LMFDB - Embedded newform 8026.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, 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("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.34399 q^{3} +1.00000 q^{4} +1.04947 q^{5} +2.34399 q^{6} -2.18495 q^{7} -1.00000 q^{8} +2.49429 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.34399 q^{3} +1.00000 q^{4} +1.04947 q^{5} +2.34399 q^{6} -2.18495 q^{7} -1.00000 q^{8} +2.49429 q^{9} -1.04947 q^{10} -1.41075 q^{11} -2.34399 q^{12} +1.55513 q^{13} +2.18495 q^{14} -2.45996 q^{15} +1.00000 q^{16} -5.65650 q^{17} -2.49429 q^{18} -3.08363 q^{19} +1.04947 q^{20} +5.12150 q^{21} +1.41075 q^{22} -7.68050 q^{23} +2.34399 q^{24} -3.89860 q^{25} -1.55513 q^{26} +1.18539 q^{27} -2.18495 q^{28} -9.05297 q^{29} +2.45996 q^{30} +0.0306546 q^{31} -1.00000 q^{32} +3.30679 q^{33} +5.65650 q^{34} -2.29305 q^{35} +2.49429 q^{36} -3.29992 q^{37} +3.08363 q^{38} -3.64522 q^{39} -1.04947 q^{40} -7.01221 q^{41} -5.12150 q^{42} -4.37246 q^{43} -1.41075 q^{44} +2.61769 q^{45} +7.68050 q^{46} +9.27923 q^{47} -2.34399 q^{48} -2.22599 q^{49} +3.89860 q^{50} +13.2588 q^{51} +1.55513 q^{52} -3.22734 q^{53} -1.18539 q^{54} -1.48055 q^{55} +2.18495 q^{56} +7.22800 q^{57} +9.05297 q^{58} +6.66120 q^{59} -2.45996 q^{60} -8.75759 q^{61} -0.0306546 q^{62} -5.44989 q^{63} +1.00000 q^{64} +1.63207 q^{65} -3.30679 q^{66} -4.41171 q^{67} -5.65650 q^{68} +18.0030 q^{69} +2.29305 q^{70} +5.29311 q^{71} -2.49429 q^{72} -15.4311 q^{73} +3.29992 q^{74} +9.13829 q^{75} -3.08363 q^{76} +3.08243 q^{77} +3.64522 q^{78} +11.0534 q^{79} +1.04947 q^{80} -10.2614 q^{81} +7.01221 q^{82} -5.20435 q^{83} +5.12150 q^{84} -5.93635 q^{85} +4.37246 q^{86} +21.2201 q^{87} +1.41075 q^{88} +12.0123 q^{89} -2.61769 q^{90} -3.39789 q^{91} -7.68050 q^{92} -0.0718540 q^{93} -9.27923 q^{94} -3.23619 q^{95} +2.34399 q^{96} -8.28067 q^{97} +2.22599 q^{98} -3.51882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * 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
$3$	−2.34399	−1.35330	−0.676651	−	0.736304i	$-0.736570\pi$
$3$	−2.34399	−1.35330	−0.676651	+	0.736304i	$0.736570\pi$
$4$	1.00000	0.500000
$5$	1.04947	0.469339	0.234670	−	0.972075i	$-0.424599\pi$
$5$	1.04947	0.469339	0.234670	+	0.972075i	$0.424599\pi$
$6$	2.34399	0.956930
$7$	−2.18495	−0.825834	−0.412917	−	0.910769i	$-0.635490\pi$
$7$	−2.18495	−0.825834	−0.412917	+	0.910769i	$0.635490\pi$
$8$	−1.00000	−0.353553
$9$	2.49429	0.831428
$10$	−1.04947	−0.331873
$11$	−1.41075	−0.425358	−0.212679	−	0.977122i	$-0.568219\pi$
$11$	−1.41075	−0.425358	−0.212679	+	0.977122i	$0.568219\pi$
$12$	−2.34399	−0.676651
$13$	1.55513	0.431316	0.215658	−	0.976469i	$-0.430810\pi$
$13$	1.55513	0.431316	0.215658	+	0.976469i	$0.430810\pi$
$14$	2.18495	0.583953
$15$	−2.45996	−0.635158
$16$	1.00000	0.250000
$17$	−5.65650	−1.37190	−0.685951	−	0.727647i	$-0.740614\pi$
$17$	−5.65650	−1.37190	−0.685951	+	0.727647i	$0.740614\pi$
$18$	−2.49429	−0.587909
$19$	−3.08363	−0.707434	−0.353717	−	0.935352i	$-0.615082\pi$
$19$	−3.08363	−0.707434	−0.353717	+	0.935352i	$0.615082\pi$
$20$	1.04947	0.234670
$21$	5.12150	1.11760
$22$	1.41075	0.300774
$23$	−7.68050	−1.60150	−0.800748	−	0.599002i	$-0.795564\pi$
$23$	−7.68050	−1.60150	−0.800748	+	0.599002i	$0.795564\pi$
$24$	2.34399	0.478465
$25$	−3.89860	−0.779721
$26$	−1.55513	−0.304987
$27$	1.18539	0.228128
$28$	−2.18495	−0.412917
$29$	−9.05297	−1.68109	−0.840547	−	0.541738i	$-0.817767\pi$
$29$	−9.05297	−1.68109	−0.840547	+	0.541738i	$0.817767\pi$
$30$	2.45996	0.449124
$31$	0.0306546	0.00550573	0.00275286	−	0.999996i	$-0.499124\pi$
$31$	0.0306546	0.00550573	0.00275286	+	0.999996i	$0.499124\pi$
$32$	−1.00000	−0.176777
$33$	3.30679	0.575638
$34$	5.65650	0.970082
$35$	−2.29305	−0.387596
$36$	2.49429	0.415714
$37$	−3.29992	−0.542504	−0.271252	−	0.962508i	$-0.587438\pi$
$37$	−3.29992	−0.542504	−0.271252	+	0.962508i	$0.587438\pi$
$38$	3.08363	0.500231
$39$	−3.64522	−0.583702
$40$	−1.04947	−0.165936
$41$	−7.01221	−1.09512	−0.547561	−	0.836766i	$-0.684444\pi$
$41$	−7.01221	−1.09512	−0.547561	+	0.836766i	$0.684444\pi$
$42$	−5.12150	−0.790265
$43$	−4.37246	−0.666795	−0.333397	−	0.942786i	$-0.608195\pi$
$43$	−4.37246	−0.666795	−0.333397	+	0.942786i	$0.608195\pi$
$44$	−1.41075	−0.212679
$45$	2.61769	0.390222
$46$	7.68050	1.13243
$47$	9.27923	1.35351	0.676757	−	0.736206i	$-0.263385\pi$
$47$	9.27923	1.35351	0.676757	+	0.736206i	$0.263385\pi$
$48$	−2.34399	−0.338326
$49$	−2.22599	−0.317999
$50$	3.89860	0.551346
$51$	13.2588	1.85660
$52$	1.55513	0.215658
$53$	−3.22734	−0.443310	−0.221655	−	0.975125i	$-0.571146\pi$
$53$	−3.22734	−0.443310	−0.221655	+	0.975125i	$0.571146\pi$
$54$	−1.18539	−0.161311
$55$	−1.48055	−0.199637
$56$	2.18495	0.291976
$57$	7.22800	0.957373
$58$	9.05297	1.18871
$59$	6.66120	0.867215	0.433608	−	0.901102i	$-0.357240\pi$
$59$	6.66120	0.867215	0.433608	+	0.901102i	$0.357240\pi$
$60$	−2.45996	−0.317579
$61$	−8.75759	−1.12129	−0.560647	−	0.828055i	$-0.689448\pi$
$61$	−8.75759	−1.12129	−0.560647	+	0.828055i	$0.689448\pi$
$62$	−0.0306546	−0.00389314
$63$	−5.44989	−0.686621
$64$	1.00000	0.125000
$65$	1.63207	0.202434
$66$	−3.30679	−0.407038
$67$	−4.41171	−0.538976	−0.269488	−	0.963004i	$-0.586855\pi$
$67$	−4.41171	−0.538976	−0.269488	+	0.963004i	$0.586855\pi$
$68$	−5.65650	−0.685951
$69$	18.0030	2.16731
$70$	2.29305	0.274072
$71$	5.29311	0.628176	0.314088	−	0.949394i	$-0.398301\pi$
$71$	5.29311	0.628176	0.314088	+	0.949394i	$0.398301\pi$
$72$	−2.49429	−0.293954
$73$	−15.4311	−1.80608	−0.903040	−	0.429557i	$-0.858670\pi$
$73$	−15.4311	−1.80608	−0.903040	+	0.429557i	$0.858670\pi$
$74$	3.29992	0.383608
$75$	9.13829	1.05520
$76$	−3.08363	−0.353717
$77$	3.08243	0.351275
$78$	3.64522	0.412739
$79$	11.0534	1.24361	0.621803	−	0.783173i	$-0.286400\pi$
$79$	11.0534	1.24361	0.621803	+	0.783173i	$0.286400\pi$
$80$	1.04947	0.117335
$81$	−10.2614	−1.14016
$82$	7.01221	0.774369
$83$	−5.20435	−0.571252	−0.285626	−	0.958341i	$-0.592202\pi$
$83$	−5.20435	−0.571252	−0.285626	+	0.958341i	$0.592202\pi$
$84$	5.12150	0.558801
$85$	−5.93635	−0.643887
$86$	4.37246	0.471495
$87$	21.2201	2.27503
$88$	1.41075	0.150387
$89$	12.0123	1.27330	0.636649	−	0.771153i	$-0.280320\pi$
$89$	12.0123	1.27330	0.636649	+	0.771153i	$0.280320\pi$
$90$	−2.61769	−0.275928
$91$	−3.39789	−0.356196
$92$	−7.68050	−0.800748
$93$	−0.0718540	−0.00745091
$94$	−9.27923	−0.957079
$95$	−3.23619	−0.332026
$96$	2.34399	0.239232
$97$	−8.28067	−0.840775	−0.420388	−	0.907345i	$-0.638106\pi$
$97$	−8.28067	−0.840775	−0.420388	+	0.907345i	$0.638106\pi$
$98$	2.22599	0.224859
$99$	−3.51882	−0.353655
$100$	−3.89860	−0.389860
$101$	−4.82528	−0.480133	−0.240067	−	0.970756i	$-0.577169\pi$
$101$	−4.82528	−0.480133	−0.240067	+	0.970756i	$0.577169\pi$
$102$	−13.2588	−1.31281
$103$	−5.80979	−0.572456	−0.286228	−	0.958162i	$-0.592401\pi$
$103$	−5.80979	−0.572456	−0.286228	+	0.958162i	$0.592401\pi$
$104$	−1.55513	−0.152493
$105$	5.37488	0.524535
$106$	3.22734	0.313467
$107$	3.60050	0.348073	0.174037	−	0.984739i	$-0.444319\pi$
$107$	3.60050	0.348073	0.174037	+	0.984739i	$0.444319\pi$
$108$	1.18539	0.114064
$109$	7.46909	0.715409	0.357704	−	0.933835i	$-0.383560\pi$
$109$	7.46909	0.715409	0.357704	+	0.933835i	$0.383560\pi$
$110$	1.48055	0.141165
$111$	7.73498	0.734172
$112$	−2.18495	−0.206458
$113$	8.83095	0.830746	0.415373	−	0.909651i	$-0.363651\pi$
$113$	8.83095	0.830746	0.415373	+	0.909651i	$0.363651\pi$
$114$	−7.22800	−0.676965
$115$	−8.06049	−0.751644
$116$	−9.05297	−0.840547
$117$	3.87895	0.358609
$118$	−6.66120	−0.613214
$119$	12.3592	1.13296
$120$	2.45996	0.224562
$121$	−9.00978	−0.819070
$122$	8.75759	0.792875
$123$	16.4365	1.48203
$124$	0.0306546	0.00275286
$125$	−9.33885	−0.835293
$126$	5.44989	0.485515
$127$	−13.0920	−1.16173	−0.580863	−	0.814001i	$-0.697285\pi$
$127$	−13.0920	−1.16173	−0.580863	+	0.814001i	$0.697285\pi$
$128$	−1.00000	−0.0883883
$129$	10.2490	0.902375
$130$	−1.63207	−0.143142
$131$	−20.3025	−1.77383	−0.886917	−	0.461928i	$-0.847158\pi$
$131$	−20.3025	−1.77383	−0.886917	+	0.461928i	$0.847158\pi$
$132$	3.30679	0.287819
$133$	6.73759	0.584223
$134$	4.41171	0.381114
$135$	1.24404	0.107070
$136$	5.65650	0.485041
$137$	13.6218	1.16379	0.581894	−	0.813265i	$-0.302312\pi$
$137$	13.6218	1.16379	0.581894	+	0.813265i	$0.302312\pi$
$138$	−18.0030	−1.53252
$139$	−11.2288	−0.952415	−0.476207	−	0.879333i	$-0.657989\pi$
$139$	−11.2288	−0.952415	−0.476207	+	0.879333i	$0.657989\pi$
$140$	−2.29305	−0.193798
$141$	−21.7504	−1.83172
$142$	−5.29311	−0.444188
$143$	−2.19391	−0.183464
$144$	2.49429	0.207857
$145$	−9.50086	−0.789003
$146$	15.4311	1.27709
$147$	5.21770	0.430349
$148$	−3.29992	−0.271252
$149$	11.6635	0.955510	0.477755	−	0.878493i	$-0.341451\pi$
$149$	11.6635	0.955510	0.477755	+	0.878493i	$0.341451\pi$
$150$	−9.13829	−0.746138
$151$	17.4128	1.41703	0.708517	−	0.705694i	$-0.249365\pi$
$151$	17.4128	1.41703	0.708517	+	0.705694i	$0.249365\pi$
$152$	3.08363	0.250116
$153$	−14.1089	−1.14064
$154$	−3.08243	−0.248389
$155$	0.0321712	0.00258405
$156$	−3.64522	−0.291851
$157$	18.7650	1.49761	0.748804	−	0.662792i	$-0.230629\pi$
$157$	18.7650	1.49761	0.748804	+	0.662792i	$0.230629\pi$
$158$	−11.0534	−0.879363
$159$	7.56486	0.599932
$160$	−1.04947	−0.0829682
$161$	16.7815	1.32257
$162$	10.2614	0.806212
$163$	−15.4664	−1.21142	−0.605709	−	0.795686i	$-0.707110\pi$
$163$	−15.4664	−1.21142	−0.605709	+	0.795686i	$0.707110\pi$
$164$	−7.01221	−0.547561
$165$	3.47039	0.270170
$166$	5.20435	0.403936
$167$	−17.5983	−1.36180	−0.680900	−	0.732377i	$-0.738411\pi$
$167$	−17.5983	−1.36180	−0.680900	+	0.732377i	$0.738411\pi$
$168$	−5.12150	−0.395132
$169$	−10.5816	−0.813966
$170$	5.93635	0.455297
$171$	−7.69146	−0.588181
$172$	−4.37246	−0.333397
$173$	−8.61548	−0.655023	−0.327511	−	0.944847i	$-0.606210\pi$
$173$	−8.61548	−0.655023	−0.327511	+	0.944847i	$0.606210\pi$
$174$	−21.2201	−1.60869
$175$	8.51826	0.643920
$176$	−1.41075	−0.106340
$177$	−15.6138	−1.17360
$178$	−12.0123	−0.900358
$179$	−0.878161	−0.0656368	−0.0328184	−	0.999461i	$-0.510448\pi$
$179$	−0.878161	−0.0656368	−0.0328184	+	0.999461i	$0.510448\pi$
$180$	2.61769	0.195111
$181$	9.61659	0.714796	0.357398	−	0.933952i	$-0.383664\pi$
$181$	9.61659	0.714796	0.357398	+	0.933952i	$0.383664\pi$
$182$	3.39789	0.251868
$183$	20.5277	1.51745
$184$	7.68050	0.566214
$185$	−3.46318	−0.254618
$186$	0.0718540	0.00526859
$187$	7.97992	0.583550
$188$	9.27923	0.676757
$189$	−2.59002	−0.188396
$190$	3.23619	0.234778
$191$	20.8588	1.50929	0.754645	−	0.656133i	$-0.227809\pi$
$191$	20.8588	1.50929	0.754645	+	0.656133i	$0.227809\pi$
$192$	−2.34399	−0.169163
$193$	−18.7552	−1.35003	−0.675014	−	0.737805i	$-0.735862\pi$
$193$	−18.7552	−1.35003	−0.675014	+	0.737805i	$0.735862\pi$
$194$	8.28067	0.594518
$195$	−3.82556	−0.273954
$196$	−2.22599	−0.158999
$197$	−21.2499	−1.51399	−0.756997	−	0.653419i	$-0.773334\pi$
$197$	−21.2499	−1.51399	−0.756997	+	0.653419i	$0.773334\pi$
$198$	3.51882	0.250072
$199$	14.3586	1.01785	0.508927	−	0.860810i	$-0.330042\pi$
$199$	14.3586	1.01785	0.508927	+	0.860810i	$0.330042\pi$
$200$	3.89860	0.275673
$201$	10.3410	0.729398
$202$	4.82528	0.339506
$203$	19.7803	1.38830
$204$	13.2588	0.928300
$205$	−7.35913	−0.513984
$206$	5.80979	0.404788
$207$	−19.1574	−1.33153
$208$	1.55513	0.107829
$209$	4.35025	0.300913
$210$	−5.37488	−0.370902
$211$	0.948037	0.0652656	0.0326328	−	0.999467i	$-0.489611\pi$
$211$	0.948037	0.0652656	0.0326328	+	0.999467i	$0.489611\pi$
$212$	−3.22734	−0.221655
$213$	−12.4070	−0.850113
$214$	−3.60050	−0.246125
$215$	−4.58879	−0.312953
$216$	−1.18539	−0.0806556
$217$	−0.0669787	−0.00454681
$218$	−7.46909	−0.505870
$219$	36.1704	2.44417
$220$	−1.48055	−0.0998186
$221$	−8.79661	−0.591724
$222$	−7.73498	−0.519138
$223$	1.73412	0.116125	0.0580625	−	0.998313i	$-0.481508\pi$
$223$	1.73412	0.116125	0.0580625	+	0.998313i	$0.481508\pi$
$224$	2.18495	0.145988
$225$	−9.72423	−0.648282
$226$	−8.83095	−0.587426
$227$	21.5834	1.43254	0.716271	−	0.697822i	$-0.245848\pi$
$227$	21.5834	1.43254	0.716271	+	0.697822i	$0.245848\pi$
$228$	7.22800	0.478686
$229$	−13.5664	−0.896493	−0.448246	−	0.893910i	$-0.647951\pi$
$229$	−13.5664	−0.896493	−0.448246	+	0.893910i	$0.647951\pi$
$230$	8.06049	0.531493
$231$	−7.22517	−0.475381
$232$	9.05297	0.594357
$233$	−26.1818	−1.71522	−0.857612	−	0.514297i	$-0.828053\pi$
$233$	−26.1818	−1.71522	−0.857612	+	0.514297i	$0.828053\pi$
$234$	−3.87895	−0.253575
$235$	9.73831	0.635257
$236$	6.66120	0.433608
$237$	−25.9091	−1.68298
$238$	−12.3592	−0.801126
$239$	−6.51518	−0.421432	−0.210716	−	0.977547i	$-0.567580\pi$
$239$	−6.51518	−0.421432	−0.210716	+	0.977547i	$0.567580\pi$
$240$	−2.45996	−0.158789
$241$	−16.3552	−1.05353	−0.526766	−	0.850010i	$-0.676595\pi$
$241$	−16.3552	−1.05353	−0.526766	+	0.850010i	$0.676595\pi$
$242$	9.00978	0.579170
$243$	20.4964	1.31485
$244$	−8.75759	−0.560647
$245$	−2.33612	−0.149249
$246$	−16.4365	−1.04796
$247$	−4.79546	−0.305128
$248$	−0.0306546	−0.00194657
$249$	12.1989	0.773077
$250$	9.33885	0.590641
$251$	12.0030	0.757624	0.378812	−	0.925474i	$-0.376333\pi$
$251$	12.0030	0.757624	0.378812	+	0.925474i	$0.376333\pi$
$252$	−5.44989	−0.343311
$253$	10.8353	0.681209
$254$	13.0920	0.821464
$255$	13.9147	0.871375
$256$	1.00000	0.0625000
$257$	−19.5817	−1.22147	−0.610737	−	0.791833i	$-0.709127\pi$
$257$	−19.5817	−1.22147	−0.610737	+	0.791833i	$0.709127\pi$
$258$	−10.2490	−0.638075
$259$	7.21016	0.448018
$260$	1.63207	0.101217
$261$	−22.5807	−1.39771
$262$	20.3025	1.25429
$263$	17.7616	1.09523	0.547614	−	0.836731i	$-0.315536\pi$
$263$	17.7616	1.09523	0.547614	+	0.836731i	$0.315536\pi$
$264$	−3.30679	−0.203519
$265$	−3.38701	−0.208062
$266$	−6.73759	−0.413108
$267$	−28.1566	−1.72316
$268$	−4.41171	−0.269488
$269$	−1.39786	−0.0852288	−0.0426144	−	0.999092i	$-0.513569\pi$
$269$	−1.39786	−0.0852288	−0.0426144	+	0.999092i	$0.513569\pi$
$270$	−1.24404	−0.0757096
$271$	−8.65894	−0.525993	−0.262996	−	0.964797i	$-0.584711\pi$
$271$	−8.65894	−0.525993	−0.262996	+	0.964797i	$0.584711\pi$
$272$	−5.65650	−0.342976
$273$	7.96461	0.482040
$274$	−13.6218	−0.822922
$275$	5.49997	0.331661
$276$	18.0030	1.08365
$277$	−0.130566	−0.00784498	−0.00392249	−	0.999992i	$-0.501249\pi$
$277$	−0.130566	−0.00784498	−0.00392249	+	0.999992i	$0.501249\pi$
$278$	11.2288	0.673459
$279$	0.0764613	0.00457762
$280$	2.29305	0.137036
$281$	−17.5677	−1.04800	−0.524002	−	0.851717i	$-0.675561\pi$
$281$	−17.5677	−1.04800	−0.524002	+	0.851717i	$0.675561\pi$
$282$	21.7504	1.29522
$283$	−7.59996	−0.451770	−0.225885	−	0.974154i	$-0.572527\pi$
$283$	−7.59996	−0.451770	−0.225885	+	0.974154i	$0.572527\pi$
$284$	5.29311	0.314088
$285$	7.58560	0.449332
$286$	2.19391	0.129729
$287$	15.3213	0.904389
$288$	−2.49429	−0.146977
$289$	14.9960	0.882117
$290$	9.50086	0.557910
$291$	19.4098	1.13782
$292$	−15.4311	−0.903040
$293$	10.7354	0.627168	0.313584	−	0.949560i	$-0.398470\pi$
$293$	10.7354	0.627168	0.313584	+	0.949560i	$0.398470\pi$
$294$	−5.21770	−0.304303
$295$	6.99076	0.407018
$296$	3.29992	0.191804
$297$	−1.67229	−0.0970363
$298$	−11.6635	−0.675647
$299$	−11.9442	−0.690751
$300$	9.13829	0.527599
$301$	9.55362	0.550661
$302$	−17.4128	−1.00199
$303$	11.3104	0.649766
$304$	−3.08363	−0.176859
$305$	−9.19086	−0.526267
$306$	14.1089	0.806553
$307$	−12.9018	−0.736346	−0.368173	−	0.929757i	$-0.620017\pi$
$307$	−12.9018	−0.736346	−0.368173	+	0.929757i	$0.620017\pi$
$308$	3.08243	0.175638
$309$	13.6181	0.774706
$310$	−0.0321712	−0.00182720
$311$	−5.19578	−0.294626	−0.147313	−	0.989090i	$-0.547062\pi$
$311$	−5.19578	−0.294626	−0.147313	+	0.989090i	$0.547062\pi$
$312$	3.64522	0.206370
$313$	−6.42747	−0.363302	−0.181651	−	0.983363i	$-0.558144\pi$
$313$	−6.42747	−0.363302	−0.181651	+	0.983363i	$0.558144\pi$
$314$	−18.7650	−1.05897
$315$	−5.71952	−0.322258
$316$	11.0534	0.621803
$317$	12.2775	0.689573	0.344787	−	0.938681i	$-0.387951\pi$
$317$	12.2775	0.689573	0.344787	+	0.938681i	$0.387951\pi$
$318$	−7.56486	−0.424216
$319$	12.7715	0.715067
$320$	1.04947	0.0586674
$321$	−8.43953	−0.471049
$322$	−16.7815	−0.935197
$323$	17.4426	0.970531
$324$	−10.2614	−0.570078
$325$	−6.06285	−0.336306
$326$	15.4664	0.856602
$327$	−17.5075	−0.968165
$328$	7.01221	0.387184
$329$	−20.2747	−1.11778
$330$	−3.47039	−0.191039
$331$	7.40674	0.407111	0.203556	−	0.979063i	$-0.434750\pi$
$331$	7.40674	0.407111	0.203556	+	0.979063i	$0.434750\pi$
$332$	−5.20435	−0.285626
$333$	−8.23094	−0.451053
$334$	17.5983	0.962938
$335$	−4.62998	−0.252963
$336$	5.12150	0.279401
$337$	−6.15145	−0.335091	−0.167545	−	0.985864i	$-0.553584\pi$
$337$	−6.15145	−0.335091	−0.167545	+	0.985864i	$0.553584\pi$
$338$	10.5816	0.575561
$339$	−20.6996	−1.12425
$340$	−5.93635	−0.321944
$341$	−0.0432461	−0.00234191
$342$	7.69146	0.415907
$343$	20.1583	1.08845
$344$	4.37246	0.235747
$345$	18.8937	1.01720
$346$	8.61548	0.463171
$347$	−3.12435	−0.167724	−0.0838620	−	0.996477i	$-0.526725\pi$
$347$	−3.12435	−0.167724	−0.0838620	+	0.996477i	$0.526725\pi$
$348$	21.2201	1.13752
$349$	−33.7342	−1.80575	−0.902876	−	0.429900i	$-0.858549\pi$
$349$	−33.7342	−1.80575	−0.902876	+	0.429900i	$0.858549\pi$
$350$	−8.51826	−0.455320
$351$	1.84344	0.0983955
$352$	1.41075	0.0751934
$353$	10.1358	0.539476	0.269738	−	0.962934i	$-0.413063\pi$
$353$	10.1358	0.539476	0.269738	+	0.962934i	$0.413063\pi$
$354$	15.6138	0.829864
$355$	5.55498	0.294828
$356$	12.0123	0.636649
$357$	−28.9698	−1.53324
$358$	0.878161	0.0464123
$359$	−22.2355	−1.17355	−0.586773	−	0.809752i	$-0.699602\pi$
$359$	−22.2355	−1.17355	−0.586773	+	0.809752i	$0.699602\pi$
$360$	−2.61769	−0.137964
$361$	−9.49120	−0.499537
$362$	−9.61659	−0.505437
$363$	21.1188	1.10845
$364$	−3.39789	−0.178098
$365$	−16.1946	−0.847663
$366$	−20.5277	−1.07300
$367$	−4.10434	−0.214245	−0.107122	−	0.994246i	$-0.534164\pi$
$367$	−4.10434	−0.214245	−0.107122	+	0.994246i	$0.534164\pi$
$368$	−7.68050	−0.400374
$369$	−17.4904	−0.910516
$370$	3.46318	0.180042
$371$	7.05158	0.366100
$372$	−0.0718540	−0.00372546
$373$	8.90918	0.461300	0.230650	−	0.973037i	$-0.425915\pi$
$373$	8.90918	0.461300	0.230650	+	0.973037i	$0.425915\pi$
$374$	−7.97992	−0.412632
$375$	21.8902	1.13040
$376$	−9.27923	−0.478540
$377$	−14.0786	−0.725084
$378$	2.59002	0.133216
$379$	19.2351	0.988041	0.494020	−	0.869450i	$-0.335527\pi$
$379$	19.2351	0.988041	0.494020	+	0.869450i	$0.335527\pi$
$380$	−3.23619	−0.166013
$381$	30.6875	1.57217
$382$	−20.8588	−1.06723
$383$	−22.5674	−1.15314	−0.576569	−	0.817048i	$-0.695609\pi$
$383$	−22.5674	−1.15314	−0.576569	+	0.817048i	$0.695609\pi$
$384$	2.34399	0.119616
$385$	3.23493	0.164867
$386$	18.7552	0.954613
$387$	−10.9062	−0.554392
$388$	−8.28067	−0.420388
$389$	−15.7463	−0.798370	−0.399185	−	0.916870i	$-0.630707\pi$
$389$	−15.7463	−0.798370	−0.399185	+	0.916870i	$0.630707\pi$
$390$	3.82556	0.193715
$391$	43.4448	2.19710
$392$	2.22599	0.112430
$393$	47.5888	2.40054
$394$	21.2499	1.07056
$395$	11.6003	0.583673
$396$	−3.51882	−0.176827
$397$	−32.2351	−1.61783	−0.808916	−	0.587924i	$-0.799945\pi$
$397$	−32.2351	−1.61783	−0.808916	+	0.587924i	$0.799945\pi$
$398$	−14.3586	−0.719732
$399$	−15.7928	−0.790630
$400$	−3.89860	−0.194930
$401$	−6.38181	−0.318692	−0.159346	−	0.987223i	$-0.550939\pi$
$401$	−6.38181	−0.318692	−0.159346	+	0.987223i	$0.550939\pi$
$402$	−10.3410	−0.515762
$403$	0.0476720	0.00237471
$404$	−4.82528	−0.240067
$405$	−10.7691	−0.535119
$406$	−19.7803	−0.981680
$407$	4.65537	0.230758
$408$	−13.2588	−0.656407
$409$	23.1706	1.14571	0.572855	−	0.819657i	$-0.305836\pi$
$409$	23.1706	1.14571	0.572855	+	0.819657i	$0.305836\pi$
$410$	7.35913	0.363441
$411$	−31.9293	−1.57496
$412$	−5.80979	−0.286228
$413$	−14.5544	−0.716175
$414$	19.1574	0.941533
$415$	−5.46183	−0.268111
$416$	−1.55513	−0.0762467
$417$	26.3202	1.28891
$418$	−4.35025	−0.212778
$419$	20.1679	0.985267	0.492633	−	0.870237i	$-0.336034\pi$
$419$	20.1679	0.985267	0.492633	+	0.870237i	$0.336034\pi$
$420$	5.37488	0.262267
$421$	−0.352628	−0.0171860	−0.00859301	−	0.999963i	$-0.502735\pi$
$421$	−0.352628	−0.0171860	−0.00859301	+	0.999963i	$0.502735\pi$
$422$	−0.948037	−0.0461497
$423$	23.1450	1.12535
$424$	3.22734	0.156734
$425$	22.0525	1.06970
$426$	12.4070	0.601121
$427$	19.1349	0.926002
$428$	3.60050	0.174037
$429$	5.14250	0.248282
$430$	4.58879	0.221291
$431$	17.2506	0.830933	0.415466	−	0.909608i	$-0.363618\pi$
$431$	17.2506	0.830933	0.415466	+	0.909608i	$0.363618\pi$
$432$	1.18539	0.0570321
$433$	22.2333	1.06846	0.534232	−	0.845338i	$-0.320601\pi$
$433$	22.2333	1.06846	0.534232	+	0.845338i	$0.320601\pi$
$434$	0.0669787	0.00321508
$435$	22.2699	1.06776
$436$	7.46909	0.357704
$437$	23.6839	1.13295
$438$	−36.1704	−1.72829
$439$	10.4878	0.500557	0.250278	−	0.968174i	$-0.419478\pi$
$439$	10.4878	0.500557	0.250278	+	0.968174i	$0.419478\pi$
$440$	1.48055	0.0705824
$441$	−5.55226	−0.264393
$442$	8.79661	0.418412
$443$	−17.4820	−0.830593	−0.415297	−	0.909686i	$-0.636322\pi$
$443$	−17.4820	−0.830593	−0.415297	+	0.909686i	$0.636322\pi$
$444$	7.73498	0.367086
$445$	12.6066	0.597609
$446$	−1.73412	−0.0821128
$447$	−27.3391	−1.29309
$448$	−2.18495	−0.103229
$449$	21.9807	1.03733	0.518666	−	0.854977i	$-0.326429\pi$
$449$	21.9807	1.03733	0.518666	+	0.854977i	$0.326429\pi$
$450$	9.72423	0.458405
$451$	9.89249	0.465819
$452$	8.83095	0.415373
$453$	−40.8154	−1.91767
$454$	−21.5834	−1.01296
$455$	−3.56600	−0.167176
$456$	−7.22800	−0.338482
$457$	2.59785	0.121522	0.0607612	−	0.998152i	$-0.480647\pi$
$457$	2.59785	0.121522	0.0607612	+	0.998152i	$0.480647\pi$
$458$	13.5664	0.633916
$459$	−6.70516	−0.312970
$460$	−8.06049	−0.375822
$461$	−0.737334	−0.0343411	−0.0171705	−	0.999853i	$-0.505466\pi$
$461$	−0.737334	−0.0343411	−0.0171705	+	0.999853i	$0.505466\pi$
$462$	7.22517	0.336145
$463$	26.1869	1.21701	0.608503	−	0.793551i	$-0.291770\pi$
$463$	26.1869	1.21701	0.608503	+	0.793551i	$0.291770\pi$
$464$	−9.05297	−0.420274
$465$	−0.0754089	−0.00349701
$466$	26.1818	1.21285
$467$	−26.0862	−1.20713	−0.603563	−	0.797315i	$-0.706253\pi$
$467$	−26.0862	−1.20713	−0.603563	+	0.797315i	$0.706253\pi$
$468$	3.87895	0.179304
$469$	9.63937	0.445105
$470$	−9.73831	−0.449195
$471$	−43.9849	−2.02672
$472$	−6.66120	−0.306607
$473$	6.16847	0.283626
$474$	25.9091	1.19004
$475$	12.0219	0.551601
$476$	12.3592	0.566482
$477$	−8.04991	−0.368580
$478$	6.51518	0.297998
$479$	−29.7741	−1.36041	−0.680207	−	0.733020i	$-0.738110\pi$
$479$	−29.7741	−1.36041	−0.680207	+	0.733020i	$0.738110\pi$
$480$	2.45996	0.112281
$481$	−5.13182	−0.233991
$482$	16.3552	0.744959
$483$	−39.3357	−1.78984
$484$	−9.00978	−0.409535
$485$	−8.69035	−0.394609
$486$	−20.4964	−0.929737
$487$	9.98926	0.452656	0.226328	−	0.974051i	$-0.427328\pi$
$487$	9.98926	0.452656	0.226328	+	0.974051i	$0.427328\pi$
$488$	8.75759	0.396437
$489$	36.2530	1.63942
$490$	2.33612	0.105535
$491$	24.9247	1.12484	0.562418	−	0.826853i	$-0.309871\pi$
$491$	24.9247	1.12484	0.562418	+	0.826853i	$0.309871\pi$
$492$	16.4365	0.741016
$493$	51.2081	2.30630
$494$	4.79546	0.215758
$495$	−3.69291	−0.165984
$496$	0.0306546	0.00137643
$497$	−11.5652	−0.518769
$498$	−12.1989	−0.546648
$499$	−10.9537	−0.490356	−0.245178	−	0.969478i	$-0.578846\pi$
$499$	−10.9537	−0.490356	−0.245178	+	0.969478i	$0.578846\pi$
$500$	−9.33885	−0.417646
$501$	41.2503	1.84293
$502$	−12.0030	−0.535721
$503$	18.7370	0.835444	0.417722	−	0.908575i	$-0.362829\pi$
$503$	18.7370	0.835444	0.417722	+	0.908575i	$0.362829\pi$
$504$	5.44989	0.242757
$505$	−5.06401	−0.225345
$506$	−10.8353	−0.481688
$507$	24.8031	1.10154
$508$	−13.0920	−0.580863
$509$	31.9270	1.41514	0.707570	−	0.706643i	$-0.249791\pi$
$509$	31.9270	1.41514	0.707570	+	0.706643i	$0.249791\pi$
$510$	−13.9147	−0.616155
$511$	33.7163	1.49152
$512$	−1.00000	−0.0441942
$513$	−3.65531	−0.161386
$514$	19.5817	0.863713
$515$	−6.09723	−0.268676
$516$	10.2490	0.451187
$517$	−13.0907	−0.575728
$518$	−7.21016	−0.316796
$519$	20.1946	0.886444
$520$	−1.63207	−0.0715711
$521$	43.8688	1.92193	0.960964	−	0.276674i	$-0.0892324\pi$
$521$	43.8688	1.92193	0.960964	+	0.276674i	$0.0892324\pi$
$522$	22.5807	0.988330
$523$	5.98030	0.261500	0.130750	−	0.991415i	$-0.458261\pi$
$523$	5.98030	0.261500	0.130750	+	0.991415i	$0.458261\pi$
$524$	−20.3025	−0.886917
$525$	−19.9667	−0.871418
$526$	−17.7616	−0.774443
$527$	−0.173398	−0.00755332
$528$	3.30679	0.143910
$529$	35.9901	1.56479
$530$	3.38701	0.147122
$531$	16.6149	0.721027
$532$	6.73759	0.292111
$533$	−10.9049	−0.472344
$534$	28.1566	1.21846
$535$	3.77863	0.163364
$536$	4.41171	0.190557
$537$	2.05840	0.0888265
$538$	1.39786	0.0602659
$539$	3.14033	0.135263
$540$	1.24404	0.0535348
$541$	−43.9110	−1.88788	−0.943941	−	0.330113i	$-0.892913\pi$
$541$	−43.9110	−1.88788	−0.943941	+	0.330113i	$0.892913\pi$
$542$	8.65894	0.371933
$543$	−22.5412	−0.967335
$544$	5.65650	0.242520
$545$	7.83861	0.335769
$546$	−7.96461	−0.340854
$547$	−20.4742	−0.875415	−0.437708	−	0.899117i	$-0.644209\pi$
$547$	−20.4742	−0.875415	−0.437708	+	0.899117i	$0.644209\pi$
$548$	13.6218	0.581894
$549$	−21.8439	−0.932276
$550$	−5.49997	−0.234519
$551$	27.9161	1.18926
$552$	−18.0030	−0.766259
$553$	−24.1512	−1.02701
$554$	0.130566	0.00554724
$555$	8.11766	0.344575
$556$	−11.2288	−0.476207
$557$	−16.7724	−0.710668	−0.355334	−	0.934739i	$-0.615633\pi$
$557$	−16.7724	−0.710668	−0.355334	+	0.934739i	$0.615633\pi$
$558$	−0.0764613	−0.00323686
$559$	−6.79976	−0.287599
$560$	−2.29305	−0.0968990
$561$	−18.7049	−0.789720
$562$	17.5677	0.741050
$563$	−13.5374	−0.570532	−0.285266	−	0.958448i	$-0.592082\pi$
$563$	−13.5374	−0.570532	−0.285266	+	0.958448i	$0.592082\pi$
$564$	−21.7504	−0.915858
$565$	9.26785	0.389901
$566$	7.59996	0.319450
$567$	22.4206	0.941578
$568$	−5.29311	−0.222094
$569$	28.9607	1.21409	0.607047	−	0.794666i	$-0.292354\pi$
$569$	28.9607	1.21409	0.607047	+	0.794666i	$0.292354\pi$
$570$	−7.58560	−0.317726
$571$	−19.0682	−0.797978	−0.398989	−	0.916956i	$-0.630639\pi$
$571$	−19.0682	−0.797978	−0.398989	+	0.916956i	$0.630639\pi$
$572$	−2.19391	−0.0917320
$573$	−48.8928	−2.04253
$574$	−15.3213	−0.639500
$575$	29.9432	1.24872
$576$	2.49429	0.103929
$577$	10.6521	0.443451	0.221725	−	0.975109i	$-0.428831\pi$
$577$	10.6521	0.443451	0.221725	+	0.975109i	$0.428831\pi$
$578$	−14.9960	−0.623751
$579$	43.9619	1.82700
$580$	−9.50086	−0.394502
$581$	11.3713	0.471759
$582$	−19.4098	−0.804563
$583$	4.55298	0.188565
$584$	15.4311	0.638545
$585$	4.07085	0.168309
$586$	−10.7354	−0.443475
$587$	−34.9923	−1.44429	−0.722144	−	0.691743i	$-0.756843\pi$
$587$	−34.9923	−1.44429	−0.722144	+	0.691743i	$0.756843\pi$
$588$	5.21770	0.215174
$589$	−0.0945275	−0.00389494
$590$	−6.99076	−0.287805
$591$	49.8096	2.04889
$592$	−3.29992	−0.135626
$593$	−14.0327	−0.576254	−0.288127	−	0.957592i	$-0.593032\pi$
$593$	−14.0327	−0.576254	−0.288127	+	0.957592i	$0.593032\pi$
$594$	1.67229	0.0686150
$595$	12.9706	0.531744
$596$	11.6635	0.477755
$597$	−33.6564	−1.37746
$598$	11.9442	0.488435
$599$	27.6781	1.13090	0.565448	−	0.824784i	$-0.308703\pi$
$599$	27.6781	1.13090	0.565448	+	0.824784i	$0.308703\pi$
$600$	−9.13829	−0.373069
$601$	35.6052	1.45237	0.726184	−	0.687500i	$-0.241292\pi$
$601$	35.6052	1.45237	0.726184	+	0.687500i	$0.241292\pi$
$602$	−9.55362	−0.389376
$603$	−11.0041	−0.448120
$604$	17.4128	0.708517
$605$	−9.45553	−0.384422
$606$	−11.3104	−0.459454
$607$	5.03024	0.204171	0.102086	−	0.994776i	$-0.467448\pi$
$607$	5.03024	0.204171	0.102086	+	0.994776i	$0.467448\pi$
$608$	3.08363	0.125058
$609$	−46.3648	−1.87880
$610$	9.19086	0.372127
$611$	14.4304	0.583793
$612$	−14.1089	−0.570319
$613$	17.0481	0.688567	0.344284	−	0.938866i	$-0.388122\pi$
$613$	17.0481	0.688567	0.344284	+	0.938866i	$0.388122\pi$
$614$	12.9018	0.520676
$615$	17.2497	0.695576
$616$	−3.08243	−0.124194
$617$	−0.892886	−0.0359462	−0.0179731	−	0.999838i	$-0.505721\pi$
$617$	−0.892886	−0.0359462	−0.0179731	+	0.999838i	$0.505721\pi$
$618$	−13.6181	−0.547800
$619$	−37.8295	−1.52050	−0.760249	−	0.649632i	$-0.774923\pi$
$619$	−37.8295	−1.52050	−0.760249	+	0.649632i	$0.774923\pi$
$620$	0.0321712	0.00129203
$621$	−9.10439	−0.365347
$622$	5.19578	0.208332
$623$	−26.2462	−1.05153
$624$	−3.64522	−0.145925
$625$	9.69214	0.387685
$626$	6.42747	0.256893
$627$	−10.1969	−0.407226
$628$	18.7650	0.748804
$629$	18.6660	0.744262
$630$	5.71952	0.227871
$631$	15.2056	0.605326	0.302663	−	0.953098i	$-0.402124\pi$
$631$	15.2056	0.605326	0.302663	+	0.953098i	$0.402124\pi$
$632$	−11.0534	−0.439681
$633$	−2.22219	−0.0883241
$634$	−12.2775	−0.487602
$635$	−13.7397	−0.545243
$636$	7.56486	0.299966
$637$	−3.46171	−0.137158
$638$	−12.7715	−0.505629
$639$	13.2025	0.522284
$640$	−1.04947	−0.0414841
$641$	−28.9376	−1.14296	−0.571482	−	0.820614i	$-0.693631\pi$
$641$	−28.9376	−1.14296	−0.571482	+	0.820614i	$0.693631\pi$
$642$	8.43953	0.333082
$643$	−18.3591	−0.724014	−0.362007	−	0.932175i	$-0.617908\pi$
$643$	−18.3591	−0.724014	−0.362007	+	0.932175i	$0.617908\pi$
$644$	16.7815	0.661284
$645$	10.7561	0.423520
$646$	−17.4426	−0.686269
$647$	−12.9403	−0.508736	−0.254368	−	0.967108i	$-0.581867\pi$
$647$	−12.9403	−0.508736	−0.254368	+	0.967108i	$0.581867\pi$
$648$	10.2614	0.403106
$649$	−9.39732	−0.368877
$650$	6.06285	0.237804
$651$	0.156997	0.00615322
$652$	−15.4664	−0.605709
$653$	−2.89510	−0.113294	−0.0566469	−	0.998394i	$-0.518041\pi$
$653$	−2.89510	−0.113294	−0.0566469	+	0.998394i	$0.518041\pi$
$654$	17.5075	0.684596
$655$	−21.3069	−0.832530
$656$	−7.01221	−0.273781
$657$	−38.4897	−1.50163
$658$	20.2747	0.790388
$659$	4.04102	0.157416	0.0787079	−	0.996898i	$-0.474921\pi$
$659$	4.04102	0.157416	0.0787079	+	0.996898i	$0.474921\pi$
$660$	3.47039	0.135085
$661$	−4.15409	−0.161576	−0.0807878	−	0.996731i	$-0.525744\pi$
$661$	−4.15409	−0.161576	−0.0807878	+	0.996731i	$0.525744\pi$
$662$	−7.40674	−0.287871
$663$	20.6192	0.800782
$664$	5.20435	0.201968
$665$	7.07092	0.274199
$666$	8.23094	0.318943
$667$	69.5314	2.69227
$668$	−17.5983	−0.680900
$669$	−4.06475	−0.157152
$670$	4.62998	0.178872
$671$	12.3548	0.476952
$672$	−5.12150	−0.197566
$673$	−5.82154	−0.224404	−0.112202	−	0.993685i	$-0.535790\pi$
$673$	−5.82154	−0.224404	−0.112202	+	0.993685i	$0.535790\pi$
$674$	6.15145	0.236945
$675$	−4.62137	−0.177877
$676$	−10.5816	−0.406983
$677$	−0.719572	−0.0276554	−0.0138277	−	0.999904i	$-0.504402\pi$
$677$	−0.719572	−0.0276554	−0.0138277	+	0.999904i	$0.504402\pi$
$678$	20.6996	0.794965
$679$	18.0929	0.694340
$680$	5.93635	0.227649
$681$	−50.5913	−1.93866
$682$	0.0432461	0.00165598
$683$	42.0362	1.60847	0.804235	−	0.594311i	$-0.202575\pi$
$683$	42.0362	1.60847	0.804235	+	0.594311i	$0.202575\pi$
$684$	−7.69146	−0.294090
$685$	14.2957	0.546211
$686$	−20.1583	−0.769649
$687$	31.7995	1.21323
$688$	−4.37246	−0.166699
$689$	−5.01895	−0.191207
$690$	−18.8937	−0.719271
$691$	0.535871	0.0203855	0.0101927	−	0.999948i	$-0.496755\pi$
$691$	0.535871	0.0203855	0.0101927	+	0.999948i	$0.496755\pi$
$692$	−8.61548	−0.327511
$693$	7.68845	0.292060
$694$	3.12435	0.118599
$695$	−11.7843	−0.447005
$696$	−21.2201	−0.804345
$697$	39.6645	1.50240
$698$	33.7342	1.27686
$699$	61.3698	2.32122
$700$	8.51826	0.321960
$701$	27.0303	1.02092	0.510461	−	0.859901i	$-0.329475\pi$
$701$	27.0303	1.02092	0.510461	+	0.859901i	$0.329475\pi$
$702$	−1.84344	−0.0695762
$703$	10.1757	0.383786
$704$	−1.41075	−0.0531698
$705$	−22.8265	−0.859695
$706$	−10.1358	−0.381467
$707$	10.5430	0.396510
$708$	−15.6138	−0.586802
$709$	44.6754	1.67782	0.838911	−	0.544269i	$-0.183193\pi$
$709$	44.6754	1.67782	0.838911	+	0.544269i	$0.183193\pi$
$710$	−5.55498	−0.208475
$711$	27.5704	1.03397
$712$	−12.0123	−0.450179
$713$	−0.235443	−0.00881740
$714$	28.9698	1.08417
$715$	−2.30245	−0.0861068
$716$	−0.878161	−0.0328184
$717$	15.2715	0.570325
$718$	22.2355	0.829822
$719$	0.144697	0.00539630	0.00269815	−	0.999996i	$-0.499141\pi$
$719$	0.144697	0.00539630	0.00269815	+	0.999996i	$0.499141\pi$
$720$	2.61769	0.0975555
$721$	12.6941	0.472753
$722$	9.49120	0.353226
$723$	38.3364	1.42575
$724$	9.61659	0.357398
$725$	35.2940	1.31078
$726$	−21.1188	−0.783793
$727$	−33.8738	−1.25631	−0.628154	−	0.778089i	$-0.716189\pi$
$727$	−33.8738	−1.25631	−0.628154	+	0.778089i	$0.716189\pi$
$728$	3.39789	0.125934
$729$	−17.2592	−0.639231
$730$	16.1946	0.599389
$731$	24.7328	0.914777
$732$	20.5277	0.758725
$733$	29.1531	1.07679	0.538396	−	0.842692i	$-0.319030\pi$
$733$	29.1531	1.07679	0.538396	+	0.842692i	$0.319030\pi$
$734$	4.10434	0.151494
$735$	5.47584	0.201980
$736$	7.68050	0.283107
$737$	6.22384	0.229258
$738$	17.4904	0.643832
$739$	18.8801	0.694516	0.347258	−	0.937770i	$-0.387113\pi$
$739$	18.8801	0.694516	0.347258	+	0.937770i	$0.387113\pi$
$740$	−3.46318	−0.127309
$741$	11.2405	0.412930
$742$	−7.05158	−0.258872
$743$	42.4345	1.55677	0.778385	−	0.627787i	$-0.216039\pi$
$743$	42.4345	1.55677	0.778385	+	0.627787i	$0.216039\pi$
$744$	0.0718540	0.00263430
$745$	12.2405	0.448458
$746$	−8.90918	−0.326188
$747$	−12.9811	−0.474955
$748$	7.97992	0.291775
$749$	−7.86691	−0.287451
$750$	−21.8902	−0.799316
$751$	47.6990	1.74056	0.870280	−	0.492558i	$-0.163938\pi$
$751$	47.6990	1.74056	0.870280	+	0.492558i	$0.163938\pi$
$752$	9.27923	0.338379
$753$	−28.1349	−1.02529
$754$	14.0786	0.512712
$755$	18.2743	0.665069
$756$	−2.59002	−0.0941981
$757$	20.4047	0.741621	0.370810	−	0.928709i	$-0.379080\pi$
$757$	20.4047	0.741621	0.370810	+	0.928709i	$0.379080\pi$
$758$	−19.2351	−0.698650
$759$	−25.3978	−0.921882
$760$	3.23619	0.117389
$761$	29.4965	1.06925	0.534623	−	0.845091i	$-0.320454\pi$
$761$	29.4965	1.06925	0.534623	+	0.845091i	$0.320454\pi$
$762$	−30.6875	−1.11169
$763$	−16.3196	−0.590809
$764$	20.8588	0.754645
$765$	−14.8069	−0.535346
$766$	22.5674	0.815392
$767$	10.3591	0.374044
$768$	−2.34399	−0.0845814
$769$	−13.8261	−0.498582	−0.249291	−	0.968429i	$-0.580198\pi$
$769$	−13.8261	−0.498582	−0.249291	+	0.968429i	$0.580198\pi$
$770$	−3.23493	−0.116579
$771$	45.8994	1.65302
$772$	−18.7552	−0.675014
$773$	31.2558	1.12419	0.562097	−	0.827071i	$-0.309995\pi$
$773$	31.2558	1.12419	0.562097	+	0.827071i	$0.309995\pi$
$774$	10.9062	0.392014
$775$	−0.119510	−0.00429293
$776$	8.28067	0.297259
$777$	−16.9005	−0.606304
$778$	15.7463	0.564533
$779$	21.6231	0.774727
$780$	−3.82556	−0.136977
$781$	−7.46727	−0.267200
$782$	−43.4448	−1.55358
$783$	−10.7313	−0.383506
$784$	−2.22599	−0.0794997
$785$	19.6933	0.702886
$786$	−47.5888	−1.69743
$787$	−23.1041	−0.823572	−0.411786	−	0.911280i	$-0.635095\pi$
$787$	−23.1041	−0.823572	−0.411786	+	0.911280i	$0.635095\pi$
$788$	−21.2499	−0.756997
$789$	−41.6330	−1.48217
$790$	−11.6003	−0.412719
$791$	−19.2952	−0.686058
$792$	3.51882	0.125036
$793$	−13.6192	−0.483632
$794$	32.2351	1.14398
$795$	7.93912	0.281572
$796$	14.3586	0.508927
$797$	3.27116	0.115870	0.0579352	−	0.998320i	$-0.481548\pi$
$797$	3.27116	0.115870	0.0579352	+	0.998320i	$0.481548\pi$
$798$	15.7928	0.559060
$799$	−52.4880	−1.85689
$800$	3.89860	0.137836
$801$	29.9620	1.05866
$802$	6.38181	0.225350
$803$	21.7695	0.768230
$804$	10.3410	0.364699
$805$	17.6118	0.620733
$806$	−0.0476720	−0.00167917
$807$	3.27656	0.115340
$808$	4.82528	0.169753
$809$	−32.9813	−1.15956	−0.579780	−	0.814773i	$-0.696862\pi$
$809$	−32.9813	−1.15956	−0.579780	+	0.814773i	$0.696862\pi$
$810$	10.7691	0.378387
$811$	−35.6142	−1.25058	−0.625292	−	0.780391i	$-0.715020\pi$
$811$	−35.6142	−1.25058	−0.625292	+	0.780391i	$0.715020\pi$
$812$	19.7803	0.694152
$813$	20.2965	0.711828
$814$	−4.65537	−0.163171
$815$	−16.2315	−0.568566
$816$	13.2588	0.464150
$817$	13.4831	0.471713
$818$	−23.1706	−0.810139
$819$	−8.47530	−0.296151
$820$	−7.35913	−0.256992
$821$	50.6260	1.76686	0.883429	−	0.468564i	$-0.155229\pi$
$821$	50.6260	1.76686	0.883429	+	0.468564i	$0.155229\pi$
$822$	31.9293	1.11366
$823$	−28.8589	−1.00596	−0.502979	−	0.864298i	$-0.667763\pi$
$823$	−28.8589	−1.00596	−0.502979	+	0.864298i	$0.667763\pi$
$824$	5.80979	0.202394
$825$	−12.8919	−0.448837
$826$	14.5544	0.506412
$827$	−23.1180	−0.803893	−0.401947	−	0.915663i	$-0.631666\pi$
$827$	−23.1180	−0.803893	−0.401947	+	0.915663i	$0.631666\pi$
$828$	−19.1574	−0.665764
$829$	−38.4205	−1.33440	−0.667200	−	0.744879i	$-0.732507\pi$
$829$	−38.4205	−1.33440	−0.667200	+	0.744879i	$0.732507\pi$
$830$	5.46183	0.189583
$831$	0.306046	0.0106166
$832$	1.55513	0.0539145
$833$	12.5913	0.436264
$834$	−26.3202	−0.911394
$835$	−18.4690	−0.639146
$836$	4.35025	0.150456
$837$	0.0363377	0.00125601
$838$	−20.1679	−0.696689
$839$	28.3429	0.978507	0.489253	−	0.872142i	$-0.337269\pi$
$839$	28.3429	0.978507	0.489253	+	0.872142i	$0.337269\pi$
$840$	−5.37488	−0.185451
$841$	52.9563	1.82608
$842$	0.352628	0.0121524
$843$	41.1786	1.41827
$844$	0.948037	0.0326328
$845$	−11.1051	−0.382026
$846$	−23.1450	−0.795743
$847$	19.6859	0.676416
$848$	−3.22734	−0.110827
$849$	17.8142	0.611382
$850$	−22.0525	−0.756393
$851$	25.3451	0.868817
$852$	−12.4070	−0.425056
$853$	−2.54129	−0.0870123	−0.0435061	−	0.999053i	$-0.513853\pi$
$853$	−2.54129	−0.0870123	−0.0435061	+	0.999053i	$0.513853\pi$
$854$	−19.1349	−0.654782
$855$	−8.07199	−0.276056
$856$	−3.60050	−0.123063
$857$	24.4635	0.835659	0.417829	−	0.908526i	$-0.362791\pi$
$857$	24.4635	0.835659	0.417829	+	0.908526i	$0.362791\pi$
$858$	−5.14250	−0.175562
$859$	−6.78867	−0.231627	−0.115813	−	0.993271i	$-0.536947\pi$
$859$	−6.78867	−0.231627	−0.115813	+	0.993271i	$0.536947\pi$
$860$	−4.58879	−0.156476
$861$	−35.9130	−1.22391
$862$	−17.2506	−0.587558
$863$	−53.4908	−1.82085	−0.910424	−	0.413676i	$-0.864245\pi$
$863$	−53.4908	−1.82085	−0.910424	+	0.413676i	$0.864245\pi$
$864$	−1.18539	−0.0403278
$865$	−9.04172	−0.307428
$866$	−22.2333	−0.755519
$867$	−35.1504	−1.19377
$868$	−0.0669787	−0.00227341
$869$	−15.5936	−0.528978
$870$	−22.2699	−0.755021
$871$	−6.86080	−0.232469
$872$	−7.46909	−0.252935
$873$	−20.6544	−0.699044
$874$	−23.6839	−0.801118
$875$	20.4049	0.689813
$876$	36.1704	1.22209
$877$	−5.69700	−0.192374	−0.0961871	−	0.995363i	$-0.530665\pi$
$877$	−5.69700	−0.192374	−0.0961871	+	0.995363i	$0.530665\pi$
$878$	−10.4878	−0.353947
$879$	−25.1636	−0.848749
$880$	−1.48055	−0.0499093
$881$	37.6137	1.26724	0.633619	−	0.773645i	$-0.281569\pi$
$881$	37.6137	1.26724	0.633619	+	0.773645i	$0.281569\pi$
$882$	5.55226	0.186954
$883$	46.6007	1.56824	0.784119	−	0.620610i	$-0.213115\pi$
$883$	46.6007	1.56824	0.784119	+	0.620610i	$0.213115\pi$
$884$	−8.79661	−0.295862
$885$	−16.3863	−0.550818
$886$	17.4820	0.587318
$887$	−8.93349	−0.299957	−0.149979	−	0.988689i	$-0.547920\pi$
$887$	−8.93349	−0.299957	−0.149979	+	0.988689i	$0.547920\pi$
$888$	−7.73498	−0.259569
$889$	28.6053	0.959392
$890$	−12.6066	−0.422573
$891$	14.4763	0.484974
$892$	1.73412	0.0580625
$893$	−28.6137	−0.957523
$894$	27.3391	0.914356
$895$	−0.921607	−0.0308059
$896$	2.18495	0.0729941
$897$	27.9971	0.934795
$898$	−21.9807	−0.733504
$899$	−0.277515	−0.00925565
$900$	−9.72423	−0.324141
$901$	18.2555	0.608178
$902$	−9.89249	−0.329384
$903$	−22.3936	−0.745211
$904$	−8.83095	−0.293713
$905$	10.0924	0.335482
$906$	40.8154	1.35600
$907$	−40.3819	−1.34086	−0.670430	−	0.741973i	$-0.733890\pi$
$907$	−40.3819	−1.34086	−0.670430	+	0.741973i	$0.733890\pi$
$908$	21.5834	0.716271
$909$	−12.0356	−0.399196
$910$	3.56600	0.118212
$911$	−42.0164	−1.39207	−0.696033	−	0.718010i	$-0.745053\pi$
$911$	−42.0164	−1.39207	−0.696033	+	0.718010i	$0.745053\pi$
$912$	7.22800	0.239343
$913$	7.34206	0.242987
$914$	−2.59785	−0.0859293
$915$	21.5433	0.712199
$916$	−13.5664	−0.448246
$917$	44.3599	1.46489
$918$	6.70516	0.221303
$919$	30.9534	1.02106	0.510530	−	0.859860i	$-0.329449\pi$
$919$	30.9534	1.02106	0.510530	+	0.859860i	$0.329449\pi$
$920$	8.06049	0.265746
$921$	30.2418	0.996500
$922$	0.737334	0.0242828
$923$	8.23149	0.270943
$924$	−7.22517	−0.237691
$925$	12.8651	0.423001
$926$	−26.1869	−0.860554
$927$	−14.4913	−0.475956
$928$	9.05297	0.297178
$929$	59.5976	1.95533	0.977666	−	0.210163i	$-0.0673994\pi$
$929$	59.5976	1.95533	0.977666	+	0.210163i	$0.0673994\pi$
$930$	0.0754089	0.00247276
$931$	6.86415	0.224963
$932$	−26.1818	−0.857612
$933$	12.1789	0.398718
$934$	26.0862	0.853567
$935$	8.37472	0.273883
$936$	−3.87895	−0.126787
$937$	−8.80122	−0.287523	−0.143762	−	0.989612i	$-0.545920\pi$
$937$	−8.80122	−0.287523	−0.143762	+	0.989612i	$0.545920\pi$
$938$	−9.63937	−0.314737
$939$	15.0659	0.491658
$940$	9.73831	0.317629
$941$	−13.1580	−0.428938	−0.214469	−	0.976731i	$-0.568802\pi$
$941$	−13.1580	−0.428938	−0.214469	+	0.976731i	$0.568802\pi$
$942$	43.9849	1.43310
$943$	53.8573	1.75383
$944$	6.66120	0.216804
$945$	−2.71816	−0.0884217
$946$	−6.16847	−0.200554
$947$	−43.0408	−1.39864	−0.699319	−	0.714810i	$-0.746513\pi$
$947$	−43.0408	−1.39864	−0.699319	+	0.714810i	$0.746513\pi$
$948$	−25.9091	−0.841488
$949$	−23.9975	−0.778991
$950$	−12.0219	−0.390041
$951$	−28.7783	−0.933201
$952$	−12.3592	−0.400563
$953$	16.9703	0.549721	0.274861	−	0.961484i	$-0.411368\pi$
$953$	16.9703	0.549721	0.274861	+	0.961484i	$0.411368\pi$
$954$	8.04991	0.260626
$955$	21.8908	0.708369
$956$	−6.51518	−0.210716
$957$	−29.9363	−0.967703
$958$	29.7741	0.961958
$959$	−29.7629	−0.961095
$960$	−2.45996	−0.0793947
$961$	−30.9991	−0.999970
$962$	5.13182	0.165456
$963$	8.98067	0.289398
$964$	−16.3552	−0.526766
$965$	−19.6831	−0.633621
$966$	39.3357	1.26561
$967$	2.30590	0.0741527	0.0370764	−	0.999312i	$-0.488196\pi$
$967$	2.30590	0.0741527	0.0370764	+	0.999312i	$0.488196\pi$
$968$	9.00978	0.289585
$969$	−40.8852	−1.31342
$970$	8.69035	0.279030
$971$	13.3048	0.426973	0.213486	−	0.976946i	$-0.431518\pi$
$971$	13.3048	0.426973	0.213486	+	0.976946i	$0.431518\pi$
$972$	20.4964	0.657423
$973$	24.5344	0.786536
$974$	−9.98926	−0.320076
$975$	14.2113	0.455124
$976$	−8.75759	−0.280324
$977$	−31.6225	−1.01169	−0.505847	−	0.862623i	$-0.668820\pi$
$977$	−31.6225	−1.01169	−0.505847	+	0.862623i	$0.668820\pi$
$978$	−36.2530	−1.15924
$979$	−16.9464	−0.541608
$980$	−2.33612	−0.0746247
$981$	18.6300	0.594811
$982$	−24.9247	−0.795379
$983$	15.2433	0.486185	0.243093	−	0.970003i	$-0.421838\pi$
$983$	15.2433	0.486185	0.243093	+	0.970003i	$0.421838\pi$
$984$	−16.4365	−0.523978
$985$	−22.3012	−0.710576
$986$	−51.2081	−1.63080
$987$	47.5236	1.51269
$988$	−4.79546	−0.152564
$989$	33.5827	1.06787
$990$	3.69291	0.117368
$991$	32.6978	1.03868	0.519341	−	0.854567i	$-0.326178\pi$
$991$	32.6978	1.03868	0.519341	+	0.854567i	$0.326178\pi$
$992$	−0.0306546	−0.000973284 0
$993$	−17.3613	−0.550945
$994$	11.5652	0.366825
$995$	15.0690	0.477719
$996$	12.1989	0.386538
$997$	19.0893	0.604565	0.302282	−	0.953218i	$-0.402251\pi$
$997$	19.0893	0.604565	0.302282	+	0.953218i	$0.402251\pi$
$998$	10.9537	0.346734
$999$	−3.91169	−0.123761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.13	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.13	✓	86	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.34399 q^{3} +1.00000 q^{4} +1.04947 q^{5} +2.34399 q^{6} -2.18495 q^{7} -1.00000 q^{8} +2.49429 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.34399 q^{3} +1.00000 q^{4} +1.04947 q^{5} +2.34399 q^{6} -2.18495 q^{7} -1.00000 q^{8} +2.49429 q^{9} -1.04947 q^{10} -1.41075 q^{11} -2.34399 q^{12} +1.55513 q^{13} +2.18495 q^{14} -2.45996 q^{15} +1.00000 q^{16} -5.65650 q^{17} -2.49429 q^{18} -3.08363 q^{19} +1.04947 q^{20} +5.12150 q^{21} +1.41075 q^{22} -7.68050 q^{23} +2.34399 q^{24} -3.89860 q^{25} -1.55513 q^{26} +1.18539 q^{27} -2.18495 q^{28} -9.05297 q^{29} +2.45996 q^{30} +0.0306546 q^{31} -1.00000 q^{32} +3.30679 q^{33} +5.65650 q^{34} -2.29305 q^{35} +2.49429 q^{36} -3.29992 q^{37} +3.08363 q^{38} -3.64522 q^{39} -1.04947 q^{40} -7.01221 q^{41} -5.12150 q^{42} -4.37246 q^{43} -1.41075 q^{44} +2.61769 q^{45} +7.68050 q^{46} +9.27923 q^{47} -2.34399 q^{48} -2.22599 q^{49} +3.89860 q^{50} +13.2588 q^{51} +1.55513 q^{52} -3.22734 q^{53} -1.18539 q^{54} -1.48055 q^{55} +2.18495 q^{56} +7.22800 q^{57} +9.05297 q^{58} +6.66120 q^{59} -2.45996 q^{60} -8.75759 q^{61} -0.0306546 q^{62} -5.44989 q^{63} +1.00000 q^{64} +1.63207 q^{65} -3.30679 q^{66} -4.41171 q^{67} -5.65650 q^{68} +18.0030 q^{69} +2.29305 q^{70} +5.29311 q^{71} -2.49429 q^{72} -15.4311 q^{73} +3.29992 q^{74} +9.13829 q^{75} -3.08363 q^{76} +3.08243 q^{77} +3.64522 q^{78} +11.0534 q^{79} +1.04947 q^{80} -10.2614 q^{81} +7.01221 q^{82} -5.20435 q^{83} +5.12150 q^{84} -5.93635 q^{85} +4.37246 q^{86} +21.2201 q^{87} +1.41075 q^{88} +12.0123 q^{89} -2.61769 q^{90} -3.39789 q^{91} -7.68050 q^{92} -0.0718540 q^{93} -9.27923 q^{94} -3.23619 q^{95} +2.34399 q^{96} -8.28067 q^{97} +2.22599 q^{98} -3.51882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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