LMFDB - Embedded newform 8002.2.a.e.1.64

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			1.64
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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.33509 q^{3} +1.00000 q^{4} -3.74704 q^{5} -2.33509 q^{6} +4.17376 q^{7} -1.00000 q^{8} +2.45266 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.33509 q^{3} +1.00000 q^{4} -3.74704 q^{5} -2.33509 q^{6} +4.17376 q^{7} -1.00000 q^{8} +2.45266 q^{9} +3.74704 q^{10} +2.63847 q^{11} +2.33509 q^{12} +1.98660 q^{13} -4.17376 q^{14} -8.74970 q^{15} +1.00000 q^{16} +7.02193 q^{17} -2.45266 q^{18} -7.23332 q^{19} -3.74704 q^{20} +9.74612 q^{21} -2.63847 q^{22} +3.22981 q^{23} -2.33509 q^{24} +9.04034 q^{25} -1.98660 q^{26} -1.27809 q^{27} +4.17376 q^{28} +3.84822 q^{29} +8.74970 q^{30} -0.655035 q^{31} -1.00000 q^{32} +6.16107 q^{33} -7.02193 q^{34} -15.6393 q^{35} +2.45266 q^{36} +2.20496 q^{37} +7.23332 q^{38} +4.63889 q^{39} +3.74704 q^{40} +6.48911 q^{41} -9.74612 q^{42} +4.44213 q^{43} +2.63847 q^{44} -9.19023 q^{45} -3.22981 q^{46} +5.02776 q^{47} +2.33509 q^{48} +10.4203 q^{49} -9.04034 q^{50} +16.3969 q^{51} +1.98660 q^{52} -5.68509 q^{53} +1.27809 q^{54} -9.88646 q^{55} -4.17376 q^{56} -16.8905 q^{57} -3.84822 q^{58} -6.73276 q^{59} -8.74970 q^{60} -11.7991 q^{61} +0.655035 q^{62} +10.2368 q^{63} +1.00000 q^{64} -7.44386 q^{65} -6.16107 q^{66} -2.89563 q^{67} +7.02193 q^{68} +7.54191 q^{69} +15.6393 q^{70} +14.0935 q^{71} -2.45266 q^{72} +4.06682 q^{73} -2.20496 q^{74} +21.1100 q^{75} -7.23332 q^{76} +11.0123 q^{77} -4.63889 q^{78} -4.93917 q^{79} -3.74704 q^{80} -10.3424 q^{81} -6.48911 q^{82} +4.80179 q^{83} +9.74612 q^{84} -26.3115 q^{85} -4.44213 q^{86} +8.98595 q^{87} -2.63847 q^{88} -3.69511 q^{89} +9.19023 q^{90} +8.29158 q^{91} +3.22981 q^{92} -1.52957 q^{93} -5.02776 q^{94} +27.1036 q^{95} -2.33509 q^{96} +5.90364 q^{97} -10.4203 q^{98} +6.47127 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.33509	1.34817	0.674083	−	0.738655i	$-0.264539\pi$
$3$	2.33509	1.34817	0.674083	+	0.738655i	$0.264539\pi$
$4$	1.00000	0.500000
$5$	−3.74704	−1.67573	−0.837865	−	0.545878i	$-0.816196\pi$
$5$	−3.74704	−1.67573	−0.837865	+	0.545878i	$0.816196\pi$
$6$	−2.33509	−0.953298
$7$	4.17376	1.57753	0.788767	−	0.614693i	$-0.210720\pi$
$7$	4.17376	1.57753	0.788767	+	0.614693i	$0.210720\pi$
$8$	−1.00000	−0.353553
$9$	2.45266	0.817554
$10$	3.74704	1.18492
$11$	2.63847	0.795528	0.397764	−	0.917488i	$-0.369786\pi$
$11$	2.63847	0.795528	0.397764	+	0.917488i	$0.369786\pi$
$12$	2.33509	0.674083
$13$	1.98660	0.550983	0.275491	−	0.961304i	$-0.411159\pi$
$13$	1.98660	0.550983	0.275491	+	0.961304i	$0.411159\pi$
$14$	−4.17376	−1.11548
$15$	−8.74970	−2.25916
$16$	1.00000	0.250000
$17$	7.02193	1.70307	0.851534	−	0.524300i	$-0.175673\pi$
$17$	7.02193	1.70307	0.851534	+	0.524300i	$0.175673\pi$
$18$	−2.45266	−0.578098
$19$	−7.23332	−1.65944	−0.829718	−	0.558182i	$-0.811499\pi$
$19$	−7.23332	−1.65944	−0.829718	+	0.558182i	$0.811499\pi$
$20$	−3.74704	−0.837865
$21$	9.74612	2.12678
$22$	−2.63847	−0.562524
$23$	3.22981	0.673462	0.336731	−	0.941601i	$-0.390679\pi$
$23$	3.22981	0.673462	0.336731	+	0.941601i	$0.390679\pi$
$24$	−2.33509	−0.476649
$25$	9.04034	1.80807
$26$	−1.98660	−0.389604
$27$	−1.27809	−0.245968
$28$	4.17376	0.788767
$29$	3.84822	0.714596	0.357298	−	0.933990i	$-0.383698\pi$
$29$	3.84822	0.714596	0.357298	+	0.933990i	$0.383698\pi$
$30$	8.74970	1.59747
$31$	−0.655035	−0.117648	−0.0588239	−	0.998268i	$-0.518735\pi$
$31$	−0.655035	−0.117648	−0.0588239	+	0.998268i	$0.518735\pi$
$32$	−1.00000	−0.176777
$33$	6.16107	1.07250
$34$	−7.02193	−1.20425
$35$	−15.6393	−2.64352
$36$	2.45266	0.408777
$37$	2.20496	0.362493	0.181247	−	0.983438i	$-0.441987\pi$
$37$	2.20496	0.362493	0.181247	+	0.983438i	$0.441987\pi$
$38$	7.23332	1.17340
$39$	4.63889	0.742816
$40$	3.74704	0.592460
$41$	6.48911	1.01343	0.506714	−	0.862114i	$-0.330860\pi$
$41$	6.48911	1.01343	0.506714	+	0.862114i	$0.330860\pi$
$42$	−9.74612	−1.50386
$43$	4.44213	0.677419	0.338710	−	0.940891i	$-0.390010\pi$
$43$	4.44213	0.677419	0.338710	+	0.940891i	$0.390010\pi$
$44$	2.63847	0.397764
$45$	−9.19023	−1.37000
$46$	−3.22981	−0.476209
$47$	5.02776	0.733375	0.366687	−	0.930344i	$-0.380492\pi$
$47$	5.02776	0.733375	0.366687	+	0.930344i	$0.380492\pi$
$48$	2.33509	0.337042
$49$	10.4203	1.48861
$50$	−9.04034	−1.27850
$51$	16.3969	2.29602
$52$	1.98660	0.275491
$53$	−5.68509	−0.780907	−0.390454	−	0.920623i	$-0.627682\pi$
$53$	−5.68509	−0.780907	−0.390454	+	0.920623i	$0.627682\pi$
$54$	1.27809	0.173926
$55$	−9.88646	−1.33309
$56$	−4.17376	−0.557742
$57$	−16.8905	−2.23720
$58$	−3.84822	−0.505296
$59$	−6.73276	−0.876531	−0.438265	−	0.898846i	$-0.644407\pi$
$59$	−6.73276	−0.876531	−0.438265	+	0.898846i	$0.644407\pi$
$60$	−8.74970	−1.12958
$61$	−11.7991	−1.51072	−0.755359	−	0.655311i	$-0.772538\pi$
$61$	−11.7991	−1.51072	−0.755359	+	0.655311i	$0.772538\pi$
$62$	0.655035	0.0831895
$63$	10.2368	1.28972
$64$	1.00000	0.125000
$65$	−7.44386	−0.923298
$66$	−6.16107	−0.758376
$67$	−2.89563	−0.353757	−0.176879	−	0.984233i	$-0.556600\pi$
$67$	−2.89563	−0.353757	−0.176879	+	0.984233i	$0.556600\pi$
$68$	7.02193	0.851534
$69$	7.54191	0.907939
$70$	15.6393	1.86925
$71$	14.0935	1.67259	0.836295	−	0.548279i	$-0.184717\pi$
$71$	14.0935	1.67259	0.836295	+	0.548279i	$0.184717\pi$
$72$	−2.45266	−0.289049
$73$	4.06682	0.475986	0.237993	−	0.971267i	$-0.423511\pi$
$73$	4.06682	0.475986	0.237993	+	0.971267i	$0.423511\pi$
$74$	−2.20496	−0.256321
$75$	21.1100	2.43758
$76$	−7.23332	−0.829718
$77$	11.0123	1.25497
$78$	−4.63889	−0.525251
$79$	−4.93917	−0.555700	−0.277850	−	0.960625i	$-0.589622\pi$
$79$	−4.93917	−0.555700	−0.277850	+	0.960625i	$0.589622\pi$
$80$	−3.74704	−0.418932
$81$	−10.3424	−1.14916
$82$	−6.48911	−0.716602
$83$	4.80179	0.527065	0.263532	−	0.964651i	$-0.415112\pi$
$83$	4.80179	0.527065	0.263532	+	0.964651i	$0.415112\pi$
$84$	9.74612	1.06339
$85$	−26.3115	−2.85388
$86$	−4.44213	−0.479008
$87$	8.98595	0.963395
$88$	−2.63847	−0.281262
$89$	−3.69511	−0.391681	−0.195840	−	0.980636i	$-0.562743\pi$
$89$	−3.69511	−0.391681	−0.195840	+	0.980636i	$0.562743\pi$
$90$	9.19023	0.968735
$91$	8.29158	0.869193
$92$	3.22981	0.336731
$93$	−1.52957	−0.158609
$94$	−5.02776	−0.518574
$95$	27.1036	2.78077
$96$	−2.33509	−0.238324
$97$	5.90364	0.599424	0.299712	−	0.954030i	$-0.403109\pi$
$97$	5.90364	0.599424	0.299712	+	0.954030i	$0.403109\pi$
$98$	−10.4203	−1.05261
$99$	6.47127	0.650387
$100$	9.04034	0.904034
$101$	4.22713	0.420615	0.210308	−	0.977635i	$-0.432553\pi$
$101$	4.22713	0.420615	0.210308	+	0.977635i	$0.432553\pi$
$102$	−16.3969	−1.62353
$103$	−20.1520	−1.98564	−0.992819	−	0.119628i	$-0.961830\pi$
$103$	−20.1520	−1.98564	−0.992819	+	0.119628i	$0.961830\pi$
$104$	−1.98660	−0.194802
$105$	−36.5192	−3.56390
$106$	5.68509	0.552185
$107$	−7.77941	−0.752064	−0.376032	−	0.926607i	$-0.622712\pi$
$107$	−7.77941	−0.752064	−0.376032	+	0.926607i	$0.622712\pi$
$108$	−1.27809	−0.122984
$109$	0.523156	0.0501092	0.0250546	−	0.999686i	$-0.492024\pi$
$109$	0.523156	0.0501092	0.0250546	+	0.999686i	$0.492024\pi$
$110$	9.88646	0.942637
$111$	5.14879	0.488701
$112$	4.17376	0.394383
$113$	11.8796	1.11754	0.558768	−	0.829324i	$-0.311274\pi$
$113$	11.8796	1.11754	0.558768	+	0.829324i	$0.311274\pi$
$114$	16.8905	1.58194
$115$	−12.1022	−1.12854
$116$	3.84822	0.357298
$117$	4.87245	0.450458
$118$	6.73276	0.619801
$119$	29.3078	2.68664
$120$	8.74970	0.798735
$121$	−4.03848	−0.367135
$122$	11.7991	1.06824
$123$	15.1527	1.36627
$124$	−0.655035	−0.0588239
$125$	−15.1393	−1.35410
$126$	−10.2368	−0.911968
$127$	8.84928	0.785247	0.392623	−	0.919699i	$-0.371568\pi$
$127$	8.84928	0.785247	0.392623	+	0.919699i	$0.371568\pi$
$128$	−1.00000	−0.0883883
$129$	10.3728	0.913274
$130$	7.44386	0.652870
$131$	16.8262	1.47012	0.735058	−	0.678004i	$-0.237155\pi$
$131$	16.8262	1.47012	0.735058	+	0.678004i	$0.237155\pi$
$132$	6.16107	0.536252
$133$	−30.1901	−2.61782
$134$	2.89563	0.250144
$135$	4.78905	0.412176
$136$	−7.02193	−0.602125
$137$	8.44361	0.721386	0.360693	−	0.932685i	$-0.382540\pi$
$137$	8.44361	0.721386	0.360693	+	0.932685i	$0.382540\pi$
$138$	−7.54191	−0.642010
$139$	−9.40265	−0.797523	−0.398761	−	0.917055i	$-0.630560\pi$
$139$	−9.40265	−0.797523	−0.398761	+	0.917055i	$0.630560\pi$
$140$	−15.6393	−1.32176
$141$	11.7403	0.988711
$142$	−14.0935	−1.18270
$143$	5.24157	0.438322
$144$	2.45266	0.204388
$145$	−14.4194	−1.19747
$146$	−4.06682	−0.336573
$147$	24.3323	2.00690
$148$	2.20496	0.181247
$149$	−1.30834	−0.107183	−0.0535917	−	0.998563i	$-0.517067\pi$
$149$	−1.30834	−0.107183	−0.0535917	+	0.998563i	$0.517067\pi$
$150$	−21.1100	−1.72363
$151$	2.01551	0.164020	0.0820100	−	0.996632i	$-0.473866\pi$
$151$	2.01551	0.164020	0.0820100	+	0.996632i	$0.473866\pi$
$152$	7.23332	0.586700
$153$	17.2224	1.39235
$154$	−11.0123	−0.887400
$155$	2.45444	0.197146
$156$	4.63889	0.371408
$157$	−6.42705	−0.512935	−0.256467	−	0.966553i	$-0.582559\pi$
$157$	−6.42705	−0.512935	−0.256467	+	0.966553i	$0.582559\pi$
$158$	4.93917	0.392939
$159$	−13.2752	−1.05279
$160$	3.74704	0.296230
$161$	13.4805	1.06241
$162$	10.3424	0.812579
$163$	−1.50466	−0.117854	−0.0589269	−	0.998262i	$-0.518768\pi$
$163$	−1.50466	−0.117854	−0.0589269	+	0.998262i	$0.518768\pi$
$164$	6.48911	0.506714
$165$	−23.0858	−1.79723
$166$	−4.80179	−0.372691
$167$	23.4395	1.81380	0.906902	−	0.421342i	$-0.138441\pi$
$167$	23.4395	1.81380	0.906902	+	0.421342i	$0.138441\pi$
$168$	−9.74612	−0.751930
$169$	−9.05344	−0.696418
$170$	26.3115	2.01800
$171$	−17.7409	−1.35668
$172$	4.44213	0.338710
$173$	−2.83392	−0.215459	−0.107729	−	0.994180i	$-0.534358\pi$
$173$	−2.83392	−0.215459	−0.107729	+	0.994180i	$0.534358\pi$
$174$	−8.98595	−0.681223
$175$	37.7322	2.85229
$176$	2.63847	0.198882
$177$	−15.7216	−1.18171
$178$	3.69511	0.276960
$179$	−14.2346	−1.06394	−0.531971	−	0.846762i	$-0.678549\pi$
$179$	−14.2346	−1.06394	−0.531971	+	0.846762i	$0.678549\pi$
$180$	−9.19023	−0.684999
$181$	19.5881	1.45598	0.727988	−	0.685590i	$-0.240456\pi$
$181$	19.5881	1.45598	0.727988	+	0.685590i	$0.240456\pi$
$182$	−8.29158	−0.614613
$183$	−27.5520	−2.03670
$184$	−3.22981	−0.238105
$185$	−8.26208	−0.607440
$186$	1.52957	0.112153
$187$	18.5271	1.35484
$188$	5.02776	0.366687
$189$	−5.33443	−0.388023
$190$	−27.1036	−1.96630
$191$	−1.53068	−0.110756	−0.0553780	−	0.998465i	$-0.517636\pi$
$191$	−1.53068	−0.110756	−0.0553780	+	0.998465i	$0.517636\pi$
$192$	2.33509	0.168521
$193$	−15.1760	−1.09239	−0.546196	−	0.837657i	$-0.683925\pi$
$193$	−15.1760	−1.09239	−0.546196	+	0.837657i	$0.683925\pi$
$194$	−5.90364	−0.423857
$195$	−17.3821	−1.24476
$196$	10.4203	0.744306
$197$	18.2132	1.29763	0.648817	−	0.760944i	$-0.275264\pi$
$197$	18.2132	1.29763	0.648817	+	0.760944i	$0.275264\pi$
$198$	−6.47127	−0.459893
$199$	21.6939	1.53784	0.768919	−	0.639346i	$-0.220795\pi$
$199$	21.6939	1.53784	0.768919	+	0.639346i	$0.220795\pi$
$200$	−9.04034	−0.639249
$201$	−6.76156	−0.476924
$202$	−4.22713	−0.297420
$203$	16.0615	1.12730
$204$	16.3969	1.14801
$205$	−24.3150	−1.69823
$206$	20.1520	1.40406
$207$	7.92163	0.550591
$208$	1.98660	0.137746
$209$	−19.0849	−1.32013
$210$	36.5192	2.52006
$211$	8.53358	0.587476	0.293738	−	0.955886i	$-0.405101\pi$
$211$	8.53358	0.587476	0.293738	+	0.955886i	$0.405101\pi$
$212$	−5.68509	−0.390454
$213$	32.9096	2.25493
$214$	7.77941	0.531789
$215$	−16.6449	−1.13517
$216$	1.27809	0.0869629
$217$	−2.73396	−0.185593
$218$	−0.523156	−0.0354326
$219$	9.49641	0.641708
$220$	−9.88646	−0.666545
$221$	13.9497	0.938360
$222$	−5.14879	−0.345564
$223$	4.00144	0.267956	0.133978	−	0.990984i	$-0.457225\pi$
$223$	4.00144	0.267956	0.133978	+	0.990984i	$0.457225\pi$
$224$	−4.17376	−0.278871
$225$	22.1729	1.47819
$226$	−11.8796	−0.790217
$227$	−10.2355	−0.679354	−0.339677	−	0.940542i	$-0.610318\pi$
$227$	−10.2355	−0.679354	−0.339677	+	0.940542i	$0.610318\pi$
$228$	−16.8905	−1.11860
$229$	−20.6882	−1.36712	−0.683558	−	0.729896i	$-0.739569\pi$
$229$	−20.6882	−1.36712	−0.683558	+	0.729896i	$0.739569\pi$
$230$	12.1022	0.797998
$231$	25.7148	1.69191
$232$	−3.84822	−0.252648
$233$	−21.2478	−1.39199	−0.695995	−	0.718047i	$-0.745036\pi$
$233$	−21.2478	−1.39199	−0.695995	+	0.718047i	$0.745036\pi$
$234$	−4.87245	−0.318522
$235$	−18.8393	−1.22894
$236$	−6.73276	−0.438265
$237$	−11.5334	−0.749176
$238$	−29.3078	−1.89974
$239$	−11.8590	−0.767094	−0.383547	−	0.923521i	$-0.625298\pi$
$239$	−11.8590	−0.767094	−0.383547	+	0.923521i	$0.625298\pi$
$240$	−8.74970	−0.564791
$241$	1.93646	0.124738	0.0623691	−	0.998053i	$-0.480134\pi$
$241$	1.93646	0.124738	0.0623691	+	0.998053i	$0.480134\pi$
$242$	4.03848	0.259603
$243$	−20.3163	−1.30329
$244$	−11.7991	−0.755359
$245$	−39.0452	−2.49451
$246$	−15.1527	−0.966099
$247$	−14.3697	−0.914321
$248$	0.655035	0.0415947
$249$	11.2126	0.710571
$250$	15.1393	0.957497
$251$	−23.7929	−1.50179	−0.750897	−	0.660420i	$-0.770378\pi$
$251$	−23.7929	−1.50179	−0.750897	+	0.660420i	$0.770378\pi$
$252$	10.2368	0.644859
$253$	8.52175	0.535758
$254$	−8.84928	−0.555253
$255$	−61.4397	−3.84751
$256$	1.00000	0.0625000
$257$	16.3636	1.02073	0.510367	−	0.859957i	$-0.329510\pi$
$257$	16.3636	1.02073	0.510367	+	0.859957i	$0.329510\pi$
$258$	−10.3728	−0.645782
$259$	9.20297	0.571845
$260$	−7.44386	−0.461649
$261$	9.43837	0.584221
$262$	−16.8262	−1.03953
$263$	17.0622	1.05210	0.526050	−	0.850454i	$-0.323673\pi$
$263$	17.0622	1.05210	0.526050	+	0.850454i	$0.323673\pi$
$264$	−6.16107	−0.379188
$265$	21.3023	1.30859
$266$	30.1901	1.85108
$267$	−8.62843	−0.528051
$268$	−2.89563	−0.176879
$269$	−3.00093	−0.182970	−0.0914850	−	0.995806i	$-0.529161\pi$
$269$	−3.00093	−0.182970	−0.0914850	+	0.995806i	$0.529161\pi$
$270$	−4.78905	−0.291452
$271$	12.4434	0.755880	0.377940	−	0.925830i	$-0.376632\pi$
$271$	12.4434	0.755880	0.377940	+	0.925830i	$0.376632\pi$
$272$	7.02193	0.425767
$273$	19.3616	1.17182
$274$	−8.44361	−0.510097
$275$	23.8527	1.43837
$276$	7.54191	0.453969
$277$	−6.53501	−0.392651	−0.196325	−	0.980539i	$-0.562901\pi$
$277$	−6.53501	−0.392651	−0.196325	+	0.980539i	$0.562901\pi$
$278$	9.40265	0.563934
$279$	−1.60658	−0.0961833
$280$	15.6393	0.934625
$281$	−23.9419	−1.42825	−0.714126	−	0.700017i	$-0.753176\pi$
$281$	−23.9419	−1.42825	−0.714126	+	0.700017i	$0.753176\pi$
$282$	−11.7403	−0.699125
$283$	−8.07052	−0.479743	−0.239871	−	0.970805i	$-0.577105\pi$
$283$	−8.07052	−0.479743	−0.239871	+	0.970805i	$0.577105\pi$
$284$	14.0935	0.836295
$285$	63.2894	3.74894
$286$	−5.24157	−0.309941
$287$	27.0840	1.59872
$288$	−2.45266	−0.144524
$289$	32.3074	1.90044
$290$	14.4194	0.846739
$291$	13.7855	0.808123
$292$	4.06682	0.237993
$293$	21.8472	1.27633	0.638164	−	0.769900i	$-0.279694\pi$
$293$	21.8472	1.27633	0.638164	+	0.769900i	$0.279694\pi$
$294$	−24.3323	−1.41909
$295$	25.2280	1.46883
$296$	−2.20496	−0.128161
$297$	−3.37220	−0.195675
$298$	1.30834	0.0757901
$299$	6.41633	0.371066
$300$	21.1100	1.21879
$301$	18.5404	1.06865
$302$	−2.01551	−0.115980
$303$	9.87075	0.567060
$304$	−7.23332	−0.414859
$305$	44.2117	2.53155
$306$	−17.2224	−0.984539
$307$	32.0926	1.83162	0.915811	−	0.401609i	$-0.131549\pi$
$307$	32.0926	1.83162	0.915811	+	0.401609i	$0.131549\pi$
$308$	11.0123	0.627486
$309$	−47.0568	−2.67697
$310$	−2.45444	−0.139403
$311$	14.4612	0.820019	0.410010	−	0.912081i	$-0.365525\pi$
$311$	14.4612	0.820019	0.410010	+	0.912081i	$0.365525\pi$
$312$	−4.63889	−0.262625
$313$	−30.3264	−1.71415	−0.857075	−	0.515191i	$-0.827721\pi$
$313$	−30.3264	−1.71415	−0.857075	+	0.515191i	$0.827721\pi$
$314$	6.42705	0.362700
$315$	−38.3578	−2.16122
$316$	−4.93917	−0.277850
$317$	−17.2415	−0.968380	−0.484190	−	0.874963i	$-0.660886\pi$
$317$	−17.2415	−0.968380	−0.484190	+	0.874963i	$0.660886\pi$
$318$	13.2752	0.744437
$319$	10.1534	0.568482
$320$	−3.74704	−0.209466
$321$	−18.1656	−1.01391
$322$	−13.4805	−0.751236
$323$	−50.7918	−2.82613
$324$	−10.3424	−0.574580
$325$	17.9595	0.996214
$326$	1.50466	0.0833352
$327$	1.22162	0.0675556
$328$	−6.48911	−0.358301
$329$	20.9847	1.15692
$330$	23.0858	1.27083
$331$	27.4163	1.50694	0.753468	−	0.657485i	$-0.228380\pi$
$331$	27.4163	1.50694	0.753468	+	0.657485i	$0.228380\pi$
$332$	4.80179	0.263532
$333$	5.40802	0.296358
$334$	−23.4395	−1.28255
$335$	10.8501	0.592802
$336$	9.74612	0.531694
$337$	−10.0815	−0.549176	−0.274588	−	0.961562i	$-0.588541\pi$
$337$	−10.0815	−0.549176	−0.274588	+	0.961562i	$0.588541\pi$
$338$	9.05344	0.492442
$339$	27.7399	1.50662
$340$	−26.3115	−1.42694
$341$	−1.72829	−0.0935921
$342$	17.7409	0.959317
$343$	14.2754	0.770800
$344$	−4.44213	−0.239504
$345$	−28.2599	−1.52146
$346$	2.83392	0.152352
$347$	−3.06331	−0.164447	−0.0822235	−	0.996614i	$-0.526202\pi$
$347$	−3.06331	−0.164447	−0.0822235	+	0.996614i	$0.526202\pi$
$348$	8.98595	0.481697
$349$	27.5940	1.47707	0.738536	−	0.674214i	$-0.235517\pi$
$349$	27.5940	1.47707	0.738536	+	0.674214i	$0.235517\pi$
$350$	−37.7322	−2.01687
$351$	−2.53904	−0.135524
$352$	−2.63847	−0.140631
$353$	17.2582	0.918563	0.459281	−	0.888291i	$-0.348107\pi$
$353$	17.2582	0.918563	0.459281	+	0.888291i	$0.348107\pi$
$354$	15.7216	0.835595
$355$	−52.8090	−2.80281
$356$	−3.69511	−0.195840
$357$	68.4365	3.62205
$358$	14.2346	0.752321
$359$	−8.98790	−0.474363	−0.237182	−	0.971465i	$-0.576224\pi$
$359$	−8.98790	−0.474363	−0.237182	+	0.971465i	$0.576224\pi$
$360$	9.19023	0.484368
$361$	33.3209	1.75373
$362$	−19.5881	−1.02953
$363$	−9.43023	−0.494959
$364$	8.29158	0.434597
$365$	−15.2386	−0.797623
$366$	27.5520	1.44016
$367$	−3.69103	−0.192670	−0.0963350	−	0.995349i	$-0.530712\pi$
$367$	−3.69103	−0.192670	−0.0963350	+	0.995349i	$0.530712\pi$
$368$	3.22981	0.168365
$369$	15.9156	0.828532
$370$	8.26208	0.429525
$371$	−23.7282	−1.23191
$372$	−1.52957	−0.0793044
$373$	−15.1096	−0.782345	−0.391173	−	0.920317i	$-0.627930\pi$
$373$	−15.1096	−0.782345	−0.391173	+	0.920317i	$0.627930\pi$
$374$	−18.5271	−0.958015
$375$	−35.3518	−1.82556
$376$	−5.02776	−0.259287
$377$	7.64485	0.393730
$378$	5.33443	0.274374
$379$	22.4116	1.15121	0.575603	−	0.817730i	$-0.304768\pi$
$379$	22.4116	1.15121	0.575603	+	0.817730i	$0.304768\pi$
$380$	27.1036	1.39038
$381$	20.6639	1.05864
$382$	1.53068	0.0783163
$383$	−13.2629	−0.677704	−0.338852	−	0.940840i	$-0.610039\pi$
$383$	−13.2629	−0.677704	−0.338852	+	0.940840i	$0.610039\pi$
$384$	−2.33509	−0.119162
$385$	−41.2637	−2.10299
$386$	15.1760	0.772438
$387$	10.8950	0.553826
$388$	5.90364	0.299712
$389$	34.8106	1.76497	0.882485	−	0.470341i	$-0.155869\pi$
$389$	34.8106	1.76497	0.882485	+	0.470341i	$0.155869\pi$
$390$	17.3821	0.880178
$391$	22.6795	1.14695
$392$	−10.4203	−0.526304
$393$	39.2908	1.98196
$394$	−18.2132	−0.917566
$395$	18.5073	0.931202
$396$	6.47127	0.325194
$397$	29.9236	1.50182	0.750911	−	0.660403i	$-0.229615\pi$
$397$	29.9236	1.50182	0.750911	+	0.660403i	$0.229615\pi$
$398$	−21.6939	−1.08742
$399$	−70.4968	−3.52925
$400$	9.04034	0.452017
$401$	24.8293	1.23992	0.619958	−	0.784635i	$-0.287150\pi$
$401$	24.8293	1.23992	0.619958	+	0.784635i	$0.287150\pi$
$402$	6.76156	0.337236
$403$	−1.30129	−0.0648218
$404$	4.22713	0.210308
$405$	38.7536	1.92568
$406$	−16.0615	−0.797121
$407$	5.81772	0.288374
$408$	−16.3969	−0.811765
$409$	18.8833	0.933720	0.466860	−	0.884331i	$-0.345385\pi$
$409$	18.8833	0.933720	0.466860	+	0.884331i	$0.345385\pi$
$410$	24.3150	1.20083
$411$	19.7166	0.972549
$412$	−20.1520	−0.992819
$413$	−28.1009	−1.38276
$414$	−7.92163	−0.389327
$415$	−17.9925	−0.883218
$416$	−1.98660	−0.0974009
$417$	−21.9561	−1.07519
$418$	19.0849	0.933472
$419$	−4.84730	−0.236806	−0.118403	−	0.992966i	$-0.537777\pi$
$419$	−4.84730	−0.236806	−0.118403	+	0.992966i	$0.537777\pi$
$420$	−36.5192	−1.78195
$421$	−29.4721	−1.43638	−0.718192	−	0.695845i	$-0.755030\pi$
$421$	−29.4721	−1.43638	−0.718192	+	0.695845i	$0.755030\pi$
$422$	−8.53358	−0.415408
$423$	12.3314	0.599573
$424$	5.68509	0.276092
$425$	63.4806	3.07926
$426$	−32.9096	−1.59448
$427$	−49.2466	−2.38321
$428$	−7.77941	−0.376032
$429$	12.2396	0.590932
$430$	16.6449	0.802687
$431$	33.1558	1.59706	0.798529	−	0.601956i	$-0.205612\pi$
$431$	33.1558	1.59706	0.798529	+	0.601956i	$0.205612\pi$
$432$	−1.27809	−0.0614920
$433$	2.69224	0.129381	0.0646903	−	0.997905i	$-0.479394\pi$
$433$	2.69224	0.129381	0.0646903	+	0.997905i	$0.479394\pi$
$434$	2.73396	0.131234
$435$	−33.6707	−1.61439
$436$	0.523156	0.0250546
$437$	−23.3622	−1.11757
$438$	−9.49641	−0.453756
$439$	−1.28491	−0.0613254	−0.0306627	−	0.999530i	$-0.509762\pi$
$439$	−1.28491	−0.0613254	−0.0306627	+	0.999530i	$0.509762\pi$
$440$	9.88646	0.471319
$441$	25.5574	1.21702
$442$	−13.9497	−0.663521
$443$	−21.7011	−1.03105	−0.515525	−	0.856874i	$-0.672403\pi$
$443$	−21.7011	−1.03105	−0.515525	+	0.856874i	$0.672403\pi$
$444$	5.14879	0.244351
$445$	13.8457	0.656351
$446$	−4.00144	−0.189474
$447$	−3.05510	−0.144501
$448$	4.17376	0.197192
$449$	5.93981	0.280317	0.140158	−	0.990129i	$-0.455239\pi$
$449$	5.93981	0.280317	0.140158	+	0.990129i	$0.455239\pi$
$450$	−22.1729	−1.04524
$451$	17.1213	0.806211
$452$	11.8796	0.558768
$453$	4.70640	0.221126
$454$	10.2355	0.480376
$455$	−31.0689	−1.45653
$456$	16.8905	0.790969
$457$	−24.8344	−1.16171	−0.580853	−	0.814009i	$-0.697281\pi$
$457$	−24.8344	−1.16171	−0.580853	+	0.814009i	$0.697281\pi$
$458$	20.6882	0.966697
$459$	−8.97464	−0.418900
$460$	−12.1022	−0.564270
$461$	−18.4340	−0.858559	−0.429279	−	0.903172i	$-0.641232\pi$
$461$	−18.4340	−0.858559	−0.429279	+	0.903172i	$0.641232\pi$
$462$	−25.7148	−1.19636
$463$	5.38909	0.250452	0.125226	−	0.992128i	$-0.460034\pi$
$463$	5.38909	0.250452	0.125226	+	0.992128i	$0.460034\pi$
$464$	3.84822	0.178649
$465$	5.73136	0.265785
$466$	21.2478	0.984285
$467$	18.4482	0.853680	0.426840	−	0.904327i	$-0.359627\pi$
$467$	18.4482	0.853680	0.426840	+	0.904327i	$0.359627\pi$
$468$	4.87245	0.225229
$469$	−12.0857	−0.558064
$470$	18.8393	0.868990
$471$	−15.0078	−0.691521
$472$	6.73276	0.309900
$473$	11.7204	0.538906
$474$	11.5334	0.529747
$475$	−65.3917	−3.00038
$476$	29.3078	1.34332
$477$	−13.9436	−0.638434
$478$	11.8590	0.542418
$479$	−14.0671	−0.642744	−0.321372	−	0.946953i	$-0.604144\pi$
$479$	−14.0671	−0.642744	−0.321372	+	0.946953i	$0.604144\pi$
$480$	8.74970	0.399367
$481$	4.38036	0.199727
$482$	−1.93646	−0.0882032
$483$	31.4781	1.43230
$484$	−4.03848	−0.183567
$485$	−22.1212	−1.00447
$486$	20.3163	0.921566
$487$	32.2434	1.46109	0.730543	−	0.682867i	$-0.239267\pi$
$487$	32.2434	1.46109	0.730543	+	0.682867i	$0.239267\pi$
$488$	11.7991	0.534120
$489$	−3.51351	−0.158887
$490$	39.0452	1.76388
$491$	9.30216	0.419801	0.209900	−	0.977723i	$-0.432686\pi$
$491$	9.30216	0.419801	0.209900	+	0.977723i	$0.432686\pi$
$492$	15.1527	0.683135
$493$	27.0219	1.21701
$494$	14.3697	0.646522
$495$	−24.2481	−1.08987
$496$	−0.655035	−0.0294119
$497$	58.8229	2.63857
$498$	−11.2126	−0.502450
$499$	14.5769	0.652550	0.326275	−	0.945275i	$-0.394206\pi$
$499$	14.5769	0.652550	0.326275	+	0.945275i	$0.394206\pi$
$500$	−15.1393	−0.677052
$501$	54.7335	2.44531
$502$	23.7929	1.06193
$503$	23.5043	1.04800	0.524001	−	0.851717i	$-0.324439\pi$
$503$	23.5043	1.04800	0.524001	+	0.851717i	$0.324439\pi$
$504$	−10.2368	−0.455984
$505$	−15.8393	−0.704837
$506$	−8.52175	−0.378838
$507$	−21.1406	−0.938888
$508$	8.84928	0.392623
$509$	38.9554	1.72667	0.863334	−	0.504633i	$-0.168372\pi$
$509$	38.9554	1.72667	0.863334	+	0.504633i	$0.168372\pi$
$510$	61.4397	2.72060
$511$	16.9739	0.750883
$512$	−1.00000	−0.0441942
$513$	9.24481	0.408169
$514$	−16.3636	−0.721768
$515$	75.5105	3.32739
$516$	10.3728	0.456637
$517$	13.2656	0.583420
$518$	−9.20297	−0.404355
$519$	−6.61746	−0.290474
$520$	7.44386	0.326435
$521$	36.4846	1.59842	0.799210	−	0.601052i	$-0.205251\pi$
$521$	36.4846	1.59842	0.799210	+	0.601052i	$0.205251\pi$
$522$	−9.43837	−0.413106
$523$	−8.53150	−0.373056	−0.186528	−	0.982450i	$-0.559724\pi$
$523$	−8.53150	−0.373056	−0.186528	+	0.982450i	$0.559724\pi$
$524$	16.8262	0.735058
$525$	88.1083	3.84536
$526$	−17.0622	−0.743947
$527$	−4.59960	−0.200362
$528$	6.16107	0.268126
$529$	−12.5683	−0.546449
$530$	−21.3023	−0.925312
$531$	−16.5132	−0.716611
$532$	−30.1901	−1.30891
$533$	12.8912	0.558381
$534$	8.62843	0.373389
$535$	29.1498	1.26025
$536$	2.89563	0.125072
$537$	−33.2391	−1.43437
$538$	3.00093	0.129379
$539$	27.4936	1.18423
$540$	4.78905	0.206088
$541$	15.6004	0.670715	0.335358	−	0.942091i	$-0.391143\pi$
$541$	15.6004	0.670715	0.335358	+	0.942091i	$0.391143\pi$
$542$	−12.4434	−0.534488
$543$	45.7401	1.96290
$544$	−7.02193	−0.301063
$545$	−1.96029	−0.0839695
$546$	−19.3616	−0.828600
$547$	−19.8035	−0.846737	−0.423368	−	0.905958i	$-0.639152\pi$
$547$	−19.8035	−0.846737	−0.423368	+	0.905958i	$0.639152\pi$
$548$	8.44361	0.360693
$549$	−28.9392	−1.23509
$550$	−23.8527	−1.01708
$551$	−27.8354	−1.18583
$552$	−7.54191	−0.321005
$553$	−20.6149	−0.876635
$554$	6.53501	0.277646
$555$	−19.2927	−0.818931
$556$	−9.40265	−0.398761
$557$	13.8628	0.587387	0.293693	−	0.955900i	$-0.405116\pi$
$557$	13.8628	0.587387	0.293693	+	0.955900i	$0.405116\pi$
$558$	1.60658	0.0680119
$559$	8.82472	0.373246
$560$	−15.6393	−0.660880
$561$	43.2626	1.82655
$562$	23.9419	1.00993
$563$	−10.3452	−0.436000	−0.218000	−	0.975949i	$-0.569953\pi$
$563$	−10.3452	−0.436000	−0.218000	+	0.975949i	$0.569953\pi$
$564$	11.7403	0.494356
$565$	−44.5133	−1.87269
$566$	8.07052	0.339229
$567$	−43.1669	−1.81284
$568$	−14.0935	−0.591350
$569$	5.82441	0.244172	0.122086	−	0.992520i	$-0.461042\pi$
$569$	5.82441	0.244172	0.122086	+	0.992520i	$0.461042\pi$
$570$	−63.2894	−2.65090
$571$	12.0860	0.505783	0.252891	−	0.967495i	$-0.418618\pi$
$571$	12.0860	0.505783	0.252891	+	0.967495i	$0.418618\pi$
$572$	5.24157	0.219161
$573$	−3.57428	−0.149318
$574$	−27.0840	−1.13046
$575$	29.1986	1.21767
$576$	2.45266	0.102194
$577$	36.1251	1.50391	0.751954	−	0.659216i	$-0.229112\pi$
$577$	36.1251	1.50391	0.751954	+	0.659216i	$0.229112\pi$
$578$	−32.3074	−1.34381
$579$	−35.4374	−1.47273
$580$	−14.4194	−0.598735
$581$	20.0415	0.831462
$582$	−13.7855	−0.571429
$583$	−14.9999	−0.621234
$584$	−4.06682	−0.168286
$585$	−18.2573	−0.754845
$586$	−21.8472	−0.902500
$587$	−41.5250	−1.71392	−0.856960	−	0.515383i	$-0.827650\pi$
$587$	−41.5250	−1.71392	−0.856960	+	0.515383i	$0.827650\pi$
$588$	24.3323	1.00345
$589$	4.73807	0.195229
$590$	−25.2280	−1.03862
$591$	42.5294	1.74943
$592$	2.20496	0.0906233
$593$	26.6012	1.09238	0.546190	−	0.837661i	$-0.316078\pi$
$593$	26.6012	1.09238	0.546190	+	0.837661i	$0.316078\pi$
$594$	3.37220	0.138363
$595$	−109.818	−4.50209
$596$	−1.30834	−0.0535917
$597$	50.6572	2.07326
$598$	−6.41633	−0.262383
$599$	−8.26651	−0.337760	−0.168880	−	0.985637i	$-0.554015\pi$
$599$	−8.26651	−0.337760	−0.168880	+	0.985637i	$0.554015\pi$
$600$	−21.1100	−0.861814
$601$	16.0801	0.655920	0.327960	−	0.944692i	$-0.393639\pi$
$601$	16.0801	0.655920	0.327960	+	0.944692i	$0.393639\pi$
$602$	−18.5404	−0.755650
$603$	−7.10200	−0.289216
$604$	2.01551	0.0820100
$605$	15.1324	0.615218
$606$	−9.87075	−0.400972
$607$	−35.4201	−1.43766	−0.718828	−	0.695188i	$-0.755321\pi$
$607$	−35.4201	−1.43766	−0.718828	+	0.695188i	$0.755321\pi$
$608$	7.23332	0.293350
$609$	37.5052	1.51979
$610$	−44.2117	−1.79008
$611$	9.98814	0.404077
$612$	17.2224	0.696174
$613$	−19.8420	−0.801411	−0.400705	−	0.916207i	$-0.631235\pi$
$613$	−19.8420	−0.801411	−0.400705	+	0.916207i	$0.631235\pi$
$614$	−32.0926	−1.29515
$615$	−56.7777	−2.28950
$616$	−11.0123	−0.443700
$617$	−19.8118	−0.797593	−0.398797	−	0.917039i	$-0.630572\pi$
$617$	−19.8118	−0.797593	−0.398797	+	0.917039i	$0.630572\pi$
$618$	47.0568	1.89290
$619$	−24.9869	−1.00431	−0.502155	−	0.864778i	$-0.667459\pi$
$619$	−24.9869	−1.00431	−0.502155	+	0.864778i	$0.667459\pi$
$620$	2.45444	0.0985729
$621$	−4.12798	−0.165650
$622$	−14.4612	−0.579841
$623$	−15.4225	−0.617890
$624$	4.63889	0.185704
$625$	11.5261	0.461044
$626$	30.3264	1.21209
$627$	−44.5650	−1.77975
$628$	−6.42705	−0.256467
$629$	15.4831	0.617350
$630$	38.3578	1.52821
$631$	3.05120	0.121466	0.0607331	−	0.998154i	$-0.480656\pi$
$631$	3.05120	0.121466	0.0607331	+	0.998154i	$0.480656\pi$
$632$	4.93917	0.196470
$633$	19.9267	0.792015
$634$	17.2415	0.684748
$635$	−33.1587	−1.31586
$636$	−13.2752	−0.526397
$637$	20.7009	0.820199
$638$	−10.1534	−0.401977
$639$	34.5666	1.36743
$640$	3.74704	0.148115
$641$	−21.8474	−0.862921	−0.431461	−	0.902132i	$-0.642002\pi$
$641$	−21.8474	−0.862921	−0.431461	+	0.902132i	$0.642002\pi$
$642$	18.1656	0.716941
$643$	3.18954	0.125783	0.0628916	−	0.998020i	$-0.479968\pi$
$643$	3.18954	0.125783	0.0628916	+	0.998020i	$0.479968\pi$
$644$	13.4805	0.531204
$645$	−38.8673	−1.53040
$646$	50.7918	1.99838
$647$	−22.1060	−0.869077	−0.434538	−	0.900653i	$-0.643088\pi$
$647$	−22.1060	−0.869077	−0.434538	+	0.900653i	$0.643088\pi$
$648$	10.3424	0.406289
$649$	−17.7642	−0.697305
$650$	−17.9595	−0.704430
$651$	−6.38405	−0.250211
$652$	−1.50466	−0.0589269
$653$	24.2123	0.947499	0.473750	−	0.880660i	$-0.342900\pi$
$653$	24.2123	0.947499	0.473750	+	0.880660i	$0.342900\pi$
$654$	−1.22162	−0.0477690
$655$	−63.0487	−2.46352
$656$	6.48911	0.253357
$657$	9.97454	0.389144
$658$	−20.9847	−0.818068
$659$	−22.5261	−0.877494	−0.438747	−	0.898611i	$-0.644578\pi$
$659$	−22.5261	−0.877494	−0.438747	+	0.898611i	$0.644578\pi$
$660$	−23.0858	−0.898614
$661$	−42.8411	−1.66633	−0.833164	−	0.553026i	$-0.813473\pi$
$661$	−42.8411	−1.66633	−0.833164	+	0.553026i	$0.813473\pi$
$662$	−27.4163	−1.06556
$663$	32.5739	1.26507
$664$	−4.80179	−0.186346
$665$	113.124	4.38675
$666$	−5.40802	−0.209556
$667$	12.4290	0.481253
$668$	23.4395	0.906902
$669$	9.34374	0.361250
$670$	−10.8501	−0.419174
$671$	−31.1315	−1.20182
$672$	−9.74612	−0.375965
$673$	−31.8900	−1.22927	−0.614635	−	0.788812i	$-0.710697\pi$
$673$	−31.8900	−1.22927	−0.614635	+	0.788812i	$0.710697\pi$
$674$	10.0815	0.388326
$675$	−11.5544	−0.444727
$676$	−9.05344	−0.348209
$677$	−33.1458	−1.27390	−0.636948	−	0.770907i	$-0.719804\pi$
$677$	−33.1458	−1.27390	−0.636948	+	0.770907i	$0.719804\pi$
$678$	−27.7399	−1.06534
$679$	24.6404	0.945611
$680$	26.3115	1.00900
$681$	−23.9009	−0.915883
$682$	1.72829	0.0661796
$683$	−16.6176	−0.635857	−0.317928	−	0.948115i	$-0.602987\pi$
$683$	−16.6176	−0.635857	−0.317928	+	0.948115i	$0.602987\pi$
$684$	−17.7409	−0.678339
$685$	−31.6386	−1.20885
$686$	−14.2754	−0.545038
$687$	−48.3089	−1.84310
$688$	4.44213	0.169355
$689$	−11.2940	−0.430266
$690$	28.2599	1.07583
$691$	9.38311	0.356950	0.178475	−	0.983944i	$-0.442884\pi$
$691$	9.38311	0.356950	0.178475	+	0.983944i	$0.442884\pi$
$692$	−2.83392	−0.107729
$693$	27.0095	1.02601
$694$	3.06331	0.116282
$695$	35.2322	1.33643
$696$	−8.98595	−0.340611
$697$	45.5660	1.72594
$698$	−27.5940	−1.04445
$699$	−49.6156	−1.87663
$700$	37.7322	1.42614
$701$	−25.1682	−0.950590	−0.475295	−	0.879827i	$-0.657659\pi$
$701$	−25.1682	−0.950590	−0.475295	+	0.879827i	$0.657659\pi$
$702$	2.53904	0.0958300
$703$	−15.9492	−0.601534
$704$	2.63847	0.0994411
$705$	−43.9914	−1.65681
$706$	−17.2582	−0.649522
$707$	17.6430	0.663535
$708$	−15.7216	−0.590855
$709$	15.4608	0.580642	0.290321	−	0.956929i	$-0.406238\pi$
$709$	15.4608	0.580642	0.290321	+	0.956929i	$0.406238\pi$
$710$	52.8090	1.98189
$711$	−12.1141	−0.454314
$712$	3.69511	0.138480
$713$	−2.11564	−0.0792312
$714$	−68.4365	−2.56117
$715$	−19.6404	−0.734510
$716$	−14.2346	−0.531971
$717$	−27.6919	−1.03417
$718$	8.98790	0.335425
$719$	5.52202	0.205936	0.102968	−	0.994685i	$-0.467166\pi$
$719$	5.52202	0.205936	0.102968	+	0.994685i	$0.467166\pi$
$720$	−9.19023	−0.342500
$721$	−84.1097	−3.13241
$722$	−33.3209	−1.24007
$723$	4.52181	0.168168
$724$	19.5881	0.727988
$725$	34.7892	1.29204
$726$	9.43023	0.349989
$727$	6.43167	0.238537	0.119269	−	0.992862i	$-0.461945\pi$
$727$	6.43167	0.238537	0.119269	+	0.992862i	$0.461945\pi$
$728$	−8.29158	−0.307306
$729$	−16.4131	−0.607894
$730$	15.2386	0.564005
$731$	31.1923	1.15369
$732$	−27.5520	−1.01835
$733$	17.4034	0.642809	0.321405	−	0.946942i	$-0.395845\pi$
$733$	17.4034	0.642809	0.321405	+	0.946942i	$0.395845\pi$
$734$	3.69103	0.136238
$735$	−91.1743	−3.36301
$736$	−3.22981	−0.119052
$737$	−7.64003	−0.281424
$738$	−15.9156	−0.585860
$739$	−1.57835	−0.0580606	−0.0290303	−	0.999579i	$-0.509242\pi$
$739$	−1.57835	−0.0580606	−0.0290303	+	0.999579i	$0.509242\pi$
$740$	−8.26208	−0.303720
$741$	−33.5545	−1.23266
$742$	23.7282	0.871090
$743$	−20.3234	−0.745595	−0.372797	−	0.927913i	$-0.621601\pi$
$743$	−20.3234	−0.745595	−0.372797	+	0.927913i	$0.621601\pi$
$744$	1.52957	0.0560767
$745$	4.90241	0.179610
$746$	15.1096	0.553202
$747$	11.7772	0.430904
$748$	18.5271	0.677419
$749$	−32.4694	−1.18641
$750$	35.3518	1.29087
$751$	−10.3571	−0.377935	−0.188967	−	0.981983i	$-0.560514\pi$
$751$	−10.3571	−0.377935	−0.188967	+	0.981983i	$0.560514\pi$
$752$	5.02776	0.183344
$753$	−55.5586	−2.02467
$754$	−7.64485	−0.278409
$755$	−7.55221	−0.274853
$756$	−5.33443	−0.194011
$757$	−45.9327	−1.66945	−0.834726	−	0.550666i	$-0.814374\pi$
$757$	−45.9327	−1.66945	−0.834726	+	0.550666i	$0.814374\pi$
$758$	−22.4116	−0.814025
$759$	19.8991	0.722291
$760$	−27.1036	−0.983150
$761$	5.64833	0.204752	0.102376	−	0.994746i	$-0.467356\pi$
$761$	5.64833	0.204752	0.102376	+	0.994746i	$0.467356\pi$
$762$	−20.6639	−0.748574
$763$	2.18353	0.0790490
$764$	−1.53068	−0.0553780
$765$	−64.5331	−2.33320
$766$	13.2629	0.479209
$767$	−13.3753	−0.482953
$768$	2.33509	0.0842604
$769$	31.7687	1.14561	0.572805	−	0.819692i	$-0.305855\pi$
$769$	31.7687	1.14561	0.572805	+	0.819692i	$0.305855\pi$
$770$	41.2637	1.48704
$771$	38.2105	1.37612
$772$	−15.1760	−0.546196
$773$	31.4854	1.13245	0.566225	−	0.824251i	$-0.308403\pi$
$773$	31.4854	1.13245	0.566225	+	0.824251i	$0.308403\pi$
$774$	−10.8950	−0.391614
$775$	−5.92174	−0.212715
$776$	−5.90364	−0.211928
$777$	21.4898	0.770942
$778$	−34.8106	−1.24802
$779$	−46.9378	−1.68172
$780$	−17.3821	−0.622380
$781$	37.1853	1.33059
$782$	−22.6795	−0.811017
$783$	−4.91836	−0.175768
$784$	10.4203	0.372153
$785$	24.0825	0.859540
$786$	−39.2908	−1.40146
$787$	−38.7438	−1.38107	−0.690533	−	0.723301i	$-0.742624\pi$
$787$	−38.7438	−1.38107	−0.690533	+	0.723301i	$0.742624\pi$
$788$	18.2132	0.648817
$789$	39.8418	1.41841
$790$	−18.5073	−0.658459
$791$	49.5825	1.76295
$792$	−6.47127	−0.229947
$793$	−23.4400	−0.832379
$794$	−29.9236	−1.06195
$795$	49.7428	1.76420
$796$	21.6939	0.768919
$797$	−37.0260	−1.31153	−0.655765	−	0.754965i	$-0.727654\pi$
$797$	−37.0260	−1.31153	−0.655765	+	0.754965i	$0.727654\pi$
$798$	70.4968	2.49556
$799$	35.3046	1.24899
$800$	−9.04034	−0.319624
$801$	−9.06285	−0.320220
$802$	−24.8293	−0.876753
$803$	10.7302	0.378660
$804$	−6.76156	−0.238462
$805$	−50.5118	−1.78031
$806$	1.30129	0.0458360
$807$	−7.00745	−0.246674
$808$	−4.22713	−0.148710
$809$	−13.8054	−0.485373	−0.242686	−	0.970105i	$-0.578029\pi$
$809$	−13.8054	−0.485373	−0.242686	+	0.970105i	$0.578029\pi$
$810$	−38.7536	−1.36166
$811$	21.8007	0.765526	0.382763	−	0.923847i	$-0.374973\pi$
$811$	21.8007	0.765526	0.382763	+	0.923847i	$0.374973\pi$
$812$	16.0615	0.563650
$813$	29.0564	1.01905
$814$	−5.81772	−0.203911
$815$	5.63802	0.197491
$816$	16.3969	0.574005
$817$	−32.1314	−1.12413
$818$	−18.8833	−0.660240
$819$	20.3364	0.710612
$820$	−24.3150	−0.849116
$821$	−47.4678	−1.65664	−0.828319	−	0.560256i	$-0.810703\pi$
$821$	−47.4678	−1.65664	−0.828319	+	0.560256i	$0.810703\pi$
$822$	−19.7166	−0.687696
$823$	3.45699	0.120503	0.0602515	−	0.998183i	$-0.480810\pi$
$823$	3.45699	0.120503	0.0602515	+	0.998183i	$0.480810\pi$
$824$	20.1520	0.702029
$825$	55.6982	1.93916
$826$	28.1009	0.977757
$827$	18.3180	0.636981	0.318490	−	0.947926i	$-0.396824\pi$
$827$	18.3180	0.636981	0.318490	+	0.947926i	$0.396824\pi$
$828$	7.92163	0.275296
$829$	44.4739	1.54464	0.772321	−	0.635233i	$-0.219096\pi$
$829$	44.4739	1.54464	0.772321	+	0.635233i	$0.219096\pi$
$830$	17.9925	0.624529
$831$	−15.2599	−0.529359
$832$	1.98660	0.0688728
$833$	73.1704	2.53520
$834$	21.9561	0.760277
$835$	−87.8289	−3.03944
$836$	−19.0849	−0.660065
$837$	0.837192	0.0289376
$838$	4.84730	0.167447
$839$	40.5086	1.39851	0.699257	−	0.714871i	$-0.253514\pi$
$839$	40.5086	1.39851	0.699257	+	0.714871i	$0.253514\pi$
$840$	36.5192	1.26003
$841$	−14.1912	−0.489352
$842$	29.4721	1.01568
$843$	−55.9065	−1.92552
$844$	8.53358	0.293738
$845$	33.9236	1.16701
$846$	−12.3314	−0.423962
$847$	−16.8556	−0.579167
$848$	−5.68509	−0.195227
$849$	−18.8454	−0.646773
$850$	−63.4806	−2.17737
$851$	7.12160	0.244125
$852$	32.9096	1.12747
$853$	40.0042	1.36972	0.684859	−	0.728675i	$-0.259864\pi$
$853$	40.0042	1.36972	0.684859	+	0.728675i	$0.259864\pi$
$854$	49.2466	1.68518
$855$	66.4759	2.27343
$856$	7.77941	0.265895
$857$	−21.3463	−0.729176	−0.364588	−	0.931169i	$-0.618790\pi$
$857$	−21.3463	−0.729176	−0.364588	+	0.931169i	$0.618790\pi$
$858$	−12.2396	−0.417852
$859$	−20.1126	−0.686233	−0.343117	−	0.939293i	$-0.611483\pi$
$859$	−20.1126	−0.686233	−0.343117	+	0.939293i	$0.611483\pi$
$860$	−16.6449	−0.567585
$861$	63.2436	2.15534
$862$	−33.1558	−1.12929
$863$	−2.34436	−0.0798029	−0.0399015	−	0.999204i	$-0.512704\pi$
$863$	−2.34436	−0.0798029	−0.0399015	+	0.999204i	$0.512704\pi$
$864$	1.27809	0.0434814
$865$	10.6188	0.361050
$866$	−2.69224	−0.0914859
$867$	75.4409	2.56211
$868$	−2.73396	−0.0927966
$869$	−13.0318	−0.442075
$870$	33.6707	1.14155
$871$	−5.75245	−0.194914
$872$	−0.523156	−0.0177163
$873$	14.4796	0.490061
$874$	23.3622	0.790239
$875$	−63.1880	−2.13615
$876$	9.49641	0.320854
$877$	−42.2742	−1.42750	−0.713748	−	0.700402i	$-0.753004\pi$
$877$	−42.2742	−1.42750	−0.713748	+	0.700402i	$0.753004\pi$
$878$	1.28491	0.0433636
$879$	51.0153	1.72070
$880$	−9.88646	−0.333273
$881$	−24.9430	−0.840352	−0.420176	−	0.907443i	$-0.638032\pi$
$881$	−24.9430	−0.840352	−0.420176	+	0.907443i	$0.638032\pi$
$882$	−25.5574	−0.860563
$883$	4.68476	0.157655	0.0788274	−	0.996888i	$-0.474882\pi$
$883$	4.68476	0.157655	0.0788274	+	0.996888i	$0.474882\pi$
$884$	13.9497	0.469180
$885$	58.9096	1.98023
$886$	21.7011	0.729063
$887$	10.2156	0.343005	0.171503	−	0.985184i	$-0.445138\pi$
$887$	10.2156	0.343005	0.171503	+	0.985184i	$0.445138\pi$
$888$	−5.14879	−0.172782
$889$	36.9348	1.23875
$890$	−13.8457	−0.464110
$891$	−27.2882	−0.914189
$892$	4.00144	0.133978
$893$	−36.3674	−1.21699
$894$	3.05510	0.102178
$895$	53.3376	1.78288
$896$	−4.17376	−0.139436
$897$	14.9827	0.500258
$898$	−5.93981	−0.198214
$899$	−2.52072	−0.0840706
$900$	22.1729	0.739097
$901$	−39.9203	−1.32994
$902$	−17.1213	−0.570077
$903$	43.2936	1.44072
$904$	−11.8796	−0.395108
$905$	−73.3976	−2.43982
$906$	−4.70640	−0.156360
$907$	43.0407	1.42914	0.714571	−	0.699563i	$-0.246622\pi$
$907$	43.0407	1.42914	0.714571	+	0.699563i	$0.246622\pi$
$908$	−10.2355	−0.339677
$909$	10.3677	0.343876
$910$	31.0689	1.02992
$911$	−52.2269	−1.73036	−0.865178	−	0.501465i	$-0.832795\pi$
$911$	−52.2269	−1.73036	−0.865178	+	0.501465i	$0.832795\pi$
$912$	−16.8905	−0.559299
$913$	12.6694	0.419295
$914$	24.8344	0.821450
$915$	103.238	3.41296
$916$	−20.6882	−0.683558
$917$	70.2287	2.31916
$918$	8.97464	0.296207
$919$	−12.5244	−0.413142	−0.206571	−	0.978432i	$-0.566231\pi$
$919$	−12.5244	−0.413142	−0.206571	+	0.978432i	$0.566231\pi$
$920$	12.1022	0.398999
$921$	74.9392	2.46933
$922$	18.4340	0.607093
$923$	27.9981	0.921568
$924$	25.7148	0.845956
$925$	19.9336	0.655412
$926$	−5.38909	−0.177096
$927$	−49.4261	−1.62337
$928$	−3.84822	−0.126324
$929$	31.1454	1.02185	0.510924	−	0.859626i	$-0.329303\pi$
$929$	31.1454	1.02185	0.510924	+	0.859626i	$0.329303\pi$
$930$	−5.73136	−0.187939
$931$	−75.3732	−2.47026
$932$	−21.2478	−0.695995
$933$	33.7682	1.10552
$934$	−18.4482	−0.603643
$935$	−69.4220	−2.27034
$936$	−4.87245	−0.159261
$937$	37.2585	1.21718	0.608591	−	0.793484i	$-0.291735\pi$
$937$	37.2585	1.21718	0.608591	+	0.793484i	$0.291735\pi$
$938$	12.0857	0.394611
$939$	−70.8150	−2.31096
$940$	−18.8393	−0.614469
$941$	4.19746	0.136833	0.0684167	−	0.997657i	$-0.478205\pi$
$941$	4.19746	0.136833	0.0684167	+	0.997657i	$0.478205\pi$
$942$	15.0078	0.488979
$943$	20.9586	0.682505
$944$	−6.73276	−0.219133
$945$	19.9884	0.650221
$946$	−11.7204	−0.381064
$947$	13.6929	0.444959	0.222479	−	0.974937i	$-0.428585\pi$
$947$	13.6929	0.444959	0.222479	+	0.974937i	$0.428585\pi$
$948$	−11.5334	−0.374588
$949$	8.07913	0.262260
$950$	65.3917	2.12159
$951$	−40.2606	−1.30554
$952$	−29.3078	−0.949872
$953$	4.49283	0.145537	0.0727685	−	0.997349i	$-0.476817\pi$
$953$	4.49283	0.145537	0.0727685	+	0.997349i	$0.476817\pi$
$954$	13.9436	0.451441
$955$	5.73552	0.185597
$956$	−11.8590	−0.383547
$957$	23.7091	0.766408
$958$	14.0671	0.454488
$959$	35.2416	1.13801
$960$	−8.74970	−0.282395
$961$	−30.5709	−0.986159
$962$	−4.38036	−0.141229
$963$	−19.0802	−0.614852
$964$	1.93646	0.0623691
$965$	56.8652	1.83055
$966$	−31.4781	−1.01279
$967$	−61.7610	−1.98610	−0.993050	−	0.117691i	$-0.962451\pi$
$967$	−61.7610	−1.98610	−0.993050	+	0.117691i	$0.962451\pi$
$968$	4.03848	0.129802
$969$	−118.604	−3.81010
$970$	22.1212	0.710269
$971$	54.9072	1.76206	0.881028	−	0.473065i	$-0.156852\pi$
$971$	54.9072	1.76206	0.881028	+	0.473065i	$0.156852\pi$
$972$	−20.3163	−0.651645
$973$	−39.2444	−1.25812
$974$	−32.2434	−1.03314
$975$	41.9371	1.34306
$976$	−11.7991	−0.377680
$977$	−41.1839	−1.31759	−0.658795	−	0.752322i	$-0.728934\pi$
$977$	−41.1839	−1.31759	−0.658795	+	0.752322i	$0.728934\pi$
$978$	3.51351	0.112350
$979$	−9.74944	−0.311593
$980$	−39.0452	−1.24725
$981$	1.28312	0.0409670
$982$	−9.30216	−0.296844
$983$	13.7773	0.439428	0.219714	−	0.975564i	$-0.429488\pi$
$983$	13.7773	0.439428	0.219714	+	0.975564i	$0.429488\pi$
$984$	−15.1527	−0.483049
$985$	−68.2455	−2.17448
$986$	−27.0219	−0.860553
$987$	49.0012	1.55973
$988$	−14.3697	−0.457160
$989$	14.3472	0.456216
$990$	24.2481	0.770656
$991$	19.5202	0.620080	0.310040	−	0.950723i	$-0.399658\pi$
$991$	19.5202	0.620080	0.310040	+	0.950723i	$0.399658\pi$
$992$	0.655035	0.0207974
$993$	64.0196	2.03160
$994$	−58.8229	−1.86575
$995$	−81.2880	−2.57700
$996$	11.2126	0.355286
$997$	17.9749	0.569269	0.284635	−	0.958636i	$-0.408128\pi$
$997$	17.9749	0.569269	0.284635	+	0.958636i	$0.408128\pi$
$998$	−14.5769	−0.461423
$999$	−2.81813	−0.0891617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.64	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.64	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.33509 q^{3} +1.00000 q^{4} -3.74704 q^{5} -2.33509 q^{6} +4.17376 q^{7} -1.00000 q^{8} +2.45266 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.33509 q^{3} +1.00000 q^{4} -3.74704 q^{5} -2.33509 q^{6} +4.17376 q^{7} -1.00000 q^{8} +2.45266 q^{9} +3.74704 q^{10} +2.63847 q^{11} +2.33509 q^{12} +1.98660 q^{13} -4.17376 q^{14} -8.74970 q^{15} +1.00000 q^{16} +7.02193 q^{17} -2.45266 q^{18} -7.23332 q^{19} -3.74704 q^{20} +9.74612 q^{21} -2.63847 q^{22} +3.22981 q^{23} -2.33509 q^{24} +9.04034 q^{25} -1.98660 q^{26} -1.27809 q^{27} +4.17376 q^{28} +3.84822 q^{29} +8.74970 q^{30} -0.655035 q^{31} -1.00000 q^{32} +6.16107 q^{33} -7.02193 q^{34} -15.6393 q^{35} +2.45266 q^{36} +2.20496 q^{37} +7.23332 q^{38} +4.63889 q^{39} +3.74704 q^{40} +6.48911 q^{41} -9.74612 q^{42} +4.44213 q^{43} +2.63847 q^{44} -9.19023 q^{45} -3.22981 q^{46} +5.02776 q^{47} +2.33509 q^{48} +10.4203 q^{49} -9.04034 q^{50} +16.3969 q^{51} +1.98660 q^{52} -5.68509 q^{53} +1.27809 q^{54} -9.88646 q^{55} -4.17376 q^{56} -16.8905 q^{57} -3.84822 q^{58} -6.73276 q^{59} -8.74970 q^{60} -11.7991 q^{61} +0.655035 q^{62} +10.2368 q^{63} +1.00000 q^{64} -7.44386 q^{65} -6.16107 q^{66} -2.89563 q^{67} +7.02193 q^{68} +7.54191 q^{69} +15.6393 q^{70} +14.0935 q^{71} -2.45266 q^{72} +4.06682 q^{73} -2.20496 q^{74} +21.1100 q^{75} -7.23332 q^{76} +11.0123 q^{77} -4.63889 q^{78} -4.93917 q^{79} -3.74704 q^{80} -10.3424 q^{81} -6.48911 q^{82} +4.80179 q^{83} +9.74612 q^{84} -26.3115 q^{85} -4.44213 q^{86} +8.98595 q^{87} -2.63847 q^{88} -3.69511 q^{89} +9.19023 q^{90} +8.29158 q^{91} +3.22981 q^{92} -1.52957 q^{93} -5.02776 q^{94} +27.1036 q^{95} -2.33509 q^{96} +5.90364 q^{97} -10.4203 q^{98} +6.47127 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 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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