LMFDB - Embedded newform 8023.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$158$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67852 q^{2} +0.688962 q^{3} +5.17445 q^{4} -3.33373 q^{5} -1.84540 q^{6} +3.78681 q^{7} -8.50280 q^{8} -2.52533 q^{9} +O(q^{10})$	\(q-2.67852 q^{2} +0.688962 q^{3} +5.17445 q^{4} -3.33373 q^{5} -1.84540 q^{6} +3.78681 q^{7} -8.50280 q^{8} -2.52533 q^{9} +8.92945 q^{10} +1.45005 q^{11} +3.56500 q^{12} +3.73900 q^{13} -10.1430 q^{14} -2.29681 q^{15} +12.4260 q^{16} -0.457265 q^{17} +6.76414 q^{18} -4.11903 q^{19} -17.2502 q^{20} +2.60897 q^{21} -3.88399 q^{22} -6.37891 q^{23} -5.85811 q^{24} +6.11376 q^{25} -10.0150 q^{26} -3.80674 q^{27} +19.5947 q^{28} -7.35059 q^{29} +6.15205 q^{30} +5.96142 q^{31} -16.2776 q^{32} +0.999033 q^{33} +1.22479 q^{34} -12.6242 q^{35} -13.0672 q^{36} +11.4442 q^{37} +11.0329 q^{38} +2.57603 q^{39} +28.3461 q^{40} +7.78118 q^{41} -6.98817 q^{42} -9.44692 q^{43} +7.50323 q^{44} +8.41877 q^{45} +17.0860 q^{46} +11.7459 q^{47} +8.56104 q^{48} +7.33996 q^{49} -16.3758 q^{50} -0.315038 q^{51} +19.3472 q^{52} -2.37933 q^{53} +10.1964 q^{54} -4.83409 q^{55} -32.1985 q^{56} -2.83785 q^{57} +19.6887 q^{58} +8.26952 q^{59} -11.8847 q^{60} -6.75010 q^{61} -15.9678 q^{62} -9.56296 q^{63} +18.7479 q^{64} -12.4648 q^{65} -2.67592 q^{66} -4.48494 q^{67} -2.36609 q^{68} -4.39483 q^{69} +33.8142 q^{70} -1.00000 q^{71} +21.4724 q^{72} -7.70485 q^{73} -30.6534 q^{74} +4.21215 q^{75} -21.3137 q^{76} +5.49109 q^{77} -6.89993 q^{78} -11.2483 q^{79} -41.4249 q^{80} +4.95329 q^{81} -20.8420 q^{82} -4.14568 q^{83} +13.5000 q^{84} +1.52440 q^{85} +25.3037 q^{86} -5.06428 q^{87} -12.3295 q^{88} +10.3144 q^{89} -22.5498 q^{90} +14.1589 q^{91} -33.0073 q^{92} +4.10719 q^{93} -31.4615 q^{94} +13.7317 q^{95} -11.2147 q^{96} -9.49652 q^{97} -19.6602 q^{98} -3.66187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) $ 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * 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 $

$2$	−2.67852	−1.89400	−0.946998	−	0.321239i	$-0.895901\pi$
$2$	−2.67852	−1.89400	−0.946998	+	0.321239i	$0.895901\pi$
$3$	0.688962	0.397772	0.198886	−	0.980023i	$-0.436268\pi$
$3$	0.688962	0.397772	0.198886	+	0.980023i	$0.436268\pi$
$4$	5.17445	2.58722
$5$	−3.33373	−1.49089	−0.745445	−	0.666567i	$-0.767763\pi$
$5$	−3.33373	−1.49089	−0.745445	+	0.666567i	$0.767763\pi$
$6$	−1.84540	−0.753380
$7$	3.78681	1.43128	0.715641	−	0.698469i	$-0.246135\pi$
$7$	3.78681	1.43128	0.715641	+	0.698469i	$0.246135\pi$
$8$	−8.50280	−3.00619
$9$	−2.52533	−0.841777
$10$	8.92945	2.82374
$11$	1.45005	0.437208	0.218604	−	0.975814i	$-0.429850\pi$
$11$	1.45005	0.437208	0.218604	+	0.975814i	$0.429850\pi$
$12$	3.56500	1.02913
$13$	3.73900	1.03701	0.518506	−	0.855074i	$-0.326488\pi$
$13$	3.73900	1.03701	0.518506	+	0.855074i	$0.326488\pi$
$14$	−10.1430	−2.71084
$15$	−2.29681	−0.593035
$16$	12.4260	3.10650
$17$	−0.457265	−0.110903	−0.0554515	−	0.998461i	$-0.517660\pi$
$17$	−0.457265	−0.110903	−0.0554515	+	0.998461i	$0.517660\pi$
$18$	6.76414	1.59432
$19$	−4.11903	−0.944969	−0.472485	−	0.881339i	$-0.656643\pi$
$19$	−4.11903	−0.944969	−0.472485	+	0.881339i	$0.656643\pi$
$20$	−17.2502	−3.85726
$21$	2.60897	0.569324
$22$	−3.88399	−0.828070
$23$	−6.37891	−1.33010	−0.665048	−	0.746801i	$-0.731589\pi$
$23$	−6.37891	−1.33010	−0.665048	+	0.746801i	$0.731589\pi$
$24$	−5.85811	−1.19578
$25$	6.11376	1.22275
$26$	−10.0150	−1.96410
$27$	−3.80674	−0.732608
$28$	19.5947	3.70304
$29$	−7.35059	−1.36497	−0.682485	−	0.730900i	$-0.739101\pi$
$29$	−7.35059	−1.36497	−0.682485	+	0.730900i	$0.739101\pi$
$30$	6.15205	1.12321
$31$	5.96142	1.07070	0.535351	−	0.844629i	$-0.320179\pi$
$31$	5.96142	1.07070	0.535351	+	0.844629i	$0.320179\pi$
$32$	−16.2776	−2.87750
$33$	0.999033	0.173909
$34$	1.22479	0.210050
$35$	−12.6242	−2.13388
$36$	−13.0672	−2.17786
$37$	11.4442	1.88141	0.940706	−	0.339222i	$-0.110164\pi$
$37$	11.4442	1.88141	0.940706	+	0.339222i	$0.110164\pi$
$38$	11.0329	1.78977
$39$	2.57603	0.412495
$40$	28.3461	4.48191
$41$	7.78118	1.21522	0.607608	−	0.794237i	$-0.292129\pi$
$41$	7.78118	1.21522	0.607608	+	0.794237i	$0.292129\pi$
$42$	−6.98817	−1.07830
$43$	−9.44692	−1.44064	−0.720321	−	0.693641i	$-0.756006\pi$
$43$	−9.44692	−1.44064	−0.720321	+	0.693641i	$0.756006\pi$
$44$	7.50323	1.13115
$45$	8.41877	1.25500
$46$	17.0860	2.51920
$47$	11.7459	1.71331	0.856655	−	0.515889i	$-0.172538\pi$
$47$	11.7459	1.71331	0.856655	+	0.515889i	$0.172538\pi$
$48$	8.56104	1.23568
$49$	7.33996	1.04857
$50$	−16.3758	−2.31589
$51$	−0.315038	−0.0441141
$52$	19.3472	2.68298
$53$	−2.37933	−0.326826	−0.163413	−	0.986558i	$-0.552250\pi$
$53$	−2.37933	−0.326826	−0.163413	+	0.986558i	$0.552250\pi$
$54$	10.1964	1.38756
$55$	−4.83409	−0.651829
$56$	−32.1985	−4.30271
$57$	−2.83785	−0.375883
$58$	19.6887	2.58525
$59$	8.26952	1.07660	0.538300	−	0.842753i	$-0.319067\pi$
$59$	8.26952	1.07660	0.538300	+	0.842753i	$0.319067\pi$
$60$	−11.8847	−1.53431
$61$	−6.75010	−0.864261	−0.432131	−	0.901811i	$-0.642238\pi$
$61$	−6.75010	−0.864261	−0.432131	+	0.901811i	$0.642238\pi$
$62$	−15.9678	−2.02791
$63$	−9.56296	−1.20482
$64$	18.7479	2.34348
$65$	−12.4648	−1.54607
$66$	−2.67592	−0.329384
$67$	−4.48494	−0.547922	−0.273961	−	0.961741i	$-0.588334\pi$
$67$	−4.48494	−0.547922	−0.273961	+	0.961741i	$0.588334\pi$
$68$	−2.36609	−0.286931
$69$	−4.39483	−0.529075
$70$	33.8142	4.04157
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	21.4724	2.53055
$73$	−7.70485	−0.901785	−0.450892	−	0.892578i	$-0.648894\pi$
$73$	−7.70485	−0.901785	−0.450892	+	0.892578i	$0.648894\pi$
$74$	−30.6534	−3.56339
$75$	4.21215	0.486377
$76$	−21.3137	−2.44485
$77$	5.49109	0.625767
$78$	−6.89993	−0.781263
$79$	−11.2483	−1.26554	−0.632768	−	0.774341i	$-0.718082\pi$
$79$	−11.2483	−1.26554	−0.632768	+	0.774341i	$0.718082\pi$
$80$	−41.4249	−4.63145
$81$	4.95329	0.550366
$82$	−20.8420	−2.30162
$83$	−4.14568	−0.455047	−0.227524	−	0.973773i	$-0.573063\pi$
$83$	−4.14568	−0.455047	−0.227524	+	0.973773i	$0.573063\pi$
$84$	13.5000	1.47297
$85$	1.52440	0.165344
$86$	25.3037	2.72857
$87$	−5.06428	−0.542947
$88$	−12.3295	−1.31433
$89$	10.3144	1.09333	0.546663	−	0.837353i	$-0.315898\pi$
$89$	10.3144	1.09333	0.546663	+	0.837353i	$0.315898\pi$
$90$	−22.5498	−2.37696
$91$	14.1589	1.48426
$92$	−33.0073	−3.44125
$93$	4.10719	0.425896
$94$	−31.4615	−3.24500
$95$	13.7317	1.40885
$96$	−11.2147	−1.14459
$97$	−9.49652	−0.964226	−0.482113	−	0.876109i	$-0.660131\pi$
$97$	−9.49652	−0.964226	−0.482113	+	0.876109i	$0.660131\pi$
$98$	−19.6602	−1.98598
$99$	−3.66187	−0.368032
$100$	31.6353	3.16353
$101$	−15.4740	−1.53972	−0.769860	−	0.638213i	$-0.779674\pi$
$101$	−15.4740	−1.53972	−0.769860	+	0.638213i	$0.779674\pi$
$102$	0.843834	0.0835520
$103$	13.4795	1.32817	0.664085	−	0.747657i	$-0.268821\pi$
$103$	13.4795	1.32817	0.664085	+	0.747657i	$0.268821\pi$
$104$	−31.7920	−3.11746
$105$	−8.69761	−0.848800
$106$	6.37306	0.619007
$107$	17.8700	1.72756	0.863779	−	0.503870i	$-0.168091\pi$
$107$	17.8700	1.72756	0.863779	+	0.503870i	$0.168091\pi$
$108$	−19.6978	−1.89542
$109$	5.37901	0.515216	0.257608	−	0.966250i	$-0.417066\pi$
$109$	5.37901	0.515216	0.257608	+	0.966250i	$0.417066\pi$
$110$	12.9482	1.23456
$111$	7.88461	0.748374
$112$	47.0549	4.44627
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	7.60123	0.711921
$115$	21.2656	1.98303
$116$	−38.0352	−3.53148
$117$	−9.44221	−0.872932
$118$	−22.1500	−2.03908
$119$	−1.73158	−0.158733
$120$	19.5294	1.78278
$121$	−8.89734	−0.808849
$122$	18.0802	1.63691
$123$	5.36094	0.483380
$124$	30.8471	2.77015
$125$	−3.71298	−0.332099
$126$	25.6145	2.28192
$127$	−9.21300	−0.817522	−0.408761	−	0.912642i	$-0.634039\pi$
$127$	−9.21300	−0.817522	−0.408761	+	0.912642i	$0.634039\pi$
$128$	−17.6612	−1.56105
$129$	−6.50857	−0.573048
$130$	33.3872	2.92825
$131$	−17.4164	−1.52168	−0.760841	−	0.648938i	$-0.775213\pi$
$131$	−17.4164	−1.52168	−0.760841	+	0.648938i	$0.775213\pi$
$132$	5.16944	0.449942
$133$	−15.5980	−1.35252
$134$	12.0130	1.03776
$135$	12.6907	1.09224
$136$	3.88803	0.333396
$137$	−8.09267	−0.691404	−0.345702	−	0.938344i	$-0.612359\pi$
$137$	−8.09267	−0.691404	−0.345702	+	0.938344i	$0.612359\pi$
$138$	11.7716	1.00207
$139$	11.1930	0.949381	0.474691	−	0.880153i	$-0.342560\pi$
$139$	11.1930	0.949381	0.474691	+	0.880153i	$0.342560\pi$
$140$	−65.3233	−5.52083
$141$	8.09246	0.681508
$142$	2.67852	0.224776
$143$	5.42175	0.453390
$144$	−31.3798	−2.61498
$145$	24.5049	2.03502
$146$	20.6376	1.70798
$147$	5.05696	0.417091
$148$	59.2173	4.86763
$149$	−17.9349	−1.46928	−0.734640	−	0.678457i	$-0.762649\pi$
$149$	−17.9349	−1.46928	−0.734640	+	0.678457i	$0.762649\pi$
$150$	−11.2823	−0.921197
$151$	−17.6506	−1.43639	−0.718194	−	0.695843i	$-0.755031\pi$
$151$	−17.6506	−1.43639	−0.718194	+	0.695843i	$0.755031\pi$
$152$	35.0233	2.84076
$153$	1.15474	0.0933556
$154$	−14.7080	−1.18520
$155$	−19.8738	−1.59630
$156$	13.3295	1.06722
$157$	11.7147	0.934933	0.467466	−	0.884011i	$-0.345167\pi$
$157$	11.7147	0.934933	0.467466	+	0.884011i	$0.345167\pi$
$158$	30.1289	2.39692
$159$	−1.63927	−0.130002
$160$	54.2652	4.29004
$161$	−24.1558	−1.90374
$162$	−13.2675	−1.04239
$163$	17.8070	1.39475	0.697377	−	0.716704i	$-0.254350\pi$
$163$	17.8070	1.39475	0.697377	+	0.716704i	$0.254350\pi$
$164$	40.2633	3.14404
$165$	−3.33051	−0.259280
$166$	11.1043	0.861858
$167$	3.69353	0.285814	0.142907	−	0.989736i	$-0.454355\pi$
$167$	3.69353	0.285814	0.142907	+	0.989736i	$0.454355\pi$
$168$	−22.1836	−1.71150
$169$	0.980105	0.0753927
$170$	−4.08312	−0.313161
$171$	10.4019	0.795454
$172$	−48.8826	−3.72726
$173$	15.8196	1.20274	0.601370	−	0.798971i	$-0.294622\pi$
$173$	15.8196	1.20274	0.601370	+	0.798971i	$0.294622\pi$
$174$	13.5647	1.02834
$175$	23.1517	1.75010
$176$	18.0184	1.35819
$177$	5.69739	0.428242
$178$	−27.6273	−2.07076
$179$	−4.59611	−0.343529	−0.171765	−	0.985138i	$-0.554947\pi$
$179$	−4.59611	−0.343529	−0.171765	+	0.985138i	$0.554947\pi$
$180$	43.5625	3.24696
$181$	3.24026	0.240847	0.120423	−	0.992723i	$-0.461575\pi$
$181$	3.24026	0.240847	0.120423	+	0.992723i	$0.461575\pi$
$182$	−37.9248	−2.81117
$183$	−4.65056	−0.343779
$184$	54.2386	3.99852
$185$	−38.1518	−2.80498
$186$	−11.0012	−0.806646
$187$	−0.663059	−0.0484876
$188$	60.7783	4.43272
$189$	−14.4154	−1.04857
$190$	−36.7806	−2.66835
$191$	3.41034	0.246764	0.123382	−	0.992359i	$-0.460626\pi$
$191$	3.41034	0.246764	0.123382	+	0.992359i	$0.460626\pi$
$192$	12.9166	0.932174
$193$	−21.8959	−1.57610	−0.788051	−	0.615610i	$-0.788910\pi$
$193$	−21.8959	−1.57610	−0.788051	+	0.615610i	$0.788910\pi$
$194$	25.4366	1.82624
$195$	−8.58778	−0.614984
$196$	37.9802	2.71287
$197$	7.48921	0.533584	0.266792	−	0.963754i	$-0.414036\pi$
$197$	7.48921	0.533584	0.266792	+	0.963754i	$0.414036\pi$
$198$	9.80837	0.697051
$199$	−18.3820	−1.30306	−0.651531	−	0.758622i	$-0.725873\pi$
$199$	−18.3820	−1.30306	−0.651531	+	0.758622i	$0.725873\pi$
$200$	−51.9841	−3.67583
$201$	−3.08995	−0.217948
$202$	41.4473	2.91622
$203$	−27.8353	−1.95366
$204$	−1.63015	−0.114133
$205$	−25.9404	−1.81175
$206$	−36.1049	−2.51555
$207$	16.1089	1.11964
$208$	46.4608	3.22148
$209$	−5.97281	−0.413148
$210$	23.2967	1.60762
$211$	14.3897	0.990626	0.495313	−	0.868714i	$-0.335053\pi$
$211$	14.3897	0.990626	0.495313	+	0.868714i	$0.335053\pi$
$212$	−12.3117	−0.845571
$213$	−0.688962	−0.0472069
$214$	−47.8651	−3.27199
$215$	31.4935	2.14784
$216$	32.3680	2.20236
$217$	22.5748	1.53248
$218$	−14.4078	−0.975817
$219$	−5.30835	−0.358705
$220$	−25.0137	−1.68643
$221$	−1.70971	−0.115008
$222$	−21.1191	−1.41742
$223$	−5.90794	−0.395625	−0.197812	−	0.980240i	$-0.563384\pi$
$223$	−5.90794	−0.395625	−0.197812	+	0.980240i	$0.563384\pi$
$224$	−61.6403	−4.11852
$225$	−15.4393	−1.02928
$226$	2.67852	0.178172
$227$	11.7556	0.780249	0.390124	−	0.920762i	$-0.372432\pi$
$227$	11.7556	0.780249	0.390124	+	0.920762i	$0.372432\pi$
$228$	−14.6843	−0.972493
$229$	3.52788	0.233129	0.116565	−	0.993183i	$-0.462812\pi$
$229$	3.52788	0.233129	0.116565	+	0.993183i	$0.462812\pi$
$230$	−56.9602	−3.75584
$231$	3.78315	0.248913
$232$	62.5006	4.10337
$233$	−17.6528	−1.15648	−0.578238	−	0.815868i	$-0.696259\pi$
$233$	−17.6528	−1.15648	−0.578238	+	0.815868i	$0.696259\pi$
$234$	25.2911	1.65333
$235$	−39.1576	−2.55436
$236$	42.7902	2.78540
$237$	−7.74968	−0.503396
$238$	4.63805	0.300640
$239$	−9.53899	−0.617026	−0.308513	−	0.951220i	$-0.599831\pi$
$239$	−9.53899	−0.617026	−0.308513	+	0.951220i	$0.599831\pi$
$240$	−28.5402	−1.84226
$241$	11.4891	0.740079	0.370040	−	0.929016i	$-0.379344\pi$
$241$	11.4891	0.740079	0.370040	+	0.929016i	$0.379344\pi$
$242$	23.8317	1.53196
$243$	14.8329	0.951529
$244$	−34.9280	−2.23604
$245$	−24.4695	−1.56330
$246$	−14.3594	−0.915519
$247$	−15.4010	−0.979944
$248$	−50.6888	−3.21874
$249$	−2.85621	−0.181005
$250$	9.94529	0.628995
$251$	21.4538	1.35415	0.677075	−	0.735914i	$-0.263247\pi$
$251$	21.4538	1.35415	0.677075	+	0.735914i	$0.263247\pi$
$252$	−49.4830	−3.11714
$253$	−9.24977	−0.581528
$254$	24.6772	1.54838
$255$	1.05025	0.0657693
$256$	9.81012	0.613133
$257$	20.2895	1.26563	0.632813	−	0.774304i	$-0.281900\pi$
$257$	20.2895	1.26563	0.632813	+	0.774304i	$0.281900\pi$
$258$	17.4333	1.08535
$259$	43.3370	2.69283
$260$	−64.4985	−4.00003
$261$	18.5627	1.14900
$262$	46.6502	2.88206
$263$	−23.9610	−1.47750	−0.738748	−	0.673982i	$-0.764583\pi$
$263$	−23.9610	−1.47750	−0.738748	+	0.673982i	$0.764583\pi$
$264$	−8.49458	−0.522805
$265$	7.93204	0.487261
$266$	41.7794	2.56166
$267$	7.10624	0.434895
$268$	−23.2071	−1.41760
$269$	18.4345	1.12397	0.561986	−	0.827147i	$-0.310037\pi$
$269$	18.4345	1.12397	0.561986	+	0.827147i	$0.310037\pi$
$270$	−33.9921	−2.06870
$271$	−4.33208	−0.263155	−0.131578	−	0.991306i	$-0.542004\pi$
$271$	−4.33208	−0.263155	−0.131578	+	0.991306i	$0.542004\pi$
$272$	−5.68197	−0.344520
$273$	9.75494	0.590396
$274$	21.6764	1.30952
$275$	8.86529	0.534597
$276$	−22.7408	−1.36884
$277$	−31.2168	−1.87564	−0.937819	−	0.347126i	$-0.887158\pi$
$277$	−31.2168	−1.87564	−0.937819	+	0.347126i	$0.887158\pi$
$278$	−29.9807	−1.79812
$279$	−15.0546	−0.901293
$280$	107.341	6.41487
$281$	15.9306	0.950338	0.475169	−	0.879895i	$-0.342387\pi$
$281$	15.9306	0.950338	0.475169	+	0.879895i	$0.342387\pi$
$282$	−21.6758	−1.29077
$283$	7.44917	0.442807	0.221404	−	0.975182i	$-0.428936\pi$
$283$	7.44917	0.442807	0.221404	+	0.975182i	$0.428936\pi$
$284$	−5.17445	−0.307047
$285$	9.46064	0.560400
$286$	−14.5222	−0.858718
$287$	29.4659	1.73932
$288$	41.1064	2.42222
$289$	−16.7909	−0.987701
$290$	−65.6367	−3.85432
$291$	−6.54275	−0.383543
$292$	−39.8683	−2.33312
$293$	−12.5486	−0.733097	−0.366548	−	0.930399i	$-0.619461\pi$
$293$	−12.5486	−0.733097	−0.366548	+	0.930399i	$0.619461\pi$
$294$	−13.5451	−0.789968
$295$	−27.5684	−1.60509
$296$	−97.3077	−5.65589
$297$	−5.51999	−0.320302
$298$	48.0388	2.78281
$299$	−23.8507	−1.37932
$300$	21.7955	1.25837
$301$	−35.7737	−2.06196
$302$	47.2775	2.72051
$303$	−10.6610	−0.612458
$304$	−51.1830	−2.93555
$305$	22.5030	1.28852
$306$	−3.09300	−0.176815
$307$	−5.83419	−0.332975	−0.166487	−	0.986044i	$-0.553243\pi$
$307$	−5.83419	−0.332975	−0.166487	+	0.986044i	$0.553243\pi$
$308$	28.4133	1.61900
$309$	9.28684	0.528310
$310$	53.2322	3.02339
$311$	17.3662	0.984747	0.492373	−	0.870384i	$-0.336129\pi$
$311$	17.3662	0.984747	0.492373	+	0.870384i	$0.336129\pi$
$312$	−21.9035	−1.24004
$313$	−32.5151	−1.83786	−0.918931	−	0.394419i	$-0.870946\pi$
$313$	−32.5151	−1.83786	−0.918931	+	0.394419i	$0.870946\pi$
$314$	−31.3779	−1.77076
$315$	31.8803	1.79625
$316$	−58.2039	−3.27423
$317$	−10.7018	−0.601075	−0.300537	−	0.953770i	$-0.597166\pi$
$317$	−10.7018	−0.601075	−0.300537	+	0.953770i	$0.597166\pi$
$318$	4.39080	0.246224
$319$	−10.6588	−0.596776
$320$	−62.5004	−3.49388
$321$	12.3118	0.687175
$322$	64.7016	3.60568
$323$	1.88348	0.104800
$324$	25.6305	1.42392
$325$	22.8593	1.26801
$326$	−47.6964	−2.64166
$327$	3.70594	0.204939
$328$	−66.1618	−3.65318
$329$	44.4794	2.45223
$330$	8.92081	0.491075
$331$	11.2927	0.620700	0.310350	−	0.950622i	$-0.399554\pi$
$331$	11.2927	0.620700	0.310350	+	0.950622i	$0.399554\pi$
$332$	−21.4516	−1.17731
$333$	−28.9004	−1.58373
$334$	−9.89317	−0.541330
$335$	14.9516	0.816892
$336$	32.4191	1.76861
$337$	20.1870	1.09965	0.549827	−	0.835279i	$-0.314694\pi$
$337$	20.1870	1.09965	0.549827	+	0.835279i	$0.314694\pi$
$338$	−2.62523	−0.142794
$339$	−0.688962	−0.0374193
$340$	7.88791	0.427782
$341$	8.64439	0.468120
$342$	−27.8617	−1.50659
$343$	1.28738	0.0695118
$344$	80.3253	4.33085
$345$	14.6512	0.788793
$346$	−42.3730	−2.27798
$347$	−24.3693	−1.30821	−0.654107	−	0.756402i	$-0.726955\pi$
$347$	−24.3693	−1.30821	−0.654107	+	0.756402i	$0.726955\pi$
$348$	−26.2048	−1.40473
$349$	2.48012	0.132758	0.0663788	−	0.997794i	$-0.478855\pi$
$349$	2.48012	0.132758	0.0663788	+	0.997794i	$0.478855\pi$
$350$	−62.0121	−3.31469
$351$	−14.2334	−0.759723
$352$	−23.6034	−1.25807
$353$	−5.10893	−0.271921	−0.135961	−	0.990714i	$-0.543412\pi$
$353$	−5.10893	−0.271921	−0.135961	+	0.990714i	$0.543412\pi$
$354$	−15.2605	−0.811088
$355$	3.33373	0.176936
$356$	53.3714	2.82868
$357$	−1.19299	−0.0631397
$358$	12.3107	0.650643
$359$	−9.80284	−0.517374	−0.258687	−	0.965961i	$-0.583290\pi$
$359$	−9.80284	−0.517374	−0.258687	+	0.965961i	$0.583290\pi$
$360$	−71.5832	−3.77276
$361$	−2.03363	−0.107033
$362$	−8.67910	−0.456163
$363$	−6.12993	−0.321738
$364$	73.2644	3.84010
$365$	25.6859	1.34446
$366$	12.4566	0.651117
$367$	20.5968	1.07515	0.537573	−	0.843217i	$-0.319341\pi$
$367$	20.5968	1.07515	0.537573	+	0.843217i	$0.319341\pi$
$368$	−79.2644	−4.13194
$369$	−19.6501	−1.02294
$370$	102.190	5.31262
$371$	−9.01007	−0.467779
$372$	21.2525	1.10189
$373$	15.8345	0.819880	0.409940	−	0.912112i	$-0.365550\pi$
$373$	15.8345	0.819880	0.409940	+	0.912112i	$0.365550\pi$
$374$	1.77601	0.0918354
$375$	−2.55811	−0.132100
$376$	−99.8728	−5.15055
$377$	−27.4838	−1.41549
$378$	38.6120	1.98599
$379$	−9.23204	−0.474218	−0.237109	−	0.971483i	$-0.576200\pi$
$379$	−9.23204	−0.474218	−0.237109	+	0.971483i	$0.576200\pi$
$380$	71.0541	3.64500
$381$	−6.34741	−0.325188
$382$	−9.13465	−0.467369
$383$	−21.1520	−1.08082	−0.540409	−	0.841403i	$-0.681730\pi$
$383$	−21.1520	−1.08082	−0.540409	+	0.841403i	$0.681730\pi$
$384$	−12.1679	−0.620941
$385$	−18.3058	−0.932950
$386$	58.6485	2.98513
$387$	23.8566	1.21270
$388$	−49.1392	−2.49467
$389$	−3.13204	−0.158801	−0.0794003	−	0.996843i	$-0.525301\pi$
$389$	−3.13204	−0.158801	−0.0794003	+	0.996843i	$0.525301\pi$
$390$	23.0025	1.16478
$391$	2.91685	0.147511
$392$	−62.4103	−3.15219
$393$	−11.9993	−0.605283
$394$	−20.0600	−1.01061
$395$	37.4989	1.88678
$396$	−18.9481	−0.952180
$397$	18.4583	0.926394	0.463197	−	0.886255i	$-0.346702\pi$
$397$	18.4583	0.926394	0.463197	+	0.886255i	$0.346702\pi$
$398$	49.2364	2.46800
$399$	−10.7464	−0.537994
$400$	75.9696	3.79848
$401$	36.3460	1.81503	0.907516	−	0.420018i	$-0.137976\pi$
$401$	36.3460	1.81503	0.907516	+	0.420018i	$0.137976\pi$
$402$	8.27649	0.412794
$403$	22.2897	1.11033
$404$	−80.0693	−3.98360
$405$	−16.5129	−0.820535
$406$	74.5573	3.70022
$407$	16.5947	0.822568
$408$	2.67871	0.132616
$409$	−19.6794	−0.973083	−0.486542	−	0.873657i	$-0.661742\pi$
$409$	−19.6794	−0.973083	−0.486542	+	0.873657i	$0.661742\pi$
$410$	69.4817	3.43146
$411$	−5.57555	−0.275021
$412$	69.7487	3.43627
$413$	31.3151	1.54092
$414$	−43.1478	−2.12060
$415$	13.8206	0.678425
$416$	−60.8620	−2.98401
$417$	7.71158	0.377638
$418$	15.9983	0.782501
$419$	−6.27320	−0.306466	−0.153233	−	0.988190i	$-0.548968\pi$
$419$	−6.27320	−0.306466	−0.153233	+	0.988190i	$0.548968\pi$
$420$	−45.0053	−2.19603
$421$	−16.1872	−0.788915	−0.394458	−	0.918914i	$-0.629068\pi$
$421$	−16.1872	−0.788915	−0.394458	+	0.918914i	$0.629068\pi$
$422$	−38.5430	−1.87624
$423$	−29.6622	−1.44223
$424$	20.2309	0.982502
$425$	−2.79561	−0.135607
$426$	1.84540	0.0894097
$427$	−25.5614	−1.23700
$428$	92.4674	4.46958
$429$	3.73538	0.180346
$430$	−84.3558	−4.06800
$431$	7.19713	0.346674	0.173337	−	0.984863i	$-0.444545\pi$
$431$	7.19713	0.346674	0.173337	+	0.984863i	$0.444545\pi$
$432$	−47.3026	−2.27585
$433$	25.2844	1.21509	0.607544	−	0.794286i	$-0.292155\pi$
$433$	25.2844	1.21509	0.607544	+	0.794286i	$0.292155\pi$
$434$	−60.4669	−2.90251
$435$	16.8829	0.809475
$436$	27.8334	1.33298
$437$	26.2749	1.25690
$438$	14.2185	0.679386
$439$	30.5362	1.45741	0.728706	−	0.684827i	$-0.240122\pi$
$439$	30.5362	1.45741	0.728706	+	0.684827i	$0.240122\pi$
$440$	41.1033	1.95952
$441$	−18.5358	−0.882659
$442$	4.57949	0.217824
$443$	31.3445	1.48922	0.744611	−	0.667499i	$-0.232635\pi$
$443$	31.3445	1.48922	0.744611	+	0.667499i	$0.232635\pi$
$444$	40.7985	1.93621
$445$	−34.3855	−1.63003
$446$	15.8245	0.749312
$447$	−12.3564	−0.584439
$448$	70.9947	3.35419
$449$	−1.33785	−0.0631372	−0.0315686	−	0.999502i	$-0.510050\pi$
$449$	−1.33785	−0.0631372	−0.0315686	+	0.999502i	$0.510050\pi$
$450$	41.3543	1.94946
$451$	11.2831	0.531302
$452$	−5.17445	−0.243385
$453$	−12.1606	−0.571356
$454$	−31.4876	−1.47779
$455$	−47.2019	−2.21286
$456$	24.1297	1.12998
$457$	−14.3544	−0.671469	−0.335735	−	0.941957i	$-0.608985\pi$
$457$	−14.3544	−0.671469	−0.335735	+	0.941957i	$0.608985\pi$
$458$	−9.44949	−0.441546
$459$	1.74069	0.0812484
$460$	110.038	5.13053
$461$	−5.97884	−0.278462	−0.139231	−	0.990260i	$-0.544463\pi$
$461$	−5.97884	−0.278462	−0.139231	+	0.990260i	$0.544463\pi$
$462$	−10.1332	−0.471441
$463$	−13.6196	−0.632959	−0.316479	−	0.948599i	$-0.602501\pi$
$463$	−13.6196	−0.632959	−0.316479	+	0.948599i	$0.602501\pi$
$464$	−91.3384	−4.24028
$465$	−13.6923	−0.634964
$466$	47.2834	2.19036
$467$	−14.1078	−0.652832	−0.326416	−	0.945226i	$-0.605841\pi$
$467$	−14.1078	−0.652832	−0.326416	+	0.945226i	$0.605841\pi$
$468$	−48.8582	−2.25847
$469$	−16.9836	−0.784231
$470$	104.884	4.83794
$471$	8.07097	0.371891
$472$	−70.3141	−3.23647
$473$	−13.6986	−0.629860
$474$	20.7576	0.953430
$475$	−25.1827	−1.15546
$476$	−8.95995	−0.410678
$477$	6.00859	0.275114
$478$	25.5503	1.16864
$479$	−14.8749	−0.679653	−0.339826	−	0.940488i	$-0.610368\pi$
$479$	−14.8749	−0.679653	−0.339826	+	0.940488i	$0.610368\pi$
$480$	37.3867	1.70646
$481$	42.7898	1.95105
$482$	−30.7738	−1.40171
$483$	−16.6424	−0.757255
$484$	−46.0388	−2.09267
$485$	31.6589	1.43755
$486$	−39.7301	−1.80219
$487$	−32.2608	−1.46188	−0.730938	−	0.682443i	$-0.760917\pi$
$487$	−32.2608	−1.46188	−0.730938	+	0.682443i	$0.760917\pi$
$488$	57.3947	2.59814
$489$	12.2684	0.554795
$490$	65.5418	2.96088
$491$	7.19456	0.324686	0.162343	−	0.986734i	$-0.448095\pi$
$491$	7.19456	0.324686	0.162343	+	0.986734i	$0.448095\pi$
$492$	27.7399	1.25061
$493$	3.36116	0.151379
$494$	41.2519	1.85601
$495$	12.2077	0.548695
$496$	74.0766	3.32614
$497$	−3.78681	−0.169862
$498$	7.65042	0.342823
$499$	−34.5718	−1.54765	−0.773823	−	0.633402i	$-0.781658\pi$
$499$	−34.5718	−1.54765	−0.773823	+	0.633402i	$0.781658\pi$
$500$	−19.2126	−0.859215
$501$	2.54470	0.113689
$502$	−57.4642	−2.56475
$503$	−34.8596	−1.55431	−0.777156	−	0.629308i	$-0.783338\pi$
$503$	−34.8596	−1.55431	−0.777156	+	0.629308i	$0.783338\pi$
$504$	81.3120	3.62192
$505$	51.5861	2.29555
$506$	24.7757	1.10141
$507$	0.675255	0.0299891
$508$	−47.6722	−2.11511
$509$	−8.94075	−0.396292	−0.198146	−	0.980173i	$-0.563492\pi$
$509$	−8.94075	−0.396292	−0.198146	+	0.980173i	$0.563492\pi$
$510$	−2.81312	−0.124567
$511$	−29.1768	−1.29071
$512$	9.04589	0.399775
$513$	15.6801	0.692292
$514$	−54.3459	−2.39709
$515$	−44.9369	−1.98016
$516$	−33.6783	−1.48260
$517$	17.0321	0.749073
$518$	−116.079	−5.10021
$519$	10.8991	0.478417
$520$	105.986	4.64779
$521$	−31.6200	−1.38530	−0.692648	−	0.721276i	$-0.743556\pi$
$521$	−31.6200	−1.38530	−0.692648	+	0.721276i	$0.743556\pi$
$522$	−49.7204	−2.17620
$523$	−1.19072	−0.0520667	−0.0260333	−	0.999661i	$-0.508288\pi$
$523$	−1.19072	−0.0520667	−0.0260333	+	0.999661i	$0.508288\pi$
$524$	−90.1205	−3.93693
$525$	15.9506	0.696143
$526$	64.1798	2.79837
$527$	−2.72595	−0.118744
$528$	12.4140	0.540249
$529$	17.6905	0.769153
$530$	−21.2461	−0.922871
$531$	−20.8833	−0.906257
$532$	−80.7109	−3.49926
$533$	29.0938	1.26019
$534$	−19.0342	−0.823690
$535$	−59.5738	−2.57560
$536$	38.1345	1.64716
$537$	−3.16654	−0.136646
$538$	−49.3771	−2.12880
$539$	10.6433	0.458441
$540$	65.6671	2.82586
$541$	−16.8249	−0.723359	−0.361680	−	0.932302i	$-0.617797\pi$
$541$	−16.8249	−0.723359	−0.361680	+	0.932302i	$0.617797\pi$
$542$	11.6036	0.498415
$543$	2.23242	0.0958023
$544$	7.44318	0.319124
$545$	−17.9322	−0.768130
$546$	−26.1288	−1.11821
$547$	−37.0439	−1.58388	−0.791941	−	0.610598i	$-0.790929\pi$
$547$	−37.0439	−1.58388	−0.791941	+	0.610598i	$0.790929\pi$
$548$	−41.8751	−1.78882
$549$	17.0462	0.727515
$550$	−23.7458	−1.01252
$551$	30.2773	1.28985
$552$	37.3684	1.59050
$553$	−42.5954	−1.81134
$554$	83.6147	3.55245
$555$	−26.2852	−1.11574
$556$	57.9178	2.45626
$557$	37.2863	1.57987	0.789935	−	0.613190i	$-0.210114\pi$
$557$	37.2863	1.57987	0.789935	+	0.613190i	$0.210114\pi$
$558$	40.3239	1.70705
$559$	−35.3220	−1.49396
$560$	−156.869	−6.62891
$561$	−0.456822	−0.0192871
$562$	−42.6703	−1.79994
$563$	41.0502	1.73006	0.865031	−	0.501719i	$-0.167299\pi$
$563$	41.0502	1.73006	0.865031	+	0.501719i	$0.167299\pi$
$564$	41.8740	1.76321
$565$	3.33373	0.140251
$566$	−19.9527	−0.838676
$567$	18.7572	0.787728
$568$	8.50280	0.356770
$569$	−27.6922	−1.16092	−0.580459	−	0.814289i	$-0.697127\pi$
$569$	−27.6922	−1.16092	−0.580459	+	0.814289i	$0.697127\pi$
$570$	−25.3405	−1.06140
$571$	−29.6663	−1.24149	−0.620747	−	0.784011i	$-0.713171\pi$
$571$	−29.6663	−1.24149	−0.620747	+	0.784011i	$0.713171\pi$
$572$	28.0546	1.17302
$573$	2.34960	0.0981558
$574$	−78.9248	−3.29426
$575$	−38.9992	−1.62638
$576$	−47.3446	−1.97269
$577$	27.8718	1.16032	0.580159	−	0.814503i	$-0.302990\pi$
$577$	27.8718	1.16032	0.580159	+	0.814503i	$0.302990\pi$
$578$	44.9747	1.87070
$579$	−15.0855	−0.626930
$580$	126.799	5.26505
$581$	−15.6989	−0.651300
$582$	17.5248	0.726428
$583$	−3.45015	−0.142891
$584$	65.5129	2.71094
$585$	31.4778	1.30145
$586$	33.6116	1.38848
$587$	−6.95666	−0.287132	−0.143566	−	0.989641i	$-0.545857\pi$
$587$	−6.95666	−0.287132	−0.143566	+	0.989641i	$0.545857\pi$
$588$	26.1669	1.07911
$589$	−24.5553	−1.01178
$590$	73.8423	3.04004
$591$	5.15978	0.212245
$592$	142.205	5.84461
$593$	−18.3748	−0.754561	−0.377280	−	0.926099i	$-0.623141\pi$
$593$	−18.3748	−0.754561	−0.377280	+	0.926099i	$0.623141\pi$
$594$	14.7854	0.606651
$595$	5.77261	0.236654
$596$	−92.8029	−3.80136
$597$	−12.6645	−0.518323
$598$	63.8846	2.61243
$599$	34.7708	1.42070	0.710348	−	0.703851i	$-0.248538\pi$
$599$	34.7708	1.42070	0.710348	+	0.703851i	$0.248538\pi$
$600$	−35.8151	−1.46214
$601$	12.8285	0.523286	0.261643	−	0.965165i	$-0.415736\pi$
$601$	12.8285	0.523286	0.261643	+	0.965165i	$0.415736\pi$
$602$	95.8205	3.90535
$603$	11.3260	0.461228
$604$	−91.3322	−3.71626
$605$	29.6613	1.20591
$606$	28.5556	1.15999
$607$	−46.6434	−1.89320	−0.946598	−	0.322417i	$-0.895505\pi$
$607$	−46.6434	−1.89320	−0.946598	+	0.322417i	$0.895505\pi$
$608$	67.0480	2.71915
$609$	−19.1775	−0.777111
$610$	−60.2746	−2.44045
$611$	43.9178	1.77672
$612$	5.97516	0.241532
$613$	−2.38315	−0.0962547	−0.0481274	−	0.998841i	$-0.515325\pi$
$613$	−2.38315	−0.0962547	−0.0481274	+	0.998841i	$0.515325\pi$
$614$	15.6270	0.630653
$615$	−17.8719	−0.720666
$616$	−46.6896	−1.88118
$617$	−12.9686	−0.522096	−0.261048	−	0.965326i	$-0.584068\pi$
$617$	−12.9686	−0.522096	−0.261048	+	0.965326i	$0.584068\pi$
$618$	−24.8749	−1.00062
$619$	−5.51505	−0.221669	−0.110834	−	0.993839i	$-0.535352\pi$
$619$	−5.51505	−0.221669	−0.110834	+	0.993839i	$0.535352\pi$
$620$	−102.836	−4.12998
$621$	24.2829	0.974439
$622$	−46.5156	−1.86511
$623$	39.0588	1.56486
$624$	32.0097	1.28141
$625$	−18.1907	−0.727629
$626$	87.0922	3.48090
$627$	−4.11504	−0.164339
$628$	60.6170	2.41888
$629$	−5.23302	−0.208654
$630$	−85.3920	−3.40210
$631$	−5.46855	−0.217699	−0.108850	−	0.994058i	$-0.534717\pi$
$631$	−5.46855	−0.217699	−0.108850	+	0.994058i	$0.534717\pi$
$632$	95.6424	3.80445
$633$	9.91394	0.394044
$634$	28.6650	1.13843
$635$	30.7137	1.21884
$636$	−8.48229	−0.336345
$637$	27.4441	1.08738
$638$	28.5496	1.13029
$639$	2.52533	0.0999006
$640$	58.8778	2.32735
$641$	−3.08693	−0.121927	−0.0609633	−	0.998140i	$-0.519417\pi$
$641$	−3.08693	−0.121927	−0.0609633	+	0.998140i	$0.519417\pi$
$642$	−32.9772	−1.30151
$643$	−29.0813	−1.14685	−0.573427	−	0.819257i	$-0.694386\pi$
$643$	−29.0813	−1.14685	−0.573427	+	0.819257i	$0.694386\pi$
$644$	−124.993	−4.92540
$645$	21.6978	0.854351
$646$	−5.04494	−0.198491
$647$	6.81408	0.267889	0.133944	−	0.990989i	$-0.457236\pi$
$647$	6.81408	0.267889	0.133944	+	0.990989i	$0.457236\pi$
$648$	−42.1169	−1.65451
$649$	11.9913	0.470698
$650$	−61.2291	−2.40160
$651$	15.5532	0.609577
$652$	92.1415	3.60854
$653$	−27.2333	−1.06572	−0.532860	−	0.846203i	$-0.678883\pi$
$653$	−27.2333	−1.06572	−0.532860	+	0.846203i	$0.678883\pi$
$654$	−9.92641	−0.388153
$655$	58.0618	2.26866
$656$	96.6889	3.77507
$657$	19.4573	0.759102
$658$	−119.139	−4.64451
$659$	−28.3944	−1.10609	−0.553045	−	0.833151i	$-0.686534\pi$
$659$	−28.3944	−1.10609	−0.553045	+	0.833151i	$0.686534\pi$
$660$	−17.2335	−0.670814
$661$	0.134294	0.00522343	0.00261172	−	0.999997i	$-0.499169\pi$
$661$	0.134294	0.00522343	0.00261172	+	0.999997i	$0.499169\pi$
$662$	−30.2475	−1.17560
$663$	−1.17793	−0.0457469
$664$	35.2499	1.36796
$665$	51.9995	2.01645
$666$	77.4101	2.99958
$667$	46.8888	1.81554
$668$	19.1120	0.739464
$669$	−4.07035	−0.157369
$670$	−40.0480	−1.54719
$671$	−9.78801	−0.377862
$672$	−42.4679	−1.63823
$673$	26.6102	1.02575	0.512874	−	0.858464i	$-0.328581\pi$
$673$	26.6102	1.02575	0.512874	+	0.858464i	$0.328581\pi$
$674$	−54.0711	−2.08274
$675$	−23.2735	−0.895799
$676$	5.07150	0.195058
$677$	10.4269	0.400737	0.200368	−	0.979721i	$-0.435786\pi$
$677$	10.4269	0.400737	0.200368	+	0.979721i	$0.435786\pi$
$678$	1.84540	0.0708720
$679$	−35.9616	−1.38008
$680$	−12.9616	−0.497056
$681$	8.09919	0.310362
$682$	−23.1541	−0.886617
$683$	−31.9126	−1.22110	−0.610551	−	0.791977i	$-0.709052\pi$
$683$	−31.9126	−1.22110	−0.610551	+	0.791977i	$0.709052\pi$
$684$	53.8241	2.05802
$685$	26.9788	1.03081
$686$	−3.44826	−0.131655
$687$	2.43058	0.0927323
$688$	−117.387	−4.47535
$689$	−8.89630	−0.338922
$690$	−39.2434	−1.49397
$691$	37.3120	1.41942	0.709708	−	0.704496i	$-0.248827\pi$
$691$	37.3120	1.41942	0.709708	+	0.704496i	$0.248827\pi$
$692$	81.8575	3.11175
$693$	−13.8668	−0.526757
$694$	65.2736	2.47775
$695$	−37.3146	−1.41542
$696$	43.0605	1.63221
$697$	−3.55806	−0.134771
$698$	−6.64303	−0.251442
$699$	−12.1621	−0.460014
$700$	119.797	4.52791
$701$	−21.1421	−0.798524	−0.399262	−	0.916837i	$-0.630734\pi$
$701$	−21.1421	−0.798524	−0.399262	+	0.916837i	$0.630734\pi$
$702$	38.1244	1.43891
$703$	−47.1389	−1.77788
$704$	27.1854	1.02459
$705$	−26.9781	−1.01605
$706$	13.6844	0.515017
$707$	−58.5971	−2.20377
$708$	29.4808	1.10796
$709$	18.2110	0.683929	0.341965	−	0.939713i	$-0.388908\pi$
$709$	18.2110	0.683929	0.341965	+	0.939713i	$0.388908\pi$
$710$	−8.92945	−0.335116
$711$	28.4058	1.06530
$712$	−87.7015	−3.28675
$713$	−38.0274	−1.42414
$714$	3.19544	0.119586
$715$	−18.0747	−0.675954
$716$	−23.7823	−0.888787
$717$	−6.57200	−0.245436
$718$	26.2571	0.979905
$719$	12.7240	0.474526	0.237263	−	0.971445i	$-0.423750\pi$
$719$	12.7240	0.474526	0.237263	+	0.971445i	$0.423750\pi$
$720$	104.612	3.89865
$721$	51.0442	1.90099
$722$	5.44710	0.202720
$723$	7.91557	0.294383
$724$	16.7666	0.623125
$725$	−44.9397	−1.66902
$726$	16.4191	0.609371
$727$	−25.9533	−0.962554	−0.481277	−	0.876568i	$-0.659827\pi$
$727$	−25.9533	−0.962554	−0.481277	+	0.876568i	$0.659827\pi$
$728$	−120.390	−4.46196
$729$	−4.64059	−0.171874
$730$	−68.8001	−2.54641
$731$	4.31974	0.159771
$732$	−24.0641	−0.889434
$733$	29.1624	1.07714	0.538569	−	0.842581i	$-0.318965\pi$
$733$	29.1624	1.07714	0.538569	+	0.842581i	$0.318965\pi$
$734$	−55.1689	−2.03632
$735$	−16.8585	−0.621836
$736$	103.834	3.82736
$737$	−6.50340	−0.239556
$738$	52.6330	1.93745
$739$	−33.0764	−1.21674	−0.608368	−	0.793655i	$-0.708176\pi$
$739$	−33.0764	−1.21674	−0.608368	+	0.793655i	$0.708176\pi$
$740$	−197.415	−7.25711
$741$	−10.6107	−0.389795
$742$	24.1336	0.885973
$743$	−16.7457	−0.614340	−0.307170	−	0.951655i	$-0.599382\pi$
$743$	−16.7457	−0.614340	−0.307170	+	0.951655i	$0.599382\pi$
$744$	−34.9227	−1.28033
$745$	59.7900	2.19054
$746$	−42.4130	−1.55285
$747$	10.4692	0.383048
$748$	−3.43096	−0.125448
$749$	67.6704	2.47262
$750$	6.85193	0.250197
$751$	31.7810	1.15971	0.579853	−	0.814721i	$-0.303110\pi$
$751$	31.7810	1.15971	0.579853	+	0.814721i	$0.303110\pi$
$752$	145.954	5.32240
$753$	14.7808	0.538643
$754$	73.6159	2.68093
$755$	58.8425	2.14150
$756$	−74.5919	−2.71288
$757$	−27.1125	−0.985422	−0.492711	−	0.870193i	$-0.663994\pi$
$757$	−27.1125	−0.985422	−0.492711	+	0.870193i	$0.663994\pi$
$758$	24.7282	0.898167
$759$	−6.37274	−0.231316
$760$	−116.758	−4.23526
$761$	8.76202	0.317623	0.158812	−	0.987309i	$-0.449234\pi$
$761$	8.76202	0.317623	0.158812	+	0.987309i	$0.449234\pi$
$762$	17.0016	0.615904
$763$	20.3693	0.737419
$764$	17.6466	0.638432
$765$	−3.84961	−0.139183
$766$	56.6560	2.04707
$767$	30.9197	1.11645
$768$	6.75880	0.243887
$769$	50.1723	1.80926	0.904630	−	0.426199i	$-0.140148\pi$
$769$	50.1723	1.80926	0.904630	+	0.426199i	$0.140148\pi$
$770$	49.0324	1.76700
$771$	13.9787	0.503432
$772$	−113.299	−4.07773
$773$	−42.9464	−1.54467	−0.772337	−	0.635213i	$-0.780912\pi$
$773$	−42.9464	−1.54467	−0.772337	+	0.635213i	$0.780912\pi$
$774$	−63.9003	−2.29685
$775$	36.4467	1.30920
$776$	80.7471	2.89865
$777$	29.8576	1.07113
$778$	8.38921	0.300768
$779$	−32.0509	−1.14834
$780$	−44.4370	−1.59110
$781$	−1.45005	−0.0518870
$782$	−7.81283	−0.279386
$783$	27.9818	0.999988
$784$	91.2064	3.25737
$785$	−39.0536	−1.39388
$786$	32.1402	1.14640
$787$	22.8026	0.812826	0.406413	−	0.913689i	$-0.366779\pi$
$787$	22.8026	0.812826	0.406413	+	0.913689i	$0.366779\pi$
$788$	38.7525	1.38050
$789$	−16.5082	−0.587707
$790$	−100.441	−3.57355
$791$	−3.78681	−0.134644
$792$	31.1361	1.10637
$793$	−25.2386	−0.896249
$794$	−49.4408	−1.75459
$795$	5.46487	0.193819
$796$	−95.1165	−3.37131
$797$	−47.0794	−1.66764	−0.833818	−	0.552039i	$-0.813850\pi$
$797$	−47.0794	−1.66764	−0.833818	+	0.552039i	$0.813850\pi$
$798$	28.7845	1.01896
$799$	−5.37097	−0.190011
$800$	−99.5175	−3.51848
$801$	−26.0473	−0.920337
$802$	−97.3533	−3.43766
$803$	−11.1725	−0.394267
$804$	−15.9888	−0.563881
$805$	80.5288	2.83827
$806$	−59.7034	−2.10296
$807$	12.7007	0.447085
$808$	131.572	4.62870
$809$	2.36449	0.0831309	0.0415655	−	0.999136i	$-0.486765\pi$
$809$	2.36449	0.0831309	0.0415655	+	0.999136i	$0.486765\pi$
$810$	44.2302	1.55409
$811$	0.354600	0.0124517	0.00622585	−	0.999981i	$-0.498018\pi$
$811$	0.354600	0.0124517	0.00622585	+	0.999981i	$0.498018\pi$
$812$	−144.032	−5.05454
$813$	−2.98464	−0.104676
$814$	−44.4491	−1.55794
$815$	−59.3638	−2.07942
$816$	−3.91466	−0.137041
$817$	38.9121	1.36136
$818$	52.7116	1.84302
$819$	−35.7559	−1.24941
$820$	−134.227	−4.68741
$821$	47.9186	1.67237	0.836186	−	0.548447i	$-0.184781\pi$
$821$	47.9186	1.67237	0.836186	+	0.548447i	$0.184781\pi$
$822$	14.9342	0.520890
$823$	−39.1141	−1.36343	−0.681716	−	0.731617i	$-0.738766\pi$
$823$	−39.1141	−1.36343	−0.681716	+	0.731617i	$0.738766\pi$
$824$	−114.613	−3.99274
$825$	6.10785	0.212648
$826$	−83.8781	−2.91849
$827$	−26.7323	−0.929574	−0.464787	−	0.885422i	$-0.653869\pi$
$827$	−26.7323	−0.929574	−0.464787	+	0.885422i	$0.653869\pi$
$828$	83.3545	2.89677
$829$	−36.6354	−1.27240	−0.636200	−	0.771524i	$-0.719495\pi$
$829$	−36.6354	−1.27240	−0.636200	+	0.771524i	$0.719495\pi$
$830$	−37.0186	−1.28493
$831$	−21.5072	−0.746077
$832$	70.0983	2.43022
$833$	−3.35630	−0.116289
$834$	−20.6556	−0.715244
$835$	−12.3132	−0.426117
$836$	−30.9060	−1.06891
$837$	−22.6936	−0.784406
$838$	16.8029	0.580445
$839$	9.12535	0.315042	0.157521	−	0.987516i	$-0.449650\pi$
$839$	9.12535	0.315042	0.157521	+	0.987516i	$0.449650\pi$
$840$	73.9541	2.55166
$841$	25.0311	0.863143
$842$	43.3576	1.49420
$843$	10.9756	0.378018
$844$	74.4586	2.56297
$845$	−3.26741	−0.112402
$846$	79.4507	2.73157
$847$	−33.6926	−1.15769
$848$	−29.5655	−1.01528
$849$	5.13220	0.176137
$850$	7.48808	0.256839
$851$	−73.0015	−2.50246
$852$	−3.56500	−0.122135
$853$	33.9057	1.16091	0.580455	−	0.814292i	$-0.302875\pi$
$853$	33.9057	1.16091	0.580455	+	0.814292i	$0.302875\pi$
$854$	68.4665	2.34288
$855$	−34.6772	−1.18593
$856$	−151.945	−5.19338
$857$	22.6440	0.773505	0.386752	−	0.922184i	$-0.373597\pi$
$857$	22.6440	0.773505	0.386752	+	0.922184i	$0.373597\pi$
$858$	−10.0053	−0.341575
$859$	46.2344	1.57750	0.788748	−	0.614717i	$-0.210730\pi$
$859$	46.2344	1.57750	0.788748	+	0.614717i	$0.210730\pi$
$860$	162.961	5.55694
$861$	20.3009	0.691852
$862$	−19.2776	−0.656599
$863$	9.03043	0.307399	0.153700	−	0.988118i	$-0.450881\pi$
$863$	9.03043	0.307399	0.153700	+	0.988118i	$0.450881\pi$
$864$	61.9648	2.10808
$865$	−52.7382	−1.79315
$866$	−67.7245	−2.30137
$867$	−11.5683	−0.392880
$868$	116.812	3.96486
$869$	−16.3107	−0.553303
$870$	−45.2212	−1.53314
$871$	−16.7692	−0.568202
$872$	−45.7367	−1.54884
$873$	23.9819	0.811663
$874$	−70.3777	−2.38056
$875$	−14.0604	−0.475328
$876$	−27.4678	−0.928050
$877$	1.89433	0.0639671	0.0319836	−	0.999488i	$-0.489818\pi$
$877$	1.89433	0.0639671	0.0319836	+	0.999488i	$0.489818\pi$
$878$	−81.7916	−2.76033
$879$	−8.64551	−0.291606
$880$	−60.0684	−2.02491
$881$	−42.2893	−1.42476	−0.712381	−	0.701793i	$-0.752383\pi$
$881$	−42.2893	−1.42476	−0.712381	+	0.701793i	$0.752383\pi$
$882$	49.6485	1.67175
$883$	−12.4612	−0.419354	−0.209677	−	0.977771i	$-0.567241\pi$
$883$	−12.4612	−0.419354	−0.209677	+	0.977771i	$0.567241\pi$
$884$	−8.84681	−0.297550
$885$	−18.9936	−0.638461
$886$	−83.9567	−2.82058
$887$	−20.4076	−0.685219	−0.342609	−	0.939478i	$-0.611311\pi$
$887$	−20.4076	−0.685219	−0.342609	+	0.939478i	$0.611311\pi$
$888$	−67.0413	−2.24976
$889$	−34.8879	−1.17010
$890$	92.1021	3.08727
$891$	7.18254	0.240624
$892$	−30.5703	−1.02357
$893$	−48.3815	−1.61903
$894$	33.0969	1.10693
$895$	15.3222	0.512164
$896$	−66.8798	−2.23430
$897$	−16.4323	−0.548657
$898$	3.58346	0.119582
$899$	−43.8200	−1.46148
$900$	−79.8897	−2.66299
$901$	1.08798	0.0362459
$902$	−30.2221	−1.00628
$903$	−24.6468	−0.820193
$904$	8.50280	0.282799
$905$	−10.8022	−0.359076
$906$	32.5724	1.08215
$907$	13.8214	0.458931	0.229465	−	0.973317i	$-0.426302\pi$
$907$	13.8214	0.458931	0.229465	+	0.973317i	$0.426302\pi$
$908$	60.8289	2.01868
$909$	39.0769	1.29610
$910$	126.431	4.19115
$911$	−42.3017	−1.40152	−0.700759	−	0.713398i	$-0.747155\pi$
$911$	−42.3017	−1.40152	−0.700759	+	0.713398i	$0.747155\pi$
$912$	−35.2632	−1.16768
$913$	−6.01146	−0.198950
$914$	38.4484	1.27176
$915$	15.5037	0.512537
$916$	18.2548	0.603157
$917$	−65.9529	−2.17796
$918$	−4.66246	−0.153884
$919$	−47.5567	−1.56875	−0.784376	−	0.620286i	$-0.787016\pi$
$919$	−47.5567	−1.56875	−0.784376	+	0.620286i	$0.787016\pi$
$920$	−180.817	−5.96136
$921$	−4.01954	−0.132448
$922$	16.0144	0.527406
$923$	−3.73900	−0.123071
$924$	19.5757	0.643994
$925$	69.9670	2.30050
$926$	36.4804	1.19882
$927$	−34.0401	−1.11802
$928$	119.650	3.92771
$929$	−40.6423	−1.33343	−0.666716	−	0.745312i	$-0.732301\pi$
$929$	−40.6423	−1.33343	−0.666716	+	0.745312i	$0.732301\pi$
$930$	36.6750	1.20262
$931$	−30.2335	−0.990863
$932$	−91.3436	−2.99206
$933$	11.9647	0.391705
$934$	37.7880	1.23646
$935$	2.21046	0.0722897
$936$	80.2852	2.62420
$937$	−36.6631	−1.19773	−0.598866	−	0.800849i	$-0.704382\pi$
$937$	−36.6631	−1.19773	−0.598866	+	0.800849i	$0.704382\pi$
$938$	45.4909	1.48533
$939$	−22.4017	−0.731051
$940$	−202.619	−6.60869
$941$	−40.8944	−1.33312	−0.666560	−	0.745452i	$-0.732234\pi$
$941$	−40.8944	−1.33312	−0.666560	+	0.745452i	$0.732234\pi$
$942$	−21.6182	−0.704359
$943$	−49.6355	−1.61635
$944$	102.757	3.34446
$945$	48.0572	1.56330
$946$	36.6918	1.19295
$947$	6.80385	0.221095	0.110548	−	0.993871i	$-0.464740\pi$
$947$	6.80385	0.221095	0.110548	+	0.993871i	$0.464740\pi$
$948$	−40.1003	−1.30240
$949$	−28.8084	−0.935161
$950$	67.4524	2.18844
$951$	−7.37316	−0.239091
$952$	14.7232	0.477183
$953$	−5.91109	−0.191479	−0.0957395	−	0.995406i	$-0.530522\pi$
$953$	−5.91109	−0.191479	−0.0957395	+	0.995406i	$0.530522\pi$
$954$	−16.0941	−0.521066
$955$	−11.3692	−0.367897
$956$	−49.3590	−1.59638
$957$	−7.34348	−0.237381
$958$	39.8427	1.28726
$959$	−30.6454	−0.989593
$960$	−43.0604	−1.38977
$961$	4.53855	0.146405
$962$	−114.613	−3.69528
$963$	−45.1277	−1.45422
$964$	59.4498	1.91475
$965$	72.9951	2.34979
$966$	44.5769	1.43424
$967$	−55.9694	−1.79986	−0.899928	−	0.436038i	$-0.856381\pi$
$967$	−55.9694	−1.79986	−0.899928	+	0.436038i	$0.856381\pi$
$968$	75.6523	2.43156
$969$	1.29765	0.0416865
$970$	−84.7987	−2.72272
$971$	−30.9489	−0.993197	−0.496599	−	0.867980i	$-0.665418\pi$
$971$	−30.9489	−0.993197	−0.496599	+	0.867980i	$0.665418\pi$
$972$	76.7518	2.46182
$973$	42.3860	1.35883
$974$	86.4111	2.76879
$975$	15.7492	0.504379
$976$	−83.8767	−2.68483
$977$	−41.9756	−1.34292	−0.671460	−	0.741041i	$-0.734332\pi$
$977$	−41.9756	−1.34292	−0.671460	+	0.741041i	$0.734332\pi$
$978$	−32.8610	−1.05078
$979$	14.9565	0.478011
$980$	−126.616	−4.04460
$981$	−13.5838	−0.433697
$982$	−19.2707	−0.614954
$983$	−24.4535	−0.779944	−0.389972	−	0.920827i	$-0.627515\pi$
$983$	−24.4535	−0.779944	−0.389972	+	0.920827i	$0.627515\pi$
$984$	−45.5830	−1.45313
$985$	−24.9670	−0.795515
$986$	−9.00293	−0.286712
$987$	30.6446	0.975429
$988$	−79.6918	−2.53533
$989$	60.2611	1.91619
$990$	−32.6985	−1.03923
$991$	−13.3971	−0.425574	−0.212787	−	0.977099i	$-0.568254\pi$
$991$	−13.3971	−0.425574	−0.212787	+	0.977099i	$0.568254\pi$
$992$	−97.0378	−3.08095
$993$	7.78021	0.246898
$994$	10.1430	0.321718
$995$	61.2805	1.94272
$996$	−14.7793	−0.468301
$997$	−31.6661	−1.00287	−0.501437	−	0.865194i	$-0.667195\pi$
$997$	−31.6661	−1.00287	−0.501437	+	0.865194i	$0.667195\pi$
$998$	92.6011	2.93124
$999$	−43.5651	−1.37834

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.9	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.9	✓	158	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67852 q^{2} +0.688962 q^{3} +5.17445 q^{4} -3.33373 q^{5} -1.84540 q^{6} +3.78681 q^{7} -8.50280 q^{8} -2.52533 q^{9} +O(q^{10})\)	\(q-2.67852 q^{2} +0.688962 q^{3} +5.17445 q^{4} -3.33373 q^{5} -1.84540 q^{6} +3.78681 q^{7} -8.50280 q^{8} -2.52533 q^{9} +8.92945 q^{10} +1.45005 q^{11} +3.56500 q^{12} +3.73900 q^{13} -10.1430 q^{14} -2.29681 q^{15} +12.4260 q^{16} -0.457265 q^{17} +6.76414 q^{18} -4.11903 q^{19} -17.2502 q^{20} +2.60897 q^{21} -3.88399 q^{22} -6.37891 q^{23} -5.85811 q^{24} +6.11376 q^{25} -10.0150 q^{26} -3.80674 q^{27} +19.5947 q^{28} -7.35059 q^{29} +6.15205 q^{30} +5.96142 q^{31} -16.2776 q^{32} +0.999033 q^{33} +1.22479 q^{34} -12.6242 q^{35} -13.0672 q^{36} +11.4442 q^{37} +11.0329 q^{38} +2.57603 q^{39} +28.3461 q^{40} +7.78118 q^{41} -6.98817 q^{42} -9.44692 q^{43} +7.50323 q^{44} +8.41877 q^{45} +17.0860 q^{46} +11.7459 q^{47} +8.56104 q^{48} +7.33996 q^{49} -16.3758 q^{50} -0.315038 q^{51} +19.3472 q^{52} -2.37933 q^{53} +10.1964 q^{54} -4.83409 q^{55} -32.1985 q^{56} -2.83785 q^{57} +19.6887 q^{58} +8.26952 q^{59} -11.8847 q^{60} -6.75010 q^{61} -15.9678 q^{62} -9.56296 q^{63} +18.7479 q^{64} -12.4648 q^{65} -2.67592 q^{66} -4.48494 q^{67} -2.36609 q^{68} -4.39483 q^{69} +33.8142 q^{70} -1.00000 q^{71} +21.4724 q^{72} -7.70485 q^{73} -30.6534 q^{74} +4.21215 q^{75} -21.3137 q^{76} +5.49109 q^{77} -6.89993 q^{78} -11.2483 q^{79} -41.4249 q^{80} +4.95329 q^{81} -20.8420 q^{82} -4.14568 q^{83} +13.5000 q^{84} +1.52440 q^{85} +25.3037 q^{86} -5.06428 q^{87} -12.3295 q^{88} +10.3144 q^{89} -22.5498 q^{90} +14.1589 q^{91} -33.0073 q^{92} +4.10719 q^{93} -31.4615 q^{94} +13.7317 q^{95} -11.2147 q^{96} -9.49652 q^{97} -19.6602 q^{98} -3.66187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

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