LMFDB - Embedded newform 4031.2.a.d.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.96419 q^{2} -0.913998 q^{3} +1.85806 q^{4} -4.29424 q^{5} +1.79527 q^{6} -2.01487 q^{7} +0.278799 q^{8} -2.16461 q^{9} +O(q^{10})$	\(q-1.96419 q^{2} -0.913998 q^{3} +1.85806 q^{4} -4.29424 q^{5} +1.79527 q^{6} -2.01487 q^{7} +0.278799 q^{8} -2.16461 q^{9} +8.43472 q^{10} +4.84729 q^{11} -1.69826 q^{12} -4.42415 q^{13} +3.95760 q^{14} +3.92492 q^{15} -4.26373 q^{16} +4.90208 q^{17} +4.25171 q^{18} +2.06684 q^{19} -7.97895 q^{20} +1.84159 q^{21} -9.52101 q^{22} -7.00395 q^{23} -0.254821 q^{24} +13.4405 q^{25} +8.68988 q^{26} +4.72044 q^{27} -3.74375 q^{28} +1.00000 q^{29} -7.70931 q^{30} -10.5113 q^{31} +7.81720 q^{32} -4.43041 q^{33} -9.62864 q^{34} +8.65234 q^{35} -4.02197 q^{36} -5.35709 q^{37} -4.05968 q^{38} +4.04366 q^{39} -1.19723 q^{40} -4.71597 q^{41} -3.61724 q^{42} +11.0231 q^{43} +9.00655 q^{44} +9.29534 q^{45} +13.7571 q^{46} -11.8372 q^{47} +3.89704 q^{48} -2.94029 q^{49} -26.3997 q^{50} -4.48049 q^{51} -8.22033 q^{52} -2.55095 q^{53} -9.27186 q^{54} -20.8154 q^{55} -0.561744 q^{56} -1.88909 q^{57} -1.96419 q^{58} -12.2624 q^{59} +7.29274 q^{60} +2.09723 q^{61} +20.6462 q^{62} +4.36141 q^{63} -6.82704 q^{64} +18.9983 q^{65} +8.70218 q^{66} -6.00381 q^{67} +9.10836 q^{68} +6.40159 q^{69} -16.9949 q^{70} +0.200111 q^{71} -0.603490 q^{72} -1.35338 q^{73} +10.5224 q^{74} -12.2846 q^{75} +3.84032 q^{76} -9.76666 q^{77} -7.94253 q^{78} +5.52797 q^{79} +18.3095 q^{80} +2.17935 q^{81} +9.26309 q^{82} -9.52213 q^{83} +3.42178 q^{84} -21.0507 q^{85} -21.6516 q^{86} -0.913998 q^{87} +1.35142 q^{88} -9.38042 q^{89} -18.2579 q^{90} +8.91409 q^{91} -13.0138 q^{92} +9.60727 q^{93} +23.2505 q^{94} -8.87552 q^{95} -7.14491 q^{96} -16.1921 q^{97} +5.77530 q^{98} -10.4925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.96419	−1.38890	−0.694448	−	0.719543i	$-0.744351\pi$
$2$	−1.96419	−1.38890	−0.694448	+	0.719543i	$0.744351\pi$
$3$	−0.913998	−0.527697	−0.263848	−	0.964564i	$-0.584992\pi$
$3$	−0.913998	−0.527697	−0.263848	+	0.964564i	$0.584992\pi$
$4$	1.85806	0.929030
$5$	−4.29424	−1.92044	−0.960221	−	0.279242i	$-0.909917\pi$
$5$	−4.29424	−1.92044	−0.960221	+	0.279242i	$0.909917\pi$
$6$	1.79527	0.732916
$7$	−2.01487	−0.761550	−0.380775	−	0.924668i	$-0.624343\pi$
$7$	−2.01487	−0.761550	−0.380775	+	0.924668i	$0.624343\pi$
$8$	0.278799	0.0985702
$9$	−2.16461	−0.721536
$10$	8.43472	2.66729
$11$	4.84729	1.46151	0.730756	−	0.682639i	$-0.239168\pi$
$11$	4.84729	1.46151	0.730756	+	0.682639i	$0.239168\pi$
$12$	−1.69826	−0.490246
$13$	−4.42415	−1.22704	−0.613519	−	0.789680i	$-0.710246\pi$
$13$	−4.42415	−1.22704	−0.613519	+	0.789680i	$0.710246\pi$
$14$	3.95760	1.05771
$15$	3.92492	1.01341
$16$	−4.26373	−1.06593
$17$	4.90208	1.18893	0.594465	−	0.804122i	$-0.297364\pi$
$17$	4.90208	1.18893	0.594465	+	0.804122i	$0.297364\pi$
$18$	4.25171	1.00214
$19$	2.06684	0.474166	0.237083	−	0.971489i	$-0.423809\pi$
$19$	2.06684	0.474166	0.237083	+	0.971489i	$0.423809\pi$
$20$	−7.97895	−1.78415
$21$	1.84159	0.401867
$22$	−9.52101	−2.02989
$23$	−7.00395	−1.46042	−0.730212	−	0.683220i	$-0.760579\pi$
$23$	−7.00395	−1.46042	−0.730212	+	0.683220i	$0.760579\pi$
$24$	−0.254821	−0.0520152
$25$	13.4405	2.68809
$26$	8.68988	1.70423
$27$	4.72044	0.908449
$28$	−3.74375	−0.707503
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−7.70931	−1.40752
$31$	−10.5113	−1.88788	−0.943939	−	0.330119i	$-0.892911\pi$
$31$	−10.5113	−1.88788	−0.943939	+	0.330119i	$0.892911\pi$
$32$	7.81720	1.38190
$33$	−4.43041	−0.771235
$34$	−9.62864	−1.65130
$35$	8.65234	1.46251
$36$	−4.02197	−0.670328
$37$	−5.35709	−0.880701	−0.440350	−	0.897826i	$-0.645146\pi$
$37$	−5.35709	−0.880701	−0.440350	+	0.897826i	$0.645146\pi$
$38$	−4.05968	−0.658567
$39$	4.04366	0.647504
$40$	−1.19723	−0.189298
$41$	−4.71597	−0.736512	−0.368256	−	0.929725i	$-0.620045\pi$
$41$	−4.71597	−0.736512	−0.368256	+	0.929725i	$0.620045\pi$
$42$	−3.61724	−0.558152
$43$	11.0231	1.68101	0.840505	−	0.541803i	$-0.182258\pi$
$43$	11.0231	1.68101	0.840505	+	0.541803i	$0.182258\pi$
$44$	9.00655	1.35779
$45$	9.29534	1.38567
$46$	13.7571	2.02838
$47$	−11.8372	−1.72663	−0.863314	−	0.504667i	$-0.831615\pi$
$47$	−11.8372	−1.72663	−0.863314	+	0.504667i	$0.831615\pi$
$48$	3.89704	0.562490
$49$	−2.94029	−0.420042
$50$	−26.3997	−3.73348
$51$	−4.48049	−0.627394
$52$	−8.22033	−1.13995
$53$	−2.55095	−0.350400	−0.175200	−	0.984533i	$-0.556057\pi$
$53$	−2.55095	−0.350400	−0.175200	+	0.984533i	$0.556057\pi$
$54$	−9.27186	−1.26174
$55$	−20.8154	−2.80675
$56$	−0.561744	−0.0750661
$57$	−1.88909	−0.250216
$58$	−1.96419	−0.257911
$59$	−12.2624	−1.59643	−0.798214	−	0.602374i	$-0.794222\pi$
$59$	−12.2624	−1.59643	−0.798214	+	0.602374i	$0.794222\pi$
$60$	7.29274	0.941489
$61$	2.09723	0.268523	0.134261	−	0.990946i	$-0.457134\pi$
$61$	2.09723	0.268523	0.134261	+	0.990946i	$0.457134\pi$
$62$	20.6462	2.62207
$63$	4.36141	0.549486
$64$	−6.82704	−0.853380
$65$	18.9983	2.35645
$66$	8.70218	1.07116
$67$	−6.00381	−0.733483	−0.366741	−	0.930323i	$-0.619527\pi$
$67$	−6.00381	−0.733483	−0.366741	+	0.930323i	$0.619527\pi$
$68$	9.10836	1.10455
$69$	6.40159	0.770661
$70$	−16.9949	−2.03128
$71$	0.200111	0.0237488	0.0118744	−	0.999929i	$-0.496220\pi$
$71$	0.200111	0.0237488	0.0118744	+	0.999929i	$0.496220\pi$
$72$	−0.603490	−0.0711220
$73$	−1.35338	−0.158402	−0.0792009	−	0.996859i	$-0.525237\pi$
$73$	−1.35338	−0.158402	−0.0792009	+	0.996859i	$0.525237\pi$
$74$	10.5224	1.22320
$75$	−12.2846	−1.41850
$76$	3.84032	0.440515
$77$	−9.76666	−1.11301
$78$	−7.94253	−0.899315
$79$	5.52797	0.621946	0.310973	−	0.950419i	$-0.399345\pi$
$79$	5.52797	0.621946	0.310973	+	0.950419i	$0.399345\pi$
$80$	18.3095	2.04706
$81$	2.17935	0.242150
$82$	9.26309	1.02294
$83$	−9.52213	−1.04519	−0.522595	−	0.852581i	$-0.675036\pi$
$83$	−9.52213	−1.04519	−0.522595	+	0.852581i	$0.675036\pi$
$84$	3.42178	0.373347
$85$	−21.0507	−2.28327
$86$	−21.6516	−2.33475
$87$	−0.913998	−0.0979908
$88$	1.35142	0.144062
$89$	−9.38042	−0.994323	−0.497161	−	0.867658i	$-0.665624\pi$
$89$	−9.38042	−0.994323	−0.497161	+	0.867658i	$0.665624\pi$
$90$	−18.2579	−1.92455
$91$	8.91409	0.934450
$92$	−13.0138	−1.35678
$93$	9.60727	0.996227
$94$	23.2505	2.39810
$95$	−8.87552	−0.910609
$96$	−7.14491	−0.729224
$97$	−16.1921	−1.64406	−0.822028	−	0.569447i	$-0.807158\pi$
$97$	−16.1921	−1.64406	−0.822028	+	0.569447i	$0.807158\pi$
$98$	5.77530	0.583394
$99$	−10.4925	−1.05453
$100$	24.9732	2.49732
$101$	−18.9121	−1.88182	−0.940912	−	0.338652i	$-0.890029\pi$
$101$	−18.9121	−1.88182	−0.940912	+	0.338652i	$0.890029\pi$
$102$	8.80056	0.871385
$103$	5.87581	0.578961	0.289480	−	0.957184i	$-0.406518\pi$
$103$	5.87581	0.578961	0.289480	+	0.957184i	$0.406518\pi$
$104$	−1.23345	−0.120949
$105$	−7.90822	−0.771763
$106$	5.01056	0.486669
$107$	−10.0865	−0.975100	−0.487550	−	0.873095i	$-0.662109\pi$
$107$	−10.0865	−0.975100	−0.487550	+	0.873095i	$0.662109\pi$
$108$	8.77086	0.843976
$109$	−3.13179	−0.299971	−0.149985	−	0.988688i	$-0.547923\pi$
$109$	−3.13179	−0.299971	−0.149985	+	0.988688i	$0.547923\pi$
$110$	40.8855	3.89828
$111$	4.89637	0.464743
$112$	8.59088	0.811762
$113$	−0.342045	−0.0321769	−0.0160884	−	0.999871i	$-0.505121\pi$
$113$	−0.342045	−0.0321769	−0.0160884	+	0.999871i	$0.505121\pi$
$114$	3.71054	0.347524
$115$	30.0766	2.80466
$116$	1.85806	0.172516
$117$	9.57654	0.885352
$118$	24.0857	2.21727
$119$	−9.87707	−0.905429
$120$	1.09426	0.0998921
$121$	12.4962	1.13602
$122$	−4.11936	−0.372950
$123$	4.31039	0.388655
$124$	−19.5306	−1.75390
$125$	−36.2454	−3.24189
$126$	−8.56665	−0.763178
$127$	−16.3838	−1.45383	−0.726915	−	0.686727i	$-0.759047\pi$
$127$	−16.3838	−1.45383	−0.726915	+	0.686727i	$0.759047\pi$
$128$	−2.22477	−0.196644
$129$	−10.0751	−0.887064
$130$	−37.3164	−3.27287
$131$	17.0472	1.48942	0.744709	−	0.667389i	$-0.232588\pi$
$131$	17.0472	1.48942	0.744709	+	0.667389i	$0.232588\pi$
$132$	−8.23196	−0.716500
$133$	−4.16442	−0.361101
$134$	11.7927	1.01873
$135$	−20.2707	−1.74462
$136$	1.36669	0.117193
$137$	1.46917	0.125520	0.0627599	−	0.998029i	$-0.480010\pi$
$137$	1.46917	0.125520	0.0627599	+	0.998029i	$0.480010\pi$
$138$	−12.5740	−1.07037
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	16.0766	1.35872
$141$	10.8191	0.911136
$142$	−0.393057	−0.0329846
$143$	−21.4451	−1.79333
$144$	9.22931	0.769109
$145$	−4.29424	−0.356617
$146$	2.65831	0.220003
$147$	2.68742	0.221655
$148$	−9.95380	−0.818197
$149$	0.400751	0.0328308	0.0164154	−	0.999865i	$-0.494775\pi$
$149$	0.400751	0.0328308	0.0164154	+	0.999865i	$0.494775\pi$
$150$	24.1293	1.97015
$151$	23.3449	1.89978	0.949890	−	0.312584i	$-0.101195\pi$
$151$	23.3449	1.89978	0.949890	+	0.312584i	$0.101195\pi$
$152$	0.576233	0.0467387
$153$	−10.6111	−0.857856
$154$	19.1836	1.54586
$155$	45.1379	3.62556
$156$	7.51336	0.601550
$157$	7.28607	0.581491	0.290746	−	0.956800i	$-0.406097\pi$
$157$	7.28607	0.581491	0.290746	+	0.956800i	$0.406097\pi$
$158$	−10.8580	−0.863817
$159$	2.33156	0.184905
$160$	−33.5689	−2.65386
$161$	14.1121	1.11219
$162$	−4.28067	−0.336322
$163$	5.05880	0.396236	0.198118	−	0.980178i	$-0.436517\pi$
$163$	5.05880	0.396236	0.198118	+	0.980178i	$0.436517\pi$
$164$	−8.76256	−0.684241
$165$	19.0252	1.48111
$166$	18.7033	1.45166
$167$	−6.55377	−0.507146	−0.253573	−	0.967316i	$-0.581606\pi$
$167$	−6.55377	−0.507146	−0.253573	+	0.967316i	$0.581606\pi$
$168$	0.513432	0.0396122
$169$	6.57307	0.505620
$170$	41.3477	3.17122
$171$	−4.47391	−0.342128
$172$	20.4816	1.56171
$173$	1.99894	0.151977	0.0759885	−	0.997109i	$-0.475789\pi$
$173$	1.99894	0.151977	0.0759885	+	0.997109i	$0.475789\pi$
$174$	1.79527	0.136099
$175$	−27.0808	−2.04712
$176$	−20.6675	−1.55787
$177$	11.2078	0.842430
$178$	18.4250	1.38101
$179$	14.8960	1.11338	0.556689	−	0.830721i	$-0.312071\pi$
$179$	14.8960	1.11338	0.556689	+	0.830721i	$0.312071\pi$
$180$	17.2713	1.28733
$181$	9.05518	0.673066	0.336533	−	0.941672i	$-0.390746\pi$
$181$	9.05518	0.673066	0.336533	+	0.941672i	$0.390746\pi$
$182$	−17.5090	−1.29785
$183$	−1.91686	−0.141698
$184$	−1.95269	−0.143954
$185$	23.0046	1.69133
$186$	−18.8705	−1.38366
$187$	23.7618	1.73763
$188$	−21.9942	−1.60409
$189$	−9.51108	−0.691829
$190$	17.4332	1.26474
$191$	4.14710	0.300073	0.150037	−	0.988680i	$-0.452061\pi$
$191$	4.14710	0.300073	0.150037	+	0.988680i	$0.452061\pi$
$192$	6.23990	0.450326
$193$	−18.8878	−1.35957	−0.679786	−	0.733411i	$-0.737927\pi$
$193$	−18.8878	−1.35957	−0.679786	+	0.733411i	$0.737927\pi$
$194$	31.8044	2.28342
$195$	−17.3644	−1.24349
$196$	−5.46324	−0.390231
$197$	−16.8664	−1.20168	−0.600839	−	0.799370i	$-0.705167\pi$
$197$	−16.8664	−1.20168	−0.600839	+	0.799370i	$0.705167\pi$
$198$	20.6093	1.46464
$199$	8.85225	0.627520	0.313760	−	0.949502i	$-0.398411\pi$
$199$	8.85225	0.627520	0.313760	+	0.949502i	$0.398411\pi$
$200$	3.74719	0.264966
$201$	5.48747	0.387056
$202$	37.1470	2.61366
$203$	−2.01487	−0.141416
$204$	−8.32502	−0.582868
$205$	20.2515	1.41443
$206$	−11.5412	−0.804116
$207$	15.1608	1.05375
$208$	18.8634	1.30794
$209$	10.0186	0.693000
$210$	15.5333	1.07190
$211$	−23.8451	−1.64156	−0.820781	−	0.571243i	$-0.806462\pi$
$211$	−23.8451	−1.64156	−0.820781	+	0.571243i	$0.806462\pi$
$212$	−4.73981	−0.325532
$213$	−0.182901	−0.0125322
$214$	19.8119	1.35431
$215$	−47.3359	−3.22828
$216$	1.31605	0.0895460
$217$	21.1788	1.43771
$218$	6.15144	0.416628
$219$	1.23699	0.0835881
$220$	−38.6762	−2.60755
$221$	−21.6875	−1.45886
$222$	−9.61742	−0.645479
$223$	−19.4375	−1.30163	−0.650816	−	0.759236i	$-0.725573\pi$
$223$	−19.4375	−1.30163	−0.650816	+	0.759236i	$0.725573\pi$
$224$	−15.7507	−1.05239
$225$	−29.0934	−1.93956
$226$	0.671842	0.0446903
$227$	−25.2445	−1.67554	−0.837768	−	0.546027i	$-0.816140\pi$
$227$	−25.2445	−1.67554	−0.837768	+	0.546027i	$0.816140\pi$
$228$	−3.51004	−0.232458
$229$	19.1548	1.26579	0.632894	−	0.774239i	$-0.281867\pi$
$229$	19.1548	1.26579	0.632894	+	0.774239i	$0.281867\pi$
$230$	−59.0763	−3.89538
$231$	8.92670	0.587334
$232$	0.278799	0.0183040
$233$	−19.9792	−1.30888	−0.654440	−	0.756114i	$-0.727096\pi$
$233$	−19.9792	−1.30888	−0.654440	+	0.756114i	$0.727096\pi$
$234$	−18.8102	−1.22966
$235$	50.8316	3.31589
$236$	−22.7843	−1.48313
$237$	−5.05256	−0.328199
$238$	19.4005	1.25755
$239$	−14.3721	−0.929654	−0.464827	−	0.885401i	$-0.653884\pi$
$239$	−14.3721	−0.929654	−0.464827	+	0.885401i	$0.653884\pi$
$240$	−16.7348	−1.08023
$241$	−4.91054	−0.316316	−0.158158	−	0.987414i	$-0.550555\pi$
$241$	−4.91054	−0.316316	−0.158158	+	0.987414i	$0.550555\pi$
$242$	−24.5449	−1.57781
$243$	−16.1532	−1.03623
$244$	3.89677	0.249465
$245$	12.6263	0.806665
$246$	−8.46644	−0.539801
$247$	−9.14402	−0.581820
$248$	−2.93053	−0.186089
$249$	8.70321	0.551543
$250$	71.1930	4.50264
$251$	26.0687	1.64544	0.822720	−	0.568446i	$-0.192455\pi$
$251$	26.0687	1.64544	0.822720	+	0.568446i	$0.192455\pi$
$252$	8.10376	0.510489
$253$	−33.9501	−2.13443
$254$	32.1810	2.01922
$255$	19.2403	1.20487
$256$	18.0240	1.12650
$257$	−11.3079	−0.705367	−0.352684	−	0.935743i	$-0.614731\pi$
$257$	−11.3079	−0.705367	−0.352684	+	0.935743i	$0.614731\pi$
$258$	19.7895	1.23204
$259$	10.7939	0.670698
$260$	35.3000	2.18922
$261$	−2.16461	−0.133986
$262$	−33.4840	−2.06865
$263$	14.4980	0.893987	0.446994	−	0.894537i	$-0.352495\pi$
$263$	14.4980	0.893987	0.446994	+	0.894537i	$0.352495\pi$
$264$	−1.23519	−0.0760208
$265$	10.9544	0.672922
$266$	8.17974	0.501532
$267$	8.57368	0.524701
$268$	−11.1554	−0.681427
$269$	−8.21607	−0.500943	−0.250471	−	0.968124i	$-0.580586\pi$
$269$	−8.21607	−0.500943	−0.250471	+	0.968124i	$0.580586\pi$
$270$	39.8156	2.42310
$271$	25.2044	1.53106	0.765528	−	0.643403i	$-0.222478\pi$
$271$	25.2044	1.53106	0.765528	+	0.643403i	$0.222478\pi$
$272$	−20.9012	−1.26732
$273$	−8.14745	−0.493106
$274$	−2.88574	−0.174334
$275$	65.1498	3.92868
$276$	11.8945	0.715967
$277$	18.5439	1.11420	0.557098	−	0.830447i	$-0.311915\pi$
$277$	18.5439	1.11420	0.557098	+	0.830447i	$0.311915\pi$
$278$	1.96419	0.117805
$279$	22.7528	1.36217
$280$	2.41226	0.144160
$281$	−1.17435	−0.0700557	−0.0350278	−	0.999386i	$-0.511152\pi$
$281$	−1.17435	−0.0700557	−0.0350278	+	0.999386i	$0.511152\pi$
$282$	−21.2509	−1.26547
$283$	−19.9083	−1.18342	−0.591712	−	0.806150i	$-0.701548\pi$
$283$	−19.9083	−1.18342	−0.591712	+	0.806150i	$0.701548\pi$
$284$	0.371818	0.0220633
$285$	8.11220	0.480525
$286$	42.1223	2.49075
$287$	9.50208	0.560890
$288$	−16.9212	−0.997090
$289$	7.03042	0.413554
$290$	8.43472	0.495304
$291$	14.7995	0.867563
$292$	−2.51467	−0.147160
$293$	−5.52736	−0.322912	−0.161456	−	0.986880i	$-0.551619\pi$
$293$	−5.52736	−0.322912	−0.161456	+	0.986880i	$0.551619\pi$
$294$	−5.27862	−0.307855
$295$	52.6577	3.06585
$296$	−1.49355	−0.0868109
$297$	22.8813	1.32771
$298$	−0.787154	−0.0455986
$299$	30.9865	1.79200
$300$	−22.8254	−1.31783
$301$	−22.2102	−1.28017
$302$	−45.8539	−2.63860
$303$	17.2856	0.993032
$304$	−8.81247	−0.505430
$305$	−9.00600	−0.515682
$306$	20.8422	1.19147
$307$	−0.0880121	−0.00502311	−0.00251156	−	0.999997i	$-0.500799\pi$
$307$	−0.0880121	−0.00502311	−0.00251156	+	0.999997i	$0.500799\pi$
$308$	−18.1470	−1.03402
$309$	−5.37048	−0.305516
$310$	−88.6595	−5.03552
$311$	−11.7198	−0.664570	−0.332285	−	0.943179i	$-0.607820\pi$
$311$	−11.7198	−0.664570	−0.332285	+	0.943179i	$0.607820\pi$
$312$	1.12737	0.0638246
$313$	−10.1758	−0.575168	−0.287584	−	0.957755i	$-0.592852\pi$
$313$	−10.1758	−0.575168	−0.287584	+	0.957755i	$0.592852\pi$
$314$	−14.3113	−0.807631
$315$	−18.7289	−1.05526
$316$	10.2713	0.577806
$317$	−12.6827	−0.712332	−0.356166	−	0.934423i	$-0.615916\pi$
$317$	−12.6827	−0.712332	−0.356166	+	0.934423i	$0.615916\pi$
$318$	−4.57964	−0.256813
$319$	4.84729	0.271396
$320$	29.3169	1.63887
$321$	9.21905	0.514557
$322$	−27.7188	−1.54471
$323$	10.1318	0.563751
$324$	4.04937	0.224965
$325$	−59.4626	−3.29839
$326$	−9.93646	−0.550330
$327$	2.86245	0.158294
$328$	−1.31481	−0.0725981
$329$	23.8504	1.31491
$330$	−37.3692	−2.05711
$331$	−3.82924	−0.210474	−0.105237	−	0.994447i	$-0.533560\pi$
$331$	−3.82924	−0.210474	−0.105237	+	0.994447i	$0.533560\pi$
$332$	−17.6927	−0.971013
$333$	11.5960	0.635457
$334$	12.8729	0.704373
$335$	25.7818	1.40861
$336$	−7.85204	−0.428364
$337$	5.99339	0.326481	0.163240	−	0.986586i	$-0.447805\pi$
$337$	5.99339	0.326481	0.163240	+	0.986586i	$0.447805\pi$
$338$	−12.9108	−0.702254
$339$	0.312628	0.0169796
$340$	−39.1135	−2.12123
$341$	−50.9511	−2.75916
$342$	8.78762	0.475180
$343$	20.0284	1.08143
$344$	3.07323	0.165698
$345$	−27.4900	−1.48001
$346$	−3.92632	−0.211080
$347$	−3.90428	−0.209593	−0.104796	−	0.994494i	$-0.533419\pi$
$347$	−3.90428	−0.209593	−0.104796	+	0.994494i	$0.533419\pi$
$348$	−1.69826	−0.0910364
$349$	15.9375	0.853113	0.426557	−	0.904461i	$-0.359726\pi$
$349$	15.9375	0.853113	0.426557	+	0.904461i	$0.359726\pi$
$350$	53.1920	2.84323
$351$	−20.8839	−1.11470
$352$	37.8922	2.01966
$353$	−1.44038	−0.0766636	−0.0383318	−	0.999265i	$-0.512204\pi$
$353$	−1.44038	−0.0766636	−0.0383318	+	0.999265i	$0.512204\pi$
$354$	−22.0143	−1.17005
$355$	−0.859324	−0.0456082
$356$	−17.4294	−0.923755
$357$	9.02762	0.477792
$358$	−29.2586	−1.54637
$359$	33.3434	1.75980	0.879898	−	0.475162i	$-0.157611\pi$
$359$	33.3434	1.75980	0.879898	+	0.475162i	$0.157611\pi$
$360$	2.59153	0.136586
$361$	−14.7282	−0.775166
$362$	−17.7861	−0.934818
$363$	−11.4215	−0.599472
$364$	16.5629	0.868132
$365$	5.81176	0.304201
$366$	3.76509	0.196804
$367$	23.5986	1.23184	0.615918	−	0.787810i	$-0.288785\pi$
$367$	23.5986	1.23184	0.615918	+	0.787810i	$0.288785\pi$
$368$	29.8630	1.55672
$369$	10.2082	0.531420
$370$	−45.1856	−2.34909
$371$	5.13983	0.266847
$372$	17.8509	0.925525
$373$	−12.0171	−0.622223	−0.311111	−	0.950373i	$-0.600701\pi$
$373$	−12.0171	−0.622223	−0.311111	+	0.950373i	$0.600701\pi$
$374$	−46.6728	−2.41339
$375$	33.1282	1.71073
$376$	−3.30019	−0.170194
$377$	−4.42415	−0.227855
$378$	18.6816	0.960878
$379$	−29.3503	−1.50762	−0.753811	−	0.657092i	$-0.771786\pi$
$379$	−29.3503	−1.50762	−0.753811	+	0.657092i	$0.771786\pi$
$380$	−16.4912	−0.845983
$381$	14.9748	0.767182
$382$	−8.14571	−0.416771
$383$	13.2904	0.679108	0.339554	−	0.940586i	$-0.389724\pi$
$383$	13.2904	0.679108	0.339554	+	0.940586i	$0.389724\pi$
$384$	2.03344	0.103768
$385$	41.9404	2.13748
$386$	37.0992	1.88830
$387$	−23.8607	−1.21291
$388$	−30.0858	−1.52738
$389$	−20.7072	−1.04990	−0.524949	−	0.851134i	$-0.675915\pi$
$389$	−20.7072	−1.04990	−0.524949	+	0.851134i	$0.675915\pi$
$390$	34.1071	1.72708
$391$	−34.3340	−1.73634
$392$	−0.819750	−0.0414036
$393$	−15.5811	−0.785962
$394$	33.1288	1.66900
$395$	−23.7384	−1.19441
$396$	−19.4956	−0.979693
$397$	30.4157	1.52652	0.763261	−	0.646090i	$-0.223597\pi$
$397$	30.4157	1.52652	0.763261	+	0.646090i	$0.223597\pi$
$398$	−17.3875	−0.871559
$399$	3.80627	0.190552
$400$	−57.3066	−2.86533
$401$	14.2664	0.712432	0.356216	−	0.934404i	$-0.384067\pi$
$401$	14.2664	0.712432	0.356216	+	0.934404i	$0.384067\pi$
$402$	−10.7785	−0.537581
$403$	46.5034	2.31650
$404$	−35.1398	−1.74827
$405$	−9.35866	−0.465036
$406$	3.95760	0.196412
$407$	−25.9674	−1.28715
$408$	−1.24916	−0.0618424
$409$	2.36044	0.116716	0.0583582	−	0.998296i	$-0.481413\pi$
$409$	2.36044	0.116716	0.0583582	+	0.998296i	$0.481413\pi$
$410$	−39.7779	−1.96449
$411$	−1.34282	−0.0662363
$412$	10.9176	0.537872
$413$	24.7072	1.21576
$414$	−29.7788	−1.46355
$415$	40.8903	2.00723
$416$	−34.5845	−1.69564
$417$	0.913998	0.0447587
$418$	−19.6784	−0.962504
$419$	−19.8938	−0.971877	−0.485938	−	0.873993i	$-0.661522\pi$
$419$	−19.8938	−0.971877	−0.485938	+	0.873993i	$0.661522\pi$
$420$	−14.6939	−0.716991
$421$	6.47978	0.315805	0.157902	−	0.987455i	$-0.449527\pi$
$421$	6.47978	0.315805	0.157902	+	0.987455i	$0.449527\pi$
$422$	46.8364	2.27996
$423$	25.6228	1.24582
$424$	−0.711201	−0.0345390
$425$	65.8863	3.19596
$426$	0.359253	0.0174059
$427$	−4.22565	−0.204493
$428$	−18.7413	−0.905897
$429$	19.6008	0.946334
$430$	92.9769	4.48375
$431$	8.86412	0.426970	0.213485	−	0.976946i	$-0.431519\pi$
$431$	8.86412	0.426970	0.213485	+	0.976946i	$0.431519\pi$
$432$	−20.1267	−0.968346
$433$	14.9819	0.719984	0.359992	−	0.932955i	$-0.382779\pi$
$433$	14.9819	0.719984	0.359992	+	0.932955i	$0.382779\pi$
$434$	−41.5994	−1.99683
$435$	3.92492	0.188186
$436$	−5.81905	−0.278682
$437$	−14.4761	−0.692484
$438$	−2.42969	−0.116095
$439$	−1.76993	−0.0844742	−0.0422371	−	0.999108i	$-0.513448\pi$
$439$	−1.76993	−0.0844742	−0.0422371	+	0.999108i	$0.513448\pi$
$440$	−5.80330	−0.276662
$441$	6.36458	0.303075
$442$	42.5985	2.02621
$443$	8.51655	0.404634	0.202317	−	0.979320i	$-0.435153\pi$
$443$	8.51655	0.404634	0.202317	+	0.979320i	$0.435153\pi$
$444$	9.09775	0.431760
$445$	40.2818	1.90954
$446$	38.1790	1.80783
$447$	−0.366286	−0.0173247
$448$	13.7556	0.649892
$449$	19.3446	0.912930	0.456465	−	0.889741i	$-0.349115\pi$
$449$	19.3446	0.912930	0.456465	+	0.889741i	$0.349115\pi$
$450$	57.1450	2.69384
$451$	−22.8597	−1.07642
$452$	−0.635540	−0.0298933
$453$	−21.3372	−1.00251
$454$	49.5851	2.32714
$455$	−38.2792	−1.79456
$456$	−0.526676	−0.0246639
$457$	−12.2197	−0.571614	−0.285807	−	0.958287i	$-0.592262\pi$
$457$	−12.2197	−0.571614	−0.285807	+	0.958287i	$0.592262\pi$
$458$	−37.6238	−1.75805
$459$	23.1400	1.08008
$460$	55.8842	2.60561
$461$	−28.5113	−1.32790	−0.663952	−	0.747775i	$-0.731122\pi$
$461$	−28.5113	−1.32790	−0.663952	+	0.747775i	$0.731122\pi$
$462$	−17.5338	−0.815745
$463$	14.9532	0.694935	0.347467	−	0.937692i	$-0.387042\pi$
$463$	14.9532	0.694935	0.347467	+	0.937692i	$0.387042\pi$
$464$	−4.26373	−0.197939
$465$	−41.2559	−1.91320
$466$	39.2430	1.81790
$467$	3.66620	0.169651	0.0848257	−	0.996396i	$-0.472967\pi$
$467$	3.66620	0.169651	0.0848257	+	0.996396i	$0.472967\pi$
$468$	17.7938	0.822518
$469$	12.0969	0.558584
$470$	−99.8431	−4.60542
$471$	−6.65945	−0.306851
$472$	−3.41874	−0.157360
$473$	53.4322	2.45682
$474$	9.92420	0.455834
$475$	27.7794	1.27460
$476$	−18.3522	−0.841171
$477$	5.52180	0.252826
$478$	28.2296	1.29119
$479$	−5.79342	−0.264708	−0.132354	−	0.991202i	$-0.542254\pi$
$479$	−5.79342	−0.264708	−0.132354	+	0.991202i	$0.542254\pi$
$480$	30.6819	1.40043
$481$	23.7006	1.08065
$482$	9.64526	0.439329
$483$	−12.8984	−0.586897
$484$	23.2186	1.05539
$485$	69.5326	3.15731
$486$	31.7281	1.43922
$487$	−10.9624	−0.496755	−0.248377	−	0.968663i	$-0.579897\pi$
$487$	−10.9624	−0.496755	−0.248377	+	0.968663i	$0.579897\pi$
$488$	0.584704	0.0264683
$489$	−4.62373	−0.209092
$490$	−24.8005	−1.12037
$491$	33.4210	1.50827	0.754134	−	0.656721i	$-0.228057\pi$
$491$	33.4210	1.50827	0.754134	+	0.656721i	$0.228057\pi$
$492$	8.00896	0.361072
$493$	4.90208	0.220779
$494$	17.9606	0.808087
$495$	45.0572	2.02517
$496$	44.8172	2.01235
$497$	−0.403198	−0.0180859
$498$	−17.0948	−0.766036
$499$	6.86197	0.307184	0.153592	−	0.988134i	$-0.450916\pi$
$499$	6.86197	0.307184	0.153592	+	0.988134i	$0.450916\pi$
$500$	−67.3461	−3.01181
$501$	5.99013	0.267619
$502$	−51.2040	−2.28534
$503$	−39.6169	−1.76643	−0.883216	−	0.468967i	$-0.844626\pi$
$503$	−39.6169	−1.76643	−0.883216	+	0.468967i	$0.844626\pi$
$504$	1.21595	0.0541629
$505$	81.2130	3.61393
$506$	66.6847	2.96450
$507$	−6.00777	−0.266814
$508$	−30.4421	−1.35065
$509$	1.13406	0.0502662	0.0251331	−	0.999684i	$-0.491999\pi$
$509$	1.13406	0.0502662	0.0251331	+	0.999684i	$0.491999\pi$
$510$	−37.7917	−1.67344
$511$	2.72690	0.120631
$512$	−30.9530	−1.36794
$513$	9.75641	0.430756
$514$	22.2109	0.979681
$515$	−25.2321	−1.11186
$516$	−18.7202	−0.824109
$517$	−57.3781	−2.52349
$518$	−21.2012	−0.931529
$519$	−1.82703	−0.0801978
$520$	5.29671	0.232276
$521$	−6.87385	−0.301149	−0.150574	−	0.988599i	$-0.548112\pi$
$521$	−6.87385	−0.301149	−0.150574	+	0.988599i	$0.548112\pi$
$522$	4.25171	0.186092
$523$	−12.5968	−0.550819	−0.275410	−	0.961327i	$-0.588814\pi$
$523$	−12.5968	−0.550819	−0.275410	+	0.961327i	$0.588814\pi$
$524$	31.6747	1.38371
$525$	24.7518	1.08026
$526$	−28.4770	−1.24165
$527$	−51.5271	−2.24456
$528$	18.8901	0.822085
$529$	26.0553	1.13284
$530$	−21.5165	−0.934618
$531$	26.5433	1.15188
$532$	−7.73775	−0.335474
$533$	20.8642	0.903727
$534$	−16.8404	−0.728755
$535$	43.3139	1.87262
$536$	−1.67386	−0.0722995
$537$	−13.6149	−0.587526
$538$	16.1380	0.695757
$539$	−14.2524	−0.613896
$540$	−37.6641	−1.62081
$541$	24.4682	1.05197	0.525986	−	0.850493i	$-0.323696\pi$
$541$	24.4682	1.05197	0.525986	+	0.850493i	$0.323696\pi$
$542$	−49.5063	−2.12648
$543$	−8.27641	−0.355175
$544$	38.3206	1.64298
$545$	13.4486	0.576076
$546$	16.0032	0.684873
$547$	41.0031	1.75316	0.876582	−	0.481252i	$-0.159818\pi$
$547$	41.0031	1.75316	0.876582	+	0.481252i	$0.159818\pi$
$548$	2.72981	0.116612
$549$	−4.53968	−0.193749
$550$	−127.967	−5.45653
$551$	2.06684	0.0880505
$552$	1.78476	0.0759643
$553$	−11.1382	−0.473643
$554$	−36.4238	−1.54750
$555$	−21.0262	−0.892512
$556$	−1.85806	−0.0787993
$557$	3.78490	0.160371	0.0801857	−	0.996780i	$-0.474449\pi$
$557$	3.78490	0.160371	0.0801857	+	0.996780i	$0.474449\pi$
$558$	−44.6909	−1.89191
$559$	−48.7679	−2.06266
$560$	−36.8913	−1.55894
$561$	−21.7182	−0.916944
$562$	2.30665	0.0973000
$563$	27.2591	1.14883	0.574417	−	0.818563i	$-0.305229\pi$
$563$	27.2591	1.14883	0.574417	+	0.818563i	$0.305229\pi$
$564$	20.1026	0.846472
$565$	1.46882	0.0617938
$566$	39.1037	1.64365
$567$	−4.39112	−0.184410
$568$	0.0557906	0.00234092
$569$	−31.6389	−1.32637	−0.663185	−	0.748456i	$-0.730796\pi$
$569$	−31.6389	−1.32637	−0.663185	+	0.748456i	$0.730796\pi$
$570$	−15.9339	−0.667399
$571$	24.9975	1.04611	0.523056	−	0.852298i	$-0.324792\pi$
$571$	24.9975	1.04611	0.523056	+	0.852298i	$0.324792\pi$
$572$	−39.8463	−1.66606
$573$	−3.79044	−0.158348
$574$	−18.6639	−0.779018
$575$	−94.1364	−3.92576
$576$	14.7779	0.615745
$577$	−1.37465	−0.0572274	−0.0286137	−	0.999591i	$-0.509109\pi$
$577$	−1.37465	−0.0572274	−0.0286137	+	0.999591i	$0.509109\pi$
$578$	−13.8091	−0.574383
$579$	17.2634	0.717441
$580$	−7.97895	−0.331308
$581$	19.1859	0.795964
$582$	−29.0691	−1.20495
$583$	−12.3652	−0.512113
$584$	−0.377322	−0.0156137
$585$	−41.1239	−1.70027
$586$	10.8568	0.448490
$587$	−12.1882	−0.503060	−0.251530	−	0.967849i	$-0.580934\pi$
$587$	−12.1882	−0.503060	−0.251530	+	0.967849i	$0.580934\pi$
$588$	4.99339	0.205924
$589$	−21.7251	−0.895168
$590$	−103.430	−4.25814
$591$	15.4158	0.634122
$592$	22.8412	0.938768
$593$	8.40049	0.344967	0.172483	−	0.985012i	$-0.444821\pi$
$593$	8.40049	0.344967	0.172483	+	0.985012i	$0.444821\pi$
$594$	−44.9434	−1.84405
$595$	42.4145	1.73882
$596$	0.744620	0.0305008
$597$	−8.09094	−0.331140
$598$	−60.8635	−2.48889
$599$	−12.0908	−0.494016	−0.247008	−	0.969013i	$-0.579447\pi$
$599$	−12.0908	−0.494016	−0.247008	+	0.969013i	$0.579447\pi$
$600$	−3.42492	−0.139822
$601$	−12.8016	−0.522186	−0.261093	−	0.965314i	$-0.584083\pi$
$601$	−12.8016	−0.522186	−0.261093	+	0.965314i	$0.584083\pi$
$602$	43.6251	1.77803
$603$	12.9959	0.529234
$604$	43.3762	1.76495
$605$	−53.6616	−2.18165
$606$	−33.9523	−1.37922
$607$	−18.4587	−0.749215	−0.374607	−	0.927184i	$-0.622222\pi$
$607$	−18.4587	−0.749215	−0.374607	+	0.927184i	$0.622222\pi$
$608$	16.1569	0.655250
$609$	1.84159	0.0746249
$610$	17.6895	0.716228
$611$	52.3693	2.11864
$612$	−19.7160	−0.796974
$613$	48.6066	1.96320	0.981601	−	0.190942i	$-0.0611543\pi$
$613$	48.6066	1.96320	0.981601	+	0.190942i	$0.0611543\pi$
$614$	0.172873	0.00697658
$615$	−18.5098	−0.746389
$616$	−2.72293	−0.109710
$617$	17.8772	0.719708	0.359854	−	0.933009i	$-0.382826\pi$
$617$	17.8772	0.719708	0.359854	+	0.933009i	$0.382826\pi$
$618$	10.5487	0.424329
$619$	21.9748	0.883243	0.441622	−	0.897201i	$-0.354403\pi$
$619$	21.9748	0.883243	0.441622	+	0.897201i	$0.354403\pi$
$620$	83.8688	3.36825
$621$	−33.0617	−1.32672
$622$	23.0200	0.923018
$623$	18.9003	0.757226
$624$	−17.2411	−0.690196
$625$	88.4440	3.53776
$626$	19.9872	0.798847
$627$	−9.15696	−0.365694
$628$	13.5379	0.540223
$629$	−26.2609	−1.04709
$630$	36.7872	1.46564
$631$	23.9159	0.952076	0.476038	−	0.879425i	$-0.342072\pi$
$631$	23.9159	0.952076	0.476038	+	0.879425i	$0.342072\pi$
$632$	1.54119	0.0613053
$633$	21.7943	0.866247
$634$	24.9113	0.989355
$635$	70.3561	2.79200
$636$	4.33218	0.171782
$637$	13.0083	0.515407
$638$	−9.52101	−0.376940
$639$	−0.433162	−0.0171356
$640$	9.55370	0.377643
$641$	21.3880	0.844774	0.422387	−	0.906416i	$-0.361192\pi$
$641$	21.3880	0.844774	0.422387	+	0.906416i	$0.361192\pi$
$642$	−18.1080	−0.714666
$643$	28.3591	1.11837	0.559186	−	0.829042i	$-0.311114\pi$
$643$	28.3591	1.11837	0.559186	+	0.829042i	$0.311114\pi$
$644$	26.2211	1.03325
$645$	43.2649	1.70355
$646$	−19.9009	−0.782990
$647$	−7.81611	−0.307283	−0.153641	−	0.988127i	$-0.549100\pi$
$647$	−7.81611	−0.307283	−0.153641	+	0.988127i	$0.549100\pi$
$648$	0.607601	0.0238688
$649$	−59.4394	−2.33320
$650$	116.796	4.58112
$651$	−19.3574	−0.758677
$652$	9.39955	0.368115
$653$	−14.7704	−0.578010	−0.289005	−	0.957328i	$-0.593324\pi$
$653$	−14.7704	−0.578010	−0.289005	+	0.957328i	$0.593324\pi$
$654$	−5.62240	−0.219853
$655$	−73.2046	−2.86034
$656$	20.1077	0.785072
$657$	2.92955	0.114293
$658$	−46.8468	−1.82628
$659$	−40.7819	−1.58864	−0.794319	−	0.607501i	$-0.792172\pi$
$659$	−40.7819	−1.58864	−0.794319	+	0.607501i	$0.792172\pi$
$660$	35.3500	1.37600
$661$	0.421158	0.0163812	0.00819058	−	0.999966i	$-0.497393\pi$
$661$	0.421158	0.0163812	0.00819058	+	0.999966i	$0.497393\pi$
$662$	7.52136	0.292326
$663$	19.8224	0.769836
$664$	−2.65476	−0.103025
$665$	17.8830	0.693474
$666$	−22.7768	−0.882584
$667$	−7.00395	−0.271194
$668$	−12.1773	−0.471154
$669$	17.7658	0.686867
$670$	−50.6405	−1.95641
$671$	10.1659	0.392449
$672$	14.3961	0.555340
$673$	−1.29954	−0.0500936	−0.0250468	−	0.999686i	$-0.507973\pi$
$673$	−1.29954	−0.0500936	−0.0250468	+	0.999686i	$0.507973\pi$
$674$	−11.7722	−0.453448
$675$	63.4450	2.44200
$676$	12.2131	0.469736
$677$	−34.0330	−1.30799	−0.653997	−	0.756497i	$-0.726909\pi$
$677$	−34.0330	−1.30799	−0.653997	+	0.756497i	$0.726909\pi$
$678$	−0.614062	−0.0235829
$679$	32.6250	1.25203
$680$	−5.86891	−0.225062
$681$	23.0734	0.884174
$682$	100.078	3.83218
$683$	−23.5841	−0.902421	−0.451210	−	0.892418i	$-0.649008\pi$
$683$	−23.5841	−0.902421	−0.451210	+	0.892418i	$0.649008\pi$
$684$	−8.31278	−0.317847
$685$	−6.30897	−0.241053
$686$	−39.3397	−1.50200
$687$	−17.5075	−0.667952
$688$	−46.9997	−1.79185
$689$	11.2858	0.429954
$690$	53.9956	2.05558
$691$	−34.3082	−1.30514	−0.652572	−	0.757727i	$-0.726310\pi$
$691$	−34.3082	−1.30514	−0.652572	+	0.757727i	$0.726310\pi$
$692$	3.71416	0.141191
$693$	21.1410	0.803080
$694$	7.66877	0.291102
$695$	4.29424	0.162890
$696$	−0.254821	−0.00965898
$697$	−23.1181	−0.875661
$698$	−31.3043	−1.18488
$699$	18.2609	0.690692
$700$	−50.3178	−1.90183
$701$	−17.0509	−0.644005	−0.322002	−	0.946739i	$-0.604356\pi$
$701$	−17.0509	−0.644005	−0.322002	+	0.946739i	$0.604356\pi$
$702$	41.0201	1.54820
$703$	−11.0723	−0.417599
$704$	−33.0926	−1.24723
$705$	−46.4600	−1.74978
$706$	2.82918	0.106478
$707$	38.1054	1.43310
$708$	20.8248	0.782643
$709$	11.7774	0.442310	0.221155	−	0.975239i	$-0.429017\pi$
$709$	11.7774	0.442310	0.221155	+	0.975239i	$0.429017\pi$
$710$	1.68788	0.0633449
$711$	−11.9659	−0.448756
$712$	−2.61525	−0.0980106
$713$	73.6204	2.75710
$714$	−17.7320	−0.663603
$715$	92.0903	3.44398
$716$	27.6776	1.03436
$717$	13.1361	0.490576
$718$	−65.4929	−2.44417
$719$	14.8789	0.554889	0.277444	−	0.960742i	$-0.410513\pi$
$719$	14.8789	0.554889	0.277444	+	0.960742i	$0.410513\pi$
$720$	−39.6329	−1.47703
$721$	−11.8390	−0.440908
$722$	28.9290	1.07662
$723$	4.48822	0.166919
$724$	16.8251	0.625298
$725$	13.4405	0.499167
$726$	22.4340	0.832604
$727$	5.44821	0.202063	0.101031	−	0.994883i	$-0.467786\pi$
$727$	5.44821	0.202063	0.101031	+	0.994883i	$0.467786\pi$
$728$	2.48524	0.0921090
$729$	8.22597	0.304665
$730$	−11.4154	−0.422504
$731$	54.0363	1.99860
$732$	−3.56164	−0.131642
$733$	−19.1051	−0.705662	−0.352831	−	0.935687i	$-0.614781\pi$
$733$	−19.1051	−0.705662	−0.352831	+	0.935687i	$0.614781\pi$
$734$	−46.3522	−1.71089
$735$	−11.5404	−0.425675
$736$	−54.7513	−2.01816
$737$	−29.1022	−1.07199
$738$	−20.0510	−0.738086
$739$	4.81846	0.177250	0.0886250	−	0.996065i	$-0.471753\pi$
$739$	4.81846	0.177250	0.0886250	+	0.996065i	$0.471753\pi$
$740$	42.7440	1.57130
$741$	8.35761	0.307024
$742$	−10.0956	−0.370622
$743$	−3.01457	−0.110594	−0.0552969	−	0.998470i	$-0.517611\pi$
$743$	−3.01457	−0.110594	−0.0552969	+	0.998470i	$0.517611\pi$
$744$	2.67849	0.0981984
$745$	−1.72092	−0.0630497
$746$	23.6039	0.864202
$747$	20.6117	0.754142
$748$	44.1508	1.61431
$749$	20.3230	0.742588
$750$	−65.0702	−2.37603
$751$	19.9755	0.728918	0.364459	−	0.931219i	$-0.381254\pi$
$751$	19.9755	0.728918	0.364459	+	0.931219i	$0.381254\pi$
$752$	50.4705	1.84047
$753$	−23.8267	−0.868294
$754$	8.68988	0.316467
$755$	−100.248	−3.64842
$756$	−17.6722	−0.642730
$757$	−13.2704	−0.482320	−0.241160	−	0.970485i	$-0.577528\pi$
$757$	−13.2704	−0.482320	−0.241160	+	0.970485i	$0.577528\pi$
$758$	57.6496	2.09393
$759$	31.0304	1.12633
$760$	−2.47448	−0.0897589
$761$	−11.1935	−0.405765	−0.202882	−	0.979203i	$-0.565031\pi$
$761$	−11.1935	−0.405765	−0.202882	+	0.979203i	$0.565031\pi$
$762$	−29.4134	−1.06554
$763$	6.31015	0.228443
$764$	7.70556	0.278777
$765$	45.5665	1.64746
$766$	−26.1050	−0.943210
$767$	54.2507	1.95888
$768$	−16.4739	−0.594449
$769$	−13.7077	−0.494311	−0.247155	−	0.968976i	$-0.579496\pi$
$769$	−13.7077	−0.494311	−0.247155	+	0.968976i	$0.579496\pi$
$770$	−82.3790	−2.96873
$771$	10.3354	0.372220
$772$	−35.0946	−1.26308
$773$	18.5996	0.668982	0.334491	−	0.942399i	$-0.391436\pi$
$773$	18.5996	0.668982	0.334491	+	0.942399i	$0.391436\pi$
$774$	46.8671	1.68460
$775$	−141.276	−5.07480
$776$	−4.51433	−0.162055
$777$	−9.86556	−0.353925
$778$	40.6730	1.45820
$779$	−9.74718	−0.349229
$780$	−32.2641	−1.15524
$781$	0.969994	0.0347091
$782$	67.4386	2.41160
$783$	4.72044	0.168695
$784$	12.5366	0.447737
$785$	−31.2881	−1.11672
$786$	30.6043	1.09162
$787$	3.80511	0.135638	0.0678188	−	0.997698i	$-0.478396\pi$
$787$	3.80511	0.135638	0.0678188	+	0.997698i	$0.478396\pi$
$788$	−31.3387	−1.11639
$789$	−13.2512	−0.471754
$790$	46.6269	1.65891
$791$	0.689176	0.0245043
$792$	−2.92529	−0.103946
$793$	−9.27844	−0.329487
$794$	−59.7424	−2.12018
$795$	−10.0123	−0.355099
$796$	16.4480	0.582984
$797$	−46.7678	−1.65660	−0.828300	−	0.560285i	$-0.810692\pi$
$797$	−46.7678	−1.65660	−0.828300	+	0.560285i	$0.810692\pi$
$798$	−7.47626	−0.264657
$799$	−58.0268	−2.05284
$800$	105.067	3.71468
$801$	20.3049	0.717440
$802$	−28.0221	−0.989494
$803$	−6.56024	−0.231506
$804$	10.1961	0.359587
$805$	−60.6005	−2.13589
$806$	−91.3416	−3.21737
$807$	7.50947	0.264346
$808$	−5.27267	−0.185492
$809$	3.21277	0.112955	0.0564775	−	0.998404i	$-0.482013\pi$
$809$	3.21277	0.112955	0.0564775	+	0.998404i	$0.482013\pi$
$810$	18.3822	0.645886
$811$	−30.3466	−1.06561	−0.532807	−	0.846236i	$-0.678863\pi$
$811$	−30.3466	−1.06561	−0.532807	+	0.846236i	$0.678863\pi$
$812$	−3.74375	−0.131380
$813$	−23.0367	−0.807933
$814$	51.0049	1.78772
$815$	−21.7237	−0.760947
$816$	19.1036	0.668761
$817$	22.7831	0.797079
$818$	−4.63637	−0.162107
$819$	−19.2955	−0.674240
$820$	37.6285	1.31404
$821$	−41.1831	−1.43730	−0.718651	−	0.695371i	$-0.755240\pi$
$821$	−41.1831	−1.43730	−0.718651	+	0.695371i	$0.755240\pi$
$822$	2.63756	0.0919953
$823$	−9.59571	−0.334485	−0.167243	−	0.985916i	$-0.553486\pi$
$823$	−9.59571	−0.334485	−0.167243	+	0.985916i	$0.553486\pi$
$824$	1.63817	0.0570683
$825$	−59.5468	−2.07315
$826$	−48.5297	−1.68856
$827$	−14.4404	−0.502142	−0.251071	−	0.967969i	$-0.580783\pi$
$827$	−14.4404	−0.502142	−0.251071	+	0.967969i	$0.580783\pi$
$828$	28.1697	0.978964
$829$	0.826632	0.0287101	0.0143551	−	0.999897i	$-0.495430\pi$
$829$	0.826632	0.0287101	0.0143551	+	0.999897i	$0.495430\pi$
$830$	−80.3165	−2.78783
$831$	−16.9491	−0.587957
$832$	30.2038	1.04713
$833$	−14.4136	−0.499400
$834$	−1.79527	−0.0621651
$835$	28.1435	0.973944
$836$	18.6151	0.643817
$837$	−49.6178	−1.71504
$838$	39.0753	1.34984
$839$	−53.4197	−1.84425	−0.922126	−	0.386889i	$-0.873550\pi$
$839$	−53.4197	−1.84425	−0.922126	+	0.386889i	$0.873550\pi$
$840$	−2.20480	−0.0760728
$841$	1.00000	0.0344828
$842$	−12.7275	−0.438620
$843$	1.07335	0.0369682
$844$	−44.3056	−1.52506
$845$	−28.2263	−0.971015
$846$	−50.3282	−1.73032
$847$	−25.1782	−0.865133
$848$	10.8766	0.373503
$849$	18.1961	0.624489
$850$	−129.414	−4.43885
$851$	37.5208	1.28620
$852$	−0.339841	−0.0116428
$853$	36.7696	1.25897	0.629484	−	0.777013i	$-0.283266\pi$
$853$	36.7696	1.25897	0.629484	+	0.777013i	$0.283266\pi$
$854$	8.29999	0.284020
$855$	19.2120	0.657037
$856$	−2.81211	−0.0961158
$857$	42.1249	1.43896	0.719480	−	0.694513i	$-0.244380\pi$
$857$	42.1249	1.43896	0.719480	+	0.694513i	$0.244380\pi$
$858$	−38.4997	−1.31436
$859$	−46.6412	−1.59138	−0.795689	−	0.605705i	$-0.792891\pi$
$859$	−46.6412	−1.59138	−0.795689	+	0.605705i	$0.792891\pi$
$860$	−87.9529	−2.99917
$861$	−8.68488	−0.295980
$862$	−17.4109	−0.593016
$863$	27.2925	0.929047	0.464524	−	0.885561i	$-0.346226\pi$
$863$	27.2925	0.929047	0.464524	+	0.885561i	$0.346226\pi$
$864$	36.9006	1.25539
$865$	−8.58394	−0.291863
$866$	−29.4273	−0.999982
$867$	−6.42579	−0.218231
$868$	39.3516	1.33568
$869$	26.7957	0.908981
$870$	−7.70931	−0.261370
$871$	26.5617	0.900011
$872$	−0.873138	−0.0295682
$873$	35.0495	1.18625
$874$	28.4338	0.961788
$875$	73.0298	2.46886
$876$	2.29840	0.0776558
$877$	−23.4429	−0.791609	−0.395805	−	0.918335i	$-0.629534\pi$
$877$	−23.4429	−0.791609	−0.395805	+	0.918335i	$0.629534\pi$
$878$	3.47649	0.117326
$879$	5.05199	0.170399
$880$	88.7513	2.99181
$881$	49.3605	1.66300	0.831499	−	0.555526i	$-0.187483\pi$
$881$	49.3605	1.66300	0.831499	+	0.555526i	$0.187483\pi$
$882$	−12.5013	−0.420940
$883$	−11.2789	−0.379566	−0.189783	−	0.981826i	$-0.560778\pi$
$883$	−11.2789	−0.379566	−0.189783	+	0.981826i	$0.560778\pi$
$884$	−40.2967	−1.35533
$885$	−48.1290	−1.61784
$886$	−16.7282	−0.561994
$887$	−1.99538	−0.0669982	−0.0334991	−	0.999439i	$-0.510665\pi$
$887$	−1.99538	−0.0669982	−0.0334991	+	0.999439i	$0.510665\pi$
$888$	1.36510	0.0458098
$889$	33.0113	1.10716
$890$	−79.1212	−2.65215
$891$	10.5639	0.353906
$892$	−36.1160	−1.20925
$893$	−24.4656	−0.818709
$894$	0.719456	0.0240622
$895$	−63.9669	−2.13818
$896$	4.48263	0.149754
$897$	−28.3216	−0.945630
$898$	−37.9966	−1.26796
$899$	−10.5113	−0.350570
$900$	−54.0572	−1.80191
$901$	−12.5050	−0.416601
$902$	44.9008	1.49503
$903$	20.3001	0.675544
$904$	−0.0953616	−0.00317168
$905$	−38.8851	−1.29258
$906$	41.9104	1.39238
$907$	−53.1720	−1.76555	−0.882774	−	0.469797i	$-0.844327\pi$
$907$	−53.1720	−1.76555	−0.882774	+	0.469797i	$0.844327\pi$
$908$	−46.9057	−1.55662
$909$	40.9373	1.35780
$910$	75.1878	2.49245
$911$	25.0668	0.830501	0.415251	−	0.909707i	$-0.363694\pi$
$911$	25.0668	0.830501	0.415251	+	0.909707i	$0.363694\pi$
$912$	8.05458	0.266714
$913$	−46.1565	−1.52756
$914$	24.0019	0.793912
$915$	8.23146	0.272124
$916$	35.5908	1.17595
$917$	−34.3479	−1.13427
$918$	−45.4514	−1.50012
$919$	8.06477	0.266032	0.133016	−	0.991114i	$-0.457534\pi$
$919$	8.06477	0.266032	0.133016	+	0.991114i	$0.457534\pi$
$920$	8.38532	0.276456
$921$	0.0804428	0.00265068
$922$	56.0018	1.84432
$923$	−0.885320	−0.0291407
$924$	16.5863	0.545651
$925$	−72.0019	−2.36741
$926$	−29.3710	−0.965192
$927$	−12.7188	−0.417741
$928$	7.81720	0.256612
$929$	−42.0447	−1.37944	−0.689721	−	0.724075i	$-0.742267\pi$
$929$	−42.0447	−1.37944	−0.689721	+	0.724075i	$0.742267\pi$
$930$	81.0346	2.65723
$931$	−6.07712	−0.199170
$932$	−37.1225	−1.21599
$933$	10.7119	0.350691
$934$	−7.20112	−0.235628
$935$	−102.039	−3.33703
$936$	2.66993	0.0872693
$937$	−5.55023	−0.181318	−0.0906591	−	0.995882i	$-0.528897\pi$
$937$	−5.55023	−0.181318	−0.0906591	+	0.995882i	$0.528897\pi$
$938$	−23.7607	−0.775814
$939$	9.30061	0.303514
$940$	94.4481	3.08056
$941$	48.0484	1.56633	0.783167	−	0.621811i	$-0.213603\pi$
$941$	48.0484	1.56633	0.783167	+	0.621811i	$0.213603\pi$
$942$	13.0805	0.426184
$943$	33.0305	1.07562
$944$	52.2836	1.70169
$945$	40.8428	1.32862
$946$	−104.951	−3.41226
$947$	25.4172	0.825947	0.412974	−	0.910743i	$-0.364490\pi$
$947$	25.4172	0.825947	0.412974	+	0.910743i	$0.364490\pi$
$948$	−9.38795	−0.304906
$949$	5.98757	0.194365
$950$	−54.5641	−1.77029
$951$	11.5920	0.375895
$952$	−2.75371	−0.0892484
$953$	14.0615	0.455497	0.227748	−	0.973720i	$-0.426864\pi$
$953$	14.0615	0.455497	0.227748	+	0.973720i	$0.426864\pi$
$954$	−10.8459	−0.351149
$955$	−17.8086	−0.576274
$956$	−26.7042	−0.863677
$957$	−4.43041	−0.143215
$958$	11.3794	0.367652
$959$	−2.96019	−0.0955895
$960$	−26.7956	−0.864825
$961$	79.4866	2.56409
$962$	−46.5525	−1.50091
$963$	21.8334	0.703570
$964$	−9.12408	−0.293867
$965$	81.1085	2.61098
$966$	25.3349	0.815139
$967$	−31.9101	−1.02616	−0.513080	−	0.858341i	$-0.671496\pi$
$967$	−31.9101	−1.02616	−0.513080	+	0.858341i	$0.671496\pi$
$968$	3.48392	0.111977
$969$	−9.26048	−0.297489
$970$	−136.576	−4.38518
$971$	26.9345	0.864369	0.432184	−	0.901785i	$-0.357743\pi$
$971$	26.9345	0.864369	0.432184	+	0.901785i	$0.357743\pi$
$972$	−30.0137	−0.962690
$973$	2.01487	0.0645938
$974$	21.5323	0.689940
$975$	54.3487	1.74055
$976$	−8.94202	−0.286227
$977$	−29.9883	−0.959412	−0.479706	−	0.877429i	$-0.659257\pi$
$977$	−29.9883	−0.959412	−0.479706	+	0.877429i	$0.659257\pi$
$978$	9.08190	0.290407
$979$	−45.4696	−1.45321
$980$	23.4604	0.749416
$981$	6.77909	0.216440
$982$	−65.6453	−2.09483
$983$	17.4124	0.555369	0.277684	−	0.960672i	$-0.410433\pi$
$983$	17.4124	0.555369	0.277684	+	0.960672i	$0.410433\pi$
$984$	1.20173	0.0383098
$985$	72.4281	2.30775
$986$	−9.62864	−0.306639
$987$	−21.7992	−0.693875
$988$	−16.9901	−0.540528
$989$	−77.2054	−2.45499
$990$	−88.5010	−2.81275
$991$	14.5422	0.461948	0.230974	−	0.972960i	$-0.425809\pi$
$991$	14.5422	0.461948	0.230974	+	0.972960i	$0.425809\pi$
$992$	−82.1687	−2.60886
$993$	3.49991	0.111066
$994$	0.791959	0.0251194
$995$	−38.0137	−1.20511
$996$	16.1711	0.512400
$997$	22.1719	0.702191	0.351095	−	0.936340i	$-0.385809\pi$
$997$	22.1719	0.702191	0.351095	+	0.936340i	$0.385809\pi$
$998$	−13.4782	−0.426646
$999$	−25.2878	−0.800072

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.18	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.96419 q^{2} -0.913998 q^{3} +1.85806 q^{4} -4.29424 q^{5} +1.79527 q^{6} -2.01487 q^{7} +0.278799 q^{8} -2.16461 q^{9} +O(q^{10})\)	\(q-1.96419 q^{2} -0.913998 q^{3} +1.85806 q^{4} -4.29424 q^{5} +1.79527 q^{6} -2.01487 q^{7} +0.278799 q^{8} -2.16461 q^{9} +8.43472 q^{10} +4.84729 q^{11} -1.69826 q^{12} -4.42415 q^{13} +3.95760 q^{14} +3.92492 q^{15} -4.26373 q^{16} +4.90208 q^{17} +4.25171 q^{18} +2.06684 q^{19} -7.97895 q^{20} +1.84159 q^{21} -9.52101 q^{22} -7.00395 q^{23} -0.254821 q^{24} +13.4405 q^{25} +8.68988 q^{26} +4.72044 q^{27} -3.74375 q^{28} +1.00000 q^{29} -7.70931 q^{30} -10.5113 q^{31} +7.81720 q^{32} -4.43041 q^{33} -9.62864 q^{34} +8.65234 q^{35} -4.02197 q^{36} -5.35709 q^{37} -4.05968 q^{38} +4.04366 q^{39} -1.19723 q^{40} -4.71597 q^{41} -3.61724 q^{42} +11.0231 q^{43} +9.00655 q^{44} +9.29534 q^{45} +13.7571 q^{46} -11.8372 q^{47} +3.89704 q^{48} -2.94029 q^{49} -26.3997 q^{50} -4.48049 q^{51} -8.22033 q^{52} -2.55095 q^{53} -9.27186 q^{54} -20.8154 q^{55} -0.561744 q^{56} -1.88909 q^{57} -1.96419 q^{58} -12.2624 q^{59} +7.29274 q^{60} +2.09723 q^{61} +20.6462 q^{62} +4.36141 q^{63} -6.82704 q^{64} +18.9983 q^{65} +8.70218 q^{66} -6.00381 q^{67} +9.10836 q^{68} +6.40159 q^{69} -16.9949 q^{70} +0.200111 q^{71} -0.603490 q^{72} -1.35338 q^{73} +10.5224 q^{74} -12.2846 q^{75} +3.84032 q^{76} -9.76666 q^{77} -7.94253 q^{78} +5.52797 q^{79} +18.3095 q^{80} +2.17935 q^{81} +9.26309 q^{82} -9.52213 q^{83} +3.42178 q^{84} -21.0507 q^{85} -21.6516 q^{86} -0.913998 q^{87} +1.35142 q^{88} -9.38042 q^{89} -18.2579 q^{90} +8.91409 q^{91} -13.0138 q^{92} +9.60727 q^{93} +23.2505 q^{94} -8.87552 q^{95} -7.14491 q^{96} -16.1921 q^{97} +5.77530 q^{98} -10.4925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 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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