LMFDB - Embedded newform 8007.2.a.j.1.46

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.46
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.59893 q^{2} -1.00000 q^{3} +0.556583 q^{4} +1.72494 q^{5} -1.59893 q^{6} -4.76527 q^{7} -2.30793 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.59893 q^{2} -1.00000 q^{3} +0.556583 q^{4} +1.72494 q^{5} -1.59893 q^{6} -4.76527 q^{7} -2.30793 q^{8} +1.00000 q^{9} +2.75807 q^{10} +5.76936 q^{11} -0.556583 q^{12} +6.38564 q^{13} -7.61934 q^{14} -1.72494 q^{15} -4.80338 q^{16} +1.00000 q^{17} +1.59893 q^{18} +6.07869 q^{19} +0.960074 q^{20} +4.76527 q^{21} +9.22481 q^{22} -1.53381 q^{23} +2.30793 q^{24} -2.02457 q^{25} +10.2102 q^{26} -1.00000 q^{27} -2.65227 q^{28} -6.74095 q^{29} -2.75807 q^{30} -0.347935 q^{31} -3.06443 q^{32} -5.76936 q^{33} +1.59893 q^{34} -8.21982 q^{35} +0.556583 q^{36} -6.53838 q^{37} +9.71942 q^{38} -6.38564 q^{39} -3.98104 q^{40} -2.27178 q^{41} +7.61934 q^{42} +9.57338 q^{43} +3.21113 q^{44} +1.72494 q^{45} -2.45246 q^{46} +4.94114 q^{47} +4.80338 q^{48} +15.7078 q^{49} -3.23715 q^{50} -1.00000 q^{51} +3.55414 q^{52} -8.79270 q^{53} -1.59893 q^{54} +9.95181 q^{55} +10.9979 q^{56} -6.07869 q^{57} -10.7783 q^{58} -10.2872 q^{59} -0.960074 q^{60} -3.48211 q^{61} -0.556325 q^{62} -4.76527 q^{63} +4.70695 q^{64} +11.0149 q^{65} -9.22481 q^{66} +10.2914 q^{67} +0.556583 q^{68} +1.53381 q^{69} -13.1429 q^{70} +5.97617 q^{71} -2.30793 q^{72} +11.4678 q^{73} -10.4544 q^{74} +2.02457 q^{75} +3.38330 q^{76} -27.4925 q^{77} -10.2102 q^{78} -13.9093 q^{79} -8.28556 q^{80} +1.00000 q^{81} -3.63243 q^{82} -5.71699 q^{83} +2.65227 q^{84} +1.72494 q^{85} +15.3072 q^{86} +6.74095 q^{87} -13.3152 q^{88} +15.5942 q^{89} +2.75807 q^{90} -30.4293 q^{91} -0.853695 q^{92} +0.347935 q^{93} +7.90054 q^{94} +10.4854 q^{95} +3.06443 q^{96} +19.2786 q^{97} +25.1157 q^{98} +5.76936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	1.59893	1.13062	0.565308	−	0.824880i	$-0.308757\pi$
$2$	1.59893	1.13062	0.565308	+	0.824880i	$0.308757\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.556583	0.278292
$5$	1.72494	0.771418	0.385709	−	0.922620i	$-0.373957\pi$
$5$	1.72494	0.771418	0.385709	+	0.922620i	$0.373957\pi$
$6$	−1.59893	−0.652761
$7$	−4.76527	−1.80110	−0.900551	−	0.434751i	$-0.856837\pi$
$7$	−4.76527	−1.80110	−0.900551	+	0.434751i	$0.856837\pi$
$8$	−2.30793	−0.815975
$9$	1.00000	0.333333
$10$	2.75807	0.872177
$11$	5.76936	1.73953	0.869763	−	0.493469i	$-0.164271\pi$
$11$	5.76936	1.73953	0.869763	+	0.493469i	$0.164271\pi$
$12$	−0.556583	−0.160672
$13$	6.38564	1.77106	0.885529	−	0.464584i	$-0.153796\pi$
$13$	6.38564	1.77106	0.885529	+	0.464584i	$0.153796\pi$
$14$	−7.61934	−2.03635
$15$	−1.72494	−0.445378
$16$	−4.80338	−1.20085
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.59893	0.376872
$19$	6.07869	1.39455	0.697274	−	0.716805i	$-0.254396\pi$
$19$	6.07869	1.39455	0.697274	+	0.716805i	$0.254396\pi$
$20$	0.960074	0.214679
$21$	4.76527	1.03987
$22$	9.22481	1.96674
$23$	−1.53381	−0.319822	−0.159911	−	0.987131i	$-0.551121\pi$
$23$	−1.53381	−0.319822	−0.159911	+	0.987131i	$0.551121\pi$
$24$	2.30793	0.471103
$25$	−2.02457	−0.404914
$26$	10.2102	2.00239
$27$	−1.00000	−0.192450
$28$	−2.65227	−0.501231
$29$	−6.74095	−1.25176	−0.625881	−	0.779918i	$-0.715261\pi$
$29$	−6.74095	−1.25176	−0.625881	+	0.779918i	$0.715261\pi$
$30$	−2.75807	−0.503552
$31$	−0.347935	−0.0624910	−0.0312455	−	0.999512i	$-0.509947\pi$
$31$	−0.347935	−0.0624910	−0.0312455	+	0.999512i	$0.509947\pi$
$32$	−3.06443	−0.541720
$33$	−5.76936	−1.00432
$34$	1.59893	0.274215
$35$	−8.21982	−1.38940
$36$	0.556583	0.0927638
$37$	−6.53838	−1.07490	−0.537452	−	0.843295i	$-0.680613\pi$
$37$	−6.53838	−1.07490	−0.537452	+	0.843295i	$0.680613\pi$
$38$	9.71942	1.57670
$39$	−6.38564	−1.02252
$40$	−3.98104	−0.629458
$41$	−2.27178	−0.354793	−0.177396	−	0.984139i	$-0.556767\pi$
$41$	−2.27178	−0.354793	−0.177396	+	0.984139i	$0.556767\pi$
$42$	7.61934	1.17569
$43$	9.57338	1.45993	0.729964	−	0.683486i	$-0.239537\pi$
$43$	9.57338	1.45993	0.729964	+	0.683486i	$0.239537\pi$
$44$	3.21113	0.484095
$45$	1.72494	0.257139
$46$	−2.45246	−0.361596
$47$	4.94114	0.720739	0.360369	−	0.932810i	$-0.382651\pi$
$47$	4.94114	0.720739	0.360369	+	0.932810i	$0.382651\pi$
$48$	4.80338	0.693308
$49$	15.7078	2.24397
$50$	−3.23715	−0.457802
$51$	−1.00000	−0.140028
$52$	3.55414	0.492870
$53$	−8.79270	−1.20777	−0.603885	−	0.797071i	$-0.706382\pi$
$53$	−8.79270	−1.20777	−0.603885	+	0.797071i	$0.706382\pi$
$54$	−1.59893	−0.217587
$55$	9.95181	1.34190
$56$	10.9979	1.46965
$57$	−6.07869	−0.805143
$58$	−10.7783	−1.41526
$59$	−10.2872	−1.33928	−0.669638	−	0.742687i	$-0.733551\pi$
$59$	−10.2872	−1.33928	−0.669638	+	0.742687i	$0.733551\pi$
$60$	−0.960074	−0.123945
$61$	−3.48211	−0.445839	−0.222920	−	0.974837i	$-0.571559\pi$
$61$	−3.48211	−0.445839	−0.222920	+	0.974837i	$0.571559\pi$
$62$	−0.556325	−0.0706533
$63$	−4.76527	−0.600367
$64$	4.70695	0.588369
$65$	11.0149	1.36623
$66$	−9.22481	−1.13550
$67$	10.2914	1.25730	0.628649	−	0.777689i	$-0.283608\pi$
$67$	10.2914	1.25730	0.628649	+	0.777689i	$0.283608\pi$
$68$	0.556583	0.0674956
$69$	1.53381	0.184649
$70$	−13.1429	−1.57088
$71$	5.97617	0.709241	0.354620	−	0.935010i	$-0.384610\pi$
$71$	5.97617	0.709241	0.354620	+	0.935010i	$0.384610\pi$
$72$	−2.30793	−0.271992
$73$	11.4678	1.34221	0.671104	−	0.741363i	$-0.265820\pi$
$73$	11.4678	1.34221	0.671104	+	0.741363i	$0.265820\pi$
$74$	−10.4544	−1.21530
$75$	2.02457	0.233777
$76$	3.38330	0.388091
$77$	−27.4925	−3.13306
$78$	−10.2102	−1.15608
$79$	−13.9093	−1.56492	−0.782461	−	0.622699i	$-0.786036\pi$
$79$	−13.9093	−1.56492	−0.782461	+	0.622699i	$0.786036\pi$
$80$	−8.28556	−0.926354
$81$	1.00000	0.111111
$82$	−3.63243	−0.401134
$83$	−5.71699	−0.627522	−0.313761	−	0.949502i	$-0.601589\pi$
$83$	−5.71699	−0.627522	−0.313761	+	0.949502i	$0.601589\pi$
$84$	2.65227	0.289386
$85$	1.72494	0.187096
$86$	15.3072	1.65062
$87$	6.74095	0.722705
$88$	−13.3152	−1.41941
$89$	15.5942	1.65299	0.826493	−	0.562946i	$-0.190332\pi$
$89$	15.5942	1.65299	0.826493	+	0.562946i	$0.190332\pi$
$90$	2.75807	0.290726
$91$	−30.4293	−3.18986
$92$	−0.853695	−0.0890038
$93$	0.347935	0.0360792
$94$	7.90054	0.814878
$95$	10.4854	1.07578
$96$	3.06443	0.312762
$97$	19.2786	1.95744	0.978721	−	0.205194i	$-0.0657824\pi$
$97$	19.2786	1.95744	0.978721	+	0.205194i	$0.0657824\pi$
$98$	25.1157	2.53706
$99$	5.76936	0.579842
$100$	−1.12684	−0.112684
$101$	15.7986	1.57202	0.786009	−	0.618216i	$-0.212144\pi$
$101$	15.7986	1.57202	0.786009	+	0.618216i	$0.212144\pi$
$102$	−1.59893	−0.158318
$103$	11.0207	1.08590	0.542949	−	0.839766i	$-0.317308\pi$
$103$	11.0207	1.08590	0.542949	+	0.839766i	$0.317308\pi$
$104$	−14.7376	−1.44514
$105$	8.21982	0.802172
$106$	−14.0589	−1.36552
$107$	−17.6687	−1.70810	−0.854049	−	0.520193i	$-0.825860\pi$
$107$	−17.6687	−1.70810	−0.854049	+	0.520193i	$0.825860\pi$
$108$	−0.556583	−0.0535572
$109$	4.24719	0.406807	0.203403	−	0.979095i	$-0.434800\pi$
$109$	4.24719	0.406807	0.203403	+	0.979095i	$0.434800\pi$
$110$	15.9123	1.51718
$111$	6.53838	0.620596
$112$	22.8894	2.16284
$113$	13.7300	1.29161	0.645807	−	0.763501i	$-0.276521\pi$
$113$	13.7300	1.29161	0.645807	+	0.763501i	$0.276521\pi$
$114$	−9.71942	−0.910307
$115$	−2.64574	−0.246717
$116$	−3.75190	−0.348355
$117$	6.38564	0.590353
$118$	−16.4485	−1.51421
$119$	−4.76527	−0.436831
$120$	3.98104	0.363418
$121$	22.2855	2.02595
$122$	−5.56766	−0.504073
$123$	2.27178	0.204840
$124$	−0.193655	−0.0173907
$125$	−12.1170	−1.08378
$126$	−7.61934	−0.678785
$127$	−6.16875	−0.547388	−0.273694	−	0.961817i	$-0.588246\pi$
$127$	−6.16875	−0.547388	−0.273694	+	0.961817i	$0.588246\pi$
$128$	13.6549	1.20694
$129$	−9.57338	−0.842890
$130$	17.6120	1.54468
$131$	−13.8311	−1.20843	−0.604216	−	0.796820i	$-0.706514\pi$
$131$	−13.8311	−1.20843	−0.604216	+	0.796820i	$0.706514\pi$
$132$	−3.21113	−0.279493
$133$	−28.9666	−2.51172
$134$	16.4553	1.42152
$135$	−1.72494	−0.148459
$136$	−2.30793	−0.197903
$137$	7.06963	0.603999	0.301999	−	0.953308i	$-0.402346\pi$
$137$	7.06963	0.603999	0.301999	+	0.953308i	$0.402346\pi$
$138$	2.45246	0.208768
$139$	−4.23660	−0.359343	−0.179672	−	0.983727i	$-0.557504\pi$
$139$	−4.23660	−0.359343	−0.179672	+	0.983727i	$0.557504\pi$
$140$	−4.57501	−0.386659
$141$	−4.94114	−0.416119
$142$	9.55549	0.801879
$143$	36.8410	3.08080
$144$	−4.80338	−0.400282
$145$	−11.6277	−0.965632
$146$	18.3363	1.51752
$147$	−15.7078	−1.29556
$148$	−3.63915	−0.299136
$149$	−7.88032	−0.645581	−0.322791	−	0.946470i	$-0.604621\pi$
$149$	−7.88032	−0.645581	−0.322791	+	0.946470i	$0.604621\pi$
$150$	3.23715	0.264312
$151$	−4.63870	−0.377492	−0.188746	−	0.982026i	$-0.560442\pi$
$151$	−4.63870	−0.377492	−0.188746	+	0.982026i	$0.560442\pi$
$152$	−14.0292	−1.13792
$153$	1.00000	0.0808452
$154$	−43.9587	−3.54229
$155$	−0.600169	−0.0482067
$156$	−3.55414	−0.284559
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−22.2401	−1.76933
$159$	8.79270	0.697307
$160$	−5.28597	−0.417892
$161$	7.30903	0.576033
$162$	1.59893	0.125624
$163$	17.9435	1.40545	0.702723	−	0.711464i	$-0.251968\pi$
$163$	17.9435	1.40545	0.702723	+	0.711464i	$0.251968\pi$
$164$	−1.26444	−0.0987359
$165$	−9.95181	−0.774748
$166$	−9.14108	−0.709486
$167$	6.73608	0.521254	0.260627	−	0.965440i	$-0.416071\pi$
$167$	6.73608	0.521254	0.260627	+	0.965440i	$0.416071\pi$
$168$	−10.9979	−0.848505
$169$	27.7764	2.13665
$170$	2.75807	0.211534
$171$	6.07869	0.464849
$172$	5.32838	0.406285
$173$	3.36376	0.255742	0.127871	−	0.991791i	$-0.459186\pi$
$173$	3.36376	0.255742	0.127871	+	0.991791i	$0.459186\pi$
$174$	10.7783	0.817102
$175$	9.64762	0.729292
$176$	−27.7124	−2.08890
$177$	10.2872	0.773232
$178$	24.9341	1.86889
$179$	−7.18405	−0.536961	−0.268481	−	0.963285i	$-0.586522\pi$
$179$	−7.18405	−0.536961	−0.268481	+	0.963285i	$0.586522\pi$
$180$	0.960074	0.0715597
$181$	5.94249	0.441702	0.220851	−	0.975308i	$-0.429117\pi$
$181$	5.94249	0.441702	0.220851	+	0.975308i	$0.429117\pi$
$182$	−48.6543	−3.60650
$183$	3.48211	0.257405
$184$	3.53993	0.260967
$185$	−11.2783	−0.829200
$186$	0.556325	0.0407917
$187$	5.76936	0.421897
$188$	2.75015	0.200575
$189$	4.76527	0.346622
$190$	16.7654	1.21629
$191$	16.1012	1.16504	0.582521	−	0.812815i	$-0.302066\pi$
$191$	16.1012	1.16504	0.582521	+	0.812815i	$0.302066\pi$
$192$	−4.70695	−0.339695
$193$	−14.4383	−1.03929	−0.519647	−	0.854381i	$-0.673937\pi$
$193$	−14.4383	−1.03929	−0.519647	+	0.854381i	$0.673937\pi$
$194$	30.8251	2.21312
$195$	−11.0149	−0.788791
$196$	8.74268	0.624477
$197$	21.1438	1.50643	0.753215	−	0.657774i	$-0.228502\pi$
$197$	21.1438	1.50643	0.753215	+	0.657774i	$0.228502\pi$
$198$	9.22481	0.655579
$199$	18.3680	1.30207	0.651036	−	0.759047i	$-0.274335\pi$
$199$	18.3680	1.30207	0.651036	+	0.759047i	$0.274335\pi$
$200$	4.67256	0.330400
$201$	−10.2914	−0.725901
$202$	25.2608	1.77735
$203$	32.1224	2.25455
$204$	−0.556583	−0.0389686
$205$	−3.91870	−0.273694
$206$	17.6213	1.22773
$207$	−1.53381	−0.106607
$208$	−30.6727	−2.12677
$209$	35.0701	2.42585
$210$	13.1429	0.906948
$211$	−2.64970	−0.182413	−0.0912063	−	0.995832i	$-0.529072\pi$
$211$	−2.64970	−0.182413	−0.0912063	+	0.995832i	$0.529072\pi$
$212$	−4.89387	−0.336112
$213$	−5.97617	−0.409480
$214$	−28.2510	−1.93120
$215$	16.5135	1.12621
$216$	2.30793	0.157034
$217$	1.65801	0.112553
$218$	6.79096	0.459942
$219$	−11.4678	−0.774925
$220$	5.53901	0.373440
$221$	6.38564	0.429545
$222$	10.4544	0.701655
$223$	13.4516	0.900787	0.450394	−	0.892830i	$-0.351284\pi$
$223$	13.4516	0.900787	0.450394	+	0.892830i	$0.351284\pi$
$224$	14.6028	0.975692
$225$	−2.02457	−0.134971
$226$	21.9534	1.46032
$227$	−7.79511	−0.517380	−0.258690	−	0.965960i	$-0.583291\pi$
$227$	−7.79511	−0.517380	−0.258690	+	0.965960i	$0.583291\pi$
$228$	−3.38330	−0.224064
$229$	−2.39914	−0.158539	−0.0792697	−	0.996853i	$-0.525259\pi$
$229$	−2.39914	−0.158539	−0.0792697	+	0.996853i	$0.525259\pi$
$230$	−4.23036	−0.278942
$231$	27.4925	1.80888
$232$	15.5576	1.02141
$233$	−1.01696	−0.0666232	−0.0333116	−	0.999445i	$-0.510605\pi$
$233$	−1.01696	−0.0666232	−0.0333116	+	0.999445i	$0.510605\pi$
$234$	10.2102	0.667462
$235$	8.52318	0.555991
$236$	−5.72567	−0.372709
$237$	13.9093	0.903508
$238$	−7.61934	−0.493888
$239$	−25.8273	−1.67063	−0.835314	−	0.549772i	$-0.814714\pi$
$239$	−25.8273	−1.67063	−0.835314	+	0.549772i	$0.814714\pi$
$240$	8.28556	0.534831
$241$	22.7891	1.46797	0.733987	−	0.679163i	$-0.237657\pi$
$241$	22.7891	1.46797	0.733987	+	0.679163i	$0.237657\pi$
$242$	35.6330	2.29057
$243$	−1.00000	−0.0641500
$244$	−1.93809	−0.124073
$245$	27.0950	1.73104
$246$	3.63243	0.231595
$247$	38.8163	2.46982
$248$	0.803009	0.0509911
$249$	5.71699	0.362300
$250$	−19.3742	−1.22533
$251$	20.2190	1.27621	0.638105	−	0.769950i	$-0.279719\pi$
$251$	20.2190	1.27621	0.638105	+	0.769950i	$0.279719\pi$
$252$	−2.65227	−0.167077
$253$	−8.84912	−0.556339
$254$	−9.86341	−0.618885
$255$	−1.72494	−0.108020
$256$	12.4194	0.776215
$257$	20.9990	1.30988	0.654942	−	0.755680i	$-0.272693\pi$
$257$	20.9990	1.30988	0.654942	+	0.755680i	$0.272693\pi$
$258$	−15.3072	−0.952984
$259$	31.1571	1.93601
$260$	6.13069	0.380209
$261$	−6.74095	−0.417254
$262$	−22.1151	−1.36627
$263$	−15.7761	−0.972798	−0.486399	−	0.873737i	$-0.661690\pi$
$263$	−15.7761	−0.972798	−0.486399	+	0.873737i	$0.661690\pi$
$264$	13.3152	0.819497
$265$	−15.1669	−0.931696
$266$	−46.3156	−2.83979
$267$	−15.5942	−0.954352
$268$	5.72803	0.349895
$269$	31.9731	1.94943	0.974717	−	0.223443i	$-0.0717296\pi$
$269$	31.9731	1.94943	0.974717	+	0.223443i	$0.0717296\pi$
$270$	−2.75807	−0.167851
$271$	−15.5271	−0.943206	−0.471603	−	0.881811i	$-0.656324\pi$
$271$	−15.5271	−0.943206	−0.471603	+	0.881811i	$0.656324\pi$
$272$	−4.80338	−0.291248
$273$	30.4293	1.84166
$274$	11.3038	0.682891
$275$	−11.6805	−0.704359
$276$	0.853695	0.0513864
$277$	−18.4498	−1.10854	−0.554272	−	0.832336i	$-0.687003\pi$
$277$	−18.4498	−1.10854	−0.554272	+	0.832336i	$0.687003\pi$
$278$	−6.77403	−0.406279
$279$	−0.347935	−0.0208303
$280$	18.9707	1.13372
$281$	5.15477	0.307508	0.153754	−	0.988109i	$-0.450864\pi$
$281$	5.15477	0.307508	0.153754	+	0.988109i	$0.450864\pi$
$282$	−7.90054	−0.470470
$283$	14.2123	0.844834	0.422417	−	0.906402i	$-0.361182\pi$
$283$	14.2123	0.844834	0.422417	+	0.906402i	$0.361182\pi$
$284$	3.32624	0.197376
$285$	−10.4854	−0.621102
$286$	58.9063	3.48320
$287$	10.8257	0.639018
$288$	−3.06443	−0.180573
$289$	1.00000	0.0588235
$290$	−18.5920	−1.09176
$291$	−19.2786	−1.13013
$292$	6.38280	0.373525
$293$	33.5190	1.95820	0.979101	−	0.203376i	$-0.0651912\pi$
$293$	33.5190	1.95820	0.979101	+	0.203376i	$0.0651912\pi$
$294$	−25.1157	−1.46478
$295$	−17.7448	−1.03314
$296$	15.0901	0.877094
$297$	−5.76936	−0.334772
$298$	−12.6001	−0.729904
$299$	−9.79438	−0.566424
$300$	1.12684	0.0650582
$301$	−45.6197	−2.62948
$302$	−7.41696	−0.426798
$303$	−15.7986	−0.907605
$304$	−29.1983	−1.67464
$305$	−6.00645	−0.343928
$306$	1.59893	0.0914049
$307$	17.3448	0.989919	0.494959	−	0.868916i	$-0.335183\pi$
$307$	17.3448	0.989919	0.494959	+	0.868916i	$0.335183\pi$
$308$	−15.3019	−0.871905
$309$	−11.0207	−0.626943
$310$	−0.959629	−0.0545033
$311$	18.9076	1.07215	0.536074	−	0.844171i	$-0.319907\pi$
$311$	18.9076	1.07215	0.536074	+	0.844171i	$0.319907\pi$
$312$	14.7376	0.834351
$313$	19.3859	1.09576	0.547879	−	0.836558i	$-0.315435\pi$
$313$	19.3859	1.09576	0.547879	+	0.836558i	$0.315435\pi$
$314$	−1.59893	−0.0902329
$315$	−8.21982	−0.463134
$316$	−7.74170	−0.435505
$317$	−3.47746	−0.195314	−0.0976568	−	0.995220i	$-0.531135\pi$
$317$	−3.47746	−0.195314	−0.0976568	+	0.995220i	$0.531135\pi$
$318$	14.0589	0.788386
$319$	−38.8909	−2.17747
$320$	8.11922	0.453878
$321$	17.6687	0.986171
$322$	11.6866	0.651271
$323$	6.07869	0.338228
$324$	0.556583	0.0309213
$325$	−12.9282	−0.717126
$326$	28.6905	1.58902
$327$	−4.24719	−0.234870
$328$	5.24311	0.289502
$329$	−23.5458	−1.29812
$330$	−15.9123	−0.875942
$331$	−1.51025	−0.0830111	−0.0415055	−	0.999138i	$-0.513215\pi$
$331$	−1.51025	−0.0830111	−0.0415055	+	0.999138i	$0.513215\pi$
$332$	−3.18198	−0.174634
$333$	−6.53838	−0.358301
$334$	10.7705	0.589338
$335$	17.7521	0.969902
$336$	−22.8894	−1.24872
$337$	−12.7099	−0.692350	−0.346175	−	0.938170i	$-0.612520\pi$
$337$	−12.7099	−0.692350	−0.346175	+	0.938170i	$0.612520\pi$
$338$	44.4126	2.41572
$339$	−13.7300	−0.745714
$340$	0.960074	0.0520673
$341$	−2.00736	−0.108705
$342$	9.71942	0.525566
$343$	−41.4949	−2.24051
$344$	−22.0947	−1.19126
$345$	2.64574	0.142442
$346$	5.37843	0.289146
$347$	6.30533	0.338488	0.169244	−	0.985574i	$-0.445867\pi$
$347$	6.30533	0.338488	0.169244	+	0.985574i	$0.445867\pi$
$348$	3.75190	0.201123
$349$	−23.0504	−1.23386	−0.616930	−	0.787018i	$-0.711624\pi$
$349$	−23.0504	−1.23386	−0.616930	+	0.787018i	$0.711624\pi$
$350$	15.4259	0.824549
$351$	−6.38564	−0.340840
$352$	−17.6798	−0.942336
$353$	−9.40724	−0.500697	−0.250348	−	0.968156i	$-0.580545\pi$
$353$	−9.40724	−0.500697	−0.250348	+	0.968156i	$0.580545\pi$
$354$	16.4485	0.874228
$355$	10.3086	0.547121
$356$	8.67949	0.460012
$357$	4.76527	0.252205
$358$	−11.4868	−0.607097
$359$	−13.3352	−0.703805	−0.351902	−	0.936037i	$-0.614465\pi$
$359$	−13.3352	−0.703805	−0.351902	+	0.936037i	$0.614465\pi$
$360$	−3.98104	−0.209819
$361$	17.9505	0.944764
$362$	9.50164	0.499395
$363$	−22.2855	−1.16968
$364$	−16.9364	−0.887710
$365$	19.7814	1.03540
$366$	5.56766	0.291026
$367$	−10.5128	−0.548762	−0.274381	−	0.961621i	$-0.588473\pi$
$367$	−10.5128	−0.548762	−0.274381	+	0.961621i	$0.588473\pi$
$368$	7.36749	0.384057
$369$	−2.27178	−0.118264
$370$	−18.0333	−0.937506
$371$	41.8996	2.17532
$372$	0.193655	0.0100405
$373$	−11.2434	−0.582159	−0.291080	−	0.956699i	$-0.594014\pi$
$373$	−11.2434	−0.582159	−0.291080	+	0.956699i	$0.594014\pi$
$374$	9.22481	0.477003
$375$	12.1170	0.625718
$376$	−11.4038	−0.588105
$377$	−43.0453	−2.21694
$378$	7.61934	0.391896
$379$	−5.22165	−0.268218	−0.134109	−	0.990967i	$-0.542817\pi$
$379$	−5.22165	−0.268218	−0.134109	+	0.990967i	$0.542817\pi$
$380$	5.83600	0.299380
$381$	6.16875	0.316035
$382$	25.7447	1.31722
$383$	30.4678	1.55683	0.778416	−	0.627749i	$-0.216024\pi$
$383$	30.4678	1.55683	0.778416	+	0.627749i	$0.216024\pi$
$384$	−13.6549	−0.696826
$385$	−47.4230	−2.41690
$386$	−23.0859	−1.17504
$387$	9.57338	0.486643
$388$	10.7301	0.544740
$389$	3.26598	0.165592	0.0827959	−	0.996567i	$-0.473615\pi$
$389$	3.26598	0.165592	0.0827959	+	0.996567i	$0.473615\pi$
$390$	−17.6120	−0.891819
$391$	−1.53381	−0.0775683
$392$	−36.2524	−1.83102
$393$	13.8311	0.697689
$394$	33.8074	1.70319
$395$	−23.9928	−1.20721
$396$	3.21113	0.161365
$397$	−26.2007	−1.31498	−0.657489	−	0.753465i	$-0.728381\pi$
$397$	−26.2007	−1.31498	−0.657489	+	0.753465i	$0.728381\pi$
$398$	29.3692	1.47214
$399$	28.9666	1.45014
$400$	9.72479	0.486239
$401$	−14.0995	−0.704098	−0.352049	−	0.935982i	$-0.614515\pi$
$401$	−14.0995	−0.704098	−0.352049	+	0.935982i	$0.614515\pi$
$402$	−16.4553	−0.820715
$403$	−2.22179	−0.110675
$404$	8.79322	0.437479
$405$	1.72494	0.0857131
$406$	51.3615	2.54903
$407$	−37.7222	−1.86982
$408$	2.30793	0.114259
$409$	1.86465	0.0922008	0.0461004	−	0.998937i	$-0.485321\pi$
$409$	1.86465	0.0922008	0.0461004	+	0.998937i	$0.485321\pi$
$410$	−6.26573	−0.309442
$411$	−7.06963	−0.348719
$412$	6.13391	0.302196
$413$	49.0212	2.41217
$414$	−2.45246	−0.120532
$415$	−9.86149	−0.484082
$416$	−19.5683	−0.959417
$417$	4.23660	0.207467
$418$	56.0748	2.74271
$419$	−7.66907	−0.374659	−0.187329	−	0.982297i	$-0.559983\pi$
$419$	−7.66907	−0.374659	−0.187329	+	0.982297i	$0.559983\pi$
$420$	4.57501	0.223238
$421$	−20.0162	−0.975528	−0.487764	−	0.872976i	$-0.662187\pi$
$421$	−20.0162	−0.975528	−0.487764	+	0.872976i	$0.662187\pi$
$422$	−4.23668	−0.206239
$423$	4.94114	0.240246
$424$	20.2929	0.985510
$425$	−2.02457	−0.0982061
$426$	−9.55549	−0.462965
$427$	16.5932	0.803002
$428$	−9.83410	−0.475349
$429$	−36.8410	−1.77870
$430$	26.4040	1.27332
$431$	8.02711	0.386652	0.193326	−	0.981135i	$-0.438072\pi$
$431$	8.02711	0.386652	0.193326	+	0.981135i	$0.438072\pi$
$432$	4.80338	0.231103
$433$	31.7904	1.52775	0.763874	−	0.645365i	$-0.223295\pi$
$433$	31.7904	1.52775	0.763874	+	0.645365i	$0.223295\pi$
$434$	2.65104	0.127254
$435$	11.6277	0.557508
$436$	2.36391	0.113211
$437$	−9.32358	−0.446008
$438$	−18.3363	−0.876142
$439$	14.4990	0.691998	0.345999	−	0.938235i	$-0.387540\pi$
$439$	14.4990	0.691998	0.345999	+	0.938235i	$0.387540\pi$
$440$	−22.9680	−1.09496
$441$	15.7078	0.747989
$442$	10.2102	0.485650
$443$	−4.72700	−0.224587	−0.112293	−	0.993675i	$-0.535820\pi$
$443$	−4.72700	−0.224587	−0.112293	+	0.993675i	$0.535820\pi$
$444$	3.63915	0.172706
$445$	26.8992	1.27514
$446$	21.5082	1.01844
$447$	7.88032	0.372726
$448$	−22.4299	−1.05971
$449$	23.6427	1.11577	0.557884	−	0.829919i	$-0.311613\pi$
$449$	23.6427	1.11577	0.557884	+	0.829919i	$0.311613\pi$
$450$	−3.23715	−0.152601
$451$	−13.1067	−0.617172
$452$	7.64191	0.359445
$453$	4.63870	0.217945
$454$	−12.4638	−0.584957
$455$	−52.4888	−2.46071
$456$	14.0292	0.656976
$457$	−8.24543	−0.385705	−0.192852	−	0.981228i	$-0.561774\pi$
$457$	−8.24543	−0.385705	−0.192852	+	0.981228i	$0.561774\pi$
$458$	−3.83606	−0.179247
$459$	−1.00000	−0.0466760
$460$	−1.47258	−0.0686592
$461$	−19.6339	−0.914443	−0.457222	−	0.889353i	$-0.651155\pi$
$461$	−19.6339	−0.914443	−0.457222	+	0.889353i	$0.651155\pi$
$462$	43.9587	2.04514
$463$	−15.8111	−0.734802	−0.367401	−	0.930063i	$-0.619752\pi$
$463$	−15.8111	−0.734802	−0.367401	+	0.930063i	$0.619752\pi$
$464$	32.3793	1.50317
$465$	0.600169	0.0278322
$466$	−1.62605	−0.0753252
$467$	−18.3411	−0.848725	−0.424362	−	0.905492i	$-0.639502\pi$
$467$	−18.3411	−0.848725	−0.424362	+	0.905492i	$0.639502\pi$
$468$	3.55414	0.164290
$469$	−49.0414	−2.26452
$470$	13.6280	0.628612
$471$	1.00000	0.0460776
$472$	23.7420	1.09282
$473$	55.2323	2.53958
$474$	22.2401	1.02152
$475$	−12.3067	−0.564672
$476$	−2.65227	−0.121566
$477$	−8.79270	−0.402590
$478$	−41.2961	−1.88884
$479$	−19.1302	−0.874081	−0.437040	−	0.899442i	$-0.643973\pi$
$479$	−19.1302	−0.874081	−0.437040	+	0.899442i	$0.643973\pi$
$480$	5.28597	0.241270
$481$	−41.7517	−1.90372
$482$	36.4382	1.65972
$483$	−7.30903	−0.332573
$484$	12.4037	0.563805
$485$	33.2544	1.51001
$486$	−1.59893	−0.0725290
$487$	2.35903	0.106898	0.0534489	−	0.998571i	$-0.482979\pi$
$487$	2.35903	0.106898	0.0534489	+	0.998571i	$0.482979\pi$
$488$	8.03646	0.363793
$489$	−17.9435	−0.811434
$490$	43.3231	1.95714
$491$	−0.639103	−0.0288423	−0.0144212	−	0.999896i	$-0.504591\pi$
$491$	−0.639103	−0.0288423	−0.0144212	+	0.999896i	$0.504591\pi$
$492$	1.26444	0.0570052
$493$	−6.74095	−0.303597
$494$	62.0647	2.79242
$495$	9.95181	0.447301
$496$	1.67127	0.0750421
$497$	−28.4781	−1.27742
$498$	9.14108	0.409622
$499$	−30.9107	−1.38375	−0.691876	−	0.722016i	$-0.743216\pi$
$499$	−30.9107	−1.38375	−0.691876	+	0.722016i	$0.743216\pi$
$500$	−6.74411	−0.301606
$501$	−6.73608	−0.300946
$502$	32.3287	1.44290
$503$	−4.68351	−0.208827	−0.104414	−	0.994534i	$-0.533297\pi$
$503$	−4.68351	−0.208827	−0.104414	+	0.994534i	$0.533297\pi$
$504$	10.9979	0.489885
$505$	27.2516	1.21268
$506$	−14.1491	−0.629006
$507$	−27.7764	−1.23359
$508$	−3.43342	−0.152333
$509$	−12.6155	−0.559173	−0.279587	−	0.960120i	$-0.590197\pi$
$509$	−12.6155	−0.559173	−0.279587	+	0.960120i	$0.590197\pi$
$510$	−2.75807	−0.122129
$511$	−54.6473	−2.41745
$512$	−7.45207	−0.329338
$513$	−6.07869	−0.268381
$514$	33.5760	1.48097
$515$	19.0100	0.837681
$516$	−5.32838	−0.234569
$517$	28.5072	1.25374
$518$	49.8181	2.18888
$519$	−3.36376	−0.147653
$520$	−25.4215	−1.11481
$521$	3.19040	0.139774	0.0698871	−	0.997555i	$-0.477736\pi$
$521$	3.19040	0.139774	0.0698871	+	0.997555i	$0.477736\pi$
$522$	−10.7783	−0.471754
$523$	21.6719	0.947647	0.473823	−	0.880620i	$-0.342874\pi$
$523$	21.6719	0.947647	0.473823	+	0.880620i	$0.342874\pi$
$524$	−7.69818	−0.336297
$525$	−9.64762	−0.421057
$526$	−25.2250	−1.09986
$527$	−0.347935	−0.0151563
$528$	27.7124	1.20603
$529$	−20.6474	−0.897714
$530$	−24.2509	−1.05339
$531$	−10.2872	−0.446426
$532$	−16.1223	−0.698991
$533$	−14.5068	−0.628359
$534$	−24.9341	−1.07901
$535$	−30.4775	−1.31766
$536$	−23.7518	−1.02592
$537$	7.18405	0.310015
$538$	51.1228	2.20406
$539$	90.6237	3.90344
$540$	−0.960074	−0.0413150
$541$	7.98124	0.343140	0.171570	−	0.985172i	$-0.445116\pi$
$541$	7.98124	0.343140	0.171570	+	0.985172i	$0.445116\pi$
$542$	−24.8268	−1.06640
$543$	−5.94249	−0.255017
$544$	−3.06443	−0.131386
$545$	7.32616	0.313818
$546$	48.6543	2.08221
$547$	−25.8270	−1.10428	−0.552141	−	0.833751i	$-0.686189\pi$
$547$	−25.8270	−1.10428	−0.552141	+	0.833751i	$0.686189\pi$
$548$	3.93483	0.168088
$549$	−3.48211	−0.148613
$550$	−18.6763	−0.796359
$551$	−40.9761	−1.74564
$552$	−3.53993	−0.150669
$553$	66.2817	2.81858
$554$	−29.5000	−1.25334
$555$	11.2783	0.478739
$556$	−2.35802	−0.100002
$557$	24.3489	1.03170	0.515848	−	0.856680i	$-0.327477\pi$
$557$	24.3489	1.03170	0.515848	+	0.856680i	$0.327477\pi$
$558$	−0.556325	−0.0235511
$559$	61.1322	2.58562
$560$	39.4829	1.66846
$561$	−5.76936	−0.243582
$562$	8.24213	0.347673
$563$	−9.04520	−0.381210	−0.190605	−	0.981667i	$-0.561045\pi$
$563$	−9.04520	−0.381210	−0.190605	+	0.981667i	$0.561045\pi$
$564$	−2.75015	−0.115802
$565$	23.6836	0.996375
$566$	22.7245	0.955183
$567$	−4.76527	−0.200122
$568$	−13.7926	−0.578723
$569$	43.0953	1.80665	0.903325	−	0.428957i	$-0.141119\pi$
$569$	43.0953	1.80665	0.903325	+	0.428957i	$0.141119\pi$
$570$	−16.7654	−0.702227
$571$	4.10639	0.171847	0.0859236	−	0.996302i	$-0.472616\pi$
$571$	4.10639	0.171847	0.0859236	+	0.996302i	$0.472616\pi$
$572$	20.5051	0.857361
$573$	−16.1012	−0.672638
$574$	17.3095	0.722484
$575$	3.10532	0.129501
$576$	4.70695	0.196123
$577$	24.6778	1.02735	0.513674	−	0.857985i	$-0.328284\pi$
$577$	24.6778	1.02735	0.513674	+	0.857985i	$0.328284\pi$
$578$	1.59893	0.0665068
$579$	14.4383	0.600037
$580$	−6.47181	−0.268727
$581$	27.2430	1.13023
$582$	−30.8251	−1.27774
$583$	−50.7282	−2.10095
$584$	−26.4669	−1.09521
$585$	11.0149	0.455409
$586$	53.5946	2.21397
$587$	3.31824	0.136958	0.0684792	−	0.997653i	$-0.478185\pi$
$587$	3.31824	0.136958	0.0684792	+	0.997653i	$0.478185\pi$
$588$	−8.74268	−0.360542
$589$	−2.11499	−0.0871468
$590$	−28.3727	−1.16809
$591$	−21.1438	−0.869738
$592$	31.4063	1.29079
$593$	−7.77003	−0.319077	−0.159539	−	0.987192i	$-0.551001\pi$
$593$	−7.77003	−0.319077	−0.159539	+	0.987192i	$0.551001\pi$
$594$	−9.22481	−0.378498
$595$	−8.21982	−0.336980
$596$	−4.38605	−0.179660
$597$	−18.3680	−0.751752
$598$	−15.6606	−0.640408
$599$	−33.3882	−1.36420	−0.682102	−	0.731257i	$-0.738934\pi$
$599$	−33.3882	−1.36420	−0.682102	+	0.731257i	$0.738934\pi$
$600$	−4.67256	−0.190756
$601$	33.0180	1.34683	0.673416	−	0.739263i	$-0.264826\pi$
$601$	33.0180	1.34683	0.673416	+	0.739263i	$0.264826\pi$
$602$	−72.9429	−2.97293
$603$	10.2914	0.419099
$604$	−2.58182	−0.105053
$605$	38.4412	1.56286
$606$	−25.2608	−1.02615
$607$	44.2615	1.79652	0.898259	−	0.439467i	$-0.144833\pi$
$607$	44.2615	1.79652	0.898259	+	0.439467i	$0.144833\pi$
$608$	−18.6277	−0.755454
$609$	−32.1224	−1.30167
$610$	−9.60390	−0.388851
$611$	31.5523	1.27647
$612$	0.556583	0.0224985
$613$	4.37889	0.176862	0.0884309	−	0.996082i	$-0.471815\pi$
$613$	4.37889	0.176862	0.0884309	+	0.996082i	$0.471815\pi$
$614$	27.7331	1.11922
$615$	3.91870	0.158017
$616$	63.4507	2.55650
$617$	−13.6938	−0.551290	−0.275645	−	0.961260i	$-0.588891\pi$
$617$	−13.6938	−0.551290	−0.275645	+	0.961260i	$0.588891\pi$
$618$	−17.6213	−0.708832
$619$	−22.2176	−0.892999	−0.446500	−	0.894784i	$-0.647330\pi$
$619$	−22.2176	−0.892999	−0.446500	+	0.894784i	$0.647330\pi$
$620$	−0.334044	−0.0134155
$621$	1.53381	0.0615498
$622$	30.2319	1.21219
$623$	−74.3108	−2.97720
$624$	30.6727	1.22789
$625$	−10.7783	−0.431130
$626$	30.9968	1.23888
$627$	−35.0701	−1.40057
$628$	−0.556583	−0.0222101
$629$	−6.53838	−0.260702
$630$	−13.1429	−0.523627
$631$	−4.68940	−0.186682	−0.0933411	−	0.995634i	$-0.529755\pi$
$631$	−4.68940	−0.186682	−0.0933411	+	0.995634i	$0.529755\pi$
$632$	32.1017	1.27694
$633$	2.64970	0.105316
$634$	−5.56022	−0.220825
$635$	−10.6407	−0.422265
$636$	4.89387	0.194055
$637$	100.304	3.97420
$638$	−62.1839	−2.46189
$639$	5.97617	0.236414
$640$	23.5540	0.931054
$641$	−27.7400	−1.09566	−0.547832	−	0.836588i	$-0.684547\pi$
$641$	−27.7400	−1.09566	−0.547832	+	0.836588i	$0.684547\pi$
$642$	28.2510	1.11498
$643$	−24.1231	−0.951323	−0.475662	−	0.879628i	$-0.657791\pi$
$643$	−24.1231	−0.951323	−0.475662	+	0.879628i	$0.657791\pi$
$644$	4.06808	0.160305
$645$	−16.5135	−0.650220
$646$	9.71942	0.382405
$647$	9.33163	0.366864	0.183432	−	0.983032i	$-0.441279\pi$
$647$	9.33163	0.366864	0.183432	+	0.983032i	$0.441279\pi$
$648$	−2.30793	−0.0906639
$649$	−59.3504	−2.32971
$650$	−20.6713	−0.810794
$651$	−1.65801	−0.0649823
$652$	9.98706	0.391123
$653$	18.2329	0.713507	0.356754	−	0.934199i	$-0.383884\pi$
$653$	18.2329	0.713507	0.356754	+	0.934199i	$0.383884\pi$
$654$	−6.79096	−0.265548
$655$	−23.8579	−0.932207
$656$	10.9122	0.426051
$657$	11.4678	0.447403
$658$	−37.6482	−1.46768
$659$	−24.6638	−0.960766	−0.480383	−	0.877059i	$-0.659502\pi$
$659$	−24.6638	−0.960766	−0.480383	+	0.877059i	$0.659502\pi$
$660$	−5.53901	−0.215606
$661$	37.8635	1.47272	0.736360	−	0.676590i	$-0.236543\pi$
$661$	37.8635	1.47272	0.736360	+	0.676590i	$0.236543\pi$
$662$	−2.41479	−0.0938536
$663$	−6.38564	−0.247998
$664$	13.1944	0.512042
$665$	−49.9657	−1.93759
$666$	−10.4544	−0.405101
$667$	10.3394	0.400342
$668$	3.74919	0.145061
$669$	−13.4516	−0.520070
$670$	28.3844	1.09659
$671$	−20.0896	−0.775549
$672$	−14.6028	−0.563316
$673$	46.5057	1.79266	0.896331	−	0.443386i	$-0.146223\pi$
$673$	46.5057	1.79266	0.896331	+	0.443386i	$0.146223\pi$
$674$	−20.3222	−0.782781
$675$	2.02457	0.0779258
$676$	15.4599	0.594610
$677$	−35.1067	−1.34926	−0.674631	−	0.738156i	$-0.735697\pi$
$677$	−35.1067	−1.34926	−0.674631	+	0.738156i	$0.735697\pi$
$678$	−21.9534	−0.843116
$679$	−91.8676	−3.52555
$680$	−3.98104	−0.152666
$681$	7.79511	0.298709
$682$	−3.20964	−0.122903
$683$	−21.6541	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$683$	−21.6541	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$684$	3.38330	0.129364
$685$	12.1947	0.465936
$686$	−66.3475	−2.53316
$687$	2.39914	0.0915328
$688$	−45.9846	−1.75315
$689$	−56.1470	−2.13903
$690$	4.23036	0.161047
$691$	−20.9106	−0.795475	−0.397738	−	0.917499i	$-0.630205\pi$
$691$	−20.9106	−0.795475	−0.397738	+	0.917499i	$0.630205\pi$
$692$	1.87221	0.0711709
$693$	−27.4925	−1.04435
$694$	10.0818	0.382700
$695$	−7.30789	−0.277204
$696$	−15.5576	−0.589709
$697$	−2.27178	−0.0860499
$698$	−36.8560	−1.39502
$699$	1.01696	0.0384649
$700$	5.36970	0.202956
$701$	−41.3258	−1.56085	−0.780426	−	0.625248i	$-0.784998\pi$
$701$	−41.3258	−1.56085	−0.780426	+	0.625248i	$0.784998\pi$
$702$	−10.2102	−0.385359
$703$	−39.7448	−1.49900
$704$	27.1561	1.02348
$705$	−8.52318	−0.321001
$706$	−15.0415	−0.566096
$707$	−75.2844	−2.83136
$708$	5.72567	0.215184
$709$	−26.3731	−0.990463	−0.495231	−	0.868761i	$-0.664917\pi$
$709$	−26.3731	−0.990463	−0.495231	+	0.868761i	$0.664917\pi$
$710$	16.4827	0.618584
$711$	−13.9093	−0.521641
$712$	−35.9904	−1.34880
$713$	0.533668	0.0199860
$714$	7.61934	0.285147
$715$	63.5487	2.37659
$716$	−3.99852	−0.149432
$717$	25.8273	0.964538
$718$	−21.3221	−0.795733
$719$	21.1724	0.789596	0.394798	−	0.918768i	$-0.370815\pi$
$719$	21.1724	0.789596	0.394798	+	0.918768i	$0.370815\pi$
$720$	−8.28556	−0.308785
$721$	−52.5164	−1.95581
$722$	28.7017	1.06816
$723$	−22.7891	−0.847536
$724$	3.30749	0.122922
$725$	13.6475	0.506856
$726$	−35.6330	−1.32246
$727$	−41.6666	−1.54533	−0.772664	−	0.634816i	$-0.781076\pi$
$727$	−41.6666	−1.54533	−0.772664	+	0.634816i	$0.781076\pi$
$728$	70.2285	2.60284
$729$	1.00000	0.0370370
$730$	31.6291	1.17064
$731$	9.57338	0.354084
$732$	1.93809	0.0716337
$733$	−28.4088	−1.04930	−0.524651	−	0.851317i	$-0.675804\pi$
$733$	−28.4088	−1.04930	−0.524651	+	0.851317i	$0.675804\pi$
$734$	−16.8092	−0.620439
$735$	−27.0950	−0.999415
$736$	4.70026	0.173254
$737$	59.3749	2.18710
$738$	−3.63243	−0.133711
$739$	−2.66358	−0.0979814	−0.0489907	−	0.998799i	$-0.515600\pi$
$739$	−2.66358	−0.0979814	−0.0489907	+	0.998799i	$0.515600\pi$
$740$	−6.27733	−0.230759
$741$	−38.8163	−1.42595
$742$	66.9946	2.45945
$743$	−48.1675	−1.76709	−0.883547	−	0.468342i	$-0.844851\pi$
$743$	−48.1675	−1.76709	−0.883547	+	0.468342i	$0.844851\pi$
$744$	−0.803009	−0.0294397
$745$	−13.5931	−0.498013
$746$	−17.9774	−0.658198
$747$	−5.71699	−0.209174
$748$	3.21113	0.117410
$749$	84.1961	3.07646
$750$	19.3742	0.707447
$751$	−6.21629	−0.226835	−0.113418	−	0.993547i	$-0.536180\pi$
$751$	−6.21629	−0.226835	−0.113418	+	0.993547i	$0.536180\pi$
$752$	−23.7342	−0.865496
$753$	−20.2190	−0.736820
$754$	−68.8264	−2.50651
$755$	−8.00149	−0.291204
$756$	2.65227	0.0964620
$757$	18.3131	0.665600	0.332800	−	0.942997i	$-0.392007\pi$
$757$	18.3131	0.665600	0.332800	+	0.942997i	$0.392007\pi$
$758$	−8.34906	−0.303252
$759$	8.84912	0.321203
$760$	−24.1995	−0.877809
$761$	30.1478	1.09286	0.546428	−	0.837506i	$-0.315987\pi$
$761$	30.1478	1.09286	0.546428	+	0.837506i	$0.315987\pi$
$762$	9.86341	0.357314
$763$	−20.2390	−0.732700
$764$	8.96166	0.324222
$765$	1.72494	0.0623655
$766$	48.7159	1.76018
$767$	−65.6902	−2.37194
$768$	−12.4194	−0.448148
$769$	46.1917	1.66572	0.832858	−	0.553487i	$-0.186703\pi$
$769$	46.1917	1.66572	0.832858	+	0.553487i	$0.186703\pi$
$770$	−75.8262	−2.73259
$771$	−20.9990	−0.756261
$772$	−8.03614	−0.289227
$773$	21.0031	0.755430	0.377715	−	0.925922i	$-0.376710\pi$
$773$	21.0031	0.755430	0.377715	+	0.925922i	$0.376710\pi$
$774$	15.3072	0.550206
$775$	0.704420	0.0253035
$776$	−44.4935	−1.59722
$777$	−31.1571	−1.11776
$778$	5.22208	0.187221
$779$	−13.8095	−0.494776
$780$	−6.13069	−0.219514
$781$	34.4787	1.23374
$782$	−2.45246	−0.0876999
$783$	6.74095	0.240902
$784$	−75.4504	−2.69466
$785$	−1.72494	−0.0615659
$786$	22.1151	0.788818
$787$	−46.6959	−1.66453	−0.832265	−	0.554378i	$-0.812956\pi$
$787$	−46.6959	−1.66453	−0.832265	+	0.554378i	$0.812956\pi$
$788$	11.7683	0.419227
$789$	15.7761	0.561645
$790$	−38.3629	−1.36489
$791$	−65.4274	−2.32633
$792$	−13.3152	−0.473137
$793$	−22.2355	−0.789607
$794$	−41.8932	−1.48673
$795$	15.1669	0.537915
$796$	10.2233	0.362356
$797$	−24.5743	−0.870467	−0.435234	−	0.900318i	$-0.643334\pi$
$797$	−24.5743	−0.870467	−0.435234	+	0.900318i	$0.643334\pi$
$798$	46.3156	1.63956
$799$	4.94114	0.174805
$800$	6.20415	0.219350
$801$	15.5942	0.550996
$802$	−22.5442	−0.796064
$803$	66.1620	2.33481
$804$	−5.72803	−0.202012
$805$	12.6077	0.444362
$806$	−3.55249	−0.125131
$807$	−31.9731	−1.12551
$808$	−36.4619	−1.28273
$809$	1.29891	0.0456674	0.0228337	−	0.999739i	$-0.492731\pi$
$809$	1.29891	0.0456674	0.0228337	+	0.999739i	$0.492731\pi$
$810$	2.75807	0.0969086
$811$	35.3116	1.23996	0.619979	−	0.784618i	$-0.287141\pi$
$811$	35.3116	1.23996	0.619979	+	0.784618i	$0.287141\pi$
$812$	17.8788	0.627423
$813$	15.5271	0.544560
$814$	−60.3153	−2.11405
$815$	30.9516	1.08419
$816$	4.80338	0.168152
$817$	58.1937	2.03594
$818$	2.98144	0.104244
$819$	−30.4293	−1.06329
$820$	−2.18108	−0.0761666
$821$	20.5414	0.716899	0.358450	−	0.933549i	$-0.383305\pi$
$821$	20.5414	0.716899	0.358450	+	0.933549i	$0.383305\pi$
$822$	−11.3038	−0.394267
$823$	−4.80021	−0.167325	−0.0836625	−	0.996494i	$-0.526662\pi$
$823$	−4.80021	−0.167325	−0.0836625	+	0.996494i	$0.526662\pi$
$824$	−25.4349	−0.886065
$825$	11.6805	0.406662
$826$	78.3815	2.72724
$827$	29.4048	1.02250	0.511252	−	0.859431i	$-0.329182\pi$
$827$	29.4048	1.02250	0.511252	+	0.859431i	$0.329182\pi$
$828$	−0.853695	−0.0296679
$829$	−30.1208	−1.04614	−0.523069	−	0.852290i	$-0.675213\pi$
$829$	−30.1208	−1.04614	−0.523069	+	0.852290i	$0.675213\pi$
$830$	−15.7679	−0.547310
$831$	18.4498	0.640018
$832$	30.0569	1.04203
$833$	15.7078	0.544242
$834$	6.77403	0.234565
$835$	11.6194	0.402105
$836$	19.5195	0.675094
$837$	0.347935	0.0120264
$838$	−12.2623	−0.423595
$839$	28.1945	0.973382	0.486691	−	0.873574i	$-0.338204\pi$
$839$	28.1945	0.973382	0.486691	+	0.873574i	$0.338204\pi$
$840$	−18.9707	−0.654552
$841$	16.4404	0.566909
$842$	−32.0045	−1.10295
$843$	−5.15477	−0.177540
$844$	−1.47478	−0.0507639
$845$	47.9127	1.64825
$846$	7.90054	0.271626
$847$	−106.196	−3.64895
$848$	42.2347	1.45035
$849$	−14.2123	−0.487765
$850$	−3.23715	−0.111033
$851$	10.0287	0.343778
$852$	−3.32624	−0.113955
$853$	6.84090	0.234228	0.117114	−	0.993118i	$-0.462636\pi$
$853$	6.84090	0.234228	0.117114	+	0.993118i	$0.462636\pi$
$854$	26.5314	0.907886
$855$	10.4854	0.358593
$856$	40.7780	1.39376
$857$	−30.8582	−1.05410	−0.527049	−	0.849835i	$-0.676702\pi$
$857$	−30.8582	−1.05410	−0.527049	+	0.849835i	$0.676702\pi$
$858$	−58.9063	−2.01103
$859$	28.1192	0.959414	0.479707	−	0.877429i	$-0.340743\pi$
$859$	28.1192	0.959414	0.479707	+	0.877429i	$0.340743\pi$
$860$	9.19116	0.313416
$861$	−10.8257	−0.368937
$862$	12.8348	0.437155
$863$	−3.58391	−0.121998	−0.0609989	−	0.998138i	$-0.519429\pi$
$863$	−3.58391	−0.121998	−0.0609989	+	0.998138i	$0.519429\pi$
$864$	3.06443	0.104254
$865$	5.80230	0.197284
$866$	50.8306	1.72730
$867$	−1.00000	−0.0339618
$868$	0.922818	0.0313225
$869$	−80.2479	−2.72222
$870$	18.5920	0.630327
$871$	65.7173	2.22675
$872$	−9.80219	−0.331944
$873$	19.2786	0.652481
$874$	−14.9078	−0.504263
$875$	57.7407	1.95199
$876$	−6.38280	−0.215655
$877$	30.8612	1.04211	0.521054	−	0.853524i	$-0.325539\pi$
$877$	30.8612	1.04211	0.521054	+	0.853524i	$0.325539\pi$
$878$	23.1829	0.782383
$879$	−33.5190	−1.13057
$880$	−47.8023	−1.61142
$881$	12.1487	0.409302	0.204651	−	0.978835i	$-0.434394\pi$
$881$	12.1487	0.409302	0.204651	+	0.978835i	$0.434394\pi$
$882$	25.1157	0.845688
$883$	10.5487	0.354990	0.177495	−	0.984122i	$-0.443201\pi$
$883$	10.5487	0.354990	0.177495	+	0.984122i	$0.443201\pi$
$884$	3.55414	0.119539
$885$	17.7448	0.596485
$886$	−7.55815	−0.253921
$887$	10.7117	0.359665	0.179833	−	0.983697i	$-0.442444\pi$
$887$	10.7117	0.359665	0.179833	+	0.983697i	$0.442444\pi$
$888$	−15.0901	−0.506390
$889$	29.3957	0.985902
$890$	43.0100	1.44170
$891$	5.76936	0.193281
$892$	7.48695	0.250681
$893$	30.0356	1.00510
$894$	12.6001	0.421410
$895$	−12.3921	−0.414222
$896$	−65.0695	−2.17382
$897$	9.79438	0.327025
$898$	37.8031	1.26150
$899$	2.34541	0.0782239
$900$	−1.12684	−0.0375614
$901$	−8.79270	−0.292927
$902$	−20.9568	−0.697784
$903$	45.6197	1.51813
$904$	−31.6879	−1.05392
$905$	10.2505	0.340737
$906$	7.41696	0.246412
$907$	−42.6152	−1.41501	−0.707507	−	0.706707i	$-0.750180\pi$
$907$	−42.6152	−1.41501	−0.707507	+	0.706707i	$0.750180\pi$
$908$	−4.33863	−0.143982
$909$	15.7986	0.524006
$910$	−83.9260	−2.78212
$911$	−16.5414	−0.548040	−0.274020	−	0.961724i	$-0.588353\pi$
$911$	−16.5414	−0.548040	−0.274020	+	0.961724i	$0.588353\pi$
$912$	29.1983	0.966852
$913$	−32.9834	−1.09159
$914$	−13.1839	−0.436084
$915$	6.00645	0.198567
$916$	−1.33532	−0.0441202
$917$	65.9091	2.17651
$918$	−1.59893	−0.0527726
$919$	0.404529	0.0133442	0.00667210	−	0.999978i	$-0.497876\pi$
$919$	0.404529	0.0133442	0.00667210	+	0.999978i	$0.497876\pi$
$920$	6.10617	0.201315
$921$	−17.3448	−0.571530
$922$	−31.3933	−1.03388
$923$	38.1617	1.25611
$924$	15.3019	0.503395
$925$	13.2374	0.435243
$926$	−25.2808	−0.830778
$927$	11.0207	0.361966
$928$	20.6572	0.678104
$929$	47.1326	1.54637	0.773186	−	0.634180i	$-0.218662\pi$
$929$	47.1326	1.54637	0.773186	+	0.634180i	$0.218662\pi$
$930$	0.959629	0.0314675
$931$	95.4827	3.12932
$932$	−0.566022	−0.0185407
$933$	−18.9076	−0.619005
$934$	−29.3262	−0.959581
$935$	9.95181	0.325459
$936$	−14.7376	−0.481713
$937$	−17.4011	−0.568470	−0.284235	−	0.958755i	$-0.591740\pi$
$937$	−17.4011	−0.568470	−0.284235	+	0.958755i	$0.591740\pi$
$938$	−78.4138	−2.56030
$939$	−19.3859	−0.632636
$940$	4.74386	0.154728
$941$	34.3548	1.11993	0.559967	−	0.828515i	$-0.310814\pi$
$941$	34.3548	1.11993	0.559967	+	0.828515i	$0.310814\pi$
$942$	1.59893	0.0520960
$943$	3.48449	0.113471
$944$	49.4133	1.60826
$945$	8.21982	0.267391
$946$	88.3126	2.87129
$947$	19.1025	0.620747	0.310374	−	0.950615i	$-0.399546\pi$
$947$	19.1025	0.620747	0.310374	+	0.950615i	$0.399546\pi$
$948$	7.74170	0.251439
$949$	73.2295	2.37713
$950$	−19.6776	−0.638427
$951$	3.47746	0.112764
$952$	10.9979	0.356443
$953$	−4.32007	−0.139941	−0.0699705	−	0.997549i	$-0.522291\pi$
$953$	−4.32007	−0.139941	−0.0699705	+	0.997549i	$0.522291\pi$
$954$	−14.0589	−0.455175
$955$	27.7737	0.898735
$956$	−14.3750	−0.464922
$957$	38.8909	1.25716
$958$	−30.5879	−0.988249
$959$	−33.6887	−1.08786
$960$	−8.11922	−0.262047
$961$	−30.8789	−0.996095
$962$	−66.7582	−2.15237
$963$	−17.6687	−0.569366
$964$	12.6840	0.408525
$965$	−24.9053	−0.801731
$966$	−11.6866	−0.376012
$967$	45.6245	1.46719	0.733593	−	0.679589i	$-0.237842\pi$
$967$	45.6245	1.46719	0.733593	+	0.679589i	$0.237842\pi$
$968$	−51.4332	−1.65313
$969$	−6.07869	−0.195276
$970$	53.1716	1.70724
$971$	−27.3574	−0.877940	−0.438970	−	0.898502i	$-0.644657\pi$
$971$	−27.3574	−0.877940	−0.438970	+	0.898502i	$0.644657\pi$
$972$	−0.556583	−0.0178524
$973$	20.1885	0.647214
$974$	3.77193	0.120860
$975$	12.9282	0.414033
$976$	16.7259	0.535384
$977$	−10.4139	−0.333172	−0.166586	−	0.986027i	$-0.553274\pi$
$977$	−10.4139	−0.333172	−0.166586	+	0.986027i	$0.553274\pi$
$978$	−28.6905	−0.917420
$979$	89.9688	2.87541
$980$	15.0806	0.481733
$981$	4.24719	0.135602
$982$	−1.02188	−0.0326096
$983$	−10.8289	−0.345390	−0.172695	−	0.984975i	$-0.555247\pi$
$983$	−10.8289	−0.345390	−0.172695	+	0.984975i	$0.555247\pi$
$984$	−5.24311	−0.167144
$985$	36.4718	1.16209
$986$	−10.7783	−0.343251
$987$	23.5458	0.749472
$988$	21.6045	0.687331
$989$	−14.6838	−0.466917
$990$	15.9123	0.505725
$991$	8.93434	0.283809	0.141904	−	0.989880i	$-0.454677\pi$
$991$	8.93434	0.283809	0.141904	+	0.989880i	$0.454677\pi$
$992$	1.06622	0.0338526
$993$	1.51025	0.0479265
$994$	−45.5345	−1.44427
$995$	31.6837	1.00444
$996$	3.18198	0.100825
$997$	−5.92530	−0.187656	−0.0938280	−	0.995588i	$-0.529910\pi$
$997$	−5.92530	−0.187656	−0.0938280	+	0.995588i	$0.529910\pi$
$998$	−49.4241	−1.56449
$999$	6.53838	0.206865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.46	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.46	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+1.59893 q^{2} -1.00000 q^{3} +0.556583 q^{4} +1.72494 q^{5} -1.59893 q^{6} -4.76527 q^{7} -2.30793 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.59893 q^{2} -1.00000 q^{3} +0.556583 q^{4} +1.72494 q^{5} -1.59893 q^{6} -4.76527 q^{7} -2.30793 q^{8} +1.00000 q^{9} +2.75807 q^{10} +5.76936 q^{11} -0.556583 q^{12} +6.38564 q^{13} -7.61934 q^{14} -1.72494 q^{15} -4.80338 q^{16} +1.00000 q^{17} +1.59893 q^{18} +6.07869 q^{19} +0.960074 q^{20} +4.76527 q^{21} +9.22481 q^{22} -1.53381 q^{23} +2.30793 q^{24} -2.02457 q^{25} +10.2102 q^{26} -1.00000 q^{27} -2.65227 q^{28} -6.74095 q^{29} -2.75807 q^{30} -0.347935 q^{31} -3.06443 q^{32} -5.76936 q^{33} +1.59893 q^{34} -8.21982 q^{35} +0.556583 q^{36} -6.53838 q^{37} +9.71942 q^{38} -6.38564 q^{39} -3.98104 q^{40} -2.27178 q^{41} +7.61934 q^{42} +9.57338 q^{43} +3.21113 q^{44} +1.72494 q^{45} -2.45246 q^{46} +4.94114 q^{47} +4.80338 q^{48} +15.7078 q^{49} -3.23715 q^{50} -1.00000 q^{51} +3.55414 q^{52} -8.79270 q^{53} -1.59893 q^{54} +9.95181 q^{55} +10.9979 q^{56} -6.07869 q^{57} -10.7783 q^{58} -10.2872 q^{59} -0.960074 q^{60} -3.48211 q^{61} -0.556325 q^{62} -4.76527 q^{63} +4.70695 q^{64} +11.0149 q^{65} -9.22481 q^{66} +10.2914 q^{67} +0.556583 q^{68} +1.53381 q^{69} -13.1429 q^{70} +5.97617 q^{71} -2.30793 q^{72} +11.4678 q^{73} -10.4544 q^{74} +2.02457 q^{75} +3.38330 q^{76} -27.4925 q^{77} -10.2102 q^{78} -13.9093 q^{79} -8.28556 q^{80} +1.00000 q^{81} -3.63243 q^{82} -5.71699 q^{83} +2.65227 q^{84} +1.72494 q^{85} +15.3072 q^{86} +6.74095 q^{87} -13.3152 q^{88} +15.5942 q^{89} +2.75807 q^{90} -30.4293 q^{91} -0.853695 q^{92} +0.347935 q^{93} +7.90054 q^{94} +10.4854 q^{95} +3.06443 q^{96} +19.2786 q^{97} +25.1157 q^{98} +5.76936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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