LMFDB - Embedded newform 8002.2.a.d.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.62360 q^{3} +1.00000 q^{4} -0.0296991 q^{5} -1.62360 q^{6} -3.06845 q^{7} +1.00000 q^{8} -0.363928 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.62360 q^{3} +1.00000 q^{4} -0.0296991 q^{5} -1.62360 q^{6} -3.06845 q^{7} +1.00000 q^{8} -0.363928 q^{9} -0.0296991 q^{10} -3.06359 q^{11} -1.62360 q^{12} +1.09107 q^{13} -3.06845 q^{14} +0.0482194 q^{15} +1.00000 q^{16} +5.55020 q^{17} -0.363928 q^{18} +3.30298 q^{19} -0.0296991 q^{20} +4.98192 q^{21} -3.06359 q^{22} +5.36563 q^{23} -1.62360 q^{24} -4.99912 q^{25} +1.09107 q^{26} +5.46167 q^{27} -3.06845 q^{28} +0.628401 q^{29} +0.0482194 q^{30} -9.14820 q^{31} +1.00000 q^{32} +4.97404 q^{33} +5.55020 q^{34} +0.0911301 q^{35} -0.363928 q^{36} +3.26148 q^{37} +3.30298 q^{38} -1.77145 q^{39} -0.0296991 q^{40} -7.10029 q^{41} +4.98192 q^{42} +4.06912 q^{43} -3.06359 q^{44} +0.0108083 q^{45} +5.36563 q^{46} +0.168206 q^{47} -1.62360 q^{48} +2.41536 q^{49} -4.99912 q^{50} -9.01129 q^{51} +1.09107 q^{52} -2.60509 q^{53} +5.46167 q^{54} +0.0909860 q^{55} -3.06845 q^{56} -5.36271 q^{57} +0.628401 q^{58} +14.4345 q^{59} +0.0482194 q^{60} -4.98440 q^{61} -9.14820 q^{62} +1.11669 q^{63} +1.00000 q^{64} -0.0324037 q^{65} +4.97404 q^{66} +8.91897 q^{67} +5.55020 q^{68} -8.71163 q^{69} +0.0911301 q^{70} -3.19384 q^{71} -0.363928 q^{72} +2.81820 q^{73} +3.26148 q^{74} +8.11656 q^{75} +3.30298 q^{76} +9.40047 q^{77} -1.77145 q^{78} -3.25476 q^{79} -0.0296991 q^{80} -7.77577 q^{81} -7.10029 q^{82} +15.7393 q^{83} +4.98192 q^{84} -0.164836 q^{85} +4.06912 q^{86} -1.02027 q^{87} -3.06359 q^{88} -13.5329 q^{89} +0.0108083 q^{90} -3.34788 q^{91} +5.36563 q^{92} +14.8530 q^{93} +0.168206 q^{94} -0.0980955 q^{95} -1.62360 q^{96} -15.9718 q^{97} +2.41536 q^{98} +1.11493 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.62360	−0.937385	−0.468692	−	0.883361i	$-0.655275\pi$
$3$	−1.62360	−0.937385	−0.468692	+	0.883361i	$0.655275\pi$
$4$	1.00000	0.500000
$5$	−0.0296991	−0.0132818	−0.00664092	−	0.999978i	$-0.502114\pi$
$5$	−0.0296991	−0.0132818	−0.00664092	+	0.999978i	$0.502114\pi$
$6$	−1.62360	−0.662831
$7$	−3.06845	−1.15976	−0.579882	−	0.814701i	$-0.696901\pi$
$7$	−3.06845	−1.15976	−0.579882	+	0.814701i	$0.696901\pi$
$8$	1.00000	0.353553
$9$	−0.363928	−0.121309
$10$	−0.0296991	−0.00939168
$11$	−3.06359	−0.923708	−0.461854	−	0.886956i	$-0.652816\pi$
$11$	−3.06359	−0.923708	−0.461854	+	0.886956i	$0.652816\pi$
$12$	−1.62360	−0.468692
$13$	1.09107	0.302607	0.151304	−	0.988487i	$-0.451653\pi$
$13$	1.09107	0.302607	0.151304	+	0.988487i	$0.451653\pi$
$14$	−3.06845	−0.820077
$15$	0.0482194	0.0124502
$16$	1.00000	0.250000
$17$	5.55020	1.34612	0.673060	−	0.739588i	$-0.264979\pi$
$17$	5.55020	1.34612	0.673060	+	0.739588i	$0.264979\pi$
$18$	−0.363928	−0.0857787
$19$	3.30298	0.757755	0.378878	−	0.925447i	$-0.376310\pi$
$19$	3.30298	0.757755	0.378878	+	0.925447i	$0.376310\pi$
$20$	−0.0296991	−0.00664092
$21$	4.98192	1.08714
$22$	−3.06359	−0.653160
$23$	5.36563	1.11881	0.559406	−	0.828894i	$-0.311029\pi$
$23$	5.36563	1.11881	0.559406	+	0.828894i	$0.311029\pi$
$24$	−1.62360	−0.331416
$25$	−4.99912	−0.999824
$26$	1.09107	0.213976
$27$	5.46167	1.05110
$28$	−3.06845	−0.579882
$29$	0.628401	0.116691	0.0583456	−	0.998296i	$-0.481417\pi$
$29$	0.628401	0.116691	0.0583456	+	0.998296i	$0.481417\pi$
$30$	0.0482194	0.00880362
$31$	−9.14820	−1.64307	−0.821533	−	0.570162i	$-0.806881\pi$
$31$	−9.14820	−1.64307	−0.821533	+	0.570162i	$0.806881\pi$
$32$	1.00000	0.176777
$33$	4.97404	0.865870
$34$	5.55020	0.951851
$35$	0.0911301	0.0154038
$36$	−0.363928	−0.0606547
$37$	3.26148	0.536184	0.268092	−	0.963393i	$-0.413607\pi$
$37$	3.26148	0.536184	0.268092	+	0.963393i	$0.413607\pi$
$38$	3.30298	0.535814
$39$	−1.77145	−0.283660
$40$	−0.0296991	−0.00469584
$41$	−7.10029	−1.10888	−0.554439	−	0.832224i	$-0.687067\pi$
$41$	−7.10029	−1.10888	−0.554439	+	0.832224i	$0.687067\pi$
$42$	4.98192	0.768727
$43$	4.06912	0.620534	0.310267	−	0.950649i	$-0.399581\pi$
$43$	4.06912	0.620534	0.310267	+	0.950649i	$0.399581\pi$
$44$	−3.06359	−0.461854
$45$	0.0108083	0.00161121
$46$	5.36563	0.791119
$47$	0.168206	0.0245354	0.0122677	−	0.999925i	$-0.496095\pi$
$47$	0.168206	0.0245354	0.0122677	+	0.999925i	$0.496095\pi$
$48$	−1.62360	−0.234346
$49$	2.41536	0.345051
$50$	−4.99912	−0.706982
$51$	−9.01129	−1.26183
$52$	1.09107	0.151304
$53$	−2.60509	−0.357837	−0.178919	−	0.983864i	$-0.557260\pi$
$53$	−2.60509	−0.357837	−0.178919	+	0.983864i	$0.557260\pi$
$54$	5.46167	0.743239
$55$	0.0909860	0.0122685
$56$	−3.06845	−0.410038
$57$	−5.36271	−0.710308
$58$	0.628401	0.0825131
$59$	14.4345	1.87921	0.939604	−	0.342265i	$-0.111194\pi$
$59$	14.4345	1.87921	0.939604	+	0.342265i	$0.111194\pi$
$60$	0.0482194	0.00622510
$61$	−4.98440	−0.638187	−0.319093	−	0.947723i	$-0.603378\pi$
$61$	−4.98440	−0.638187	−0.319093	+	0.947723i	$0.603378\pi$
$62$	−9.14820	−1.16182
$63$	1.11669	0.140690
$64$	1.00000	0.125000
$65$	−0.0324037	−0.00401918
$66$	4.97404	0.612263
$67$	8.91897	1.08963	0.544813	−	0.838558i	$-0.316601\pi$
$67$	8.91897	1.08963	0.544813	+	0.838558i	$0.316601\pi$
$68$	5.55020	0.673060
$69$	−8.71163	−1.04876
$70$	0.0911301	0.0108921
$71$	−3.19384	−0.379039	−0.189519	−	0.981877i	$-0.560693\pi$
$71$	−3.19384	−0.379039	−0.189519	+	0.981877i	$0.560693\pi$
$72$	−0.363928	−0.0428894
$73$	2.81820	0.329845	0.164923	−	0.986307i	$-0.447263\pi$
$73$	2.81820	0.329845	0.164923	+	0.986307i	$0.447263\pi$
$74$	3.26148	0.379139
$75$	8.11656	0.937220
$76$	3.30298	0.378878
$77$	9.40047	1.07128
$78$	−1.77145	−0.200578
$79$	−3.25476	−0.366189	−0.183095	−	0.983095i	$-0.558611\pi$
$79$	−3.25476	−0.366189	−0.183095	+	0.983095i	$0.558611\pi$
$80$	−0.0296991	−0.00332046
$81$	−7.77577	−0.863975
$82$	−7.10029	−0.784096
$83$	15.7393	1.72761	0.863805	−	0.503825i	$-0.168075\pi$
$83$	15.7393	1.72761	0.863805	+	0.503825i	$0.168075\pi$
$84$	4.98192	0.543572
$85$	−0.164836	−0.0178790
$86$	4.06912	0.438784
$87$	−1.02027	−0.109385
$88$	−3.06359	−0.326580
$89$	−13.5329	−1.43448	−0.717241	−	0.696826i	$-0.754595\pi$
$89$	−13.5329	−1.43448	−0.717241	+	0.696826i	$0.754595\pi$
$90$	0.0108083	0.00113930
$91$	−3.34788	−0.350953
$92$	5.36563	0.559406
$93$	14.8530	1.54018
$94$	0.168206	0.0173492
$95$	−0.0980955	−0.0100644
$96$	−1.62360	−0.165708
$97$	−15.9718	−1.62169	−0.810845	−	0.585261i	$-0.800992\pi$
$97$	−15.9718	−1.62169	−0.810845	+	0.585261i	$0.800992\pi$
$98$	2.41536	0.243988
$99$	1.11493	0.112055
$100$	−4.99912	−0.499912
$101$	9.58171	0.953415	0.476708	−	0.879062i	$-0.341830\pi$
$101$	9.58171	0.953415	0.476708	+	0.879062i	$0.341830\pi$
$102$	−9.01129	−0.892251
$103$	−1.59719	−0.157376	−0.0786881	−	0.996899i	$-0.525073\pi$
$103$	−1.59719	−0.157376	−0.0786881	+	0.996899i	$0.525073\pi$
$104$	1.09107	0.106988
$105$	−0.147959	−0.0144393
$106$	−2.60509	−0.253029
$107$	−2.33635	−0.225863	−0.112932	−	0.993603i	$-0.536024\pi$
$107$	−2.33635	−0.225863	−0.112932	+	0.993603i	$0.536024\pi$
$108$	5.46167	0.525549
$109$	−4.52501	−0.433418	−0.216709	−	0.976236i	$-0.569532\pi$
$109$	−4.52501	−0.433418	−0.216709	+	0.976236i	$0.569532\pi$
$110$	0.0909860	0.00867517
$111$	−5.29533	−0.502611
$112$	−3.06845	−0.289941
$113$	19.7441	1.85737	0.928686	−	0.370867i	$-0.120939\pi$
$113$	19.7441	1.85737	0.928686	+	0.370867i	$0.120939\pi$
$114$	−5.36271	−0.502264
$115$	−0.159354	−0.0148599
$116$	0.628401	0.0583456
$117$	−0.397070	−0.0367091
$118$	14.4345	1.32880
$119$	−17.0305	−1.56118
$120$	0.0482194	0.00440181
$121$	−1.61440	−0.146763
$122$	−4.98440	−0.451266
$123$	11.5280	1.03945
$124$	−9.14820	−0.821533
$125$	0.296965	0.0265613
$126$	1.11669	0.0994830
$127$	0.906314	0.0804224	0.0402112	−	0.999191i	$-0.487197\pi$
$127$	0.906314	0.0804224	0.0402112	+	0.999191i	$0.487197\pi$
$128$	1.00000	0.0883883
$129$	−6.60661	−0.581680
$130$	−0.0324037	−0.00284199
$131$	−6.78992	−0.593238	−0.296619	−	0.954996i	$-0.595859\pi$
$131$	−6.78992	−0.593238	−0.296619	+	0.954996i	$0.595859\pi$
$132$	4.97404	0.432935
$133$	−10.1350	−0.878817
$134$	8.91897	0.770482
$135$	−0.162207	−0.0139605
$136$	5.55020	0.475926
$137$	−21.9962	−1.87926	−0.939629	−	0.342194i	$-0.888830\pi$
$137$	−21.9962	−1.87926	−0.939629	+	0.342194i	$0.888830\pi$
$138$	−8.71163	−0.741583
$139$	−17.3679	−1.47312	−0.736561	−	0.676371i	$-0.763552\pi$
$139$	−17.3679	−1.47312	−0.736561	+	0.676371i	$0.763552\pi$
$140$	0.0911301	0.00770190
$141$	−0.273100	−0.0229991
$142$	−3.19384	−0.268021
$143$	−3.34258	−0.279521
$144$	−0.363928	−0.0303274
$145$	−0.0186629	−0.00154987
$146$	2.81820	0.233236
$147$	−3.92157	−0.323446
$148$	3.26148	0.268092
$149$	−9.64344	−0.790021	−0.395011	−	0.918677i	$-0.629259\pi$
$149$	−9.64344	−0.790021	−0.395011	+	0.918677i	$0.629259\pi$
$150$	8.11656	0.662714
$151$	−16.5063	−1.34327	−0.671633	−	0.740884i	$-0.734407\pi$
$151$	−16.5063	−1.34327	−0.671633	+	0.740884i	$0.734407\pi$
$152$	3.30298	0.267907
$153$	−2.01987	−0.163297
$154$	9.40047	0.757511
$155$	0.271693	0.0218229
$156$	−1.77145	−0.141830
$157$	16.6764	1.33092	0.665462	−	0.746431i	$-0.268234\pi$
$157$	16.6764	1.33092	0.665462	+	0.746431i	$0.268234\pi$
$158$	−3.25476	−0.258935
$159$	4.22963	0.335431
$160$	−0.0296991	−0.00234792
$161$	−16.4641	−1.29756
$162$	−7.77577	−0.610922
$163$	1.92983	0.151156	0.0755778	−	0.997140i	$-0.475920\pi$
$163$	1.92983	0.151156	0.0755778	+	0.997140i	$0.475920\pi$
$164$	−7.10029	−0.554439
$165$	−0.147725	−0.0115004
$166$	15.7393	1.22161
$167$	−4.62632	−0.357995	−0.178998	−	0.983850i	$-0.557285\pi$
$167$	−4.62632	−0.357995	−0.178998	+	0.983850i	$0.557285\pi$
$168$	4.98192	0.384364
$169$	−11.8096	−0.908429
$170$	−0.164836	−0.0126423
$171$	−1.20205	−0.0919229
$172$	4.06912	0.310267
$173$	−3.65661	−0.278007	−0.139003	−	0.990292i	$-0.544390\pi$
$173$	−3.65661	−0.278007	−0.139003	+	0.990292i	$0.544390\pi$
$174$	−1.02027	−0.0773465
$175$	15.3395	1.15956
$176$	−3.06359	−0.230927
$177$	−23.4358	−1.76154
$178$	−13.5329	−1.01433
$179$	−1.93475	−0.144610	−0.0723049	−	0.997383i	$-0.523035\pi$
$179$	−1.93475	−0.144610	−0.0723049	+	0.997383i	$0.523035\pi$
$180$	0.0108083	0.000805607 0
$181$	−21.7813	−1.61899	−0.809496	−	0.587126i	$-0.800259\pi$
$181$	−21.7813	−1.61899	−0.809496	+	0.587126i	$0.800259\pi$
$182$	−3.34788	−0.248161
$183$	8.09266	0.598227
$184$	5.36563	0.395560
$185$	−0.0968630	−0.00712151
$186$	14.8530	1.08907
$187$	−17.0035	−1.24342
$188$	0.168206	0.0122677
$189$	−16.7588	−1.21903
$190$	−0.0980955	−0.00711660
$191$	−2.82708	−0.204560	−0.102280	−	0.994756i	$-0.532614\pi$
$191$	−2.82708	−0.204560	−0.102280	+	0.994756i	$0.532614\pi$
$192$	−1.62360	−0.117173
$193$	−16.2685	−1.17103	−0.585515	−	0.810661i	$-0.699108\pi$
$193$	−16.2685	−1.17103	−0.585515	+	0.810661i	$0.699108\pi$
$194$	−15.9718	−1.14671
$195$	0.0526106	0.00376752
$196$	2.41536	0.172526
$197$	−11.0819	−0.789554	−0.394777	−	0.918777i	$-0.629178\pi$
$197$	−11.0819	−0.789554	−0.394777	+	0.918777i	$0.629178\pi$
$198$	1.11493	0.0792345
$199$	16.3825	1.16132	0.580661	−	0.814145i	$-0.302794\pi$
$199$	16.3825	1.16132	0.580661	+	0.814145i	$0.302794\pi$
$200$	−4.99912	−0.353491
$201$	−14.4808	−1.02140
$202$	9.58171	0.674167
$203$	−1.92821	−0.135334
$204$	−9.01129	−0.630917
$205$	0.210872	0.0147280
$206$	−1.59719	−0.111282
$207$	−1.95271	−0.135722
$208$	1.09107	0.0756518
$209$	−10.1190	−0.699945
$210$	−0.147959	−0.0102101
$211$	10.2386	0.704851	0.352426	−	0.935840i	$-0.385357\pi$
$211$	10.2386	0.704851	0.352426	+	0.935840i	$0.385357\pi$
$212$	−2.60509	−0.178919
$213$	5.18551	0.355305
$214$	−2.33635	−0.159710
$215$	−0.120849	−0.00824184
$216$	5.46167	0.371619
$217$	28.0708	1.90557
$218$	−4.52501	−0.306473
$219$	−4.57562	−0.309192
$220$	0.0909860	0.00613427
$221$	6.05563	0.407346
$222$	−5.29533	−0.355399
$223$	23.8752	1.59880	0.799399	−	0.600800i	$-0.205151\pi$
$223$	23.8752	1.59880	0.799399	+	0.600800i	$0.205151\pi$
$224$	−3.06845	−0.205019
$225$	1.81932	0.121288
$226$	19.7441	1.31336
$227$	−0.0475735	−0.00315757	−0.00157878	−	0.999999i	$-0.500503\pi$
$227$	−0.0475735	−0.00315757	−0.00157878	+	0.999999i	$0.500503\pi$
$228$	−5.36271	−0.355154
$229$	−1.67375	−0.110604	−0.0553022	−	0.998470i	$-0.517612\pi$
$229$	−1.67375	−0.110604	−0.0553022	+	0.998470i	$0.517612\pi$
$230$	−0.159354	−0.0105075
$231$	−15.2626	−1.00420
$232$	0.628401	0.0412566
$233$	4.88184	0.319820	0.159910	−	0.987132i	$-0.448880\pi$
$233$	4.88184	0.319820	0.159910	+	0.987132i	$0.448880\pi$
$234$	−0.397070	−0.0259573
$235$	−0.00499558	−0.000325876 0
$236$	14.4345	0.939604
$237$	5.28442	0.343260
$238$	−17.0305	−1.10392
$239$	−25.7668	−1.66671	−0.833357	−	0.552736i	$-0.813584\pi$
$239$	−25.7668	−1.66671	−0.833357	+	0.552736i	$0.813584\pi$
$240$	0.0482194	0.00311255
$241$	−23.8956	−1.53925	−0.769625	−	0.638496i	$-0.779557\pi$
$241$	−23.8956	−1.53925	−0.769625	+	0.638496i	$0.779557\pi$
$242$	−1.61440	−0.103777
$243$	−3.76028	−0.241222
$244$	−4.98440	−0.319093
$245$	−0.0717340	−0.00458292
$246$	11.5280	0.735000
$247$	3.60377	0.229302
$248$	−9.14820	−0.580911
$249$	−25.5543	−1.61944
$250$	0.296965	0.0187817
$251$	13.5862	0.857551	0.428775	−	0.903411i	$-0.358945\pi$
$251$	13.5862	0.857551	0.428775	+	0.903411i	$0.358945\pi$
$252$	1.11669	0.0703451
$253$	−16.4381	−1.03346
$254$	0.906314	0.0568672
$255$	0.267627	0.0167595
$256$	1.00000	0.0625000
$257$	−21.9532	−1.36940	−0.684701	−	0.728824i	$-0.740067\pi$
$257$	−21.9532	−1.36940	−0.684701	+	0.728824i	$0.740067\pi$
$258$	−6.60661	−0.411310
$259$	−10.0077	−0.621847
$260$	−0.0324037	−0.00200959
$261$	−0.228693	−0.0141557
$262$	−6.78992	−0.419483
$263$	−4.68788	−0.289067	−0.144534	−	0.989500i	$-0.546168\pi$
$263$	−4.68788	−0.289067	−0.144534	+	0.989500i	$0.546168\pi$
$264$	4.97404	0.306131
$265$	0.0773690	0.00475274
$266$	−10.1350	−0.621417
$267$	21.9719	1.34466
$268$	8.91897	0.544813
$269$	14.8047	0.902661	0.451330	−	0.892357i	$-0.350950\pi$
$269$	14.8047	0.902661	0.451330	+	0.892357i	$0.350950\pi$
$270$	−0.162207	−0.00987158
$271$	−0.497467	−0.0302190	−0.0151095	−	0.999886i	$-0.504810\pi$
$271$	−0.497467	−0.0302190	−0.0151095	+	0.999886i	$0.504810\pi$
$272$	5.55020	0.336530
$273$	5.43561	0.328978
$274$	−21.9962	−1.32884
$275$	15.3153	0.923545
$276$	−8.71163	−0.524378
$277$	−23.8249	−1.43150	−0.715751	−	0.698355i	$-0.753916\pi$
$277$	−23.8249	−1.43150	−0.715751	+	0.698355i	$0.753916\pi$
$278$	−17.3679	−1.04165
$279$	3.32929	0.199319
$280$	0.0911301	0.00544606
$281$	−17.5501	−1.04695	−0.523477	−	0.852040i	$-0.675365\pi$
$281$	−17.5501	−1.04695	−0.523477	+	0.852040i	$0.675365\pi$
$282$	−0.273100	−0.0162629
$283$	−16.2301	−0.964782	−0.482391	−	0.875956i	$-0.660232\pi$
$283$	−16.2301	−0.964782	−0.482391	+	0.875956i	$0.660232\pi$
$284$	−3.19384	−0.189519
$285$	0.159268	0.00943420
$286$	−3.34258	−0.197651
$287$	21.7869	1.28604
$288$	−0.363928	−0.0214447
$289$	13.8047	0.812041
$290$	−0.0186629	−0.00109593
$291$	25.9318	1.52015
$292$	2.81820	0.164923
$293$	4.44171	0.259487	0.129744	−	0.991548i	$-0.458585\pi$
$293$	4.44171	0.259487	0.129744	+	0.991548i	$0.458585\pi$
$294$	−3.92157	−0.228711
$295$	−0.428691	−0.0249593
$296$	3.26148	0.189570
$297$	−16.7323	−0.970908
$298$	−9.64344	−0.558630
$299$	5.85426	0.338561
$300$	8.11656	0.468610
$301$	−12.4859	−0.719673
$302$	−16.5063	−0.949833
$303$	−15.5568	−0.893717
$304$	3.30298	0.189439
$305$	0.148032	0.00847630
$306$	−2.01987	−0.115469
$307$	−11.7417	−0.670132	−0.335066	−	0.942195i	$-0.608759\pi$
$307$	−11.7417	−0.670132	−0.335066	+	0.942195i	$0.608759\pi$
$308$	9.40047	0.535641
$309$	2.59320	0.147522
$310$	0.271693	0.0154311
$311$	21.3109	1.20843	0.604215	−	0.796821i	$-0.293487\pi$
$311$	21.3109	1.20843	0.604215	+	0.796821i	$0.293487\pi$
$312$	−1.77145	−0.100289
$313$	−18.4766	−1.04436	−0.522180	−	0.852835i	$-0.674881\pi$
$313$	−18.4766	−1.04436	−0.522180	+	0.852835i	$0.674881\pi$
$314$	16.6764	0.941106
$315$	−0.0331648	−0.00186863
$316$	−3.25476	−0.183095
$317$	8.27275	0.464644	0.232322	−	0.972639i	$-0.425368\pi$
$317$	8.27275	0.464644	0.232322	+	0.972639i	$0.425368\pi$
$318$	4.22963	0.237186
$319$	−1.92517	−0.107789
$320$	−0.0296991	−0.00166023
$321$	3.79329	0.211721
$322$	−16.4641	−0.917511
$323$	18.3322	1.02003
$324$	−7.77577	−0.431987
$325$	−5.45437	−0.302554
$326$	1.92983	0.106883
$327$	7.34681	0.406279
$328$	−7.10029	−0.392048
$329$	−0.516132	−0.0284553
$330$	−0.147725	−0.00813198
$331$	−17.1338	−0.941761	−0.470880	−	0.882197i	$-0.656064\pi$
$331$	−17.1338	−0.941761	−0.470880	+	0.882197i	$0.656064\pi$
$332$	15.7393	0.863805
$333$	−1.18694	−0.0650442
$334$	−4.62632	−0.253141
$335$	−0.264885	−0.0144722
$336$	4.98192	0.271786
$337$	−2.25294	−0.122726	−0.0613628	−	0.998116i	$-0.519545\pi$
$337$	−2.25294	−0.122726	−0.0613628	+	0.998116i	$0.519545\pi$
$338$	−11.8096	−0.642356
$339$	−32.0565	−1.74107
$340$	−0.164836	−0.00893948
$341$	28.0264	1.51771
$342$	−1.20205	−0.0649993
$343$	14.0677	0.759586
$344$	4.06912	0.219392
$345$	0.258728	0.0139294
$346$	−3.65661	−0.196580
$347$	−13.2925	−0.713581	−0.356791	−	0.934184i	$-0.616129\pi$
$347$	−13.2925	−0.713581	−0.356791	+	0.934184i	$0.616129\pi$
$348$	−1.02027	−0.0546923
$349$	−28.1461	−1.50663	−0.753313	−	0.657662i	$-0.771546\pi$
$349$	−28.1461	−1.50663	−0.753313	+	0.657662i	$0.771546\pi$
$350$	15.3395	0.819932
$351$	5.95904	0.318070
$352$	−3.06359	−0.163290
$353$	−17.5825	−0.935824	−0.467912	−	0.883775i	$-0.654994\pi$
$353$	−17.5825	−0.935824	−0.467912	+	0.883775i	$0.654994\pi$
$354$	−23.4358	−1.24560
$355$	0.0948541	0.00503434
$356$	−13.5329	−0.717241
$357$	27.6507	1.46343
$358$	−1.93475	−0.102255
$359$	27.4919	1.45097	0.725484	−	0.688240i	$-0.241616\pi$
$359$	27.4919	1.45097	0.725484	+	0.688240i	$0.241616\pi$
$360$	0.0108083	0.000569650 0
$361$	−8.09033	−0.425807
$362$	−21.7813	−1.14480
$363$	2.62113	0.137574
$364$	−3.34788	−0.175476
$365$	−0.0836979	−0.00438095
$366$	8.09266	0.423010
$367$	23.8446	1.24468	0.622340	−	0.782747i	$-0.286182\pi$
$367$	23.8446	1.24468	0.622340	+	0.782747i	$0.286182\pi$
$368$	5.36563	0.279703
$369$	2.58400	0.134517
$370$	−0.0968630	−0.00503567
$371$	7.99359	0.415007
$372$	14.8530	0.770092
$373$	−1.76461	−0.0913682	−0.0456841	−	0.998956i	$-0.514547\pi$
$373$	−1.76461	−0.0913682	−0.0456841	+	0.998956i	$0.514547\pi$
$374$	−17.0035	−0.879233
$375$	−0.482152	−0.0248982
$376$	0.168206	0.00867459
$377$	0.685627	0.0353116
$378$	−16.7588	−0.861981
$379$	−27.9440	−1.43539	−0.717694	−	0.696359i	$-0.754802\pi$
$379$	−27.9440	−1.43539	−0.717694	+	0.696359i	$0.754802\pi$
$380$	−0.0980955	−0.00503219
$381$	−1.47149	−0.0753868
$382$	−2.82708	−0.144646
$383$	−4.48945	−0.229400	−0.114700	−	0.993400i	$-0.536591\pi$
$383$	−4.48945	−0.229400	−0.114700	+	0.993400i	$0.536591\pi$
$384$	−1.62360	−0.0828539
$385$	−0.279186	−0.0142286
$386$	−16.2685	−0.828044
$387$	−1.48087	−0.0752767
$388$	−15.9718	−0.810845
$389$	25.5804	1.29698	0.648490	−	0.761223i	$-0.275401\pi$
$389$	25.5804	1.29698	0.648490	+	0.761223i	$0.275401\pi$
$390$	0.0526106	0.00266404
$391$	29.7803	1.50606
$392$	2.41536	0.121994
$393$	11.0241	0.556092
$394$	−11.0819	−0.558299
$395$	0.0966635	0.00486367
$396$	1.11493	0.0560273
$397$	7.76224	0.389575	0.194788	−	0.980845i	$-0.437598\pi$
$397$	7.76224	0.389575	0.194788	+	0.980845i	$0.437598\pi$
$398$	16.3825	0.821179
$399$	16.4552	0.823790
$400$	−4.99912	−0.249956
$401$	−5.30628	−0.264983	−0.132492	−	0.991184i	$-0.542298\pi$
$401$	−5.30628	−0.264983	−0.132492	+	0.991184i	$0.542298\pi$
$402$	−14.4808	−0.722238
$403$	−9.98129	−0.497204
$404$	9.58171	0.476708
$405$	0.230933	0.0114752
$406$	−1.92821	−0.0956957
$407$	−9.99185	−0.495277
$408$	−9.01129	−0.446125
$409$	18.7552	0.927387	0.463694	−	0.885996i	$-0.346524\pi$
$409$	18.7552	0.927387	0.463694	+	0.885996i	$0.346524\pi$
$410$	0.210872	0.0104142
$411$	35.7129	1.76159
$412$	−1.59719	−0.0786881
$413$	−44.2914	−2.17944
$414$	−1.95271	−0.0959702
$415$	−0.467443	−0.0229459
$416$	1.09107	0.0534939
$417$	28.1984	1.38088
$418$	−10.1190	−0.494936
$419$	−5.86784	−0.286663	−0.143331	−	0.989675i	$-0.545781\pi$
$419$	−5.86784	−0.286663	−0.143331	+	0.989675i	$0.545781\pi$
$420$	−0.147959	−0.00721964
$421$	18.0391	0.879171	0.439585	−	0.898201i	$-0.355125\pi$
$421$	18.0391	0.879171	0.439585	+	0.898201i	$0.355125\pi$
$422$	10.2386	0.498405
$423$	−0.0612151	−0.00297638
$424$	−2.60509	−0.126515
$425$	−27.7461	−1.34588
$426$	5.18551	0.251239
$427$	15.2944	0.740146
$428$	−2.33635	−0.112932
$429$	5.42701	0.262019
$430$	−0.120849	−0.00582786
$431$	−17.5008	−0.842982	−0.421491	−	0.906833i	$-0.638493\pi$
$431$	−17.5008	−0.842982	−0.421491	+	0.906833i	$0.638493\pi$
$432$	5.46167	0.262775
$433$	31.9651	1.53614	0.768072	−	0.640363i	$-0.221216\pi$
$433$	31.9651	1.53614	0.768072	+	0.640363i	$0.221216\pi$
$434$	28.0708	1.34744
$435$	0.0303011	0.00145283
$436$	−4.52501	−0.216709
$437$	17.7226	0.847785
$438$	−4.57562	−0.218632
$439$	10.4049	0.496600	0.248300	−	0.968683i	$-0.420128\pi$
$439$	10.4049	0.496600	0.248300	+	0.968683i	$0.420128\pi$
$440$	0.0909860	0.00433759
$441$	−0.879018	−0.0418580
$442$	6.05563	0.288037
$443$	30.9506	1.47051	0.735253	−	0.677793i	$-0.237063\pi$
$443$	30.9506	1.47051	0.735253	+	0.677793i	$0.237063\pi$
$444$	−5.29533	−0.251305
$445$	0.401914	0.0190526
$446$	23.8752	1.13052
$447$	15.6571	0.740554
$448$	−3.06845	−0.144970
$449$	29.8608	1.40922	0.704608	−	0.709596i	$-0.251123\pi$
$449$	29.8608	1.40922	0.704608	+	0.709596i	$0.251123\pi$
$450$	1.81932	0.0857636
$451$	21.7524	1.02428
$452$	19.7441	0.928686
$453$	26.7997	1.25916
$454$	−0.0475735	−0.00223274
$455$	0.0994290	0.00466130
$456$	−5.36271	−0.251132
$457$	0.557953	0.0260999	0.0130500	−	0.999915i	$-0.495846\pi$
$457$	0.557953	0.0260999	0.0130500	+	0.999915i	$0.495846\pi$
$458$	−1.67375	−0.0782092
$459$	30.3133	1.41491
$460$	−0.159354	−0.00742994
$461$	−1.88430	−0.0877608	−0.0438804	−	0.999037i	$-0.513972\pi$
$461$	−1.88430	−0.0877608	−0.0438804	+	0.999037i	$0.513972\pi$
$462$	−15.2626	−0.710080
$463$	−17.9782	−0.835517	−0.417759	−	0.908558i	$-0.637184\pi$
$463$	−17.9782	−0.835517	−0.417759	+	0.908558i	$0.637184\pi$
$464$	0.628401	0.0291728
$465$	−0.441121	−0.0204565
$466$	4.88184	0.226147
$467$	3.44813	0.159560	0.0797801	−	0.996812i	$-0.474578\pi$
$467$	3.44813	0.159560	0.0797801	+	0.996812i	$0.474578\pi$
$468$	−0.397070	−0.0183546
$469$	−27.3674	−1.26371
$470$	−0.00499558	−0.000230429 0
$471$	−27.0758	−1.24759
$472$	14.4345	0.664400
$473$	−12.4661	−0.573193
$474$	5.28442	0.242722
$475$	−16.5120	−0.757622
$476$	−17.0305	−0.780591
$477$	0.948068	0.0434090
$478$	−25.7668	−1.17854
$479$	−23.1502	−1.05776	−0.528880	−	0.848697i	$-0.677388\pi$
$479$	−23.1502	−1.05776	−0.528880	+	0.848697i	$0.677388\pi$
$480$	0.0482194	0.00220091
$481$	3.55849	0.162253
$482$	−23.8956	−1.08841
$483$	26.7312	1.21631
$484$	−1.61440	−0.0733817
$485$	0.474348	0.0215390
$486$	−3.76028	−0.170570
$487$	−39.4945	−1.78967	−0.894834	−	0.446400i	$-0.852706\pi$
$487$	−39.4945	−1.78967	−0.894834	+	0.446400i	$0.852706\pi$
$488$	−4.98440	−0.225633
$489$	−3.13326	−0.141691
$490$	−0.0717340	−0.00324061
$491$	−3.99129	−0.180125	−0.0900623	−	0.995936i	$-0.528707\pi$
$491$	−3.99129	−0.180125	−0.0900623	+	0.995936i	$0.528707\pi$
$492$	11.5280	0.519723
$493$	3.48775	0.157080
$494$	3.60377	0.162141
$495$	−0.0331124	−0.00148829
$496$	−9.14820	−0.410766
$497$	9.80012	0.439596
$498$	−25.5543	−1.14511
$499$	2.88875	0.129318	0.0646592	−	0.997907i	$-0.479404\pi$
$499$	2.88875	0.129318	0.0646592	+	0.997907i	$0.479404\pi$
$500$	0.296965	0.0132807
$501$	7.51128	0.335579
$502$	13.5862	0.606380
$503$	−6.30147	−0.280969	−0.140484	−	0.990083i	$-0.544866\pi$
$503$	−6.30147	−0.280969	−0.140484	+	0.990083i	$0.544866\pi$
$504$	1.11669	0.0497415
$505$	−0.284568	−0.0126631
$506$	−16.4381	−0.730763
$507$	19.1740	0.851547
$508$	0.906314	0.0402112
$509$	−22.6814	−1.00534	−0.502669	−	0.864479i	$-0.667648\pi$
$509$	−22.6814	−1.00534	−0.502669	+	0.864479i	$0.667648\pi$
$510$	0.267627	0.0118507
$511$	−8.64749	−0.382542
$512$	1.00000	0.0441942
$513$	18.0398	0.796475
$514$	−21.9532	−0.968313
$515$	0.0474352	0.00209025
$516$	−6.60661	−0.290840
$517$	−0.515316	−0.0226636
$518$	−10.0077	−0.439712
$519$	5.93686	0.260599
$520$	−0.0324037	−0.00142100
$521$	−12.7444	−0.558341	−0.279170	−	0.960242i	$-0.590059\pi$
$521$	−12.7444	−0.558341	−0.279170	+	0.960242i	$0.590059\pi$
$522$	−0.228693	−0.0100096
$523$	−3.70312	−0.161926	−0.0809630	−	0.996717i	$-0.525800\pi$
$523$	−3.70312	−0.161926	−0.0809630	+	0.996717i	$0.525800\pi$
$524$	−6.78992	−0.296619
$525$	−24.9052	−1.08695
$526$	−4.68788	−0.204401
$527$	−50.7743	−2.21176
$528$	4.97404	0.216468
$529$	5.78999	0.251739
$530$	0.0773690	0.00336069
$531$	−5.25311	−0.227966
$532$	−10.1350	−0.439408
$533$	−7.74689	−0.335555
$534$	21.9719	0.950819
$535$	0.0693875	0.00299988
$536$	8.91897	0.385241
$537$	3.14125	0.135555
$538$	14.8047	0.638278
$539$	−7.39968	−0.318727
$540$	−0.162207	−0.00698026
$541$	17.5041	0.752562	0.376281	−	0.926506i	$-0.377203\pi$
$541$	17.5041	0.752562	0.376281	+	0.926506i	$0.377203\pi$
$542$	−0.497467	−0.0213680
$543$	35.3641	1.51762
$544$	5.55020	0.237963
$545$	0.134389	0.00575659
$546$	5.43561	0.232623
$547$	21.4714	0.918053	0.459026	−	0.888423i	$-0.348198\pi$
$547$	21.4714	0.918053	0.459026	+	0.888423i	$0.348198\pi$
$548$	−21.9962	−0.939629
$549$	1.81396	0.0774181
$550$	15.3153	0.653045
$551$	2.07560	0.0884233
$552$	−8.71163	−0.370792
$553$	9.98706	0.424693
$554$	−23.8249	−1.01222
$555$	0.157267	0.00667560
$556$	−17.3679	−0.736561
$557$	−38.4487	−1.62912	−0.814561	−	0.580077i	$-0.803022\pi$
$557$	−38.4487	−1.62912	−0.814561	+	0.580077i	$0.803022\pi$
$558$	3.32929	0.140940
$559$	4.43968	0.187778
$560$	0.0911301	0.00385095
$561$	27.6069	1.16557
$562$	−17.5501	−0.740308
$563$	−41.8008	−1.76169	−0.880847	−	0.473400i	$-0.843026\pi$
$563$	−41.8008	−1.76169	−0.880847	+	0.473400i	$0.843026\pi$
$564$	−0.273100	−0.0114996
$565$	−0.586383	−0.0246693
$566$	−16.2301	−0.682204
$567$	23.8595	1.00201
$568$	−3.19384	−0.134010
$569$	25.8954	1.08559	0.542796	−	0.839865i	$-0.317366\pi$
$569$	25.8954	1.08559	0.542796	+	0.839865i	$0.317366\pi$
$570$	0.159268	0.00667099
$571$	3.03341	0.126944	0.0634721	−	0.997984i	$-0.479783\pi$
$571$	3.03341	0.126944	0.0634721	+	0.997984i	$0.479783\pi$
$572$	−3.34258	−0.139760
$573$	4.59005	0.191752
$574$	21.7869	0.909366
$575$	−26.8234	−1.11861
$576$	−0.363928	−0.0151637
$577$	20.0565	0.834964	0.417482	−	0.908685i	$-0.362913\pi$
$577$	20.0565	0.834964	0.417482	+	0.908685i	$0.362913\pi$
$578$	13.8047	0.574200
$579$	26.4135	1.09771
$580$	−0.0186629	−0.000774937 0
$581$	−48.2951	−2.00362
$582$	25.9318	1.07491
$583$	7.98095	0.330537
$584$	2.81820	0.116618
$585$	0.0117926	0.000487565 0
$586$	4.44171	0.183485
$587$	−17.4302	−0.719421	−0.359710	−	0.933064i	$-0.617124\pi$
$587$	−17.4302	−0.719421	−0.359710	+	0.933064i	$0.617124\pi$
$588$	−3.92157	−0.161723
$589$	−30.2163	−1.24504
$590$	−0.428691	−0.0176489
$591$	17.9926	0.740116
$592$	3.26148	0.134046
$593$	18.1026	0.743384	0.371692	−	0.928356i	$-0.378778\pi$
$593$	18.1026	0.743384	0.371692	+	0.928356i	$0.378778\pi$
$594$	−16.7323	−0.686536
$595$	0.505790	0.0207354
$596$	−9.64344	−0.395011
$597$	−26.5986	−1.08861
$598$	5.85426	0.239398
$599$	7.20374	0.294337	0.147168	−	0.989111i	$-0.452984\pi$
$599$	7.20374	0.294337	0.147168	+	0.989111i	$0.452984\pi$
$600$	8.11656	0.331357
$601$	8.58219	0.350075	0.175037	−	0.984562i	$-0.443995\pi$
$601$	8.58219	0.350075	0.175037	+	0.984562i	$0.443995\pi$
$602$	−12.4859	−0.508886
$603$	−3.24587	−0.132182
$604$	−16.5063	−0.671633
$605$	0.0479462	0.00194929
$606$	−15.5568	−0.631954
$607$	−2.35851	−0.0957289	−0.0478645	−	0.998854i	$-0.515242\pi$
$607$	−2.35851	−0.0957289	−0.0478645	+	0.998854i	$0.515242\pi$
$608$	3.30298	0.133953
$609$	3.13065	0.126860
$610$	0.148032	0.00599365
$611$	0.183524	0.00742460
$612$	−2.01987	−0.0816486
$613$	−19.1109	−0.771883	−0.385942	−	0.922523i	$-0.626123\pi$
$613$	−19.1109	−0.771883	−0.385942	+	0.922523i	$0.626123\pi$
$614$	−11.7417	−0.473855
$615$	−0.342372	−0.0138058
$616$	9.40047	0.378756
$617$	−13.1148	−0.527982	−0.263991	−	0.964525i	$-0.585039\pi$
$617$	−13.1148	−0.527982	−0.263991	+	0.964525i	$0.585039\pi$
$618$	2.59320	0.104314
$619$	−38.9049	−1.56372	−0.781861	−	0.623453i	$-0.785729\pi$
$619$	−38.9049	−1.56372	−0.781861	+	0.623453i	$0.785729\pi$
$620$	0.271693	0.0109115
$621$	29.3053	1.17598
$622$	21.3109	0.854490
$623$	41.5249	1.66366
$624$	−1.77145	−0.0709149
$625$	24.9868	0.999471
$626$	−18.4766	−0.738474
$627$	16.4292	0.656118
$628$	16.6764	0.665462
$629$	18.1019	0.721768
$630$	−0.0331648	−0.00132132
$631$	−5.08681	−0.202503	−0.101251	−	0.994861i	$-0.532285\pi$
$631$	−5.08681	−0.202503	−0.101251	+	0.994861i	$0.532285\pi$
$632$	−3.25476	−0.129467
$633$	−16.6233	−0.660717
$634$	8.27275	0.328553
$635$	−0.0269167	−0.00106816
$636$	4.22963	0.167716
$637$	2.63532	0.104415
$638$	−1.92517	−0.0762180
$639$	1.16233	0.0459810
$640$	−0.0296991	−0.00117396
$641$	−0.711126	−0.0280878	−0.0140439	−	0.999901i	$-0.504470\pi$
$641$	−0.711126	−0.0280878	−0.0140439	+	0.999901i	$0.504470\pi$
$642$	3.79329	0.149709
$643$	−20.9710	−0.827017	−0.413508	−	0.910500i	$-0.635697\pi$
$643$	−20.9710	−0.827017	−0.413508	+	0.910500i	$0.635697\pi$
$644$	−16.4641	−0.648778
$645$	0.196210	0.00772578
$646$	18.3322	0.721270
$647$	−20.2405	−0.795735	−0.397867	−	0.917443i	$-0.630250\pi$
$647$	−20.2405	−0.795735	−0.397867	+	0.917443i	$0.630250\pi$
$648$	−7.77577	−0.305461
$649$	−44.2213	−1.73584
$650$	−5.45437	−0.213938
$651$	−45.5756	−1.78625
$652$	1.92983	0.0755778
$653$	38.0145	1.48762	0.743811	−	0.668390i	$-0.233016\pi$
$653$	38.0145	1.48762	0.743811	+	0.668390i	$0.233016\pi$
$654$	7.34681	0.287283
$655$	0.201654	0.00787929
$656$	−7.10029	−0.277220
$657$	−1.02562	−0.0400133
$658$	−0.516132	−0.0201209
$659$	−12.3610	−0.481517	−0.240759	−	0.970585i	$-0.577396\pi$
$659$	−12.3610	−0.481517	−0.240759	+	0.970585i	$0.577396\pi$
$660$	−0.147725	−0.00575018
$661$	−19.3211	−0.751502	−0.375751	−	0.926721i	$-0.622615\pi$
$661$	−19.3211	−0.751502	−0.375751	+	0.926721i	$0.622615\pi$
$662$	−17.1338	−0.665925
$663$	−9.83192	−0.381840
$664$	15.7393	0.610803
$665$	0.301001	0.0116723
$666$	−1.18694	−0.0459932
$667$	3.37177	0.130555
$668$	−4.62632	−0.178998
$669$	−38.7637	−1.49869
$670$	−0.264885	−0.0102334
$671$	15.2702	0.589498
$672$	4.98192	0.192182
$673$	9.33159	0.359706	0.179853	−	0.983693i	$-0.442438\pi$
$673$	9.33159	0.359706	0.179853	+	0.983693i	$0.442438\pi$
$674$	−2.25294	−0.0867801
$675$	−27.3035	−1.05091
$676$	−11.8096	−0.454214
$677$	9.35270	0.359454	0.179727	−	0.983717i	$-0.442479\pi$
$677$	9.35270	0.359454	0.179727	+	0.983717i	$0.442479\pi$
$678$	−32.0565	−1.23112
$679$	49.0086	1.88078
$680$	−0.164836	−0.00632117
$681$	0.0772403	0.00295986
$682$	28.0264	1.07318
$683$	−25.2949	−0.967882	−0.483941	−	0.875101i	$-0.660795\pi$
$683$	−25.2949	−0.967882	−0.483941	+	0.875101i	$0.660795\pi$
$684$	−1.20205	−0.0459614
$685$	0.653266	0.0249600
$686$	14.0677	0.537108
$687$	2.71750	0.103679
$688$	4.06912	0.155134
$689$	−2.84233	−0.108284
$690$	0.258728	0.00984959
$691$	8.92001	0.339333	0.169667	−	0.985502i	$-0.445731\pi$
$691$	8.92001	0.339333	0.169667	+	0.985502i	$0.445731\pi$
$692$	−3.65661	−0.139003
$693$	−3.42110	−0.129957
$694$	−13.2925	−0.504578
$695$	0.515810	0.0195658
$696$	−1.02027	−0.0386733
$697$	−39.4080	−1.49268
$698$	−28.1461	−1.06535
$699$	−7.92615	−0.299794
$700$	15.3395	0.579779
$701$	−9.21822	−0.348167	−0.174084	−	0.984731i	$-0.555696\pi$
$701$	−9.21822	−0.348167	−0.174084	+	0.984731i	$0.555696\pi$
$702$	5.95904	0.224910
$703$	10.7726	0.406296
$704$	−3.06359	−0.115464
$705$	0.00811082	0.000305471 0
$706$	−17.5825	−0.661728
$707$	−29.4009	−1.10574
$708$	−23.4358	−0.880770
$709$	−8.38423	−0.314876	−0.157438	−	0.987529i	$-0.550324\pi$
$709$	−8.38423	−0.314876	−0.157438	+	0.987529i	$0.550324\pi$
$710$	0.0948541	0.00355981
$711$	1.18450	0.0444222
$712$	−13.5329	−0.507166
$713$	−49.0859	−1.83828
$714$	27.6507	1.03480
$715$	0.0992717	0.00371255
$716$	−1.93475	−0.0723049
$717$	41.8349	1.56235
$718$	27.4919	1.02599
$719$	47.9403	1.78787	0.893936	−	0.448195i	$-0.147933\pi$
$719$	47.9403	1.78787	0.893936	+	0.448195i	$0.147933\pi$
$720$	0.0108083	0.000402803 0
$721$	4.90090	0.182519
$722$	−8.09033	−0.301091
$723$	38.7968	1.44287
$724$	−21.7813	−0.809496
$725$	−3.14145	−0.116671
$726$	2.62113	0.0972794
$727$	−2.04077	−0.0756879	−0.0378440	−	0.999284i	$-0.512049\pi$
$727$	−2.04077	−0.0756879	−0.0378440	+	0.999284i	$0.512049\pi$
$728$	−3.34788	−0.124081
$729$	29.4325	1.09009
$730$	−0.0836979	−0.00309780
$731$	22.5844	0.835314
$732$	8.09266	0.299113
$733$	−29.0618	−1.07342	−0.536710	−	0.843767i	$-0.680333\pi$
$733$	−29.0618	−1.07342	−0.536710	+	0.843767i	$0.680333\pi$
$734$	23.8446	0.880122
$735$	0.116467	0.00429596
$736$	5.36563	0.197780
$737$	−27.3241	−1.00650
$738$	2.58400	0.0951182
$739$	31.8782	1.17266	0.586329	−	0.810073i	$-0.300572\pi$
$739$	31.8782	1.17266	0.586329	+	0.810073i	$0.300572\pi$
$740$	−0.0968630	−0.00356076
$741$	−5.85107	−0.214945
$742$	7.99359	0.293454
$743$	38.9248	1.42801	0.714007	−	0.700139i	$-0.246879\pi$
$743$	38.9248	1.42801	0.714007	+	0.700139i	$0.246879\pi$
$744$	14.8530	0.544537
$745$	0.286402	0.0104929
$746$	−1.76461	−0.0646071
$747$	−5.72797	−0.209576
$748$	−17.0035	−0.621711
$749$	7.16896	0.261948
$750$	−0.482152	−0.0176057
$751$	13.2124	0.482128	0.241064	−	0.970509i	$-0.422504\pi$
$751$	13.2124	0.482128	0.241064	+	0.970509i	$0.422504\pi$
$752$	0.168206	0.00613386
$753$	−22.0585	−0.803855
$754$	0.685627	0.0249691
$755$	0.490223	0.0178411
$756$	−16.7588	−0.609513
$757$	−7.55110	−0.274449	−0.137225	−	0.990540i	$-0.543818\pi$
$757$	−7.55110	−0.274449	−0.137225	+	0.990540i	$0.543818\pi$
$758$	−27.9440	−1.01497
$759$	26.6889	0.968745
$760$	−0.0980955	−0.00355830
$761$	34.2578	1.24185	0.620923	−	0.783872i	$-0.286758\pi$
$761$	34.2578	1.24185	0.620923	+	0.783872i	$0.286758\pi$
$762$	−1.47149	−0.0533065
$763$	13.8848	0.502662
$764$	−2.82708	−0.102280
$765$	0.0599885	0.00216889
$766$	−4.48945	−0.162210
$767$	15.7490	0.568662
$768$	−1.62360	−0.0585866
$769$	−46.6397	−1.68187	−0.840935	−	0.541136i	$-0.817994\pi$
$769$	−46.6397	−1.68187	−0.840935	+	0.541136i	$0.817994\pi$
$770$	−0.279186	−0.0100611
$771$	35.6431	1.28366
$772$	−16.2685	−0.585515
$773$	−23.4807	−0.844542	−0.422271	−	0.906470i	$-0.638767\pi$
$773$	−23.4807	−0.844542	−0.422271	+	0.906470i	$0.638767\pi$
$774$	−1.48087	−0.0532287
$775$	45.7329	1.64278
$776$	−15.9718	−0.573354
$777$	16.2484	0.582910
$778$	25.5804	0.917103
$779$	−23.4521	−0.840259
$780$	0.0526106	0.00188376
$781$	9.78462	0.350121
$782$	29.7803	1.06494
$783$	3.43212	0.122654
$784$	2.41536	0.0862628
$785$	−0.495275	−0.0176771
$786$	11.0241	0.393217
$787$	11.8630	0.422870	0.211435	−	0.977392i	$-0.432186\pi$
$787$	11.8630	0.422870	0.211435	+	0.977392i	$0.432186\pi$
$788$	−11.0819	−0.394777
$789$	7.61124	0.270967
$790$	0.0966635	0.00343913
$791$	−60.5838	−2.15411
$792$	1.11493	0.0396173
$793$	−5.43831	−0.193120
$794$	7.76224	0.275471
$795$	−0.125616	−0.00445515
$796$	16.3825	0.580661
$797$	52.5884	1.86278	0.931388	−	0.364028i	$-0.118599\pi$
$797$	52.5884	1.86278	0.931388	+	0.364028i	$0.118599\pi$
$798$	16.4552	0.582507
$799$	0.933579	0.0330277
$800$	−4.99912	−0.176746
$801$	4.92499	0.174016
$802$	−5.30628	−0.187371
$803$	−8.63381	−0.304681
$804$	−14.4808	−0.510699
$805$	0.488970	0.0172339
$806$	−9.98129	−0.351576
$807$	−24.0370	−0.846141
$808$	9.58171	0.337083
$809$	−18.3053	−0.643580	−0.321790	−	0.946811i	$-0.604285\pi$
$809$	−18.3053	−0.643580	−0.321790	+	0.946811i	$0.604285\pi$
$810$	0.230933	0.00811417
$811$	−17.9579	−0.630585	−0.315293	−	0.948994i	$-0.602103\pi$
$811$	−17.9579	−0.630585	−0.315293	+	0.948994i	$0.602103\pi$
$812$	−1.92821	−0.0676671
$813$	0.807687	0.0283268
$814$	−9.99185	−0.350214
$815$	−0.0573141	−0.00200763
$816$	−9.01129	−0.315458
$817$	13.4402	0.470213
$818$	18.7552	0.655762
$819$	1.21839	0.0425739
$820$	0.210872	0.00736398
$821$	2.11187	0.0737047	0.0368524	−	0.999321i	$-0.488267\pi$
$821$	2.11187	0.0737047	0.0368524	+	0.999321i	$0.488267\pi$
$822$	35.7129	1.24563
$823$	41.6790	1.45284	0.726419	−	0.687252i	$-0.241183\pi$
$823$	41.6790	1.45284	0.726419	+	0.687252i	$0.241183\pi$
$824$	−1.59719	−0.0556409
$825$	−24.8658	−0.865717
$826$	−44.2914	−1.54109
$827$	−17.0773	−0.593837	−0.296918	−	0.954903i	$-0.595959\pi$
$827$	−17.0773	−0.593837	−0.296918	+	0.954903i	$0.595959\pi$
$828$	−1.95271	−0.0678612
$829$	16.6387	0.577887	0.288943	−	0.957346i	$-0.406696\pi$
$829$	16.6387	0.577887	0.288943	+	0.957346i	$0.406696\pi$
$830$	−0.467443	−0.0162252
$831$	38.6821	1.34187
$832$	1.09107	0.0378259
$833$	13.4057	0.464481
$834$	28.1984	0.976431
$835$	0.137397	0.00475483
$836$	−10.1190	−0.349972
$837$	−49.9644	−1.72702
$838$	−5.86784	−0.202701
$839$	−33.5423	−1.15801	−0.579004	−	0.815325i	$-0.696558\pi$
$839$	−33.5423	−1.15801	−0.579004	+	0.815325i	$0.696558\pi$
$840$	−0.147959	−0.00510506
$841$	−28.6051	−0.986383
$842$	18.0391	0.621668
$843$	28.4944	0.981398
$844$	10.2386	0.352426
$845$	0.350734	0.0120656
$846$	−0.0612151	−0.00210462
$847$	4.95369	0.170211
$848$	−2.60509	−0.0894593
$849$	26.3512	0.904372
$850$	−27.7461	−0.951683
$851$	17.4999	0.599889
$852$	5.18551	0.177653
$853$	−3.93647	−0.134782	−0.0673912	−	0.997727i	$-0.521468\pi$
$853$	−3.93647	−0.134782	−0.0673912	+	0.997727i	$0.521468\pi$
$854$	15.2944	0.523362
$855$	0.0356997	0.00122091
$856$	−2.33635	−0.0798548
$857$	−9.01158	−0.307830	−0.153915	−	0.988084i	$-0.549188\pi$
$857$	−9.01158	−0.307830	−0.153915	+	0.988084i	$0.549188\pi$
$858$	5.42701	0.185275
$859$	50.3233	1.71701	0.858505	−	0.512805i	$-0.171394\pi$
$859$	50.3233	1.71701	0.858505	+	0.512805i	$0.171394\pi$
$860$	−0.120849	−0.00412092
$861$	−35.3731	−1.20551
$862$	−17.5008	−0.596078
$863$	−4.64075	−0.157973	−0.0789866	−	0.996876i	$-0.525168\pi$
$863$	−4.64075	−0.157973	−0.0789866	+	0.996876i	$0.525168\pi$
$864$	5.46167	0.185810
$865$	0.108598	0.00369244
$866$	31.9651	1.08622
$867$	−22.4133	−0.761195
$868$	28.0708	0.952783
$869$	9.97126	0.338252
$870$	0.0303011	0.00102730
$871$	9.73119	0.329729
$872$	−4.52501	−0.153236
$873$	5.81259	0.196726
$874$	17.7226	0.599475
$875$	−0.911221	−0.0308049
$876$	−4.57562	−0.154596
$877$	13.1459	0.443906	0.221953	−	0.975057i	$-0.428757\pi$
$877$	13.1459	0.443906	0.221953	+	0.975057i	$0.428757\pi$
$878$	10.4049	0.351149
$879$	−7.21155	−0.243239
$880$	0.0909860	0.00306714
$881$	−40.5439	−1.36596	−0.682980	−	0.730437i	$-0.739316\pi$
$881$	−40.5439	−1.36596	−0.682980	+	0.730437i	$0.739316\pi$
$882$	−0.879018	−0.0295981
$883$	14.0882	0.474107	0.237054	−	0.971497i	$-0.423818\pi$
$883$	14.0882	0.474107	0.237054	+	0.971497i	$0.423818\pi$
$884$	6.05563	0.203673
$885$	0.696021	0.0233965
$886$	30.9506	1.03980
$887$	7.42734	0.249386	0.124693	−	0.992195i	$-0.460205\pi$
$887$	7.42734	0.249386	0.124693	+	0.992195i	$0.460205\pi$
$888$	−5.29533	−0.177700
$889$	−2.78098	−0.0932710
$890$	0.401914	0.0134722
$891$	23.8218	0.798060
$892$	23.8752	0.799399
$893$	0.555582	0.0185919
$894$	15.6571	0.523651
$895$	0.0574603	0.00192069
$896$	−3.06845	−0.102510
$897$	−9.50497	−0.317362
$898$	29.8608	0.996467
$899$	−5.74874	−0.191731
$900$	1.81932	0.0606440
$901$	−14.4588	−0.481692
$902$	21.7524	0.724276
$903$	20.2720	0.674611
$904$	19.7441	0.656680
$905$	0.646885	0.0215032
$906$	26.7997	0.890359
$907$	33.1963	1.10226	0.551132	−	0.834418i	$-0.314196\pi$
$907$	33.1963	1.10226	0.551132	+	0.834418i	$0.314196\pi$
$908$	−0.0475735	−0.00157878
$909$	−3.48705	−0.115658
$910$	0.0994290	0.00329604
$911$	−38.7815	−1.28489	−0.642444	−	0.766333i	$-0.722079\pi$
$911$	−38.7815	−1.28489	−0.642444	+	0.766333i	$0.722079\pi$
$912$	−5.36271	−0.177577
$913$	−48.2188	−1.59581
$914$	0.557953	0.0184554
$915$	−0.240345	−0.00794555
$916$	−1.67375	−0.0553022
$917$	20.8345	0.688016
$918$	30.3133	1.00049
$919$	24.1823	0.797701	0.398850	−	0.917016i	$-0.369409\pi$
$919$	24.1823	0.797701	0.398850	+	0.917016i	$0.369409\pi$
$920$	−0.159354	−0.00525376
$921$	19.0637	0.628172
$922$	−1.88430	−0.0620562
$923$	−3.48469	−0.114700
$924$	−15.2626	−0.502102
$925$	−16.3045	−0.536089
$926$	−17.9782	−0.590800
$927$	0.581264	0.0190912
$928$	0.628401	0.0206283
$929$	0.600157	0.0196905	0.00984526	−	0.999952i	$-0.496866\pi$
$929$	0.600157	0.0196905	0.00984526	+	0.999952i	$0.496866\pi$
$930$	−0.441121	−0.0144649
$931$	7.97788	0.261464
$932$	4.88184	0.159910
$933$	−34.6004	−1.13276
$934$	3.44813	0.112826
$935$	0.504990	0.0165149
$936$	−0.397070	−0.0129786
$937$	3.00277	0.0980963	0.0490481	−	0.998796i	$-0.484381\pi$
$937$	3.00277	0.0980963	0.0490481	+	0.998796i	$0.484381\pi$
$938$	−27.3674	−0.893576
$939$	29.9986	0.978967
$940$	−0.00499558	−0.000162938 0
$941$	−7.94838	−0.259110	−0.129555	−	0.991572i	$-0.541355\pi$
$941$	−7.94838	−0.259110	−0.129555	+	0.991572i	$0.541355\pi$
$942$	−27.0758	−0.882178
$943$	−38.0975	−1.24063
$944$	14.4345	0.469802
$945$	0.497722	0.0161909
$946$	−12.4661	−0.405308
$947$	−16.9212	−0.549865	−0.274933	−	0.961463i	$-0.588656\pi$
$947$	−16.9212	−0.549865	−0.274933	+	0.961463i	$0.588656\pi$
$948$	5.28442	0.171630
$949$	3.07484	0.0998135
$950$	−16.5120	−0.535719
$951$	−13.4316	−0.435550
$952$	−17.0305	−0.551961
$953$	15.4653	0.500970	0.250485	−	0.968120i	$-0.419410\pi$
$953$	15.4653	0.500970	0.250485	+	0.968120i	$0.419410\pi$
$954$	0.948068	0.0306948
$955$	0.0839618	0.00271694
$956$	−25.7668	−0.833357
$957$	3.12569	0.101039
$958$	−23.1502	−0.747949
$959$	67.4940	2.17950
$960$	0.0482194	0.00155627
$961$	52.6896	1.69966
$962$	3.55849	0.114730
$963$	0.850264	0.0273994
$964$	−23.8956	−0.769625
$965$	0.483159	0.0155534
$966$	26.7312	0.860061
$967$	−42.5324	−1.36775	−0.683874	−	0.729600i	$-0.739706\pi$
$967$	−42.5324	−1.36775	−0.683874	+	0.729600i	$0.739706\pi$
$968$	−1.61440	−0.0518887
$969$	−29.7641	−0.956161
$970$	0.474348	0.0152304
$971$	−31.4852	−1.01041	−0.505204	−	0.863000i	$-0.668583\pi$
$971$	−31.4852	−1.01041	−0.505204	+	0.863000i	$0.668583\pi$
$972$	−3.76028	−0.120611
$973$	53.2923	1.70847
$974$	−39.4945	−1.26549
$975$	8.85571	0.283610
$976$	−4.98440	−0.159547
$977$	35.0383	1.12097	0.560487	−	0.828163i	$-0.310614\pi$
$977$	35.0383	1.12097	0.560487	+	0.828163i	$0.310614\pi$
$978$	−3.13326	−0.100191
$979$	41.4592	1.32504
$980$	−0.0717340	−0.00229146
$981$	1.64678	0.0525777
$982$	−3.99129	−0.127367
$983$	−2.56201	−0.0817155	−0.0408578	−	0.999165i	$-0.513009\pi$
$983$	−2.56201	−0.0817155	−0.0408578	+	0.999165i	$0.513009\pi$
$984$	11.5280	0.367500
$985$	0.329123	0.0104867
$986$	3.48775	0.111073
$987$	0.837992	0.0266736
$988$	3.60377	0.114651
$989$	21.8334	0.694261
$990$	−0.0331124	−0.00105238
$991$	−23.3684	−0.742323	−0.371161	−	0.928568i	$-0.621040\pi$
$991$	−23.3684	−0.742323	−0.371161	+	0.928568i	$0.621040\pi$
$992$	−9.14820	−0.290456
$993$	27.8185	0.882792
$994$	9.80012	0.310841
$995$	−0.486545	−0.0154245
$996$	−25.5543	−0.809718
$997$	−40.5159	−1.28315	−0.641576	−	0.767060i	$-0.721719\pi$
$997$	−40.5159	−1.28315	−0.641576	+	0.767060i	$0.721719\pi$
$998$	2.88875	0.0914419
$999$	17.8131	0.563582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.25	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.25	✓	69	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.62360 q^{3} +1.00000 q^{4} -0.0296991 q^{5} -1.62360 q^{6} -3.06845 q^{7} +1.00000 q^{8} -0.363928 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.62360 q^{3} +1.00000 q^{4} -0.0296991 q^{5} -1.62360 q^{6} -3.06845 q^{7} +1.00000 q^{8} -0.363928 q^{9} -0.0296991 q^{10} -3.06359 q^{11} -1.62360 q^{12} +1.09107 q^{13} -3.06845 q^{14} +0.0482194 q^{15} +1.00000 q^{16} +5.55020 q^{17} -0.363928 q^{18} +3.30298 q^{19} -0.0296991 q^{20} +4.98192 q^{21} -3.06359 q^{22} +5.36563 q^{23} -1.62360 q^{24} -4.99912 q^{25} +1.09107 q^{26} +5.46167 q^{27} -3.06845 q^{28} +0.628401 q^{29} +0.0482194 q^{30} -9.14820 q^{31} +1.00000 q^{32} +4.97404 q^{33} +5.55020 q^{34} +0.0911301 q^{35} -0.363928 q^{36} +3.26148 q^{37} +3.30298 q^{38} -1.77145 q^{39} -0.0296991 q^{40} -7.10029 q^{41} +4.98192 q^{42} +4.06912 q^{43} -3.06359 q^{44} +0.0108083 q^{45} +5.36563 q^{46} +0.168206 q^{47} -1.62360 q^{48} +2.41536 q^{49} -4.99912 q^{50} -9.01129 q^{51} +1.09107 q^{52} -2.60509 q^{53} +5.46167 q^{54} +0.0909860 q^{55} -3.06845 q^{56} -5.36271 q^{57} +0.628401 q^{58} +14.4345 q^{59} +0.0482194 q^{60} -4.98440 q^{61} -9.14820 q^{62} +1.11669 q^{63} +1.00000 q^{64} -0.0324037 q^{65} +4.97404 q^{66} +8.91897 q^{67} +5.55020 q^{68} -8.71163 q^{69} +0.0911301 q^{70} -3.19384 q^{71} -0.363928 q^{72} +2.81820 q^{73} +3.26148 q^{74} +8.11656 q^{75} +3.30298 q^{76} +9.40047 q^{77} -1.77145 q^{78} -3.25476 q^{79} -0.0296991 q^{80} -7.77577 q^{81} -7.10029 q^{82} +15.7393 q^{83} +4.98192 q^{84} -0.164836 q^{85} +4.06912 q^{86} -1.02027 q^{87} -3.06359 q^{88} -13.5329 q^{89} +0.0108083 q^{90} -3.34788 q^{91} +5.36563 q^{92} +14.8530 q^{93} +0.168206 q^{94} -0.0980955 q^{95} -1.62360 q^{96} -15.9718 q^{97} +2.41536 q^{98} +1.11493 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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