LMFDB - Embedded newform 1441.2.a.d.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.06686 q^{2} -1.75987 q^{3} +2.27189 q^{4} -3.28939 q^{5} +3.63739 q^{6} +1.71043 q^{7} -0.561957 q^{8} +0.0971338 q^{9} +O(q^{10})$	\(q-2.06686 q^{2} -1.75987 q^{3} +2.27189 q^{4} -3.28939 q^{5} +3.63739 q^{6} +1.71043 q^{7} -0.561957 q^{8} +0.0971338 q^{9} +6.79870 q^{10} -1.00000 q^{11} -3.99823 q^{12} -0.888858 q^{13} -3.53521 q^{14} +5.78889 q^{15} -3.38230 q^{16} -3.91293 q^{17} -0.200761 q^{18} +4.66703 q^{19} -7.47314 q^{20} -3.01013 q^{21} +2.06686 q^{22} -1.83812 q^{23} +0.988970 q^{24} +5.82010 q^{25} +1.83714 q^{26} +5.10866 q^{27} +3.88591 q^{28} -3.68986 q^{29} -11.9648 q^{30} +4.99113 q^{31} +8.11463 q^{32} +1.75987 q^{33} +8.08747 q^{34} -5.62628 q^{35} +0.220677 q^{36} +10.3016 q^{37} -9.64608 q^{38} +1.56427 q^{39} +1.84850 q^{40} +5.34159 q^{41} +6.22151 q^{42} +3.85171 q^{43} -2.27189 q^{44} -0.319511 q^{45} +3.79913 q^{46} +3.02305 q^{47} +5.95239 q^{48} -4.07442 q^{49} -12.0293 q^{50} +6.88625 q^{51} -2.01939 q^{52} +3.10542 q^{53} -10.5589 q^{54} +3.28939 q^{55} -0.961189 q^{56} -8.21336 q^{57} +7.62640 q^{58} +5.11732 q^{59} +13.1517 q^{60} -9.85925 q^{61} -10.3159 q^{62} +0.166141 q^{63} -10.0072 q^{64} +2.92380 q^{65} -3.63739 q^{66} +0.818983 q^{67} -8.88976 q^{68} +3.23485 q^{69} +11.6287 q^{70} +4.11340 q^{71} -0.0545850 q^{72} -4.99865 q^{73} -21.2919 q^{74} -10.2426 q^{75} +10.6030 q^{76} -1.71043 q^{77} -3.23313 q^{78} -8.24990 q^{79} +11.1257 q^{80} -9.28197 q^{81} -11.0403 q^{82} +7.27751 q^{83} -6.83869 q^{84} +12.8712 q^{85} -7.96092 q^{86} +6.49366 q^{87} +0.561957 q^{88} -7.61243 q^{89} +0.660383 q^{90} -1.52033 q^{91} -4.17601 q^{92} -8.78373 q^{93} -6.24820 q^{94} -15.3517 q^{95} -14.2807 q^{96} -6.15264 q^{97} +8.42124 q^{98} -0.0971338 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * 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 $

$2$	−2.06686	−1.46149	−0.730744	−	0.682652i	$-0.760827\pi$
$2$	−2.06686	−1.46149	−0.730744	+	0.682652i	$0.760827\pi$
$3$	−1.75987	−1.01606	−0.508030	−	0.861339i	$-0.669626\pi$
$3$	−1.75987	−1.01606	−0.508030	+	0.861339i	$0.669626\pi$
$4$	2.27189	1.13594
$5$	−3.28939	−1.47106	−0.735530	−	0.677492i	$-0.763067\pi$
$5$	−3.28939	−1.47106	−0.735530	+	0.677492i	$0.763067\pi$
$6$	3.63739	1.48496
$7$	1.71043	0.646482	0.323241	−	0.946317i	$-0.395227\pi$
$7$	1.71043	0.646482	0.323241	+	0.946317i	$0.395227\pi$
$8$	−0.561957	−0.198682
$9$	0.0971338	0.0323779
$10$	6.79870	2.14994
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.99823	−1.15419
$13$	−0.888858	−0.246525	−0.123262	−	0.992374i	$-0.539336\pi$
$13$	−0.888858	−0.246525	−0.123262	+	0.992374i	$0.539336\pi$
$14$	−3.53521	−0.944826
$15$	5.78889	1.49469
$16$	−3.38230	−0.845574
$17$	−3.91293	−0.949026	−0.474513	−	0.880249i	$-0.657376\pi$
$17$	−3.91293	−0.949026	−0.474513	+	0.880249i	$0.657376\pi$
$18$	−0.200761	−0.0473199
$19$	4.66703	1.07069	0.535345	−	0.844633i	$-0.320181\pi$
$19$	4.66703	1.07069	0.535345	+	0.844633i	$0.320181\pi$
$20$	−7.47314	−1.67104
$21$	−3.01013	−0.656865
$22$	2.06686	0.440655
$23$	−1.83812	−0.383275	−0.191637	−	0.981466i	$-0.561380\pi$
$23$	−1.83812	−0.383275	−0.191637	+	0.981466i	$0.561380\pi$
$24$	0.988970	0.201873
$25$	5.82010	1.16402
$26$	1.83714	0.360293
$27$	5.10866	0.983162
$28$	3.88591	0.734368
$29$	−3.68986	−0.685190	−0.342595	−	0.939483i	$-0.611306\pi$
$29$	−3.68986	−0.685190	−0.342595	+	0.939483i	$0.611306\pi$
$30$	−11.9648	−2.18446
$31$	4.99113	0.896433	0.448217	−	0.893925i	$-0.352059\pi$
$31$	4.99113	0.896433	0.448217	+	0.893925i	$0.352059\pi$
$32$	8.11463	1.43448
$33$	1.75987	0.306354
$34$	8.08747	1.38699
$35$	−5.62628	−0.951015
$36$	0.220677	0.0367795
$37$	10.3016	1.69357	0.846785	−	0.531935i	$-0.178535\pi$
$37$	10.3016	1.69357	0.846785	+	0.531935i	$0.178535\pi$
$38$	−9.64608	−1.56480
$39$	1.56427	0.250484
$40$	1.84850	0.292273
$41$	5.34159	0.834216	0.417108	−	0.908857i	$-0.363044\pi$
$41$	5.34159	0.834216	0.417108	+	0.908857i	$0.363044\pi$
$42$	6.22151	0.960000
$43$	3.85171	0.587380	0.293690	−	0.955901i	$-0.405117\pi$
$43$	3.85171	0.587380	0.293690	+	0.955901i	$0.405117\pi$
$44$	−2.27189	−0.342500
$45$	−0.319511	−0.0476299
$46$	3.79913	0.560151
$47$	3.02305	0.440957	0.220478	−	0.975392i	$-0.429238\pi$
$47$	3.02305	0.440957	0.220478	+	0.975392i	$0.429238\pi$
$48$	5.95239	0.859154
$49$	−4.07442	−0.582061
$50$	−12.0293	−1.70120
$51$	6.88625	0.964267
$52$	−2.01939	−0.280039
$53$	3.10542	0.426563	0.213281	−	0.976991i	$-0.431585\pi$
$53$	3.10542	0.426563	0.213281	+	0.976991i	$0.431585\pi$
$54$	−10.5589	−1.43688
$55$	3.28939	0.443542
$56$	−0.961189	−0.128444
$57$	−8.21336	−1.08789
$58$	7.62640	1.00140
$59$	5.11732	0.666219	0.333109	−	0.942888i	$-0.391902\pi$
$59$	5.11732	0.666219	0.333109	+	0.942888i	$0.391902\pi$
$60$	13.1517	1.69788
$61$	−9.85925	−1.26235	−0.631174	−	0.775642i	$-0.717426\pi$
$61$	−9.85925	−1.26235	−0.631174	+	0.775642i	$0.717426\pi$
$62$	−10.3159	−1.31013
$63$	0.166141	0.0209318
$64$	−10.0072	−1.25090
$65$	2.92380	0.362653
$66$	−3.63739	−0.447732
$67$	0.818983	0.100055	0.0500274	−	0.998748i	$-0.484069\pi$
$67$	0.818983	0.100055	0.0500274	+	0.998748i	$0.484069\pi$
$68$	−8.88976	−1.07804
$69$	3.23485	0.389430
$70$	11.6287	1.38990
$71$	4.11340	0.488171	0.244086	−	0.969754i	$-0.421512\pi$
$71$	4.11340	0.488171	0.244086	+	0.969754i	$0.421512\pi$
$72$	−0.0545850	−0.00643291
$73$	−4.99865	−0.585048	−0.292524	−	0.956258i	$-0.594495\pi$
$73$	−4.99865	−0.585048	−0.292524	+	0.956258i	$0.594495\pi$
$74$	−21.2919	−2.47513
$75$	−10.2426	−1.18271
$76$	10.6030	1.21625
$77$	−1.71043	−0.194922
$78$	−3.23313	−0.366079
$79$	−8.24990	−0.928187	−0.464093	−	0.885786i	$-0.653620\pi$
$79$	−8.24990	−0.928187	−0.464093	+	0.885786i	$0.653620\pi$
$80$	11.1257	1.24389
$81$	−9.28197	−1.03133
$82$	−11.0403	−1.21920
$83$	7.27751	0.798810	0.399405	−	0.916775i	$-0.369217\pi$
$83$	7.27751	0.798810	0.399405	+	0.916775i	$0.369217\pi$
$84$	−6.83869	−0.746162
$85$	12.8712	1.39608
$86$	−7.96092	−0.858448
$87$	6.49366	0.696194
$88$	0.561957	0.0599048
$89$	−7.61243	−0.806916	−0.403458	−	0.914998i	$-0.632192\pi$
$89$	−7.61243	−0.806916	−0.403458	+	0.914998i	$0.632192\pi$
$90$	0.660383	0.0696105
$91$	−1.52033	−0.159374
$92$	−4.17601	−0.435379
$93$	−8.78373	−0.910830
$94$	−6.24820	−0.644453
$95$	−15.3517	−1.57505
$96$	−14.2807	−1.45752
$97$	−6.15264	−0.624706	−0.312353	−	0.949966i	$-0.601117\pi$
$97$	−6.15264	−0.624706	−0.312353	+	0.949966i	$0.601117\pi$
$98$	8.42124	0.850674
$99$	−0.0971338	−0.00976231
$100$	13.2226	1.32226
$101$	−2.66264	−0.264942	−0.132471	−	0.991187i	$-0.542291\pi$
$101$	−2.66264	−0.264942	−0.132471	+	0.991187i	$0.542291\pi$
$102$	−14.2329	−1.40926
$103$	−0.0978393	−0.00964039	−0.00482020	−	0.999988i	$-0.501534\pi$
$103$	−0.0978393	−0.00964039	−0.00482020	+	0.999988i	$0.501534\pi$
$104$	0.499500	0.0489800
$105$	9.90151	0.966288
$106$	−6.41846	−0.623416
$107$	−1.37891	−0.133304	−0.0666522	−	0.997776i	$-0.521232\pi$
$107$	−1.37891	−0.133304	−0.0666522	+	0.997776i	$0.521232\pi$
$108$	11.6063	1.11682
$109$	−2.35602	−0.225666	−0.112833	−	0.993614i	$-0.535992\pi$
$109$	−2.35602	−0.225666	−0.112833	+	0.993614i	$0.535992\pi$
$110$	−6.79870	−0.648230
$111$	−18.1294	−1.72077
$112$	−5.78519	−0.546649
$113$	1.08127	0.101717	0.0508587	−	0.998706i	$-0.483804\pi$
$113$	1.08127	0.101717	0.0508587	+	0.998706i	$0.483804\pi$
$114$	16.9758	1.58993
$115$	6.04630	0.563820
$116$	−8.38295	−0.778338
$117$	−0.0863382	−0.00798197
$118$	−10.5768	−0.973670
$119$	−6.69281	−0.613529
$120$	−3.25311	−0.296967
$121$	1.00000	0.0909091
$122$	20.3776	1.84490
$123$	−9.40049	−0.847614
$124$	11.3393	1.01830
$125$	−2.69764	−0.241284
$126$	−0.343389	−0.0305915
$127$	6.65700	0.590713	0.295356	−	0.955387i	$-0.404562\pi$
$127$	6.65700	0.590713	0.295356	+	0.955387i	$0.404562\pi$
$128$	4.45411	0.393692
$129$	−6.77850	−0.596813
$130$	−6.04308	−0.530013
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	3.99823	0.348001
$133$	7.98264	0.692183
$134$	−1.69272	−0.146229
$135$	−16.8044	−1.44629
$136$	2.19890	0.188554
$137$	−21.7844	−1.86116	−0.930582	−	0.366084i	$-0.880698\pi$
$137$	−21.7844	−1.86116	−0.930582	+	0.366084i	$0.880698\pi$
$138$	−6.68596	−0.569147
$139$	5.78600	0.490762	0.245381	−	0.969427i	$-0.421087\pi$
$139$	5.78600	0.490762	0.245381	+	0.969427i	$0.421087\pi$
$140$	−12.7823	−1.08030
$141$	−5.32016	−0.448038
$142$	−8.50181	−0.713456
$143$	0.888858	0.0743301
$144$	−0.328535	−0.0273779
$145$	12.1374	1.00796
$146$	10.3315	0.855040
$147$	7.17045	0.591408
$148$	23.4041	1.92380
$149$	−7.06627	−0.578891	−0.289446	−	0.957194i	$-0.593471\pi$
$149$	−7.06627	−0.578891	−0.289446	+	0.957194i	$0.593471\pi$
$150$	21.1700	1.72852
$151$	−2.50933	−0.204206	−0.102103	−	0.994774i	$-0.532557\pi$
$151$	−2.50933	−0.204206	−0.102103	+	0.994774i	$0.532557\pi$
$152$	−2.62267	−0.212727
$153$	−0.380078	−0.0307275
$154$	3.53521	0.284876
$155$	−16.4178	−1.31871
$156$	3.55386	0.284536
$157$	5.58366	0.445624	0.222812	−	0.974861i	$-0.428476\pi$
$157$	5.58366	0.445624	0.222812	+	0.974861i	$0.428476\pi$
$158$	17.0514	1.35653
$159$	−5.46513	−0.433413
$160$	−26.6922	−2.11020
$161$	−3.14398	−0.247780
$162$	19.1845	1.50728
$163$	−7.07717	−0.554327	−0.277164	−	0.960823i	$-0.589394\pi$
$163$	−7.07717	−0.554327	−0.277164	+	0.960823i	$0.589394\pi$
$164$	12.1355	0.947624
$165$	−5.78889	−0.450665
$166$	−15.0416	−1.16745
$167$	−5.58526	−0.432201	−0.216100	−	0.976371i	$-0.569334\pi$
$167$	−5.58526	−0.432201	−0.216100	+	0.976371i	$0.569334\pi$
$168$	1.69157	0.130507
$169$	−12.2099	−0.939225
$170$	−26.6029	−2.04035
$171$	0.453327	0.0346668
$172$	8.75066	0.667231
$173$	−16.9160	−1.28610	−0.643051	−	0.765824i	$-0.722331\pi$
$173$	−16.9160	−1.28610	−0.643051	+	0.765824i	$0.722331\pi$
$174$	−13.4215	−1.01748
$175$	9.95489	0.752519
$176$	3.38230	0.254950
$177$	−9.00581	−0.676918
$178$	15.7338	1.17930
$179$	7.44249	0.556278	0.278139	−	0.960541i	$-0.410282\pi$
$179$	7.44249	0.556278	0.278139	+	0.960541i	$0.410282\pi$
$180$	−0.725894	−0.0541049
$181$	−14.0378	−1.04342	−0.521712	−	0.853122i	$-0.674706\pi$
$181$	−14.0378	−1.04342	−0.521712	+	0.853122i	$0.674706\pi$
$182$	3.14230	0.232923
$183$	17.3510	1.28262
$184$	1.03294	0.0761497
$185$	−33.8860	−2.49135
$186$	18.1547	1.33117
$187$	3.91293	0.286142
$188$	6.86803	0.500903
$189$	8.73801	0.635597
$190$	31.7297	2.30192
$191$	−21.8093	−1.57807	−0.789033	−	0.614350i	$-0.789418\pi$
$191$	−21.8093	−1.57807	−0.789033	+	0.614350i	$0.789418\pi$
$192$	17.6113	1.27099
$193$	15.4299	1.11066	0.555332	−	0.831628i	$-0.312591\pi$
$193$	15.4299	1.11066	0.555332	+	0.831628i	$0.312591\pi$
$194$	12.7166	0.913000
$195$	−5.14551	−0.368477
$196$	−9.25664	−0.661189
$197$	15.3104	1.09082	0.545409	−	0.838170i	$-0.316374\pi$
$197$	15.3104	1.09082	0.545409	+	0.838170i	$0.316374\pi$
$198$	0.200761	0.0142675
$199$	−7.27852	−0.515960	−0.257980	−	0.966150i	$-0.583057\pi$
$199$	−7.27852	−0.515960	−0.257980	+	0.966150i	$0.583057\pi$
$200$	−3.27065	−0.231270
$201$	−1.44130	−0.101662
$202$	5.50329	0.387210
$203$	−6.31125	−0.442963
$204$	15.6448	1.09535
$205$	−17.5706	−1.22718
$206$	0.202220	0.0140893
$207$	−0.178544	−0.0124096
$208$	3.00638	0.208455
$209$	−4.66703	−0.322825
$210$	−20.4650	−1.41222
$211$	−19.9739	−1.37506	−0.687530	−	0.726156i	$-0.741305\pi$
$211$	−19.9739	−1.37506	−0.687530	+	0.726156i	$0.741305\pi$
$212$	7.05518	0.484552
$213$	−7.23905	−0.496011
$214$	2.85001	0.194823
$215$	−12.6698	−0.864072
$216$	−2.87085	−0.195336
$217$	8.53699	0.579528
$218$	4.86955	0.329808
$219$	8.79696	0.594444
$220$	7.47314	0.503839
$221$	3.47804	0.233959
$222$	37.4709	2.51488
$223$	27.1059	1.81515	0.907573	−	0.419894i	$-0.137933\pi$
$223$	27.1059	1.81515	0.907573	+	0.419894i	$0.137933\pi$
$224$	13.8795	0.927364
$225$	0.565328	0.0376886
$226$	−2.23483	−0.148659
$227$	12.3795	0.821659	0.410829	−	0.911712i	$-0.365239\pi$
$227$	12.3795	0.821659	0.410829	+	0.911712i	$0.365239\pi$
$228$	−18.6599	−1.23578
$229$	3.63019	0.239890	0.119945	−	0.992781i	$-0.461728\pi$
$229$	3.63019	0.239890	0.119945	+	0.992781i	$0.461728\pi$
$230$	−12.4968	−0.824016
$231$	3.01013	0.198052
$232$	2.07354	0.136135
$233$	−13.7767	−0.902539	−0.451270	−	0.892388i	$-0.649029\pi$
$233$	−13.7767	−0.902539	−0.451270	+	0.892388i	$0.649029\pi$
$234$	0.178448	0.0116655
$235$	−9.94399	−0.648674
$236$	11.6260	0.756788
$237$	14.5187	0.943093
$238$	13.8331	0.896664
$239$	−23.2307	−1.50267	−0.751334	−	0.659922i	$-0.770589\pi$
$239$	−23.2307	−1.50267	−0.751334	+	0.659922i	$0.770589\pi$
$240$	−19.5798	−1.26387
$241$	18.8150	1.21198	0.605989	−	0.795473i	$-0.292777\pi$
$241$	18.8150	1.21198	0.605989	+	0.795473i	$0.292777\pi$
$242$	−2.06686	−0.132862
$243$	1.00905	0.0647307
$244$	−22.3991	−1.43396
$245$	13.4024	0.856247
$246$	19.4295	1.23878
$247$	−4.14833	−0.263952
$248$	−2.80480	−0.178105
$249$	−12.8074	−0.811639
$250$	5.57563	0.352633
$251$	−8.83010	−0.557351	−0.278675	−	0.960385i	$-0.589895\pi$
$251$	−8.83010	−0.557351	−0.278675	+	0.960385i	$0.589895\pi$
$252$	0.377453	0.0237773
$253$	1.83812	0.115562
$254$	−13.7590	−0.863320
$255$	−22.6516	−1.41850
$256$	10.8083	0.675521
$257$	−15.0503	−0.938812	−0.469406	−	0.882982i	$-0.655532\pi$
$257$	−15.0503	−0.938812	−0.469406	+	0.882982i	$0.655532\pi$
$258$	14.0102	0.872235
$259$	17.6202	1.09486
$260$	6.64256	0.411954
$261$	−0.358410	−0.0221850
$262$	2.06686	0.127691
$263$	−29.9674	−1.84787	−0.923934	−	0.382551i	$-0.875046\pi$
$263$	−29.9674	−1.84787	−0.923934	+	0.382551i	$0.875046\pi$
$264$	−0.988970	−0.0608669
$265$	−10.2150	−0.627500
$266$	−16.4990	−1.01162
$267$	13.3969	0.819875
$268$	1.86064	0.113657
$269$	16.1102	0.982258	0.491129	−	0.871087i	$-0.336584\pi$
$269$	16.1102	0.982258	0.491129	+	0.871087i	$0.336584\pi$
$270$	34.7322	2.11374
$271$	−22.4616	−1.36445	−0.682223	−	0.731144i	$-0.738987\pi$
$271$	−22.4616	−1.36445	−0.682223	+	0.731144i	$0.738987\pi$
$272$	13.2347	0.802472
$273$	2.67558	0.161934
$274$	45.0251	2.72007
$275$	−5.82010	−0.350965
$276$	7.34922	0.442371
$277$	2.84932	0.171199	0.0855995	−	0.996330i	$-0.472719\pi$
$277$	2.84932	0.171199	0.0855995	+	0.996330i	$0.472719\pi$
$278$	−11.9588	−0.717242
$279$	0.484807	0.0290247
$280$	3.16173	0.188949
$281$	9.17490	0.547329	0.273664	−	0.961825i	$-0.411764\pi$
$281$	9.17490	0.547329	0.273664	+	0.961825i	$0.411764\pi$
$282$	10.9960	0.654802
$283$	−12.8825	−0.765787	−0.382894	−	0.923792i	$-0.625072\pi$
$283$	−12.8825	−0.765787	−0.382894	+	0.923792i	$0.625072\pi$
$284$	9.34520	0.554536
$285$	27.0170	1.60035
$286$	−1.83714	−0.108632
$287$	9.13643	0.539306
$288$	0.788205	0.0464454
$289$	−1.68894	−0.0993497
$290$	−25.0862	−1.47311
$291$	10.8278	0.634739
$292$	−11.3564	−0.664582
$293$	20.2066	1.18048	0.590240	−	0.807228i	$-0.299033\pi$
$293$	20.2066	1.18048	0.590240	+	0.807228i	$0.299033\pi$
$294$	−14.8203	−0.864336
$295$	−16.8329	−0.980048
$296$	−5.78905	−0.336482
$297$	−5.10866	−0.296435
$298$	14.6050	0.846042
$299$	1.63383	0.0944867
$300$	−23.2701	−1.34350
$301$	6.58808	0.379731
$302$	5.18642	0.298445
$303$	4.68589	0.269197
$304$	−15.7853	−0.905348
$305$	32.4309	1.85699
$306$	0.785566	0.0449078
$307$	19.1881	1.09512	0.547561	−	0.836766i	$-0.315556\pi$
$307$	19.1881	1.09512	0.547561	+	0.836766i	$0.315556\pi$
$308$	−3.88591	−0.221420
$309$	0.172184	0.00979522
$310$	33.9332	1.92728
$311$	−5.50562	−0.312195	−0.156097	−	0.987742i	$-0.549891\pi$
$311$	−5.50562	−0.312195	−0.156097	+	0.987742i	$0.549891\pi$
$312$	−0.879054	−0.0497666
$313$	−18.8596	−1.06600	−0.533002	−	0.846114i	$-0.678936\pi$
$313$	−18.8596	−1.06600	−0.533002	+	0.846114i	$0.678936\pi$
$314$	−11.5406	−0.651274
$315$	−0.546502	−0.0307919
$316$	−18.7429	−1.05437
$317$	14.5952	0.819750	0.409875	−	0.912142i	$-0.365572\pi$
$317$	14.5952	0.819750	0.409875	+	0.912142i	$0.365572\pi$
$318$	11.2956	0.633428
$319$	3.68986	0.206592
$320$	32.9175	1.84014
$321$	2.42670	0.135445
$322$	6.49815	0.362128
$323$	−18.2618	−1.01611
$324$	−21.0876	−1.17153
$325$	−5.17325	−0.286960
$326$	14.6275	0.810142
$327$	4.14628	0.229290
$328$	−3.00174	−0.165744
$329$	5.17071	0.285071
$330$	11.9648	0.658641
$331$	−6.78069	−0.372700	−0.186350	−	0.982483i	$-0.559666\pi$
$331$	−6.78069	−0.372700	−0.186350	+	0.982483i	$0.559666\pi$
$332$	16.5337	0.907404
$333$	1.00063	0.0548343
$334$	11.5439	0.631656
$335$	−2.69396	−0.147187
$336$	10.1812	0.555428
$337$	36.1740	1.97053	0.985263	−	0.171047i	$-0.0547151\pi$
$337$	36.1740	1.97053	0.985263	+	0.171047i	$0.0547151\pi$
$338$	25.2362	1.37267
$339$	−1.90289	−0.103351
$340$	29.2419	1.58586
$341$	−4.99113	−0.270285
$342$	−0.936960	−0.0506650
$343$	−18.9420	−1.02277
$344$	−2.16449	−0.116702
$345$	−10.6407	−0.572875
$346$	34.9630	1.87962
$347$	25.8552	1.38798	0.693989	−	0.719986i	$-0.255852\pi$
$347$	25.8552	1.38798	0.693989	+	0.719986i	$0.255852\pi$
$348$	14.7529	0.790838
$349$	5.31861	0.284699	0.142349	−	0.989816i	$-0.454534\pi$
$349$	5.31861	0.284699	0.142349	+	0.989816i	$0.454534\pi$
$350$	−20.5753	−1.09980
$351$	−4.54087	−0.242374
$352$	−8.11463	−0.432511
$353$	24.8670	1.32354	0.661769	−	0.749708i	$-0.269806\pi$
$353$	24.8670	1.32354	0.661769	+	0.749708i	$0.269806\pi$
$354$	18.6137	0.989307
$355$	−13.5306	−0.718130
$356$	−17.2946	−0.916612
$357$	11.7785	0.623382
$358$	−15.3826	−0.812993
$359$	−7.73524	−0.408250	−0.204125	−	0.978945i	$-0.565435\pi$
$359$	−7.73524	−0.408250	−0.204125	+	0.978945i	$0.565435\pi$
$360$	0.179552	0.00946320
$361$	2.78120	0.146379
$362$	29.0142	1.52495
$363$	−1.75987	−0.0923691
$364$	−3.45402	−0.181040
$365$	16.4425	0.860641
$366$	−35.8619	−1.87453
$367$	−24.1383	−1.26001	−0.630005	−	0.776591i	$-0.716947\pi$
$367$	−24.1383	−1.26001	−0.630005	+	0.776591i	$0.716947\pi$
$368$	6.21707	0.324087
$369$	0.518849	0.0270102
$370$	70.0374	3.64107
$371$	5.31161	0.275765
$372$	−19.9557	−1.03465
$373$	23.3693	1.21002	0.605008	−	0.796219i	$-0.293170\pi$
$373$	23.3693	1.21002	0.605008	+	0.796219i	$0.293170\pi$
$374$	−8.08747	−0.418193
$375$	4.74748	0.245159
$376$	−1.69882	−0.0876101
$377$	3.27976	0.168916
$378$	−18.0602	−0.928917
$379$	1.86750	0.0959269	0.0479635	−	0.998849i	$-0.484727\pi$
$379$	1.86750	0.0959269	0.0479635	+	0.998849i	$0.484727\pi$
$380$	−34.8774	−1.78917
$381$	−11.7154	−0.600200
$382$	45.0767	2.30632
$383$	25.0117	1.27804	0.639019	−	0.769191i	$-0.279340\pi$
$383$	25.0117	1.27804	0.639019	+	0.769191i	$0.279340\pi$
$384$	−7.83865	−0.400014
$385$	5.62628	0.286742
$386$	−31.8913	−1.62322
$387$	0.374131	0.0190181
$388$	−13.9781	−0.709632
$389$	−20.5551	−1.04218	−0.521092	−	0.853500i	$-0.674475\pi$
$389$	−20.5551	−1.04218	−0.521092	+	0.853500i	$0.674475\pi$
$390$	10.6350	0.538525
$391$	7.19244	0.363738
$392$	2.28965	0.115645
$393$	1.75987	0.0887736
$394$	−31.6443	−1.59422
$395$	27.1372	1.36542
$396$	−0.220677	−0.0110894
$397$	9.11866	0.457653	0.228826	−	0.973467i	$-0.426511\pi$
$397$	9.11866	0.457653	0.228826	+	0.973467i	$0.426511\pi$
$398$	15.0436	0.754070
$399$	−14.0484	−0.703299
$400$	−19.6853	−0.984265
$401$	11.8882	0.593669	0.296835	−	0.954929i	$-0.404069\pi$
$401$	11.8882	0.593669	0.296835	+	0.954929i	$0.404069\pi$
$402$	2.97896	0.148577
$403$	−4.43641	−0.220993
$404$	−6.04922	−0.300960
$405$	30.5320	1.51715
$406$	13.0444	0.647385
$407$	−10.3016	−0.510631
$408$	−3.86977	−0.191582
$409$	15.9052	0.786460	0.393230	−	0.919440i	$-0.371358\pi$
$409$	15.9052	0.786460	0.393230	+	0.919440i	$0.371358\pi$
$410$	36.3159	1.79351
$411$	38.3376	1.89105
$412$	−0.222280	−0.0109510
$413$	8.75283	0.430699
$414$	0.369024	0.0181365
$415$	−23.9386	−1.17510
$416$	−7.21276	−0.353634
$417$	−10.1826	−0.498644
$418$	9.64608	0.471805
$419$	−4.19811	−0.205091	−0.102545	−	0.994728i	$-0.532699\pi$
$419$	−4.19811	−0.205091	−0.102545	+	0.994728i	$0.532699\pi$
$420$	22.4951	1.09765
$421$	−34.5660	−1.68464	−0.842321	−	0.538976i	$-0.818811\pi$
$421$	−34.5660	−1.68464	−0.842321	+	0.538976i	$0.818811\pi$
$422$	41.2832	2.00963
$423$	0.293640	0.0142773
$424$	−1.74511	−0.0847503
$425$	−22.7737	−1.10469
$426$	14.9621	0.724914
$427$	−16.8636	−0.816085
$428$	−3.13273	−0.151426
$429$	−1.56427	−0.0755238
$430$	26.1866	1.26283
$431$	15.2043	0.732365	0.366183	−	0.930543i	$-0.380665\pi$
$431$	15.2043	0.732365	0.366183	+	0.930543i	$0.380665\pi$
$432$	−17.2790	−0.831336
$433$	−19.2083	−0.923092	−0.461546	−	0.887116i	$-0.652705\pi$
$433$	−19.2083	−0.923092	−0.461546	+	0.887116i	$0.652705\pi$
$434$	−17.6447	−0.846973
$435$	−21.3602	−1.02414
$436$	−5.35262	−0.256344
$437$	−8.57857	−0.410369
$438$	−18.1821	−0.868772
$439$	−23.7248	−1.13232	−0.566161	−	0.824295i	$-0.691572\pi$
$439$	−23.7248	−1.13232	−0.566161	+	0.824295i	$0.691572\pi$
$440$	−1.84850	−0.0881236
$441$	−0.395764	−0.0188459
$442$	−7.18861	−0.341927
$443$	−26.8487	−1.27562	−0.637810	−	0.770193i	$-0.720160\pi$
$443$	−26.8487	−1.27562	−0.637810	+	0.770193i	$0.720160\pi$
$444$	−41.1881	−1.95470
$445$	25.0403	1.18702
$446$	−56.0240	−2.65281
$447$	12.4357	0.588188
$448$	−17.1166	−0.808682
$449$	−5.17734	−0.244334	−0.122167	−	0.992510i	$-0.538984\pi$
$449$	−5.17734	−0.244334	−0.122167	+	0.992510i	$0.538984\pi$
$450$	−1.16845	−0.0550814
$451$	−5.34159	−0.251526
$452$	2.45653	0.115545
$453$	4.41608	0.207486
$454$	−25.5867	−1.20084
$455$	5.00097	0.234449
$456$	4.61556	0.216143
$457$	−3.22875	−0.151035	−0.0755173	−	0.997144i	$-0.524061\pi$
$457$	−3.22875	−0.151035	−0.0755173	+	0.997144i	$0.524061\pi$
$458$	−7.50308	−0.350596
$459$	−19.9899	−0.933046
$460$	13.7365	0.640469
$461$	−6.15481	−0.286658	−0.143329	−	0.989675i	$-0.545781\pi$
$461$	−6.15481	−0.286658	−0.143329	+	0.989675i	$0.545781\pi$
$462$	−6.22151	−0.289451
$463$	3.66765	0.170450	0.0852250	−	0.996362i	$-0.472839\pi$
$463$	3.66765	0.170450	0.0852250	+	0.996362i	$0.472839\pi$
$464$	12.4802	0.579379
$465$	28.8931	1.33989
$466$	28.4744	1.31905
$467$	0.285061	0.0131910	0.00659552	−	0.999978i	$-0.497901\pi$
$467$	0.285061	0.0131910	0.00659552	+	0.999978i	$0.497901\pi$
$468$	−0.196151	−0.00906707
$469$	1.40081	0.0646836
$470$	20.5528	0.948029
$471$	−9.82649	−0.452781
$472$	−2.87572	−0.132366
$473$	−3.85171	−0.177102
$474$	−30.0081	−1.37832
$475$	27.1626	1.24631
$476$	−15.2053	−0.696935
$477$	0.301642	0.0138112
$478$	48.0145	2.19613
$479$	6.01839	0.274987	0.137494	−	0.990503i	$-0.456095\pi$
$479$	6.01839	0.274987	0.137494	+	0.990503i	$0.456095\pi$
$480$	46.9747	2.14409
$481$	−9.15665	−0.417507
$482$	−38.8878	−1.77129
$483$	5.53299	0.251760
$484$	2.27189	0.103268
$485$	20.2385	0.918981
$486$	−2.08556	−0.0946030
$487$	−31.3817	−1.42204	−0.711020	−	0.703172i	$-0.751766\pi$
$487$	−31.3817	−1.42204	−0.711020	+	0.703172i	$0.751766\pi$
$488$	5.54047	0.250805
$489$	12.4549	0.563230
$490$	−27.7008	−1.25139
$491$	−6.78173	−0.306055	−0.153028	−	0.988222i	$-0.548902\pi$
$491$	−6.78173	−0.306055	−0.153028	+	0.988222i	$0.548902\pi$
$492$	−21.3569	−0.962843
$493$	14.4382	0.650263
$494$	8.57400	0.385762
$495$	0.319511	0.0143610
$496$	−16.8815	−0.758001
$497$	7.03570	0.315594
$498$	26.4711	1.18620
$499$	−15.8765	−0.710730	−0.355365	−	0.934728i	$-0.615643\pi$
$499$	−15.8765	−0.710730	−0.355365	+	0.934728i	$0.615643\pi$
$500$	−6.12873	−0.274085
$501$	9.82932	0.439142
$502$	18.2505	0.814561
$503$	23.3961	1.04318	0.521589	−	0.853197i	$-0.325339\pi$
$503$	23.3961	1.04318	0.521589	+	0.853197i	$0.325339\pi$
$504$	−0.0933639	−0.00415876
$505$	8.75846	0.389746
$506$	−3.79913	−0.168892
$507$	21.4879	0.954309
$508$	15.1240	0.671017
$509$	−24.6722	−1.09357	−0.546787	−	0.837272i	$-0.684149\pi$
$509$	−24.6722	−1.09357	−0.546787	+	0.837272i	$0.684149\pi$
$510$	46.8175	2.07311
$511$	−8.54985	−0.378223
$512$	−31.2475	−1.38096
$513$	23.8423	1.05266
$514$	31.1068	1.37206
$515$	0.321832	0.0141816
$516$	−15.4000	−0.677947
$517$	−3.02305	−0.132953
$518$	−36.4183	−1.60013
$519$	29.7700	1.30676
$520$	−1.64305	−0.0720526
$521$	37.4555	1.64095	0.820477	−	0.571680i	$-0.193708\pi$
$521$	37.4555	1.64095	0.820477	+	0.571680i	$0.193708\pi$
$522$	0.740781	0.0324231
$523$	16.7446	0.732191	0.366096	−	0.930577i	$-0.380694\pi$
$523$	16.7446	0.732191	0.366096	+	0.930577i	$0.380694\pi$
$524$	−2.27189	−0.0992480
$525$	−17.5193	−0.764604
$526$	61.9383	2.70064
$527$	−19.5300	−0.850739
$528$	−5.95239	−0.259045
$529$	−19.6213	−0.853101
$530$	21.1128	0.917083
$531$	0.497065	0.0215708
$532$	18.1357	0.786282
$533$	−4.74792	−0.205655
$534$	−27.6894	−1.19824
$535$	4.53578	0.196099
$536$	−0.460233	−0.0198791
$537$	−13.0978	−0.565212
$538$	−33.2975	−1.43556
$539$	4.07442	0.175498
$540$	−38.1777	−1.64291
$541$	−20.3564	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$541$	−20.3564	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$542$	46.4249	1.99412
$543$	24.7047	1.06018
$544$	−31.7520	−1.36136
$545$	7.74987	0.331968
$546$	−5.53004	−0.236664
$547$	−25.6063	−1.09484	−0.547422	−	0.836856i	$-0.684391\pi$
$547$	−25.6063	−1.09484	−0.547422	+	0.836856i	$0.684391\pi$
$548$	−49.4917	−2.11418
$549$	−0.957666	−0.0408722
$550$	12.0293	0.512931
$551$	−17.2207	−0.733626
$552$	−1.81785	−0.0773727
$553$	−14.1109	−0.600056
$554$	−5.88913	−0.250205
$555$	59.6348	2.53136
$556$	13.1452	0.557479
$557$	−6.31758	−0.267684	−0.133842	−	0.991003i	$-0.542732\pi$
$557$	−6.31758	−0.267684	−0.133842	+	0.991003i	$0.542732\pi$
$558$	−1.00203	−0.0424192
$559$	−3.42362	−0.144804
$560$	19.0297	0.804154
$561$	−6.88625	−0.290738
$562$	−18.9632	−0.799914
$563$	−38.1282	−1.60691	−0.803455	−	0.595365i	$-0.797007\pi$
$563$	−38.1282	−1.60691	−0.803455	+	0.595365i	$0.797007\pi$
$564$	−12.0868	−0.508947
$565$	−3.55672	−0.149632
$566$	26.6263	1.11919
$567$	−15.8762	−0.666736
$568$	−2.31156	−0.0969908
$569$	−22.3302	−0.936133	−0.468066	−	0.883693i	$-0.655049\pi$
$569$	−22.3302	−0.936133	−0.468066	+	0.883693i	$0.655049\pi$
$570$	−55.8402	−2.33889
$571$	−0.521203	−0.0218117	−0.0109058	−	0.999941i	$-0.503472\pi$
$571$	−0.521203	−0.0218117	−0.0109058	+	0.999941i	$0.503472\pi$
$572$	2.01939	0.0844349
$573$	38.3815	1.60341
$574$	−18.8837	−0.788189
$575$	−10.6980	−0.446139
$576$	−0.972034	−0.0405014
$577$	−4.30680	−0.179294	−0.0896471	−	0.995974i	$-0.528574\pi$
$577$	−4.30680	−0.179294	−0.0896471	+	0.995974i	$0.528574\pi$
$578$	3.49080	0.145198
$579$	−27.1545	−1.12850
$580$	27.5748	1.14498
$581$	12.4477	0.516417
$582$	−22.3796	−0.927663
$583$	−3.10542	−0.128614
$584$	2.80903	0.116238
$585$	0.284000	0.0117420
$586$	−41.7640	−1.72526
$587$	−18.5751	−0.766676	−0.383338	−	0.923608i	$-0.625225\pi$
$587$	−18.5751	−0.766676	−0.383338	+	0.923608i	$0.625225\pi$
$588$	16.2905	0.671807
$589$	23.2938	0.959803
$590$	34.7911	1.43233
$591$	−26.9442	−1.10834
$592$	−34.8430	−1.43204
$593$	−38.4795	−1.58016	−0.790082	−	0.613001i	$-0.789962\pi$
$593$	−38.4795	−1.58016	−0.790082	+	0.613001i	$0.789962\pi$
$594$	10.5589	0.433235
$595$	22.0153	0.902538
$596$	−16.0538	−0.657589
$597$	12.8092	0.524247
$598$	−3.37689	−0.138091
$599$	33.1899	1.35610	0.678051	−	0.735015i	$-0.262825\pi$
$599$	33.1899	1.35610	0.678051	+	0.735015i	$0.262825\pi$
$600$	5.75591	0.234984
$601$	−26.4853	−1.08036	−0.540179	−	0.841550i	$-0.681644\pi$
$601$	−26.4853	−1.08036	−0.540179	+	0.841550i	$0.681644\pi$
$602$	−13.6166	−0.554972
$603$	0.0795509	0.00323956
$604$	−5.70091	−0.231967
$605$	−3.28939	−0.133733
$606$	−9.68506	−0.393429
$607$	−8.93905	−0.362825	−0.181413	−	0.983407i	$-0.558067\pi$
$607$	−8.93905	−0.362825	−0.181413	+	0.983407i	$0.558067\pi$
$608$	37.8713	1.53588
$609$	11.1070	0.450077
$610$	−67.0300	−2.71397
$611$	−2.68706	−0.108707
$612$	−0.863496	−0.0349047
$613$	−36.3573	−1.46846	−0.734229	−	0.678901i	$-0.762456\pi$
$613$	−36.3573	−1.46846	−0.734229	+	0.678901i	$0.762456\pi$
$614$	−39.6590	−1.60051
$615$	30.9219	1.24689
$616$	0.961189	0.0387274
$617$	43.0726	1.73404	0.867019	−	0.498276i	$-0.166033\pi$
$617$	43.0726	1.73404	0.867019	+	0.498276i	$0.166033\pi$
$618$	−0.355880	−0.0143156
$619$	41.2081	1.65629	0.828147	−	0.560511i	$-0.189395\pi$
$619$	41.2081	1.65629	0.828147	+	0.560511i	$0.189395\pi$
$620$	−37.2994	−1.49798
$621$	−9.39033	−0.376821
$622$	11.3793	0.456269
$623$	−13.0205	−0.521657
$624$	−5.29083	−0.211803
$625$	−20.2269	−0.809077
$626$	38.9800	1.55795
$627$	8.21336	0.328010
$628$	12.6855	0.506205
$629$	−40.3094	−1.60724
$630$	1.12954	0.0450020
$631$	−8.98294	−0.357605	−0.178803	−	0.983885i	$-0.557222\pi$
$631$	−8.98294	−0.357605	−0.178803	+	0.983885i	$0.557222\pi$
$632$	4.63609	0.184414
$633$	35.1514	1.39714
$634$	−30.1662	−1.19805
$635$	−21.8975	−0.868975
$636$	−12.4162	−0.492334
$637$	3.62159	0.143492
$638$	−7.62640	−0.301932
$639$	0.399551	0.0158060
$640$	−14.6513	−0.579145
$641$	−50.4021	−1.99076	−0.995381	−	0.0960026i	$-0.969394\pi$
$641$	−50.4021	−1.99076	−0.995381	+	0.0960026i	$0.969394\pi$
$642$	−5.01564	−0.197951
$643$	−5.72478	−0.225763	−0.112882	−	0.993608i	$-0.536008\pi$
$643$	−5.72478	−0.225763	−0.112882	+	0.993608i	$0.536008\pi$
$644$	−7.14277	−0.281465
$645$	22.2971	0.877949
$646$	37.7445	1.48504
$647$	2.06881	0.0813333	0.0406666	−	0.999173i	$-0.487052\pi$
$647$	2.06881	0.0813333	0.0406666	+	0.999173i	$0.487052\pi$
$648$	5.21607	0.204906
$649$	−5.11732	−0.200872
$650$	10.6923	0.419388
$651$	−15.0240	−0.588836
$652$	−16.0786	−0.629685
$653$	13.4548	0.526526	0.263263	−	0.964724i	$-0.415201\pi$
$653$	13.4548	0.526526	0.263263	+	0.964724i	$0.415201\pi$
$654$	−8.56976	−0.335104
$655$	3.28939	0.128527
$656$	−18.0668	−0.705392
$657$	−0.485538	−0.0189426
$658$	−10.6871	−0.416627
$659$	18.6520	0.726579	0.363290	−	0.931676i	$-0.381654\pi$
$659$	18.6520	0.726579	0.363290	+	0.931676i	$0.381654\pi$
$660$	−13.1517	−0.511930
$661$	−2.82140	−0.109740	−0.0548699	−	0.998494i	$-0.517474\pi$
$661$	−2.82140	−0.109740	−0.0548699	+	0.998494i	$0.517474\pi$
$662$	14.0147	0.544697
$663$	−6.12090	−0.237716
$664$	−4.08965	−0.158709
$665$	−26.2580	−1.01824
$666$	−2.06816	−0.0801396
$667$	6.78241	0.262616
$668$	−12.6891	−0.490956
$669$	−47.7028	−1.84430
$670$	5.56802	0.215111
$671$	9.85925	0.380612
$672$	−24.4261	−0.942258
$673$	−21.7193	−0.837219	−0.418609	−	0.908166i	$-0.637482\pi$
$673$	−21.7193	−0.837219	−0.418609	+	0.908166i	$0.637482\pi$
$674$	−74.7665	−2.87990
$675$	29.7329	1.14442
$676$	−27.7396	−1.06691
$677$	43.9682	1.68984	0.844918	−	0.534895i	$-0.179649\pi$
$677$	43.9682	1.68984	0.844918	+	0.534895i	$0.179649\pi$
$678$	3.93300	0.151046
$679$	−10.5237	−0.403861
$680$	−7.23305	−0.277375
$681$	−21.7863	−0.834855
$682$	10.3159	0.395018
$683$	−40.6460	−1.55528	−0.777638	−	0.628712i	$-0.783582\pi$
$683$	−40.6460	−1.55528	−0.777638	+	0.628712i	$0.783582\pi$
$684$	1.02991	0.0393795
$685$	71.6573	2.73788
$686$	39.1505	1.49477
$687$	−6.38866	−0.243742
$688$	−13.0276	−0.496673
$689$	−2.76028	−0.105158
$690$	21.9928	0.837250
$691$	−20.1579	−0.766842	−0.383421	−	0.923574i	$-0.625254\pi$
$691$	−20.1579	−0.766842	−0.383421	+	0.923574i	$0.625254\pi$
$692$	−38.4313	−1.46094
$693$	−0.166141	−0.00631116
$694$	−53.4389	−2.02851
$695$	−19.0324	−0.721941
$696$	−3.64916	−0.138321
$697$	−20.9013	−0.791693
$698$	−10.9928	−0.416084
$699$	24.2451	0.917034
$700$	22.6164	0.854820
$701$	48.4299	1.82917	0.914585	−	0.404393i	$-0.132517\pi$
$701$	48.4299	1.82917	0.914585	+	0.404393i	$0.132517\pi$
$702$	9.38533	0.354226
$703$	48.0779	1.81329
$704$	10.0072	0.377159
$705$	17.5001	0.659092
$706$	−51.3965	−1.93433
$707$	−4.55426	−0.171281
$708$	−20.4602	−0.768942
$709$	11.1683	0.419434	0.209717	−	0.977762i	$-0.432746\pi$
$709$	11.1683	0.419434	0.209717	+	0.977762i	$0.432746\pi$
$710$	27.9658	1.04954
$711$	−0.801344	−0.0300528
$712$	4.27786	0.160320
$713$	−9.17430	−0.343580
$714$	−24.3444	−0.911065
$715$	−2.92380	−0.109344
$716$	16.9085	0.631901
$717$	40.8829	1.52680
$718$	15.9876	0.596653
$719$	−13.3948	−0.499541	−0.249771	−	0.968305i	$-0.580355\pi$
$719$	−13.3948	−0.499541	−0.249771	+	0.968305i	$0.580355\pi$
$720$	1.08068	0.0402746
$721$	−0.167347	−0.00623234
$722$	−5.74834	−0.213931
$723$	−33.1118	−1.23144
$724$	−31.8924	−1.18527
$725$	−21.4754	−0.797575
$726$	3.63739	0.134996
$727$	36.9829	1.37162	0.685810	−	0.727780i	$-0.259448\pi$
$727$	36.9829	1.37162	0.685810	+	0.727780i	$0.259448\pi$
$728$	0.854361	0.0316647
$729$	26.0701	0.965559
$730$	−33.9843	−1.25782
$731$	−15.0715	−0.557439
$732$	39.4195	1.45699
$733$	−45.0843	−1.66523	−0.832613	−	0.553855i	$-0.813156\pi$
$733$	−45.0843	−1.66523	−0.832613	+	0.553855i	$0.813156\pi$
$734$	49.8904	1.84149
$735$	−23.5864	−0.869998
$736$	−14.9157	−0.549799
$737$	−0.818983	−0.0301676
$738$	−1.07239	−0.0394751
$739$	4.72308	0.173741	0.0868707	−	0.996220i	$-0.472313\pi$
$739$	4.72308	0.173741	0.0868707	+	0.996220i	$0.472313\pi$
$740$	−76.9852	−2.83003
$741$	7.30051	0.268191
$742$	−10.9783	−0.403027
$743$	−33.7735	−1.23903	−0.619514	−	0.784985i	$-0.712670\pi$
$743$	−33.7735	−1.23903	−0.619514	+	0.784985i	$0.712670\pi$
$744$	4.93608	0.180965
$745$	23.2437	0.851585
$746$	−48.3009	−1.76842
$747$	0.706892	0.0258638
$748$	8.88976	0.325042
$749$	−2.35853	−0.0861789
$750$	−9.81236	−0.358297
$751$	−27.4070	−1.00010	−0.500048	−	0.865998i	$-0.666684\pi$
$751$	−27.4070	−1.00010	−0.500048	+	0.865998i	$0.666684\pi$
$752$	−10.2248	−0.372862
$753$	15.5398	0.566302
$754$	−6.77879	−0.246869
$755$	8.25416	0.300400
$756$	19.8518	0.722003
$757$	−27.2990	−0.992200	−0.496100	−	0.868265i	$-0.665235\pi$
$757$	−27.2990	−0.992200	−0.496100	+	0.868265i	$0.665235\pi$
$758$	−3.85985	−0.140196
$759$	−3.23485	−0.117418
$760$	8.62700	0.312934
$761$	30.4101	1.10237	0.551183	−	0.834385i	$-0.314177\pi$
$761$	30.4101	1.10237	0.551183	+	0.834385i	$0.314177\pi$
$762$	24.2141	0.877184
$763$	−4.02981	−0.145889
$764$	−49.5484	−1.79260
$765$	1.25023	0.0452020
$766$	−51.6956	−1.86784
$767$	−4.54857	−0.164239
$768$	−19.0212	−0.686370
$769$	−44.2539	−1.59584	−0.797919	−	0.602765i	$-0.794066\pi$
$769$	−44.2539	−1.59584	−0.797919	+	0.602765i	$0.794066\pi$
$770$	−11.6287	−0.419069
$771$	26.4865	0.953889
$772$	35.0549	1.26165
$773$	−39.9642	−1.43741	−0.718707	−	0.695313i	$-0.755266\pi$
$773$	−39.9642	−1.43741	−0.718707	+	0.695313i	$0.755266\pi$
$774$	−0.773274	−0.0277948
$775$	29.0489	1.04347
$776$	3.45752	0.124118
$777$	−31.0092	−1.11245
$778$	42.4844	1.52314
$779$	24.9294	0.893188
$780$	−11.6900	−0.418570
$781$	−4.11340	−0.147189
$782$	−14.8657	−0.531598
$783$	−18.8502	−0.673653
$784$	13.7809	0.492175
$785$	−18.3668	−0.655540
$786$	−3.63739	−0.129741
$787$	43.4611	1.54922	0.774610	−	0.632439i	$-0.217946\pi$
$787$	43.4611	1.54922	0.774610	+	0.632439i	$0.217946\pi$
$788$	34.7835	1.23911
$789$	52.7386	1.87755
$790$	−56.0886	−1.99554
$791$	1.84944	0.0657585
$792$	0.0545850	0.00193959
$793$	8.76347	0.311200
$794$	−18.8470	−0.668853
$795$	17.9770	0.637577
$796$	−16.5360	−0.586103
$797$	27.0242	0.957248	0.478624	−	0.878020i	$-0.341136\pi$
$797$	27.0242	0.957248	0.478624	+	0.878020i	$0.341136\pi$
$798$	29.0360	1.02786
$799$	−11.8290	−0.418479
$800$	47.2280	1.66976
$801$	−0.739424	−0.0261263
$802$	−24.5712	−0.867640
$803$	4.99865	0.176399
$804$	−3.27448	−0.115482
$805$	10.3418	0.364500
$806$	9.16941	0.322979
$807$	−28.3519	−0.998033
$808$	1.49629	0.0526392
$809$	15.0514	0.529180	0.264590	−	0.964361i	$-0.414763\pi$
$809$	15.0514	0.529180	0.264590	+	0.964361i	$0.414763\pi$
$810$	−63.1053	−2.21729
$811$	−4.99794	−0.175502	−0.0877508	−	0.996142i	$-0.527968\pi$
$811$	−4.99794	−0.175502	−0.0877508	+	0.996142i	$0.527968\pi$
$812$	−14.3385	−0.503182
$813$	39.5295	1.38636
$814$	21.2919	0.746280
$815$	23.2796	0.815449
$816$	−23.2913	−0.815359
$817$	17.9760	0.628902
$818$	−32.8737	−1.14940
$819$	−0.147676	−0.00516020
$820$	−39.9184	−1.39401
$821$	33.4491	1.16738	0.583691	−	0.811976i	$-0.301608\pi$
$821$	33.4491	1.16738	0.583691	+	0.811976i	$0.301608\pi$
$822$	−79.2382	−2.76375
$823$	27.1870	0.947680	0.473840	−	0.880611i	$-0.342867\pi$
$823$	27.1870	0.947680	0.473840	+	0.880611i	$0.342867\pi$
$824$	0.0549815	0.00191537
$825$	10.2426	0.356602
$826$	−18.0908	−0.629460
$827$	14.1336	0.491472	0.245736	−	0.969337i	$-0.420970\pi$
$827$	14.1336	0.491472	0.245736	+	0.969337i	$0.420970\pi$
$828$	−0.405631	−0.0140967
$829$	−7.35030	−0.255287	−0.127643	−	0.991820i	$-0.540741\pi$
$829$	−7.35030	−0.255287	−0.127643	+	0.991820i	$0.540741\pi$
$830$	49.4776	1.71739
$831$	−5.01443	−0.173949
$832$	8.89496	0.308377
$833$	15.9430	0.552391
$834$	21.0459	0.728761
$835$	18.3721	0.635793
$836$	−10.6030	−0.366712
$837$	25.4980	0.881339
$838$	8.67688	0.299738
$839$	6.62382	0.228680	0.114340	−	0.993442i	$-0.463525\pi$
$839$	6.62382	0.228680	0.114340	+	0.993442i	$0.463525\pi$
$840$	−5.56422	−0.191984
$841$	−15.3849	−0.530515
$842$	71.4428	2.46208
$843$	−16.1466	−0.556119
$844$	−45.3785	−1.56199
$845$	40.1633	1.38166
$846$	−0.606911	−0.0208660
$847$	1.71043	0.0587711
$848$	−10.5035	−0.360690
$849$	22.6716	0.778086
$850$	47.0699	1.61448
$851$	−18.9356	−0.649103
$852$	−16.4463	−0.563442
$853$	40.0325	1.37069	0.685343	−	0.728221i	$-0.259652\pi$
$853$	40.0325	1.37069	0.685343	+	0.728221i	$0.259652\pi$
$854$	34.8546	1.19270
$855$	−1.49117	−0.0509969
$856$	0.774888	0.0264851
$857$	4.06798	0.138960	0.0694798	−	0.997583i	$-0.477866\pi$
$857$	4.06798	0.138960	0.0694798	+	0.997583i	$0.477866\pi$
$858$	3.23313	0.110377
$859$	22.1540	0.755885	0.377943	−	0.925829i	$-0.376632\pi$
$859$	22.1540	0.755885	0.377943	+	0.925829i	$0.376632\pi$
$860$	−28.7843	−0.981538
$861$	−16.0789	−0.547967
$862$	−31.4251	−1.07034
$863$	8.95724	0.304908	0.152454	−	0.988311i	$-0.451282\pi$
$863$	8.95724	0.304908	0.152454	+	0.988311i	$0.451282\pi$
$864$	41.4549	1.41032
$865$	55.6434	1.89193
$866$	39.7008	1.34909
$867$	2.97232	0.100945
$868$	19.3951	0.658312
$869$	8.24990	0.279859
$870$	44.1485	1.49677
$871$	−0.727960	−0.0246660
$872$	1.32398	0.0448357
$873$	−0.597629	−0.0202267
$874$	17.7307	0.599749
$875$	−4.61412	−0.155986
$876$	19.9857	0.675255
$877$	51.2708	1.73129	0.865645	−	0.500658i	$-0.166909\pi$
$877$	51.2708	1.73129	0.865645	+	0.500658i	$0.166909\pi$
$878$	49.0357	1.65487
$879$	−35.5609	−1.19944
$880$	−11.1257	−0.375047
$881$	12.2147	0.411523	0.205761	−	0.978602i	$-0.434033\pi$
$881$	12.2147	0.411523	0.205761	+	0.978602i	$0.434033\pi$
$882$	0.817987	0.0275431
$883$	20.6772	0.695843	0.347921	−	0.937524i	$-0.386888\pi$
$883$	20.6772	0.695843	0.347921	+	0.937524i	$0.386888\pi$
$884$	7.90173	0.265764
$885$	29.6236	0.995788
$886$	55.4924	1.86430
$887$	9.51086	0.319343	0.159672	−	0.987170i	$-0.448956\pi$
$887$	9.51086	0.319343	0.159672	+	0.987170i	$0.448956\pi$
$888$	10.1880	0.341886
$889$	11.3863	0.381886
$890$	−51.7546	−1.73482
$891$	9.28197	0.310958
$892$	61.5817	2.06191
$893$	14.1087	0.472128
$894$	−25.7028	−0.859630
$895$	−24.4813	−0.818319
$896$	7.61846	0.254515
$897$	−2.87532	−0.0960042
$898$	10.7008	0.357090
$899$	−18.4166	−0.614227
$900$	1.28436	0.0428121
$901$	−12.1513	−0.404819
$902$	11.0403	0.367602
$903$	−11.5942	−0.385829
$904$	−0.607628	−0.0202094
$905$	46.1759	1.53494
$906$	−9.12740	−0.303238
$907$	9.63520	0.319931	0.159966	−	0.987123i	$-0.448862\pi$
$907$	9.63520	0.319931	0.159966	+	0.987123i	$0.448862\pi$
$908$	28.1249	0.933359
$909$	−0.258632	−0.00857829
$910$	−10.3363	−0.342644
$911$	20.9870	0.695329	0.347665	−	0.937619i	$-0.386975\pi$
$911$	20.9870	0.695329	0.347665	+	0.937619i	$0.386975\pi$
$912$	27.7800	0.919888
$913$	−7.27751	−0.240850
$914$	6.67336	0.220735
$915$	−57.0742	−1.88681
$916$	8.24740	0.272502
$917$	−1.71043	−0.0564834
$918$	41.3161	1.36364
$919$	47.5912	1.56989	0.784945	−	0.619566i	$-0.212691\pi$
$919$	47.5912	1.56989	0.784945	+	0.619566i	$0.212691\pi$
$920$	−3.39776	−0.112021
$921$	−33.7685	−1.11271
$922$	12.7211	0.418947
$923$	−3.65623	−0.120346
$924$	6.83869	0.224976
$925$	59.9563	1.97135
$926$	−7.58049	−0.249110
$927$	−0.00950350	−0.000312136 0
$928$	−29.9418	−0.982889
$929$	15.6727	0.514203	0.257102	−	0.966384i	$-0.417232\pi$
$929$	15.6727	0.514203	0.257102	+	0.966384i	$0.417232\pi$
$930$	−59.7179	−1.95823
$931$	−19.0155	−0.623207
$932$	−31.2991	−1.02523
$933$	9.68915	0.317209
$934$	−0.589179	−0.0192785
$935$	−12.8712	−0.420932
$936$	0.0485183	0.00158587
$937$	20.2378	0.661139	0.330569	−	0.943782i	$-0.392759\pi$
$937$	20.2378	0.661139	0.330569	+	0.943782i	$0.392759\pi$
$938$	−2.89528	−0.0945343
$939$	33.1903	1.08312
$940$	−22.5916	−0.736858
$941$	−40.3738	−1.31615	−0.658075	−	0.752953i	$-0.728629\pi$
$941$	−40.3738	−1.31615	−0.658075	+	0.752953i	$0.728629\pi$
$942$	20.3099	0.661734
$943$	−9.81849	−0.319734
$944$	−17.3083	−0.563337
$945$	−28.7428	−0.935002
$946$	7.96092	0.258832
$947$	−43.5956	−1.41667	−0.708333	−	0.705878i	$-0.750552\pi$
$947$	−43.5956	−1.41667	−0.708333	+	0.705878i	$0.750552\pi$
$948$	32.9850	1.07130
$949$	4.44309	0.144229
$950$	−56.1412	−1.82146
$951$	−25.6857	−0.832915
$952$	3.76107	0.121897
$953$	18.1882	0.589172	0.294586	−	0.955625i	$-0.404818\pi$
$953$	18.1882	0.589172	0.294586	+	0.955625i	$0.404818\pi$
$954$	−0.623449	−0.0201849
$955$	71.7394	2.32143
$956$	−52.7776	−1.70695
$957$	−6.49366	−0.209910
$958$	−12.4391	−0.401891
$959$	−37.2607	−1.20321
$960$	−57.9305	−1.86970
$961$	−6.08862	−0.196407
$962$	18.9255	0.610182
$963$	−0.133939	−0.00431612
$964$	42.7455	1.37674
$965$	−50.7548	−1.63386
$966$	−11.4359	−0.367943
$967$	−50.0614	−1.60986	−0.804932	−	0.593366i	$-0.797799\pi$
$967$	−50.0614	−1.60986	−0.804932	+	0.593366i	$0.797799\pi$
$968$	−0.561957	−0.0180620
$969$	32.1383	1.03243
$970$	−41.8299	−1.34308
$971$	−9.10794	−0.292288	−0.146144	−	0.989263i	$-0.546686\pi$
$971$	−9.10794	−0.292288	−0.146144	+	0.989263i	$0.546686\pi$
$972$	2.29245	0.0735305
$973$	9.89655	0.317269
$974$	64.8614	2.07829
$975$	9.10423	0.291569
$976$	33.3469	1.06741
$977$	−38.7008	−1.23815	−0.619074	−	0.785332i	$-0.712492\pi$
$977$	−38.7008	−1.23815	−0.619074	+	0.785332i	$0.712492\pi$
$978$	−25.7425	−0.823153
$979$	7.61243	0.243294
$980$	30.4487	0.972649
$981$	−0.228849	−0.00730659
$982$	14.0169	0.447296
$983$	−15.0694	−0.480639	−0.240319	−	0.970694i	$-0.577252\pi$
$983$	−15.0694	−0.480639	−0.240319	+	0.970694i	$0.577252\pi$
$984$	5.28267	0.168405
$985$	−50.3618	−1.60466
$986$	−29.8416	−0.950351
$987$	−9.09977	−0.289649
$988$	−9.42455	−0.299835
$989$	−7.07990	−0.225128
$990$	−0.660383	−0.0209884
$991$	−25.7639	−0.818416	−0.409208	−	0.912441i	$-0.634195\pi$
$991$	−25.7639	−0.818416	−0.409208	+	0.912441i	$0.634195\pi$
$992$	40.5012	1.28591
$993$	11.9331	0.378686
$994$	−14.5418	−0.461237
$995$	23.9419	0.759009
$996$	−29.0971	−0.921977
$997$	−6.18203	−0.195787	−0.0978934	−	0.995197i	$-0.531210\pi$
$997$	−6.18203	−0.195787	−0.0978934	+	0.995197i	$0.531210\pi$
$998$	32.8144	1.03872
$999$	52.6273	1.66505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.d.1.6	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.d.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.06686 q^{2} -1.75987 q^{3} +2.27189 q^{4} -3.28939 q^{5} +3.63739 q^{6} +1.71043 q^{7} -0.561957 q^{8} +0.0971338 q^{9} +O(q^{10})\)	\(q-2.06686 q^{2} -1.75987 q^{3} +2.27189 q^{4} -3.28939 q^{5} +3.63739 q^{6} +1.71043 q^{7} -0.561957 q^{8} +0.0971338 q^{9} +6.79870 q^{10} -1.00000 q^{11} -3.99823 q^{12} -0.888858 q^{13} -3.53521 q^{14} +5.78889 q^{15} -3.38230 q^{16} -3.91293 q^{17} -0.200761 q^{18} +4.66703 q^{19} -7.47314 q^{20} -3.01013 q^{21} +2.06686 q^{22} -1.83812 q^{23} +0.988970 q^{24} +5.82010 q^{25} +1.83714 q^{26} +5.10866 q^{27} +3.88591 q^{28} -3.68986 q^{29} -11.9648 q^{30} +4.99113 q^{31} +8.11463 q^{32} +1.75987 q^{33} +8.08747 q^{34} -5.62628 q^{35} +0.220677 q^{36} +10.3016 q^{37} -9.64608 q^{38} +1.56427 q^{39} +1.84850 q^{40} +5.34159 q^{41} +6.22151 q^{42} +3.85171 q^{43} -2.27189 q^{44} -0.319511 q^{45} +3.79913 q^{46} +3.02305 q^{47} +5.95239 q^{48} -4.07442 q^{49} -12.0293 q^{50} +6.88625 q^{51} -2.01939 q^{52} +3.10542 q^{53} -10.5589 q^{54} +3.28939 q^{55} -0.961189 q^{56} -8.21336 q^{57} +7.62640 q^{58} +5.11732 q^{59} +13.1517 q^{60} -9.85925 q^{61} -10.3159 q^{62} +0.166141 q^{63} -10.0072 q^{64} +2.92380 q^{65} -3.63739 q^{66} +0.818983 q^{67} -8.88976 q^{68} +3.23485 q^{69} +11.6287 q^{70} +4.11340 q^{71} -0.0545850 q^{72} -4.99865 q^{73} -21.2919 q^{74} -10.2426 q^{75} +10.6030 q^{76} -1.71043 q^{77} -3.23313 q^{78} -8.24990 q^{79} +11.1257 q^{80} -9.28197 q^{81} -11.0403 q^{82} +7.27751 q^{83} -6.83869 q^{84} +12.8712 q^{85} -7.96092 q^{86} +6.49366 q^{87} +0.561957 q^{88} -7.61243 q^{89} +0.660383 q^{90} -1.52033 q^{91} -4.17601 q^{92} -8.78373 q^{93} -6.24820 q^{94} -15.3517 q^{95} -14.2807 q^{96} -6.15264 q^{97} +8.42124 q^{98} -0.0971338 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * q^99

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