LMFDB - Embedded newform 867.2.a.o.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(1,867)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("867.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.3418281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} - 4x^{3} + 18x^{2} + 12x - 1 $ x^6 - 9x^4 - 4x^3 + 18x^2 + 12x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.71374$ of defining polynomial
Character	$\chi$	$=$	867.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.44395 q^{2} -1.00000 q^{3} +3.97290 q^{4} -2.87349 q^{5} -2.44395 q^{6} +1.56252 q^{7} +4.82168 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.44395 q^{2} -1.00000 q^{3} +3.97290 q^{4} -2.87349 q^{5} -2.44395 q^{6} +1.56252 q^{7} +4.82168 q^{8} +1.00000 q^{9} -7.02266 q^{10} +6.34249 q^{11} -3.97290 q^{12} +0.803928 q^{13} +3.81872 q^{14} +2.87349 q^{15} +3.83815 q^{16} +2.44395 q^{18} +3.25173 q^{19} -11.4161 q^{20} -1.56252 q^{21} +15.5007 q^{22} +6.17389 q^{23} -4.82168 q^{24} +3.25692 q^{25} +1.96476 q^{26} -1.00000 q^{27} +6.20773 q^{28} +1.52895 q^{29} +7.02266 q^{30} -2.17313 q^{31} -0.263112 q^{32} -6.34249 q^{33} -4.48987 q^{35} +3.97290 q^{36} -0.636236 q^{37} +7.94707 q^{38} -0.803928 q^{39} -13.8550 q^{40} -5.61579 q^{41} -3.81872 q^{42} -11.0241 q^{43} +25.1981 q^{44} -2.87349 q^{45} +15.0887 q^{46} +7.46399 q^{47} -3.83815 q^{48} -4.55854 q^{49} +7.95975 q^{50} +3.19393 q^{52} +1.34692 q^{53} -2.44395 q^{54} -18.2250 q^{55} +7.53396 q^{56} -3.25173 q^{57} +3.73668 q^{58} +4.03412 q^{59} +11.4161 q^{60} -8.36818 q^{61} -5.31104 q^{62} +1.56252 q^{63} -8.31932 q^{64} -2.31008 q^{65} -15.5007 q^{66} +7.75709 q^{67} -6.17389 q^{69} -10.9730 q^{70} +4.51749 q^{71} +4.82168 q^{72} -8.28093 q^{73} -1.55493 q^{74} -3.25692 q^{75} +12.9188 q^{76} +9.91025 q^{77} -1.96476 q^{78} -1.50720 q^{79} -11.0289 q^{80} +1.00000 q^{81} -13.7247 q^{82} +7.52521 q^{83} -6.20773 q^{84} -26.9424 q^{86} -1.52895 q^{87} +30.5814 q^{88} -6.12748 q^{89} -7.02266 q^{90} +1.25615 q^{91} +24.5282 q^{92} +2.17313 q^{93} +18.2416 q^{94} -9.34380 q^{95} +0.263112 q^{96} -4.84158 q^{97} -11.1408 q^{98} +6.34249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 + 12 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{10} + 9 q^{11} - 9 q^{12} + 9 q^{13} + 6 q^{14} - 3 q^{15} + 15 q^{16} + 3 q^{18} + 9 q^{19} - 6 q^{20} + 3 q^{21} + 18 q^{22} + 9 q^{23} - 12 q^{24} + 15 q^{25} - 12 q^{26} - 6 q^{27} + 15 q^{28} + 6 q^{29} + 12 q^{30} - 24 q^{31} + 42 q^{32} - 9 q^{33} + 9 q^{36} + 3 q^{37} - 6 q^{38} - 9 q^{39} + 3 q^{40} + 18 q^{41} - 6 q^{42} + 3 q^{44} + 3 q^{45} - 15 q^{46} + 24 q^{47} - 15 q^{48} + 21 q^{49} + 12 q^{50} - 18 q^{52} + 24 q^{53} - 3 q^{54} - 24 q^{55} + 54 q^{56} - 9 q^{57} - 3 q^{58} - 9 q^{59} + 6 q^{60} - 21 q^{61} + 30 q^{62} - 3 q^{63} + 24 q^{64} - 9 q^{65} - 18 q^{66} - 6 q^{67} - 9 q^{69} - 3 q^{70} + 27 q^{71} + 12 q^{72} - 18 q^{73} + 36 q^{74} - 15 q^{75} - 3 q^{76} + 33 q^{77} + 12 q^{78} - 24 q^{79} + 3 q^{80} + 6 q^{81} + 15 q^{82} + 6 q^{83} - 15 q^{84} + 6 q^{86} - 6 q^{87} + 24 q^{88} - 12 q^{90} - 39 q^{91} + 24 q^{93} - 15 q^{94} + 42 q^{95} - 42 q^{96} + 33 q^{97} - 57 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^10 + 9 * q^11 - 9 * q^12 + 9 * q^13 + 6 * q^14 - 3 * q^15 + 15 * q^16 + 3 * q^18 + 9 * q^19 - 6 * q^20 + 3 * q^21 + 18 * q^22 + 9 * q^23 - 12 * q^24 + 15 * q^25 - 12 * q^26 - 6 * q^27 + 15 * q^28 + 6 * q^29 + 12 * q^30 - 24 * q^31 + 42 * q^32 - 9 * q^33 + 9 * q^36 + 3 * q^37 - 6 * q^38 - 9 * q^39 + 3 * q^40 + 18 * q^41 - 6 * q^42 + 3 * q^44 + 3 * q^45 - 15 * q^46 + 24 * q^47 - 15 * q^48 + 21 * q^49 + 12 * q^50 - 18 * q^52 + 24 * q^53 - 3 * q^54 - 24 * q^55 + 54 * q^56 - 9 * q^57 - 3 * q^58 - 9 * q^59 + 6 * q^60 - 21 * q^61 + 30 * q^62 - 3 * q^63 + 24 * q^64 - 9 * q^65 - 18 * q^66 - 6 * q^67 - 9 * q^69 - 3 * q^70 + 27 * q^71 + 12 * q^72 - 18 * q^73 + 36 * q^74 - 15 * q^75 - 3 * q^76 + 33 * q^77 + 12 * q^78 - 24 * q^79 + 3 * q^80 + 6 * q^81 + 15 * q^82 + 6 * q^83 - 15 * q^84 + 6 * q^86 - 6 * q^87 + 24 * q^88 - 12 * q^90 - 39 * q^91 + 24 * q^93 - 15 * q^94 + 42 * q^95 - 42 * q^96 + 33 * q^97 - 57 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	2.44395	1.72814	0.864068	−	0.503376i	$-0.167909\pi$
$2$	2.44395	1.72814	0.864068	+	0.503376i	$0.167909\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.97290	1.98645
$5$	−2.87349	−1.28506	−0.642531	−	0.766260i	$-0.722116\pi$
$5$	−2.87349	−1.28506	−0.642531	+	0.766260i	$0.722116\pi$
$6$	−2.44395	−0.997739
$7$	1.56252	0.590576	0.295288	−	0.955408i	$-0.404584\pi$
$7$	1.56252	0.590576	0.295288	+	0.955408i	$0.404584\pi$
$8$	4.82168	1.70472
$9$	1.00000	0.333333
$10$	−7.02266	−2.22076
$11$	6.34249	1.91233	0.956166	−	0.292826i	$-0.0945955\pi$
$11$	6.34249	1.91233	0.956166	+	0.292826i	$0.0945955\pi$
$12$	−3.97290	−1.14688
$13$	0.803928	0.222970	0.111485	−	0.993766i	$-0.464439\pi$
$13$	0.803928	0.222970	0.111485	+	0.993766i	$0.464439\pi$
$14$	3.81872	1.02060
$15$	2.87349	0.741931
$16$	3.83815	0.959536
$17$	0	0
$17$	0	0
$18$	2.44395	0.576045
$19$	3.25173	0.745998	0.372999	−	0.927832i	$-0.378329\pi$
$19$	3.25173	0.745998	0.372999	+	0.927832i	$0.378329\pi$
$20$	−11.4161	−2.55271
$21$	−1.56252	−0.340969
$22$	15.5007	3.30477
$23$	6.17389	1.28734	0.643672	−	0.765301i	$-0.277410\pi$
$23$	6.17389	1.28734	0.643672	+	0.765301i	$0.277410\pi$
$24$	−4.82168	−0.984221
$25$	3.25692	0.651384
$26$	1.96476	0.385321
$27$	−1.00000	−0.192450
$28$	6.20773	1.17315
$29$	1.52895	0.283919	0.141959	−	0.989872i	$-0.454660\pi$
$29$	1.52895	0.283919	0.141959	+	0.989872i	$0.454660\pi$
$30$	7.02266	1.28216
$31$	−2.17313	−0.390306	−0.195153	−	0.980773i	$-0.562520\pi$
$31$	−2.17313	−0.390306	−0.195153	+	0.980773i	$0.562520\pi$
$32$	−0.263112	−0.0465121
$33$	−6.34249	−1.10409
$34$	0	0
$35$	−4.48987	−0.758927
$36$	3.97290	0.662150
$37$	−0.636236	−0.104597	−0.0522983	−	0.998632i	$-0.516655\pi$
$37$	−0.636236	−0.104597	−0.0522983	+	0.998632i	$0.516655\pi$
$38$	7.94707	1.28919
$39$	−0.803928	−0.128732
$40$	−13.8550	−2.19067
$41$	−5.61579	−0.877039	−0.438519	−	0.898722i	$-0.644497\pi$
$41$	−5.61579	−0.877039	−0.438519	+	0.898722i	$0.644497\pi$
$42$	−3.81872	−0.589241
$43$	−11.0241	−1.68116	−0.840582	−	0.541685i	$-0.817787\pi$
$43$	−11.0241	−1.68116	−0.840582	+	0.541685i	$0.817787\pi$
$44$	25.1981	3.79875
$45$	−2.87349	−0.428354
$46$	15.0887	2.22470
$47$	7.46399	1.08874	0.544368	−	0.838847i	$-0.316770\pi$
$47$	7.46399	1.08874	0.544368	+	0.838847i	$0.316770\pi$
$48$	−3.83815	−0.553989
$49$	−4.55854	−0.651220
$50$	7.95975	1.12568
$51$	0	0
$52$	3.19393	0.442918
$53$	1.34692	0.185014	0.0925071	−	0.995712i	$-0.470512\pi$
$53$	1.34692	0.185014	0.0925071	+	0.995712i	$0.470512\pi$
$54$	−2.44395	−0.332580
$55$	−18.2250	−2.45746
$56$	7.53396	1.00677
$57$	−3.25173	−0.430702
$58$	3.73668	0.490650
$59$	4.03412	0.525198	0.262599	−	0.964905i	$-0.415420\pi$
$59$	4.03412	0.525198	0.262599	+	0.964905i	$0.415420\pi$
$60$	11.4161	1.47381
$61$	−8.36818	−1.07144	−0.535718	−	0.844397i	$-0.679959\pi$
$61$	−8.36818	−1.07144	−0.535718	+	0.844397i	$0.679959\pi$
$62$	−5.31104	−0.674502
$63$	1.56252	0.196859
$64$	−8.31932	−1.03992
$65$	−2.31008	−0.286530
$66$	−15.5007	−1.90801
$67$	7.75709	0.947680	0.473840	−	0.880611i	$-0.342868\pi$
$67$	7.75709	0.947680	0.473840	+	0.880611i	$0.342868\pi$
$68$	0	0
$69$	−6.17389	−0.743248
$70$	−10.9730	−1.31153
$71$	4.51749	0.536127	0.268064	−	0.963401i	$-0.413616\pi$
$71$	4.51749	0.536127	0.268064	+	0.963401i	$0.413616\pi$
$72$	4.82168	0.568240
$73$	−8.28093	−0.969209	−0.484605	−	0.874733i	$-0.661037\pi$
$73$	−8.28093	−0.969209	−0.484605	+	0.874733i	$0.661037\pi$
$74$	−1.55493	−0.180757
$75$	−3.25692	−0.376077
$76$	12.9188	1.48189
$77$	9.91025	1.12938
$78$	−1.96476	−0.222465
$79$	−1.50720	−0.169573	−0.0847865	−	0.996399i	$-0.527021\pi$
$79$	−1.50720	−0.169573	−0.0847865	+	0.996399i	$0.527021\pi$
$80$	−11.0289	−1.23306
$81$	1.00000	0.111111
$82$	−13.7247	−1.51564
$83$	7.52521	0.825999	0.413000	−	0.910731i	$-0.364481\pi$
$83$	7.52521	0.825999	0.413000	+	0.910731i	$0.364481\pi$
$84$	−6.20773	−0.677319
$85$	0	0
$86$	−26.9424	−2.90528
$87$	−1.52895	−0.163921
$88$	30.5814	3.25999
$89$	−6.12748	−0.649511	−0.324756	−	0.945798i	$-0.605282\pi$
$89$	−6.12748	−0.649511	−0.324756	+	0.945798i	$0.605282\pi$
$90$	−7.02266	−0.740253
$91$	1.25615	0.131680
$92$	24.5282	2.55725
$93$	2.17313	0.225344
$94$	18.2416	1.88148
$95$	−9.34380	−0.958654
$96$	0.263112	0.0268538
$97$	−4.84158	−0.491588	−0.245794	−	0.969322i	$-0.579049\pi$
$97$	−4.84158	−0.491588	−0.245794	+	0.969322i	$0.579049\pi$
$98$	−11.1408	−1.12540
$99$	6.34249	0.637444
$100$	12.9394	1.29394
$101$	−15.8161	−1.57376	−0.786882	−	0.617104i	$-0.788306\pi$
$101$	−15.8161	−1.57376	−0.786882	+	0.617104i	$0.788306\pi$
$102$	0	0
$103$	−7.19272	−0.708720	−0.354360	−	0.935109i	$-0.615301\pi$
$103$	−7.19272	−0.708720	−0.354360	+	0.935109i	$0.615301\pi$
$104$	3.87628	0.380101
$105$	4.48987	0.438167
$106$	3.29182	0.319730
$107$	−3.67769	−0.355535	−0.177768	−	0.984072i	$-0.556888\pi$
$107$	−3.67769	−0.355535	−0.177768	+	0.984072i	$0.556888\pi$
$108$	−3.97290	−0.382293
$109$	−10.2836	−0.984992	−0.492496	−	0.870315i	$-0.663915\pi$
$109$	−10.2836	−0.984992	−0.492496	+	0.870315i	$0.663915\pi$
$110$	−44.5411	−4.24683
$111$	0.636236	0.0603889
$112$	5.99717	0.566679
$113$	−13.9303	−1.31045	−0.655226	−	0.755433i	$-0.727427\pi$
$113$	−13.9303	−1.31045	−0.655226	+	0.755433i	$0.727427\pi$
$114$	−7.94707	−0.744312
$115$	−17.7406	−1.65432
$116$	6.07437	0.563991
$117$	0.803928	0.0743232
$118$	9.85920	0.907613
$119$	0	0
$120$	13.8550	1.26478
$121$	29.2271	2.65701
$122$	−20.4514	−1.85159
$123$	5.61579	0.506359
$124$	−8.63365	−0.775325
$125$	5.00872	0.447993
$126$	3.81872	0.340199
$127$	2.17742	0.193215	0.0966076	−	0.995323i	$-0.469201\pi$
$127$	2.17742	0.193215	0.0966076	+	0.995323i	$0.469201\pi$
$128$	−19.8058	−1.75060
$129$	11.0241	0.970620
$130$	−5.64571	−0.495162
$131$	4.40863	0.385184	0.192592	−	0.981279i	$-0.438311\pi$
$131$	4.40863	0.385184	0.192592	+	0.981279i	$0.438311\pi$
$132$	−25.1981	−2.19321
$133$	5.08089	0.440569
$134$	18.9580	1.63772
$135$	2.87349	0.247310
$136$	0	0
$137$	0.311499	0.0266131	0.0133066	−	0.999911i	$-0.495764\pi$
$137$	0.311499	0.0266131	0.0133066	+	0.999911i	$0.495764\pi$
$138$	−15.0887	−1.28443
$139$	10.8097	0.916871	0.458435	−	0.888728i	$-0.348410\pi$
$139$	10.8097	0.916871	0.458435	+	0.888728i	$0.348410\pi$
$140$	−17.8378	−1.50757
$141$	−7.46399	−0.628582
$142$	11.0405	0.926501
$143$	5.09890	0.426392
$144$	3.83815	0.319845
$145$	−4.39341	−0.364853
$146$	−20.2382	−1.67492
$147$	4.55854	0.375982
$148$	−2.52770	−0.207776
$149$	17.7269	1.45225	0.726123	−	0.687565i	$-0.241320\pi$
$149$	17.7269	1.45225	0.726123	+	0.687565i	$0.241320\pi$
$150$	−7.95975	−0.649911
$151$	−16.1244	−1.31219	−0.656093	−	0.754680i	$-0.727792\pi$
$151$	−16.1244	−1.31219	−0.656093	+	0.754680i	$0.727792\pi$
$152$	15.6788	1.27172
$153$	0	0
$154$	24.2202	1.95172
$155$	6.24447	0.501568
$156$	−3.19393	−0.255719
$157$	19.6347	1.56702	0.783510	−	0.621380i	$-0.213428\pi$
$157$	19.6347	1.56702	0.783510	+	0.621380i	$0.213428\pi$
$158$	−3.68352	−0.293045
$159$	−1.34692	−0.106818
$160$	0.756049	0.0597709
$161$	9.64681	0.760275
$162$	2.44395	0.192015
$163$	10.8776	0.852002	0.426001	−	0.904723i	$-0.359922\pi$
$163$	10.8776	0.852002	0.426001	+	0.904723i	$0.359922\pi$
$164$	−22.3110	−1.74219
$165$	18.2250	1.41882
$166$	18.3913	1.42744
$167$	10.5141	0.813603	0.406802	−	0.913517i	$-0.366644\pi$
$167$	10.5141	0.813603	0.406802	+	0.913517i	$0.366644\pi$
$168$	−7.53396	−0.581257
$169$	−12.3537	−0.950285
$170$	0	0
$171$	3.25173	0.248666
$172$	−43.7978	−3.33955
$173$	7.74845	0.589104	0.294552	−	0.955635i	$-0.404830\pi$
$173$	7.74845	0.589104	0.294552	+	0.955635i	$0.404830\pi$
$174$	−3.73668	−0.283277
$175$	5.08899	0.384692
$176$	24.3434	1.83495
$177$	−4.03412	−0.303223
$178$	−14.9753	−1.12244
$179$	−11.9475	−0.893001	−0.446501	−	0.894783i	$-0.647330\pi$
$179$	−11.9475	−0.893001	−0.446501	+	0.894783i	$0.647330\pi$
$180$	−11.4161	−0.850904
$181$	1.75313	0.130309	0.0651544	−	0.997875i	$-0.479246\pi$
$181$	1.75313	0.130309	0.0651544	+	0.997875i	$0.479246\pi$
$182$	3.06997	0.227562
$183$	8.36818	0.618594
$184$	29.7685	2.19456
$185$	1.82822	0.134413
$186$	5.31104	0.389424
$187$	0	0
$188$	29.6537	2.16272
$189$	−1.56252	−0.113656
$190$	−22.8358	−1.65668
$191$	−22.3232	−1.61525	−0.807627	−	0.589694i	$-0.799248\pi$
$191$	−22.3232	−1.61525	−0.807627	+	0.589694i	$0.799248\pi$
$192$	8.31932	0.600395
$193$	26.1577	1.88287	0.941435	−	0.337195i	$-0.109478\pi$
$193$	26.1577	1.88287	0.941435	+	0.337195i	$0.109478\pi$
$194$	−11.8326	−0.849530
$195$	2.31008	0.165428
$196$	−18.1106	−1.29362
$197$	17.7960	1.26791	0.633957	−	0.773368i	$-0.281429\pi$
$197$	17.7960	1.26791	0.633957	+	0.773368i	$0.281429\pi$
$198$	15.5007	1.10159
$199$	−22.6540	−1.60590	−0.802951	−	0.596045i	$-0.796738\pi$
$199$	−22.6540	−1.60590	−0.802951	+	0.596045i	$0.796738\pi$
$200$	15.7038	1.11043
$201$	−7.75709	−0.547143
$202$	−38.6538	−2.71968
$203$	2.38901	0.167676
$204$	0	0
$205$	16.1369	1.12705
$206$	−17.5787	−1.22476
$207$	6.17389	0.429115
$208$	3.08559	0.213947
$209$	20.6241	1.42660
$210$	10.9730	0.757211
$211$	−22.7255	−1.56449	−0.782245	−	0.622971i	$-0.785925\pi$
$211$	−22.7255	−1.56449	−0.782245	+	0.622971i	$0.785925\pi$
$212$	5.35120	0.367522
$213$	−4.51749	−0.309533
$214$	−8.98809	−0.614413
$215$	31.6777	2.16040
$216$	−4.82168	−0.328074
$217$	−3.39556	−0.230506
$218$	−25.1327	−1.70220
$219$	8.28093	0.559573
$220$	−72.4063	−4.88163
$221$	0	0
$222$	1.55493	0.104360
$223$	0.594738	0.0398266	0.0199133	−	0.999802i	$-0.493661\pi$
$223$	0.594738	0.0398266	0.0199133	+	0.999802i	$0.493661\pi$
$224$	−0.411118	−0.0274690
$225$	3.25692	0.217128
$226$	−34.0450	−2.26464
$227$	−20.0429	−1.33030	−0.665148	−	0.746711i	$-0.731632\pi$
$227$	−20.0429	−1.33030	−0.665148	+	0.746711i	$0.731632\pi$
$228$	−12.9188	−0.855569
$229$	1.93974	0.128182	0.0640909	−	0.997944i	$-0.479585\pi$
$229$	1.93974	0.128182	0.0640909	+	0.997944i	$0.479585\pi$
$230$	−43.3571	−2.85888
$231$	−9.91025	−0.652047
$232$	7.37210	0.484002
$233$	−8.44275	−0.553103	−0.276551	−	0.960999i	$-0.589192\pi$
$233$	−8.44275	−0.553103	−0.276551	+	0.960999i	$0.589192\pi$
$234$	1.96476	0.128440
$235$	−21.4477	−1.39909
$236$	16.0272	1.04328
$237$	1.50720	0.0979031
$238$	0	0
$239$	15.5030	1.00281	0.501403	−	0.865214i	$-0.332817\pi$
$239$	15.5030	1.00281	0.501403	+	0.865214i	$0.332817\pi$
$240$	11.0289	0.711909
$241$	−29.7917	−1.91906	−0.959528	−	0.281615i	$-0.909130\pi$
$241$	−29.7917	−1.91906	−0.959528	+	0.281615i	$0.909130\pi$
$242$	71.4297	4.59168
$243$	−1.00000	−0.0641500
$244$	−33.2460	−2.12836
$245$	13.0989	0.836858
$246$	13.7247	0.875056
$247$	2.61416	0.166335
$248$	−10.4782	−0.665363
$249$	−7.52521	−0.476891
$250$	12.2411	0.774193
$251$	−4.59133	−0.289802	−0.144901	−	0.989446i	$-0.546286\pi$
$251$	−4.59133	−0.289802	−0.144901	+	0.989446i	$0.546286\pi$
$252$	6.20773	0.391050
$253$	39.1578	2.46183
$254$	5.32152	0.333902
$255$	0	0
$256$	−31.7658	−1.98536
$257$	−29.0731	−1.81353	−0.906765	−	0.421637i	$-0.861456\pi$
$257$	−29.0731	−1.81353	−0.906765	+	0.421637i	$0.861456\pi$
$258$	26.9424	1.67736
$259$	−0.994130	−0.0617722
$260$	−9.17770	−0.569177
$261$	1.52895	0.0946396
$262$	10.7745	0.665649
$263$	−1.07458	−0.0662617	−0.0331308	−	0.999451i	$-0.510548\pi$
$263$	−1.07458	−0.0662617	−0.0331308	+	0.999451i	$0.510548\pi$
$264$	−30.5814	−1.88216
$265$	−3.87037	−0.237755
$266$	12.4174	0.761362
$267$	6.12748	0.374995
$268$	30.8182	1.88252
$269$	25.3189	1.54372	0.771860	−	0.635793i	$-0.219327\pi$
$269$	25.3189	1.54372	0.771860	+	0.635793i	$0.219327\pi$
$270$	7.02266	0.427386
$271$	19.4812	1.18340	0.591699	−	0.806159i	$-0.298458\pi$
$271$	19.4812	1.18340	0.591699	+	0.806159i	$0.298458\pi$
$272$	0	0
$273$	−1.25615	−0.0760258
$274$	0.761288	0.0459911
$275$	20.6570	1.24566
$276$	−24.5282	−1.47643
$277$	9.50313	0.570988	0.285494	−	0.958381i	$-0.407842\pi$
$277$	9.50313	0.570988	0.285494	+	0.958381i	$0.407842\pi$
$278$	26.4185	1.58448
$279$	−2.17313	−0.130102
$280$	−21.6487	−1.29376
$281$	14.4217	0.860329	0.430164	−	0.902751i	$-0.358456\pi$
$281$	14.4217	0.860329	0.430164	+	0.902751i	$0.358456\pi$
$282$	−18.2416	−1.08627
$283$	−19.4109	−1.15386	−0.576928	−	0.816795i	$-0.695749\pi$
$283$	−19.4109	−1.15386	−0.576928	+	0.816795i	$0.695749\pi$
$284$	17.9475	1.06499
$285$	9.34380	0.553479
$286$	12.4615	0.736862
$287$	−8.77477	−0.517958
$288$	−0.263112	−0.0155040
$289$	0	0
$290$	−10.7373	−0.630516
$291$	4.84158	0.283818
$292$	−32.8993	−1.92529
$293$	−1.07338	−0.0627076	−0.0313538	−	0.999508i	$-0.509982\pi$
$293$	−1.07338	−0.0627076	−0.0313538	+	0.999508i	$0.509982\pi$
$294$	11.1408	0.649747
$295$	−11.5920	−0.674912
$296$	−3.06772	−0.178308
$297$	−6.34249	−0.368028
$298$	43.3238	2.50968
$299$	4.96336	0.287038
$300$	−12.9394	−0.747058
$301$	−17.2254	−0.992855
$302$	−39.4073	−2.26764
$303$	15.8161	0.908613
$304$	12.4806	0.715812
$305$	24.0459	1.37686
$306$	0	0
$307$	14.5796	0.832104	0.416052	−	0.909341i	$-0.363413\pi$
$307$	14.5796	0.832104	0.416052	+	0.909341i	$0.363413\pi$
$308$	39.3724	2.24345
$309$	7.19272	0.409180
$310$	15.2612	0.866777
$311$	−14.3449	−0.813427	−0.406714	−	0.913556i	$-0.633325\pi$
$311$	−14.3449	−0.813427	−0.406714	+	0.913556i	$0.633325\pi$
$312$	−3.87628	−0.219451
$313$	11.3185	0.639757	0.319879	−	0.947458i	$-0.396358\pi$
$313$	11.3185	0.639757	0.319879	+	0.947458i	$0.396358\pi$
$314$	47.9863	2.70802
$315$	−4.48987	−0.252976
$316$	−5.98795	−0.336849
$317$	−11.7623	−0.660635	−0.330317	−	0.943870i	$-0.607156\pi$
$317$	−11.7623	−0.660635	−0.330317	+	0.943870i	$0.607156\pi$
$318$	−3.29182	−0.184596
$319$	9.69734	0.542947
$320$	23.9055	1.33636
$321$	3.67769	0.205268
$322$	23.5763	1.31386
$323$	0	0
$324$	3.97290	0.220717
$325$	2.61833	0.145239
$326$	26.5844	1.47237
$327$	10.2836	0.568686
$328$	−27.0775	−1.49511
$329$	11.6626	0.642981
$330$	44.5411	2.45191
$331$	−20.2084	−1.11075	−0.555376	−	0.831600i	$-0.687426\pi$
$331$	−20.2084	−1.11075	−0.555376	+	0.831600i	$0.687426\pi$
$332$	29.8969	1.64081
$333$	−0.636236	−0.0348655
$334$	25.6959	1.40602
$335$	−22.2899	−1.21783
$336$	−5.99717	−0.327172
$337$	−6.40801	−0.349067	−0.174533	−	0.984651i	$-0.555842\pi$
$337$	−6.40801	−0.349067	−0.174533	+	0.984651i	$0.555842\pi$
$338$	−30.1919	−1.64222
$339$	13.9303	0.756590
$340$	0	0
$341$	−13.7831	−0.746395
$342$	7.94707	0.429729
$343$	−18.0604	−0.975171
$344$	−53.1548	−2.86591
$345$	17.7406	0.955120
$346$	18.9368	1.01805
$347$	11.7291	0.629649	0.314824	−	0.949150i	$-0.398054\pi$
$347$	11.7291	0.629649	0.314824	+	0.949150i	$0.398054\pi$
$348$	−6.07437	−0.325620
$349$	25.7808	1.38001	0.690007	−	0.723803i	$-0.257607\pi$
$349$	25.7808	1.38001	0.690007	+	0.723803i	$0.257607\pi$
$350$	12.4373	0.664799
$351$	−0.803928	−0.0429105
$352$	−1.66879	−0.0889466
$353$	−3.96309	−0.210934	−0.105467	−	0.994423i	$-0.533634\pi$
$353$	−3.96309	−0.210934	−0.105467	+	0.994423i	$0.533634\pi$
$354$	−9.85920	−0.524010
$355$	−12.9809	−0.688957
$356$	−24.3439	−1.29022
$357$	0	0
$358$	−29.1992	−1.54323
$359$	−11.2422	−0.593340	−0.296670	−	0.954980i	$-0.595876\pi$
$359$	−11.2422	−0.593340	−0.296670	+	0.954980i	$0.595876\pi$
$360$	−13.8550	−0.730224
$361$	−8.42625	−0.443487
$362$	4.28455	0.225191
$363$	−29.2271	−1.53403
$364$	4.99057	0.261577
$365$	23.7951	1.24549
$366$	20.4514	1.06901
$367$	15.4532	0.806649	0.403324	−	0.915057i	$-0.367855\pi$
$367$	15.4532	0.806649	0.403324	+	0.915057i	$0.367855\pi$
$368$	23.6963	1.23525
$369$	−5.61579	−0.292346
$370$	4.46807	0.232284
$371$	2.10459	0.109265
$372$	8.63365	0.447634
$373$	−5.14892	−0.266601	−0.133300	−	0.991076i	$-0.542558\pi$
$373$	−5.14892	−0.266601	−0.133300	+	0.991076i	$0.542558\pi$
$374$	0	0
$375$	−5.00872	−0.258649
$376$	35.9890	1.85599
$377$	1.22917	0.0633052
$378$	−3.81872	−0.196414
$379$	−11.8468	−0.608531	−0.304265	−	0.952587i	$-0.598411\pi$
$379$	−11.8468	−0.608531	−0.304265	+	0.952587i	$0.598411\pi$
$380$	−37.1220	−1.90432
$381$	−2.17742	−0.111553
$382$	−54.5569	−2.79138
$383$	30.7346	1.57047	0.785234	−	0.619200i	$-0.212543\pi$
$383$	30.7346	1.57047	0.785234	+	0.619200i	$0.212543\pi$
$384$	19.8058	1.01071
$385$	−28.4770	−1.45132
$386$	63.9281	3.25385
$387$	−11.0241	−0.560388
$388$	−19.2351	−0.976515
$389$	19.3503	0.981099	0.490549	−	0.871413i	$-0.336796\pi$
$389$	19.3503	0.981099	0.490549	+	0.871413i	$0.336796\pi$
$390$	5.64571	0.285882
$391$	0	0
$392$	−21.9798	−1.11015
$393$	−4.40863	−0.222386
$394$	43.4926	2.19113
$395$	4.33091	0.217912
$396$	25.1981	1.26625
$397$	−13.5426	−0.679681	−0.339841	−	0.940483i	$-0.610373\pi$
$397$	−13.5426	−0.679681	−0.339841	+	0.940483i	$0.610373\pi$
$398$	−55.3654	−2.77522
$399$	−5.08089	−0.254363
$400$	12.5005	0.625026
$401$	8.65508	0.432214	0.216107	−	0.976370i	$-0.430664\pi$
$401$	8.65508	0.432214	0.216107	+	0.976370i	$0.430664\pi$
$402$	−18.9580	−0.945537
$403$	−1.74704	−0.0870264
$404$	−62.8359	−3.12620
$405$	−2.87349	−0.142785
$406$	5.83863	0.289766
$407$	−4.03532	−0.200023
$408$	0	0
$409$	20.2269	1.00015	0.500077	−	0.865981i	$-0.333305\pi$
$409$	20.2269	1.00015	0.500077	+	0.865981i	$0.333305\pi$
$410$	39.4378	1.94769
$411$	−0.311499	−0.0153651
$412$	−28.5760	−1.40784
$413$	6.30339	0.310169
$414$	15.0887	0.741568
$415$	−21.6236	−1.06146
$416$	−0.211523	−0.0103708
$417$	−10.8097	−0.529356
$418$	50.4042	2.46535
$419$	27.8667	1.36138	0.680690	−	0.732572i	$-0.261680\pi$
$419$	27.8667	1.36138	0.680690	+	0.732572i	$0.261680\pi$
$420$	17.8378	0.870397
$421$	−30.5071	−1.48682	−0.743411	−	0.668834i	$-0.766794\pi$
$421$	−30.5071	−1.48682	−0.743411	+	0.668834i	$0.766794\pi$
$422$	−55.5401	−2.70365
$423$	7.46399	0.362912
$424$	6.49443	0.315398
$425$	0	0
$426$	−11.0405	−0.534915
$427$	−13.0754	−0.632765
$428$	−14.6111	−0.706254
$429$	−5.09890	−0.246177
$430$	77.4187	3.73346
$431$	11.8366	0.570151	0.285075	−	0.958505i	$-0.407981\pi$
$431$	11.8366	0.570151	0.285075	+	0.958505i	$0.407981\pi$
$432$	−3.83815	−0.184663
$433$	24.9436	1.19871	0.599355	−	0.800483i	$-0.295424\pi$
$433$	24.9436	1.19871	0.599355	+	0.800483i	$0.295424\pi$
$434$	−8.29859	−0.398345
$435$	4.39341	0.210648
$436$	−40.8558	−1.95664
$437$	20.0758	0.960356
$438$	20.2382	0.967018
$439$	−14.2845	−0.681763	−0.340882	−	0.940106i	$-0.610726\pi$
$439$	−14.2845	−0.681763	−0.340882	+	0.940106i	$0.610726\pi$
$440$	−87.8753	−4.18929
$441$	−4.55854	−0.217073
$442$	0	0
$443$	3.36806	0.160021	0.0800107	−	0.996794i	$-0.474505\pi$
$443$	3.36806	0.160021	0.0800107	+	0.996794i	$0.474505\pi$
$444$	2.52770	0.119959
$445$	17.6072	0.834662
$446$	1.45351	0.0688257
$447$	−17.7269	−0.838455
$448$	−12.9991	−0.614149
$449$	3.93610	0.185756	0.0928781	−	0.995677i	$-0.470393\pi$
$449$	3.93610	0.185756	0.0928781	+	0.995677i	$0.470393\pi$
$450$	7.95975	0.375226
$451$	−35.6181	−1.67719
$452$	−55.3437	−2.60315
$453$	16.1244	0.757591
$454$	−48.9840	−2.29893
$455$	−3.60953	−0.169218
$456$	−15.6788	−0.734227
$457$	−14.8175	−0.693132	−0.346566	−	0.938026i	$-0.612652\pi$
$457$	−14.8175	−0.693132	−0.346566	+	0.938026i	$0.612652\pi$
$458$	4.74064	0.221515
$459$	0	0
$460$	−70.4815	−3.28622
$461$	−33.2839	−1.55019	−0.775093	−	0.631847i	$-0.782297\pi$
$461$	−33.2839	−1.55019	−0.775093	+	0.631847i	$0.782297\pi$
$462$	−24.2202	−1.12682
$463$	19.1509	0.890018	0.445009	−	0.895526i	$-0.353201\pi$
$463$	19.1509	0.890018	0.445009	+	0.895526i	$0.353201\pi$
$464$	5.86833	0.272430
$465$	−6.24447	−0.289580
$466$	−20.6337	−0.955837
$467$	−37.8301	−1.75057	−0.875285	−	0.483607i	$-0.839326\pi$
$467$	−37.8301	−1.75057	−0.875285	+	0.483607i	$0.839326\pi$
$468$	3.19393	0.147639
$469$	12.1206	0.559677
$470$	−52.4171	−2.41782
$471$	−19.6347	−0.904719
$472$	19.4512	0.895315
$473$	−69.9204	−3.21494
$474$	3.68352	0.169190
$475$	10.5906	0.485931
$476$	0	0
$477$	1.34692	0.0616714
$478$	37.8886	1.73298
$479$	−0.429488	−0.0196238	−0.00981191	−	0.999952i	$-0.503123\pi$
$479$	−0.429488	−0.0196238	−0.00981191	+	0.999952i	$0.503123\pi$
$480$	−0.756049	−0.0345088
$481$	−0.511488	−0.0233218
$482$	−72.8096	−3.31639
$483$	−9.64681	−0.438945
$484$	116.117	5.27803
$485$	13.9122	0.631721
$486$	−2.44395	−0.110860
$487$	0.195626	0.00886466	0.00443233	−	0.999990i	$-0.498589\pi$
$487$	0.195626	0.00886466	0.00443233	+	0.999990i	$0.498589\pi$
$488$	−40.3487	−1.82650
$489$	−10.8776	−0.491903
$490$	32.0131	1.44620
$491$	−9.32805	−0.420969	−0.210485	−	0.977597i	$-0.567504\pi$
$491$	−9.32805	−0.420969	−0.210485	+	0.977597i	$0.567504\pi$
$492$	22.3110	1.00586
$493$	0	0
$494$	6.38888	0.287449
$495$	−18.2250	−0.819155
$496$	−8.34081	−0.374513
$497$	7.05866	0.316624
$498$	−18.3913	−0.824132
$499$	−8.21386	−0.367703	−0.183851	−	0.982954i	$-0.558857\pi$
$499$	−8.21386	−0.367703	−0.183851	+	0.982954i	$0.558857\pi$
$500$	19.8991	0.889917
$501$	−10.5141	−0.469734
$502$	−11.2210	−0.500818
$503$	29.9327	1.33463	0.667316	−	0.744775i	$-0.267443\pi$
$503$	29.9327	1.33463	0.667316	+	0.744775i	$0.267443\pi$
$504$	7.53396	0.335589
$505$	45.4474	2.02238
$506$	95.6998	4.25437
$507$	12.3537	0.548647
$508$	8.65069	0.383812
$509$	2.71603	0.120386	0.0601929	−	0.998187i	$-0.480828\pi$
$509$	2.71603	0.120386	0.0601929	+	0.998187i	$0.480828\pi$
$510$	0	0
$511$	−12.9391	−0.572392
$512$	−38.0225	−1.68037
$513$	−3.25173	−0.143567
$514$	−71.0532	−3.13402
$515$	20.6682	0.910749
$516$	43.7978	1.92809
$517$	47.3403	2.08202
$518$	−2.42961	−0.106751
$519$	−7.74845	−0.340119
$520$	−11.1384	−0.488453
$521$	2.07489	0.0909026	0.0454513	−	0.998967i	$-0.485527\pi$
$521$	2.07489	0.0909026	0.0454513	+	0.998967i	$0.485527\pi$
$522$	3.73668	0.163550
$523$	17.2333	0.753558	0.376779	−	0.926303i	$-0.377032\pi$
$523$	17.2333	0.753558	0.376779	+	0.926303i	$0.377032\pi$
$524$	17.5150	0.765148
$525$	−5.08899	−0.222102
$526$	−2.62623	−0.114509
$527$	0	0
$528$	−24.3434	−1.05941
$529$	15.1169	0.657255
$530$	−9.45899	−0.410872
$531$	4.03412	0.175066
$532$	20.1859	0.875168
$533$	−4.51469	−0.195553
$534$	14.9753	0.648043
$535$	10.5678	0.456885
$536$	37.4022	1.61553
$537$	11.9475	0.515575
$538$	61.8782	2.66776
$539$	−28.9125	−1.24535
$540$	11.4161	0.491270
$541$	3.53584	0.152018	0.0760088	−	0.997107i	$-0.475782\pi$
$541$	3.53584	0.152018	0.0760088	+	0.997107i	$0.475782\pi$
$542$	47.6111	2.04507
$543$	−1.75313	−0.0752338
$544$	0	0
$545$	29.5498	1.26578
$546$	−3.06997	−0.131383
$547$	−19.5703	−0.836766	−0.418383	−	0.908271i	$-0.637403\pi$
$547$	−19.5703	−0.836766	−0.418383	+	0.908271i	$0.637403\pi$
$548$	1.23755	0.0528657
$549$	−8.36818	−0.357145
$550$	50.4846	2.15267
$551$	4.97173	0.211803
$552$	−29.7685	−1.26703
$553$	−2.35502	−0.100146
$554$	23.2252	0.986744
$555$	−1.82822	−0.0776034
$556$	42.9461	1.82132
$557$	15.0835	0.639110	0.319555	−	0.947568i	$-0.396467\pi$
$557$	15.0835	0.639110	0.319555	+	0.947568i	$0.396467\pi$
$558$	−5.31104	−0.224834
$559$	−8.86260	−0.374848
$560$	−17.2328	−0.728218
$561$	0	0
$562$	35.2460	1.48676
$563$	38.6507	1.62893	0.814466	−	0.580212i	$-0.197030\pi$
$563$	38.6507	1.62893	0.814466	+	0.580212i	$0.197030\pi$
$564$	−29.6537	−1.24865
$565$	40.0285	1.68401
$566$	−47.4392	−1.99402
$567$	1.56252	0.0656196
$568$	21.7819	0.913947
$569$	−3.19348	−0.133878	−0.0669389	−	0.997757i	$-0.521323\pi$
$569$	−3.19348	−0.133878	−0.0669389	+	0.997757i	$0.521323\pi$
$570$	22.8358	0.956487
$571$	−5.32142	−0.222695	−0.111347	−	0.993782i	$-0.535517\pi$
$571$	−5.32142	−0.222695	−0.111347	+	0.993782i	$0.535517\pi$
$572$	20.2574	0.847006
$573$	22.3232	0.932567
$574$	−21.4451	−0.895102
$575$	20.1078	0.838555
$576$	−8.31932	−0.346638
$577$	−10.4307	−0.434236	−0.217118	−	0.976145i	$-0.569666\pi$
$577$	−10.4307	−0.434236	−0.217118	+	0.976145i	$0.569666\pi$
$578$	0	0
$579$	−26.1577	−1.08708
$580$	−17.4546	−0.724763
$581$	11.7583	0.487816
$582$	11.8326	0.490476
$583$	8.54285	0.353809
$584$	−39.9280	−1.65223
$585$	−2.31008	−0.0955099
$586$	−2.62329	−0.108367
$587$	−18.7387	−0.773427	−0.386714	−	0.922200i	$-0.626390\pi$
$587$	−18.7387	−0.773427	−0.386714	+	0.922200i	$0.626390\pi$
$588$	18.1106	0.746870
$589$	−7.06645	−0.291168
$590$	−28.3303	−1.16634
$591$	−17.7960	−0.732031
$592$	−2.44197	−0.100364
$593$	−7.29409	−0.299533	−0.149766	−	0.988721i	$-0.547852\pi$
$593$	−7.29409	−0.299533	−0.149766	+	0.988721i	$0.547852\pi$
$594$	−15.5007	−0.636003
$595$	0	0
$596$	70.4273	2.88482
$597$	22.6540	0.927168
$598$	12.1302	0.496041
$599$	31.8625	1.30187	0.650933	−	0.759135i	$-0.274378\pi$
$599$	31.8625	1.30187	0.650933	+	0.759135i	$0.274378\pi$
$600$	−15.7038	−0.641105
$601$	0.524164	0.0213811	0.0106905	−	0.999943i	$-0.496597\pi$
$601$	0.524164	0.0213811	0.0106905	+	0.999943i	$0.496597\pi$
$602$	−42.0980	−1.71579
$603$	7.75709	0.315893
$604$	−64.0607	−2.60659
$605$	−83.9838	−3.41443
$606$	38.6538	1.57021
$607$	0.949127	0.0385239	0.0192619	−	0.999814i	$-0.493868\pi$
$607$	0.949127	0.0385239	0.0192619	+	0.999814i	$0.493868\pi$
$608$	−0.855570	−0.0346980
$609$	−2.38901	−0.0968076
$610$	58.7669	2.37940
$611$	6.00051	0.242755
$612$	0	0
$613$	3.89703	0.157399	0.0786997	−	0.996898i	$-0.474923\pi$
$613$	3.89703	0.157399	0.0786997	+	0.996898i	$0.474923\pi$
$614$	35.6319	1.43799
$615$	−16.1369	−0.650702
$616$	47.7840	1.92527
$617$	19.3509	0.779037	0.389518	−	0.921019i	$-0.372641\pi$
$617$	19.3509	0.779037	0.389518	+	0.921019i	$0.372641\pi$
$618$	17.5787	0.707118
$619$	19.6749	0.790803	0.395401	−	0.918508i	$-0.370606\pi$
$619$	19.6749	0.790803	0.395401	+	0.918508i	$0.370606\pi$
$620$	24.8087	0.996340
$621$	−6.17389	−0.247749
$622$	−35.0584	−1.40571
$623$	−9.57429	−0.383586
$624$	−3.08559	−0.123523
$625$	−30.6771	−1.22708
$626$	27.6618	1.10559
$627$	−20.6241	−0.823646
$628$	78.0067	3.11281
$629$	0	0
$630$	−10.9730	−0.437176
$631$	−2.77834	−0.110604	−0.0553019	−	0.998470i	$-0.517612\pi$
$631$	−2.77834	−0.110604	−0.0553019	+	0.998470i	$0.517612\pi$
$632$	−7.26722	−0.289075
$633$	22.7255	0.903258
$634$	−28.7464	−1.14167
$635$	−6.25680	−0.248293
$636$	−5.35120	−0.212189
$637$	−3.66474	−0.145202
$638$	23.6998	0.938286
$639$	4.51749	0.178709
$640$	56.9117	2.24963
$641$	−21.5166	−0.849855	−0.424928	−	0.905227i	$-0.639700\pi$
$641$	−21.5166	−0.849855	−0.424928	+	0.905227i	$0.639700\pi$
$642$	8.98809	0.354732
$643$	44.4358	1.75238	0.876188	−	0.481970i	$-0.160078\pi$
$643$	44.4358	1.75238	0.876188	+	0.481970i	$0.160078\pi$
$644$	38.3258	1.51025
$645$	−31.6777	−1.24731
$646$	0	0
$647$	−43.8840	−1.72526	−0.862629	−	0.505838i	$-0.831183\pi$
$647$	−43.8840	−1.72526	−0.862629	+	0.505838i	$0.831183\pi$
$648$	4.82168	0.189413
$649$	25.5864	1.00435
$650$	6.39907	0.250992
$651$	3.39556	0.133083
$652$	43.2158	1.69246
$653$	−8.54832	−0.334522	−0.167261	−	0.985913i	$-0.553492\pi$
$653$	−8.54832	−0.334522	−0.167261	+	0.985913i	$0.553492\pi$
$654$	25.1327	0.982766
$655$	−12.6681	−0.494985
$656$	−21.5542	−0.841551
$657$	−8.28093	−0.323070
$658$	28.5029	1.11116
$659$	36.1408	1.40785	0.703924	−	0.710276i	$-0.251430\pi$
$659$	36.1408	1.40785	0.703924	+	0.710276i	$0.251430\pi$
$660$	72.4063	2.81841
$661$	46.4203	1.80554	0.902771	−	0.430122i	$-0.141529\pi$
$661$	46.4203	1.80554	0.902771	+	0.430122i	$0.141529\pi$
$662$	−49.3882	−1.91953
$663$	0	0
$664$	36.2841	1.40810
$665$	−14.5999	−0.566158
$666$	−1.55493	−0.0602523
$667$	9.43956	0.365501
$668$	41.7714	1.61618
$669$	−0.594738	−0.0229939
$670$	−54.4754	−2.10457
$671$	−53.0751	−2.04894
$672$	0.411118	0.0158592
$673$	−45.1306	−1.73966	−0.869829	−	0.493353i	$-0.835771\pi$
$673$	−45.1306	−1.73966	−0.869829	+	0.493353i	$0.835771\pi$
$674$	−15.6609	−0.603234
$675$	−3.25692	−0.125359
$676$	−49.0800	−1.88769
$677$	36.2356	1.39265	0.696324	−	0.717727i	$-0.254818\pi$
$677$	36.2356	1.39265	0.696324	+	0.717727i	$0.254818\pi$
$678$	34.0450	1.30749
$679$	−7.56505	−0.290320
$680$	0	0
$681$	20.0429	0.768047
$682$	−33.6852	−1.28987
$683$	−24.3296	−0.930947	−0.465474	−	0.885062i	$-0.654116\pi$
$683$	−24.3296	−0.930947	−0.465474	+	0.885062i	$0.654116\pi$
$684$	12.9188	0.493963
$685$	−0.895087	−0.0341995
$686$	−44.1388	−1.68523
$687$	−1.93974	−0.0740058
$688$	−42.3122	−1.61314
$689$	1.08283	0.0412525
$690$	43.3571	1.65058
$691$	21.3887	0.813666	0.406833	−	0.913503i	$-0.366633\pi$
$691$	21.3887	0.813666	0.406833	+	0.913503i	$0.366633\pi$
$692$	30.7838	1.17023
$693$	9.91025	0.376459
$694$	28.6652	1.08812
$695$	−31.0617	−1.17824
$696$	−7.37210	−0.279439
$697$	0	0
$698$	63.0070	2.38485
$699$	8.44275	0.319334
$700$	20.2181	0.764171
$701$	−15.3315	−0.579063	−0.289532	−	0.957168i	$-0.593500\pi$
$701$	−15.3315	−0.579063	−0.289532	+	0.957168i	$0.593500\pi$
$702$	−1.96476	−0.0741551
$703$	−2.06887	−0.0780288
$704$	−52.7652	−1.98866
$705$	21.4477	0.807766
$706$	−9.68560	−0.364522
$707$	−24.7130	−0.929427
$708$	−16.0272	−0.602338
$709$	38.5013	1.44595	0.722974	−	0.690875i	$-0.242775\pi$
$709$	38.5013	1.44595	0.722974	+	0.690875i	$0.242775\pi$
$710$	−31.7248	−1.19061
$711$	−1.50720	−0.0565244
$712$	−29.5447	−1.10723
$713$	−13.4167	−0.502459
$714$	0	0
$715$	−14.6516	−0.547940
$716$	−47.4664	−1.77390
$717$	−15.5030	−0.578970
$718$	−27.4754	−1.02537
$719$	−15.2312	−0.568028	−0.284014	−	0.958820i	$-0.591666\pi$
$719$	−15.2312	−0.568028	−0.284014	+	0.958820i	$0.591666\pi$
$720$	−11.0289	−0.411021
$721$	−11.2388	−0.418553
$722$	−20.5933	−0.766405
$723$	29.7917	1.10797
$724$	6.96499	0.258852
$725$	4.97967	0.184940
$726$	−71.4297	−2.65101
$727$	11.2839	0.418495	0.209248	−	0.977863i	$-0.432899\pi$
$727$	11.2839	0.418495	0.209248	+	0.977863i	$0.432899\pi$
$728$	6.05676	0.224478
$729$	1.00000	0.0370370
$730$	58.1542	2.15238
$731$	0	0
$732$	33.2460	1.22881
$733$	−26.5213	−0.979585	−0.489793	−	0.871839i	$-0.662927\pi$
$733$	−26.5213	−0.979585	−0.489793	+	0.871839i	$0.662927\pi$
$734$	37.7668	1.39400
$735$	−13.0989	−0.483160
$736$	−1.62443	−0.0598771
$737$	49.1993	1.81228
$738$	−13.7247	−0.505214
$739$	0.861682	0.0316975	0.0158487	−	0.999874i	$-0.494955\pi$
$739$	0.861682	0.0316975	0.0158487	+	0.999874i	$0.494955\pi$
$740$	7.26332	0.267005
$741$	−2.61416	−0.0960335
$742$	5.14352	0.188825
$743$	−4.33692	−0.159106	−0.0795531	−	0.996831i	$-0.525349\pi$
$743$	−4.33692	−0.159106	−0.0795531	+	0.996831i	$0.525349\pi$
$744$	10.4782	0.384148
$745$	−50.9381	−1.86623
$746$	−12.5837	−0.460722
$747$	7.52521	0.275333
$748$	0	0
$749$	−5.74645	−0.209971
$750$	−12.2411	−0.446981
$751$	−34.0949	−1.24414	−0.622071	−	0.782961i	$-0.713709\pi$
$751$	−34.0949	−1.24414	−0.622071	+	0.782961i	$0.713709\pi$
$752$	28.6479	1.04468
$753$	4.59133	0.167317
$754$	3.00402	0.109400
$755$	46.3333	1.68624
$756$	−6.20773	−0.225773
$757$	35.7904	1.30082	0.650412	−	0.759581i	$-0.274596\pi$
$757$	35.7904	1.30082	0.650412	+	0.759581i	$0.274596\pi$
$758$	−28.9531	−1.05162
$759$	−39.1578	−1.42134
$760$	−45.0528	−1.63424
$761$	24.8283	0.900025	0.450013	−	0.893022i	$-0.351420\pi$
$761$	24.8283	0.900025	0.450013	+	0.893022i	$0.351420\pi$
$762$	−5.32152	−0.192778
$763$	−16.0683	−0.581713
$764$	−88.6880	−3.20862
$765$	0	0
$766$	75.1140	2.71398
$767$	3.24314	0.117103
$768$	31.7658	1.14625
$769$	−47.0234	−1.69571	−0.847854	−	0.530230i	$-0.822106\pi$
$769$	−47.0234	−1.69571	−0.847854	+	0.530230i	$0.822106\pi$
$770$	−69.5963	−2.50808
$771$	29.0731	1.04704
$772$	103.922	3.74023
$773$	41.7490	1.50161	0.750804	−	0.660525i	$-0.229666\pi$
$773$	41.7490	1.50161	0.750804	+	0.660525i	$0.229666\pi$
$774$	−26.9424	−0.968426
$775$	−7.07772	−0.254239
$776$	−23.3445	−0.838020
$777$	0.994130	0.0356642
$778$	47.2912	1.69547
$779$	−18.2610	−0.654269
$780$	9.17770	0.328614
$781$	28.6521	1.02525
$782$	0	0
$783$	−1.52895	−0.0546402
$784$	−17.4963	−0.624869
$785$	−56.4200	−2.01372
$786$	−10.7745	−0.384313
$787$	−2.38063	−0.0848604	−0.0424302	−	0.999099i	$-0.513510\pi$
$787$	−2.38063	−0.0848604	−0.0424302	+	0.999099i	$0.513510\pi$
$788$	70.7019	2.51865
$789$	1.07458	0.0382562
$790$	10.5845	0.376581
$791$	−21.7663	−0.773922
$792$	30.5814	1.08666
$793$	−6.72742	−0.238898
$794$	−33.0974	−1.17458
$795$	3.87037	0.137268
$796$	−90.0023	−3.19005
$797$	−38.4308	−1.36129	−0.680645	−	0.732614i	$-0.738300\pi$
$797$	−38.4308	−1.36129	−0.680645	+	0.732614i	$0.738300\pi$
$798$	−12.4174	−0.439573
$799$	0	0
$800$	−0.856935	−0.0302972
$801$	−6.12748	−0.216504
$802$	21.1526	0.746924
$803$	−52.5217	−1.85345
$804$	−30.8182	−1.08687
$805$	−27.7200	−0.977000
$806$	−4.26969	−0.150393
$807$	−25.3189	−0.891267
$808$	−76.2602	−2.68283
$809$	14.5807	0.512630	0.256315	−	0.966593i	$-0.417492\pi$
$809$	14.5807	0.512630	0.256315	+	0.966593i	$0.417492\pi$
$810$	−7.02266	−0.246751
$811$	−0.278172	−0.00976792	−0.00488396	−	0.999988i	$-0.501555\pi$
$811$	−0.278172	−0.00976792	−0.00488396	+	0.999988i	$0.501555\pi$
$812$	9.49131	0.333080
$813$	−19.4812	−0.683235
$814$	−9.86213	−0.345667
$815$	−31.2567	−1.09487
$816$	0	0
$817$	−35.8475	−1.25414
$818$	49.4335	1.72840
$819$	1.25615	0.0438935
$820$	64.1103	2.23883
$821$	−12.4495	−0.434492	−0.217246	−	0.976117i	$-0.569707\pi$
$821$	−12.4495	−0.434492	−0.217246	+	0.976117i	$0.569707\pi$
$822$	−0.761288	−0.0265530
$823$	−20.9324	−0.729659	−0.364829	−	0.931074i	$-0.618873\pi$
$823$	−20.9324	−0.729659	−0.364829	+	0.931074i	$0.618873\pi$
$824$	−34.6810	−1.20817
$825$	−20.6570	−0.719183
$826$	15.4052	0.536015
$827$	30.9351	1.07572	0.537859	−	0.843035i	$-0.319233\pi$
$827$	30.9351	1.07572	0.537859	+	0.843035i	$0.319233\pi$
$828$	24.5282	0.852415
$829$	5.04799	0.175324	0.0876620	−	0.996150i	$-0.472060\pi$
$829$	5.04799	0.175324	0.0876620	+	0.996150i	$0.472060\pi$
$830$	−52.8470	−1.83435
$831$	−9.50313	−0.329660
$832$	−6.68814	−0.231869
$833$	0	0
$834$	−26.4185	−0.914798
$835$	−30.2120	−1.04553
$836$	81.9374	2.83386
$837$	2.17313	0.0751145
$838$	68.1050	2.35265
$839$	−10.9660	−0.378589	−0.189294	−	0.981920i	$-0.560620\pi$
$839$	−10.9660	−0.378589	−0.189294	+	0.981920i	$0.560620\pi$
$840$	21.6487	0.746952
$841$	−26.6623	−0.919390
$842$	−74.5578	−2.56943
$843$	−14.4217	−0.496711
$844$	−90.2863	−3.10778
$845$	35.4982	1.22117
$846$	18.2416	0.627161
$847$	45.6679	1.56917
$848$	5.16969	0.177528
$849$	19.4109	0.666180
$850$	0	0
$851$	−3.92805	−0.134652
$852$	−17.9475	−0.614873
$853$	26.6307	0.911819	0.455910	−	0.890026i	$-0.349314\pi$
$853$	26.6307	0.911819	0.455910	+	0.890026i	$0.349314\pi$
$854$	−31.9557	−1.09350
$855$	−9.34380	−0.319551
$856$	−17.7326	−0.606088
$857$	−1.33422	−0.0455762	−0.0227881	−	0.999740i	$-0.507254\pi$
$857$	−1.33422	−0.0455762	−0.0227881	+	0.999740i	$0.507254\pi$
$858$	−12.4615	−0.425428
$859$	−24.4857	−0.835441	−0.417721	−	0.908575i	$-0.637171\pi$
$859$	−24.4857	−0.835441	−0.417721	+	0.908575i	$0.637171\pi$
$860$	125.852	4.29153
$861$	8.77477	0.299043
$862$	28.9282	0.985297
$863$	−39.3336	−1.33893	−0.669465	−	0.742843i	$-0.733477\pi$
$863$	−39.3336	−1.33893	−0.669465	+	0.742843i	$0.733477\pi$
$864$	0.263112	0.00895126
$865$	−22.2651	−0.757035
$866$	60.9609	2.07153
$867$	0	0
$868$	−13.4902	−0.457888
$869$	−9.55939	−0.324280
$870$	10.7373	0.364028
$871$	6.23614	0.211304
$872$	−49.5843	−1.67914
$873$	−4.84158	−0.163863
$874$	49.0643	1.65963
$875$	7.82621	0.264574
$876$	32.8993	1.11156
$877$	3.86722	0.130587	0.0652934	−	0.997866i	$-0.479202\pi$
$877$	3.86722	0.130587	0.0652934	+	0.997866i	$0.479202\pi$
$878$	−34.9107	−1.17818
$879$	1.07338	0.0362042
$880$	−69.9504	−2.35803
$881$	16.3448	0.550670	0.275335	−	0.961348i	$-0.411211\pi$
$881$	16.3448	0.550670	0.275335	+	0.961348i	$0.411211\pi$
$882$	−11.1408	−0.375132
$883$	−33.5409	−1.12874	−0.564370	−	0.825522i	$-0.690881\pi$
$883$	−33.5409	−1.12874	−0.564370	+	0.825522i	$0.690881\pi$
$884$	0	0
$885$	11.5920	0.389660
$886$	8.23138	0.276539
$887$	25.1866	0.845683	0.422841	−	0.906204i	$-0.361033\pi$
$887$	25.1866	0.845683	0.422841	+	0.906204i	$0.361033\pi$
$888$	3.06772	0.102946
$889$	3.40226	0.114108
$890$	43.0312	1.44241
$891$	6.34249	0.212481
$892$	2.36283	0.0791135
$893$	24.2709	0.812195
$894$	−43.3238	−1.44896
$895$	34.3311	1.14756
$896$	−30.9469	−1.03386
$897$	−4.96336	−0.165722
$898$	9.61965	0.321012
$899$	−3.32261	−0.110815
$900$	12.9394	0.431314
$901$	0	0
$902$	−87.0488	−2.89841
$903$	17.2254	0.573225
$904$	−67.1674	−2.23395
$905$	−5.03758	−0.167455
$906$	39.4073	1.30922
$907$	45.0671	1.49643	0.748214	−	0.663457i	$-0.230911\pi$
$907$	45.0671	1.49643	0.748214	+	0.663457i	$0.230911\pi$
$908$	−79.6286	−2.64257
$909$	−15.8161	−0.524588
$910$	−8.82153	−0.292431
$911$	45.0324	1.49199	0.745995	−	0.665952i	$-0.231974\pi$
$911$	45.0324	1.49199	0.745995	+	0.665952i	$0.231974\pi$
$912$	−12.4806	−0.413274
$913$	47.7286	1.57958
$914$	−36.2132	−1.19783
$915$	−24.0459	−0.794932
$916$	7.70640	0.254627
$917$	6.88856	0.227480
$918$	0	0
$919$	−56.5601	−1.86574	−0.932872	−	0.360208i	$-0.882706\pi$
$919$	−56.5601	−1.86574	−0.932872	+	0.360208i	$0.882706\pi$
$920$	−85.5393	−2.82015
$921$	−14.5796	−0.480415
$922$	−81.3443	−2.67893
$923$	3.63174	0.119540
$924$	−39.3724	−1.29526
$925$	−2.07217	−0.0681325
$926$	46.8039	1.53807
$927$	−7.19272	−0.236240
$928$	−0.402285	−0.0132057
$929$	−33.6201	−1.10304	−0.551520	−	0.834161i	$-0.685952\pi$
$929$	−33.6201	−1.10304	−0.551520	+	0.834161i	$0.685952\pi$
$930$	−15.2612	−0.500434
$931$	−14.8231	−0.485809
$932$	−33.5422	−1.09871
$933$	14.3449	0.469633
$934$	−92.4550	−3.02522
$935$	0	0
$936$	3.87628	0.126700
$937$	−2.08118	−0.0679891	−0.0339946	−	0.999422i	$-0.510823\pi$
$937$	−2.08118	−0.0679891	−0.0339946	+	0.999422i	$0.510823\pi$
$938$	29.6222	0.967198
$939$	−11.3185	−0.369364
$940$	−85.2095	−2.77923
$941$	5.76562	0.187954	0.0939769	−	0.995574i	$-0.470042\pi$
$941$	5.76562	0.187954	0.0939769	+	0.995574i	$0.470042\pi$
$942$	−47.9863	−1.56348
$943$	−34.6712	−1.12905
$944$	15.4835	0.503946
$945$	4.48987	0.146056
$946$	−170.882	−5.55585
$947$	24.5255	0.796971	0.398486	−	0.917175i	$-0.369536\pi$
$947$	24.5255	0.796971	0.398486	+	0.917175i	$0.369536\pi$
$948$	5.98795	0.194480
$949$	−6.65727	−0.216104
$950$	25.8830	0.839755
$951$	11.7623	0.381418
$952$	0	0
$953$	13.3063	0.431033	0.215517	−	0.976500i	$-0.430856\pi$
$953$	13.3063	0.431033	0.215517	+	0.976500i	$0.430856\pi$
$954$	3.29182	0.106577
$955$	64.1455	2.07570
$956$	61.5919	1.99202
$957$	−9.69734	−0.313471
$958$	−1.04965	−0.0339126
$959$	0.486722	0.0157171
$960$	−23.9055	−0.771545
$961$	−26.2775	−0.847661
$962$	−1.25005	−0.0403033
$963$	−3.67769	−0.118512
$964$	−118.360	−3.81211
$965$	−75.1637	−2.41960
$966$	−23.5763	−0.758556
$967$	−18.0996	−0.582044	−0.291022	−	0.956716i	$-0.593995\pi$
$967$	−18.0996	−0.582044	−0.291022	+	0.956716i	$0.593995\pi$
$968$	140.924	4.52946
$969$	0	0
$970$	34.0008	1.09170
$971$	2.40360	0.0771352	0.0385676	−	0.999256i	$-0.487721\pi$
$971$	2.40360	0.0771352	0.0385676	+	0.999256i	$0.487721\pi$
$972$	−3.97290	−0.127431
$973$	16.8904	0.541482
$974$	0.478101	0.0153193
$975$	−2.61833	−0.0838536
$976$	−32.1183	−1.02808
$977$	41.4410	1.32581	0.662907	−	0.748701i	$-0.269322\pi$
$977$	41.4410	1.32581	0.662907	+	0.748701i	$0.269322\pi$
$978$	−26.5844	−0.850076
$979$	−38.8634	−1.24208
$980$	52.0406	1.66238
$981$	−10.2836	−0.328331
$982$	−22.7973	−0.727491
$983$	−37.8963	−1.20870	−0.604352	−	0.796718i	$-0.706568\pi$
$983$	−37.8963	−1.20870	−0.604352	+	0.796718i	$0.706568\pi$
$984$	27.0775	0.863200
$985$	−51.1366	−1.62935
$986$	0	0
$987$	−11.6626	−0.371225
$988$	10.3858	0.330416
$989$	−68.0617	−2.16424
$990$	−44.5411	−1.41561
$991$	25.3455	0.805127	0.402563	−	0.915392i	$-0.368119\pi$
$991$	25.3455	0.805127	0.402563	+	0.915392i	$0.368119\pi$
$992$	0.571778	0.0181540
$993$	20.2084	0.641293
$994$	17.2510	0.547169
$995$	65.0960	2.06368
$996$	−29.8969	−0.947321
$997$	33.7990	1.07043	0.535213	−	0.844717i	$-0.320231\pi$
$997$	33.7990	1.07043	0.535213	+	0.844717i	$0.320231\pi$
$998$	−20.0743	−0.635440
$999$	0.636236	0.0201296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.a.o.1.5	✓	6
3.2	odd	2		2601.2.a.bh.1.2		6
17.2	even	8		867.2.e.k.616.9		24
17.3	odd	16		867.2.h.m.757.9		48
17.4	even	4		867.2.d.g.577.4		12
17.5	odd	16		867.2.h.m.688.4		48
17.6	odd	16		867.2.h.m.733.9		48
17.7	odd	16		867.2.h.m.712.4		48
17.8	even	8		867.2.e.k.829.4		24
17.9	even	8		867.2.e.k.829.3		24
17.10	odd	16		867.2.h.m.712.3		48
17.11	odd	16		867.2.h.m.733.10		48
17.12	odd	16		867.2.h.m.688.3		48
17.13	even	4		867.2.d.g.577.3		12
17.14	odd	16		867.2.h.m.757.10		48
17.15	even	8		867.2.e.k.616.10		24
17.16	even	2		867.2.a.p.1.5	yes	6
51.50	odd	2		2601.2.a.bi.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.5	✓	6	1.1	even	1	trivial
867.2.a.p.1.5	yes	6	17.16	even	2
867.2.d.g.577.3		12	17.13	even	4
867.2.d.g.577.4		12	17.4	even	4
867.2.e.k.616.9		24	17.2	even	8
867.2.e.k.616.10		24	17.15	even	8
867.2.e.k.829.3		24	17.9	even	8
867.2.e.k.829.4		24	17.8	even	8
867.2.h.m.688.3		48	17.12	odd	16
867.2.h.m.688.4		48	17.5	odd	16
867.2.h.m.712.3		48	17.10	odd	16
867.2.h.m.712.4		48	17.7	odd	16
867.2.h.m.733.9		48	17.6	odd	16
867.2.h.m.733.10		48	17.11	odd	16
867.2.h.m.757.9		48	17.3	odd	16
867.2.h.m.757.10		48	17.14	odd	16
2601.2.a.bh.1.2		6	3.2	odd	2
2601.2.a.bi.1.2		6	51.50	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.a (trivial)

\(f(q)\)	\(=\)	\(q+2.44395 q^{2} -1.00000 q^{3} +3.97290 q^{4} -2.87349 q^{5} -2.44395 q^{6} +1.56252 q^{7} +4.82168 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.44395 q^{2} -1.00000 q^{3} +3.97290 q^{4} -2.87349 q^{5} -2.44395 q^{6} +1.56252 q^{7} +4.82168 q^{8} +1.00000 q^{9} -7.02266 q^{10} +6.34249 q^{11} -3.97290 q^{12} +0.803928 q^{13} +3.81872 q^{14} +2.87349 q^{15} +3.83815 q^{16} +2.44395 q^{18} +3.25173 q^{19} -11.4161 q^{20} -1.56252 q^{21} +15.5007 q^{22} +6.17389 q^{23} -4.82168 q^{24} +3.25692 q^{25} +1.96476 q^{26} -1.00000 q^{27} +6.20773 q^{28} +1.52895 q^{29} +7.02266 q^{30} -2.17313 q^{31} -0.263112 q^{32} -6.34249 q^{33} -4.48987 q^{35} +3.97290 q^{36} -0.636236 q^{37} +7.94707 q^{38} -0.803928 q^{39} -13.8550 q^{40} -5.61579 q^{41} -3.81872 q^{42} -11.0241 q^{43} +25.1981 q^{44} -2.87349 q^{45} +15.0887 q^{46} +7.46399 q^{47} -3.83815 q^{48} -4.55854 q^{49} +7.95975 q^{50} +3.19393 q^{52} +1.34692 q^{53} -2.44395 q^{54} -18.2250 q^{55} +7.53396 q^{56} -3.25173 q^{57} +3.73668 q^{58} +4.03412 q^{59} +11.4161 q^{60} -8.36818 q^{61} -5.31104 q^{62} +1.56252 q^{63} -8.31932 q^{64} -2.31008 q^{65} -15.5007 q^{66} +7.75709 q^{67} -6.17389 q^{69} -10.9730 q^{70} +4.51749 q^{71} +4.82168 q^{72} -8.28093 q^{73} -1.55493 q^{74} -3.25692 q^{75} +12.9188 q^{76} +9.91025 q^{77} -1.96476 q^{78} -1.50720 q^{79} -11.0289 q^{80} +1.00000 q^{81} -13.7247 q^{82} +7.52521 q^{83} -6.20773 q^{84} -26.9424 q^{86} -1.52895 q^{87} +30.5814 q^{88} -6.12748 q^{89} -7.02266 q^{90} +1.25615 q^{91} +24.5282 q^{92} +2.17313 q^{93} +18.2416 q^{94} -9.34380 q^{95} +0.263112 q^{96} -4.84158 q^{97} -11.1408 q^{98} +6.34249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 + 12 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{10} + 9 q^{11} - 9 q^{12} + 9 q^{13} + 6 q^{14} - 3 q^{15} + 15 q^{16} + 3 q^{18} + 9 q^{19} - 6 q^{20} + 3 q^{21} + 18 q^{22} + 9 q^{23} - 12 q^{24} + 15 q^{25} - 12 q^{26} - 6 q^{27} + 15 q^{28} + 6 q^{29} + 12 q^{30} - 24 q^{31} + 42 q^{32} - 9 q^{33} + 9 q^{36} + 3 q^{37} - 6 q^{38} - 9 q^{39} + 3 q^{40} + 18 q^{41} - 6 q^{42} + 3 q^{44} + 3 q^{45} - 15 q^{46} + 24 q^{47} - 15 q^{48} + 21 q^{49} + 12 q^{50} - 18 q^{52} + 24 q^{53} - 3 q^{54} - 24 q^{55} + 54 q^{56} - 9 q^{57} - 3 q^{58} - 9 q^{59} + 6 q^{60} - 21 q^{61} + 30 q^{62} - 3 q^{63} + 24 q^{64} - 9 q^{65} - 18 q^{66} - 6 q^{67} - 9 q^{69} - 3 q^{70} + 27 q^{71} + 12 q^{72} - 18 q^{73} + 36 q^{74} - 15 q^{75} - 3 q^{76} + 33 q^{77} + 12 q^{78} - 24 q^{79} + 3 q^{80} + 6 q^{81} + 15 q^{82} + 6 q^{83} - 15 q^{84} + 6 q^{86} - 6 q^{87} + 24 q^{88} - 12 q^{90} - 39 q^{91} + 24 q^{93} - 15 q^{94} + 42 q^{95} - 42 q^{96} + 33 q^{97} - 57 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 3 * q^6 - 3 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^10 + 9 * q^11 - 9 * q^12 + 9 * q^13 + 6 * q^14 - 3 * q^15 + 15 * q^16 + 3 * q^18 + 9 * q^19 - 6 * q^20 + 3 * q^21 + 18 * q^22 + 9 * q^23 - 12 * q^24 + 15 * q^25 - 12 * q^26 - 6 * q^27 + 15 * q^28 + 6 * q^29 + 12 * q^30 - 24 * q^31 + 42 * q^32 - 9 * q^33 + 9 * q^36 + 3 * q^37 - 6 * q^38 - 9 * q^39 + 3 * q^40 + 18 * q^41 - 6 * q^42 + 3 * q^44 + 3 * q^45 - 15 * q^46 + 24 * q^47 - 15 * q^48 + 21 * q^49 + 12 * q^50 - 18 * q^52 + 24 * q^53 - 3 * q^54 - 24 * q^55 + 54 * q^56 - 9 * q^57 - 3 * q^58 - 9 * q^59 + 6 * q^60 - 21 * q^61 + 30 * q^62 - 3 * q^63 + 24 * q^64 - 9 * q^65 - 18 * q^66 - 6 * q^67 - 9 * q^69 - 3 * q^70 + 27 * q^71 + 12 * q^72 - 18 * q^73 + 36 * q^74 - 15 * q^75 - 3 * q^76 + 33 * q^77 + 12 * q^78 - 24 * q^79 + 3 * q^80 + 6 * q^81 + 15 * q^82 + 6 * q^83 - 15 * q^84 + 6 * q^86 - 6 * q^87 + 24 * q^88 - 12 * q^90 - 39 * q^91 + 24 * q^93 - 15 * q^94 + 42 * q^95 - 42 * q^96 + 33 * q^97 - 57 * q^98 + 9 * q^99

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