LMFDB - Embedded newform 4031.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.11438 q^{2} +2.42067 q^{3} +2.47061 q^{4} +1.02780 q^{5} -5.11822 q^{6} +0.853130 q^{7} -0.995051 q^{8} +2.85965 q^{9} +O(q^{10})$	\(q-2.11438 q^{2} +2.42067 q^{3} +2.47061 q^{4} +1.02780 q^{5} -5.11822 q^{6} +0.853130 q^{7} -0.995051 q^{8} +2.85965 q^{9} -2.17316 q^{10} +6.11407 q^{11} +5.98054 q^{12} +5.66977 q^{13} -1.80384 q^{14} +2.48796 q^{15} -2.83730 q^{16} +1.13232 q^{17} -6.04639 q^{18} -0.339258 q^{19} +2.53929 q^{20} +2.06515 q^{21} -12.9275 q^{22} +2.37533 q^{23} -2.40869 q^{24} -3.94363 q^{25} -11.9881 q^{26} -0.339743 q^{27} +2.10775 q^{28} +1.00000 q^{29} -5.26050 q^{30} -1.94017 q^{31} +7.98925 q^{32} +14.8002 q^{33} -2.39416 q^{34} +0.876846 q^{35} +7.06508 q^{36} +8.04855 q^{37} +0.717321 q^{38} +13.7247 q^{39} -1.02271 q^{40} -3.29461 q^{41} -4.36651 q^{42} +5.98133 q^{43} +15.1055 q^{44} +2.93914 q^{45} -5.02235 q^{46} +12.1567 q^{47} -6.86818 q^{48} -6.27217 q^{49} +8.33834 q^{50} +2.74097 q^{51} +14.0078 q^{52} -8.54311 q^{53} +0.718346 q^{54} +6.28404 q^{55} -0.848907 q^{56} -0.821232 q^{57} -2.11438 q^{58} +9.53124 q^{59} +6.14679 q^{60} -15.1226 q^{61} +4.10227 q^{62} +2.43965 q^{63} -11.2177 q^{64} +5.82739 q^{65} -31.2932 q^{66} +15.1469 q^{67} +2.79752 q^{68} +5.74989 q^{69} -1.85399 q^{70} -2.17447 q^{71} -2.84550 q^{72} -1.22657 q^{73} -17.0177 q^{74} -9.54623 q^{75} -0.838174 q^{76} +5.21610 q^{77} -29.0192 q^{78} -7.28144 q^{79} -2.91618 q^{80} -9.40135 q^{81} +6.96607 q^{82} -9.00104 q^{83} +5.10217 q^{84} +1.16380 q^{85} -12.6468 q^{86} +2.42067 q^{87} -6.08381 q^{88} -11.9321 q^{89} -6.21447 q^{90} +4.83705 q^{91} +5.86851 q^{92} -4.69652 q^{93} -25.7038 q^{94} -0.348689 q^{95} +19.3393 q^{96} -5.51546 q^{97} +13.2618 q^{98} +17.4841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) $ 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.11438	−1.49509	−0.747547	−	0.664209i	$-0.768768\pi$
$2$	−2.11438	−1.49509	−0.747547	+	0.664209i	$0.768768\pi$
$3$	2.42067	1.39758	0.698788	−	0.715329i	$-0.253723\pi$
$3$	2.42067	1.39758	0.698788	+	0.715329i	$0.253723\pi$
$4$	2.47061	1.23531
$5$	1.02780	0.459646	0.229823	−	0.973232i	$-0.426185\pi$
$5$	1.02780	0.459646	0.229823	+	0.973232i	$0.426185\pi$
$6$	−5.11822	−2.08951
$7$	0.853130	0.322453	0.161226	−	0.986917i	$-0.448455\pi$
$7$	0.853130	0.322453	0.161226	+	0.986917i	$0.448455\pi$
$8$	−0.995051	−0.351804
$9$	2.85965	0.953216
$10$	−2.17316	−0.687213
$11$	6.11407	1.84346	0.921731	−	0.387829i	$-0.126775\pi$
$11$	6.11407	1.84346	0.921731	+	0.387829i	$0.126775\pi$
$12$	5.98054	1.72643
$13$	5.66977	1.57251	0.786256	−	0.617900i	$-0.212017\pi$
$13$	5.66977	1.57251	0.786256	+	0.617900i	$0.212017\pi$
$14$	−1.80384	−0.482097
$15$	2.48796	0.642389
$16$	−2.83730	−0.709326
$17$	1.13232	0.274628	0.137314	−	0.990528i	$-0.456153\pi$
$17$	1.13232	0.274628	0.137314	+	0.990528i	$0.456153\pi$
$18$	−6.04639	−1.42515
$19$	−0.339258	−0.0778311	−0.0389155	−	0.999243i	$-0.512390\pi$
$19$	−0.339258	−0.0778311	−0.0389155	+	0.999243i	$0.512390\pi$
$20$	2.53929	0.567803
$21$	2.06515	0.450652
$22$	−12.9275	−2.75615
$23$	2.37533	0.495290	0.247645	−	0.968851i	$-0.420343\pi$
$23$	2.37533	0.495290	0.247645	+	0.968851i	$0.420343\pi$
$24$	−2.40869	−0.491672
$25$	−3.94363	−0.788726
$26$	−11.9881	−2.35105
$27$	−0.339743	−0.0653835
$28$	2.10775	0.398328
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−5.26050	−0.960432
$31$	−1.94017	−0.348466	−0.174233	−	0.984704i	$-0.555745\pi$
$31$	−1.94017	−0.348466	−0.174233	+	0.984704i	$0.555745\pi$
$32$	7.98925	1.41231
$33$	14.8002	2.57638
$34$	−2.39416	−0.410594
$35$	0.876846	0.148214
$36$	7.06508	1.17751
$37$	8.04855	1.32317	0.661587	−	0.749869i	$-0.269883\pi$
$37$	8.04855	1.32317	0.661587	+	0.749869i	$0.269883\pi$
$38$	0.717321	0.116365
$39$	13.7247	2.19770
$40$	−1.02271	−0.161705
$41$	−3.29461	−0.514532	−0.257266	−	0.966341i	$-0.582822\pi$
$41$	−3.29461	−0.514532	−0.257266	+	0.966341i	$0.582822\pi$
$42$	−4.36651	−0.673767
$43$	5.98133	0.912145	0.456072	−	0.889943i	$-0.349256\pi$
$43$	5.98133	0.912145	0.456072	+	0.889943i	$0.349256\pi$
$44$	15.1055	2.27724
$45$	2.93914	0.438142
$46$	−5.02235	−0.740505
$47$	12.1567	1.77323	0.886616	−	0.462506i	$-0.153049\pi$
$47$	12.1567	1.77323	0.886616	+	0.462506i	$0.153049\pi$
$48$	−6.86818	−0.991336
$49$	−6.27217	−0.896024
$50$	8.33834	1.17922
$51$	2.74097	0.383813
$52$	14.0078	1.94253
$53$	−8.54311	−1.17349	−0.586743	−	0.809773i	$-0.699590\pi$
$53$	−8.54311	−1.17349	−0.586743	+	0.809773i	$0.699590\pi$
$54$	0.718346	0.0977545
$55$	6.28404	0.847340
$56$	−0.848907	−0.113440
$57$	−0.821232	−0.108775
$58$	−2.11438	−0.277632
$59$	9.53124	1.24086	0.620431	−	0.784261i	$-0.286958\pi$
$59$	9.53124	1.24086	0.620431	+	0.784261i	$0.286958\pi$
$60$	6.14679	0.793547
$61$	−15.1226	−1.93625	−0.968123	−	0.250476i	$-0.919413\pi$
$61$	−15.1226	−1.93625	−0.968123	+	0.250476i	$0.919413\pi$
$62$	4.10227	0.520989
$63$	2.43965	0.307367
$64$	−11.2177	−1.40221
$65$	5.82739	0.722799
$66$	−31.2932	−3.85193
$67$	15.1469	1.85049	0.925243	−	0.379375i	$-0.123861\pi$
$67$	15.1469	1.85049	0.925243	+	0.379375i	$0.123861\pi$
$68$	2.79752	0.339249
$69$	5.74989	0.692205
$70$	−1.85399	−0.221594
$71$	−2.17447	−0.258062	−0.129031	−	0.991641i	$-0.541187\pi$
$71$	−2.17447	−0.258062	−0.129031	+	0.991641i	$0.541187\pi$
$72$	−2.84550	−0.335345
$73$	−1.22657	−0.143559	−0.0717795	−	0.997421i	$-0.522868\pi$
$73$	−1.22657	−0.143559	−0.0717795	+	0.997421i	$0.522868\pi$
$74$	−17.0177	−1.97827
$75$	−9.54623	−1.10230
$76$	−0.838174	−0.0961451
$77$	5.21610	0.594430
$78$	−29.0192	−3.28577
$79$	−7.28144	−0.819226	−0.409613	−	0.912259i	$-0.634336\pi$
$79$	−7.28144	−0.819226	−0.409613	+	0.912259i	$0.634336\pi$
$80$	−2.91618	−0.326039
$81$	−9.40135	−1.04459
$82$	6.96607	0.769273
$83$	−9.00104	−0.987993	−0.493996	−	0.869464i	$-0.664464\pi$
$83$	−9.00104	−0.987993	−0.493996	+	0.869464i	$0.664464\pi$
$84$	5.10217	0.556693
$85$	1.16380	0.126232
$86$	−12.6468	−1.36374
$87$	2.42067	0.259523
$88$	−6.08381	−0.648537
$89$	−11.9321	−1.26480	−0.632398	−	0.774643i	$-0.717929\pi$
$89$	−11.9321	−1.26480	−0.632398	+	0.774643i	$0.717929\pi$
$90$	−6.21447	−0.655063
$91$	4.83705	0.507061
$92$	5.86851	0.611834
$93$	−4.69652	−0.487007
$94$	−25.7038	−2.65115
$95$	−0.348689	−0.0357747
$96$	19.3393	1.97381
$97$	−5.51546	−0.560010	−0.280005	−	0.959999i	$-0.590336\pi$
$97$	−5.51546	−0.560010	−0.280005	+	0.959999i	$0.590336\pi$
$98$	13.2618	1.33964
$99$	17.4841	1.75722
$100$	−9.74317	−0.974317
$101$	−15.0593	−1.49845	−0.749227	−	0.662313i	$-0.769575\pi$
$101$	−15.0593	−1.49845	−0.749227	+	0.662313i	$0.769575\pi$
$102$	−5.79547	−0.573837
$103$	7.09871	0.699457	0.349728	−	0.936851i	$-0.386274\pi$
$103$	7.09871	0.699457	0.349728	+	0.936851i	$0.386274\pi$
$104$	−5.64171	−0.553216
$105$	2.12256	0.207140
$106$	18.0634	1.75447
$107$	−8.69620	−0.840694	−0.420347	−	0.907363i	$-0.638092\pi$
$107$	−8.69620	−0.840694	−0.420347	+	0.907363i	$0.638092\pi$
$108$	−0.839372	−0.0807686
$109$	9.92020	0.950183	0.475091	−	0.879936i	$-0.342415\pi$
$109$	9.92020	0.950183	0.475091	+	0.879936i	$0.342415\pi$
$110$	−13.2869	−1.26685
$111$	19.4829	1.84923
$112$	−2.42059	−0.228724
$113$	−1.22728	−0.115452	−0.0577262	−	0.998332i	$-0.518385\pi$
$113$	−1.22728	−0.115452	−0.0577262	+	0.998332i	$0.518385\pi$
$114$	1.73640	0.162628
$115$	2.44136	0.227658
$116$	2.47061	0.229390
$117$	16.2136	1.49894
$118$	−20.1527	−1.85520
$119$	0.966016	0.0885545
$120$	−2.47565	−0.225995
$121$	26.3819	2.39836
$122$	31.9749	2.89487
$123$	−7.97517	−0.719097
$124$	−4.79341	−0.430461
$125$	−9.19225	−0.822180
$126$	−5.15836	−0.459543
$127$	−0.616958	−0.0547462	−0.0273731	−	0.999625i	$-0.508714\pi$
$127$	−0.616958	−0.0547462	−0.0273731	+	0.999625i	$0.508714\pi$
$128$	7.74003	0.684128
$129$	14.4788	1.27479
$130$	−12.3213	−1.08065
$131$	−13.0617	−1.14121	−0.570604	−	0.821225i	$-0.693291\pi$
$131$	−13.0617	−1.14121	−0.570604	+	0.821225i	$0.693291\pi$
$132$	36.5654	3.18261
$133$	−0.289431	−0.0250968
$134$	−32.0263	−2.76665
$135$	−0.349187	−0.0300532
$136$	−1.12672	−0.0966151
$137$	−0.797244	−0.0681132	−0.0340566	−	0.999420i	$-0.510843\pi$
$137$	−0.797244	−0.0681132	−0.0340566	+	0.999420i	$0.510843\pi$
$138$	−12.1575	−1.03491
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	2.16634	0.183090
$141$	29.4273	2.47823
$142$	4.59766	0.385827
$143$	34.6654	2.89887
$144$	−8.11370	−0.676141
$145$	1.02780	0.0853540
$146$	2.59343	0.214634
$147$	−15.1829	−1.25226
$148$	19.8848	1.63452
$149$	−18.9495	−1.55240	−0.776201	−	0.630485i	$-0.782856\pi$
$149$	−18.9495	−1.55240	−0.776201	+	0.630485i	$0.782856\pi$
$150$	20.1844	1.64805
$151$	10.2173	0.831469	0.415735	−	0.909486i	$-0.363525\pi$
$151$	10.2173	0.831469	0.415735	+	0.909486i	$0.363525\pi$
$152$	0.337579	0.0273812
$153$	3.23804	0.261780
$154$	−11.0288	−0.888728
$155$	−1.99411	−0.160171
$156$	33.9083	2.71484
$157$	−13.9869	−1.11627	−0.558136	−	0.829749i	$-0.688483\pi$
$157$	−13.9869	−1.11627	−0.558136	+	0.829749i	$0.688483\pi$
$158$	15.3957	1.22482
$159$	−20.6800	−1.64003
$160$	8.21134	0.649163
$161$	2.02646	0.159708
$162$	19.8781	1.56177
$163$	−20.7731	−1.62707	−0.813535	−	0.581515i	$-0.802460\pi$
$163$	−20.7731	−1.62707	−0.813535	+	0.581515i	$0.802460\pi$
$164$	−8.13970	−0.635604
$165$	15.2116	1.18422
$166$	19.0316	1.47714
$167$	4.15505	0.321528	0.160764	−	0.986993i	$-0.448604\pi$
$167$	4.15505	0.321528	0.160764	+	0.986993i	$0.448604\pi$
$168$	−2.05493	−0.158541
$169$	19.1463	1.47280
$170$	−2.46071	−0.188728
$171$	−0.970158	−0.0741899
$172$	14.7775	1.12678
$173$	−22.2634	−1.69266	−0.846328	−	0.532662i	$-0.821192\pi$
$173$	−22.2634	−1.69266	−0.846328	+	0.532662i	$0.821192\pi$
$174$	−5.11822	−0.388012
$175$	−3.36443	−0.254327
$176$	−17.3475	−1.30762
$177$	23.0720	1.73420
$178$	25.2289	1.89099
$179$	15.9365	1.19115	0.595575	−	0.803300i	$-0.296924\pi$
$179$	15.9365	1.19115	0.595575	+	0.803300i	$0.296924\pi$
$180$	7.26148	0.541239
$181$	16.3123	1.21248	0.606242	−	0.795280i	$-0.292676\pi$
$181$	16.3123	1.21248	0.606242	+	0.795280i	$0.292676\pi$
$182$	−10.2274	−0.758104
$183$	−36.6067	−2.70605
$184$	−2.36357	−0.174245
$185$	8.27229	0.608191
$186$	9.93024	0.728121
$187$	6.92309	0.506266
$188$	30.0344	2.19048
$189$	−0.289845	−0.0210831
$190$	0.737261	0.0534865
$191$	−18.0974	−1.30948	−0.654739	−	0.755855i	$-0.727222\pi$
$191$	−18.0974	−1.30948	−0.654739	+	0.755855i	$0.727222\pi$
$192$	−27.1544	−1.95970
$193$	18.1369	1.30552	0.652760	−	0.757565i	$-0.273611\pi$
$193$	18.1369	1.30552	0.652760	+	0.757565i	$0.273611\pi$
$194$	11.6618	0.837268
$195$	14.1062	1.01017
$196$	−15.4961	−1.10686
$197$	19.8599	1.41496	0.707479	−	0.706734i	$-0.249832\pi$
$197$	19.8599	1.41496	0.707479	+	0.706734i	$0.249832\pi$
$198$	−36.9681	−2.62721
$199$	−18.8221	−1.33426	−0.667130	−	0.744941i	$-0.732478\pi$
$199$	−18.8221	−1.33426	−0.667130	+	0.744941i	$0.732478\pi$
$200$	3.92411	0.277477
$201$	36.6656	2.58619
$202$	31.8411	2.24033
$203$	0.853130	0.0598780
$204$	6.77188	0.474126
$205$	−3.38620	−0.236502
$206$	−15.0094	−1.04575
$207$	6.79260	0.472119
$208$	−16.0869	−1.11542
$209$	−2.07425	−0.143479
$210$	−4.48789	−0.309694
$211$	7.08566	0.487797	0.243898	−	0.969801i	$-0.421574\pi$
$211$	7.08566	0.487797	0.243898	+	0.969801i	$0.421574\pi$
$212$	−21.1067	−1.44961
$213$	−5.26368	−0.360661
$214$	18.3871	1.25692
$215$	6.14761	0.419263
$216$	0.338061	0.0230022
$217$	−1.65522	−0.112364
$218$	−20.9751	−1.42061
$219$	−2.96912	−0.200635
$220$	15.5254	1.04672
$221$	6.42000	0.431856
$222$	−41.1943	−2.76478
$223$	−8.68785	−0.581781	−0.290891	−	0.956756i	$-0.593952\pi$
$223$	−8.68785	−0.581781	−0.290891	+	0.956756i	$0.593952\pi$
$224$	6.81586	0.455404
$225$	−11.2774	−0.751827
$226$	2.59493	0.172612
$227$	19.3656	1.28534	0.642671	−	0.766142i	$-0.277826\pi$
$227$	19.3656	1.28534	0.642671	+	0.766142i	$0.277826\pi$
$228$	−2.02894	−0.134370
$229$	3.76897	0.249061	0.124530	−	0.992216i	$-0.460258\pi$
$229$	3.76897	0.249061	0.124530	+	0.992216i	$0.460258\pi$
$230$	−5.16196	−0.340370
$231$	12.6265	0.830760
$232$	−0.995051	−0.0653283
$233$	10.8450	0.710478	0.355239	−	0.934776i	$-0.384400\pi$
$233$	10.8450	0.710478	0.355239	+	0.934776i	$0.384400\pi$
$234$	−34.2817	−2.24106
$235$	12.4946	0.815059
$236$	23.5480	1.53284
$237$	−17.6260	−1.14493
$238$	−2.04253	−0.132397
$239$	−22.9558	−1.48489	−0.742443	−	0.669910i	$-0.766333\pi$
$239$	−22.9558	−1.48489	−0.742443	+	0.669910i	$0.766333\pi$
$240$	−7.05911	−0.455663
$241$	−28.9056	−1.86197	−0.930986	−	0.365054i	$-0.881050\pi$
$241$	−28.9056	−1.86197	−0.930986	+	0.365054i	$0.881050\pi$
$242$	−55.7814	−3.58577
$243$	−21.7384	−1.39452
$244$	−37.3620	−2.39185
$245$	−6.44653	−0.411854
$246$	16.8626	1.07512
$247$	−1.92352	−0.122390
$248$	1.93057	0.122591
$249$	−21.7886	−1.38079
$250$	19.4359	1.22924
$251$	−12.6980	−0.801492	−0.400746	−	0.916189i	$-0.631249\pi$
$251$	−12.6980	−0.801492	−0.400746	+	0.916189i	$0.631249\pi$
$252$	6.02743	0.379692
$253$	14.5229	0.913049
$254$	1.30449	0.0818507
$255$	2.81717	0.176418
$256$	6.07004	0.379378
$257$	−23.1040	−1.44119	−0.720594	−	0.693358i	$-0.756131\pi$
$257$	−23.1040	−1.44119	−0.720594	+	0.693358i	$0.756131\pi$
$258$	−30.6138	−1.90593
$259$	6.86646	0.426661
$260$	14.3972	0.892877
$261$	2.85965	0.177008
$262$	27.6175	1.70621
$263$	9.15873	0.564751	0.282376	−	0.959304i	$-0.408878\pi$
$263$	9.15873	0.564751	0.282376	+	0.959304i	$0.408878\pi$
$264$	−14.7269	−0.906379
$265$	−8.78059	−0.539388
$266$	0.611968	0.0375221
$267$	−28.8836	−1.76765
$268$	37.4221	2.28592
$269$	18.8266	1.14788	0.573938	−	0.818899i	$-0.305415\pi$
$269$	18.8266	1.14788	0.573938	+	0.818899i	$0.305415\pi$
$270$	0.738315	0.0449324
$271$	8.19112	0.497575	0.248788	−	0.968558i	$-0.419968\pi$
$271$	8.19112	0.497575	0.248788	+	0.968558i	$0.419968\pi$
$272$	−3.21274	−0.194801
$273$	11.7089	0.708656
$274$	1.68568	0.101836
$275$	−24.1116	−1.45399
$276$	14.2057	0.855084
$277$	11.7995	0.708965	0.354482	−	0.935063i	$-0.384657\pi$
$277$	11.7995	0.708965	0.354482	+	0.935063i	$0.384657\pi$
$278$	2.11438	0.126812
$279$	−5.54822	−0.332163
$280$	−0.872506	−0.0521422
$281$	11.2944	0.673765	0.336883	−	0.941547i	$-0.390627\pi$
$281$	11.2944	0.673765	0.336883	+	0.941547i	$0.390627\pi$
$282$	−62.2206	−3.70518
$283$	−3.34947	−0.199105	−0.0995525	−	0.995032i	$-0.531741\pi$
$283$	−3.34947	−0.199105	−0.0995525	+	0.995032i	$0.531741\pi$
$284$	−5.37227	−0.318786
$285$	−0.844061	−0.0499978
$286$	−73.2960	−4.33408
$287$	−2.81073	−0.165912
$288$	22.8464	1.34624
$289$	−15.7179	−0.924580
$290$	−2.17316	−0.127612
$291$	−13.3511	−0.782656
$292$	−3.03037	−0.177339
$293$	−1.03700	−0.0605821	−0.0302910	−	0.999541i	$-0.509643\pi$
$293$	−1.03700	−0.0605821	−0.0302910	+	0.999541i	$0.509643\pi$
$294$	32.1024	1.87225
$295$	9.79620	0.570357
$296$	−8.00872	−0.465497
$297$	−2.07721	−0.120532
$298$	40.0664	2.32099
$299$	13.4676	0.778850
$300$	−23.5850	−1.36168
$301$	5.10285	0.294124
$302$	−21.6032	−1.24312
$303$	−36.4536	−2.09420
$304$	0.962578	0.0552076
$305$	−15.5429	−0.889987
$306$	−6.84645	−0.391385
$307$	−1.10352	−0.0629810	−0.0314905	−	0.999504i	$-0.510025\pi$
$307$	−1.10352	−0.0629810	−0.0314905	+	0.999504i	$0.510025\pi$
$308$	12.8870	0.734302
$309$	17.1836	0.977543
$310$	4.21631	0.239470
$311$	−5.15507	−0.292317	−0.146159	−	0.989261i	$-0.546691\pi$
$311$	−5.15507	−0.292317	−0.146159	+	0.989261i	$0.546691\pi$
$312$	−13.6567	−0.773160
$313$	−11.8296	−0.668646	−0.334323	−	0.942458i	$-0.608508\pi$
$313$	−11.8296	−0.668646	−0.334323	+	0.942458i	$0.608508\pi$
$314$	29.5736	1.66893
$315$	2.50747	0.141280
$316$	−17.9896	−1.01199
$317$	11.2193	0.630138	0.315069	−	0.949069i	$-0.397972\pi$
$317$	11.2193	0.630138	0.315069	+	0.949069i	$0.397972\pi$
$318$	43.7255	2.45201
$319$	6.11407	0.342322
$320$	−11.5295	−0.644521
$321$	−21.0507	−1.17493
$322$	−4.28472	−0.238778
$323$	−0.384148	−0.0213746
$324$	−23.2271	−1.29039
$325$	−22.3595	−1.24028
$326$	43.9222	2.43262
$327$	24.0135	1.32795
$328$	3.27831	0.181014
$329$	10.3712	0.571784
$330$	−32.1631	−1.77052
$331$	31.0354	1.70586	0.852931	−	0.522024i	$-0.174823\pi$
$331$	31.0354	1.70586	0.852931	+	0.522024i	$0.174823\pi$
$332$	−22.2381	−1.22047
$333$	23.0160	1.26127
$334$	−8.78537	−0.480714
$335$	15.5679	0.850568
$336$	−5.85945	−0.319659
$337$	22.5854	1.23030	0.615152	−	0.788409i	$-0.289095\pi$
$337$	22.5854	1.23030	0.615152	+	0.788409i	$0.289095\pi$
$338$	−40.4827	−2.20197
$339$	−2.97083	−0.161354
$340$	2.87529	0.155934
$341$	−11.8624	−0.642383
$342$	2.05129	0.110921
$343$	−11.3229	−0.611378
$344$	−5.95173	−0.320896
$345$	5.90973	0.318169
$346$	47.0734	2.53068
$347$	−22.9338	−1.23115	−0.615575	−	0.788078i	$-0.711076\pi$
$347$	−22.9338	−1.23115	−0.615575	+	0.788078i	$0.711076\pi$
$348$	5.98054	0.320590
$349$	13.6314	0.729670	0.364835	−	0.931072i	$-0.381125\pi$
$349$	13.6314	0.729670	0.364835	+	0.931072i	$0.381125\pi$
$350$	7.11369	0.380242
$351$	−1.92626	−0.102816
$352$	48.8468	2.60355
$353$	−9.46693	−0.503874	−0.251937	−	0.967744i	$-0.581068\pi$
$353$	−9.46693	−0.503874	−0.251937	+	0.967744i	$0.581068\pi$
$354$	−48.7830	−2.59279
$355$	−2.23492	−0.118617
$356$	−29.4795	−1.56241
$357$	2.33841	0.123762
$358$	−33.6959	−1.78088
$359$	35.3532	1.86587	0.932935	−	0.360045i	$-0.117239\pi$
$359$	35.3532	1.86587	0.932935	+	0.360045i	$0.117239\pi$
$360$	−2.92460	−0.154140
$361$	−18.8849	−0.993942
$362$	−34.4904	−1.81278
$363$	63.8619	3.35188
$364$	11.9505	0.626375
$365$	−1.26067	−0.0659863
$366$	77.4006	4.04580
$367$	5.47594	0.285842	0.142921	−	0.989734i	$-0.454351\pi$
$367$	5.47594	0.285842	0.142921	+	0.989734i	$0.454351\pi$
$368$	−6.73953	−0.351322
$369$	−9.42143	−0.490460
$370$	−17.4908	−0.909302
$371$	−7.28838	−0.378394
$372$	−11.6033	−0.601602
$373$	12.4581	0.645054	0.322527	−	0.946560i	$-0.395468\pi$
$373$	12.4581	0.645054	0.322527	+	0.946560i	$0.395468\pi$
$374$	−14.6381	−0.756916
$375$	−22.2514	−1.14906
$376$	−12.0965	−0.623830
$377$	5.66977	0.292008
$378$	0.612842	0.0315212
$379$	34.8084	1.78798	0.893992	−	0.448082i	$-0.147893\pi$
$379$	34.8084	1.78798	0.893992	+	0.448082i	$0.147893\pi$
$380$	−0.861474	−0.0441927
$381$	−1.49345	−0.0765119
$382$	38.2647	1.95779
$383$	8.01574	0.409585	0.204793	−	0.978805i	$-0.434348\pi$
$383$	8.01574	0.409585	0.204793	+	0.978805i	$0.434348\pi$
$384$	18.7361	0.956121
$385$	5.36110	0.273227
$386$	−38.3482	−1.95187
$387$	17.1045	0.869471
$388$	−13.6266	−0.691784
$389$	7.70583	0.390701	0.195351	−	0.980733i	$-0.437416\pi$
$389$	7.70583	0.390701	0.195351	+	0.980733i	$0.437416\pi$
$390$	−29.8259	−1.51029
$391$	2.68963	0.136020
$392$	6.24113	0.315225
$393$	−31.6181	−1.59492
$394$	−41.9914	−2.11550
$395$	−7.48386	−0.376554
$396$	43.1964	2.17070
$397$	−1.91244	−0.0959827	−0.0479914	−	0.998848i	$-0.515282\pi$
$397$	−1.91244	−0.0959827	−0.0479914	+	0.998848i	$0.515282\pi$
$398$	39.7970	1.99484
$399$	−0.700617	−0.0350747
$400$	11.1893	0.559464
$401$	2.75717	0.137687	0.0688433	−	0.997627i	$-0.478069\pi$
$401$	2.75717	0.137687	0.0688433	+	0.997627i	$0.478069\pi$
$402$	−77.5251	−3.86660
$403$	−11.0003	−0.547966
$404$	−37.2056	−1.85105
$405$	−9.66270	−0.480143
$406$	−1.80384	−0.0895232
$407$	49.2094	2.43922
$408$	−2.72741	−0.135027
$409$	−7.66688	−0.379103	−0.189551	−	0.981871i	$-0.560703\pi$
$409$	−7.66688	−0.379103	−0.189551	+	0.981871i	$0.560703\pi$
$410$	7.15972	0.353593
$411$	−1.92987	−0.0951933
$412$	17.5382	0.864043
$413$	8.13139	0.400119
$414$	−14.3622	−0.705861
$415$	−9.25126	−0.454127
$416$	45.2972	2.22088
$417$	−2.42067	−0.118541
$418$	4.38575	0.214514
$419$	20.6680	1.00970	0.504850	−	0.863207i	$-0.331548\pi$
$419$	20.6680	1.00970	0.504850	+	0.863207i	$0.331548\pi$
$420$	5.24401	0.255881
$421$	−2.17425	−0.105966	−0.0529832	−	0.998595i	$-0.516873\pi$
$421$	−2.17425	−0.105966	−0.0529832	+	0.998595i	$0.516873\pi$
$422$	−14.9818	−0.729302
$423$	34.7638	1.69027
$424$	8.50082	0.412836
$425$	−4.46545	−0.216606
$426$	11.1294	0.539222
$427$	−12.9015	−0.624348
$428$	−21.4849	−1.03851
$429$	83.9136	4.05139
$430$	−12.9984	−0.626838
$431$	25.9105	1.24806	0.624032	−	0.781399i	$-0.285494\pi$
$431$	25.9105	1.24806	0.624032	+	0.781399i	$0.285494\pi$
$432$	0.963953	0.0463782
$433$	19.4605	0.935210	0.467605	−	0.883938i	$-0.345117\pi$
$433$	19.4605	0.935210	0.467605	+	0.883938i	$0.345117\pi$
$434$	3.49977	0.167994
$435$	2.48796	0.119289
$436$	24.5090	1.17377
$437$	−0.805848	−0.0385489
$438$	6.27785	0.299967
$439$	−2.70547	−0.129125	−0.0645624	−	0.997914i	$-0.520565\pi$
$439$	−2.70547	−0.129125	−0.0645624	+	0.997914i	$0.520565\pi$
$440$	−6.25294	−0.298097
$441$	−17.9362	−0.854105
$442$	−13.5743	−0.645665
$443$	−36.1723	−1.71860	−0.859299	−	0.511474i	$-0.829100\pi$
$443$	−36.1723	−1.71860	−0.859299	+	0.511474i	$0.829100\pi$
$444$	48.1346	2.28437
$445$	−12.2638	−0.581358
$446$	18.3694	0.869818
$447$	−45.8705	−2.16960
$448$	−9.57016	−0.452148
$449$	−17.1391	−0.808845	−0.404423	−	0.914572i	$-0.632528\pi$
$449$	−17.1391	−0.808845	−0.404423	+	0.914572i	$0.632528\pi$
$450$	23.8447	1.12405
$451$	−20.1435	−0.948520
$452$	−3.03212	−0.142619
$453$	24.7326	1.16204
$454$	−40.9464	−1.92171
$455$	4.97152	0.233068
$456$	0.817167	0.0382674
$457$	−34.4787	−1.61285	−0.806423	−	0.591339i	$-0.798599\pi$
$457$	−34.4787	−1.61285	−0.806423	+	0.591339i	$0.798599\pi$
$458$	−7.96905	−0.372369
$459$	−0.384697	−0.0179561
$460$	6.03165	0.281227
$461$	−27.8712	−1.29809	−0.649047	−	0.760749i	$-0.724832\pi$
$461$	−27.8712	−1.29809	−0.649047	+	0.760749i	$0.724832\pi$
$462$	−26.6972	−1.24206
$463$	8.31579	0.386468	0.193234	−	0.981153i	$-0.438102\pi$
$463$	8.31579	0.386468	0.193234	+	0.981153i	$0.438102\pi$
$464$	−2.83730	−0.131719
$465$	−4.82708	−0.223851
$466$	−22.9304	−1.06223
$467$	−17.3970	−0.805037	−0.402519	−	0.915412i	$-0.631865\pi$
$467$	−17.3970	−0.805037	−0.402519	+	0.915412i	$0.631865\pi$
$468$	40.0574	1.85165
$469$	12.9223	0.596694
$470$	−26.4184	−1.21859
$471$	−33.8576	−1.56008
$472$	−9.48407	−0.436540
$473$	36.5703	1.68150
$474$	37.2680	1.71178
$475$	1.33791	0.0613874
$476$	2.38665	0.109392
$477$	−24.4303	−1.11859
$478$	48.5373	2.22004
$479$	−2.17928	−0.0995737	−0.0497869	−	0.998760i	$-0.515854\pi$
$479$	−2.17928	−0.0995737	−0.0497869	+	0.998760i	$0.515854\pi$
$480$	19.8769	0.907254
$481$	45.6335	2.08071
$482$	61.1174	2.78382
$483$	4.90540	0.223203
$484$	65.1794	2.96270
$485$	−5.66878	−0.257406
$486$	45.9632	2.08493
$487$	2.99512	0.135722	0.0678610	−	0.997695i	$-0.478383\pi$
$487$	2.99512	0.135722	0.0678610	+	0.997695i	$0.478383\pi$
$488$	15.0477	0.681178
$489$	−50.2847	−2.27395
$490$	13.6304	0.615760
$491$	−9.18339	−0.414440	−0.207220	−	0.978294i	$-0.566442\pi$
$491$	−9.18339	−0.414440	−0.207220	+	0.978294i	$0.566442\pi$
$492$	−19.7035	−0.888304
$493$	1.13232	0.0509971
$494$	4.06705	0.182985
$495$	17.9701	0.807698
$496$	5.50486	0.247176
$497$	−1.85511	−0.0832129
$498$	46.0693	2.06442
$499$	30.5195	1.36624	0.683120	−	0.730306i	$-0.260622\pi$
$499$	30.5195	1.36624	0.683120	+	0.730306i	$0.260622\pi$
$500$	−22.7105	−1.01564
$501$	10.0580	0.449359
$502$	26.8485	1.19831
$503$	30.3106	1.35148	0.675742	−	0.737138i	$-0.263823\pi$
$503$	30.3106	1.35148	0.675742	+	0.737138i	$0.263823\pi$
$504$	−2.42758	−0.108133
$505$	−15.4779	−0.688758
$506$	−30.7070	−1.36509
$507$	46.3470	2.05834
$508$	−1.52426	−0.0676283
$509$	−39.3024	−1.74205	−0.871024	−	0.491241i	$-0.836544\pi$
$509$	−39.3024	−1.74205	−0.871024	+	0.491241i	$0.836544\pi$
$510$	−5.95657	−0.263762
$511$	−1.04642	−0.0462910
$512$	−28.3144	−1.25133
$513$	0.115260	0.00508887
$514$	48.8506	2.15471
$515$	7.29605	0.321502
$516$	35.7716	1.57476
$517$	74.3268	3.26889
$518$	−14.5183	−0.637898
$519$	−53.8924	−2.36561
$520$	−5.79855	−0.254283
$521$	−23.1329	−1.01347	−0.506734	−	0.862102i	$-0.669148\pi$
$521$	−23.1329	−1.01347	−0.506734	+	0.862102i	$0.669148\pi$
$522$	−6.04639	−0.264643
$523$	−10.6871	−0.467316	−0.233658	−	0.972319i	$-0.575070\pi$
$523$	−10.6871	−0.467316	−0.233658	+	0.972319i	$0.575070\pi$
$524$	−32.2704	−1.40974
$525$	−8.14417	−0.355441
$526$	−19.3650	−0.844356
$527$	−2.19690	−0.0956984
$528$	−41.9926	−1.82749
$529$	−17.3578	−0.754688
$530$	18.5655	0.806435
$531$	27.2560	1.18281
$532$	−0.715071	−0.0310023
$533$	−18.6797	−0.809108
$534$	61.0710	2.64280
$535$	−8.93795	−0.386421
$536$	−15.0719	−0.651008
$537$	38.5770	1.66472
$538$	−39.8065	−1.71618
$539$	−38.3485	−1.65179
$540$	−0.862705	−0.0371249
$541$	28.4349	1.22251	0.611257	−	0.791432i	$-0.290664\pi$
$541$	28.4349	1.22251	0.611257	+	0.791432i	$0.290664\pi$
$542$	−17.3192	−0.743922
$543$	39.4867	1.69454
$544$	9.04638	0.387860
$545$	10.1960	0.436747
$546$	−24.7571	−1.05951
$547$	29.7111	1.27035	0.635177	−	0.772367i	$-0.280927\pi$
$547$	29.7111	1.27035	0.635177	+	0.772367i	$0.280927\pi$
$548$	−1.96968	−0.0841406
$549$	−43.2452	−1.84566
$550$	50.9812	2.17385
$551$	−0.339258	−0.0144529
$552$	−5.72143	−0.243520
$553$	−6.21201	−0.264162
$554$	−24.9487	−1.05997
$555$	20.0245	0.849993
$556$	−2.47061	−0.104777
$557$	33.0242	1.39928	0.699641	−	0.714495i	$-0.253343\pi$
$557$	33.0242	1.39928	0.699641	+	0.714495i	$0.253343\pi$
$558$	11.7311	0.496615
$559$	33.9128	1.43436
$560$	−2.48788	−0.105132
$561$	16.7585	0.707545
$562$	−23.8806	−1.00734
$563$	42.3931	1.78666	0.893329	−	0.449404i	$-0.148364\pi$
$563$	42.3931	1.78666	0.893329	+	0.449404i	$0.148364\pi$
$564$	72.7034	3.06137
$565$	−1.26139	−0.0530672
$566$	7.08205	0.297681
$567$	−8.02058	−0.336832
$568$	2.16371	0.0907872
$569$	−10.6978	−0.448474	−0.224237	−	0.974535i	$-0.571989\pi$
$569$	−10.6978	−0.448474	−0.224237	+	0.974535i	$0.571989\pi$
$570$	1.78467	0.0747515
$571$	41.6446	1.74277	0.871386	−	0.490599i	$-0.163222\pi$
$571$	41.6446	1.74277	0.871386	+	0.490599i	$0.163222\pi$
$572$	85.6448	3.58099
$573$	−43.8078	−1.83010
$574$	5.94296	0.248054
$575$	−9.36741	−0.390648
$576$	−32.0787	−1.33661
$577$	26.4713	1.10201	0.551007	−	0.834501i	$-0.314244\pi$
$577$	26.4713	1.10201	0.551007	+	0.834501i	$0.314244\pi$
$578$	33.2335	1.38233
$579$	43.9034	1.82456
$580$	2.53929	0.105438
$581$	−7.67906	−0.318581
$582$	28.2294	1.17014
$583$	−52.2332	−2.16328
$584$	1.22050	0.0505046
$585$	16.6643	0.688983
$586$	2.19261	0.0905759
$587$	−19.4246	−0.801739	−0.400869	−	0.916135i	$-0.631292\pi$
$587$	−19.4246	−0.801739	−0.400869	+	0.916135i	$0.631292\pi$
$588$	−37.5109	−1.54693
$589$	0.658219	0.0271214
$590$	−20.7129	−0.852737
$591$	48.0743	1.97751
$592$	−22.8362	−0.938561
$593$	−11.5462	−0.474147	−0.237073	−	0.971492i	$-0.576188\pi$
$593$	−11.5462	−0.474147	−0.237073	+	0.971492i	$0.576188\pi$
$594$	4.39202	0.180207
$595$	0.992870	0.0407037
$596$	−46.8168	−1.91769
$597$	−45.5620	−1.86473
$598$	−28.4756	−1.16445
$599$	−5.65967	−0.231248	−0.115624	−	0.993293i	$-0.536887\pi$
$599$	−5.65967	−0.231248	−0.115624	+	0.993293i	$0.536887\pi$
$600$	9.49898	0.387794
$601$	47.9241	1.95487	0.977433	−	0.211245i	$-0.0677516\pi$
$601$	47.9241	1.95487	0.977433	+	0.211245i	$0.0677516\pi$
$602$	−10.7894	−0.439742
$603$	43.3148	1.76391
$604$	25.2429	1.02712
$605$	27.1153	1.10239
$606$	77.0768	3.13103
$607$	15.8830	0.644671	0.322336	−	0.946625i	$-0.395532\pi$
$607$	15.8830	0.644671	0.322336	+	0.946625i	$0.395532\pi$
$608$	−2.71041	−0.109922
$609$	2.06515	0.0836840
$610$	32.8637	1.33061
$611$	68.9256	2.78843
$612$	7.99993	0.323378
$613$	24.3458	0.983316	0.491658	−	0.870788i	$-0.336391\pi$
$613$	24.3458	0.983316	0.491658	+	0.870788i	$0.336391\pi$
$614$	2.33325	0.0941624
$615$	−8.19687	−0.330530
$616$	−5.19028	−0.209122
$617$	17.1132	0.688953	0.344476	−	0.938795i	$-0.388056\pi$
$617$	17.1132	0.688953	0.344476	+	0.938795i	$0.388056\pi$
$618$	−36.3328	−1.46152
$619$	−45.9358	−1.84632	−0.923158	−	0.384420i	$-0.874401\pi$
$619$	−45.9358	−1.84632	−0.923158	+	0.384420i	$0.874401\pi$
$620$	−4.92667	−0.197860
$621$	−0.807000	−0.0323838
$622$	10.8998	0.437042
$623$	−10.1796	−0.407837
$624$	−38.9410	−1.55889
$625$	10.2704	0.410814
$626$	25.0122	0.999689
$627$	−5.02107	−0.200522
$628$	−34.5561	−1.37894
$629$	9.11353	0.363380
$630$	−5.30175	−0.211227
$631$	−5.45553	−0.217181	−0.108591	−	0.994087i	$-0.534634\pi$
$631$	−5.45553	−0.217181	−0.108591	+	0.994087i	$0.534634\pi$
$632$	7.24540	0.288207
$633$	17.1520	0.681733
$634$	−23.7219	−0.942115
$635$	−0.634109	−0.0251639
$636$	−51.0924	−2.02594
$637$	−35.5618	−1.40901
$638$	−12.9275	−0.511804
$639$	−6.21822	−0.245989
$640$	7.95519	0.314457
$641$	0.440854	0.0174127	0.00870635	−	0.999962i	$-0.497229\pi$
$641$	0.440854	0.0174127	0.00870635	+	0.999962i	$0.497229\pi$
$642$	44.5091	1.75663
$643$	15.7655	0.621730	0.310865	−	0.950454i	$-0.399381\pi$
$643$	15.7655	0.621730	0.310865	+	0.950454i	$0.399381\pi$
$644$	5.00660	0.197288
$645$	14.8813	0.585952
$646$	0.812236	0.0319570
$647$	21.3871	0.840815	0.420407	−	0.907335i	$-0.361887\pi$
$647$	21.3871	0.840815	0.420407	+	0.907335i	$0.361887\pi$
$648$	9.35482	0.367492
$649$	58.2747	2.28748
$650$	47.2765	1.85434
$651$	−4.00674	−0.157037
$652$	−51.3221	−2.00993
$653$	19.2216	0.752199	0.376099	−	0.926579i	$-0.377265\pi$
$653$	19.2216	0.752199	0.376099	+	0.926579i	$0.377265\pi$
$654$	−50.7738	−1.98541
$655$	−13.4248	−0.524551
$656$	9.34782	0.364971
$657$	−3.50756	−0.136843
$658$	−21.9287	−0.854870
$659$	23.1565	0.902048	0.451024	−	0.892512i	$-0.351059\pi$
$659$	23.1565	0.902048	0.451024	+	0.892512i	$0.351059\pi$
$660$	37.5819	1.46287
$661$	−30.8488	−1.19988	−0.599940	−	0.800045i	$-0.704809\pi$
$661$	−30.8488	−1.19988	−0.599940	+	0.800045i	$0.704809\pi$
$662$	−65.6207	−2.55042
$663$	15.5407	0.603551
$664$	8.95649	0.347579
$665$	−0.297477	−0.0115357
$666$	−48.6647	−1.88572
$667$	2.37533	0.0919730
$668$	10.2655	0.397185
$669$	−21.0304	−0.813083
$670$	−32.9166	−1.27168
$671$	−92.4605	−3.56940
$672$	16.4990	0.636461
$673$	6.05161	0.233272	0.116636	−	0.993175i	$-0.462789\pi$
$673$	6.05161	0.233272	0.116636	+	0.993175i	$0.462789\pi$
$674$	−47.7541	−1.83942
$675$	1.33982	0.0515697
$676$	47.3032	1.81935
$677$	−26.2323	−1.00819	−0.504095	−	0.863648i	$-0.668174\pi$
$677$	−26.2323	−1.00819	−0.504095	+	0.863648i	$0.668174\pi$
$678$	6.28148	0.241239
$679$	−4.70540	−0.180577
$680$	−1.15804	−0.0444087
$681$	46.8779	1.79636
$682$	25.0816	0.960423
$683$	−36.0520	−1.37949	−0.689745	−	0.724052i	$-0.742277\pi$
$683$	−36.0520	−1.37949	−0.689745	+	0.724052i	$0.742277\pi$
$684$	−2.39688	−0.0916471
$685$	−0.819407	−0.0313079
$686$	23.9409	0.914068
$687$	9.12345	0.348081
$688$	−16.9709	−0.647008
$689$	−48.4375	−1.84532
$690$	−12.4954	−0.475692
$691$	42.3945	1.61276	0.806381	−	0.591396i	$-0.201423\pi$
$691$	42.3945	1.61276	0.806381	+	0.591396i	$0.201423\pi$
$692$	−55.0042	−2.09095
$693$	14.9162	0.566620
$694$	48.4908	1.84068
$695$	−1.02780	−0.0389866
$696$	−2.40869	−0.0913012
$697$	−3.73055	−0.141305
$698$	−28.8219	−1.09093
$699$	26.2521	0.992946
$700$	−8.31219	−0.314171
$701$	−2.51041	−0.0948168	−0.0474084	−	0.998876i	$-0.515096\pi$
$701$	−2.51041	−0.0948168	−0.0474084	+	0.998876i	$0.515096\pi$
$702$	4.07286	0.153720
$703$	−2.73053	−0.102984
$704$	−68.5859	−2.58493
$705$	30.2454	1.13911
$706$	20.0167	0.753339
$707$	−12.8475	−0.483181
$708$	57.0019	2.14226
$709$	24.2743	0.911639	0.455820	−	0.890072i	$-0.349346\pi$
$709$	24.2743	0.911639	0.455820	+	0.890072i	$0.349346\pi$
$710$	4.72547	0.177344
$711$	−20.8224	−0.780900
$712$	11.8730	0.444960
$713$	−4.60855	−0.172591
$714$	−4.94429	−0.185035
$715$	35.6291	1.33245
$716$	39.3729	1.47143
$717$	−55.5684	−2.07524
$718$	−74.7501	−2.78965
$719$	−4.17948	−0.155868	−0.0779342	−	0.996959i	$-0.524832\pi$
$719$	−4.17948	−0.155868	−0.0779342	+	0.996959i	$0.524832\pi$
$720$	−8.33925	−0.310785
$721$	6.05612	0.225542
$722$	39.9299	1.48604
$723$	−69.9709	−2.60225
$724$	40.3014	1.49779
$725$	−3.94363	−0.146463
$726$	−135.029	−5.01138
$727$	−5.91841	−0.219501	−0.109751	−	0.993959i	$-0.535005\pi$
$727$	−5.91841	−0.219501	−0.109751	+	0.993959i	$0.535005\pi$
$728$	−4.81311	−0.178386
$729$	−24.4174	−0.904347
$730$	2.66553	0.0986557
$731$	6.77278	0.250500
$732$	−90.4410	−3.34280
$733$	18.8222	0.695216	0.347608	−	0.937640i	$-0.386994\pi$
$733$	18.8222	0.695216	0.347608	+	0.937640i	$0.386994\pi$
$734$	−11.5782	−0.427360
$735$	−15.6049	−0.575596
$736$	18.9771	0.699504
$737$	92.6092	3.41130
$738$	19.9205	0.733284
$739$	3.98984	0.146769	0.0733843	−	0.997304i	$-0.476620\pi$
$739$	3.98984	0.146769	0.0733843	+	0.997304i	$0.476620\pi$
$740$	20.4376	0.751301
$741$	−4.65620	−0.171050
$742$	15.4104	0.565734
$743$	−21.7969	−0.799652	−0.399826	−	0.916591i	$-0.630930\pi$
$743$	−21.7969	−0.799652	−0.399826	+	0.916591i	$0.630930\pi$
$744$	4.67328	0.171331
$745$	−19.4763	−0.713555
$746$	−26.3411	−0.964416
$747$	−25.7398	−0.941771
$748$	17.1043	0.625394
$749$	−7.41899	−0.271084
$750$	47.0480	1.71795
$751$	−32.8477	−1.19863	−0.599314	−	0.800514i	$-0.704560\pi$
$751$	−32.8477	−1.19863	−0.599314	+	0.800514i	$0.704560\pi$
$752$	−34.4922	−1.25780
$753$	−30.7377	−1.12014
$754$	−11.9881	−0.436580
$755$	10.5013	0.382181
$756$	−0.716093	−0.0260441
$757$	−4.64660	−0.168884	−0.0844418	−	0.996428i	$-0.526911\pi$
$757$	−4.64660	−0.168884	−0.0844418	+	0.996428i	$0.526911\pi$
$758$	−73.5981	−2.67321
$759$	35.1552	1.27605
$760$	0.346963	0.0125857
$761$	−43.7344	−1.58537	−0.792686	−	0.609630i	$-0.791318\pi$
$761$	−43.7344	−1.58537	−0.792686	+	0.609630i	$0.791318\pi$
$762$	3.15773	0.114393
$763$	8.46322	0.306389
$764$	−44.7115	−1.61761
$765$	3.32805	0.120326
$766$	−16.9483	−0.612368
$767$	54.0400	1.95127
$768$	14.6936	0.530209
$769$	12.6727	0.456989	0.228494	−	0.973545i	$-0.426620\pi$
$769$	12.6727	0.456989	0.228494	+	0.973545i	$0.426620\pi$
$770$	−11.3354	−0.408500
$771$	−55.9272	−2.01417
$772$	44.8091	1.61271
$773$	−52.2079	−1.87779	−0.938893	−	0.344208i	$-0.888147\pi$
$773$	−52.2079	−1.87779	−0.938893	+	0.344208i	$0.888147\pi$
$774$	−36.1655	−1.29994
$775$	7.65133	0.274844
$776$	5.48816	0.197014
$777$	16.6214	0.596291
$778$	−16.2931	−0.584135
$779$	1.11772	0.0400466
$780$	34.8509	1.24786
$781$	−13.2949	−0.475728
$782$	−5.68691	−0.203363
$783$	−0.339743	−0.0121414
$784$	17.7961	0.635573
$785$	−14.3757	−0.513090
$786$	66.8528	2.38456
$787$	50.5443	1.80171	0.900855	−	0.434120i	$-0.142941\pi$
$787$	50.5443	1.80171	0.900855	+	0.434120i	$0.142941\pi$
$788$	49.0661	1.74791
$789$	22.1703	0.789282
$790$	15.8237	0.562983
$791$	−1.04703	−0.0372280
$792$	−17.3976	−0.618196
$793$	−85.7415	−3.04477
$794$	4.04363	0.143503
$795$	−21.2549	−0.753835
$796$	−46.5020	−1.64822
$797$	−27.8903	−0.987924	−0.493962	−	0.869483i	$-0.664452\pi$
$797$	−27.8903	−0.987924	−0.493962	+	0.869483i	$0.664452\pi$
$798$	1.48137	0.0524400
$799$	13.7652	0.486979
$800$	−31.5066	−1.11393
$801$	−34.1215	−1.20562
$802$	−5.82972	−0.205854
$803$	−7.49933	−0.264646
$804$	90.5865	3.19474
$805$	2.08280	0.0734089
$806$	23.2589	0.819261
$807$	45.5729	1.60424
$808$	14.9848	0.527162
$809$	36.7248	1.29117	0.645587	−	0.763686i	$-0.276613\pi$
$809$	36.7248	1.29117	0.645587	+	0.763686i	$0.276613\pi$
$810$	20.4306	0.717859
$811$	−23.1067	−0.811387	−0.405693	−	0.914009i	$-0.632970\pi$
$811$	−23.1067	−0.811387	−0.405693	+	0.914009i	$0.632970\pi$
$812$	2.10775	0.0739676
$813$	19.8280	0.695399
$814$	−104.048	−3.64686
$815$	−21.3505	−0.747876
$816$	−7.77698	−0.272249
$817$	−2.02921	−0.0709932
$818$	16.2107	0.566794
$819$	13.8323	0.483339
$820$	−8.36598	−0.292153
$821$	−13.5430	−0.472656	−0.236328	−	0.971673i	$-0.575944\pi$
$821$	−13.5430	−0.472656	−0.236328	+	0.971673i	$0.575944\pi$
$822$	4.08047	0.142323
$823$	−26.4540	−0.922129	−0.461065	−	0.887367i	$-0.652532\pi$
$823$	−26.4540	−0.922129	−0.461065	+	0.887367i	$0.652532\pi$
$824$	−7.06358	−0.246071
$825$	−58.3664	−2.03206
$826$	−17.1929	−0.598216
$827$	27.2058	0.946039	0.473020	−	0.881052i	$-0.343164\pi$
$827$	27.2058	0.946039	0.473020	+	0.881052i	$0.343164\pi$
$828$	16.7819	0.583211
$829$	−44.0112	−1.52857	−0.764286	−	0.644877i	$-0.776908\pi$
$829$	−44.0112	−1.52857	−0.764286	+	0.644877i	$0.776908\pi$
$830$	19.5607	0.678962
$831$	28.5628	0.990831
$832$	−63.6019	−2.20500
$833$	−7.10210	−0.246073
$834$	5.11822	0.177230
$835$	4.27056	0.147789
$836$	−5.12466	−0.177240
$837$	0.659160	0.0227839
$838$	−43.7001	−1.50960
$839$	−48.9839	−1.69111	−0.845557	−	0.533886i	$-0.820731\pi$
$839$	−48.9839	−1.69111	−0.845557	+	0.533886i	$0.820731\pi$
$840$	−2.11205	−0.0728727
$841$	1.00000	0.0344828
$842$	4.59720	0.158430
$843$	27.3399	0.941637
$844$	17.5059	0.602578
$845$	19.6786	0.676964
$846$	−73.5040	−2.52712
$847$	22.5072	0.773356
$848$	24.2394	0.832384
$849$	−8.10796	−0.278264
$850$	9.44167	0.323847
$851$	19.1179	0.655355
$852$	−13.0045	−0.445527
$853$	7.72326	0.264439	0.132220	−	0.991220i	$-0.457790\pi$
$853$	7.72326	0.264439	0.132220	+	0.991220i	$0.457790\pi$
$854$	27.2787	0.933458
$855$	−0.997128	−0.0341010
$856$	8.65316	0.295759
$857$	15.0517	0.514156	0.257078	−	0.966391i	$-0.417240\pi$
$857$	15.0517	0.514156	0.257078	+	0.966391i	$0.417240\pi$
$858$	−177.425	−6.05720
$859$	4.08698	0.139446	0.0697230	−	0.997566i	$-0.477788\pi$
$859$	4.08698	0.139446	0.0697230	+	0.997566i	$0.477788\pi$
$860$	15.1883	0.517918
$861$	−6.80386	−0.231875
$862$	−54.7846	−1.86597
$863$	13.6491	0.464620	0.232310	−	0.972642i	$-0.425372\pi$
$863$	13.6491	0.464620	0.232310	+	0.972642i	$0.425372\pi$
$864$	−2.71429	−0.0923419
$865$	−22.8823	−0.778022
$866$	−41.1468	−1.39823
$867$	−38.0478	−1.29217
$868$	−4.08941	−0.138803
$869$	−44.5193	−1.51021
$870$	−5.26050	−0.178348
$871$	85.8794	2.90991
$872$	−9.87110	−0.334278
$873$	−15.7723	−0.533811
$874$	1.70387	0.0576343
$875$	−7.84218	−0.265114
$876$	−7.33554	−0.247845
$877$	24.8938	0.840603	0.420302	−	0.907384i	$-0.361924\pi$
$877$	24.8938	0.840603	0.420302	+	0.907384i	$0.361924\pi$
$878$	5.72039	0.193054
$879$	−2.51023	−0.0846680
$880$	−17.8297	−0.601040
$881$	2.32536	0.0783433	0.0391716	−	0.999232i	$-0.487528\pi$
$881$	2.32536	0.0783433	0.0391716	+	0.999232i	$0.487528\pi$
$882$	37.9240	1.27697
$883$	−3.46228	−0.116515	−0.0582576	−	0.998302i	$-0.518554\pi$
$883$	−3.46228	−0.116515	−0.0582576	+	0.998302i	$0.518554\pi$
$884$	15.8613	0.533474
$885$	23.7134	0.797116
$886$	76.4820	2.56946
$887$	−38.8905	−1.30581	−0.652907	−	0.757438i	$-0.726451\pi$
$887$	−38.8905	−1.30581	−0.652907	+	0.757438i	$0.726451\pi$
$888$	−19.3865	−0.650567
$889$	−0.526346	−0.0176531
$890$	25.9303	0.869185
$891$	−57.4806	−1.92567
$892$	−21.4643	−0.718678
$893$	−4.12425	−0.138013
$894$	96.9877	3.24375
$895$	16.3795	0.547507
$896$	6.60325	0.220599
$897$	32.6006	1.08850
$898$	36.2387	1.20930
$899$	−1.94017	−0.0647084
$900$	−27.8621	−0.928735
$901$	−9.67353	−0.322272
$902$	42.5911	1.41813
$903$	12.3523	0.411060
$904$	1.22120	0.0406166
$905$	16.7658	0.557313
$906$	−52.2942	−1.73736
$907$	−5.65199	−0.187671	−0.0938356	−	0.995588i	$-0.529913\pi$
$907$	−5.65199	−0.187671	−0.0938356	+	0.995588i	$0.529913\pi$
$908$	47.8450	1.58779
$909$	−43.0643	−1.42835
$910$	−10.5117	−0.348459
$911$	−18.1809	−0.602359	−0.301179	−	0.953568i	$-0.597380\pi$
$911$	−18.1809	−0.602359	−0.301179	+	0.953568i	$0.597380\pi$
$912$	2.33008	0.0771568
$913$	−55.0330	−1.82133
$914$	72.9011	2.41136
$915$	−37.6244	−1.24382
$916$	9.31167	0.307666
$917$	−11.1433	−0.367986
$918$	0.813397	0.0268461
$919$	−54.2671	−1.79011	−0.895054	−	0.445958i	$-0.852863\pi$
$919$	−54.2671	−1.79011	−0.895054	+	0.445958i	$0.852863\pi$
$920$	−2.42928	−0.0800908
$921$	−2.67125	−0.0880206
$922$	58.9304	1.94077
$923$	−12.3288	−0.405806
$924$	31.1951	1.02624
$925$	−31.7405	−1.04362
$926$	−17.5828	−0.577805
$927$	20.2998	0.666734
$928$	7.98925	0.262260
$929$	−56.6071	−1.85722	−0.928610	−	0.371058i	$-0.878995\pi$
$929$	−56.6071	−1.85722	−0.928610	+	0.371058i	$0.878995\pi$
$930$	10.2063	0.334678
$931$	2.12788	0.0697385
$932$	26.7937	0.877657
$933$	−12.4787	−0.408535
$934$	36.7839	1.20361
$935$	7.11554	0.232703
$936$	−16.1333	−0.527334
$937$	48.2628	1.57668	0.788339	−	0.615242i	$-0.210942\pi$
$937$	48.2628	1.57668	0.788339	+	0.615242i	$0.210942\pi$
$938$	−27.3226	−0.892114
$939$	−28.6355	−0.934484
$940$	30.8693	1.00685
$941$	50.6634	1.65158	0.825790	−	0.563978i	$-0.190730\pi$
$941$	50.6634	1.65158	0.825790	+	0.563978i	$0.190730\pi$
$942$	71.5879	2.33246
$943$	−7.82578	−0.254842
$944$	−27.0430	−0.880176
$945$	−0.297902	−0.00969075
$946$	−77.3236	−2.51401
$947$	26.2123	0.851784	0.425892	−	0.904774i	$-0.359960\pi$
$947$	26.2123	0.851784	0.425892	+	0.904774i	$0.359960\pi$
$948$	−43.5469	−1.41434
$949$	−6.95437	−0.225748
$950$	−2.82885	−0.0917799
$951$	27.1582	0.880665
$952$	−0.961235	−0.0311538
$953$	−43.2872	−1.40221	−0.701105	−	0.713059i	$-0.747309\pi$
$953$	−43.2872	−1.40221	−0.701105	+	0.713059i	$0.747309\pi$
$954$	51.6550	1.67239
$955$	−18.6004	−0.601896
$956$	−56.7148	−1.83429
$957$	14.8002	0.478421
$958$	4.60782	0.148872
$959$	−0.680153	−0.0219633
$960$	−27.9092	−0.900767
$961$	−27.2357	−0.878572
$962$	−96.4866	−3.11085
$963$	−24.8681	−0.801363
$964$	−71.4144	−2.30010
$965$	18.6410	0.600076
$966$	−10.3719	−0.333710
$967$	−5.08244	−0.163440	−0.0817201	−	0.996655i	$-0.526041\pi$
$967$	−5.08244	−0.163440	−0.0817201	+	0.996655i	$0.526041\pi$
$968$	−26.2513	−0.843750
$969$	−0.929897	−0.0298726
$970$	11.9860	0.384846
$971$	18.5674	0.595856	0.297928	−	0.954588i	$-0.403704\pi$
$971$	18.5674	0.595856	0.297928	+	0.954588i	$0.403704\pi$
$972$	−53.7070	−1.72265
$973$	−0.853130	−0.0273501
$974$	−6.33283	−0.202917
$975$	−54.1250	−1.73339
$976$	42.9073	1.37343
$977$	22.4189	0.717244	0.358622	−	0.933483i	$-0.383247\pi$
$977$	22.4189	0.717244	0.358622	+	0.933483i	$0.383247\pi$
$978$	106.321	3.39977
$979$	−72.9535	−2.33161
$980$	−15.9269	−0.508765
$981$	28.3683	0.905730
$982$	19.4172	0.619627
$983$	−17.8881	−0.570541	−0.285271	−	0.958447i	$-0.592083\pi$
$983$	−17.8881	−0.570541	−0.285271	+	0.958447i	$0.592083\pi$
$984$	7.93570	0.252981
$985$	20.4120	0.650379
$986$	−2.39416	−0.0762455
$987$	25.1053	0.799111
$988$	−4.75226	−0.151189
$989$	14.2076	0.451776
$990$	−37.9958	−1.20758
$991$	−9.34571	−0.296876	−0.148438	−	0.988922i	$-0.547425\pi$
$991$	−9.34571	−0.296876	−0.148438	+	0.988922i	$0.547425\pi$
$992$	−15.5005	−0.492142
$993$	75.1266	2.38407
$994$	3.92240	0.124411
$995$	−19.3453	−0.613287
$996$	−53.8311	−1.70570
$997$	13.6589	0.432583	0.216291	−	0.976329i	$-0.430604\pi$
$997$	13.6589	0.432583	0.216291	+	0.976329i	$0.430604\pi$
$998$	−64.5299	−2.04266
$999$	−2.73444	−0.0865137

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.13	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.13	✓	98	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.11438 q^{2} +2.42067 q^{3} +2.47061 q^{4} +1.02780 q^{5} -5.11822 q^{6} +0.853130 q^{7} -0.995051 q^{8} +2.85965 q^{9} +O(q^{10})\)	\(q-2.11438 q^{2} +2.42067 q^{3} +2.47061 q^{4} +1.02780 q^{5} -5.11822 q^{6} +0.853130 q^{7} -0.995051 q^{8} +2.85965 q^{9} -2.17316 q^{10} +6.11407 q^{11} +5.98054 q^{12} +5.66977 q^{13} -1.80384 q^{14} +2.48796 q^{15} -2.83730 q^{16} +1.13232 q^{17} -6.04639 q^{18} -0.339258 q^{19} +2.53929 q^{20} +2.06515 q^{21} -12.9275 q^{22} +2.37533 q^{23} -2.40869 q^{24} -3.94363 q^{25} -11.9881 q^{26} -0.339743 q^{27} +2.10775 q^{28} +1.00000 q^{29} -5.26050 q^{30} -1.94017 q^{31} +7.98925 q^{32} +14.8002 q^{33} -2.39416 q^{34} +0.876846 q^{35} +7.06508 q^{36} +8.04855 q^{37} +0.717321 q^{38} +13.7247 q^{39} -1.02271 q^{40} -3.29461 q^{41} -4.36651 q^{42} +5.98133 q^{43} +15.1055 q^{44} +2.93914 q^{45} -5.02235 q^{46} +12.1567 q^{47} -6.86818 q^{48} -6.27217 q^{49} +8.33834 q^{50} +2.74097 q^{51} +14.0078 q^{52} -8.54311 q^{53} +0.718346 q^{54} +6.28404 q^{55} -0.848907 q^{56} -0.821232 q^{57} -2.11438 q^{58} +9.53124 q^{59} +6.14679 q^{60} -15.1226 q^{61} +4.10227 q^{62} +2.43965 q^{63} -11.2177 q^{64} +5.82739 q^{65} -31.2932 q^{66} +15.1469 q^{67} +2.79752 q^{68} +5.74989 q^{69} -1.85399 q^{70} -2.17447 q^{71} -2.84550 q^{72} -1.22657 q^{73} -17.0177 q^{74} -9.54623 q^{75} -0.838174 q^{76} +5.21610 q^{77} -29.0192 q^{78} -7.28144 q^{79} -2.91618 q^{80} -9.40135 q^{81} +6.96607 q^{82} -9.00104 q^{83} +5.10217 q^{84} +1.16380 q^{85} -12.6468 q^{86} +2.42067 q^{87} -6.08381 q^{88} -11.9321 q^{89} -6.21447 q^{90} +4.83705 q^{91} +5.86851 q^{92} -4.69652 q^{93} -25.7038 q^{94} -0.348689 q^{95} +19.3393 q^{96} -5.51546 q^{97} +13.2618 q^{98} +17.4841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

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