LMFDB - Embedded newform 275.3.c.f.76.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			76.4
Root			$-1.46104i$ of defining polynomial
Character	$\chi$	$=$	275.76
Dual form			275.3.c.f.76.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.46104i q^{2} -0.114554 q^{3} +1.86536 q^{4} +0.167368i q^{6} -4.56066i q^{7} -8.56953i q^{8} -8.98688 q^{9} +(5.89241 - 9.28868i) q^{11} -0.213685 q^{12} +16.5645i q^{13} -6.66330 q^{14} -5.05897 q^{16} -17.2939i q^{17} +13.1302i q^{18} -35.8838i q^{19} +0.522441i q^{21} +(-13.5711 - 8.60904i) q^{22} +29.3902 q^{23} +0.981674i q^{24} +24.2014 q^{26} +2.06047 q^{27} -8.50728i q^{28} +8.51985i q^{29} -26.3476 q^{31} -26.8868i q^{32} +(-0.674999 + 1.06406i) q^{33} -25.2670 q^{34} -16.7638 q^{36} -44.4227 q^{37} -52.4276 q^{38} -1.89753i q^{39} +52.2243i q^{41} +0.763308 q^{42} -6.77375i q^{43} +(10.9915 - 17.3268i) q^{44} -42.9402i q^{46} -15.0434 q^{47} +0.579525 q^{48} +28.2004 q^{49} +1.98108i q^{51} +30.8989i q^{52} +33.1498 q^{53} -3.01043i q^{54} -39.0827 q^{56} +4.11063i q^{57} +12.4478 q^{58} +51.5447 q^{59} +23.1889i q^{61} +38.4948i q^{62} +40.9861i q^{63} -59.5185 q^{64} +(1.55463 + 0.986200i) q^{66} +113.668 q^{67} -32.2593i q^{68} -3.36676 q^{69} +8.00364 q^{71} +77.0133i q^{72} -32.5342i q^{73} +64.9034i q^{74} -66.9363i q^{76} +(-42.3625 - 26.8732i) q^{77} -2.77237 q^{78} +52.0160i q^{79} +80.6459 q^{81} +76.3018 q^{82} +43.3699i q^{83} +0.974543i q^{84} -9.89672 q^{86} -0.975983i q^{87} +(-79.5996 - 50.4951i) q^{88} +73.8028 q^{89} +75.5451 q^{91} +54.8233 q^{92} +3.01822 q^{93} +21.9790i q^{94} +3.07999i q^{96} -22.0298 q^{97} -41.2019i q^{98} +(-52.9543 + 83.4762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.46104i		−	0.730520i	−0.930906	−	0.365260i	$-0.880980\pi$
$2$		−	1.46104i		−	0.730520i	0.930906	−	0.365260i	$-0.119020\pi$
$3$	−0.114554			−0.0381847			−0.0190923	−	0.999818i	$-0.506078\pi$
$3$	−0.114554			−0.0381847			−0.0190923	+	0.999818i	$0.506078\pi$
$4$	1.86536			0.466341
$5$		0			0
$5$		0			0
$6$			0.167368i			0.0278947i
$7$		−	4.56066i		−	0.651522i	−0.945452	−	0.325761i	$-0.894379\pi$
$7$		−	4.56066i		−	0.651522i	0.945452	−	0.325761i	$-0.105621\pi$
$8$		−	8.56953i		−	1.07119i
$9$	−8.98688			−0.998542
$10$		0			0
$11$	5.89241	−	9.28868i	0.535673	−	0.844425i
$11$	5.89241	−	9.28868i	0.535673	−	0.844425i
$12$	−0.213685			−0.0178071
$13$			16.5645i			1.27420i	0.770783	+	0.637098i	$0.219865\pi$
$13$			16.5645i			1.27420i	−0.770783	+	0.637098i	$0.780135\pi$
$14$	−6.66330			−0.475950
$15$		0			0
$16$	−5.05897			−0.316185
$17$		−	17.2939i		−	1.01729i	−0.860978	−	0.508643i	$-0.830147\pi$
$17$		−	17.2939i		−	1.01729i	0.860978	−	0.508643i	$-0.169853\pi$
$18$			13.1302i			0.729455i
$19$		−	35.8838i		−	1.88862i	−0.329057	−	0.944310i	$-0.606731\pi$
$19$		−	35.8838i		−	1.88862i	0.329057	−	0.944310i	$-0.393269\pi$
$20$		0			0
$21$			0.522441i			0.0248782i
$22$	−13.5711	−	8.60904i	−0.616869	−	0.391320i
$23$	29.3902			1.27783			0.638917	−	0.769276i	$-0.279383\pi$
$23$	29.3902			1.27783			0.638917	+	0.769276i	$0.279383\pi$
$24$			0.981674i			0.0409031i
$25$		0			0
$26$	24.2014			0.930825
$27$	2.06047			0.0763137
$28$		−	8.50728i		−	0.303831i
$29$			8.51985i			0.293788i	0.989152	+	0.146894i	$0.0469276\pi$
$29$			8.51985i			0.293788i	−0.989152	+	0.146894i	$0.953072\pi$
$30$		0			0
$31$	−26.3476			−0.849921			−0.424961	−	0.905212i	$-0.639712\pi$
$31$	−26.3476			−0.849921			−0.424961	+	0.905212i	$0.639712\pi$
$32$		−	26.8868i		−	0.840211i
$33$	−0.674999	+	1.06406i	−0.0204545	+	0.0322441i
$34$	−25.2670			−0.743147
$35$		0			0
$36$	−16.7638			−0.465661
$37$	−44.4227			−1.20061			−0.600307	−	0.799769i	$-0.704955\pi$
$37$	−44.4227			−1.20061			−0.600307	+	0.799769i	$0.704955\pi$
$38$	−52.4276			−1.37967
$39$		−	1.89753i		−	0.0486547i
$40$		0			0
$41$			52.2243i			1.27376i	0.770961	+	0.636882i	$0.219776\pi$
$41$			52.2243i			1.27376i	−0.770961	+	0.636882i	$0.780224\pi$
$42$	0.763308			0.0181740
$43$		−	6.77375i		−	0.157529i	−0.996893	−	0.0787646i	$-0.974902\pi$
$43$		−	6.77375i		−	0.157529i	0.996893	−	0.0787646i	$-0.0250975\pi$
$44$	10.9915	−	17.3268i	0.249806	−	0.393790i
$45$		0			0
$46$		−	42.9402i		−	0.933482i
$47$	−15.0434			−0.320072			−0.160036	−	0.987111i	$-0.551161\pi$
$47$	−15.0434			−0.320072			−0.160036	+	0.987111i	$0.551161\pi$
$48$	0.579525			0.0120734
$49$	28.2004			0.575519
$50$		0			0
$51$			1.98108i			0.0388447i
$52$			30.8989i			0.594209i
$53$	33.1498			0.625468			0.312734	−	0.949841i	$-0.398755\pi$
$53$	33.1498			0.625468			0.312734	+	0.949841i	$0.398755\pi$
$54$		−	3.01043i		−	0.0557486i
$55$		0			0
$56$	−39.0827			−0.697905
$57$			4.11063i			0.0721163i
$58$	12.4478			0.214618
$59$	51.5447			0.873639			0.436819	−	0.899549i	$-0.356105\pi$
$59$	51.5447			0.873639			0.436819	+	0.899549i	$0.356105\pi$
$60$		0			0
$61$			23.1889i			0.380146i	0.981770	+	0.190073i	$0.0608725\pi$
$61$			23.1889i			0.380146i	−0.981770	+	0.190073i	$0.939127\pi$
$62$			38.4948i			0.620884i
$63$			40.9861i			0.650572i
$64$	−59.5185			−0.929976
$65$		0			0
$66$	1.55463	+	0.986200i	0.0235550	+	0.0149424i
$67$	113.668			1.69653			0.848265	−	0.529572i	$-0.177647\pi$
$67$	113.668			1.69653			0.848265	+	0.529572i	$0.177647\pi$
$68$		−	32.2593i		−	0.474402i
$69$	−3.36676			−0.0487936
$70$		0			0
$71$	8.00364			0.112727			0.0563637	−	0.998410i	$-0.482049\pi$
$71$	8.00364			0.112727			0.0563637	+	0.998410i	$0.482049\pi$
$72$			77.0133i			1.06963i
$73$		−	32.5342i		−	0.445674i	−0.974856	−	0.222837i	$-0.928468\pi$
$73$		−	32.5342i		−	0.445674i	0.974856	−	0.222837i	$-0.0715318\pi$
$74$			64.9034i			0.877073i
$75$		0			0
$76$		−	66.9363i		−	0.880741i
$77$	−42.3625	−	26.8732i	−0.550162	−	0.349003i
$78$	−2.77237			−0.0355432
$79$			52.0160i			0.658431i	0.944255	+	0.329215i	$0.106784\pi$
$79$			52.0160i			0.658431i	−0.944255	+	0.329215i	$0.893216\pi$
$80$		0			0
$81$	80.6459			0.995628
$82$	76.3018			0.930510
$83$			43.3699i			0.522529i	0.965267	+	0.261264i	$0.0841394\pi$
$83$			43.3699i			0.522529i	−0.965267	+	0.261264i	$0.915861\pi$
$84$			0.974543i			0.0116017i
$85$		0			0
$86$	−9.89672			−0.115078
$87$		−	0.975983i		−	0.0112182i
$88$	−79.5996	−	50.4951i	−0.904541	−	0.573808i
$89$	73.8028			0.829245			0.414623	−	0.909993i	$-0.363914\pi$
$89$	73.8028			0.829245			0.414623	+	0.909993i	$0.363914\pi$
$90$		0			0
$91$	75.5451			0.830166
$92$	54.8233			0.595906
$93$	3.01822			0.0324540
$94$			21.9790i			0.233819i
$95$		0			0
$96$			3.07999i			0.0320832i
$97$	−22.0298			−0.227111			−0.113556	−	0.993532i	$-0.536224\pi$
$97$	−22.0298			−0.227111			−0.113556	+	0.993532i	$0.536224\pi$
$98$		−	41.2019i		−	0.420428i
$99$	−52.9543	+	83.4762i	−0.534892	+	0.843194i
$100$		0			0
$101$			163.013i			1.61399i	0.590561	+	0.806993i	$0.298906\pi$
$101$			163.013i			1.61399i	−0.590561	+	0.806993i	$0.701094\pi$
$102$	2.89444			0.0283768
$103$	−42.6423			−0.414003			−0.207001	−	0.978341i	$-0.566370\pi$
$103$	−42.6423			−0.414003			−0.207001	+	0.978341i	$0.566370\pi$
$104$	141.950			1.36491
$105$		0			0
$106$		−	48.4332i		−	0.456917i
$107$			131.098i			1.22522i	0.790387	+	0.612608i	$0.209879\pi$
$107$			131.098i			1.22522i	−0.790387	+	0.612608i	$0.790121\pi$
$108$	3.84352			0.0355882
$109$			54.5201i			0.500184i	0.968222	+	0.250092i	$0.0804609\pi$
$109$			54.5201i			0.500184i	−0.968222	+	0.250092i	$0.919539\pi$
$110$		0			0
$111$	5.08880			0.0458451
$112$			23.0722i			0.206002i
$113$	117.985			1.04412			0.522058	−	0.852910i	$-0.325164\pi$
$113$	117.985			1.04412			0.522058	+	0.852910i	$0.325164\pi$
$114$	6.00579			0.0526824
$115$		0			0
$116$			15.8926i			0.137005i
$117$		−	148.863i		−	1.27234i
$118$		−	75.3088i		−	0.638210i
$119$	−78.8713			−0.662784
$120$		0			0
$121$	−51.5591	−	109.465i	−0.426108	−	0.904672i
$122$	33.8799			0.277704
$123$		−	5.98251i		−	0.0486383i
$124$	−49.1478			−0.396353
$125$		0			0
$126$	59.8822			0.475256
$127$			113.764i			0.895782i	0.894088	+	0.447891i	$0.147825\pi$
$127$			113.764i			0.895782i	−0.894088	+	0.447891i	$0.852175\pi$
$128$		−	20.5882i		−	0.160845i
$129$			0.775961i			0.00601520i
$130$		0			0
$131$		−	115.599i		−	0.882435i	−0.897400	−	0.441218i	$-0.854547\pi$
$131$		−	115.599i		−	0.882435i	0.897400	−	0.441218i	$-0.145453\pi$
$132$	−1.25912	+	1.98485i	−0.00953877	+	0.0150367i
$133$	−163.654			−1.23048
$134$		−	166.073i		−	1.23935i
$135$		0			0
$136$	−148.200			−1.08971
$137$	216.355			1.57924			0.789618	−	0.613598i	$-0.210279\pi$
$137$	216.355			1.57924			0.789618	+	0.613598i	$0.210279\pi$
$138$			4.91897i			0.0356447i
$139$		−	5.08013i		−	0.0365477i	−0.999833	−	0.0182738i	$-0.994183\pi$
$139$		−	5.08013i		−	0.0365477i	0.999833	−	0.0182738i	$-0.00581707\pi$
$140$		0			0
$141$	1.72328			0.0122219
$142$		−	11.6936i		−	0.0823495i
$143$	153.863	+	97.6050i	1.07596	+	0.682552i
$144$	45.4643			0.315724
$145$		0			0
$146$	−47.5338			−0.325574
$147$	−3.23047			−0.0219760
$148$	−82.8646			−0.559896
$149$		−	187.947i		−	1.26139i	−0.776030	−	0.630696i	$-0.782769\pi$
$149$		−	187.947i		−	1.26139i	0.776030	−	0.630696i	$-0.217231\pi$
$150$		0			0
$151$			136.741i			0.905571i	0.891620	+	0.452785i	$0.149570\pi$
$151$			136.741i			0.905571i	−0.891620	+	0.452785i	$0.850430\pi$
$152$	−307.507			−2.02307
$153$			155.418i			1.01580i
$154$	−39.2629	+	61.8932i	−0.254954	+	0.401904i
$155$		0			0
$156$		−	3.53959i		−	0.0226897i
$157$	−256.057			−1.63094			−0.815470	−	0.578800i	$-0.803521\pi$
$157$	−256.057			−1.63094			−0.815470	+	0.578800i	$0.803521\pi$
$158$	75.9975			0.480997
$159$	−3.79744			−0.0238833
$160$		0			0
$161$		−	134.038i		−	0.832537i
$162$		−	117.827i		−	0.727326i
$163$	25.1370			0.154215			0.0771075	−	0.997023i	$-0.475432\pi$
$163$	25.1370			0.154215			0.0771075	+	0.997023i	$0.475432\pi$
$164$			97.4174i			0.594008i
$165$		0			0
$166$	63.3651			0.381718
$167$			4.21038i			0.0252119i	0.999921	+	0.0126059i	$0.00401270\pi$
$167$			4.21038i			0.0252119i	−0.999921	+	0.0126059i	$0.995987\pi$
$168$	4.47708			0.0266493
$169$	−105.384			−0.623573
$170$		0			0
$171$			322.483i			1.88587i
$172$		−	12.6355i		−	0.0734623i
$173$			168.015i			0.971185i	0.874185	+	0.485592i	$0.161396\pi$
$173$			168.015i			0.971185i	−0.874185	+	0.485592i	$0.838604\pi$
$174$	−1.42595			−0.00819511
$175$		0			0
$176$	−29.8095	+	46.9911i	−0.169372	+	0.266995i
$177$	−5.90465			−0.0333596
$178$		−	107.829i		−	0.605780i
$179$	−34.5542			−0.193040			−0.0965200	−	0.995331i	$-0.530771\pi$
$179$	−34.5542			−0.193040			−0.0965200	+	0.995331i	$0.530771\pi$
$180$		0			0
$181$	−107.349			−0.593091			−0.296545	−	0.955019i	$-0.595835\pi$
$181$	−107.349			−0.593091			−0.296545	+	0.955019i	$0.595835\pi$
$182$		−	110.374i		−	0.606453i
$183$		−	2.65638i		−	0.0145158i
$184$		−	251.860i		−	1.36880i
$185$		0			0
$186$		−	4.40974i		−	0.0237083i
$187$	−160.637	−	101.902i	−0.859022	−	0.544933i
$188$	−28.0614			−0.149263
$189$		−	9.39709i		−	0.0497200i
$190$		0			0
$191$	−75.4470			−0.395011			−0.197505	−	0.980302i	$-0.563284\pi$
$191$	−75.4470			−0.395011			−0.197505	+	0.980302i	$0.563284\pi$
$192$	6.81808			0.0355108
$193$		−	167.064i		−	0.865617i	−0.901486	−	0.432809i	$-0.857523\pi$
$193$		−	167.064i		−	0.865617i	0.901486	−	0.432809i	$-0.142477\pi$
$194$			32.1864i			0.165909i
$195$		0			0
$196$	52.6040			0.268388
$197$		−	362.777i		−	1.84151i	−0.390145	−	0.920754i	$-0.627575\pi$
$197$		−	362.777i		−	1.84151i	0.390145	−	0.920754i	$-0.372425\pi$
$198$	121.962	+	77.3684i	0.615970	+	0.390749i
$199$	337.735			1.69716			0.848580	−	0.529068i	$-0.177458\pi$
$199$	337.735			1.69716			0.848580	+	0.529068i	$0.177458\pi$
$200$		0			0
$201$	−13.0211			−0.0647814
$202$	238.168			1.17905
$203$	38.8561			0.191409
$204$			3.69543i			0.0181149i
$205$		0			0
$206$			62.3021i			0.302437i
$207$	−264.126			−1.27597
$208$		−	83.7994i		−	0.402882i
$209$	−333.313	−	211.442i	−1.59480	−	1.01168i
$210$		0			0
$211$		−	317.915i		−	1.50670i	−0.657617	−	0.753352i	$-0.728436\pi$
$211$		−	317.915i		−	1.50670i	0.657617	−	0.753352i	$-0.271564\pi$
$212$	61.8364			0.291681
$213$	−0.916849			−0.00430446
$214$	191.539			0.895044
$215$		0			0
$216$		−	17.6572i		−	0.0817465i
$217$			120.162i			0.553743i
$218$	79.6560			0.365395
$219$			3.72692i			0.0170179i
$220$		0			0
$221$	286.465			1.29622
$222$		−	7.43494i		−	0.0334907i
$223$	−292.643			−1.31230			−0.656151	−	0.754630i	$-0.727817\pi$
$223$	−292.643			−1.31230			−0.656151	+	0.754630i	$0.727817\pi$
$224$	−122.621			−0.547416
$225$		0			0
$226$		−	172.381i		−	0.762747i
$227$		−	9.54908i		−	0.0420664i	−0.999779	−	0.0210332i	$-0.993304\pi$
$227$		−	9.54908i		−	0.0420664i	0.999779	−	0.0210332i	$-0.00669557\pi$
$228$			7.66782i			0.0336308i
$229$	−355.912			−1.55420			−0.777100	−	0.629377i	$-0.783310\pi$
$229$	−355.912			−1.55420			−0.777100	+	0.629377i	$0.783310\pi$
$230$		0			0
$231$	4.85279	+	3.07844i	0.0210077	+	0.0133266i
$232$	73.0111			0.314703
$233$			270.961i			1.16292i	0.813573	+	0.581462i	$0.197519\pi$
$233$			270.961i			1.16292i	−0.813573	+	0.581462i	$0.802481\pi$
$234$	−217.495			−0.929467
$235$		0			0
$236$	96.1496			0.407413
$237$		−	5.95864i		−	0.0251420i
$238$			115.234i			0.484177i
$239$			79.1374i			0.331119i	0.986200	+	0.165560i	$0.0529430\pi$
$239$			79.1374i			0.331119i	−0.986200	+	0.165560i	$0.947057\pi$
$240$		0			0
$241$		−	146.567i		−	0.608164i	−0.952646	−	0.304082i	$-0.901650\pi$
$241$		−	146.567i		−	0.608164i	0.952646	−	0.304082i	$-0.0983496\pi$
$242$	−159.933	+	75.3299i	−0.660881	+	0.311281i
$243$	−27.7825			−0.114331
$244$			43.2558i			0.177278i
$245$		0			0
$246$	−8.74068			−0.0355312
$247$	594.398			2.40647
$248$			225.786i			0.910428i
$249$		−	4.96819i		−	0.0199526i
$250$		0			0
$251$	52.7485			0.210154			0.105077	−	0.994464i	$-0.466491\pi$
$251$	52.7485			0.210154			0.105077	+	0.994464i	$0.466491\pi$
$252$			76.4539i			0.303388i
$253$	173.179	−	272.996i	0.684501	−	1.07903i
$254$	166.214			0.654386
$255$		0			0
$256$	−268.154			−1.04748
$257$	−41.8668			−0.162906			−0.0814529	−	0.996677i	$-0.525956\pi$
$257$	−41.8668			−0.162906			−0.0814529	+	0.996677i	$0.525956\pi$
$258$	1.13371			0.00439422
$259$			202.597i			0.782227i
$260$		0			0
$261$		−	76.5668i		−	0.293360i
$262$	−168.895			−0.644636
$263$		−	289.448i		−	1.10056i	−0.834979	−	0.550282i	$-0.814520\pi$
$263$		−	289.448i		−	1.10056i	0.834979	−	0.550282i	$-0.185480\pi$
$264$	9.11845	+	5.78442i	0.0345396	+	0.0219107i
$265$		0			0
$266$			239.104i			0.898888i
$267$	−8.45441			−0.0316645
$268$	212.031			0.791161
$269$	297.640			1.10647			0.553234	−	0.833026i	$-0.313393\pi$
$269$	297.640			1.10647			0.553234	+	0.833026i	$0.313393\pi$
$270$		0			0
$271$			277.488i			1.02394i	0.859003	+	0.511970i	$0.171084\pi$
$271$			277.488i			1.02394i	−0.859003	+	0.511970i	$0.828916\pi$
$272$			87.4890i			0.321651i
$273$	−8.65400			−0.0316996
$274$		−	316.104i		−	1.15366i
$275$		0			0
$276$	−6.28023			−0.0227545
$277$		−	22.6740i		−	0.0818556i	−0.999162	−	0.0409278i	$-0.986969\pi$
$277$		−	22.6740i		−	0.0818556i	0.999162	−	0.0409278i	$-0.0130314\pi$
$278$	−7.42227			−0.0266988
$279$	236.782			0.848682
$280$		0			0
$281$		−	182.887i		−	0.650845i	−0.945569	−	0.325422i	$-0.894494\pi$
$281$		−	182.887i		−	0.650845i	0.945569	−	0.325422i	$-0.105506\pi$
$282$		−	2.51778i		−	0.00892831i
$283$		−	367.233i		−	1.29764i	−0.760941	−	0.648821i	$-0.775262\pi$
$283$		−	367.233i		−	1.29764i	0.760941	−	0.648821i	$-0.224738\pi$
$284$	14.9297			0.0525694
$285$		0			0
$286$	142.605	−	224.799i	0.498618	−	0.786012i
$287$	238.177			0.829886
$288$			241.628i			0.838986i
$289$	−10.0774			−0.0348699
$290$		0			0
$291$	2.52360			0.00867218
$292$		−	60.6881i		−	0.207836i
$293$			10.3180i			0.0352150i	0.999845	+	0.0176075i	$0.00560493\pi$
$293$			10.3180i			0.0352150i	−0.999845	+	0.0176075i	$0.994395\pi$
$294$			4.71985i			0.0160539i
$295$		0			0
$296$			380.682i			1.28609i
$297$	12.1411	−	19.1390i	0.0408792	−	0.0644412i
$298$	−274.599			−0.921472
$299$			486.834i			1.62821i
$300$		0			0
$301$	−30.8928			−0.102634
$302$	199.784			0.661537
$303$		−	18.6737i		−	0.0616295i
$304$			181.535i			0.597154i
$305$		0			0
$306$	227.071			0.742064
$307$			459.671i			1.49730i	0.662966	+	0.748649i	$0.269297\pi$
$307$			459.671i			1.49730i	−0.662966	+	0.748649i	$0.730703\pi$
$308$	−79.0214	−	50.1283i	−0.256563	−	0.162754i
$309$	4.88484			0.0158086
$310$		0			0
$311$	101.131			0.325181			0.162590	−	0.986694i	$-0.448015\pi$
$311$	101.131			0.325181			0.162590	+	0.986694i	$0.448015\pi$
$312$	−16.2610			−0.0521185
$313$	−288.760			−0.922556			−0.461278	−	0.887256i	$-0.652609\pi$
$313$	−288.760			−0.922556			−0.461278	+	0.887256i	$0.652609\pi$
$314$			374.110i			1.19143i
$315$		0			0
$316$			97.0288i			0.307053i
$317$	−242.929			−0.766338			−0.383169	−	0.923678i	$-0.625167\pi$
$317$	−242.929			−0.766338			−0.383169	+	0.923678i	$0.625167\pi$
$318$			5.54821i			0.0174472i
$319$	79.1381	+	50.2024i	0.248082	+	0.157374i
$320$		0			0
$321$		−	15.0178i		−	0.0467845i
$322$	−195.835			−0.608185
$323$	−620.569			−1.92127
$324$	150.434			0.464302
$325$		0			0
$326$		−	36.7262i		−	0.112657i
$327$		−	6.24550i		−	0.0190994i
$328$	447.538			1.36445
$329$			68.6078i			0.208534i
$330$		0			0
$331$	−241.395			−0.729291			−0.364646	−	0.931146i	$-0.618810\pi$
$331$	−241.395			−0.729291			−0.364646	+	0.931146i	$0.618810\pi$
$332$			80.9006i			0.243676i
$333$	399.222			1.19886
$334$	6.15154			0.0184178
$335$		0			0
$336$		−	2.64301i		−	0.00786611i
$337$			527.662i			1.56576i	0.622171	+	0.782881i	$0.286251\pi$
$337$			527.662i			1.56576i	−0.622171	+	0.782881i	$0.713749\pi$
$338$			153.970i			0.455532i
$339$	−13.5157			−0.0398692
$340$		0			0
$341$	−155.251	+	244.734i	−0.455280	+	0.717695i
$342$	471.161			1.37766
$343$		−	352.085i		−	1.02649i
$344$	−58.0479			−0.168744
$345$		0			0
$346$	245.476			0.709470
$347$			214.531i			0.618244i	0.951022	+	0.309122i	$0.100035\pi$
$347$			214.531i			0.618244i	−0.951022	+	0.309122i	$0.899965\pi$
$348$		−	1.82056i		−	0.00523150i
$349$			76.4945i			0.219182i	0.993977	+	0.109591i	$0.0349541\pi$
$349$			76.4945i			0.219182i	−0.993977	+	0.109591i	$0.965046\pi$
$350$		0			0
$351$			34.1307i			0.0972385i
$352$	−249.743	−	158.428i	−0.709496	−	0.450079i
$353$	176.689			0.500535			0.250268	−	0.968177i	$-0.419481\pi$
$353$	176.689			0.500535			0.250268	+	0.968177i	$0.419481\pi$
$354$			8.62693i			0.0243699i
$355$		0			0
$356$	137.669			0.386711
$357$	9.03503			0.0253082
$358$			50.4850i			0.141020i
$359$		−	357.810i		−	0.996686i	−0.866980	−	0.498343i	$-0.833942\pi$
$359$		−	357.810i		−	0.996686i	0.866980	−	0.498343i	$-0.166058\pi$
$360$		0			0
$361$	−926.646			−2.56689
$362$			156.842i			0.433265i
$363$	5.90630	+	12.5397i	0.0162708	+	0.0345446i
$364$	140.919			0.387140
$365$		0			0
$366$	−3.88108			−0.0106041
$367$	314.687			0.857458			0.428729	−	0.903433i	$-0.358962\pi$
$367$	314.687			0.857458			0.428729	+	0.903433i	$0.358962\pi$
$368$	−148.684			−0.404032
$369$		−	469.334i		−	1.27191i
$370$		0			0
$371$		−	151.185i		−	0.407506i
$372$	5.63007			0.0151346
$373$			420.645i			1.12773i	0.825865	+	0.563867i	$0.190687\pi$
$373$			420.645i			1.12773i	−0.825865	+	0.563867i	$0.809313\pi$
$374$	−148.883	+	234.697i	−0.398084	+	0.627532i
$375$		0			0
$376$			128.915i			0.342859i
$377$	−141.127			−0.374343
$378$	−13.7295			−0.0363215
$379$	401.667			1.05981			0.529904	−	0.848058i	$-0.322228\pi$
$379$	401.667			1.05981			0.529904	+	0.848058i	$0.322228\pi$
$380$		0			0
$381$		−	13.0322i		−	0.0342051i
$382$			110.231i			0.288563i
$383$	−60.0864			−0.156884			−0.0784418	−	0.996919i	$-0.524994\pi$
$383$	−60.0864			−0.156884			−0.0784418	+	0.996919i	$0.524994\pi$
$384$			2.35846i			0.00614182i
$385$		0			0
$386$	−244.087			−0.632350
$387$			60.8749i			0.157299i
$388$	−41.0936			−0.105911
$389$	411.464			1.05775			0.528874	−	0.848700i	$-0.322614\pi$
$389$	411.464			1.05775			0.528874	+	0.848700i	$0.322614\pi$
$390$		0			0
$391$		−	508.269i		−	1.29992i
$392$		−	241.664i		−	0.616491i
$393$			13.2423i			0.0336955i
$394$	−530.031			−1.34526
$395$		0			0
$396$	−98.7791	+	155.713i	−0.249442	+	0.393216i
$397$	237.517			0.598279			0.299140	−	0.954209i	$-0.403300\pi$
$397$	237.517			0.598279			0.299140	+	0.954209i	$0.403300\pi$
$398$		−	493.444i		−	1.23981i
$399$	18.7472			0.0469854
$400$		0			0
$401$	101.501			0.253120			0.126560	−	0.991959i	$-0.459606\pi$
$401$	101.501			0.253120			0.126560	+	0.991959i	$0.459606\pi$
$402$			19.0243i			0.0473241i
$403$		−	436.435i		−	1.08297i
$404$			304.078i			0.752667i
$405$		0			0
$406$		−	56.7703i		−	0.139828i
$407$	−261.757	+	412.629i	−0.643137	+	1.01383i
$408$	16.9769			0.0416101
$409$		−	694.176i		−	1.69725i	−0.528993	−	0.848626i	$-0.677430\pi$
$409$		−	694.176i		−	1.69725i	0.528993	−	0.848626i	$-0.322570\pi$
$410$		0			0
$411$	−24.7844			−0.0603026
$412$	−79.5433			−0.193066
$413$		−	235.078i		−	0.569195i
$414$			385.898i			0.932121i
$415$		0			0
$416$	445.367			1.07059
$417$			0.581949i			0.00139556i
$418$	−308.925	+	486.983i	−0.739055	+	1.16503i
$419$	−416.354			−0.993686			−0.496843	−	0.867841i	$-0.665507\pi$
$419$	−416.354			−0.993686			−0.496843	+	0.867841i	$0.665507\pi$
$420$		0			0
$421$	539.341			1.28110			0.640548	−	0.767918i	$-0.278707\pi$
$421$	539.341			1.28110			0.640548	+	0.767918i	$0.278707\pi$
$422$	−464.486			−1.10068
$423$	135.193			0.319606
$424$		−	284.078i		−	0.669995i
$425$		0			0
$426$			1.33955i			0.00314449i
$427$	105.757			0.247674
$428$			244.546i			0.571368i
$429$	−17.6256	−	11.1810i	−0.0410853	−	0.0260630i
$430$		0			0
$431$		−	343.493i		−	0.796967i	−0.917176	−	0.398483i	$-0.869537\pi$
$431$		−	343.493i		−	0.796967i	0.917176	−	0.398483i	$-0.130463\pi$
$432$	−10.4238			−0.0241293
$433$	−18.0353			−0.0416520			−0.0208260	−	0.999783i	$-0.506630\pi$
$433$	−18.0353			−0.0416520			−0.0208260	+	0.999783i	$0.506630\pi$
$434$	175.562			0.404520
$435$		0			0
$436$			101.700i			0.233256i
$437$		−	1054.63i		−	2.41334i
$438$	5.44518			0.0124319
$439$			693.839i			1.58050i	0.612786	+	0.790249i	$0.290049\pi$
$439$			693.839i			1.58050i	−0.612786	+	0.790249i	$0.709951\pi$
$440$		0			0
$441$	−253.434			−0.574680
$442$		−	418.536i		−	0.946914i
$443$	359.314			0.811092			0.405546	−	0.914075i	$-0.367081\pi$
$443$	359.314			0.811092			0.405546	+	0.914075i	$0.367081\pi$
$444$	9.49247			0.0213794
$445$		0			0
$446$			427.564i			0.958663i
$447$			21.5301i			0.0481658i
$448$			271.443i			0.605900i
$449$	−567.882			−1.26477			−0.632385	−	0.774654i	$-0.717924\pi$
$449$	−567.882			−1.26477			−0.632385	+	0.774654i	$0.717924\pi$
$450$		0			0
$451$	485.095	+	307.727i	1.07560	+	0.682322i
$452$	220.085			0.486914
$453$		−	15.6643i		−	0.0345789i
$454$	−13.9516			−0.0307303
$455$		0			0
$456$	35.2262			0.0772504
$457$		−	797.218i		−	1.74446i	−0.489096	−	0.872230i	$-0.662673\pi$
$457$		−	797.218i		−	1.74446i	0.489096	−	0.872230i	$-0.337327\pi$
$458$			520.001i			1.13537i
$459$		−	35.6335i		−	0.0776328i
$460$		0			0
$461$			87.9144i			0.190704i	0.995444	+	0.0953518i	$0.0303976\pi$
$461$			87.9144i			0.190704i	−0.995444	+	0.0953518i	$0.969602\pi$
$462$	4.49772	−	7.09012i	0.00973532	−	0.0153466i
$463$	50.9282			0.109996			0.0549981	−	0.998486i	$-0.482485\pi$
$463$	50.9282			0.109996			0.0549981	+	0.998486i	$0.482485\pi$
$464$		−	43.1016i		−	0.0928914i
$465$		0			0
$466$	395.885			0.849539
$467$	463.064			0.991572			0.495786	−	0.868445i	$-0.334880\pi$
$467$	463.064			0.991572			0.495786	+	0.868445i	$0.334880\pi$
$468$		−	277.684i		−	0.593343i
$469$		−	518.398i		−	1.10533i
$470$		0			0
$471$	29.3324			0.0622769
$472$		−	441.714i		−	0.935834i
$473$	−62.9192	−	39.9137i	−0.133022	−	0.0843841i
$474$	−8.70581			−0.0183667
$475$		0			0
$476$	−147.124			−0.309083
$477$	−297.913			−0.624556
$478$	115.623			0.241889
$479$			182.184i			0.380343i	0.981751	+	0.190171i	$0.0609044\pi$
$479$			182.184i			0.380343i	−0.981751	+	0.190171i	$0.939096\pi$
$480$		0			0
$481$		−	735.842i		−	1.52982i
$482$	−214.141			−0.444276
$483$			15.3546i			0.0317901i
$484$	−96.1765	−	204.193i	−0.198712	−	0.421886i
$485$		0			0
$486$			40.5914i			0.0835213i
$487$	−366.810			−0.753203			−0.376602	−	0.926375i	$-0.622907\pi$
$487$	−366.810			−0.753203			−0.376602	+	0.926375i	$0.622907\pi$
$488$	198.718			0.407209
$489$	−2.87955			−0.00588865
$490$		0			0
$491$			42.0181i			0.0855766i	0.999084	+	0.0427883i	$0.0136241\pi$
$491$			42.0181i			0.0855766i	−0.999084	+	0.0427883i	$0.986376\pi$
$492$		−	11.1596i		−	0.0226820i
$493$	147.341			0.298866
$494$		−	868.439i		−	1.75797i
$495$		0			0
$496$	133.291			0.268733
$497$		−	36.5018i		−	0.0734444i
$498$	−7.25873			−0.0145758
$499$	−229.963			−0.460848			−0.230424	−	0.973090i	$-0.574011\pi$
$499$	−229.963			−0.460848			−0.230424	+	0.973090i	$0.574011\pi$
$500$		0			0
$501$		−	0.482316i		−	0.000962707i
$502$		−	77.0677i		−	0.153521i
$503$		−	9.38400i		−	0.0186561i	−0.999956	−	0.00932803i	$-0.997031\pi$
$503$		−	9.38400i		−	0.0186561i	0.999956	−	0.00932803i	$-0.00296925\pi$
$504$	351.231			0.696887
$505$		0			0
$506$	−398.858	−	253.021i	−0.788256	−	0.500042i
$507$	12.0721			0.0238109
$508$			212.212i			0.417740i
$509$	−584.355			−1.14804			−0.574022	−	0.818840i	$-0.694618\pi$
$509$	−584.355			−1.14804			−0.574022	+	0.818840i	$0.694618\pi$
$510$		0			0
$511$	−148.377			−0.290367
$512$			309.431i			0.604357i
$513$		−	73.9374i		−	0.144128i
$514$			61.1691i			0.119006i
$515$		0			0
$516$			1.44745i			0.00280513i
$517$	−88.6418	+	139.733i	−0.171454	+	0.270277i
$518$	296.002			0.571432
$519$		−	19.2468i		−	0.0370844i
$520$		0			0
$521$	121.060			0.232361			0.116180	−	0.993228i	$-0.462935\pi$
$521$	121.060			0.232361			0.116180	+	0.993228i	$0.462935\pi$
$522$	−111.867			−0.214305
$523$			446.636i			0.853988i	0.904254	+	0.426994i	$0.140428\pi$
$523$			446.636i			0.853988i	−0.904254	+	0.426994i	$0.859572\pi$
$524$		−	215.634i		−	0.411516i
$525$		0			0
$526$	−422.896			−0.803984
$527$			455.651i			0.864613i
$528$	3.41480	−	5.38302i	0.00646742	−	0.0101951i
$529$	334.782			0.632858
$530$		0			0
$531$	−463.226			−0.872365
$532$	−305.273			−0.573822
$533$	−865.072			−1.62302
$534$			12.3522i			0.0231315i
$535$		0			0
$536$		−	974.077i		−	1.81731i
$537$	3.95832			0.00737117
$538$		−	434.864i		−	0.808297i
$539$	166.168	−	261.945i	0.308290	−	0.485983i
$540$		0			0
$541$			472.750i			0.873846i	0.899499	+	0.436923i	$0.143932\pi$
$541$			472.750i			0.873846i	−0.899499	+	0.436923i	$0.856068\pi$
$542$	405.421			0.748009
$543$	12.2973			0.0226470
$544$	−464.976			−0.854735
$545$		0			0
$546$			12.6438i			0.0231572i
$547$		−	24.2342i		−	0.0443039i	−0.999755	−	0.0221520i	$-0.992948\pi$
$547$		−	24.2342i		−	0.0443039i	0.999755	−	0.0221520i	$-0.00705176\pi$
$548$	403.582			0.736463
$549$		−	208.396i		−	0.379592i
$550$		0			0
$551$	305.724			0.554854
$552$			28.8516i			0.0522673i
$553$	237.227			0.428982
$554$	−33.1276			−0.0597972
$555$		0			0
$556$		−	9.47629i		−	0.0170437i
$557$		−	597.483i		−	1.07268i	−0.844002	−	0.536340i	$-0.819807\pi$
$557$		−	597.483i		−	1.07268i	0.844002	−	0.536340i	$-0.180193\pi$
$558$		−	345.948i		−	0.619979i
$559$	112.204			0.200723
$560$		0			0
$561$	18.4016	+	11.6733i	0.0328015	+	0.0208081i
$562$	−267.206			−0.475455
$563$			963.269i			1.71096i	0.517838	+	0.855479i	$0.326737\pi$
$563$			963.269i			1.71096i	−0.517838	+	0.855479i	$0.673263\pi$
$564$	3.21455			0.00569955
$565$		0			0
$566$	−536.541			−0.947953
$567$		−	367.798i		−	0.648674i
$568$		−	68.5874i		−	0.120753i
$569$			136.737i			0.240310i	0.992755	+	0.120155i	$0.0383392\pi$
$569$			136.737i			0.240310i	−0.992755	+	0.120155i	$0.961661\pi$
$570$		0			0
$571$			829.845i			1.45332i	0.686998	+	0.726659i	$0.258928\pi$
$571$			829.845i			1.45332i	−0.686998	+	0.726659i	$0.741072\pi$
$572$	287.010	+	182.069i	0.501765	+	0.318302i
$573$	8.64276			0.0150833
$574$		−	347.986i		−	0.606248i
$575$		0			0
$576$	534.885			0.928620
$577$	−636.305			−1.10278			−0.551391	−	0.834247i	$-0.685903\pi$
$577$	−636.305			−1.10278			−0.551391	+	0.834247i	$0.685903\pi$
$578$			14.7235i			0.0254732i
$579$			19.1379i			0.0330533i
$580$		0			0
$581$	197.795			0.340439
$582$		−	3.68708i		−	0.00633520i
$583$	195.332	−	307.918i	0.335046	−	0.528161i
$584$	−278.803			−0.477402
$585$		0			0
$586$	15.0750			0.0257253
$587$	455.242			0.775540			0.387770	−	0.921756i	$-0.373246\pi$
$587$	455.242			0.775540			0.387770	+	0.921756i	$0.373246\pi$
$588$	−6.02600			−0.0102483
$589$			945.450i			1.60518i
$590$		0			0
$591$			41.5576i			0.0703173i
$592$	224.733			0.379617
$593$		−	219.359i		−	0.369914i	−0.982747	−	0.184957i	$-0.940785\pi$
$593$		−	219.359i		−	0.369914i	0.982747	−	0.184957i	$-0.0592146\pi$
$594$	−27.9629	−	17.7387i	−0.0470756	−	0.0298631i
$595$		0			0
$596$		−	350.590i		−	0.588239i
$597$	−38.6889			−0.0648055
$598$	711.284			1.18944
$599$	−260.846			−0.435470			−0.217735	−	0.976008i	$-0.569867\pi$
$599$	−260.846			−0.435470			−0.217735	+	0.976008i	$0.569867\pi$
$600$		0			0
$601$			314.178i			0.522759i	0.965236	+	0.261379i	$0.0841773\pi$
$601$			314.178i			0.522759i	−0.965236	+	0.261379i	$0.915823\pi$
$602$			45.1355i			0.0749760i
$603$	−1021.52			−1.69406
$604$			255.072i			0.422305i
$605$		0			0
$606$	−27.2831			−0.0450216
$607$			423.627i			0.697903i	0.937141	+	0.348951i	$0.113462\pi$
$607$			423.627i			0.697903i	−0.937141	+	0.348951i	$0.886538\pi$
$608$	−964.799			−1.58684
$609$	−4.45112			−0.00730890
$610$		0			0
$611$		−	249.187i		−	0.407835i
$612$			289.911i			0.473710i
$613$			144.866i			0.236323i	0.992994	+	0.118162i	$0.0377001\pi$
$613$			144.866i			0.236323i	−0.992994	+	0.118162i	$0.962300\pi$
$614$	671.597			1.09381
$615$		0			0
$616$	−230.291	+	363.026i	−0.373849	+	0.589328i
$617$	−988.195			−1.60161			−0.800806	−	0.598923i	$-0.795595\pi$
$617$	−988.195			−1.60161			−0.800806	+	0.598923i	$0.795595\pi$
$618$		−	7.13695i		−	0.0115485i
$619$	822.930			1.32945			0.664725	−	0.747088i	$-0.268549\pi$
$619$	822.930			1.32945			0.664725	+	0.747088i	$0.268549\pi$
$620$		0			0
$621$	60.5575			0.0975161
$622$		−	147.757i		−	0.237551i
$623$		−	336.589i		−	0.540272i
$624$			9.59956i			0.0153839i
$625$		0			0
$626$			421.890i			0.673946i
$627$	38.1823	+	24.2215i	0.0608969	+	0.0386308i
$628$	−477.640			−0.760574
$629$			768.240i			1.22137i
$630$		0			0
$631$	−854.486			−1.35418			−0.677089	−	0.735902i	$-0.736759\pi$
$631$	−854.486			−1.35418			−0.677089	+	0.735902i	$0.736759\pi$
$632$	445.753			0.705305
$633$			36.4184i			0.0575330i
$634$			354.929i			0.559825i
$635$		0			0
$636$	−7.08361			−0.0111377
$637$			467.127i			0.733323i
$638$	73.3477	−	115.624i	0.114965	−	0.181229i
$639$	−71.9277			−0.112563
$640$		0			0
$641$	−70.2095			−0.109531			−0.0547656	−	0.998499i	$-0.517441\pi$
$641$	−70.2095			−0.109531			−0.0547656	+	0.998499i	$0.517441\pi$
$642$	−21.9416			−0.0341770
$643$	560.759			0.872097			0.436049	−	0.899923i	$-0.356378\pi$
$643$	560.759			0.872097			0.436049	+	0.899923i	$0.356378\pi$
$644$		−	250.030i		−	0.388246i
$645$		0			0
$646$			906.676i			1.40352i
$647$	−73.2119			−0.113156			−0.0565780	−	0.998398i	$-0.518019\pi$
$647$	−73.2119			−0.113156			−0.0565780	+	0.998398i	$0.518019\pi$
$648$		−	691.097i		−	1.06651i
$649$	303.722	−	478.782i	0.467985	−	0.737723i
$650$		0			0
$651$		−	13.7651i		−	0.0211445i
$652$	46.8897			0.0719167
$653$	52.7951			0.0808500			0.0404250	−	0.999183i	$-0.487129\pi$
$653$	52.7951			0.0808500			0.0404250	+	0.999183i	$0.487129\pi$
$654$	−9.12492			−0.0139525
$655$		0			0
$656$		−	264.201i		−	0.402746i
$657$			292.381i			0.445024i
$658$	100.239			0.152338
$659$		−	466.110i		−	0.707299i	−0.935378	−	0.353649i	$-0.884941\pi$
$659$		−	466.110i		−	0.707299i	0.935378	−	0.353649i	$-0.115059\pi$
$660$		0			0
$661$	759.575			1.14913			0.574565	−	0.818459i	$-0.305171\pi$
$661$	759.575			1.14913			0.574565	+	0.818459i	$0.305171\pi$
$662$			352.688i			0.532762i
$663$	−32.8157			−0.0494957
$664$	371.659			0.559728
$665$		0			0
$666$		−	583.279i		−	0.875794i
$667$			250.400i			0.375412i
$668$			7.85389i			0.0117573i
$669$	33.5235			0.0501098
$670$		0			0
$671$	215.394	+	136.639i	0.321005	+	0.203634i
$672$	14.0468			0.0209029
$673$		−	608.412i		−	0.904030i	−0.892010	−	0.452015i	$-0.850705\pi$
$673$		−	608.412i		−	0.904030i	0.892010	−	0.452015i	$-0.149295\pi$
$674$	770.935			1.14382
$675$		0			0
$676$	−196.579			−0.290798
$677$			557.900i			0.824077i	0.911166	+	0.412038i	$0.135183\pi$
$677$			557.900i			0.824077i	−0.911166	+	0.412038i	$0.864817\pi$
$678$			19.7469i			0.0291253i
$679$			100.470i			0.147968i
$680$		0			0
$681$			1.09388i			0.00160629i
$682$	357.566	+	226.827i	0.524290	+	0.332591i
$683$	785.901			1.15066			0.575330	−	0.817921i	$-0.304874\pi$
$683$	785.901			1.15066			0.575330	+	0.817921i	$0.304874\pi$
$684$			601.548i			0.879457i
$685$		0			0
$686$	−514.409			−0.749868
$687$	40.7711			0.0593466
$688$			34.2682i			0.0498084i
$689$			549.111i			0.796968i
$690$		0			0
$691$	480.448			0.695293			0.347647	−	0.937626i	$-0.386981\pi$
$691$	480.448			0.695293			0.347647	+	0.937626i	$0.386981\pi$
$692$			313.409i			0.452903i
$693$	380.706	+	241.506i	0.549360	+	0.348494i
$694$	313.438			0.451640
$695$		0			0
$696$	−8.36371			−0.0120168
$697$	903.160			1.29578
$698$	111.762			0.160117
$699$		−	31.0397i		−	0.0444059i
$700$		0			0
$701$			284.947i			0.406486i	0.979128	+	0.203243i	$0.0651481\pi$
$701$			284.947i			0.406486i	−0.979128	+	0.203243i	$0.934852\pi$
$702$	49.8663			0.0710346
$703$			1594.06i			2.26750i
$704$	−350.707	+	552.848i	−0.498163	+	0.785296i
$705$		0			0
$706$		−	258.150i		−	0.365651i
$707$	743.444			1.05155
$708$	−11.0143			−0.0155570
$709$	−313.418			−0.442057			−0.221028	−	0.975267i	$-0.570941\pi$
$709$	−313.418			−0.442057			−0.221028	+	0.975267i	$0.570941\pi$
$710$		0			0
$711$		−	467.462i		−	0.657471i
$712$		−	632.455i		−	0.888280i
$713$	−774.359			−1.08606
$714$		−	13.2005i		−	0.0184881i
$715$		0			0
$716$	−64.4561			−0.0900224
$717$		−	9.06551i		−	0.0126437i
$718$	−522.775			−0.728099
$719$	−1198.70			−1.66718			−0.833590	−	0.552384i	$-0.813718\pi$
$719$	−1198.70			−1.66718			−0.833590	+	0.552384i	$0.813718\pi$
$720$		0			0
$721$			194.477i			0.269732i
$722$			1353.87i			1.87516i
$723$			16.7899i			0.0232225i
$724$	−200.246			−0.276583
$725$		0			0
$726$	18.3210	−	8.62934i	0.0252355	−	0.0118861i
$727$	−152.540			−0.209821			−0.104910	−	0.994482i	$-0.533456\pi$
$727$	−152.540			−0.209821			−0.104910	+	0.994482i	$0.533456\pi$
$728$		−	647.386i		−	0.889267i
$729$	−722.630			−0.991262
$730$		0			0
$731$	−117.144			−0.160252
$732$		−	4.95512i		−	0.00676929i
$733$			1107.11i			1.51039i	0.655501	+	0.755194i	$0.272457\pi$
$733$			1107.11i			1.51039i	−0.655501	+	0.755194i	$0.727543\pi$
$734$		−	459.770i		−	0.626390i
$735$		0			0
$736$		−	790.206i		−	1.07365i
$737$	669.775	−	1055.82i	0.908786	−	1.43259i
$738$	−685.715			−0.929153
$739$			438.677i			0.593609i	0.954938	+	0.296805i	$0.0959210\pi$
$739$			438.677i			0.593609i	−0.954938	+	0.296805i	$0.904079\pi$
$740$		0			0
$741$	−68.0907			−0.0918903
$742$	−220.887			−0.297691
$743$		−	764.284i		−	1.02865i	−0.857597	−	0.514323i	$-0.828043\pi$
$743$		−	764.284i		−	1.02865i	0.857597	−	0.514323i	$-0.171957\pi$
$744$		−	25.8647i		−	0.0347644i
$745$		0			0
$746$	614.579			0.823832
$747$		−	389.760i		−	0.521767i
$748$	−299.646	−	190.085i	−0.400597	−	0.254124i
$749$	597.893			0.798255
$750$		0			0
$751$	1224.32			1.63025			0.815126	−	0.579283i	$-0.196668\pi$
$751$	1224.32			1.63025			0.815126	+	0.579283i	$0.196668\pi$
$752$	76.1041			0.101202
$753$	−6.04256			−0.00802464
$754$			206.193i			0.273465i
$755$		0			0
$756$		−	17.5290i		−	0.0231865i
$757$	1346.79			1.77911			0.889555	−	0.456828i	$-0.151014\pi$
$757$	1346.79			1.77911			0.889555	+	0.456828i	$0.151014\pi$
$758$		−	586.852i		−	0.774211i
$759$	−19.8383	+	31.2728i	−0.0261374	+	0.0412026i
$760$		0			0
$761$		−	642.215i		−	0.843909i	−0.906617	−	0.421954i	$-0.861344\pi$
$761$		−	642.215i		−	0.843909i	0.906617	−	0.421954i	$-0.138656\pi$
$762$	−19.0405			−0.0249875
$763$	248.647			0.325881
$764$	−140.736			−0.184210
$765$		0			0
$766$			87.7886i			0.114607i
$767$			853.814i			1.11319i
$768$	30.7181			0.0399976
$769$			786.000i			1.02211i	0.859549	+	0.511053i	$0.170744\pi$
$769$			786.000i			1.02211i	−0.859549	+	0.511053i	$0.829256\pi$
$770$		0			0
$771$	4.79601			0.00622051
$772$		−	311.635i		−	0.403673i
$773$	1311.57			1.69672			0.848360	−	0.529419i	$-0.177590\pi$
$773$	1311.57			1.69672			0.848360	+	0.529419i	$0.177590\pi$
$774$	88.9406			0.114910
$775$		0			0
$776$			188.785i			0.243280i
$777$		−	23.2083i		−	0.0298691i
$778$		−	601.166i		−	0.772706i
$779$	1874.01			2.40566
$780$		0			0
$781$	47.1607	−	74.3432i	0.0603850	−	0.0951898i
$782$	−742.601			−0.949618
$783$			17.5549i			0.0224200i
$784$	−142.665			−0.181971
$785$		0			0
$786$	19.3476			0.0246152
$787$			658.660i			0.836925i	0.908234	+	0.418462i	$0.137431\pi$
$787$			658.660i			0.836925i	−0.908234	+	0.418462i	$0.862569\pi$
$788$		−	676.711i		−	0.858770i
$789$			33.1575i			0.0420247i
$790$		0			0
$791$		−	538.089i		−	0.680265i
$792$	715.352	+	453.794i	0.903222	+	0.572972i
$793$	−384.114			−0.484381
$794$		−	347.022i		−	0.437055i
$795$		0			0
$796$	629.998			0.791455
$797$	−1499.40			−1.88130			−0.940651	−	0.339376i	$-0.889784\pi$
$797$	−1499.40			−1.88130			−0.940651	+	0.339376i	$0.889784\pi$
$798$		−	27.3904i		−	0.0343238i
$799$			260.158i			0.325605i
$800$		0			0
$801$	−663.257			−0.828036
$802$		−	148.297i		−	0.184909i
$803$	−302.200	−	191.705i	−0.376339	−	0.238736i
$804$	−24.2890			−0.0302102
$805$		0			0
$806$	−637.649			−0.791128
$807$	−34.0959			−0.0422501
$808$	1396.94			1.72889
$809$		−	1400.12i		−	1.73068i	−0.501186	−	0.865340i	$-0.667103\pi$
$809$		−	1400.12i		−	1.73068i	0.501186	−	0.865340i	$-0.332897\pi$
$810$		0			0
$811$			611.795i			0.754371i	0.926138	+	0.377186i	$0.123108\pi$
$811$			611.795i			0.754371i	−0.926138	+	0.377186i	$0.876892\pi$
$812$	72.4807			0.0892620
$813$		−	31.7873i		−	0.0390988i
$814$	602.867	+	382.437i	0.740622	+	0.469824i
$815$		0			0
$816$		−	10.0222i		−	0.0122821i
$817$	−243.068			−0.297513
$818$	−1014.22			−1.23988
$819$	−678.915			−0.828956
$820$		0			0
$821$			1249.80i			1.52230i	0.648579	+	0.761148i	$0.275364\pi$
$821$			1249.80i			1.52230i	−0.648579	+	0.761148i	$0.724636\pi$
$822$			36.2110i			0.0440523i
$823$	−899.845			−1.09337			−0.546686	−	0.837338i	$-0.684111\pi$
$823$	−899.845			−1.09337			−0.546686	+	0.837338i	$0.684111\pi$
$824$			365.424i			0.443476i
$825$		0			0
$826$	−343.458			−0.415808
$827$		−	1331.57i		−	1.61012i	−0.593193	−	0.805060i	$-0.702133\pi$
$827$		−	1331.57i		−	1.61012i	0.593193	−	0.805060i	$-0.297867\pi$
$828$	−492.691			−0.595037
$829$	−578.195			−0.697461			−0.348730	−	0.937223i	$-0.613387\pi$
$829$	−578.195			−0.697461			−0.348730	+	0.937223i	$0.613387\pi$
$830$		0			0
$831$			2.59740i			0.00312563i
$832$		−	985.896i		−	1.18497i
$833$		−	487.694i		−	0.585467i
$834$	0.850251			0.00101949
$835$		0			0
$836$	−621.750	−	394.416i	−0.743720	−	0.471789i
$837$	−54.2883			−0.0648606
$838$			608.310i			0.725907i
$839$	779.704			0.929325			0.464663	−	0.885488i	$-0.346176\pi$
$839$	779.704			0.929325			0.464663	+	0.885488i	$0.346176\pi$
$840$		0			0
$841$	768.412			0.913689
$842$		−	787.999i		−	0.935866i
$843$			20.9505i			0.0248523i
$844$		−	593.026i		−	0.702638i
$845$		0			0
$846$		−	197.523i		−	0.233478i
$847$	−499.234	+	235.143i	−0.589414	+	0.277619i
$848$	−167.704			−0.197764
$849$			42.0680i			0.0495500i
$850$		0			0
$851$	−1305.59			−1.53419
$852$	−1.71026			−0.00200734
$853$			1330.04i			1.55925i	0.626250	+	0.779623i	$0.284589\pi$
$853$			1330.04i			1.55925i	−0.626250	+	0.779623i	$0.715411\pi$
$854$		−	154.515i		−	0.180931i
$855$		0			0
$856$	1123.45			1.31244
$857$		−	223.662i		−	0.260983i	−0.991449	−	0.130491i	$-0.958345\pi$
$857$		−	223.662i		−	0.260983i	0.991449	−	0.130491i	$-0.0416555\pi$
$858$	−16.3359	+	25.7517i	−0.0190396	+	0.0300136i
$859$	−1512.14			−1.76035			−0.880174	−	0.474651i	$-0.842574\pi$
$859$	−1512.14			−1.76035			−0.880174	+	0.474651i	$0.842574\pi$
$860$		0			0
$861$	−27.2842			−0.0316889
$862$	−501.857			−0.582200
$863$	815.242			0.944661			0.472330	−	0.881422i	$-0.343413\pi$
$863$	815.242			0.944661			0.472330	+	0.881422i	$0.343413\pi$
$864$		−	55.3993i		−	0.0641196i
$865$		0			0
$866$			26.3503i			0.0304276i
$867$	1.15441			0.00133150
$868$			224.146i			0.258233i
$869$	483.160	+	306.500i	0.555996	+	0.352704i
$870$		0			0
$871$			1882.85i			2.16171i
$872$	467.211			0.535793
$873$	197.979			0.226780
$874$	−1540.86			−1.76299
$875$		0			0
$876$			6.95207i			0.00793615i
$877$			138.555i			0.157987i	0.996875	+	0.0789935i	$0.0251706\pi$
$877$			138.555i			0.157987i	−0.996875	+	0.0789935i	$0.974829\pi$
$878$	1013.73			1.15459
$879$		−	1.18197i		−	0.00134467i
$880$		0			0
$881$	415.019			0.471077			0.235538	−	0.971865i	$-0.424315\pi$
$881$	415.019			0.471077			0.235538	+	0.971865i	$0.424315\pi$
$882$			370.277i			0.419815i
$883$	285.257			0.323055			0.161527	−	0.986868i	$-0.448358\pi$
$883$	285.257			0.323055			0.161527	+	0.986868i	$0.448358\pi$
$884$	534.361			0.604480
$885$		0			0
$886$		−	524.972i		−	0.592519i
$887$		−	405.942i		−	0.457657i	−0.973467	−	0.228829i	$-0.926510\pi$
$887$		−	405.942i		−	0.457657i	0.973467	−	0.228829i	$-0.0734895\pi$
$888$		−	43.6086i		−	0.0491088i
$889$	518.840			0.583622
$890$		0			0
$891$	475.198	−	749.093i	0.533331	−	0.840733i
$892$	−545.886			−0.611980
$893$			539.814i			0.604495i
$894$	31.4564			0.0351861
$895$		0			0
$896$	−93.8956			−0.104794
$897$		−	55.7688i		−	0.0621726i
$898$			829.697i			0.923939i
$899$		−	224.477i		−	0.249697i
$900$		0			0
$901$		−	573.288i		−	0.636279i
$902$	449.601	−	708.743i	0.498449	−	0.785746i
$903$	3.53889			0.00391903
$904$		−	1011.08i		−	1.11845i
$905$		0			0
$906$	−22.8861			−0.0252606
$907$	−1577.64			−1.73940			−0.869700	−	0.493581i	$-0.835688\pi$
$907$	−1577.64			−1.73940			−0.869700	+	0.493581i	$0.835688\pi$
$908$		−	17.8125i		−	0.0196173i
$909$		−	1464.97i		−	1.61163i
$910$		0			0
$911$	−574.512			−0.630639			−0.315319	−	0.948986i	$-0.602112\pi$
$911$	−574.512			−0.630639			−0.315319	+	0.948986i	$0.602112\pi$
$912$		−	20.7955i		−	0.0228021i
$913$	402.849	+	255.553i	0.441236	+	0.279905i
$914$	−1164.77			−1.27436
$915$		0			0
$916$	−663.905			−0.724787
$917$	−527.207			−0.574926
$918$	−52.0619			−0.0567123
$919$			354.240i			0.385462i	0.981252	+	0.192731i	$0.0617345\pi$
$919$			354.240i			0.385462i	−0.981252	+	0.192731i	$0.938266\pi$
$920$		0			0
$921$		−	52.6571i		−	0.0571739i
$922$	128.446			0.139313
$923$			132.577i			0.143637i
$924$	9.05222	+	5.74240i	0.00979677	+	0.00621472i
$925$		0			0
$926$		−	74.4082i		−	0.0803544i
$927$	383.221			0.413399
$928$	229.071			0.246844
$929$	−230.873			−0.248518			−0.124259	−	0.992250i	$-0.539655\pi$
$929$	−230.873			−0.248518			−0.124259	+	0.992250i	$0.539655\pi$
$930$		0			0
$931$		−	1011.94i		−	1.08694i
$932$			505.442i			0.542319i
$933$	−11.5850			−0.0124169
$934$		−	676.555i		−	0.724363i
$935$		0			0
$936$	−1275.69			−1.36292
$937$			414.814i			0.442704i	0.975194	+	0.221352i	$0.0710470\pi$
$937$			414.814i			0.442704i	−0.975194	+	0.221352i	$0.928953\pi$
$938$	−757.400			−0.807463
$939$	33.0786			0.0352275
$940$		0			0
$941$			1428.08i			1.51762i	0.651315	+	0.758808i	$0.274218\pi$
$941$			1428.08i			1.51762i	−0.651315	+	0.758808i	$0.725782\pi$
$942$		−	42.8558i		−	0.0454945i
$943$			1534.88i			1.62766i
$944$	−260.763			−0.276232
$945$		0			0
$946$	−58.3155	+	91.9275i	−0.0616443	+	0.0971749i
$947$	−976.020			−1.03064			−0.515322	−	0.856997i	$-0.672328\pi$
$947$	−976.020			−1.03064			−0.515322	+	0.856997i	$0.672328\pi$
$948$		−	11.1150i		−	0.0117247i
$949$	538.914			0.567876
$950$		0			0
$951$	27.8285			0.0292624
$952$			675.890i			0.709968i
$953$		−	1273.90i		−	1.33673i	−0.743834	−	0.668364i	$-0.766995\pi$
$953$		−	1273.90i		−	1.33673i	0.743834	−	0.668364i	$-0.233005\pi$
$954$			435.263i			0.456250i
$955$		0			0
$956$			147.620i			0.154414i
$957$	−9.06559	−	5.75089i	−0.00947293	−	0.00600929i
$958$	266.178			0.277848
$959$		−	986.723i		−	1.02891i
$960$		0			0
$961$	−266.806			−0.277634
$962$	−1075.09			−1.11756
$963$		−	1178.16i		−	1.22343i
$964$		−	273.402i		−	0.283612i
$965$		0			0
$966$	22.4337			0.0232233
$967$		−	1586.32i		−	1.64045i	−0.572038	−	0.820227i	$-0.693847\pi$
$967$		−	1586.32i		−	1.64045i	0.572038	−	0.820227i	$-0.306153\pi$
$968$	−938.066	+	441.837i	−0.969077	+	0.456443i
$969$	71.0887			0.0733629
$970$		0			0
$971$	662.523			0.682310			0.341155	−	0.940007i	$-0.389182\pi$
$971$	662.523			0.682310			0.341155	+	0.940007i	$0.389182\pi$
$972$	−51.8245			−0.0533174
$973$	−23.1687			−0.0238116
$974$			535.924i			0.550230i
$975$		0			0
$976$		−	117.312i		−	0.120197i
$977$	1552.47			1.58902			0.794508	−	0.607254i	$-0.207729\pi$
$977$	1552.47			1.58902			0.794508	+	0.607254i	$0.207729\pi$
$978$			4.20713i			0.00430177i
$979$	434.876	−	685.531i	0.444204	−	0.700236i
$980$		0			0
$981$		−	489.965i		−	0.499455i
$982$	61.3901			0.0625154
$983$	−862.208			−0.877119			−0.438560	−	0.898702i	$-0.644511\pi$
$983$	−862.208			−0.877119			−0.438560	+	0.898702i	$0.644511\pi$
$984$	−51.2673			−0.0521009
$985$		0			0
$986$		−	215.271i		−	0.218328i
$987$		−	7.85930i		−	0.00796281i
$988$	1108.77			1.12224
$989$		−	199.082i		−	0.201296i
$990$		0			0
$991$	−1075.74			−1.08551			−0.542755	−	0.839891i	$-0.682619\pi$
$991$	−1075.74			−1.08551			−0.542755	+	0.839891i	$0.682619\pi$
$992$			708.401i			0.714113i
$993$	27.6528			0.0278477
$994$	−53.3306			−0.0536526
$995$		0			0
$996$		−	9.26749i		−	0.00930470i
$997$		−	872.880i		−	0.875507i	−0.899095	−	0.437753i	$-0.855774\pi$
$997$		−	872.880i		−	0.875507i	0.899095	−	0.437753i	$-0.144226\pi$
$998$			335.985i			0.336658i
$999$	−91.5317			−0.0916233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.c.f.76.4		8
5.2	odd	4		275.3.d.c.274.10		16
5.3	odd	4		275.3.d.c.274.7		16
5.4	even	2		55.3.c.a.21.5	yes	8
11.10	odd	2	inner	275.3.c.f.76.5		8
15.14	odd	2		495.3.b.a.406.4		8
20.19	odd	2		880.3.j.a.241.5		8
55.32	even	4		275.3.d.c.274.8		16
55.43	even	4		275.3.d.c.274.9		16
55.54	odd	2		55.3.c.a.21.4	✓	8
165.164	even	2		495.3.b.a.406.5		8
220.219	even	2		880.3.j.a.241.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.c.a.21.4	✓	8	55.54	odd	2
55.3.c.a.21.5	yes	8	5.4	even	2
275.3.c.f.76.4		8	1.1	even	1	trivial
275.3.c.f.76.5		8	11.10	odd	2	inner
275.3.d.c.274.7		16	5.3	odd	4
275.3.d.c.274.8		16	55.32	even	4
275.3.d.c.274.9		16	55.43	even	4
275.3.d.c.274.10		16	5.2	odd	4
495.3.b.a.406.4		8	15.14	odd	2
495.3.b.a.406.5		8	165.164	even	2
880.3.j.a.241.5		8	20.19	odd	2
880.3.j.a.241.6		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)

\(f(q)\)	\(=\)	\(q-1.46104i q^{2} -0.114554 q^{3} +1.86536 q^{4} +0.167368i q^{6} -4.56066i q^{7} -8.56953i q^{8} -8.98688 q^{9} +(5.89241 - 9.28868i) q^{11} -0.213685 q^{12} +16.5645i q^{13} -6.66330 q^{14} -5.05897 q^{16} -17.2939i q^{17} +13.1302i q^{18} -35.8838i q^{19} +0.522441i q^{21} +(-13.5711 - 8.60904i) q^{22} +29.3902 q^{23} +0.981674i q^{24} +24.2014 q^{26} +2.06047 q^{27} -8.50728i q^{28} +8.51985i q^{29} -26.3476 q^{31} -26.8868i q^{32} +(-0.674999 + 1.06406i) q^{33} -25.2670 q^{34} -16.7638 q^{36} -44.4227 q^{37} -52.4276 q^{38} -1.89753i q^{39} +52.2243i q^{41} +0.763308 q^{42} -6.77375i q^{43} +(10.9915 - 17.3268i) q^{44} -42.9402i q^{46} -15.0434 q^{47} +0.579525 q^{48} +28.2004 q^{49} +1.98108i q^{51} +30.8989i q^{52} +33.1498 q^{53} -3.01043i q^{54} -39.0827 q^{56} +4.11063i q^{57} +12.4478 q^{58} +51.5447 q^{59} +23.1889i q^{61} +38.4948i q^{62} +40.9861i q^{63} -59.5185 q^{64} +(1.55463 + 0.986200i) q^{66} +113.668 q^{67} -32.2593i q^{68} -3.36676 q^{69} +8.00364 q^{71} +77.0133i q^{72} -32.5342i q^{73} +64.9034i q^{74} -66.9363i q^{76} +(-42.3625 - 26.8732i) q^{77} -2.77237 q^{78} +52.0160i q^{79} +80.6459 q^{81} +76.3018 q^{82} +43.3699i q^{83} +0.974543i q^{84} -9.89672 q^{86} -0.975983i q^{87} +(-79.5996 - 50.4951i) q^{88} +73.8028 q^{89} +75.5451 q^{91} +54.8233 q^{92} +3.01822 q^{93} +21.9790i q^{94} +3.07999i q^{96} -22.0298 q^{97} -41.2019i q^{98} +(-52.9543 + 83.4762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} - 28 q^{4} - 4 q^{9} + 8 q^{11} + 48 q^{12} + 88 q^{16} - 80 q^{22} - 8 q^{23} - 100 q^{26} + 16 q^{27} + 36 q^{31} + 152 q^{33} + 80 q^{34} - 216 q^{36} + 88 q^{37} + 160 q^{38} - 280 q^{42}+ \cdots - 184 q^{99}+O(q^{100}) \) 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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