LMFDB - Embedded newform 1441.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.660505 q^{2} +2.12062 q^{3} -1.56373 q^{4} +2.37769 q^{5} -1.40068 q^{6} +3.00733 q^{7} +2.35386 q^{8} +1.49703 q^{9} +O(q^{10})$	\(q-0.660505 q^{2} +2.12062 q^{3} -1.56373 q^{4} +2.37769 q^{5} -1.40068 q^{6} +3.00733 q^{7} +2.35386 q^{8} +1.49703 q^{9} -1.57048 q^{10} +1.00000 q^{11} -3.31608 q^{12} -0.736252 q^{13} -1.98636 q^{14} +5.04217 q^{15} +1.57273 q^{16} +1.25246 q^{17} -0.988795 q^{18} -0.110974 q^{19} -3.71807 q^{20} +6.37741 q^{21} -0.660505 q^{22} +3.25960 q^{23} +4.99165 q^{24} +0.653403 q^{25} +0.486298 q^{26} -3.18723 q^{27} -4.70267 q^{28} -0.486844 q^{29} -3.33038 q^{30} +7.87356 q^{31} -5.74652 q^{32} +2.12062 q^{33} -0.827258 q^{34} +7.15050 q^{35} -2.34095 q^{36} +1.08677 q^{37} +0.0732991 q^{38} -1.56131 q^{39} +5.59675 q^{40} +6.21368 q^{41} -4.21231 q^{42} -3.39036 q^{43} -1.56373 q^{44} +3.55947 q^{45} -2.15298 q^{46} -11.7300 q^{47} +3.33516 q^{48} +2.04406 q^{49} -0.431576 q^{50} +2.65600 q^{51} +1.15130 q^{52} -6.11837 q^{53} +2.10518 q^{54} +2.37769 q^{55} +7.07885 q^{56} -0.235334 q^{57} +0.321563 q^{58} -0.348609 q^{59} -7.88461 q^{60} -0.211686 q^{61} -5.20052 q^{62} +4.50206 q^{63} +0.650149 q^{64} -1.75058 q^{65} -1.40068 q^{66} +1.98218 q^{67} -1.95852 q^{68} +6.91238 q^{69} -4.72294 q^{70} -6.68283 q^{71} +3.52380 q^{72} +1.98560 q^{73} -0.717818 q^{74} +1.38562 q^{75} +0.173534 q^{76} +3.00733 q^{77} +1.03125 q^{78} +5.38749 q^{79} +3.73946 q^{80} -11.2500 q^{81} -4.10417 q^{82} +7.07572 q^{83} -9.97257 q^{84} +2.97797 q^{85} +2.23935 q^{86} -1.03241 q^{87} +2.35386 q^{88} +13.4745 q^{89} -2.35105 q^{90} -2.21415 q^{91} -5.09715 q^{92} +16.6968 q^{93} +7.74769 q^{94} -0.263862 q^{95} -12.1862 q^{96} -0.429909 q^{97} -1.35011 q^{98} +1.49703 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * 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 $

$2$	−0.660505	−0.467048	−0.233524	−	0.972351i	$-0.575026\pi$
$2$	−0.660505	−0.467048	−0.233524	+	0.972351i	$0.575026\pi$
$3$	2.12062	1.22434	0.612170	−	0.790726i	$-0.290297\pi$
$3$	2.12062	1.22434	0.612170	+	0.790726i	$0.290297\pi$
$4$	−1.56373	−0.781867
$5$	2.37769	1.06333	0.531667	−	0.846953i	$-0.321566\pi$
$5$	2.37769	1.06333	0.531667	+	0.846953i	$0.321566\pi$
$6$	−1.40068	−0.571825
$7$	3.00733	1.13667	0.568333	−	0.822799i	$-0.307589\pi$
$7$	3.00733	1.13667	0.568333	+	0.822799i	$0.307589\pi$
$8$	2.35386	0.832216
$9$	1.49703	0.499009
$10$	−1.57048	−0.496628
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.31608	−0.957271
$13$	−0.736252	−0.204199	−0.102100	−	0.994774i	$-0.532556\pi$
$13$	−0.736252	−0.204199	−0.102100	+	0.994774i	$0.532556\pi$
$14$	−1.98636	−0.530877
$15$	5.04217	1.30188
$16$	1.57273	0.393182
$17$	1.25246	0.303767	0.151883	−	0.988398i	$-0.451466\pi$
$17$	1.25246	0.303767	0.151883	+	0.988398i	$0.451466\pi$
$18$	−0.988795	−0.233061
$19$	−0.110974	−0.0254592	−0.0127296	−	0.999919i	$-0.504052\pi$
$19$	−0.110974	−0.0254592	−0.0127296	+	0.999919i	$0.504052\pi$
$20$	−3.71807	−0.831386
$21$	6.37741	1.39167
$22$	−0.660505	−0.140820
$23$	3.25960	0.679675	0.339837	−	0.940484i	$-0.389628\pi$
$23$	3.25960	0.679675	0.339837	+	0.940484i	$0.389628\pi$
$24$	4.99165	1.01892
$25$	0.653403	0.130681
$26$	0.486298	0.0953709
$27$	−3.18723	−0.613383
$28$	−4.70267	−0.888721
$29$	−0.486844	−0.0904048	−0.0452024	−	0.998978i	$-0.514393\pi$
$29$	−0.486844	−0.0904048	−0.0452024	+	0.998978i	$0.514393\pi$
$30$	−3.33038	−0.608042
$31$	7.87356	1.41413	0.707066	−	0.707147i	$-0.250018\pi$
$31$	7.87356	1.41413	0.707066	+	0.707147i	$0.250018\pi$
$32$	−5.74652	−1.01585
$33$	2.12062	0.369153
$34$	−0.827258	−0.141874
$35$	7.15050	1.20866
$36$	−2.34095	−0.390159
$37$	1.08677	0.178664	0.0893321	−	0.996002i	$-0.471527\pi$
$37$	1.08677	0.178664	0.0893321	+	0.996002i	$0.471527\pi$
$38$	0.0732991	0.0118907
$39$	−1.56131	−0.250010
$40$	5.59675	0.884925
$41$	6.21368	0.970414	0.485207	−	0.874399i	$-0.338744\pi$
$41$	6.21368	0.970414	0.485207	+	0.874399i	$0.338744\pi$
$42$	−4.21231	−0.649974
$43$	−3.39036	−0.517025	−0.258512	−	0.966008i	$-0.583232\pi$
$43$	−3.39036	−0.517025	−0.258512	+	0.966008i	$0.583232\pi$
$44$	−1.56373	−0.235742
$45$	3.55947	0.530614
$46$	−2.15298	−0.317440
$47$	−11.7300	−1.71099	−0.855495	−	0.517811i	$-0.826747\pi$
$47$	−11.7300	−1.71099	−0.855495	+	0.517811i	$0.826747\pi$
$48$	3.33516	0.481389
$49$	2.04406	0.292008
$50$	−0.431576	−0.0610341
$51$	2.65600	0.371914
$52$	1.15130	0.159657
$53$	−6.11837	−0.840422	−0.420211	−	0.907426i	$-0.638044\pi$
$53$	−6.11837	−0.840422	−0.420211	+	0.907426i	$0.638044\pi$
$54$	2.10518	0.286479
$55$	2.37769	0.320607
$56$	7.07885	0.945951
$57$	−0.235334	−0.0311708
$58$	0.321563	0.0422233
$59$	−0.348609	−0.0453850	−0.0226925	−	0.999742i	$-0.507224\pi$
$59$	−0.348609	−0.0453850	−0.0226925	+	0.999742i	$0.507224\pi$
$60$	−7.88461	−1.01790
$61$	−0.211686	−0.0271036	−0.0135518	−	0.999908i	$-0.504314\pi$
$61$	−0.211686	−0.0271036	−0.0135518	+	0.999908i	$0.504314\pi$
$62$	−5.20052	−0.660467
$63$	4.50206	0.567207
$64$	0.650149	0.0812687
$65$	−1.75058	−0.217132
$66$	−1.40068	−0.172412
$67$	1.98218	0.242162	0.121081	−	0.992643i	$-0.461364\pi$
$67$	1.98218	0.242162	0.121081	+	0.992643i	$0.461364\pi$
$68$	−1.95852	−0.237505
$69$	6.91238	0.832153
$70$	−4.72294	−0.564500
$71$	−6.68283	−0.793106	−0.396553	−	0.918012i	$-0.629794\pi$
$71$	−6.68283	−0.793106	−0.396553	+	0.918012i	$0.629794\pi$
$72$	3.52380	0.415284
$73$	1.98560	0.232397	0.116199	−	0.993226i	$-0.462929\pi$
$73$	1.98560	0.232397	0.116199	+	0.993226i	$0.462929\pi$
$74$	−0.717818	−0.0834447
$75$	1.38562	0.159998
$76$	0.173534	0.0199057
$77$	3.00733	0.342717
$78$	1.03125	0.116766
$79$	5.38749	0.606140	0.303070	−	0.952968i	$-0.401988\pi$
$79$	5.38749	0.606140	0.303070	+	0.952968i	$0.401988\pi$
$80$	3.73946	0.418084
$81$	−11.2500	−1.25000
$82$	−4.10417	−0.453230
$83$	7.07572	0.776661	0.388331	−	0.921520i	$-0.373052\pi$
$83$	7.07572	0.776661	0.388331	+	0.921520i	$0.373052\pi$
$84$	−9.97257	−1.08810
$85$	2.97797	0.323006
$86$	2.23935	0.241475
$87$	−1.03241	−0.110686
$88$	2.35386	0.250923
$89$	13.4745	1.42830	0.714148	−	0.699995i	$-0.246814\pi$
$89$	13.4745	1.42830	0.714148	+	0.699995i	$0.246814\pi$
$90$	−2.35105	−0.247822
$91$	−2.21415	−0.232106
$92$	−5.09715	−0.531415
$93$	16.6968	1.73138
$94$	7.74769	0.799113
$95$	−0.263862	−0.0270717
$96$	−12.1862	−1.24375
$97$	−0.429909	−0.0436506	−0.0218253	−	0.999762i	$-0.506948\pi$
$97$	−0.429909	−0.0436506	−0.0218253	+	0.999762i	$0.506948\pi$
$98$	−1.35011	−0.136382
$99$	1.49703	0.150457
$100$	−1.02175	−0.102175
$101$	16.7710	1.66877	0.834387	−	0.551179i	$-0.185822\pi$
$101$	16.7710	1.66877	0.834387	+	0.551179i	$0.185822\pi$
$102$	−1.75430	−0.173702
$103$	−3.40447	−0.335453	−0.167726	−	0.985834i	$-0.553643\pi$
$103$	−3.40447	−0.335453	−0.167726	+	0.985834i	$0.553643\pi$
$104$	−1.73304	−0.169938
$105$	15.1635	1.47981
$106$	4.04121	0.392517
$107$	−10.6669	−1.03121	−0.515605	−	0.856826i	$-0.672433\pi$
$107$	−10.6669	−1.03121	−0.515605	+	0.856826i	$0.672433\pi$
$108$	4.98398	0.479584
$109$	−0.896970	−0.0859141	−0.0429571	−	0.999077i	$-0.513678\pi$
$109$	−0.896970	−0.0859141	−0.0429571	+	0.999077i	$0.513678\pi$
$110$	−1.57048	−0.149739
$111$	2.30463	0.218746
$112$	4.72972	0.446916
$113$	−0.776215	−0.0730202	−0.0365101	−	0.999333i	$-0.511624\pi$
$113$	−0.776215	−0.0730202	−0.0365101	+	0.999333i	$0.511624\pi$
$114$	0.155439	0.0145582
$115$	7.75032	0.722721
$116$	0.761295	0.0706845
$117$	−1.10219	−0.101897
$118$	0.230258	0.0211970
$119$	3.76657	0.345281
$120$	11.8686	1.08345
$121$	1.00000	0.0909091
$122$	0.139819	0.0126587
$123$	13.1769	1.18812
$124$	−12.3121	−1.10566
$125$	−10.3349	−0.924377
$126$	−2.97364	−0.264912
$127$	5.36007	0.475629	0.237815	−	0.971311i	$-0.423569\pi$
$127$	5.36007	0.475629	0.237815	+	0.971311i	$0.423569\pi$
$128$	11.0636	0.977895
$129$	−7.18966	−0.633014
$130$	1.15626	0.101411
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−3.31608	−0.288628
$133$	−0.333737	−0.0289386
$134$	−1.30924	−0.113101
$135$	−7.57824	−0.652231
$136$	2.94813	0.252800
$137$	14.0554	1.20084	0.600418	−	0.799686i	$-0.295001\pi$
$137$	14.0554	1.20084	0.600418	+	0.799686i	$0.295001\pi$
$138$	−4.56566	−0.388655
$139$	15.3736	1.30397	0.651987	−	0.758231i	$-0.273936\pi$
$139$	15.3736	1.30397	0.651987	+	0.758231i	$0.273936\pi$
$140$	−11.1815	−0.945008
$141$	−24.8748	−2.09483
$142$	4.41404	0.370418
$143$	−0.736252	−0.0615685
$144$	2.35442	0.196202
$145$	−1.15756	−0.0961305
$146$	−1.31150	−0.108541
$147$	4.33467	0.357517
$148$	−1.69942	−0.139692
$149$	−11.5801	−0.948682	−0.474341	−	0.880341i	$-0.657314\pi$
$149$	−11.5801	−0.948682	−0.474341	+	0.880341i	$0.657314\pi$
$150$	−0.915209	−0.0747265
$151$	−14.4883	−1.17904	−0.589519	−	0.807754i	$-0.700683\pi$
$151$	−14.4883	−1.17904	−0.589519	+	0.807754i	$0.700683\pi$
$152$	−0.261218	−0.0211876
$153$	1.87497	0.151583
$154$	−1.98636	−0.160065
$155$	18.7209	1.50370
$156$	2.44147	0.195474
$157$	−9.64613	−0.769845	−0.384923	−	0.922949i	$-0.625772\pi$
$157$	−9.64613	−0.769845	−0.384923	+	0.922949i	$0.625772\pi$
$158$	−3.55847	−0.283096
$159$	−12.9747	−1.02896
$160$	−13.6634	−1.08019
$161$	9.80272	0.772562
$162$	7.43067	0.583809
$163$	−13.3412	−1.04496	−0.522481	−	0.852651i	$-0.674993\pi$
$163$	−13.3412	−1.04496	−0.522481	+	0.852651i	$0.674993\pi$
$164$	−9.71654	−0.758734
$165$	5.04217	0.392533
$166$	−4.67355	−0.362738
$167$	10.6205	0.821840	0.410920	−	0.911671i	$-0.365208\pi$
$167$	10.6205	0.821840	0.410920	+	0.911671i	$0.365208\pi$
$168$	15.0116	1.15817
$169$	−12.4579	−0.958303
$170$	−1.96696	−0.150859
$171$	−0.166132	−0.0127044
$172$	5.30162	0.404244
$173$	−5.34954	−0.406718	−0.203359	−	0.979104i	$-0.565186\pi$
$173$	−5.34954	−0.406718	−0.203359	+	0.979104i	$0.565186\pi$
$174$	0.681913	0.0516957
$175$	1.96500	0.148540
$176$	1.57273	0.118549
$177$	−0.739267	−0.0555667
$178$	−8.89998	−0.667082
$179$	−18.2367	−1.36307	−0.681537	−	0.731784i	$-0.738688\pi$
$179$	−18.2367	−1.36307	−0.681537	+	0.731784i	$0.738688\pi$
$180$	−5.56606	−0.414869
$181$	7.63946	0.567836	0.283918	−	0.958849i	$-0.408366\pi$
$181$	7.63946	0.567836	0.283918	+	0.958849i	$0.408366\pi$
$182$	1.46246	0.108405
$183$	−0.448905	−0.0331840
$184$	7.67266	0.565636
$185$	2.58401	0.189980
$186$	−11.0283	−0.808636
$187$	1.25246	0.0915892
$188$	18.3425	1.33777
$189$	−9.58507	−0.697211
$190$	0.174282	0.0126438
$191$	16.3909	1.18600	0.593002	−	0.805201i	$-0.297943\pi$
$191$	16.3909	1.18600	0.593002	+	0.805201i	$0.297943\pi$
$192$	1.37872	0.0995005
$193$	11.7411	0.845145	0.422573	−	0.906329i	$-0.361127\pi$
$193$	11.7411	0.845145	0.422573	+	0.906329i	$0.361127\pi$
$194$	0.283957	0.0203869
$195$	−3.71231	−0.265844
$196$	−3.19636	−0.228311
$197$	−19.0920	−1.36025	−0.680123	−	0.733098i	$-0.738074\pi$
$197$	−19.0920	−1.36025	−0.680123	+	0.733098i	$0.738074\pi$
$198$	−0.988795	−0.0702706
$199$	1.71426	0.121521	0.0607604	−	0.998152i	$-0.480647\pi$
$199$	1.71426	0.121521	0.0607604	+	0.998152i	$0.480647\pi$
$200$	1.53802	0.108755
$201$	4.20346	0.296489
$202$	−11.0773	−0.779397
$203$	−1.46410	−0.102760
$204$	−4.15327	−0.290787
$205$	14.7742	1.03187
$206$	2.24867	0.156672
$207$	4.87972	0.339164
$208$	−1.15792	−0.0802876
$209$	−0.110974	−0.00767625
$210$	−10.0156	−0.691140
$211$	2.88704	0.198752	0.0993760	−	0.995050i	$-0.468315\pi$
$211$	2.88704	0.198752	0.0993760	+	0.995050i	$0.468315\pi$
$212$	9.56750	0.657098
$213$	−14.1717	−0.971031
$214$	7.04555	0.481624
$215$	−8.06122	−0.549770
$216$	−7.50231	−0.510467
$217$	23.6784	1.60740
$218$	0.592453	0.0401260
$219$	4.21071	0.284533
$220$	−3.71807	−0.250672
$221$	−0.922128	−0.0620290
$222$	−1.52222	−0.102165
$223$	−6.21044	−0.415882	−0.207941	−	0.978141i	$-0.566676\pi$
$223$	−6.21044	−0.415882	−0.207941	+	0.978141i	$0.566676\pi$
$224$	−17.2817	−1.15468
$225$	0.978163	0.0652109
$226$	0.512694	0.0341039
$227$	−9.74658	−0.646903	−0.323452	−	0.946245i	$-0.604843\pi$
$227$	−9.74658	−0.646903	−0.323452	+	0.946245i	$0.604843\pi$
$228$	0.368000	0.0243714
$229$	−6.81189	−0.450142	−0.225071	−	0.974342i	$-0.572261\pi$
$229$	−6.81189	−0.450142	−0.225071	+	0.974342i	$0.572261\pi$
$230$	−5.11913	−0.337545
$231$	6.37741	0.419603
$232$	−1.14597	−0.0752363
$233$	22.0084	1.44182	0.720910	−	0.693029i	$-0.243724\pi$
$233$	22.0084	1.44182	0.720910	+	0.693029i	$0.243724\pi$
$234$	0.728002	0.0475910
$235$	−27.8902	−1.81935
$236$	0.545132	0.0354851
$237$	11.4248	0.742122
$238$	−2.48784	−0.161263
$239$	−26.2325	−1.69684	−0.848419	−	0.529325i	$-0.822445\pi$
$239$	−26.2325	−1.69684	−0.848419	+	0.529325i	$0.822445\pi$
$240$	7.92997	0.511877
$241$	1.12310	0.0723454	0.0361727	−	0.999346i	$-0.488483\pi$
$241$	1.12310	0.0723454	0.0361727	+	0.999346i	$0.488483\pi$
$242$	−0.660505	−0.0424589
$243$	−14.2953	−0.917041
$244$	0.331020	0.0211914
$245$	4.86013	0.310502
$246$	−8.70338	−0.554907
$247$	0.0817050	0.00519876
$248$	18.5333	1.17686
$249$	15.0049	0.950898
$250$	6.82622	0.431728
$251$	−18.1112	−1.14317	−0.571583	−	0.820544i	$-0.693671\pi$
$251$	−18.1112	−1.14317	−0.571583	+	0.820544i	$0.693671\pi$
$252$	−7.04003	−0.443480
$253$	3.25960	0.204930
$254$	−3.54035	−0.222142
$255$	6.31514	0.395469
$256$	−8.60787	−0.537992
$257$	−8.19457	−0.511163	−0.255582	−	0.966787i	$-0.582267\pi$
$257$	−8.19457	−0.511163	−0.255582	+	0.966787i	$0.582267\pi$
$258$	4.74881	0.295648
$259$	3.26829	0.203081
$260$	2.73744	0.169769
$261$	−0.728820	−0.0451128
$262$	0.660505	0.0408061
$263$	14.0220	0.864631	0.432316	−	0.901722i	$-0.357697\pi$
$263$	14.0220	0.864631	0.432316	+	0.901722i	$0.357697\pi$
$264$	4.99165	0.307215
$265$	−14.5476	−0.893650
$266$	0.220435	0.0135157
$267$	28.5743	1.74872
$268$	−3.09961	−0.189339
$269$	−5.28256	−0.322083	−0.161042	−	0.986948i	$-0.551485\pi$
$269$	−5.28256	−0.322083	−0.161042	+	0.986948i	$0.551485\pi$
$270$	5.00547	0.304623
$271$	27.1521	1.64937	0.824686	−	0.565591i	$-0.191352\pi$
$271$	27.1521	1.64937	0.824686	+	0.565591i	$0.191352\pi$
$272$	1.96978	0.119436
$273$	−4.69538	−0.284177
$274$	−9.28368	−0.560848
$275$	0.653403	0.0394017
$276$	−10.8091	−0.650633
$277$	−14.0111	−0.841847	−0.420923	−	0.907096i	$-0.638294\pi$
$277$	−14.0111	−0.841847	−0.420923	+	0.907096i	$0.638294\pi$
$278$	−10.1543	−0.609017
$279$	11.7869	0.705665
$280$	16.8313	1.00586
$281$	28.2453	1.68498	0.842488	−	0.538715i	$-0.181090\pi$
$281$	28.2453	1.68498	0.842488	+	0.538715i	$0.181090\pi$
$282$	16.4299	0.978387
$283$	−6.00505	−0.356963	−0.178482	−	0.983943i	$-0.557118\pi$
$283$	−6.00505	−0.356963	−0.178482	+	0.983943i	$0.557118\pi$
$284$	10.4502	0.620103
$285$	−0.559552	−0.0331450
$286$	0.486298	0.0287554
$287$	18.6866	1.10304
$288$	−8.60271	−0.506919
$289$	−15.4313	−0.907726
$290$	0.764577	0.0448975
$291$	−0.911673	−0.0534432
$292$	−3.10495	−0.181704
$293$	10.2366	0.598026	0.299013	−	0.954249i	$-0.403343\pi$
$293$	10.2366	0.598026	0.299013	+	0.954249i	$0.403343\pi$
$294$	−2.86307	−0.166978
$295$	−0.828884	−0.0482595
$296$	2.55811	0.148687
$297$	−3.18723	−0.184942
$298$	7.64874	0.443080
$299$	−2.39989	−0.138789
$300$	−2.16674	−0.125097
$301$	−10.1959	−0.587684
$302$	9.56957	0.550667
$303$	35.5648	2.04315
$304$	−0.174532	−0.0100101
$305$	−0.503323	−0.0288202
$306$	−1.23843	−0.0707963
$307$	−1.11657	−0.0637261	−0.0318630	−	0.999492i	$-0.510144\pi$
$307$	−1.11657	−0.0637261	−0.0318630	+	0.999492i	$0.510144\pi$
$308$	−4.70267	−0.267959
$309$	−7.21960	−0.410709
$310$	−12.3652	−0.702297
$311$	−14.6495	−0.830699	−0.415350	−	0.909662i	$-0.636341\pi$
$311$	−14.6495	−0.830699	−0.415350	+	0.909662i	$0.636341\pi$
$312$	−3.67511	−0.208062
$313$	−28.1510	−1.59119	−0.795594	−	0.605831i	$-0.792841\pi$
$313$	−28.1510	−1.59119	−0.795594	+	0.605831i	$0.792841\pi$
$314$	6.37132	0.359554
$315$	10.7045	0.603131
$316$	−8.42460	−0.473921
$317$	9.16635	0.514834	0.257417	−	0.966300i	$-0.417129\pi$
$317$	9.16635	0.514834	0.257417	+	0.966300i	$0.417129\pi$
$318$	8.56987	0.480575
$319$	−0.486844	−0.0272581
$320$	1.54585	0.0864158
$321$	−22.6205	−1.26255
$322$	−6.47474	−0.360823
$323$	−0.138991	−0.00773368
$324$	17.5920	0.977333
$325$	−0.481069	−0.0266849
$326$	8.81191	0.488046
$327$	−1.90213	−0.105188
$328$	14.6262	0.807595
$329$	−35.2759	−1.94482
$330$	−3.33038	−0.183331
$331$	−13.2824	−0.730067	−0.365034	−	0.930994i	$-0.618942\pi$
$331$	−13.2824	−0.730067	−0.365034	+	0.930994i	$0.618942\pi$
$332$	−11.0645	−0.607245
$333$	1.62693	0.0891551
$334$	−7.01490	−0.383838
$335$	4.71302	0.257500
$336$	10.0299	0.547178
$337$	−25.5410	−1.39130	−0.695652	−	0.718379i	$-0.744885\pi$
$337$	−25.5410	−1.39130	−0.695652	+	0.718379i	$0.744885\pi$
$338$	8.22853	0.447573
$339$	−1.64606	−0.0894016
$340$	−4.65675	−0.252548
$341$	7.87356	0.426377
$342$	0.109731	0.00593356
$343$	−14.9042	−0.804750
$344$	−7.98044	−0.430277
$345$	16.4355	0.884857
$346$	3.53339	0.189956
$347$	14.8776	0.798674	0.399337	−	0.916804i	$-0.369240\pi$
$347$	14.8776	0.798674	0.399337	+	0.916804i	$0.369240\pi$
$348$	1.61442	0.0865418
$349$	−22.3139	−1.19443	−0.597217	−	0.802080i	$-0.703727\pi$
$349$	−22.3139	−1.19443	−0.597217	+	0.802080i	$0.703727\pi$
$350$	−1.29789	−0.0693753
$351$	2.34660	0.125252
$352$	−5.74652	−0.306291
$353$	−16.1471	−0.859423	−0.429711	−	0.902966i	$-0.641385\pi$
$353$	−16.1471	−0.859423	−0.429711	+	0.902966i	$0.641385\pi$
$354$	0.488290	0.0259523
$355$	−15.8897	−0.843337
$356$	−21.0705	−1.11674
$357$	7.98747	0.422742
$358$	12.0454	0.636620
$359$	−7.17495	−0.378679	−0.189340	−	0.981912i	$-0.560635\pi$
$359$	−7.17495	−0.378679	−0.189340	+	0.981912i	$0.560635\pi$
$360$	8.37850	0.441586
$361$	−18.9877	−0.999352
$362$	−5.04590	−0.265207
$363$	2.12062	0.111304
$364$	3.46235	0.181476
$365$	4.72115	0.247116
$366$	0.296504	0.0154985
$367$	−14.9196	−0.778796	−0.389398	−	0.921070i	$-0.627317\pi$
$367$	−14.9196	−0.778796	−0.389398	+	0.921070i	$0.627317\pi$
$368$	5.12647	0.267236
$369$	9.30206	0.484246
$370$	−1.70675	−0.0887296
$371$	−18.4000	−0.955279
$372$	−26.1094	−1.35371
$373$	−0.408941	−0.0211742	−0.0105871	−	0.999944i	$-0.503370\pi$
$373$	−0.408941	−0.0211742	−0.0105871	+	0.999944i	$0.503370\pi$
$374$	−0.827258	−0.0427765
$375$	−21.9163	−1.13175
$376$	−27.6107	−1.42391
$377$	0.358440	0.0184606
$378$	6.33099	0.325631
$379$	−14.5864	−0.749252	−0.374626	−	0.927176i	$-0.622229\pi$
$379$	−14.5864	−0.749252	−0.374626	+	0.927176i	$0.622229\pi$
$380$	0.412610	0.0211665
$381$	11.3667	0.582332
$382$	−10.8263	−0.553920
$383$	−26.5867	−1.35852	−0.679258	−	0.733899i	$-0.737698\pi$
$383$	−26.5867	−1.35852	−0.679258	+	0.733899i	$0.737698\pi$
$384$	23.4617	1.19728
$385$	7.15050	0.364423
$386$	−7.75508	−0.394723
$387$	−5.07546	−0.258000
$388$	0.672263	0.0341290
$389$	−0.801249	−0.0406249	−0.0203125	−	0.999794i	$-0.506466\pi$
$389$	−0.801249	−0.0406249	−0.0203125	+	0.999794i	$0.506466\pi$
$390$	2.45200	0.124162
$391$	4.08253	0.206463
$392$	4.81143	0.243014
$393$	−2.12062	−0.106971
$394$	12.6103	0.635300
$395$	12.8098	0.644530
$396$	−2.34095	−0.117637
$397$	−21.5131	−1.07971	−0.539855	−	0.841758i	$-0.681521\pi$
$397$	−21.5131	−1.07971	−0.539855	+	0.841758i	$0.681521\pi$
$398$	−1.13228	−0.0567560
$399$	−0.707729	−0.0354307
$400$	1.02763	0.0513813
$401$	−14.0023	−0.699240	−0.349620	−	0.936892i	$-0.613689\pi$
$401$	−14.0023	−0.699240	−0.349620	+	0.936892i	$0.613689\pi$
$402$	−2.77641	−0.138475
$403$	−5.79692	−0.288765
$404$	−26.2253	−1.30476
$405$	−26.7490	−1.32917
$406$	0.967048	0.0479938
$407$	1.08677	0.0538693
$408$	6.25186	0.309513
$409$	−24.9669	−1.23453	−0.617267	−	0.786754i	$-0.711760\pi$
$409$	−24.9669	−1.23453	−0.617267	+	0.786754i	$0.711760\pi$
$410$	−9.75843	−0.481935
$411$	29.8062	1.47023
$412$	5.32369	0.262279
$413$	−1.04838	−0.0515876
$414$	−3.22308	−0.158406
$415$	16.8239	0.825851
$416$	4.23089	0.207436
$417$	32.6016	1.59651
$418$	0.0732991	0.00358517
$419$	15.1859	0.741879	0.370939	−	0.928657i	$-0.379036\pi$
$419$	15.1859	0.741879	0.370939	+	0.928657i	$0.379036\pi$
$420$	−23.7117	−1.15701
$421$	−28.1825	−1.37353	−0.686766	−	0.726879i	$-0.740970\pi$
$421$	−28.1825	−1.37353	−0.686766	+	0.726879i	$0.740970\pi$
$422$	−1.90690	−0.0928266
$423$	−17.5601	−0.853800
$424$	−14.4018	−0.699413
$425$	0.818363	0.0396965
$426$	9.36050	0.453518
$427$	−0.636610	−0.0308077
$428$	16.6802	0.806268
$429$	−1.56131	−0.0753807
$430$	5.32447	0.256769
$431$	−12.4323	−0.598843	−0.299422	−	0.954121i	$-0.596794\pi$
$431$	−12.4323	−0.598843	−0.299422	+	0.954121i	$0.596794\pi$
$432$	−5.01265	−0.241171
$433$	11.3096	0.543502	0.271751	−	0.962368i	$-0.412397\pi$
$433$	11.3096	0.543502	0.271751	+	0.962368i	$0.412397\pi$
$434$	−15.6397	−0.750730
$435$	−2.45475	−0.117696
$436$	1.40262	0.0671734
$437$	−0.361732	−0.0173040
$438$	−2.78119	−0.132891
$439$	−1.43861	−0.0686613	−0.0343307	−	0.999411i	$-0.510930\pi$
$439$	−1.43861	−0.0686613	−0.0343307	+	0.999411i	$0.510930\pi$
$440$	5.59675	0.266815
$441$	3.06001	0.145715
$442$	0.609070	0.0289705
$443$	22.9456	1.09018	0.545088	−	0.838379i	$-0.316496\pi$
$443$	22.9456	1.09018	0.545088	+	0.838379i	$0.316496\pi$
$444$	−3.60383	−0.171030
$445$	32.0382	1.51876
$446$	4.10202	0.194236
$447$	−24.5571	−1.16151
$448$	1.95522	0.0923753
$449$	31.8979	1.50536	0.752678	−	0.658389i	$-0.228762\pi$
$449$	31.8979	1.50536	0.752678	+	0.658389i	$0.228762\pi$
$450$	−0.646082	−0.0304566
$451$	6.21368	0.292591
$452$	1.21379	0.0570920
$453$	−30.7241	−1.44354
$454$	6.43766	0.302135
$455$	−5.26457	−0.246807
$456$	−0.553945	−0.0259408
$457$	0.526400	0.0246239	0.0123120	−	0.999924i	$-0.496081\pi$
$457$	0.526400	0.0246239	0.0123120	+	0.999924i	$0.496081\pi$
$458$	4.49929	0.210238
$459$	−3.99189	−0.186325
$460$	−12.1194	−0.565072
$461$	24.1279	1.12375	0.561873	−	0.827223i	$-0.310081\pi$
$461$	24.1279	1.12375	0.561873	+	0.827223i	$0.310081\pi$
$462$	−4.21231	−0.195974
$463$	14.2619	0.662807	0.331404	−	0.943489i	$-0.392478\pi$
$463$	14.2619	0.662807	0.331404	+	0.943489i	$0.392478\pi$
$464$	−0.765674	−0.0355455
$465$	39.6998	1.84104
$466$	−14.5367	−0.673398
$467$	28.4175	1.31500	0.657502	−	0.753452i	$-0.271613\pi$
$467$	28.4175	1.31500	0.657502	+	0.753452i	$0.271613\pi$
$468$	1.72353	0.0796702
$469$	5.96109	0.275258
$470$	18.4216	0.849725
$471$	−20.4558	−0.942553
$472$	−0.820578	−0.0377702
$473$	−3.39036	−0.155889
$474$	−7.54615	−0.346606
$475$	−0.0725109	−0.00332703
$476$	−5.88992	−0.269964
$477$	−9.15937	−0.419379
$478$	17.3267	0.792504
$479$	18.4156	0.841428	0.420714	−	0.907193i	$-0.361780\pi$
$479$	18.4156	0.841428	0.420714	+	0.907193i	$0.361780\pi$
$480$	−28.9750	−1.32252
$481$	−0.800138	−0.0364831
$482$	−0.741815	−0.0337887
$483$	20.7878	0.945879
$484$	−1.56373	−0.0710788
$485$	−1.02219	−0.0464152
$486$	9.44209	0.428302
$487$	−24.1638	−1.09497	−0.547483	−	0.836817i	$-0.684414\pi$
$487$	−24.1638	−1.09497	−0.547483	+	0.836817i	$0.684414\pi$
$488$	−0.498279	−0.0225560
$489$	−28.2915	−1.27939
$490$	−3.21014	−0.145019
$491$	36.3107	1.63868	0.819340	−	0.573307i	$-0.194340\pi$
$491$	36.3107	1.63868	0.819340	+	0.573307i	$0.194340\pi$
$492$	−20.6051	−0.928949
$493$	−0.609755	−0.0274620
$494$	−0.0539665	−0.00242807
$495$	3.55947	0.159986
$496$	12.3830	0.556011
$497$	−20.0975	−0.901496
$498$	−9.91082	−0.444114
$499$	−17.7206	−0.793285	−0.396642	−	0.917973i	$-0.629825\pi$
$499$	−17.7206	−0.793285	−0.396642	+	0.917973i	$0.629825\pi$
$500$	16.1610	0.722740
$501$	22.5221	1.00621
$502$	11.9625	0.533913
$503$	24.4092	1.08835	0.544176	−	0.838971i	$-0.316842\pi$
$503$	24.4092	1.08835	0.544176	+	0.838971i	$0.316842\pi$
$504$	10.5972	0.472039
$505$	39.8761	1.77446
$506$	−2.15298	−0.0957119
$507$	−26.4185	−1.17329
$508$	−8.38172	−0.371879
$509$	−17.5457	−0.777702	−0.388851	−	0.921301i	$-0.627128\pi$
$509$	−17.5457	−0.777702	−0.388851	+	0.921301i	$0.627128\pi$
$510$	−4.17118	−0.184703
$511$	5.97137	0.264158
$512$	−16.4417	−0.726627
$513$	0.353701	0.0156163
$514$	5.41256	0.238738
$515$	−8.09478	−0.356699
$516$	11.2427	0.494933
$517$	−11.7300	−0.515883
$518$	−2.15872	−0.0948487
$519$	−11.3443	−0.497961
$520$	−4.12062	−0.180701
$521$	32.1500	1.40851	0.704257	−	0.709945i	$-0.251280\pi$
$521$	32.1500	1.40851	0.704257	+	0.709945i	$0.251280\pi$
$522$	0.481389	0.0210698
$523$	−7.20277	−0.314955	−0.157478	−	0.987523i	$-0.550336\pi$
$523$	−7.20277	−0.314955	−0.157478	+	0.987523i	$0.550336\pi$
$524$	1.56373	0.0683120
$525$	4.16702	0.181864
$526$	−9.26157	−0.403824
$527$	9.86134	0.429567
$528$	3.33516	0.145144
$529$	−12.3750	−0.538043
$530$	9.60874	0.417377
$531$	−0.521878	−0.0226476
$532$	0.521875	0.0226262
$533$	−4.57483	−0.198158
$534$	−18.8735	−0.816735
$535$	−25.3626	−1.09652
$536$	4.66579	0.201531
$537$	−38.6731	−1.66887
$538$	3.48915	0.150428
$539$	2.04406	0.0880437
$540$	11.8504	0.509958
$541$	−3.85240	−0.165627	−0.0828137	−	0.996565i	$-0.526391\pi$
$541$	−3.85240	−0.165627	−0.0828137	+	0.996565i	$0.526391\pi$
$542$	−17.9341	−0.770335
$543$	16.2004	0.695225
$544$	−7.19731	−0.308582
$545$	−2.13271	−0.0913555
$546$	3.10132	0.132724
$547$	−2.52004	−0.107749	−0.0538746	−	0.998548i	$-0.517157\pi$
$547$	−2.52004	−0.107749	−0.0538746	+	0.998548i	$0.517157\pi$
$548$	−21.9789	−0.938894
$549$	−0.316899	−0.0135249
$550$	−0.431576	−0.0184025
$551$	0.0540272	0.00230164
$552$	16.2708	0.692531
$553$	16.2020	0.688979
$554$	9.25442	0.393182
$555$	5.47969	0.232600
$556$	−24.0402	−1.01953
$557$	−6.58445	−0.278992	−0.139496	−	0.990223i	$-0.544548\pi$
$557$	−6.58445	−0.278992	−0.139496	+	0.990223i	$0.544548\pi$
$558$	−7.78533	−0.329579
$559$	2.49616	0.105576
$560$	11.2458	0.475222
$561$	2.65600	0.112136
$562$	−18.6562	−0.786964
$563$	−27.3464	−1.15251	−0.576257	−	0.817269i	$-0.695487\pi$
$563$	−27.3464	−1.15251	−0.576257	+	0.817269i	$0.695487\pi$
$564$	38.8975	1.63788
$565$	−1.84560	−0.0776449
$566$	3.96636	0.166719
$567$	−33.8325	−1.42083
$568$	−15.7305	−0.660036
$569$	−16.4288	−0.688732	−0.344366	−	0.938835i	$-0.611906\pi$
$569$	−16.4288	−0.688732	−0.344366	+	0.938835i	$0.611906\pi$
$570$	0.369587	0.0154803
$571$	−15.7589	−0.659491	−0.329746	−	0.944070i	$-0.606963\pi$
$571$	−15.7589	−0.659491	−0.329746	+	0.944070i	$0.606963\pi$
$572$	1.15130	0.0481383
$573$	34.7589	1.45207
$574$	−12.3426	−0.515170
$575$	2.12984	0.0888203
$576$	0.973292	0.0405538
$577$	12.2614	0.510449	0.255224	−	0.966882i	$-0.417851\pi$
$577$	12.2614	0.510449	0.255224	+	0.966882i	$0.417851\pi$
$578$	10.1925	0.423951
$579$	24.8985	1.03475
$580$	1.81012	0.0751612
$581$	21.2791	0.882804
$582$	0.602165	0.0249605
$583$	−6.11837	−0.253397
$584$	4.67384	0.193405
$585$	−2.62066	−0.108351
$586$	−6.76130	−0.279307
$587$	−16.2780	−0.671864	−0.335932	−	0.941886i	$-0.609051\pi$
$587$	−16.2780	−0.671864	−0.335932	+	0.941886i	$0.609051\pi$
$588$	−6.77826	−0.279531
$589$	−0.873762	−0.0360027
$590$	0.547482	0.0225395
$591$	−40.4868	−1.66540
$592$	1.70920	0.0702476
$593$	27.1579	1.11524	0.557621	−	0.830096i	$-0.311714\pi$
$593$	27.1579	1.11524	0.557621	+	0.830096i	$0.311714\pi$
$594$	2.10518	0.0863767
$595$	8.95574	0.367150
$596$	18.1083	0.741743
$597$	3.63530	0.148783
$598$	1.58514	0.0648211
$599$	−19.8009	−0.809043	−0.404522	−	0.914528i	$-0.632562\pi$
$599$	−19.8009	−0.809043	−0.404522	+	0.914528i	$0.632562\pi$
$600$	3.26156	0.133153
$601$	−12.4979	−0.509798	−0.254899	−	0.966968i	$-0.582042\pi$
$601$	−12.4979	−0.509798	−0.254899	+	0.966968i	$0.582042\pi$
$602$	6.73447	0.274476
$603$	2.96739	0.120841
$604$	22.6558	0.921851
$605$	2.37769	0.0966668
$606$	−23.4908	−0.954247
$607$	34.7690	1.41123	0.705615	−	0.708595i	$-0.250671\pi$
$607$	34.7690	1.41123	0.705615	+	0.708595i	$0.250671\pi$
$608$	0.637716	0.0258628
$609$	−3.10481	−0.125813
$610$	0.332447	0.0134604
$611$	8.63620	0.349383
$612$	−2.93196	−0.118517
$613$	29.8041	1.20378	0.601889	−	0.798580i	$-0.294415\pi$
$613$	29.8041	1.20378	0.601889	+	0.798580i	$0.294415\pi$
$614$	0.737501	0.0297631
$615$	31.3305	1.26337
$616$	7.07885	0.285215
$617$	−7.40609	−0.298158	−0.149079	−	0.988825i	$-0.547631\pi$
$617$	−7.40609	−0.298158	−0.149079	+	0.988825i	$0.547631\pi$
$618$	4.76858	0.191820
$619$	4.24520	0.170629	0.0853146	−	0.996354i	$-0.472810\pi$
$619$	4.24520	0.170629	0.0853146	+	0.996354i	$0.472810\pi$
$620$	−29.2744	−1.17569
$621$	−10.3891	−0.416901
$622$	9.67609	0.387976
$623$	40.5224	1.62349
$624$	−2.45552	−0.0982993
$625$	−27.8401	−1.11360
$626$	18.5939	0.743160
$627$	−0.235334	−0.00939834
$628$	15.0840	0.601916
$629$	1.36114	0.0542723
$630$	−7.07038	−0.281691
$631$	22.3197	0.888532	0.444266	−	0.895895i	$-0.353464\pi$
$631$	22.3197	0.888532	0.444266	+	0.895895i	$0.353464\pi$
$632$	12.6814	0.504440
$633$	6.12231	0.243340
$634$	−6.05442	−0.240452
$635$	12.7446	0.505753
$636$	20.2890	0.804512
$637$	−1.50494	−0.0596279
$638$	0.321563	0.0127308
$639$	−10.0044	−0.395767
$640$	26.3058	1.03983
$641$	22.9791	0.907621	0.453810	−	0.891098i	$-0.350064\pi$
$641$	22.9791	0.907621	0.453810	+	0.891098i	$0.350064\pi$
$642$	14.9409	0.589672
$643$	−26.5893	−1.04858	−0.524290	−	0.851540i	$-0.675669\pi$
$643$	−26.5893	−1.04858	−0.524290	+	0.851540i	$0.675669\pi$
$644$	−15.3288	−0.604041
$645$	−17.0948	−0.673106
$646$	0.0918044	0.00361199
$647$	45.7871	1.80008	0.900038	−	0.435811i	$-0.143538\pi$
$647$	45.7871	1.80008	0.900038	+	0.435811i	$0.143538\pi$
$648$	−26.4809	−1.04027
$649$	−0.348609	−0.0136841
$650$	0.317749	0.0124631
$651$	50.2129	1.96800
$652$	20.8620	0.817020
$653$	14.7714	0.578049	0.289024	−	0.957322i	$-0.406669\pi$
$653$	14.7714	0.578049	0.289024	+	0.957322i	$0.406669\pi$
$654$	1.25637	0.0491279
$655$	−2.37769	−0.0929040
$656$	9.77243	0.381549
$657$	2.97250	0.115968
$658$	23.2999	0.908325
$659$	14.2556	0.555318	0.277659	−	0.960680i	$-0.410441\pi$
$659$	14.2556	0.555318	0.277659	+	0.960680i	$0.410441\pi$
$660$	−7.88461	−0.306908
$661$	−35.7596	−1.39089	−0.695444	−	0.718581i	$-0.744792\pi$
$661$	−35.7596	−1.39089	−0.695444	+	0.718581i	$0.744792\pi$
$662$	8.77310	0.340976
$663$	−1.95548	−0.0759447
$664$	16.6553	0.646350
$665$	−0.793522	−0.0307715
$666$	−1.07459	−0.0416397
$667$	−1.58692	−0.0614458
$668$	−16.6077	−0.642569
$669$	−13.1700	−0.509181
$670$	−3.11297	−0.120265
$671$	−0.211686	−0.00817204
$672$	−36.6479	−1.41372
$673$	−11.1401	−0.429420	−0.214710	−	0.976678i	$-0.568881\pi$
$673$	−11.1401	−0.429420	−0.214710	+	0.976678i	$0.568881\pi$
$674$	16.8699	0.649805
$675$	−2.08255	−0.0801573
$676$	19.4809	0.749265
$677$	−23.2402	−0.893195	−0.446598	−	0.894735i	$-0.647364\pi$
$677$	−23.2402	−0.893195	−0.446598	+	0.894735i	$0.647364\pi$
$678$	1.08723	0.0417548
$679$	−1.29288	−0.0496161
$680$	7.00973	0.268811
$681$	−20.6688	−0.792030
$682$	−5.20052	−0.199138
$683$	−8.54607	−0.327006	−0.163503	−	0.986543i	$-0.552279\pi$
$683$	−8.54607	−0.327006	−0.163503	+	0.986543i	$0.552279\pi$
$684$	0.259786	0.00993315
$685$	33.4194	1.27689
$686$	9.84428	0.375856
$687$	−14.4454	−0.551128
$688$	−5.33211	−0.203285
$689$	4.50466	0.171614
$690$	−10.8557	−0.413270
$691$	−7.59211	−0.288818	−0.144409	−	0.989518i	$-0.546128\pi$
$691$	−7.59211	−0.288818	−0.144409	+	0.989518i	$0.546128\pi$
$692$	8.36525	0.317999
$693$	4.50206	0.171019
$694$	−9.82675	−0.373019
$695$	36.5537	1.38656
$696$	−2.43016	−0.0921149
$697$	7.78241	0.294780
$698$	14.7384	0.557857
$699$	46.6715	1.76528
$700$	−3.07274	−0.116139
$701$	−21.5310	−0.813216	−0.406608	−	0.913603i	$-0.633288\pi$
$701$	−21.5310	−0.813216	−0.406608	+	0.913603i	$0.633288\pi$
$702$	−1.54994	−0.0584989
$703$	−0.120604	−0.00454866
$704$	0.650149	0.0245034
$705$	−59.1445	−2.22751
$706$	10.6652	0.401391
$707$	50.4359	1.89684
$708$	1.15602	0.0434458
$709$	11.7163	0.440015	0.220007	−	0.975498i	$-0.429392\pi$
$709$	11.7163	0.440015	0.220007	+	0.975498i	$0.429392\pi$
$710$	10.4952	0.393878
$711$	8.06523	0.302470
$712$	31.7172	1.18865
$713$	25.6647	0.961150
$714$	−5.27577	−0.197441
$715$	−1.75058	−0.0654679
$716$	28.5173	1.06574
$717$	−55.6291	−2.07751
$718$	4.73909	0.176861
$719$	28.0538	1.04623	0.523115	−	0.852262i	$-0.324770\pi$
$719$	28.0538	1.04623	0.523115	+	0.852262i	$0.324770\pi$
$720$	5.59807	0.208628
$721$	−10.2384	−0.381298
$722$	12.5415	0.466745
$723$	2.38167	0.0885754
$724$	−11.9461	−0.443972
$725$	−0.318106	−0.0118142
$726$	−1.40068	−0.0519841
$727$	30.0192	1.11335	0.556674	−	0.830731i	$-0.312077\pi$
$727$	30.0192	1.11335	0.556674	+	0.830731i	$0.312077\pi$
$728$	−5.21182	−0.193163
$729$	3.43516	0.127228
$730$	−3.11834	−0.115415
$731$	−4.24630	−0.157055
$732$	0.701967	0.0259455
$733$	31.3940	1.15956	0.579782	−	0.814772i	$-0.303138\pi$
$733$	31.3940	1.15956	0.579782	+	0.814772i	$0.303138\pi$
$734$	9.85446	0.363735
$735$	10.3065	0.380161
$736$	−18.7314	−0.690448
$737$	1.98218	0.0730147
$738$	−6.14406	−0.226166
$739$	13.0271	0.479209	0.239604	−	0.970871i	$-0.422982\pi$
$739$	13.0271	0.479209	0.239604	+	0.970871i	$0.422982\pi$
$740$	−4.04070	−0.148539
$741$	0.173265	0.00636506
$742$	12.1533	0.446161
$743$	5.70462	0.209282	0.104641	−	0.994510i	$-0.466631\pi$
$743$	5.70462	0.209282	0.104641	+	0.994510i	$0.466631\pi$
$744$	39.3020	1.44088
$745$	−27.5340	−1.00877
$746$	0.270107	0.00988934
$747$	10.5926	0.387561
$748$	−1.95852	−0.0716105
$749$	−32.0790	−1.17214
$750$	14.4758	0.528582
$751$	2.14802	0.0783823	0.0391912	−	0.999232i	$-0.487522\pi$
$751$	2.14802	0.0783823	0.0391912	+	0.999232i	$0.487522\pi$
$752$	−18.4480	−0.672730
$753$	−38.4069	−1.39963
$754$	−0.236751	−0.00862198
$755$	−34.4486	−1.25371
$756$	14.9885	0.545126
$757$	27.0639	0.983653	0.491826	−	0.870693i	$-0.336330\pi$
$757$	27.0639	0.983653	0.491826	+	0.870693i	$0.336330\pi$
$758$	9.63437	0.349936
$759$	6.91238	0.250904
$760$	−0.621096	−0.0225295
$761$	35.3954	1.28308	0.641541	−	0.767089i	$-0.278295\pi$
$761$	35.3954	1.28308	0.641541	+	0.767089i	$0.278295\pi$
$762$	−7.50774	−0.271977
$763$	−2.69749	−0.0976556
$764$	−25.6310	−0.927296
$765$	4.45810	0.161183
$766$	17.5606	0.634492
$767$	0.256664	0.00926760
$768$	−18.2540	−0.658685
$769$	−28.3511	−1.02237	−0.511184	−	0.859471i	$-0.670793\pi$
$769$	−28.3511	−1.02237	−0.511184	+	0.859471i	$0.670793\pi$
$770$	−4.72294	−0.170203
$771$	−17.3776	−0.625838
$772$	−18.3600	−0.660791
$773$	6.43894	0.231592	0.115796	−	0.993273i	$-0.463058\pi$
$773$	6.43894	0.231592	0.115796	+	0.993273i	$0.463058\pi$
$774$	3.35237	0.120498
$775$	5.14461	0.184800
$776$	−1.01195	−0.0363268
$777$	6.93079	0.248641
$778$	0.529229	0.0189738
$779$	−0.689559	−0.0247060
$780$	5.80506	0.207855
$781$	−6.68283	−0.239130
$782$	−2.69653	−0.0964279
$783$	1.55169	0.0554527
$784$	3.21474	0.114812
$785$	−22.9355	−0.818603
$786$	1.40068	0.0499606
$787$	4.24103	0.151176	0.0755882	−	0.997139i	$-0.475917\pi$
$787$	4.24103	0.151176	0.0755882	+	0.997139i	$0.475917\pi$
$788$	29.8547	1.06353
$789$	29.7352	1.05860
$790$	−8.46092	−0.301026
$791$	−2.33434	−0.0829995
$792$	3.52380	0.125213
$793$	0.155854	0.00553454
$794$	14.2095	0.504276
$795$	−30.8499	−1.09413
$796$	−2.68065	−0.0950130
$797$	19.2696	0.682563	0.341281	−	0.939961i	$-0.389139\pi$
$797$	19.2696	0.682563	0.341281	+	0.939961i	$0.389139\pi$
$798$	0.467458	0.0165478
$799$	−14.6913	−0.519742
$800$	−3.75480	−0.132752
$801$	20.1717	0.712733
$802$	9.24857	0.326578
$803$	1.98560	0.0700704
$804$	−6.57309	−0.231815
$805$	23.3078	0.821492
$806$	3.82889	0.134867
$807$	−11.2023	−0.394339
$808$	39.4766	1.38878
$809$	−1.99901	−0.0702815	−0.0351407	−	0.999382i	$-0.511188\pi$
$809$	−1.99901	−0.0702815	−0.0351407	+	0.999382i	$0.511188\pi$
$810$	17.6678	0.620784
$811$	34.4402	1.20936	0.604680	−	0.796468i	$-0.293301\pi$
$811$	34.4402	1.20936	0.604680	+	0.796468i	$0.293301\pi$
$812$	2.28947	0.0803446
$813$	57.5792	2.01939
$814$	−0.717818	−0.0251595
$815$	−31.7211	−1.11114
$816$	4.17716	0.146230
$817$	0.376243	0.0131631
$818$	16.4908	0.576586
$819$	−3.31465	−0.115823
$820$	−23.1029	−0.806789
$821$	30.7219	1.07220	0.536101	−	0.844154i	$-0.319897\pi$
$821$	30.7219	1.07220	0.536101	+	0.844154i	$0.319897\pi$
$822$	−19.6872	−0.686669
$823$	−3.52505	−0.122875	−0.0614377	−	0.998111i	$-0.519569\pi$
$823$	−3.52505	−0.122875	−0.0614377	+	0.998111i	$0.519569\pi$
$824$	−8.01367	−0.279169
$825$	1.38562	0.0482411
$826$	0.692463	0.0240939
$827$	−7.10614	−0.247105	−0.123552	−	0.992338i	$-0.539429\pi$
$827$	−7.10614	−0.247105	−0.123552	+	0.992338i	$0.539429\pi$
$828$	−7.63058	−0.265181
$829$	26.7739	0.929896	0.464948	−	0.885338i	$-0.346073\pi$
$829$	26.7739	0.929896	0.464948	+	0.885338i	$0.346073\pi$
$830$	−11.1122	−0.385712
$831$	−29.7123	−1.03071
$832$	−0.478674	−0.0165950
$833$	2.56011	0.0887024
$834$	−21.5335	−0.745645
$835$	25.2523	0.873891
$836$	0.173534	0.00600180
$837$	−25.0948	−0.867405
$838$	−10.0303	−0.346493
$839$	39.7215	1.37134	0.685669	−	0.727914i	$-0.259510\pi$
$839$	39.7215	1.37134	0.685669	+	0.727914i	$0.259510\pi$
$840$	35.6928	1.23152
$841$	−28.7630	−0.991827
$842$	18.6147	0.641504
$843$	59.8976	2.06298
$844$	−4.51456	−0.155398
$845$	−29.6211	−1.01900
$846$	11.5985	0.398765
$847$	3.00733	0.103333
$848$	−9.62253	−0.330439
$849$	−12.7344	−0.437044
$850$	−0.540533	−0.0185401
$851$	3.54245	0.121434
$852$	22.1608	0.759217
$853$	−10.8371	−0.371055	−0.185528	−	0.982639i	$-0.559399\pi$
$853$	−10.8371	−0.371055	−0.185528	+	0.982639i	$0.559399\pi$
$854$	0.420484	0.0143887
$855$	−0.395009	−0.0135090
$856$	−25.1085	−0.858190
$857$	26.5036	0.905344	0.452672	−	0.891677i	$-0.350471\pi$
$857$	26.5036	0.905344	0.452672	+	0.891677i	$0.350471\pi$
$858$	1.03125	0.0352064
$859$	54.5171	1.86010	0.930049	−	0.367435i	$-0.119764\pi$
$859$	54.5171	1.86010	0.930049	+	0.367435i	$0.119764\pi$
$860$	12.6056	0.429847
$861$	39.6272	1.35049
$862$	8.21160	0.279688
$863$	−4.08743	−0.139138	−0.0695688	−	0.997577i	$-0.522162\pi$
$863$	−4.08743	−0.139138	−0.0695688	+	0.997577i	$0.522162\pi$
$864$	18.3155	0.623106
$865$	−12.7195	−0.432477
$866$	−7.47002	−0.253841
$867$	−32.7240	−1.11137
$868$	−37.0267	−1.25677
$869$	5.38749	0.182758
$870$	1.62138	0.0549698
$871$	−1.45939	−0.0494494
$872$	−2.11134	−0.0714991
$873$	−0.643586	−0.0217821
$874$	0.238926	0.00808179
$875$	−31.0804	−1.05071
$876$	−6.58443	−0.222467
$877$	21.3329	0.720360	0.360180	−	0.932883i	$-0.382715\pi$
$877$	21.3329	0.720360	0.360180	+	0.932883i	$0.382715\pi$
$878$	0.950212	0.0320681
$879$	21.7079	0.732188
$880$	3.73946	0.126057
$881$	21.0694	0.709846	0.354923	−	0.934896i	$-0.384507\pi$
$881$	21.0694	0.709846	0.354923	+	0.934896i	$0.384507\pi$
$882$	−2.02115	−0.0680557
$883$	−2.32643	−0.0782907	−0.0391453	−	0.999234i	$-0.512464\pi$
$883$	−2.32643	−0.0782907	−0.0391453	+	0.999234i	$0.512464\pi$
$884$	1.44196	0.0484984
$885$	−1.75775	−0.0590860
$886$	−15.1557	−0.509164
$887$	−31.9942	−1.07426	−0.537131	−	0.843499i	$-0.680492\pi$
$887$	−31.9942	−1.07426	−0.537131	+	0.843499i	$0.680492\pi$
$888$	5.42479	0.182044
$889$	16.1195	0.540632
$890$	−21.1614	−0.709331
$891$	−11.2500	−0.376889
$892$	9.71147	0.325164
$893$	1.30172	0.0435605
$894$	16.2201	0.542480
$895$	−43.3612	−1.44940
$896$	33.2720	1.11154
$897$	−5.08925	−0.169925
$898$	−21.0687	−0.703073
$899$	−3.83320	−0.127844
$900$	−1.52959	−0.0509862
$901$	−7.66303	−0.255293
$902$	−4.10417	−0.136654
$903$	−21.6217	−0.719525
$904$	−1.82710	−0.0607686
$905$	18.1642	0.603800
$906$	20.2934	0.674204
$907$	−12.0985	−0.401725	−0.200863	−	0.979619i	$-0.564374\pi$
$907$	−12.0985	−0.401725	−0.200863	+	0.979619i	$0.564374\pi$
$908$	15.2411	0.505792
$909$	25.1066	0.832734
$910$	3.47727	0.115271
$911$	−2.35994	−0.0781884	−0.0390942	−	0.999236i	$-0.512447\pi$
$911$	−2.35994	−0.0781884	−0.0390942	+	0.999236i	$0.512447\pi$
$912$	−0.370117	−0.0122558
$913$	7.07572	0.234172
$914$	−0.347690	−0.0115005
$915$	−1.06736	−0.0352857
$916$	10.6520	0.351951
$917$	−3.00733	−0.0993109
$918$	2.63666	0.0870228
$919$	40.8290	1.34682	0.673412	−	0.739268i	$-0.264828\pi$
$919$	40.8290	1.34682	0.673412	+	0.739268i	$0.264828\pi$
$920$	18.2432	0.601461
$921$	−2.36782	−0.0780224
$922$	−15.9366	−0.524843
$923$	4.92024	0.161952
$924$	−9.97257	−0.328073
$925$	0.710100	0.0233480
$926$	−9.42006	−0.309562
$927$	−5.09660	−0.167394
$928$	2.79766	0.0918378
$929$	32.3748	1.06218	0.531091	−	0.847315i	$-0.321782\pi$
$929$	32.3748	1.06218	0.531091	+	0.847315i	$0.321782\pi$
$930$	−26.2219	−0.859851
$931$	−0.226838	−0.00743430
$932$	−34.4153	−1.12731
$933$	−31.0661	−1.01706
$934$	−18.7699	−0.614170
$935$	2.97797	0.0973900
$936$	−2.59440	−0.0848007
$937$	−41.4569	−1.35434	−0.677169	−	0.735827i	$-0.736793\pi$
$937$	−41.4569	−1.35434	−0.677169	+	0.735827i	$0.736793\pi$
$938$	−3.93733	−0.128558
$939$	−59.6975	−1.94815
$940$	43.6128	1.42249
$941$	0.0998449	0.00325485	0.00162743	−	0.999999i	$-0.499482\pi$
$941$	0.0998449	0.00325485	0.00162743	+	0.999999i	$0.499482\pi$
$942$	13.5111	0.440217
$943$	20.2541	0.659566
$944$	−0.548267	−0.0178446
$945$	−22.7903	−0.741369
$946$	2.23935	0.0728075
$947$	−20.5172	−0.666721	−0.333361	−	0.942799i	$-0.608183\pi$
$947$	−20.5172	−0.666721	−0.333361	+	0.942799i	$0.608183\pi$
$948$	−17.8654	−0.580240
$949$	−1.46190	−0.0474554
$950$	0.0478938	0.00155388
$951$	19.4383	0.630331
$952$	8.86600	0.287349
$953$	19.0768	0.617958	0.308979	−	0.951069i	$-0.400013\pi$
$953$	19.0768	0.617958	0.308979	+	0.951069i	$0.400013\pi$
$954$	6.04981	0.195870
$955$	38.9724	1.26112
$956$	41.0206	1.32670
$957$	−1.03241	−0.0333731
$958$	−12.1636	−0.392987
$959$	42.2694	1.36495
$960$	3.27817	0.105802
$961$	30.9929	0.999770
$962$	0.528495	0.0170394
$963$	−15.9687	−0.514583
$964$	−1.75623	−0.0565644
$965$	27.9168	0.898672
$966$	−13.7305	−0.441771
$967$	−32.9995	−1.06119	−0.530596	−	0.847625i	$-0.678032\pi$
$967$	−32.9995	−1.06119	−0.530596	+	0.847625i	$0.678032\pi$
$968$	2.35386	0.0756560
$969$	−0.294747	−0.00946865
$970$	0.675161	0.0216781
$971$	19.4216	0.623267	0.311634	−	0.950202i	$-0.399124\pi$
$971$	19.4216	0.623267	0.311634	+	0.950202i	$0.399124\pi$
$972$	22.3540	0.717004
$973$	46.2336	1.48218
$974$	15.9603	0.511401
$975$	−1.02016	−0.0326714
$976$	−0.332924	−0.0106566
$977$	−30.9258	−0.989404	−0.494702	−	0.869063i	$-0.664723\pi$
$977$	−30.9258	−0.989404	−0.494702	+	0.869063i	$0.664723\pi$
$978$	18.6867	0.597535
$979$	13.4745	0.430647
$980$	−7.59995	−0.242771
$981$	−1.34279	−0.0428720
$982$	−23.9834	−0.765342
$983$	36.0180	1.14880	0.574399	−	0.818576i	$-0.305236\pi$
$983$	36.0180	1.14880	0.574399	+	0.818576i	$0.305236\pi$
$984$	31.0165	0.988771
$985$	−45.3948	−1.44640
$986$	0.402746	0.0128260
$987$	−74.8067	−2.38112
$988$	−0.127765	−0.00406474
$989$	−11.0512	−0.351409
$990$	−2.35105	−0.0747211
$991$	31.4209	0.998119	0.499059	−	0.866568i	$-0.333679\pi$
$991$	31.4209	0.998119	0.499059	+	0.866568i	$0.333679\pi$
$992$	−45.2456	−1.43655
$993$	−28.1669	−0.893851
$994$	13.2745	0.421041
$995$	4.07598	0.129217
$996$	−23.4637	−0.743475
$997$	−6.70348	−0.212301	−0.106151	−	0.994350i	$-0.533853\pi$
$997$	−6.70348	−0.212301	−0.106151	+	0.994350i	$0.533853\pi$
$998$	11.7046	0.370502
$999$	−3.46379	−0.109590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.10	✓	28	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-0.660505 q^{2} +2.12062 q^{3} -1.56373 q^{4} +2.37769 q^{5} -1.40068 q^{6} +3.00733 q^{7} +2.35386 q^{8} +1.49703 q^{9} +O(q^{10})\)	\(q-0.660505 q^{2} +2.12062 q^{3} -1.56373 q^{4} +2.37769 q^{5} -1.40068 q^{6} +3.00733 q^{7} +2.35386 q^{8} +1.49703 q^{9} -1.57048 q^{10} +1.00000 q^{11} -3.31608 q^{12} -0.736252 q^{13} -1.98636 q^{14} +5.04217 q^{15} +1.57273 q^{16} +1.25246 q^{17} -0.988795 q^{18} -0.110974 q^{19} -3.71807 q^{20} +6.37741 q^{21} -0.660505 q^{22} +3.25960 q^{23} +4.99165 q^{24} +0.653403 q^{25} +0.486298 q^{26} -3.18723 q^{27} -4.70267 q^{28} -0.486844 q^{29} -3.33038 q^{30} +7.87356 q^{31} -5.74652 q^{32} +2.12062 q^{33} -0.827258 q^{34} +7.15050 q^{35} -2.34095 q^{36} +1.08677 q^{37} +0.0732991 q^{38} -1.56131 q^{39} +5.59675 q^{40} +6.21368 q^{41} -4.21231 q^{42} -3.39036 q^{43} -1.56373 q^{44} +3.55947 q^{45} -2.15298 q^{46} -11.7300 q^{47} +3.33516 q^{48} +2.04406 q^{49} -0.431576 q^{50} +2.65600 q^{51} +1.15130 q^{52} -6.11837 q^{53} +2.10518 q^{54} +2.37769 q^{55} +7.07885 q^{56} -0.235334 q^{57} +0.321563 q^{58} -0.348609 q^{59} -7.88461 q^{60} -0.211686 q^{61} -5.20052 q^{62} +4.50206 q^{63} +0.650149 q^{64} -1.75058 q^{65} -1.40068 q^{66} +1.98218 q^{67} -1.95852 q^{68} +6.91238 q^{69} -4.72294 q^{70} -6.68283 q^{71} +3.52380 q^{72} +1.98560 q^{73} -0.717818 q^{74} +1.38562 q^{75} +0.173534 q^{76} +3.00733 q^{77} +1.03125 q^{78} +5.38749 q^{79} +3.73946 q^{80} -11.2500 q^{81} -4.10417 q^{82} +7.07572 q^{83} -9.97257 q^{84} +2.97797 q^{85} +2.23935 q^{86} -1.03241 q^{87} +2.35386 q^{88} +13.4745 q^{89} -2.35105 q^{90} -2.21415 q^{91} -5.09715 q^{92} +16.6968 q^{93} +7.74769 q^{94} -0.263862 q^{95} -12.1862 q^{96} -0.429909 q^{97} -1.35011 q^{98} +1.49703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * q^99

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