LMFDB - Embedded newform 8002.2.a.e.1.8

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			1.8
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.61328 q^{3} +1.00000 q^{4} -3.49569 q^{5} +2.61328 q^{6} -0.478818 q^{7} -1.00000 q^{8} +3.82924 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.61328 q^{3} +1.00000 q^{4} -3.49569 q^{5} +2.61328 q^{6} -0.478818 q^{7} -1.00000 q^{8} +3.82924 q^{9} +3.49569 q^{10} -0.518766 q^{11} -2.61328 q^{12} +0.394051 q^{13} +0.478818 q^{14} +9.13523 q^{15} +1.00000 q^{16} -1.63145 q^{17} -3.82924 q^{18} -1.57912 q^{19} -3.49569 q^{20} +1.25129 q^{21} +0.518766 q^{22} -1.44805 q^{23} +2.61328 q^{24} +7.21987 q^{25} -0.394051 q^{26} -2.16703 q^{27} -0.478818 q^{28} +6.68629 q^{29} -9.13523 q^{30} +0.0346656 q^{31} -1.00000 q^{32} +1.35568 q^{33} +1.63145 q^{34} +1.67380 q^{35} +3.82924 q^{36} -0.471003 q^{37} +1.57912 q^{38} -1.02977 q^{39} +3.49569 q^{40} -1.81254 q^{41} -1.25129 q^{42} +0.346409 q^{43} -0.518766 q^{44} -13.3858 q^{45} +1.44805 q^{46} +13.5266 q^{47} -2.61328 q^{48} -6.77073 q^{49} -7.21987 q^{50} +4.26343 q^{51} +0.394051 q^{52} +0.660429 q^{53} +2.16703 q^{54} +1.81344 q^{55} +0.478818 q^{56} +4.12669 q^{57} -6.68629 q^{58} +2.43140 q^{59} +9.13523 q^{60} -6.58531 q^{61} -0.0346656 q^{62} -1.83351 q^{63} +1.00000 q^{64} -1.37748 q^{65} -1.35568 q^{66} -15.0872 q^{67} -1.63145 q^{68} +3.78417 q^{69} -1.67380 q^{70} -3.80058 q^{71} -3.82924 q^{72} -4.71638 q^{73} +0.471003 q^{74} -18.8675 q^{75} -1.57912 q^{76} +0.248394 q^{77} +1.02977 q^{78} -7.31985 q^{79} -3.49569 q^{80} -5.82465 q^{81} +1.81254 q^{82} -1.54698 q^{83} +1.25129 q^{84} +5.70304 q^{85} -0.346409 q^{86} -17.4732 q^{87} +0.518766 q^{88} +15.2625 q^{89} +13.3858 q^{90} -0.188679 q^{91} -1.44805 q^{92} -0.0905911 q^{93} -13.5266 q^{94} +5.52012 q^{95} +2.61328 q^{96} +6.19777 q^{97} +6.77073 q^{98} -1.98648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.61328	−1.50878	−0.754389	−	0.656427i	$-0.772067\pi$
$3$	−2.61328	−1.50878	−0.754389	+	0.656427i	$0.772067\pi$
$4$	1.00000	0.500000
$5$	−3.49569	−1.56332	−0.781661	−	0.623704i	$-0.785627\pi$
$5$	−3.49569	−1.56332	−0.781661	+	0.623704i	$0.785627\pi$
$6$	2.61328	1.06687
$7$	−0.478818	−0.180976	−0.0904881	−	0.995898i	$-0.528843\pi$
$7$	−0.478818	−0.180976	−0.0904881	+	0.995898i	$0.528843\pi$
$8$	−1.00000	−0.353553
$9$	3.82924	1.27641
$10$	3.49569	1.10544
$11$	−0.518766	−0.156414	−0.0782068	−	0.996937i	$-0.524919\pi$
$11$	−0.518766	−0.156414	−0.0782068	+	0.996937i	$0.524919\pi$
$12$	−2.61328	−0.754389
$13$	0.394051	0.109290	0.0546451	−	0.998506i	$-0.482597\pi$
$13$	0.394051	0.109290	0.0546451	+	0.998506i	$0.482597\pi$
$14$	0.478818	0.127969
$15$	9.13523	2.35871
$16$	1.00000	0.250000
$17$	−1.63145	−0.395684	−0.197842	−	0.980234i	$-0.563393\pi$
$17$	−1.63145	−0.395684	−0.197842	+	0.980234i	$0.563393\pi$
$18$	−3.82924	−0.902560
$19$	−1.57912	−0.362275	−0.181138	−	0.983458i	$-0.557978\pi$
$19$	−1.57912	−0.362275	−0.181138	+	0.983458i	$0.557978\pi$
$20$	−3.49569	−0.781661
$21$	1.25129	0.273053
$22$	0.518766	0.110601
$23$	−1.44805	−0.301940	−0.150970	−	0.988538i	$-0.548240\pi$
$23$	−1.44805	−0.301940	−0.150970	+	0.988538i	$0.548240\pi$
$24$	2.61328	0.533434
$25$	7.21987	1.44397
$26$	−0.394051	−0.0772799
$27$	−2.16703	−0.417046
$28$	−0.478818	−0.0904881
$29$	6.68629	1.24161	0.620806	−	0.783964i	$-0.286805\pi$
$29$	6.68629	1.24161	0.620806	+	0.783964i	$0.286805\pi$
$30$	−9.13523	−1.66786
$31$	0.0346656	0.00622613	0.00311307	−	0.999995i	$-0.499009\pi$
$31$	0.0346656	0.00622613	0.00311307	+	0.999995i	$0.499009\pi$
$32$	−1.00000	−0.176777
$33$	1.35568	0.235994
$34$	1.63145	0.279791
$35$	1.67380	0.282924
$36$	3.82924	0.638206
$37$	−0.471003	−0.0774323	−0.0387162	−	0.999250i	$-0.512327\pi$
$37$	−0.471003	−0.0774323	−0.0387162	+	0.999250i	$0.512327\pi$
$38$	1.57912	0.256167
$39$	−1.02977	−0.164895
$40$	3.49569	0.552718
$41$	−1.81254	−0.283071	−0.141536	−	0.989933i	$-0.545204\pi$
$41$	−1.81254	−0.283071	−0.141536	+	0.989933i	$0.545204\pi$
$42$	−1.25129	−0.193078
$43$	0.346409	0.0528268	0.0264134	−	0.999651i	$-0.491591\pi$
$43$	0.346409	0.0528268	0.0264134	+	0.999651i	$0.491591\pi$
$44$	−0.518766	−0.0782068
$45$	−13.3858	−1.99544
$46$	1.44805	0.213504
$47$	13.5266	1.97305	0.986526	−	0.163606i	$-0.0523125\pi$
$47$	13.5266	1.97305	0.986526	+	0.163606i	$0.0523125\pi$
$48$	−2.61328	−0.377195
$49$	−6.77073	−0.967248
$50$	−7.21987	−1.02104
$51$	4.26343	0.597000
$52$	0.394051	0.0546451
$53$	0.660429	0.0907169	0.0453585	−	0.998971i	$-0.485557\pi$
$53$	0.660429	0.0907169	0.0453585	+	0.998971i	$0.485557\pi$
$54$	2.16703	0.294896
$55$	1.81344	0.244525
$56$	0.478818	0.0639847
$57$	4.12669	0.546593
$58$	−6.68629	−0.877953
$59$	2.43140	0.316541	0.158271	−	0.987396i	$-0.449408\pi$
$59$	2.43140	0.316541	0.158271	+	0.987396i	$0.449408\pi$
$60$	9.13523	1.17935
$61$	−6.58531	−0.843163	−0.421581	−	0.906791i	$-0.638525\pi$
$61$	−6.58531	−0.843163	−0.421581	+	0.906791i	$0.638525\pi$
$62$	−0.0346656	−0.00440254
$63$	−1.83351	−0.231000
$64$	1.00000	0.125000
$65$	−1.37748	−0.170856
$66$	−1.35568	−0.166873
$67$	−15.0872	−1.84320	−0.921600	−	0.388142i	$-0.873117\pi$
$67$	−15.0872	−1.84320	−0.921600	+	0.388142i	$0.873117\pi$
$68$	−1.63145	−0.197842
$69$	3.78417	0.455561
$70$	−1.67380	−0.200057
$71$	−3.80058	−0.451046	−0.225523	−	0.974238i	$-0.572409\pi$
$71$	−3.80058	−0.451046	−0.225523	+	0.974238i	$0.572409\pi$
$72$	−3.82924	−0.451280
$73$	−4.71638	−0.552011	−0.276005	−	0.961156i	$-0.589011\pi$
$73$	−4.71638	−0.552011	−0.276005	+	0.961156i	$0.589011\pi$
$74$	0.471003	0.0547529
$75$	−18.8675	−2.17864
$76$	−1.57912	−0.181138
$77$	0.248394	0.0283071
$78$	1.02977	0.116598
$79$	−7.31985	−0.823548	−0.411774	−	0.911286i	$-0.635091\pi$
$79$	−7.31985	−0.823548	−0.411774	+	0.911286i	$0.635091\pi$
$80$	−3.49569	−0.390830
$81$	−5.82465	−0.647183
$82$	1.81254	0.200162
$83$	−1.54698	−0.169803	−0.0849017	−	0.996389i	$-0.527058\pi$
$83$	−1.54698	−0.169803	−0.0849017	+	0.996389i	$0.527058\pi$
$84$	1.25129	0.136526
$85$	5.70304	0.618582
$86$	−0.346409	−0.0373542
$87$	−17.4732	−1.87332
$88$	0.518766	0.0553006
$89$	15.2625	1.61782	0.808909	−	0.587934i	$-0.200059\pi$
$89$	15.2625	1.61782	0.808909	+	0.587934i	$0.200059\pi$
$90$	13.3858	1.41099
$91$	−0.188679	−0.0197789
$92$	−1.44805	−0.150970
$93$	−0.0905911	−0.00939386
$94$	−13.5266	−1.39516
$95$	5.52012	0.566352
$96$	2.61328	0.266717
$97$	6.19777	0.629288	0.314644	−	0.949210i	$-0.398115\pi$
$97$	6.19777	0.629288	0.314644	+	0.949210i	$0.398115\pi$
$98$	6.77073	0.683947
$99$	−1.98648	−0.199648
$100$	7.21987	0.721987
$101$	−9.37856	−0.933201	−0.466601	−	0.884468i	$-0.654521\pi$
$101$	−9.37856	−0.933201	−0.466601	+	0.884468i	$0.654521\pi$
$102$	−4.26343	−0.422143
$103$	15.4375	1.52110	0.760552	−	0.649277i	$-0.224928\pi$
$103$	15.4375	1.52110	0.760552	+	0.649277i	$0.224928\pi$
$104$	−0.394051	−0.0386399
$105$	−4.37411	−0.426869
$106$	−0.660429	−0.0641465
$107$	15.5729	1.50549	0.752744	−	0.658313i	$-0.228730\pi$
$107$	15.5729	1.50549	0.752744	+	0.658313i	$0.228730\pi$
$108$	−2.16703	−0.208523
$109$	−4.04637	−0.387572	−0.193786	−	0.981044i	$-0.562077\pi$
$109$	−4.04637	−0.387572	−0.193786	+	0.981044i	$0.562077\pi$
$110$	−1.81344	−0.172905
$111$	1.23086	0.116828
$112$	−0.478818	−0.0452440
$113$	16.3223	1.53547	0.767735	−	0.640768i	$-0.221384\pi$
$113$	16.3223	1.53547	0.767735	+	0.640768i	$0.221384\pi$
$114$	−4.12669	−0.386500
$115$	5.06195	0.472029
$116$	6.68629	0.620806
$117$	1.50892	0.139499
$118$	−2.43140	−0.223828
$119$	0.781167	0.0716094
$120$	−9.13523	−0.833928
$121$	−10.7309	−0.975535
$122$	6.58531	0.596206
$123$	4.73668	0.427092
$124$	0.0346656	0.00311307
$125$	−7.75997	−0.694073
$126$	1.83351	0.163342
$127$	−0.835001	−0.0740944	−0.0370472	−	0.999314i	$-0.511795\pi$
$127$	−0.835001	−0.0740944	−0.0370472	+	0.999314i	$0.511795\pi$
$128$	−1.00000	−0.0883883
$129$	−0.905263	−0.0797039
$130$	1.37748	0.120813
$131$	−16.8384	−1.47118	−0.735589	−	0.677428i	$-0.763094\pi$
$131$	−16.8384	−1.47118	−0.735589	+	0.677428i	$0.763094\pi$
$132$	1.35568	0.117997
$133$	0.756111	0.0655631
$134$	15.0872	1.30334
$135$	7.57528	0.651977
$136$	1.63145	0.139896
$137$	−20.0997	−1.71723	−0.858615	−	0.512622i	$-0.828674\pi$
$137$	−20.0997	−1.71723	−0.858615	+	0.512622i	$0.828674\pi$
$138$	−3.78417	−0.322130
$139$	−8.90098	−0.754971	−0.377486	−	0.926015i	$-0.623211\pi$
$139$	−8.90098	−0.754971	−0.377486	+	0.926015i	$0.623211\pi$
$140$	1.67380	0.141462
$141$	−35.3487	−2.97690
$142$	3.80058	0.318937
$143$	−0.204420	−0.0170945
$144$	3.82924	0.319103
$145$	−23.3732	−1.94104
$146$	4.71638	0.390331
$147$	17.6938	1.45936
$148$	−0.471003	−0.0387162
$149$	−15.4223	−1.26345	−0.631724	−	0.775194i	$-0.717652\pi$
$149$	−15.4223	−1.26345	−0.631724	+	0.775194i	$0.717652\pi$
$150$	18.8675	1.54053
$151$	−23.7803	−1.93521	−0.967607	−	0.252460i	$-0.918760\pi$
$151$	−23.7803	−1.93521	−0.967607	+	0.252460i	$0.918760\pi$
$152$	1.57912	0.128084
$153$	−6.24721	−0.505057
$154$	−0.248394	−0.0200162
$155$	−0.121180	−0.00973345
$156$	−1.02977	−0.0824474
$157$	7.41881	0.592085	0.296043	−	0.955175i	$-0.404333\pi$
$157$	7.41881	0.592085	0.296043	+	0.955175i	$0.404333\pi$
$158$	7.31985	0.582336
$159$	−1.72589	−0.136872
$160$	3.49569	0.276359
$161$	0.693354	0.0546439
$162$	5.82465	0.457627
$163$	−19.8529	−1.55500	−0.777500	−	0.628883i	$-0.783512\pi$
$163$	−19.8529	−1.55500	−0.777500	+	0.628883i	$0.783512\pi$
$164$	−1.81254	−0.141536
$165$	−4.73904	−0.368934
$166$	1.54698	0.120069
$167$	2.89092	0.223706	0.111853	−	0.993725i	$-0.464321\pi$
$167$	2.89092	0.223706	0.111853	+	0.993725i	$0.464321\pi$
$168$	−1.25129	−0.0965388
$169$	−12.8447	−0.988056
$170$	−5.70304	−0.437403
$171$	−6.04683	−0.462413
$172$	0.346409	0.0264134
$173$	−10.7517	−0.817435	−0.408718	−	0.912661i	$-0.634024\pi$
$173$	−10.7517	−0.817435	−0.408718	+	0.912661i	$0.634024\pi$
$174$	17.4732	1.32464
$175$	−3.45700	−0.261325
$176$	−0.518766	−0.0391034
$177$	−6.35393	−0.477590
$178$	−15.2625	−1.14397
$179$	−1.79236	−0.133967	−0.0669836	−	0.997754i	$-0.521338\pi$
$179$	−1.79236	−0.133967	−0.0669836	+	0.997754i	$0.521338\pi$
$180$	−13.3858	−0.997722
$181$	−9.37633	−0.696937	−0.348468	−	0.937320i	$-0.613298\pi$
$181$	−9.37633	−0.696937	−0.348468	+	0.937320i	$0.613298\pi$
$182$	0.188679	0.0139858
$183$	17.2093	1.27215
$184$	1.44805	0.106752
$185$	1.64648	0.121052
$186$	0.0905911	0.00664246
$187$	0.846339	0.0618905
$188$	13.5266	0.986526
$189$	1.03761	0.0754753
$190$	−5.52012	−0.400472
$191$	−8.09957	−0.586064	−0.293032	−	0.956103i	$-0.594664\pi$
$191$	−8.09957	−0.586064	−0.293032	+	0.956103i	$0.594664\pi$
$192$	−2.61328	−0.188597
$193$	−15.3567	−1.10540	−0.552700	−	0.833381i	$-0.686402\pi$
$193$	−15.3567	−1.10540	−0.552700	+	0.833381i	$0.686402\pi$
$194$	−6.19777	−0.444974
$195$	3.59975	0.257783
$196$	−6.77073	−0.483624
$197$	7.45842	0.531390	0.265695	−	0.964057i	$-0.414399\pi$
$197$	7.45842	0.531390	0.265695	+	0.964057i	$0.414399\pi$
$198$	1.98648	0.141173
$199$	1.82888	0.129646	0.0648230	−	0.997897i	$-0.479352\pi$
$199$	1.82888	0.129646	0.0648230	+	0.997897i	$0.479352\pi$
$200$	−7.21987	−0.510522
$201$	39.4272	2.78098
$202$	9.37856	0.659873
$203$	−3.20151	−0.224702
$204$	4.26343	0.298500
$205$	6.33609	0.442531
$206$	−15.4375	−1.07558
$207$	−5.54494	−0.385400
$208$	0.394051	0.0273226
$209$	0.819193	0.0566648
$210$	4.37411	0.301842
$211$	12.8834	0.886930	0.443465	−	0.896292i	$-0.353749\pi$
$211$	12.8834	0.886930	0.443465	+	0.896292i	$0.353749\pi$
$212$	0.660429	0.0453585
$213$	9.93198	0.680528
$214$	−15.5729	−1.06454
$215$	−1.21094	−0.0825853
$216$	2.16703	0.147448
$217$	−0.0165985	−0.00112678
$218$	4.04637	0.274055
$219$	12.3252	0.832862
$220$	1.81344	0.122262
$221$	−0.642875	−0.0432444
$222$	−1.23086	−0.0826101
$223$	−14.3736	−0.962527	−0.481263	−	0.876576i	$-0.659822\pi$
$223$	−14.3736	−0.962527	−0.481263	+	0.876576i	$0.659822\pi$
$224$	0.478818	0.0319924
$225$	27.6466	1.84311
$226$	−16.3223	−1.08574
$227$	25.8048	1.71272	0.856362	−	0.516376i	$-0.172719\pi$
$227$	25.8048	1.71272	0.856362	+	0.516376i	$0.172719\pi$
$228$	4.12669	0.273296
$229$	−9.81575	−0.648643	−0.324321	−	0.945947i	$-0.605136\pi$
$229$	−9.81575	−0.648643	−0.324321	+	0.945947i	$0.605136\pi$
$230$	−5.06195	−0.333775
$231$	−0.649124	−0.0427092
$232$	−6.68629	−0.438976
$233$	27.4265	1.79677	0.898384	−	0.439210i	$-0.144742\pi$
$233$	27.4265	1.79677	0.898384	+	0.439210i	$0.144742\pi$
$234$	−1.50892	−0.0986410
$235$	−47.2847	−3.08451
$236$	2.43140	0.158271
$237$	19.1288	1.24255
$238$	−0.781167	−0.0506355
$239$	−11.9191	−0.770985	−0.385493	−	0.922711i	$-0.625968\pi$
$239$	−11.9191	−0.770985	−0.385493	+	0.922711i	$0.625968\pi$
$240$	9.13523	0.589676
$241$	−3.75561	−0.241920	−0.120960	−	0.992657i	$-0.538597\pi$
$241$	−3.75561	−0.241920	−0.120960	+	0.992657i	$0.538597\pi$
$242$	10.7309	0.689807
$243$	21.7225	1.39350
$244$	−6.58531	−0.421581
$245$	23.6684	1.51212
$246$	−4.73668	−0.302000
$247$	−0.622255	−0.0395931
$248$	−0.0346656	−0.00220127
$249$	4.04270	0.256196
$250$	7.75997	0.490784
$251$	−22.7390	−1.43527	−0.717636	−	0.696418i	$-0.754776\pi$
$251$	−22.7390	−1.43527	−0.717636	+	0.696418i	$0.754776\pi$
$252$	−1.83351	−0.115500
$253$	0.751200	0.0472275
$254$	0.835001	0.0523926
$255$	−14.9037	−0.933303
$256$	1.00000	0.0625000
$257$	15.7572	0.982905	0.491452	−	0.870904i	$-0.336466\pi$
$257$	15.7572	0.982905	0.491452	+	0.870904i	$0.336466\pi$
$258$	0.905263	0.0563592
$259$	0.225524	0.0140134
$260$	−1.37748	−0.0854279
$261$	25.6034	1.58481
$262$	16.8384	1.04028
$263$	−3.72559	−0.229730	−0.114865	−	0.993381i	$-0.536644\pi$
$263$	−3.72559	−0.229730	−0.114865	+	0.993381i	$0.536644\pi$
$264$	−1.35568	−0.0834363
$265$	−2.30866	−0.141820
$266$	−0.756111	−0.0463601
$267$	−39.8851	−2.44093
$268$	−15.0872	−0.921600
$269$	−11.7094	−0.713934	−0.356967	−	0.934117i	$-0.616189\pi$
$269$	−11.7094	−0.713934	−0.356967	+	0.934117i	$0.616189\pi$
$270$	−7.57528	−0.461017
$271$	17.9900	1.09281	0.546407	−	0.837520i	$-0.315995\pi$
$271$	17.9900	1.09281	0.546407	+	0.837520i	$0.315995\pi$
$272$	−1.63145	−0.0989211
$273$	0.493071	0.0298420
$274$	20.0997	1.21426
$275$	−3.74542	−0.225857
$276$	3.78417	0.227780
$277$	−20.7574	−1.24719	−0.623597	−	0.781746i	$-0.714329\pi$
$277$	−20.7574	−1.24719	−0.623597	+	0.781746i	$0.714329\pi$
$278$	8.90098	0.533845
$279$	0.132743	0.00794712
$280$	−1.67380	−0.100029
$281$	27.2542	1.62585	0.812924	−	0.582369i	$-0.197874\pi$
$281$	27.2542	1.62585	0.812924	+	0.582369i	$0.197874\pi$
$282$	35.3487	2.10498
$283$	17.5891	1.04556	0.522782	−	0.852466i	$-0.324894\pi$
$283$	17.5891	1.04556	0.522782	+	0.852466i	$0.324894\pi$
$284$	−3.80058	−0.225523
$285$	−14.4256	−0.854500
$286$	0.204420	0.0120876
$287$	0.867877	0.0512292
$288$	−3.82924	−0.225640
$289$	−14.3384	−0.843434
$290$	23.3732	1.37252
$291$	−16.1965	−0.949457
$292$	−4.71638	−0.276005
$293$	−29.2878	−1.71101	−0.855505	−	0.517794i	$-0.826753\pi$
$293$	−29.2878	−1.71101	−0.855505	+	0.517794i	$0.826753\pi$
$294$	−17.6938	−1.03193
$295$	−8.49942	−0.494855
$296$	0.471003	0.0273765
$297$	1.12418	0.0652317
$298$	15.4223	0.893392
$299$	−0.570608	−0.0329991
$300$	−18.8675	−1.08932
$301$	−0.165867	−0.00956039
$302$	23.7803	1.36840
$303$	24.5088	1.40799
$304$	−1.57912	−0.0905688
$305$	23.0202	1.31813
$306$	6.24721	0.357129
$307$	1.91738	0.109431	0.0547154	−	0.998502i	$-0.482575\pi$
$307$	1.91738	0.109431	0.0547154	+	0.998502i	$0.482575\pi$
$308$	0.248394	0.0141536
$309$	−40.3426	−2.29501
$310$	0.121180	0.00688259
$311$	−2.28986	−0.129846	−0.0649230	−	0.997890i	$-0.520680\pi$
$311$	−2.28986	−0.129846	−0.0649230	+	0.997890i	$0.520680\pi$
$312$	1.02977	0.0582991
$313$	12.8454	0.726067	0.363034	−	0.931776i	$-0.381741\pi$
$313$	12.8454	0.726067	0.363034	+	0.931776i	$0.381741\pi$
$314$	−7.41881	−0.418668
$315$	6.40938	0.361128
$316$	−7.31985	−0.411774
$317$	2.01283	0.113052	0.0565259	−	0.998401i	$-0.481998\pi$
$317$	2.01283	0.113052	0.0565259	+	0.998401i	$0.481998\pi$
$318$	1.72589	0.0967829
$319$	−3.46862	−0.194205
$320$	−3.49569	−0.195415
$321$	−40.6964	−2.27145
$322$	−0.693354	−0.0386391
$323$	2.57625	0.143347
$324$	−5.82465	−0.323592
$325$	2.84500	0.157812
$326$	19.8529	1.09955
$327$	10.5743	0.584761
$328$	1.81254	0.100081
$329$	−6.47676	−0.357075
$330$	4.73904	0.260876
$331$	23.5787	1.29600	0.648001	−	0.761640i	$-0.275605\pi$
$331$	23.5787	1.29600	0.648001	+	0.761640i	$0.275605\pi$
$332$	−1.54698	−0.0849017
$333$	−1.80358	−0.0988356
$334$	−2.89092	−0.158184
$335$	52.7403	2.88151
$336$	1.25129	0.0682632
$337$	−26.4651	−1.44164	−0.720822	−	0.693120i	$-0.756236\pi$
$337$	−26.4651	−1.44164	−0.720822	+	0.693120i	$0.756236\pi$
$338$	12.8447	0.698661
$339$	−42.6547	−2.31668
$340$	5.70304	0.309291
$341$	−0.0179833	−0.000973852 0
$342$	6.04683	0.326975
$343$	6.59367	0.356025
$344$	−0.346409	−0.0186771
$345$	−13.2283	−0.712187
$346$	10.7517	0.578014
$347$	−13.2596	−0.711811	−0.355905	−	0.934522i	$-0.615827\pi$
$347$	−13.2596	−0.711811	−0.355905	+	0.934522i	$0.615827\pi$
$348$	−17.4732	−0.936659
$349$	13.0888	0.700625	0.350313	−	0.936633i	$-0.386075\pi$
$349$	13.0888	0.700625	0.350313	+	0.936633i	$0.386075\pi$
$350$	3.45700	0.184784
$351$	−0.853923	−0.0455790
$352$	0.518766	0.0276503
$353$	13.9656	0.743316	0.371658	−	0.928370i	$-0.378789\pi$
$353$	13.9656	0.743316	0.371658	+	0.928370i	$0.378789\pi$
$354$	6.35393	0.337707
$355$	13.2856	0.705129
$356$	15.2625	0.808909
$357$	−2.04141	−0.108043
$358$	1.79236	0.0947291
$359$	26.5440	1.40094	0.700470	−	0.713681i	$-0.252974\pi$
$359$	26.5440	1.40094	0.700470	+	0.713681i	$0.252974\pi$
$360$	13.3858	0.705496
$361$	−16.5064	−0.868757
$362$	9.37633	0.492809
$363$	28.0428	1.47187
$364$	−0.188679	−0.00988946
$365$	16.4870	0.862970
$366$	−17.2093	−0.899543
$367$	16.0040	0.835400	0.417700	−	0.908585i	$-0.362836\pi$
$367$	16.0040	0.835400	0.417700	+	0.908585i	$0.362836\pi$
$368$	−1.44805	−0.0754850
$369$	−6.94065	−0.361316
$370$	−1.64648	−0.0855964
$371$	−0.316225	−0.0164176
$372$	−0.0905911	−0.00469693
$373$	−28.3811	−1.46952	−0.734759	−	0.678328i	$-0.762705\pi$
$373$	−28.3811	−1.46952	−0.734759	+	0.678328i	$0.762705\pi$
$374$	−0.846339	−0.0437632
$375$	20.2790	1.04720
$376$	−13.5266	−0.697579
$377$	2.63474	0.135696
$378$	−1.03761	−0.0533691
$379$	36.9387	1.89741	0.948707	−	0.316158i	$-0.102393\pi$
$379$	36.9387	1.89741	0.948707	+	0.316158i	$0.102393\pi$
$380$	5.52012	0.283176
$381$	2.18209	0.111792
$382$	8.09957	0.414410
$383$	14.6807	0.750147	0.375073	−	0.926995i	$-0.377618\pi$
$383$	14.6807	0.750147	0.375073	+	0.926995i	$0.377618\pi$
$384$	2.61328	0.133358
$385$	−0.868310	−0.0442532
$386$	15.3567	0.781635
$387$	1.32648	0.0674288
$388$	6.19777	0.314644
$389$	8.06683	0.409005	0.204502	−	0.978866i	$-0.434442\pi$
$389$	8.06683	0.409005	0.204502	+	0.978866i	$0.434442\pi$
$390$	−3.59975	−0.182280
$391$	2.36242	0.119473
$392$	6.77073	0.341974
$393$	44.0035	2.21968
$394$	−7.45842	−0.375750
$395$	25.5879	1.28747
$396$	−1.98648	−0.0998242
$397$	−31.6162	−1.58677	−0.793386	−	0.608719i	$-0.791684\pi$
$397$	−31.6162	−1.58677	−0.793386	+	0.608719i	$0.791684\pi$
$398$	−1.82888	−0.0916735
$399$	−1.97593	−0.0989203
$400$	7.21987	0.360993
$401$	2.91703	0.145669	0.0728347	−	0.997344i	$-0.476795\pi$
$401$	2.91703	0.145669	0.0728347	+	0.997344i	$0.476795\pi$
$402$	−39.4272	−1.96645
$403$	0.0136600	0.000680455 0
$404$	−9.37856	−0.466601
$405$	20.3612	1.01175
$406$	3.20151	0.158888
$407$	0.244340	0.0121115
$408$	−4.26343	−0.211071
$409$	28.1151	1.39020	0.695102	−	0.718911i	$-0.255359\pi$
$409$	28.1151	1.39020	0.695102	+	0.718911i	$0.255359\pi$
$410$	−6.33609	−0.312917
$411$	52.5260	2.59092
$412$	15.4375	0.760552
$413$	−1.16420	−0.0572864
$414$	5.54494	0.272519
$415$	5.40777	0.265457
$416$	−0.394051	−0.0193200
$417$	23.2608	1.13908
$418$	−0.819193	−0.0400681
$419$	−34.8537	−1.70271	−0.851356	−	0.524588i	$-0.824219\pi$
$419$	−34.8537	−1.70271	−0.851356	+	0.524588i	$0.824219\pi$
$420$	−4.37411	−0.213435
$421$	−25.8122	−1.25801	−0.629005	−	0.777401i	$-0.716537\pi$
$421$	−25.8122	−1.25801	−0.629005	+	0.777401i	$0.716537\pi$
$422$	−12.8834	−0.627154
$423$	51.7964	2.51843
$424$	−0.660429	−0.0320733
$425$	−11.7788	−0.571358
$426$	−9.93198	−0.481206
$427$	3.15317	0.152592
$428$	15.5729	0.752744
$429$	0.534208	0.0257918
$430$	1.21094	0.0583966
$431$	16.4844	0.794028	0.397014	−	0.917813i	$-0.370046\pi$
$431$	16.4844	0.794028	0.397014	+	0.917813i	$0.370046\pi$
$432$	−2.16703	−0.104261
$433$	36.0861	1.73419	0.867094	−	0.498145i	$-0.165985\pi$
$433$	36.0861	1.73419	0.867094	+	0.498145i	$0.165985\pi$
$434$	0.0165985	0.000796755 0
$435$	61.0808	2.92860
$436$	−4.04637	−0.193786
$437$	2.28665	0.109385
$438$	−12.3252	−0.588923
$439$	12.2932	0.586721	0.293361	−	0.956002i	$-0.405226\pi$
$439$	12.2932	0.586721	0.293361	+	0.956002i	$0.405226\pi$
$440$	−1.81344	−0.0864526
$441$	−25.9268	−1.23461
$442$	0.642875	0.0305784
$443$	−10.7849	−0.512405	−0.256202	−	0.966623i	$-0.582471\pi$
$443$	−10.7849	−0.512405	−0.256202	+	0.966623i	$0.582471\pi$
$444$	1.23086	0.0584141
$445$	−53.3529	−2.52917
$446$	14.3736	0.680609
$447$	40.3029	1.90626
$448$	−0.478818	−0.0226220
$449$	−34.6427	−1.63489	−0.817446	−	0.576006i	$-0.804611\pi$
$449$	−34.6427	−1.63489	−0.817446	+	0.576006i	$0.804611\pi$
$450$	−27.6466	−1.30327
$451$	0.940284	0.0442762
$452$	16.3223	0.767735
$453$	62.1447	2.91981
$454$	−25.8048	−1.21108
$455$	0.659563	0.0309208
$456$	−4.12669	−0.193250
$457$	10.9190	0.510770	0.255385	−	0.966839i	$-0.417798\pi$
$457$	10.9190	0.510770	0.255385	+	0.966839i	$0.417798\pi$
$458$	9.81575	0.458660
$459$	3.53540	0.165019
$460$	5.06195	0.236015
$461$	−12.4177	−0.578349	−0.289175	−	0.957276i	$-0.593381\pi$
$461$	−12.4177	−0.578349	−0.289175	+	0.957276i	$0.593381\pi$
$462$	0.649124	0.0302000
$463$	−10.9578	−0.509251	−0.254626	−	0.967040i	$-0.581952\pi$
$463$	−10.9578	−0.509251	−0.254626	+	0.967040i	$0.581952\pi$
$464$	6.68629	0.310403
$465$	0.316679	0.0146856
$466$	−27.4265	−1.27051
$467$	1.70410	0.0788561	0.0394281	−	0.999222i	$-0.487446\pi$
$467$	1.70410	0.0788561	0.0394281	+	0.999222i	$0.487446\pi$
$468$	1.50892	0.0697497
$469$	7.22404	0.333575
$470$	47.2847	2.18108
$471$	−19.3874	−0.893326
$472$	−2.43140	−0.111914
$473$	−0.179705	−0.00826283
$474$	−19.1288	−0.878616
$475$	−11.4010	−0.523116
$476$	0.781167	0.0358047
$477$	2.52894	0.115792
$478$	11.9191	0.545169
$479$	−12.8413	−0.586736	−0.293368	−	0.956000i	$-0.594776\pi$
$479$	−12.8413	−0.586736	−0.293368	+	0.956000i	$0.594776\pi$
$480$	−9.13523	−0.416964
$481$	−0.185599	−0.00846260
$482$	3.75561	0.171063
$483$	−1.81193	−0.0824456
$484$	−10.7309	−0.487767
$485$	−21.6655	−0.983780
$486$	−21.7225	−0.985355
$487$	12.2065	0.553127	0.276564	−	0.960996i	$-0.410804\pi$
$487$	12.2065	0.553127	0.276564	+	0.960996i	$0.410804\pi$
$488$	6.58531	0.298103
$489$	51.8812	2.34615
$490$	−23.6684	−1.06923
$491$	−8.79930	−0.397107	−0.198554	−	0.980090i	$-0.563624\pi$
$491$	−8.79930	−0.397107	−0.198554	+	0.980090i	$0.563624\pi$
$492$	4.73668	0.213546
$493$	−10.9083	−0.491287
$494$	0.622255	0.0279966
$495$	6.94411	0.312115
$496$	0.0346656	0.00155653
$497$	1.81978	0.0816285
$498$	−4.04270	−0.181158
$499$	23.9035	1.07007	0.535033	−	0.844831i	$-0.320299\pi$
$499$	23.9035	1.07007	0.535033	+	0.844831i	$0.320299\pi$
$500$	−7.75997	−0.347036
$501$	−7.55478	−0.337523
$502$	22.7390	1.01489
$503$	−3.64287	−0.162428	−0.0812138	−	0.996697i	$-0.525880\pi$
$503$	−3.64287	−0.162428	−0.0812138	+	0.996697i	$0.525880\pi$
$504$	1.83351	0.0816709
$505$	32.7845	1.45889
$506$	−0.751200	−0.0333949
$507$	33.5669	1.49076
$508$	−0.835001	−0.0370472
$509$	25.7731	1.14237	0.571186	−	0.820821i	$-0.306484\pi$
$509$	25.7731	1.14237	0.571186	+	0.820821i	$0.306484\pi$
$510$	14.9037	0.659945
$511$	2.25829	0.0999008
$512$	−1.00000	−0.0441942
$513$	3.42201	0.151085
$514$	−15.7572	−0.695019
$515$	−53.9649	−2.37798
$516$	−0.905263	−0.0398520
$517$	−7.01711	−0.308612
$518$	−0.225524	−0.00990897
$519$	28.0972	1.23333
$520$	1.37748	0.0604066
$521$	10.9232	0.478554	0.239277	−	0.970951i	$-0.423090\pi$
$521$	10.9232	0.478554	0.239277	+	0.970951i	$0.423090\pi$
$522$	−25.6034	−1.12063
$523$	3.92120	0.171462	0.0857311	−	0.996318i	$-0.472677\pi$
$523$	3.92120	0.171462	0.0857311	+	0.996318i	$0.472677\pi$
$524$	−16.8384	−0.735589
$525$	9.03411	0.394281
$526$	3.72559	0.162444
$527$	−0.0565552	−0.00246358
$528$	1.35568	0.0589984
$529$	−20.9031	−0.908832
$530$	2.30866	0.100282
$531$	9.31040	0.404037
$532$	0.756111	0.0327816
$533$	−0.714234	−0.0309369
$534$	39.8851	1.72600
$535$	−54.4381	−2.35356
$536$	15.0872	0.651669
$537$	4.68394	0.202127
$538$	11.7094	0.504828
$539$	3.51242	0.151291
$540$	7.57528	0.325988
$541$	33.3609	1.43430	0.717149	−	0.696920i	$-0.245447\pi$
$541$	33.3609	1.43430	0.717149	+	0.696920i	$0.245447\pi$
$542$	−17.9900	−0.772736
$543$	24.5030	1.05152
$544$	1.63145	0.0699478
$545$	14.1449	0.605900
$546$	−0.493071	−0.0211015
$547$	−17.5347	−0.749729	−0.374865	−	0.927080i	$-0.622311\pi$
$547$	−17.5347	−0.749729	−0.374865	+	0.927080i	$0.622311\pi$
$548$	−20.0997	−0.858615
$549$	−25.2167	−1.07622
$550$	3.74542	0.159705
$551$	−10.5585	−0.449805
$552$	−3.78417	−0.161065
$553$	3.50487	0.149042
$554$	20.7574	0.881899
$555$	−4.30272	−0.182640
$556$	−8.90098	−0.377486
$557$	14.0175	0.593940	0.296970	−	0.954887i	$-0.404024\pi$
$557$	14.0175	0.593940	0.296970	+	0.954887i	$0.404024\pi$
$558$	−0.132743	−0.00561946
$559$	0.136503	0.00577345
$560$	1.67380	0.0707310
$561$	−2.21172	−0.0933790
$562$	−27.2542	−1.14965
$563$	−15.2895	−0.644377	−0.322188	−	0.946676i	$-0.604418\pi$
$563$	−15.2895	−0.644377	−0.322188	+	0.946676i	$0.604418\pi$
$564$	−35.3487	−1.48845
$565$	−57.0576	−2.40043
$566$	−17.5891	−0.739326
$567$	2.78894	0.117125
$568$	3.80058	0.159469
$569$	21.0722	0.883392	0.441696	−	0.897165i	$-0.354377\pi$
$569$	21.0722	0.883392	0.441696	+	0.897165i	$0.354377\pi$
$570$	14.4256	0.604223
$571$	−13.4449	−0.562650	−0.281325	−	0.959613i	$-0.590774\pi$
$571$	−13.4449	−0.562650	−0.281325	+	0.959613i	$0.590774\pi$
$572$	−0.204420	−0.00854724
$573$	21.1664	0.884241
$574$	−0.867877	−0.0362245
$575$	−10.4548	−0.435993
$576$	3.82924	0.159552
$577$	33.8215	1.40801	0.704004	−	0.710196i	$-0.251394\pi$
$577$	33.8215	1.40801	0.704004	+	0.710196i	$0.251394\pi$
$578$	14.3384	0.596398
$579$	40.1314	1.66780
$580$	−23.3732	−0.970520
$581$	0.740723	0.0307304
$582$	16.1965	0.671367
$583$	−0.342608	−0.0141894
$584$	4.71638	0.195165
$585$	−5.27471	−0.218082
$586$	29.2878	1.20987
$587$	−18.8414	−0.777669	−0.388835	−	0.921308i	$-0.627122\pi$
$587$	−18.8414	−0.777669	−0.388835	+	0.921308i	$0.627122\pi$
$588$	17.6938	0.729681
$589$	−0.0547412	−0.00225557
$590$	8.49942	0.349916
$591$	−19.4909	−0.801750
$592$	−0.471003	−0.0193581
$593$	7.62865	0.313271	0.156636	−	0.987656i	$-0.449935\pi$
$593$	7.62865	0.313271	0.156636	+	0.987656i	$0.449935\pi$
$594$	−1.12418	−0.0461258
$595$	−2.73072	−0.111949
$596$	−15.4223	−0.631724
$597$	−4.77938	−0.195607
$598$	0.570608	0.0233339
$599$	−5.73731	−0.234420	−0.117210	−	0.993107i	$-0.537395\pi$
$599$	−5.73731	−0.234420	−0.117210	+	0.993107i	$0.537395\pi$
$600$	18.8675	0.770264
$601$	27.0126	1.10187	0.550933	−	0.834550i	$-0.314272\pi$
$601$	27.0126	1.10187	0.550933	+	0.834550i	$0.314272\pi$
$602$	0.165867	0.00676022
$603$	−57.7726	−2.35268
$604$	−23.7803	−0.967607
$605$	37.5119	1.52507
$606$	−24.5088	−0.995602
$607$	10.3655	0.420722	0.210361	−	0.977624i	$-0.432536\pi$
$607$	10.3655	0.420722	0.210361	+	0.977624i	$0.432536\pi$
$608$	1.57912	0.0640418
$609$	8.36646	0.339026
$610$	−23.0202	−0.932062
$611$	5.33016	0.215635
$612$	−6.24721	−0.252528
$613$	32.3862	1.30807	0.654034	−	0.756465i	$-0.273075\pi$
$613$	32.3862	1.30807	0.654034	+	0.756465i	$0.273075\pi$
$614$	−1.91738	−0.0773792
$615$	−16.5580	−0.667682
$616$	−0.248394	−0.0100081
$617$	40.2542	1.62057	0.810287	−	0.586034i	$-0.199311\pi$
$617$	40.2542	1.62057	0.810287	+	0.586034i	$0.199311\pi$
$618$	40.3426	1.62282
$619$	37.7354	1.51671	0.758357	−	0.651839i	$-0.226002\pi$
$619$	37.7354	1.51671	0.758357	+	0.651839i	$0.226002\pi$
$620$	−0.121180	−0.00486672
$621$	3.13798	0.125923
$622$	2.28986	0.0918149
$623$	−7.30794	−0.292786
$624$	−1.02977	−0.0412237
$625$	−8.97286	−0.358914
$626$	−12.8454	−0.513407
$627$	−2.14078	−0.0854946
$628$	7.41881	0.296043
$629$	0.768417	0.0306388
$630$	−6.40938	−0.255356
$631$	−25.7914	−1.02674	−0.513369	−	0.858168i	$-0.671603\pi$
$631$	−25.7914	−1.02674	−0.513369	+	0.858168i	$0.671603\pi$
$632$	7.31985	0.291168
$633$	−33.6680	−1.33818
$634$	−2.01283	−0.0799397
$635$	2.91891	0.115833
$636$	−1.72589	−0.0684359
$637$	−2.66802	−0.105711
$638$	3.46862	0.137324
$639$	−14.5533	−0.575720
$640$	3.49569	0.138179
$641$	−26.0187	−1.02768	−0.513838	−	0.857887i	$-0.671777\pi$
$641$	−26.0187	−1.02768	−0.513838	+	0.857887i	$0.671777\pi$
$642$	40.6964	1.60616
$643$	−0.311293	−0.0122762	−0.00613810	−	0.999981i	$-0.501954\pi$
$643$	−0.311293	−0.0122762	−0.00613810	+	0.999981i	$0.501954\pi$
$644$	0.693354	0.0273220
$645$	3.16452	0.124603
$646$	−2.57625	−0.101361
$647$	27.6951	1.08881	0.544403	−	0.838824i	$-0.316756\pi$
$647$	27.6951	1.08881	0.544403	+	0.838824i	$0.316756\pi$
$648$	5.82465	0.228814
$649$	−1.26133	−0.0495113
$650$	−2.84500	−0.111590
$651$	0.0433766	0.00170006
$652$	−19.8529	−0.777500
$653$	−19.7464	−0.772736	−0.386368	−	0.922345i	$-0.626271\pi$
$653$	−19.7464	−0.772736	−0.386368	+	0.922345i	$0.626271\pi$
$654$	−10.5743	−0.413488
$655$	58.8619	2.29992
$656$	−1.81254	−0.0707678
$657$	−18.0602	−0.704594
$658$	6.47676	0.252490
$659$	10.9891	0.428075	0.214037	−	0.976825i	$-0.431339\pi$
$659$	10.9891	0.428075	0.214037	+	0.976825i	$0.431339\pi$
$660$	−4.73904	−0.184467
$661$	39.8747	1.55095	0.775473	−	0.631381i	$-0.217512\pi$
$661$	39.8747	1.55095	0.775473	+	0.631381i	$0.217512\pi$
$662$	−23.5787	−0.916412
$663$	1.68001	0.0652463
$664$	1.54698	0.0600346
$665$	−2.64313	−0.102496
$666$	1.80358	0.0698873
$667$	−9.68210	−0.374892
$668$	2.89092	0.111853
$669$	37.5622	1.45224
$670$	−52.7403	−2.03754
$671$	3.41623	0.131882
$672$	−1.25129	−0.0482694
$673$	1.84249	0.0710227	0.0355114	−	0.999369i	$-0.488694\pi$
$673$	1.84249	0.0710227	0.0355114	+	0.999369i	$0.488694\pi$
$674$	26.4651	1.01940
$675$	−15.6457	−0.602203
$676$	−12.8447	−0.494028
$677$	5.72080	0.219868	0.109934	−	0.993939i	$-0.464936\pi$
$677$	5.72080	0.219868	0.109934	+	0.993939i	$0.464936\pi$
$678$	42.6547	1.63814
$679$	−2.96760	−0.113886
$680$	−5.70304	−0.218702
$681$	−67.4352	−2.58412
$682$	0.0179833	0.000688618 0
$683$	−3.41671	−0.130737	−0.0653684	−	0.997861i	$-0.520822\pi$
$683$	−3.41671	−0.130737	−0.0653684	+	0.997861i	$0.520822\pi$
$684$	−6.04683	−0.231206
$685$	70.2622	2.68458
$686$	−6.59367	−0.251748
$687$	25.6513	0.978658
$688$	0.346409	0.0132067
$689$	0.260243	0.00991447
$690$	13.2283	0.503593
$691$	39.0725	1.48639	0.743194	−	0.669076i	$-0.233310\pi$
$691$	39.0725	1.48639	0.743194	+	0.669076i	$0.233310\pi$
$692$	−10.7517	−0.408718
$693$	0.951161	0.0361316
$694$	13.2596	0.503326
$695$	31.1151	1.18026
$696$	17.4732	0.662318
$697$	2.95707	0.112007
$698$	−13.0888	−0.495417
$699$	−71.6731	−2.71093
$700$	−3.45700	−0.130662
$701$	23.3894	0.883404	0.441702	−	0.897162i	$-0.354375\pi$
$701$	23.3894	0.883404	0.441702	+	0.897162i	$0.354375\pi$
$702$	0.853923	0.0322292
$703$	0.743770	0.0280518
$704$	−0.518766	−0.0195517
$705$	123.568	4.65385
$706$	−13.9656	−0.525604
$707$	4.49062	0.168887
$708$	−6.35393	−0.238795
$709$	2.90057	0.108933	0.0544665	−	0.998516i	$-0.482654\pi$
$709$	2.90057	0.108933	0.0544665	+	0.998516i	$0.482654\pi$
$710$	−13.2856	−0.498602
$711$	−28.0295	−1.05119
$712$	−15.2625	−0.571985
$713$	−0.0501977	−0.00187992
$714$	2.04141	0.0763978
$715$	0.714591	0.0267242
$716$	−1.79236	−0.0669836
$717$	31.1481	1.16325
$718$	−26.5440	−0.990615
$719$	48.8678	1.82246	0.911231	−	0.411896i	$-0.135133\pi$
$719$	48.8678	1.82246	0.911231	+	0.411896i	$0.135133\pi$
$720$	−13.3858	−0.498861
$721$	−7.39176	−0.275284
$722$	16.5064	0.614304
$723$	9.81446	0.365004
$724$	−9.37633	−0.348468
$725$	48.2741	1.79286
$726$	−28.0428	−1.04077
$727$	−10.0723	−0.373559	−0.186780	−	0.982402i	$-0.559805\pi$
$727$	−10.0723	−0.373559	−0.186780	+	0.982402i	$0.559805\pi$
$728$	0.188679	0.00699290
$729$	−39.2932	−1.45530
$730$	−16.4870	−0.610212
$731$	−0.565148	−0.0209027
$732$	17.2093	0.636073
$733$	−29.4406	−1.08741	−0.543706	−	0.839276i	$-0.682979\pi$
$733$	−29.4406	−1.08741	−0.543706	+	0.839276i	$0.682979\pi$
$734$	−16.0040	−0.590717
$735$	−61.8522	−2.28145
$736$	1.44805	0.0533759
$737$	7.82674	0.288302
$738$	6.94065	0.255489
$739$	8.37310	0.308009	0.154005	−	0.988070i	$-0.450783\pi$
$739$	8.37310	0.308009	0.154005	+	0.988070i	$0.450783\pi$
$740$	1.64648	0.0605258
$741$	1.62613	0.0597373
$742$	0.316225	0.0116090
$743$	−6.24975	−0.229281	−0.114641	−	0.993407i	$-0.536572\pi$
$743$	−6.24975	−0.229281	−0.114641	+	0.993407i	$0.536572\pi$
$744$	0.0905911	0.00332123
$745$	53.9118	1.97517
$746$	28.3811	1.03911
$747$	−5.92376	−0.216739
$748$	0.846339	0.0309452
$749$	−7.45658	−0.272458
$750$	−20.2790	−0.740484
$751$	19.6809	0.718166	0.359083	−	0.933306i	$-0.383089\pi$
$751$	19.6809	0.718166	0.359083	+	0.933306i	$0.383089\pi$
$752$	13.5266	0.493263
$753$	59.4234	2.16551
$754$	−2.63474	−0.0959517
$755$	83.1287	3.02536
$756$	1.03761	0.0377377
$757$	−43.2565	−1.57219	−0.786093	−	0.618109i	$-0.787899\pi$
$757$	−43.2565	−1.57219	−0.786093	+	0.618109i	$0.787899\pi$
$758$	−36.9387	−1.34167
$759$	−1.96310	−0.0712559
$760$	−5.52012	−0.200236
$761$	−29.2839	−1.06154	−0.530771	−	0.847515i	$-0.678098\pi$
$761$	−29.2839	−1.06154	−0.530771	+	0.847515i	$0.678098\pi$
$762$	−2.18209	−0.0790489
$763$	1.93748	0.0701414
$764$	−8.09957	−0.293032
$765$	21.8383	0.789566
$766$	−14.6807	−0.530434
$767$	0.958096	0.0345948
$768$	−2.61328	−0.0942987
$769$	−25.1196	−0.905836	−0.452918	−	0.891552i	$-0.649617\pi$
$769$	−25.1196	−0.905836	−0.452918	+	0.891552i	$0.649617\pi$
$770$	0.868310	0.0312917
$771$	−41.1779	−1.48299
$772$	−15.3567	−0.552700
$773$	−26.1489	−0.940511	−0.470256	−	0.882530i	$-0.655838\pi$
$773$	−26.1489	−0.940511	−0.470256	+	0.882530i	$0.655838\pi$
$774$	−1.32648	−0.0476794
$775$	0.250281	0.00899037
$776$	−6.19777	−0.222487
$777$	−0.589359	−0.0211431
$778$	−8.06683	−0.289210
$779$	2.86222	0.102550
$780$	3.59975	0.128892
$781$	1.97161	0.0705497
$782$	−2.36242	−0.0844801
$783$	−14.4894	−0.517809
$784$	−6.77073	−0.241812
$785$	−25.9339	−0.925620
$786$	−44.0035	−1.56955
$787$	19.9910	0.712602	0.356301	−	0.934371i	$-0.384038\pi$
$787$	19.9910	0.712602	0.356301	+	0.934371i	$0.384038\pi$
$788$	7.45842	0.265695
$789$	9.73602	0.346612
$790$	−25.5879	−0.910378
$791$	−7.81539	−0.277883
$792$	1.98648	0.0705864
$793$	−2.59495	−0.0921495
$794$	31.6162	1.12202
$795$	6.03317	0.213974
$796$	1.82888	0.0648230
$797$	−45.4739	−1.61077	−0.805385	−	0.592752i	$-0.798041\pi$
$797$	−45.4739	−1.61077	−0.805385	+	0.592752i	$0.798041\pi$
$798$	1.97593	0.0699472
$799$	−22.0679	−0.780706
$800$	−7.21987	−0.255261
$801$	58.4436	2.06500
$802$	−2.91703	−0.103004
$803$	2.44670	0.0863421
$804$	39.4272	1.39049
$805$	−2.42375	−0.0854260
$806$	−0.0136600	−0.000481155 0
$807$	30.5999	1.07717
$808$	9.37856	0.329936
$809$	5.29557	0.186182	0.0930912	−	0.995658i	$-0.470325\pi$
$809$	5.29557	0.186182	0.0930912	+	0.995658i	$0.470325\pi$
$810$	−20.3612	−0.715419
$811$	38.0242	1.33521	0.667605	−	0.744516i	$-0.267320\pi$
$811$	38.0242	1.33521	0.667605	+	0.744516i	$0.267320\pi$
$812$	−3.20151	−0.112351
$813$	−47.0129	−1.64881
$814$	−0.244340	−0.00856411
$815$	69.3997	2.43096
$816$	4.26343	0.149250
$817$	−0.547021	−0.0191378
$818$	−28.1151	−0.983023
$819$	−0.722496	−0.0252461
$820$	6.33609	0.221266
$821$	−0.494361	−0.0172533	−0.00862665	−	0.999963i	$-0.502746\pi$
$821$	−0.494361	−0.0172533	−0.00862665	+	0.999963i	$0.502746\pi$
$822$	−52.5260	−1.83206
$823$	−20.8898	−0.728171	−0.364085	−	0.931366i	$-0.618618\pi$
$823$	−20.8898	−0.728171	−0.364085	+	0.931366i	$0.618618\pi$
$824$	−15.4375	−0.537792
$825$	9.78783	0.340768
$826$	1.16420	0.0405076
$827$	−41.5104	−1.44346	−0.721728	−	0.692176i	$-0.756652\pi$
$827$	−41.5104	−1.44346	−0.721728	+	0.692176i	$0.756652\pi$
$828$	−5.54494	−0.192700
$829$	−45.4324	−1.57793	−0.788967	−	0.614436i	$-0.789384\pi$
$829$	−45.4324	−1.57793	−0.788967	+	0.614436i	$0.789384\pi$
$830$	−5.40777	−0.187707
$831$	54.2450	1.88174
$832$	0.394051	0.0136613
$833$	11.0461	0.382725
$834$	−23.2608	−0.805454
$835$	−10.1058	−0.349724
$836$	0.819193	0.0283324
$837$	−0.0751216	−0.00259658
$838$	34.8537	1.20400
$839$	12.5944	0.434806	0.217403	−	0.976082i	$-0.430241\pi$
$839$	12.5944	0.434806	0.217403	+	0.976082i	$0.430241\pi$
$840$	4.37411	0.150921
$841$	15.7065	0.541602
$842$	25.8122	0.889547
$843$	−71.2229	−2.45305
$844$	12.8834	0.443465
$845$	44.9012	1.54465
$846$	−51.7964	−1.78080
$847$	5.13814	0.176548
$848$	0.660429	0.0226792
$849$	−45.9653	−1.57752
$850$	11.7788	0.404011
$851$	0.682037	0.0233799
$852$	9.93198	0.340264
$853$	13.0591	0.447135	0.223567	−	0.974688i	$-0.428230\pi$
$853$	13.0591	0.447135	0.223567	+	0.974688i	$0.428230\pi$
$854$	−3.15317	−0.107899
$855$	21.1379	0.722899
$856$	−15.5729	−0.532271
$857$	−39.1314	−1.33670	−0.668352	−	0.743846i	$-0.733000\pi$
$857$	−39.1314	−1.33670	−0.668352	+	0.743846i	$0.733000\pi$
$858$	−0.534208	−0.0182376
$859$	−38.4392	−1.31153	−0.655763	−	0.754966i	$-0.727653\pi$
$859$	−38.4392	−1.31153	−0.655763	+	0.754966i	$0.727653\pi$
$860$	−1.21094	−0.0412926
$861$	−2.26801	−0.0772934
$862$	−16.4844	−0.561463
$863$	−4.04441	−0.137673	−0.0688367	−	0.997628i	$-0.521929\pi$
$863$	−4.04441	−0.137673	−0.0688367	+	0.997628i	$0.521929\pi$
$864$	2.16703	0.0737240
$865$	37.5846	1.27791
$866$	−36.0861	−1.22626
$867$	37.4702	1.27255
$868$	−0.0165985	−0.000563391 0
$869$	3.79729	0.128814
$870$	−61.0808	−2.07083
$871$	−5.94515	−0.201444
$872$	4.04637	0.137028
$873$	23.7327	0.803232
$874$	−2.28665	−0.0773471
$875$	3.71561	0.125611
$876$	12.3252	0.416431
$877$	39.3482	1.32870	0.664348	−	0.747424i	$-0.268709\pi$
$877$	39.3482	1.32870	0.664348	+	0.747424i	$0.268709\pi$
$878$	−12.2932	−0.414875
$879$	76.5372	2.58154
$880$	1.81344	0.0611312
$881$	−28.2778	−0.952703	−0.476351	−	0.879255i	$-0.658041\pi$
$881$	−28.2778	−0.952703	−0.476351	+	0.879255i	$0.658041\pi$
$882$	25.9268	0.872999
$883$	18.9825	0.638813	0.319407	−	0.947618i	$-0.396516\pi$
$883$	18.9825	0.638813	0.319407	+	0.947618i	$0.396516\pi$
$884$	−0.642875	−0.0216222
$885$	22.2114	0.746627
$886$	10.7849	0.362325
$887$	16.8953	0.567289	0.283645	−	0.958929i	$-0.408456\pi$
$887$	16.8953	0.567289	0.283645	+	0.958929i	$0.408456\pi$
$888$	−1.23086	−0.0413050
$889$	0.399813	0.0134093
$890$	53.3529	1.78839
$891$	3.02163	0.101228
$892$	−14.3736	−0.481263
$893$	−21.3601	−0.714787
$894$	−40.3029	−1.34793
$895$	6.26554	0.209434
$896$	0.478818	0.0159962
$897$	1.49116	0.0497883
$898$	34.6427	1.15604
$899$	0.231785	0.00773045
$900$	27.6466	0.921553
$901$	−1.07746	−0.0358953
$902$	−0.940284	−0.0313080
$903$	0.433456	0.0144245
$904$	−16.3223	−0.542871
$905$	32.7768	1.08954
$906$	−62.1447	−2.06462
$907$	0.764870	0.0253971	0.0126986	−	0.999919i	$-0.495958\pi$
$907$	0.764870	0.0253971	0.0126986	+	0.999919i	$0.495958\pi$
$908$	25.8048	0.856362
$909$	−35.9127	−1.19115
$910$	−0.659563	−0.0218643
$911$	10.3890	0.344202	0.172101	−	0.985079i	$-0.444944\pi$
$911$	10.3890	0.344202	0.172101	+	0.985079i	$0.444944\pi$
$912$	4.12669	0.136648
$913$	0.802521	0.0265596
$914$	−10.9190	−0.361169
$915$	−60.1583	−1.98877
$916$	−9.81575	−0.324321
$917$	8.06252	0.266248
$918$	−3.53540	−0.116686
$919$	−31.8574	−1.05088	−0.525439	−	0.850831i	$-0.676099\pi$
$919$	−31.8574	−1.05088	−0.525439	+	0.850831i	$0.676099\pi$
$920$	−5.06195	−0.166888
$921$	−5.01066	−0.165107
$922$	12.4177	0.408955
$923$	−1.49762	−0.0492949
$924$	−0.649124	−0.0213546
$925$	−3.40058	−0.111810
$926$	10.9578	0.360095
$927$	59.1140	1.94156
$928$	−6.68629	−0.219488
$929$	35.6028	1.16809	0.584046	−	0.811721i	$-0.301469\pi$
$929$	35.6028	1.16809	0.584046	+	0.811721i	$0.301469\pi$
$930$	−0.316679	−0.0103843
$931$	10.6918	0.350410
$932$	27.4265	0.898384
$933$	5.98404	0.195909
$934$	−1.70410	−0.0557597
$935$	−2.95854	−0.0967547
$936$	−1.50892	−0.0493205
$937$	−20.9413	−0.684122	−0.342061	−	0.939678i	$-0.611125\pi$
$937$	−20.9413	−0.684122	−0.342061	+	0.939678i	$0.611125\pi$
$938$	−7.22404	−0.235873
$939$	−33.5688	−1.09547
$940$	−47.2847	−1.54226
$941$	−22.3639	−0.729043	−0.364522	−	0.931195i	$-0.618767\pi$
$941$	−22.3639	−0.729043	−0.364522	+	0.931195i	$0.618767\pi$
$942$	19.3874	0.631677
$943$	2.62466	0.0854705
$944$	2.43140	0.0791353
$945$	−3.62718	−0.117992
$946$	0.179705	0.00584271
$947$	36.8400	1.19714	0.598569	−	0.801071i	$-0.295736\pi$
$947$	36.8400	1.19714	0.598569	+	0.801071i	$0.295736\pi$
$948$	19.1288	0.621275
$949$	−1.85850	−0.0603294
$950$	11.4010	0.369899
$951$	−5.26009	−0.170570
$952$	−0.781167	−0.0253178
$953$	38.3828	1.24334	0.621671	−	0.783279i	$-0.286454\pi$
$953$	38.3828	1.24334	0.621671	+	0.783279i	$0.286454\pi$
$954$	−2.52894	−0.0818775
$955$	28.3136	0.916206
$956$	−11.9191	−0.385493
$957$	9.06447	0.293013
$958$	12.8413	0.414885
$959$	9.62407	0.310777
$960$	9.13523	0.294838
$961$	−30.9988	−0.999961
$962$	0.185599	0.00598396
$963$	59.6323	1.92163
$964$	−3.75561	−0.120960
$965$	53.6823	1.72809
$966$	1.81193	0.0582978
$967$	19.3292	0.621586	0.310793	−	0.950478i	$-0.399405\pi$
$967$	19.3292	0.621586	0.310793	+	0.950478i	$0.399405\pi$
$968$	10.7309	0.344904
$969$	−6.73248	−0.216278
$970$	21.6655	0.695637
$971$	−18.8060	−0.603512	−0.301756	−	0.953385i	$-0.597573\pi$
$971$	−18.8060	−0.603512	−0.301756	+	0.953385i	$0.597573\pi$
$972$	21.7225	0.696751
$973$	4.26195	0.136632
$974$	−12.2065	−0.391120
$975$	−7.43478	−0.238104
$976$	−6.58531	−0.210791
$977$	−25.7961	−0.825290	−0.412645	−	0.910892i	$-0.635395\pi$
$977$	−25.7961	−0.825290	−0.412645	+	0.910892i	$0.635395\pi$
$978$	−51.8812	−1.65898
$979$	−7.91764	−0.253049
$980$	23.6684	0.756059
$981$	−15.4945	−0.494702
$982$	8.79930	0.280797
$983$	−32.5300	−1.03755	−0.518773	−	0.854912i	$-0.673611\pi$
$983$	−32.5300	−1.03755	−0.518773	+	0.854912i	$0.673611\pi$
$984$	−4.73668	−0.151000
$985$	−26.0723	−0.830734
$986$	10.9083	0.347392
$987$	16.9256	0.538747
$988$	−0.622255	−0.0197966
$989$	−0.501618	−0.0159505
$990$	−6.94411	−0.220698
$991$	44.3905	1.41011	0.705055	−	0.709153i	$-0.250922\pi$
$991$	44.3905	1.41011	0.705055	+	0.709153i	$0.250922\pi$
$992$	−0.0346656	−0.00110064
$993$	−61.6177	−1.95538
$994$	−1.81978	−0.0577200
$995$	−6.39320	−0.202678
$996$	4.04270	0.128098
$997$	−49.4824	−1.56712	−0.783562	−	0.621314i	$-0.786599\pi$
$997$	−49.4824	−1.56712	−0.783562	+	0.621314i	$0.786599\pi$
$998$	−23.9035	−0.756651
$999$	1.02068	0.0322928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.8	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.61328 q^{3} +1.00000 q^{4} -3.49569 q^{5} +2.61328 q^{6} -0.478818 q^{7} -1.00000 q^{8} +3.82924 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.61328 q^{3} +1.00000 q^{4} -3.49569 q^{5} +2.61328 q^{6} -0.478818 q^{7} -1.00000 q^{8} +3.82924 q^{9} +3.49569 q^{10} -0.518766 q^{11} -2.61328 q^{12} +0.394051 q^{13} +0.478818 q^{14} +9.13523 q^{15} +1.00000 q^{16} -1.63145 q^{17} -3.82924 q^{18} -1.57912 q^{19} -3.49569 q^{20} +1.25129 q^{21} +0.518766 q^{22} -1.44805 q^{23} +2.61328 q^{24} +7.21987 q^{25} -0.394051 q^{26} -2.16703 q^{27} -0.478818 q^{28} +6.68629 q^{29} -9.13523 q^{30} +0.0346656 q^{31} -1.00000 q^{32} +1.35568 q^{33} +1.63145 q^{34} +1.67380 q^{35} +3.82924 q^{36} -0.471003 q^{37} +1.57912 q^{38} -1.02977 q^{39} +3.49569 q^{40} -1.81254 q^{41} -1.25129 q^{42} +0.346409 q^{43} -0.518766 q^{44} -13.3858 q^{45} +1.44805 q^{46} +13.5266 q^{47} -2.61328 q^{48} -6.77073 q^{49} -7.21987 q^{50} +4.26343 q^{51} +0.394051 q^{52} +0.660429 q^{53} +2.16703 q^{54} +1.81344 q^{55} +0.478818 q^{56} +4.12669 q^{57} -6.68629 q^{58} +2.43140 q^{59} +9.13523 q^{60} -6.58531 q^{61} -0.0346656 q^{62} -1.83351 q^{63} +1.00000 q^{64} -1.37748 q^{65} -1.35568 q^{66} -15.0872 q^{67} -1.63145 q^{68} +3.78417 q^{69} -1.67380 q^{70} -3.80058 q^{71} -3.82924 q^{72} -4.71638 q^{73} +0.471003 q^{74} -18.8675 q^{75} -1.57912 q^{76} +0.248394 q^{77} +1.02977 q^{78} -7.31985 q^{79} -3.49569 q^{80} -5.82465 q^{81} +1.81254 q^{82} -1.54698 q^{83} +1.25129 q^{84} +5.70304 q^{85} -0.346409 q^{86} -17.4732 q^{87} +0.518766 q^{88} +15.2625 q^{89} +13.3858 q^{90} -0.188679 q^{91} -1.44805 q^{92} -0.0905911 q^{93} -13.5266 q^{94} +5.52012 q^{95} +2.61328 q^{96} +6.19777 q^{97} +6.77073 q^{98} -1.98648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 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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