LMFDB - Embedded newform 275.3.d.c.274.1

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			274.1
Root			$2.44303 - 2.44303i$ of defining polynomial
Character	$\chi$	$=$	275.274
Dual form			275.3.d.c.274.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.88606 q^{2} -4.12151i q^{3} +11.1014 q^{4} +16.0164i q^{6} +3.44089 q^{7} -27.5966 q^{8} -7.98688 q^{9} +(-6.12847 - 9.13465i) q^{11} -45.7547i q^{12} +6.33153 q^{13} -13.3715 q^{14} +62.8361 q^{16} +0.715819 q^{17} +31.0375 q^{18} -20.9074i q^{19} -14.1817i q^{21} +(23.8156 + 35.4978i) q^{22} -4.55735i q^{23} +113.740i q^{24} -24.6047 q^{26} -4.17560i q^{27} +38.1988 q^{28} +0.262032i q^{29} -9.37380 q^{31} -133.798 q^{32} +(-37.6486 + 25.2586i) q^{33} -2.78171 q^{34} -88.6658 q^{36} -19.4653i q^{37} +81.2473i q^{38} -26.0955i q^{39} -24.1588i q^{41} +55.1108i q^{42} -63.5155 q^{43} +(-68.0348 - 101.408i) q^{44} +17.7101i q^{46} -34.9319i q^{47} -258.980i q^{48} -37.1603 q^{49} -2.95026i q^{51} +70.2891 q^{52} +60.7519i q^{53} +16.2266i q^{54} -94.9568 q^{56} -86.1701 q^{57} -1.01827i q^{58} -47.3144 q^{59} +108.391i q^{61} +36.4271 q^{62} -27.4820 q^{63} +268.603 q^{64} +(146.304 - 98.1563i) q^{66} +96.1396i q^{67} +7.94662 q^{68} -18.7832 q^{69} +20.7471 q^{71} +220.410 q^{72} +98.4295 q^{73} +75.6433i q^{74} -232.102i q^{76} +(-21.0874 - 31.4313i) q^{77} +101.409i q^{78} -114.561i q^{79} -89.0917 q^{81} +93.8823i q^{82} -127.250 q^{83} -157.437i q^{84} +246.825 q^{86} +1.07997 q^{87} +(169.125 + 252.085i) q^{88} +3.05204 q^{89} +21.7861 q^{91} -50.5931i q^{92} +38.6343i q^{93} +135.748i q^{94} +551.451i q^{96} -91.6103i q^{97} +144.407 q^{98} +(48.9474 + 72.9573i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.88606			−1.94303			−0.971514	−	0.236982i	$-0.923842\pi$
$2$	−3.88606			−1.94303			−0.971514	+	0.236982i	$0.923842\pi$
$3$		−	4.12151i		−	1.37384i	−0.726734	−	0.686919i	$-0.758963\pi$
$3$		−	4.12151i		−	1.37384i	0.726734	−	0.686919i	$-0.241037\pi$
$4$	11.1014			2.77536
$5$		0			0
$5$		0			0
$6$			16.0164i			2.66941i
$7$	3.44089			0.491556			0.245778	−	0.969326i	$-0.420957\pi$
$7$	3.44089			0.491556			0.245778	+	0.969326i	$0.420957\pi$
$8$	−27.5966			−3.44957
$9$	−7.98688			−0.887431
$10$		0			0
$11$	−6.12847	−	9.13465i	−0.557134	−	0.830423i
$11$	−6.12847	−	9.13465i	−0.557134	−	0.830423i
$12$		−	45.7547i		−	3.81289i
$13$	6.33153			0.487041			0.243521	−	0.969896i	$-0.421698\pi$
$13$	6.33153			0.487041			0.243521	+	0.969896i	$0.421698\pi$
$14$	−13.3715			−0.955107
$15$		0			0
$16$	62.8361			3.92725
$17$	0.715819			0.0421070			0.0210535	−	0.999778i	$-0.493298\pi$
$17$	0.715819			0.0421070			0.0210535	+	0.999778i	$0.493298\pi$
$18$	31.0375			1.72430
$19$		−	20.9074i		−	1.10039i	−0.835037	−	0.550194i	$-0.814554\pi$
$19$		−	20.9074i		−	1.10039i	0.835037	−	0.550194i	$-0.185446\pi$
$20$		0			0
$21$		−	14.1817i		−	0.675318i
$22$	23.8156	+	35.4978i	1.08253	+	1.61353i
$23$		−	4.55735i		−	0.198146i	−0.995080	−	0.0990728i	$-0.968412\pi$
$23$		−	4.55735i		−	0.198146i	0.995080	−	0.0990728i	$-0.0315877\pi$
$24$			113.740i			4.73915i
$25$		0			0
$26$	−24.6047			−0.946334
$27$		−	4.17560i		−	0.154652i
$28$	38.1988			1.36424
$29$			0.262032i			0.00903560i	0.999990	+	0.00451780i	$0.00143807\pi$
$29$			0.262032i			0.00903560i	−0.999990	+	0.00451780i	$0.998562\pi$
$30$		0			0
$31$	−9.37380			−0.302381			−0.151190	−	0.988505i	$-0.548311\pi$
$31$	−9.37380			−0.302381			−0.151190	+	0.988505i	$0.548311\pi$
$32$	−133.798			−4.18119
$33$	−37.6486	+	25.2586i	−1.14087	+	0.765412i
$34$	−2.78171			−0.0818151
$35$		0			0
$36$	−88.6658			−2.46294
$37$		−	19.4653i		−	0.526090i	−0.964784	−	0.263045i	$-0.915273\pi$
$37$		−	19.4653i		−	0.526090i	0.964784	−	0.263045i	$-0.0847267\pi$
$38$			81.2473i			2.13809i
$39$		−	26.0955i		−	0.669115i
$40$		0			0
$41$		−	24.1588i		−	0.589238i	−0.955615	−	0.294619i	$-0.904807\pi$
$41$		−	24.1588i		−	0.589238i	0.955615	−	0.294619i	$-0.0951928\pi$
$42$			55.1108i			1.31216i
$43$	−63.5155			−1.47710			−0.738552	−	0.674196i	$-0.764490\pi$
$43$	−63.5155			−1.47710			−0.738552	+	0.674196i	$0.764490\pi$
$44$	−68.0348	−	101.408i	−1.54625	−	2.30472i
$45$		0			0
$46$			17.7101i			0.385002i
$47$		−	34.9319i		−	0.743233i	−0.928386	−	0.371616i	$-0.878804\pi$
$47$		−	34.9319i		−	0.743233i	0.928386	−	0.371616i	$-0.121196\pi$
$48$		−	258.980i		−	5.39541i
$49$	−37.1603			−0.758373
$50$		0			0
$51$		−	2.95026i		−	0.0578482i
$52$	70.2891			1.35171
$53$			60.7519i			1.14626i	0.819464	+	0.573131i	$0.194271\pi$
$53$			60.7519i			1.14626i	−0.819464	+	0.573131i	$0.805729\pi$
$54$			16.2266i			0.300493i
$55$		0			0
$56$	−94.9568			−1.69566
$57$	−86.1701			−1.51176
$58$		−	1.01827i		−	0.0175564i
$59$	−47.3144			−0.801940			−0.400970	−	0.916091i	$-0.631327\pi$
$59$	−47.3144			−0.801940			−0.400970	+	0.916091i	$0.631327\pi$
$60$		0			0
$61$			108.391i			1.77691i	0.458965	+	0.888455i	$0.348220\pi$
$61$			108.391i			1.77691i	−0.458965	+	0.888455i	$0.651780\pi$
$62$	36.4271			0.587534
$63$	−27.4820			−0.436222
$64$	268.603			4.19692
$65$		0			0
$66$	146.304	−	98.1563i	2.21673	−	1.48722i
$67$			96.1396i			1.43492i	0.696600	+	0.717460i	$0.254695\pi$
$67$			96.1396i			1.43492i	−0.696600	+	0.717460i	$0.745305\pi$
$68$	7.94662			0.116862
$69$	−18.7832			−0.272220
$70$		0			0
$71$	20.7471			0.292213			0.146107	−	0.989269i	$-0.453326\pi$
$71$	20.7471			0.292213			0.146107	+	0.989269i	$0.453326\pi$
$72$	220.410			3.06125
$73$	98.4295			1.34835			0.674175	−	0.738572i	$-0.264499\pi$
$73$	98.4295			1.34835			0.674175	+	0.738572i	$0.264499\pi$
$74$			75.6433i			1.02221i
$75$		0			0
$76$		−	232.102i		−	3.05397i
$77$	−21.0874	−	31.4313i	−0.273863	−	0.408199i
$78$			101.409i			1.30011i
$79$		−	114.561i		−	1.45014i	−0.688677	−	0.725069i	$-0.741808\pi$
$79$		−	114.561i		−	1.45014i	0.688677	−	0.725069i	$-0.258192\pi$
$80$		0			0
$81$	−89.0917			−1.09990
$82$			93.8823i			1.14491i
$83$	−127.250			−1.53313			−0.766567	−	0.642165i	$-0.778037\pi$
$83$	−127.250			−1.53313			−0.766567	+	0.642165i	$0.778037\pi$
$84$		−	157.437i		−	1.87425i
$85$		0			0
$86$	246.825			2.87006
$87$	1.07997			0.0124135
$88$	169.125	+	252.085i	1.92187	+	2.86460i
$89$	3.05204			0.0342926			0.0171463	−	0.999853i	$-0.494542\pi$
$89$	3.05204			0.0342926			0.0171463	+	0.999853i	$0.494542\pi$
$90$		0			0
$91$	21.7861			0.239408
$92$		−	50.5931i		−	0.549925i
$93$			38.6343i			0.415422i
$94$			135.748i			1.44412i
$95$		0			0
$96$			551.451i			5.74428i
$97$		−	91.6103i		−	0.944436i	−0.881482	−	0.472218i	$-0.843453\pi$
$97$		−	91.6103i		−	0.944436i	0.881482	−	0.472218i	$-0.156547\pi$
$98$	144.407			1.47354
$99$	48.9474	+	72.9573i	0.494418	+	0.736943i
$100$		0			0
$101$			100.098i			0.991071i	0.868588	+	0.495535i	$0.165028\pi$
$101$			100.098i			0.991071i	−0.868588	+	0.495535i	$0.834972\pi$
$102$			11.4649i			0.112401i
$103$		−	118.551i		−	1.15098i	−0.817808	−	0.575491i	$-0.804811\pi$
$103$		−	118.551i		−	1.15098i	0.817808	−	0.575491i	$-0.195189\pi$
$104$	−174.729			−1.68008
$105$		0			0
$106$		−	236.085i		−	2.22722i
$107$	159.030			1.48626			0.743130	−	0.669148i	$-0.233341\pi$
$107$	159.030			1.48626			0.743130	+	0.669148i	$0.233341\pi$
$108$		−	46.3551i		−	0.429214i
$109$		−	36.8808i		−	0.338356i	−0.985586	−	0.169178i	$-0.945889\pi$
$109$		−	36.8808i		−	0.338356i	0.985586	−	0.169178i	$-0.0541112\pi$
$110$		0			0
$111$	−80.2266			−0.722762
$112$	216.212			1.93047
$113$		−	121.539i		−	1.07557i	−0.843082	−	0.537784i	$-0.819261\pi$
$113$		−	121.539i		−	1.07557i	0.843082	−	0.537784i	$-0.180739\pi$
$114$	334.862			2.93738
$115$		0			0
$116$			2.90894i			0.0250770i
$117$	−50.5692			−0.432215
$118$	183.867			1.55819
$119$	2.46306			0.0206980
$120$		0			0
$121$	−45.8836	+	111.963i	−0.379203	+	0.925313i
$122$		−	421.215i		−	3.45258i
$123$	−99.5707			−0.809518
$124$	−104.063			−0.839215
$125$		0			0
$126$	106.797			0.847592
$127$	3.05895			0.0240862			0.0120431	−	0.999927i	$-0.496166\pi$
$127$	3.05895			0.0240862			0.0120431	+	0.999927i	$0.496166\pi$
$128$	−508.614			−3.97354
$129$			261.780i			2.02930i
$130$		0			0
$131$		−	44.4928i		−	0.339640i	−0.985475	−	0.169820i	$-0.945681\pi$
$131$		−	44.4928i		−	0.339640i	0.985475	−	0.169820i	$-0.0543186\pi$
$132$	−417.953	+	280.407i	−3.16631	+	2.12429i
$133$		−	71.9401i		−	0.540903i
$134$		−	373.604i		−	2.78809i
$135$		0			0
$136$	−19.7542			−0.145251
$137$		−	75.3365i		−	0.549902i	−0.961458	−	0.274951i	$-0.911338\pi$
$137$		−	75.3365i		−	0.549902i	0.961458	−	0.274951i	$-0.0886616\pi$
$138$	72.9924			0.528931
$139$		−	8.54320i		−	0.0614619i	−0.999528	−	0.0307309i	$-0.990216\pi$
$139$		−	8.54320i		−	0.0614619i	0.999528	−	0.0307309i	$-0.00978350\pi$
$140$		0			0
$141$	−143.973			−1.02108
$142$	−80.6245			−0.567778
$143$	−38.8026	−	57.8363i	−0.271347	−	0.404450i
$144$	−501.864			−3.48517
$145$		0			0
$146$	−382.503			−2.61988
$147$			153.157i			1.04188i
$148$		−	216.093i		−	1.46009i
$149$			88.5634i			0.594385i	0.954818	+	0.297192i	$0.0960503\pi$
$149$			88.5634i			0.594385i	−0.954818	+	0.297192i	$0.903950\pi$
$150$		0			0
$151$		−	171.337i		−	1.13468i	−0.823483	−	0.567340i	$-0.807972\pi$
$151$		−	171.337i		−	1.13468i	0.823483	−	0.567340i	$-0.192028\pi$
$152$			576.972i			3.79587i
$153$	−5.71716			−0.0373671
$154$	81.9469	+	122.144i	0.532123	+	0.793143i
$155$		0			0
$156$		−	289.697i		−	1.85703i
$157$		−	44.0180i		−	0.280369i	−0.990125	−	0.140185i	$-0.955230\pi$
$157$		−	44.0180i		−	0.280369i	0.990125	−	0.140185i	$-0.0447696\pi$
$158$			445.190i			2.81766i
$159$	250.390			1.57478
$160$		0			0
$161$		−	15.6813i		−	0.0973996i
$162$	346.215			2.13713
$163$		−	174.094i		−	1.06806i	−0.845464	−	0.534032i	$-0.820676\pi$
$163$		−	174.094i		−	1.06806i	0.845464	−	0.534032i	$-0.179324\pi$
$164$		−	268.197i		−	1.63535i
$165$		0			0
$166$	494.501			2.97892
$167$	12.0665			0.0722544			0.0361272	−	0.999347i	$-0.488498\pi$
$167$	12.0665			0.0722544			0.0361272	+	0.999347i	$0.488498\pi$
$168$			391.366i			2.32956i
$169$	−128.912			−0.762791
$170$		0			0
$171$			166.985i			0.976519i
$172$	−705.113			−4.09949
$173$	132.929			0.768374			0.384187	−	0.923255i	$-0.374482\pi$
$173$	132.929			0.768374			0.384187	+	0.923255i	$0.374482\pi$
$174$	−4.19683			−0.0241197
$175$		0			0
$176$	−385.089	−	573.985i	−2.18801	−	3.26128i
$177$			195.007i			1.10174i
$178$	−11.8604			−0.0666314
$179$	132.613			0.740855			0.370427	−	0.928861i	$-0.379211\pi$
$179$	132.613			0.740855			0.370427	+	0.928861i	$0.379211\pi$
$180$		0			0
$181$	23.2117			0.128241			0.0641207	−	0.997942i	$-0.479576\pi$
$181$	23.2117			0.128241			0.0641207	+	0.997942i	$0.479576\pi$
$182$	−84.6621			−0.465176
$183$	446.737			2.44119
$184$			125.767i			0.683517i
$185$		0			0
$186$		−	150.135i		−	0.807177i
$187$	−4.38688	−	6.53876i	−0.0234593	−	0.0349666i
$188$		−	387.795i		−	2.06274i
$189$		−	14.3678i		−	0.0760200i
$190$		0			0
$191$	265.473			1.38991			0.694956	−	0.719052i	$-0.255424\pi$
$191$	265.473			1.38991			0.694956	+	0.719052i	$0.255424\pi$
$192$		−	1107.05i		−	5.76589i
$193$	−208.771			−1.08171			−0.540856	−	0.841115i	$-0.681900\pi$
$193$	−208.771			−1.08171			−0.540856	+	0.841115i	$0.681900\pi$
$194$			356.003i			1.83507i
$195$		0			0
$196$	−412.532			−2.10476
$197$	49.1632			0.249559			0.124780	−	0.992184i	$-0.460178\pi$
$197$	49.1632			0.249559			0.124780	+	0.992184i	$0.460178\pi$
$198$	−190.212	−	283.516i	−0.960668	−	1.43190i
$199$	241.764			1.21490			0.607448	−	0.794360i	$-0.292194\pi$
$199$	241.764			1.21490			0.607448	+	0.794360i	$0.292194\pi$
$200$		0			0
$201$	396.241			1.97135
$202$		−	388.987i		−	1.92568i
$203$			0.901626i			0.00444151i
$204$		−	32.7521i		−	0.160550i
$205$		0			0
$206$			460.697i			2.23639i
$207$			36.3990i			0.175840i
$208$	397.849			1.91273
$209$	−190.982	+	128.130i	−0.913788	+	0.613064i
$210$		0			0
$211$			304.085i			1.44116i	0.693371	+	0.720581i	$0.256125\pi$
$211$			304.085i			1.44116i	−0.693371	+	0.720581i	$0.743875\pi$
$212$			674.433i			3.18129i
$213$		−	85.5096i		−	0.401454i
$214$	−617.998			−2.88784
$215$		0			0
$216$			115.232i			0.533482i
$217$	−32.2542			−0.148637
$218$			143.321i			0.657435i
$219$		−	405.679i		−	1.85241i
$220$		0			0
$221$	4.53223			0.0205078
$222$	311.765			1.40435
$223$			198.650i			0.890805i	0.895330	+	0.445403i	$0.146939\pi$
$223$			198.650i			0.890805i	−0.895330	+	0.445403i	$0.853061\pi$
$224$	−460.385			−2.05529
$225$		0			0
$226$			472.308i			2.08986i
$227$	164.265			0.723634			0.361817	−	0.932249i	$-0.382157\pi$
$227$	164.265			0.723634			0.361817	+	0.932249i	$0.382157\pi$
$228$	−956.611			−4.19566
$229$	181.944			0.794516			0.397258	−	0.917707i	$-0.369962\pi$
$229$	181.944			0.794516			0.397258	+	0.917707i	$0.369962\pi$
$230$		0			0
$231$	−129.545	+	86.9121i	−0.560800	+	0.376243i
$232$		−	7.23120i		−	0.0311689i
$233$	−124.243			−0.533233			−0.266617	−	0.963803i	$-0.585906\pi$
$233$	−124.243			−0.533233			−0.266617	+	0.963803i	$0.585906\pi$
$234$	196.515			0.839806
$235$		0			0
$236$	−525.258			−2.22567
$237$	−472.164			−1.99225
$238$	−9.57158			−0.0402167
$239$		−	278.390i		−	1.16481i	−0.812898	−	0.582406i	$-0.802111\pi$
$239$		−	278.390i		−	1.16481i	0.812898	−	0.582406i	$-0.197889\pi$
$240$		0			0
$241$		−	334.905i		−	1.38965i	−0.719180	−	0.694824i	$-0.755482\pi$
$241$		−	334.905i		−	1.38965i	0.719180	−	0.694824i	$-0.244518\pi$
$242$	178.306	−	435.094i	0.736803	−	1.79791i
$243$			329.612i			1.35643i
$244$			1203.30i			4.93156i
$245$		0			0
$246$	386.937			1.57292
$247$		−	132.376i		−	0.535935i
$248$	258.685			1.04308
$249$			524.463i			2.10628i
$250$		0			0
$251$	180.078			0.717442			0.358721	−	0.933445i	$-0.383213\pi$
$251$	180.078			0.717442			0.358721	+	0.933445i	$0.383213\pi$
$252$	−305.089			−1.21067
$253$	−41.6298	+	27.9296i	−0.164545	+	0.110394i
$254$	−11.8873			−0.0468002
$255$		0			0
$256$	902.089			3.52379
$257$		−	46.2863i		−	0.180102i	−0.995937	−	0.0900512i	$-0.971297\pi$
$257$		−	46.2863i		−	0.180102i	0.995937	−	0.0900512i	$-0.0287031\pi$
$258$		−	1017.29i		−	3.94299i
$259$		−	66.9781i		−	0.258603i
$260$		0			0
$261$		−	2.09282i		−	0.00801847i
$262$			172.902i			0.659930i
$263$	−269.933			−1.02636			−0.513180	−	0.858281i	$-0.671533\pi$
$263$	−269.933			−1.02636			−0.513180	+	0.858281i	$0.671533\pi$
$264$	1038.97	−	697.050i	3.93550	−	2.64034i
$265$		0			0
$266$			279.563i			1.05099i
$267$		−	12.5790i		−	0.0471124i
$268$			1067.29i			3.98242i
$269$	284.250			1.05669			0.528346	−	0.849029i	$-0.322813\pi$
$269$	284.250			1.05669			0.528346	+	0.849029i	$0.322813\pi$
$270$		0			0
$271$		−	363.163i		−	1.34008i	−0.742323	−	0.670042i	$-0.766276\pi$
$271$		−	363.163i		−	1.34008i	0.742323	−	0.670042i	$-0.233724\pi$
$272$	44.9793			0.165365
$273$		−	89.7918i		−	0.328908i
$274$			292.762i			1.06847i
$275$		0			0
$276$	−208.520			−0.755507
$277$	−4.30214			−0.0155312			−0.00776559	−	0.999970i	$-0.502472\pi$
$277$	−4.30214			−0.0155312			−0.00776559	+	0.999970i	$0.502472\pi$
$278$			33.1994i			0.119422i
$279$	74.8674			0.268342
$280$		0			0
$281$		−	65.1496i		−	0.231849i	−0.993258	−	0.115925i	$-0.963017\pi$
$281$		−	65.1496i		−	0.231849i	0.993258	−	0.115925i	$-0.0369831\pi$
$282$	559.485			1.98399
$283$	297.904			1.05267			0.526333	−	0.850279i	$-0.323567\pi$
$283$	297.904			1.05267			0.526333	+	0.850279i	$0.323567\pi$
$284$	230.323			0.810996
$285$		0			0
$286$	150.789	+	224.755i	0.527235	+	0.785857i
$287$		−	83.1277i		−	0.289644i
$288$	1068.63			3.71052
$289$	−288.488			−0.998227
$290$		0			0
$291$	−377.573			−1.29750
$292$	1092.71			3.74215
$293$	286.790			0.978805			0.489402	−	0.872058i	$-0.337215\pi$
$293$	286.790			0.978805			0.489402	+	0.872058i	$0.337215\pi$
$294$		−	595.175i		−	2.02440i
$295$		0			0
$296$			537.176i			1.81478i
$297$	−38.1426	+	25.5900i	−0.128426	+	0.0861618i
$298$		−	344.162i		−	1.15491i
$299$		−	28.8550i		−	0.0965050i
$300$		0			0
$301$	−218.550			−0.726080
$302$			665.824i			2.20472i
$303$	412.556			1.36157
$304$		−	1313.74i		−	4.32151i
$305$		0			0
$306$	22.2172			0.0726053
$307$	89.5999			0.291856			0.145928	−	0.989295i	$-0.453383\pi$
$307$	89.5999			0.291856			0.145928	+	0.989295i	$0.453383\pi$
$308$	−234.101	−	348.933i	−0.760067	−	1.13290i
$309$	−488.610			−1.58126
$310$		0			0
$311$	507.003			1.63024			0.815118	−	0.579295i	$-0.196672\pi$
$311$	507.003			1.63024			0.815118	+	0.579295i	$0.196672\pi$
$312$			720.146i			2.30816i
$313$			265.646i			0.848708i	0.905496	+	0.424354i	$0.139499\pi$
$313$			265.646i			0.848708i	−0.905496	+	0.424354i	$0.860501\pi$
$314$			171.056i			0.544765i
$315$		0			0
$316$		−	1271.79i		−	4.02465i
$317$		−	547.546i		−	1.72727i	−0.504114	−	0.863637i	$-0.668181\pi$
$317$		−	547.546i		−	1.72727i	0.504114	−	0.863637i	$-0.331819\pi$
$318$	−973.029			−3.05984
$319$	2.39357	−	1.60586i	0.00750337	−	0.00503404i
$320$		0			0
$321$		−	655.443i		−	2.04188i
$322$			60.9386i			0.189250i
$323$		−	14.9659i		−	0.0463341i
$324$	−989.045			−3.05261
$325$		0			0
$326$			676.541i			2.07528i
$327$	−152.005			−0.464846
$328$			666.699i			2.03262i
$329$		−	120.197i		−	0.365341i
$330$		0			0
$331$	−518.651			−1.56692			−0.783461	−	0.621441i	$-0.786547\pi$
$331$	−518.651			−1.56692			−0.783461	+	0.621441i	$0.786547\pi$
$332$	−1412.66			−4.25499
$333$			155.467i			0.466868i
$334$	−46.8910			−0.140392
$335$		0			0
$336$		−	891.121i		−	2.65215i
$337$	−23.0137			−0.0682900			−0.0341450	−	0.999417i	$-0.510871\pi$
$337$	−23.0137			−0.0682900			−0.0341450	+	0.999417i	$0.510871\pi$
$338$	500.958			1.48212
$339$	−500.926			−1.47766
$340$		0			0
$341$	57.4471	+	85.6264i	0.168467	+	0.251104i
$342$		−	648.912i		−	1.89740i
$343$	−296.468			−0.864339
$344$	1752.81			5.09537
$345$		0			0
$346$	−516.569			−1.49297
$347$	395.647			1.14019			0.570096	−	0.821578i	$-0.306906\pi$
$347$	395.647			1.14019			0.570096	+	0.821578i	$0.306906\pi$
$348$	11.9892			0.0344518
$349$		−	282.183i		−	0.808548i	−0.914638	−	0.404274i	$-0.867524\pi$
$349$		−	282.183i		−	0.808548i	0.914638	−	0.404274i	$-0.132476\pi$
$350$		0			0
$351$		−	26.4379i		−	0.0753218i
$352$	819.979	+	1222.20i	2.32948	+	3.47216i
$353$		−	265.522i		−	0.752186i	−0.926582	−	0.376093i	$-0.877267\pi$
$353$		−	265.522i		−	0.752186i	0.926582	−	0.376093i	$-0.122733\pi$
$354$		−	757.809i		−	2.14070i
$355$		0			0
$356$	33.8820			0.0951742
$357$		−	10.1515i		−	0.0284356i
$358$	−515.342			−1.43950
$359$			206.014i			0.573856i	0.957952	+	0.286928i	$0.0926340\pi$
$359$			206.014i			0.573856i	−0.957952	+	0.286928i	$0.907366\pi$
$360$		0			0
$361$	−76.1189			−0.210856
$362$	−90.2019			−0.249177
$363$	461.457	+	189.110i	1.27123	+	0.520964i
$364$	241.857			0.664443
$365$		0			0
$366$	−1736.04			−4.74329
$367$			604.681i			1.64763i	0.566858	+	0.823816i	$0.308159\pi$
$367$			604.681i			1.64763i	−0.566858	+	0.823816i	$0.691841\pi$
$368$		−	286.366i		−	0.778168i
$369$			192.953i			0.522908i
$370$		0			0
$371$			209.041i			0.563452i
$372$			428.896i			1.15295i
$373$	−247.498			−0.663534			−0.331767	−	0.943361i	$-0.607645\pi$
$373$	−247.498			−0.663534			−0.331767	+	0.943361i	$0.607645\pi$
$374$	17.0477	+	25.4100i	0.0455820	+	0.0679411i
$375$		0			0
$376$			964.002i			2.56383i
$377$			1.65907i			0.00440071i
$378$			55.8340i			0.147709i
$379$	268.717			0.709016			0.354508	−	0.935053i	$-0.384648\pi$
$379$	268.717			0.709016			0.354508	+	0.935053i	$0.384648\pi$
$380$		0			0
$381$		−	12.6075i		−	0.0330906i
$382$	−1031.64			−2.70064
$383$		−	202.104i		−	0.527687i	−0.964566	−	0.263843i	$-0.915010\pi$
$383$		−	202.104i		−	0.527687i	0.964566	−	0.263843i	$-0.0849902\pi$
$384$			2096.26i			5.45901i
$385$		0			0
$386$	811.294			2.10180
$387$	507.290			1.31083
$388$		−	1017.01i		−	2.62115i
$389$	−186.969			−0.480640			−0.240320	−	0.970694i	$-0.577252\pi$
$389$	−186.969			−0.480640			−0.240320	+	0.970694i	$0.577252\pi$
$390$		0			0
$391$		−	3.26224i		−	0.00834332i
$392$	1025.50			2.61606
$393$	−183.378			−0.466610
$394$	−191.051			−0.484900
$395$		0			0
$396$	543.386	+	809.931i	1.37219	+	2.04528i
$397$			361.294i			0.910061i	0.890476	+	0.455030i	$0.150372\pi$
$397$			361.294i			0.910061i	−0.890476	+	0.455030i	$0.849628\pi$
$398$	−939.509			−2.36058
$399$	−296.502			−0.743113
$400$		0			0
$401$	719.624			1.79457			0.897287	−	0.441447i	$-0.145535\pi$
$401$	719.624			1.79457			0.897287	+	0.441447i	$0.145535\pi$
$402$	−1539.81			−3.83038
$403$	−59.3505			−0.147272
$404$			1111.23i			2.75058i
$405$		0			0
$406$		−	3.50377i		−	0.00862997i
$407$	−177.809	+	119.293i	−0.436877	+	0.293102i
$408$			81.4170i			0.199551i
$409$		−	412.750i		−	1.00917i	−0.863362	−	0.504584i	$-0.831646\pi$
$409$		−	412.750i		−	1.00917i	0.863362	−	0.504584i	$-0.168354\pi$
$410$		0			0
$411$	−310.500			−0.755476
$412$		−	1316.09i		−	3.19439i
$413$	−162.804			−0.394198
$414$		−	141.448i		−	0.341663i
$415$		0			0
$416$	−847.148			−2.03641
$417$	−35.2109			−0.0844387
$418$	742.165	−	497.922i	1.77552	−	1.19120i
$419$	−432.780			−1.03289			−0.516444	−	0.856321i	$-0.672745\pi$
$419$	−432.780			−1.03289			−0.516444	+	0.856321i	$0.672745\pi$
$420$		0			0
$421$	−38.3182			−0.0910172			−0.0455086	−	0.998964i	$-0.514491\pi$
$421$	−38.3182			−0.0910172			−0.0455086	+	0.998964i	$0.514491\pi$
$422$		−	1181.69i		−	2.80022i
$423$			278.997i			0.659568i
$424$		−	1676.54i		−	3.95411i
$425$		0			0
$426$			332.295i			0.780036i
$427$			372.963i			0.873450i
$428$	1765.46			4.12490
$429$	−238.373	+	159.926i	−0.555649	+	0.372787i
$430$		0			0
$431$		−	576.666i		−	1.33797i	−0.743275	−	0.668986i	$-0.766728\pi$
$431$		−	576.666i		−	1.33797i	0.743275	−	0.668986i	$-0.233272\pi$
$432$		−	262.378i		−	0.607357i
$433$		−	127.997i		−	0.295606i	−0.989017	−	0.147803i	$-0.952780\pi$
$433$		−	127.997i		−	0.295606i	0.989017	−	0.147803i	$-0.0472201\pi$
$434$	125.342			0.288806
$435$		0			0
$436$		−	409.429i		−	0.939058i
$437$	−95.2822			−0.218037
$438$			1576.49i			3.59929i
$439$		−	502.454i		−	1.14454i	−0.820065	−	0.572271i	$-0.806063\pi$
$439$		−	502.454i		−	1.14454i	0.820065	−	0.572271i	$-0.193937\pi$
$440$		0			0
$441$	296.794			0.673003
$442$	−17.6125			−0.0398473
$443$			617.205i			1.39324i	0.717441	+	0.696619i	$0.245313\pi$
$443$			617.205i			1.39324i	−0.717441	+	0.696619i	$0.754687\pi$
$444$	−890.630			−2.00592
$445$		0			0
$446$		−	771.963i		−	1.73086i
$447$	365.015			0.816589
$448$	924.234			2.06302
$449$	428.860			0.955145			0.477572	−	0.878592i	$-0.341517\pi$
$449$	428.860			0.955145			0.477572	+	0.878592i	$0.341517\pi$
$450$		0			0
$451$	−220.682	+	148.056i	−0.489317	+	0.328285i
$452$		−	1349.26i		−	2.98509i
$453$	−706.167			−1.55887
$454$	−638.342			−1.40604
$455$		0			0
$456$	2378.00			5.21491
$457$	601.480			1.31615			0.658074	−	0.752953i	$-0.271371\pi$
$457$	601.480			1.31615			0.658074	+	0.752953i	$0.271371\pi$
$458$	−707.045			−1.54377
$459$		−	2.98897i		−	0.00651193i
$460$		0			0
$461$			547.862i			1.18842i	0.804309	+	0.594211i	$0.202535\pi$
$461$			547.862i			1.18842i	−0.804309	+	0.594211i	$0.797465\pi$
$462$	503.418	−	337.745i	1.08965	−	0.731050i
$463$			752.922i			1.62618i	0.582138	+	0.813090i	$0.302216\pi$
$463$			752.922i			1.62618i	−0.582138	+	0.813090i	$0.697784\pi$
$464$			16.4651i			0.0354851i
$465$		0			0
$466$	482.817			1.03609
$467$		−	129.382i		−	0.277050i	−0.990359	−	0.138525i	$-0.955764\pi$
$467$		−	129.382i		−	0.277050i	0.990359	−	0.138525i	$-0.0442362\pi$
$468$	−561.390			−1.19955
$469$			330.806i			0.705344i
$470$		0			0
$471$	−181.421			−0.385182
$472$	1305.72			2.76635
$473$	389.253	+	580.192i	0.822945	+	1.22662i
$474$	1834.86			3.87100
$475$		0			0
$476$	27.3435			0.0574443
$477$		−	485.218i		−	1.01723i
$478$			1081.84i			2.26326i
$479$			643.912i			1.34428i	0.740422	+	0.672142i	$0.234625\pi$
$479$			643.912i			1.34428i	−0.740422	+	0.672142i	$0.765375\pi$
$480$		0			0
$481$		−	123.245i		−	0.256227i
$482$			1301.46i			2.70012i
$483$	−64.6309			−0.133811
$484$	−509.374	+	1242.95i	−1.05243	+	2.56808i
$485$		0			0
$486$		−	1280.89i		−	2.63558i
$487$		−	289.544i		−	0.594546i	−0.954793	−	0.297273i	$-0.903923\pi$
$487$		−	289.544i		−	0.594546i	0.954793	−	0.297273i	$-0.0960771\pi$
$488$		−	2991.23i		−	6.12957i
$489$	−717.533			−1.46735
$490$		0			0
$491$			969.915i			1.97539i	0.156404	+	0.987693i	$0.450010\pi$
$491$			969.915i			1.97539i	−0.156404	+	0.987693i	$0.549990\pi$
$492$	−1105.38			−2.24670
$493$			0.187568i			0.000380462i
$494$			514.420i			1.04134i
$495$		0			0
$496$	−589.013			−1.18753
$497$	71.3887			0.143639
$498$		−	2038.09i		−	4.09256i
$499$	390.136			0.781836			0.390918	−	0.920426i	$-0.372158\pi$
$499$	390.136			0.781836			0.390918	+	0.920426i	$0.372158\pi$
$500$		0			0
$501$		−	49.7322i		−	0.0992658i
$502$	−699.793			−1.39401
$503$	−40.1337			−0.0797888			−0.0398944	−	0.999204i	$-0.512702\pi$
$503$	−40.1337			−0.0797888			−0.0398944	+	0.999204i	$0.512702\pi$
$504$	758.408			1.50478
$505$		0			0
$506$	161.776	−	108.536i	0.319715	−	0.214498i
$507$			531.311i			1.04795i
$508$	33.9587			0.0668479
$509$	655.246			1.28732			0.643660	−	0.765312i	$-0.277415\pi$
$509$	655.246			1.28732			0.643660	+	0.765312i	$0.277415\pi$
$510$		0			0
$511$	338.685			0.662789
$512$	−1471.11			−2.87327
$513$	−87.3009			−0.170177
$514$			179.871i			0.349944i
$515$		0			0
$516$			2906.13i			5.63204i
$517$	−319.091	+	214.080i	−0.617197	+	0.414080i
$518$			260.281i			0.502472i
$519$		−	547.868i		−	1.05562i
$520$		0			0
$521$	−544.201			−1.04453			−0.522266	−	0.852783i	$-0.674913\pi$
$521$	−544.201			−1.04453			−0.522266	+	0.852783i	$0.674913\pi$
$522$			8.13282i			0.0155801i
$523$	912.634			1.74500			0.872499	−	0.488616i	$-0.162498\pi$
$523$	912.634			1.74500			0.872499	+	0.488616i	$0.162498\pi$
$524$		−	493.934i		−	0.942623i
$525$		0			0
$526$	1048.97			1.99425
$527$	−6.70995			−0.0127324
$528$	−2365.69	+	1587.15i	−4.48047	+	3.00597i
$529$	508.231			0.960738
$530$		0			0
$531$	377.895			0.711666
$532$		−	798.638i		−	1.50120i
$533$		−	152.962i		−	0.286983i
$534$			48.8828i			0.0915408i
$535$		0			0
$536$		−	2653.12i		−	4.94986i
$537$		−	546.566i		−	1.01781i
$538$	−1104.61			−2.05318
$539$	227.736	+	339.446i	0.422515	+	0.629770i
$540$		0			0
$541$		−	344.689i		−	0.637134i	−0.947900	−	0.318567i	$-0.896798\pi$
$541$		−	344.689i		−	0.637134i	0.947900	−	0.318567i	$-0.103202\pi$
$542$			1411.27i			2.60382i
$543$		−	95.6673i		−	0.176183i
$544$	−95.7753			−0.176058
$545$		0			0
$546$			348.936i			0.639077i
$547$	163.700			0.299268			0.149634	−	0.988741i	$-0.452190\pi$
$547$	163.700			0.299268			0.149634	+	0.988741i	$0.452190\pi$
$548$		−	836.343i		−	1.52617i
$549$		−	865.709i		−	1.57688i
$550$		0			0
$551$	5.47841			0.00994268
$552$	518.351			0.939041
$553$		−	394.192i		−	0.712824i
$554$	16.7183			0.0301775
$555$		0			0
$556$		−	94.8418i		−	0.170579i
$557$	−912.056			−1.63744			−0.818722	−	0.574190i	$-0.805317\pi$
$557$	−912.056			−1.63744			−0.818722	+	0.574190i	$0.805317\pi$
$558$	−290.939			−0.521396
$559$	−402.150			−0.719410
$560$		0			0
$561$	−26.9496	+	18.0806i	−0.0480385	+	0.0322292i
$562$			253.175i			0.450489i
$563$	225.781			0.401031			0.200516	−	0.979690i	$-0.435738\pi$
$563$	225.781			0.401031			0.200516	+	0.979690i	$0.435738\pi$
$564$	−1598.30			−2.83387
$565$		0			0
$566$	−1157.67			−2.04536
$567$	−306.555			−0.540661
$568$	−572.550			−1.00801
$569$		−	341.635i		−	0.600413i	−0.953874	−	0.300206i	$-0.902944\pi$
$569$		−	341.635i		−	0.600413i	0.953874	−	0.300206i	$-0.0970556\pi$
$570$		0			0
$571$		−	323.963i		−	0.567362i	−0.958919	−	0.283681i	$-0.908444\pi$
$571$		−	323.963i		−	0.567362i	0.958919	−	0.283681i	$-0.0915556\pi$
$572$	−430.765	−	642.066i	−0.753085	−	1.12249i
$573$		−	1094.15i		−	1.90951i
$574$			323.039i			0.562786i
$575$		0			0
$576$	−2145.30			−3.72448
$577$			851.342i			1.47546i	0.675095	+	0.737731i	$0.264103\pi$
$577$			851.342i			1.47546i	−0.675095	+	0.737731i	$0.735897\pi$
$578$	1121.08			1.93958
$579$			860.451i			1.48610i
$580$		0			0
$581$	−437.854			−0.753621
$582$	1467.27			2.52108
$583$	554.947	−	372.316i	0.951882	−	0.638622i
$584$	−2716.32			−4.65123
$585$		0			0
$586$	−1114.48			−1.90185
$587$		−	7.13211i		−	0.0121501i	−0.999982	−	0.00607505i	$-0.998066\pi$
$587$		−	7.13211i		−	0.0121501i	0.999982	−	0.00607505i	$-0.00193376\pi$
$588$			1700.26i			2.89159i
$589$			195.982i			0.332736i
$590$		0			0
$591$		−	202.627i		−	0.342854i
$592$		−	1223.12i		−	2.06609i
$593$	−705.700			−1.19005			−0.595026	−	0.803707i	$-0.702858\pi$
$593$	−705.700			−1.19005			−0.595026	+	0.803707i	$0.702858\pi$
$594$	148.224	−	99.4444i	0.249536	−	0.167415i
$595$		0			0
$596$			983.180i			1.64963i
$597$		−	996.434i		−	1.66907i
$598$			112.132i			0.187512i
$599$	560.646			0.935970			0.467985	−	0.883737i	$-0.344980\pi$
$599$	560.646			0.935970			0.467985	+	0.883737i	$0.344980\pi$
$600$		0			0
$601$			478.375i			0.795966i	0.917393	+	0.397983i	$0.130290\pi$
$601$			478.375i			0.795966i	−0.917393	+	0.397983i	$0.869710\pi$
$602$	849.297			1.41079
$603$		−	767.856i		−	1.27339i
$604$		−	1902.08i		−	3.14915i
$605$		0			0
$606$	−1603.22			−2.64557
$607$	64.8986			0.106917			0.0534585	−	0.998570i	$-0.482976\pi$
$607$	64.8986			0.106917			0.0534585	+	0.998570i	$0.482976\pi$
$608$			2797.37i			4.60094i
$609$	3.71606			0.00610191
$610$		0			0
$611$		−	221.173i		−	0.361985i
$612$	−63.4687			−0.103707
$613$	−589.680			−0.961958			−0.480979	−	0.876732i	$-0.659719\pi$
$613$	−589.680			−0.961958			−0.480979	+	0.876732i	$0.659719\pi$
$614$	−348.190			−0.567085
$615$		0			0
$616$	581.940	+	867.397i	0.944708	+	1.40811i
$617$		−	409.434i		−	0.663588i	−0.943352	−	0.331794i	$-0.892346\pi$
$617$		−	409.434i		−	0.663588i	0.943352	−	0.331794i	$-0.107654\pi$
$618$	1898.77			3.07244
$619$	239.349			0.386670			0.193335	−	0.981133i	$-0.438070\pi$
$619$	239.349			0.386670			0.193335	+	0.981133i	$0.438070\pi$
$620$		0			0
$621$	−19.0297			−0.0306436
$622$	−1970.24			−3.16759
$623$	10.5017			0.0168567
$624$		−	1639.74i		−	2.62779i
$625$		0			0
$626$		−	1032.31i		−	1.64906i
$627$	528.091	+	787.134i	0.842251	+	1.25540i
$628$		−	488.662i		−	0.778125i
$629$		−	13.9336i		−	0.0221521i
$630$		0			0
$631$	−105.355			−0.166965			−0.0834824	−	0.996509i	$-0.526604\pi$
$631$	−105.355			−0.166965			−0.0834824	+	0.996509i	$0.526604\pi$
$632$			3161.48i			5.00235i
$633$	1253.29			1.97992
$634$			2127.79i			3.35614i
$635$		0			0
$636$	2779.69			4.37057
$637$	−235.281			−0.369359
$638$	−9.30157	+	6.24046i	−0.0145793	+	0.00978128i
$639$	−165.705			−0.259319
$640$		0			0
$641$	161.248			0.251557			0.125779	−	0.992058i	$-0.459857\pi$
$641$	161.248			0.251557			0.125779	+	0.992058i	$0.459857\pi$
$642$			2547.09i			3.96743i
$643$		−	840.772i		−	1.30758i	−0.756678	−	0.653788i	$-0.773179\pi$
$643$		−	840.772i		−	1.30758i	0.756678	−	0.653788i	$-0.226821\pi$
$644$		−	174.085i		−	0.270319i
$645$		0			0
$646$			58.1584i			0.0900284i
$647$		−	547.749i		−	0.846598i	−0.905990	−	0.423299i	$-0.860872\pi$
$647$		−	547.749i		−	0.846598i	0.905990	−	0.423299i	$-0.139128\pi$
$648$	2458.62			3.79417
$649$	289.965	+	432.201i	0.446788	+	0.665949i
$650$		0			0
$651$			132.936i			0.204203i
$652$		−	1932.70i		−	2.96426i
$653$		−	718.762i		−	1.10071i	−0.834932	−	0.550354i	$-0.814493\pi$
$653$		−	718.762i		−	1.10071i	0.834932	−	0.550354i	$-0.185507\pi$
$654$	590.699			0.903209
$655$		0			0
$656$		−	1518.04i		−	2.31409i
$657$	−786.144			−1.19657
$658$			467.093i			0.709867i
$659$			9.21340i			0.0139809i	0.999976	+	0.00699044i	$0.00222515\pi$
$659$			9.21340i			0.0139809i	−0.999976	+	0.00699044i	$0.997775\pi$
$660$		0			0
$661$	298.105			0.450990			0.225495	−	0.974244i	$-0.427600\pi$
$661$	298.105			0.450990			0.225495	+	0.974244i	$0.427600\pi$
$662$	2015.51			3.04457
$663$		−	18.6797i		−	0.0281745i
$664$	3511.66			5.28865
$665$		0			0
$666$		−	604.154i		−	0.907138i
$667$	1.19417			0.00179036
$668$	133.955			0.200532
$669$	818.737			1.22382
$670$		0			0
$671$	990.118	−	664.274i	1.47559	−	0.989976i
$672$			1897.48i			2.82364i
$673$	470.312			0.698829			0.349415	−	0.936968i	$-0.386380\pi$
$673$	470.312			0.698829			0.349415	+	0.936968i	$0.386380\pi$
$674$	89.4326			0.132689
$675$		0			0
$676$	−1431.10			−2.11702
$677$	−395.226			−0.583790			−0.291895	−	0.956450i	$-0.594286\pi$
$677$	−395.226			−0.583790			−0.291895	+	0.956450i	$0.594286\pi$
$678$	1946.63			2.87113
$679$		−	315.221i		−	0.464243i
$680$		0			0
$681$		−	677.020i		−	0.994155i
$682$	−223.243	−	332.749i	−0.327335	−	0.487902i
$683$			356.945i			0.522614i	0.965256	+	0.261307i	$0.0841535\pi$
$683$			356.945i			0.522614i	−0.965256	+	0.261307i	$0.915847\pi$
$684$			1853.77i			2.71019i
$685$		0			0
$686$	1152.09			1.67943
$687$		−	749.885i		−	1.09154i
$688$	−3991.06			−5.80096
$689$			384.653i			0.558277i
$690$		0			0
$691$	−445.935			−0.645348			−0.322674	−	0.946510i	$-0.604582\pi$
$691$	−445.935			−0.645348			−0.322674	+	0.946510i	$0.604582\pi$
$692$	1475.70			2.13251
$693$	168.423	+	251.038i	0.243034	+	0.362249i
$694$	−1537.51			−2.21543
$695$		0			0
$696$	−29.8035			−0.0428211
$697$		−	17.2933i		−	0.0248111i
$698$			1096.58i			1.57103i
$699$			512.071i			0.732576i
$700$		0			0
$701$			1196.50i			1.70684i	0.521222	+	0.853421i	$0.325476\pi$
$701$			1196.50i			1.70684i	−0.521222	+	0.853421i	$0.674524\pi$
$702$			102.739i			0.146352i
$703$	−406.969			−0.578903
$704$	−1646.13	−	2453.59i	−2.33825	−	3.48522i
$705$		0			0
$706$			1031.83i			1.46152i
$707$			344.427i			0.487167i
$708$			2164.86i			3.05771i
$709$	−753.537			−1.06282			−0.531409	−	0.847116i	$-0.678337\pi$
$709$	−753.537			−1.06282			−0.531409	+	0.847116i	$0.678337\pi$
$710$		0			0
$711$			914.983i			1.28690i
$712$	−84.2258			−0.118295
$713$			42.7197i			0.0599154i
$714$			39.4494i			0.0552513i
$715$		0			0
$716$	1472.19			2.05614
$717$	−1147.39			−1.60026
$718$		−	800.583i		−	1.11502i
$719$	815.663			1.13444			0.567220	−	0.823566i	$-0.308019\pi$
$719$	815.663			1.13444			0.567220	+	0.823566i	$0.308019\pi$
$720$		0			0
$721$		−	407.922i		−	0.565773i
$722$	295.802			0.409699
$723$	−1380.32			−1.90915
$724$	257.683			0.355916
$725$		0			0
$726$	−1793.25	−	734.892i	−2.47004	−	1.01225i
$727$			255.827i			0.351895i	0.984400	+	0.175947i	$0.0562988\pi$
$727$			255.827i			0.351895i	−0.984400	+	0.175947i	$0.943701\pi$
$728$	−601.222			−0.825855
$729$	556.676			0.763616
$730$		0			0
$731$	−45.4656			−0.0621965
$732$	4959.42			6.77516
$733$	−354.905			−0.484182			−0.242091	−	0.970254i	$-0.577833\pi$
$733$	−354.905			−0.484182			−0.242091	+	0.970254i	$0.577833\pi$
$734$		−	2349.82i		−	3.20139i
$735$		0			0
$736$			609.765i			0.828485i
$737$	878.202	−	589.189i	1.19159	−	0.799443i
$738$		−	749.827i		−	1.01603i
$739$		−	269.271i		−	0.364372i	−0.983264	−	0.182186i	$-0.941683\pi$
$739$		−	269.271i		−	0.364372i	0.983264	−	0.182186i	$-0.0583174\pi$
$740$		0			0
$741$	−545.589			−0.736287
$742$		−	812.344i		−	1.09480i
$743$	−245.731			−0.330728			−0.165364	−	0.986233i	$-0.552880\pi$
$743$	−245.731			−0.330728			−0.165364	+	0.986233i	$0.552880\pi$
$744$		−	1066.17i		−	1.43303i
$745$		0			0
$746$	961.792			1.28927
$747$	1016.33			1.36055
$748$	−48.7006	−	72.5896i	−0.0651078	−	0.0970449i
$749$	547.204			0.730580
$750$		0			0
$751$	484.753			0.645477			0.322738	−	0.946488i	$-0.395397\pi$
$751$	484.753			0.645477			0.322738	+	0.946488i	$0.395397\pi$
$752$		−	2194.99i		−	2.91886i
$753$		−	742.194i		−	0.985650i
$754$		−	6.44723i		−	0.00855070i
$755$		0			0
$756$		−	159.503i		−	0.210983i
$757$			373.291i			0.493119i	0.969128	+	0.246559i	$0.0793001\pi$
$757$			373.291i			0.493119i	−0.969128	+	0.246559i	$0.920700\pi$
$758$	−1044.25			−1.37764
$759$	115.112	+	171.578i	0.151663	+	0.226058i
$760$		0			0
$761$			503.375i			0.661466i	0.943724	+	0.330733i	$0.107296\pi$
$761$			503.375i			0.661466i	−0.943724	+	0.330733i	$0.892704\pi$
$762$			48.9935i			0.0642959i
$763$		−	126.903i		−	0.166321i
$764$	2947.13			3.85751
$765$		0			0
$766$			785.387i			1.02531i
$767$	−299.573			−0.390577
$768$		−	3717.97i		−	4.84111i
$769$			91.5300i			0.119025i	0.998228	+	0.0595124i	$0.0189546\pi$
$769$			91.5300i			0.119025i	−0.998228	+	0.0595124i	$0.981045\pi$
$770$		0			0
$771$	−190.770			−0.247432
$772$	−2317.65			−3.00214
$773$			1147.94i			1.48504i	0.669823	+	0.742521i	$0.266370\pi$
$773$			1147.94i			1.48504i	−0.669823	+	0.742521i	$0.733630\pi$
$774$	−1971.36			−2.54698
$775$		0			0
$776$			2528.13i			3.25790i
$777$	−276.051			−0.355278
$778$	726.572			0.933898
$779$	−505.097			−0.648391
$780$		0			0
$781$	−127.148	−	189.518i	−0.162802	−	0.242660i
$782$			12.6772i			0.0162113i
$783$	1.09414			0.00139737
$784$	−2335.00			−2.97832
$785$		0			0
$786$	712.617			0.906637
$787$	−275.997			−0.350695			−0.175348	−	0.984507i	$-0.556105\pi$
$787$	−275.997			−0.350695			−0.175348	+	0.984507i	$0.556105\pi$
$788$	545.781			0.692616
$789$			1112.53i			1.41005i
$790$		0			0
$791$		−	418.204i		−	0.528702i
$792$	−1350.78	−	2013.37i	−1.70553	−	2.54214i
$793$			686.284i			0.865428i
$794$		−	1404.01i		−	1.76827i
$795$		0			0
$796$	2683.93			3.37177
$797$		−	191.515i		−	0.240295i	−0.992756	−	0.120147i	$-0.961663\pi$
$797$		−	191.515i		−	0.240295i	0.992756	−	0.120147i	$-0.0383367\pi$
$798$	1152.22			1.44389
$799$		−	25.0050i		−	0.0312953i
$800$		0			0
$801$	−24.3763			−0.0304323
$802$	−2796.50			−3.48691
$803$	−603.223	−	899.119i	−0.751211	−	1.11970i
$804$	4398.84			5.47120
$805$		0			0
$806$	230.640			0.286153
$807$		−	1171.54i		−	1.45172i
$808$		−	2762.36i		−	3.41877i
$809$			92.9030i			0.114837i	0.998350	+	0.0574184i	$0.0182869\pi$
$809$			92.9030i			0.114837i	−0.998350	+	0.0574184i	$0.981713\pi$
$810$		0			0
$811$		−	38.8804i		−	0.0479413i	−0.999713	−	0.0239706i	$-0.992369\pi$
$811$		−	38.8804i		−	0.0479413i	0.999713	−	0.0239706i	$-0.00763082\pi$
$812$			10.0093i			0.0123268i
$813$	−1496.78			−1.84106
$814$	690.975	−	463.578i	0.848864	−	0.569506i
$815$		0			0
$816$		−	185.383i		−	0.227185i
$817$			1327.94i			1.62539i
$818$			1603.97i			1.96084i
$819$	−174.003			−0.212458
$820$		0			0
$821$			766.646i			0.933796i	0.884311	+	0.466898i	$0.154628\pi$
$821$			766.646i			0.933796i	−0.884311	+	0.466898i	$0.845372\pi$
$822$	1206.62			1.46791
$823$		−	160.909i		−	0.195515i	−0.995210	−	0.0977573i	$-0.968833\pi$
$823$		−	160.909i		−	0.195515i	0.995210	−	0.0977573i	$-0.0311669\pi$
$824$			3271.61i			3.97040i
$825$		0			0
$826$	632.665			0.765938
$827$	488.410			0.590581			0.295290	−	0.955408i	$-0.404584\pi$
$827$	488.410			0.590581			0.295290	+	0.955408i	$0.404584\pi$
$828$			404.081i			0.488020i
$829$	−1310.28			−1.58056			−0.790278	−	0.612749i	$-0.790064\pi$
$829$	−1310.28			−1.58056			−0.790278	+	0.612749i	$0.790064\pi$
$830$		0			0
$831$			17.7313i			0.0213373i
$832$	1700.67			2.04407
$833$	−26.6000			−0.0319328
$834$	136.832			0.164067
$835$		0			0
$836$	−2120.17	+	1422.43i	−2.53609	+	1.70147i
$837$			39.1412i			0.0467637i
$838$	1681.81			2.00693
$839$	−728.730			−0.868569			−0.434285	−	0.900776i	$-0.642999\pi$
$839$	−728.730			−0.868569			−0.434285	+	0.900776i	$0.642999\pi$
$840$		0			0
$841$	840.931			0.999918
$842$	148.907			0.176849
$843$	−268.515			−0.318523
$844$			3375.78i			3.99974i
$845$		0			0
$846$		−	1084.20i		−	1.28156i
$847$	−157.881	+	385.252i	−0.186400	+	0.454843i
$848$			3817.41i			4.50166i
$849$		−	1227.82i		−	1.44619i
$850$		0			0
$851$	−88.7102			−0.104242
$852$		−	949.279i		−	1.11418i
$853$	756.332			0.886673			0.443337	−	0.896355i	$-0.353795\pi$
$853$	756.332			0.886673			0.443337	+	0.896355i	$0.353795\pi$
$854$		−	1449.36i		−	1.69714i
$855$		0			0
$856$	−4388.67			−5.12696
$857$	−437.904			−0.510973			−0.255486	−	0.966813i	$-0.582236\pi$
$857$	−437.904			−0.510973			−0.255486	+	0.966813i	$0.582236\pi$
$858$	926.332	−	621.480i	1.07964	−	0.724336i
$859$	8.64857			0.0100682			0.00503409	−	0.999987i	$-0.498398\pi$
$859$	8.64857			0.0100682			0.00503409	+	0.999987i	$0.498398\pi$
$860$		0			0
$861$	−342.612			−0.397923
$862$			2240.96i			2.59972i
$863$		−	134.736i		−	0.156125i	−0.996948	−	0.0780626i	$-0.975127\pi$
$863$		−	134.736i		−	0.156125i	0.996948	−	0.0780626i	$-0.0248734\pi$
$864$			558.688i			0.646629i
$865$		0			0
$866$			497.404i			0.574370i
$867$			1189.01i			1.37140i
$868$	−358.068			−0.412521
$869$	−1046.47	+	702.083i	−1.20423	+	0.807921i
$870$		0			0
$871$			608.711i			0.698865i
$872$			1017.78i			1.16718i
$873$			731.680i			0.838122i
$874$	370.272			0.423652
$875$		0			0
$876$		−	4503.61i		−	5.14111i
$877$	1710.46			1.95036			0.975179	−	0.221420i	$-0.0710692\pi$
$877$	1710.46			1.95036			0.975179	+	0.221420i	$0.0710692\pi$
$878$			1952.56i			2.22388i
$879$		−	1182.01i		−	1.34472i
$880$		0			0
$881$	−70.0218			−0.0794800			−0.0397400	−	0.999210i	$-0.512653\pi$
$881$	−70.0218			−0.0794800			−0.0397400	+	0.999210i	$0.512653\pi$
$882$	−1153.36			−1.30766
$883$			173.732i			0.196753i	0.995149	+	0.0983763i	$0.0313649\pi$
$883$			173.732i			0.196753i	−0.995149	+	0.0983763i	$0.968635\pi$
$884$	50.3143			0.0569166
$885$		0			0
$886$		−	2398.49i		−	2.70710i
$887$	−1416.42			−1.59686			−0.798432	−	0.602085i	$-0.794337\pi$
$887$	−1416.42			−1.59686			−0.798432	+	0.602085i	$0.794337\pi$
$888$	2213.98			2.49322
$889$	10.5255			0.0118397
$890$		0			0
$891$	545.996	+	813.821i	0.612790	+	0.913380i
$892$			2205.29i			2.47230i
$893$	−730.336			−0.817845
$894$	−1418.47			−1.58665
$895$		0			0
$896$	−1750.09			−1.95322
$897$	−118.926			−0.132582
$898$	−1666.57			−1.85587
$899$		−	2.45624i		−	0.00273219i
$900$		0			0
$901$			43.4874i			0.0482657i
$902$	857.582	−	575.355i	0.950756	−	0.637866i
$903$			900.757i			0.997516i
$904$			3354.07i			3.71025i
$905$		0			0
$906$	2744.20			3.02892
$907$		−	900.626i		−	0.992972i	−0.868045	−	0.496486i	$-0.834623\pi$
$907$		−	900.626i		−	0.992972i	0.868045	−	0.496486i	$-0.165377\pi$
$908$	1823.57			2.00834
$909$		−	799.472i		−	0.879507i
$910$		0			0
$911$	−617.866			−0.678228			−0.339114	−	0.940745i	$-0.610127\pi$
$911$	−617.866			−0.678228			−0.339114	+	0.940745i	$0.610127\pi$
$912$	−5414.59			−5.93705
$913$	779.849	+	1162.38i	0.854161	+	1.27315i
$914$	−2337.38			−2.55731
$915$		0			0
$916$	2019.84			2.20507
$917$		−	153.095i		−	0.166952i
$918$			11.6153i			0.0126529i
$919$		−	1434.87i		−	1.56133i	−0.624947	−	0.780667i	$-0.714879\pi$
$919$		−	1434.87i		−	1.56133i	0.624947	−	0.780667i	$-0.285121\pi$
$920$		0			0
$921$		−	369.287i		−	0.400963i
$922$		−	2129.02i		−	2.30914i
$923$	131.361			0.142320
$924$	−1438.13	+	964.849i	−1.55642	+	1.04421i
$925$		0			0
$926$		−	2925.90i		−	3.15971i
$927$			946.854i			1.02142i
$928$		−	35.0595i		−	0.0377796i
$929$	−962.019			−1.03554			−0.517771	−	0.855519i	$-0.673238\pi$
$929$	−962.019			−1.03554			−0.517771	+	0.855519i	$0.673238\pi$
$930$		0			0
$931$			776.924i			0.834505i
$932$	−1379.28			−1.47991
$933$		−	2089.62i		−	2.23968i
$934$			502.787i			0.538316i
$935$		0			0
$936$	1395.54			1.49096
$937$	954.293			1.01846			0.509228	−	0.860632i	$-0.329931\pi$
$937$	954.293			1.01846			0.509228	+	0.860632i	$0.329931\pi$
$938$		−	1285.53i		−	1.37050i
$939$	1094.86			1.16599
$940$		0			0
$941$			34.4712i			0.0366325i	0.999832	+	0.0183163i	$0.00583058\pi$
$941$			34.4712i			0.0366325i	−0.999832	+	0.0183163i	$0.994169\pi$
$942$	705.011			0.748419
$943$	−110.100			−0.116755
$944$	−2973.05			−3.14942
$945$		0			0
$946$	−1512.66	−	2254.66i	−1.59901	−	2.38336i
$947$		−	1448.61i		−	1.52969i	−0.644217	−	0.764843i	$-0.722817\pi$
$947$		−	1448.61i		−	1.52969i	0.644217	−	0.764843i	$-0.277183\pi$
$948$	−5241.70			−5.52922
$949$	623.210			0.656702
$950$		0			0
$951$	−2256.72			−2.37300
$952$	−67.9719			−0.0713991
$953$	1393.91			1.46266			0.731328	−	0.682026i	$-0.238901\pi$
$953$	1393.91			1.46266			0.731328	+	0.682026i	$0.238901\pi$
$954$			1885.58i			1.97650i
$955$		0			0
$956$		−	3090.53i		−	3.23277i
$957$	−6.61857	−	9.86515i	−0.00691596	−	0.0103084i
$958$		−	2502.28i		−	2.61198i
$959$		−	259.225i		−	0.270307i
$960$		0			0
$961$	−873.132			−0.908566
$962$			478.938i			0.497857i
$963$	−1270.15			−1.31895
$964$		−	3717.93i		−	3.85677i
$965$		0			0
$966$	251.159			0.259999
$967$	−733.093			−0.758110			−0.379055	−	0.925374i	$-0.623751\pi$
$967$	−733.093			−0.758110			−0.379055	+	0.925374i	$0.623751\pi$
$968$	1266.23	−	3089.79i	1.30809	−	3.19193i
$969$	−61.6822			−0.0636555
$970$		0			0
$971$	−400.649			−0.412614			−0.206307	−	0.978487i	$-0.566145\pi$
$971$	−400.649			−0.412614			−0.206307	+	0.978487i	$0.566145\pi$
$972$			3659.17i			3.76458i
$973$		−	29.3962i		−	0.0302120i
$974$			1125.18i			1.15522i
$975$		0			0
$976$			6810.89i			6.97837i
$977$			717.785i			0.734683i	0.930086	+	0.367341i	$0.119732\pi$
$977$			717.785i			0.734683i	−0.930086	+	0.367341i	$0.880268\pi$
$978$	2788.37			2.85110
$979$	−18.7043	−	27.8793i	−0.0191056	−	0.0284773i
$980$		0			0
$981$			294.562i			0.300267i
$982$		−	3769.14i		−	3.83823i
$983$			124.372i			0.126523i	0.997997	+	0.0632616i	$0.0201502\pi$
$983$			124.372i			0.126523i	−0.997997	+	0.0632616i	$0.979850\pi$
$984$	2747.81			2.79249
$985$		0			0
$986$		−	0.728899i		−	0.000739249i
$987$	−495.394			−0.501919
$988$		−	1469.56i		−	1.48741i
$989$			289.462i			0.292682i
$990$		0			0
$991$	−224.819			−0.226861			−0.113430	−	0.993546i	$-0.536184\pi$
$991$	−224.819			−0.226861			−0.113430	+	0.993546i	$0.536184\pi$
$992$	1254.20			1.26431
$993$			2137.63i			2.15270i
$994$	−277.420			−0.279095
$995$		0			0
$996$			5822.29i			5.84567i
$997$	1800.12			1.80553			0.902767	−	0.430129i	$-0.141532\pi$
$997$	1800.12			1.80553			0.902767	+	0.430129i	$0.141532\pi$
$998$	−1516.09			−1.51913
$999$	−81.2794			−0.0813607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.d.c.274.1		16
5.2	odd	4		275.3.c.f.76.1		8
5.3	odd	4		55.3.c.a.21.8	yes	8
5.4	even	2	inner	275.3.d.c.274.16		16
11.10	odd	2	inner	275.3.d.c.274.15		16
15.8	even	4		495.3.b.a.406.1		8
20.3	even	4		880.3.j.a.241.2		8
55.32	even	4		275.3.c.f.76.8		8
55.43	even	4		55.3.c.a.21.1	✓	8
55.54	odd	2	inner	275.3.d.c.274.2		16
165.98	odd	4		495.3.b.a.406.8		8
220.43	odd	4		880.3.j.a.241.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.c.a.21.1	✓	8	55.43	even	4
55.3.c.a.21.8	yes	8	5.3	odd	4
275.3.c.f.76.1		8	5.2	odd	4
275.3.c.f.76.8		8	55.32	even	4
275.3.d.c.274.1		16	1.1	even	1	trivial
275.3.d.c.274.2		16	55.54	odd	2	inner
275.3.d.c.274.15		16	11.10	odd	2	inner
275.3.d.c.274.16		16	5.4	even	2	inner
495.3.b.a.406.1		8	15.8	even	4
495.3.b.a.406.8		8	165.98	odd	4
880.3.j.a.241.1		8	220.43	odd	4
880.3.j.a.241.2		8	20.3	even	4

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-3.88606 q^{2} -4.12151i q^{3} +11.1014 q^{4} +16.0164i q^{6} +3.44089 q^{7} -27.5966 q^{8} -7.98688 q^{9} +(-6.12847 - 9.13465i) q^{11} -45.7547i q^{12} +6.33153 q^{13} -13.3715 q^{14} +62.8361 q^{16} +0.715819 q^{17} +31.0375 q^{18} -20.9074i q^{19} -14.1817i q^{21} +(23.8156 + 35.4978i) q^{22} -4.55735i q^{23} +113.740i q^{24} -24.6047 q^{26} -4.17560i q^{27} +38.1988 q^{28} +0.262032i q^{29} -9.37380 q^{31} -133.798 q^{32} +(-37.6486 + 25.2586i) q^{33} -2.78171 q^{34} -88.6658 q^{36} -19.4653i q^{37} +81.2473i q^{38} -26.0955i q^{39} -24.1588i q^{41} +55.1108i q^{42} -63.5155 q^{43} +(-68.0348 - 101.408i) q^{44} +17.7101i q^{46} -34.9319i q^{47} -258.980i q^{48} -37.1603 q^{49} -2.95026i q^{51} +70.2891 q^{52} +60.7519i q^{53} +16.2266i q^{54} -94.9568 q^{56} -86.1701 q^{57} -1.01827i q^{58} -47.3144 q^{59} +108.391i q^{61} +36.4271 q^{62} -27.4820 q^{63} +268.603 q^{64} +(146.304 - 98.1563i) q^{66} +96.1396i q^{67} +7.94662 q^{68} -18.7832 q^{69} +20.7471 q^{71} +220.410 q^{72} +98.4295 q^{73} +75.6433i q^{74} -232.102i q^{76} +(-21.0874 - 31.4313i) q^{77} +101.409i q^{78} -114.561i q^{79} -89.0917 q^{81} +93.8823i q^{82} -127.250 q^{83} -157.437i q^{84} +246.825 q^{86} +1.07997 q^{87} +(169.125 + 252.085i) q^{88} +3.05204 q^{89} +21.7861 q^{91} -50.5931i q^{92} +38.6343i q^{93} +135.748i q^{94} +551.451i q^{96} -91.6103i q^{97} +144.407 q^{98} +(48.9474 + 72.9573i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 56 q^{4} + 8 q^{9} + 16 q^{11} + 176 q^{16} - 200 q^{26} + 72 q^{31} - 160 q^{34} - 432 q^{36} - 24 q^{44} - 344 q^{49} - 160 q^{56} + 32 q^{59} + 1176 q^{64} + 360 q^{66} - 16 q^{69} + 552 q^{71}+ \cdots + 368 q^{99}+O(q^{100}) \) 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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