LMFDB - Embedded newform 8026.2.a.d.1.17

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:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.32778 q^{3} +1.00000 q^{4} +2.23848 q^{5} -2.32778 q^{6} +3.76217 q^{7} +1.00000 q^{8} +2.41856 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.32778 q^{3} +1.00000 q^{4} +2.23848 q^{5} -2.32778 q^{6} +3.76217 q^{7} +1.00000 q^{8} +2.41856 q^{9} +2.23848 q^{10} +6.14419 q^{11} -2.32778 q^{12} -5.81764 q^{13} +3.76217 q^{14} -5.21069 q^{15} +1.00000 q^{16} -3.87026 q^{17} +2.41856 q^{18} -4.78653 q^{19} +2.23848 q^{20} -8.75750 q^{21} +6.14419 q^{22} +2.82768 q^{23} -2.32778 q^{24} +0.0107930 q^{25} -5.81764 q^{26} +1.35347 q^{27} +3.76217 q^{28} -7.67062 q^{29} -5.21069 q^{30} +4.46847 q^{31} +1.00000 q^{32} -14.3023 q^{33} -3.87026 q^{34} +8.42154 q^{35} +2.41856 q^{36} -9.15399 q^{37} -4.78653 q^{38} +13.5422 q^{39} +2.23848 q^{40} +7.89125 q^{41} -8.75750 q^{42} +6.40589 q^{43} +6.14419 q^{44} +5.41389 q^{45} +2.82768 q^{46} +12.4966 q^{47} -2.32778 q^{48} +7.15391 q^{49} +0.0107930 q^{50} +9.00911 q^{51} -5.81764 q^{52} +4.99068 q^{53} +1.35347 q^{54} +13.7536 q^{55} +3.76217 q^{56} +11.1420 q^{57} -7.67062 q^{58} +12.3424 q^{59} -5.21069 q^{60} +2.17480 q^{61} +4.46847 q^{62} +9.09902 q^{63} +1.00000 q^{64} -13.0227 q^{65} -14.3023 q^{66} -4.39550 q^{67} -3.87026 q^{68} -6.58222 q^{69} +8.42154 q^{70} -14.3691 q^{71} +2.41856 q^{72} +7.97567 q^{73} -9.15399 q^{74} -0.0251236 q^{75} -4.78653 q^{76} +23.1155 q^{77} +13.5422 q^{78} +14.2764 q^{79} +2.23848 q^{80} -10.4063 q^{81} +7.89125 q^{82} -10.6606 q^{83} -8.75750 q^{84} -8.66350 q^{85} +6.40589 q^{86} +17.8555 q^{87} +6.14419 q^{88} +3.72489 q^{89} +5.41389 q^{90} -21.8869 q^{91} +2.82768 q^{92} -10.4016 q^{93} +12.4966 q^{94} -10.7146 q^{95} -2.32778 q^{96} +17.7726 q^{97} +7.15391 q^{98} +14.8601 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * 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
$3$	−2.32778	−1.34394	−0.671972	−	0.740577i	$-0.734553\pi$
$3$	−2.32778	−1.34394	−0.671972	+	0.740577i	$0.734553\pi$
$4$	1.00000	0.500000
$5$	2.23848	1.00108	0.500539	−	0.865714i	$-0.333135\pi$
$5$	2.23848	1.00108	0.500539	+	0.865714i	$0.333135\pi$
$6$	−2.32778	−0.950312
$7$	3.76217	1.42197	0.710983	−	0.703209i	$-0.248250\pi$
$7$	3.76217	1.42197	0.710983	+	0.703209i	$0.248250\pi$
$8$	1.00000	0.353553
$9$	2.41856	0.806186
$10$	2.23848	0.707870
$11$	6.14419	1.85254	0.926271	−	0.376859i	$-0.122996\pi$
$11$	6.14419	1.85254	0.926271	+	0.376859i	$0.122996\pi$
$12$	−2.32778	−0.671972
$13$	−5.81764	−1.61352	−0.806762	−	0.590877i	$-0.798782\pi$
$13$	−5.81764	−1.61352	−0.806762	+	0.590877i	$0.798782\pi$
$14$	3.76217	1.00548
$15$	−5.21069	−1.34539
$16$	1.00000	0.250000
$17$	−3.87026	−0.938675	−0.469338	−	0.883019i	$-0.655507\pi$
$17$	−3.87026	−0.938675	−0.469338	+	0.883019i	$0.655507\pi$
$18$	2.41856	0.570059
$19$	−4.78653	−1.09811	−0.549053	−	0.835788i	$-0.685011\pi$
$19$	−4.78653	−1.09811	−0.549053	+	0.835788i	$0.685011\pi$
$20$	2.23848	0.500539
$21$	−8.75750	−1.91104
$22$	6.14419	1.30994
$23$	2.82768	0.589613	0.294806	−	0.955557i	$-0.404745\pi$
$23$	2.82768	0.589613	0.294806	+	0.955557i	$0.404745\pi$
$24$	−2.32778	−0.475156
$25$	0.0107930	0.00215859
$26$	−5.81764	−1.14093
$27$	1.35347	0.260476
$28$	3.76217	0.710983
$29$	−7.67062	−1.42440	−0.712199	−	0.701978i	$-0.752301\pi$
$29$	−7.67062	−1.42440	−0.712199	+	0.701978i	$0.752301\pi$
$30$	−5.21069	−0.951337
$31$	4.46847	0.802561	0.401280	−	0.915955i	$-0.368565\pi$
$31$	4.46847	0.802561	0.401280	+	0.915955i	$0.368565\pi$
$32$	1.00000	0.176777
$33$	−14.3023	−2.48971
$34$	−3.87026	−0.663744
$35$	8.42154	1.42350
$36$	2.41856	0.403093
$37$	−9.15399	−1.50491	−0.752453	−	0.658645i	$-0.771130\pi$
$37$	−9.15399	−1.50491	−0.752453	+	0.658645i	$0.771130\pi$
$38$	−4.78653	−0.776478
$39$	13.5422	2.16849
$40$	2.23848	0.353935
$41$	7.89125	1.23241	0.616203	−	0.787588i	$-0.288670\pi$
$41$	7.89125	1.23241	0.616203	+	0.787588i	$0.288670\pi$
$42$	−8.75750	−1.35131
$43$	6.40589	0.976889	0.488445	−	0.872595i	$-0.337564\pi$
$43$	6.40589	0.976889	0.488445	+	0.872595i	$0.337564\pi$
$44$	6.14419	0.926271
$45$	5.41389	0.807055
$46$	2.82768	0.416919
$47$	12.4966	1.82281	0.911407	−	0.411507i	$-0.134997\pi$
$47$	12.4966	1.82281	0.911407	+	0.411507i	$0.134997\pi$
$48$	−2.32778	−0.335986
$49$	7.15391	1.02199
$50$	0.0107930	0.00152635
$51$	9.00911	1.26153
$52$	−5.81764	−0.806762
$53$	4.99068	0.685522	0.342761	−	0.939423i	$-0.388638\pi$
$53$	4.99068	0.685522	0.342761	+	0.939423i	$0.388638\pi$
$54$	1.35347	0.184184
$55$	13.7536	1.85454
$56$	3.76217	0.502741
$57$	11.1420	1.47579
$58$	−7.67062	−1.00720
$59$	12.3424	1.60684	0.803422	−	0.595411i	$-0.203011\pi$
$59$	12.3424	1.60684	0.803422	+	0.595411i	$0.203011\pi$
$60$	−5.21069	−0.672697
$61$	2.17480	0.278454	0.139227	−	0.990260i	$-0.455538\pi$
$61$	2.17480	0.278454	0.139227	+	0.990260i	$0.455538\pi$
$62$	4.46847	0.567496
$63$	9.09902	1.14637
$64$	1.00000	0.125000
$65$	−13.0227	−1.61526
$66$	−14.3023	−1.76049
$67$	−4.39550	−0.536995	−0.268498	−	0.963280i	$-0.586527\pi$
$67$	−4.39550	−0.536995	−0.268498	+	0.963280i	$0.586527\pi$
$68$	−3.87026	−0.469338
$69$	−6.58222	−0.792407
$70$	8.42154	1.00657
$71$	−14.3691	−1.70530	−0.852648	−	0.522486i	$-0.825005\pi$
$71$	−14.3691	−1.70530	−0.852648	+	0.522486i	$0.825005\pi$
$72$	2.41856	0.285030
$73$	7.97567	0.933482	0.466741	−	0.884394i	$-0.345428\pi$
$73$	7.97567	0.933482	0.466741	+	0.884394i	$0.345428\pi$
$74$	−9.15399	−1.06413
$75$	−0.0251236	−0.00290103
$76$	−4.78653	−0.549053
$77$	23.1155	2.63425
$78$	13.5422	1.53335
$79$	14.2764	1.60622	0.803112	−	0.595828i	$-0.203176\pi$
$79$	14.2764	1.60622	0.803112	+	0.595828i	$0.203176\pi$
$80$	2.23848	0.250270
$81$	−10.4063	−1.15625
$82$	7.89125	0.871442
$83$	−10.6606	−1.17015	−0.585076	−	0.810979i	$-0.698935\pi$
$83$	−10.6606	−1.17015	−0.585076	+	0.810979i	$0.698935\pi$
$84$	−8.75750	−0.955521
$85$	−8.66350	−0.939688
$86$	6.40589	0.690765
$87$	17.8555	1.91431
$88$	6.14419	0.654972
$89$	3.72489	0.394838	0.197419	−	0.980319i	$-0.436744\pi$
$89$	3.72489	0.394838	0.197419	+	0.980319i	$0.436744\pi$
$90$	5.41389	0.570674
$91$	−21.8869	−2.29438
$92$	2.82768	0.294806
$93$	−10.4016	−1.07860
$94$	12.4966	1.28892
$95$	−10.7146	−1.09929
$96$	−2.32778	−0.237578
$97$	17.7726	1.80454	0.902268	−	0.431177i	$-0.141901\pi$
$97$	17.7726	1.80454	0.902268	+	0.431177i	$0.141901\pi$
$98$	7.15391	0.722654
$99$	14.8601	1.49349
$100$	0.0107930	0.00107930
$101$	11.3521	1.12958	0.564790	−	0.825235i	$-0.308957\pi$
$101$	11.3521	1.12958	0.564790	+	0.825235i	$0.308957\pi$
$102$	9.00911	0.892034
$103$	13.0873	1.28953	0.644763	−	0.764382i	$-0.276956\pi$
$103$	13.0873	1.28953	0.644763	+	0.764382i	$0.276956\pi$
$104$	−5.81764	−0.570467
$105$	−19.6035	−1.91310
$106$	4.99068	0.484737
$107$	−1.95101	−0.188611	−0.0943055	−	0.995543i	$-0.530063\pi$
$107$	−1.95101	−0.188611	−0.0943055	+	0.995543i	$0.530063\pi$
$108$	1.35347	0.130238
$109$	−1.08621	−0.104040	−0.0520202	−	0.998646i	$-0.516566\pi$
$109$	−1.08621	−0.104040	−0.0520202	+	0.998646i	$0.516566\pi$
$110$	13.7536	1.31136
$111$	21.3085	2.02251
$112$	3.76217	0.355491
$113$	4.38494	0.412501	0.206250	−	0.978499i	$-0.433874\pi$
$113$	4.38494	0.412501	0.206250	+	0.978499i	$0.433874\pi$
$114$	11.1420	1.04354
$115$	6.32971	0.590249
$116$	−7.67062	−0.712199
$117$	−14.0703	−1.30080
$118$	12.3424	1.13621
$119$	−14.5606	−1.33476
$120$	−5.21069	−0.475669
$121$	26.7510	2.43191
$122$	2.17480	0.196897
$123$	−18.3691	−1.65628
$124$	4.46847	0.401280
$125$	−11.1682	−0.998918
$126$	9.09902	0.810605
$127$	14.2819	1.26731	0.633656	−	0.773615i	$-0.281553\pi$
$127$	14.2819	1.26731	0.633656	+	0.773615i	$0.281553\pi$
$128$	1.00000	0.0883883
$129$	−14.9115	−1.31288
$130$	−13.0227	−1.14216
$131$	3.57181	0.312071	0.156035	−	0.987751i	$-0.450129\pi$
$131$	3.57181	0.312071	0.156035	+	0.987751i	$0.450129\pi$
$132$	−14.3023	−1.24486
$133$	−18.0077	−1.56147
$134$	−4.39550	−0.379713
$135$	3.02972	0.260757
$136$	−3.87026	−0.331872
$137$	17.3345	1.48099	0.740495	−	0.672062i	$-0.234591\pi$
$137$	17.3345	1.48099	0.740495	+	0.672062i	$0.234591\pi$
$138$	−6.58222	−0.560316
$139$	15.5260	1.31690	0.658449	−	0.752626i	$-0.271213\pi$
$139$	15.5260	1.31690	0.658449	+	0.752626i	$0.271213\pi$
$140$	8.42154	0.711750
$141$	−29.0893	−2.44976
$142$	−14.3691	−1.20583
$143$	−35.7447	−2.98912
$144$	2.41856	0.201546
$145$	−17.1705	−1.42593
$146$	7.97567	0.660072
$147$	−16.6527	−1.37349
$148$	−9.15399	−0.752453
$149$	−10.7217	−0.878353	−0.439176	−	0.898401i	$-0.644730\pi$
$149$	−10.7217	−0.878353	−0.439176	+	0.898401i	$0.644730\pi$
$150$	−0.0251236	−0.00205133
$151$	7.60064	0.618531	0.309266	−	0.950976i	$-0.399917\pi$
$151$	7.60064	0.618531	0.309266	+	0.950976i	$0.399917\pi$
$152$	−4.78653	−0.388239
$153$	−9.36044	−0.756747
$154$	23.1155	1.86270
$155$	10.0026	0.803426
$156$	13.5422	1.08424
$157$	−7.70318	−0.614781	−0.307390	−	0.951584i	$-0.599456\pi$
$157$	−7.70318	−0.614781	−0.307390	+	0.951584i	$0.599456\pi$
$158$	14.2764	1.13577
$159$	−11.6172	−0.921303
$160$	2.23848	0.176967
$161$	10.6382	0.838409
$162$	−10.4063	−0.817592
$163$	−14.6647	−1.14863	−0.574315	−	0.818635i	$-0.694731\pi$
$163$	−14.6647	−1.14863	−0.574315	+	0.818635i	$0.694731\pi$
$164$	7.89125	0.616203
$165$	−32.0154	−2.49240
$166$	−10.6606	−0.827422
$167$	−12.4530	−0.963643	−0.481822	−	0.876269i	$-0.660025\pi$
$167$	−12.4530	−0.963643	−0.481822	+	0.876269i	$0.660025\pi$
$168$	−8.75750	−0.675656
$169$	20.8450	1.60346
$170$	−8.66350	−0.664460
$171$	−11.5765	−0.885277
$172$	6.40589	0.488445
$173$	−18.6737	−1.41974	−0.709869	−	0.704334i	$-0.751246\pi$
$173$	−18.6737	−1.41974	−0.709869	+	0.704334i	$0.751246\pi$
$174$	17.8555	1.35362
$175$	0.0406049	0.00306944
$176$	6.14419	0.463135
$177$	−28.7304	−2.15951
$178$	3.72489	0.279193
$179$	−3.34502	−0.250019	−0.125009	−	0.992156i	$-0.539896\pi$
$179$	−3.34502	−0.250019	−0.125009	+	0.992156i	$0.539896\pi$
$180$	5.41389	0.403528
$181$	−14.7391	−1.09555	−0.547775	−	0.836626i	$-0.684525\pi$
$181$	−14.7391	−1.09555	−0.547775	+	0.836626i	$0.684525\pi$
$182$	−21.8869	−1.62237
$183$	−5.06245	−0.374227
$184$	2.82768	0.208460
$185$	−20.4910	−1.50653
$186$	−10.4016	−0.762683
$187$	−23.7796	−1.73894
$188$	12.4966	0.911407
$189$	5.09199	0.370387
$190$	−10.7146	−0.777315
$191$	−0.613531	−0.0443935	−0.0221968	−	0.999754i	$-0.507066\pi$
$191$	−0.613531	−0.0443935	−0.0221968	+	0.999754i	$0.507066\pi$
$192$	−2.32778	−0.167993
$193$	−24.3012	−1.74924	−0.874621	−	0.484807i	$-0.838890\pi$
$193$	−24.3012	−1.74924	−0.874621	+	0.484807i	$0.838890\pi$
$194$	17.7726	1.27600
$195$	30.3139	2.17083
$196$	7.15391	0.510993
$197$	21.3675	1.52237	0.761185	−	0.648535i	$-0.224618\pi$
$197$	21.3675	1.52237	0.761185	+	0.648535i	$0.224618\pi$
$198$	14.8601	1.05606
$199$	19.4410	1.37813	0.689067	−	0.724698i	$-0.258021\pi$
$199$	19.4410	1.37813	0.689067	+	0.724698i	$0.258021\pi$
$200$	0.0107930	0.000763177 0
$201$	10.2317	0.721692
$202$	11.3521	0.798733
$203$	−28.8581	−2.02544
$204$	9.00911	0.630764
$205$	17.6644	1.23373
$206$	13.0873	0.911833
$207$	6.83891	0.475337
$208$	−5.81764	−0.403381
$209$	−29.4093	−2.03429
$210$	−19.6035	−1.35277
$211$	11.7401	0.808224	0.404112	−	0.914709i	$-0.367581\pi$
$211$	11.7401	0.808224	0.404112	+	0.914709i	$0.367581\pi$
$212$	4.99068	0.342761
$213$	33.4480	2.29182
$214$	−1.95101	−0.133368
$215$	14.3395	0.977943
$216$	1.35347	0.0920921
$217$	16.8111	1.14121
$218$	−1.08621	−0.0735677
$219$	−18.5656	−1.25455
$220$	13.7536	0.927270
$221$	22.5158	1.51458
$222$	21.3085	1.43013
$223$	2.81240	0.188332	0.0941662	−	0.995556i	$-0.469981\pi$
$223$	2.81240	0.188332	0.0941662	+	0.995556i	$0.469981\pi$
$224$	3.76217	0.251370
$225$	0.0261034	0.00174022
$226$	4.38494	0.291682
$227$	−13.7013	−0.909389	−0.454695	−	0.890647i	$-0.650252\pi$
$227$	−13.7013	−0.909389	−0.454695	+	0.890647i	$0.650252\pi$
$228$	11.1420	0.737896
$229$	−11.7658	−0.777508	−0.388754	−	0.921342i	$-0.627094\pi$
$229$	−11.7658	−0.777508	−0.388754	+	0.921342i	$0.627094\pi$
$230$	6.32971	0.417369
$231$	−53.8077	−3.54029
$232$	−7.67062	−0.503601
$233$	−9.20396	−0.602971	−0.301486	−	0.953471i	$-0.597483\pi$
$233$	−9.20396	−0.602971	−0.301486	+	0.953471i	$0.597483\pi$
$234$	−14.0703	−0.919804
$235$	27.9733	1.82478
$236$	12.3424	0.803422
$237$	−33.2324	−2.15867
$238$	−14.5606	−0.943821
$239$	−15.9774	−1.03349	−0.516745	−	0.856139i	$-0.672857\pi$
$239$	−15.9774	−1.03349	−0.516745	+	0.856139i	$0.672857\pi$
$240$	−5.21069	−0.336348
$241$	−9.59903	−0.618328	−0.309164	−	0.951009i	$-0.600049\pi$
$241$	−9.59903	−0.618328	−0.309164	+	0.951009i	$0.600049\pi$
$242$	26.7510	1.71962
$243$	20.1630	1.29346
$244$	2.17480	0.139227
$245$	16.0139	1.02309
$246$	−18.3691	−1.17117
$247$	27.8463	1.77182
$248$	4.46847	0.283748
$249$	24.8155	1.57262
$250$	−11.1682	−0.706342
$251$	26.0829	1.64634	0.823170	−	0.567795i	$-0.192203\pi$
$251$	26.0829	1.64634	0.823170	+	0.567795i	$0.192203\pi$
$252$	9.09902	0.573184
$253$	17.3738	1.09228
$254$	14.2819	0.896125
$255$	20.1667	1.26289
$256$	1.00000	0.0625000
$257$	−4.95062	−0.308811	−0.154406	−	0.988008i	$-0.549346\pi$
$257$	−4.95062	−0.308811	−0.154406	+	0.988008i	$0.549346\pi$
$258$	−14.9115	−0.928349
$259$	−34.4389	−2.13993
$260$	−13.0227	−0.807632
$261$	−18.5518	−1.14833
$262$	3.57181	0.220667
$263$	1.32741	0.0818517	0.0409258	−	0.999162i	$-0.486969\pi$
$263$	1.32741	0.0818517	0.0409258	+	0.999162i	$0.486969\pi$
$264$	−14.3023	−0.880246
$265$	11.1715	0.686261
$266$	−18.0077	−1.10412
$267$	−8.67073	−0.530640
$268$	−4.39550	−0.268498
$269$	18.0902	1.10298	0.551489	−	0.834182i	$-0.314060\pi$
$269$	18.0902	1.10298	0.551489	+	0.834182i	$0.314060\pi$
$270$	3.02972	0.184383
$271$	−0.519857	−0.0315791	−0.0157895	−	0.999875i	$-0.505026\pi$
$271$	−0.519857	−0.0315791	−0.0157895	+	0.999875i	$0.505026\pi$
$272$	−3.87026	−0.234669
$273$	50.9480	3.08351
$274$	17.3345	1.04722
$275$	0.0663139	0.00399888
$276$	−6.58222	−0.396203
$277$	15.7594	0.946889	0.473445	−	0.880824i	$-0.343010\pi$
$277$	15.7594	0.946889	0.473445	+	0.880824i	$0.343010\pi$
$278$	15.5260	0.931187
$279$	10.8072	0.647013
$280$	8.42154	0.503283
$281$	−10.2295	−0.610242	−0.305121	−	0.952314i	$-0.598697\pi$
$281$	−10.2295	−0.610242	−0.305121	+	0.952314i	$0.598697\pi$
$282$	−29.0893	−1.73224
$283$	23.7316	1.41070	0.705350	−	0.708860i	$-0.250790\pi$
$283$	23.7316	1.41070	0.705350	+	0.708860i	$0.250790\pi$
$284$	−14.3691	−0.852648
$285$	24.9411	1.47738
$286$	−35.7447	−2.11363
$287$	29.6882	1.75244
$288$	2.41856	0.142515
$289$	−2.02110	−0.118888
$290$	−17.1705	−1.00829
$291$	−41.3707	−2.42519
$292$	7.97567	0.466741
$293$	14.8856	0.869628	0.434814	−	0.900520i	$-0.356814\pi$
$293$	14.8856	0.869628	0.434814	+	0.900520i	$0.356814\pi$
$294$	−16.6527	−0.971206
$295$	27.6282	1.60858
$296$	−9.15399	−0.532065
$297$	8.31598	0.482542
$298$	−10.7217	−0.621089
$299$	−16.4505	−0.951354
$300$	−0.0251236	−0.00145051
$301$	24.1000	1.38910
$302$	7.60064	0.437368
$303$	−26.4253	−1.51809
$304$	−4.78653	−0.274526
$305$	4.86824	0.278755
$306$	−9.36044	−0.535101
$307$	5.45593	0.311386	0.155693	−	0.987805i	$-0.450239\pi$
$307$	5.45593	0.311386	0.155693	+	0.987805i	$0.450239\pi$
$308$	23.1155	1.31713
$309$	−30.4643	−1.73305
$310$	10.0026	0.568108
$311$	0.240454	0.0136349	0.00681744	−	0.999977i	$-0.497830\pi$
$311$	0.240454	0.0136349	0.00681744	+	0.999977i	$0.497830\pi$
$312$	13.5422	0.766676
$313$	−18.8480	−1.06535	−0.532676	−	0.846319i	$-0.678814\pi$
$313$	−18.8480	−1.06535	−0.532676	+	0.846319i	$0.678814\pi$
$314$	−7.70318	−0.434716
$315$	20.3680	1.14760
$316$	14.2764	0.803112
$317$	−31.8103	−1.78665	−0.893323	−	0.449415i	$-0.851632\pi$
$317$	−31.8103	−1.78665	−0.893323	+	0.449415i	$0.851632\pi$
$318$	−11.6172	−0.651460
$319$	−47.1297	−2.63876
$320$	2.23848	0.125135
$321$	4.54152	0.253483
$322$	10.6382	0.592845
$323$	18.5251	1.03076
$324$	−10.4063	−0.578125
$325$	−0.0627896	−0.00348294
$326$	−14.6647	−0.812204
$327$	2.52847	0.139825
$328$	7.89125	0.435721
$329$	47.0142	2.59198
$330$	−32.0154	−1.76239
$331$	23.8489	1.31085	0.655427	−	0.755259i	$-0.272489\pi$
$331$	23.8489	1.31085	0.655427	+	0.755259i	$0.272489\pi$
$332$	−10.6606	−0.585076
$333$	−22.1394	−1.21323
$334$	−12.4530	−0.681399
$335$	−9.83923	−0.537575
$336$	−8.75750	−0.477761
$337$	25.9468	1.41341	0.706706	−	0.707507i	$-0.250180\pi$
$337$	25.9468	1.41341	0.706706	+	0.707507i	$0.250180\pi$
$338$	20.8450	1.13382
$339$	−10.2072	−0.554378
$340$	−8.66350	−0.469844
$341$	27.4551	1.48678
$342$	−11.5765	−0.625985
$343$	0.579022	0.0312643
$344$	6.40589	0.345382
$345$	−14.7342	−0.793261
$346$	−18.6737	−1.00391
$347$	−25.6126	−1.37495	−0.687477	−	0.726206i	$-0.741282\pi$
$347$	−25.6126	−1.37495	−0.687477	+	0.726206i	$0.741282\pi$
$348$	17.8555	0.957155
$349$	14.9622	0.800910	0.400455	−	0.916316i	$-0.368852\pi$
$349$	14.9622	0.800910	0.400455	+	0.916316i	$0.368852\pi$
$350$	0.0406049	0.00217042
$351$	−7.87401	−0.420284
$352$	6.14419	0.327486
$353$	14.7072	0.782785	0.391393	−	0.920224i	$-0.371993\pi$
$353$	14.7072	0.782785	0.391393	+	0.920224i	$0.371993\pi$
$354$	−28.7304	−1.52700
$355$	−32.1649	−1.70714
$356$	3.72489	0.197419
$357$	33.8938	1.79385
$358$	−3.34502	−0.176790
$359$	−12.0146	−0.634107	−0.317053	−	0.948408i	$-0.602693\pi$
$359$	−12.0146	−0.634107	−0.317053	+	0.948408i	$0.602693\pi$
$360$	5.41389	0.285337
$361$	3.91086	0.205835
$362$	−14.7391	−0.774671
$363$	−62.2705	−3.26835
$364$	−21.8869	−1.14719
$365$	17.8534	0.934489
$366$	−5.06245	−0.264618
$367$	23.5449	1.22903	0.614517	−	0.788903i	$-0.289351\pi$
$367$	23.5449	1.22903	0.614517	+	0.788903i	$0.289351\pi$
$368$	2.82768	0.147403
$369$	19.0854	0.993548
$370$	−20.4910	−1.06528
$371$	18.7758	0.974789
$372$	−10.4016	−0.539298
$373$	−15.5586	−0.805593	−0.402796	−	0.915290i	$-0.631962\pi$
$373$	−15.5586	−0.805593	−0.402796	+	0.915290i	$0.631962\pi$
$374$	−23.7796	−1.22961
$375$	25.9972	1.34249
$376$	12.4966	0.644462
$377$	44.6249	2.29830
$378$	5.09199	0.261904
$379$	11.9453	0.613587	0.306793	−	0.951776i	$-0.400744\pi$
$379$	11.9453	0.613587	0.306793	+	0.951776i	$0.400744\pi$
$380$	−10.7146	−0.549645
$381$	−33.2451	−1.70320
$382$	−0.613531	−0.0313910
$383$	23.5107	1.20134	0.600669	−	0.799498i	$-0.294901\pi$
$383$	23.5107	1.20134	0.600669	+	0.799498i	$0.294901\pi$
$384$	−2.32778	−0.118789
$385$	51.7435	2.63709
$386$	−24.3012	−1.23690
$387$	15.4930	0.787554
$388$	17.7726	0.902268
$389$	0.953367	0.0483376	0.0241688	−	0.999708i	$-0.492306\pi$
$389$	0.953367	0.0483376	0.0241688	+	0.999708i	$0.492306\pi$
$390$	30.3139	1.53501
$391$	−10.9439	−0.553455
$392$	7.15391	0.361327
$393$	−8.31440	−0.419406
$394$	21.3675	1.07648
$395$	31.9575	1.60796
$396$	14.8601	0.746746
$397$	18.5528	0.931140	0.465570	−	0.885011i	$-0.345849\pi$
$397$	18.5528	0.931140	0.465570	+	0.885011i	$0.345849\pi$
$398$	19.4410	0.974488
$399$	41.9180	2.09853
$400$	0.0107930	0.000539648 0
$401$	−8.46983	−0.422963	−0.211482	−	0.977382i	$-0.567829\pi$
$401$	−8.46983	−0.422963	−0.211482	+	0.977382i	$0.567829\pi$
$402$	10.2317	0.510313
$403$	−25.9960	−1.29495
$404$	11.3521	0.564790
$405$	−23.2942	−1.15750
$406$	−28.8581	−1.43221
$407$	−56.2438	−2.78790
$408$	9.00911	0.446017
$409$	−4.23102	−0.209211	−0.104605	−	0.994514i	$-0.533358\pi$
$409$	−4.23102	−0.209211	−0.104605	+	0.994514i	$0.533358\pi$
$410$	17.6644	0.872382
$411$	−40.3510	−1.99037
$412$	13.0873	0.644763
$413$	46.4342	2.28488
$414$	6.83891	0.336114
$415$	−23.8635	−1.17141
$416$	−5.81764	−0.285233
$417$	−36.1411	−1.76984
$418$	−29.4093	−1.43846
$419$	−28.2469	−1.37995	−0.689976	−	0.723832i	$-0.742379\pi$
$419$	−28.2469	−1.37995	−0.689976	+	0.723832i	$0.742379\pi$
$420$	−19.6035	−0.956552
$421$	−25.3478	−1.23537	−0.617687	−	0.786424i	$-0.711930\pi$
$421$	−25.3478	−1.23537	−0.617687	+	0.786424i	$0.711930\pi$
$422$	11.7401	0.571501
$423$	30.2237	1.46953
$424$	4.99068	0.242369
$425$	−0.0417715	−0.00202622
$426$	33.4480	1.62056
$427$	8.18195	0.395952
$428$	−1.95101	−0.0943055
$429$	83.2057	4.01721
$430$	14.3395	0.691510
$431$	−1.44212	−0.0694647	−0.0347323	−	0.999397i	$-0.511058\pi$
$431$	−1.44212	−0.0694647	−0.0347323	+	0.999397i	$0.511058\pi$
$432$	1.35347	0.0651189
$433$	4.35600	0.209336	0.104668	−	0.994507i	$-0.466622\pi$
$433$	4.35600	0.209336	0.104668	+	0.994507i	$0.466622\pi$
$434$	16.8111	0.806960
$435$	39.9692	1.91638
$436$	−1.08621	−0.0520202
$437$	−13.5348	−0.647457
$438$	−18.5656	−0.887099
$439$	−21.0080	−1.00266	−0.501328	−	0.865257i	$-0.667155\pi$
$439$	−21.0080	−1.00266	−0.501328	+	0.865257i	$0.667155\pi$
$440$	13.7536	0.655679
$441$	17.3021	0.823911
$442$	22.5158	1.07097
$443$	−5.01145	−0.238101	−0.119051	−	0.992888i	$-0.537985\pi$
$443$	−5.01145	−0.238101	−0.119051	+	0.992888i	$0.537985\pi$
$444$	21.3085	1.01126
$445$	8.33810	0.395264
$446$	2.81240	0.133171
$447$	24.9577	1.18046
$448$	3.76217	0.177746
$449$	0.231032	0.0109031	0.00545154	−	0.999985i	$-0.498265\pi$
$449$	0.231032	0.0109031	0.00545154	+	0.999985i	$0.498265\pi$
$450$	0.0261034	0.00123052
$451$	48.4853	2.28308
$452$	4.38494	0.206250
$453$	−17.6926	−0.831271
$454$	−13.7013	−0.643035
$455$	−48.9935	−2.29685
$456$	11.1420	0.521771
$457$	4.55848	0.213237	0.106618	−	0.994300i	$-0.465998\pi$
$457$	4.55848	0.213237	0.106618	+	0.994300i	$0.465998\pi$
$458$	−11.7658	−0.549781
$459$	−5.23828	−0.244502
$460$	6.32971	0.295124
$461$	27.0936	1.26188	0.630938	−	0.775833i	$-0.282670\pi$
$461$	27.0936	1.26188	0.630938	+	0.775833i	$0.282670\pi$
$462$	−53.8077	−2.50336
$463$	−40.0458	−1.86109	−0.930543	−	0.366182i	$-0.880665\pi$
$463$	−40.0458	−1.86109	−0.930543	+	0.366182i	$0.880665\pi$
$464$	−7.67062	−0.356099
$465$	−23.2838	−1.07976
$466$	−9.20396	−0.426365
$467$	11.8868	0.550056	0.275028	−	0.961436i	$-0.411313\pi$
$467$	11.8868	0.550056	0.275028	+	0.961436i	$0.411313\pi$
$468$	−14.0703	−0.650400
$469$	−16.5366	−0.763589
$470$	27.9733	1.29031
$471$	17.9313	0.826231
$472$	12.3424	0.568105
$473$	39.3590	1.80973
$474$	−33.2324	−1.52641
$475$	−0.0516608	−0.00237036
$476$	−14.5606	−0.667382
$477$	12.0702	0.552658
$478$	−15.9774	−0.730788
$479$	−15.0067	−0.685671	−0.342836	−	0.939395i	$-0.611387\pi$
$479$	−15.0067	−0.685671	−0.342836	+	0.939395i	$0.611387\pi$
$480$	−5.21069	−0.237834
$481$	53.2547	2.42820
$482$	−9.59903	−0.437224
$483$	−24.7634	−1.12678
$484$	26.7510	1.21596
$485$	39.7836	1.80648
$486$	20.1630	0.914614
$487$	−27.3691	−1.24021	−0.620106	−	0.784518i	$-0.712911\pi$
$487$	−27.3691	−1.24021	−0.620106	+	0.784518i	$0.712911\pi$
$488$	2.17480	0.0984485
$489$	34.1362	1.54369
$490$	16.0139	0.723433
$491$	24.9688	1.12683	0.563414	−	0.826175i	$-0.309488\pi$
$491$	24.9688	1.12683	0.563414	+	0.826175i	$0.309488\pi$
$492$	−18.3691	−0.828142
$493$	29.6873	1.33705
$494$	27.8463	1.25287
$495$	33.2640	1.49510
$496$	4.46847	0.200640
$497$	−54.0589	−2.42487
$498$	24.8155	1.11201
$499$	−39.4181	−1.76460	−0.882299	−	0.470689i	$-0.844005\pi$
$499$	−39.4181	−1.76460	−0.882299	+	0.470689i	$0.844005\pi$
$500$	−11.1682	−0.499459
$501$	28.9879	1.29508
$502$	26.0829	1.16414
$503$	28.3702	1.26496	0.632481	−	0.774576i	$-0.282036\pi$
$503$	28.3702	1.26496	0.632481	+	0.774576i	$0.282036\pi$
$504$	9.09902	0.405302
$505$	25.4115	1.13080
$506$	17.3738	0.772360
$507$	−48.5225	−2.15496
$508$	14.2819	0.633656
$509$	22.3014	0.988493	0.494246	−	0.869322i	$-0.335444\pi$
$509$	22.3014	0.988493	0.494246	+	0.869322i	$0.335444\pi$
$510$	20.1667	0.892997
$511$	30.0058	1.32738
$512$	1.00000	0.0441942
$513$	−6.47843	−0.286030
$514$	−4.95062	−0.218363
$515$	29.2956	1.29092
$516$	−14.9115	−0.656442
$517$	76.7813	3.37684
$518$	−34.4389	−1.51316
$519$	43.4683	1.90805
$520$	−13.0227	−0.571082
$521$	−25.9354	−1.13625	−0.568125	−	0.822942i	$-0.692331\pi$
$521$	−25.9354	−1.13625	−0.568125	+	0.822942i	$0.692331\pi$
$522$	−18.5518	−0.811991
$523$	−11.3672	−0.497052	−0.248526	−	0.968625i	$-0.579946\pi$
$523$	−11.3672	−0.497052	−0.248526	+	0.968625i	$0.579946\pi$
$524$	3.57181	0.156035
$525$	−0.0945193	−0.00412516
$526$	1.32741	0.0578779
$527$	−17.2941	−0.753344
$528$	−14.3023	−0.622428
$529$	−15.0042	−0.652357
$530$	11.1715	0.485260
$531$	29.8508	1.29541
$532$	−18.0077	−0.780734
$533$	−45.9084	−1.98852
$534$	−8.67073	−0.375219
$535$	−4.36729	−0.188814
$536$	−4.39550	−0.189857
$537$	7.78648	0.336011
$538$	18.0902	0.779923
$539$	43.9549	1.89327
$540$	3.02972	0.130378
$541$	21.0198	0.903711	0.451855	−	0.892091i	$-0.350762\pi$
$541$	21.0198	0.903711	0.451855	+	0.892091i	$0.350762\pi$
$542$	−0.519857	−0.0223298
$543$	34.3094	1.47236
$544$	−3.87026	−0.165936
$545$	−2.43147	−0.104153
$546$	50.9480	2.18037
$547$	−3.55300	−0.151915	−0.0759576	−	0.997111i	$-0.524201\pi$
$547$	−3.55300	−0.151915	−0.0759576	+	0.997111i	$0.524201\pi$
$548$	17.3345	0.740495
$549$	5.25987	0.224486
$550$	0.0663139	0.00282763
$551$	36.7156	1.56414
$552$	−6.58222	−0.280158
$553$	53.7103	2.28399
$554$	15.7594	0.669552
$555$	47.6986	2.02469
$556$	15.5260	0.658449
$557$	−12.8822	−0.545837	−0.272919	−	0.962037i	$-0.587989\pi$
$557$	−12.8822	−0.545837	−0.272919	+	0.962037i	$0.587989\pi$
$558$	10.8072	0.457507
$559$	−37.2672	−1.57623
$560$	8.42154	0.355875
$561$	55.3536	2.33703
$562$	−10.2295	−0.431506
$563$	−45.3345	−1.91062	−0.955311	−	0.295604i	$-0.904479\pi$
$563$	−45.3345	−1.91062	−0.955311	+	0.295604i	$0.904479\pi$
$564$	−29.0893	−1.22488
$565$	9.81561	0.412946
$566$	23.7316	0.997515
$567$	−39.1501	−1.64415
$568$	−14.3691	−0.602913
$569$	11.0206	0.462006	0.231003	−	0.972953i	$-0.425799\pi$
$569$	11.0206	0.462006	0.231003	+	0.972953i	$0.425799\pi$
$570$	24.9411	1.04467
$571$	22.9266	0.959446	0.479723	−	0.877420i	$-0.340737\pi$
$571$	22.9266	0.959446	0.479723	+	0.877420i	$0.340737\pi$
$572$	−35.7447	−1.49456
$573$	1.42816	0.0596624
$574$	29.6882	1.23916
$575$	0.0305191	0.00127273
$576$	2.41856	0.100773
$577$	−14.6844	−0.611321	−0.305660	−	0.952141i	$-0.598877\pi$
$577$	−14.6844	−0.611321	−0.305660	+	0.952141i	$0.598877\pi$
$578$	−2.02110	−0.0840668
$579$	56.5679	2.35088
$580$	−17.1705	−0.712967
$581$	−40.1069	−1.66392
$582$	−41.3707	−1.71487
$583$	30.6636	1.26996
$584$	7.97567	0.330036
$585$	−31.4961	−1.30220
$586$	14.8856	0.614920
$587$	−34.1443	−1.40929	−0.704643	−	0.709562i	$-0.748893\pi$
$587$	−34.1443	−1.40929	−0.704643	+	0.709562i	$0.748893\pi$
$588$	−16.6527	−0.686746
$589$	−21.3885	−0.881296
$590$	27.6282	1.13744
$591$	−49.7388	−2.04598
$592$	−9.15399	−0.376227
$593$	−20.6894	−0.849612	−0.424806	−	0.905284i	$-0.639658\pi$
$593$	−20.6894	−0.849612	−0.424806	+	0.905284i	$0.639658\pi$
$594$	8.31598	0.341209
$595$	−32.5935	−1.33620
$596$	−10.7217	−0.439176
$597$	−45.2543	−1.85214
$598$	−16.4505	−0.672709
$599$	−8.07531	−0.329948	−0.164974	−	0.986298i	$-0.552754\pi$
$599$	−8.07531	−0.329948	−0.164974	+	0.986298i	$0.552754\pi$
$600$	−0.0251236	−0.00102567
$601$	−19.4784	−0.794540	−0.397270	−	0.917702i	$-0.630042\pi$
$601$	−19.4784	−0.794540	−0.397270	+	0.917702i	$0.630042\pi$
$602$	24.1000	0.982244
$603$	−10.6308	−0.432918
$604$	7.60064	0.309266
$605$	59.8816	2.43453
$606$	−26.4253	−1.07345
$607$	−17.2744	−0.701147	−0.350573	−	0.936535i	$-0.614013\pi$
$607$	−17.2744	−0.701147	−0.350573	+	0.936535i	$0.614013\pi$
$608$	−4.78653	−0.194119
$609$	67.1754	2.72208
$610$	4.86824	0.197109
$611$	−72.7006	−2.94115
$612$	−9.36044	−0.378373
$613$	−15.5483	−0.627991	−0.313995	−	0.949425i	$-0.601668\pi$
$613$	−15.5483	−0.627991	−0.313995	+	0.949425i	$0.601668\pi$
$614$	5.45593	0.220183
$615$	−41.1188	−1.65807
$616$	23.1155	0.931348
$617$	−22.0246	−0.886676	−0.443338	−	0.896355i	$-0.646206\pi$
$617$	−22.0246	−0.886676	−0.443338	+	0.896355i	$0.646206\pi$
$618$	−30.4643	−1.22545
$619$	19.9425	0.801558	0.400779	−	0.916175i	$-0.368739\pi$
$619$	19.9425	0.801558	0.400779	+	0.916175i	$0.368739\pi$
$620$	10.0026	0.401713
$621$	3.82719	0.153580
$622$	0.240454	0.00964131
$623$	14.0137	0.561446
$624$	13.5422	0.542121
$625$	−25.0538	−1.00215
$626$	−18.8480	−0.753318
$627$	68.4584	2.73397
$628$	−7.70318	−0.307390
$629$	35.4283	1.41262
$630$	20.3680	0.811479
$631$	−17.3322	−0.689983	−0.344991	−	0.938606i	$-0.612118\pi$
$631$	−17.3322	−0.689983	−0.344991	+	0.938606i	$0.612118\pi$
$632$	14.2764	0.567886
$633$	−27.3285	−1.08621
$634$	−31.8103	−1.26335
$635$	31.9697	1.26868
$636$	−11.6172	−0.460652
$637$	−41.6189	−1.64900
$638$	−47.1297	−1.86588
$639$	−34.7524	−1.37478
$640$	2.23848	0.0884837
$641$	−4.77570	−0.188629	−0.0943144	−	0.995542i	$-0.530066\pi$
$641$	−4.77570	−0.188629	−0.0943144	+	0.995542i	$0.530066\pi$
$642$	4.54152	0.179239
$643$	−40.4929	−1.59689	−0.798443	−	0.602071i	$-0.794342\pi$
$643$	−40.4929	−1.59689	−0.798443	+	0.602071i	$0.794342\pi$
$644$	10.6382	0.419205
$645$	−33.3791	−1.31430
$646$	18.5251	0.728860
$647$	−18.5181	−0.728020	−0.364010	−	0.931395i	$-0.618593\pi$
$647$	−18.5181	−0.728020	−0.364010	+	0.931395i	$0.618593\pi$
$648$	−10.4063	−0.408796
$649$	75.8340	2.97674
$650$	−0.0627896	−0.00246281
$651$	−39.1326	−1.53373
$652$	−14.6647	−0.574315
$653$	−37.1159	−1.45246	−0.726229	−	0.687453i	$-0.758729\pi$
$653$	−37.1159	−1.45246	−0.726229	+	0.687453i	$0.758729\pi$
$654$	2.52847	0.0988709
$655$	7.99544	0.312408
$656$	7.89125	0.308101
$657$	19.2896	0.752560
$658$	47.0142	1.83281
$659$	18.5669	0.723263	0.361631	−	0.932321i	$-0.382220\pi$
$659$	18.5669	0.723263	0.361631	+	0.932321i	$0.382220\pi$
$660$	−32.0154	−1.24620
$661$	36.5134	1.42021	0.710103	−	0.704098i	$-0.248648\pi$
$661$	36.5134	1.42021	0.710103	+	0.704098i	$0.248648\pi$
$662$	23.8489	0.926913
$663$	−52.4118	−2.03550
$664$	−10.6606	−0.413711
$665$	−40.3099	−1.56315
$666$	−22.1394	−0.857886
$667$	−21.6901	−0.839843
$668$	−12.4530	−0.481822
$669$	−6.54666	−0.253108
$670$	−9.83923	−0.380123
$671$	13.3624	0.515848
$672$	−8.75750	−0.337828
$673$	−15.7361	−0.606580	−0.303290	−	0.952898i	$-0.598085\pi$
$673$	−15.7361	−0.606580	−0.303290	+	0.952898i	$0.598085\pi$
$674$	25.9468	0.999434
$675$	0.0146080	0.000562260 0
$676$	20.8450	0.801730
$677$	16.7835	0.645042	0.322521	−	0.946562i	$-0.395470\pi$
$677$	16.7835	0.645042	0.322521	+	0.946562i	$0.395470\pi$
$678$	−10.2072	−0.392004
$679$	66.8635	2.56599
$680$	−8.66350	−0.332230
$681$	31.8937	1.22217
$682$	27.4551	1.05131
$683$	−21.8493	−0.836042	−0.418021	−	0.908437i	$-0.637276\pi$
$683$	−21.8493	−0.836042	−0.418021	+	0.908437i	$0.637276\pi$
$684$	−11.5765	−0.442638
$685$	38.8030	1.48259
$686$	0.579022	0.0221072
$687$	27.3883	1.04493
$688$	6.40589	0.244222
$689$	−29.0340	−1.10611
$690$	−14.7342	−0.560921
$691$	15.8807	0.604132	0.302066	−	0.953287i	$-0.402324\pi$
$691$	15.8807	0.604132	0.302066	+	0.953287i	$0.402324\pi$
$692$	−18.6737	−0.709869
$693$	55.9060	2.12370
$694$	−25.6126	−0.972240
$695$	34.7546	1.31832
$696$	17.8555	0.676811
$697$	−30.5412	−1.15683
$698$	14.9622	0.566329
$699$	21.4248	0.810360
$700$	0.0406049	0.00153472
$701$	24.9333	0.941716	0.470858	−	0.882209i	$-0.343944\pi$
$701$	24.9333	0.941716	0.470858	+	0.882209i	$0.343944\pi$
$702$	−7.87401	−0.297185
$703$	43.8158	1.65255
$704$	6.14419	0.231568
$705$	−65.1158	−2.45240
$706$	14.7072	0.553513
$707$	42.7086	1.60622
$708$	−28.7304	−1.07975
$709$	−0.183400	−0.00688773	−0.00344387	−	0.999994i	$-0.501096\pi$
$709$	−0.183400	−0.00688773	−0.00344387	+	0.999994i	$0.501096\pi$
$710$	−32.1649	−1.20713
$711$	34.5284	1.29491
$712$	3.72489	0.139596
$713$	12.6354	0.473200
$714$	33.8938	1.26844
$715$	−80.0137	−2.99234
$716$	−3.34502	−0.125009
$717$	37.1918	1.38895
$718$	−12.0146	−0.448381
$719$	30.6586	1.14337	0.571686	−	0.820473i	$-0.306290\pi$
$719$	30.6586	1.14337	0.571686	+	0.820473i	$0.306290\pi$
$720$	5.41389	0.201764
$721$	49.2365	1.83366
$722$	3.91086	0.145547
$723$	22.3444	0.830998
$724$	−14.7391	−0.547775
$725$	−0.0827886	−0.00307469
$726$	−62.2705	−2.31107
$727$	15.5495	0.576699	0.288349	−	0.957525i	$-0.406894\pi$
$727$	15.5495	0.576699	0.288349	+	0.957525i	$0.406894\pi$
$728$	−21.8869	−0.811184
$729$	−15.7164	−0.582088
$730$	17.8534	0.660784
$731$	−24.7924	−0.916982
$732$	−5.06245	−0.187114
$733$	−0.768140	−0.0283719	−0.0141860	−	0.999899i	$-0.504516\pi$
$733$	−0.768140	−0.0283719	−0.0141860	+	0.999899i	$0.504516\pi$
$734$	23.5449	0.869059
$735$	−37.2768	−1.37497
$736$	2.82768	0.104230
$737$	−27.0067	−0.994806
$738$	19.0854	0.702544
$739$	10.3712	0.381513	0.190756	−	0.981637i	$-0.438906\pi$
$739$	10.3712	0.381513	0.190756	+	0.981637i	$0.438906\pi$
$740$	−20.4910	−0.753265
$741$	−64.8201	−2.38123
$742$	18.7758	0.689280
$743$	50.3838	1.84840	0.924202	−	0.381905i	$-0.124732\pi$
$743$	50.3838	1.84840	0.924202	+	0.381905i	$0.124732\pi$
$744$	−10.4016	−0.381341
$745$	−24.0002	−0.879300
$746$	−15.5586	−0.569640
$747$	−25.7832	−0.943359
$748$	−23.7796	−0.869468
$749$	−7.34002	−0.268198
$750$	25.9972	0.949284
$751$	16.4936	0.601861	0.300931	−	0.953646i	$-0.402703\pi$
$751$	16.4936	0.601861	0.300931	+	0.953646i	$0.402703\pi$
$752$	12.4966	0.455703
$753$	−60.7153	−2.21259
$754$	44.6249	1.62514
$755$	17.0139	0.619198
$756$	5.09199	0.185194
$757$	35.8728	1.30382	0.651910	−	0.758297i	$-0.273968\pi$
$757$	35.8728	1.30382	0.651910	+	0.758297i	$0.273968\pi$
$758$	11.9453	0.433871
$759$	−40.4424	−1.46797
$760$	−10.7146	−0.388658
$761$	−5.29631	−0.191991	−0.0959955	−	0.995382i	$-0.530603\pi$
$761$	−5.29631	−0.191991	−0.0959955	+	0.995382i	$0.530603\pi$
$762$	−33.2451	−1.20434
$763$	−4.08652	−0.147942
$764$	−0.613531	−0.0221968
$765$	−20.9532	−0.757563
$766$	23.5107	0.849475
$767$	−71.8037	−2.59268
$768$	−2.32778	−0.0839965
$769$	−10.3984	−0.374975	−0.187487	−	0.982267i	$-0.560034\pi$
$769$	−10.3984	−0.374975	−0.187487	+	0.982267i	$0.560034\pi$
$770$	51.7435	1.86471
$771$	11.5240	0.415025
$772$	−24.3012	−0.874621
$773$	−33.8663	−1.21809	−0.609043	−	0.793137i	$-0.708446\pi$
$773$	−33.8663	−1.21809	−0.609043	+	0.793137i	$0.708446\pi$
$774$	15.4930	0.556885
$775$	0.0482280	0.00173240
$776$	17.7726	0.638000
$777$	80.1661	2.87594
$778$	0.953367	0.0341799
$779$	−37.7717	−1.35331
$780$	30.3139	1.08541
$781$	−88.2863	−3.15913
$782$	−10.9439	−0.391352
$783$	−10.3820	−0.371021
$784$	7.15391	0.255497
$785$	−17.2434	−0.615444
$786$	−8.31440	−0.296565
$787$	−31.9215	−1.13788	−0.568939	−	0.822380i	$-0.692646\pi$
$787$	−31.9215	−1.13788	−0.568939	+	0.822380i	$0.692646\pi$
$788$	21.3675	0.761185
$789$	−3.08992	−0.110004
$790$	31.9575	1.13700
$791$	16.4969	0.586562
$792$	14.8601	0.528029
$793$	−12.6522	−0.449293
$794$	18.5528	0.658416
$795$	−26.0049	−0.922297
$796$	19.4410	0.689067
$797$	22.9149	0.811688	0.405844	−	0.913942i	$-0.366978\pi$
$797$	22.9149	0.811688	0.405844	+	0.913942i	$0.366978\pi$
$798$	41.9180	1.48388
$799$	−48.3650	−1.71103
$800$	0.0107930	0.000381589 0
$801$	9.00886	0.318313
$802$	−8.46983	−0.299080
$803$	49.0040	1.72931
$804$	10.2317	0.360846
$805$	23.8134	0.839314
$806$	−25.9960	−0.915668
$807$	−42.1099	−1.48234
$808$	11.3521	0.399367
$809$	4.98644	0.175314	0.0876569	−	0.996151i	$-0.472062\pi$
$809$	4.98644	0.175314	0.0876569	+	0.996151i	$0.472062\pi$
$810$	−23.2942	−0.818474
$811$	−46.2719	−1.62483	−0.812413	−	0.583083i	$-0.801846\pi$
$811$	−46.2719	−1.62483	−0.812413	+	0.583083i	$0.801846\pi$
$812$	−28.8581	−1.01272
$813$	1.21011	0.0424405
$814$	−56.2438	−1.97134
$815$	−32.8267	−1.14987
$816$	9.00911	0.315382
$817$	−30.6620	−1.07273
$818$	−4.23102	−0.147934
$819$	−52.9348	−1.84969
$820$	17.6644	0.616867
$821$	49.3879	1.72365	0.861826	−	0.507205i	$-0.169321\pi$
$821$	49.3879	1.72365	0.861826	+	0.507205i	$0.169321\pi$
$822$	−40.3510	−1.40740
$823$	12.9187	0.450317	0.225159	−	0.974322i	$-0.427710\pi$
$823$	12.9187	0.450317	0.225159	+	0.974322i	$0.427710\pi$
$824$	13.0873	0.455916
$825$	−0.154364	−0.00537427
$826$	46.4342	1.61565
$827$	19.3284	0.672116	0.336058	−	0.941841i	$-0.390906\pi$
$827$	19.3284	0.672116	0.336058	+	0.941841i	$0.390906\pi$
$828$	6.83891	0.237669
$829$	−6.73189	−0.233808	−0.116904	−	0.993143i	$-0.537297\pi$
$829$	−6.73189	−0.233808	−0.116904	+	0.993143i	$0.537297\pi$
$830$	−23.8635	−0.828314
$831$	−36.6843	−1.27257
$832$	−5.81764	−0.201690
$833$	−27.6875	−0.959314
$834$	−36.1411	−1.25146
$835$	−27.8758	−0.964683
$836$	−29.4093	−1.01714
$837$	6.04794	0.209048
$838$	−28.2469	−0.975774
$839$	2.20109	0.0759902	0.0379951	−	0.999278i	$-0.487903\pi$
$839$	2.20109	0.0759902	0.0379951	+	0.999278i	$0.487903\pi$
$840$	−19.6035	−0.676384
$841$	29.8384	1.02891
$842$	−25.3478	−0.873542
$843$	23.8121	0.820131
$844$	11.7401	0.404112
$845$	46.6611	1.60519
$846$	30.2237	1.03911
$847$	100.642	3.45809
$848$	4.99068	0.171380
$849$	−55.2420	−1.89590
$850$	−0.0417715	−0.00143275
$851$	−25.8846	−0.887313
$852$	33.4480	1.14591
$853$	−31.8462	−1.09039	−0.545196	−	0.838309i	$-0.683545\pi$
$853$	−31.8462	−1.09039	−0.545196	+	0.838309i	$0.683545\pi$
$854$	8.18195	0.279981
$855$	−25.9137	−0.886232
$856$	−1.95101	−0.0666841
$857$	−35.2837	−1.20527	−0.602634	−	0.798017i	$-0.705882\pi$
$857$	−35.2837	−1.20527	−0.602634	+	0.798017i	$0.705882\pi$
$858$	83.2057	2.84060
$859$	20.8990	0.713064	0.356532	−	0.934283i	$-0.383959\pi$
$859$	20.8990	0.713064	0.356532	+	0.934283i	$0.383959\pi$
$860$	14.3395	0.488971
$861$	−69.1076	−2.35518
$862$	−1.44212	−0.0491189
$863$	14.8275	0.504732	0.252366	−	0.967632i	$-0.418791\pi$
$863$	14.8275	0.504732	0.252366	+	0.967632i	$0.418791\pi$
$864$	1.35347	0.0460460
$865$	−41.8008	−1.42127
$866$	4.35600	0.148023
$867$	4.70468	0.159779
$868$	16.8111	0.570607
$869$	87.7170	2.97560
$870$	39.9692	1.35508
$871$	25.5714	0.866455
$872$	−1.08621	−0.0367839
$873$	42.9841	1.45479
$874$	−13.5348	−0.457821
$875$	−42.0168	−1.42043
$876$	−18.5656	−0.627274
$877$	−20.4132	−0.689305	−0.344652	−	0.938730i	$-0.612003\pi$
$877$	−20.4132	−0.689305	−0.344652	+	0.938730i	$0.612003\pi$
$878$	−21.0080	−0.708985
$879$	−34.6505	−1.16873
$880$	13.7536	0.463635
$881$	−26.6630	−0.898298	−0.449149	−	0.893457i	$-0.648273\pi$
$881$	−26.6630	−0.898298	−0.449149	+	0.893457i	$0.648273\pi$
$882$	17.3021	0.582593
$883$	6.74789	0.227085	0.113542	−	0.993533i	$-0.463780\pi$
$883$	6.74789	0.227085	0.113542	+	0.993533i	$0.463780\pi$
$884$	22.5158	0.757288
$885$	−64.3124	−2.16184
$886$	−5.01145	−0.168363
$887$	20.0074	0.671782	0.335891	−	0.941901i	$-0.390963\pi$
$887$	20.0074	0.671782	0.335891	+	0.941901i	$0.390963\pi$
$888$	21.3085	0.715066
$889$	53.7309	1.80208
$890$	8.33810	0.279494
$891$	−63.9379	−2.14200
$892$	2.81240	0.0941662
$893$	−59.8152	−2.00164
$894$	24.9577	0.834709
$895$	−7.48777	−0.250289
$896$	3.76217	0.125685
$897$	38.2930	1.27857
$898$	0.231032	0.00770964
$899$	−34.2759	−1.14317
$900$	0.0261034	0.000870112 0
$901$	−19.3152	−0.643483
$902$	48.4853	1.61438
$903$	−56.0996	−1.86688
$904$	4.38494	0.145841
$905$	−32.9932	−1.09673
$906$	−17.6926	−0.587798
$907$	8.28194	0.274997	0.137499	−	0.990502i	$-0.456094\pi$
$907$	8.28194	0.274997	0.137499	+	0.990502i	$0.456094\pi$
$908$	−13.7013	−0.454695
$909$	27.4558	0.910651
$910$	−48.9935	−1.62412
$911$	−39.5210	−1.30939	−0.654695	−	0.755894i	$-0.727203\pi$
$911$	−39.5210	−1.30939	−0.654695	+	0.755894i	$0.727203\pi$
$912$	11.1420	0.368948
$913$	−65.5006	−2.16775
$914$	4.55848	0.150781
$915$	−11.3322	−0.374631
$916$	−11.7658	−0.388754
$917$	13.4378	0.443754
$918$	−5.23828	−0.172889
$919$	−5.86154	−0.193354	−0.0966772	−	0.995316i	$-0.530821\pi$
$919$	−5.86154	−0.193354	−0.0966772	+	0.995316i	$0.530821\pi$
$920$	6.32971	0.208684
$921$	−12.7002	−0.418486
$922$	27.0936	0.892281
$923$	83.5942	2.75154
$924$	−53.8077	−1.77014
$925$	−0.0987986	−0.00324848
$926$	−40.0458	−1.31599
$927$	31.6523	1.03960
$928$	−7.67062	−0.251800
$929$	56.4654	1.85257	0.926285	−	0.376824i	$-0.122984\pi$
$929$	56.4654	1.85257	0.926285	+	0.376824i	$0.122984\pi$
$930$	−23.2838	−0.763506
$931$	−34.2424	−1.12225
$932$	−9.20396	−0.301486
$933$	−0.559723	−0.0183245
$934$	11.8868	0.388948
$935$	−53.2301	−1.74081
$936$	−14.0703	−0.459902
$937$	15.4762	0.505587	0.252793	−	0.967520i	$-0.418651\pi$
$937$	15.4762	0.505587	0.252793	+	0.967520i	$0.418651\pi$
$938$	−16.5366	−0.539939
$939$	43.8740	1.43177
$940$	27.9733	0.912390
$941$	−25.3483	−0.826332	−0.413166	−	0.910656i	$-0.635577\pi$
$941$	−25.3483	−0.826332	−0.413166	+	0.910656i	$0.635577\pi$
$942$	17.9313	0.584233
$943$	22.3139	0.726642
$944$	12.3424	0.401711
$945$	11.3983	0.370787
$946$	39.3590	1.27967
$947$	−51.9510	−1.68818	−0.844090	−	0.536201i	$-0.819859\pi$
$947$	−51.9510	−1.68818	−0.844090	+	0.536201i	$0.819859\pi$
$948$	−33.2324	−1.07934
$949$	−46.3996	−1.50620
$950$	−0.0516608	−0.00167610
$951$	74.0474	2.40115
$952$	−14.5606	−0.471910
$953$	5.39885	0.174886	0.0874430	−	0.996170i	$-0.472130\pi$
$953$	5.39885	0.174886	0.0874430	+	0.996170i	$0.472130\pi$
$954$	12.0702	0.390788
$955$	−1.37338	−0.0444414
$956$	−15.9774	−0.516745
$957$	109.708	3.54634
$958$	−15.0067	−0.484843
$959$	65.2155	2.10592
$960$	−5.21069	−0.168174
$961$	−11.0328	−0.355897
$962$	53.2547	1.71700
$963$	−4.71862	−0.152055
$964$	−9.59903	−0.309164
$965$	−54.3979	−1.75113
$966$	−24.7634	−0.796750
$967$	−9.11979	−0.293273	−0.146636	−	0.989190i	$-0.546845\pi$
$967$	−9.11979	−0.293273	−0.146636	+	0.989190i	$0.546845\pi$
$968$	26.7510	0.859810
$969$	−43.1224	−1.38529
$970$	39.7836	1.27738
$971$	24.7415	0.793994	0.396997	−	0.917820i	$-0.370052\pi$
$971$	24.7415	0.793994	0.396997	+	0.917820i	$0.370052\pi$
$972$	20.1630	0.646730
$973$	58.4114	1.87258
$974$	−27.3691	−0.876963
$975$	0.146160	0.00468087
$976$	2.17480	0.0696136
$977$	−54.9785	−1.75892	−0.879459	−	0.475975i	$-0.842095\pi$
$977$	−54.9785	−1.75892	−0.879459	+	0.475975i	$0.842095\pi$
$978$	34.1362	1.09156
$979$	22.8864	0.731453
$980$	16.0139	0.511545
$981$	−2.62707	−0.0838759
$982$	24.9688	0.796788
$983$	18.1849	0.580007	0.290003	−	0.957026i	$-0.406344\pi$
$983$	18.1849	0.580007	0.290003	+	0.957026i	$0.406344\pi$
$984$	−18.3691	−0.585585
$985$	47.8307	1.52401
$986$	29.6873	0.945435
$987$	−109.439	−3.48347
$988$	27.8463	0.885909
$989$	18.1138	0.575986
$990$	33.2640	1.05720
$991$	−0.341680	−0.0108538	−0.00542692	−	0.999985i	$-0.501727\pi$
$991$	−0.341680	−0.0108538	−0.00542692	+	0.999985i	$0.501727\pi$
$992$	4.46847	0.141874
$993$	−55.5149	−1.76171
$994$	−54.0589	−1.71464
$995$	43.5182	1.37962
$996$	24.8155	0.786309
$997$	−19.7175	−0.624458	−0.312229	−	0.950007i	$-0.601076\pi$
$997$	−19.7175	−0.624458	−0.312229	+	0.950007i	$0.601076\pi$
$998$	−39.4181	−1.24776
$999$	−12.3897	−0.391992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.17	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.17	✓	96	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.32778 q^{3} +1.00000 q^{4} +2.23848 q^{5} -2.32778 q^{6} +3.76217 q^{7} +1.00000 q^{8} +2.41856 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.32778 q^{3} +1.00000 q^{4} +2.23848 q^{5} -2.32778 q^{6} +3.76217 q^{7} +1.00000 q^{8} +2.41856 q^{9} +2.23848 q^{10} +6.14419 q^{11} -2.32778 q^{12} -5.81764 q^{13} +3.76217 q^{14} -5.21069 q^{15} +1.00000 q^{16} -3.87026 q^{17} +2.41856 q^{18} -4.78653 q^{19} +2.23848 q^{20} -8.75750 q^{21} +6.14419 q^{22} +2.82768 q^{23} -2.32778 q^{24} +0.0107930 q^{25} -5.81764 q^{26} +1.35347 q^{27} +3.76217 q^{28} -7.67062 q^{29} -5.21069 q^{30} +4.46847 q^{31} +1.00000 q^{32} -14.3023 q^{33} -3.87026 q^{34} +8.42154 q^{35} +2.41856 q^{36} -9.15399 q^{37} -4.78653 q^{38} +13.5422 q^{39} +2.23848 q^{40} +7.89125 q^{41} -8.75750 q^{42} +6.40589 q^{43} +6.14419 q^{44} +5.41389 q^{45} +2.82768 q^{46} +12.4966 q^{47} -2.32778 q^{48} +7.15391 q^{49} +0.0107930 q^{50} +9.00911 q^{51} -5.81764 q^{52} +4.99068 q^{53} +1.35347 q^{54} +13.7536 q^{55} +3.76217 q^{56} +11.1420 q^{57} -7.67062 q^{58} +12.3424 q^{59} -5.21069 q^{60} +2.17480 q^{61} +4.46847 q^{62} +9.09902 q^{63} +1.00000 q^{64} -13.0227 q^{65} -14.3023 q^{66} -4.39550 q^{67} -3.87026 q^{68} -6.58222 q^{69} +8.42154 q^{70} -14.3691 q^{71} +2.41856 q^{72} +7.97567 q^{73} -9.15399 q^{74} -0.0251236 q^{75} -4.78653 q^{76} +23.1155 q^{77} +13.5422 q^{78} +14.2764 q^{79} +2.23848 q^{80} -10.4063 q^{81} +7.89125 q^{82} -10.6606 q^{83} -8.75750 q^{84} -8.66350 q^{85} +6.40589 q^{86} +17.8555 q^{87} +6.14419 q^{88} +3.72489 q^{89} +5.41389 q^{90} -21.8869 q^{91} +2.82768 q^{92} -10.4016 q^{93} +12.4966 q^{94} -10.7146 q^{95} -2.32778 q^{96} +17.7726 q^{97} +7.15391 q^{98} +14.8601 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

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