LMFDB - Embedded newform 1441.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.169669 q^{2} -1.85024 q^{3} -1.97121 q^{4} -3.73136 q^{5} +0.313927 q^{6} +1.69497 q^{7} +0.673790 q^{8} +0.423370 q^{9} +O(q^{10})$	\(q-0.169669 q^{2} -1.85024 q^{3} -1.97121 q^{4} -3.73136 q^{5} +0.313927 q^{6} +1.69497 q^{7} +0.673790 q^{8} +0.423370 q^{9} +0.633095 q^{10} +1.00000 q^{11} +3.64721 q^{12} +0.706466 q^{13} -0.287584 q^{14} +6.90390 q^{15} +3.82810 q^{16} -0.521224 q^{17} -0.0718326 q^{18} +5.59979 q^{19} +7.35531 q^{20} -3.13610 q^{21} -0.169669 q^{22} +3.04720 q^{23} -1.24667 q^{24} +8.92307 q^{25} -0.119865 q^{26} +4.76737 q^{27} -3.34115 q^{28} -8.02530 q^{29} -1.17137 q^{30} +1.55904 q^{31} -1.99709 q^{32} -1.85024 q^{33} +0.0884353 q^{34} -6.32456 q^{35} -0.834552 q^{36} -7.66615 q^{37} -0.950109 q^{38} -1.30713 q^{39} -2.51416 q^{40} -5.80718 q^{41} +0.532098 q^{42} +5.42776 q^{43} -1.97121 q^{44} -1.57975 q^{45} -0.517015 q^{46} -9.01069 q^{47} -7.08289 q^{48} -4.12707 q^{49} -1.51396 q^{50} +0.964386 q^{51} -1.39259 q^{52} +7.15431 q^{53} -0.808873 q^{54} -3.73136 q^{55} +1.14206 q^{56} -10.3609 q^{57} +1.36164 q^{58} +15.1410 q^{59} -13.6090 q^{60} +9.76953 q^{61} -0.264520 q^{62} +0.717601 q^{63} -7.31736 q^{64} -2.63608 q^{65} +0.313927 q^{66} +3.25036 q^{67} +1.02744 q^{68} -5.63805 q^{69} +1.07308 q^{70} -10.0834 q^{71} +0.285262 q^{72} -9.77990 q^{73} +1.30071 q^{74} -16.5098 q^{75} -11.0384 q^{76} +1.69497 q^{77} +0.221779 q^{78} +10.7868 q^{79} -14.2840 q^{80} -10.0909 q^{81} +0.985297 q^{82} -6.21910 q^{83} +6.18192 q^{84} +1.94487 q^{85} -0.920920 q^{86} +14.8487 q^{87} +0.673790 q^{88} -2.41089 q^{89} +0.268033 q^{90} +1.19744 q^{91} -6.00669 q^{92} -2.88459 q^{93} +1.52883 q^{94} -20.8948 q^{95} +3.69509 q^{96} +15.0150 q^{97} +0.700234 q^{98} +0.423370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * 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 $

$2$	−0.169669	−0.119974	−0.0599869	−	0.998199i	$-0.519106\pi$
$2$	−0.169669	−0.119974	−0.0599869	+	0.998199i	$0.519106\pi$
$3$	−1.85024	−1.06823	−0.534117	−	0.845411i	$-0.679356\pi$
$3$	−1.85024	−1.06823	−0.534117	+	0.845411i	$0.679356\pi$
$4$	−1.97121	−0.985606
$5$	−3.73136	−1.66872	−0.834358	−	0.551223i	$-0.814161\pi$
$5$	−3.73136	−1.66872	−0.834358	+	0.551223i	$0.814161\pi$
$6$	0.313927	0.128160
$7$	1.69497	0.640640	0.320320	−	0.947309i	$-0.396210\pi$
$7$	1.69497	0.640640	0.320320	+	0.947309i	$0.396210\pi$
$8$	0.673790	0.238221
$9$	0.423370	0.141123
$10$	0.633095	0.200202
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.64721	1.05286
$13$	0.706466	0.195938	0.0979691	−	0.995189i	$-0.468765\pi$
$13$	0.706466	0.195938	0.0979691	+	0.995189i	$0.468765\pi$
$14$	−0.287584	−0.0768600
$15$	6.90390	1.78258
$16$	3.82810	0.957026
$17$	−0.521224	−0.126415	−0.0632077	−	0.998000i	$-0.520133\pi$
$17$	−0.521224	−0.126415	−0.0632077	+	0.998000i	$0.520133\pi$
$18$	−0.0718326	−0.0169311
$19$	5.59979	1.28468	0.642340	−	0.766420i	$-0.277964\pi$
$19$	5.59979	1.28468	0.642340	+	0.766420i	$0.277964\pi$
$20$	7.35531	1.64470
$21$	−3.13610	−0.684353
$22$	−0.169669	−0.0361735
$23$	3.04720	0.635386	0.317693	−	0.948194i	$-0.397092\pi$
$23$	3.04720	0.635386	0.317693	+	0.948194i	$0.397092\pi$
$24$	−1.24667	−0.254476
$25$	8.92307	1.78461
$26$	−0.119865	−0.0235075
$27$	4.76737	0.917481
$28$	−3.34115	−0.631418
$29$	−8.02530	−1.49026	−0.745130	−	0.666919i	$-0.767613\pi$
$29$	−8.02530	−1.49026	−0.745130	+	0.666919i	$0.767613\pi$
$30$	−1.17137	−0.213863
$31$	1.55904	0.280012	0.140006	−	0.990151i	$-0.455288\pi$
$31$	1.55904	0.280012	0.140006	+	0.990151i	$0.455288\pi$
$32$	−1.99709	−0.353039
$33$	−1.85024	−0.322085
$34$	0.0884353	0.0151665
$35$	−6.32456	−1.06905
$36$	−0.834552	−0.139092
$37$	−7.66615	−1.26031	−0.630154	−	0.776471i	$-0.717008\pi$
$37$	−7.66615	−1.26031	−0.630154	+	0.776471i	$0.717008\pi$
$38$	−0.950109	−0.154128
$39$	−1.30713	−0.209308
$40$	−2.51416	−0.397523
$41$	−5.80718	−0.906929	−0.453465	−	0.891274i	$-0.649812\pi$
$41$	−5.80718	−0.906929	−0.453465	+	0.891274i	$0.649812\pi$
$42$	0.532098	0.0821044
$43$	5.42776	0.827725	0.413863	−	0.910339i	$-0.364179\pi$
$43$	5.42776	0.827725	0.413863	+	0.910339i	$0.364179\pi$
$44$	−1.97121	−0.297171
$45$	−1.57975	−0.235495
$46$	−0.517015	−0.0762297
$47$	−9.01069	−1.31434	−0.657172	−	0.753740i	$-0.728248\pi$
$47$	−9.01069	−1.31434	−0.657172	+	0.753740i	$0.728248\pi$
$48$	−7.08289	−1.02233
$49$	−4.12707	−0.589581
$50$	−1.51396	−0.214107
$51$	0.964386	0.135041
$52$	−1.39259	−0.193118
$53$	7.15431	0.982720	0.491360	−	0.870957i	$-0.336500\pi$
$53$	7.15431	0.982720	0.491360	+	0.870957i	$0.336500\pi$
$54$	−0.808873	−0.110074
$55$	−3.73136	−0.503137
$56$	1.14206	0.152614
$57$	−10.3609	−1.37234
$58$	1.36164	0.178792
$59$	15.1410	1.97119	0.985597	−	0.169111i	$-0.0540897\pi$
$59$	15.1410	1.97119	0.985597	+	0.169111i	$0.0540897\pi$
$60$	−13.6090	−1.75692
$61$	9.76953	1.25086	0.625430	−	0.780280i	$-0.284924\pi$
$61$	9.76953	1.25086	0.625430	+	0.780280i	$0.284924\pi$
$62$	−0.264520	−0.0335941
$63$	0.717601	0.0904092
$64$	−7.31736	−0.914671
$65$	−2.63608	−0.326965
$66$	0.313927	0.0386417
$67$	3.25036	0.397095	0.198547	−	0.980091i	$-0.436378\pi$
$67$	3.25036	0.397095	0.198547	+	0.980091i	$0.436378\pi$
$68$	1.02744	0.124596
$69$	−5.63805	−0.678741
$70$	1.07308	0.128257
$71$	−10.0834	−1.19668	−0.598341	−	0.801241i	$-0.704173\pi$
$71$	−10.0834	−1.19668	−0.598341	+	0.801241i	$0.704173\pi$
$72$	0.285262	0.0336185
$73$	−9.77990	−1.14465	−0.572325	−	0.820027i	$-0.693959\pi$
$73$	−9.77990	−1.14465	−0.572325	+	0.820027i	$0.693959\pi$
$74$	1.30071	0.151204
$75$	−16.5098	−1.90638
$76$	−11.0384	−1.26619
$77$	1.69497	0.193160
$78$	0.221779	0.0251115
$79$	10.7868	1.21361	0.606807	−	0.794849i	$-0.292450\pi$
$79$	10.7868	1.21361	0.606807	+	0.794849i	$0.292450\pi$
$80$	−14.2840	−1.59700
$81$	−10.0909	−1.12121
$82$	0.985297	0.108808
$83$	−6.21910	−0.682635	−0.341317	−	0.939948i	$-0.610873\pi$
$83$	−6.21910	−0.682635	−0.341317	+	0.939948i	$0.610873\pi$
$84$	6.18192	0.674502
$85$	1.94487	0.210951
$86$	−0.920920	−0.0993054
$87$	14.8487	1.59195
$88$	0.673790	0.0718263
$89$	−2.41089	−0.255553	−0.127777	−	0.991803i	$-0.540784\pi$
$89$	−2.41089	−0.255553	−0.127777	+	0.991803i	$0.540784\pi$
$90$	0.268033	0.0282532
$91$	1.19744	0.125526
$92$	−6.00669	−0.626241
$93$	−2.88459	−0.299118
$94$	1.52883	0.157687
$95$	−20.8948	−2.14377
$96$	3.69509	0.377128
$97$	15.0150	1.52454	0.762272	−	0.647257i	$-0.224084\pi$
$97$	15.0150	1.52454	0.762272	+	0.647257i	$0.224084\pi$
$98$	0.700234	0.0707343
$99$	0.423370	0.0425503
$100$	−17.5893	−1.75893
$101$	1.26835	0.126205	0.0631026	−	0.998007i	$-0.479900\pi$
$101$	1.26835	0.126205	0.0631026	+	0.998007i	$0.479900\pi$
$102$	−0.163626	−0.0162014
$103$	−17.8358	−1.75741	−0.878707	−	0.477362i	$-0.841593\pi$
$103$	−17.8358	−1.75741	−0.878707	+	0.477362i	$0.841593\pi$
$104$	0.476010	0.0466766
$105$	11.7019	1.14199
$106$	−1.21386	−0.117901
$107$	14.2338	1.37604	0.688018	−	0.725694i	$-0.258481\pi$
$107$	14.2338	1.37604	0.688018	+	0.725694i	$0.258481\pi$
$108$	−9.39750	−0.904275
$109$	−19.1489	−1.83413	−0.917065	−	0.398738i	$-0.869448\pi$
$109$	−19.1489	−1.83413	−0.917065	+	0.398738i	$0.869448\pi$
$110$	0.633095	0.0603633
$111$	14.1842	1.34630
$112$	6.48853	0.613109
$113$	−13.0974	−1.23210	−0.616048	−	0.787709i	$-0.711267\pi$
$113$	−13.0974	−1.23210	−0.616048	+	0.787709i	$0.711267\pi$
$114$	1.75792	0.164645
$115$	−11.3702	−1.06028
$116$	15.8196	1.46881
$117$	0.299096	0.0276515
$118$	−2.56896	−0.236492
$119$	−0.883460	−0.0809867
$120$	4.65178	0.424647
$121$	1.00000	0.0909091
$122$	−1.65758	−0.150070
$123$	10.7447	0.968813
$124$	−3.07320	−0.275981
$125$	−14.6384	−1.30930
$126$	−0.121754	−0.0108467
$127$	−0.202132	−0.0179363	−0.00896816	−	0.999960i	$-0.502855\pi$
$127$	−0.202132	−0.0179363	−0.00896816	+	0.999960i	$0.502855\pi$
$128$	5.23571	0.462775
$129$	−10.0426	−0.884204
$130$	0.447260	0.0392273
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	3.64721	0.317449
$133$	9.49149	0.823017
$134$	−0.551484	−0.0476410
$135$	−17.7888	−1.53102
$136$	−0.351195	−0.0301148
$137$	−8.05468	−0.688158	−0.344079	−	0.938941i	$-0.611809\pi$
$137$	−8.05468	−0.688158	−0.344079	+	0.938941i	$0.611809\pi$
$138$	0.956599	0.0814311
$139$	−6.95248	−0.589702	−0.294851	−	0.955543i	$-0.595270\pi$
$139$	−6.95248	−0.589702	−0.294851	+	0.955543i	$0.595270\pi$
$140$	12.4670	1.05366
$141$	16.6719	1.40403
$142$	1.71084	0.143571
$143$	0.706466	0.0590776
$144$	1.62070	0.135059
$145$	29.9453	2.48682
$146$	1.65934	0.137328
$147$	7.63604	0.629810
$148$	15.1116	1.24217
$149$	−10.8467	−0.888599	−0.444299	−	0.895878i	$-0.646547\pi$
$149$	−10.8467	−0.888599	−0.444299	+	0.895878i	$0.646547\pi$
$150$	2.80119	0.228716
$151$	16.9912	1.38273	0.691364	−	0.722507i	$-0.257010\pi$
$151$	16.9912	1.38273	0.691364	+	0.722507i	$0.257010\pi$
$152$	3.77308	0.306038
$153$	−0.220670	−0.0178401
$154$	−0.287584	−0.0231742
$155$	−5.81734	−0.467260
$156$	2.57663	0.206295
$157$	−12.2112	−0.974563	−0.487282	−	0.873245i	$-0.662012\pi$
$157$	−12.2112	−0.974563	−0.487282	+	0.873245i	$0.662012\pi$
$158$	−1.83019	−0.145602
$159$	−13.2371	−1.04977
$160$	7.45187	0.589122
$161$	5.16493	0.407053
$162$	1.71210	0.134516
$163$	−7.17497	−0.561987	−0.280993	−	0.959710i	$-0.590664\pi$
$163$	−7.17497	−0.561987	−0.280993	+	0.959710i	$0.590664\pi$
$164$	11.4472	0.893875
$165$	6.90390	0.537468
$166$	1.05519	0.0818983
$167$	−3.96016	−0.306446	−0.153223	−	0.988192i	$-0.548965\pi$
$167$	−3.96016	−0.306446	−0.153223	+	0.988192i	$0.548965\pi$
$168$	−2.11307	−0.163027
$169$	−12.5009	−0.961608
$170$	−0.329984	−0.0253086
$171$	2.37078	0.181298
$172$	−10.6993	−0.815811
$173$	10.5669	0.803386	0.401693	−	0.915774i	$-0.368422\pi$
$173$	10.5669	0.803386	0.401693	+	0.915774i	$0.368422\pi$
$174$	−2.51936	−0.190992
$175$	15.1244	1.14329
$176$	3.82810	0.288554
$177$	−28.0145	−2.10570
$178$	0.409052	0.0306597
$179$	−15.2272	−1.13813	−0.569066	−	0.822292i	$-0.692695\pi$
$179$	−15.2272	−1.13813	−0.569066	+	0.822292i	$0.692695\pi$
$180$	3.11402	0.232105
$181$	1.23727	0.0919657	0.0459829	−	0.998942i	$-0.485358\pi$
$181$	1.23727	0.0919657	0.0459829	+	0.998942i	$0.485358\pi$
$182$	−0.203168	−0.0150598
$183$	−18.0759	−1.33621
$184$	2.05318	0.151362
$185$	28.6052	2.10309
$186$	0.489424	0.0358863
$187$	−0.521224	−0.0381157
$188$	17.7620	1.29543
$189$	8.08057	0.587775
$190$	3.54520	0.257196
$191$	6.30901	0.456504	0.228252	−	0.973602i	$-0.426699\pi$
$191$	6.30901	0.456504	0.228252	+	0.973602i	$0.426699\pi$
$192$	13.5388	0.977082
$193$	9.66439	0.695658	0.347829	−	0.937558i	$-0.386919\pi$
$193$	9.66439	0.695658	0.347829	+	0.937558i	$0.386919\pi$
$194$	−2.54758	−0.182905
$195$	4.87737	0.349275
$196$	8.13533	0.581095
$197$	2.80309	0.199712	0.0998560	−	0.995002i	$-0.468162\pi$
$197$	2.80309	0.199712	0.0998560	+	0.995002i	$0.468162\pi$
$198$	−0.0718326	−0.00510492
$199$	14.2375	1.00927	0.504634	−	0.863333i	$-0.331627\pi$
$199$	14.2375	1.00927	0.504634	+	0.863333i	$0.331627\pi$
$200$	6.01227	0.425132
$201$	−6.01393	−0.424190
$202$	−0.215199	−0.0151413
$203$	−13.6027	−0.954720
$204$	−1.90101	−0.133097
$205$	21.6687	1.51341
$206$	3.02618	0.210844
$207$	1.29009	0.0896678
$208$	2.70442	0.187518
$209$	5.59979	0.387346
$210$	−1.98545	−0.137009
$211$	19.1971	1.32158	0.660790	−	0.750571i	$-0.270221\pi$
$211$	19.1971	1.32158	0.660790	+	0.750571i	$0.270221\pi$
$212$	−14.1027	−0.968575
$213$	18.6567	1.27834
$214$	−2.41503	−0.165088
$215$	−20.2529	−1.38124
$216$	3.21221	0.218563
$217$	2.64253	0.179387
$218$	3.24896	0.220048
$219$	18.0951	1.22275
$220$	7.35531	0.495895
$221$	−0.368227	−0.0247696
$222$	−2.40661	−0.161521
$223$	−17.8071	−1.19245	−0.596225	−	0.802817i	$-0.703333\pi$
$223$	−17.8071	−1.19245	−0.596225	+	0.802817i	$0.703333\pi$
$224$	−3.38501	−0.226171
$225$	3.77776	0.251850
$226$	2.22221	0.147819
$227$	8.57424	0.569092	0.284546	−	0.958662i	$-0.408157\pi$
$227$	8.57424	0.569092	0.284546	+	0.958662i	$0.408157\pi$
$228$	20.4236	1.35259
$229$	−23.5161	−1.55399	−0.776995	−	0.629506i	$-0.783257\pi$
$229$	−23.5161	−1.55399	−0.776995	+	0.629506i	$0.783257\pi$
$230$	1.92917	0.127206
$231$	−3.13610	−0.206340
$232$	−5.40737	−0.355011
$233$	−4.28472	−0.280701	−0.140351	−	0.990102i	$-0.544823\pi$
$233$	−4.28472	−0.280701	−0.140351	+	0.990102i	$0.544823\pi$
$234$	−0.0507473	−0.00331745
$235$	33.6222	2.19327
$236$	−29.8462	−1.94282
$237$	−19.9582	−1.29642
$238$	0.149895	0.00971628
$239$	−29.0657	−1.88011	−0.940054	−	0.341027i	$-0.889225\pi$
$239$	−29.0657	−1.88011	−0.940054	+	0.341027i	$0.889225\pi$
$240$	26.4288	1.70597
$241$	21.2610	1.36954	0.684771	−	0.728758i	$-0.259902\pi$
$241$	21.2610	1.36954	0.684771	+	0.728758i	$0.259902\pi$
$242$	−0.169669	−0.0109067
$243$	4.36836	0.280231
$244$	−19.2578	−1.23286
$245$	15.3996	0.983843
$246$	−1.82303	−0.116232
$247$	3.95606	0.251718
$248$	1.05046	0.0667046
$249$	11.5068	0.729213
$250$	2.48367	0.157081
$251$	10.6137	0.669934	0.334967	−	0.942230i	$-0.391275\pi$
$251$	10.6137	0.669934	0.334967	+	0.942230i	$0.391275\pi$
$252$	−1.41454	−0.0891078
$253$	3.04720	0.191576
$254$	0.0342955	0.00215189
$255$	−3.59848	−0.225345
$256$	13.7464	0.859150
$257$	10.6188	0.662383	0.331191	−	0.943564i	$-0.392549\pi$
$257$	10.6188	0.662383	0.331191	+	0.943564i	$0.392549\pi$
$258$	1.70392	0.106081
$259$	−12.9939	−0.807403
$260$	5.19627	0.322259
$261$	−3.39767	−0.210310
$262$	−0.169669	−0.0104822
$263$	−17.4277	−1.07464	−0.537318	−	0.843380i	$-0.680562\pi$
$263$	−17.4277	−1.07464	−0.537318	+	0.843380i	$0.680562\pi$
$264$	−1.24667	−0.0767273
$265$	−26.6953	−1.63988
$266$	−1.61041	−0.0987405
$267$	4.46071	0.272991
$268$	−6.40715	−0.391379
$269$	−19.9432	−1.21596	−0.607979	−	0.793953i	$-0.708019\pi$
$269$	−19.9432	−1.21596	−0.607979	+	0.793953i	$0.708019\pi$
$270$	3.01820	0.183682
$271$	−5.94312	−0.361019	−0.180510	−	0.983573i	$-0.557775\pi$
$271$	−5.94312	−0.361019	−0.180510	+	0.983573i	$0.557775\pi$
$272$	−1.99530	−0.120983
$273$	−2.21555	−0.134091
$274$	1.36663	0.0825609
$275$	8.92307	0.538081
$276$	11.1138	0.668971
$277$	8.29721	0.498531	0.249266	−	0.968435i	$-0.419811\pi$
$277$	8.29721	0.498531	0.249266	+	0.968435i	$0.419811\pi$
$278$	1.17962	0.0707488
$279$	0.660050	0.0395162
$280$	−4.26143	−0.254669
$281$	−25.1363	−1.49951	−0.749754	−	0.661717i	$-0.769828\pi$
$281$	−25.1363	−1.49951	−0.749754	+	0.661717i	$0.769828\pi$
$282$	−2.82870	−0.168447
$283$	32.6083	1.93836	0.969180	−	0.246353i	$-0.0792323\pi$
$283$	32.6083	1.93836	0.969180	+	0.246353i	$0.0792323\pi$
$284$	19.8766	1.17946
$285$	38.6604	2.29004
$286$	−0.119865	−0.00708777
$287$	−9.84302	−0.581015
$288$	−0.845508	−0.0498220
$289$	−16.7283	−0.984019
$290$	−5.08078	−0.298353
$291$	−27.7813	−1.62857
$292$	19.2783	1.12817
$293$	−13.0820	−0.764258	−0.382129	−	0.924109i	$-0.624809\pi$
$293$	−13.0820	−0.764258	−0.382129	+	0.924109i	$0.624809\pi$
$294$	−1.29560	−0.0755608
$295$	−56.4967	−3.28936
$296$	−5.16538	−0.300231
$297$	4.76737	0.276631
$298$	1.84035	0.106609
$299$	2.15275	0.124496
$300$	32.5443	1.87894
$301$	9.19990	0.530274
$302$	−2.88288	−0.165891
$303$	−2.34674	−0.134817
$304$	21.4366	1.22947
$305$	−36.4537	−2.08733
$306$	0.0374409	0.00214035
$307$	−27.6124	−1.57592	−0.787962	−	0.615724i	$-0.788864\pi$
$307$	−27.6124	−1.57592	−0.787962	+	0.615724i	$0.788864\pi$
$308$	−3.34115	−0.190380
$309$	33.0004	1.87733
$310$	0.987020	0.0560590
$311$	−0.798921	−0.0453027	−0.0226513	−	0.999743i	$-0.507211\pi$
$311$	−0.798921	−0.0453027	−0.0226513	+	0.999743i	$0.507211\pi$
$312$	−0.880730	−0.0498615
$313$	14.7962	0.836332	0.418166	−	0.908371i	$-0.362673\pi$
$313$	14.7962	0.836332	0.418166	+	0.908371i	$0.362673\pi$
$314$	2.07187	0.116922
$315$	−2.67763	−0.150867
$316$	−21.2632	−1.19615
$317$	21.2000	1.19071	0.595356	−	0.803462i	$-0.297011\pi$
$317$	21.2000	1.19071	0.595356	+	0.803462i	$0.297011\pi$
$318$	2.24593	0.125945
$319$	−8.02530	−0.449330
$320$	27.3037	1.52633
$321$	−26.3359	−1.46993
$322$	−0.876327	−0.0488358
$323$	−2.91874	−0.162403
$324$	19.8912	1.10507
$325$	6.30384	0.349674
$326$	1.21737	0.0674237
$327$	35.4299	1.95928
$328$	−3.91282	−0.216049
$329$	−15.2729	−0.842021
$330$	−1.17137	−0.0644821
$331$	−23.1324	−1.27147	−0.635735	−	0.771907i	$-0.719303\pi$
$331$	−23.1324	−1.27147	−0.635735	+	0.771907i	$0.719303\pi$
$332$	12.2592	0.672809
$333$	−3.24562	−0.177859
$334$	0.671915	0.0367655
$335$	−12.1283	−0.662639
$336$	−12.0053	−0.654943
$337$	−15.3775	−0.837666	−0.418833	−	0.908063i	$-0.637561\pi$
$337$	−15.3775	−0.837666	−0.418833	+	0.908063i	$0.637561\pi$
$338$	2.12101	0.115368
$339$	24.2332	1.31617
$340$	−3.83376	−0.207915
$341$	1.55904	0.0844267
$342$	−0.402247	−0.0217511
$343$	−18.8601	−1.01835
$344$	3.65717	0.197181
$345$	21.0376	1.13263
$346$	−1.79287	−0.0963853
$347$	23.5512	1.26430	0.632148	−	0.774848i	$-0.282174\pi$
$347$	23.5512	1.26430	0.632148	+	0.774848i	$0.282174\pi$
$348$	−29.2699	−1.56903
$349$	−18.8954	−1.01145	−0.505723	−	0.862696i	$-0.668774\pi$
$349$	−18.8954	−1.01145	−0.505723	+	0.862696i	$0.668774\pi$
$350$	−2.56613	−0.137165
$351$	3.36798	0.179770
$352$	−1.99709	−0.106445
$353$	4.74491	0.252546	0.126273	−	0.991996i	$-0.459698\pi$
$353$	4.74491	0.252546	0.126273	+	0.991996i	$0.459698\pi$
$354$	4.75318	0.252628
$355$	37.6249	1.99692
$356$	4.75237	0.251875
$357$	1.63461	0.0865127
$358$	2.58357	0.136546
$359$	−22.4361	−1.18413	−0.592067	−	0.805889i	$-0.701688\pi$
$359$	−22.4361	−1.18413	−0.592067	+	0.805889i	$0.701688\pi$
$360$	−1.06442	−0.0560997
$361$	12.3577	0.650403
$362$	−0.209926	−0.0110335
$363$	−1.85024	−0.0971122
$364$	−2.36041	−0.123719
$365$	36.4923	1.91010
$366$	3.06692	0.160310
$367$	−22.9276	−1.19681	−0.598407	−	0.801193i	$-0.704199\pi$
$367$	−22.9276	−1.19681	−0.598407	+	0.801193i	$0.704199\pi$
$368$	11.6650	0.608081
$369$	−2.45859	−0.127989
$370$	−4.85340	−0.252316
$371$	12.1264	0.629569
$372$	5.68614	0.294812
$373$	−25.0533	−1.29721	−0.648605	−	0.761125i	$-0.724647\pi$
$373$	−25.0533	−1.29721	−0.648605	+	0.761125i	$0.724647\pi$
$374$	0.0884353	0.00457288
$375$	27.0844	1.39863
$376$	−6.07132	−0.313104
$377$	−5.66960	−0.291999
$378$	−1.37102	−0.0705176
$379$	−23.8218	−1.22364	−0.611822	−	0.790995i	$-0.709563\pi$
$379$	−23.8218	−1.22364	−0.611822	+	0.790995i	$0.709563\pi$
$380$	41.1882	2.11291
$381$	0.373992	0.0191602
$382$	−1.07044	−0.0547686
$383$	−21.9958	−1.12393	−0.561966	−	0.827160i	$-0.689955\pi$
$383$	−21.9958	−1.12393	−0.561966	+	0.827160i	$0.689955\pi$
$384$	−9.68729	−0.494352
$385$	−6.32456	−0.322329
$386$	−1.63974	−0.0834608
$387$	2.29795	0.116811
$388$	−29.5978	−1.50260
$389$	8.51697	0.431827	0.215914	−	0.976412i	$-0.430727\pi$
$389$	8.51697	0.431827	0.215914	+	0.976412i	$0.430727\pi$
$390$	−0.827536	−0.0419039
$391$	−1.58828	−0.0803225
$392$	−2.78078	−0.140450
$393$	−1.85024	−0.0933320
$394$	−0.475597	−0.0239602
$395$	−40.2496	−2.02518
$396$	−0.834552	−0.0419378
$397$	15.0440	0.755036	0.377518	−	0.926002i	$-0.376778\pi$
$397$	15.0440	0.755036	0.377518	+	0.926002i	$0.376778\pi$
$398$	−2.41565	−0.121086
$399$	−17.5615	−0.879174
$400$	34.1584	1.70792
$401$	−9.69600	−0.484195	−0.242098	−	0.970252i	$-0.577835\pi$
$401$	−9.69600	−0.484195	−0.242098	+	0.970252i	$0.577835\pi$
$402$	1.02038	0.0508917
$403$	1.10141	0.0548650
$404$	−2.50018	−0.124389
$405$	37.6527	1.87098
$406$	2.30794	0.114541
$407$	−7.66615	−0.379997
$408$	0.649794	0.0321696
$409$	18.2291	0.901372	0.450686	−	0.892683i	$-0.351179\pi$
$409$	18.2291	0.901372	0.450686	+	0.892683i	$0.351179\pi$
$410$	−3.67650	−0.181569
$411$	14.9031	0.735113
$412$	35.1582	1.73212
$413$	25.6636	1.26282
$414$	−0.218889	−0.0107578
$415$	23.2057	1.13912
$416$	−1.41088	−0.0691738
$417$	12.8637	0.629939
$418$	−0.950109	−0.0464713
$419$	22.1174	1.08050	0.540252	−	0.841503i	$-0.318329\pi$
$419$	22.1174	1.08050	0.540252	+	0.841503i	$0.318329\pi$
$420$	−23.0670	−1.12555
$421$	9.04911	0.441026	0.220513	−	0.975384i	$-0.429227\pi$
$421$	9.04911	0.441026	0.220513	+	0.975384i	$0.429227\pi$
$422$	−3.25714	−0.158555
$423$	−3.81486	−0.185485
$424$	4.82050	0.234104
$425$	−4.65091	−0.225602
$426$	−3.16546	−0.153367
$427$	16.5591	0.801351
$428$	−28.0579	−1.35623
$429$	−1.30713	−0.0631087
$430$	3.43629	0.165712
$431$	−17.3177	−0.834163	−0.417082	−	0.908869i	$-0.636947\pi$
$431$	−17.3177	−0.834163	−0.417082	+	0.908869i	$0.636947\pi$
$432$	18.2500	0.878053
$433$	11.8615	0.570029	0.285014	−	0.958523i	$-0.408002\pi$
$433$	11.8615	0.570029	0.285014	+	0.958523i	$0.408002\pi$
$434$	−0.448354	−0.0215217
$435$	−55.4058	−2.65651
$436$	37.7465	1.80773
$437$	17.0637	0.816268
$438$	−3.07017	−0.146699
$439$	−5.35065	−0.255373	−0.127686	−	0.991815i	$-0.540755\pi$
$439$	−5.35065	−0.255373	−0.127686	+	0.991815i	$0.540755\pi$
$440$	−2.51416	−0.119858
$441$	−1.74728	−0.0832036
$442$	0.0624765	0.00297170
$443$	−19.0560	−0.905380	−0.452690	−	0.891668i	$-0.649536\pi$
$443$	−19.0560	−0.905380	−0.452690	+	0.891668i	$0.649536\pi$
$444$	−27.9600	−1.32692
$445$	8.99589	0.426446
$446$	3.02130	0.143063
$447$	20.0690	0.949231
$448$	−12.4027	−0.585974
$449$	−31.5950	−1.49106	−0.745530	−	0.666472i	$-0.767804\pi$
$449$	−31.5950	−1.49106	−0.745530	+	0.666472i	$0.767804\pi$
$450$	−0.640967	−0.0302155
$451$	−5.80718	−0.273450
$452$	25.8177	1.21436
$453$	−31.4378	−1.47708
$454$	−1.45478	−0.0682761
$455$	−4.46808	−0.209467
$456$	−6.98109	−0.326920
$457$	−4.73166	−0.221338	−0.110669	−	0.993857i	$-0.535299\pi$
$457$	−4.73166	−0.221338	−0.110669	+	0.993857i	$0.535299\pi$
$458$	3.98995	0.186438
$459$	−2.48487	−0.115984
$460$	22.4131	1.04502
$461$	18.2439	0.849704	0.424852	−	0.905263i	$-0.360326\pi$
$461$	18.2439	0.849704	0.424852	+	0.905263i	$0.360326\pi$
$462$	0.532098	0.0247554
$463$	−7.03634	−0.327006	−0.163503	−	0.986543i	$-0.552279\pi$
$463$	−7.03634	−0.327006	−0.163503	+	0.986543i	$0.552279\pi$
$464$	−30.7217	−1.42622
$465$	10.7634	0.499143
$466$	0.726982	0.0336768
$467$	−13.1043	−0.606397	−0.303198	−	0.952927i	$-0.598054\pi$
$467$	−13.1043	−0.606397	−0.303198	+	0.952927i	$0.598054\pi$
$468$	−0.589582	−0.0272535
$469$	5.50928	0.254395
$470$	−5.70463	−0.263135
$471$	22.5937	1.04106
$472$	10.2019	0.469579
$473$	5.42776	0.249569
$474$	3.38628	0.155537
$475$	49.9673	2.29266
$476$	1.74149	0.0798210
$477$	3.02892	0.138685
$478$	4.93155	0.225564
$479$	10.2936	0.470326	0.235163	−	0.971956i	$-0.424438\pi$
$479$	10.2936	0.470326	0.235163	+	0.971956i	$0.424438\pi$
$480$	−13.7877	−0.629320
$481$	−5.41587	−0.246942
$482$	−3.60733	−0.164309
$483$	−9.55633	−0.434828
$484$	−1.97121	−0.0896006
$485$	−56.0265	−2.54403
$486$	−0.741174	−0.0336203
$487$	25.3382	1.14818	0.574092	−	0.818791i	$-0.305355\pi$
$487$	25.3382	1.14818	0.574092	+	0.818791i	$0.305355\pi$
$488$	6.58261	0.297981
$489$	13.2754	0.600333
$490$	−2.61283	−0.118035
$491$	5.67127	0.255941	0.127970	−	0.991778i	$-0.459154\pi$
$491$	5.67127	0.255941	0.127970	+	0.991778i	$0.459154\pi$
$492$	−21.1800	−0.954868
$493$	4.18298	0.188392
$494$	−0.671219	−0.0301996
$495$	−1.57975	−0.0710043
$496$	5.96816	0.267978
$497$	−17.0911	−0.766642
$498$	−1.95234	−0.0874865
$499$	−4.67814	−0.209422	−0.104711	−	0.994503i	$-0.533392\pi$
$499$	−4.67814	−0.209422	−0.104711	+	0.994503i	$0.533392\pi$
$500$	28.8554	1.29045
$501$	7.32722	0.327356
$502$	−1.80082	−0.0803745
$503$	2.94166	0.131162	0.0655810	−	0.997847i	$-0.479110\pi$
$503$	2.94166	0.131162	0.0655810	+	0.997847i	$0.479110\pi$
$504$	0.483512	0.0215373
$505$	−4.73266	−0.210601
$506$	−0.517015	−0.0229841
$507$	23.1296	1.02722
$508$	0.398445	0.0176781
$509$	−3.58093	−0.158722	−0.0793611	−	0.996846i	$-0.525288\pi$
$509$	−3.58093	−0.158722	−0.0793611	+	0.996846i	$0.525288\pi$
$510$	0.610548	0.0270355
$511$	−16.5767	−0.733308
$512$	−12.8037	−0.565851
$513$	26.6963	1.17867
$514$	−1.80168	−0.0794686
$515$	66.5518	2.93262
$516$	19.7962	0.871477
$517$	−9.01069	−0.396290
$518$	2.20466	0.0968672
$519$	−19.5512	−0.858204
$520$	−1.77616	−0.0778900
$521$	−16.0319	−0.702372	−0.351186	−	0.936306i	$-0.614222\pi$
$521$	−16.0319	−0.702372	−0.351186	+	0.936306i	$0.614222\pi$
$522$	0.576478	0.0252317
$523$	−4.51329	−0.197353	−0.0986763	−	0.995120i	$-0.531461\pi$
$523$	−4.51329	−0.197353	−0.0986763	+	0.995120i	$0.531461\pi$
$524$	−1.97121	−0.0861128
$525$	−27.9836	−1.22130
$526$	2.95693	0.128928
$527$	−0.812608	−0.0353978
$528$	−7.08289	−0.308243
$529$	−13.7145	−0.596284
$530$	4.52936	0.196743
$531$	6.41026	0.278181
$532$	−18.7098	−0.811171
$533$	−4.10257	−0.177702
$534$	−0.756842	−0.0327517
$535$	−53.1115	−2.29621
$536$	2.19006	0.0945963
$537$	28.1739	1.21579
$538$	3.38373	0.145883
$539$	−4.12707	−0.177765
$540$	35.0655	1.50898
$541$	16.6375	0.715304	0.357652	−	0.933855i	$-0.383577\pi$
$541$	16.6375	0.715304	0.357652	+	0.933855i	$0.383577\pi$
$542$	1.00836	0.0433128
$543$	−2.28924	−0.0982409
$544$	1.04093	0.0446295
$545$	71.4514	3.06064
$546$	0.375909	0.0160874
$547$	−19.7965	−0.846436	−0.423218	−	0.906028i	$-0.639100\pi$
$547$	−19.7965	−0.846436	−0.423218	+	0.906028i	$0.639100\pi$
$548$	15.8775	0.678253
$549$	4.13612	0.176526
$550$	−1.51396	−0.0645557
$551$	−44.9400	−1.91451
$552$	−3.79886	−0.161690
$553$	18.2834	0.777489
$554$	−1.40778	−0.0598107
$555$	−52.9263	−2.24660
$556$	13.7048	0.581214
$557$	16.9738	0.719201	0.359601	−	0.933106i	$-0.382913\pi$
$557$	16.9738	0.719201	0.359601	+	0.933106i	$0.382913\pi$
$558$	−0.111990	−0.00474091
$559$	3.83452	0.162183
$560$	−24.2111	−1.02310
$561$	0.964386	0.0407164
$562$	4.26485	0.179902
$563$	30.8525	1.30028	0.650138	−	0.759816i	$-0.274711\pi$
$563$	30.8525	1.30028	0.650138	+	0.759816i	$0.274711\pi$
$564$	−32.8639	−1.38382
$565$	48.8710	2.05602
$566$	−5.53260	−0.232553
$567$	−17.1037	−0.718290
$568$	−6.79411	−0.285075
$569$	−40.8503	−1.71253	−0.856266	−	0.516535i	$-0.827222\pi$
$569$	−40.8503	−1.71253	−0.856266	+	0.516535i	$0.827222\pi$
$570$	−6.55945	−0.274745
$571$	21.3968	0.895429	0.447714	−	0.894177i	$-0.352238\pi$
$571$	21.3968	0.895429	0.447714	+	0.894177i	$0.352238\pi$
$572$	−1.39259	−0.0582273
$573$	−11.6732	−0.487653
$574$	1.67005	0.0697066
$575$	27.1904	1.13392
$576$	−3.09795	−0.129081
$577$	−39.5247	−1.64544	−0.822718	−	0.568449i	$-0.807543\pi$
$577$	−39.5247	−1.64544	−0.822718	+	0.568449i	$0.807543\pi$
$578$	2.83827	0.118057
$579$	−17.8814	−0.743125
$580$	−59.0285	−2.45103
$581$	−10.5412	−0.437323
$582$	4.71362	0.195386
$583$	7.15431	0.296301
$584$	−6.58960	−0.272680
$585$	−1.11604	−0.0461424
$586$	2.21960	0.0916910
$587$	−43.1312	−1.78021	−0.890107	−	0.455751i	$-0.849371\pi$
$587$	−43.1312	−1.78021	−0.890107	+	0.455751i	$0.849371\pi$
$588$	−15.0523	−0.620745
$589$	8.73029	0.359725
$590$	9.58571	0.394638
$591$	−5.18638	−0.213339
$592$	−29.3468	−1.20615
$593$	31.6926	1.30146	0.650729	−	0.759310i	$-0.274463\pi$
$593$	31.6926	1.30146	0.650729	+	0.759310i	$0.274463\pi$
$594$	−0.808873	−0.0331885
$595$	3.29651	0.135144
$596$	21.3812	0.875809
$597$	−26.3427	−1.07813
$598$	−0.365253	−0.0149363
$599$	−7.66688	−0.313260	−0.156630	−	0.987657i	$-0.550063\pi$
$599$	−7.66688	−0.313260	−0.156630	+	0.987657i	$0.550063\pi$
$600$	−11.1241	−0.454140
$601$	−44.1467	−1.80078	−0.900390	−	0.435084i	$-0.856719\pi$
$601$	−44.1467	−1.80078	−0.900390	+	0.435084i	$0.856719\pi$
$602$	−1.56093	−0.0636190
$603$	1.37611	0.0560393
$604$	−33.4933	−1.36283
$605$	−3.73136	−0.151701
$606$	0.398168	0.0161745
$607$	45.0640	1.82909	0.914546	−	0.404481i	$-0.132548\pi$
$607$	45.0640	1.82909	0.914546	+	0.404481i	$0.132548\pi$
$608$	−11.1833	−0.453542
$609$	25.1681	1.01986
$610$	6.18504	0.250425
$611$	−6.36574	−0.257530
$612$	0.434988	0.0175834
$613$	−18.1499	−0.733068	−0.366534	−	0.930405i	$-0.619456\pi$
$613$	−18.1499	−0.733068	−0.366534	+	0.930405i	$0.619456\pi$
$614$	4.68496	0.189070
$615$	−40.0922	−1.61667
$616$	1.14206	0.0460148
$617$	−18.6177	−0.749522	−0.374761	−	0.927121i	$-0.622275\pi$
$617$	−18.6177	−0.749522	−0.374761	+	0.927121i	$0.622275\pi$
$618$	−5.59914	−0.225230
$619$	7.95905	0.319901	0.159951	−	0.987125i	$-0.448866\pi$
$619$	7.95905	0.319901	0.159951	+	0.987125i	$0.448866\pi$
$620$	11.4672	0.460534
$621$	14.5272	0.582955
$622$	0.135552	0.00543513
$623$	−4.08639	−0.163718
$624$	−5.00382	−0.200313
$625$	10.0058	0.400231
$626$	−2.51046	−0.100338
$627$	−10.3609	−0.413776
$628$	24.0710	0.960536
$629$	3.99578	0.159322
$630$	0.454309	0.0181001
$631$	6.83700	0.272177	0.136088	−	0.990697i	$-0.456547\pi$
$631$	6.83700	0.272177	0.136088	+	0.990697i	$0.456547\pi$
$632$	7.26807	0.289108
$633$	−35.5191	−1.41176
$634$	−3.59698	−0.142854
$635$	0.754228	0.0299306
$636$	26.0932	1.03466
$637$	−2.91563	−0.115521
$638$	1.36164	0.0539079
$639$	−4.26902	−0.168880
$640$	−19.5363	−0.772241
$641$	3.02283	0.119394	0.0596972	−	0.998217i	$-0.480986\pi$
$641$	3.02283	0.119394	0.0596972	+	0.998217i	$0.480986\pi$
$642$	4.46838	0.176353
$643$	−9.62454	−0.379555	−0.189777	−	0.981827i	$-0.560777\pi$
$643$	−9.62454	−0.379555	−0.189777	+	0.981827i	$0.560777\pi$
$644$	−10.1812	−0.401194
$645$	37.4727	1.47549
$646$	0.495219	0.0194841
$647$	−21.1105	−0.829939	−0.414970	−	0.909835i	$-0.636208\pi$
$647$	−21.1105	−0.829939	−0.414970	+	0.909835i	$0.636208\pi$
$648$	−6.79913	−0.267095
$649$	15.1410	0.594337
$650$	−1.06956	−0.0419517
$651$	−4.88930	−0.191627
$652$	14.1434	0.553898
$653$	−9.03588	−0.353601	−0.176801	−	0.984247i	$-0.556575\pi$
$653$	−9.03588	−0.353601	−0.176801	+	0.984247i	$0.556575\pi$
$654$	−6.01135	−0.235062
$655$	−3.73136	−0.145796
$656$	−22.2305	−0.867955
$657$	−4.14051	−0.161537
$658$	2.59133	0.101021
$659$	−46.2534	−1.80178	−0.900888	−	0.434052i	$-0.857083\pi$
$659$	−46.2534	−1.80178	−0.900888	+	0.434052i	$0.857083\pi$
$660$	−13.6090	−0.529732
$661$	−10.3055	−0.400838	−0.200419	−	0.979710i	$-0.564230\pi$
$661$	−10.3055	−0.400838	−0.200419	+	0.979710i	$0.564230\pi$
$662$	3.92484	0.152543
$663$	0.681306	0.0264597
$664$	−4.19037	−0.162618
$665$	−35.4162	−1.37338
$666$	0.550679	0.0213384
$667$	−24.4547	−0.946891
$668$	7.80631	0.302035
$669$	32.9473	1.27382
$670$	2.05779	0.0794993
$671$	9.76953	0.377149
$672$	6.26307	0.241603
$673$	3.83786	0.147939	0.0739693	−	0.997261i	$-0.476433\pi$
$673$	3.83786	0.147939	0.0739693	+	0.997261i	$0.476433\pi$
$674$	2.60908	0.100498
$675$	42.5396	1.63735
$676$	24.6419	0.947767
$677$	20.9587	0.805507	0.402753	−	0.915309i	$-0.368053\pi$
$677$	20.9587	0.805507	0.402753	+	0.915309i	$0.368053\pi$
$678$	−4.11161	−0.157906
$679$	25.4501	0.976683
$680$	1.31044	0.0502530
$681$	−15.8644	−0.607923
$682$	−0.264520	−0.0101290
$683$	−6.73646	−0.257763	−0.128882	−	0.991660i	$-0.541139\pi$
$683$	−6.73646	−0.257763	−0.128882	+	0.991660i	$0.541139\pi$
$684$	−4.67332	−0.178689
$685$	30.0549	1.14834
$686$	3.19996	0.122175
$687$	43.5104	1.66003
$688$	20.7780	0.792155
$689$	5.05427	0.192552
$690$	−3.56942	−0.135885
$691$	5.38833	0.204982	0.102491	−	0.994734i	$-0.467319\pi$
$691$	5.38833	0.204982	0.102491	+	0.994734i	$0.467319\pi$
$692$	−20.8296	−0.791822
$693$	0.717601	0.0272594
$694$	−3.99590	−0.151682
$695$	25.9422	0.984045
$696$	10.0049	0.379235
$697$	3.02684	0.114650
$698$	3.20595	0.121347
$699$	7.92774	0.299855
$700$	−29.8133	−1.12684
$701$	−7.23905	−0.273415	−0.136708	−	0.990611i	$-0.543652\pi$
$701$	−7.23905	−0.273415	−0.136708	+	0.990611i	$0.543652\pi$
$702$	−0.571441	−0.0215677
$703$	−42.9288	−1.61909
$704$	−7.31736	−0.275784
$705$	−62.2089	−2.34292
$706$	−0.805062	−0.0302989
$707$	2.14981	0.0808521
$708$	55.2225	2.07539
$709$	−19.5149	−0.732898	−0.366449	−	0.930438i	$-0.619427\pi$
$709$	−19.5149	−0.732898	−0.366449	+	0.930438i	$0.619427\pi$
$710$	−6.38377	−0.239579
$711$	4.56682	0.171269
$712$	−1.62443	−0.0608781
$713$	4.75071	0.177915
$714$	−0.277342	−0.0103793
$715$	−2.63608	−0.0985838
$716$	30.0160	1.12175
$717$	53.7785	2.00839
$718$	3.80671	0.142065
$719$	−17.1330	−0.638952	−0.319476	−	0.947594i	$-0.603507\pi$
$719$	−17.1330	−0.638952	−0.319476	+	0.947594i	$0.603507\pi$
$720$	−6.04743	−0.225375
$721$	−30.2312	−1.12587
$722$	−2.09671	−0.0780313
$723$	−39.3379	−1.46299
$724$	−2.43893	−0.0906420
$725$	−71.6102	−2.65954
$726$	0.313927	0.0116509
$727$	21.8597	0.810732	0.405366	−	0.914155i	$-0.367144\pi$
$727$	21.8597	0.810732	0.405366	+	0.914155i	$0.367144\pi$
$728$	0.806823	0.0299029
$729$	22.1901	0.821856
$730$	−6.19161	−0.229162
$731$	−2.82908	−0.104637
$732$	35.6315	1.31698
$733$	23.2014	0.856965	0.428482	−	0.903550i	$-0.359048\pi$
$733$	23.2014	0.856965	0.428482	+	0.903550i	$0.359048\pi$
$734$	3.89010	0.143586
$735$	−28.4928	−1.05097
$736$	−6.08554	−0.224316
$737$	3.25036	0.119729
$738$	0.417145	0.0153553
$739$	5.25297	0.193234	0.0966168	−	0.995322i	$-0.469198\pi$
$739$	5.25297	0.193234	0.0966168	+	0.995322i	$0.469198\pi$
$740$	−56.3869	−2.07282
$741$	−7.31964	−0.268894
$742$	−2.05746	−0.0755318
$743$	−18.3377	−0.672744	−0.336372	−	0.941729i	$-0.609200\pi$
$743$	−18.3377	−0.672744	−0.336372	+	0.941729i	$0.609200\pi$
$744$	−1.94361	−0.0712561
$745$	40.4731	1.48282
$746$	4.25076	0.155631
$747$	−2.63298	−0.0963357
$748$	1.02744	0.0375670
$749$	24.1259	0.881543
$750$	−4.59538	−0.167800
$751$	33.0227	1.20502	0.602508	−	0.798113i	$-0.294168\pi$
$751$	33.0227	1.20502	0.602508	+	0.798113i	$0.294168\pi$
$752$	−34.4939	−1.25786
$753$	−19.6379	−0.715646
$754$	0.961953	0.0350322
$755$	−63.4005	−2.30738
$756$	−15.9285	−0.579314
$757$	−30.7380	−1.11719	−0.558597	−	0.829439i	$-0.688660\pi$
$757$	−30.7380	−1.11719	−0.558597	+	0.829439i	$0.688660\pi$
$758$	4.04182	0.146805
$759$	−5.63805	−0.204648
$760$	−14.0787	−0.510690
$761$	41.6276	1.50900	0.754499	−	0.656301i	$-0.227880\pi$
$761$	41.6276	1.50900	0.754499	+	0.656301i	$0.227880\pi$
$762$	−0.0634547	−0.00229872
$763$	−32.4568	−1.17502
$764$	−12.4364	−0.449933
$765$	0.823401	0.0297701
$766$	3.73200	0.134842
$767$	10.6966	0.386232
$768$	−25.4341	−0.917773
$769$	22.3836	0.807173	0.403587	−	0.914941i	$-0.367763\pi$
$769$	22.3836	0.807173	0.403587	+	0.914941i	$0.367763\pi$
$770$	1.07308	0.0386711
$771$	−19.6473	−0.707580
$772$	−19.0506	−0.685645
$773$	43.0000	1.54660	0.773302	−	0.634038i	$-0.218604\pi$
$773$	43.0000	1.54660	0.773302	+	0.634038i	$0.218604\pi$
$774$	−0.389890	−0.0140143
$775$	13.9114	0.499712
$776$	10.1170	0.363178
$777$	24.0418	0.862495
$778$	−1.44506	−0.0518080
$779$	−32.5190	−1.16511
$780$	−9.61433	−0.344248
$781$	−10.0834	−0.360813
$782$	0.269481	0.00963660
$783$	−38.2596	−1.36729
$784$	−15.7988	−0.564244
$785$	45.5646	1.62627
$786$	0.313927	0.0111974
$787$	−46.4223	−1.65478	−0.827388	−	0.561631i	$-0.810174\pi$
$787$	−46.4223	−1.65478	−0.827388	+	0.561631i	$0.810174\pi$
$788$	−5.52549	−0.196837
$789$	32.2453	1.14796
$790$	6.82910	0.242968
$791$	−22.1997	−0.789329
$792$	0.285262	0.0101364
$793$	6.90184	0.245091
$794$	−2.55249	−0.0905846
$795$	49.3926	1.75178
$796$	−28.0651	−0.994742
$797$	19.6731	0.696857	0.348428	−	0.937335i	$-0.386715\pi$
$797$	19.6731	0.696857	0.348428	+	0.937335i	$0.386715\pi$
$798$	2.97963	0.105478
$799$	4.69659	0.166153
$800$	−17.8202	−0.630038
$801$	−1.02070	−0.0360645
$802$	1.64511	0.0580908
$803$	−9.77990	−0.345125
$804$	11.8547	0.418084
$805$	−19.2722	−0.679257
$806$	−0.186874	−0.00658236
$807$	36.8996	1.29893
$808$	0.854600	0.0300647
$809$	−15.6349	−0.549694	−0.274847	−	0.961488i	$-0.588627\pi$
$809$	−15.6349	−0.549694	−0.274847	+	0.961488i	$0.588627\pi$
$810$	−6.38848	−0.224468
$811$	23.4806	0.824516	0.412258	−	0.911067i	$-0.364740\pi$
$811$	23.4806	0.824516	0.412258	+	0.911067i	$0.364740\pi$
$812$	26.8137	0.940978
$813$	10.9962	0.385653
$814$	1.30071	0.0455897
$815$	26.7724	0.937796
$816$	3.69177	0.129238
$817$	30.3943	1.06336
$818$	−3.09291	−0.108141
$819$	0.506960	0.0177146
$820$	−42.7136	−1.49162
$821$	−19.3735	−0.676139	−0.338070	−	0.941121i	$-0.609774\pi$
$821$	−19.3735	−0.676139	−0.338070	+	0.941121i	$0.609774\pi$
$822$	−2.52858	−0.0881944
$823$	41.2602	1.43824	0.719120	−	0.694886i	$-0.244545\pi$
$823$	41.2602	1.43824	0.719120	+	0.694886i	$0.244545\pi$
$824$	−12.0176	−0.418653
$825$	−16.5098	−0.574796
$826$	−4.35431	−0.151506
$827$	−31.5500	−1.09710	−0.548551	−	0.836117i	$-0.684820\pi$
$827$	−31.5500	−1.09710	−0.548551	+	0.836117i	$0.684820\pi$
$828$	−2.54305	−0.0883771
$829$	42.0294	1.45974	0.729870	−	0.683586i	$-0.239581\pi$
$829$	42.0294	1.45974	0.729870	+	0.683586i	$0.239581\pi$
$830$	−3.93728	−0.136665
$831$	−15.3518	−0.532548
$832$	−5.16947	−0.179219
$833$	2.15113	0.0745321
$834$	−2.18257	−0.0755762
$835$	14.7768	0.511372
$836$	−11.0384	−0.381770
$837$	7.43252	0.256905
$838$	−3.75262	−0.129632
$839$	−1.20123	−0.0414711	−0.0207355	−	0.999785i	$-0.506601\pi$
$839$	−1.20123	−0.0414711	−0.0207355	+	0.999785i	$0.506601\pi$
$840$	7.88464	0.272046
$841$	35.4054	1.22088
$842$	−1.53535	−0.0529116
$843$	46.5081	1.60182
$844$	−37.8415	−1.30256
$845$	46.6454	1.60465
$846$	0.647261	0.0222533
$847$	1.69497	0.0582400
$848$	27.3874	0.940488
$849$	−60.3330	−2.07062
$850$	0.789114	0.0270664
$851$	−23.3603	−0.800782
$852$	−36.7763	−1.25994
$853$	9.60648	0.328920	0.164460	−	0.986384i	$-0.447412\pi$
$853$	9.60648	0.328920	0.164460	+	0.986384i	$0.447412\pi$
$854$	−2.80956	−0.0961411
$855$	−8.84625	−0.302535
$856$	9.59061	0.327800
$857$	45.1086	1.54088	0.770441	−	0.637511i	$-0.220036\pi$
$857$	45.1086	1.54088	0.770441	+	0.637511i	$0.220036\pi$
$858$	0.221779	0.00757139
$859$	54.0072	1.84270	0.921350	−	0.388733i	$-0.127087\pi$
$859$	54.0072	1.84270	0.921350	+	0.388733i	$0.127087\pi$
$860$	39.9228	1.36136
$861$	18.2119	0.620660
$862$	2.93827	0.100078
$863$	33.0125	1.12376	0.561879	−	0.827220i	$-0.310079\pi$
$863$	33.0125	1.12376	0.561879	+	0.827220i	$0.310079\pi$
$864$	−9.52087	−0.323907
$865$	−39.4289	−1.34062
$866$	−2.01253	−0.0683886
$867$	30.9513	1.05116
$868$	−5.20899	−0.176804
$869$	10.7868	0.365919
$870$	9.40063	0.318711
$871$	2.29627	0.0778061
$872$	−12.9023	−0.436928
$873$	6.35691	0.215149
$874$	−2.89518	−0.0979308
$875$	−24.8117	−0.838787
$876$	−35.6693	−1.20515
$877$	−33.3170	−1.12504	−0.562518	−	0.826785i	$-0.690167\pi$
$877$	−33.3170	−1.12504	−0.562518	+	0.826785i	$0.690167\pi$
$878$	0.907838	0.0306380
$879$	24.2048	0.816406
$880$	−14.2840	−0.481515
$881$	−50.5974	−1.70467	−0.852334	−	0.522998i	$-0.824814\pi$
$881$	−50.5974	−1.70467	−0.852334	+	0.522998i	$0.824814\pi$
$882$	0.296458	0.00998226
$883$	−0.190888	−0.00642388	−0.00321194	−	0.999995i	$-0.501022\pi$
$883$	−0.190888	−0.00642388	−0.00321194	+	0.999995i	$0.501022\pi$
$884$	0.725853	0.0244131
$885$	104.532	3.51381
$886$	3.23321	0.108622
$887$	24.0851	0.808697	0.404349	−	0.914605i	$-0.367498\pi$
$887$	24.0851	0.808697	0.404349	+	0.914605i	$0.367498\pi$
$888$	9.55716	0.320717
$889$	−0.342608	−0.0114907
$890$	−1.52632	−0.0511624
$891$	−10.0909	−0.338057
$892$	35.1015	1.17529
$893$	−50.4580	−1.68851
$894$	−3.40508	−0.113883
$895$	56.8181	1.89922
$896$	8.87438	0.296472
$897$	−3.98308	−0.132991
$898$	5.36068	0.178888
$899$	−12.5117	−0.417290
$900$	−7.44676	−0.248225
$901$	−3.72899	−0.124231
$902$	0.985297	0.0328068
$903$	−17.0220	−0.566456
$904$	−8.82487	−0.293511
$905$	−4.61671	−0.153465
$906$	5.33401	0.177211
$907$	−0.0488386	−0.00162166	−0.000810830	−	1.00000i	$-0.500258\pi$
$907$	−0.0488386	−0.00162166	−0.000810830		1.00000i	$0.500258\pi$
$908$	−16.9016	−0.560901
$909$	0.536980	0.0178105
$910$	0.758094	0.0251306
$911$	−39.1384	−1.29671	−0.648356	−	0.761337i	$-0.724543\pi$
$911$	−39.1384	−1.29671	−0.648356	+	0.761337i	$0.724543\pi$
$912$	−39.6627	−1.31336
$913$	−6.21910	−0.205822
$914$	0.802814	0.0265547
$915$	67.4478	2.22976
$916$	46.3553	1.53162
$917$	1.69497	0.0559729
$918$	0.421604	0.0139150
$919$	−29.7830	−0.982451	−0.491225	−	0.871033i	$-0.663451\pi$
$919$	−29.7830	−0.982451	−0.491225	+	0.871033i	$0.663451\pi$
$920$	−7.66115	−0.252581
$921$	51.0895	1.68345
$922$	−3.09542	−0.101942
$923$	−7.12359	−0.234476
$924$	6.18192	0.203370
$925$	−68.4056	−2.24916
$926$	1.19385	0.0392322
$927$	−7.55114	−0.248012
$928$	16.0272	0.526120
$929$	7.57004	0.248365	0.124183	−	0.992259i	$-0.460369\pi$
$929$	7.57004	0.248365	0.124183	+	0.992259i	$0.460369\pi$
$930$	−1.82622	−0.0598841
$931$	−23.1107	−0.757423
$932$	8.44609	0.276661
$933$	1.47819	0.0483938
$934$	2.22340	0.0727517
$935$	1.94487	0.0636042
$936$	0.201528	0.00658715
$937$	54.2383	1.77189	0.885944	−	0.463793i	$-0.153512\pi$
$937$	54.2383	1.77189	0.885944	+	0.463793i	$0.153512\pi$
$938$	−0.934751	−0.0305207
$939$	−27.3765	−0.893399
$940$	−66.2764	−2.16170
$941$	−18.7474	−0.611146	−0.305573	−	0.952169i	$-0.598848\pi$
$941$	−18.7474	−0.611146	−0.305573	+	0.952169i	$0.598848\pi$
$942$	−3.83344	−0.124900
$943$	−17.6957	−0.576250
$944$	57.9614	1.88648
$945$	−30.1515	−0.980829
$946$	−0.920920	−0.0299417
$947$	−5.67738	−0.184490	−0.0922451	−	0.995736i	$-0.529404\pi$
$947$	−5.67738	−0.184490	−0.0922451	+	0.995736i	$0.529404\pi$
$948$	39.3418	1.27776
$949$	−6.90916	−0.224281
$950$	−8.47788	−0.275059
$951$	−39.2251	−1.27196
$952$	−0.595267	−0.0192927
$953$	−4.83583	−0.156648	−0.0783240	−	0.996928i	$-0.524957\pi$
$953$	−4.83583	−0.156648	−0.0783240	+	0.996928i	$0.524957\pi$
$954$	−0.513912	−0.0166385
$955$	−23.5412	−0.761776
$956$	57.2948	1.85305
$957$	14.8487	0.479990
$958$	−1.74650	−0.0564268
$959$	−13.6525	−0.440861
$960$	−50.5183	−1.63047
$961$	−28.5694	−0.921594
$962$	0.918903	0.0296266
$963$	6.02617	0.194191
$964$	−41.9100	−1.34983
$965$	−36.0613	−1.16086
$966$	1.62141	0.0521680
$967$	58.0129	1.86557	0.932784	−	0.360436i	$-0.117372\pi$
$967$	58.0129	1.86557	0.932784	+	0.360436i	$0.117372\pi$
$968$	0.673790	0.0216564
$969$	5.40036	0.173485
$970$	9.50594	0.305217
$971$	−24.1014	−0.773452	−0.386726	−	0.922195i	$-0.626394\pi$
$971$	−24.1014	−0.773452	−0.386726	+	0.922195i	$0.626394\pi$
$972$	−8.61097	−0.276197
$973$	−11.7843	−0.377786
$974$	−4.29910	−0.137752
$975$	−11.6636	−0.373534
$976$	37.3988	1.19711
$977$	20.9187	0.669249	0.334625	−	0.942352i	$-0.391391\pi$
$977$	20.9187	0.669249	0.334625	+	0.942352i	$0.391391\pi$
$978$	−2.25241	−0.0720243
$979$	−2.41089	−0.0770522
$980$	−30.3558	−0.969682
$981$	−8.10706	−0.258838
$982$	−0.962237	−0.0307062
$983$	−6.65887	−0.212385	−0.106193	−	0.994346i	$-0.533866\pi$
$983$	−6.65887	−0.212385	−0.106193	+	0.994346i	$0.533866\pi$
$984$	7.23964	0.230791
$985$	−10.4594	−0.333263
$986$	−0.709720	−0.0226021
$987$	28.2584	0.899476
$988$	−7.79823	−0.248095
$989$	16.5395	0.525925
$990$	0.268033	0.00851866
$991$	−19.3853	−0.615794	−0.307897	−	0.951420i	$-0.599625\pi$
$991$	−19.3853	−0.615794	−0.307897	+	0.951420i	$0.599625\pi$
$992$	−3.11354	−0.0988550
$993$	42.8003	1.35823
$994$	2.89983	0.0919770
$995$	−53.1252	−1.68418
$996$	−22.6823	−0.718717
$997$	1.44161	0.0456562	0.0228281	−	0.999739i	$-0.492733\pi$
$997$	1.44161	0.0456562	0.0228281	+	0.999739i	$0.492733\pi$
$998$	0.793734	0.0251252
$999$	−36.5474	−1.15631

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.c.1.13	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.c.1.13	✓	23	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-0.169669 q^{2} -1.85024 q^{3} -1.97121 q^{4} -3.73136 q^{5} +0.313927 q^{6} +1.69497 q^{7} +0.673790 q^{8} +0.423370 q^{9} +O(q^{10})\)	\(q-0.169669 q^{2} -1.85024 q^{3} -1.97121 q^{4} -3.73136 q^{5} +0.313927 q^{6} +1.69497 q^{7} +0.673790 q^{8} +0.423370 q^{9} +0.633095 q^{10} +1.00000 q^{11} +3.64721 q^{12} +0.706466 q^{13} -0.287584 q^{14} +6.90390 q^{15} +3.82810 q^{16} -0.521224 q^{17} -0.0718326 q^{18} +5.59979 q^{19} +7.35531 q^{20} -3.13610 q^{21} -0.169669 q^{22} +3.04720 q^{23} -1.24667 q^{24} +8.92307 q^{25} -0.119865 q^{26} +4.76737 q^{27} -3.34115 q^{28} -8.02530 q^{29} -1.17137 q^{30} +1.55904 q^{31} -1.99709 q^{32} -1.85024 q^{33} +0.0884353 q^{34} -6.32456 q^{35} -0.834552 q^{36} -7.66615 q^{37} -0.950109 q^{38} -1.30713 q^{39} -2.51416 q^{40} -5.80718 q^{41} +0.532098 q^{42} +5.42776 q^{43} -1.97121 q^{44} -1.57975 q^{45} -0.517015 q^{46} -9.01069 q^{47} -7.08289 q^{48} -4.12707 q^{49} -1.51396 q^{50} +0.964386 q^{51} -1.39259 q^{52} +7.15431 q^{53} -0.808873 q^{54} -3.73136 q^{55} +1.14206 q^{56} -10.3609 q^{57} +1.36164 q^{58} +15.1410 q^{59} -13.6090 q^{60} +9.76953 q^{61} -0.264520 q^{62} +0.717601 q^{63} -7.31736 q^{64} -2.63608 q^{65} +0.313927 q^{66} +3.25036 q^{67} +1.02744 q^{68} -5.63805 q^{69} +1.07308 q^{70} -10.0834 q^{71} +0.285262 q^{72} -9.77990 q^{73} +1.30071 q^{74} -16.5098 q^{75} -11.0384 q^{76} +1.69497 q^{77} +0.221779 q^{78} +10.7868 q^{79} -14.2840 q^{80} -10.0909 q^{81} +0.985297 q^{82} -6.21910 q^{83} +6.18192 q^{84} +1.94487 q^{85} -0.920920 q^{86} +14.8487 q^{87} +0.673790 q^{88} -2.41089 q^{89} +0.268033 q^{90} +1.19744 q^{91} -6.00669 q^{92} -2.88459 q^{93} +1.52883 q^{94} -20.8948 q^{95} +3.69509 q^{96} +15.0150 q^{97} +0.700234 q^{98} +0.423370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

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