LMFDB - Embedded newform 4031.2.a.e.1.6

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:	$103$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.63961 q^{2} +1.15663 q^{3} +4.96757 q^{4} -1.20001 q^{5} -3.05306 q^{6} -2.18899 q^{7} -7.83323 q^{8} -1.66221 q^{9} +O(q^{10})$	\(q-2.63961 q^{2} +1.15663 q^{3} +4.96757 q^{4} -1.20001 q^{5} -3.05306 q^{6} -2.18899 q^{7} -7.83323 q^{8} -1.66221 q^{9} +3.16755 q^{10} +0.568551 q^{11} +5.74563 q^{12} -6.43848 q^{13} +5.77808 q^{14} -1.38796 q^{15} +10.7416 q^{16} -4.60595 q^{17} +4.38759 q^{18} -0.514144 q^{19} -5.96111 q^{20} -2.53185 q^{21} -1.50076 q^{22} -6.42980 q^{23} -9.06015 q^{24} -3.55999 q^{25} +16.9951 q^{26} -5.39245 q^{27} -10.8739 q^{28} -1.00000 q^{29} +3.66369 q^{30} +0.530218 q^{31} -12.6872 q^{32} +0.657603 q^{33} +12.1579 q^{34} +2.62680 q^{35} -8.25712 q^{36} +3.36909 q^{37} +1.35714 q^{38} -7.44694 q^{39} +9.39992 q^{40} +7.91104 q^{41} +6.68310 q^{42} +8.49731 q^{43} +2.82432 q^{44} +1.99466 q^{45} +16.9722 q^{46} -9.31760 q^{47} +12.4240 q^{48} -2.20834 q^{49} +9.39699 q^{50} -5.32738 q^{51} -31.9836 q^{52} -12.6643 q^{53} +14.2340 q^{54} -0.682265 q^{55} +17.1468 q^{56} -0.594674 q^{57} +2.63961 q^{58} -8.17228 q^{59} -6.89479 q^{60} -1.02214 q^{61} -1.39957 q^{62} +3.63855 q^{63} +12.0061 q^{64} +7.72622 q^{65} -1.73582 q^{66} +15.5243 q^{67} -22.8803 q^{68} -7.43689 q^{69} -6.93373 q^{70} -1.79261 q^{71} +13.0205 q^{72} -10.9579 q^{73} -8.89309 q^{74} -4.11759 q^{75} -2.55404 q^{76} -1.24455 q^{77} +19.6571 q^{78} +12.2212 q^{79} -12.8900 q^{80} -1.25044 q^{81} -20.8821 q^{82} -7.38566 q^{83} -12.5771 q^{84} +5.52716 q^{85} -22.4296 q^{86} -1.15663 q^{87} -4.45359 q^{88} +5.76227 q^{89} -5.26513 q^{90} +14.0938 q^{91} -31.9404 q^{92} +0.613266 q^{93} +24.5949 q^{94} +0.616975 q^{95} -14.6743 q^{96} -7.66437 q^{97} +5.82917 q^{98} -0.945050 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) $ 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * 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 $

$2$	−2.63961	−1.86649	−0.933245	−	0.359241i	$-0.883035\pi$
$2$	−2.63961	−1.86649	−0.933245	+	0.359241i	$0.883035\pi$
$3$	1.15663	0.667781	0.333890	−	0.942612i	$-0.391639\pi$
$3$	1.15663	0.667781	0.333890	+	0.942612i	$0.391639\pi$
$4$	4.96757	2.48378
$5$	−1.20001	−0.536659	−0.268329	−	0.963327i	$-0.586472\pi$
$5$	−1.20001	−0.536659	−0.268329	+	0.963327i	$0.586472\pi$
$6$	−3.05306	−1.24641
$7$	−2.18899	−0.827359	−0.413679	−	0.910423i	$-0.635757\pi$
$7$	−2.18899	−0.827359	−0.413679	+	0.910423i	$0.635757\pi$
$8$	−7.83323	−2.76946
$9$	−1.66221	−0.554069
$10$	3.16755	1.00167
$11$	0.568551	0.171425	0.0857123	−	0.996320i	$-0.472683\pi$
$11$	0.568551	0.171425	0.0857123	+	0.996320i	$0.472683\pi$
$12$	5.74563	1.65862
$13$	−6.43848	−1.78571	−0.892857	−	0.450340i	$-0.851303\pi$
$13$	−6.43848	−1.78571	−0.892857	+	0.450340i	$0.851303\pi$
$14$	5.77808	1.54426
$15$	−1.38796	−0.358370
$16$	10.7416	2.68539
$17$	−4.60595	−1.11711	−0.558553	−	0.829469i	$-0.688643\pi$
$17$	−4.60595	−1.11711	−0.558553	+	0.829469i	$0.688643\pi$
$18$	4.38759	1.03416
$19$	−0.514144	−0.117953	−0.0589763	−	0.998259i	$-0.518784\pi$
$19$	−0.514144	−0.117953	−0.0589763	+	0.998259i	$0.518784\pi$
$20$	−5.96111	−1.33294
$21$	−2.53185	−0.552494
$22$	−1.50076	−0.319962
$23$	−6.42980	−1.34070	−0.670352	−	0.742043i	$-0.733857\pi$
$23$	−6.42980	−1.34070	−0.670352	+	0.742043i	$0.733857\pi$
$24$	−9.06015	−1.84939
$25$	−3.55999	−0.711997
$26$	16.9951	3.33302
$27$	−5.39245	−1.03778
$28$	−10.8739	−2.05498
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.66369	0.668894
$31$	0.530218	0.0952299	0.0476150	−	0.998866i	$-0.484838\pi$
$31$	0.530218	0.0952299	0.0476150	+	0.998866i	$0.484838\pi$
$32$	−12.6872	−2.24279
$33$	0.657603	0.114474
$34$	12.1579	2.08507
$35$	2.62680	0.444010
$36$	−8.25712	−1.37619
$37$	3.36909	0.553874	0.276937	−	0.960888i	$-0.410681\pi$
$37$	3.36909	0.553874	0.276937	+	0.960888i	$0.410681\pi$
$38$	1.35714	0.220157
$39$	−7.44694	−1.19247
$40$	9.39992	1.48626
$41$	7.91104	1.23550	0.617749	−	0.786376i	$-0.288045\pi$
$41$	7.91104	1.23550	0.617749	+	0.786376i	$0.288045\pi$
$42$	6.68310	1.03122
$43$	8.49731	1.29583	0.647913	−	0.761714i	$-0.275642\pi$
$43$	8.49731	1.29583	0.647913	+	0.761714i	$0.275642\pi$
$44$	2.82432	0.425782
$45$	1.99466	0.297346
$46$	16.9722	2.50241
$47$	−9.31760	−1.35911	−0.679556	−	0.733624i	$-0.737827\pi$
$47$	−9.31760	−1.35911	−0.679556	+	0.733624i	$0.737827\pi$
$48$	12.4240	1.79325
$49$	−2.20834	−0.315477
$50$	9.39699	1.32894
$51$	−5.32738	−0.745982
$52$	−31.9836	−4.43533
$53$	−12.6643	−1.73957	−0.869785	−	0.493431i	$-0.835742\pi$
$53$	−12.6643	−1.73957	−0.869785	+	0.493431i	$0.835742\pi$
$54$	14.2340	1.93700
$55$	−0.682265	−0.0919966
$56$	17.1468	2.29134
$57$	−0.594674	−0.0787665
$58$	2.63961	0.346598
$59$	−8.17228	−1.06394	−0.531970	−	0.846763i	$-0.678548\pi$
$59$	−8.17228	−1.06394	−0.531970	+	0.846763i	$0.678548\pi$
$60$	−6.89479	−0.890114
$61$	−1.02214	−0.130872	−0.0654360	−	0.997857i	$-0.520844\pi$
$61$	−1.02214	−0.130872	−0.0654360	+	0.997857i	$0.520844\pi$
$62$	−1.39957	−0.177746
$63$	3.63855	0.458414
$64$	12.0061	1.50076
$65$	7.72622	0.958320
$66$	−1.73582	−0.213665
$67$	15.5243	1.89660	0.948299	−	0.317377i	$-0.102802\pi$
$67$	15.5243	1.89660	0.948299	+	0.317377i	$0.102802\pi$
$68$	−22.8803	−2.77465
$69$	−7.43689	−0.895297
$70$	−6.93373	−0.828739
$71$	−1.79261	−0.212744	−0.106372	−	0.994326i	$-0.533923\pi$
$71$	−1.79261	−0.212744	−0.106372	+	0.994326i	$0.533923\pi$
$72$	13.0205	1.53447
$73$	−10.9579	−1.28253	−0.641265	−	0.767319i	$-0.721590\pi$
$73$	−10.9579	−1.28253	−0.641265	+	0.767319i	$0.721590\pi$
$74$	−8.89309	−1.03380
$75$	−4.11759	−0.475458
$76$	−2.55404	−0.292969
$77$	−1.24455	−0.141830
$78$	19.6571	2.22572
$79$	12.2212	1.37500	0.687499	−	0.726186i	$-0.258709\pi$
$79$	12.2212	1.37500	0.687499	+	0.726186i	$0.258709\pi$
$80$	−12.8900	−1.44114
$81$	−1.25044	−0.138938
$82$	−20.8821	−2.30604
$83$	−7.38566	−0.810681	−0.405341	−	0.914166i	$-0.632847\pi$
$83$	−7.38566	−0.810681	−0.405341	+	0.914166i	$0.632847\pi$
$84$	−12.5771	−1.37228
$85$	5.52716	0.599505
$86$	−22.4296	−2.41865
$87$	−1.15663	−0.124004
$88$	−4.45359	−0.474754
$89$	5.76227	0.610800	0.305400	−	0.952224i	$-0.401210\pi$
$89$	5.76227	0.610800	0.305400	+	0.952224i	$0.401210\pi$
$90$	−5.26513	−0.554993
$91$	14.0938	1.47743
$92$	−31.9404	−3.33002
$93$	0.613266	0.0635927
$94$	24.5949	2.53677
$95$	0.616975	0.0633003
$96$	−14.6743	−1.49769
$97$	−7.66437	−0.778199	−0.389100	−	0.921196i	$-0.627214\pi$
$97$	−7.66437	−0.778199	−0.389100	+	0.921196i	$0.627214\pi$
$98$	5.82917	0.588835
$99$	−0.945050	−0.0949811
$100$	−17.6845	−1.76845
$101$	16.5441	1.64620	0.823098	−	0.567899i	$-0.192244\pi$
$101$	16.5441	1.64620	0.823098	+	0.567899i	$0.192244\pi$
$102$	14.0622	1.39237
$103$	−2.08812	−0.205748	−0.102874	−	0.994694i	$-0.532804\pi$
$103$	−2.08812	−0.205748	−0.102874	+	0.994694i	$0.532804\pi$
$104$	50.4341	4.94547
$105$	3.03823	0.296501
$106$	33.4288	3.24689
$107$	11.2595	1.08850	0.544249	−	0.838924i	$-0.316815\pi$
$107$	11.2595	1.08850	0.544249	+	0.838924i	$0.316815\pi$
$108$	−26.7873	−2.57761
$109$	8.81915	0.844721	0.422361	−	0.906428i	$-0.361202\pi$
$109$	8.81915	0.844721	0.422361	+	0.906428i	$0.361202\pi$
$110$	1.80092	0.171711
$111$	3.89679	0.369867
$112$	−23.5132	−2.22178
$113$	20.9357	1.96947	0.984733	−	0.174073i	$-0.0556929\pi$
$113$	20.9357	1.96947	0.984733	+	0.174073i	$0.0556929\pi$
$114$	1.56971	0.147017
$115$	7.71579	0.719501
$116$	−4.96757	−0.461227
$117$	10.7021	0.989409
$118$	21.5717	1.98583
$119$	10.0824	0.924248
$120$	10.8722	0.992494
$121$	−10.6767	−0.970614
$122$	2.69806	0.244271
$123$	9.15015	0.825041
$124$	2.63389	0.236530
$125$	10.2720	0.918759
$126$	−9.60437	−0.855625
$127$	7.64847	0.678692	0.339346	−	0.940662i	$-0.389794\pi$
$127$	7.64847	0.678692	0.339346	+	0.940662i	$0.389794\pi$
$128$	−6.31706	−0.558354
$129$	9.82824	0.865328
$130$	−20.3942	−1.78869
$131$	−5.53048	−0.483200	−0.241600	−	0.970376i	$-0.577672\pi$
$131$	−5.53048	−0.483200	−0.241600	+	0.970376i	$0.577672\pi$
$132$	3.26669	0.284329
$133$	1.12545	0.0975892
$134$	−40.9783	−3.53998
$135$	6.47097	0.556932
$136$	36.0794	3.09379
$137$	−12.1601	−1.03890	−0.519452	−	0.854500i	$-0.673864\pi$
$137$	−12.1601	−1.03890	−0.519452	+	0.854500i	$0.673864\pi$
$138$	19.6305	1.67106
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	13.0488	1.10282
$141$	−10.7770	−0.907588
$142$	4.73180	0.397084
$143$	−3.66061	−0.306115
$144$	−17.8547	−1.48789
$145$	1.20001	0.0996551
$146$	28.9247	2.39383
$147$	−2.55423	−0.210669
$148$	16.7362	1.37570
$149$	−21.5455	−1.76508	−0.882539	−	0.470238i	$-0.844168\pi$
$149$	−21.5455	−1.76508	−0.882539	+	0.470238i	$0.844168\pi$
$150$	10.8688	0.887437
$151$	0.581630	0.0473323	0.0236662	−	0.999720i	$-0.492466\pi$
$151$	0.581630	0.0473323	0.0236662	+	0.999720i	$0.492466\pi$
$152$	4.02740	0.326666
$153$	7.65604	0.618954
$154$	3.28513	0.264724
$155$	−0.636264	−0.0511060
$156$	−36.9932	−2.96182
$157$	−6.08516	−0.485648	−0.242824	−	0.970070i	$-0.578074\pi$
$157$	−6.08516	−0.485648	−0.242824	+	0.970070i	$0.578074\pi$
$158$	−32.2594	−2.56642
$159$	−14.6479	−1.16165
$160$	15.2247	1.20362
$161$	14.0747	1.10924
$162$	3.30069	0.259327
$163$	8.10025	0.634461	0.317230	−	0.948348i	$-0.397247\pi$
$163$	8.10025	0.634461	0.317230	+	0.948348i	$0.397247\pi$
$164$	39.2986	3.06871
$165$	−0.789128	−0.0614335
$166$	19.4953	1.51313
$167$	−4.54734	−0.351884	−0.175942	−	0.984401i	$-0.556297\pi$
$167$	−4.54734	−0.351884	−0.175942	+	0.984401i	$0.556297\pi$
$168$	19.8325	1.53011
$169$	28.4541	2.18878
$170$	−14.5896	−1.11897
$171$	0.854613	0.0653539
$172$	42.2109	3.21855
$173$	−11.8569	−0.901463	−0.450731	−	0.892660i	$-0.648837\pi$
$173$	−11.8569	−0.901463	−0.450731	+	0.892660i	$0.648837\pi$
$174$	3.05306	0.231452
$175$	7.79276	0.589077
$176$	6.10713	0.460343
$177$	−9.45230	−0.710478
$178$	−15.2102	−1.14005
$179$	18.5972	1.39002	0.695009	−	0.719001i	$-0.255401\pi$
$179$	18.5972	1.39002	0.695009	+	0.719001i	$0.255401\pi$
$180$	9.90860	0.738543
$181$	4.46126	0.331603	0.165801	−	0.986159i	$-0.446979\pi$
$181$	4.46126	0.331603	0.165801	+	0.986159i	$0.446979\pi$
$182$	−37.2021	−2.75760
$183$	−1.18224	−0.0873938
$184$	50.3661	3.71303
$185$	−4.04292	−0.297242
$186$	−1.61878	−0.118695
$187$	−2.61872	−0.191500
$188$	−46.2858	−3.37574
$189$	11.8040	0.858614
$190$	−1.62858	−0.118149
$191$	−5.84416	−0.422869	−0.211434	−	0.977392i	$-0.567813\pi$
$191$	−5.84416	−0.422869	−0.211434	+	0.977392i	$0.567813\pi$
$192$	13.8866	1.00218
$193$	0.0843536	0.00607190	0.00303595	−	0.999995i	$-0.499034\pi$
$193$	0.0843536	0.00607190	0.00303595	+	0.999995i	$0.499034\pi$
$194$	20.2310	1.45250
$195$	8.93638	0.639947
$196$	−10.9701	−0.783577
$197$	−24.9965	−1.78093	−0.890465	−	0.455052i	$-0.849621\pi$
$197$	−24.9965	−1.78093	−0.890465	+	0.455052i	$0.849621\pi$
$198$	2.49457	0.177281
$199$	−20.7764	−1.47280	−0.736400	−	0.676546i	$-0.763476\pi$
$199$	−20.7764	−1.47280	−0.736400	+	0.676546i	$0.763476\pi$
$200$	27.8862	1.97185
$201$	17.9559	1.26651
$202$	−43.6700	−3.07261
$203$	2.18899	0.153637
$204$	−26.4641	−1.85286
$205$	−9.49330	−0.663041
$206$	5.51182	0.384027
$207$	10.6877	0.742843
$208$	−69.1595	−4.79535
$209$	−0.292317	−0.0202200
$210$	−8.01976	−0.553416
$211$	11.0107	0.758011	0.379005	−	0.925394i	$-0.376266\pi$
$211$	11.0107	0.758011	0.379005	+	0.925394i	$0.376266\pi$
$212$	−62.9105	−4.32071
$213$	−2.07339	−0.142066
$214$	−29.7208	−2.03167
$215$	−10.1968	−0.695417
$216$	42.2403	2.87409
$217$	−1.16064	−0.0787893
$218$	−23.2792	−1.57666
$219$	−12.6743	−0.856449
$220$	−3.38919	−0.228499
$221$	29.6553	1.99483
$222$	−10.2860	−0.690352
$223$	29.2061	1.95579	0.977893	−	0.209107i	$-0.0670556\pi$
$223$	29.2061	1.95579	0.977893	+	0.209107i	$0.0670556\pi$
$224$	27.7720	1.85560
$225$	5.91744	0.394496
$226$	−55.2622	−3.67599
$227$	−3.41809	−0.226867	−0.113433	−	0.993546i	$-0.536185\pi$
$227$	−3.41809	−0.226867	−0.113433	+	0.993546i	$0.536185\pi$
$228$	−2.95408	−0.195639
$229$	19.0466	1.25863	0.629317	−	0.777149i	$-0.283335\pi$
$229$	19.0466	1.25863	0.629317	+	0.777149i	$0.283335\pi$
$230$	−20.3667	−1.34294
$231$	−1.43948	−0.0947111
$232$	7.83323	0.514277
$233$	−3.45567	−0.226388	−0.113194	−	0.993573i	$-0.536108\pi$
$233$	−3.45567	−0.226388	−0.113194	+	0.993573i	$0.536108\pi$
$234$	−28.2494	−1.84672
$235$	11.1812	0.729379
$236$	−40.5963	−2.64260
$237$	14.1355	0.918197
$238$	−26.6135	−1.72510
$239$	−7.76648	−0.502372	−0.251186	−	0.967939i	$-0.580821\pi$
$239$	−7.76648	−0.502372	−0.251186	+	0.967939i	$0.580821\pi$
$240$	−14.9089	−0.962365
$241$	−26.4123	−1.70137	−0.850684	−	0.525678i	$-0.823812\pi$
$241$	−26.4123	−1.70137	−0.850684	+	0.525678i	$0.823812\pi$
$242$	28.1825	1.81164
$243$	14.7310	0.944997
$244$	−5.07756	−0.325058
$245$	2.65002	0.169304
$246$	−24.1529	−1.53993
$247$	3.31031	0.210630
$248$	−4.15332	−0.263736
$249$	−8.54247	−0.541357
$250$	−27.1142	−1.71485
$251$	−17.2497	−1.08879	−0.544395	−	0.838829i	$-0.683241\pi$
$251$	−17.2497	−1.08879	−0.544395	+	0.838829i	$0.683241\pi$
$252$	18.0747	1.13860
$253$	−3.65567	−0.229830
$254$	−20.1890	−1.26677
$255$	6.39288	0.400338
$256$	−7.33753	−0.458595
$257$	−11.3893	−0.710447	−0.355223	−	0.934781i	$-0.615595\pi$
$257$	−11.3893	−0.710447	−0.355223	+	0.934781i	$0.615595\pi$
$258$	−25.9428	−1.61513
$259$	−7.37488	−0.458253
$260$	38.3805	2.38026
$261$	1.66221	0.102888
$262$	14.5983	0.901888
$263$	24.7194	1.52427	0.762133	−	0.647420i	$-0.224152\pi$
$263$	24.7194	1.52427	0.762133	+	0.647420i	$0.224152\pi$
$264$	−5.15116	−0.317032
$265$	15.1972	0.933556
$266$	−2.97076	−0.182149
$267$	6.66482	0.407880
$268$	77.1181	4.71074
$269$	−16.3345	−0.995930	−0.497965	−	0.867197i	$-0.665919\pi$
$269$	−16.3345	−0.995930	−0.497965	+	0.867197i	$0.665919\pi$
$270$	−17.0809	−1.03951
$271$	−19.0273	−1.15583	−0.577913	−	0.816098i	$-0.696133\pi$
$271$	−19.0273	−1.15583	−0.577913	+	0.816098i	$0.696133\pi$
$272$	−49.4751	−2.99987
$273$	16.3013	0.986597
$274$	32.0979	1.93910
$275$	−2.02403	−0.122054
$276$	−36.9432	−2.22372
$277$	31.1564	1.87200	0.936002	−	0.351994i	$-0.114496\pi$
$277$	31.1564	1.87200	0.936002	+	0.351994i	$0.114496\pi$
$278$	−2.63961	−0.158314
$279$	−0.881332	−0.0527640
$280$	−20.5763	−1.22967
$281$	−16.0962	−0.960221	−0.480111	−	0.877208i	$-0.659403\pi$
$281$	−16.0962	−0.960221	−0.480111	+	0.877208i	$0.659403\pi$
$282$	28.4472	1.69400
$283$	2.43020	0.144460	0.0722302	−	0.997388i	$-0.476988\pi$
$283$	2.43020	0.144460	0.0722302	+	0.997388i	$0.476988\pi$
$284$	−8.90490	−0.528409
$285$	0.713612	0.0422707
$286$	9.66260	0.571361
$287$	−17.3172	−1.02220
$288$	21.0887	1.24266
$289$	4.21476	0.247927
$290$	−3.16755	−0.186005
$291$	−8.86484	−0.519666
$292$	−54.4343	−3.18553
$293$	−33.2301	−1.94132	−0.970661	−	0.240450i	$-0.922705\pi$
$293$	−33.2301	−1.94132	−0.970661	+	0.240450i	$0.922705\pi$
$294$	6.74219	0.393212
$295$	9.80678	0.570973
$296$	−26.3908	−1.53394
$297$	−3.06588	−0.177901
$298$	56.8719	3.29450
$299$	41.3981	2.39412
$300$	−20.4544	−1.18093
$301$	−18.6005	−1.07211
$302$	−1.53528	−0.0883453
$303$	19.1354	1.09930
$304$	−5.52271	−0.316749
$305$	1.22658	0.0702336
$306$	−20.2090	−1.15527
$307$	15.8276	0.903330	0.451665	−	0.892188i	$-0.350830\pi$
$307$	15.8276	0.903330	0.451665	+	0.892188i	$0.350830\pi$
$308$	−6.18239	−0.352274
$309$	−2.41518	−0.137395
$310$	1.67949	0.0953888
$311$	−2.26147	−0.128236	−0.0641182	−	0.997942i	$-0.520423\pi$
$311$	−2.26147	−0.128236	−0.0641182	+	0.997942i	$0.520423\pi$
$312$	58.3336	3.30249
$313$	−34.1284	−1.92905	−0.964526	−	0.263987i	$-0.914962\pi$
$313$	−34.1284	−1.92905	−0.964526	+	0.263987i	$0.914962\pi$
$314$	16.0625	0.906457
$315$	−4.36628	−0.246012
$316$	60.7098	3.41519
$317$	−22.8880	−1.28552	−0.642759	−	0.766068i	$-0.722210\pi$
$317$	−22.8880	−1.28552	−0.642759	+	0.766068i	$0.722210\pi$
$318$	38.6647	2.16821
$319$	−0.568551	−0.0318328
$320$	−14.4073	−0.805395
$321$	13.0231	0.726878
$322$	−37.1519	−2.07039
$323$	2.36812	0.131766
$324$	−6.21166	−0.345092
$325$	22.9209	1.27142
$326$	−21.3815	−1.18421
$327$	10.2005	0.564089
$328$	−61.9690	−3.42167
$329$	20.3961	1.12447
$330$	2.08299	0.114665
$331$	22.9493	1.26141	0.630704	−	0.776024i	$-0.282766\pi$
$331$	22.9493	1.26141	0.630704	+	0.776024i	$0.282766\pi$
$332$	−36.6887	−2.01356
$333$	−5.60012	−0.306885
$334$	12.0032	0.656788
$335$	−18.6293	−1.01783
$336$	−27.1960	−1.48366
$337$	31.9223	1.73892	0.869459	−	0.494005i	$-0.164468\pi$
$337$	31.9223	1.73892	0.869459	+	0.494005i	$0.164468\pi$
$338$	−75.1078	−4.08533
$339$	24.2149	1.31517
$340$	27.4566	1.48904
$341$	0.301456	0.0163248
$342$	−2.25585	−0.121982
$343$	20.1569	1.08837
$344$	−66.5613	−3.58875
$345$	8.92431	0.480469
$346$	31.2976	1.68257
$347$	15.2531	0.818830	0.409415	−	0.912348i	$-0.365733\pi$
$347$	15.2531	0.818830	0.409415	+	0.912348i	$0.365733\pi$
$348$	−5.74563	−0.307998
$349$	−7.98972	−0.427680	−0.213840	−	0.976869i	$-0.568597\pi$
$349$	−7.98972	−0.427680	−0.213840	+	0.976869i	$0.568597\pi$
$350$	−20.5699	−1.09951
$351$	34.7192	1.85317
$352$	−7.21330	−0.384470
$353$	−19.1272	−1.01804	−0.509019	−	0.860755i	$-0.669992\pi$
$353$	−19.1272	−1.01804	−0.509019	+	0.860755i	$0.669992\pi$
$354$	24.9504	1.32610
$355$	2.15114	0.114171
$356$	28.6245	1.51709
$357$	11.6616	0.617195
$358$	−49.0893	−2.59445
$359$	−36.2364	−1.91248	−0.956242	−	0.292578i	$-0.905487\pi$
$359$	−36.2364	−1.91248	−0.956242	+	0.292578i	$0.905487\pi$
$360$	−15.6246	−0.823490
$361$	−18.7357	−0.986087
$362$	−11.7760	−0.618933
$363$	−12.3490	−0.648157
$364$	70.0116	3.66961
$365$	13.1496	0.688281
$366$	3.12066	0.163120
$367$	0.806419	0.0420947	0.0210474	−	0.999778i	$-0.493300\pi$
$367$	0.806419	0.0420947	0.0210474	+	0.999778i	$0.493300\pi$
$368$	−69.0661	−3.60032
$369$	−13.1498	−0.684551
$370$	10.6718	0.554798
$371$	27.7219	1.43925
$372$	3.04644	0.157950
$373$	14.8443	0.768609	0.384305	−	0.923206i	$-0.374441\pi$
$373$	14.8443	0.768609	0.384305	+	0.923206i	$0.374441\pi$
$374$	6.91240	0.357432
$375$	11.8809	0.613529
$376$	72.9869	3.76401
$377$	6.43848	0.331599
$378$	−31.1580	−1.60259
$379$	3.61902	0.185896	0.0929482	−	0.995671i	$-0.470371\pi$
$379$	3.61902	0.185896	0.0929482	+	0.995671i	$0.470371\pi$
$380$	3.06487	0.157224
$381$	8.84645	0.453218
$382$	15.4263	0.789280
$383$	−29.5461	−1.50973	−0.754867	−	0.655878i	$-0.772299\pi$
$383$	−29.5461	−1.50973	−0.754867	+	0.655878i	$0.772299\pi$
$384$	−7.30650	−0.372858
$385$	1.49347	0.0761142
$386$	−0.222661	−0.0113331
$387$	−14.1243	−0.717978
$388$	−38.0733	−1.93288
$389$	19.5556	0.991506	0.495753	−	0.868463i	$-0.334892\pi$
$389$	19.5556	0.991506	0.495753	+	0.868463i	$0.334892\pi$
$390$	−23.5886	−1.19445
$391$	29.6153	1.49771
$392$	17.2984	0.873703
$393$	−6.39672	−0.322672
$394$	65.9812	3.32409
$395$	−14.6656	−0.737905
$396$	−4.69460	−0.235912
$397$	−23.1321	−1.16097	−0.580484	−	0.814272i	$-0.697137\pi$
$397$	−23.1321	−1.16097	−0.580484	+	0.814272i	$0.697137\pi$
$398$	54.8417	2.74897
$399$	1.30173	0.0651682
$400$	−38.2399	−1.91199
$401$	28.4451	1.42048	0.710241	−	0.703959i	$-0.248586\pi$
$401$	28.4451	1.42048	0.710241	+	0.703959i	$0.248586\pi$
$402$	−47.3967	−2.36393
$403$	−3.41380	−0.170053
$404$	82.1838	4.08879
$405$	1.50054	0.0745624
$406$	−5.77808	−0.286761
$407$	1.91550	0.0949477
$408$	41.7306	2.06597
$409$	−11.1737	−0.552506	−0.276253	−	0.961085i	$-0.589093\pi$
$409$	−11.1737	−0.552506	−0.276253	+	0.961085i	$0.589093\pi$
$410$	25.0587	1.23756
$411$	−14.0647	−0.693760
$412$	−10.3729	−0.511034
$413$	17.8890	0.880260
$414$	−28.2113	−1.38651
$415$	8.86283	0.435059
$416$	81.6861	4.00499
$417$	1.15663	0.0566404
$418$	0.771604	0.0377404
$419$	27.4333	1.34020	0.670101	−	0.742270i	$-0.266251\pi$
$419$	27.4333	1.34020	0.670101	+	0.742270i	$0.266251\pi$
$420$	15.0926	0.736444
$421$	−36.4000	−1.77403	−0.887014	−	0.461743i	$-0.847224\pi$
$421$	−36.4000	−1.77403	−0.887014	+	0.461743i	$0.847224\pi$
$422$	−29.0641	−1.41482
$423$	15.4878	0.753042
$424$	99.2020	4.81768
$425$	16.3971	0.795377
$426$	5.47294	0.265165
$427$	2.23746	0.108278
$428$	55.9324	2.70359
$429$	−4.23397	−0.204418
$430$	26.9157	1.29799
$431$	12.2620	0.590641	0.295321	−	0.955398i	$-0.404574\pi$
$431$	12.2620	0.590641	0.295321	+	0.955398i	$0.404574\pi$
$432$	−57.9234	−2.78684
$433$	2.48457	0.119401	0.0597004	−	0.998216i	$-0.480985\pi$
$433$	2.48457	0.119401	0.0597004	+	0.998216i	$0.480985\pi$
$434$	3.06364	0.147059
$435$	1.38796	0.0665477
$436$	43.8097	2.09810
$437$	3.30584	0.158140
$438$	33.4552	1.59855
$439$	13.9415	0.665390	0.332695	−	0.943035i	$-0.392042\pi$
$439$	13.9415	0.665390	0.332695	+	0.943035i	$0.392042\pi$
$440$	5.34434	0.254781
$441$	3.67072	0.174796
$442$	−78.2786	−3.72334
$443$	−20.2263	−0.960979	−0.480489	−	0.877001i	$-0.659541\pi$
$443$	−20.2263	−0.960979	−0.480489	+	0.877001i	$0.659541\pi$
$444$	19.3575	0.918668
$445$	−6.91476	−0.327791
$446$	−77.0929	−3.65045
$447$	−24.9202	−1.17869
$448$	−26.2811	−1.24167
$449$	5.40272	0.254970	0.127485	−	0.991841i	$-0.459310\pi$
$449$	5.40272	0.254970	0.127485	+	0.991841i	$0.459310\pi$
$450$	−15.6197	−0.736322
$451$	4.49783	0.211795
$452$	103.999	4.89172
$453$	0.672730	0.0316076
$454$	9.02245	0.423445
$455$	−16.9126	−0.792874
$456$	4.65822	0.218141
$457$	17.3080	0.809635	0.404818	−	0.914397i	$-0.367335\pi$
$457$	17.3080	0.809635	0.404818	+	0.914397i	$0.367335\pi$
$458$	−50.2756	−2.34923
$459$	24.8373	1.15931
$460$	38.3287	1.78708
$461$	17.5160	0.815801	0.407900	−	0.913026i	$-0.366261\pi$
$461$	17.5160	0.815801	0.407900	+	0.913026i	$0.366261\pi$
$462$	3.79968	0.176777
$463$	−19.3197	−0.897861	−0.448930	−	0.893567i	$-0.648195\pi$
$463$	−19.3197	−0.897861	−0.448930	+	0.893567i	$0.648195\pi$
$464$	−10.7416	−0.498665
$465$	−0.735922	−0.0341276
$466$	9.12163	0.422551
$467$	−35.3133	−1.63411	−0.817053	−	0.576562i	$-0.804394\pi$
$467$	−35.3133	−1.63411	−0.817053	+	0.576562i	$0.804394\pi$
$468$	53.1634	2.45748
$469$	−33.9825	−1.56917
$470$	−29.5140	−1.36138
$471$	−7.03827	−0.324307
$472$	64.0153	2.94654
$473$	4.83115	0.222137
$474$	−37.3122	−1.71380
$475$	1.83034	0.0839820
$476$	50.0848	2.29563
$477$	21.0506	0.963842
$478$	20.5005	0.937672
$479$	4.54644	0.207732	0.103866	−	0.994591i	$-0.466879\pi$
$479$	4.54644	0.207732	0.103866	+	0.994591i	$0.466879\pi$
$480$	17.6093	0.803751
$481$	−21.6918	−0.989062
$482$	69.7184	3.17558
$483$	16.2793	0.740732
$484$	−53.0374	−2.41079
$485$	9.19729	0.417628
$486$	−38.8843	−1.76383
$487$	41.2540	1.86940	0.934698	−	0.355442i	$-0.115670\pi$
$487$	41.2540	1.86940	0.934698	+	0.355442i	$0.115670\pi$
$488$	8.00668	0.362445
$489$	9.36900	0.423681
$490$	−6.99503	−0.316003
$491$	11.6704	0.526679	0.263339	−	0.964703i	$-0.415176\pi$
$491$	11.6704	0.526679	0.263339	+	0.964703i	$0.415176\pi$
$492$	45.4540	2.04922
$493$	4.60595	0.207441
$494$	−8.73793	−0.393138
$495$	1.13407	0.0509725
$496$	5.69537	0.255730
$497$	3.92400	0.176015
$498$	22.5488	1.01044
$499$	−27.5386	−1.23280	−0.616398	−	0.787434i	$-0.711409\pi$
$499$	−27.5386	−1.23280	−0.616398	+	0.787434i	$0.711409\pi$
$500$	51.0270	2.28200
$501$	−5.25959	−0.234981
$502$	45.5325	2.03221
$503$	−7.47753	−0.333407	−0.166703	−	0.986007i	$-0.553312\pi$
$503$	−7.47753	−0.333407	−0.166703	+	0.986007i	$0.553312\pi$
$504$	−28.5016	−1.26956
$505$	−19.8530	−0.883446
$506$	9.64955	0.428975
$507$	32.9108	1.46162
$508$	37.9943	1.68572
$509$	11.7518	0.520887	0.260444	−	0.965489i	$-0.416131\pi$
$509$	11.7518	0.520887	0.260444	+	0.965489i	$0.416131\pi$
$510$	−16.8747	−0.747226
$511$	23.9868	1.06111
$512$	32.0024	1.41432
$513$	2.77249	0.122409
$514$	30.0634	1.32604
$515$	2.50575	0.110417
$516$	48.8224	2.14929
$517$	−5.29753	−0.232985
$518$	19.4669	0.855324
$519$	−13.7140	−0.601979
$520$	−60.5212	−2.65403
$521$	34.3349	1.50424	0.752119	−	0.659028i	$-0.229032\pi$
$521$	34.3349	1.50424	0.752119	+	0.659028i	$0.229032\pi$
$522$	−4.38759	−0.192039
$523$	12.1641	0.531900	0.265950	−	0.963987i	$-0.414314\pi$
$523$	12.1641	0.531900	0.265950	+	0.963987i	$0.414314\pi$
$524$	−27.4730	−1.20016
$525$	9.01334	0.393374
$526$	−65.2498	−2.84503
$527$	−2.44216	−0.106382
$528$	7.06369	0.307408
$529$	18.3423	0.797490
$530$	−40.1147	−1.74247
$531$	13.5840	0.589496
$532$	5.59076	0.242390
$533$	−50.9351	−2.20625
$534$	−17.5926	−0.761304
$535$	−13.5115	−0.584152
$536$	−121.606	−5.25256
$537$	21.5100	0.928226
$538$	43.1167	1.85889
$539$	−1.25555	−0.0540806
$540$	32.1450	1.38330
$541$	22.2257	0.955558	0.477779	−	0.878480i	$-0.341442\pi$
$541$	22.2257	0.955558	0.477779	+	0.878480i	$0.341442\pi$
$542$	50.2247	2.15734
$543$	5.16002	0.221438
$544$	58.4364	2.50544
$545$	−10.5830	−0.453327
$546$	−43.0290	−1.84147
$547$	41.5392	1.77609	0.888043	−	0.459760i	$-0.152064\pi$
$547$	41.5392	1.77609	0.888043	+	0.459760i	$0.152064\pi$
$548$	−60.4059	−2.58041
$549$	1.69901	0.0725121
$550$	5.34267	0.227812
$551$	0.514144	0.0219033
$552$	58.2549	2.47949
$553$	−26.7521	−1.13762
$554$	−82.2408	−3.49408
$555$	−4.67617	−0.198492
$556$	4.96757	0.210672
$557$	8.12358	0.344207	0.172103	−	0.985079i	$-0.444944\pi$
$557$	8.12358	0.344207	0.172103	+	0.985079i	$0.444944\pi$
$558$	2.32638	0.0984834
$559$	−54.7098	−2.31398
$560$	28.2159	1.19234
$561$	−3.02889	−0.127880
$562$	42.4879	1.79224
$563$	26.5617	1.11944	0.559721	−	0.828681i	$-0.310908\pi$
$563$	26.5617	1.11944	0.559721	+	0.828681i	$0.310908\pi$
$564$	−53.5355	−2.25425
$565$	−25.1230	−1.05693
$566$	−6.41479	−0.269634
$567$	2.73720	0.114952
$568$	14.0419	0.589186
$569$	−16.3424	−0.685108	−0.342554	−	0.939498i	$-0.611292\pi$
$569$	−16.3424	−0.685108	−0.342554	+	0.939498i	$0.611292\pi$
$570$	−1.88366	−0.0788979
$571$	11.8953	0.497804	0.248902	−	0.968529i	$-0.419930\pi$
$571$	11.8953	0.497804	0.248902	+	0.968529i	$0.419930\pi$
$572$	−18.1843	−0.760324
$573$	−6.75953	−0.282384
$574$	45.7106	1.90793
$575$	22.8900	0.954578
$576$	−19.9566	−0.831524
$577$	3.27763	0.136449	0.0682247	−	0.997670i	$-0.478267\pi$
$577$	3.27763	0.136449	0.0682247	+	0.997670i	$0.478267\pi$
$578$	−11.1253	−0.462753
$579$	0.0975659	0.00405470
$580$	5.96111	0.247521
$581$	16.1671	0.670725
$582$	23.3998	0.969952
$583$	−7.20028	−0.298205
$584$	85.8361	3.55192
$585$	−12.8426	−0.530975
$586$	87.7146	3.62346
$587$	−2.87128	−0.118510	−0.0592552	−	0.998243i	$-0.518873\pi$
$587$	−2.87128	−0.118510	−0.0592552	+	0.998243i	$0.518873\pi$
$588$	−12.6883	−0.523257
$589$	−0.272608	−0.0112326
$590$	−25.8861	−1.06571
$591$	−28.9117	−1.18927
$592$	36.1893	1.48737
$593$	27.6439	1.13520	0.567600	−	0.823304i	$-0.307872\pi$
$593$	27.6439	1.13520	0.567600	+	0.823304i	$0.307872\pi$
$594$	8.09275	0.332050
$595$	−12.0989	−0.496006
$596$	−107.029	−4.38407
$597$	−24.0306	−0.983507
$598$	−109.275	−4.46859
$599$	−21.7947	−0.890509	−0.445255	−	0.895404i	$-0.646887\pi$
$599$	−21.7947	−0.890509	−0.445255	+	0.895404i	$0.646887\pi$
$600$	32.2540	1.31676
$601$	−35.5881	−1.45167	−0.725835	−	0.687869i	$-0.758546\pi$
$601$	−35.5881	−1.45167	−0.725835	+	0.687869i	$0.758546\pi$
$602$	49.0981	2.00109
$603$	−25.8047	−1.05085
$604$	2.88928	0.117563
$605$	12.8122	0.520888
$606$	−50.5100	−2.05183
$607$	34.1747	1.38711	0.693554	−	0.720405i	$-0.256044\pi$
$607$	34.1747	1.38711	0.693554	+	0.720405i	$0.256044\pi$
$608$	6.52302	0.264543
$609$	2.53185	0.102596
$610$	−3.23769	−0.131090
$611$	59.9912	2.42698
$612$	38.0319	1.53735
$613$	−12.0701	−0.487505	−0.243752	−	0.969837i	$-0.578378\pi$
$613$	−12.0701	−0.487505	−0.243752	+	0.969837i	$0.578378\pi$
$614$	−41.7788	−1.68606
$615$	−10.9802	−0.442766
$616$	9.74885	0.392792
$617$	−9.44732	−0.380335	−0.190167	−	0.981752i	$-0.560903\pi$
$617$	−9.44732	−0.380335	−0.190167	+	0.981752i	$0.560903\pi$
$618$	6.37514	0.256446
$619$	25.3970	1.02079	0.510396	−	0.859940i	$-0.329499\pi$
$619$	25.3970	1.02079	0.510396	+	0.859940i	$0.329499\pi$
$620$	−3.16068	−0.126936
$621$	34.6723	1.39135
$622$	5.96942	0.239352
$623$	−12.6135	−0.505351
$624$	−79.9919	−3.20224
$625$	5.47343	0.218937
$626$	90.0859	3.60056
$627$	−0.338103	−0.0135025
$628$	−30.2284	−1.20624
$629$	−15.5178	−0.618737
$630$	11.5253	0.459179
$631$	−16.4780	−0.655980	−0.327990	−	0.944681i	$-0.606371\pi$
$631$	−16.4780	−0.655980	−0.327990	+	0.944681i	$0.606371\pi$
$632$	−95.7318	−3.80801
$633$	12.7354	0.506185
$634$	60.4155	2.39941
$635$	−9.17821	−0.364226
$636$	−72.7642	−2.88529
$637$	14.2184	0.563352
$638$	1.50076	0.0594155
$639$	2.97969	0.117875
$640$	7.58050	0.299646
$641$	6.60761	0.260985	0.130492	−	0.991449i	$-0.458344\pi$
$641$	6.60761	0.260985	0.130492	+	0.991449i	$0.458344\pi$
$642$	−34.3759	−1.35671
$643$	−11.8836	−0.468645	−0.234322	−	0.972159i	$-0.575287\pi$
$643$	−11.8836	−0.468645	−0.234322	+	0.972159i	$0.575287\pi$
$644$	69.9171	2.75512
$645$	−11.7939	−0.464386
$646$	−6.25092	−0.245939
$647$	45.9566	1.80674	0.903370	−	0.428863i	$-0.141086\pi$
$647$	45.9566	1.80674	0.903370	+	0.428863i	$0.141086\pi$
$648$	9.79501	0.384784
$649$	−4.64636	−0.182386
$650$	−60.5024	−2.37310
$651$	−1.34243	−0.0526140
$652$	40.2385	1.57586
$653$	21.7184	0.849906	0.424953	−	0.905215i	$-0.360291\pi$
$653$	21.7184	0.849906	0.424953	+	0.905215i	$0.360291\pi$
$654$	−26.9254	−1.05287
$655$	6.63661	0.259314
$656$	84.9771	3.31780
$657$	18.2144	0.710610
$658$	−53.8378	−2.09882
$659$	−6.95417	−0.270896	−0.135448	−	0.990784i	$-0.543247\pi$
$659$	−6.95417	−0.270896	−0.135448	+	0.990784i	$0.543247\pi$
$660$	−3.92004	−0.152587
$661$	−11.7802	−0.458198	−0.229099	−	0.973403i	$-0.573578\pi$
$661$	−11.7802	−0.458198	−0.229099	+	0.973403i	$0.573578\pi$
$662$	−60.5773	−2.35440
$663$	34.3002	1.33211
$664$	57.8536	2.24515
$665$	−1.35055	−0.0523721
$666$	14.7822	0.572797
$667$	6.42980	0.248963
$668$	−22.5892	−0.874004
$669$	33.7807	1.30604
$670$	49.1741	1.89976
$671$	−0.581141	−0.0224347
$672$	32.1219	1.23913
$673$	−7.42938	−0.286381	−0.143191	−	0.989695i	$-0.545736\pi$
$673$	−7.42938	−0.286381	−0.143191	+	0.989695i	$0.545736\pi$
$674$	−84.2625	−3.24567
$675$	19.1970	0.738894
$676$	141.348	5.43644
$677$	46.6069	1.79125	0.895624	−	0.444812i	$-0.146729\pi$
$677$	46.6069	1.79125	0.895624	+	0.444812i	$0.146729\pi$
$678$	−63.9179	−2.45475
$679$	16.7772	0.643850
$680$	−43.2955	−1.66031
$681$	−3.95347	−0.151497
$682$	−0.795728	−0.0304700
$683$	16.2506	0.621810	0.310905	−	0.950441i	$-0.399368\pi$
$683$	16.2506	0.621810	0.310905	+	0.950441i	$0.399368\pi$
$684$	4.24535	0.162325
$685$	14.5921	0.557537
$686$	−53.2065	−2.03143
$687$	22.0298	0.840491
$688$	91.2744	3.47981
$689$	81.5386	3.10637
$690$	−23.5568	−0.896790
$691$	28.7539	1.09385	0.546924	−	0.837182i	$-0.315799\pi$
$691$	28.7539	1.09385	0.546924	+	0.837182i	$0.315799\pi$
$692$	−58.8999	−2.23904
$693$	2.06870	0.0785835
$694$	−40.2623	−1.52834
$695$	−1.20001	−0.0455188
$696$	9.06015	0.343424
$697$	−36.4379	−1.38018
$698$	21.0898	0.798260
$699$	−3.99693	−0.151178
$700$	38.7110	1.46314
$701$	12.4556	0.470442	0.235221	−	0.971942i	$-0.424419\pi$
$701$	12.4556	0.470442	0.235221	+	0.971942i	$0.424419\pi$
$702$	−91.6453	−3.45893
$703$	−1.73219	−0.0653309
$704$	6.82606	0.257267
$705$	12.9325	0.487065
$706$	50.4884	1.90016
$707$	−36.2147	−1.36200
$708$	−46.9549	−1.76467
$709$	−45.5928	−1.71227	−0.856136	−	0.516750i	$-0.827142\pi$
$709$	−45.5928	−1.71227	−0.856136	+	0.516750i	$0.827142\pi$
$710$	−5.67819	−0.213098
$711$	−20.3142	−0.761844
$712$	−45.1372	−1.69159
$713$	−3.40919	−0.127675
$714$	−30.7820	−1.15199
$715$	4.39275	0.164280
$716$	92.3826	3.45250
$717$	−8.98294	−0.335474
$718$	95.6501	3.56963
$719$	−47.1283	−1.75759	−0.878794	−	0.477201i	$-0.841651\pi$
$719$	−47.1283	−1.75759	−0.878794	+	0.477201i	$0.841651\pi$
$720$	21.4258	0.798491
$721$	4.57086	0.170228
$722$	49.4549	1.84052
$723$	−30.5493	−1.13614
$724$	22.1616	0.823629
$725$	3.55999	0.132215
$726$	32.5967	1.20978
$727$	−21.9517	−0.814144	−0.407072	−	0.913396i	$-0.633450\pi$
$727$	−21.9517	−0.814144	−0.407072	+	0.913396i	$0.633450\pi$
$728$	−110.400	−4.09168
$729$	20.7897	0.769989
$730$	−34.7099	−1.28467
$731$	−39.1382	−1.44758
$732$	−5.87286	−0.217067
$733$	29.3761	1.08503	0.542515	−	0.840046i	$-0.317472\pi$
$733$	29.3761	1.08503	0.542515	+	0.840046i	$0.317472\pi$
$734$	−2.12864	−0.0785694
$735$	3.06509	0.113058
$736$	81.5758	3.00692
$737$	8.82638	0.325124
$738$	34.7104	1.27771
$739$	−5.66094	−0.208241	−0.104120	−	0.994565i	$-0.533203\pi$
$739$	−5.66094	−0.208241	−0.104120	+	0.994565i	$0.533203\pi$
$740$	−20.0835	−0.738284
$741$	3.82880	0.140654
$742$	−73.1751	−2.68634
$743$	0.917544	0.0336614	0.0168307	−	0.999858i	$-0.494642\pi$
$743$	0.917544	0.0336614	0.0168307	+	0.999858i	$0.494642\pi$
$744$	−4.80385	−0.176118
$745$	25.8548	0.947245
$746$	−39.1833	−1.43460
$747$	12.2765	0.449174
$748$	−13.0086	−0.475643
$749$	−24.6469	−0.900579
$750$	−31.3611	−1.14515
$751$	−51.4052	−1.87580	−0.937902	−	0.346900i	$-0.887234\pi$
$751$	−51.4052	−1.87580	−0.937902	+	0.346900i	$0.887234\pi$
$752$	−100.086	−3.64975
$753$	−19.9515	−0.727073
$754$	−16.9951	−0.618926
$755$	−0.697959	−0.0254013
$756$	58.6371	2.13261
$757$	−1.69185	−0.0614912	−0.0307456	−	0.999527i	$-0.509788\pi$
$757$	−1.69185	−0.0614912	−0.0307456	+	0.999527i	$0.509788\pi$
$758$	−9.55281	−0.346974
$759$	−4.22825	−0.153476
$760$	−4.83291	−0.175308
$761$	18.9252	0.686038	0.343019	−	0.939328i	$-0.388551\pi$
$761$	18.9252	0.686038	0.343019	+	0.939328i	$0.388551\pi$
$762$	−23.3512	−0.845926
$763$	−19.3050	−0.698888
$764$	−29.0313	−1.05031
$765$	−9.18729	−0.332167
$766$	77.9902	2.81790
$767$	52.6171	1.89989
$768$	−8.48680	−0.306241
$769$	7.30115	0.263286	0.131643	−	0.991297i	$-0.457975\pi$
$769$	7.30115	0.263286	0.131643	+	0.991297i	$0.457975\pi$
$770$	−3.94218	−0.142066
$771$	−13.1732	−0.474423
$772$	0.419032	0.0150813
$773$	−33.5468	−1.20659	−0.603297	−	0.797516i	$-0.706147\pi$
$773$	−33.5468	−1.20659	−0.603297	+	0.797516i	$0.706147\pi$
$774$	37.2827	1.34010
$775$	−1.88757	−0.0678034
$776$	60.0368	2.15520
$777$	−8.53001	−0.306012
$778$	−51.6192	−1.85064
$779$	−4.06741	−0.145730
$780$	44.3920	1.58949
$781$	−1.01919	−0.0364695
$782$	−78.1730	−2.79546
$783$	5.39245	0.192710
$784$	−23.7210	−0.847180
$785$	7.30222	0.260628
$786$	16.8849	0.602263
$787$	−21.6280	−0.770953	−0.385477	−	0.922718i	$-0.625963\pi$
$787$	−21.6280	−0.770953	−0.385477	+	0.922718i	$0.625963\pi$
$788$	−124.172	−4.42344
$789$	28.5912	1.01788
$790$	38.7114	1.37729
$791$	−45.8280	−1.62945
$792$	7.40279	0.263047
$793$	6.58105	0.233700
$794$	61.0599	2.16693
$795$	17.5775	0.623410
$796$	−103.208	−3.65812
$797$	−3.23704	−0.114662	−0.0573310	−	0.998355i	$-0.518259\pi$
$797$	−3.23704	−0.114662	−0.0573310	+	0.998355i	$0.518259\pi$
$798$	−3.43607	−0.121636
$799$	42.9164	1.51827
$800$	45.1661	1.59686
$801$	−9.57810	−0.338425
$802$	−75.0842	−2.65131
$803$	−6.23015	−0.219857
$804$	89.1971	3.14574
$805$	−16.8898	−0.595286
$806$	9.01111	0.317403
$807$	−18.8929	−0.665063
$808$	−129.594	−4.55908
$809$	37.7578	1.32749	0.663746	−	0.747958i	$-0.268965\pi$
$809$	37.7578	1.32749	0.663746	+	0.747958i	$0.268965\pi$
$810$	−3.96085	−0.139170
$811$	−20.2750	−0.711953	−0.355976	−	0.934495i	$-0.615852\pi$
$811$	−20.2750	−0.711953	−0.355976	+	0.934495i	$0.615852\pi$
$812$	10.8739	0.381600
$813$	−22.0075	−0.771838
$814$	−5.05618	−0.177219
$815$	−9.72035	−0.340489
$816$	−57.2244	−2.00326
$817$	−4.36884	−0.152846
$818$	29.4944	1.03125
$819$	−23.4267	−0.818597
$820$	−47.1586	−1.64685
$821$	−8.64760	−0.301803	−0.150902	−	0.988549i	$-0.548218\pi$
$821$	−8.64760	−0.301803	−0.150902	+	0.988549i	$0.548218\pi$
$822$	37.1254	1.29490
$823$	−43.9439	−1.53179	−0.765894	−	0.642966i	$-0.777703\pi$
$823$	−43.9439	−1.53179	−0.765894	+	0.642966i	$0.777703\pi$
$824$	16.3567	0.569813
$825$	−2.34106	−0.0815052
$826$	−47.2201	−1.64300
$827$	32.8910	1.14373	0.571866	−	0.820347i	$-0.306220\pi$
$827$	32.8910	1.14373	0.571866	+	0.820347i	$0.306220\pi$
$828$	53.0916	1.84506
$829$	−32.0007	−1.11143	−0.555716	−	0.831372i	$-0.687556\pi$
$829$	−32.0007	−1.11143	−0.555716	+	0.831372i	$0.687556\pi$
$830$	−23.3945	−0.812034
$831$	36.0364	1.25009
$832$	−77.3008	−2.67992
$833$	10.1715	0.352422
$834$	−3.05306	−0.105719
$835$	5.45684	0.188842
$836$	−1.45210	−0.0502221
$837$	−2.85917	−0.0988274
$838$	−72.4132	−2.50147
$839$	−38.0767	−1.31455	−0.657277	−	0.753649i	$-0.728292\pi$
$839$	−38.0767	−1.31455	−0.657277	+	0.753649i	$0.728292\pi$
$840$	−23.7992	−0.821149
$841$	1.00000	0.0344828
$842$	96.0820	3.31120
$843$	−18.6174	−0.641217
$844$	54.6966	1.88273
$845$	−34.1451	−1.17463
$846$	−40.8818	−1.40554
$847$	23.3713	0.803046
$848$	−136.034	−4.67143
$849$	2.81084	0.0964679
$850$	−43.2821	−1.48456
$851$	−21.6625	−0.742582
$852$	−10.2997	−0.352861
$853$	−4.64021	−0.158878	−0.0794389	−	0.996840i	$-0.525313\pi$
$853$	−4.64021	−0.158878	−0.0794389	+	0.996840i	$0.525313\pi$
$854$	−5.90602	−0.202100
$855$	−1.02554	−0.0350728
$856$	−88.1983	−3.01456
$857$	−36.5823	−1.24963	−0.624813	−	0.780774i	$-0.714825\pi$
$857$	−36.5823	−1.24963	−0.624813	+	0.780774i	$0.714825\pi$
$858$	11.1760	0.381544
$859$	10.0748	0.343748	0.171874	−	0.985119i	$-0.445018\pi$
$859$	10.0748	0.343748	0.171874	+	0.985119i	$0.445018\pi$
$860$	−50.6533	−1.72726
$861$	−20.0296	−0.682605
$862$	−32.3670	−1.10243
$863$	−32.5132	−1.10676	−0.553381	−	0.832928i	$-0.686663\pi$
$863$	−32.5132	−1.10676	−0.553381	+	0.832928i	$0.686663\pi$
$864$	68.4148	2.32752
$865$	14.2283	0.483778
$866$	−6.55831	−0.222860
$867$	4.87492	0.165561
$868$	−5.76555	−0.195696
$869$	6.94840	0.235708
$870$	−3.66369	−0.124211
$871$	−99.9532	−3.38678
$872$	−69.0824	−2.33943
$873$	12.7398	0.431176
$874$	−8.72614	−0.295166
$875$	−22.4853	−0.760143
$876$	−62.9603	−2.12723
$877$	8.93453	0.301698	0.150849	−	0.988557i	$-0.451799\pi$
$877$	8.93453	0.301698	0.150849	+	0.988557i	$0.451799\pi$
$878$	−36.8001	−1.24194
$879$	−38.4349	−1.29638
$880$	−7.32860	−0.247047
$881$	5.16899	0.174148	0.0870739	−	0.996202i	$-0.472248\pi$
$881$	5.16899	0.174148	0.0870739	+	0.996202i	$0.472248\pi$
$882$	−9.68928	−0.326255
$883$	−9.72825	−0.327382	−0.163691	−	0.986512i	$-0.552340\pi$
$883$	−9.72825	−0.327382	−0.163691	+	0.986512i	$0.552340\pi$
$884$	147.315	4.95473
$885$	11.3428	0.381285
$886$	53.3895	1.79366
$887$	16.3258	0.548166	0.274083	−	0.961706i	$-0.411626\pi$
$887$	16.3258	0.548166	0.274083	+	0.961706i	$0.411626\pi$
$888$	−30.5244	−1.02433
$889$	−16.7424	−0.561522
$890$	18.2523	0.611819
$891$	−0.710941	−0.0238174
$892$	145.083	4.85775
$893$	4.79058	0.160311
$894$	65.7797	2.20000
$895$	−22.3167	−0.745965
$896$	13.8279	0.461959
$897$	47.8823	1.59874
$898$	−14.2611	−0.475899
$899$	−0.530218	−0.0176838
$900$	29.3952	0.979842
$901$	58.3309	1.94328
$902$	−11.8725	−0.395313
$903$	−21.5139	−0.715937
$904$	−163.994	−5.45436
$905$	−5.35353	−0.177958
$906$	−1.77575	−0.0589953
$907$	24.5305	0.814521	0.407261	−	0.913312i	$-0.366484\pi$
$907$	24.5305	0.814521	0.407261	+	0.913312i	$0.366484\pi$
$908$	−16.9796	−0.563488
$909$	−27.4997	−0.912107
$910$	44.6427	1.47989
$911$	19.0673	0.631727	0.315863	−	0.948805i	$-0.397706\pi$
$911$	19.0673	0.631727	0.315863	+	0.948805i	$0.397706\pi$
$912$	−6.38773	−0.211519
$913$	−4.19913	−0.138971
$914$	−45.6865	−1.51118
$915$	1.41870	0.0469006
$916$	94.6151	3.12617
$917$	12.1061	0.399780
$918$	−65.5610	−2.16384
$919$	−7.20122	−0.237546	−0.118773	−	0.992921i	$-0.537896\pi$
$919$	−7.20122	−0.237546	−0.118773	+	0.992921i	$0.537896\pi$
$920$	−60.4396	−1.99263
$921$	18.3067	0.603226
$922$	−46.2355	−1.52268
$923$	11.5417	0.379899
$924$	−7.15073	−0.235242
$925$	−11.9939	−0.394357
$926$	50.9965	1.67585
$927$	3.47088	0.113999
$928$	12.6872	0.416476
$929$	28.1132	0.922364	0.461182	−	0.887306i	$-0.347426\pi$
$929$	28.1132	0.922364	0.461182	+	0.887306i	$0.347426\pi$
$930$	1.94255	0.0636988
$931$	1.13540	0.0372114
$932$	−17.1663	−0.562300
$933$	−2.61569	−0.0856337
$934$	93.2136	3.05004
$935$	3.14248	0.102770
$936$	−83.8320	−2.74013
$937$	−0.626374	−0.0204627	−0.0102314	−	0.999948i	$-0.503257\pi$
$937$	−0.626374	−0.0204627	−0.0102314	+	0.999948i	$0.503257\pi$
$938$	89.7008	2.92884
$939$	−39.4739	−1.28818
$940$	55.5432	1.81162
$941$	−3.87750	−0.126403	−0.0632015	−	0.998001i	$-0.520131\pi$
$941$	−3.87750	−0.126403	−0.0632015	+	0.998001i	$0.520131\pi$
$942$	18.5783	0.605315
$943$	−50.8664	−1.65644
$944$	−87.7831	−2.85710
$945$	−14.1649	−0.460783
$946$	−12.7524	−0.414616
$947$	13.4392	0.436715	0.218357	−	0.975869i	$-0.429930\pi$
$947$	13.4392	0.436715	0.218357	+	0.975869i	$0.429930\pi$
$948$	70.2188	2.28060
$949$	70.5526	2.29023
$950$	−4.83140	−0.156751
$951$	−26.4729	−0.858444
$952$	−78.9774	−2.55967
$953$	18.2431	0.590953	0.295477	−	0.955350i	$-0.404522\pi$
$953$	18.2431	0.590953	0.295477	+	0.955350i	$0.404522\pi$
$954$	−55.5655	−1.79900
$955$	7.01303	0.226936
$956$	−38.5805	−1.24778
$957$	−0.657603	−0.0212573
$958$	−12.0009	−0.387730
$959$	26.6182	0.859547
$960$	−16.6640	−0.537827
$961$	−30.7189	−0.990931
$962$	57.2580	1.84607
$963$	−18.7156	−0.603103
$964$	−131.205	−4.22583
$965$	−0.101225	−0.00325854
$966$	−42.9710	−1.38257
$967$	−42.6881	−1.37276	−0.686378	−	0.727245i	$-0.740800\pi$
$967$	−42.6881	−1.37276	−0.686378	+	0.727245i	$0.740800\pi$
$968$	83.6334	2.68808
$969$	2.73904	0.0879905
$970$	−24.2773	−0.779497
$971$	22.8681	0.733872	0.366936	−	0.930246i	$-0.380407\pi$
$971$	22.8681	0.733872	0.366936	+	0.930246i	$0.380407\pi$
$972$	73.1774	2.34717
$973$	−2.18899	−0.0701757
$974$	−108.895	−3.48921
$975$	26.5110	0.849032
$976$	−10.9794	−0.351443
$977$	−10.9155	−0.349217	−0.174609	−	0.984638i	$-0.555866\pi$
$977$	−10.9155	−0.349217	−0.174609	+	0.984638i	$0.555866\pi$
$978$	−24.7305	−0.790795
$979$	3.27615	0.104706
$980$	13.1642	0.420513
$981$	−14.6593	−0.468034
$982$	−30.8054	−0.983041
$983$	3.01412	0.0961356	0.0480678	−	0.998844i	$-0.484694\pi$
$983$	3.01412	0.0961356	0.0480678	+	0.998844i	$0.484694\pi$
$984$	−71.6752	−2.28492
$985$	29.9960	0.955752
$986$	−12.1579	−0.387187
$987$	23.5907	0.750901
$988$	16.4442	0.523158
$989$	−54.6359	−1.73732
$990$	−2.99350	−0.0951395
$991$	−1.93253	−0.0613890	−0.0306945	−	0.999529i	$-0.509772\pi$
$991$	−1.93253	−0.0613890	−0.0306945	+	0.999529i	$0.509772\pi$
$992$	−6.72696	−0.213581
$993$	26.5438	0.842343
$994$	−10.3578	−0.328531
$995$	24.9318	0.790391
$996$	−42.4353	−1.34461
$997$	−9.04502	−0.286459	−0.143229	−	0.989690i	$-0.545749\pi$
$997$	−9.04502	−0.286459	−0.143229	+	0.989690i	$0.545749\pi$
$998$	72.6913	2.30100
$999$	−18.1676	−0.574798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.6	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.6	✓	103	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)

\(f(q)\)	\(=\)	\(q-2.63961 q^{2} +1.15663 q^{3} +4.96757 q^{4} -1.20001 q^{5} -3.05306 q^{6} -2.18899 q^{7} -7.83323 q^{8} -1.66221 q^{9} +O(q^{10})\)	\(q-2.63961 q^{2} +1.15663 q^{3} +4.96757 q^{4} -1.20001 q^{5} -3.05306 q^{6} -2.18899 q^{7} -7.83323 q^{8} -1.66221 q^{9} +3.16755 q^{10} +0.568551 q^{11} +5.74563 q^{12} -6.43848 q^{13} +5.77808 q^{14} -1.38796 q^{15} +10.7416 q^{16} -4.60595 q^{17} +4.38759 q^{18} -0.514144 q^{19} -5.96111 q^{20} -2.53185 q^{21} -1.50076 q^{22} -6.42980 q^{23} -9.06015 q^{24} -3.55999 q^{25} +16.9951 q^{26} -5.39245 q^{27} -10.8739 q^{28} -1.00000 q^{29} +3.66369 q^{30} +0.530218 q^{31} -12.6872 q^{32} +0.657603 q^{33} +12.1579 q^{34} +2.62680 q^{35} -8.25712 q^{36} +3.36909 q^{37} +1.35714 q^{38} -7.44694 q^{39} +9.39992 q^{40} +7.91104 q^{41} +6.68310 q^{42} +8.49731 q^{43} +2.82432 q^{44} +1.99466 q^{45} +16.9722 q^{46} -9.31760 q^{47} +12.4240 q^{48} -2.20834 q^{49} +9.39699 q^{50} -5.32738 q^{51} -31.9836 q^{52} -12.6643 q^{53} +14.2340 q^{54} -0.682265 q^{55} +17.1468 q^{56} -0.594674 q^{57} +2.63961 q^{58} -8.17228 q^{59} -6.89479 q^{60} -1.02214 q^{61} -1.39957 q^{62} +3.63855 q^{63} +12.0061 q^{64} +7.72622 q^{65} -1.73582 q^{66} +15.5243 q^{67} -22.8803 q^{68} -7.43689 q^{69} -6.93373 q^{70} -1.79261 q^{71} +13.0205 q^{72} -10.9579 q^{73} -8.89309 q^{74} -4.11759 q^{75} -2.55404 q^{76} -1.24455 q^{77} +19.6571 q^{78} +12.2212 q^{79} -12.8900 q^{80} -1.25044 q^{81} -20.8821 q^{82} -7.38566 q^{83} -12.5771 q^{84} +5.52716 q^{85} -22.4296 q^{86} -1.15663 q^{87} -4.45359 q^{88} +5.76227 q^{89} -5.26513 q^{90} +14.0938 q^{91} -31.9404 q^{92} +0.613266 q^{93} +24.5949 q^{94} +0.616975 q^{95} -14.6743 q^{96} -7.66437 q^{97} +5.82917 q^{98} -0.945050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

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