LMFDB - Embedded newform 8023.2.a.e.1.12

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:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-2.44664 q^{2} -2.78774 q^{3} +3.98604 q^{4} -0.315327 q^{5} +6.82060 q^{6} -4.26739 q^{7} -4.85913 q^{8} +4.77151 q^{9} +O(q^{10})$	\(q-2.44664 q^{2} -2.78774 q^{3} +3.98604 q^{4} -0.315327 q^{5} +6.82060 q^{6} -4.26739 q^{7} -4.85913 q^{8} +4.77151 q^{9} +0.771492 q^{10} -4.54521 q^{11} -11.1121 q^{12} +6.49457 q^{13} +10.4408 q^{14} +0.879051 q^{15} +3.91644 q^{16} +0.800118 q^{17} -11.6742 q^{18} +1.02466 q^{19} -1.25691 q^{20} +11.8964 q^{21} +11.1205 q^{22} -0.107821 q^{23} +13.5460 q^{24} -4.90057 q^{25} -15.8899 q^{26} -4.93853 q^{27} -17.0100 q^{28} +5.30590 q^{29} -2.15072 q^{30} -3.46331 q^{31} +0.136130 q^{32} +12.6709 q^{33} -1.95760 q^{34} +1.34562 q^{35} +19.0195 q^{36} +7.43821 q^{37} -2.50698 q^{38} -18.1052 q^{39} +1.53221 q^{40} +2.42286 q^{41} -29.1061 q^{42} -1.36564 q^{43} -18.1174 q^{44} -1.50459 q^{45} +0.263798 q^{46} +6.81845 q^{47} -10.9180 q^{48} +11.2106 q^{49} +11.9899 q^{50} -2.23052 q^{51} +25.8876 q^{52} +5.16392 q^{53} +12.0828 q^{54} +1.43323 q^{55} +20.7358 q^{56} -2.85650 q^{57} -12.9816 q^{58} +11.9728 q^{59} +3.50393 q^{60} -2.69663 q^{61} +8.47346 q^{62} -20.3619 q^{63} -8.16595 q^{64} -2.04791 q^{65} -31.0011 q^{66} +1.78579 q^{67} +3.18930 q^{68} +0.300576 q^{69} -3.29225 q^{70} -1.00000 q^{71} -23.1854 q^{72} +4.30976 q^{73} -18.1986 q^{74} +13.6615 q^{75} +4.08435 q^{76} +19.3962 q^{77} +44.2968 q^{78} -5.27895 q^{79} -1.23496 q^{80} -0.547192 q^{81} -5.92785 q^{82} +2.76412 q^{83} +47.4195 q^{84} -0.252299 q^{85} +3.34123 q^{86} -14.7915 q^{87} +22.0858 q^{88} -15.0687 q^{89} +3.68118 q^{90} -27.7148 q^{91} -0.429777 q^{92} +9.65481 q^{93} -16.6823 q^{94} -0.323104 q^{95} -0.379496 q^{96} -3.32618 q^{97} -27.4283 q^{98} -21.6875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) $ 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * 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 $

$2$	−2.44664	−1.73003	−0.865017	−	0.501742i	$-0.832693\pi$
$2$	−2.44664	−1.73003	−0.865017	+	0.501742i	$0.832693\pi$
$3$	−2.78774	−1.60950	−0.804752	−	0.593611i	$-0.797702\pi$
$3$	−2.78774	−1.60950	−0.804752	+	0.593611i	$0.797702\pi$
$4$	3.98604	1.99302
$5$	−0.315327	−0.141019	−0.0705093	−	0.997511i	$-0.522462\pi$
$5$	−0.315327	−0.141019	−0.0705093	+	0.997511i	$0.522462\pi$
$6$	6.82060	2.78450
$7$	−4.26739	−1.61292	−0.806460	−	0.591288i	$-0.798620\pi$
$7$	−4.26739	−1.61292	−0.806460	+	0.591288i	$0.798620\pi$
$8$	−4.85913	−1.71796
$9$	4.77151	1.59050
$10$	0.771492	0.243967
$11$	−4.54521	−1.37043	−0.685216	−	0.728340i	$-0.740292\pi$
$11$	−4.54521	−1.37043	−0.685216	+	0.728340i	$0.740292\pi$
$12$	−11.1121	−3.20778
$13$	6.49457	1.80127	0.900634	−	0.434578i	$-0.143102\pi$
$13$	6.49457	1.80127	0.900634	+	0.434578i	$0.143102\pi$
$14$	10.4408	2.79041
$15$	0.879051	0.226970
$16$	3.91644	0.979111
$17$	0.800118	0.194057	0.0970285	−	0.995282i	$-0.469066\pi$
$17$	0.800118	0.194057	0.0970285	+	0.995282i	$0.469066\pi$
$18$	−11.6742	−2.75163
$19$	1.02466	0.235074	0.117537	−	0.993069i	$-0.462500\pi$
$19$	1.02466	0.235074	0.117537	+	0.993069i	$0.462500\pi$
$20$	−1.25691	−0.281053
$21$	11.8964	2.59600
$22$	11.1205	2.37090
$23$	−0.107821	−0.0224821	−0.0112411	−	0.999937i	$-0.503578\pi$
$23$	−0.107821	−0.0224821	−0.0112411	+	0.999937i	$0.503578\pi$
$24$	13.5460	2.76507
$25$	−4.90057	−0.980114
$26$	−15.8899	−3.11626
$27$	−4.93853	−0.950420
$28$	−17.0100	−3.21458
$29$	5.30590	0.985281	0.492641	−	0.870233i	$-0.336032\pi$
$29$	5.30590	0.985281	0.492641	+	0.870233i	$0.336032\pi$
$30$	−2.15072	−0.392666
$31$	−3.46331	−0.622028	−0.311014	−	0.950405i	$-0.600669\pi$
$31$	−3.46331	−0.622028	−0.311014	+	0.950405i	$0.600669\pi$
$32$	0.136130	0.0240646
$33$	12.6709	2.20572
$34$	−1.95760	−0.335725
$35$	1.34562	0.227452
$36$	19.0195	3.16991
$37$	7.43821	1.22283	0.611417	−	0.791308i	$-0.290600\pi$
$37$	7.43821	1.22283	0.611417	+	0.791308i	$0.290600\pi$
$38$	−2.50698	−0.406686
$39$	−18.1052	−2.89915
$40$	1.53221	0.242264
$41$	2.42286	0.378387	0.189193	−	0.981940i	$-0.439413\pi$
$41$	2.42286	0.378387	0.189193	+	0.981940i	$0.439413\pi$
$42$	−29.1061	−4.49118
$43$	−1.36564	−0.208259	−0.104129	−	0.994564i	$-0.533206\pi$
$43$	−1.36564	−0.208259	−0.104129	+	0.994564i	$0.533206\pi$
$44$	−18.1174	−2.73130
$45$	−1.50459	−0.224291
$46$	0.263798	0.0388949
$47$	6.81845	0.994573	0.497287	−	0.867586i	$-0.334330\pi$
$47$	6.81845	0.994573	0.497287	+	0.867586i	$0.334330\pi$
$48$	−10.9180	−1.57588
$49$	11.2106	1.60151
$50$	11.9899	1.69563
$51$	−2.23052	−0.312336
$52$	25.8876	3.58997
$53$	5.16392	0.709319	0.354659	−	0.934996i	$-0.384597\pi$
$53$	5.16392	0.709319	0.354659	+	0.934996i	$0.384597\pi$
$54$	12.0828	1.64426
$55$	1.43323	0.193257
$56$	20.7358	2.77093
$57$	−2.85650	−0.378353
$58$	−12.9816	−1.70457
$59$	11.9728	1.55872	0.779360	−	0.626576i	$-0.215544\pi$
$59$	11.9728	1.55872	0.779360	+	0.626576i	$0.215544\pi$
$60$	3.50393	0.452356
$61$	−2.69663	−0.345268	−0.172634	−	0.984986i	$-0.555228\pi$
$61$	−2.69663	−0.345268	−0.172634	+	0.984986i	$0.555228\pi$
$62$	8.47346	1.07613
$63$	−20.3619	−2.56536
$64$	−8.16595	−1.02074
$65$	−2.04791	−0.254012
$66$	−31.0011	−3.81597
$67$	1.78579	0.218168	0.109084	−	0.994033i	$-0.465208\pi$
$67$	1.78579	0.218168	0.109084	+	0.994033i	$0.465208\pi$
$68$	3.18930	0.386760
$69$	0.300576	0.0361851
$70$	−3.29225	−0.393499
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−23.1854	−2.73242
$73$	4.30976	0.504419	0.252209	−	0.967673i	$-0.418843\pi$
$73$	4.30976	0.504419	0.252209	+	0.967673i	$0.418843\pi$
$74$	−18.1986	−2.11555
$75$	13.6615	1.57750
$76$	4.08435	0.468507
$77$	19.3962	2.21040
$78$	44.2968	5.01563
$79$	−5.27895	−0.593928	−0.296964	−	0.954889i	$-0.595974\pi$
$79$	−5.27895	−0.593928	−0.296964	+	0.954889i	$0.595974\pi$
$80$	−1.23496	−0.138073
$81$	−0.547192	−0.0607991
$82$	−5.92785	−0.654622
$83$	2.76412	0.303402	0.151701	−	0.988426i	$-0.451525\pi$
$83$	2.76412	0.303402	0.151701	+	0.988426i	$0.451525\pi$
$84$	47.4195	5.17389
$85$	−0.252299	−0.0273656
$86$	3.34123	0.360295
$87$	−14.7915	−1.58581
$88$	22.0858	2.35435
$89$	−15.0687	−1.59728	−0.798638	−	0.601811i	$-0.794446\pi$
$89$	−15.0687	−1.59728	−0.798638	+	0.601811i	$0.794446\pi$
$90$	3.68118	0.388031
$91$	−27.7148	−2.90530
$92$	−0.429777	−0.0448073
$93$	9.65481	1.00116
$94$	−16.6823	−1.72065
$95$	−0.323104	−0.0331498
$96$	−0.379496	−0.0387321
$97$	−3.32618	−0.337722	−0.168861	−	0.985640i	$-0.554009\pi$
$97$	−3.32618	−0.337722	−0.168861	+	0.985640i	$0.554009\pi$
$98$	−27.4283	−2.77067
$99$	−21.6875	−2.17968
$100$	−19.5339	−1.95339
$101$	13.9513	1.38821	0.694103	−	0.719876i	$-0.255801\pi$
$101$	13.9513	1.38821	0.694103	+	0.719876i	$0.255801\pi$
$102$	5.45728	0.540352
$103$	5.73063	0.564656	0.282328	−	0.959318i	$-0.408893\pi$
$103$	5.73063	0.564656	0.282328	+	0.959318i	$0.408893\pi$
$104$	−31.5579	−3.09451
$105$	−3.75125	−0.366085
$106$	−12.6342	−1.22715
$107$	7.45939	0.721126	0.360563	−	0.932735i	$-0.382585\pi$
$107$	7.45939	0.721126	0.360563	+	0.932735i	$0.382585\pi$
$108$	−19.6852	−1.89421
$109$	−14.4098	−1.38021	−0.690106	−	0.723709i	$-0.742436\pi$
$109$	−14.4098	−1.38021	−0.690106	+	0.723709i	$0.742436\pi$
$110$	−3.50659	−0.334340
$111$	−20.7358	−1.96816
$112$	−16.7130	−1.57923
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	6.98882	0.654563
$115$	0.0339987	0.00317040
$116$	21.1495	1.96369
$117$	30.9889	2.86493
$118$	−29.2930	−2.69664
$119$	−3.41441	−0.312999
$120$	−4.27142	−0.389926
$121$	9.65895	0.878086
$122$	6.59767	0.597325
$123$	−6.75430	−0.609015
$124$	−13.8049	−1.23972
$125$	3.12192	0.279233
$126$	49.8182	4.43816
$127$	8.68103	0.770316	0.385158	−	0.922851i	$-0.374147\pi$
$127$	8.68103	0.770316	0.385158	+	0.922851i	$0.374147\pi$
$128$	19.7069	1.74186
$129$	3.80706	0.335193
$130$	5.01050	0.439450
$131$	−1.67797	−0.146605	−0.0733025	−	0.997310i	$-0.523354\pi$
$131$	−1.67797	−0.146605	−0.0733025	+	0.997310i	$0.523354\pi$
$132$	50.5067	4.39604
$133$	−4.37264	−0.379156
$134$	−4.36917	−0.377439
$135$	1.55725	0.134027
$136$	−3.88787	−0.333382
$137$	4.23704	0.361995	0.180997	−	0.983484i	$-0.442067\pi$
$137$	4.23704	0.361995	0.180997	+	0.983484i	$0.442067\pi$
$138$	−0.735401	−0.0626015
$139$	−16.6535	−1.41253	−0.706267	−	0.707946i	$-0.749622\pi$
$139$	−16.6535	−1.41253	−0.706267	+	0.707946i	$0.749622\pi$
$140$	5.36371	0.453316
$141$	−19.0081	−1.60077
$142$	2.44664	0.205317
$143$	−29.5192	−2.46852
$144$	18.6874	1.55728
$145$	−1.67309	−0.138943
$146$	−10.5444	−0.872662
$147$	−31.2522	−2.57764
$148$	29.6490	2.43714
$149$	18.4558	1.51196	0.755979	−	0.654595i	$-0.227161\pi$
$149$	18.4558	1.51196	0.755979	+	0.654595i	$0.227161\pi$
$150$	−33.4248	−2.72913
$151$	8.08572	0.658007	0.329003	−	0.944329i	$-0.393287\pi$
$151$	8.08572	0.658007	0.329003	+	0.944329i	$0.393287\pi$
$152$	−4.97897	−0.403848
$153$	3.81777	0.308649
$154$	−47.4554	−3.82407
$155$	1.09207	0.0877175
$156$	−72.1680	−5.77807
$157$	15.9398	1.27214	0.636068	−	0.771633i	$-0.280560\pi$
$157$	15.9398	1.27214	0.636068	+	0.771633i	$0.280560\pi$
$158$	12.9157	1.02752
$159$	−14.3957	−1.14165
$160$	−0.0429255	−0.00339356
$161$	0.460112	0.0362619
$162$	1.33878	0.105185
$163$	18.2458	1.42912	0.714561	−	0.699573i	$-0.246627\pi$
$163$	18.2458	1.42912	0.714561	+	0.699573i	$0.246627\pi$
$164$	9.65760	0.754132
$165$	−3.99547	−0.311047
$166$	−6.76281	−0.524896
$167$	−6.50935	−0.503709	−0.251854	−	0.967765i	$-0.581040\pi$
$167$	−6.50935	−0.503709	−0.251854	+	0.967765i	$0.581040\pi$
$168$	−57.8060	−4.45983
$169$	29.1794	2.24457
$170$	0.617284	0.0473435
$171$	4.88920	0.373886
$172$	−5.44351	−0.415064
$173$	18.3269	1.39337	0.696685	−	0.717377i	$-0.254658\pi$
$173$	18.3269	1.39337	0.696685	+	0.717377i	$0.254658\pi$
$174$	36.1894	2.74351
$175$	20.9126	1.58085
$176$	−17.8011	−1.34181
$177$	−33.3770	−2.50877
$178$	36.8676	2.76334
$179$	−1.21192	−0.0905832	−0.0452916	−	0.998974i	$-0.514422\pi$
$179$	−1.21192	−0.0905832	−0.0452916	+	0.998974i	$0.514422\pi$
$180$	−5.99735	−0.447016
$181$	−16.1498	−1.20041	−0.600204	−	0.799847i	$-0.704914\pi$
$181$	−16.1498	−1.20041	−0.600204	+	0.799847i	$0.704914\pi$
$182$	67.8082	5.02628
$183$	7.51750	0.555710
$184$	0.523913	0.0386234
$185$	−2.34547	−0.172442
$186$	−23.6218	−1.73204
$187$	−3.63670	−0.265942
$188$	27.1786	1.98221
$189$	21.0746	1.53295
$190$	0.790519	0.0573503
$191$	21.4680	1.55337	0.776687	−	0.629887i	$-0.216899\pi$
$191$	21.4680	1.55337	0.776687	+	0.629887i	$0.216899\pi$
$192$	22.7646	1.64289
$193$	−22.2868	−1.60424	−0.802121	−	0.597162i	$-0.796295\pi$
$193$	−22.2868	−1.60424	−0.802121	+	0.597162i	$0.796295\pi$
$194$	8.13796	0.584271
$195$	5.70906	0.408834
$196$	44.6859	3.19185
$197$	−0.819456	−0.0583838	−0.0291919	−	0.999574i	$-0.509293\pi$
$197$	−0.819456	−0.0583838	−0.0291919	+	0.999574i	$0.509293\pi$
$198$	53.0616	3.77092
$199$	−13.1318	−0.930886	−0.465443	−	0.885078i	$-0.654105\pi$
$199$	−13.1318	−0.930886	−0.465443	+	0.885078i	$0.654105\pi$
$200$	23.8125	1.68380
$201$	−4.97831	−0.351143
$202$	−34.1338	−2.40164
$203$	−22.6423	−1.58918
$204$	−8.89096	−0.622491
$205$	−0.763992	−0.0533595
$206$	−14.0208	−0.976874
$207$	−0.514467	−0.0357579
$208$	25.4356	1.76364
$209$	−4.65731	−0.322153
$210$	9.17796	0.633339
$211$	−17.2874	−1.19012	−0.595059	−	0.803682i	$-0.702871\pi$
$211$	−17.2874	−1.19012	−0.595059	+	0.803682i	$0.702871\pi$
$212$	20.5836	1.41369
$213$	2.78774	0.191013
$214$	−18.2504	−1.24757
$215$	0.430624	0.0293683
$216$	23.9969	1.63278
$217$	14.7793	1.00328
$218$	35.2556	2.38781
$219$	−12.0145	−0.811865
$220$	5.71291	0.385164
$221$	5.19642	0.349549
$222$	50.7331	3.40498
$223$	−15.2054	−1.01823	−0.509116	−	0.860698i	$-0.670027\pi$
$223$	−15.2054	−1.01823	−0.509116	+	0.860698i	$0.670027\pi$
$224$	−0.580919	−0.0388143
$225$	−23.3831	−1.55888
$226$	−2.44664	−0.162748
$227$	−12.2684	−0.814283	−0.407141	−	0.913365i	$-0.633474\pi$
$227$	−12.2684	−0.814283	−0.407141	+	0.913365i	$0.633474\pi$
$228$	−11.3861	−0.754065
$229$	8.82904	0.583439	0.291720	−	0.956504i	$-0.405773\pi$
$229$	8.82904	0.583439	0.291720	+	0.956504i	$0.405773\pi$
$230$	−0.0831826	−0.00548490
$231$	−54.0716	−3.55765
$232$	−25.7820	−1.69267
$233$	−25.2388	−1.65345	−0.826724	−	0.562608i	$-0.809798\pi$
$233$	−25.2388	−1.65345	−0.826724	+	0.562608i	$0.809798\pi$
$234$	−75.8187	−4.95642
$235$	−2.15004	−0.140253
$236$	47.7239	3.10656
$237$	14.7163	0.955929
$238$	8.35383	0.541498
$239$	−6.06919	−0.392583	−0.196292	−	0.980546i	$-0.562890\pi$
$239$	−6.06919	−0.392583	−0.196292	+	0.980546i	$0.562890\pi$
$240$	3.44275	0.222229
$241$	−12.7397	−0.820634	−0.410317	−	0.911943i	$-0.634582\pi$
$241$	−12.7397	−0.820634	−0.410317	+	0.911943i	$0.634582\pi$
$242$	−23.6320	−1.51912
$243$	16.3410	1.04828
$244$	−10.7489	−0.688125
$245$	−3.53500	−0.225843
$246$	16.5253	1.05362
$247$	6.65475	0.423431
$248$	16.8286	1.06862
$249$	−7.70566	−0.488327
$250$	−7.63821	−0.483083
$251$	−5.37407	−0.339209	−0.169604	−	0.985512i	$-0.554249\pi$
$251$	−5.37407	−0.339209	−0.169604	+	0.985512i	$0.554249\pi$
$252$	−81.1634	−5.11281
$253$	0.490067	0.0308102
$254$	−21.2393	−1.33267
$255$	0.703344	0.0440451
$256$	−31.8837	−1.99273
$257$	−20.5965	−1.28477	−0.642387	−	0.766380i	$-0.722056\pi$
$257$	−20.5965	−1.28477	−0.642387	+	0.766380i	$0.722056\pi$
$258$	−9.31450	−0.579896
$259$	−31.7417	−1.97234
$260$	−8.16307	−0.506252
$261$	25.3172	1.56709
$262$	4.10539	0.253632
$263$	8.65092	0.533439	0.266719	−	0.963774i	$-0.414060\pi$
$263$	8.65092	0.533439	0.266719	+	0.963774i	$0.414060\pi$
$264$	−61.5694	−3.78934
$265$	−1.62832	−0.100027
$266$	10.6983	0.655952
$267$	42.0076	2.57082
$268$	7.11822	0.434814
$269$	−10.1998	−0.621895	−0.310948	−	0.950427i	$-0.600646\pi$
$269$	−10.1998	−0.621895	−0.310948	+	0.950427i	$0.600646\pi$
$270$	−3.81003	−0.231871
$271$	−7.25431	−0.440668	−0.220334	−	0.975424i	$-0.570715\pi$
$271$	−7.25431	−0.440668	−0.220334	+	0.975424i	$0.570715\pi$
$272$	3.13362	0.190003
$273$	77.2618	4.67610
$274$	−10.3665	−0.626263
$275$	22.2741	1.34318
$276$	1.19811	0.0721176
$277$	9.71207	0.583542	0.291771	−	0.956488i	$-0.405756\pi$
$277$	9.71207	0.583542	0.291771	+	0.956488i	$0.405756\pi$
$278$	40.7451	2.44373
$279$	−16.5252	−0.989339
$280$	−6.53855	−0.390753
$281$	14.3047	0.853346	0.426673	−	0.904406i	$-0.359686\pi$
$281$	14.3047	0.853346	0.426673	+	0.904406i	$0.359686\pi$
$282$	46.5059	2.76939
$283$	−1.99551	−0.118621	−0.0593103	−	0.998240i	$-0.518890\pi$
$283$	−1.99551	−0.118621	−0.0593103	+	0.998240i	$0.518890\pi$
$284$	−3.98604	−0.236528
$285$	0.900732	0.0533547
$286$	72.2228	4.27062
$287$	−10.3393	−0.610307
$288$	0.649546	0.0382749
$289$	−16.3598	−0.962342
$290$	4.09346	0.240376
$291$	9.27254	0.543566
$292$	17.1789	1.00532
$293$	9.19780	0.537341	0.268671	−	0.963232i	$-0.413416\pi$
$293$	9.19780	0.537341	0.268671	+	0.963232i	$0.413416\pi$
$294$	76.4629	4.45941
$295$	−3.77534	−0.219809
$296$	−36.1432	−2.10078
$297$	22.4467	1.30249
$298$	−45.1547	−2.61574
$299$	−0.700247	−0.0404964
$300$	54.4554	3.14399
$301$	5.82772	0.335904
$302$	−19.7828	−1.13837
$303$	−38.8926	−2.23432
$304$	4.01304	0.230163
$305$	0.850319	0.0486891
$306$	−9.34071	−0.533973
$307$	−2.26011	−0.128991	−0.0644957	−	0.997918i	$-0.520544\pi$
$307$	−2.26011	−0.128991	−0.0644957	+	0.997918i	$0.520544\pi$
$308$	77.3140	4.40537
$309$	−15.9755	−0.908816
$310$	−2.67191	−0.151754
$311$	−25.8709	−1.46701	−0.733503	−	0.679686i	$-0.762116\pi$
$311$	−25.8709	−1.46701	−0.733503	+	0.679686i	$0.762116\pi$
$312$	87.9754	4.98062
$313$	2.89013	0.163360	0.0816799	−	0.996659i	$-0.473971\pi$
$313$	2.89013	0.163360	0.0816799	+	0.996659i	$0.473971\pi$
$314$	−38.9990	−2.20084
$315$	6.42066	0.361763
$316$	−21.0421	−1.18371
$317$	−19.7421	−1.10883	−0.554413	−	0.832242i	$-0.687057\pi$
$317$	−19.7421	−1.10883	−0.554413	+	0.832242i	$0.687057\pi$
$318$	35.2210	1.97510
$319$	−24.1164	−1.35026
$320$	2.57494	0.143944
$321$	−20.7949	−1.16066
$322$	−1.12573	−0.0627343
$323$	0.819851	0.0456178
$324$	−2.18113	−0.121174
$325$	−31.8271	−1.76545
$326$	−44.6409	−2.47243
$327$	40.1709	2.22146
$328$	−11.7730	−0.650053
$329$	−29.0970	−1.60417
$330$	9.77548	0.538123
$331$	8.08838	0.444577	0.222289	−	0.974981i	$-0.428647\pi$
$331$	8.08838	0.444577	0.222289	+	0.974981i	$0.428647\pi$
$332$	11.0179	0.604686
$333$	35.4915	1.94492
$334$	15.9260	0.871434
$335$	−0.563107	−0.0307658
$336$	46.5915	2.54177
$337$	−23.3109	−1.26982	−0.634912	−	0.772584i	$-0.718964\pi$
$337$	−23.3109	−1.26982	−0.634912	+	0.772584i	$0.718964\pi$
$338$	−71.3914	−3.88318
$339$	−2.78774	−0.151409
$340$	−1.00567	−0.0545403
$341$	15.7415	0.852448
$342$	−11.9621	−0.646836
$343$	−17.9682	−0.970191
$344$	6.63583	0.357780
$345$	−0.0947797	−0.00510277
$346$	−44.8393	−2.41058
$347$	−17.1364	−0.919930	−0.459965	−	0.887937i	$-0.652138\pi$
$347$	−17.1364	−0.919930	−0.459965	+	0.887937i	$0.652138\pi$
$348$	−58.9595	−3.16056
$349$	−2.86962	−0.153607	−0.0768035	−	0.997046i	$-0.524471\pi$
$349$	−2.86962	−0.153607	−0.0768035	+	0.997046i	$0.524471\pi$
$350$	−51.1656	−2.73492
$351$	−32.0736	−1.71196
$352$	−0.618740	−0.0329789
$353$	−6.48296	−0.345053	−0.172526	−	0.985005i	$-0.555193\pi$
$353$	−6.48296	−0.345053	−0.172526	+	0.985005i	$0.555193\pi$
$354$	81.6614	4.34025
$355$	0.315327	0.0167358
$356$	−60.0644	−3.18340
$357$	9.51850	0.503773
$358$	2.96513	0.156712
$359$	6.56063	0.346257	0.173128	−	0.984899i	$-0.444612\pi$
$359$	6.56063	0.346257	0.173128	+	0.984899i	$0.444612\pi$
$360$	7.31098	0.385323
$361$	−17.9501	−0.944740
$362$	39.5128	2.07675
$363$	−26.9267	−1.41328
$364$	−110.472	−5.79033
$365$	−1.35898	−0.0711324
$366$	−18.3926	−0.961397
$367$	15.8517	0.827454	0.413727	−	0.910401i	$-0.364227\pi$
$367$	15.8517	0.827454	0.413727	+	0.910401i	$0.364227\pi$
$368$	−0.422273	−0.0220125
$369$	11.5607	0.601826
$370$	5.73852	0.298331
$371$	−22.0364	−1.14407
$372$	38.4845	1.99533
$373$	3.73837	0.193565	0.0967827	−	0.995306i	$-0.469145\pi$
$373$	3.73837	0.193565	0.0967827	+	0.995306i	$0.469145\pi$
$374$	8.89770	0.460089
$375$	−8.70311	−0.449427
$376$	−33.1317	−1.70864
$377$	34.4595	1.77476
$378$	−51.5620	−2.65206
$379$	−1.52067	−0.0781115	−0.0390558	−	0.999237i	$-0.512435\pi$
$379$	−1.52067	−0.0781115	−0.0390558	+	0.999237i	$0.512435\pi$
$380$	−1.28791	−0.0660682
$381$	−24.2005	−1.23983
$382$	−52.5246	−2.68739
$383$	8.73449	0.446312	0.223156	−	0.974783i	$-0.428364\pi$
$383$	8.73449	0.446312	0.223156	+	0.974783i	$0.428364\pi$
$384$	−54.9377	−2.80353
$385$	−6.11614	−0.311707
$386$	54.5278	2.77539
$387$	−6.51618	−0.331236
$388$	−13.2583	−0.673088
$389$	−7.99985	−0.405609	−0.202804	−	0.979219i	$-0.565006\pi$
$389$	−7.99985	−0.405609	−0.202804	+	0.979219i	$0.565006\pi$
$390$	−13.9680	−0.707297
$391$	−0.0862691	−0.00436282
$392$	−54.4736	−2.75133
$393$	4.67775	0.235961
$394$	2.00491	0.101006
$395$	1.66459	0.0837548
$396$	−86.4474	−4.34415
$397$	14.3619	0.720804	0.360402	−	0.932797i	$-0.382639\pi$
$397$	14.3619	0.720804	0.360402	+	0.932797i	$0.382639\pi$
$398$	32.1287	1.61047
$399$	12.1898	0.610253
$400$	−19.1928	−0.959640
$401$	−7.53357	−0.376209	−0.188104	−	0.982149i	$-0.560234\pi$
$401$	−7.53357	−0.376209	−0.188104	+	0.982149i	$0.560234\pi$
$402$	12.1801	0.607490
$403$	−22.4927	−1.12044
$404$	55.6104	2.76672
$405$	0.172544	0.00857380
$406$	55.3976	2.74934
$407$	−33.8083	−1.67581
$408$	10.8384	0.536580
$409$	−36.6911	−1.81426	−0.907129	−	0.420853i	$-0.861731\pi$
$409$	−36.6911	−1.81426	−0.907129	+	0.420853i	$0.861731\pi$
$410$	1.86921	0.0923139
$411$	−11.8118	−0.582632
$412$	22.8425	1.12537
$413$	−51.0924	−2.51409
$414$	1.25872	0.0618625
$415$	−0.871603	−0.0427853
$416$	0.884106	0.0433468
$417$	46.4257	2.27348
$418$	11.3948	0.557336
$419$	6.33462	0.309466	0.154733	−	0.987956i	$-0.450548\pi$
$419$	6.33462	0.309466	0.154733	+	0.987956i	$0.450548\pi$
$420$	−14.9526	−0.729614
$421$	13.9938	0.682014	0.341007	−	0.940061i	$-0.389232\pi$
$421$	13.9938	0.682014	0.341007	+	0.940061i	$0.389232\pi$
$422$	42.2961	2.05894
$423$	32.5343	1.58187
$424$	−25.0921	−1.21858
$425$	−3.92103	−0.190198
$426$	−6.82060	−0.330459
$427$	11.5075	0.556889
$428$	29.7334	1.43722
$429$	82.2919	3.97309
$430$	−1.05358	−0.0508082
$431$	7.52545	0.362488	0.181244	−	0.983438i	$-0.441988\pi$
$431$	7.52545	0.362488	0.181244	+	0.983438i	$0.441988\pi$
$432$	−19.3415	−0.930567
$433$	7.67929	0.369043	0.184522	−	0.982828i	$-0.440926\pi$
$433$	7.67929	0.369043	0.184522	+	0.982828i	$0.440926\pi$
$434$	−36.1595	−1.73571
$435$	4.66416	0.223629
$436$	−57.4382	−2.75079
$437$	−0.110480	−0.00528496
$438$	29.3951	1.40455
$439$	25.3340	1.20912	0.604562	−	0.796558i	$-0.293348\pi$
$439$	25.3340	1.20912	0.604562	+	0.796558i	$0.293348\pi$
$440$	−6.96424	−0.332007
$441$	53.4915	2.54721
$442$	−12.7138	−0.604732
$443$	−39.4186	−1.87283	−0.936417	−	0.350890i	$-0.885879\pi$
$443$	−39.4186	−1.87283	−0.936417	+	0.350890i	$0.885879\pi$
$444$	−82.6539	−3.92258
$445$	4.75156	0.225246
$446$	37.2022	1.76158
$447$	−51.4501	−2.43350
$448$	34.8473	1.64638
$449$	26.0439	1.22909	0.614544	−	0.788882i	$-0.289340\pi$
$449$	26.0439	1.22909	0.614544	+	0.788882i	$0.289340\pi$
$450$	57.2101	2.69691
$451$	−11.0124	−0.518553
$452$	3.98604	0.187488
$453$	−22.5409	−1.05907
$454$	30.0164	1.40874
$455$	8.73924	0.409702
$456$	13.8801	0.649995
$457$	5.02611	0.235112	0.117556	−	0.993066i	$-0.462494\pi$
$457$	5.02611	0.235112	0.117556	+	0.993066i	$0.462494\pi$
$458$	−21.6015	−1.00937
$459$	−3.95140	−0.184436
$460$	0.135520	0.00631867
$461$	28.0477	1.30631	0.653156	−	0.757223i	$-0.273444\pi$
$461$	28.0477	1.30631	0.653156	+	0.757223i	$0.273444\pi$
$462$	132.294	6.15485
$463$	21.7362	1.01017	0.505083	−	0.863071i	$-0.331462\pi$
$463$	21.7362	1.01017	0.505083	+	0.863071i	$0.331462\pi$
$464$	20.7803	0.964699
$465$	−3.04442	−0.141182
$466$	61.7502	2.86052
$467$	−17.5965	−0.814270	−0.407135	−	0.913368i	$-0.633472\pi$
$467$	−17.5965	−0.814270	−0.407135	+	0.913368i	$0.633472\pi$
$468$	123.523	5.70986
$469$	−7.62064	−0.351888
$470$	5.26038	0.242643
$471$	−44.4361	−2.04751
$472$	−58.1771	−2.67782
$473$	6.20714	0.285404
$474$	−36.0056	−1.65379
$475$	−5.02143	−0.230399
$476$	−13.6100	−0.623813
$477$	24.6397	1.12817
$478$	14.8491	0.679183
$479$	−0.236164	−0.0107906	−0.00539530	−	0.999985i	$-0.501717\pi$
$479$	−0.236164	−0.0107906	−0.00539530	+	0.999985i	$0.501717\pi$
$480$	0.119665	0.00546195
$481$	48.3080	2.20265
$482$	31.1693	1.41972
$483$	−1.28267	−0.0583637
$484$	38.5010	1.75004
$485$	1.04883	0.0476251
$486$	−39.9806	−1.81356
$487$	3.50032	0.158614	0.0793072	−	0.996850i	$-0.474729\pi$
$487$	3.50032	0.158614	0.0793072	+	0.996850i	$0.474729\pi$
$488$	13.1032	0.593156
$489$	−50.8646	−2.30018
$490$	8.64887	0.390716
$491$	29.5327	1.33279	0.666396	−	0.745598i	$-0.267836\pi$
$491$	29.5327	1.33279	0.666396	+	0.745598i	$0.267836\pi$
$492$	−26.9229	−1.21378
$493$	4.24535	0.191201
$494$	−16.2818	−0.732551
$495$	6.83867	0.307375
$496$	−13.5638	−0.609035
$497$	4.26739	0.191418
$498$	18.8530	0.844822
$499$	14.4259	0.645794	0.322897	−	0.946434i	$-0.395343\pi$
$499$	14.4259	0.645794	0.322897	+	0.946434i	$0.395343\pi$
$500$	12.4441	0.556517
$501$	18.1464	0.810721
$502$	13.1484	0.586843
$503$	−24.7666	−1.10429	−0.552144	−	0.833749i	$-0.686190\pi$
$503$	−24.7666	−1.10429	−0.552144	+	0.833749i	$0.686190\pi$
$504$	98.9410	4.40718
$505$	−4.39922	−0.195763
$506$	−1.19902	−0.0533028
$507$	−81.3447	−3.61264
$508$	34.6029	1.53526
$509$	14.8897	0.659976	0.329988	−	0.943985i	$-0.392955\pi$
$509$	14.8897	0.659976	0.329988	+	0.943985i	$0.392955\pi$
$510$	−1.72083	−0.0761996
$511$	−18.3914	−0.813588
$512$	38.5941	1.70564
$513$	−5.06033	−0.223419
$514$	50.3922	2.22270
$515$	−1.80702	−0.0796270
$516$	15.1751	0.668047
$517$	−30.9913	−1.36300
$518$	77.6606	3.41221
$519$	−51.0907	−2.24263
$520$	9.95107	0.436383
$521$	−7.47189	−0.327349	−0.163675	−	0.986514i	$-0.552335\pi$
$521$	−7.47189	−0.327349	−0.163675	+	0.986514i	$0.552335\pi$
$522$	−61.9420	−2.71113
$523$	31.2812	1.36783	0.683915	−	0.729562i	$-0.260276\pi$
$523$	31.2812	1.36783	0.683915	+	0.729562i	$0.260276\pi$
$524$	−6.68846	−0.292187
$525$	−58.2990	−2.54438
$526$	−21.1657	−0.922868
$527$	−2.77105	−0.120709
$528$	49.6248	2.15964
$529$	−22.9884	−0.999495
$530$	3.98392	0.173050
$531$	57.1282	2.47915
$532$	−17.4295	−0.755665
$533$	15.7354	0.681576
$534$	−102.777	−4.44761
$535$	−2.35215	−0.101692
$536$	−8.67736	−0.374805
$537$	3.37852	0.145794
$538$	24.9553	1.07590
$539$	−50.9545	−2.19477
$540$	6.20727	0.267118
$541$	25.6757	1.10388	0.551942	−	0.833882i	$-0.313887\pi$
$541$	25.6757	1.10388	0.551942	+	0.833882i	$0.313887\pi$
$542$	17.7487	0.762371
$543$	45.0216	1.93206
$544$	0.108920	0.00466991
$545$	4.54381	0.194635
$546$	−189.032	−8.08981
$547$	−21.4516	−0.917203	−0.458601	−	0.888642i	$-0.651649\pi$
$547$	−21.4516	−0.917203	−0.458601	+	0.888642i	$0.651649\pi$
$548$	16.8890	0.721463
$549$	−12.8670	−0.549150
$550$	−54.4967	−2.32375
$551$	5.43676	0.231614
$552$	−1.46054	−0.0621646
$553$	22.5273	0.957958
$554$	−23.7619	−1.00955
$555$	6.53857	0.277547
$556$	−66.3816	−2.81521
$557$	−40.1676	−1.70196	−0.850978	−	0.525201i	$-0.823990\pi$
$557$	−40.1676	−1.70196	−0.850978	+	0.525201i	$0.823990\pi$
$558$	40.4312	1.71159
$559$	−8.86926	−0.375130
$560$	5.27005	0.222700
$561$	10.1382	0.428035
$562$	−34.9984	−1.47632
$563$	−33.9291	−1.42994	−0.714970	−	0.699155i	$-0.753560\pi$
$563$	−33.9291	−1.42994	−0.714970	+	0.699155i	$0.753560\pi$
$564$	−75.7670	−3.19037
$565$	−0.315327	−0.0132659
$566$	4.88229	0.205218
$567$	2.33508	0.0980641
$568$	4.85913	0.203884
$569$	9.67842	0.405740	0.202870	−	0.979206i	$-0.434973\pi$
$569$	9.67842	0.405740	0.202870	+	0.979206i	$0.434973\pi$
$570$	−2.20377	−0.0923056
$571$	23.4686	0.982131	0.491066	−	0.871123i	$-0.336607\pi$
$571$	23.4686	0.982131	0.491066	+	0.871123i	$0.336607\pi$
$572$	−117.665	−4.91981
$573$	−59.8474	−2.50016
$574$	25.2964	1.05585
$575$	0.528382	0.0220350
$576$	−38.9639	−1.62350
$577$	12.2604	0.510408	0.255204	−	0.966887i	$-0.417857\pi$
$577$	12.2604	0.510408	0.255204	+	0.966887i	$0.417857\pi$
$578$	40.0266	1.66488
$579$	62.1300	2.58203
$580$	−6.66902	−0.276916
$581$	−11.7956	−0.489363
$582$	−22.6865	−0.940388
$583$	−23.4711	−0.972073
$584$	−20.9417	−0.866572
$585$	−9.77165	−0.404008
$586$	−22.5037	−0.929619
$587$	34.7726	1.43522	0.717609	−	0.696446i	$-0.245237\pi$
$587$	34.7726	1.43522	0.717609	+	0.696446i	$0.245237\pi$
$588$	−124.573	−5.13729
$589$	−3.54872	−0.146223
$590$	9.23688	0.380276
$591$	2.28443	0.0939691
$592$	29.1313	1.19729
$593$	42.5395	1.74689	0.873445	−	0.486923i	$-0.161881\pi$
$593$	42.5395	1.74689	0.873445	+	0.486923i	$0.161881\pi$
$594$	−54.9189	−2.25335
$595$	1.07666	0.0441386
$596$	73.5656	3.01337
$597$	36.6080	1.49827
$598$	1.71325	0.0700601
$599$	−25.8255	−1.05520	−0.527601	−	0.849492i	$-0.676908\pi$
$599$	−25.8255	−1.05520	−0.527601	+	0.849492i	$0.676908\pi$
$600$	−66.3831	−2.71008
$601$	3.03991	0.124000	0.0620002	−	0.998076i	$-0.480252\pi$
$601$	3.03991	0.124000	0.0620002	+	0.998076i	$0.480252\pi$
$602$	−14.2583	−0.581126
$603$	8.52090	0.346998
$604$	32.2300	1.31142
$605$	−3.04573	−0.123826
$606$	95.1562	3.86546
$607$	−25.6868	−1.04260	−0.521298	−	0.853374i	$-0.674552\pi$
$607$	−25.6868	−1.04260	−0.521298	+	0.853374i	$0.674552\pi$
$608$	0.139487	0.00565696
$609$	63.1210	2.55779
$610$	−2.08042	−0.0842339
$611$	44.2829	1.79149
$612$	15.2178	0.615143
$613$	−9.75497	−0.393999	−0.197000	−	0.980404i	$-0.563120\pi$
$613$	−9.75497	−0.393999	−0.197000	+	0.980404i	$0.563120\pi$
$614$	5.52968	0.223160
$615$	2.12981	0.0858824
$616$	−94.2485	−3.79738
$617$	21.5637	0.868124	0.434062	−	0.900883i	$-0.357080\pi$
$617$	21.5637	0.868124	0.434062	+	0.900883i	$0.357080\pi$
$618$	39.0864	1.57228
$619$	−35.8854	−1.44236	−0.721179	−	0.692749i	$-0.756399\pi$
$619$	−35.8854	−1.44236	−0.721179	+	0.692749i	$0.756399\pi$
$620$	4.35305	0.174823
$621$	0.532475	0.0213675
$622$	63.2968	2.53797
$623$	64.3039	2.57628
$624$	−70.9079	−2.83859
$625$	23.5184	0.940737
$626$	−7.07110	−0.282618
$627$	12.9834	0.518507
$628$	63.5368	2.53539
$629$	5.95145	0.237300
$630$	−15.7090	−0.625863
$631$	−21.5307	−0.857122	−0.428561	−	0.903513i	$-0.640979\pi$
$631$	−21.5307	−0.857122	−0.428561	+	0.903513i	$0.640979\pi$
$632$	25.6511	1.02034
$633$	48.1930	1.91550
$634$	48.3018	1.91831
$635$	−2.73736	−0.108629
$636$	−57.3818	−2.27533
$637$	72.8079	2.88475
$638$	59.0042	2.33600
$639$	−4.77151	−0.188758
$640$	−6.21411	−0.245634
$641$	16.5597	0.654068	0.327034	−	0.945013i	$-0.393951\pi$
$641$	16.5597	0.654068	0.327034	+	0.945013i	$0.393951\pi$
$642$	50.8775	2.00798
$643$	12.5052	0.493156	0.246578	−	0.969123i	$-0.420694\pi$
$643$	12.5052	0.493156	0.246578	+	0.969123i	$0.420694\pi$
$644$	1.83402	0.0722707
$645$	−1.20047	−0.0472685
$646$	−2.00588	−0.0789203
$647$	22.0360	0.866325	0.433162	−	0.901316i	$-0.357398\pi$
$647$	22.0360	0.866325	0.433162	+	0.901316i	$0.357398\pi$
$648$	2.65887	0.104450
$649$	−54.4187	−2.13612
$650$	77.8693	3.05429
$651$	−41.2008	−1.61479
$652$	72.7285	2.84827
$653$	15.2127	0.595317	0.297659	−	0.954672i	$-0.403794\pi$
$653$	15.2127	0.595317	0.297659	+	0.954672i	$0.403794\pi$
$654$	−98.2837	−3.84320
$655$	0.529110	0.0206740
$656$	9.48898	0.370482
$657$	20.5641	0.802281
$658$	71.1898	2.77527
$659$	−10.1627	−0.395881	−0.197940	−	0.980214i	$-0.563425\pi$
$659$	−10.1627	−0.395881	−0.197940	+	0.980214i	$0.563425\pi$
$660$	−15.9261	−0.619924
$661$	−25.5598	−0.994161	−0.497081	−	0.867704i	$-0.665595\pi$
$661$	−25.5598	−0.994161	−0.497081	+	0.867704i	$0.665595\pi$
$662$	−19.7893	−0.769135
$663$	−14.4863	−0.562600
$664$	−13.4312	−0.521232
$665$	1.37881	0.0534680
$666$	−86.8350	−3.36479
$667$	−0.572085	−0.0221512
$668$	−25.9465	−1.00390
$669$	42.3889	1.63885
$670$	1.37772	0.0532259
$671$	12.2567	0.473166
$672$	1.61945	0.0624718
$673$	16.9802	0.654537	0.327269	−	0.944931i	$-0.393872\pi$
$673$	16.9802	0.654537	0.327269	+	0.944931i	$0.393872\pi$
$674$	57.0333	2.19684
$675$	24.2016	0.931520
$676$	116.310	4.47347
$677$	34.5332	1.32722	0.663609	−	0.748080i	$-0.269024\pi$
$677$	34.5332	1.32722	0.663609	+	0.748080i	$0.269024\pi$
$678$	6.82060	0.261944
$679$	14.1941	0.544719
$680$	1.22595	0.0470131
$681$	34.2012	1.31059
$682$	−38.5137	−1.47476
$683$	38.4698	1.47201	0.736004	−	0.676977i	$-0.236711\pi$
$683$	38.4698	1.47201	0.736004	+	0.676977i	$0.236711\pi$
$684$	19.4885	0.745163
$685$	−1.33605	−0.0510480
$686$	43.9617	1.67846
$687$	−24.6131	−0.939048
$688$	−5.34846	−0.203908
$689$	33.5374	1.27767
$690$	0.231892	0.00882797
$691$	−29.7599	−1.13212	−0.566059	−	0.824364i	$-0.691533\pi$
$691$	−29.7599	−1.13212	−0.566059	+	0.824364i	$0.691533\pi$
$692$	73.0518	2.77701
$693$	92.5491	3.51565
$694$	41.9266	1.59151
$695$	5.25131	0.199193
$696$	71.8737	2.72437
$697$	1.93857	0.0734286
$698$	7.02092	0.265746
$699$	70.3592	2.66123
$700$	83.3586	3.15066
$701$	32.6423	1.23288	0.616442	−	0.787400i	$-0.288574\pi$
$701$	32.6423	1.23288	0.616442	+	0.787400i	$0.288574\pi$
$702$	78.4725	2.96175
$703$	7.62167	0.287457
$704$	37.1160	1.39886
$705$	5.99377	0.225738
$706$	15.8615	0.596954
$707$	−59.5356	−2.23906
$708$	−133.042	−5.00003
$709$	−12.1621	−0.456759	−0.228380	−	0.973572i	$-0.573343\pi$
$709$	−12.1621	−0.456759	−0.228380	+	0.973572i	$0.573343\pi$
$710$	−0.771492	−0.0289536
$711$	−25.1886	−0.944645
$712$	73.2206	2.74406
$713$	0.373415	0.0139845
$714$	−23.2883	−0.871544
$715$	9.30820	0.348107
$716$	−4.83077	−0.180534
$717$	16.9194	0.631865
$718$	−16.0515	−0.599036
$719$	−7.84869	−0.292707	−0.146353	−	0.989232i	$-0.546754\pi$
$719$	−7.84869	−0.292707	−0.146353	+	0.989232i	$0.546754\pi$
$720$	−5.89263	−0.219605
$721$	−24.4548	−0.910745
$722$	43.9173	1.63443
$723$	35.5149	1.32081
$724$	−64.3740	−2.39244
$725$	−26.0019	−0.965688
$726$	65.8798	2.44503
$727$	−40.0577	−1.48566	−0.742829	−	0.669482i	$-0.766516\pi$
$727$	−40.0577	−1.48566	−0.742829	+	0.669482i	$0.766516\pi$
$728$	134.670	4.99120
$729$	−43.9130	−1.62641
$730$	3.32494	0.123062
$731$	−1.09267	−0.0404140
$732$	29.9651	1.10754
$733$	−25.0505	−0.925260	−0.462630	−	0.886551i	$-0.653094\pi$
$733$	−25.0505	−0.925260	−0.462630	+	0.886551i	$0.653094\pi$
$734$	−38.7835	−1.43152
$735$	9.85468	0.363495
$736$	−0.0146776	−0.000541024 0
$737$	−8.11677	−0.298985
$738$	−28.2848	−1.04118
$739$	−30.4673	−1.12076	−0.560379	−	0.828236i	$-0.689345\pi$
$739$	−30.4673	−1.12076	−0.560379	+	0.828236i	$0.689345\pi$
$740$	−9.34914	−0.343681
$741$	−18.5517	−0.681515
$742$	53.9152	1.97929
$743$	1.52522	0.0559549	0.0279775	−	0.999609i	$-0.491093\pi$
$743$	1.52522	0.0559549	0.0279775	+	0.999609i	$0.491093\pi$
$744$	−46.9139	−1.71995
$745$	−5.81962	−0.213214
$746$	−9.14644	−0.334875
$747$	13.1890	0.482562
$748$	−14.4961	−0.530028
$749$	−31.8321	−1.16312
$750$	21.2934	0.777524
$751$	52.8928	1.93008	0.965042	−	0.262094i	$-0.0844130\pi$
$751$	52.8928	1.93008	0.965042	+	0.262094i	$0.0844130\pi$
$752$	26.7041	0.973797
$753$	14.9815	0.545958
$754$	−84.3100	−3.07039
$755$	−2.54965	−0.0927912
$756$	84.0043	3.05521
$757$	12.1135	0.440273	0.220136	−	0.975469i	$-0.429350\pi$
$757$	12.1135	0.440273	0.220136	+	0.975469i	$0.429350\pi$
$758$	3.72053	0.135136
$759$	−1.36618	−0.0495892
$760$	1.57000	0.0569500
$761$	32.8071	1.18926	0.594628	−	0.804001i	$-0.297299\pi$
$761$	32.8071	1.18926	0.594628	+	0.804001i	$0.297299\pi$
$762$	59.2098	2.14495
$763$	61.4923	2.22617
$764$	85.5725	3.09591
$765$	−1.20385	−0.0435252
$766$	−21.3701	−0.772135
$767$	77.7579	2.80767
$768$	88.8835	3.20731
$769$	16.4356	0.592682	0.296341	−	0.955082i	$-0.404234\pi$
$769$	16.4356	0.592682	0.296341	+	0.955082i	$0.404234\pi$
$770$	14.9640	0.539265
$771$	57.4178	2.06785
$772$	−88.8362	−3.19729
$773$	−22.4934	−0.809030	−0.404515	−	0.914531i	$-0.632560\pi$
$773$	−22.4934	−0.809030	−0.404515	+	0.914531i	$0.632560\pi$
$774$	15.9427	0.573050
$775$	16.9722	0.609658
$776$	16.1623	0.580194
$777$	88.4878	3.17448
$778$	19.5727	0.701717
$779$	2.48261	0.0889488
$780$	22.7565	0.814815
$781$	4.54521	0.162640
$782$	0.211069	0.00754782
$783$	−26.2033	−0.936431
$784$	43.9056	1.56806
$785$	−5.02626	−0.179395
$786$	−11.4448	−0.408221
$787$	14.0888	0.502212	0.251106	−	0.967960i	$-0.419206\pi$
$787$	14.0888	0.502212	0.251106	+	0.967960i	$0.419206\pi$
$788$	−3.26639	−0.116360
$789$	−24.1166	−0.858572
$790$	−4.07266	−0.144899
$791$	−4.26739	−0.151731
$792$	105.383	3.74460
$793$	−17.5134	−0.621920
$794$	−35.1384	−1.24702
$795$	4.53935	0.160994
$796$	−52.3438	−1.85528
$797$	−42.2643	−1.49708	−0.748540	−	0.663090i	$-0.769245\pi$
$797$	−42.2643	−1.49708	−0.748540	+	0.663090i	$0.769245\pi$
$798$	−29.8240	−1.05576
$799$	5.45556	0.193004
$800$	−0.667115	−0.0235861
$801$	−71.9004	−2.54048
$802$	18.4319	0.650854
$803$	−19.5888	−0.691272
$804$	−19.8438	−0.699835
$805$	−0.145086	−0.00511360
$806$	55.0314	1.93840
$807$	28.4345	1.00094
$808$	−67.7911	−2.38488
$809$	9.40832	0.330779	0.165390	−	0.986228i	$-0.447112\pi$
$809$	9.40832	0.330779	0.165390	+	0.986228i	$0.447112\pi$
$810$	−0.422154	−0.0148330
$811$	6.46548	0.227034	0.113517	−	0.993536i	$-0.463788\pi$
$811$	6.46548	0.227034	0.113517	+	0.993536i	$0.463788\pi$
$812$	−90.2533	−3.16727
$813$	20.2232	0.709257
$814$	82.7166	2.89922
$815$	−5.75340	−0.201533
$816$	−8.73572	−0.305811
$817$	−1.39932	−0.0489562
$818$	89.7699	3.13873
$819$	−132.242	−4.62090
$820$	−3.04530	−0.106347
$821$	48.5453	1.69424	0.847121	−	0.531399i	$-0.178334\pi$
$821$	48.5453	1.69424	0.847121	+	0.531399i	$0.178334\pi$
$822$	28.8991	1.00797
$823$	1.07967	0.0376349	0.0188174	−	0.999823i	$-0.494010\pi$
$823$	1.07967	0.0376349	0.0188174	+	0.999823i	$0.494010\pi$
$824$	−27.8459	−0.970056
$825$	−62.0945	−2.16185
$826$	125.005	4.34947
$827$	25.7679	0.896037	0.448019	−	0.894024i	$-0.352130\pi$
$827$	25.7679	0.896037	0.448019	+	0.894024i	$0.352130\pi$
$828$	−2.05069	−0.0712663
$829$	35.5970	1.23634	0.618168	−	0.786046i	$-0.287875\pi$
$829$	35.5970	1.23634	0.618168	+	0.786046i	$0.287875\pi$
$830$	2.13250	0.0740200
$831$	−27.0748	−0.939213
$832$	−53.0343	−1.83863
$833$	8.96979	0.310785
$834$	−113.587	−3.93320
$835$	2.05257	0.0710323
$836$	−18.5642	−0.642058
$837$	17.1036	0.591188
$838$	−15.4985	−0.535387
$839$	5.50175	0.189941	0.0949707	−	0.995480i	$-0.469724\pi$
$839$	5.50175	0.189941	0.0949707	+	0.995480i	$0.469724\pi$
$840$	18.2278	0.628919
$841$	−0.847412	−0.0292211
$842$	−34.2377	−1.17991
$843$	−39.8778	−1.37346
$844$	−68.9085	−2.37193
$845$	−9.20105	−0.316526
$846$	−79.5998	−2.73670
$847$	−41.2185	−1.41628
$848$	20.2242	0.694501
$849$	5.56297	0.190920
$850$	9.59335	0.329049
$851$	−0.801992	−0.0274919
$852$	11.1121	0.380693
$853$	30.3737	1.03998	0.519988	−	0.854173i	$-0.325936\pi$
$853$	30.3737	1.03998	0.519988	+	0.854173i	$0.325936\pi$
$854$	−28.1548	−0.963438
$855$	−1.54170	−0.0527249
$856$	−36.2461	−1.23887
$857$	17.4857	0.597301	0.298650	−	0.954363i	$-0.403464\pi$
$857$	17.4857	0.597301	0.298650	+	0.954363i	$0.403464\pi$
$858$	−201.339	−6.87358
$859$	1.38843	0.0473726	0.0236863	−	0.999719i	$-0.492460\pi$
$859$	1.38843	0.0473726	0.0236863	+	0.999719i	$0.492460\pi$
$860$	1.71649	0.0585317
$861$	28.8232	0.982292
$862$	−18.4121	−0.627117
$863$	−16.5576	−0.563627	−0.281814	−	0.959469i	$-0.590936\pi$
$863$	−16.5576	−0.563627	−0.281814	+	0.959469i	$0.590936\pi$
$864$	−0.672282	−0.0228715
$865$	−5.77897	−0.196491
$866$	−18.7884	−0.638457
$867$	45.6070	1.54889
$868$	58.9108	1.99956
$869$	23.9939	0.813938
$870$	−11.4115	−0.386887
$871$	11.5979	0.392980
$872$	70.0192	2.37115
$873$	−15.8709	−0.537149
$874$	0.270304	0.00914317
$875$	−13.3224	−0.450380
$876$	−47.8903	−1.61806
$877$	23.2617	0.785492	0.392746	−	0.919647i	$-0.371525\pi$
$877$	23.2617	0.785492	0.392746	+	0.919647i	$0.371525\pi$
$878$	−61.9830	−2.09183
$879$	−25.6411	−0.864853
$880$	5.61316	0.189220
$881$	6.86105	0.231155	0.115577	−	0.993298i	$-0.463128\pi$
$881$	6.86105	0.231155	0.115577	+	0.993298i	$0.463128\pi$
$882$	−130.874	−4.40677
$883$	−26.3365	−0.886293	−0.443146	−	0.896449i	$-0.646138\pi$
$883$	−26.3365	−0.886293	−0.443146	+	0.896449i	$0.646138\pi$
$884$	20.7131	0.696658
$885$	10.5247	0.353783
$886$	96.4430	3.24007
$887$	36.7439	1.23374	0.616871	−	0.787065i	$-0.288400\pi$
$887$	36.7439	1.23374	0.616871	+	0.787065i	$0.288400\pi$
$888$	100.758	3.38122
$889$	−37.0453	−1.24246
$890$	−11.6254	−0.389683
$891$	2.48710	0.0833211
$892$	−60.6095	−2.02936
$893$	6.98662	0.233798
$894$	125.880	4.21005
$895$	0.382151	0.0127739
$896$	−84.0968	−2.80948
$897$	1.95211	0.0651791
$898$	−63.7201	−2.12637
$899$	−18.3760	−0.612873
$900$	−93.2061	−3.10687
$901$	4.13174	0.137648
$902$	26.9433	0.897115
$903$	−16.2462	−0.540640
$904$	−4.85913	−0.161612
$905$	5.09249	0.169280
$906$	55.1495	1.83222
$907$	16.6655	0.553369	0.276684	−	0.960961i	$-0.410764\pi$
$907$	16.6655	0.553369	0.276684	+	0.960961i	$0.410764\pi$
$908$	−48.9024	−1.62288
$909$	66.5688	2.20795
$910$	−21.3818	−0.708798
$911$	8.96141	0.296905	0.148452	−	0.988920i	$-0.452571\pi$
$911$	8.96141	0.296905	0.148452	+	0.988920i	$0.452571\pi$
$912$	−11.1873	−0.370449
$913$	−12.5635	−0.415792
$914$	−12.2971	−0.406751
$915$	−2.37047	−0.0783654
$916$	35.1929	1.16281
$917$	7.16055	0.236462
$918$	9.66766	0.319080
$919$	−36.4313	−1.20176	−0.600879	−	0.799340i	$-0.705183\pi$
$919$	−36.4313	−1.20176	−0.600879	+	0.799340i	$0.705183\pi$
$920$	−0.165204	−0.00544662
$921$	6.30061	0.207612
$922$	−68.6226	−2.25997
$923$	−6.49457	−0.213771
$924$	−215.531	−7.09047
$925$	−36.4515	−1.19852
$926$	−53.1806	−1.74762
$927$	27.3438	0.898088
$928$	0.722293	0.0237104
$929$	−35.2477	−1.15644	−0.578220	−	0.815881i	$-0.696252\pi$
$929$	−35.2477	−1.15644	−0.578220	+	0.815881i	$0.696252\pi$
$930$	7.44861	0.244249
$931$	11.4871	0.376474
$932$	−100.603	−3.29535
$933$	72.1215	2.36115
$934$	43.0523	1.40872
$935$	1.14675	0.0375028
$936$	−150.579	−4.92183
$937$	−7.31953	−0.239119	−0.119559	−	0.992827i	$-0.538148\pi$
$937$	−7.31953	−0.239119	−0.119559	+	0.992827i	$0.538148\pi$
$938$	18.6449	0.608779
$939$	−8.05694	−0.262928
$940$	−8.57016	−0.279528
$941$	−3.36466	−0.109685	−0.0548424	−	0.998495i	$-0.517466\pi$
$941$	−3.36466	−0.109685	−0.0548424	+	0.998495i	$0.517466\pi$
$942$	108.719	3.54226
$943$	−0.261234	−0.00850693
$944$	46.8906	1.52616
$945$	−6.64540	−0.216175
$946$	−15.1866	−0.493760
$947$	30.5907	0.994063	0.497032	−	0.867732i	$-0.334423\pi$
$947$	30.5907	0.994063	0.497032	+	0.867732i	$0.334423\pi$
$948$	58.6600	1.90519
$949$	27.9900	0.908594
$950$	12.2856	0.398599
$951$	55.0359	1.78466
$952$	16.5911	0.537719
$953$	−55.6531	−1.80278	−0.901390	−	0.433008i	$-0.857452\pi$
$953$	−55.6531	−1.80278	−0.901390	+	0.433008i	$0.857452\pi$
$954$	−60.2845	−1.95178
$955$	−6.76946	−0.219055
$956$	−24.1921	−0.782427
$957$	67.2305	2.17325
$958$	0.577807	0.0186681
$959$	−18.0811	−0.583868
$960$	−7.17829	−0.231678
$961$	−19.0055	−0.613081
$962$	−118.192	−3.81067
$963$	35.5926	1.14695
$964$	−50.7808	−1.63554
$965$	7.02764	0.226228
$966$	3.13824	0.100971
$967$	−47.8761	−1.53959	−0.769796	−	0.638290i	$-0.779642\pi$
$967$	−47.8761	−1.53959	−0.769796	+	0.638290i	$0.779642\pi$
$968$	−46.9340	−1.50852
$969$	−2.28554	−0.0734220
$970$	−2.56612	−0.0823931
$971$	14.3337	0.459990	0.229995	−	0.973192i	$-0.426129\pi$
$971$	14.3337	0.459990	0.229995	+	0.973192i	$0.426129\pi$
$972$	65.1360	2.08924
$973$	71.0670	2.27830
$974$	−8.56401	−0.274409
$975$	88.7257	2.84150
$976$	−10.5612	−0.338055
$977$	32.2469	1.03167	0.515836	−	0.856688i	$-0.327482\pi$
$977$	32.2469	1.03167	0.515836	+	0.856688i	$0.327482\pi$
$978$	124.447	3.97939
$979$	68.4903	2.18896
$980$	−14.0907	−0.450110
$981$	−68.7567	−2.19523
$982$	−72.2558	−2.30578
$983$	10.5985	0.338041	0.169021	−	0.985613i	$-0.445940\pi$
$983$	10.5985	0.338041	0.169021	+	0.985613i	$0.445940\pi$
$984$	32.8200	1.04626
$985$	0.258397	0.00823321
$986$	−10.3868	−0.330784
$987$	81.1149	2.58191
$988$	26.5261	0.843907
$989$	0.147244	0.00468210
$990$	−16.7318	−0.531770
$991$	54.3825	1.72752	0.863758	−	0.503906i	$-0.168104\pi$
$991$	54.3825	1.72752	0.863758	+	0.503906i	$0.168104\pi$
$992$	−0.471460	−0.0149689
$993$	−22.5483	−0.715550
$994$	−10.4408	−0.331161
$995$	4.14080	0.131272
$996$	−30.7151	−0.973245
$997$	−49.1665	−1.55712	−0.778559	−	0.627572i	$-0.784049\pi$
$997$	−49.1665	−1.55712	−0.778559	+	0.627572i	$0.784049\pi$
$998$	−35.2951	−1.11725
$999$	−36.7338	−1.16221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.e.1.12	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.e.1.12	✓	172	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)

\(f(q)\)	\(=\)	\(q-2.44664 q^{2} -2.78774 q^{3} +3.98604 q^{4} -0.315327 q^{5} +6.82060 q^{6} -4.26739 q^{7} -4.85913 q^{8} +4.77151 q^{9} +O(q^{10})\)	\(q-2.44664 q^{2} -2.78774 q^{3} +3.98604 q^{4} -0.315327 q^{5} +6.82060 q^{6} -4.26739 q^{7} -4.85913 q^{8} +4.77151 q^{9} +0.771492 q^{10} -4.54521 q^{11} -11.1121 q^{12} +6.49457 q^{13} +10.4408 q^{14} +0.879051 q^{15} +3.91644 q^{16} +0.800118 q^{17} -11.6742 q^{18} +1.02466 q^{19} -1.25691 q^{20} +11.8964 q^{21} +11.1205 q^{22} -0.107821 q^{23} +13.5460 q^{24} -4.90057 q^{25} -15.8899 q^{26} -4.93853 q^{27} -17.0100 q^{28} +5.30590 q^{29} -2.15072 q^{30} -3.46331 q^{31} +0.136130 q^{32} +12.6709 q^{33} -1.95760 q^{34} +1.34562 q^{35} +19.0195 q^{36} +7.43821 q^{37} -2.50698 q^{38} -18.1052 q^{39} +1.53221 q^{40} +2.42286 q^{41} -29.1061 q^{42} -1.36564 q^{43} -18.1174 q^{44} -1.50459 q^{45} +0.263798 q^{46} +6.81845 q^{47} -10.9180 q^{48} +11.2106 q^{49} +11.9899 q^{50} -2.23052 q^{51} +25.8876 q^{52} +5.16392 q^{53} +12.0828 q^{54} +1.43323 q^{55} +20.7358 q^{56} -2.85650 q^{57} -12.9816 q^{58} +11.9728 q^{59} +3.50393 q^{60} -2.69663 q^{61} +8.47346 q^{62} -20.3619 q^{63} -8.16595 q^{64} -2.04791 q^{65} -31.0011 q^{66} +1.78579 q^{67} +3.18930 q^{68} +0.300576 q^{69} -3.29225 q^{70} -1.00000 q^{71} -23.1854 q^{72} +4.30976 q^{73} -18.1986 q^{74} +13.6615 q^{75} +4.08435 q^{76} +19.3962 q^{77} +44.2968 q^{78} -5.27895 q^{79} -1.23496 q^{80} -0.547192 q^{81} -5.92785 q^{82} +2.76412 q^{83} +47.4195 q^{84} -0.252299 q^{85} +3.34123 q^{86} -14.7915 q^{87} +22.0858 q^{88} -15.0687 q^{89} +3.68118 q^{90} -27.7148 q^{91} -0.429777 q^{92} +9.65481 q^{93} -16.6823 q^{94} -0.323104 q^{95} -0.379496 q^{96} -3.32618 q^{97} -27.4283 q^{98} -21.6875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * q^99

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