LMFDB - Embedded newform 8029.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$1$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29935 q^{2} +0.411617 q^{3} -0.311677 q^{4} -1.65503 q^{5} -0.534837 q^{6} +1.00000 q^{7} +3.00369 q^{8} -2.83057 q^{9} +O(q^{10})$	\(q-1.29935 q^{2} +0.411617 q^{3} -0.311677 q^{4} -1.65503 q^{5} -0.534837 q^{6} +1.00000 q^{7} +3.00369 q^{8} -2.83057 q^{9} +2.15047 q^{10} +5.55363 q^{11} -0.128292 q^{12} +0.124639 q^{13} -1.29935 q^{14} -0.681238 q^{15} -3.27950 q^{16} +4.96963 q^{17} +3.67792 q^{18} +4.40919 q^{19} +0.515834 q^{20} +0.411617 q^{21} -7.21614 q^{22} -4.17375 q^{23} +1.23637 q^{24} -2.26089 q^{25} -0.161951 q^{26} -2.39996 q^{27} -0.311677 q^{28} -8.73214 q^{29} +0.885169 q^{30} +1.00000 q^{31} -1.74614 q^{32} +2.28597 q^{33} -6.45732 q^{34} -1.65503 q^{35} +0.882224 q^{36} -1.00000 q^{37} -5.72910 q^{38} +0.0513037 q^{39} -4.97118 q^{40} +1.10194 q^{41} -0.534837 q^{42} -8.94632 q^{43} -1.73094 q^{44} +4.68467 q^{45} +5.42318 q^{46} +5.52054 q^{47} -1.34990 q^{48} +1.00000 q^{49} +2.93770 q^{50} +2.04559 q^{51} -0.0388472 q^{52} +9.17419 q^{53} +3.11841 q^{54} -9.19141 q^{55} +3.00369 q^{56} +1.81490 q^{57} +11.3462 q^{58} -5.71332 q^{59} +0.212326 q^{60} -1.82450 q^{61} -1.29935 q^{62} -2.83057 q^{63} +8.82786 q^{64} -0.206281 q^{65} -2.97029 q^{66} -15.9453 q^{67} -1.54892 q^{68} -1.71799 q^{69} +2.15047 q^{70} -13.4829 q^{71} -8.50215 q^{72} -8.51241 q^{73} +1.29935 q^{74} -0.930621 q^{75} -1.37424 q^{76} +5.55363 q^{77} -0.0666617 q^{78} +5.18640 q^{79} +5.42766 q^{80} +7.50385 q^{81} -1.43181 q^{82} +15.7479 q^{83} -0.128292 q^{84} -8.22487 q^{85} +11.6244 q^{86} -3.59430 q^{87} +16.6814 q^{88} -16.9916 q^{89} -6.08705 q^{90} +0.124639 q^{91} +1.30086 q^{92} +0.411617 q^{93} -7.17314 q^{94} -7.29732 q^{95} -0.718741 q^{96} -7.56618 q^{97} -1.29935 q^{98} -15.7200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) $ 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * 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 $

$2$	−1.29935	−0.918783	−0.459391	−	0.888234i	$-0.651932\pi$
$2$	−1.29935	−0.918783	−0.459391	+	0.888234i	$0.651932\pi$
$3$	0.411617	0.237647	0.118824	−	0.992915i	$-0.462088\pi$
$3$	0.411617	0.237647	0.118824	+	0.992915i	$0.462088\pi$
$4$	−0.311677	−0.155839
$5$	−1.65503	−0.740150	−0.370075	−	0.929002i	$-0.620668\pi$
$5$	−1.65503	−0.740150	−0.370075	+	0.929002i	$0.620668\pi$
$6$	−0.534837	−0.218346
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.00369	1.06196
$9$	−2.83057	−0.943524
$10$	2.15047	0.680037
$11$	5.55363	1.67448	0.837242	−	0.546833i	$-0.184167\pi$
$11$	5.55363	1.67448	0.837242	+	0.546833i	$0.184167\pi$
$12$	−0.128292	−0.0370346
$13$	0.124639	0.0345687	0.0172844	−	0.999851i	$-0.494498\pi$
$13$	0.124639	0.0345687	0.0172844	+	0.999851i	$0.494498\pi$
$14$	−1.29935	−0.347267
$15$	−0.681238	−0.175895
$16$	−3.27950	−0.819876
$17$	4.96963	1.20531	0.602657	−	0.798001i	$-0.294109\pi$
$17$	4.96963	1.20531	0.602657	+	0.798001i	$0.294109\pi$
$18$	3.67792	0.866893
$19$	4.40919	1.01154	0.505768	−	0.862669i	$-0.331209\pi$
$19$	4.40919	1.01154	0.505768	+	0.862669i	$0.331209\pi$
$20$	0.515834	0.115344
$21$	0.411617	0.0898223
$22$	−7.21614	−1.53849
$23$	−4.17375	−0.870287	−0.435143	−	0.900361i	$-0.643302\pi$
$23$	−4.17375	−0.870287	−0.435143	+	0.900361i	$0.643302\pi$
$24$	1.23637	0.252373
$25$	−2.26089	−0.452178
$26$	−0.161951	−0.0317612
$27$	−2.39996	−0.461873
$28$	−0.311677	−0.0589014
$29$	−8.73214	−1.62152	−0.810759	−	0.585380i	$-0.800945\pi$
$29$	−8.73214	−1.62152	−0.810759	+	0.585380i	$0.800945\pi$
$30$	0.885169	0.161609
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.74614	−0.308677
$33$	2.28597	0.397937
$34$	−6.45732	−1.10742
$35$	−1.65503	−0.279750
$36$	0.882224	0.147037
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−5.72910	−0.929382
$39$	0.0513037	0.00821517
$40$	−4.97118	−0.786013
$41$	1.10194	0.172094	0.0860468	−	0.996291i	$-0.472577\pi$
$41$	1.10194	0.172094	0.0860468	+	0.996291i	$0.472577\pi$
$42$	−0.534837	−0.0825272
$43$	−8.94632	−1.36430	−0.682150	−	0.731212i	$-0.738955\pi$
$43$	−8.94632	−1.36430	−0.682150	+	0.731212i	$0.738955\pi$
$44$	−1.73094	−0.260949
$45$	4.68467	0.698349
$46$	5.42318	0.799604
$47$	5.52054	0.805253	0.402627	−	0.915364i	$-0.368097\pi$
$47$	5.52054	0.805253	0.402627	+	0.915364i	$0.368097\pi$
$48$	−1.34990	−0.194841
$49$	1.00000	0.142857
$50$	2.93770	0.415453
$51$	2.04559	0.286440
$52$	−0.0388472	−0.00538714
$53$	9.17419	1.26017	0.630086	−	0.776526i	$-0.283020\pi$
$53$	9.17419	1.26017	0.630086	+	0.776526i	$0.283020\pi$
$54$	3.11841	0.424361
$55$	−9.19141	−1.23937
$56$	3.00369	0.401385
$57$	1.81490	0.240389
$58$	11.3462	1.48982
$59$	−5.71332	−0.743811	−0.371905	−	0.928271i	$-0.621295\pi$
$59$	−5.71332	−0.743811	−0.371905	+	0.928271i	$0.621295\pi$
$60$	0.212326	0.0274112
$61$	−1.82450	−0.233604	−0.116802	−	0.993155i	$-0.537264\pi$
$61$	−1.82450	−0.233604	−0.116802	+	0.993155i	$0.537264\pi$
$62$	−1.29935	−0.165018
$63$	−2.83057	−0.356618
$64$	8.82786	1.10348
$65$	−0.206281	−0.0255861
$66$	−2.97029	−0.365617
$67$	−15.9453	−1.94803	−0.974014	−	0.226488i	$-0.927276\pi$
$67$	−15.9453	−1.94803	−0.974014	+	0.226488i	$0.927276\pi$
$68$	−1.54892	−0.187834
$69$	−1.71799	−0.206821
$70$	2.15047	0.257030
$71$	−13.4829	−1.60012	−0.800061	−	0.599919i	$-0.795199\pi$
$71$	−13.4829	−1.60012	−0.800061	+	0.599919i	$0.795199\pi$
$72$	−8.50215	−1.00199
$73$	−8.51241	−0.996302	−0.498151	−	0.867090i	$-0.665987\pi$
$73$	−8.51241	−0.996302	−0.498151	+	0.867090i	$0.665987\pi$
$74$	1.29935	0.151047
$75$	−0.930621	−0.107459
$76$	−1.37424	−0.157636
$77$	5.55363	0.632895
$78$	−0.0666617	−0.00754796
$79$	5.18640	0.583515	0.291758	−	0.956492i	$-0.405760\pi$
$79$	5.18640	0.583515	0.291758	+	0.956492i	$0.405760\pi$
$80$	5.42766	0.606831
$81$	7.50385	0.833761
$82$	−1.43181	−0.158117
$83$	15.7479	1.72855	0.864276	−	0.503018i	$-0.167777\pi$
$83$	15.7479	1.72855	0.864276	+	0.503018i	$0.167777\pi$
$84$	−0.128292	−0.0139978
$85$	−8.22487	−0.892113
$86$	11.6244	1.25350
$87$	−3.59430	−0.385350
$88$	16.6814	1.77824
$89$	−16.9916	−1.80110	−0.900552	−	0.434748i	$-0.856837\pi$
$89$	−16.9916	−1.80110	−0.900552	+	0.434748i	$0.856837\pi$
$90$	−6.08705	−0.641631
$91$	0.124639	0.0130658
$92$	1.30086	0.135624
$93$	0.411617	0.0426827
$94$	−7.17314	−0.739853
$95$	−7.29732	−0.748689
$96$	−0.718741	−0.0733562
$97$	−7.56618	−0.768230	−0.384115	−	0.923285i	$-0.625493\pi$
$97$	−7.56618	−0.768230	−0.384115	+	0.923285i	$0.625493\pi$
$98$	−1.29935	−0.131255
$99$	−15.7200	−1.57991
$100$	0.704667	0.0704667
$101$	10.4528	1.04010	0.520048	−	0.854137i	$-0.325914\pi$
$101$	10.4528	1.04010	0.520048	+	0.854137i	$0.325914\pi$
$102$	−2.65794	−0.263176
$103$	20.0229	1.97292	0.986460	−	0.164003i	$-0.0524406\pi$
$103$	20.0229	1.97292	0.986460	+	0.164003i	$0.0524406\pi$
$104$	0.374378	0.0367108
$105$	−0.681238	−0.0664820
$106$	−11.9205	−1.15782
$107$	2.81907	0.272530	0.136265	−	0.990672i	$-0.456490\pi$
$107$	2.81907	0.272530	0.136265	+	0.990672i	$0.456490\pi$
$108$	0.748014	0.0719777
$109$	−6.29627	−0.603073	−0.301536	−	0.953455i	$-0.597499\pi$
$109$	−6.29627	−0.603073	−0.301536	+	0.953455i	$0.597499\pi$
$110$	11.9429	1.13871
$111$	−0.411617	−0.0390690
$112$	−3.27950	−0.309884
$113$	1.19283	0.112212	0.0561058	−	0.998425i	$-0.482132\pi$
$113$	1.19283	0.112212	0.0561058	+	0.998425i	$0.482132\pi$
$114$	−2.35820	−0.220865
$115$	6.90766	0.644143
$116$	2.72161	0.252695
$117$	−0.352801	−0.0326164
$118$	7.42363	0.683400
$119$	4.96963	0.455566
$120$	−2.04623	−0.186794
$121$	19.8428	1.80389
$122$	2.37068	0.214631
$123$	0.453577	0.0408976
$124$	−0.311677	−0.0279894
$125$	12.0170	1.07483
$126$	3.67792	0.327655
$127$	−16.2261	−1.43983	−0.719916	−	0.694061i	$-0.755820\pi$
$127$	−16.2261	−1.43983	−0.719916	+	0.694061i	$0.755820\pi$
$128$	−7.97824	−0.705184
$129$	−3.68246	−0.324222
$130$	0.268033	0.0235080
$131$	11.3530	0.991912	0.495956	−	0.868348i	$-0.334818\pi$
$131$	11.3530	0.991912	0.495956	+	0.868348i	$0.334818\pi$
$132$	−0.712485	−0.0620139
$133$	4.40919	0.382325
$134$	20.7186	1.78981
$135$	3.97200	0.341856
$136$	14.9272	1.28000
$137$	−3.34912	−0.286135	−0.143067	−	0.989713i	$-0.545697\pi$
$137$	−3.34912	−0.286135	−0.143067	+	0.989713i	$0.545697\pi$
$138$	2.23228	0.190024
$139$	13.1651	1.11665	0.558325	−	0.829622i	$-0.311444\pi$
$139$	13.1651	1.11665	0.558325	+	0.829622i	$0.311444\pi$
$140$	0.515834	0.0435959
$141$	2.27235	0.191366
$142$	17.5190	1.47016
$143$	0.692201	0.0578848
$144$	9.28287	0.773572
$145$	14.4519	1.20017
$146$	11.0606	0.915385
$147$	0.411617	0.0339496
$148$	0.311677	0.0256197
$149$	12.3024	1.00785	0.503925	−	0.863747i	$-0.331889\pi$
$149$	12.3024	1.00785	0.503925	+	0.863747i	$0.331889\pi$
$150$	1.20921	0.0987314
$151$	6.58464	0.535850	0.267925	−	0.963440i	$-0.413662\pi$
$151$	6.58464	0.535850	0.267925	+	0.963440i	$0.413662\pi$
$152$	13.2438	1.07422
$153$	−14.0669	−1.13724
$154$	−7.21614	−0.581493
$155$	−1.65503	−0.132935
$156$	−0.0159902	−0.00128024
$157$	−2.62497	−0.209496	−0.104748	−	0.994499i	$-0.533404\pi$
$157$	−2.62497	−0.209496	−0.104748	+	0.994499i	$0.533404\pi$
$158$	−6.73897	−0.536124
$159$	3.77626	0.299477
$160$	2.88991	0.228467
$161$	−4.17375	−0.328937
$162$	−9.75016	−0.766045
$163$	−1.12905	−0.0884341	−0.0442171	−	0.999022i	$-0.514079\pi$
$163$	−1.12905	−0.0884341	−0.0442171	+	0.999022i	$0.514079\pi$
$164$	−0.343449	−0.0268188
$165$	−3.78334	−0.294533
$166$	−20.4621	−1.58816
$167$	2.25865	0.174779	0.0873897	−	0.996174i	$-0.472147\pi$
$167$	2.25865	0.174779	0.0873897	+	0.996174i	$0.472147\pi$
$168$	1.23637	0.0953881
$169$	−12.9845	−0.998805
$170$	10.6870	0.819658
$171$	−12.4805	−0.954409
$172$	2.78836	0.212611
$173$	−14.7289	−1.11982	−0.559908	−	0.828555i	$-0.689164\pi$
$173$	−14.7289	−1.11982	−0.559908	+	0.828555i	$0.689164\pi$
$174$	4.67027	0.354053
$175$	−2.26089	−0.170907
$176$	−18.2132	−1.37287
$177$	−2.35170	−0.176765
$178$	22.0781	1.65482
$179$	−12.4853	−0.933194	−0.466597	−	0.884470i	$-0.654520\pi$
$179$	−12.4853	−0.933194	−0.466597	+	0.884470i	$0.654520\pi$
$180$	−1.46010	−0.108830
$181$	−11.1200	−0.826543	−0.413272	−	0.910608i	$-0.635614\pi$
$181$	−11.1200	−0.826543	−0.413272	+	0.910608i	$0.635614\pi$
$182$	−0.161951	−0.0120046
$183$	−0.750998	−0.0555153
$184$	−12.5366	−0.924213
$185$	1.65503	0.121680
$186$	−0.534837	−0.0392162
$187$	27.5995	2.01828
$188$	−1.72063	−0.125490
$189$	−2.39996	−0.174572
$190$	9.48180	0.687882
$191$	−19.5685	−1.41593	−0.707965	−	0.706248i	$-0.750387\pi$
$191$	−19.5685	−1.41593	−0.707965	+	0.706248i	$0.750387\pi$
$192$	3.63370	0.262240
$193$	24.1515	1.73846	0.869230	−	0.494408i	$-0.164615\pi$
$193$	24.1515	1.73846	0.869230	+	0.494408i	$0.164615\pi$
$194$	9.83116	0.705836
$195$	−0.0849090	−0.00608046
$196$	−0.311677	−0.0222627
$197$	−21.8118	−1.55402	−0.777012	−	0.629486i	$-0.783265\pi$
$197$	−21.8118	−1.55402	−0.777012	+	0.629486i	$0.783265\pi$
$198$	20.4258	1.45160
$199$	3.43796	0.243710	0.121855	−	0.992548i	$-0.461116\pi$
$199$	3.43796	0.243710	0.121855	+	0.992548i	$0.461116\pi$
$200$	−6.79101	−0.480197
$201$	−6.56336	−0.462944
$202$	−13.5819	−0.955622
$203$	−8.73214	−0.612876
$204$	−0.637563	−0.0446383
$205$	−1.82373	−0.127375
$206$	−26.0169	−1.81268
$207$	11.8141	0.821136
$208$	−0.408755	−0.0283421
$209$	24.4870	1.69380
$210$	0.885169	0.0610825
$211$	−9.40807	−0.647678	−0.323839	−	0.946112i	$-0.604974\pi$
$211$	−9.40807	−0.647678	−0.323839	+	0.946112i	$0.604974\pi$
$212$	−2.85938	−0.196383
$213$	−5.54978	−0.380265
$214$	−3.66298	−0.250396
$215$	14.8064	1.00979
$216$	−7.20875	−0.490493
$217$	1.00000	0.0678844
$218$	8.18108	0.554093
$219$	−3.50385	−0.236769
$220$	2.86475	0.193141
$221$	0.619412	0.0416662
$222$	0.534837	0.0358959
$223$	10.4877	0.702307	0.351153	−	0.936318i	$-0.385790\pi$
$223$	10.4877	0.702307	0.351153	+	0.936318i	$0.385790\pi$
$224$	−1.74614	−0.116669
$225$	6.39961	0.426640
$226$	−1.54990	−0.103098
$227$	−18.6790	−1.23977	−0.619886	−	0.784692i	$-0.712821\pi$
$227$	−18.6790	−1.23977	−0.619886	+	0.784692i	$0.712821\pi$
$228$	−0.565662	−0.0374619
$229$	24.1632	1.59675	0.798375	−	0.602160i	$-0.205693\pi$
$229$	24.1632	1.59675	0.798375	+	0.602160i	$0.205693\pi$
$230$	−8.97550	−0.591827
$231$	2.28597	0.150406
$232$	−26.2286	−1.72199
$233$	−2.80549	−0.183794	−0.0918969	−	0.995769i	$-0.529293\pi$
$233$	−2.80549	−0.183794	−0.0918969	+	0.995769i	$0.529293\pi$
$234$	0.458413	0.0299674
$235$	−9.13664	−0.596008
$236$	1.78071	0.115914
$237$	2.13481	0.138671
$238$	−6.45732	−0.418566
$239$	15.3720	0.994329	0.497165	−	0.867656i	$-0.334374\pi$
$239$	15.3720	0.994329	0.497165	+	0.867656i	$0.334374\pi$
$240$	2.23412	0.144212
$241$	16.3063	1.05038	0.525192	−	0.850984i	$-0.323994\pi$
$241$	16.3063	1.05038	0.525192	+	0.850984i	$0.323994\pi$
$242$	−25.7829	−1.65739
$243$	10.2886	0.660014
$244$	0.568656	0.0364045
$245$	−1.65503	−0.105736
$246$	−0.589357	−0.0375760
$247$	0.549558	0.0349675
$248$	3.00369	0.190734
$249$	6.48209	0.410786
$250$	−15.6143	−0.987535
$251$	−15.2466	−0.962359	−0.481179	−	0.876622i	$-0.659791\pi$
$251$	−15.2466	−0.962359	−0.481179	+	0.876622i	$0.659791\pi$
$252$	0.882224	0.0555749
$253$	−23.1795	−1.45728
$254$	21.0834	1.32289
$255$	−3.38550	−0.212008
$256$	−7.28915	−0.455572
$257$	−15.3916	−0.960100	−0.480050	−	0.877241i	$-0.659382\pi$
$257$	−15.3916	−0.960100	−0.480050	+	0.877241i	$0.659382\pi$
$258$	4.78482	0.297890
$259$	−1.00000	−0.0621370
$260$	0.0642932	0.00398729
$261$	24.7170	1.52994
$262$	−14.7515	−0.911352
$263$	−11.1415	−0.687014	−0.343507	−	0.939150i	$-0.611615\pi$
$263$	−11.1415	−0.687014	−0.343507	+	0.939150i	$0.611615\pi$
$264$	6.86635	0.422595
$265$	−15.1835	−0.932716
$266$	−5.72910	−0.351273
$267$	−6.99403	−0.428028
$268$	4.96978	0.303578
$269$	−17.1723	−1.04701	−0.523507	−	0.852021i	$-0.675377\pi$
$269$	−17.1723	−1.04701	−0.523507	+	0.852021i	$0.675377\pi$
$270$	−5.16104	−0.314091
$271$	−0.625968	−0.0380249	−0.0190124	−	0.999819i	$-0.506052\pi$
$271$	−0.625968	−0.0380249	−0.0190124	+	0.999819i	$0.506052\pi$
$272$	−16.2979	−0.988207
$273$	0.0513037	0.00310504
$274$	4.35170	0.262896
$275$	−12.5561	−0.757164
$276$	0.535457	0.0322307
$277$	−30.9185	−1.85771	−0.928856	−	0.370441i	$-0.879207\pi$
$277$	−30.9185	−1.85771	−0.928856	+	0.370441i	$0.879207\pi$
$278$	−17.1061	−1.02596
$279$	−2.83057	−0.169462
$280$	−4.97118	−0.297085
$281$	−6.73402	−0.401718	−0.200859	−	0.979620i	$-0.564373\pi$
$281$	−6.73402	−0.401718	−0.200859	+	0.979620i	$0.564373\pi$
$282$	−2.95259	−0.175824
$283$	25.2069	1.49839	0.749197	−	0.662347i	$-0.230440\pi$
$283$	25.2069	1.49839	0.749197	+	0.662347i	$0.230440\pi$
$284$	4.20230	0.249361
$285$	−3.00370	−0.177924
$286$	−0.899415	−0.0531835
$287$	1.10194	0.0650453
$288$	4.94257	0.291244
$289$	7.69727	0.452781
$290$	−18.7782	−1.10269
$291$	−3.11437	−0.182568
$292$	2.65312	0.155262
$293$	6.21763	0.363238	0.181619	−	0.983369i	$-0.441866\pi$
$293$	6.21763	0.363238	0.181619	+	0.983369i	$0.441866\pi$
$294$	−0.534837	−0.0311923
$295$	9.45569	0.550531
$296$	−3.00369	−0.174586
$297$	−13.3285	−0.773399
$298$	−15.9852	−0.925995
$299$	−0.520213	−0.0300847
$300$	0.290053	0.0167462
$301$	−8.94632	−0.515657
$302$	−8.55578	−0.492330
$303$	4.30257	0.247176
$304$	−14.4599	−0.829334
$305$	3.01960	0.172902
$306$	18.2779	1.04488
$307$	−0.474891	−0.0271034	−0.0135517	−	0.999908i	$-0.504314\pi$
$307$	−0.474891	−0.0271034	−0.0135517	+	0.999908i	$0.504314\pi$
$308$	−1.73094	−0.0986295
$309$	8.24179	0.468859
$310$	2.15047	0.122138
$311$	28.2344	1.60102	0.800512	−	0.599317i	$-0.204561\pi$
$311$	28.2344	1.60102	0.800512	+	0.599317i	$0.204561\pi$
$312$	0.154100	0.00872422
$313$	−34.0233	−1.92311	−0.961555	−	0.274613i	$-0.911450\pi$
$313$	−34.0233	−1.92311	−0.961555	+	0.274613i	$0.911450\pi$
$314$	3.41077	0.192481
$315$	4.68467	0.263951
$316$	−1.61648	−0.0909341
$317$	22.4144	1.25892	0.629460	−	0.777033i	$-0.283276\pi$
$317$	22.4144	1.25892	0.629460	+	0.777033i	$0.283276\pi$
$318$	−4.90670	−0.275154
$319$	−48.4951	−2.71521
$320$	−14.6103	−0.816743
$321$	1.16038	0.0647661
$322$	5.42318	0.302222
$323$	21.9120	1.21922
$324$	−2.33878	−0.129932
$325$	−0.281796	−0.0156312
$326$	1.46704	0.0812518
$327$	−2.59165	−0.143319
$328$	3.30988	0.182757
$329$	5.52054	0.304357
$330$	4.91591	0.270612
$331$	−24.5204	−1.34776	−0.673881	−	0.738840i	$-0.735374\pi$
$331$	−24.5204	−1.34776	−0.673881	+	0.738840i	$0.735374\pi$
$332$	−4.90825	−0.269375
$333$	2.83057	0.155114
$334$	−2.93479	−0.160584
$335$	26.3899	1.44183
$336$	−1.34990	−0.0736431
$337$	18.6575	1.01634	0.508169	−	0.861258i	$-0.330323\pi$
$337$	18.6575	1.01634	0.508169	+	0.861258i	$0.330323\pi$
$338$	16.8714	0.917685
$339$	0.490988	0.0266668
$340$	2.56351	0.139026
$341$	5.55363	0.300746
$342$	16.2166	0.876894
$343$	1.00000	0.0539949
$344$	−26.8719	−1.44884
$345$	2.84331	0.153079
$346$	19.1380	1.02887
$347$	6.54502	0.351355	0.175677	−	0.984448i	$-0.443788\pi$
$347$	6.54502	0.351355	0.175677	+	0.984448i	$0.443788\pi$
$348$	1.12026	0.0600523
$349$	−23.0414	−1.23338	−0.616690	−	0.787206i	$-0.711527\pi$
$349$	−23.0414	−1.23338	−0.616690	+	0.787206i	$0.711527\pi$
$350$	2.93770	0.157027
$351$	−0.299130	−0.0159664
$352$	−9.69742	−0.516874
$353$	−23.9678	−1.27568	−0.637838	−	0.770171i	$-0.720171\pi$
$353$	−23.9678	−1.27568	−0.637838	+	0.770171i	$0.720171\pi$
$354$	3.05569	0.162408
$355$	22.3145	1.18433
$356$	5.29589	0.280681
$357$	2.04559	0.108264
$358$	16.2228	0.857402
$359$	25.3628	1.33860	0.669298	−	0.742994i	$-0.266595\pi$
$359$	25.3628	1.33860	0.669298	+	0.742994i	$0.266595\pi$
$360$	14.0713	0.741622
$361$	0.440916	0.0232061
$362$	14.4488	0.759414
$363$	8.16766	0.428691
$364$	−0.0388472	−0.00203615
$365$	14.0883	0.737413
$366$	0.975812	0.0510065
$367$	−19.9725	−1.04256	−0.521279	−	0.853387i	$-0.674545\pi$
$367$	−19.9725	−1.04256	−0.521279	+	0.853387i	$0.674545\pi$
$368$	13.6878	0.713527
$369$	−3.11911	−0.162374
$370$	−2.15047	−0.111797
$371$	9.17419	0.476300
$372$	−0.128292	−0.00665162
$373$	−5.41498	−0.280377	−0.140188	−	0.990125i	$-0.544771\pi$
$373$	−5.41498	−0.280377	−0.140188	+	0.990125i	$0.544771\pi$
$374$	−35.8616	−1.85436
$375$	4.94639	0.255430
$376$	16.5820	0.855150
$377$	−1.08837	−0.0560538
$378$	3.11841	0.160393
$379$	−10.5136	−0.540050	−0.270025	−	0.962853i	$-0.587032\pi$
$379$	−10.5136	−0.540050	−0.270025	+	0.962853i	$0.587032\pi$
$380$	2.27441	0.116675
$381$	−6.67894	−0.342172
$382$	25.4265	1.30093
$383$	0.814302	0.0416089	0.0208044	−	0.999784i	$-0.493377\pi$
$383$	0.814302	0.0416089	0.0208044	+	0.999784i	$0.493377\pi$
$384$	−3.28398	−0.167585
$385$	−9.19141	−0.468437
$386$	−31.3813	−1.59727
$387$	25.3232	1.28725
$388$	2.35821	0.119720
$389$	−14.0323	−0.711465	−0.355732	−	0.934588i	$-0.615769\pi$
$389$	−14.0323	−0.711465	−0.355732	+	0.934588i	$0.615769\pi$
$390$	0.110327	0.00558662
$391$	−20.7420	−1.04897
$392$	3.00369	0.151709
$393$	4.67307	0.235725
$394$	28.3412	1.42781
$395$	−8.58362	−0.431889
$396$	4.89955	0.246212
$397$	6.05799	0.304042	0.152021	−	0.988377i	$-0.451422\pi$
$397$	6.05799	0.304042	0.152021	+	0.988377i	$0.451422\pi$
$398$	−4.46713	−0.223917
$399$	1.81490	0.0908585
$400$	7.41459	0.370730
$401$	−21.1763	−1.05749	−0.528747	−	0.848780i	$-0.677338\pi$
$401$	−21.1763	−1.05749	−0.528747	+	0.848780i	$0.677338\pi$
$402$	8.52814	0.425345
$403$	0.124639	0.00620873
$404$	−3.25791	−0.162087
$405$	−12.4191	−0.617108
$406$	11.3462	0.563100
$407$	−5.55363	−0.275283
$408$	6.14431	0.304189
$409$	−31.8184	−1.57332	−0.786658	−	0.617388i	$-0.788191\pi$
$409$	−31.8184	−1.57332	−0.786658	+	0.617388i	$0.788191\pi$
$410$	2.36968	0.117030
$411$	−1.37856	−0.0679992
$412$	−6.24069	−0.307457
$413$	−5.71332	−0.281134
$414$	−15.3507	−0.754446
$415$	−26.0631	−1.27939
$416$	−0.217638	−0.0106706
$417$	5.41899	0.265369
$418$	−31.8173	−1.55623
$419$	−16.7563	−0.818597	−0.409298	−	0.912401i	$-0.634226\pi$
$419$	−16.7563	−0.818597	−0.409298	+	0.912401i	$0.634226\pi$
$420$	0.212326	0.0103605
$421$	−10.5823	−0.515752	−0.257876	−	0.966178i	$-0.583023\pi$
$421$	−10.5823	−0.515752	−0.257876	+	0.966178i	$0.583023\pi$
$422$	12.2244	0.595076
$423$	−15.6263	−0.759776
$424$	27.5564	1.33826
$425$	−11.2358	−0.545016
$426$	7.21113	0.349381
$427$	−1.82450	−0.0882939
$428$	−0.878641	−0.0424707
$429$	0.284922	0.0137562
$430$	−19.2387	−0.927775
$431$	−17.3197	−0.834261	−0.417130	−	0.908847i	$-0.636964\pi$
$431$	−17.3197	−0.834261	−0.417130	+	0.908847i	$0.636964\pi$
$432$	7.87069	0.378679
$433$	−2.08628	−0.100260	−0.0501300	−	0.998743i	$-0.515964\pi$
$433$	−2.08628	−0.100260	−0.0501300	+	0.998743i	$0.515964\pi$
$434$	−1.29935	−0.0623710
$435$	5.94866	0.285217
$436$	1.96240	0.0939820
$437$	−18.4028	−0.880327
$438$	4.55275	0.217539
$439$	−29.2024	−1.39375	−0.696877	−	0.717191i	$-0.745428\pi$
$439$	−29.2024	−1.39375	−0.696877	+	0.717191i	$0.745428\pi$
$440$	−27.6081	−1.31617
$441$	−2.83057	−0.134789
$442$	−0.804836	−0.0382821
$443$	34.9571	1.66086	0.830432	−	0.557120i	$-0.188094\pi$
$443$	34.9571	1.66086	0.830432	+	0.557120i	$0.188094\pi$
$444$	0.128292	0.00608846
$445$	28.1215	1.33309
$446$	−13.6272	−0.645267
$447$	5.06387	0.239513
$448$	8.82786	0.417077
$449$	−19.4930	−0.919930	−0.459965	−	0.887937i	$-0.652138\pi$
$449$	−19.4930	−0.919930	−0.459965	+	0.887937i	$0.652138\pi$
$450$	−8.31536	−0.391990
$451$	6.11975	0.288168
$452$	−0.371776	−0.0174869
$453$	2.71035	0.127343
$454$	24.2707	1.13908
$455$	−0.206281	−0.00967062
$456$	5.45139	0.255285
$457$	−1.54558	−0.0722992	−0.0361496	−	0.999346i	$-0.511509\pi$
$457$	−1.54558	−0.0722992	−0.0361496	+	0.999346i	$0.511509\pi$
$458$	−31.3966	−1.46707
$459$	−11.9269	−0.556702
$460$	−2.15296	−0.100382
$461$	−10.7290	−0.499700	−0.249850	−	0.968285i	$-0.580381\pi$
$461$	−10.7290	−0.499700	−0.249850	+	0.968285i	$0.580381\pi$
$462$	−2.97029	−0.138190
$463$	15.6216	0.725999	0.362999	−	0.931789i	$-0.381753\pi$
$463$	15.6216	0.725999	0.362999	+	0.931789i	$0.381753\pi$
$464$	28.6371	1.32944
$465$	−0.681238	−0.0315916
$466$	3.64533	0.168866
$467$	−3.61336	−0.167206	−0.0836032	−	0.996499i	$-0.526643\pi$
$467$	−3.61336	−0.167206	−0.0836032	+	0.996499i	$0.526643\pi$
$468$	0.109960	0.00508290
$469$	−15.9453	−0.736285
$470$	11.8717	0.547602
$471$	−1.08048	−0.0497861
$472$	−17.1610	−0.789900
$473$	−49.6846	−2.28450
$474$	−2.77388	−0.127408
$475$	−9.96868	−0.457394
$476$	−1.54892	−0.0709947
$477$	−25.9682	−1.18900
$478$	−19.9736	−0.913573
$479$	17.2641	0.788818	0.394409	−	0.918935i	$-0.370949\pi$
$479$	17.2641	0.788818	0.394409	+	0.918935i	$0.370949\pi$
$480$	1.18954	0.0542946
$481$	−0.124639	−0.00568307
$482$	−21.1877	−0.965074
$483$	−1.71799	−0.0781711
$484$	−6.18456	−0.281116
$485$	12.5222	0.568605
$486$	−13.3686	−0.606410
$487$	−16.4361	−0.744793	−0.372396	−	0.928074i	$-0.621464\pi$
$487$	−16.4361	−0.744793	−0.372396	+	0.928074i	$0.621464\pi$
$488$	−5.48024	−0.248079
$489$	−0.464737	−0.0210161
$490$	2.15047	0.0971481
$491$	13.1594	0.593875	0.296937	−	0.954897i	$-0.404035\pi$
$491$	13.1594	0.593875	0.296937	+	0.954897i	$0.404035\pi$
$492$	−0.141369	−0.00637343
$493$	−43.3956	−1.95444
$494$	−0.714071	−0.0321276
$495$	26.0169	1.16937
$496$	−3.27950	−0.147254
$497$	−13.4829	−0.604789
$498$	−8.42254	−0.377423
$499$	31.4162	1.40638	0.703192	−	0.711000i	$-0.251758\pi$
$499$	31.4162	1.40638	0.703192	+	0.711000i	$0.251758\pi$
$500$	−3.74541	−0.167500
$501$	0.929699	0.0415359
$502$	19.8108	0.884199
$503$	29.1002	1.29752	0.648758	−	0.760995i	$-0.275289\pi$
$503$	29.1002	1.29752	0.648758	+	0.760995i	$0.275289\pi$
$504$	−8.50215	−0.378716
$505$	−17.2997	−0.769827
$506$	30.1184	1.33892
$507$	−5.34463	−0.237363
$508$	5.05730	0.224381
$509$	−28.0825	−1.24474	−0.622368	−	0.782725i	$-0.713829\pi$
$509$	−28.0825	−1.24474	−0.622368	+	0.782725i	$0.713829\pi$
$510$	4.39897	0.194790
$511$	−8.51241	−0.376567
$512$	25.4277	1.12376
$513$	−10.5819	−0.467202
$514$	19.9991	0.882123
$515$	−33.1385	−1.46026
$516$	1.14774	0.0505264
$517$	30.6591	1.34838
$518$	1.29935	0.0570904
$519$	−6.06266	−0.266121
$520$	−0.619605	−0.0271715
$521$	20.7334	0.908345	0.454172	−	0.890914i	$-0.349935\pi$
$521$	20.7334	0.908345	0.454172	+	0.890914i	$0.349935\pi$
$522$	−32.1161	−1.40568
$523$	−19.0319	−0.832205	−0.416103	−	0.909318i	$-0.636604\pi$
$523$	−19.0319	−0.832205	−0.416103	+	0.909318i	$0.636604\pi$
$524$	−3.53846	−0.154578
$525$	−0.930621	−0.0406156
$526$	14.4768	0.631216
$527$	4.96963	0.216481
$528$	−7.49685	−0.326259
$529$	−5.57983	−0.242601
$530$	19.7288	0.856963
$531$	16.1720	0.701803
$532$	−1.37424	−0.0595810
$533$	0.137345	0.00594906
$534$	9.08773	0.393264
$535$	−4.66564	−0.201713
$536$	−47.8947	−2.06874
$537$	−5.13916	−0.221771
$538$	22.3129	0.961979
$539$	5.55363	0.239212
$540$	−1.23798	−0.0532743
$541$	41.3769	1.77893	0.889466	−	0.457001i	$-0.151077\pi$
$541$	41.3769	1.77893	0.889466	+	0.457001i	$0.151077\pi$
$542$	0.813355	0.0349366
$543$	−4.57719	−0.196426
$544$	−8.67767	−0.372052
$545$	10.4205	0.446364
$546$	−0.0666617	−0.00285286
$547$	41.0161	1.75372	0.876860	−	0.480745i	$-0.159634\pi$
$547$	41.0161	1.75372	0.876860	+	0.480745i	$0.159634\pi$
$548$	1.04384	0.0445908
$549$	5.16439	0.220411
$550$	16.3149	0.695669
$551$	−38.5016	−1.64022
$552$	−5.16030	−0.219637
$553$	5.18640	0.220548
$554$	40.1741	1.70683
$555$	0.681238	0.0289169
$556$	−4.10326	−0.174017
$557$	−1.53441	−0.0650149	−0.0325075	−	0.999471i	$-0.510349\pi$
$557$	−1.53441	−0.0650149	−0.0325075	+	0.999471i	$0.510349\pi$
$558$	3.67792	0.155699
$559$	−1.11506	−0.0471621
$560$	5.42766	0.229361
$561$	11.3604	0.479638
$562$	8.74988	0.369091
$563$	−15.9186	−0.670887	−0.335444	−	0.942060i	$-0.608886\pi$
$563$	−15.9186	−0.670887	−0.335444	+	0.942060i	$0.608886\pi$
$564$	−0.708240	−0.0298223
$565$	−1.97416	−0.0830534
$566$	−32.7527	−1.37670
$567$	7.50385	0.315132
$568$	−40.4983	−1.69927
$569$	−27.5321	−1.15421	−0.577103	−	0.816671i	$-0.695817\pi$
$569$	−27.5321	−1.15421	−0.577103	+	0.816671i	$0.695817\pi$
$570$	3.90288	0.163473
$571$	−19.5538	−0.818301	−0.409151	−	0.912467i	$-0.634175\pi$
$571$	−19.5538	−0.818301	−0.409151	+	0.912467i	$0.634175\pi$
$572$	−0.215743	−0.00902068
$573$	−8.05475	−0.336492
$574$	−1.43181	−0.0597625
$575$	9.43638	0.393524
$576$	−24.9879	−1.04116
$577$	22.0013	0.915928	0.457964	−	0.888971i	$-0.348579\pi$
$577$	22.0013	0.915928	0.457964	+	0.888971i	$0.348579\pi$
$578$	−10.0015	−0.416007
$579$	9.94116	0.413140
$580$	−4.50433	−0.187032
$581$	15.7479	0.653331
$582$	4.04668	0.167740
$583$	50.9501	2.11014
$584$	−25.5686	−1.05804
$585$	0.583894	0.0241411
$586$	−8.07891	−0.333737
$587$	22.4491	0.926574	0.463287	−	0.886208i	$-0.346670\pi$
$587$	22.4491	0.926574	0.463287	+	0.886208i	$0.346670\pi$
$588$	−0.128292	−0.00529066
$589$	4.40919	0.181677
$590$	−12.2863	−0.505819
$591$	−8.97810	−0.369310
$592$	3.27950	0.134787
$593$	−47.7770	−1.96197	−0.980983	−	0.194094i	$-0.937823\pi$
$593$	−47.7770	−1.96197	−0.980983	+	0.194094i	$0.937823\pi$
$594$	17.3185	0.710586
$595$	−8.22487	−0.337187
$596$	−3.83437	−0.157062
$597$	1.41512	0.0579171
$598$	0.675942	0.0276413
$599$	14.4026	0.588474	0.294237	−	0.955733i	$-0.404935\pi$
$599$	14.4026	0.588474	0.294237	+	0.955733i	$0.404935\pi$
$600$	−2.79530	−0.114118
$601$	−6.03064	−0.245995	−0.122997	−	0.992407i	$-0.539251\pi$
$601$	−6.03064	−0.245995	−0.122997	+	0.992407i	$0.539251\pi$
$602$	11.6244	0.473777
$603$	45.1343	1.83801
$604$	−2.05228	−0.0835061
$605$	−32.8404	−1.33515
$606$	−5.59056	−0.227101
$607$	−9.97740	−0.404970	−0.202485	−	0.979285i	$-0.564902\pi$
$607$	−9.97740	−0.404970	−0.202485	+	0.979285i	$0.564902\pi$
$608$	−7.69905	−0.312238
$609$	−3.59430	−0.145648
$610$	−3.92353	−0.158859
$611$	0.688077	0.0278366
$612$	4.38433	0.177226
$613$	30.9130	1.24857	0.624283	−	0.781198i	$-0.285391\pi$
$613$	30.9130	1.24857	0.624283	+	0.781198i	$0.285391\pi$
$614$	0.617051	0.0249022
$615$	−0.750681	−0.0302704
$616$	16.6814	0.672112
$617$	−27.0175	−1.08768	−0.543842	−	0.839188i	$-0.683031\pi$
$617$	−27.0175	−1.08768	−0.543842	+	0.839188i	$0.683031\pi$
$618$	−10.7090	−0.430780
$619$	2.31773	0.0931575	0.0465787	−	0.998915i	$-0.485168\pi$
$619$	2.31773	0.0931575	0.0465787	+	0.998915i	$0.485168\pi$
$620$	0.515834	0.0207164
$621$	10.0168	0.401962
$622$	−36.6865	−1.47099
$623$	−16.9916	−0.680753
$624$	−0.168251	−0.00673542
$625$	−8.58394	−0.343357
$626$	44.2083	1.76692
$627$	10.0793	0.402527
$628$	0.818144	0.0326475
$629$	−4.96963	−0.198152
$630$	−6.08705	−0.242514
$631$	26.4609	1.05339	0.526695	−	0.850054i	$-0.323431\pi$
$631$	26.4609	1.05339	0.526695	+	0.850054i	$0.323431\pi$
$632$	15.5783	0.619672
$633$	−3.87253	−0.153919
$634$	−29.1243	−1.15667
$635$	26.8546	1.06569
$636$	−1.17697	−0.0466700
$637$	0.124639	0.00493839
$638$	63.0124	2.49468
$639$	38.1642	1.50975
$640$	13.2042	0.521942
$641$	8.90319	0.351655	0.175828	−	0.984421i	$-0.443740\pi$
$641$	8.90319	0.351655	0.175828	+	0.984421i	$0.443740\pi$
$642$	−1.50775	−0.0595059
$643$	−20.9437	−0.825940	−0.412970	−	0.910745i	$-0.635509\pi$
$643$	−20.9437	−0.825940	−0.412970	+	0.910745i	$0.635509\pi$
$644$	1.30086	0.0512611
$645$	6.09457	0.239973
$646$	−28.4715	−1.12020
$647$	−7.69406	−0.302485	−0.151242	−	0.988497i	$-0.548327\pi$
$647$	−7.69406	−0.302485	−0.151242	+	0.988497i	$0.548327\pi$
$648$	22.5392	0.885424
$649$	−31.7297	−1.24550
$650$	0.366153	0.0143617
$651$	0.411617	0.0161326
$652$	0.351900	0.0137815
$653$	20.7275	0.811128	0.405564	−	0.914067i	$-0.367075\pi$
$653$	20.7275	0.811128	0.405564	+	0.914067i	$0.367075\pi$
$654$	3.36748	0.131679
$655$	−18.7894	−0.734164
$656$	−3.61381	−0.141095
$657$	24.0950	0.940034
$658$	−7.17314	−0.279638
$659$	−27.7786	−1.08210	−0.541051	−	0.840990i	$-0.681973\pi$
$659$	−27.7786	−1.08210	−0.541051	+	0.840990i	$0.681973\pi$
$660$	1.17918	0.0458996
$661$	35.5496	1.38272	0.691360	−	0.722511i	$-0.257012\pi$
$661$	35.5496	1.38272	0.691360	+	0.722511i	$0.257012\pi$
$662$	31.8607	1.23830
$663$	0.254961	0.00990186
$664$	47.3017	1.83566
$665$	−7.29732	−0.282978
$666$	−3.67792	−0.142516
$667$	36.4458	1.41119
$668$	−0.703969	−0.0272374
$669$	4.31691	0.166901
$670$	−34.2898	−1.32473
$671$	−10.1326	−0.391166
$672$	−0.718741	−0.0277260
$673$	−46.2965	−1.78460	−0.892300	−	0.451442i	$-0.850910\pi$
$673$	−46.2965	−1.78460	−0.892300	+	0.451442i	$0.850910\pi$
$674$	−24.2427	−0.933793
$675$	5.42605	0.208849
$676$	4.04696	0.155652
$677$	−37.5563	−1.44341	−0.721703	−	0.692203i	$-0.756640\pi$
$677$	−37.5563	−1.44341	−0.721703	+	0.692203i	$0.756640\pi$
$678$	−0.637967	−0.0245010
$679$	−7.56618	−0.290364
$680$	−24.7050	−0.947392
$681$	−7.68862	−0.294629
$682$	−7.21614	−0.276320
$683$	−36.4621	−1.39518	−0.697592	−	0.716495i	$-0.745745\pi$
$683$	−36.4621	−1.39518	−0.697592	+	0.716495i	$0.745745\pi$
$684$	3.88989	0.148734
$685$	5.54289	0.211783
$686$	−1.29935	−0.0496096
$687$	9.94600	0.379464
$688$	29.3395	1.11856
$689$	1.14346	0.0435625
$690$	−3.69447	−0.140646
$691$	23.3368	0.887773	0.443886	−	0.896083i	$-0.353599\pi$
$691$	23.3368	0.887773	0.443886	+	0.896083i	$0.353599\pi$
$692$	4.59066	0.174511
$693$	−15.7200	−0.597152
$694$	−8.50430	−0.322819
$695$	−21.7886	−0.826488
$696$	−10.7962	−0.409228
$697$	5.47623	0.207427
$698$	29.9390	1.13321
$699$	−1.15479	−0.0436781
$700$	0.704667	0.0266339
$701$	−38.0688	−1.43784	−0.718919	−	0.695094i	$-0.755363\pi$
$701$	−38.0688	−1.43784	−0.718919	+	0.695094i	$0.755363\pi$
$702$	0.388676	0.0146696
$703$	−4.40919	−0.166296
$704$	49.0267	1.84776
$705$	−3.76080	−0.141640
$706$	31.1426	1.17207
$707$	10.4528	0.393119
$708$	0.732971	0.0275467
$709$	10.1028	0.379420	0.189710	−	0.981840i	$-0.439245\pi$
$709$	10.1028	0.379420	0.189710	+	0.981840i	$0.439245\pi$
$710$	−28.9944	−1.08814
$711$	−14.6805	−0.550560
$712$	−51.0374	−1.91271
$713$	−4.17375	−0.156308
$714$	−2.65794	−0.0994711
$715$	−1.14561	−0.0428434
$716$	3.89138	0.145428
$717$	6.32737	0.236300
$718$	−32.9552	−1.22988
$719$	38.1048	1.42107	0.710535	−	0.703662i	$-0.248453\pi$
$719$	38.1048	1.42107	0.710535	+	0.703662i	$0.248453\pi$
$720$	−15.3634	−0.572560
$721$	20.0229	0.745694
$722$	−0.572907	−0.0213214
$723$	6.71197	0.249621
$724$	3.46585	0.128807
$725$	19.7424	0.733215
$726$	−10.6127	−0.393874
$727$	−21.6983	−0.804744	−0.402372	−	0.915476i	$-0.631814\pi$
$727$	−21.6983	−0.804744	−0.402372	+	0.915476i	$0.631814\pi$
$728$	0.374378	0.0138754
$729$	−18.2766	−0.676910
$730$	−18.3056	−0.677522
$731$	−44.4599	−1.64441
$732$	0.234069	0.00865143
$733$	−21.0963	−0.779209	−0.389605	−	0.920982i	$-0.627388\pi$
$733$	−21.0963	−0.779209	−0.389605	+	0.920982i	$0.627388\pi$
$734$	25.9514	0.957883
$735$	−0.681238	−0.0251278
$736$	7.28795	0.268637
$737$	−88.5543	−3.26194
$738$	4.05283	0.149187
$739$	0.944666	0.0347501	0.0173750	−	0.999849i	$-0.494469\pi$
$739$	0.944666	0.0347501	0.0173750	+	0.999849i	$0.494469\pi$
$740$	−0.515834	−0.0189624
$741$	0.226208	0.00830995
$742$	−11.9205	−0.437616
$743$	−20.3755	−0.747503	−0.373751	−	0.927529i	$-0.621929\pi$
$743$	−20.3755	−0.747503	−0.373751	+	0.927529i	$0.621929\pi$
$744$	1.23637	0.0453275
$745$	−20.3608	−0.745960
$746$	7.03598	0.257605
$747$	−44.5754	−1.63093
$748$	−8.60214	−0.314525
$749$	2.81907	0.103007
$750$	−6.42712	−0.234685
$751$	−13.6189	−0.496960	−0.248480	−	0.968637i	$-0.579931\pi$
$751$	−13.6189	−0.496960	−0.248480	+	0.968637i	$0.579931\pi$
$752$	−18.1046	−0.660208
$753$	−6.27578	−0.228702
$754$	1.41418	0.0515013
$755$	−10.8977	−0.396609
$756$	0.748014	0.0272050
$757$	34.4125	1.25074	0.625372	−	0.780327i	$-0.284947\pi$
$757$	34.4125	1.25074	0.625372	+	0.780327i	$0.284947\pi$
$758$	13.6610	0.496188
$759$	−9.54107	−0.346319
$760$	−21.9189	−0.795081
$761$	39.7756	1.44186	0.720932	−	0.693006i	$-0.243714\pi$
$761$	39.7756	1.44186	0.720932	+	0.693006i	$0.243714\pi$
$762$	8.67831	0.314382
$763$	−6.29627	−0.227940
$764$	6.09907	0.220656
$765$	23.2811	0.841730
$766$	−1.05807	−0.0382295
$767$	−0.712104	−0.0257126
$768$	−3.00034	−0.108266
$769$	18.0611	0.651298	0.325649	−	0.945491i	$-0.394417\pi$
$769$	18.0611	0.651298	0.325649	+	0.945491i	$0.394417\pi$
$770$	11.9429	0.430392
$771$	−6.33544	−0.228165
$772$	−7.52745	−0.270919
$773$	−10.1006	−0.363295	−0.181647	−	0.983364i	$-0.558143\pi$
$773$	−10.1006	−0.363295	−0.181647	+	0.983364i	$0.558143\pi$
$774$	−32.9038	−1.18270
$775$	−2.26089	−0.0812135
$776$	−22.7265	−0.815832
$777$	−0.411617	−0.0147667
$778$	18.2329	0.653681
$779$	4.85865	0.174079
$780$	0.0264642	0.000947570 0
$781$	−74.8789	−2.67938
$782$	26.9512	0.963774
$783$	20.9568	0.748936
$784$	−3.27950	−0.117125
$785$	4.34440	0.155058
$786$	−6.07198	−0.216580
$787$	9.21887	0.328617	0.164309	−	0.986409i	$-0.447461\pi$
$787$	9.21887	0.328617	0.164309	+	0.986409i	$0.447461\pi$
$788$	6.79823	0.242177
$789$	−4.58603	−0.163267
$790$	11.1532	0.396812
$791$	1.19283	0.0424120
$792$	−47.2178	−1.67781
$793$	−0.227405	−0.00807539
$794$	−7.87147	−0.279348
$795$	−6.24980	−0.221658
$796$	−1.07153	−0.0379795
$797$	−36.7069	−1.30023	−0.650113	−	0.759838i	$-0.725278\pi$
$797$	−36.7069	−1.30023	−0.650113	+	0.759838i	$0.725278\pi$
$798$	−2.35820	−0.0834792
$799$	27.4351	0.970583
$800$	3.94783	0.139577
$801$	48.0959	1.69938
$802$	27.5155	0.971607
$803$	−47.2748	−1.66829
$804$	2.04565	0.0721445
$805$	6.90766	0.243463
$806$	−0.161951	−0.00570447
$807$	−7.06842	−0.248820
$808$	31.3971	1.10454
$809$	−15.1667	−0.533233	−0.266616	−	0.963803i	$-0.585906\pi$
$809$	−15.1667	−0.533233	−0.266616	+	0.963803i	$0.585906\pi$
$810$	16.1368	0.566988
$811$	5.79986	0.203661	0.101830	−	0.994802i	$-0.467530\pi$
$811$	5.79986	0.203661	0.101830	+	0.994802i	$0.467530\pi$
$812$	2.72161	0.0955097
$813$	−0.257659	−0.00903651
$814$	7.21614	0.252926
$815$	1.86861	0.0654545
$816$	−6.70851	−0.234845
$817$	−39.4460	−1.38004
$818$	41.3433	1.44554
$819$	−0.352801	−0.0123278
$820$	0.568416	0.0198500
$821$	−24.1025	−0.841184	−0.420592	−	0.907250i	$-0.638178\pi$
$821$	−24.1025	−0.841184	−0.420592	+	0.907250i	$0.638178\pi$
$822$	1.79124	0.0624765
$823$	53.2506	1.85620	0.928099	−	0.372334i	$-0.121442\pi$
$823$	53.2506	1.85620	0.928099	+	0.372334i	$0.121442\pi$
$824$	60.1427	2.09517
$825$	−5.16833	−0.179938
$826$	7.42363	0.258301
$827$	−39.0569	−1.35814	−0.679071	−	0.734073i	$-0.737617\pi$
$827$	−39.0569	−1.35814	−0.679071	+	0.734073i	$0.737617\pi$
$828$	−3.68218	−0.127965
$829$	−21.3772	−0.742461	−0.371231	−	0.928541i	$-0.621064\pi$
$829$	−21.3772	−0.742461	−0.371231	+	0.928541i	$0.621064\pi$
$830$	33.8652	1.17548
$831$	−12.7266	−0.441481
$832$	1.10030	0.0381460
$833$	4.96963	0.172188
$834$	−7.04119	−0.243816
$835$	−3.73812	−0.129363
$836$	−7.63204	−0.263960
$837$	−2.39996	−0.0829549
$838$	21.7723	0.752112
$839$	41.9198	1.44723	0.723616	−	0.690203i	$-0.242479\pi$
$839$	41.9198	1.44723	0.723616	+	0.690203i	$0.242479\pi$
$840$	−2.04623	−0.0706015
$841$	47.2503	1.62932
$842$	13.7502	0.473864
$843$	−2.77184	−0.0954672
$844$	2.93228	0.100933
$845$	21.4896	0.739266
$846$	20.3041	0.698069
$847$	19.8428	0.681808
$848$	−30.0868	−1.03318
$849$	10.3756	0.356090
$850$	14.5993	0.500751
$851$	4.17375	0.143074
$852$	1.72974	0.0592599
$853$	17.1245	0.586332	0.293166	−	0.956062i	$-0.405291\pi$
$853$	17.1245	0.586332	0.293166	+	0.956062i	$0.405291\pi$
$854$	2.37068	0.0811229
$855$	20.6556	0.706406
$856$	8.46762	0.289417
$857$	40.7078	1.39055	0.695275	−	0.718743i	$-0.255282\pi$
$857$	40.7078	1.39055	0.695275	+	0.718743i	$0.255282\pi$
$858$	−0.370215	−0.0126389
$859$	3.33476	0.113781	0.0568903	−	0.998380i	$-0.481881\pi$
$859$	3.33476	0.113781	0.0568903	+	0.998380i	$0.481881\pi$
$860$	−4.61481	−0.157364
$861$	0.453577	0.0154578
$862$	22.5044	0.766504
$863$	−24.5417	−0.835410	−0.417705	−	0.908583i	$-0.637166\pi$
$863$	−24.5417	−0.835410	−0.417705	+	0.908583i	$0.637166\pi$
$864$	4.19067	0.142570
$865$	24.3767	0.828832
$866$	2.71081	0.0921171
$867$	3.16833	0.107602
$868$	−0.311677	−0.0105790
$869$	28.8033	0.977086
$870$	−7.72942	−0.262052
$871$	−1.98741	−0.0673409
$872$	−18.9120	−0.640442
$873$	21.4166	0.724843
$874$	23.9118	0.808829
$875$	12.0170	0.406247
$876$	1.09207	0.0368977
$877$	−36.9072	−1.24627	−0.623134	−	0.782115i	$-0.714141\pi$
$877$	−36.9072	−1.24627	−0.623134	+	0.782115i	$0.714141\pi$
$878$	37.9443	1.28056
$879$	2.55929	0.0863226
$880$	30.1432	1.01613
$881$	−24.2593	−0.817317	−0.408658	−	0.912687i	$-0.634003\pi$
$881$	−24.2593	−0.817317	−0.408658	+	0.912687i	$0.634003\pi$
$882$	3.67792	0.123842
$883$	10.7139	0.360551	0.180276	−	0.983616i	$-0.442301\pi$
$883$	10.7139	0.360551	0.180276	+	0.983616i	$0.442301\pi$
$884$	−0.193057	−0.00649320
$885$	3.89213	0.130832
$886$	−45.4217	−1.52597
$887$	28.0640	0.942298	0.471149	−	0.882054i	$-0.343839\pi$
$887$	28.0640	0.942298	0.471149	+	0.882054i	$0.343839\pi$
$888$	−1.23637	−0.0414899
$889$	−16.2261	−0.544205
$890$	−36.5398	−1.22482
$891$	41.6736	1.39612
$892$	−3.26877	−0.109446
$893$	24.3411	0.814543
$894$	−6.57977	−0.220060
$895$	20.6635	0.690704
$896$	−7.97824	−0.266534
$897$	−0.214129	−0.00714955
$898$	25.3283	0.845215
$899$	−8.73214	−0.291233
$900$	−1.99461	−0.0664870
$901$	45.5924	1.51890
$902$	−7.95173	−0.264764
$903$	−3.68246	−0.122545
$904$	3.58288	0.119165
$905$	18.4039	0.611766
$906$	−3.52171	−0.117001
$907$	−5.99349	−0.199011	−0.0995053	−	0.995037i	$-0.531726\pi$
$907$	−5.99349	−0.199011	−0.0995053	+	0.995037i	$0.531726\pi$
$908$	5.82183	0.193204
$909$	−29.5875	−0.981355
$910$	0.268033	0.00888520
$911$	−4.21467	−0.139638	−0.0698191	−	0.997560i	$-0.522242\pi$
$911$	−4.21467	−0.139638	−0.0698191	+	0.997560i	$0.522242\pi$
$912$	−5.95196	−0.197089
$913$	87.4578	2.89443
$914$	2.00826	0.0664273
$915$	1.24292	0.0410897
$916$	−7.53112	−0.248835
$917$	11.3530	0.374908
$918$	15.4973	0.511488
$919$	35.0052	1.15472	0.577358	−	0.816491i	$-0.304084\pi$
$919$	35.0052	1.15472	0.577358	+	0.816491i	$0.304084\pi$
$920$	20.7485	0.684057
$921$	−0.195473	−0.00644106
$922$	13.9408	0.459115
$923$	−1.68050	−0.0553142
$924$	−0.712485	−0.0234390
$925$	2.26089	0.0743376
$926$	−20.2980	−0.667035
$927$	−56.6764	−1.86150
$928$	15.2475	0.500525
$929$	−4.47082	−0.146683	−0.0733414	−	0.997307i	$-0.523366\pi$
$929$	−4.47082	−0.146683	−0.0733414	+	0.997307i	$0.523366\pi$
$930$	0.885169	0.0290258
$931$	4.40919	0.144505
$932$	0.874407	0.0286422
$933$	11.6218	0.380479
$934$	4.69504	0.153626
$935$	−45.6779	−1.49383
$936$	−1.05970	−0.0346375
$937$	−47.0672	−1.53762	−0.768810	−	0.639478i	$-0.779151\pi$
$937$	−47.0672	−1.53762	−0.768810	+	0.639478i	$0.779151\pi$
$938$	20.7186	0.676486
$939$	−14.0046	−0.457022
$940$	2.84768	0.0928811
$941$	−51.8128	−1.68905	−0.844524	−	0.535518i	$-0.820116\pi$
$941$	−51.8128	−1.68905	−0.844524	+	0.535518i	$0.820116\pi$
$942$	1.40393	0.0457426
$943$	−4.59921	−0.149771
$944$	18.7368	0.609832
$945$	3.97200	0.129209
$946$	64.5579	2.09896
$947$	−34.0567	−1.10669	−0.553347	−	0.832951i	$-0.686650\pi$
$947$	−34.0567	−1.10669	−0.553347	+	0.832951i	$0.686650\pi$
$948$	−0.665372	−0.0216103
$949$	−1.06098	−0.0344409
$950$	12.9529	0.420246
$951$	9.22618	0.299179
$952$	14.9272	0.483795
$953$	−45.3242	−1.46820	−0.734098	−	0.679044i	$-0.762395\pi$
$953$	−45.3242	−1.46820	−0.734098	+	0.679044i	$0.762395\pi$
$954$	33.7419	1.09243
$955$	32.3864	1.04800
$956$	−4.79109	−0.154955
$957$	−19.9614	−0.645262
$958$	−22.4322	−0.724752
$959$	−3.34912	−0.108149
$960$	−6.01387	−0.194097
$961$	1.00000	0.0322581
$962$	0.161951	0.00522150
$963$	−7.97959	−0.257139
$964$	−5.08231	−0.163690
$965$	−39.9713	−1.28672
$966$	2.23228	0.0718223
$967$	−15.5676	−0.500621	−0.250311	−	0.968166i	$-0.580533\pi$
$967$	−15.5676	−0.500621	−0.250311	+	0.968166i	$0.580533\pi$
$968$	59.6017	1.91567
$969$	9.01938	0.289744
$970$	−16.2708	−0.522425
$971$	−47.8512	−1.53562	−0.767808	−	0.640680i	$-0.778653\pi$
$971$	−47.8512	−1.53562	−0.767808	+	0.640680i	$0.778653\pi$
$972$	−3.20672	−0.102856
$973$	13.1651	0.422054
$974$	21.3564	0.684303
$975$	−0.115992	−0.00371472
$976$	5.98347	0.191526
$977$	−19.0552	−0.609631	−0.304815	−	0.952411i	$-0.598595\pi$
$977$	−19.0552	−0.609631	−0.304815	+	0.952411i	$0.598595\pi$
$978$	0.603859	0.0193093
$979$	−94.3650	−3.01592
$980$	0.515834	0.0164777
$981$	17.8220	0.569014
$982$	−17.0987	−0.545642
$983$	−6.17169	−0.196846	−0.0984232	−	0.995145i	$-0.531380\pi$
$983$	−6.17169	−0.196846	−0.0984232	+	0.995145i	$0.531380\pi$
$984$	1.36240	0.0434318
$985$	36.0990	1.15021
$986$	56.3862	1.79570
$987$	2.27235	0.0723297
$988$	−0.171285	−0.00544929
$989$	37.3397	1.18733
$990$	−33.8052	−1.07440
$991$	38.7251	1.23014	0.615071	−	0.788471i	$-0.289127\pi$
$991$	38.7251	1.23014	0.615071	+	0.788471i	$0.289127\pi$
$992$	−1.74614	−0.0554400
$993$	−10.0930	−0.320292
$994$	17.5190	0.555670
$995$	−5.68991	−0.180382
$996$	−2.02032	−0.0640163
$997$	−59.7779	−1.89319	−0.946593	−	0.322432i	$-0.895500\pi$
$997$	−59.7779	−1.89319	−0.946593	+	0.322432i	$0.895500\pi$
$998$	−40.8208	−1.29216
$999$	2.39996	0.0759315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.d.1.20	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.d.1.20	✓	66	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.29935 q^{2} +0.411617 q^{3} -0.311677 q^{4} -1.65503 q^{5} -0.534837 q^{6} +1.00000 q^{7} +3.00369 q^{8} -2.83057 q^{9} +O(q^{10})\)	\(q-1.29935 q^{2} +0.411617 q^{3} -0.311677 q^{4} -1.65503 q^{5} -0.534837 q^{6} +1.00000 q^{7} +3.00369 q^{8} -2.83057 q^{9} +2.15047 q^{10} +5.55363 q^{11} -0.128292 q^{12} +0.124639 q^{13} -1.29935 q^{14} -0.681238 q^{15} -3.27950 q^{16} +4.96963 q^{17} +3.67792 q^{18} +4.40919 q^{19} +0.515834 q^{20} +0.411617 q^{21} -7.21614 q^{22} -4.17375 q^{23} +1.23637 q^{24} -2.26089 q^{25} -0.161951 q^{26} -2.39996 q^{27} -0.311677 q^{28} -8.73214 q^{29} +0.885169 q^{30} +1.00000 q^{31} -1.74614 q^{32} +2.28597 q^{33} -6.45732 q^{34} -1.65503 q^{35} +0.882224 q^{36} -1.00000 q^{37} -5.72910 q^{38} +0.0513037 q^{39} -4.97118 q^{40} +1.10194 q^{41} -0.534837 q^{42} -8.94632 q^{43} -1.73094 q^{44} +4.68467 q^{45} +5.42318 q^{46} +5.52054 q^{47} -1.34990 q^{48} +1.00000 q^{49} +2.93770 q^{50} +2.04559 q^{51} -0.0388472 q^{52} +9.17419 q^{53} +3.11841 q^{54} -9.19141 q^{55} +3.00369 q^{56} +1.81490 q^{57} +11.3462 q^{58} -5.71332 q^{59} +0.212326 q^{60} -1.82450 q^{61} -1.29935 q^{62} -2.83057 q^{63} +8.82786 q^{64} -0.206281 q^{65} -2.97029 q^{66} -15.9453 q^{67} -1.54892 q^{68} -1.71799 q^{69} +2.15047 q^{70} -13.4829 q^{71} -8.50215 q^{72} -8.51241 q^{73} +1.29935 q^{74} -0.930621 q^{75} -1.37424 q^{76} +5.55363 q^{77} -0.0666617 q^{78} +5.18640 q^{79} +5.42766 q^{80} +7.50385 q^{81} -1.43181 q^{82} +15.7479 q^{83} -0.128292 q^{84} -8.22487 q^{85} +11.6244 q^{86} -3.59430 q^{87} +16.6814 q^{88} -16.9916 q^{89} -6.08705 q^{90} +0.124639 q^{91} +1.30086 q^{92} +0.411617 q^{93} -7.17314 q^{94} -7.29732 q^{95} -0.718741 q^{96} -7.56618 q^{97} -1.29935 q^{98} -15.7200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * q^99

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