LMFDB - Embedded newform 1441.2.a.e.1.14

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			1.14
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.235116 q^{2} -2.49285 q^{3} -1.94472 q^{4} +2.71737 q^{5} -0.586108 q^{6} +3.95783 q^{7} -0.927465 q^{8} +3.21431 q^{9} +O(q^{10})$	\(q+0.235116 q^{2} -2.49285 q^{3} -1.94472 q^{4} +2.71737 q^{5} -0.586108 q^{6} +3.95783 q^{7} -0.927465 q^{8} +3.21431 q^{9} +0.638897 q^{10} +1.00000 q^{11} +4.84790 q^{12} +0.639559 q^{13} +0.930546 q^{14} -6.77401 q^{15} +3.67138 q^{16} +0.272796 q^{17} +0.755734 q^{18} +3.04103 q^{19} -5.28453 q^{20} -9.86627 q^{21} +0.235116 q^{22} -5.44151 q^{23} +2.31203 q^{24} +2.38411 q^{25} +0.150370 q^{26} -0.534240 q^{27} -7.69686 q^{28} -1.40364 q^{29} -1.59267 q^{30} +2.14918 q^{31} +2.71813 q^{32} -2.49285 q^{33} +0.0641385 q^{34} +10.7549 q^{35} -6.25093 q^{36} -9.80229 q^{37} +0.714993 q^{38} -1.59433 q^{39} -2.52027 q^{40} +7.06002 q^{41} -2.31971 q^{42} -10.9346 q^{43} -1.94472 q^{44} +8.73448 q^{45} -1.27938 q^{46} +12.8451 q^{47} -9.15220 q^{48} +8.66438 q^{49} +0.560543 q^{50} -0.680039 q^{51} -1.24376 q^{52} -3.48952 q^{53} -0.125608 q^{54} +2.71737 q^{55} -3.67075 q^{56} -7.58083 q^{57} -0.330018 q^{58} +14.0747 q^{59} +13.1736 q^{60} +5.76935 q^{61} +0.505305 q^{62} +12.7217 q^{63} -6.70368 q^{64} +1.73792 q^{65} -0.586108 q^{66} +14.5840 q^{67} -0.530512 q^{68} +13.5649 q^{69} +2.52864 q^{70} -5.94853 q^{71} -2.98116 q^{72} +7.80607 q^{73} -2.30467 q^{74} -5.94324 q^{75} -5.91395 q^{76} +3.95783 q^{77} -0.374851 q^{78} +3.58772 q^{79} +9.97651 q^{80} -8.31115 q^{81} +1.65992 q^{82} +7.68472 q^{83} +19.1871 q^{84} +0.741288 q^{85} -2.57090 q^{86} +3.49907 q^{87} -0.927465 q^{88} -0.625182 q^{89} +2.05361 q^{90} +2.53126 q^{91} +10.5822 q^{92} -5.35758 q^{93} +3.02009 q^{94} +8.26361 q^{95} -6.77589 q^{96} -10.4645 q^{97} +2.03713 q^{98} +3.21431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.235116	0.166252	0.0831259	−	0.996539i	$-0.473510\pi$
$2$	0.235116	0.166252	0.0831259	+	0.996539i	$0.473510\pi$
$3$	−2.49285	−1.43925	−0.719624	−	0.694364i	$-0.755686\pi$
$3$	−2.49285	−1.43925	−0.719624	+	0.694364i	$0.755686\pi$
$4$	−1.94472	−0.972360
$5$	2.71737	1.21525	0.607623	−	0.794226i	$-0.292123\pi$
$5$	2.71737	1.21525	0.607623	+	0.794226i	$0.292123\pi$
$6$	−0.586108	−0.239278
$7$	3.95783	1.49592	0.747959	−	0.663745i	$-0.231034\pi$
$7$	3.95783	1.49592	0.747959	+	0.663745i	$0.231034\pi$
$8$	−0.927465	−0.327909
$9$	3.21431	1.07144
$10$	0.638897	0.202037
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.84790	1.39947
$13$	0.639559	0.177382	0.0886909	−	0.996059i	$-0.471732\pi$
$13$	0.639559	0.177382	0.0886909	+	0.996059i	$0.471732\pi$
$14$	0.930546	0.248699
$15$	−6.77401	−1.74904
$16$	3.67138	0.917845
$17$	0.272796	0.0661627	0.0330813	−	0.999453i	$-0.489468\pi$
$17$	0.272796	0.0661627	0.0330813	+	0.999453i	$0.489468\pi$
$18$	0.755734	0.178128
$19$	3.04103	0.697660	0.348830	−	0.937186i	$-0.386579\pi$
$19$	3.04103	0.697660	0.348830	+	0.937186i	$0.386579\pi$
$20$	−5.28453	−1.18166
$21$	−9.86627	−2.15300
$22$	0.235116	0.0501268
$23$	−5.44151	−1.13463	−0.567316	−	0.823500i	$-0.692018\pi$
$23$	−5.44151	−1.13463	−0.567316	+	0.823500i	$0.692018\pi$
$24$	2.31203	0.471942
$25$	2.38411	0.476823
$26$	0.150370	0.0294900
$27$	−0.534240	−0.102815
$28$	−7.69686	−1.45457
$29$	−1.40364	−0.260650	−0.130325	−	0.991471i	$-0.541602\pi$
$29$	−1.40364	−0.260650	−0.130325	+	0.991471i	$0.541602\pi$
$30$	−1.59267	−0.290781
$31$	2.14918	0.386003	0.193002	−	0.981198i	$-0.438178\pi$
$31$	2.14918	0.386003	0.193002	+	0.981198i	$0.438178\pi$
$32$	2.71813	0.480502
$33$	−2.49285	−0.433950
$34$	0.0641385	0.0109997
$35$	10.7549	1.81791
$36$	−6.25093	−1.04182
$37$	−9.80229	−1.61149	−0.805743	−	0.592265i	$-0.798234\pi$
$37$	−9.80229	−1.61149	−0.805743	+	0.592265i	$0.798234\pi$
$38$	0.714993	0.115987
$39$	−1.59433	−0.255296
$40$	−2.52027	−0.398490
$41$	7.06002	1.10259	0.551295	−	0.834311i	$-0.314134\pi$
$41$	7.06002	1.10259	0.551295	+	0.834311i	$0.314134\pi$
$42$	−2.31971	−0.357940
$43$	−10.9346	−1.66751	−0.833756	−	0.552133i	$-0.813814\pi$
$43$	−10.9346	−1.66751	−0.833756	+	0.552133i	$0.813814\pi$
$44$	−1.94472	−0.293178
$45$	8.73448	1.30206
$46$	−1.27938	−0.188635
$47$	12.8451	1.87365	0.936826	−	0.349796i	$-0.113749\pi$
$47$	12.8451	1.87365	0.936826	+	0.349796i	$0.113749\pi$
$48$	−9.15220	−1.32101
$49$	8.66438	1.23777
$50$	0.560543	0.0792727
$51$	−0.680039	−0.0952246
$52$	−1.24376	−0.172479
$53$	−3.48952	−0.479322	−0.239661	−	0.970857i	$-0.577036\pi$
$53$	−3.48952	−0.479322	−0.239661	+	0.970857i	$0.577036\pi$
$54$	−0.125608	−0.0170931
$55$	2.71737	0.366410
$56$	−3.67075	−0.490524
$57$	−7.58083	−1.00411
$58$	−0.330018	−0.0433335
$59$	14.0747	1.83237	0.916184	−	0.400758i	$-0.131253\pi$
$59$	14.0747	1.83237	0.916184	+	0.400758i	$0.131253\pi$
$60$	13.1736	1.70070
$61$	5.76935	0.738690	0.369345	−	0.929292i	$-0.379582\pi$
$61$	5.76935	0.738690	0.369345	+	0.929292i	$0.379582\pi$
$62$	0.505305	0.0641738
$63$	12.7217	1.60278
$64$	−6.70368	−0.837961
$65$	1.73792	0.215563
$66$	−0.586108	−0.0721449
$67$	14.5840	1.78172	0.890861	−	0.454275i	$-0.150102\pi$
$67$	14.5840	1.78172	0.890861	+	0.454275i	$0.150102\pi$
$68$	−0.530512	−0.0643340
$69$	13.5649	1.63302
$70$	2.52864	0.302230
$71$	−5.94853	−0.705961	−0.352980	−	0.935631i	$-0.614832\pi$
$71$	−5.94853	−0.705961	−0.352980	+	0.935631i	$0.614832\pi$
$72$	−2.98116	−0.351333
$73$	7.80607	0.913631	0.456815	−	0.889561i	$-0.348990\pi$
$73$	7.80607	0.913631	0.456815	+	0.889561i	$0.348990\pi$
$74$	−2.30467	−0.267913
$75$	−5.94324	−0.686267
$76$	−5.91395	−0.678377
$77$	3.95783	0.451036
$78$	−0.374851	−0.0424435
$79$	3.58772	0.403650	0.201825	−	0.979422i	$-0.435313\pi$
$79$	3.58772	0.403650	0.201825	+	0.979422i	$0.435313\pi$
$80$	9.97651	1.11541
$81$	−8.31115	−0.923461
$82$	1.65992	0.183307
$83$	7.68472	0.843507	0.421754	−	0.906710i	$-0.361415\pi$
$83$	7.68472	0.843507	0.421754	+	0.906710i	$0.361415\pi$
$84$	19.1871	2.09349
$85$	0.741288	0.0804039
$86$	−2.57090	−0.277227
$87$	3.49907	0.375140
$88$	−0.927465	−0.0988681
$89$	−0.625182	−0.0662692	−0.0331346	−	0.999451i	$-0.510549\pi$
$89$	−0.625182	−0.0662692	−0.0331346	+	0.999451i	$0.510549\pi$
$90$	2.05361	0.216470
$91$	2.53126	0.265348
$92$	10.5822	1.10327
$93$	−5.35758	−0.555555
$94$	3.02009	0.311498
$95$	8.26361	0.847828
$96$	−6.77589	−0.691562
$97$	−10.4645	−1.06251	−0.531253	−	0.847213i	$-0.678279\pi$
$97$	−10.4645	−1.06251	−0.531253	+	0.847213i	$0.678279\pi$
$98$	2.03713	0.205781
$99$	3.21431	0.323050
$100$	−4.63644	−0.463644
$101$	−3.79625	−0.377741	−0.188870	−	0.982002i	$-0.560483\pi$
$101$	−3.79625	−0.377741	−0.188870	+	0.982002i	$0.560483\pi$
$102$	−0.159888	−0.0158313
$103$	9.42271	0.928447	0.464224	−	0.885718i	$-0.346333\pi$
$103$	9.42271	0.928447	0.464224	+	0.885718i	$0.346333\pi$
$104$	−0.593169	−0.0581650
$105$	−26.8103	−2.61642
$106$	−0.820440	−0.0796881
$107$	−5.79195	−0.559929	−0.279965	−	0.960010i	$-0.590323\pi$
$107$	−5.79195	−0.559929	−0.279965	+	0.960010i	$0.590323\pi$
$108$	1.03895	0.0999728
$109$	9.83702	0.942215	0.471108	−	0.882076i	$-0.343854\pi$
$109$	9.83702	0.942215	0.471108	+	0.882076i	$0.343854\pi$
$110$	0.638897	0.0609164
$111$	24.4356	2.31933
$112$	14.5307	1.37302
$113$	8.52540	0.802002	0.401001	−	0.916078i	$-0.368662\pi$
$113$	8.52540	0.802002	0.401001	+	0.916078i	$0.368662\pi$
$114$	−1.78237	−0.166934
$115$	−14.7866	−1.37886
$116$	2.72969	0.253446
$117$	2.05574	0.190053
$118$	3.30918	0.304635
$119$	1.07968	0.0989739
$120$	6.28266	0.573525
$121$	1.00000	0.0909091
$122$	1.35646	0.122809
$123$	−17.5996	−1.58690
$124$	−4.17955	−0.375334
$125$	−7.10834	−0.635789
$126$	2.99106	0.266465
$127$	9.26519	0.822152	0.411076	−	0.911601i	$-0.365153\pi$
$127$	9.26519	0.822152	0.411076	+	0.911601i	$0.365153\pi$
$128$	−7.01240	−0.619814
$129$	27.2584	2.39996
$130$	0.408612	0.0358377
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	4.84790	0.421956
$133$	12.0359	1.04364
$134$	3.42893	0.296215
$135$	−1.45173	−0.124945
$136$	−0.253009	−0.0216953
$137$	9.95318	0.850357	0.425179	−	0.905109i	$-0.360211\pi$
$137$	9.95318	0.850357	0.425179	+	0.905109i	$0.360211\pi$
$138$	3.18931	0.271492
$139$	−11.2360	−0.953025	−0.476512	−	0.879168i	$-0.658099\pi$
$139$	−11.2360	−0.953025	−0.476512	+	0.879168i	$0.658099\pi$
$140$	−20.9153	−1.76766
$141$	−32.0209	−2.69665
$142$	−1.39859	−0.117367
$143$	0.639559	0.0534826
$144$	11.8009	0.983412
$145$	−3.81422	−0.316754
$146$	1.83533	0.151893
$147$	−21.5990	−1.78146
$148$	19.0627	1.56695
$149$	−8.85539	−0.725462	−0.362731	−	0.931894i	$-0.618156\pi$
$149$	−8.85539	−0.725462	−0.362731	+	0.931894i	$0.618156\pi$
$150$	−1.39735	−0.114093
$151$	16.6577	1.35559	0.677793	−	0.735252i	$-0.262936\pi$
$151$	16.6577	1.35559	0.677793	+	0.735252i	$0.262936\pi$
$152$	−2.82045	−0.228769
$153$	0.876850	0.0708891
$154$	0.930546	0.0749856
$155$	5.84011	0.469089
$156$	3.10052	0.248240
$157$	8.52200	0.680129	0.340065	−	0.940402i	$-0.389551\pi$
$157$	8.52200	0.680129	0.340065	+	0.940402i	$0.389551\pi$
$158$	0.843529	0.0671075
$159$	8.69884	0.689863
$160$	7.38617	0.583928
$161$	−21.5365	−1.69732
$162$	−1.95408	−0.153527
$163$	1.64649	0.128963	0.0644814	−	0.997919i	$-0.479461\pi$
$163$	1.64649	0.128963	0.0644814	+	0.997919i	$0.479461\pi$
$164$	−13.7298	−1.07211
$165$	−6.77401	−0.527356
$166$	1.80680	0.140235
$167$	6.84151	0.529412	0.264706	−	0.964329i	$-0.414725\pi$
$167$	6.84151	0.529412	0.264706	+	0.964329i	$0.414725\pi$
$168$	9.15062	0.705986
$169$	−12.5910	−0.968536
$170$	0.174288	0.0133673
$171$	9.77480	0.747498
$172$	21.2648	1.62142
$173$	−5.51409	−0.419228	−0.209614	−	0.977784i	$-0.567221\pi$
$173$	−5.51409	−0.419228	−0.209614	+	0.977784i	$0.567221\pi$
$174$	0.822686	0.0623677
$175$	9.43591	0.713288
$176$	3.67138	0.276741
$177$	−35.0861	−2.63723
$178$	−0.146990	−0.0110174
$179$	9.48285	0.708781	0.354391	−	0.935097i	$-0.384688\pi$
$179$	9.48285	0.708781	0.354391	+	0.935097i	$0.384688\pi$
$180$	−16.9861	−1.26607
$181$	9.71950	0.722445	0.361222	−	0.932480i	$-0.382360\pi$
$181$	9.71950	0.722445	0.361222	+	0.932480i	$0.382360\pi$
$182$	0.595139	0.0441147
$183$	−14.3821	−1.06316
$184$	5.04681	0.372056
$185$	−26.6365	−1.95835
$186$	−1.25965	−0.0923620
$187$	0.272796	0.0199488
$188$	−24.9801	−1.82186
$189$	−2.11443	−0.153802
$190$	1.94290	0.140953
$191$	10.5216	0.761313	0.380656	−	0.924717i	$-0.375698\pi$
$191$	10.5216	0.761313	0.380656	+	0.924717i	$0.375698\pi$
$192$	16.7113	1.20603
$193$	−12.9784	−0.934209	−0.467105	−	0.884202i	$-0.654703\pi$
$193$	−12.9784	−0.934209	−0.467105	+	0.884202i	$0.654703\pi$
$194$	−2.46036	−0.176643
$195$	−4.33238	−0.310248
$196$	−16.8498	−1.20356
$197$	2.64628	0.188539	0.0942697	−	0.995547i	$-0.469948\pi$
$197$	2.64628	0.188539	0.0942697	+	0.995547i	$0.469948\pi$
$198$	0.755734	0.0537077
$199$	−5.15790	−0.365634	−0.182817	−	0.983147i	$-0.558522\pi$
$199$	−5.15790	−0.365634	−0.182817	+	0.983147i	$0.558522\pi$
$200$	−2.21118	−0.156354
$201$	−36.3558	−2.56434
$202$	−0.892557	−0.0628001
$203$	−5.55537	−0.389911
$204$	1.32249	0.0925926
$205$	19.1847	1.33992
$206$	2.21543	0.154356
$207$	−17.4907	−1.21569
$208$	2.34806	0.162809
$209$	3.04103	0.210352
$210$	−6.30353	−0.434985
$211$	−23.9623	−1.64963	−0.824817	−	0.565400i	$-0.808722\pi$
$211$	−23.9623	−1.64963	−0.824817	+	0.565400i	$0.808722\pi$
$212$	6.78613	0.466074
$213$	14.8288	1.01605
$214$	−1.36178	−0.0930892
$215$	−29.7134	−2.02644
$216$	0.495489	0.0337138
$217$	8.50606	0.577429
$218$	2.31284	0.156645
$219$	−19.4594	−1.31494
$220$	−5.28453	−0.356283
$221$	0.174469	0.0117361
$222$	5.74520	0.385593
$223$	4.25284	0.284791	0.142396	−	0.989810i	$-0.454519\pi$
$223$	4.25284	0.284791	0.142396	+	0.989810i	$0.454519\pi$
$224$	10.7579	0.718791
$225$	7.66328	0.510885
$226$	2.00445	0.133334
$227$	3.56009	0.236291	0.118146	−	0.992996i	$-0.462305\pi$
$227$	3.56009	0.236291	0.118146	+	0.992996i	$0.462305\pi$
$228$	14.7426	0.976352
$229$	15.1828	1.00331	0.501653	−	0.865069i	$-0.332725\pi$
$229$	15.1828	1.00331	0.501653	+	0.865069i	$0.332725\pi$
$230$	−3.47656	−0.229238
$231$	−9.86627	−0.649153
$232$	1.30183	0.0854693
$233$	−7.33561	−0.480572	−0.240286	−	0.970702i	$-0.577241\pi$
$233$	−7.33561	−0.480572	−0.240286	+	0.970702i	$0.577241\pi$
$234$	0.483337	0.0315967
$235$	34.9049	2.27695
$236$	−27.3713	−1.78172
$237$	−8.94365	−0.580953
$238$	0.253849	0.0164546
$239$	8.35921	0.540713	0.270356	−	0.962760i	$-0.412858\pi$
$239$	8.35921	0.540713	0.270356	+	0.962760i	$0.412858\pi$
$240$	−24.8700	−1.60535
$241$	−18.8459	−1.21397	−0.606986	−	0.794713i	$-0.707621\pi$
$241$	−18.8459	−1.21397	−0.606986	+	0.794713i	$0.707621\pi$
$242$	0.235116	0.0151138
$243$	22.3212	1.43190
$244$	−11.2198	−0.718273
$245$	23.5444	1.50419
$246$	−4.13793	−0.263825
$247$	1.94492	0.123752
$248$	−1.99329	−0.126574
$249$	−19.1569	−1.21402
$250$	−1.67128	−0.105701
$251$	21.9204	1.38360	0.691800	−	0.722089i	$-0.256818\pi$
$251$	21.9204	1.38360	0.691800	+	0.722089i	$0.256818\pi$
$252$	−24.7401	−1.55848
$253$	−5.44151	−0.342105
$254$	2.17839	0.136684
$255$	−1.84792	−0.115721
$256$	11.7586	0.734915
$257$	10.3538	0.645853	0.322927	−	0.946424i	$-0.395333\pi$
$257$	10.3538	0.645853	0.322927	+	0.946424i	$0.395333\pi$
$258$	6.40886	0.398998
$259$	−38.7957	−2.41065
$260$	−3.37977	−0.209604
$261$	−4.51174	−0.279270
$262$	−0.235116	−0.0145255
$263$	−20.5224	−1.26546	−0.632731	−	0.774371i	$-0.718066\pi$
$263$	−20.5224	−1.26546	−0.632731	+	0.774371i	$0.718066\pi$
$264$	2.31203	0.142296
$265$	−9.48232	−0.582494
$266$	2.82982	0.173507
$267$	1.55849	0.0953778
$268$	−28.3619	−1.73248
$269$	−16.6120	−1.01285	−0.506427	−	0.862283i	$-0.669034\pi$
$269$	−16.6120	−1.01285	−0.506427	+	0.862283i	$0.669034\pi$
$270$	−0.341324	−0.0207723
$271$	−12.7716	−0.775821	−0.387910	−	0.921697i	$-0.626803\pi$
$271$	−12.7716	−0.775821	−0.387910	+	0.921697i	$0.626803\pi$
$272$	1.00154	0.0607271
$273$	−6.31006	−0.381902
$274$	2.34015	0.141373
$275$	2.38411	0.143768
$276$	−26.3799	−1.58788
$277$	−23.9871	−1.44125	−0.720624	−	0.693326i	$-0.756144\pi$
$277$	−23.9871	−1.44125	−0.720624	+	0.693326i	$0.756144\pi$
$278$	−2.64176	−0.158442
$279$	6.90812	0.413578
$280$	−9.97478	−0.596107
$281$	27.1767	1.62123	0.810613	−	0.585582i	$-0.199134\pi$
$281$	27.1767	1.62123	0.810613	+	0.585582i	$0.199134\pi$
$282$	−7.52862	−0.448323
$283$	6.43498	0.382520	0.191260	−	0.981539i	$-0.438743\pi$
$283$	6.43498	0.382520	0.191260	+	0.981539i	$0.438743\pi$
$284$	11.5682	0.686448
$285$	−20.5999	−1.22024
$286$	0.150370	0.00889158
$287$	27.9423	1.64938
$288$	8.73691	0.514827
$289$	−16.9256	−0.995622
$290$	−0.896783	−0.0526609
$291$	26.0864	1.52921
$292$	−15.1806	−0.888379
$293$	−13.2580	−0.774539	−0.387270	−	0.921966i	$-0.626582\pi$
$293$	−13.2580	−0.774539	−0.387270	+	0.921966i	$0.626582\pi$
$294$	−5.07827	−0.296170
$295$	38.2462	2.22678
$296$	9.09128	0.528420
$297$	−0.534240	−0.0309998
$298$	−2.08204	−0.120609
$299$	−3.48017	−0.201263
$300$	11.5579	0.667299
$301$	−43.2773	−2.49446
$302$	3.91649	0.225369
$303$	9.46348	0.543663
$304$	11.1648	0.640343
$305$	15.6775	0.897690
$306$	0.206161	0.0117854
$307$	28.8129	1.64444	0.822220	−	0.569170i	$-0.192735\pi$
$307$	28.8129	1.64444	0.822220	+	0.569170i	$0.192735\pi$
$308$	−7.69686	−0.438570
$309$	−23.4894	−1.33627
$310$	1.37310	0.0779869
$311$	−3.80397	−0.215703	−0.107852	−	0.994167i	$-0.534397\pi$
$311$	−3.80397	−0.215703	−0.107852	+	0.994167i	$0.534397\pi$
$312$	1.47868	0.0837139
$313$	−21.3374	−1.20606	−0.603029	−	0.797719i	$-0.706040\pi$
$313$	−21.3374	−1.20606	−0.603029	+	0.797719i	$0.706040\pi$
$314$	2.00365	0.113073
$315$	34.5695	1.94777
$316$	−6.97711	−0.392493
$317$	−8.66391	−0.486614	−0.243307	−	0.969949i	$-0.578232\pi$
$317$	−8.66391	−0.486614	−0.243307	+	0.969949i	$0.578232\pi$
$318$	2.04523	0.114691
$319$	−1.40364	−0.0785889
$320$	−18.2164	−1.01833
$321$	14.4385	0.805877
$322$	−5.06358	−0.282182
$323$	0.829580	0.0461590
$324$	16.1629	0.897936
$325$	1.52478	0.0845797
$326$	0.387115	0.0214403
$327$	−24.5222	−1.35608
$328$	−6.54792	−0.361548
$329$	50.8387	2.80283
$330$	−1.59267	−0.0876739
$331$	−11.5484	−0.634757	−0.317378	−	0.948299i	$-0.602803\pi$
$331$	−11.5484	−0.634757	−0.317378	+	0.948299i	$0.602803\pi$
$332$	−14.9446	−0.820193
$333$	−31.5076	−1.72660
$334$	1.60855	0.0880158
$335$	39.6302	2.16523
$336$	−36.2228	−1.97612
$337$	−1.06922	−0.0582440	−0.0291220	−	0.999576i	$-0.509271\pi$
$337$	−1.06922	−0.0582440	−0.0291220	+	0.999576i	$0.509271\pi$
$338$	−2.96033	−0.161021
$339$	−21.2526	−1.15428
$340$	−1.44160	−0.0781816
$341$	2.14918	0.116384
$342$	2.29821	0.124273
$343$	6.58733	0.355682
$344$	10.1415	0.546791
$345$	36.8608	1.98452
$346$	−1.29645	−0.0696975
$347$	−32.7702	−1.75919	−0.879597	−	0.475720i	$-0.842188\pi$
$347$	−32.7702	−1.75919	−0.879597	+	0.475720i	$0.842188\pi$
$348$	−6.80472	−0.364771
$349$	24.5752	1.31548	0.657741	−	0.753244i	$-0.271512\pi$
$349$	24.5752	1.31548	0.657741	+	0.753244i	$0.271512\pi$
$350$	2.21853	0.118585
$351$	−0.341678	−0.0182374
$352$	2.71813	0.144877
$353$	25.9818	1.38287	0.691435	−	0.722439i	$-0.256979\pi$
$353$	25.9818	1.38287	0.691435	+	0.722439i	$0.256979\pi$
$354$	−8.24929	−0.438445
$355$	−16.1644	−0.857916
$356$	1.21580	0.0644375
$357$	−2.69148	−0.142448
$358$	2.22957	0.117836
$359$	13.3589	0.705057	0.352528	−	0.935801i	$-0.385322\pi$
$359$	13.3589	0.705057	0.352528	+	0.935801i	$0.385322\pi$
$360$	−8.10092	−0.426956
$361$	−9.75215	−0.513271
$362$	2.28521	0.120108
$363$	−2.49285	−0.130841
$364$	−4.92260	−0.258014
$365$	21.2120	1.11029
$366$	−3.38146	−0.176752
$367$	−16.3063	−0.851181	−0.425590	−	0.904916i	$-0.639934\pi$
$367$	−16.3063	−0.851181	−0.425590	+	0.904916i	$0.639934\pi$
$368$	−19.9778	−1.04142
$369$	22.6931	1.18135
$370$	−6.26265	−0.325580
$371$	−13.8109	−0.717026
$372$	10.4190	0.540200
$373$	9.67697	0.501054	0.250527	−	0.968110i	$-0.419396\pi$
$373$	9.67697	0.501054	0.250527	+	0.968110i	$0.419396\pi$
$374$	0.0641385	0.00331652
$375$	17.7200	0.915058
$376$	−11.9134	−0.614386
$377$	−0.897712	−0.0462345
$378$	−0.497135	−0.0255699
$379$	22.4795	1.15469	0.577347	−	0.816499i	$-0.304088\pi$
$379$	22.4795	1.15469	0.577347	+	0.816499i	$0.304088\pi$
$380$	−16.0704	−0.824394
$381$	−23.0967	−1.18328
$382$	2.47378	0.126570
$383$	13.9042	0.710470	0.355235	−	0.934777i	$-0.384401\pi$
$383$	13.9042	0.710470	0.355235	+	0.934777i	$0.384401\pi$
$384$	17.4809	0.892067
$385$	10.7549	0.548120
$386$	−3.05144	−0.155314
$387$	−35.1472	−1.78663
$388$	20.3505	1.03314
$389$	33.4146	1.69419	0.847093	−	0.531445i	$-0.178351\pi$
$389$	33.4146	1.69419	0.847093	+	0.531445i	$0.178351\pi$
$390$	−1.01861	−0.0515793
$391$	−1.48442	−0.0750704
$392$	−8.03591	−0.405875
$393$	2.49285	0.125748
$394$	0.622181	0.0313450
$395$	9.74917	0.490534
$396$	−6.25093	−0.314121
$397$	1.32046	0.0662718	0.0331359	−	0.999451i	$-0.489451\pi$
$397$	1.32046	0.0662718	0.0331359	+	0.999451i	$0.489451\pi$
$398$	−1.21270	−0.0607873
$399$	−30.0036	−1.50206
$400$	8.75299	0.437650
$401$	30.8199	1.53907	0.769536	−	0.638603i	$-0.220487\pi$
$401$	30.8199	1.53907	0.769536	+	0.638603i	$0.220487\pi$
$402$	−8.54782	−0.426327
$403$	1.37453	0.0684700
$404$	7.38264	0.367300
$405$	−22.5845	−1.12223
$406$	−1.30615	−0.0648234
$407$	−9.80229	−0.485881
$408$	0.630713	0.0312249
$409$	−3.46168	−0.171169	−0.0855845	−	0.996331i	$-0.527276\pi$
$409$	−3.46168	−0.171169	−0.0855845	+	0.996331i	$0.527276\pi$
$410$	4.51062	0.222764
$411$	−24.8118	−1.22388
$412$	−18.3245	−0.902785
$413$	55.7051	2.74107
$414$	−4.11233	−0.202110
$415$	20.8822	1.02507
$416$	1.73840	0.0852323
$417$	28.0097	1.37164
$418$	0.714993	0.0349715
$419$	−0.564012	−0.0275538	−0.0137769	−	0.999905i	$-0.504385\pi$
$419$	−0.564012	−0.0275538	−0.0137769	+	0.999905i	$0.504385\pi$
$420$	52.1386	2.54410
$421$	21.5184	1.04874	0.524371	−	0.851490i	$-0.324300\pi$
$421$	21.5184	1.04874	0.524371	+	0.851490i	$0.324300\pi$
$422$	−5.63391	−0.274255
$423$	41.2881	2.00750
$424$	3.23641	0.157174
$425$	0.650376	0.0315479
$426$	3.48648	0.168921
$427$	22.8341	1.10502
$428$	11.2637	0.544453
$429$	−1.59433	−0.0769748
$430$	−6.98609	−0.336899
$431$	29.7128	1.43122	0.715608	−	0.698502i	$-0.246150\pi$
$431$	29.7128	1.43122	0.715608	+	0.698502i	$0.246150\pi$
$432$	−1.96140	−0.0943678
$433$	18.4605	0.887157	0.443578	−	0.896236i	$-0.353709\pi$
$433$	18.4605	0.887157	0.443578	+	0.896236i	$0.353709\pi$
$434$	1.99991	0.0959987
$435$	9.50828	0.455887
$436$	−19.1302	−0.916173
$437$	−16.5478	−0.791587
$438$	−4.57520	−0.218612
$439$	37.1916	1.77506	0.887529	−	0.460752i	$-0.152420\pi$
$439$	37.1916	1.77506	0.887529	+	0.460752i	$0.152420\pi$
$440$	−2.52027	−0.120149
$441$	27.8500	1.32619
$442$	0.0410204	0.00195114
$443$	−15.5151	−0.737143	−0.368572	−	0.929599i	$-0.620153\pi$
$443$	−15.5151	−0.737143	−0.368572	+	0.929599i	$0.620153\pi$
$444$	−47.5205	−2.25522
$445$	−1.69885	−0.0805334
$446$	0.999909	0.0473471
$447$	22.0752	1.04412
$448$	−26.5320	−1.25352
$449$	6.28196	0.296464	0.148232	−	0.988953i	$-0.452642\pi$
$449$	6.28196	0.296464	0.148232	+	0.988953i	$0.452642\pi$
$450$	1.80176	0.0849356
$451$	7.06002	0.332443
$452$	−16.5795	−0.779835
$453$	−41.5253	−1.95103
$454$	0.837032	0.0392838
$455$	6.87839	0.322464
$456$	7.03096	0.329255
$457$	−40.4823	−1.89368	−0.946841	−	0.321702i	$-0.895745\pi$
$457$	−40.4823	−1.89368	−0.946841	+	0.321702i	$0.895745\pi$
$458$	3.56971	0.166801
$459$	−0.145738	−0.00680249
$460$	28.7558	1.34075
$461$	−26.2538	−1.22276	−0.611380	−	0.791337i	$-0.709385\pi$
$461$	−26.2538	−1.22276	−0.611380	+	0.791337i	$0.709385\pi$
$462$	−2.31971	−0.107923
$463$	−35.7361	−1.66080	−0.830399	−	0.557169i	$-0.811888\pi$
$463$	−35.7361	−1.66080	−0.830399	+	0.557169i	$0.811888\pi$
$464$	−5.15330	−0.239236
$465$	−14.5585	−0.675136
$466$	−1.72472	−0.0798960
$467$	−30.8077	−1.42561	−0.712805	−	0.701363i	$-0.752575\pi$
$467$	−30.8077	−1.42561	−0.712805	+	0.701363i	$0.752575\pi$
$468$	−3.99784	−0.184800
$469$	57.7210	2.66531
$470$	8.20670	0.378547
$471$	−21.2441	−0.978875
$472$	−13.0538	−0.600849
$473$	−10.9346	−0.502774
$474$	−2.10279	−0.0965844
$475$	7.25016	0.332660
$476$	−2.09967	−0.0962383
$477$	−11.2164	−0.513563
$478$	1.96538	0.0898945
$479$	36.5501	1.67002	0.835009	−	0.550236i	$-0.185462\pi$
$479$	36.5501	1.67002	0.835009	+	0.550236i	$0.185462\pi$
$480$	−18.4126	−0.840418
$481$	−6.26914	−0.285848
$482$	−4.43096	−0.201825
$483$	53.6874	2.44286
$484$	−1.94472	−0.0883964
$485$	−28.4358	−1.29121
$486$	5.24806	0.238057
$487$	0.784778	0.0355617	0.0177808	−	0.999842i	$-0.494340\pi$
$487$	0.784778	0.0355617	0.0177808	+	0.999842i	$0.494340\pi$
$488$	−5.35087	−0.242223
$489$	−4.10445	−0.185610
$490$	5.53564	0.250075
$491$	−4.64306	−0.209539	−0.104769	−	0.994497i	$-0.533410\pi$
$491$	−4.64306	−0.209539	−0.104769	+	0.994497i	$0.533410\pi$
$492$	34.2262	1.54304
$493$	−0.382908	−0.0172453
$494$	0.457280	0.0205740
$495$	8.73448	0.392585
$496$	7.89044	0.354291
$497$	−23.5432	−1.05606
$498$	−4.50408	−0.201832
$499$	−17.6860	−0.791736	−0.395868	−	0.918307i	$-0.629556\pi$
$499$	−17.6860	−0.791736	−0.395868	+	0.918307i	$0.629556\pi$
$500$	13.8237	0.618216
$501$	−17.0549	−0.761956
$502$	5.15382	0.230026
$503$	−15.6533	−0.697947	−0.348974	−	0.937133i	$-0.613470\pi$
$503$	−15.6533	−0.697947	−0.348974	+	0.937133i	$0.613470\pi$
$504$	−11.7989	−0.525565
$505$	−10.3158	−0.459048
$506$	−1.27938	−0.0568755
$507$	31.3874	1.39396
$508$	−18.0182	−0.799428
$509$	−42.7530	−1.89499	−0.947497	−	0.319764i	$-0.896396\pi$
$509$	−42.7530	−1.89499	−0.947497	+	0.319764i	$0.896396\pi$
$510$	−0.434475	−0.0192389
$511$	30.8950	1.36672
$512$	16.7894	0.741995
$513$	−1.62464	−0.0717296
$514$	2.43434	0.107374
$515$	25.6050	1.12829
$516$	−53.0099	−2.33363
$517$	12.8451	0.564927
$518$	−9.12148	−0.400775
$519$	13.7458	0.603374
$520$	−1.61186	−0.0706848
$521$	−40.1948	−1.76096	−0.880482	−	0.474079i	$-0.842781\pi$
$521$	−40.1948	−1.76096	−0.880482	+	0.474079i	$0.842781\pi$
$522$	−1.06078	−0.0464291
$523$	−26.0441	−1.13883	−0.569415	−	0.822050i	$-0.692830\pi$
$523$	−26.0441	−1.13883	−0.569415	+	0.822050i	$0.692830\pi$
$524$	1.94472	0.0849555
$525$	−23.5223	−1.02660
$526$	−4.82513	−0.210386
$527$	0.586286	0.0255390
$528$	−9.15220	−0.398299
$529$	6.61000	0.287391
$530$	−2.22944	−0.0968407
$531$	45.2404	1.96327
$532$	−23.4064	−1.01480
$533$	4.51530	0.195579
$534$	0.366424	0.0158567
$535$	−15.7389	−0.680452
$536$	−13.5262	−0.584242
$537$	−23.6393	−1.02011
$538$	−3.90575	−0.168389
$539$	8.66438	0.373201
$540$	2.82321	0.121492
$541$	−29.9304	−1.28681	−0.643404	−	0.765527i	$-0.722479\pi$
$541$	−29.9304	−1.28681	−0.643404	+	0.765527i	$0.722479\pi$
$542$	−3.00281	−0.128982
$543$	−24.2293	−1.03978
$544$	0.741494	0.0317913
$545$	26.7308	1.14502
$546$	−1.48359	−0.0634920
$547$	−28.6045	−1.22304	−0.611520	−	0.791229i	$-0.709441\pi$
$547$	−28.6045	−1.22304	−0.611520	+	0.791229i	$0.709441\pi$
$548$	−19.3562	−0.826854
$549$	18.5445	0.791459
$550$	0.560543	0.0239016
$551$	−4.26852	−0.181845
$552$	−12.5809	−0.535481
$553$	14.1996	0.603827
$554$	−5.63975	−0.239610
$555$	66.4008	2.81856
$556$	21.8509	0.926683
$557$	26.5541	1.12513	0.562567	−	0.826752i	$-0.309814\pi$
$557$	26.5541	1.12513	0.562567	+	0.826752i	$0.309814\pi$
$558$	1.62421	0.0687581
$559$	−6.99333	−0.295786
$560$	39.4853	1.66856
$561$	−0.680039	−0.0287113
$562$	6.38967	0.269532
$563$	6.42622	0.270833	0.135416	−	0.990789i	$-0.456763\pi$
$563$	6.42622	0.270833	0.135416	+	0.990789i	$0.456763\pi$
$564$	62.2718	2.62212
$565$	23.1667	0.974630
$566$	1.51297	0.0635947
$567$	−32.8941	−1.38142
$568$	5.51706	0.231491
$569$	0.326335	0.0136807	0.00684034	−	0.999977i	$-0.497823\pi$
$569$	0.326335	0.0136807	0.00684034	+	0.999977i	$0.497823\pi$
$570$	−4.84337	−0.202866
$571$	18.8620	0.789352	0.394676	−	0.918820i	$-0.370857\pi$
$571$	18.8620	0.789352	0.394676	+	0.918820i	$0.370857\pi$
$572$	−1.24376	−0.0520044
$573$	−26.2287	−1.09572
$574$	6.56967	0.274213
$575$	−12.9732	−0.541019
$576$	−21.5477	−0.897821
$577$	11.9797	0.498720	0.249360	−	0.968411i	$-0.419780\pi$
$577$	11.9797	0.498720	0.249360	+	0.968411i	$0.419780\pi$
$578$	−3.97947	−0.165524
$579$	32.3533	1.34456
$580$	7.41759	0.307999
$581$	30.4148	1.26182
$582$	6.13331	0.254234
$583$	−3.48952	−0.144521
$584$	−7.23986	−0.299587
$585$	5.58621	0.230962
$586$	−3.11716	−0.128769
$587$	−5.69413	−0.235022	−0.117511	−	0.993072i	$-0.537492\pi$
$587$	−5.69413	−0.235022	−0.117511	+	0.993072i	$0.537492\pi$
$588$	42.0041	1.73222
$589$	6.53570	0.269299
$590$	8.99227	0.370206
$591$	−6.59677	−0.271355
$592$	−35.9879	−1.47909
$593$	18.4035	0.755740	0.377870	−	0.925859i	$-0.376657\pi$
$593$	18.4035	0.755740	0.377870	+	0.925859i	$0.376657\pi$
$594$	−0.125608	−0.00515377
$595$	2.93389	0.120278
$596$	17.2213	0.705411
$597$	12.8579	0.526238
$598$	−0.818241	−0.0334604
$599$	19.0427	0.778065	0.389033	−	0.921224i	$-0.372809\pi$
$599$	19.0427	0.778065	0.389033	+	0.921224i	$0.372809\pi$
$600$	5.51215	0.225033
$601$	−38.9274	−1.58788	−0.793940	−	0.607995i	$-0.791974\pi$
$601$	−38.9274	−1.58788	−0.793940	+	0.607995i	$0.791974\pi$
$602$	−10.1752	−0.414709
$603$	46.8776	1.90900
$604$	−32.3946	−1.31812
$605$	2.71737	0.110477
$606$	2.22501	0.0903849
$607$	−28.0094	−1.13687	−0.568434	−	0.822729i	$-0.692450\pi$
$607$	−28.0094	−1.13687	−0.568434	+	0.822729i	$0.692450\pi$
$608$	8.26591	0.335227
$609$	13.8487	0.561178
$610$	3.68602	0.149243
$611$	8.21521	0.332352
$612$	−1.70523	−0.0689298
$613$	−27.4990	−1.11067	−0.555337	−	0.831626i	$-0.687411\pi$
$613$	−27.4990	−1.11067	−0.555337	+	0.831626i	$0.687411\pi$
$614$	6.77437	0.273391
$615$	−47.8246	−1.92847
$616$	−3.67075	−0.147899
$617$	−1.90908	−0.0768567	−0.0384284	−	0.999261i	$-0.512235\pi$
$617$	−1.90908	−0.0768567	−0.0384284	+	0.999261i	$0.512235\pi$
$618$	−5.52273	−0.222157
$619$	21.9025	0.880336	0.440168	−	0.897916i	$-0.354919\pi$
$619$	21.9025	0.880336	0.440168	+	0.897916i	$0.354919\pi$
$620$	−11.3574	−0.456124
$621$	2.90707	0.116657
$622$	−0.894372	−0.0358611
$623$	−2.47436	−0.0991332
$624$	−5.85338	−0.234323
$625$	−31.2366	−1.24946
$626$	−5.01674	−0.200509
$627$	−7.58083	−0.302749
$628$	−16.5729	−0.661331
$629$	−2.67402	−0.106620
$630$	8.12784	0.323821
$631$	46.6219	1.85599	0.927994	−	0.372594i	$-0.121532\pi$
$631$	46.6219	1.85599	0.927994	+	0.372594i	$0.121532\pi$
$632$	−3.32749	−0.132360
$633$	59.7345	2.37423
$634$	−2.03702	−0.0809004
$635$	25.1770	0.999117
$636$	−16.9168	−0.670796
$637$	5.54138	0.219558
$638$	−0.330018	−0.0130655
$639$	−19.1204	−0.756392
$640$	−19.0553	−0.753227
$641$	−27.3954	−1.08205	−0.541026	−	0.841006i	$-0.681964\pi$
$641$	−27.3954	−1.08205	−0.541026	+	0.841006i	$0.681964\pi$
$642$	3.39471	0.133979
$643$	8.97966	0.354123	0.177062	−	0.984200i	$-0.443341\pi$
$643$	8.97966	0.354123	0.177062	+	0.984200i	$0.443341\pi$
$644$	41.8825	1.65040
$645$	74.0711	2.91655
$646$	0.195047	0.00767403
$647$	−7.21947	−0.283827	−0.141913	−	0.989879i	$-0.545325\pi$
$647$	−7.21947	−0.283827	−0.141913	+	0.989879i	$0.545325\pi$
$648$	7.70830	0.302811
$649$	14.0747	0.552480
$650$	0.358500	0.0140615
$651$	−21.2044	−0.831064
$652$	−3.20196	−0.125398
$653$	−27.5381	−1.07765	−0.538824	−	0.842418i	$-0.681131\pi$
$653$	−27.5381	−1.07765	−0.538824	+	0.842418i	$0.681131\pi$
$654$	−5.76556	−0.225451
$655$	−2.71737	−0.106177
$656$	25.9200	1.01201
$657$	25.0911	0.978897
$658$	11.9530	0.465975
$659$	−26.7170	−1.04075	−0.520374	−	0.853939i	$-0.674207\pi$
$659$	−26.7170	−1.04075	−0.520374	+	0.853939i	$0.674207\pi$
$660$	13.1736	0.512780
$661$	−12.0202	−0.467531	−0.233766	−	0.972293i	$-0.575105\pi$
$661$	−12.0202	−0.467531	−0.233766	+	0.972293i	$0.575105\pi$
$662$	−2.71521	−0.105529
$663$	−0.434925	−0.0168911
$664$	−7.12731	−0.276593
$665$	32.7059	1.26828
$666$	−7.40792	−0.287051
$667$	7.63793	0.295742
$668$	−13.3048	−0.514779
$669$	−10.6017	−0.409885
$670$	9.31769	0.359974
$671$	5.76935	0.222723
$672$	−26.8178	−1.03452
$673$	4.46705	0.172192	0.0860961	−	0.996287i	$-0.472561\pi$
$673$	4.46705	0.172192	0.0860961	+	0.996287i	$0.472561\pi$
$674$	−0.251390	−0.00968316
$675$	−1.27369	−0.0490243
$676$	24.4859	0.941766
$677$	−8.12166	−0.312141	−0.156070	−	0.987746i	$-0.549883\pi$
$677$	−8.12166	−0.312141	−0.156070	+	0.987746i	$0.549883\pi$
$678$	−4.99681	−0.191901
$679$	−41.4165	−1.58942
$680$	−0.687519	−0.0263651
$681$	−8.87476	−0.340082
$682$	0.505305	0.0193491
$683$	−14.3931	−0.550735	−0.275368	−	0.961339i	$-0.588800\pi$
$683$	−14.3931	−0.550735	−0.275368	+	0.961339i	$0.588800\pi$
$684$	−19.0093	−0.726837
$685$	27.0465	1.03339
$686$	1.54878	0.0591328
$687$	−37.8484	−1.44401
$688$	−40.1451	−1.53052
$689$	−2.23175	−0.0850230
$690$	8.66655	0.329930
$691$	7.37931	0.280722	0.140361	−	0.990100i	$-0.455174\pi$
$691$	7.37931	0.280722	0.140361	+	0.990100i	$0.455174\pi$
$692$	10.7234	0.407641
$693$	12.7217	0.483256
$694$	−7.70477	−0.292469
$695$	−30.5324	−1.15816
$696$	−3.24527	−0.123012
$697$	1.92594	0.0729503
$698$	5.77802	0.218701
$699$	18.2866	0.691663
$700$	−18.3502	−0.693573
$701$	−40.8952	−1.54459	−0.772295	−	0.635263i	$-0.780892\pi$
$701$	−40.8952	−1.54459	−0.772295	+	0.635263i	$0.780892\pi$
$702$	−0.0803339	−0.00303201
$703$	−29.8090	−1.12427
$704$	−6.70368	−0.252655
$705$	−87.0128	−3.27709
$706$	6.10872	0.229905
$707$	−15.0249	−0.565069
$708$	68.2327	2.56434
$709$	−41.3283	−1.55212	−0.776058	−	0.630661i	$-0.782784\pi$
$709$	−41.3283	−1.55212	−0.776058	+	0.630661i	$0.782784\pi$
$710$	−3.80050	−0.142630
$711$	11.5320	0.432485
$712$	0.579835	0.0217302
$713$	−11.6948	−0.437972
$714$	−0.632808	−0.0236823
$715$	1.73792	0.0649945
$716$	−18.4415	−0.689191
$717$	−20.8383	−0.778220
$718$	3.14089	0.117217
$719$	−22.1369	−0.825566	−0.412783	−	0.910829i	$-0.635443\pi$
$719$	−22.1369	−0.825566	−0.412783	+	0.910829i	$0.635443\pi$
$720$	32.0676	1.19509
$721$	37.2934	1.38888
$722$	−2.29288	−0.0853322
$723$	46.9800	1.74721
$724$	−18.9017	−0.702476
$725$	−3.34644	−0.124284
$726$	−0.586108	−0.0217525
$727$	−29.9003	−1.10894	−0.554471	−	0.832203i	$-0.687079\pi$
$727$	−29.9003	−1.10894	−0.554471	+	0.832203i	$0.687079\pi$
$728$	−2.34766	−0.0870100
$729$	−30.7099	−1.13740
$730$	4.98727	0.184587
$731$	−2.98291	−0.110327
$732$	27.9692	1.03377
$733$	−29.4205	−1.08667	−0.543336	−	0.839515i	$-0.682839\pi$
$733$	−29.4205	−1.08667	−0.543336	+	0.839515i	$0.682839\pi$
$734$	−3.83386	−0.141510
$735$	−58.6926	−2.16491
$736$	−14.7907	−0.545193
$737$	14.5840	0.537210
$738$	5.33549	0.196402
$739$	−38.0047	−1.39802	−0.699012	−	0.715110i	$-0.746377\pi$
$739$	−38.0047	−1.39802	−0.699012	+	0.715110i	$0.746377\pi$
$740$	51.8005	1.90422
$741$	−4.84839	−0.178110
$742$	−3.24716	−0.119207
$743$	12.5466	0.460291	0.230146	−	0.973156i	$-0.426080\pi$
$743$	12.5466	0.460291	0.230146	+	0.973156i	$0.426080\pi$
$744$	4.96897	0.182171
$745$	−24.0634	−0.881615
$746$	2.27521	0.0833012
$747$	24.7011	0.903764
$748$	−0.530512	−0.0193974
$749$	−22.9235	−0.837608
$750$	4.16625	0.152130
$751$	−35.1687	−1.28332	−0.641662	−	0.766988i	$-0.721755\pi$
$751$	−35.1687	−1.28332	−0.641662	+	0.766988i	$0.721755\pi$
$752$	47.1593	1.71972
$753$	−54.6442	−1.99135
$754$	−0.211066	−0.00768658
$755$	45.2653	1.64737
$756$	4.11197	0.149551
$757$	−46.3555	−1.68482	−0.842409	−	0.538839i	$-0.818863\pi$
$757$	−46.3555	−1.68482	−0.842409	+	0.538839i	$0.818863\pi$
$758$	5.28528	0.191970
$759$	13.5649	0.492374
$760$	−7.66421	−0.278010
$761$	39.7295	1.44019	0.720097	−	0.693874i	$-0.244097\pi$
$761$	39.7295	1.44019	0.720097	+	0.693874i	$0.244097\pi$
$762$	−5.43040	−0.196723
$763$	38.9332	1.40948
$764$	−20.4615	−0.740270
$765$	2.38273	0.0861477
$766$	3.26909	0.118117
$767$	9.00159	0.325029
$768$	−29.3126	−1.05773
$769$	−9.25006	−0.333566	−0.166783	−	0.985994i	$-0.553338\pi$
$769$	−9.25006	−0.333566	−0.166783	+	0.985994i	$0.553338\pi$
$770$	2.52864	0.0911259
$771$	−25.8105	−0.929543
$772$	25.2395	0.908388
$773$	−37.8465	−1.36125	−0.680623	−	0.732634i	$-0.738291\pi$
$773$	−37.8465	−1.36125	−0.680623	+	0.732634i	$0.738291\pi$
$774$	−8.26366	−0.297031
$775$	5.12388	0.184055
$776$	9.70543	0.348405
$777$	96.7120	3.46952
$778$	7.85629	0.281662
$779$	21.4697	0.769232
$780$	8.42526	0.301673
$781$	−5.94853	−0.212855
$782$	−0.349010	−0.0124806
$783$	0.749882	0.0267986
$784$	31.8102	1.13608
$785$	23.1574	0.826525
$786$	0.586108	0.0209058
$787$	−5.57661	−0.198785	−0.0993923	−	0.995048i	$-0.531690\pi$
$787$	−5.57661	−0.198785	−0.0993923	+	0.995048i	$0.531690\pi$
$788$	−5.14627	−0.183328
$789$	51.1592	1.82132
$790$	2.29218	0.0815522
$791$	33.7420	1.19973
$792$	−2.98116	−0.105931
$793$	3.68984	0.131030
$794$	0.310460	0.0110178
$795$	23.6380	0.838354
$796$	10.0307	0.355528
$797$	8.43299	0.298712	0.149356	−	0.988783i	$-0.452280\pi$
$797$	8.43299	0.298712	0.149356	+	0.988783i	$0.452280\pi$
$798$	−7.05432	−0.249720
$799$	3.50409	0.123966
$800$	6.48033	0.229114
$801$	−2.00953	−0.0710032
$802$	7.24624	0.255874
$803$	7.80607	0.275470
$804$	70.7019	2.49346
$805$	−58.5228	−2.06266
$806$	0.323172	0.0113833
$807$	41.4114	1.45775
$808$	3.52089	0.123864
$809$	3.93790	0.138449	0.0692245	−	0.997601i	$-0.477948\pi$
$809$	3.93790	0.138449	0.0692245	+	0.997601i	$0.477948\pi$
$810$	−5.30996	−0.186573
$811$	44.4428	1.56060	0.780298	−	0.625408i	$-0.215067\pi$
$811$	44.4428	1.56060	0.780298	+	0.625408i	$0.215067\pi$
$812$	10.8036	0.379134
$813$	31.8378	1.11660
$814$	−2.30467	−0.0807787
$815$	4.47412	0.156722
$816$	−2.49668	−0.0874014
$817$	−33.2524	−1.16336
$818$	−0.813895	−0.0284572
$819$	8.13626	0.284304
$820$	−37.3089	−1.30288
$821$	46.4501	1.62112	0.810559	−	0.585656i	$-0.199163\pi$
$821$	46.4501	1.62112	0.810559	+	0.585656i	$0.199163\pi$
$822$	−5.83364	−0.203472
$823$	8.93094	0.311313	0.155656	−	0.987811i	$-0.450251\pi$
$823$	8.93094	0.311313	0.155656	+	0.987811i	$0.450251\pi$
$824$	−8.73924	−0.304446
$825$	−5.94324	−0.206917
$826$	13.0971	0.455708
$827$	−33.2978	−1.15788	−0.578939	−	0.815371i	$-0.696533\pi$
$827$	−33.2978	−1.15788	−0.578939	+	0.815371i	$0.696533\pi$
$828$	34.0145	1.18209
$829$	−33.1086	−1.14991	−0.574955	−	0.818185i	$-0.694980\pi$
$829$	−33.1086	−1.14991	−0.574955	+	0.818185i	$0.694980\pi$
$830$	4.90974	0.170420
$831$	59.7964	2.07431
$832$	−4.28740	−0.148639
$833$	2.36361	0.0818941
$834$	6.58551	0.228038
$835$	18.5909	0.643366
$836$	−5.91395	−0.204538
$837$	−1.14818	−0.0396868
$838$	−0.132608	−0.00458087
$839$	1.09163	0.0376873	0.0188437	−	0.999822i	$-0.494002\pi$
$839$	1.09163	0.0376873	0.0188437	+	0.999822i	$0.494002\pi$
$840$	24.8657	0.857947
$841$	−27.0298	−0.932062
$842$	5.05931	0.174355
$843$	−67.7475	−2.33335
$844$	46.6000	1.60404
$845$	−34.2143	−1.17701
$846$	9.70749	0.333750
$847$	3.95783	0.135992
$848$	−12.8113	−0.439943
$849$	−16.0415	−0.550541
$850$	0.152914	0.00524489
$851$	53.3392	1.82844
$852$	−28.8379	−0.987969
$853$	25.3615	0.868363	0.434181	−	0.900825i	$-0.357038\pi$
$853$	25.3615	0.868363	0.434181	+	0.900825i	$0.357038\pi$
$854$	5.36865	0.183711
$855$	26.5618	0.908394
$856$	5.37183	0.183606
$857$	48.0815	1.64243	0.821216	−	0.570617i	$-0.193296\pi$
$857$	48.0815	1.64243	0.821216	+	0.570617i	$0.193296\pi$
$858$	−0.374851	−0.0127972
$859$	−38.0202	−1.29723	−0.648617	−	0.761115i	$-0.724652\pi$
$859$	−38.0202	−1.29723	−0.648617	+	0.761115i	$0.724652\pi$
$860$	57.7843	1.97043
$861$	−69.6560	−2.37387
$862$	6.98595	0.237942
$863$	10.7314	0.365300	0.182650	−	0.983178i	$-0.441532\pi$
$863$	10.7314	0.365300	0.182650	+	0.983178i	$0.441532\pi$
$864$	−1.45213	−0.0494026
$865$	−14.9838	−0.509466
$866$	4.34036	0.147491
$867$	42.1930	1.43295
$868$	−16.5419	−0.561469
$869$	3.58772	0.121705
$870$	2.23555	0.0757921
$871$	9.32735	0.316045
$872$	−9.12349	−0.308960
$873$	−33.6360	−1.13841
$874$	−3.89064	−0.131603
$875$	−28.1335	−0.951088
$876$	37.8430	1.27860
$877$	−33.0842	−1.11718	−0.558588	−	0.829445i	$-0.688657\pi$
$877$	−33.0842	−1.11718	−0.558588	+	0.829445i	$0.688657\pi$
$878$	8.74432	0.295107
$879$	33.0502	1.11475
$880$	9.97651	0.336308
$881$	32.2750	1.08737	0.543686	−	0.839289i	$-0.317028\pi$
$881$	32.2750	1.08737	0.543686	+	0.839289i	$0.317028\pi$
$882$	6.54797	0.220482
$883$	4.01893	0.135248	0.0676238	−	0.997711i	$-0.478458\pi$
$883$	4.01893	0.135248	0.0676238	+	0.997711i	$0.478458\pi$
$884$	−0.339294	−0.0114117
$885$	−95.3420	−3.20489
$886$	−3.64783	−0.122551
$887$	−8.61547	−0.289279	−0.144640	−	0.989484i	$-0.546202\pi$
$887$	−8.61547	−0.289279	−0.144640	+	0.989484i	$0.546202\pi$
$888$	−22.6632	−0.760528
$889$	36.6700	1.22987
$890$	−0.399427	−0.0133888
$891$	−8.31115	−0.278434
$892$	−8.27058	−0.276920
$893$	39.0623	1.30717
$894$	5.19022	0.173587
$895$	25.7684	0.861344
$896$	−27.7539	−0.927191
$897$	8.67554	0.289668
$898$	1.47699	0.0492877
$899$	−3.01667	−0.100612
$900$	−14.9029	−0.496765
$901$	−0.951925	−0.0317132
$902$	1.65992	0.0552693
$903$	107.884	3.59015
$904$	−7.90701	−0.262983
$905$	26.4115	0.877948
$906$	−9.76323	−0.324362
$907$	2.87135	0.0953417	0.0476709	−	0.998863i	$-0.484820\pi$
$907$	2.87135	0.0953417	0.0476709	+	0.998863i	$0.484820\pi$
$908$	−6.92337	−0.229760
$909$	−12.2023	−0.404725
$910$	1.61722	0.0536102
$911$	−30.9811	−1.02645	−0.513224	−	0.858255i	$-0.671549\pi$
$911$	−30.9811	−1.02645	−0.513224	+	0.858255i	$0.671549\pi$
$912$	−27.8321	−0.921613
$913$	7.68472	0.254327
$914$	−9.51802	−0.314828
$915$	−39.0816	−1.29200
$916$	−29.5262	−0.975575
$917$	−3.95783	−0.130699
$918$	−0.0342654	−0.00113093
$919$	40.3993	1.33265	0.666325	−	0.745661i	$-0.267866\pi$
$919$	40.3993	1.33265	0.666325	+	0.745661i	$0.267866\pi$
$920$	13.7141	0.452139
$921$	−71.8263	−2.36676
$922$	−6.17267	−0.203286
$923$	−3.80444	−0.125225
$924$	19.1871	0.631211
$925$	−23.3698	−0.768394
$926$	−8.40212	−0.276111
$927$	30.2875	0.994772
$928$	−3.81528	−0.125243
$929$	−17.2834	−0.567050	−0.283525	−	0.958965i	$-0.591504\pi$
$929$	−17.2834	−0.567050	−0.283525	+	0.958965i	$0.591504\pi$
$930$	−3.42294	−0.112243
$931$	26.3486	0.863541
$932$	14.2657	0.467289
$933$	9.48273	0.310451
$934$	−7.24336	−0.237010
$935$	0.741288	0.0242427
$936$	−1.90663	−0.0623201
$937$	18.4692	0.603363	0.301682	−	0.953409i	$-0.402452\pi$
$937$	18.4692	0.603363	0.301682	+	0.953409i	$0.402452\pi$
$938$	13.5711	0.443113
$939$	53.1908	1.73582
$940$	−67.8804	−2.21401
$941$	47.2841	1.54142	0.770709	−	0.637187i	$-0.219902\pi$
$941$	47.2841	1.54142	0.770709	+	0.637187i	$0.219902\pi$
$942$	−4.99481	−0.162740
$943$	−38.4171	−1.25103
$944$	51.6735	1.68183
$945$	−5.74569	−0.186907
$946$	−2.57090	−0.0835871
$947$	−33.2460	−1.08035	−0.540174	−	0.841553i	$-0.681642\pi$
$947$	−33.2460	−1.08035	−0.540174	+	0.841553i	$0.681642\pi$
$948$	17.3929	0.564895
$949$	4.99244	0.162061
$950$	1.70463	0.0553054
$951$	21.5978	0.700358
$952$	−1.00136	−0.0324544
$953$	48.9817	1.58667	0.793337	−	0.608783i	$-0.208342\pi$
$953$	48.9817	1.58667	0.793337	+	0.608783i	$0.208342\pi$
$954$	−2.63715	−0.0853808
$955$	28.5910	0.925182
$956$	−16.2563	−0.525768
$957$	3.49907	0.113109
$958$	8.59351	0.277644
$959$	39.3929	1.27206
$960$	45.4108	1.46563
$961$	−26.3810	−0.851001
$962$	−1.47397	−0.0475228
$963$	−18.6171	−0.599928
$964$	36.6500	1.18042
$965$	−35.2673	−1.13529
$966$	12.6227	0.406130
$967$	1.66064	0.0534026	0.0267013	−	0.999643i	$-0.491500\pi$
$967$	1.66064	0.0534026	0.0267013	+	0.999643i	$0.491500\pi$
$968$	−0.927465	−0.0298099
$969$	−2.06802	−0.0664343
$970$	−6.68571	−0.214665
$971$	1.77727	0.0570352	0.0285176	−	0.999593i	$-0.490921\pi$
$971$	1.77727	0.0570352	0.0285176	+	0.999593i	$0.490921\pi$
$972$	−43.4084	−1.39233
$973$	−44.4701	−1.42565
$974$	0.184514	0.00591220
$975$	−3.80106	−0.121731
$976$	21.1815	0.678003
$977$	18.0919	0.578812	0.289406	−	0.957206i	$-0.406542\pi$
$977$	18.0919	0.578812	0.289406	+	0.957206i	$0.406542\pi$
$978$	−0.965020	−0.0308579
$979$	−0.625182	−0.0199809
$980$	−45.7872	−1.46262
$981$	31.6192	1.00952
$982$	−1.09166	−0.0348362
$983$	−7.39904	−0.235993	−0.117996	−	0.993014i	$-0.537647\pi$
$983$	−7.39904	−0.235993	−0.117996	+	0.993014i	$0.537647\pi$
$984$	16.3230	0.520358
$985$	7.19092	0.229122
$986$	−0.0900276	−0.00286706
$987$	−126.733	−4.03397
$988$	−3.78232	−0.120332
$989$	59.5008	1.89201
$990$	2.05361	0.0652681
$991$	−32.7011	−1.03878	−0.519392	−	0.854536i	$-0.673842\pi$
$991$	−32.7011	−1.03878	−0.519392	+	0.854536i	$0.673842\pi$
$992$	5.84174	0.185475
$993$	28.7884	0.913573
$994$	−5.53538	−0.175572
$995$	−14.0159	−0.444335
$996$	37.2547	1.18046
$997$	−39.6821	−1.25674	−0.628372	−	0.777913i	$-0.716279\pi$
$997$	−39.6821	−1.25674	−0.628372	+	0.777913i	$0.716279\pi$
$998$	−4.15826	−0.131628
$999$	5.23678	0.165684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.14	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+0.235116 q^{2} -2.49285 q^{3} -1.94472 q^{4} +2.71737 q^{5} -0.586108 q^{6} +3.95783 q^{7} -0.927465 q^{8} +3.21431 q^{9} +O(q^{10})\)	\(q+0.235116 q^{2} -2.49285 q^{3} -1.94472 q^{4} +2.71737 q^{5} -0.586108 q^{6} +3.95783 q^{7} -0.927465 q^{8} +3.21431 q^{9} +0.638897 q^{10} +1.00000 q^{11} +4.84790 q^{12} +0.639559 q^{13} +0.930546 q^{14} -6.77401 q^{15} +3.67138 q^{16} +0.272796 q^{17} +0.755734 q^{18} +3.04103 q^{19} -5.28453 q^{20} -9.86627 q^{21} +0.235116 q^{22} -5.44151 q^{23} +2.31203 q^{24} +2.38411 q^{25} +0.150370 q^{26} -0.534240 q^{27} -7.69686 q^{28} -1.40364 q^{29} -1.59267 q^{30} +2.14918 q^{31} +2.71813 q^{32} -2.49285 q^{33} +0.0641385 q^{34} +10.7549 q^{35} -6.25093 q^{36} -9.80229 q^{37} +0.714993 q^{38} -1.59433 q^{39} -2.52027 q^{40} +7.06002 q^{41} -2.31971 q^{42} -10.9346 q^{43} -1.94472 q^{44} +8.73448 q^{45} -1.27938 q^{46} +12.8451 q^{47} -9.15220 q^{48} +8.66438 q^{49} +0.560543 q^{50} -0.680039 q^{51} -1.24376 q^{52} -3.48952 q^{53} -0.125608 q^{54} +2.71737 q^{55} -3.67075 q^{56} -7.58083 q^{57} -0.330018 q^{58} +14.0747 q^{59} +13.1736 q^{60} +5.76935 q^{61} +0.505305 q^{62} +12.7217 q^{63} -6.70368 q^{64} +1.73792 q^{65} -0.586108 q^{66} +14.5840 q^{67} -0.530512 q^{68} +13.5649 q^{69} +2.52864 q^{70} -5.94853 q^{71} -2.98116 q^{72} +7.80607 q^{73} -2.30467 q^{74} -5.94324 q^{75} -5.91395 q^{76} +3.95783 q^{77} -0.374851 q^{78} +3.58772 q^{79} +9.97651 q^{80} -8.31115 q^{81} +1.65992 q^{82} +7.68472 q^{83} +19.1871 q^{84} +0.741288 q^{85} -2.57090 q^{86} +3.49907 q^{87} -0.927465 q^{88} -0.625182 q^{89} +2.05361 q^{90} +2.53126 q^{91} +10.5822 q^{92} -5.35758 q^{93} +3.02009 q^{94} +8.26361 q^{95} -6.77589 q^{96} -10.4645 q^{97} +2.03713 q^{98} +3.21431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 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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