LMFDB - Embedded newform 8029.2.a.h.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38302 q^{2} +3.20550 q^{3} +3.67879 q^{4} -2.71243 q^{5} -7.63877 q^{6} -1.00000 q^{7} -4.00058 q^{8} +7.27524 q^{9} +O(q^{10})$	\(q-2.38302 q^{2} +3.20550 q^{3} +3.67879 q^{4} -2.71243 q^{5} -7.63877 q^{6} -1.00000 q^{7} -4.00058 q^{8} +7.27524 q^{9} +6.46378 q^{10} +1.70346 q^{11} +11.7924 q^{12} -4.94138 q^{13} +2.38302 q^{14} -8.69471 q^{15} +2.17589 q^{16} -5.84765 q^{17} -17.3370 q^{18} +0.253583 q^{19} -9.97846 q^{20} -3.20550 q^{21} -4.05937 q^{22} -5.66146 q^{23} -12.8239 q^{24} +2.35729 q^{25} +11.7754 q^{26} +13.7043 q^{27} -3.67879 q^{28} +9.01245 q^{29} +20.7197 q^{30} -1.00000 q^{31} +2.81596 q^{32} +5.46044 q^{33} +13.9351 q^{34} +2.71243 q^{35} +26.7640 q^{36} +1.00000 q^{37} -0.604294 q^{38} -15.8396 q^{39} +10.8513 q^{40} +9.12094 q^{41} +7.63877 q^{42} +1.64815 q^{43} +6.26666 q^{44} -19.7336 q^{45} +13.4914 q^{46} -6.84863 q^{47} +6.97483 q^{48} +1.00000 q^{49} -5.61748 q^{50} -18.7446 q^{51} -18.1783 q^{52} +4.15565 q^{53} -32.6576 q^{54} -4.62052 q^{55} +4.00058 q^{56} +0.812862 q^{57} -21.4769 q^{58} +3.14438 q^{59} -31.9860 q^{60} -14.7323 q^{61} +2.38302 q^{62} -7.27524 q^{63} -11.0623 q^{64} +13.4032 q^{65} -13.0123 q^{66} +10.5328 q^{67} -21.5122 q^{68} -18.1478 q^{69} -6.46378 q^{70} -0.0847724 q^{71} -29.1052 q^{72} -5.24257 q^{73} -2.38302 q^{74} +7.55631 q^{75} +0.932879 q^{76} -1.70346 q^{77} +37.7461 q^{78} +0.574501 q^{79} -5.90196 q^{80} +22.1034 q^{81} -21.7354 q^{82} -3.50055 q^{83} -11.7924 q^{84} +15.8613 q^{85} -3.92758 q^{86} +28.8894 q^{87} -6.81482 q^{88} -0.267085 q^{89} +47.0256 q^{90} +4.94138 q^{91} -20.8273 q^{92} -3.20550 q^{93} +16.3204 q^{94} -0.687828 q^{95} +9.02657 q^{96} +17.3924 q^{97} -2.38302 q^{98} +12.3931 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) $ 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * 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 $

$2$	−2.38302	−1.68505	−0.842525	−	0.538657i	$-0.818932\pi$
$2$	−2.38302	−1.68505	−0.842525	+	0.538657i	$0.818932\pi$
$3$	3.20550	1.85070	0.925348	−	0.379118i	$-0.123772\pi$
$3$	3.20550	1.85070	0.925348	+	0.379118i	$0.123772\pi$
$4$	3.67879	1.83939
$5$	−2.71243	−1.21304	−0.606519	−	0.795069i	$-0.707434\pi$
$5$	−2.71243	−1.21304	−0.606519	+	0.795069i	$0.707434\pi$
$6$	−7.63877	−3.11852
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−4.00058	−1.41442
$9$	7.27524	2.42508
$10$	6.46378	2.04403
$11$	1.70346	0.513612	0.256806	−	0.966463i	$-0.417330\pi$
$11$	1.70346	0.513612	0.256806	+	0.966463i	$0.417330\pi$
$12$	11.7924	3.40416
$13$	−4.94138	−1.37049	−0.685246	−	0.728312i	$-0.740305\pi$
$13$	−4.94138	−1.37049	−0.685246	+	0.728312i	$0.740305\pi$
$14$	2.38302	0.636889
$15$	−8.69471	−2.24496
$16$	2.17589	0.543973
$17$	−5.84765	−1.41826	−0.709131	−	0.705077i	$-0.750913\pi$
$17$	−5.84765	−1.41826	−0.709131	+	0.705077i	$0.750913\pi$
$18$	−17.3370	−4.08638
$19$	0.253583	0.0581760	0.0290880	−	0.999577i	$-0.490740\pi$
$19$	0.253583	0.0581760	0.0290880	+	0.999577i	$0.490740\pi$
$20$	−9.97846	−2.23125
$21$	−3.20550	−0.699498
$22$	−4.05937	−0.865462
$23$	−5.66146	−1.18050	−0.590248	−	0.807222i	$-0.700970\pi$
$23$	−5.66146	−1.18050	−0.590248	+	0.807222i	$0.700970\pi$
$24$	−12.8239	−2.61766
$25$	2.35729	0.471459
$26$	11.7754	2.30935
$27$	13.7043	2.63739
$28$	−3.67879	−0.695225
$29$	9.01245	1.67357	0.836785	−	0.547531i	$-0.184432\pi$
$29$	9.01245	1.67357	0.836785	+	0.547531i	$0.184432\pi$
$30$	20.7197	3.78288
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	2.81596	0.497797
$33$	5.46044	0.950540
$34$	13.9351	2.38984
$35$	2.71243	0.458485
$36$	26.7640	4.46067
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−0.604294	−0.0980295
$39$	−15.8396	−2.53636
$40$	10.8513	1.71574
$41$	9.12094	1.42445	0.712226	−	0.701950i	$-0.247687\pi$
$41$	9.12094	1.42445	0.712226	+	0.701950i	$0.247687\pi$
$42$	7.63877	1.17869
$43$	1.64815	0.251341	0.125670	−	0.992072i	$-0.459892\pi$
$43$	1.64815	0.251341	0.125670	+	0.992072i	$0.459892\pi$
$44$	6.26666	0.944734
$45$	−19.7336	−2.94171
$46$	13.4914	1.98919
$47$	−6.84863	−0.998975	−0.499488	−	0.866321i	$-0.666478\pi$
$47$	−6.84863	−0.998975	−0.499488	+	0.866321i	$0.666478\pi$
$48$	6.97483	1.00673
$49$	1.00000	0.142857
$50$	−5.61748	−0.794432
$51$	−18.7446	−2.62477
$52$	−18.1783	−2.52087
$53$	4.15565	0.570822	0.285411	−	0.958405i	$-0.407870\pi$
$53$	4.15565	0.570822	0.285411	+	0.958405i	$0.407870\pi$
$54$	−32.6576	−4.44413
$55$	−4.62052	−0.623030
$56$	4.00058	0.534600
$57$	0.812862	0.107666
$58$	−21.4769	−2.82005
$59$	3.14438	0.409363	0.204682	−	0.978829i	$-0.434384\pi$
$59$	3.14438	0.409363	0.204682	+	0.978829i	$0.434384\pi$
$60$	−31.9860	−4.12937
$61$	−14.7323	−1.88628	−0.943139	−	0.332400i	$-0.892142\pi$
$61$	−14.7323	−1.88628	−0.943139	+	0.332400i	$0.892142\pi$
$62$	2.38302	0.302644
$63$	−7.27524	−0.916594
$64$	−11.0623	−1.38279
$65$	13.4032	1.66246
$66$	−13.0123	−1.60171
$67$	10.5328	1.28679	0.643393	−	0.765536i	$-0.277526\pi$
$67$	10.5328	1.28679	0.643393	+	0.765536i	$0.277526\pi$
$68$	−21.5122	−2.60874
$69$	−18.1478	−2.18474
$70$	−6.46378	−0.772570
$71$	−0.0847724	−0.0100606	−0.00503032	−	0.999987i	$-0.501601\pi$
$71$	−0.0847724	−0.0100606	−0.00503032	+	0.999987i	$0.501601\pi$
$72$	−29.1052	−3.43008
$73$	−5.24257	−0.613597	−0.306798	−	0.951775i	$-0.599258\pi$
$73$	−5.24257	−0.613597	−0.306798	+	0.951775i	$0.599258\pi$
$74$	−2.38302	−0.277020
$75$	7.55631	0.872528
$76$	0.932879	0.107009
$77$	−1.70346	−0.194127
$78$	37.7461	4.27390
$79$	0.574501	0.0646365	0.0323182	−	0.999478i	$-0.489711\pi$
$79$	0.574501	0.0646365	0.0323182	+	0.999478i	$0.489711\pi$
$80$	−5.90196	−0.659860
$81$	22.1034	2.45593
$82$	−21.7354	−2.40027
$83$	−3.50055	−0.384235	−0.192118	−	0.981372i	$-0.561535\pi$
$83$	−3.50055	−0.384235	−0.192118	+	0.981372i	$0.561535\pi$
$84$	−11.7924	−1.28665
$85$	15.8613	1.72040
$86$	−3.92758	−0.423522
$87$	28.8894	3.09727
$88$	−6.81482	−0.726462
$89$	−0.267085	−0.0283109	−0.0141555	−	0.999900i	$-0.504506\pi$
$89$	−0.267085	−0.0283109	−0.0141555	+	0.999900i	$0.504506\pi$
$90$	47.0256	4.95693
$91$	4.94138	0.517997
$92$	−20.8273	−2.17140
$93$	−3.20550	−0.332395
$94$	16.3204	1.68332
$95$	−0.687828	−0.0705696
$96$	9.02657	0.921271
$97$	17.3924	1.76593	0.882963	−	0.469442i	$-0.155545\pi$
$97$	17.3924	1.76593	0.882963	+	0.469442i	$0.155545\pi$
$98$	−2.38302	−0.240721
$99$	12.3931	1.24555
$100$	8.67198	0.867198
$101$	−8.60516	−0.856246	−0.428123	−	0.903721i	$-0.640825\pi$
$101$	−8.60516	−0.856246	−0.428123	+	0.903721i	$0.640825\pi$
$102$	44.6688	4.42287
$103$	−16.2964	−1.60573	−0.802867	−	0.596158i	$-0.796693\pi$
$103$	−16.2964	−1.60573	−0.802867	+	0.596158i	$0.796693\pi$
$104$	19.7684	1.93845
$105$	8.69471	0.848517
$106$	−9.90300	−0.961864
$107$	−0.549816	−0.0531527	−0.0265764	−	0.999647i	$-0.508461\pi$
$107$	−0.549816	−0.0531527	−0.0265764	+	0.999647i	$0.508461\pi$
$108$	50.4151	4.85120
$109$	8.21386	0.786745	0.393373	−	0.919379i	$-0.371308\pi$
$109$	8.21386	0.786745	0.393373	+	0.919379i	$0.371308\pi$
$110$	11.0108	1.04984
$111$	3.20550	0.304253
$112$	−2.17589	−0.205603
$113$	17.9210	1.68587	0.842934	−	0.538016i	$-0.180826\pi$
$113$	17.9210	1.68587	0.842934	+	0.538016i	$0.180826\pi$
$114$	−1.93707	−0.181423
$115$	15.3563	1.43199
$116$	33.1549	3.07835
$117$	−35.9497	−3.32355
$118$	−7.49311	−0.689797
$119$	5.84765	0.536053
$120$	34.7839	3.17532
$121$	−8.09823	−0.736203
$122$	35.1074	3.17847
$123$	29.2372	2.63623
$124$	−3.67879	−0.330365
$125$	7.16816	0.641140
$126$	17.3370	1.54451
$127$	13.7379	1.21904	0.609520	−	0.792771i	$-0.291362\pi$
$127$	13.7379	1.21904	0.609520	+	0.792771i	$0.291362\pi$
$128$	20.7297	1.83227
$129$	5.28316	0.465156
$130$	−31.9400	−2.80132
$131$	−2.57971	−0.225390	−0.112695	−	0.993630i	$-0.535948\pi$
$131$	−2.57971	−0.225390	−0.112695	+	0.993630i	$0.535948\pi$
$132$	20.0878	1.74842
$133$	−0.253583	−0.0219885
$134$	−25.0999	−2.16830
$135$	−37.1719	−3.19925
$136$	23.3940	2.00602
$137$	5.55455	0.474557	0.237279	−	0.971442i	$-0.423745\pi$
$137$	5.55455	0.474557	0.237279	+	0.971442i	$0.423745\pi$
$138$	43.2466	3.68140
$139$	0.424288	0.0359876	0.0179938	−	0.999838i	$-0.494272\pi$
$139$	0.424288	0.0359876	0.0179938	+	0.999838i	$0.494272\pi$
$140$	9.97846	0.843334
$141$	−21.9533	−1.84880
$142$	0.202014	0.0169527
$143$	−8.41743	−0.703901
$144$	15.8301	1.31918
$145$	−24.4457	−2.03010
$146$	12.4932	1.03394
$147$	3.20550	0.264385
$148$	3.67879	0.302394
$149$	20.0780	1.64486	0.822429	−	0.568868i	$-0.192618\pi$
$149$	20.0780	1.64486	0.822429	+	0.568868i	$0.192618\pi$
$150$	−18.0068	−1.47025
$151$	6.47492	0.526921	0.263461	−	0.964670i	$-0.415136\pi$
$151$	6.47492	0.526921	0.263461	+	0.964670i	$0.415136\pi$
$152$	−1.01448	−0.0822852
$153$	−42.5430	−3.43940
$154$	4.05937	0.327114
$155$	2.71243	0.217868
$156$	−58.2705	−4.66537
$157$	2.54892	0.203426	0.101713	−	0.994814i	$-0.467568\pi$
$157$	2.54892	0.203426	0.101713	+	0.994814i	$0.467568\pi$
$158$	−1.36905	−0.108916
$159$	13.3209	1.05642
$160$	−7.63811	−0.603846
$161$	5.66146	0.446186
$162$	−52.6728	−4.13836
$163$	9.91620	0.776696	0.388348	−	0.921513i	$-0.373046\pi$
$163$	9.91620	0.776696	0.388348	+	0.921513i	$0.373046\pi$
$164$	33.5540	2.62013
$165$	−14.8111	−1.15304
$166$	8.34188	0.647455
$167$	15.0873	1.16749	0.583744	−	0.811938i	$-0.301587\pi$
$167$	15.0873	1.16749	0.583744	+	0.811938i	$0.301587\pi$
$168$	12.8239	0.989383
$169$	11.4172	0.878247
$170$	−37.7979	−2.89897
$171$	1.84488	0.141081
$172$	6.06320	0.462315
$173$	−12.1092	−0.920643	−0.460321	−	0.887752i	$-0.652266\pi$
$173$	−12.1092	−0.920643	−0.460321	+	0.887752i	$0.652266\pi$
$174$	−68.8441	−5.21906
$175$	−2.35729	−0.178195
$176$	3.70654	0.279391
$177$	10.0793	0.757607
$178$	0.636468	0.0477053
$179$	7.82450	0.584831	0.292415	−	0.956291i	$-0.405541\pi$
$179$	7.82450	0.584831	0.292415	+	0.956291i	$0.405541\pi$
$180$	−72.5957	−5.41096
$181$	10.2120	0.759049	0.379525	−	0.925182i	$-0.376088\pi$
$181$	10.2120	0.759049	0.379525	+	0.925182i	$0.376088\pi$
$182$	−11.7754	−0.872851
$183$	−47.2244	−3.49093
$184$	22.6491	1.66972
$185$	−2.71243	−0.199422
$186$	7.63877	0.560102
$187$	−9.96122	−0.728436
$188$	−25.1946	−1.83751
$189$	−13.7043	−0.996840
$190$	1.63911	0.118913
$191$	25.0505	1.81259	0.906295	−	0.422647i	$-0.138899\pi$
$191$	25.0505	1.81259	0.906295	+	0.422647i	$0.138899\pi$
$192$	−35.4602	−2.55912
$193$	−15.6635	−1.12748	−0.563740	−	0.825952i	$-0.690638\pi$
$193$	−15.6635	−1.12748	−0.563740	+	0.825952i	$0.690638\pi$
$194$	−41.4464	−2.97567
$195$	42.9638	3.07670
$196$	3.67879	0.262770
$197$	−24.1803	−1.72277	−0.861386	−	0.507950i	$-0.830403\pi$
$197$	−24.1803	−1.72277	−0.861386	+	0.507950i	$0.830403\pi$
$198$	−29.5329	−2.09881
$199$	21.7767	1.54371	0.771855	−	0.635798i	$-0.219329\pi$
$199$	21.7767	1.54371	0.771855	+	0.635798i	$0.219329\pi$
$200$	−9.43055	−0.666840
$201$	33.7629	2.38145
$202$	20.5063	1.44282
$203$	−9.01245	−0.632550
$204$	−68.9575	−4.82799
$205$	−24.7399	−1.72791
$206$	38.8347	2.70574
$207$	−41.1885	−2.86280
$208$	−10.7519	−0.745511
$209$	0.431968	0.0298799
$210$	−20.7197	−1.42979
$211$	7.44872	0.512791	0.256395	−	0.966572i	$-0.417465\pi$
$211$	7.44872	0.512791	0.256395	+	0.966572i	$0.417465\pi$
$212$	15.2877	1.04997
$213$	−0.271738	−0.0186192
$214$	1.31022	0.0895650
$215$	−4.47050	−0.304886
$216$	−54.8251	−3.73037
$217$	1.00000	0.0678844
$218$	−19.5738	−1.32571
$219$	−16.8051	−1.13558
$220$	−16.9979	−1.14600
$221$	28.8954	1.94372
$222$	−7.63877	−0.512681
$223$	4.19328	0.280803	0.140401	−	0.990095i	$-0.455161\pi$
$223$	4.19328	0.280803	0.140401	+	0.990095i	$0.455161\pi$
$224$	−2.81596	−0.188149
$225$	17.1499	1.14333
$226$	−42.7062	−2.84077
$227$	22.3829	1.48560	0.742802	−	0.669511i	$-0.233496\pi$
$227$	22.3829	1.48560	0.742802	+	0.669511i	$0.233496\pi$
$228$	2.99034	0.198040
$229$	−27.0853	−1.78985	−0.894924	−	0.446219i	$-0.852770\pi$
$229$	−27.0853	−1.78985	−0.894924	+	0.446219i	$0.852770\pi$
$230$	−36.5945	−2.41297
$231$	−5.46044	−0.359270
$232$	−36.0550	−2.36713
$233$	22.8982	1.50011	0.750056	−	0.661375i	$-0.230027\pi$
$233$	22.8982	1.50011	0.750056	+	0.661375i	$0.230027\pi$
$234$	85.6688	5.60035
$235$	18.5765	1.21179
$236$	11.5675	0.752979
$237$	1.84156	0.119622
$238$	−13.9351	−0.903276
$239$	10.5318	0.681247	0.340623	−	0.940200i	$-0.389362\pi$
$239$	10.5318	0.681247	0.340623	+	0.940200i	$0.389362\pi$
$240$	−18.9188	−1.22120
$241$	−13.6304	−0.878013	−0.439007	−	0.898484i	$-0.644669\pi$
$241$	−13.6304	−0.878013	−0.439007	+	0.898484i	$0.644669\pi$
$242$	19.2982	1.24054
$243$	29.7395	1.90779
$244$	−54.1970	−3.46961
$245$	−2.71243	−0.173291
$246$	−69.6728	−4.44218
$247$	−1.25305	−0.0797297
$248$	4.00058	0.254037
$249$	−11.2210	−0.711103
$250$	−17.0819	−1.08035
$251$	24.7158	1.56005	0.780023	−	0.625751i	$-0.215207\pi$
$251$	24.7158	1.56005	0.780023	+	0.625751i	$0.215207\pi$
$252$	−26.7640	−1.68598
$253$	−9.64406	−0.606317
$254$	−32.7376	−2.05414
$255$	50.8436	3.18395
$256$	−27.2748	−1.70467
$257$	−12.4448	−0.776288	−0.388144	−	0.921599i	$-0.626884\pi$
$257$	−12.4448	−0.776288	−0.388144	+	0.921599i	$0.626884\pi$
$258$	−12.5899	−0.783811
$259$	−1.00000	−0.0621370
$260$	49.3073	3.05791
$261$	65.5677	4.05854
$262$	6.14751	0.379794
$263$	−10.4106	−0.641946	−0.320973	−	0.947088i	$-0.604010\pi$
$263$	−10.4106	−0.641946	−0.320973	+	0.947088i	$0.604010\pi$
$264$	−21.8449	−1.34446
$265$	−11.2719	−0.692429
$266$	0.604294	0.0370517
$267$	−0.856140	−0.0523949
$268$	38.7479	2.36691
$269$	3.40694	0.207725	0.103862	−	0.994592i	$-0.466880\pi$
$269$	3.40694	0.207725	0.103862	+	0.994592i	$0.466880\pi$
$270$	88.5815	5.39090
$271$	3.48330	0.211595	0.105798	−	0.994388i	$-0.466260\pi$
$271$	3.48330	0.211595	0.105798	+	0.994388i	$0.466260\pi$
$272$	−12.7239	−0.771497
$273$	15.8396	0.958656
$274$	−13.2366	−0.799652
$275$	4.01555	0.242147
$276$	−66.7619	−4.01860
$277$	−27.1853	−1.63341	−0.816704	−	0.577056i	$-0.804201\pi$
$277$	−27.1853	−1.63341	−0.816704	+	0.577056i	$0.804201\pi$
$278$	−1.01109	−0.0606410
$279$	−7.27524	−0.435557
$280$	−10.8513	−0.648490
$281$	25.4517	1.51832	0.759161	−	0.650902i	$-0.225609\pi$
$281$	25.4517	1.51832	0.759161	+	0.650902i	$0.225609\pi$
$282$	52.3151	3.11532
$283$	−16.6914	−0.992202	−0.496101	−	0.868265i	$-0.665235\pi$
$283$	−16.6914	−0.992202	−0.496101	+	0.868265i	$0.665235\pi$
$284$	−0.311860	−0.0185055
$285$	−2.20483	−0.130603
$286$	20.0589	1.18611
$287$	−9.12094	−0.538392
$288$	20.4868	1.20720
$289$	17.1950	1.01147
$290$	58.2545	3.42082
$291$	55.7512	3.26820
$292$	−19.2863	−1.12865
$293$	24.2923	1.41917	0.709585	−	0.704620i	$-0.248883\pi$
$293$	24.2923	1.41917	0.709585	+	0.704620i	$0.248883\pi$
$294$	−7.63877	−0.445502
$295$	−8.52891	−0.496573
$296$	−4.00058	−0.232529
$297$	23.3447	1.35459
$298$	−47.8464	−2.77167
$299$	27.9754	1.61786
$300$	27.7981	1.60492
$301$	−1.64815	−0.0949979
$302$	−15.4299	−0.887888
$303$	−27.5839	−1.58465
$304$	0.551770	0.0316462
$305$	39.9604	2.28812
$306$	101.381	5.79556
$307$	−3.54662	−0.202416	−0.101208	−	0.994865i	$-0.532271\pi$
$307$	−3.54662	−0.202416	−0.101208	+	0.994865i	$0.532271\pi$
$308$	−6.26666	−0.357076
$309$	−52.2382	−2.97173
$310$	−6.46378	−0.367118
$311$	16.6229	0.942599	0.471299	−	0.881973i	$-0.343785\pi$
$311$	16.6229	0.942599	0.471299	+	0.881973i	$0.343785\pi$
$312$	63.3676	3.58748
$313$	11.3666	0.642479	0.321239	−	0.946998i	$-0.395901\pi$
$313$	11.3666	0.642479	0.321239	+	0.946998i	$0.395901\pi$
$314$	−6.07413	−0.342783
$315$	19.7336	1.11186
$316$	2.11347	0.118892
$317$	32.1862	1.80775	0.903877	−	0.427792i	$-0.140708\pi$
$317$	32.1862	1.80775	0.903877	+	0.427792i	$0.140708\pi$
$318$	−31.7441	−1.78012
$319$	15.3523	0.859566
$320$	30.0057	1.67737
$321$	−1.76244	−0.0983696
$322$	−13.4914	−0.751845
$323$	−1.48287	−0.0825088
$324$	81.3135	4.51742
$325$	−11.6483	−0.646130
$326$	−23.6305	−1.30877
$327$	26.3295	1.45603
$328$	−36.4891	−2.01477
$329$	6.84863	0.377577
$330$	35.2951	1.94293
$331$	6.05038	0.332559	0.166280	−	0.986079i	$-0.446825\pi$
$331$	6.05038	0.332559	0.166280	+	0.986079i	$0.446825\pi$
$332$	−12.8778	−0.706759
$333$	7.27524	0.398681
$334$	−35.9533	−1.96727
$335$	−28.5695	−1.56092
$336$	−6.97483	−0.380508
$337$	7.12833	0.388305	0.194152	−	0.980971i	$-0.437804\pi$
$337$	7.12833	0.388305	0.194152	+	0.980971i	$0.437804\pi$
$338$	−27.2074	−1.47989
$339$	57.4459	3.12003
$340$	58.3505	3.16450
$341$	−1.70346	−0.0922474
$342$	−4.39638	−0.237729
$343$	−1.00000	−0.0539949
$344$	−6.59357	−0.355501
$345$	49.2248	2.65017
$346$	28.8564	1.55133
$347$	−36.5484	−1.96202	−0.981012	−	0.193949i	$-0.937870\pi$
$347$	−36.5484	−1.96202	−0.981012	+	0.193949i	$0.937870\pi$
$348$	106.278	5.69710
$349$	13.1523	0.704026	0.352013	−	0.935995i	$-0.385497\pi$
$349$	13.1523	0.704026	0.352013	+	0.935995i	$0.385497\pi$
$350$	5.61748	0.300267
$351$	−67.7180	−3.61452
$352$	4.79688	0.255674
$353$	29.8757	1.59012	0.795061	−	0.606529i	$-0.207439\pi$
$353$	29.8757	1.59012	0.795061	+	0.606529i	$0.207439\pi$
$354$	−24.0192	−1.27661
$355$	0.229940	0.0122039
$356$	−0.982547	−0.0520749
$357$	18.7446	0.992071
$358$	−18.6459	−0.985469
$359$	−28.2981	−1.49352	−0.746760	−	0.665094i	$-0.768391\pi$
$359$	−28.2981	−1.49352	−0.746760	+	0.665094i	$0.768391\pi$
$360$	78.9458	4.16081
$361$	−18.9357	−0.996616
$362$	−24.3353	−1.27904
$363$	−25.9589	−1.36249
$364$	18.1783	0.952800
$365$	14.2201	0.744316
$366$	112.537	5.88239
$367$	−18.8649	−0.984740	−0.492370	−	0.870386i	$-0.663869\pi$
$367$	−18.8649	−0.984740	−0.492370	+	0.870386i	$0.663869\pi$
$368$	−12.3187	−0.642158
$369$	66.3570	3.45441
$370$	6.46378	0.336036
$371$	−4.15565	−0.215751
$372$	−11.7924	−0.611405
$373$	5.95184	0.308174	0.154087	−	0.988057i	$-0.450756\pi$
$373$	5.95184	0.308174	0.154087	+	0.988057i	$0.450756\pi$
$374$	23.7378	1.22745
$375$	22.9776	1.18656
$376$	27.3985	1.41297
$377$	−44.5339	−2.29361
$378$	32.6576	1.67972
$379$	−24.8283	−1.27535	−0.637673	−	0.770307i	$-0.720103\pi$
$379$	−24.8283	−1.27535	−0.637673	+	0.770307i	$0.720103\pi$
$380$	−2.53037	−0.129805
$381$	44.0368	2.25607
$382$	−59.6958	−3.05430
$383$	−30.7537	−1.57144	−0.785720	−	0.618583i	$-0.787707\pi$
$383$	−30.7537	−1.57144	−0.785720	+	0.618583i	$0.787707\pi$
$384$	66.4491	3.39097
$385$	4.62052	0.235483
$386$	37.3263	1.89986
$387$	11.9907	0.609522
$388$	63.9828	3.24823
$389$	4.60203	0.233332	0.116666	−	0.993171i	$-0.462779\pi$
$389$	4.60203	0.233332	0.116666	+	0.993171i	$0.462779\pi$
$390$	−102.384	−5.18440
$391$	33.1062	1.67425
$392$	−4.00058	−0.202060
$393$	−8.26927	−0.417129
$394$	57.6221	2.90296
$395$	−1.55830	−0.0784064
$396$	45.5914	2.29105
$397$	−13.2768	−0.666342	−0.333171	−	0.942866i	$-0.608119\pi$
$397$	−13.2768	−0.666342	−0.333171	+	0.942866i	$0.608119\pi$
$398$	−51.8944	−2.60123
$399$	−0.812862	−0.0406940
$400$	5.12922	0.256461
$401$	−10.4264	−0.520668	−0.260334	−	0.965519i	$-0.583833\pi$
$401$	−10.4264	−0.520668	−0.260334	+	0.965519i	$0.583833\pi$
$402$	−80.4577	−4.01287
$403$	4.94138	0.246148
$404$	−31.6566	−1.57497
$405$	−59.9539	−2.97913
$406$	21.4769	1.06588
$407$	1.70346	0.0844373
$408$	74.9894	3.71253
$409$	−10.8422	−0.536112	−0.268056	−	0.963403i	$-0.586381\pi$
$409$	−10.8422	−0.536112	−0.268056	+	0.963403i	$0.586381\pi$
$410$	58.9558	2.91162
$411$	17.8051	0.878261
$412$	−59.9511	−2.95358
$413$	−3.14438	−0.154725
$414$	98.1530	4.82396
$415$	9.49500	0.466091
$416$	−13.9147	−0.682226
$417$	1.36006	0.0666022
$418$	−1.02939	−0.0503491
$419$	7.61747	0.372138	0.186069	−	0.982537i	$-0.440425\pi$
$419$	7.61747	0.372138	0.186069	+	0.982537i	$0.440425\pi$
$420$	31.9860	1.56076
$421$	21.8925	1.06698	0.533488	−	0.845808i	$-0.320881\pi$
$421$	21.8925	1.06698	0.533488	+	0.845808i	$0.320881\pi$
$422$	−17.7504	−0.864078
$423$	−49.8254	−2.42259
$424$	−16.6250	−0.807382
$425$	−13.7846	−0.668652
$426$	0.647557	0.0313743
$427$	14.7323	0.712946
$428$	−2.02266	−0.0977687
$429$	−26.9821	−1.30271
$430$	10.6533	0.513748
$431$	21.4064	1.03111	0.515555	−	0.856857i	$-0.327586\pi$
$431$	21.4064	1.03111	0.515555	+	0.856857i	$0.327586\pi$
$432$	29.8190	1.43467
$433$	−17.4677	−0.839443	−0.419722	−	0.907653i	$-0.637872\pi$
$433$	−17.4677	−0.839443	−0.419722	+	0.907653i	$0.637872\pi$
$434$	−2.38302	−0.114389
$435$	−78.3606	−3.75711
$436$	30.2170	1.44713
$437$	−1.43565	−0.0686765
$438$	40.0468	1.91351
$439$	0.641901	0.0306363	0.0153181	−	0.999883i	$-0.495124\pi$
$439$	0.641901	0.0306363	0.0153181	+	0.999883i	$0.495124\pi$
$440$	18.4847	0.881226
$441$	7.27524	0.346440
$442$	−68.8584	−3.27526
$443$	3.67818	0.174755	0.0873777	−	0.996175i	$-0.472151\pi$
$443$	3.67818	0.174755	0.0873777	+	0.996175i	$0.472151\pi$
$444$	11.7924	0.559640
$445$	0.724449	0.0343422
$446$	−9.99267	−0.473167
$447$	64.3602	3.04413
$448$	11.0623	0.522644
$449$	−6.10657	−0.288187	−0.144093	−	0.989564i	$-0.546027\pi$
$449$	−6.10657	−0.288187	−0.144093	+	0.989564i	$0.546027\pi$
$450$	−40.8685	−1.92656
$451$	15.5371	0.731615
$452$	65.9276	3.10098
$453$	20.7553	0.975171
$454$	−53.3389	−2.50332
$455$	−13.4032	−0.628350
$456$	−3.25192	−0.152285
$457$	13.2577	0.620170	0.310085	−	0.950709i	$-0.399642\pi$
$457$	13.2577	0.620170	0.310085	+	0.950709i	$0.399642\pi$
$458$	64.5448	3.01598
$459$	−80.1378	−3.74051
$460$	56.4927	2.63398
$461$	21.5242	1.00248	0.501242	−	0.865307i	$-0.332877\pi$
$461$	21.5242	1.00248	0.501242	+	0.865307i	$0.332877\pi$
$462$	13.0123	0.605388
$463$	21.8605	1.01594	0.507971	−	0.861374i	$-0.330396\pi$
$463$	21.8605	1.01594	0.507971	+	0.861374i	$0.330396\pi$
$464$	19.6101	0.910378
$465$	8.69471	0.403207
$466$	−54.5669	−2.52776
$467$	10.0996	0.467354	0.233677	−	0.972314i	$-0.424924\pi$
$467$	10.0996	0.467354	0.233677	+	0.972314i	$0.424924\pi$
$468$	−132.251	−6.11331
$469$	−10.5328	−0.486360
$470$	−44.2681	−2.04193
$471$	8.17057	0.376480
$472$	−12.5793	−0.579011
$473$	2.80756	0.129092
$474$	−4.38849	−0.201570
$475$	0.597771	0.0274276
$476$	21.5122	0.986012
$477$	30.2333	1.38429
$478$	−25.0975	−1.14793
$479$	−12.8366	−0.586521	−0.293260	−	0.956033i	$-0.594740\pi$
$479$	−12.8366	−0.586521	−0.293260	+	0.956033i	$0.594740\pi$
$480$	−24.4840	−1.11754
$481$	−4.94138	−0.225307
$482$	32.4816	1.47950
$483$	18.1478	0.825754
$484$	−29.7917	−1.35417
$485$	−47.1756	−2.14213
$486$	−70.8699	−3.21472
$487$	−9.62194	−0.436012	−0.218006	−	0.975947i	$-0.569955\pi$
$487$	−9.62194	−0.436012	−0.218006	+	0.975947i	$0.569955\pi$
$488$	58.9377	2.66799
$489$	31.7864	1.43743
$490$	6.46378	0.292004
$491$	−5.03618	−0.227279	−0.113640	−	0.993522i	$-0.536251\pi$
$491$	−5.03618	−0.227279	−0.113640	+	0.993522i	$0.536251\pi$
$492$	107.557	4.84906
$493$	−52.7016	−2.37356
$494$	2.98605	0.134349
$495$	−33.6154	−1.51090
$496$	−2.17589	−0.0977005
$497$	0.0847724	0.00380256
$498$	26.7399	1.19824
$499$	−14.8475	−0.664666	−0.332333	−	0.943162i	$-0.607836\pi$
$499$	−14.8475	−0.664666	−0.332333	+	0.943162i	$0.607836\pi$
$500$	26.3701	1.17931
$501$	48.3622	2.16067
$502$	−58.8982	−2.62876
$503$	−6.03336	−0.269014	−0.134507	−	0.990913i	$-0.542945\pi$
$503$	−6.03336	−0.269014	−0.134507	+	0.990913i	$0.542945\pi$
$504$	29.1052	1.29645
$505$	23.3409	1.03866
$506$	22.9820	1.02167
$507$	36.5979	1.62537
$508$	50.5387	2.24229
$509$	24.4567	1.08403	0.542013	−	0.840370i	$-0.317662\pi$
$509$	24.4567	1.08403	0.542013	+	0.840370i	$0.317662\pi$
$510$	−121.161	−5.36511
$511$	5.24257	0.231918
$512$	23.5369	1.04019
$513$	3.47518	0.153433
$514$	29.6563	1.30808
$515$	44.2030	1.94782
$516$	19.4356	0.855604
$517$	−11.6664	−0.513086
$518$	2.38302	0.104704
$519$	−38.8159	−1.70383
$520$	−53.6204	−2.35141
$521$	−29.6610	−1.29947	−0.649737	−	0.760159i	$-0.725121\pi$
$521$	−29.6610	−1.29947	−0.649737	+	0.760159i	$0.725121\pi$
$522$	−156.249	−6.83884
$523$	−9.62483	−0.420865	−0.210432	−	0.977608i	$-0.567487\pi$
$523$	−9.62483	−0.420865	−0.210432	+	0.977608i	$0.567487\pi$
$524$	−9.49021	−0.414582
$525$	−7.55631	−0.329784
$526$	24.8087	1.08171
$527$	5.84765	0.254727
$528$	11.8813	0.517068
$529$	9.05214	0.393571
$530$	26.8612	1.16678
$531$	22.8761	0.992738
$532$	−0.932879	−0.0404454
$533$	−45.0700	−1.95220
$534$	2.04020	0.0882880
$535$	1.49134	0.0644762
$536$	−42.1373	−1.82006
$537$	25.0815	1.08234
$538$	−8.11880	−0.350026
$539$	1.70346	0.0733731
$540$	−136.748	−5.88468
$541$	−3.89566	−0.167487	−0.0837437	−	0.996487i	$-0.526688\pi$
$541$	−3.89566	−0.167487	−0.0837437	+	0.996487i	$0.526688\pi$
$542$	−8.30076	−0.356548
$543$	32.7345	1.40477
$544$	−16.4668	−0.706006
$545$	−22.2796	−0.954351
$546$	−37.7461	−1.61538
$547$	19.1440	0.818539	0.409269	−	0.912414i	$-0.365784\pi$
$547$	19.1440	0.818539	0.409269	+	0.912414i	$0.365784\pi$
$548$	20.4340	0.872897
$549$	−107.181	−4.57437
$550$	−9.56914	−0.408030
$551$	2.28541	0.0973616
$552$	72.6018	3.09014
$553$	−0.574501	−0.0244303
$554$	64.7832	2.75238
$555$	−8.69471	−0.369070
$556$	1.56086	0.0661954
$557$	−1.11413	−0.0472073	−0.0236036	−	0.999721i	$-0.507514\pi$
$557$	−1.11413	−0.0472073	−0.0236036	+	0.999721i	$0.507514\pi$
$558$	17.3370	0.733935
$559$	−8.14414	−0.344461
$560$	5.90196	0.249404
$561$	−31.9307	−1.34811
$562$	−60.6520	−2.55845
$563$	−0.190545	−0.00803052	−0.00401526	−	0.999992i	$-0.501278\pi$
$563$	−0.190545	−0.00803052	−0.00401526	+	0.999992i	$0.501278\pi$
$564$	−80.7615	−3.40067
$565$	−48.6096	−2.04502
$566$	39.7760	1.67191
$567$	−22.1034	−0.928254
$568$	0.339139	0.0142300
$569$	0.654013	0.0274176	0.0137088	−	0.999906i	$-0.495636\pi$
$569$	0.654013	0.0274176	0.0137088	+	0.999906i	$0.495636\pi$
$570$	5.25416	0.220073
$571$	30.8698	1.29186	0.645931	−	0.763396i	$-0.276469\pi$
$571$	30.8698	1.29186	0.645931	+	0.763396i	$0.276469\pi$
$572$	−30.9659	−1.29475
$573$	80.2993	3.35455
$574$	21.7354	0.907217
$575$	−13.3457	−0.556556
$576$	−80.4807	−3.35336
$577$	−10.1358	−0.421958	−0.210979	−	0.977491i	$-0.567665\pi$
$577$	−10.1358	−0.421958	−0.210979	+	0.977491i	$0.567665\pi$
$578$	−40.9759	−1.70437
$579$	−50.2092	−2.08662
$580$	−89.9304	−3.73416
$581$	3.50055	0.145227
$582$	−132.856	−5.50707
$583$	7.07897	0.293181
$584$	20.9733	0.867883
$585$	97.5111	4.03159
$586$	−57.8890	−2.39137
$587$	24.0577	0.992969	0.496484	−	0.868046i	$-0.334624\pi$
$587$	24.0577	0.992969	0.496484	+	0.868046i	$0.334624\pi$
$588$	11.7924	0.486308
$589$	−0.253583	−0.0104487
$590$	20.3246	0.836750
$591$	−77.5099	−3.18833
$592$	2.17589	0.0894287
$593$	−45.8773	−1.88396	−0.941978	−	0.335675i	$-0.891036\pi$
$593$	−45.8773	−1.88396	−0.941978	+	0.335675i	$0.891036\pi$
$594$	−55.6308	−2.28256
$595$	−15.8613	−0.650252
$596$	73.8628	3.02554
$597$	69.8053	2.85694
$598$	−66.6660	−2.72617
$599$	17.9496	0.733401	0.366700	−	0.930339i	$-0.380487\pi$
$599$	17.9496	0.733401	0.366700	+	0.930339i	$0.380487\pi$
$600$	−30.2296	−1.23412
$601$	45.7540	1.86634	0.933172	−	0.359429i	$-0.117029\pi$
$601$	45.7540	1.86634	0.933172	+	0.359429i	$0.117029\pi$
$602$	3.92758	0.160076
$603$	76.6286	3.12056
$604$	23.8198	0.969215
$605$	21.9659	0.893041
$606$	65.7329	2.67022
$607$	17.0266	0.691089	0.345545	−	0.938402i	$-0.387694\pi$
$607$	17.0266	0.691089	0.345545	+	0.938402i	$0.387694\pi$
$608$	0.714081	0.0289598
$609$	−28.8894	−1.17066
$610$	−95.2264	−3.85560
$611$	33.8417	1.36909
$612$	−156.507	−6.32640
$613$	24.2356	0.978868	0.489434	−	0.872040i	$-0.337203\pi$
$613$	24.2356	0.978868	0.489434	+	0.872040i	$0.337203\pi$
$614$	8.45166	0.341081
$615$	−79.3039	−3.19784
$616$	6.81482	0.274577
$617$	29.6576	1.19397	0.596986	−	0.802252i	$-0.296365\pi$
$617$	29.6576	1.19397	0.596986	+	0.802252i	$0.296365\pi$
$618$	124.485	5.00751
$619$	41.3363	1.66145	0.830723	−	0.556687i	$-0.187928\pi$
$619$	41.3363	1.66145	0.830723	+	0.556687i	$0.187928\pi$
$620$	9.97846	0.400745
$621$	−77.5862	−3.11343
$622$	−39.6127	−1.58833
$623$	0.267085	0.0107005
$624$	−34.4653	−1.37971
$625$	−31.2296	−1.24919
$626$	−27.0869	−1.08261
$627$	1.38468	0.0552986
$628$	9.37694	0.374181
$629$	−5.84765	−0.233161
$630$	−47.0256	−1.87354
$631$	−21.6720	−0.862749	−0.431374	−	0.902173i	$-0.641971\pi$
$631$	−21.6720	−0.862749	−0.431374	+	0.902173i	$0.641971\pi$
$632$	−2.29834	−0.0914230
$633$	23.8769	0.949020
$634$	−76.7003	−3.04616
$635$	−37.2631	−1.47874
$636$	49.0049	1.94317
$637$	−4.94138	−0.195784
$638$	−36.5849	−1.44841
$639$	−0.616740	−0.0243978
$640$	−56.2280	−2.22261
$641$	0.903313	0.0356787	0.0178394	−	0.999841i	$-0.494321\pi$
$641$	0.903313	0.0356787	0.0178394	+	0.999841i	$0.494321\pi$
$642$	4.19992	0.165758
$643$	−34.8890	−1.37589	−0.687944	−	0.725764i	$-0.741487\pi$
$643$	−34.8890	−1.37589	−0.687944	+	0.725764i	$0.741487\pi$
$644$	20.8273	0.820711
$645$	−14.3302	−0.564251
$646$	3.53370	0.139031
$647$	29.8231	1.17247	0.586234	−	0.810142i	$-0.300610\pi$
$647$	29.8231	1.17247	0.586234	+	0.810142i	$0.300610\pi$
$648$	−88.4263	−3.47371
$649$	5.35631	0.210254
$650$	27.7581	1.08876
$651$	3.20550	0.125633
$652$	36.4796	1.42865
$653$	−21.7153	−0.849785	−0.424892	−	0.905244i	$-0.639688\pi$
$653$	−21.7153	−0.849785	−0.424892	+	0.905244i	$0.639688\pi$
$654$	−62.7438	−2.45348
$655$	6.99730	0.273407
$656$	19.8462	0.774864
$657$	−38.1410	−1.48802
$658$	−16.3204	−0.636236
$659$	−37.3908	−1.45654	−0.728269	−	0.685292i	$-0.759675\pi$
$659$	−37.3908	−1.45654	−0.728269	+	0.685292i	$0.759675\pi$
$660$	−54.4867	−2.12089
$661$	31.3113	1.21787	0.608935	−	0.793220i	$-0.291597\pi$
$661$	31.3113	1.21787	0.608935	+	0.793220i	$0.291597\pi$
$662$	−14.4182	−0.560379
$663$	92.6243	3.59723
$664$	14.0042	0.543469
$665$	0.687828	0.0266728
$666$	−17.3370	−0.671797
$667$	−51.0236	−1.97564
$668$	55.5028	2.14747
$669$	13.4416	0.519681
$670$	68.0818	2.63023
$671$	−25.0958	−0.968814
$672$	−9.02657	−0.348208
$673$	−3.33631	−0.128605	−0.0643027	−	0.997930i	$-0.520482\pi$
$673$	−3.33631	−0.128605	−0.0643027	+	0.997930i	$0.520482\pi$
$674$	−16.9869	−0.654313
$675$	32.3050	1.24342
$676$	42.0015	1.61544
$677$	16.1830	0.621964	0.310982	−	0.950416i	$-0.399342\pi$
$677$	16.1830	0.621964	0.310982	+	0.950416i	$0.399342\pi$
$678$	−136.895	−5.25741
$679$	−17.3924	−0.667458
$680$	−63.4546	−2.43337
$681$	71.7484	2.74940
$682$	4.05937	0.155441
$683$	−2.50862	−0.0959897	−0.0479948	−	0.998848i	$-0.515283\pi$
$683$	−2.50862	−0.0959897	−0.0479948	+	0.998848i	$0.515283\pi$
$684$	6.78691	0.259504
$685$	−15.0663	−0.575655
$686$	2.38302	0.0909841
$687$	−86.8220	−3.31247
$688$	3.58620	0.136723
$689$	−20.5346	−0.782307
$690$	−117.304	−4.46567
$691$	19.3480	0.736031	0.368016	−	0.929820i	$-0.380037\pi$
$691$	19.3480	0.736031	0.368016	+	0.929820i	$0.380037\pi$
$692$	−44.5470	−1.69342
$693$	−12.3931	−0.470773
$694$	87.0957	3.30611
$695$	−1.15085	−0.0436543
$696$	−115.574	−4.38084
$697$	−53.3360	−2.02025
$698$	−31.3422	−1.18632
$699$	73.4002	2.77625
$700$	−8.67198	−0.327770
$701$	8.87306	0.335131	0.167565	−	0.985861i	$-0.446409\pi$
$701$	8.87306	0.335131	0.167565	+	0.985861i	$0.446409\pi$
$702$	161.373	6.09065
$703$	0.253583	0.00956408
$704$	−18.8441	−0.710215
$705$	59.5468	2.24266
$706$	−71.1944	−2.67943
$707$	8.60516	0.323631
$708$	37.0796	1.39354
$709$	29.9266	1.12392	0.561958	−	0.827166i	$-0.310048\pi$
$709$	29.9266	1.12392	0.561958	+	0.827166i	$0.310048\pi$
$710$	−0.547951	−0.0205642
$711$	4.17963	0.156749
$712$	1.06849	0.0400435
$713$	5.66146	0.212023
$714$	−44.6688	−1.67169
$715$	22.8317	0.853858
$716$	28.7847	1.07573
$717$	33.7597	1.26078
$718$	67.4351	2.51665
$719$	45.6521	1.70254	0.851268	−	0.524731i	$-0.175834\pi$
$719$	45.6521	1.70254	0.851268	+	0.524731i	$0.175834\pi$
$720$	−42.9382	−1.60021
$721$	16.2964	0.606911
$722$	45.1241	1.67935
$723$	−43.6923	−1.62494
$724$	37.5676	1.39619
$725$	21.2450	0.789020
$726$	61.8606	2.29586
$727$	7.12851	0.264382	0.132191	−	0.991224i	$-0.457799\pi$
$727$	7.12851	0.264382	0.132191	+	0.991224i	$0.457799\pi$
$728$	−19.7684	−0.732665
$729$	29.0200	1.07481
$730$	−33.8869	−1.25421
$731$	−9.63781	−0.356467
$732$	−173.728	−6.42119
$733$	−3.52379	−0.130154	−0.0650770	−	0.997880i	$-0.520729\pi$
$733$	−3.52379	−0.130154	−0.0650770	+	0.997880i	$0.520729\pi$
$734$	44.9554	1.65934
$735$	−8.69471	−0.320709
$736$	−15.9425	−0.587647
$737$	17.9422	0.660909
$738$	−158.130	−5.82085
$739$	27.2217	1.00137	0.500683	−	0.865631i	$-0.333082\pi$
$739$	27.2217	1.00137	0.500683	+	0.865631i	$0.333082\pi$
$740$	−9.97846	−0.366816
$741$	−4.01666	−0.147556
$742$	9.90300	0.363550
$743$	16.1155	0.591220	0.295610	−	0.955309i	$-0.404477\pi$
$743$	16.1155	0.591220	0.295610	+	0.955309i	$0.404477\pi$
$744$	12.8239	0.470146
$745$	−54.4604	−1.99527
$746$	−14.1833	−0.519289
$747$	−25.4673	−0.931800
$748$	−36.6452	−1.33988
$749$	0.549816	0.0200898
$750$	−54.7560	−1.99941
$751$	−29.7674	−1.08623	−0.543114	−	0.839659i	$-0.682755\pi$
$751$	−29.7674	−1.08623	−0.543114	+	0.839659i	$0.682755\pi$
$752$	−14.9019	−0.543416
$753$	79.2265	2.88717
$754$	106.125	3.86485
$755$	−17.5628	−0.639175
$756$	−50.4151	−1.83358
$757$	−8.54173	−0.310455	−0.155227	−	0.987879i	$-0.549611\pi$
$757$	−8.54173	−0.310455	−0.155227	+	0.987879i	$0.549611\pi$
$758$	59.1664	2.14902
$759$	−30.9140	−1.12211
$760$	2.75171	0.0998150
$761$	−17.7206	−0.642372	−0.321186	−	0.947016i	$-0.604082\pi$
$761$	−17.7206	−0.642372	−0.321186	+	0.947016i	$0.604082\pi$
$762$	−104.941	−3.80160
$763$	−8.21386	−0.297362
$764$	92.1553	3.33406
$765$	115.395	4.17212
$766$	73.2866	2.64795
$767$	−15.5376	−0.561029
$768$	−87.4293	−3.15483
$769$	25.1928	0.908477	0.454239	−	0.890880i	$-0.349911\pi$
$769$	25.1928	0.908477	0.454239	+	0.890880i	$0.349911\pi$
$770$	−11.0108	−0.396801
$771$	−39.8920	−1.43667
$772$	−57.6225	−2.07388
$773$	19.1802	0.689866	0.344933	−	0.938627i	$-0.387902\pi$
$773$	19.1802	0.689866	0.344933	+	0.938627i	$0.387902\pi$
$774$	−28.5741	−1.02707
$775$	−2.35729	−0.0846765
$776$	−69.5795	−2.49776
$777$	−3.20550	−0.114997
$778$	−10.9667	−0.393176
$779$	2.31292	0.0828689
$780$	158.055	5.65927
$781$	−0.144406	−0.00516726
$782$	−78.8928	−2.82120
$783$	123.509	4.41386
$784$	2.17589	0.0777105
$785$	−6.91378	−0.246763
$786$	19.7058	0.702884
$787$	−38.1434	−1.35966	−0.679832	−	0.733368i	$-0.737947\pi$
$787$	−38.1434	−1.35966	−0.679832	+	0.733368i	$0.737947\pi$
$788$	−88.9540	−3.16886
$789$	−33.3712	−1.18805
$790$	3.71345	0.132119
$791$	−17.9210	−0.637199
$792$	−49.5794	−1.76173
$793$	72.7978	2.58513
$794$	31.6388	1.12282
$795$	−36.1322	−1.28148
$796$	80.1119	2.83949
$797$	−26.3670	−0.933968	−0.466984	−	0.884266i	$-0.654659\pi$
$797$	−26.3670	−0.933968	−0.466984	+	0.884266i	$0.654659\pi$
$798$	1.93707	0.0685714
$799$	40.0484	1.41681
$800$	6.63806	0.234691
$801$	−1.94310	−0.0686562
$802$	24.8462	0.877351
$803$	−8.93050	−0.315151
$804$	124.207	4.38043
$805$	−15.3563	−0.541240
$806$	−11.7754	−0.414771
$807$	10.9209	0.384435
$808$	34.4257	1.21109
$809$	−23.4999	−0.826212	−0.413106	−	0.910683i	$-0.635556\pi$
$809$	−23.4999	−0.826212	−0.413106	+	0.910683i	$0.635556\pi$
$810$	142.871	5.01999
$811$	25.0803	0.880690	0.440345	−	0.897829i	$-0.354856\pi$
$811$	25.0803	0.880690	0.440345	+	0.897829i	$0.354856\pi$
$812$	−33.1549	−1.16351
$813$	11.1657	0.391598
$814$	−4.05937	−0.142281
$815$	−26.8970	−0.942162
$816$	−40.7863	−1.42781
$817$	0.417944	0.0146220
$818$	25.8372	0.903376
$819$	35.9497	1.25618
$820$	−91.0129	−3.17831
$821$	−40.9245	−1.42828	−0.714138	−	0.700005i	$-0.753181\pi$
$821$	−40.9245	−1.42828	−0.714138	+	0.700005i	$0.753181\pi$
$822$	−42.4299	−1.47991
$823$	46.2913	1.61361	0.806807	−	0.590815i	$-0.201194\pi$
$823$	46.2913	1.61361	0.806807	+	0.590815i	$0.201194\pi$
$824$	65.1952	2.27118
$825$	12.8719	0.448141
$826$	7.49311	0.260719
$827$	12.7847	0.444567	0.222284	−	0.974982i	$-0.428649\pi$
$827$	12.7847	0.444567	0.222284	+	0.974982i	$0.428649\pi$
$828$	−151.524	−5.26581
$829$	−12.6959	−0.440947	−0.220474	−	0.975393i	$-0.570760\pi$
$829$	−12.6959	−0.440947	−0.220474	+	0.975393i	$0.570760\pi$
$830$	−22.6268	−0.785387
$831$	−87.1426	−3.02294
$832$	54.6629	1.89510
$833$	−5.84765	−0.202609
$834$	−3.24104	−0.112228
$835$	−40.9232	−1.41621
$836$	1.58912	0.0549608
$837$	−13.7043	−0.473689
$838$	−18.1526	−0.627071
$839$	12.9666	0.447658	0.223829	−	0.974628i	$-0.428144\pi$
$839$	12.9666	0.447658	0.223829	+	0.974628i	$0.428144\pi$
$840$	−34.7839	−1.20016
$841$	52.2243	1.80084
$842$	−52.1703	−1.79791
$843$	81.5855	2.80996
$844$	27.4022	0.943224
$845$	−30.9684	−1.06535
$846$	118.735	4.08219
$847$	8.09823	0.278259
$848$	9.04225	0.310512
$849$	−53.5043	−1.83626
$850$	32.8490	1.12671
$851$	−5.66146	−0.194072
$852$	−0.999666	−0.0342480
$853$	50.5626	1.73123	0.865616	−	0.500709i	$-0.166927\pi$
$853$	50.5626	1.73123	0.865616	+	0.500709i	$0.166927\pi$
$854$	−35.1074	−1.20135
$855$	−5.00411	−0.171137
$856$	2.19958	0.0751802
$857$	3.07178	0.104930	0.0524650	−	0.998623i	$-0.483292\pi$
$857$	3.07178	0.104930	0.0524650	+	0.998623i	$0.483292\pi$
$858$	64.2988	2.19513
$859$	43.3178	1.47798	0.738992	−	0.673714i	$-0.235302\pi$
$859$	43.3178	1.47798	0.738992	+	0.673714i	$0.235302\pi$
$860$	−16.4460	−0.560805
$861$	−29.2372	−0.996401
$862$	−51.0118	−1.73747
$863$	24.9165	0.848167	0.424083	−	0.905623i	$-0.360596\pi$
$863$	24.9165	0.848167	0.424083	+	0.905623i	$0.360596\pi$
$864$	38.5907	1.31288
$865$	32.8453	1.11677
$866$	41.6258	1.41450
$867$	55.1184	1.87192
$868$	3.67879	0.124866
$869$	0.978639	0.0331980
$870$	186.735	6.33091
$871$	−52.0466	−1.76353
$872$	−32.8602	−1.11279
$873$	126.534	4.28251
$874$	3.42119	0.115723
$875$	−7.16816	−0.242328
$876$	−61.8223	−2.08878
$877$	−0.376863	−0.0127257	−0.00636287	−	0.999980i	$-0.502025\pi$
$877$	−0.376863	−0.0127257	−0.00636287	+	0.999980i	$0.502025\pi$
$878$	−1.52966	−0.0516236
$879$	77.8689	2.62645
$880$	−10.0537	−0.338912
$881$	−11.1055	−0.374153	−0.187077	−	0.982345i	$-0.559901\pi$
$881$	−11.1055	−0.374153	−0.187077	+	0.982345i	$0.559901\pi$
$882$	−17.3370	−0.583768
$883$	4.37332	0.147174	0.0735869	−	0.997289i	$-0.476555\pi$
$883$	4.37332	0.147174	0.0735869	+	0.997289i	$0.476555\pi$
$884$	106.300	3.57526
$885$	−27.3394	−0.919005
$886$	−8.76517	−0.294472
$887$	−42.3259	−1.42116	−0.710582	−	0.703615i	$-0.751568\pi$
$887$	−42.3259	−1.42116	−0.710582	+	0.703615i	$0.751568\pi$
$888$	−12.8239	−0.430341
$889$	−13.7379	−0.460754
$890$	−1.72638	−0.0578683
$891$	37.6522	1.26139
$892$	15.4262	0.516507
$893$	−1.73670	−0.0581164
$894$	−153.372	−5.12952
$895$	−21.2234	−0.709421
$896$	−20.7297	−0.692531
$897$	89.6752	2.99417
$898$	14.5521	0.485609
$899$	−9.01245	−0.300582
$900$	63.0907	2.10302
$901$	−24.3008	−0.809576
$902$	−37.0253	−1.23281
$903$	−5.28316	−0.175812
$904$	−71.6945	−2.38452
$905$	−27.6993	−0.920755
$906$	−49.4604	−1.64321
$907$	−32.7972	−1.08901	−0.544506	−	0.838757i	$-0.683283\pi$
$907$	−32.7972	−1.08901	−0.544506	+	0.838757i	$0.683283\pi$
$908$	82.3419	2.73261
$909$	−62.6046	−2.07646
$910$	31.9400	1.05880
$911$	22.5118	0.745850	0.372925	−	0.927861i	$-0.378355\pi$
$911$	22.5118	0.745850	0.372925	+	0.927861i	$0.378355\pi$
$912$	1.76870	0.0585675
$913$	−5.96304	−0.197348
$914$	−31.5934	−1.04502
$915$	128.093	4.23462
$916$	−99.6411	−3.29223
$917$	2.57971	0.0851896
$918$	190.970	6.30295
$919$	−2.78009	−0.0917066	−0.0458533	−	0.998948i	$-0.514601\pi$
$919$	−2.78009	−0.0917066	−0.0458533	+	0.998948i	$0.514601\pi$
$920$	−61.4343	−2.02543
$921$	−11.3687	−0.374611
$922$	−51.2927	−1.68924
$923$	0.418893	0.0137880
$924$	−20.0878	−0.660839
$925$	2.35729	0.0775074
$926$	−52.0939	−1.71191
$927$	−118.560	−3.89403
$928$	25.3787	0.833098
$929$	42.6764	1.40017	0.700084	−	0.714061i	$-0.253146\pi$
$929$	42.6764	1.40017	0.700084	+	0.714061i	$0.253146\pi$
$930$	−20.7197	−0.679425
$931$	0.253583	0.00831086
$932$	84.2376	2.75929
$933$	53.2847	1.74446
$934$	−24.0676	−0.787515
$935$	27.0191	0.883620
$936$	143.820	4.70089
$937$	−32.8346	−1.07266	−0.536330	−	0.844009i	$-0.680190\pi$
$937$	−32.8346	−1.07266	−0.536330	+	0.844009i	$0.680190\pi$
$938$	25.0999	0.819540
$939$	36.4357	1.18903
$940$	68.3388	2.22897
$941$	11.7552	0.383209	0.191605	−	0.981472i	$-0.438631\pi$
$941$	11.7552	0.383209	0.191605	+	0.981472i	$0.438631\pi$
$942$	−19.4706	−0.634388
$943$	−51.6378	−1.68156
$944$	6.84183	0.222683
$945$	37.1719	1.20920
$946$	−6.69047	−0.217526
$947$	52.8895	1.71868	0.859339	−	0.511406i	$-0.170875\pi$
$947$	52.8895	1.71868	0.859339	+	0.511406i	$0.170875\pi$
$948$	6.77472	0.220033
$949$	25.9055	0.840929
$950$	−1.42450	−0.0462169
$951$	103.173	3.34561
$952$	−23.3940	−0.758203
$953$	−4.06460	−0.131665	−0.0658326	−	0.997831i	$-0.520970\pi$
$953$	−4.06460	−0.131665	−0.0658326	+	0.997831i	$0.520970\pi$
$954$	−72.0467	−2.33260
$955$	−67.9478	−2.19874
$956$	38.7443	1.25308
$957$	49.2119	1.59080
$958$	30.5900	0.988317
$959$	−5.55455	−0.179366
$960$	96.1833	3.10430
$961$	1.00000	0.0322581
$962$	11.7754	0.379654
$963$	−4.00004	−0.128900
$964$	−50.1434	−1.61501
$965$	42.4861	1.36768
$966$	−43.2466	−1.39144
$967$	0.473716	0.0152337	0.00761684	−	0.999971i	$-0.497575\pi$
$967$	0.473716	0.0152337	0.00761684	+	0.999971i	$0.497575\pi$
$968$	32.3976	1.04130
$969$	−4.75333	−0.152699
$970$	112.420	3.60960
$971$	22.0691	0.708230	0.354115	−	0.935202i	$-0.384782\pi$
$971$	22.0691	0.708230	0.354115	+	0.935202i	$0.384782\pi$
$972$	109.405	3.50918
$973$	−0.424288	−0.0136021
$974$	22.9293	0.734701
$975$	−37.3386	−1.19579
$976$	−32.0559	−1.02608
$977$	42.9313	1.37349	0.686747	−	0.726897i	$-0.259038\pi$
$977$	42.9313	1.37349	0.686747	+	0.726897i	$0.259038\pi$
$978$	−75.7476	−2.42214
$979$	−0.454967	−0.0145408
$980$	−9.97846	−0.318750
$981$	59.7578	1.90792
$982$	12.0013	0.382977
$983$	−55.7236	−1.77731	−0.888654	−	0.458578i	$-0.848359\pi$
$983$	−55.7236	−1.77731	−0.888654	+	0.458578i	$0.848359\pi$
$984$	−116.966	−3.72873
$985$	65.5874	2.08979
$986$	125.589	3.99957
$987$	21.9533	0.698781
$988$	−4.60970	−0.146654
$989$	−9.33095	−0.296707
$990$	80.1061	2.54594
$991$	−0.209233	−0.00664650	−0.00332325	−	0.999994i	$-0.501058\pi$
$991$	−0.209233	−0.00664650	−0.00332325	+	0.999994i	$0.501058\pi$
$992$	−2.81596	−0.0894069
$993$	19.3945	0.615466
$994$	−0.202014	−0.00640751
$995$	−59.0679	−1.87258
$996$	−41.2797	−1.30800
$997$	−44.1485	−1.39820	−0.699099	−	0.715025i	$-0.746415\pi$
$997$	−44.1485	−1.39820	−0.699099	+	0.715025i	$0.746415\pi$
$998$	35.3819	1.11999
$999$	13.7043	0.433584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.h.1.6	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.h.1.6	✓	71	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38302 q^{2} +3.20550 q^{3} +3.67879 q^{4} -2.71243 q^{5} -7.63877 q^{6} -1.00000 q^{7} -4.00058 q^{8} +7.27524 q^{9} +O(q^{10})\)	\(q-2.38302 q^{2} +3.20550 q^{3} +3.67879 q^{4} -2.71243 q^{5} -7.63877 q^{6} -1.00000 q^{7} -4.00058 q^{8} +7.27524 q^{9} +6.46378 q^{10} +1.70346 q^{11} +11.7924 q^{12} -4.94138 q^{13} +2.38302 q^{14} -8.69471 q^{15} +2.17589 q^{16} -5.84765 q^{17} -17.3370 q^{18} +0.253583 q^{19} -9.97846 q^{20} -3.20550 q^{21} -4.05937 q^{22} -5.66146 q^{23} -12.8239 q^{24} +2.35729 q^{25} +11.7754 q^{26} +13.7043 q^{27} -3.67879 q^{28} +9.01245 q^{29} +20.7197 q^{30} -1.00000 q^{31} +2.81596 q^{32} +5.46044 q^{33} +13.9351 q^{34} +2.71243 q^{35} +26.7640 q^{36} +1.00000 q^{37} -0.604294 q^{38} -15.8396 q^{39} +10.8513 q^{40} +9.12094 q^{41} +7.63877 q^{42} +1.64815 q^{43} +6.26666 q^{44} -19.7336 q^{45} +13.4914 q^{46} -6.84863 q^{47} +6.97483 q^{48} +1.00000 q^{49} -5.61748 q^{50} -18.7446 q^{51} -18.1783 q^{52} +4.15565 q^{53} -32.6576 q^{54} -4.62052 q^{55} +4.00058 q^{56} +0.812862 q^{57} -21.4769 q^{58} +3.14438 q^{59} -31.9860 q^{60} -14.7323 q^{61} +2.38302 q^{62} -7.27524 q^{63} -11.0623 q^{64} +13.4032 q^{65} -13.0123 q^{66} +10.5328 q^{67} -21.5122 q^{68} -18.1478 q^{69} -6.46378 q^{70} -0.0847724 q^{71} -29.1052 q^{72} -5.24257 q^{73} -2.38302 q^{74} +7.55631 q^{75} +0.932879 q^{76} -1.70346 q^{77} +37.7461 q^{78} +0.574501 q^{79} -5.90196 q^{80} +22.1034 q^{81} -21.7354 q^{82} -3.50055 q^{83} -11.7924 q^{84} +15.8613 q^{85} -3.92758 q^{86} +28.8894 q^{87} -6.81482 q^{88} -0.267085 q^{89} +47.0256 q^{90} +4.94138 q^{91} -20.8273 q^{92} -3.20550 q^{93} +16.3204 q^{94} -0.687828 q^{95} +9.02657 q^{96} +17.3924 q^{97} -2.38302 q^{98} +12.3931 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * q^99

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