LMFDB - Embedded newform 1441.2.a.e.1.27

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:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.27
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)

$f(q)$	$=$	$q+2.67178 q^{2} -1.26231 q^{3} +5.13839 q^{4} -0.362334 q^{5} -3.37261 q^{6} +0.0617708 q^{7} +8.38506 q^{8} -1.40657 q^{9} +O(q^{10})$	\(q+2.67178 q^{2} -1.26231 q^{3} +5.13839 q^{4} -0.362334 q^{5} -3.37261 q^{6} +0.0617708 q^{7} +8.38506 q^{8} -1.40657 q^{9} -0.968075 q^{10} +1.00000 q^{11} -6.48623 q^{12} +3.38570 q^{13} +0.165038 q^{14} +0.457377 q^{15} +12.1262 q^{16} +3.44123 q^{17} -3.75805 q^{18} +1.54031 q^{19} -1.86181 q^{20} -0.0779739 q^{21} +2.67178 q^{22} +6.24144 q^{23} -10.5845 q^{24} -4.86871 q^{25} +9.04584 q^{26} +5.56246 q^{27} +0.317402 q^{28} +2.65024 q^{29} +1.22201 q^{30} -3.16079 q^{31} +15.6285 q^{32} -1.26231 q^{33} +9.19419 q^{34} -0.0223817 q^{35} -7.22752 q^{36} +7.14203 q^{37} +4.11537 q^{38} -4.27381 q^{39} -3.03819 q^{40} -5.84051 q^{41} -0.208329 q^{42} +1.61375 q^{43} +5.13839 q^{44} +0.509650 q^{45} +16.6757 q^{46} -7.80153 q^{47} -15.3071 q^{48} -6.99618 q^{49} -13.0081 q^{50} -4.34390 q^{51} +17.3971 q^{52} +4.33413 q^{53} +14.8616 q^{54} -0.362334 q^{55} +0.517952 q^{56} -1.94435 q^{57} +7.08084 q^{58} -1.45377 q^{59} +2.35018 q^{60} -4.89476 q^{61} -8.44493 q^{62} -0.0868853 q^{63} +17.5033 q^{64} -1.22676 q^{65} -3.37261 q^{66} +6.96091 q^{67} +17.6824 q^{68} -7.87862 q^{69} -0.0597988 q^{70} -14.2913 q^{71} -11.7942 q^{72} +3.77596 q^{73} +19.0819 q^{74} +6.14582 q^{75} +7.91473 q^{76} +0.0617708 q^{77} -11.4187 q^{78} -4.66074 q^{79} -4.39375 q^{80} -2.80182 q^{81} -15.6045 q^{82} -9.72154 q^{83} -0.400660 q^{84} -1.24687 q^{85} +4.31159 q^{86} -3.34542 q^{87} +8.38506 q^{88} -1.46223 q^{89} +1.36167 q^{90} +0.209138 q^{91} +32.0709 q^{92} +3.98990 q^{93} -20.8439 q^{94} -0.558108 q^{95} -19.7279 q^{96} -9.53019 q^{97} -18.6922 q^{98} -1.40657 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * 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 $

$2$	2.67178	1.88923	0.944615	−	0.328180i	$-0.106435\pi$
$2$	2.67178	1.88923	0.944615	+	0.328180i	$0.106435\pi$
$3$	−1.26231	−0.728795	−0.364397	−	0.931244i	$-0.618725\pi$
$3$	−1.26231	−0.728795	−0.364397	+	0.931244i	$0.618725\pi$
$4$	5.13839	2.56919
$5$	−0.362334	−0.162041	−0.0810203	−	0.996712i	$-0.525818\pi$
$5$	−0.362334	−0.162041	−0.0810203	+	0.996712i	$0.525818\pi$
$6$	−3.37261	−1.37686
$7$	0.0617708	0.0233472	0.0116736	−	0.999932i	$-0.496284\pi$
$7$	0.0617708	0.0233472	0.0116736	+	0.999932i	$0.496284\pi$
$8$	8.38506	2.96457
$9$	−1.40657	−0.468858
$10$	−0.968075	−0.306132
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−6.48623	−1.87241
$13$	3.38570	0.939025	0.469513	−	0.882926i	$-0.344430\pi$
$13$	3.38570	0.939025	0.469513	+	0.882926i	$0.344430\pi$
$14$	0.165038	0.0441082
$15$	0.457377	0.118094
$16$	12.1262	3.03156
$17$	3.44123	0.834621	0.417310	−	0.908764i	$-0.362973\pi$
$17$	3.44123	0.834621	0.417310	+	0.908764i	$0.362973\pi$
$18$	−3.75805	−0.885781
$19$	1.54031	0.353372	0.176686	−	0.984267i	$-0.443462\pi$
$19$	1.54031	0.353372	0.176686	+	0.984267i	$0.443462\pi$
$20$	−1.86181	−0.416314
$21$	−0.0779739	−0.0170153
$22$	2.67178	0.569625
$23$	6.24144	1.30143	0.650715	−	0.759322i	$-0.274469\pi$
$23$	6.24144	1.30143	0.650715	+	0.759322i	$0.274469\pi$
$24$	−10.5845	−2.16056
$25$	−4.86871	−0.973743
$26$	9.04584	1.77404
$27$	5.56246	1.07050
$28$	0.317402	0.0599834
$29$	2.65024	0.492137	0.246068	−	0.969252i	$-0.420861\pi$
$29$	2.65024	0.492137	0.246068	+	0.969252i	$0.420861\pi$
$30$	1.22201	0.223107
$31$	−3.16079	−0.567695	−0.283848	−	0.958869i	$-0.591611\pi$
$31$	−3.16079	−0.567695	−0.283848	+	0.958869i	$0.591611\pi$
$32$	15.6285	2.76275
$33$	−1.26231	−0.219740
$34$	9.19419	1.57679
$35$	−0.0223817	−0.00378319
$36$	−7.22752	−1.20459
$37$	7.14203	1.17414	0.587071	−	0.809535i	$-0.300281\pi$
$37$	7.14203	1.17414	0.587071	+	0.809535i	$0.300281\pi$
$38$	4.11537	0.667602
$39$	−4.27381	−0.684357
$40$	−3.03819	−0.480380
$41$	−5.84051	−0.912135	−0.456067	−	0.889945i	$-0.650742\pi$
$41$	−5.84051	−0.912135	−0.456067	+	0.889945i	$0.650742\pi$
$42$	−0.208329	−0.0321458
$43$	1.61375	0.246095	0.123048	−	0.992401i	$-0.460733\pi$
$43$	1.61375	0.246095	0.123048	+	0.992401i	$0.460733\pi$
$44$	5.13839	0.774641
$45$	0.509650	0.0759741
$46$	16.6757	2.45870
$47$	−7.80153	−1.13797	−0.568985	−	0.822348i	$-0.692664\pi$
$47$	−7.80153	−1.13797	−0.568985	+	0.822348i	$0.692664\pi$
$48$	−15.3071	−2.20938
$49$	−6.99618	−0.999455
$50$	−13.0081	−1.83962
$51$	−4.34390	−0.608267
$52$	17.3971	2.41254
$53$	4.33413	0.595338	0.297669	−	0.954669i	$-0.403791\pi$
$53$	4.33413	0.595338	0.297669	+	0.954669i	$0.403791\pi$
$54$	14.8616	2.02241
$55$	−0.362334	−0.0488571
$56$	0.517952	0.0692143
$57$	−1.94435	−0.257536
$58$	7.08084	0.929760
$59$	−1.45377	−0.189265	−0.0946323	−	0.995512i	$-0.530168\pi$
$59$	−1.45377	−0.189265	−0.0946323	+	0.995512i	$0.530168\pi$
$60$	2.35018	0.303407
$61$	−4.89476	−0.626710	−0.313355	−	0.949636i	$-0.601453\pi$
$61$	−4.89476	−0.626710	−0.313355	+	0.949636i	$0.601453\pi$
$62$	−8.44493	−1.07251
$63$	−0.0868853	−0.0109465
$64$	17.5033	2.18791
$65$	−1.22676	−0.152160
$66$	−3.37261	−0.415139
$67$	6.96091	0.850410	0.425205	−	0.905097i	$-0.360202\pi$
$67$	6.96091	0.850410	0.425205	+	0.905097i	$0.360202\pi$
$68$	17.6824	2.14430
$69$	−7.87862	−0.948475
$70$	−0.0597988	−0.00714732
$71$	−14.2913	−1.69606	−0.848030	−	0.529949i	$-0.822211\pi$
$71$	−14.2913	−1.69606	−0.848030	+	0.529949i	$0.822211\pi$
$72$	−11.7942	−1.38996
$73$	3.77596	0.441943	0.220971	−	0.975280i	$-0.429077\pi$
$73$	3.77596	0.441943	0.220971	+	0.975280i	$0.429077\pi$
$74$	19.0819	2.21823
$75$	6.14582	0.709659
$76$	7.91473	0.907882
$77$	0.0617708	0.00703944
$78$	−11.4187	−1.29291
$79$	−4.66074	−0.524374	−0.262187	−	0.965017i	$-0.584444\pi$
$79$	−4.66074	−0.524374	−0.262187	+	0.965017i	$0.584444\pi$
$80$	−4.39375	−0.491236
$81$	−2.80182	−0.311314
$82$	−15.6045	−1.72323
$83$	−9.72154	−1.06708	−0.533539	−	0.845776i	$-0.679138\pi$
$83$	−9.72154	−1.06708	−0.533539	+	0.845776i	$0.679138\pi$
$84$	−0.400660	−0.0437156
$85$	−1.24687	−0.135242
$86$	4.31159	0.464930
$87$	−3.34542	−0.358667
$88$	8.38506	0.893851
$89$	−1.46223	−0.154997	−0.0774983	−	0.996992i	$-0.524693\pi$
$89$	−1.46223	−0.154997	−0.0774983	+	0.996992i	$0.524693\pi$
$90$	1.36167	0.143533
$91$	0.209138	0.0219236
$92$	32.0709	3.34362
$93$	3.98990	0.413733
$94$	−20.8439	−2.14989
$95$	−0.558108	−0.0572607
$96$	−19.7279	−2.01348
$97$	−9.53019	−0.967644	−0.483822	−	0.875166i	$-0.660752\pi$
$97$	−9.53019	−0.967644	−0.483822	+	0.875166i	$0.660752\pi$
$98$	−18.6922	−1.88820
$99$	−1.40657	−0.141366
$100$	−25.0173	−2.50173
$101$	−1.26659	−0.126031	−0.0630153	−	0.998013i	$-0.520072\pi$
$101$	−1.26659	−0.126031	−0.0630153	+	0.998013i	$0.520072\pi$
$102$	−11.6059	−1.14916
$103$	5.89359	0.580712	0.290356	−	0.956919i	$-0.406226\pi$
$103$	5.89359	0.580712	0.290356	+	0.956919i	$0.406226\pi$
$104$	28.3893	2.78380
$105$	0.0282526	0.00275717
$106$	11.5798	1.12473
$107$	−0.264352	−0.0255559	−0.0127779	−	0.999918i	$-0.504067\pi$
$107$	−0.264352	−0.0255559	−0.0127779	+	0.999918i	$0.504067\pi$
$108$	28.5821	2.75031
$109$	−7.24105	−0.693566	−0.346783	−	0.937945i	$-0.612726\pi$
$109$	−7.24105	−0.693566	−0.346783	+	0.937945i	$0.612726\pi$
$110$	−0.968075	−0.0923023
$111$	−9.01545	−0.855709
$112$	0.749048	0.0707784
$113$	4.51580	0.424811	0.212405	−	0.977182i	$-0.431870\pi$
$113$	4.51580	0.424811	0.212405	+	0.977182i	$0.431870\pi$
$114$	−5.19488	−0.486545
$115$	−2.26148	−0.210884
$116$	13.6179	1.26439
$117$	−4.76225	−0.440270
$118$	−3.88414	−0.357564
$119$	0.212568	0.0194860
$120$	3.83514	0.350099
$121$	1.00000	0.0909091
$122$	−13.0777	−1.18400
$123$	7.37253	0.664759
$124$	−16.2414	−1.45852
$125$	3.57577	0.319827
$126$	−0.232138	−0.0206805
$127$	15.5630	1.38099	0.690495	−	0.723337i	$-0.257393\pi$
$127$	15.5630	1.38099	0.690495	+	0.723337i	$0.257393\pi$
$128$	15.5079	1.37072
$129$	−2.03706	−0.179353
$130$	−3.27761	−0.287466
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−6.48623	−0.564554
$133$	0.0951465	0.00825025
$134$	18.5980	1.60662
$135$	−2.01547	−0.173464
$136$	28.8549	2.47429
$137$	10.5481	0.901189	0.450594	−	0.892729i	$-0.351212\pi$
$137$	10.5481	0.901189	0.450594	+	0.892729i	$0.351212\pi$
$138$	−21.0499	−1.79189
$139$	−10.3031	−0.873897	−0.436949	−	0.899486i	$-0.643941\pi$
$139$	−10.3031	−0.873897	−0.436949	+	0.899486i	$0.643941\pi$
$140$	−0.115006	−0.00971975
$141$	9.84795	0.829347
$142$	−38.1830	−3.20425
$143$	3.38570	0.283127
$144$	−17.0565	−1.42137
$145$	−0.960271	−0.0797461
$146$	10.0885	0.834932
$147$	8.83135	0.728397
$148$	36.6985	3.01660
$149$	−20.3503	−1.66716	−0.833580	−	0.552398i	$-0.813713\pi$
$149$	−20.3503	−1.66716	−0.833580	+	0.552398i	$0.813713\pi$
$150$	16.4203	1.34071
$151$	6.64718	0.540940	0.270470	−	0.962728i	$-0.412821\pi$
$151$	6.64718	0.540940	0.270470	+	0.962728i	$0.412821\pi$
$152$	12.9156	1.04760
$153$	−4.84035	−0.391319
$154$	0.165038	0.0132991
$155$	1.14526	0.0919897
$156$	−21.9605	−1.75824
$157$	−20.1466	−1.60788	−0.803938	−	0.594713i	$-0.797266\pi$
$157$	−20.1466	−1.60788	−0.803938	+	0.594713i	$0.797266\pi$
$158$	−12.4525	−0.990664
$159$	−5.47101	−0.433879
$160$	−5.66272	−0.447677
$161$	0.385539	0.0303847
$162$	−7.48584	−0.588143
$163$	12.8598	1.00726	0.503630	−	0.863919i	$-0.331997\pi$
$163$	12.8598	1.00726	0.503630	+	0.863919i	$0.331997\pi$
$164$	−30.0108	−2.34345
$165$	0.457377	0.0356068
$166$	−25.9738	−2.01596
$167$	−15.5537	−1.20358	−0.601792	−	0.798653i	$-0.705547\pi$
$167$	−15.5537	−1.20358	−0.601792	+	0.798653i	$0.705547\pi$
$168$	−0.653816	−0.0504430
$169$	−1.53701	−0.118231
$170$	−3.33137	−0.255504
$171$	−2.16657	−0.165682
$172$	8.29209	0.632266
$173$	−12.1416	−0.923108	−0.461554	−	0.887112i	$-0.652708\pi$
$173$	−12.1416	−0.923108	−0.461554	+	0.887112i	$0.652708\pi$
$174$	−8.93821	−0.677604
$175$	−0.300745	−0.0227342
$176$	12.1262	0.914049
$177$	1.83511	0.137935
$178$	−3.90676	−0.292824
$179$	23.2337	1.73657	0.868284	−	0.496067i	$-0.165223\pi$
$179$	23.2337	1.73657	0.868284	+	0.496067i	$0.165223\pi$
$180$	2.61878	0.195192
$181$	2.82673	0.210109	0.105054	−	0.994466i	$-0.466498\pi$
$181$	2.82673	0.210109	0.105054	+	0.994466i	$0.466498\pi$
$182$	0.558769	0.0414187
$183$	6.17871	0.456743
$184$	52.3348	3.85818
$185$	−2.58780	−0.190259
$186$	10.6601	0.781638
$187$	3.44123	0.251648
$188$	−40.0873	−2.92367
$189$	0.343598	0.0249931
$190$	−1.49114	−0.108179
$191$	−3.83470	−0.277469	−0.138735	−	0.990330i	$-0.544304\pi$
$191$	−3.83470	−0.277469	−0.138735	+	0.990330i	$0.544304\pi$
$192$	−22.0945	−1.59454
$193$	−14.3896	−1.03578	−0.517892	−	0.855446i	$-0.673283\pi$
$193$	−14.3896	−1.03578	−0.517892	+	0.855446i	$0.673283\pi$
$194$	−25.4625	−1.82810
$195$	1.54854	0.110894
$196$	−35.9491	−2.56779
$197$	5.58262	0.397745	0.198873	−	0.980025i	$-0.436272\pi$
$197$	5.58262	0.397745	0.198873	+	0.980025i	$0.436272\pi$
$198$	−3.75805	−0.267073
$199$	−11.1174	−0.788094	−0.394047	−	0.919090i	$-0.628925\pi$
$199$	−11.1174	−0.788094	−0.394047	+	0.919090i	$0.628925\pi$
$200$	−40.8245	−2.88673
$201$	−8.78682	−0.619775
$202$	−3.38405	−0.238101
$203$	0.163707	0.0114900
$204$	−22.3206	−1.56276
$205$	2.11622	0.147803
$206$	15.7463	1.09710
$207$	−8.77905	−0.610186
$208$	41.0558	2.84671
$209$	1.54031	0.106546
$210$	0.0754846	0.00520893
$211$	8.83808	0.608438	0.304219	−	0.952602i	$-0.401604\pi$
$211$	8.83808	0.608438	0.304219	+	0.952602i	$0.401604\pi$
$212$	22.2704	1.52954
$213$	18.0400	1.23608
$214$	−0.706290	−0.0482810
$215$	−0.584717	−0.0398774
$216$	46.6416	3.17356
$217$	−0.195245	−0.0132541
$218$	−19.3465	−1.31031
$219$	−4.76643	−0.322086
$220$	−1.86181	−0.125523
$221$	11.6510	0.783730
$222$	−24.0873	−1.61663
$223$	−2.75777	−0.184674	−0.0923370	−	0.995728i	$-0.529434\pi$
$223$	−2.75777	−0.184674	−0.0923370	+	0.995728i	$0.529434\pi$
$224$	0.965383	0.0645024
$225$	6.84821	0.456547
$226$	12.0652	0.802565
$227$	20.2075	1.34122	0.670609	−	0.741811i	$-0.266033\pi$
$227$	20.2075	1.34122	0.670609	+	0.741811i	$0.266033\pi$
$228$	−9.99084	−0.661659
$229$	16.9438	1.11968	0.559840	−	0.828601i	$-0.310863\pi$
$229$	16.9438	1.11968	0.559840	+	0.828601i	$0.310863\pi$
$230$	−6.04218	−0.398409
$231$	−0.0779739	−0.00513031
$232$	22.2224	1.45897
$233$	−18.2780	−1.19743	−0.598717	−	0.800960i	$-0.704323\pi$
$233$	−18.2780	−1.19743	−0.598717	+	0.800960i	$0.704323\pi$
$234$	−12.7237	−0.831771
$235$	2.82676	0.184397
$236$	−7.47002	−0.486257
$237$	5.88330	0.382161
$238$	0.567933	0.0368136
$239$	−3.51197	−0.227170	−0.113585	−	0.993528i	$-0.536234\pi$
$239$	−3.51197	−0.227170	−0.113585	+	0.993528i	$0.536234\pi$
$240$	5.54627	0.358010
$241$	−12.8997	−0.830944	−0.415472	−	0.909606i	$-0.636384\pi$
$241$	−12.8997	−0.830944	−0.415472	+	0.909606i	$0.636384\pi$
$242$	2.67178	0.171748
$243$	−13.1506	−0.843612
$244$	−25.1512	−1.61014
$245$	2.53495	0.161952
$246$	19.6978	1.25588
$247$	5.21505	0.331826
$248$	−26.5035	−1.68297
$249$	12.2716	0.777681
$250$	9.55365	0.604226
$251$	26.6418	1.68162	0.840808	−	0.541333i	$-0.182080\pi$
$251$	26.6418	1.68162	0.840808	+	0.541333i	$0.182080\pi$
$252$	−0.446450	−0.0281237
$253$	6.24144	0.392396
$254$	41.5808	2.60901
$255$	1.57394	0.0985640
$256$	6.42704	0.401690
$257$	8.17989	0.510248	0.255124	−	0.966908i	$-0.417884\pi$
$257$	8.17989	0.510248	0.255124	+	0.966908i	$0.417884\pi$
$258$	−5.44256	−0.338839
$259$	0.441169	0.0274129
$260$	−6.30354	−0.390929
$261$	−3.72776	−0.230742
$262$	−2.67178	−0.165063
$263$	25.5379	1.57474	0.787368	−	0.616484i	$-0.211443\pi$
$263$	25.5379	1.57474	0.787368	+	0.616484i	$0.211443\pi$
$264$	−10.5845	−0.651434
$265$	−1.57040	−0.0964689
$266$	0.254210	0.0155866
$267$	1.84579	0.112961
$268$	35.7678	2.18487
$269$	−29.3129	−1.78724	−0.893618	−	0.448827i	$-0.851842\pi$
$269$	−29.3129	−1.78724	−0.893618	+	0.448827i	$0.851842\pi$
$270$	−5.38488	−0.327713
$271$	6.23258	0.378602	0.189301	−	0.981919i	$-0.439378\pi$
$271$	6.23258	0.378602	0.189301	+	0.981919i	$0.439378\pi$
$272$	41.7292	2.53020
$273$	−0.263997	−0.0159778
$274$	28.1823	1.70255
$275$	−4.86871	−0.293595
$276$	−40.4834	−2.43682
$277$	−7.20129	−0.432683	−0.216342	−	0.976318i	$-0.569413\pi$
$277$	−7.20129	−0.432683	−0.216342	+	0.976318i	$0.569413\pi$
$278$	−27.5276	−1.65099
$279$	4.44589	0.266169
$280$	−0.187672	−0.0112155
$281$	15.6597	0.934182	0.467091	−	0.884209i	$-0.345302\pi$
$281$	15.6597	0.934182	0.467091	+	0.884209i	$0.345302\pi$
$282$	26.3115	1.56683
$283$	−13.0602	−0.776348	−0.388174	−	0.921586i	$-0.626894\pi$
$283$	−13.0602	−0.776348	−0.388174	+	0.921586i	$0.626894\pi$
$284$	−73.4340	−4.35750
$285$	0.704505	0.0417313
$286$	9.04584	0.534892
$287$	−0.360773	−0.0212958
$288$	−21.9826	−1.29534
$289$	−5.15794	−0.303408
$290$	−2.56563	−0.150659
$291$	12.0300	0.705214
$292$	19.4023	1.13544
$293$	−12.0268	−0.702612	−0.351306	−	0.936261i	$-0.614262\pi$
$293$	−12.0268	−0.702612	−0.351306	+	0.936261i	$0.614262\pi$
$294$	23.5954	1.37611
$295$	0.526749	0.0306685
$296$	59.8864	3.48082
$297$	5.56246	0.322767
$298$	−54.3714	−3.14965
$299$	21.1317	1.22208
$300$	31.5796	1.82325
$301$	0.0996829	0.00574563
$302$	17.7598	1.02196
$303$	1.59883	0.0918505
$304$	18.6782	1.07127
$305$	1.77354	0.101553
$306$	−12.9323	−0.739292
$307$	−9.02517	−0.515093	−0.257547	−	0.966266i	$-0.582914\pi$
$307$	−9.02517	−0.515093	−0.257547	+	0.966266i	$0.582914\pi$
$308$	0.317402	0.0180857
$309$	−7.43953	−0.423220
$310$	3.05989	0.173790
$311$	20.4716	1.16084	0.580418	−	0.814319i	$-0.302889\pi$
$311$	20.4716	1.16084	0.580418	+	0.814319i	$0.302889\pi$
$312$	−35.8361	−2.02882
$313$	−19.9927	−1.13005	−0.565026	−	0.825073i	$-0.691134\pi$
$313$	−19.9927	−1.13005	−0.565026	+	0.825073i	$0.691134\pi$
$314$	−53.8273	−3.03765
$315$	0.0314815	0.00177378
$316$	−23.9487	−1.34722
$317$	11.4354	0.642275	0.321138	−	0.947033i	$-0.395935\pi$
$317$	11.4354	0.642275	0.321138	+	0.947033i	$0.395935\pi$
$318$	−14.6173	−0.819698
$319$	2.65024	0.148385
$320$	−6.34202	−0.354530
$321$	0.333694	0.0186250
$322$	1.03007	0.0574037
$323$	5.30057	0.294932
$324$	−14.3968	−0.799825
$325$	−16.4840	−0.914369
$326$	34.3586	1.90295
$327$	9.14044	0.505468
$328$	−48.9731	−2.70409
$329$	−0.481907	−0.0265684
$330$	1.22201	0.0672694
$331$	−11.3434	−0.623488	−0.311744	−	0.950166i	$-0.600913\pi$
$331$	−11.3434	−0.623488	−0.311744	+	0.950166i	$0.600913\pi$
$332$	−49.9530	−2.74153
$333$	−10.0458	−0.550506
$334$	−41.5561	−2.27385
$335$	−2.52217	−0.137801
$336$	−0.945530	−0.0515829
$337$	19.1201	1.04154	0.520768	−	0.853698i	$-0.325646\pi$
$337$	19.1201	1.04154	0.520768	+	0.853698i	$0.325646\pi$
$338$	−4.10654	−0.223366
$339$	−5.70034	−0.309600
$340$	−6.40692	−0.347464
$341$	−3.16079	−0.171167
$342$	−5.78858	−0.313011
$343$	−0.864556	−0.0466816
$344$	13.5314	0.729565
$345$	2.85469	0.153691
$346$	−32.4396	−1.74396
$347$	−28.1563	−1.51151	−0.755756	−	0.654854i	$-0.772730\pi$
$347$	−28.1563	−1.51151	−0.755756	+	0.654854i	$0.772730\pi$
$348$	−17.1901	−0.921484
$349$	−3.42026	−0.183083	−0.0915413	−	0.995801i	$-0.529179\pi$
$349$	−3.42026	−0.183083	−0.0915413	+	0.995801i	$0.529179\pi$
$350$	−0.803522	−0.0429501
$351$	18.8328	1.00522
$352$	15.6285	0.833000
$353$	14.7900	0.787193	0.393596	−	0.919283i	$-0.371231\pi$
$353$	14.7900	0.787193	0.393596	+	0.919283i	$0.371231\pi$
$354$	4.90299	0.260591
$355$	5.17820	0.274831
$356$	−7.51352	−0.398216
$357$	−0.268326	−0.0142013
$358$	62.0752	3.28078
$359$	36.3037	1.91604	0.958019	−	0.286706i	$-0.0925604\pi$
$359$	36.3037	1.91604	0.958019	+	0.286706i	$0.0925604\pi$
$360$	4.27344	0.225230
$361$	−16.6274	−0.875128
$362$	7.55238	0.396944
$363$	−1.26231	−0.0662541
$364$	1.07463	0.0563260
$365$	−1.36816	−0.0716127
$366$	16.5081	0.862893
$367$	−13.9395	−0.727637	−0.363819	−	0.931470i	$-0.618527\pi$
$367$	−13.9395	−0.727637	−0.363819	+	0.931470i	$0.618527\pi$
$368$	75.6851	3.94536
$369$	8.21512	0.427662
$370$	−6.91402	−0.359443
$371$	0.267723	0.0138995
$372$	20.5017	1.06296
$373$	−36.1906	−1.87388	−0.936939	−	0.349493i	$-0.886354\pi$
$373$	−36.1906	−1.87388	−0.936939	+	0.349493i	$0.886354\pi$
$374$	9.19419	0.475420
$375$	−4.51373	−0.233088
$376$	−65.4163	−3.37359
$377$	8.97292	0.462129
$378$	0.918017	0.0472177
$379$	−26.4443	−1.35835	−0.679175	−	0.733976i	$-0.737662\pi$
$379$	−26.4443	−1.35835	−0.679175	+	0.733976i	$0.737662\pi$
$380$	−2.86777	−0.147114
$381$	−19.6453	−1.00646
$382$	−10.2455	−0.524203
$383$	−22.1632	−1.13249	−0.566244	−	0.824238i	$-0.691604\pi$
$383$	−22.1632	−1.13249	−0.566244	+	0.824238i	$0.691604\pi$
$384$	−19.5757	−0.998970
$385$	−0.0223817	−0.00114068
$386$	−38.4457	−1.95684
$387$	−2.26986	−0.115384
$388$	−48.9698	−2.48606
$389$	7.43397	0.376917	0.188459	−	0.982081i	$-0.439651\pi$
$389$	7.43397	0.376917	0.188459	+	0.982081i	$0.439651\pi$
$390$	4.13736	0.209504
$391$	21.4782	1.08620
$392$	−58.6634	−2.96295
$393$	1.26231	0.0636751
$394$	14.9155	0.751433
$395$	1.68874	0.0849699
$396$	−7.22752	−0.363197
$397$	32.7419	1.64327	0.821634	−	0.570016i	$-0.193063\pi$
$397$	32.7419	1.64327	0.821634	+	0.570016i	$0.193063\pi$
$398$	−29.7033	−1.48889
$399$	−0.120104	−0.00601274
$400$	−59.0392	−2.95196
$401$	−10.0162	−0.500188	−0.250094	−	0.968222i	$-0.580461\pi$
$401$	−10.0162	−0.500188	−0.250094	+	0.968222i	$0.580461\pi$
$402$	−23.4764	−1.17090
$403$	−10.7015	−0.533080
$404$	−6.50824	−0.323797
$405$	1.01520	0.0504455
$406$	0.437389	0.0217073
$407$	7.14203	0.354017
$408$	−36.4238	−1.80325
$409$	18.2136	0.900605	0.450302	−	0.892876i	$-0.351316\pi$
$409$	18.2136	0.900605	0.450302	+	0.892876i	$0.351316\pi$
$410$	5.65405	0.279234
$411$	−13.3150	−0.656782
$412$	30.2835	1.49196
$413$	−0.0898005	−0.00441879
$414$	−23.4556	−1.15278
$415$	3.52244	0.172910
$416$	52.9133	2.59429
$417$	13.0057	0.636892
$418$	4.11537	0.201290
$419$	17.2145	0.840981	0.420491	−	0.907297i	$-0.361858\pi$
$419$	17.2145	0.840981	0.420491	+	0.907297i	$0.361858\pi$
$420$	0.145173	0.00708370
$421$	−14.0564	−0.685065	−0.342532	−	0.939506i	$-0.611285\pi$
$421$	−14.0564	−0.685065	−0.342532	+	0.939506i	$0.611285\pi$
$422$	23.6134	1.14948
$423$	10.9734	0.533547
$424$	36.3419	1.76492
$425$	−16.7544	−0.812706
$426$	48.1988	2.33524
$427$	−0.302354	−0.0146319
$428$	−1.35834	−0.0656580
$429$	−4.27381	−0.206341
$430$	−1.56223	−0.0753376
$431$	2.13221	0.102705	0.0513525	−	0.998681i	$-0.483647\pi$
$431$	2.13221	0.102705	0.0513525	+	0.998681i	$0.483647\pi$
$432$	67.4517	3.24527
$433$	18.0792	0.868830	0.434415	−	0.900713i	$-0.356955\pi$
$433$	18.0792	0.868830	0.434415	+	0.900713i	$0.356955\pi$
$434$	−0.521651	−0.0250400
$435$	1.21216	0.0581186
$436$	−37.2073	−1.78191
$437$	9.61377	0.459889
$438$	−12.7348	−0.608494
$439$	−15.4440	−0.737103	−0.368552	−	0.929607i	$-0.620146\pi$
$439$	−15.4440	−0.737103	−0.368552	+	0.929607i	$0.620146\pi$
$440$	−3.03819	−0.144840
$441$	9.84066	0.468603
$442$	31.1288	1.48065
$443$	5.61909	0.266971	0.133485	−	0.991051i	$-0.457383\pi$
$443$	5.61909	0.266971	0.133485	+	0.991051i	$0.457383\pi$
$444$	−46.3249	−2.19848
$445$	0.529817	0.0251157
$446$	−7.36814	−0.348892
$447$	25.6884	1.21502
$448$	1.08119	0.0510815
$449$	39.2975	1.85457	0.927283	−	0.374362i	$-0.122138\pi$
$449$	39.2975	1.85457	0.927283	+	0.374362i	$0.122138\pi$
$450$	18.2969	0.862523
$451$	−5.84051	−0.275019
$452$	23.2039	1.09142
$453$	−8.39080	−0.394234
$454$	53.9898	2.53387
$455$	−0.0757777	−0.00355251
$456$	−16.3035	−0.763482
$457$	36.8812	1.72523	0.862616	−	0.505860i	$-0.168825\pi$
$457$	36.8812	1.72523	0.862616	+	0.505860i	$0.168825\pi$
$458$	45.2701	2.11533
$459$	19.1417	0.893458
$460$	−11.6204	−0.541803
$461$	15.6920	0.730848	0.365424	−	0.930841i	$-0.380924\pi$
$461$	15.6920	0.730848	0.365424	+	0.930841i	$0.380924\pi$
$462$	−0.208329	−0.00969234
$463$	18.5445	0.861835	0.430918	−	0.902391i	$-0.358190\pi$
$463$	18.5445	0.861835	0.430918	+	0.902391i	$0.358190\pi$
$464$	32.1374	1.49194
$465$	−1.44568	−0.0670416
$466$	−48.8348	−2.26223
$467$	34.4834	1.59570	0.797850	−	0.602856i	$-0.205971\pi$
$467$	34.4834	1.59570	0.797850	+	0.602856i	$0.205971\pi$
$468$	−24.4703	−1.13114
$469$	0.429981	0.0198547
$470$	7.55247	0.348369
$471$	25.4313	1.17181
$472$	−12.1899	−0.561087
$473$	1.61375	0.0742005
$474$	15.7188	0.721991
$475$	−7.49935	−0.344094
$476$	1.09225	0.0500634
$477$	−6.09627	−0.279129
$478$	−9.38320	−0.429177
$479$	26.9256	1.23026	0.615131	−	0.788425i	$-0.289103\pi$
$479$	26.9256	1.23026	0.615131	+	0.788425i	$0.289103\pi$
$480$	7.14810	0.326265
$481$	24.1808	1.10255
$482$	−34.4652	−1.56985
$483$	−0.486669	−0.0221442
$484$	5.13839	0.233563
$485$	3.45311	0.156798
$486$	−35.1355	−1.59378
$487$	−1.22364	−0.0554485	−0.0277243	−	0.999616i	$-0.508826\pi$
$487$	−1.22364	−0.0554485	−0.0277243	+	0.999616i	$0.508826\pi$
$488$	−41.0429	−1.85792
$489$	−16.2331	−0.734086
$490$	6.77283	0.305965
$491$	14.2588	0.643490	0.321745	−	0.946826i	$-0.395731\pi$
$491$	14.2588	0.643490	0.321745	+	0.946826i	$0.395731\pi$
$492$	37.8829	1.70789
$493$	9.12008	0.410748
$494$	13.9334	0.626895
$495$	0.509650	0.0229070
$496$	−38.3285	−1.72100
$497$	−0.882783	−0.0395982
$498$	32.7869	1.46922
$499$	−36.6354	−1.64003	−0.820014	−	0.572344i	$-0.806034\pi$
$499$	−36.6354	−1.64003	−0.820014	+	0.572344i	$0.806034\pi$
$500$	18.3737	0.821696
$501$	19.6336	0.877166
$502$	71.1810	3.17696
$503$	13.1902	0.588124	0.294062	−	0.955786i	$-0.404993\pi$
$503$	13.1902	0.588124	0.294062	+	0.955786i	$0.404993\pi$
$504$	−0.728539	−0.0324517
$505$	0.458929	0.0204221
$506$	16.6757	0.741326
$507$	1.94018	0.0861663
$508$	79.9686	3.54803
$509$	−24.5919	−1.09002	−0.545009	−	0.838430i	$-0.683474\pi$
$509$	−24.5919	−1.09002	−0.545009	+	0.838430i	$0.683474\pi$
$510$	4.20522	0.186210
$511$	0.233244	0.0103181
$512$	−13.8441	−0.611831
$513$	8.56794	0.378284
$514$	21.8548	0.963975
$515$	−2.13545	−0.0940990
$516$	−10.4672	−0.460792
$517$	−7.80153	−0.343111
$518$	1.17871	0.0517893
$519$	15.3264	0.672756
$520$	−10.2864	−0.451089
$521$	−3.13351	−0.137282	−0.0686409	−	0.997641i	$-0.521866\pi$
$521$	−3.13351	−0.137282	−0.0686409	+	0.997641i	$0.521866\pi$
$522$	−9.95973	−0.435926
$523$	4.59195	0.200792	0.100396	−	0.994948i	$-0.467989\pi$
$523$	4.59195	0.200792	0.100396	+	0.994948i	$0.467989\pi$
$524$	−5.13839	−0.224471
$525$	0.379633	0.0165685
$526$	68.2316	2.97504
$527$	−10.8770	−0.473810
$528$	−15.3071	−0.666154
$529$	15.9555	0.693719
$530$	−4.19576	−0.182252
$531$	2.04483	0.0887382
$532$	0.488899	0.0211965
$533$	−19.7742	−0.856518
$534$	4.93154	0.213409
$535$	0.0957837	0.00414109
$536$	58.3677	2.52110
$537$	−29.3281	−1.26560
$538$	−78.3174	−3.37650
$539$	−6.99618	−0.301347
$540$	−10.3563	−0.445662
$541$	0.197899	0.00850833	0.00425417	−	0.999991i	$-0.498646\pi$
$541$	0.197899	0.00850833	0.00425417	+	0.999991i	$0.498646\pi$
$542$	16.6521	0.715267
$543$	−3.56820	−0.153126
$544$	53.7811	2.30585
$545$	2.62368	0.112386
$546$	−0.705340	−0.0301858
$547$	28.9378	1.23729	0.618646	−	0.785670i	$-0.287682\pi$
$547$	28.9378	1.23729	0.618646	+	0.785670i	$0.287682\pi$
$548$	54.2004	2.31533
$549$	6.88485	0.293838
$550$	−13.0081	−0.554668
$551$	4.08220	0.173907
$552$	−66.0628	−2.81182
$553$	−0.287898	−0.0122427
$554$	−19.2402	−0.817439
$555$	3.26660	0.138660
$556$	−52.9413	−2.24521
$557$	21.1726	0.897112	0.448556	−	0.893755i	$-0.351938\pi$
$557$	21.1726	0.897112	0.448556	+	0.893755i	$0.351938\pi$
$558$	11.8784	0.502854
$559$	5.46369	0.231090
$560$	−0.271405	−0.0114690
$561$	−4.34390	−0.183399
$562$	41.8393	1.76489
$563$	−12.3698	−0.521323	−0.260662	−	0.965430i	$-0.583941\pi$
$563$	−12.3698	−0.521323	−0.260662	+	0.965430i	$0.583941\pi$
$564$	50.6026	2.13075
$565$	−1.63623	−0.0688366
$566$	−34.8939	−1.46670
$567$	−0.173071	−0.00726830
$568$	−119.833	−5.02808
$569$	−14.2348	−0.596754	−0.298377	−	0.954448i	$-0.596445\pi$
$569$	−14.2348	−0.596754	−0.298377	+	0.954448i	$0.596445\pi$
$570$	1.88228	0.0788400
$571$	9.07399	0.379735	0.189867	−	0.981810i	$-0.439194\pi$
$571$	9.07399	0.379735	0.189867	+	0.981810i	$0.439194\pi$
$572$	17.3971	0.727407
$573$	4.84058	0.202218
$574$	−0.963906	−0.0402326
$575$	−30.3878	−1.26726
$576$	−24.6196	−1.02582
$577$	25.6025	1.06585	0.532923	−	0.846164i	$-0.321094\pi$
$577$	25.6025	1.06585	0.532923	+	0.846164i	$0.321094\pi$
$578$	−13.7809	−0.573208
$579$	18.1641	0.754874
$580$	−4.93424	−0.204883
$581$	−0.600508	−0.0249133
$582$	32.1416	1.33231
$583$	4.33413	0.179501
$584$	31.6617	1.31017
$585$	1.72552	0.0713416
$586$	−32.1328	−1.32740
$587$	29.8738	1.23302	0.616512	−	0.787345i	$-0.288545\pi$
$587$	29.8738	1.23302	0.616512	+	0.787345i	$0.288545\pi$
$588$	45.3789	1.87139
$589$	−4.86862	−0.200608
$590$	1.40736	0.0579400
$591$	−7.04700	−0.289875
$592$	86.6059	3.55948
$593$	−38.9969	−1.60141	−0.800705	−	0.599059i	$-0.795542\pi$
$593$	−38.9969	−1.60141	−0.800705	+	0.599059i	$0.795542\pi$
$594$	14.8616	0.609781
$595$	−0.0770205	−0.00315753
$596$	−104.568	−4.28326
$597$	14.0336	0.574359
$598$	56.4591	2.30878
$599$	29.4681	1.20403	0.602017	−	0.798483i	$-0.294364\pi$
$599$	29.4681	1.20403	0.602017	+	0.798483i	$0.294364\pi$
$600$	51.5331	2.10383
$601$	5.41893	0.221043	0.110521	−	0.993874i	$-0.464748\pi$
$601$	5.41893	0.221043	0.110521	+	0.993874i	$0.464748\pi$
$602$	0.266330	0.0108548
$603$	−9.79104	−0.398722
$604$	34.1558	1.38978
$605$	−0.362334	−0.0147310
$606$	4.27172	0.173527
$607$	−5.67374	−0.230290	−0.115145	−	0.993349i	$-0.536733\pi$
$607$	−5.67374	−0.230290	−0.115145	+	0.993349i	$0.536733\pi$
$608$	24.0727	0.976278
$609$	−0.206649	−0.00837386
$610$	4.73850	0.191856
$611$	−26.4137	−1.06858
$612$	−24.8716	−1.00537
$613$	6.79571	0.274476	0.137238	−	0.990538i	$-0.456177\pi$
$613$	6.79571	0.274476	0.137238	+	0.990538i	$0.456177\pi$
$614$	−24.1132	−0.973130
$615$	−2.67132	−0.107718
$616$	0.517952	0.0208689
$617$	9.85497	0.396746	0.198373	−	0.980127i	$-0.436434\pi$
$617$	9.85497	0.396746	0.198373	+	0.980127i	$0.436434\pi$
$618$	−19.8768	−0.799560
$619$	8.89018	0.357327	0.178663	−	0.983910i	$-0.442823\pi$
$619$	8.89018	0.357327	0.178663	+	0.983910i	$0.442823\pi$
$620$	5.88480	0.236339
$621$	34.7177	1.39318
$622$	54.6954	2.19309
$623$	−0.0903234	−0.00361873
$624$	−51.8252	−2.07467
$625$	23.0479	0.921918
$626$	−53.4159	−2.13493
$627$	−1.94435	−0.0776500
$628$	−103.521	−4.13094
$629$	24.5774	0.979964
$630$	0.0841115	0.00335108
$631$	−15.4776	−0.616153	−0.308076	−	0.951362i	$-0.599685\pi$
$631$	−15.4776	−0.616153	−0.308076	+	0.951362i	$0.599685\pi$
$632$	−39.0806	−1.55454
$633$	−11.1564	−0.443427
$634$	30.5528	1.21341
$635$	−5.63899	−0.223777
$636$	−28.1122	−1.11472
$637$	−23.6870	−0.938514
$638$	7.08084	0.280333
$639$	20.1017	0.795212
$640$	−5.61903	−0.222112
$641$	−28.2724	−1.11669	−0.558346	−	0.829608i	$-0.688564\pi$
$641$	−28.2724	−1.11669	−0.558346	+	0.829608i	$0.688564\pi$
$642$	0.891556	0.0351869
$643$	11.3126	0.446124	0.223062	−	0.974804i	$-0.428395\pi$
$643$	11.3126	0.446124	0.223062	+	0.974804i	$0.428395\pi$
$644$	1.98105	0.0780642
$645$	0.738094	0.0290624
$646$	14.1619	0.557194
$647$	36.6234	1.43981	0.719907	−	0.694070i	$-0.244184\pi$
$647$	36.6234	1.43981	0.719907	+	0.694070i	$0.244184\pi$
$648$	−23.4935	−0.922910
$649$	−1.45377	−0.0570654
$650$	−44.0416	−1.72745
$651$	0.246460	0.00965951
$652$	66.0788	2.58785
$653$	−16.0980	−0.629964	−0.314982	−	0.949098i	$-0.601998\pi$
$653$	−16.0980	−0.629964	−0.314982	+	0.949098i	$0.601998\pi$
$654$	24.4212	0.954945
$655$	0.362334	0.0141576
$656$	−70.8234	−2.76519
$657$	−5.31117	−0.207209
$658$	−1.28755	−0.0501939
$659$	−26.1107	−1.01713	−0.508565	−	0.861024i	$-0.669824\pi$
$659$	−26.1107	−1.01713	−0.508565	+	0.861024i	$0.669824\pi$
$660$	2.35018	0.0914807
$661$	10.4885	0.407954	0.203977	−	0.978976i	$-0.434613\pi$
$661$	10.4885	0.407954	0.203977	+	0.978976i	$0.434613\pi$
$662$	−30.3070	−1.17791
$663$	−14.7072	−0.571178
$664$	−81.5157	−3.16342
$665$	−0.0344748	−0.00133688
$666$	−26.8401	−1.04003
$667$	16.5413	0.640481
$668$	−79.9211	−3.09224
$669$	3.48116	0.134589
$670$	−6.73868	−0.260338
$671$	−4.89476	−0.188960
$672$	−1.21861	−0.0470090
$673$	0.717453	0.0276558	0.0138279	−	0.999904i	$-0.495598\pi$
$673$	0.717453	0.0276558	0.0138279	+	0.999904i	$0.495598\pi$
$674$	51.0845	1.96770
$675$	−27.0820	−1.04239
$676$	−7.89773	−0.303759
$677$	−47.4107	−1.82214	−0.911070	−	0.412251i	$-0.864743\pi$
$677$	−47.4107	−1.82214	−0.911070	+	0.412251i	$0.864743\pi$
$678$	−15.2300	−0.584905
$679$	−0.588688	−0.0225918
$680$	−10.4551	−0.400935
$681$	−25.5081	−0.977472
$682$	−8.44493	−0.323373
$683$	11.7603	0.449997	0.224999	−	0.974359i	$-0.427762\pi$
$683$	11.7603	0.449997	0.224999	+	0.974359i	$0.427762\pi$
$684$	−11.1327	−0.425668
$685$	−3.82195	−0.146029
$686$	−2.30990	−0.0881924
$687$	−21.3884	−0.816017
$688$	19.5688	0.746052
$689$	14.6741	0.559038
$690$	7.62710	0.290359
$691$	−51.2945	−1.95134	−0.975668	−	0.219254i	$-0.929638\pi$
$691$	−51.2945	−1.95134	−0.975668	+	0.219254i	$0.929638\pi$
$692$	−62.3882	−2.37164
$693$	−0.0868853	−0.00330050
$694$	−75.2274	−2.85559
$695$	3.73316	0.141607
$696$	−28.0516	−1.06329
$697$	−20.0985	−0.761287
$698$	−9.13818	−0.345885
$699$	23.0726	0.872684
$700$	−1.54534	−0.0584084
$701$	28.3838	1.07204	0.536021	−	0.844205i	$-0.319927\pi$
$701$	28.3838	1.07204	0.536021	+	0.844205i	$0.319927\pi$
$702$	50.3171	1.89910
$703$	11.0010	0.414909
$704$	17.5033	0.659679
$705$	−3.56825	−0.134388
$706$	39.5156	1.48719
$707$	−0.0782385	−0.00294246
$708$	9.42948	0.354382
$709$	−2.57869	−0.0968448	−0.0484224	−	0.998827i	$-0.515419\pi$
$709$	−2.57869	−0.0968448	−0.0484224	+	0.998827i	$0.515419\pi$
$710$	13.8350	0.519218
$711$	6.55568	0.245857
$712$	−12.2609	−0.459498
$713$	−19.7279	−0.738816
$714$	−0.716907	−0.0268296
$715$	−1.22676	−0.0458780
$716$	119.384	4.46158
$717$	4.43319	0.165561
$718$	96.9954	3.61984
$719$	5.68219	0.211910	0.105955	−	0.994371i	$-0.466210\pi$
$719$	5.68219	0.211910	0.105955	+	0.994371i	$0.466210\pi$
$720$	6.18013	0.230320
$721$	0.364052	0.0135580
$722$	−44.4248	−1.65332
$723$	16.2834	0.605588
$724$	14.5248	0.539810
$725$	−12.9032	−0.479215
$726$	−3.37261	−0.125169
$727$	14.9429	0.554200	0.277100	−	0.960841i	$-0.410627\pi$
$727$	14.9429	0.554200	0.277100	+	0.960841i	$0.410627\pi$
$728$	1.75363	0.0649940
$729$	25.0056	0.926134
$730$	−3.65541	−0.135293
$731$	5.55330	0.205396
$732$	31.7486	1.17346
$733$	4.57422	0.168953	0.0844763	−	0.996425i	$-0.473078\pi$
$733$	4.57422	0.168953	0.0844763	+	0.996425i	$0.473078\pi$
$734$	−37.2433	−1.37468
$735$	−3.19990	−0.118030
$736$	97.5440	3.59552
$737$	6.96091	0.256408
$738$	21.9490	0.807952
$739$	41.3271	1.52024	0.760120	−	0.649782i	$-0.225140\pi$
$739$	41.3271	1.52024	0.760120	+	0.649782i	$0.225140\pi$
$740$	−13.2971	−0.488811
$741$	−6.58300	−0.241833
$742$	0.715295	0.0262593
$743$	−14.1869	−0.520466	−0.260233	−	0.965546i	$-0.583799\pi$
$743$	−14.1869	−0.520466	−0.260233	+	0.965546i	$0.583799\pi$
$744$	33.4556	1.22654
$745$	7.37360	0.270148
$746$	−96.6932	−3.54019
$747$	13.6741	0.500308
$748$	17.6824	0.646531
$749$	−0.0163293	−0.000596658 0
$750$	−12.0597	−0.440357
$751$	7.69984	0.280971	0.140486	−	0.990083i	$-0.455134\pi$
$751$	7.69984	0.280971	0.140486	+	0.990083i	$0.455134\pi$
$752$	−94.6032	−3.44982
$753$	−33.6302	−1.22555
$754$	23.9736	0.873068
$755$	−2.40850	−0.0876543
$756$	1.76554	0.0642120
$757$	−21.2383	−0.771918	−0.385959	−	0.922516i	$-0.626129\pi$
$757$	−21.2383	−0.771918	−0.385959	+	0.922516i	$0.626129\pi$
$758$	−70.6531	−2.56624
$759$	−7.87862	−0.285976
$760$	−4.67977	−0.169753
$761$	−24.3557	−0.882893	−0.441447	−	0.897287i	$-0.645535\pi$
$761$	−24.3557	−0.882893	−0.441447	+	0.897287i	$0.645535\pi$
$762$	−52.4878	−1.90143
$763$	−0.447286	−0.0161928
$764$	−19.7042	−0.712872
$765$	1.75382	0.0634096
$766$	−59.2151	−2.13953
$767$	−4.92203	−0.177724
$768$	−8.11291	−0.292749
$769$	−39.5851	−1.42747	−0.713737	−	0.700413i	$-0.752999\pi$
$769$	−39.5851	−1.42747	−0.713737	+	0.700413i	$0.752999\pi$
$770$	−0.0597988	−0.00215500
$771$	−10.3256	−0.371866
$772$	−73.9392	−2.66113
$773$	−38.8121	−1.39597	−0.697987	−	0.716110i	$-0.745921\pi$
$773$	−38.8121	−1.39597	−0.697987	+	0.716110i	$0.745921\pi$
$774$	−6.06457	−0.217986
$775$	15.3890	0.552789
$776$	−79.9112	−2.86865
$777$	−0.556892	−0.0199784
$778$	19.8619	0.712083
$779$	−8.99622	−0.322323
$780$	7.95702	0.284907
$781$	−14.2913	−0.511381
$782$	57.3850	2.05208
$783$	14.7418	0.526830
$784$	−84.8374	−3.02991
$785$	7.29981	0.260541
$786$	3.37261	0.120297
$787$	23.5647	0.839989	0.419995	−	0.907527i	$-0.362032\pi$
$787$	23.5647	0.839989	0.419995	+	0.907527i	$0.362032\pi$
$788$	28.6857	1.02188
$789$	−32.2368	−1.14766
$790$	4.51194	0.160528
$791$	0.278945	0.00991813
$792$	−11.7942	−0.419089
$793$	−16.5722	−0.588497
$794$	87.4789	3.10451
$795$	1.98233	0.0703061
$796$	−57.1257	−2.02477
$797$	−0.201689	−0.00714420	−0.00357210	−	0.999994i	$-0.501137\pi$
$797$	−0.201689	−0.00714420	−0.00357210	+	0.999994i	$0.501137\pi$
$798$	−0.320892	−0.0113594
$799$	−26.8469	−0.949774
$800$	−76.0905	−2.69020
$801$	2.05674	0.0726714
$802$	−26.7612	−0.944970
$803$	3.77596	0.133251
$804$	−45.1501	−1.59232
$805$	−0.139694	−0.00492356
$806$	−28.5921	−1.00711
$807$	37.0019	1.30253
$808$	−10.6205	−0.373626
$809$	−22.7813	−0.800948	−0.400474	−	0.916308i	$-0.631155\pi$
$809$	−22.7813	−0.800948	−0.400474	+	0.916308i	$0.631155\pi$
$810$	2.71237	0.0953031
$811$	1.30949	0.0459825	0.0229912	−	0.999736i	$-0.492681\pi$
$811$	1.30949	0.0459825	0.0229912	+	0.999736i	$0.492681\pi$
$812$	0.841192	0.0295200
$813$	−7.86745	−0.275923
$814$	19.0819	0.668820
$815$	−4.65955	−0.163217
$816$	−52.6751	−1.84400
$817$	2.48569	0.0869632
$818$	48.6627	1.70145
$819$	−0.294168	−0.0102791
$820$	10.8739	0.379734
$821$	14.0984	0.492039	0.246019	−	0.969265i	$-0.420877\pi$
$821$	14.0984	0.492039	0.246019	+	0.969265i	$0.420877\pi$
$822$	−35.5748	−1.24081
$823$	−5.57139	−0.194206	−0.0971032	−	0.995274i	$-0.530958\pi$
$823$	−5.57139	−0.194206	−0.0971032	+	0.995274i	$0.530958\pi$
$824$	49.4181	1.72156
$825$	6.14582	0.213970
$826$	−0.239927	−0.00834812
$827$	−28.5741	−0.993618	−0.496809	−	0.867860i	$-0.665495\pi$
$827$	−28.5741	−0.993618	−0.496809	+	0.867860i	$0.665495\pi$
$828$	−45.1101	−1.56769
$829$	35.0682	1.21797	0.608984	−	0.793182i	$-0.291577\pi$
$829$	35.0682	1.21797	0.608984	+	0.793182i	$0.291577\pi$
$830$	9.41118	0.326667
$831$	9.09025	0.315337
$832$	59.2609	2.05450
$833$	−24.0755	−0.834166
$834$	34.7483	1.20324
$835$	5.63565	0.195030
$836$	7.91473	0.273737
$837$	−17.5818	−0.607716
$838$	45.9932	1.58881
$839$	27.3368	0.943771	0.471886	−	0.881660i	$-0.343574\pi$
$839$	27.3368	0.943771	0.471886	+	0.881660i	$0.343574\pi$
$840$	0.236900	0.00817382
$841$	−21.9762	−0.757801
$842$	−37.5554	−1.29425
$843$	−19.7674	−0.680827
$844$	45.4134	1.56320
$845$	0.556910	0.0191583
$846$	29.3186	1.00799
$847$	0.0617708	0.00212247
$848$	52.5566	1.80480
$849$	16.4860	0.565798
$850$	−44.7639	−1.53539
$851$	44.5765	1.52806
$852$	92.6964	3.17573
$853$	−15.7514	−0.539316	−0.269658	−	0.962956i	$-0.586911\pi$
$853$	−15.7514	−0.539316	−0.269658	+	0.962956i	$0.586911\pi$
$854$	−0.807821	−0.0276431
$855$	0.785020	0.0268471
$856$	−2.21661	−0.0757622
$857$	−35.0388	−1.19690	−0.598451	−	0.801159i	$-0.704217\pi$
$857$	−35.0388	−1.19690	−0.598451	+	0.801159i	$0.704217\pi$
$858$	−11.4187	−0.389826
$859$	−34.4884	−1.17673	−0.588365	−	0.808595i	$-0.700228\pi$
$859$	−34.4884	−1.17673	−0.588365	+	0.808595i	$0.700228\pi$
$860$	−3.00450	−0.102453
$861$	0.455408	0.0155203
$862$	5.69680	0.194034
$863$	34.4711	1.17341	0.586705	−	0.809800i	$-0.300425\pi$
$863$	34.4711	1.17341	0.586705	+	0.809800i	$0.300425\pi$
$864$	86.9327	2.95751
$865$	4.39931	0.149581
$866$	48.3035	1.64142
$867$	6.51091	0.221122
$868$	−1.00324	−0.0340523
$869$	−4.66074	−0.158105
$870$	3.23862	0.109799
$871$	23.5676	0.798557
$872$	−60.7166	−2.05612
$873$	13.4049	0.453688
$874$	25.6858	0.868837
$875$	0.220878	0.00746705
$876$	−24.4918	−0.827500
$877$	−45.0624	−1.52165	−0.760824	−	0.648958i	$-0.775205\pi$
$877$	−45.0624	−1.52165	−0.760824	+	0.648958i	$0.775205\pi$
$878$	−41.2630	−1.39256
$879$	15.1815	0.512060
$880$	−4.39375	−0.148113
$881$	−8.59302	−0.289506	−0.144753	−	0.989468i	$-0.546239\pi$
$881$	−8.59302	−0.289506	−0.144753	+	0.989468i	$0.546239\pi$
$882$	26.2920	0.885299
$883$	−31.6322	−1.06451	−0.532255	−	0.846584i	$-0.678655\pi$
$883$	−31.6322	−1.06451	−0.532255	+	0.846584i	$0.678655\pi$
$884$	59.8673	2.01355
$885$	−0.664921	−0.0223511
$886$	15.0129	0.504370
$887$	39.2355	1.31740	0.658699	−	0.752406i	$-0.271107\pi$
$887$	39.2355	1.31740	0.658699	+	0.752406i	$0.271107\pi$
$888$	−75.5951	−2.53681
$889$	0.961338	0.0322423
$890$	1.41555	0.0474494
$891$	−2.80182	−0.0938646
$892$	−14.1705	−0.474463
$893$	−12.0168	−0.402127
$894$	68.6335	2.29545
$895$	−8.41836	−0.281395
$896$	0.957934	0.0320023
$897$	−26.6747	−0.890642
$898$	104.994	3.50370
$899$	−8.37686	−0.279384
$900$	35.1887	1.17296
$901$	14.9147	0.496882
$902$	−15.6045	−0.519574
$903$	−0.125831	−0.00418738
$904$	37.8653	1.25938
$905$	−1.02422	−0.0340462
$906$	−22.4183	−0.744799
$907$	34.5977	1.14880	0.574398	−	0.818576i	$-0.305236\pi$
$907$	34.5977	1.14880	0.574398	+	0.818576i	$0.305236\pi$
$908$	103.834	3.44585
$909$	1.78156	0.0590905
$910$	−0.202461	−0.00671152
$911$	25.4890	0.844488	0.422244	−	0.906482i	$-0.361243\pi$
$911$	25.4890	0.844488	0.422244	+	0.906482i	$0.361243\pi$
$912$	−23.5777	−0.780735
$913$	−9.72154	−0.321736
$914$	98.5384	3.25936
$915$	−2.23875	−0.0740109
$916$	87.0640	2.87667
$917$	−0.0617708	−0.00203985
$918$	51.1423	1.68795
$919$	−8.12354	−0.267971	−0.133985	−	0.990983i	$-0.542778\pi$
$919$	−8.12354	−0.267971	−0.133985	+	0.990983i	$0.542778\pi$
$920$	−18.9627	−0.625181
$921$	11.3926	0.375397
$922$	41.9255	1.38074
$923$	−48.3860	−1.59264
$924$	−0.400660	−0.0131807
$925$	−34.7725	−1.14331
$926$	49.5467	1.62821
$927$	−8.28977	−0.272272
$928$	41.4191	1.35965
$929$	31.9219	1.04732	0.523662	−	0.851926i	$-0.324565\pi$
$929$	31.9219	1.04732	0.523662	+	0.851926i	$0.324565\pi$
$930$	−3.86252	−0.126657
$931$	−10.7763	−0.353180
$932$	−93.9197	−3.07644
$933$	−25.8414	−0.846011
$934$	92.1318	3.01464
$935$	−1.24687	−0.0407771
$936$	−39.9317	−1.30521
$937$	−17.9348	−0.585903	−0.292952	−	0.956127i	$-0.594637\pi$
$937$	−17.9348	−0.585903	−0.292952	+	0.956127i	$0.594637\pi$
$938$	1.14881	0.0375101
$939$	25.2369	0.823576
$940$	14.5250	0.473753
$941$	17.1106	0.557788	0.278894	−	0.960322i	$-0.410032\pi$
$941$	17.1106	0.557788	0.278894	+	0.960322i	$0.410032\pi$
$942$	67.9467	2.21382
$943$	−36.4532	−1.18708
$944$	−17.6287	−0.573767
$945$	−0.124497	−0.00404989
$946$	4.31159	0.140182
$947$	17.0969	0.555575	0.277788	−	0.960643i	$-0.410399\pi$
$947$	17.0969	0.555575	0.277788	+	0.960643i	$0.410399\pi$
$948$	30.2306	0.981846
$949$	12.7843	0.414996
$950$	−20.0366	−0.650072
$951$	−14.4350	−0.468087
$952$	1.78239	0.0577677
$953$	26.4772	0.857679	0.428840	−	0.903381i	$-0.358923\pi$
$953$	26.4772	0.857679	0.428840	+	0.903381i	$0.358923\pi$
$954$	−16.2879	−0.527339
$955$	1.38944	0.0449613
$956$	−18.0459	−0.583645
$957$	−3.34542	−0.108142
$958$	71.9391	2.32425
$959$	0.651568	0.0210402
$960$	8.00560	0.258379
$961$	−21.0094	−0.677722
$962$	64.6057	2.08297
$963$	0.371831	0.0119821
$964$	−66.2837	−2.13486
$965$	5.21383	0.167839
$966$	−1.30027	−0.0418355
$967$	42.4478	1.36503	0.682514	−	0.730872i	$-0.260887\pi$
$967$	42.4478	1.36503	0.682514	+	0.730872i	$0.260887\pi$
$968$	8.38506	0.269506
$969$	−6.69097	−0.214945
$970$	9.22593	0.296227
$971$	−43.2156	−1.38685	−0.693427	−	0.720527i	$-0.743900\pi$
$971$	−43.2156	−1.38685	−0.693427	+	0.720527i	$0.743900\pi$
$972$	−67.5729	−2.16740
$973$	−0.636431	−0.0204030
$974$	−3.26930	−0.104755
$975$	20.8079	0.666387
$976$	−59.3551	−1.89991
$977$	17.7521	0.567941	0.283971	−	0.958833i	$-0.408348\pi$
$977$	17.7521	0.567941	0.283971	+	0.958833i	$0.408348\pi$
$978$	−43.3712	−1.38686
$979$	−1.46223	−0.0467332
$980$	13.0256	0.416087
$981$	10.1851	0.325184
$982$	38.0963	1.21570
$983$	18.2539	0.582208	0.291104	−	0.956691i	$-0.405977\pi$
$983$	18.2539	0.582208	0.291104	+	0.956691i	$0.405977\pi$
$984$	61.8192	1.97072
$985$	−2.02277	−0.0644509
$986$	24.3668	0.775997
$987$	0.608316	0.0193629
$988$	26.7969	0.852524
$989$	10.0721	0.320275
$990$	1.36167	0.0432767
$991$	23.9485	0.760748	0.380374	−	0.924833i	$-0.375795\pi$
$991$	23.9485	0.760748	0.380374	+	0.924833i	$0.375795\pi$
$992$	−49.3983	−1.56840
$993$	14.3189	0.454395
$994$	−2.35860	−0.0748102
$995$	4.02822	0.127703
$996$	63.0562	1.99801
$997$	−41.6105	−1.31782	−0.658910	−	0.752222i	$-0.728982\pi$
$997$	−41.6105	−1.31782	−0.658910	+	0.752222i	$0.728982\pi$
$998$	−97.8817	−3.09839
$999$	39.7273	1.25691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.27	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.27	✓	28	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)

\(f(q)\)	\(=\)	\(q+2.67178 q^{2} -1.26231 q^{3} +5.13839 q^{4} -0.362334 q^{5} -3.37261 q^{6} +0.0617708 q^{7} +8.38506 q^{8} -1.40657 q^{9} +O(q^{10})\)	\(q+2.67178 q^{2} -1.26231 q^{3} +5.13839 q^{4} -0.362334 q^{5} -3.37261 q^{6} +0.0617708 q^{7} +8.38506 q^{8} -1.40657 q^{9} -0.968075 q^{10} +1.00000 q^{11} -6.48623 q^{12} +3.38570 q^{13} +0.165038 q^{14} +0.457377 q^{15} +12.1262 q^{16} +3.44123 q^{17} -3.75805 q^{18} +1.54031 q^{19} -1.86181 q^{20} -0.0779739 q^{21} +2.67178 q^{22} +6.24144 q^{23} -10.5845 q^{24} -4.86871 q^{25} +9.04584 q^{26} +5.56246 q^{27} +0.317402 q^{28} +2.65024 q^{29} +1.22201 q^{30} -3.16079 q^{31} +15.6285 q^{32} -1.26231 q^{33} +9.19419 q^{34} -0.0223817 q^{35} -7.22752 q^{36} +7.14203 q^{37} +4.11537 q^{38} -4.27381 q^{39} -3.03819 q^{40} -5.84051 q^{41} -0.208329 q^{42} +1.61375 q^{43} +5.13839 q^{44} +0.509650 q^{45} +16.6757 q^{46} -7.80153 q^{47} -15.3071 q^{48} -6.99618 q^{49} -13.0081 q^{50} -4.34390 q^{51} +17.3971 q^{52} +4.33413 q^{53} +14.8616 q^{54} -0.362334 q^{55} +0.517952 q^{56} -1.94435 q^{57} +7.08084 q^{58} -1.45377 q^{59} +2.35018 q^{60} -4.89476 q^{61} -8.44493 q^{62} -0.0868853 q^{63} +17.5033 q^{64} -1.22676 q^{65} -3.37261 q^{66} +6.96091 q^{67} +17.6824 q^{68} -7.87862 q^{69} -0.0597988 q^{70} -14.2913 q^{71} -11.7942 q^{72} +3.77596 q^{73} +19.0819 q^{74} +6.14582 q^{75} +7.91473 q^{76} +0.0617708 q^{77} -11.4187 q^{78} -4.66074 q^{79} -4.39375 q^{80} -2.80182 q^{81} -15.6045 q^{82} -9.72154 q^{83} -0.400660 q^{84} -1.24687 q^{85} +4.31159 q^{86} -3.34542 q^{87} +8.38506 q^{88} -1.46223 q^{89} +1.36167 q^{90} +0.209138 q^{91} +32.0709 q^{92} +3.98990 q^{93} -20.8439 q^{94} -0.558108 q^{95} -19.7279 q^{96} -9.53019 q^{97} -18.6922 q^{98} -1.40657 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * q^99

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