^{88} -84.8892 q^{89} -19.5825 q^{91} +15.8945i q^{92} -73.1549i q^{93} -3.89022i q^{94} -52.3739i q^{96} +160.450i q^{97} -6.34690 q^{98} +(-7.86394 - 10.4327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.66769			0.833846			0.416923	−	0.908942i	$-0.363109\pi$
$2$	1.66769			0.833846			0.416923	+	0.908942i	$0.363109\pi$
$3$		−	2.79505i		−	0.931684i	−0.884868	−	0.465842i	$-0.845752\pi$
$3$		−	2.79505i		−	0.931684i	0.884868	−	0.465842i	$-0.154248\pi$
$4$	−1.21881			−0.304701
$5$		0			0
$5$		0			0
$6$		−	4.66128i		−	0.776881i
$7$	−6.72266			−0.960380			−0.480190	−	0.877164i	$-0.659432\pi$
$7$	−6.72266			−0.960380			−0.480190	+	0.877164i	$0.659432\pi$
$8$	−8.70336			−1.08792
$9$	1.18769			0.131965
$10$		0			0
$11$	−6.62122	−	8.78404i	−0.601929	−	0.798549i
$11$	−6.62122	−	8.78404i	−0.601929	−	0.798549i
$12$			3.40663i			0.283885i
$13$	2.91291			0.224070			0.112035	−	0.993704i	$-0.464263\pi$
$13$	2.91291			0.224070			0.112035	+	0.993704i	$0.464263\pi$
$14$	−11.2113			−0.800809
$15$		0			0
$16$	−9.63929			−0.602456
$17$	−30.9615			−1.82127			−0.910633	−	0.413217i	$-0.864405\pi$
$17$	−30.9615			−1.82127			−0.910633	+	0.413217i	$0.864405\pi$
$18$	1.98069			0.110039
$19$		−	4.49991i		−	0.236837i	−0.992964	−	0.118419i	$-0.962217\pi$
$19$		−	4.49991i		−	0.236837i	0.992964	−	0.118419i	$-0.0377825\pi$
$20$		0			0
$21$			18.7902i			0.894771i
$22$	−11.0422	−	14.6491i	−0.501916	−	0.665867i
$23$		−	13.0410i		−	0.567002i	−0.958972	−	0.283501i	$-0.908504\pi$
$23$		−	13.0410i		−	0.567002i	0.958972	−	0.283501i	$-0.0914959\pi$
$24$			24.3263i			1.01360i
$25$		0			0
$26$	4.85783			0.186840
$27$		−	28.4751i		−	1.05463i
$28$	8.19362			0.292629
$29$			44.8359i			1.54607i	0.634366	+	0.773033i	$0.281261\pi$
$29$			44.8359i			1.54607i	−0.634366	+	0.773033i	$0.718739\pi$
$30$		0			0
$31$	26.1730			0.844290			0.422145	−	0.906528i	$-0.361277\pi$
$31$	26.1730			0.844290			0.422145	+	0.906528i	$0.361277\pi$
$32$	18.7381			0.585565
$33$	−24.5519	+	18.5067i	−0.743996	+	0.560808i
$34$	−51.6342			−1.51865
$35$		0			0
$36$	−1.44756			−0.0402100
$37$		−	28.8149i		−	0.778781i	−0.921073	−	0.389390i	$-0.872686\pi$
$37$		−	28.8149i		−	0.778781i	0.921073	−	0.389390i	$-0.127314\pi$
$38$		−	7.50446i		−	0.197486i
$39$		−	8.14172i		−	0.208762i
$40$		0			0
$41$		−	24.6573i		−	0.601397i	−0.953719	−	0.300698i	$-0.902780\pi$
$41$		−	24.6573i		−	0.601397i	0.953719	−	0.300698i	$-0.0972197\pi$
$42$			31.3362i			0.746101i
$43$	2.28690			0.0531837			0.0265919	−	0.999646i	$-0.491535\pi$
$43$	2.28690			0.0531837			0.0265919	+	0.999646i	$0.491535\pi$
$44$	8.06999	+	10.7060i	0.183409	+	0.243319i
$45$		0			0
$46$		−	21.7484i		−	0.472792i
$47$		−	2.33270i		−	0.0496319i	−0.999692	−	0.0248159i	$-0.992100\pi$
$47$		−	2.33270i		−	0.0496319i	0.999692	−	0.0248159i	$-0.00789997\pi$
$48$			26.9423i			0.561298i
$49$	−3.80580			−0.0776694
$50$		0			0
$51$			86.5390i			1.69684i
$52$	−3.55027			−0.0682744
$53$		−	93.1057i		−	1.75671i	−0.478009	−	0.878355i	$-0.658641\pi$
$53$		−	93.1057i		−	1.75671i	0.478009	−	0.878355i	$-0.341359\pi$
$54$		−	47.4877i		−	0.879402i
$55$		0			0
$56$	58.5097			1.04482
$57$	−12.5775			−0.220658
$58$			74.7724i			1.28918i
$59$	108.616			1.84095			0.920473	−	0.390805i	$-0.127803\pi$
$59$	108.616			1.84095			0.920473	+	0.390805i	$0.127803\pi$
$60$		0			0
$61$		−	54.7958i		−	0.898292i	−0.893458	−	0.449146i	$-0.851728\pi$
$61$		−	54.7958i		−	0.898292i	0.893458	−	0.449146i	$-0.148272\pi$
$62$	43.6485			0.704008
$63$	−7.98441			−0.126737
$64$	69.8065			1.09073
$65$		0			0
$66$	−40.9449	+	30.8634i	−0.620377	+	0.467627i
$67$			9.01793i			0.134596i	0.997733	+	0.0672980i	$0.0214378\pi$
$67$			9.01793i			0.134596i	−0.997733	+	0.0672980i	$0.978562\pi$
$68$	37.7361			0.554942
$69$	−36.4504			−0.528266
$70$		0			0
$71$	−1.24936			−0.0175966			−0.00879832	−	0.999961i	$-0.502801\pi$
$71$	−1.24936			−0.0175966			−0.00879832	+	0.999961i	$0.502801\pi$
$72$	−10.3369			−0.143567
$73$	−24.1060			−0.330220			−0.165110	−	0.986275i	$-0.552798\pi$
$73$	−24.1060			−0.330220			−0.165110	+	0.986275i	$0.552798\pi$
$74$		−	48.0543i		−	0.649383i
$75$		0			0
$76$			5.48452i			0.0721647i
$77$	44.5123	+	59.0522i	0.578081	+	0.766911i
$78$		−	13.5779i		−	0.174075i
$79$		−	108.479i		−	1.37315i	−0.727060	−	0.686574i	$-0.759114\pi$
$79$		−	108.479i		−	1.37315i	0.727060	−	0.686574i	$-0.240886\pi$
$80$		0			0
$81$	−68.9002			−0.850620
$82$		−	41.1207i		−	0.501472i
$83$	−8.27453			−0.0996931			−0.0498466	−	0.998757i	$-0.515873\pi$
$83$	−8.27453			−0.0996931			−0.0498466	+	0.998757i	$0.515873\pi$
$84$		−	22.9016i		−	0.272638i
$85$		0			0
$86$	3.81384			0.0443470
$87$	125.319			1.44044
$88$	57.6269	+	76.4507i	0.654851	+	0.868757i
$89$	−84.8892			−0.953811			−0.476906	−	0.878954i	$-0.658242\pi$
$89$	−84.8892			−0.953811			−0.476906	+	0.878954i	$0.658242\pi$
$90$		0			0
$91$	−19.5825			−0.215192
$92$			15.8945i			0.172766i
$93$		−	73.1549i		−	0.786611i
$94$		−	3.89022i		−	0.0413853i
$95$		0			0
$96$		−	52.3739i		−	0.545561i
$97$			160.450i			1.65413i	0.562109	+	0.827063i	$0.309990\pi$
$97$			160.450i			1.65413i	−0.562109	+	0.827063i	$0.690010\pi$
$98$	−6.34690			−0.0647643
$99$	−7.86394	−	10.4327i	−0.0794337	−	0.105381i
$100$		0			0
$101$			38.1687i			0.377908i	0.981986	+	0.188954i	$0.0605098\pi$
$101$			38.1687i			0.377908i	−0.981986	+	0.188954i	$0.939490\pi$
$102$			144.320i			1.41491i
$103$		−	34.4787i		−	0.334744i	−0.985894	−	0.167372i	$-0.946472\pi$
$103$		−	34.4787i		−	0.334744i	0.985894	−	0.167372i	$-0.0535282\pi$
$104$	−25.3521			−0.243770
$105$		0			0
$106$		−	155.271i		−	1.46483i
$107$	−132.298			−1.23643			−0.618214	−	0.786009i	$-0.712144\pi$
$107$	−132.298			−1.23643			−0.618214	+	0.786009i	$0.712144\pi$
$108$			34.7056i			0.321348i
$109$			174.238i			1.59851i	0.600992	+	0.799255i	$0.294772\pi$
$109$			174.238i			1.59851i	−0.600992	+	0.799255i	$0.705228\pi$
$110$		0			0
$111$	−80.5391			−0.725577
$112$	64.8017			0.578587
$113$			104.085i			0.921104i	0.887633	+	0.460552i	$0.152349\pi$
$113$			104.085i			0.921104i	−0.887633	+	0.460552i	$0.847651\pi$
$114$	−20.9754			−0.183994
$115$		0			0
$116$		−	54.6462i		−	0.471088i
$117$	3.45962			0.0295694
$118$	181.138			1.53507
$119$	208.144			1.74911
$120$		0			0
$121$	−33.3188	+	116.322i	−0.275362	+	0.961341i
$122$		−	91.3825i		−	0.749037i
$123$	−68.9183			−0.560312
$124$	−31.8998			−0.257256
$125$		0			0
$126$	−13.3155			−0.105679
$127$	32.2445			0.253894			0.126947	−	0.991910i	$-0.459482\pi$
$127$	32.2445			0.253894			0.126947	+	0.991910i	$0.459482\pi$
$128$	41.4634			0.323933
$129$		−	6.39201i		−	0.0495504i
$130$		0			0
$131$			253.053i			1.93170i	0.259093	+	0.965852i	$0.416577\pi$
$131$			253.053i			1.93170i	−0.259093	+	0.965852i	$0.583423\pi$
$132$	29.9239	−	22.5560i	0.226697	−	0.170879i
$133$			30.2514i			0.227454i
$134$			15.0391i			0.112232i
$135$		0			0
$136$	269.469			1.98139
$137$		−	200.242i		−	1.46162i	−0.682580	−	0.730811i	$-0.739142\pi$
$137$		−	200.242i		−	1.46162i	0.682580	−	0.730811i	$-0.260858\pi$
$138$	−60.7880			−0.440492
$139$		−	199.124i		−	1.43255i	−0.697821	−	0.716273i	$-0.745847\pi$
$139$		−	199.124i		−	1.43255i	0.697821	−	0.716273i	$-0.254153\pi$
$140$		0			0
$141$	−6.52001			−0.0462412
$142$	−2.08355			−0.0146729
$143$	−19.2870	−	25.5871i	−0.134874	−	0.178931i
$144$	−11.4485			−0.0795031
$145$		0			0
$146$	−40.2014			−0.275352
$147$			10.6374i			0.0723634i
$148$			35.1197i			0.237296i
$149$		−	42.5232i		−	0.285391i	−0.989767	−	0.142695i	$-0.954423\pi$
$149$		−	42.5232i		−	0.285391i	0.989767	−	0.142695i	$-0.0455769\pi$
$150$		0			0
$151$		−	225.857i		−	1.49574i	−0.663845	−	0.747870i	$-0.731077\pi$
$151$		−	225.857i		−	1.49574i	0.663845	−	0.747870i	$-0.268923\pi$
$152$			39.1643i			0.257660i
$153$	−36.7726			−0.240344
$154$	74.2327	+	98.4808i	0.482030	+	0.639486i
$155$		0			0
$156$			9.92318i			0.0636101i
$157$		−	121.955i		−	0.776782i	−0.921495	−	0.388391i	$-0.873031\pi$
$157$		−	121.955i		−	0.776782i	0.921495	−	0.388391i	$-0.126969\pi$
$158$		−	180.909i		−	1.14499i
$159$	−260.235			−1.63670
$160$		0			0
$161$			87.6705i			0.544537i
$162$	−114.904			−0.709286
$163$			88.1904i			0.541046i	0.962714	+	0.270523i	$0.0871966\pi$
$163$			88.1904i			0.541046i	−0.962714	+	0.270523i	$0.912803\pi$
$164$			30.0524i			0.183246i
$165$		0			0
$166$	−13.7994			−0.0831287
$167$	−155.562			−0.931508			−0.465754	−	0.884914i	$-0.654217\pi$
$167$	−155.562			−0.931508			−0.465754	+	0.884914i	$0.654217\pi$
$168$		−	163.538i		−	0.973439i
$169$	−160.515			−0.949793
$170$		0			0
$171$		−	5.34448i		−	0.0312543i
$172$	−2.78729			−0.0162052
$173$	−214.864			−1.24199			−0.620995	−	0.783815i	$-0.713271\pi$
$173$	−214.864			−1.24199			−0.620995	+	0.783815i	$0.713271\pi$
$174$	208.993			1.20111
$175$		0			0
$176$	63.8239	+	84.6719i	0.362636	+	0.481090i
$177$		−	303.587i		−	1.71518i
$178$	−141.569			−0.795331
$179$	155.650			0.869555			0.434778	−	0.900538i	$-0.356827\pi$
$179$	155.650			0.869555			0.434778	+	0.900538i	$0.356827\pi$
$180$		0			0
$181$	189.154			1.04505			0.522525	−	0.852624i	$-0.324990\pi$
$181$	189.154			1.04505			0.522525	+	0.852624i	$0.324990\pi$
$182$	−32.6575			−0.179437
$183$	−153.157			−0.836924
$184$			113.501i			0.616852i
$185$		0			0
$186$		−	122.000i		−	0.655913i
$187$	205.003	+	271.967i	1.09627	+	1.45437i
$188$			2.84311i			0.0151229i
$189$			191.429i			1.01285i
$190$		0			0
$191$	−123.993			−0.649180			−0.324590	−	0.945855i	$-0.605226\pi$
$191$	−123.993			−0.649180			−0.324590	+	0.945855i	$0.605226\pi$
$192$		−	195.113i		−	1.01621i
$193$	234.124			1.21308			0.606538	−	0.795054i	$-0.292558\pi$
$193$	234.124			1.21308			0.606538	+	0.795054i	$0.292558\pi$
$194$			267.582i			1.37929i
$195$		0			0
$196$	4.63853			0.0236660
$197$	−218.949			−1.11142			−0.555709	−	0.831377i	$-0.687553\pi$
$197$	−218.949			−1.11142			−0.555709	+	0.831377i	$0.687553\pi$
$198$	−13.1146	−	17.3985i	−0.0662354	−	0.0878712i
$199$	−127.963			−0.643028			−0.321514	−	0.946905i	$-0.604192\pi$
$199$	−127.963			−0.643028			−0.321514	+	0.946905i	$0.604192\pi$
$200$		0			0
$201$	25.2056			0.125401
$202$			63.6537i			0.315117i
$203$		−	301.417i		−	1.48481i
$204$		−	105.474i		−	0.517031i
$205$		0			0
$206$		−	57.4998i		−	0.279125i
$207$		−	15.4887i		−	0.0748244i
$208$	−28.0783			−0.134992
$209$	−39.5274	+	29.7949i	−0.189126	+	0.142559i
$210$		0			0
$211$		−	224.173i		−	1.06243i	−0.847237	−	0.531215i	$-0.821736\pi$
$211$		−	224.173i		−	1.06243i	0.847237	−	0.531215i	$-0.178264\pi$
$212$			113.478i			0.535272i
$213$			3.49203i			0.0163945i
$214$	−220.632			−1.03099
$215$		0			0
$216$			247.829i			1.14736i
$217$	−175.952			−0.810840
$218$			290.575i			1.33291i
$219$			67.3776i			0.307660i
$220$		0			0
$221$	−90.1880			−0.408090
$222$	−134.314			−0.605020
$223$			267.394i			1.19908i	0.800346	+	0.599538i	$0.204649\pi$
$223$			267.394i			1.19908i	−0.800346	+	0.599538i	$0.795351\pi$
$224$	−125.970			−0.562365
$225$		0			0
$226$			173.581i			0.768059i
$227$	157.636			0.694431			0.347216	−	0.937785i	$-0.387127\pi$
$227$	157.636			0.694431			0.347216	+	0.937785i	$0.387127\pi$
$228$	15.3295			0.0672347
$229$	−43.2374			−0.188810			−0.0944049	−	0.995534i	$-0.530095\pi$
$229$	−43.2374			−0.188810			−0.0944049	+	0.995534i	$0.530095\pi$
$230$		0			0
$231$	165.054	−	124.414i	0.714519	−	0.538589i
$232$		−	390.223i		−	1.68199i
$233$	213.611			0.916784			0.458392	−	0.888750i	$-0.348426\pi$
$233$	213.611			0.916784			0.458392	+	0.888750i	$0.348426\pi$
$234$	5.76958			0.0246563
$235$		0			0
$236$	−132.382			−0.560939
$237$	−303.204			−1.27934
$238$	347.120			1.45849
$239$		−	277.630i		−	1.16163i	−0.814035	−	0.580816i	$-0.802733\pi$
$239$		−	277.630i		−	1.16163i	0.814035	−	0.580816i	$-0.197267\pi$
$240$		0			0
$241$		−	39.3269i		−	0.163182i	−0.996666	−	0.0815910i	$-0.974000\pi$
$241$		−	39.3269i		−	0.163182i	0.996666	−	0.0815910i	$-0.0260001\pi$
$242$	−55.5655	+	193.990i	−0.229609	+	0.801610i
$243$		−	63.6963i		−	0.262125i
$244$			66.7855i			0.273711i
$245$		0			0
$246$	−114.934			−0.467213
$247$		−	13.1078i		−	0.0530681i
$248$	−227.793			−0.918520
$249$			23.1277i			0.0928825i
$250$		0			0
$251$	−348.287			−1.38760			−0.693800	−	0.720168i	$-0.744065\pi$
$251$	−348.287			−1.38760			−0.693800	+	0.720168i	$0.744065\pi$
$252$	9.73145			0.0386169
$253$	−114.553	+	86.3476i	−0.452779	+	0.341295i
$254$	53.7739			0.211708
$255$		0			0
$256$	−210.078			−0.820616
$257$		−	213.878i		−	0.832211i	−0.909316	−	0.416105i	$-0.863395\pi$
$257$		−	213.878i		−	0.832211i	0.909316	−	0.416105i	$-0.136605\pi$
$258$		−	10.6599i		−	0.0413174i
$259$			193.713i			0.747926i
$260$		0			0
$261$			53.2510i			0.204027i
$262$			422.015i			1.61074i
$263$	164.115			0.624012			0.312006	−	0.950080i	$-0.398999\pi$
$263$	164.115			0.624012			0.312006	+	0.950080i	$0.398999\pi$
$264$	213.684	−	161.070i	0.809407	−	0.610114i
$265$		0			0
$266$			50.4500i			0.189662i
$267$			237.270i			0.888651i
$268$		−	10.9911i		−	0.0410116i
$269$	−375.819			−1.39710			−0.698549	−	0.715562i	$-0.746171\pi$
$269$	−375.819			−1.39710			−0.698549	+	0.715562i	$0.746171\pi$
$270$		0			0
$271$		−	163.935i		−	0.604928i	−0.953161	−	0.302464i	$-0.902191\pi$
$271$		−	163.935i		−	0.604928i	0.953161	−	0.302464i	$-0.0978092\pi$
$272$	298.447			1.09723
$273$			54.7341i			0.200491i
$274$		−	333.942i		−	1.21877i
$275$		0			0
$276$	44.4259			0.160963
$277$	336.063			1.21323			0.606613	−	0.794998i	$-0.292528\pi$
$277$	336.063			1.21323			0.606613	+	0.794998i	$0.292528\pi$
$278$		−	332.077i		−	1.19452i
$279$	31.0853			0.111417
$280$		0			0
$281$		−	383.397i		−	1.36440i	−0.731164	−	0.682202i	$-0.761023\pi$
$281$		−	383.397i		−	1.36440i	0.731164	−	0.682202i	$-0.238977\pi$
$282$	−10.8734			−0.0385580
$283$	31.1879			0.110204			0.0551022	−	0.998481i	$-0.482452\pi$
$283$	31.1879			0.110204			0.0551022	+	0.998481i	$0.482452\pi$
$284$	1.52273			0.00536172
$285$		0			0
$286$	−32.1648	−	42.6714i	−0.112464	−	0.149201i
$287$			165.762i			0.577570i
$288$	22.2549			0.0772741
$289$	669.615			2.31701
$290$		0			0
$291$	448.467			1.54112
$292$	29.3806			0.100618
$293$	−175.574			−0.599229			−0.299614	−	0.954060i	$-0.596858\pi$
$293$	−175.574			−0.599229			−0.299614	+	0.954060i	$0.596858\pi$
$294$			17.7399i			0.0603399i
$295$		0			0
$296$			250.786i			0.847251i
$297$	−250.127	+	188.540i	−0.842177	+	0.634815i
$298$		−	70.9156i		−	0.237972i
$299$		−	37.9873i		−	0.127048i
$300$		0			0
$301$	−15.3741			−0.0510766
$302$		−	376.659i		−	1.24722i
$303$	106.684			0.352091
$304$			43.3759i			0.142684i
$305$		0			0
$306$	−61.3253			−0.200409
$307$	515.038			1.67765			0.838825	−	0.544402i	$-0.183243\pi$
$307$	515.038			1.67765			0.838825	+	0.544402i	$0.183243\pi$
$308$	−54.2518	−	71.9731i	−0.176142	−	0.233679i
$309$	−96.3697			−0.311876
$310$		0			0
$311$	419.087			1.34755			0.673774	−	0.738937i	$-0.264672\pi$
$311$	419.087			1.34755			0.673774	+	0.738937i	$0.264672\pi$
$312$			70.8603i			0.227116i
$313$			82.3366i			0.263056i	0.991312	+	0.131528i	$0.0419884\pi$
$313$			82.3366i			0.263056i	−0.991312	+	0.131528i	$0.958012\pi$
$314$		−	203.383i		−	0.647716i
$315$		0			0
$316$			132.215i			0.418400i
$317$			373.069i			1.17687i	0.808543	+	0.588437i	$0.200257\pi$
$317$			373.069i			1.17687i	−0.808543	+	0.588437i	$0.799743\pi$
$318$	−433.992			−1.36475
$319$	393.840	−	296.868i	1.23461	−	0.930622i
$320$		0			0
$321$			369.779i			1.15196i
$322$			146.207i			0.454060i
$323$			139.324i			0.431344i
$324$	83.9760			0.259185
$325$		0			0
$326$			147.074i			0.451149i
$327$	487.003			1.48931
$328$			214.601i			0.654271i
$329$			15.6819i			0.0476655i
$330$		0			0
$331$	179.066			0.540986			0.270493	−	0.962722i	$-0.412813\pi$
$331$	179.066			0.540986			0.270493	+	0.962722i	$0.412813\pi$
$332$	10.0850			0.0303766
$333$		−	34.2230i		−	0.102772i
$334$	−259.429			−0.776734
$335$		0			0
$336$		−	181.124i		−	0.539060i
$337$	−187.268			−0.555693			−0.277846	−	0.960626i	$-0.589621\pi$
$337$	−187.268			−0.555693			−0.277846	+	0.960626i	$0.589621\pi$
$338$	−267.689			−0.791981
$339$	290.922			0.858178
$340$		0			0
$341$	−173.297	−	229.905i	−0.508203	−	0.674207i
$342$		−	8.91295i		−	0.0260613i
$343$	354.996			1.03497
$344$	−19.9037			−0.0578596
$345$		0			0
$346$	−358.327			−1.03563
$347$	388.617			1.11993			0.559967	−	0.828515i	$-0.310814\pi$
$347$	388.617			1.11993			0.559967	+	0.828515i	$0.310814\pi$
$348$	−152.739			−0.438905
$349$			73.9677i			0.211942i	0.994369	+	0.105971i	$0.0337950\pi$
$349$			73.9677i			0.211942i	−0.994369	+	0.105971i	$0.966205\pi$
$350$		0			0
$351$		−	82.9453i		−	0.236311i
$352$	−124.069	−	164.596i	−0.352469	−	0.467602i
$353$		−	208.797i		−	0.591492i	−0.955267	−	0.295746i	$-0.904432\pi$
$353$		−	208.797i		−	0.591492i	0.955267	−	0.295746i	$-0.0955681\pi$
$354$		−	506.289i		−	1.43020i
$355$		0			0
$356$	103.463			0.290628
$357$		−	581.773i		−	1.62962i
$358$	259.577			0.725075
$359$		−	32.9550i		−	0.0917967i	−0.998946	−	0.0458984i	$-0.985385\pi$
$359$		−	32.9550i		−	0.0917967i	0.998946	−	0.0458984i	$-0.0146150\pi$
$360$		0			0
$361$	340.751			0.943908
$362$	315.450			0.871410
$363$	325.127	+	93.1278i	0.895666	+	0.256550i
$364$	23.8672			0.0655694
$365$		0			0
$366$	−255.419			−0.697866
$367$		−	29.7192i		−	0.0809788i	−0.999180	−	0.0404894i	$-0.987108\pi$
$367$		−	29.7192i		−	0.0809788i	0.999180	−	0.0404894i	$-0.0128917\pi$
$368$			125.706i			0.341593i
$369$		−	29.2851i		−	0.0793634i
$370$		0			0
$371$			625.918i			1.68711i
$372$			89.1616i			0.239682i
$373$	436.560			1.17040			0.585201	−	0.810889i	$-0.301016\pi$
$373$	436.560			1.17040			0.585201	+	0.810889i	$0.301016\pi$
$374$	341.882	+	453.557i	0.914123	+	1.21272i
$375$		0			0
$376$			20.3023i			0.0539955i
$377$			130.603i			0.346426i
$378$			319.244i			0.844560i
$379$	−74.5391			−0.196673			−0.0983366	−	0.995153i	$-0.531352\pi$
$379$	−74.5391			−0.196673			−0.0983366	+	0.995153i	$0.531352\pi$
$380$		0			0
$381$		−	90.1251i		−	0.236549i
$382$	−206.783			−0.541316
$383$			496.956i			1.29754i	0.760986	+	0.648768i	$0.224715\pi$
$383$			496.956i			1.29754i	−0.760986	+	0.648768i	$0.775285\pi$
$384$		−	115.892i		−	0.301803i
$385$		0			0
$386$	390.446			1.01152
$387$	2.71612			0.00701840
$388$		−	195.558i		−	0.504015i
$389$	−6.51617			−0.0167511			−0.00837554	−	0.999965i	$-0.502666\pi$
$389$	−6.51617			−0.0167511			−0.00837554	+	0.999965i	$0.502666\pi$
$390$		0			0
$391$			403.770i			1.03266i
$392$	33.1233			0.0844981
$393$	707.297			1.79974
$394$	−365.140			−0.926751
$395$		0			0
$396$	9.58461	+	12.7154i	0.0242036	+	0.0321096i
$397$		−	59.6577i		−	0.150271i	−0.997173	−	0.0751357i	$-0.976061\pi$
$397$		−	59.6577i		−	0.150271i	0.997173	−	0.0751357i	$-0.0239390\pi$
$398$	−213.402			−0.536186
$399$	84.5542			0.211915
$400$		0			0
$401$	−298.153			−0.743524			−0.371762	−	0.928328i	$-0.621246\pi$
$401$	−298.153			−0.743524			−0.371762	+	0.928328i	$0.621246\pi$
$402$	42.0351			0.104565
$403$	76.2395			0.189180
$404$		−	46.5203i		−	0.115149i
$405$		0			0
$406$		−	502.670i		−	1.23810i
$407$	−253.111	+	190.790i	−0.621895	+	0.468771i
$408$		−	753.180i		−	1.84603i
$409$			170.539i			0.416967i	0.978026	+	0.208483i	$0.0668528\pi$
$409$			170.539i			0.416967i	−0.978026	+	0.208483i	$0.933147\pi$
$410$		0			0
$411$	−559.687			−1.36177
$412$			42.0228i			0.101997i
$413$	−730.188			−1.76801
$414$		−	25.8303i		−	0.0623920i
$415$		0			0
$416$	54.5822			0.131207
$417$	−556.561			−1.33468
$418$	−65.9195	+	49.6887i	−0.157702	+	0.118873i
$419$	−547.949			−1.30775			−0.653877	−	0.756601i	$-0.726859\pi$
$419$	−547.949			−1.30775			−0.653877	+	0.756601i	$0.726859\pi$
$420$		0			0
$421$	375.189			0.891185			0.445593	−	0.895236i	$-0.352993\pi$
$421$	375.189			0.891185			0.445593	+	0.895236i	$0.352993\pi$
$422$		−	373.851i		−	0.885902i
$423$		−	2.77051i		−	0.00654968i
$424$			810.332i			1.91116i
$425$		0			0
$426$			5.82363i			0.0136705i
$427$			368.374i			0.862702i
$428$	161.245			0.376742
$429$	−71.5172	+	53.9082i	−0.166707	+	0.125660i
$430$		0			0
$431$		−	405.352i		−	0.940493i	−0.882535	−	0.470246i	$-0.844165\pi$
$431$		−	405.352i		−	0.940493i	0.882535	−	0.470246i	$-0.155835\pi$
$432$			274.480i			0.635370i
$433$			122.182i			0.282175i	0.989997	+	0.141088i	$0.0450599\pi$
$433$			122.182i			0.282175i	−0.989997	+	0.141088i	$0.954940\pi$
$434$	−293.434			−0.676115
$435$		0			0
$436$		−	212.362i		−	0.487068i
$437$	−58.6835			−0.134287
$438$			112.365i			0.256541i
$439$			125.331i			0.285492i	0.989759	+	0.142746i	$0.0455931\pi$
$439$			125.331i			0.285492i	−0.989759	+	0.142746i	$0.954407\pi$
$440$		0			0
$441$	−4.52010			−0.0102497
$442$	−150.406			−0.340284
$443$			66.9517i			0.151133i	0.997141	+	0.0755663i	$0.0240765\pi$
$443$			66.9517i			0.151133i	−0.997141	+	0.0755663i	$0.975924\pi$
$444$	98.1615			0.221084
$445$		0			0
$446$			445.931i			0.999845i
$447$	−118.855			−0.265894
$448$	−469.285			−1.04751
$449$	−227.828			−0.507413			−0.253706	−	0.967281i	$-0.581650\pi$
$449$	−227.828			−0.507413			−0.253706	+	0.967281i	$0.581650\pi$
$450$		0			0
$451$	−216.590	+	163.261i	−0.480245	+	0.361998i
$452$		−	126.859i		−	0.280662i
$453$	−631.281			−1.39356
$454$	262.888			0.579049
$455$		0			0
$456$	109.466			0.240058
$457$	328.089			0.717919			0.358959	−	0.933353i	$-0.383132\pi$
$457$	328.089			0.717919			0.358959	+	0.933353i	$0.383132\pi$
$458$	−72.1067			−0.157438
$459$			881.632i			1.92077i
$460$		0			0
$461$		−	634.564i		−	1.37649i	−0.725476	−	0.688247i	$-0.758381\pi$
$461$		−	634.564i		−	1.37649i	0.725476	−	0.688247i	$-0.241619\pi$
$462$	275.259	−	207.484i	0.595798	−	0.449100i
$463$			39.8190i			0.0860022i	0.999075	+	0.0430011i	$0.0136919\pi$
$463$			39.8190i			0.0860022i	−0.999075	+	0.0430011i	$0.986308\pi$
$464$		−	432.186i		−	0.931436i
$465$		0			0
$466$	356.237			0.764456
$467$		−	120.629i		−	0.258307i	−0.991625	−	0.129153i	$-0.958774\pi$
$467$		−	120.629i		−	0.258307i	0.991625	−	0.129153i	$-0.0412259\pi$
$468$	−4.21660			−0.00900984
$469$		−	60.6245i		−	0.129263i
$470$		0			0
$471$	−340.870			−0.723715
$472$	−945.323			−2.00280
$473$	−15.1421	−	20.0882i	−0.0320129	−	0.0424698i
$474$	−505.650			−1.06677
$475$		0			0
$476$	−253.687			−0.532956
$477$		−	110.580i		−	0.231825i
$478$		−	463.002i		−	0.968623i
$479$		−	611.310i		−	1.27622i	−0.769945	−	0.638110i	$-0.779716\pi$
$479$		−	611.310i		−	1.27622i	0.769945	−	0.638110i	$-0.220284\pi$
$480$		0			0
$481$		−	83.9351i		−	0.174501i
$482$		−	65.5851i		−	0.136069i
$483$	245.044			0.507337
$484$	40.6092	−	141.774i	0.0839032	−	0.292922i
$485$		0			0
$486$		−	106.226i		−	0.218572i
$487$		−	386.421i		−	0.793472i	−0.917933	−	0.396736i	$-0.870143\pi$
$487$		−	386.421i		−	0.793472i	0.917933	−	0.396736i	$-0.129857\pi$
$488$			476.908i			0.977270i
$489$	246.497			0.504083
$490$		0			0
$491$		−	699.750i		−	1.42515i	−0.701594	−	0.712577i	$-0.747528\pi$
$491$		−	699.750i		−	1.42515i	0.701594	−	0.712577i	$-0.252472\pi$
$492$	83.9981			0.170728
$493$		−	1388.19i		−	2.81580i
$494$		−	21.8598i		−	0.0442506i
$495$		0			0
$496$	−252.289			−0.508647
$497$	8.39903			0.0168995
$498$			38.5699i			0.0774496i
$499$	243.340			0.487654			0.243827	−	0.969819i	$-0.421597\pi$
$499$	243.340			0.487654			0.243827	+	0.969819i	$0.421597\pi$
$500$		0			0
$501$			434.803i			0.867871i
$502$	−580.836			−1.15704
$503$	90.1999			0.179324			0.0896620	−	0.995972i	$-0.471421\pi$
$503$	90.1999			0.179324			0.0896620	+	0.995972i	$0.471421\pi$
$504$	69.4912			0.137879
$505$		0			0
$506$	−191.039	+	144.001i	−0.377548	+	0.284587i
$507$			448.648i			0.884907i
$508$	−39.2998			−0.0773619
$509$	−629.870			−1.23746			−0.618732	−	0.785602i	$-0.712353\pi$
$509$	−629.870			−1.23746			−0.618732	+	0.785602i	$0.712353\pi$
$510$		0			0
$511$	162.057			0.317137
$512$	−516.198			−1.00820
$513$	−128.135			−0.249777
$514$		−	356.683i		−	0.693935i
$515$		0			0
$516$			7.79061i			0.0150981i
$517$	−20.4905	+	15.4453i	−0.0396335	+	0.0298749i
$518$			323.053i			0.623655i
$519$			600.556i			1.15714i
$520$		0			0
$521$	−355.136			−0.681643			−0.340822	−	0.940128i	$-0.610705\pi$
$521$	−355.136			−0.681643			−0.340822	+	0.940128i	$0.610705\pi$
$522$			88.8062i			0.170127i
$523$	107.213			0.204996			0.102498	−	0.994733i	$-0.467317\pi$
$523$	107.213			0.204996			0.102498	+	0.994733i	$0.467317\pi$
$524$		−	308.423i		−	0.588593i
$525$		0			0
$526$	273.693			0.520330
$527$	−810.355			−1.53768
$528$	236.662	−	178.391i	0.448224	−	0.337862i
$529$	358.931			0.678509
$530$		0			0
$531$	129.002			0.242941
$532$		−	36.8706i		−	0.0693056i
$533$		−	71.8243i		−	0.134755i
$534$			395.693i			0.740998i
$535$		0			0
$536$		−	78.4862i		−	0.146430i
$537$		−	435.051i		−	0.810151i
$538$	−626.750			−1.16496
$539$	25.1991	+	33.4303i	0.0467515	+	0.0620229i
$540$		0			0
$541$			365.120i			0.674899i	0.941344	+	0.337449i	$0.109564\pi$
$541$			365.120i			0.674899i	−0.941344	+	0.337449i	$0.890436\pi$
$542$		−	273.394i		−	0.504417i
$543$		−	528.695i		−	0.973656i
$544$	−580.159			−1.06647
$545$		0			0
$546$			91.2795i			0.167179i
$547$	384.034			0.702074			0.351037	−	0.936362i	$-0.385829\pi$
$547$	384.034			0.702074			0.351037	+	0.936362i	$0.385829\pi$
$548$			244.056i			0.445358i
$549$		−	65.0802i		−	0.118543i
$550$		0			0
$551$	201.758			0.366166
$552$	317.241			0.574711
$553$			729.266i			1.31874i
$554$	560.450			1.01164
$555$		0			0
$556$			242.693i			0.436499i
$557$	−93.3430			−0.167582			−0.0837908	−	0.996483i	$-0.526703\pi$
$557$	−93.3430			−0.167582			−0.0837908	+	0.996483i	$0.526703\pi$
$558$	51.8407			0.0929045
$559$	6.66153			0.0119169
$560$		0			0
$561$	760.163	−	572.994i	1.35501	−	1.02138i
$562$		−	639.388i		−	1.13770i
$563$	325.624			0.578373			0.289187	−	0.957273i	$-0.406615\pi$
$563$	325.624			0.578373			0.289187	+	0.957273i	$0.406615\pi$
$564$	7.94663			0.0140898
$565$		0			0
$566$	52.0117			0.0918935
$567$	463.193			0.816919
$568$	10.8736			0.0191437
$569$			409.067i			0.718923i	0.933160	+	0.359461i	$0.117040\pi$
$569$			409.067i			0.718923i	−0.933160	+	0.359461i	$0.882960\pi$
$570$		0			0
$571$			395.169i			0.692065i	0.938223	+	0.346032i	$0.112471\pi$
$571$			395.169i			0.692065i	−0.938223	+	0.346032i	$0.887529\pi$
$572$	23.5071	+	31.1857i	0.0410963	+	0.0545205i
$573$			346.568i			0.604830i
$574$			276.441i			0.481604i
$575$		0			0
$576$	82.9082			0.143938
$577$		−	432.156i		−	0.748971i	−0.927233	−	0.374485i	$-0.877819\pi$
$577$		−	432.156i		−	0.748971i	0.927233	−	0.374485i	$-0.122181\pi$
$578$	1116.71			1.93203
$579$		−	654.388i		−	1.13020i
$580$		0			0
$581$	55.6269			0.0957433
$582$	747.904			1.28506
$583$	−817.844	+	616.473i	−1.40282	+	1.05742i
$584$	209.804			0.359253
$585$		0			0
$586$	−292.803			−0.499664
$587$		−	1.36709i		−	0.00232895i	−0.999999	−	0.00116447i	$-0.999629\pi$
$587$		−	1.36709i		−	0.00232895i	0.999999	−	0.00116447i	$-0.000370664\pi$
$588$		−	12.9649i		−	0.0220492i
$589$		−	117.776i		−	0.199960i
$590$		0			0
$591$			611.974i			1.03549i
$592$			277.755i			0.469181i
$593$	−232.591			−0.392228			−0.196114	−	0.980581i	$-0.562832\pi$
$593$	−232.591			−0.392228			−0.196114	+	0.980581i	$0.562832\pi$
$594$	−417.134	+	314.427i	−0.702246	+	0.529338i
$595$		0			0
$596$			51.8275i			0.0869590i
$597$			357.662i			0.599099i
$598$		−	63.3511i		−	0.105938i
$599$	291.349			0.486392			0.243196	−	0.969977i	$-0.421804\pi$
$599$	291.349			0.486392			0.243196	+	0.969977i	$0.421804\pi$
$600$		0			0
$601$		−	160.437i		−	0.266951i	−0.991052	−	0.133475i	$-0.957386\pi$
$601$		−	160.437i		−	0.266951i	0.991052	−	0.133475i	$-0.0426137\pi$
$602$	−25.6392			−0.0425900
$603$			10.7105i			0.0177620i
$604$			275.275i			0.455754i
$605$		0			0
$606$	177.915			0.293590
$607$	−107.785			−0.177571			−0.0887854	−	0.996051i	$-0.528299\pi$
$607$	−107.785			−0.177571			−0.0887854	+	0.996051i	$0.528299\pi$
$608$		−	84.3197i		−	0.138684i
$609$	−842.475			−1.38337
$610$		0			0
$611$		−	6.79493i		−	0.0111210i
$612$	44.8186			0.0732330
$613$	−552.780			−0.901761			−0.450881	−	0.892584i	$-0.648890\pi$
$613$	−552.780			−0.901761			−0.450881	+	0.892584i	$0.648890\pi$
$614$	858.925			1.39890
$615$		0			0
$616$	−387.406	−	513.952i	−0.628906	−	0.834338i
$617$			21.9153i			0.0355192i	0.999842	+	0.0177596i	$0.00565335\pi$
$617$			21.9153i			0.0355192i	−0.999842	+	0.0177596i	$0.994347\pi$
$618$	−160.715			−0.260056
$619$	−205.700			−0.332310			−0.166155	−	0.986100i	$-0.553135\pi$
$619$	−205.700			−0.332310			−0.166155	+	0.986100i	$0.553135\pi$
$620$		0			0
$621$	−371.345			−0.597979
$622$	698.909			1.12365
$623$	570.682			0.916022
$624$			78.4804i			0.125770i
$625$		0			0
$626$			137.312i			0.219348i
$627$	83.2783	+	110.481i	0.132820	+	0.176206i
$628$			148.639i			0.236687i
$629$			892.152i			1.41837i
$630$		0			0
$631$	859.961			1.36285			0.681427	−	0.731886i	$-0.261360\pi$
$631$	859.961			1.36285			0.681427	+	0.731886i	$0.261360\pi$
$632$			944.129i			1.49388i
$633$	−626.574			−0.989848
$634$			622.164i			0.981331i
$635$		0			0
$636$	317.176			0.498705
$637$	−11.0859			−0.0174034
$638$	656.804	−	495.085i	1.02947	−	0.775995i
$639$	−1.48385			−0.00232214
$640$		0			0
$641$	794.780			1.23991			0.619953	−	0.784639i	$-0.287152\pi$
$641$	794.780			1.23991			0.619953	+	0.784639i	$0.287152\pi$
$642$			616.678i			0.960558i
$643$			25.5239i			0.0396951i	0.999803	+	0.0198475i	$0.00631808\pi$
$643$			25.5239i			0.0396951i	−0.999803	+	0.0198475i	$0.993682\pi$
$644$		−	106.853i		−	0.165921i
$645$		0			0
$646$			232.350i			0.359674i
$647$		−	681.121i		−	1.05274i	−0.850257	−	0.526368i	$-0.823553\pi$
$647$		−	681.121i		−	1.05274i	0.850257	−	0.526368i	$-0.176447\pi$
$648$	599.663			0.925406
$649$	−719.170	−	954.086i	−1.10812	−	1.47009i
$650$		0			0
$651$			491.796i			0.755446i
$652$		−	107.487i		−	0.164857i
$653$		−	913.057i		−	1.39825i	−0.715000	−	0.699124i	$-0.753573\pi$
$653$		−	913.057i		−	1.39825i	0.715000	−	0.699124i	$-0.246427\pi$
$654$	812.171			1.24185
$655$		0			0
$656$			237.678i			0.362315i
$657$	−28.6304			−0.0435775
$658$			26.1526i			0.0397457i
$659$		−	126.800i		−	0.192413i	−0.995361	−	0.0962065i	$-0.969329\pi$
$659$		−	126.800i		−	0.192413i	0.995361	−	0.0962065i	$-0.0306709\pi$
$660$		0			0
$661$	−736.664			−1.11447			−0.557235	−	0.830355i	$-0.688138\pi$
$661$	−736.664			−1.11447			−0.557235	+	0.830355i	$0.688138\pi$
$662$	298.627			0.451099
$663$			252.080i			0.380211i
$664$	72.0162			0.108458
$665$		0			0
$666$		−	57.0735i		−	0.0856959i
$667$	584.706			0.876621
$668$	189.600			0.283832
$669$	747.380			1.11716
$670$		0			0
$671$	−481.329	+	362.815i	−0.717331	+	0.540708i
$672$			352.092i			0.523946i
$673$	225.017			0.334349			0.167174	−	0.985927i	$-0.446536\pi$
$673$	225.017			0.334349			0.167174	+	0.985927i	$0.446536\pi$
$674$	−312.306			−0.463362
$675$		0			0
$676$	195.637			0.289403
$677$	−109.258			−0.161386			−0.0806931	−	0.996739i	$-0.525713\pi$
$677$	−109.258			−0.161386			−0.0806931	+	0.996739i	$0.525713\pi$
$678$	485.169			0.715588
$679$		−	1078.65i		−	1.58859i
$680$		0			0
$681$		−	440.601i		−	0.646991i
$682$	−289.006	−	383.410i	−0.423763	−	0.562185i
$683$			1080.61i			1.58215i	0.611719	+	0.791075i	$0.290478\pi$
$683$			1080.61i			1.58215i	−0.611719	+	0.791075i	$0.709522\pi$
$684$			6.51389i			0.00952323i
$685$		0			0
$686$	592.023			0.863007
$687$			120.851i			0.175911i
$688$	−22.0441			−0.0320408
$689$		−	271.208i		−	0.393626i
$690$		0			0
$691$	−1170.13			−1.69339			−0.846695	−	0.532078i	$-0.821411\pi$
$691$	−1170.13			−1.69339			−0.846695	+	0.532078i	$0.821411\pi$
$692$	261.878			0.378436
$693$	52.8666	+	70.1354i	0.0762866	+	0.101206i
$694$	648.093			0.933852
$695$		0			0
$696$	−1090.69			−1.56709
$697$			763.426i			1.09530i
$698$			123.355i			0.176727i
$699$		−	597.053i		−	0.854153i
$700$		0			0
$701$		−	328.408i		−	0.468485i	−0.972178	−	0.234242i	$-0.924739\pi$
$701$		−	328.408i		−	0.468485i	0.972178	−	0.234242i	$-0.0752609\pi$
$702$		−	138.327i		−	0.197047i
$703$	−129.664			−0.184444
$704$	−462.204	−	613.183i	−0.656540	−	0.870999i
$705$		0			0
$706$		−	348.208i		−	0.493213i
$707$		−	256.596i		−	0.362936i
$708$			370.014i			0.522618i
$709$	705.817			0.995511			0.497756	−	0.867317i	$-0.334158\pi$
$709$	705.817			0.995511			0.497756	+	0.867317i	$0.334158\pi$
$710$		0			0
$711$		−	128.839i		−	0.181208i
$712$	738.821			1.03767
$713$		−	341.323i		−	0.478714i
$714$		−	970.217i		−	1.35885i
$715$		0			0
$716$	−189.708			−0.264955
$717$	−775.991			−1.08227
$718$		−	54.9588i		−	0.0765443i
$719$	584.645			0.813137			0.406568	−	0.913620i	$-0.366725\pi$
$719$	584.645			0.813137			0.406568	+	0.913620i	$0.366725\pi$
$720$		0			0
$721$			231.789i			0.321482i
$722$	568.267			0.787074
$723$	−109.921			−0.152034
$724$	−230.542			−0.318428
$725$		0			0
$726$	542.211	+	155.308i	0.746847	+	0.213923i
$727$			370.464i			0.509579i	0.966997	+	0.254790i	$0.0820062\pi$
$727$			370.464i			0.509579i	−0.966997	+	0.254790i	$0.917994\pi$
$728$	170.433			0.234112
$729$	−798.136			−1.09484
$730$		0			0
$731$	−70.8059			−0.0968617
$732$	186.669			0.255012
$733$	−407.221			−0.555554			−0.277777	−	0.960646i	$-0.589598\pi$
$733$	−407.221			−0.555554			−0.277777	+	0.960646i	$0.589598\pi$
$734$		−	49.5625i		−	0.0675238i
$735$		0			0
$736$		−	244.364i		−	0.332016i
$737$	79.2138	−	59.7097i	0.107481	−	0.0810172i
$738$		−	48.8385i		−	0.0661768i
$739$		−	1382.44i		−	1.87069i	−0.353731	−	0.935347i	$-0.615087\pi$
$739$		−	1382.44i		−	1.87069i	0.353731	−	0.935347i	$-0.384913\pi$
$740$		0			0
$741$	−36.6370			−0.0494427
$742$			1043.84i			1.40679i
$743$	−748.989			−1.00806			−0.504030	−	0.863686i	$-0.668150\pi$
$743$	−748.989			−1.00806			−0.504030	+	0.863686i	$0.668150\pi$
$744$			636.693i			0.855770i
$745$		0			0
$746$	728.047			0.975934
$747$	−9.82754			−0.0131560
$748$	−249.859	−	331.475i	−0.334036	−	0.443149i
$749$	889.394			1.18744
$750$		0			0
$751$	−532.843			−0.709512			−0.354756	−	0.934959i	$-0.615436\pi$
$751$	−532.843			−0.709512			−0.354756	+	0.934959i	$0.615436\pi$
$752$			22.4856i			0.0299010i
$753$			973.481i			1.29280i
$754$			217.805i			0.288866i
$755$		0			0
$756$		−	233.314i		−	0.308617i
$757$		−	610.182i		−	0.806052i	−0.915188	−	0.403026i	$-0.867958\pi$
$757$		−	610.182i		−	0.806052i	0.915188	−	0.403026i	$-0.132042\pi$
$758$	−124.308			−0.163995
$759$	241.346	+	320.182i	0.317979	+	0.421847i
$760$		0			0
$761$			180.435i			0.237102i	0.992948	+	0.118551i	$0.0378249\pi$
$761$			180.435i			0.237102i	−0.992948	+	0.118551i	$0.962175\pi$
$762$		−	150.301i		−	0.197245i
$763$		−	1171.34i		−	1.53518i
$764$	151.124			0.197806
$765$		0			0
$766$			828.769i			1.08194i
$767$	316.388			0.412500
$768$			587.178i			0.764555i
$769$			559.139i			0.727099i	0.931575	+	0.363550i	$0.118435\pi$
$769$			559.139i			0.727099i	−0.931575	+	0.363550i	$0.881565\pi$
$770$		0			0
$771$	−597.800			−0.775357
$772$	−285.351			−0.369626
$773$		−	272.373i		−	0.352358i	−0.984358	−	0.176179i	$-0.943626\pi$
$773$		−	272.373i		−	0.352358i	0.984358	−	0.176179i	$-0.0563737\pi$
$774$	4.52965			0.00585226
$775$		0			0
$776$		−	1396.46i		−	1.79956i
$777$	541.437			0.696830
$778$	−10.8670			−0.0139678
$779$	−110.956			−0.142433
$780$		0			0
$781$	8.27230	+	10.9744i	0.0105919	+	0.0140518i
$782$			673.364i			0.861079i
$783$	1276.71			1.63053
$784$	36.6852			0.0467924
$785$		0			0
$786$	1179.55			1.50070
$787$	−1415.45			−1.79854			−0.899268	−	0.437398i	$-0.855900\pi$
$787$	−1415.45			−1.79854			−0.899268	+	0.437398i	$0.855900\pi$
$788$	266.857			0.338651
$789$		−	458.710i		−	0.581382i
$790$		0			0
$791$		−	699.727i		−	0.884610i
$792$	68.4426	+	90.7994i	0.0864175	+	0.114646i
$793$		−	159.615i		−	0.201280i
$794$		−	99.4906i		−	0.125303i
$795$		0			0
$796$	155.961			0.195932
$797$			960.746i			1.20545i	0.797948	+	0.602726i	$0.205919\pi$
$797$			960.746i			1.20545i	−0.797948	+	0.602726i	$0.794081\pi$
$798$	141.010			0.176705
$799$			72.2239i			0.0903928i
$800$		0			0
$801$	−100.822			−0.125870
$802$	−497.227			−0.619984
$803$	159.611	+	211.749i	0.198769	+	0.263697i
$804$	−30.7207			−0.0382098
$805$		0			0
$806$	127.144			0.157747
$807$			1050.43i			1.30165i
$808$		−	332.196i		−	0.411134i
$809$			850.203i			1.05093i	0.850815	+	0.525465i	$0.176109\pi$
$809$			850.203i			1.05093i	−0.850815	+	0.525465i	$0.823891\pi$
$810$		0			0
$811$			316.974i			0.390843i	0.980719	+	0.195422i	$0.0626075\pi$
$811$			316.974i			0.390843i	−0.980719	+	0.195422i	$0.937392\pi$
$812$			367.368i			0.452424i
$813$	−458.208			−0.563602
$814$	−422.111	+	318.178i	−0.518564	+	0.390883i
$815$		0			0
$816$		−	834.175i		−	1.02227i
$817$		−	10.2909i		−	0.0125959i
$818$			284.407i			0.347686i
$819$	−23.2578			−0.0283979
$820$		0			0
$821$			1214.62i			1.47944i	0.672915	+	0.739720i	$0.265042\pi$
$821$			1214.62i			1.47944i	−0.672915	+	0.739720i	$0.734958\pi$
$822$	−933.385			−1.13550
$823$		−	1210.57i		−	1.47093i	−0.677564	−	0.735464i	$-0.736964\pi$
$823$		−	1210.57i		−	1.47093i	0.677564	−	0.735464i	$-0.263036\pi$
$824$			300.080i			0.364175i
$825$		0			0
$826$	−1217.73			−1.47425
$827$	305.273			0.369133			0.184566	−	0.982820i	$-0.440912\pi$
$827$	305.273			0.369133			0.184566	+	0.982820i	$0.440912\pi$
$828$			18.8777i			0.0227991i
$829$	225.488			0.272000			0.136000	−	0.990709i	$-0.456575\pi$
$829$	225.488			0.272000			0.136000	+	0.990709i	$0.456575\pi$
$830$		0			0
$831$		−	939.315i		−	1.13034i
$832$	203.340			0.244399
$833$	117.833			0.141457
$834$	−928.172			−1.11292
$835$		0			0
$836$	48.1762	−	36.3142i	0.0576271	−	0.0434381i
$837$		−	745.279i		−	0.890417i
$838$	−913.810			−1.09047
$839$	−405.279			−0.483050			−0.241525	−	0.970395i	$-0.577648\pi$
$839$	−405.279			−0.483050			−0.241525	+	0.970395i	$0.577648\pi$
$840$		0			0
$841$	−1169.26			−1.39032
$842$	625.699			0.743111
$843$	−1071.62			−1.27119
$844$			273.223i			0.323724i
$845$		0			0
$846$		−	4.62036i		−	0.00546142i
$847$	223.991	−	781.995i	0.264452	−	0.923253i
$848$			897.472i			1.05834i
$849$		−	87.1717i		−	0.102676i
$850$		0			0
$851$	−375.776			−0.441570
$852$		−	4.25610i		−	0.00499543i
$853$	788.482			0.924364			0.462182	−	0.886785i	$-0.347067\pi$
$853$	788.482			0.924364			0.462182	+	0.886785i	$0.347067\pi$
$854$			614.334i			0.719360i
$855$		0			0
$856$	1151.44			1.34514
$857$	1365.13			1.59292			0.796460	−	0.604691i	$-0.206703\pi$
$857$	1365.13			1.59292			0.796460	+	0.604691i	$0.206703\pi$
$858$	−119.269	+	89.9022i	−0.139008	+	0.104781i
$859$	−519.889			−0.605226			−0.302613	−	0.953113i	$-0.597859\pi$
$859$	−519.889			−0.605226			−0.302613	+	0.953113i	$0.597859\pi$
$860$		0			0
$861$	463.315			0.538112
$862$		−	676.003i		−	0.784226i
$863$		−	1082.06i		−	1.25384i	−0.779085	−	0.626919i	$-0.784316\pi$
$863$		−	1082.06i		−	1.25384i	0.779085	−	0.626919i	$-0.215684\pi$
$864$		−	533.569i		−	0.617556i
$865$		0			0
$866$			203.762i			0.235291i
$867$		−	1871.61i		−	2.15872i
$868$	214.452			0.247064
$869$	−952.882	+	718.262i	−1.09653	+	0.826538i
$870$		0			0
$871$			26.2684i			0.0301589i
$872$		−	1516.45i		−	1.73905i
$873$			190.565i			0.218287i
$874$	−97.8660			−0.111975
$875$		0			0
$876$		−	82.1203i		−	0.0937446i
$877$	−819.535			−0.934475			−0.467238	−	0.884132i	$-0.654751\pi$
$877$	−819.535			−0.934475			−0.467238	+	0.884132i	$0.654751\pi$
$878$			209.013i			0.238056i
$879$			490.738i			0.558292i
$880$		0			0
$881$	1482.75			1.68304			0.841518	−	0.540230i	$-0.181663\pi$
$881$	1482.75			1.68304			0.841518	+	0.540230i	$0.181663\pi$
$882$	−7.53813			−0.00854663
$883$			503.758i			0.570508i	0.958452	+	0.285254i	$0.0920779\pi$
$883$			503.758i			0.570508i	−0.958452	+	0.285254i	$0.907922\pi$
$884$	109.922			0.124346
$885$		0			0
$886$			111.655i			0.126021i
$887$	−1653.39			−1.86402			−0.932011	−	0.362429i	$-0.881947\pi$
$887$	−1653.39			−1.86402			−0.932011	+	0.362429i	$0.881947\pi$
$888$	700.960			0.789370
$889$	−216.769			−0.243835
$890$		0			0
$891$	456.204	+	605.223i	0.512013	+	0.679262i
$892$		−	325.901i		−	0.365360i
$893$	−10.4969			−0.0117547
$894$	−198.213			−0.221714
$895$		0			0
$896$	−278.744			−0.311098
$897$	−106.176			−0.118368
$898$	−379.947			−0.423104
$899$			1173.49i			1.30533i
$900$		0			0
$901$			2882.69i			3.19944i
$902$	−361.206	+	272.269i	−0.400450	+	0.301851i
$903$			42.9713i			0.0475873i
$904$		−	905.887i		−	1.00209i
$905$		0			0
$906$	−1052.78			−1.16201
$907$			1620.77i			1.78695i	0.449109	+	0.893477i	$0.351742\pi$
$907$			1620.77i			1.78695i	−0.449109	+	0.893477i	$0.648258\pi$
$908$	−192.128			−0.211594
$909$			45.3325i			0.0498707i
$910$		0			0
$911$	−111.468			−0.122358			−0.0611791	−	0.998127i	$-0.519486\pi$
$911$	−111.468			−0.122358			−0.0611791	+	0.998127i	$0.519486\pi$
$912$	121.238			0.132936
$913$	54.7875	+	72.6838i	0.0600082	+	0.0796099i
$914$	547.151			0.598633
$915$		0			0
$916$	52.6980			0.0575306
$917$		−	1701.19i		−	1.85517i
$918$			1470.29i			1.60162i
$919$			664.740i			0.723330i	0.932308	+	0.361665i	$0.117792\pi$
$919$			664.740i			0.723330i	−0.932308	+	0.361665i	$0.882208\pi$
$920$		0			0
$921$		−	1439.56i		−	1.56304i
$922$		−	1058.26i		−	1.14778i
$923$	−3.63927			−0.00394287
$924$	−201.169	+	151.637i	−0.217715	+	0.164109i
$925$		0			0
$926$			66.4058i			0.0717126i
$927$		−	40.9499i		−	0.0441746i
$928$			840.138i			0.905321i
$929$	844.411			0.908946			0.454473	−	0.890760i	$-0.349828\pi$
$929$	844.411			0.908946			0.454473	+	0.890760i	$0.349828\pi$
$930$		0			0
$931$			17.1258i			0.0183950i
$932$	−260.350			−0.279345
$933$		−	1171.37i		−	1.25549i
$934$		−	201.172i		−	0.215388i
$935$		0			0
$936$	−30.1103			−0.0321691
$937$	175.541			0.187343			0.0936716	−	0.995603i	$-0.470140\pi$
$937$	175.541			0.187343			0.0936716	+	0.995603i	$0.470140\pi$
$938$		−	101.103i		−	0.107786i
$939$	230.135			0.245085
$940$		0			0
$941$			838.440i			0.891010i	0.895279	+	0.445505i	$0.146976\pi$
$941$			838.440i			0.891010i	−0.895279	+	0.445505i	$0.853024\pi$
$942$	−568.466			−0.603467
$943$	−321.556			−0.340993
$944$	−1046.98			−1.10909
$945$		0			0
$946$	−25.2523	−	33.5010i	−0.0266938	−	0.0354133i
$947$			1483.34i			1.56636i	0.621796	+	0.783179i	$0.286403\pi$
$947$			1483.34i			1.56636i	−0.621796	+	0.783179i	$0.713597\pi$
$948$	369.546			0.389817
$949$	−70.2186			−0.0739922
$950$		0			0
$951$	1042.75			1.09647
$952$	−1811.55			−1.90289
$953$	186.094			0.195272			0.0976359	−	0.995222i	$-0.468872\pi$
$953$	186.094			0.195272			0.0976359	+	0.995222i	$0.468872\pi$
$954$		−	184.414i		−	0.193306i
$955$		0			0
$956$			338.377i			0.353951i
$957$	−829.763	−	1100.80i	−0.867046	−	1.15027i
$958$		−	1019.48i		−	1.06417i
$959$			1346.16i			1.40371i
$960$		0			0
$961$	−275.974			−0.287174
$962$		−	139.978i		−	0.145507i
$963$	−157.128			−0.163166
$964$			47.9318i			0.0497218i
$965$		0			0
$966$	408.657			0.423040
$967$	948.621			0.980994			0.490497	−	0.871443i	$-0.336815\pi$
$967$	948.621			0.980994			0.490497	+	0.871443i	$0.336815\pi$
$968$	289.986	−	1012.39i	0.299572	−	1.04586i
$969$	389.418			0.401876
$970$		0			0
$971$	685.460			0.705932			0.352966	−	0.935636i	$-0.385173\pi$
$971$	685.460			0.705932			0.352966	+	0.935636i	$0.385173\pi$
$972$			77.6334i			0.0798698i
$973$			1338.64i			1.37579i
$974$		−	644.430i		−	0.661633i
$975$		0			0
$976$			528.193i			0.541181i
$977$			48.0051i			0.0491352i	0.999698	+	0.0245676i	$0.00782089\pi$
$977$			48.0051i			0.0491352i	−0.999698	+	0.0245676i	$0.992179\pi$
$978$	411.081			0.420328
$979$	562.070	+	745.670i	0.574127	+	0.761665i
$980$		0			0
$981$			206.940i			0.210948i
$982$		−	1166.97i		−	1.18836i
$983$		−	1453.38i		−	1.47851i	−0.673423	−	0.739257i	$-0.735177\pi$
$983$		−	1453.38i		−	1.47851i	0.673423	−	0.739257i	$-0.264823\pi$
$984$	599.821			0.609574
$985$		0			0
$986$		−	2315.07i		−	2.34794i
$987$	43.8318			0.0444092
$988$			15.9759i			0.0161699i
$989$		−	29.8236i		−	0.0301553i
$990$		0			0
$991$	1112.63			1.12273			0.561366	−	0.827568i	$-0.310276\pi$
$991$	1112.63			1.12273			0.561366	+	0.827568i	$0.310276\pi$
$992$	490.431			0.494386
$993$		−	500.500i		−	0.504028i
$994$	14.0070			0.0140915
$995$		0			0
$996$		−	28.1882i		−	0.0283014i
$997$	846.960			0.849508			0.424754	−	0.905309i	$-0.360361\pi$
$997$	846.960			0.849508			0.424754	+	0.905309i	$0.360361\pi$
$998$	405.815			0.406629
$999$	−820.507			−0.821328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.d.c.274.11		16
5.2	odd	4		275.3.c.f.76.6		8
5.3	odd	4		55.3.c.a.21.3	✓	8
5.4	even	2	inner	275.3.d.c.274.6		16
11.10	odd	2	inner	275.3.d.c.274.5		16
15.8	even	4		495.3.b.a.406.6		8
20.3	even	4		880.3.j.a.241.3		8
55.32	even	4		275.3.c.f.76.3		8
55.43	even	4		55.3.c.a.21.6	yes	8
55.54	odd	2	inner	275.3.d.c.274.12		16
165.98	odd	4		495.3.b.a.406.3		8
220.43	odd	4		880.3.j.a.241.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.c.a.21.3	✓	8	5.3	odd	4
55.3.c.a.21.6	yes	8	55.43	even	4
275.3.c.f.76.3		8	55.32	even	4
275.3.c.f.76.6		8	5.2	odd	4
275.3.d.c.274.5		16	11.10	odd	2	inner
275.3.d.c.274.6		16	5.4	even	2	inner
275.3.d.c.274.11		16	1.1	even	1	trivial
275.3.d.c.274.12		16	55.54	odd	2	inner
495.3.b.a.406.3		8	165.98	odd	4
495.3.b.a.406.6		8	15.8	even	4
880.3.j.a.241.3		8	20.3	even	4
880.3.j.a.241.4		8	220.43	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)

\(f(q)\)	\(=\)	\(q+1.66769 q^{2} -2.79505i q^{3} -1.21881 q^{4} -4.66128i q^{6} -6.72266 q^{7} -8.70336 q^{8} +1.18769 q^{9} +(-6.62122 - 8.78404i) q^{11} +3.40663i q^{12} +2.91291 q^{13} -11.2113 q^{14} -9.63929 q^{16} -30.9615 q^{17} +1.98069 q^{18} -4.49991i q^{19} +18.7902i q^{21} +(-11.0422 - 14.6491i) q^{22} -13.0410i q^{23} +24.3263i q^{24} +4.85783 q^{26} -28.4751i q^{27} +8.19362 q^{28} +44.8359i q^{29} +26.1730 q^{31} +18.7381 q^{32} +(-24.5519 + 18.5067i) q^{33} -51.6342 q^{34} -1.44756 q^{36} -28.8149i q^{37} -7.50446i q^{38} -8.14172i q^{39} -24.6573i q^{41} +31.3362i q^{42} +2.28690 q^{43} +(8.06999 + 10.7060i) q^{44} -21.7484i q^{46} -2.33270i q^{47} +26.9423i q^{48} -3.80580 q^{49} +86.5390i q^{51} -3.55027 q^{52} -93.1057i q^{53} -47.4877i q^{54} +58.5097 q^{56} -12.5775 q^{57} +74.7724i q^{58} +108.616 q^{59} -54.7958i q^{61} +43.6485 q^{62} -7.98441 q^{63} +69.8065 q^{64} +(-40.9449 + 30.8634i) q^{66} +9.01793i q^{67} +37.7361 q^{68} -36.4504 q^{69} -1.24936 q^{71} -10.3369 q^{72} -24.1060 q^{73} -48.0543i q^{74} +5.48452i q^{76} +(44.5123 + 59.0522i) q^{77} -13.5779i q^{78} -108.479i q^{79} -68.9002 q^{81} -41.1207i q^{82} -8.27453 q^{83} -22.9016i q^{84} +3.81384 q^{86} +125.319 q^{87} +(57.6269 + 76.4507i) q^{88} -84.8892 q^{89} -19.5825 q^{91} +15.8945i q^{92} -73.1549i q^{93} -3.89022i q^{94} -52.3739i q^{96} +160.450i q^{97} -6.34690 q^{98} +(-7.86394 - 10.4327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 56 q^{4} + 8 q^{9} + 16 q^{11} + 176 q^{16} - 200 q^{26} + 72 q^{31} - 160 q^{34} - 432 q^{36} - 24 q^{44} - 344 q^{49} - 160 q^{56} + 32 q^{59} + 1176 q^{64} + 360 q^{66} - 16 q^{69} + 552 q^{71}+ \cdots + 368 q^{99}+O(q^{100}) \) 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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