LMFDB - Embedded newform 9251.2.a.ba.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, 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("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54144 q^{2} +0.626545 q^{3} +4.45893 q^{4} -0.217422 q^{5} -1.59233 q^{6} -0.803024 q^{7} -6.24924 q^{8} -2.60744 q^{9} +O(q^{10})$	\(q-2.54144 q^{2} +0.626545 q^{3} +4.45893 q^{4} -0.217422 q^{5} -1.59233 q^{6} -0.803024 q^{7} -6.24924 q^{8} -2.60744 q^{9} +0.552566 q^{10} +1.00000 q^{11} +2.79373 q^{12} +0.170339 q^{13} +2.04084 q^{14} -0.136225 q^{15} +6.96423 q^{16} -1.26956 q^{17} +6.62666 q^{18} +6.74600 q^{19} -0.969470 q^{20} -0.503131 q^{21} -2.54144 q^{22} +8.79133 q^{23} -3.91544 q^{24} -4.95273 q^{25} -0.432908 q^{26} -3.51332 q^{27} -3.58063 q^{28} +0.346207 q^{30} +1.57449 q^{31} -5.20071 q^{32} +0.626545 q^{33} +3.22652 q^{34} +0.174595 q^{35} -11.6264 q^{36} +1.10437 q^{37} -17.1446 q^{38} +0.106725 q^{39} +1.35872 q^{40} -0.226890 q^{41} +1.27868 q^{42} -6.11646 q^{43} +4.45893 q^{44} +0.566915 q^{45} -22.3427 q^{46} +4.77355 q^{47} +4.36341 q^{48} -6.35515 q^{49} +12.5871 q^{50} -0.795438 q^{51} +0.759533 q^{52} -5.39913 q^{53} +8.92889 q^{54} -0.217422 q^{55} +5.01829 q^{56} +4.22667 q^{57} -11.0438 q^{59} -0.607417 q^{60} -0.258433 q^{61} -4.00148 q^{62} +2.09384 q^{63} -0.711148 q^{64} -0.0370355 q^{65} -1.59233 q^{66} -6.23627 q^{67} -5.66089 q^{68} +5.50816 q^{69} -0.443724 q^{70} -10.6354 q^{71} +16.2945 q^{72} -6.08350 q^{73} -2.80670 q^{74} -3.10311 q^{75} +30.0800 q^{76} -0.803024 q^{77} -0.271237 q^{78} -1.45269 q^{79} -1.51418 q^{80} +5.62107 q^{81} +0.576628 q^{82} -9.36412 q^{83} -2.24343 q^{84} +0.276030 q^{85} +15.5446 q^{86} -6.24924 q^{88} +11.4432 q^{89} -1.44078 q^{90} -0.136787 q^{91} +39.2000 q^{92} +0.986491 q^{93} -12.1317 q^{94} -1.46673 q^{95} -3.25848 q^{96} -1.95848 q^{97} +16.1513 q^{98} -2.60744 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) $ 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * 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 $

$2$	−2.54144	−1.79707	−0.898536	−	0.438900i	$-0.855368\pi$
$2$	−2.54144	−1.79707	−0.898536	+	0.438900i	$0.855368\pi$
$3$	0.626545	0.361736	0.180868	−	0.983507i	$-0.442109\pi$
$3$	0.626545	0.361736	0.180868	+	0.983507i	$0.442109\pi$
$4$	4.45893	2.22947
$5$	−0.217422	−0.0972341	−0.0486170	−	0.998817i	$-0.515481\pi$
$5$	−0.217422	−0.0972341	−0.0486170	+	0.998817i	$0.515481\pi$
$6$	−1.59233	−0.650066
$7$	−0.803024	−0.303515	−0.151757	−	0.988418i	$-0.548493\pi$
$7$	−0.803024	−0.303515	−0.151757	+	0.988418i	$0.548493\pi$
$8$	−6.24924	−2.20944
$9$	−2.60744	−0.869147
$10$	0.552566	0.174737
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.79373	0.806479
$13$	0.170339	0.0472437	0.0236218	−	0.999721i	$-0.492480\pi$
$13$	0.170339	0.0472437	0.0236218	+	0.999721i	$0.492480\pi$
$14$	2.04084	0.545438
$15$	−0.136225	−0.0351731
$16$	6.96423	1.74106
$17$	−1.26956	−0.307914	−0.153957	−	0.988078i	$-0.549202\pi$
$17$	−1.26956	−0.307914	−0.153957	+	0.988078i	$0.549202\pi$
$18$	6.62666	1.56192
$19$	6.74600	1.54764	0.773819	−	0.633407i	$-0.218344\pi$
$19$	6.74600	1.54764	0.773819	+	0.633407i	$0.218344\pi$
$20$	−0.969470	−0.216780
$21$	−0.503131	−0.109792
$22$	−2.54144	−0.541838
$23$	8.79133	1.83312	0.916559	−	0.399899i	$-0.130955\pi$
$23$	8.79133	1.83312	0.916559	+	0.399899i	$0.130955\pi$
$24$	−3.91544	−0.799235
$25$	−4.95273	−0.990546
$26$	−0.432908	−0.0849003
$27$	−3.51332	−0.676138
$28$	−3.58063	−0.676676
$29$	0	0
$29$	0	0
$30$	0.346207	0.0632085
$31$	1.57449	0.282787	0.141394	−	0.989953i	$-0.454842\pi$
$31$	1.57449	0.282787	0.141394	+	0.989953i	$0.454842\pi$
$32$	−5.20071	−0.919365
$33$	0.626545	0.109068
$34$	3.22652	0.553343
$35$	0.174595	0.0295120
$36$	−11.6264	−1.93773
$37$	1.10437	0.181558	0.0907790	−	0.995871i	$-0.471064\pi$
$37$	1.10437	0.181558	0.0907790	+	0.995871i	$0.471064\pi$
$38$	−17.1446	−2.78122
$39$	0.106725	0.0170897
$40$	1.35872	0.214833
$41$	−0.226890	−0.0354342	−0.0177171	−	0.999843i	$-0.505640\pi$
$41$	−0.226890	−0.0354342	−0.0177171	+	0.999843i	$0.505640\pi$
$42$	1.27868	0.197304
$43$	−6.11646	−0.932751	−0.466375	−	0.884587i	$-0.654440\pi$
$43$	−6.11646	−0.932751	−0.466375	+	0.884587i	$0.654440\pi$
$44$	4.45893	0.672210
$45$	0.566915	0.0845107
$46$	−22.3427	−3.29425
$47$	4.77355	0.696294	0.348147	−	0.937440i	$-0.386811\pi$
$47$	4.77355	0.696294	0.348147	+	0.937440i	$0.386811\pi$
$48$	4.36341	0.629804
$49$	−6.35515	−0.907879
$50$	12.5871	1.78008
$51$	−0.795438	−0.111384
$52$	0.759533	0.105328
$53$	−5.39913	−0.741628	−0.370814	−	0.928707i	$-0.620921\pi$
$53$	−5.39913	−0.741628	−0.370814	+	0.928707i	$0.620921\pi$
$54$	8.92889	1.21507
$55$	−0.217422	−0.0293172
$56$	5.01829	0.670598
$57$	4.22667	0.559837
$58$	0	0
$59$	−11.0438	−1.43778	−0.718889	−	0.695125i	$-0.755349\pi$
$59$	−11.0438	−1.43778	−0.718889	+	0.695125i	$0.755349\pi$
$60$	−0.607417	−0.0784172
$61$	−0.258433	−0.0330889	−0.0165445	−	0.999863i	$-0.505267\pi$
$61$	−0.258433	−0.0330889	−0.0165445	+	0.999863i	$0.505267\pi$
$62$	−4.00148	−0.508189
$63$	2.09384	0.263799
$64$	−0.711148	−0.0888935
$65$	−0.0370355	−0.00459369
$66$	−1.59233	−0.196002
$67$	−6.23627	−0.761882	−0.380941	−	0.924599i	$-0.624400\pi$
$67$	−6.23627	−0.761882	−0.380941	+	0.924599i	$0.624400\pi$
$68$	−5.66089	−0.686484
$69$	5.50816	0.663105
$70$	−0.443724	−0.0530351
$71$	−10.6354	−1.26219	−0.631096	−	0.775704i	$-0.717395\pi$
$71$	−10.6354	−1.26219	−0.631096	+	0.775704i	$0.717395\pi$
$72$	16.2945	1.92033
$73$	−6.08350	−0.712020	−0.356010	−	0.934482i	$-0.615863\pi$
$73$	−6.08350	−0.712020	−0.356010	+	0.934482i	$0.615863\pi$
$74$	−2.80670	−0.326273
$75$	−3.10311	−0.358316
$76$	30.0800	3.45041
$77$	−0.803024	−0.0915131
$78$	−0.271237	−0.0307115
$79$	−1.45269	−0.163441	−0.0817203	−	0.996655i	$-0.526041\pi$
$79$	−1.45269	−0.163441	−0.0817203	+	0.996655i	$0.526041\pi$
$80$	−1.51418	−0.169290
$81$	5.62107	0.624563
$82$	0.576628	0.0636779
$83$	−9.36412	−1.02785	−0.513923	−	0.857836i	$-0.671808\pi$
$83$	−9.36412	−1.02785	−0.513923	+	0.857836i	$0.671808\pi$
$84$	−2.24343	−0.244778
$85$	0.276030	0.0299397
$86$	15.5446	1.67622
$87$	0	0
$88$	−6.24924	−0.666172
$89$	11.4432	1.21298	0.606488	−	0.795093i	$-0.292578\pi$
$89$	11.4432	1.21298	0.606488	+	0.795093i	$0.292578\pi$
$90$	−1.44078	−0.151872
$91$	−0.136787	−0.0143391
$92$	39.2000	4.08688
$93$	0.986491	0.102294
$94$	−12.1317	−1.25129
$95$	−1.46673	−0.150483
$96$	−3.25848	−0.332567
$97$	−1.95848	−0.198853	−0.0994266	−	0.995045i	$-0.531701\pi$
$97$	−1.95848	−0.198853	−0.0994266	+	0.995045i	$0.531701\pi$
$98$	16.1513	1.63152
$99$	−2.60744	−0.262058
$100$	−22.0839	−2.20839
$101$	9.23028	0.918447	0.459223	−	0.888321i	$-0.348128\pi$
$101$	9.23028	0.918447	0.459223	+	0.888321i	$0.348128\pi$
$102$	2.02156	0.200164
$103$	9.53197	0.939213	0.469607	−	0.882876i	$-0.344396\pi$
$103$	9.53197	0.939213	0.469607	+	0.882876i	$0.344396\pi$
$104$	−1.06449	−0.104382
$105$	0.109392	0.0106755
$106$	13.7216	1.33276
$107$	1.23255	0.119155	0.0595774	−	0.998224i	$-0.481025\pi$
$107$	1.23255	0.119155	0.0595774	+	0.998224i	$0.481025\pi$
$108$	−15.6656	−1.50743
$109$	−1.87590	−0.179679	−0.0898394	−	0.995956i	$-0.528635\pi$
$109$	−1.87590	−0.179679	−0.0898394	+	0.995956i	$0.528635\pi$
$110$	0.552566	0.0526851
$111$	0.691940	0.0656761
$112$	−5.59245	−0.528437
$113$	−5.39324	−0.507353	−0.253677	−	0.967289i	$-0.581640\pi$
$113$	−5.39324	−0.507353	−0.253677	+	0.967289i	$0.581640\pi$
$114$	−10.7419	−1.00607
$115$	−1.91143	−0.178242
$116$	0	0
$117$	−0.444150	−0.0410617
$118$	28.0672	2.58379
$119$	1.01949	0.0934563
$120$	0.851301	0.0777128
$121$	1.00000	0.0909091
$122$	0.656792	0.0594632
$123$	−0.142157	−0.0128178
$124$	7.02056	0.630465
$125$	2.16394	0.193549
$126$	−5.32137	−0.474065
$127$	16.0096	1.42062	0.710310	−	0.703889i	$-0.248555\pi$
$127$	16.0096	1.42062	0.710310	+	0.703889i	$0.248555\pi$
$128$	12.2088	1.07911
$129$	−3.83224	−0.337410
$130$	0.0941237	0.00825520
$131$	0.162091	0.0141619	0.00708097	−	0.999975i	$-0.497746\pi$
$131$	0.162091	0.0141619	0.00708097	+	0.999975i	$0.497746\pi$
$132$	2.79373	0.243163
$133$	−5.41720	−0.469731
$134$	15.8491	1.36916
$135$	0.763872	0.0657436
$136$	7.93380	0.680318
$137$	7.68888	0.656905	0.328453	−	0.944520i	$-0.393473\pi$
$137$	7.68888	0.656905	0.328453	+	0.944520i	$0.393473\pi$
$138$	−13.9987	−1.19165
$139$	−22.3848	−1.89866	−0.949328	−	0.314288i	$-0.898234\pi$
$139$	−22.3848	−1.89866	−0.949328	+	0.314288i	$0.898234\pi$
$140$	0.778508	0.0657959
$141$	2.99085	0.251875
$142$	27.0293	2.26825
$143$	0.170339	0.0142445
$144$	−18.1588	−1.51324
$145$	0	0
$146$	15.4609	1.27955
$147$	−3.98179	−0.328413
$148$	4.92433	0.404778
$149$	13.3559	1.09416	0.547078	−	0.837082i	$-0.315740\pi$
$149$	13.3559	1.09416	0.547078	+	0.837082i	$0.315740\pi$
$150$	7.88638	0.643920
$151$	14.8002	1.20442	0.602212	−	0.798336i	$-0.294286\pi$
$151$	14.8002	1.20442	0.602212	+	0.798336i	$0.294286\pi$
$152$	−42.1574	−3.41942
$153$	3.31031	0.267622
$154$	2.04084	0.164456
$155$	−0.342329	−0.0274966
$156$	0.475882	0.0381010
$157$	17.1435	1.36820	0.684101	−	0.729387i	$-0.260195\pi$
$157$	17.1435	1.36820	0.684101	+	0.729387i	$0.260195\pi$
$158$	3.69193	0.293714
$159$	−3.38280	−0.268274
$160$	1.13075	0.0893935
$161$	−7.05965	−0.556378
$162$	−14.2856	−1.12239
$163$	10.8343	0.848611	0.424306	−	0.905519i	$-0.360518\pi$
$163$	10.8343	0.848611	0.424306	+	0.905519i	$0.360518\pi$
$164$	−1.01169	−0.0789995
$165$	−0.136225	−0.0106051
$166$	23.7984	1.84711
$167$	18.4578	1.42831	0.714154	−	0.699989i	$-0.246812\pi$
$167$	18.4578	1.42831	0.714154	+	0.699989i	$0.246812\pi$
$168$	3.14419	0.242579
$169$	−12.9710	−0.997768
$170$	−0.701516	−0.0538038
$171$	−17.5898	−1.34512
$172$	−27.2729	−2.07954
$173$	11.3415	0.862279	0.431139	−	0.902285i	$-0.358112\pi$
$173$	11.3415	0.862279	0.431139	+	0.902285i	$0.358112\pi$
$174$	0	0
$175$	3.97716	0.300645
$176$	6.96423	0.524949
$177$	−6.91943	−0.520096
$178$	−29.0822	−2.17980
$179$	3.27987	0.245149	0.122575	−	0.992459i	$-0.460885\pi$
$179$	3.27987	0.245149	0.122575	+	0.992459i	$0.460885\pi$
$180$	2.52784	0.188414
$181$	−18.8698	−1.40258	−0.701292	−	0.712874i	$-0.747393\pi$
$181$	−18.8698	−1.40258	−0.701292	+	0.712874i	$0.747393\pi$
$182$	0.347636	0.0257685
$183$	−0.161920	−0.0119695
$184$	−54.9391	−4.05017
$185$	−0.240115	−0.0176536
$186$	−2.50711	−0.183830
$187$	−1.26956	−0.0928395
$188$	21.2850	1.55237
$189$	2.82128	0.205218
$190$	3.72761	0.270429
$191$	22.5015	1.62815	0.814077	−	0.580757i	$-0.197243\pi$
$191$	22.5015	1.62815	0.814077	+	0.580757i	$0.197243\pi$
$192$	−0.445567	−0.0321560
$193$	−4.32159	−0.311075	−0.155537	−	0.987830i	$-0.549711\pi$
$193$	−4.32159	−0.311075	−0.155537	+	0.987830i	$0.549711\pi$
$194$	4.97736	0.357354
$195$	−0.0232044	−0.00166170
$196$	−28.3372	−2.02409
$197$	−9.25610	−0.659470	−0.329735	−	0.944074i	$-0.606959\pi$
$197$	−9.25610	−0.659470	−0.329735	+	0.944074i	$0.606959\pi$
$198$	6.62666	0.470936
$199$	3.40926	0.241676	0.120838	−	0.992672i	$-0.461442\pi$
$199$	3.40926	0.241676	0.120838	+	0.992672i	$0.461442\pi$
$200$	30.9508	2.18855
$201$	−3.90731	−0.275600
$202$	−23.4582	−1.65052
$203$	0	0
$204$	−3.54680	−0.248326
$205$	0.0493308	0.00344542
$206$	−24.2250	−1.68783
$207$	−22.9229	−1.59325
$208$	1.18628	0.0822540
$209$	6.74600	0.466630
$210$	−0.278013	−0.0191847
$211$	−25.8340	−1.77848	−0.889242	−	0.457436i	$-0.848768\pi$
$211$	−25.8340	−1.77848	−0.889242	+	0.457436i	$0.848768\pi$
$212$	−24.0744	−1.65344
$213$	−6.66358	−0.456581
$214$	−3.13245	−0.214130
$215$	1.32985	0.0906952
$216$	21.9556	1.49389
$217$	−1.26436	−0.0858301
$218$	4.76750	0.322896
$219$	−3.81159	−0.257563
$220$	−0.969470	−0.0653617
$221$	−0.216256	−0.0145470
$222$	−1.75853	−0.118025
$223$	−8.15968	−0.546413	−0.273206	−	0.961955i	$-0.588084\pi$
$223$	−8.15968	−0.546413	−0.273206	+	0.961955i	$0.588084\pi$
$224$	4.17630	0.279041
$225$	12.9139	0.860930
$226$	13.7066	0.911750
$227$	−20.4727	−1.35882	−0.679412	−	0.733757i	$-0.737765\pi$
$227$	−20.4727	−1.35882	−0.679412	+	0.733757i	$0.737765\pi$
$228$	18.8465	1.24814
$229$	−7.70259	−0.509001	−0.254501	−	0.967073i	$-0.581911\pi$
$229$	−7.70259	−0.509001	−0.254501	+	0.967073i	$0.581911\pi$
$230$	4.85778	0.320313
$231$	−0.503131	−0.0331036
$232$	0	0
$233$	25.5267	1.67231	0.836154	−	0.548495i	$-0.184799\pi$
$233$	25.5267	1.67231	0.836154	+	0.548495i	$0.184799\pi$
$234$	1.12878	0.0737908
$235$	−1.03788	−0.0677035
$236$	−49.2435	−3.20548
$237$	−0.910177	−0.0591224
$238$	−2.59097	−0.167948
$239$	20.7504	1.34223	0.671116	−	0.741352i	$-0.265815\pi$
$239$	20.7504	1.34223	0.671116	+	0.741352i	$0.265815\pi$
$240$	−0.948700	−0.0612383
$241$	13.8387	0.891427	0.445714	−	0.895176i	$-0.352950\pi$
$241$	13.8387	0.891427	0.445714	+	0.895176i	$0.352950\pi$
$242$	−2.54144	−0.163370
$243$	14.0618	0.902065
$244$	−1.15234	−0.0737707
$245$	1.38175	0.0882767
$246$	0.361283	0.0230346
$247$	1.14911	0.0731161
$248$	−9.83939	−0.624802
$249$	−5.86705	−0.371809
$250$	−5.49953	−0.347821
$251$	−27.4711	−1.73396	−0.866980	−	0.498343i	$-0.833942\pi$
$251$	−27.4711	−1.73396	−0.866980	+	0.498343i	$0.833942\pi$
$252$	9.33629	0.588131
$253$	8.79133	0.552706
$254$	−40.6874	−2.55295
$255$	0.172946	0.0108303
$256$	−29.6056	−1.85035
$257$	−19.3436	−1.20662	−0.603309	−	0.797508i	$-0.706151\pi$
$257$	−19.3436	−1.20662	−0.603309	+	0.797508i	$0.706151\pi$
$258$	9.73942	0.606350
$259$	−0.886839	−0.0551055
$260$	−0.165139	−0.0102415
$261$	0	0
$262$	−0.411944	−0.0254500
$263$	7.53119	0.464393	0.232197	−	0.972669i	$-0.425409\pi$
$263$	7.53119	0.464393	0.232197	+	0.972669i	$0.425409\pi$
$264$	−3.91544	−0.240978
$265$	1.17389	0.0721115
$266$	13.7675	0.844140
$267$	7.16968	0.438777
$268$	−27.8071	−1.69859
$269$	−28.7512	−1.75299	−0.876497	−	0.481407i	$-0.840126\pi$
$269$	−28.7512	−1.75299	−0.876497	+	0.481407i	$0.840126\pi$
$270$	−1.94134	−0.118146
$271$	−9.94450	−0.604086	−0.302043	−	0.953294i	$-0.597669\pi$
$271$	−9.94450	−0.604086	−0.302043	+	0.953294i	$0.597669\pi$
$272$	−8.84152	−0.536096
$273$	−0.0857031	−0.00518699
$274$	−19.5408	−1.18051
$275$	−4.95273	−0.298661
$276$	24.5605	1.47837
$277$	13.6643	0.821011	0.410505	−	0.911858i	$-0.365352\pi$
$277$	13.6643	0.821011	0.410505	+	0.911858i	$0.365352\pi$
$278$	56.8897	3.41202
$279$	−4.10540	−0.245784
$280$	−1.09109	−0.0652049
$281$	21.8787	1.30517	0.652587	−	0.757714i	$-0.273684\pi$
$281$	21.8787	1.30517	0.652587	+	0.757714i	$0.273684\pi$
$282$	−7.60107	−0.452637
$283$	−27.8958	−1.65824	−0.829118	−	0.559074i	$-0.811157\pi$
$283$	−27.8958	−1.65824	−0.829118	+	0.559074i	$0.811157\pi$
$284$	−47.4227	−2.81402
$285$	−0.918972	−0.0544352
$286$	−0.432908	−0.0255984
$287$	0.182198	0.0107548
$288$	13.5605	0.799063
$289$	−15.3882	−0.905189
$290$	0	0
$291$	−1.22708	−0.0719324
$292$	−27.1260	−1.58743
$293$	32.1475	1.87808	0.939040	−	0.343808i	$-0.111717\pi$
$293$	32.1475	1.87808	0.939040	+	0.343808i	$0.111717\pi$
$294$	10.1195	0.590181
$295$	2.40116	0.139801
$296$	−6.90150	−0.401142
$297$	−3.51332	−0.203863
$298$	−33.9432	−1.96628
$299$	1.49751	0.0866032
$300$	−13.8366	−0.798854
$301$	4.91166	0.283104
$302$	−37.6139	−2.16444
$303$	5.78319	0.332235
$304$	46.9807	2.69453
$305$	0.0561890	0.00321737
$306$	−8.41295	−0.480937
$307$	−16.1775	−0.923302	−0.461651	−	0.887062i	$-0.652743\pi$
$307$	−16.1775	−0.923302	−0.461651	+	0.887062i	$0.652743\pi$
$308$	−3.58063	−0.204025
$309$	5.97221	0.339747
$310$	0.870011	0.0494133
$311$	−27.2290	−1.54402	−0.772008	−	0.635613i	$-0.780747\pi$
$311$	−27.2290	−1.54402	−0.772008	+	0.635613i	$0.780747\pi$
$312$	−0.666953	−0.0377588
$313$	9.20963	0.520559	0.260280	−	0.965533i	$-0.416185\pi$
$313$	9.20963	0.520559	0.260280	+	0.965533i	$0.416185\pi$
$314$	−43.5693	−2.45876
$315$	−0.455246	−0.0256502
$316$	−6.47746	−0.364385
$317$	−7.53753	−0.423350	−0.211675	−	0.977340i	$-0.567892\pi$
$317$	−7.53753	−0.423350	−0.211675	+	0.977340i	$0.567892\pi$
$318$	8.59720	0.482107
$319$	0	0
$320$	0.154619	0.00864348
$321$	0.772246	0.0431026
$322$	17.9417	0.999852
$323$	−8.56446	−0.476539
$324$	25.0640	1.39244
$325$	−0.843645	−0.0467970
$326$	−27.5349	−1.52502
$327$	−1.17534	−0.0649963
$328$	1.41789	0.0782899
$329$	−3.83328	−0.211336
$330$	0.346207	0.0190581
$331$	−16.5777	−0.911191	−0.455596	−	0.890187i	$-0.650574\pi$
$331$	−16.5777	−0.911191	−0.455596	+	0.890187i	$0.650574\pi$
$332$	−41.7540	−2.29155
$333$	−2.87959	−0.157801
$334$	−46.9094	−2.56677
$335$	1.35590	0.0740808
$336$	−3.50392	−0.191155
$337$	−11.5895	−0.631322	−0.315661	−	0.948872i	$-0.602226\pi$
$337$	−11.5895	−0.631322	−0.315661	+	0.948872i	$0.602226\pi$
$338$	32.9650	1.79306
$339$	−3.37911	−0.183528
$340$	1.23080	0.0667496
$341$	1.57449	0.0852636
$342$	44.7035	2.41729
$343$	10.7245	0.579069
$344$	38.2232	2.06086
$345$	−1.19760	−0.0644764
$346$	−28.8238	−1.54958
$347$	−3.12557	−0.167789	−0.0838947	−	0.996475i	$-0.526736\pi$
$347$	−3.12557	−0.167789	−0.0838947	+	0.996475i	$0.526736\pi$
$348$	0	0
$349$	27.3368	1.46330	0.731652	−	0.681679i	$-0.238750\pi$
$349$	27.3368	1.46330	0.731652	+	0.681679i	$0.238750\pi$
$350$	−10.1077	−0.540281
$351$	−0.598456	−0.0319432
$352$	−5.20071	−0.277199
$353$	−23.5299	−1.25237	−0.626185	−	0.779674i	$-0.715385\pi$
$353$	−23.5299	−1.25237	−0.626185	+	0.779674i	$0.715385\pi$
$354$	17.5853	0.934650
$355$	2.31237	0.122728
$356$	51.0244	2.70429
$357$	0.638756	0.0338065
$358$	−8.33561	−0.440551
$359$	18.6067	0.982026	0.491013	−	0.871152i	$-0.336627\pi$
$359$	18.6067	0.982026	0.491013	+	0.871152i	$0.336627\pi$
$360$	−3.54279	−0.186721
$361$	26.5085	1.39518
$362$	47.9567	2.52055
$363$	0.626545	0.0328851
$364$	−0.609923	−0.0319687
$365$	1.32269	0.0692326
$366$	0.411510	0.0215100
$367$	−32.4847	−1.69569	−0.847844	−	0.530246i	$-0.822100\pi$
$367$	−32.4847	−1.69569	−0.847844	+	0.530246i	$0.822100\pi$
$368$	61.2248	3.19156
$369$	0.591602	0.0307976
$370$	0.610239	0.0317248
$371$	4.33564	0.225095
$372$	4.39870	0.228062
$373$	2.73854	0.141796	0.0708982	−	0.997484i	$-0.477413\pi$
$373$	2.73854	0.141796	0.0708982	+	0.997484i	$0.477413\pi$
$374$	3.22652	0.166839
$375$	1.35581	0.0700136
$376$	−29.8311	−1.53842
$377$	0	0
$378$	−7.17012	−0.368791
$379$	−28.6354	−1.47090	−0.735450	−	0.677579i	$-0.763029\pi$
$379$	−28.6354	−1.47090	−0.735450	+	0.677579i	$0.763029\pi$
$380$	−6.54004	−0.335497
$381$	10.0307	0.513889
$382$	−57.1864	−2.92591
$383$	−21.2031	−1.08343	−0.541714	−	0.840563i	$-0.682224\pi$
$383$	−21.2031	−1.08343	−0.541714	+	0.840563i	$0.682224\pi$
$384$	7.64935	0.390354
$385$	0.174595	0.00889819
$386$	10.9831	0.559023
$387$	15.9483	0.810698
$388$	−8.73272	−0.443337
$389$	−19.9463	−1.01132	−0.505659	−	0.862734i	$-0.668750\pi$
$389$	−19.9463	−1.01132	−0.505659	+	0.862734i	$0.668750\pi$
$390$	0.0589728	0.00298620
$391$	−11.1611	−0.564442
$392$	39.7149	2.00591
$393$	0.101557	0.00512288
$394$	23.5238	1.18511
$395$	0.315847	0.0158920
$396$	−11.6264	−0.584249
$397$	8.88552	0.445951	0.222976	−	0.974824i	$-0.428423\pi$
$397$	8.88552	0.445951	0.222976	+	0.974824i	$0.428423\pi$
$398$	−8.66444	−0.434309
$399$	−3.39412	−0.169919
$400$	−34.4919	−1.72460
$401$	−21.2279	−1.06007	−0.530036	−	0.847975i	$-0.677822\pi$
$401$	−21.2279	−1.06007	−0.530036	+	0.847975i	$0.677822\pi$
$402$	9.93020	0.495273
$403$	0.268198	0.0133599
$404$	41.1572	2.04765
$405$	−1.22214	−0.0607288
$406$	0	0
$407$	1.10437	0.0547418
$408$	4.97088	0.246095
$409$	18.0793	0.893962	0.446981	−	0.894543i	$-0.352499\pi$
$409$	18.0793	0.893962	0.446981	+	0.894543i	$0.352499\pi$
$410$	−0.125372	−0.00619166
$411$	4.81743	0.237626
$412$	42.5025	2.09395
$413$	8.86843	0.436387
$414$	58.2572	2.86318
$415$	2.03597	0.0999416
$416$	−0.885886	−0.0434342
$417$	−14.0251	−0.686812
$418$	−17.1446	−0.838568
$419$	−1.75974	−0.0859689	−0.0429844	−	0.999076i	$-0.513687\pi$
$419$	−1.75974	−0.0859689	−0.0429844	+	0.999076i	$0.513687\pi$
$420$	0.487771	0.0238008
$421$	−24.9418	−1.21559	−0.607795	−	0.794094i	$-0.707946\pi$
$421$	−24.9418	−1.21559	−0.607795	+	0.794094i	$0.707946\pi$
$422$	65.6556	3.19607
$423$	−12.4468	−0.605182
$424$	33.7405	1.63858
$425$	6.28779	0.305003
$426$	16.9351	0.820508
$427$	0.207528	0.0100430
$428$	5.49584	0.265652
$429$	0.106725	0.00515275
$430$	−3.37974	−0.162986
$431$	14.3422	0.690838	0.345419	−	0.938448i	$-0.387737\pi$
$431$	14.3422	0.690838	0.345419	+	0.938448i	$0.387737\pi$
$432$	−24.4675	−1.17720
$433$	−13.1229	−0.630647	−0.315324	−	0.948984i	$-0.602113\pi$
$433$	−13.1229	−0.630647	−0.315324	+	0.948984i	$0.602113\pi$
$434$	3.21329	0.154243
$435$	0	0
$436$	−8.36452	−0.400588
$437$	59.3063	2.83700
$438$	9.68694	0.462860
$439$	−7.87764	−0.375979	−0.187990	−	0.982171i	$-0.560197\pi$
$439$	−7.87764	−0.375979	−0.187990	+	0.982171i	$0.560197\pi$
$440$	1.35872	0.0647746
$441$	16.5707	0.789080
$442$	0.549603	0.0261420
$443$	21.2184	1.00812	0.504058	−	0.863670i	$-0.331840\pi$
$443$	21.2184	1.00812	0.504058	+	0.863670i	$0.331840\pi$
$444$	3.08532	0.146423
$445$	−2.48800	−0.117943
$446$	20.7374	0.981943
$447$	8.36806	0.395796
$448$	0.571069	0.0269805
$449$	14.0109	0.661213	0.330607	−	0.943769i	$-0.392747\pi$
$449$	14.0109	0.661213	0.330607	+	0.943769i	$0.392747\pi$
$450$	−32.8201	−1.54715
$451$	−0.226890	−0.0106838
$452$	−24.0481	−1.13113
$453$	9.27300	0.435684
$454$	52.0303	2.44190
$455$	0.0297404	0.00139425
$456$	−26.4135	−1.23693
$457$	−26.6265	−1.24554	−0.622769	−	0.782406i	$-0.713992\pi$
$457$	−26.6265	−1.24554	−0.622769	+	0.782406i	$0.713992\pi$
$458$	19.5757	0.914712
$459$	4.46037	0.208192
$460$	−8.52293	−0.397384
$461$	−2.78751	−0.129827	−0.0649136	−	0.997891i	$-0.520677\pi$
$461$	−2.78751	−0.129827	−0.0649136	+	0.997891i	$0.520677\pi$
$462$	1.27868	0.0594895
$463$	−20.0996	−0.934109	−0.467055	−	0.884228i	$-0.654685\pi$
$463$	−20.0996	−0.934109	−0.467055	+	0.884228i	$0.654685\pi$
$464$	0	0
$465$	−0.214485	−0.00994650
$466$	−64.8746	−3.00526
$467$	29.9057	1.38387	0.691935	−	0.721960i	$-0.256759\pi$
$467$	29.9057	1.38387	0.691935	+	0.721960i	$0.256759\pi$
$468$	−1.98044	−0.0915457
$469$	5.00788	0.231242
$470$	2.63770	0.121668
$471$	10.7412	0.494928
$472$	69.0153	3.17669
$473$	−6.11646	−0.281235
$474$	2.31316	0.106247
$475$	−33.4111	−1.53301
$476$	4.54583	0.208358
$477$	14.0779	0.644584
$478$	−52.7360	−2.41209
$479$	−22.1133	−1.01038	−0.505191	−	0.863007i	$-0.668578\pi$
$479$	−22.1133	−1.01038	−0.505191	+	0.863007i	$0.668578\pi$
$480$	0.708465	0.0323369
$481$	0.188118	0.00857746
$482$	−35.1702	−1.60196
$483$	−4.42319	−0.201262
$484$	4.45893	0.202679
$485$	0.425816	0.0193353
$486$	−35.7373	−1.62108
$487$	−13.1785	−0.597173	−0.298586	−	0.954383i	$-0.596515\pi$
$487$	−13.1785	−0.597173	−0.298586	+	0.954383i	$0.596515\pi$
$488$	1.61501	0.0731081
$489$	6.78821	0.306973
$490$	−3.51164	−0.158640
$491$	26.1470	1.18000	0.589999	−	0.807404i	$-0.299128\pi$
$491$	26.1470	1.18000	0.589999	+	0.807404i	$0.299128\pi$
$492$	−0.633868	−0.0285770
$493$	0	0
$494$	−2.92040	−0.131395
$495$	0.566915	0.0254809
$496$	10.9651	0.492349
$497$	8.54050	0.383094
$498$	14.9108	0.668167
$499$	−18.6290	−0.833950	−0.416975	−	0.908918i	$-0.636910\pi$
$499$	−18.6290	−0.833950	−0.416975	+	0.908918i	$0.636910\pi$
$500$	9.64887	0.431511
$501$	11.5646	0.516670
$502$	69.8162	3.11605
$503$	−14.6267	−0.652173	−0.326087	−	0.945340i	$-0.605730\pi$
$503$	−14.6267	−0.652173	−0.326087	+	0.945340i	$0.605730\pi$
$504$	−13.0849	−0.582848
$505$	−2.00686	−0.0893043
$506$	−22.3427	−0.993252
$507$	−8.12691	−0.360929
$508$	71.3856	3.16722
$509$	−13.8343	−0.613196	−0.306598	−	0.951839i	$-0.599191\pi$
$509$	−13.8343	−0.613196	−0.306598	+	0.951839i	$0.599191\pi$
$510$	−0.439531	−0.0194628
$511$	4.88520	0.216109
$512$	50.8234	2.24610
$513$	−23.7008	−1.04642
$514$	49.1605	2.16838
$515$	−2.07246	−0.0913235
$516$	−17.0877	−0.752244
$517$	4.77355	0.209941
$518$	2.25385	0.0990285
$519$	7.10597	0.311917
$520$	0.231444	0.0101495
$521$	28.4790	1.24769	0.623844	−	0.781549i	$-0.285570\pi$
$521$	28.4790	1.24769	0.623844	+	0.781549i	$0.285570\pi$
$522$	0	0
$523$	−9.30812	−0.407016	−0.203508	−	0.979073i	$-0.565234\pi$
$523$	−9.30812	−0.407016	−0.203508	+	0.979073i	$0.565234\pi$
$524$	0.722752	0.0315736
$525$	2.49187	0.108754
$526$	−19.1401	−0.834548
$527$	−1.99891	−0.0870741
$528$	4.36341	0.189893
$529$	54.2874	2.36032
$530$	−2.98338	−0.129590
$531$	28.7960	1.24964
$532$	−24.1549	−1.04725
$533$	−0.0386483	−0.00167404
$534$	−18.2213	−0.788514
$535$	−0.267983	−0.0115859
$536$	38.9720	1.68333
$537$	2.05499	0.0886794
$538$	73.0697	3.15026
$539$	−6.35515	−0.273736
$540$	3.40606	0.146573
$541$	−43.8460	−1.88508	−0.942542	−	0.334087i	$-0.891572\pi$
$541$	−43.8460	−1.88508	−0.942542	+	0.334087i	$0.891572\pi$
$542$	25.2734	1.08559
$543$	−11.8228	−0.507366
$544$	6.60262	0.283085
$545$	0.407862	0.0174709
$546$	0.217810	0.00932139
$547$	−24.4609	−1.04587	−0.522937	−	0.852371i	$-0.675164\pi$
$547$	−24.4609	−1.04587	−0.522937	+	0.852371i	$0.675164\pi$
$548$	34.2842	1.46455
$549$	0.673848	0.0287591
$550$	12.5871	0.536715
$551$	0	0
$552$	−34.4219	−1.46509
$553$	1.16655	0.0496066
$554$	−34.7271	−1.47541
$555$	−0.150443	−0.00638595
$556$	−99.8124	−4.23299
$557$	−28.1340	−1.19208	−0.596039	−	0.802956i	$-0.703259\pi$
$557$	−28.1340	−1.19208	−0.596039	+	0.802956i	$0.703259\pi$
$558$	10.4336	0.441691
$559$	−1.04187	−0.0440666
$560$	1.21592	0.0513820
$561$	−0.795438	−0.0335834
$562$	−55.6035	−2.34549
$563$	−41.1929	−1.73607	−0.868037	−	0.496500i	$-0.834618\pi$
$563$	−41.1929	−1.73607	−0.868037	+	0.496500i	$0.834618\pi$
$564$	13.3360	0.561547
$565$	1.17261	0.0493320
$566$	70.8957	2.97997
$567$	−4.51386	−0.189564
$568$	66.4634	2.78874
$569$	21.5392	0.902971	0.451486	−	0.892278i	$-0.350894\pi$
$569$	21.5392	0.902971	0.451486	+	0.892278i	$0.350894\pi$
$570$	2.33551	0.0978239
$571$	−43.5574	−1.82282	−0.911410	−	0.411499i	$-0.865005\pi$
$571$	−43.5574	−1.82282	−0.911410	+	0.411499i	$0.865005\pi$
$572$	0.759533	0.0317577
$573$	14.0982	0.588962
$574$	−0.463046	−0.0193272
$575$	−43.5410	−1.81579
$576$	1.85428	0.0772615
$577$	16.7791	0.698522	0.349261	−	0.937025i	$-0.386433\pi$
$577$	16.7791	0.698522	0.349261	+	0.937025i	$0.386433\pi$
$578$	39.1083	1.62669
$579$	−2.70767	−0.112527
$580$	0	0
$581$	7.51962	0.311966
$582$	3.11854	0.129268
$583$	−5.39913	−0.223609
$584$	38.0173	1.57317
$585$	0.0965680	0.00399259
$586$	−81.7012	−3.37504
$587$	−22.1731	−0.915183	−0.457591	−	0.889163i	$-0.651288\pi$
$587$	−22.1731	−0.915183	−0.457591	+	0.889163i	$0.651288\pi$
$588$	−17.7545	−0.732185
$589$	10.6215	0.437652
$590$	−6.10241	−0.251232
$591$	−5.79936	−0.238554
$592$	7.69112	0.316103
$593$	−25.8769	−1.06263	−0.531317	−	0.847173i	$-0.678303\pi$
$593$	−25.8769	−1.06263	−0.531317	+	0.847173i	$0.678303\pi$
$594$	8.92889	0.366357
$595$	−0.221659	−0.00908714
$596$	59.5530	2.43938
$597$	2.13606	0.0874229
$598$	−3.80584	−0.155632
$599$	−17.0480	−0.696562	−0.348281	−	0.937390i	$-0.613235\pi$
$599$	−17.0480	−0.696562	−0.348281	+	0.937390i	$0.613235\pi$
$600$	19.3921	0.791678
$601$	−10.4352	−0.425661	−0.212830	−	0.977089i	$-0.568268\pi$
$601$	−10.4352	−0.425661	−0.212830	+	0.977089i	$0.568268\pi$
$602$	−12.4827	−0.508757
$603$	16.2607	0.662187
$604$	65.9932	2.68522
$605$	−0.217422	−0.00883946
$606$	−14.6976	−0.597051
$607$	−44.6367	−1.81175	−0.905874	−	0.423548i	$-0.860784\pi$
$607$	−44.6367	−1.81175	−0.905874	+	0.423548i	$0.860784\pi$
$608$	−35.0840	−1.42284
$609$	0	0
$610$	−0.142801	−0.00578185
$611$	0.813125	0.0328955
$612$	14.7604	0.596655
$613$	28.1092	1.13532	0.567660	−	0.823263i	$-0.307849\pi$
$613$	28.1092	1.13532	0.567660	+	0.823263i	$0.307849\pi$
$614$	41.1143	1.65924
$615$	0.0309080	0.00124633
$616$	5.01829	0.202193
$617$	−21.9146	−0.882247	−0.441123	−	0.897446i	$-0.645420\pi$
$617$	−21.9146	−0.882247	−0.441123	+	0.897446i	$0.645420\pi$
$618$	−15.1780	−0.610551
$619$	35.3420	1.42051	0.710257	−	0.703942i	$-0.248579\pi$
$619$	35.3420	1.42051	0.710257	+	0.703942i	$0.248579\pi$
$620$	−1.52642	−0.0613027
$621$	−30.8867	−1.23944
$622$	69.2010	2.77471
$623$	−9.18916	−0.368156
$624$	0.743260	0.0297542
$625$	24.2932	0.971726
$626$	−23.4058	−0.935482
$627$	4.22667	0.168797
$628$	76.4419	3.05036
$629$	−1.40207	−0.0559042
$630$	1.15698	0.0460953
$631$	22.4197	0.892515	0.446257	−	0.894905i	$-0.352757\pi$
$631$	22.4197	0.892515	0.446257	+	0.894905i	$0.352757\pi$
$632$	9.07822	0.361112
$633$	−16.1862	−0.643342
$634$	19.1562	0.760790
$635$	−3.48083	−0.138133
$636$	−15.0837	−0.598107
$637$	−1.08253	−0.0428915
$638$	0	0
$639$	27.7312	1.09703
$640$	−2.65445	−0.104926
$641$	13.2714	0.524191	0.262095	−	0.965042i	$-0.415587\pi$
$641$	13.2714	0.524191	0.262095	+	0.965042i	$0.415587\pi$
$642$	−1.96262	−0.0774584
$643$	−2.87817	−0.113504	−0.0567520	−	0.998388i	$-0.518074\pi$
$643$	−2.87817	−0.113504	−0.0567520	+	0.998388i	$0.518074\pi$
$644$	−31.4785	−1.24043
$645$	0.833213	0.0328077
$646$	21.7661	0.856375
$647$	19.2932	0.758494	0.379247	−	0.925295i	$-0.376183\pi$
$647$	19.2932	0.758494	0.379247	+	0.925295i	$0.376183\pi$
$648$	−35.1274	−1.37994
$649$	−11.0438	−0.433506
$650$	2.14408	0.0840976
$651$	−0.792176	−0.0310478
$652$	48.3096	1.89195
$653$	−13.1981	−0.516482	−0.258241	−	0.966081i	$-0.583143\pi$
$653$	−13.1981	−0.516482	−0.258241	+	0.966081i	$0.583143\pi$
$654$	2.98705	0.116803
$655$	−0.0352421	−0.00137702
$656$	−1.58011	−0.0616931
$657$	15.8624	0.618850
$658$	9.74206	0.379785
$659$	11.1998	0.436280	0.218140	−	0.975917i	$-0.430001\pi$
$659$	11.1998	0.436280	0.218140	+	0.975917i	$0.430001\pi$
$660$	−0.607417	−0.0236437
$661$	3.88236	0.151006	0.0755032	−	0.997146i	$-0.475944\pi$
$661$	3.88236	0.151006	0.0755032	+	0.997146i	$0.475944\pi$
$662$	42.1312	1.63748
$663$	−0.135494	−0.00526217
$664$	58.5187	2.27097
$665$	1.17782	0.0456738
$666$	7.31831	0.283579
$667$	0	0
$668$	82.3021	3.18436
$669$	−5.11241	−0.197657
$670$	−3.44595	−0.133129
$671$	−0.258433	−0.00997669
$672$	2.61664	0.100939
$673$	4.21684	0.162547	0.0812737	−	0.996692i	$-0.474101\pi$
$673$	4.21684	0.162547	0.0812737	+	0.996692i	$0.474101\pi$
$674$	29.4542	1.13453
$675$	17.4005	0.669745
$676$	−57.8368	−2.22449
$677$	21.5767	0.829261	0.414631	−	0.909990i	$-0.363911\pi$
$677$	21.5767	0.829261	0.414631	+	0.909990i	$0.363911\pi$
$678$	8.58781	0.329813
$679$	1.57271	0.0603549
$680$	−1.72498	−0.0661500
$681$	−12.8271	−0.491535
$682$	−4.00148	−0.153225
$683$	35.7718	1.36877	0.684384	−	0.729122i	$-0.260071\pi$
$683$	35.7718	1.36877	0.684384	+	0.729122i	$0.260071\pi$
$684$	−78.4317	−2.99891
$685$	−1.67173	−0.0638735
$686$	−27.2557	−1.04063
$687$	−4.82602	−0.184124
$688$	−42.5964	−1.62397
$689$	−0.919686	−0.0350372
$690$	3.04362	0.115869
$691$	−28.5979	−1.08791	−0.543957	−	0.839113i	$-0.683075\pi$
$691$	−28.5979	−1.08791	−0.543957	+	0.839113i	$0.683075\pi$
$692$	50.5710	1.92242
$693$	2.09384	0.0795383
$694$	7.94346	0.301530
$695$	4.86695	0.184614
$696$	0	0
$697$	0.288051	0.0109107
$698$	−69.4748	−2.62966
$699$	15.9936	0.604934
$700$	17.7339	0.670278
$701$	−35.1146	−1.32626	−0.663130	−	0.748504i	$-0.730773\pi$
$701$	−35.1146	−1.32626	−0.663130	+	0.748504i	$0.730773\pi$
$702$	1.52094	0.0574043
$703$	7.45010	0.280986
$704$	−0.711148	−0.0268024
$705$	−0.650276	−0.0244908
$706$	59.7999	2.25060
$707$	−7.41214	−0.278762
$708$	−30.8533	−1.15954
$709$	−47.5462	−1.78563	−0.892817	−	0.450420i	$-0.851274\pi$
$709$	−47.5462	−1.78563	−0.892817	+	0.450420i	$0.851274\pi$
$710$	−5.87677	−0.220551
$711$	3.78781	0.142054
$712$	−71.5113	−2.68000
$713$	13.8419	0.518383
$714$	−1.62336	−0.0607528
$715$	−0.0370355	−0.00138505
$716$	14.6247	0.546552
$717$	13.0011	0.485534
$718$	−47.2880	−1.76477
$719$	−27.9174	−1.04114	−0.520572	−	0.853818i	$-0.674281\pi$
$719$	−27.9174	−1.04114	−0.520572	+	0.853818i	$0.674281\pi$
$720$	3.94813	0.147138
$721$	−7.65441	−0.285065
$722$	−67.3698	−2.50724
$723$	8.67056	0.322461
$724$	−84.1394	−3.12702
$725$	0	0
$726$	−1.59233	−0.0590969
$727$	30.8418	1.14386	0.571930	−	0.820302i	$-0.306195\pi$
$727$	30.8418	1.14386	0.571930	+	0.820302i	$0.306195\pi$
$728$	0.854814	0.0316815
$729$	−8.05285	−0.298254
$730$	−3.36154	−0.124416
$731$	7.76522	0.287207
$732$	−0.721990	−0.0266855
$733$	15.2062	0.561652	0.280826	−	0.959759i	$-0.409392\pi$
$733$	15.2062	0.561652	0.280826	+	0.959759i	$0.409392\pi$
$734$	82.5580	3.04727
$735$	0.865729	0.0319329
$736$	−45.7212	−1.68530
$737$	−6.23627	−0.229716
$738$	−1.50352	−0.0553454
$739$	−1.77513	−0.0652994	−0.0326497	−	0.999467i	$-0.510395\pi$
$739$	−1.77513	−0.0652994	−0.0326497	+	0.999467i	$0.510395\pi$
$740$	−1.07066	−0.0393582
$741$	0.719969	0.0264487
$742$	−11.0188	−0.404512
$743$	2.29756	0.0842894	0.0421447	−	0.999112i	$-0.486581\pi$
$743$	2.29756	0.0842894	0.0421447	+	0.999112i	$0.486581\pi$
$744$	−6.16482	−0.226013
$745$	−2.90386	−0.106389
$746$	−6.95986	−0.254818
$747$	24.4164	0.893349
$748$	−5.66089	−0.206983
$749$	−0.989765	−0.0361652
$750$	−3.44571	−0.125819
$751$	−43.1865	−1.57590	−0.787949	−	0.615741i	$-0.788857\pi$
$751$	−43.1865	−1.57590	−0.787949	+	0.615741i	$0.788857\pi$
$752$	33.2441	1.21229
$753$	−17.2119	−0.627236
$754$	0	0
$755$	−3.21789	−0.117111
$756$	12.5799	0.457526
$757$	−1.13516	−0.0412582	−0.0206291	−	0.999787i	$-0.506567\pi$
$757$	−1.13516	−0.0412582	−0.0206291	+	0.999787i	$0.506567\pi$
$758$	72.7751	2.64331
$759$	5.50816	0.199934
$760$	9.16594	0.332484
$761$	−24.6408	−0.893228	−0.446614	−	0.894727i	$-0.647370\pi$
$761$	−24.6408	−0.893228	−0.446614	+	0.894727i	$0.647370\pi$
$762$	−25.4925	−0.923496
$763$	1.50639	0.0545352
$764$	100.333	3.62992
$765$	−0.719733	−0.0260220
$766$	53.8864	1.94700
$767$	−1.88119	−0.0679259
$768$	−18.5492	−0.669338
$769$	−0.422111	−0.0152217	−0.00761086	−	0.999971i	$-0.502423\pi$
$769$	−0.422111	−0.0152217	−0.00761086	+	0.999971i	$0.502423\pi$
$770$	−0.443724	−0.0159907
$771$	−12.1196	−0.436477
$772$	−19.2697	−0.693531
$773$	−0.245052	−0.00881392	−0.00440696	−	0.999990i	$-0.501403\pi$
$773$	−0.245052	−0.00881392	−0.00440696	+	0.999990i	$0.501403\pi$
$774$	−40.5317	−1.45688
$775$	−7.79803	−0.280114
$776$	12.2390	0.439355
$777$	−0.555645	−0.0199336
$778$	50.6924	1.81741
$779$	−1.53060	−0.0548394
$780$	−0.103467	−0.00370472
$781$	−10.6354	−0.380565
$782$	28.3654	1.01434
$783$	0	0
$784$	−44.2587	−1.58067
$785$	−3.72738	−0.133036
$786$	−0.258102	−0.00920619
$787$	19.8503	0.707586	0.353793	−	0.935324i	$-0.384892\pi$
$787$	19.8503	0.707586	0.353793	+	0.935324i	$0.384892\pi$
$788$	−41.2723	−1.47027
$789$	4.71863	0.167988
$790$	−0.802707	−0.0285590
$791$	4.33090	0.153989
$792$	16.2945	0.579001
$793$	−0.0440213	−0.00156324
$794$	−22.5820	−0.801407
$795$	0.735496	0.0260853
$796$	15.2017	0.538809
$797$	−24.1991	−0.857177	−0.428589	−	0.903500i	$-0.640989\pi$
$797$	−24.1991	−0.857177	−0.428589	+	0.903500i	$0.640989\pi$
$798$	8.62597	0.305356
$799$	−6.06032	−0.214399
$800$	25.7577	0.910672
$801$	−29.8374	−1.05425
$802$	53.9496	1.90503
$803$	−6.08350	−0.214682
$804$	−17.4224	−0.614441
$805$	1.53492	0.0540989
$806$	−0.681611	−0.0240087
$807$	−18.0140	−0.634121
$808$	−57.6823	−2.02925
$809$	−38.7298	−1.36167	−0.680833	−	0.732439i	$-0.738382\pi$
$809$	−38.7298	−1.36167	−0.680833	+	0.732439i	$0.738382\pi$
$810$	3.10601	0.109134
$811$	23.2724	0.817206	0.408603	−	0.912712i	$-0.366016\pi$
$811$	23.2724	0.817206	0.408603	+	0.912712i	$0.366016\pi$
$812$	0	0
$813$	−6.23068	−0.218520
$814$	−2.80670	−0.0983749
$815$	−2.35562	−0.0825139
$816$	−5.53961	−0.193925
$817$	−41.2616	−1.44356
$818$	−45.9474	−1.60651
$819$	0.356663	0.0124628
$820$	0.219963	0.00768144
$821$	−20.0059	−0.698209	−0.349104	−	0.937084i	$-0.613514\pi$
$821$	−20.0059	−0.698209	−0.349104	+	0.937084i	$0.613514\pi$
$822$	−12.2432	−0.427032
$823$	−5.58365	−0.194634	−0.0973168	−	0.995253i	$-0.531026\pi$
$823$	−5.58365	−0.194634	−0.0973168	+	0.995253i	$0.531026\pi$
$824$	−59.5676	−2.07514
$825$	−3.10311	−0.108036
$826$	−22.5386	−0.784218
$827$	6.39041	0.222216	0.111108	−	0.993808i	$-0.464560\pi$
$827$	6.39041	0.222216	0.111108	+	0.993808i	$0.464560\pi$
$828$	−102.212	−3.55210
$829$	−6.54807	−0.227424	−0.113712	−	0.993514i	$-0.536274\pi$
$829$	−6.54807	−0.227424	−0.113712	+	0.993514i	$0.536274\pi$
$830$	−5.17429	−0.179602
$831$	8.56133	0.296989
$832$	−0.121137	−0.00419966
$833$	8.06825	0.279548
$834$	35.6440	1.23425
$835$	−4.01313	−0.138880
$836$	30.0800	1.04034
$837$	−5.53169	−0.191203
$838$	4.47228	0.154492
$839$	−29.9216	−1.03301	−0.516504	−	0.856285i	$-0.672767\pi$
$839$	−29.9216	−1.03301	−0.516504	+	0.856285i	$0.672767\pi$
$840$	−0.683616	−0.0235870
$841$	0	0
$842$	63.3883	2.18450
$843$	13.7080	0.472129
$844$	−115.192	−3.96507
$845$	2.82018	0.0970170
$846$	31.6327	1.08756
$847$	−0.803024	−0.0275922
$848$	−37.6008	−1.29122
$849$	−17.4780	−0.599844
$850$	−15.9801	−0.548112
$851$	9.70891	0.332817
$852$	−29.7125	−1.01793
$853$	27.0469	0.926068	0.463034	−	0.886341i	$-0.346761\pi$
$853$	27.0469	0.926068	0.463034	+	0.886341i	$0.346761\pi$
$854$	−0.527420	−0.0180479
$855$	3.82441	0.130792
$856$	−7.70248	−0.263265
$857$	−27.1427	−0.927178	−0.463589	−	0.886050i	$-0.653439\pi$
$857$	−27.1427	−0.927178	−0.463589	+	0.886050i	$0.653439\pi$
$858$	−0.271237	−0.00925986
$859$	−1.18721	−0.0405072	−0.0202536	−	0.999795i	$-0.506447\pi$
$859$	−1.18721	−0.0405072	−0.0202536	+	0.999795i	$0.506447\pi$
$860$	5.92972	0.202202
$861$	0.114155	0.00389040
$862$	−36.4498	−1.24149
$863$	48.3617	1.64625	0.823125	−	0.567860i	$-0.192228\pi$
$863$	48.3617	1.64625	0.823125	+	0.567860i	$0.192228\pi$
$864$	18.2717	0.621617
$865$	−2.46589	−0.0838429
$866$	33.3512	1.13332
$867$	−9.64141	−0.327440
$868$	−5.63768	−0.191355
$869$	−1.45269	−0.0492792
$870$	0	0
$871$	−1.06228	−0.0359941
$872$	11.7230	0.396990
$873$	5.10662	0.172833
$874$	−150.724	−5.09830
$875$	−1.73770	−0.0587449
$876$	−16.9956	−0.574229
$877$	21.2731	0.718343	0.359172	−	0.933272i	$-0.383059\pi$
$877$	21.2731	0.718343	0.359172	+	0.933272i	$0.383059\pi$
$878$	20.0206	0.675662
$879$	20.1419	0.679369
$880$	−1.51418	−0.0510429
$881$	12.5029	0.421232	0.210616	−	0.977569i	$-0.432453\pi$
$881$	12.5029	0.421232	0.210616	+	0.977569i	$0.432453\pi$
$882$	−42.1135	−1.41803
$883$	16.5777	0.557883	0.278941	−	0.960308i	$-0.410016\pi$
$883$	16.5777	0.557883	0.278941	+	0.960308i	$0.410016\pi$
$884$	−0.964273	−0.0324320
$885$	1.50444	0.0505711
$886$	−53.9253	−1.81166
$887$	52.8421	1.77427	0.887133	−	0.461514i	$-0.152694\pi$
$887$	52.8421	1.77427	0.887133	+	0.461514i	$0.152694\pi$
$888$	−4.32410	−0.145107
$889$	−12.8561	−0.431179
$890$	6.32311	0.211951
$891$	5.62107	0.188313
$892$	−36.3835	−1.21821
$893$	32.2024	1.07761
$894$	−21.2670	−0.711273
$895$	−0.713117	−0.0238369
$896$	−9.80394	−0.327526
$897$	0.938258	0.0313275
$898$	−35.6078	−1.18825
$899$	0	0
$900$	57.5824	1.91941
$901$	6.85453	0.228358
$902$	0.576628	0.0191996
$903$	3.07738	0.102409
$904$	33.7037	1.12097
$905$	4.10272	0.136379
$906$	−23.5668	−0.782955
$907$	−46.3966	−1.54057	−0.770287	−	0.637698i	$-0.779887\pi$
$907$	−46.3966	−1.54057	−0.770287	+	0.637698i	$0.779887\pi$
$908$	−91.2866	−3.02945
$909$	−24.0674	−0.798265
$910$	−0.0755836	−0.00250557
$911$	−23.0416	−0.763401	−0.381700	−	0.924286i	$-0.624661\pi$
$911$	−23.0416	−0.763401	−0.381700	+	0.924286i	$0.624661\pi$
$912$	29.4355	0.974708
$913$	−9.36412	−0.309907
$914$	67.6699	2.23832
$915$	0.0352049	0.00116384
$916$	−34.3453	−1.13480
$917$	−0.130163	−0.00429835
$918$	−11.3358	−0.374136
$919$	18.2562	0.602216	0.301108	−	0.953590i	$-0.402644\pi$
$919$	18.2562	0.602216	0.301108	+	0.953590i	$0.402644\pi$
$920$	11.9450	0.393814
$921$	−10.1360	−0.333992
$922$	7.08429	0.233309
$923$	−1.81163	−0.0596306
$924$	−2.24343	−0.0738034
$925$	−5.46966	−0.179841
$926$	51.0821	1.67866
$927$	−24.8541	−0.816314
$928$	0	0
$929$	−15.9750	−0.524123	−0.262062	−	0.965051i	$-0.584402\pi$
$929$	−15.9750	−0.524123	−0.262062	+	0.965051i	$0.584402\pi$
$930$	0.545101	0.0178746
$931$	−42.8718	−1.40507
$932$	113.822	3.72835
$933$	−17.0602	−0.558526
$934$	−76.0036	−2.48691
$935$	0.276030	0.00902716
$936$	2.77560	0.0907234
$937$	−11.4427	−0.373817	−0.186908	−	0.982377i	$-0.559847\pi$
$937$	−11.4427	−0.373817	−0.186908	+	0.982377i	$0.559847\pi$
$938$	−12.7272	−0.415559
$939$	5.77025	0.188305
$940$	−4.62782	−0.150943
$941$	−42.3349	−1.38008	−0.690039	−	0.723772i	$-0.742407\pi$
$941$	−42.3349	−1.38008	−0.690039	+	0.723772i	$0.742407\pi$
$942$	−27.2982	−0.889422
$943$	−1.99466	−0.0649552
$944$	−76.9115	−2.50325
$945$	−0.613408	−0.0199542
$946$	15.5446	0.505400
$947$	−16.6447	−0.540882	−0.270441	−	0.962737i	$-0.587169\pi$
$947$	−16.6447	−0.540882	−0.270441	+	0.962737i	$0.587169\pi$
$948$	−4.05842	−0.131811
$949$	−1.03626	−0.0336385
$950$	84.9124	2.75492
$951$	−4.72260	−0.153141
$952$	−6.37103	−0.206486
$953$	−32.1357	−1.04098	−0.520489	−	0.853869i	$-0.674250\pi$
$953$	−32.1357	−1.04098	−0.520489	+	0.853869i	$0.674250\pi$
$954$	−35.7782	−1.15836
$955$	−4.89233	−0.158312
$956$	92.5247	2.99246
$957$	0	0
$958$	56.1997	1.81573
$959$	−6.17435	−0.199380
$960$	0.0968760	0.00312666
$961$	−28.5210	−0.920031
$962$	−0.478092	−0.0154143
$963$	−3.21379	−0.103563
$964$	61.7057	1.98741
$965$	0.939608	0.0302470
$966$	11.2413	0.361682
$967$	−58.5099	−1.88155	−0.940776	−	0.339028i	$-0.889902\pi$
$967$	−58.5099	−1.88155	−0.940776	+	0.339028i	$0.889902\pi$
$968$	−6.24924	−0.200858
$969$	−5.36602	−0.172381
$970$	−1.08219	−0.0347469
$971$	−28.4321	−0.912431	−0.456216	−	0.889869i	$-0.650795\pi$
$971$	−28.4321	−0.912431	−0.456216	+	0.889869i	$0.650795\pi$
$972$	62.7007	2.01112
$973$	17.9756	0.576270
$974$	33.4923	1.07316
$975$	−0.528582	−0.0169282
$976$	−1.79979	−0.0576097
$977$	−8.76606	−0.280451	−0.140226	−	0.990120i	$-0.544783\pi$
$977$	−8.76606	−0.280451	−0.140226	+	0.990120i	$0.544783\pi$
$978$	−17.2518	−0.551653
$979$	11.4432	0.365726
$980$	6.16113	0.196810
$981$	4.89130	0.156167
$982$	−66.4511	−2.12054
$983$	37.7626	1.20444	0.602219	−	0.798331i	$-0.294283\pi$
$983$	37.7626	1.20444	0.602219	+	0.798331i	$0.294283\pi$
$984$	0.888373	0.0283203
$985$	2.01248	0.0641229
$986$	0	0
$987$	−2.40172	−0.0764477
$988$	5.12381	0.163010
$989$	−53.7718	−1.70984
$990$	−1.44078	−0.0457911
$991$	−39.9176	−1.26803	−0.634013	−	0.773323i	$-0.718593\pi$
$991$	−39.9176	−1.26803	−0.634013	+	0.773323i	$0.718593\pi$
$992$	−8.18848	−0.259985
$993$	−10.3867	−0.329611
$994$	−21.7052	−0.688447
$995$	−0.741248	−0.0234991
$996$	−26.1608	−0.828936
$997$	55.1885	1.74784	0.873919	−	0.486071i	$-0.161570\pi$
$997$	55.1885	1.74784	0.873919	+	0.486071i	$0.161570\pi$
$998$	47.3447	1.49867
$999$	−3.88001	−0.122758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.ba.1.2	✓	40
29.28	even	2		9251.2.a.bb.1.39	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.ba.1.2	✓	40	1.1	even	1	trivial
9251.2.a.bb.1.39	yes	40	29.28	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54144 q^{2} +0.626545 q^{3} +4.45893 q^{4} -0.217422 q^{5} -1.59233 q^{6} -0.803024 q^{7} -6.24924 q^{8} -2.60744 q^{9} +O(q^{10})\)	\(q-2.54144 q^{2} +0.626545 q^{3} +4.45893 q^{4} -0.217422 q^{5} -1.59233 q^{6} -0.803024 q^{7} -6.24924 q^{8} -2.60744 q^{9} +0.552566 q^{10} +1.00000 q^{11} +2.79373 q^{12} +0.170339 q^{13} +2.04084 q^{14} -0.136225 q^{15} +6.96423 q^{16} -1.26956 q^{17} +6.62666 q^{18} +6.74600 q^{19} -0.969470 q^{20} -0.503131 q^{21} -2.54144 q^{22} +8.79133 q^{23} -3.91544 q^{24} -4.95273 q^{25} -0.432908 q^{26} -3.51332 q^{27} -3.58063 q^{28} +0.346207 q^{30} +1.57449 q^{31} -5.20071 q^{32} +0.626545 q^{33} +3.22652 q^{34} +0.174595 q^{35} -11.6264 q^{36} +1.10437 q^{37} -17.1446 q^{38} +0.106725 q^{39} +1.35872 q^{40} -0.226890 q^{41} +1.27868 q^{42} -6.11646 q^{43} +4.45893 q^{44} +0.566915 q^{45} -22.3427 q^{46} +4.77355 q^{47} +4.36341 q^{48} -6.35515 q^{49} +12.5871 q^{50} -0.795438 q^{51} +0.759533 q^{52} -5.39913 q^{53} +8.92889 q^{54} -0.217422 q^{55} +5.01829 q^{56} +4.22667 q^{57} -11.0438 q^{59} -0.607417 q^{60} -0.258433 q^{61} -4.00148 q^{62} +2.09384 q^{63} -0.711148 q^{64} -0.0370355 q^{65} -1.59233 q^{66} -6.23627 q^{67} -5.66089 q^{68} +5.50816 q^{69} -0.443724 q^{70} -10.6354 q^{71} +16.2945 q^{72} -6.08350 q^{73} -2.80670 q^{74} -3.10311 q^{75} +30.0800 q^{76} -0.803024 q^{77} -0.271237 q^{78} -1.45269 q^{79} -1.51418 q^{80} +5.62107 q^{81} +0.576628 q^{82} -9.36412 q^{83} -2.24343 q^{84} +0.276030 q^{85} +15.5446 q^{86} -6.24924 q^{88} +11.4432 q^{89} -1.44078 q^{90} -0.136787 q^{91} +39.2000 q^{92} +0.986491 q^{93} -12.1317 q^{94} -1.46673 q^{95} -3.25848 q^{96} -1.95848 q^{97} +16.1513 q^{98} -2.60744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * q^99

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