LMFDB - Embedded newform 8047.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8047,2,Mod(1,8047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8047, 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("8047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8047 = 13 \cdot 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8047.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:	$64.2556185065$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34671 q^{2} +2.23237 q^{3} +3.50704 q^{4} -1.50112 q^{5} -5.23873 q^{6} -4.09520 q^{7} -3.53658 q^{8} +1.98350 q^{9} +O(q^{10})$	\(q-2.34671 q^{2} +2.23237 q^{3} +3.50704 q^{4} -1.50112 q^{5} -5.23873 q^{6} -4.09520 q^{7} -3.53658 q^{8} +1.98350 q^{9} +3.52269 q^{10} +5.11060 q^{11} +7.82903 q^{12} -1.00000 q^{13} +9.61024 q^{14} -3.35106 q^{15} +1.28525 q^{16} +3.04379 q^{17} -4.65469 q^{18} +0.373462 q^{19} -5.26449 q^{20} -9.14202 q^{21} -11.9931 q^{22} +4.35028 q^{23} -7.89498 q^{24} -2.74664 q^{25} +2.34671 q^{26} -2.26922 q^{27} -14.3620 q^{28} +1.71238 q^{29} +7.86397 q^{30} -6.62184 q^{31} +4.05706 q^{32} +11.4088 q^{33} -7.14289 q^{34} +6.14738 q^{35} +6.95620 q^{36} +5.18380 q^{37} -0.876406 q^{38} -2.23237 q^{39} +5.30884 q^{40} -7.03871 q^{41} +21.4536 q^{42} -2.60892 q^{43} +17.9231 q^{44} -2.97747 q^{45} -10.2088 q^{46} -4.10331 q^{47} +2.86916 q^{48} +9.77065 q^{49} +6.44556 q^{50} +6.79488 q^{51} -3.50704 q^{52} +1.89762 q^{53} +5.32519 q^{54} -7.67163 q^{55} +14.4830 q^{56} +0.833707 q^{57} -4.01845 q^{58} +2.11771 q^{59} -11.7523 q^{60} +12.2996 q^{61} +15.5395 q^{62} -8.12281 q^{63} -12.0912 q^{64} +1.50112 q^{65} -26.7731 q^{66} -14.1602 q^{67} +10.6747 q^{68} +9.71146 q^{69} -14.4261 q^{70} +12.2594 q^{71} -7.01480 q^{72} -5.58795 q^{73} -12.1649 q^{74} -6.13153 q^{75} +1.30975 q^{76} -20.9289 q^{77} +5.23873 q^{78} -0.667905 q^{79} -1.92931 q^{80} -11.0162 q^{81} +16.5178 q^{82} -15.0876 q^{83} -32.0614 q^{84} -4.56910 q^{85} +6.12237 q^{86} +3.82267 q^{87} -18.0741 q^{88} -7.66860 q^{89} +6.98724 q^{90} +4.09520 q^{91} +15.2566 q^{92} -14.7824 q^{93} +9.62928 q^{94} -0.560611 q^{95} +9.05688 q^{96} -5.89508 q^{97} -22.9289 q^{98} +10.1369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) $ 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * 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 $

$2$	−2.34671	−1.65937	−0.829687	−	0.558229i	$-0.811481\pi$
$2$	−2.34671	−1.65937	−0.829687	+	0.558229i	$0.811481\pi$
$3$	2.23237	1.28886	0.644431	−	0.764662i	$-0.277094\pi$
$3$	2.23237	1.28886	0.644431	+	0.764662i	$0.277094\pi$
$4$	3.50704	1.75352
$5$	−1.50112	−0.671321	−0.335661	−	0.941983i	$-0.608960\pi$
$5$	−1.50112	−0.671321	−0.335661	+	0.941983i	$0.608960\pi$
$6$	−5.23873	−2.13870
$7$	−4.09520	−1.54784	−0.773920	−	0.633284i	$-0.781707\pi$
$7$	−4.09520	−1.54784	−0.773920	+	0.633284i	$0.781707\pi$
$8$	−3.53658	−1.25037
$9$	1.98350	0.661165
$10$	3.52269	1.11397
$11$	5.11060	1.54090	0.770452	−	0.637497i	$-0.220030\pi$
$11$	5.11060	1.54090	0.770452	+	0.637497i	$0.220030\pi$
$12$	7.82903	2.26005
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	9.61024	2.56844
$15$	−3.35106	−0.865241
$16$	1.28525	0.321313
$17$	3.04379	0.738228	0.369114	−	0.929384i	$-0.379661\pi$
$17$	3.04379	0.738228	0.369114	+	0.929384i	$0.379661\pi$
$18$	−4.65469	−1.09712
$19$	0.373462	0.0856780	0.0428390	−	0.999082i	$-0.486360\pi$
$19$	0.373462	0.0856780	0.0428390	+	0.999082i	$0.486360\pi$
$20$	−5.26449	−1.17718
$21$	−9.14202	−1.99495
$22$	−11.9931	−2.55694
$23$	4.35028	0.907097	0.453548	−	0.891232i	$-0.350158\pi$
$23$	4.35028	0.907097	0.453548	+	0.891232i	$0.350158\pi$
$24$	−7.89498	−1.61156
$25$	−2.74664	−0.549328
$26$	2.34671	0.460227
$27$	−2.26922	−0.436711
$28$	−14.3620	−2.71417
$29$	1.71238	0.317981	0.158990	−	0.987280i	$-0.449176\pi$
$29$	1.71238	0.317981	0.158990	+	0.987280i	$0.449176\pi$
$30$	7.86397	1.43576
$31$	−6.62184	−1.18932	−0.594658	−	0.803978i	$-0.702713\pi$
$31$	−6.62184	−1.18932	−0.594658	+	0.803978i	$0.702713\pi$
$32$	4.05706	0.717194
$33$	11.4088	1.98601
$34$	−7.14289	−1.22500
$35$	6.14738	1.03910
$36$	6.95620	1.15937
$37$	5.18380	0.852211	0.426106	−	0.904673i	$-0.359885\pi$
$37$	5.18380	0.852211	0.426106	+	0.904673i	$0.359885\pi$
$38$	−0.876406	−0.142172
$39$	−2.23237	−0.357466
$40$	5.30884	0.839401
$41$	−7.03871	−1.09926	−0.549631	−	0.835408i	$-0.685232\pi$
$41$	−7.03871	−1.09926	−0.549631	+	0.835408i	$0.685232\pi$
$42$	21.4536	3.31037
$43$	−2.60892	−0.397857	−0.198928	−	0.980014i	$-0.563746\pi$
$43$	−2.60892	−0.397857	−0.198928	+	0.980014i	$0.563746\pi$
$44$	17.9231	2.70201
$45$	−2.97747	−0.443854
$46$	−10.2088	−1.50521
$47$	−4.10331	−0.598530	−0.299265	−	0.954170i	$-0.596741\pi$
$47$	−4.10331	−0.598530	−0.299265	+	0.954170i	$0.596741\pi$
$48$	2.86916	0.414128
$49$	9.77065	1.39581
$50$	6.44556	0.911540
$51$	6.79488	0.951474
$52$	−3.50704	−0.486339
$53$	1.89762	0.260658	0.130329	−	0.991471i	$-0.458397\pi$
$53$	1.89762	0.260658	0.130329	+	0.991471i	$0.458397\pi$
$54$	5.32519	0.724667
$55$	−7.67163	−1.03444
$56$	14.4830	1.93537
$57$	0.833707	0.110427
$58$	−4.01845	−0.527649
$59$	2.11771	0.275702	0.137851	−	0.990453i	$-0.455980\pi$
$59$	2.11771	0.275702	0.137851	+	0.990453i	$0.455980\pi$
$60$	−11.7523	−1.51722
$61$	12.2996	1.57480	0.787402	−	0.616440i	$-0.211426\pi$
$61$	12.2996	1.57480	0.787402	+	0.616440i	$0.211426\pi$
$62$	15.5395	1.97352
$63$	−8.12281	−1.02338
$64$	−12.0912	−1.51140
$65$	1.50112	0.186191
$66$	−26.7731	−3.29554
$67$	−14.1602	−1.72994	−0.864970	−	0.501823i	$-0.832663\pi$
$67$	−14.1602	−1.72994	−0.864970	+	0.501823i	$0.832663\pi$
$68$	10.6747	1.29450
$69$	9.71146	1.16912
$70$	−14.4261	−1.72425
$71$	12.2594	1.45492	0.727462	−	0.686148i	$-0.240700\pi$
$71$	12.2594	1.45492	0.727462	+	0.686148i	$0.240700\pi$
$72$	−7.01480	−0.826702
$73$	−5.58795	−0.654020	−0.327010	−	0.945021i	$-0.606041\pi$
$73$	−5.58795	−0.654020	−0.327010	+	0.945021i	$0.606041\pi$
$74$	−12.1649	−1.41414
$75$	−6.13153	−0.708008
$76$	1.30975	0.150238
$77$	−20.9289	−2.38507
$78$	5.23873	0.593170
$79$	−0.667905	−0.0751452	−0.0375726	−	0.999294i	$-0.511963\pi$
$79$	−0.667905	−0.0751452	−0.0375726	+	0.999294i	$0.511963\pi$
$80$	−1.92931	−0.215704
$81$	−11.0162	−1.22403
$82$	16.5178	1.82408
$83$	−15.0876	−1.65607	−0.828037	−	0.560673i	$-0.810542\pi$
$83$	−15.0876	−1.65607	−0.828037	+	0.560673i	$0.810542\pi$
$84$	−32.0614	−3.49819
$85$	−4.56910	−0.495588
$86$	6.12237	0.660193
$87$	3.82267	0.409833
$88$	−18.0741	−1.92670
$89$	−7.66860	−0.812870	−0.406435	−	0.913680i	$-0.633228\pi$
$89$	−7.66860	−0.812870	−0.406435	+	0.913680i	$0.633228\pi$
$90$	6.98724	0.736520
$91$	4.09520	0.429293
$92$	15.2566	1.59061
$93$	−14.7824	−1.53287
$94$	9.62928	0.993184
$95$	−0.560611	−0.0575175
$96$	9.05688	0.924364
$97$	−5.89508	−0.598555	−0.299277	−	0.954166i	$-0.596746\pi$
$97$	−5.89508	−0.598555	−0.299277	+	0.954166i	$0.596746\pi$
$98$	−22.9289	−2.31617
$99$	10.1369	1.01879
$100$	−9.63257	−0.963257
$101$	3.75592	0.373728	0.186864	−	0.982386i	$-0.440168\pi$
$101$	3.75592	0.373728	0.186864	+	0.982386i	$0.440168\pi$
$102$	−15.9456	−1.57885
$103$	4.44228	0.437711	0.218855	−	0.975757i	$-0.429768\pi$
$103$	4.44228	0.437711	0.218855	+	0.975757i	$0.429768\pi$
$104$	3.53658	0.346791
$105$	13.7233	1.33925
$106$	−4.45315	−0.432528
$107$	17.5992	1.70138	0.850688	−	0.525671i	$-0.176186\pi$
$107$	17.5992	1.70138	0.850688	+	0.525671i	$0.176186\pi$
$108$	−7.95824	−0.765782
$109$	4.09339	0.392076	0.196038	−	0.980596i	$-0.437192\pi$
$109$	4.09339	0.392076	0.196038	+	0.980596i	$0.437192\pi$
$110$	18.0031	1.71653
$111$	11.5722	1.09838
$112$	−5.26335	−0.497340
$113$	−2.30488	−0.216825	−0.108413	−	0.994106i	$-0.534577\pi$
$113$	−2.30488	−0.216825	−0.108413	+	0.994106i	$0.534577\pi$
$114$	−1.95647	−0.183240
$115$	−6.53030	−0.608953
$116$	6.00538	0.557586
$117$	−1.98350	−0.183374
$118$	−4.96964	−0.457493
$119$	−12.4649	−1.14266
$120$	11.8513	1.08187
$121$	15.1183	1.37439
$122$	−28.8636	−2.61319
$123$	−15.7130	−1.41680
$124$	−23.2230	−2.08549
$125$	11.6286	1.04010
$126$	19.0619	1.69817
$127$	5.88548	0.522252	0.261126	−	0.965305i	$-0.415906\pi$
$127$	5.88548	0.522252	0.261126	+	0.965305i	$0.415906\pi$
$128$	20.2605	1.79079
$129$	−5.82409	−0.512782
$130$	−3.52269	−0.308960
$131$	−5.10388	−0.445928	−0.222964	−	0.974827i	$-0.571573\pi$
$131$	−5.10388	−0.445928	−0.222964	+	0.974827i	$0.571573\pi$
$132$	40.0111	3.48252
$133$	−1.52940	−0.132616
$134$	33.2298	2.87062
$135$	3.40637	0.293173
$136$	−10.7646	−0.923059
$137$	−1.95908	−0.167376	−0.0836879	−	0.996492i	$-0.526670\pi$
$137$	−1.95908	−0.167376	−0.0836879	+	0.996492i	$0.526670\pi$
$138$	−22.7900	−1.94001
$139$	−13.9332	−1.18180	−0.590899	−	0.806746i	$-0.701227\pi$
$139$	−13.9332	−1.18180	−0.590899	+	0.806746i	$0.701227\pi$
$140$	21.5591	1.82208
$141$	−9.16013	−0.771422
$142$	−28.7693	−2.41426
$143$	−5.11060	−0.427370
$144$	2.54929	0.212441
$145$	−2.57049	−0.213467
$146$	13.1133	1.08526
$147$	21.8118	1.79900
$148$	18.1798	1.49437
$149$	−4.52680	−0.370850	−0.185425	−	0.982658i	$-0.559366\pi$
$149$	−4.52680	−0.370850	−0.185425	+	0.982658i	$0.559366\pi$
$150$	14.3889	1.17485
$151$	8.86817	0.721681	0.360841	−	0.932627i	$-0.382490\pi$
$151$	8.86817	0.721681	0.360841	+	0.932627i	$0.382490\pi$
$152$	−1.32078	−0.107129
$153$	6.03735	0.488091
$154$	49.1141	3.95773
$155$	9.94017	0.798414
$156$	−7.82903	−0.626824
$157$	8.26147	0.659337	0.329668	−	0.944097i	$-0.393063\pi$
$157$	8.26147	0.659337	0.329668	+	0.944097i	$0.393063\pi$
$158$	1.56738	0.124694
$159$	4.23619	0.335952
$160$	−6.09013	−0.481467
$161$	−17.8153	−1.40404
$162$	25.8519	2.03112
$163$	13.5443	1.06087	0.530435	−	0.847726i	$-0.322029\pi$
$163$	13.5443	1.06087	0.530435	+	0.847726i	$0.322029\pi$
$164$	−24.6850	−1.92758
$165$	−17.1259	−1.33325
$166$	35.4061	2.74805
$167$	12.2981	0.951652	0.475826	−	0.879539i	$-0.342149\pi$
$167$	12.2981	0.951652	0.475826	+	0.879539i	$0.342149\pi$
$168$	32.3315	2.49443
$169$	1.00000	0.0769231
$170$	10.7223	0.822366
$171$	0.740760	0.0566474
$172$	−9.14959	−0.697649
$173$	−11.3902	−0.865978	−0.432989	−	0.901399i	$-0.642541\pi$
$173$	−11.3902	−0.865978	−0.432989	+	0.901399i	$0.642541\pi$
$174$	−8.97069	−0.680066
$175$	11.2480	0.850271
$176$	6.56840	0.495112
$177$	4.72752	0.355342
$178$	17.9960	1.34885
$179$	15.1661	1.13357	0.566786	−	0.823865i	$-0.308187\pi$
$179$	15.1661	1.13357	0.566786	+	0.823865i	$0.308187\pi$
$180$	−10.4421	−0.778308
$181$	−3.25894	−0.242235	−0.121117	−	0.992638i	$-0.538648\pi$
$181$	−3.25894	−0.242235	−0.121117	+	0.992638i	$0.538648\pi$
$182$	−9.61024	−0.712358
$183$	27.4573	2.02970
$184$	−15.3851	−1.13421
$185$	−7.78151	−0.572108
$186$	34.6900	2.54360
$187$	15.5556	1.13754
$188$	−14.3905	−1.04953
$189$	9.29289	0.675959
$190$	1.31559	0.0954430
$191$	20.9962	1.51923	0.759616	−	0.650372i	$-0.225387\pi$
$191$	20.9962	1.51923	0.759616	+	0.650372i	$0.225387\pi$
$192$	−26.9922	−1.94799
$193$	−9.45489	−0.680578	−0.340289	−	0.940321i	$-0.610525\pi$
$193$	−9.45489	−0.680578	−0.340289	+	0.940321i	$0.610525\pi$
$194$	13.8340	0.993226
$195$	3.35106	0.239975
$196$	34.2661	2.44758
$197$	−8.48258	−0.604359	−0.302179	−	0.953251i	$-0.597714\pi$
$197$	−8.48258	−0.604359	−0.302179	+	0.953251i	$0.597714\pi$
$198$	−23.7883	−1.69056
$199$	−0.930591	−0.0659679	−0.0329839	−	0.999456i	$-0.510501\pi$
$199$	−0.930591	−0.0659679	−0.0329839	+	0.999456i	$0.510501\pi$
$200$	9.71372	0.686864
$201$	−31.6108	−2.22966
$202$	−8.81406	−0.620155
$203$	−7.01253	−0.492183
$204$	23.8299	1.66843
$205$	10.5659	0.737957
$206$	−10.4247	−0.726326
$207$	8.62877	0.599741
$208$	−1.28525	−0.0891161
$209$	1.90862	0.132022
$210$	−32.2045	−2.22232
$211$	3.29653	0.226943	0.113471	−	0.993541i	$-0.463803\pi$
$211$	3.29653	0.226943	0.113471	+	0.993541i	$0.463803\pi$
$212$	6.65501	0.457068
$213$	27.3676	1.87520
$214$	−41.3001	−2.82322
$215$	3.91630	0.267090
$216$	8.02528	0.546051
$217$	27.1177	1.84087
$218$	−9.60600	−0.650601
$219$	−12.4744	−0.842942
$220$	−26.9047	−1.81392
$221$	−3.04379	−0.204748
$222$	−27.1565	−1.82263
$223$	−16.3019	−1.09166	−0.545828	−	0.837897i	$-0.683785\pi$
$223$	−16.3019	−1.09166	−0.545828	+	0.837897i	$0.683785\pi$
$224$	−16.6145	−1.11010
$225$	−5.44795	−0.363196
$226$	5.40889	0.359794
$227$	−6.48782	−0.430611	−0.215306	−	0.976547i	$-0.569075\pi$
$227$	−6.48782	−0.430611	−0.215306	+	0.976547i	$0.569075\pi$
$228$	2.92384	0.193636
$229$	−2.30267	−0.152164	−0.0760822	−	0.997102i	$-0.524241\pi$
$229$	−2.30267	−0.152164	−0.0760822	+	0.997102i	$0.524241\pi$
$230$	15.3247	1.01048
$231$	−46.7212	−3.07403
$232$	−6.05597	−0.397594
$233$	−14.6326	−0.958615	−0.479307	−	0.877647i	$-0.659112\pi$
$233$	−14.6326	−0.958615	−0.479307	+	0.877647i	$0.659112\pi$
$234$	4.65469	0.304286
$235$	6.15957	0.401806
$236$	7.42689	0.483449
$237$	−1.49101	−0.0968518
$238$	29.2516	1.89610
$239$	−2.97023	−0.192128	−0.0960642	−	0.995375i	$-0.530625\pi$
$239$	−2.97023	−0.192128	−0.0960642	+	0.995375i	$0.530625\pi$
$240$	−4.30695	−0.278013
$241$	−2.95230	−0.190174	−0.0950870	−	0.995469i	$-0.530313\pi$
$241$	−2.95230	−0.190174	−0.0950870	+	0.995469i	$0.530313\pi$
$242$	−35.4782	−2.28062
$243$	−17.7847	−1.14089
$244$	43.1352	2.76145
$245$	−14.6669	−0.937035
$246$	36.8739	2.35099
$247$	−0.373462	−0.0237628
$248$	23.4187	1.48709
$249$	−33.6811	−2.13445
$250$	−27.2890	−1.72591
$251$	−2.28997	−0.144541	−0.0722707	−	0.997385i	$-0.523025\pi$
$251$	−2.28997	−0.144541	−0.0722707	+	0.997385i	$0.523025\pi$
$252$	−28.4870	−1.79451
$253$	22.2326	1.39775
$254$	−13.8115	−0.866611
$255$	−10.1999	−0.638745
$256$	−23.3630	−1.46019
$257$	−25.3333	−1.58025	−0.790125	−	0.612946i	$-0.789984\pi$
$257$	−25.3333	−1.58025	−0.790125	+	0.612946i	$0.789984\pi$
$258$	13.6674	0.850897
$259$	−21.2287	−1.31909
$260$	5.26449	0.326490
$261$	3.39650	0.210238
$262$	11.9773	0.739961
$263$	−31.8900	−1.96642	−0.983211	−	0.182470i	$-0.941591\pi$
$263$	−31.8900	−1.96642	−0.983211	+	0.182470i	$0.941591\pi$
$264$	−40.3481	−2.48325
$265$	−2.84855	−0.174985
$266$	3.58906	0.220059
$267$	−17.1192	−1.04768
$268$	−49.6603	−3.03349
$269$	−31.9250	−1.94650	−0.973251	−	0.229745i	$-0.926211\pi$
$269$	−31.9250	−1.94650	−0.973251	+	0.229745i	$0.926211\pi$
$270$	−7.99375	−0.486484
$271$	1.05163	0.0638817	0.0319409	−	0.999490i	$-0.489831\pi$
$271$	1.05163	0.0638817	0.0319409	+	0.999490i	$0.489831\pi$
$272$	3.91203	0.237202
$273$	9.14202	0.553300
$274$	4.59740	0.277739
$275$	−14.0370	−0.846462
$276$	34.0585	2.05008
$277$	21.2627	1.27755	0.638776	−	0.769393i	$-0.279441\pi$
$277$	21.2627	1.27755	0.638776	+	0.769393i	$0.279441\pi$
$278$	32.6971	1.96104
$279$	−13.1344	−0.786335
$280$	−21.7407	−1.29926
$281$	4.90835	0.292808	0.146404	−	0.989225i	$-0.453230\pi$
$281$	4.90835	0.292808	0.146404	+	0.989225i	$0.453230\pi$
$282$	21.4962	1.28008
$283$	−20.5601	−1.22217	−0.611085	−	0.791565i	$-0.709267\pi$
$283$	−20.5601	−1.22217	−0.611085	+	0.791565i	$0.709267\pi$
$284$	42.9942	2.55124
$285$	−1.25149	−0.0741321
$286$	11.9931	0.709167
$287$	28.8249	1.70148
$288$	8.04716	0.474184
$289$	−7.73533	−0.455020
$290$	6.03218	0.354222
$291$	−13.1600	−0.771454
$292$	−19.5972	−1.14684
$293$	4.24615	0.248063	0.124031	−	0.992278i	$-0.460418\pi$
$293$	4.24615	0.248063	0.124031	+	0.992278i	$0.460418\pi$
$294$	−51.1858	−2.98522
$295$	−3.17893	−0.185085
$296$	−18.3329	−1.06558
$297$	−11.5971	−0.672930
$298$	10.6231	0.615378
$299$	−4.35028	−0.251583
$300$	−21.5035	−1.24151
$301$	10.6840	0.615818
$302$	−20.8110	−1.19754
$303$	8.38463	0.481684
$304$	0.479992	0.0275294
$305$	−18.4632	−1.05720
$306$	−14.1679	−0.809925
$307$	−11.2510	−0.642131	−0.321065	−	0.947057i	$-0.604041\pi$
$307$	−11.2510	−0.642131	−0.321065	+	0.947057i	$0.604041\pi$
$308$	−73.3986	−4.18227
$309$	9.91683	0.564149
$310$	−23.3267	−1.32487
$311$	−0.248013	−0.0140635	−0.00703176	−	0.999975i	$-0.502238\pi$
$311$	−0.248013	−0.0140635	−0.00703176	+	0.999975i	$0.502238\pi$
$312$	7.89498	0.446965
$313$	−13.1723	−0.744542	−0.372271	−	0.928124i	$-0.621421\pi$
$313$	−13.1723	−0.744542	−0.372271	+	0.928124i	$0.621421\pi$
$314$	−19.3873	−1.09409
$315$	12.1933	0.687015
$316$	−2.34237	−0.131769
$317$	−17.1692	−0.964320	−0.482160	−	0.876083i	$-0.660148\pi$
$317$	−17.1692	−0.964320	−0.482160	+	0.876083i	$0.660148\pi$
$318$	−9.94110	−0.557469
$319$	8.75129	0.489978
$320$	18.1504	1.01464
$321$	39.2879	2.19284
$322$	41.8072	2.32983
$323$	1.13674	0.0632499
$324$	−38.6344	−2.14635
$325$	2.74664	0.152356
$326$	−31.7845	−1.76038
$327$	9.13799	0.505332
$328$	24.8930	1.37448
$329$	16.8039	0.926428
$330$	40.1896	2.21237
$331$	−17.0478	−0.937034	−0.468517	−	0.883454i	$-0.655212\pi$
$331$	−17.0478	−0.937034	−0.468517	+	0.883454i	$0.655212\pi$
$332$	−52.9127	−2.90396
$333$	10.2820	0.563453
$334$	−28.8600	−1.57915
$335$	21.2561	1.16135
$336$	−11.7498	−0.641003
$337$	8.75399	0.476860	0.238430	−	0.971160i	$-0.423367\pi$
$337$	8.75399	0.476860	0.238430	+	0.971160i	$0.423367\pi$
$338$	−2.34671	−0.127644
$339$	−5.14537	−0.279458
$340$	−16.0240	−0.869024
$341$	−33.8416	−1.83262
$342$	−1.73835	−0.0939991
$343$	−11.3464	−0.612646
$344$	9.22666	0.497468
$345$	−14.5781	−0.784857
$346$	26.7294	1.43698
$347$	2.10443	0.112971	0.0564857	−	0.998403i	$-0.482010\pi$
$347$	2.10443	0.112971	0.0564857	+	0.998403i	$0.482010\pi$
$348$	13.4063	0.718651
$349$	−8.83864	−0.473122	−0.236561	−	0.971617i	$-0.576020\pi$
$349$	−8.83864	−0.473122	−0.236561	+	0.971617i	$0.576020\pi$
$350$	−26.3958	−1.41092
$351$	2.26922	0.121122
$352$	20.7340	1.10513
$353$	33.5442	1.78538	0.892689	−	0.450674i	$-0.148816\pi$
$353$	33.5442	1.78538	0.892689	+	0.450674i	$0.148816\pi$
$354$	−11.0941	−0.589645
$355$	−18.4028	−0.976721
$356$	−26.8941	−1.42538
$357$	−27.8264	−1.47273
$358$	−35.5905	−1.88102
$359$	−33.0998	−1.74694	−0.873469	−	0.486880i	$-0.838135\pi$
$359$	−33.0998	−1.74694	−0.873469	+	0.486880i	$0.838135\pi$
$360$	10.5301	0.554983
$361$	−18.8605	−0.992659
$362$	7.64777	0.401958
$363$	33.7496	1.77140
$364$	14.3620	0.752775
$365$	8.38819	0.439058
$366$	−64.4344	−3.36804
$367$	−27.3351	−1.42688	−0.713441	−	0.700716i	$-0.752864\pi$
$367$	−27.3351	−1.42688	−0.713441	+	0.700716i	$0.752864\pi$
$368$	5.59120	0.291462
$369$	−13.9612	−0.726793
$370$	18.2609	0.949340
$371$	−7.77111	−0.403456
$372$	−51.8425	−2.68791
$373$	19.6589	1.01790	0.508949	−	0.860797i	$-0.330034\pi$
$373$	19.6589	1.01790	0.508949	+	0.860797i	$0.330034\pi$
$374$	−36.5045	−1.88760
$375$	25.9595	1.34054
$376$	14.5117	0.748384
$377$	−1.71238	−0.0881920
$378$	−21.8077	−1.12167
$379$	15.4858	0.795451	0.397725	−	0.917504i	$-0.369800\pi$
$379$	15.4858	0.795451	0.397725	+	0.917504i	$0.369800\pi$
$380$	−1.96609	−0.100858
$381$	13.1386	0.673111
$382$	−49.2720	−2.52097
$383$	−37.3459	−1.90828	−0.954142	−	0.299355i	$-0.903229\pi$
$383$	−37.3459	−1.90828	−0.954142	+	0.299355i	$0.903229\pi$
$384$	45.2290	2.30808
$385$	31.4168	1.60115
$386$	22.1879	1.12933
$387$	−5.17478	−0.263049
$388$	−20.6743	−1.04958
$389$	−2.62774	−0.133232	−0.0666159	−	0.997779i	$-0.521220\pi$
$389$	−2.62774	−0.133232	−0.0666159	+	0.997779i	$0.521220\pi$
$390$	−7.86397	−0.398207
$391$	13.2414	0.669644
$392$	−34.5547	−1.74528
$393$	−11.3938	−0.574739
$394$	19.9061	1.00286
$395$	1.00261	0.0504465
$396$	35.5504	1.78647
$397$	−17.2568	−0.866092	−0.433046	−	0.901372i	$-0.642561\pi$
$397$	−17.2568	−0.866092	−0.433046	+	0.901372i	$0.642561\pi$
$398$	2.18383	0.109465
$399$	−3.41419	−0.170924
$400$	−3.53012	−0.176506
$401$	−16.9827	−0.848074	−0.424037	−	0.905645i	$-0.639387\pi$
$401$	−16.9827	−0.848074	−0.424037	+	0.905645i	$0.639387\pi$
$402$	74.1814	3.69983
$403$	6.62184	0.329857
$404$	13.1722	0.655340
$405$	16.5367	0.821715
$406$	16.4564	0.816716
$407$	26.4923	1.31318
$408$	−24.0307	−1.18970
$409$	−15.4315	−0.763041	−0.381520	−	0.924360i	$-0.624599\pi$
$409$	−15.4315	−0.763041	−0.381520	+	0.924360i	$0.624599\pi$
$410$	−24.7952	−1.22455
$411$	−4.37341	−0.215724
$412$	15.5793	0.767535
$413$	−8.67243	−0.426743
$414$	−20.2492	−0.995194
$415$	22.6482	1.11176
$416$	−4.05706	−0.198914
$417$	−31.1041	−1.52317
$418$	−4.47896	−0.219073
$419$	2.98781	0.145964	0.0729821	−	0.997333i	$-0.476748\pi$
$419$	2.98781	0.145964	0.0729821	+	0.997333i	$0.476748\pi$
$420$	48.1280	2.34841
$421$	−21.1452	−1.03055	−0.515276	−	0.857024i	$-0.672311\pi$
$421$	−21.1452	−1.03055	−0.515276	+	0.857024i	$0.672311\pi$
$422$	−7.73601	−0.376583
$423$	−8.13891	−0.395727
$424$	−6.71108	−0.325919
$425$	−8.36020	−0.405529
$426$	−64.2237	−3.11165
$427$	−50.3693	−2.43754
$428$	61.7210	2.98340
$429$	−11.4088	−0.550821
$430$	−9.19042	−0.443201
$431$	8.15856	0.392984	0.196492	−	0.980505i	$-0.437045\pi$
$431$	8.15856	0.392984	0.196492	+	0.980505i	$0.437045\pi$
$432$	−2.91651	−0.140321
$433$	−9.64457	−0.463488	−0.231744	−	0.972777i	$-0.574443\pi$
$433$	−9.64457	−0.463488	−0.231744	+	0.972777i	$0.574443\pi$
$434$	−63.6374	−3.05469
$435$	−5.73829	−0.275130
$436$	14.3557	0.687513
$437$	1.62466	0.0777183
$438$	29.2738	1.39876
$439$	−12.2940	−0.586760	−0.293380	−	0.955996i	$-0.594780\pi$
$439$	−12.2940	−0.586760	−0.293380	+	0.955996i	$0.594780\pi$
$440$	27.1314	1.29344
$441$	19.3800	0.922859
$442$	7.14289	0.339753
$443$	5.79798	0.275470	0.137735	−	0.990469i	$-0.456018\pi$
$443$	5.79798	0.275470	0.137735	+	0.990469i	$0.456018\pi$
$444$	40.5841	1.92604
$445$	11.5115	0.545697
$446$	38.2558	1.81146
$447$	−10.1055	−0.477974
$448$	49.5160	2.33941
$449$	−18.2913	−0.863222	−0.431611	−	0.902060i	$-0.642055\pi$
$449$	−18.2913	−0.863222	−0.431611	+	0.902060i	$0.642055\pi$
$450$	12.7847	0.602679
$451$	−35.9720	−1.69386
$452$	−8.08332	−0.380208
$453$	19.7971	0.930148
$454$	15.2250	0.714545
$455$	−6.14738	−0.288194
$456$	−2.94847	−0.138075
$457$	19.4025	0.907613	0.453806	−	0.891100i	$-0.350066\pi$
$457$	19.4025	0.907613	0.453806	+	0.891100i	$0.350066\pi$
$458$	5.40369	0.252498
$459$	−6.90702	−0.322392
$460$	−22.9020	−1.06781
$461$	25.4020	1.18309	0.591546	−	0.806272i	$-0.298518\pi$
$461$	25.4020	1.18309	0.591546	+	0.806272i	$0.298518\pi$
$462$	109.641	5.10096
$463$	−26.4491	−1.22920	−0.614598	−	0.788841i	$-0.710682\pi$
$463$	−26.4491	−1.22920	−0.614598	+	0.788841i	$0.710682\pi$
$464$	2.20083	0.102171
$465$	22.1902	1.02905
$466$	34.3385	1.59070
$467$	5.86283	0.271300	0.135650	−	0.990757i	$-0.456688\pi$
$467$	5.86283	0.271300	0.135650	+	0.990757i	$0.456688\pi$
$468$	−6.95620	−0.321550
$469$	57.9887	2.67767
$470$	−14.4547	−0.666746
$471$	18.4427	0.849794
$472$	−7.48945	−0.344730
$473$	−13.3332	−0.613059
$474$	3.49897	0.160713
$475$	−1.02576	−0.0470653
$476$	−43.7150	−2.00367
$477$	3.76391	0.172338
$478$	6.97027	0.318813
$479$	−29.3478	−1.34094	−0.670468	−	0.741939i	$-0.733907\pi$
$479$	−29.3478	−1.34094	−0.670468	+	0.741939i	$0.733907\pi$
$480$	−13.5955	−0.620545
$481$	−5.18380	−0.236361
$482$	6.92818	0.315570
$483$	−39.7704	−1.80961
$484$	53.0204	2.41002
$485$	8.84922	0.401823
$486$	41.7355	1.89316
$487$	27.4486	1.24382	0.621908	−	0.783090i	$-0.286358\pi$
$487$	27.4486	1.24382	0.621908	+	0.783090i	$0.286358\pi$
$488$	−43.4986	−1.96909
$489$	30.2359	1.36731
$490$	34.4190	1.55489
$491$	3.94748	0.178147	0.0890736	−	0.996025i	$-0.471609\pi$
$491$	3.94748	0.178147	0.0890736	+	0.996025i	$0.471609\pi$
$492$	−55.1062	−2.48438
$493$	5.21212	0.234742
$494$	0.876406	0.0394314
$495$	−15.2166	−0.683937
$496$	−8.51072	−0.382142
$497$	−50.2047	−2.25199
$498$	79.0397	3.54185
$499$	−1.18535	−0.0530636	−0.0265318	−	0.999648i	$-0.508446\pi$
$499$	−1.18535	−0.0530636	−0.0265318	+	0.999648i	$0.508446\pi$
$500$	40.7821	1.82383
$501$	27.4539	1.22655
$502$	5.37389	0.239848
$503$	−10.1367	−0.451974	−0.225987	−	0.974130i	$-0.572561\pi$
$503$	−10.1367	−0.451974	−0.225987	+	0.974130i	$0.572561\pi$
$504$	28.7270	1.27960
$505$	−5.63809	−0.250892
$506$	−52.1734	−2.31939
$507$	2.23237	0.0991432
$508$	20.6406	0.915780
$509$	−4.60537	−0.204129	−0.102065	−	0.994778i	$-0.532545\pi$
$509$	−4.60537	−0.204129	−0.102065	+	0.994778i	$0.532545\pi$
$510$	23.9363	1.05992
$511$	22.8838	1.01232
$512$	14.3051	0.632203
$513$	−0.847466	−0.0374165
$514$	59.4500	2.62223
$515$	−6.66840	−0.293845
$516$	−20.4253	−0.899174
$517$	−20.9704	−0.922278
$518$	49.8175	2.18886
$519$	−25.4271	−1.11613
$520$	−5.30884	−0.232808
$521$	−14.9469	−0.654838	−0.327419	−	0.944879i	$-0.606179\pi$
$521$	−14.9469	−0.654838	−0.327419	+	0.944879i	$0.606179\pi$
$522$	−7.97059	−0.348863
$523$	−21.0396	−0.919996	−0.459998	−	0.887920i	$-0.652150\pi$
$523$	−21.0396	−0.919996	−0.459998	+	0.887920i	$0.652150\pi$
$524$	−17.8995	−0.781943
$525$	25.1098	1.09588
$526$	74.8366	3.26303
$527$	−20.1555	−0.877987
$528$	14.6631	0.638131
$529$	−4.07504	−0.177176
$530$	6.68471	0.290365
$531$	4.20047	0.182285
$532$	−5.36367	−0.232545
$533$	7.03871	0.304880
$534$	40.1737	1.73849
$535$	−26.4185	−1.14217
$536$	50.0786	2.16307
$537$	33.8565	1.46102
$538$	74.9187	3.22997
$539$	49.9339	2.15081
$540$	11.9463	0.514085
$541$	40.0565	1.72216	0.861081	−	0.508468i	$-0.169788\pi$
$541$	40.0565	1.72216	0.861081	+	0.508468i	$0.169788\pi$
$542$	−2.46786	−0.106004
$543$	−7.27517	−0.312207
$544$	12.3488	0.529452
$545$	−6.14468	−0.263209
$546$	−21.4536	−0.918131
$547$	24.3150	1.03963	0.519817	−	0.854277i	$-0.326000\pi$
$547$	24.3150	1.03963	0.519817	+	0.854277i	$0.326000\pi$
$548$	−6.87058	−0.293497
$549$	24.3962	1.04121
$550$	32.9407	1.40460
$551$	0.639508	0.0272440
$552$	−34.3454	−1.46184
$553$	2.73520	0.116313
$554$	−49.8973	−2.11993
$555$	−17.3712	−0.737368
$556$	−48.8642	−2.07231
$557$	−31.4030	−1.33059	−0.665294	−	0.746582i	$-0.731694\pi$
$557$	−31.4030	−1.33059	−0.665294	+	0.746582i	$0.731694\pi$
$558$	30.8226	1.30482
$559$	2.60892	0.110346
$560$	7.90093	0.333875
$561$	34.7260	1.46613
$562$	−11.5185	−0.485878
$563$	−38.1534	−1.60797	−0.803987	−	0.594647i	$-0.797292\pi$
$563$	−38.1534	−1.60797	−0.803987	+	0.594647i	$0.797292\pi$
$564$	−32.1250	−1.35270
$565$	3.45991	0.145559
$566$	48.2485	2.02804
$567$	45.1137	1.89460
$568$	−43.3564	−1.81919
$569$	23.2901	0.976373	0.488187	−	0.872739i	$-0.337659\pi$
$569$	23.2901	0.976373	0.488187	+	0.872739i	$0.337659\pi$
$570$	2.93689	0.123013
$571$	13.8812	0.580912	0.290456	−	0.956888i	$-0.406193\pi$
$571$	13.8812	0.580912	0.290456	+	0.956888i	$0.406193\pi$
$572$	−17.9231	−0.749402
$573$	46.8714	1.95808
$574$	−67.6436	−2.82339
$575$	−11.9487	−0.498293
$576$	−23.9829	−0.999288
$577$	21.4637	0.893547	0.446774	−	0.894647i	$-0.352573\pi$
$577$	21.4637	0.893547	0.446774	+	0.894647i	$0.352573\pi$
$578$	18.1526	0.755047
$579$	−21.1069	−0.877171
$580$	−9.01480	−0.374319
$581$	61.7865	2.56334
$582$	30.8827	1.28013
$583$	9.69796	0.401649
$584$	19.7623	0.817768
$585$	2.97747	0.123103
$586$	−9.96448	−0.411629
$587$	−23.2573	−0.959930	−0.479965	−	0.877288i	$-0.659351\pi$
$587$	−23.2573	−0.959930	−0.479965	+	0.877288i	$0.659351\pi$
$588$	76.4947	3.15459
$589$	−2.47300	−0.101898
$590$	7.46003	0.307125
$591$	−18.9363	−0.778935
$592$	6.66248	0.273826
$593$	9.13742	0.375229	0.187614	−	0.982243i	$-0.439924\pi$
$593$	9.13742	0.375229	0.187614	+	0.982243i	$0.439924\pi$
$594$	27.2149	1.11664
$595$	18.7114	0.767091
$596$	−15.8757	−0.650293
$597$	−2.07743	−0.0850235
$598$	10.2088	0.417471
$599$	−36.6551	−1.49769	−0.748844	−	0.662746i	$-0.769391\pi$
$599$	−36.6551	−1.49769	−0.748844	+	0.662746i	$0.769391\pi$
$600$	21.6847	0.885272
$601$	13.7620	0.561364	0.280682	−	0.959801i	$-0.409439\pi$
$601$	13.7620	0.561364	0.280682	+	0.959801i	$0.409439\pi$
$602$	−25.0723	−1.02187
$603$	−28.0867	−1.14378
$604$	31.1010	1.26548
$605$	−22.6943	−0.922656
$606$	−19.6763	−0.799294
$607$	17.1926	0.697826	0.348913	−	0.937155i	$-0.386551\pi$
$607$	17.1926	0.697826	0.348913	+	0.937155i	$0.386551\pi$
$608$	1.51516	0.0614477
$609$	−15.6546	−0.634356
$610$	43.3277	1.75429
$611$	4.10331	0.166002
$612$	21.1732	0.855877
$613$	−6.27845	−0.253584	−0.126792	−	0.991929i	$-0.540468\pi$
$613$	−6.27845	−0.253584	−0.126792	+	0.991929i	$0.540468\pi$
$614$	26.4029	1.06553
$615$	23.5871	0.951125
$616$	74.0169	2.98223
$617$	−22.5789	−0.908991	−0.454496	−	0.890749i	$-0.650181\pi$
$617$	−22.5789	−0.908991	−0.454496	+	0.890749i	$0.650181\pi$
$618$	−23.2719	−0.936134
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	34.8606	1.40003
$621$	−9.87174	−0.396139
$622$	0.582014	0.0233366
$623$	31.4044	1.25819
$624$	−2.86916	−0.114858
$625$	−3.72278	−0.148911
$626$	30.9115	1.23547
$627$	4.26074	0.170158
$628$	28.9733	1.15616
$629$	15.7784	0.629126
$630$	−28.6142	−1.14002
$631$	6.54013	0.260359	0.130179	−	0.991490i	$-0.458445\pi$
$631$	6.54013	0.260359	0.130179	+	0.991490i	$0.458445\pi$
$632$	2.36210	0.0939593
$633$	7.35910	0.292498
$634$	40.2912	1.60017
$635$	−8.83482	−0.350599
$636$	14.8565	0.589098
$637$	−9.77065	−0.387127
$638$	−20.5367	−0.813057
$639$	24.3165	0.961945
$640$	−30.4134	−1.20220
$641$	−3.32754	−0.131430	−0.0657149	−	0.997838i	$-0.520933\pi$
$641$	−3.32754	−0.131430	−0.0657149	+	0.997838i	$0.520933\pi$
$642$	−92.1973	−3.63874
$643$	−8.57425	−0.338136	−0.169068	−	0.985604i	$-0.554076\pi$
$643$	−8.57425	−0.338136	−0.169068	+	0.985604i	$0.554076\pi$
$644$	−62.4789	−2.46201
$645$	8.74265	0.344242
$646$	−2.66760	−0.104955
$647$	39.2090	1.54146	0.770732	−	0.637159i	$-0.219891\pi$
$647$	39.2090	1.54146	0.770732	+	0.637159i	$0.219891\pi$
$648$	38.9598	1.53049
$649$	10.8228	0.424831
$650$	−6.44556	−0.252816
$651$	60.5369	2.37263
$652$	47.5003	1.86026
$653$	−43.2482	−1.69243	−0.846216	−	0.532840i	$-0.821125\pi$
$653$	−43.2482	−1.69243	−0.846216	+	0.532840i	$0.821125\pi$
$654$	−21.4442	−0.838534
$655$	7.66153	0.299361
$656$	−9.04650	−0.353206
$657$	−11.0837	−0.432416
$658$	−39.4338	−1.53729
$659$	−42.2728	−1.64671	−0.823357	−	0.567523i	$-0.807902\pi$
$659$	−42.2728	−1.64671	−0.823357	+	0.567523i	$0.807902\pi$
$660$	−60.0614	−2.33789
$661$	20.8607	0.811387	0.405694	−	0.914009i	$-0.367030\pi$
$661$	20.8607	0.811387	0.405694	+	0.914009i	$0.367030\pi$
$662$	40.0063	1.55489
$663$	−6.79488	−0.263891
$664$	53.3584	2.07071
$665$	2.29581	0.0890278
$666$	−24.1290	−0.934979
$667$	7.44933	0.288439
$668$	43.1298	1.66874
$669$	−36.3919	−1.40699
$670$	−49.8819	−1.92711
$671$	62.8584	2.42662
$672$	−37.0897	−1.43077
$673$	1.11450	0.0429608	0.0214804	−	0.999769i	$-0.493162\pi$
$673$	1.11450	0.0429608	0.0214804	+	0.999769i	$0.493162\pi$
$674$	−20.5431	−0.791289
$675$	6.23272	0.239897
$676$	3.50704	0.134886
$677$	−15.0756	−0.579403	−0.289702	−	0.957117i	$-0.593556\pi$
$677$	−15.0756	−0.579403	−0.289702	+	0.957117i	$0.593556\pi$
$678$	12.0747	0.463725
$679$	24.1415	0.926467
$680$	16.1590	0.619669
$681$	−14.4832	−0.554999
$682$	79.4163	3.04101
$683$	−35.4799	−1.35760	−0.678801	−	0.734322i	$-0.737500\pi$
$683$	−35.4799	−1.35760	−0.678801	+	0.734322i	$0.737500\pi$
$684$	2.59788	0.0993323
$685$	2.94082	0.112363
$686$	26.6266	1.01661
$687$	−5.14041	−0.196119
$688$	−3.35311	−0.127836
$689$	−1.89762	−0.0722934
$690$	34.2105	1.30237
$691$	22.6286	0.860831	0.430415	−	0.902631i	$-0.358367\pi$
$691$	22.6286	0.860831	0.430415	+	0.902631i	$0.358367\pi$
$692$	−39.9457	−1.51851
$693$	−41.5125	−1.57693
$694$	−4.93847	−0.187462
$695$	20.9154	0.793366
$696$	−13.5192	−0.512444
$697$	−21.4244	−0.811505
$698$	20.7417	0.785086
$699$	−32.6655	−1.23552
$700$	39.4473	1.49097
$701$	−0.743396	−0.0280777	−0.0140388	−	0.999901i	$-0.504469\pi$
$701$	−0.743396	−0.0280777	−0.0140388	+	0.999901i	$0.504469\pi$
$702$	−5.32519	−0.200986
$703$	1.93595	0.0730158
$704$	−61.7935	−2.32893
$705$	13.7505	0.517872
$706$	−78.7184	−2.96261
$707$	−15.3813	−0.578472
$708$	16.5796	0.623099
$709$	−20.8929	−0.784651	−0.392325	−	0.919827i	$-0.628329\pi$
$709$	−20.8929	−0.784651	−0.392325	+	0.919827i	$0.628329\pi$
$710$	43.1861	1.62075
$711$	−1.32479	−0.0496834
$712$	27.1206	1.01639
$713$	−28.8069	−1.07883
$714$	65.3004	2.44381
$715$	7.67163	0.286903
$716$	53.1883	1.98774
$717$	−6.63067	−0.247627
$718$	77.6755	2.89882
$719$	26.4815	0.987592	0.493796	−	0.869578i	$-0.335609\pi$
$719$	26.4815	0.987592	0.493796	+	0.869578i	$0.335609\pi$
$720$	−3.82679	−0.142616
$721$	−18.1920	−0.677506
$722$	44.2602	1.64719
$723$	−6.59063	−0.245108
$724$	−11.4292	−0.424764
$725$	−4.70329	−0.174676
$726$	−79.2006	−2.93941
$727$	−23.0906	−0.856383	−0.428191	−	0.903688i	$-0.640849\pi$
$727$	−23.0906	−0.856383	−0.428191	+	0.903688i	$0.640849\pi$
$728$	−14.4830	−0.536776
$729$	−6.65342	−0.246423
$730$	−19.6846	−0.728561
$731$	−7.94101	−0.293709
$732$	96.2940	3.55913
$733$	−22.3947	−0.827168	−0.413584	−	0.910466i	$-0.635723\pi$
$733$	−22.3947	−0.827168	−0.413584	+	0.910466i	$0.635723\pi$
$734$	64.1475	2.36773
$735$	−32.7421	−1.20771
$736$	17.6494	0.650564
$737$	−72.3670	−2.66567
$738$	32.7630	1.20602
$739$	29.9327	1.10109	0.550546	−	0.834805i	$-0.314420\pi$
$739$	29.9327	1.10109	0.550546	+	0.834805i	$0.314420\pi$
$740$	−27.2901	−1.00320
$741$	−0.833707	−0.0306270
$742$	18.2365	0.669484
$743$	6.57981	0.241390	0.120695	−	0.992690i	$-0.461488\pi$
$743$	6.57981	0.241390	0.120695	+	0.992690i	$0.461488\pi$
$744$	52.2793	1.91665
$745$	6.79527	0.248959
$746$	−46.1337	−1.68907
$747$	−29.9261	−1.09494
$748$	54.5542	1.99470
$749$	−72.0721	−2.63346
$750$	−60.9193	−2.22446
$751$	4.01776	0.146610	0.0733051	−	0.997310i	$-0.476645\pi$
$751$	4.01776	0.146610	0.0733051	+	0.997310i	$0.476645\pi$
$752$	−5.27378	−0.192315
$753$	−5.11206	−0.186294
$754$	4.01845	0.146343
$755$	−13.3122	−0.484480
$756$	32.5906	1.18531
$757$	−17.8723	−0.649581	−0.324790	−	0.945786i	$-0.605294\pi$
$757$	−17.8723	−0.649581	−0.324790	+	0.945786i	$0.605294\pi$
$758$	−36.3406	−1.31995
$759$	49.6314	1.80151
$760$	1.98265	0.0719182
$761$	25.1494	0.911667	0.455833	−	0.890065i	$-0.349341\pi$
$761$	25.1494	0.911667	0.455833	+	0.890065i	$0.349341\pi$
$762$	−30.8325	−1.11694
$763$	−16.7633	−0.606871
$764$	73.6345	2.66400
$765$	−9.06278	−0.327666
$766$	87.6398	3.16656
$767$	−2.11771	−0.0764660
$768$	−52.1549	−1.88198
$769$	−28.1798	−1.01619	−0.508094	−	0.861302i	$-0.669650\pi$
$769$	−28.1798	−1.01619	−0.508094	+	0.861302i	$0.669650\pi$
$770$	−73.7262	−2.65691
$771$	−56.5535	−2.03672
$772$	−33.1587	−1.19341
$773$	−49.6175	−1.78462	−0.892310	−	0.451424i	$-0.850916\pi$
$773$	−49.6175	−1.78462	−0.892310	+	0.451424i	$0.850916\pi$
$774$	12.1437	0.436496
$775$	18.1878	0.653325
$776$	20.8484	0.748416
$777$	−47.3904	−1.70012
$778$	6.16654	0.221081
$779$	−2.62869	−0.0941825
$780$	11.7523	0.420800
$781$	62.6530	2.24190
$782$	−31.0736	−1.11119
$783$	−3.88576	−0.138866
$784$	12.5577	0.448490
$785$	−12.4015	−0.442627
$786$	26.7378	0.953707
$787$	−46.9552	−1.67377	−0.836886	−	0.547377i	$-0.815626\pi$
$787$	−46.9552	−1.67377	−0.836886	+	0.547377i	$0.815626\pi$
$788$	−29.7487	−1.05976
$789$	−71.1905	−2.53445
$790$	−2.35282	−0.0837097
$791$	9.43896	0.335611
$792$	−35.8499	−1.27387
$793$	−12.2996	−0.436772
$794$	40.4966	1.43717
$795$	−6.35903	−0.225531
$796$	−3.26362	−0.115676
$797$	24.3842	0.863731	0.431866	−	0.901938i	$-0.357856\pi$
$797$	24.3842	0.863731	0.431866	+	0.901938i	$0.357856\pi$
$798$	8.01212	0.283626
$799$	−12.4896	−0.441851
$800$	−11.1433	−0.393974
$801$	−15.2106	−0.537441
$802$	39.8534	1.40727
$803$	−28.5578	−1.00778
$804$	−110.860	−3.90974
$805$	26.7429	0.942562
$806$	−15.5395	−0.547356
$807$	−71.2686	−2.50877
$808$	−13.2831	−0.467299
$809$	−11.6372	−0.409142	−0.204571	−	0.978852i	$-0.565580\pi$
$809$	−11.6372	−0.409142	−0.204571	+	0.978852i	$0.565580\pi$
$810$	−38.8068	−1.36353
$811$	−38.6906	−1.35861	−0.679305	−	0.733856i	$-0.737719\pi$
$811$	−38.6906	−1.35861	−0.679305	+	0.733856i	$0.737719\pi$
$812$	−24.5932	−0.863053
$813$	2.34762	0.0823348
$814$	−62.1698	−2.17905
$815$	−20.3316	−0.712184
$816$	8.73312	0.305720
$817$	−0.974332	−0.0340876
$818$	36.2133	1.26617
$819$	8.12281	0.283834
$820$	37.0552	1.29402
$821$	24.3860	0.851079	0.425539	−	0.904940i	$-0.360084\pi$
$821$	24.3860	0.851079	0.425539	+	0.904940i	$0.360084\pi$
$822$	10.2631	0.357967
$823$	17.3455	0.604626	0.302313	−	0.953209i	$-0.402241\pi$
$823$	17.3455	0.604626	0.302313	+	0.953209i	$0.402241\pi$
$824$	−15.7105	−0.547301
$825$	−31.3358	−1.09097
$826$	20.3517	0.708125
$827$	52.4814	1.82496	0.912478	−	0.409125i	$-0.134166\pi$
$827$	52.4814	1.82496	0.912478	+	0.409125i	$0.134166\pi$
$828$	30.2614	1.05166
$829$	10.9150	0.379094	0.189547	−	0.981872i	$-0.439298\pi$
$829$	10.9150	0.379094	0.189547	+	0.981872i	$0.439298\pi$
$830$	−53.1488	−1.84482
$831$	47.4663	1.64659
$832$	12.0912	0.419188
$833$	29.7398	1.03042
$834$	72.9922	2.52751
$835$	−18.4609	−0.638865
$836$	6.69359	0.231503
$837$	15.0264	0.519388
$838$	−7.01153	−0.242209
$839$	42.1386	1.45479	0.727394	−	0.686220i	$-0.240731\pi$
$839$	42.1386	1.45479	0.727394	+	0.686220i	$0.240731\pi$
$840$	−48.5335	−1.67456
$841$	−26.0678	−0.898888
$842$	49.6215	1.71007
$843$	10.9573	0.377389
$844$	11.5611	0.397949
$845$	−1.50112	−0.0516401
$846$	19.0996	0.656659
$847$	−61.9123	−2.12733
$848$	2.43891	0.0837525
$849$	−45.8978	−1.57521
$850$	19.6189	0.672924
$851$	22.5510	0.773038
$852$	95.9792	3.28819
$853$	−52.2244	−1.78813	−0.894064	−	0.447939i	$-0.852158\pi$
$853$	−52.2244	−1.78813	−0.894064	+	0.447939i	$0.852158\pi$
$854$	118.202	4.04479
$855$	−1.11197	−0.0380286
$856$	−62.2409	−2.12735
$857$	47.8414	1.63423	0.817115	−	0.576475i	$-0.195572\pi$
$857$	47.8414	1.63423	0.817115	+	0.576475i	$0.195572\pi$
$858$	26.7731	0.914018
$859$	−33.3044	−1.13633	−0.568167	−	0.822914i	$-0.692347\pi$
$859$	−33.3044	−1.13633	−0.568167	+	0.822914i	$0.692347\pi$
$860$	13.7346	0.468347
$861$	64.3480	2.19297
$862$	−19.1458	−0.652107
$863$	−16.5764	−0.564266	−0.282133	−	0.959375i	$-0.591042\pi$
$863$	−16.5764	−0.564266	−0.282133	+	0.959375i	$0.591042\pi$
$864$	−9.20635	−0.313206
$865$	17.0980	0.581349
$866$	22.6330	0.769100
$867$	−17.2682	−0.586458
$868$	95.1030	3.22801
$869$	−3.41340	−0.115792
$870$	13.4661	0.456543
$871$	14.1602	0.479799
$872$	−14.4766	−0.490241
$873$	−11.6929	−0.395744
$874$	−3.81261	−0.128964
$875$	−47.6216	−1.60990
$876$	−43.7482	−1.47812
$877$	4.61648	0.155887	0.0779436	−	0.996958i	$-0.475165\pi$
$877$	4.61648	0.155887	0.0779436	+	0.996958i	$0.475165\pi$
$878$	28.8504	0.973654
$879$	9.47900	0.319719
$880$	−9.85996	−0.332379
$881$	−3.88478	−0.130882	−0.0654408	−	0.997856i	$-0.520845\pi$
$881$	−3.88478	−0.130882	−0.0654408	+	0.997856i	$0.520845\pi$
$882$	−45.4793	−1.53137
$883$	−53.9554	−1.81575	−0.907873	−	0.419246i	$-0.862295\pi$
$883$	−53.9554	−1.81575	−0.907873	+	0.419246i	$0.862295\pi$
$884$	−10.6747	−0.359029
$885$	−7.09657	−0.238549
$886$	−13.6062	−0.457108
$887$	−42.5041	−1.42715	−0.713573	−	0.700581i	$-0.752924\pi$
$887$	−42.5041	−1.42715	−0.713573	+	0.700581i	$0.752924\pi$
$888$	−40.9260	−1.37339
$889$	−24.1022	−0.808363
$890$	−27.0141	−0.905514
$891$	−56.2996	−1.88611
$892$	−57.1714	−1.91424
$893$	−1.53243	−0.0512809
$894$	23.7147	0.793138
$895$	−22.7662	−0.760990
$896$	−82.9707	−2.77186
$897$	−9.71146	−0.324256
$898$	42.9244	1.43241
$899$	−11.3391	−0.378180
$900$	−19.1062	−0.636872
$901$	5.77595	0.192425
$902$	84.4159	2.81074
$903$	23.8508	0.793705
$904$	8.15142	0.271112
$905$	4.89205	0.162617
$906$	−46.4580	−1.54346
$907$	24.6460	0.818357	0.409179	−	0.912454i	$-0.365815\pi$
$907$	24.6460	0.818357	0.409179	+	0.912454i	$0.365815\pi$
$908$	−22.7530	−0.755086
$909$	7.44986	0.247096
$910$	14.4261	0.478221
$911$	−7.55295	−0.250240	−0.125120	−	0.992142i	$-0.539932\pi$
$911$	−7.55295	−0.250240	−0.125120	+	0.992142i	$0.539932\pi$
$912$	1.07152	0.0354816
$913$	−77.1065	−2.55185
$914$	−45.5321	−1.50607
$915$	−41.2168	−1.36258
$916$	−8.07554	−0.266823
$917$	20.9014	0.690225
$918$	16.2088	0.534969
$919$	26.3209	0.868248	0.434124	−	0.900853i	$-0.357058\pi$
$919$	26.3209	0.868248	0.434124	+	0.900853i	$0.357058\pi$
$920$	23.0949	0.761418
$921$	−25.1165	−0.827618
$922$	−59.6112	−1.96319
$923$	−12.2594	−0.403523
$924$	−163.853	−5.39037
$925$	−14.2380	−0.468143
$926$	62.0684	2.03969
$927$	8.81125	0.289399
$928$	6.94722	0.228054
$929$	21.3035	0.698944	0.349472	−	0.936947i	$-0.386361\pi$
$929$	21.3035	0.698944	0.349472	+	0.936947i	$0.386361\pi$
$930$	−52.0739	−1.70757
$931$	3.64897	0.119590
$932$	−51.3172	−1.68095
$933$	−0.553658	−0.0181259
$934$	−13.7584	−0.450187
$935$	−23.3508	−0.763654
$936$	7.01480	0.229286
$937$	−4.99993	−0.163341	−0.0816703	−	0.996659i	$-0.526025\pi$
$937$	−4.99993	−0.163341	−0.0816703	+	0.996659i	$0.526025\pi$
$938$	−136.083	−4.44326
$939$	−29.4055	−0.959612
$940$	21.6018	0.704575
$941$	37.6976	1.22891	0.614453	−	0.788953i	$-0.289377\pi$
$941$	37.6976	1.22891	0.614453	+	0.788953i	$0.289377\pi$
$942$	−43.2796	−1.41013
$943$	−30.6204	−0.997136
$944$	2.72178	0.0885865
$945$	−13.9498	−0.453785
$946$	31.2890	1.01729
$947$	49.1714	1.59785	0.798927	−	0.601428i	$-0.205401\pi$
$947$	49.1714	1.59785	0.798927	+	0.601428i	$0.205401\pi$
$948$	−5.22905	−0.169831
$949$	5.58795	0.181393
$950$	2.40717	0.0780989
$951$	−38.3281	−1.24288
$952$	44.0833	1.42875
$953$	50.8967	1.64871	0.824353	−	0.566076i	$-0.191539\pi$
$953$	50.8967	1.64871	0.824353	+	0.566076i	$0.191539\pi$
$954$	−8.83281	−0.285973
$955$	−31.5178	−1.01989
$956$	−10.4167	−0.336901
$957$	19.5362	0.631514
$958$	68.8708	2.22511
$959$	8.02284	0.259071
$960$	40.5185	1.30773
$961$	12.8487	0.414474
$962$	12.1649	0.392211
$963$	34.9079	1.12489
$964$	−10.3538	−0.333474
$965$	14.1929	0.456886
$966$	93.3294	3.00283
$967$	14.3751	0.462273	0.231136	−	0.972921i	$-0.425756\pi$
$967$	14.3751	0.462273	0.231136	+	0.972921i	$0.425756\pi$
$968$	−53.4670	−1.71850
$969$	2.53763	0.0815204
$970$	−20.7665	−0.666774
$971$	−13.2779	−0.426109	−0.213054	−	0.977040i	$-0.568341\pi$
$971$	−13.2779	−0.426109	−0.213054	+	0.977040i	$0.568341\pi$
$972$	−62.3717	−2.00057
$973$	57.0591	1.82923
$974$	−64.4139	−2.06396
$975$	6.13153	0.196366
$976$	15.8081	0.506004
$977$	27.8744	0.891782	0.445891	−	0.895087i	$-0.352887\pi$
$977$	27.8744	0.891782	0.445891	+	0.895087i	$0.352887\pi$
$978$	−70.9548	−2.26888
$979$	−39.1912	−1.25255
$980$	−51.4375	−1.64311
$981$	8.11923	0.259227
$982$	−9.26358	−0.295613
$983$	−41.4189	−1.32106	−0.660529	−	0.750801i	$-0.729668\pi$
$983$	−41.4189	−1.32106	−0.660529	+	0.750801i	$0.729668\pi$
$984$	55.5704	1.77152
$985$	12.7334	0.405719
$986$	−12.2313	−0.389525
$987$	37.5126	1.19404
$988$	−1.30975	−0.0416686
$989$	−11.3495	−0.360894
$990$	35.7090	1.13491
$991$	13.4076	0.425906	0.212953	−	0.977062i	$-0.431692\pi$
$991$	13.4076	0.425906	0.212953	+	0.977062i	$0.431692\pi$
$992$	−26.8652	−0.852970
$993$	−38.0572	−1.20771
$994$	117.816	3.73689
$995$	1.39693	0.0442856
$996$	−118.121	−3.74280
$997$	−6.39362	−0.202488	−0.101244	−	0.994862i	$-0.532282\pi$
$997$	−6.39362	−0.202488	−0.101244	+	0.994862i	$0.532282\pi$
$998$	2.78167	0.0880523
$999$	−11.7632	−0.372170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8047.2.a.c.1.17	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8047.2.a.c.1.17	✓	151	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:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34671 q^{2} +2.23237 q^{3} +3.50704 q^{4} -1.50112 q^{5} -5.23873 q^{6} -4.09520 q^{7} -3.53658 q^{8} +1.98350 q^{9} +O(q^{10})\)	\(q-2.34671 q^{2} +2.23237 q^{3} +3.50704 q^{4} -1.50112 q^{5} -5.23873 q^{6} -4.09520 q^{7} -3.53658 q^{8} +1.98350 q^{9} +3.52269 q^{10} +5.11060 q^{11} +7.82903 q^{12} -1.00000 q^{13} +9.61024 q^{14} -3.35106 q^{15} +1.28525 q^{16} +3.04379 q^{17} -4.65469 q^{18} +0.373462 q^{19} -5.26449 q^{20} -9.14202 q^{21} -11.9931 q^{22} +4.35028 q^{23} -7.89498 q^{24} -2.74664 q^{25} +2.34671 q^{26} -2.26922 q^{27} -14.3620 q^{28} +1.71238 q^{29} +7.86397 q^{30} -6.62184 q^{31} +4.05706 q^{32} +11.4088 q^{33} -7.14289 q^{34} +6.14738 q^{35} +6.95620 q^{36} +5.18380 q^{37} -0.876406 q^{38} -2.23237 q^{39} +5.30884 q^{40} -7.03871 q^{41} +21.4536 q^{42} -2.60892 q^{43} +17.9231 q^{44} -2.97747 q^{45} -10.2088 q^{46} -4.10331 q^{47} +2.86916 q^{48} +9.77065 q^{49} +6.44556 q^{50} +6.79488 q^{51} -3.50704 q^{52} +1.89762 q^{53} +5.32519 q^{54} -7.67163 q^{55} +14.4830 q^{56} +0.833707 q^{57} -4.01845 q^{58} +2.11771 q^{59} -11.7523 q^{60} +12.2996 q^{61} +15.5395 q^{62} -8.12281 q^{63} -12.0912 q^{64} +1.50112 q^{65} -26.7731 q^{66} -14.1602 q^{67} +10.6747 q^{68} +9.71146 q^{69} -14.4261 q^{70} +12.2594 q^{71} -7.01480 q^{72} -5.58795 q^{73} -12.1649 q^{74} -6.13153 q^{75} +1.30975 q^{76} -20.9289 q^{77} +5.23873 q^{78} -0.667905 q^{79} -1.92931 q^{80} -11.0162 q^{81} +16.5178 q^{82} -15.0876 q^{83} -32.0614 q^{84} -4.56910 q^{85} +6.12237 q^{86} +3.82267 q^{87} -18.0741 q^{88} -7.66860 q^{89} +6.98724 q^{90} +4.09520 q^{91} +15.2566 q^{92} -14.7824 q^{93} +9.62928 q^{94} -0.560611 q^{95} +9.05688 q^{96} -5.89508 q^{97} -22.9289 q^{98} +10.1369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * q^99

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