LMFDB - Embedded newform 8002.2.a.e.1.36

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			1.36
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.196706 q^{3} +1.00000 q^{4} -2.53024 q^{5} +0.196706 q^{6} -1.48415 q^{7} -1.00000 q^{8} -2.96131 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.196706 q^{3} +1.00000 q^{4} -2.53024 q^{5} +0.196706 q^{6} -1.48415 q^{7} -1.00000 q^{8} -2.96131 q^{9} +2.53024 q^{10} +3.96474 q^{11} -0.196706 q^{12} +0.949511 q^{13} +1.48415 q^{14} +0.497713 q^{15} +1.00000 q^{16} +6.20158 q^{17} +2.96131 q^{18} +1.18145 q^{19} -2.53024 q^{20} +0.291942 q^{21} -3.96474 q^{22} -3.51875 q^{23} +0.196706 q^{24} +1.40210 q^{25} -0.949511 q^{26} +1.17263 q^{27} -1.48415 q^{28} +1.18927 q^{29} -0.497713 q^{30} +10.7070 q^{31} -1.00000 q^{32} -0.779890 q^{33} -6.20158 q^{34} +3.75526 q^{35} -2.96131 q^{36} -0.827260 q^{37} -1.18145 q^{38} -0.186775 q^{39} +2.53024 q^{40} +0.701178 q^{41} -0.291942 q^{42} -1.78316 q^{43} +3.96474 q^{44} +7.49281 q^{45} +3.51875 q^{46} -1.53229 q^{47} -0.196706 q^{48} -4.79729 q^{49} -1.40210 q^{50} -1.21989 q^{51} +0.949511 q^{52} +0.648027 q^{53} -1.17263 q^{54} -10.0317 q^{55} +1.48415 q^{56} -0.232399 q^{57} -1.18927 q^{58} -13.5490 q^{59} +0.497713 q^{60} -5.98145 q^{61} -10.7070 q^{62} +4.39503 q^{63} +1.00000 q^{64} -2.40249 q^{65} +0.779890 q^{66} -11.3687 q^{67} +6.20158 q^{68} +0.692161 q^{69} -3.75526 q^{70} +5.32807 q^{71} +2.96131 q^{72} +9.57628 q^{73} +0.827260 q^{74} -0.275802 q^{75} +1.18145 q^{76} -5.88428 q^{77} +0.186775 q^{78} +5.61503 q^{79} -2.53024 q^{80} +8.65326 q^{81} -0.701178 q^{82} +8.59090 q^{83} +0.291942 q^{84} -15.6915 q^{85} +1.78316 q^{86} -0.233937 q^{87} -3.96474 q^{88} -12.3987 q^{89} -7.49281 q^{90} -1.40922 q^{91} -3.51875 q^{92} -2.10614 q^{93} +1.53229 q^{94} -2.98936 q^{95} +0.196706 q^{96} +0.511154 q^{97} +4.79729 q^{98} -11.7408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.196706	−0.113568	−0.0567842	−	0.998386i	$-0.518085\pi$
$3$	−0.196706	−0.113568	−0.0567842	+	0.998386i	$0.518085\pi$
$4$	1.00000	0.500000
$5$	−2.53024	−1.13156	−0.565778	−	0.824557i	$-0.691424\pi$
$5$	−2.53024	−1.13156	−0.565778	+	0.824557i	$0.691424\pi$
$6$	0.196706	0.0803050
$7$	−1.48415	−0.560957	−0.280478	−	0.959860i	$-0.590493\pi$
$7$	−1.48415	−0.560957	−0.280478	+	0.959860i	$0.590493\pi$
$8$	−1.00000	−0.353553
$9$	−2.96131	−0.987102
$10$	2.53024	0.800131
$11$	3.96474	1.19542	0.597708	−	0.801714i	$-0.296078\pi$
$11$	3.96474	1.19542	0.597708	+	0.801714i	$0.296078\pi$
$12$	−0.196706	−0.0567842
$13$	0.949511	0.263347	0.131674	−	0.991293i	$-0.457965\pi$
$13$	0.949511	0.263347	0.131674	+	0.991293i	$0.457965\pi$
$14$	1.48415	0.396656
$15$	0.497713	0.128509
$16$	1.00000	0.250000
$17$	6.20158	1.50411	0.752053	−	0.659103i	$-0.229064\pi$
$17$	6.20158	1.50411	0.752053	+	0.659103i	$0.229064\pi$
$18$	2.96131	0.697987
$19$	1.18145	0.271044	0.135522	−	0.990774i	$-0.456729\pi$
$19$	1.18145	0.271044	0.135522	+	0.990774i	$0.456729\pi$
$20$	−2.53024	−0.565778
$21$	0.291942	0.0637070
$22$	−3.96474	−0.845286
$23$	−3.51875	−0.733711	−0.366855	−	0.930278i	$-0.619566\pi$
$23$	−3.51875	−0.733711	−0.366855	+	0.930278i	$0.619566\pi$
$24$	0.196706	0.0401525
$25$	1.40210	0.280420
$26$	−0.949511	−0.186214
$27$	1.17263	0.225672
$28$	−1.48415	−0.280478
$29$	1.18927	0.220842	0.110421	−	0.993885i	$-0.464780\pi$
$29$	1.18927	0.220842	0.110421	+	0.993885i	$0.464780\pi$
$30$	−0.497713	−0.0908696
$31$	10.7070	1.92304	0.961520	−	0.274736i	$-0.0885906\pi$
$31$	10.7070	1.92304	0.961520	+	0.274736i	$0.0885906\pi$
$32$	−1.00000	−0.176777
$33$	−0.779890	−0.135761
$34$	−6.20158	−1.06356
$35$	3.75526	0.634754
$36$	−2.96131	−0.493551
$37$	−0.827260	−0.136001	−0.0680003	−	0.997685i	$-0.521662\pi$
$37$	−0.827260	−0.136001	−0.0680003	+	0.997685i	$0.521662\pi$
$38$	−1.18145	−0.191657
$39$	−0.186775	−0.0299079
$40$	2.53024	0.400066
$41$	0.701178	0.109506	0.0547528	−	0.998500i	$-0.482563\pi$
$41$	0.701178	0.109506	0.0547528	+	0.998500i	$0.482563\pi$
$42$	−0.291942	−0.0450476
$43$	−1.78316	−0.271930	−0.135965	−	0.990714i	$-0.543413\pi$
$43$	−1.78316	−0.271930	−0.135965	+	0.990714i	$0.543413\pi$
$44$	3.96474	0.597708
$45$	7.49281	1.11696
$46$	3.51875	0.518812
$47$	−1.53229	−0.223508	−0.111754	−	0.993736i	$-0.535647\pi$
$47$	−1.53229	−0.223508	−0.111754	+	0.993736i	$0.535647\pi$
$48$	−0.196706	−0.0283921
$49$	−4.79729	−0.685327
$50$	−1.40210	−0.198287
$51$	−1.21989	−0.170819
$52$	0.949511	0.131674
$53$	0.648027	0.0890133	0.0445067	−	0.999009i	$-0.485828\pi$
$53$	0.648027	0.0890133	0.0445067	+	0.999009i	$0.485828\pi$
$54$	−1.17263	−0.159574
$55$	−10.0317	−1.35268
$56$	1.48415	0.198328
$57$	−0.232399	−0.0307821
$58$	−1.18927	−0.156159
$59$	−13.5490	−1.76393	−0.881963	−	0.471319i	$-0.843778\pi$
$59$	−13.5490	−1.76393	−0.881963	+	0.471319i	$0.843778\pi$
$60$	0.497713	0.0642545
$61$	−5.98145	−0.765846	−0.382923	−	0.923780i	$-0.625083\pi$
$61$	−5.98145	−0.765846	−0.382923	+	0.923780i	$0.625083\pi$
$62$	−10.7070	−1.35979
$63$	4.39503	0.553722
$64$	1.00000	0.125000
$65$	−2.40249	−0.297992
$66$	0.779890	0.0959978
$67$	−11.3687	−1.38891	−0.694456	−	0.719535i	$-0.744355\pi$
$67$	−11.3687	−1.38891	−0.694456	+	0.719535i	$0.744355\pi$
$68$	6.20158	0.752053
$69$	0.692161	0.0833263
$70$	−3.75526	−0.448839
$71$	5.32807	0.632325	0.316163	−	0.948705i	$-0.397605\pi$
$71$	5.32807	0.632325	0.316163	+	0.948705i	$0.397605\pi$
$72$	2.96131	0.348993
$73$	9.57628	1.12082	0.560409	−	0.828216i	$-0.310644\pi$
$73$	9.57628	1.12082	0.560409	+	0.828216i	$0.310644\pi$
$74$	0.827260	0.0961670
$75$	−0.275802	−0.0318469
$76$	1.18145	0.135522
$77$	−5.88428	−0.670576
$78$	0.186775	0.0211481
$79$	5.61503	0.631740	0.315870	−	0.948802i	$-0.397704\pi$
$79$	5.61503	0.631740	0.315870	+	0.948802i	$0.397704\pi$
$80$	−2.53024	−0.282889
$81$	8.65326	0.961473
$82$	−0.701178	−0.0774322
$83$	8.59090	0.942974	0.471487	−	0.881873i	$-0.343717\pi$
$83$	8.59090	0.942974	0.471487	+	0.881873i	$0.343717\pi$
$84$	0.291942	0.0318535
$85$	−15.6915	−1.70198
$86$	1.78316	0.192283
$87$	−0.233937	−0.0250807
$88$	−3.96474	−0.422643
$89$	−12.3987	−1.31426	−0.657132	−	0.753776i	$-0.728231\pi$
$89$	−12.3987	−1.31426	−0.657132	+	0.753776i	$0.728231\pi$
$90$	−7.49281	−0.789811
$91$	−1.40922	−0.147726
$92$	−3.51875	−0.366855
$93$	−2.10614	−0.218396
$94$	1.53229	0.158044
$95$	−2.98936	−0.306702
$96$	0.196706	0.0200762
$97$	0.511154	0.0518998	0.0259499	−	0.999663i	$-0.491739\pi$
$97$	0.511154	0.0518998	0.0259499	+	0.999663i	$0.491739\pi$
$98$	4.79729	0.484600
$99$	−11.7408	−1.18000
$100$	1.40210	0.140210
$101$	−2.72432	−0.271080	−0.135540	−	0.990772i	$-0.543277\pi$
$101$	−2.72432	−0.271080	−0.135540	+	0.990772i	$0.543277\pi$
$102$	1.21989	0.120787
$103$	−9.11869	−0.898491	−0.449246	−	0.893408i	$-0.648307\pi$
$103$	−9.11869	−0.898491	−0.449246	+	0.893408i	$0.648307\pi$
$104$	−0.949511	−0.0931072
$105$	−0.738683	−0.0720880
$106$	−0.648027	−0.0629419
$107$	12.9005	1.24714	0.623571	−	0.781767i	$-0.285681\pi$
$107$	12.9005	1.24714	0.623571	+	0.781767i	$0.285681\pi$
$108$	1.17263	0.112836
$109$	−0.0963773	−0.00923127	−0.00461563	−	0.999989i	$-0.501469\pi$
$109$	−0.0963773	−0.00923127	−0.00461563	+	0.999989i	$0.501469\pi$
$110$	10.0317	0.956489
$111$	0.162727	0.0154454
$112$	−1.48415	−0.140239
$113$	−9.28616	−0.873568	−0.436784	−	0.899566i	$-0.643883\pi$
$113$	−9.28616	−0.873568	−0.436784	+	0.899566i	$0.643883\pi$
$114$	0.232399	0.0217662
$115$	8.90328	0.830235
$116$	1.18927	0.110421
$117$	−2.81179	−0.259950
$118$	13.5490	1.24728
$119$	−9.20410	−0.843738
$120$	−0.497713	−0.0454348
$121$	4.71919	0.429017
$122$	5.98145	0.541535
$123$	−0.137926	−0.0124364
$124$	10.7070	0.961520
$125$	9.10354	0.814245
$126$	−4.39503	−0.391540
$127$	4.83606	0.429131	0.214565	−	0.976710i	$-0.431166\pi$
$127$	4.83606	0.429131	0.214565	+	0.976710i	$0.431166\pi$
$128$	−1.00000	−0.0883883
$129$	0.350759	0.0308826
$130$	2.40249	0.210712
$131$	−10.0157	−0.875072	−0.437536	−	0.899201i	$-0.644149\pi$
$131$	−10.0157	−0.875072	−0.437536	+	0.899201i	$0.644149\pi$
$132$	−0.779890	−0.0678807
$133$	−1.75346	−0.152044
$134$	11.3687	0.982110
$135$	−2.96702	−0.255361
$136$	−6.20158	−0.531781
$137$	21.7569	1.85882	0.929409	−	0.369052i	$-0.120318\pi$
$137$	21.7569	1.85882	0.929409	+	0.369052i	$0.120318\pi$
$138$	−0.692161	−0.0589206
$139$	−17.8129	−1.51087	−0.755437	−	0.655221i	$-0.772575\pi$
$139$	−17.8129	−1.51087	−0.755437	+	0.655221i	$0.772575\pi$
$140$	3.75526	0.317377
$141$	0.301412	0.0253835
$142$	−5.32807	−0.447121
$143$	3.76457	0.314809
$144$	−2.96131	−0.246776
$145$	−3.00914	−0.249895
$146$	−9.57628	−0.792539
$147$	0.943657	0.0778315
$148$	−0.827260	−0.0680003
$149$	−19.1650	−1.57006	−0.785030	−	0.619457i	$-0.787353\pi$
$149$	−19.1650	−1.57006	−0.785030	+	0.619457i	$0.787353\pi$
$150$	0.275802	0.0225191
$151$	12.8566	1.04626	0.523128	−	0.852254i	$-0.324765\pi$
$151$	12.8566	1.04626	0.523128	+	0.852254i	$0.324765\pi$
$152$	−1.18145	−0.0958286
$153$	−18.3648	−1.48471
$154$	5.88428	0.474169
$155$	−27.0913	−2.17603
$156$	−0.186775	−0.0149540
$157$	7.02079	0.560320	0.280160	−	0.959953i	$-0.409613\pi$
$157$	7.02079	0.560320	0.280160	+	0.959953i	$0.409613\pi$
$158$	−5.61503	−0.446708
$159$	−0.127471	−0.0101091
$160$	2.53024	0.200033
$161$	5.22236	0.411580
$162$	−8.65326	−0.679864
$163$	−16.0734	−1.25896	−0.629482	−	0.777015i	$-0.716733\pi$
$163$	−16.0734	−1.25896	−0.629482	+	0.777015i	$0.716733\pi$
$164$	0.701178	0.0547528
$165$	1.97331	0.153622
$166$	−8.59090	−0.666783
$167$	−9.50328	−0.735386	−0.367693	−	0.929947i	$-0.619852\pi$
$167$	−9.50328	−0.735386	−0.367693	+	0.929947i	$0.619852\pi$
$168$	−0.291942	−0.0225238
$169$	−12.0984	−0.930648
$170$	15.6915	1.20348
$171$	−3.49865	−0.267548
$172$	−1.78316	−0.135965
$173$	3.94335	0.299807	0.149904	−	0.988701i	$-0.452104\pi$
$173$	3.94335	0.299807	0.149904	+	0.988701i	$0.452104\pi$
$174$	0.233937	0.0177347
$175$	−2.08093	−0.157304
$176$	3.96474	0.298854
$177$	2.66517	0.200326
$178$	12.3987	0.929325
$179$	14.0950	1.05351	0.526755	−	0.850017i	$-0.323408\pi$
$179$	14.0950	1.05351	0.526755	+	0.850017i	$0.323408\pi$
$180$	7.49281	0.558481
$181$	19.5259	1.45135	0.725673	−	0.688039i	$-0.241528\pi$
$181$	19.5259	1.45135	0.725673	+	0.688039i	$0.241528\pi$
$182$	1.40922	0.104458
$183$	1.17659	0.0869759
$184$	3.51875	0.259406
$185$	2.09316	0.153892
$186$	2.10614	0.154430
$187$	24.5877	1.79803
$188$	−1.53229	−0.111754
$189$	−1.74036	−0.126592
$190$	2.98936	0.216871
$191$	11.9746	0.866453	0.433227	−	0.901285i	$-0.357375\pi$
$191$	11.9746	0.866453	0.433227	+	0.901285i	$0.357375\pi$
$192$	−0.196706	−0.0141960
$193$	11.2116	0.807030	0.403515	−	0.914973i	$-0.367788\pi$
$193$	11.2116	0.807030	0.403515	+	0.914973i	$0.367788\pi$
$194$	−0.511154	−0.0366987
$195$	0.472585	0.0338425
$196$	−4.79729	−0.342664
$197$	−16.4458	−1.17172	−0.585858	−	0.810414i	$-0.699242\pi$
$197$	−16.4458	−1.17172	−0.585858	+	0.810414i	$0.699242\pi$
$198$	11.7408	0.834384
$199$	−22.6196	−1.60346	−0.801729	−	0.597687i	$-0.796086\pi$
$199$	−22.6196	−1.60346	−0.801729	+	0.597687i	$0.796086\pi$
$200$	−1.40210	−0.0991435
$201$	2.23630	0.157737
$202$	2.72432	0.191682
$203$	−1.76506	−0.123883
$204$	−1.21989	−0.0854094
$205$	−1.77415	−0.123912
$206$	9.11869	0.635329
$207$	10.4201	0.724247
$208$	0.949511	0.0658368
$209$	4.68416	0.324010
$210$	0.738683	0.0509739
$211$	14.5558	1.00206	0.501031	−	0.865429i	$-0.332954\pi$
$211$	14.5558	1.00206	0.501031	+	0.865429i	$0.332954\pi$
$212$	0.648027	0.0445067
$213$	−1.04806	−0.0718122
$214$	−12.9005	−0.881862
$215$	4.51182	0.307704
$216$	−1.17263	−0.0797871
$217$	−15.8909	−1.07874
$218$	0.0963773	0.00652749
$219$	−1.88371	−0.127290
$220$	−10.0317	−0.676340
$221$	5.88847	0.396102
$222$	−0.162727	−0.0109215
$223$	−10.9253	−0.731615	−0.365807	−	0.930691i	$-0.619207\pi$
$223$	−10.9253	−0.731615	−0.365807	+	0.930691i	$0.619207\pi$
$224$	1.48415	0.0991641
$225$	−4.15205	−0.276803
$226$	9.28616	0.617706
$227$	17.4302	1.15688	0.578440	−	0.815725i	$-0.303662\pi$
$227$	17.4302	1.15688	0.578440	+	0.815725i	$0.303662\pi$
$228$	−0.232399	−0.0153910
$229$	28.3464	1.87318	0.936592	−	0.350423i	$-0.113962\pi$
$229$	28.3464	1.87318	0.936592	+	0.350423i	$0.113962\pi$
$230$	−8.90328	−0.587065
$231$	1.15748	0.0761563
$232$	−1.18927	−0.0780794
$233$	11.3259	0.741984	0.370992	−	0.928636i	$-0.379018\pi$
$233$	11.3259	0.741984	0.370992	+	0.928636i	$0.379018\pi$
$234$	2.81179	0.183813
$235$	3.87707	0.252912
$236$	−13.5490	−0.881963
$237$	−1.10451	−0.0717457
$238$	9.20410	0.596613
$239$	4.08725	0.264382	0.132191	−	0.991224i	$-0.457799\pi$
$239$	4.08725	0.264382	0.132191	+	0.991224i	$0.457799\pi$
$240$	0.497713	0.0321273
$241$	−26.0055	−1.67516	−0.837581	−	0.546313i	$-0.816031\pi$
$241$	−26.0055	−1.67516	−0.837581	+	0.546313i	$0.816031\pi$
$242$	−4.71919	−0.303361
$243$	−5.22003	−0.334865
$244$	−5.98145	−0.382923
$245$	12.1383	0.775487
$246$	0.137926	0.00879385
$247$	1.12180	0.0713787
$248$	−10.7070	−0.679897
$249$	−1.68988	−0.107092
$250$	−9.10354	−0.575758
$251$	2.88206	0.181914	0.0909570	−	0.995855i	$-0.471007\pi$
$251$	2.88206	0.181914	0.0909570	+	0.995855i	$0.471007\pi$
$252$	4.39503	0.276861
$253$	−13.9510	−0.877089
$254$	−4.83606	−0.303441
$255$	3.08661	0.193291
$256$	1.00000	0.0625000
$257$	26.6394	1.66172	0.830859	−	0.556483i	$-0.187849\pi$
$257$	26.6394	1.66172	0.830859	+	0.556483i	$0.187849\pi$
$258$	−0.350759	−0.0218373
$259$	1.22778	0.0762905
$260$	−2.40249	−0.148996
$261$	−3.52179	−0.217994
$262$	10.0157	0.618769
$263$	29.5840	1.82423	0.912113	−	0.409938i	$-0.134450\pi$
$263$	29.5840	1.82423	0.912113	+	0.409938i	$0.134450\pi$
$264$	0.779890	0.0479989
$265$	−1.63966	−0.100724
$266$	1.75346	0.107511
$267$	2.43891	0.149259
$268$	−11.3687	−0.694456
$269$	14.3376	0.874176	0.437088	−	0.899419i	$-0.356010\pi$
$269$	14.3376	0.874176	0.437088	+	0.899419i	$0.356010\pi$
$270$	2.96702	0.180567
$271$	−4.07088	−0.247288	−0.123644	−	0.992327i	$-0.539458\pi$
$271$	−4.07088	−0.247288	−0.123644	+	0.992327i	$0.539458\pi$
$272$	6.20158	0.376026
$273$	0.277202	0.0167770
$274$	−21.7569	−1.31438
$275$	5.55897	0.335219
$276$	0.692161	0.0416632
$277$	14.0443	0.843843	0.421921	−	0.906632i	$-0.361356\pi$
$277$	14.0443	0.843843	0.421921	+	0.906632i	$0.361356\pi$
$278$	17.8129	1.06835
$279$	−31.7068	−1.89824
$280$	−3.75526	−0.224420
$281$	7.80829	0.465804	0.232902	−	0.972500i	$-0.425178\pi$
$281$	7.80829	0.465804	0.232902	+	0.972500i	$0.425178\pi$
$282$	−0.301412	−0.0179488
$283$	−13.8225	−0.821664	−0.410832	−	0.911711i	$-0.634762\pi$
$283$	−13.8225	−0.821664	−0.410832	+	0.911711i	$0.634762\pi$
$284$	5.32807	0.316163
$285$	0.588026	0.0348316
$286$	−3.76457	−0.222604
$287$	−1.04066	−0.0614279
$288$	2.96131	0.174497
$289$	21.4597	1.26233
$290$	3.00914	0.176703
$291$	−0.100547	−0.00589418
$292$	9.57628	0.560409
$293$	20.6351	1.20552	0.602759	−	0.797923i	$-0.294068\pi$
$293$	20.6351	1.20552	0.602759	+	0.797923i	$0.294068\pi$
$294$	−0.943657	−0.0550352
$295$	34.2821	1.99598
$296$	0.827260	0.0480835
$297$	4.64916	0.269772
$298$	19.1650	1.11020
$299$	−3.34110	−0.193221
$300$	−0.275802	−0.0159234
$301$	2.64648	0.152541
$302$	−12.8566	−0.739815
$303$	0.535891	0.0307861
$304$	1.18145	0.0677611
$305$	15.1345	0.866598
$306$	18.3648	1.04985
$307$	1.79671	0.102543	0.0512717	−	0.998685i	$-0.483673\pi$
$307$	1.79671	0.102543	0.0512717	+	0.998685i	$0.483673\pi$
$308$	−5.88428	−0.335288
$309$	1.79370	0.102040
$310$	27.0913	1.53868
$311$	27.9620	1.58558	0.792790	−	0.609494i	$-0.208628\pi$
$311$	27.9620	1.58558	0.792790	+	0.609494i	$0.208628\pi$
$312$	0.186775	0.0105740
$313$	10.1029	0.571052	0.285526	−	0.958371i	$-0.407832\pi$
$313$	10.1029	0.571052	0.285526	+	0.958371i	$0.407832\pi$
$314$	−7.02079	−0.396206
$315$	−11.1205	−0.626567
$316$	5.61503	0.315870
$317$	7.73770	0.434592	0.217296	−	0.976106i	$-0.430276\pi$
$317$	7.73770	0.434592	0.217296	+	0.976106i	$0.430276\pi$
$318$	0.127471	0.00714822
$319$	4.71515	0.263998
$320$	−2.53024	−0.141445
$321$	−2.53761	−0.141636
$322$	−5.22236	−0.291031
$323$	7.32689	0.407679
$324$	8.65326	0.480737
$325$	1.33131	0.0738478
$326$	16.0734	0.890222
$327$	0.0189580	0.00104838
$328$	−0.701178	−0.0387161
$329$	2.27416	0.125378
$330$	−1.97331	−0.108627
$331$	12.0598	0.662868	0.331434	−	0.943478i	$-0.392468\pi$
$331$	12.0598	0.662868	0.331434	+	0.943478i	$0.392468\pi$
$332$	8.59090	0.471487
$333$	2.44977	0.134247
$334$	9.50328	0.519996
$335$	28.7656	1.57163
$336$	0.291942	0.0159267
$337$	9.71045	0.528962	0.264481	−	0.964391i	$-0.414799\pi$
$337$	9.71045	0.528962	0.264481	+	0.964391i	$0.414799\pi$
$338$	12.0984	0.658068
$339$	1.82665	0.0992097
$340$	−15.6915	−0.850990
$341$	42.4506	2.29883
$342$	3.49865	0.189185
$343$	17.5090	0.945396
$344$	1.78316	0.0961416
$345$	−1.75133	−0.0942885
$346$	−3.94335	−0.211996
$347$	−5.78396	−0.310499	−0.155250	−	0.987875i	$-0.549618\pi$
$347$	−5.78396	−0.310499	−0.155250	+	0.987875i	$0.549618\pi$
$348$	−0.233937	−0.0125403
$349$	15.3184	0.819977	0.409988	−	0.912091i	$-0.365533\pi$
$349$	15.3184	0.819977	0.409988	+	0.912091i	$0.365533\pi$
$350$	2.08093	0.111230
$351$	1.11342	0.0594301
$352$	−3.96474	−0.211322
$353$	22.9510	1.22156	0.610779	−	0.791801i	$-0.290856\pi$
$353$	22.9510	1.22156	0.610779	+	0.791801i	$0.290856\pi$
$354$	−2.66517	−0.141652
$355$	−13.4813	−0.715512
$356$	−12.3987	−0.657132
$357$	1.81050	0.0958220
$358$	−14.0950	−0.744945
$359$	2.71270	0.143171	0.0715854	−	0.997434i	$-0.477194\pi$
$359$	2.71270	0.143171	0.0715854	+	0.997434i	$0.477194\pi$
$360$	−7.49281	−0.394906
$361$	−17.6042	−0.926535
$362$	−19.5259	−1.02626
$363$	−0.928294	−0.0487228
$364$	−1.40922	−0.0738632
$365$	−24.2303	−1.26827
$366$	−1.17659	−0.0615013
$367$	33.1913	1.73257	0.866286	−	0.499548i	$-0.166501\pi$
$367$	33.1913	1.73257	0.866286	+	0.499548i	$0.166501\pi$
$368$	−3.51875	−0.183428
$369$	−2.07640	−0.108093
$370$	−2.09316	−0.108818
$371$	−0.961771	−0.0499326
$372$	−2.10614	−0.109198
$373$	−13.6329	−0.705884	−0.352942	−	0.935645i	$-0.614819\pi$
$373$	−13.6329	−0.705884	−0.352942	+	0.935645i	$0.614819\pi$
$374$	−24.5877	−1.27140
$375$	−1.79072	−0.0924725
$376$	1.53229	0.0790220
$377$	1.12923	0.0581581
$378$	1.74036	0.0895142
$379$	11.3297	0.581968	0.290984	−	0.956728i	$-0.406017\pi$
$379$	11.3297	0.581968	0.290984	+	0.956728i	$0.406017\pi$
$380$	−2.98936	−0.153351
$381$	−0.951283	−0.0487357
$382$	−11.9746	−0.612675
$383$	−25.9302	−1.32497	−0.662485	−	0.749075i	$-0.730498\pi$
$383$	−25.9302	−1.32497	−0.662485	+	0.749075i	$0.730498\pi$
$384$	0.196706	0.0100381
$385$	14.8886	0.758795
$386$	−11.2116	−0.570657
$387$	5.28049	0.268422
$388$	0.511154	0.0259499
$389$	−19.3844	−0.982827	−0.491413	−	0.870926i	$-0.663520\pi$
$389$	−19.3844	−0.982827	−0.491413	+	0.870926i	$0.663520\pi$
$390$	−0.472585	−0.0239302
$391$	−21.8218	−1.10358
$392$	4.79729	0.242300
$393$	1.97014	0.0993805
$394$	16.4458	0.828528
$395$	−14.2074	−0.714850
$396$	−11.7408	−0.589998
$397$	−13.4610	−0.675590	−0.337795	−	0.941220i	$-0.609681\pi$
$397$	−13.4610	−0.675590	−0.337795	+	0.941220i	$0.609681\pi$
$398$	22.6196	1.13382
$399$	0.344916	0.0172674
$400$	1.40210	0.0701050
$401$	−27.8345	−1.38999	−0.694995	−	0.719015i	$-0.744593\pi$
$401$	−27.8345	−1.38999	−0.694995	+	0.719015i	$0.744593\pi$
$402$	−2.23630	−0.111537
$403$	10.1664	0.506427
$404$	−2.72432	−0.135540
$405$	−21.8948	−1.08796
$406$	1.76506	0.0875984
$407$	−3.27987	−0.162577
$408$	1.21989	0.0603936
$409$	−36.3552	−1.79765	−0.898824	−	0.438310i	$-0.855577\pi$
$409$	−36.3552	−1.79765	−0.898824	+	0.438310i	$0.855577\pi$
$410$	1.77415	0.0876189
$411$	−4.27972	−0.211103
$412$	−9.11869	−0.449246
$413$	20.1087	0.989486
$414$	−10.4201	−0.512120
$415$	−21.7370	−1.06703
$416$	−0.949511	−0.0465536
$417$	3.50392	0.171588
$418$	−4.68416	−0.229110
$419$	−31.8630	−1.55661	−0.778305	−	0.627887i	$-0.783920\pi$
$419$	−31.8630	−1.55661	−0.778305	+	0.627887i	$0.783920\pi$
$420$	−0.738683	−0.0360440
$421$	21.8011	1.06252	0.531261	−	0.847208i	$-0.321718\pi$
$421$	21.8011	1.06252	0.531261	+	0.847208i	$0.321718\pi$
$422$	−14.5558	−0.708565
$423$	4.53759	0.220625
$424$	−0.648027	−0.0314710
$425$	8.69525	0.421781
$426$	1.04806	0.0507789
$427$	8.87738	0.429607
$428$	12.9005	0.623571
$429$	−0.740514	−0.0357524
$430$	−4.51182	−0.217579
$431$	3.45331	0.166340	0.0831701	−	0.996535i	$-0.473496\pi$
$431$	3.45331	0.166340	0.0831701	+	0.996535i	$0.473496\pi$
$432$	1.17263	0.0564180
$433$	36.8866	1.77266	0.886328	−	0.463058i	$-0.153248\pi$
$433$	36.8866	1.77266	0.886328	+	0.463058i	$0.153248\pi$
$434$	15.8909	0.762786
$435$	0.591916	0.0283802
$436$	−0.0963773	−0.00461563
$437$	−4.15725	−0.198868
$438$	1.88371	0.0900073
$439$	−26.3450	−1.25738	−0.628689	−	0.777657i	$-0.716408\pi$
$439$	−26.3450	−1.25738	−0.628689	+	0.777657i	$0.716408\pi$
$440$	10.0317	0.478245
$441$	14.2063	0.676488
$442$	−5.88847	−0.280086
$443$	−8.66729	−0.411795	−0.205898	−	0.978574i	$-0.566011\pi$
$443$	−8.66729	−0.411795	−0.205898	+	0.978574i	$0.566011\pi$
$444$	0.162727	0.00772269
$445$	31.3718	1.48716
$446$	10.9253	0.517330
$447$	3.76988	0.178309
$448$	−1.48415	−0.0701196
$449$	25.9238	1.22342	0.611711	−	0.791082i	$-0.290482\pi$
$449$	25.9238	1.22342	0.611711	+	0.791082i	$0.290482\pi$
$450$	4.15205	0.195730
$451$	2.77999	0.130905
$452$	−9.28616	−0.436784
$453$	−2.52898	−0.118822
$454$	−17.4302	−0.818038
$455$	3.56566	0.167161
$456$	0.232399	0.0108831
$457$	−10.8245	−0.506348	−0.253174	−	0.967421i	$-0.581475\pi$
$457$	−10.8245	−0.506348	−0.253174	+	0.967421i	$0.581475\pi$
$458$	−28.3464	−1.32454
$459$	7.27214	0.339434
$460$	8.90328	0.415118
$461$	−38.1997	−1.77914	−0.889569	−	0.456801i	$-0.848995\pi$
$461$	−38.1997	−1.77914	−0.889569	+	0.456801i	$0.848995\pi$
$462$	−1.15748	−0.0538506
$463$	−6.55923	−0.304833	−0.152417	−	0.988316i	$-0.548706\pi$
$463$	−6.55923	−0.304833	−0.152417	+	0.988316i	$0.548706\pi$
$464$	1.18927	0.0552105
$465$	5.32903	0.247128
$466$	−11.3259	−0.524662
$467$	2.51078	0.116185	0.0580926	−	0.998311i	$-0.481498\pi$
$467$	2.51078	0.116185	0.0580926	+	0.998311i	$0.481498\pi$
$468$	−2.81179	−0.129975
$469$	16.8729	0.779120
$470$	−3.87707	−0.178836
$471$	−1.38103	−0.0636346
$472$	13.5490	0.623642
$473$	−7.06978	−0.325069
$474$	1.10451	0.0507319
$475$	1.65652	0.0760063
$476$	−9.20410	−0.421869
$477$	−1.91901	−0.0878653
$478$	−4.08725	−0.186946
$479$	−4.95903	−0.226584	−0.113292	−	0.993562i	$-0.536140\pi$
$479$	−4.95903	−0.226584	−0.113292	+	0.993562i	$0.536140\pi$
$480$	−0.497713	−0.0227174
$481$	−0.785492	−0.0358154
$482$	26.0055	1.18452
$483$	−1.02727	−0.0467425
$484$	4.71919	0.214509
$485$	−1.29334	−0.0587276
$486$	5.22003	0.236785
$487$	−24.2797	−1.10022	−0.550109	−	0.835093i	$-0.685414\pi$
$487$	−24.2797	−1.10022	−0.550109	+	0.835093i	$0.685414\pi$
$488$	5.98145	0.270768
$489$	3.16173	0.142979
$490$	−12.1383	−0.548352
$491$	2.61299	0.117923	0.0589614	−	0.998260i	$-0.481221\pi$
$491$	2.61299	0.117923	0.0589614	+	0.998260i	$0.481221\pi$
$492$	−0.137926	−0.00621819
$493$	7.37536	0.332170
$494$	−1.12180	−0.0504724
$495$	29.7071	1.33523
$496$	10.7070	0.480760
$497$	−7.90766	−0.354707
$498$	1.68988	0.0757255
$499$	26.2223	1.17387	0.586937	−	0.809633i	$-0.300334\pi$
$499$	26.2223	1.17387	0.586937	+	0.809633i	$0.300334\pi$
$500$	9.10354	0.407123
$501$	1.86935	0.0835166
$502$	−2.88206	−0.128633
$503$	−19.4582	−0.867598	−0.433799	−	0.901010i	$-0.642827\pi$
$503$	−19.4582	−0.867598	−0.433799	+	0.901010i	$0.642827\pi$
$504$	−4.39503	−0.195770
$505$	6.89318	0.306742
$506$	13.9510	0.620195
$507$	2.37984	0.105692
$508$	4.83606	0.214565
$509$	33.3527	1.47833	0.739166	−	0.673524i	$-0.235220\pi$
$509$	33.3527	1.47833	0.739166	+	0.673524i	$0.235220\pi$
$510$	−3.08661	−0.136677
$511$	−14.2127	−0.628731
$512$	−1.00000	−0.0441942
$513$	1.38540	0.0611671
$514$	−26.6394	−1.17501
$515$	23.0725	1.01669
$516$	0.350759	0.0154413
$517$	−6.07515	−0.267185
$518$	−1.22778	−0.0539455
$519$	−0.775681	−0.0340486
$520$	2.40249	0.105356
$521$	−13.2667	−0.581223	−0.290611	−	0.956841i	$-0.593859\pi$
$521$	−13.2667	−0.581223	−0.290611	+	0.956841i	$0.593859\pi$
$522$	3.52179	0.154145
$523$	17.7211	0.774889	0.387444	−	0.921893i	$-0.373358\pi$
$523$	17.7211	0.774889	0.387444	+	0.921893i	$0.373358\pi$
$524$	−10.0157	−0.437536
$525$	0.409332	0.0178647
$526$	−29.5840	−1.28992
$527$	66.4005	2.89245
$528$	−0.779890	−0.0339403
$529$	−10.6184	−0.461669
$530$	1.63966	0.0712224
$531$	40.1227	1.74117
$532$	−1.75346	−0.0760221
$533$	0.665777	0.0288380
$534$	−2.43891	−0.105542
$535$	−32.6414	−1.41121
$536$	11.3687	0.491055
$537$	−2.77258	−0.119646
$538$	−14.3376	−0.618136
$539$	−19.0200	−0.819251
$540$	−2.96702	−0.127680
$541$	−31.5380	−1.35593	−0.677963	−	0.735096i	$-0.737137\pi$
$541$	−31.5380	−1.35593	−0.677963	+	0.735096i	$0.737137\pi$
$542$	4.07088	0.174859
$543$	−3.84086	−0.164827
$544$	−6.20158	−0.265891
$545$	0.243857	0.0104457
$546$	−0.277202	−0.0118632
$547$	−44.7027	−1.91135	−0.955674	−	0.294428i	$-0.904871\pi$
$547$	−44.7027	−1.91135	−0.955674	+	0.294428i	$0.904871\pi$
$548$	21.7569	0.929409
$549$	17.7129	0.755968
$550$	−5.55897	−0.237035
$551$	1.40507	0.0598580
$552$	−0.692161	−0.0294603
$553$	−8.33356	−0.354379
$554$	−14.0443	−0.596687
$555$	−0.411738	−0.0174773
$556$	−17.8129	−0.755437
$557$	−0.645677	−0.0273582	−0.0136791	−	0.999906i	$-0.504354\pi$
$557$	−0.645677	−0.0273582	−0.0136791	+	0.999906i	$0.504354\pi$
$558$	31.7068	1.34226
$559$	−1.69313	−0.0716118
$560$	3.75526	0.158689
$561$	−4.83655	−0.204199
$562$	−7.80829	−0.329373
$563$	−7.43875	−0.313506	−0.156753	−	0.987638i	$-0.550103\pi$
$563$	−7.43875	−0.313506	−0.156753	+	0.987638i	$0.550103\pi$
$564$	0.301412	0.0126917
$565$	23.4962	0.988492
$566$	13.8225	0.581004
$567$	−12.8428	−0.539345
$568$	−5.32807	−0.223561
$569$	−0.568198	−0.0238201	−0.0119101	−	0.999929i	$-0.503791\pi$
$569$	−0.568198	−0.0238201	−0.0119101	+	0.999929i	$0.503791\pi$
$570$	−0.588026	−0.0246297
$571$	16.0485	0.671611	0.335805	−	0.941931i	$-0.390992\pi$
$571$	16.0485	0.671611	0.335805	+	0.941931i	$0.390992\pi$
$572$	3.76457	0.157405
$573$	−2.35548	−0.0984017
$574$	1.04066	0.0434361
$575$	−4.93365	−0.205747
$576$	−2.96131	−0.123388
$577$	−25.5322	−1.06292	−0.531459	−	0.847084i	$-0.678356\pi$
$577$	−25.5322	−1.06292	−0.531459	+	0.847084i	$0.678356\pi$
$578$	−21.4597	−0.892604
$579$	−2.20540	−0.0916531
$580$	−3.00914	−0.124948
$581$	−12.7502	−0.528968
$582$	0.100547	0.00416781
$583$	2.56926	0.106408
$584$	−9.57628	−0.396269
$585$	7.11451	0.294149
$586$	−20.6351	−0.852430
$587$	−1.11221	−0.0459059	−0.0229530	−	0.999737i	$-0.507307\pi$
$587$	−1.11221	−0.0459059	−0.0229530	+	0.999737i	$0.507307\pi$
$588$	0.943657	0.0389158
$589$	12.6499	0.521229
$590$	−34.2821	−1.41137
$591$	3.23499	0.133070
$592$	−0.827260	−0.0340002
$593$	22.4051	0.920067	0.460034	−	0.887902i	$-0.347837\pi$
$593$	22.4051	0.920067	0.460034	+	0.887902i	$0.347837\pi$
$594$	−4.64916	−0.190757
$595$	23.2885	0.954737
$596$	−19.1650	−0.785030
$597$	4.44941	0.182102
$598$	3.34110	0.136628
$599$	23.5568	0.962505	0.481252	−	0.876582i	$-0.340182\pi$
$599$	23.5568	0.962505	0.481252	+	0.876582i	$0.340182\pi$
$600$	0.275802	0.0112596
$601$	35.8966	1.46425	0.732127	−	0.681168i	$-0.238528\pi$
$601$	35.8966	1.46425	0.732127	+	0.681168i	$0.238528\pi$
$602$	−2.64648	−0.107863
$603$	33.6663	1.37100
$604$	12.8566	0.523128
$605$	−11.9407	−0.485457
$606$	−0.535891	−0.0217691
$607$	25.7863	1.04663	0.523317	−	0.852138i	$-0.324694\pi$
$607$	25.7863	1.04663	0.523317	+	0.852138i	$0.324694\pi$
$608$	−1.18145	−0.0479143
$609$	0.347198	0.0140692
$610$	−15.1345	−0.612778
$611$	−1.45493	−0.0588602
$612$	−18.3648	−0.742353
$613$	40.4130	1.63227	0.816134	−	0.577863i	$-0.196113\pi$
$613$	40.4130	1.63227	0.816134	+	0.577863i	$0.196113\pi$
$614$	−1.79671	−0.0725091
$615$	0.348986	0.0140725
$616$	5.88428	0.237084
$617$	14.3012	0.575745	0.287873	−	0.957669i	$-0.407052\pi$
$617$	14.3012	0.575745	0.287873	+	0.957669i	$0.407052\pi$
$618$	−1.79370	−0.0721533
$619$	21.9481	0.882168	0.441084	−	0.897466i	$-0.354594\pi$
$619$	21.9481	0.882168	0.441084	+	0.897466i	$0.354594\pi$
$620$	−27.0913	−1.08801
$621$	−4.12618	−0.165578
$622$	−27.9620	−1.12117
$623$	18.4016	0.737245
$624$	−0.186775	−0.00747698
$625$	−30.0446	−1.20178
$626$	−10.1029	−0.403795
$627$	−0.921404	−0.0367973
$628$	7.02079	0.280160
$629$	−5.13032	−0.204559
$630$	11.1205	0.443050
$631$	−25.1441	−1.00097	−0.500485	−	0.865745i	$-0.666845\pi$
$631$	−25.1441	−1.00097	−0.500485	+	0.865745i	$0.666845\pi$
$632$	−5.61503	−0.223354
$633$	−2.86321	−0.113803
$634$	−7.73770	−0.307303
$635$	−12.2364	−0.485586
$636$	−0.127471	−0.00505455
$637$	−4.55508	−0.180479
$638$	−4.71515	−0.186675
$639$	−15.7780	−0.624170
$640$	2.53024	0.100016
$641$	−13.0862	−0.516874	−0.258437	−	0.966028i	$-0.583207\pi$
$641$	−13.0862	−0.516874	−0.258437	+	0.966028i	$0.583207\pi$
$642$	2.53761	0.100152
$643$	−2.73439	−0.107834	−0.0539168	−	0.998545i	$-0.517171\pi$
$643$	−2.73439	−0.107834	−0.0539168	+	0.998545i	$0.517171\pi$
$644$	5.22236	0.205790
$645$	−0.887503	−0.0349454
$646$	−7.32689	−0.288273
$647$	6.63241	0.260747	0.130374	−	0.991465i	$-0.458382\pi$
$647$	6.63241	0.260747	0.130374	+	0.991465i	$0.458382\pi$
$648$	−8.65326	−0.339932
$649$	−53.7182	−2.10862
$650$	−1.33131	−0.0522183
$651$	3.12583	0.122511
$652$	−16.0734	−0.629482
$653$	22.9073	0.896430	0.448215	−	0.893926i	$-0.352060\pi$
$653$	22.9073	0.896430	0.448215	+	0.893926i	$0.352060\pi$
$654$	−0.0189580	−0.000741317 0
$655$	25.3420	0.990194
$656$	0.701178	0.0273764
$657$	−28.3583	−1.10636
$658$	−2.27416	−0.0886559
$659$	45.8928	1.78773	0.893865	−	0.448337i	$-0.147984\pi$
$659$	45.8928	1.78773	0.893865	+	0.448337i	$0.147984\pi$
$660$	1.97331	0.0768108
$661$	16.0962	0.626070	0.313035	−	0.949742i	$-0.398654\pi$
$661$	16.0962	0.626070	0.313035	+	0.949742i	$0.398654\pi$
$662$	−12.0598	−0.468719
$663$	−1.15830	−0.0449846
$664$	−8.59090	−0.333392
$665$	4.43667	0.172047
$666$	−2.44977	−0.0949266
$667$	−4.18475	−0.162034
$668$	−9.50328	−0.367693
$669$	2.14908	0.0830883
$670$	−28.7656	−1.11131
$671$	−23.7149	−0.915504
$672$	−0.291942	−0.0112619
$673$	−14.7430	−0.568300	−0.284150	−	0.958780i	$-0.591711\pi$
$673$	−14.7430	−0.568300	−0.284150	+	0.958780i	$0.591711\pi$
$674$	−9.71045	−0.374033
$675$	1.64414	0.0632830
$676$	−12.0984	−0.465324
$677$	45.1572	1.73553	0.867765	−	0.496974i	$-0.165556\pi$
$677$	45.1572	1.73553	0.867765	+	0.496974i	$0.165556\pi$
$678$	−1.82665	−0.0701519
$679$	−0.758630	−0.0291136
$680$	15.6915	0.601741
$681$	−3.42862	−0.131385
$682$	−42.4506	−1.62552
$683$	21.3543	0.817100	0.408550	−	0.912736i	$-0.366035\pi$
$683$	21.3543	0.817100	0.408550	+	0.912736i	$0.366035\pi$
$684$	−3.49865	−0.133774
$685$	−55.0501	−2.10336
$686$	−17.5090	−0.668496
$687$	−5.57591	−0.212734
$688$	−1.78316	−0.0679824
$689$	0.615309	0.0234414
$690$	1.75133	0.0666720
$691$	19.9640	0.759466	0.379733	−	0.925096i	$-0.376016\pi$
$691$	19.9640	0.759466	0.379733	+	0.925096i	$0.376016\pi$
$692$	3.94335	0.149904
$693$	17.4252	0.661927
$694$	5.78396	0.219556
$695$	45.0710	1.70964
$696$	0.233937	0.00886736
$697$	4.34842	0.164708
$698$	−15.3184	−0.579811
$699$	−2.22787	−0.0842659
$700$	−2.08093	−0.0786518
$701$	17.4973	0.660862	0.330431	−	0.943830i	$-0.392806\pi$
$701$	17.4973	0.660862	0.330431	+	0.943830i	$0.392806\pi$
$702$	−1.11342	−0.0420234
$703$	−0.977370	−0.0368622
$704$	3.96474	0.149427
$705$	−0.762644	−0.0287228
$706$	−22.9510	−0.863772
$707$	4.04331	0.152064
$708$	2.66517	0.100163
$709$	−39.3846	−1.47912	−0.739560	−	0.673091i	$-0.764966\pi$
$709$	−39.3846	−1.47912	−0.739560	+	0.673091i	$0.764966\pi$
$710$	13.4813	0.505943
$711$	−16.6278	−0.623592
$712$	12.3987	0.464662
$713$	−37.6754	−1.41095
$714$	−1.81050	−0.0677564
$715$	−9.52525	−0.356224
$716$	14.0950	0.526755
$717$	−0.803987	−0.0300254
$718$	−2.71270	−0.101237
$719$	33.7078	1.25709	0.628544	−	0.777774i	$-0.283651\pi$
$719$	33.7078	1.25709	0.628544	+	0.777774i	$0.283651\pi$
$720$	7.49281	0.279240
$721$	13.5335	0.504015
$722$	17.6042	0.655159
$723$	5.11545	0.190245
$724$	19.5259	0.725673
$725$	1.66748	0.0619286
$726$	0.928294	0.0344522
$727$	35.8495	1.32958	0.664792	−	0.747028i	$-0.268520\pi$
$727$	35.8495	1.32958	0.664792	+	0.747028i	$0.268520\pi$
$728$	1.40922	0.0522291
$729$	−24.9330	−0.923443
$730$	24.2303	0.896802
$731$	−11.0584	−0.409011
$732$	1.17659	0.0434880
$733$	−19.0877	−0.705020	−0.352510	−	0.935808i	$-0.614672\pi$
$733$	−19.0877	−0.705020	−0.352510	+	0.935808i	$0.614672\pi$
$734$	−33.1913	−1.22511
$735$	−2.38768	−0.0880708
$736$	3.51875	0.129703
$737$	−45.0741	−1.66033
$738$	2.07640	0.0764335
$739$	31.0722	1.14301	0.571505	−	0.820599i	$-0.306360\pi$
$739$	31.0722	1.14301	0.571505	+	0.820599i	$0.306360\pi$
$740$	2.09316	0.0769462
$741$	−0.220666	−0.00810637
$742$	0.961771	0.0353077
$743$	−1.40074	−0.0513883	−0.0256942	−	0.999670i	$-0.508180\pi$
$743$	−1.40074	−0.0513883	−0.0256942	+	0.999670i	$0.508180\pi$
$744$	2.10614	0.0772148
$745$	48.4921	1.77661
$746$	13.6329	0.499135
$747$	−25.4403	−0.930812
$748$	24.5877	0.899015
$749$	−19.1463	−0.699592
$750$	1.79072	0.0653880
$751$	14.3183	0.522484	0.261242	−	0.965273i	$-0.415868\pi$
$751$	14.3183	0.522484	0.261242	+	0.965273i	$0.415868\pi$
$752$	−1.53229	−0.0558770
$753$	−0.566919	−0.0206597
$754$	−1.12923	−0.0411240
$755$	−32.5303	−1.18390
$756$	−1.74036	−0.0632961
$757$	21.7797	0.791597	0.395798	−	0.918337i	$-0.370468\pi$
$757$	21.7797	0.791597	0.395798	+	0.918337i	$0.370468\pi$
$758$	−11.3297	−0.411514
$759$	2.74424	0.0996096
$760$	2.98936	0.108436
$761$	25.5770	0.927166	0.463583	−	0.886053i	$-0.346564\pi$
$761$	25.5770	0.927166	0.463583	+	0.886053i	$0.346564\pi$
$762$	0.951283	0.0344614
$763$	0.143039	0.00517834
$764$	11.9746	0.433227
$765$	46.4673	1.68003
$766$	25.9302	0.936896
$767$	−12.8649	−0.464525
$768$	−0.196706	−0.00709802
$769$	2.39501	0.0863664	0.0431832	−	0.999067i	$-0.486250\pi$
$769$	2.39501	0.0863664	0.0431832	+	0.999067i	$0.486250\pi$
$770$	−14.8886	−0.536549
$771$	−5.24013	−0.188719
$772$	11.2116	0.403515
$773$	46.6511	1.67792	0.838962	−	0.544190i	$-0.183163\pi$
$773$	46.6511	1.67792	0.838962	+	0.544190i	$0.183163\pi$
$774$	−5.28049	−0.189803
$775$	15.0123	0.539259
$776$	−0.511154	−0.0183494
$777$	−0.241512	−0.00866419
$778$	19.3844	0.694964
$779$	0.828410	0.0296809
$780$	0.472585	0.0169212
$781$	21.1244	0.755891
$782$	21.8218	0.780347
$783$	1.39457	0.0498379
$784$	−4.79729	−0.171332
$785$	−17.7643	−0.634034
$786$	−1.97014	−0.0702727
$787$	−13.1807	−0.469842	−0.234921	−	0.972014i	$-0.575483\pi$
$787$	−13.1807	−0.469842	−0.234921	+	0.972014i	$0.575483\pi$
$788$	−16.4458	−0.585858
$789$	−5.81935	−0.207174
$790$	14.2074	0.505475
$791$	13.7821	0.490034
$792$	11.7408	0.417192
$793$	−5.67945	−0.201683
$794$	13.4610	0.477714
$795$	0.322532	0.0114390
$796$	−22.6196	−0.801729
$797$	45.3358	1.60588	0.802938	−	0.596063i	$-0.203269\pi$
$797$	45.3358	1.60588	0.802938	+	0.596063i	$0.203269\pi$
$798$	−0.344916	−0.0122099
$799$	−9.50265	−0.336180
$800$	−1.40210	−0.0495718
$801$	36.7165	1.29731
$802$	27.8345	0.982871
$803$	37.9675	1.33984
$804$	2.23630	0.0788683
$805$	−13.2138	−0.465726
$806$	−10.1664	−0.358098
$807$	−2.82029	−0.0992788
$808$	2.72432	0.0958412
$809$	41.5853	1.46206	0.731030	−	0.682345i	$-0.239040\pi$
$809$	41.5853	1.46206	0.731030	+	0.682345i	$0.239040\pi$
$810$	21.8948	0.769305
$811$	−46.6608	−1.63848	−0.819241	−	0.573449i	$-0.805605\pi$
$811$	−46.6608	−1.63848	−0.819241	+	0.573449i	$0.805605\pi$
$812$	−1.76506	−0.0619414
$813$	0.800768	0.0280842
$814$	3.27987	0.114959
$815$	40.6695	1.42459
$816$	−1.21989	−0.0427047
$817$	−2.10672	−0.0737049
$818$	36.3552	1.27113
$819$	4.17313	0.145821
$820$	−1.77415	−0.0619559
$821$	40.0418	1.39747	0.698734	−	0.715381i	$-0.253747\pi$
$821$	40.0418	1.39747	0.698734	+	0.715381i	$0.253747\pi$
$822$	4.27972	0.149272
$823$	6.03011	0.210196	0.105098	−	0.994462i	$-0.466484\pi$
$823$	6.03011	0.210196	0.105098	+	0.994462i	$0.466484\pi$
$824$	9.11869	0.317665
$825$	−1.09348	−0.0380702
$826$	−20.1087	−0.699672
$827$	−33.8059	−1.17555	−0.587773	−	0.809026i	$-0.699995\pi$
$827$	−33.8059	−1.17555	−0.587773	+	0.809026i	$0.699995\pi$
$828$	10.4201	0.362124
$829$	−9.29497	−0.322828	−0.161414	−	0.986887i	$-0.551605\pi$
$829$	−9.29497	−0.322828	−0.161414	+	0.986887i	$0.551605\pi$
$830$	21.7370	0.754503
$831$	−2.76261	−0.0958339
$832$	0.949511	0.0329184
$833$	−29.7508	−1.03080
$834$	−3.50392	−0.121331
$835$	24.0456	0.832131
$836$	4.68416	0.162005
$837$	12.5553	0.433976
$838$	31.8630	1.10069
$839$	−4.89998	−0.169166	−0.0845830	−	0.996416i	$-0.526956\pi$
$839$	−4.89998	−0.169166	−0.0845830	+	0.996416i	$0.526956\pi$
$840$	0.738683	0.0254870
$841$	−27.5856	−0.951229
$842$	−21.8011	−0.751316
$843$	−1.53594	−0.0529006
$844$	14.5558	0.501031
$845$	30.6119	1.05308
$846$	−4.53759	−0.156006
$847$	−7.00399	−0.240660
$848$	0.648027	0.0222533
$849$	2.71898	0.0933151
$850$	−8.69525	−0.298245
$851$	2.91092	0.0997851
$852$	−1.04806	−0.0359061
$853$	−24.0972	−0.825072	−0.412536	−	0.910941i	$-0.635357\pi$
$853$	−24.0972	−0.825072	−0.412536	+	0.910941i	$0.635357\pi$
$854$	−8.87738	−0.303778
$855$	8.85241	0.302746
$856$	−12.9005	−0.440931
$857$	27.7473	0.947831	0.473916	−	0.880570i	$-0.342840\pi$
$857$	27.7473	0.947831	0.473916	+	0.880570i	$0.342840\pi$
$858$	0.740514	0.0252807
$859$	33.6333	1.14755	0.573777	−	0.819011i	$-0.305478\pi$
$859$	33.6333	1.14755	0.573777	+	0.819011i	$0.305478\pi$
$860$	4.51182	0.153852
$861$	0.204703	0.00697627
$862$	−3.45331	−0.117620
$863$	23.7334	0.807896	0.403948	−	0.914782i	$-0.367638\pi$
$863$	23.7334	0.807896	0.403948	+	0.914782i	$0.367638\pi$
$864$	−1.17263	−0.0398936
$865$	−9.97761	−0.339249
$866$	−36.8866	−1.25346
$867$	−4.22125	−0.143361
$868$	−15.8909	−0.539371
$869$	22.2621	0.755192
$870$	−0.591916	−0.0200678
$871$	−10.7947	−0.365766
$872$	0.0963773	0.00326375
$873$	−1.51368	−0.0512304
$874$	4.15725	0.140621
$875$	−13.5110	−0.456756
$876$	−1.88371	−0.0636448
$877$	−21.7268	−0.733663	−0.366832	−	0.930287i	$-0.619557\pi$
$877$	−21.7268	−0.733663	−0.366832	+	0.930287i	$0.619557\pi$
$878$	26.3450	0.889101
$879$	−4.05906	−0.136909
$880$	−10.0317	−0.338170
$881$	8.07430	0.272030	0.136015	−	0.990707i	$-0.456570\pi$
$881$	8.07430	0.272030	0.136015	+	0.990707i	$0.456570\pi$
$882$	−14.2063	−0.478349
$883$	−24.9659	−0.840170	−0.420085	−	0.907485i	$-0.638000\pi$
$883$	−24.9659	−0.840170	−0.420085	+	0.907485i	$0.638000\pi$
$884$	5.88847	0.198051
$885$	−6.74350	−0.226680
$886$	8.66729	0.291183
$887$	−19.3930	−0.651153	−0.325576	−	0.945516i	$-0.605558\pi$
$887$	−19.3930	−0.651153	−0.325576	+	0.945516i	$0.605558\pi$
$888$	−0.162727	−0.00546076
$889$	−7.17745	−0.240724
$890$	−31.3718	−1.05158
$891$	34.3079	1.14936
$892$	−10.9253	−0.365807
$893$	−1.81034	−0.0605806
$894$	−3.76988	−0.126084
$895$	−35.6637	−1.19211
$896$	1.48415	0.0495820
$897$	0.657214	0.0219437
$898$	−25.9238	−0.865089
$899$	12.7336	0.424688
$900$	−4.15205	−0.138402
$901$	4.01879	0.133885
$902$	−2.77999	−0.0925636
$903$	−0.520580	−0.0173238
$904$	9.28616	0.308853
$905$	−49.4051	−1.64228
$906$	2.52898	0.0840196
$907$	−22.2447	−0.738624	−0.369312	−	0.929305i	$-0.620407\pi$
$907$	−22.2447	−0.738624	−0.369312	+	0.929305i	$0.620407\pi$
$908$	17.4302	0.578440
$909$	8.06755	0.267584
$910$	−3.56566	−0.118200
$911$	31.9208	1.05758	0.528792	−	0.848752i	$-0.322645\pi$
$911$	31.9208	1.05758	0.528792	+	0.848752i	$0.322645\pi$
$912$	−0.232399	−0.00769552
$913$	34.0607	1.12725
$914$	10.8245	0.358042
$915$	−2.97705	−0.0984182
$916$	28.3464	0.936592
$917$	14.8648	0.490878
$918$	−7.27214	−0.240016
$919$	−0.802259	−0.0264641	−0.0132320	−	0.999912i	$-0.504212\pi$
$919$	−0.802259	−0.0264641	−0.0132320	+	0.999912i	$0.504212\pi$
$920$	−8.90328	−0.293532
$921$	−0.353423	−0.0116457
$922$	38.1997	1.25804
$923$	5.05906	0.166521
$924$	1.15748	0.0380781
$925$	−1.15990	−0.0381373
$926$	6.55923	0.215550
$927$	27.0032	0.886903
$928$	−1.18927	−0.0390397
$929$	−5.61545	−0.184237	−0.0921184	−	0.995748i	$-0.529364\pi$
$929$	−5.61545	−0.184237	−0.0921184	+	0.995748i	$0.529364\pi$
$930$	−5.32903	−0.174746
$931$	−5.66778	−0.185754
$932$	11.3259	0.370992
$933$	−5.50030	−0.180072
$934$	−2.51078	−0.0821554
$935$	−62.2127	−2.03457
$936$	2.81179	0.0919064
$937$	−42.0191	−1.37270	−0.686352	−	0.727269i	$-0.740789\pi$
$937$	−42.0191	−1.37270	−0.686352	+	0.727269i	$0.740789\pi$
$938$	−16.8729	−0.550921
$939$	−1.98731	−0.0648535
$940$	3.87707	0.126456
$941$	16.5191	0.538507	0.269254	−	0.963069i	$-0.413223\pi$
$941$	16.5191	0.538507	0.269254	+	0.963069i	$0.413223\pi$
$942$	1.38103	0.0449965
$943$	−2.46727	−0.0803454
$944$	−13.5490	−0.440981
$945$	4.40351	0.143246
$946$	7.06978	0.229858
$947$	46.7428	1.51894	0.759468	−	0.650545i	$-0.225459\pi$
$947$	46.7428	1.51894	0.759468	+	0.650545i	$0.225459\pi$
$948$	−1.10451	−0.0358729
$949$	9.09279	0.295164
$950$	−1.65652	−0.0537446
$951$	−1.52205	−0.0493560
$952$	9.20410	0.298306
$953$	−17.6993	−0.573337	−0.286669	−	0.958030i	$-0.592548\pi$
$953$	−17.6993	−0.573337	−0.286669	+	0.958030i	$0.592548\pi$
$954$	1.91901	0.0621301
$955$	−30.2986	−0.980441
$956$	4.08725	0.132191
$957$	−0.927500	−0.0299818
$958$	4.95903	0.160219
$959$	−32.2905	−1.04272
$960$	0.497713	0.0160636
$961$	83.6405	2.69808
$962$	0.785492	0.0253253
$963$	−38.2024	−1.23106
$964$	−26.0055	−0.837581
$965$	−28.3681	−0.913200
$966$	1.02727	0.0330519
$967$	3.36003	0.108051	0.0540256	−	0.998540i	$-0.482795\pi$
$967$	3.36003	0.108051	0.0540256	+	0.998540i	$0.482795\pi$
$968$	−4.71919	−0.151680
$969$	−1.44125	−0.0462995
$970$	1.29334	0.0415267
$971$	−23.3651	−0.749822	−0.374911	−	0.927061i	$-0.622327\pi$
$971$	−23.3651	−0.749822	−0.374911	+	0.927061i	$0.622327\pi$
$972$	−5.22003	−0.167432
$973$	26.4371	0.847535
$974$	24.2797	0.777971
$975$	−0.261877	−0.00838678
$976$	−5.98145	−0.191462
$977$	20.8059	0.665641	0.332821	−	0.942990i	$-0.392000\pi$
$977$	20.8059	0.665641	0.332821	+	0.942990i	$0.392000\pi$
$978$	−3.16173	−0.101101
$979$	−49.1578	−1.57109
$980$	12.1383	0.387743
$981$	0.285403	0.00911221
$982$	−2.61299	−0.0833840
$983$	−6.31706	−0.201483	−0.100741	−	0.994913i	$-0.532121\pi$
$983$	−6.31706	−0.201483	−0.100741	+	0.994913i	$0.532121\pi$
$984$	0.137926	0.00439692
$985$	41.6118	1.32586
$986$	−7.37536	−0.234879
$987$	−0.447341	−0.0142390
$988$	1.12180	0.0356894
$989$	6.27450	0.199518
$990$	−29.7071	−0.944152
$991$	−5.46988	−0.173756	−0.0868782	−	0.996219i	$-0.527689\pi$
$991$	−5.46988	−0.173756	−0.0868782	+	0.996219i	$0.527689\pi$
$992$	−10.7070	−0.339949
$993$	−2.37224	−0.0752809
$994$	7.90766	0.250816
$995$	57.2329	1.81440
$996$	−1.68988	−0.0535460
$997$	3.04160	0.0963285	0.0481643	−	0.998839i	$-0.484663\pi$
$997$	3.04160	0.0963285	0.0481643	+	0.998839i	$0.484663\pi$
$998$	−26.2223	−0.830054
$999$	−0.970066	−0.0306915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.36	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.36	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.196706 q^{3} +1.00000 q^{4} -2.53024 q^{5} +0.196706 q^{6} -1.48415 q^{7} -1.00000 q^{8} -2.96131 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.196706 q^{3} +1.00000 q^{4} -2.53024 q^{5} +0.196706 q^{6} -1.48415 q^{7} -1.00000 q^{8} -2.96131 q^{9} +2.53024 q^{10} +3.96474 q^{11} -0.196706 q^{12} +0.949511 q^{13} +1.48415 q^{14} +0.497713 q^{15} +1.00000 q^{16} +6.20158 q^{17} +2.96131 q^{18} +1.18145 q^{19} -2.53024 q^{20} +0.291942 q^{21} -3.96474 q^{22} -3.51875 q^{23} +0.196706 q^{24} +1.40210 q^{25} -0.949511 q^{26} +1.17263 q^{27} -1.48415 q^{28} +1.18927 q^{29} -0.497713 q^{30} +10.7070 q^{31} -1.00000 q^{32} -0.779890 q^{33} -6.20158 q^{34} +3.75526 q^{35} -2.96131 q^{36} -0.827260 q^{37} -1.18145 q^{38} -0.186775 q^{39} +2.53024 q^{40} +0.701178 q^{41} -0.291942 q^{42} -1.78316 q^{43} +3.96474 q^{44} +7.49281 q^{45} +3.51875 q^{46} -1.53229 q^{47} -0.196706 q^{48} -4.79729 q^{49} -1.40210 q^{50} -1.21989 q^{51} +0.949511 q^{52} +0.648027 q^{53} -1.17263 q^{54} -10.0317 q^{55} +1.48415 q^{56} -0.232399 q^{57} -1.18927 q^{58} -13.5490 q^{59} +0.497713 q^{60} -5.98145 q^{61} -10.7070 q^{62} +4.39503 q^{63} +1.00000 q^{64} -2.40249 q^{65} +0.779890 q^{66} -11.3687 q^{67} +6.20158 q^{68} +0.692161 q^{69} -3.75526 q^{70} +5.32807 q^{71} +2.96131 q^{72} +9.57628 q^{73} +0.827260 q^{74} -0.275802 q^{75} +1.18145 q^{76} -5.88428 q^{77} +0.186775 q^{78} +5.61503 q^{79} -2.53024 q^{80} +8.65326 q^{81} -0.701178 q^{82} +8.59090 q^{83} +0.291942 q^{84} -15.6915 q^{85} +1.78316 q^{86} -0.233937 q^{87} -3.96474 q^{88} -12.3987 q^{89} -7.49281 q^{90} -1.40922 q^{91} -3.51875 q^{92} -2.10614 q^{93} +1.53229 q^{94} -2.98936 q^{95} +0.196706 q^{96} +0.511154 q^{97} +4.79729 q^{98} -11.7408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 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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