LMFDB - Embedded newform 841.2.a.g.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(1,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$6.71541880999$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.11973625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 8x^{4} + 15x^{3} + 13x^{2} - 27x + 9 $ x^6 - 2x^5 - 8x^4 + 15x^3 + 13x^2 - 27*x + 9
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			1.4
Root			$0.511256$ of defining polynomial
Character	$\chi$	$=$	841.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.511256 q^{2} -2.69256 q^{3} -1.73862 q^{4} +2.20381 q^{5} +1.37659 q^{6} -1.30206 q^{7} +1.91139 q^{8} +4.24987 q^{9} -1.12671 q^{10} -5.00853 q^{11} +4.68133 q^{12} +3.13782 q^{13} +0.665686 q^{14} -5.93390 q^{15} +2.50003 q^{16} +1.37659 q^{17} -2.17277 q^{18} +5.95217 q^{19} -3.83159 q^{20} +3.50588 q^{21} +2.56064 q^{22} +0.865330 q^{23} -5.14653 q^{24} -0.143202 q^{25} -1.60423 q^{26} -3.36536 q^{27} +2.26379 q^{28} +3.03374 q^{30} -2.74400 q^{31} -5.10093 q^{32} +13.4858 q^{33} -0.703787 q^{34} -2.86950 q^{35} -7.38891 q^{36} -5.89999 q^{37} -3.04308 q^{38} -8.44877 q^{39} +4.21235 q^{40} +1.90869 q^{41} -1.79240 q^{42} -11.0143 q^{43} +8.70792 q^{44} +9.36593 q^{45} -0.442405 q^{46} +2.87661 q^{47} -6.73147 q^{48} -5.30464 q^{49} +0.0732129 q^{50} -3.70654 q^{51} -5.45547 q^{52} -5.80302 q^{53} +1.72056 q^{54} -11.0379 q^{55} -2.48874 q^{56} -16.0266 q^{57} -4.35304 q^{59} +10.3168 q^{60} +5.43545 q^{61} +1.40288 q^{62} -5.53359 q^{63} -2.39218 q^{64} +6.91518 q^{65} -6.89467 q^{66} -2.36278 q^{67} -2.39336 q^{68} -2.32995 q^{69} +1.46705 q^{70} -15.5897 q^{71} +8.12316 q^{72} -3.39645 q^{73} +3.01640 q^{74} +0.385580 q^{75} -10.3486 q^{76} +6.52141 q^{77} +4.31948 q^{78} -2.11612 q^{79} +5.50960 q^{80} -3.68820 q^{81} -0.975830 q^{82} +6.35906 q^{83} -6.09538 q^{84} +3.03374 q^{85} +5.63110 q^{86} -9.57325 q^{88} -11.9328 q^{89} -4.78838 q^{90} -4.08563 q^{91} -1.50448 q^{92} +7.38838 q^{93} -1.47068 q^{94} +13.1175 q^{95} +13.7346 q^{96} +11.4236 q^{97} +2.71203 q^{98} -21.2856 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 6 q^{9} - 15 q^{10} - 13 q^{11} + 4 q^{12} - 6 q^{13} + 6 q^{14} - 19 q^{15} + 4 q^{16} - 3 q^{17} - 17 q^{18} + 6 q^{19} - 5 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 6 * q^9 - 15 * q^10 - 13 * q^11 + 4 * q^12 - 6 * q^13 + 6 * q^14 - 19 * q^15 + 4 * q^16 - 3 * q^17 - 17 * q^18 + 6 * q^19 - 5 * q^20 + 2 * q^21 - 4 * q^22 - 5 * q^23 - 10 * q^24 + 6 * q^25 - 9 * q^26 + q^27 - 5 * q^28 + 26 * q^30 - 16 * q^31 - 33 * q^32 + 27 * q^33 - 4 * q^35 - 21 * q^36 + 10 * q^37 + 41 * q^38 - 17 * q^39 - 7 * q^40 - 30 * q^41 - 21 * q^42 + 2 * q^43 - 16 * q^44 + 16 * q^45 + 20 * q^46 - 5 * q^47 + 30 * q^48 - 12 * q^49 + 8 * q^50 - 23 * q^51 - 13 * q^53 + 19 * q^54 - 10 * q^55 - 16 * q^56 - 16 * q^57 - 17 * q^59 + 9 * q^60 + 4 * q^61 - 9 * q^63 + q^64 + 32 * q^65 + 8 * q^66 - 9 * q^67 - 16 * q^68 - 26 * q^69 + 28 * q^70 + 21 * q^72 - 9 * q^73 - 36 * q^74 - 7 * q^75 - 24 * q^76 - 13 * q^77 - 6 * q^79 + 5 * q^80 - 22 * q^81 + 19 * q^82 - 24 * q^83 + 26 * q^85 + 17 * q^86 + 21 * q^88 - 9 * q^89 + 16 * q^90 + 16 * q^91 - 23 * q^92 - 12 * q^93 - 37 * q^94 - 31 * q^95 - 37 * q^96 + 10 * q^97 + 42 * q^98 - 6 * q^99

Coefficient data

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

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

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

$2$	−0.511256	−0.361512	−0.180756	−	0.983528i	$-0.557854\pi$
$2$	−0.511256	−0.361512	−0.180756	+	0.983528i	$0.557854\pi$
$3$	−2.69256	−1.55455	−0.777275	−	0.629161i	$-0.783399\pi$
$3$	−2.69256	−1.55455	−0.777275	+	0.629161i	$0.783399\pi$
$4$	−1.73862	−0.869309
$5$	2.20381	0.985576	0.492788	−	0.870149i	$-0.335978\pi$
$5$	2.20381	0.985576	0.492788	+	0.870149i	$0.335978\pi$
$6$	1.37659	0.561989
$7$	−1.30206	−0.492133	−0.246066	−	0.969253i	$-0.579138\pi$
$7$	−1.30206	−0.492133	−0.246066	+	0.969253i	$0.579138\pi$
$8$	1.91139	0.675778
$9$	4.24987	1.41662
$10$	−1.12671	−0.356298
$11$	−5.00853	−1.51013	−0.755065	−	0.655650i	$-0.772395\pi$
$11$	−5.00853	−1.51013	−0.755065	+	0.655650i	$0.772395\pi$
$12$	4.68133	1.35138
$13$	3.13782	0.870275	0.435138	−	0.900364i	$-0.356700\pi$
$13$	3.13782	0.870275	0.435138	+	0.900364i	$0.356700\pi$
$14$	0.665686	0.177912
$15$	−5.93390	−1.53213
$16$	2.50003	0.625007
$17$	1.37659	0.333871	0.166936	−	0.985968i	$-0.446613\pi$
$17$	1.37659	0.333871	0.166936	+	0.985968i	$0.446613\pi$
$18$	−2.17277	−0.512127
$19$	5.95217	1.36552	0.682761	−	0.730642i	$-0.260779\pi$
$19$	5.95217	1.36552	0.682761	+	0.730642i	$0.260779\pi$
$20$	−3.83159	−0.856770
$21$	3.50588	0.765045
$22$	2.56064	0.545930
$23$	0.865330	0.180434	0.0902169	−	0.995922i	$-0.471244\pi$
$23$	0.865330	0.180434	0.0902169	+	0.995922i	$0.471244\pi$
$24$	−5.14653	−1.05053
$25$	−0.143202	−0.0286404
$26$	−1.60423	−0.314615
$27$	−3.36536	−0.647663
$28$	2.26379	0.427815
$29$	0	0
$29$	0	0
$30$	3.03374	0.553882
$31$	−2.74400	−0.492837	−0.246418	−	0.969164i	$-0.579254\pi$
$31$	−2.74400	−0.492837	−0.246418	+	0.969164i	$0.579254\pi$
$32$	−5.10093	−0.901726
$33$	13.4858	2.34757
$34$	−0.703787	−0.120698
$35$	−2.86950	−0.485034
$36$	−7.38891	−1.23148
$37$	−5.89999	−0.969952	−0.484976	−	0.874527i	$-0.661172\pi$
$37$	−5.89999	−0.969952	−0.484976	+	0.874527i	$0.661172\pi$
$38$	−3.04308	−0.493653
$39$	−8.44877	−1.35289
$40$	4.21235	0.666030
$41$	1.90869	0.298088	0.149044	−	0.988831i	$-0.452380\pi$
$41$	1.90869	0.298088	0.149044	+	0.988831i	$0.452380\pi$
$42$	−1.79240	−0.276573
$43$	−11.0143	−1.67966	−0.839830	−	0.542850i	$-0.817345\pi$
$43$	−11.0143	−1.67966	−0.839830	+	0.542850i	$0.817345\pi$
$44$	8.70792	1.31277
$45$	9.36593	1.39619
$46$	−0.442405	−0.0652290
$47$	2.87661	0.419597	0.209799	−	0.977745i	$-0.432719\pi$
$47$	2.87661	0.419597	0.209799	+	0.977745i	$0.432719\pi$
$48$	−6.73147	−0.971604
$49$	−5.30464	−0.757805
$50$	0.0732129	0.0103539
$51$	−3.70654	−0.519019
$52$	−5.45547	−0.756538
$53$	−5.80302	−0.797106	−0.398553	−	0.917145i	$-0.630487\pi$
$53$	−5.80302	−0.797106	−0.398553	+	0.917145i	$0.630487\pi$
$54$	1.72056	0.234138
$55$	−11.0379	−1.48835
$56$	−2.48874	−0.332572
$57$	−16.0266	−2.12277
$58$	0	0
$59$	−4.35304	−0.566717	−0.283359	−	0.959014i	$-0.591449\pi$
$59$	−4.35304	−0.566717	−0.283359	+	0.959014i	$0.591449\pi$
$60$	10.3168	1.33189
$61$	5.43545	0.695939	0.347969	−	0.937506i	$-0.386871\pi$
$61$	5.43545	0.695939	0.347969	+	0.937506i	$0.386871\pi$
$62$	1.40288	0.178166
$63$	−5.53359	−0.697167
$64$	−2.39218	−0.299022
$65$	6.91518	0.857722
$66$	−6.89467	−0.848676
$67$	−2.36278	−0.288660	−0.144330	−	0.989530i	$-0.546103\pi$
$67$	−2.36278	−0.288660	−0.144330	+	0.989530i	$0.546103\pi$
$68$	−2.39336	−0.290237
$69$	−2.32995	−0.280493
$70$	1.46705	0.175346
$71$	−15.5897	−1.85016	−0.925081	−	0.379770i	$-0.876003\pi$
$71$	−15.5897	−1.85016	−0.925081	+	0.379770i	$0.876003\pi$
$72$	8.12316	0.957324
$73$	−3.39645	−0.397525	−0.198762	−	0.980048i	$-0.563692\pi$
$73$	−3.39645	−0.397525	−0.198762	+	0.980048i	$0.563692\pi$
$74$	3.01640	0.350650
$75$	0.385580	0.0445230
$76$	−10.3486	−1.18706
$77$	6.52141	0.743184
$78$	4.31948	0.489085
$79$	−2.11612	−0.238083	−0.119041	−	0.992889i	$-0.537982\pi$
$79$	−2.11612	−0.238083	−0.119041	+	0.992889i	$0.537982\pi$
$80$	5.50960	0.615992
$81$	−3.68820	−0.409800
$82$	−0.975830	−0.107762
$83$	6.35906	0.697997	0.348999	−	0.937123i	$-0.386522\pi$
$83$	6.35906	0.697997	0.348999	+	0.937123i	$0.386522\pi$
$84$	−6.09538	−0.665060
$85$	3.03374	0.329055
$86$	5.63110	0.607217
$87$	0	0
$88$	−9.57325	−1.02051
$89$	−11.9328	−1.26488	−0.632438	−	0.774611i	$-0.717946\pi$
$89$	−11.9328	−1.26488	−0.632438	+	0.774611i	$0.717946\pi$
$90$	−4.78838	−0.504740
$91$	−4.08563	−0.428291
$92$	−1.50448	−0.156853
$93$	7.38838	0.766139
$94$	−1.47068	−0.151690
$95$	13.1175	1.34583
$96$	13.7346	1.40178
$97$	11.4236	1.15989	0.579944	−	0.814657i	$-0.303075\pi$
$97$	11.4236	1.15989	0.579944	+	0.814657i	$0.303075\pi$
$98$	2.71203	0.273956
$99$	−21.2856	−2.13929
$100$	0.248974	0.0248974
$101$	0.974512	0.0969676	0.0484838	−	0.998824i	$-0.484561\pi$
$101$	0.974512	0.0969676	0.0484838	+	0.998824i	$0.484561\pi$
$102$	1.89499	0.187632
$103$	−7.77717	−0.766308	−0.383154	−	0.923685i	$-0.625162\pi$
$103$	−7.77717	−0.766308	−0.383154	+	0.923685i	$0.625162\pi$
$104$	5.99760	0.588113
$105$	7.72630	0.754009
$106$	2.96682	0.288164
$107$	−5.44933	−0.526806	−0.263403	−	0.964686i	$-0.584845\pi$
$107$	−5.44933	−0.526806	−0.263403	+	0.964686i	$0.584845\pi$
$108$	5.85107	0.563020
$109$	−7.89151	−0.755870	−0.377935	−	0.925832i	$-0.623366\pi$
$109$	−7.89151	−0.755870	−0.377935	+	0.925832i	$0.623366\pi$
$110$	5.64317	0.538056
$111$	15.8861	1.50784
$112$	−3.25519	−0.307586
$113$	17.3009	1.62753	0.813767	−	0.581191i	$-0.197413\pi$
$113$	17.3009	1.62753	0.813767	+	0.581191i	$0.197413\pi$
$114$	8.19368	0.767408
$115$	1.90703	0.177831
$116$	0	0
$117$	13.3353	1.23285
$118$	2.22551	0.204875
$119$	−1.79240	−0.164309
$120$	−11.3420	−1.03538
$121$	14.0854	1.28049
$122$	−2.77891	−0.251590
$123$	−5.13927	−0.463392
$124$	4.77076	0.428427
$125$	−11.3347	−1.01380
$126$	2.82908	0.252034
$127$	−5.51617	−0.489481	−0.244741	−	0.969589i	$-0.578703\pi$
$127$	−5.51617	−0.489481	−0.244741	+	0.969589i	$0.578703\pi$
$128$	11.4249	1.00983
$129$	29.6565	2.61111
$130$	−3.53542	−0.310077
$131$	0.0282924	0.00247192	0.00123596	−	0.999999i	$-0.499607\pi$
$131$	0.0282924	0.00247192	0.00123596	+	0.999999i	$0.499607\pi$
$132$	−23.4466	−2.04076
$133$	−7.75009	−0.672018
$134$	1.20798	0.104354
$135$	−7.41662	−0.638321
$136$	2.63119	0.225623
$137$	−6.15467	−0.525829	−0.262914	−	0.964819i	$-0.584684\pi$
$137$	−6.15467	−0.525829	−0.262914	+	0.964819i	$0.584684\pi$
$138$	1.19120	0.101402
$139$	12.4082	1.05245	0.526223	−	0.850347i	$-0.323608\pi$
$139$	12.4082	1.05245	0.526223	+	0.850347i	$0.323608\pi$
$140$	4.98896	0.421644
$141$	−7.74545	−0.652285
$142$	7.97034	0.668856
$143$	−15.7159	−1.31423
$144$	10.6248	0.885400
$145$	0	0
$146$	1.73646	0.143710
$147$	14.2830	1.17805
$148$	10.2578	0.843188
$149$	−20.8077	−1.70464	−0.852318	−	0.523024i	$-0.824804\pi$
$149$	−20.8077	−1.70464	−0.852318	+	0.523024i	$0.824804\pi$
$150$	−0.197130	−0.0160956
$151$	20.0283	1.62988	0.814941	−	0.579544i	$-0.196769\pi$
$151$	20.0283	1.62988	0.814941	+	0.579544i	$0.196769\pi$
$152$	11.3769	0.922790
$153$	5.85031	0.472970
$154$	−3.33411	−0.268670
$155$	−6.04726	−0.485728
$156$	14.6892	1.17608
$157$	11.7893	0.940890	0.470445	−	0.882429i	$-0.344093\pi$
$157$	11.7893	0.940890	0.470445	+	0.882429i	$0.344093\pi$
$158$	1.08188	0.0860698
$159$	15.6250	1.23914
$160$	−11.2415	−0.888719
$161$	−1.12671	−0.0887974
$162$	1.88561	0.148148
$163$	2.50662	0.196333	0.0981667	−	0.995170i	$-0.468702\pi$
$163$	2.50662	0.196333	0.0981667	+	0.995170i	$0.468702\pi$
$164$	−3.31849	−0.259130
$165$	29.7201	2.31371
$166$	−3.25110	−0.252334
$167$	−2.67090	−0.206681	−0.103340	−	0.994646i	$-0.532953\pi$
$167$	−2.67090	−0.206681	−0.103340	+	0.994646i	$0.532953\pi$
$168$	6.70109	0.517000
$169$	−3.15408	−0.242621
$170$	−1.55102	−0.118957
$171$	25.2960	1.93443
$172$	19.1496	1.46014
$173$	23.5982	1.79414	0.897071	−	0.441887i	$-0.145691\pi$
$173$	23.5982	1.79414	0.897071	+	0.441887i	$0.145691\pi$
$174$	0	0
$175$	0.186458	0.0140949
$176$	−12.5215	−0.943841
$177$	11.7208	0.880990
$178$	6.10072	0.457268
$179$	−20.9584	−1.56651	−0.783253	−	0.621704i	$-0.786441\pi$
$179$	−20.9584	−1.56651	−0.783253	+	0.621704i	$0.786441\pi$
$180$	−16.2838	−1.21372
$181$	9.09389	0.675944	0.337972	−	0.941156i	$-0.390259\pi$
$181$	9.09389	0.675944	0.337972	+	0.941156i	$0.390259\pi$
$182$	2.08880	0.154832
$183$	−14.6353	−1.08187
$184$	1.65398	0.121933
$185$	−13.0025	−0.955961
$186$	−3.77735	−0.276969
$187$	−6.89467	−0.504188
$188$	−5.00133	−0.364760
$189$	4.38190	0.318736
$190$	−6.70639	−0.486533
$191$	−19.2700	−1.39433	−0.697163	−	0.716912i	$-0.745555\pi$
$191$	−19.2700	−1.39433	−0.697163	+	0.716912i	$0.745555\pi$
$192$	6.44107	0.464844
$193$	−5.31806	−0.382802	−0.191401	−	0.981512i	$-0.561303\pi$
$193$	−5.31806	−0.382802	−0.191401	+	0.981512i	$0.561303\pi$
$194$	−5.84036	−0.419313
$195$	−18.6195	−1.33337
$196$	9.22274	0.658767
$197$	−9.97263	−0.710521	−0.355260	−	0.934767i	$-0.615608\pi$
$197$	−9.97263	−0.710521	−0.355260	+	0.934767i	$0.615608\pi$
$198$	10.8824	0.773378
$199$	−22.1902	−1.57302	−0.786510	−	0.617578i	$-0.788114\pi$
$199$	−22.1902	−1.57302	−0.786510	+	0.617578i	$0.788114\pi$
$200$	−0.273715	−0.0193546
$201$	6.36192	0.448736
$202$	−0.498225	−0.0350550
$203$	0	0
$204$	6.44425	0.451188
$205$	4.20641	0.293788
$206$	3.97612	0.277030
$207$	3.67754	0.255607
$208$	7.84464	0.543928
$209$	−29.8117	−2.06212
$210$	−3.95011	−0.272584
$211$	−7.31033	−0.503264	−0.251632	−	0.967823i	$-0.580967\pi$
$211$	−7.31033	−0.503264	−0.251632	+	0.967823i	$0.580967\pi$
$212$	10.0892	0.692931
$213$	41.9763	2.87617
$214$	2.78600	0.190447
$215$	−24.2734	−1.65543
$216$	−6.43251	−0.437677
$217$	3.57285	0.242541
$218$	4.03458	0.273256
$219$	9.14515	0.617972
$220$	19.1906	1.29383
$221$	4.31948	0.290560
$222$	−8.12184	−0.545102
$223$	5.50016	0.368318	0.184159	−	0.982896i	$-0.441044\pi$
$223$	5.50016	0.368318	0.184159	+	0.982896i	$0.441044\pi$
$224$	6.64172	0.443769
$225$	−0.608591	−0.0405727
$226$	−8.84519	−0.588373
$227$	15.7510	1.04543	0.522716	−	0.852507i	$-0.324919\pi$
$227$	15.7510	1.04543	0.522716	+	0.852507i	$0.324919\pi$
$228$	27.8641	1.84535
$229$	−14.8322	−0.980140	−0.490070	−	0.871683i	$-0.663029\pi$
$229$	−14.8322	−0.980140	−0.490070	+	0.871683i	$0.663029\pi$
$230$	−0.974978	−0.0642881
$231$	−17.5593	−1.15532
$232$	0	0
$233$	−15.8867	−1.04078	−0.520388	−	0.853930i	$-0.674213\pi$
$233$	−15.8867	−1.04078	−0.520388	+	0.853930i	$0.674213\pi$
$234$	−6.81777	−0.445691
$235$	6.33952	0.413545
$236$	7.56827	0.492652
$237$	5.69779	0.370111
$238$	0.916373	0.0593997
$239$	9.39994	0.608032	0.304016	−	0.952667i	$-0.401672\pi$
$239$	9.39994	0.608032	0.304016	+	0.952667i	$0.401672\pi$
$240$	−14.8349	−0.957590
$241$	−10.4403	−0.672518	−0.336259	−	0.941769i	$-0.609162\pi$
$241$	−10.4403	−0.672518	−0.336259	+	0.941769i	$0.609162\pi$
$242$	−7.20124	−0.462913
$243$	20.0268	1.28472
$244$	−9.45018	−0.604986
$245$	−11.6904	−0.746875
$246$	2.62748	0.167522
$247$	18.6769	1.18838
$248$	−5.24485	−0.333048
$249$	−17.1221	−1.08507
$250$	5.79491	0.366502
$251$	−14.7822	−0.933042	−0.466521	−	0.884510i	$-0.654493\pi$
$251$	−14.7822	−0.933042	−0.466521	+	0.884510i	$0.654493\pi$
$252$	9.62080	0.606054
$253$	−4.33403	−0.272478
$254$	2.82017	0.176953
$255$	−8.16852	−0.511533
$256$	−1.05668	−0.0660424
$257$	1.73053	0.107948	0.0539739	−	0.998542i	$-0.482811\pi$
$257$	1.73053	0.107948	0.0539739	+	0.998542i	$0.482811\pi$
$258$	−15.1621	−0.943949
$259$	7.68214	0.477345
$260$	−12.0228	−0.745625
$261$	0	0
$262$	−0.0144647	−0.000893630 0
$263$	−13.5311	−0.834362	−0.417181	−	0.908824i	$-0.636982\pi$
$263$	−13.5311	−0.834362	−0.417181	+	0.908824i	$0.636982\pi$
$264$	25.7765	1.58644
$265$	−12.7888	−0.785608
$266$	3.96228	0.242943
$267$	32.1298	1.96631
$268$	4.10797	0.250934
$269$	−29.8893	−1.82239	−0.911193	−	0.411980i	$-0.864837\pi$
$269$	−29.8893	−1.82239	−0.911193	+	0.411980i	$0.864837\pi$
$270$	3.79179	0.230761
$271$	−9.36397	−0.568821	−0.284410	−	0.958703i	$-0.591798\pi$
$271$	−9.36397	−0.568821	−0.284410	+	0.958703i	$0.591798\pi$
$272$	3.44150	0.208672
$273$	11.0008	0.665799
$274$	3.14661	0.190093
$275$	0.717232	0.0432507
$276$	4.05090	0.243835
$277$	22.4222	1.34722	0.673610	−	0.739087i	$-0.264743\pi$
$277$	22.4222	1.34722	0.673610	+	0.739087i	$0.264743\pi$
$278$	−6.34374	−0.380472
$279$	−11.6616	−0.698164
$280$	−5.48473	−0.327775
$281$	−8.71205	−0.519717	−0.259859	−	0.965647i	$-0.583676\pi$
$281$	−8.71205	−0.519717	−0.259859	+	0.965647i	$0.583676\pi$
$282$	3.95990	0.235809
$283$	−14.4581	−0.859444	−0.429722	−	0.902961i	$-0.641388\pi$
$283$	−14.4581	−0.859444	−0.429722	+	0.902961i	$0.641388\pi$
$284$	27.1046	1.60836
$285$	−35.3196	−2.09215
$286$	8.03483	0.475110
$287$	−2.48523	−0.146699
$288$	−21.6783	−1.27741
$289$	−15.1050	−0.888530
$290$	0	0
$291$	−30.7586	−1.80310
$292$	5.90513	0.345572
$293$	−32.7560	−1.91363	−0.956813	−	0.290706i	$-0.906110\pi$
$293$	−32.7560	−1.91363	−0.956813	+	0.290706i	$0.906110\pi$
$294$	−7.30229	−0.425878
$295$	−9.59329	−0.558543
$296$	−11.2772	−0.655472
$297$	16.8555	0.978055
$298$	10.6381	0.616247
$299$	2.71525	0.157027
$300$	−0.670376	−0.0387042
$301$	14.3412	0.826615
$302$	−10.2396	−0.589222
$303$	−2.62393	−0.150741
$304$	14.8806	0.853461
$305$	11.9787	0.685900
$306$	−2.99101	−0.170984
$307$	28.4921	1.62613	0.813065	−	0.582173i	$-0.197798\pi$
$307$	28.4921	1.62613	0.813065	+	0.582173i	$0.197798\pi$
$308$	−11.3382	−0.646056
$309$	20.9405	1.19126
$310$	3.09170	0.175597
$311$	21.8076	1.23660	0.618298	−	0.785944i	$-0.287823\pi$
$311$	21.8076	1.23660	0.618298	+	0.785944i	$0.287823\pi$
$312$	−16.1489	−0.914251
$313$	−23.9276	−1.35247	−0.676234	−	0.736687i	$-0.736389\pi$
$313$	−23.9276	−1.35247	−0.676234	+	0.736687i	$0.736389\pi$
$314$	−6.02735	−0.340143
$315$	−12.1950	−0.687111
$316$	3.67913	0.206967
$317$	−9.35254	−0.525291	−0.262646	−	0.964892i	$-0.584595\pi$
$317$	−9.35254	−0.525291	−0.262646	+	0.964892i	$0.584595\pi$
$318$	−7.98835	−0.447964
$319$	0	0
$320$	−5.27191	−0.294709
$321$	14.6726	0.818946
$322$	0.576038	0.0321013
$323$	8.19368	0.455908
$324$	6.41236	0.356242
$325$	−0.449343	−0.0249250
$326$	−1.28152	−0.0709770
$327$	21.2484	1.17504
$328$	3.64825	0.201441
$329$	−3.74552	−0.206497
$330$	−15.1946	−0.836434
$331$	10.2474	0.563247	0.281623	−	0.959525i	$-0.409127\pi$
$331$	10.2474	0.563247	0.281623	+	0.959525i	$0.409127\pi$
$332$	−11.0560	−0.606775
$333$	−25.0742	−1.37406
$334$	1.36551	0.0747176
$335$	−5.20713	−0.284496
$336$	8.76478	0.478158
$337$	15.9436	0.868502	0.434251	−	0.900792i	$-0.357013\pi$
$337$	15.9436	0.868502	0.434251	+	0.900792i	$0.357013\pi$
$338$	1.61254	0.0877105
$339$	−46.5838	−2.53008
$340$	−5.27451	−0.286051
$341$	13.7434	0.744247
$342$	−12.9327	−0.699321
$343$	16.0214	0.865074
$344$	−21.0525	−1.13508
$345$	−5.13478	−0.276447
$346$	−12.0647	−0.648604
$347$	36.7925	1.97513	0.987563	−	0.157224i	$-0.0502544\pi$
$347$	36.7925	1.97513	0.987563	+	0.157224i	$0.0502544\pi$
$348$	0	0
$349$	32.4894	1.73912	0.869558	−	0.493831i	$-0.164404\pi$
$349$	32.4894	1.73912	0.869558	+	0.493831i	$0.164404\pi$
$350$	−0.0953276	−0.00509547
$351$	−10.5599	−0.563645
$352$	25.5482	1.36172
$353$	−12.0171	−0.639604	−0.319802	−	0.947484i	$-0.603616\pi$
$353$	−12.0171	−0.639604	−0.319802	+	0.947484i	$0.603616\pi$
$354$	−5.99233	−0.318489
$355$	−34.3569	−1.82347
$356$	20.7466	1.09957
$357$	4.82614	0.255426
$358$	10.7151	0.566311
$359$	−3.90861	−0.206288	−0.103144	−	0.994666i	$-0.532890\pi$
$359$	−3.90861	−0.206288	−0.103144	+	0.994666i	$0.532890\pi$
$360$	17.9019	0.943515
$361$	16.4284	0.864652
$362$	−4.64930	−0.244362
$363$	−37.9258	−1.99059
$364$	7.10336	0.372317
$365$	−7.48515	−0.391791
$366$	7.48237	0.391110
$367$	12.7874	0.667495	0.333747	−	0.942663i	$-0.391687\pi$
$367$	12.7874	0.667495	0.333747	+	0.942663i	$0.391687\pi$
$368$	2.16335	0.112772
$369$	8.11170	0.422278
$370$	6.64759	0.345592
$371$	7.55588	0.392282
$372$	−12.8456	−0.666011
$373$	24.9865	1.29375	0.646876	−	0.762596i	$-0.276075\pi$
$373$	24.9865	1.29375	0.646876	+	0.762596i	$0.276075\pi$
$374$	3.52494	0.182270
$375$	30.5192	1.57601
$376$	5.49833	0.283555
$377$	0	0
$378$	−2.24027	−0.115227
$379$	13.0352	0.669574	0.334787	−	0.942294i	$-0.391336\pi$
$379$	13.0352	0.669574	0.334787	+	0.942294i	$0.391336\pi$
$380$	−22.8063	−1.16994
$381$	14.8526	0.760923
$382$	9.85188	0.504066
$383$	24.0350	1.22813	0.614066	−	0.789254i	$-0.289533\pi$
$383$	24.0350	1.22813	0.614066	+	0.789254i	$0.289533\pi$
$384$	−30.7621	−1.56982
$385$	14.3720	0.732464
$386$	2.71889	0.138388
$387$	−46.8092	−2.37945
$388$	−19.8612	−1.00830
$389$	−17.6717	−0.895991	−0.447995	−	0.894036i	$-0.647862\pi$
$389$	−17.6717	−0.895991	−0.447995	+	0.894036i	$0.647862\pi$
$390$	9.51933	0.482030
$391$	1.19120	0.0602416
$392$	−10.1392	−0.512108
$393$	−0.0761791	−0.00384272
$394$	5.09856	0.256862
$395$	−4.66355	−0.234648
$396$	37.0076	1.85970
$397$	30.2526	1.51833	0.759167	−	0.650896i	$-0.225607\pi$
$397$	30.2526	1.51833	0.759167	+	0.650896i	$0.225607\pi$
$398$	11.3448	0.568666
$399$	20.8676	1.04469
$400$	−0.358009	−0.0179005
$401$	−12.3573	−0.617092	−0.308546	−	0.951209i	$-0.599842\pi$
$401$	−12.3573	−0.617092	−0.308546	+	0.951209i	$0.599842\pi$
$402$	−3.25257	−0.162223
$403$	−8.61018	−0.428903
$404$	−1.69430	−0.0842948
$405$	−8.12810	−0.403889
$406$	0	0
$407$	29.5503	1.46475
$408$	−7.08464	−0.350742
$409$	−6.10698	−0.301971	−0.150985	−	0.988536i	$-0.548245\pi$
$409$	−6.10698	−0.301971	−0.150985	+	0.988536i	$0.548245\pi$
$410$	−2.15055	−0.106208
$411$	16.5718	0.817427
$412$	13.5215	0.666158
$413$	5.66792	0.278900
$414$	−1.88016	−0.0924050
$415$	14.0142	0.687929
$416$	−16.0058	−0.784749
$417$	−33.4097	−1.63608
$418$	15.2414	0.745480
$419$	11.6075	0.567062	0.283531	−	0.958963i	$-0.408494\pi$
$419$	11.6075	0.567062	0.283531	+	0.958963i	$0.408494\pi$
$420$	−13.4331	−0.655467
$421$	−20.2867	−0.988715	−0.494357	−	0.869259i	$-0.664597\pi$
$421$	−20.2867	−0.988715	−0.494357	+	0.869259i	$0.664597\pi$
$422$	3.73745	0.181936
$423$	12.2252	0.594412
$424$	−11.0918	−0.538667
$425$	−0.197130	−0.00956221
$426$	−21.4606	−1.03977
$427$	−7.07729	−0.342494
$428$	9.47429	0.457957
$429$	42.3159	2.04303
$430$	12.4099	0.598459
$431$	16.9837	0.818077	0.409038	−	0.912517i	$-0.365864\pi$
$431$	16.9837	0.818077	0.409038	+	0.912517i	$0.365864\pi$
$432$	−8.41349	−0.404794
$433$	−15.9353	−0.765800	−0.382900	−	0.923790i	$-0.625075\pi$
$433$	−15.9353	−0.765800	−0.382900	+	0.923790i	$0.625075\pi$
$434$	−1.82664	−0.0876815
$435$	0	0
$436$	13.7203	0.657084
$437$	5.15060	0.246386
$438$	−4.67551	−0.223404
$439$	−5.40352	−0.257896	−0.128948	−	0.991651i	$-0.541160\pi$
$439$	−5.40352	−0.257896	−0.128948	+	0.991651i	$0.541160\pi$
$440$	−21.0977	−1.00579
$441$	−22.5440	−1.07353
$442$	−2.20836	−0.105041
$443$	−19.0514	−0.905159	−0.452579	−	0.891724i	$-0.649496\pi$
$443$	−19.0514	−0.905159	−0.452579	+	0.891724i	$0.649496\pi$
$444$	−27.6198	−1.31078
$445$	−26.2977	−1.24663
$446$	−2.81199	−0.133151
$447$	56.0260	2.64994
$448$	3.11476	0.147158
$449$	−17.6874	−0.834721	−0.417360	−	0.908741i	$-0.637045\pi$
$449$	−17.6874	−0.834721	−0.417360	+	0.908741i	$0.637045\pi$
$450$	0.311145	0.0146675
$451$	−9.55975	−0.450151
$452$	−30.0797	−1.41483
$453$	−53.9274	−2.53373
$454$	−8.05279	−0.377936
$455$	−9.00398	−0.422113
$456$	−30.6330	−1.43452
$457$	−15.0980	−0.706255	−0.353127	−	0.935575i	$-0.614882\pi$
$457$	−15.0980	−0.706255	−0.353127	+	0.935575i	$0.614882\pi$
$458$	7.58305	0.354333
$459$	−4.63270	−0.216236
$460$	−3.31559	−0.154590
$461$	22.3018	1.03870	0.519349	−	0.854562i	$-0.326175\pi$
$461$	22.3018	1.03870	0.519349	+	0.854562i	$0.326175\pi$
$462$	8.97728	0.417661
$463$	−26.7391	−1.24267	−0.621335	−	0.783545i	$-0.713409\pi$
$463$	−26.7391	−1.24267	−0.621335	+	0.783545i	$0.713409\pi$
$464$	0	0
$465$	16.2826	0.755088
$466$	8.12219	0.376253
$467$	−11.5613	−0.534991	−0.267496	−	0.963559i	$-0.586196\pi$
$467$	−11.5613	−0.534991	−0.267496	+	0.963559i	$0.586196\pi$
$468$	−23.1851	−1.07173
$469$	3.07648	0.142059
$470$	−3.24112	−0.149501
$471$	−31.7434	−1.46266
$472$	−8.32035	−0.382975
$473$	55.1653	2.53650
$474$	−2.91303	−0.133800
$475$	−0.852364	−0.0391091
$476$	3.11630	0.142835
$477$	−24.6621	−1.12920
$478$	−4.80577	−0.219811
$479$	−24.3280	−1.11158	−0.555788	−	0.831324i	$-0.687583\pi$
$479$	−24.3280	−1.11158	−0.555788	+	0.831324i	$0.687583\pi$
$480$	30.2684	1.38156
$481$	−18.5131	−0.844125
$482$	5.33766	0.243124
$483$	3.03374	0.138040
$484$	−24.4891	−1.11314
$485$	25.1754	1.14316
$486$	−10.2388	−0.464441
$487$	1.28689	0.0583144	0.0291572	−	0.999575i	$-0.490718\pi$
$487$	1.28689	0.0583144	0.0291572	+	0.999575i	$0.490718\pi$
$488$	10.3893	0.470300
$489$	−6.74922	−0.305210
$490$	5.97680	0.270004
$491$	−32.6584	−1.47385	−0.736927	−	0.675972i	$-0.763724\pi$
$491$	−32.6584	−1.47385	−0.736927	+	0.675972i	$0.763724\pi$
$492$	8.93522	0.402831
$493$	0	0
$494$	−9.54865	−0.429614
$495$	−46.9096	−2.10843
$496$	−6.86007	−0.308026
$497$	20.2988	0.910525
$498$	8.75378	0.392266
$499$	−10.4832	−0.469291	−0.234646	−	0.972081i	$-0.575393\pi$
$499$	−10.4832	−0.469291	−0.234646	+	0.972081i	$0.575393\pi$
$500$	19.7066	0.881308
$501$	7.19156	0.321295
$502$	7.55746	0.337306
$503$	3.79036	0.169004	0.0845019	−	0.996423i	$-0.473070\pi$
$503$	3.79036	0.169004	0.0845019	+	0.996423i	$0.473070\pi$
$504$	−10.5768	−0.471130
$505$	2.14764	0.0955689
$506$	2.21580	0.0985043
$507$	8.49253	0.377167
$508$	9.59052	0.425510
$509$	−8.01829	−0.355404	−0.177702	−	0.984084i	$-0.556866\pi$
$509$	−8.01829	−0.355404	−0.177702	+	0.984084i	$0.556866\pi$
$510$	4.17620	0.184925
$511$	4.42239	0.195635
$512$	−22.3095	−0.985951
$513$	−20.0312	−0.884399
$514$	−0.884745	−0.0390244
$515$	−17.1394	−0.755254
$516$	−51.5614	−2.26986
$517$	−14.4076	−0.633646
$518$	−3.92754	−0.172566
$519$	−63.5397	−2.78908
$520$	13.2176	0.579630
$521$	−6.39024	−0.279962	−0.139981	−	0.990154i	$-0.544704\pi$
$521$	−6.39024	−0.279962	−0.139981	+	0.990154i	$0.544704\pi$
$522$	0	0
$523$	−16.3261	−0.713891	−0.356946	−	0.934125i	$-0.616182\pi$
$523$	−16.3261	−0.713891	−0.356946	+	0.934125i	$0.616182\pi$
$524$	−0.0491897	−0.00214886
$525$	−0.502049	−0.0219112
$526$	6.91783	0.301632
$527$	−3.77735	−0.164544
$528$	33.7148	1.46725
$529$	−22.2512	−0.967444
$530$	6.53833	0.284007
$531$	−18.4999	−0.802825
$532$	13.4744	0.584191
$533$	5.98914	0.259418
$534$	−16.4265	−0.710846
$535$	−12.0093	−0.519207
$536$	−4.51619	−0.195070
$537$	56.4318	2.43521
$538$	15.2811	0.658815
$539$	26.5684	1.14438
$540$	12.8947	0.554898
$541$	21.9611	0.944182	0.472091	−	0.881550i	$-0.343499\pi$
$541$	21.9611	0.944182	0.472091	+	0.881550i	$0.343499\pi$
$542$	4.78738	0.205636
$543$	−24.4858	−1.05079
$544$	−7.02187	−0.301060
$545$	−17.3914	−0.744967
$546$	−5.62423	−0.240695
$547$	4.10519	0.175525	0.0877626	−	0.996141i	$-0.472028\pi$
$547$	4.10519	0.175525	0.0877626	+	0.996141i	$0.472028\pi$
$548$	10.7006	0.457108
$549$	23.1000	0.985884
$550$	−0.366689	−0.0156357
$551$	0	0
$552$	−4.45344	−0.189551
$553$	2.75532	0.117168
$554$	−11.4635	−0.487037
$555$	35.0099	1.48609
$556$	−21.5730	−0.914900
$557$	−24.8912	−1.05467	−0.527337	−	0.849656i	$-0.676810\pi$
$557$	−24.8912	−1.05467	−0.527337	+	0.849656i	$0.676810\pi$
$558$	5.96208	0.252395
$559$	−34.5608	−1.46177
$560$	−7.17383	−0.303150
$561$	18.5643	0.783786
$562$	4.45408	0.187884
$563$	−22.6338	−0.953902	−0.476951	−	0.878930i	$-0.658258\pi$
$563$	−22.6338	−0.953902	−0.476951	+	0.878930i	$0.658258\pi$
$564$	13.4664	0.567037
$565$	38.1280	1.60406
$566$	7.39178	0.310700
$567$	4.80226	0.201676
$568$	−29.7981	−1.25030
$569$	−10.3978	−0.435897	−0.217948	−	0.975960i	$-0.569936\pi$
$569$	−10.3978	−0.435897	−0.217948	+	0.975960i	$0.569936\pi$
$570$	18.0573	0.756339
$571$	35.6768	1.49303	0.746514	−	0.665370i	$-0.231726\pi$
$571$	35.6768	1.49303	0.746514	+	0.665370i	$0.231726\pi$
$572$	27.3239	1.14247
$573$	51.8856	2.16755
$574$	1.27059	0.0530334
$575$	−0.123917	−0.00516770
$576$	−10.1664	−0.423602
$577$	−1.60879	−0.0669750	−0.0334875	−	0.999439i	$-0.510661\pi$
$577$	−1.60879	−0.0669750	−0.0334875	+	0.999439i	$0.510661\pi$
$578$	7.72252	0.321215
$579$	14.3192	0.595085
$580$	0	0
$581$	−8.27988	−0.343507
$582$	15.7255	0.651843
$583$	29.0646	1.20373
$584$	−6.49194	−0.268639
$585$	29.3886	1.21507
$586$	16.7467	0.691799
$587$	24.7543	1.02172	0.510859	−	0.859664i	$-0.329327\pi$
$587$	24.7543	1.02172	0.510859	+	0.859664i	$0.329327\pi$
$588$	−24.8328	−1.02409
$589$	−16.3328	−0.672980
$590$	4.90462	0.201920
$591$	26.8519	1.10454
$592$	−14.7501	−0.606227
$593$	−10.2075	−0.419171	−0.209586	−	0.977790i	$-0.567211\pi$
$593$	−10.2075	−0.419171	−0.209586	+	0.977790i	$0.567211\pi$
$594$	−8.61747	−0.353579
$595$	−3.95011	−0.161939
$596$	36.1767	1.48185
$597$	59.7483	2.44534
$598$	−1.38819	−0.0567672
$599$	−18.7742	−0.767093	−0.383546	−	0.923522i	$-0.625297\pi$
$599$	−18.7742	−0.767093	−0.383546	+	0.923522i	$0.625297\pi$
$600$	0.736994	0.0300876
$601$	40.8108	1.66471	0.832355	−	0.554243i	$-0.186992\pi$
$601$	40.8108	1.66471	0.832355	+	0.554243i	$0.186992\pi$
$602$	−7.33204	−0.298831
$603$	−10.0415	−0.408922
$604$	−34.8216	−1.41687
$605$	31.0416	1.26202
$606$	1.34150	0.0544947
$607$	−11.7038	−0.475043	−0.237522	−	0.971382i	$-0.576335\pi$
$607$	−11.7038	−0.475043	−0.237522	+	0.971382i	$0.576335\pi$
$608$	−30.3616	−1.23133
$609$	0	0
$610$	−6.12419	−0.247961
$611$	9.02630	0.365165
$612$	−10.1715	−0.411157
$613$	13.8696	0.560187	0.280094	−	0.959973i	$-0.409634\pi$
$613$	13.8696	0.560187	0.280094	+	0.959973i	$0.409634\pi$
$614$	−14.5667	−0.587866
$615$	−11.3260	−0.456708
$616$	12.4650	0.502227
$617$	25.2302	1.01573	0.507866	−	0.861436i	$-0.330435\pi$
$617$	25.2302	1.01573	0.507866	+	0.861436i	$0.330435\pi$
$618$	−10.7059	−0.430656
$619$	28.9034	1.16173	0.580863	−	0.814001i	$-0.302715\pi$
$619$	28.9034	1.16173	0.580863	+	0.814001i	$0.302715\pi$
$620$	10.5139	0.422248
$621$	−2.91215	−0.116860
$622$	−11.1493	−0.447045
$623$	15.5373	0.622487
$624$	−21.1222	−0.845563
$625$	−24.2635	−0.970539
$626$	12.2331	0.488934
$627$	80.2696	3.20566
$628$	−20.4971	−0.817924
$629$	−8.12184	−0.323839
$630$	6.23477	0.248399
$631$	15.6970	0.624889	0.312445	−	0.949936i	$-0.398852\pi$
$631$	15.6970	0.624889	0.312445	+	0.949936i	$0.398852\pi$
$632$	−4.04474	−0.160891
$633$	19.6835	0.782349
$634$	4.78154	0.189899
$635$	−12.1566	−0.482421
$636$	−27.1658	−1.07720
$637$	−16.6450	−0.659499
$638$	0	0
$639$	−66.2544	−2.62098
$640$	25.1783	0.995260
$641$	32.5456	1.28547	0.642737	−	0.766087i	$-0.277799\pi$
$641$	32.5456	1.28547	0.642737	+	0.766087i	$0.277799\pi$
$642$	−7.50146	−0.296059
$643$	24.5655	0.968768	0.484384	−	0.874856i	$-0.339044\pi$
$643$	24.5655	0.968768	0.484384	+	0.874856i	$0.339044\pi$
$644$	1.95892	0.0771923
$645$	65.3575	2.57345
$646$	−4.18906	−0.164816
$647$	13.0218	0.511939	0.255970	−	0.966685i	$-0.417605\pi$
$647$	13.0218	0.511939	0.255970	+	0.966685i	$0.417605\pi$
$648$	−7.04958	−0.276934
$649$	21.8023	0.855816
$650$	0.229729	0.00901071
$651$	−9.62012	−0.377042
$652$	−4.35805	−0.170674
$653$	29.9591	1.17239	0.586195	−	0.810170i	$-0.300625\pi$
$653$	29.9591	1.17239	0.586195	+	0.810170i	$0.300625\pi$
$654$	−10.8633	−0.424790
$655$	0.0623513	0.00243627
$656$	4.77178	0.186307
$657$	−14.4345	−0.563143
$658$	1.91492	0.0746514
$659$	−14.2014	−0.553206	−0.276603	−	0.960984i	$-0.589209\pi$
$659$	−14.2014	−0.553206	−0.276603	+	0.960984i	$0.589209\pi$
$660$	−51.6719	−2.01133
$661$	40.3814	1.57066	0.785328	−	0.619080i	$-0.212494\pi$
$661$	40.3814	1.57066	0.785328	+	0.619080i	$0.212494\pi$
$662$	−5.23903	−0.203621
$663$	−11.6305	−0.451689
$664$	12.1546	0.471691
$665$	−17.0798	−0.662325
$666$	12.8193	0.496739
$667$	0	0
$668$	4.64368	0.179669
$669$	−14.8095	−0.572568
$670$	2.66217	0.102849
$671$	−27.2236	−1.05096
$672$	−17.8832	−0.689860
$673$	−40.7941	−1.57250	−0.786249	−	0.617910i	$-0.787980\pi$
$673$	−40.7941	−1.57250	−0.786249	+	0.617910i	$0.787980\pi$
$674$	−8.15124	−0.313974
$675$	0.481926	0.0185493
$676$	5.48373	0.210913
$677$	−20.5887	−0.791288	−0.395644	−	0.918404i	$-0.629479\pi$
$677$	−20.5887	−0.791288	−0.395644	+	0.918404i	$0.629479\pi$
$678$	23.8162	0.914656
$679$	−14.8742	−0.570818
$680$	5.79866	0.222368
$681$	−42.4105	−1.62518
$682$	−7.02639	−0.269054
$683$	12.6374	0.483555	0.241778	−	0.970332i	$-0.422270\pi$
$683$	12.6374	0.483555	0.241778	+	0.970332i	$0.422270\pi$
$684$	−43.9801	−1.68162
$685$	−13.5637	−0.518244
$686$	−8.19102	−0.312735
$687$	39.9366	1.52368
$688$	−27.5360	−1.04980
$689$	−18.2088	−0.693701
$690$	2.62519	0.0999391
$691$	−22.1174	−0.841385	−0.420692	−	0.907203i	$-0.638213\pi$
$691$	−22.1174	−0.841385	−0.420692	+	0.907203i	$0.638213\pi$
$692$	−41.0283	−1.55966
$693$	27.7152	1.05281
$694$	−18.8104	−0.714032
$695$	27.3453	1.03726
$696$	0	0
$697$	2.62748	0.0995229
$698$	−16.6104	−0.628712
$699$	42.7760	1.61794
$700$	−0.324179	−0.0122528
$701$	2.18774	0.0826296	0.0413148	−	0.999146i	$-0.486845\pi$
$701$	2.18774	0.0826296	0.0413148	+	0.999146i	$0.486845\pi$
$702$	5.39880	0.203765
$703$	−35.1178	−1.32449
$704$	11.9813	0.451562
$705$	−17.0695	−0.642876
$706$	6.14380	0.231225
$707$	−1.26887	−0.0477209
$708$	−20.3780	−0.765852
$709$	29.7979	1.11908	0.559541	−	0.828803i	$-0.310977\pi$
$709$	29.7979	1.11908	0.559541	+	0.828803i	$0.310977\pi$
$710$	17.5652	0.659209
$711$	−8.99326	−0.337274
$712$	−22.8083	−0.854775
$713$	−2.37446	−0.0889244
$714$	−2.46739	−0.0923397
$715$	−34.6349	−1.29527
$716$	36.4387	1.36178
$717$	−25.3099	−0.945215
$718$	1.99830	0.0745758
$719$	8.13140	0.303250	0.151625	−	0.988438i	$-0.451549\pi$
$719$	8.13140	0.303250	0.151625	+	0.988438i	$0.451549\pi$
$720$	23.4151	0.872629
$721$	10.1264	0.377125
$722$	−8.39910	−0.312582
$723$	28.1111	1.04546
$724$	−15.8108	−0.587604
$725$	0	0
$726$	19.3898	0.719621
$727$	−10.2040	−0.378447	−0.189223	−	0.981934i	$-0.560597\pi$
$727$	−10.2040	−0.378447	−0.189223	+	0.981934i	$0.560597\pi$
$728$	−7.80924	−0.289430
$729$	−42.8586	−1.58736
$730$	3.82683	0.141637
$731$	−15.1621	−0.560790
$732$	25.4452	0.940480
$733$	24.6598	0.910829	0.455415	−	0.890279i	$-0.349491\pi$
$733$	24.6598	0.910829	0.455415	+	0.890279i	$0.349491\pi$
$734$	−6.53761	−0.241307
$735$	31.4772	1.16105
$736$	−4.41399	−0.162702
$737$	11.8341	0.435913
$738$	−4.14715	−0.152659
$739$	4.17165	0.153457	0.0767283	−	0.997052i	$-0.475553\pi$
$739$	4.17165	0.153457	0.0767283	+	0.997052i	$0.475553\pi$
$740$	22.6063	0.831026
$741$	−50.2886	−1.84740
$742$	−3.86299	−0.141815
$743$	2.79854	0.102668	0.0513342	−	0.998682i	$-0.483653\pi$
$743$	2.79854	0.102668	0.0513342	+	0.998682i	$0.483653\pi$
$744$	14.1221	0.517740
$745$	−45.8564	−1.68005
$746$	−12.7745	−0.467707
$747$	27.0252	0.988800
$748$	11.9872	0.438295
$749$	7.09535	0.259259
$750$	−15.6031	−0.569746
$751$	14.7008	0.536441	0.268220	−	0.963358i	$-0.413564\pi$
$751$	14.7008	0.536441	0.268220	+	0.963358i	$0.413564\pi$
$752$	7.19161	0.262251
$753$	39.8019	1.45046
$754$	0	0
$755$	44.1387	1.60637
$756$	−7.61845	−0.277080
$757$	−22.9360	−0.833623	−0.416811	−	0.908993i	$-0.636852\pi$
$757$	−22.9360	−0.833623	−0.416811	+	0.908993i	$0.636852\pi$
$758$	−6.66432	−0.242059
$759$	11.6696	0.423581
$760$	25.0726	0.909480
$761$	−12.6222	−0.457553	−0.228777	−	0.973479i	$-0.573473\pi$
$761$	−12.6222	−0.457553	−0.228777	+	0.973479i	$0.573473\pi$
$762$	−7.59349	−0.275083
$763$	10.2752	0.371988
$764$	33.5031	1.21210
$765$	12.8930	0.466148
$766$	−12.2880	−0.443985
$767$	−13.6591	−0.493200
$768$	2.84517	0.102666
$769$	−3.52741	−0.127202	−0.0636009	−	0.997975i	$-0.520258\pi$
$769$	−3.52741	−0.127202	−0.0636009	+	0.997975i	$0.520258\pi$
$770$	−7.34776	−0.264795
$771$	−4.65956	−0.167810
$772$	9.24607	0.332773
$773$	26.2076	0.942623	0.471311	−	0.881967i	$-0.343781\pi$
$773$	26.2076	0.942623	0.471311	+	0.881967i	$0.343781\pi$
$774$	23.9315	0.860199
$775$	0.392946	0.0141150
$776$	21.8349	0.783826
$777$	−20.6846	−0.742057
$778$	9.03476	0.323912
$779$	11.3609	0.407046
$780$	32.3722	1.15911
$781$	78.0817	2.79398
$782$	−0.609008	−0.0217781
$783$	0	0
$784$	−13.2617	−0.473634
$785$	25.9815	0.927318
$786$	0.0389470	0.00138919
$787$	−18.0121	−0.642061	−0.321031	−	0.947069i	$-0.604029\pi$
$787$	−18.0121	−0.642061	−0.321031	+	0.947069i	$0.604029\pi$
$788$	17.3386	0.617662
$789$	36.4332	1.29706
$790$	2.38426	0.0848283
$791$	−22.5269	−0.800963
$792$	−40.6851	−1.44568
$793$	17.0555	0.605658
$794$	−15.4668	−0.548896
$795$	34.4345	1.22127
$796$	38.5802	1.36744
$797$	34.9738	1.23884	0.619419	−	0.785061i	$-0.287368\pi$
$797$	34.9738	1.23884	0.619419	+	0.785061i	$0.287368\pi$
$798$	−10.6687	−0.377667
$799$	3.95990	0.140091
$800$	0.730464	0.0258258
$801$	−50.7130	−1.79185
$802$	6.31772	0.223086
$803$	17.0112	0.600314
$804$	−11.0610	−0.390090
$805$	−2.48306	−0.0875165
$806$	4.40200	0.155054
$807$	80.4788	2.83299
$808$	1.86267	0.0655286
$809$	38.2616	1.34521	0.672603	−	0.740003i	$-0.265176\pi$
$809$	38.2616	1.34521	0.672603	+	0.740003i	$0.265176\pi$
$810$	4.15554	0.146011
$811$	31.7116	1.11354	0.556772	−	0.830665i	$-0.312040\pi$
$811$	31.7116	1.11354	0.556772	+	0.830665i	$0.312040\pi$
$812$	0	0
$813$	25.2130	0.884260
$814$	−15.1077	−0.529526
$815$	5.52412	0.193502
$816$	−9.26645	−0.324390
$817$	−65.5588	−2.29361
$818$	3.12223	0.109166
$819$	−17.3634	−0.606727
$820$	−7.31333	−0.255393
$821$	−21.4880	−0.749938	−0.374969	−	0.927037i	$-0.622347\pi$
$821$	−21.4880	−0.749938	−0.374969	+	0.927037i	$0.622347\pi$
$822$	−8.47243	−0.295510
$823$	−8.90285	−0.310334	−0.155167	−	0.987888i	$-0.549592\pi$
$823$	−8.90285	−0.310334	−0.155167	+	0.987888i	$0.549592\pi$
$824$	−14.8652	−0.517854
$825$	−1.93119	−0.0672354
$826$	−2.89776	−0.100826
$827$	−27.4341	−0.953976	−0.476988	−	0.878910i	$-0.658271\pi$
$827$	−27.4341	−0.953976	−0.476988	+	0.878910i	$0.658271\pi$
$828$	−6.39384	−0.222201
$829$	−40.4211	−1.40388	−0.701942	−	0.712234i	$-0.747683\pi$
$829$	−40.4211	−1.40388	−0.701942	+	0.712234i	$0.747683\pi$
$830$	−7.16483	−0.248695
$831$	−60.3731	−2.09432
$832$	−7.50622	−0.260231
$833$	−7.30229	−0.253009
$834$	17.0809	0.591463
$835$	−5.88617	−0.203699
$836$	51.8311	1.79262
$837$	9.23453	0.319192
$838$	−5.93438	−0.205000
$839$	8.10537	0.279829	0.139914	−	0.990164i	$-0.455317\pi$
$839$	8.10537	0.279829	0.139914	+	0.990164i	$0.455317\pi$
$840$	14.7680	0.509543
$841$	0	0
$842$	10.3717	0.357432
$843$	23.4577	0.807926
$844$	12.7099	0.437492
$845$	−6.95100	−0.239122
$846$	−6.25022	−0.214887
$847$	−18.3400	−0.630171
$848$	−14.5077	−0.498197
$849$	38.9292	1.33605
$850$	0.100784	0.00345685
$851$	−5.10544	−0.175012
$852$	−72.9807	−2.50028
$853$	−12.7043	−0.434988	−0.217494	−	0.976062i	$-0.569788\pi$
$853$	−12.7043	−0.434988	−0.217494	+	0.976062i	$0.569788\pi$
$854$	3.61830	0.123816
$855$	55.7477	1.90653
$856$	−10.4158	−0.356004
$857$	−46.2188	−1.57881	−0.789403	−	0.613876i	$-0.789610\pi$
$857$	−46.2188	−1.57881	−0.789403	+	0.613876i	$0.789610\pi$
$858$	−21.6343	−0.738581
$859$	−6.05228	−0.206501	−0.103251	−	0.994655i	$-0.532924\pi$
$859$	−6.05228	−0.206501	−0.103251	+	0.994655i	$0.532924\pi$
$860$	42.2021	1.43908
$861$	6.69164	0.228050
$862$	−8.68302	−0.295745
$863$	−13.1316	−0.447004	−0.223502	−	0.974704i	$-0.571749\pi$
$863$	−13.1316	−0.447004	−0.223502	+	0.974704i	$0.571749\pi$
$864$	17.1665	0.584015
$865$	52.0061	1.76826
$866$	8.14699	0.276846
$867$	40.6711	1.38126
$868$	−6.21182	−0.210843
$869$	10.5987	0.359536
$870$	0	0
$871$	−7.41398	−0.251213
$872$	−15.0837	−0.510800
$873$	48.5487	1.64312
$874$	−2.63327	−0.0890717
$875$	14.7584	0.498926
$876$	−15.8999	−0.537209
$877$	30.7758	1.03923	0.519613	−	0.854402i	$-0.326076\pi$
$877$	30.7758	1.03923	0.519613	+	0.854402i	$0.326076\pi$
$878$	2.76258	0.0932325
$879$	88.1974	2.97483
$880$	−27.5950	−0.930227
$881$	−29.5206	−0.994574	−0.497287	−	0.867586i	$-0.665670\pi$
$881$	−29.5206	−0.994574	−0.497287	+	0.867586i	$0.665670\pi$
$882$	11.5258	0.388093
$883$	36.0213	1.21221	0.606107	−	0.795383i	$-0.292730\pi$
$883$	36.0213	1.21221	0.606107	+	0.795383i	$0.292730\pi$
$884$	−7.50992	−0.252586
$885$	25.8305	0.868282
$886$	9.74013	0.327226
$887$	14.2942	0.479952	0.239976	−	0.970779i	$-0.422860\pi$
$887$	14.2942	0.479952	0.239976	+	0.970779i	$0.422860\pi$
$888$	30.3644	1.01896
$889$	7.18239	0.240890
$890$	13.4448	0.450672
$891$	18.4725	0.618850
$892$	−9.56267	−0.320182
$893$	17.1221	0.572969
$894$	−28.6436	−0.957986
$895$	−46.1884	−1.54391
$896$	−14.8759	−0.496968
$897$	−7.31097	−0.244106
$898$	9.04279	0.301762
$899$	0	0
$900$	1.05811	0.0352702
$901$	−7.98835	−0.266131
$902$	4.88748	0.162735
$903$	−38.6146	−1.28501
$904$	33.0688	1.09985
$905$	20.0412	0.666194
$906$	27.5707	0.915975
$907$	20.1496	0.669056	0.334528	−	0.942386i	$-0.391423\pi$
$907$	20.1496	0.669056	0.334528	+	0.942386i	$0.391423\pi$
$908$	−27.3850	−0.908803
$909$	4.14155	0.137367
$910$	4.60333	0.152599
$911$	18.4045	0.609769	0.304885	−	0.952389i	$-0.401382\pi$
$911$	18.4045	0.609769	0.304885	+	0.952389i	$0.401382\pi$
$912$	−40.0669	−1.32675
$913$	−31.8495	−1.05407
$914$	7.71894	0.255320
$915$	−32.2534	−1.06627
$916$	25.7875	0.852044
$917$	−0.0368385	−0.00121651
$918$	2.36849	0.0781720
$919$	5.31764	0.175413	0.0877063	−	0.996146i	$-0.472046\pi$
$919$	5.31764	0.175413	0.0877063	+	0.996146i	$0.472046\pi$
$920$	3.64507	0.120174
$921$	−76.7166	−2.52790
$922$	−11.4019	−0.375502
$923$	−48.9178	−1.61015
$924$	30.5289	1.00433
$925$	0.844891	0.0277798
$926$	13.6705	0.449240
$927$	−33.0520	−1.08557
$928$	0	0
$929$	−1.90689	−0.0625630	−0.0312815	−	0.999511i	$-0.509959\pi$
$929$	−1.90689	−0.0625630	−0.0312815	+	0.999511i	$0.509959\pi$
$930$	−8.32457	−0.272974
$931$	−31.5741	−1.03480
$932$	27.6210	0.904755
$933$	−58.7183	−1.92235
$934$	5.91076	0.193406
$935$	−15.1946	−0.496916
$936$	25.4890	0.833135
$937$	−3.37308	−0.110194	−0.0550969	−	0.998481i	$-0.517547\pi$
$937$	−3.37308	−0.110194	−0.0550969	+	0.998481i	$0.517547\pi$
$938$	−1.57287	−0.0513560
$939$	64.4265	2.10248
$940$	−11.0220	−0.359498
$941$	−19.8305	−0.646456	−0.323228	−	0.946321i	$-0.604768\pi$
$941$	−19.8305	−0.646456	−0.323228	+	0.946321i	$0.604768\pi$
$942$	16.2290	0.528769
$943$	1.65165	0.0537851
$944$	−10.8827	−0.354202
$945$	9.65689	0.314139
$946$	−28.2036	−0.916977
$947$	−40.5147	−1.31655	−0.658275	−	0.752778i	$-0.728714\pi$
$947$	−40.5147	−1.31655	−0.658275	+	0.752778i	$0.728714\pi$
$948$	−9.90628	−0.321741
$949$	−10.6575	−0.345956
$950$	0.435776	0.0141384
$951$	25.1823	0.816591
$952$	−3.42597	−0.111036
$953$	−2.34193	−0.0758624	−0.0379312	−	0.999280i	$-0.512077\pi$
$953$	−2.34193	−0.0758624	−0.0379312	+	0.999280i	$0.512077\pi$
$954$	12.6086	0.408219
$955$	−42.4675	−1.37421
$956$	−16.3429	−0.528567
$957$	0	0
$958$	12.4378	0.401848
$959$	8.01375	0.258777
$960$	14.1949	0.458139
$961$	−23.4705	−0.757112
$962$	9.46493	0.305162
$963$	−23.1589	−0.746287
$964$	18.1517	0.584626
$965$	−11.7200	−0.377280
$966$	−1.55102	−0.0499031
$967$	−13.2287	−0.425407	−0.212703	−	0.977117i	$-0.568227\pi$
$967$	−13.2287	−0.425407	−0.212703	+	0.977117i	$0.568227\pi$
$968$	26.9227	0.865327
$969$	−22.0620	−0.708732
$970$	−12.8711	−0.413265
$971$	−20.6402	−0.662374	−0.331187	−	0.943565i	$-0.607449\pi$
$971$	−20.6402	−0.662374	−0.331187	+	0.943565i	$0.607449\pi$
$972$	−34.8189	−1.11682
$973$	−16.1562	−0.517943
$974$	−0.657928	−0.0210814
$975$	1.20988	0.0387472
$976$	13.5888	0.434966
$977$	−2.70257	−0.0864630	−0.0432315	−	0.999065i	$-0.513765\pi$
$977$	−2.70257	−0.0864630	−0.0432315	+	0.999065i	$0.513765\pi$
$978$	3.45057	0.110337
$979$	59.7659	1.91013
$980$	20.3252	0.649265
$981$	−33.5379	−1.07078
$982$	16.6968	0.532816
$983$	−14.5855	−0.465207	−0.232603	−	0.972572i	$-0.574724\pi$
$983$	−14.5855	−0.465207	−0.232603	+	0.972572i	$0.574724\pi$
$984$	−9.82314	−0.313150
$985$	−21.9778	−0.700272
$986$	0	0
$987$	10.0850	0.321011
$988$	−32.4719	−1.03307
$989$	−9.53097	−0.303067
$990$	23.9828	0.762223
$991$	22.3492	0.709945	0.354973	−	0.934877i	$-0.384490\pi$
$991$	22.3492	0.709945	0.354973	+	0.934877i	$0.384490\pi$
$992$	13.9969	0.444403
$993$	−27.5917	−0.875595
$994$	−10.3779	−0.329166
$995$	−48.9030	−1.55033
$996$	29.7688	0.943262
$997$	54.4178	1.72343	0.861715	−	0.507392i	$-0.169391\pi$
$997$	54.4178	1.72343	0.861715	+	0.507392i	$0.169391\pi$
$998$	5.35958	0.169655
$999$	19.8556	0.628202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.a.g.1.4	✓	6
3.2	odd	2		7569.2.a.bc.1.3		6
29.2	odd	28		841.2.e.l.236.6		72
29.3	odd	28		841.2.e.l.270.6		72
29.4	even	14		841.2.d.n.190.4		36
29.5	even	14		841.2.d.n.605.4		36
29.6	even	14		841.2.d.n.645.4		36
29.7	even	7		841.2.d.o.571.3		36
29.8	odd	28		841.2.e.l.267.6		72
29.9	even	14		841.2.d.n.574.3		36
29.10	odd	28		841.2.e.l.651.6		72
29.11	odd	28		841.2.e.l.63.6		72
29.12	odd	4		841.2.b.d.840.6		12
29.13	even	14		841.2.d.n.778.3		36
29.14	odd	28		841.2.e.l.196.7		72
29.15	odd	28		841.2.e.l.196.6		72
29.16	even	7		841.2.d.o.778.4		36
29.17	odd	4		841.2.b.d.840.7		12
29.18	odd	28		841.2.e.l.63.7		72
29.19	odd	28		841.2.e.l.651.7		72
29.20	even	7		841.2.d.o.574.4		36
29.21	odd	28		841.2.e.l.267.7		72
29.22	even	14		841.2.d.n.571.4		36
29.23	even	7		841.2.d.o.645.3		36
29.24	even	7		841.2.d.o.605.3		36
29.25	even	7		841.2.d.o.190.3		36
29.26	odd	28		841.2.e.l.270.7		72
29.27	odd	28		841.2.e.l.236.7		72
29.28	even	2		841.2.a.h.1.3	yes	6
87.86	odd	2		7569.2.a.y.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.g.1.4	✓	6	1.1	even	1	trivial
841.2.a.h.1.3	yes	6	29.28	even	2
841.2.b.d.840.6		12	29.12	odd	4
841.2.b.d.840.7		12	29.17	odd	4
841.2.d.n.190.4		36	29.4	even	14
841.2.d.n.571.4		36	29.22	even	14
841.2.d.n.574.3		36	29.9	even	14
841.2.d.n.605.4		36	29.5	even	14
841.2.d.n.645.4		36	29.6	even	14
841.2.d.n.778.3		36	29.13	even	14
841.2.d.o.190.3		36	29.25	even	7
841.2.d.o.571.3		36	29.7	even	7
841.2.d.o.574.4		36	29.20	even	7
841.2.d.o.605.3		36	29.24	even	7
841.2.d.o.645.3		36	29.23	even	7
841.2.d.o.778.4		36	29.16	even	7
841.2.e.l.63.6		72	29.11	odd	28
841.2.e.l.63.7		72	29.18	odd	28
841.2.e.l.196.6		72	29.15	odd	28
841.2.e.l.196.7		72	29.14	odd	28
841.2.e.l.236.6		72	29.2	odd	28
841.2.e.l.236.7		72	29.27	odd	28
841.2.e.l.267.6		72	29.8	odd	28
841.2.e.l.267.7		72	29.21	odd	28
841.2.e.l.270.6		72	29.3	odd	28
841.2.e.l.270.7		72	29.26	odd	28
841.2.e.l.651.6		72	29.10	odd	28
841.2.e.l.651.7		72	29.19	odd	28
7569.2.a.y.1.4		6	87.86	odd	2
7569.2.a.bc.1.3		6	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q-0.511256 q^{2} -2.69256 q^{3} -1.73862 q^{4} +2.20381 q^{5} +1.37659 q^{6} -1.30206 q^{7} +1.91139 q^{8} +4.24987 q^{9} -1.12671 q^{10} -5.00853 q^{11} +4.68133 q^{12} +3.13782 q^{13} +0.665686 q^{14} -5.93390 q^{15} +2.50003 q^{16} +1.37659 q^{17} -2.17277 q^{18} +5.95217 q^{19} -3.83159 q^{20} +3.50588 q^{21} +2.56064 q^{22} +0.865330 q^{23} -5.14653 q^{24} -0.143202 q^{25} -1.60423 q^{26} -3.36536 q^{27} +2.26379 q^{28} +3.03374 q^{30} -2.74400 q^{31} -5.10093 q^{32} +13.4858 q^{33} -0.703787 q^{34} -2.86950 q^{35} -7.38891 q^{36} -5.89999 q^{37} -3.04308 q^{38} -8.44877 q^{39} +4.21235 q^{40} +1.90869 q^{41} -1.79240 q^{42} -11.0143 q^{43} +8.70792 q^{44} +9.36593 q^{45} -0.442405 q^{46} +2.87661 q^{47} -6.73147 q^{48} -5.30464 q^{49} +0.0732129 q^{50} -3.70654 q^{51} -5.45547 q^{52} -5.80302 q^{53} +1.72056 q^{54} -11.0379 q^{55} -2.48874 q^{56} -16.0266 q^{57} -4.35304 q^{59} +10.3168 q^{60} +5.43545 q^{61} +1.40288 q^{62} -5.53359 q^{63} -2.39218 q^{64} +6.91518 q^{65} -6.89467 q^{66} -2.36278 q^{67} -2.39336 q^{68} -2.32995 q^{69} +1.46705 q^{70} -15.5897 q^{71} +8.12316 q^{72} -3.39645 q^{73} +3.01640 q^{74} +0.385580 q^{75} -10.3486 q^{76} +6.52141 q^{77} +4.31948 q^{78} -2.11612 q^{79} +5.50960 q^{80} -3.68820 q^{81} -0.975830 q^{82} +6.35906 q^{83} -6.09538 q^{84} +3.03374 q^{85} +5.63110 q^{86} -9.57325 q^{88} -11.9328 q^{89} -4.78838 q^{90} -4.08563 q^{91} -1.50448 q^{92} +7.38838 q^{93} -1.47068 q^{94} +13.1175 q^{95} +13.7346 q^{96} +11.4236 q^{97} +2.71203 q^{98} -21.2856 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 6 q^{9} - 15 q^{10} - 13 q^{11} + 4 q^{12} - 6 q^{13} + 6 q^{14} - 19 q^{15} + 4 q^{16} - 3 q^{17} - 17 q^{18} + 6 q^{19} - 5 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 6 * q^9 - 15 * q^10 - 13 * q^11 + 4 * q^12 - 6 * q^13 + 6 * q^14 - 19 * q^15 + 4 * q^16 - 3 * q^17 - 17 * q^18 + 6 * q^19 - 5 * q^20 + 2 * q^21 - 4 * q^22 - 5 * q^23 - 10 * q^24 + 6 * q^25 - 9 * q^26 + q^27 - 5 * q^28 + 26 * q^30 - 16 * q^31 - 33 * q^32 + 27 * q^33 - 4 * q^35 - 21 * q^36 + 10 * q^37 + 41 * q^38 - 17 * q^39 - 7 * q^40 - 30 * q^41 - 21 * q^42 + 2 * q^43 - 16 * q^44 + 16 * q^45 + 20 * q^46 - 5 * q^47 + 30 * q^48 - 12 * q^49 + 8 * q^50 - 23 * q^51 - 13 * q^53 + 19 * q^54 - 10 * q^55 - 16 * q^56 - 16 * q^57 - 17 * q^59 + 9 * q^60 + 4 * q^61 - 9 * q^63 + q^64 + 32 * q^65 + 8 * q^66 - 9 * q^67 - 16 * q^68 - 26 * q^69 + 28 * q^70 + 21 * q^72 - 9 * q^73 - 36 * q^74 - 7 * q^75 - 24 * q^76 - 13 * q^77 - 6 * q^79 + 5 * q^80 - 22 * q^81 + 19 * q^82 - 24 * q^83 + 26 * q^85 + 17 * q^86 + 21 * q^88 - 9 * q^89 + 16 * q^90 + 16 * q^91 - 23 * q^92 - 12 * q^93 - 37 * q^94 - 31 * q^95 - 37 * q^96 + 10 * q^97 + 42 * q^98 - 6 * q^99

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