LMFDB - Embedded newform 8002.2.a.e.1.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.61
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.20430 q^{3} +1.00000 q^{4} -2.30939 q^{5} -2.20430 q^{6} -3.47075 q^{7} -1.00000 q^{8} +1.85892 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.20430 q^{3} +1.00000 q^{4} -2.30939 q^{5} -2.20430 q^{6} -3.47075 q^{7} -1.00000 q^{8} +1.85892 q^{9} +2.30939 q^{10} +1.06995 q^{11} +2.20430 q^{12} -2.45895 q^{13} +3.47075 q^{14} -5.09059 q^{15} +1.00000 q^{16} +0.439796 q^{17} -1.85892 q^{18} -5.10287 q^{19} -2.30939 q^{20} -7.65056 q^{21} -1.06995 q^{22} +2.64585 q^{23} -2.20430 q^{24} +0.333298 q^{25} +2.45895 q^{26} -2.51528 q^{27} -3.47075 q^{28} +2.14555 q^{29} +5.09059 q^{30} +5.54152 q^{31} -1.00000 q^{32} +2.35848 q^{33} -0.439796 q^{34} +8.01533 q^{35} +1.85892 q^{36} +11.2443 q^{37} +5.10287 q^{38} -5.42025 q^{39} +2.30939 q^{40} +0.0632186 q^{41} +7.65056 q^{42} -1.73296 q^{43} +1.06995 q^{44} -4.29298 q^{45} -2.64585 q^{46} -9.80320 q^{47} +2.20430 q^{48} +5.04612 q^{49} -0.333298 q^{50} +0.969439 q^{51} -2.45895 q^{52} -13.0233 q^{53} +2.51528 q^{54} -2.47093 q^{55} +3.47075 q^{56} -11.2482 q^{57} -2.14555 q^{58} -13.9155 q^{59} -5.09059 q^{60} -2.95703 q^{61} -5.54152 q^{62} -6.45185 q^{63} +1.00000 q^{64} +5.67868 q^{65} -2.35848 q^{66} +6.14925 q^{67} +0.439796 q^{68} +5.83223 q^{69} -8.01533 q^{70} +5.83615 q^{71} -1.85892 q^{72} -9.72900 q^{73} -11.2443 q^{74} +0.734688 q^{75} -5.10287 q^{76} -3.71352 q^{77} +5.42025 q^{78} -3.66633 q^{79} -2.30939 q^{80} -11.1212 q^{81} -0.0632186 q^{82} +10.5986 q^{83} -7.65056 q^{84} -1.01566 q^{85} +1.73296 q^{86} +4.72943 q^{87} -1.06995 q^{88} +14.3358 q^{89} +4.29298 q^{90} +8.53441 q^{91} +2.64585 q^{92} +12.2152 q^{93} +9.80320 q^{94} +11.7845 q^{95} -2.20430 q^{96} +13.4031 q^{97} -5.04612 q^{98} +1.98894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.20430	1.27265	0.636325	−	0.771421i	$-0.280454\pi$
$3$	2.20430	1.27265	0.636325	+	0.771421i	$0.280454\pi$
$4$	1.00000	0.500000
$5$	−2.30939	−1.03279	−0.516396	−	0.856350i	$-0.672727\pi$
$5$	−2.30939	−1.03279	−0.516396	+	0.856350i	$0.672727\pi$
$6$	−2.20430	−0.899900
$7$	−3.47075	−1.31182	−0.655910	−	0.754839i	$-0.727715\pi$
$7$	−3.47075	−1.31182	−0.655910	+	0.754839i	$0.727715\pi$
$8$	−1.00000	−0.353553
$9$	1.85892	0.619640
$10$	2.30939	0.730294
$11$	1.06995	0.322601	0.161300	−	0.986905i	$-0.448431\pi$
$11$	1.06995	0.322601	0.161300	+	0.986905i	$0.448431\pi$
$12$	2.20430	0.636325
$13$	−2.45895	−0.681990	−0.340995	−	0.940065i	$-0.610764\pi$
$13$	−2.45895	−0.681990	−0.340995	+	0.940065i	$0.610764\pi$
$14$	3.47075	0.927597
$15$	−5.09059	−1.31438
$16$	1.00000	0.250000
$17$	0.439796	0.106666	0.0533330	−	0.998577i	$-0.483016\pi$
$17$	0.439796	0.106666	0.0533330	+	0.998577i	$0.483016\pi$
$18$	−1.85892	−0.438152
$19$	−5.10287	−1.17068	−0.585339	−	0.810789i	$-0.699039\pi$
$19$	−5.10287	−1.17068	−0.585339	+	0.810789i	$0.699039\pi$
$20$	−2.30939	−0.516396
$21$	−7.65056	−1.66949
$22$	−1.06995	−0.228113
$23$	2.64585	0.551697	0.275849	−	0.961201i	$-0.411041\pi$
$23$	2.64585	0.551697	0.275849	+	0.961201i	$0.411041\pi$
$24$	−2.20430	−0.449950
$25$	0.333298	0.0666597
$26$	2.45895	0.482240
$27$	−2.51528	−0.484065
$28$	−3.47075	−0.655910
$29$	2.14555	0.398418	0.199209	−	0.979957i	$-0.436163\pi$
$29$	2.14555	0.398418	0.199209	+	0.979957i	$0.436163\pi$
$30$	5.09059	0.929410
$31$	5.54152	0.995287	0.497644	−	0.867382i	$-0.334199\pi$
$31$	5.54152	0.995287	0.497644	+	0.867382i	$0.334199\pi$
$32$	−1.00000	−0.176777
$33$	2.35848	0.410558
$34$	−0.439796	−0.0754243
$35$	8.01533	1.35484
$36$	1.85892	0.309820
$37$	11.2443	1.84855	0.924274	−	0.381731i	$-0.124672\pi$
$37$	11.2443	1.84855	0.924274	+	0.381731i	$0.124672\pi$
$38$	5.10287	0.827795
$39$	−5.42025	−0.867935
$40$	2.30939	0.365147
$41$	0.0632186	0.00987309	0.00493654	−	0.999988i	$-0.498429\pi$
$41$	0.0632186	0.00987309	0.00493654	+	0.999988i	$0.498429\pi$
$42$	7.65056	1.18051
$43$	−1.73296	−0.264274	−0.132137	−	0.991231i	$-0.542184\pi$
$43$	−1.73296	−0.264274	−0.132137	+	0.991231i	$0.542184\pi$
$44$	1.06995	0.161300
$45$	−4.29298	−0.639959
$46$	−2.64585	−0.390109
$47$	−9.80320	−1.42994	−0.714971	−	0.699154i	$-0.753560\pi$
$47$	−9.80320	−1.42994	−0.714971	+	0.699154i	$0.753560\pi$
$48$	2.20430	0.318163
$49$	5.04612	0.720874
$50$	−0.333298	−0.0471355
$51$	0.969439	0.135749
$52$	−2.45895	−0.340995
$53$	−13.0233	−1.78889	−0.894447	−	0.447174i	$-0.852430\pi$
$53$	−13.0233	−1.78889	−0.894447	+	0.447174i	$0.852430\pi$
$54$	2.51528	0.342286
$55$	−2.47093	−0.333180
$56$	3.47075	0.463799
$57$	−11.2482	−1.48986
$58$	−2.14555	−0.281724
$59$	−13.9155	−1.81165	−0.905824	−	0.423655i	$-0.860747\pi$
$59$	−13.9155	−1.81165	−0.905824	+	0.423655i	$0.860747\pi$
$60$	−5.09059	−0.657192
$61$	−2.95703	−0.378608	−0.189304	−	0.981919i	$-0.560623\pi$
$61$	−2.95703	−0.378608	−0.189304	+	0.981919i	$0.560623\pi$
$62$	−5.54152	−0.703774
$63$	−6.45185	−0.812857
$64$	1.00000	0.125000
$65$	5.67868	0.704354
$66$	−2.35848	−0.290309
$67$	6.14925	0.751250	0.375625	−	0.926772i	$-0.377428\pi$
$67$	6.14925	0.751250	0.375625	+	0.926772i	$0.377428\pi$
$68$	0.439796	0.0533330
$69$	5.83223	0.702118
$70$	−8.01533	−0.958015
$71$	5.83615	0.692623	0.346312	−	0.938120i	$-0.387434\pi$
$71$	5.83615	0.692623	0.346312	+	0.938120i	$0.387434\pi$
$72$	−1.85892	−0.219076
$73$	−9.72900	−1.13869	−0.569347	−	0.822097i	$-0.692804\pi$
$73$	−9.72900	−1.13869	−0.569347	+	0.822097i	$0.692804\pi$
$74$	−11.2443	−1.30712
$75$	0.734688	0.0848345
$76$	−5.10287	−0.585339
$77$	−3.71352	−0.423195
$78$	5.42025	0.613723
$79$	−3.66633	−0.412494	−0.206247	−	0.978500i	$-0.566125\pi$
$79$	−3.66633	−0.412494	−0.206247	+	0.978500i	$0.566125\pi$
$80$	−2.30939	−0.258198
$81$	−11.1212	−1.23569
$82$	−0.0632186	−0.00698133
$83$	10.5986	1.16335	0.581676	−	0.813421i	$-0.302397\pi$
$83$	10.5986	1.16335	0.581676	+	0.813421i	$0.302397\pi$
$84$	−7.65056	−0.834745
$85$	−1.01566	−0.110164
$86$	1.73296	0.186870
$87$	4.72943	0.507048
$88$	−1.06995	−0.114057
$89$	14.3358	1.51959	0.759795	−	0.650163i	$-0.225299\pi$
$89$	14.3358	1.51959	0.759795	+	0.650163i	$0.225299\pi$
$90$	4.29298	0.452520
$91$	8.53441	0.894649
$92$	2.64585	0.275849
$93$	12.2152	1.26665
$94$	9.80320	1.01112
$95$	11.7845	1.20907
$96$	−2.20430	−0.224975
$97$	13.4031	1.36088	0.680441	−	0.732803i	$-0.261788\pi$
$97$	13.4031	1.36088	0.680441	+	0.732803i	$0.261788\pi$
$98$	−5.04612	−0.509735
$99$	1.98894	0.199896
$100$	0.333298	0.0333298
$101$	−0.507978	−0.0505457	−0.0252728	−	0.999681i	$-0.508045\pi$
$101$	−0.507978	−0.0505457	−0.0252728	+	0.999681i	$0.508045\pi$
$102$	−0.969439	−0.0959888
$103$	9.55632	0.941612	0.470806	−	0.882237i	$-0.343963\pi$
$103$	9.55632	0.941612	0.470806	+	0.882237i	$0.343963\pi$
$104$	2.45895	0.241120
$105$	17.6682	1.72424
$106$	13.0233	1.26494
$107$	8.24230	0.796813	0.398407	−	0.917209i	$-0.369563\pi$
$107$	8.24230	0.796813	0.398407	+	0.917209i	$0.369563\pi$
$108$	−2.51528	−0.242033
$109$	−1.89158	−0.181180	−0.0905902	−	0.995888i	$-0.528875\pi$
$109$	−1.89158	−0.181180	−0.0905902	+	0.995888i	$0.528875\pi$
$110$	2.47093	0.235594
$111$	24.7857	2.35256
$112$	−3.47075	−0.327955
$113$	−16.5754	−1.55928	−0.779639	−	0.626229i	$-0.784597\pi$
$113$	−16.5754	−1.55928	−0.779639	+	0.626229i	$0.784597\pi$
$114$	11.2482	1.05349
$115$	−6.11030	−0.569789
$116$	2.14555	0.199209
$117$	−4.57099	−0.422588
$118$	13.9155	1.28103
$119$	−1.52642	−0.139927
$120$	5.09059	0.464705
$121$	−9.85521	−0.895929
$122$	2.95703	0.267716
$123$	0.139353	0.0125650
$124$	5.54152	0.497644
$125$	10.7773	0.963947
$126$	6.45185	0.574776
$127$	−1.56665	−0.139018	−0.0695088	−	0.997581i	$-0.522143\pi$
$127$	−1.56665	−0.139018	−0.0695088	+	0.997581i	$0.522143\pi$
$128$	−1.00000	−0.0883883
$129$	−3.81996	−0.336328
$130$	−5.67868	−0.498054
$131$	−11.3130	−0.988419	−0.494210	−	0.869343i	$-0.664543\pi$
$131$	−11.3130	−0.988419	−0.494210	+	0.869343i	$0.664543\pi$
$132$	2.35848	0.205279
$133$	17.7108	1.53572
$134$	−6.14925	−0.531214
$135$	5.80877	0.499939
$136$	−0.439796	−0.0377122
$137$	8.72664	0.745567	0.372784	−	0.927918i	$-0.378403\pi$
$137$	8.72664	0.745567	0.372784	+	0.927918i	$0.378403\pi$
$138$	−5.83223	−0.496472
$139$	17.1058	1.45090	0.725448	−	0.688277i	$-0.241632\pi$
$139$	17.1058	1.45090	0.725448	+	0.688277i	$0.241632\pi$
$140$	8.01533	0.677419
$141$	−21.6091	−1.81982
$142$	−5.83615	−0.489759
$143$	−2.63094	−0.220011
$144$	1.85892	0.154910
$145$	−4.95492	−0.411483
$146$	9.72900	0.805178
$147$	11.1231	0.917421
$148$	11.2443	0.924274
$149$	18.3777	1.50556	0.752779	−	0.658273i	$-0.228713\pi$
$149$	18.3777	1.50556	0.752779	+	0.658273i	$0.228713\pi$
$150$	−0.734688	−0.0599870
$151$	6.62709	0.539305	0.269652	−	0.962958i	$-0.413091\pi$
$151$	6.62709	0.539305	0.269652	+	0.962958i	$0.413091\pi$
$152$	5.10287	0.413897
$153$	0.817545	0.0660946
$154$	3.71352	0.299244
$155$	−12.7976	−1.02792
$156$	−5.42025	−0.433968
$157$	−1.59309	−0.127143	−0.0635713	−	0.997977i	$-0.520249\pi$
$157$	−1.59309	−0.127143	−0.0635713	+	0.997977i	$0.520249\pi$
$158$	3.66633	0.291677
$159$	−28.7073	−2.27664
$160$	2.30939	0.182574
$161$	−9.18308	−0.723728
$162$	11.1212	0.873762
$163$	−14.6767	−1.14957	−0.574784	−	0.818305i	$-0.694914\pi$
$163$	−14.6767	−1.14957	−0.574784	+	0.818305i	$0.694914\pi$
$164$	0.0632186	0.00493654
$165$	−5.44665	−0.424021
$166$	−10.5986	−0.822613
$167$	6.71789	0.519846	0.259923	−	0.965629i	$-0.416303\pi$
$167$	6.71789	0.519846	0.259923	+	0.965629i	$0.416303\pi$
$168$	7.65056	0.590254
$169$	−6.95356	−0.534889
$170$	1.01566	0.0778976
$171$	−9.48582	−0.725399
$172$	−1.73296	−0.132137
$173$	21.7323	1.65228	0.826139	−	0.563466i	$-0.190532\pi$
$173$	21.7323	1.65228	0.826139	+	0.563466i	$0.190532\pi$
$174$	−4.72943	−0.358537
$175$	−1.15680	−0.0874456
$176$	1.06995	0.0806502
$177$	−30.6739	−2.30559
$178$	−14.3358	−1.07451
$179$	9.58002	0.716044	0.358022	−	0.933713i	$-0.383451\pi$
$179$	9.58002	0.716044	0.358022	+	0.933713i	$0.383451\pi$
$180$	−4.29298	−0.319980
$181$	−7.85596	−0.583929	−0.291965	−	0.956429i	$-0.594309\pi$
$181$	−7.85596	−0.583929	−0.291965	+	0.956429i	$0.594309\pi$
$182$	−8.53441	−0.632612
$183$	−6.51816	−0.481836
$184$	−2.64585	−0.195054
$185$	−25.9675	−1.90917
$186$	−12.2152	−0.895659
$187$	0.470558	0.0344106
$188$	−9.80320	−0.714971
$189$	8.72990	0.635007
$190$	−11.7845	−0.854940
$191$	−5.78027	−0.418246	−0.209123	−	0.977889i	$-0.567061\pi$
$191$	−5.78027	−0.418246	−0.209123	+	0.977889i	$0.567061\pi$
$192$	2.20430	0.159081
$193$	8.15108	0.586727	0.293364	−	0.956001i	$-0.405225\pi$
$193$	8.15108	0.586727	0.293364	+	0.956001i	$0.405225\pi$
$194$	−13.4031	−0.962289
$195$	12.5175	0.896397
$196$	5.04612	0.360437
$197$	27.4967	1.95906	0.979528	−	0.201306i	$-0.0645187\pi$
$197$	27.4967	1.95906	0.979528	+	0.201306i	$0.0645187\pi$
$198$	−1.98894	−0.141348
$199$	12.1311	0.859950	0.429975	−	0.902841i	$-0.358522\pi$
$199$	12.1311	0.859950	0.429975	+	0.902841i	$0.358522\pi$
$200$	−0.333298	−0.0235678
$201$	13.5548	0.956079
$202$	0.507978	0.0357412
$203$	−7.44667	−0.522654
$204$	0.969439	0.0678743
$205$	−0.145997	−0.0101968
$206$	−9.55632	−0.665821
$207$	4.91842	0.341854
$208$	−2.45895	−0.170498
$209$	−5.45979	−0.377662
$210$	−17.6682	−1.21922
$211$	−0.515681	−0.0355009	−0.0177505	−	0.999842i	$-0.505650\pi$
$211$	−0.515681	−0.0355009	−0.0177505	+	0.999842i	$0.505650\pi$
$212$	−13.0233	−0.894447
$213$	12.8646	0.881468
$214$	−8.24230	−0.563432
$215$	4.00209	0.272940
$216$	2.51528	0.171143
$217$	−19.2333	−1.30564
$218$	1.89158	0.128114
$219$	−21.4456	−1.44916
$220$	−2.47093	−0.166590
$221$	−1.08144	−0.0727452
$222$	−24.7857	−1.66351
$223$	21.3057	1.42673	0.713367	−	0.700791i	$-0.247170\pi$
$223$	21.3057	1.42673	0.713367	+	0.700791i	$0.247170\pi$
$224$	3.47075	0.231899
$225$	0.619575	0.0413050
$226$	16.5754	1.10258
$227$	4.60848	0.305875	0.152938	−	0.988236i	$-0.451127\pi$
$227$	4.60848	0.305875	0.152938	+	0.988236i	$0.451127\pi$
$228$	−11.2482	−0.744932
$229$	−4.02324	−0.265863	−0.132931	−	0.991125i	$-0.542439\pi$
$229$	−4.02324	−0.265863	−0.132931	+	0.991125i	$0.542439\pi$
$230$	6.11030	0.402901
$231$	−8.18569	−0.538579
$232$	−2.14555	−0.140862
$233$	16.2200	1.06261	0.531303	−	0.847182i	$-0.321702\pi$
$233$	16.2200	1.06261	0.531303	+	0.847182i	$0.321702\pi$
$234$	4.57099	0.298815
$235$	22.6394	1.47683
$236$	−13.9155	−0.905824
$237$	−8.08167	−0.524961
$238$	1.52642	0.0989432
$239$	22.7057	1.46871	0.734353	−	0.678767i	$-0.237486\pi$
$239$	22.7057	1.46871	0.734353	+	0.678767i	$0.237486\pi$
$240$	−5.09059	−0.328596
$241$	22.6643	1.45994	0.729969	−	0.683480i	$-0.239535\pi$
$241$	22.6643	1.45994	0.729969	+	0.683480i	$0.239535\pi$
$242$	9.85521	0.633517
$243$	−16.9685	−1.08853
$244$	−2.95703	−0.189304
$245$	−11.6535	−0.744513
$246$	−0.139353	−0.00888479
$247$	12.5477	0.798391
$248$	−5.54152	−0.351887
$249$	23.3625	1.48054
$250$	−10.7773	−0.681613
$251$	9.63237	0.607990	0.303995	−	0.952674i	$-0.401679\pi$
$251$	9.63237	0.607990	0.303995	+	0.952674i	$0.401679\pi$
$252$	−6.45185	−0.406428
$253$	2.83091	0.177978
$254$	1.56665	0.0983002
$255$	−2.23882	−0.140200
$256$	1.00000	0.0625000
$257$	−13.9153	−0.868012	−0.434006	−	0.900910i	$-0.642900\pi$
$257$	−13.9153	−0.868012	−0.434006	+	0.900910i	$0.642900\pi$
$258$	3.81996	0.237820
$259$	−39.0261	−2.42496
$260$	5.67868	0.352177
$261$	3.98840	0.246876
$262$	11.3130	0.698918
$263$	16.4731	1.01577	0.507887	−	0.861424i	$-0.330427\pi$
$263$	16.4731	1.01577	0.507887	+	0.861424i	$0.330427\pi$
$264$	−2.35848	−0.145154
$265$	30.0760	1.84756
$266$	−17.7108	−1.08592
$267$	31.6003	1.93391
$268$	6.14925	0.375625
$269$	−14.1228	−0.861079	−0.430540	−	0.902572i	$-0.641677\pi$
$269$	−14.1228	−0.861079	−0.430540	+	0.902572i	$0.641677\pi$
$270$	−5.80877	−0.353510
$271$	14.9566	0.908551	0.454275	−	0.890861i	$-0.349898\pi$
$271$	14.9566	0.908551	0.454275	+	0.890861i	$0.349898\pi$
$272$	0.439796	0.0266665
$273$	18.8124	1.13858
$274$	−8.72664	−0.527196
$275$	0.356611	0.0215045
$276$	5.83223	0.351059
$277$	30.0410	1.80499	0.902494	−	0.430703i	$-0.141734\pi$
$277$	30.0410	1.80499	0.902494	+	0.430703i	$0.141734\pi$
$278$	−17.1058	−1.02594
$279$	10.3013	0.616720
$280$	−8.01533	−0.479008
$281$	1.66335	0.0992270	0.0496135	−	0.998768i	$-0.484201\pi$
$281$	1.66335	0.0992270	0.0496135	+	0.998768i	$0.484201\pi$
$282$	21.6091	1.28681
$283$	33.1541	1.97081	0.985403	−	0.170236i	$-0.0544529\pi$
$283$	33.1541	1.97081	0.985403	+	0.170236i	$0.0544529\pi$
$284$	5.83615	0.346312
$285$	25.9766	1.53872
$286$	2.63094	0.155571
$287$	−0.219416	−0.0129517
$288$	−1.85892	−0.109538
$289$	−16.8066	−0.988622
$290$	4.95492	0.290963
$291$	29.5445	1.73193
$292$	−9.72900	−0.569347
$293$	−9.13612	−0.533738	−0.266869	−	0.963733i	$-0.585989\pi$
$293$	−9.13612	−0.533738	−0.266869	+	0.963733i	$0.585989\pi$
$294$	−11.1231	−0.648714
$295$	32.1364	1.87106
$296$	−11.2443	−0.653560
$297$	−2.69121	−0.156160
$298$	−18.3777	−1.06459
$299$	−6.50601	−0.376252
$300$	0.734688	0.0424172
$301$	6.01467	0.346680
$302$	−6.62709	−0.381346
$303$	−1.11973	−0.0643270
$304$	−5.10287	−0.292670
$305$	6.82893	0.391024
$306$	−0.817545	−0.0467359
$307$	−15.0119	−0.856776	−0.428388	−	0.903595i	$-0.640918\pi$
$307$	−15.0119	−0.856776	−0.428388	+	0.903595i	$0.640918\pi$
$308$	−3.71352	−0.211597
$309$	21.0650	1.19834
$310$	12.7976	0.726853
$311$	−8.32976	−0.472337	−0.236169	−	0.971712i	$-0.575892\pi$
$311$	−8.32976	−0.472337	−0.236169	+	0.971712i	$0.575892\pi$
$312$	5.42025	0.306861
$313$	21.2712	1.20232	0.601161	−	0.799128i	$-0.294705\pi$
$313$	21.2712	1.20232	0.601161	+	0.799128i	$0.294705\pi$
$314$	1.59309	0.0899034
$315$	14.8999	0.839512
$316$	−3.66633	−0.206247
$317$	−12.9023	−0.724663	−0.362332	−	0.932049i	$-0.618019\pi$
$317$	−12.9023	−0.724663	−0.362332	+	0.932049i	$0.618019\pi$
$318$	28.7073	1.60983
$319$	2.29562	0.128530
$320$	−2.30939	−0.129099
$321$	18.1685	1.01406
$322$	9.18308	0.511753
$323$	−2.24422	−0.124872
$324$	−11.1212	−0.617843
$325$	−0.819564	−0.0454612
$326$	14.6767	0.812868
$327$	−4.16960	−0.230579
$328$	−0.0632186	−0.00349066
$329$	34.0245	1.87583
$330$	5.44665	0.299828
$331$	−27.2285	−1.49661	−0.748306	−	0.663354i	$-0.769132\pi$
$331$	−27.2285	−1.49661	−0.748306	+	0.663354i	$0.769132\pi$
$332$	10.5986	0.581676
$333$	20.9022	1.14543
$334$	−6.71789	−0.367586
$335$	−14.2010	−0.775885
$336$	−7.65056	−0.417372
$337$	−3.02187	−0.164612	−0.0823060	−	0.996607i	$-0.526228\pi$
$337$	−3.02187	−0.164612	−0.0823060	+	0.996607i	$0.526228\pi$
$338$	6.95356	0.378224
$339$	−36.5370	−1.98442
$340$	−1.01566	−0.0550820
$341$	5.92913	0.321081
$342$	9.48582	0.512935
$343$	6.78144	0.366164
$344$	1.73296	0.0934349
$345$	−13.4689	−0.725142
$346$	−21.7323	−1.16834
$347$	9.35278	0.502083	0.251042	−	0.967976i	$-0.419227\pi$
$347$	9.35278	0.502083	0.251042	+	0.967976i	$0.419227\pi$
$348$	4.72943	0.253524
$349$	1.54566	0.0827375	0.0413688	−	0.999144i	$-0.486828\pi$
$349$	1.54566	0.0827375	0.0413688	+	0.999144i	$0.486828\pi$
$350$	1.15680	0.0618333
$351$	6.18494	0.330128
$352$	−1.06995	−0.0570283
$353$	−13.3029	−0.708043	−0.354021	−	0.935237i	$-0.615186\pi$
$353$	−13.3029	−0.708043	−0.354021	+	0.935237i	$0.615186\pi$
$354$	30.6739	1.63030
$355$	−13.4780	−0.715336
$356$	14.3358	0.759795
$357$	−3.36468	−0.178078
$358$	−9.58002	−0.506320
$359$	17.3891	0.917760	0.458880	−	0.888498i	$-0.348251\pi$
$359$	17.3891	0.917760	0.458880	+	0.888498i	$0.348251\pi$
$360$	4.29298	0.226260
$361$	7.03926	0.370488
$362$	7.85596	0.412900
$363$	−21.7238	−1.14020
$364$	8.53441	0.447324
$365$	22.4681	1.17603
$366$	6.51816	0.340710
$367$	17.0579	0.890417	0.445209	−	0.895427i	$-0.353129\pi$
$367$	17.0579	0.890417	0.445209	+	0.895427i	$0.353129\pi$
$368$	2.64585	0.137924
$369$	0.117518	0.00611776
$370$	25.9675	1.34998
$371$	45.2008	2.34671
$372$	12.2152	0.633327
$373$	−2.69948	−0.139774	−0.0698869	−	0.997555i	$-0.522264\pi$
$373$	−2.69948	−0.139774	−0.0698869	+	0.997555i	$0.522264\pi$
$374$	−0.470558	−0.0243320
$375$	23.7562	1.22677
$376$	9.80320	0.505561
$377$	−5.27580	−0.271717
$378$	−8.72990	−0.449018
$379$	−23.6358	−1.21409	−0.607044	−	0.794668i	$-0.707645\pi$
$379$	−23.6358	−1.21409	−0.607044	+	0.794668i	$0.707645\pi$
$380$	11.7845	0.604534
$381$	−3.45336	−0.176921
$382$	5.78027	0.295744
$383$	0.430014	0.0219727	0.0109864	−	0.999940i	$-0.496503\pi$
$383$	0.430014	0.0219727	0.0109864	+	0.999940i	$0.496503\pi$
$384$	−2.20430	−0.112487
$385$	8.57597	0.437072
$386$	−8.15108	−0.414879
$387$	−3.22143	−0.163755
$388$	13.4031	0.680441
$389$	32.2276	1.63401	0.817003	−	0.576634i	$-0.195634\pi$
$389$	32.2276	1.63401	0.817003	+	0.576634i	$0.195634\pi$
$390$	−12.5175	−0.633848
$391$	1.16363	0.0588474
$392$	−5.04612	−0.254867
$393$	−24.9371	−1.25791
$394$	−27.4967	−1.38526
$395$	8.46699	0.426020
$396$	1.98894	0.0999482
$397$	−0.557780	−0.0279942	−0.0139971	−	0.999902i	$-0.504456\pi$
$397$	−0.557780	−0.0279942	−0.0139971	+	0.999902i	$0.504456\pi$
$398$	−12.1311	−0.608077
$399$	39.0398	1.95444
$400$	0.333298	0.0166649
$401$	6.50199	0.324694	0.162347	−	0.986734i	$-0.448094\pi$
$401$	6.50199	0.324694	0.162347	+	0.986734i	$0.448094\pi$
$402$	−13.5548	−0.676050
$403$	−13.6263	−0.678776
$404$	−0.507978	−0.0252728
$405$	25.6832	1.27621
$406$	7.44667	0.369572
$407$	12.0308	0.596343
$408$	−0.969439	−0.0479944
$409$	8.71043	0.430703	0.215351	−	0.976537i	$-0.430910\pi$
$409$	8.71043	0.430703	0.215351	+	0.976537i	$0.430910\pi$
$410$	0.145997	0.00721026
$411$	19.2361	0.948847
$412$	9.55632	0.470806
$413$	48.2973	2.37656
$414$	−4.91842	−0.241727
$415$	−24.4764	−1.20150
$416$	2.45895	0.120560
$417$	37.7063	1.84648
$418$	5.45979	0.267047
$419$	−25.8624	−1.26346	−0.631730	−	0.775189i	$-0.717655\pi$
$419$	−25.8624	−1.26346	−0.631730	+	0.775189i	$0.717655\pi$
$420$	17.6682	0.862118
$421$	−33.3883	−1.62724	−0.813622	−	0.581394i	$-0.802508\pi$
$421$	−33.3883	−1.62724	−0.813622	+	0.581394i	$0.802508\pi$
$422$	0.515681	0.0251030
$423$	−18.2234	−0.886050
$424$	13.0233	0.632470
$425$	0.146583	0.00711033
$426$	−12.8646	−0.623292
$427$	10.2631	0.496666
$428$	8.24230	0.398407
$429$	−5.79938	−0.279997
$430$	−4.00209	−0.192998
$431$	−2.24901	−0.108331	−0.0541655	−	0.998532i	$-0.517250\pi$
$431$	−2.24901	−0.108331	−0.0541655	+	0.998532i	$0.517250\pi$
$432$	−2.51528	−0.121016
$433$	4.34204	0.208665	0.104333	−	0.994542i	$-0.466729\pi$
$433$	4.34204	0.208665	0.104333	+	0.994542i	$0.466729\pi$
$434$	19.2333	0.923226
$435$	−10.9221	−0.523675
$436$	−1.89158	−0.0905902
$437$	−13.5014	−0.645860
$438$	21.4456	1.02471
$439$	−3.63163	−0.173328	−0.0866641	−	0.996238i	$-0.527621\pi$
$439$	−3.63163	−0.173328	−0.0866641	+	0.996238i	$0.527621\pi$
$440$	2.47093	0.117797
$441$	9.38033	0.446682
$442$	1.08144	0.0514386
$443$	−25.9286	−1.23191	−0.615953	−	0.787783i	$-0.711229\pi$
$443$	−25.9286	−1.23191	−0.615953	+	0.787783i	$0.711229\pi$
$444$	24.7857	1.17628
$445$	−33.1070	−1.56942
$446$	−21.3057	−1.00885
$447$	40.5099	1.91605
$448$	−3.47075	−0.163978
$449$	3.26202	0.153944	0.0769721	−	0.997033i	$-0.475475\pi$
$449$	3.26202	0.153944	0.0769721	+	0.997033i	$0.475475\pi$
$450$	−0.619575	−0.0292070
$451$	0.0676405	0.00318507
$452$	−16.5754	−0.779639
$453$	14.6081	0.686346
$454$	−4.60848	−0.216286
$455$	−19.7093	−0.923986
$456$	11.2482	0.526747
$457$	−37.3409	−1.74674	−0.873368	−	0.487061i	$-0.838069\pi$
$457$	−37.3409	−1.74674	−0.873368	+	0.487061i	$0.838069\pi$
$458$	4.02324	0.187993
$459$	−1.10621	−0.0516334
$460$	−6.11030	−0.284894
$461$	34.8843	1.62472	0.812361	−	0.583155i	$-0.198182\pi$
$461$	34.8843	1.62472	0.812361	+	0.583155i	$0.198182\pi$
$462$	8.18569	0.380833
$463$	−19.1210	−0.888629	−0.444315	−	0.895871i	$-0.646553\pi$
$463$	−19.1210	−0.888629	−0.444315	+	0.895871i	$0.646553\pi$
$464$	2.14555	0.0996046
$465$	−28.2096	−1.30819
$466$	−16.2200	−0.751376
$467$	−18.0828	−0.836771	−0.418386	−	0.908269i	$-0.637404\pi$
$467$	−18.0828	−0.836771	−0.418386	+	0.908269i	$0.637404\pi$
$468$	−4.57099	−0.211294
$469$	−21.3425	−0.985506
$470$	−22.6394	−1.04428
$471$	−3.51165	−0.161808
$472$	13.9155	0.640514
$473$	−1.85417	−0.0852550
$474$	8.08167	0.371203
$475$	−1.70078	−0.0780370
$476$	−1.52642	−0.0699634
$477$	−24.2094	−1.10847
$478$	−22.7057	−1.03853
$479$	3.92278	0.179237	0.0896183	−	0.995976i	$-0.471435\pi$
$479$	3.92278	0.179237	0.0896183	+	0.995976i	$0.471435\pi$
$480$	5.09059	0.232352
$481$	−27.6491	−1.26069
$482$	−22.6643	−1.03233
$483$	−20.2422	−0.921053
$484$	−9.85521	−0.447964
$485$	−30.9531	−1.40551
$486$	16.9685	0.769708
$487$	−28.0592	−1.27149	−0.635743	−	0.771901i	$-0.719306\pi$
$487$	−28.0592	−1.27149	−0.635743	+	0.771901i	$0.719306\pi$
$488$	2.95703	0.133858
$489$	−32.3518	−1.46300
$490$	11.6535	0.526450
$491$	33.4631	1.51017	0.755084	−	0.655628i	$-0.227596\pi$
$491$	33.4631	1.51017	0.755084	+	0.655628i	$0.227596\pi$
$492$	0.139353	0.00628250
$493$	0.943603	0.0424977
$494$	−12.5477	−0.564548
$495$	−4.59326	−0.206451
$496$	5.54152	0.248822
$497$	−20.2558	−0.908598
$498$	−23.3625	−1.04690
$499$	15.4024	0.689505	0.344752	−	0.938694i	$-0.387963\pi$
$499$	15.4024	0.689505	0.344752	+	0.938694i	$0.387963\pi$
$500$	10.7773	0.481973
$501$	14.8082	0.661582
$502$	−9.63237	−0.429914
$503$	−34.3202	−1.53026	−0.765130	−	0.643876i	$-0.777325\pi$
$503$	−34.3202	−1.53026	−0.765130	+	0.643876i	$0.777325\pi$
$504$	6.45185	0.287388
$505$	1.17312	0.0522032
$506$	−2.83091	−0.125849
$507$	−15.3277	−0.680727
$508$	−1.56665	−0.0695088
$509$	23.0882	1.02336	0.511682	−	0.859175i	$-0.329022\pi$
$509$	23.0882	1.02336	0.511682	+	0.859175i	$0.329022\pi$
$510$	2.23882	0.0991365
$511$	33.7670	1.49376
$512$	−1.00000	−0.0441942
$513$	12.8351	0.566685
$514$	13.9153	0.613777
$515$	−22.0693	−0.972490
$516$	−3.81996	−0.168164
$517$	−10.4889	−0.461301
$518$	39.0261	1.71471
$519$	47.9045	2.10277
$520$	−5.67868	−0.249027
$521$	−30.9493	−1.35592	−0.677958	−	0.735101i	$-0.737135\pi$
$521$	−30.9493	−1.35592	−0.677958	+	0.735101i	$0.737135\pi$
$522$	−3.98840	−0.174568
$523$	7.31707	0.319953	0.159977	−	0.987121i	$-0.448858\pi$
$523$	7.31707	0.319953	0.159977	+	0.987121i	$0.448858\pi$
$524$	−11.3130	−0.494210
$525$	−2.54992	−0.111288
$526$	−16.4731	−0.718260
$527$	2.43714	0.106163
$528$	2.35848	0.102640
$529$	−15.9995	−0.695630
$530$	−30.0760	−1.30642
$531$	−25.8679	−1.12257
$532$	17.7108	0.767860
$533$	−0.155451	−0.00673335
$534$	−31.6003	−1.36748
$535$	−19.0347	−0.822942
$536$	−6.14925	−0.265607
$537$	21.1172	0.911274
$538$	14.1228	0.608875
$539$	5.39907	0.232555
$540$	5.80877	0.249970
$541$	18.5459	0.797350	0.398675	−	0.917092i	$-0.369470\pi$
$541$	18.5459	0.797350	0.398675	+	0.917092i	$0.369470\pi$
$542$	−14.9566	−0.642442
$543$	−17.3169	−0.743138
$544$	−0.439796	−0.0188561
$545$	4.36840	0.187122
$546$	−18.8124	−0.805094
$547$	4.06277	0.173712	0.0868558	−	0.996221i	$-0.472318\pi$
$547$	4.06277	0.173712	0.0868558	+	0.996221i	$0.472318\pi$
$548$	8.72664	0.372784
$549$	−5.49687	−0.234601
$550$	−0.356611	−0.0152060
$551$	−10.9485	−0.466420
$552$	−5.83223	−0.248236
$553$	12.7249	0.541118
$554$	−30.0410	−1.27632
$555$	−57.2399	−2.42970
$556$	17.1058	0.725448
$557$	25.6616	1.08732	0.543659	−	0.839306i	$-0.317038\pi$
$557$	25.6616	1.08732	0.543659	+	0.839306i	$0.317038\pi$
$558$	−10.3013	−0.436087
$559$	4.26126	0.180232
$560$	8.01533	0.338710
$561$	1.03725	0.0437927
$562$	−1.66335	−0.0701641
$563$	12.7666	0.538048	0.269024	−	0.963134i	$-0.413299\pi$
$563$	12.7666	0.538048	0.269024	+	0.963134i	$0.413299\pi$
$564$	−21.6091	−0.909909
$565$	38.2790	1.61041
$566$	−33.1541	−1.39357
$567$	38.5988	1.62100
$568$	−5.83615	−0.244879
$569$	9.73544	0.408131	0.204065	−	0.978957i	$-0.434584\pi$
$569$	9.73544	0.408131	0.204065	+	0.978957i	$0.434584\pi$
$570$	−25.9766	−1.08804
$571$	−34.1343	−1.42848	−0.714238	−	0.699902i	$-0.753227\pi$
$571$	−34.1343	−1.42848	−0.714238	+	0.699902i	$0.753227\pi$
$572$	−2.63094	−0.110005
$573$	−12.7414	−0.532281
$574$	0.219416	0.00915825
$575$	0.881857	0.0367760
$576$	1.85892	0.0774550
$577$	−12.9989	−0.541152	−0.270576	−	0.962699i	$-0.587214\pi$
$577$	−12.9989	−0.541152	−0.270576	+	0.962699i	$0.587214\pi$
$578$	16.8066	0.699062
$579$	17.9674	0.746699
$580$	−4.95492	−0.205742
$581$	−36.7852	−1.52611
$582$	−29.5445	−1.22466
$583$	−13.9343	−0.577099
$584$	9.72900	0.402589
$585$	10.5562	0.436446
$586$	9.13612	0.377410
$587$	15.6291	0.645084	0.322542	−	0.946555i	$-0.395463\pi$
$587$	15.6291	0.645084	0.322542	+	0.946555i	$0.395463\pi$
$588$	11.1231	0.458710
$589$	−28.2777	−1.16516
$590$	−32.1364	−1.32304
$591$	60.6108	2.49319
$592$	11.2443	0.462137
$593$	−3.91297	−0.160686	−0.0803431	−	0.996767i	$-0.525602\pi$
$593$	−3.91297	−0.160686	−0.0803431	+	0.996767i	$0.525602\pi$
$594$	2.69121	0.110422
$595$	3.52511	0.144515
$596$	18.3777	0.752779
$597$	26.7405	1.09442
$598$	6.50601	0.266050
$599$	44.3863	1.81358	0.906788	−	0.421587i	$-0.138527\pi$
$599$	44.3863	1.81358	0.906788	+	0.421587i	$0.138527\pi$
$600$	−0.734688	−0.0299935
$601$	−1.57184	−0.0641166	−0.0320583	−	0.999486i	$-0.510206\pi$
$601$	−1.57184	−0.0641166	−0.0320583	+	0.999486i	$0.510206\pi$
$602$	−6.01467	−0.245140
$603$	11.4310	0.465505
$604$	6.62709	0.269652
$605$	22.7596	0.925308
$606$	1.11973	0.0454860
$607$	42.5531	1.72718	0.863588	−	0.504198i	$-0.168212\pi$
$607$	42.5531	1.72718	0.863588	+	0.504198i	$0.168212\pi$
$608$	5.10287	0.206949
$609$	−16.4147	−0.665156
$610$	−6.82893	−0.276495
$611$	24.1056	0.975207
$612$	0.817545	0.0330473
$613$	−38.7350	−1.56449	−0.782245	−	0.622970i	$-0.785926\pi$
$613$	−38.7350	−1.56449	−0.782245	+	0.622970i	$0.785926\pi$
$614$	15.0119	0.605832
$615$	−0.321820	−0.0129770
$616$	3.71352	0.149622
$617$	36.0824	1.45262	0.726311	−	0.687367i	$-0.241233\pi$
$617$	36.0824	1.45262	0.726311	+	0.687367i	$0.241233\pi$
$618$	−21.0650	−0.847357
$619$	6.78949	0.272893	0.136446	−	0.990647i	$-0.456432\pi$
$619$	6.78949	0.272893	0.136446	+	0.990647i	$0.456432\pi$
$620$	−12.7976	−0.513962
$621$	−6.65504	−0.267058
$622$	8.32976	0.333993
$623$	−49.7559	−1.99343
$624$	−5.42025	−0.216984
$625$	−26.5554	−1.06222
$626$	−21.2712	−0.850170
$627$	−12.0350	−0.480632
$628$	−1.59309	−0.0635713
$629$	4.94518	0.197177
$630$	−14.8999	−0.593625
$631$	−14.9853	−0.596555	−0.298277	−	0.954479i	$-0.596412\pi$
$631$	−14.9853	−0.596555	−0.298277	+	0.954479i	$0.596412\pi$
$632$	3.66633	0.145839
$633$	−1.13671	−0.0451803
$634$	12.9023	0.512414
$635$	3.61801	0.143576
$636$	−28.7073	−1.13832
$637$	−12.4081	−0.491629
$638$	−2.29562	−0.0908846
$639$	10.8489	0.429177
$640$	2.30939	0.0912868
$641$	−18.7212	−0.739444	−0.369722	−	0.929142i	$-0.620547\pi$
$641$	−18.7212	−0.739444	−0.369722	+	0.929142i	$0.620547\pi$
$642$	−18.1685	−0.717052
$643$	−28.8560	−1.13797	−0.568984	−	0.822349i	$-0.692663\pi$
$643$	−28.8560	−1.13797	−0.568984	+	0.822349i	$0.692663\pi$
$644$	−9.18308	−0.361864
$645$	8.82178	0.347357
$646$	2.24422	0.0882976
$647$	46.3226	1.82113	0.910565	−	0.413367i	$-0.135647\pi$
$647$	46.3226	1.82113	0.910565	+	0.413367i	$0.135647\pi$
$648$	11.1212	0.436881
$649$	−14.8889	−0.584439
$650$	0.819564	0.0321460
$651$	−42.3958	−1.66162
$652$	−14.6767	−0.574784
$653$	−41.8465	−1.63758	−0.818789	−	0.574094i	$-0.805354\pi$
$653$	−41.8465	−1.63758	−0.818789	+	0.574094i	$0.805354\pi$
$654$	4.16960	0.163044
$655$	26.1261	1.02083
$656$	0.0632186	0.00246827
$657$	−18.0854	−0.705580
$658$	−34.0245	−1.32641
$659$	−39.1089	−1.52347	−0.761733	−	0.647891i	$-0.775651\pi$
$659$	−39.1089	−1.52347	−0.761733	+	0.647891i	$0.775651\pi$
$660$	−5.44665	−0.212011
$661$	−43.7325	−1.70100	−0.850499	−	0.525977i	$-0.823700\pi$
$661$	−43.7325	−1.70100	−0.850499	+	0.525977i	$0.823700\pi$
$662$	27.2285	1.05826
$663$	−2.38380	−0.0925793
$664$	−10.5986	−0.411307
$665$	−40.9012	−1.58608
$666$	−20.9022	−0.809944
$667$	5.67680	0.219806
$668$	6.71789	0.259923
$669$	46.9640	1.81573
$670$	14.2010	0.548634
$671$	−3.16386	−0.122139
$672$	7.65056	0.295127
$673$	21.0563	0.811660	0.405830	−	0.913949i	$-0.366983\pi$
$673$	21.0563	0.811660	0.405830	+	0.913949i	$0.366983\pi$
$674$	3.02187	0.116398
$675$	−0.838338	−0.0322676
$676$	−6.95356	−0.267445
$677$	40.4015	1.55275	0.776377	−	0.630268i	$-0.217055\pi$
$677$	40.4015	1.55275	0.776377	+	0.630268i	$0.217055\pi$
$678$	36.5370	1.40319
$679$	−46.5189	−1.78523
$680$	1.01566	0.0389488
$681$	10.1584	0.389272
$682$	−5.92913	−0.227038
$683$	30.5522	1.16905	0.584524	−	0.811376i	$-0.301281\pi$
$683$	30.5522	1.16905	0.584524	+	0.811376i	$0.301281\pi$
$684$	−9.48582	−0.362700
$685$	−20.1533	−0.770016
$686$	−6.78144	−0.258917
$687$	−8.86840	−0.338351
$688$	−1.73296	−0.0660685
$689$	32.0238	1.22001
$690$	13.4689	0.512753
$691$	−8.36067	−0.318055	−0.159027	−	0.987274i	$-0.550836\pi$
$691$	−8.36067	−0.318055	−0.159027	+	0.987274i	$0.550836\pi$
$692$	21.7323	0.826139
$693$	−6.90313	−0.262228
$694$	−9.35278	−0.355027
$695$	−39.5041	−1.49847
$696$	−4.72943	−0.179268
$697$	0.0278033	0.00105312
$698$	−1.54566	−0.0585043
$699$	35.7536	1.35233
$700$	−1.15680	−0.0437228
$701$	−17.1477	−0.647659	−0.323830	−	0.946115i	$-0.604970\pi$
$701$	−17.1477	−0.647659	−0.323830	+	0.946115i	$0.604970\pi$
$702$	−6.18494	−0.233436
$703$	−57.3780	−2.16405
$704$	1.06995	0.0403251
$705$	49.9040	1.87949
$706$	13.3029	0.500662
$707$	1.76306	0.0663068
$708$	−30.6739	−1.15280
$709$	−9.32864	−0.350345	−0.175172	−	0.984538i	$-0.556048\pi$
$709$	−9.32864	−0.350345	−0.175172	+	0.984538i	$0.556048\pi$
$710$	13.4780	0.505819
$711$	−6.81541	−0.255598
$712$	−14.3358	−0.537256
$713$	14.6620	0.549097
$714$	3.36468	0.125920
$715$	6.07589	0.227225
$716$	9.58002	0.358022
$717$	50.0500	1.86915
$718$	−17.3891	−0.648955
$719$	−2.53841	−0.0946669	−0.0473334	−	0.998879i	$-0.515072\pi$
$719$	−2.53841	−0.0946669	−0.0473334	+	0.998879i	$0.515072\pi$
$720$	−4.29298	−0.159990
$721$	−33.1676	−1.23523
$722$	−7.03926	−0.261974
$723$	49.9589	1.85799
$724$	−7.85596	−0.291965
$725$	0.715108	0.0265584
$726$	21.7238	0.806246
$727$	16.7547	0.621397	0.310699	−	0.950508i	$-0.399437\pi$
$727$	16.7547	0.621397	0.310699	+	0.950508i	$0.399437\pi$
$728$	−8.53441	−0.316306
$729$	−4.04013	−0.149634
$730$	−22.4681	−0.831582
$731$	−0.762148	−0.0281891
$732$	−6.51816	−0.240918
$733$	27.3126	1.00881	0.504407	−	0.863466i	$-0.331711\pi$
$733$	27.3126	1.00881	0.504407	+	0.863466i	$0.331711\pi$
$734$	−17.0579	−0.629620
$735$	−25.6877	−0.947505
$736$	−2.64585	−0.0975272
$737$	6.57936	0.242354
$738$	−0.117518	−0.00432591
$739$	17.6357	0.648738	0.324369	−	0.945931i	$-0.394848\pi$
$739$	17.6357	0.648738	0.324369	+	0.945931i	$0.394848\pi$
$740$	−25.9675	−0.954583
$741$	27.6588	1.01607
$742$	−45.2008	−1.65937
$743$	−28.6620	−1.05151	−0.525754	−	0.850637i	$-0.676217\pi$
$743$	−28.6620	−1.05151	−0.525754	+	0.850637i	$0.676217\pi$
$744$	−12.2152	−0.447829
$745$	−42.4413	−1.55493
$746$	2.69948	0.0988351
$747$	19.7020	0.720859
$748$	0.470558	0.0172053
$749$	−28.6070	−1.04528
$750$	−23.7562	−0.867456
$751$	−45.7035	−1.66775	−0.833873	−	0.551956i	$-0.813882\pi$
$751$	−45.7035	−1.66775	−0.833873	+	0.551956i	$0.813882\pi$
$752$	−9.80320	−0.357486
$753$	21.2326	0.773759
$754$	5.27580	0.192133
$755$	−15.3045	−0.556990
$756$	8.72990	0.317504
$757$	−38.7954	−1.41004	−0.705021	−	0.709186i	$-0.749062\pi$
$757$	−38.7954	−1.41004	−0.705021	+	0.709186i	$0.749062\pi$
$758$	23.6358	0.858490
$759$	6.24017	0.226504
$760$	−11.7845	−0.427470
$761$	21.3616	0.774356	0.387178	−	0.922005i	$-0.373450\pi$
$761$	21.3616	0.774356	0.387178	+	0.922005i	$0.373450\pi$
$762$	3.45336	0.125102
$763$	6.56520	0.237676
$764$	−5.78027	−0.209123
$765$	−1.88803	−0.0682620
$766$	−0.430014	−0.0155371
$767$	34.2176	1.23553
$768$	2.20430	0.0795407
$769$	9.09245	0.327882	0.163941	−	0.986470i	$-0.447579\pi$
$769$	9.09245	0.327882	0.163941	+	0.986470i	$0.447579\pi$
$770$	−8.57597	−0.309057
$771$	−30.6734	−1.10468
$772$	8.15108	0.293364
$773$	24.9311	0.896710	0.448355	−	0.893855i	$-0.352010\pi$
$773$	24.9311	0.896710	0.448355	+	0.893855i	$0.352010\pi$
$774$	3.22143	0.115792
$775$	1.84698	0.0663455
$776$	−13.4031	−0.481144
$777$	−86.0250	−3.08613
$778$	−32.2276	−1.15542
$779$	−0.322596	−0.0115582
$780$	12.5175	0.448198
$781$	6.24436	0.223441
$782$	−1.16363	−0.0416114
$783$	−5.39665	−0.192861
$784$	5.04612	0.180218
$785$	3.67908	0.131312
$786$	24.9371	0.889479
$787$	17.1708	0.612072	0.306036	−	0.952020i	$-0.400997\pi$
$787$	17.1708	0.612072	0.306036	+	0.952020i	$0.400997\pi$
$788$	27.4967	0.979528
$789$	36.3115	1.29273
$790$	−8.46699	−0.301242
$791$	57.5289	2.04549
$792$	−1.98894	−0.0706741
$793$	7.27118	0.258207
$794$	0.557780	0.0197949
$795$	66.2965	2.35129
$796$	12.1311	0.429975
$797$	6.13444	0.217293	0.108647	−	0.994080i	$-0.465348\pi$
$797$	6.13444	0.217293	0.108647	+	0.994080i	$0.465348\pi$
$798$	−39.0398	−1.38199
$799$	−4.31140	−0.152526
$800$	−0.333298	−0.0117839
$801$	26.6491	0.941599
$802$	−6.50199	−0.229593
$803$	−10.4095	−0.367344
$804$	13.5548	0.478040
$805$	21.2073	0.747461
$806$	13.6263	0.479967
$807$	−31.1307	−1.09585
$808$	0.507978	0.0178706
$809$	−52.2545	−1.83717	−0.918585	−	0.395223i	$-0.870667\pi$
$809$	−52.2545	−1.83717	−0.918585	+	0.395223i	$0.870667\pi$
$810$	−25.6832	−0.902415
$811$	−31.4153	−1.10314	−0.551571	−	0.834128i	$-0.685971\pi$
$811$	−31.4153	−1.10314	−0.551571	+	0.834128i	$0.685971\pi$
$812$	−7.44667	−0.261327
$813$	32.9688	1.15627
$814$	−12.0308	−0.421678
$815$	33.8943	1.18727
$816$	0.969439	0.0339372
$817$	8.84307	0.309380
$818$	−8.71043	−0.304553
$819$	15.8648	0.554360
$820$	−0.145997	−0.00509842
$821$	−34.3881	−1.20015	−0.600076	−	0.799943i	$-0.704863\pi$
$821$	−34.3881	−1.20015	−0.600076	+	0.799943i	$0.704863\pi$
$822$	−19.2361	−0.670936
$823$	−25.9712	−0.905299	−0.452650	−	0.891688i	$-0.649521\pi$
$823$	−25.9712	−0.905299	−0.452650	+	0.891688i	$0.649521\pi$
$824$	−9.55632	−0.332910
$825$	0.786077	0.0273677
$826$	−48.2973	−1.68048
$827$	−13.2370	−0.460294	−0.230147	−	0.973156i	$-0.573921\pi$
$827$	−13.2370	−0.460294	−0.230147	+	0.973156i	$0.573921\pi$
$828$	4.91842	0.170927
$829$	−34.1761	−1.18698	−0.593492	−	0.804840i	$-0.702251\pi$
$829$	−34.1761	−1.18698	−0.593492	+	0.804840i	$0.702251\pi$
$830$	24.4764	0.849589
$831$	66.2192	2.29712
$832$	−2.45895	−0.0852488
$833$	2.21926	0.0768928
$834$	−37.7063	−1.30566
$835$	−15.5142	−0.536893
$836$	−5.45979	−0.188831
$837$	−13.9385	−0.481784
$838$	25.8624	0.893401
$839$	−12.8998	−0.445351	−0.222676	−	0.974893i	$-0.571479\pi$
$839$	−12.8998	−0.445351	−0.222676	+	0.974893i	$0.571479\pi$
$840$	−17.6682	−0.609609
$841$	−24.3966	−0.841263
$842$	33.3883	1.15064
$843$	3.66651	0.126281
$844$	−0.515681	−0.0177505
$845$	16.0585	0.552430
$846$	18.2234	0.626532
$847$	34.2050	1.17530
$848$	−13.0233	−0.447224
$849$	73.0814	2.50815
$850$	−0.146583	−0.00502776
$851$	29.7506	1.01984
$852$	12.8646	0.440734
$853$	−30.9052	−1.05817	−0.529087	−	0.848567i	$-0.677466\pi$
$853$	−30.9052	−1.05817	−0.529087	+	0.848567i	$0.677466\pi$
$854$	−10.2631	−0.351196
$855$	21.9065	0.749186
$856$	−8.24230	−0.281716
$857$	46.7570	1.59719	0.798594	−	0.601870i	$-0.205578\pi$
$857$	46.7570	1.59719	0.798594	+	0.601870i	$0.205578\pi$
$858$	5.79938	0.197988
$859$	24.5843	0.838806	0.419403	−	0.907800i	$-0.362239\pi$
$859$	24.5843	0.838806	0.419403	+	0.907800i	$0.362239\pi$
$860$	4.00209	0.136470
$861$	−0.483658	−0.0164830
$862$	2.24901	0.0766015
$863$	0.307708	0.0104745	0.00523725	−	0.999986i	$-0.498333\pi$
$863$	0.307708	0.0104745	0.00523725	+	0.999986i	$0.498333\pi$
$864$	2.51528	0.0855715
$865$	−50.1885	−1.70646
$866$	−4.34204	−0.147549
$867$	−37.0467	−1.25817
$868$	−19.2333	−0.652819
$869$	−3.92277	−0.133071
$870$	10.9221	0.370294
$871$	−15.1207	−0.512345
$872$	1.89158	0.0640569
$873$	24.9153	0.843257
$874$	13.5014	0.456692
$875$	−37.4052	−1.26453
$876$	−21.4456	−0.724580
$877$	18.2939	0.617743	0.308871	−	0.951104i	$-0.400049\pi$
$877$	18.2939	0.617743	0.308871	+	0.951104i	$0.400049\pi$
$878$	3.63163	0.122562
$879$	−20.1387	−0.679262
$880$	−2.47093	−0.0832949
$881$	28.9441	0.975151	0.487576	−	0.873081i	$-0.337881\pi$
$881$	28.9441	0.975151	0.487576	+	0.873081i	$0.337881\pi$
$882$	−9.38033	−0.315852
$883$	−7.44021	−0.250383	−0.125192	−	0.992133i	$-0.539955\pi$
$883$	−7.44021	−0.250383	−0.125192	+	0.992133i	$0.539955\pi$
$884$	−1.08144	−0.0363726
$885$	70.8382	2.38120
$886$	25.9286	0.871089
$887$	−25.2527	−0.847904	−0.423952	−	0.905685i	$-0.639357\pi$
$887$	−25.2527	−0.847904	−0.423952	+	0.905685i	$0.639357\pi$
$888$	−24.7857	−0.831754
$889$	5.43745	0.182366
$890$	33.1070	1.10975
$891$	−11.8991	−0.398634
$892$	21.3057	0.713367
$893$	50.0244	1.67400
$894$	−40.5099	−1.35485
$895$	−22.1240	−0.739525
$896$	3.47075	0.115950
$897$	−14.3412	−0.478838
$898$	−3.26202	−0.108855
$899$	11.8896	0.396541
$900$	0.619575	0.0206525
$901$	−5.72761	−0.190814
$902$	−0.0676405	−0.00225218
$903$	13.2581	0.441203
$904$	16.5754	0.551288
$905$	18.1425	0.603077
$906$	−14.6081	−0.485320
$907$	−13.4356	−0.446123	−0.223062	−	0.974804i	$-0.571605\pi$
$907$	−13.4356	−0.446123	−0.223062	+	0.974804i	$0.571605\pi$
$908$	4.60848	0.152938
$909$	−0.944290	−0.0313201
$910$	19.7093	0.653357
$911$	8.04234	0.266455	0.133227	−	0.991085i	$-0.457466\pi$
$911$	8.04234	0.266455	0.133227	+	0.991085i	$0.457466\pi$
$912$	−11.2482	−0.372466
$913$	11.3400	0.375298
$914$	37.3409	1.23513
$915$	15.0530	0.497637
$916$	−4.02324	−0.132931
$917$	39.2645	1.29663
$918$	1.10621	0.0365103
$919$	38.2262	1.26097	0.630483	−	0.776203i	$-0.282857\pi$
$919$	38.2262	1.26097	0.630483	+	0.776203i	$0.282857\pi$
$920$	6.11030	0.201451
$921$	−33.0907	−1.09038
$922$	−34.8843	−1.14885
$923$	−14.3508	−0.472362
$924$	−8.18569	−0.269289
$925$	3.74770	0.123224
$926$	19.1210	0.628356
$927$	17.7644	0.583461
$928$	−2.14555	−0.0704311
$929$	37.0077	1.21418	0.607091	−	0.794632i	$-0.292336\pi$
$929$	37.0077	1.21418	0.607091	+	0.794632i	$0.292336\pi$
$930$	28.2096	0.925030
$931$	−25.7497	−0.843911
$932$	16.2200	0.531303
$933$	−18.3613	−0.601120
$934$	18.0828	0.591687
$935$	−1.08670	−0.0355390
$936$	4.57099	0.149408
$937$	2.35432	0.0769124	0.0384562	−	0.999260i	$-0.487756\pi$
$937$	2.35432	0.0769124	0.0384562	+	0.999260i	$0.487756\pi$
$938$	21.3425	0.696858
$939$	46.8881	1.53014
$940$	22.6394	0.738417
$941$	−26.6580	−0.869025	−0.434512	−	0.900666i	$-0.643079\pi$
$941$	−26.6580	−0.869025	−0.434512	+	0.900666i	$0.643079\pi$
$942$	3.51165	0.114416
$943$	0.167267	0.00544696
$944$	−13.9155	−0.452912
$945$	−20.1608	−0.655830
$946$	1.85417	0.0602844
$947$	−21.0971	−0.685563	−0.342781	−	0.939415i	$-0.611369\pi$
$947$	−21.0971	−0.685563	−0.342781	+	0.939415i	$0.611369\pi$
$948$	−8.08167	−0.262480
$949$	23.9231	0.776578
$950$	1.70078	0.0551805
$951$	−28.4404	−0.922243
$952$	1.52642	0.0494716
$953$	−15.2279	−0.493280	−0.246640	−	0.969107i	$-0.579327\pi$
$953$	−15.2279	−0.493280	−0.246640	+	0.969107i	$0.579327\pi$
$954$	24.2094	0.783807
$955$	13.3489	0.431961
$956$	22.7057	0.734353
$957$	5.06023	0.163574
$958$	−3.92278	−0.126739
$959$	−30.2880	−0.978051
$960$	−5.09059	−0.164298
$961$	−0.291505	−0.00940338
$962$	27.6491	0.891443
$963$	15.3218	0.493737
$964$	22.6643	0.729969
$965$	−18.8240	−0.605967
$966$	20.2422	0.651283
$967$	13.7075	0.440804	0.220402	−	0.975409i	$-0.429263\pi$
$967$	13.7075	0.440804	0.220402	+	0.975409i	$0.429263\pi$
$968$	9.85521	0.316759
$969$	−4.94692	−0.158918
$970$	30.9531	0.993844
$971$	−13.5731	−0.435580	−0.217790	−	0.975996i	$-0.569885\pi$
$971$	−13.5731	−0.435580	−0.217790	+	0.975996i	$0.569885\pi$
$972$	−16.9685	−0.544266
$973$	−59.3700	−1.90332
$974$	28.0592	0.899076
$975$	−1.80656	−0.0578563
$976$	−2.95703	−0.0946521
$977$	53.0740	1.69799	0.848993	−	0.528404i	$-0.177209\pi$
$977$	53.0740	1.69799	0.848993	+	0.528404i	$0.177209\pi$
$978$	32.3518	1.03450
$979$	15.3385	0.490221
$980$	−11.6535	−0.372256
$981$	−3.51629	−0.112267
$982$	−33.4631	−1.06785
$983$	32.0891	1.02348	0.511742	−	0.859139i	$-0.329000\pi$
$983$	32.0891	1.02348	0.511742	+	0.859139i	$0.329000\pi$
$984$	−0.139353	−0.00444240
$985$	−63.5006	−2.02330
$986$	−0.943603	−0.0300504
$987$	75.0000	2.38728
$988$	12.5477	0.399196
$989$	−4.58515	−0.145799
$990$	4.59326	0.145983
$991$	0.289060	0.00918229	0.00459115	−	0.999989i	$-0.498539\pi$
$991$	0.289060	0.00918229	0.00459115	+	0.999989i	$0.498539\pi$
$992$	−5.54152	−0.175944
$993$	−60.0196	−1.90466
$994$	20.2558	0.642476
$995$	−28.0155	−0.888150
$996$	23.3625	0.740270
$997$	−54.4217	−1.72355	−0.861776	−	0.507289i	$-0.830648\pi$
$997$	−54.4217	−1.72355	−0.861776	+	0.507289i	$0.830648\pi$
$998$	−15.4024	−0.487553
$999$	−28.2825	−0.894818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.61	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.61	✓	77	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.20430 q^{3} +1.00000 q^{4} -2.30939 q^{5} -2.20430 q^{6} -3.47075 q^{7} -1.00000 q^{8} +1.85892 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.20430 q^{3} +1.00000 q^{4} -2.30939 q^{5} -2.20430 q^{6} -3.47075 q^{7} -1.00000 q^{8} +1.85892 q^{9} +2.30939 q^{10} +1.06995 q^{11} +2.20430 q^{12} -2.45895 q^{13} +3.47075 q^{14} -5.09059 q^{15} +1.00000 q^{16} +0.439796 q^{17} -1.85892 q^{18} -5.10287 q^{19} -2.30939 q^{20} -7.65056 q^{21} -1.06995 q^{22} +2.64585 q^{23} -2.20430 q^{24} +0.333298 q^{25} +2.45895 q^{26} -2.51528 q^{27} -3.47075 q^{28} +2.14555 q^{29} +5.09059 q^{30} +5.54152 q^{31} -1.00000 q^{32} +2.35848 q^{33} -0.439796 q^{34} +8.01533 q^{35} +1.85892 q^{36} +11.2443 q^{37} +5.10287 q^{38} -5.42025 q^{39} +2.30939 q^{40} +0.0632186 q^{41} +7.65056 q^{42} -1.73296 q^{43} +1.06995 q^{44} -4.29298 q^{45} -2.64585 q^{46} -9.80320 q^{47} +2.20430 q^{48} +5.04612 q^{49} -0.333298 q^{50} +0.969439 q^{51} -2.45895 q^{52} -13.0233 q^{53} +2.51528 q^{54} -2.47093 q^{55} +3.47075 q^{56} -11.2482 q^{57} -2.14555 q^{58} -13.9155 q^{59} -5.09059 q^{60} -2.95703 q^{61} -5.54152 q^{62} -6.45185 q^{63} +1.00000 q^{64} +5.67868 q^{65} -2.35848 q^{66} +6.14925 q^{67} +0.439796 q^{68} +5.83223 q^{69} -8.01533 q^{70} +5.83615 q^{71} -1.85892 q^{72} -9.72900 q^{73} -11.2443 q^{74} +0.734688 q^{75} -5.10287 q^{76} -3.71352 q^{77} +5.42025 q^{78} -3.66633 q^{79} -2.30939 q^{80} -11.1212 q^{81} -0.0632186 q^{82} +10.5986 q^{83} -7.65056 q^{84} -1.01566 q^{85} +1.73296 q^{86} +4.72943 q^{87} -1.06995 q^{88} +14.3358 q^{89} +4.29298 q^{90} +8.53441 q^{91} +2.64585 q^{92} +12.2152 q^{93} +9.80320 q^{94} +11.7845 q^{95} -2.20430 q^{96} +13.4031 q^{97} -5.04612 q^{98} +1.98894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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