LMFDB - Embedded newform 8041.2.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59406 q^{2} -1.64341 q^{3} +4.72913 q^{4} -1.77081 q^{5} +4.26309 q^{6} -2.35395 q^{7} -7.07951 q^{8} -0.299219 q^{9} +O(q^{10})$	\(q-2.59406 q^{2} -1.64341 q^{3} +4.72913 q^{4} -1.77081 q^{5} +4.26309 q^{6} -2.35395 q^{7} -7.07951 q^{8} -0.299219 q^{9} +4.59358 q^{10} +1.00000 q^{11} -7.77187 q^{12} -1.76785 q^{13} +6.10628 q^{14} +2.91016 q^{15} +8.90639 q^{16} -1.00000 q^{17} +0.776190 q^{18} +4.33043 q^{19} -8.37439 q^{20} +3.86850 q^{21} -2.59406 q^{22} -1.79914 q^{23} +11.6345 q^{24} -1.86423 q^{25} +4.58590 q^{26} +5.42195 q^{27} -11.1321 q^{28} +5.71752 q^{29} -7.54912 q^{30} +0.869088 q^{31} -8.94467 q^{32} -1.64341 q^{33} +2.59406 q^{34} +4.16840 q^{35} -1.41504 q^{36} +1.69519 q^{37} -11.2334 q^{38} +2.90529 q^{39} +12.5365 q^{40} +8.84725 q^{41} -10.0351 q^{42} -1.00000 q^{43} +4.72913 q^{44} +0.529860 q^{45} +4.66707 q^{46} -5.13726 q^{47} -14.6368 q^{48} -1.45891 q^{49} +4.83591 q^{50} +1.64341 q^{51} -8.36039 q^{52} +4.78070 q^{53} -14.0649 q^{54} -1.77081 q^{55} +16.6648 q^{56} -7.11666 q^{57} -14.8316 q^{58} +0.969361 q^{59} +13.7625 q^{60} +6.54259 q^{61} -2.25446 q^{62} +0.704346 q^{63} +5.39018 q^{64} +3.13053 q^{65} +4.26309 q^{66} -4.15695 q^{67} -4.72913 q^{68} +2.95671 q^{69} -10.8131 q^{70} -3.14680 q^{71} +2.11832 q^{72} -9.63659 q^{73} -4.39743 q^{74} +3.06368 q^{75} +20.4792 q^{76} -2.35395 q^{77} -7.53650 q^{78} -9.32988 q^{79} -15.7715 q^{80} -8.01281 q^{81} -22.9503 q^{82} +10.0262 q^{83} +18.2946 q^{84} +1.77081 q^{85} +2.59406 q^{86} -9.39621 q^{87} -7.07951 q^{88} +2.23814 q^{89} -1.37449 q^{90} +4.16143 q^{91} -8.50835 q^{92} -1.42826 q^{93} +13.3263 q^{94} -7.66838 q^{95} +14.6997 q^{96} -16.1140 q^{97} +3.78451 q^{98} -0.299219 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * 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 $

$2$	−2.59406	−1.83427	−0.917137	−	0.398571i	$-0.869506\pi$
$2$	−2.59406	−1.83427	−0.917137	+	0.398571i	$0.869506\pi$
$3$	−1.64341	−0.948821	−0.474410	−	0.880304i	$-0.657339\pi$
$3$	−1.64341	−0.948821	−0.474410	+	0.880304i	$0.657339\pi$
$4$	4.72913	2.36456
$5$	−1.77081	−0.791931	−0.395965	−	0.918265i	$-0.629590\pi$
$5$	−1.77081	−0.791931	−0.395965	+	0.918265i	$0.629590\pi$
$6$	4.26309	1.74040
$7$	−2.35395	−0.889710	−0.444855	−	0.895603i	$-0.646745\pi$
$7$	−2.35395	−0.889710	−0.444855	+	0.895603i	$0.646745\pi$
$8$	−7.07951	−2.50299
$9$	−0.299219	−0.0997395
$10$	4.59358	1.45262
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−7.77187	−2.24355
$13$	−1.76785	−0.490313	−0.245157	−	0.969483i	$-0.578839\pi$
$13$	−1.76785	−0.490313	−0.245157	+	0.969483i	$0.578839\pi$
$14$	6.10628	1.63197
$15$	2.91016	0.751400
$16$	8.90639	2.22660
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.776190	0.182950
$19$	4.33043	0.993469	0.496735	−	0.867902i	$-0.334532\pi$
$19$	4.33043	0.993469	0.496735	+	0.867902i	$0.334532\pi$
$20$	−8.37439	−1.87257
$21$	3.86850	0.844175
$22$	−2.59406	−0.553055
$23$	−1.79914	−0.375146	−0.187573	−	0.982251i	$-0.560062\pi$
$23$	−1.79914	−0.375146	−0.187573	+	0.982251i	$0.560062\pi$
$24$	11.6345	2.37488
$25$	−1.86423	−0.372846
$26$	4.58590	0.899369
$27$	5.42195	1.04346
$28$	−11.1321	−2.10378
$29$	5.71752	1.06172	0.530859	−	0.847460i	$-0.321870\pi$
$29$	5.71752	1.06172	0.530859	+	0.847460i	$0.321870\pi$
$30$	−7.54912	−1.37827
$31$	0.869088	0.156093	0.0780464	−	0.996950i	$-0.475132\pi$
$31$	0.869088	0.156093	0.0780464	+	0.996950i	$0.475132\pi$
$32$	−8.94467	−1.58121
$33$	−1.64341	−0.286080
$34$	2.59406	0.444877
$35$	4.16840	0.704589
$36$	−1.41504	−0.235841
$37$	1.69519	0.278688	0.139344	−	0.990244i	$-0.455501\pi$
$37$	1.69519	0.278688	0.139344	+	0.990244i	$0.455501\pi$
$38$	−11.2334	−1.82230
$39$	2.90529	0.465219
$40$	12.5365	1.98219
$41$	8.84725	1.38171	0.690854	−	0.722995i	$-0.257235\pi$
$41$	8.84725	1.38171	0.690854	+	0.722995i	$0.257235\pi$
$42$	−10.0351	−1.54845
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	4.72913	0.712943
$45$	0.529860	0.0789868
$46$	4.66707	0.688121
$47$	−5.13726	−0.749346	−0.374673	−	0.927157i	$-0.622245\pi$
$47$	−5.13726	−0.749346	−0.374673	+	0.927157i	$0.622245\pi$
$48$	−14.6368	−2.11264
$49$	−1.45891	−0.208416
$50$	4.83591	0.683901
$51$	1.64341	0.230123
$52$	−8.36039	−1.15938
$53$	4.78070	0.656680	0.328340	−	0.944560i	$-0.393511\pi$
$53$	4.78070	0.656680	0.328340	+	0.944560i	$0.393511\pi$
$54$	−14.0649	−1.91398
$55$	−1.77081	−0.238776
$56$	16.6648	2.22693
$57$	−7.11666	−0.942624
$58$	−14.8316	−1.94748
$59$	0.969361	0.126200	0.0631000	−	0.998007i	$-0.479901\pi$
$59$	0.969361	0.126200	0.0631000	+	0.998007i	$0.479901\pi$
$60$	13.7625	1.77673
$61$	6.54259	0.837693	0.418846	−	0.908057i	$-0.362435\pi$
$61$	6.54259	0.837693	0.418846	+	0.908057i	$0.362435\pi$
$62$	−2.25446	−0.286317
$63$	0.704346	0.0887393
$64$	5.39018	0.673772
$65$	3.13053	0.388294
$66$	4.26309	0.524750
$67$	−4.15695	−0.507852	−0.253926	−	0.967224i	$-0.581722\pi$
$67$	−4.15695	−0.507852	−0.253926	+	0.967224i	$0.581722\pi$
$68$	−4.72913	−0.573491
$69$	2.95671	0.355946
$70$	−10.8131	−1.29241
$71$	−3.14680	−0.373457	−0.186728	−	0.982412i	$-0.559788\pi$
$71$	−3.14680	−0.373457	−0.186728	+	0.982412i	$0.559788\pi$
$72$	2.11832	0.249647
$73$	−9.63659	−1.12788	−0.563939	−	0.825817i	$-0.690715\pi$
$73$	−9.63659	−1.12788	−0.563939	+	0.825817i	$0.690715\pi$
$74$	−4.39743	−0.511191
$75$	3.06368	0.353764
$76$	20.4792	2.34912
$77$	−2.35395	−0.268258
$78$	−7.53650	−0.853340
$79$	−9.32988	−1.04969	−0.524847	−	0.851197i	$-0.675877\pi$
$79$	−9.32988	−1.04969	−0.524847	+	0.851197i	$0.675877\pi$
$80$	−15.7715	−1.76331
$81$	−8.01281	−0.890312
$82$	−22.9503	−2.53443
$83$	10.0262	1.10051	0.550257	−	0.834995i	$-0.314530\pi$
$83$	10.0262	1.10051	0.550257	+	0.834995i	$0.314530\pi$
$84$	18.2946	1.99611
$85$	1.77081	0.192071
$86$	2.59406	0.279724
$87$	−9.39621	−1.00738
$88$	−7.07951	−0.754678
$89$	2.23814	0.237242	0.118621	−	0.992940i	$-0.462153\pi$
$89$	2.23814	0.237242	0.118621	+	0.992940i	$0.462153\pi$
$90$	−1.37449	−0.144884
$91$	4.16143	0.436237
$92$	−8.50835	−0.887057
$93$	−1.42826	−0.148104
$94$	13.3263	1.37451
$95$	−7.66838	−0.786759
$96$	14.6997	1.50028
$97$	−16.1140	−1.63613	−0.818065	−	0.575126i	$-0.804953\pi$
$97$	−16.1140	−1.63613	−0.818065	+	0.575126i	$0.804953\pi$
$98$	3.78451	0.382293
$99$	−0.299219	−0.0300726
$100$	−8.81617	−0.881617
$101$	16.6742	1.65915	0.829573	−	0.558398i	$-0.188584\pi$
$101$	16.6742	1.65915	0.829573	+	0.558398i	$0.188584\pi$
$102$	−4.26309	−0.422108
$103$	16.8928	1.66450	0.832249	−	0.554402i	$-0.187053\pi$
$103$	16.8928	1.66450	0.832249	+	0.554402i	$0.187053\pi$
$104$	12.5155	1.22725
$105$	−6.85038	−0.668528
$106$	−12.4014	−1.20453
$107$	−9.65261	−0.933153	−0.466577	−	0.884481i	$-0.654513\pi$
$107$	−9.65261	−0.933153	−0.466577	+	0.884481i	$0.654513\pi$
$108$	25.6411	2.46732
$109$	−8.99504	−0.861569	−0.430784	−	0.902455i	$-0.641763\pi$
$109$	−8.99504	−0.861569	−0.430784	+	0.902455i	$0.641763\pi$
$110$	4.59358	0.437981
$111$	−2.78589	−0.264425
$112$	−20.9652	−1.98103
$113$	−15.1017	−1.42065	−0.710326	−	0.703873i	$-0.751453\pi$
$113$	−15.1017	−1.42065	−0.710326	+	0.703873i	$0.751453\pi$
$114$	18.4610	1.72903
$115$	3.18593	0.297090
$116$	27.0389	2.51050
$117$	0.528974	0.0489036
$118$	−2.51458	−0.231486
$119$	2.35395	0.215786
$120$	−20.6025	−1.88074
$121$	1.00000	0.0909091
$122$	−16.9718	−1.53656
$123$	−14.5396	−1.31099
$124$	4.11003	0.369091
$125$	12.1553	1.08720
$126$	−1.82711	−0.162772
$127$	−13.9568	−1.23846	−0.619232	−	0.785208i	$-0.712556\pi$
$127$	−13.9568	−1.23846	−0.619232	+	0.785208i	$0.712556\pi$
$128$	3.90691	0.345325
$129$	1.64341	0.144694
$130$	−8.12077	−0.712238
$131$	11.2799	0.985529	0.492764	−	0.870163i	$-0.335986\pi$
$131$	11.2799	0.985529	0.492764	+	0.870163i	$0.335986\pi$
$132$	−7.77187	−0.676455
$133$	−10.1936	−0.883900
$134$	10.7834	0.931540
$135$	−9.60126	−0.826345
$136$	7.07951	0.607063
$137$	6.91902	0.591132	0.295566	−	0.955322i	$-0.404492\pi$
$137$	6.91902	0.591132	0.295566	+	0.955322i	$0.404492\pi$
$138$	−7.66988	−0.652904
$139$	−18.9516	−1.60745	−0.803726	−	0.595000i	$-0.797152\pi$
$139$	−18.9516	−1.60745	−0.803726	+	0.595000i	$0.797152\pi$
$140$	19.7129	1.66605
$141$	8.44260	0.710995
$142$	8.16298	0.685022
$143$	−1.76785	−0.147835
$144$	−2.66496	−0.222080
$145$	−10.1247	−0.840807
$146$	24.9978	2.06884
$147$	2.39759	0.197750
$148$	8.01679	0.658976
$149$	−21.1530	−1.73292	−0.866459	−	0.499248i	$-0.833610\pi$
$149$	−21.1530	−1.73292	−0.866459	+	0.499248i	$0.833610\pi$
$150$	−7.94736	−0.648900
$151$	−22.3134	−1.81584	−0.907919	−	0.419146i	$-0.862329\pi$
$151$	−22.3134	−1.81584	−0.907919	+	0.419146i	$0.862329\pi$
$152$	−30.6573	−2.48664
$153$	0.299219	0.0241904
$154$	6.10628	0.492058
$155$	−1.53899	−0.123615
$156$	13.7395	1.10004
$157$	−0.508352	−0.0405709	−0.0202854	−	0.999794i	$-0.506458\pi$
$157$	−0.508352	−0.0405709	−0.0202854	+	0.999794i	$0.506458\pi$
$158$	24.2022	1.92543
$159$	−7.85663	−0.623071
$160$	15.8393	1.25221
$161$	4.23508	0.333771
$162$	20.7857	1.63308
$163$	21.4027	1.67639	0.838195	−	0.545371i	$-0.183611\pi$
$163$	21.4027	1.67639	0.838195	+	0.545371i	$0.183611\pi$
$164$	41.8398	3.26714
$165$	2.91016	0.226556
$166$	−26.0084	−2.01864
$167$	−3.33393	−0.257987	−0.128994	−	0.991645i	$-0.541175\pi$
$167$	−3.33393	−0.257987	−0.128994	+	0.991645i	$0.541175\pi$
$168$	−27.3871	−2.11296
$169$	−9.87471	−0.759593
$170$	−4.59358	−0.352312
$171$	−1.29575	−0.0990882
$172$	−4.72913	−0.360593
$173$	−21.1513	−1.60810	−0.804052	−	0.594560i	$-0.797326\pi$
$173$	−21.1513	−1.60810	−0.804052	+	0.594560i	$0.797326\pi$
$174$	24.3743	1.84781
$175$	4.38830	0.331724
$176$	8.90639	0.671345
$177$	−1.59305	−0.119741
$178$	−5.80586	−0.435167
$179$	−11.0187	−0.823579	−0.411790	−	0.911279i	$-0.635096\pi$
$179$	−11.0187	−0.823579	−0.411790	+	0.911279i	$0.635096\pi$
$180$	2.50577	0.186769
$181$	16.7846	1.24759	0.623795	−	0.781588i	$-0.285590\pi$
$181$	16.7846	1.24759	0.623795	+	0.781588i	$0.285590\pi$
$182$	−10.7950	−0.800178
$183$	−10.7521	−0.794820
$184$	12.7370	0.938986
$185$	−3.00187	−0.220702
$186$	3.70500	0.271664
$187$	−1.00000	−0.0731272
$188$	−24.2947	−1.77188
$189$	−12.7630	−0.928373
$190$	19.8922	1.44313
$191$	16.2603	1.17656	0.588278	−	0.808658i	$-0.299806\pi$
$191$	16.2603	1.17656	0.588278	+	0.808658i	$0.299806\pi$
$192$	−8.85825	−0.639289
$193$	−4.36012	−0.313848	−0.156924	−	0.987611i	$-0.550158\pi$
$193$	−4.36012	−0.313848	−0.156924	+	0.987611i	$0.550158\pi$
$194$	41.8006	3.00111
$195$	−5.14473	−0.368422
$196$	−6.89939	−0.492814
$197$	11.5518	0.823031	0.411516	−	0.911403i	$-0.365000\pi$
$197$	11.5518	0.823031	0.411516	+	0.911403i	$0.365000\pi$
$198$	0.776190	0.0551614
$199$	15.4184	1.09298	0.546492	−	0.837464i	$-0.315963\pi$
$199$	15.4184	1.09298	0.546492	+	0.837464i	$0.315963\pi$
$200$	13.1978	0.933227
$201$	6.83155	0.481860
$202$	−43.2538	−3.04333
$203$	−13.4588	−0.944620
$204$	7.77187	0.544140
$205$	−15.6668	−1.09422
$206$	−43.8209	−3.05315
$207$	0.538336	0.0374169
$208$	−15.7452	−1.09173
$209$	4.33043	0.299542
$210$	17.7703	1.22626
$211$	11.3624	0.782220	0.391110	−	0.920344i	$-0.372091\pi$
$211$	11.3624	0.782220	0.391110	+	0.920344i	$0.372091\pi$
$212$	22.6085	1.55276
$213$	5.17147	0.354343
$214$	25.0394	1.71166
$215$	1.77081	0.120768
$216$	−38.3848	−2.61175
$217$	−2.04579	−0.138877
$218$	23.3336	1.58035
$219$	15.8368	1.07015
$220$	−8.37439	−0.564601
$221$	1.76785	0.118918
$222$	7.22676	0.485028
$223$	22.9403	1.53620	0.768098	−	0.640333i	$-0.221204\pi$
$223$	22.9403	1.53620	0.768098	+	0.640333i	$0.221204\pi$
$224$	21.0553	1.40682
$225$	0.557812	0.0371874
$226$	39.1748	2.60587
$227$	21.8044	1.44721	0.723603	−	0.690216i	$-0.242484\pi$
$227$	21.8044	1.44721	0.723603	+	0.690216i	$0.242484\pi$
$228$	−33.6556	−2.22890
$229$	8.39753	0.554925	0.277462	−	0.960737i	$-0.410507\pi$
$229$	8.39753	0.554925	0.277462	+	0.960737i	$0.410507\pi$
$230$	−8.26449	−0.544944
$231$	3.86850	0.254528
$232$	−40.4773	−2.65746
$233$	−10.4308	−0.683341	−0.341671	−	0.939820i	$-0.610993\pi$
$233$	−10.4308	−0.683341	−0.341671	+	0.939820i	$0.610993\pi$
$234$	−1.37219	−0.0897027
$235$	9.09711	0.593430
$236$	4.58423	0.298408
$237$	15.3328	0.995971
$238$	−6.10628	−0.395811
$239$	−5.29141	−0.342273	−0.171137	−	0.985247i	$-0.554744\pi$
$239$	−5.29141	−0.342273	−0.171137	+	0.985247i	$0.554744\pi$
$240$	25.9190	1.67307
$241$	−3.09953	−0.199658	−0.0998290	−	0.995005i	$-0.531830\pi$
$241$	−3.09953	−0.199658	−0.0998290	+	0.995005i	$0.531830\pi$
$242$	−2.59406	−0.166752
$243$	−3.09756	−0.198709
$244$	30.9407	1.98078
$245$	2.58346	0.165051
$246$	37.7166	2.40472
$247$	−7.65556	−0.487111
$248$	−6.15272	−0.390698
$249$	−16.4770	−1.04419
$250$	−31.5314	−1.99422
$251$	−21.2617	−1.34203	−0.671015	−	0.741444i	$-0.734141\pi$
$251$	−21.2617	−1.34203	−0.671015	+	0.741444i	$0.734141\pi$
$252$	3.33094	0.209830
$253$	−1.79914	−0.113111
$254$	36.2047	2.27168
$255$	−2.91016	−0.182241
$256$	−20.9151	−1.30719
$257$	28.2627	1.76298	0.881489	−	0.472204i	$-0.156541\pi$
$257$	28.2627	1.76298	0.881489	+	0.472204i	$0.156541\pi$
$258$	−4.26309	−0.265408
$259$	−3.99041	−0.247952
$260$	14.8047	0.918147
$261$	−1.71079	−0.105895
$262$	−29.2607	−1.80773
$263$	−3.19795	−0.197194	−0.0985970	−	0.995127i	$-0.531435\pi$
$263$	−3.19795	−0.197194	−0.0985970	+	0.995127i	$0.531435\pi$
$264$	11.6345	0.716054
$265$	−8.46572	−0.520045
$266$	26.4428	1.62131
$267$	−3.67817	−0.225100
$268$	−19.6587	−1.20085
$269$	10.4584	0.637662	0.318831	−	0.947812i	$-0.396710\pi$
$269$	10.4584	0.637662	0.318831	+	0.947812i	$0.396710\pi$
$270$	24.9062	1.51574
$271$	−25.6942	−1.56081	−0.780407	−	0.625272i	$-0.784988\pi$
$271$	−25.6942	−1.56081	−0.780407	+	0.625272i	$0.784988\pi$
$272$	−8.90639	−0.540029
$273$	−6.83892	−0.413910
$274$	−17.9483	−1.08430
$275$	−1.86423	−0.112417
$276$	13.9827	0.841658
$277$	−3.47693	−0.208909	−0.104454	−	0.994530i	$-0.533310\pi$
$277$	−3.47693	−0.208909	−0.104454	+	0.994530i	$0.533310\pi$
$278$	49.1614	2.94851
$279$	−0.260047	−0.0155686
$280$	−29.5103	−1.76358
$281$	21.7493	1.29746	0.648728	−	0.761020i	$-0.275301\pi$
$281$	21.7493	1.29746	0.648728	+	0.761020i	$0.275301\pi$
$282$	−21.9006	−1.30416
$283$	−10.7828	−0.640971	−0.320486	−	0.947253i	$-0.603846\pi$
$283$	−10.7828	−0.640971	−0.320486	+	0.947253i	$0.603846\pi$
$284$	−14.8816	−0.883062
$285$	12.6023	0.746493
$286$	4.58590	0.271170
$287$	−20.8260	−1.22932
$288$	2.67641	0.157709
$289$	1.00000	0.0588235
$290$	26.2639	1.54227
$291$	26.4818	1.55239
$292$	−45.5727	−2.66694
$293$	−22.6856	−1.32531	−0.662654	−	0.748926i	$-0.730570\pi$
$293$	−22.6856	−1.32531	−0.662654	+	0.748926i	$0.730570\pi$
$294$	−6.21948	−0.362727
$295$	−1.71656	−0.0999417
$296$	−12.0011	−0.697553
$297$	5.42195	0.314614
$298$	54.8720	3.17865
$299$	3.18061	0.183939
$300$	14.4885	0.836496
$301$	2.35395	0.135679
$302$	57.8822	3.33074
$303$	−27.4025	−1.57423
$304$	38.5685	2.21206
$305$	−11.5857	−0.663395
$306$	−0.776190	−0.0443718
$307$	−6.99874	−0.399439	−0.199720	−	0.979853i	$-0.564003\pi$
$307$	−6.99874	−0.399439	−0.199720	+	0.979853i	$0.564003\pi$
$308$	−11.1321	−0.634312
$309$	−27.7617	−1.57931
$310$	3.99223	0.226743
$311$	−30.2215	−1.71370	−0.856852	−	0.515562i	$-0.827583\pi$
$311$	−30.2215	−1.71370	−0.856852	+	0.515562i	$0.827583\pi$
$312$	−20.5681	−1.16444
$313$	−22.1100	−1.24973	−0.624865	−	0.780733i	$-0.714846\pi$
$313$	−22.1100	−1.24973	−0.624865	+	0.780733i	$0.714846\pi$
$314$	1.31869	0.0744182
$315$	−1.24726	−0.0702754
$316$	−44.1222	−2.48207
$317$	−24.1783	−1.35799	−0.678995	−	0.734143i	$-0.737584\pi$
$317$	−24.1783	−1.35799	−0.678995	+	0.734143i	$0.737584\pi$
$318$	20.3805	1.14288
$319$	5.71752	0.320120
$320$	−9.54499	−0.533581
$321$	15.8632	0.885395
$322$	−10.9860	−0.612228
$323$	−4.33043	−0.240952
$324$	−37.8936	−2.10520
$325$	3.29567	0.182811
$326$	−55.5198	−3.07496
$327$	14.7825	0.817474
$328$	−62.6342	−3.45839
$329$	12.0929	0.666700
$330$	−7.54912	−0.415565
$331$	−19.1308	−1.05152	−0.525762	−	0.850632i	$-0.676220\pi$
$331$	−19.1308	−1.05152	−0.525762	+	0.850632i	$0.676220\pi$
$332$	47.4150	2.60223
$333$	−0.507234	−0.0277962
$334$	8.64841	0.473220
$335$	7.36117	0.402184
$336$	34.4544	1.87964
$337$	−4.59630	−0.250376	−0.125188	−	0.992133i	$-0.539953\pi$
$337$	−4.59630	−0.250376	−0.125188	+	0.992133i	$0.539953\pi$
$338$	25.6155	1.39330
$339$	24.8183	1.34794
$340$	8.37439	0.454165
$341$	0.869088	0.0470638
$342$	3.36124	0.181755
$343$	19.9119	1.07514
$344$	7.07951	0.381702
$345$	−5.23578	−0.281885
$346$	54.8676	2.94970
$347$	3.63707	0.195248	0.0976242	−	0.995223i	$-0.468876\pi$
$347$	3.63707	0.195248	0.0976242	+	0.995223i	$0.468876\pi$
$348$	−44.4359	−2.38201
$349$	8.60989	0.460877	0.230439	−	0.973087i	$-0.425984\pi$
$349$	8.60989	0.460877	0.230439	+	0.973087i	$0.425984\pi$
$350$	−11.3835	−0.608474
$351$	−9.58520	−0.511620
$352$	−8.94467	−0.476752
$353$	1.80228	0.0959258	0.0479629	−	0.998849i	$-0.484727\pi$
$353$	1.80228	0.0959258	0.0479629	+	0.998849i	$0.484727\pi$
$354$	4.13247	0.219638
$355$	5.57239	0.295752
$356$	10.5844	0.560974
$357$	−3.86850	−0.204743
$358$	28.5832	1.51067
$359$	−20.0871	−1.06016	−0.530079	−	0.847948i	$-0.677838\pi$
$359$	−20.0871	−1.06016	−0.530079	+	0.847948i	$0.677838\pi$
$360$	−3.75115	−0.197703
$361$	−0.247350	−0.0130184
$362$	−43.5402	−2.28842
$363$	−1.64341	−0.0862564
$364$	19.6799	1.03151
$365$	17.0646	0.893201
$366$	27.8916	1.45792
$367$	−3.51832	−0.183655	−0.0918274	−	0.995775i	$-0.529271\pi$
$367$	−3.51832	−0.183655	−0.0918274	+	0.995775i	$0.529271\pi$
$368$	−16.0238	−0.835300
$369$	−2.64726	−0.137811
$370$	7.78702	0.404828
$371$	−11.2535	−0.584254
$372$	−6.75444	−0.350202
$373$	−8.51299	−0.440786	−0.220393	−	0.975411i	$-0.570734\pi$
$373$	−8.51299	−0.440786	−0.220393	+	0.975411i	$0.570734\pi$
$374$	2.59406	0.134135
$375$	−19.9760	−1.03156
$376$	36.3693	1.87560
$377$	−10.1077	−0.520574
$378$	33.1080	1.70289
$379$	24.2790	1.24713	0.623565	−	0.781772i	$-0.285684\pi$
$379$	24.2790	1.24713	0.623565	+	0.781772i	$0.285684\pi$
$380$	−36.2647	−1.86034
$381$	22.9366	1.17508
$382$	−42.1802	−2.15813
$383$	−26.5810	−1.35822	−0.679112	−	0.734035i	$-0.737635\pi$
$383$	−26.5810	−1.35822	−0.679112	+	0.734035i	$0.737635\pi$
$384$	−6.42063	−0.327652
$385$	4.16840	0.212441
$386$	11.3104	0.575684
$387$	0.299219	0.0152101
$388$	−76.2052	−3.86873
$389$	29.5823	1.49988	0.749941	−	0.661504i	$-0.230082\pi$
$389$	29.5823	1.49988	0.749941	+	0.661504i	$0.230082\pi$
$390$	13.3457	0.675786
$391$	1.79914	0.0909863
$392$	10.3284	0.521663
$393$	−18.5374	−0.935090
$394$	−29.9660	−1.50967
$395$	16.5215	0.831284
$396$	−1.41504	−0.0711086
$397$	4.74354	0.238072	0.119036	−	0.992890i	$-0.462020\pi$
$397$	4.74354	0.238072	0.119036	+	0.992890i	$0.462020\pi$
$398$	−39.9963	−2.00483
$399$	16.7523	0.838662
$400$	−16.6035	−0.830177
$401$	2.65784	0.132726	0.0663631	−	0.997796i	$-0.478860\pi$
$401$	2.65784	0.132726	0.0663631	+	0.997796i	$0.478860\pi$
$402$	−17.7214	−0.883864
$403$	−1.53642	−0.0765344
$404$	78.8545	3.92316
$405$	14.1892	0.705066
$406$	34.9128	1.73269
$407$	1.69519	0.0840277
$408$	−11.6345	−0.575994
$409$	−19.7444	−0.976297	−0.488149	−	0.872761i	$-0.662328\pi$
$409$	−19.7444	−0.976297	−0.488149	+	0.872761i	$0.662328\pi$
$410$	40.6406	2.00709
$411$	−11.3708	−0.560878
$412$	79.8882	3.93581
$413$	−2.28183	−0.112281
$414$	−1.39647	−0.0686329
$415$	−17.7544	−0.871531
$416$	15.8128	0.775288
$417$	31.1451	1.52518
$418$	−11.2334	−0.549443
$419$	27.1836	1.32801	0.664004	−	0.747729i	$-0.268856\pi$
$419$	27.1836	1.32801	0.664004	+	0.747729i	$0.268856\pi$
$420$	−32.3963	−1.58078
$421$	−10.9269	−0.532545	−0.266273	−	0.963898i	$-0.585792\pi$
$421$	−10.9269	−0.532545	−0.266273	+	0.963898i	$0.585792\pi$
$422$	−29.4747	−1.43481
$423$	1.53716	0.0747394
$424$	−33.8450	−1.64366
$425$	1.86423	0.0904283
$426$	−13.4151	−0.649963
$427$	−15.4009	−0.745304
$428$	−45.6484	−2.20650
$429$	2.90529	0.140269
$430$	−4.59358	−0.221522
$431$	−24.3193	−1.17142	−0.585711	−	0.810520i	$-0.699185\pi$
$431$	−24.3193	−1.17142	−0.585711	+	0.810520i	$0.699185\pi$
$432$	48.2901	2.32336
$433$	−17.0035	−0.817134	−0.408567	−	0.912728i	$-0.633971\pi$
$433$	−17.0035	−0.817134	−0.408567	+	0.912728i	$0.633971\pi$
$434$	5.30690	0.254739
$435$	16.6389	0.797775
$436$	−42.5387	−2.03723
$437$	−7.79105	−0.372696
$438$	−41.0816	−1.96295
$439$	−9.75346	−0.465507	−0.232754	−	0.972536i	$-0.574774\pi$
$439$	−9.75346	−0.465507	−0.232754	+	0.972536i	$0.574774\pi$
$440$	12.5365	0.597653
$441$	0.436534	0.0207873
$442$	−4.58590	−0.218129
$443$	12.4883	0.593337	0.296668	−	0.954981i	$-0.404124\pi$
$443$	12.4883	0.593337	0.296668	+	0.954981i	$0.404124\pi$
$444$	−13.1748	−0.625250
$445$	−3.96332	−0.187879
$446$	−59.5084	−2.81780
$447$	34.7629	1.64423
$448$	−12.6882	−0.599462
$449$	−32.1774	−1.51855	−0.759274	−	0.650771i	$-0.774446\pi$
$449$	−32.1774	−1.51855	−0.759274	+	0.650771i	$0.774446\pi$
$450$	−1.44699	−0.0682120
$451$	8.84725	0.416601
$452$	−71.4181	−3.35922
$453$	36.6699	1.72290
$454$	−56.5618	−2.65458
$455$	−7.36911	−0.345469
$456$	50.3825	2.35937
$457$	10.0173	0.468591	0.234296	−	0.972165i	$-0.424722\pi$
$457$	10.0173	0.468591	0.234296	+	0.972165i	$0.424722\pi$
$458$	−21.7837	−1.01788
$459$	−5.42195	−0.253075
$460$	15.0667	0.702488
$461$	20.5438	0.956821	0.478411	−	0.878136i	$-0.341213\pi$
$461$	20.5438	0.956821	0.478411	+	0.878136i	$0.341213\pi$
$462$	−10.0351	−0.466875
$463$	−24.9672	−1.16033	−0.580163	−	0.814500i	$-0.697011\pi$
$463$	−24.9672	−1.16033	−0.580163	+	0.814500i	$0.697011\pi$
$464$	50.9225	2.36402
$465$	2.52919	0.117288
$466$	27.0580	1.25344
$467$	−13.7110	−0.634470	−0.317235	−	0.948347i	$-0.602754\pi$
$467$	−13.7110	−0.634470	−0.317235	+	0.948347i	$0.602754\pi$
$468$	2.50158	0.115636
$469$	9.78525	0.451841
$470$	−23.5984	−1.08851
$471$	0.835428	0.0384945
$472$	−6.86260	−0.315877
$473$	−1.00000	−0.0459800
$474$	−39.7741	−1.82688
$475$	−8.07291	−0.370411
$476$	11.1321	0.510241
$477$	−1.43047	−0.0654969
$478$	13.7262	0.627823
$479$	19.2584	0.879941	0.439970	−	0.898012i	$-0.354989\pi$
$479$	19.2584	0.879941	0.439970	+	0.898012i	$0.354989\pi$
$480$	−26.0304	−1.18812
$481$	−2.99685	−0.136645
$482$	8.04035	0.366228
$483$	−6.95996	−0.316689
$484$	4.72913	0.214960
$485$	28.5349	1.29570
$486$	8.03525	0.364486
$487$	20.3357	0.921500	0.460750	−	0.887530i	$-0.347580\pi$
$487$	20.3357	0.921500	0.460750	+	0.887530i	$0.347580\pi$
$488$	−46.3183	−2.09673
$489$	−35.1733	−1.59059
$490$	−6.70164	−0.302749
$491$	−36.0798	−1.62826	−0.814128	−	0.580685i	$-0.802785\pi$
$491$	−36.0798	−1.62826	−0.814128	+	0.580685i	$0.802785\pi$
$492$	−68.7597	−3.09993
$493$	−5.71752	−0.257504
$494$	19.8589	0.893496
$495$	0.529860	0.0238154
$496$	7.74044	0.347556
$497$	7.40742	0.332268
$498$	42.7424	1.91533
$499$	38.0641	1.70398	0.851991	−	0.523557i	$-0.175395\pi$
$499$	38.0641	1.70398	0.851991	+	0.523557i	$0.175395\pi$
$500$	57.4837	2.57075
$501$	5.47900	0.244784
$502$	55.1542	2.46165
$503$	−2.83444	−0.126381	−0.0631907	−	0.998001i	$-0.520128\pi$
$503$	−2.83444	−0.126381	−0.0631907	+	0.998001i	$0.520128\pi$
$504$	−4.98643	−0.222113
$505$	−29.5269	−1.31393
$506$	4.66707	0.207476
$507$	16.2281	0.720717
$508$	−66.0034	−2.92843
$509$	−36.8478	−1.63325	−0.816624	−	0.577170i	$-0.804157\pi$
$509$	−36.8478	−1.63325	−0.816624	+	0.577170i	$0.804157\pi$
$510$	7.54912	0.334281
$511$	22.6841	1.00348
$512$	46.4411	2.05243
$513$	23.4794	1.03664
$514$	−73.3150	−3.23379
$515$	−29.9140	−1.31817
$516$	7.77187	0.342138
$517$	−5.13726	−0.225936
$518$	10.3513	0.454812
$519$	34.7602	1.52580
$520$	−22.1626	−0.971895
$521$	7.62742	0.334163	0.167082	−	0.985943i	$-0.446566\pi$
$521$	7.62742	0.334163	0.167082	+	0.985943i	$0.446566\pi$
$522$	4.43788	0.194241
$523$	−31.6745	−1.38503	−0.692515	−	0.721403i	$-0.743497\pi$
$523$	−31.6745	−1.38503	−0.692515	+	0.721403i	$0.743497\pi$
$524$	53.3440	2.33035
$525$	−7.21176	−0.314747
$526$	8.29566	0.361708
$527$	−0.869088	−0.0378581
$528$	−14.6368	−0.636986
$529$	−19.7631	−0.859265
$530$	21.9605	0.953905
$531$	−0.290051	−0.0125871
$532$	−48.2070	−2.09004
$533$	−15.6406	−0.677470
$534$	9.54138	0.412896
$535$	17.0930	0.738993
$536$	29.4292	1.27115
$537$	18.1083	0.781429
$538$	−27.1298	−1.16965
$539$	−1.45891	−0.0628399
$540$	−45.4056	−1.95394
$541$	−36.1665	−1.55492	−0.777460	−	0.628933i	$-0.783492\pi$
$541$	−36.1665	−1.55492	−0.777460	+	0.628933i	$0.783492\pi$
$542$	66.6523	2.86296
$543$	−27.5839	−1.18374
$544$	8.94467	0.383499
$545$	15.9285	0.682303
$546$	17.7405	0.759225
$547$	−18.3970	−0.786598	−0.393299	−	0.919411i	$-0.628666\pi$
$547$	−18.3970	−0.786598	−0.393299	+	0.919411i	$0.628666\pi$
$548$	32.7209	1.39777
$549$	−1.95767	−0.0835511
$550$	4.83591	0.206204
$551$	24.7593	1.05478
$552$	−20.9321	−0.890929
$553$	21.9621	0.933922
$554$	9.01936	0.383196
$555$	4.93329	0.209406
$556$	−89.6244	−3.80092
$557$	46.8486	1.98504	0.992519	−	0.122091i	$-0.0389600\pi$
$557$	46.8486	1.98504	0.992519	+	0.122091i	$0.0389600\pi$
$558$	0.674578	0.0285571
$559$	1.76785	0.0747721
$560$	37.1254	1.56884
$561$	1.64341	0.0693846
$562$	−56.4190	−2.37989
$563$	35.9278	1.51418	0.757089	−	0.653312i	$-0.226621\pi$
$563$	35.9278	1.51418	0.757089	+	0.653312i	$0.226621\pi$
$564$	39.9261	1.68119
$565$	26.7423	1.12506
$566$	27.9712	1.17572
$567$	18.8618	0.792120
$568$	22.2778	0.934756
$569$	14.1740	0.594205	0.297102	−	0.954846i	$-0.403980\pi$
$569$	14.1740	0.594205	0.297102	+	0.954846i	$0.403980\pi$
$570$	−32.6910	−1.36927
$571$	−11.0064	−0.460603	−0.230302	−	0.973119i	$-0.573971\pi$
$571$	−11.0064	−0.460603	−0.230302	+	0.973119i	$0.573971\pi$
$572$	−8.36039	−0.349565
$573$	−26.7223	−1.11634
$574$	54.0238	2.25491
$575$	3.35400	0.139872
$576$	−1.61284	−0.0672017
$577$	25.3508	1.05537	0.527684	−	0.849441i	$-0.323060\pi$
$577$	25.3508	1.05537	0.527684	+	0.849441i	$0.323060\pi$
$578$	−2.59406	−0.107899
$579$	7.16544	0.297786
$580$	−47.8808	−1.98814
$581$	−23.6011	−0.979138
$582$	−68.6954	−2.84752
$583$	4.78070	0.197996
$584$	68.2223	2.82306
$585$	−0.936712	−0.0387283
$586$	58.8477	2.43098
$587$	37.7421	1.55778	0.778891	−	0.627159i	$-0.215782\pi$
$587$	37.7421	1.55778	0.778891	+	0.627159i	$0.215782\pi$
$588$	11.3385	0.467592
$589$	3.76353	0.155073
$590$	4.45284	0.183321
$591$	−18.9843	−0.780909
$592$	15.0981	0.620527
$593$	−31.7640	−1.30439	−0.652195	−	0.758051i	$-0.726152\pi$
$593$	−31.7640	−1.30439	−0.652195	+	0.758051i	$0.726152\pi$
$594$	−14.0649	−0.577088
$595$	−4.16840	−0.170888
$596$	−100.035	−4.09760
$597$	−25.3387	−1.03705
$598$	−8.25067	−0.337395
$599$	4.36378	0.178299	0.0891497	−	0.996018i	$-0.471585\pi$
$599$	4.36378	0.178299	0.0891497	+	0.996018i	$0.471585\pi$
$600$	−21.6894	−0.885465
$601$	40.7997	1.66425	0.832127	−	0.554585i	$-0.187123\pi$
$601$	40.7997	1.66425	0.832127	+	0.554585i	$0.187123\pi$
$602$	−6.10628	−0.248873
$603$	1.24384	0.0506529
$604$	−105.523	−4.29366
$605$	−1.77081	−0.0719937
$606$	71.0836	2.88757
$607$	−44.8498	−1.82040	−0.910198	−	0.414173i	$-0.864071\pi$
$607$	−44.8498	−1.82040	−0.910198	+	0.414173i	$0.864071\pi$
$608$	−38.7343	−1.57088
$609$	22.1182	0.896275
$610$	30.0539	1.21685
$611$	9.08190	0.367414
$612$	1.41504	0.0571997
$613$	33.5626	1.35558	0.677790	−	0.735256i	$-0.262938\pi$
$613$	33.5626	1.35558	0.677790	+	0.735256i	$0.262938\pi$
$614$	18.1551	0.732682
$615$	25.7469	1.03822
$616$	16.6648	0.671445
$617$	−7.63772	−0.307483	−0.153742	−	0.988111i	$-0.549132\pi$
$617$	−7.63772	−0.307483	−0.153742	+	0.988111i	$0.549132\pi$
$618$	72.0155	2.89689
$619$	23.7717	0.955467	0.477733	−	0.878505i	$-0.341458\pi$
$619$	23.7717	0.955467	0.477733	+	0.878505i	$0.341458\pi$
$620$	−7.27809	−0.292295
$621$	−9.75484	−0.391448
$622$	78.3963	3.14340
$623$	−5.26847	−0.211077
$624$	25.8757	1.03586
$625$	−12.2035	−0.488141
$626$	57.3545	2.29235
$627$	−7.11666	−0.284212
$628$	−2.40406	−0.0959325
$629$	−1.69519	−0.0675918
$630$	3.23547	0.128904
$631$	7.42487	0.295579	0.147790	−	0.989019i	$-0.452784\pi$
$631$	7.42487	0.295579	0.147790	+	0.989019i	$0.452784\pi$
$632$	66.0510	2.62737
$633$	−18.6730	−0.742187
$634$	62.7200	2.49093
$635$	24.7148	0.980777
$636$	−37.1550	−1.47329
$637$	2.57914	0.102189
$638$	−14.8316	−0.587188
$639$	0.941582	0.0372484
$640$	−6.91840	−0.273474
$641$	26.3072	1.03907	0.519536	−	0.854448i	$-0.326105\pi$
$641$	26.3072	1.03907	0.519536	+	0.854448i	$0.326105\pi$
$642$	−41.1499	−1.62406
$643$	12.5432	0.494657	0.247328	−	0.968932i	$-0.420447\pi$
$643$	12.5432	0.494657	0.247328	+	0.968932i	$0.420447\pi$
$644$	20.0283	0.789224
$645$	−2.91016	−0.114587
$646$	11.2334	0.441972
$647$	−30.4398	−1.19671	−0.598356	−	0.801231i	$-0.704179\pi$
$647$	−30.4398	−1.19671	−0.598356	+	0.801231i	$0.704179\pi$
$648$	56.7268	2.22844
$649$	0.969361	0.0380507
$650$	−8.54917	−0.335326
$651$	3.36206	0.131770
$652$	101.216	3.96393
$653$	38.8313	1.51959	0.759793	−	0.650165i	$-0.225300\pi$
$653$	38.8313	1.51959	0.759793	+	0.650165i	$0.225300\pi$
$654$	−38.3466	−1.49947
$655$	−19.9746	−0.780470
$656$	78.7971	3.07651
$657$	2.88345	0.112494
$658$	−31.3695	−1.22291
$659$	22.3417	0.870308	0.435154	−	0.900356i	$-0.356694\pi$
$659$	22.3417	0.870308	0.435154	+	0.900356i	$0.356694\pi$
$660$	13.7625	0.535705
$661$	9.03348	0.351362	0.175681	−	0.984447i	$-0.443787\pi$
$661$	9.03348	0.351362	0.175681	+	0.984447i	$0.443787\pi$
$662$	49.6264	1.92878
$663$	−2.90529	−0.112832
$664$	−70.9803	−2.75457
$665$	18.0510	0.699987
$666$	1.31579	0.0509859
$667$	−10.2866	−0.398299
$668$	−15.7666	−0.610028
$669$	−37.7002	−1.45757
$670$	−19.0953	−0.737715
$671$	6.54259	0.252574
$672$	−34.6024	−1.33482
$673$	−3.59899	−0.138731	−0.0693654	−	0.997591i	$-0.522097\pi$
$673$	−3.59899	−0.138731	−0.0693654	+	0.997591i	$0.522097\pi$
$674$	11.9231	0.459259
$675$	−10.1078	−0.389048
$676$	−46.6988	−1.79611
$677$	46.4096	1.78367	0.891833	−	0.452364i	$-0.149419\pi$
$677$	46.4096	1.78367	0.891833	+	0.452364i	$0.149419\pi$
$678$	−64.3800	−2.47250
$679$	37.9316	1.45568
$680$	−12.5365	−0.480752
$681$	−35.8334	−1.37314
$682$	−2.25446	−0.0863279
$683$	36.0032	1.37763	0.688813	−	0.724939i	$-0.258132\pi$
$683$	36.0032	1.37763	0.688813	+	0.724939i	$0.258132\pi$
$684$	−6.12775	−0.234300
$685$	−12.2523	−0.468135
$686$	−51.6525	−1.97210
$687$	−13.8005	−0.526524
$688$	−8.90639	−0.339553
$689$	−8.45156	−0.321979
$690$	13.5819	0.517055
$691$	21.2682	0.809082	0.404541	−	0.914520i	$-0.367431\pi$
$691$	21.2682	0.809082	0.404541	+	0.914520i	$0.367431\pi$
$692$	−100.027	−3.80246
$693$	0.704346	0.0267559
$694$	−9.43477	−0.358139
$695$	33.5597	1.27299
$696$	66.5205	2.52145
$697$	−8.84725	−0.335113
$698$	−22.3345	−0.845375
$699$	17.1420	0.648368
$700$	20.7528	0.784383
$701$	34.3275	1.29653	0.648266	−	0.761414i	$-0.275495\pi$
$701$	34.3275	1.29653	0.648266	+	0.761414i	$0.275495\pi$
$702$	24.8645	0.938452
$703$	7.34093	0.276868
$704$	5.39018	0.203150
$705$	−14.9502	−0.563059
$706$	−4.67522	−0.175954
$707$	−39.2503	−1.47616
$708$	−7.53375	−0.283136
$709$	29.6094	1.11200	0.556002	−	0.831181i	$-0.312335\pi$
$709$	29.6094	1.11200	0.556002	+	0.831181i	$0.312335\pi$
$710$	−14.4551	−0.542490
$711$	2.79167	0.104696
$712$	−15.8449	−0.593814
$713$	−1.56361	−0.0585576
$714$	10.0351	0.375554
$715$	3.13053	0.117075
$716$	−52.1090	−1.94741
$717$	8.69594	0.324756
$718$	52.1072	1.94462
$719$	−15.5793	−0.581009	−0.290504	−	0.956874i	$-0.593823\pi$
$719$	−15.5793	−0.581009	−0.290504	+	0.956874i	$0.593823\pi$
$720$	4.71914	0.175872
$721$	−39.7648	−1.48092
$722$	0.641641	0.0238794
$723$	5.09378	0.189440
$724$	79.3765	2.95000
$725$	−10.6588	−0.395857
$726$	4.26309	0.158218
$727$	−25.7451	−0.954835	−0.477417	−	0.878677i	$-0.658427\pi$
$727$	−25.7451	−0.954835	−0.477417	+	0.878677i	$0.658427\pi$
$728$	−29.4609	−1.09189
$729$	29.1290	1.07885
$730$	−44.2665	−1.63838
$731$	1.00000	0.0369863
$732$	−50.8482	−1.87940
$733$	14.8898	0.549968	0.274984	−	0.961449i	$-0.411327\pi$
$733$	14.8898	0.549968	0.274984	+	0.961449i	$0.411327\pi$
$734$	9.12672	0.336873
$735$	−4.24567	−0.156604
$736$	16.0927	0.593184
$737$	−4.15695	−0.153123
$738$	6.86714	0.252783
$739$	−0.538480	−0.0198083	−0.00990415	−	0.999951i	$-0.503153\pi$
$739$	−0.538480	−0.0198083	−0.00990415	+	0.999951i	$0.503153\pi$
$740$	−14.1962	−0.521864
$741$	12.5812	0.462181
$742$	29.1923	1.07168
$743$	7.30325	0.267930	0.133965	−	0.990986i	$-0.457229\pi$
$743$	7.30325	0.267930	0.133965	+	0.990986i	$0.457229\pi$
$744$	10.1114	0.370702
$745$	37.4579	1.37235
$746$	22.0832	0.808523
$747$	−3.00001	−0.109765
$748$	−4.72913	−0.172914
$749$	22.7218	0.830236
$750$	51.8189	1.89216
$751$	−13.3879	−0.488530	−0.244265	−	0.969709i	$-0.578547\pi$
$751$	−13.3879	−0.488530	−0.244265	+	0.969709i	$0.578547\pi$
$752$	−45.7544	−1.66849
$753$	34.9417	1.27335
$754$	26.2200	0.954876
$755$	39.5128	1.43802
$756$	−60.3579	−2.19520
$757$	29.8102	1.08347	0.541736	−	0.840549i	$-0.317767\pi$
$757$	29.8102	1.08347	0.541736	+	0.840549i	$0.317767\pi$
$758$	−62.9811	−2.28758
$759$	2.95671	0.107322
$760$	54.2884	1.96925
$761$	3.68559	0.133602	0.0668012	−	0.997766i	$-0.478721\pi$
$761$	3.68559	0.133602	0.0668012	+	0.997766i	$0.478721\pi$
$762$	−59.4989	−2.15542
$763$	21.1739	0.766546
$764$	76.8972	2.78204
$765$	−0.529860	−0.0191571
$766$	68.9525	2.49136
$767$	−1.71368	−0.0618776
$768$	34.3720	1.24029
$769$	0.646832	0.0233253	0.0116627	−	0.999932i	$-0.496288\pi$
$769$	0.646832	0.0233253	0.0116627	+	0.999932i	$0.496288\pi$
$770$	−10.8131	−0.389676
$771$	−46.4471	−1.67275
$772$	−20.6196	−0.742114
$773$	−47.1254	−1.69498	−0.847491	−	0.530809i	$-0.821888\pi$
$773$	−47.1254	−1.69498	−0.847491	+	0.530809i	$0.821888\pi$
$774$	−0.776190	−0.0278996
$775$	−1.62018	−0.0581985
$776$	114.079	4.09521
$777$	6.55785	0.235262
$778$	−76.7382	−2.75120
$779$	38.3124	1.37268
$780$	−24.3301	−0.871156
$781$	−3.14680	−0.112601
$782$	−4.66707	−0.166894
$783$	31.0001	1.10785
$784$	−12.9937	−0.464059
$785$	0.900195	0.0321293
$786$	48.0871	1.71521
$787$	18.0132	0.642101	0.321050	−	0.947062i	$-0.395964\pi$
$787$	18.0132	0.642101	0.321050	+	0.947062i	$0.395964\pi$
$788$	54.6299	1.94611
$789$	5.25553	0.187102
$790$	−42.8576	−1.52480
$791$	35.5488	1.26397
$792$	2.11832	0.0752713
$793$	−11.5663	−0.410732
$794$	−12.3050	−0.436689
$795$	13.9126	0.493429
$796$	72.9158	2.58443
$797$	54.1709	1.91883	0.959416	−	0.281994i	$-0.0909957\pi$
$797$	54.1709	1.91883	0.959416	+	0.281994i	$0.0909957\pi$
$798$	−43.4563	−1.53834
$799$	5.13726	0.181743
$800$	16.6749	0.589547
$801$	−0.669693	−0.0236624
$802$	−6.89459	−0.243456
$803$	−9.63659	−0.340068
$804$	32.3073	1.13939
$805$	−7.49953	−0.264324
$806$	3.98555	0.140385
$807$	−17.1874	−0.605027
$808$	−118.045	−4.15282
$809$	−37.3147	−1.31191	−0.655957	−	0.754798i	$-0.727735\pi$
$809$	−37.3147	−1.31191	−0.655957	+	0.754798i	$0.727735\pi$
$810$	−36.8075	−1.29328
$811$	−10.7021	−0.375802	−0.187901	−	0.982188i	$-0.560168\pi$
$811$	−10.7021	−0.375802	−0.187901	+	0.982188i	$0.560168\pi$
$812$	−63.6482	−2.23361
$813$	42.2261	1.48093
$814$	−4.39743	−0.154130
$815$	−37.9002	−1.32758
$816$	14.6368	0.512391
$817$	−4.33043	−0.151503
$818$	51.2181	1.79080
$819$	−1.24518	−0.0435100
$820$	−74.0903	−2.58735
$821$	−30.5621	−1.06662	−0.533312	−	0.845919i	$-0.679053\pi$
$821$	−30.5621	−1.06662	−0.533312	+	0.845919i	$0.679053\pi$
$822$	29.4964	1.02880
$823$	4.44634	0.154990	0.0774949	−	0.996993i	$-0.475308\pi$
$823$	4.44634	0.154990	0.0774949	+	0.996993i	$0.475308\pi$
$824$	−119.593	−4.16621
$825$	3.06368	0.106664
$826$	5.91919	0.205955
$827$	45.4792	1.58147	0.790734	−	0.612160i	$-0.209699\pi$
$827$	45.4792	1.58147	0.790734	+	0.612160i	$0.209699\pi$
$828$	2.54586	0.0884747
$829$	−19.7929	−0.687435	−0.343718	−	0.939073i	$-0.611686\pi$
$829$	−19.7929	−0.687435	−0.343718	+	0.939073i	$0.611686\pi$
$830$	46.0560	1.59863
$831$	5.71401	0.198217
$832$	−9.52903	−0.330360
$833$	1.45891	0.0505484
$834$	−80.7922	−2.79760
$835$	5.90376	0.204308
$836$	20.4792	0.708287
$837$	4.71216	0.162876
$838$	−70.5159	−2.43593
$839$	31.8806	1.10064	0.550321	−	0.834953i	$-0.314506\pi$
$839$	31.8806	1.10064	0.550321	+	0.834953i	$0.314506\pi$
$840$	48.4973	1.67332
$841$	3.69006	0.127243
$842$	28.3450	0.976834
$843$	−35.7430	−1.23105
$844$	53.7343	1.84961
$845$	17.4862	0.601545
$846$	−3.98749	−0.137093
$847$	−2.35395	−0.0808827
$848$	42.5788	1.46216
$849$	17.7205	0.608167
$850$	−4.83591	−0.165870
$851$	−3.04989	−0.104549
$852$	24.4565	0.837867
$853$	13.5097	0.462562	0.231281	−	0.972887i	$-0.425708\pi$
$853$	13.5097	0.462562	0.231281	+	0.972887i	$0.425708\pi$
$854$	39.9509	1.36709
$855$	2.29452	0.0784710
$856$	68.3358	2.33567
$857$	−12.4690	−0.425932	−0.212966	−	0.977060i	$-0.568312\pi$
$857$	−12.4690	−0.425932	−0.212966	+	0.977060i	$0.568312\pi$
$858$	−7.53650	−0.257292
$859$	−15.8552	−0.540974	−0.270487	−	0.962724i	$-0.587185\pi$
$859$	−15.8552	−0.540974	−0.270487	+	0.962724i	$0.587185\pi$
$860$	8.37439	0.285564
$861$	34.2255	1.16640
$862$	63.0857	2.14871
$863$	18.7812	0.639320	0.319660	−	0.947532i	$-0.396431\pi$
$863$	18.7812	0.639320	0.319660	+	0.947532i	$0.396431\pi$
$864$	−48.4976	−1.64992
$865$	37.4549	1.27351
$866$	44.1079	1.49885
$867$	−1.64341	−0.0558130
$868$	−9.67481	−0.328384
$869$	−9.32988	−0.316494
$870$	−43.1623	−1.46334
$871$	7.34886	0.249007
$872$	63.6805	2.15649
$873$	4.82161	0.163187
$874$	20.2104	0.683628
$875$	−28.6129	−0.967291
$876$	74.8943	2.53045
$877$	−5.90719	−0.199472	−0.0997358	−	0.995014i	$-0.531800\pi$
$877$	−5.90719	−0.199472	−0.0997358	+	0.995014i	$0.531800\pi$
$878$	25.3010	0.853868
$879$	37.2816	1.25748
$880$	−15.7715	−0.531659
$881$	9.71106	0.327174	0.163587	−	0.986529i	$-0.447694\pi$
$881$	9.71106	0.327174	0.163587	+	0.986529i	$0.447694\pi$
$882$	−1.13239	−0.0381297
$883$	25.3470	0.852994	0.426497	−	0.904489i	$-0.359747\pi$
$883$	25.3470	0.852994	0.426497	+	0.904489i	$0.359747\pi$
$884$	8.36039	0.281190
$885$	2.82100	0.0948268
$886$	−32.3953	−1.08834
$887$	−30.2617	−1.01609	−0.508044	−	0.861331i	$-0.669631\pi$
$887$	−30.2617	−1.01609	−0.508044	+	0.861331i	$0.669631\pi$
$888$	19.7228	0.661852
$889$	32.8536	1.10187
$890$	10.2811	0.344623
$891$	−8.01281	−0.268439
$892$	108.488	3.63243
$893$	−22.2465	−0.744452
$894$	−90.1769	−3.01597
$895$	19.5121	0.652218
$896$	−9.19667	−0.307239
$897$	−5.22703	−0.174525
$898$	83.4701	2.78543
$899$	4.96903	0.165726
$900$	2.63796	0.0879321
$901$	−4.78070	−0.159268
$902$	−22.9503	−0.764160
$903$	−3.86850	−0.128735
$904$	106.913	3.55587
$905$	−29.7223	−0.988004
$906$	−95.1239	−3.16028
$907$	−21.9127	−0.727598	−0.363799	−	0.931477i	$-0.618521\pi$
$907$	−21.9127	−0.727598	−0.363799	+	0.931477i	$0.618521\pi$
$908$	103.116	3.42201
$909$	−4.98923	−0.165482
$910$	19.1159	0.633685
$911$	51.0713	1.69207	0.846034	−	0.533129i	$-0.178984\pi$
$911$	51.0713	1.69207	0.846034	+	0.533129i	$0.178984\pi$
$912$	−63.3838	−2.09885
$913$	10.0262	0.331817
$914$	−25.9855	−0.859525
$915$	19.0400	0.629443
$916$	39.7130	1.31215
$917$	−26.5523	−0.876835
$918$	14.0649	0.464209
$919$	45.7616	1.50954	0.754769	−	0.655991i	$-0.227749\pi$
$919$	45.7616	1.50954	0.754769	+	0.655991i	$0.227749\pi$
$920$	−22.5549	−0.743612
$921$	11.5018	0.378996
$922$	−53.2918	−1.75507
$923$	5.56307	0.183111
$924$	18.2946	0.601849
$925$	−3.16023	−0.103908
$926$	64.7664	2.12836
$927$	−5.05464	−0.166016
$928$	−51.1413	−1.67880
$929$	−38.3311	−1.25760	−0.628801	−	0.777566i	$-0.716454\pi$
$929$	−38.3311	−1.25760	−0.628801	+	0.777566i	$0.716454\pi$
$930$	−6.56085	−0.215139
$931$	−6.31773	−0.207055
$932$	−49.3284	−1.61580
$933$	49.6662	1.62600
$934$	35.5671	1.16379
$935$	1.77081	0.0579117
$936$	−3.74487	−0.122405
$937$	−39.5695	−1.29268	−0.646340	−	0.763050i	$-0.723701\pi$
$937$	−39.5695	−1.29268	−0.646340	+	0.763050i	$0.723701\pi$
$938$	−25.3835	−0.828800
$939$	36.3357	1.18577
$940$	43.0214	1.40320
$941$	15.1877	0.495105	0.247553	−	0.968874i	$-0.420374\pi$
$941$	15.1877	0.495105	0.247553	+	0.968874i	$0.420374\pi$
$942$	−2.16715	−0.0706095
$943$	−15.9174	−0.518342
$944$	8.63351	0.280997
$945$	22.6009	0.735207
$946$	2.59406	0.0843400
$947$	−28.4202	−0.923533	−0.461766	−	0.887002i	$-0.652784\pi$
$947$	−28.4202	−0.923533	−0.461766	+	0.887002i	$0.652784\pi$
$948$	72.5106	2.35504
$949$	17.0360	0.553013
$950$	20.9416	0.679435
$951$	39.7348	1.28849
$952$	−16.6648	−0.540110
$953$	35.4448	1.14817	0.574084	−	0.818796i	$-0.305358\pi$
$953$	35.4448	1.14817	0.574084	+	0.818796i	$0.305358\pi$
$954$	3.71073	0.120139
$955$	−28.7940	−0.931752
$956$	−25.0238	−0.809327
$957$	−9.39621	−0.303736
$958$	−49.9575	−1.61405
$959$	−16.2870	−0.525936
$960$	15.6863	0.506273
$961$	−30.2447	−0.975635
$962$	7.77400	0.250644
$963$	2.88824	0.0930723
$964$	−14.6581	−0.472104
$965$	7.72095	0.248546
$966$	18.0545	0.580895
$967$	9.20500	0.296013	0.148006	−	0.988986i	$-0.452714\pi$
$967$	9.20500	0.296013	0.148006	+	0.988986i	$0.452714\pi$
$968$	−7.07951	−0.227544
$969$	7.11666	0.228620
$970$	−74.0210	−2.37667
$971$	36.1652	1.16060	0.580299	−	0.814404i	$-0.302936\pi$
$971$	36.1652	1.16060	0.580299	+	0.814404i	$0.302936\pi$
$972$	−14.6488	−0.469859
$973$	44.6111	1.43017
$974$	−52.7521	−1.69028
$975$	−5.41613	−0.173455
$976$	58.2709	1.86521
$977$	39.7847	1.27283	0.636413	−	0.771348i	$-0.280417\pi$
$977$	39.7847	1.27283	0.636413	+	0.771348i	$0.280417\pi$
$978$	91.2416	2.91758
$979$	2.23814	0.0715312
$980$	12.2175	0.390274
$981$	2.69148	0.0859325
$982$	93.5929	2.98667
$983$	9.58359	0.305669	0.152835	−	0.988252i	$-0.451160\pi$
$983$	9.58359	0.305669	0.152835	+	0.988252i	$0.451160\pi$
$984$	102.933	3.28139
$985$	−20.4561	−0.651784
$986$	14.8316	0.472334
$987$	−19.8735	−0.632579
$988$	−36.2041	−1.15181
$989$	1.79914	0.0572093
$990$	−1.37449	−0.0436840
$991$	46.2252	1.46839	0.734196	−	0.678938i	$-0.237559\pi$
$991$	46.2252	1.46839	0.734196	+	0.678938i	$0.237559\pi$
$992$	−7.77370	−0.246815
$993$	31.4397	0.997707
$994$	−19.2153	−0.609471
$995$	−27.3031	−0.865568
$996$	−77.9220	−2.46905
$997$	−21.1554	−0.669997	−0.334999	−	0.942219i	$-0.608736\pi$
$997$	−21.1554	−0.669997	−0.334999	+	0.942219i	$0.608736\pi$
$998$	−98.7403	−3.12557
$999$	9.19127	0.290799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.4	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.4	✓	78	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59406 q^{2} -1.64341 q^{3} +4.72913 q^{4} -1.77081 q^{5} +4.26309 q^{6} -2.35395 q^{7} -7.07951 q^{8} -0.299219 q^{9} +O(q^{10})\)	\(q-2.59406 q^{2} -1.64341 q^{3} +4.72913 q^{4} -1.77081 q^{5} +4.26309 q^{6} -2.35395 q^{7} -7.07951 q^{8} -0.299219 q^{9} +4.59358 q^{10} +1.00000 q^{11} -7.77187 q^{12} -1.76785 q^{13} +6.10628 q^{14} +2.91016 q^{15} +8.90639 q^{16} -1.00000 q^{17} +0.776190 q^{18} +4.33043 q^{19} -8.37439 q^{20} +3.86850 q^{21} -2.59406 q^{22} -1.79914 q^{23} +11.6345 q^{24} -1.86423 q^{25} +4.58590 q^{26} +5.42195 q^{27} -11.1321 q^{28} +5.71752 q^{29} -7.54912 q^{30} +0.869088 q^{31} -8.94467 q^{32} -1.64341 q^{33} +2.59406 q^{34} +4.16840 q^{35} -1.41504 q^{36} +1.69519 q^{37} -11.2334 q^{38} +2.90529 q^{39} +12.5365 q^{40} +8.84725 q^{41} -10.0351 q^{42} -1.00000 q^{43} +4.72913 q^{44} +0.529860 q^{45} +4.66707 q^{46} -5.13726 q^{47} -14.6368 q^{48} -1.45891 q^{49} +4.83591 q^{50} +1.64341 q^{51} -8.36039 q^{52} +4.78070 q^{53} -14.0649 q^{54} -1.77081 q^{55} +16.6648 q^{56} -7.11666 q^{57} -14.8316 q^{58} +0.969361 q^{59} +13.7625 q^{60} +6.54259 q^{61} -2.25446 q^{62} +0.704346 q^{63} +5.39018 q^{64} +3.13053 q^{65} +4.26309 q^{66} -4.15695 q^{67} -4.72913 q^{68} +2.95671 q^{69} -10.8131 q^{70} -3.14680 q^{71} +2.11832 q^{72} -9.63659 q^{73} -4.39743 q^{74} +3.06368 q^{75} +20.4792 q^{76} -2.35395 q^{77} -7.53650 q^{78} -9.32988 q^{79} -15.7715 q^{80} -8.01281 q^{81} -22.9503 q^{82} +10.0262 q^{83} +18.2946 q^{84} +1.77081 q^{85} +2.59406 q^{86} -9.39621 q^{87} -7.07951 q^{88} +2.23814 q^{89} -1.37449 q^{90} +4.16143 q^{91} -8.50835 q^{92} -1.42826 q^{93} +13.3263 q^{94} -7.66838 q^{95} +14.6997 q^{96} -16.1140 q^{97} +3.78451 q^{98} -0.299219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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