LMFDB - Embedded newform 8002.2.a.d.1.13

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			1.13
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.42898 q^{3} +1.00000 q^{4} -1.63165 q^{5} -2.42898 q^{6} +3.93412 q^{7} +1.00000 q^{8} +2.89993 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.42898 q^{3} +1.00000 q^{4} -1.63165 q^{5} -2.42898 q^{6} +3.93412 q^{7} +1.00000 q^{8} +2.89993 q^{9} -1.63165 q^{10} -6.50822 q^{11} -2.42898 q^{12} +2.44292 q^{13} +3.93412 q^{14} +3.96325 q^{15} +1.00000 q^{16} -2.35205 q^{17} +2.89993 q^{18} +6.25808 q^{19} -1.63165 q^{20} -9.55589 q^{21} -6.50822 q^{22} -9.09408 q^{23} -2.42898 q^{24} -2.33771 q^{25} +2.44292 q^{26} +0.243076 q^{27} +3.93412 q^{28} +4.33849 q^{29} +3.96325 q^{30} +9.17000 q^{31} +1.00000 q^{32} +15.8083 q^{33} -2.35205 q^{34} -6.41912 q^{35} +2.89993 q^{36} +1.52912 q^{37} +6.25808 q^{38} -5.93380 q^{39} -1.63165 q^{40} +5.51590 q^{41} -9.55589 q^{42} -7.93779 q^{43} -6.50822 q^{44} -4.73167 q^{45} -9.09408 q^{46} -3.89046 q^{47} -2.42898 q^{48} +8.47732 q^{49} -2.33771 q^{50} +5.71307 q^{51} +2.44292 q^{52} -8.11651 q^{53} +0.243076 q^{54} +10.6192 q^{55} +3.93412 q^{56} -15.2007 q^{57} +4.33849 q^{58} +3.46092 q^{59} +3.96325 q^{60} -10.3917 q^{61} +9.17000 q^{62} +11.4087 q^{63} +1.00000 q^{64} -3.98600 q^{65} +15.8083 q^{66} +2.22144 q^{67} -2.35205 q^{68} +22.0893 q^{69} -6.41912 q^{70} -2.67169 q^{71} +2.89993 q^{72} -6.75657 q^{73} +1.52912 q^{74} +5.67824 q^{75} +6.25808 q^{76} -25.6041 q^{77} -5.93380 q^{78} +17.1301 q^{79} -1.63165 q^{80} -9.29021 q^{81} +5.51590 q^{82} -7.38539 q^{83} -9.55589 q^{84} +3.83773 q^{85} -7.93779 q^{86} -10.5381 q^{87} -6.50822 q^{88} +15.6397 q^{89} -4.73167 q^{90} +9.61075 q^{91} -9.09408 q^{92} -22.2737 q^{93} -3.89046 q^{94} -10.2110 q^{95} -2.42898 q^{96} -9.53508 q^{97} +8.47732 q^{98} -18.8734 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.42898	−1.40237	−0.701185	−	0.712979i	$-0.747345\pi$
$3$	−2.42898	−1.40237	−0.701185	+	0.712979i	$0.747345\pi$
$4$	1.00000	0.500000
$5$	−1.63165	−0.729697	−0.364849	−	0.931067i	$-0.618879\pi$
$5$	−1.63165	−0.729697	−0.364849	+	0.931067i	$0.618879\pi$
$6$	−2.42898	−0.991625
$7$	3.93412	1.48696	0.743479	−	0.668759i	$-0.233174\pi$
$7$	3.93412	1.48696	0.743479	+	0.668759i	$0.233174\pi$
$8$	1.00000	0.353553
$9$	2.89993	0.966642
$10$	−1.63165	−0.515974
$11$	−6.50822	−1.96230	−0.981152	−	0.193240i	$-0.938101\pi$
$11$	−6.50822	−1.96230	−0.981152	+	0.193240i	$0.938101\pi$
$12$	−2.42898	−0.701185
$13$	2.44292	0.677545	0.338772	−	0.940868i	$-0.389988\pi$
$13$	2.44292	0.677545	0.338772	+	0.940868i	$0.389988\pi$
$14$	3.93412	1.05144
$15$	3.96325	1.02331
$16$	1.00000	0.250000
$17$	−2.35205	−0.570456	−0.285228	−	0.958460i	$-0.592069\pi$
$17$	−2.35205	−0.570456	−0.285228	+	0.958460i	$0.592069\pi$
$18$	2.89993	0.683519
$19$	6.25808	1.43570	0.717851	−	0.696197i	$-0.245126\pi$
$19$	6.25808	1.43570	0.717851	+	0.696197i	$0.245126\pi$
$20$	−1.63165	−0.364849
$21$	−9.55589	−2.08527
$22$	−6.50822	−1.38756
$23$	−9.09408	−1.89625	−0.948123	−	0.317904i	$-0.897021\pi$
$23$	−9.09408	−1.89625	−0.948123	+	0.317904i	$0.897021\pi$
$24$	−2.42898	−0.495813
$25$	−2.33771	−0.467542
$26$	2.44292	0.479096
$27$	0.243076	0.0467800
$28$	3.93412	0.743479
$29$	4.33849	0.805637	0.402819	−	0.915280i	$-0.368031\pi$
$29$	4.33849	0.805637	0.402819	+	0.915280i	$0.368031\pi$
$30$	3.96325	0.723586
$31$	9.17000	1.64698	0.823490	−	0.567331i	$-0.192024\pi$
$31$	9.17000	1.64698	0.823490	+	0.567331i	$0.192024\pi$
$32$	1.00000	0.176777
$33$	15.8083	2.75188
$34$	−2.35205	−0.403373
$35$	−6.41912	−1.08503
$36$	2.89993	0.483321
$37$	1.52912	0.251385	0.125693	−	0.992069i	$-0.459885\pi$
$37$	1.52912	0.251385	0.125693	+	0.992069i	$0.459885\pi$
$38$	6.25808	1.01519
$39$	−5.93380	−0.950168
$40$	−1.63165	−0.257987
$41$	5.51590	0.861439	0.430720	−	0.902486i	$-0.358260\pi$
$41$	5.51590	0.861439	0.430720	+	0.902486i	$0.358260\pi$
$42$	−9.55589	−1.47451
$43$	−7.93779	−1.21050	−0.605251	−	0.796035i	$-0.706927\pi$
$43$	−7.93779	−1.21050	−0.605251	+	0.796035i	$0.706927\pi$
$44$	−6.50822	−0.981152
$45$	−4.73167	−0.705356
$46$	−9.09408	−1.34085
$47$	−3.89046	−0.567482	−0.283741	−	0.958901i	$-0.591576\pi$
$47$	−3.89046	−0.567482	−0.283741	+	0.958901i	$0.591576\pi$
$48$	−2.42898	−0.350593
$49$	8.47732	1.21105
$50$	−2.33771	−0.330602
$51$	5.71307	0.799990
$52$	2.44292	0.338772
$53$	−8.11651	−1.11489	−0.557444	−	0.830214i	$-0.688218\pi$
$53$	−8.11651	−1.11489	−0.557444	+	0.830214i	$0.688218\pi$
$54$	0.243076	0.0330784
$55$	10.6192	1.43189
$56$	3.93412	0.525719
$57$	−15.2007	−2.01339
$58$	4.33849	0.569672
$59$	3.46092	0.450573	0.225286	−	0.974293i	$-0.427668\pi$
$59$	3.46092	0.450573	0.225286	+	0.974293i	$0.427668\pi$
$60$	3.96325	0.511653
$61$	−10.3917	−1.33052	−0.665261	−	0.746610i	$-0.731680\pi$
$61$	−10.3917	−1.33052	−0.665261	+	0.746610i	$0.731680\pi$
$62$	9.17000	1.16459
$63$	11.4087	1.43736
$64$	1.00000	0.125000
$65$	−3.98600	−0.494403
$66$	15.8083	1.94587
$67$	2.22144	0.271392	0.135696	−	0.990751i	$-0.456673\pi$
$67$	2.22144	0.271392	0.135696	+	0.990751i	$0.456673\pi$
$68$	−2.35205	−0.285228
$69$	22.0893	2.65924
$70$	−6.41912	−0.767232
$71$	−2.67169	−0.317071	−0.158536	−	0.987353i	$-0.550677\pi$
$71$	−2.67169	−0.317071	−0.158536	+	0.987353i	$0.550677\pi$
$72$	2.89993	0.341760
$73$	−6.75657	−0.790796	−0.395398	−	0.918510i	$-0.629393\pi$
$73$	−6.75657	−0.790796	−0.395398	+	0.918510i	$0.629393\pi$
$74$	1.52912	0.177756
$75$	5.67824	0.655667
$76$	6.25808	0.717851
$77$	−25.6041	−2.91786
$78$	−5.93380	−0.671871
$79$	17.1301	1.92729	0.963645	−	0.267186i	$-0.0860937\pi$
$79$	17.1301	1.92729	0.963645	+	0.267186i	$0.0860937\pi$
$80$	−1.63165	−0.182424
$81$	−9.29021	−1.03225
$82$	5.51590	0.609130
$83$	−7.38539	−0.810652	−0.405326	−	0.914172i	$-0.632842\pi$
$83$	−7.38539	−0.810652	−0.405326	+	0.914172i	$0.632842\pi$
$84$	−9.55589	−1.04263
$85$	3.83773	0.416260
$86$	−7.93779	−0.855954
$87$	−10.5381	−1.12980
$88$	−6.50822	−0.693779
$89$	15.6397	1.65780	0.828901	−	0.559396i	$-0.188967\pi$
$89$	15.6397	1.65780	0.828901	+	0.559396i	$0.188967\pi$
$90$	−4.73167	−0.498762
$91$	9.61075	1.00748
$92$	−9.09408	−0.948123
$93$	−22.2737	−2.30968
$94$	−3.89046	−0.401270
$95$	−10.2110	−1.04763
$96$	−2.42898	−0.247906
$97$	−9.53508	−0.968141	−0.484070	−	0.875029i	$-0.660842\pi$
$97$	−9.53508	−0.968141	−0.484070	+	0.875029i	$0.660842\pi$
$98$	8.47732	0.856338
$99$	−18.8734	−1.89685
$100$	−2.33771	−0.233771
$101$	7.22405	0.718820	0.359410	−	0.933180i	$-0.382978\pi$
$101$	7.22405	0.718820	0.359410	+	0.933180i	$0.382978\pi$
$102$	5.71307	0.565678
$103$	−13.2094	−1.30156	−0.650782	−	0.759265i	$-0.725559\pi$
$103$	−13.2094	−1.30156	−0.650782	+	0.759265i	$0.725559\pi$
$104$	2.44292	0.239548
$105$	15.5919	1.52161
$106$	−8.11651	−0.788345
$107$	8.95921	0.866120	0.433060	−	0.901365i	$-0.357434\pi$
$107$	8.95921	0.866120	0.433060	+	0.901365i	$0.357434\pi$
$108$	0.243076	0.0233900
$109$	−15.1403	−1.45018	−0.725090	−	0.688654i	$-0.758202\pi$
$109$	−15.1403	−1.45018	−0.725090	+	0.688654i	$0.758202\pi$
$110$	10.6192	1.01250
$111$	−3.71419	−0.352535
$112$	3.93412	0.371740
$113$	4.09684	0.385398	0.192699	−	0.981258i	$-0.438276\pi$
$113$	4.09684	0.385398	0.192699	+	0.981258i	$0.438276\pi$
$114$	−15.2007	−1.42368
$115$	14.8384	1.38369
$116$	4.33849	0.402819
$117$	7.08429	0.654943
$118$	3.46092	0.318603
$119$	−9.25325	−0.848244
$120$	3.96325	0.361793
$121$	31.3570	2.85063
$122$	−10.3917	−0.940822
$123$	−13.3980	−1.20806
$124$	9.17000	0.823490
$125$	11.9726	1.07086
$126$	11.4087	1.01636
$127$	−0.451099	−0.0400286	−0.0200143	−	0.999800i	$-0.506371\pi$
$127$	−0.451099	−0.0400286	−0.0200143	+	0.999800i	$0.506371\pi$
$128$	1.00000	0.0883883
$129$	19.2807	1.69757
$130$	−3.98600	−0.349595
$131$	6.87675	0.600825	0.300412	−	0.953809i	$-0.402876\pi$
$131$	6.87675	0.600825	0.300412	+	0.953809i	$0.402876\pi$
$132$	15.8083	1.37594
$133$	24.6200	2.13483
$134$	2.22144	0.191903
$135$	−0.396615	−0.0341352
$136$	−2.35205	−0.201687
$137$	−19.6896	−1.68220	−0.841098	−	0.540883i	$-0.818090\pi$
$137$	−19.6896	−1.68220	−0.841098	+	0.540883i	$0.818090\pi$
$138$	22.0893	1.88037
$139$	−11.5087	−0.976159	−0.488080	−	0.872799i	$-0.662302\pi$
$139$	−11.5087	−0.976159	−0.488080	+	0.872799i	$0.662302\pi$
$140$	−6.41912	−0.542515
$141$	9.44983	0.795820
$142$	−2.67169	−0.224203
$143$	−15.8991	−1.32955
$144$	2.89993	0.241661
$145$	−7.07891	−0.587871
$146$	−6.75657	−0.559178
$147$	−20.5912	−1.69833
$148$	1.52912	0.125693
$149$	2.39346	0.196080	0.0980398	−	0.995182i	$-0.468743\pi$
$149$	2.39346	0.196080	0.0980398	+	0.995182i	$0.468743\pi$
$150$	5.67824	0.463626
$151$	6.19252	0.503940	0.251970	−	0.967735i	$-0.418922\pi$
$151$	6.19252	0.503940	0.251970	+	0.967735i	$0.418922\pi$
$152$	6.25808	0.507597
$153$	−6.82077	−0.551427
$154$	−25.6041	−2.06324
$155$	−14.9622	−1.20180
$156$	−5.93380	−0.475084
$157$	7.02873	0.560954	0.280477	−	0.959861i	$-0.409507\pi$
$157$	7.02873	0.560954	0.280477	+	0.959861i	$0.409507\pi$
$158$	17.1301	1.36280
$159$	19.7148	1.56349
$160$	−1.63165	−0.128993
$161$	−35.7772	−2.81964
$162$	−9.29021	−0.729907
$163$	−7.85085	−0.614926	−0.307463	−	0.951560i	$-0.599480\pi$
$163$	−7.85085	−0.614926	−0.307463	+	0.951560i	$0.599480\pi$
$164$	5.51590	0.430720
$165$	−25.7937	−2.00804
$166$	−7.38539	−0.573218
$167$	8.77288	0.678866	0.339433	−	0.940630i	$-0.389765\pi$
$167$	8.77288	0.678866	0.339433	+	0.940630i	$0.389765\pi$
$168$	−9.55589	−0.737253
$169$	−7.03213	−0.540933
$170$	3.83773	0.294340
$171$	18.1480	1.38781
$172$	−7.93779	−0.605251
$173$	20.0977	1.52800	0.764001	−	0.645215i	$-0.223232\pi$
$173$	20.0977	1.52800	0.764001	+	0.645215i	$0.223232\pi$
$174$	−10.5381	−0.798890
$175$	−9.19683	−0.695215
$176$	−6.50822	−0.490576
$177$	−8.40648	−0.631870
$178$	15.6397	1.17224
$179$	−22.0836	−1.65060	−0.825301	−	0.564693i	$-0.808995\pi$
$179$	−22.0836	−1.65060	−0.825301	+	0.564693i	$0.808995\pi$
$180$	−4.73167	−0.352678
$181$	0.504009	0.0374627	0.0187313	−	0.999825i	$-0.494037\pi$
$181$	0.504009	0.0374627	0.0187313	+	0.999825i	$0.494037\pi$
$182$	9.61075	0.712396
$183$	25.2412	1.86589
$184$	−9.09408	−0.670424
$185$	−2.49499	−0.183435
$186$	−22.2737	−1.63319
$187$	15.3077	1.11941
$188$	−3.89046	−0.283741
$189$	0.956290	0.0695599
$190$	−10.2110	−0.740785
$191$	13.0768	0.946203	0.473101	−	0.881008i	$-0.343134\pi$
$191$	13.0768	0.946203	0.473101	+	0.881008i	$0.343134\pi$
$192$	−2.42898	−0.175296
$193$	6.83261	0.491822	0.245911	−	0.969292i	$-0.420913\pi$
$193$	6.83261	0.491822	0.245911	+	0.969292i	$0.420913\pi$
$194$	−9.53508	−0.684579
$195$	9.68190	0.693335
$196$	8.47732	0.605523
$197$	−25.5654	−1.82146	−0.910730	−	0.413002i	$-0.864480\pi$
$197$	−25.5654	−1.82146	−0.910730	+	0.413002i	$0.864480\pi$
$198$	−18.8734	−1.34127
$199$	14.2658	1.01127	0.505637	−	0.862746i	$-0.331258\pi$
$199$	14.2658	1.01127	0.505637	+	0.862746i	$0.331258\pi$
$200$	−2.33771	−0.165301
$201$	−5.39582	−0.380592
$202$	7.22405	0.508282
$203$	17.0681	1.19795
$204$	5.71307	0.399995
$205$	−9.00004	−0.628590
$206$	−13.2094	−0.920345
$207$	−26.3722	−1.83299
$208$	2.44292	0.169386
$209$	−40.7290	−2.81728
$210$	15.5919	1.07594
$211$	−20.9173	−1.44001	−0.720005	−	0.693969i	$-0.755860\pi$
$211$	−20.9173	−1.44001	−0.720005	+	0.693969i	$0.755860\pi$
$212$	−8.11651	−0.557444
$213$	6.48947	0.444651
$214$	8.95921	0.612439
$215$	12.9517	0.883300
$216$	0.243076	0.0165392
$217$	36.0759	2.44899
$218$	−15.1403	−1.02543
$219$	16.4115	1.10899
$220$	10.6192	0.715944
$221$	−5.74587	−0.386509
$222$	−3.71419	−0.249280
$223$	−22.7105	−1.52081	−0.760405	−	0.649449i	$-0.774999\pi$
$223$	−22.7105	−1.52081	−0.760405	+	0.649449i	$0.774999\pi$
$224$	3.93412	0.262860
$225$	−6.77919	−0.451946
$226$	4.09684	0.272518
$227$	−25.5465	−1.69558	−0.847791	−	0.530330i	$-0.822068\pi$
$227$	−25.5465	−1.69558	−0.847791	+	0.530330i	$0.822068\pi$
$228$	−15.2007	−1.00669
$229$	0.0691195	0.00456754	0.00228377	−	0.999997i	$-0.499273\pi$
$229$	0.0691195	0.00456754	0.00228377	+	0.999997i	$0.499273\pi$
$230$	14.8384	0.978414
$231$	62.1919	4.09192
$232$	4.33849	0.284836
$233$	−4.53012	−0.296778	−0.148389	−	0.988929i	$-0.547409\pi$
$233$	−4.53012	−0.296778	−0.148389	+	0.988929i	$0.547409\pi$
$234$	7.08429	0.463115
$235$	6.34788	0.414090
$236$	3.46092	0.225286
$237$	−41.6087	−2.70277
$238$	−9.25325	−0.599799
$239$	3.09460	0.200173	0.100087	−	0.994979i	$-0.468088\pi$
$239$	3.09460	0.200173	0.100087	+	0.994979i	$0.468088\pi$
$240$	3.96325	0.255826
$241$	9.49765	0.611797	0.305899	−	0.952064i	$-0.401043\pi$
$241$	9.49765	0.611797	0.305899	+	0.952064i	$0.401043\pi$
$242$	31.3570	2.01570
$243$	21.8365	1.40081
$244$	−10.3917	−0.665261
$245$	−13.8320	−0.883697
$246$	−13.3980	−0.854225
$247$	15.2880	0.972752
$248$	9.17000	0.582295
$249$	17.9389	1.13683
$250$	11.9726	0.757213
$251$	15.2680	0.963711	0.481855	−	0.876251i	$-0.339963\pi$
$251$	15.2680	0.963711	0.481855	+	0.876251i	$0.339963\pi$
$252$	11.4087	0.718678
$253$	59.1863	3.72101
$254$	−0.451099	−0.0283045
$255$	−9.32175	−0.583751
$256$	1.00000	0.0625000
$257$	−22.4339	−1.39939	−0.699695	−	0.714442i	$-0.746681\pi$
$257$	−22.4339	−1.39939	−0.699695	+	0.714442i	$0.746681\pi$
$258$	19.2807	1.20036
$259$	6.01573	0.373799
$260$	−3.98600	−0.247201
$261$	12.5813	0.778763
$262$	6.87675	0.424847
$263$	11.5457	0.711937	0.355969	−	0.934498i	$-0.384151\pi$
$263$	11.5457	0.711937	0.355969	+	0.934498i	$0.384151\pi$
$264$	15.8083	0.972935
$265$	13.2433	0.813531
$266$	24.6200	1.50955
$267$	−37.9884	−2.32485
$268$	2.22144	0.135696
$269$	−15.5778	−0.949795	−0.474898	−	0.880041i	$-0.657515\pi$
$269$	−15.5778	−0.949795	−0.474898	+	0.880041i	$0.657515\pi$
$270$	−0.396615	−0.0241372
$271$	14.6625	0.890685	0.445342	−	0.895360i	$-0.353082\pi$
$271$	14.6625	0.890685	0.445342	+	0.895360i	$0.353082\pi$
$272$	−2.35205	−0.142614
$273$	−23.3443	−1.41286
$274$	−19.6896	−1.18949
$275$	15.2143	0.917459
$276$	22.0893	1.32962
$277$	−28.2531	−1.69757	−0.848783	−	0.528742i	$-0.822664\pi$
$277$	−28.2531	−1.69757	−0.848783	+	0.528742i	$0.822664\pi$
$278$	−11.5087	−0.690249
$279$	26.5923	1.59204
$280$	−6.41912	−0.383616
$281$	21.9228	1.30780	0.653902	−	0.756579i	$-0.273131\pi$
$281$	21.9228	1.30780	0.653902	+	0.756579i	$0.273131\pi$
$282$	9.44983	0.562729
$283$	−10.8414	−0.644457	−0.322228	−	0.946662i	$-0.604432\pi$
$283$	−10.8414	−0.644457	−0.322228	+	0.946662i	$0.604432\pi$
$284$	−2.67169	−0.158536
$285$	24.8023	1.46916
$286$	−15.8991	−0.940132
$287$	21.7002	1.28092
$288$	2.89993	0.170880
$289$	−11.4679	−0.674580
$290$	−7.07891	−0.415688
$291$	23.1605	1.35769
$292$	−6.75657	−0.395398
$293$	−30.1137	−1.75926	−0.879632	−	0.475655i	$-0.842211\pi$
$293$	−30.1137	−1.75926	−0.879632	+	0.475655i	$0.842211\pi$
$294$	−20.5912	−1.20090
$295$	−5.64701	−0.328782
$296$	1.52912	0.0888781
$297$	−1.58199	−0.0917965
$298$	2.39346	0.138649
$299$	−22.2161	−1.28479
$300$	5.67824	0.327833
$301$	−31.2282	−1.79997
$302$	6.19252	0.356339
$303$	−17.5470	−1.00805
$304$	6.25808	0.358925
$305$	16.9557	0.970879
$306$	−6.82077	−0.389917
$307$	−22.2556	−1.27019	−0.635097	−	0.772433i	$-0.719040\pi$
$307$	−22.2556	−1.27019	−0.635097	+	0.772433i	$0.719040\pi$
$308$	−25.6041	−1.45893
$309$	32.0854	1.82527
$310$	−14.9622	−0.849799
$311$	−5.16239	−0.292732	−0.146366	−	0.989230i	$-0.546758\pi$
$311$	−5.16239	−0.292732	−0.146366	+	0.989230i	$0.546758\pi$
$312$	−5.93380	−0.335935
$313$	−34.3839	−1.94349	−0.971745	−	0.236033i	$-0.924153\pi$
$313$	−34.3839	−1.94349	−0.971745	+	0.236033i	$0.924153\pi$
$314$	7.02873	0.396654
$315$	−18.6150	−1.04884
$316$	17.1301	0.963645
$317$	−15.6821	−0.880797	−0.440398	−	0.897802i	$-0.645163\pi$
$317$	−15.6821	−0.880797	−0.440398	+	0.897802i	$0.645163\pi$
$318$	19.7148	1.10555
$319$	−28.2359	−1.58090
$320$	−1.63165	−0.0912122
$321$	−21.7617	−1.21462
$322$	−35.7772	−1.99379
$323$	−14.7193	−0.819004
$324$	−9.29021	−0.516123
$325$	−5.71084	−0.316780
$326$	−7.85085	−0.434818
$327$	36.7755	2.03369
$328$	5.51590	0.304565
$329$	−15.3055	−0.843822
$330$	−25.7937	−1.41990
$331$	−31.1154	−1.71026	−0.855128	−	0.518417i	$-0.826522\pi$
$331$	−31.1154	−1.71026	−0.855128	+	0.518417i	$0.826522\pi$
$332$	−7.38539	−0.405326
$333$	4.43433	0.243000
$334$	8.77288	0.480030
$335$	−3.62461	−0.198034
$336$	−9.55589	−0.521317
$337$	−16.3637	−0.891387	−0.445694	−	0.895186i	$-0.647043\pi$
$337$	−16.3637	−0.891387	−0.445694	+	0.895186i	$0.647043\pi$
$338$	−7.03213	−0.382498
$339$	−9.95113	−0.540471
$340$	3.83773	0.208130
$341$	−59.6804	−3.23187
$342$	18.1480	0.981330
$343$	5.81195	0.313816
$344$	−7.93779	−0.427977
$345$	−36.0421	−1.94044
$346$	20.0977	1.08046
$347$	4.10189	0.220201	0.110100	−	0.993920i	$-0.464883\pi$
$347$	4.10189	0.220201	0.110100	+	0.993920i	$0.464883\pi$
$348$	−10.5381	−0.564901
$349$	−21.0142	−1.12486	−0.562432	−	0.826843i	$-0.690134\pi$
$349$	−21.0142	−1.12486	−0.562432	+	0.826843i	$0.690134\pi$
$350$	−9.19683	−0.491591
$351$	0.593815	0.0316955
$352$	−6.50822	−0.346889
$353$	−15.0533	−0.801208	−0.400604	−	0.916251i	$-0.631200\pi$
$353$	−15.0533	−0.801208	−0.400604	+	0.916251i	$0.631200\pi$
$354$	−8.40648	−0.446799
$355$	4.35927	0.231366
$356$	15.6397	0.828901
$357$	22.4759	1.18955
$358$	−22.0836	−1.16715
$359$	−8.27864	−0.436930	−0.218465	−	0.975845i	$-0.570105\pi$
$359$	−8.27864	−0.436930	−0.218465	+	0.975845i	$0.570105\pi$
$360$	−4.73167	−0.249381
$361$	20.1636	1.06124
$362$	0.504009	0.0264901
$363$	−76.1653	−3.99764
$364$	9.61075	0.503740
$365$	11.0244	0.577042
$366$	25.2412	1.31938
$367$	10.7723	0.562311	0.281156	−	0.959662i	$-0.409282\pi$
$367$	10.7723	0.562311	0.281156	+	0.959662i	$0.409282\pi$
$368$	−9.09408	−0.474062
$369$	15.9957	0.832704
$370$	−2.49499	−0.129708
$371$	−31.9313	−1.65779
$372$	−22.2737	−1.15484
$373$	0.104352	0.00540316	0.00270158	−	0.999996i	$-0.499140\pi$
$373$	0.104352	0.00540316	0.00270158	+	0.999996i	$0.499140\pi$
$374$	15.3077	0.791540
$375$	−29.0811	−1.50174
$376$	−3.89046	−0.200635
$377$	10.5986	0.545855
$378$	0.956290	0.0491862
$379$	9.03615	0.464156	0.232078	−	0.972697i	$-0.425448\pi$
$379$	9.03615	0.464156	0.232078	+	0.972697i	$0.425448\pi$
$380$	−10.2110	−0.523814
$381$	1.09571	0.0561349
$382$	13.0768	0.669066
$383$	27.7505	1.41798	0.708992	−	0.705216i	$-0.249150\pi$
$383$	27.7505	1.41798	0.708992	+	0.705216i	$0.249150\pi$
$384$	−2.42898	−0.123953
$385$	41.7771	2.12916
$386$	6.83261	0.347771
$387$	−23.0190	−1.17012
$388$	−9.53508	−0.484070
$389$	−25.7264	−1.30438	−0.652191	−	0.758055i	$-0.726150\pi$
$389$	−25.7264	−1.30438	−0.652191	+	0.758055i	$0.726150\pi$
$390$	9.68190	0.490262
$391$	21.3897	1.08172
$392$	8.47732	0.428169
$393$	−16.7035	−0.842579
$394$	−25.5654	−1.28797
$395$	−27.9504	−1.40634
$396$	−18.8734	−0.948423
$397$	−21.5241	−1.08026	−0.540131	−	0.841581i	$-0.681625\pi$
$397$	−21.5241	−1.08026	−0.540131	+	0.841581i	$0.681625\pi$
$398$	14.2658	0.715079
$399$	−59.8015	−2.99382
$400$	−2.33771	−0.116885
$401$	−11.7675	−0.587641	−0.293820	−	0.955861i	$-0.594927\pi$
$401$	−11.7675	−0.587641	−0.293820	+	0.955861i	$0.594927\pi$
$402$	−5.39582	−0.269119
$403$	22.4016	1.11590
$404$	7.22405	0.359410
$405$	15.1584	0.753226
$406$	17.0681	0.847078
$407$	−9.95183	−0.493294
$408$	5.71307	0.282839
$409$	25.5443	1.26309	0.631543	−	0.775341i	$-0.282422\pi$
$409$	25.5443	1.26309	0.631543	+	0.775341i	$0.282422\pi$
$410$	−9.00004	−0.444480
$411$	47.8256	2.35906
$412$	−13.2094	−0.650782
$413$	13.6157	0.669983
$414$	−26.3722	−1.29612
$415$	12.0504	0.591531
$416$	2.44292	0.119774
$417$	27.9545	1.36894
$418$	−40.7290	−1.99212
$419$	−19.7092	−0.962856	−0.481428	−	0.876486i	$-0.659882\pi$
$419$	−19.7092	−0.962856	−0.481428	+	0.876486i	$0.659882\pi$
$420$	15.5919	0.760807
$421$	30.2532	1.47445	0.737225	−	0.675648i	$-0.236136\pi$
$421$	30.2532	1.47445	0.737225	+	0.675648i	$0.236136\pi$
$422$	−20.9173	−1.01824
$423$	−11.2820	−0.548552
$424$	−8.11651	−0.394173
$425$	5.49841	0.266712
$426$	6.48947	0.314416
$427$	−40.8823	−1.97843
$428$	8.95921	0.433060
$429$	38.6185	1.86452
$430$	12.9517	0.624587
$431$	−34.8805	−1.68013	−0.840067	−	0.542483i	$-0.817484\pi$
$431$	−34.8805	−1.68013	−0.840067	+	0.542483i	$0.817484\pi$
$432$	0.243076	0.0116950
$433$	14.8819	0.715176	0.357588	−	0.933879i	$-0.383599\pi$
$433$	14.8819	0.715176	0.357588	+	0.933879i	$0.383599\pi$
$434$	36.0759	1.73170
$435$	17.1945	0.824413
$436$	−15.1403	−0.725090
$437$	−56.9115	−2.72244
$438$	16.4115	0.784174
$439$	10.0693	0.480581	0.240291	−	0.970701i	$-0.422757\pi$
$439$	10.0693	0.480581	0.240291	+	0.970701i	$0.422757\pi$
$440$	10.6192	0.506249
$441$	24.5836	1.17065
$442$	−5.74587	−0.273303
$443$	26.5038	1.25923	0.629617	−	0.776905i	$-0.283212\pi$
$443$	26.5038	1.25923	0.629617	+	0.776905i	$0.283212\pi$
$444$	−3.71419	−0.176268
$445$	−25.5185	−1.20969
$446$	−22.7105	−1.07537
$447$	−5.81365	−0.274976
$448$	3.93412	0.185870
$449$	−28.6134	−1.35035	−0.675174	−	0.737659i	$-0.735931\pi$
$449$	−28.6134	−1.35035	−0.675174	+	0.737659i	$0.735931\pi$
$450$	−6.77919	−0.319574
$451$	−35.8987	−1.69041
$452$	4.09684	0.192699
$453$	−15.0415	−0.706710
$454$	−25.5465	−1.19896
$455$	−15.6814	−0.735156
$456$	−15.2007	−0.711839
$457$	0.264389	0.0123676	0.00618379	−	0.999981i	$-0.498032\pi$
$457$	0.264389	0.0123676	0.00618379	+	0.999981i	$0.498032\pi$
$458$	0.0691195	0.00322974
$459$	−0.571726	−0.0266859
$460$	14.8384	0.691843
$461$	−25.3513	−1.18073	−0.590364	−	0.807137i	$-0.701016\pi$
$461$	−25.3513	−1.18073	−0.590364	+	0.807137i	$0.701016\pi$
$462$	62.1919	2.89343
$463$	38.7891	1.80268	0.901342	−	0.433108i	$-0.142583\pi$
$463$	38.7891	1.80268	0.901342	+	0.433108i	$0.142583\pi$
$464$	4.33849	0.201409
$465$	36.3430	1.68536
$466$	−4.53012	−0.209854
$467$	−38.7430	−1.79281	−0.896406	−	0.443233i	$-0.853831\pi$
$467$	−38.7430	−1.79281	−0.896406	+	0.443233i	$0.853831\pi$
$468$	7.08429	0.327472
$469$	8.73941	0.403548
$470$	6.34788	0.292806
$471$	−17.0726	−0.786665
$472$	3.46092	0.159302
$473$	51.6609	2.37537
$474$	−41.6087	−1.91115
$475$	−14.6296	−0.671251
$476$	−9.25325	−0.424122
$477$	−23.5373	−1.07770
$478$	3.09460	0.141544
$479$	7.52557	0.343852	0.171926	−	0.985110i	$-0.445001\pi$
$479$	7.52557	0.343852	0.171926	+	0.985110i	$0.445001\pi$
$480$	3.96325	0.180897
$481$	3.73551	0.170325
$482$	9.49765	0.432606
$483$	86.9020	3.95418
$484$	31.3570	1.42532
$485$	15.5579	0.706450
$486$	21.8365	0.990522
$487$	−27.9026	−1.26439	−0.632193	−	0.774811i	$-0.717845\pi$
$487$	−27.9026	−1.26439	−0.632193	+	0.774811i	$0.717845\pi$
$488$	−10.3917	−0.470411
$489$	19.0695	0.862354
$490$	−13.8320	−0.624868
$491$	−11.2908	−0.509548	−0.254774	−	0.967001i	$-0.582001\pi$
$491$	−11.2908	−0.509548	−0.254774	+	0.967001i	$0.582001\pi$
$492$	−13.3980	−0.604028
$493$	−10.2043	−0.459580
$494$	15.2880	0.687840
$495$	30.7948	1.38412
$496$	9.17000	0.411745
$497$	−10.5108	−0.471472
$498$	17.9389	0.803863
$499$	−10.2253	−0.457748	−0.228874	−	0.973456i	$-0.573504\pi$
$499$	−10.2253	−0.457748	−0.228874	+	0.973456i	$0.573504\pi$
$500$	11.9726	0.535431
$501$	−21.3091	−0.952021
$502$	15.2680	0.681446
$503$	−29.7579	−1.32684	−0.663420	−	0.748247i	$-0.730896\pi$
$503$	−29.7579	−1.32684	−0.663420	+	0.748247i	$0.730896\pi$
$504$	11.4087	0.508182
$505$	−11.7871	−0.524521
$506$	59.1863	2.63115
$507$	17.0809	0.758589
$508$	−0.451099	−0.0200143
$509$	−13.5647	−0.601244	−0.300622	−	0.953743i	$-0.597194\pi$
$509$	−13.5647	−0.601244	−0.300622	+	0.953743i	$0.597194\pi$
$510$	−9.32175	−0.412774
$511$	−26.5812	−1.17588
$512$	1.00000	0.0441942
$513$	1.52119	0.0671621
$514$	−22.4339	−0.989518
$515$	21.5532	0.949748
$516$	19.2807	0.848786
$517$	25.3200	1.11357
$518$	6.01573	0.264316
$519$	−48.8169	−2.14282
$520$	−3.98600	−0.174798
$521$	−1.70687	−0.0747792	−0.0373896	−	0.999301i	$-0.511904\pi$
$521$	−1.70687	−0.0747792	−0.0373896	+	0.999301i	$0.511904\pi$
$522$	12.5813	0.550669
$523$	21.2928	0.931070	0.465535	−	0.885030i	$-0.345862\pi$
$523$	21.2928	0.931070	0.465535	+	0.885030i	$0.345862\pi$
$524$	6.87675	0.300412
$525$	22.3389	0.974949
$526$	11.5457	0.503416
$527$	−21.5683	−0.939529
$528$	15.8083	0.687969
$529$	59.7022	2.59575
$530$	13.2433	0.575253
$531$	10.0364	0.435543
$532$	24.6200	1.06741
$533$	13.4749	0.583664
$534$	−37.9884	−1.64392
$535$	−14.6183	−0.632005
$536$	2.22144	0.0959515
$537$	53.6404	2.31476
$538$	−15.5778	−0.671607
$539$	−55.1723	−2.37644
$540$	−0.396615	−0.0170676
$541$	40.6056	1.74577	0.872886	−	0.487925i	$-0.162246\pi$
$541$	40.6056	1.74577	0.872886	+	0.487925i	$0.162246\pi$
$542$	14.6625	0.629809
$543$	−1.22423	−0.0525365
$544$	−2.35205	−0.100843
$545$	24.7038	1.05819
$546$	−23.3443	−0.999044
$547$	12.7634	0.545726	0.272863	−	0.962053i	$-0.412029\pi$
$547$	12.7634	0.545726	0.272863	+	0.962053i	$0.412029\pi$
$548$	−19.6896	−0.841098
$549$	−30.1352	−1.28614
$550$	15.2143	0.648741
$551$	27.1506	1.15665
$552$	22.0893	0.940183
$553$	67.3920	2.86580
$554$	−28.2531	−1.20036
$555$	6.06027	0.257244
$556$	−11.5087	−0.488080
$557$	−1.40014	−0.0593260	−0.0296630	−	0.999560i	$-0.509443\pi$
$557$	−1.40014	−0.0593260	−0.0296630	+	0.999560i	$0.509443\pi$
$558$	26.5923	1.12574
$559$	−19.3914	−0.820169
$560$	−6.41912	−0.271257
$561$	−37.1819	−1.56982
$562$	21.9228	0.924757
$563$	29.1661	1.22920	0.614602	−	0.788837i	$-0.289317\pi$
$563$	29.1661	1.22920	0.614602	+	0.788837i	$0.289317\pi$
$564$	9.44983	0.397910
$565$	−6.68462	−0.281224
$566$	−10.8414	−0.455700
$567$	−36.5488	−1.53491
$568$	−2.67169	−0.112102
$569$	−6.70361	−0.281030	−0.140515	−	0.990079i	$-0.544876\pi$
$569$	−6.70361	−0.281030	−0.140515	+	0.990079i	$0.544876\pi$
$570$	24.8023	1.03885
$571$	0.996288	0.0416934	0.0208467	−	0.999783i	$-0.493364\pi$
$571$	0.996288	0.0416934	0.0208467	+	0.999783i	$0.493364\pi$
$572$	−15.8991	−0.664774
$573$	−31.7632	−1.32693
$574$	21.7002	0.905750
$575$	21.2593	0.886574
$576$	2.89993	0.120830
$577$	39.9708	1.66401	0.832004	−	0.554770i	$-0.187194\pi$
$577$	39.9708	1.66401	0.832004	+	0.554770i	$0.187194\pi$
$578$	−11.4679	−0.477000
$579$	−16.5963	−0.689717
$580$	−7.07891	−0.293936
$581$	−29.0550	−1.20541
$582$	23.1605	0.960033
$583$	52.8241	2.18775
$584$	−6.75657	−0.279589
$585$	−11.5591	−0.477910
$586$	−30.1137	−1.24399
$587$	3.85518	0.159120	0.0795601	−	0.996830i	$-0.474648\pi$
$587$	3.85518	0.159120	0.0795601	+	0.996830i	$0.474648\pi$
$588$	−20.5912	−0.849167
$589$	57.3866	2.36457
$590$	−5.64701	−0.232484
$591$	62.0978	2.55436
$592$	1.52912	0.0628463
$593$	−3.95459	−0.162395	−0.0811977	−	0.996698i	$-0.525875\pi$
$593$	−3.95459	−0.162395	−0.0811977	+	0.996698i	$0.525875\pi$
$594$	−1.58199	−0.0649099
$595$	15.0981	0.618961
$596$	2.39346	0.0980398
$597$	−34.6512	−1.41818
$598$	−22.2161	−0.908485
$599$	−27.6817	−1.13104	−0.565521	−	0.824734i	$-0.691325\pi$
$599$	−27.6817	−1.13104	−0.565521	+	0.824734i	$0.691325\pi$
$600$	5.67824	0.231813
$601$	−41.7687	−1.70378	−0.851891	−	0.523718i	$-0.824544\pi$
$601$	−41.7687	−1.70378	−0.851891	+	0.523718i	$0.824544\pi$
$602$	−31.2282	−1.27277
$603$	6.44201	0.262339
$604$	6.19252	0.251970
$605$	−51.1637	−2.08010
$606$	−17.5470	−0.712800
$607$	−30.6562	−1.24430	−0.622148	−	0.782900i	$-0.713740\pi$
$607$	−30.6562	−1.24430	−0.622148	+	0.782900i	$0.713740\pi$
$608$	6.25808	0.253799
$609$	−41.4581	−1.67997
$610$	16.9557	0.686515
$611$	−9.50409	−0.384494
$612$	−6.82077	−0.275713
$613$	17.5748	0.709841	0.354920	−	0.934897i	$-0.384508\pi$
$613$	17.5748	0.709841	0.354920	+	0.934897i	$0.384508\pi$
$614$	−22.2556	−0.898162
$615$	21.8609	0.881516
$616$	−25.6041	−1.03162
$617$	10.0730	0.405522	0.202761	−	0.979228i	$-0.435009\pi$
$617$	10.0730	0.405522	0.202761	+	0.979228i	$0.435009\pi$
$618$	32.0854	1.29066
$619$	−12.2522	−0.492459	−0.246230	−	0.969212i	$-0.579192\pi$
$619$	−12.2522	−0.492459	−0.246230	+	0.969212i	$0.579192\pi$
$620$	−14.9622	−0.600898
$621$	−2.21055	−0.0887063
$622$	−5.16239	−0.206993
$623$	61.5284	2.46508
$624$	−5.93380	−0.237542
$625$	−7.84657	−0.313863
$626$	−34.3839	−1.37426
$627$	98.9297	3.95087
$628$	7.02873	0.280477
$629$	−3.59656	−0.143404
$630$	−18.6150	−0.741639
$631$	−38.5619	−1.53513	−0.767563	−	0.640973i	$-0.778531\pi$
$631$	−38.5619	−1.53513	−0.767563	+	0.640973i	$0.778531\pi$
$632$	17.1301	0.681400
$633$	50.8077	2.01943
$634$	−15.6821	−0.622817
$635$	0.736037	0.0292088
$636$	19.7148	0.781743
$637$	20.7094	0.820537
$638$	−28.2359	−1.11787
$639$	−7.74770	−0.306494
$640$	−1.63165	−0.0644967
$641$	18.1661	0.717519	0.358759	−	0.933430i	$-0.383200\pi$
$641$	18.1661	0.717519	0.358759	+	0.933430i	$0.383200\pi$
$642$	−21.7617	−0.858867
$643$	−7.80555	−0.307821	−0.153910	−	0.988085i	$-0.549187\pi$
$643$	−7.80555	−0.307821	−0.153910	+	0.988085i	$0.549187\pi$
$644$	−35.7772	−1.40982
$645$	−31.4594	−1.23871
$646$	−14.7193	−0.579123
$647$	−6.58881	−0.259033	−0.129516	−	0.991577i	$-0.541342\pi$
$647$	−6.58881	−0.259033	−0.129516	+	0.991577i	$0.541342\pi$
$648$	−9.29021	−0.364954
$649$	−22.5244	−0.884160
$650$	−5.71084	−0.223998
$651$	−87.6275	−3.43439
$652$	−7.85085	−0.307463
$653$	35.6242	1.39408	0.697041	−	0.717031i	$-0.254499\pi$
$653$	35.6242	1.39408	0.697041	+	0.717031i	$0.254499\pi$
$654$	36.7755	1.43804
$655$	−11.2205	−0.438420
$656$	5.51590	0.215360
$657$	−19.5936	−0.764417
$658$	−15.3055	−0.596672
$659$	0.604088	0.0235319	0.0117660	−	0.999931i	$-0.496255\pi$
$659$	0.604088	0.0235319	0.0117660	+	0.999931i	$0.496255\pi$
$660$	−25.7937	−1.00402
$661$	−23.8552	−0.927858	−0.463929	−	0.885872i	$-0.653561\pi$
$661$	−23.8552	−0.927858	−0.463929	+	0.885872i	$0.653561\pi$
$662$	−31.1154	−1.20933
$663$	13.9566	0.542029
$664$	−7.38539	−0.286609
$665$	−40.1714	−1.55778
$666$	4.43433	0.171827
$667$	−39.4546	−1.52769
$668$	8.77288	0.339433
$669$	55.1633	2.13274
$670$	−3.62461	−0.140031
$671$	67.6316	2.61089
$672$	−9.55589	−0.368626
$673$	28.6740	1.10530	0.552651	−	0.833413i	$-0.313616\pi$
$673$	28.6740	1.10530	0.552651	+	0.833413i	$0.313616\pi$
$674$	−16.3637	−0.630306
$675$	−0.568241	−0.0218716
$676$	−7.03213	−0.270467
$677$	−26.4862	−1.01795	−0.508973	−	0.860783i	$-0.669975\pi$
$677$	−26.4862	−1.01795	−0.508973	+	0.860783i	$0.669975\pi$
$678$	−9.95113	−0.382171
$679$	−37.5122	−1.43959
$680$	3.83773	0.147170
$681$	62.0519	2.37783
$682$	−59.6804	−2.28528
$683$	26.9505	1.03123	0.515615	−	0.856820i	$-0.327563\pi$
$683$	26.9505	1.03123	0.515615	+	0.856820i	$0.327563\pi$
$684$	18.1480	0.693905
$685$	32.1266	1.22749
$686$	5.81195	0.221901
$687$	−0.167890	−0.00640539
$688$	−7.93779	−0.302625
$689$	−19.8280	−0.755387
$690$	−36.0421	−1.37210
$691$	−0.960197	−0.0365276	−0.0182638	−	0.999833i	$-0.505814\pi$
$691$	−0.960197	−0.0365276	−0.0182638	+	0.999833i	$0.505814\pi$
$692$	20.0977	0.764001
$693$	−74.2501	−2.82053
$694$	4.10189	0.155705
$695$	18.7783	0.712301
$696$	−10.5381	−0.399445
$697$	−12.9737	−0.491413
$698$	−21.0142	−0.795399
$699$	11.0036	0.416193
$700$	−9.19683	−0.347608
$701$	−17.0425	−0.643685	−0.321842	−	0.946793i	$-0.604302\pi$
$701$	−17.0425	−0.643685	−0.321842	+	0.946793i	$0.604302\pi$
$702$	0.593815	0.0224121
$703$	9.56933	0.360914
$704$	−6.50822	−0.245288
$705$	−15.4188	−0.580707
$706$	−15.0533	−0.566540
$707$	28.4203	1.06886
$708$	−8.40648	−0.315935
$709$	−28.3692	−1.06543	−0.532715	−	0.846295i	$-0.678828\pi$
$709$	−28.3692	−1.06543	−0.532715	+	0.846295i	$0.678828\pi$
$710$	4.35927	0.163600
$711$	49.6761	1.86300
$712$	15.6397	0.586121
$713$	−83.3926	−3.12308
$714$	22.4759	0.841140
$715$	25.9418	0.970168
$716$	−22.0836	−0.825301
$717$	−7.51671	−0.280717
$718$	−8.27864	−0.308956
$719$	24.8035	0.925014	0.462507	−	0.886616i	$-0.346950\pi$
$719$	24.8035	0.925014	0.462507	+	0.886616i	$0.346950\pi$
$720$	−4.73167	−0.176339
$721$	−51.9675	−1.93537
$722$	20.1636	0.750410
$723$	−23.0696	−0.857966
$724$	0.504009	0.0187313
$725$	−10.1421	−0.376669
$726$	−76.1653	−2.82676
$727$	30.3174	1.12441	0.562206	−	0.826998i	$-0.309953\pi$
$727$	30.3174	1.12441	0.562206	+	0.826998i	$0.309953\pi$
$728$	9.61075	0.356198
$729$	−25.1696	−0.932209
$730$	11.0244	0.408030
$731$	18.6701	0.690538
$732$	25.2412	0.932943
$733$	−42.1520	−1.55692	−0.778460	−	0.627694i	$-0.783999\pi$
$733$	−42.1520	−1.55692	−0.778460	+	0.627694i	$0.783999\pi$
$734$	10.7723	0.397614
$735$	33.5977	1.23927
$736$	−9.09408	−0.335212
$737$	−14.4576	−0.532553
$738$	15.9957	0.588810
$739$	3.94245	0.145025	0.0725126	−	0.997367i	$-0.476898\pi$
$739$	3.94245	0.145025	0.0725126	+	0.997367i	$0.476898\pi$
$740$	−2.49499	−0.0917176
$741$	−37.1342	−1.36416
$742$	−31.9313	−1.17224
$743$	22.2927	0.817840	0.408920	−	0.912570i	$-0.365906\pi$
$743$	22.2927	0.817840	0.408920	+	0.912570i	$0.365906\pi$
$744$	−22.2737	−0.816594
$745$	−3.90529	−0.143079
$746$	0.104352	0.00382061
$747$	−21.4171	−0.783610
$748$	15.3077	0.559704
$749$	35.2466	1.28788
$750$	−29.0811	−1.06189
$751$	21.3230	0.778086	0.389043	−	0.921219i	$-0.372806\pi$
$751$	21.3230	0.778086	0.389043	+	0.921219i	$0.372806\pi$
$752$	−3.89046	−0.141870
$753$	−37.0857	−1.35148
$754$	10.5986	0.385978
$755$	−10.1040	−0.367724
$756$	0.956290	0.0347799
$757$	−5.03001	−0.182819	−0.0914095	−	0.995813i	$-0.529137\pi$
$757$	−5.03001	−0.182819	−0.0914095	+	0.995813i	$0.529137\pi$
$758$	9.03615	0.328208
$759$	−143.762	−5.21823
$760$	−10.2110	−0.370392
$761$	−34.9027	−1.26522	−0.632612	−	0.774469i	$-0.718017\pi$
$761$	−34.9027	−1.26522	−0.632612	+	0.774469i	$0.718017\pi$
$762$	1.09571	0.0396934
$763$	−59.5639	−2.15636
$764$	13.0768	0.473101
$765$	11.1291	0.402374
$766$	27.7505	1.00267
$767$	8.45475	0.305283
$768$	−2.42898	−0.0876481
$769$	21.1588	0.763005	0.381503	−	0.924368i	$-0.375407\pi$
$769$	21.1588	0.763005	0.381503	+	0.924368i	$0.375407\pi$
$770$	41.7771	1.50554
$771$	54.4915	1.96246
$772$	6.83261	0.245911
$773$	28.3876	1.02103	0.510515	−	0.859869i	$-0.329455\pi$
$773$	28.3876	1.02103	0.510515	+	0.859869i	$0.329455\pi$
$774$	−23.0190	−0.827401
$775$	−21.4368	−0.770032
$776$	−9.53508	−0.342289
$777$	−14.6121	−0.524205
$778$	−25.7264	−0.922338
$779$	34.5190	1.23677
$780$	9.68190	0.346668
$781$	17.3880	0.622190
$782$	21.3897	0.764895
$783$	1.05458	0.0376877
$784$	8.47732	0.302761
$785$	−11.4684	−0.409326
$786$	−16.7035	−0.595793
$787$	−8.25891	−0.294398	−0.147199	−	0.989107i	$-0.547026\pi$
$787$	−8.25891	−0.294398	−0.147199	+	0.989107i	$0.547026\pi$
$788$	−25.5654	−0.910730
$789$	−28.0442	−0.998399
$790$	−27.9504	−0.994431
$791$	16.1175	0.573071
$792$	−18.8734	−0.670636
$793$	−25.3862	−0.901489
$794$	−21.5241	−0.763861
$795$	−32.1677	−1.14087
$796$	14.2658	0.505637
$797$	−15.8016	−0.559721	−0.279861	−	0.960041i	$-0.590288\pi$
$797$	−15.8016	−0.559721	−0.279861	+	0.960041i	$0.590288\pi$
$798$	−59.8015	−2.11695
$799$	9.15055	0.323723
$800$	−2.33771	−0.0826505
$801$	45.3539	1.60250
$802$	−11.7675	−0.415525
$803$	43.9733	1.55178
$804$	−5.39582	−0.190296
$805$	58.3760	2.05748
$806$	22.4016	0.789062
$807$	37.8381	1.33196
$808$	7.22405	0.254141
$809$	36.4376	1.28108	0.640539	−	0.767926i	$-0.278711\pi$
$809$	36.4376	1.28108	0.640539	+	0.767926i	$0.278711\pi$
$810$	15.1584	0.532612
$811$	49.4947	1.73800	0.868998	−	0.494816i	$-0.164765\pi$
$811$	49.4947	1.73800	0.868998	+	0.494816i	$0.164765\pi$
$812$	17.0681	0.598974
$813$	−35.6149	−1.24907
$814$	−9.95183	−0.348812
$815$	12.8099	0.448710
$816$	5.71307	0.199998
$817$	−49.6753	−1.73792
$818$	25.5443	0.893137
$819$	27.8705	0.973873
$820$	−9.00004	−0.314295
$821$	−7.75605	−0.270688	−0.135344	−	0.990799i	$-0.543214\pi$
$821$	−7.75605	−0.270688	−0.135344	+	0.990799i	$0.543214\pi$
$822$	47.8256	1.66811
$823$	−47.1461	−1.64341	−0.821705	−	0.569914i	$-0.806977\pi$
$823$	−47.1461	−1.64341	−0.821705	+	0.569914i	$0.806977\pi$
$824$	−13.2094	−0.460172
$825$	−36.9553	−1.28662
$826$	13.6157	0.473750
$827$	−40.4001	−1.40485	−0.702425	−	0.711758i	$-0.747899\pi$
$827$	−40.4001	−1.40485	−0.702425	+	0.711758i	$0.747899\pi$
$828$	−26.3722	−0.916496
$829$	−36.0373	−1.25163	−0.625814	−	0.779973i	$-0.715233\pi$
$829$	−36.0373	−1.25163	−0.625814	+	0.779973i	$0.715233\pi$
$830$	12.0504	0.418275
$831$	68.6262	2.38062
$832$	2.44292	0.0846931
$833$	−19.9391	−0.690848
$834$	27.9545	0.967984
$835$	−14.3143	−0.495366
$836$	−40.7290	−1.40864
$837$	2.22900	0.0770457
$838$	−19.7092	−0.680842
$839$	−55.0706	−1.90125	−0.950623	−	0.310347i	$-0.899555\pi$
$839$	−55.0706	−1.90125	−0.950623	+	0.310347i	$0.899555\pi$
$840$	15.5919	0.537971
$841$	−10.1775	−0.350949
$842$	30.2532	1.04259
$843$	−53.2500	−1.83403
$844$	−20.9173	−0.720005
$845$	11.4740	0.394718
$846$	−11.2820	−0.387885
$847$	123.362	4.23877
$848$	−8.11651	−0.278722
$849$	26.3336	0.903767
$850$	5.49841	0.188594
$851$	−13.9059	−0.476688
$852$	6.48947	0.222326
$853$	15.9079	0.544677	0.272338	−	0.962202i	$-0.412203\pi$
$853$	15.9079	0.544677	0.272338	+	0.962202i	$0.412203\pi$
$854$	−40.8823	−1.39896
$855$	−29.6112	−1.01268
$856$	8.95921	0.306220
$857$	−50.3694	−1.72059	−0.860293	−	0.509801i	$-0.829719\pi$
$857$	−50.3694	−1.72059	−0.860293	+	0.509801i	$0.829719\pi$
$858$	38.6185	1.31841
$859$	29.0510	0.991206	0.495603	−	0.868549i	$-0.334947\pi$
$859$	29.0510	0.991206	0.495603	+	0.868549i	$0.334947\pi$
$860$	12.9517	0.441650
$861$	−52.7094	−1.79633
$862$	−34.8805	−1.18803
$863$	24.6713	0.839822	0.419911	−	0.907565i	$-0.362061\pi$
$863$	24.6713	0.839822	0.419911	+	0.907565i	$0.362061\pi$
$864$	0.243076	0.00826961
$865$	−32.7925	−1.11498
$866$	14.8819	0.505706
$867$	27.8552	0.946011
$868$	36.0759	1.22450
$869$	−111.487	−3.78193
$870$	17.1945	0.582948
$871$	5.42680	0.183880
$872$	−15.1403	−0.512716
$873$	−27.6510	−0.935846
$874$	−56.9115	−1.92506
$875$	47.1016	1.59233
$876$	16.4115	0.554495
$877$	−34.2934	−1.15801	−0.579004	−	0.815325i	$-0.696558\pi$
$877$	−34.2934	−1.15801	−0.579004	+	0.815325i	$0.696558\pi$
$878$	10.0693	0.339822
$879$	73.1456	2.46714
$880$	10.6192	0.357972
$881$	−2.98833	−0.100680	−0.0503398	−	0.998732i	$-0.516030\pi$
$881$	−2.98833	−0.100680	−0.0503398	+	0.998732i	$0.516030\pi$
$882$	24.5836	0.827773
$883$	48.0252	1.61618	0.808089	−	0.589061i	$-0.200502\pi$
$883$	48.0252	1.61618	0.808089	+	0.589061i	$0.200502\pi$
$884$	−5.74587	−0.193255
$885$	13.7165	0.461074
$886$	26.5038	0.890414
$887$	19.1642	0.643471	0.321735	−	0.946830i	$-0.395734\pi$
$887$	19.1642	0.643471	0.321735	+	0.946830i	$0.395734\pi$
$888$	−3.71419	−0.124640
$889$	−1.77468	−0.0595209
$890$	−25.5185	−0.855382
$891$	60.4627	2.02558
$892$	−22.7105	−0.760405
$893$	−24.3468	−0.814735
$894$	−5.81365	−0.194438
$895$	36.0327	1.20444
$896$	3.93412	0.131430
$897$	53.9624	1.80175
$898$	−28.6134	−0.954840
$899$	39.7839	1.32687
$900$	−6.77919	−0.225973
$901$	19.0904	0.635994
$902$	−35.8987	−1.19530
$903$	75.8527	2.52422
$904$	4.09684	0.136259
$905$	−0.822367	−0.0273364
$906$	−15.0415	−0.499720
$907$	3.57374	0.118664	0.0593321	−	0.998238i	$-0.481103\pi$
$907$	3.57374	0.118664	0.0593321	+	0.998238i	$0.481103\pi$
$908$	−25.5465	−0.847791
$909$	20.9492	0.694842
$910$	−15.6814	−0.519834
$911$	20.0567	0.664507	0.332253	−	0.943190i	$-0.392191\pi$
$911$	20.0567	0.664507	0.332253	+	0.943190i	$0.392191\pi$
$912$	−15.2007	−0.503346
$913$	48.0658	1.59075
$914$	0.264389	0.00874520
$915$	−41.1849	−1.36153
$916$	0.0691195	0.00228377
$917$	27.0540	0.893401
$918$	−0.571726	−0.0188698
$919$	−0.392125	−0.0129350	−0.00646751	−	0.999979i	$-0.502059\pi$
$919$	−0.392125	−0.0129350	−0.00646751	+	0.999979i	$0.502059\pi$
$920$	14.8384	0.489207
$921$	54.0583	1.78128
$922$	−25.3513	−0.834901
$923$	−6.52673	−0.214830
$924$	62.1919	2.04596
$925$	−3.57463	−0.117533
$926$	38.7891	1.27469
$927$	−38.3064	−1.25815
$928$	4.33849	0.142418
$929$	−19.3263	−0.634075	−0.317037	−	0.948413i	$-0.602688\pi$
$929$	−19.3263	−0.634075	−0.317037	+	0.948413i	$0.602688\pi$
$930$	36.3430	1.19173
$931$	53.0517	1.73870
$932$	−4.53012	−0.148389
$933$	12.5393	0.410519
$934$	−38.7430	−1.26771
$935$	−24.9768	−0.816828
$936$	7.08429	0.231557
$937$	54.2433	1.77205	0.886026	−	0.463636i	$-0.153455\pi$
$937$	54.2433	1.77205	0.886026	+	0.463636i	$0.153455\pi$
$938$	8.73941	0.285352
$939$	83.5176	2.72549
$940$	6.34788	0.207045
$941$	29.0862	0.948183	0.474092	−	0.880476i	$-0.342777\pi$
$941$	29.0862	0.948183	0.474092	+	0.880476i	$0.342777\pi$
$942$	−17.0726	−0.556256
$943$	−50.1620	−1.63350
$944$	3.46092	0.112643
$945$	−1.56033	−0.0507576
$946$	51.6609	1.67964
$947$	51.9951	1.68961	0.844807	−	0.535072i	$-0.179715\pi$
$947$	51.9951	1.68961	0.844807	+	0.535072i	$0.179715\pi$
$948$	−41.6087	−1.35139
$949$	−16.5058	−0.535800
$950$	−14.6296	−0.474646
$951$	38.0916	1.23520
$952$	−9.25325	−0.299900
$953$	3.97607	0.128798	0.0643988	−	0.997924i	$-0.479487\pi$
$953$	3.97607	0.128798	0.0643988	+	0.997924i	$0.479487\pi$
$954$	−23.5373	−0.762048
$955$	−21.3368	−0.690442
$956$	3.09460	0.100087
$957$	68.5842	2.21701
$958$	7.52557	0.243140
$959$	−77.4613	−2.50136
$960$	3.96325	0.127913
$961$	53.0888	1.71254
$962$	3.73551	0.120438
$963$	25.9811	0.837228
$964$	9.49765	0.305899
$965$	−11.1484	−0.358881
$966$	86.9020	2.79603
$967$	50.2201	1.61497	0.807485	−	0.589889i	$-0.200828\pi$
$967$	50.2201	1.61497	0.807485	+	0.589889i	$0.200828\pi$
$968$	31.3570	1.00785
$969$	35.7529	1.14855
$970$	15.5579	0.499535
$971$	−1.89168	−0.0607070	−0.0303535	−	0.999539i	$-0.509663\pi$
$971$	−1.89168	−0.0607070	−0.0303535	+	0.999539i	$0.509663\pi$
$972$	21.8365	0.700405
$973$	−45.2768	−1.45151
$974$	−27.9026	−0.894055
$975$	13.8715	0.444243
$976$	−10.3917	−0.332631
$977$	41.2310	1.31910	0.659548	−	0.751663i	$-0.270748\pi$
$977$	41.2310	1.31910	0.659548	+	0.751663i	$0.270748\pi$
$978$	19.0695	0.609776
$979$	−101.786	−3.25311
$980$	−13.8320	−0.441848
$981$	−43.9059	−1.40181
$982$	−11.2908	−0.360305
$983$	−11.6824	−0.372610	−0.186305	−	0.982492i	$-0.559651\pi$
$983$	−11.6824	−0.372610	−0.186305	+	0.982492i	$0.559651\pi$
$984$	−13.3980	−0.427113
$985$	41.7139	1.32911
$986$	−10.2043	−0.324972
$987$	37.1768	1.18335
$988$	15.2880	0.486376
$989$	72.1869	2.29541
$990$	30.7948	0.978723
$991$	27.6633	0.878754	0.439377	−	0.898303i	$-0.355199\pi$
$991$	27.6633	0.878754	0.439377	+	0.898303i	$0.355199\pi$
$992$	9.17000	0.291148
$993$	75.5785	2.39841
$994$	−10.5108	−0.333381
$995$	−23.2768	−0.737924
$996$	17.9389	0.568417
$997$	5.23529	0.165803	0.0829017	−	0.996558i	$-0.473581\pi$
$997$	5.23529	0.165803	0.0829017	+	0.996558i	$0.473581\pi$
$998$	−10.2253	−0.323677
$999$	0.371691	0.0117598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.13	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.42898 q^{3} +1.00000 q^{4} -1.63165 q^{5} -2.42898 q^{6} +3.93412 q^{7} +1.00000 q^{8} +2.89993 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.42898 q^{3} +1.00000 q^{4} -1.63165 q^{5} -2.42898 q^{6} +3.93412 q^{7} +1.00000 q^{8} +2.89993 q^{9} -1.63165 q^{10} -6.50822 q^{11} -2.42898 q^{12} +2.44292 q^{13} +3.93412 q^{14} +3.96325 q^{15} +1.00000 q^{16} -2.35205 q^{17} +2.89993 q^{18} +6.25808 q^{19} -1.63165 q^{20} -9.55589 q^{21} -6.50822 q^{22} -9.09408 q^{23} -2.42898 q^{24} -2.33771 q^{25} +2.44292 q^{26} +0.243076 q^{27} +3.93412 q^{28} +4.33849 q^{29} +3.96325 q^{30} +9.17000 q^{31} +1.00000 q^{32} +15.8083 q^{33} -2.35205 q^{34} -6.41912 q^{35} +2.89993 q^{36} +1.52912 q^{37} +6.25808 q^{38} -5.93380 q^{39} -1.63165 q^{40} +5.51590 q^{41} -9.55589 q^{42} -7.93779 q^{43} -6.50822 q^{44} -4.73167 q^{45} -9.09408 q^{46} -3.89046 q^{47} -2.42898 q^{48} +8.47732 q^{49} -2.33771 q^{50} +5.71307 q^{51} +2.44292 q^{52} -8.11651 q^{53} +0.243076 q^{54} +10.6192 q^{55} +3.93412 q^{56} -15.2007 q^{57} +4.33849 q^{58} +3.46092 q^{59} +3.96325 q^{60} -10.3917 q^{61} +9.17000 q^{62} +11.4087 q^{63} +1.00000 q^{64} -3.98600 q^{65} +15.8083 q^{66} +2.22144 q^{67} -2.35205 q^{68} +22.0893 q^{69} -6.41912 q^{70} -2.67169 q^{71} +2.89993 q^{72} -6.75657 q^{73} +1.52912 q^{74} +5.67824 q^{75} +6.25808 q^{76} -25.6041 q^{77} -5.93380 q^{78} +17.1301 q^{79} -1.63165 q^{80} -9.29021 q^{81} +5.51590 q^{82} -7.38539 q^{83} -9.55589 q^{84} +3.83773 q^{85} -7.93779 q^{86} -10.5381 q^{87} -6.50822 q^{88} +15.6397 q^{89} -4.73167 q^{90} +9.61075 q^{91} -9.09408 q^{92} -22.2737 q^{93} -3.89046 q^{94} -10.2110 q^{95} -2.42898 q^{96} -9.53508 q^{97} +8.47732 q^{98} -18.8734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 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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