LMFDB - Embedded newform 8033.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62733 q^{2} +2.34750 q^{3} +4.90284 q^{4} -3.13713 q^{5} -6.16764 q^{6} -4.86517 q^{7} -7.62672 q^{8} +2.51073 q^{9} +O(q^{10})$	\(q-2.62733 q^{2} +2.34750 q^{3} +4.90284 q^{4} -3.13713 q^{5} -6.16764 q^{6} -4.86517 q^{7} -7.62672 q^{8} +2.51073 q^{9} +8.24227 q^{10} +3.23567 q^{11} +11.5094 q^{12} -4.09779 q^{13} +12.7824 q^{14} -7.36440 q^{15} +10.2322 q^{16} +2.85368 q^{17} -6.59652 q^{18} +4.57593 q^{19} -15.3809 q^{20} -11.4210 q^{21} -8.50117 q^{22} -5.15309 q^{23} -17.9037 q^{24} +4.84160 q^{25} +10.7662 q^{26} -1.14855 q^{27} -23.8532 q^{28} -1.00000 q^{29} +19.3487 q^{30} +0.0329587 q^{31} -11.6299 q^{32} +7.59573 q^{33} -7.49755 q^{34} +15.2627 q^{35} +12.3097 q^{36} +10.1388 q^{37} -12.0225 q^{38} -9.61953 q^{39} +23.9260 q^{40} +5.37131 q^{41} +30.0066 q^{42} -5.88423 q^{43} +15.8640 q^{44} -7.87650 q^{45} +13.5388 q^{46} +6.65167 q^{47} +24.0200 q^{48} +16.6699 q^{49} -12.7205 q^{50} +6.69900 q^{51} -20.0908 q^{52} -13.9066 q^{53} +3.01761 q^{54} -10.1507 q^{55} +37.1053 q^{56} +10.7420 q^{57} +2.62733 q^{58} +14.6537 q^{59} -36.1065 q^{60} -2.42549 q^{61} -0.0865932 q^{62} -12.2151 q^{63} +10.0911 q^{64} +12.8553 q^{65} -19.9565 q^{66} -5.34866 q^{67} +13.9911 q^{68} -12.0968 q^{69} -40.1000 q^{70} +4.29396 q^{71} -19.1487 q^{72} +14.1346 q^{73} -26.6379 q^{74} +11.3656 q^{75} +22.4351 q^{76} -15.7421 q^{77} +25.2737 q^{78} -2.47592 q^{79} -32.0997 q^{80} -10.2284 q^{81} -14.1122 q^{82} -14.2541 q^{83} -55.9952 q^{84} -8.95237 q^{85} +15.4598 q^{86} -2.34750 q^{87} -24.6776 q^{88} +6.53199 q^{89} +20.6941 q^{90} +19.9364 q^{91} -25.2648 q^{92} +0.0773703 q^{93} -17.4761 q^{94} -14.3553 q^{95} -27.3010 q^{96} -12.8286 q^{97} -43.7972 q^{98} +8.12392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) $ 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.62733	−1.85780	−0.928900	−	0.370330i	$-0.879244\pi$
$2$	−2.62733	−1.85780	−0.928900	+	0.370330i	$0.879244\pi$
$3$	2.34750	1.35533	0.677664	−	0.735372i	$-0.262993\pi$
$3$	2.34750	1.35533	0.677664	+	0.735372i	$0.262993\pi$
$4$	4.90284	2.45142
$5$	−3.13713	−1.40297	−0.701484	−	0.712685i	$-0.747479\pi$
$5$	−3.13713	−1.40297	−0.701484	+	0.712685i	$0.747479\pi$
$6$	−6.16764	−2.51793
$7$	−4.86517	−1.83886	−0.919431	−	0.393252i	$-0.871350\pi$
$7$	−4.86517	−1.83886	−0.919431	+	0.393252i	$0.871350\pi$
$8$	−7.62672	−2.69645
$9$	2.51073	0.836911
$10$	8.24227	2.60643
$11$	3.23567	0.975593	0.487796	−	0.872958i	$-0.337801\pi$
$11$	3.23567	0.975593	0.487796	+	0.872958i	$0.337801\pi$
$12$	11.5094	3.32248
$13$	−4.09779	−1.13652	−0.568261	−	0.822849i	$-0.692384\pi$
$13$	−4.09779	−1.13652	−0.568261	+	0.822849i	$0.692384\pi$
$14$	12.7824	3.41624
$15$	−7.36440	−1.90148
$16$	10.2322	2.55805
$17$	2.85368	0.692119	0.346059	−	0.938213i	$-0.387520\pi$
$17$	2.85368	0.692119	0.346059	+	0.938213i	$0.387520\pi$
$18$	−6.59652	−1.55481
$19$	4.57593	1.04979	0.524895	−	0.851167i	$-0.324104\pi$
$19$	4.57593	1.04979	0.524895	+	0.851167i	$0.324104\pi$
$20$	−15.3809	−3.43927
$21$	−11.4210	−2.49226
$22$	−8.50117	−1.81246
$23$	−5.15309	−1.07449	−0.537246	−	0.843425i	$-0.680535\pi$
$23$	−5.15309	−1.07449	−0.537246	+	0.843425i	$0.680535\pi$
$24$	−17.9037	−3.65457
$25$	4.84160	0.968319
$26$	10.7662	2.11143
$27$	−1.14855	−0.221038
$28$	−23.8532	−4.50783
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	19.3487	3.53257
$31$	0.0329587	0.00591955	0.00295978	−	0.999996i	$-0.499058\pi$
$31$	0.0329587	0.00591955	0.00295978	+	0.999996i	$0.499058\pi$
$32$	−11.6299	−2.05589
$33$	7.59573	1.32225
$34$	−7.49755	−1.28582
$35$	15.2627	2.57986
$36$	12.3097	2.05162
$37$	10.1388	1.66680	0.833402	−	0.552667i	$-0.186390\pi$
$37$	10.1388	1.66680	0.833402	+	0.552667i	$0.186390\pi$
$38$	−12.0225	−1.95030
$39$	−9.61953	−1.54036
$40$	23.9260	3.78303
$41$	5.37131	0.838857	0.419429	−	0.907788i	$-0.362230\pi$
$41$	5.37131	0.838857	0.419429	+	0.907788i	$0.362230\pi$
$42$	30.0066	4.63012
$43$	−5.88423	−0.897337	−0.448668	−	0.893698i	$-0.648102\pi$
$43$	−5.88423	−0.897337	−0.448668	+	0.893698i	$0.648102\pi$
$44$	15.8640	2.39159
$45$	−7.87650	−1.17416
$46$	13.5388	1.99619
$47$	6.65167	0.970245	0.485123	−	0.874446i	$-0.338775\pi$
$47$	6.65167	0.970245	0.485123	+	0.874446i	$0.338775\pi$
$48$	24.0200	3.46699
$49$	16.6699	2.38141
$50$	−12.7205	−1.79894
$51$	6.69900	0.938047
$52$	−20.0908	−2.78609
$53$	−13.9066	−1.91022	−0.955111	−	0.296249i	$-0.904264\pi$
$53$	−13.9066	−1.91022	−0.955111	+	0.296249i	$0.904264\pi$
$54$	3.01761	0.410645
$55$	−10.1507	−1.36873
$56$	37.1053	4.95840
$57$	10.7420	1.42281
$58$	2.62733	0.344985
$59$	14.6537	1.90775	0.953877	−	0.300198i	$-0.0970529\pi$
$59$	14.6537	1.90775	0.953877	+	0.300198i	$0.0970529\pi$
$60$	−36.1065	−4.66133
$61$	−2.42549	−0.310552	−0.155276	−	0.987871i	$-0.549627\pi$
$61$	−2.42549	−0.310552	−0.155276	+	0.987871i	$0.549627\pi$
$62$	−0.0865932	−0.0109973
$63$	−12.2151	−1.53896
$64$	10.0911	1.26138
$65$	12.8553	1.59450
$66$	−19.9565	−2.45647
$67$	−5.34866	−0.653443	−0.326721	−	0.945121i	$-0.605944\pi$
$67$	−5.34866	−0.653443	−0.326721	+	0.945121i	$0.605944\pi$
$68$	13.9911	1.69668
$69$	−12.0968	−1.45629
$70$	−40.1000	−4.79287
$71$	4.29396	0.509600	0.254800	−	0.966994i	$-0.417990\pi$
$71$	4.29396	0.509600	0.254800	+	0.966994i	$0.417990\pi$
$72$	−19.1487	−2.25669
$73$	14.1346	1.65433	0.827167	−	0.561956i	$-0.189951\pi$
$73$	14.1346	1.65433	0.827167	+	0.561956i	$0.189951\pi$
$74$	−26.6379	−3.09659
$75$	11.3656	1.31239
$76$	22.4351	2.57348
$77$	−15.7421	−1.79398
$78$	25.2737	2.86168
$79$	−2.47592	−0.278563	−0.139281	−	0.990253i	$-0.544479\pi$
$79$	−2.47592	−0.278563	−0.139281	+	0.990253i	$0.544479\pi$
$80$	−32.0997	−3.58886
$81$	−10.2284	−1.13649
$82$	−14.1122	−1.55843
$83$	−14.2541	−1.56459	−0.782295	−	0.622908i	$-0.785951\pi$
$83$	−14.2541	−1.56459	−0.782295	+	0.622908i	$0.785951\pi$
$84$	−55.9952	−6.10958
$85$	−8.95237	−0.971021
$86$	15.4598	1.66707
$87$	−2.34750	−0.251678
$88$	−24.6776	−2.63064
$89$	6.53199	0.692390	0.346195	−	0.938163i	$-0.387474\pi$
$89$	6.53199	0.692390	0.346195	+	0.938163i	$0.387474\pi$
$90$	20.6941	2.18135
$91$	19.9364	2.08991
$92$	−25.2648	−2.63403
$93$	0.0773703	0.00802293
$94$	−17.4761	−1.80252
$95$	−14.3553	−1.47282
$96$	−27.3010	−2.78640
$97$	−12.8286	−1.30255	−0.651273	−	0.758844i	$-0.725765\pi$
$97$	−12.8286	−1.30255	−0.651273	+	0.758844i	$0.725765\pi$
$98$	−43.7972	−4.42419
$99$	8.12392	0.816484
$100$	23.7376	2.37376
$101$	18.9967	1.89025	0.945124	−	0.326713i	$-0.105941\pi$
$101$	18.9967	1.89025	0.945124	+	0.326713i	$0.105941\pi$
$102$	−17.6005	−1.74270
$103$	17.8209	1.75594	0.877970	−	0.478715i	$-0.158897\pi$
$103$	17.8209	1.75594	0.877970	+	0.478715i	$0.158897\pi$
$104$	31.2527	3.06458
$105$	35.8291	3.49656
$106$	36.5372	3.54881
$107$	−6.10792	−0.590475	−0.295237	−	0.955424i	$-0.595399\pi$
$107$	−6.10792	−0.590475	−0.295237	+	0.955424i	$0.595399\pi$
$108$	−5.63116	−0.541858
$109$	−12.5817	−1.20511	−0.602556	−	0.798077i	$-0.705851\pi$
$109$	−12.5817	−1.20511	−0.602556	+	0.798077i	$0.705851\pi$
$110$	26.6693	2.54282
$111$	23.8007	2.25907
$112$	−49.7813	−4.70389
$113$	0.0651181	0.00612579	0.00306290	−	0.999995i	$-0.499025\pi$
$113$	0.0651181	0.00612579	0.00306290	+	0.999995i	$0.499025\pi$
$114$	−28.2227	−2.64330
$115$	16.1659	1.50748
$116$	−4.90284	−0.455218
$117$	−10.2885	−0.951168
$118$	−38.5001	−3.54423
$119$	−13.8836	−1.27271
$120$	56.1662	5.12725
$121$	−0.530411	−0.0482192
$122$	6.37254	0.576943
$123$	12.6091	1.13693
$124$	0.161591	0.0145113
$125$	0.496936	0.0444473
$126$	32.0932	2.85909
$127$	−10.4595	−0.928129	−0.464064	−	0.885801i	$-0.653609\pi$
$127$	−10.4595	−0.928129	−0.464064	+	0.885801i	$0.653609\pi$
$128$	−3.25279	−0.287509
$129$	−13.8132	−1.21618
$130$	−33.7751	−2.96227
$131$	11.4667	1.00185	0.500924	−	0.865491i	$-0.332994\pi$
$131$	11.4667	1.00185	0.500924	+	0.865491i	$0.332994\pi$
$132$	37.2407	3.24138
$133$	−22.2627	−1.93042
$134$	14.0527	1.21397
$135$	3.60315	0.310110
$136$	−21.7642	−1.86626
$137$	−3.34918	−0.286140	−0.143070	−	0.989713i	$-0.545697\pi$
$137$	−3.34918	−0.286140	−0.143070	+	0.989713i	$0.545697\pi$
$138$	31.7824	2.70549
$139$	−19.6164	−1.66384	−0.831921	−	0.554894i	$-0.812759\pi$
$139$	−19.6164	−1.66384	−0.831921	+	0.554894i	$0.812759\pi$
$140$	74.8305	6.32433
$141$	15.6148	1.31500
$142$	−11.2816	−0.946734
$143$	−13.2591	−1.10878
$144$	25.6903	2.14086
$145$	3.13713	0.260525
$146$	−37.1363	−3.07342
$147$	39.1325	3.22759
$148$	49.7088	4.08604
$149$	7.54351	0.617988	0.308994	−	0.951064i	$-0.400008\pi$
$149$	7.54351	0.617988	0.308994	+	0.951064i	$0.400008\pi$
$150$	−29.8612	−2.43816
$151$	−5.89775	−0.479952	−0.239976	−	0.970779i	$-0.577140\pi$
$151$	−5.89775	−0.479952	−0.239976	+	0.970779i	$0.577140\pi$
$152$	−34.8993	−2.83071
$153$	7.16483	0.579242
$154$	41.3597	3.33286
$155$	−0.103396	−0.00830494
$156$	−47.1631	−3.77607
$157$	22.7853	1.81847	0.909234	−	0.416285i	$-0.136668\pi$
$157$	22.7853	1.81847	0.909234	+	0.416285i	$0.136668\pi$
$158$	6.50505	0.517514
$159$	−32.6457	−2.58897
$160$	36.4844	2.88434
$161$	25.0706	1.97584
$162$	26.8734	2.11137
$163$	1.27085	0.0995403	0.0497701	−	0.998761i	$-0.484151\pi$
$163$	1.27085	0.0995403	0.0497701	+	0.998761i	$0.484151\pi$
$164$	26.3347	2.05639
$165$	−23.8288	−1.85507
$166$	37.4502	2.90670
$167$	12.9948	1.00556	0.502782	−	0.864413i	$-0.332310\pi$
$167$	12.9948	1.00556	0.502782	+	0.864413i	$0.332310\pi$
$168$	87.1045	6.72026
$169$	3.79185	0.291681
$170$	23.5208	1.80396
$171$	11.4889	0.878582
$172$	−28.8495	−2.19975
$173$	−11.5180	−0.875696	−0.437848	−	0.899049i	$-0.644259\pi$
$173$	−11.5180	−0.875696	−0.437848	+	0.899049i	$0.644259\pi$
$174$	6.16764	0.467567
$175$	−23.5552	−1.78060
$176$	33.1080	2.49561
$177$	34.3996	2.58563
$178$	−17.1617	−1.28632
$179$	15.8966	1.18816	0.594082	−	0.804404i	$-0.297515\pi$
$179$	15.8966	1.18816	0.594082	+	0.804404i	$0.297515\pi$
$180$	−38.6173	−2.87836
$181$	16.8109	1.24954	0.624771	−	0.780808i	$-0.285192\pi$
$181$	16.8109	1.24954	0.624771	+	0.780808i	$0.285192\pi$
$182$	−52.3795	−3.88263
$183$	−5.69381	−0.420899
$184$	39.3011	2.89732
$185$	−31.8067	−2.33847
$186$	−0.203277	−0.0149050
$187$	9.23358	0.675226
$188$	32.6121	2.37848
$189$	5.58789	0.406459
$190$	37.7161	2.73621
$191$	2.41132	0.174477	0.0872383	−	0.996187i	$-0.472196\pi$
$191$	2.41132	0.174477	0.0872383	+	0.996187i	$0.472196\pi$
$192$	23.6887	1.70959
$193$	18.6316	1.34113	0.670565	−	0.741851i	$-0.266052\pi$
$193$	18.6316	1.34113	0.670565	+	0.741851i	$0.266052\pi$
$194$	33.7049	2.41987
$195$	30.1777	2.16107
$196$	81.7298	5.83785
$197$	−11.5370	−0.821978	−0.410989	−	0.911640i	$-0.634817\pi$
$197$	−11.5370	−0.821978	−0.410989	+	0.911640i	$0.634817\pi$
$198$	−21.3442	−1.51686
$199$	−15.6223	−1.10744	−0.553718	−	0.832704i	$-0.686791\pi$
$199$	−15.6223	−1.10744	−0.553718	+	0.832704i	$0.686791\pi$
$200$	−36.9255	−2.61103
$201$	−12.5560	−0.885629
$202$	−49.9107	−3.51170
$203$	4.86517	0.341468
$204$	32.8441	2.29955
$205$	−16.8505	−1.17689
$206$	−46.8212	−3.26219
$207$	−12.9380	−0.899255
$208$	−41.9293	−2.90727
$209$	14.8062	1.02417
$210$	−94.1347	−6.49591
$211$	−23.7994	−1.63842	−0.819210	−	0.573494i	$-0.805588\pi$
$211$	−23.7994	−1.63842	−0.819210	+	0.573494i	$0.805588\pi$
$212$	−68.1820	−4.68276
$213$	10.0801	0.690674
$214$	16.0475	1.09698
$215$	18.4596	1.25893
$216$	8.75966	0.596019
$217$	−0.160350	−0.0108852
$218$	33.0563	2.23886
$219$	33.1810	2.24216
$220$	−49.7675	−3.35532
$221$	−11.6938	−0.786608
$222$	−62.5323	−4.19689
$223$	−16.1912	−1.08424	−0.542120	−	0.840301i	$-0.682378\pi$
$223$	−16.1912	−1.08424	−0.542120	+	0.840301i	$0.682378\pi$
$224$	56.5812	3.78049
$225$	12.1560	0.810397
$226$	−0.171086	−0.0113805
$227$	16.1048	1.06891	0.534457	−	0.845196i	$-0.320516\pi$
$227$	16.1048	1.06891	0.534457	+	0.845196i	$0.320516\pi$
$228$	52.6662	3.48791
$229$	−5.31999	−0.351555	−0.175777	−	0.984430i	$-0.556244\pi$
$229$	−5.31999	−0.351555	−0.175777	+	0.984430i	$0.556244\pi$
$230$	−42.4731	−2.80059
$231$	−36.9545	−2.43143
$232$	7.62672	0.500718
$233$	11.4146	0.747795	0.373897	−	0.927470i	$-0.378021\pi$
$233$	11.4146	0.747795	0.373897	+	0.927470i	$0.378021\pi$
$234$	27.0311	1.76708
$235$	−20.8671	−1.36122
$236$	71.8450	4.67671
$237$	−5.81221	−0.377544
$238$	36.4768	2.36444
$239$	5.34773	0.345916	0.172958	−	0.984929i	$-0.444668\pi$
$239$	5.34773	0.345916	0.172958	+	0.984929i	$0.444668\pi$
$240$	−75.3539	−4.86408
$241$	−22.3271	−1.43821	−0.719107	−	0.694899i	$-0.755449\pi$
$241$	−22.3271	−1.43821	−0.719107	+	0.694899i	$0.755449\pi$
$242$	1.39356	0.0895817
$243$	−20.5655	−1.31928
$244$	−11.8918	−0.761293
$245$	−52.2956	−3.34105
$246$	−33.1283	−2.11218
$247$	−18.7512	−1.19311
$248$	−0.251366	−0.0159618
$249$	−33.4614	−2.12053
$250$	−1.30561	−0.0825741
$251$	−22.1691	−1.39930	−0.699651	−	0.714485i	$-0.746661\pi$
$251$	−22.1691	−1.39930	−0.699651	+	0.714485i	$0.746661\pi$
$252$	−59.8890	−3.77265
$253$	−16.6737	−1.04827
$254$	27.4805	1.72428
$255$	−21.0156	−1.31605
$256$	−11.6360	−0.727249
$257$	7.37507	0.460044	0.230022	−	0.973185i	$-0.426120\pi$
$257$	7.37507	0.460044	0.230022	+	0.973185i	$0.426120\pi$
$258$	36.2918	2.25943
$259$	−49.3269	−3.06502
$260$	63.0275	3.90880
$261$	−2.51073	−0.155411
$262$	−30.1267	−1.86123
$263$	−29.9704	−1.84806	−0.924028	−	0.382325i	$-0.875123\pi$
$263$	−29.9704	−1.84806	−0.924028	+	0.382325i	$0.875123\pi$
$264$	−57.9305	−3.56537
$265$	43.6269	2.67998
$266$	58.4913	3.58633
$267$	15.3338	0.938415
$268$	−26.2236	−1.60186
$269$	−10.5037	−0.640424	−0.320212	−	0.947346i	$-0.603754\pi$
$269$	−10.5037	−0.640424	−0.320212	+	0.947346i	$0.603754\pi$
$270$	−9.46665	−0.576122
$271$	−18.8471	−1.14488	−0.572441	−	0.819946i	$-0.694003\pi$
$271$	−18.8471	−1.14488	−0.572441	+	0.819946i	$0.694003\pi$
$272$	29.1994	1.77047
$273$	46.8007	2.83251
$274$	8.79940	0.531591
$275$	15.6658	0.944685
$276$	−59.3089	−3.56998
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	51.5387	3.09109
$279$	0.0827504	0.00495414
$280$	−116.404	−6.95648
$281$	8.16665	0.487182	0.243591	−	0.969878i	$-0.421675\pi$
$281$	8.16665	0.487182	0.243591	+	0.969878i	$0.421675\pi$
$282$	−41.0250	−2.44301
$283$	−12.8814	−0.765719	−0.382860	−	0.923807i	$-0.625061\pi$
$283$	−12.8814	−0.765719	−0.382860	+	0.923807i	$0.625061\pi$
$284$	21.0526	1.24924
$285$	−33.6990	−1.99616
$286$	34.8360	2.05990
$287$	−26.1323	−1.54254
$288$	−29.1995	−1.72060
$289$	−8.85652	−0.520972
$290$	−8.24227	−0.484003
$291$	−30.1150	−1.76538
$292$	69.2999	4.05547
$293$	12.5880	0.735399	0.367700	−	0.929945i	$-0.380145\pi$
$293$	12.5880	0.735399	0.367700	+	0.929945i	$0.380145\pi$
$294$	−102.814	−5.99622
$295$	−45.9707	−2.67652
$296$	−77.3256	−4.49446
$297$	−3.71633	−0.215643
$298$	−19.8193	−1.14810
$299$	21.1162	1.22118
$300$	55.7239	3.21722
$301$	28.6278	1.65008
$302$	15.4953	0.891656
$303$	44.5948	2.56190
$304$	46.8218	2.68541
$305$	7.60907	0.435694
$306$	−18.8243	−1.07612
$307$	2.81852	0.160861	0.0804306	−	0.996760i	$-0.474370\pi$
$307$	2.81852	0.160861	0.0804306	+	0.996760i	$0.474370\pi$
$308$	−77.1811	−4.39780
$309$	41.8344	2.37987
$310$	0.271654	0.0154289
$311$	18.0923	1.02592	0.512961	−	0.858412i	$-0.328549\pi$
$311$	18.0923	1.02592	0.512961	+	0.858412i	$0.328549\pi$
$312$	73.3655	4.15350
$313$	−27.0067	−1.52651	−0.763253	−	0.646099i	$-0.776399\pi$
$313$	−27.0067	−1.52651	−0.763253	+	0.646099i	$0.776399\pi$
$314$	−59.8645	−3.37835
$315$	38.3205	2.15912
$316$	−12.1391	−0.682875
$317$	−5.76049	−0.323542	−0.161771	−	0.986828i	$-0.551721\pi$
$317$	−5.76049	−0.323542	−0.161771	+	0.986828i	$0.551721\pi$
$318$	85.7710	4.80980
$319$	−3.23567	−0.181163
$320$	−31.6570	−1.76968
$321$	−14.3383	−0.800287
$322$	−65.8687	−3.67072
$323$	13.0582	0.726580
$324$	−50.1483	−2.78602
$325$	−19.8398	−1.10052
$326$	−3.33892	−0.184926
$327$	−29.5356	−1.63332
$328$	−40.9654	−2.26194
$329$	−32.3615	−1.78415
$330$	62.6060	3.44635
$331$	−27.7780	−1.52682	−0.763409	−	0.645915i	$-0.776476\pi$
$331$	−27.7780	−1.52682	−0.763409	+	0.645915i	$0.776476\pi$
$332$	−69.8856	−3.83547
$333$	25.4558	1.39497
$334$	−34.1415	−1.86814
$335$	16.7795	0.916760
$336$	−116.861	−6.37531
$337$	−3.58563	−0.195322	−0.0976608	−	0.995220i	$-0.531136\pi$
$337$	−3.58563	−0.195322	−0.0976608	+	0.995220i	$0.531136\pi$
$338$	−9.96244	−0.541885
$339$	0.152864	0.00830245
$340$	−43.8921	−2.38038
$341$	0.106643	0.00577507
$342$	−30.1852	−1.63223
$343$	−47.0456	−2.54023
$344$	44.8774	2.41963
$345$	37.9494	2.04313
$346$	30.2615	1.62687
$347$	−2.28305	−0.122561	−0.0612803	−	0.998121i	$-0.519518\pi$
$347$	−2.28305	−0.122561	−0.0612803	+	0.998121i	$0.519518\pi$
$348$	−11.5094	−0.616969
$349$	16.8543	0.902188	0.451094	−	0.892476i	$-0.351034\pi$
$349$	16.8543	0.902188	0.451094	+	0.892476i	$0.351034\pi$
$350$	61.8872	3.30801
$351$	4.70651	0.251215
$352$	−37.6304	−2.00571
$353$	24.6536	1.31218	0.656089	−	0.754683i	$-0.272209\pi$
$353$	24.6536	1.31218	0.656089	+	0.754683i	$0.272209\pi$
$354$	−90.3789	−4.80358
$355$	−13.4707	−0.714952
$356$	32.0253	1.69734
$357$	−32.5918	−1.72494
$358$	−41.7655	−2.20737
$359$	−21.6946	−1.14500	−0.572498	−	0.819906i	$-0.694026\pi$
$359$	−21.6946	−1.14500	−0.572498	+	0.819906i	$0.694026\pi$
$360$	60.0719	3.16606
$361$	1.93915	0.102060
$362$	−44.1677	−2.32140
$363$	−1.24514	−0.0653528
$364$	97.7452	5.12324
$365$	−44.3422	−2.32098
$366$	14.9595	0.781946
$367$	4.33693	0.226386	0.113193	−	0.993573i	$-0.463892\pi$
$367$	4.33693	0.226386	0.113193	+	0.993573i	$0.463892\pi$
$368$	−52.7273	−2.74860
$369$	13.4859	0.702049
$370$	83.5665	4.34442
$371$	67.6581	3.51263
$372$	0.379334	0.0196676
$373$	11.4265	0.591643	0.295821	−	0.955243i	$-0.404407\pi$
$373$	11.4265	0.591643	0.295821	+	0.955243i	$0.404407\pi$
$374$	−24.2596	−1.25443
$375$	1.16655	0.0602406
$376$	−50.7304	−2.61622
$377$	4.09779	0.211047
$378$	−14.6812	−0.755120
$379$	12.2132	0.627352	0.313676	−	0.949530i	$-0.398439\pi$
$379$	12.2132	0.627352	0.313676	+	0.949530i	$0.398439\pi$
$380$	−70.3818	−3.61051
$381$	−24.5536	−1.25792
$382$	−6.33531	−0.324143
$383$	−2.03234	−0.103848	−0.0519239	−	0.998651i	$-0.516535\pi$
$383$	−2.03234	−0.103848	−0.0519239	+	0.998651i	$0.516535\pi$
$384$	−7.63590	−0.389668
$385$	49.3851	2.51690
$386$	−48.9512	−2.49155
$387$	−14.7737	−0.750991
$388$	−62.8966	−3.19309
$389$	−6.04761	−0.306626	−0.153313	−	0.988178i	$-0.548994\pi$
$389$	−6.04761	−0.306626	−0.153313	+	0.988178i	$0.548994\pi$
$390$	−79.2868	−4.01484
$391$	−14.7053	−0.743677
$392$	−127.136	−6.42136
$393$	26.9180	1.35783
$394$	30.3115	1.52707
$395$	7.76729	0.390815
$396$	39.8303	2.00155
$397$	3.56934	0.179140	0.0895701	−	0.995981i	$-0.471451\pi$
$397$	3.56934	0.179140	0.0895701	+	0.995981i	$0.471451\pi$
$398$	41.0449	2.05740
$399$	−52.2616	−2.61635
$400$	49.5401	2.47701
$401$	−17.2414	−0.860995	−0.430497	−	0.902592i	$-0.641662\pi$
$401$	−17.2414	−0.860995	−0.430497	+	0.902592i	$0.641662\pi$
$402$	32.9886	1.64532
$403$	−0.135058	−0.00672770
$404$	93.1381	4.63379
$405$	32.0879	1.59446
$406$	−12.7824	−0.634379
$407$	32.8058	1.62612
$408$	−51.0914	−2.52940
$409$	−27.6623	−1.36781	−0.683905	−	0.729571i	$-0.739720\pi$
$409$	−27.6623	−1.36781	−0.683905	+	0.729571i	$0.739720\pi$
$410$	44.2718	2.18643
$411$	−7.86219	−0.387813
$412$	87.3728	4.30455
$413$	−71.2929	−3.50809
$414$	33.9924	1.67064
$415$	44.7170	2.19507
$416$	47.6567	2.33656
$417$	−46.0494	−2.25505
$418$	−38.9008	−1.90270
$419$	31.8032	1.55369	0.776844	−	0.629693i	$-0.216819\pi$
$419$	31.8032	1.55369	0.776844	+	0.629693i	$0.216819\pi$
$420$	175.664	8.57154
$421$	−27.1558	−1.32349	−0.661747	−	0.749727i	$-0.730185\pi$
$421$	−27.1558	−1.32349	−0.661747	+	0.749727i	$0.730185\pi$
$422$	62.5288	3.04386
$423$	16.7006	0.812009
$424$	106.062	5.15082
$425$	13.8164	0.670192
$426$	−26.4836	−1.28313
$427$	11.8004	0.571061
$428$	−29.9462	−1.44750
$429$	−31.1257	−1.50276
$430$	−48.4994	−2.33885
$431$	−4.77858	−0.230176	−0.115088	−	0.993355i	$-0.536715\pi$
$431$	−4.77858	−0.230176	−0.115088	+	0.993355i	$0.536715\pi$
$432$	−11.7522	−0.565427
$433$	2.71210	0.130335	0.0651675	−	0.997874i	$-0.479242\pi$
$433$	2.71210	0.130335	0.0651675	+	0.997874i	$0.479242\pi$
$434$	0.421290	0.0202226
$435$	7.36440	0.353096
$436$	−61.6863	−2.95424
$437$	−23.5802	−1.12799
$438$	−87.1773	−4.16549
$439$	6.36235	0.303658	0.151829	−	0.988407i	$-0.451484\pi$
$439$	6.36235	0.303658	0.151829	+	0.988407i	$0.451484\pi$
$440$	77.4168	3.69070
$441$	41.8536	1.99303
$442$	30.7233	1.46136
$443$	16.4697	0.782499	0.391249	−	0.920285i	$-0.372043\pi$
$443$	16.4697	0.782499	0.391249	+	0.920285i	$0.372043\pi$
$444$	116.691	5.53792
$445$	−20.4917	−0.971401
$446$	42.5395	2.01430
$447$	17.7083	0.837576
$448$	−49.0947	−2.31951
$449$	−29.3421	−1.38474	−0.692369	−	0.721544i	$-0.743433\pi$
$449$	−29.3421	−1.38474	−0.692369	+	0.721544i	$0.743433\pi$
$450$	−31.9377	−1.50556
$451$	17.3798	0.818383
$452$	0.319264	0.0150169
$453$	−13.8449	−0.650492
$454$	−42.3126	−1.98583
$455$	−62.5432	−2.93207
$456$	−81.9260	−3.83654
$457$	−11.2685	−0.527118	−0.263559	−	0.964643i	$-0.584896\pi$
$457$	−11.2685	−0.527118	−0.263559	+	0.964643i	$0.584896\pi$
$458$	13.9773	0.653119
$459$	−3.27759	−0.152985
$460$	79.2589	3.69547
$461$	−6.46359	−0.301039	−0.150520	−	0.988607i	$-0.548095\pi$
$461$	−6.46359	−0.301039	−0.150520	+	0.988607i	$0.548095\pi$
$462$	97.0916	4.51711
$463$	26.6118	1.23676	0.618378	−	0.785881i	$-0.287790\pi$
$463$	26.6118	1.23676	0.618378	+	0.785881i	$0.287790\pi$
$464$	−10.2322	−0.475017
$465$	−0.242721	−0.0112559
$466$	−29.9899	−1.38925
$467$	−19.2865	−0.892473	−0.446237	−	0.894915i	$-0.647236\pi$
$467$	−19.2865	−0.892473	−0.446237	+	0.894915i	$0.647236\pi$
$468$	−50.4427	−2.33171
$469$	26.0221	1.20159
$470$	54.8248	2.52888
$471$	53.4885	2.46462
$472$	−111.760	−5.14416
$473$	−19.0395	−0.875435
$474$	15.2706	0.701401
$475$	22.1548	1.01653
$476$	−68.0693	−3.11995
$477$	−34.9158	−1.59869
$478$	−14.0502	−0.642643
$479$	−21.7969	−0.995924	−0.497962	−	0.867199i	$-0.665918\pi$
$479$	−21.7969	−0.995924	−0.497962	+	0.867199i	$0.665918\pi$
$480$	85.6469	3.90923
$481$	−41.5465	−1.89436
$482$	58.6606	2.67192
$483$	58.8532	2.67791
$484$	−2.60052	−0.118206
$485$	40.2450	1.82743
$486$	54.0323	2.45096
$487$	19.2441	0.872032	0.436016	−	0.899939i	$-0.356389\pi$
$487$	19.2441	0.872032	0.436016	+	0.899939i	$0.356389\pi$
$488$	18.4985	0.837387
$489$	2.98330	0.134910
$490$	137.398	6.20699
$491$	−8.01689	−0.361797	−0.180899	−	0.983502i	$-0.557901\pi$
$491$	−8.01689	−0.361797	−0.180899	+	0.983502i	$0.557901\pi$
$492$	61.8205	2.78708
$493$	−2.85368	−0.128523
$494$	49.2655	2.21656
$495$	−25.4858	−1.14550
$496$	0.337239	0.0151425
$497$	−20.8909	−0.937083
$498$	87.9141	3.93952
$499$	−17.2088	−0.770373	−0.385187	−	0.922839i	$-0.625863\pi$
$499$	−17.2088	−0.770373	−0.385187	+	0.922839i	$0.625863\pi$
$500$	2.43640	0.108959
$501$	30.5051	1.36287
$502$	58.2455	2.59962
$503$	2.54692	0.113561	0.0567807	−	0.998387i	$-0.481916\pi$
$503$	2.54692	0.113561	0.0567807	+	0.998387i	$0.481916\pi$
$504$	93.1615	4.14974
$505$	−59.5953	−2.65196
$506$	43.8073	1.94747
$507$	8.90136	0.395323
$508$	−51.2812	−2.27523
$509$	22.1270	0.980762	0.490381	−	0.871508i	$-0.336858\pi$
$509$	22.1270	0.980762	0.490381	+	0.871508i	$0.336858\pi$
$510$	55.2149	2.44496
$511$	−68.7675	−3.04209
$512$	37.0771	1.63859
$513$	−5.25568	−0.232044
$514$	−19.3767	−0.854671
$515$	−55.9064	−2.46353
$516$	−67.7240	−2.98138
$517$	21.5226	0.946564
$518$	129.598	5.69420
$519$	−27.0384	−1.18685
$520$	−98.0437	−4.29950
$521$	−16.6435	−0.729166	−0.364583	−	0.931171i	$-0.618788\pi$
$521$	−16.6435	−0.729166	−0.364583	+	0.931171i	$0.618788\pi$
$522$	6.59652	0.288722
$523$	−42.5072	−1.85871	−0.929354	−	0.369189i	$-0.879636\pi$
$523$	−42.5072	−1.85871	−0.929354	+	0.369189i	$0.879636\pi$
$524$	56.2193	2.45595
$525$	−55.2957	−2.41330
$526$	78.7421	3.43332
$527$	0.0940534	0.00409703
$528$	77.7209	3.38237
$529$	3.55429	0.154534
$530$	−114.622	−4.97887
$531$	36.7916	1.59662
$532$	−109.150	−4.73227
$533$	−22.0105	−0.953379
$534$	−40.2870	−1.74339
$535$	19.1613	0.828417
$536$	40.7927	1.76198
$537$	37.3171	1.61035
$538$	27.5967	1.18978
$539$	53.9383	2.32329
$540$	17.6657	0.760210
$541$	−8.40944	−0.361550	−0.180775	−	0.983524i	$-0.557861\pi$
$541$	−8.40944	−0.361550	−0.180775	+	0.983524i	$0.557861\pi$
$542$	49.5176	2.12696
$543$	39.4634	1.69354
$544$	−33.1879	−1.42292
$545$	39.4706	1.69073
$546$	−122.961	−5.26223
$547$	−34.5535	−1.47740	−0.738700	−	0.674034i	$-0.764560\pi$
$547$	−34.5535	−1.47740	−0.738700	+	0.674034i	$0.764560\pi$
$548$	−16.4205	−0.701450
$549$	−6.08975	−0.259904
$550$	−41.1592	−1.75504
$551$	−4.57593	−0.194941
$552$	92.2592	3.92681
$553$	12.0458	0.512239
$554$	2.62733	0.111624
$555$	−74.6660	−3.16940
$556$	−96.1761	−4.07878
$557$	−35.6974	−1.51255	−0.756274	−	0.654255i	$-0.772982\pi$
$557$	−35.6974	−1.51255	−0.756274	+	0.654255i	$0.772982\pi$
$558$	−0.217412	−0.00920380
$559$	24.1123	1.01984
$560$	156.171	6.59941
$561$	21.6758	0.915152
$562$	−21.4565	−0.905086
$563$	−3.85171	−0.162330	−0.0811650	−	0.996701i	$-0.525864\pi$
$563$	−3.85171	−0.162330	−0.0811650	+	0.996701i	$0.525864\pi$
$564$	76.5567	3.22362
$565$	−0.204284	−0.00859429
$566$	33.8436	1.42255
$567$	49.7630	2.08985
$568$	−32.7488	−1.37411
$569$	−0.810620	−0.0339830	−0.0169915	−	0.999856i	$-0.505409\pi$
$569$	−0.810620	−0.0339830	−0.0169915	+	0.999856i	$0.505409\pi$
$570$	88.5383	3.70846
$571$	37.8767	1.58509	0.792544	−	0.609814i	$-0.208756\pi$
$571$	37.8767	1.58509	0.792544	+	0.609814i	$0.208756\pi$
$572$	−65.0073	−2.71809
$573$	5.66055	0.236473
$574$	68.6581	2.86574
$575$	−24.9492	−1.04045
$576$	25.3360	1.05567
$577$	1.48150	0.0616756	0.0308378	−	0.999524i	$-0.490182\pi$
$577$	1.48150	0.0616756	0.0308378	+	0.999524i	$0.490182\pi$
$578$	23.2690	0.967861
$579$	43.7375	1.81767
$580$	15.3809	0.638656
$581$	69.3486	2.87707
$582$	79.1221	3.27971
$583$	−44.9973	−1.86360
$584$	−107.801	−4.46083
$585$	32.2762	1.33446
$586$	−33.0728	−1.36622
$587$	12.8643	0.530966	0.265483	−	0.964116i	$-0.414469\pi$
$587$	12.8643	0.530966	0.265483	+	0.964116i	$0.414469\pi$
$588$	191.860	7.91219
$589$	0.150817	0.00621429
$590$	120.780	4.97243
$591$	−27.0831	−1.11405
$592$	103.742	4.26376
$593$	−15.0409	−0.617655	−0.308828	−	0.951118i	$-0.599937\pi$
$593$	−15.0409	−0.617655	−0.308828	+	0.951118i	$0.599937\pi$
$594$	9.76402	0.400622
$595$	43.5548	1.78557
$596$	36.9846	1.51495
$597$	−36.6733	−1.50094
$598$	−55.4793	−2.26872
$599$	−8.86064	−0.362036	−0.181018	−	0.983480i	$-0.557939\pi$
$599$	−8.86064	−0.362036	−0.181018	+	0.983480i	$0.557939\pi$
$600$	−86.6824	−3.53879
$601$	−17.0671	−0.696182	−0.348091	−	0.937461i	$-0.613170\pi$
$601$	−17.0671	−0.696182	−0.348091	+	0.937461i	$0.613170\pi$
$602$	−75.2145	−3.06552
$603$	−13.4291	−0.546874
$604$	−28.9158	−1.17657
$605$	1.66397	0.0676500
$606$	−117.165	−4.75950
$607$	−22.1215	−0.897883	−0.448941	−	0.893561i	$-0.648199\pi$
$607$	−22.1215	−0.897883	−0.448941	+	0.893561i	$0.648199\pi$
$608$	−53.2174	−2.15825
$609$	11.4210	0.462801
$610$	−19.9915	−0.809432
$611$	−27.2571	−1.10270
$612$	35.1280	1.41997
$613$	−12.7811	−0.516225	−0.258112	−	0.966115i	$-0.583100\pi$
$613$	−12.7811	−0.516225	−0.258112	+	0.966115i	$0.583100\pi$
$614$	−7.40516	−0.298848
$615$	−39.5565	−1.59507
$616$	120.061	4.83738
$617$	0.580925	0.0233871	0.0116936	−	0.999932i	$-0.496278\pi$
$617$	0.580925	0.0233871	0.0116936	+	0.999932i	$0.496278\pi$
$618$	−109.913	−4.42133
$619$	−5.05500	−0.203177	−0.101589	−	0.994826i	$-0.532393\pi$
$619$	−5.05500	−0.203177	−0.101589	+	0.994826i	$0.532393\pi$
$620$	−0.506933	−0.0203589
$621$	5.91857	0.237504
$622$	−47.5345	−1.90596
$623$	−31.7793	−1.27321
$624$	−98.4289	−3.94031
$625$	−25.7669	−1.03068
$626$	70.9553	2.83594
$627$	34.7575	1.38808
$628$	111.713	4.45783
$629$	28.9328	1.15363
$630$	−100.681	−4.01121
$631$	10.1293	0.403241	0.201620	−	0.979464i	$-0.435379\pi$
$631$	10.1293	0.403241	0.201620	+	0.979464i	$0.435379\pi$
$632$	18.8831	0.751131
$633$	−55.8690	−2.22059
$634$	15.1347	0.601076
$635$	32.8128	1.30213
$636$	−160.057	−6.34667
$637$	−68.3096	−2.70653
$638$	8.50117	0.336565
$639$	10.7810	0.426490
$640$	10.2044	0.403365
$641$	−24.3257	−0.960806	−0.480403	−	0.877048i	$-0.659509\pi$
$641$	−24.3257	−0.960806	−0.480403	+	0.877048i	$0.659509\pi$
$642$	37.6714	1.48677
$643$	−23.8111	−0.939018	−0.469509	−	0.882928i	$-0.655569\pi$
$643$	−23.8111	−0.939018	−0.469509	+	0.882928i	$0.655569\pi$
$644$	122.917	4.84362
$645$	43.3338	1.70627
$646$	−34.3083	−1.34984
$647$	−48.3257	−1.89988	−0.949940	−	0.312433i	$-0.898856\pi$
$647$	−48.3257	−1.89988	−0.949940	+	0.312433i	$0.898856\pi$
$648$	78.0092	3.06449
$649$	47.4147	1.86119
$650$	52.1257	2.04454
$651$	−0.376420	−0.0147531
$652$	6.23075	0.244015
$653$	41.9323	1.64094	0.820470	−	0.571690i	$-0.193712\pi$
$653$	41.9323	1.64094	0.820470	+	0.571690i	$0.193712\pi$
$654$	77.5996	3.03438
$655$	−35.9725	−1.40556
$656$	54.9602	2.14584
$657$	35.4883	1.38453
$658$	85.0242	3.31459
$659$	29.5103	1.14956	0.574778	−	0.818309i	$-0.305088\pi$
$659$	29.5103	1.14956	0.574778	+	0.818309i	$0.305088\pi$
$660$	−116.829	−4.54756
$661$	17.1108	0.665534	0.332767	−	0.943009i	$-0.392018\pi$
$661$	17.1108	0.665534	0.332767	+	0.943009i	$0.392018\pi$
$662$	72.9819	2.83652
$663$	−27.4511	−1.06611
$664$	108.712	4.21884
$665$	69.8410	2.70832
$666$	−66.8806	−2.59157
$667$	5.15309	0.199528
$668$	63.7113	2.46506
$669$	−38.0087	−1.46950
$670$	−44.0851	−1.70316
$671$	−7.84808	−0.302972
$672$	132.824	5.12380
$673$	19.2093	0.740464	0.370232	−	0.928939i	$-0.379278\pi$
$673$	19.2093	0.740464	0.370232	+	0.928939i	$0.379278\pi$
$674$	9.42062	0.362869
$675$	−5.56081	−0.214036
$676$	18.5909	0.715033
$677$	−21.0494	−0.808996	−0.404498	−	0.914539i	$-0.632554\pi$
$677$	−21.0494	−0.808996	−0.404498	+	0.914539i	$0.632554\pi$
$678$	−0.401625	−0.0154243
$679$	62.4133	2.39520
$680$	68.2772	2.61831
$681$	37.8060	1.44873
$682$	−0.280187	−0.0107289
$683$	30.5031	1.16717	0.583585	−	0.812052i	$-0.301650\pi$
$683$	30.5031	1.16717	0.583585	+	0.812052i	$0.301650\pi$
$684$	56.3285	2.15377
$685$	10.5068	0.401445
$686$	123.604	4.71923
$687$	−12.4887	−0.476472
$688$	−60.2085	−2.29543
$689$	56.9864	2.17101
$690$	−99.7054	−3.79572
$691$	41.8201	1.59091	0.795455	−	0.606012i	$-0.207232\pi$
$691$	41.8201	1.59091	0.795455	+	0.606012i	$0.207232\pi$
$692$	−56.4708	−2.14670
$693$	−39.5242	−1.50140
$694$	5.99832	0.227693
$695$	61.5392	2.33432
$696$	17.9037	0.678637
$697$	15.3280	0.580589
$698$	−44.2816	−1.67609
$699$	26.7957	1.01351
$700$	−115.487	−4.36501
$701$	−10.4862	−0.396056	−0.198028	−	0.980196i	$-0.563454\pi$
$701$	−10.4862	−0.396056	−0.198028	+	0.980196i	$0.563454\pi$
$702$	−12.3655	−0.466707
$703$	46.3944	1.74980
$704$	32.6514	1.23060
$705$	−48.9855	−1.84490
$706$	−64.7731	−2.43777
$707$	−92.4224	−3.47590
$708$	168.656	6.33847
$709$	26.0658	0.978922	0.489461	−	0.872025i	$-0.337194\pi$
$709$	26.0658	0.978922	0.489461	+	0.872025i	$0.337194\pi$
$710$	35.3920	1.32824
$711$	−6.21638	−0.233132
$712$	−49.8177	−1.86700
$713$	−0.169839	−0.00636051
$714$	85.6292	3.20459
$715$	41.5956	1.55559
$716$	77.9384	2.91269
$717$	12.5538	0.468829
$718$	56.9988	2.12717
$719$	−38.7730	−1.44599	−0.722995	−	0.690854i	$-0.757235\pi$
$719$	−38.7730	−1.44599	−0.722995	+	0.690854i	$0.757235\pi$
$720$	−80.5938	−3.00356
$721$	−86.7015	−3.22893
$722$	−5.09478	−0.189608
$723$	−52.4128	−1.94925
$724$	82.4211	3.06316
$725$	−4.84160	−0.179812
$726$	3.27138	0.121412
$727$	−7.85839	−0.291452	−0.145726	−	0.989325i	$-0.546552\pi$
$727$	−7.85839	−0.291452	−0.145726	+	0.989325i	$0.546552\pi$
$728$	−152.050	−5.63533
$729$	−17.5922	−0.651563
$730$	116.502	4.31192
$731$	−16.7917	−0.621064
$732$	−27.9159	−1.03180
$733$	39.9939	1.47721	0.738604	−	0.674140i	$-0.235485\pi$
$733$	39.9939	1.47721	0.738604	+	0.674140i	$0.235485\pi$
$734$	−11.3945	−0.420580
$735$	−122.764	−4.52821
$736$	59.9296	2.20904
$737$	−17.3065	−0.637494
$738$	−35.4319	−1.30427
$739$	−0.409742	−0.0150726	−0.00753630	−	0.999972i	$-0.502399\pi$
$739$	−0.409742	−0.0150726	−0.00753630	+	0.999972i	$0.502399\pi$
$740$	−155.943	−5.73259
$741$	−44.0183	−1.61705
$742$	−177.760	−6.52577
$743$	−32.8813	−1.20630	−0.603149	−	0.797629i	$-0.706087\pi$
$743$	−32.8813	−1.20630	−0.603149	+	0.797629i	$0.706087\pi$
$744$	−0.590081	−0.0216334
$745$	−23.6650	−0.867018
$746$	−30.0212	−1.09915
$747$	−35.7882	−1.30942
$748$	45.2708	1.65526
$749$	29.7161	1.08580
$750$	−3.06492	−0.111915
$751$	−24.2104	−0.883451	−0.441725	−	0.897150i	$-0.645633\pi$
$751$	−24.2104	−0.883451	−0.441725	+	0.897150i	$0.645633\pi$
$752$	68.0611	2.48193
$753$	−52.0419	−1.89651
$754$	−10.7662	−0.392083
$755$	18.5020	0.673358
$756$	27.3965	0.996403
$757$	−41.5183	−1.50901	−0.754504	−	0.656295i	$-0.772123\pi$
$757$	−41.5183	−1.50901	−0.754504	+	0.656295i	$0.772123\pi$
$758$	−32.0882	−1.16549
$759$	−39.1414	−1.42074
$760$	109.484	3.97139
$761$	5.71596	0.207203	0.103602	−	0.994619i	$-0.466963\pi$
$761$	5.71596	0.207203	0.103602	+	0.994619i	$0.466963\pi$
$762$	64.5103	2.33696
$763$	61.2123	2.21603
$764$	11.8223	0.427716
$765$	−22.4770	−0.812658
$766$	5.33962	0.192928
$767$	−60.0479	−2.16820
$768$	−27.3154	−0.985660
$769$	12.8469	0.463271	0.231635	−	0.972803i	$-0.425592\pi$
$769$	12.8469	0.463271	0.231635	+	0.972803i	$0.425592\pi$
$770$	−129.751	−4.67589
$771$	17.3130	0.623511
$772$	91.3476	3.28767
$773$	4.05774	0.145947	0.0729734	−	0.997334i	$-0.476751\pi$
$773$	4.05774	0.145947	0.0729734	+	0.997334i	$0.476751\pi$
$774$	38.8154	1.39519
$775$	0.159573	0.00573201
$776$	97.8400	3.51225
$777$	−115.795	−4.15411
$778$	15.8890	0.569650
$779$	24.5787	0.880625
$780$	147.957	5.29770
$781$	13.8939	0.497162
$782$	38.6355	1.38160
$783$	1.14855	0.0410458
$784$	170.569	6.09176
$785$	−71.4806	−2.55125
$786$	−70.7222	−2.52258
$787$	−22.7182	−0.809818	−0.404909	−	0.914357i	$-0.632697\pi$
$787$	−22.7182	−0.809818	−0.404909	+	0.914357i	$0.632697\pi$
$788$	−56.5641	−2.01501
$789$	−70.3554	−2.50472
$790$	−20.4072	−0.726056
$791$	−0.316811	−0.0112645
$792$	−61.9588	−2.20161
$793$	9.93912	0.352949
$794$	−9.37783	−0.332807
$795$	102.414	3.63225
$796$	−76.5937	−2.71479
$797$	0.591222	0.0209422	0.0104711	−	0.999945i	$-0.496667\pi$
$797$	0.591222	0.0209422	0.0104711	+	0.999945i	$0.496667\pi$
$798$	137.308	4.86066
$799$	18.9817	0.671525
$800$	−56.3071	−1.99076
$801$	16.4001	0.579469
$802$	45.2988	1.59956
$803$	45.7351	1.61396
$804$	−61.5599	−2.17105
$805$	−78.6499	−2.77204
$806$	0.354840	0.0124987
$807$	−24.6575	−0.867984
$808$	−144.883	−5.09696
$809$	4.13957	0.145540	0.0727698	−	0.997349i	$-0.476816\pi$
$809$	4.13957	0.145540	0.0727698	+	0.997349i	$0.476816\pi$
$810$	−84.3054	−2.96219
$811$	−41.2657	−1.44904	−0.724518	−	0.689256i	$-0.757938\pi$
$811$	−41.2657	−1.44904	−0.724518	+	0.689256i	$0.757938\pi$
$812$	23.8532	0.837082
$813$	−44.2436	−1.55169
$814$	−86.1915	−3.02101
$815$	−3.98681	−0.139652
$816$	68.5454	2.39957
$817$	−26.9258	−0.942016
$818$	72.6778	2.54112
$819$	50.0551	1.74907
$820$	−82.6154	−2.88505
$821$	−43.5123	−1.51859	−0.759295	−	0.650747i	$-0.774456\pi$
$821$	−43.5123	−1.51859	−0.759295	+	0.650747i	$0.774456\pi$
$822$	20.6565	0.720480
$823$	−5.37175	−0.187247	−0.0936236	−	0.995608i	$-0.529845\pi$
$823$	−5.37175	−0.187247	−0.0936236	+	0.995608i	$0.529845\pi$
$824$	−135.915	−4.73481
$825$	36.7755	1.28036
$826$	187.310	6.51734
$827$	−7.82279	−0.272025	−0.136012	−	0.990707i	$-0.543429\pi$
$827$	−7.82279	−0.272025	−0.136012	+	0.990707i	$0.543429\pi$
$828$	−63.4331	−2.20445
$829$	6.79456	0.235985	0.117992	−	0.993015i	$-0.462354\pi$
$829$	6.79456	0.235985	0.117992	+	0.993015i	$0.462354\pi$
$830$	−117.486	−4.07800
$831$	−2.34750	−0.0814337
$832$	−41.3510	−1.43359
$833$	47.5705	1.64822
$834$	120.987	4.18943
$835$	−40.7663	−1.41077
$836$	72.5926	2.51067
$837$	−0.0378547	−0.00130845
$838$	−83.5574	−2.88644
$839$	−0.354714	−0.0122461	−0.00612304	−	0.999981i	$-0.501949\pi$
$839$	−0.354714	−0.0122461	−0.00612304	+	0.999981i	$0.501949\pi$
$840$	−273.258	−9.42830
$841$	1.00000	0.0344828
$842$	71.3472	2.45879
$843$	19.1712	0.660290
$844$	−116.685	−4.01646
$845$	−11.8955	−0.409219
$846$	−43.8778	−1.50855
$847$	2.58054	0.0886685
$848$	−142.295	−4.88644
$849$	−30.2390	−1.03780
$850$	−36.3001	−1.24508
$851$	−52.2460	−1.79097
$852$	49.4209	1.69313
$853$	22.7040	0.777369	0.388685	−	0.921371i	$-0.372930\pi$
$853$	22.7040	0.777369	0.388685	+	0.921371i	$0.372930\pi$
$854$	−31.0035	−1.06092
$855$	−36.0423	−1.23262
$856$	46.5834	1.59219
$857$	31.6215	1.08017	0.540084	−	0.841611i	$-0.318392\pi$
$857$	31.6215	1.08017	0.540084	+	0.841611i	$0.318392\pi$
$858$	81.7773	2.79183
$859$	−12.8810	−0.439494	−0.219747	−	0.975557i	$-0.570523\pi$
$859$	−12.8810	−0.439494	−0.219747	+	0.975557i	$0.570523\pi$
$860$	90.5046	3.08618
$861$	−61.3455	−2.09065
$862$	12.5549	0.427622
$863$	−20.7359	−0.705859	−0.352930	−	0.935650i	$-0.614815\pi$
$863$	−20.7359	−0.705859	−0.352930	+	0.935650i	$0.614815\pi$
$864$	13.3575	0.454430
$865$	36.1334	1.22857
$866$	−7.12556	−0.242136
$867$	−20.7906	−0.706087
$868$	−0.786169	−0.0266843
$869$	−8.01128	−0.271764
$870$	−19.3487	−0.655982
$871$	21.9177	0.742652
$872$	95.9573	3.24953
$873$	−32.2092	−1.09012
$874$	61.9528	2.09558
$875$	−2.41768	−0.0817324
$876$	162.681	5.49649
$877$	−16.1605	−0.545700	−0.272850	−	0.962057i	$-0.587966\pi$
$877$	−16.1605	−0.545700	−0.272850	+	0.962057i	$0.587966\pi$
$878$	−16.7160	−0.564137
$879$	29.5503	0.996707
$880$	−103.864	−3.50126
$881$	16.3669	0.551415	0.275708	−	0.961242i	$-0.411088\pi$
$881$	16.3669	0.551415	0.275708	+	0.961242i	$0.411088\pi$
$882$	−109.963	−3.70265
$883$	8.47380	0.285166	0.142583	−	0.989783i	$-0.454459\pi$
$883$	8.47380	0.285166	0.142583	+	0.989783i	$0.454459\pi$
$884$	−57.3327	−1.92831
$885$	−107.916	−3.62756
$886$	−43.2713	−1.45373
$887$	55.2853	1.85630	0.928150	−	0.372207i	$-0.121399\pi$
$887$	55.2853	1.85630	0.928150	+	0.372207i	$0.121399\pi$
$888$	−181.521	−6.09146
$889$	50.8872	1.70670
$890$	53.8384	1.80467
$891$	−33.0958	−1.10875
$892$	−79.3828	−2.65793
$893$	30.4376	1.01855
$894$	−46.5256	−1.55605
$895$	−49.8696	−1.66696
$896$	15.8254	0.528688
$897$	49.5703	1.65510
$898$	77.0911	2.57256
$899$	−0.0329587	−0.00109923
$900$	59.5988	1.98663
$901$	−39.6850	−1.32210
$902$	−45.6624	−1.52039
$903$	67.2036	2.23640
$904$	−0.496637	−0.0165179
$905$	−52.7379	−1.75307
$906$	36.3752	1.20848
$907$	31.2787	1.03859	0.519296	−	0.854594i	$-0.326194\pi$
$907$	31.2787	1.03859	0.519296	+	0.854594i	$0.326194\pi$
$908$	78.9594	2.62036
$909$	47.6958	1.58197
$910$	164.321	5.44720
$911$	−16.1419	−0.534804	−0.267402	−	0.963585i	$-0.586165\pi$
$911$	−16.1419	−0.534804	−0.267402	+	0.963585i	$0.586165\pi$
$912$	109.914	3.63961
$913$	−46.1216	−1.52640
$914$	29.6060	0.979280
$915$	17.8622	0.590508
$916$	−26.0831	−0.861809
$917$	−55.7873	−1.84226
$918$	8.61130	0.284215
$919$	38.5261	1.27086	0.635429	−	0.772159i	$-0.280823\pi$
$919$	38.5261	1.27086	0.635429	+	0.772159i	$0.280823\pi$
$920$	−123.293	−4.06484
$921$	6.61646	0.218020
$922$	16.9820	0.559271
$923$	−17.5957	−0.579171
$924$	−181.182	−5.96046
$925$	49.0879	1.61400
$926$	−69.9179	−2.29765
$927$	44.7434	1.46957
$928$	11.6299	0.381769
$929$	7.00435	0.229805	0.114903	−	0.993377i	$-0.463344\pi$
$929$	7.00435	0.229805	0.114903	+	0.993377i	$0.463344\pi$
$930$	0.637707	0.0209112
$931$	76.2803	2.49998
$932$	55.9640	1.83316
$933$	42.4717	1.39046
$934$	50.6720	1.65804
$935$	−28.9669	−0.947320
$936$	78.4671	2.56478
$937$	−17.7271	−0.579120	−0.289560	−	0.957160i	$-0.593509\pi$
$937$	−17.7271	−0.579120	−0.289560	+	0.957160i	$0.593509\pi$
$938$	−68.3687	−2.23232
$939$	−63.3980	−2.06892
$940$	−102.308	−3.33693
$941$	22.4270	0.731098	0.365549	−	0.930792i	$-0.380881\pi$
$941$	22.4270	0.731098	0.365549	+	0.930792i	$0.380881\pi$
$942$	−140.532	−4.57877
$943$	−27.6788	−0.901346
$944$	149.940	4.88012
$945$	−17.5299	−0.570249
$946$	50.0229	1.62638
$947$	32.3846	1.05236	0.526178	−	0.850374i	$-0.323624\pi$
$947$	32.3846	1.05236	0.526178	+	0.850374i	$0.323624\pi$
$948$	−28.4964	−0.925519
$949$	−57.9208	−1.88019
$950$	−58.2079	−1.88851
$951$	−13.5227	−0.438505
$952$	105.887	3.43180
$953$	55.1063	1.78507	0.892534	−	0.450980i	$-0.148925\pi$
$953$	55.1063	1.78507	0.892534	+	0.450980i	$0.148925\pi$
$954$	91.7353	2.97004
$955$	−7.56461	−0.244785
$956$	26.2191	0.847986
$957$	−7.59573	−0.245535
$958$	57.2674	1.85023
$959$	16.2943	0.526172
$960$	−74.3146	−2.39849
$961$	−30.9989	−0.999965
$962$	109.156	3.51934
$963$	−15.3354	−0.494175
$964$	−109.466	−3.52567
$965$	−58.4497	−1.88156
$966$	−154.627	−4.97503
$967$	−34.0491	−1.09494	−0.547472	−	0.836824i	$-0.684410\pi$
$967$	−34.0491	−1.09494	−0.547472	+	0.836824i	$0.684410\pi$
$968$	4.04530	0.130021
$969$	30.6542	0.984753
$970$	−105.737	−3.39500
$971$	−16.3143	−0.523550	−0.261775	−	0.965129i	$-0.584308\pi$
$971$	−16.3143	−0.523550	−0.261775	+	0.965129i	$0.584308\pi$
$972$	−100.829	−3.23411
$973$	95.4371	3.05957
$974$	−50.5604	−1.62006
$975$	−46.5739	−1.49156
$976$	−24.8180	−0.794405
$977$	19.4826	0.623303	0.311652	−	0.950196i	$-0.399118\pi$
$977$	19.4826	0.623303	0.311652	+	0.950196i	$0.399118\pi$
$978$	−7.83811	−0.250635
$979$	21.1354	0.675490
$980$	−256.397	−8.19031
$981$	−31.5894	−1.00857
$982$	21.0630	0.672147
$983$	14.3547	0.457844	0.228922	−	0.973445i	$-0.426480\pi$
$983$	14.3547	0.457844	0.228922	+	0.973445i	$0.426480\pi$
$984$	−96.1662	−3.06567
$985$	36.1931	1.15321
$986$	7.49755	0.238770
$987$	−75.9684	−2.41810
$988$	−91.9341	−2.92481
$989$	30.3219	0.964182
$990$	66.9595	2.12811
$991$	40.9032	1.29933	0.649666	−	0.760219i	$-0.274909\pi$
$991$	40.9032	1.29933	0.649666	+	0.760219i	$0.274909\pi$
$992$	−0.383305	−0.0121699
$993$	−65.2088	−2.06934
$994$	54.8871	1.74091
$995$	49.0092	1.55370
$996$	−164.056	−5.19832
$997$	57.5309	1.82202	0.911011	−	0.412383i	$-0.135303\pi$
$997$	57.5309	1.82202	0.911011	+	0.412383i	$0.135303\pi$
$998$	45.2132	1.43120
$999$	−11.6449	−0.368428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.b.1.6	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.b.1.6	✓	153	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62733 q^{2} +2.34750 q^{3} +4.90284 q^{4} -3.13713 q^{5} -6.16764 q^{6} -4.86517 q^{7} -7.62672 q^{8} +2.51073 q^{9} +O(q^{10})\)	\(q-2.62733 q^{2} +2.34750 q^{3} +4.90284 q^{4} -3.13713 q^{5} -6.16764 q^{6} -4.86517 q^{7} -7.62672 q^{8} +2.51073 q^{9} +8.24227 q^{10} +3.23567 q^{11} +11.5094 q^{12} -4.09779 q^{13} +12.7824 q^{14} -7.36440 q^{15} +10.2322 q^{16} +2.85368 q^{17} -6.59652 q^{18} +4.57593 q^{19} -15.3809 q^{20} -11.4210 q^{21} -8.50117 q^{22} -5.15309 q^{23} -17.9037 q^{24} +4.84160 q^{25} +10.7662 q^{26} -1.14855 q^{27} -23.8532 q^{28} -1.00000 q^{29} +19.3487 q^{30} +0.0329587 q^{31} -11.6299 q^{32} +7.59573 q^{33} -7.49755 q^{34} +15.2627 q^{35} +12.3097 q^{36} +10.1388 q^{37} -12.0225 q^{38} -9.61953 q^{39} +23.9260 q^{40} +5.37131 q^{41} +30.0066 q^{42} -5.88423 q^{43} +15.8640 q^{44} -7.87650 q^{45} +13.5388 q^{46} +6.65167 q^{47} +24.0200 q^{48} +16.6699 q^{49} -12.7205 q^{50} +6.69900 q^{51} -20.0908 q^{52} -13.9066 q^{53} +3.01761 q^{54} -10.1507 q^{55} +37.1053 q^{56} +10.7420 q^{57} +2.62733 q^{58} +14.6537 q^{59} -36.1065 q^{60} -2.42549 q^{61} -0.0865932 q^{62} -12.2151 q^{63} +10.0911 q^{64} +12.8553 q^{65} -19.9565 q^{66} -5.34866 q^{67} +13.9911 q^{68} -12.0968 q^{69} -40.1000 q^{70} +4.29396 q^{71} -19.1487 q^{72} +14.1346 q^{73} -26.6379 q^{74} +11.3656 q^{75} +22.4351 q^{76} -15.7421 q^{77} +25.2737 q^{78} -2.47592 q^{79} -32.0997 q^{80} -10.2284 q^{81} -14.1122 q^{82} -14.2541 q^{83} -55.9952 q^{84} -8.95237 q^{85} +15.4598 q^{86} -2.34750 q^{87} -24.6776 q^{88} +6.53199 q^{89} +20.6941 q^{90} +19.9364 q^{91} -25.2648 q^{92} +0.0773703 q^{93} -17.4761 q^{94} -14.3553 q^{95} -27.3010 q^{96} -12.8286 q^{97} -43.7972 q^{98} +8.12392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * q^99

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