LMFDB - Embedded newform 9251.2.a.ba.1.8

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			1.8
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)

$f(q)$	$=$	$q-1.62004 q^{2} -2.62880 q^{3} +0.624541 q^{4} -2.73623 q^{5} +4.25878 q^{6} +0.785723 q^{7} +2.22830 q^{8} +3.91061 q^{9} +O(q^{10})$	\(q-1.62004 q^{2} -2.62880 q^{3} +0.624541 q^{4} -2.73623 q^{5} +4.25878 q^{6} +0.785723 q^{7} +2.22830 q^{8} +3.91061 q^{9} +4.43281 q^{10} +1.00000 q^{11} -1.64180 q^{12} +2.10631 q^{13} -1.27291 q^{14} +7.19302 q^{15} -4.85903 q^{16} +1.06034 q^{17} -6.33536 q^{18} +6.41611 q^{19} -1.70889 q^{20} -2.06551 q^{21} -1.62004 q^{22} +7.44529 q^{23} -5.85777 q^{24} +2.48697 q^{25} -3.41231 q^{26} -2.39382 q^{27} +0.490716 q^{28} -11.6530 q^{30} -5.81019 q^{31} +3.41524 q^{32} -2.62880 q^{33} -1.71781 q^{34} -2.14992 q^{35} +2.44234 q^{36} +3.23706 q^{37} -10.3944 q^{38} -5.53708 q^{39} -6.09715 q^{40} +9.99376 q^{41} +3.34622 q^{42} -9.22083 q^{43} +0.624541 q^{44} -10.7003 q^{45} -12.0617 q^{46} +0.760121 q^{47} +12.7734 q^{48} -6.38264 q^{49} -4.02899 q^{50} -2.78744 q^{51} +1.31548 q^{52} -12.4322 q^{53} +3.87809 q^{54} -2.73623 q^{55} +1.75083 q^{56} -16.8667 q^{57} -7.43058 q^{59} +4.49234 q^{60} +2.54450 q^{61} +9.41276 q^{62} +3.07266 q^{63} +4.18523 q^{64} -5.76335 q^{65} +4.25878 q^{66} -8.12863 q^{67} +0.662229 q^{68} -19.5722 q^{69} +3.48297 q^{70} +5.44049 q^{71} +8.71403 q^{72} +13.1146 q^{73} -5.24418 q^{74} -6.53774 q^{75} +4.00713 q^{76} +0.785723 q^{77} +8.97031 q^{78} +5.52190 q^{79} +13.2954 q^{80} -5.43895 q^{81} -16.1903 q^{82} -12.8268 q^{83} -1.29000 q^{84} -2.90135 q^{85} +14.9381 q^{86} +2.22830 q^{88} +2.55628 q^{89} +17.3350 q^{90} +1.65498 q^{91} +4.64989 q^{92} +15.2738 q^{93} -1.23143 q^{94} -17.5560 q^{95} -8.97798 q^{96} -1.11533 q^{97} +10.3402 q^{98} +3.91061 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.62004	−1.14554	−0.572772	−	0.819715i	$-0.694132\pi$
$2$	−1.62004	−1.14554	−0.572772	+	0.819715i	$0.694132\pi$
$3$	−2.62880	−1.51774	−0.758870	−	0.651242i	$-0.774248\pi$
$3$	−2.62880	−1.51774	−0.758870	+	0.651242i	$0.774248\pi$
$4$	0.624541	0.312271
$5$	−2.73623	−1.22368	−0.611840	−	0.790982i	$-0.709570\pi$
$5$	−2.73623	−1.22368	−0.611840	+	0.790982i	$0.709570\pi$
$6$	4.25878	1.73864
$7$	0.785723	0.296975	0.148488	−	0.988914i	$-0.452559\pi$
$7$	0.785723	0.296975	0.148488	+	0.988914i	$0.452559\pi$
$8$	2.22830	0.787824
$9$	3.91061	1.30354
$10$	4.43281	1.40178
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.64180	−0.473946
$13$	2.10631	0.584185	0.292093	−	0.956390i	$-0.405648\pi$
$13$	2.10631	0.584185	0.292093	+	0.956390i	$0.405648\pi$
$14$	−1.27291	−0.340198
$15$	7.19302	1.85723
$16$	−4.85903	−1.21476
$17$	1.06034	0.257171	0.128586	−	0.991698i	$-0.458956\pi$
$17$	1.06034	0.257171	0.128586	+	0.991698i	$0.458956\pi$
$18$	−6.33536	−1.49326
$19$	6.41611	1.47196	0.735979	−	0.677005i	$-0.236722\pi$
$19$	6.41611	1.47196	0.735979	+	0.677005i	$0.236722\pi$
$20$	−1.70889	−0.382119
$21$	−2.06551	−0.450732
$22$	−1.62004	−0.345394
$23$	7.44529	1.55245	0.776225	−	0.630456i	$-0.217132\pi$
$23$	7.44529	1.55245	0.776225	+	0.630456i	$0.217132\pi$
$24$	−5.85777	−1.19571
$25$	2.48697	0.497393
$26$	−3.41231	−0.669210
$27$	−2.39382	−0.460690
$28$	0.490716	0.0927367
$29$	0	0
$29$	0	0
$30$	−11.6530	−2.12754
$31$	−5.81019	−1.04354	−0.521770	−	0.853086i	$-0.674728\pi$
$31$	−5.81019	−1.04354	−0.521770	+	0.853086i	$0.674728\pi$
$32$	3.41524	0.603734
$33$	−2.62880	−0.457616
$34$	−1.71781	−0.294601
$35$	−2.14992	−0.363403
$36$	2.44234	0.407056
$37$	3.23706	0.532169	0.266085	−	0.963950i	$-0.414270\pi$
$37$	3.23706	0.532169	0.266085	+	0.963950i	$0.414270\pi$
$38$	−10.3944	−1.68619
$39$	−5.53708	−0.886642
$40$	−6.09715	−0.964045
$41$	9.99376	1.56076	0.780382	−	0.625304i	$-0.215025\pi$
$41$	9.99376	1.56076	0.780382	+	0.625304i	$0.215025\pi$
$42$	3.34622	0.516333
$43$	−9.22083	−1.40616	−0.703081	−	0.711109i	$-0.748193\pi$
$43$	−9.22083	−1.40616	−0.703081	+	0.711109i	$0.748193\pi$
$44$	0.624541	0.0941531
$45$	−10.7003	−1.59511
$46$	−12.0617	−1.77840
$47$	0.760121	0.110875	0.0554376	−	0.998462i	$-0.482345\pi$
$47$	0.760121	0.110875	0.0554376	+	0.998462i	$0.482345\pi$
$48$	12.7734	1.84369
$49$	−6.38264	−0.911806
$50$	−4.02899	−0.569786
$51$	−2.78744	−0.390320
$52$	1.31548	0.182424
$53$	−12.4322	−1.70769	−0.853845	−	0.520527i	$-0.825736\pi$
$53$	−12.4322	−1.70769	−0.853845	+	0.520527i	$0.825736\pi$
$54$	3.87809	0.527741
$55$	−2.73623	−0.368953
$56$	1.75083	0.233964
$57$	−16.8667	−2.23405
$58$	0	0
$59$	−7.43058	−0.967379	−0.483690	−	0.875240i	$-0.660704\pi$
$59$	−7.43058	−0.967379	−0.483690	+	0.875240i	$0.660704\pi$
$60$	4.49234	0.579958
$61$	2.54450	0.325790	0.162895	−	0.986643i	$-0.447917\pi$
$61$	2.54450	0.325790	0.162895	+	0.986643i	$0.447917\pi$
$62$	9.41276	1.19542
$63$	3.07266	0.387118
$64$	4.18523	0.523154
$65$	−5.76335	−0.714856
$66$	4.25878	0.524219
$67$	−8.12863	−0.993070	−0.496535	−	0.868017i	$-0.665395\pi$
$67$	−8.12863	−0.993070	−0.496535	+	0.868017i	$0.665395\pi$
$68$	0.662229	0.0803071
$69$	−19.5722	−2.35622
$70$	3.48297	0.416294
$71$	5.44049	0.645667	0.322834	−	0.946456i	$-0.395365\pi$
$71$	5.44049	0.645667	0.322834	+	0.946456i	$0.395365\pi$
$72$	8.71403	1.02696
$73$	13.1146	1.53495	0.767474	−	0.641080i	$-0.221513\pi$
$73$	13.1146	1.53495	0.767474	+	0.641080i	$0.221513\pi$
$74$	−5.24418	−0.609623
$75$	−6.53774	−0.754914
$76$	4.00713	0.459649
$77$	0.785723	0.0895415
$78$	8.97031	1.01569
$79$	5.52190	0.621262	0.310631	−	0.950531i	$-0.399460\pi$
$79$	5.52190	0.621262	0.310631	+	0.950531i	$0.399460\pi$
$80$	13.2954	1.48647
$81$	−5.43895	−0.604328
$82$	−16.1903	−1.78792
$83$	−12.8268	−1.40792	−0.703962	−	0.710238i	$-0.748588\pi$
$83$	−12.8268	−1.40792	−0.703962	+	0.710238i	$0.748588\pi$
$84$	−1.29000	−0.140750
$85$	−2.90135	−0.314696
$86$	14.9381	1.61082
$87$	0	0
$88$	2.22830	0.237538
$89$	2.55628	0.270965	0.135482	−	0.990780i	$-0.456742\pi$
$89$	2.55628	0.270965	0.135482	+	0.990780i	$0.456742\pi$
$90$	17.3350	1.82727
$91$	1.65498	0.173489
$92$	4.64989	0.484784
$93$	15.2738	1.58382
$94$	−1.23143	−0.127012
$95$	−17.5560	−1.80120
$96$	−8.97798	−0.916312
$97$	−1.11533	−0.113245	−0.0566224	−	0.998396i	$-0.518033\pi$
$97$	−1.11533	−0.113245	−0.0566224	+	0.998396i	$0.518033\pi$
$98$	10.3402	1.04451
$99$	3.91061	0.393031
$100$	1.55321	0.155321
$101$	−15.6207	−1.55431	−0.777157	−	0.629306i	$-0.783339\pi$
$101$	−15.6207	−1.55431	−0.777157	+	0.629306i	$0.783339\pi$
$102$	4.51577	0.447128
$103$	3.69454	0.364034	0.182017	−	0.983295i	$-0.441737\pi$
$103$	3.69454	0.364034	0.182017	+	0.983295i	$0.441737\pi$
$104$	4.69350	0.460235
$105$	5.65172	0.551551
$106$	20.1407	1.95623
$107$	−3.36445	−0.325253	−0.162627	−	0.986688i	$-0.551997\pi$
$107$	−3.36445	−0.325253	−0.162627	+	0.986688i	$0.551997\pi$
$108$	−1.49504	−0.143860
$109$	−1.78303	−0.170783	−0.0853915	−	0.996347i	$-0.527214\pi$
$109$	−1.78303	−0.170783	−0.0853915	+	0.996347i	$0.527214\pi$
$110$	4.43281	0.422652
$111$	−8.50959	−0.807695
$112$	−3.81785	−0.360753
$113$	7.99763	0.752353	0.376177	−	0.926548i	$-0.377239\pi$
$113$	7.99763	0.752353	0.376177	+	0.926548i	$0.377239\pi$
$114$	27.3248	2.55920
$115$	−20.3720	−1.89970
$116$	0	0
$117$	8.23696	0.761507
$118$	12.0379	1.10818
$119$	0.833138	0.0763736
$120$	16.0282	1.46317
$121$	1.00000	0.0909091
$122$	−4.12221	−0.373207
$123$	−26.2716	−2.36883
$124$	−3.62870	−0.325867
$125$	6.87625	0.615030
$126$	−4.97784	−0.443461
$127$	6.49841	0.576640	0.288320	−	0.957534i	$-0.406903\pi$
$127$	6.49841	0.576640	0.288320	+	0.957534i	$0.406903\pi$
$128$	−13.6107	−1.20303
$129$	24.2397	2.13419
$130$	9.33688	0.818899
$131$	6.92552	0.605085	0.302543	−	0.953136i	$-0.402165\pi$
$131$	6.92552	0.605085	0.302543	+	0.953136i	$0.402165\pi$
$132$	−1.64180	−0.142900
$133$	5.04129	0.437135
$134$	13.1687	1.13761
$135$	6.55004	0.563738
$136$	2.36277	0.202606
$137$	−19.0501	−1.62756	−0.813781	−	0.581172i	$-0.802595\pi$
$137$	−19.0501	−1.62756	−0.813781	+	0.581172i	$0.802595\pi$
$138$	31.7078	2.69915
$139$	2.34169	0.198619	0.0993096	−	0.995057i	$-0.468337\pi$
$139$	2.34169	0.198619	0.0993096	+	0.995057i	$0.468337\pi$
$140$	−1.34271	−0.113480
$141$	−1.99821	−0.168280
$142$	−8.81383	−0.739640
$143$	2.10631	0.176139
$144$	−19.0018	−1.58348
$145$	0	0
$146$	−21.2462	−1.75835
$147$	16.7787	1.38388
$148$	2.02168	0.166181
$149$	−2.46105	−0.201617	−0.100809	−	0.994906i	$-0.532143\pi$
$149$	−2.46105	−0.201617	−0.100809	+	0.994906i	$0.532143\pi$
$150$	10.5914	0.864787
$151$	−10.9481	−0.890942	−0.445471	−	0.895296i	$-0.646964\pi$
$151$	−10.9481	−0.890942	−0.445471	+	0.895296i	$0.646964\pi$
$152$	14.2970	1.15964
$153$	4.14660	0.335232
$154$	−1.27291	−0.102574
$155$	15.8980	1.27696
$156$	−3.45813	−0.276872
$157$	−15.8212	−1.26267	−0.631333	−	0.775512i	$-0.717492\pi$
$157$	−15.8212	−1.26267	−0.631333	+	0.775512i	$0.717492\pi$
$158$	−8.94572	−0.711683
$159$	32.6818	2.59183
$160$	−9.34488	−0.738777
$161$	5.84993	0.461039
$162$	8.81134	0.692285
$163$	6.99057	0.547544	0.273772	−	0.961795i	$-0.411729\pi$
$163$	6.99057	0.547544	0.273772	+	0.961795i	$0.411729\pi$
$164$	6.24152	0.487380
$165$	7.19302	0.559976
$166$	20.7800	1.61284
$167$	−20.0023	−1.54782	−0.773912	−	0.633293i	$-0.781703\pi$
$167$	−20.0023	−1.54782	−0.773912	+	0.633293i	$0.781703\pi$
$168$	−4.60259	−0.355097
$169$	−8.56346	−0.658727
$170$	4.70031	0.360498
$171$	25.0909	1.91875
$172$	−5.75879	−0.439103
$173$	−8.49697	−0.646012	−0.323006	−	0.946397i	$-0.604693\pi$
$173$	−8.49697	−0.646012	−0.323006	+	0.946397i	$0.604693\pi$
$174$	0	0
$175$	1.95407	0.147714
$176$	−4.85903	−0.366263
$177$	19.5335	1.46823
$178$	−4.14128	−0.310402
$179$	9.72799	0.727104	0.363552	−	0.931574i	$-0.381564\pi$
$179$	9.72799	0.727104	0.363552	+	0.931574i	$0.381564\pi$
$180$	−6.68280	−0.498107
$181$	−24.1224	−1.79301	−0.896503	−	0.443038i	$-0.853901\pi$
$181$	−24.1224	−1.79301	−0.896503	+	0.443038i	$0.853901\pi$
$182$	−2.68113	−0.198739
$183$	−6.68900	−0.494465
$184$	16.5904	1.22306
$185$	−8.85734	−0.651205
$186$	−24.7443	−1.81434
$187$	1.06034	0.0775401
$188$	0.474727	0.0346230
$189$	−1.88088	−0.136814
$190$	28.4414	2.06336
$191$	−12.0383	−0.871062	−0.435531	−	0.900174i	$-0.643439\pi$
$191$	−12.0383	−0.871062	−0.435531	+	0.900174i	$0.643439\pi$
$192$	−11.0022	−0.794012
$193$	24.3435	1.75228	0.876140	−	0.482056i	$-0.160110\pi$
$193$	24.3435	1.75228	0.876140	+	0.482056i	$0.160110\pi$
$194$	1.80689	0.129727
$195$	15.1507	1.08497
$196$	−3.98622	−0.284730
$197$	12.9781	0.924654	0.462327	−	0.886710i	$-0.347015\pi$
$197$	12.9781	0.924654	0.462327	+	0.886710i	$0.347015\pi$
$198$	−6.33536	−0.450234
$199$	13.0320	0.923812	0.461906	−	0.886929i	$-0.347166\pi$
$199$	13.0320	0.923812	0.461906	+	0.886929i	$0.347166\pi$
$200$	5.54171	0.391858
$201$	21.3686	1.50722
$202$	25.3062	1.78054
$203$	0	0
$204$	−1.74087	−0.121885
$205$	−27.3452	−1.90987
$206$	−5.98532	−0.417017
$207$	29.1156	2.02368
$208$	−10.2346	−0.709644
$209$	6.41611	0.443812
$210$	−9.15603	−0.631826
$211$	4.61113	0.317444	0.158722	−	0.987323i	$-0.449263\pi$
$211$	4.61113	0.317444	0.158722	+	0.987323i	$0.449263\pi$
$212$	−7.76440	−0.533262
$213$	−14.3020	−0.979956
$214$	5.45055	0.372592
$215$	25.2303	1.72069
$216$	−5.33415	−0.362943
$217$	−4.56520	−0.309906
$218$	2.88858	0.195640
$219$	−34.4757	−2.32965
$220$	−1.70889	−0.115213
$221$	2.23342	0.150236
$222$	13.7859	0.925250
$223$	−15.0267	−1.00626	−0.503130	−	0.864211i	$-0.667818\pi$
$223$	−15.0267	−1.00626	−0.503130	+	0.864211i	$0.667818\pi$
$224$	2.68343	0.179294
$225$	9.72555	0.648370
$226$	−12.9565	−0.861854
$227$	27.1505	1.80204	0.901021	−	0.433775i	$-0.142819\pi$
$227$	27.1505	1.80204	0.901021	+	0.433775i	$0.142819\pi$
$228$	−10.5339	−0.697628
$229$	−10.1693	−0.672004	−0.336002	−	0.941861i	$-0.609075\pi$
$229$	−10.1693	−0.672004	−0.336002	+	0.941861i	$0.609075\pi$
$230$	33.0036	2.17619
$231$	−2.06551	−0.135901
$232$	0	0
$233$	19.6036	1.28427	0.642137	−	0.766590i	$-0.278048\pi$
$233$	19.6036	1.28427	0.642137	+	0.766590i	$0.278048\pi$
$234$	−13.3442	−0.872340
$235$	−2.07987	−0.135676
$236$	−4.64070	−0.302084
$237$	−14.5160	−0.942915
$238$	−1.34972	−0.0874893
$239$	−3.87405	−0.250591	−0.125296	−	0.992119i	$-0.539988\pi$
$239$	−3.87405	−0.250591	−0.125296	+	0.992119i	$0.539988\pi$
$240$	−34.9511	−2.25608
$241$	−7.01960	−0.452172	−0.226086	−	0.974107i	$-0.572593\pi$
$241$	−7.01960	−0.452172	−0.226086	+	0.974107i	$0.572593\pi$
$242$	−1.62004	−0.104140
$243$	21.4794	1.37790
$244$	1.58915	0.101735
$245$	17.4644	1.11576
$246$	42.5612	2.71360
$247$	13.5143	0.859896
$248$	−12.9469	−0.822127
$249$	33.7191	2.13686
$250$	−11.1398	−0.704544
$251$	14.8880	0.939720	0.469860	−	0.882741i	$-0.344304\pi$
$251$	14.8880	0.939720	0.469860	+	0.882741i	$0.344304\pi$
$252$	1.91900	0.120886
$253$	7.44529	0.468081
$254$	−10.5277	−0.660567
$255$	7.62708	0.477626
$256$	13.6795	0.854969
$257$	23.2172	1.44825	0.724125	−	0.689669i	$-0.242244\pi$
$257$	23.2172	1.44825	0.724125	+	0.689669i	$0.242244\pi$
$258$	−39.2694	−2.44481
$259$	2.54343	0.158041
$260$	−3.59945	−0.223229
$261$	0	0
$262$	−11.2196	−0.693152
$263$	−15.0817	−0.929976	−0.464988	−	0.885317i	$-0.653941\pi$
$263$	−15.0817	−0.929976	−0.464988	+	0.885317i	$0.653941\pi$
$264$	−5.85777	−0.360521
$265$	34.0173	2.08967
$266$	−8.16711	−0.500757
$267$	−6.71995	−0.411254
$268$	−5.07666	−0.310107
$269$	1.12034	0.0683086	0.0341543	−	0.999417i	$-0.489126\pi$
$269$	1.12034	0.0683086	0.0341543	+	0.999417i	$0.489126\pi$
$270$	−10.6114	−0.645786
$271$	−7.63747	−0.463943	−0.231972	−	0.972723i	$-0.574518\pi$
$271$	−7.63747	−0.463943	−0.231972	+	0.972723i	$0.574518\pi$
$272$	−5.15225	−0.312401
$273$	−4.35061	−0.263311
$274$	30.8620	1.86444
$275$	2.48697	0.149970
$276$	−12.2236	−0.735777
$277$	3.78644	0.227505	0.113753	−	0.993509i	$-0.463713\pi$
$277$	3.78644	0.227505	0.113753	+	0.993509i	$0.463713\pi$
$278$	−3.79363	−0.227527
$279$	−22.7214	−1.36029
$280$	−4.79068	−0.286298
$281$	12.2123	0.728527	0.364263	−	0.931296i	$-0.381321\pi$
$281$	12.2123	0.728527	0.364263	+	0.931296i	$0.381321\pi$
$282$	3.23719	0.192772
$283$	−23.3525	−1.38816	−0.694082	−	0.719896i	$-0.744190\pi$
$283$	−23.3525	−1.38816	−0.694082	+	0.719896i	$0.744190\pi$
$284$	3.39781	0.201623
$285$	46.1512	2.73376
$286$	−3.41231	−0.201774
$287$	7.85233	0.463508
$288$	13.3557	0.786990
$289$	−15.8757	−0.933863
$290$	0	0
$291$	2.93199	0.171876
$292$	8.19061	0.479319
$293$	−0.939265	−0.0548725	−0.0274362	−	0.999624i	$-0.508734\pi$
$293$	−0.939265	−0.0548725	−0.0274362	+	0.999624i	$0.508734\pi$
$294$	−27.1822	−1.58530
$295$	20.3318	1.18376
$296$	7.21315	0.419256
$297$	−2.39382	−0.138903
$298$	3.98701	0.230961
$299$	15.6821	0.906918
$300$	−4.08309	−0.235737
$301$	−7.24502	−0.417596
$302$	17.7364	1.02061
$303$	41.0637	2.35905
$304$	−31.1761	−1.78807
$305$	−6.96235	−0.398663
$306$	−6.71767	−0.384023
$307$	−6.90854	−0.394291	−0.197146	−	0.980374i	$-0.563167\pi$
$307$	−6.90854	−0.394291	−0.197146	+	0.980374i	$0.563167\pi$
$308$	0.490716	0.0279612
$309$	−9.71223	−0.552509
$310$	−25.7555	−1.46281
$311$	25.1331	1.42516	0.712582	−	0.701588i	$-0.247525\pi$
$311$	25.1331	1.42516	0.712582	+	0.701588i	$0.247525\pi$
$312$	−12.3383	−0.698518
$313$	−25.6529	−1.44999	−0.724994	−	0.688756i	$-0.758157\pi$
$313$	−25.6529	−1.44999	−0.724994	+	0.688756i	$0.758157\pi$
$314$	25.6310	1.44644
$315$	−8.40750	−0.473709
$316$	3.44865	0.194002
$317$	23.1136	1.29819	0.649096	−	0.760707i	$-0.275147\pi$
$317$	23.1136	1.29819	0.649096	+	0.760707i	$0.275147\pi$
$318$	−52.9459	−2.96906
$319$	0	0
$320$	−11.4518	−0.640173
$321$	8.84447	0.493650
$322$	−9.47715	−0.528141
$323$	6.80329	0.378545
$324$	−3.39685	−0.188714
$325$	5.23832	0.290570
$326$	−11.3250	−0.627235
$327$	4.68723	0.259204
$328$	22.2691	1.22961
$329$	0.597245	0.0329272
$330$	−11.6530	−0.641477
$331$	1.52489	0.0838154	0.0419077	−	0.999121i	$-0.486656\pi$
$331$	1.52489	0.0838154	0.0419077	+	0.999121i	$0.486656\pi$
$332$	−8.01087	−0.439653
$333$	12.6589	0.693702
$334$	32.4046	1.77310
$335$	22.2418	1.21520
$336$	10.0364	0.547530
$337$	−31.6482	−1.72399	−0.861994	−	0.506918i	$-0.830785\pi$
$337$	−31.6482	−1.72399	−0.861994	+	0.506918i	$0.830785\pi$
$338$	13.8732	0.754601
$339$	−21.0242	−1.14188
$340$	−1.81201	−0.0982702
$341$	−5.81019	−0.314639
$342$	−40.6484	−2.19801
$343$	−10.5150	−0.567759
$344$	−20.5468	−1.10781
$345$	53.5541	2.88325
$346$	13.7655	0.740035
$347$	26.3148	1.41265	0.706325	−	0.707887i	$-0.250352\pi$
$347$	26.3148	1.41265	0.706325	+	0.707887i	$0.250352\pi$
$348$	0	0
$349$	−17.4773	−0.935538	−0.467769	−	0.883851i	$-0.654942\pi$
$349$	−17.4773	−0.935538	−0.467769	+	0.883851i	$0.654942\pi$
$350$	−3.16567	−0.169212
$351$	−5.04212	−0.269129
$352$	3.41524	0.182033
$353$	28.1084	1.49606	0.748029	−	0.663666i	$-0.231001\pi$
$353$	28.1084	1.49606	0.748029	+	0.663666i	$0.231001\pi$
$354$	−31.6452	−1.68192
$355$	−14.8864	−0.790090
$356$	1.59650	0.0846144
$357$	−2.19016	−0.115915
$358$	−15.7598	−0.832929
$359$	−15.2613	−0.805460	−0.402730	−	0.915319i	$-0.631939\pi$
$359$	−15.2613	−0.805460	−0.402730	+	0.915319i	$0.631939\pi$
$360$	−23.8436	−1.25667
$361$	22.1665	1.16666
$362$	39.0794	2.05397
$363$	−2.62880	−0.137976
$364$	1.03360	0.0541754
$365$	−35.8846	−1.87828
$366$	10.8365	0.566431
$367$	−23.1710	−1.20952	−0.604759	−	0.796409i	$-0.706731\pi$
$367$	−23.1710	−1.20952	−0.604759	+	0.796409i	$0.706731\pi$
$368$	−36.1769	−1.88585
$369$	39.0817	2.03451
$370$	14.3493	0.745984
$371$	−9.76825	−0.507142
$372$	9.53915	0.494582
$373$	32.2299	1.66880	0.834399	−	0.551160i	$-0.185815\pi$
$373$	32.2299	1.66880	0.834399	+	0.551160i	$0.185815\pi$
$374$	−1.71781	−0.0888256
$375$	−18.0763	−0.933456
$376$	1.69378	0.0873501
$377$	0	0
$378$	3.04710	0.156726
$379$	−38.0599	−1.95501	−0.977504	−	0.210917i	$-0.932355\pi$
$379$	−38.0599	−1.95501	−0.977504	+	0.210917i	$0.932355\pi$
$380$	−10.9644	−0.562463
$381$	−17.0830	−0.875191
$382$	19.5026	0.997840
$383$	−9.65021	−0.493103	−0.246551	−	0.969130i	$-0.579297\pi$
$383$	−9.65021	−0.493103	−0.246551	+	0.969130i	$0.579297\pi$
$384$	35.7799	1.82589
$385$	−2.14992	−0.109570
$386$	−39.4375	−2.00731
$387$	−36.0591	−1.83299
$388$	−0.696571	−0.0353630
$389$	31.8725	1.61600	0.807999	−	0.589183i	$-0.200550\pi$
$389$	31.8725	1.61600	0.807999	+	0.589183i	$0.200550\pi$
$390$	−24.5448	−1.24288
$391$	7.89457	0.399246
$392$	−14.2225	−0.718342
$393$	−18.2058	−0.918363
$394$	−21.0251	−1.05923
$395$	−15.1092	−0.760226
$396$	2.44234	0.122732
$397$	25.0157	1.25550	0.627751	−	0.778414i	$-0.283976\pi$
$397$	25.0157	1.25550	0.627751	+	0.778414i	$0.283976\pi$
$398$	−21.1124	−1.05827
$399$	−13.2526	−0.663458
$400$	−12.0842	−0.604212
$401$	25.5039	1.27360	0.636801	−	0.771028i	$-0.280257\pi$
$401$	25.5039	1.27360	0.636801	+	0.771028i	$0.280257\pi$
$402$	−34.6180	−1.72659
$403$	−12.2381	−0.609621
$404$	−9.75575	−0.485367
$405$	14.8822	0.739505
$406$	0	0
$407$	3.23706	0.160455
$408$	−6.21126	−0.307503
$409$	6.47613	0.320224	0.160112	−	0.987099i	$-0.448814\pi$
$409$	6.47613	0.320224	0.160112	+	0.987099i	$0.448814\pi$
$410$	44.3005	2.18785
$411$	50.0790	2.47022
$412$	2.30739	0.113677
$413$	−5.83838	−0.287288
$414$	−47.1686	−2.31821
$415$	35.0971	1.72285
$416$	7.19354	0.352693
$417$	−6.15583	−0.301453
$418$	−10.3944	−0.508406
$419$	21.4308	1.04696	0.523482	−	0.852037i	$-0.324633\pi$
$419$	21.4308	1.04696	0.523482	+	0.852037i	$0.324633\pi$
$420$	3.52973	0.172233
$421$	−16.2053	−0.789797	−0.394898	−	0.918725i	$-0.629220\pi$
$421$	−16.2053	−0.789797	−0.394898	+	0.918725i	$0.629220\pi$
$422$	−7.47024	−0.363645
$423$	2.97254	0.144530
$424$	−27.7027	−1.34536
$425$	2.63704	0.127915
$426$	23.1698	1.12258
$427$	1.99927	0.0967517
$428$	−2.10123	−0.101567
$429$	−5.53708	−0.267333
$430$	−40.8742	−1.97113
$431$	−37.0223	−1.78330	−0.891650	−	0.452725i	$-0.850452\pi$
$431$	−37.0223	−1.78330	−0.891650	+	0.452725i	$0.850452\pi$
$432$	11.6316	0.559627
$433$	−23.3658	−1.12289	−0.561445	−	0.827514i	$-0.689754\pi$
$433$	−23.3658	−1.12289	−0.561445	+	0.827514i	$0.689754\pi$
$434$	7.39582	0.355011
$435$	0	0
$436$	−1.11357	−0.0533305
$437$	47.7698	2.28514
$438$	55.8521	2.66872
$439$	−40.3714	−1.92682	−0.963412	−	0.268025i	$-0.913629\pi$
$439$	−40.3714	−1.92682	−0.963412	+	0.268025i	$0.913629\pi$
$440$	−6.09715	−0.290670
$441$	−24.9600	−1.18857
$442$	−3.61823	−0.172102
$443$	12.6403	0.600561	0.300280	−	0.953851i	$-0.402920\pi$
$443$	12.6403	0.600561	0.300280	+	0.953851i	$0.402920\pi$
$444$	−5.31459	−0.252219
$445$	−6.99457	−0.331574
$446$	24.3439	1.15271
$447$	6.46962	0.306003
$448$	3.28843	0.155364
$449$	11.3532	0.535792	0.267896	−	0.963448i	$-0.413672\pi$
$449$	11.3532	0.535792	0.267896	+	0.963448i	$0.413672\pi$
$450$	−15.7558	−0.742736
$451$	9.99376	0.470588
$452$	4.99485	0.234938
$453$	28.7804	1.35222
$454$	−43.9850	−2.06432
$455$	−4.52840	−0.212295
$456$	−37.5841	−1.76004
$457$	−11.5331	−0.539497	−0.269749	−	0.962931i	$-0.586941\pi$
$457$	−11.5331	−0.539497	−0.269749	+	0.962931i	$0.586941\pi$
$458$	16.4747	0.769810
$459$	−2.53827	−0.118476
$460$	−12.7232	−0.593221
$461$	1.88423	0.0877574	0.0438787	−	0.999037i	$-0.486028\pi$
$461$	1.88423	0.0877574	0.0438787	+	0.999037i	$0.486028\pi$
$462$	3.34622	0.155680
$463$	25.2344	1.17274	0.586371	−	0.810043i	$-0.300556\pi$
$463$	25.2344	1.17274	0.586371	+	0.810043i	$0.300556\pi$
$464$	0	0
$465$	−41.7928	−1.93809
$466$	−31.7587	−1.47119
$467$	−42.1149	−1.94885	−0.974423	−	0.224723i	$-0.927852\pi$
$467$	−42.1149	−1.94885	−0.974423	+	0.224723i	$0.927852\pi$
$468$	5.14432	0.237796
$469$	−6.38685	−0.294917
$470$	3.36948	0.155422
$471$	41.5907	1.91640
$472$	−16.5576	−0.762125
$473$	−9.22083	−0.423974
$474$	23.5165	1.08015
$475$	15.9566	0.732141
$476$	0.520329	0.0238492
$477$	−48.6174	−2.22604
$478$	6.27612	0.287063
$479$	−9.47635	−0.432986	−0.216493	−	0.976284i	$-0.569462\pi$
$479$	−9.47635	−0.432986	−0.216493	+	0.976284i	$0.569462\pi$
$480$	24.5658	1.12127
$481$	6.81825	0.310885
$482$	11.3721	0.517983
$483$	−15.3783	−0.699738
$484$	0.624541	0.0283882
$485$	3.05181	0.138575
$486$	−34.7976	−1.57845
$487$	41.6812	1.88875	0.944377	−	0.328865i	$-0.106666\pi$
$487$	41.6812	1.88875	0.944377	+	0.328865i	$0.106666\pi$
$488$	5.66992	0.256665
$489$	−18.3768	−0.831029
$490$	−28.2931	−1.27815
$491$	−31.9752	−1.44302	−0.721510	−	0.692404i	$-0.756552\pi$
$491$	−31.9752	−1.44302	−0.721510	+	0.692404i	$0.756552\pi$
$492$	−16.4077	−0.739717
$493$	0	0
$494$	−21.8938	−0.985048
$495$	−10.7003	−0.480944
$496$	28.2319	1.26765
$497$	4.27472	0.191747
$498$	−54.6265	−2.44787
$499$	−24.9335	−1.11618	−0.558089	−	0.829781i	$-0.688465\pi$
$499$	−24.9335	−1.11618	−0.558089	+	0.829781i	$0.688465\pi$
$500$	4.29450	0.192056
$501$	52.5821	2.34920
$502$	−24.1192	−1.07649
$503$	−9.69952	−0.432480	−0.216240	−	0.976340i	$-0.569379\pi$
$503$	−9.69952	−0.432480	−0.216240	+	0.976340i	$0.569379\pi$
$504$	6.84681	0.304981
$505$	42.7418	1.90198
$506$	−12.0617	−0.536207
$507$	22.5117	0.999778
$508$	4.05852	0.180068
$509$	17.2806	0.765949	0.382975	−	0.923759i	$-0.374900\pi$
$509$	17.2806	0.765949	0.382975	+	0.923759i	$0.374900\pi$
$510$	−12.3562	−0.547142
$511$	10.3044	0.455842
$512$	5.06006	0.223625
$513$	−15.3590	−0.678117
$514$	−37.6129	−1.65903
$515$	−10.1091	−0.445461
$516$	15.1387	0.666445
$517$	0.760121	0.0334301
$518$	−4.12047	−0.181043
$519$	22.3369	0.980479
$520$	−12.8425	−0.563181
$521$	−25.1530	−1.10197	−0.550985	−	0.834515i	$-0.685748\pi$
$521$	−25.1530	−1.10197	−0.550985	+	0.834515i	$0.685748\pi$
$522$	0	0
$523$	−21.9871	−0.961428	−0.480714	−	0.876877i	$-0.659622\pi$
$523$	−21.9871	−0.961428	−0.480714	+	0.876877i	$0.659622\pi$
$524$	4.32527	0.188950
$525$	−5.13686	−0.224191
$526$	24.4330	1.06533
$527$	−6.16080	−0.268369
$528$	12.7734	0.555893
$529$	32.4323	1.41010
$530$	−55.1095	−2.39380
$531$	−29.0581	−1.26101
$532$	3.14849	0.136504
$533$	21.0500	0.911775
$534$	10.8866	0.471110
$535$	9.20590	0.398006
$536$	−18.1130	−0.782364
$537$	−25.5730	−1.10356
$538$	−1.81501	−0.0782505
$539$	−6.38264	−0.274920
$540$	4.09077	0.176039
$541$	−29.9555	−1.28789	−0.643944	−	0.765073i	$-0.722703\pi$
$541$	−29.9555	−1.28789	−0.643944	+	0.765073i	$0.722703\pi$
$542$	12.3730	0.531467
$543$	63.4131	2.72132
$544$	3.62133	0.155263
$545$	4.87878	0.208984
$546$	7.04818	0.301634
$547$	−31.3392	−1.33997	−0.669983	−	0.742377i	$-0.733699\pi$
$547$	−31.3392	−1.33997	−0.669983	+	0.742377i	$0.733699\pi$
$548$	−11.8976	−0.508240
$549$	9.95056	0.424680
$550$	−4.02899	−0.171797
$551$	0	0
$552$	−43.6128	−1.85628
$553$	4.33869	0.184500
$554$	−6.13420	−0.260617
$555$	23.2842	0.988360
$556$	1.46248	0.0620230
$557$	−24.2926	−1.02931	−0.514655	−	0.857397i	$-0.672080\pi$
$557$	−24.2926	−1.02931	−0.514655	+	0.857397i	$0.672080\pi$
$558$	36.8096	1.55828
$559$	−19.4219	−0.821460
$560$	10.4465	0.441447
$561$	−2.78744	−0.117686
$562$	−19.7845	−0.834559
$563$	28.2626	1.19113	0.595564	−	0.803308i	$-0.296929\pi$
$563$	28.2626	1.19113	0.595564	+	0.803308i	$0.296929\pi$
$564$	−1.24796	−0.0525488
$565$	−21.8834	−0.920640
$566$	37.8321	1.59020
$567$	−4.27351	−0.179471
$568$	12.1231	0.508672
$569$	−22.3770	−0.938095	−0.469047	−	0.883173i	$-0.655403\pi$
$569$	−22.3770	−0.938095	−0.469047	+	0.883173i	$0.655403\pi$
$570$	−74.7670	−3.13164
$571$	19.4372	0.813422	0.406711	−	0.913557i	$-0.366676\pi$
$571$	19.4372	0.813422	0.406711	+	0.913557i	$0.366676\pi$
$572$	1.31548	0.0550029
$573$	31.6464	1.32205
$574$	−12.7211	−0.530969
$575$	18.5162	0.772177
$576$	16.3668	0.681951
$577$	−23.0834	−0.960976	−0.480488	−	0.877001i	$-0.659541\pi$
$577$	−23.0834	−0.960976	−0.480488	+	0.877001i	$0.659541\pi$
$578$	25.7193	1.06978
$579$	−63.9942	−2.65951
$580$	0	0
$581$	−10.0783	−0.418119
$582$	−4.74995	−0.196892
$583$	−12.4322	−0.514888
$584$	29.2233	1.20927
$585$	−22.5382	−0.931841
$586$	1.52165	0.0628588
$587$	−11.5250	−0.475687	−0.237843	−	0.971304i	$-0.576440\pi$
$587$	−11.5250	−0.475687	−0.237843	+	0.971304i	$0.576440\pi$
$588$	10.4790	0.432146
$589$	−37.2788	−1.53605
$590$	−32.9384	−1.35605
$591$	−34.1170	−1.40338
$592$	−15.7290	−0.646457
$593$	−31.3047	−1.28553	−0.642765	−	0.766063i	$-0.722213\pi$
$593$	−31.3047	−1.28553	−0.642765	+	0.766063i	$0.722213\pi$
$594$	3.87809	0.159120
$595$	−2.27966	−0.0934569
$596$	−1.53703	−0.0629591
$597$	−34.2585	−1.40211
$598$	−25.4057	−1.03891
$599$	18.0884	0.739070	0.369535	−	0.929217i	$-0.379517\pi$
$599$	18.0884	0.739070	0.369535	+	0.929217i	$0.379517\pi$
$600$	−14.5681	−0.594739
$601$	3.70140	0.150983	0.0754917	−	0.997146i	$-0.475947\pi$
$601$	3.70140	0.150983	0.0754917	+	0.997146i	$0.475947\pi$
$602$	11.7372	0.478374
$603$	−31.7879	−1.29450
$604$	−6.83753	−0.278215
$605$	−2.73623	−0.111244
$606$	−66.5250	−2.70239
$607$	8.00712	0.324999	0.162499	−	0.986709i	$-0.448044\pi$
$607$	8.00712	0.324999	0.162499	+	0.986709i	$0.448044\pi$
$608$	21.9125	0.888670
$609$	0	0
$610$	11.2793	0.456686
$611$	1.60105	0.0647716
$612$	2.58972	0.104683
$613$	14.4578	0.583943	0.291972	−	0.956427i	$-0.405689\pi$
$613$	14.4578	0.583943	0.291972	+	0.956427i	$0.405689\pi$
$614$	11.1921	0.451678
$615$	71.8853	2.89869
$616$	1.75083	0.0705429
$617$	18.1534	0.730830	0.365415	−	0.930845i	$-0.380927\pi$
$617$	18.1534	0.730830	0.365415	+	0.930845i	$0.380927\pi$
$618$	15.7342	0.632924
$619$	45.3081	1.82109	0.910543	−	0.413414i	$-0.135664\pi$
$619$	45.3081	1.82109	0.910543	+	0.413414i	$0.135664\pi$
$620$	9.92897	0.398757
$621$	−17.8227	−0.715199
$622$	−40.7166	−1.63259
$623$	2.00853	0.0804699
$624$	26.9048	1.07706
$625$	−31.2498	−1.24999
$626$	41.5588	1.66102
$627$	−16.8667	−0.673591
$628$	−9.88096	−0.394293
$629$	3.43240	0.136859
$630$	13.6205	0.542655
$631$	−12.3496	−0.491628	−0.245814	−	0.969317i	$-0.579055\pi$
$631$	−12.3496	−0.491628	−0.245814	+	0.969317i	$0.579055\pi$
$632$	12.3045	0.489446
$633$	−12.1218	−0.481797
$634$	−37.4451	−1.48714
$635$	−17.7812	−0.705623
$636$	20.4111	0.809353
$637$	−13.4438	−0.532663
$638$	0	0
$639$	21.2756	0.841651
$640$	37.2421	1.47212
$641$	−5.95307	−0.235132	−0.117566	−	0.993065i	$-0.537509\pi$
$641$	−5.95307	−0.235132	−0.117566	+	0.993065i	$0.537509\pi$
$642$	−14.3284	−0.565498
$643$	−35.2490	−1.39008	−0.695042	−	0.718969i	$-0.744614\pi$
$643$	−35.2490	−1.39008	−0.695042	+	0.718969i	$0.744614\pi$
$644$	3.65352	0.143969
$645$	−66.3256	−2.61157
$646$	−11.0216	−0.433640
$647$	20.6353	0.811259	0.405630	−	0.914038i	$-0.367052\pi$
$647$	20.6353	0.811259	0.405630	+	0.914038i	$0.367052\pi$
$648$	−12.1196	−0.476104
$649$	−7.43058	−0.291676
$650$	−8.48631	−0.332860
$651$	12.0010	0.470357
$652$	4.36590	0.170982
$653$	−46.2092	−1.80830	−0.904152	−	0.427210i	$-0.859497\pi$
$653$	−46.2092	−1.80830	−0.904152	+	0.427210i	$0.859497\pi$
$654$	−7.59352	−0.296930
$655$	−18.9498	−0.740431
$656$	−48.5600	−1.89595
$657$	51.2861	2.00086
$658$	−0.967563	−0.0377195
$659$	−24.0457	−0.936686	−0.468343	−	0.883547i	$-0.655149\pi$
$659$	−24.0457	−0.936686	−0.468343	+	0.883547i	$0.655149\pi$
$660$	4.49234	0.174864
$661$	−20.1091	−0.782152	−0.391076	−	0.920358i	$-0.627897\pi$
$661$	−20.1091	−0.782152	−0.391076	+	0.920358i	$0.627897\pi$
$662$	−2.47038	−0.0960142
$663$	−5.87121	−0.228019
$664$	−28.5820	−1.10920
$665$	−13.7941	−0.534914
$666$	−20.5079	−0.794666
$667$	0	0
$668$	−12.4923	−0.483340
$669$	39.5022	1.52724
$670$	−36.0327	−1.39206
$671$	2.54450	0.0982294
$672$	−7.05421	−0.272122
$673$	−37.2985	−1.43775	−0.718876	−	0.695138i	$-0.755343\pi$
$673$	−37.2985	−1.43775	−0.718876	+	0.695138i	$0.755343\pi$
$674$	51.2715	1.97490
$675$	−5.95334	−0.229144
$676$	−5.34823	−0.205701
$677$	15.4323	0.593112	0.296556	−	0.955015i	$-0.404162\pi$
$677$	15.4323	0.593112	0.296556	+	0.955015i	$0.404162\pi$
$678$	34.0601	1.30807
$679$	−0.876342	−0.0336309
$680$	−6.46509	−0.247925
$681$	−71.3734	−2.73503
$682$	9.41276	0.360433
$683$	28.2944	1.08266	0.541328	−	0.840811i	$-0.317922\pi$
$683$	28.2944	1.08266	0.541328	+	0.840811i	$0.317922\pi$
$684$	15.6703	0.599169
$685$	52.1256	1.99162
$686$	17.0348	0.650393
$687$	26.7330	1.01993
$688$	44.8043	1.70815
$689$	−26.1860	−0.997608
$690$	−86.7599	−3.30289
$691$	15.5077	0.589940	0.294970	−	0.955507i	$-0.404690\pi$
$691$	15.5077	0.589940	0.294970	+	0.955507i	$0.404690\pi$
$692$	−5.30671	−0.201731
$693$	3.07266	0.116721
$694$	−42.6311	−1.61825
$695$	−6.40740	−0.243046
$696$	0	0
$697$	10.5968	0.401384
$698$	28.3140	1.07170
$699$	−51.5340	−1.94920
$700$	1.22039	0.0461266
$701$	−32.4206	−1.22451	−0.612254	−	0.790661i	$-0.709737\pi$
$701$	−32.4206	−1.22451	−0.612254	+	0.790661i	$0.709737\pi$
$702$	8.16846	0.308299
$703$	20.7693	0.783330
$704$	4.18523	0.157737
$705$	5.46757	0.205920
$706$	−45.5368	−1.71380
$707$	−12.2735	−0.461593
$708$	12.1995	0.458485
$709$	−5.27767	−0.198207	−0.0991036	−	0.995077i	$-0.531598\pi$
$709$	−5.27767	−0.198207	−0.0991036	+	0.995077i	$0.531598\pi$
$710$	24.1167	0.905083
$711$	21.5940	0.809839
$712$	5.69616	0.213473
$713$	−43.2585	−1.62004
$714$	3.54815	0.132786
$715$	−5.76335	−0.215537
$716$	6.07553	0.227053
$717$	10.1841	0.380332
$718$	24.7239	0.922689
$719$	−32.8105	−1.22362	−0.611812	−	0.791003i	$-0.709559\pi$
$719$	−32.8105	−1.22362	−0.611812	+	0.791003i	$0.709559\pi$
$720$	51.9933	1.93767
$721$	2.90289	0.108109
$722$	−35.9107	−1.33646
$723$	18.4531	0.686280
$724$	−15.0654	−0.559903
$725$	0	0
$726$	4.25878	0.158058
$727$	4.50575	0.167109	0.0835546	−	0.996503i	$-0.473373\pi$
$727$	4.50575	0.167109	0.0835546	+	0.996503i	$0.473373\pi$
$728$	3.68779	0.136679
$729$	−40.1483	−1.48697
$730$	58.1346	2.15166
$731$	−9.77726	−0.361625
$732$	−4.17756	−0.154407
$733$	18.6664	0.689458	0.344729	−	0.938702i	$-0.387971\pi$
$733$	18.6664	0.689458	0.344729	+	0.938702i	$0.387971\pi$
$734$	37.5381	1.38556
$735$	−45.9104	−1.69343
$736$	25.4274	0.937266
$737$	−8.12863	−0.299422
$738$	−63.3141	−2.33062
$739$	−6.94044	−0.255308	−0.127654	−	0.991819i	$-0.540745\pi$
$739$	−6.94044	−0.255308	−0.127654	+	0.991819i	$0.540745\pi$
$740$	−5.53178	−0.203352
$741$	−35.5265	−1.30510
$742$	15.8250	0.580954
$743$	26.0367	0.955195	0.477597	−	0.878579i	$-0.341508\pi$
$743$	26.0367	0.955195	0.477597	+	0.878579i	$0.341508\pi$
$744$	34.0348	1.24777
$745$	6.73401	0.246715
$746$	−52.2138	−1.91168
$747$	−50.1606	−1.83528
$748$	0.662229	0.0242135
$749$	−2.64352	−0.0965922
$750$	29.2844	1.06932
$751$	−22.3641	−0.816079	−0.408040	−	0.912964i	$-0.633788\pi$
$751$	−22.3641	−0.816079	−0.408040	+	0.912964i	$0.633788\pi$
$752$	−3.69345	−0.134686
$753$	−39.1376	−1.42625
$754$	0	0
$755$	29.9565	1.09023
$756$	−1.17469	−0.0427229
$757$	16.0122	0.581973	0.290987	−	0.956727i	$-0.406016\pi$
$757$	16.0122	0.581973	0.290987	+	0.956727i	$0.406016\pi$
$758$	61.6588	2.23955
$759$	−19.5722	−0.710426
$760$	−39.1200	−1.41903
$761$	16.8935	0.612389	0.306194	−	0.951969i	$-0.400944\pi$
$761$	16.8935	0.612389	0.306194	+	0.951969i	$0.400944\pi$
$762$	27.6753	1.00257
$763$	−1.40097	−0.0507184
$764$	−7.51842	−0.272007
$765$	−11.3461	−0.410217
$766$	15.6338	0.564871
$767$	−15.6511	−0.565129
$768$	−35.9607	−1.29762
$769$	−13.7267	−0.494997	−0.247499	−	0.968888i	$-0.579609\pi$
$769$	−13.7267	−0.494997	−0.247499	+	0.968888i	$0.579609\pi$
$770$	3.48297	0.125517
$771$	−61.0335	−2.19807
$772$	15.2035	0.547186
$773$	14.4619	0.520159	0.260079	−	0.965587i	$-0.416251\pi$
$773$	14.4619	0.520159	0.260079	+	0.965587i	$0.416251\pi$
$774$	58.4173	2.09976
$775$	−14.4497	−0.519050
$776$	−2.48530	−0.0892170
$777$	−6.68618	−0.239866
$778$	−51.6348	−1.85120
$779$	64.1211	2.29738
$780$	9.46225	0.338803
$781$	5.44049	0.194676
$782$	−12.7895	−0.457353
$783$	0	0
$784$	31.0134	1.10762
$785$	43.2903	1.54510
$786$	29.4942	1.05202
$787$	−22.0845	−0.787227	−0.393614	−	0.919276i	$-0.628775\pi$
$787$	−22.0845	−0.787227	−0.393614	+	0.919276i	$0.628775\pi$
$788$	8.10538	0.288742
$789$	39.6468	1.41146
$790$	24.4776	0.870873
$791$	6.28392	0.223430
$792$	8.71403	0.309639
$793$	5.35951	0.190322
$794$	−40.5265	−1.43823
$795$	−89.4248	−3.17157
$796$	8.13901	0.288479
$797$	23.8471	0.844709	0.422355	−	0.906431i	$-0.361204\pi$
$797$	23.8471	0.844709	0.422355	+	0.906431i	$0.361204\pi$
$798$	21.4697	0.760020
$799$	0.805991	0.0285139
$800$	8.49357	0.300293
$801$	9.99661	0.353213
$802$	−41.3174	−1.45897
$803$	13.1146	0.462804
$804$	13.3456	0.470661
$805$	−16.0068	−0.564165
$806$	19.8262	0.698348
$807$	−2.94517	−0.103675
$808$	−34.8076	−1.22453
$809$	−9.18602	−0.322963	−0.161482	−	0.986876i	$-0.551627\pi$
$809$	−9.18602	−0.322963	−0.161482	+	0.986876i	$0.551627\pi$
$810$	−24.1099	−0.847135
$811$	27.4236	0.962973	0.481486	−	0.876454i	$-0.340097\pi$
$811$	27.4236	0.962973	0.481486	+	0.876454i	$0.340097\pi$
$812$	0	0
$813$	20.0774	0.704145
$814$	−5.24418	−0.183808
$815$	−19.1278	−0.670018
$816$	13.5443	0.474144
$817$	−59.1619	−2.06981
$818$	−10.4916	−0.366831
$819$	6.47197	0.226149
$820$	−17.0782	−0.596398
$821$	−27.1223	−0.946575	−0.473288	−	0.880908i	$-0.656933\pi$
$821$	−27.1223	−0.946575	−0.473288	+	0.880908i	$0.656933\pi$
$822$	−81.1302	−2.82974
$823$	41.7081	1.45385	0.726927	−	0.686715i	$-0.240948\pi$
$823$	41.7081	1.45385	0.726927	+	0.686715i	$0.240948\pi$
$824$	8.23256	0.286795
$825$	−6.53774	−0.227615
$826$	9.45843	0.329101
$827$	−37.9451	−1.31948	−0.659739	−	0.751494i	$-0.729333\pi$
$827$	−37.9451	−1.31948	−0.659739	+	0.751494i	$0.729333\pi$
$828$	18.1839	0.631934
$829$	−28.2740	−0.981998	−0.490999	−	0.871160i	$-0.663368\pi$
$829$	−28.2740	−0.981998	−0.490999	+	0.871160i	$0.663368\pi$
$830$	−56.8588	−1.97360
$831$	−9.95380	−0.345294
$832$	8.81540	0.305619
$833$	−6.76780	−0.234490
$834$	9.97272	0.345327
$835$	54.7309	1.89404
$836$	4.00713	0.138589
$837$	13.9085	0.480749
$838$	−34.7189	−1.19934
$839$	−19.2269	−0.663785	−0.331892	−	0.943317i	$-0.607687\pi$
$839$	−19.2269	−0.663785	−0.331892	+	0.943317i	$0.607687\pi$
$840$	12.5937	0.434526
$841$	0	0
$842$	26.2532	0.904746
$843$	−32.1038	−1.10571
$844$	2.87984	0.0991283
$845$	23.4316	0.806072
$846$	−4.81564	−0.165565
$847$	0.785723	0.0269978
$848$	60.4083	2.07443
$849$	61.3893	2.10687
$850$	−4.27212	−0.146533
$851$	24.1008	0.826166
$852$	−8.93218	−0.306011
$853$	−5.43396	−0.186055	−0.0930277	−	0.995664i	$-0.529655\pi$
$853$	−5.43396	−0.186055	−0.0930277	+	0.995664i	$0.529655\pi$
$854$	−3.23891	−0.110833
$855$	−68.6546	−2.34794
$856$	−7.49701	−0.256242
$857$	6.37473	0.217757	0.108878	−	0.994055i	$-0.465274\pi$
$857$	6.37473	0.217757	0.108878	+	0.994055i	$0.465274\pi$
$858$	8.97031	0.306241
$859$	24.3830	0.831938	0.415969	−	0.909379i	$-0.363442\pi$
$859$	24.3830	0.831938	0.415969	+	0.909379i	$0.363442\pi$
$860$	15.7574	0.537322
$861$	−20.6422	−0.703485
$862$	59.9777	2.04285
$863$	24.3068	0.827412	0.413706	−	0.910411i	$-0.364234\pi$
$863$	24.3068	0.827412	0.413706	+	0.910411i	$0.364234\pi$
$864$	−8.17545	−0.278134
$865$	23.2497	0.790512
$866$	37.8537	1.28632
$867$	41.7340	1.41736
$868$	−2.85116	−0.0967745
$869$	5.52190	0.187318
$870$	0	0
$871$	−17.1214	−0.580137
$872$	−3.97313	−0.134547
$873$	−4.36163	−0.147619
$874$	−77.3891	−2.61773
$875$	5.40283	0.182649
$876$	−21.5315	−0.727482
$877$	−10.6284	−0.358896	−0.179448	−	0.983767i	$-0.557431\pi$
$877$	−10.6284	−0.358896	−0.179448	+	0.983767i	$0.557431\pi$
$878$	65.4035	2.20726
$879$	2.46914	0.0832822
$880$	13.2954	0.448189
$881$	−41.7274	−1.40583	−0.702916	−	0.711273i	$-0.748119\pi$
$881$	−41.7274	−1.40583	−0.702916	+	0.711273i	$0.748119\pi$
$882$	40.4363	1.36156
$883$	19.5691	0.658551	0.329276	−	0.944234i	$-0.393196\pi$
$883$	19.5691	0.658551	0.329276	+	0.944234i	$0.393196\pi$
$884$	1.39486	0.0469142
$885$	−53.4483	−1.79664
$886$	−20.4779	−0.687969
$887$	35.0562	1.17707	0.588536	−	0.808471i	$-0.299705\pi$
$887$	35.0562	1.17707	0.588536	+	0.808471i	$0.299705\pi$
$888$	−18.9620	−0.636322
$889$	5.10595	0.171248
$890$	11.3315	0.379833
$891$	−5.43895	−0.182212
$892$	−9.38477	−0.314225
$893$	4.87702	0.163203
$894$	−10.4811	−0.350539
$895$	−26.6180	−0.889743
$896$	−10.6943	−0.357270
$897$	−41.2251	−1.37647
$898$	−18.3927	−0.613773
$899$	0	0
$900$	6.07401	0.202467
$901$	−13.1824	−0.439169
$902$	−16.1903	−0.539079
$903$	19.0457	0.633802
$904$	17.8211	0.592722
$905$	66.0045	2.19407
$906$	−46.6254	−1.54903
$907$	8.54278	0.283658	0.141829	−	0.989891i	$-0.454702\pi$
$907$	8.54278	0.283658	0.141829	+	0.989891i	$0.454702\pi$
$908$	16.9566	0.562725
$909$	−61.0864	−2.02611
$910$	7.33621	0.243193
$911$	2.13556	0.0707544	0.0353772	−	0.999374i	$-0.488737\pi$
$911$	2.13556	0.0707544	0.0353772	+	0.999374i	$0.488737\pi$
$912$	81.9558	2.71383
$913$	−12.8268	−0.424505
$914$	18.6842	0.618018
$915$	18.3027	0.605067
$916$	−6.35113	−0.209847
$917$	5.44154	0.179695
$918$	4.11211	0.135720
$919$	−5.91078	−0.194979	−0.0974894	−	0.995237i	$-0.531081\pi$
$919$	−5.91078	−0.194979	−0.0974894	+	0.995237i	$0.531081\pi$
$920$	−45.3951	−1.49663
$921$	18.1612	0.598432
$922$	−3.05254	−0.100530
$923$	11.4594	0.377189
$924$	−1.29000	−0.0424378
$925$	8.05045	0.264697
$926$	−40.8808	−1.34343
$927$	14.4479	0.474532
$928$	0	0
$929$	32.9337	1.08052	0.540261	−	0.841498i	$-0.318326\pi$
$929$	32.9337	1.08052	0.540261	+	0.841498i	$0.318326\pi$
$930$	67.7061	2.22017
$931$	−40.9517	−1.34214
$932$	12.2433	0.401041
$933$	−66.0699	−2.16303
$934$	68.2280	2.23249
$935$	−2.90135	−0.0948843
$936$	18.3544	0.599934
$937$	57.1865	1.86820	0.934100	−	0.357012i	$-0.116204\pi$
$937$	57.1865	1.86820	0.934100	+	0.357012i	$0.116204\pi$
$938$	10.3470	0.337841
$939$	67.4364	2.20070
$940$	−1.29896	−0.0423675
$941$	−23.7062	−0.772800	−0.386400	−	0.922331i	$-0.626282\pi$
$941$	−23.7062	−0.772800	−0.386400	+	0.922331i	$0.626282\pi$
$942$	−67.3788	−2.19532
$943$	74.4064	2.42301
$944$	36.1054	1.17513
$945$	5.14652	0.167416
$946$	14.9381	0.485681
$947$	40.3984	1.31277	0.656386	−	0.754426i	$-0.272084\pi$
$947$	40.3984	1.31277	0.656386	+	0.754426i	$0.272084\pi$
$948$	−9.06584	−0.294445
$949$	27.6234	0.896694
$950$	−25.8505	−0.838700
$951$	−60.7612	−1.97032
$952$	1.85648	0.0601690
$953$	54.8597	1.77708	0.888539	−	0.458801i	$-0.151721\pi$
$953$	54.8597	1.77708	0.888539	+	0.458801i	$0.151721\pi$
$954$	78.7623	2.55002
$955$	32.9396	1.06590
$956$	−2.41950	−0.0782523
$957$	0	0
$958$	15.3521	0.496004
$959$	−14.9681	−0.483346
$960$	30.1044	0.971617
$961$	2.75829	0.0889772
$962$	−11.0459	−0.356133
$963$	−13.1570	−0.423980
$964$	−4.38403	−0.141200
$965$	−66.6094	−2.14423
$966$	24.9136	0.801581
$967$	24.8017	0.797568	0.398784	−	0.917045i	$-0.369432\pi$
$967$	24.8017	0.797568	0.398784	+	0.917045i	$0.369432\pi$
$968$	2.22830	0.0716204
$969$	−17.8845	−0.574534
$970$	−4.94406	−0.158744
$971$	21.3891	0.686409	0.343204	−	0.939261i	$-0.388488\pi$
$971$	21.3891	0.686409	0.343204	+	0.939261i	$0.388488\pi$
$972$	13.4148	0.430279
$973$	1.83992	0.0589850
$974$	−67.5253	−2.16365
$975$	−13.7705	−0.441010
$976$	−12.3638	−0.395756
$977$	−5.00421	−0.160099	−0.0800495	−	0.996791i	$-0.525508\pi$
$977$	−5.00421	−0.160099	−0.0800495	+	0.996791i	$0.525508\pi$
$978$	29.7713	0.951980
$979$	2.55628	0.0816990
$980$	10.9072	0.348419
$981$	−6.97273	−0.222622
$982$	51.8012	1.65304
$983$	41.9710	1.33867	0.669333	−	0.742963i	$-0.266580\pi$
$983$	41.9710	1.33867	0.669333	+	0.742963i	$0.266580\pi$
$984$	−58.5412	−1.86622
$985$	−35.5112	−1.13148
$986$	0	0
$987$	−1.57004	−0.0499749
$988$	8.44025	0.268520
$989$	−68.6517	−2.18300
$990$	17.3350	0.550943
$991$	14.1313	0.448895	0.224448	−	0.974486i	$-0.427942\pi$
$991$	14.1313	0.448895	0.224448	+	0.974486i	$0.427942\pi$
$992$	−19.8432	−0.630021
$993$	−4.00863	−0.127210
$994$	−6.92523	−0.219655
$995$	−35.6585	−1.13045
$996$	21.0590	0.667280
$997$	−37.2141	−1.17858	−0.589292	−	0.807920i	$-0.700593\pi$
$997$	−37.2141	−1.17858	−0.589292	+	0.807920i	$0.700593\pi$
$998$	40.3934	1.27863
$999$	−7.74893	−0.245165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.ba.1.8	✓	40
29.28	even	2		9251.2.a.bb.1.33	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.ba.1.8	✓	40	1.1	even	1	trivial
9251.2.a.bb.1.33	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)

\(f(q)\)	\(=\)	\(q-1.62004 q^{2} -2.62880 q^{3} +0.624541 q^{4} -2.73623 q^{5} +4.25878 q^{6} +0.785723 q^{7} +2.22830 q^{8} +3.91061 q^{9} +O(q^{10})\)	\(q-1.62004 q^{2} -2.62880 q^{3} +0.624541 q^{4} -2.73623 q^{5} +4.25878 q^{6} +0.785723 q^{7} +2.22830 q^{8} +3.91061 q^{9} +4.43281 q^{10} +1.00000 q^{11} -1.64180 q^{12} +2.10631 q^{13} -1.27291 q^{14} +7.19302 q^{15} -4.85903 q^{16} +1.06034 q^{17} -6.33536 q^{18} +6.41611 q^{19} -1.70889 q^{20} -2.06551 q^{21} -1.62004 q^{22} +7.44529 q^{23} -5.85777 q^{24} +2.48697 q^{25} -3.41231 q^{26} -2.39382 q^{27} +0.490716 q^{28} -11.6530 q^{30} -5.81019 q^{31} +3.41524 q^{32} -2.62880 q^{33} -1.71781 q^{34} -2.14992 q^{35} +2.44234 q^{36} +3.23706 q^{37} -10.3944 q^{38} -5.53708 q^{39} -6.09715 q^{40} +9.99376 q^{41} +3.34622 q^{42} -9.22083 q^{43} +0.624541 q^{44} -10.7003 q^{45} -12.0617 q^{46} +0.760121 q^{47} +12.7734 q^{48} -6.38264 q^{49} -4.02899 q^{50} -2.78744 q^{51} +1.31548 q^{52} -12.4322 q^{53} +3.87809 q^{54} -2.73623 q^{55} +1.75083 q^{56} -16.8667 q^{57} -7.43058 q^{59} +4.49234 q^{60} +2.54450 q^{61} +9.41276 q^{62} +3.07266 q^{63} +4.18523 q^{64} -5.76335 q^{65} +4.25878 q^{66} -8.12863 q^{67} +0.662229 q^{68} -19.5722 q^{69} +3.48297 q^{70} +5.44049 q^{71} +8.71403 q^{72} +13.1146 q^{73} -5.24418 q^{74} -6.53774 q^{75} +4.00713 q^{76} +0.785723 q^{77} +8.97031 q^{78} +5.52190 q^{79} +13.2954 q^{80} -5.43895 q^{81} -16.1903 q^{82} -12.8268 q^{83} -1.29000 q^{84} -2.90135 q^{85} +14.9381 q^{86} +2.22830 q^{88} +2.55628 q^{89} +17.3350 q^{90} +1.65498 q^{91} +4.64989 q^{92} +15.2738 q^{93} -1.23143 q^{94} -17.5560 q^{95} -8.97798 q^{96} -1.11533 q^{97} +10.3402 q^{98} +3.91061 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) \) 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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