LMFDB - Embedded newform 8002.2.a.d.1.35

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:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.35
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.584396 q^{3} +1.00000 q^{4} -0.560788 q^{5} -0.584396 q^{6} +3.93814 q^{7} +1.00000 q^{8} -2.65848 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.584396 q^{3} +1.00000 q^{4} -0.560788 q^{5} -0.584396 q^{6} +3.93814 q^{7} +1.00000 q^{8} -2.65848 q^{9} -0.560788 q^{10} -4.85646 q^{11} -0.584396 q^{12} -0.127690 q^{13} +3.93814 q^{14} +0.327723 q^{15} +1.00000 q^{16} -2.19863 q^{17} -2.65848 q^{18} +3.03212 q^{19} -0.560788 q^{20} -2.30144 q^{21} -4.85646 q^{22} +3.99210 q^{23} -0.584396 q^{24} -4.68552 q^{25} -0.127690 q^{26} +3.30679 q^{27} +3.93814 q^{28} +6.10879 q^{29} +0.327723 q^{30} -10.2659 q^{31} +1.00000 q^{32} +2.83810 q^{33} -2.19863 q^{34} -2.20846 q^{35} -2.65848 q^{36} +4.45107 q^{37} +3.03212 q^{38} +0.0746213 q^{39} -0.560788 q^{40} -9.60494 q^{41} -2.30144 q^{42} +11.1038 q^{43} -4.85646 q^{44} +1.49085 q^{45} +3.99210 q^{46} -11.6896 q^{47} -0.584396 q^{48} +8.50896 q^{49} -4.68552 q^{50} +1.28487 q^{51} -0.127690 q^{52} +0.463797 q^{53} +3.30679 q^{54} +2.72345 q^{55} +3.93814 q^{56} -1.77196 q^{57} +6.10879 q^{58} -2.82915 q^{59} +0.327723 q^{60} +6.32064 q^{61} -10.2659 q^{62} -10.4695 q^{63} +1.00000 q^{64} +0.0716068 q^{65} +2.83810 q^{66} -6.62825 q^{67} -2.19863 q^{68} -2.33297 q^{69} -2.20846 q^{70} -1.58179 q^{71} -2.65848 q^{72} -8.61849 q^{73} +4.45107 q^{74} +2.73820 q^{75} +3.03212 q^{76} -19.1254 q^{77} +0.0746213 q^{78} +9.09881 q^{79} -0.560788 q^{80} +6.04297 q^{81} -9.60494 q^{82} -3.52906 q^{83} -2.30144 q^{84} +1.23296 q^{85} +11.1038 q^{86} -3.56995 q^{87} -4.85646 q^{88} -5.85365 q^{89} +1.49085 q^{90} -0.502860 q^{91} +3.99210 q^{92} +5.99934 q^{93} -11.6896 q^{94} -1.70038 q^{95} -0.584396 q^{96} +1.91743 q^{97} +8.50896 q^{98} +12.9108 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.584396	−0.337401	−0.168701	−	0.985667i	$-0.553957\pi$
$3$	−0.584396	−0.337401	−0.168701	+	0.985667i	$0.553957\pi$
$4$	1.00000	0.500000
$5$	−0.560788	−0.250792	−0.125396	−	0.992107i	$-0.540020\pi$
$5$	−0.560788	−0.250792	−0.125396	+	0.992107i	$0.540020\pi$
$6$	−0.584396	−0.238579
$7$	3.93814	1.48848	0.744239	−	0.667914i	$-0.232812\pi$
$7$	3.93814	1.48848	0.744239	+	0.667914i	$0.232812\pi$
$8$	1.00000	0.353553
$9$	−2.65848	−0.886160
$10$	−0.560788	−0.177337
$11$	−4.85646	−1.46428	−0.732139	−	0.681155i	$-0.761478\pi$
$11$	−4.85646	−1.46428	−0.732139	+	0.681155i	$0.761478\pi$
$12$	−0.584396	−0.168701
$13$	−0.127690	−0.0354147	−0.0177074	−	0.999843i	$-0.505637\pi$
$13$	−0.127690	−0.0354147	−0.0177074	+	0.999843i	$0.505637\pi$
$14$	3.93814	1.05251
$15$	0.327723	0.0846176
$16$	1.00000	0.250000
$17$	−2.19863	−0.533245	−0.266623	−	0.963801i	$-0.585908\pi$
$17$	−2.19863	−0.533245	−0.266623	+	0.963801i	$0.585908\pi$
$18$	−2.65848	−0.626610
$19$	3.03212	0.695617	0.347809	−	0.937566i	$-0.386926\pi$
$19$	3.03212	0.695617	0.347809	+	0.937566i	$0.386926\pi$
$20$	−0.560788	−0.125396
$21$	−2.30144	−0.502214
$22$	−4.85646	−1.03540
$23$	3.99210	0.832410	0.416205	−	0.909271i	$-0.363360\pi$
$23$	3.99210	0.832410	0.416205	+	0.909271i	$0.363360\pi$
$24$	−0.584396	−0.119289
$25$	−4.68552	−0.937103
$26$	−0.127690	−0.0250420
$27$	3.30679	0.636393
$28$	3.93814	0.744239
$29$	6.10879	1.13437	0.567187	−	0.823589i	$-0.308032\pi$
$29$	6.10879	1.13437	0.567187	+	0.823589i	$0.308032\pi$
$30$	0.327723	0.0598337
$31$	−10.2659	−1.84381	−0.921903	−	0.387420i	$-0.873366\pi$
$31$	−10.2659	−1.84381	−0.921903	+	0.387420i	$0.873366\pi$
$32$	1.00000	0.176777
$33$	2.83810	0.494050
$34$	−2.19863	−0.377061
$35$	−2.20846	−0.373299
$36$	−2.65848	−0.443080
$37$	4.45107	0.731751	0.365875	−	0.930664i	$-0.380770\pi$
$37$	4.45107	0.731751	0.365875	+	0.930664i	$0.380770\pi$
$38$	3.03212	0.491876
$39$	0.0746213	0.0119490
$40$	−0.560788	−0.0886684
$41$	−9.60494	−1.50004	−0.750020	−	0.661415i	$-0.769956\pi$
$41$	−9.60494	−1.50004	−0.750020	+	0.661415i	$0.769956\pi$
$42$	−2.30144	−0.355119
$43$	11.1038	1.69332	0.846660	−	0.532135i	$-0.178610\pi$
$43$	11.1038	1.69332	0.846660	+	0.532135i	$0.178610\pi$
$44$	−4.85646	−0.732139
$45$	1.49085	0.222242
$46$	3.99210	0.588603
$47$	−11.6896	−1.70511	−0.852554	−	0.522640i	$-0.824947\pi$
$47$	−11.6896	−1.70511	−0.852554	+	0.522640i	$0.824947\pi$
$48$	−0.584396	−0.0843503
$49$	8.50896	1.21557
$50$	−4.68552	−0.662632
$51$	1.28487	0.179918
$52$	−0.127690	−0.0177074
$53$	0.463797	0.0637074	0.0318537	−	0.999493i	$-0.489859\pi$
$53$	0.463797	0.0637074	0.0318537	+	0.999493i	$0.489859\pi$
$54$	3.30679	0.449998
$55$	2.72345	0.367230
$56$	3.93814	0.526256
$57$	−1.77196	−0.234702
$58$	6.10879	0.802123
$59$	−2.82915	−0.368324	−0.184162	−	0.982896i	$-0.558957\pi$
$59$	−2.82915	−0.368324	−0.184162	+	0.982896i	$0.558957\pi$
$60$	0.327723	0.0423088
$61$	6.32064	0.809276	0.404638	−	0.914477i	$-0.367398\pi$
$61$	6.32064	0.809276	0.404638	+	0.914477i	$0.367398\pi$
$62$	−10.2659	−1.30377
$63$	−10.4695	−1.31903
$64$	1.00000	0.125000
$65$	0.0716068	0.00888174
$66$	2.83810	0.349346
$67$	−6.62825	−0.809769	−0.404885	−	0.914368i	$-0.632688\pi$
$67$	−6.62825	−0.809769	−0.404885	+	0.914368i	$0.632688\pi$
$68$	−2.19863	−0.266623
$69$	−2.33297	−0.280856
$70$	−2.20846	−0.263962
$71$	−1.58179	−0.187724	−0.0938619	−	0.995585i	$-0.529921\pi$
$71$	−1.58179	−0.187724	−0.0938619	+	0.995585i	$0.529921\pi$
$72$	−2.65848	−0.313305
$73$	−8.61849	−1.00872	−0.504359	−	0.863494i	$-0.668271\pi$
$73$	−8.61849	−1.00872	−0.504359	+	0.863494i	$0.668271\pi$
$74$	4.45107	0.517426
$75$	2.73820	0.316180
$76$	3.03212	0.347809
$77$	−19.1254	−2.17955
$78$	0.0746213	0.00844920
$79$	9.09881	1.02370	0.511848	−	0.859076i	$-0.328961\pi$
$79$	9.09881	1.02370	0.511848	+	0.859076i	$0.328961\pi$
$80$	−0.560788	−0.0626980
$81$	6.04297	0.671441
$82$	−9.60494	−1.06069
$83$	−3.52906	−0.387364	−0.193682	−	0.981064i	$-0.562043\pi$
$83$	−3.52906	−0.387364	−0.193682	+	0.981064i	$0.562043\pi$
$84$	−2.30144	−0.251107
$85$	1.23296	0.133734
$86$	11.1038	1.19736
$87$	−3.56995	−0.382739
$88$	−4.85646	−0.517701
$89$	−5.85365	−0.620485	−0.310243	−	0.950657i	$-0.600410\pi$
$89$	−5.85365	−0.620485	−0.310243	+	0.950657i	$0.600410\pi$
$90$	1.49085	0.157149
$91$	−0.502860	−0.0527140
$92$	3.99210	0.416205
$93$	5.99934	0.622103
$94$	−11.6896	−1.20569
$95$	−1.70038	−0.174455
$96$	−0.584396	−0.0596447
$97$	1.91743	0.194686	0.0973430	−	0.995251i	$-0.468966\pi$
$97$	1.91743	0.194686	0.0973430	+	0.995251i	$0.468966\pi$
$98$	8.50896	0.859535
$99$	12.9108	1.29759
$100$	−4.68552	−0.468552
$101$	−16.5904	−1.65081	−0.825403	−	0.564544i	$-0.809052\pi$
$101$	−16.5904	−1.65081	−0.825403	+	0.564544i	$0.809052\pi$
$102$	1.28487	0.127221
$103$	−6.51494	−0.641936	−0.320968	−	0.947090i	$-0.604008\pi$
$103$	−6.51494	−0.641936	−0.320968	+	0.947090i	$0.604008\pi$
$104$	−0.127690	−0.0125210
$105$	1.29062	0.125951
$106$	0.463797	0.0450479
$107$	−12.1443	−1.17403	−0.587015	−	0.809576i	$-0.699697\pi$
$107$	−12.1443	−1.17403	−0.587015	+	0.809576i	$0.699697\pi$
$108$	3.30679	0.318196
$109$	−0.181587	−0.0173929	−0.00869645	−	0.999962i	$-0.502768\pi$
$109$	−0.181587	−0.0173929	−0.00869645	+	0.999962i	$0.502768\pi$
$110$	2.72345	0.259671
$111$	−2.60119	−0.246894
$112$	3.93814	0.372119
$113$	−20.3459	−1.91398	−0.956992	−	0.290113i	$-0.906307\pi$
$113$	−20.3459	−1.91398	−0.956992	+	0.290113i	$0.906307\pi$
$114$	−1.77196	−0.165959
$115$	−2.23872	−0.208762
$116$	6.10879	0.567187
$117$	0.339460	0.0313831
$118$	−2.82915	−0.260444
$119$	−8.65851	−0.793724
$120$	0.327723	0.0299168
$121$	12.5852	1.14411
$122$	6.32064	0.572244
$123$	5.61309	0.506115
$124$	−10.2659	−0.921903
$125$	5.43152	0.485810
$126$	−10.4695	−0.932695
$127$	5.01253	0.444790	0.222395	−	0.974957i	$-0.428613\pi$
$127$	5.01253	0.444790	0.222395	+	0.974957i	$0.428613\pi$
$128$	1.00000	0.0883883
$129$	−6.48904	−0.571328
$130$	0.0716068	0.00628034
$131$	−19.0779	−1.66684	−0.833422	−	0.552637i	$-0.813622\pi$
$131$	−19.0779	−1.66684	−0.833422	+	0.552637i	$0.813622\pi$
$132$	2.83810	0.247025
$133$	11.9409	1.03541
$134$	−6.62825	−0.572593
$135$	−1.85441	−0.159602
$136$	−2.19863	−0.188531
$137$	8.71966	0.744971	0.372486	−	0.928038i	$-0.378506\pi$
$137$	8.71966	0.744971	0.372486	+	0.928038i	$0.378506\pi$
$138$	−2.33297	−0.198595
$139$	−21.3904	−1.81431	−0.907156	−	0.420794i	$-0.861751\pi$
$139$	−21.3904	−1.81431	−0.907156	+	0.420794i	$0.861751\pi$
$140$	−2.20846	−0.186649
$141$	6.83137	0.575305
$142$	−1.58179	−0.132741
$143$	0.620120	0.0518570
$144$	−2.65848	−0.221540
$145$	−3.42574	−0.284492
$146$	−8.61849	−0.713271
$147$	−4.97261	−0.410134
$148$	4.45107	0.365875
$149$	−2.78509	−0.228163	−0.114082	−	0.993471i	$-0.536393\pi$
$149$	−2.78509	−0.228163	−0.114082	+	0.993471i	$0.536393\pi$
$150$	2.73820	0.223573
$151$	14.4004	1.17189	0.585943	−	0.810352i	$-0.300724\pi$
$151$	14.4004	1.17189	0.585943	+	0.810352i	$0.300724\pi$
$152$	3.03212	0.245938
$153$	5.84501	0.472541
$154$	−19.1254	−1.54117
$155$	5.75699	0.462412
$156$	0.0746213	0.00597449
$157$	−2.28093	−0.182038	−0.0910192	−	0.995849i	$-0.529012\pi$
$157$	−2.28093	−0.182038	−0.0910192	+	0.995849i	$0.529012\pi$
$158$	9.09881	0.723862
$159$	−0.271041	−0.0214949
$160$	−0.560788	−0.0443342
$161$	15.7215	1.23902
$162$	6.04297	0.474780
$163$	−2.95499	−0.231453	−0.115726	−	0.993281i	$-0.536920\pi$
$163$	−2.95499	−0.231453	−0.115726	+	0.993281i	$0.536920\pi$
$164$	−9.60494	−0.750020
$165$	−1.59157	−0.123904
$166$	−3.52906	−0.273908
$167$	−6.64375	−0.514108	−0.257054	−	0.966397i	$-0.582752\pi$
$167$	−6.64375	−0.514108	−0.257054	+	0.966397i	$0.582752\pi$
$168$	−2.30144	−0.177560
$169$	−12.9837	−0.998746
$170$	1.23296	0.0945641
$171$	−8.06085	−0.616428
$172$	11.1038	0.846660
$173$	11.2534	0.855577	0.427788	−	0.903879i	$-0.359293\pi$
$173$	11.2534	0.855577	0.427788	+	0.903879i	$0.359293\pi$
$174$	−3.56995	−0.270637
$175$	−18.4522	−1.39486
$176$	−4.85646	−0.366070
$177$	1.65334	0.124273
$178$	−5.85365	−0.438749
$179$	22.3923	1.67368	0.836841	−	0.547446i	$-0.184400\pi$
$179$	22.3923	1.67368	0.836841	+	0.547446i	$0.184400\pi$
$180$	1.49085	0.111121
$181$	−8.75738	−0.650931	−0.325465	−	0.945554i	$-0.605521\pi$
$181$	−8.75738	−0.650931	−0.325465	+	0.945554i	$0.605521\pi$
$182$	−0.502860	−0.0372745
$183$	−3.69376	−0.273051
$184$	3.99210	0.294302
$185$	−2.49611	−0.183517
$186$	5.99934	0.439893
$187$	10.6776	0.780820
$188$	−11.6896	−0.852554
$189$	13.0226	0.947257
$190$	−1.70038	−0.123359
$191$	−8.28381	−0.599395	−0.299698	−	0.954034i	$-0.596886\pi$
$191$	−8.28381	−0.599395	−0.299698	+	0.954034i	$0.596886\pi$
$192$	−0.584396	−0.0421752
$193$	5.93477	0.427194	0.213597	−	0.976922i	$-0.431482\pi$
$193$	5.93477	0.427194	0.213597	+	0.976922i	$0.431482\pi$
$194$	1.91743	0.137664
$195$	−0.0418468	−0.00299671
$196$	8.50896	0.607783
$197$	−8.31700	−0.592562	−0.296281	−	0.955101i	$-0.595746\pi$
$197$	−8.31700	−0.592562	−0.296281	+	0.955101i	$0.595746\pi$
$198$	12.9108	0.917532
$199$	−3.54217	−0.251098	−0.125549	−	0.992087i	$-0.540069\pi$
$199$	−3.54217	−0.251098	−0.125549	+	0.992087i	$0.540069\pi$
$200$	−4.68552	−0.331316
$201$	3.87352	0.273217
$202$	−16.5904	−1.16730
$203$	24.0573	1.68849
$204$	1.28487	0.0899588
$205$	5.38634	0.376198
$206$	−6.51494	−0.453917
$207$	−10.6129	−0.737649
$208$	−0.127690	−0.00885368
$209$	−14.7254	−1.01858
$210$	1.29062	0.0890611
$211$	−20.9005	−1.43885	−0.719426	−	0.694569i	$-0.755595\pi$
$211$	−20.9005	−1.43885	−0.719426	+	0.694569i	$0.755595\pi$
$212$	0.463797	0.0318537
$213$	0.924391	0.0633382
$214$	−12.1443	−0.830164
$215$	−6.22690	−0.424671
$216$	3.30679	0.224999
$217$	−40.4285	−2.74447
$218$	−0.181587	−0.0122986
$219$	5.03661	0.340343
$220$	2.72345	0.183615
$221$	0.280742	0.0188847
$222$	−2.60119	−0.174580
$223$	10.6413	0.712596	0.356298	−	0.934372i	$-0.384039\pi$
$223$	10.6413	0.712596	0.356298	+	0.934372i	$0.384039\pi$
$224$	3.93814	0.263128
$225$	12.4564	0.830424
$226$	−20.3459	−1.35339
$227$	−6.24929	−0.414780	−0.207390	−	0.978258i	$-0.566497\pi$
$227$	−6.24929	−0.414780	−0.207390	+	0.978258i	$0.566497\pi$
$228$	−1.77196	−0.117351
$229$	8.04511	0.531636	0.265818	−	0.964023i	$-0.414358\pi$
$229$	8.04511	0.531636	0.265818	+	0.964023i	$0.414358\pi$
$230$	−2.23872	−0.147617
$231$	11.1768	0.735382
$232$	6.10879	0.401062
$233$	12.7337	0.834215	0.417108	−	0.908857i	$-0.363044\pi$
$233$	12.7337	0.834215	0.417108	+	0.908857i	$0.363044\pi$
$234$	0.339460	0.0221912
$235$	6.55541	0.427628
$236$	−2.82915	−0.184162
$237$	−5.31731	−0.345396
$238$	−8.65851	−0.561248
$239$	−0.398618	−0.0257844	−0.0128922	−	0.999917i	$-0.504104\pi$
$239$	−0.398618	−0.0257844	−0.0128922	+	0.999917i	$0.504104\pi$
$240$	0.327723	0.0211544
$241$	6.34213	0.408532	0.204266	−	0.978915i	$-0.434519\pi$
$241$	6.34213	0.408532	0.204266	+	0.978915i	$0.434519\pi$
$242$	12.5852	0.809010
$243$	−13.4519	−0.862938
$244$	6.32064	0.404638
$245$	−4.77173	−0.304854
$246$	5.61309	0.357878
$247$	−0.387171	−0.0246351
$248$	−10.2659	−0.651884
$249$	2.06237	0.130697
$250$	5.43152	0.343520
$251$	−13.8330	−0.873130	−0.436565	−	0.899673i	$-0.643805\pi$
$251$	−13.8330	−0.873130	−0.436565	+	0.899673i	$0.643805\pi$
$252$	−10.4695	−0.659515
$253$	−19.3875	−1.21888
$254$	5.01253	0.314514
$255$	−0.720540	−0.0451219
$256$	1.00000	0.0625000
$257$	12.4761	0.778236	0.389118	−	0.921188i	$-0.372780\pi$
$257$	12.4761	0.778236	0.389118	+	0.921188i	$0.372780\pi$
$258$	−6.48904	−0.403990
$259$	17.5289	1.08920
$260$	0.0716068	0.00444087
$261$	−16.2401	−1.00524
$262$	−19.0779	−1.17864
$263$	2.30815	0.142326	0.0711632	−	0.997465i	$-0.477329\pi$
$263$	2.30815	0.142326	0.0711632	+	0.997465i	$0.477329\pi$
$264$	2.83810	0.174673
$265$	−0.260092	−0.0159773
$266$	11.9409	0.732146
$267$	3.42085	0.209352
$268$	−6.62825	−0.404885
$269$	−29.4858	−1.79778	−0.898890	−	0.438175i	$-0.855625\pi$
$269$	−29.4858	−1.79778	−0.898890	+	0.438175i	$0.855625\pi$
$270$	−1.85441	−0.112856
$271$	−9.32430	−0.566411	−0.283205	−	0.959059i	$-0.591398\pi$
$271$	−9.32430	−0.566411	−0.283205	+	0.959059i	$0.591398\pi$
$272$	−2.19863	−0.133311
$273$	0.293869	0.0177858
$274$	8.71966	0.526774
$275$	22.7550	1.37218
$276$	−2.33297	−0.140428
$277$	−3.42010	−0.205494	−0.102747	−	0.994708i	$-0.532763\pi$
$277$	−3.42010	−0.205494	−0.102747	+	0.994708i	$0.532763\pi$
$278$	−21.3904	−1.28291
$279$	27.2917	1.63391
$280$	−2.20846	−0.131981
$281$	9.59039	0.572115	0.286057	−	0.958212i	$-0.407655\pi$
$281$	9.59039	0.572115	0.286057	+	0.958212i	$0.407655\pi$
$282$	6.83137	0.406802
$283$	28.1245	1.67183	0.835915	−	0.548860i	$-0.184938\pi$
$283$	28.1245	1.67183	0.835915	+	0.548860i	$0.184938\pi$
$284$	−1.58179	−0.0938619
$285$	0.993695	0.0588614
$286$	0.620120	0.0366685
$287$	−37.8256	−2.23278
$288$	−2.65848	−0.156653
$289$	−12.1660	−0.715649
$290$	−3.42574	−0.201166
$291$	−1.12054	−0.0656873
$292$	−8.61849	−0.504359
$293$	18.6035	1.08683	0.543415	−	0.839464i	$-0.317131\pi$
$293$	18.6035	1.08683	0.543415	+	0.839464i	$0.317131\pi$
$294$	−4.97261	−0.290008
$295$	1.58655	0.0923728
$296$	4.45107	0.258713
$297$	−16.0593	−0.931857
$298$	−2.78509	−0.161336
$299$	−0.509750	−0.0294796
$300$	2.73820	0.158090
$301$	43.7285	2.52047
$302$	14.4004	0.828649
$303$	9.69536	0.556984
$304$	3.03212	0.173904
$305$	−3.54454	−0.202960
$306$	5.84501	0.334137
$307$	−27.5303	−1.57124	−0.785619	−	0.618710i	$-0.787656\pi$
$307$	−27.5303	−1.57124	−0.785619	+	0.618710i	$0.787656\pi$
$308$	−19.1254	−1.08977
$309$	3.80731	0.216590
$310$	5.75699	0.326975
$311$	8.48905	0.481370	0.240685	−	0.970603i	$-0.422628\pi$
$311$	8.48905	0.481370	0.240685	+	0.970603i	$0.422628\pi$
$312$	0.0746213	0.00422460
$313$	13.9384	0.787845	0.393922	−	0.919144i	$-0.371118\pi$
$313$	13.9384	0.787845	0.393922	+	0.919144i	$0.371118\pi$
$314$	−2.28093	−0.128721
$315$	5.87116	0.330802
$316$	9.09881	0.511848
$317$	28.0023	1.57277	0.786383	−	0.617739i	$-0.211951\pi$
$317$	28.0023	1.57277	0.786383	+	0.617739i	$0.211951\pi$
$318$	−0.271041	−0.0151992
$319$	−29.6671	−1.66104
$320$	−0.560788	−0.0313490
$321$	7.09706	0.396119
$322$	15.7215	0.876123
$323$	−6.66651	−0.370935
$324$	6.04297	0.335720
$325$	0.598292	0.0331873
$326$	−2.95499	−0.163662
$327$	0.106119	0.00586839
$328$	−9.60494	−0.530344
$329$	−46.0354	−2.53801
$330$	−1.59157	−0.0876132
$331$	5.02954	0.276449	0.138224	−	0.990401i	$-0.455861\pi$
$331$	5.02954	0.276449	0.138224	+	0.990401i	$0.455861\pi$
$332$	−3.52906	−0.193682
$333$	−11.8331	−0.648449
$334$	−6.64375	−0.363530
$335$	3.71704	0.203084
$336$	−2.30144	−0.125554
$337$	−11.4870	−0.625736	−0.312868	−	0.949797i	$-0.601290\pi$
$337$	−11.4870	−0.625736	−0.312868	+	0.949797i	$0.601290\pi$
$338$	−12.9837	−0.706220
$339$	11.8901	0.645781
$340$	1.23296	0.0668669
$341$	49.8559	2.69985
$342$	−8.06085	−0.435881
$343$	5.94251	0.320865
$344$	11.1038	0.598679
$345$	1.30830	0.0704366
$346$	11.2534	0.604984
$347$	−12.0999	−0.649559	−0.324780	−	0.945790i	$-0.605290\pi$
$347$	−12.0999	−0.649559	−0.324780	+	0.945790i	$0.605290\pi$
$348$	−3.56995	−0.191370
$349$	−6.25886	−0.335029	−0.167515	−	0.985870i	$-0.553574\pi$
$349$	−6.25886	−0.335029	−0.167515	+	0.985870i	$0.553574\pi$
$350$	−18.4522	−0.986313
$351$	−0.422243	−0.0225377
$352$	−4.85646	−0.258850
$353$	31.9690	1.70154	0.850770	−	0.525539i	$-0.176136\pi$
$353$	31.9690	1.70154	0.850770	+	0.525539i	$0.176136\pi$
$354$	1.65334	0.0878743
$355$	0.887048	0.0470796
$356$	−5.85365	−0.310243
$357$	5.06000	0.267803
$358$	22.3923	1.18347
$359$	−7.41873	−0.391545	−0.195773	−	0.980649i	$-0.562721\pi$
$359$	−7.41873	−0.391545	−0.195773	+	0.980649i	$0.562721\pi$
$360$	1.49085	0.0785744
$361$	−9.80622	−0.516117
$362$	−8.75738	−0.460278
$363$	−7.35477	−0.386025
$364$	−0.502860	−0.0263570
$365$	4.83315	0.252978
$366$	−3.69376	−0.193076
$367$	−12.9330	−0.675098	−0.337549	−	0.941308i	$-0.609598\pi$
$367$	−12.9330	−0.675098	−0.337549	+	0.941308i	$0.609598\pi$
$368$	3.99210	0.208103
$369$	25.5346	1.32928
$370$	−2.49611	−0.129766
$371$	1.82650	0.0948270
$372$	5.99934	0.311051
$373$	−10.9350	−0.566193	−0.283096	−	0.959091i	$-0.591362\pi$
$373$	−10.9350	−0.566193	−0.283096	+	0.959091i	$0.591362\pi$
$374$	10.6776	0.552123
$375$	−3.17416	−0.163913
$376$	−11.6896	−0.602846
$377$	−0.780029	−0.0401735
$378$	13.0226	0.669812
$379$	−25.6617	−1.31815	−0.659077	−	0.752075i	$-0.729053\pi$
$379$	−25.6617	−1.31815	−0.659077	+	0.752075i	$0.729053\pi$
$380$	−1.70038	−0.0872276
$381$	−2.92930	−0.150073
$382$	−8.28381	−0.423836
$383$	−3.72099	−0.190134	−0.0950669	−	0.995471i	$-0.530307\pi$
$383$	−3.72099	−0.190134	−0.0950669	+	0.995471i	$0.530307\pi$
$384$	−0.584396	−0.0298223
$385$	10.7253	0.546613
$386$	5.93477	0.302072
$387$	−29.5193	−1.50055
$388$	1.91743	0.0973430
$389$	15.2793	0.774693	0.387346	−	0.921934i	$-0.373392\pi$
$389$	15.2793	0.774693	0.387346	+	0.921934i	$0.373392\pi$
$390$	−0.0418468	−0.00211899
$391$	−8.77714	−0.443879
$392$	8.50896	0.429768
$393$	11.1491	0.562395
$394$	−8.31700	−0.419004
$395$	−5.10250	−0.256735
$396$	12.9108	0.648793
$397$	15.1873	0.762228	0.381114	−	0.924528i	$-0.375541\pi$
$397$	15.1873	0.762228	0.381114	+	0.924528i	$0.375541\pi$
$398$	−3.54217	−0.177553
$399$	−6.97824	−0.349349
$400$	−4.68552	−0.234276
$401$	8.04190	0.401593	0.200797	−	0.979633i	$-0.435647\pi$
$401$	8.04190	0.401593	0.200797	+	0.979633i	$0.435647\pi$
$402$	3.87352	0.193194
$403$	1.31085	0.0652979
$404$	−16.5904	−0.825403
$405$	−3.38882	−0.168392
$406$	24.0573	1.19394
$407$	−21.6164	−1.07149
$408$	1.28487	0.0636105
$409$	23.1580	1.14509	0.572545	−	0.819873i	$-0.305956\pi$
$409$	23.1580	1.14509	0.572545	+	0.819873i	$0.305956\pi$
$410$	5.38634	0.266012
$411$	−5.09574	−0.251354
$412$	−6.51494	−0.320968
$413$	−11.1416	−0.548242
$414$	−10.6129	−0.521597
$415$	1.97905	0.0971480
$416$	−0.127690	−0.00626050
$417$	12.5005	0.612151
$418$	−14.7254	−0.720243
$419$	−27.6656	−1.35155	−0.675777	−	0.737106i	$-0.736192\pi$
$419$	−27.6656	−1.35155	−0.675777	+	0.737106i	$0.736192\pi$
$420$	1.29062	0.0629757
$421$	−40.0705	−1.95291	−0.976457	−	0.215710i	$-0.930793\pi$
$421$	−40.0705	−1.95291	−0.976457	+	0.215710i	$0.930793\pi$
$422$	−20.9005	−1.01742
$423$	31.0767	1.51100
$424$	0.463797	0.0225240
$425$	10.3017	0.499706
$426$	0.924391	0.0447869
$427$	24.8916	1.20459
$428$	−12.1443	−0.587015
$429$	−0.362396	−0.0174966
$430$	−6.22690	−0.300288
$431$	−12.2836	−0.591680	−0.295840	−	0.955237i	$-0.595600\pi$
$431$	−12.2836	−0.591680	−0.295840	+	0.955237i	$0.595600\pi$
$432$	3.30679	0.159098
$433$	23.2722	1.11839	0.559196	−	0.829036i	$-0.311110\pi$
$433$	23.2722	1.11839	0.559196	+	0.829036i	$0.311110\pi$
$434$	−40.4285	−1.94063
$435$	2.00199	0.0959879
$436$	−0.181587	−0.00869645
$437$	12.1045	0.579039
$438$	5.03661	0.240659
$439$	−25.2111	−1.20326	−0.601631	−	0.798774i	$-0.705482\pi$
$439$	−25.2111	−1.20326	−0.601631	+	0.798774i	$0.705482\pi$
$440$	2.72345	0.129835
$441$	−22.6209	−1.07719
$442$	0.280742	0.0133535
$443$	23.1042	1.09771	0.548857	−	0.835916i	$-0.315063\pi$
$443$	23.1042	1.09771	0.548857	+	0.835916i	$0.315063\pi$
$444$	−2.60119	−0.123447
$445$	3.28266	0.155613
$446$	10.6413	0.503881
$447$	1.62759	0.0769826
$448$	3.93814	0.186060
$449$	−33.0528	−1.55986	−0.779930	−	0.625867i	$-0.784745\pi$
$449$	−33.0528	−1.55986	−0.779930	+	0.625867i	$0.784745\pi$
$450$	12.4564	0.587198
$451$	46.6460	2.19648
$452$	−20.3459	−0.956992
$453$	−8.41553	−0.395396
$454$	−6.24929	−0.293293
$455$	0.281998	0.0132203
$456$	−1.77196	−0.0829797
$457$	30.9278	1.44674	0.723371	−	0.690460i	$-0.242592\pi$
$457$	30.9278	1.44674	0.723371	+	0.690460i	$0.242592\pi$
$458$	8.04511	0.375923
$459$	−7.27041	−0.339354
$460$	−2.23872	−0.104381
$461$	−22.7585	−1.05997	−0.529985	−	0.848007i	$-0.677803\pi$
$461$	−22.7585	−1.05997	−0.529985	+	0.848007i	$0.677803\pi$
$462$	11.1768	0.519993
$463$	11.9167	0.553817	0.276909	−	0.960896i	$-0.410690\pi$
$463$	11.9167	0.553817	0.276909	+	0.960896i	$0.410690\pi$
$464$	6.10879	0.283593
$465$	−3.36436	−0.156018
$466$	12.7337	0.589879
$467$	−34.6898	−1.60525	−0.802627	−	0.596481i	$-0.796565\pi$
$467$	−34.6898	−1.60525	−0.802627	+	0.596481i	$0.796565\pi$
$468$	0.339460	0.0156916
$469$	−26.1030	−1.20532
$470$	6.55541	0.302378
$471$	1.33297	0.0614200
$472$	−2.82915	−0.130222
$473$	−53.9254	−2.47949
$474$	−5.31731	−0.244232
$475$	−14.2071	−0.651865
$476$	−8.65851	−0.396862
$477$	−1.23299	−0.0564549
$478$	−0.398618	−0.0182323
$479$	2.63821	0.120543	0.0602714	−	0.998182i	$-0.480803\pi$
$479$	2.63821	0.120543	0.0602714	+	0.998182i	$0.480803\pi$
$480$	0.327723	0.0149584
$481$	−0.568355	−0.0259148
$482$	6.34213	0.288876
$483$	−9.18756	−0.418048
$484$	12.5852	0.572056
$485$	−1.07527	−0.0488257
$486$	−13.4519	−0.610189
$487$	−12.0586	−0.546428	−0.273214	−	0.961953i	$-0.588087\pi$
$487$	−12.0586	−0.546428	−0.273214	+	0.961953i	$0.588087\pi$
$488$	6.32064	0.286122
$489$	1.72688	0.0780924
$490$	−4.77173	−0.215565
$491$	29.5821	1.33502	0.667510	−	0.744601i	$-0.267360\pi$
$491$	29.5821	1.33502	0.667510	+	0.744601i	$0.267360\pi$
$492$	5.61309	0.253058
$493$	−13.4309	−0.604899
$494$	−0.387171	−0.0174196
$495$	−7.24023	−0.325424
$496$	−10.2659	−0.460952
$497$	−6.22931	−0.279423
$498$	2.06237	0.0924169
$499$	40.5374	1.81470	0.907351	−	0.420374i	$-0.138101\pi$
$499$	40.5374	1.81470	0.907351	+	0.420374i	$0.138101\pi$
$500$	5.43152	0.242905
$501$	3.88258	0.173461
$502$	−13.8330	−0.617396
$503$	17.8840	0.797410	0.398705	−	0.917079i	$-0.369460\pi$
$503$	17.8840	0.797410	0.398705	+	0.917079i	$0.369460\pi$
$504$	−10.4695	−0.466348
$505$	9.30370	0.414009
$506$	−19.3875	−0.861879
$507$	7.58762	0.336978
$508$	5.01253	0.222395
$509$	−5.02324	−0.222651	−0.111326	−	0.993784i	$-0.535510\pi$
$509$	−5.02324	−0.222651	−0.111326	+	0.993784i	$0.535510\pi$
$510$	−0.720540	−0.0319060
$511$	−33.9408	−1.50145
$512$	1.00000	0.0441942
$513$	10.0266	0.442686
$514$	12.4761	0.550296
$515$	3.65350	0.160993
$516$	−6.48904	−0.285664
$517$	56.7702	2.49675
$518$	17.5289	0.770177
$519$	−6.57642	−0.288673
$520$	0.0716068	0.00314017
$521$	20.3667	0.892281	0.446141	−	0.894963i	$-0.352798\pi$
$521$	20.3667	0.892281	0.446141	+	0.894963i	$0.352798\pi$
$522$	−16.2401	−0.710810
$523$	5.19121	0.226996	0.113498	−	0.993538i	$-0.463794\pi$
$523$	5.19121	0.226996	0.113498	+	0.993538i	$0.463794\pi$
$524$	−19.0779	−0.833422
$525$	10.7834	0.470627
$526$	2.30815	0.100640
$527$	22.5708	0.983202
$528$	2.83810	0.123512
$529$	−7.06313	−0.307093
$530$	−0.260092	−0.0112977
$531$	7.52124	0.326394
$532$	11.9409	0.517705
$533$	1.22645	0.0531235
$534$	3.42085	0.148035
$535$	6.81036	0.294437
$536$	−6.62825	−0.286297
$537$	−13.0860	−0.564702
$538$	−29.4858	−1.27122
$539$	−41.3235	−1.77993
$540$	−1.85441	−0.0798012
$541$	9.68311	0.416309	0.208155	−	0.978096i	$-0.433254\pi$
$541$	9.68311	0.416309	0.208155	+	0.978096i	$0.433254\pi$
$542$	−9.32430	−0.400513
$543$	5.11778	0.219625
$544$	−2.19863	−0.0942654
$545$	0.101832	0.00436200
$546$	0.293869	0.0125764
$547$	13.4547	0.575280	0.287640	−	0.957739i	$-0.407129\pi$
$547$	13.4547	0.575280	0.287640	+	0.957739i	$0.407129\pi$
$548$	8.71966	0.372486
$549$	−16.8033	−0.717148
$550$	22.7550	0.970278
$551$	18.5226	0.789090
$552$	−2.33297	−0.0992977
$553$	35.8324	1.52375
$554$	−3.42010	−0.145306
$555$	1.45871	0.0619190
$556$	−21.3904	−0.907156
$557$	1.63805	0.0694062	0.0347031	−	0.999398i	$-0.488951\pi$
$557$	1.63805	0.0694062	0.0347031	+	0.999398i	$0.488951\pi$
$558$	27.2917	1.15535
$559$	−1.41784	−0.0599684
$560$	−2.20846	−0.0933246
$561$	−6.23992	−0.263450
$562$	9.59039	0.404546
$563$	42.0191	1.77090	0.885448	−	0.464739i	$-0.153852\pi$
$563$	42.0191	1.77090	0.885448	+	0.464739i	$0.153852\pi$
$564$	6.83137	0.287653
$565$	11.4098	0.480012
$566$	28.1245	1.18216
$567$	23.7981	0.999424
$568$	−1.58179	−0.0663704
$569$	−31.4022	−1.31645	−0.658224	−	0.752822i	$-0.728692\pi$
$569$	−31.4022	−1.31645	−0.658224	+	0.752822i	$0.728692\pi$
$570$	0.993695	0.0416213
$571$	−11.2682	−0.471560	−0.235780	−	0.971806i	$-0.575764\pi$
$571$	−11.2682	−0.471560	−0.235780	+	0.971806i	$0.575764\pi$
$572$	0.620120	0.0259285
$573$	4.84103	0.202237
$574$	−37.8256	−1.57881
$575$	−18.7051	−0.780055
$576$	−2.65848	−0.110770
$577$	−20.4344	−0.850697	−0.425349	−	0.905030i	$-0.639848\pi$
$577$	−20.4344	−0.850697	−0.425349	+	0.905030i	$0.639848\pi$
$578$	−12.1660	−0.506040
$579$	−3.46826	−0.144136
$580$	−3.42574	−0.142246
$581$	−13.8979	−0.576583
$582$	−1.12054	−0.0464479
$583$	−2.25241	−0.0932854
$584$	−8.61849	−0.356636
$585$	−0.190365	−0.00787064
$586$	18.6035	0.768504
$587$	19.3919	0.800388	0.400194	−	0.916430i	$-0.368943\pi$
$587$	19.3919	0.800388	0.400194	+	0.916430i	$0.368943\pi$
$588$	−4.97261	−0.205067
$589$	−31.1274	−1.28258
$590$	1.58655	0.0653174
$591$	4.86042	0.199931
$592$	4.45107	0.182938
$593$	5.41056	0.222185	0.111093	−	0.993810i	$-0.464565\pi$
$593$	5.41056	0.222185	0.111093	+	0.993810i	$0.464565\pi$
$594$	−16.0593	−0.658922
$595$	4.85559	0.199060
$596$	−2.78509	−0.114082
$597$	2.07003	0.0847207
$598$	−0.509750	−0.0208452
$599$	−25.4222	−1.03872	−0.519362	−	0.854554i	$-0.673830\pi$
$599$	−25.4222	−1.03872	−0.519362	+	0.854554i	$0.673830\pi$
$600$	2.73820	0.111786
$601$	−46.2446	−1.88636	−0.943178	−	0.332288i	$-0.892179\pi$
$601$	−46.2446	−1.88636	−0.943178	+	0.332288i	$0.892179\pi$
$602$	43.7285	1.78224
$603$	17.6211	0.717585
$604$	14.4004	0.585943
$605$	−7.05765	−0.286934
$606$	9.69536	0.393847
$607$	20.6946	0.839966	0.419983	−	0.907532i	$-0.362036\pi$
$607$	20.6946	0.839966	0.419983	+	0.907532i	$0.362036\pi$
$608$	3.03212	0.122969
$609$	−14.0590	−0.569699
$610$	−3.54454	−0.143514
$611$	1.49264	0.0603859
$612$	5.84501	0.236270
$613$	−11.5026	−0.464584	−0.232292	−	0.972646i	$-0.574622\pi$
$613$	−11.5026	−0.464584	−0.232292	+	0.972646i	$0.574622\pi$
$614$	−27.5303	−1.11103
$615$	−3.14775	−0.126930
$616$	−19.1254	−0.770586
$617$	−39.6494	−1.59622	−0.798111	−	0.602510i	$-0.794167\pi$
$617$	−39.6494	−1.59622	−0.798111	+	0.602510i	$0.794167\pi$
$618$	3.80731	0.153152
$619$	17.5987	0.707353	0.353677	−	0.935368i	$-0.384931\pi$
$619$	17.5987	0.707353	0.353677	+	0.935368i	$0.384931\pi$
$620$	5.75699	0.231206
$621$	13.2011	0.529740
$622$	8.48905	0.340380
$623$	−23.0525	−0.923578
$624$	0.0746213	0.00298724
$625$	20.3816	0.815266
$626$	13.9384	0.557090
$627$	8.60547	0.343669
$628$	−2.28093	−0.0910192
$629$	−9.78624	−0.390203
$630$	5.87116	0.233913
$631$	−14.8473	−0.591061	−0.295531	−	0.955333i	$-0.595496\pi$
$631$	−14.8473	−0.591061	−0.295531	+	0.955333i	$0.595496\pi$
$632$	9.09881	0.361931
$633$	12.2142	0.485471
$634$	28.0023	1.11211
$635$	−2.81097	−0.111550
$636$	−0.271041	−0.0107475
$637$	−1.08651	−0.0430489
$638$	−29.6671	−1.17453
$639$	4.20515	0.166353
$640$	−0.560788	−0.0221671
$641$	10.2894	0.406409	0.203204	−	0.979136i	$-0.434864\pi$
$641$	10.2894	0.406409	0.203204	+	0.979136i	$0.434864\pi$
$642$	7.09706	0.280098
$643$	2.90757	0.114663	0.0573316	−	0.998355i	$-0.481741\pi$
$643$	2.90757	0.114663	0.0573316	+	0.998355i	$0.481741\pi$
$644$	15.7215	0.619512
$645$	3.63898	0.143285
$646$	−6.66651	−0.262290
$647$	22.1322	0.870105	0.435053	−	0.900405i	$-0.356730\pi$
$647$	22.1322	0.870105	0.435053	+	0.900405i	$0.356730\pi$
$648$	6.04297	0.237390
$649$	13.7397	0.539329
$650$	0.598292	0.0234669
$651$	23.6263	0.925986
$652$	−2.95499	−0.115726
$653$	−41.6453	−1.62971	−0.814854	−	0.579666i	$-0.803183\pi$
$653$	−41.6453	−1.62971	−0.814854	+	0.579666i	$0.803183\pi$
$654$	0.106119	0.00414958
$655$	10.6987	0.418031
$656$	−9.60494	−0.375010
$657$	22.9121	0.893886
$658$	−46.0354	−1.79465
$659$	−3.09330	−0.120498	−0.0602490	−	0.998183i	$-0.519189\pi$
$659$	−3.09330	−0.120498	−0.0602490	+	0.998183i	$0.519189\pi$
$660$	−1.59157	−0.0619519
$661$	−37.0667	−1.44173	−0.720863	−	0.693077i	$-0.756254\pi$
$661$	−37.0667	−1.44173	−0.720863	+	0.693077i	$0.756254\pi$
$662$	5.02954	0.195479
$663$	−0.164064	−0.00637174
$664$	−3.52906	−0.136954
$665$	−6.69634	−0.259673
$666$	−11.8331	−0.458522
$667$	24.3869	0.944264
$668$	−6.64375	−0.257054
$669$	−6.21875	−0.240431
$670$	3.71704	0.143602
$671$	−30.6960	−1.18501
$672$	−2.30144	−0.0887798
$673$	−19.5783	−0.754690	−0.377345	−	0.926073i	$-0.623163\pi$
$673$	−19.5783	−0.754690	−0.377345	+	0.926073i	$0.623163\pi$
$674$	−11.4870	−0.442462
$675$	−15.4940	−0.596366
$676$	−12.9837	−0.499373
$677$	2.23398	0.0858589	0.0429295	−	0.999078i	$-0.486331\pi$
$677$	2.23398	0.0858589	0.0429295	+	0.999078i	$0.486331\pi$
$678$	11.8901	0.456636
$679$	7.55113	0.289786
$680$	1.23296	0.0472820
$681$	3.65206	0.139947
$682$	49.8559	1.90908
$683$	1.92592	0.0736934	0.0368467	−	0.999321i	$-0.488269\pi$
$683$	1.92592	0.0736934	0.0368467	+	0.999321i	$0.488269\pi$
$684$	−8.06085	−0.308214
$685$	−4.88988	−0.186833
$686$	5.94251	0.226886
$687$	−4.70153	−0.179375
$688$	11.1038	0.423330
$689$	−0.0592220	−0.00225618
$690$	1.30830	0.0498062
$691$	4.90516	0.186601	0.0933006	−	0.995638i	$-0.470258\pi$
$691$	4.90516	0.186601	0.0933006	+	0.995638i	$0.470258\pi$
$692$	11.2534	0.427788
$693$	50.8446	1.93143
$694$	−12.0999	−0.459308
$695$	11.9955	0.455015
$696$	−3.56995	−0.135319
$697$	21.1177	0.799889
$698$	−6.25886	−0.236901
$699$	−7.44155	−0.281465
$700$	−18.4522	−0.697429
$701$	−42.2043	−1.59403	−0.797017	−	0.603956i	$-0.793590\pi$
$701$	−42.2043	−1.59403	−0.797017	+	0.603956i	$0.793590\pi$
$702$	−0.422243	−0.0159365
$703$	13.4962	0.509018
$704$	−4.85646	−0.183035
$705$	−3.83095	−0.144282
$706$	31.9690	1.20317
$707$	−65.3353	−2.45719
$708$	1.65334	0.0621365
$709$	−10.5984	−0.398030	−0.199015	−	0.979996i	$-0.563774\pi$
$709$	−10.5984	−0.398030	−0.199015	+	0.979996i	$0.563774\pi$
$710$	0.887048	0.0332903
$711$	−24.1890	−0.907158
$712$	−5.85365	−0.219375
$713$	−40.9824	−1.53480
$714$	5.06000	0.189366
$715$	−0.347756	−0.0130053
$716$	22.3923	0.836841
$717$	0.232951	0.00869970
$718$	−7.41873	−0.276864
$719$	−20.0800	−0.748859	−0.374429	−	0.927255i	$-0.622161\pi$
$719$	−20.0800	−0.748859	−0.374429	+	0.927255i	$0.622161\pi$
$720$	1.49085	0.0555605
$721$	−25.6568	−0.955508
$722$	−9.80622	−0.364950
$723$	−3.70632	−0.137839
$724$	−8.75738	−0.325465
$725$	−28.6228	−1.06303
$726$	−7.35477	−0.272961
$727$	−23.2177	−0.861097	−0.430549	−	0.902567i	$-0.641680\pi$
$727$	−23.2177	−0.861097	−0.430549	+	0.902567i	$0.641680\pi$
$728$	−0.502860	−0.0186372
$729$	−10.2677	−0.380284
$730$	4.83315	0.178883
$731$	−24.4132	−0.902955
$732$	−3.69376	−0.136525
$733$	28.1145	1.03843	0.519216	−	0.854643i	$-0.326224\pi$
$733$	28.1145	1.03843	0.519216	+	0.854643i	$0.326224\pi$
$734$	−12.9330	−0.477366
$735$	2.78858	0.102858
$736$	3.99210	0.147151
$737$	32.1898	1.18573
$738$	25.5346	0.939940
$739$	12.1118	0.445539	0.222769	−	0.974871i	$-0.428490\pi$
$739$	12.1118	0.445539	0.222769	+	0.974871i	$0.428490\pi$
$740$	−2.49611	−0.0917587
$741$	0.226261	0.00831191
$742$	1.82650	0.0670528
$743$	−36.8277	−1.35108	−0.675539	−	0.737325i	$-0.736089\pi$
$743$	−36.8277	−1.35108	−0.675539	+	0.737325i	$0.736089\pi$
$744$	5.99934	0.219947
$745$	1.56184	0.0572216
$746$	−10.9350	−0.400359
$747$	9.38193	0.343267
$748$	10.6776	0.390410
$749$	−47.8258	−1.74752
$750$	−3.17416	−0.115904
$751$	43.2461	1.57807	0.789036	−	0.614346i	$-0.210580\pi$
$751$	43.2461	1.57807	0.789036	+	0.614346i	$0.210580\pi$
$752$	−11.6896	−0.426277
$753$	8.08394	0.294595
$754$	−0.780029	−0.0284070
$755$	−8.07557	−0.293900
$756$	13.0226	0.473628
$757$	1.00712	0.0366042	0.0183021	−	0.999833i	$-0.494174\pi$
$757$	1.00712	0.0366042	0.0183021	+	0.999833i	$0.494174\pi$
$758$	−25.6617	−0.932076
$759$	11.3300	0.411252
$760$	−1.70038	−0.0616793
$761$	−24.9373	−0.903978	−0.451989	−	0.892024i	$-0.649285\pi$
$761$	−24.9373	−0.903978	−0.451989	+	0.892024i	$0.649285\pi$
$762$	−2.92930	−0.106117
$763$	−0.715117	−0.0258890
$764$	−8.28381	−0.299698
$765$	−3.27781	−0.118510
$766$	−3.72099	−0.134445
$767$	0.361253	0.0130441
$768$	−0.584396	−0.0210876
$769$	−20.0086	−0.721529	−0.360764	−	0.932657i	$-0.617484\pi$
$769$	−20.0086	−0.721529	−0.360764	+	0.932657i	$0.617484\pi$
$770$	10.7253	0.386514
$771$	−7.29097	−0.262578
$772$	5.93477	0.213597
$773$	−12.2007	−0.438830	−0.219415	−	0.975632i	$-0.570415\pi$
$773$	−12.2007	−0.438830	−0.219415	+	0.975632i	$0.570415\pi$
$774$	−29.5193	−1.06105
$775$	48.1010	1.72784
$776$	1.91743	0.0688319
$777$	−10.2438	−0.367496
$778$	15.2793	0.547791
$779$	−29.1234	−1.04345
$780$	−0.0418468	−0.00149835
$781$	7.68190	0.274880
$782$	−8.77714	−0.313870
$783$	20.2005	0.721907
$784$	8.50896	0.303892
$785$	1.27912	0.0456538
$786$	11.1491	0.397673
$787$	9.75990	0.347903	0.173951	−	0.984754i	$-0.444346\pi$
$787$	9.75990	0.347903	0.173951	+	0.984754i	$0.444346\pi$
$788$	−8.31700	−0.296281
$789$	−1.34887	−0.0480211
$790$	−5.10250	−0.181539
$791$	−80.1252	−2.84892
$792$	12.9108	0.458766
$793$	−0.807081	−0.0286603
$794$	15.1873	0.538976
$795$	0.151997	0.00539076
$796$	−3.54217	−0.125549
$797$	0.860043	0.0304643	0.0152321	−	0.999884i	$-0.495151\pi$
$797$	0.860043	0.0304643	0.0152321	+	0.999884i	$0.495151\pi$
$798$	−6.97824	−0.247027
$799$	25.7011	0.909241
$800$	−4.68552	−0.165658
$801$	15.5618	0.549849
$802$	8.04190	0.283969
$803$	41.8554	1.47704
$804$	3.87352	0.136609
$805$	−8.81641	−0.310738
$806$	1.31085	0.0461726
$807$	17.2314	0.606573
$808$	−16.5904	−0.583648
$809$	31.3466	1.10209	0.551044	−	0.834476i	$-0.314230\pi$
$809$	31.3466	1.10209	0.551044	+	0.834476i	$0.314230\pi$
$810$	−3.38882	−0.119071
$811$	−19.5427	−0.686238	−0.343119	−	0.939292i	$-0.611483\pi$
$811$	−19.5427	−0.686238	−0.343119	+	0.939292i	$0.611483\pi$
$812$	24.0573	0.844245
$813$	5.44908	0.191108
$814$	−21.6164	−0.757656
$815$	1.65712	0.0580465
$816$	1.28487	0.0449794
$817$	33.6682	1.17790
$818$	23.1580	0.809701
$819$	1.33684	0.0467131
$820$	5.38634	0.188099
$821$	−43.7991	−1.52860	−0.764299	−	0.644862i	$-0.776915\pi$
$821$	−43.7991	−1.52860	−0.764299	+	0.644862i	$0.776915\pi$
$822$	−5.09574	−0.177734
$823$	37.0187	1.29039	0.645195	−	0.764018i	$-0.276776\pi$
$823$	37.0187	1.29039	0.645195	+	0.764018i	$0.276776\pi$
$824$	−6.51494	−0.226959
$825$	−13.2980	−0.462975
$826$	−11.1416	−0.387666
$827$	37.8759	1.31707	0.658537	−	0.752548i	$-0.271175\pi$
$827$	37.8759	1.31707	0.658537	+	0.752548i	$0.271175\pi$
$828$	−10.6129	−0.368825
$829$	23.1512	0.804074	0.402037	−	0.915623i	$-0.368302\pi$
$829$	23.1512	0.804074	0.402037	+	0.915623i	$0.368302\pi$
$830$	1.97905	0.0686940
$831$	1.99869	0.0693338
$832$	−0.127690	−0.00442684
$833$	−18.7080	−0.648195
$834$	12.5005	0.432856
$835$	3.72573	0.128934
$836$	−14.7254	−0.509289
$837$	−33.9472	−1.17339
$838$	−27.6656	−0.955693
$839$	27.6458	0.954440	0.477220	−	0.878784i	$-0.341644\pi$
$839$	27.6458	0.954440	0.477220	+	0.878784i	$0.341644\pi$
$840$	1.29062	0.0445305
$841$	8.31729	0.286803
$842$	−40.0705	−1.38092
$843$	−5.60459	−0.193032
$844$	−20.9005	−0.719426
$845$	7.28110	0.250478
$846$	31.0767	1.06844
$847$	49.5625	1.70299
$848$	0.463797	0.0159268
$849$	−16.4359	−0.564077
$850$	10.3017	0.353346
$851$	17.7691	0.609117
$852$	0.924391	0.0316691
$853$	1.93862	0.0663770	0.0331885	−	0.999449i	$-0.489434\pi$
$853$	1.93862	0.0663770	0.0331885	+	0.999449i	$0.489434\pi$
$854$	24.8916	0.851773
$855$	4.52043	0.154595
$856$	−12.1443	−0.415082
$857$	33.3224	1.13827	0.569135	−	0.822244i	$-0.307278\pi$
$857$	33.3224	1.13827	0.569135	+	0.822244i	$0.307278\pi$
$858$	−0.362396	−0.0123720
$859$	7.52858	0.256872	0.128436	−	0.991718i	$-0.459004\pi$
$859$	7.52858	0.256872	0.128436	+	0.991718i	$0.459004\pi$
$860$	−6.22690	−0.212336
$861$	22.1051	0.753341
$862$	−12.2836	−0.418381
$863$	20.8839	0.710896	0.355448	−	0.934696i	$-0.384328\pi$
$863$	20.8839	0.710896	0.355448	+	0.934696i	$0.384328\pi$
$864$	3.30679	0.112499
$865$	−6.31075	−0.214572
$866$	23.2722	0.790822
$867$	7.10979	0.241461
$868$	−40.4285	−1.37223
$869$	−44.1880	−1.49898
$870$	2.00199	0.0678737
$871$	0.846358	0.0286778
$872$	−0.181587	−0.00614932
$873$	−5.09746	−0.172523
$874$	12.1045	0.409442
$875$	21.3901	0.723118
$876$	5.03661	0.170171
$877$	46.0057	1.55350	0.776750	−	0.629809i	$-0.216867\pi$
$877$	46.0057	1.55350	0.776750	+	0.629809i	$0.216867\pi$
$878$	−25.2111	−0.850835
$879$	−10.8718	−0.366698
$880$	2.72345	0.0918074
$881$	−11.7774	−0.396792	−0.198396	−	0.980122i	$-0.563573\pi$
$881$	−11.7774	−0.396792	−0.198396	+	0.980122i	$0.563573\pi$
$882$	−22.6209	−0.761686
$883$	−18.5423	−0.623996	−0.311998	−	0.950083i	$-0.600998\pi$
$883$	−18.5423	−0.623996	−0.311998	+	0.950083i	$0.600998\pi$
$884$	0.280742	0.00944237
$885$	−0.927176	−0.0311667
$886$	23.1042	0.776201
$887$	−13.9382	−0.467997	−0.233999	−	0.972237i	$-0.575181\pi$
$887$	−13.9382	−0.467997	−0.233999	+	0.972237i	$0.575181\pi$
$888$	−2.60119	−0.0872901
$889$	19.7400	0.662060
$890$	3.28266	0.110035
$891$	−29.3474	−0.983176
$892$	10.6413	0.356298
$893$	−35.4444	−1.18610
$894$	1.62759	0.0544349
$895$	−12.5574	−0.419746
$896$	3.93814	0.131564
$897$	0.297896	0.00994645
$898$	−33.0528	−1.10299
$899$	−62.7121	−2.09157
$900$	12.4564	0.415212
$901$	−1.01972	−0.0339717
$902$	46.6460	1.55314
$903$	−25.5548	−0.850409
$904$	−20.3459	−0.676696
$905$	4.91103	0.163248
$906$	−8.41553	−0.279587
$907$	49.4031	1.64040	0.820202	−	0.572074i	$-0.193861\pi$
$907$	49.4031	1.64040	0.820202	+	0.572074i	$0.193861\pi$
$908$	−6.24929	−0.207390
$909$	44.1053	1.46288
$910$	0.281998	0.00934814
$911$	40.1612	1.33060	0.665300	−	0.746576i	$-0.268304\pi$
$911$	40.1612	1.33060	0.665300	+	0.746576i	$0.268304\pi$
$912$	−1.77196	−0.0586755
$913$	17.1387	0.567210
$914$	30.9278	1.02300
$915$	2.07142	0.0684789
$916$	8.04511	0.265818
$917$	−75.1315	−2.48106
$918$	−7.27041	−0.239959
$919$	−4.12660	−0.136124	−0.0680620	−	0.997681i	$-0.521682\pi$
$919$	−4.12660	−0.136124	−0.0680620	+	0.997681i	$0.521682\pi$
$920$	−2.23872	−0.0738085
$921$	16.0886	0.530138
$922$	−22.7585	−0.749512
$923$	0.201978	0.00664818
$924$	11.1768	0.367691
$925$	−20.8555	−0.685726
$926$	11.9167	0.391608
$927$	17.3198	0.568858
$928$	6.10879	0.200531
$929$	26.3861	0.865701	0.432850	−	0.901466i	$-0.357508\pi$
$929$	26.3861	0.865701	0.432850	+	0.901466i	$0.357508\pi$
$930$	−3.36436	−0.110322
$931$	25.8002	0.845569
$932$	12.7337	0.417108
$933$	−4.96097	−0.162415
$934$	−34.6898	−1.13509
$935$	−5.98785	−0.195824
$936$	0.339460	0.0110956
$937$	−0.156161	−0.00510156	−0.00255078	−	0.999997i	$-0.500812\pi$
$937$	−0.156161	−0.00510156	−0.00255078	+	0.999997i	$0.500812\pi$
$938$	−26.1030	−0.852292
$939$	−8.14554	−0.265820
$940$	6.55541	0.213814
$941$	−22.2586	−0.725609	−0.362805	−	0.931865i	$-0.618181\pi$
$941$	−22.2586	−0.725609	−0.362805	+	0.931865i	$0.618181\pi$
$942$	1.33297	0.0434305
$943$	−38.3439	−1.24865
$944$	−2.82915	−0.0920810
$945$	−7.30294	−0.237565
$946$	−53.9254	−1.75327
$947$	7.41158	0.240844	0.120422	−	0.992723i	$-0.461575\pi$
$947$	7.41158	0.240844	0.120422	+	0.992723i	$0.461575\pi$
$948$	−5.31731	−0.172698
$949$	1.10049	0.0357235
$950$	−14.2071	−0.460938
$951$	−16.3644	−0.530654
$952$	−8.65851	−0.280624
$953$	−0.522019	−0.0169099	−0.00845493	−	0.999964i	$-0.502691\pi$
$953$	−0.522019	−0.0169099	−0.00845493	+	0.999964i	$0.502691\pi$
$954$	−1.23299	−0.0399197
$955$	4.64546	0.150324
$956$	−0.398618	−0.0128922
$957$	17.3373	0.560437
$958$	2.63821	0.0852367
$959$	34.3393	1.10887
$960$	0.327723	0.0105772
$961$	74.3883	2.39962
$962$	−0.568355	−0.0183245
$963$	32.2853	1.04038
$964$	6.34213	0.204266
$965$	−3.32815	−0.107137
$966$	−9.18756	−0.295605
$967$	47.5432	1.52889	0.764444	−	0.644690i	$-0.223014\pi$
$967$	47.5432	1.52889	0.764444	+	0.644690i	$0.223014\pi$
$968$	12.5852	0.404505
$969$	3.89588	0.125154
$970$	−1.07527	−0.0345250
$971$	26.3982	0.847157	0.423579	−	0.905859i	$-0.360774\pi$
$971$	26.3982	0.847157	0.423579	+	0.905859i	$0.360774\pi$
$972$	−13.4519	−0.431469
$973$	−84.2385	−2.70056
$974$	−12.0586	−0.386383
$975$	−0.349639	−0.0111974
$976$	6.32064	0.202319
$977$	−5.55205	−0.177626	−0.0888128	−	0.996048i	$-0.528307\pi$
$977$	−5.55205	−0.177626	−0.0888128	+	0.996048i	$0.528307\pi$
$978$	1.72688	0.0552197
$979$	28.4280	0.908563
$980$	−4.77173	−0.152427
$981$	0.482746	0.0154129
$982$	29.5821	0.944001
$983$	18.3961	0.586746	0.293373	−	0.955998i	$-0.405222\pi$
$983$	18.3961	0.586746	0.293373	+	0.955998i	$0.405222\pi$
$984$	5.61309	0.178939
$985$	4.66408	0.148610
$986$	−13.4309	−0.427729
$987$	26.9029	0.856329
$988$	−0.387171	−0.0123175
$989$	44.3276	1.40954
$990$	−7.24023	−0.230110
$991$	−53.7979	−1.70895	−0.854473	−	0.519497i	$-0.826119\pi$
$991$	−53.7979	−1.70895	−0.854473	+	0.519497i	$0.826119\pi$
$992$	−10.2659	−0.325942
$993$	−2.93925	−0.0932741
$994$	−6.22931	−0.197582
$995$	1.98641	0.0629733
$996$	2.06237	0.0653486
$997$	38.1071	1.20687	0.603433	−	0.797414i	$-0.293799\pi$
$997$	38.1071	1.20687	0.603433	+	0.797414i	$0.293799\pi$
$998$	40.5374	1.28319
$999$	14.7188	0.465681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.35	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.35	✓	69	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.584396 q^{3} +1.00000 q^{4} -0.560788 q^{5} -0.584396 q^{6} +3.93814 q^{7} +1.00000 q^{8} -2.65848 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.584396 q^{3} +1.00000 q^{4} -0.560788 q^{5} -0.584396 q^{6} +3.93814 q^{7} +1.00000 q^{8} -2.65848 q^{9} -0.560788 q^{10} -4.85646 q^{11} -0.584396 q^{12} -0.127690 q^{13} +3.93814 q^{14} +0.327723 q^{15} +1.00000 q^{16} -2.19863 q^{17} -2.65848 q^{18} +3.03212 q^{19} -0.560788 q^{20} -2.30144 q^{21} -4.85646 q^{22} +3.99210 q^{23} -0.584396 q^{24} -4.68552 q^{25} -0.127690 q^{26} +3.30679 q^{27} +3.93814 q^{28} +6.10879 q^{29} +0.327723 q^{30} -10.2659 q^{31} +1.00000 q^{32} +2.83810 q^{33} -2.19863 q^{34} -2.20846 q^{35} -2.65848 q^{36} +4.45107 q^{37} +3.03212 q^{38} +0.0746213 q^{39} -0.560788 q^{40} -9.60494 q^{41} -2.30144 q^{42} +11.1038 q^{43} -4.85646 q^{44} +1.49085 q^{45} +3.99210 q^{46} -11.6896 q^{47} -0.584396 q^{48} +8.50896 q^{49} -4.68552 q^{50} +1.28487 q^{51} -0.127690 q^{52} +0.463797 q^{53} +3.30679 q^{54} +2.72345 q^{55} +3.93814 q^{56} -1.77196 q^{57} +6.10879 q^{58} -2.82915 q^{59} +0.327723 q^{60} +6.32064 q^{61} -10.2659 q^{62} -10.4695 q^{63} +1.00000 q^{64} +0.0716068 q^{65} +2.83810 q^{66} -6.62825 q^{67} -2.19863 q^{68} -2.33297 q^{69} -2.20846 q^{70} -1.58179 q^{71} -2.65848 q^{72} -8.61849 q^{73} +4.45107 q^{74} +2.73820 q^{75} +3.03212 q^{76} -19.1254 q^{77} +0.0746213 q^{78} +9.09881 q^{79} -0.560788 q^{80} +6.04297 q^{81} -9.60494 q^{82} -3.52906 q^{83} -2.30144 q^{84} +1.23296 q^{85} +11.1038 q^{86} -3.56995 q^{87} -4.85646 q^{88} -5.85365 q^{89} +1.49085 q^{90} -0.502860 q^{91} +3.99210 q^{92} +5.99934 q^{93} -11.6896 q^{94} -1.70038 q^{95} -0.584396 q^{96} +1.91743 q^{97} +8.50896 q^{98} +12.9108 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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