LMFDB - Embedded newform 7935.2.a.bu.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.79106 q^{2} -1.00000 q^{3} +1.20789 q^{4} +1.00000 q^{5} -1.79106 q^{6} -4.79732 q^{7} -1.41871 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.79106 q^{2} -1.00000 q^{3} +1.20789 q^{4} +1.00000 q^{5} -1.79106 q^{6} -4.79732 q^{7} -1.41871 q^{8} +1.00000 q^{9} +1.79106 q^{10} -6.14357 q^{11} -1.20789 q^{12} -1.49041 q^{13} -8.59228 q^{14} -1.00000 q^{15} -4.95678 q^{16} -5.08181 q^{17} +1.79106 q^{18} -2.83343 q^{19} +1.20789 q^{20} +4.79732 q^{21} -11.0035 q^{22} +1.41871 q^{24} +1.00000 q^{25} -2.66941 q^{26} -1.00000 q^{27} -5.79464 q^{28} +5.95729 q^{29} -1.79106 q^{30} -7.06318 q^{31} -6.04046 q^{32} +6.14357 q^{33} -9.10183 q^{34} -4.79732 q^{35} +1.20789 q^{36} -1.77364 q^{37} -5.07484 q^{38} +1.49041 q^{39} -1.41871 q^{40} +4.42596 q^{41} +8.59228 q^{42} -0.0523310 q^{43} -7.42077 q^{44} +1.00000 q^{45} +9.00757 q^{47} +4.95678 q^{48} +16.0143 q^{49} +1.79106 q^{50} +5.08181 q^{51} -1.80025 q^{52} +12.1173 q^{53} -1.79106 q^{54} -6.14357 q^{55} +6.80602 q^{56} +2.83343 q^{57} +10.6699 q^{58} +1.48633 q^{59} -1.20789 q^{60} -2.61779 q^{61} -12.6506 q^{62} -4.79732 q^{63} -0.905260 q^{64} -1.49041 q^{65} +11.0035 q^{66} +2.39482 q^{67} -6.13828 q^{68} -8.59228 q^{70} -14.8098 q^{71} -1.41871 q^{72} -3.46573 q^{73} -3.17670 q^{74} -1.00000 q^{75} -3.42248 q^{76} +29.4727 q^{77} +2.66941 q^{78} +1.41858 q^{79} -4.95678 q^{80} +1.00000 q^{81} +7.92716 q^{82} +9.77212 q^{83} +5.79464 q^{84} -5.08181 q^{85} -0.0937279 q^{86} -5.95729 q^{87} +8.71596 q^{88} +6.02452 q^{89} +1.79106 q^{90} +7.14997 q^{91} +7.06318 q^{93} +16.1331 q^{94} -2.83343 q^{95} +6.04046 q^{96} -0.574626 q^{97} +28.6825 q^{98} -6.14357 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19} + 31 q^{20} + 15 q^{21} - 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} - 41 q^{28} + q^{29} - q^{30} + 18 q^{31} + 17 q^{32} - 15 q^{33} + 7 q^{34} - 15 q^{35} + 31 q^{36} - 8 q^{37} + 15 q^{38} - 24 q^{39} + 3 q^{40} + 36 q^{41} - 5 q^{42} - 36 q^{43} + 90 q^{44} + 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} + 6 q^{51} + 35 q^{52} + 6 q^{53} - q^{54} + 15 q^{55} + 15 q^{56} - 13 q^{57} + 42 q^{58} - 3 q^{59} - 31 q^{60} + 71 q^{61} - 7 q^{62} - 15 q^{63} + 47 q^{64} + 24 q^{65} + 21 q^{66} - 10 q^{67} - 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} + 67 q^{74} - 25 q^{75} - 12 q^{76} + 27 q^{77} - 21 q^{78} + 33 q^{79} + 39 q^{80} + 25 q^{81} + 49 q^{82} - 2 q^{83} + 41 q^{84} - 6 q^{85} - 35 q^{86} - q^{87} - 33 q^{88} + 11 q^{89} + q^{90} + 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} - 48 q^{97} + 4 q^{98} + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * 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 $

$2$	1.79106	1.26647	0.633235	−	0.773960i	$-0.281727\pi$
$2$	1.79106	1.26647	0.633235	+	0.773960i	$0.281727\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.20789	0.603946
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.79106	−0.731197
$7$	−4.79732	−1.81322	−0.906608	−	0.421973i	$-0.861338\pi$
$7$	−4.79732	−1.81322	−0.906608	+	0.421973i	$0.861338\pi$
$8$	−1.41871	−0.501591
$9$	1.00000	0.333333
$10$	1.79106	0.566383
$11$	−6.14357	−1.85236	−0.926179	−	0.377085i	$-0.876926\pi$
$11$	−6.14357	−1.85236	−0.926179	+	0.377085i	$0.876926\pi$
$12$	−1.20789	−0.348688
$13$	−1.49041	−0.413365	−0.206683	−	0.978408i	$-0.566267\pi$
$13$	−1.49041	−0.413365	−0.206683	+	0.978408i	$0.566267\pi$
$14$	−8.59228	−2.29638
$15$	−1.00000	−0.258199
$16$	−4.95678	−1.23920
$17$	−5.08181	−1.23252	−0.616260	−	0.787542i	$-0.711353\pi$
$17$	−5.08181	−1.23252	−0.616260	+	0.787542i	$0.711353\pi$
$18$	1.79106	0.422157
$19$	−2.83343	−0.650034	−0.325017	−	0.945708i	$-0.605370\pi$
$19$	−2.83343	−0.650034	−0.325017	+	0.945708i	$0.605370\pi$
$20$	1.20789	0.270093
$21$	4.79732	1.04686
$22$	−11.0035	−2.34595
$23$	0	0
$23$	0	0
$24$	1.41871	0.289593
$25$	1.00000	0.200000
$26$	−2.66941	−0.523515
$27$	−1.00000	−0.192450
$28$	−5.79464	−1.09508
$29$	5.95729	1.10624	0.553121	−	0.833101i	$-0.313437\pi$
$29$	5.95729	1.10624	0.553121	+	0.833101i	$0.313437\pi$
$30$	−1.79106	−0.327001
$31$	−7.06318	−1.26858	−0.634292	−	0.773093i	$-0.718708\pi$
$31$	−7.06318	−1.26858	−0.634292	+	0.773093i	$0.718708\pi$
$32$	−6.04046	−1.06781
$33$	6.14357	1.06946
$34$	−9.10183	−1.56095
$35$	−4.79732	−0.810895
$36$	1.20789	0.201315
$37$	−1.77364	−0.291585	−0.145793	−	0.989315i	$-0.546573\pi$
$37$	−1.77364	−0.291585	−0.145793	+	0.989315i	$0.546573\pi$
$38$	−5.07484	−0.823248
$39$	1.49041	0.238657
$40$	−1.41871	−0.224318
$41$	4.42596	0.691219	0.345609	−	0.938378i	$-0.387672\pi$
$41$	4.42596	0.691219	0.345609	+	0.938378i	$0.387672\pi$
$42$	8.59228	1.32582
$43$	−0.0523310	−0.00798040	−0.00399020	−	0.999992i	$-0.501270\pi$
$43$	−0.0523310	−0.00798040	−0.00399020	+	0.999992i	$0.501270\pi$
$44$	−7.42077	−1.11872
$45$	1.00000	0.149071
$46$	0	0
$47$	9.00757	1.31389	0.656945	−	0.753939i	$-0.271849\pi$
$47$	9.00757	1.31389	0.656945	+	0.753939i	$0.271849\pi$
$48$	4.95678	0.715450
$49$	16.0143	2.28775
$50$	1.79106	0.253294
$51$	5.08181	0.711596
$52$	−1.80025	−0.249650
$53$	12.1173	1.66443	0.832217	−	0.554450i	$-0.187071\pi$
$53$	12.1173	1.66443	0.832217	+	0.554450i	$0.187071\pi$
$54$	−1.79106	−0.243732
$55$	−6.14357	−0.828399
$56$	6.80602	0.909492
$57$	2.83343	0.375297
$58$	10.6699	1.40102
$59$	1.48633	0.193503	0.0967517	−	0.995309i	$-0.469155\pi$
$59$	1.48633	0.193503	0.0967517	+	0.995309i	$0.469155\pi$
$60$	−1.20789	−0.155938
$61$	−2.61779	−0.335174	−0.167587	−	0.985857i	$-0.553598\pi$
$61$	−2.61779	−0.335174	−0.167587	+	0.985857i	$0.553598\pi$
$62$	−12.6506	−1.60662
$63$	−4.79732	−0.604405
$64$	−0.905260	−0.113158
$65$	−1.49041	−0.184863
$66$	11.0035	1.35444
$67$	2.39482	0.292573	0.146287	−	0.989242i	$-0.453268\pi$
$67$	2.39482	0.292573	0.146287	+	0.989242i	$0.453268\pi$
$68$	−6.13828	−0.744376
$69$	0	0
$70$	−8.59228	−1.02697
$71$	−14.8098	−1.75759	−0.878797	−	0.477195i	$-0.841654\pi$
$71$	−14.8098	−1.75759	−0.878797	+	0.477195i	$0.841654\pi$
$72$	−1.41871	−0.167197
$73$	−3.46573	−0.405633	−0.202817	−	0.979217i	$-0.565010\pi$
$73$	−3.46573	−0.405633	−0.202817	+	0.979217i	$0.565010\pi$
$74$	−3.17670	−0.369284
$75$	−1.00000	−0.115470
$76$	−3.42248	−0.392585
$77$	29.4727	3.35872
$78$	2.66941	0.302251
$79$	1.41858	0.159603	0.0798015	−	0.996811i	$-0.474571\pi$
$79$	1.41858	0.159603	0.0798015	+	0.996811i	$0.474571\pi$
$80$	−4.95678	−0.554185
$81$	1.00000	0.111111
$82$	7.92716	0.875408
$83$	9.77212	1.07263	0.536315	−	0.844018i	$-0.319816\pi$
$83$	9.77212	1.07263	0.536315	+	0.844018i	$0.319816\pi$
$84$	5.79464	0.632247
$85$	−5.08181	−0.551200
$86$	−0.0937279	−0.0101069
$87$	−5.95729	−0.638689
$88$	8.71596	0.929125
$89$	6.02452	0.638597	0.319299	−	0.947654i	$-0.396553\pi$
$89$	6.02452	0.638597	0.319299	+	0.947654i	$0.396553\pi$
$90$	1.79106	0.188794
$91$	7.14997	0.749521
$92$	0	0
$93$	7.06318	0.732418
$94$	16.1331	1.66400
$95$	−2.83343	−0.290704
$96$	6.04046	0.616502
$97$	−0.574626	−0.0583444	−0.0291722	−	0.999574i	$-0.509287\pi$
$97$	−0.574626	−0.0583444	−0.0291722	+	0.999574i	$0.509287\pi$
$98$	28.6825	2.89737
$99$	−6.14357	−0.617452
$100$	1.20789	0.120789
$101$	−3.94553	−0.392595	−0.196297	−	0.980544i	$-0.562892\pi$
$101$	−3.94553	−0.392595	−0.196297	+	0.980544i	$0.562892\pi$
$102$	9.10183	0.901215
$103$	−4.88292	−0.481128	−0.240564	−	0.970633i	$-0.577332\pi$
$103$	−4.88292	−0.481128	−0.240564	+	0.970633i	$0.577332\pi$
$104$	2.11446	0.207340
$105$	4.79732	0.468170
$106$	21.7027	2.10796
$107$	−16.6853	−1.61303	−0.806515	−	0.591213i	$-0.798649\pi$
$107$	−16.6853	−1.61303	−0.806515	+	0.591213i	$0.798649\pi$
$108$	−1.20789	−0.116229
$109$	7.67038	0.734689	0.367345	−	0.930085i	$-0.380267\pi$
$109$	7.67038	0.734689	0.367345	+	0.930085i	$0.380267\pi$
$110$	−11.0035	−1.04914
$111$	1.77364	0.168347
$112$	23.7793	2.24693
$113$	−10.4413	−0.982234	−0.491117	−	0.871094i	$-0.663411\pi$
$113$	−10.4413	−0.982234	−0.491117	+	0.871094i	$0.663411\pi$
$114$	5.07484	0.475302
$115$	0	0
$116$	7.19577	0.668110
$117$	−1.49041	−0.137788
$118$	2.66210	0.245066
$119$	24.3791	2.23483
$120$	1.41871	0.129510
$121$	26.7435	2.43123
$122$	−4.68862	−0.424488
$123$	−4.42596	−0.399075
$124$	−8.53156	−0.766157
$125$	1.00000	0.0894427
$126$	−8.59228	−0.765461
$127$	1.93734	0.171911	0.0859556	−	0.996299i	$-0.472606\pi$
$127$	1.93734	0.171911	0.0859556	+	0.996299i	$0.472606\pi$
$128$	10.4595	0.924502
$129$	0.0523310	0.00460749
$130$	−2.66941	−0.234123
$131$	2.57437	0.224923	0.112462	−	0.993656i	$-0.464126\pi$
$131$	2.57437	0.224923	0.112462	+	0.993656i	$0.464126\pi$
$132$	7.42077	0.645895
$133$	13.5929	1.17865
$134$	4.28926	0.370535
$135$	−1.00000	−0.0860663
$136$	7.20963	0.618221
$137$	−13.8526	−1.18351	−0.591755	−	0.806118i	$-0.701565\pi$
$137$	−13.8526	−1.18351	−0.591755	+	0.806118i	$0.701565\pi$
$138$	0	0
$139$	−7.71491	−0.654370	−0.327185	−	0.944960i	$-0.606100\pi$
$139$	−7.71491	−0.654370	−0.327185	+	0.944960i	$0.606100\pi$
$140$	−5.79464	−0.489737
$141$	−9.00757	−0.758574
$142$	−26.5251	−2.22594
$143$	9.15644	0.765700
$144$	−4.95678	−0.413065
$145$	5.95729	0.494726
$146$	−6.20733	−0.513723
$147$	−16.0143	−1.32084
$148$	−2.14237	−0.176102
$149$	8.85312	0.725276	0.362638	−	0.931930i	$-0.381876\pi$
$149$	8.85312	0.725276	0.362638	+	0.931930i	$0.381876\pi$
$150$	−1.79106	−0.146239
$151$	−2.75598	−0.224279	−0.112139	−	0.993692i	$-0.535770\pi$
$151$	−2.75598	−0.224279	−0.112139	+	0.993692i	$0.535770\pi$
$152$	4.01982	0.326051
$153$	−5.08181	−0.410840
$154$	52.7873	4.25372
$155$	−7.06318	−0.567328
$156$	1.80025	0.144136
$157$	−14.5043	−1.15757	−0.578785	−	0.815480i	$-0.696473\pi$
$157$	−14.5043	−1.15757	−0.578785	+	0.815480i	$0.696473\pi$
$158$	2.54077	0.202132
$159$	−12.1173	−0.960961
$160$	−6.04046	−0.477540
$161$	0	0
$162$	1.79106	0.140719
$163$	−21.1162	−1.65395	−0.826975	−	0.562238i	$-0.809940\pi$
$163$	−21.1162	−1.65395	−0.826975	+	0.562238i	$0.809940\pi$
$164$	5.34608	0.417459
$165$	6.14357	0.478277
$166$	17.5024	1.35845
$167$	−2.24724	−0.173896	−0.0869482	−	0.996213i	$-0.527711\pi$
$167$	−2.24724	−0.173896	−0.0869482	+	0.996213i	$0.527711\pi$
$168$	−6.80602	−0.525096
$169$	−10.7787	−0.829129
$170$	−9.10183	−0.698078
$171$	−2.83343	−0.216678
$172$	−0.0632102	−0.00481973
$173$	14.9788	1.13881	0.569407	−	0.822056i	$-0.307173\pi$
$173$	14.9788	1.13881	0.569407	+	0.822056i	$0.307173\pi$
$174$	−10.6699	−0.808880
$175$	−4.79732	−0.362643
$176$	30.4523	2.29543
$177$	−1.48633	−0.111719
$178$	10.7903	0.808764
$179$	−8.62582	−0.644724	−0.322362	−	0.946616i	$-0.604477\pi$
$179$	−8.62582	−0.644724	−0.322362	+	0.946616i	$0.604477\pi$
$180$	1.20789	0.0900309
$181$	−2.26434	−0.168307	−0.0841534	−	0.996453i	$-0.526819\pi$
$181$	−2.26434	−0.168307	−0.0841534	+	0.996453i	$0.526819\pi$
$182$	12.8060	0.949246
$183$	2.61779	0.193513
$184$	0	0
$185$	−1.77364	−0.130401
$186$	12.6506	0.927585
$187$	31.2205	2.28307
$188$	10.8802	0.793518
$189$	4.79732	0.348954
$190$	−5.07484	−0.368168
$191$	−9.97822	−0.721999	−0.360999	−	0.932566i	$-0.617564\pi$
$191$	−9.97822	−0.721999	−0.360999	+	0.932566i	$0.617564\pi$
$192$	0.905260	0.0653315
$193$	−4.59577	−0.330810	−0.165405	−	0.986226i	$-0.552893\pi$
$193$	−4.59577	−0.330810	−0.165405	+	0.986226i	$0.552893\pi$
$194$	−1.02919	−0.0738915
$195$	1.49041	0.106730
$196$	19.3435	1.38168
$197$	−20.0189	−1.42629	−0.713143	−	0.701018i	$-0.752729\pi$
$197$	−20.0189	−1.42629	−0.713143	+	0.701018i	$0.752729\pi$
$198$	−11.0035	−0.781985
$199$	−24.3391	−1.72535	−0.862676	−	0.505756i	$-0.831213\pi$
$199$	−24.3391	−1.72535	−0.862676	+	0.505756i	$0.831213\pi$
$200$	−1.41871	−0.100318
$201$	−2.39482	−0.168917
$202$	−7.06667	−0.497209
$203$	−28.5790	−2.00586
$204$	6.13828	0.429766
$205$	4.42596	0.309122
$206$	−8.74559	−0.609334
$207$	0	0
$208$	7.38764	0.512240
$209$	17.4074	1.20409
$210$	8.59228	0.592924
$211$	27.4941	1.89277	0.946385	−	0.323041i	$-0.104705\pi$
$211$	27.4941	1.89277	0.946385	+	0.323041i	$0.104705\pi$
$212$	14.6363	1.00523
$213$	14.8098	1.01475
$214$	−29.8844	−2.04285
$215$	−0.0523310	−0.00356894
$216$	1.41871	0.0965312
$217$	33.8843	2.30022
$218$	13.7381	0.930462
$219$	3.46573	0.234193
$220$	−7.42077	−0.500308
$221$	7.57399	0.509482
$222$	3.17670	0.213206
$223$	13.3191	0.891915	0.445957	−	0.895054i	$-0.352863\pi$
$223$	13.3191	0.891915	0.445957	+	0.895054i	$0.352863\pi$
$224$	28.9780	1.93618
$225$	1.00000	0.0666667
$226$	−18.7010	−1.24397
$227$	10.3331	0.685835	0.342918	−	0.939366i	$-0.388585\pi$
$227$	10.3331	0.685835	0.342918	+	0.939366i	$0.388585\pi$
$228$	3.42248	0.226659
$229$	22.7145	1.50101	0.750507	−	0.660862i	$-0.229809\pi$
$229$	22.7145	1.50101	0.750507	+	0.660862i	$0.229809\pi$
$230$	0	0
$231$	−29.4727	−1.93916
$232$	−8.45169	−0.554880
$233$	−7.31191	−0.479019	−0.239510	−	0.970894i	$-0.576987\pi$
$233$	−7.31191	−0.479019	−0.239510	+	0.970894i	$0.576987\pi$
$234$	−2.66941	−0.174505
$235$	9.00757	0.587589
$236$	1.79532	0.116866
$237$	−1.41858	−0.0921469
$238$	43.6644	2.83034
$239$	11.6690	0.754803	0.377401	−	0.926050i	$-0.376818\pi$
$239$	11.6690	0.754803	0.377401	+	0.926050i	$0.376818\pi$
$240$	4.95678	0.319959
$241$	−12.7851	−0.823560	−0.411780	−	0.911283i	$-0.635093\pi$
$241$	−12.7851	−0.823560	−0.411780	+	0.911283i	$0.635093\pi$
$242$	47.8992	3.07908
$243$	−1.00000	−0.0641500
$244$	−3.16201	−0.202427
$245$	16.0143	1.02311
$246$	−7.92716	−0.505417
$247$	4.22297	0.268701
$248$	10.0206	0.636310
$249$	−9.77212	−0.619283
$250$	1.79106	0.113277
$251$	−11.7699	−0.742911	−0.371455	−	0.928451i	$-0.621141\pi$
$251$	−11.7699	−0.742911	−0.371455	+	0.928451i	$0.621141\pi$
$252$	−5.79464	−0.365028
$253$	0	0
$254$	3.46989	0.217720
$255$	5.08181	0.318236
$256$	20.5442	1.28401
$257$	10.1369	0.632324	0.316162	−	0.948705i	$-0.397606\pi$
$257$	10.1369	0.632324	0.316162	+	0.948705i	$0.397606\pi$
$258$	0.0937279	0.00583524
$259$	8.50874	0.528707
$260$	−1.80025	−0.111647
$261$	5.95729	0.368747
$262$	4.61084	0.284859
$263$	−2.27769	−0.140448	−0.0702242	−	0.997531i	$-0.522371\pi$
$263$	−2.27769	−0.140448	−0.0702242	+	0.997531i	$0.522371\pi$
$264$	−8.71596	−0.536431
$265$	12.1173	0.744357
$266$	24.3456	1.49273
$267$	−6.02452	−0.368694
$268$	2.89268	0.176698
$269$	−16.0257	−0.977105	−0.488553	−	0.872534i	$-0.662475\pi$
$269$	−16.0257	−0.977105	−0.488553	+	0.872534i	$0.662475\pi$
$270$	−1.79106	−0.109000
$271$	20.6004	1.25139	0.625694	−	0.780069i	$-0.284816\pi$
$271$	20.6004	1.25139	0.625694	+	0.780069i	$0.284816\pi$
$272$	25.1894	1.52733
$273$	−7.14997	−0.432736
$274$	−24.8109	−1.49888
$275$	−6.14357	−0.370471
$276$	0	0
$277$	−23.0023	−1.38207	−0.691036	−	0.722821i	$-0.742845\pi$
$277$	−23.0023	−1.38207	−0.691036	+	0.722821i	$0.742845\pi$
$278$	−13.8179	−0.828740
$279$	−7.06318	−0.422862
$280$	6.80602	0.406737
$281$	−13.8157	−0.824177	−0.412089	−	0.911144i	$-0.635201\pi$
$281$	−13.8157	−0.824177	−0.412089	+	0.911144i	$0.635201\pi$
$282$	−16.1331	−0.960711
$283$	−25.1002	−1.49205	−0.746027	−	0.665916i	$-0.768041\pi$
$283$	−25.1002	−1.49205	−0.746027	+	0.665916i	$0.768041\pi$
$284$	−17.8886	−1.06149
$285$	2.83343	0.167838
$286$	16.3997	0.969736
$287$	−21.2327	−1.25333
$288$	−6.04046	−0.355938
$289$	8.82483	0.519108
$290$	10.6699	0.626556
$291$	0.574626	0.0336852
$292$	−4.18623	−0.244981
$293$	3.92640	0.229383	0.114691	−	0.993401i	$-0.463412\pi$
$293$	3.92640	0.229383	0.114691	+	0.993401i	$0.463412\pi$
$294$	−28.6825	−1.67280
$295$	1.48633	0.0865373
$296$	2.51629	0.146256
$297$	6.14357	0.356486
$298$	15.8565	0.918540
$299$	0	0
$300$	−1.20789	−0.0697377
$301$	0.251048	0.0144702
$302$	−4.93613	−0.284042
$303$	3.94553	0.226665
$304$	14.0447	0.805518
$305$	−2.61779	−0.149894
$306$	−9.10183	−0.520317
$307$	0.589552	0.0336475	0.0168237	−	0.999858i	$-0.494645\pi$
$307$	0.589552	0.0336475	0.0168237	+	0.999858i	$0.494645\pi$
$308$	35.5998	2.02849
$309$	4.88292	0.277779
$310$	−12.6506	−0.718504
$311$	5.85652	0.332093	0.166046	−	0.986118i	$-0.446900\pi$
$311$	5.85652	0.332093	0.166046	+	0.986118i	$0.446900\pi$
$312$	−2.11446	−0.119708
$313$	−20.5501	−1.16156	−0.580781	−	0.814060i	$-0.697253\pi$
$313$	−20.5501	−1.16156	−0.580781	+	0.814060i	$0.697253\pi$
$314$	−25.9781	−1.46603
$315$	−4.79732	−0.270298
$316$	1.71349	0.0963916
$317$	31.9354	1.79367	0.896834	−	0.442367i	$-0.145861\pi$
$317$	31.9354	1.79367	0.896834	+	0.442367i	$0.145861\pi$
$318$	−21.7027	−1.21703
$319$	−36.5991	−2.04915
$320$	−0.905260	−0.0506056
$321$	16.6853	0.931284
$322$	0	0
$323$	14.3990	0.801180
$324$	1.20789	0.0671051
$325$	−1.49041	−0.0826731
$326$	−37.8204	−2.09468
$327$	−7.67038	−0.424173
$328$	−6.27916	−0.346709
$329$	−43.2122	−2.38237
$330$	11.0035	0.605723
$331$	10.2498	0.563377	0.281689	−	0.959506i	$-0.409105\pi$
$331$	10.2498	0.563377	0.281689	+	0.959506i	$0.409105\pi$
$332$	11.8037	0.647810
$333$	−1.77364	−0.0971951
$334$	−4.02493	−0.220235
$335$	2.39482	0.130843
$336$	−23.7793	−1.29727
$337$	23.9963	1.30716	0.653580	−	0.756857i	$-0.273266\pi$
$337$	23.9963	1.30716	0.653580	+	0.756857i	$0.273266\pi$
$338$	−19.3052	−1.05007
$339$	10.4413	0.567093
$340$	−6.13828	−0.332895
$341$	43.3932	2.34987
$342$	−5.07484	−0.274416
$343$	−43.2444	−2.33498
$344$	0.0742426	0.00400289
$345$	0	0
$346$	26.8279	1.44227
$347$	15.4158	0.827563	0.413781	−	0.910376i	$-0.364208\pi$
$347$	15.4158	0.827563	0.413781	+	0.910376i	$0.364208\pi$
$348$	−7.19577	−0.385734
$349$	22.2867	1.19298	0.596491	−	0.802620i	$-0.296561\pi$
$349$	22.2867	1.19298	0.596491	+	0.802620i	$0.296561\pi$
$350$	−8.59228	−0.459277
$351$	1.49041	0.0795522
$352$	37.1100	1.97797
$353$	−22.1847	−1.18077	−0.590385	−	0.807122i	$-0.701024\pi$
$353$	−22.1847	−1.18077	−0.590385	+	0.807122i	$0.701024\pi$
$354$	−2.66210	−0.141489
$355$	−14.8098	−0.786020
$356$	7.27696	0.385678
$357$	−24.3791	−1.29028
$358$	−15.4494	−0.816524
$359$	26.1337	1.37929	0.689643	−	0.724150i	$-0.257767\pi$
$359$	26.1337	1.37929	0.689643	+	0.724150i	$0.257767\pi$
$360$	−1.41871	−0.0747727
$361$	−10.9717	−0.577456
$362$	−4.05556	−0.213156
$363$	−26.7435	−1.40367
$364$	8.63639	0.452670
$365$	−3.46573	−0.181405
$366$	4.68862	0.245078
$367$	−29.5472	−1.54235	−0.771175	−	0.636623i	$-0.780331\pi$
$367$	−29.5472	−1.54235	−0.771175	+	0.636623i	$0.780331\pi$
$368$	0	0
$369$	4.42596	0.230406
$370$	−3.17670	−0.165149
$371$	−58.1304	−3.01798
$372$	8.53156	0.442341
$373$	−16.5290	−0.855840	−0.427920	−	0.903817i	$-0.640754\pi$
$373$	−16.5290	−0.855840	−0.427920	+	0.903817i	$0.640754\pi$
$374$	55.9178	2.89144
$375$	−1.00000	−0.0516398
$376$	−12.7792	−0.659034
$377$	−8.87881	−0.457282
$378$	8.59228	0.441939
$379$	9.53718	0.489892	0.244946	−	0.969537i	$-0.421230\pi$
$379$	9.53718	0.489892	0.244946	+	0.969537i	$0.421230\pi$
$380$	−3.42248	−0.175569
$381$	−1.93734	−0.0992530
$382$	−17.8716	−0.914390
$383$	27.0301	1.38117	0.690586	−	0.723250i	$-0.257353\pi$
$383$	27.0301	1.38117	0.690586	+	0.723250i	$0.257353\pi$
$384$	−10.4595	−0.533762
$385$	29.4727	1.50207
$386$	−8.23129	−0.418962
$387$	−0.0523310	−0.00266013
$388$	−0.694086	−0.0352369
$389$	16.8778	0.855737	0.427869	−	0.903841i	$-0.359265\pi$
$389$	16.8778	0.855737	0.427869	+	0.903841i	$0.359265\pi$
$390$	2.66941	0.135171
$391$	0	0
$392$	−22.7197	−1.14752
$393$	−2.57437	−0.129860
$394$	−35.8550	−1.80635
$395$	1.41858	0.0713767
$396$	−7.42077	−0.372908
$397$	−9.42922	−0.473239	−0.236619	−	0.971602i	$-0.576039\pi$
$397$	−9.42922	−0.473239	−0.236619	+	0.971602i	$0.576039\pi$
$398$	−43.5927	−2.18511
$399$	−13.5929	−0.680495
$400$	−4.95678	−0.247839
$401$	13.1636	0.657359	0.328680	−	0.944441i	$-0.393396\pi$
$401$	13.1636	0.657359	0.328680	+	0.944441i	$0.393396\pi$
$402$	−4.28926	−0.213929
$403$	10.5270	0.524389
$404$	−4.76577	−0.237106
$405$	1.00000	0.0496904
$406$	−51.1867	−2.54036
$407$	10.8965	0.540120
$408$	−7.20963	−0.356930
$409$	−5.29082	−0.261614	−0.130807	−	0.991408i	$-0.541757\pi$
$409$	−5.29082	−0.261614	−0.130807	+	0.991408i	$0.541757\pi$
$410$	7.92716	0.391494
$411$	13.8526	0.683299
$412$	−5.89804	−0.290575
$413$	−7.13039	−0.350863
$414$	0	0
$415$	9.77212	0.479695
$416$	9.00276	0.441397
$417$	7.71491	0.377801
$418$	31.1777	1.52495
$419$	9.94793	0.485988	0.242994	−	0.970028i	$-0.421870\pi$
$419$	9.94793	0.485988	0.242994	+	0.970028i	$0.421870\pi$
$420$	5.79464	0.282750
$421$	2.89894	0.141286	0.0706428	−	0.997502i	$-0.477495\pi$
$421$	2.89894	0.141286	0.0706428	+	0.997502i	$0.477495\pi$
$422$	49.2435	2.39714
$423$	9.00757	0.437963
$424$	−17.1909	−0.834864
$425$	−5.08181	−0.246504
$426$	26.5251	1.28515
$427$	12.5584	0.607743
$428$	−20.1541	−0.974183
$429$	−9.15644	−0.442077
$430$	−0.0937279	−0.00451996
$431$	22.9411	1.10504	0.552518	−	0.833501i	$-0.313667\pi$
$431$	22.9411	1.10504	0.552518	+	0.833501i	$0.313667\pi$
$432$	4.95678	0.238483
$433$	11.4893	0.552138	0.276069	−	0.961138i	$-0.410968\pi$
$433$	11.4893	0.552138	0.276069	+	0.961138i	$0.410968\pi$
$434$	60.6888	2.91316
$435$	−5.95729	−0.285630
$436$	9.26499	0.443712
$437$	0	0
$438$	6.20733	0.296598
$439$	1.44743	0.0690821	0.0345411	−	0.999403i	$-0.489003\pi$
$439$	1.44743	0.0690821	0.0345411	+	0.999403i	$0.489003\pi$
$440$	8.71596	0.415517
$441$	16.0143	0.762585
$442$	13.5655	0.645243
$443$	18.0941	0.859677	0.429838	−	0.902906i	$-0.358571\pi$
$443$	18.0941	0.859677	0.429838	+	0.902906i	$0.358571\pi$
$444$	2.14237	0.101672
$445$	6.02452	0.285589
$446$	23.8553	1.12958
$447$	−8.85312	−0.418738
$448$	4.34282	0.205179
$449$	−4.34573	−0.205088	−0.102544	−	0.994728i	$-0.532698\pi$
$449$	−4.34573	−0.205088	−0.102544	+	0.994728i	$0.532698\pi$
$450$	1.79106	0.0844313
$451$	−27.1912	−1.28038
$452$	−12.6119	−0.593216
$453$	2.75598	0.129487
$454$	18.5073	0.868589
$455$	7.14997	0.335196
$456$	−4.01982	−0.188245
$457$	−21.5170	−1.00652	−0.503262	−	0.864134i	$-0.667867\pi$
$457$	−21.5170	−1.00652	−0.503262	+	0.864134i	$0.667867\pi$
$458$	40.6829	1.90099
$459$	5.08181	0.237199
$460$	0	0
$461$	17.3853	0.809715	0.404857	−	0.914380i	$-0.367321\pi$
$461$	17.3853	0.809715	0.404857	+	0.914380i	$0.367321\pi$
$462$	−52.7873	−2.45589
$463$	−13.8927	−0.645647	−0.322823	−	0.946459i	$-0.604632\pi$
$463$	−13.8927	−0.645647	−0.322823	+	0.946459i	$0.604632\pi$
$464$	−29.5290	−1.37085
$465$	7.06318	0.327547
$466$	−13.0961	−0.606663
$467$	22.6331	1.04734	0.523668	−	0.851923i	$-0.324563\pi$
$467$	22.6331	1.04734	0.523668	+	0.851923i	$0.324563\pi$
$468$	−1.80025	−0.0832168
$469$	−11.4887	−0.530499
$470$	16.1331	0.744164
$471$	14.5043	0.668323
$472$	−2.10867	−0.0970595
$473$	0.321499	0.0147826
$474$	−2.54077	−0.116701
$475$	−2.83343	−0.130007
$476$	29.4473	1.34971
$477$	12.1173	0.554811
$478$	20.8998	0.955935
$479$	3.85429	0.176107	0.0880534	−	0.996116i	$-0.471935\pi$
$479$	3.85429	0.176107	0.0880534	+	0.996116i	$0.471935\pi$
$480$	6.04046	0.275708
$481$	2.64346	0.120531
$482$	−22.8988	−1.04301
$483$	0	0
$484$	32.3033	1.46833
$485$	−0.574626	−0.0260924
$486$	−1.79106	−0.0812441
$487$	20.5081	0.929312	0.464656	−	0.885491i	$-0.346178\pi$
$487$	20.5081	0.929312	0.464656	+	0.885491i	$0.346178\pi$
$488$	3.71389	0.168120
$489$	21.1162	0.954909
$490$	28.6825	1.29574
$491$	8.51788	0.384407	0.192203	−	0.981355i	$-0.438437\pi$
$491$	8.51788	0.384407	0.192203	+	0.981355i	$0.438437\pi$
$492$	−5.34608	−0.241020
$493$	−30.2739	−1.36347
$494$	7.56359	0.340302
$495$	−6.14357	−0.276133
$496$	35.0106	1.57202
$497$	71.0471	3.18690
$498$	−17.5024	−0.784303
$499$	13.2927	0.595065	0.297532	−	0.954712i	$-0.403836\pi$
$499$	13.2927	0.595065	0.297532	+	0.954712i	$0.403836\pi$
$500$	1.20789	0.0540186
$501$	2.24724	0.100399
$502$	−21.0806	−0.940874
$503$	2.73832	0.122095	0.0610477	−	0.998135i	$-0.480556\pi$
$503$	2.73832	0.122095	0.0610477	+	0.998135i	$0.480556\pi$
$504$	6.80602	0.303164
$505$	−3.94553	−0.175574
$506$	0	0
$507$	10.7787	0.478698
$508$	2.34010	0.103825
$509$	−34.8173	−1.54325	−0.771624	−	0.636079i	$-0.780555\pi$
$509$	−34.8173	−1.54325	−0.771624	+	0.636079i	$0.780555\pi$
$510$	9.10183	0.403036
$511$	16.6262	0.735501
$512$	15.8768	0.701660
$513$	2.83343	0.125099
$514$	18.1558	0.800819
$515$	−4.88292	−0.215167
$516$	0.0632102	0.00278267
$517$	−55.3387	−2.43379
$518$	15.2396	0.669592
$519$	−14.9788	−0.657495
$520$	2.11446	0.0927254
$521$	38.9520	1.70652	0.853259	−	0.521487i	$-0.174622\pi$
$521$	38.9520	1.70652	0.853259	+	0.521487i	$0.174622\pi$
$522$	10.6699	0.467007
$523$	−19.5834	−0.856321	−0.428160	−	0.903703i	$-0.640838\pi$
$523$	−19.5834	−0.856321	−0.428160	+	0.903703i	$0.640838\pi$
$524$	3.10955	0.135842
$525$	4.79732	0.209372
$526$	−4.07948	−0.177874
$527$	35.8938	1.56356
$528$	−30.4523	−1.32527
$529$	0	0
$530$	21.7027	0.942706
$531$	1.48633	0.0645011
$532$	16.4187	0.711842
$533$	−6.59650	−0.285726
$534$	−10.7903	−0.466940
$535$	−16.6853	−0.721369
$536$	−3.39755	−0.146752
$537$	8.62582	0.372232
$538$	−28.7030	−1.23747
$539$	−98.3849	−4.23774
$540$	−1.20789	−0.0519794
$541$	23.8345	1.02473	0.512363	−	0.858769i	$-0.328770\pi$
$541$	23.8345	1.02473	0.512363	+	0.858769i	$0.328770\pi$
$542$	36.8966	1.58484
$543$	2.26434	0.0971720
$544$	30.6965	1.31610
$545$	7.67038	0.328563
$546$	−12.8060	−0.548047
$547$	−8.78004	−0.375407	−0.187704	−	0.982226i	$-0.560104\pi$
$547$	−8.78004	−0.375407	−0.187704	+	0.982226i	$0.560104\pi$
$548$	−16.7325	−0.714776
$549$	−2.61779	−0.111725
$550$	−11.0035	−0.469191
$551$	−16.8796	−0.719094
$552$	0	0
$553$	−6.80540	−0.289395
$554$	−41.1984	−1.75035
$555$	1.77364	0.0752870
$556$	−9.31878	−0.395204
$557$	−28.4141	−1.20394	−0.601972	−	0.798517i	$-0.705618\pi$
$557$	−28.4141	−1.20394	−0.601972	+	0.798517i	$0.705618\pi$
$558$	−12.6506	−0.535541
$559$	0.0779946	0.00329882
$560$	23.7793	1.00486
$561$	−31.2205	−1.31813
$562$	−24.7448	−1.04380
$563$	−9.82226	−0.413959	−0.206980	−	0.978345i	$-0.566363\pi$
$563$	−9.82226	−0.413959	−0.206980	+	0.978345i	$0.566363\pi$
$564$	−10.8802	−0.458138
$565$	−10.4413	−0.439268
$566$	−44.9560	−1.88964
$567$	−4.79732	−0.201468
$568$	21.0108	0.881593
$569$	14.9848	0.628195	0.314098	−	0.949391i	$-0.398298\pi$
$569$	14.9848	0.628195	0.314098	+	0.949391i	$0.398298\pi$
$570$	5.07484	0.212562
$571$	24.5098	1.02570	0.512851	−	0.858478i	$-0.328589\pi$
$571$	24.5098	1.02570	0.512851	+	0.858478i	$0.328589\pi$
$572$	11.0600	0.462442
$573$	9.97822	0.416846
$574$	−38.0291	−1.58730
$575$	0	0
$576$	−0.905260	−0.0377192
$577$	17.6235	0.733677	0.366838	−	0.930285i	$-0.380440\pi$
$577$	17.6235	0.733677	0.366838	+	0.930285i	$0.380440\pi$
$578$	15.8058	0.657435
$579$	4.59577	0.190994
$580$	7.19577	0.298788
$581$	−46.8800	−1.94491
$582$	1.02919	0.0426613
$583$	−74.4433	−3.08313
$584$	4.91688	0.203462
$585$	−1.49041	−0.0616209
$586$	7.03242	0.290507
$587$	−6.01569	−0.248294	−0.124147	−	0.992264i	$-0.539619\pi$
$587$	−6.01569	−0.248294	−0.124147	+	0.992264i	$0.539619\pi$
$588$	−19.3435	−0.797713
$589$	20.0130	0.824623
$590$	2.66210	0.109597
$591$	20.0189	0.823467
$592$	8.79156	0.361331
$593$	11.0366	0.453219	0.226610	−	0.973986i	$-0.427236\pi$
$593$	11.0366	0.453219	0.226610	+	0.973986i	$0.427236\pi$
$594$	11.0035	0.451479
$595$	24.3791	0.999445
$596$	10.6936	0.438027
$597$	24.3391	0.996133
$598$	0	0
$599$	−18.0396	−0.737079	−0.368540	−	0.929612i	$-0.620142\pi$
$599$	−18.0396	−0.737079	−0.368540	+	0.929612i	$0.620142\pi$
$600$	1.41871	0.0579187
$601$	23.3045	0.950609	0.475305	−	0.879821i	$-0.342338\pi$
$601$	23.3045	0.950609	0.475305	+	0.879821i	$0.342338\pi$
$602$	0.449643	0.0183261
$603$	2.39482	0.0975244
$604$	−3.32893	−0.135452
$605$	26.7435	1.08728
$606$	7.06667	0.287064
$607$	−7.75042	−0.314580	−0.157290	−	0.987552i	$-0.550276\pi$
$607$	−7.75042	−0.314580	−0.157290	+	0.987552i	$0.550276\pi$
$608$	17.1152	0.694114
$609$	28.5790	1.15808
$610$	−4.68862	−0.189837
$611$	−13.4250	−0.543116
$612$	−6.13828	−0.248125
$613$	1.66497	0.0672476	0.0336238	−	0.999435i	$-0.489295\pi$
$613$	1.66497	0.0672476	0.0336238	+	0.999435i	$0.489295\pi$
$614$	1.05592	0.0426135
$615$	−4.42596	−0.178472
$616$	−41.8133	−1.68470
$617$	6.84666	0.275636	0.137818	−	0.990458i	$-0.455991\pi$
$617$	6.84666	0.275636	0.137818	+	0.990458i	$0.455991\pi$
$618$	8.74559	0.351799
$619$	25.9342	1.04238	0.521191	−	0.853440i	$-0.325488\pi$
$619$	25.9342	1.04238	0.521191	+	0.853440i	$0.325488\pi$
$620$	−8.53156	−0.342636
$621$	0	0
$622$	10.4894	0.420586
$623$	−28.9015	−1.15792
$624$	−7.38764	−0.295742
$625$	1.00000	0.0400000
$626$	−36.8065	−1.47108
$627$	−17.4074	−0.695184
$628$	−17.5196	−0.699109
$629$	9.01333	0.359385
$630$	−8.59228	−0.342325
$631$	45.0066	1.79169	0.895843	−	0.444371i	$-0.146573\pi$
$631$	45.0066	1.79169	0.895843	+	0.444371i	$0.146573\pi$
$632$	−2.01256	−0.0800554
$633$	−27.4941	−1.09279
$634$	57.1981	2.27163
$635$	1.93734	0.0768811
$636$	−14.6363	−0.580369
$637$	−23.8678	−0.945678
$638$	−65.5511	−2.59519
$639$	−14.8098	−0.585865
$640$	10.4595	0.413450
$641$	9.66092	0.381583	0.190792	−	0.981631i	$-0.438895\pi$
$641$	9.66092	0.381583	0.190792	+	0.981631i	$0.438895\pi$
$642$	29.8844	1.17944
$643$	18.1752	0.716761	0.358381	−	0.933576i	$-0.383329\pi$
$643$	18.1752	0.716761	0.358381	+	0.933576i	$0.383329\pi$
$644$	0	0
$645$	0.0523310	0.00206053
$646$	25.7894	1.01467
$647$	−23.9495	−0.941552	−0.470776	−	0.882253i	$-0.656026\pi$
$647$	−23.9495	−0.941552	−0.470776	+	0.882253i	$0.656026\pi$
$648$	−1.41871	−0.0557323
$649$	−9.13136	−0.358437
$650$	−2.66941	−0.104703
$651$	−33.8843	−1.32803
$652$	−25.5061	−0.998896
$653$	−38.6858	−1.51389	−0.756946	−	0.653478i	$-0.773309\pi$
$653$	−38.6858	−1.51389	−0.756946	+	0.653478i	$0.773309\pi$
$654$	−13.7381	−0.537202
$655$	2.57437	0.100589
$656$	−21.9385	−0.856555
$657$	−3.46573	−0.135211
$658$	−77.3956	−3.01719
$659$	−12.7163	−0.495356	−0.247678	−	0.968842i	$-0.579668\pi$
$659$	−12.7163	−0.495356	−0.247678	+	0.968842i	$0.579668\pi$
$660$	7.42077	0.288853
$661$	20.2247	0.786651	0.393325	−	0.919399i	$-0.371325\pi$
$661$	20.2247	0.786651	0.393325	+	0.919399i	$0.371325\pi$
$662$	18.3579	0.713501
$663$	−7.57399	−0.294149
$664$	−13.8638	−0.538021
$665$	13.5929	0.527109
$666$	−3.17670	−0.123095
$667$	0	0
$668$	−2.71442	−0.105024
$669$	−13.3191	−0.514947
$670$	4.28926	0.165708
$671$	16.0826	0.620862
$672$	−28.9780	−1.11785
$673$	−1.66654	−0.0642405	−0.0321203	−	0.999484i	$-0.510226\pi$
$673$	−1.66654	−0.0642405	−0.0321203	+	0.999484i	$0.510226\pi$
$674$	42.9788	1.65548
$675$	−1.00000	−0.0384900
$676$	−13.0195	−0.500749
$677$	36.6586	1.40890	0.704452	−	0.709752i	$-0.251193\pi$
$677$	36.6586	1.40890	0.704452	+	0.709752i	$0.251193\pi$
$678$	18.7010	0.718206
$679$	2.75667	0.105791
$680$	7.20963	0.276477
$681$	−10.3331	−0.395967
$682$	77.7197	2.97604
$683$	−12.5530	−0.480328	−0.240164	−	0.970732i	$-0.577201\pi$
$683$	−12.5530	−0.480328	−0.240164	+	0.970732i	$0.577201\pi$
$684$	−3.42248	−0.130862
$685$	−13.8526	−0.529281
$686$	−77.4532	−2.95718
$687$	−22.7145	−0.866611
$688$	0.259393	0.00988927
$689$	−18.0597	−0.688019
$690$	0	0
$691$	47.0592	1.79021	0.895107	−	0.445851i	$-0.147099\pi$
$691$	47.0592	1.79021	0.895107	+	0.445851i	$0.147099\pi$
$692$	18.0927	0.687782
$693$	29.4727	1.11957
$694$	27.6106	1.04808
$695$	−7.71491	−0.292643
$696$	8.45169	0.320360
$697$	−22.4919	−0.851942
$698$	39.9169	1.51088
$699$	7.31191	0.276562
$700$	−5.79464	−0.219017
$701$	48.4173	1.82869	0.914347	−	0.404931i	$-0.132705\pi$
$701$	48.4173	1.82869	0.914347	+	0.404931i	$0.132705\pi$
$702$	2.66941	0.100750
$703$	5.02550	0.189540
$704$	5.56153	0.209608
$705$	−9.00757	−0.339245
$706$	−39.7340	−1.49541
$707$	18.9280	0.711859
$708$	−1.79532	−0.0674724
$709$	10.3995	0.390562	0.195281	−	0.980747i	$-0.437438\pi$
$709$	10.3995	0.390562	0.195281	+	0.980747i	$0.437438\pi$
$710$	−26.5251	−0.995471
$711$	1.41858	0.0532010
$712$	−8.54706	−0.320314
$713$	0	0
$714$	−43.6644	−1.63410
$715$	9.15644	0.342432
$716$	−10.4191	−0.389379
$717$	−11.6690	−0.435786
$718$	46.8071	1.74682
$719$	45.0109	1.67862	0.839312	−	0.543650i	$-0.182958\pi$
$719$	45.0109	1.67862	0.839312	+	0.543650i	$0.182958\pi$
$720$	−4.95678	−0.184728
$721$	23.4249	0.872389
$722$	−19.6509	−0.731331
$723$	12.7851	0.475482
$724$	−2.73507	−0.101648
$725$	5.95729	0.221248
$726$	−47.8992	−1.77771
$727$	47.1391	1.74829	0.874147	−	0.485661i	$-0.161421\pi$
$727$	47.1391	1.74829	0.874147	+	0.485661i	$0.161421\pi$
$728$	−10.1438	−0.375953
$729$	1.00000	0.0370370
$730$	−6.20733	−0.229744
$731$	0.265936	0.00983601
$732$	3.16201	0.116871
$733$	−38.1432	−1.40885	−0.704426	−	0.709777i	$-0.748796\pi$
$733$	−38.1432	−1.40885	−0.704426	+	0.709777i	$0.748796\pi$
$734$	−52.9207	−1.95334
$735$	−16.0143	−0.590695
$736$	0	0
$737$	−14.7127	−0.541950
$738$	7.92716	0.291803
$739$	−4.21544	−0.155067	−0.0775336	−	0.996990i	$-0.524705\pi$
$739$	−4.21544	−0.155067	−0.0775336	+	0.996990i	$0.524705\pi$
$740$	−2.14237	−0.0787551
$741$	−4.22297	−0.155135
$742$	−104.115	−3.82218
$743$	−4.15480	−0.152425	−0.0762125	−	0.997092i	$-0.524283\pi$
$743$	−4.15480	−0.152425	−0.0762125	+	0.997092i	$0.524283\pi$
$744$	−10.0206	−0.367374
$745$	8.85312	0.324353
$746$	−29.6045	−1.08390
$747$	9.77212	0.357543
$748$	37.7110	1.37885
$749$	80.0448	2.92477
$750$	−1.79106	−0.0654002
$751$	17.0999	0.623983	0.311992	−	0.950085i	$-0.399004\pi$
$751$	17.0999	0.623983	0.311992	+	0.950085i	$0.399004\pi$
$752$	−44.6486	−1.62817
$753$	11.7699	0.428920
$754$	−15.9025	−0.579134
$755$	−2.75598	−0.100300
$756$	5.79464	0.210749
$757$	1.60726	0.0584167	0.0292084	−	0.999573i	$-0.490701\pi$
$757$	1.60726	0.0584167	0.0292084	+	0.999573i	$0.490701\pi$
$758$	17.0816	0.620433
$759$	0	0
$760$	4.01982	0.145814
$761$	−42.3670	−1.53580	−0.767902	−	0.640568i	$-0.778699\pi$
$761$	−42.3670	−1.53580	−0.767902	+	0.640568i	$0.778699\pi$
$762$	−3.46989	−0.125701
$763$	−36.7973	−1.33215
$764$	−12.0526	−0.436048
$765$	−5.08181	−0.183733
$766$	48.4124	1.74921
$767$	−2.21524	−0.0799876
$768$	−20.5442	−0.741325
$769$	−15.4236	−0.556191	−0.278095	−	0.960553i	$-0.589703\pi$
$769$	−15.4236	−0.556191	−0.278095	+	0.960553i	$0.589703\pi$
$770$	52.7873	1.90232
$771$	−10.1369	−0.365072
$772$	−5.55119	−0.199792
$773$	−17.4864	−0.628941	−0.314470	−	0.949267i	$-0.601827\pi$
$773$	−17.4864	−0.628941	−0.314470	+	0.949267i	$0.601827\pi$
$774$	−0.0937279	−0.00336898
$775$	−7.06318	−0.253717
$776$	0.815229	0.0292650
$777$	−8.50874	−0.305249
$778$	30.2291	1.08377
$779$	−12.5407	−0.449315
$780$	1.80025	0.0644594
$781$	90.9848	3.25569
$782$	0	0
$783$	−5.95729	−0.212896
$784$	−79.3793	−2.83497
$785$	−14.5043	−0.517681
$786$	−4.61084	−0.164463
$787$	−7.16133	−0.255274	−0.127637	−	0.991821i	$-0.540739\pi$
$787$	−7.16133	−0.255274	−0.127637	+	0.991821i	$0.540739\pi$
$788$	−24.1807	−0.861400
$789$	2.27769	0.0810879
$790$	2.54077	0.0903964
$791$	50.0902	1.78100
$792$	8.71596	0.309708
$793$	3.90158	0.138549
$794$	−16.8883	−0.599343
$795$	−12.1173	−0.429755
$796$	−29.3990	−1.04202
$797$	9.47692	0.335690	0.167845	−	0.985813i	$-0.446319\pi$
$797$	9.47692	0.335690	0.167845	+	0.985813i	$0.446319\pi$
$798$	−24.3456	−0.861826
$799$	−45.7748	−1.61940
$800$	−6.04046	−0.213563
$801$	6.02452	0.212866
$802$	23.5768	0.832526
$803$	21.2920	0.751378
$804$	−2.89268	−0.102017
$805$	0	0
$806$	18.8545	0.664123
$807$	16.0257	0.564132
$808$	5.59757	0.196922
$809$	5.10354	0.179431	0.0897155	−	0.995967i	$-0.471404\pi$
$809$	5.10354	0.179431	0.0897155	+	0.995967i	$0.471404\pi$
$810$	1.79106	0.0629314
$811$	−1.56102	−0.0548149	−0.0274074	−	0.999624i	$-0.508725\pi$
$811$	−1.56102	−0.0548149	−0.0274074	+	0.999624i	$0.508725\pi$
$812$	−34.5204	−1.21143
$813$	−20.6004	−0.722489
$814$	19.5163	0.684046
$815$	−21.1162	−0.739669
$816$	−25.1894	−0.881807
$817$	0.148276	0.00518753
$818$	−9.47618	−0.331327
$819$	7.14997	0.249840
$820$	5.34608	0.186693
$821$	1.85328	0.0646797	0.0323399	−	0.999477i	$-0.489704\pi$
$821$	1.85328	0.0646797	0.0323399	+	0.999477i	$0.489704\pi$
$822$	24.8109	0.865378
$823$	−10.7202	−0.373684	−0.186842	−	0.982390i	$-0.559825\pi$
$823$	−10.7202	−0.373684	−0.186842	+	0.982390i	$0.559825\pi$
$824$	6.92746	0.241329
$825$	6.14357	0.213892
$826$	−12.7709	−0.444358
$827$	35.4376	1.23229	0.616143	−	0.787634i	$-0.288694\pi$
$827$	35.4376	1.23229	0.616143	+	0.787634i	$0.288694\pi$
$828$	0	0
$829$	18.1429	0.630130	0.315065	−	0.949070i	$-0.397974\pi$
$829$	18.1429	0.630130	0.315065	+	0.949070i	$0.397974\pi$
$830$	17.5024	0.607519
$831$	23.0023	0.797939
$832$	1.34921	0.0467754
$833$	−81.3816	−2.81970
$834$	13.8179	0.478474
$835$	−2.24724	−0.0777688
$836$	21.0262	0.727208
$837$	7.06318	0.244139
$838$	17.8173	0.615489
$839$	−40.2707	−1.39030	−0.695149	−	0.718865i	$-0.744662\pi$
$839$	−40.2707	−1.39030	−0.695149	+	0.718865i	$0.744662\pi$
$840$	−6.80602	−0.234830
$841$	6.48935	0.223771
$842$	5.19217	0.178934
$843$	13.8157	0.475839
$844$	33.2099	1.14313
$845$	−10.7787	−0.370798
$846$	16.1331	0.554667
$847$	−128.297	−4.40834
$848$	−60.0626	−2.06256
$849$	25.1002	0.861437
$850$	−9.10183	−0.312190
$851$	0	0
$852$	17.8886	0.612853
$853$	27.9795	0.958001	0.479001	−	0.877815i	$-0.340999\pi$
$853$	27.9795	0.958001	0.479001	+	0.877815i	$0.340999\pi$
$854$	22.4928	0.769688
$855$	−2.83343	−0.0969013
$856$	23.6717	0.809081
$857$	10.4321	0.356353	0.178177	−	0.983999i	$-0.442980\pi$
$857$	10.4321	0.356353	0.178177	+	0.983999i	$0.442980\pi$
$858$	−16.3997	−0.559878
$859$	−39.9963	−1.36466	−0.682329	−	0.731045i	$-0.739033\pi$
$859$	−39.9963	−1.36466	−0.682329	+	0.731045i	$0.739033\pi$
$860$	−0.0632102	−0.00215545
$861$	21.2327	0.723610
$862$	41.0889	1.39949
$863$	6.04363	0.205727	0.102864	−	0.994695i	$-0.467199\pi$
$863$	6.04363	0.205727	0.102864	+	0.994695i	$0.467199\pi$
$864$	6.04046	0.205501
$865$	14.9788	0.509293
$866$	20.5779	0.699267
$867$	−8.82483	−0.299707
$868$	40.9286	1.38921
$869$	−8.71517	−0.295642
$870$	−10.6699	−0.361742
$871$	−3.56926	−0.120940
$872$	−10.8821	−0.368513
$873$	−0.574626	−0.0194481
$874$	0	0
$875$	−4.79732	−0.162179
$876$	4.18623	0.141440
$877$	−34.8778	−1.17774	−0.588869	−	0.808228i	$-0.700427\pi$
$877$	−34.8778	−1.17774	−0.588869	+	0.808228i	$0.700427\pi$
$878$	2.59244	0.0874905
$879$	−3.92640	−0.132434
$880$	30.4523	1.02655
$881$	−28.3940	−0.956619	−0.478310	−	0.878191i	$-0.658750\pi$
$881$	−28.3940	−0.956619	−0.478310	+	0.878191i	$0.658750\pi$
$882$	28.6825	0.965790
$883$	33.0238	1.11134	0.555670	−	0.831403i	$-0.312462\pi$
$883$	33.0238	1.11134	0.555670	+	0.831403i	$0.312462\pi$
$884$	9.14856	0.307699
$885$	−1.48633	−0.0499624
$886$	32.4076	1.08875
$887$	−25.9081	−0.869910	−0.434955	−	0.900452i	$-0.643236\pi$
$887$	−25.9081	−0.869910	−0.434955	+	0.900452i	$0.643236\pi$
$888$	−2.51629	−0.0844412
$889$	−9.29405	−0.311712
$890$	10.7903	0.361690
$891$	−6.14357	−0.205817
$892$	16.0881	0.538668
$893$	−25.5223	−0.854072
$894$	−15.8565	−0.530319
$895$	−8.62582	−0.288330
$896$	−50.1778	−1.67632
$897$	0	0
$898$	−7.78346	−0.259737
$899$	−42.0774	−1.40336
$900$	1.20789	0.0402631
$901$	−61.5777	−2.05145
$902$	−48.7011	−1.62157
$903$	−0.251048	−0.00835437
$904$	14.8132	0.492679
$905$	−2.26434	−0.0752691
$906$	4.93613	0.163992
$907$	30.0454	0.997641	0.498821	−	0.866705i	$-0.333767\pi$
$907$	30.0454	0.997641	0.498821	+	0.866705i	$0.333767\pi$
$908$	12.4813	0.414207
$909$	−3.94553	−0.130865
$910$	12.8060	0.424516
$911$	−22.7213	−0.752790	−0.376395	−	0.926459i	$-0.622836\pi$
$911$	−22.7213	−0.752790	−0.376395	+	0.926459i	$0.622836\pi$
$912$	−14.0447	−0.465066
$913$	−60.0358	−1.98689
$914$	−38.5382	−1.27473
$915$	2.61779	0.0865415
$916$	27.4366	0.906531
$917$	−12.3501	−0.407835
$918$	9.10183	0.300405
$919$	29.1508	0.961596	0.480798	−	0.876831i	$-0.340347\pi$
$919$	29.1508	0.961596	0.480798	+	0.876831i	$0.340347\pi$
$920$	0	0
$921$	−0.589552	−0.0194264
$922$	31.1381	1.02548
$923$	22.0726	0.726529
$924$	−35.5998	−1.17115
$925$	−1.77364	−0.0583170
$926$	−24.8826	−0.817692
$927$	−4.88292	−0.160376
$928$	−35.9848	−1.18126
$929$	49.2099	1.61453	0.807263	−	0.590192i	$-0.200948\pi$
$929$	49.2099	1.61453	0.807263	+	0.590192i	$0.200948\pi$
$930$	12.6506	0.414829
$931$	−45.3753	−1.48712
$932$	−8.83200	−0.289302
$933$	−5.85652	−0.191734
$934$	40.5372	1.32642
$935$	31.2205	1.02102
$936$	2.11446	0.0691134
$937$	14.6192	0.477590	0.238795	−	0.971070i	$-0.423248\pi$
$937$	14.6192	0.477590	0.238795	+	0.971070i	$0.423248\pi$
$938$	−20.5769	−0.671861
$939$	20.5501	0.670628
$940$	10.8802	0.354872
$941$	−19.3697	−0.631436	−0.315718	−	0.948853i	$-0.602245\pi$
$941$	−19.3697	−0.631436	−0.315718	+	0.948853i	$0.602245\pi$
$942$	25.9781	0.846411
$943$	0	0
$944$	−7.36740	−0.239788
$945$	4.79732	0.156057
$946$	0.575824	0.0187217
$947$	−36.3166	−1.18013	−0.590066	−	0.807355i	$-0.700898\pi$
$947$	−36.3166	−1.18013	−0.590066	+	0.807355i	$0.700898\pi$
$948$	−1.71349	−0.0556517
$949$	5.16536	0.167675
$950$	−5.07484	−0.164650
$951$	−31.9354	−1.03557
$952$	−34.5869	−1.12097
$953$	−7.63400	−0.247289	−0.123645	−	0.992327i	$-0.539458\pi$
$953$	−7.63400	−0.247289	−0.123645	+	0.992327i	$0.539458\pi$
$954$	21.7027	0.702652
$955$	−9.97822	−0.322888
$956$	14.0948	0.455860
$957$	36.5991	1.18308
$958$	6.90325	0.223034
$959$	66.4555	2.14596
$960$	0.905260	0.0292171
$961$	18.8885	0.609307
$962$	4.73459	0.152649
$963$	−16.6853	−0.537677
$964$	−15.4430	−0.497385
$965$	−4.59577	−0.147943
$966$	0	0
$967$	11.0672	0.355897	0.177949	−	0.984040i	$-0.443054\pi$
$967$	11.0672	0.355897	0.177949	+	0.984040i	$0.443054\pi$
$968$	−37.9413	−1.21948
$969$	−14.3990	−0.462561
$970$	−1.02919	−0.0330453
$971$	−0.839353	−0.0269361	−0.0134681	−	0.999909i	$-0.504287\pi$
$971$	−0.839353	−0.0269361	−0.0134681	+	0.999909i	$0.504287\pi$
$972$	−1.20789	−0.0387431
$973$	37.0109	1.18652
$974$	36.7313	1.17695
$975$	1.49041	0.0477313
$976$	12.9758	0.415346
$977$	−7.47748	−0.239226	−0.119613	−	0.992821i	$-0.538165\pi$
$977$	−7.47748	−0.239226	−0.119613	+	0.992821i	$0.538165\pi$
$978$	37.8204	1.20936
$979$	−37.0121	−1.18291
$980$	19.3435	0.617906
$981$	7.67038	0.244896
$982$	15.2560	0.486840
$983$	55.1310	1.75841	0.879203	−	0.476447i	$-0.158075\pi$
$983$	55.1310	1.75841	0.879203	+	0.476447i	$0.158075\pi$
$984$	6.27916	0.200172
$985$	−20.0189	−0.637855
$986$	−54.2223	−1.72679
$987$	43.2122	1.37546
$988$	5.10089	0.162281
$989$	0	0
$990$	−11.0035	−0.349714
$991$	−12.2863	−0.390286	−0.195143	−	0.980775i	$-0.562517\pi$
$991$	−12.2863	−0.390286	−0.195143	+	0.980775i	$0.562517\pi$
$992$	42.6649	1.35461
$993$	−10.2498	−0.325266
$994$	127.250	4.03611
$995$	−24.3391	−0.771601
$996$	−11.8037	−0.374013
$997$	16.1083	0.510156	0.255078	−	0.966920i	$-0.417899\pi$
$997$	16.1083	0.510156	0.255078	+	0.966920i	$0.417899\pi$
$998$	23.8081	0.753632
$999$	1.77364	0.0561156

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bu.1.20		25
23.4	even	11		345.2.m.d.16.2	✓	50
23.6	even	11		345.2.m.d.151.2	yes	50
23.22	odd	2		7935.2.a.bt.1.20		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.16.2	✓	50	23.4	even	11
345.2.m.d.151.2	yes	50	23.6	even	11
7935.2.a.bt.1.20		25	23.22	odd	2
7935.2.a.bu.1.20		25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+1.79106 q^{2} -1.00000 q^{3} +1.20789 q^{4} +1.00000 q^{5} -1.79106 q^{6} -4.79732 q^{7} -1.41871 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.79106 q^{2} -1.00000 q^{3} +1.20789 q^{4} +1.00000 q^{5} -1.79106 q^{6} -4.79732 q^{7} -1.41871 q^{8} +1.00000 q^{9} +1.79106 q^{10} -6.14357 q^{11} -1.20789 q^{12} -1.49041 q^{13} -8.59228 q^{14} -1.00000 q^{15} -4.95678 q^{16} -5.08181 q^{17} +1.79106 q^{18} -2.83343 q^{19} +1.20789 q^{20} +4.79732 q^{21} -11.0035 q^{22} +1.41871 q^{24} +1.00000 q^{25} -2.66941 q^{26} -1.00000 q^{27} -5.79464 q^{28} +5.95729 q^{29} -1.79106 q^{30} -7.06318 q^{31} -6.04046 q^{32} +6.14357 q^{33} -9.10183 q^{34} -4.79732 q^{35} +1.20789 q^{36} -1.77364 q^{37} -5.07484 q^{38} +1.49041 q^{39} -1.41871 q^{40} +4.42596 q^{41} +8.59228 q^{42} -0.0523310 q^{43} -7.42077 q^{44} +1.00000 q^{45} +9.00757 q^{47} +4.95678 q^{48} +16.0143 q^{49} +1.79106 q^{50} +5.08181 q^{51} -1.80025 q^{52} +12.1173 q^{53} -1.79106 q^{54} -6.14357 q^{55} +6.80602 q^{56} +2.83343 q^{57} +10.6699 q^{58} +1.48633 q^{59} -1.20789 q^{60} -2.61779 q^{61} -12.6506 q^{62} -4.79732 q^{63} -0.905260 q^{64} -1.49041 q^{65} +11.0035 q^{66} +2.39482 q^{67} -6.13828 q^{68} -8.59228 q^{70} -14.8098 q^{71} -1.41871 q^{72} -3.46573 q^{73} -3.17670 q^{74} -1.00000 q^{75} -3.42248 q^{76} +29.4727 q^{77} +2.66941 q^{78} +1.41858 q^{79} -4.95678 q^{80} +1.00000 q^{81} +7.92716 q^{82} +9.77212 q^{83} +5.79464 q^{84} -5.08181 q^{85} -0.0937279 q^{86} -5.95729 q^{87} +8.71596 q^{88} +6.02452 q^{89} +1.79106 q^{90} +7.14997 q^{91} +7.06318 q^{93} +16.1331 q^{94} -2.83343 q^{95} +6.04046 q^{96} -0.574626 q^{97} +28.6825 q^{98} -6.14357 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19} + 31 q^{20} + 15 q^{21} - 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} - 41 q^{28} + q^{29} - q^{30} + 18 q^{31} + 17 q^{32} - 15 q^{33} + 7 q^{34} - 15 q^{35} + 31 q^{36} - 8 q^{37} + 15 q^{38} - 24 q^{39} + 3 q^{40} + 36 q^{41} - 5 q^{42} - 36 q^{43} + 90 q^{44} + 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} + 6 q^{51} + 35 q^{52} + 6 q^{53} - q^{54} + 15 q^{55} + 15 q^{56} - 13 q^{57} + 42 q^{58} - 3 q^{59} - 31 q^{60} + 71 q^{61} - 7 q^{62} - 15 q^{63} + 47 q^{64} + 24 q^{65} + 21 q^{66} - 10 q^{67} - 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} + 67 q^{74} - 25 q^{75} - 12 q^{76} + 27 q^{77} - 21 q^{78} + 33 q^{79} + 39 q^{80} + 25 q^{81} + 49 q^{82} - 2 q^{83} + 41 q^{84} - 6 q^{85} - 35 q^{86} - q^{87} - 33 q^{88} + 11 q^{89} + q^{90} + 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} - 48 q^{97} + 4 q^{98} + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * q^99

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