LMFDB - Embedded newform 136.2.c.b.69.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [136,2,Mod(69,136)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(136, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("136.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-1,0,1,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.4469724736.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 2x^{5} - 4x^{4} + 4x^{3} - 8x + 16 $ x^8 - x^7 + 2x^5 - 4x^4 + 4x^3 - 8x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.4
Root			$0.733159 - 1.20933i$ of defining polynomial
Character	$\chi$	$=$	136.69
Dual form			136.2.c.b.69.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.733159 + 1.20933i) q^{2} -0.826905i q^{3} +(-0.924955 - 1.77326i) q^{4} -1.12786i q^{5} +(1.00000 + 0.606253i) q^{6} +1.74755 q^{7} +(2.82260 + 0.181508i) q^{8} +2.31623 q^{9} +(1.36396 + 0.826905i) q^{10} -5.05364i q^{11} +(-1.46632 + 0.764850i) q^{12} +3.09887i q^{13} +(-1.28123 + 2.11337i) q^{14} -0.932637 q^{15} +(-2.28892 + 3.28038i) q^{16} +1.00000 q^{17} +(-1.69816 + 2.80108i) q^{18} +1.04322i q^{19} +(-2.00000 + 1.04322i) q^{20} -1.44506i q^{21} +(6.11151 + 3.70512i) q^{22} -7.54284 q^{23} +(0.150089 - 2.33402i) q^{24} +3.72792 q^{25} +(-3.74755 - 2.27196i) q^{26} -4.39601i q^{27} +(-1.61641 - 3.09887i) q^{28} +1.12786i q^{29} +(0.683771 - 1.12786i) q^{30} -2.68019 q^{31} +(-2.28892 - 5.17309i) q^{32} -4.17888 q^{33} +(-0.733159 + 1.20933i) q^{34} -1.97100i q^{35} +(-2.14241 - 4.10728i) q^{36} +9.14869i q^{37} +(-1.26160 - 0.764850i) q^{38} +2.56247 q^{39} +(0.204716 - 3.18351i) q^{40} -4.72792 q^{41} +(1.74755 + 1.05946i) q^{42} +1.52970i q^{43} +(-8.96142 + 4.67439i) q^{44} -2.61239i q^{45} +(5.53010 - 9.12177i) q^{46} +7.66056 q^{47} +(2.71256 + 1.89271i) q^{48} -3.94606 q^{49} +(-2.73316 + 4.50828i) q^{50} -0.826905i q^{51} +(5.49510 - 2.86631i) q^{52} +3.90954i q^{53} +(5.31623 + 3.22298i) q^{54} -5.69982 q^{55} +(4.93264 + 0.317194i) q^{56} +0.862647 q^{57} +(-1.36396 - 0.826905i) q^{58} +11.0351i q^{59} +(0.862647 + 1.65381i) q^{60} +1.12786i q^{61} +(1.96501 - 3.24123i) q^{62} +4.04773 q^{63} +(7.93411 + 1.02465i) q^{64} +3.49510 q^{65} +(3.06378 - 5.05364i) q^{66} +2.86631i q^{67} +(-0.924955 - 1.77326i) q^{68} +6.23721i q^{69} +(2.38359 + 1.44506i) q^{70} -3.01963 q^{71} +(6.53778 + 0.420413i) q^{72} +12.2230 q^{73} +(-11.0638 - 6.70745i) q^{74} -3.08263i q^{75} +(1.84991 - 0.964936i) q^{76} -8.83150i q^{77} +(-1.87870 + 3.09887i) q^{78} +3.95227 q^{79} +(3.69982 + 2.58159i) q^{80} +3.31360 q^{81} +(3.46632 - 5.71761i) q^{82} +9.34878i q^{83} +(-2.56247 + 1.33662i) q^{84} -1.12786i q^{85} +(-1.84991 - 1.12151i) q^{86} +0.932637 q^{87} +(0.917274 - 14.2644i) q^{88} -18.2672 q^{89} +(3.15924 + 1.91530i) q^{90} +5.41543i q^{91} +(6.97679 + 13.3754i) q^{92} +2.21626i q^{93} +(-5.61641 + 9.26414i) q^{94} +1.17662 q^{95} +(-4.27765 + 1.89271i) q^{96} -1.13735 q^{97} +(2.89309 - 4.77209i) q^{98} -11.7054i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{4} + 8 q^{6} - 12 q^{7} + 5 q^{8} - 8 q^{9} - 8 q^{10} - 2 q^{12} + 6 q^{14} + 12 q^{15} + 9 q^{16} + 8 q^{17} - 19 q^{18} - 16 q^{20} + 4 q^{22} - 16 q^{23} + 18 q^{24} - 8 q^{25} - 4 q^{26}+ \cdots - 57 q^{98}+O(q^{100}) $ 8 * q - q^2 + q^4 + 8 * q^6 - 12 * q^7 + 5 * q^8 - 8 * q^9 - 8 * q^10 - 2 * q^12 + 6 * q^14 + 12 * q^15 + 9 * q^16 + 8 * q^17 - 19 * q^18 - 16 * q^20 + 4 * q^22 - 16 * q^23 + 18 * q^24 - 8 * q^25 - 4 * q^26 - 20 * q^28 + 32 * q^30 + 24 * q^31 + 9 * q^32 - 8 * q^33 - q^34 - 45 * q^36 + 18 * q^38 - 12 * q^39 + 20 * q^40 - 12 * q^42 - 10 * q^44 - 18 * q^46 + 4 * q^47 + 6 * q^48 + 8 * q^49 - 17 * q^50 - 8 * q^52 + 16 * q^54 - 12 * q^55 + 20 * q^56 + 8 * q^57 + 8 * q^58 + 8 * q^60 + 26 * q^62 + 40 * q^63 + q^64 - 24 * q^65 - 28 * q^66 + q^68 + 12 * q^70 - 36 * q^71 - 21 * q^72 + 8 * q^73 - 36 * q^74 - 2 * q^76 + 44 * q^78 + 24 * q^79 - 4 * q^80 + 40 * q^81 + 18 * q^82 + 12 * q^84 + 2 * q^86 - 12 * q^87 + 10 * q^88 + 8 * q^89 - 12 * q^90 - 28 * q^92 - 52 * q^94 + 32 * q^95 + 54 * q^96 - 8 * q^97 - 57 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	−0.733159	+	1.20933i	−0.518422	+	0.855125i
$2$	−0.733159	+	1.20933i	−0.518422	+	0.855125i
$3$		−	0.826905i		−	0.477414i	−0.971092	−	0.238707i	$-0.923277\pi$
$3$		−	0.826905i		−	0.477414i	0.971092	−	0.238707i	$-0.0767235\pi$
$4$	−0.924955	−	1.77326i	−0.462478	−	0.886631i
$5$		−	1.12786i		−	0.504397i	−0.967676	−	0.252198i	$-0.918846\pi$
$5$		−	1.12786i		−	0.504397i	0.967676	−	0.252198i	$-0.0811535\pi$
$6$	1.00000	+	0.606253i	0.408248	+	0.247502i
$7$	1.74755			0.660513			0.330256	−	0.943891i	$-0.392865\pi$
$7$	1.74755			0.660513			0.330256	+	0.943891i	$0.392865\pi$
$8$	2.82260	+	0.181508i	0.997939	+	0.0641726i
$9$	2.31623			0.772076
$10$	1.36396	+	0.826905i	0.431322	+	0.261490i
$11$		−	5.05364i		−	1.52373i	−0.647736	−	0.761865i	$-0.724284\pi$
$11$		−	5.05364i		−	1.52373i	0.647736	−	0.761865i	$-0.275716\pi$
$12$	−1.46632	+	0.764850i	−0.423290	+	0.220793i
$13$			3.09887i			0.859471i	0.902955	+	0.429736i	$0.141393\pi$
$13$			3.09887i			0.859471i	−0.902955	+	0.429736i	$0.858607\pi$
$14$	−1.28123	+	2.11337i	−0.342424	+	0.564821i
$15$	−0.932637			−0.240806
$16$	−2.28892	+	3.28038i	−0.572229	+	0.820094i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	−1.69816	+	2.80108i	−0.400261	+	0.660222i
$19$			1.04322i			0.239332i	0.992814	+	0.119666i	$0.0381824\pi$
$19$			1.04322i			0.239332i	−0.992814	+	0.119666i	$0.961818\pi$
$20$	−2.00000	+	1.04322i	−0.447214	+	0.233272i
$21$		−	1.44506i		−	0.315338i
$22$	6.11151	+	3.70512i	1.30298	+	0.789934i
$23$	−7.54284			−1.57279			−0.786395	−	0.617724i	$-0.788055\pi$
$23$	−7.54284			−1.57279			−0.786395	+	0.617724i	$0.788055\pi$
$24$	0.150089	−	2.33402i	0.0306369	−	0.476430i
$25$	3.72792			0.745584
$26$	−3.74755	−	2.27196i	−0.734956	−	0.445569i
$27$		−	4.39601i		−	0.846013i
$28$	−1.61641	−	3.09887i	−0.305472	−	0.585631i
$29$			1.12786i			0.209439i	0.994502	+	0.104720i	$0.0333945\pi$
$29$			1.12786i			0.209439i	−0.994502	+	0.104720i	$0.966605\pi$
$30$	0.683771	−	1.12786i	0.124839	−	0.205919i
$31$	−2.68019			−0.481376			−0.240688	−	0.970603i	$-0.577373\pi$
$31$	−2.68019			−0.481376			−0.240688	+	0.970603i	$0.577373\pi$
$32$	−2.28892	−	5.17309i	−0.404627	−	0.914482i
$33$	−4.17888			−0.727449
$34$	−0.733159	+	1.20933i	−0.125736	+	0.207398i
$35$		−	1.97100i		−	0.333160i
$36$	−2.14241	−	4.10728i	−0.357068	−	0.684547i
$37$			9.14869i			1.50404i	0.659143	+	0.752018i	$0.270919\pi$
$37$			9.14869i			1.50404i	−0.659143	+	0.752018i	$0.729081\pi$
$38$	−1.26160	−	0.764850i	−0.204659	−	0.124075i
$39$	2.56247			0.410323
$40$	0.204716	−	3.18351i	0.0323685	−	0.503357i
$41$	−4.72792			−0.738377			−0.369189	−	0.929355i	$-0.620364\pi$
$41$	−4.72792			−0.738377			−0.369189	+	0.929355i	$0.620364\pi$
$42$	1.74755	+	1.05946i	0.269653	+	0.163478i
$43$			1.52970i			0.233277i	0.993174	+	0.116638i	$0.0372119\pi$
$43$			1.52970i			0.233277i	−0.993174	+	0.116638i	$0.962788\pi$
$44$	−8.96142	+	4.67439i	−1.35099	+	0.704691i
$45$		−	2.61239i		−	0.389433i
$46$	5.53010	−	9.12177i	0.815369	−	1.34493i
$47$	7.66056			1.11741			0.558704	−	0.829367i	$-0.311299\pi$
$47$	7.66056			1.11741			0.558704	+	0.829367i	$0.311299\pi$
$48$	2.71256	+	1.89271i	0.391524	+	0.273190i
$49$	−3.94606			−0.563723
$50$	−2.73316	+	4.50828i	−0.386527	+	0.637568i
$51$		−	0.826905i		−	0.115790i
$52$	5.49510	−	2.86631i	0.762034	−	0.397486i
$53$			3.90954i			0.537016i	0.963277	+	0.268508i	$0.0865307\pi$
$53$			3.90954i			0.537016i	−0.963277	+	0.268508i	$0.913469\pi$
$54$	5.31623	+	3.22298i	0.723447	+	0.438592i
$55$	−5.69982			−0.768564
$56$	4.93264	+	0.317194i	0.659151	+	0.0423868i
$57$	0.862647			0.114260
$58$	−1.36396	−	0.826905i	−0.179097	−	0.108578i
$59$			11.0351i			1.43664i	0.695712	+	0.718321i	$0.255089\pi$
$59$			11.0351i			1.43664i	−0.695712	+	0.718321i	$0.744911\pi$
$60$	0.862647	+	1.65381i	0.111367	+	0.213506i
$61$			1.12786i			0.144408i	0.997390	+	0.0722042i	$0.0230033\pi$
$61$			1.12786i			0.144408i	−0.997390	+	0.0722042i	$0.976997\pi$
$62$	1.96501	−	3.24123i	0.249556	−	0.411637i
$63$	4.04773			0.509966
$64$	7.93411	+	1.02465i	0.991764	+	0.128081i
$65$	3.49510			0.433514
$66$	3.06378	−	5.05364i	0.377125	−	0.622060i
$67$			2.86631i			0.350176i	0.984553	+	0.175088i	$0.0560210\pi$
$67$			2.86631i			0.350176i	−0.984553	+	0.175088i	$0.943979\pi$
$68$	−0.924955	−	1.77326i	−0.112167	−	0.215040i
$69$			6.23721i			0.750871i
$70$	2.38359	+	1.44506i	0.284894	+	0.172718i
$71$	−3.01963			−0.358364			−0.179182	−	0.983816i	$-0.557345\pi$
$71$	−3.01963			−0.358364			−0.179182	+	0.983816i	$0.557345\pi$
$72$	6.53778	+	0.420413i	0.770485	+	0.0495462i
$73$	12.2230			1.43060			0.715298	−	0.698819i	$-0.246291\pi$
$73$	12.2230			1.43060			0.715298	+	0.698819i	$0.246291\pi$
$74$	−11.0638	−	6.70745i	−1.28614	−	0.779725i
$75$		−	3.08263i		−	0.355952i
$76$	1.84991	−	0.964936i	0.212199	−	0.110686i
$77$		−	8.83150i		−	1.00644i
$78$	−1.87870	+	3.09887i	−0.212721	+	0.350878i
$79$	3.95227			0.444665			0.222332	−	0.974971i	$-0.428633\pi$
$79$	3.95227			0.444665			0.222332	+	0.974971i	$0.428633\pi$
$80$	3.69982	+	2.58159i	0.413653	+	0.288630i
$81$	3.31360			0.368178
$82$	3.46632	−	5.71761i	0.382791	−	0.631405i
$83$			9.34878i			1.02616i	0.858340	+	0.513081i	$0.171496\pi$
$83$			9.34878i			1.02616i	−0.858340	+	0.513081i	$0.828504\pi$
$84$	−2.56247	+	1.33662i	−0.279588	+	0.145837i
$85$		−	1.12786i		−	0.122334i
$86$	−1.84991	−	1.12151i	−0.199481	−	0.120936i
$87$	0.932637			0.0999891
$88$	0.917274	−	14.2644i	0.0977817	−	1.52059i
$89$	−18.2672			−1.93632			−0.968158	−	0.250339i	$-0.919458\pi$
$89$	−18.2672			−1.93632			−0.968158	+	0.250339i	$0.919458\pi$
$90$	3.15924	+	1.91530i	0.333014	+	0.201890i
$91$			5.41543i			0.567692i
$92$	6.97679	+	13.3754i	0.727380	+	1.39448i
$93$			2.21626i			0.229816i
$94$	−5.61641	+	9.26414i	−0.579288	+	0.955523i
$95$	1.17662			0.120718
$96$	−4.27765	+	1.89271i	−0.436586	+	0.193174i
$97$	−1.13735			−0.115481			−0.0577403	−	0.998332i	$-0.518390\pi$
$97$	−1.13735			−0.115481			−0.0577403	+	0.998332i	$0.518390\pi$
$98$	2.89309	−	4.77209i	0.292246	−	0.482054i
$99$		−	11.7054i		−	1.17644i
$100$	−3.44816	−	6.61058i	−0.344816	−	0.661058i
$101$		−	15.1985i		−	1.51231i	−0.654393	−	0.756154i	$-0.727076\pi$
$101$		−	15.1985i		−	1.51231i	0.654393	−	0.756154i	$-0.272924\pi$
$102$	1.00000	+	0.606253i	0.0990148	+	0.0600280i
$103$	−14.6325			−1.44178			−0.720889	−	0.693050i	$-0.756266\pi$
$103$	−14.6325			−1.44178			−0.720889	+	0.693050i	$0.756266\pi$
$104$	−0.562468	+	8.74686i	−0.0551545	+	0.857700i
$105$	−1.62983			−0.159055
$106$	−4.72792	−	2.86631i	−0.459216	−	0.278401i
$107$		−	3.08263i		−	0.298010i	−0.988836	−	0.149005i	$-0.952393\pi$
$107$		−	3.08263i		−	0.298010i	0.988836	−	0.149005i	$-0.0476070\pi$
$108$	−7.79528	+	4.06612i	−0.750102	+	0.391262i
$109$		−	17.6022i		−	1.68598i	−0.537929	−	0.842990i	$-0.680793\pi$
$109$		−	17.6022i		−	1.68598i	0.537929	−	0.842990i	$-0.319207\pi$
$110$	4.17888	−	6.89296i	0.398440	−	0.657218i
$111$	7.56509			0.718047
$112$	−4.00000	+	5.73263i	−0.377964	+	0.541683i
$113$	5.49510			0.516936			0.258468	−	0.966020i	$-0.416782\pi$
$113$	5.49510			0.516936			0.258468	+	0.966020i	$0.416782\pi$
$114$	−0.632458	+	1.04322i	−0.0592351	+	0.0977069i
$115$			8.50730i			0.793310i
$116$	2.00000	−	1.04322i	0.185695	−	0.0968610i
$117$			7.17769i			0.663577i
$118$	−13.3450	−	8.09045i	−1.22851	−	0.744786i
$119$	1.74755			0.160198
$120$	−2.63246	−	0.169281i	−0.240309	−	0.0154531i
$121$	−14.5393			−1.32175
$122$	−1.36396	−	0.826905i	−0.123487	−	0.0748644i
$123$			3.90954i			0.352511i
$124$	2.47906	+	4.75268i	0.222626	+	0.426803i
$125$		−	9.84392i		−	0.880467i
$126$	−2.96763	+	4.89504i	−0.264378	+	0.436085i
$127$	14.7279			1.30689			0.653446	−	0.756973i	$-0.273323\pi$
$127$	14.7279			1.30689			0.653446	+	0.756973i	$0.273323\pi$
$128$	−7.05610	+	8.84372i	−0.623677	+	0.781682i
$129$	1.26492			0.111370
$130$	−2.56247	+	4.22673i	−0.224743	+	0.370709i
$131$			10.5015i			0.917524i	0.888559	+	0.458762i	$0.151707\pi$
$131$			10.5015i			0.917524i	−0.888559	+	0.458762i	$0.848293\pi$
$132$	3.86527	+	7.41024i	0.336429	+	0.644979i
$133$			1.82309i			0.158082i
$134$	−3.46632	−	2.10146i	−0.299444	−	0.181539i
$135$	−4.95811			−0.426726
$136$	2.82260	+	0.181508i	0.242036	+	0.0155642i
$137$	5.31623			0.454196			0.227098	−	0.973872i	$-0.427076\pi$
$137$	5.31623			0.454196			0.227098	+	0.973872i	$0.427076\pi$
$138$	−7.54284	−	4.57286i	−0.642089	−	0.389268i
$139$		−	2.36527i		−	0.200619i	−0.994956	−	0.100310i	$-0.968017\pi$
$139$		−	2.36527i		−	0.200619i	0.994956	−	0.100310i	$-0.0319834\pi$
$140$	−3.49510	+	1.82309i	−0.295390	+	0.154079i
$141$		−	6.33455i		−	0.533465i
$142$	2.21387	−	3.65173i	0.185784	−	0.306446i
$143$	15.6606			1.30960
$144$	−5.30165	+	7.59810i	−0.441804	+	0.633175i
$145$	1.27208			0.105640
$146$	−8.96142	+	14.7817i	−0.741653	+	1.22334i
$147$			3.26302i			0.269129i
$148$	16.2230	−	8.46213i	1.33352	−	0.695583i
$149$		−	21.4357i		−	1.75608i	−0.478585	−	0.878041i	$-0.658850\pi$
$149$		−	21.4357i		−	1.75608i	0.478585	−	0.878041i	$-0.341150\pi$
$150$	3.72792	+	2.26006i	0.304383	+	0.184533i
$151$	−18.1276			−1.47520			−0.737600	−	0.675238i	$-0.764041\pi$
$151$	−18.1276			−1.47520			−0.737600	+	0.675238i	$0.764041\pi$
$152$	−0.189353	+	2.94460i	−0.0153586	+	0.238839i
$153$	2.31623			0.187256
$154$	10.6802	+	6.47489i	0.860634	+	0.521762i
$155$			3.02289i			0.242804i
$156$	−2.37017	−	4.54393i	−0.189765	−	0.363805i
$157$			14.6187i			1.16670i	0.812220	+	0.583351i	$0.198259\pi$
$157$			14.6187i			1.16670i	−0.812220	+	0.583351i	$0.801741\pi$
$158$	−2.89764	+	4.77959i	−0.230524	+	0.380244i
$159$	3.23282			0.256379
$160$	−5.83455	+	2.58159i	−0.461261	+	0.204092i
$161$	−13.1815			−1.03885
$162$	−2.42940	+	4.00724i	−0.190872	+	0.314838i
$163$		−	19.4090i		−	1.52023i	−0.649788	−	0.760116i	$-0.725142\pi$
$163$		−	19.4090i		−	1.52023i	0.649788	−	0.760116i	$-0.274858\pi$
$164$	4.37311	+	8.38384i	0.341483	+	0.654668i
$165$			4.71321i			0.366923i
$166$	−11.3058	−	6.85414i	−0.877497	−	0.531985i
$167$	11.8751			0.918924			0.459462	−	0.888197i	$-0.348042\pi$
$167$	11.8751			0.918924			0.459462	+	0.888197i	$0.348042\pi$
$168$	0.262289	−	4.07882i	0.0202361	−	0.314688i
$169$	3.39702			0.261309
$170$	1.36396	+	0.826905i	0.104611	+	0.0634207i
$171$			2.41635i			0.184783i
$172$	2.71256	−	1.41490i	0.206831	−	0.107885i
$173$			18.0197i			1.37001i	0.728539	+	0.685005i	$0.240200\pi$
$173$			18.0197i			1.37001i	−0.728539	+	0.685005i	$0.759800\pi$
$174$	−0.683771	+	1.12786i	−0.0518366	+	0.0855032i
$175$	6.51474			0.492468
$176$	16.5778	+	11.5673i	1.24960	+	0.871922i
$177$	9.12494			0.685872
$178$	13.3927	−	22.0910i	1.00383	−	1.65579i
$179$		−	15.8637i		−	1.18571i	−0.805310	−	0.592855i	$-0.798001\pi$
$179$		−	15.8637i		−	1.18571i	0.805310	−	0.592855i	$-0.201999\pi$
$180$	−4.63246	+	2.41635i	−0.345283	+	0.180104i
$181$			11.0659i			0.822519i	0.911518	+	0.411259i	$0.134911\pi$
$181$			11.0659i			0.822519i	−0.911518	+	0.411259i	$0.865089\pi$
$182$	−6.54904	−	3.97038i	−0.485447	−	0.294304i
$183$	0.932637			0.0689425
$184$	−21.2904	−	1.36908i	−1.56955	−	0.100930i
$185$	10.3185			0.758630
$186$	−2.68019	−	1.62487i	−0.196521	−	0.119141i
$187$		−	5.05364i		−	0.369559i
$188$	−7.08567	−	13.5842i	−0.516776	−	0.990728i
$189$		−	7.68226i		−	0.558803i
$190$	−0.862647	+	1.42292i	−0.0625830	+	0.103229i
$191$	14.2930			1.03421			0.517103	−	0.855923i	$-0.327010\pi$
$191$	14.2930			1.03421			0.517103	+	0.855923i	$0.327010\pi$
$192$	0.847284	−	6.56075i	0.0611475	−	0.473481i
$193$	−21.3480			−1.53666			−0.768330	−	0.640054i	$-0.778912\pi$
$193$	−21.3480			−1.53666			−0.768330	+	0.640054i	$0.778912\pi$
$194$	0.833861	−	1.37543i	0.0598677	−	0.0987504i
$195$		−	2.89012i		−	0.206966i
$196$	3.64993	+	6.99740i	0.260709	+	0.499814i
$197$		−	22.8269i		−	1.62635i	−0.582018	−	0.813176i	$-0.697737\pi$
$197$		−	22.8269i		−	1.62635i	0.582018	−	0.813176i	$-0.302263\pi$
$198$	14.1557	+	8.58191i	1.00600	+	0.609890i
$199$	−8.81492			−0.624873			−0.312436	−	0.949939i	$-0.601145\pi$
$199$	−8.81492			−0.624873			−0.312436	+	0.949939i	$0.601145\pi$
$200$	10.5224	+	0.676646i	0.744047	+	0.0478461i
$201$	2.37017			0.167179
$202$	18.3800	+	11.1429i	1.29321	+	0.784014i
$203$			1.97100i			0.138337i
$204$	−1.46632	+	0.764850i	−0.102663	+	0.0535502i
$205$			5.33246i			0.372435i
$206$	10.7279	−	17.6955i	0.747450	−	1.23290i
$207$	−17.4709			−1.21431
$208$	−10.1655	−	7.09305i	−0.704847	−	0.491814i
$209$	5.27208			0.364677
$210$	1.19493	−	1.97100i	0.0824577	−	0.136012i
$211$			8.67845i			0.597449i	0.954339	+	0.298725i	$0.0965612\pi$
$211$			8.67845i			0.597449i	−0.954339	+	0.298725i	$0.903439\pi$
$212$	6.93264	−	3.61615i	0.476135	−	0.248358i
$213$			2.49695i			0.171088i
$214$	3.72792	+	2.26006i	0.254835	+	0.154495i
$215$	1.72529			0.117664
$216$	0.797910	−	12.4082i	0.0542909	−	0.844269i
$217$	−4.68377			−0.317955
$218$	21.2868	+	12.9052i	1.44172	+	0.874049i
$219$		−	10.1073i		−	0.682986i
$220$	5.27208	+	10.1073i	0.355444	+	0.681432i
$221$			3.09887i			0.208452i
$222$	−5.54642	+	9.14869i	−0.372251	+	0.614020i
$223$	−4.33228			−0.290111			−0.145055	−	0.989424i	$-0.546336\pi$
$223$	−4.33228			−0.290111			−0.145055	+	0.989424i	$0.546336\pi$
$224$	−4.00000	−	9.04025i	−0.267261	−	0.604027i
$225$	8.63472			0.575648
$226$	−4.02879	+	6.64539i	−0.267991	+	0.442045i
$227$			25.6392i			1.70173i	0.525381	+	0.850867i	$0.323923\pi$
$227$			25.6392i			1.70173i	−0.525381	+	0.850867i	$0.676077\pi$
$228$	−0.797910	−	1.52970i	−0.0528429	−	0.101307i
$229$			2.46448i			0.162857i	0.996679	+	0.0814287i	$0.0259483\pi$
$229$			2.46448i			0.162857i	−0.996679	+	0.0814287i	$0.974052\pi$
$230$	−10.2881	−	6.23721i	−0.678379	−	0.411269i
$231$	−7.30281			−0.480489
$232$	−0.204716	+	3.18351i	−0.0134403	+	0.209008i
$233$	−2.67172			−0.175030			−0.0875151	−	0.996163i	$-0.527893\pi$
$233$	−2.67172			−0.175030			−0.0875151	+	0.996163i	$0.527893\pi$
$234$	−8.68019	−	5.26239i	−0.567442	−	0.344013i
$235$		−	8.64007i		−	0.563616i
$236$	19.5680	−	10.2069i	1.27377	−	0.664415i
$237$		−	3.26815i		−	0.212289i
$238$	−1.28123	+	2.11337i	−0.0830501	+	0.136989i
$239$	−2.89337			−0.187157			−0.0935784	−	0.995612i	$-0.529831\pi$
$239$	−2.89337			−0.187157			−0.0935784	+	0.995612i	$0.529831\pi$
$240$	2.13473	−	3.05940i	0.137796	−	0.197483i
$241$	13.8260			0.890612			0.445306	−	0.895379i	$-0.353095\pi$
$241$	13.8260			0.890612			0.445306	+	0.895379i	$0.353095\pi$
$242$	10.6596	−	17.5827i	0.685224	−	1.13026i
$243$		−	15.9281i		−	1.02179i
$244$	2.00000	−	1.04322i	0.128037	−	0.0667856i
$245$			4.45062i			0.284340i
$246$	−4.72792	−	2.86631i	−0.301441	−	0.182750i
$247$	−3.23282			−0.205699
$248$	−7.56509	−	0.486475i	−0.480384	−	0.0308912i
$249$	7.73055			0.489903
$250$	11.9045	+	7.21716i	0.752909	+	0.456453i
$251$			26.7270i			1.68700i	0.537132	+	0.843498i	$0.319508\pi$
$251$			26.7270i			1.68700i	−0.537132	+	0.843498i	$0.680492\pi$
$252$	−3.74397	−	7.17769i	−0.235848	−	0.452152i
$253$			38.1188i			2.39651i
$254$	−10.7979	+	17.8109i	−0.677521	+	1.11756i
$255$	−0.932637			−0.0584040
$256$	−5.52173	−	15.0170i	−0.345108	−	0.938563i
$257$	−0.460746			−0.0287405			−0.0143703	−	0.999897i	$-0.504574\pi$
$257$	−0.460746			−0.0287405			−0.0143703	+	0.999897i	$0.504574\pi$
$258$	−0.927384	+	1.52970i	−0.0577364	+	0.0952349i
$259$			15.9878i			0.993435i
$260$	−3.23282	−	6.19774i	−0.200491	−	0.384367i
$261$			2.61239i			0.161703i
$262$	−12.6998	−	7.69930i	−0.784598	−	0.475664i
$263$	−16.2623			−1.00278			−0.501388	−	0.865223i	$-0.667177\pi$
$263$	−16.2623			−1.00278			−0.501388	+	0.865223i	$0.667177\pi$
$264$	−11.7953	−	0.758498i	−0.725950	−	0.0466823i
$265$	4.40943			0.270869
$266$	−2.20472	−	1.33662i	−0.135180	−	0.0819531i
$267$			15.1052i			0.924424i
$268$	5.08273	−	2.65121i	0.310477	−	0.161949i
$269$			20.0596i			1.22306i	0.791222	+	0.611529i	$0.209445\pi$
$269$			20.0596i			1.22306i	−0.791222	+	0.611529i	$0.790555\pi$
$270$	3.63508	−	5.99599i	0.221224	−	0.364904i
$271$	0.670347			0.0407207			0.0203604	−	0.999793i	$-0.493519\pi$
$271$	0.670347			0.0407207			0.0203604	+	0.999793i	$0.493519\pi$
$272$	−2.28892	+	3.28038i	−0.138786	+	0.198902i
$273$	4.47805			0.271024
$274$	−3.89764	+	6.42907i	−0.235465	+	0.388394i
$275$		−	18.8396i		−	1.13607i
$276$	11.0602	−	5.76914i	0.665746	−	0.347261i
$277$			3.58534i			0.215422i	0.994182	+	0.107711i	$0.0343522\pi$
$277$			3.58534i			0.215422i	−0.994182	+	0.107711i	$0.965648\pi$
$278$	2.86039	+	1.73412i	0.171555	+	0.104005i
$279$	−6.20793			−0.371659
$280$	0.357752	−	5.56335i	0.0213798	−	0.332474i
$281$	0.397016			0.0236840			0.0118420	−	0.999930i	$-0.496230\pi$
$281$	0.397016			0.0236840			0.0118420	+	0.999930i	$0.496230\pi$
$282$	7.66056	+	4.64423i	0.456180	+	0.276560i
$283$		−	9.96859i		−	0.592571i	−0.955099	−	0.296286i	$-0.904252\pi$
$283$		−	9.96859i		−	0.592571i	0.955099	−	0.296286i	$-0.0957481\pi$
$284$	2.79302	+	5.35460i	0.165736	+	0.317737i
$285$		−	0.972950i		−	0.0576326i
$286$	−11.4817	+	18.9388i	−0.678926	+	1.11987i
$287$	−8.26229			−0.487708
$288$	−5.30165	−	11.9821i	−0.312403	−	0.706050i
$289$	1.00000			0.0588235
$290$	−0.932637	+	1.53836i	−0.0547663	+	0.0903358i
$291$			0.940482i			0.0551320i
$292$	−11.3058	−	21.6746i	−0.661619	−	1.26841i
$293$		−	5.39407i		−	0.315125i	−0.987509	−	0.157562i	$-0.949636\pi$
$293$		−	5.39407i		−	0.315125i	0.987509	−	0.157562i	$-0.0503635\pi$
$294$	−3.94606	−	2.39231i	−0.230139	−	0.139522i
$295$	12.4461			0.724637
$296$	−1.66056	+	25.8231i	−0.0965179	+	1.50094i
$297$	−22.2159			−1.28910
$298$	25.9228	+	15.7158i	1.50167	+	0.910392i
$299$		−	23.3743i		−	1.35177i
$300$	−5.46632	+	2.85130i	−0.315598	+	0.164620i
$301$			2.67323i			0.154082i
$302$	13.2904	−	21.9222i	0.764776	−	1.26148i
$303$	−12.5677			−0.721997
$304$	−3.42217	−	2.38785i	−0.196275	−	0.136953i
$305$	1.27208			0.0728391
$306$	−1.69816	+	2.80108i	−0.0970776	+	0.160127i
$307$		−	28.9614i		−	1.65291i	−0.562999	−	0.826457i	$-0.690353\pi$
$307$		−	28.9614i		−	1.65291i	0.562999	−	0.826457i	$-0.309647\pi$
$308$	−15.6606	+	8.16874i	−0.892343	+	0.465457i
$309$			12.0996i			0.688325i
$310$	−3.65567	−	2.21626i	−0.207628	−	0.125875i
$311$	−13.5049			−0.765795			−0.382898	−	0.923791i	$-0.625074\pi$
$311$	−13.5049			−0.765795			−0.382898	+	0.923791i	$0.625074\pi$
$312$	7.23282	+	0.465108i	0.409478	+	0.0263315i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−17.6789	−	10.7179i	−0.997676	−	0.604844i
$315$		−	4.56529i		−	0.257225i
$316$	−3.65567	−	7.00841i	−0.205648	−	0.394254i
$317$		−	14.7272i		−	0.827161i	−0.910468	−	0.413580i	$-0.864278\pi$
$317$		−	14.7272i		−	0.827161i	0.910468	−	0.413580i	$-0.135722\pi$
$318$	−2.37017	+	3.90954i	−0.132912	+	0.219236i
$319$	5.69982			0.319129
$320$	1.15566	−	8.94860i	0.0646035	−	0.500242i
$321$	−2.54904			−0.142274
$322$	9.66414	−	15.9408i	0.538561	−	0.888345i
$323$			1.04322i			0.0580466i
$324$	−3.06493	−	5.87589i	−0.170274	−	0.326438i
$325$			11.5523i			0.640808i
$326$	23.4719	+	14.2299i	1.29999	+	0.788121i
$327$	−14.5553			−0.804910
$328$	−13.3450	−	0.858154i	−0.736855	−	0.0473836i
$329$	13.3872			0.738062
$330$	−5.69982	−	3.45553i	−0.313765	−	0.190221i
$331$			2.58159i			0.141897i	0.997480	+	0.0709484i	$0.0226026\pi$
$331$			2.58159i			0.141897i	−0.997480	+	0.0709484i	$0.977397\pi$
$332$	16.5778	−	8.64720i	0.909827	−	0.474577i
$333$			21.1905i			1.16123i
$334$	−8.70635	+	14.3609i	−0.476390	+	0.785795i
$335$	3.23282			0.176628
$336$	4.74034	+	3.30762i	0.258607	+	0.180445i
$337$	7.00263			0.381457			0.190729	−	0.981643i	$-0.438915\pi$
$337$	7.00263			0.381457			0.190729	+	0.981643i	$0.438915\pi$
$338$	−2.49055	+	4.10811i	−0.135468	+	0.223452i
$339$		−	4.54393i		−	0.246792i
$340$	−2.00000	+	1.04322i	−0.108465	+	0.0565768i
$341$			13.5447i			0.733487i
$342$	−2.92216	−	1.77157i	−0.158012	−	0.0957954i
$343$	−19.1288			−1.03286
$344$	−0.277652	+	4.31773i	−0.0149700	+	0.232796i
$345$	7.03473			0.378737
$346$	−21.7917	−	13.2113i	−1.17153	−	0.710243i
$347$			1.76335i			0.0946614i	0.998879	+	0.0473307i	$0.0150715\pi$
$347$			1.76335i			0.0946614i	−0.998879	+	0.0473307i	$0.984929\pi$
$348$	−0.862647	−	1.65381i	−0.0462427	−	0.0886535i
$349$		−	36.8581i		−	1.97297i	−0.163851	−	0.986485i	$-0.552392\pi$
$349$		−	36.8581i		−	1.97297i	0.163851	−	0.986485i	$-0.447608\pi$
$350$	−4.77634	+	7.87846i	−0.255306	+	0.421122i
$351$	13.6227			0.727124
$352$	−26.1429	+	11.5673i	−1.39342	+	0.616542i
$353$	−32.9830			−1.75551			−0.877755	−	0.479109i	$-0.840960\pi$
$353$	−32.9830			−1.75551			−0.877755	+	0.479109i	$0.840960\pi$
$354$	−6.69003	+	11.0351i	−0.355571	+	0.586507i
$355$			3.40574i			0.180758i
$356$	16.8963	+	32.3925i	0.895503	+	1.71680i
$357$		−	1.44506i		−	0.0764806i
$358$	19.1844	+	11.6306i	1.01393	+	0.614698i
$359$	10.1093			0.533546			0.266773	−	0.963759i	$-0.414043\pi$
$359$	10.1093			0.533546			0.266773	+	0.963759i	$0.414043\pi$
$360$	0.474169	−	7.37373i	0.0249909	−	0.388630i
$361$	17.9117			0.942720
$362$	−13.3823	−	8.11304i	−0.703356	−	0.426412i
$363$			12.0226i			0.631022i
$364$	9.60298	−	5.00903i	0.503333	−	0.262545i
$365$		−	13.7859i		−	0.721588i
$366$	−0.683771	+	1.12786i	−0.0357413	+	0.0589544i
$367$	36.8261			1.92230			0.961152	−	0.276018i	$-0.0890150\pi$
$367$	36.8261			1.92230			0.961152	+	0.276018i	$0.0890150\pi$
$368$	17.2649	−	24.7433i	0.899996	−	1.28984i
$369$	−10.9509			−0.570083
$370$	−7.56509	+	12.4785i	−0.393291	+	0.648724i
$371$			6.83212i			0.354706i
$372$	3.93001	−	2.04994i	0.203762	−	0.106285i
$373$		−	15.2775i		−	0.791037i	−0.918458	−	0.395518i	$-0.870565\pi$
$373$		−	15.2775i		−	0.791037i	0.918458	−	0.395518i	$-0.129435\pi$
$374$	6.11151	+	3.70512i	0.316019	+	0.191587i
$375$	−8.13998			−0.420347
$376$	21.6227	+	1.39045i	1.11510	+	0.0717070i
$377$	−3.49510			−0.180007
$378$	9.29039	+	5.63232i	0.477846	+	0.289695i
$379$		−	14.9805i		−	0.769498i	−0.923021	−	0.384749i	$-0.874288\pi$
$379$		−	14.9805i		−	0.769498i	0.923021	−	0.384749i	$-0.125712\pi$
$380$	−1.08832	−	2.08645i	−0.0558295	−	0.107033i
$381$		−	12.1786i		−	0.623928i
$382$	−10.4791	+	17.2850i	−0.536155	+	0.884376i
$383$	−5.19355			−0.265378			−0.132689	−	0.991158i	$-0.542361\pi$
$383$	−5.19355			−0.265378			−0.132689	+	0.991158i	$0.542361\pi$
$384$	7.31292	+	5.83472i	0.373186	+	0.297752i
$385$	−9.96074			−0.507646
$386$	15.6515	−	25.8167i	0.796638	−	1.31404i
$387$			3.54313i			0.180108i
$388$	1.05200	+	2.01682i	0.0534072	+	0.102389i
$389$			9.29660i			0.471357i	0.971831	+	0.235678i	$0.0757312\pi$
$389$			9.29660i			0.471357i	−0.971831	+	0.235678i	$0.924269\pi$
$390$	3.49510	+	2.11892i	0.176982	+	0.107296i
$391$	−7.54284			−0.381458
$392$	−11.1381	−	0.716240i	−0.562561	−	0.0361756i
$393$	8.68377			0.438038
$394$	27.6053	+	16.7358i	1.39073	+	0.843137i
$395$		−	4.45763i		−	0.224287i
$396$	−20.7567	+	10.8270i	−1.04306	+	0.544075i
$397$		−	12.1177i		−	0.608172i	−0.952645	−	0.304086i	$-0.901649\pi$
$397$		−	12.1177i		−	0.608172i	0.952645	−	0.304086i	$-0.0983511\pi$
$398$	6.46274	−	10.6601i	0.323948	−	0.534344i
$399$	1.50752			0.0754705
$400$	−8.53290	+	12.2290i	−0.426645	+	0.611449i
$401$	30.3506			1.51564			0.757818	−	0.652466i	$-0.226265\pi$
$401$	30.3506			1.51564			0.757818	+	0.652466i	$0.226265\pi$
$402$	−1.73771	+	2.86631i	−0.0866691	+	0.142959i
$403$		−	8.30555i		−	0.413729i
$404$	−26.9509	+	14.0579i	−1.34086	+	0.699409i
$405$		−	3.73730i		−	0.185708i
$406$	−2.38359	−	1.44506i	−0.118296	−	0.0717171i
$407$	46.2342			2.29174
$408$	0.150089	−	2.33402i	0.00743054	−	0.115551i
$409$	23.3015			1.15219			0.576093	−	0.817384i	$-0.304576\pi$
$409$	23.3015			1.15219			0.576093	+	0.817384i	$0.304576\pi$
$410$	−6.44870	−	3.90954i	−0.318478	−	0.193078i
$411$		−	4.39601i		−	0.216839i
$412$	13.5344	+	25.9472i	0.666790	+	1.27833i
$413$			19.2843i			0.948920i
$414$	12.8090	−	21.1281i	0.629527	−	1.03839i
$415$	10.5442			0.517592
$416$	16.0307	−	7.09305i	0.785971	−	0.347765i
$417$	−1.95585			−0.0957784
$418$	−3.86527	+	6.37568i	−0.189057	+	0.311845i
$419$		−	8.50917i		−	0.415700i	−0.978161	−	0.207850i	$-0.933353\pi$
$419$		−	8.50917i		−	0.415700i	0.978161	−	0.207850i	$-0.0666466\pi$
$420$	1.50752	+	2.89012i	0.0735595	+	0.141023i
$421$		−	31.3191i		−	1.52640i	−0.646162	−	0.763200i	$-0.723627\pi$
$421$		−	31.3191i		−	1.52640i	0.646162	−	0.763200i	$-0.276373\pi$
$422$	−10.4951	−	6.36269i	−0.510894	−	0.309731i
$423$	17.7436			0.862724
$424$	−0.709611	+	11.0351i	−0.0344618	+	0.535910i
$425$	3.72792			0.180831
$426$	−3.01963	−	1.83066i	−0.146302	−	0.0886958i
$427$			1.97100i			0.0953835i
$428$	−5.46632	+	2.85130i	−0.264224	+	0.137823i
$429$		−	12.9498i		−	0.625222i
$430$	−1.26492	+	2.08645i	−0.0609996	+	0.100618i
$431$	19.2734			0.928366			0.464183	−	0.885739i	$-0.346348\pi$
$431$	19.2734			0.928366			0.464183	+	0.885739i	$0.346348\pi$
$432$	14.4206	+	10.0621i	0.693810	+	0.484113i
$433$	21.9363			1.05419			0.527095	−	0.849806i	$-0.323281\pi$
$433$	21.9363			1.05419			0.527095	+	0.849806i	$0.323281\pi$
$434$	3.43395	−	5.66422i	0.164835	−	0.271891i
$435$		−	1.05189i		−	0.0504342i
$436$	−31.2132	+	16.2812i	−1.49484	+	0.779728i
$437$		−	7.86887i		−	0.376419i
$438$	12.2230	+	7.41024i	0.584039	+	0.354075i
$439$	−5.43358			−0.259331			−0.129665	−	0.991558i	$-0.541390\pi$
$439$	−5.43358			−0.259331			−0.129665	+	0.991558i	$0.541390\pi$
$440$	−16.0883	−	1.03456i	−0.766980	−	0.0493208i
$441$	−9.13998			−0.435237
$442$	−3.74755	−	2.27196i	−0.178253	−	0.108066i
$443$		−	5.06043i		−	0.240428i	−0.992748	−	0.120214i	$-0.961642\pi$
$443$		−	5.06043i		−	0.240428i	0.992748	−	0.120214i	$-0.0383581\pi$
$444$	−6.99737	−	13.4149i	−0.332081	−	0.636643i
$445$			20.6029i			0.976671i
$446$	3.17625	−	5.23915i	0.150400	−	0.248081i
$447$	−17.7253			−0.838378
$448$	13.8653	+	1.79062i	0.655073	+	0.0845990i
$449$	−15.8653			−0.748729			−0.374364	−	0.927282i	$-0.622139\pi$
$449$	−15.8653			−0.748729			−0.374364	+	0.927282i	$0.622139\pi$
$450$	−6.33062	+	10.4422i	−0.298428	+	0.492251i
$451$			23.8932i			1.12509i
$452$	−5.08273	−	9.74426i	−0.239071	−	0.458331i
$453$			14.9898i			0.704281i
$454$	−31.0063	−	18.7976i	−1.45520	−	0.882216i
$455$	6.10788			0.286342
$456$	2.43491	+	0.156577i	0.114025	+	0.00733239i
$457$	−10.1272			−0.473730			−0.236865	−	0.971543i	$-0.576120\pi$
$457$	−10.1272			−0.473730			−0.236865	+	0.971543i	$0.576120\pi$
$458$	−2.98037	−	1.80686i	−0.139263	−	0.0844288i
$459$		−	4.39601i		−	0.205188i
$460$	15.0857	−	7.86887i	0.703373	−	0.366888i
$461$		−	22.6244i		−	1.05372i	−0.849951	−	0.526862i	$-0.823368\pi$
$461$		−	22.6244i		−	1.05372i	0.849951	−	0.526862i	$-0.176632\pi$
$462$	5.35412	−	8.83150i	0.249096	−	0.410878i
$463$	−7.18114			−0.333736			−0.166868	−	0.985979i	$-0.553365\pi$
$463$	−7.18114			−0.333736			−0.166868	+	0.985979i	$0.553365\pi$
$464$	−3.69982	−	2.58159i	−0.171760	−	0.119847i
$465$	2.49964			0.115918
$466$	1.95880	−	3.23099i	0.0907395	−	0.149673i
$467$			38.2074i			1.76803i	0.467459	+	0.884015i	$0.345170\pi$
$467$			38.2074i			1.76803i	−0.467459	+	0.884015i	$0.654830\pi$
$468$	12.7279	−	6.63904i	0.588348	−	0.306890i
$469$			5.00903i			0.231296i
$470$	10.4487	+	6.33455i	0.481962	+	0.292191i
$471$	12.0883			0.556999
$472$	−2.00295	+	31.1475i	−0.0921931	+	1.43368i
$473$	7.73055			0.355451
$474$	3.95227	+	2.39607i	0.181534	+	0.110055i
$475$			3.88906i			0.178442i
$476$	−1.61641	−	3.09887i	−0.0740879	−	0.142036i
$477$			9.05539i			0.414618i
$478$	2.12130	−	3.49904i	0.0970261	−	0.160042i
$479$	0.136030			0.00621538			0.00310769	−	0.999995i	$-0.499011\pi$
$479$	0.136030			0.00621538			0.00310769	+	0.999995i	$0.499011\pi$
$480$	2.13473	+	4.82461i	0.0974365	+	0.220212i
$481$	−28.3506			−1.29268
$482$	−10.1367	+	16.7202i	−0.461712	+	0.761584i
$483$			10.8998i			0.495960i
$484$	13.4482	+	25.7819i	0.611280	+	1.17190i
$485$			1.28278i			0.0582481i
$486$	19.2623	+	11.6778i	0.873755	+	0.529716i
$487$	−38.5514			−1.74693			−0.873464	−	0.486888i	$-0.838132\pi$
$487$	−38.5514			−1.74693			−0.873464	+	0.486888i	$0.838132\pi$
$488$	−0.204716	+	3.18351i	−0.00926706	+	0.144111i
$489$	−16.0494			−0.725779
$490$	−5.38227	−	3.26302i	−0.243146	−	0.147408i
$491$		−	18.6889i		−	0.843418i	−0.906731	−	0.421709i	$-0.861430\pi$
$491$		−	18.6889i		−	0.843418i	0.906731	−	0.421709i	$-0.138570\pi$
$492$	6.93264	−	3.61615i	0.312547	−	0.163029i
$493$			1.12786i			0.0507965i
$494$	2.37017	−	3.90954i	0.106639	−	0.175898i
$495$	−13.2021			−0.593390
$496$	6.13473	−	8.79203i	0.275457	−	0.394774i
$497$	−5.27697			−0.236704
$498$	−5.66772	+	9.34878i	−0.253977	+	0.418929i
$499$		−	18.3033i		−	0.819368i	−0.912228	−	0.409684i	$-0.865639\pi$
$499$		−	18.3033i		−	0.819368i	0.912228	−	0.409684i	$-0.134361\pi$
$500$	−17.4558	+	9.10518i	−0.780649	+	0.407196i
$501$		−	9.81959i		−	0.438707i
$502$	−32.3218	−	19.5952i	−1.44259	−	0.874576i
$503$	−26.6030			−1.18617			−0.593085	−	0.805140i	$-0.702090\pi$
$503$	−26.6030			−1.18617			−0.593085	+	0.805140i	$0.702090\pi$
$504$	11.4251	+	0.734694i	0.508915	+	0.0327259i
$505$	−17.1419			−0.762803
$506$	−46.0981	−	27.9471i	−2.04931	−	1.24240i
$507$		−	2.80901i		−	0.124752i
$508$	−13.6227	−	26.1165i	−0.604408	−	1.15873i
$509$		−	7.57086i		−	0.335572i	−0.985823	−	0.167786i	$-0.946338\pi$
$509$		−	7.57086i		−	0.335572i	0.985823	−	0.167786i	$-0.0536618\pi$
$510$	0.683771	−	1.12786i	0.0302779	−	0.0499427i
$511$	21.3604			0.944928
$512$	22.2088	+	4.33226i	0.981500	+	0.191461i
$513$	4.58603			0.202478
$514$	0.337800	−	0.557193i	0.0148997	−	0.0245767i
$515$			16.5034i			0.727228i
$516$	−1.16999	−	2.24303i	−0.0515059	−	0.0987437i
$517$		−	38.7137i		−	1.70263i
$518$	−19.3345	−	11.7216i	−0.849511	−	0.515018i
$519$	14.9005			0.654061
$520$	9.86527	+	0.634388i	0.432621	+	0.0278198i
$521$	−22.4389			−0.983065			−0.491533	−	0.870859i	$-0.663563\pi$
$521$	−22.4389			−0.983065			−0.491533	+	0.870859i	$0.663563\pi$
$522$	−3.15924	−	1.91530i	−0.138276	−	0.0838304i
$523$			13.5755i			0.593616i	0.954937	+	0.296808i	$0.0959221\pi$
$523$			13.5755i			0.593616i	−0.954937	+	0.296808i	$0.904078\pi$
$524$	18.6220	−	9.71345i	0.813505	−	0.424334i
$525$		−	5.38707i		−	0.235111i
$526$	11.9228	−	19.6665i	0.519861	−	0.857499i
$527$	−2.68019			−0.116751
$528$	9.56509	−	13.7083i	0.416267	−	0.596576i
$529$	33.8944			1.47367
$530$	−3.23282	+	5.33246i	−0.140425	+	0.231627i
$531$			25.5597i			1.10920i
$532$	3.23282	−	1.68628i	0.140160	−	0.0731094i
$533$		−	14.6512i		−	0.634614i
$534$	−18.2672	−	11.0745i	−0.790498	−	0.479241i
$535$	−3.47680			−0.150315
$536$	−0.520258	+	8.09045i	−0.0224717	+	0.349454i
$537$	−13.1178			−0.566074
$538$	−24.2587	−	14.7069i	−1.04587	−	0.634060i
$539$			19.9420i			0.858961i
$540$	4.58603	+	8.79203i	0.197351	+	0.378349i
$541$		−	14.1426i		−	0.608037i	−0.952666	−	0.304019i	$-0.901671\pi$
$541$		−	14.1426i		−	0.608037i	0.952666	−	0.304019i	$-0.0983285\pi$
$542$	−0.491471	+	0.810671i	−0.0211105	+	0.0348213i
$543$	9.15041			0.392682
$544$	−2.28892	−	5.17309i	−0.0981364	−	0.221794i
$545$	−19.8529			−0.850403
$546$	−3.28312	+	5.41543i	−0.140505	+	0.231759i
$547$		−	29.0623i		−	1.24261i	−0.783567	−	0.621307i	$-0.786602\pi$
$547$		−	29.0623i		−	1.24261i	0.783567	−	0.621307i	$-0.213398\pi$
$548$	−4.91727	−	9.42707i	−0.210056	−	0.402704i
$549$			2.61239i			0.111494i
$550$	22.7832	+	13.8124i	0.971480	+	0.588963i
$551$	−1.17662			−0.0501255
$552$	−1.13210	+	17.6051i	−0.0481854	+	0.749324i
$553$	6.90680			0.293707
$554$	−4.33586	−	2.62863i	−0.184213	−	0.111680i
$555$		−	8.53241i		−	0.362180i
$556$	−4.19424	+	2.18777i	−0.177875	+	0.0927820i
$557$			26.1386i			1.10753i	0.832674	+	0.553764i	$0.186809\pi$
$557$			26.1386i			1.10753i	−0.832674	+	0.553764i	$0.813191\pi$
$558$	4.55140	−	7.50743i	0.192676	−	0.317815i
$559$	−4.74034			−0.200495
$560$	6.46563	+	4.51146i	0.273223	+	0.190644i
$561$	−4.17888			−0.176432
$562$	−0.291076	+	0.480123i	−0.0122783	+	0.0202528i
$563$			17.8812i			0.753602i	0.926294	+	0.376801i	$0.122976\pi$
$563$			17.8812i			0.753602i	−0.926294	+	0.376801i	$0.877024\pi$
$564$	−11.2328	+	5.85918i	−0.472987	+	0.246716i
$565$		−	6.19774i		−	0.260741i
$566$	12.0553	+	7.30857i	0.506723	+	0.307202i
$567$	5.79069			0.243186
$568$	−8.52320	−	0.548086i	−0.357626	−	0.0229972i
$569$	−21.4434			−0.898955			−0.449478	−	0.893292i	$-0.648390\pi$
$569$	−21.4434			−0.898955			−0.449478	+	0.893292i	$0.648390\pi$
$570$	1.17662	+	0.713327i	0.0492830	+	0.0298780i
$571$			34.9469i			1.46248i	0.682120	+	0.731240i	$0.261058\pi$
$571$			34.9469i			1.46248i	−0.682120	+	0.731240i	$0.738942\pi$
$572$	−14.4853	−	27.7703i	−0.605661	−	1.16113i
$573$		−	11.8190i		−	0.493744i
$574$	6.05757	−	9.99183i	0.252838	−	0.417051i
$575$	−28.1191			−1.17265
$576$	18.3772	+	2.37331i	0.765717	+	0.0988881i
$577$	−8.95848			−0.372946			−0.186473	−	0.982460i	$-0.559706\pi$
$577$	−8.95848			−0.372946			−0.186473	+	0.982460i	$0.559706\pi$
$578$	−0.733159	+	1.20933i	−0.0304954	+	0.0503015i
$579$			17.6527i			0.733622i
$580$	−1.17662	−	2.25573i	−0.0488563	−	0.0936641i
$581$			16.3375i			0.677793i
$582$	−1.13735	−	0.689523i	−0.0471448	−	0.0285817i
$583$	19.7574			0.818268
$584$	34.5007	+	2.21857i	1.42765	+	0.0918052i
$585$	8.09546			0.334706
$586$	6.52320	+	3.95471i	0.269471	+	0.163368i
$587$			6.94513i			0.286656i	0.989675	+	0.143328i	$0.0457804\pi$
$587$			6.94513i			0.286656i	−0.989675	+	0.143328i	$0.954220\pi$
$588$	5.78618	−	3.01814i	0.238618	−	0.124466i
$589$		−	2.79604i		−	0.115209i
$590$	−9.12494	+	15.0514i	−0.375668	+	0.619655i
$591$	−18.8757			−0.776443
$592$	−30.0111	−	20.9406i	−1.23345	−	0.860653i
$593$	18.5932			0.763531			0.381765	−	0.924259i	$-0.375316\pi$
$593$	18.5932			0.763531			0.381765	+	0.924259i	$0.375316\pi$
$594$	16.2878	−	26.8663i	0.668295	−	1.10234i
$595$		−	1.97100i		−	0.0808033i
$596$	−38.0111	+	19.8271i	−1.55700	+	0.812149i
$597$			7.28909i			0.298323i
$598$	28.2672	+	17.1370i	1.15593	+	0.700786i
$599$	31.7057			1.29546			0.647730	−	0.761870i	$-0.275718\pi$
$599$	31.7057			1.29546			0.647730	+	0.761870i	$0.275718\pi$
$600$	0.559522	−	8.70104i	0.0228424	−	0.355218i
$601$	−29.2257			−1.19214			−0.596070	−	0.802933i	$-0.703272\pi$
$601$	−29.2257			−1.19214			−0.596070	+	0.802933i	$0.703272\pi$
$602$	−3.23282	−	1.95990i	−0.131760	−	0.0798797i
$603$			6.63904i			0.270363i
$604$	16.7672	+	32.1449i	0.682247	+	1.30796i
$605$			16.3983i			0.666686i
$606$	9.21414	−	15.1985i	0.374299	−	0.617397i
$607$	−4.90321			−0.199015			−0.0995077	−	0.995037i	$-0.531727\pi$
$607$	−4.90321			−0.199015			−0.0995077	+	0.995037i	$0.531727\pi$
$608$	5.39670	−	2.38785i	0.218865	−	0.0968402i
$609$	1.62983			0.0660441
$610$	−0.932637	+	1.53836i	−0.0377614	+	0.0622865i
$611$			23.7391i			0.960379i
$612$	−2.14241	−	4.10728i	−0.0866017	−	0.166027i
$613$			33.8739i			1.36816i	0.729409	+	0.684078i	$0.239795\pi$
$613$			33.8739i			1.36816i	−0.729409	+	0.684078i	$0.760205\pi$
$614$	35.0239	+	21.2333i	1.41345	+	0.856907i
$615$	4.40943			0.177805
$616$	1.60298	−	24.9278i	0.0645861	−	1.00437i
$617$	−34.5174			−1.38962			−0.694809	−	0.719194i	$-0.744511\pi$
$617$	−34.5174			−1.38962			−0.694809	+	0.719194i	$0.744511\pi$
$618$	−14.6325	−	8.87097i	−0.588604	−	0.356843i
$619$			21.3435i			0.857868i	0.903336	+	0.428934i	$0.141111\pi$
$619$			21.3435i			0.857868i	−0.903336	+	0.428934i	$0.858889\pi$
$620$	5.36038	−	2.79604i	0.215278	−	0.112292i
$621$			33.1584i			1.33060i
$622$	9.90128	−	16.3319i	0.397005	−	0.654851i
$623$	−31.9228			−1.27896
$624$	−5.86527	+	8.40586i	−0.234799	+	0.336504i
$625$	7.53699			0.301480
$626$	4.39896	−	7.25598i	0.175818	−	0.290007i
$627$		−	4.35951i		−	0.174102i
$628$	25.9228	−	13.5217i	1.03443	−	0.539574i
$629$			9.14869i			0.364782i
$630$	5.52094	+	3.34709i	0.219960	+	0.133351i
$631$	44.3689			1.76630			0.883149	−	0.469093i	$-0.155419\pi$
$631$	44.3689			1.76630			0.883149	+	0.469093i	$0.155419\pi$
$632$	11.1557	+	0.717367i	0.443748	+	0.0285353i
$633$	7.17625			0.285230
$634$	17.8100	+	10.7974i	0.707326	+	0.428818i
$635$		−	16.6111i		−	0.659192i
$636$	−2.99021	−	5.73263i	−0.118570	−	0.227314i
$637$		−	12.2283i		−	0.484504i
$638$	−4.17888	+	6.89296i	−0.165443	+	0.272895i
$639$	−6.99416			−0.276685
$640$	9.97453	+	7.95833i	0.394278	+	0.314581i
$641$	−3.68151			−0.145411			−0.0727055	−	0.997353i	$-0.523163\pi$
$641$	−3.68151			−0.145411			−0.0727055	+	0.997353i	$0.523163\pi$
$642$	1.86886	−	3.08263i	0.0737578	−	0.121662i
$643$		−	30.6988i		−	1.21064i	−0.795982	−	0.605321i	$-0.793045\pi$
$643$		−	30.6988i		−	1.21064i	0.795982	−	0.605321i	$-0.206955\pi$
$644$	12.1923	+	23.3743i	0.480444	+	0.921075i
$645$		−	1.42665i		−	0.0561744i
$646$	−1.26160	−	0.764850i	−0.0496371	−	0.0300926i
$647$	−20.1066			−0.790472			−0.395236	−	0.918580i	$-0.629337\pi$
$647$	−20.1066			−0.790472			−0.395236	+	0.918580i	$0.629337\pi$
$648$	9.35297	+	0.601444i	0.367419	+	0.0236270i
$649$	55.7672			2.18905
$650$	−13.9706	−	8.46970i	−0.547971	−	0.332209i
$651$			3.87303i			0.151796i
$652$	−34.4173	+	17.9525i	−1.34788	+	0.703073i
$653$			4.85298i			0.189912i	0.995481	+	0.0949560i	$0.0302710\pi$
$653$			4.85298i			0.189912i	−0.995481	+	0.0949560i	$0.969729\pi$
$654$	10.6714	−	17.6022i	0.417283	−	0.688299i
$655$	11.8443			0.462796
$656$	10.8218	−	15.5094i	0.422521	−	0.605539i
$657$	28.3113			1.10453
$658$	−9.81497	+	16.1896i	−0.382627	+	0.631135i
$659$		−	0.820109i		−	0.0319469i	−0.999872	−	0.0159735i	$-0.994915\pi$
$659$		−	0.820109i		−	0.0319469i	0.999872	−	0.0159735i	$-0.00508473\pi$
$660$	8.35775	−	4.35951i	0.325325	−	0.169694i
$661$		−	33.6446i		−	1.30862i	−0.756225	−	0.654311i	$-0.772959\pi$
$661$		−	33.6446i		−	1.30862i	0.756225	−	0.654311i	$-0.227041\pi$
$662$	−3.12199	−	1.89271i	−0.121340	−	0.0735624i
$663$	2.56247			0.0995180
$664$	−1.69687	+	26.3878i	−0.0658515	+	1.02405i
$665$	2.05620			0.0797360
$666$	−25.6262	−	15.5360i	−0.992997	−	0.602007i
$667$		−	8.50730i		−	0.329404i
$668$	−10.9840	−	21.0577i	−0.424982	−	0.814746i
$669$			3.58238i			0.138503i
$670$	−2.37017	+	3.90954i	−0.0915676	+	0.151039i
$671$	5.69982			0.220039
$672$	−7.47542	+	3.30762i	−0.288371	+	0.127594i
$673$	14.3061			0.551459			0.275729	−	0.961235i	$-0.411081\pi$
$673$	14.3061			0.551459			0.275729	+	0.961235i	$0.411081\pi$
$674$	−5.13404	+	8.46848i	−0.197756	+	0.326194i
$675$		−	16.3880i		−	0.630774i
$676$	−3.14209	−	6.02380i	−0.120850	−	0.231685i
$677$			25.2693i			0.971177i	0.874187	+	0.485589i	$0.161395\pi$
$677$			25.2693i			0.971177i	−0.874187	+	0.485589i	$0.838605\pi$
$678$	5.49510	+	3.33142i	0.211038	+	0.127942i
$679$	−1.98758			−0.0762765
$680$	0.204716	−	3.18351i	0.00785050	−	0.122082i
$681$	21.2012			0.812431
$682$	−16.3800	−	9.93042i	−0.627223	−	0.380256i
$683$		−	16.5149i		−	0.631923i	−0.948772	−	0.315962i	$-0.897673\pi$
$683$		−	16.5149i		−	0.631923i	0.948772	−	0.315962i	$-0.102327\pi$
$684$	4.28482	−	2.23501i	0.163834	−	0.0854579i
$685$		−	5.99599i		−	0.229095i
$686$	14.0245	−	23.1330i	0.535457	−	0.883224i
$687$	2.03789			0.0777503
$688$	−5.01799	−	3.50135i	−0.191309	−	0.133488i
$689$	−12.1151			−0.461550
$690$	−5.15757	+	8.50730i	−0.196345	+	0.323867i
$691$			3.61558i			0.137543i	0.997632	+	0.0687716i	$0.0219080\pi$
$691$			3.61558i			0.137543i	−0.997632	+	0.0687716i	$0.978092\pi$
$692$	31.9536	−	16.6674i	1.21469	−	0.633599i
$693$		−	20.4558i		−	0.777050i
$694$	−2.13247	−	1.29281i	−0.0809473	−	0.0490745i
$695$	−2.66770			−0.101192
$696$	2.63246	+	0.169281i	0.0997831	+	0.00641657i
$697$	−4.72792			−0.179083
$698$	44.5736	+	27.0229i	1.68714	+	1.02283i
$699$			2.20926i			0.0835618i
$700$	−6.02584	−	11.5523i	−0.227755	−	0.436637i
$701$		−	20.4233i		−	0.771377i	−0.922629	−	0.385689i	$-0.873964\pi$
$701$		−	20.4233i		−	0.771377i	0.922629	−	0.385689i	$-0.126036\pi$
$702$	−9.98758	+	16.4743i	−0.376957	+	0.621782i
$703$	−9.54414			−0.359964
$704$	5.17819	−	40.0961i	0.195160	−	1.51118i
$705$	−7.14452			−0.269078
$706$	24.1818	−	39.8874i	0.910095	−	1.50118i
$707$		−	26.5602i		−	0.998899i
$708$	−8.44016	−	16.1809i	−0.317201	−	0.608116i
$709$		−	1.88393i		−	0.0707523i	−0.999374	−	0.0353762i	$-0.988737\pi$
$709$		−	1.88393i		−	0.0707523i	0.999374	−	0.0353762i	$-0.0112629\pi$
$710$	−4.11866	−	2.49695i	−0.154570	−	0.0937088i
$711$	9.15436			0.343315
$712$	−51.5609	−	3.31563i	−1.93233	−	0.124259i
$713$	20.2162			0.757104
$714$	1.74755	+	1.05946i	0.0654005	+	0.0396492i
$715$		−	17.6630i		−	0.660559i
$716$	−28.1305	+	14.6732i	−1.05129	+	0.548364i
$717$			2.39254i			0.0893512i
$718$	−7.41169	+	12.2254i	−0.276602	+	0.456249i
$719$	−29.2872			−1.09223			−0.546114	−	0.837711i	$-0.683893\pi$
$719$	−29.2872			−1.09223			−0.546114	+	0.837711i	$0.683893\pi$
$720$	8.56963	+	5.97955i	0.319371	+	0.222845i
$721$	−25.5710			−0.952313
$722$	−13.1321	+	21.6611i	−0.488727	+	0.806144i
$723$		−	11.4328i		−	0.425190i
$724$	19.6227	−	10.2354i	0.729271	−	0.380397i
$725$			4.20459i			0.156155i
$726$	−14.5393	−	8.81446i	−0.539602	−	0.327135i
$727$	31.1485			1.15523			0.577617	−	0.816308i	$-0.303983\pi$
$727$	31.1485			1.15523			0.577617	+	0.816308i	$0.303983\pi$
$728$	−0.982943	+	15.2856i	−0.0364303	+	0.566522i
$729$	−3.23019			−0.119637
$730$	16.6717	+	10.1073i	0.617048	+	0.374087i
$731$			1.52970i			0.0565780i
$732$	−0.862647	−	1.65381i	−0.0318844	−	0.0611265i
$733$			6.44596i			0.238087i	0.992889	+	0.119043i	$0.0379828\pi$
$733$			6.44596i			0.238087i	−0.992889	+	0.119043i	$0.962017\pi$
$734$	−26.9994	+	44.5348i	−0.996565	+	1.64381i
$735$	3.68024			0.135748
$736$	17.2649	+	39.0198i	0.636393	+	1.43829i
$737$	14.4853			0.533573
$738$	8.02879	−	13.2433i	0.295544	−	0.487493i
$739$		−	19.5888i		−	0.720587i	−0.932839	−	0.360293i	$-0.882677\pi$
$739$		−	19.5888i		−	0.720587i	0.932839	−	0.360293i	$-0.117323\pi$
$740$	−9.54414	−	18.2974i	−0.350850	−	0.672625i
$741$			2.67323i			0.0982036i
$742$	−8.26229	−	5.00903i	−0.303318	−	0.183887i
$743$	−16.2315			−0.595476			−0.297738	−	0.954648i	$-0.596232\pi$
$743$	−16.2315			−0.595476			−0.297738	+	0.954648i	$0.596232\pi$
$744$	−0.402268	+	6.25561i	−0.0147479	+	0.229342i
$745$	−24.1766			−0.885762
$746$	18.4755	+	11.2008i	0.676435	+	0.410091i
$747$			21.6539i			0.792275i
$748$	−8.96142	+	4.67439i	−0.327662	+	0.170913i
$749$		−	5.38707i		−	0.196839i
$750$	5.96790	−	9.84392i	0.217917	−	0.359449i
$751$	2.87965			0.105080			0.0525400	−	0.998619i	$-0.483268\pi$
$751$	2.87965			0.105080			0.0525400	+	0.998619i	$0.483268\pi$
$752$	−17.5344	+	25.1295i	−0.639413	+	0.916379i
$753$	22.1007			0.805395
$754$	2.56247	−	4.22673i	0.0933196	−	0.153929i
$755$			20.4454i			0.744086i
$756$	−13.6227	+	7.10575i	−0.495452	+	0.258434i
$757$			19.8538i			0.721600i	0.932643	+	0.360800i	$0.117496\pi$
$757$			19.8538i			0.721600i	−0.932643	+	0.360800i	$0.882504\pi$
$758$	18.1164	+	10.9831i	0.658017	+	0.398925i
$759$	31.5206			1.14412
$760$	3.32111	+	0.213565i	0.120469	+	0.00774681i
$761$	21.1619			0.767119			0.383560	−	0.923516i	$-0.374698\pi$
$761$	21.1619			0.767119			0.383560	+	0.923516i	$0.374698\pi$
$762$	14.7279	+	8.92884i	0.533536	+	0.323458i
$763$		−	30.7607i		−	1.11361i
$764$	−13.2204	−	25.3453i	−0.478297	−	0.916959i
$765$		−	2.61239i		−	0.0944513i
$766$	3.80770	−	6.28072i	0.137578	−	0.226931i
$767$	−34.1962			−1.23475
$768$	−12.4176	+	4.56594i	−0.448083	+	0.164759i
$769$	−28.0879			−1.01288			−0.506438	−	0.862276i	$-0.669038\pi$
$769$	−28.0879			−1.01288			−0.506438	+	0.862276i	$0.669038\pi$
$770$	7.30281	−	12.0458i	0.263175	−	0.434101i
$771$			0.380993i			0.0137211i
$772$	19.7459	+	37.8555i	0.710671	+	1.36245i
$773$			21.4752i			0.772409i	0.922413	+	0.386204i	$0.126214\pi$
$773$			21.4752i			0.772409i	−0.922413	+	0.386204i	$0.873786\pi$
$774$	−4.28482	−	2.59768i	−0.154015	−	0.0933717i
$775$	−9.99153			−0.358906
$776$	−3.21029	−	0.206438i	−0.115243	−	0.00741070i
$777$	13.2204			0.474279
$778$	−11.2427	−	6.81589i	−0.403069	−	0.244362i
$779$		−	4.93228i		−	0.176717i
$780$	−5.12494	+	2.67323i	−0.183502	+	0.0957170i
$781$			15.2601i			0.546050i
$782$	5.53010	−	9.12177i	0.197756	−	0.326194i
$783$	4.95811			0.177188
$784$	9.03220	−	12.9446i	0.322579	−	0.462306i
$785$	16.4880			0.588481
$786$	−6.36659	+	10.5015i	−0.227089	+	0.374578i
$787$			1.22304i			0.0435966i	0.999762	+	0.0217983i	$0.00693916\pi$
$787$			1.22304i			0.0435966i	−0.999762	+	0.0217983i	$0.993061\pi$
$788$	−40.4782	+	21.1139i	−1.44197	+	0.752152i
$789$			13.4474i			0.478739i
$790$	5.39074	+	3.26815i	0.191794	+	0.116276i
$791$	9.60298			0.341443
$792$	2.12462	−	33.0396i	0.0754949	−	1.17401i
$793$	−3.49510			−0.124115
$794$	14.6543	+	8.88424i	0.520063	+	0.315290i
$795$		−	3.64618i		−	0.129317i
$796$	8.15340	+	15.6312i	0.288990	+	0.554032i
$797$		−	27.2300i		−	0.964535i	−0.876024	−	0.482267i	$-0.839813\pi$
$797$		−	27.2300i		−	0.964535i	0.876024	−	0.482267i	$-0.160187\pi$
$798$	−1.10525	+	1.82309i	−0.0391255	+	0.0645367i
$799$	7.66056			0.271011
$800$	−8.53290	−	19.2849i	−0.301683	−	0.681823i
$801$	−42.3110			−1.49498
$802$	−22.2518	+	36.7039i	−0.785739	+	1.29606i
$803$		−	61.7707i		−	2.17984i
$804$	−2.19230	−	4.20293i	−0.0773165	−	0.148226i
$805$			14.8670i			0.523991i
$806$	10.0441	+	6.08929i	0.353790	+	0.214486i
$807$	16.5874			0.583904
$808$	2.75865	−	42.8993i	0.0970488	−	1.50919i
$809$	12.6939			0.446294			0.223147	−	0.974785i	$-0.428367\pi$
$809$	12.6939			0.446294			0.223147	+	0.974785i	$0.428367\pi$
$810$	4.51962	+	2.74003i	0.158803	+	0.0962750i
$811$		−	30.6006i		−	1.07453i	−0.843412	−	0.537267i	$-0.819457\pi$
$811$		−	30.6006i		−	1.07453i	0.843412	−	0.537267i	$-0.180543\pi$
$812$	3.49510	−	1.82309i	0.122654	−	0.0639779i
$813$		−	0.554313i		−	0.0194406i
$814$	−33.8970	+	55.9123i	−1.18809	+	1.95973i
$815$	−21.8907			−0.766799
$816$	2.71256	+	1.89271i	0.0949585	+	0.0662583i
$817$	−1.59582			−0.0558307
$818$	−17.0837	+	28.1792i	−0.597319	+	0.985264i
$819$			12.5434i			0.438301i
$820$	9.45584	−	4.93228i	0.330212	−	0.172243i
$821$			34.8617i			1.21668i	0.793676	+	0.608340i	$0.208164\pi$
$821$			34.8617i			1.21668i	−0.793676	+	0.608340i	$0.791836\pi$
$822$	5.31623	+	3.22298i	0.185425	+	0.112414i
$823$	−25.7292			−0.896865			−0.448433	−	0.893817i	$-0.648018\pi$
$823$	−25.7292			−0.896865			−0.448433	+	0.893817i	$0.648018\pi$
$824$	−41.3015	−	2.65590i	−1.43881	−	0.0925228i
$825$	−15.5785			−0.542374
$826$	−23.3211	−	14.1385i	−0.811445	−	0.491941i
$827$			31.5024i			1.09545i	0.836659	+	0.547723i	$0.184505\pi$
$827$			31.5024i			1.09545i	−0.836659	+	0.547723i	$0.815495\pi$
$828$	16.1598	+	30.9805i	0.561593	+	1.07665i
$829$		−	24.2760i		−	0.843142i	−0.906795	−	0.421571i	$-0.861479\pi$
$829$		−	24.2760i		−	0.843142i	0.906795	−	0.421571i	$-0.138521\pi$
$830$	−7.73055	+	12.7514i	−0.268331	+	0.442606i
$831$	2.96474			0.102846
$832$	−3.17524	+	24.5868i	−0.110082	+	0.852393i
$833$	−3.94606			−0.136723
$834$	1.43395	−	2.36527i	0.0496536	−	0.0819025i
$835$		−	13.3935i		−	0.463502i
$836$	−4.87644	−	9.34878i	−0.168655	−	0.323334i
$837$			11.7821i			0.407251i
$838$	10.2904	+	6.23858i	0.355476	+	0.215508i
$839$	34.6299			1.19556			0.597778	−	0.801662i	$-0.296050\pi$
$839$	34.6299			1.19556			0.597778	+	0.801662i	$0.296050\pi$
$840$	−4.60036	−	0.295827i	−0.158727	−	0.0102070i
$841$	27.7279			0.956135
$842$	37.8751	+	22.9619i	1.30526	+	0.791319i
$843$		−	0.328294i		−	0.0113071i
$844$	15.3892	−	8.02718i	0.529717	−	0.276307i
$845$		−	3.83138i		−	0.131803i
$846$	−13.0089	+	21.4579i	−0.447255	+	0.737736i
$847$	−25.4081			−0.873033
$848$	−12.8248	−	8.94860i	−0.440404	−	0.307296i
$849$	−8.24308			−0.282902
$850$	−2.73316	+	4.50828i	−0.0937466	+	0.154633i
$851$		−	69.0071i		−	2.36553i
$852$	4.42774	−	2.30956i	0.151692	−	0.0791244i
$853$		−	24.3542i		−	0.833872i	−0.908936	−	0.416936i	$-0.863104\pi$
$853$		−	24.3542i		−	0.833872i	0.908936	−	0.416936i	$-0.136896\pi$
$854$	−2.38359	−	1.44506i	−0.0815648	−	0.0494489i
$855$	2.72531			0.0932037
$856$	0.559522	−	8.70104i	0.0191241	−	0.297395i
$857$	1.86002			0.0635371			0.0317686	−	0.999495i	$-0.489886\pi$
$857$	1.86002			0.0635371			0.0317686	+	0.999495i	$0.489886\pi$
$858$	15.6606	+	9.49425i	0.534643	+	0.324129i
$859$			20.8140i			0.710166i	0.934835	+	0.355083i	$0.115547\pi$
$859$			20.8140i			0.710166i	−0.934835	+	0.355083i	$0.884453\pi$
$860$	−1.59582	−	3.05940i	−0.0544170	−	0.104325i
$861$			6.83212i			0.232838i
$862$	−14.1305	+	23.3079i	−0.481285	+	0.793869i
$863$	−31.1302			−1.05968			−0.529842	−	0.848096i	$-0.677749\pi$
$863$	−31.1302			−1.05968			−0.529842	+	0.848096i	$0.677749\pi$
$864$	−22.7410	+	10.0621i	−0.773664	+	0.342320i
$865$	20.3237			0.691028
$866$	−16.0828	+	26.5282i	−0.546515	+	0.901464i
$867$		−	0.826905i		−	0.0280832i
$868$	4.33228	+	8.30555i	0.147047	+	0.281909i
$869$		−	19.9733i		−	0.677549i
$870$	1.27208	+	0.771202i	0.0431275	+	0.0261462i
$871$	−8.88233			−0.300966
$872$	3.19493	−	49.6838i	0.108194	−	1.68251i
$873$	−2.63437			−0.0891599
$874$	9.51606	+	5.76914i	0.321886	+	0.195144i
$875$		−	17.2028i		−	0.581559i
$876$	−17.9228	+	9.34878i	−0.605557	+	0.315866i
$877$		−	0.991052i		−	0.0334654i	−0.999860	−	0.0167327i	$-0.994674\pi$
$877$		−	0.991052i		−	0.0334654i	0.999860	−	0.0167327i	$-0.00532644\pi$
$878$	3.98368	−	6.57099i	0.134443	−	0.221760i
$879$	−4.46038			−0.150445
$880$	13.0464	−	18.6976i	0.439794	−	0.630294i
$881$	19.3087			0.650527			0.325263	−	0.945623i	$-0.394547\pi$
$881$	19.3087			0.650527			0.325263	+	0.945623i	$0.394547\pi$
$882$	6.70106	−	11.0532i	0.225636	−	0.372182i
$883$			23.9889i			0.807290i	0.914916	+	0.403645i	$0.132257\pi$
$883$			23.9889i			0.807290i	−0.914916	+	0.403645i	$0.867743\pi$
$884$	5.49510	−	2.86631i	0.184820	−	0.0964046i
$885$		−	10.2917i		−	0.345952i
$886$	6.11973	+	3.71010i	0.205596	+	0.124643i
$887$	2.58473			0.0867866			0.0433933	−	0.999058i	$-0.486183\pi$
$887$	2.58473			0.0867866			0.0433933	+	0.999058i	$0.486183\pi$
$888$	21.3532	+	1.37312i	0.716567	+	0.0460790i
$889$	25.7378			0.863219
$890$	−24.9157	−	15.1052i	−0.835176	−	0.506328i
$891$		−	16.7457i		−	0.561004i
$892$	4.00716	+	7.68226i	0.134170	+	0.257221i
$893$			7.99168i			0.267431i
$894$	12.9955	−	21.4357i	0.434633	−	0.716918i
$895$	−17.8921			−0.598068
$896$	−12.3309	+	15.4549i	−0.411947	+	0.516311i
$897$	−19.3283			−0.645352
$898$	11.6318	−	19.1863i	0.388157	−	0.640257i
$899$		−	3.02289i		−	0.100819i
$900$	−7.98673	−	15.3116i	−0.266224	−	0.510387i
$901$			3.90954i			0.130246i
$902$	−28.8947	−	17.5175i	−0.962090	−	0.583270i
$903$	2.21051			0.0735610
$904$	15.5105	+	0.997403i	0.515870	+	0.0331731i
$905$	12.4808			0.414876
$906$	−18.1276	−	10.9899i	−0.602248	−	0.365114i
$907$			42.7770i			1.42039i	0.704006	+	0.710194i	$0.251393\pi$
$907$			42.7770i			1.42039i	−0.704006	+	0.710194i	$0.748607\pi$
$908$	45.4650	−	23.7151i	1.50881	−	0.787014i
$909$		−	35.2032i		−	1.16762i
$910$	−4.47805	+	7.38644i	−0.148446	+	0.244858i
$911$	−42.6128			−1.41183			−0.705913	−	0.708299i	$-0.749463\pi$
$911$	−42.6128			−1.41183			−0.705913	+	0.708299i	$0.749463\pi$
$912$	−1.97453	+	2.82981i	−0.0653831	+	0.0937043i
$913$	47.2453			1.56359
$914$	7.42485	−	12.2471i	0.245592	−	0.405099i
$915$		−	1.05189i		−	0.0347744i
$916$	4.37017	−	2.27953i	0.144394	−	0.0753179i
$917$			18.3520i			0.606036i
$918$	5.31623	+	3.22298i	0.175462	+	0.106374i
$919$	4.78549			0.157859			0.0789294	−	0.996880i	$-0.474850\pi$
$919$	4.78549			0.157859			0.0789294	+	0.996880i	$0.474850\pi$
$920$	−1.54414	+	24.0127i	−0.0509088	+	0.791675i
$921$	−23.9483			−0.789124
$922$	27.3604	+	16.5873i	0.901066	+	0.546274i
$923$		−	9.35744i		−	0.308004i
$924$	6.75477	+	12.9498i	0.222216	+	0.426017i
$925$			34.1056i			1.12139i
$926$	5.26492	−	8.68436i	0.173016	−	0.285386i
$927$	−33.8921			−1.11316
$928$	5.83455	−	2.58159i	0.191528	−	0.0847448i
$929$	27.2819			0.895088			0.447544	−	0.894262i	$-0.352299\pi$
$929$	27.2819			0.895088			0.447544	+	0.894262i	$0.352299\pi$
$930$	−1.83264	+	3.02289i	−0.0600945	+	0.0991245i
$931$		−	4.11663i		−	0.134917i
$932$	2.47122	+	4.73766i	0.0809476	+	0.155187i
$933$			11.1673i			0.365601i
$934$	−46.2054	−	28.0121i	−1.51189	−	0.916585i
$935$	−5.69982			−0.186404
$936$	−1.30281	+	20.2597i	−0.0425835	+	0.662210i
$937$	0.0837798			0.00273697			0.00136848	−	0.999999i	$-0.499564\pi$
$937$	0.0837798			0.00273697			0.00136848	+	0.999999i	$0.499564\pi$
$938$	−6.05757	−	3.67242i	−0.197787	−	0.119909i
$939$			4.96143i			0.161910i
$940$	−15.3211	+	7.99168i	−0.499720	+	0.260660i
$941$		−	22.3002i		−	0.726967i	−0.931601	−	0.363483i	$-0.881587\pi$
$941$		−	22.3002i		−	0.726967i	0.931601	−	0.363483i	$-0.118413\pi$
$942$	−8.86265	+	14.6187i	−0.288761	+	0.476304i
$943$	35.6619			1.16131
$944$	−36.1991	−	25.2583i	−1.17818	−	0.822088i
$945$	−8.66456			−0.281858
$946$	−5.66772	+	9.34878i	−0.184274	+	0.303955i
$947$			18.5335i			0.602257i	0.953584	+	0.301128i	$0.0973633\pi$
$947$			18.5335i			0.602257i	−0.953584	+	0.301128i	$0.902637\pi$
$948$	−5.79528	+	3.02289i	−0.188222	+	0.0981790i
$949$			37.8775i			1.22956i
$950$	−4.70315	−	2.85130i	−0.152590	−	0.0925084i
$951$	−12.1780			−0.394898
$952$	4.93264	+	0.317194i	0.159868	+	0.0102803i
$953$	−20.9782			−0.679549			−0.339775	−	0.940507i	$-0.610351\pi$
$953$	−20.9782			−0.679549			−0.339775	+	0.940507i	$0.610351\pi$
$954$	−10.9509	−	6.63904i	−0.354550	−	0.214947i
$955$		−	16.1206i		−	0.521650i
$956$	2.67624	+	5.13071i	0.0865558	+	0.165939i
$957$		−	4.71321i		−	0.152356i
$958$	−0.0997319	+	0.164505i	−0.00322219	+	0.00531493i
$959$	9.29039			0.300002
$960$	−7.39964	−	0.955622i	−0.238822	−	0.0308426i
$961$	−23.8166			−0.768277
$962$	20.7855	−	34.2852i	0.670151	−	1.10540i
$963$		−	7.14009i		−	0.230086i
$964$	−12.7884	−	24.5171i	−0.411888	−	0.789644i
$965$			24.0776i			0.775086i
$966$	−13.1815	−	7.99132i	−0.424108	−	0.257117i
$967$	7.73192			0.248642			0.124321	−	0.992242i	$-0.460325\pi$
$967$	7.73192			0.248642			0.124321	+	0.992242i	$0.460325\pi$
$968$	−41.0385	−	2.63899i	−1.31903	−	0.0848202i
$969$	0.862647			0.0277122
$970$	−1.55130	−	0.940482i	−0.0498094	−	0.0301971i
$971$		−	17.2155i		−	0.552471i	−0.961090	−	0.276235i	$-0.910913\pi$
$971$		−	17.2155i		−	0.552471i	0.961090	−	0.276235i	$-0.0890869\pi$
$972$	−28.2446	+	14.7328i	−0.905948	+	0.472553i
$973$		−	4.13343i		−	0.132512i
$974$	28.2643	−	46.6213i	0.905646	−	1.49384i
$975$	9.55268			0.305931
$976$	−3.69982	−	2.58159i	−0.118428	−	0.0826346i
$977$	25.7377			0.823422			0.411711	−	0.911314i	$-0.364931\pi$
$977$	25.7377			0.823422			0.411711	+	0.911314i	$0.364931\pi$
$978$	11.7668	−	19.4090i	0.376260	−	0.620632i
$979$			92.3157i			2.95042i
$980$	7.89212	−	4.11663i	0.252105	−	0.131501i
$981$		−	40.7706i		−	1.30171i
$982$	22.6010	+	13.7019i	0.721228	+	0.437246i
$983$	33.9385			1.08247			0.541235	−	0.840872i	$-0.317957\pi$
$983$	33.9385			1.08247			0.541235	+	0.840872i	$0.317957\pi$
$984$	−0.709611	+	11.0351i	−0.0226216	+	0.351785i
$985$	−25.7457			−0.820327
$986$	−1.36396	−	0.826905i	−0.0434373	−	0.0263340i
$987$		−	11.0700i		−	0.352361i
$988$	2.99021	+	5.73263i	0.0951312	+	0.182379i
$989$		−	11.5383i		−	0.366896i
$990$	9.67923	−	15.9657i	0.307626	−	0.507422i
$991$	3.70829			0.117798			0.0588988	−	0.998264i	$-0.481241\pi$
$991$	3.70829			0.117798			0.0588988	+	0.998264i	$0.481241\pi$
$992$	6.13473	+	13.8649i	0.194778	+	0.440210i
$993$	2.13473			0.0677435
$994$	3.86886	−	6.38159i	0.122713	−	0.202412i
$995$			9.94203i			0.315184i
$996$	−7.15041	−	13.7083i	−0.226569	−	0.434364i
$997$		−	26.8766i		−	0.851191i	−0.904913	−	0.425596i	$-0.860065\pi$
$997$		−	26.8766i		−	0.851191i	0.904913	−	0.425596i	$-0.139935\pi$
$998$	22.1347	+	13.4192i	0.700662	+	0.424778i
$999$	40.2178			1.27243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.c.b.69.4	yes	8
3.2	odd	2		1224.2.f.c.613.5		8
4.3	odd	2		544.2.c.b.273.6		8
8.3	odd	2		544.2.c.b.273.3		8
8.5	even	2	inner	136.2.c.b.69.3	✓	8
12.11	even	2		4896.2.f.d.2449.5		8
16.3	odd	4		4352.2.a.bb.1.3		8
16.5	even	4		4352.2.a.bf.1.3		8
16.11	odd	4		4352.2.a.bb.1.6		8
16.13	even	4		4352.2.a.bf.1.6		8
24.5	odd	2		1224.2.f.c.613.6		8
24.11	even	2		4896.2.f.d.2449.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.c.b.69.3	✓	8	8.5	even	2	inner
136.2.c.b.69.4	yes	8	1.1	even	1	trivial
544.2.c.b.273.3		8	8.3	odd	2
544.2.c.b.273.6		8	4.3	odd	2
1224.2.f.c.613.5		8	3.2	odd	2
1224.2.f.c.613.6		8	24.5	odd	2
4352.2.a.bb.1.3		8	16.3	odd	4
4352.2.a.bb.1.6		8	16.11	odd	4
4352.2.a.bf.1.3		8	16.5	even	4
4352.2.a.bf.1.6		8	16.13	even	4
4896.2.f.d.2449.4		8	24.11	even	2
4896.2.f.d.2449.5		8	12.11	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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.733159 + 1.20933i) q^{2} -0.826905i q^{3} +(-0.924955 - 1.77326i) q^{4} -1.12786i q^{5} +(1.00000 + 0.606253i) q^{6} +1.74755 q^{7} +(2.82260 + 0.181508i) q^{8} +2.31623 q^{9} +(1.36396 + 0.826905i) q^{10} -5.05364i q^{11} +(-1.46632 + 0.764850i) q^{12} +3.09887i q^{13} +(-1.28123 + 2.11337i) q^{14} -0.932637 q^{15} +(-2.28892 + 3.28038i) q^{16} +1.00000 q^{17} +(-1.69816 + 2.80108i) q^{18} +1.04322i q^{19} +(-2.00000 + 1.04322i) q^{20} -1.44506i q^{21} +(6.11151 + 3.70512i) q^{22} -7.54284 q^{23} +(0.150089 - 2.33402i) q^{24} +3.72792 q^{25} +(-3.74755 - 2.27196i) q^{26} -4.39601i q^{27} +(-1.61641 - 3.09887i) q^{28} +1.12786i q^{29} +(0.683771 - 1.12786i) q^{30} -2.68019 q^{31} +(-2.28892 - 5.17309i) q^{32} -4.17888 q^{33} +(-0.733159 + 1.20933i) q^{34} -1.97100i q^{35} +(-2.14241 - 4.10728i) q^{36} +9.14869i q^{37} +(-1.26160 - 0.764850i) q^{38} +2.56247 q^{39} +(0.204716 - 3.18351i) q^{40} -4.72792 q^{41} +(1.74755 + 1.05946i) q^{42} +1.52970i q^{43} +(-8.96142 + 4.67439i) q^{44} -2.61239i q^{45} +(5.53010 - 9.12177i) q^{46} +7.66056 q^{47} +(2.71256 + 1.89271i) q^{48} -3.94606 q^{49} +(-2.73316 + 4.50828i) q^{50} -0.826905i q^{51} +(5.49510 - 2.86631i) q^{52} +3.90954i q^{53} +(5.31623 + 3.22298i) q^{54} -5.69982 q^{55} +(4.93264 + 0.317194i) q^{56} +0.862647 q^{57} +(-1.36396 - 0.826905i) q^{58} +11.0351i q^{59} +(0.862647 + 1.65381i) q^{60} +1.12786i q^{61} +(1.96501 - 3.24123i) q^{62} +4.04773 q^{63} +(7.93411 + 1.02465i) q^{64} +3.49510 q^{65} +(3.06378 - 5.05364i) q^{66} +2.86631i q^{67} +(-0.924955 - 1.77326i) q^{68} +6.23721i q^{69} +(2.38359 + 1.44506i) q^{70} -3.01963 q^{71} +(6.53778 + 0.420413i) q^{72} +12.2230 q^{73} +(-11.0638 - 6.70745i) q^{74} -3.08263i q^{75} +(1.84991 - 0.964936i) q^{76} -8.83150i q^{77} +(-1.87870 + 3.09887i) q^{78} +3.95227 q^{79} +(3.69982 + 2.58159i) q^{80} +3.31360 q^{81} +(3.46632 - 5.71761i) q^{82} +9.34878i q^{83} +(-2.56247 + 1.33662i) q^{84} -1.12786i q^{85} +(-1.84991 - 1.12151i) q^{86} +0.932637 q^{87} +(0.917274 - 14.2644i) q^{88} -18.2672 q^{89} +(3.15924 + 1.91530i) q^{90} +5.41543i q^{91} +(6.97679 + 13.3754i) q^{92} +2.21626i q^{93} +(-5.61641 + 9.26414i) q^{94} +1.17662 q^{95} +(-4.27765 + 1.89271i) q^{96} -1.13735 q^{97} +(2.89309 - 4.77209i) q^{98} -11.7054i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{4} + 8 q^{6} - 12 q^{7} + 5 q^{8} - 8 q^{9} - 8 q^{10} - 2 q^{12} + 6 q^{14} + 12 q^{15} + 9 q^{16} + 8 q^{17} - 19 q^{18} - 16 q^{20} + 4 q^{22} - 16 q^{23} + 18 q^{24} - 8 q^{25} - 4 q^{26}+ \cdots - 57 q^{98}+O(q^{100}) \) 8 * q - q^2 + q^4 + 8 * q^6 - 12 * q^7 + 5 * q^8 - 8 * q^9 - 8 * q^10 - 2 * q^12 + 6 * q^14 + 12 * q^15 + 9 * q^16 + 8 * q^17 - 19 * q^18 - 16 * q^20 + 4 * q^22 - 16 * q^23 + 18 * q^24 - 8 * q^25 - 4 * q^26 - 20 * q^28 + 32 * q^30 + 24 * q^31 + 9 * q^32 - 8 * q^33 - q^34 - 45 * q^36 + 18 * q^38 - 12 * q^39 + 20 * q^40 - 12 * q^42 - 10 * q^44 - 18 * q^46 + 4 * q^47 + 6 * q^48 + 8 * q^49 - 17 * q^50 - 8 * q^52 + 16 * q^54 - 12 * q^55 + 20 * q^56 + 8 * q^57 + 8 * q^58 + 8 * q^60 + 26 * q^62 + 40 * q^63 + q^64 - 24 * q^65 - 28 * q^66 + q^68 + 12 * q^70 - 36 * q^71 - 21 * q^72 + 8 * q^73 - 36 * q^74 - 2 * q^76 + 44 * q^78 + 24 * q^79 - 4 * q^80 + 40 * q^81 + 18 * q^82 + 12 * q^84 + 2 * q^86 - 12 * q^87 + 10 * q^88 + 8 * q^89 - 12 * q^90 - 28 * q^92 - 52 * q^94 + 32 * q^95 + 54 * q^96 - 8 * q^97 - 57 * q^98

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