LMFDB - Embedded newform 275.3.c.f.76.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(76,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.76"); S:= CuspForms(chi, 3); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			76.8
Root			$3.88606i$ of defining polynomial
Character	$\chi$	$=$	275.76
Dual form			275.3.c.f.76.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.88606i q^{2} -4.12151 q^{3} -11.1014 q^{4} -16.0164i q^{6} -3.44089i q^{7} -27.5966i q^{8} +7.98688 q^{9} +(-6.12847 + 9.13465i) q^{11} +45.7547 q^{12} +6.33153i q^{13} +13.3715 q^{14} +62.8361 q^{16} -0.715819i q^{17} +31.0375i q^{18} -20.9074i q^{19} +14.1817i q^{21} +(-35.4978 - 23.8156i) q^{22} -4.55735 q^{23} +113.740i q^{24} -24.6047 q^{26} +4.17560 q^{27} +38.1988i q^{28} +0.262032i q^{29} -9.37380 q^{31} +133.798i q^{32} +(25.2586 - 37.6486i) q^{33} +2.78171 q^{34} -88.6658 q^{36} +19.4653 q^{37} +81.2473 q^{38} -26.0955i q^{39} +24.1588i q^{41} -55.1108 q^{42} -63.5155i q^{43} +(68.0348 - 101.408i) q^{44} -17.7101i q^{46} +34.9319 q^{47} -258.980 q^{48} +37.1603 q^{49} +2.95026i q^{51} -70.2891i q^{52} +60.7519 q^{53} +16.2266i q^{54} -94.9568 q^{56} +86.1701i q^{57} -1.01827 q^{58} +47.3144 q^{59} -108.391i q^{61} -36.4271i q^{62} -27.4820i q^{63} -268.603 q^{64} +(146.304 + 98.1563i) q^{66} -96.1396 q^{67} +7.94662i q^{68} +18.7832 q^{69} +20.7471 q^{71} -220.410i q^{72} +98.4295i q^{73} +75.6433i q^{74} +232.102i q^{76} +(31.4313 + 21.0874i) q^{77} +101.409 q^{78} -114.561i q^{79} -89.0917 q^{81} -93.8823 q^{82} -127.250i q^{83} -157.437i q^{84} +246.825 q^{86} -1.07997i q^{87} +(252.085 + 169.125i) q^{88} -3.05204 q^{89} +21.7861 q^{91} +50.5931 q^{92} +38.6343 q^{93} +135.748i q^{94} -551.451i q^{96} +91.6103 q^{97} +144.407i q^{98} +(-48.9474 + 72.9573i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} - 28 q^{4} - 4 q^{9} + 8 q^{11} + 48 q^{12} + 88 q^{16} - 80 q^{22} - 8 q^{23} - 100 q^{26} + 16 q^{27} + 36 q^{31} + 152 q^{33} + 80 q^{34} - 216 q^{36} + 88 q^{37} + 160 q^{38} - 280 q^{42}+ \cdots - 184 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 - 28 * q^4 - 4 * q^9 + 8 * q^11 + 48 * q^12 + 88 * q^16 - 80 * q^22 - 8 * q^23 - 100 * q^26 + 16 * q^27 + 36 * q^31 + 152 * q^33 + 80 * q^34 - 216 * q^36 + 88 * q^37 + 160 * q^38 - 280 * q^42 + 12 * q^44 + 8 * q^47 - 488 * q^48 + 172 * q^49 + 152 * q^53 - 80 * q^56 - 160 * q^58 - 16 * q^59 - 588 * q^64 + 180 * q^66 + 88 * q^67 + 8 * q^69 + 276 * q^71 - 160 * q^77 - 160 * q^78 - 320 * q^81 + 520 * q^82 + 420 * q^86 + 520 * q^88 + 444 * q^89 - 40 * q^91 + 368 * q^92 + 104 * q^93 - 312 * q^97 - 184 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			3.88606i			1.94303i	0.236982	+	0.971514i	$0.423842\pi$
$2$			3.88606i			1.94303i	−0.236982	+	0.971514i	$0.576158\pi$
$3$	−4.12151			−1.37384			−0.686919	−	0.726734i	$-0.741037\pi$
$3$	−4.12151			−1.37384			−0.686919	+	0.726734i	$0.741037\pi$
$4$	−11.1014			−2.77536
$5$		0			0
$5$		0			0
$6$		−	16.0164i		−	2.66941i
$7$		−	3.44089i		−	0.491556i	−0.969326	−	0.245778i	$-0.920957\pi$
$7$		−	3.44089i		−	0.491556i	0.969326	−	0.245778i	$-0.0790434\pi$
$8$		−	27.5966i		−	3.44957i
$9$	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
$12$	45.7547			3.81289
$13$			6.33153i			0.487041i	0.969896	+	0.243521i	$0.0783023\pi$
$13$			6.33153i			0.487041i	−0.969896	+	0.243521i	$0.921698\pi$
$14$	13.3715			0.955107
$15$		0			0
$16$	62.8361			3.92725
$17$		−	0.715819i		−	0.0421070i	−0.999778	−	0.0210535i	$-0.993298\pi$
$17$		−	0.715819i		−	0.0421070i	0.999778	−	0.0210535i	$-0.00670204\pi$
$18$			31.0375i			1.72430i
$19$		−	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
$22$	−35.4978	−	23.8156i	−1.61353	−	1.08253i
$23$	−4.55735			−0.198146			−0.0990728	−	0.995080i	$-0.531588\pi$
$23$	−4.55735			−0.198146			−0.0990728	+	0.995080i	$0.531588\pi$
$24$			113.740i			4.73915i
$25$		0			0
$26$	−24.6047			−0.946334
$27$	4.17560			0.154652
$28$			38.1988i			1.36424i
$29$			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	$0.548311\pi$
$32$			133.798i			4.18119i
$33$	25.2586	−	37.6486i	0.765412	−	1.14087i
$34$	2.78171			0.0818151
$35$		0			0
$36$	−88.6658			−2.46294
$37$	19.4653			0.526090			0.263045	−	0.964784i	$-0.415273\pi$
$37$	19.4653			0.526090			0.263045	+	0.964784i	$0.415273\pi$
$38$	81.2473			2.13809
$39$		−	26.0955i		−	0.669115i
$40$		0			0
$41$			24.1588i			0.589238i	0.955615	+	0.294619i	$0.0951928\pi$
$41$			24.1588i			0.589238i	−0.955615	+	0.294619i	$0.904807\pi$
$42$	−55.1108			−1.31216
$43$		−	63.5155i		−	1.47710i	−0.674196	−	0.738552i	$-0.735510\pi$
$43$		−	63.5155i		−	1.47710i	0.674196	−	0.738552i	$-0.264490\pi$
$44$	68.0348	−	101.408i	1.54625	−	2.30472i
$45$		0			0
$46$		−	17.7101i		−	0.385002i
$47$	34.9319			0.743233			0.371616	−	0.928386i	$-0.378804\pi$
$47$	34.9319			0.743233			0.371616	+	0.928386i	$0.378804\pi$
$48$	−258.980			−5.39541
$49$	37.1603			0.758373
$50$		0			0
$51$			2.95026i			0.0578482i
$52$		−	70.2891i		−	1.35171i
$53$	60.7519			1.14626			0.573131	−	0.819464i	$-0.305729\pi$
$53$	60.7519			1.14626			0.573131	+	0.819464i	$0.305729\pi$
$54$			16.2266i			0.300493i
$55$		0			0
$56$	−94.9568			−1.69566
$57$			86.1701i			1.51176i
$58$	−1.01827			−0.0175564
$59$	47.3144			0.801940			0.400970	−	0.916091i	$-0.368673\pi$
$59$	47.3144			0.801940			0.400970	+	0.916091i	$0.368673\pi$
$60$		0			0
$61$		−	108.391i		−	1.77691i	−0.458965	−	0.888455i	$-0.651780\pi$
$61$		−	108.391i		−	1.77691i	0.458965	−	0.888455i	$-0.348220\pi$
$62$		−	36.4271i		−	0.587534i
$63$		−	27.4820i		−	0.436222i
$64$	−268.603			−4.19692
$65$		0			0
$66$	146.304	+	98.1563i	2.21673	+	1.48722i
$67$	−96.1396			−1.43492			−0.717460	−	0.696600i	$-0.754695\pi$
$67$	−96.1396			−1.43492			−0.717460	+	0.696600i	$0.754695\pi$
$68$			7.94662i			0.116862i
$69$	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	$0.453326\pi$
$72$		−	220.410i		−	3.06125i
$73$			98.4295i			1.34835i	0.738572	+	0.674175i	$0.235501\pi$
$73$			98.4295i			1.34835i	−0.738572	+	0.674175i	$0.764499\pi$
$74$			75.6433i			1.02221i
$75$		0			0
$76$			232.102i			3.05397i
$77$	31.4313	+	21.0874i	0.408199	+	0.273863i
$78$	101.409			1.30011
$79$		−	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
$82$	−93.8823			−1.14491
$83$		−	127.250i		−	1.53313i	−0.642165	−	0.766567i	$-0.721963\pi$
$83$		−	127.250i		−	1.53313i	0.642165	−	0.766567i	$-0.278037\pi$
$84$		−	157.437i		−	1.87425i
$85$		0			0
$86$	246.825			2.87006
$87$		−	1.07997i		−	0.0124135i
$88$	252.085	+	169.125i	2.86460	+	1.92187i
$89$	−3.05204			−0.0342926			−0.0171463	−	0.999853i	$-0.505458\pi$
$89$	−3.05204			−0.0342926			−0.0171463	+	0.999853i	$0.505458\pi$
$90$		0			0
$91$	21.7861			0.239408
$92$	50.5931			0.549925
$93$	38.6343			0.415422
$94$			135.748i			1.44412i
$95$		0			0
$96$		−	551.451i		−	5.74428i
$97$	91.6103			0.944436			0.472218	−	0.881482i	$-0.343453\pi$
$97$	91.6103			0.944436			0.472218	+	0.881482i	$0.343453\pi$
$98$			144.407i			1.47354i
$99$	−48.9474	+	72.9573i	−0.494418	+	0.736943i
$100$		0			0
$101$		−	100.098i		−	0.991071i	−0.868588	−	0.495535i	$-0.834972\pi$
$101$		−	100.098i		−	0.991071i	0.868588	−	0.495535i	$-0.165028\pi$
$102$	−11.4649			−0.112401
$103$	−118.551			−1.15098			−0.575491	−	0.817808i	$-0.695189\pi$
$103$	−118.551			−1.15098			−0.575491	+	0.817808i	$0.695189\pi$
$104$	174.729			1.68008
$105$		0			0
$106$			236.085i			2.22722i
$107$		−	159.030i		−	1.48626i	−0.669148	−	0.743130i	$-0.733341\pi$
$107$		−	159.030i		−	1.48626i	0.669148	−	0.743130i	$-0.266659\pi$
$108$	−46.3551			−0.429214
$109$		−	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
$112$		−	216.212i		−	1.93047i
$113$	−121.539			−1.07557			−0.537784	−	0.843082i	$-0.680739\pi$
$113$	−121.539			−1.07557			−0.537784	+	0.843082i	$0.680739\pi$
$114$	−334.862			−2.93738
$115$		0			0
$116$		−	2.90894i		−	0.0250770i
$117$			50.5692i			0.432215i
$118$			183.867i			1.55819i
$119$	−2.46306			−0.0206980
$120$		0			0
$121$	−45.8836	−	111.963i	−0.379203	−	0.925313i
$122$	421.215			3.45258
$123$		−	99.5707i		−	0.809518i
$124$	104.063			0.839215
$125$		0			0
$126$	106.797			0.847592
$127$		−	3.05895i		−	0.0240862i	−0.999927	−	0.0120431i	$-0.996166\pi$
$127$		−	3.05895i		−	0.0240862i	0.999927	−	0.0120431i	$-0.00383354\pi$
$128$		−	508.614i		−	3.97354i
$129$			261.780i			2.02930i
$130$		0			0
$131$			44.4928i			0.339640i	0.985475	+	0.169820i	$0.0543186\pi$
$131$			44.4928i			0.339640i	−0.985475	+	0.169820i	$0.945681\pi$
$132$	−280.407	+	417.953i	−2.12429	+	3.16631i
$133$	−71.9401			−0.540903
$134$		−	373.604i		−	2.78809i
$135$		0			0
$136$	−19.7542			−0.145251
$137$	75.3365			0.549902			0.274951	−	0.961458i	$-0.411338\pi$
$137$	75.3365			0.549902			0.274951	+	0.961458i	$0.411338\pi$
$138$			72.9924i			0.528931i
$139$		−	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
$142$			80.6245i			0.567778i
$143$	−57.8363	−	38.8026i	−0.404450	−	0.271347i
$144$	501.864			3.48517
$145$		0			0
$146$	−382.503			−2.61988
$147$	−153.157			−1.04188
$148$	−216.093			−1.46009
$149$			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	$0.192028\pi$
$151$			171.337i			1.13468i	−0.823483	+	0.567340i	$0.807972\pi$
$152$	−576.972			−3.79587
$153$		−	5.71716i		−	0.0373671i
$154$	−81.9469	+	122.144i	−0.532123	+	0.793143i
$155$		0			0
$156$			289.697i			1.85703i
$157$	44.0180			0.280369			0.140185	−	0.990125i	$-0.455230\pi$
$157$	44.0180			0.280369			0.140185	+	0.990125i	$0.455230\pi$
$158$	445.190			2.81766
$159$	−250.390			−1.57478
$160$		0			0
$161$			15.6813i			0.0973996i
$162$		−	346.215i		−	2.13713i
$163$	−174.094			−1.06806			−0.534032	−	0.845464i	$-0.679324\pi$
$163$	−174.094			−1.06806			−0.534032	+	0.845464i	$0.679324\pi$
$164$		−	268.197i		−	1.63535i
$165$		0			0
$166$	494.501			2.97892
$167$		−	12.0665i		−	0.0722544i	−0.999347	−	0.0361272i	$-0.988498\pi$
$167$		−	12.0665i		−	0.0722544i	0.999347	−	0.0361272i	$-0.0115021\pi$
$168$	391.366			2.32956
$169$	128.912			0.762791
$170$		0			0
$171$		−	166.985i		−	0.976519i
$172$			705.113i			4.09949i
$173$			132.929i			0.768374i	0.923255	+	0.384187i	$0.125518\pi$
$173$			132.929i			0.768374i	−0.923255	+	0.384187i	$0.874482\pi$
$174$	4.19683			0.0241197
$175$		0			0
$176$	−385.089	+	573.985i	−2.18801	+	3.26128i
$177$	−195.007			−1.10174
$178$		−	11.8604i		−	0.0666314i
$179$	−132.613			−0.740855			−0.370427	−	0.928861i	$-0.620789\pi$
$179$	−132.613			−0.740855			−0.370427	+	0.928861i	$0.620789\pi$
$180$		0			0
$181$	23.2117			0.128241			0.0641207	−	0.997942i	$-0.479576\pi$
$181$	23.2117			0.128241			0.0641207	+	0.997942i	$0.479576\pi$
$182$			84.6621i			0.465176i
$183$			446.737i			2.44119i
$184$			125.767i			0.683517i
$185$		0			0
$186$			150.135i			0.807177i
$187$	6.53876	+	4.38688i	0.0349666	+	0.0234593i
$188$	−387.795			−2.06274
$189$		−	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	$0.255424\pi$
$192$	1107.05			5.76589
$193$		−	208.771i		−	1.08171i	−0.841115	−	0.540856i	$-0.818100\pi$
$193$		−	208.771i		−	1.08171i	0.841115	−	0.540856i	$-0.181900\pi$
$194$			356.003i			1.83507i
$195$		0			0
$196$	−412.532			−2.10476
$197$		−	49.1632i		−	0.249559i	−0.992184	−	0.124780i	$-0.960178\pi$
$197$		−	49.1632i		−	0.249559i	0.992184	−	0.124780i	$-0.0398224\pi$
$198$	−283.516	−	190.212i	−1.43190	−	0.960668i
$199$	−241.764			−1.21490			−0.607448	−	0.794360i	$-0.707806\pi$
$199$	−241.764			−1.21490			−0.607448	+	0.794360i	$0.707806\pi$
$200$		0			0
$201$	396.241			1.97135
$202$	388.987			1.92568
$203$	0.901626			0.00444151
$204$		−	32.7521i		−	0.160550i
$205$		0			0
$206$		−	460.697i		−	2.23639i
$207$	−36.3990			−0.175840
$208$			397.849i			1.91273i
$209$	190.982	+	128.130i	0.913788	+	0.613064i
$210$		0			0
$211$		−	304.085i		−	1.44116i	−0.693371	−	0.720581i	$-0.743875\pi$
$211$		−	304.085i		−	1.44116i	0.693371	−	0.720581i	$-0.256125\pi$
$212$	−674.433			−3.18129
$213$	−85.5096			−0.401454
$214$	617.998			2.88784
$215$		0			0
$216$		−	115.232i		−	0.533482i
$217$			32.2542i			0.148637i
$218$	143.321			0.657435
$219$		−	405.679i		−	1.85241i
$220$		0			0
$221$	4.53223			0.0205078
$222$		−	311.765i		−	1.40435i
$223$	198.650			0.890805			0.445403	−	0.895330i	$-0.353061\pi$
$223$	198.650			0.890805			0.445403	+	0.895330i	$0.353061\pi$
$224$	460.385			2.05529
$225$		0			0
$226$		−	472.308i		−	2.08986i
$227$		−	164.265i		−	0.723634i	−0.932249	−	0.361817i	$-0.882157\pi$
$227$		−	164.265i		−	0.723634i	0.932249	−	0.361817i	$-0.117843\pi$
$228$		−	956.611i		−	4.19566i
$229$	−181.944			−0.794516			−0.397258	−	0.917707i	$-0.630038\pi$
$229$	−181.944			−0.794516			−0.397258	+	0.917707i	$0.630038\pi$
$230$		0			0
$231$	−129.545	−	86.9121i	−0.560800	−	0.376243i
$232$	7.23120			0.0311689
$233$		−	124.243i		−	0.533233i	−0.963803	−	0.266617i	$-0.914094\pi$
$233$		−	124.243i		−	0.533233i	0.963803	−	0.266617i	$-0.0859057\pi$
$234$	−196.515			−0.839806
$235$		0			0
$236$	−525.258			−2.22567
$237$			472.164i			1.99225i
$238$		−	9.57158i		−	0.0402167i
$239$		−	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	$0.244518\pi$
$241$			334.905i			1.38965i	−0.719180	+	0.694824i	$0.755482\pi$
$242$	435.094	−	178.306i	1.79791	−	0.736803i
$243$	329.612			1.35643
$244$			1203.30i			4.93156i
$245$		0			0
$246$	386.937			1.57292
$247$	132.376			0.535935
$248$			258.685i			1.04308i
$249$			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	$0.383213\pi$
$252$			305.089i			1.21067i
$253$	27.9296	−	41.6298i	0.110394	−	0.164545i
$254$	11.8873			0.0468002
$255$		0			0
$256$	902.089			3.52379
$257$	46.2863			0.180102			0.0900512	−	0.995937i	$-0.471297\pi$
$257$	46.2863			0.180102			0.0900512	+	0.995937i	$0.471297\pi$
$258$	−1017.29			−3.94299
$259$		−	66.9781i		−	0.258603i
$260$		0			0
$261$			2.09282i			0.00801847i
$262$	−172.902			−0.659930
$263$		−	269.933i		−	1.02636i	−0.858281	−	0.513180i	$-0.828467\pi$
$263$		−	269.933i		−	1.02636i	0.858281	−	0.513180i	$-0.171533\pi$
$264$	−1038.97	−	697.050i	−3.93550	−	2.64034i
$265$		0			0
$266$		−	279.563i		−	1.05099i
$267$	12.5790			0.0471124
$268$	1067.29			3.98242
$269$	−284.250			−1.05669			−0.528346	−	0.849029i	$-0.677187\pi$
$269$	−284.250			−1.05669			−0.528346	+	0.849029i	$0.677187\pi$
$270$		0			0
$271$			363.163i			1.34008i	0.742323	+	0.670042i	$0.233724\pi$
$271$			363.163i			1.34008i	−0.742323	+	0.670042i	$0.766276\pi$
$272$		−	44.9793i		−	0.165365i
$273$	−89.7918			−0.328908
$274$			292.762i			1.06847i
$275$		0			0
$276$	−208.520			−0.755507
$277$			4.30214i			0.0155312i	0.999970	+	0.00776559i	$0.00247189\pi$
$277$			4.30214i			0.0155312i	−0.999970	+	0.00776559i	$0.997528\pi$
$278$	33.1994			0.119422
$279$	−74.8674			−0.268342
$280$		0			0
$281$			65.1496i			0.231849i	0.993258	+	0.115925i	$0.0369831\pi$
$281$			65.1496i			0.231849i	−0.993258	+	0.115925i	$0.963017\pi$
$282$		−	559.485i		−	1.98399i
$283$			297.904i			1.05267i	0.850279	+	0.526333i	$0.176433\pi$
$283$			297.904i			1.05267i	−0.850279	+	0.526333i	$0.823567\pi$
$284$	−230.323			−0.810996
$285$		0			0
$286$	150.789	−	224.755i	0.527235	−	0.785857i
$287$	83.1277			0.289644
$288$			1068.63i			3.71052i
$289$	288.488			0.998227
$290$		0			0
$291$	−377.573			−1.29750
$292$		−	1092.71i		−	3.74215i
$293$			286.790i			0.978805i	0.872058	+	0.489402i	$0.162785\pi$
$293$			286.790i			0.978805i	−0.872058	+	0.489402i	$0.837215\pi$
$294$		−	595.175i		−	2.02440i
$295$		0			0
$296$		−	537.176i		−	1.81478i
$297$	−25.5900	+	38.1426i	−0.0861618	+	0.128426i
$298$	−344.162			−1.15491
$299$		−	28.8550i		−	0.0965050i
$300$		0			0
$301$	−218.550			−0.726080
$302$	−665.824			−2.20472
$303$			412.556i			1.36157i
$304$		−	1313.74i		−	4.32151i
$305$		0			0
$306$	22.2172			0.0726053
$307$		−	89.5999i		−	0.291856i	−0.989295	−	0.145928i	$-0.953383\pi$
$307$		−	89.5999i		−	0.291856i	0.989295	−	0.145928i	$-0.0466168\pi$
$308$	−348.933	−	234.101i	−1.13290	−	0.760067i
$309$	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	$0.196672\pi$
$312$	−720.146			−2.30816
$313$	265.646			0.848708			0.424354	−	0.905496i	$-0.360501\pi$
$313$	265.646			0.848708			0.424354	+	0.905496i	$0.360501\pi$
$314$			171.056i			0.544765i
$315$		0			0
$316$			1271.79i			4.02465i
$317$	547.546			1.72727			0.863637	−	0.504114i	$-0.168181\pi$
$317$	547.546			1.72727			0.863637	+	0.504114i	$0.168181\pi$
$318$		−	973.029i		−	3.05984i
$319$	−2.39357	−	1.60586i	−0.00750337	−	0.00503404i
$320$		0			0
$321$			655.443i			2.04188i
$322$	−60.9386			−0.189250
$323$	−14.9659			−0.0463341
$324$	989.045			3.05261
$325$		0			0
$326$		−	676.541i		−	2.07528i
$327$			152.005i			0.464846i
$328$	666.699			2.03262
$329$		−	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	$0.786547\pi$
$332$			1412.66i			4.25499i
$333$	155.467			0.466868
$334$	46.8910			0.140392
$335$		0			0
$336$			891.121i			2.65215i
$337$			23.0137i			0.0682900i	0.999417	+	0.0341450i	$0.0108708\pi$
$337$			23.0137i			0.0682900i	−0.999417	+	0.0341450i	$0.989129\pi$
$338$			500.958i			1.48212i
$339$	500.926			1.47766
$340$		0			0
$341$	57.4471	−	85.6264i	0.168467	−	0.251104i
$342$	648.912			1.89740
$343$		−	296.468i		−	0.864339i
$344$	−1752.81			−5.09537
$345$		0			0
$346$	−516.569			−1.49297
$347$		−	395.647i		−	1.14019i	−0.821578	−	0.570096i	$-0.806906\pi$
$347$		−	395.647i		−	1.14019i	0.821578	−	0.570096i	$-0.193094\pi$
$348$			11.9892i			0.0344518i
$349$		−	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
$352$	−1222.20	−	819.979i	−3.47216	−	2.32948i
$353$	−265.522			−0.752186			−0.376093	−	0.926582i	$-0.622733\pi$
$353$	−265.522			−0.752186			−0.376093	+	0.926582i	$0.622733\pi$
$354$		−	757.809i		−	2.14070i
$355$		0			0
$356$	33.8820			0.0951742
$357$	10.1515			0.0284356
$358$		−	515.342i		−	1.43950i
$359$			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
$362$			90.2019i			0.249177i
$363$	189.110	+	461.457i	0.520964	+	1.27123i
$364$	−241.857			−0.664443
$365$		0			0
$366$	−1736.04			−4.74329
$367$	−604.681			−1.64763			−0.823816	−	0.566858i	$-0.808159\pi$
$367$	−604.681			−1.64763			−0.823816	+	0.566858i	$0.808159\pi$
$368$	−286.366			−0.778168
$369$			192.953i			0.522908i
$370$		0			0
$371$		−	209.041i		−	0.563452i
$372$	−428.896			−1.15295
$373$		−	247.498i		−	0.663534i	−0.943361	−	0.331767i	$-0.892355\pi$
$373$		−	247.498i		−	0.663534i	0.943361	−	0.331767i	$-0.107645\pi$
$374$	−17.0477	+	25.4100i	−0.0455820	+	0.0679411i
$375$		0			0
$376$		−	964.002i		−	2.56383i
$377$	−1.65907			−0.00440071
$378$	55.8340			0.147709
$379$	−268.717			−0.709016			−0.354508	−	0.935053i	$-0.615352\pi$
$379$	−268.717			−0.709016			−0.354508	+	0.935053i	$0.615352\pi$
$380$		0			0
$381$			12.6075i			0.0330906i
$382$			1031.64i			2.70064i
$383$	−202.104			−0.527687			−0.263843	−	0.964566i	$-0.584990\pi$
$383$	−202.104			−0.527687			−0.263843	+	0.964566i	$0.584990\pi$
$384$			2096.26i			5.45901i
$385$		0			0
$386$	811.294			2.10180
$387$		−	507.290i		−	1.31083i
$388$	−1017.01			−2.62115
$389$	186.969			0.480640			0.240320	−	0.970694i	$-0.422748\pi$
$389$	186.969			0.480640			0.240320	+	0.970694i	$0.422748\pi$
$390$		0			0
$391$			3.26224i			0.00834332i
$392$		−	1025.50i		−	2.61606i
$393$		−	183.378i		−	0.466610i
$394$	191.051			0.484900
$395$		0			0
$396$	543.386	−	809.931i	1.37219	−	2.04528i
$397$	−361.294			−0.910061			−0.455030	−	0.890476i	$-0.650372\pi$
$397$	−361.294			−0.910061			−0.455030	+	0.890476i	$0.650372\pi$
$398$		−	939.509i		−	2.36058i
$399$	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	$0.145535\pi$
$402$			1539.81i			3.83038i
$403$		−	59.3505i		−	0.147272i
$404$			1111.23i			2.75058i
$405$		0			0
$406$			3.50377i			0.00862997i
$407$	−119.293	+	177.809i	−0.293102	+	0.436877i
$408$	81.4170			0.199551
$409$		−	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
$412$	1316.09			3.19439
$413$		−	162.804i		−	0.394198i
$414$		−	141.448i		−	0.341663i
$415$		0			0
$416$	−847.148			−2.03641
$417$			35.2109i			0.0844387i
$418$	−497.922	+	742.165i	−1.19120	+	1.77552i
$419$	432.780			1.03289			0.516444	−	0.856321i	$-0.327255\pi$
$419$	432.780			1.03289			0.516444	+	0.856321i	$0.327255\pi$
$420$		0			0
$421$	−38.3182			−0.0910172			−0.0455086	−	0.998964i	$-0.514491\pi$
$421$	−38.3182			−0.0910172			−0.0455086	+	0.998964i	$0.514491\pi$
$422$	1181.69			2.80022
$423$	278.997			0.659568
$424$		−	1676.54i		−	3.95411i
$425$		0			0
$426$		−	332.295i		−	0.780036i
$427$	−372.963			−0.873450
$428$			1765.46i			4.12490i
$429$	238.373	+	159.926i	0.555649	+	0.372787i
$430$		0			0
$431$			576.666i			1.33797i	0.743275	+	0.668986i	$0.233272\pi$
$431$			576.666i			1.33797i	−0.743275	+	0.668986i	$0.766728\pi$
$432$	262.378			0.607357
$433$	−127.997			−0.295606			−0.147803	−	0.989017i	$-0.547220\pi$
$433$	−127.997			−0.295606			−0.147803	+	0.989017i	$0.547220\pi$
$434$	−125.342			−0.288806
$435$		0			0
$436$			409.429i			0.939058i
$437$			95.2822i			0.218037i
$438$	1576.49			3.59929
$439$		−	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
$442$			17.6125i			0.0398473i
$443$	617.205			1.39324			0.696619	−	0.717441i	$-0.254687\pi$
$443$	617.205			1.39324			0.696619	+	0.717441i	$0.254687\pi$
$444$	890.630			2.00592
$445$		0			0
$446$			771.963i			1.73086i
$447$		−	365.015i		−	0.816589i
$448$			924.234i			2.06302i
$449$	−428.860			−0.955145			−0.477572	−	0.878592i	$-0.658483\pi$
$449$	−428.860			−0.955145			−0.477572	+	0.878592i	$0.658483\pi$
$450$		0			0
$451$	−220.682	−	148.056i	−0.489317	−	0.328285i
$452$	1349.26			2.98509
$453$		−	706.167i		−	1.55887i
$454$	638.342			1.40604
$455$		0			0
$456$	2378.00			5.21491
$457$		−	601.480i		−	1.31615i	−0.752953	−	0.658074i	$-0.771371\pi$
$457$		−	601.480i		−	1.31615i	0.752953	−	0.658074i	$-0.228629\pi$
$458$		−	707.045i		−	1.54377i
$459$		−	2.98897i		−	0.00651193i
$460$		0			0
$461$		−	547.862i		−	1.18842i	−0.804309	−	0.594211i	$-0.797465\pi$
$461$		−	547.862i		−	1.18842i	0.804309	−	0.594211i	$-0.202535\pi$
$462$	337.745	−	503.418i	0.731050	−	1.08965i
$463$	752.922			1.62618			0.813090	−	0.582138i	$-0.197784\pi$
$463$	752.922			1.62618			0.813090	+	0.582138i	$0.197784\pi$
$464$			16.4651i			0.0354851i
$465$		0			0
$466$	482.817			1.03609
$467$	129.382			0.277050			0.138525	−	0.990359i	$-0.455764\pi$
$467$	129.382			0.277050			0.138525	+	0.990359i	$0.455764\pi$
$468$		−	561.390i		−	1.19955i
$469$			330.806i			0.705344i
$470$		0			0
$471$	−181.421			−0.385182
$472$		−	1305.72i		−	2.76635i
$473$	580.192	+	389.253i	1.22662	+	0.822945i
$474$	−1834.86			−3.87100
$475$		0			0
$476$	27.3435			0.0574443
$477$	485.218			1.01723
$478$	1081.84			2.26326
$479$			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
$482$	−1301.46			−2.70012
$483$		−	64.6309i		−	0.133811i
$484$	509.374	+	1242.95i	1.05243	+	2.56808i
$485$		0			0
$486$			1280.89i			2.63558i
$487$	289.544			0.594546			0.297273	−	0.954793i	$-0.403923\pi$
$487$	289.544			0.594546			0.297273	+	0.954793i	$0.403923\pi$
$488$	−2991.23			−6.12957
$489$	717.533			1.46735
$490$		0			0
$491$		−	969.915i		−	1.97539i	−0.156404	−	0.987693i	$-0.549990\pi$
$491$		−	969.915i		−	1.97539i	0.156404	−	0.987693i	$-0.450010\pi$
$492$			1105.38i			2.24670i
$493$	0.187568			0.000380462
$494$			514.420i			1.04134i
$495$		0			0
$496$	−589.013			−1.18753
$497$		−	71.3887i		−	0.143639i
$498$	−2038.09			−4.09256
$499$	−390.136			−0.781836			−0.390918	−	0.920426i	$-0.627842\pi$
$499$	−390.136			−0.781836			−0.390918	+	0.920426i	$0.627842\pi$
$500$		0			0
$501$			49.7322i			0.0992658i
$502$			699.793i			1.39401i
$503$		−	40.1337i		−	0.0797888i	−0.999204	−	0.0398944i	$-0.987298\pi$
$503$		−	40.1337i		−	0.0797888i	0.999204	−	0.0398944i	$-0.0127021\pi$
$504$	−758.408			−1.50478
$505$		0			0
$506$	161.776	+	108.536i	0.319715	+	0.214498i
$507$	−531.311			−1.04795
$508$			33.9587i			0.0668479i
$509$	−655.246			−1.28732			−0.643660	−	0.765312i	$-0.722585\pi$
$509$	−655.246			−1.28732			−0.643660	+	0.765312i	$0.722585\pi$
$510$		0			0
$511$	338.685			0.662789
$512$			1471.11i			2.87327i
$513$		−	87.3009i		−	0.170177i
$514$			179.871i			0.349944i
$515$		0			0
$516$		−	2906.13i		−	5.63204i
$517$	−214.080	+	319.091i	−0.414080	+	0.617197i
$518$	260.281			0.502472
$519$		−	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	$0.674913\pi$
$522$	−8.13282			−0.0155801
$523$			912.634i			1.74500i	0.488616	+	0.872499i	$0.337502\pi$
$523$			912.634i			1.74500i	−0.488616	+	0.872499i	$0.662498\pi$
$524$		−	493.934i		−	0.942623i
$525$		0			0
$526$	1048.97			1.99425
$527$			6.70995i			0.0127324i
$528$	1587.15	−	2365.69i	3.00597	−	4.48047i
$529$	−508.231			−0.960738
$530$		0			0
$531$	377.895			0.711666
$532$	798.638			1.50120
$533$	−152.962			−0.286983
$534$			48.8828i			0.0915408i
$535$		0			0
$536$			2653.12i			4.94986i
$537$	546.566			1.01781
$538$		−	1104.61i		−	2.05318i
$539$	−227.736	+	339.446i	−0.422515	+	0.629770i
$540$		0			0
$541$			344.689i			0.637134i	0.947900	+	0.318567i	$0.103202\pi$
$541$			344.689i			0.637134i	−0.947900	+	0.318567i	$0.896798\pi$
$542$	−1411.27			−2.60382
$543$	−95.6673			−0.176183
$544$	95.7753			0.176058
$545$		0			0
$546$		−	348.936i		−	0.639077i
$547$		−	163.700i		−	0.299268i	−0.988741	−	0.149634i	$-0.952190\pi$
$547$		−	163.700i		−	0.299268i	0.988741	−	0.149634i	$-0.0478096\pi$
$548$	−836.343			−1.52617
$549$		−	865.709i		−	1.57688i
$550$		0			0
$551$	5.47841			0.00994268
$552$		−	518.351i		−	0.939041i
$553$	−394.192			−0.712824
$554$	−16.7183			−0.0301775
$555$		0			0
$556$			94.8418i			0.170579i
$557$			912.056i			1.63744i	0.574190	+	0.818722i	$0.305317\pi$
$557$			912.056i			1.63744i	−0.574190	+	0.818722i	$0.694683\pi$
$558$		−	290.939i		−	0.521396i
$559$	402.150			0.719410
$560$		0			0
$561$	−26.9496	−	18.0806i	−0.0480385	−	0.0322292i
$562$	−253.175			−0.450489
$563$			225.781i			0.401031i	0.979690	+	0.200516i	$0.0642618\pi$
$563$			225.781i			0.401031i	−0.979690	+	0.200516i	$0.935738\pi$
$564$	1598.30			2.83387
$565$		0			0
$566$	−1157.67			−2.04536
$567$			306.555i			0.540661i
$568$		−	572.550i		−	1.00801i
$569$		−	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	$0.0915556\pi$
$571$			323.963i			0.567362i	−0.958919	+	0.283681i	$0.908444\pi$
$572$	642.066	+	430.765i	1.12249	+	0.753085i
$573$	−1094.15			−1.90951
$574$			323.039i			0.562786i
$575$		0			0
$576$	−2145.30			−3.72448
$577$	−851.342			−1.47546			−0.737731	−	0.675095i	$-0.764103\pi$
$577$	−851.342			−1.47546			−0.737731	+	0.675095i	$0.764103\pi$
$578$			1121.08i			1.93958i
$579$			860.451i			1.48610i
$580$		0			0
$581$	−437.854			−0.753621
$582$		−	1467.27i		−	2.52108i
$583$	−372.316	+	554.947i	−0.638622	+	0.951882i
$584$	2716.32			4.65123
$585$		0			0
$586$	−1114.48			−1.90185
$587$	7.13211			0.0121501			0.00607505	−	0.999982i	$-0.498066\pi$
$587$	7.13211			0.0121501			0.00607505	+	0.999982i	$0.498066\pi$
$588$	1700.26			2.89159
$589$			195.982i			0.332736i
$590$		0			0
$591$			202.627i			0.342854i
$592$	1223.12			2.06609
$593$		−	705.700i		−	1.19005i	−0.803707	−	0.595026i	$-0.797142\pi$
$593$		−	705.700i		−	1.19005i	0.803707	−	0.595026i	$-0.202858\pi$
$594$	−148.224	−	99.4444i	−0.249536	−	0.167415i
$595$		0			0
$596$		−	983.180i		−	1.64963i
$597$	996.434			1.66907
$598$	112.132			0.187512
$599$	−560.646			−0.935970			−0.467985	−	0.883737i	$-0.655020\pi$
$599$	−560.646			−0.935970			−0.467985	+	0.883737i	$0.655020\pi$
$600$		0			0
$601$		−	478.375i		−	0.795966i	−0.917393	−	0.397983i	$-0.869710\pi$
$601$		−	478.375i		−	0.795966i	0.917393	−	0.397983i	$-0.130290\pi$
$602$		−	849.297i		−	1.41079i
$603$	−767.856			−1.27339
$604$		−	1902.08i		−	3.14915i
$605$		0			0
$606$	−1603.22			−2.64557
$607$		−	64.8986i		−	0.106917i	−0.998570	−	0.0534585i	$-0.982976\pi$
$607$		−	64.8986i		−	0.106917i	0.998570	−	0.0534585i	$-0.0170245\pi$
$608$	2797.37			4.60094
$609$	−3.71606			−0.00610191
$610$		0			0
$611$			221.173i			0.361985i
$612$			63.4687i			0.103707i
$613$		−	589.680i		−	0.961958i	−0.876732	−	0.480979i	$-0.840281\pi$
$613$		−	589.680i		−	0.961958i	0.876732	−	0.480979i	$-0.159719\pi$
$614$	348.190			0.567085
$615$		0			0
$616$	581.940	−	867.397i	0.944708	−	1.40811i
$617$	409.434			0.663588			0.331794	−	0.943352i	$-0.392346\pi$
$617$	409.434			0.663588			0.331794	+	0.943352i	$0.392346\pi$
$618$			1898.77i			3.07244i
$619$	−239.349			−0.386670			−0.193335	−	0.981133i	$-0.561930\pi$
$619$	−239.349			−0.386670			−0.193335	+	0.981133i	$0.561930\pi$
$620$		0			0
$621$	−19.0297			−0.0306436
$622$			1970.24i			3.16759i
$623$			10.5017i			0.0168567i
$624$		−	1639.74i		−	2.62779i
$625$		0			0
$626$			1032.31i			1.64906i
$627$	−787.134	−	528.091i	−1.25540	−	0.842251i
$628$	−488.662			−0.778125
$629$		−	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	$0.526604\pi$
$632$	−3161.48			−5.00235
$633$			1253.29i			1.97992i
$634$			2127.79i			3.35614i
$635$		0			0
$636$	2779.69			4.37057
$637$			235.281i			0.369359i
$638$	6.24046	−	9.30157i	0.00978128	−	0.0145793i
$639$	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	$0.459857\pi$
$642$	−2547.09			−3.96743
$643$	−840.772			−1.30758			−0.653788	−	0.756678i	$-0.726821\pi$
$643$	−840.772			−1.30758			−0.653788	+	0.756678i	$0.726821\pi$
$644$		−	174.085i		−	0.270319i
$645$		0			0
$646$		−	58.1584i		−	0.0900284i
$647$	547.749			0.846598			0.423299	−	0.905990i	$-0.360872\pi$
$647$	547.749			0.846598			0.423299	+	0.905990i	$0.360872\pi$
$648$			2458.62i			3.79417i
$649$	−289.965	+	432.201i	−0.446788	+	0.665949i
$650$		0			0
$651$		−	132.936i		−	0.204203i
$652$	1932.70			2.96426
$653$	−718.762			−1.10071			−0.550354	−	0.834932i	$-0.685507\pi$
$653$	−718.762			−1.10071			−0.550354	+	0.834932i	$0.685507\pi$
$654$	−590.699			−0.903209
$655$		0			0
$656$			1518.04i			2.31409i
$657$			786.144i			1.19657i
$658$	467.093			0.709867
$659$			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	$0.427600\pi$
$662$		−	2015.51i		−	3.04457i
$663$	−18.6797			−0.0281745
$664$	−3511.66			−5.28865
$665$		0			0
$666$			604.154i			0.907138i
$667$		−	1.19417i		−	0.00179036i
$668$			133.955i			0.200532i
$669$	−818.737			−1.22382
$670$		0			0
$671$	990.118	+	664.274i	1.47559	+	0.989976i
$672$	−1897.48			−2.82364
$673$			470.312i			0.698829i	0.936968	+	0.349415i	$0.113620\pi$
$673$			470.312i			0.698829i	−0.936968	+	0.349415i	$0.886380\pi$
$674$	−89.4326			−0.132689
$675$		0			0
$676$	−1431.10			−2.11702
$677$			395.226i			0.583790i	0.956450	+	0.291895i	$0.0942858\pi$
$677$			395.226i			0.583790i	−0.956450	+	0.291895i	$0.905714\pi$
$678$			1946.63i			2.87113i
$679$		−	315.221i		−	0.464243i
$680$		0			0
$681$			677.020i			0.994155i
$682$	332.749	+	223.243i	0.487902	+	0.327335i
$683$	356.945			0.522614			0.261307	−	0.965256i	$-0.415847\pi$
$683$	356.945			0.522614			0.261307	+	0.965256i	$0.415847\pi$
$684$			1853.77i			2.71019i
$685$		0			0
$686$	1152.09			1.67943
$687$	749.885			1.09154
$688$		−	3991.06i		−	5.80096i
$689$			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	$0.604582\pi$
$692$		−	1475.70i		−	2.13251i
$693$	251.038	+	168.423i	0.362249	+	0.243034i
$694$	1537.51			2.21543
$695$		0			0
$696$	−29.8035			−0.0428211
$697$	17.2933			0.0248111
$698$	1096.58			1.57103
$699$			512.071i			0.732576i
$700$		0			0
$701$		−	1196.50i		−	1.70684i	−0.521222	−	0.853421i	$-0.674524\pi$
$701$		−	1196.50i		−	1.70684i	0.521222	−	0.853421i	$-0.325476\pi$
$702$	−102.739			−0.146352
$703$		−	406.969i		−	0.578903i
$704$	1646.13	−	2453.59i	2.33825	−	3.48522i
$705$		0			0
$706$		−	1031.83i		−	1.46152i
$707$	−344.427			−0.487167
$708$	2164.86			3.05771
$709$	753.537			1.06282			0.531409	−	0.847116i	$-0.321663\pi$
$709$	753.537			1.06282			0.531409	+	0.847116i	$0.321663\pi$
$710$		0			0
$711$		−	914.983i		−	1.28690i
$712$			84.2258i			0.118295i
$713$	42.7197			0.0599154
$714$			39.4494i			0.0552513i
$715$		0			0
$716$	1472.19			2.05614
$717$			1147.39i			1.60026i
$718$	−800.583			−1.11502
$719$	−815.663			−1.13444			−0.567220	−	0.823566i	$-0.691981\pi$
$719$	−815.663			−1.13444			−0.567220	+	0.823566i	$0.691981\pi$
$720$		0			0
$721$			407.922i			0.565773i
$722$		−	295.802i		−	0.409699i
$723$		−	1380.32i		−	1.90915i
$724$	−257.683			−0.355916
$725$		0			0
$726$	−1793.25	+	734.892i	−2.47004	+	1.01225i
$727$	−255.827			−0.351895			−0.175947	−	0.984400i	$-0.556299\pi$
$727$	−255.827			−0.351895			−0.175947	+	0.984400i	$0.556299\pi$
$728$		−	601.222i		−	0.825855i
$729$	−556.676			−0.763616
$730$		0			0
$731$	−45.4656			−0.0621965
$732$		−	4959.42i		−	6.77516i
$733$		−	354.905i		−	0.484182i	−0.970254	−	0.242091i	$-0.922167\pi$
$733$		−	354.905i		−	0.484182i	0.970254	−	0.242091i	$-0.0778333\pi$
$734$		−	2349.82i		−	3.20139i
$735$		0			0
$736$		−	609.765i		−	0.828485i
$737$	589.189	−	878.202i	0.799443	−	1.19159i
$738$	−749.827			−1.01603
$739$		−	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
$742$	812.344			1.09480
$743$		−	245.731i		−	0.330728i	−0.986233	−	0.165364i	$-0.947120\pi$
$743$		−	245.731i		−	0.330728i	0.986233	−	0.165364i	$-0.0528799\pi$
$744$		−	1066.17i		−	1.43303i
$745$		0			0
$746$	961.792			1.28927
$747$		−	1016.33i		−	1.36055i
$748$	−72.5896	−	48.7006i	−0.0970449	−	0.0651078i
$749$	−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	$0.395397\pi$
$752$	2194.99			2.91886
$753$	−742.194			−0.985650
$754$		−	6.44723i		−	0.00855070i
$755$		0			0
$756$			159.503i			0.210983i
$757$	−373.291			−0.493119			−0.246559	−	0.969128i	$-0.579300\pi$
$757$	−373.291			−0.493119			−0.246559	+	0.969128i	$0.579300\pi$
$758$		−	1044.25i		−	1.37764i
$759$	−115.112	+	171.578i	−0.151663	+	0.226058i
$760$		0			0
$761$		−	503.375i		−	0.661466i	−0.943724	−	0.330733i	$-0.892704\pi$
$761$		−	503.375i		−	0.661466i	0.943724	−	0.330733i	$-0.107296\pi$
$762$	−48.9935			−0.0642959
$763$	−126.903			−0.166321
$764$	−2947.13			−3.85751
$765$		0			0
$766$		−	785.387i		−	1.02531i
$767$			299.573i			0.390577i
$768$	−3717.97			−4.84111
$769$			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
$772$			2317.65i			3.00214i
$773$	1147.94			1.48504			0.742521	−	0.669823i	$-0.233630\pi$
$773$	1147.94			1.48504			0.742521	+	0.669823i	$0.233630\pi$
$774$	1971.36			2.54698
$775$		0			0
$776$		−	2528.13i		−	3.25790i
$777$			276.051i			0.355278i
$778$			726.572i			0.933898i
$779$	505.097			0.648391
$780$		0			0
$781$	−127.148	+	189.518i	−0.162802	+	0.242660i
$782$	−12.6772			−0.0162113
$783$			1.09414i			0.00139737i
$784$	2335.00			2.97832
$785$		0			0
$786$	712.617			0.906637
$787$			275.997i			0.350695i	0.984507	+	0.175348i	$0.0561050\pi$
$787$			275.997i			0.350695i	−0.984507	+	0.175348i	$0.943895\pi$
$788$			545.781i			0.692616i
$789$			1112.53i			1.41005i
$790$		0			0
$791$			418.204i			0.528702i
$792$	2013.37	+	1350.78i	2.54214	+	1.70553i
$793$	686.284			0.865428
$794$		−	1404.01i		−	1.76827i
$795$		0			0
$796$	2683.93			3.37177
$797$	191.515			0.240295			0.120147	−	0.992756i	$-0.461663\pi$
$797$	191.515			0.240295			0.120147	+	0.992756i	$0.461663\pi$
$798$			1152.22i			1.44389i
$799$		−	25.0050i		−	0.0312953i
$800$		0			0
$801$	−24.3763			−0.0304323
$802$			2796.50i			3.48691i
$803$	−899.119	−	603.223i	−1.11970	−	0.751211i
$804$	−4398.84			−5.47120
$805$		0			0
$806$	230.640			0.286153
$807$	1171.54			1.45172
$808$	−2762.36			−3.41877
$809$			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	$0.00763082\pi$
$811$			38.8804i			0.0479413i	−0.999713	+	0.0239706i	$0.992369\pi$
$812$	−10.0093			−0.0123268
$813$		−	1496.78i		−	1.84106i
$814$	−690.975	−	463.578i	−0.848864	−	0.569506i
$815$		0			0
$816$			185.383i			0.227185i
$817$	−1327.94			−1.62539
$818$	1603.97			1.96084
$819$	174.003			0.212458
$820$		0			0
$821$		−	766.646i		−	0.933796i	−0.884311	−	0.466898i	$-0.845372\pi$
$821$		−	766.646i		−	0.933796i	0.884311	−	0.466898i	$-0.154628\pi$
$822$		−	1206.62i		−	1.46791i
$823$	−160.909			−0.195515			−0.0977573	−	0.995210i	$-0.531167\pi$
$823$	−160.909			−0.195515			−0.0977573	+	0.995210i	$0.531167\pi$
$824$			3271.61i			3.97040i
$825$		0			0
$826$	632.665			0.765938
$827$		−	488.410i		−	0.590581i	−0.955408	−	0.295290i	$-0.904584\pi$
$827$		−	488.410i		−	0.590581i	0.955408	−	0.295290i	$-0.0954164\pi$
$828$	404.081			0.488020
$829$	1310.28			1.58056			0.790278	−	0.612749i	$-0.209936\pi$
$829$	1310.28			1.58056			0.790278	+	0.612749i	$0.209936\pi$
$830$		0			0
$831$		−	17.7313i		−	0.0213373i
$832$		−	1700.67i		−	2.04407i
$833$		−	26.6000i		−	0.0319328i
$834$	−136.832			−0.164067
$835$		0			0
$836$	−2120.17	−	1422.43i	−2.53609	−	1.70147i
$837$	−39.1412			−0.0467637
$838$			1681.81i			2.00693i
$839$	728.730			0.868569			0.434285	−	0.900776i	$-0.357001\pi$
$839$	728.730			0.868569			0.434285	+	0.900776i	$0.357001\pi$
$840$		0			0
$841$	840.931			0.999918
$842$		−	148.907i		−	0.176849i
$843$		−	268.515i		−	0.318523i
$844$			3375.78i			3.99974i
$845$		0			0
$846$			1084.20i			1.28156i
$847$	−385.252	+	157.881i	−0.454843	+	0.186400i
$848$	3817.41			4.50166
$849$		−	1227.82i		−	1.44619i
$850$		0			0
$851$	−88.7102			−0.104242
$852$	949.279			1.11418
$853$			756.332i			0.886673i	0.896355	+	0.443337i	$0.146205\pi$
$853$			756.332i			0.886673i	−0.896355	+	0.443337i	$0.853795\pi$
$854$		−	1449.36i		−	1.69714i
$855$		0			0
$856$	−4388.67			−5.12696
$857$			437.904i			0.510973i	0.966813	+	0.255486i	$0.0822356\pi$
$857$			437.904i			0.510973i	−0.966813	+	0.255486i	$0.917764\pi$
$858$	−621.480	+	926.332i	−0.724336	+	1.07964i
$859$	−8.64857			−0.0100682			−0.00503409	−	0.999987i	$-0.501602\pi$
$859$	−8.64857			−0.0100682			−0.00503409	+	0.999987i	$0.501602\pi$
$860$		0			0
$861$	−342.612			−0.397923
$862$	−2240.96			−2.59972
$863$	−134.736			−0.156125			−0.0780626	−	0.996948i	$-0.524873\pi$
$863$	−134.736			−0.156125			−0.0780626	+	0.996948i	$0.524873\pi$
$864$			558.688i			0.646629i
$865$		0			0
$866$		−	497.404i		−	0.574370i
$867$	−1189.01			−1.37140
$868$		−	358.068i		−	0.412521i
$869$	1046.47	+	702.083i	1.20423	+	0.807921i
$870$		0			0
$871$		−	608.711i		−	0.698865i
$872$	−1017.78			−1.16718
$873$	731.680			0.838122
$874$	−370.272			−0.423652
$875$		0			0
$876$			4503.61i			5.14111i
$877$		−	1710.46i		−	1.95036i	−0.221420	−	0.975179i	$-0.571069\pi$
$877$		−	1710.46i		−	1.95036i	0.221420	−	0.975179i	$-0.428931\pi$
$878$	1952.56			2.22388
$879$		−	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	$0.512653\pi$
$882$			1153.36i			1.30766i
$883$	173.732			0.196753			0.0983763	−	0.995149i	$-0.468635\pi$
$883$	173.732			0.196753			0.0983763	+	0.995149i	$0.468635\pi$
$884$	−50.3143			−0.0569166
$885$		0			0
$886$			2398.49i			2.70710i
$887$			1416.42i			1.59686i	0.602085	+	0.798432i	$0.294337\pi$
$887$			1416.42i			1.59686i	−0.602085	+	0.798432i	$0.705663\pi$
$888$			2213.98i			2.49322i
$889$	−10.5255			−0.0118397
$890$		0			0
$891$	545.996	−	813.821i	0.612790	−	0.913380i
$892$	−2205.29			−2.47230
$893$		−	730.336i		−	0.817845i
$894$	1418.47			1.58665
$895$		0			0
$896$	−1750.09			−1.95322
$897$			118.926i			0.132582i
$898$		−	1666.57i		−	1.85587i
$899$		−	2.45624i		−	0.00273219i
$900$		0			0
$901$		−	43.4874i		−	0.0482657i
$902$	575.355	−	857.582i	0.637866	−	0.950756i
$903$	900.757			0.997516
$904$			3354.07i			3.71025i
$905$		0			0
$906$	2744.20			3.02892
$907$	900.626			0.992972			0.496486	−	0.868045i	$-0.334623\pi$
$907$	900.626			0.992972			0.496486	+	0.868045i	$0.334623\pi$
$908$			1823.57i			2.00834i
$909$		−	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	$0.610127\pi$
$912$			5414.59i			5.93705i
$913$	1162.38	+	779.849i	1.27315	+	0.854161i
$914$	2337.38			2.55731
$915$		0			0
$916$	2019.84			2.20507
$917$	153.095			0.166952
$918$	11.6153			0.0126529
$919$		−	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
$922$	2129.02			2.30914
$923$			131.361i			0.142320i
$924$	1438.13	+	964.849i	1.55642	+	1.04421i
$925$		0			0
$926$			2925.90i			3.15971i
$927$	−946.854			−1.02142
$928$	−35.0595			−0.0377796
$929$	962.019			1.03554			0.517771	−	0.855519i	$-0.326762\pi$
$929$	962.019			1.03554			0.517771	+	0.855519i	$0.326762\pi$
$930$		0			0
$931$		−	776.924i		−	0.834505i
$932$			1379.28i			1.47991i
$933$	−2089.62			−2.23968
$934$			502.787i			0.538316i
$935$		0			0
$936$	1395.54			1.49096
$937$		−	954.293i		−	1.01846i	−0.860632	−	0.509228i	$-0.829931\pi$
$937$		−	954.293i		−	1.01846i	0.860632	−	0.509228i	$-0.170069\pi$
$938$	−1285.53			−1.37050
$939$	−1094.86			−1.16599
$940$		0			0
$941$		−	34.4712i		−	0.0366325i	−0.999832	−	0.0183163i	$-0.994169\pi$
$941$		−	34.4712i		−	0.0366325i	0.999832	−	0.0183163i	$-0.00583058\pi$
$942$		−	705.011i		−	0.748419i
$943$		−	110.100i		−	0.116755i
$944$	2973.05			3.14942
$945$		0			0
$946$	−1512.66	+	2254.66i	−1.59901	+	2.38336i
$947$	1448.61			1.52969			0.764843	−	0.644217i	$-0.222817\pi$
$947$	1448.61			1.52969			0.764843	+	0.644217i	$0.222817\pi$
$948$		−	5241.70i		−	5.52922i
$949$	−623.210			−0.656702
$950$		0			0
$951$	−2256.72			−2.37300
$952$			67.9719i			0.0713991i
$953$			1393.91i			1.46266i	0.682026	+	0.731328i	$0.261099\pi$
$953$			1393.91i			1.46266i	−0.682026	+	0.731328i	$0.738901\pi$
$954$			1885.58i			1.97650i
$955$		0			0
$956$			3090.53i			3.23277i
$957$	9.86515	+	6.61857i	0.0103084	+	0.00691596i
$958$	−2502.28			−2.61198
$959$		−	259.225i		−	0.270307i
$960$		0			0
$961$	−873.132			−0.908566
$962$	−478.938			−0.497857
$963$		−	1270.15i		−	1.31895i
$964$		−	3717.93i		−	3.85677i
$965$		0			0
$966$	251.159			0.259999
$967$			733.093i			0.758110i	0.925374	+	0.379055i	$0.123751\pi$
$967$			733.093i			0.758110i	−0.925374	+	0.379055i	$0.876249\pi$
$968$	−3089.79	+	1266.23i	−3.19193	+	1.30809i
$969$	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	$0.566145\pi$
$972$	−3659.17			−3.76458
$973$	−29.3962			−0.0302120
$974$			1125.18i			1.15522i
$975$		0			0
$976$		−	6810.89i		−	6.97837i
$977$	−717.785			−0.734683			−0.367341	−	0.930086i	$-0.619732\pi$
$977$	−717.785			−0.734683			−0.367341	+	0.930086i	$0.619732\pi$
$978$			2788.37i			2.85110i
$979$	18.7043	−	27.8793i	0.0191056	−	0.0284773i
$980$		0			0
$981$		−	294.562i		−	0.300267i
$982$	3769.14			3.83823
$983$	124.372			0.126523			0.0632616	−	0.997997i	$-0.479850\pi$
$983$	124.372			0.126523			0.0632616	+	0.997997i	$0.479850\pi$
$984$	−2747.81			−2.79249
$985$		0			0
$986$			0.728899i			0.000739249i
$987$			495.394i			0.501919i
$988$	−1469.56			−1.48741
$989$			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	$0.536184\pi$
$992$		−	1254.20i		−	1.26431i
$993$	2137.63			2.15270
$994$	277.420			0.279095
$995$		0			0
$996$		−	5822.29i		−	5.84567i
$997$		−	1800.12i		−	1.80553i	−0.430129	−	0.902767i	$-0.641532\pi$
$997$		−	1800.12i		−	1.80553i	0.430129	−	0.902767i	$-0.358468\pi$
$998$		−	1516.09i		−	1.51913i
$999$	81.2794			0.0813607

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.c.a.21.1	✓	8	5.4	even	2
55.3.c.a.21.8	yes	8	55.54	odd	2
275.3.c.f.76.1		8	11.10	odd	2	inner
275.3.c.f.76.8		8	1.1	even	1	trivial
275.3.d.c.274.1		16	55.43	even	4
275.3.d.c.274.2		16	5.2	odd	4
275.3.d.c.274.15		16	5.3	odd	4
275.3.d.c.274.16		16	55.32	even	4
495.3.b.a.406.1		8	165.164	even	2
495.3.b.a.406.8		8	15.14	odd	2
880.3.j.a.241.1		8	20.19	odd	2
880.3.j.a.241.2		8	220.219	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+3.88606i q^{2} -4.12151 q^{3} -11.1014 q^{4} -16.0164i q^{6} -3.44089i q^{7} -27.5966i q^{8} +7.98688 q^{9} +(-6.12847 + 9.13465i) q^{11} +45.7547 q^{12} +6.33153i q^{13} +13.3715 q^{14} +62.8361 q^{16} -0.715819i q^{17} +31.0375i q^{18} -20.9074i q^{19} +14.1817i q^{21} +(-35.4978 - 23.8156i) q^{22} -4.55735 q^{23} +113.740i q^{24} -24.6047 q^{26} +4.17560 q^{27} +38.1988i q^{28} +0.262032i q^{29} -9.37380 q^{31} +133.798i q^{32} +(25.2586 - 37.6486i) q^{33} +2.78171 q^{34} -88.6658 q^{36} +19.4653 q^{37} +81.2473 q^{38} -26.0955i q^{39} +24.1588i q^{41} -55.1108 q^{42} -63.5155i q^{43} +(68.0348 - 101.408i) q^{44} -17.7101i q^{46} +34.9319 q^{47} -258.980 q^{48} +37.1603 q^{49} +2.95026i q^{51} -70.2891i q^{52} +60.7519 q^{53} +16.2266i q^{54} -94.9568 q^{56} +86.1701i q^{57} -1.01827 q^{58} +47.3144 q^{59} -108.391i q^{61} -36.4271i q^{62} -27.4820i q^{63} -268.603 q^{64} +(146.304 + 98.1563i) q^{66} -96.1396 q^{67} +7.94662i q^{68} +18.7832 q^{69} +20.7471 q^{71} -220.410i q^{72} +98.4295i q^{73} +75.6433i q^{74} +232.102i q^{76} +(31.4313 + 21.0874i) q^{77} +101.409 q^{78} -114.561i q^{79} -89.0917 q^{81} -93.8823 q^{82} -127.250i q^{83} -157.437i q^{84} +246.825 q^{86} -1.07997i q^{87} +(252.085 + 169.125i) q^{88} -3.05204 q^{89} +21.7861 q^{91} +50.5931 q^{92} +38.6343 q^{93} +135.748i q^{94} -551.451i q^{96} +91.6103 q^{97} +144.407i q^{98} +(-48.9474 + 72.9573i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} - 28 q^{4} - 4 q^{9} + 8 q^{11} + 48 q^{12} + 88 q^{16} - 80 q^{22} - 8 q^{23} - 100 q^{26} + 16 q^{27} + 36 q^{31} + 152 q^{33} + 80 q^{34} - 216 q^{36} + 88 q^{37} + 160 q^{38} - 280 q^{42}+ \cdots - 184 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 - 28 * q^4 - 4 * q^9 + 8 * q^11 + 48 * q^12 + 88 * q^16 - 80 * q^22 - 8 * q^23 - 100 * q^26 + 16 * q^27 + 36 * q^31 + 152 * q^33 + 80 * q^34 - 216 * q^36 + 88 * q^37 + 160 * q^38 - 280 * q^42 + 12 * q^44 + 8 * q^47 - 488 * q^48 + 172 * q^49 + 152 * q^53 - 80 * q^56 - 160 * q^58 - 16 * q^59 - 588 * q^64 + 180 * q^66 + 88 * q^67 + 8 * q^69 + 276 * q^71 - 160 * q^77 - 160 * q^78 - 320 * q^81 + 520 * q^82 + 420 * q^86 + 520 * q^88 + 444 * q^89 - 40 * q^91 + 368 * q^92 + 104 * q^93 - 312 * q^97 - 184 * q^99

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