LMFDB - Embedded newform 8041.2.a.i.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.66059 q^{2} -0.870455 q^{3} +5.07876 q^{4} -2.53728 q^{5} +2.31593 q^{6} +1.57807 q^{7} -8.19134 q^{8} -2.24231 q^{9} +O(q^{10})$	\(q-2.66059 q^{2} -0.870455 q^{3} +5.07876 q^{4} -2.53728 q^{5} +2.31593 q^{6} +1.57807 q^{7} -8.19134 q^{8} -2.24231 q^{9} +6.75067 q^{10} +1.00000 q^{11} -4.42083 q^{12} -5.54559 q^{13} -4.19860 q^{14} +2.20859 q^{15} +11.6363 q^{16} -1.00000 q^{17} +5.96587 q^{18} -7.29705 q^{19} -12.8862 q^{20} -1.37364 q^{21} -2.66059 q^{22} +7.87110 q^{23} +7.13019 q^{24} +1.43779 q^{25} +14.7546 q^{26} +4.56319 q^{27} +8.01463 q^{28} +1.60580 q^{29} -5.87616 q^{30} +5.64012 q^{31} -14.5768 q^{32} -0.870455 q^{33} +2.66059 q^{34} -4.00400 q^{35} -11.3881 q^{36} -2.01159 q^{37} +19.4145 q^{38} +4.82719 q^{39} +20.7837 q^{40} -8.14727 q^{41} +3.65469 q^{42} -1.00000 q^{43} +5.07876 q^{44} +5.68936 q^{45} -20.9418 q^{46} +3.48904 q^{47} -10.1289 q^{48} -4.50970 q^{49} -3.82537 q^{50} +0.870455 q^{51} -28.1647 q^{52} -4.47992 q^{53} -12.1408 q^{54} -2.53728 q^{55} -12.9265 q^{56} +6.35175 q^{57} -4.27238 q^{58} +4.63908 q^{59} +11.2169 q^{60} +1.59035 q^{61} -15.0061 q^{62} -3.53851 q^{63} +15.5103 q^{64} +14.0707 q^{65} +2.31593 q^{66} -14.5722 q^{67} -5.07876 q^{68} -6.85144 q^{69} +10.6530 q^{70} -2.40885 q^{71} +18.3675 q^{72} -12.2347 q^{73} +5.35202 q^{74} -1.25153 q^{75} -37.0600 q^{76} +1.57807 q^{77} -12.8432 q^{78} -12.1757 q^{79} -29.5245 q^{80} +2.75487 q^{81} +21.6766 q^{82} -4.85369 q^{83} -6.97637 q^{84} +2.53728 q^{85} +2.66059 q^{86} -1.39777 q^{87} -8.19134 q^{88} +18.3671 q^{89} -15.1371 q^{90} -8.75132 q^{91} +39.9754 q^{92} -4.90947 q^{93} -9.28292 q^{94} +18.5147 q^{95} +12.6884 q^{96} -2.70432 q^{97} +11.9985 q^{98} -2.24231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.66059	−1.88132	−0.940662	−	0.339345i	$-0.889795\pi$
$2$	−2.66059	−1.88132	−0.940662	+	0.339345i	$0.889795\pi$
$3$	−0.870455	−0.502557	−0.251279	−	0.967915i	$-0.580851\pi$
$3$	−0.870455	−0.502557	−0.251279	+	0.967915i	$0.580851\pi$
$4$	5.07876	2.53938
$5$	−2.53728	−1.13471	−0.567353	−	0.823475i	$-0.692032\pi$
$5$	−2.53728	−1.13471	−0.567353	+	0.823475i	$0.692032\pi$
$6$	2.31593	0.945474
$7$	1.57807	0.596453	0.298227	−	0.954495i	$-0.403605\pi$
$7$	1.57807	0.596453	0.298227	+	0.954495i	$0.403605\pi$
$8$	−8.19134	−2.89607
$9$	−2.24231	−0.747436
$10$	6.75067	2.13475
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.42083	−1.27618
$13$	−5.54559	−1.53807	−0.769035	−	0.639206i	$-0.779263\pi$
$13$	−5.54559	−1.53807	−0.769035	+	0.639206i	$0.779263\pi$
$14$	−4.19860	−1.12212
$15$	2.20859	0.570255
$16$	11.6363	2.90907
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	5.96587	1.40617
$19$	−7.29705	−1.67406	−0.837029	−	0.547159i	$-0.815709\pi$
$19$	−7.29705	−1.67406	−0.837029	+	0.547159i	$0.815709\pi$
$20$	−12.8862	−2.88145
$21$	−1.37364	−0.299752
$22$	−2.66059	−0.567241
$23$	7.87110	1.64124	0.820619	−	0.571476i	$-0.193629\pi$
$23$	7.87110	1.64124	0.820619	+	0.571476i	$0.193629\pi$
$24$	7.13019	1.45544
$25$	1.43779	0.287558
$26$	14.7546	2.89361
$27$	4.56319	0.878187
$28$	8.01463	1.51462
$29$	1.60580	0.298189	0.149095	−	0.988823i	$-0.452364\pi$
$29$	1.60580	0.298189	0.149095	+	0.988823i	$0.452364\pi$
$30$	−5.87616	−1.07283
$31$	5.64012	1.01300	0.506498	−	0.862241i	$-0.330940\pi$
$31$	5.64012	1.01300	0.506498	+	0.862241i	$0.330940\pi$
$32$	−14.5768	−2.57684
$33$	−0.870455	−0.151527
$34$	2.66059	0.456288
$35$	−4.00400	−0.676799
$36$	−11.3881	−1.89802
$37$	−2.01159	−0.330703	−0.165351	−	0.986235i	$-0.552876\pi$
$37$	−2.01159	−0.330703	−0.165351	+	0.986235i	$0.552876\pi$
$38$	19.4145	3.14945
$39$	4.82719	0.772969
$40$	20.7837	3.28619
$41$	−8.14727	−1.27239	−0.636195	−	0.771528i	$-0.719493\pi$
$41$	−8.14727	−1.27239	−0.636195	+	0.771528i	$0.719493\pi$
$42$	3.65469	0.563931
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	5.07876	0.765652
$45$	5.68936	0.848120
$46$	−20.9418	−3.08770
$47$	3.48904	0.508929	0.254464	−	0.967082i	$-0.418101\pi$
$47$	3.48904	0.508929	0.254464	+	0.967082i	$0.418101\pi$
$48$	−10.1289	−1.46198
$49$	−4.50970	−0.644243
$50$	−3.82537	−0.540989
$51$	0.870455	0.121888
$52$	−28.1647	−3.90575
$53$	−4.47992	−0.615364	−0.307682	−	0.951489i	$-0.599553\pi$
$53$	−4.47992	−0.615364	−0.307682	+	0.951489i	$0.599553\pi$
$54$	−12.1408	−1.65215
$55$	−2.53728	−0.342127
$56$	−12.9265	−1.72737
$57$	6.35175	0.841310
$58$	−4.27238	−0.560990
$59$	4.63908	0.603956	0.301978	−	0.953315i	$-0.402353\pi$
$59$	4.63908	0.603956	0.301978	+	0.953315i	$0.402353\pi$
$60$	11.2169	1.44809
$61$	1.59035	0.203624	0.101812	−	0.994804i	$-0.467536\pi$
$61$	1.59035	0.203624	0.101812	+	0.994804i	$0.467536\pi$
$62$	−15.0061	−1.90577
$63$	−3.53851	−0.445811
$64$	15.5103	1.93879
$65$	14.0707	1.74526
$66$	2.31593	0.285071
$67$	−14.5722	−1.78028	−0.890139	−	0.455689i	$-0.849393\pi$
$67$	−14.5722	−1.78028	−0.890139	+	0.455689i	$0.849393\pi$
$68$	−5.07876	−0.615890
$69$	−6.85144	−0.824816
$70$	10.6530	1.27328
$71$	−2.40885	−0.285877	−0.142939	−	0.989732i	$-0.545655\pi$
$71$	−2.40885	−0.285877	−0.142939	+	0.989732i	$0.545655\pi$
$72$	18.3675	2.16463
$73$	−12.2347	−1.43196	−0.715980	−	0.698121i	$-0.754020\pi$
$73$	−12.2347	−1.43196	−0.715980	+	0.698121i	$0.754020\pi$
$74$	5.35202	0.622159
$75$	−1.25153	−0.144514
$76$	−37.0600	−4.25107
$77$	1.57807	0.179837
$78$	−12.8432	−1.45420
$79$	−12.1757	−1.36987	−0.684935	−	0.728604i	$-0.740169\pi$
$79$	−12.1757	−1.36987	−0.684935	+	0.728604i	$0.740169\pi$
$80$	−29.5245	−3.30094
$81$	2.75487	0.306097
$82$	21.6766	2.39378
$83$	−4.85369	−0.532762	−0.266381	−	0.963868i	$-0.585828\pi$
$83$	−4.85369	−0.532762	−0.266381	+	0.963868i	$0.585828\pi$
$84$	−6.97637	−0.761185
$85$	2.53728	0.275207
$86$	2.66059	0.286899
$87$	−1.39777	−0.149857
$88$	−8.19134	−0.873199
$89$	18.3671	1.94690	0.973452	−	0.228891i	$-0.0735098\pi$
$89$	18.3671	1.94690	0.973452	+	0.228891i	$0.0735098\pi$
$90$	−15.1371	−1.59559
$91$	−8.75132	−0.917387
$92$	39.9754	4.16773
$93$	−4.90947	−0.509089
$94$	−9.28292	−0.957460
$95$	18.5147	1.89956
$96$	12.6884	1.29501
$97$	−2.70432	−0.274582	−0.137291	−	0.990531i	$-0.543840\pi$
$97$	−2.70432	−0.274582	−0.137291	+	0.990531i	$0.543840\pi$
$98$	11.9985	1.21203
$99$	−2.24231	−0.225360
$100$	7.30218	0.730218
$101$	−15.5569	−1.54797	−0.773986	−	0.633202i	$-0.781740\pi$
$101$	−15.5569	−1.54797	−0.773986	+	0.633202i	$0.781740\pi$
$102$	−2.31593	−0.229311
$103$	−10.3576	−1.02056	−0.510282	−	0.860007i	$-0.670459\pi$
$103$	−10.3576	−1.02056	−0.510282	+	0.860007i	$0.670459\pi$
$104$	45.4258	4.45437
$105$	3.48530	0.340130
$106$	11.9193	1.15770
$107$	−10.5750	−1.02232	−0.511161	−	0.859485i	$-0.670784\pi$
$107$	−10.5750	−1.02232	−0.511161	+	0.859485i	$0.670784\pi$
$108$	23.1754	2.23005
$109$	−10.7814	−1.03267	−0.516333	−	0.856388i	$-0.672703\pi$
$109$	−10.7814	−1.03267	−0.516333	+	0.856388i	$0.672703\pi$
$110$	6.75067	0.643651
$111$	1.75100	0.166197
$112$	18.3629	1.73513
$113$	15.4711	1.45540	0.727701	−	0.685894i	$-0.240589\pi$
$113$	15.4711	1.45540	0.727701	+	0.685894i	$0.240589\pi$
$114$	−16.8994	−1.58278
$115$	−19.9712	−1.86232
$116$	8.15546	0.757216
$117$	12.4349	1.14961
$118$	−12.3427	−1.13624
$119$	−1.57807	−0.144661
$120$	−18.0913	−1.65150
$121$	1.00000	0.0909091
$122$	−4.23128	−0.383082
$123$	7.09184	0.639449
$124$	28.6448	2.57238
$125$	9.03833	0.808413
$126$	9.41455	0.838714
$127$	17.1175	1.51893	0.759467	−	0.650546i	$-0.225460\pi$
$127$	17.1175	1.51893	0.759467	+	0.650546i	$0.225460\pi$
$128$	−12.1131	−1.07066
$129$	0.870455	0.0766393
$130$	−37.4365	−3.28340
$131$	−0.830164	−0.0725318	−0.0362659	−	0.999342i	$-0.511546\pi$
$131$	−0.830164	−0.0725318	−0.0362659	+	0.999342i	$0.511546\pi$
$132$	−4.42083	−0.384784
$133$	−11.5152	−0.998497
$134$	38.7707	3.34928
$135$	−11.5781	−0.996484
$136$	8.19134	0.702401
$137$	−14.4097	−1.23110	−0.615550	−	0.788098i	$-0.711066\pi$
$137$	−14.4097	−1.23110	−0.615550	+	0.788098i	$0.711066\pi$
$138$	18.2289	1.55175
$139$	−19.3602	−1.64211	−0.821053	−	0.570851i	$-0.806613\pi$
$139$	−19.3602	−1.64211	−0.821053	+	0.570851i	$0.806613\pi$
$140$	−20.3354	−1.71865
$141$	−3.03705	−0.255766
$142$	6.40896	0.537828
$143$	−5.54559	−0.463746
$144$	−26.0922	−2.17435
$145$	−4.07436	−0.338357
$146$	32.5515	2.69398
$147$	3.92549	0.323769
$148$	−10.2164	−0.839780
$149$	19.9891	1.63757	0.818786	−	0.574099i	$-0.194648\pi$
$149$	19.9891	1.63757	0.818786	+	0.574099i	$0.194648\pi$
$150$	3.32981	0.271878
$151$	16.8923	1.37468	0.687338	−	0.726337i	$-0.258779\pi$
$151$	16.8923	1.37468	0.687338	+	0.726337i	$0.258779\pi$
$152$	59.7726	4.84820
$153$	2.24231	0.181280
$154$	−4.19860	−0.338333
$155$	−14.3106	−1.14945
$156$	24.5161	1.96286
$157$	−16.6329	−1.32745	−0.663726	−	0.747976i	$-0.731026\pi$
$157$	−16.6329	−1.32745	−0.663726	+	0.747976i	$0.731026\pi$
$158$	32.3945	2.57717
$159$	3.89957	0.309256
$160$	36.9854	2.92395
$161$	12.4211	0.978921
$162$	−7.32959	−0.575867
$163$	−13.0658	−1.02339	−0.511694	−	0.859168i	$-0.670982\pi$
$163$	−13.0658	−1.02339	−0.511694	+	0.859168i	$0.670982\pi$
$164$	−41.3781	−3.23108
$165$	2.20859	0.171938
$166$	12.9137	1.00230
$167$	−18.8842	−1.46131	−0.730653	−	0.682749i	$-0.760784\pi$
$167$	−18.8842	−1.46131	−0.730653	+	0.682749i	$0.760784\pi$
$168$	11.2519	0.868104
$169$	17.7536	1.36566
$170$	−6.75067	−0.517753
$171$	16.3622	1.25125
$172$	−5.07876	−0.387252
$173$	−13.9903	−1.06366	−0.531832	−	0.846850i	$-0.678496\pi$
$173$	−13.9903	−1.06366	−0.531832	+	0.846850i	$0.678496\pi$
$174$	3.71891	0.281930
$175$	2.26893	0.171515
$176$	11.6363	0.877119
$177$	−4.03811	−0.303523
$178$	−48.8673	−3.66276
$179$	5.09962	0.381163	0.190582	−	0.981671i	$-0.438963\pi$
$179$	5.09962	0.381163	0.190582	+	0.981671i	$0.438963\pi$
$180$	28.8949	2.15370
$181$	−15.7689	−1.17209	−0.586046	−	0.810277i	$-0.699316\pi$
$181$	−15.7689	−1.17209	−0.586046	+	0.810277i	$0.699316\pi$
$182$	23.2837	1.72590
$183$	−1.38433	−0.102333
$184$	−64.4748	−4.75315
$185$	5.10396	0.375250
$186$	13.0621	0.957761
$187$	−1.00000	−0.0731272
$188$	17.7200	1.29236
$189$	7.20103	0.523798
$190$	−49.2600	−3.57369
$191$	−24.3575	−1.76245	−0.881223	−	0.472702i	$-0.843279\pi$
$191$	−24.3575	−1.76245	−0.881223	+	0.472702i	$0.843279\pi$
$192$	−13.5011	−0.974355
$193$	6.37501	0.458883	0.229442	−	0.973322i	$-0.426310\pi$
$193$	6.37501	0.458883	0.229442	+	0.973322i	$0.426310\pi$
$194$	7.19510	0.516578
$195$	−12.2479	−0.877092
$196$	−22.9037	−1.63598
$197$	3.81198	0.271592	0.135796	−	0.990737i	$-0.456641\pi$
$197$	3.81198	0.271592	0.135796	+	0.990737i	$0.456641\pi$
$198$	5.96587	0.423976
$199$	−17.0808	−1.21082	−0.605412	−	0.795913i	$-0.706991\pi$
$199$	−17.0808	−1.21082	−0.605412	+	0.795913i	$0.706991\pi$
$200$	−11.7774	−0.832788
$201$	12.6844	0.894692
$202$	41.3907	2.91224
$203$	2.53406	0.177856
$204$	4.42083	0.309520
$205$	20.6719	1.44379
$206$	27.5574	1.92001
$207$	−17.6494	−1.22672
$208$	−64.5302	−4.47436
$209$	−7.29705	−0.504747
$210$	−9.27297	−0.639896
$211$	21.9914	1.51395	0.756977	−	0.653442i	$-0.226676\pi$
$211$	21.9914	1.51395	0.756977	+	0.653442i	$0.226676\pi$
$212$	−22.7525	−1.56264
$213$	2.09679	0.143670
$214$	28.1357	1.92332
$215$	2.53728	0.173041
$216$	−37.3787	−2.54330
$217$	8.90049	0.604205
$218$	28.6848	1.94278
$219$	10.6497	0.719642
$220$	−12.8862	−0.868790
$221$	5.54559	0.373037
$222$	−4.65869	−0.312671
$223$	13.4686	0.901926	0.450963	−	0.892543i	$-0.351081\pi$
$223$	13.4686	0.901926	0.450963	+	0.892543i	$0.351081\pi$
$224$	−23.0032	−1.53696
$225$	−3.22396	−0.214931
$226$	−41.1624	−2.73808
$227$	−7.93654	−0.526767	−0.263383	−	0.964691i	$-0.584838\pi$
$227$	−7.93654	−0.526767	−0.263383	+	0.964691i	$0.584838\pi$
$228$	32.2590	2.13641
$229$	4.11295	0.271792	0.135896	−	0.990723i	$-0.456609\pi$
$229$	4.11295	0.271792	0.135896	+	0.990723i	$0.456609\pi$
$230$	53.1352	3.50363
$231$	−1.37364	−0.0903787
$232$	−13.1536	−0.863578
$233$	11.7614	0.770517	0.385258	−	0.922809i	$-0.374112\pi$
$233$	11.7614	0.770517	0.385258	+	0.922809i	$0.374112\pi$
$234$	−33.0843	−2.16279
$235$	−8.85267	−0.577484
$236$	23.5608	1.53368
$237$	10.5984	0.688438
$238$	4.19860	0.272155
$239$	22.2846	1.44147	0.720737	−	0.693209i	$-0.243804\pi$
$239$	22.2846	1.44147	0.720737	+	0.693209i	$0.243804\pi$
$240$	25.6998	1.65891
$241$	20.2341	1.30339	0.651695	−	0.758481i	$-0.274058\pi$
$241$	20.2341	1.30339	0.651695	+	0.758481i	$0.274058\pi$
$242$	−2.66059	−0.171029
$243$	−16.0876	−1.03202
$244$	8.07702	0.517078
$245$	11.4424	0.731027
$246$	−18.8685	−1.20301
$247$	40.4664	2.57482
$248$	−46.2001	−2.93371
$249$	4.22492	0.267743
$250$	−24.0473	−1.52089
$251$	9.69461	0.611918	0.305959	−	0.952045i	$-0.401023\pi$
$251$	9.69461	0.611918	0.305959	+	0.952045i	$0.401023\pi$
$252$	−17.9713	−1.13208
$253$	7.87110	0.494852
$254$	−45.5428	−2.85761
$255$	−2.20859	−0.138307
$256$	1.20747	0.0754671
$257$	−26.8705	−1.67613	−0.838067	−	0.545568i	$-0.816314\pi$
$257$	−26.8705	−1.67613	−0.838067	+	0.545568i	$0.816314\pi$
$258$	−2.31593	−0.144183
$259$	−3.17442	−0.197249
$260$	71.4618	4.43187
$261$	−3.60069	−0.222877
$262$	2.20873	0.136456
$263$	−30.2390	−1.86461	−0.932307	−	0.361668i	$-0.882207\pi$
$263$	−30.2390	−1.86461	−0.932307	+	0.361668i	$0.882207\pi$
$264$	7.13019	0.438833
$265$	11.3668	0.698258
$266$	30.6374	1.87850
$267$	−15.9877	−0.978431
$268$	−74.0088	−4.52080
$269$	−15.5140	−0.945903	−0.472952	−	0.881088i	$-0.656811\pi$
$269$	−15.5140	−0.945903	−0.472952	+	0.881088i	$0.656811\pi$
$270$	30.8046	1.87471
$271$	−14.6783	−0.891644	−0.445822	−	0.895122i	$-0.647088\pi$
$271$	−14.6783	−0.891644	−0.445822	+	0.895122i	$0.647088\pi$
$272$	−11.6363	−0.705554
$273$	7.61763	0.461040
$274$	38.3383	2.31610
$275$	1.43779	0.0867019
$276$	−34.7968	−2.09452
$277$	−3.14366	−0.188884	−0.0944422	−	0.995530i	$-0.530107\pi$
$277$	−3.14366	−0.188884	−0.0944422	+	0.995530i	$0.530107\pi$
$278$	51.5095	3.08934
$279$	−12.6469	−0.757150
$280$	32.7981	1.96006
$281$	1.01999	0.0608473	0.0304236	−	0.999537i	$-0.490314\pi$
$281$	1.01999	0.0608473	0.0304236	+	0.999537i	$0.490314\pi$
$282$	8.08036	0.481178
$283$	3.69869	0.219865	0.109932	−	0.993939i	$-0.464937\pi$
$283$	3.69869	0.219865	0.109932	+	0.993939i	$0.464937\pi$
$284$	−12.2340	−0.725952
$285$	−16.1162	−0.954640
$286$	14.7546	0.872456
$287$	−12.8569	−0.758921
$288$	32.6857	1.92602
$289$	1.00000	0.0588235
$290$	10.8402	0.636559
$291$	2.35399	0.137993
$292$	−62.1370	−3.63629
$293$	1.45167	0.0848075	0.0424037	−	0.999101i	$-0.486498\pi$
$293$	1.45167	0.0848075	0.0424037	+	0.999101i	$0.486498\pi$
$294$	−10.4441	−0.609115
$295$	−11.7706	−0.685313
$296$	16.4776	0.957740
$297$	4.56319	0.264783
$298$	−53.1829	−3.08080
$299$	−43.6499	−2.52434
$300$	−6.35622	−0.366977
$301$	−1.57807	−0.0909583
$302$	−44.9436	−2.58621
$303$	13.5416	0.777945
$304$	−84.9106	−4.86996
$305$	−4.03517	−0.231053
$306$	−5.96587	−0.341046
$307$	8.53719	0.487243	0.243622	−	0.969870i	$-0.421664\pi$
$307$	8.53719	0.487243	0.243622	+	0.969870i	$0.421664\pi$
$308$	8.01463	0.456676
$309$	9.01582	0.512892
$310$	38.0746	2.16249
$311$	10.0213	0.568258	0.284129	−	0.958786i	$-0.408296\pi$
$311$	10.0213	0.568258	0.284129	+	0.958786i	$0.408296\pi$
$312$	−39.5411	−2.23858
$313$	14.2659	0.806359	0.403180	−	0.915121i	$-0.367905\pi$
$313$	14.2659	0.806359	0.403180	+	0.915121i	$0.367905\pi$
$314$	44.2535	2.49737
$315$	8.97820	0.505864
$316$	−61.8373	−3.47862
$317$	−23.8586	−1.34003	−0.670015	−	0.742347i	$-0.733713\pi$
$317$	−23.8586	−1.34003	−0.670015	+	0.742347i	$0.733713\pi$
$318$	−10.3752	−0.581811
$319$	1.60580	0.0899074
$320$	−39.3541	−2.19996
$321$	9.20504	0.513775
$322$	−33.0476	−1.84167
$323$	7.29705	0.406019
$324$	13.9913	0.777296
$325$	−7.97338	−0.442284
$326$	34.7627	1.92533
$327$	9.38469	0.518974
$328$	66.7371	3.68494
$329$	5.50594	0.303552
$330$	−5.87616	−0.323472
$331$	23.6822	1.30169	0.650846	−	0.759210i	$-0.274414\pi$
$331$	23.6822	1.30169	0.650846	+	0.759210i	$0.274414\pi$
$332$	−24.6507	−1.35288
$333$	4.51060	0.247179
$334$	50.2433	2.74919
$335$	36.9738	2.02009
$336$	−15.9840	−0.872001
$337$	−7.38517	−0.402296	−0.201148	−	0.979561i	$-0.564467\pi$
$337$	−7.38517	−0.402296	−0.201148	+	0.979561i	$0.564467\pi$
$338$	−47.2351	−2.56925
$339$	−13.4669	−0.731423
$340$	12.8862	0.698854
$341$	5.64012	0.305430
$342$	−43.5333	−2.35401
$343$	−18.1631	−0.980714
$344$	8.19134	0.441647
$345$	17.3840	0.935924
$346$	37.2225	2.00110
$347$	−25.9513	−1.39314	−0.696570	−	0.717489i	$-0.745291\pi$
$347$	−25.9513	−1.39314	−0.696570	+	0.717489i	$0.745291\pi$
$348$	−7.09896	−0.380544
$349$	3.22080	0.172405	0.0862027	−	0.996278i	$-0.472527\pi$
$349$	3.22080	0.172405	0.0862027	+	0.996278i	$0.472527\pi$
$350$	−6.03669	−0.322675
$351$	−25.3056	−1.35071
$352$	−14.5768	−0.776946
$353$	17.6835	0.941198	0.470599	−	0.882347i	$-0.344038\pi$
$353$	17.6835	0.941198	0.470599	+	0.882347i	$0.344038\pi$
$354$	10.7438	0.571025
$355$	6.11192	0.324387
$356$	93.2819	4.94393
$357$	1.37364	0.0727006
$358$	−13.5680	−0.717092
$359$	0.130807	0.00690375	0.00345187	−	0.999994i	$-0.498901\pi$
$359$	0.130807	0.00690375	0.00345187	+	0.999994i	$0.498901\pi$
$360$	−46.6035	−2.45622
$361$	34.2469	1.80247
$362$	41.9546	2.20509
$363$	−0.870455	−0.0456870
$364$	−44.4459	−2.32960
$365$	31.0428	1.62485
$366$	3.68314	0.192521
$367$	−2.06773	−0.107935	−0.0539673	−	0.998543i	$-0.517187\pi$
$367$	−2.06773	−0.107935	−0.0539673	+	0.998543i	$0.517187\pi$
$368$	91.5904	4.77448
$369$	18.2687	0.951030
$370$	−13.5796	−0.705968
$371$	−7.06962	−0.367036
$372$	−24.9340	−1.29277
$373$	3.04369	0.157596	0.0787982	−	0.996891i	$-0.474892\pi$
$373$	3.04369	0.157596	0.0787982	+	0.996891i	$0.474892\pi$
$374$	2.66059	0.137576
$375$	−7.86746	−0.406274
$376$	−28.5799	−1.47390
$377$	−8.90510	−0.458636
$378$	−19.1590	−0.985433
$379$	−19.1476	−0.983545	−0.491772	−	0.870724i	$-0.663651\pi$
$379$	−19.1476	−0.983545	−0.491772	+	0.870724i	$0.663651\pi$
$380$	94.0315	4.82371
$381$	−14.9000	−0.763352
$382$	64.8054	3.31573
$383$	−27.1862	−1.38915	−0.694574	−	0.719421i	$-0.744407\pi$
$383$	−27.1862	−1.38915	−0.694574	+	0.719421i	$0.744407\pi$
$384$	10.5440	0.538069
$385$	−4.00400	−0.204063
$386$	−16.9613	−0.863308
$387$	2.24231	0.113983
$388$	−13.7346	−0.697269
$389$	−11.6206	−0.589190	−0.294595	−	0.955622i	$-0.595185\pi$
$389$	−11.6206	−0.589190	−0.294595	+	0.955622i	$0.595185\pi$
$390$	32.5868	1.65009
$391$	−7.87110	−0.398058
$392$	36.9405	1.86578
$393$	0.722621	0.0364514
$394$	−10.1421	−0.510953
$395$	30.8931	1.55440
$396$	−11.3881	−0.572276
$397$	−2.83727	−0.142398	−0.0711992	−	0.997462i	$-0.522683\pi$
$397$	−2.83727	−0.142398	−0.0711992	+	0.997462i	$0.522683\pi$
$398$	45.4450	2.27795
$399$	10.0235	0.501802
$400$	16.7305	0.836526
$401$	28.6063	1.42853	0.714265	−	0.699876i	$-0.246761\pi$
$401$	28.6063	1.42853	0.714265	+	0.699876i	$0.246761\pi$
$402$	−33.7482	−1.68321
$403$	−31.2778	−1.55806
$404$	−79.0099	−3.93089
$405$	−6.98987	−0.347330
$406$	−6.74210	−0.334605
$407$	−2.01159	−0.0997106
$408$	−7.13019	−0.352997
$409$	7.05543	0.348868	0.174434	−	0.984669i	$-0.444190\pi$
$409$	7.05543	0.348868	0.174434	+	0.984669i	$0.444190\pi$
$410$	−54.9996	−2.71624
$411$	12.5430	0.618699
$412$	−52.6038	−2.59160
$413$	7.32077	0.360232
$414$	46.9580	2.30786
$415$	12.3152	0.604528
$416$	80.8370	3.96336
$417$	16.8521	0.825253
$418$	19.4145	0.949593
$419$	16.6105	0.811478	0.405739	−	0.913989i	$-0.367014\pi$
$419$	16.6105	0.811478	0.405739	+	0.913989i	$0.367014\pi$
$420$	17.7010	0.863721
$421$	34.4380	1.67840	0.839202	−	0.543819i	$-0.183022\pi$
$421$	34.4380	1.67840	0.839202	+	0.543819i	$0.183022\pi$
$422$	−58.5103	−2.84824
$423$	−7.82350	−0.380391
$424$	36.6965	1.78214
$425$	−1.43779	−0.0697430
$426$	−5.57871	−0.270290
$427$	2.50968	0.121452
$428$	−53.7078	−2.59606
$429$	4.82719	0.233059
$430$	−6.75067	−0.325546
$431$	12.9384	0.623220	0.311610	−	0.950210i	$-0.399132\pi$
$431$	12.9384	0.623220	0.311610	+	0.950210i	$0.399132\pi$
$432$	53.0987	2.55471
$433$	23.7005	1.13897	0.569486	−	0.822001i	$-0.307142\pi$
$433$	23.7005	1.13897	0.569486	+	0.822001i	$0.307142\pi$
$434$	−23.6806	−1.13671
$435$	3.54654	0.170044
$436$	−54.7560	−2.62233
$437$	−57.4358	−2.74753
$438$	−28.3346	−1.35388
$439$	−12.5017	−0.596674	−0.298337	−	0.954461i	$-0.596432\pi$
$439$	−12.5017	−0.596674	−0.298337	+	0.954461i	$0.596432\pi$
$440$	20.7837	0.990825
$441$	10.1121	0.481531
$442$	−14.7546	−0.701803
$443$	28.6698	1.36214	0.681072	−	0.732217i	$-0.261514\pi$
$443$	28.6698	1.36214	0.681072	+	0.732217i	$0.261514\pi$
$444$	8.89289	0.422038
$445$	−46.6024	−2.20916
$446$	−35.8345	−1.69682
$447$	−17.3996	−0.822974
$448$	24.4764	1.15640
$449$	−19.9595	−0.941945	−0.470972	−	0.882148i	$-0.656097\pi$
$449$	−19.9595	−0.941945	−0.470972	+	0.882148i	$0.656097\pi$
$450$	8.57766	0.404355
$451$	−8.14727	−0.383640
$452$	78.5742	3.69582
$453$	−14.7040	−0.690854
$454$	21.1159	0.991019
$455$	22.2045	1.04096
$456$	−52.0293	−2.43650
$457$	−26.9453	−1.26045	−0.630224	−	0.776414i	$-0.717037\pi$
$457$	−26.9453	−1.26045	−0.630224	+	0.776414i	$0.717037\pi$
$458$	−10.9429	−0.511328
$459$	−4.56319	−0.212992
$460$	−101.429	−4.72914
$461$	−26.1593	−1.21836	−0.609179	−	0.793033i	$-0.708501\pi$
$461$	−26.1593	−1.21836	−0.609179	+	0.793033i	$0.708501\pi$
$462$	3.65469	0.170032
$463$	−30.0923	−1.39851	−0.699254	−	0.714873i	$-0.746484\pi$
$463$	−30.0923	−1.39851	−0.699254	+	0.714873i	$0.746484\pi$
$464$	18.6855	0.867454
$465$	12.4567	0.577666
$466$	−31.2924	−1.44959
$467$	−38.0326	−1.75994	−0.879969	−	0.475031i	$-0.842437\pi$
$467$	−38.0326	−1.75994	−0.879969	+	0.475031i	$0.842437\pi$
$468$	63.1540	2.91930
$469$	−22.9959	−1.06185
$470$	23.5534	1.08644
$471$	14.4782	0.667121
$472$	−38.0002	−1.74910
$473$	−1.00000	−0.0459800
$474$	−28.1980	−1.29518
$475$	−10.4916	−0.481388
$476$	−8.01463	−0.367350
$477$	10.0454	0.459946
$478$	−59.2904	−2.71188
$479$	−15.3441	−0.701090	−0.350545	−	0.936546i	$-0.614004\pi$
$479$	−15.3441	−0.701090	−0.350545	+	0.936546i	$0.614004\pi$
$480$	−32.1941	−1.46945
$481$	11.1554	0.508644
$482$	−53.8346	−2.45210
$483$	−10.8120	−0.491964
$484$	5.07876	0.230853
$485$	6.86162	0.311570
$486$	42.8025	1.94156
$487$	−4.98060	−0.225693	−0.112846	−	0.993612i	$-0.535997\pi$
$487$	−4.98060	−0.225693	−0.112846	+	0.993612i	$0.535997\pi$
$488$	−13.0271	−0.589710
$489$	11.3731	0.514312
$490$	−30.4435	−1.37530
$491$	24.3655	1.09960	0.549801	−	0.835296i	$-0.314704\pi$
$491$	24.3655	1.09960	0.549801	+	0.835296i	$0.314704\pi$
$492$	36.0177	1.62381
$493$	−1.60580	−0.0723215
$494$	−107.665	−4.84407
$495$	5.68936	0.255718
$496$	65.6302	2.94688
$497$	−3.80132	−0.170513
$498$	−11.2408	−0.503712
$499$	−15.6279	−0.699599	−0.349800	−	0.936825i	$-0.613750\pi$
$499$	−15.6279	−0.699599	−0.349800	+	0.936825i	$0.613750\pi$
$500$	45.9035	2.05287
$501$	16.4379	0.734390
$502$	−25.7934	−1.15122
$503$	−4.60234	−0.205208	−0.102604	−	0.994722i	$-0.532717\pi$
$503$	−4.60234	−0.205208	−0.102604	+	0.994722i	$0.532717\pi$
$504$	28.9851	1.29110
$505$	39.4723	1.75649
$506$	−20.9418	−0.930976
$507$	−15.4537	−0.686323
$508$	86.9358	3.85715
$509$	18.2928	0.810816	0.405408	−	0.914136i	$-0.367130\pi$
$509$	18.2928	0.810816	0.405408	+	0.914136i	$0.367130\pi$
$510$	5.87616	0.260201
$511$	−19.3071	−0.854097
$512$	21.0137	0.928683
$513$	−33.2978	−1.47014
$514$	71.4914	3.15335
$515$	26.2801	1.15804
$516$	4.42083	0.194616
$517$	3.48904	0.153448
$518$	8.44584	0.371089
$519$	12.1779	0.534552
$520$	−115.258	−5.05440
$521$	−2.19257	−0.0960584	−0.0480292	−	0.998846i	$-0.515294\pi$
$521$	−2.19257	−0.0960584	−0.0480292	+	0.998846i	$0.515294\pi$
$522$	9.57998	0.419304
$523$	13.2329	0.578636	0.289318	−	0.957233i	$-0.406571\pi$
$523$	13.2329	0.578636	0.289318	+	0.957233i	$0.406571\pi$
$524$	−4.21621	−0.184186
$525$	−1.97500	−0.0861960
$526$	80.4536	3.50794
$527$	−5.64012	−0.245688
$528$	−10.1289	−0.440803
$529$	38.9542	1.69366
$530$	−30.2425	−1.31365
$531$	−10.4022	−0.451419
$532$	−58.4831	−2.53556
$533$	45.1815	1.95703
$534$	42.5368	1.84075
$535$	26.8317	1.16003
$536$	119.366	5.15582
$537$	−4.43899	−0.191556
$538$	41.2764	1.77955
$539$	−4.50970	−0.194247
$540$	−58.8024	−2.53045
$541$	−14.6820	−0.631228	−0.315614	−	0.948888i	$-0.602211\pi$
$541$	−14.6820	−0.631228	−0.315614	+	0.948888i	$0.602211\pi$
$542$	39.0530	1.67747
$543$	13.7261	0.589044
$544$	14.5768	0.624975
$545$	27.3553	1.17177
$546$	−20.2674	−0.867365
$547$	−0.0899527	−0.00384610	−0.00192305	−	0.999998i	$-0.500612\pi$
$547$	−0.0899527	−0.00384610	−0.00192305	+	0.999998i	$0.500612\pi$
$548$	−73.1832	−3.12623
$549$	−3.56606	−0.152196
$550$	−3.82537	−0.163114
$551$	−11.7176	−0.499186
$552$	56.1224	2.38873
$553$	−19.2140	−0.817063
$554$	8.36401	0.355353
$555$	−4.44277	−0.188585
$556$	−98.3256	−4.16993
$557$	21.5747	0.914150	0.457075	−	0.889428i	$-0.348897\pi$
$557$	21.5747	0.914150	0.457075	+	0.889428i	$0.348897\pi$
$558$	33.6482	1.42444
$559$	5.54559	0.234554
$560$	−46.5917	−1.96886
$561$	0.870455	0.0367506
$562$	−2.71377	−0.114473
$563$	18.8013	0.792382	0.396191	−	0.918168i	$-0.370332\pi$
$563$	18.8013	0.792382	0.396191	+	0.918168i	$0.370332\pi$
$564$	−15.4245	−0.649487
$565$	−39.2546	−1.65145
$566$	−9.84072	−0.413637
$567$	4.34737	0.182572
$568$	19.7317	0.827923
$569$	−26.6804	−1.11850	−0.559251	−	0.828998i	$-0.688911\pi$
$569$	−26.6804	−1.11850	−0.559251	+	0.828998i	$0.688911\pi$
$570$	42.8786	1.79599
$571$	−3.77200	−0.157853	−0.0789267	−	0.996880i	$-0.525149\pi$
$571$	−3.77200	−0.157853	−0.0789267	+	0.996880i	$0.525149\pi$
$572$	−28.1647	−1.17763
$573$	21.2021	0.885730
$574$	34.2071	1.42778
$575$	11.3170	0.471950
$576$	−34.7790	−1.44912
$577$	−21.6186	−0.899994	−0.449997	−	0.893030i	$-0.648575\pi$
$577$	−21.6186	−0.899994	−0.449997	+	0.893030i	$0.648575\pi$
$578$	−2.66059	−0.110666
$579$	−5.54916	−0.230615
$580$	−20.6927	−0.859217
$581$	−7.65945	−0.317767
$582$	−6.26301	−0.259610
$583$	−4.47992	−0.185539
$584$	100.218	4.14706
$585$	−31.5509	−1.30447
$586$	−3.86231	−0.159550
$587$	−24.0630	−0.993187	−0.496594	−	0.867983i	$-0.665416\pi$
$587$	−24.0630	−0.993187	−0.496594	+	0.867983i	$0.665416\pi$
$588$	19.9367	0.822174
$589$	−41.1562	−1.69581
$590$	31.3169	1.28930
$591$	−3.31816	−0.136491
$592$	−23.4074	−0.962039
$593$	22.3368	0.917264	0.458632	−	0.888626i	$-0.348340\pi$
$593$	22.3368	0.917264	0.458632	+	0.888626i	$0.348340\pi$
$594$	−12.1408	−0.498143
$595$	4.00400	0.164148
$596$	101.520	4.15842
$597$	14.8680	0.608508
$598$	116.135	4.74910
$599$	18.5635	0.758484	0.379242	−	0.925297i	$-0.376185\pi$
$599$	18.5635	0.758484	0.379242	+	0.925297i	$0.376185\pi$
$600$	10.2517	0.418524
$601$	−2.90206	−0.118377	−0.0591887	−	0.998247i	$-0.518851\pi$
$601$	−2.90206	−0.118377	−0.0591887	+	0.998247i	$0.518851\pi$
$602$	4.19860	0.171122
$603$	32.6754	1.33064
$604$	85.7920	3.49083
$605$	−2.53728	−0.103155
$606$	−36.0287	−1.46357
$607$	−34.9208	−1.41739	−0.708696	−	0.705514i	$-0.750716\pi$
$607$	−34.9208	−1.41739	−0.708696	+	0.705514i	$0.750716\pi$
$608$	106.368	4.31378
$609$	−2.20578	−0.0893828
$610$	10.7359	0.434686
$611$	−19.3488	−0.782768
$612$	11.3881	0.460339
$613$	−32.4176	−1.30934	−0.654668	−	0.755917i	$-0.727191\pi$
$613$	−32.4176	−1.30934	−0.654668	+	0.755917i	$0.727191\pi$
$614$	−22.7140	−0.916663
$615$	−17.9940	−0.725587
$616$	−12.9265	−0.520823
$617$	0.469553	0.0189035	0.00945174	−	0.999955i	$-0.496991\pi$
$617$	0.469553	0.0189035	0.00945174	+	0.999955i	$0.496991\pi$
$618$	−23.9874	−0.964916
$619$	33.4134	1.34300	0.671500	−	0.741005i	$-0.265650\pi$
$619$	33.4134	1.34300	0.671500	+	0.741005i	$0.265650\pi$
$620$	−72.6800	−2.91890
$621$	35.9173	1.44131
$622$	−26.6627	−1.06908
$623$	28.9845	1.16124
$624$	56.1706	2.24862
$625$	−30.1217	−1.20487
$626$	−37.9559	−1.51702
$627$	6.35175	0.253665
$628$	−84.4747	−3.37091
$629$	2.01159	0.0802072
$630$	−23.8873	−0.951694
$631$	33.8593	1.34792	0.673959	−	0.738769i	$-0.264592\pi$
$631$	33.8593	1.34792	0.673959	+	0.738769i	$0.264592\pi$
$632$	99.7350	3.96724
$633$	−19.1426	−0.760849
$634$	63.4780	2.52103
$635$	−43.4319	−1.72354
$636$	19.8050	0.785319
$637$	25.0090	0.990892
$638$	−4.27238	−0.169145
$639$	5.40138	0.213675
$640$	30.7344	1.21489
$641$	6.38117	0.252041	0.126021	−	0.992028i	$-0.459779\pi$
$641$	6.38117	0.252041	0.126021	+	0.992028i	$0.459779\pi$
$642$	−24.4909	−0.966578
$643$	17.3845	0.685577	0.342788	−	0.939413i	$-0.388629\pi$
$643$	17.3845	0.685577	0.342788	+	0.939413i	$0.388629\pi$
$644$	63.0839	2.48585
$645$	−2.20859	−0.0869631
$646$	−19.4145	−0.763853
$647$	18.5926	0.730949	0.365475	−	0.930821i	$-0.380907\pi$
$647$	18.5926	0.730949	0.365475	+	0.930821i	$0.380907\pi$
$648$	−22.5661	−0.886478
$649$	4.63908	0.182100
$650$	21.2139	0.832079
$651$	−7.74748	−0.303648
$652$	−66.3578	−2.59877
$653$	40.0788	1.56840	0.784202	−	0.620505i	$-0.213073\pi$
$653$	40.0788	1.56840	0.784202	+	0.620505i	$0.213073\pi$
$654$	−24.9688	−0.976359
$655$	2.10636	0.0823023
$656$	−94.8041	−3.70148
$657$	27.4339	1.07030
$658$	−14.6491	−0.571080
$659$	−36.6028	−1.42584	−0.712921	−	0.701244i	$-0.752628\pi$
$659$	−36.6028	−1.42584	−0.712921	+	0.701244i	$0.752628\pi$
$660$	11.2169	0.436617
$661$	−12.3226	−0.479293	−0.239646	−	0.970860i	$-0.577031\pi$
$661$	−12.3226	−0.479293	−0.239646	+	0.970860i	$0.577031\pi$
$662$	−63.0087	−2.44890
$663$	−4.82719	−0.187472
$664$	39.7582	1.54292
$665$	29.2174	1.13300
$666$	−12.0009	−0.465024
$667$	12.6394	0.489399
$668$	−95.9085	−3.71081
$669$	−11.7238	−0.453270
$670$	−98.3722	−3.80045
$671$	1.59035	0.0613949
$672$	20.0232	0.772413
$673$	47.4646	1.82962	0.914812	−	0.403880i	$-0.132339\pi$
$673$	47.4646	1.82962	0.914812	+	0.403880i	$0.132339\pi$
$674$	19.6489	0.756849
$675$	6.56090	0.252529
$676$	90.1662	3.46793
$677$	0.548743	0.0210899	0.0105449	−	0.999944i	$-0.496643\pi$
$677$	0.548743	0.0210899	0.0105449	+	0.999944i	$0.496643\pi$
$678$	35.8300	1.37604
$679$	−4.26760	−0.163776
$680$	−20.7837	−0.797019
$681$	6.90840	0.264731
$682$	−15.0061	−0.574612
$683$	14.6486	0.560512	0.280256	−	0.959925i	$-0.409581\pi$
$683$	14.6486	0.560512	0.280256	+	0.959925i	$0.409581\pi$
$684$	83.0999	3.17740
$685$	36.5613	1.39694
$686$	48.3246	1.84504
$687$	−3.58014	−0.136591
$688$	−11.6363	−0.443630
$689$	24.8438	0.946474
$690$	−46.2518	−1.76078
$691$	−30.2219	−1.14969	−0.574847	−	0.818261i	$-0.694939\pi$
$691$	−30.2219	−1.14969	−0.574847	+	0.818261i	$0.694939\pi$
$692$	−71.0534	−2.70105
$693$	−3.53851	−0.134417
$694$	69.0459	2.62095
$695$	49.1221	1.86331
$696$	11.4496	0.433998
$697$	8.14727	0.308600
$698$	−8.56924	−0.324350
$699$	−10.2378	−0.387229
$700$	11.5233	0.435541
$701$	−46.9706	−1.77406	−0.887028	−	0.461716i	$-0.847234\pi$
$701$	−46.9706	−1.77406	−0.887028	+	0.461716i	$0.847234\pi$
$702$	67.3280	2.54113
$703$	14.6786	0.553616
$704$	15.5103	0.584568
$705$	7.70585	0.290219
$706$	−47.0486	−1.77070
$707$	−24.5499	−0.923293
$708$	−20.5086	−0.770760
$709$	35.2164	1.32258	0.661290	−	0.750130i	$-0.270009\pi$
$709$	35.2164	1.32258	0.661290	+	0.750130i	$0.270009\pi$
$710$	−16.2613	−0.610277
$711$	27.3016	1.02389
$712$	−150.451	−5.63838
$713$	44.3940	1.66257
$714$	−3.65469	−0.136773
$715$	14.0707	0.526215
$716$	25.8997	0.967919
$717$	−19.3978	−0.724423
$718$	−0.348025	−0.0129882
$719$	42.6654	1.59115	0.795576	−	0.605854i	$-0.207168\pi$
$719$	42.6654	1.59115	0.795576	+	0.605854i	$0.207168\pi$
$720$	66.2031	2.46724
$721$	−16.3450	−0.608719
$722$	−91.1171	−3.39103
$723$	−17.6128	−0.655029
$724$	−80.0865	−2.97639
$725$	2.30880	0.0857465
$726$	2.31593	0.0859521
$727$	−41.1159	−1.52490	−0.762452	−	0.647045i	$-0.776005\pi$
$727$	−41.1159	−1.52490	−0.762452	+	0.647045i	$0.776005\pi$
$728$	71.6850	2.65682
$729$	5.73890	0.212552
$730$	−82.5922	−3.05688
$731$	1.00000	0.0369863
$732$	−7.03068	−0.259862
$733$	29.0554	1.07319	0.536593	−	0.843841i	$-0.319711\pi$
$733$	29.0554	1.07319	0.536593	+	0.843841i	$0.319711\pi$
$734$	5.50139	0.203060
$735$	−9.96008	−0.367383
$736$	−114.735	−4.22920
$737$	−14.5722	−0.536774
$738$	−48.6056	−1.78920
$739$	15.3390	0.564253	0.282127	−	0.959377i	$-0.408960\pi$
$739$	15.3390	0.564253	0.282127	+	0.959377i	$0.408960\pi$
$740$	25.9218	0.952904
$741$	−35.2242	−1.29399
$742$	18.8094	0.690514
$743$	−7.58541	−0.278282	−0.139141	−	0.990273i	$-0.544434\pi$
$743$	−7.58541	−0.278282	−0.139141	+	0.990273i	$0.544434\pi$
$744$	40.2151	1.47436
$745$	−50.7179	−1.85816
$746$	−8.09803	−0.296490
$747$	10.8835	0.398205
$748$	−5.07876	−0.185698
$749$	−16.6880	−0.609767
$750$	20.9321	0.764333
$751$	22.8706	0.834559	0.417279	−	0.908778i	$-0.362984\pi$
$751$	22.8706	0.834559	0.417279	+	0.908778i	$0.362984\pi$
$752$	40.5995	1.48051
$753$	−8.43872	−0.307524
$754$	23.6928	0.862843
$755$	−42.8605	−1.55985
$756$	36.5723	1.33012
$757$	−32.4872	−1.18077	−0.590384	−	0.807123i	$-0.701024\pi$
$757$	−32.4872	−1.18077	−0.590384	+	0.807123i	$0.701024\pi$
$758$	50.9439	1.85037
$759$	−6.85144	−0.248691
$760$	−151.660	−5.50128
$761$	38.9926	1.41348	0.706740	−	0.707474i	$-0.250165\pi$
$761$	38.9926	1.41348	0.706740	+	0.707474i	$0.250165\pi$
$762$	39.6429	1.43611
$763$	−17.0137	−0.615938
$764$	−123.706	−4.47552
$765$	−5.68936	−0.205699
$766$	72.3313	2.61344
$767$	−25.7264	−0.928927
$768$	−1.05105	−0.0379265
$769$	−9.05845	−0.326656	−0.163328	−	0.986572i	$-0.552223\pi$
$769$	−9.05845	−0.326656	−0.163328	+	0.986572i	$0.552223\pi$
$770$	10.6530	0.383908
$771$	23.3895	0.842353
$772$	32.3771	1.16528
$773$	−5.78595	−0.208106	−0.104053	−	0.994572i	$-0.533181\pi$
$773$	−5.78595	−0.208106	−0.104053	+	0.994572i	$0.533181\pi$
$774$	−5.96587	−0.214439
$775$	8.10930	0.291295
$776$	22.1520	0.795211
$777$	2.76319	0.0991289
$778$	30.9178	1.10846
$779$	59.4510	2.13005
$780$	−62.2043	−2.22727
$781$	−2.40885	−0.0861953
$782$	20.9418	0.748877
$783$	7.32756	0.261866
$784$	−52.4763	−1.87415
$785$	42.2024	1.50627
$786$	−1.92260	−0.0685769
$787$	−13.3593	−0.476207	−0.238104	−	0.971240i	$-0.576526\pi$
$787$	−13.3593	−0.476207	−0.238104	+	0.971240i	$0.576526\pi$
$788$	19.3601	0.689676
$789$	26.3217	0.937076
$790$	−82.1939	−2.92433
$791$	24.4145	0.868079
$792$	18.3675	0.652661
$793$	−8.81944	−0.313188
$794$	7.54882	0.267898
$795$	−9.89430	−0.350915
$796$	−86.7491	−3.07474
$797$	8.87297	0.314297	0.157148	−	0.987575i	$-0.449770\pi$
$797$	8.87297	0.314297	0.157148	+	0.987575i	$0.449770\pi$
$798$	−26.6684	−0.944053
$799$	−3.48904	−0.123433
$800$	−20.9583	−0.740989
$801$	−41.1846	−1.45519
$802$	−76.1097	−2.68753
$803$	−12.2347	−0.431752
$804$	64.4213	2.27196
$805$	−31.5159	−1.11079
$806$	83.2176	2.93121
$807$	13.5042	0.475371
$808$	127.432	4.48304
$809$	−12.3372	−0.433754	−0.216877	−	0.976199i	$-0.569587\pi$
$809$	−12.3372	−0.433754	−0.216877	+	0.976199i	$0.569587\pi$
$810$	18.5972	0.653440
$811$	31.3233	1.09991	0.549955	−	0.835194i	$-0.314645\pi$
$811$	31.3233	1.09991	0.549955	+	0.835194i	$0.314645\pi$
$812$	12.8699	0.451644
$813$	12.7768	0.448102
$814$	5.35202	0.187588
$815$	33.1515	1.16125
$816$	10.1289	0.354582
$817$	7.29705	0.255291
$818$	−18.7716	−0.656335
$819$	19.6231	0.685688
$820$	104.988	3.66633
$821$	56.9650	1.98809	0.994047	−	0.108956i	$-0.0347507\pi$
$821$	56.9650	1.98809	0.994047	+	0.108956i	$0.0347507\pi$
$822$	−33.3717	−1.16397
$823$	−6.52318	−0.227384	−0.113692	−	0.993516i	$-0.536268\pi$
$823$	−6.52318	−0.227384	−0.113692	+	0.993516i	$0.536268\pi$
$824$	84.8425	2.95563
$825$	−1.25153	−0.0435727
$826$	−19.4776	−0.677713
$827$	34.5198	1.20037	0.600185	−	0.799861i	$-0.295093\pi$
$827$	34.5198	1.20037	0.600185	+	0.799861i	$0.295093\pi$
$828$	−89.6372	−3.11511
$829$	13.1429	0.456473	0.228237	−	0.973606i	$-0.426704\pi$
$829$	13.1429	0.456473	0.228237	+	0.973606i	$0.426704\pi$
$830$	−32.7657	−1.13731
$831$	2.73642	0.0949253
$832$	−86.0141	−2.98200
$833$	4.50970	0.156252
$834$	−44.8367	−1.55257
$835$	47.9146	1.65815
$836$	−37.0600	−1.28175
$837$	25.7370	0.889600
$838$	−44.1939	−1.52665
$839$	29.5728	1.02097	0.510483	−	0.859888i	$-0.329467\pi$
$839$	29.5728	1.02097	0.510483	+	0.859888i	$0.329467\pi$
$840$	−28.5493	−0.985043
$841$	−26.4214	−0.911083
$842$	−91.6255	−3.15762
$843$	−0.887852	−0.0305792
$844$	111.689	3.84450
$845$	−45.0458	−1.54962
$846$	20.8152	0.715640
$847$	1.57807	0.0542230
$848$	−52.1297	−1.79014
$849$	−3.21955	−0.110495
$850$	3.82537	0.131209
$851$	−15.8334	−0.542762
$852$	10.6491	0.364833
$853$	29.4565	1.00857	0.504285	−	0.863537i	$-0.331756\pi$
$853$	29.4565	1.00857	0.504285	+	0.863537i	$0.331756\pi$
$854$	−6.67725	−0.228491
$855$	−41.5155	−1.41980
$856$	86.6232	2.96072
$857$	15.0929	0.515564	0.257782	−	0.966203i	$-0.417008\pi$
$857$	15.0929	0.515564	0.257782	+	0.966203i	$0.417008\pi$
$858$	−12.8432	−0.438459
$859$	8.36317	0.285348	0.142674	−	0.989770i	$-0.454430\pi$
$859$	8.36317	0.285348	0.142674	+	0.989770i	$0.454430\pi$
$860$	12.8862	0.439417
$861$	11.1914	0.381402
$862$	−34.4238	−1.17248
$863$	3.72873	0.126927	0.0634637	−	0.997984i	$-0.479785\pi$
$863$	3.72873	0.126927	0.0634637	+	0.997984i	$0.479785\pi$
$864$	−66.5168	−2.26295
$865$	35.4973	1.20694
$866$	−63.0574	−2.14278
$867$	−0.870455	−0.0295622
$868$	45.2035	1.53431
$869$	−12.1757	−0.413031
$870$	−9.43592	−0.319908
$871$	80.8115	2.73819
$872$	88.3137	2.99068
$873$	6.06392	0.205233
$874$	152.813	5.16899
$875$	14.2631	0.482180
$876$	54.0875	1.82745
$877$	42.0489	1.41989	0.709945	−	0.704257i	$-0.248720\pi$
$877$	42.0489	1.41989	0.709945	+	0.704257i	$0.248720\pi$
$878$	33.2620	1.12254
$879$	−1.26361	−0.0426206
$880$	−29.5245	−0.995272
$881$	3.70250	0.124740	0.0623702	−	0.998053i	$-0.480134\pi$
$881$	3.70250	0.124740	0.0623702	+	0.998053i	$0.480134\pi$
$882$	−26.9043	−0.905915
$883$	5.52888	0.186062	0.0930309	−	0.995663i	$-0.470344\pi$
$883$	5.52888	0.186062	0.0930309	+	0.995663i	$0.470344\pi$
$884$	28.1647	0.947283
$885$	10.2458	0.344409
$886$	−76.2787	−2.56263
$887$	38.8050	1.30294	0.651472	−	0.758673i	$-0.274152\pi$
$887$	38.8050	1.30294	0.651472	+	0.758673i	$0.274152\pi$
$888$	−14.3430	−0.481319
$889$	27.0126	0.905973
$890$	123.990	4.15615
$891$	2.75487	0.0922916
$892$	68.4039	2.29033
$893$	−25.4597	−0.851976
$894$	46.2933	1.54828
$895$	−12.9392	−0.432508
$896$	−19.1154	−0.638599
$897$	37.9953	1.26863
$898$	53.1040	1.77210
$899$	9.05689	0.302064
$900$	−16.3737	−0.545791
$901$	4.47992	0.149248
$902$	21.6766	0.721751
$903$	1.37364	0.0457118
$904$	−126.729	−4.21495
$905$	40.0101	1.32998
$906$	39.1214	1.29972
$907$	15.8936	0.527737	0.263869	−	0.964559i	$-0.415001\pi$
$907$	15.8936	0.527737	0.263869	+	0.964559i	$0.415001\pi$
$908$	−40.3078	−1.33766
$909$	34.8834	1.15701
$910$	−59.0773	−1.95839
$911$	−17.9616	−0.595094	−0.297547	−	0.954707i	$-0.596169\pi$
$911$	−17.9616	−0.595094	−0.297547	+	0.954707i	$0.596169\pi$
$912$	73.9109	2.44743
$913$	−4.85369	−0.160634
$914$	71.6905	2.37131
$915$	3.51243	0.116117
$916$	20.8887	0.690182
$917$	−1.31006	−0.0432618
$918$	12.1408	0.400706
$919$	−49.0097	−1.61668	−0.808340	−	0.588715i	$-0.799634\pi$
$919$	−49.0097	−1.61668	−0.808340	+	0.588715i	$0.799634\pi$
$920$	163.591	5.39342
$921$	−7.43124	−0.244868
$922$	69.5992	2.29213
$923$	13.3585	0.439700
$924$	−6.97637	−0.229506
$925$	−2.89223	−0.0950961
$926$	80.0635	2.63105
$927$	23.2249	0.762806
$928$	−23.4074	−0.768385
$929$	−27.1642	−0.891228	−0.445614	−	0.895225i	$-0.647015\pi$
$929$	−27.1642	−0.891228	−0.445614	+	0.895225i	$0.647015\pi$
$930$	−33.1422	−1.08678
$931$	32.9075	1.07850
$932$	59.7335	1.95664
$933$	−8.72313	−0.285582
$934$	101.189	3.31101
$935$	2.53728	0.0829779
$936$	−101.859	−3.32935
$937$	19.4721	0.636124	0.318062	−	0.948070i	$-0.396968\pi$
$937$	19.4721	0.636124	0.318062	+	0.948070i	$0.396968\pi$
$938$	61.1828	1.99769
$939$	−12.4179	−0.405242
$940$	−44.9606	−1.46645
$941$	31.3309	1.02136	0.510679	−	0.859772i	$-0.329394\pi$
$941$	31.3309	1.02136	0.510679	+	0.859772i	$0.329394\pi$
$942$	−38.5206	−1.25507
$943$	−64.1280	−2.08829
$944$	53.9817	1.75695
$945$	−18.2710	−0.594356
$946$	2.66059	0.0865034
$947$	14.5406	0.472505	0.236253	−	0.971692i	$-0.424081\pi$
$947$	14.5406	0.472505	0.236253	+	0.971692i	$0.424081\pi$
$948$	53.8266	1.74821
$949$	67.8485	2.20246
$950$	27.9139	0.905647
$951$	20.7678	0.673443
$952$	12.9265	0.418950
$953$	30.6007	0.991254	0.495627	−	0.868535i	$-0.334938\pi$
$953$	30.6007	0.991254	0.495627	+	0.868535i	$0.334938\pi$
$954$	−26.7266	−0.865307
$955$	61.8017	1.99986
$956$	113.178	3.66045
$957$	−1.39777	−0.0451836
$958$	40.8244	1.31898
$959$	−22.7394	−0.734294
$960$	34.2560	1.10561
$961$	0.810984	0.0261608
$962$	−29.6801	−0.956925
$963$	23.7124	0.764120
$964$	102.764	3.30981
$965$	−16.1752	−0.520697
$966$	28.7664	0.925544
$967$	23.5641	0.757770	0.378885	−	0.925444i	$-0.376308\pi$
$967$	23.5641	0.757770	0.378885	+	0.925444i	$0.376308\pi$
$968$	−8.19134	−0.263280
$969$	−6.35175	−0.204048
$970$	−18.2560	−0.586165
$971$	25.4869	0.817913	0.408957	−	0.912554i	$-0.365893\pi$
$971$	25.4869	0.817913	0.408957	+	0.912554i	$0.365893\pi$
$972$	−81.7049	−2.62069
$973$	−30.5516	−0.979440
$974$	13.2514	0.424601
$975$	6.94047	0.222273
$976$	18.5058	0.592357
$977$	17.4287	0.557592	0.278796	−	0.960350i	$-0.410065\pi$
$977$	17.4287	0.557592	0.278796	+	0.960350i	$0.410065\pi$
$978$	−30.2593	−0.967587
$979$	18.3671	0.587014
$980$	58.1131	1.85636
$981$	24.1751	0.771852
$982$	−64.8268	−2.06871
$983$	24.3019	0.775110	0.387555	−	0.921847i	$-0.373320\pi$
$983$	24.3019	0.775110	0.387555	+	0.921847i	$0.373320\pi$
$984$	−58.0916	−1.85189
$985$	−9.67206	−0.308177
$986$	4.27238	0.136060
$987$	−4.79267	−0.152552
$988$	205.519	6.53845
$989$	−7.87110	−0.250286
$990$	−15.1371	−0.481088
$991$	46.5378	1.47832	0.739161	−	0.673529i	$-0.235222\pi$
$991$	46.5378	1.47832	0.739161	+	0.673529i	$0.235222\pi$
$992$	−82.2149	−2.61033
$993$	−20.6143	−0.654175
$994$	10.1138	0.320789
$995$	43.3387	1.37393
$996$	21.4574	0.679902
$997$	−52.3932	−1.65931	−0.829654	−	0.558278i	$-0.811462\pi$
$997$	−52.3932	−1.65931	−0.829654	+	0.558278i	$0.811462\pi$
$998$	41.5794	1.31617
$999$	−9.17926	−0.290419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.3	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.66059 q^{2} -0.870455 q^{3} +5.07876 q^{4} -2.53728 q^{5} +2.31593 q^{6} +1.57807 q^{7} -8.19134 q^{8} -2.24231 q^{9} +O(q^{10})\)	\(q-2.66059 q^{2} -0.870455 q^{3} +5.07876 q^{4} -2.53728 q^{5} +2.31593 q^{6} +1.57807 q^{7} -8.19134 q^{8} -2.24231 q^{9} +6.75067 q^{10} +1.00000 q^{11} -4.42083 q^{12} -5.54559 q^{13} -4.19860 q^{14} +2.20859 q^{15} +11.6363 q^{16} -1.00000 q^{17} +5.96587 q^{18} -7.29705 q^{19} -12.8862 q^{20} -1.37364 q^{21} -2.66059 q^{22} +7.87110 q^{23} +7.13019 q^{24} +1.43779 q^{25} +14.7546 q^{26} +4.56319 q^{27} +8.01463 q^{28} +1.60580 q^{29} -5.87616 q^{30} +5.64012 q^{31} -14.5768 q^{32} -0.870455 q^{33} +2.66059 q^{34} -4.00400 q^{35} -11.3881 q^{36} -2.01159 q^{37} +19.4145 q^{38} +4.82719 q^{39} +20.7837 q^{40} -8.14727 q^{41} +3.65469 q^{42} -1.00000 q^{43} +5.07876 q^{44} +5.68936 q^{45} -20.9418 q^{46} +3.48904 q^{47} -10.1289 q^{48} -4.50970 q^{49} -3.82537 q^{50} +0.870455 q^{51} -28.1647 q^{52} -4.47992 q^{53} -12.1408 q^{54} -2.53728 q^{55} -12.9265 q^{56} +6.35175 q^{57} -4.27238 q^{58} +4.63908 q^{59} +11.2169 q^{60} +1.59035 q^{61} -15.0061 q^{62} -3.53851 q^{63} +15.5103 q^{64} +14.0707 q^{65} +2.31593 q^{66} -14.5722 q^{67} -5.07876 q^{68} -6.85144 q^{69} +10.6530 q^{70} -2.40885 q^{71} +18.3675 q^{72} -12.2347 q^{73} +5.35202 q^{74} -1.25153 q^{75} -37.0600 q^{76} +1.57807 q^{77} -12.8432 q^{78} -12.1757 q^{79} -29.5245 q^{80} +2.75487 q^{81} +21.6766 q^{82} -4.85369 q^{83} -6.97637 q^{84} +2.53728 q^{85} +2.66059 q^{86} -1.39777 q^{87} -8.19134 q^{88} +18.3671 q^{89} -15.1371 q^{90} -8.75132 q^{91} +39.9754 q^{92} -4.90947 q^{93} -9.28292 q^{94} +18.5147 q^{95} +12.6884 q^{96} -2.70432 q^{97} +11.9985 q^{98} -2.24231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 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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