LMFDB - Embedded newform 4029.2.a.l.1.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.38616 q^{2} -1.00000 q^{3} -0.0785713 q^{4} +0.223881 q^{5} -1.38616 q^{6} -1.36218 q^{7} -2.88122 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.38616 q^{2} -1.00000 q^{3} -0.0785713 q^{4} +0.223881 q^{5} -1.38616 q^{6} -1.36218 q^{7} -2.88122 q^{8} +1.00000 q^{9} +0.310335 q^{10} -1.81746 q^{11} +0.0785713 q^{12} -6.19716 q^{13} -1.88819 q^{14} -0.223881 q^{15} -3.83668 q^{16} -1.00000 q^{17} +1.38616 q^{18} +0.302242 q^{19} -0.0175906 q^{20} +1.36218 q^{21} -2.51929 q^{22} +3.55266 q^{23} +2.88122 q^{24} -4.94988 q^{25} -8.59023 q^{26} -1.00000 q^{27} +0.107028 q^{28} +5.25703 q^{29} -0.310335 q^{30} +2.62536 q^{31} +0.444206 q^{32} +1.81746 q^{33} -1.38616 q^{34} -0.304966 q^{35} -0.0785713 q^{36} +9.66362 q^{37} +0.418955 q^{38} +6.19716 q^{39} -0.645052 q^{40} +4.75400 q^{41} +1.88819 q^{42} -0.704181 q^{43} +0.142800 q^{44} +0.223881 q^{45} +4.92455 q^{46} -3.93071 q^{47} +3.83668 q^{48} -5.14447 q^{49} -6.86130 q^{50} +1.00000 q^{51} +0.486919 q^{52} +3.80473 q^{53} -1.38616 q^{54} -0.406896 q^{55} +3.92474 q^{56} -0.302242 q^{57} +7.28706 q^{58} +9.63461 q^{59} +0.0175906 q^{60} +13.6681 q^{61} +3.63916 q^{62} -1.36218 q^{63} +8.28911 q^{64} -1.38743 q^{65} +2.51929 q^{66} -13.4090 q^{67} +0.0785713 q^{68} -3.55266 q^{69} -0.422731 q^{70} +7.08887 q^{71} -2.88122 q^{72} -10.8473 q^{73} +13.3953 q^{74} +4.94988 q^{75} -0.0237476 q^{76} +2.47571 q^{77} +8.59023 q^{78} +1.00000 q^{79} -0.858962 q^{80} +1.00000 q^{81} +6.58979 q^{82} +6.16234 q^{83} -0.107028 q^{84} -0.223881 q^{85} -0.976105 q^{86} -5.25703 q^{87} +5.23652 q^{88} +0.122798 q^{89} +0.310335 q^{90} +8.44163 q^{91} -0.279137 q^{92} -2.62536 q^{93} -5.44857 q^{94} +0.0676664 q^{95} -0.444206 q^{96} -2.12619 q^{97} -7.13104 q^{98} -1.81746 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * 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 $

$2$	1.38616	0.980160	0.490080	−	0.871677i	$-0.336967\pi$
$2$	1.38616	0.980160	0.490080	+	0.871677i	$0.336967\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.0785713	−0.0392856
$5$	0.223881	0.100123	0.0500614	−	0.998746i	$-0.484058\pi$
$5$	0.223881	0.100123	0.0500614	+	0.998746i	$0.484058\pi$
$6$	−1.38616	−0.565896
$7$	−1.36218	−0.514855	−0.257428	−	0.966298i	$-0.582875\pi$
$7$	−1.36218	−0.514855	−0.257428	+	0.966298i	$0.582875\pi$
$8$	−2.88122	−1.01867
$9$	1.00000	0.333333
$10$	0.310335	0.0981364
$11$	−1.81746	−0.547986	−0.273993	−	0.961732i	$-0.588344\pi$
$11$	−1.81746	−0.547986	−0.273993	+	0.961732i	$0.588344\pi$
$12$	0.0785713	0.0226816
$13$	−6.19716	−1.71878	−0.859391	−	0.511319i	$-0.829157\pi$
$13$	−6.19716	−1.71878	−0.859391	+	0.511319i	$0.829157\pi$
$14$	−1.88819	−0.504641
$15$	−0.223881	−0.0578059
$16$	−3.83668	−0.959171
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.38616	0.326720
$19$	0.302242	0.0693391	0.0346696	−	0.999399i	$-0.488962\pi$
$19$	0.302242	0.0693391	0.0346696	+	0.999399i	$0.488962\pi$
$20$	−0.0175906	−0.00393339
$21$	1.36218	0.297252
$22$	−2.51929	−0.537114
$23$	3.55266	0.740781	0.370391	−	0.928876i	$-0.379224\pi$
$23$	3.55266	0.740781	0.370391	+	0.928876i	$0.379224\pi$
$24$	2.88122	0.588127
$25$	−4.94988	−0.989975
$26$	−8.59023	−1.68468
$27$	−1.00000	−0.192450
$28$	0.107028	0.0202264
$29$	5.25703	0.976206	0.488103	−	0.872786i	$-0.337689\pi$
$29$	5.25703	0.976206	0.488103	+	0.872786i	$0.337689\pi$
$30$	−0.310335	−0.0566591
$31$	2.62536	0.471528	0.235764	−	0.971810i	$-0.424241\pi$
$31$	2.62536	0.471528	0.235764	+	0.971810i	$0.424241\pi$
$32$	0.444206	0.0785252
$33$	1.81746	0.316380
$34$	−1.38616	−0.237724
$35$	−0.304966	−0.0515487
$36$	−0.0785713	−0.0130952
$37$	9.66362	1.58869	0.794345	−	0.607467i	$-0.207814\pi$
$37$	9.66362	1.58869	0.794345	+	0.607467i	$0.207814\pi$
$38$	0.418955	0.0679635
$39$	6.19716	0.992339
$40$	−0.645052	−0.101992
$41$	4.75400	0.742450	0.371225	−	0.928543i	$-0.378938\pi$
$41$	4.75400	0.742450	0.371225	+	0.928543i	$0.378938\pi$
$42$	1.88819	0.291354
$43$	−0.704181	−0.107387	−0.0536933	−	0.998557i	$-0.517099\pi$
$43$	−0.704181	−0.107387	−0.0536933	+	0.998557i	$0.517099\pi$
$44$	0.142800	0.0215280
$45$	0.223881	0.0333743
$46$	4.92455	0.726085
$47$	−3.93071	−0.573353	−0.286676	−	0.958027i	$-0.592550\pi$
$47$	−3.93071	−0.573353	−0.286676	+	0.958027i	$0.592550\pi$
$48$	3.83668	0.553778
$49$	−5.14447	−0.734924
$50$	−6.86130	−0.970335
$51$	1.00000	0.140028
$52$	0.486919	0.0675235
$53$	3.80473	0.522620	0.261310	−	0.965255i	$-0.415846\pi$
$53$	3.80473	0.522620	0.261310	+	0.965255i	$0.415846\pi$
$54$	−1.38616	−0.188632
$55$	−0.406896	−0.0548659
$56$	3.92474	0.524466
$57$	−0.302242	−0.0400330
$58$	7.28706	0.956838
$59$	9.63461	1.25432	0.627160	−	0.778891i	$-0.284217\pi$
$59$	9.63461	1.25432	0.627160	+	0.778891i	$0.284217\pi$
$60$	0.0175906	0.00227094
$61$	13.6681	1.75002	0.875008	−	0.484108i	$-0.160856\pi$
$61$	13.6681	1.75002	0.875008	+	0.484108i	$0.160856\pi$
$62$	3.63916	0.462173
$63$	−1.36218	−0.171618
$64$	8.28911	1.03614
$65$	−1.38743	−0.172089
$66$	2.51929	0.310103
$67$	−13.4090	−1.63817	−0.819085	−	0.573672i	$-0.805518\pi$
$67$	−13.4090	−1.63817	−0.819085	+	0.573672i	$0.805518\pi$
$68$	0.0785713	0.00952817
$69$	−3.55266	−0.427690
$70$	−0.422731	−0.0505260
$71$	7.08887	0.841294	0.420647	−	0.907224i	$-0.361803\pi$
$71$	7.08887	0.841294	0.420647	+	0.907224i	$0.361803\pi$
$72$	−2.88122	−0.339556
$73$	−10.8473	−1.26958	−0.634788	−	0.772687i	$-0.718912\pi$
$73$	−10.8473	−1.26958	−0.634788	+	0.772687i	$0.718912\pi$
$74$	13.3953	1.55717
$75$	4.94988	0.571563
$76$	−0.0237476	−0.00272403
$77$	2.47571	0.282133
$78$	8.59023	0.972652
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−0.858962	−0.0960349
$81$	1.00000	0.111111
$82$	6.58979	0.727720
$83$	6.16234	0.676404	0.338202	−	0.941073i	$-0.390181\pi$
$83$	6.16234	0.676404	0.338202	+	0.941073i	$0.390181\pi$
$84$	−0.107028	−0.0116777
$85$	−0.223881	−0.0242833
$86$	−0.976105	−0.105256
$87$	−5.25703	−0.563613
$88$	5.23652	0.558215
$89$	0.122798	0.0130166	0.00650830	−	0.999979i	$-0.497928\pi$
$89$	0.122798	0.0130166	0.00650830	+	0.999979i	$0.497928\pi$
$90$	0.310335	0.0327121
$91$	8.44163	0.884924
$92$	−0.279137	−0.0291021
$93$	−2.62536	−0.272237
$94$	−5.44857	−0.561978
$95$	0.0676664	0.00694243
$96$	−0.444206	−0.0453366
$97$	−2.12619	−0.215881	−0.107941	−	0.994157i	$-0.534426\pi$
$97$	−2.12619	−0.215881	−0.107941	+	0.994157i	$0.534426\pi$
$98$	−7.13104	−0.720344
$99$	−1.81746	−0.182662
$100$	0.388918	0.0388918
$101$	5.37663	0.534995	0.267497	−	0.963559i	$-0.413803\pi$
$101$	5.37663	0.534995	0.267497	+	0.963559i	$0.413803\pi$
$102$	1.38616	0.137250
$103$	17.8158	1.75544	0.877719	−	0.479175i	$-0.159064\pi$
$103$	17.8158	1.75544	0.877719	+	0.479175i	$0.159064\pi$
$104$	17.8554	1.75087
$105$	0.304966	0.0297617
$106$	5.27395	0.512251
$107$	−11.2381	−1.08643	−0.543214	−	0.839594i	$-0.682793\pi$
$107$	−11.2381	−1.08643	−0.543214	+	0.839594i	$0.682793\pi$
$108$	0.0785713	0.00756053
$109$	−6.80910	−0.652194	−0.326097	−	0.945336i	$-0.605734\pi$
$109$	−6.80910	−0.652194	−0.326097	+	0.945336i	$0.605734\pi$
$110$	−0.564022	−0.0537774
$111$	−9.66362	−0.917230
$112$	5.22625	0.493834
$113$	−3.05178	−0.287087	−0.143544	−	0.989644i	$-0.545850\pi$
$113$	−3.05178	−0.287087	−0.143544	+	0.989644i	$0.545850\pi$
$114$	−0.418955	−0.0392387
$115$	0.795375	0.0741691
$116$	−0.413051	−0.0383509
$117$	−6.19716	−0.572927
$118$	13.3551	1.22943
$119$	1.36218	0.124871
$120$	0.645052	0.0588850
$121$	−7.69683	−0.699712
$122$	18.9461	1.71530
$123$	−4.75400	−0.428654
$124$	−0.206278	−0.0185243
$125$	−2.22759	−0.199242
$126$	−1.88819	−0.168214
$127$	7.14875	0.634349	0.317174	−	0.948367i	$-0.397266\pi$
$127$	7.14875	0.634349	0.317174	+	0.948367i	$0.397266\pi$
$128$	10.6016	0.937056
$129$	0.704181	0.0619997
$130$	−1.92319	−0.168675
$131$	−12.4247	−1.08555	−0.542774	−	0.839879i	$-0.682626\pi$
$131$	−12.4247	−1.08555	−0.542774	+	0.839879i	$0.682626\pi$
$132$	−0.142800	−0.0124292
$133$	−0.411708	−0.0356996
$134$	−18.5870	−1.60567
$135$	−0.223881	−0.0192686
$136$	2.88122	0.247063
$137$	0.923061	0.0788624	0.0394312	−	0.999222i	$-0.487445\pi$
$137$	0.923061	0.0788624	0.0394312	+	0.999222i	$0.487445\pi$
$138$	−4.92455	−0.419205
$139$	17.3651	1.47289	0.736444	−	0.676499i	$-0.236504\pi$
$139$	17.3651	1.47289	0.736444	+	0.676499i	$0.236504\pi$
$140$	0.0239616	0.00202513
$141$	3.93071	0.331025
$142$	9.82628	0.824603
$143$	11.2631	0.941868
$144$	−3.83668	−0.319724
$145$	1.17695	0.0977404
$146$	−15.0360	−1.24439
$147$	5.14447	0.424309
$148$	−0.759283	−0.0624127
$149$	20.9917	1.71971	0.859855	−	0.510539i	$-0.170554\pi$
$149$	20.9917	1.71971	0.859855	+	0.510539i	$0.170554\pi$
$150$	6.86130	0.560223
$151$	1.92496	0.156651	0.0783254	−	0.996928i	$-0.475043\pi$
$151$	1.92496	0.156651	0.0783254	+	0.996928i	$0.475043\pi$
$152$	−0.870828	−0.0706334
$153$	−1.00000	−0.0808452
$154$	3.43172	0.276536
$155$	0.587769	0.0472107
$156$	−0.486919	−0.0389847
$157$	−11.3114	−0.902747	−0.451374	−	0.892335i	$-0.649066\pi$
$157$	−11.3114	−0.902747	−0.451374	+	0.892335i	$0.649066\pi$
$158$	1.38616	0.110277
$159$	−3.80473	−0.301735
$160$	0.0994494	0.00786216
$161$	−4.83936	−0.381395
$162$	1.38616	0.108907
$163$	0.0522065	0.00408913	0.00204457	−	0.999998i	$-0.499349\pi$
$163$	0.0522065	0.00408913	0.00204457	+	0.999998i	$0.499349\pi$
$164$	−0.373528	−0.0291676
$165$	0.406896	0.0316768
$166$	8.54196	0.662985
$167$	8.92034	0.690276	0.345138	−	0.938552i	$-0.387832\pi$
$167$	8.92034	0.690276	0.345138	+	0.938552i	$0.387832\pi$
$168$	−3.92474	−0.302800
$169$	25.4047	1.95421
$170$	−0.310335	−0.0238016
$171$	0.302242	0.0231130
$172$	0.0553284	0.00421875
$173$	−7.78743	−0.592068	−0.296034	−	0.955177i	$-0.595664\pi$
$173$	−7.78743	−0.592068	−0.296034	+	0.955177i	$0.595664\pi$
$174$	−7.28706	−0.552431
$175$	6.74262	0.509694
$176$	6.97303	0.525612
$177$	−9.63461	−0.724182
$178$	0.170218	0.0127584
$179$	−12.1122	−0.905309	−0.452654	−	0.891686i	$-0.649523\pi$
$179$	−12.1122	−0.905309	−0.452654	+	0.891686i	$0.649523\pi$
$180$	−0.0175906	−0.00131113
$181$	0.496934	0.0369368	0.0184684	−	0.999829i	$-0.494121\pi$
$181$	0.496934	0.0369368	0.0184684	+	0.999829i	$0.494121\pi$
$182$	11.7014	0.867367
$183$	−13.6681	−1.01037
$184$	−10.2360	−0.754609
$185$	2.16350	0.159064
$186$	−3.63916	−0.266836
$187$	1.81746	0.132906
$188$	0.308841	0.0225245
$189$	1.36218	0.0990839
$190$	0.0937962	0.00680469
$191$	11.8021	0.853967	0.426983	−	0.904260i	$-0.359576\pi$
$191$	11.8021	0.853967	0.426983	+	0.904260i	$0.359576\pi$
$192$	−8.28911	−0.598215
$193$	13.7533	0.989987	0.494993	−	0.868897i	$-0.335171\pi$
$193$	13.7533	0.989987	0.494993	+	0.868897i	$0.335171\pi$
$194$	−2.94722	−0.211598
$195$	1.38743	0.0993558
$196$	0.404208	0.0288720
$197$	−7.71956	−0.549996	−0.274998	−	0.961445i	$-0.588677\pi$
$197$	−7.71956	−0.549996	−0.274998	+	0.961445i	$0.588677\pi$
$198$	−2.51929	−0.179038
$199$	3.43961	0.243828	0.121914	−	0.992541i	$-0.461097\pi$
$199$	3.43961	0.243828	0.121914	+	0.992541i	$0.461097\pi$
$200$	14.2617	1.00845
$201$	13.4090	0.945798
$202$	7.45285	0.524380
$203$	−7.16101	−0.502604
$204$	−0.0785713	−0.00550109
$205$	1.06433	0.0743362
$206$	24.6954	1.72061
$207$	3.55266	0.246927
$208$	23.7765	1.64861
$209$	−0.549314	−0.0379969
$210$	0.422731	0.0291712
$211$	−10.8476	−0.746781	−0.373390	−	0.927674i	$-0.621805\pi$
$211$	−10.8476	−0.746781	−0.373390	+	0.927674i	$0.621805\pi$
$212$	−0.298942	−0.0205315
$213$	−7.08887	−0.485721
$214$	−15.5778	−1.06487
$215$	−0.157653	−0.0107518
$216$	2.88122	0.196042
$217$	−3.57621	−0.242769
$218$	−9.43848	−0.639254
$219$	10.8473	0.732990
$220$	0.0319704	0.00215544
$221$	6.19716	0.416866
$222$	−13.3953	−0.899033
$223$	−2.53298	−0.169621	−0.0848106	−	0.996397i	$-0.527029\pi$
$223$	−2.53298	−0.169621	−0.0848106	+	0.996397i	$0.527029\pi$
$224$	−0.605087	−0.0404291
$225$	−4.94988	−0.329992
$226$	−4.23024	−0.281392
$227$	−4.73378	−0.314192	−0.157096	−	0.987583i	$-0.550213\pi$
$227$	−4.73378	−0.314192	−0.157096	+	0.987583i	$0.550213\pi$
$228$	0.0237476	0.00157272
$229$	−1.37192	−0.0906588	−0.0453294	−	0.998972i	$-0.514434\pi$
$229$	−1.37192	−0.0906588	−0.0453294	+	0.998972i	$0.514434\pi$
$230$	1.10251	0.0726976
$231$	−2.47571	−0.162890
$232$	−15.1467	−0.994428
$233$	−7.97874	−0.522705	−0.261352	−	0.965243i	$-0.584168\pi$
$233$	−7.97874	−0.522705	−0.261352	+	0.965243i	$0.584168\pi$
$234$	−8.59023	−0.561561
$235$	−0.880012	−0.0574057
$236$	−0.757004	−0.0492767
$237$	−1.00000	−0.0649570
$238$	1.88819	0.122393
$239$	18.2413	1.17993	0.589967	−	0.807427i	$-0.299141\pi$
$239$	18.2413	1.17993	0.589967	+	0.807427i	$0.299141\pi$
$240$	0.858962	0.0554458
$241$	15.9318	1.02626	0.513129	−	0.858311i	$-0.328486\pi$
$241$	15.9318	1.02626	0.513129	+	0.858311i	$0.328486\pi$
$242$	−10.6690	−0.685829
$243$	−1.00000	−0.0641500
$244$	−1.07392	−0.0687505
$245$	−1.15175	−0.0735827
$246$	−6.58979	−0.420150
$247$	−1.87304	−0.119179
$248$	−7.56425	−0.480330
$249$	−6.16234	−0.390522
$250$	−3.08779	−0.195289
$251$	13.7772	0.869607	0.434804	−	0.900525i	$-0.356818\pi$
$251$	13.7772	0.869607	0.434804	+	0.900525i	$0.356818\pi$
$252$	0.107028	0.00674214
$253$	−6.45684	−0.405938
$254$	9.90928	0.621764
$255$	0.223881	0.0140200
$256$	−1.88276	−0.117673
$257$	8.81666	0.549968	0.274984	−	0.961449i	$-0.411327\pi$
$257$	8.81666	0.549968	0.274984	+	0.961449i	$0.411327\pi$
$258$	0.976105	0.0607696
$259$	−13.1636	−0.817945
$260$	0.109012	0.00676064
$261$	5.25703	0.325402
$262$	−17.2225	−1.06401
$263$	11.6884	0.720738	0.360369	−	0.932810i	$-0.382651\pi$
$263$	11.6884	0.720738	0.360369	+	0.932810i	$0.382651\pi$
$264$	−5.23652	−0.322286
$265$	0.851808	0.0523261
$266$	−0.570691	−0.0349913
$267$	−0.122798	−0.00751514
$268$	1.05356	0.0643565
$269$	10.0881	0.615082	0.307541	−	0.951535i	$-0.400494\pi$
$269$	10.0881	0.615082	0.307541	+	0.951535i	$0.400494\pi$
$270$	−0.310335	−0.0188864
$271$	16.9762	1.03123	0.515615	−	0.856820i	$-0.327563\pi$
$271$	16.9762	1.03123	0.515615	+	0.856820i	$0.327563\pi$
$272$	3.83668	0.232633
$273$	−8.44163	−0.510911
$274$	1.27951	0.0772978
$275$	8.99622	0.542493
$276$	0.279137	0.0168021
$277$	−12.3310	−0.740897	−0.370449	−	0.928853i	$-0.620796\pi$
$277$	−12.3310	−0.740897	−0.370449	+	0.928853i	$0.620796\pi$
$278$	24.0707	1.44367
$279$	2.62536	0.157176
$280$	0.878677	0.0525110
$281$	−8.66438	−0.516874	−0.258437	−	0.966028i	$-0.583207\pi$
$281$	−8.66438	−0.516874	−0.258437	+	0.966028i	$0.583207\pi$
$282$	5.44857	0.324458
$283$	−6.22886	−0.370267	−0.185134	−	0.982713i	$-0.559272\pi$
$283$	−6.22886	−0.370267	−0.185134	+	0.982713i	$0.559272\pi$
$284$	−0.556981	−0.0330508
$285$	−0.0676664	−0.00400821
$286$	15.6124	0.923182
$287$	−6.47580	−0.382254
$288$	0.444206	0.0261751
$289$	1.00000	0.0588235
$290$	1.63144	0.0958013
$291$	2.12619	0.124639
$292$	0.852283	0.0498761
$293$	30.2742	1.76864	0.884318	−	0.466884i	$-0.154623\pi$
$293$	30.2742	1.76864	0.884318	+	0.466884i	$0.154623\pi$
$294$	7.13104	0.415891
$295$	2.15701	0.125586
$296$	−27.8431	−1.61834
$297$	1.81746	0.105460
$298$	29.0978	1.68559
$299$	−22.0164	−1.27324
$300$	−0.388918	−0.0224542
$301$	0.959220	0.0552885
$302$	2.66829	0.153543
$303$	−5.37663	−0.308879
$304$	−1.15961	−0.0665081
$305$	3.06003	0.175217
$306$	−1.38616	−0.0792413
$307$	−11.9329	−0.681049	−0.340524	−	0.940236i	$-0.610605\pi$
$307$	−11.9329	−0.681049	−0.340524	+	0.940236i	$0.610605\pi$
$308$	−0.194520	−0.0110838
$309$	−17.8158	−1.01350
$310$	0.814739	0.0462741
$311$	1.92318	0.109054	0.0545269	−	0.998512i	$-0.482635\pi$
$311$	1.92318	0.109054	0.0545269	+	0.998512i	$0.482635\pi$
$312$	−17.8554	−1.01086
$313$	24.5266	1.38633	0.693163	−	0.720781i	$-0.256217\pi$
$313$	24.5266	1.38633	0.693163	+	0.720781i	$0.256217\pi$
$314$	−15.6793	−0.884837
$315$	−0.304966	−0.0171829
$316$	−0.0785713	−0.00441998
$317$	10.9845	0.616950	0.308475	−	0.951232i	$-0.400181\pi$
$317$	10.9845	0.616950	0.308475	+	0.951232i	$0.400181\pi$
$318$	−5.27395	−0.295748
$319$	−9.55446	−0.534947
$320$	1.85578	0.103741
$321$	11.2381	0.627249
$322$	−6.70811	−0.373828
$323$	−0.302242	−0.0168172
$324$	−0.0785713	−0.00436507
$325$	30.6752	1.70155
$326$	0.0723664	0.00400801
$327$	6.80910	0.376544
$328$	−13.6973	−0.756309
$329$	5.35433	0.295194
$330$	0.564022	0.0310484
$331$	25.8360	1.42007	0.710036	−	0.704165i	$-0.248678\pi$
$331$	25.8360	1.42007	0.710036	+	0.704165i	$0.248678\pi$
$332$	−0.484183	−0.0265730
$333$	9.66362	0.529563
$334$	12.3650	0.676582
$335$	−3.00202	−0.164018
$336$	−5.22625	−0.285115
$337$	−25.3753	−1.38228	−0.691141	−	0.722720i	$-0.742892\pi$
$337$	−25.3753	−1.38228	−0.691141	+	0.722720i	$0.742892\pi$
$338$	35.2149	1.91544
$339$	3.05178	0.165750
$340$	0.0175906	0.000953987 0
$341$	−4.77149	−0.258391
$342$	0.418955	0.0226545
$343$	16.5429	0.893235
$344$	2.02890	0.109391
$345$	−0.795375	−0.0428216
$346$	−10.7946	−0.580321
$347$	−1.27642	−0.0685217	−0.0342609	−	0.999413i	$-0.510908\pi$
$347$	−1.27642	−0.0685217	−0.0342609	+	0.999413i	$0.510908\pi$
$348$	0.413051	0.0221419
$349$	−14.0988	−0.754691	−0.377346	−	0.926072i	$-0.623163\pi$
$349$	−14.0988	−0.754691	−0.377346	+	0.926072i	$0.623163\pi$
$350$	9.34632	0.499582
$351$	6.19716	0.330780
$352$	−0.807328	−0.0430307
$353$	13.8259	0.735881	0.367940	−	0.929849i	$-0.380063\pi$
$353$	13.8259	0.735881	0.367940	+	0.929849i	$0.380063\pi$
$354$	−13.3551	−0.709814
$355$	1.58707	0.0842327
$356$	−0.00964843	−0.000511366 0
$357$	−1.36218	−0.0720941
$358$	−16.7894	−0.887348
$359$	28.7264	1.51612	0.758060	−	0.652184i	$-0.226147\pi$
$359$	28.7264	1.51612	0.758060	+	0.652184i	$0.226147\pi$
$360$	−0.645052	−0.0339973
$361$	−18.9086	−0.995192
$362$	0.688828	0.0362040
$363$	7.69683	0.403979
$364$	−0.663270	−0.0347648
$365$	−2.42850	−0.127113
$366$	−18.9461	−0.990327
$367$	1.58748	0.0828660	0.0414330	−	0.999141i	$-0.486808\pi$
$367$	1.58748	0.0828660	0.0414330	+	0.999141i	$0.486808\pi$
$368$	−13.6304	−0.710536
$369$	4.75400	0.247483
$370$	2.99896	0.155908
$371$	−5.18272	−0.269073
$372$	0.206278	0.0106950
$373$	29.2177	1.51283	0.756417	−	0.654090i	$-0.226948\pi$
$373$	29.2177	1.51283	0.756417	+	0.654090i	$0.226948\pi$
$374$	2.51929	0.130269
$375$	2.22759	0.115032
$376$	11.3253	0.584055
$377$	−32.5786	−1.67788
$378$	1.88819	0.0971181
$379$	−22.3278	−1.14690	−0.573452	−	0.819239i	$-0.694396\pi$
$379$	−22.3278	−1.14690	−0.573452	+	0.819239i	$0.694396\pi$
$380$	−0.00531664	−0.000272738 0
$381$	−7.14875	−0.366242
$382$	16.3595	0.837024
$383$	−34.0913	−1.74198	−0.870991	−	0.491299i	$-0.836522\pi$
$383$	−34.0913	−1.74198	−0.870991	+	0.491299i	$0.836522\pi$
$384$	−10.6016	−0.541010
$385$	0.554265	0.0282480
$386$	19.0643	0.970346
$387$	−0.704181	−0.0357955
$388$	0.167057	0.00848104
$389$	−34.3667	−1.74246	−0.871230	−	0.490875i	$-0.836677\pi$
$389$	−34.3667	−1.74246	−0.871230	+	0.490875i	$0.836677\pi$
$390$	1.92319	0.0973846
$391$	−3.55266	−0.179666
$392$	14.8224	0.748643
$393$	12.4247	0.626741
$394$	−10.7005	−0.539084
$395$	0.223881	0.0112647
$396$	0.142800	0.00717599
$397$	−0.795380	−0.0399190	−0.0199595	−	0.999801i	$-0.506354\pi$
$397$	−0.795380	−0.0399190	−0.0199595	+	0.999801i	$0.506354\pi$
$398$	4.76784	0.238990
$399$	0.411708	0.0206112
$400$	18.9911	0.949556
$401$	−29.1086	−1.45361	−0.726806	−	0.686842i	$-0.758996\pi$
$401$	−29.1086	−1.45361	−0.726806	+	0.686842i	$0.758996\pi$
$402$	18.5870	0.927033
$403$	−16.2698	−0.810454
$404$	−0.422449	−0.0210176
$405$	0.223881	0.0111248
$406$	−9.92628	−0.492633
$407$	−17.5633	−0.870579
$408$	−2.88122	−0.142642
$409$	−22.1399	−1.09475	−0.547375	−	0.836888i	$-0.684373\pi$
$409$	−22.1399	−1.09475	−0.547375	+	0.836888i	$0.684373\pi$
$410$	1.47533	0.0728614
$411$	−0.923061	−0.0455312
$412$	−1.39981	−0.0689635
$413$	−13.1241	−0.645793
$414$	4.92455	0.242028
$415$	1.37963	0.0677235
$416$	−2.75281	−0.134968
$417$	−17.3651	−0.850372
$418$	−0.761435	−0.0372430
$419$	−37.7338	−1.84342	−0.921709	−	0.387883i	$-0.873207\pi$
$419$	−37.7338	−1.84342	−0.921709	+	0.387883i	$0.873207\pi$
$420$	−0.0239616	−0.00116921
$421$	−10.3066	−0.502311	−0.251156	−	0.967947i	$-0.580811\pi$
$421$	−10.3066	−0.502311	−0.251156	+	0.967947i	$0.580811\pi$
$422$	−15.0365	−0.731965
$423$	−3.93071	−0.191118
$424$	−10.9623	−0.532375
$425$	4.94988	0.240104
$426$	−9.82628	−0.476085
$427$	−18.6183	−0.901005
$428$	0.882992	0.0426810
$429$	−11.2631	−0.543788
$430$	−0.218532	−0.0105385
$431$	−20.8517	−1.00439	−0.502196	−	0.864754i	$-0.667474\pi$
$431$	−20.8517	−1.00439	−0.502196	+	0.864754i	$0.667474\pi$
$432$	3.83668	0.184593
$433$	19.0724	0.916559	0.458279	−	0.888808i	$-0.348466\pi$
$433$	19.0724	0.916559	0.458279	+	0.888808i	$0.348466\pi$
$434$	−4.95718	−0.237952
$435$	−1.17695	−0.0564305
$436$	0.535000	0.0256219
$437$	1.07376	0.0513651
$438$	15.0360	0.718447
$439$	−12.8727	−0.614382	−0.307191	−	0.951648i	$-0.599389\pi$
$439$	−12.8727	−0.614382	−0.307191	+	0.951648i	$0.599389\pi$
$440$	1.17236	0.0558900
$441$	−5.14447	−0.244975
$442$	8.59023	0.408595
$443$	16.5102	0.784425	0.392213	−	0.919875i	$-0.371710\pi$
$443$	16.5102	0.784425	0.392213	+	0.919875i	$0.371710\pi$
$444$	0.759283	0.0360340
$445$	0.0274923	0.00130326
$446$	−3.51111	−0.166256
$447$	−20.9917	−0.992875
$448$	−11.2912	−0.533461
$449$	4.35578	0.205562	0.102781	−	0.994704i	$-0.467226\pi$
$449$	4.35578	0.205562	0.102781	+	0.994704i	$0.467226\pi$
$450$	−6.86130	−0.323445
$451$	−8.64023	−0.406852
$452$	0.239782	0.0112784
$453$	−1.92496	−0.0904424
$454$	−6.56176	−0.307959
$455$	1.88992	0.0886010
$456$	0.870828	0.0407802
$457$	2.28846	0.107049	0.0535247	−	0.998567i	$-0.482954\pi$
$457$	2.28846	0.107049	0.0535247	+	0.998567i	$0.482954\pi$
$458$	−1.90169	−0.0888602
$459$	1.00000	0.0466760
$460$	−0.0624937	−0.00291378
$461$	0.106706	0.00496980	0.00248490	−	0.999997i	$-0.499209\pi$
$461$	0.106706	0.00496980	0.00248490	+	0.999997i	$0.499209\pi$
$462$	−3.43172	−0.159658
$463$	12.4912	0.580517	0.290258	−	0.956948i	$-0.406259\pi$
$463$	12.4912	0.580517	0.290258	+	0.956948i	$0.406259\pi$
$464$	−20.1696	−0.936348
$465$	−0.587769	−0.0272571
$466$	−11.0598	−0.512334
$467$	24.1747	1.11867	0.559335	−	0.828942i	$-0.311056\pi$
$467$	24.1747	1.11867	0.559335	+	0.828942i	$0.311056\pi$
$468$	0.486919	0.0225078
$469$	18.2654	0.843420
$470$	−1.21983	−0.0562668
$471$	11.3114	0.521201
$472$	−27.7595	−1.27773
$473$	1.27982	0.0588463
$474$	−1.38616	−0.0636683
$475$	−1.49606	−0.0686440
$476$	−0.107028	−0.00490563
$477$	3.80473	0.174207
$478$	25.2853	1.15652
$479$	34.4118	1.57232	0.786158	−	0.618025i	$-0.212067\pi$
$479$	34.4118	1.57232	0.786158	+	0.618025i	$0.212067\pi$
$480$	−0.0994494	−0.00453922
$481$	−59.8870	−2.73061
$482$	22.0840	1.00590
$483$	4.83936	0.220199
$484$	0.604750	0.0274886
$485$	−0.476013	−0.0216147
$486$	−1.38616	−0.0628773
$487$	0.396378	0.0179616	0.00898080	−	0.999960i	$-0.497141\pi$
$487$	0.396378	0.0179616	0.00898080	+	0.999960i	$0.497141\pi$
$488$	−39.3808	−1.78268
$489$	−0.0522065	−0.00236086
$490$	−1.59651	−0.0721228
$491$	20.7877	0.938135	0.469068	−	0.883162i	$-0.344590\pi$
$491$	20.7877	0.938135	0.469068	+	0.883162i	$0.344590\pi$
$492$	0.373528	0.0168399
$493$	−5.25703	−0.236765
$494$	−2.59633	−0.116814
$495$	−0.406896	−0.0182886
$496$	−10.0727	−0.452276
$497$	−9.65630	−0.433144
$498$	−8.54196	−0.382774
$499$	−1.48325	−0.0663993	−0.0331996	−	0.999449i	$-0.510570\pi$
$499$	−1.48325	−0.0663993	−0.0331996	+	0.999449i	$0.510570\pi$
$500$	0.175025	0.00782735
$501$	−8.92034	−0.398531
$502$	19.0973	0.852355
$503$	8.64959	0.385666	0.192833	−	0.981232i	$-0.438232\pi$
$503$	8.64959	0.385666	0.192833	+	0.981232i	$0.438232\pi$
$504$	3.92474	0.174822
$505$	1.20373	0.0535652
$506$	−8.95018	−0.397884
$507$	−25.4047	−1.12826
$508$	−0.561687	−0.0249208
$509$	37.3483	1.65543	0.827717	−	0.561146i	$-0.189639\pi$
$509$	37.3483	1.65543	0.827717	+	0.561146i	$0.189639\pi$
$510$	0.310335	0.0137418
$511$	14.7759	0.653647
$512$	−23.8130	−1.05239
$513$	−0.302242	−0.0133443
$514$	12.2213	0.539057
$515$	3.98862	0.175759
$516$	−0.0553284	−0.00243570
$517$	7.14392	0.314189
$518$	−18.2468	−0.801717
$519$	7.78743	0.341830
$520$	3.99749	0.175302
$521$	24.1834	1.05949	0.529746	−	0.848156i	$-0.322287\pi$
$521$	24.1834	1.05949	0.529746	+	0.848156i	$0.322287\pi$
$522$	7.28706	0.318946
$523$	41.1323	1.79859	0.899295	−	0.437343i	$-0.144080\pi$
$523$	41.1323	1.79859	0.899295	+	0.437343i	$0.144080\pi$
$524$	0.976222	0.0426464
$525$	−6.74262	−0.294272
$526$	16.2020	0.706439
$527$	−2.62536	−0.114362
$528$	−6.97303	−0.303462
$529$	−10.3786	−0.451243
$530$	1.18074	0.0512880
$531$	9.63461	0.418106
$532$	0.0323484	0.00140248
$533$	−29.4613	−1.27611
$534$	−0.170218	−0.00736604
$535$	−2.51600	−0.108776
$536$	38.6343	1.66875
$537$	12.1122	0.522680
$538$	13.9837	0.602879
$539$	9.34989	0.402728
$540$	0.0175906	0.000756981 0
$541$	13.1697	0.566211	0.283106	−	0.959089i	$-0.408635\pi$
$541$	13.1697	0.566211	0.283106	+	0.959089i	$0.408635\pi$
$542$	23.5317	1.01077
$543$	−0.496934	−0.0213255
$544$	−0.444206	−0.0190452
$545$	−1.52443	−0.0652995
$546$	−11.7014	−0.500775
$547$	30.4234	1.30081	0.650406	−	0.759587i	$-0.274599\pi$
$547$	30.4234	1.30081	0.650406	+	0.759587i	$0.274599\pi$
$548$	−0.0725261	−0.00309816
$549$	13.6681	0.583339
$550$	12.4702	0.531730
$551$	1.58890	0.0676892
$552$	10.2360	0.435674
$553$	−1.36218	−0.0579257
$554$	−17.0927	−0.726198
$555$	−2.16350	−0.0918357
$556$	−1.36440	−0.0578633
$557$	−43.8799	−1.85925	−0.929626	−	0.368505i	$-0.879870\pi$
$557$	−43.8799	−1.85925	−0.929626	+	0.368505i	$0.879870\pi$
$558$	3.63916	0.154058
$559$	4.36392	0.184574
$560$	1.17006	0.0494440
$561$	−1.81746	−0.0767334
$562$	−12.0102	−0.506619
$563$	−31.5598	−1.33009	−0.665044	−	0.746804i	$-0.731587\pi$
$563$	−31.5598	−1.33009	−0.665044	+	0.746804i	$0.731587\pi$
$564$	−0.308841	−0.0130045
$565$	−0.683237	−0.0287440
$566$	−8.63417	−0.362921
$567$	−1.36218	−0.0572061
$568$	−20.4246	−0.856998
$569$	21.5907	0.905128	0.452564	−	0.891732i	$-0.350509\pi$
$569$	21.5907	0.905128	0.452564	+	0.891732i	$0.350509\pi$
$570$	−0.0937962	−0.00392869
$571$	34.5411	1.44550	0.722750	−	0.691110i	$-0.242878\pi$
$571$	34.5411	1.44550	0.722750	+	0.691110i	$0.242878\pi$
$572$	−0.884957	−0.0370019
$573$	−11.8021	−0.493038
$574$	−8.97647	−0.374671
$575$	−17.5852	−0.733355
$576$	8.28911	0.345379
$577$	−33.1215	−1.37887	−0.689433	−	0.724349i	$-0.742140\pi$
$577$	−33.1215	−1.37887	−0.689433	+	0.724349i	$0.742140\pi$
$578$	1.38616	0.0576565
$579$	−13.7533	−0.571569
$580$	−0.0924745	−0.00383980
$581$	−8.39420	−0.348250
$582$	2.94722	0.122166
$583$	−6.91495	−0.286388
$584$	31.2534	1.29327
$585$	−1.38743	−0.0573631
$586$	41.9648	1.73355
$587$	3.12920	0.129156	0.0645779	−	0.997913i	$-0.479430\pi$
$587$	3.12920	0.129156	0.0645779	+	0.997913i	$0.479430\pi$
$588$	−0.404208	−0.0166692
$589$	0.793494	0.0326954
$590$	2.98995	0.123094
$591$	7.71956	0.317540
$592$	−37.0763	−1.52382
$593$	−23.7575	−0.975602	−0.487801	−	0.872955i	$-0.662201\pi$
$593$	−23.7575	−0.975602	−0.487801	+	0.872955i	$0.662201\pi$
$594$	2.51929	0.103368
$595$	0.304966	0.0125024
$596$	−1.64935	−0.0675599
$597$	−3.43961	−0.140774
$598$	−30.5182	−1.24798
$599$	−34.9459	−1.42785	−0.713925	−	0.700222i	$-0.753084\pi$
$599$	−34.9459	−1.42785	−0.713925	+	0.700222i	$0.753084\pi$
$600$	−14.2617	−0.582232
$601$	7.23127	0.294970	0.147485	−	0.989064i	$-0.452882\pi$
$601$	7.23127	0.294970	0.147485	+	0.989064i	$0.452882\pi$
$602$	1.32963	0.0541916
$603$	−13.4090	−0.546057
$604$	−0.151246	−0.00615413
$605$	−1.72318	−0.0700571
$606$	−7.45285	−0.302751
$607$	7.74840	0.314498	0.157249	−	0.987559i	$-0.449737\pi$
$607$	7.74840	0.314498	0.157249	+	0.987559i	$0.449737\pi$
$608$	0.134258	0.00544487
$609$	7.16101	0.290179
$610$	4.24167	0.171740
$611$	24.3592	0.985468
$612$	0.0785713	0.00317606
$613$	−17.0824	−0.689950	−0.344975	−	0.938612i	$-0.612113\pi$
$613$	−17.0824	−0.689950	−0.344975	+	0.938612i	$0.612113\pi$
$614$	−16.5409	−0.667537
$615$	−1.06433	−0.0429180
$616$	−7.13307	−0.287400
$617$	−39.9020	−1.60639	−0.803197	−	0.595713i	$-0.796870\pi$
$617$	−39.9020	−1.60639	−0.803197	+	0.595713i	$0.796870\pi$
$618$	−24.6954	−0.993395
$619$	21.7622	0.874697	0.437348	−	0.899292i	$-0.355918\pi$
$619$	21.7622	0.874697	0.437348	+	0.899292i	$0.355918\pi$
$620$	−0.0461818	−0.00185470
$621$	−3.55266	−0.142563
$622$	2.66583	0.106890
$623$	−0.167273	−0.00670166
$624$	−23.7765	−0.951823
$625$	24.2507	0.970027
$626$	33.9977	1.35882
$627$	0.549314	0.0219375
$628$	0.888750	0.0354650
$629$	−9.66362	−0.385314
$630$	−0.422731	−0.0168420
$631$	−8.43240	−0.335689	−0.167844	−	0.985814i	$-0.553681\pi$
$631$	−8.43240	−0.335689	−0.167844	+	0.985814i	$0.553681\pi$
$632$	−2.88122	−0.114609
$633$	10.8476	0.431154
$634$	15.2262	0.604710
$635$	1.60047	0.0635128
$636$	0.298942	0.0118538
$637$	31.8811	1.26317
$638$	−13.2440	−0.524334
$639$	7.08887	0.280431
$640$	2.37350	0.0938207
$641$	−14.5069	−0.572989	−0.286494	−	0.958082i	$-0.592490\pi$
$641$	−14.5069	−0.572989	−0.286494	+	0.958082i	$0.592490\pi$
$642$	15.5778	0.614805
$643$	33.1471	1.30719	0.653597	−	0.756843i	$-0.273259\pi$
$643$	33.1471	1.30719	0.653597	+	0.756843i	$0.273259\pi$
$644$	0.380235	0.0149834
$645$	0.157653	0.00620758
$646$	−0.418955	−0.0164836
$647$	−33.8276	−1.32990	−0.664949	−	0.746888i	$-0.731547\pi$
$647$	−33.8276	−1.32990	−0.664949	+	0.746888i	$0.731547\pi$
$648$	−2.88122	−0.113185
$649$	−17.5106	−0.687349
$650$	42.5206	1.66779
$651$	3.57621	0.140163
$652$	−0.00410194	−0.000160644 0
$653$	14.9942	0.586768	0.293384	−	0.955995i	$-0.405219\pi$
$653$	14.9942	0.586768	0.293384	+	0.955995i	$0.405219\pi$
$654$	9.43848	0.369074
$655$	−2.78165	−0.108688
$656$	−18.2396	−0.712137
$657$	−10.8473	−0.423192
$658$	7.42193	0.289337
$659$	4.84891	0.188887	0.0944433	−	0.995530i	$-0.469893\pi$
$659$	4.84891	0.188887	0.0944433	+	0.995530i	$0.469893\pi$
$660$	−0.0319704	−0.00124444
$661$	−14.9110	−0.579969	−0.289984	−	0.957031i	$-0.593650\pi$
$661$	−14.9110	−0.579969	−0.289984	+	0.957031i	$0.593650\pi$
$662$	35.8127	1.39190
$663$	−6.19716	−0.240678
$664$	−17.7551	−0.689031
$665$	−0.0921737	−0.00357434
$666$	13.3953	0.519057
$667$	18.6764	0.723155
$668$	−0.700882	−0.0271180
$669$	2.53298	0.0979308
$670$	−4.16127	−0.160764
$671$	−24.8412	−0.958984
$672$	0.605087	0.0233418
$673$	2.45881	0.0947800	0.0473900	−	0.998876i	$-0.484910\pi$
$673$	2.45881	0.0947800	0.0473900	+	0.998876i	$0.484910\pi$
$674$	−35.1742	−1.35486
$675$	4.94988	0.190521
$676$	−1.99608	−0.0767725
$677$	−25.4623	−0.978596	−0.489298	−	0.872117i	$-0.662747\pi$
$677$	−25.4623	−0.978596	−0.489298	+	0.872117i	$0.662747\pi$
$678$	4.23024	0.162462
$679$	2.89624	0.111148
$680$	0.645052	0.0247366
$681$	4.73378	0.181399
$682$	−6.61403	−0.253264
$683$	−1.46913	−0.0562148	−0.0281074	−	0.999605i	$-0.508948\pi$
$683$	−1.46913	−0.0562148	−0.0281074	+	0.999605i	$0.508948\pi$
$684$	−0.0237476	−0.000908011 0
$685$	0.206656	0.00789592
$686$	22.9311	0.875513
$687$	1.37192	0.0523419
$688$	2.70172	0.103002
$689$	−23.5785	−0.898269
$690$	−1.10251	−0.0419720
$691$	38.3147	1.45756	0.728779	−	0.684749i	$-0.240088\pi$
$691$	38.3147	1.45756	0.728779	+	0.684749i	$0.240088\pi$
$692$	0.611869	0.0232598
$693$	2.47571	0.0940444
$694$	−1.76932	−0.0671623
$695$	3.88772	0.147470
$696$	15.1467	0.574133
$697$	−4.75400	−0.180071
$698$	−19.5431	−0.739719
$699$	7.97874	0.301784
$700$	−0.529776	−0.0200237
$701$	−22.7062	−0.857603	−0.428801	−	0.903399i	$-0.641064\pi$
$701$	−22.7062	−0.857603	−0.428801	+	0.903399i	$0.641064\pi$
$702$	8.59023	0.324217
$703$	2.92075	0.110158
$704$	−15.0651	−0.567789
$705$	0.880012	0.0331432
$706$	19.1649	0.721281
$707$	−7.32393	−0.275445
$708$	0.757004	0.0284499
$709$	14.7843	0.555235	0.277618	−	0.960692i	$-0.410455\pi$
$709$	14.7843	0.555235	0.277618	+	0.960692i	$0.410455\pi$
$710$	2.19992	0.0825615
$711$	1.00000	0.0375029
$712$	−0.353810	−0.0132596
$713$	9.32701	0.349299
$714$	−1.88819	−0.0706638
$715$	2.52160	0.0943025
$716$	0.951672	0.0355656
$717$	−18.2413	−0.681235
$718$	39.8193	1.48604
$719$	28.1389	1.04940	0.524702	−	0.851286i	$-0.324177\pi$
$719$	28.1389	1.04940	0.524702	+	0.851286i	$0.324177\pi$
$720$	−0.858962	−0.0320116
$721$	−24.2682	−0.903796
$722$	−26.2103	−0.975448
$723$	−15.9318	−0.592511
$724$	−0.0390448	−0.00145109
$725$	−26.0216	−0.966419
$726$	10.6690	0.395964
$727$	27.5861	1.02311	0.511556	−	0.859250i	$-0.329069\pi$
$727$	27.5861	1.02311	0.511556	+	0.859250i	$0.329069\pi$
$728$	−24.3222	−0.901442
$729$	1.00000	0.0370370
$730$	−3.36628	−0.124592
$731$	0.704181	0.0260451
$732$	1.07392	0.0396931
$733$	−28.5987	−1.05632	−0.528159	−	0.849145i	$-0.677118\pi$
$733$	−28.5987	−1.05632	−0.528159	+	0.849145i	$0.677118\pi$
$734$	2.20050	0.0812220
$735$	1.15175	0.0424830
$736$	1.57811	0.0581700
$737$	24.3704	0.897694
$738$	6.58979	0.242573
$739$	−6.26136	−0.230328	−0.115164	−	0.993346i	$-0.536739\pi$
$739$	−6.26136	−0.230328	−0.115164	+	0.993346i	$0.536739\pi$
$740$	−0.169989	−0.00624893
$741$	1.87304	0.0688079
$742$	−7.18406	−0.263735
$743$	2.85189	0.104626	0.0523128	−	0.998631i	$-0.483341\pi$
$743$	2.85189	0.104626	0.0523128	+	0.998631i	$0.483341\pi$
$744$	7.56425	0.277319
$745$	4.69966	0.172182
$746$	40.5003	1.48282
$747$	6.16234	0.225468
$748$	−0.142800	−0.00522130
$749$	15.3083	0.559353
$750$	3.08779	0.112750
$751$	14.7099	0.536771	0.268386	−	0.963312i	$-0.413510\pi$
$751$	14.7099	0.536771	0.268386	+	0.963312i	$0.413510\pi$
$752$	15.0809	0.549943
$753$	−13.7772	−0.502068
$754$	−45.1591	−1.64460
$755$	0.430962	0.0156843
$756$	−0.107028	−0.00389258
$757$	26.5982	0.966728	0.483364	−	0.875419i	$-0.339415\pi$
$757$	26.5982	0.966728	0.483364	+	0.875419i	$0.339415\pi$
$758$	−30.9499	−1.12415
$759$	6.45684	0.234368
$760$	−0.194962	−0.00707202
$761$	−16.0688	−0.582494	−0.291247	−	0.956648i	$-0.594070\pi$
$761$	−16.0688	−0.582494	−0.291247	+	0.956648i	$0.594070\pi$
$762$	−9.90928	−0.358975
$763$	9.27521	0.335785
$764$	−0.927302	−0.0335486
$765$	−0.223881	−0.00809445
$766$	−47.2558	−1.70742
$767$	−59.7072	−2.15590
$768$	1.88276	0.0679383
$769$	25.7059	0.926977	0.463489	−	0.886103i	$-0.346597\pi$
$769$	25.7059	0.926977	0.463489	+	0.886103i	$0.346597\pi$
$770$	0.768298	0.0276875
$771$	−8.81666	−0.317524
$772$	−1.08062	−0.0388923
$773$	−18.3624	−0.660450	−0.330225	−	0.943902i	$-0.607125\pi$
$773$	−18.3624	−0.660450	−0.330225	+	0.943902i	$0.607125\pi$
$774$	−0.976105	−0.0350854
$775$	−12.9952	−0.466801
$776$	6.12602	0.219911
$777$	13.1636	0.472241
$778$	−47.6376	−1.70789
$779$	1.43686	0.0514809
$780$	−0.109012	−0.00390326
$781$	−12.8838	−0.461017
$782$	−4.92455	−0.176101
$783$	−5.25703	−0.187871
$784$	19.7377	0.704918
$785$	−2.53241	−0.0903856
$786$	17.2225	0.614307
$787$	16.4478	0.586302	0.293151	−	0.956066i	$-0.405296\pi$
$787$	16.4478	0.586302	0.293151	+	0.956066i	$0.405296\pi$
$788$	0.606536	0.0216069
$789$	−11.6884	−0.416118
$790$	0.310335	0.0110412
$791$	4.15707	0.147808
$792$	5.23652	0.186072
$793$	−84.7031	−3.00790
$794$	−1.10252	−0.0391270
$795$	−0.851808	−0.0302105
$796$	−0.270255	−0.00957893
$797$	5.95430	0.210912	0.105456	−	0.994424i	$-0.466370\pi$
$797$	5.95430	0.210912	0.105456	+	0.994424i	$0.466370\pi$
$798$	0.570691	0.0202023
$799$	3.93071	0.139058
$800$	−2.19876	−0.0777380
$801$	0.122798	0.00433887
$802$	−40.3490	−1.42477
$803$	19.7145	0.695709
$804$	−1.05356	−0.0371563
$805$	−1.08344	−0.0381863
$806$	−22.5524	−0.794375
$807$	−10.0881	−0.355118
$808$	−15.4913	−0.544981
$809$	−4.03485	−0.141858	−0.0709288	−	0.997481i	$-0.522596\pi$
$809$	−4.03485	−0.141858	−0.0709288	+	0.997481i	$0.522596\pi$
$810$	0.310335	0.0109040
$811$	20.9607	0.736029	0.368014	−	0.929820i	$-0.380038\pi$
$811$	20.9607	0.736029	0.368014	+	0.929820i	$0.380038\pi$
$812$	0.562650	0.0197451
$813$	−16.9762	−0.595381
$814$	−24.3454	−0.853307
$815$	0.0116881	0.000409415 0
$816$	−3.83668	−0.134311
$817$	−0.212833	−0.00744609
$818$	−30.6894	−1.07303
$819$	8.44163	0.294975
$820$	−0.0836260	−0.00292035
$821$	24.5243	0.855905	0.427953	−	0.903801i	$-0.359235\pi$
$821$	24.5243	0.855905	0.427953	+	0.903801i	$0.359235\pi$
$822$	−1.27951	−0.0446279
$823$	−38.5000	−1.34203	−0.671013	−	0.741446i	$-0.734140\pi$
$823$	−38.5000	−1.34203	−0.671013	+	0.741446i	$0.734140\pi$
$824$	−51.3312	−1.78821
$825$	−8.99622	−0.313208
$826$	−18.1920	−0.632980
$827$	−10.9211	−0.379762	−0.189881	−	0.981807i	$-0.560810\pi$
$827$	−10.9211	−0.379762	−0.189881	+	0.981807i	$0.560810\pi$
$828$	−0.279137	−0.00970069
$829$	−6.90274	−0.239742	−0.119871	−	0.992789i	$-0.538248\pi$
$829$	−6.90274	−0.239742	−0.119871	+	0.992789i	$0.538248\pi$
$830$	1.91239	0.0663799
$831$	12.3310	0.427757
$832$	−51.3689	−1.78090
$833$	5.14447	0.178245
$834$	−24.0707	−0.833501
$835$	1.99710	0.0691124
$836$	0.0431603	0.00149273
$837$	−2.62536	−0.0907457
$838$	−52.3050	−1.80684
$839$	−52.0644	−1.79746	−0.898732	−	0.438498i	$-0.855511\pi$
$839$	−52.0644	−1.79746	−0.898732	+	0.438498i	$0.855511\pi$
$840$	−0.878677	−0.0303172
$841$	−1.36366	−0.0470227
$842$	−14.2865	−0.492346
$843$	8.66438	0.298417
$844$	0.852311	0.0293378
$845$	5.68765	0.195661
$846$	−5.44857	−0.187326
$847$	10.4845	0.360250
$848$	−14.5975	−0.501282
$849$	6.22886	0.213774
$850$	6.86130	0.235341
$851$	34.3316	1.17687
$852$	0.556981	0.0190819
$853$	45.9189	1.57223	0.786117	−	0.618077i	$-0.212088\pi$
$853$	45.9189	1.57223	0.786117	+	0.618077i	$0.212088\pi$
$854$	−25.8079	−0.883129
$855$	0.0676664	0.00231414
$856$	32.3795	1.10671
$857$	−29.6138	−1.01159	−0.505795	−	0.862654i	$-0.668801\pi$
$857$	−29.6138	−1.01159	−0.505795	+	0.862654i	$0.668801\pi$
$858$	−15.6124	−0.532999
$859$	−6.42056	−0.219067	−0.109533	−	0.993983i	$-0.534936\pi$
$859$	−6.42056	−0.219067	−0.109533	+	0.993983i	$0.534936\pi$
$860$	0.0123870	0.000422393 0
$861$	6.47580	0.220695
$862$	−28.9037	−0.984464
$863$	0.886625	0.0301811	0.0150905	−	0.999886i	$-0.495196\pi$
$863$	0.886625	0.0301811	0.0150905	+	0.999886i	$0.495196\pi$
$864$	−0.444206	−0.0151122
$865$	−1.74346	−0.0592795
$866$	26.4373	0.898375
$867$	−1.00000	−0.0339618
$868$	0.280987	0.00953733
$869$	−1.81746	−0.0616532
$870$	−1.63144	−0.0553109
$871$	83.0976	2.81566
$872$	19.6186	0.664368
$873$	−2.12619	−0.0719605
$874$	1.48841	0.0503461
$875$	3.03438	0.102581
$876$	−0.852283	−0.0287960
$877$	33.4860	1.13074	0.565371	−	0.824837i	$-0.308733\pi$
$877$	33.4860	1.13074	0.565371	+	0.824837i	$0.308733\pi$
$878$	−17.8436	−0.602193
$879$	−30.2742	−1.02112
$880$	1.56113	0.0526258
$881$	−21.3029	−0.717713	−0.358856	−	0.933393i	$-0.616833\pi$
$881$	−21.3029	−0.717713	−0.358856	+	0.933393i	$0.616833\pi$
$882$	−7.13104	−0.240115
$883$	7.59181	0.255485	0.127742	−	0.991807i	$-0.459227\pi$
$883$	7.59181	0.255485	0.127742	+	0.991807i	$0.459227\pi$
$884$	−0.486919	−0.0163768
$885$	−2.15701	−0.0725071
$886$	22.8858	0.768863
$887$	−3.49706	−0.117420	−0.0587099	−	0.998275i	$-0.518699\pi$
$887$	−3.49706	−0.117420	−0.0587099	+	0.998275i	$0.518699\pi$
$888$	27.8431	0.934352
$889$	−9.73787	−0.326598
$890$	0.0381086	0.00127740
$891$	−1.81746	−0.0608873
$892$	0.199020	0.00666368
$893$	−1.18803	−0.0397558
$894$	−29.0978	−0.973177
$895$	−2.71170	−0.0906421
$896$	−14.4412	−0.482448
$897$	22.0164	0.735106
$898$	6.03780	0.201484
$899$	13.8016	0.460309
$900$	0.388918	0.0129639
$901$	−3.80473	−0.126754
$902$	−11.9767	−0.398781
$903$	−0.959220	−0.0319208
$904$	8.79286	0.292446
$905$	0.111254	0.00369822
$906$	−2.66829	−0.0886480
$907$	56.7009	1.88272	0.941361	−	0.337400i	$-0.109548\pi$
$907$	56.7009	1.88272	0.941361	+	0.337400i	$0.109548\pi$
$908$	0.371940	0.0123432
$909$	5.37663	0.178332
$910$	2.61973	0.0868432
$911$	19.2580	0.638045	0.319022	−	0.947747i	$-0.396646\pi$
$911$	19.2580	0.638045	0.319022	+	0.947747i	$0.396646\pi$
$912$	1.15961	0.0383985
$913$	−11.1998	−0.370660
$914$	3.17216	0.104926
$915$	−3.06003	−0.101161
$916$	0.107793	0.00356159
$917$	16.9246	0.558900
$918$	1.38616	0.0457500
$919$	22.8109	0.752461	0.376231	−	0.926526i	$-0.377220\pi$
$919$	22.8109	0.752461	0.376231	+	0.926526i	$0.377220\pi$
$920$	−2.29165	−0.0755536
$921$	11.9329	0.393204
$922$	0.147911	0.00487120
$923$	−43.9308	−1.44600
$924$	0.194520	0.00639923
$925$	−47.8337	−1.57276
$926$	17.3148	0.568999
$927$	17.8158	0.585146
$928$	2.33520	0.0766567
$929$	50.3301	1.65128	0.825638	−	0.564200i	$-0.190815\pi$
$929$	50.3301	1.65128	0.825638	+	0.564200i	$0.190815\pi$
$930$	−0.814739	−0.0267164
$931$	−1.55488	−0.0509590
$932$	0.626900	0.0205348
$933$	−1.92318	−0.0629622
$934$	33.5099	1.09648
$935$	0.406896	0.0133069
$936$	17.8554	0.583622
$937$	−22.3262	−0.729367	−0.364683	−	0.931132i	$-0.618823\pi$
$937$	−22.3262	−0.729367	−0.364683	+	0.931132i	$0.618823\pi$
$938$	25.3188	0.826687
$939$	−24.5266	−0.800395
$940$	0.0691437	0.00225522
$941$	−20.1620	−0.657262	−0.328631	−	0.944458i	$-0.606587\pi$
$941$	−20.1620	−0.657262	−0.328631	+	0.944458i	$0.606587\pi$
$942$	15.6793	0.510861
$943$	16.8894	0.549994
$944$	−36.9650	−1.20311
$945$	0.304966	0.00992056
$946$	1.77403	0.0576788
$947$	3.85129	0.125150	0.0625750	−	0.998040i	$-0.480069\pi$
$947$	3.85129	0.125150	0.0625750	+	0.998040i	$0.480069\pi$
$948$	0.0785713	0.00255188
$949$	67.2221	2.18212
$950$	−2.07378	−0.0672822
$951$	−10.9845	−0.356196
$952$	−3.92474	−0.127202
$953$	38.1214	1.23487	0.617437	−	0.786620i	$-0.288171\pi$
$953$	38.1214	1.23487	0.617437	+	0.786620i	$0.288171\pi$
$954$	5.27395	0.170750
$955$	2.64226	0.0855015
$956$	−1.43325	−0.0463545
$957$	9.55446	0.308852
$958$	47.7002	1.54112
$959$	−1.25737	−0.0406027
$960$	−1.85578	−0.0598949
$961$	−24.1075	−0.777661
$962$	−83.0127	−2.67644
$963$	−11.2381	−0.362143
$964$	−1.25178	−0.0403172
$965$	3.07912	0.0991202
$966$	6.70811	0.215830
$967$	26.8361	0.862990	0.431495	−	0.902115i	$-0.357986\pi$
$967$	26.8361	0.862990	0.431495	+	0.902115i	$0.357986\pi$
$968$	22.1763	0.712773
$969$	0.302242	0.00970942
$970$	−0.659829	−0.0211858
$971$	36.6217	1.17525	0.587623	−	0.809135i	$-0.300064\pi$
$971$	36.6217	1.17525	0.587623	+	0.809135i	$0.300064\pi$
$972$	0.0785713	0.00252018
$973$	−23.6544	−0.758324
$974$	0.549442	0.0176053
$975$	−30.6752	−0.982391
$976$	−52.4400	−1.67857
$977$	−31.8230	−1.01811	−0.509054	−	0.860735i	$-0.670005\pi$
$977$	−31.8230	−1.01811	−0.509054	+	0.860735i	$0.670005\pi$
$978$	−0.0723664	−0.00231402
$979$	−0.223182	−0.00713291
$980$	0.0904946	0.00289074
$981$	−6.80910	−0.217398
$982$	28.8150	0.919523
$983$	−10.3811	−0.331104	−0.165552	−	0.986201i	$-0.552941\pi$
$983$	−10.3811	−0.331104	−0.165552	+	0.986201i	$0.552941\pi$
$984$	13.6973	0.436655
$985$	−1.72827	−0.0550671
$986$	−7.28706	−0.232067
$987$	−5.35433	−0.170430
$988$	0.147167	0.00468202
$989$	−2.50172	−0.0795500
$990$	−0.564022	−0.0179258
$991$	−22.8275	−0.725140	−0.362570	−	0.931957i	$-0.618101\pi$
$991$	−22.8275	−0.725140	−0.362570	+	0.931957i	$0.618101\pi$
$992$	1.16620	0.0370269
$993$	−25.8360	−0.819879
$994$	−13.3851	−0.424551
$995$	0.770065	0.0244127
$996$	0.484183	0.0153419
$997$	−45.6747	−1.44653	−0.723266	−	0.690569i	$-0.757360\pi$
$997$	−45.6747	−1.44653	−0.723266	+	0.690569i	$0.757360\pi$
$998$	−2.05601	−0.0650819
$999$	−9.66362	−0.305743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.24	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.24	✓	32	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+1.38616 q^{2} -1.00000 q^{3} -0.0785713 q^{4} +0.223881 q^{5} -1.38616 q^{6} -1.36218 q^{7} -2.88122 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.38616 q^{2} -1.00000 q^{3} -0.0785713 q^{4} +0.223881 q^{5} -1.38616 q^{6} -1.36218 q^{7} -2.88122 q^{8} +1.00000 q^{9} +0.310335 q^{10} -1.81746 q^{11} +0.0785713 q^{12} -6.19716 q^{13} -1.88819 q^{14} -0.223881 q^{15} -3.83668 q^{16} -1.00000 q^{17} +1.38616 q^{18} +0.302242 q^{19} -0.0175906 q^{20} +1.36218 q^{21} -2.51929 q^{22} +3.55266 q^{23} +2.88122 q^{24} -4.94988 q^{25} -8.59023 q^{26} -1.00000 q^{27} +0.107028 q^{28} +5.25703 q^{29} -0.310335 q^{30} +2.62536 q^{31} +0.444206 q^{32} +1.81746 q^{33} -1.38616 q^{34} -0.304966 q^{35} -0.0785713 q^{36} +9.66362 q^{37} +0.418955 q^{38} +6.19716 q^{39} -0.645052 q^{40} +4.75400 q^{41} +1.88819 q^{42} -0.704181 q^{43} +0.142800 q^{44} +0.223881 q^{45} +4.92455 q^{46} -3.93071 q^{47} +3.83668 q^{48} -5.14447 q^{49} -6.86130 q^{50} +1.00000 q^{51} +0.486919 q^{52} +3.80473 q^{53} -1.38616 q^{54} -0.406896 q^{55} +3.92474 q^{56} -0.302242 q^{57} +7.28706 q^{58} +9.63461 q^{59} +0.0175906 q^{60} +13.6681 q^{61} +3.63916 q^{62} -1.36218 q^{63} +8.28911 q^{64} -1.38743 q^{65} +2.51929 q^{66} -13.4090 q^{67} +0.0785713 q^{68} -3.55266 q^{69} -0.422731 q^{70} +7.08887 q^{71} -2.88122 q^{72} -10.8473 q^{73} +13.3953 q^{74} +4.94988 q^{75} -0.0237476 q^{76} +2.47571 q^{77} +8.59023 q^{78} +1.00000 q^{79} -0.858962 q^{80} +1.00000 q^{81} +6.58979 q^{82} +6.16234 q^{83} -0.107028 q^{84} -0.223881 q^{85} -0.976105 q^{86} -5.25703 q^{87} +5.23652 q^{88} +0.122798 q^{89} +0.310335 q^{90} +8.44163 q^{91} -0.279137 q^{92} -2.62536 q^{93} -5.44857 q^{94} +0.0676664 q^{95} -0.444206 q^{96} -2.12619 q^{97} -7.13104 q^{98} -1.81746 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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