LMFDB - Embedded newform 8027.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60584 q^{2} -2.87607 q^{3} +4.79042 q^{4} -4.02377 q^{5} +7.49460 q^{6} +0.529095 q^{7} -7.27140 q^{8} +5.27181 q^{9} +O(q^{10})$	\(q-2.60584 q^{2} -2.87607 q^{3} +4.79042 q^{4} -4.02377 q^{5} +7.49460 q^{6} +0.529095 q^{7} -7.27140 q^{8} +5.27181 q^{9} +10.4853 q^{10} -1.18156 q^{11} -13.7776 q^{12} +1.16621 q^{13} -1.37874 q^{14} +11.5727 q^{15} +9.36729 q^{16} -3.73439 q^{17} -13.7375 q^{18} -5.24303 q^{19} -19.2756 q^{20} -1.52172 q^{21} +3.07897 q^{22} -1.00000 q^{23} +20.9131 q^{24} +11.1908 q^{25} -3.03897 q^{26} -6.53389 q^{27} +2.53459 q^{28} -1.73586 q^{29} -30.1566 q^{30} -6.15727 q^{31} -9.86689 q^{32} +3.39827 q^{33} +9.73124 q^{34} -2.12896 q^{35} +25.2542 q^{36} +1.60108 q^{37} +13.6625 q^{38} -3.35412 q^{39} +29.2585 q^{40} -9.34482 q^{41} +3.96536 q^{42} +10.2455 q^{43} -5.66019 q^{44} -21.2126 q^{45} +2.60584 q^{46} +2.07811 q^{47} -26.9410 q^{48} -6.72006 q^{49} -29.1614 q^{50} +10.7404 q^{51} +5.58665 q^{52} -13.4836 q^{53} +17.0263 q^{54} +4.75435 q^{55} -3.84726 q^{56} +15.0793 q^{57} +4.52339 q^{58} +5.38943 q^{59} +55.4380 q^{60} -5.85924 q^{61} +16.0449 q^{62} +2.78929 q^{63} +6.97700 q^{64} -4.69258 q^{65} -8.85535 q^{66} +4.97594 q^{67} -17.8893 q^{68} +2.87607 q^{69} +5.54774 q^{70} +2.77058 q^{71} -38.3334 q^{72} +9.87762 q^{73} -4.17215 q^{74} -32.1855 q^{75} -25.1163 q^{76} -0.625160 q^{77} +8.74030 q^{78} -7.22750 q^{79} -37.6919 q^{80} +2.97653 q^{81} +24.3511 q^{82} -1.50450 q^{83} -7.28967 q^{84} +15.0263 q^{85} -26.6982 q^{86} +4.99247 q^{87} +8.59163 q^{88} -7.68319 q^{89} +55.2766 q^{90} +0.617038 q^{91} -4.79042 q^{92} +17.7088 q^{93} -5.41524 q^{94} +21.0968 q^{95} +28.3779 q^{96} +10.1921 q^{97} +17.5114 q^{98} -6.22898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * 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 $

$2$	−2.60584	−1.84261	−0.921305	−	0.388841i	$-0.872876\pi$
$2$	−2.60584	−1.84261	−0.921305	+	0.388841i	$0.872876\pi$
$3$	−2.87607	−1.66050	−0.830251	−	0.557389i	$-0.811803\pi$
$3$	−2.87607	−1.66050	−0.830251	+	0.557389i	$0.811803\pi$
$4$	4.79042	2.39521
$5$	−4.02377	−1.79949	−0.899743	−	0.436419i	$-0.856246\pi$
$5$	−4.02377	−1.79949	−0.899743	+	0.436419i	$0.856246\pi$
$6$	7.49460	3.05966
$7$	0.529095	0.199979	0.0999896	−	0.994988i	$-0.468119\pi$
$7$	0.529095	0.199979	0.0999896	+	0.994988i	$0.468119\pi$
$8$	−7.27140	−2.57083
$9$	5.27181	1.75727
$10$	10.4853	3.31575
$11$	−1.18156	−0.356255	−0.178127	−	0.984007i	$-0.557004\pi$
$11$	−1.18156	−0.356255	−0.178127	+	0.984007i	$0.557004\pi$
$12$	−13.7776	−3.97725
$13$	1.16621	0.323449	0.161725	−	0.986836i	$-0.448294\pi$
$13$	1.16621	0.323449	0.161725	+	0.986836i	$0.448294\pi$
$14$	−1.37874	−0.368484
$15$	11.5727	2.98805
$16$	9.36729	2.34182
$17$	−3.73439	−0.905723	−0.452861	−	0.891581i	$-0.649597\pi$
$17$	−3.73439	−0.905723	−0.452861	+	0.891581i	$0.649597\pi$
$18$	−13.7375	−3.23796
$19$	−5.24303	−1.20283	−0.601416	−	0.798936i	$-0.705397\pi$
$19$	−5.24303	−1.20283	−0.601416	+	0.798936i	$0.705397\pi$
$20$	−19.2756	−4.31015
$21$	−1.52172	−0.332066
$22$	3.07897	0.656439
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	20.9131	4.26887
$25$	11.1908	2.23815
$26$	−3.03897	−0.595991
$27$	−6.53389	−1.25745
$28$	2.53459	0.478992
$29$	−1.73586	−0.322342	−0.161171	−	0.986927i	$-0.551527\pi$
$29$	−1.73586	−0.322342	−0.161171	+	0.986927i	$0.551527\pi$
$30$	−30.1566	−5.50581
$31$	−6.15727	−1.10588	−0.552939	−	0.833222i	$-0.686494\pi$
$31$	−6.15727	−1.10588	−0.552939	+	0.833222i	$0.686494\pi$
$32$	−9.86689	−1.74424
$33$	3.39827	0.591562
$34$	9.73124	1.66889
$35$	−2.12896	−0.359860
$36$	25.2542	4.20903
$37$	1.60108	0.263215	0.131608	−	0.991302i	$-0.457986\pi$
$37$	1.60108	0.263215	0.131608	+	0.991302i	$0.457986\pi$
$38$	13.6625	2.21635
$39$	−3.35412	−0.537088
$40$	29.2585	4.62617
$41$	−9.34482	−1.45942	−0.729708	−	0.683759i	$-0.760344\pi$
$41$	−9.34482	−1.45942	−0.729708	+	0.683759i	$0.760344\pi$
$42$	3.96536	0.611868
$43$	10.2455	1.56242	0.781212	−	0.624266i	$-0.214602\pi$
$43$	10.2455	1.56242	0.781212	+	0.624266i	$0.214602\pi$
$44$	−5.66019	−0.853306
$45$	−21.2126	−3.16218
$46$	2.60584	0.384211
$47$	2.07811	0.303124	0.151562	−	0.988448i	$-0.451570\pi$
$47$	2.07811	0.303124	0.151562	+	0.988448i	$0.451570\pi$
$48$	−26.9410	−3.88860
$49$	−6.72006	−0.960008
$50$	−29.1614	−4.12404
$51$	10.7404	1.50395
$52$	5.58665	0.774729
$53$	−13.4836	−1.85211	−0.926055	−	0.377389i	$-0.876822\pi$
$53$	−13.4836	−1.85211	−0.926055	+	0.377389i	$0.876822\pi$
$54$	17.0263	2.31698
$55$	4.75435	0.641076
$56$	−3.84726	−0.514112
$57$	15.0793	1.99731
$58$	4.52339	0.593950
$59$	5.38943	0.701644	0.350822	−	0.936442i	$-0.385902\pi$
$59$	5.38943	0.701644	0.350822	+	0.936442i	$0.385902\pi$
$60$	55.4380	7.15702
$61$	−5.85924	−0.750199	−0.375099	−	0.926985i	$-0.622391\pi$
$61$	−5.85924	−0.750199	−0.375099	+	0.926985i	$0.622391\pi$
$62$	16.0449	2.03770
$63$	2.78929	0.351417
$64$	6.97700	0.872125
$65$	−4.69258	−0.582043
$66$	−8.85535	−1.09002
$67$	4.97594	0.607908	0.303954	−	0.952687i	$-0.401693\pi$
$67$	4.97594	0.607908	0.303954	+	0.952687i	$0.401693\pi$
$68$	−17.8893	−2.16940
$69$	2.87607	0.346239
$70$	5.54774	0.663081
$71$	2.77058	0.328807	0.164404	−	0.986393i	$-0.447430\pi$
$71$	2.77058	0.328807	0.164404	+	0.986393i	$0.447430\pi$
$72$	−38.3334	−4.51764
$73$	9.87762	1.15609	0.578044	−	0.816006i	$-0.303816\pi$
$73$	9.87762	1.15609	0.578044	+	0.816006i	$0.303816\pi$
$74$	−4.17215	−0.485003
$75$	−32.1855	−3.71646
$76$	−25.1163	−2.88104
$77$	−0.625160	−0.0712436
$78$	8.74030	0.989644
$79$	−7.22750	−0.813157	−0.406578	−	0.913616i	$-0.633278\pi$
$79$	−7.22750	−0.813157	−0.406578	+	0.913616i	$0.633278\pi$
$80$	−37.6919	−4.21408
$81$	2.97653	0.330725
$82$	24.3511	2.68913
$83$	−1.50450	−0.165140	−0.0825701	−	0.996585i	$-0.526313\pi$
$83$	−1.50450	−0.165140	−0.0825701	+	0.996585i	$0.526313\pi$
$84$	−7.28967	−0.795368
$85$	15.0263	1.62984
$86$	−26.6982	−2.87894
$87$	4.99247	0.535249
$88$	8.59163	0.915870
$89$	−7.68319	−0.814417	−0.407208	−	0.913335i	$-0.633498\pi$
$89$	−7.68319	−0.814417	−0.407208	+	0.913335i	$0.633498\pi$
$90$	55.2766	5.82667
$91$	0.617038	0.0646831
$92$	−4.79042	−0.499436
$93$	17.7088	1.83631
$94$	−5.41524	−0.558539
$95$	21.0968	2.16448
$96$	28.3779	2.89631
$97$	10.1921	1.03485	0.517425	−	0.855729i	$-0.326891\pi$
$97$	10.1921	1.03485	0.517425	+	0.855729i	$0.326891\pi$
$98$	17.5114	1.76892
$99$	−6.22898	−0.626036
$100$	53.6085	5.36085
$101$	15.6779	1.56001	0.780004	−	0.625774i	$-0.215217\pi$
$101$	15.6779	1.56001	0.780004	+	0.625774i	$0.215217\pi$
$102$	−27.9878	−2.77120
$103$	2.30134	0.226758	0.113379	−	0.993552i	$-0.463833\pi$
$103$	2.30134	0.226758	0.113379	+	0.993552i	$0.463833\pi$
$104$	−8.48000	−0.831533
$105$	6.12305	0.597548
$106$	35.1361	3.41272
$107$	8.73768	0.844704	0.422352	−	0.906432i	$-0.361205\pi$
$107$	8.73768	0.844704	0.422352	+	0.906432i	$0.361205\pi$
$108$	−31.3001	−3.01185
$109$	11.8666	1.13661	0.568307	−	0.822817i	$-0.307599\pi$
$109$	11.8666	1.13661	0.568307	+	0.822817i	$0.307599\pi$
$110$	−12.3891	−1.18125
$111$	−4.60481	−0.437069
$112$	4.95619	0.468316
$113$	0.252377	0.0237416	0.0118708	−	0.999930i	$-0.496221\pi$
$113$	0.252377	0.0237416	0.0118708	+	0.999930i	$0.496221\pi$
$114$	−39.2944	−3.68026
$115$	4.02377	0.375219
$116$	−8.31551	−0.772076
$117$	6.14805	0.568387
$118$	−14.0440	−1.29286
$119$	−1.97585	−0.181126
$120$	−84.1496	−7.68177
$121$	−9.60391	−0.873082
$122$	15.2683	1.38232
$123$	26.8764	2.42336
$124$	−29.4959	−2.64881
$125$	−24.9102	−2.22804
$126$	−7.26845	−0.647525
$127$	−9.97542	−0.885175	−0.442588	−	0.896725i	$-0.645939\pi$
$127$	−9.97542	−0.885175	−0.442588	+	0.896725i	$0.645939\pi$
$128$	1.55282	0.137251
$129$	−29.4668	−2.59441
$130$	12.2281	1.07248
$131$	−6.07742	−0.530986	−0.265493	−	0.964113i	$-0.585535\pi$
$131$	−6.07742	−0.530986	−0.265493	+	0.964113i	$0.585535\pi$
$132$	16.2791	1.41692
$133$	−2.77406	−0.240541
$134$	−12.9665	−1.12014
$135$	26.2909	2.26276
$136$	27.1542	2.32846
$137$	−22.1822	−1.89515	−0.947577	−	0.319529i	$-0.896475\pi$
$137$	−22.1822	−1.89515	−0.947577	+	0.319529i	$0.896475\pi$
$138$	−7.49460	−0.637983
$139$	−16.5911	−1.40724	−0.703619	−	0.710578i	$-0.748434\pi$
$139$	−16.5911	−1.40724	−0.703619	+	0.710578i	$0.748434\pi$
$140$	−10.1986	−0.861940
$141$	−5.97681	−0.503338
$142$	−7.21970	−0.605864
$143$	−1.37796	−0.115230
$144$	49.3825	4.11521
$145$	6.98472	0.580050
$146$	−25.7395	−2.13022
$147$	19.3274	1.59410
$148$	7.66982	0.630456
$149$	−2.95149	−0.241796	−0.120898	−	0.992665i	$-0.538577\pi$
$149$	−2.95149	−0.241796	−0.120898	+	0.992665i	$0.538577\pi$
$150$	83.8703	6.84798
$151$	−18.5959	−1.51331	−0.756656	−	0.653813i	$-0.773168\pi$
$151$	−18.5959	−1.51331	−0.756656	+	0.653813i	$0.773168\pi$
$152$	38.1241	3.09228
$153$	−19.6870	−1.59160
$154$	1.62907	0.131274
$155$	24.7755	1.99001
$156$	−16.0676	−1.28644
$157$	−5.66901	−0.452436	−0.226218	−	0.974077i	$-0.572636\pi$
$157$	−5.66901	−0.452436	−0.226218	+	0.974077i	$0.572636\pi$
$158$	18.8337	1.49833
$159$	38.7797	3.07543
$160$	39.7022	3.13873
$161$	−0.529095	−0.0416985
$162$	−7.75637	−0.609398
$163$	−9.57944	−0.750320	−0.375160	−	0.926960i	$-0.622412\pi$
$163$	−9.57944	−0.750320	−0.375160	+	0.926960i	$0.622412\pi$
$164$	−44.7656	−3.49561
$165$	−13.6739	−1.06451
$166$	3.92049	0.304289
$167$	−18.0619	−1.39767	−0.698836	−	0.715282i	$-0.746298\pi$
$167$	−18.0619	−1.39767	−0.698836	+	0.715282i	$0.746298\pi$
$168$	11.0650	0.853685
$169$	−11.6399	−0.895381
$170$	−39.1563	−3.00315
$171$	−27.6402	−2.11370
$172$	49.0802	3.74233
$173$	18.2715	1.38915	0.694577	−	0.719418i	$-0.255592\pi$
$173$	18.2715	1.38915	0.694577	+	0.719418i	$0.255592\pi$
$174$	−13.0096	−0.986255
$175$	5.92098	0.447584
$176$	−11.0681	−0.834286
$177$	−15.5004	−1.16508
$178$	20.0212	1.50065
$179$	3.86330	0.288757	0.144378	−	0.989523i	$-0.453882\pi$
$179$	3.86330	0.288757	0.144378	+	0.989523i	$0.453882\pi$
$180$	−101.617	−7.57409
$181$	−2.80765	−0.208691	−0.104346	−	0.994541i	$-0.533275\pi$
$181$	−2.80765	−0.208691	−0.104346	+	0.994541i	$0.533275\pi$
$182$	−1.60790	−0.119186
$183$	16.8516	1.24571
$184$	7.27140	0.536055
$185$	−6.44237	−0.473652
$186$	−46.1463	−3.38361
$187$	4.41242	0.322668
$188$	9.95504	0.726046
$189$	−3.45705	−0.251463
$190$	−54.9748	−3.98829
$191$	−15.7872	−1.14232	−0.571162	−	0.820838i	$-0.693507\pi$
$191$	−15.7872	−1.14232	−0.571162	+	0.820838i	$0.693507\pi$
$192$	−20.0664	−1.44817
$193$	−6.22396	−0.448010	−0.224005	−	0.974588i	$-0.571913\pi$
$193$	−6.22396	−0.448010	−0.224005	+	0.974588i	$0.571913\pi$
$194$	−26.5590	−1.90682
$195$	13.4962	0.966483
$196$	−32.1919	−2.29942
$197$	20.8861	1.48808	0.744038	−	0.668138i	$-0.232908\pi$
$197$	20.8861	1.48808	0.744038	+	0.668138i	$0.232908\pi$
$198$	16.2317	1.15354
$199$	−16.6820	−1.18255	−0.591276	−	0.806469i	$-0.701376\pi$
$199$	−16.6820	−1.18255	−0.591276	+	0.806469i	$0.701376\pi$
$200$	−81.3725	−5.75391
$201$	−14.3112	−1.00943
$202$	−40.8541	−2.87449
$203$	−0.918437	−0.0644616
$204$	51.4510	3.60229
$205$	37.6014	2.62620
$206$	−5.99693	−0.417826
$207$	−5.27181	−0.366416
$208$	10.9243	0.757461
$209$	6.19497	0.428515
$210$	−15.9557	−1.10105
$211$	−9.17539	−0.631660	−0.315830	−	0.948816i	$-0.602283\pi$
$211$	−9.17539	−0.631660	−0.315830	+	0.948816i	$0.602283\pi$
$212$	−64.5919	−4.43619
$213$	−7.96840	−0.545986
$214$	−22.7690	−1.55646
$215$	−41.2256	−2.81156
$216$	47.5105	3.23268
$217$	−3.25778	−0.221153
$218$	−30.9225	−2.09434
$219$	−28.4088	−1.91969
$220$	22.7753	1.53551
$221$	−4.35509	−0.292955
$222$	11.9994	0.805348
$223$	−16.1754	−1.08318	−0.541591	−	0.840642i	$-0.682178\pi$
$223$	−16.1754	−1.08318	−0.541591	+	0.840642i	$0.682178\pi$
$224$	−5.22053	−0.348811
$225$	58.9956	3.93304
$226$	−0.657654	−0.0437465
$227$	15.2966	1.01527	0.507636	−	0.861571i	$-0.330519\pi$
$227$	15.2966	1.01527	0.507636	+	0.861571i	$0.330519\pi$
$228$	72.2364	4.78397
$229$	−2.55758	−0.169009	−0.0845047	−	0.996423i	$-0.526931\pi$
$229$	−2.55758	−0.169009	−0.0845047	+	0.996423i	$0.526931\pi$
$230$	−10.4853	−0.691382
$231$	1.79801	0.118300
$232$	12.6222	0.828685
$233$	−3.04109	−0.199229	−0.0996143	−	0.995026i	$-0.531761\pi$
$233$	−3.04109	−0.199229	−0.0996143	+	0.995026i	$0.531761\pi$
$234$	−16.0209	−1.04732
$235$	−8.36186	−0.545468
$236$	25.8176	1.68058
$237$	20.7868	1.35025
$238$	5.14875	0.333744
$239$	21.1922	1.37081	0.685403	−	0.728164i	$-0.259626\pi$
$239$	21.1922	1.37081	0.685403	+	0.728164i	$0.259626\pi$
$240$	108.405	6.99749
$241$	24.2313	1.56087	0.780436	−	0.625236i	$-0.214997\pi$
$241$	24.2313	1.56087	0.780436	+	0.625236i	$0.214997\pi$
$242$	25.0263	1.60875
$243$	11.0409	0.708277
$244$	−28.0682	−1.79688
$245$	27.0400	1.72752
$246$	−70.0357	−4.46531
$247$	−6.11448	−0.389055
$248$	44.7720	2.84302
$249$	4.32705	0.274216
$250$	64.9122	4.10541
$251$	−13.3512	−0.842723	−0.421362	−	0.906893i	$-0.638448\pi$
$251$	−13.3512	−0.842723	−0.421362	+	0.906893i	$0.638448\pi$
$252$	13.3619	0.841718
$253$	1.18156	0.0742843
$254$	25.9944	1.63103
$255$	−43.2169	−2.70635
$256$	−18.0004	−1.12502
$257$	−27.6921	−1.72739	−0.863694	−	0.504017i	$-0.831855\pi$
$257$	−27.6921	−1.72739	−0.863694	+	0.504017i	$0.831855\pi$
$258$	76.7859	4.78048
$259$	0.847121	0.0526376
$260$	−22.4794	−1.39411
$261$	−9.15113	−0.566441
$262$	15.8368	0.978401
$263$	−3.26129	−0.201100	−0.100550	−	0.994932i	$-0.532060\pi$
$263$	−3.26129	−0.201100	−0.100550	+	0.994932i	$0.532060\pi$
$264$	−24.7102	−1.52081
$265$	54.2548	3.33285
$266$	7.22877	0.443224
$267$	22.0974	1.35234
$268$	23.8368	1.45607
$269$	−1.10447	−0.0673406	−0.0336703	−	0.999433i	$-0.510720\pi$
$269$	−1.10447	−0.0673406	−0.0336703	+	0.999433i	$0.510720\pi$
$270$	−68.5100	−4.16938
$271$	−6.75823	−0.410533	−0.205267	−	0.978706i	$-0.565806\pi$
$271$	−6.75823	−0.410533	−0.205267	+	0.978706i	$0.565806\pi$
$272$	−34.9811	−2.12104
$273$	−1.77465	−0.107407
$274$	57.8033	3.49203
$275$	−13.2226	−0.797353
$276$	13.7776	0.829315
$277$	−4.39977	−0.264356	−0.132178	−	0.991226i	$-0.542197\pi$
$277$	−4.39977	−0.264356	−0.132178	+	0.991226i	$0.542197\pi$
$278$	43.2338	2.59299
$279$	−32.4599	−1.94332
$280$	15.4805	0.925138
$281$	−14.5113	−0.865671	−0.432836	−	0.901473i	$-0.642487\pi$
$281$	−14.5113	−0.865671	−0.432836	+	0.901473i	$0.642487\pi$
$282$	15.5746	0.927456
$283$	−2.07166	−0.123147	−0.0615737	−	0.998103i	$-0.519612\pi$
$283$	−2.07166	−0.123147	−0.0615737	+	0.998103i	$0.519612\pi$
$284$	13.2722	0.787563
$285$	−60.6758	−3.59413
$286$	3.59074	0.212325
$287$	−4.94430	−0.291853
$288$	−52.0164	−3.06509
$289$	−3.05433	−0.179666
$290$	−18.2011	−1.06880
$291$	−29.3132	−1.71837
$292$	47.3179	2.76907
$293$	−10.2080	−0.596356	−0.298178	−	0.954510i	$-0.596379\pi$
$293$	−10.2080	−0.596356	−0.298178	+	0.954510i	$0.596379\pi$
$294$	−50.3642	−2.93730
$295$	−21.6858	−1.26260
$296$	−11.6421	−0.676681
$297$	7.72021	0.447972
$298$	7.69113	0.445535
$299$	−1.16621	−0.0674438
$300$	−154.182	−8.90170
$301$	5.42084	0.312452
$302$	48.4580	2.78844
$303$	−45.0908	−2.59040
$304$	−49.1129	−2.81682
$305$	23.5763	1.34997
$306$	51.3012	2.93269
$307$	−13.3504	−0.761945	−0.380973	−	0.924586i	$-0.624411\pi$
$307$	−13.3504	−0.761945	−0.380973	+	0.924586i	$0.624411\pi$
$308$	−2.99478	−0.170643
$309$	−6.61882	−0.376531
$310$	−64.5610	−3.66682
$311$	−28.0363	−1.58979	−0.794896	−	0.606745i	$-0.792475\pi$
$311$	−28.0363	−1.58979	−0.794896	+	0.606745i	$0.792475\pi$
$312$	24.3891	1.38076
$313$	−18.6299	−1.05302	−0.526512	−	0.850167i	$-0.676501\pi$
$313$	−18.6299	−1.05302	−0.526512	+	0.850167i	$0.676501\pi$
$314$	14.7726	0.833664
$315$	−11.2235	−0.632371
$316$	−34.6227	−1.94768
$317$	−22.0159	−1.23654	−0.618269	−	0.785967i	$-0.712166\pi$
$317$	−22.0159	−1.23654	−0.618269	+	0.785967i	$0.712166\pi$
$318$	−101.054	−5.66682
$319$	2.05103	0.114836
$320$	−28.0739	−1.56938
$321$	−25.1302	−1.40263
$322$	1.37874	0.0768342
$323$	19.5795	1.08943
$324$	14.2588	0.792157
$325$	13.0508	0.723929
$326$	24.9625	1.38255
$327$	−34.1292	−1.88735
$328$	67.9499	3.75191
$329$	1.09952	0.0606185
$330$	35.6319	1.96147
$331$	−9.51627	−0.523061	−0.261531	−	0.965195i	$-0.584227\pi$
$331$	−9.51627	−0.523061	−0.261531	+	0.965195i	$0.584227\pi$
$332$	−7.20718	−0.395545
$333$	8.44056	0.462540
$334$	47.0665	2.57536
$335$	−20.0221	−1.09392
$336$	−14.2544	−0.777640
$337$	3.74073	0.203771	0.101885	−	0.994796i	$-0.467512\pi$
$337$	3.74073	0.203771	0.101885	+	0.994796i	$0.467512\pi$
$338$	30.3319	1.64984
$339$	−0.725854	−0.0394230
$340$	71.9825	3.90380
$341$	7.27521	0.393975
$342$	72.0261	3.89472
$343$	−7.25922	−0.391961
$344$	−74.4991	−4.01672
$345$	−11.5727	−0.623052
$346$	−47.6126	−2.55967
$347$	−10.2336	−0.549367	−0.274684	−	0.961535i	$-0.588573\pi$
$347$	−10.2336	−0.549367	−0.274684	+	0.961535i	$0.588573\pi$
$348$	23.9160	1.28203
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−15.4292	−0.824723
$351$	−7.61990	−0.406720
$352$	11.6584	0.621393
$353$	−16.1435	−0.859234	−0.429617	−	0.903011i	$-0.641351\pi$
$353$	−16.1435	−0.859234	−0.429617	+	0.903011i	$0.641351\pi$
$354$	40.3916	2.14679
$355$	−11.1482	−0.591685
$356$	−36.8057	−1.95070
$357$	5.68269	0.300760
$358$	−10.0672	−0.532066
$359$	−11.6856	−0.616745	−0.308372	−	0.951266i	$-0.599784\pi$
$359$	−11.6856	−0.616745	−0.308372	+	0.951266i	$0.599784\pi$
$360$	154.245	8.12943
$361$	8.48931	0.446806
$362$	7.31630	0.384536
$363$	27.6216	1.44976
$364$	2.95587	0.154930
$365$	−39.7453	−2.08036
$366$	−43.9127	−2.29535
$367$	−12.7889	−0.667576	−0.333788	−	0.942648i	$-0.608327\pi$
$367$	−12.7889	−0.667576	−0.333788	+	0.942648i	$0.608327\pi$
$368$	−9.36729	−0.488304
$369$	−49.2641	−2.56459
$370$	16.7878	0.872756
$371$	−7.13409	−0.370383
$372$	84.8324	4.39836
$373$	−25.9694	−1.34464	−0.672321	−	0.740259i	$-0.734703\pi$
$373$	−25.9694	−1.34464	−0.672321	+	0.740259i	$0.734703\pi$
$374$	−11.4981	−0.594552
$375$	71.6437	3.69967
$376$	−15.1108	−0.779280
$377$	−2.02439	−0.104261
$378$	9.00853	0.463349
$379$	12.9441	0.664896	0.332448	−	0.943122i	$-0.392125\pi$
$379$	12.9441	0.664896	0.332448	+	0.943122i	$0.392125\pi$
$380$	101.062	5.18439
$381$	28.6900	1.46984
$382$	41.1390	2.10486
$383$	−14.6288	−0.747495	−0.373747	−	0.927531i	$-0.621927\pi$
$383$	−14.6288	−0.747495	−0.373747	+	0.927531i	$0.621927\pi$
$384$	−4.46602	−0.227905
$385$	2.51550	0.128202
$386$	16.2187	0.825508
$387$	54.0123	2.74560
$388$	48.8244	2.47868
$389$	−3.04040	−0.154154	−0.0770772	−	0.997025i	$-0.524559\pi$
$389$	−3.04040	−0.154154	−0.0770772	+	0.997025i	$0.524559\pi$
$390$	−35.1690	−1.78085
$391$	3.73439	0.188856
$392$	48.8642	2.46802
$393$	17.4791	0.881704
$394$	−54.4260	−2.74194
$395$	29.0818	1.46326
$396$	−29.8394	−1.49949
$397$	−26.1010	−1.30997	−0.654985	−	0.755642i	$-0.727325\pi$
$397$	−26.1010	−1.30997	−0.654985	+	0.755642i	$0.727325\pi$
$398$	43.4706	2.17898
$399$	7.97840	0.399420
$400$	104.827	5.24136
$401$	−13.4816	−0.673239	−0.336620	−	0.941641i	$-0.609284\pi$
$401$	−13.4816	−0.673239	−0.336620	+	0.941641i	$0.609284\pi$
$402$	37.2927	1.85999
$403$	−7.18068	−0.357695
$404$	75.1037	3.73655
$405$	−11.9769	−0.595136
$406$	2.39330	0.118778
$407$	−1.89177	−0.0937717
$408$	−78.0977	−3.86641
$409$	−34.8789	−1.72465	−0.862325	−	0.506356i	$-0.830992\pi$
$409$	−34.8789	−1.72465	−0.862325	+	0.506356i	$0.830992\pi$
$410$	−97.9835	−4.83906
$411$	63.7977	3.14691
$412$	11.0244	0.543132
$413$	2.85152	0.140314
$414$	13.7375	0.675162
$415$	6.05376	0.297168
$416$	−11.5069	−0.564172
$417$	47.7172	2.33672
$418$	−16.1431	−0.789586
$419$	−16.7740	−0.819463	−0.409732	−	0.912206i	$-0.634378\pi$
$419$	−16.7740	−0.819463	−0.409732	+	0.912206i	$0.634378\pi$
$420$	29.3320	1.43125
$421$	32.6131	1.58947	0.794733	−	0.606959i	$-0.207611\pi$
$421$	32.6131	1.58947	0.794733	+	0.606959i	$0.207611\pi$
$422$	23.9096	1.16390
$423$	10.9554	0.532670
$424$	98.0444	4.76146
$425$	−41.7907	−2.02715
$426$	20.7644	1.00604
$427$	−3.10010	−0.150024
$428$	41.8572	2.02324
$429$	3.96310	0.191340
$430$	107.427	5.18061
$431$	37.1892	1.79134	0.895671	−	0.444718i	$-0.146696\pi$
$431$	37.1892	1.79134	0.895671	+	0.444718i	$0.146696\pi$
$432$	−61.2048	−2.94472
$433$	4.29527	0.206418	0.103209	−	0.994660i	$-0.467089\pi$
$433$	4.29527	0.206418	0.103209	+	0.994660i	$0.467089\pi$
$434$	8.48927	0.407498
$435$	−20.0886	−0.963174
$436$	56.8460	2.72243
$437$	5.24303	0.250808
$438$	74.0288	3.53723
$439$	−12.3725	−0.590508	−0.295254	−	0.955419i	$-0.595404\pi$
$439$	−12.3725	−0.590508	−0.295254	+	0.955419i	$0.595404\pi$
$440$	−34.5708	−1.64810
$441$	−35.4269	−1.68699
$442$	11.3487	0.539802
$443$	5.26727	0.250256	0.125128	−	0.992141i	$-0.460066\pi$
$443$	5.26727	0.250256	0.125128	+	0.992141i	$0.460066\pi$
$444$	−22.0590	−1.04687
$445$	30.9154	1.46553
$446$	42.1504	1.99588
$447$	8.48871	0.401502
$448$	3.69150	0.174407
$449$	−29.9131	−1.41169	−0.705843	−	0.708368i	$-0.749432\pi$
$449$	−29.9131	−1.41169	−0.705843	+	0.708368i	$0.749432\pi$
$450$	−153.733	−7.24705
$451$	11.0415	0.519924
$452$	1.20899	0.0568661
$453$	53.4832	2.51286
$454$	−39.8606	−1.87075
$455$	−2.48282	−0.116396
$456$	−109.648	−5.13473
$457$	0.267516	0.0125139	0.00625694	−	0.999980i	$-0.498008\pi$
$457$	0.267516	0.0125139	0.00625694	+	0.999980i	$0.498008\pi$
$458$	6.66464	0.311418
$459$	24.4001	1.13890
$460$	19.2756	0.898728
$461$	−16.1539	−0.752361	−0.376180	−	0.926546i	$-0.622763\pi$
$461$	−16.1539	−0.752361	−0.376180	+	0.926546i	$0.622763\pi$
$462$	−4.68533	−0.217981
$463$	−16.3214	−0.758520	−0.379260	−	0.925290i	$-0.623821\pi$
$463$	−16.3214	−0.758520	−0.379260	+	0.925290i	$0.623821\pi$
$464$	−16.2603	−0.754867
$465$	−71.2561	−3.30442
$466$	7.92461	0.367101
$467$	−12.2034	−0.564705	−0.282353	−	0.959311i	$-0.591115\pi$
$467$	−12.2034	−0.564705	−0.282353	+	0.959311i	$0.591115\pi$
$468$	29.4517	1.36141
$469$	2.63275	0.121569
$470$	21.7897	1.00508
$471$	16.3045	0.751272
$472$	−39.1887	−1.80381
$473$	−12.1057	−0.556621
$474$	−54.1672	−2.48798
$475$	−58.6735	−2.69212
$476$	−9.46515	−0.433834
$477$	−71.0827	−3.25466
$478$	−55.2234	−2.52586
$479$	14.7747	0.675072	0.337536	−	0.941313i	$-0.390407\pi$
$479$	14.7747	0.675072	0.337536	+	0.941313i	$0.390407\pi$
$480$	−114.186	−5.21187
$481$	1.86719	0.0851367
$482$	−63.1429	−2.87608
$483$	1.52172	0.0692406
$484$	−46.0068	−2.09122
$485$	−41.0107	−1.86220
$486$	−28.7710	−1.30508
$487$	29.1641	1.32155	0.660776	−	0.750583i	$-0.270227\pi$
$487$	29.1641	1.32155	0.660776	+	0.750583i	$0.270227\pi$
$488$	42.6049	1.92863
$489$	27.5512	1.24591
$490$	−70.4620	−3.18315
$491$	−38.1350	−1.72101	−0.860504	−	0.509444i	$-0.829851\pi$
$491$	−38.1350	−1.72101	−0.860504	+	0.509444i	$0.829851\pi$
$492$	128.749	5.80446
$493$	6.48239	0.291952
$494$	15.9334	0.716877
$495$	25.0640	1.12654
$496$	−57.6769	−2.58977
$497$	1.46590	0.0657547
$498$	−11.2756	−0.505272
$499$	32.2722	1.44470	0.722351	−	0.691526i	$-0.243061\pi$
$499$	32.2722	1.44470	0.722351	+	0.691526i	$0.243061\pi$
$500$	−119.331	−5.33662
$501$	51.9474	2.32084
$502$	34.7913	1.55281
$503$	−21.5891	−0.962611	−0.481305	−	0.876553i	$-0.659837\pi$
$503$	−21.5891	−0.962611	−0.481305	+	0.876553i	$0.659837\pi$
$504$	−20.2820	−0.903434
$505$	−63.0843	−2.80721
$506$	−3.07897	−0.136877
$507$	33.4774	1.48678
$508$	−47.7864	−2.12018
$509$	21.2684	0.942703	0.471352	−	0.881945i	$-0.343766\pi$
$509$	21.2684	0.942703	0.471352	+	0.881945i	$0.343766\pi$
$510$	112.616	4.98674
$511$	5.22620	0.231193
$512$	43.8006	1.93573
$513$	34.2573	1.51250
$514$	72.1614	3.18290
$515$	−9.26006	−0.408047
$516$	−141.158	−6.21415
$517$	−2.45542	−0.107989
$518$	−2.20747	−0.0969905
$519$	−52.5501	−2.30669
$520$	34.1216	1.49633
$521$	39.6336	1.73638	0.868189	−	0.496233i	$-0.165284\pi$
$521$	39.6336	1.73638	0.868189	+	0.496233i	$0.165284\pi$
$522$	23.8464	1.04373
$523$	−37.8383	−1.65455	−0.827276	−	0.561796i	$-0.810111\pi$
$523$	−37.8383	−1.65455	−0.827276	+	0.561796i	$0.810111\pi$
$524$	−29.1134	−1.27182
$525$	−17.0292	−0.743215
$526$	8.49841	0.370548
$527$	22.9936	1.00162
$528$	31.8326	1.38533
$529$	1.00000	0.0434783
$530$	−141.380	−6.14114
$531$	28.4120	1.23298
$532$	−13.2889	−0.576147
$533$	−10.8980	−0.472047
$534$	−57.5825	−2.49184
$535$	−35.1585	−1.52003
$536$	−36.1821	−1.56283
$537$	−11.1111	−0.479481
$538$	2.87807	0.124082
$539$	7.94018	0.342008
$540$	125.944	5.41979
$541$	15.1424	0.651024	0.325512	−	0.945538i	$-0.394463\pi$
$541$	15.1424	0.651024	0.325512	+	0.945538i	$0.394463\pi$
$542$	17.6109	0.756453
$543$	8.07501	0.346532
$544$	36.8468	1.57979
$545$	−47.7485	−2.04532
$546$	4.62445	0.197908
$547$	43.2569	1.84953	0.924766	−	0.380536i	$-0.124260\pi$
$547$	43.2569	1.84953	0.924766	+	0.380536i	$0.124260\pi$
$548$	−106.262	−4.53929
$549$	−30.8888	−1.31830
$550$	34.4560	1.46921
$551$	9.10117	0.387723
$552$	−20.9131	−0.890120
$553$	−3.82403	−0.162614
$554$	11.4651	0.487106
$555$	18.5287	0.786501
$556$	−79.4783	−3.37063
$557$	−2.59269	−0.109856	−0.0549280	−	0.998490i	$-0.517493\pi$
$557$	−2.59269	−0.109856	−0.0549280	+	0.998490i	$0.517493\pi$
$558$	84.5855	3.58079
$559$	11.9484	0.505365
$560$	−19.9426	−0.842728
$561$	−12.6905	−0.535791
$562$	37.8142	1.59509
$563$	−18.4868	−0.779126	−0.389563	−	0.921000i	$-0.627374\pi$
$563$	−18.4868	−0.779126	−0.389563	+	0.921000i	$0.627374\pi$
$564$	−28.6314	−1.20560
$565$	−1.01551	−0.0427227
$566$	5.39842	0.226912
$567$	1.57487	0.0661382
$568$	−20.1460	−0.845308
$569$	−17.8434	−0.748035	−0.374017	−	0.927422i	$-0.622020\pi$
$569$	−17.8434	−0.748035	−0.374017	+	0.927422i	$0.622020\pi$
$570$	158.112	6.62257
$571$	−14.1185	−0.590841	−0.295420	−	0.955367i	$-0.595460\pi$
$571$	−14.1185	−0.590841	−0.295420	+	0.955367i	$0.595460\pi$
$572$	−6.60099	−0.276001
$573$	45.4052	1.89683
$574$	12.8841	0.537771
$575$	−11.1908	−0.466687
$576$	36.7814	1.53256
$577$	32.7421	1.36307	0.681536	−	0.731785i	$-0.261312\pi$
$577$	32.7421	1.36307	0.681536	+	0.731785i	$0.261312\pi$
$578$	7.95910	0.331055
$579$	17.9006	0.743922
$580$	33.4598	1.38934
$581$	−0.796023	−0.0330246
$582$	76.3857	3.16629
$583$	15.9317	0.659823
$584$	−71.8241	−2.97210
$585$	−24.7384	−1.02281
$586$	26.6004	1.09885
$587$	−23.8884	−0.985979	−0.492989	−	0.870035i	$-0.664096\pi$
$587$	−23.8884	−0.985979	−0.492989	+	0.870035i	$0.664096\pi$
$588$	92.5863	3.81820
$589$	32.2827	1.33019
$590$	56.5099	2.32648
$591$	−60.0701	−2.47095
$592$	14.9977	0.616403
$593$	4.96252	0.203786	0.101893	−	0.994795i	$-0.467510\pi$
$593$	4.96252	0.203786	0.101893	+	0.994795i	$0.467510\pi$
$594$	−20.1177	−0.825437
$595$	7.95037	0.325933
$596$	−14.1389	−0.579151
$597$	47.9785	1.96363
$598$	3.03897	0.124273
$599$	29.5437	1.20712	0.603561	−	0.797317i	$-0.293748\pi$
$599$	29.5437	1.20712	0.603561	+	0.797317i	$0.293748\pi$
$600$	234.034	9.55438
$601$	−21.1136	−0.861242	−0.430621	−	0.902533i	$-0.641705\pi$
$601$	−21.1136	−0.861242	−0.430621	+	0.902533i	$0.641705\pi$
$602$	−14.1259	−0.575728
$603$	26.2322	1.06826
$604$	−89.0821	−3.62470
$605$	38.6440	1.57110
$606$	117.500	4.77309
$607$	−46.1934	−1.87493	−0.937467	−	0.348075i	$-0.886836\pi$
$607$	−46.1934	−1.87493	−0.937467	+	0.348075i	$0.886836\pi$
$608$	51.7324	2.09802
$609$	2.64149	0.107039
$610$	−61.4361	−2.48747
$611$	2.42352	0.0980452
$612$	−94.3089	−3.81221
$613$	−13.0917	−0.528767	−0.264384	−	0.964418i	$-0.585169\pi$
$613$	−13.0917	−0.528767	−0.264384	+	0.964418i	$0.585169\pi$
$614$	34.7889	1.40397
$615$	−108.145	−4.36081
$616$	4.54579	0.183155
$617$	31.3920	1.26379	0.631897	−	0.775052i	$-0.282277\pi$
$617$	31.3920	1.26379	0.631897	+	0.775052i	$0.282277\pi$
$618$	17.2476	0.693800
$619$	−2.48137	−0.0997346	−0.0498673	−	0.998756i	$-0.515880\pi$
$619$	−2.48137	−0.0997346	−0.0498673	+	0.998756i	$0.515880\pi$
$620$	118.685	4.76650
$621$	6.53389	0.262196
$622$	73.0582	2.92937
$623$	−4.06514	−0.162866
$624$	−31.4190	−1.25777
$625$	44.2794	1.77118
$626$	48.5466	1.94031
$627$	−17.8172	−0.711550
$628$	−27.1569	−1.08368
$629$	−5.97904	−0.238400
$630$	29.2466	1.16521
$631$	13.6548	0.543588	0.271794	−	0.962355i	$-0.412383\pi$
$631$	13.6548	0.543588	0.271794	+	0.962355i	$0.412383\pi$
$632$	52.5540	2.09049
$633$	26.3891	1.04887
$634$	57.3700	2.27846
$635$	40.1388	1.59286
$636$	185.771	7.36631
$637$	−7.83702	−0.310514
$638$	−5.34467	−0.211598
$639$	14.6060	0.577803
$640$	−6.24818	−0.246981
$641$	−22.5159	−0.889323	−0.444662	−	0.895699i	$-0.646676\pi$
$641$	−22.5159	−0.889323	−0.444662	+	0.895699i	$0.646676\pi$
$642$	65.4855	2.58450
$643$	2.72666	0.107529	0.0537645	−	0.998554i	$-0.482878\pi$
$643$	2.72666	0.107529	0.0537645	+	0.998554i	$0.482878\pi$
$644$	−2.53459	−0.0998768
$645$	118.568	4.66860
$646$	−51.0211	−2.00740
$647$	−35.3858	−1.39116	−0.695579	−	0.718449i	$-0.744852\pi$
$647$	−35.3858	−1.39116	−0.695579	+	0.718449i	$0.744852\pi$
$648$	−21.6435	−0.850238
$649$	−6.36796	−0.249964
$650$	−34.0084	−1.33392
$651$	9.36962	0.367224
$652$	−45.8896	−1.79717
$653$	−26.2408	−1.02688	−0.513441	−	0.858125i	$-0.671629\pi$
$653$	−26.2408	−1.02688	−0.513441	+	0.858125i	$0.671629\pi$
$654$	88.9354	3.47765
$655$	24.4542	0.955503
$656$	−87.5356	−3.41769
$657$	52.0729	2.03156
$658$	−2.86518	−0.111696
$659$	25.3871	0.988942	0.494471	−	0.869194i	$-0.335362\pi$
$659$	25.3871	0.988942	0.494471	+	0.869194i	$0.335362\pi$
$660$	−65.5036	−2.54972
$661$	3.84386	0.149509	0.0747544	−	0.997202i	$-0.476183\pi$
$661$	3.84386	0.149509	0.0747544	+	0.997202i	$0.476183\pi$
$662$	24.7979	0.963798
$663$	12.5256	0.486453
$664$	10.9398	0.424547
$665$	11.1622	0.432851
$666$	−21.9948	−0.852280
$667$	1.73586	0.0672129
$668$	−86.5241	−3.34772
$669$	46.5215	1.79863
$670$	52.1744	2.01567
$671$	6.92307	0.267262
$672$	15.0146	0.579202
$673$	19.7313	0.760585	0.380292	−	0.924866i	$-0.375823\pi$
$673$	19.7313	0.760585	0.380292	+	0.924866i	$0.375823\pi$
$674$	−9.74777	−0.375470
$675$	−73.1192	−2.81436
$676$	−55.7602	−2.14462
$677$	14.2218	0.546590	0.273295	−	0.961930i	$-0.411887\pi$
$677$	14.2218	0.546590	0.273295	+	0.961930i	$0.411887\pi$
$678$	1.89146	0.0726411
$679$	5.39259	0.206949
$680$	−109.263	−4.19003
$681$	−43.9942	−1.68586
$682$	−18.9580	−0.725941
$683$	33.0142	1.26325	0.631627	−	0.775272i	$-0.282387\pi$
$683$	33.0142	1.26325	0.631627	+	0.775272i	$0.282387\pi$
$684$	−132.408	−5.06276
$685$	89.2562	3.41030
$686$	18.9164	0.722231
$687$	7.35578	0.280641
$688$	95.9725	3.65892
$689$	−15.7247	−0.599064
$690$	30.1566	1.14804
$691$	−32.8222	−1.24861	−0.624307	−	0.781179i	$-0.714618\pi$
$691$	−32.8222	−1.24861	−0.624307	+	0.781179i	$0.714618\pi$
$692$	87.5280	3.32732
$693$	−3.29572	−0.125194
$694$	26.6671	1.01227
$695$	66.7588	2.53230
$696$	−36.3023	−1.37603
$697$	34.8972	1.32183
$698$	−2.60584	−0.0986326
$699$	8.74641	0.330820
$700$	28.3640	1.07206
$701$	35.2583	1.33169	0.665844	−	0.746091i	$-0.268072\pi$
$701$	35.2583	1.33169	0.665844	+	0.746091i	$0.268072\pi$
$702$	19.8563	0.749427
$703$	−8.39448	−0.316604
$704$	−8.24377	−0.310699
$705$	24.0493	0.905750
$706$	42.0676	1.58323
$707$	8.29510	0.311969
$708$	−74.2534	−2.79062
$709$	17.6909	0.664395	0.332197	−	0.943210i	$-0.392210\pi$
$709$	17.6909	0.664395	0.332197	+	0.943210i	$0.392210\pi$
$710$	29.0505	1.09024
$711$	−38.1020	−1.42894
$712$	55.8676	2.09373
$713$	6.15727	0.230591
$714$	−14.8082	−0.554183
$715$	5.54458	0.207356
$716$	18.5068	0.691633
$717$	−60.9502	−2.27623
$718$	30.4510	1.13642
$719$	−35.7622	−1.33371	−0.666853	−	0.745189i	$-0.732359\pi$
$719$	−35.7622	−1.33371	−0.666853	+	0.745189i	$0.732359\pi$
$720$	−198.704	−7.40527
$721$	1.21763	0.0453468
$722$	−22.1218	−0.823289
$723$	−69.6909	−2.59183
$724$	−13.4498	−0.499859
$725$	−19.4256	−0.721450
$726$	−71.9774	−2.67133
$727$	2.60341	0.0965552	0.0482776	−	0.998834i	$-0.484627\pi$
$727$	2.60341	0.0965552	0.0482776	+	0.998834i	$0.484627\pi$
$728$	−4.48673	−0.166289
$729$	−40.6842	−1.50682
$730$	103.570	3.83330
$731$	−38.2607	−1.41512
$732$	80.7263	2.98373
$733$	−3.77512	−0.139437	−0.0697186	−	0.997567i	$-0.522210\pi$
$733$	−3.77512	−0.139437	−0.0697186	+	0.997567i	$0.522210\pi$
$734$	33.3259	1.23008
$735$	−77.7691	−2.86856
$736$	9.86689	0.363699
$737$	−5.87939	−0.216570
$738$	128.374	4.72553
$739$	−11.4822	−0.422379	−0.211189	−	0.977445i	$-0.567734\pi$
$739$	−11.4822	−0.422379	−0.211189	+	0.977445i	$0.567734\pi$
$740$	−30.8616	−1.13450
$741$	17.5857	0.646027
$742$	18.5903	0.682472
$743$	−28.0625	−1.02951	−0.514757	−	0.857336i	$-0.672118\pi$
$743$	−28.0625	−1.02951	−0.514757	+	0.857336i	$0.672118\pi$
$744$	−128.768	−4.72085
$745$	11.8761	0.435108
$746$	67.6721	2.47765
$747$	−7.93143	−0.290196
$748$	21.1374	0.772858
$749$	4.62307	0.168923
$750$	−186.692	−6.81704
$751$	36.8156	1.34342	0.671710	−	0.740814i	$-0.265560\pi$
$751$	36.8156	1.34342	0.671710	+	0.740814i	$0.265560\pi$
$752$	19.4663	0.709862
$753$	38.3992	1.39934
$754$	5.27523	0.192113
$755$	74.8257	2.72319
$756$	−16.5607	−0.602308
$757$	9.28858	0.337599	0.168800	−	0.985650i	$-0.446011\pi$
$757$	9.28858	0.337599	0.168800	+	0.985650i	$0.446011\pi$
$758$	−33.7304	−1.22514
$759$	−3.39827	−0.123349
$760$	−153.403	−5.56451
$761$	25.8784	0.938093	0.469046	−	0.883174i	$-0.344598\pi$
$761$	25.8784	0.938093	0.469046	+	0.883174i	$0.344598\pi$
$762$	−74.7618	−2.70833
$763$	6.27856	0.227299
$764$	−75.6274	−2.73610
$765$	79.2160	2.86406
$766$	38.1203	1.37734
$767$	6.28522	0.226946
$768$	51.7705	1.86811
$769$	13.2286	0.477036	0.238518	−	0.971138i	$-0.423338\pi$
$769$	13.2286	0.477036	0.238518	+	0.971138i	$0.423338\pi$
$770$	−6.55501	−0.236226
$771$	79.6446	2.86833
$772$	−29.8154	−1.07308
$773$	−7.43379	−0.267375	−0.133687	−	0.991024i	$-0.542682\pi$
$773$	−7.43379	−0.267375	−0.133687	+	0.991024i	$0.542682\pi$
$774$	−140.748	−5.05907
$775$	−68.9045	−2.47512
$776$	−74.1108	−2.66042
$777$	−2.43638	−0.0874048
$778$	7.92281	0.284046
$779$	48.9951	1.75543
$780$	64.6525	2.31493
$781$	−3.27362	−0.117139
$782$	−9.73124	−0.347988
$783$	11.3419	0.405328
$784$	−62.9487	−2.24817
$785$	22.8108	0.814153
$786$	−45.5478	−1.62464
$787$	−37.8198	−1.34813	−0.674065	−	0.738672i	$-0.735453\pi$
$787$	−37.8198	−1.34813	−0.674065	+	0.738672i	$0.735453\pi$
$788$	100.053	3.56425
$789$	9.37972	0.333927
$790$	−75.7827	−2.69623
$791$	0.133531	0.00474782
$792$	45.2934	1.60943
$793$	−6.83312	−0.242651
$794$	68.0150	2.41376
$795$	−156.041	−5.53420
$796$	−79.9136	−2.83246
$797$	8.21204	0.290886	0.145443	−	0.989367i	$-0.453539\pi$
$797$	8.21204	0.290886	0.145443	+	0.989367i	$0.453539\pi$
$798$	−20.7905	−0.735975
$799$	−7.76048	−0.274546
$800$	−110.418	−3.90387
$801$	−40.5043	−1.43115
$802$	35.1309	1.24052
$803$	−11.6710	−0.411862
$804$	−68.5566	−2.41780
$805$	2.12896	0.0750360
$806$	18.7117	0.659093
$807$	3.17653	0.111819
$808$	−114.000	−4.01051
$809$	46.9992	1.65240	0.826202	−	0.563374i	$-0.190497\pi$
$809$	46.9992	1.65240	0.826202	+	0.563374i	$0.190497\pi$
$810$	31.2099	1.09660
$811$	22.1039	0.776173	0.388087	−	0.921623i	$-0.373136\pi$
$811$	22.1039	0.776173	0.388087	+	0.921623i	$0.373136\pi$
$812$	−4.39970	−0.154399
$813$	19.4372	0.681692
$814$	4.92966	0.172785
$815$	38.5455	1.35019
$816$	100.608	3.52200
$817$	−53.7174	−1.87933
$818$	90.8889	3.17786
$819$	3.25290	0.113666
$820$	180.127	6.29030
$821$	−11.8570	−0.413813	−0.206906	−	0.978361i	$-0.566340\pi$
$821$	−11.8570	−0.413813	−0.206906	+	0.978361i	$0.566340\pi$
$822$	−166.247	−5.79852
$823$	28.9310	1.00847	0.504235	−	0.863566i	$-0.331774\pi$
$823$	28.9310	1.00847	0.504235	+	0.863566i	$0.331774\pi$
$824$	−16.7339	−0.582955
$825$	38.0292	1.32401
$826$	−7.43062	−0.258544
$827$	−13.1987	−0.458965	−0.229483	−	0.973313i	$-0.573703\pi$
$827$	−13.1987	−0.458965	−0.229483	+	0.973313i	$0.573703\pi$
$828$	−25.2542	−0.877643
$829$	−0.865918	−0.0300746	−0.0150373	−	0.999887i	$-0.504787\pi$
$829$	−0.865918	−0.0300746	−0.0150373	+	0.999887i	$0.504787\pi$
$830$	−15.7752	−0.547564
$831$	12.6541	0.438964
$832$	8.13667	0.282088
$833$	25.0953	0.869501
$834$	−124.344	−4.30566
$835$	72.6770	2.51509
$836$	29.6765	1.02638
$837$	40.2309	1.39058
$838$	43.7104	1.50995
$839$	18.3317	0.632879	0.316440	−	0.948613i	$-0.397512\pi$
$839$	18.3317	0.632879	0.316440	+	0.948613i	$0.397512\pi$
$840$	−44.5231	−1.53619
$841$	−25.9868	−0.896096
$842$	−84.9847	−2.92877
$843$	41.7356	1.43745
$844$	−43.9540	−1.51296
$845$	46.8365	1.61123
$846$	−28.5481	−0.981503
$847$	−5.08138	−0.174598
$848$	−126.304	−4.33731
$849$	5.95825	0.204486
$850$	108.900	3.73524
$851$	−1.60108	−0.0548842
$852$	−38.1720	−1.30775
$853$	24.1024	0.825249	0.412625	−	0.910901i	$-0.364612\pi$
$853$	24.1024	0.825249	0.412625	+	0.910901i	$0.364612\pi$
$854$	8.07837	0.276436
$855$	111.218	3.80358
$856$	−63.5352	−2.17159
$857$	21.5007	0.734449	0.367224	−	0.930132i	$-0.380308\pi$
$857$	21.5007	0.734449	0.367224	+	0.930132i	$0.380308\pi$
$858$	−10.3272	−0.352566
$859$	−13.2788	−0.453066	−0.226533	−	0.974003i	$-0.572739\pi$
$859$	−13.2788	−0.453066	−0.226533	+	0.974003i	$0.572739\pi$
$860$	−197.488	−6.73428
$861$	14.2202	0.484622
$862$	−96.9093	−3.30074
$863$	11.5011	0.391503	0.195752	−	0.980654i	$-0.437285\pi$
$863$	11.5011	0.391503	0.195752	+	0.980654i	$0.437285\pi$
$864$	64.4692	2.19329
$865$	−73.5203	−2.49976
$866$	−11.1928	−0.380347
$867$	8.78448	0.298336
$868$	−15.6061	−0.529707
$869$	8.53975	0.289691
$870$	52.3477	1.77475
$871$	5.80301	0.196627
$872$	−86.2868	−2.92204
$873$	53.7307	1.81851
$874$	−13.6625	−0.462141
$875$	−13.1799	−0.445562
$876$	−136.090	−4.59805
$877$	3.33935	0.112762	0.0563810	−	0.998409i	$-0.482044\pi$
$877$	3.33935	0.112762	0.0563810	+	0.998409i	$0.482044\pi$
$878$	32.2408	1.08808
$879$	29.3589	0.990251
$880$	44.5354	1.50129
$881$	−18.5373	−0.624539	−0.312269	−	0.949994i	$-0.601089\pi$
$881$	−18.5373	−0.624539	−0.312269	+	0.949994i	$0.601089\pi$
$882$	92.3168	3.10847
$883$	7.56444	0.254564	0.127282	−	0.991867i	$-0.459375\pi$
$883$	7.56444	0.254564	0.127282	+	0.991867i	$0.459375\pi$
$884$	−20.8627	−0.701690
$885$	62.3701	2.09655
$886$	−13.7257	−0.461124
$887$	11.9713	0.401956	0.200978	−	0.979596i	$-0.435588\pi$
$887$	11.9713	0.401956	0.200978	+	0.979596i	$0.435588\pi$
$888$	33.4834	1.12363
$889$	−5.27795	−0.177017
$890$	−80.5608	−2.70040
$891$	−3.51696	−0.117823
$892$	−77.4867	−2.59445
$893$	−10.8956	−0.364607
$894$	−22.1203	−0.739812
$895$	−15.5451	−0.519614
$896$	0.821588	0.0274473
$897$	3.35412	0.111991
$898$	77.9488	2.60119
$899$	10.6882	0.356470
$900$	282.614	9.42045
$901$	50.3529	1.67750
$902$	−28.7724	−0.958017
$903$	−15.5908	−0.518828
$904$	−1.83513	−0.0610355
$905$	11.2974	0.375537
$906$	−139.369	−4.63022
$907$	−11.0099	−0.365578	−0.182789	−	0.983152i	$-0.558513\pi$
$907$	−11.0099	−0.365578	−0.182789	+	0.983152i	$0.558513\pi$
$908$	73.2773	2.43179
$909$	82.6508	2.74135
$910$	6.46984	0.214473
$911$	−9.94415	−0.329464	−0.164732	−	0.986338i	$-0.552676\pi$
$911$	−9.94415	−0.329464	−0.164732	+	0.986338i	$0.552676\pi$
$912$	141.252	4.67734
$913$	1.77766	0.0588320
$914$	−0.697105	−0.0230582
$915$	−67.8071	−2.24163
$916$	−12.2519	−0.404813
$917$	−3.21553	−0.106186
$918$	−63.5828	−2.09855
$919$	−4.00147	−0.131996	−0.0659981	−	0.997820i	$-0.521023\pi$
$919$	−4.00147	−0.131996	−0.0659981	+	0.997820i	$0.521023\pi$
$920$	−29.2585	−0.964623
$921$	38.3966	1.26521
$922$	42.0944	1.38631
$923$	3.23109	0.106353
$924$	8.61321	0.283354
$925$	17.9173	0.589116
$926$	42.5310	1.39766
$927$	12.1322	0.398474
$928$	17.1276	0.562240
$929$	−32.9597	−1.08137	−0.540687	−	0.841224i	$-0.681836\pi$
$929$	−32.9597	−1.08137	−0.540687	+	0.841224i	$0.681836\pi$
$930$	185.682	6.08876
$931$	35.2334	1.15473
$932$	−14.5681	−0.477195
$933$	80.6345	2.63986
$934$	31.8001	1.04053
$935$	−17.7546	−0.580637
$936$	−44.7049	−1.46123
$937$	−2.05324	−0.0670764	−0.0335382	−	0.999437i	$-0.510678\pi$
$937$	−2.05324	−0.0670764	−0.0335382	+	0.999437i	$0.510678\pi$
$938$	−6.86053	−0.224004
$939$	53.5810	1.74855
$940$	−40.0568	−1.30651
$941$	−39.9286	−1.30164	−0.650818	−	0.759234i	$-0.725574\pi$
$941$	−39.9286	−1.30164	−0.650818	+	0.759234i	$0.725574\pi$
$942$	−42.4870	−1.38430
$943$	9.34482	0.304309
$944$	50.4843	1.64313
$945$	13.9104	0.452505
$946$	31.5456	1.02564
$947$	−53.1709	−1.72782	−0.863912	−	0.503644i	$-0.831992\pi$
$947$	−53.1709	−1.72782	−0.863912	+	0.503644i	$0.831992\pi$
$948$	99.5776	3.23413
$949$	11.5194	0.373936
$950$	152.894	4.96053
$951$	63.3194	2.05327
$952$	14.3672	0.465643
$953$	37.2468	1.20654	0.603271	−	0.797536i	$-0.293864\pi$
$953$	37.2468	1.20654	0.603271	+	0.797536i	$0.293864\pi$
$954$	185.231	5.99706
$955$	63.5242	2.05560
$956$	101.519	3.28337
$957$	−5.89893	−0.190685
$958$	−38.5005	−1.24389
$959$	−11.7365	−0.378991
$960$	80.7426	2.60596
$961$	6.91194	0.222966
$962$	−4.86562	−0.156874
$963$	46.0634	1.48437
$964$	116.078	3.73862
$965$	25.0438	0.806188
$966$	−3.96536	−0.127583
$967$	−48.2098	−1.55032	−0.775161	−	0.631764i	$-0.782331\pi$
$967$	−48.2098	−1.55032	−0.775161	+	0.631764i	$0.782331\pi$
$968$	69.8338	2.24454
$969$	−56.3121	−1.80901
$970$	106.867	3.43131
$971$	−9.64763	−0.309607	−0.154804	−	0.987945i	$-0.549474\pi$
$971$	−9.64763	−0.309607	−0.154804	+	0.987945i	$0.549474\pi$
$972$	52.8908	1.69647
$973$	−8.77826	−0.281418
$974$	−75.9971	−2.43511
$975$	−37.5351	−1.20209
$976$	−54.8852	−1.75683
$977$	10.1054	0.323301	0.161651	−	0.986848i	$-0.448318\pi$
$977$	10.1054	0.323301	0.161651	+	0.986848i	$0.448318\pi$
$978$	−71.7941	−2.29572
$979$	9.07819	0.290140
$980$	129.533	4.13778
$981$	62.5584	1.99734
$982$	99.3738	3.17115
$983$	19.2744	0.614757	0.307379	−	0.951587i	$-0.400548\pi$
$983$	19.2744	0.614757	0.307379	+	0.951587i	$0.400548\pi$
$984$	−195.429	−6.23005
$985$	−84.0411	−2.67777
$986$	−16.8921	−0.537954
$987$	−3.16230	−0.100657
$988$	−29.2910	−0.931869
$989$	−10.2455	−0.325788
$990$	−65.3129	−2.07578
$991$	25.7573	0.818207	0.409103	−	0.912488i	$-0.365842\pi$
$991$	25.7573	0.818207	0.409103	+	0.912488i	$0.365842\pi$
$992$	60.7531	1.92891
$993$	27.3695	0.868545
$994$	−3.81991	−0.121160
$995$	67.1244	2.12799
$996$	20.7284	0.656804
$997$	36.3673	1.15176	0.575882	−	0.817533i	$-0.304659\pi$
$997$	36.3673	1.15176	0.575882	+	0.817533i	$0.304659\pi$
$998$	−84.0963	−2.66202
$999$	−10.4612	−0.330979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.10	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.10	✓	169	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60584 q^{2} -2.87607 q^{3} +4.79042 q^{4} -4.02377 q^{5} +7.49460 q^{6} +0.529095 q^{7} -7.27140 q^{8} +5.27181 q^{9} +O(q^{10})\)	\(q-2.60584 q^{2} -2.87607 q^{3} +4.79042 q^{4} -4.02377 q^{5} +7.49460 q^{6} +0.529095 q^{7} -7.27140 q^{8} +5.27181 q^{9} +10.4853 q^{10} -1.18156 q^{11} -13.7776 q^{12} +1.16621 q^{13} -1.37874 q^{14} +11.5727 q^{15} +9.36729 q^{16} -3.73439 q^{17} -13.7375 q^{18} -5.24303 q^{19} -19.2756 q^{20} -1.52172 q^{21} +3.07897 q^{22} -1.00000 q^{23} +20.9131 q^{24} +11.1908 q^{25} -3.03897 q^{26} -6.53389 q^{27} +2.53459 q^{28} -1.73586 q^{29} -30.1566 q^{30} -6.15727 q^{31} -9.86689 q^{32} +3.39827 q^{33} +9.73124 q^{34} -2.12896 q^{35} +25.2542 q^{36} +1.60108 q^{37} +13.6625 q^{38} -3.35412 q^{39} +29.2585 q^{40} -9.34482 q^{41} +3.96536 q^{42} +10.2455 q^{43} -5.66019 q^{44} -21.2126 q^{45} +2.60584 q^{46} +2.07811 q^{47} -26.9410 q^{48} -6.72006 q^{49} -29.1614 q^{50} +10.7404 q^{51} +5.58665 q^{52} -13.4836 q^{53} +17.0263 q^{54} +4.75435 q^{55} -3.84726 q^{56} +15.0793 q^{57} +4.52339 q^{58} +5.38943 q^{59} +55.4380 q^{60} -5.85924 q^{61} +16.0449 q^{62} +2.78929 q^{63} +6.97700 q^{64} -4.69258 q^{65} -8.85535 q^{66} +4.97594 q^{67} -17.8893 q^{68} +2.87607 q^{69} +5.54774 q^{70} +2.77058 q^{71} -38.3334 q^{72} +9.87762 q^{73} -4.17215 q^{74} -32.1855 q^{75} -25.1163 q^{76} -0.625160 q^{77} +8.74030 q^{78} -7.22750 q^{79} -37.6919 q^{80} +2.97653 q^{81} +24.3511 q^{82} -1.50450 q^{83} -7.28967 q^{84} +15.0263 q^{85} -26.6982 q^{86} +4.99247 q^{87} +8.59163 q^{88} -7.68319 q^{89} +55.2766 q^{90} +0.617038 q^{91} -4.79042 q^{92} +17.7088 q^{93} -5.41524 q^{94} +21.0968 q^{95} +28.3779 q^{96} +10.1921 q^{97} +17.5114 q^{98} -6.22898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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