LMFDB - Embedded newform 8009.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8009,2,Mod(1,8009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8009, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8009 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8009.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:	$63.9521869788$
Analytic rank:	$1$
Dimension:	$306$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56252 q^{2} +1.99928 q^{3} +4.56650 q^{4} -3.64858 q^{5} -5.12319 q^{6} -3.78692 q^{7} -6.57671 q^{8} +0.997123 q^{9} +O(q^{10})$	\(q-2.56252 q^{2} +1.99928 q^{3} +4.56650 q^{4} -3.64858 q^{5} -5.12319 q^{6} -3.78692 q^{7} -6.57671 q^{8} +0.997123 q^{9} +9.34955 q^{10} +4.03811 q^{11} +9.12972 q^{12} +4.74175 q^{13} +9.70405 q^{14} -7.29453 q^{15} +7.71993 q^{16} +7.35966 q^{17} -2.55515 q^{18} -1.99850 q^{19} -16.6612 q^{20} -7.57112 q^{21} -10.3477 q^{22} -7.47178 q^{23} -13.1487 q^{24} +8.31212 q^{25} -12.1508 q^{26} -4.00431 q^{27} -17.2930 q^{28} -5.79597 q^{29} +18.6924 q^{30} -4.61623 q^{31} -6.62906 q^{32} +8.07332 q^{33} -18.8593 q^{34} +13.8169 q^{35} +4.55337 q^{36} +1.14866 q^{37} +5.12120 q^{38} +9.48009 q^{39} +23.9956 q^{40} +11.6777 q^{41} +19.4011 q^{42} -5.16267 q^{43} +18.4400 q^{44} -3.63808 q^{45} +19.1466 q^{46} +5.04508 q^{47} +15.4343 q^{48} +7.34076 q^{49} -21.3000 q^{50} +14.7140 q^{51} +21.6532 q^{52} -9.80966 q^{53} +10.2611 q^{54} -14.7334 q^{55} +24.9055 q^{56} -3.99557 q^{57} +14.8523 q^{58} -2.86738 q^{59} -33.3105 q^{60} -13.4879 q^{61} +11.8292 q^{62} -3.77603 q^{63} +1.54722 q^{64} -17.3006 q^{65} -20.6880 q^{66} -6.82278 q^{67} +33.6079 q^{68} -14.9382 q^{69} -35.4060 q^{70} +13.4018 q^{71} -6.55779 q^{72} +12.4765 q^{73} -2.94347 q^{74} +16.6183 q^{75} -9.12616 q^{76} -15.2920 q^{77} -24.2929 q^{78} -1.60487 q^{79} -28.1668 q^{80} -10.9971 q^{81} -29.9243 q^{82} +5.72530 q^{83} -34.5735 q^{84} -26.8523 q^{85} +13.2294 q^{86} -11.5878 q^{87} -26.5575 q^{88} +7.10777 q^{89} +9.32265 q^{90} -17.9566 q^{91} -34.1199 q^{92} -9.22913 q^{93} -12.9281 q^{94} +7.29169 q^{95} -13.2533 q^{96} -1.53145 q^{97} -18.8108 q^{98} +4.02650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 306 q - 13 q^{2} - 25 q^{3} + 253 q^{4} - 25 q^{5} - 49 q^{6} - 102 q^{7} - 33 q^{8} + 251 q^{9}+O(q^{10}) $ 306 * q - 13 * q^2 - 25 * q^3 + 253 * q^4 - 25 * q^5 - 49 * q^6 - 102 * q^7 - 33 * q^8 + 251 * q^9	\( 306 q - 13 q^{2} - 25 q^{3} + 253 q^{4} - 25 q^{5} - 49 q^{6} - 102 q^{7} - 33 q^{8} + 251 q^{9} - 61 q^{10} - 43 q^{11} - 50 q^{12} - 89 q^{13} - 40 q^{14} - 61 q^{15} + 151 q^{16} - 52 q^{17} - 57 q^{18} - 185 q^{19} - 66 q^{20} - 63 q^{21} - 55 q^{22} - 62 q^{23} - 131 q^{24} + 209 q^{25} - 57 q^{26} - 88 q^{27} - 182 q^{28} - 67 q^{29} - 68 q^{30} - 240 q^{31} - 64 q^{32} - 52 q^{33} - 128 q^{34} - 99 q^{35} + 106 q^{36} - 49 q^{37} - 45 q^{38} - 190 q^{39} - 158 q^{40} - 72 q^{41} - 36 q^{42} - 141 q^{43} - 80 q^{44} - 100 q^{45} - 91 q^{46} - 105 q^{47} - 85 q^{48} + 116 q^{49} - 51 q^{50} - 145 q^{51} - 237 q^{52} - 48 q^{53} - 156 q^{54} - 420 q^{55} - 116 q^{56} - 35 q^{57} - 43 q^{58} - 139 q^{59} - 73 q^{60} - 233 q^{61} - 58 q^{62} - 252 q^{63} - 3 q^{64} - 45 q^{65} - 127 q^{66} - 108 q^{67} - 85 q^{68} - 164 q^{69} - 56 q^{70} - 131 q^{71} - 117 q^{72} - 118 q^{73} - 47 q^{74} - 112 q^{75} - 389 q^{76} - 36 q^{77} + 9 q^{78} - 382 q^{79} - 119 q^{80} + 102 q^{81} - 131 q^{82} - 59 q^{83} - 144 q^{84} - 140 q^{85} - 38 q^{86} - 301 q^{87} - 131 q^{88} - 98 q^{89} - 138 q^{90} - 176 q^{91} - 97 q^{92} - 60 q^{93} - 342 q^{94} - 154 q^{95} - 243 q^{96} - 109 q^{97} - 21 q^{98} - 173 q^{99}+O(q^{100}) \) 306 * q - 13 * q^2 - 25 * q^3 + 253 * q^4 - 25 * q^5 - 49 * q^6 - 102 * q^7 - 33 * q^8 + 251 * q^9 - 61 * q^10 - 43 * q^11 - 50 * q^12 - 89 * q^13 - 40 * q^14 - 61 * q^15 + 151 * q^16 - 52 * q^17 - 57 * q^18 - 185 * q^19 - 66 * q^20 - 63 * q^21 - 55 * q^22 - 62 * q^23 - 131 * q^24 + 209 * q^25 - 57 * q^26 - 88 * q^27 - 182 * q^28 - 67 * q^29 - 68 * q^30 - 240 * q^31 - 64 * q^32 - 52 * q^33 - 128 * q^34 - 99 * q^35 + 106 * q^36 - 49 * q^37 - 45 * q^38 - 190 * q^39 - 158 * q^40 - 72 * q^41 - 36 * q^42 - 141 * q^43 - 80 * q^44 - 100 * q^45 - 91 * q^46 - 105 * q^47 - 85 * q^48 + 116 * q^49 - 51 * q^50 - 145 * q^51 - 237 * q^52 - 48 * q^53 - 156 * q^54 - 420 * q^55 - 116 * q^56 - 35 * q^57 - 43 * q^58 - 139 * q^59 - 73 * q^60 - 233 * q^61 - 58 * q^62 - 252 * q^63 - 3 * q^64 - 45 * q^65 - 127 * q^66 - 108 * q^67 - 85 * q^68 - 164 * q^69 - 56 * q^70 - 131 * q^71 - 117 * q^72 - 118 * q^73 - 47 * q^74 - 112 * q^75 - 389 * q^76 - 36 * q^77 + 9 * q^78 - 382 * q^79 - 119 * q^80 + 102 * q^81 - 131 * q^82 - 59 * q^83 - 144 * q^84 - 140 * q^85 - 38 * q^86 - 301 * q^87 - 131 * q^88 - 98 * q^89 - 138 * q^90 - 176 * q^91 - 97 * q^92 - 60 * q^93 - 342 * q^94 - 154 * q^95 - 243 * q^96 - 109 * q^97 - 21 * q^98 - 173 * 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 $

$2$	−2.56252	−1.81197	−0.905987	−	0.423305i	$-0.860870\pi$
$2$	−2.56252	−1.81197	−0.905987	+	0.423305i	$0.860870\pi$
$3$	1.99928	1.15429	0.577143	−	0.816643i	$-0.304168\pi$
$3$	1.99928	1.15429	0.577143	+	0.816643i	$0.304168\pi$
$4$	4.56650	2.28325
$5$	−3.64858	−1.63169	−0.815847	−	0.578268i	$-0.803729\pi$
$5$	−3.64858	−1.63169	−0.815847	+	0.578268i	$0.803729\pi$
$6$	−5.12319	−2.09154
$7$	−3.78692	−1.43132	−0.715661	−	0.698448i	$-0.753874\pi$
$7$	−3.78692	−1.43132	−0.715661	+	0.698448i	$0.753874\pi$
$8$	−6.57671	−2.32522
$9$	0.997123	0.332374
$10$	9.34955	2.95659
$11$	4.03811	1.21754	0.608768	−	0.793348i	$-0.291664\pi$
$11$	4.03811	1.21754	0.608768	+	0.793348i	$0.291664\pi$
$12$	9.12972	2.63552
$13$	4.74175	1.31513	0.657563	−	0.753400i	$-0.271587\pi$
$13$	4.74175	1.31513	0.657563	+	0.753400i	$0.271587\pi$
$14$	9.70405	2.59352
$15$	−7.29453	−1.88344
$16$	7.71993	1.92998
$17$	7.35966	1.78498	0.892489	−	0.451069i	$-0.148957\pi$
$17$	7.35966	1.78498	0.892489	+	0.451069i	$0.148957\pi$
$18$	−2.55515	−0.602254
$19$	−1.99850	−0.458488	−0.229244	−	0.973369i	$-0.573625\pi$
$19$	−1.99850	−0.458488	−0.229244	+	0.973369i	$0.573625\pi$
$20$	−16.6612	−3.72557
$21$	−7.57112	−1.65215
$22$	−10.3477	−2.20615
$23$	−7.47178	−1.55797	−0.778987	−	0.627040i	$-0.784266\pi$
$23$	−7.47178	−1.55797	−0.778987	+	0.627040i	$0.784266\pi$
$24$	−13.1487	−2.68396
$25$	8.31212	1.66242
$26$	−12.1508	−2.38297
$27$	−4.00431	−0.770630
$28$	−17.2930	−3.26807
$29$	−5.79597	−1.07628	−0.538142	−	0.842854i	$-0.680874\pi$
$29$	−5.79597	−1.07628	−0.538142	+	0.842854i	$0.680874\pi$
$30$	18.6924	3.41274
$31$	−4.61623	−0.829099	−0.414549	−	0.910027i	$-0.636061\pi$
$31$	−4.61623	−0.829099	−0.414549	+	0.910027i	$0.636061\pi$
$32$	−6.62906	−1.17186
$33$	8.07332	1.40538
$34$	−18.8593	−3.23434
$35$	13.8169	2.33548
$36$	4.55337	0.758894
$37$	1.14866	0.188839	0.0944195	−	0.995533i	$-0.469901\pi$
$37$	1.14866	0.188839	0.0944195	+	0.995533i	$0.469901\pi$
$38$	5.12120	0.830768
$39$	9.48009	1.51803
$40$	23.9956	3.79404
$41$	11.6777	1.82375	0.911875	−	0.410469i	$-0.134635\pi$
$41$	11.6777	1.82375	0.911875	+	0.410469i	$0.134635\pi$
$42$	19.4011	2.99366
$43$	−5.16267	−0.787299	−0.393650	−	0.919261i	$-0.628788\pi$
$43$	−5.16267	−0.787299	−0.393650	+	0.919261i	$0.628788\pi$
$44$	18.4400	2.77994
$45$	−3.63808	−0.542333
$46$	19.1466	2.82301
$47$	5.04508	0.735901	0.367950	−	0.929845i	$-0.380060\pi$
$47$	5.04508	0.735901	0.367950	+	0.929845i	$0.380060\pi$
$48$	15.4343	2.22775
$49$	7.34076	1.04868
$50$	−21.3000	−3.01227
$51$	14.7140	2.06037
$52$	21.6532	3.00276
$53$	−9.80966	−1.34746	−0.673730	−	0.738977i	$-0.735309\pi$
$53$	−9.80966	−1.34746	−0.673730	+	0.738977i	$0.735309\pi$
$54$	10.2611	1.39636
$55$	−14.7334	−1.98665
$56$	24.9055	3.32813
$57$	−3.99557	−0.529226
$58$	14.8523	1.95020
$59$	−2.86738	−0.373301	−0.186651	−	0.982426i	$-0.559763\pi$
$59$	−2.86738	−0.373301	−0.186651	+	0.982426i	$0.559763\pi$
$60$	−33.3105	−4.30036
$61$	−13.4879	−1.72695	−0.863476	−	0.504390i	$-0.831717\pi$
$61$	−13.4879	−1.72695	−0.863476	+	0.504390i	$0.831717\pi$
$62$	11.8292	1.50231
$63$	−3.77603	−0.475735
$64$	1.54722	0.193402
$65$	−17.3006	−2.14588
$66$	−20.6880	−2.54652
$67$	−6.82278	−0.833535	−0.416767	−	0.909013i	$-0.636837\pi$
$67$	−6.82278	−0.833535	−0.416767	+	0.909013i	$0.636837\pi$
$68$	33.6079	4.07555
$69$	−14.9382	−1.79835
$70$	−35.4060	−4.23182
$71$	13.4018	1.59050	0.795251	−	0.606280i	$-0.207339\pi$
$71$	13.4018	1.59050	0.795251	+	0.606280i	$0.207339\pi$
$72$	−6.55779	−0.772843
$73$	12.4765	1.46027	0.730133	−	0.683305i	$-0.239458\pi$
$73$	12.4765	1.46027	0.730133	+	0.683305i	$0.239458\pi$
$74$	−2.94347	−0.342171
$75$	16.6183	1.91891
$76$	−9.12616	−1.04684
$77$	−15.2920	−1.74269
$78$	−24.2929	−2.75063
$79$	−1.60487	−0.180561	−0.0902807	−	0.995916i	$-0.528776\pi$
$79$	−1.60487	−0.180561	−0.0902807	+	0.995916i	$0.528776\pi$
$80$	−28.1668	−3.14914
$81$	−10.9971	−1.22190
$82$	−29.9243	−3.30459
$83$	5.72530	0.628434	0.314217	−	0.949351i	$-0.398258\pi$
$83$	5.72530	0.628434	0.314217	+	0.949351i	$0.398258\pi$
$84$	−34.5735	−3.77228
$85$	−26.8523	−2.91254
$86$	13.2294	1.42657
$87$	−11.5878	−1.24234
$88$	−26.5575	−2.83104
$89$	7.10777	0.753422	0.376711	−	0.926331i	$-0.377055\pi$
$89$	7.10777	0.753422	0.376711	+	0.926331i	$0.377055\pi$
$90$	9.32265	0.982694
$91$	−17.9566	−1.88237
$92$	−34.1199	−3.55725
$93$	−9.22913	−0.957016
$94$	−12.9281	−1.33343
$95$	7.29169	0.748112
$96$	−13.2533	−1.35266
$97$	−1.53145	−0.155495	−0.0777477	−	0.996973i	$-0.524773\pi$
$97$	−1.53145	−0.155495	−0.0777477	+	0.996973i	$0.524773\pi$
$98$	−18.8108	−1.90018
$99$	4.02650	0.404678
$100$	37.9573	3.79573
$101$	12.4889	1.24269	0.621345	−	0.783537i	$-0.286587\pi$
$101$	12.4889	1.24269	0.621345	+	0.783537i	$0.286587\pi$
$102$	−37.7049	−3.73335
$103$	10.2071	1.00573	0.502867	−	0.864364i	$-0.332279\pi$
$103$	10.2071	1.00573	0.502867	+	0.864364i	$0.332279\pi$
$104$	−31.1851	−3.05795
$105$	27.6238	2.69581
$106$	25.1374	2.44156
$107$	16.8075	1.62485	0.812423	−	0.583068i	$-0.198148\pi$
$107$	16.8075	1.62485	0.812423	+	0.583068i	$0.198148\pi$
$108$	−18.2857	−1.75954
$109$	11.4951	1.10103	0.550513	−	0.834826i	$-0.314432\pi$
$109$	11.4951	1.10103	0.550513	+	0.834826i	$0.314432\pi$
$110$	37.7545	3.59975
$111$	2.29650	0.217974
$112$	−29.2348	−2.76243
$113$	−16.2184	−1.52570	−0.762849	−	0.646576i	$-0.776200\pi$
$113$	−16.2184	−1.52570	−0.762849	+	0.646576i	$0.776200\pi$
$114$	10.2387	0.958944
$115$	27.2614	2.54214
$116$	−26.4673	−2.45743
$117$	4.72811	0.437114
$118$	7.34771	0.676412
$119$	−27.8704	−2.55488
$120$	47.9740	4.37941
$121$	5.30635	0.482396
$122$	34.5631	3.12919
$123$	23.3470	2.10513
$124$	−21.0800	−1.89304
$125$	−12.0845	−1.08087
$126$	9.67614	0.862019
$127$	7.19217	0.638202	0.319101	−	0.947721i	$-0.396619\pi$
$127$	7.19217	0.638202	0.319101	+	0.947721i	$0.396619\pi$
$128$	9.29334	0.821423
$129$	−10.3216	−0.908768
$130$	44.3332	3.88828
$131$	−5.37780	−0.469861	−0.234930	−	0.972012i	$-0.575486\pi$
$131$	−5.37780	−0.469861	−0.234930	+	0.972012i	$0.575486\pi$
$132$	36.8668	3.20885
$133$	7.56817	0.656243
$134$	17.4835	1.51034
$135$	14.6100	1.25743
$136$	−48.4023	−4.15046
$137$	3.43726	0.293665	0.146833	−	0.989161i	$-0.453092\pi$
$137$	3.43726	0.293665	0.146833	+	0.989161i	$0.453092\pi$
$138$	38.2794	3.25856
$139$	−1.28825	−0.109268	−0.0546339	−	0.998506i	$-0.517399\pi$
$139$	−1.28825	−0.109268	−0.0546339	+	0.998506i	$0.517399\pi$
$140$	63.0948	5.33248
$141$	10.0865	0.849439
$142$	−34.3424	−2.88195
$143$	19.1477	1.60121
$144$	7.69773	0.641477
$145$	21.1470	1.75617
$146$	−31.9713	−2.64596
$147$	14.6762	1.21048
$148$	5.24537	0.431167
$149$	1.04719	0.0857892	0.0428946	−	0.999080i	$-0.486342\pi$
$149$	1.04719	0.0857892	0.0428946	+	0.999080i	$0.486342\pi$
$150$	−42.5846	−3.47702
$151$	−10.3582	−0.842936	−0.421468	−	0.906843i	$-0.638485\pi$
$151$	−10.3582	−0.842936	−0.421468	+	0.906843i	$0.638485\pi$
$152$	13.1436	1.06608
$153$	7.33848	0.593281
$154$	39.1861	3.15770
$155$	16.8427	1.35283
$156$	43.2909	3.46604
$157$	4.04749	0.323025	0.161512	−	0.986871i	$-0.448363\pi$
$157$	4.04749	0.323025	0.161512	+	0.986871i	$0.448363\pi$
$158$	4.11250	0.327173
$159$	−19.6123	−1.55535
$160$	24.1866	1.91212
$161$	28.2950	2.22996
$162$	28.1803	2.21405
$163$	9.62088	0.753565	0.376783	−	0.926302i	$-0.377030\pi$
$163$	9.62088	0.753565	0.376783	+	0.926302i	$0.377030\pi$
$164$	53.3262	4.16408
$165$	−29.4561	−2.29316
$166$	−14.6712	−1.13871
$167$	−9.57887	−0.741235	−0.370617	−	0.928786i	$-0.620854\pi$
$167$	−9.57887	−0.741235	−0.370617	+	0.928786i	$0.620854\pi$
$168$	49.7930	3.84162
$169$	9.48421	0.729555
$170$	68.8094	5.27744
$171$	−1.99275	−0.152390
$172$	−23.5753	−1.79760
$173$	5.10238	0.387927	0.193963	−	0.981009i	$-0.437866\pi$
$173$	5.10238	0.387927	0.193963	+	0.981009i	$0.437866\pi$
$174$	29.6939	2.25109
$175$	−31.4773	−2.37946
$176$	31.1740	2.34983
$177$	−5.73270	−0.430896
$178$	−18.2138	−1.36518
$179$	−11.1715	−0.834998	−0.417499	−	0.908677i	$-0.637093\pi$
$179$	−11.1715	−0.834998	−0.417499	+	0.908677i	$0.637093\pi$
$180$	−16.6133	−1.23828
$181$	−11.4604	−0.851842	−0.425921	−	0.904760i	$-0.640050\pi$
$181$	−11.4604	−0.851842	−0.425921	+	0.904760i	$0.640050\pi$
$182$	46.0142	3.41080
$183$	−26.9661	−1.99339
$184$	49.1397	3.62263
$185$	−4.19098	−0.308127
$186$	23.6498	1.73409
$187$	29.7191	2.17328
$188$	23.0384	1.68025
$189$	15.1640	1.10302
$190$	−18.6851	−1.35556
$191$	−18.2587	−1.32115	−0.660577	−	0.750758i	$-0.729688\pi$
$191$	−18.2587	−1.32115	−0.660577	+	0.750758i	$0.729688\pi$
$192$	3.09332	0.223241
$193$	−10.4478	−0.752050	−0.376025	−	0.926610i	$-0.622709\pi$
$193$	−10.4478	−0.752050	−0.376025	+	0.926610i	$0.622709\pi$
$194$	3.92438	0.281754
$195$	−34.5889	−2.47696
$196$	33.5216	2.39440
$197$	4.26859	0.304124	0.152062	−	0.988371i	$-0.451409\pi$
$197$	4.26859	0.304124	0.152062	+	0.988371i	$0.451409\pi$
$198$	−10.3180	−0.733266
$199$	−22.7149	−1.61022	−0.805108	−	0.593128i	$-0.797893\pi$
$199$	−22.7149	−1.61022	−0.805108	+	0.593128i	$0.797893\pi$
$200$	−54.6664	−3.86550
$201$	−13.6406	−0.962137
$202$	−32.0030	−2.25172
$203$	21.9489	1.54051
$204$	67.1916	4.70435
$205$	−42.6070	−2.97580
$206$	−26.1558	−1.82236
$207$	−7.45029	−0.517831
$208$	36.6060	2.53817
$209$	−8.07018	−0.558226
$210$	−70.7865	−4.88473
$211$	−22.0283	−1.51649	−0.758246	−	0.651969i	$-0.773943\pi$
$211$	−22.0283	−1.51649	−0.758246	+	0.651969i	$0.773943\pi$
$212$	−44.7958	−3.07659
$213$	26.7940	1.83589
$214$	−43.0696	−2.94418
$215$	18.8364	1.28463
$216$	26.3352	1.79188
$217$	17.4813	1.18671
$218$	−29.4563	−1.99503
$219$	24.9441	1.68556
$220$	−67.2799	−4.53601
$221$	34.8977	2.34747
$222$	−5.88482	−0.394963
$223$	−18.6250	−1.24722	−0.623612	−	0.781734i	$-0.714336\pi$
$223$	−18.6250	−1.24722	−0.623612	+	0.781734i	$0.714336\pi$
$224$	25.1037	1.67731
$225$	8.28820	0.552547
$226$	41.5600	2.76453
$227$	18.4556	1.22494	0.612470	−	0.790494i	$-0.290176\pi$
$227$	18.4556	1.22494	0.612470	+	0.790494i	$0.290176\pi$
$228$	−18.2458	−1.20836
$229$	26.8423	1.77379	0.886894	−	0.461972i	$-0.152858\pi$
$229$	26.8423	1.77379	0.886894	+	0.461972i	$0.152858\pi$
$230$	−69.8578	−4.60628
$231$	−30.5730	−2.01156
$232$	38.1184	2.50260
$233$	17.7052	1.15991	0.579955	−	0.814649i	$-0.303070\pi$
$233$	17.7052	1.15991	0.579955	+	0.814649i	$0.303070\pi$
$234$	−12.1159	−0.792039
$235$	−18.4074	−1.20076
$236$	−13.0939	−0.852340
$237$	−3.20858	−0.208419
$238$	71.4185	4.62937
$239$	6.43743	0.416403	0.208201	−	0.978086i	$-0.433239\pi$
$239$	6.43743	0.416403	0.208201	+	0.978086i	$0.433239\pi$
$240$	−56.3133	−3.63501
$241$	1.41300	0.0910195	0.0455097	−	0.998964i	$-0.485509\pi$
$241$	1.41300	0.0910195	0.0455097	+	0.998964i	$0.485509\pi$
$242$	−13.5976	−0.874089
$243$	−9.97338	−0.639793
$244$	−61.5926	−3.94306
$245$	−26.7833	−1.71112
$246$	−59.8271	−3.81444
$247$	−9.47640	−0.602969
$248$	30.3596	1.92784
$249$	11.4465	0.725392
$250$	30.9668	1.95851
$251$	4.27848	0.270056	0.135028	−	0.990842i	$-0.456888\pi$
$251$	4.27848	0.270056	0.135028	+	0.990842i	$0.456888\pi$
$252$	−17.2432	−1.08622
$253$	−30.1719	−1.89689
$254$	−18.4301	−1.15640
$255$	−53.6852	−3.36190
$256$	−26.9088	−1.68180
$257$	12.4944	0.779378	0.389689	−	0.920947i	$-0.372583\pi$
$257$	12.4944	0.779378	0.389689	+	0.920947i	$0.372583\pi$
$258$	26.4493	1.64666
$259$	−4.34989	−0.270289
$260$	−79.0034	−4.89959
$261$	−5.77930	−0.357730
$262$	13.7807	0.851375
$263$	9.48409	0.584814	0.292407	−	0.956294i	$-0.405544\pi$
$263$	9.48409	0.584814	0.292407	+	0.956294i	$0.405544\pi$
$264$	−53.0959	−3.26783
$265$	35.7913	2.19864
$266$	−19.3936	−1.18910
$267$	14.2104	0.869664
$268$	−31.1562	−1.90317
$269$	15.7026	0.957406	0.478703	−	0.877977i	$-0.341107\pi$
$269$	15.7026	0.957406	0.478703	+	0.877977i	$0.341107\pi$
$270$	−37.4385	−2.27844
$271$	−9.54786	−0.579991	−0.289996	−	0.957028i	$-0.593654\pi$
$271$	−9.54786	−0.579991	−0.289996	+	0.957028i	$0.593654\pi$
$272$	56.8161	3.44498
$273$	−35.9004	−2.17279
$274$	−8.80805	−0.532114
$275$	33.5653	2.02406
$276$	−68.2153	−4.10608
$277$	9.05708	0.544187	0.272093	−	0.962271i	$-0.412284\pi$
$277$	9.05708	0.544187	0.272093	+	0.962271i	$0.412284\pi$
$278$	3.30116	0.197991
$279$	−4.60295	−0.275571
$280$	−90.8695	−5.43049
$281$	17.9479	1.07068	0.535340	−	0.844637i	$-0.320183\pi$
$281$	17.9479	1.07068	0.535340	+	0.844637i	$0.320183\pi$
$282$	−25.8469	−1.53916
$283$	−26.7580	−1.59060	−0.795298	−	0.606218i	$-0.792686\pi$
$283$	−26.7580	−1.59060	−0.795298	+	0.606218i	$0.792686\pi$
$284$	61.1994	3.63152
$285$	14.5781	0.863534
$286$	−49.0664	−2.90136
$287$	−44.2225	−2.61037
$288$	−6.60999	−0.389497
$289$	37.1645	2.18615
$290$	−54.1897	−3.18213
$291$	−3.06180	−0.179486
$292$	56.9740	3.33415
$293$	−29.0674	−1.69813	−0.849067	−	0.528285i	$-0.822835\pi$
$293$	−29.0674	−1.69813	−0.849067	+	0.528285i	$0.822835\pi$
$294$	−37.6082	−2.19335
$295$	10.4619	0.609113
$296$	−7.55442	−0.439092
$297$	−16.1699	−0.938271
$298$	−2.68345	−0.155448
$299$	−35.4293	−2.04893
$300$	75.8873	4.38135
$301$	19.5506	1.12688
$302$	26.5430	1.52738
$303$	24.9688	1.43442
$304$	−15.4283	−0.884874
$305$	49.2117	2.81786
$306$	−18.8050	−1.07501
$307$	−2.98317	−0.170259	−0.0851293	−	0.996370i	$-0.527130\pi$
$307$	−2.98317	−0.170259	−0.0851293	+	0.996370i	$0.527130\pi$
$308$	−69.8310	−3.97899
$309$	20.4068	1.16090
$310$	−43.1596	−2.45130
$311$	−9.92271	−0.562665	−0.281333	−	0.959610i	$-0.590776\pi$
$311$	−9.92271	−0.562665	−0.281333	+	0.959610i	$0.590776\pi$
$312$	−62.3478	−3.52975
$313$	−1.08514	−0.0613356	−0.0306678	−	0.999530i	$-0.509763\pi$
$313$	−1.08514	−0.0613356	−0.0306678	+	0.999530i	$0.509763\pi$
$314$	−10.3718	−0.585313
$315$	13.7771	0.776253
$316$	−7.32862	−0.412267
$317$	4.89322	0.274830	0.137415	−	0.990514i	$-0.456121\pi$
$317$	4.89322	0.274830	0.137415	+	0.990514i	$0.456121\pi$
$318$	50.2568	2.81826
$319$	−23.4048	−1.31042
$320$	−5.64514	−0.315573
$321$	33.6030	1.87554
$322$	−72.5066	−4.04063
$323$	−14.7083	−0.818391
$324$	−50.2183	−2.78991
$325$	39.4140	2.18630
$326$	−24.6537	−1.36544
$327$	22.9818	1.27090
$328$	−76.8008	−4.24061
$329$	−19.1053	−1.05331
$330$	75.4819	4.15514
$331$	−30.6616	−1.68531	−0.842656	−	0.538452i	$-0.819009\pi$
$331$	−30.6616	−1.68531	−0.842656	+	0.538452i	$0.819009\pi$
$332$	26.1446	1.43487
$333$	1.14536	0.0627652
$334$	24.5460	1.34310
$335$	24.8934	1.36007
$336$	−58.4485	−3.18863
$337$	−16.5286	−0.900369	−0.450185	−	0.892935i	$-0.648642\pi$
$337$	−16.5286	−0.900369	−0.450185	+	0.892935i	$0.648642\pi$
$338$	−24.3035	−1.32193
$339$	−32.4251	−1.76109
$340$	−122.621	−6.65005
$341$	−18.6408	−1.00946
$342$	5.10647	0.276126
$343$	−1.29044	−0.0696773
$344$	33.9533	1.83064
$345$	54.5031	2.93435
$346$	−13.0750	−0.702914
$347$	−33.0336	−1.77334	−0.886668	−	0.462407i	$-0.846986\pi$
$347$	−33.0336	−1.77334	−0.886668	+	0.462407i	$0.846986\pi$
$348$	−52.9156	−2.83657
$349$	−16.5686	−0.886896	−0.443448	−	0.896300i	$-0.646245\pi$
$349$	−16.5686	−0.886896	−0.443448	+	0.896300i	$0.646245\pi$
$350$	80.6612	4.31152
$351$	−18.9875	−1.01348
$352$	−26.7689	−1.42679
$353$	−34.8472	−1.85473	−0.927365	−	0.374157i	$-0.877932\pi$
$353$	−34.8472	−1.85473	−0.927365	+	0.374157i	$0.877932\pi$
$354$	14.6901	0.780772
$355$	−48.8975	−2.59521
$356$	32.4577	1.72025
$357$	−55.7208	−2.94906
$358$	28.6272	1.51299
$359$	−35.5939	−1.87857	−0.939286	−	0.343135i	$-0.888511\pi$
$359$	−35.5939	−1.87857	−0.939286	+	0.343135i	$0.888511\pi$
$360$	23.9266	1.26104
$361$	−15.0060	−0.789789
$362$	29.3674	1.54352
$363$	10.6089	0.556822
$364$	−81.9990	−4.29792
$365$	−45.5215	−2.38271
$366$	69.1012	3.61198
$367$	13.5857	0.709168	0.354584	−	0.935024i	$-0.384622\pi$
$367$	13.5857	0.709168	0.354584	+	0.935024i	$0.384622\pi$
$368$	−57.6817	−3.00686
$369$	11.6441	0.606168
$370$	10.7395	0.558319
$371$	37.1484	1.92865
$372$	−42.1449	−2.18511
$373$	7.04992	0.365031	0.182516	−	0.983203i	$-0.441576\pi$
$373$	7.04992	0.365031	0.182516	+	0.983203i	$0.441576\pi$
$374$	−76.1558	−3.93792
$375$	−24.1603	−1.24763
$376$	−33.1800	−1.71113
$377$	−27.4831	−1.41545
$378$	−38.8581	−1.99864
$379$	35.1826	1.80721	0.903605	−	0.428366i	$-0.140911\pi$
$379$	35.1826	1.80721	0.903605	+	0.428366i	$0.140911\pi$
$380$	33.2975	1.70813
$381$	14.3792	0.736667
$382$	46.7883	2.39390
$383$	9.32328	0.476397	0.238199	−	0.971216i	$-0.423443\pi$
$383$	9.32328	0.476397	0.238199	+	0.971216i	$0.423443\pi$
$384$	18.5800	0.948157
$385$	55.7941	2.84353
$386$	26.7727	1.36269
$387$	−5.14781	−0.261678
$388$	−6.99338	−0.355035
$389$	13.4761	0.683267	0.341633	−	0.939833i	$-0.389020\pi$
$389$	13.4761	0.683267	0.341633	+	0.939833i	$0.389020\pi$
$390$	88.6346	4.48819
$391$	−54.9897	−2.78095
$392$	−48.2781	−2.43841
$393$	−10.7517	−0.542353
$394$	−10.9383	−0.551065
$395$	5.85548	0.294621
$396$	18.3870	0.923982
$397$	−35.1226	−1.76275	−0.881376	−	0.472415i	$-0.843382\pi$
$397$	−35.1226	−1.76275	−0.881376	+	0.472415i	$0.843382\pi$
$398$	58.2073	2.91767
$399$	15.1309	0.757492
$400$	64.1690	3.20845
$401$	−31.1427	−1.55519	−0.777596	−	0.628764i	$-0.783561\pi$
$401$	−31.1427	−1.55519	−0.777596	+	0.628764i	$0.783561\pi$
$402$	34.9544	1.74337
$403$	−21.8890	−1.09037
$404$	57.0305	2.83737
$405$	40.1238	1.99377
$406$	−56.2444	−2.79136
$407$	4.63843	0.229918
$408$	−96.7698	−4.79082
$409$	−33.9809	−1.68025	−0.840124	−	0.542394i	$-0.817518\pi$
$409$	−33.9809	−1.68025	−0.840124	+	0.542394i	$0.817518\pi$
$410$	109.181	5.39207
$411$	6.87205	0.338973
$412$	46.6107	2.29634
$413$	10.8585	0.534314
$414$	19.0915	0.938296
$415$	−20.8892	−1.02541
$416$	−31.4334	−1.54115
$417$	−2.57557	−0.126126
$418$	20.6800	1.01149
$419$	−7.73120	−0.377694	−0.188847	−	0.982007i	$-0.560475\pi$
$419$	−7.73120	−0.377694	−0.188847	+	0.982007i	$0.560475\pi$
$420$	126.144	6.15520
$421$	13.8686	0.675916	0.337958	−	0.941161i	$-0.390264\pi$
$421$	13.8686	0.675916	0.337958	+	0.941161i	$0.390264\pi$
$422$	56.4480	2.74784
$423$	5.03057	0.244595
$424$	64.5153	3.13314
$425$	61.1743	2.96739
$426$	−68.6601	−3.32659
$427$	51.0777	2.47182
$428$	76.7517	3.70993
$429$	38.2817	1.84826
$430$	−48.2686	−2.32772
$431$	−29.1324	−1.40326	−0.701630	−	0.712542i	$-0.747544\pi$
$431$	−29.1324	−1.40326	−0.701630	+	0.712542i	$0.747544\pi$
$432$	−30.9130	−1.48730
$433$	3.19141	0.153369	0.0766846	−	0.997055i	$-0.475567\pi$
$433$	3.19141	0.153369	0.0766846	+	0.997055i	$0.475567\pi$
$434$	−44.7961	−2.15028
$435$	42.2789	2.02712
$436$	52.4922	2.51392
$437$	14.9324	0.714312
$438$	−63.9196	−3.05420
$439$	−5.47547	−0.261330	−0.130665	−	0.991427i	$-0.541711\pi$
$439$	−5.47547	−0.261330	−0.130665	+	0.991427i	$0.541711\pi$
$440$	96.8971	4.61939
$441$	7.31965	0.348555
$442$	−89.4259	−4.25356
$443$	−10.4066	−0.494430	−0.247215	−	0.968961i	$-0.579515\pi$
$443$	−10.4066	−0.494430	−0.247215	+	0.968961i	$0.579515\pi$
$444$	10.4870	0.497689
$445$	−25.9333	−1.22935
$446$	47.7270	2.25994
$447$	2.09363	0.0990252
$448$	−5.85919	−0.276821
$449$	−27.1862	−1.28300	−0.641499	−	0.767124i	$-0.721687\pi$
$449$	−27.1862	−1.28300	−0.641499	+	0.767124i	$0.721687\pi$
$450$	−21.2387	−1.00120
$451$	47.1558	2.22048
$452$	−74.0613	−3.48355
$453$	−20.7089	−0.972989
$454$	−47.2928	−2.21956
$455$	65.5162	3.07145
$456$	26.2777	1.23057
$457$	0.700067	0.0327478	0.0163739	−	0.999866i	$-0.494788\pi$
$457$	0.700067	0.0327478	0.0163739	+	0.999866i	$0.494788\pi$
$458$	−68.7839	−3.21406
$459$	−29.4704	−1.37556
$460$	124.489	5.80433
$461$	8.31285	0.387168	0.193584	−	0.981084i	$-0.437989\pi$
$461$	8.31285	0.387168	0.193584	+	0.981084i	$0.437989\pi$
$462$	78.3439	3.64489
$463$	−38.9224	−1.80888	−0.904439	−	0.426602i	$-0.859711\pi$
$463$	−38.9224	−1.80888	−0.904439	+	0.426602i	$0.859711\pi$
$464$	−44.7445	−2.07721
$465$	33.6732	1.56156
$466$	−45.3700	−2.10173
$467$	25.8743	1.19732	0.598659	−	0.801004i	$-0.295700\pi$
$467$	25.8743	1.19732	0.598659	+	0.801004i	$0.295700\pi$
$468$	21.5909	0.998041
$469$	25.8373	1.19306
$470$	47.1692	2.17575
$471$	8.09207	0.372863
$472$	18.8579	0.868006
$473$	−20.8474	−0.958566
$474$	8.22204	0.377651
$475$	−16.6118	−0.762201
$476$	−127.270	−5.83343
$477$	−9.78144	−0.447861
$478$	−16.4960	−0.754511
$479$	17.0108	0.777243	0.388622	−	0.921397i	$-0.372951\pi$
$479$	17.0108	0.777243	0.388622	+	0.921397i	$0.372951\pi$
$480$	48.3559	2.20713
$481$	5.44667	0.248347
$482$	−3.62084	−0.164925
$483$	56.5697	2.57401
$484$	24.2315	1.10143
$485$	5.58762	0.253721
$486$	25.5570	1.15929
$487$	−39.8753	−1.80692	−0.903461	−	0.428670i	$-0.858982\pi$
$487$	−39.8753	−1.80692	−0.903461	+	0.428670i	$0.858982\pi$
$488$	88.7061	4.01554
$489$	19.2348	0.869829
$490$	68.6328	3.10051
$491$	−30.4411	−1.37379	−0.686894	−	0.726758i	$-0.741026\pi$
$491$	−30.4411	−1.37379	−0.686894	+	0.726758i	$0.741026\pi$
$492$	106.614	4.80653
$493$	−42.6563	−1.92115
$494$	24.2835	1.09256
$495$	−14.6910	−0.660311
$496$	−35.6370	−1.60015
$497$	−50.7516	−2.27652
$498$	−29.3318	−1.31439
$499$	3.11654	0.139516	0.0697578	−	0.997564i	$-0.477777\pi$
$499$	3.11654	0.139516	0.0697578	+	0.997564i	$0.477777\pi$
$500$	−55.1839	−2.46790
$501$	−19.1508	−0.855597
$502$	−10.9637	−0.489334
$503$	−8.10216	−0.361257	−0.180629	−	0.983551i	$-0.557813\pi$
$503$	−8.10216	−0.361257	−0.180629	+	0.983551i	$0.557813\pi$
$504$	24.8338	1.10619
$505$	−45.5666	−2.02769
$506$	77.3160	3.43712
$507$	18.9616	0.842114
$508$	32.8430	1.45717
$509$	−2.83343	−0.125590	−0.0627948	−	0.998026i	$-0.520001\pi$
$509$	−2.83343	−0.125590	−0.0627948	+	0.998026i	$0.520001\pi$
$510$	137.569	6.09168
$511$	−47.2476	−2.09011
$512$	50.3676	2.22596
$513$	8.00263	0.353325
$514$	−32.0171	−1.41221
$515$	−37.2413	−1.64105
$516$	−47.1337	−2.07494
$517$	20.3726	0.895986
$518$	11.1467	0.489757
$519$	10.2011	0.447778
$520$	113.781	4.98964
$521$	9.98452	0.437430	0.218715	−	0.975789i	$-0.429814\pi$
$521$	9.98452	0.437430	0.218715	+	0.975789i	$0.429814\pi$
$522$	14.8096	0.648197
$523$	−17.4991	−0.765184	−0.382592	−	0.923917i	$-0.624968\pi$
$523$	−17.4991	−0.765184	−0.382592	+	0.923917i	$0.624968\pi$
$524$	−24.5577	−1.07281
$525$	−62.9320	−2.74658
$526$	−24.3032	−1.05967
$527$	−33.9738	−1.47992
$528$	62.3255	2.71237
$529$	32.8275	1.42728
$530$	−91.7159	−3.98388
$531$	−2.85913	−0.124076
$532$	34.5601	1.49837
$533$	55.3727	2.39846
$534$	−36.4145	−1.57581
$535$	−61.3236	−2.65125
$536$	44.8714	1.93815
$537$	−22.3350	−0.963826
$538$	−40.2383	−1.73479
$539$	29.6428	1.27681
$540$	66.7168	2.87103
$541$	−38.8368	−1.66972	−0.834862	−	0.550459i	$-0.814453\pi$
$541$	−38.8368	−1.66972	−0.834862	+	0.550459i	$0.814453\pi$
$542$	24.4666	1.05093
$543$	−22.9125	−0.983269
$544$	−48.7876	−2.09175
$545$	−41.9406	−1.79654
$546$	91.9953	3.93704
$547$	2.06735	0.0883935	0.0441968	−	0.999023i	$-0.485927\pi$
$547$	2.06735	0.0883935	0.0441968	+	0.999023i	$0.485927\pi$
$548$	15.6963	0.670511
$549$	−13.4491	−0.573995
$550$	−86.0116	−3.66755
$551$	11.5833	0.493464
$552$	98.2441	4.18155
$553$	6.07750	0.258441
$554$	−23.2089	−0.986053
$555$	−8.37895	−0.355667
$556$	−5.88279	−0.249486
$557$	27.8992	1.18213	0.591064	−	0.806624i	$-0.298708\pi$
$557$	27.8992	1.18213	0.591064	+	0.806624i	$0.298708\pi$
$558$	11.7951	0.499328
$559$	−24.4801	−1.03540
$560$	106.665	4.50743
$561$	59.4169	2.50858
$562$	−45.9918	−1.94005
$563$	25.8573	1.08976	0.544879	−	0.838515i	$-0.316576\pi$
$563$	25.8573	1.08976	0.544879	+	0.838515i	$0.316576\pi$
$564$	46.0602	1.93948
$565$	59.1741	2.48947
$566$	68.5678	2.88212
$567$	41.6452	1.74893
$568$	−88.1398	−3.69826
$569$	2.20255	0.0923357	0.0461678	−	0.998934i	$-0.485299\pi$
$569$	2.20255	0.0923357	0.0461678	+	0.998934i	$0.485299\pi$
$570$	−37.3567	−1.56470
$571$	21.9761	0.919673	0.459837	−	0.888004i	$-0.347908\pi$
$571$	21.9761	0.919673	0.459837	+	0.888004i	$0.347908\pi$
$572$	87.4381	3.65597
$573$	−36.5043	−1.52499
$574$	113.321	4.72993
$575$	−62.1063	−2.59001
$576$	1.54277	0.0642819
$577$	−3.55614	−0.148044	−0.0740221	−	0.997257i	$-0.523584\pi$
$577$	−3.55614	−0.148044	−0.0740221	+	0.997257i	$0.523584\pi$
$578$	−95.2348	−3.96125
$579$	−20.8881	−0.868080
$580$	96.5680	4.00977
$581$	−21.6813	−0.899490
$582$	7.84593	0.325224
$583$	−39.6125	−1.64058
$584$	−82.0544	−3.39544
$585$	−17.2509	−0.713236
$586$	74.4857	3.07698
$587$	−5.36561	−0.221462	−0.110731	−	0.993850i	$-0.535319\pi$
$587$	−5.36561	−0.221462	−0.110731	+	0.993850i	$0.535319\pi$
$588$	67.0191	2.76382
$589$	9.22554	0.380132
$590$	−26.8087	−1.10370
$591$	8.53410	0.351046
$592$	8.86760	0.364456
$593$	−14.8041	−0.607930	−0.303965	−	0.952683i	$-0.598311\pi$
$593$	−14.8041	−0.607930	−0.303965	+	0.952683i	$0.598311\pi$
$594$	41.4356	1.70012
$595$	101.687	4.16878
$596$	4.78200	0.195878
$597$	−45.4134	−1.85865
$598$	90.7883	3.71261
$599$	−37.1080	−1.51619	−0.758095	−	0.652144i	$-0.773870\pi$
$599$	−37.1080	−1.51619	−0.758095	+	0.652144i	$0.773870\pi$
$600$	−109.293	−4.46188
$601$	13.0395	0.531892	0.265946	−	0.963988i	$-0.414316\pi$
$601$	13.0395	0.531892	0.265946	+	0.963988i	$0.414316\pi$
$602$	−50.0988	−2.04187
$603$	−6.80315	−0.277046
$604$	−47.3006	−1.92463
$605$	−19.3606	−0.787122
$606$	−63.9829	−2.59913
$607$	40.8492	1.65802	0.829010	−	0.559234i	$-0.188905\pi$
$607$	40.8492	1.65802	0.829010	+	0.559234i	$0.188905\pi$
$608$	13.2482	0.537285
$609$	43.8820	1.77819
$610$	−126.106	−5.10588
$611$	23.9225	0.967802
$612$	33.5112	1.35461
$613$	2.70154	0.109114	0.0545571	−	0.998511i	$-0.482625\pi$
$613$	2.70154	0.109114	0.0545571	+	0.998511i	$0.482625\pi$
$614$	7.64443	0.308504
$615$	−85.1833	−3.43492
$616$	100.571	4.05212
$617$	1.57922	0.0635772	0.0317886	−	0.999495i	$-0.489880\pi$
$617$	1.57922	0.0635772	0.0317886	+	0.999495i	$0.489880\pi$
$618$	−52.2929	−2.10353
$619$	39.2244	1.57656	0.788281	−	0.615315i	$-0.210971\pi$
$619$	39.2244	1.57656	0.788281	+	0.615315i	$0.210971\pi$
$620$	76.9120	3.08886
$621$	29.9193	1.20062
$622$	25.4271	1.01953
$623$	−26.9166	−1.07839
$624$	73.1857	2.92977
$625$	2.53069	0.101228
$626$	2.78068	0.111139
$627$	−16.1346	−0.644352
$628$	18.4829	0.737547
$629$	8.45376	0.337073
$630$	−35.3041	−1.40655
$631$	−0.251740	−0.0100216	−0.00501081	−	0.999987i	$-0.501595\pi$
$631$	−0.251740	−0.0100216	−0.00501081	+	0.999987i	$0.501595\pi$
$632$	10.5547	0.419845
$633$	−44.0408	−1.75046
$634$	−12.5390	−0.497986
$635$	−26.2412	−1.04135
$636$	−89.5594	−3.55126
$637$	34.8081	1.37915
$638$	59.9752	2.37444
$639$	13.3633	0.528642
$640$	−33.9075	−1.34031
$641$	−27.8777	−1.10110	−0.550551	−	0.834802i	$-0.685582\pi$
$641$	−27.8777	−1.10110	−0.550551	+	0.834802i	$0.685582\pi$
$642$	−86.1083	−3.39842
$643$	−7.54386	−0.297501	−0.148750	−	0.988875i	$-0.547525\pi$
$643$	−7.54386	−0.297501	−0.148750	+	0.988875i	$0.547525\pi$
$644$	129.209	5.09156
$645$	37.6592	1.48283
$646$	37.6903	1.48290
$647$	41.6958	1.63923	0.819615	−	0.572915i	$-0.194187\pi$
$647$	41.6958	1.63923	0.819615	+	0.572915i	$0.194187\pi$
$648$	72.3248	2.84119
$649$	−11.5788	−0.454508
$650$	−100.999	−3.96151
$651$	34.9500	1.36980
$652$	43.9337	1.72058
$653$	−39.8482	−1.55938	−0.779691	−	0.626165i	$-0.784624\pi$
$653$	−39.8482	−1.55938	−0.779691	+	0.626165i	$0.784624\pi$
$654$	−58.8914	−2.30284
$655$	19.6213	0.766669
$656$	90.1510	3.51981
$657$	12.4406	0.485355
$658$	48.9577	1.90857
$659$	−40.2236	−1.56689	−0.783445	−	0.621461i	$-0.786539\pi$
$659$	−40.2236	−1.56689	−0.783445	+	0.621461i	$0.786539\pi$
$660$	−134.511	−5.23585
$661$	−6.79137	−0.264154	−0.132077	−	0.991239i	$-0.542165\pi$
$661$	−6.79137	−0.264154	−0.132077	+	0.991239i	$0.542165\pi$
$662$	78.5708	3.05374
$663$	69.7702	2.70965
$664$	−37.6536	−1.46124
$665$	−27.6130	−1.07079
$666$	−2.93500	−0.113729
$667$	43.3062	1.67682
$668$	−43.7419	−1.69243
$669$	−37.2367	−1.43965
$670$	−63.7899	−2.46442
$671$	−54.4658	−2.10263
$672$	50.1894	1.93610
$673$	−10.6718	−0.411370	−0.205685	−	0.978618i	$-0.565942\pi$
$673$	−10.6718	−0.411370	−0.205685	+	0.978618i	$0.565942\pi$
$674$	42.3548	1.63145
$675$	−33.2843	−1.28111
$676$	43.3097	1.66576
$677$	12.4214	0.477392	0.238696	−	0.971094i	$-0.423280\pi$
$677$	12.4214	0.477392	0.238696	+	0.971094i	$0.423280\pi$
$678$	83.0900	3.19105
$679$	5.79949	0.222564
$680$	176.600	6.77228
$681$	36.8979	1.41393
$682$	47.7675	1.82911
$683$	−8.42900	−0.322527	−0.161263	−	0.986911i	$-0.551557\pi$
$683$	−8.42900	−0.322527	−0.161263	+	0.986911i	$0.551557\pi$
$684$	−9.09991	−0.347944
$685$	−12.5411	−0.479171
$686$	3.30678	0.126254
$687$	53.6653	2.04746
$688$	−39.8554	−1.51947
$689$	−46.5150	−1.77208
$690$	−139.665	−5.31697
$691$	−25.4363	−0.967642	−0.483821	−	0.875167i	$-0.660751\pi$
$691$	−25.4363	−0.967642	−0.483821	+	0.875167i	$0.660751\pi$
$692$	23.3000	0.885735
$693$	−15.2480	−0.579224
$694$	84.6492	3.21324
$695$	4.70028	0.178292
$696$	76.2094	2.88871
$697$	85.9438	3.25535
$698$	42.4573	1.60703
$699$	35.3978	1.33887
$700$	−143.741	−5.43291
$701$	−15.8883	−0.600093	−0.300047	−	0.953925i	$-0.597002\pi$
$701$	−15.8883	−0.600093	−0.300047	+	0.953925i	$0.597002\pi$
$702$	48.6557	1.83639
$703$	−2.29560	−0.0865804
$704$	6.24784	0.235474
$705$	−36.8015	−1.38602
$706$	89.2967	3.36072
$707$	−47.2944	−1.77869
$708$	−26.1784	−0.983843
$709$	−6.78401	−0.254779	−0.127389	−	0.991853i	$-0.540660\pi$
$709$	−6.78401	−0.254779	−0.127389	+	0.991853i	$0.540660\pi$
$710$	125.301	4.70246
$711$	−1.60025	−0.0600140
$712$	−46.7457	−1.75187
$713$	34.4914	1.29171
$714$	142.786	5.34362
$715$	−69.8620	−2.61269
$716$	−51.0147	−1.90651
$717$	12.8702	0.480648
$718$	91.2099	3.40392
$719$	34.4841	1.28604	0.643019	−	0.765850i	$-0.277682\pi$
$719$	34.4841	1.28604	0.643019	+	0.765850i	$0.277682\pi$
$720$	−28.0857	−1.04669
$721$	−38.6534	−1.43953
$722$	38.4531	1.43108
$723$	2.82499	0.105062
$724$	−52.3338	−1.94497
$725$	−48.1768	−1.78924
$726$	−27.1855	−1.00895
$727$	10.1026	0.374686	0.187343	−	0.982295i	$-0.440012\pi$
$727$	10.1026	0.374686	0.187343	+	0.982295i	$0.440012\pi$
$728$	118.096	4.37691
$729$	13.0518	0.483398
$730$	116.650	4.31740
$731$	−37.9954	−1.40531
$732$	−123.141	−4.55142
$733$	−19.6269	−0.724935	−0.362467	−	0.931996i	$-0.618066\pi$
$733$	−19.6269	−0.724935	−0.362467	+	0.931996i	$0.618066\pi$
$734$	−34.8136	−1.28500
$735$	−53.5474	−1.97513
$736$	49.5309	1.82573
$737$	−27.5511	−1.01486
$738$	−29.8382	−1.09836
$739$	−29.3946	−1.08130	−0.540649	−	0.841248i	$-0.681821\pi$
$739$	−29.3946	−1.08130	−0.540649	+	0.841248i	$0.681821\pi$
$740$	−19.1381	−0.703532
$741$	−18.9460	−0.695998
$742$	−95.1935	−3.49466
$743$	−31.1176	−1.14160	−0.570798	−	0.821091i	$-0.693366\pi$
$743$	−31.1176	−1.14160	−0.570798	+	0.821091i	$0.693366\pi$
$744$	60.6973	2.22527
$745$	−3.82076	−0.139982
$746$	−18.0656	−0.661427
$747$	5.70883	0.208875
$748$	135.712	4.96214
$749$	−63.6488	−2.32568
$750$	61.9113	2.26068
$751$	23.6843	0.864252	0.432126	−	0.901813i	$-0.357764\pi$
$751$	23.6843	0.864252	0.432126	+	0.901813i	$0.357764\pi$
$752$	38.9477	1.42028
$753$	8.55389	0.311721
$754$	70.4259	2.56476
$755$	37.7926	1.37541
$756$	69.2465	2.51847
$757$	16.3398	0.593881	0.296941	−	0.954896i	$-0.404034\pi$
$757$	16.3398	0.593881	0.296941	+	0.954896i	$0.404034\pi$
$758$	−90.1562	−3.27462
$759$	−60.3221	−2.18955
$760$	−47.9553	−1.73952
$761$	−31.1931	−1.13075	−0.565374	−	0.824835i	$-0.691268\pi$
$761$	−31.1931	−1.13075	−0.565374	+	0.824835i	$0.691268\pi$
$762$	−36.8469	−1.33482
$763$	−43.5309	−1.57592
$764$	−83.3785	−3.01653
$765$	−26.7750	−0.968053
$766$	−23.8911	−0.863220
$767$	−13.5964	−0.490938
$768$	−53.7982	−1.94128
$769$	17.1503	0.618454	0.309227	−	0.950988i	$-0.399930\pi$
$769$	17.1503	0.618454	0.309227	+	0.950988i	$0.399930\pi$
$770$	−142.973	−5.15240
$771$	24.9798	0.899624
$772$	−47.7099	−1.71712
$773$	32.5809	1.17185	0.585927	−	0.810364i	$-0.300731\pi$
$773$	32.5809	1.17185	0.585927	+	0.810364i	$0.300731\pi$
$774$	13.1914	0.474154
$775$	−38.3706	−1.37831
$776$	10.0719	0.361561
$777$	−8.69666	−0.311991
$778$	−34.5328	−1.23806
$779$	−23.3379	−0.836167
$780$	−157.950	−5.65552
$781$	54.1180	1.93649
$782$	140.912	5.03901
$783$	23.2089	0.829418
$784$	56.6702	2.02394
$785$	−14.7676	−0.527077
$786$	27.5515	0.982730
$787$	−24.0077	−0.855781	−0.427891	−	0.903830i	$-0.640743\pi$
$787$	−24.0077	−0.855781	−0.427891	+	0.903830i	$0.640743\pi$
$788$	19.4925	0.694392
$789$	18.9614	0.675042
$790$	−15.0048	−0.533846
$791$	61.4178	2.18376
$792$	−26.4811	−0.940965
$793$	−63.9564	−2.27116
$794$	90.0023	3.19406
$795$	71.5569	2.53786
$796$	−103.728	−3.67653
$797$	3.14903	0.111544	0.0557721	−	0.998444i	$-0.482238\pi$
$797$	3.14903	0.111544	0.0557721	+	0.998444i	$0.482238\pi$
$798$	−38.7732	−1.37256
$799$	37.1301	1.31357
$800$	−55.1015	−1.94813
$801$	7.08732	0.250418
$802$	79.8037	2.81797
$803$	50.3816	1.77793
$804$	−62.2900	−2.19680
$805$	−103.237	−3.63861
$806$	56.0910	1.97572
$807$	31.3939	1.10512
$808$	−82.1357	−2.88952
$809$	44.1303	1.55154	0.775770	−	0.631016i	$-0.217362\pi$
$809$	44.1303	1.55154	0.775770	+	0.631016i	$0.217362\pi$
$810$	−102.818	−3.61266
$811$	−38.6741	−1.35803	−0.679015	−	0.734124i	$-0.737593\pi$
$811$	−38.6741	−1.35803	−0.679015	+	0.734124i	$0.737593\pi$
$812$	100.230	3.51737
$813$	−19.0889	−0.669476
$814$	−11.8861	−0.416606
$815$	−35.1025	−1.22959
$816$	113.591	3.97649
$817$	10.3176	0.360967
$818$	87.0768	3.04457
$819$	−17.9050	−0.625651
$820$	−194.565	−6.79450
$821$	7.93274	0.276854	0.138427	−	0.990373i	$-0.455795\pi$
$821$	7.93274	0.276854	0.138427	+	0.990373i	$0.455795\pi$
$822$	−17.6098	−0.614211
$823$	−24.9428	−0.869452	−0.434726	−	0.900563i	$-0.643155\pi$
$823$	−24.9428	−0.869452	−0.434726	+	0.900563i	$0.643155\pi$
$824$	−67.1290	−2.33855
$825$	67.1064	2.33634
$826$	−27.8252	−0.968163
$827$	−53.7131	−1.86779	−0.933894	−	0.357550i	$-0.883612\pi$
$827$	−53.7131	−1.86779	−0.933894	+	0.357550i	$0.883612\pi$
$828$	−34.0217	−1.18234
$829$	−8.90971	−0.309447	−0.154724	−	0.987958i	$-0.549449\pi$
$829$	−8.90971	−0.309447	−0.154724	+	0.987958i	$0.549449\pi$
$830$	53.5290	1.85802
$831$	18.1076	0.628147
$832$	7.33652	0.254348
$833$	54.0255	1.87187
$834$	6.59995	0.228538
$835$	34.9492	1.20947
$836$	−36.8525	−1.27457
$837$	18.4848	0.638929
$838$	19.8114	0.684372
$839$	−4.90408	−0.169308	−0.0846539	−	0.996410i	$-0.526978\pi$
$839$	−4.90408	−0.169308	−0.0846539	+	0.996410i	$0.526978\pi$
$840$	−181.674	−6.26834
$841$	4.59328	0.158389
$842$	−35.5386	−1.22474
$843$	35.8828	1.23587
$844$	−100.592	−3.46253
$845$	−34.6039	−1.19041
$846$	−12.8909	−0.443199
$847$	−20.0947	−0.690463
$848$	−75.7299	−2.60058
$849$	−53.4967	−1.83600
$850$	−156.760	−5.37683
$851$	−8.58255	−0.294206
$852$	122.355	4.19180
$853$	45.2073	1.54787	0.773935	−	0.633265i	$-0.218286\pi$
$853$	45.2073	1.54787	0.773935	+	0.633265i	$0.218286\pi$
$854$	−130.888	−4.47888
$855$	7.27071	0.248653
$856$	−110.538	−3.77812
$857$	−5.29397	−0.180839	−0.0904193	−	0.995904i	$-0.528821\pi$
$857$	−5.29397	−0.180839	−0.0904193	+	0.995904i	$0.528821\pi$
$858$	−98.0975	−3.34899
$859$	20.6098	0.703197	0.351599	−	0.936151i	$-0.385638\pi$
$859$	20.6098	0.703197	0.351599	+	0.936151i	$0.385638\pi$
$860$	86.0164	2.93313
$861$	−88.4132	−3.01311
$862$	74.6524	2.54267
$863$	56.7528	1.93189	0.965944	−	0.258750i	$-0.0833106\pi$
$863$	56.7528	1.93189	0.965944	+	0.258750i	$0.0833106\pi$
$864$	26.5448	0.903073
$865$	−18.6164	−0.632978
$866$	−8.17804	−0.277901
$867$	74.3023	2.52344
$868$	79.8283	2.70955
$869$	−6.48063	−0.219840
$870$	−108.340	−3.67308
$871$	−32.3519	−1.09620
$872$	−75.5996	−2.56013
$873$	−1.52705	−0.0516827
$874$	−38.2645	−1.29432
$875$	45.7631	1.54707
$876$	113.907	3.84856
$877$	6.32395	0.213544	0.106772	−	0.994284i	$-0.465948\pi$
$877$	6.32395	0.213544	0.106772	+	0.994284i	$0.465948\pi$
$878$	14.0310	0.473523
$879$	−58.1138	−1.96013
$880$	−113.741	−3.83420
$881$	−9.40081	−0.316721	−0.158361	−	0.987381i	$-0.550621\pi$
$881$	−9.40081	−0.316721	−0.158361	+	0.987381i	$0.550621\pi$
$882$	−18.7567	−0.631572
$883$	−22.9879	−0.773603	−0.386802	−	0.922163i	$-0.626420\pi$
$883$	−22.9879	−0.773603	−0.386802	+	0.922163i	$0.626420\pi$
$884$	159.360	5.35986
$885$	20.9162	0.703090
$886$	26.6670	0.895895
$887$	51.7701	1.73827	0.869135	−	0.494574i	$-0.164676\pi$
$887$	51.7701	1.73827	0.869135	+	0.494574i	$0.164676\pi$
$888$	−15.1034	−0.506837
$889$	−27.2362	−0.913472
$890$	66.4544	2.22756
$891$	−44.4076	−1.48771
$892$	−85.0512	−2.84773
$893$	−10.0826	−0.337402
$894$	−5.36496	−0.179431
$895$	40.7601	1.36246
$896$	−35.1931	−1.17572
$897$	−70.8332	−2.36505
$898$	69.6652	2.32476
$899$	26.7555	0.892346
$900$	37.8481	1.26160
$901$	−72.1957	−2.40519
$902$	−120.838	−4.02346
$903$	39.0871	1.30074
$904$	106.664	3.54758
$905$	41.8140	1.38995
$906$	53.0669	1.76303
$907$	0.306251	0.0101689	0.00508445	−	0.999987i	$-0.498382\pi$
$907$	0.306251	0.0101689	0.00508445	+	0.999987i	$0.498382\pi$
$908$	84.2775	2.79685
$909$	12.4529	0.413038
$910$	−167.886	−5.56538
$911$	10.0181	0.331914	0.165957	−	0.986133i	$-0.446929\pi$
$911$	10.0181	0.331914	0.165957	+	0.986133i	$0.446929\pi$
$912$	−30.8455	−1.02140
$913$	23.1194	0.765141
$914$	−1.79394	−0.0593381
$915$	98.3881	3.25261
$916$	122.575	4.05000
$917$	20.3653	0.672522
$918$	75.5183	2.49248
$919$	−34.9562	−1.15310	−0.576550	−	0.817062i	$-0.695601\pi$
$919$	−34.9562	−1.15310	−0.576550	+	0.817062i	$0.695601\pi$
$920$	−179.290	−5.91102
$921$	−5.96420	−0.196527
$922$	−21.3018	−0.701538
$923$	63.5481	2.09171
$924$	−139.612	−4.59289
$925$	9.54781	0.313930
$926$	99.7395	3.27764
$927$	10.1777	0.334280
$928$	38.4218	1.26126
$929$	−0.0878788	−0.00288321	−0.00144161	−	0.999999i	$-0.500459\pi$
$929$	−0.0878788	−0.00288321	−0.00144161	+	0.999999i	$0.500459\pi$
$930$	−86.2882	−2.82950
$931$	−14.6705	−0.480807
$932$	80.8510	2.64836
$933$	−19.8383	−0.649476
$934$	−66.3033	−2.16951
$935$	−108.432	−3.54612
$936$	−31.0954	−1.01639
$937$	−41.1895	−1.34560	−0.672801	−	0.739823i	$-0.734909\pi$
$937$	−41.1895	−1.34560	−0.672801	+	0.739823i	$0.734909\pi$
$938$	−66.2086	−2.16179
$939$	−2.16949	−0.0707988
$940$	−84.0573	−2.74165
$941$	41.0877	1.33942	0.669711	−	0.742622i	$-0.266418\pi$
$941$	41.0877	1.33942	0.669711	+	0.742622i	$0.266418\pi$
$942$	−20.7361	−0.675618
$943$	−87.2532	−2.84135
$944$	−22.1360	−0.720465
$945$	−55.3271	−1.79979
$946$	53.4219	1.73690
$947$	10.6646	0.346552	0.173276	−	0.984873i	$-0.444565\pi$
$947$	10.6646	0.346552	0.173276	+	0.984873i	$0.444565\pi$
$948$	−14.6520	−0.475874
$949$	59.1606	1.92043
$950$	42.5680	1.38109
$951$	9.78292	0.317233
$952$	183.296	5.94065
$953$	−20.4420	−0.662180	−0.331090	−	0.943599i	$-0.607416\pi$
$953$	−20.4420	−0.662180	−0.331090	+	0.943599i	$0.607416\pi$
$954$	25.0651	0.811513
$955$	66.6184	2.15572
$956$	29.3965	0.950752
$957$	−46.7927	−1.51259
$958$	−43.5905	−1.40834
$959$	−13.0166	−0.420329
$960$	−11.2862	−0.364261
$961$	−9.69045	−0.312595
$962$	−13.9572	−0.449998
$963$	16.7592	0.540057
$964$	6.45248	0.207820
$965$	38.1196	1.22711
$966$	−144.961	−4.66404
$967$	−15.0872	−0.485172	−0.242586	−	0.970130i	$-0.577996\pi$
$967$	−15.0872	−0.485172	−0.242586	+	0.970130i	$0.577996\pi$
$968$	−34.8983	−1.12168
$969$	−29.4060	−0.944657
$970$	−14.3184	−0.459736
$971$	−35.5421	−1.14060	−0.570300	−	0.821436i	$-0.693173\pi$
$971$	−35.5421	−1.14060	−0.570300	+	0.821436i	$0.693173\pi$
$972$	−45.5435	−1.46081
$973$	4.87850	0.156397
$974$	102.181	3.27410
$975$	78.7996	2.52361
$976$	−104.126	−3.33299
$977$	−7.31856	−0.234141	−0.117071	−	0.993124i	$-0.537350\pi$
$977$	−7.31856	−0.234141	−0.117071	+	0.993124i	$0.537350\pi$
$978$	−49.2896	−1.57611
$979$	28.7020	0.917319
$980$	−122.306	−3.90693
$981$	11.4620	0.365953
$982$	78.0059	2.48927
$983$	−0.447522	−0.0142737	−0.00713687	−	0.999975i	$-0.502272\pi$
$983$	−0.447522	−0.0142737	−0.00713687	+	0.999975i	$0.502272\pi$
$984$	−153.546	−4.89488
$985$	−15.5743	−0.496237
$986$	109.308	3.48107
$987$	−38.1969	−1.21582
$988$	−43.2740	−1.37673
$989$	38.5743	1.22659
$990$	37.6459	1.19647
$991$	−29.8166	−0.947157	−0.473578	−	0.880752i	$-0.657038\pi$
$991$	−29.8166	−0.947157	−0.473578	+	0.880752i	$0.657038\pi$
$992$	30.6012	0.971590
$993$	−61.3011	−1.94533
$994$	130.052	4.12499
$995$	82.8770	2.62738
$996$	52.2704	1.65625
$997$	11.8684	0.375875	0.187937	−	0.982181i	$-0.439820\pi$
$997$	11.8684	0.375875	0.187937	+	0.982181i	$0.439820\pi$
$998$	−7.98620	−0.252799
$999$	−4.59960	−0.145525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8009.2.a.a.1.16	✓	306

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8009.2.a.a.1.16	✓	306	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:	\( N \)	\(=\)	\( 8009 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56252 q^{2} +1.99928 q^{3} +4.56650 q^{4} -3.64858 q^{5} -5.12319 q^{6} -3.78692 q^{7} -6.57671 q^{8} +0.997123 q^{9} +O(q^{10})\)	\(q-2.56252 q^{2} +1.99928 q^{3} +4.56650 q^{4} -3.64858 q^{5} -5.12319 q^{6} -3.78692 q^{7} -6.57671 q^{8} +0.997123 q^{9} +9.34955 q^{10} +4.03811 q^{11} +9.12972 q^{12} +4.74175 q^{13} +9.70405 q^{14} -7.29453 q^{15} +7.71993 q^{16} +7.35966 q^{17} -2.55515 q^{18} -1.99850 q^{19} -16.6612 q^{20} -7.57112 q^{21} -10.3477 q^{22} -7.47178 q^{23} -13.1487 q^{24} +8.31212 q^{25} -12.1508 q^{26} -4.00431 q^{27} -17.2930 q^{28} -5.79597 q^{29} +18.6924 q^{30} -4.61623 q^{31} -6.62906 q^{32} +8.07332 q^{33} -18.8593 q^{34} +13.8169 q^{35} +4.55337 q^{36} +1.14866 q^{37} +5.12120 q^{38} +9.48009 q^{39} +23.9956 q^{40} +11.6777 q^{41} +19.4011 q^{42} -5.16267 q^{43} +18.4400 q^{44} -3.63808 q^{45} +19.1466 q^{46} +5.04508 q^{47} +15.4343 q^{48} +7.34076 q^{49} -21.3000 q^{50} +14.7140 q^{51} +21.6532 q^{52} -9.80966 q^{53} +10.2611 q^{54} -14.7334 q^{55} +24.9055 q^{56} -3.99557 q^{57} +14.8523 q^{58} -2.86738 q^{59} -33.3105 q^{60} -13.4879 q^{61} +11.8292 q^{62} -3.77603 q^{63} +1.54722 q^{64} -17.3006 q^{65} -20.6880 q^{66} -6.82278 q^{67} +33.6079 q^{68} -14.9382 q^{69} -35.4060 q^{70} +13.4018 q^{71} -6.55779 q^{72} +12.4765 q^{73} -2.94347 q^{74} +16.6183 q^{75} -9.12616 q^{76} -15.2920 q^{77} -24.2929 q^{78} -1.60487 q^{79} -28.1668 q^{80} -10.9971 q^{81} -29.9243 q^{82} +5.72530 q^{83} -34.5735 q^{84} -26.8523 q^{85} +13.2294 q^{86} -11.5878 q^{87} -26.5575 q^{88} +7.10777 q^{89} +9.32265 q^{90} -17.9566 q^{91} -34.1199 q^{92} -9.22913 q^{93} -12.9281 q^{94} +7.29169 q^{95} -13.2533 q^{96} -1.53145 q^{97} -18.8108 q^{98} +4.02650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 306 q - 13 q^{2} - 25 q^{3} + 253 q^{4} - 25 q^{5} - 49 q^{6} - 102 q^{7} - 33 q^{8} + 251 q^{9}+O(q^{10}) \) 306 * q - 13 * q^2 - 25 * q^3 + 253 * q^4 - 25 * q^5 - 49 * q^6 - 102 * q^7 - 33 * q^8 + 251 * q^9	\( 306 q - 13 q^{2} - 25 q^{3} + 253 q^{4} - 25 q^{5} - 49 q^{6} - 102 q^{7} - 33 q^{8} + 251 q^{9} - 61 q^{10} - 43 q^{11} - 50 q^{12} - 89 q^{13} - 40 q^{14} - 61 q^{15} + 151 q^{16} - 52 q^{17} - 57 q^{18} - 185 q^{19} - 66 q^{20} - 63 q^{21} - 55 q^{22} - 62 q^{23} - 131 q^{24} + 209 q^{25} - 57 q^{26} - 88 q^{27} - 182 q^{28} - 67 q^{29} - 68 q^{30} - 240 q^{31} - 64 q^{32} - 52 q^{33} - 128 q^{34} - 99 q^{35} + 106 q^{36} - 49 q^{37} - 45 q^{38} - 190 q^{39} - 158 q^{40} - 72 q^{41} - 36 q^{42} - 141 q^{43} - 80 q^{44} - 100 q^{45} - 91 q^{46} - 105 q^{47} - 85 q^{48} + 116 q^{49} - 51 q^{50} - 145 q^{51} - 237 q^{52} - 48 q^{53} - 156 q^{54} - 420 q^{55} - 116 q^{56} - 35 q^{57} - 43 q^{58} - 139 q^{59} - 73 q^{60} - 233 q^{61} - 58 q^{62} - 252 q^{63} - 3 q^{64} - 45 q^{65} - 127 q^{66} - 108 q^{67} - 85 q^{68} - 164 q^{69} - 56 q^{70} - 131 q^{71} - 117 q^{72} - 118 q^{73} - 47 q^{74} - 112 q^{75} - 389 q^{76} - 36 q^{77} + 9 q^{78} - 382 q^{79} - 119 q^{80} + 102 q^{81} - 131 q^{82} - 59 q^{83} - 144 q^{84} - 140 q^{85} - 38 q^{86} - 301 q^{87} - 131 q^{88} - 98 q^{89} - 138 q^{90} - 176 q^{91} - 97 q^{92} - 60 q^{93} - 342 q^{94} - 154 q^{95} - 243 q^{96} - 109 q^{97} - 21 q^{98} - 173 q^{99}+O(q^{100}) \) 306 * q - 13 * q^2 - 25 * q^3 + 253 * q^4 - 25 * q^5 - 49 * q^6 - 102 * q^7 - 33 * q^8 + 251 * q^9 - 61 * q^10 - 43 * q^11 - 50 * q^12 - 89 * q^13 - 40 * q^14 - 61 * q^15 + 151 * q^16 - 52 * q^17 - 57 * q^18 - 185 * q^19 - 66 * q^20 - 63 * q^21 - 55 * q^22 - 62 * q^23 - 131 * q^24 + 209 * q^25 - 57 * q^26 - 88 * q^27 - 182 * q^28 - 67 * q^29 - 68 * q^30 - 240 * q^31 - 64 * q^32 - 52 * q^33 - 128 * q^34 - 99 * q^35 + 106 * q^36 - 49 * q^37 - 45 * q^38 - 190 * q^39 - 158 * q^40 - 72 * q^41 - 36 * q^42 - 141 * q^43 - 80 * q^44 - 100 * q^45 - 91 * q^46 - 105 * q^47 - 85 * q^48 + 116 * q^49 - 51 * q^50 - 145 * q^51 - 237 * q^52 - 48 * q^53 - 156 * q^54 - 420 * q^55 - 116 * q^56 - 35 * q^57 - 43 * q^58 - 139 * q^59 - 73 * q^60 - 233 * q^61 - 58 * q^62 - 252 * q^63 - 3 * q^64 - 45 * q^65 - 127 * q^66 - 108 * q^67 - 85 * q^68 - 164 * q^69 - 56 * q^70 - 131 * q^71 - 117 * q^72 - 118 * q^73 - 47 * q^74 - 112 * q^75 - 389 * q^76 - 36 * q^77 + 9 * q^78 - 382 * q^79 - 119 * q^80 + 102 * q^81 - 131 * q^82 - 59 * q^83 - 144 * q^84 - 140 * q^85 - 38 * q^86 - 301 * q^87 - 131 * q^88 - 98 * q^89 - 138 * q^90 - 176 * q^91 - 97 * q^92 - 60 * q^93 - 342 * q^94 - 154 * q^95 - 243 * q^96 - 109 * q^97 - 21 * q^98 - 173 * q^99

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