LMFDB - Embedded newform 867.2.a.i.1.2

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:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ 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)

$f(q)$	$=$	$q-1.34730 q^{2} -1.00000 q^{3} -0.184793 q^{4} +2.53209 q^{5} +1.34730 q^{6} -0.184793 q^{7} +2.94356 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.34730 q^{2} -1.00000 q^{3} -0.184793 q^{4} +2.53209 q^{5} +1.34730 q^{6} -0.184793 q^{7} +2.94356 q^{8} +1.00000 q^{9} -3.41147 q^{10} -3.57398 q^{11} +0.184793 q^{12} -6.53209 q^{13} +0.248970 q^{14} -2.53209 q^{15} -3.59627 q^{16} -1.34730 q^{18} +4.63816 q^{19} -0.467911 q^{20} +0.184793 q^{21} +4.81521 q^{22} +3.10607 q^{23} -2.94356 q^{24} +1.41147 q^{25} +8.80066 q^{26} -1.00000 q^{27} +0.0341483 q^{28} -6.35504 q^{29} +3.41147 q^{30} +7.41147 q^{31} -1.04189 q^{32} +3.57398 q^{33} -0.467911 q^{35} -0.184793 q^{36} +8.39693 q^{37} -6.24897 q^{38} +6.53209 q^{39} +7.45336 q^{40} -7.18479 q^{41} -0.248970 q^{42} -4.93582 q^{43} +0.660444 q^{44} +2.53209 q^{45} -4.18479 q^{46} -9.04963 q^{47} +3.59627 q^{48} -6.96585 q^{49} -1.90167 q^{50} +1.20708 q^{52} -7.65270 q^{53} +1.34730 q^{54} -9.04963 q^{55} -0.543948 q^{56} -4.63816 q^{57} +8.56212 q^{58} -6.55438 q^{59} +0.467911 q^{60} -2.98545 q^{61} -9.98545 q^{62} -0.184793 q^{63} +8.59627 q^{64} -16.5398 q^{65} -4.81521 q^{66} -13.5175 q^{67} -3.10607 q^{69} +0.630415 q^{70} +3.61081 q^{71} +2.94356 q^{72} -8.41147 q^{73} -11.3131 q^{74} -1.41147 q^{75} -0.857097 q^{76} +0.660444 q^{77} -8.80066 q^{78} +7.82295 q^{79} -9.10607 q^{80} +1.00000 q^{81} +9.68004 q^{82} +2.51249 q^{83} -0.0341483 q^{84} +6.65002 q^{86} +6.35504 q^{87} -10.5202 q^{88} +1.32770 q^{89} -3.41147 q^{90} +1.20708 q^{91} -0.573978 q^{92} -7.41147 q^{93} +12.1925 q^{94} +11.7442 q^{95} +1.04189 q^{96} +8.75877 q^{97} +9.38507 q^{98} -3.57398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 3 q^{11} - 3 q^{12} - 15 q^{13} - 12 q^{14} - 3 q^{15} + 3 q^{16} - 3 q^{18} - 3 q^{19} - 6 q^{20} - 3 q^{21} + 18 q^{22} - 3 q^{23} + 6 q^{24} - 6 q^{25} + 12 q^{26} - 3 q^{27} + 21 q^{28} + 6 q^{29} + 12 q^{31} + 3 q^{33} - 6 q^{35} + 3 q^{36} - 3 q^{37} - 6 q^{38} + 15 q^{39} + 9 q^{40} - 18 q^{41} + 12 q^{42} - 24 q^{43} - 21 q^{44} + 3 q^{45} - 9 q^{46} - 3 q^{48} + 6 q^{50} - 6 q^{52} - 24 q^{53} + 3 q^{54} - 24 q^{56} + 3 q^{57} - 9 q^{58} - 9 q^{59} + 6 q^{60} + 9 q^{61} - 12 q^{62} + 3 q^{63} + 12 q^{64} - 21 q^{65} - 18 q^{66} - 18 q^{67} + 3 q^{69} + 9 q^{70} + 15 q^{71} - 6 q^{72} - 15 q^{73} - 12 q^{74} + 6 q^{75} - 3 q^{76} - 21 q^{77} - 12 q^{78} + 3 q^{79} - 15 q^{80} + 3 q^{81} + 9 q^{82} - 21 q^{84} + 30 q^{86} - 6 q^{87} - 6 q^{91} + 6 q^{92} - 12 q^{93} + 9 q^{94} + 6 q^{95} + 15 q^{97} - 27 q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 3 * q^11 - 3 * q^12 - 15 * q^13 - 12 * q^14 - 3 * q^15 + 3 * q^16 - 3 * q^18 - 3 * q^19 - 6 * q^20 - 3 * q^21 + 18 * q^22 - 3 * q^23 + 6 * q^24 - 6 * q^25 + 12 * q^26 - 3 * q^27 + 21 * q^28 + 6 * q^29 + 12 * q^31 + 3 * q^33 - 6 * q^35 + 3 * q^36 - 3 * q^37 - 6 * q^38 + 15 * q^39 + 9 * q^40 - 18 * q^41 + 12 * q^42 - 24 * q^43 - 21 * q^44 + 3 * q^45 - 9 * q^46 - 3 * q^48 + 6 * q^50 - 6 * q^52 - 24 * q^53 + 3 * q^54 - 24 * q^56 + 3 * q^57 - 9 * q^58 - 9 * q^59 + 6 * q^60 + 9 * q^61 - 12 * q^62 + 3 * q^63 + 12 * q^64 - 21 * q^65 - 18 * q^66 - 18 * q^67 + 3 * q^69 + 9 * q^70 + 15 * q^71 - 6 * q^72 - 15 * q^73 - 12 * q^74 + 6 * q^75 - 3 * q^76 - 21 * q^77 - 12 * q^78 + 3 * q^79 - 15 * q^80 + 3 * q^81 + 9 * q^82 - 21 * q^84 + 30 * q^86 - 6 * q^87 - 6 * q^91 + 6 * q^92 - 12 * q^93 + 9 * q^94 + 6 * q^95 + 15 * q^97 - 27 * q^98 - 3 * 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 $

$2$	−1.34730	−0.952682	−0.476341	−	0.879261i	$-0.658037\pi$
$2$	−1.34730	−0.952682	−0.476341	+	0.879261i	$0.658037\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.184793	−0.0923963
$5$	2.53209	1.13238	0.566192	−	0.824273i	$-0.308416\pi$
$5$	2.53209	1.13238	0.566192	+	0.824273i	$0.308416\pi$
$6$	1.34730	0.550031
$7$	−0.184793	−0.0698450	−0.0349225	−	0.999390i	$-0.511118\pi$
$7$	−0.184793	−0.0698450	−0.0349225	+	0.999390i	$0.511118\pi$
$8$	2.94356	1.04071
$9$	1.00000	0.333333
$10$	−3.41147	−1.07880
$11$	−3.57398	−1.07759	−0.538797	−	0.842435i	$-0.681121\pi$
$11$	−3.57398	−1.07759	−0.538797	+	0.842435i	$0.681121\pi$
$12$	0.184793	0.0533450
$13$	−6.53209	−1.81168	−0.905838	−	0.423625i	$-0.860758\pi$
$13$	−6.53209	−1.81168	−0.905838	+	0.423625i	$0.860758\pi$
$14$	0.248970	0.0665401
$15$	−2.53209	−0.653783
$16$	−3.59627	−0.899067
$17$	0	0
$17$	0	0
$18$	−1.34730	−0.317561
$19$	4.63816	1.06407	0.532033	−	0.846724i	$-0.321428\pi$
$19$	4.63816	1.06407	0.532033	+	0.846724i	$0.321428\pi$
$20$	−0.467911	−0.104628
$21$	0.184793	0.0403250
$22$	4.81521	1.02661
$23$	3.10607	0.647660	0.323830	−	0.946115i	$-0.395029\pi$
$23$	3.10607	0.647660	0.323830	+	0.946115i	$0.395029\pi$
$24$	−2.94356	−0.600852
$25$	1.41147	0.282295
$26$	8.80066	1.72595
$27$	−1.00000	−0.192450
$28$	0.0341483	0.00645342
$29$	−6.35504	−1.18010	−0.590050	−	0.807366i	$-0.700892\pi$
$29$	−6.35504	−1.18010	−0.590050	+	0.807366i	$0.700892\pi$
$30$	3.41147	0.622847
$31$	7.41147	1.33114	0.665570	−	0.746335i	$-0.268188\pi$
$31$	7.41147	1.33114	0.665570	+	0.746335i	$0.268188\pi$
$32$	−1.04189	−0.184182
$33$	3.57398	0.622150
$34$	0	0
$35$	−0.467911	−0.0790914
$36$	−0.184793	−0.0307988
$37$	8.39693	1.38045	0.690223	−	0.723597i	$-0.257512\pi$
$37$	8.39693	1.38045	0.690223	+	0.723597i	$0.257512\pi$
$38$	−6.24897	−1.01372
$39$	6.53209	1.04597
$40$	7.45336	1.17848
$41$	−7.18479	−1.12208	−0.561038	−	0.827790i	$-0.689598\pi$
$41$	−7.18479	−1.12208	−0.561038	+	0.827790i	$0.689598\pi$
$42$	−0.248970	−0.0384170
$43$	−4.93582	−0.752706	−0.376353	−	0.926476i	$-0.622822\pi$
$43$	−4.93582	−0.752706	−0.376353	+	0.926476i	$0.622822\pi$
$44$	0.660444	0.0995657
$45$	2.53209	0.377462
$46$	−4.18479	−0.617014
$47$	−9.04963	−1.32002	−0.660012	−	0.751255i	$-0.729449\pi$
$47$	−9.04963	−1.32002	−0.660012	+	0.751255i	$0.729449\pi$
$48$	3.59627	0.519076
$49$	−6.96585	−0.995122
$50$	−1.90167	−0.268937
$51$	0	0
$52$	1.20708	0.167392
$53$	−7.65270	−1.05118	−0.525590	−	0.850738i	$-0.676155\pi$
$53$	−7.65270	−1.05118	−0.525590	+	0.850738i	$0.676155\pi$
$54$	1.34730	0.183344
$55$	−9.04963	−1.22025
$56$	−0.543948	−0.0726882
$57$	−4.63816	−0.614339
$58$	8.56212	1.12426
$59$	−6.55438	−0.853307	−0.426654	−	0.904415i	$-0.640308\pi$
$59$	−6.55438	−0.853307	−0.426654	+	0.904415i	$0.640308\pi$
$60$	0.467911	0.0604071
$61$	−2.98545	−0.382248	−0.191124	−	0.981566i	$-0.561213\pi$
$61$	−2.98545	−0.382248	−0.191124	+	0.981566i	$0.561213\pi$
$62$	−9.98545	−1.26815
$63$	−0.184793	−0.0232817
$64$	8.59627	1.07453
$65$	−16.5398	−2.05151
$66$	−4.81521	−0.592711
$67$	−13.5175	−1.65143	−0.825715	−	0.564087i	$-0.809228\pi$
$67$	−13.5175	−1.65143	−0.825715	+	0.564087i	$0.809228\pi$
$68$	0	0
$69$	−3.10607	−0.373927
$70$	0.630415	0.0753490
$71$	3.61081	0.428525	0.214262	−	0.976776i	$-0.431265\pi$
$71$	3.61081	0.428525	0.214262	+	0.976776i	$0.431265\pi$
$72$	2.94356	0.346902
$73$	−8.41147	−0.984489	−0.492244	−	0.870457i	$-0.663823\pi$
$73$	−8.41147	−0.984489	−0.492244	+	0.870457i	$0.663823\pi$
$74$	−11.3131	−1.31513
$75$	−1.41147	−0.162983
$76$	−0.857097	−0.0983157
$77$	0.660444	0.0752646
$78$	−8.80066	−0.996478
$79$	7.82295	0.880150	0.440075	−	0.897961i	$-0.354952\pi$
$79$	7.82295	0.880150	0.440075	+	0.897961i	$0.354952\pi$
$80$	−9.10607	−1.01809
$81$	1.00000	0.111111
$82$	9.68004	1.06898
$83$	2.51249	0.275781	0.137891	−	0.990447i	$-0.455968\pi$
$83$	2.51249	0.275781	0.137891	+	0.990447i	$0.455968\pi$
$84$	−0.0341483	−0.00372588
$85$	0	0
$86$	6.65002	0.717090
$87$	6.35504	0.681331
$88$	−10.5202	−1.12146
$89$	1.32770	0.140735	0.0703677	−	0.997521i	$-0.477583\pi$
$89$	1.32770	0.140735	0.0703677	+	0.997521i	$0.477583\pi$
$90$	−3.41147	−0.359601
$91$	1.20708	0.126536
$92$	−0.573978	−0.0598413
$93$	−7.41147	−0.768534
$94$	12.1925	1.25756
$95$	11.7442	1.20493
$96$	1.04189	0.106337
$97$	8.75877	0.889318	0.444659	−	0.895700i	$-0.353325\pi$
$97$	8.75877	0.889318	0.444659	+	0.895700i	$0.353325\pi$
$98$	9.38507	0.948035
$99$	−3.57398	−0.359198
$100$	−0.260830	−0.0260830
$101$	−11.0273	−1.09726	−0.548631	−	0.836065i	$-0.684851\pi$
$101$	−11.0273	−1.09726	−0.548631	+	0.836065i	$0.684851\pi$
$102$	0	0
$103$	6.27126	0.617926	0.308963	−	0.951074i	$-0.400018\pi$
$103$	6.27126	0.617926	0.308963	+	0.951074i	$0.400018\pi$
$104$	−19.2276	−1.88542
$105$	0.467911	0.0456634
$106$	10.3105	1.00144
$107$	−3.55438	−0.343615	−0.171807	−	0.985131i	$-0.554961\pi$
$107$	−3.55438	−0.343615	−0.171807	+	0.985131i	$0.554961\pi$
$108$	0.184793	0.0177817
$109$	−3.59627	−0.344460	−0.172230	−	0.985057i	$-0.555097\pi$
$109$	−3.59627	−0.344460	−0.172230	+	0.985057i	$0.555097\pi$
$110$	12.1925	1.16251
$111$	−8.39693	−0.797001
$112$	0.664563	0.0627953
$113$	−4.70914	−0.442999	−0.221499	−	0.975161i	$-0.571095\pi$
$113$	−4.70914	−0.442999	−0.221499	+	0.975161i	$0.571095\pi$
$114$	6.24897	0.585270
$115$	7.86484	0.733400
$116$	1.17436	0.109037
$117$	−6.53209	−0.603892
$118$	8.83069	0.812931
$119$	0	0
$120$	−7.45336	−0.680396
$121$	1.77332	0.161211
$122$	4.02229	0.364161
$123$	7.18479	0.647831
$124$	−1.36959	−0.122992
$125$	−9.08647	−0.812718
$126$	0.248970	0.0221800
$127$	−7.76651	−0.689166	−0.344583	−	0.938756i	$-0.611980\pi$
$127$	−7.76651	−0.689166	−0.344583	+	0.938756i	$0.611980\pi$
$128$	−9.49794	−0.839507
$129$	4.93582	0.434575
$130$	22.2841	1.95444
$131$	4.95130	0.432597	0.216299	−	0.976327i	$-0.430601\pi$
$131$	4.95130	0.432597	0.216299	+	0.976327i	$0.430601\pi$
$132$	−0.660444	−0.0574843
$133$	−0.857097	−0.0743197
$134$	18.2121	1.57329
$135$	−2.53209	−0.217928
$136$	0	0
$137$	−11.5885	−0.990075	−0.495037	−	0.868872i	$-0.664846\pi$
$137$	−11.5885	−0.990075	−0.495037	+	0.868872i	$0.664846\pi$
$138$	4.18479	0.356233
$139$	2.68954	0.228124	0.114062	−	0.993474i	$-0.463614\pi$
$139$	2.68954	0.228124	0.114062	+	0.993474i	$0.463614\pi$
$140$	0.0864665	0.00730775
$141$	9.04963	0.762116
$142$	−4.86484	−0.408248
$143$	23.3455	1.95225
$144$	−3.59627	−0.299689
$145$	−16.0915	−1.33633
$146$	11.3327	0.937905
$147$	6.96585	0.574534
$148$	−1.55169	−0.127548
$149$	−15.9290	−1.30496	−0.652478	−	0.757808i	$-0.726270\pi$
$149$	−15.9290	−1.30496	−0.652478	+	0.757808i	$0.726270\pi$
$150$	1.90167	0.155271
$151$	1.38919	0.113050	0.0565252	−	0.998401i	$-0.481998\pi$
$151$	1.38919	0.113050	0.0565252	+	0.998401i	$0.481998\pi$
$152$	13.6527	1.10738
$153$	0	0
$154$	−0.889814	−0.0717033
$155$	18.7665	1.50736
$156$	−1.20708	−0.0966438
$157$	1.78106	0.142144	0.0710720	−	0.997471i	$-0.477358\pi$
$157$	1.78106	0.142144	0.0710720	+	0.997471i	$0.477358\pi$
$158$	−10.5398	−0.838504
$159$	7.65270	0.606899
$160$	−2.63816	−0.208565
$161$	−0.573978	−0.0452358
$162$	−1.34730	−0.105854
$163$	3.15064	0.246778	0.123389	−	0.992358i	$-0.460624\pi$
$163$	3.15064	0.246778	0.123389	+	0.992358i	$0.460624\pi$
$164$	1.32770	0.103676
$165$	9.04963	0.704513
$166$	−3.38507	−0.262732
$167$	−24.3482	−1.88412	−0.942061	−	0.335441i	$-0.891115\pi$
$167$	−24.3482	−1.88412	−0.942061	+	0.335441i	$0.891115\pi$
$168$	0.543948	0.0419665
$169$	29.6682	2.28217
$170$	0	0
$171$	4.63816	0.354689
$172$	0.912103	0.0695472
$173$	−15.0692	−1.14569	−0.572846	−	0.819663i	$-0.694161\pi$
$173$	−15.0692	−1.14569	−0.572846	+	0.819663i	$0.694161\pi$
$174$	−8.56212	−0.649093
$175$	−0.260830	−0.0197169
$176$	12.8530	0.968830
$177$	6.55438	0.492657
$178$	−1.78880	−0.134076
$179$	16.9017	1.26329	0.631645	−	0.775258i	$-0.282380\pi$
$179$	16.9017	1.26329	0.631645	+	0.775258i	$0.282380\pi$
$180$	−0.467911	−0.0348760
$181$	−10.6682	−0.792960	−0.396480	−	0.918043i	$-0.629768\pi$
$181$	−10.6682	−0.792960	−0.396480	+	0.918043i	$0.629768\pi$
$182$	−1.62630	−0.120549
$183$	2.98545	0.220691
$184$	9.14290	0.674024
$185$	21.2618	1.56320
$186$	9.98545	0.732169
$187$	0	0
$188$	1.67230	0.121965
$189$	0.184793	0.0134417
$190$	−15.8229	−1.14792
$191$	1.77837	0.128678	0.0643392	−	0.997928i	$-0.479506\pi$
$191$	1.77837	0.128678	0.0643392	+	0.997928i	$0.479506\pi$
$192$	−8.59627	−0.620382
$193$	−5.06923	−0.364891	−0.182446	−	0.983216i	$-0.558401\pi$
$193$	−5.06923	−0.364891	−0.182446	+	0.983216i	$0.558401\pi$
$194$	−11.8007	−0.847238
$195$	16.5398	1.18444
$196$	1.28724	0.0919455
$197$	−8.04458	−0.573152	−0.286576	−	0.958057i	$-0.592517\pi$
$197$	−8.04458	−0.573152	−0.286576	+	0.958057i	$0.592517\pi$
$198$	4.81521	0.342202
$199$	11.9409	0.846466	0.423233	−	0.906021i	$-0.360895\pi$
$199$	11.9409	0.846466	0.423233	+	0.906021i	$0.360895\pi$
$200$	4.15476	0.293786
$201$	13.5175	0.953454
$202$	14.8571	1.04534
$203$	1.17436	0.0824242
$204$	0	0
$205$	−18.1925	−1.27062
$206$	−8.44924	−0.588687
$207$	3.10607	0.215887
$208$	23.4911	1.62882
$209$	−16.5767	−1.14663
$210$	−0.630415	−0.0435028
$211$	2.54664	0.175318	0.0876589	−	0.996151i	$-0.472061\pi$
$211$	2.54664	0.175318	0.0876589	+	0.996151i	$0.472061\pi$
$212$	1.41416	0.0971251
$213$	−3.61081	−0.247409
$214$	4.78880	0.327356
$215$	−12.4979	−0.852352
$216$	−2.94356	−0.200284
$217$	−1.36959	−0.0929735
$218$	4.84524	0.328161
$219$	8.41147	0.568395
$220$	1.67230	0.112747
$221$	0	0
$222$	11.3131	0.759289
$223$	4.44562	0.297701	0.148850	−	0.988860i	$-0.452443\pi$
$223$	4.44562	0.297701	0.148850	+	0.988860i	$0.452443\pi$
$224$	0.192533	0.0128642
$225$	1.41147	0.0940983
$226$	6.34461	0.422037
$227$	7.52023	0.499135	0.249568	−	0.968357i	$-0.419712\pi$
$227$	7.52023	0.499135	0.249568	+	0.968357i	$0.419712\pi$
$228$	0.857097	0.0567626
$229$	13.7374	0.907794	0.453897	−	0.891054i	$-0.350033\pi$
$229$	13.7374	0.907794	0.453897	+	0.891054i	$0.350033\pi$
$230$	−10.5963	−0.698697
$231$	−0.660444	−0.0434541
$232$	−18.7065	−1.22814
$233$	20.5253	1.34466	0.672328	−	0.740253i	$-0.265294\pi$
$233$	20.5253	1.34466	0.672328	+	0.740253i	$0.265294\pi$
$234$	8.80066	0.575317
$235$	−22.9145	−1.49478
$236$	1.21120	0.0788424
$237$	−7.82295	−0.508155
$238$	0	0
$239$	25.9145	1.67627	0.838134	−	0.545465i	$-0.183647\pi$
$239$	25.9145	1.67627	0.838134	+	0.545465i	$0.183647\pi$
$240$	9.10607	0.587794
$241$	11.3773	0.732878	0.366439	−	0.930442i	$-0.380577\pi$
$241$	11.3773	0.732878	0.366439	+	0.930442i	$0.380577\pi$
$242$	−2.38919	−0.153583
$243$	−1.00000	−0.0641500
$244$	0.551689	0.0353183
$245$	−17.6382	−1.12686
$246$	−9.68004	−0.617177
$247$	−30.2968	−1.92774
$248$	21.8161	1.38533
$249$	−2.51249	−0.159222
$250$	12.2422	0.774262
$251$	−0.859785	−0.0542691	−0.0271346	−	0.999632i	$-0.508638\pi$
$251$	−0.859785	−0.0542691	−0.0271346	+	0.999632i	$0.508638\pi$
$252$	0.0341483	0.00215114
$253$	−11.1010	−0.697915
$254$	10.4638	0.656557
$255$	0	0
$256$	−4.39599	−0.274750
$257$	0.0300295	0.00187319	0.000936594	−	1.00000i	$-0.499702\pi$
$257$	0.0300295	0.00187319	0.000936594		1.00000i	$0.499702\pi$
$258$	−6.65002	−0.414012
$259$	−1.55169	−0.0964173
$260$	3.05644	0.189552
$261$	−6.35504	−0.393367
$262$	−6.67087	−0.412128
$263$	12.2422	0.754884	0.377442	−	0.926033i	$-0.376804\pi$
$263$	12.2422	0.754884	0.377442	+	0.926033i	$0.376804\pi$
$264$	10.5202	0.647475
$265$	−19.3773	−1.19034
$266$	1.15476	0.0708031
$267$	−1.32770	−0.0812537
$268$	2.49794	0.152586
$269$	21.5672	1.31497	0.657487	−	0.753466i	$-0.271620\pi$
$269$	21.5672	1.31497	0.657487	+	0.753466i	$0.271620\pi$
$270$	3.41147	0.207616
$271$	3.39693	0.206349	0.103174	−	0.994663i	$-0.467100\pi$
$271$	3.39693	0.206349	0.103174	+	0.994663i	$0.467100\pi$
$272$	0	0
$273$	−1.20708	−0.0730559
$274$	15.6132	0.943227
$275$	−5.04458	−0.304199
$276$	0.573978	0.0345494
$277$	15.9172	0.956369	0.478185	−	0.878259i	$-0.341295\pi$
$277$	15.9172	0.956369	0.478185	+	0.878259i	$0.341295\pi$
$278$	−3.62361	−0.217330
$279$	7.41147	0.443713
$280$	−1.37733	−0.0823110
$281$	−16.0155	−0.955404	−0.477702	−	0.878522i	$-0.658530\pi$
$281$	−16.0155	−0.955404	−0.477702	+	0.878522i	$0.658530\pi$
$282$	−12.1925	−0.726055
$283$	−26.8357	−1.59522	−0.797610	−	0.603174i	$-0.793902\pi$
$283$	−26.8357	−1.59522	−0.797610	+	0.603174i	$0.793902\pi$
$284$	−0.667252	−0.0395941
$285$	−11.7442	−0.695668
$286$	−31.4534	−1.85988
$287$	1.32770	0.0783714
$288$	−1.04189	−0.0613939
$289$	0	0
$290$	21.6800	1.27310
$291$	−8.75877	−0.513448
$292$	1.55438	0.0909631
$293$	2.40879	0.140723	0.0703614	−	0.997522i	$-0.477585\pi$
$293$	2.40879	0.140723	0.0703614	+	0.997522i	$0.477585\pi$
$294$	−9.38507	−0.547348
$295$	−16.5963	−0.966272
$296$	24.7169	1.43664
$297$	3.57398	0.207383
$298$	21.4611	1.24321
$299$	−20.2891	−1.17335
$300$	0.260830	0.0150590
$301$	0.912103	0.0525727
$302$	−1.87164	−0.107701
$303$	11.0273	0.633504
$304$	−16.6800	−0.956666
$305$	−7.55943	−0.432852
$306$	0	0
$307$	−6.41921	−0.366364	−0.183182	−	0.983079i	$-0.558640\pi$
$307$	−6.41921	−0.366364	−0.183182	+	0.983079i	$0.558640\pi$
$308$	−0.122045	−0.00695417
$309$	−6.27126	−0.356759
$310$	−25.2841	−1.43604
$311$	−0.543948	−0.0308445	−0.0154222	−	0.999881i	$-0.504909\pi$
$311$	−0.543948	−0.0308445	−0.0154222	+	0.999881i	$0.504909\pi$
$312$	19.2276	1.08855
$313$	−16.6186	−0.939336	−0.469668	−	0.882843i	$-0.655626\pi$
$313$	−16.6186	−0.939336	−0.469668	+	0.882843i	$0.655626\pi$
$314$	−2.39961	−0.135418
$315$	−0.467911	−0.0263638
$316$	−1.44562	−0.0813226
$317$	26.0574	1.46353	0.731764	−	0.681558i	$-0.238697\pi$
$317$	26.0574	1.46353	0.731764	+	0.681558i	$0.238697\pi$
$318$	−10.3105	−0.578182
$319$	22.7128	1.27167
$320$	21.7665	1.21678
$321$	3.55438	0.198386
$322$	0.773318	0.0430953
$323$	0	0
$324$	−0.184793	−0.0102663
$325$	−9.21987	−0.511427
$326$	−4.24485	−0.235101
$327$	3.59627	0.198874
$328$	−21.1489	−1.16775
$329$	1.67230	0.0921971
$330$	−12.1925	−0.671177
$331$	−22.5107	−1.23730	−0.618651	−	0.785666i	$-0.712320\pi$
$331$	−22.5107	−1.23730	−0.618651	+	0.785666i	$0.712320\pi$
$332$	−0.464289	−0.0254812
$333$	8.39693	0.460149
$334$	32.8043	1.79497
$335$	−34.2276	−1.87005
$336$	−0.664563	−0.0362549
$337$	−0.497007	−0.0270737	−0.0135368	−	0.999908i	$-0.504309\pi$
$337$	−0.497007	−0.0270737	−0.0135368	+	0.999908i	$0.504309\pi$
$338$	−39.9718	−2.17418
$339$	4.70914	0.255765
$340$	0	0
$341$	−26.4884	−1.43443
$342$	−6.24897	−0.337906
$343$	2.58079	0.139349
$344$	−14.5289	−0.783346
$345$	−7.86484	−0.423429
$346$	20.3027	1.09148
$347$	13.8648	0.744303	0.372152	−	0.928172i	$-0.378620\pi$
$347$	13.8648	0.744303	0.372152	+	0.928172i	$0.378620\pi$
$348$	−1.17436	−0.0629525
$349$	27.0479	1.44784	0.723920	−	0.689884i	$-0.242339\pi$
$349$	27.0479	1.44784	0.723920	+	0.689884i	$0.242339\pi$
$350$	0.351415	0.0187839
$351$	6.53209	0.348657
$352$	3.72369	0.198473
$353$	8.96997	0.477423	0.238712	−	0.971090i	$-0.423275\pi$
$353$	8.96997	0.477423	0.238712	+	0.971090i	$0.423275\pi$
$354$	−8.83069	−0.469346
$355$	9.14290	0.485255
$356$	−0.245348	−0.0130034
$357$	0	0
$358$	−22.7716	−1.20351
$359$	6.12567	0.323300	0.161650	−	0.986848i	$-0.448318\pi$
$359$	6.12567	0.323300	0.161650	+	0.986848i	$0.448318\pi$
$360$	7.45336	0.392827
$361$	2.51249	0.132236
$362$	14.3732	0.755439
$363$	−1.77332	−0.0930751
$364$	−0.223060	−0.0116915
$365$	−21.2986	−1.11482
$366$	−4.02229	−0.210248
$367$	17.9213	0.935483	0.467741	−	0.883865i	$-0.345068\pi$
$367$	17.9213	0.935483	0.467741	+	0.883865i	$0.345068\pi$
$368$	−11.1702	−0.582289
$369$	−7.18479	−0.374025
$370$	−28.6459	−1.48923
$371$	1.41416	0.0734197
$372$	1.36959	0.0710097
$373$	−15.5389	−0.804574	−0.402287	−	0.915514i	$-0.631785\pi$
$373$	−15.5389	−0.804574	−0.402287	+	0.915514i	$0.631785\pi$
$374$	0	0
$375$	9.08647	0.469223
$376$	−26.6382	−1.37376
$377$	41.5117	2.13796
$378$	−0.248970	−0.0128057
$379$	38.0087	1.95237	0.976187	−	0.216930i	$-0.0696042\pi$
$379$	38.0087	1.95237	0.976187	+	0.216930i	$0.0696042\pi$
$380$	−2.17024	−0.111331
$381$	7.76651	0.397890
$382$	−2.39599	−0.122590
$383$	21.2686	1.08677	0.543387	−	0.839483i	$-0.317142\pi$
$383$	21.2686	1.08677	0.543387	+	0.839483i	$0.317142\pi$
$384$	9.49794	0.484690
$385$	1.67230	0.0852285
$386$	6.82976	0.347625
$387$	−4.93582	−0.250902
$388$	−1.61856	−0.0821697
$389$	13.8016	0.699769	0.349884	−	0.936793i	$-0.386221\pi$
$389$	13.8016	0.699769	0.349884	+	0.936793i	$0.386221\pi$
$390$	−22.2841	−1.12840
$391$	0	0
$392$	−20.5044	−1.03563
$393$	−4.95130	−0.249760
$394$	10.8384	0.546032
$395$	19.8084	0.996669
$396$	0.660444	0.0331886
$397$	−28.5621	−1.43349	−0.716746	−	0.697335i	$-0.754369\pi$
$397$	−28.5621	−1.43349	−0.716746	+	0.697335i	$0.754369\pi$
$398$	−16.0879	−0.806413
$399$	0.857097	0.0429085
$400$	−5.07604	−0.253802
$401$	−26.7766	−1.33716	−0.668580	−	0.743640i	$-0.733098\pi$
$401$	−26.7766	−1.33716	−0.668580	+	0.743640i	$0.733098\pi$
$402$	−18.2121	−0.908339
$403$	−48.4124	−2.41159
$404$	2.03777	0.101383
$405$	2.53209	0.125821
$406$	−1.58222	−0.0785240
$407$	−30.0104	−1.48756
$408$	0	0
$409$	38.8357	1.92030	0.960152	−	0.279479i	$-0.0901616\pi$
$409$	38.8357	1.92030	0.960152	+	0.279479i	$0.0901616\pi$
$410$	24.5107	1.21050
$411$	11.5885	0.571620
$412$	−1.15888	−0.0570940
$413$	1.21120	0.0595993
$414$	−4.18479	−0.205671
$415$	6.36184	0.312291
$416$	6.80571	0.333677
$417$	−2.68954	−0.131707
$418$	22.3337	1.09238
$419$	19.0351	0.929925	0.464962	−	0.885330i	$-0.346068\pi$
$419$	19.0351	0.929925	0.464962	+	0.885330i	$0.346068\pi$
$420$	−0.0864665	−0.00421913
$421$	6.41653	0.312722	0.156361	−	0.987700i	$-0.450024\pi$
$421$	6.41653	0.312722	0.156361	+	0.987700i	$0.450024\pi$
$422$	−3.43107	−0.167022
$423$	−9.04963	−0.440008
$424$	−22.5262	−1.09397
$425$	0	0
$426$	4.86484	0.235702
$427$	0.551689	0.0266981
$428$	0.656822	0.0317487
$429$	−23.3455	−1.12713
$430$	16.8384	0.812021
$431$	8.65095	0.416702	0.208351	−	0.978054i	$-0.433190\pi$
$431$	8.65095	0.416702	0.208351	+	0.978054i	$0.433190\pi$
$432$	3.59627	0.173025
$433$	23.3182	1.12060	0.560301	−	0.828289i	$-0.310686\pi$
$433$	23.3182	1.12060	0.560301	+	0.828289i	$0.310686\pi$
$434$	1.84524	0.0885742
$435$	16.0915	0.771529
$436$	0.664563	0.0318268
$437$	14.4064	0.689153
$438$	−11.3327	−0.541500
$439$	13.1993	0.629970	0.314985	−	0.949097i	$-0.398000\pi$
$439$	13.1993	0.629970	0.314985	+	0.949097i	$0.398000\pi$
$440$	−26.6382	−1.26992
$441$	−6.96585	−0.331707
$442$	0	0
$443$	−30.5235	−1.45022	−0.725108	−	0.688635i	$-0.758210\pi$
$443$	−30.5235	−1.45022	−0.725108	+	0.688635i	$0.758210\pi$
$444$	1.55169	0.0736399
$445$	3.36184	0.159367
$446$	−5.98957	−0.283614
$447$	15.9290	0.753417
$448$	−1.58853	−0.0750508
$449$	2.71183	0.127979	0.0639896	−	0.997951i	$-0.479618\pi$
$449$	2.71183	0.127979	0.0639896	+	0.997951i	$0.479618\pi$
$450$	−1.90167	−0.0896458
$451$	25.6783	1.20914
$452$	0.870214	0.0409314
$453$	−1.38919	−0.0652696
$454$	−10.1320	−0.475517
$455$	3.05644	0.143288
$456$	−13.6527	−0.639346
$457$	−26.2668	−1.22871	−0.614355	−	0.789030i	$-0.710584\pi$
$457$	−26.2668	−1.22871	−0.614355	+	0.789030i	$0.710584\pi$
$458$	−18.5084	−0.864839
$459$	0	0
$460$	−1.45336	−0.0677634
$461$	−25.5202	−1.18860	−0.594298	−	0.804245i	$-0.702570\pi$
$461$	−25.5202	−1.18860	−0.594298	+	0.804245i	$0.702570\pi$
$462$	0.889814	0.0413979
$463$	−2.82564	−0.131318	−0.0656592	−	0.997842i	$-0.520915\pi$
$463$	−2.82564	−0.131318	−0.0656592	+	0.997842i	$0.520915\pi$
$464$	22.8544	1.06099
$465$	−18.7665	−0.870276
$466$	−27.6536	−1.28103
$467$	−32.9992	−1.52702	−0.763510	−	0.645796i	$-0.776526\pi$
$467$	−32.9992	−1.52702	−0.763510	+	0.645796i	$0.776526\pi$
$468$	1.20708	0.0557973
$469$	2.49794	0.115344
$470$	30.8726	1.42405
$471$	−1.78106	−0.0820669
$472$	−19.2932	−0.888043
$473$	17.6405	0.811112
$474$	10.5398	0.484110
$475$	6.54664	0.300380
$476$	0	0
$477$	−7.65270	−0.350393
$478$	−34.9145	−1.59695
$479$	−34.8188	−1.59091	−0.795456	−	0.606011i	$-0.792769\pi$
$479$	−34.8188	−1.59091	−0.795456	+	0.606011i	$0.792769\pi$
$480$	2.63816	0.120415
$481$	−54.8495	−2.50092
$482$	−15.3286	−0.698200
$483$	0.573978	0.0261169
$484$	−0.327696	−0.0148953
$485$	22.1780	1.00705
$486$	1.34730	0.0611146
$487$	−21.5827	−0.978003	−0.489002	−	0.872283i	$-0.662639\pi$
$487$	−21.5827	−0.978003	−0.489002	+	0.872283i	$0.662639\pi$
$488$	−8.78787	−0.397808
$489$	−3.15064	−0.142477
$490$	23.7638	1.07354
$491$	−34.3209	−1.54888	−0.774440	−	0.632647i	$-0.781968\pi$
$491$	−34.3209	−1.54888	−0.774440	+	0.632647i	$0.781968\pi$
$492$	−1.32770	−0.0598572
$493$	0	0
$494$	40.8188	1.83653
$495$	−9.04963	−0.406751
$496$	−26.6536	−1.19678
$497$	−0.667252	−0.0299303
$498$	3.38507	0.151688
$499$	18.1462	0.812336	0.406168	−	0.913799i	$-0.366865\pi$
$499$	18.1462	0.812336	0.406168	+	0.913799i	$0.366865\pi$
$500$	1.67911	0.0750921
$501$	24.3482	1.08780
$502$	1.15839	0.0517013
$503$	−25.2148	−1.12427	−0.562137	−	0.827044i	$-0.690021\pi$
$503$	−25.2148	−1.12427	−0.562137	+	0.827044i	$0.690021\pi$
$504$	−0.543948	−0.0242294
$505$	−27.9222	−1.24252
$506$	14.9564	0.664891
$507$	−29.6682	−1.31761
$508$	1.43519	0.0636764
$509$	−2.82026	−0.125006	−0.0625029	−	0.998045i	$-0.519908\pi$
$509$	−2.82026	−0.125006	−0.0625029	+	0.998045i	$0.519908\pi$
$510$	0	0
$511$	1.55438	0.0687616
$512$	24.9186	1.10126
$513$	−4.63816	−0.204780
$514$	−0.0404586	−0.00178455
$515$	15.8794	0.699729
$516$	−0.912103	−0.0401531
$517$	32.3432	1.42245
$518$	2.09059	0.0918550
$519$	15.0692	0.661466
$520$	−48.6860	−2.13502
$521$	−1.05232	−0.0461029	−0.0230514	−	0.999734i	$-0.507338\pi$
$521$	−1.05232	−0.0461029	−0.0230514	+	0.999734i	$0.507338\pi$
$522$	8.56212	0.374754
$523$	15.0915	0.659906	0.329953	−	0.943997i	$-0.392967\pi$
$523$	15.0915	0.659906	0.329953	+	0.943997i	$0.392967\pi$
$524$	−0.914964	−0.0399704
$525$	0.260830	0.0113835
$526$	−16.4938	−0.719165
$527$	0	0
$528$	−12.8530	−0.559354
$529$	−13.3523	−0.580537
$530$	26.1070	1.13402
$531$	−6.55438	−0.284436
$532$	0.158385	0.00686686
$533$	46.9317	2.03284
$534$	1.78880	0.0774089
$535$	−9.00000	−0.389104
$536$	−39.7897	−1.71865
$537$	−16.9017	−0.729361
$538$	−29.0574	−1.25275
$539$	24.8958	1.07234
$540$	0.467911	0.0201357
$541$	19.3182	0.830554	0.415277	−	0.909695i	$-0.363685\pi$
$541$	19.3182	0.830554	0.415277	+	0.909695i	$0.363685\pi$
$542$	−4.57667	−0.196585
$543$	10.6682	0.457816
$544$	0	0
$545$	−9.10607	−0.390061
$546$	1.62630	0.0695991
$547$	−16.7419	−0.715830	−0.357915	−	0.933754i	$-0.616512\pi$
$547$	−16.7419	−0.715830	−0.357915	+	0.933754i	$0.616512\pi$
$548$	2.14147	0.0914792
$549$	−2.98545	−0.127416
$550$	6.79654	0.289805
$551$	−29.4757	−1.25570
$552$	−9.14290	−0.389148
$553$	−1.44562	−0.0614741
$554$	−21.4451	−0.911116
$555$	−21.2618	−0.902512
$556$	−0.497007	−0.0210778
$557$	−19.8084	−0.839309	−0.419654	−	0.907684i	$-0.637849\pi$
$557$	−19.8084	−0.839309	−0.419654	+	0.907684i	$0.637849\pi$
$558$	−9.98545	−0.422718
$559$	32.2412	1.36366
$560$	1.68273	0.0711085
$561$	0	0
$562$	21.5776	0.910196
$563$	35.4020	1.49202	0.746008	−	0.665937i	$-0.231968\pi$
$563$	35.4020	1.49202	0.746008	+	0.665937i	$0.231968\pi$
$564$	−1.67230	−0.0704167
$565$	−11.9240	−0.501645
$566$	36.1557	1.51974
$567$	−0.184793	−0.00776056
$568$	10.6287	0.445969
$569$	18.0060	0.754850	0.377425	−	0.926040i	$-0.376810\pi$
$569$	18.0060	0.754850	0.377425	+	0.926040i	$0.376810\pi$
$570$	15.8229	0.662750
$571$	13.8922	0.581370	0.290685	−	0.956819i	$-0.406117\pi$
$571$	13.8922	0.581370	0.290685	+	0.956819i	$0.406117\pi$
$572$	−4.31408	−0.180381
$573$	−1.77837	−0.0742925
$574$	−1.78880	−0.0746631
$575$	4.38413	0.182831
$576$	8.59627	0.358178
$577$	−4.15570	−0.173004	−0.0865020	−	0.996252i	$-0.527569\pi$
$577$	−4.15570	−0.173004	−0.0865020	+	0.996252i	$0.527569\pi$
$578$	0	0
$579$	5.06923	0.210670
$580$	2.97359	0.123472
$581$	−0.464289	−0.0192620
$582$	11.8007	0.489153
$583$	27.3506	1.13275
$584$	−24.7597	−1.02456
$585$	−16.5398	−0.683838
$586$	−3.24535	−0.134064
$587$	−25.9341	−1.07041	−0.535207	−	0.844721i	$-0.679766\pi$
$587$	−25.9341	−1.07041	−0.535207	+	0.844721i	$0.679766\pi$
$588$	−1.28724	−0.0530848
$589$	34.3756	1.41642
$590$	22.3601	0.920550
$591$	8.04458	0.330910
$592$	−30.1976	−1.24111
$593$	−37.6459	−1.54593	−0.772966	−	0.634448i	$-0.781228\pi$
$593$	−37.6459	−1.54593	−0.772966	+	0.634448i	$0.781228\pi$
$594$	−4.81521	−0.197570
$595$	0	0
$596$	2.94356	0.120573
$597$	−11.9409	−0.488707
$598$	27.3354	1.11783
$599$	−9.59720	−0.392131	−0.196065	−	0.980591i	$-0.562817\pi$
$599$	−9.59720	−0.392131	−0.196065	+	0.980591i	$0.562817\pi$
$600$	−4.15476	−0.169617
$601$	28.1625	1.14877	0.574386	−	0.818584i	$-0.305241\pi$
$601$	28.1625	1.14877	0.574386	+	0.818584i	$0.305241\pi$
$602$	−1.22887	−0.0500851
$603$	−13.5175	−0.550477
$604$	−0.256711	−0.0104454
$605$	4.49020	0.182553
$606$	−14.8571	−0.603528
$607$	16.2686	0.660321	0.330160	−	0.943925i	$-0.392897\pi$
$607$	16.2686	0.660321	0.330160	+	0.943925i	$0.392897\pi$
$608$	−4.83244	−0.195981
$609$	−1.17436	−0.0475876
$610$	10.1848	0.412370
$611$	59.1130	2.39146
$612$	0	0
$613$	−4.12330	−0.166539	−0.0832693	−	0.996527i	$-0.526536\pi$
$613$	−4.12330	−0.166539	−0.0832693	+	0.996527i	$0.526536\pi$
$614$	8.64858	0.349028
$615$	18.1925	0.733594
$616$	1.94406	0.0783284
$617$	−12.6928	−0.510994	−0.255497	−	0.966810i	$-0.582239\pi$
$617$	−12.6928	−0.510994	−0.255497	+	0.966810i	$0.582239\pi$
$618$	8.44924	0.339878
$619$	−25.9240	−1.04197	−0.520986	−	0.853565i	$-0.674436\pi$
$619$	−25.9240	−1.04197	−0.520986	+	0.853565i	$0.674436\pi$
$620$	−3.46791	−0.139275
$621$	−3.10607	−0.124642
$622$	0.732860	0.0293850
$623$	−0.245348	−0.00982967
$624$	−23.4911	−0.940398
$625$	−30.0651	−1.20260
$626$	22.3901	0.894889
$627$	16.5767	0.662008
$628$	−0.329126	−0.0131336
$629$	0	0
$630$	0.630415	0.0251163
$631$	30.1411	1.19990	0.599950	−	0.800037i	$-0.295187\pi$
$631$	30.1411	1.19990	0.599950	+	0.800037i	$0.295187\pi$
$632$	23.0273	0.915978
$633$	−2.54664	−0.101220
$634$	−35.1070	−1.39428
$635$	−19.6655	−0.780401
$636$	−1.41416	−0.0560752
$637$	45.5016	1.80284
$638$	−30.6008	−1.21150
$639$	3.61081	0.142842
$640$	−24.0496	−0.950645
$641$	0.598021	0.0236204	0.0118102	−	0.999930i	$-0.496241\pi$
$641$	0.598021	0.0236204	0.0118102	+	0.999930i	$0.496241\pi$
$642$	−4.78880	−0.188999
$643$	32.5827	1.28493	0.642467	−	0.766313i	$-0.277911\pi$
$643$	32.5827	1.28493	0.642467	+	0.766313i	$0.277911\pi$
$644$	0.106067	0.00417962
$645$	12.4979	0.492106
$646$	0	0
$647$	−13.8648	−0.545083	−0.272542	−	0.962144i	$-0.587864\pi$
$647$	−13.8648	−0.545083	−0.272542	+	0.962144i	$0.587864\pi$
$648$	2.94356	0.115634
$649$	23.4252	0.919520
$650$	12.4219	0.487227
$651$	1.36959	0.0536783
$652$	−0.582216	−0.0228013
$653$	−1.49619	−0.0585503	−0.0292751	−	0.999571i	$-0.509320\pi$
$653$	−1.49619	−0.0585503	−0.0292751	+	0.999571i	$0.509320\pi$
$654$	−4.84524	−0.189464
$655$	12.5371	0.489867
$656$	25.8384	1.00882
$657$	−8.41147	−0.328163
$658$	−2.25309	−0.0878346
$659$	49.3441	1.92217	0.961087	−	0.276246i	$-0.0890906\pi$
$659$	49.3441	1.92217	0.961087	+	0.276246i	$0.0890906\pi$
$660$	−1.67230	−0.0650943
$661$	45.9077	1.78560	0.892801	−	0.450452i	$-0.148737\pi$
$661$	45.9077	1.78560	0.892801	+	0.450452i	$0.148737\pi$
$662$	30.3286	1.17876
$663$	0	0
$664$	7.39567	0.287008
$665$	−2.17024	−0.0841585
$666$	−11.3131	−0.438376
$667$	−19.7392	−0.764304
$668$	4.49937	0.174086
$669$	−4.44562	−0.171878
$670$	46.1147	1.78157
$671$	10.6699	0.411908
$672$	−0.192533	−0.00742713
$673$	34.7965	1.34131	0.670654	−	0.741770i	$-0.266014\pi$
$673$	34.7965	1.34131	0.670654	+	0.741770i	$0.266014\pi$
$674$	0.669616	0.0257926
$675$	−1.41147	−0.0543277
$676$	−5.48246	−0.210864
$677$	14.1875	0.545269	0.272635	−	0.962118i	$-0.412105\pi$
$677$	14.1875	0.545269	0.272635	+	0.962118i	$0.412105\pi$
$678$	−6.34461	−0.243663
$679$	−1.61856	−0.0621145
$680$	0	0
$681$	−7.52023	−0.288176
$682$	35.6878	1.36656
$683$	−44.5289	−1.70385	−0.851926	−	0.523663i	$-0.824565\pi$
$683$	−44.5289	−1.70385	−0.851926	+	0.523663i	$0.824565\pi$
$684$	−0.857097	−0.0327719
$685$	−29.3432	−1.12115
$686$	−3.47708	−0.132756
$687$	−13.7374	−0.524115
$688$	17.7505	0.676733
$689$	49.9881	1.90440
$690$	10.5963	0.403393
$691$	−5.98782	−0.227787	−0.113894	−	0.993493i	$-0.536332\pi$
$691$	−5.98782	−0.227787	−0.113894	+	0.993493i	$0.536332\pi$
$692$	2.78468	0.105858
$693$	0.660444	0.0250882
$694$	−18.6800	−0.709085
$695$	6.81016	0.258324
$696$	18.7065	0.709066
$697$	0	0
$698$	−36.4415	−1.37933
$699$	−20.5253	−0.776337
$700$	0.0481994	0.00182177
$701$	15.4739	0.584441	0.292221	−	0.956351i	$-0.405606\pi$
$701$	15.4739	0.584441	0.292221	+	0.956351i	$0.405606\pi$
$702$	−8.80066	−0.332159
$703$	38.9463	1.46889
$704$	−30.7229	−1.15791
$705$	22.9145	0.863009
$706$	−12.0852	−0.454833
$707$	2.03777	0.0766382
$708$	−1.21120	−0.0455197
$709$	31.9982	1.20172	0.600860	−	0.799355i	$-0.294825\pi$
$709$	31.9982	1.20172	0.600860	+	0.799355i	$0.294825\pi$
$710$	−12.3182	−0.462294
$711$	7.82295	0.293383
$712$	3.90816	0.146464
$713$	23.0205	0.862126
$714$	0	0
$715$	59.1130	2.21070
$716$	−3.12330	−0.116723
$717$	−25.9145	−0.967794
$718$	−8.25309	−0.308003
$719$	−23.3364	−0.870300	−0.435150	−	0.900358i	$-0.643305\pi$
$719$	−23.3364	−0.870300	−0.435150	+	0.900358i	$0.643305\pi$
$720$	−9.10607	−0.339363
$721$	−1.15888	−0.0431590
$722$	−3.38507	−0.125979
$723$	−11.3773	−0.423127
$724$	1.97140	0.0732665
$725$	−8.96997	−0.333136
$726$	2.38919	0.0886710
$727$	−4.75372	−0.176306	−0.0881528	−	0.996107i	$-0.528096\pi$
$727$	−4.75372	−0.176306	−0.0881528	+	0.996107i	$0.528096\pi$
$728$	3.55312	0.131687
$729$	1.00000	0.0370370
$730$	28.6955	1.06207
$731$	0	0
$732$	−0.551689	−0.0203910
$733$	−0.982764	−0.0362992	−0.0181496	−	0.999835i	$-0.505778\pi$
$733$	−0.982764	−0.0362992	−0.0181496	+	0.999835i	$0.505778\pi$
$734$	−24.1453	−0.891218
$735$	17.6382	0.650593
$736$	−3.23618	−0.119287
$737$	48.3114	1.77957
$738$	9.68004	0.356327
$739$	−9.95636	−0.366250	−0.183125	−	0.983090i	$-0.558621\pi$
$739$	−9.95636	−0.366250	−0.183125	+	0.983090i	$0.558621\pi$
$740$	−3.92902	−0.144433
$741$	30.2968	1.11298
$742$	−1.90530	−0.0699456
$743$	−46.5262	−1.70688	−0.853441	−	0.521190i	$-0.825488\pi$
$743$	−46.5262	−1.70688	−0.853441	+	0.521190i	$0.825488\pi$
$744$	−21.8161	−0.799819
$745$	−40.3337	−1.47771
$746$	20.9355	0.766503
$747$	2.51249	0.0919271
$748$	0	0
$749$	0.656822	0.0239998
$750$	−12.2422	−0.447021
$751$	−13.3155	−0.485890	−0.242945	−	0.970040i	$-0.578113\pi$
$751$	−13.3155	−0.485890	−0.242945	+	0.970040i	$0.578113\pi$
$752$	32.5449	1.18679
$753$	0.859785	0.0313323
$754$	−55.9285	−2.03680
$755$	3.51754	0.128016
$756$	−0.0341483	−0.00124196
$757$	−45.0874	−1.63873	−0.819365	−	0.573273i	$-0.805674\pi$
$757$	−45.0874	−1.63873	−0.819365	+	0.573273i	$0.805674\pi$
$758$	−51.2089	−1.85999
$759$	11.1010	0.402941
$760$	34.5699	1.25398
$761$	24.0036	0.870131	0.435065	−	0.900399i	$-0.356725\pi$
$761$	24.0036	0.870131	0.435065	+	0.900399i	$0.356725\pi$
$762$	−10.4638	−0.379063
$763$	0.664563	0.0240588
$764$	−0.328630	−0.0118894
$765$	0	0
$766$	−28.6551	−1.03535
$767$	42.8138	1.54592
$768$	4.39599	0.158627
$769$	−30.5773	−1.10264	−0.551322	−	0.834292i	$-0.685877\pi$
$769$	−30.5773	−1.10264	−0.551322	+	0.834292i	$0.685877\pi$
$770$	−2.25309	−0.0811957
$771$	−0.0300295	−0.00108149
$772$	0.936756	0.0337146
$773$	−45.3346	−1.63057	−0.815286	−	0.579058i	$-0.803421\pi$
$773$	−45.3346	−1.63057	−0.815286	+	0.579058i	$0.803421\pi$
$774$	6.65002	0.239030
$775$	10.4611	0.375774
$776$	25.7820	0.925520
$777$	1.55169	0.0556665
$778$	−18.5948	−0.666657
$779$	−33.3242	−1.19396
$780$	−3.05644	−0.109438
$781$	−12.9050	−0.461776
$782$	0	0
$783$	6.35504	0.227110
$784$	25.0511	0.894681
$785$	4.50980	0.160962
$786$	6.67087	0.237942
$787$	18.7442	0.668159	0.334080	−	0.942545i	$-0.391575\pi$
$787$	18.7442	0.668159	0.334080	+	0.942545i	$0.391575\pi$
$788$	1.48658	0.0529571
$789$	−12.2422	−0.435833
$790$	−26.6878	−0.949509
$791$	0.870214	0.0309412
$792$	−10.5202	−0.373820
$793$	19.5012	0.692509
$794$	38.4816	1.36566
$795$	19.3773	0.687243
$796$	−2.20658	−0.0782103
$797$	44.5681	1.57868	0.789342	−	0.613954i	$-0.210422\pi$
$797$	44.5681	1.57868	0.789342	+	0.613954i	$0.210422\pi$
$798$	−1.15476	−0.0408782
$799$	0	0
$800$	−1.47060	−0.0519935
$801$	1.32770	0.0469118
$802$	36.0760	1.27389
$803$	30.0624	1.06088
$804$	−2.49794	−0.0880956
$805$	−1.45336	−0.0512243
$806$	65.2259	2.29748
$807$	−21.5672	−0.759200
$808$	−32.4597	−1.14193
$809$	−8.46522	−0.297621	−0.148811	−	0.988866i	$-0.547545\pi$
$809$	−8.46522	−0.297621	−0.148811	+	0.988866i	$0.547545\pi$
$810$	−3.41147	−0.119867
$811$	10.9314	0.383853	0.191926	−	0.981409i	$-0.438527\pi$
$811$	10.9314	0.383853	0.191926	+	0.981409i	$0.438527\pi$
$812$	−0.217014	−0.00761568
$813$	−3.39693	−0.119135
$814$	40.4329	1.41717
$815$	7.97771	0.279447
$816$	0	0
$817$	−22.8931	−0.800929
$818$	−52.3233	−1.82944
$819$	1.20708	0.0421788
$820$	3.36184	0.117401
$821$	−12.5680	−0.438626	−0.219313	−	0.975655i	$-0.570382\pi$
$821$	−12.5680	−0.438626	−0.219313	+	0.975655i	$0.570382\pi$
$822$	−15.6132	−0.544572
$823$	51.2695	1.78714	0.893571	−	0.448921i	$-0.148192\pi$
$823$	51.2695	1.78714	0.893571	+	0.448921i	$0.148192\pi$
$824$	18.4598	0.643079
$825$	5.04458	0.175630
$826$	−1.63185	−0.0567792
$827$	28.5458	0.992635	0.496318	−	0.868141i	$-0.334685\pi$
$827$	28.5458	0.992635	0.496318	+	0.868141i	$0.334685\pi$
$828$	−0.573978	−0.0199471
$829$	4.09865	0.142352	0.0711760	−	0.997464i	$-0.477325\pi$
$829$	4.09865	0.142352	0.0711760	+	0.997464i	$0.477325\pi$
$830$	−8.57129	−0.297514
$831$	−15.9172	−0.552160
$832$	−56.1516	−1.94671
$833$	0	0
$834$	3.62361	0.125475
$835$	−61.6519	−2.13355
$836$	3.06324	0.105945
$837$	−7.41147	−0.256178
$838$	−25.6459	−0.885923
$839$	−37.3969	−1.29109	−0.645543	−	0.763724i	$-0.723369\pi$
$839$	−37.3969	−1.29109	−0.645543	+	0.763724i	$0.723369\pi$
$840$	1.37733	0.0475223
$841$	11.3865	0.392638
$842$	−8.64496	−0.297925
$843$	16.0155	0.551602
$844$	−0.470599	−0.0161987
$845$	75.1225	2.58429
$846$	12.1925	0.419188
$847$	−0.327696	−0.0112598
$848$	27.5212	0.945081
$849$	26.8357	0.921000
$850$	0	0
$851$	26.0814	0.894059
$852$	0.667252	0.0228597
$853$	−56.2586	−1.92626	−0.963129	−	0.269042i	$-0.913293\pi$
$853$	−56.2586	−1.92626	−0.963129	+	0.269042i	$0.913293\pi$
$854$	−0.743289	−0.0254348
$855$	11.7442	0.401644
$856$	−10.4625	−0.357602
$857$	−17.8203	−0.608728	−0.304364	−	0.952556i	$-0.598444\pi$
$857$	−17.8203	−0.608728	−0.304364	+	0.952556i	$0.598444\pi$
$858$	31.4534	1.07380
$859$	−5.45935	−0.186271	−0.0931353	−	0.995653i	$-0.529689\pi$
$859$	−5.45935	−0.186271	−0.0931353	+	0.995653i	$0.529689\pi$
$860$	2.30953	0.0787542
$861$	−1.32770	−0.0452478
$862$	−11.6554	−0.396984
$863$	8.23947	0.280475	0.140237	−	0.990118i	$-0.455213\pi$
$863$	8.23947	0.280475	0.140237	+	0.990118i	$0.455213\pi$
$864$	1.04189	0.0354458
$865$	−38.1566	−1.29736
$866$	−31.4165	−1.06758
$867$	0	0
$868$	0.253089	0.00859040
$869$	−27.9590	−0.948446
$870$	−21.6800	−0.735022
$871$	88.2978	2.99186
$872$	−10.5858	−0.358482
$873$	8.75877	0.296439
$874$	−19.4097	−0.656544
$875$	1.67911	0.0567643
$876$	−1.55438	−0.0525176
$877$	8.15032	0.275217	0.137608	−	0.990487i	$-0.456058\pi$
$877$	8.15032	0.275217	0.137608	+	0.990487i	$0.456058\pi$
$878$	−17.7834	−0.600161
$879$	−2.40879	−0.0812463
$880$	32.5449	1.09709
$881$	18.8553	0.635253	0.317626	−	0.948216i	$-0.397114\pi$
$881$	18.8553	0.635253	0.317626	+	0.948216i	$0.397114\pi$
$882$	9.38507	0.316012
$883$	17.2189	0.579463	0.289732	−	0.957108i	$-0.406434\pi$
$883$	17.2189	0.579463	0.289732	+	0.957108i	$0.406434\pi$
$884$	0	0
$885$	16.5963	0.557877
$886$	41.1242	1.38160
$887$	−11.1898	−0.375718	−0.187859	−	0.982196i	$-0.560155\pi$
$887$	−11.1898	−0.375718	−0.187859	+	0.982196i	$0.560155\pi$
$888$	−24.7169	−0.829444
$889$	1.43519	0.0481348
$890$	−4.52940	−0.151826
$891$	−3.57398	−0.119733
$892$	−0.821518	−0.0275065
$893$	−41.9736	−1.40459
$894$	−21.4611	−0.717767
$895$	42.7965	1.43053
$896$	1.75515	0.0586354
$897$	20.2891	0.677433
$898$	−3.65364	−0.121923
$899$	−47.1002	−1.57088
$900$	−0.260830	−0.00869433
$901$	0	0
$902$	−34.5963	−1.15193
$903$	−0.912103	−0.0303529
$904$	−13.8617	−0.461032
$905$	−27.0128	−0.897936
$906$	1.87164	0.0621812
$907$	−41.0797	−1.36403	−0.682014	−	0.731339i	$-0.738896\pi$
$907$	−41.0797	−1.36403	−0.682014	+	0.731339i	$0.738896\pi$
$908$	−1.38968	−0.0461182
$909$	−11.0273	−0.365754
$910$	−4.11793	−0.136508
$911$	38.3688	1.27121	0.635607	−	0.772013i	$-0.280750\pi$
$911$	38.3688	1.27121	0.635607	+	0.772013i	$0.280750\pi$
$912$	16.6800	0.552331
$913$	−8.97958	−0.297181
$914$	35.3892	1.17057
$915$	7.55943	0.249907
$916$	−2.53857	−0.0838768
$917$	−0.914964	−0.0302148
$918$	0	0
$919$	22.7110	0.749167	0.374584	−	0.927193i	$-0.377786\pi$
$919$	22.7110	0.749167	0.374584	+	0.927193i	$0.377786\pi$
$920$	23.1506	0.763254
$921$	6.41921	0.211520
$922$	34.3833	1.13235
$923$	−23.5862	−0.776348
$924$	0.122045	0.00401499
$925$	11.8520	0.389693
$926$	3.80697	0.125105
$927$	6.27126	0.205975
$928$	6.62124	0.217353
$929$	21.5439	0.706834	0.353417	−	0.935466i	$-0.385020\pi$
$929$	21.5439	0.706834	0.353417	+	0.935466i	$0.385020\pi$
$930$	25.2841	0.829097
$931$	−32.3087	−1.05888
$932$	−3.79292	−0.124241
$933$	0.543948	0.0178081
$934$	44.4597	1.45476
$935$	0	0
$936$	−19.2276	−0.628474
$937$	−37.5476	−1.22663	−0.613313	−	0.789840i	$-0.710163\pi$
$937$	−37.5476	−1.22663	−0.613313	+	0.789840i	$0.710163\pi$
$938$	−3.36547	−0.109886
$939$	16.6186	0.542326
$940$	4.23442	0.138112
$941$	−38.8735	−1.26724	−0.633620	−	0.773644i	$-0.718432\pi$
$941$	−38.8735	−1.26724	−0.633620	+	0.773644i	$0.718432\pi$
$942$	2.39961	0.0781837
$943$	−22.3164	−0.726723
$944$	23.5713	0.767180
$945$	0.467911	0.0152211
$946$	−23.7670	−0.772732
$947$	−47.5313	−1.54456	−0.772279	−	0.635283i	$-0.780883\pi$
$947$	−47.5313	−1.54456	−0.772279	+	0.635283i	$0.780883\pi$
$948$	1.44562	0.0469516
$949$	54.9445	1.78357
$950$	−8.82026	−0.286167
$951$	−26.0574	−0.844968
$952$	0	0
$953$	48.6332	1.57538	0.787692	−	0.616069i	$-0.211276\pi$
$953$	48.6332	1.57538	0.787692	+	0.616069i	$0.211276\pi$
$954$	10.3105	0.333813
$955$	4.50299	0.145713
$956$	−4.78880	−0.154881
$957$	−22.7128	−0.734199
$958$	46.9113	1.51563
$959$	2.14147	0.0691518
$960$	−21.7665	−0.702511
$961$	23.9299	0.771934
$962$	73.8985	2.38258
$963$	−3.55438	−0.114538
$964$	−2.10244	−0.0677152
$965$	−12.8357	−0.413197
$966$	−0.773318	−0.0248811
$967$	1.39281	0.0447897	0.0223948	−	0.999749i	$-0.492871\pi$
$967$	1.39281	0.0447897	0.0223948	+	0.999749i	$0.492871\pi$
$968$	5.21987	0.167773
$969$	0	0
$970$	−29.8803	−0.959399
$971$	13.0892	0.420051	0.210025	−	0.977696i	$-0.432645\pi$
$971$	13.0892	0.420051	0.210025	+	0.977696i	$0.432645\pi$
$972$	0.184793	0.00592722
$973$	−0.497007	−0.0159333
$974$	29.0782	0.931727
$975$	9.21987	0.295272
$976$	10.7365	0.343666
$977$	3.40230	0.108849	0.0544247	−	0.998518i	$-0.482668\pi$
$977$	3.40230	0.108849	0.0544247	+	0.998518i	$0.482668\pi$
$978$	4.24485	0.135735
$979$	−4.74516	−0.151656
$980$	3.25940	0.104118
$981$	−3.59627	−0.114820
$982$	46.2404	1.47559
$983$	−14.6622	−0.467652	−0.233826	−	0.972279i	$-0.575125\pi$
$983$	−14.6622	−0.467652	−0.233826	+	0.972279i	$0.575125\pi$
$984$	21.1489	0.674202
$985$	−20.3696	−0.649029
$986$	0	0
$987$	−1.67230	−0.0532300
$988$	5.59863	0.178116
$989$	−15.3310	−0.487497
$990$	12.1925	0.387504
$991$	−46.6674	−1.48244	−0.741219	−	0.671263i	$-0.765752\pi$
$991$	−46.6674	−1.48244	−0.741219	+	0.671263i	$0.765752\pi$
$992$	−7.72193	−0.245172
$993$	22.5107	0.714357
$994$	0.898986	0.0285141
$995$	30.2354	0.958525
$996$	0.464289	0.0147116
$997$	1.54993	0.0490869	0.0245435	−	0.999699i	$-0.492187\pi$
$997$	1.54993	0.0490869	0.0245435	+	0.999699i	$0.492187\pi$
$998$	−24.4483	−0.773898
$999$	−8.39693	−0.265667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.a.i.1.2	✓	3
3.2	odd	2		2601.2.a.y.1.2		3
17.2	even	8		867.2.e.j.616.3		12
17.3	odd	16		867.2.h.l.757.3		24
17.4	even	4		867.2.d.d.577.4		6
17.5	odd	16		867.2.h.l.688.4		24
17.6	odd	16		867.2.h.l.733.3		24
17.7	odd	16		867.2.h.l.712.4		24
17.8	even	8		867.2.e.j.829.4		12
17.9	even	8		867.2.e.j.829.3		12
17.10	odd	16		867.2.h.l.712.3		24
17.11	odd	16		867.2.h.l.733.4		24
17.12	odd	16		867.2.h.l.688.3		24
17.13	even	4		867.2.d.d.577.3		6
17.14	odd	16		867.2.h.l.757.4		24
17.15	even	8		867.2.e.j.616.4		12
17.16	even	2		867.2.a.j.1.2	yes	3
51.50	odd	2		2601.2.a.z.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.i.1.2	✓	3	1.1	even	1	trivial
867.2.a.j.1.2	yes	3	17.16	even	2
867.2.d.d.577.3		6	17.13	even	4
867.2.d.d.577.4		6	17.4	even	4
867.2.e.j.616.3		12	17.2	even	8
867.2.e.j.616.4		12	17.15	even	8
867.2.e.j.829.3		12	17.9	even	8
867.2.e.j.829.4		12	17.8	even	8
867.2.h.l.688.3		24	17.12	odd	16
867.2.h.l.688.4		24	17.5	odd	16
867.2.h.l.712.3		24	17.10	odd	16
867.2.h.l.712.4		24	17.7	odd	16
867.2.h.l.733.3		24	17.6	odd	16
867.2.h.l.733.4		24	17.11	odd	16
867.2.h.l.757.3		24	17.3	odd	16
867.2.h.l.757.4		24	17.14	odd	16
2601.2.a.y.1.2		3	3.2	odd	2
2601.2.a.z.1.2		3	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)

\(f(q)\)	\(=\)	\(q-1.34730 q^{2} -1.00000 q^{3} -0.184793 q^{4} +2.53209 q^{5} +1.34730 q^{6} -0.184793 q^{7} +2.94356 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.34730 q^{2} -1.00000 q^{3} -0.184793 q^{4} +2.53209 q^{5} +1.34730 q^{6} -0.184793 q^{7} +2.94356 q^{8} +1.00000 q^{9} -3.41147 q^{10} -3.57398 q^{11} +0.184793 q^{12} -6.53209 q^{13} +0.248970 q^{14} -2.53209 q^{15} -3.59627 q^{16} -1.34730 q^{18} +4.63816 q^{19} -0.467911 q^{20} +0.184793 q^{21} +4.81521 q^{22} +3.10607 q^{23} -2.94356 q^{24} +1.41147 q^{25} +8.80066 q^{26} -1.00000 q^{27} +0.0341483 q^{28} -6.35504 q^{29} +3.41147 q^{30} +7.41147 q^{31} -1.04189 q^{32} +3.57398 q^{33} -0.467911 q^{35} -0.184793 q^{36} +8.39693 q^{37} -6.24897 q^{38} +6.53209 q^{39} +7.45336 q^{40} -7.18479 q^{41} -0.248970 q^{42} -4.93582 q^{43} +0.660444 q^{44} +2.53209 q^{45} -4.18479 q^{46} -9.04963 q^{47} +3.59627 q^{48} -6.96585 q^{49} -1.90167 q^{50} +1.20708 q^{52} -7.65270 q^{53} +1.34730 q^{54} -9.04963 q^{55} -0.543948 q^{56} -4.63816 q^{57} +8.56212 q^{58} -6.55438 q^{59} +0.467911 q^{60} -2.98545 q^{61} -9.98545 q^{62} -0.184793 q^{63} +8.59627 q^{64} -16.5398 q^{65} -4.81521 q^{66} -13.5175 q^{67} -3.10607 q^{69} +0.630415 q^{70} +3.61081 q^{71} +2.94356 q^{72} -8.41147 q^{73} -11.3131 q^{74} -1.41147 q^{75} -0.857097 q^{76} +0.660444 q^{77} -8.80066 q^{78} +7.82295 q^{79} -9.10607 q^{80} +1.00000 q^{81} +9.68004 q^{82} +2.51249 q^{83} -0.0341483 q^{84} +6.65002 q^{86} +6.35504 q^{87} -10.5202 q^{88} +1.32770 q^{89} -3.41147 q^{90} +1.20708 q^{91} -0.573978 q^{92} -7.41147 q^{93} +12.1925 q^{94} +11.7442 q^{95} +1.04189 q^{96} +8.75877 q^{97} +9.38507 q^{98} -3.57398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 3 q^{11} - 3 q^{12} - 15 q^{13} - 12 q^{14} - 3 q^{15} + 3 q^{16} - 3 q^{18} - 3 q^{19} - 6 q^{20} - 3 q^{21} + 18 q^{22} - 3 q^{23} + 6 q^{24} - 6 q^{25} + 12 q^{26} - 3 q^{27} + 21 q^{28} + 6 q^{29} + 12 q^{31} + 3 q^{33} - 6 q^{35} + 3 q^{36} - 3 q^{37} - 6 q^{38} + 15 q^{39} + 9 q^{40} - 18 q^{41} + 12 q^{42} - 24 q^{43} - 21 q^{44} + 3 q^{45} - 9 q^{46} - 3 q^{48} + 6 q^{50} - 6 q^{52} - 24 q^{53} + 3 q^{54} - 24 q^{56} + 3 q^{57} - 9 q^{58} - 9 q^{59} + 6 q^{60} + 9 q^{61} - 12 q^{62} + 3 q^{63} + 12 q^{64} - 21 q^{65} - 18 q^{66} - 18 q^{67} + 3 q^{69} + 9 q^{70} + 15 q^{71} - 6 q^{72} - 15 q^{73} - 12 q^{74} + 6 q^{75} - 3 q^{76} - 21 q^{77} - 12 q^{78} + 3 q^{79} - 15 q^{80} + 3 q^{81} + 9 q^{82} - 21 q^{84} + 30 q^{86} - 6 q^{87} - 6 q^{91} + 6 q^{92} - 12 q^{93} + 9 q^{94} + 6 q^{95} + 15 q^{97} - 27 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 3 * q^11 - 3 * q^12 - 15 * q^13 - 12 * q^14 - 3 * q^15 + 3 * q^16 - 3 * q^18 - 3 * q^19 - 6 * q^20 - 3 * q^21 + 18 * q^22 - 3 * q^23 + 6 * q^24 - 6 * q^25 + 12 * q^26 - 3 * q^27 + 21 * q^28 + 6 * q^29 + 12 * q^31 + 3 * q^33 - 6 * q^35 + 3 * q^36 - 3 * q^37 - 6 * q^38 + 15 * q^39 + 9 * q^40 - 18 * q^41 + 12 * q^42 - 24 * q^43 - 21 * q^44 + 3 * q^45 - 9 * q^46 - 3 * q^48 + 6 * q^50 - 6 * q^52 - 24 * q^53 + 3 * q^54 - 24 * q^56 + 3 * q^57 - 9 * q^58 - 9 * q^59 + 6 * q^60 + 9 * q^61 - 12 * q^62 + 3 * q^63 + 12 * q^64 - 21 * q^65 - 18 * q^66 - 18 * q^67 + 3 * q^69 + 9 * q^70 + 15 * q^71 - 6 * q^72 - 15 * q^73 - 12 * q^74 + 6 * q^75 - 3 * q^76 - 21 * q^77 - 12 * q^78 + 3 * q^79 - 15 * q^80 + 3 * q^81 + 9 * q^82 - 21 * q^84 + 30 * q^86 - 6 * q^87 - 6 * q^91 + 6 * q^92 - 12 * q^93 + 9 * q^94 + 6 * q^95 + 15 * q^97 - 27 * q^98 - 3 * q^99

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