LMFDB - Embedded newform 2005.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.31024 q^{2} -1.68649 q^{3} -0.283271 q^{4} +1.00000 q^{5} -2.20970 q^{6} +0.0877260 q^{7} -2.99163 q^{8} -0.155757 q^{9} +O(q^{10})$	\(q+1.31024 q^{2} -1.68649 q^{3} -0.283271 q^{4} +1.00000 q^{5} -2.20970 q^{6} +0.0877260 q^{7} -2.99163 q^{8} -0.155757 q^{9} +1.31024 q^{10} -1.38343 q^{11} +0.477733 q^{12} +7.14201 q^{13} +0.114942 q^{14} -1.68649 q^{15} -3.35322 q^{16} +3.36739 q^{17} -0.204079 q^{18} -2.67096 q^{19} -0.283271 q^{20} -0.147949 q^{21} -1.81263 q^{22} -7.08384 q^{23} +5.04535 q^{24} +1.00000 q^{25} +9.35775 q^{26} +5.32215 q^{27} -0.0248502 q^{28} +2.68724 q^{29} -2.20970 q^{30} -8.69445 q^{31} +1.58975 q^{32} +2.33314 q^{33} +4.41209 q^{34} +0.0877260 q^{35} +0.0441214 q^{36} +1.13900 q^{37} -3.49960 q^{38} -12.0449 q^{39} -2.99163 q^{40} -5.71093 q^{41} -0.193849 q^{42} -7.92378 q^{43} +0.391886 q^{44} -0.155757 q^{45} -9.28154 q^{46} -11.3179 q^{47} +5.65516 q^{48} -6.99230 q^{49} +1.31024 q^{50} -5.67906 q^{51} -2.02312 q^{52} +2.52059 q^{53} +6.97329 q^{54} -1.38343 q^{55} -0.262444 q^{56} +4.50455 q^{57} +3.52093 q^{58} -9.78089 q^{59} +0.477733 q^{60} +2.48430 q^{61} -11.3918 q^{62} -0.0136639 q^{63} +8.78938 q^{64} +7.14201 q^{65} +3.05698 q^{66} +11.1066 q^{67} -0.953883 q^{68} +11.9468 q^{69} +0.114942 q^{70} +3.17119 q^{71} +0.465967 q^{72} -11.8519 q^{73} +1.49237 q^{74} -1.68649 q^{75} +0.756605 q^{76} -0.121363 q^{77} -15.7817 q^{78} -6.21451 q^{79} -3.35322 q^{80} -8.50847 q^{81} -7.48269 q^{82} -11.4266 q^{83} +0.0419096 q^{84} +3.36739 q^{85} -10.3821 q^{86} -4.53200 q^{87} +4.13872 q^{88} +5.50933 q^{89} -0.204079 q^{90} +0.626540 q^{91} +2.00665 q^{92} +14.6631 q^{93} -14.8291 q^{94} -2.67096 q^{95} -2.68109 q^{96} -0.0219065 q^{97} -9.16160 q^{98} +0.215479 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9}+O(q^{10}) $ 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9	\( 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9} - 5 q^{10} - 30 q^{11} - 29 q^{12} - 18 q^{13} + 6 q^{14} - 10 q^{15} + 21 q^{16} - 18 q^{17} - 30 q^{18} - 17 q^{19} + 25 q^{20} + 6 q^{21} - 2 q^{22} - 44 q^{23} + 11 q^{24} + 25 q^{25} - 14 q^{26} - 25 q^{27} - 50 q^{28} - 9 q^{29} + 2 q^{30} - 13 q^{31} - 45 q^{32} - 21 q^{33} - 21 q^{34} - 31 q^{35} + 5 q^{36} - 28 q^{37} - 32 q^{38} + 9 q^{39} - 30 q^{40} + 28 q^{41} - 67 q^{42} - 61 q^{43} - 49 q^{44} + 17 q^{45} + 18 q^{46} - 53 q^{47} - 44 q^{48} + 28 q^{49} - 5 q^{50} - 30 q^{51} - 3 q^{52} - 36 q^{53} + 17 q^{54} - 30 q^{55} - 3 q^{56} - 13 q^{57} + 2 q^{58} - 39 q^{59} - 29 q^{60} + 10 q^{61} - 30 q^{62} - 44 q^{63} - 4 q^{64} - 18 q^{65} + 33 q^{66} - 10 q^{67} - 18 q^{68} - 6 q^{69} + 6 q^{70} - 7 q^{71} - q^{72} - 26 q^{73} - 3 q^{74} - 10 q^{75} + 12 q^{76} + 29 q^{77} - 5 q^{78} - 6 q^{79} + 21 q^{80} + 13 q^{81} - 30 q^{82} - 35 q^{83} + 117 q^{84} - 18 q^{85} + 14 q^{86} - 104 q^{87} + 53 q^{88} + 7 q^{89} - 30 q^{90} - 25 q^{91} - 31 q^{92} + 2 q^{93} + 68 q^{94} - 17 q^{95} + 92 q^{96} + 6 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9 - 5 * q^10 - 30 * q^11 - 29 * q^12 - 18 * q^13 + 6 * q^14 - 10 * q^15 + 21 * q^16 - 18 * q^17 - 30 * q^18 - 17 * q^19 + 25 * q^20 + 6 * q^21 - 2 * q^22 - 44 * q^23 + 11 * q^24 + 25 * q^25 - 14 * q^26 - 25 * q^27 - 50 * q^28 - 9 * q^29 + 2 * q^30 - 13 * q^31 - 45 * q^32 - 21 * q^33 - 21 * q^34 - 31 * q^35 + 5 * q^36 - 28 * q^37 - 32 * q^38 + 9 * q^39 - 30 * q^40 + 28 * q^41 - 67 * q^42 - 61 * q^43 - 49 * q^44 + 17 * q^45 + 18 * q^46 - 53 * q^47 - 44 * q^48 + 28 * q^49 - 5 * q^50 - 30 * q^51 - 3 * q^52 - 36 * q^53 + 17 * q^54 - 30 * q^55 - 3 * q^56 - 13 * q^57 + 2 * q^58 - 39 * q^59 - 29 * q^60 + 10 * q^61 - 30 * q^62 - 44 * q^63 - 4 * q^64 - 18 * q^65 + 33 * q^66 - 10 * q^67 - 18 * q^68 - 6 * q^69 + 6 * q^70 - 7 * q^71 - q^72 - 26 * q^73 - 3 * q^74 - 10 * q^75 + 12 * q^76 + 29 * q^77 - 5 * q^78 - 6 * q^79 + 21 * q^80 + 13 * q^81 - 30 * q^82 - 35 * q^83 + 117 * q^84 - 18 * q^85 + 14 * q^86 - 104 * q^87 + 53 * q^88 + 7 * q^89 - 30 * q^90 - 25 * q^91 - 31 * q^92 + 2 * q^93 + 68 * q^94 - 17 * q^95 + 92 * q^96 + 6 * q^97 + 15 * q^98 - 36 * 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 $

$2$	1.31024	0.926480	0.463240	−	0.886233i	$-0.346687\pi$
$2$	1.31024	0.926480	0.463240	+	0.886233i	$0.346687\pi$
$3$	−1.68649	−0.973695	−0.486847	−	0.873487i	$-0.661853\pi$
$3$	−1.68649	−0.973695	−0.486847	+	0.873487i	$0.661853\pi$
$4$	−0.283271	−0.141635
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.20970	−0.902108
$7$	0.0877260	0.0331573	0.0165787	−	0.999863i	$-0.494723\pi$
$7$	0.0877260	0.0331573	0.0165787	+	0.999863i	$0.494723\pi$
$8$	−2.99163	−1.05770
$9$	−0.155757	−0.0519190
$10$	1.31024	0.414334
$11$	−1.38343	−0.417121	−0.208560	−	0.978010i	$-0.566878\pi$
$11$	−1.38343	−0.417121	−0.208560	+	0.978010i	$0.566878\pi$
$12$	0.477733	0.137910
$13$	7.14201	1.98084	0.990419	−	0.138096i	$-0.0440982\pi$
$13$	7.14201	1.98084	0.990419	+	0.138096i	$0.0440982\pi$
$14$	0.114942	0.0307196
$15$	−1.68649	−0.435449
$16$	−3.35322	−0.838304
$17$	3.36739	0.816712	0.408356	−	0.912823i	$-0.366102\pi$
$17$	3.36739	0.816712	0.408356	+	0.912823i	$0.366102\pi$
$18$	−0.204079	−0.0481019
$19$	−2.67096	−0.612761	−0.306380	−	0.951909i	$-0.599118\pi$
$19$	−2.67096	−0.612761	−0.306380	+	0.951909i	$0.599118\pi$
$20$	−0.283271	−0.0633413
$21$	−0.147949	−0.0322851
$22$	−1.81263	−0.386454
$23$	−7.08384	−1.47708	−0.738542	−	0.674208i	$-0.764485\pi$
$23$	−7.08384	−1.47708	−0.738542	+	0.674208i	$0.764485\pi$
$24$	5.04535	1.02988
$25$	1.00000	0.200000
$26$	9.35775	1.83521
$27$	5.32215	1.02425
$28$	−0.0248502	−0.00469625
$29$	2.68724	0.499009	0.249504	−	0.968374i	$-0.419732\pi$
$29$	2.68724	0.499009	0.249504	+	0.968374i	$0.419732\pi$
$30$	−2.20970	−0.403435
$31$	−8.69445	−1.56157	−0.780784	−	0.624801i	$-0.785180\pi$
$31$	−8.69445	−1.56157	−0.780784	+	0.624801i	$0.785180\pi$
$32$	1.58975	0.281030
$33$	2.33314	0.406148
$34$	4.41209	0.756667
$35$	0.0877260	0.0148284
$36$	0.0441214	0.00735356
$37$	1.13900	0.187251	0.0936254	−	0.995607i	$-0.470154\pi$
$37$	1.13900	0.187251	0.0936254	+	0.995607i	$0.470154\pi$
$38$	−3.49960	−0.567710
$39$	−12.0449	−1.92873
$40$	−2.99163	−0.473019
$41$	−5.71093	−0.891897	−0.445949	−	0.895058i	$-0.647134\pi$
$41$	−5.71093	−0.891897	−0.445949	+	0.895058i	$0.647134\pi$
$42$	−0.193849	−0.0299115
$43$	−7.92378	−1.20837	−0.604183	−	0.796846i	$-0.706500\pi$
$43$	−7.92378	−1.20837	−0.604183	+	0.796846i	$0.706500\pi$
$44$	0.391886	0.0590790
$45$	−0.155757	−0.0232189
$46$	−9.28154	−1.36849
$47$	−11.3179	−1.65088	−0.825440	−	0.564491i	$-0.809073\pi$
$47$	−11.3179	−1.65088	−0.825440	+	0.564491i	$0.809073\pi$
$48$	5.65516	0.816252
$49$	−6.99230	−0.998901
$50$	1.31024	0.185296
$51$	−5.67906	−0.795228
$52$	−2.02312	−0.280557
$53$	2.52059	0.346230	0.173115	−	0.984902i	$-0.444617\pi$
$53$	2.52059	0.346230	0.173115	+	0.984902i	$0.444617\pi$
$54$	6.97329	0.948945
$55$	−1.38343	−0.186542
$56$	−0.262444	−0.0350706
$57$	4.50455	0.596642
$58$	3.52093	0.462321
$59$	−9.78089	−1.27336	−0.636682	−	0.771127i	$-0.719693\pi$
$59$	−9.78089	−1.27336	−0.636682	+	0.771127i	$0.719693\pi$
$60$	0.477733	0.0616751
$61$	2.48430	0.318083	0.159041	−	0.987272i	$-0.449160\pi$
$61$	2.48430	0.318083	0.159041	+	0.987272i	$0.449160\pi$
$62$	−11.3918	−1.44676
$63$	−0.0136639	−0.00172149
$64$	8.78938	1.09867
$65$	7.14201	0.885858
$66$	3.05698	0.376288
$67$	11.1066	1.35689	0.678444	−	0.734653i	$-0.262655\pi$
$67$	11.1066	1.35689	0.678444	+	0.734653i	$0.262655\pi$
$68$	−0.953883	−0.115675
$69$	11.9468	1.43823
$70$	0.114942	0.0137382
$71$	3.17119	0.376351	0.188176	−	0.982135i	$-0.439743\pi$
$71$	3.17119	0.376351	0.188176	+	0.982135i	$0.439743\pi$
$72$	0.465967	0.0549148
$73$	−11.8519	−1.38716	−0.693581	−	0.720379i	$-0.743968\pi$
$73$	−11.8519	−1.38716	−0.693581	+	0.720379i	$0.743968\pi$
$74$	1.49237	0.173484
$75$	−1.68649	−0.194739
$76$	0.756605	0.0867886
$77$	−0.121363	−0.0138306
$78$	−15.7817	−1.78693
$79$	−6.21451	−0.699187	−0.349594	−	0.936901i	$-0.613680\pi$
$79$	−6.21451	−0.699187	−0.349594	+	0.936901i	$0.613680\pi$
$80$	−3.35322	−0.374901
$81$	−8.50847	−0.945385
$82$	−7.48269	−0.826325
$83$	−11.4266	−1.25423	−0.627114	−	0.778928i	$-0.715764\pi$
$83$	−11.4266	−1.25423	−0.627114	+	0.778928i	$0.715764\pi$
$84$	0.0419096	0.00457271
$85$	3.36739	0.365245
$86$	−10.3821	−1.11953
$87$	−4.53200	−0.485882
$88$	4.13872	0.441189
$89$	5.50933	0.583988	0.291994	−	0.956420i	$-0.405681\pi$
$89$	5.50933	0.583988	0.291994	+	0.956420i	$0.405681\pi$
$90$	−0.204079	−0.0215118
$91$	0.626540	0.0656793
$92$	2.00665	0.209207
$93$	14.6631	1.52049
$94$	−14.8291	−1.52951
$95$	−2.67096	−0.274035
$96$	−2.68109	−0.273638
$97$	−0.0219065	−0.00222427	−0.00111213	−	0.999999i	$-0.500354\pi$
$97$	−0.0219065	−0.00222427	−0.00111213	+	0.999999i	$0.500354\pi$
$98$	−9.16160	−0.925461
$99$	0.215479	0.0216565
$100$	−0.283271	−0.0283271
$101$	−13.2926	−1.32266	−0.661330	−	0.750095i	$-0.730008\pi$
$101$	−13.2926	−1.32266	−0.661330	+	0.750095i	$0.730008\pi$
$102$	−7.44093	−0.736762
$103$	4.04565	0.398630	0.199315	−	0.979935i	$-0.436128\pi$
$103$	4.04565	0.398630	0.199315	+	0.979935i	$0.436128\pi$
$104$	−21.3663	−2.09514
$105$	−0.147949	−0.0144383
$106$	3.30258	0.320775
$107$	−7.59480	−0.734217	−0.367108	−	0.930178i	$-0.619652\pi$
$107$	−7.59480	−0.734217	−0.367108	+	0.930178i	$0.619652\pi$
$108$	−1.50761	−0.145070
$109$	5.23248	0.501180	0.250590	−	0.968093i	$-0.419375\pi$
$109$	5.23248	0.501180	0.250590	+	0.968093i	$0.419375\pi$
$110$	−1.81263	−0.172827
$111$	−1.92091	−0.182325
$112$	−0.294164	−0.0277959
$113$	−2.17548	−0.204652	−0.102326	−	0.994751i	$-0.532628\pi$
$113$	−2.17548	−0.204652	−0.102326	+	0.994751i	$0.532628\pi$
$114$	5.90204	0.552776
$115$	−7.08384	−0.660572
$116$	−0.761217	−0.0706773
$117$	−1.11242	−0.102843
$118$	−12.8153	−1.17975
$119$	0.295408	0.0270800
$120$	5.04535	0.460576
$121$	−9.08611	−0.826010
$122$	3.25504	0.294697
$123$	9.63142	0.868436
$124$	2.46288	0.221173
$125$	1.00000	0.0894427
$126$	−0.0179030	−0.00159493
$127$	8.53193	0.757087	0.378543	−	0.925584i	$-0.376425\pi$
$127$	8.53193	0.757087	0.378543	+	0.925584i	$0.376425\pi$
$128$	8.33671	0.736868
$129$	13.3634	1.17658
$130$	9.35775	0.820729
$131$	20.0695	1.75348	0.876740	−	0.480964i	$-0.159713\pi$
$131$	20.0695	1.75348	0.876740	+	0.480964i	$0.159713\pi$
$132$	−0.660911	−0.0575249
$133$	−0.234313	−0.0203175
$134$	14.5523	1.25713
$135$	5.32215	0.458058
$136$	−10.0740	−0.863838
$137$	−15.2235	−1.30063	−0.650317	−	0.759663i	$-0.725364\pi$
$137$	−15.2235	−1.30063	−0.650317	+	0.759663i	$0.725364\pi$
$138$	15.6532	1.33249
$139$	5.17208	0.438690	0.219345	−	0.975647i	$-0.429608\pi$
$139$	5.17208	0.438690	0.219345	+	0.975647i	$0.429608\pi$
$140$	−0.0248502	−0.00210023
$141$	19.0874	1.60745
$142$	4.15502	0.348682
$143$	−9.88049	−0.826248
$144$	0.522286	0.0435239
$145$	2.68724	0.223163
$146$	−15.5288	−1.28518
$147$	11.7924	0.972624
$148$	−0.322646	−0.0265213
$149$	−2.39249	−0.196001	−0.0980004	−	0.995186i	$-0.531245\pi$
$149$	−2.39249	−0.196001	−0.0980004	+	0.995186i	$0.531245\pi$
$150$	−2.20970	−0.180422
$151$	−15.3120	−1.24607	−0.623035	−	0.782194i	$-0.714101\pi$
$151$	−15.3120	−1.24607	−0.623035	+	0.782194i	$0.714101\pi$
$152$	7.99054	0.648118
$153$	−0.524494	−0.0424028
$154$	−0.159015	−0.0128138
$155$	−8.69445	−0.698355
$156$	3.41197	0.273177
$157$	7.64180	0.609882	0.304941	−	0.952371i	$-0.401363\pi$
$157$	7.64180	0.609882	0.304941	+	0.952371i	$0.401363\pi$
$158$	−8.14250	−0.647783
$159$	−4.25095	−0.337122
$160$	1.58975	0.125681
$161$	−0.621438	−0.0489761
$162$	−11.1481	−0.875880
$163$	6.90452	0.540804	0.270402	−	0.962747i	$-0.412843\pi$
$163$	6.90452	0.540804	0.270402	+	0.962747i	$0.412843\pi$
$164$	1.61774	0.126324
$165$	2.33314	0.181635
$166$	−14.9715	−1.16202
$167$	−14.9769	−1.15895	−0.579475	−	0.814990i	$-0.696742\pi$
$167$	−14.9769	−1.15895	−0.579475	+	0.814990i	$0.696742\pi$
$168$	0.442609	0.0341480
$169$	38.0083	2.92372
$170$	4.41209	0.338392
$171$	0.416021	0.0318139
$172$	2.24458	0.171147
$173$	−23.5476	−1.79029	−0.895144	−	0.445777i	$-0.852928\pi$
$173$	−23.5476	−1.79029	−0.895144	+	0.445777i	$0.852928\pi$
$174$	−5.93801	−0.450160
$175$	0.0877260	0.00663147
$176$	4.63895	0.349674
$177$	16.4954	1.23987
$178$	7.21854	0.541053
$179$	21.3814	1.59812	0.799060	−	0.601251i	$-0.205331\pi$
$179$	21.3814	1.59812	0.799060	+	0.601251i	$0.205331\pi$
$180$	0.0441214	0.00328861
$181$	−12.8656	−0.956291	−0.478145	−	0.878281i	$-0.658691\pi$
$181$	−12.8656	−0.956291	−0.478145	+	0.878281i	$0.658691\pi$
$182$	0.820918	0.0608505
$183$	−4.18975	−0.309715
$184$	21.1923	1.56231
$185$	1.13900	0.0837411
$186$	19.2122	1.40870
$187$	−4.65855	−0.340667
$188$	3.20602	0.233823
$189$	0.466891	0.0339613
$190$	−3.49960	−0.253888
$191$	5.71744	0.413699	0.206850	−	0.978373i	$-0.433679\pi$
$191$	5.71744	0.413699	0.206850	+	0.978373i	$0.433679\pi$
$192$	−14.8232	−1.06977
$193$	2.44394	0.175919	0.0879594	−	0.996124i	$-0.471965\pi$
$193$	2.44394	0.175919	0.0879594	+	0.996124i	$0.471965\pi$
$194$	−0.0287027	−0.00206074
$195$	−12.0449	−0.862555
$196$	1.98072	0.141480
$197$	0.617556	0.0439990	0.0219995	−	0.999758i	$-0.492997\pi$
$197$	0.617556	0.0439990	0.0219995	+	0.999758i	$0.492997\pi$
$198$	0.282329	0.0200643
$199$	21.0851	1.49468	0.747340	−	0.664441i	$-0.231330\pi$
$199$	21.0851	1.49468	0.747340	+	0.664441i	$0.231330\pi$
$200$	−2.99163	−0.211540
$201$	−18.7312	−1.32119
$202$	−17.4165	−1.22542
$203$	0.235741	0.0165458
$204$	1.60871	0.112632
$205$	−5.71093	−0.398869
$206$	5.30078	0.369323
$207$	1.10336	0.0766886
$208$	−23.9487	−1.66054
$209$	3.69509	0.255595
$210$	−0.193849	−0.0133768
$211$	−22.4102	−1.54278	−0.771392	−	0.636360i	$-0.780439\pi$
$211$	−22.4102	−1.54278	−0.771392	+	0.636360i	$0.780439\pi$
$212$	−0.714010	−0.0490384
$213$	−5.34818	−0.366451
$214$	−9.95101	−0.680237
$215$	−7.92378	−0.540397
$216$	−15.9219	−1.08335
$217$	−0.762729	−0.0517774
$218$	6.85580	0.464333
$219$	19.9881	1.35067
$220$	0.391886	0.0264209
$221$	24.0499	1.61777
$222$	−2.51686	−0.168921
$223$	−10.9642	−0.734219	−0.367110	−	0.930178i	$-0.619653\pi$
$223$	−10.9642	−0.734219	−0.367110	+	0.930178i	$0.619653\pi$
$224$	0.139462	0.00931822
$225$	−0.155757	−0.0103838
$226$	−2.85040	−0.189605
$227$	10.7301	0.712182	0.356091	−	0.934451i	$-0.384109\pi$
$227$	10.7301	0.712182	0.356091	+	0.934451i	$0.384109\pi$
$228$	−1.27601	−0.0845056
$229$	18.7951	1.24202	0.621009	−	0.783803i	$-0.286723\pi$
$229$	18.7951	1.24202	0.621009	+	0.783803i	$0.286723\pi$
$230$	−9.28154	−0.612006
$231$	0.204677	0.0134668
$232$	−8.03925	−0.527802
$233$	−24.8423	−1.62748	−0.813738	−	0.581232i	$-0.802571\pi$
$233$	−24.8423	−1.62748	−0.813738	+	0.581232i	$0.802571\pi$
$234$	−1.45753	−0.0952820
$235$	−11.3179	−0.738296
$236$	2.77064	0.180353
$237$	10.4807	0.680795
$238$	0.387055	0.0250890
$239$	−2.93276	−0.189704	−0.0948522	−	0.995491i	$-0.530238\pi$
$239$	−2.93276	−0.189704	−0.0948522	+	0.995491i	$0.530238\pi$
$240$	5.65516	0.365039
$241$	−16.5262	−1.06455	−0.532274	−	0.846572i	$-0.678662\pi$
$241$	−16.5262	−1.06455	−0.532274	+	0.846572i	$0.678662\pi$
$242$	−11.9050	−0.765282
$243$	−1.61701	−0.103731
$244$	−0.703731	−0.0450518
$245$	−6.99230	−0.446722
$246$	12.6195	0.804588
$247$	−19.0760	−1.21378
$248$	26.0106	1.65167
$249$	19.2707	1.22123
$250$	1.31024	0.0828669
$251$	19.3869	1.22369	0.611845	−	0.790978i	$-0.290428\pi$
$251$	19.3869	1.22369	0.611845	+	0.790978i	$0.290428\pi$
$252$	0.00387059	0.000243824 0
$253$	9.80002	0.616122
$254$	11.1789	0.701425
$255$	−5.67906	−0.355637
$256$	−6.65568	−0.415980
$257$	−21.4279	−1.33664	−0.668319	−	0.743875i	$-0.732986\pi$
$257$	−21.4279	−1.33664	−0.668319	+	0.743875i	$0.732986\pi$
$258$	17.5092	1.09008
$259$	0.0999202	0.00620874
$260$	−2.02312	−0.125469
$261$	−0.418557	−0.0259080
$262$	26.2959	1.62456
$263$	20.3534	1.25505	0.627523	−	0.778598i	$-0.284069\pi$
$263$	20.3534	1.25505	0.627523	+	0.778598i	$0.284069\pi$
$264$	−6.97991	−0.429584
$265$	2.52059	0.154839
$266$	−0.307006	−0.0188238
$267$	−9.29142	−0.568626
$268$	−3.14618	−0.192183
$269$	10.0115	0.610410	0.305205	−	0.952287i	$-0.401275\pi$
$269$	10.0115	0.610410	0.305205	+	0.952287i	$0.401275\pi$
$270$	6.97329	0.424381
$271$	20.8155	1.26445	0.632227	−	0.774784i	$-0.282141\pi$
$271$	20.8155	1.26445	0.632227	+	0.774784i	$0.282141\pi$
$272$	−11.2916	−0.684653
$273$	−1.05665	−0.0639516
$274$	−19.9465	−1.20501
$275$	−1.38343	−0.0834241
$276$	−3.38419	−0.203704
$277$	−10.3198	−0.620055	−0.310028	−	0.950728i	$-0.600338\pi$
$277$	−10.3198	−0.620055	−0.310028	+	0.950728i	$0.600338\pi$
$278$	6.77666	0.406437
$279$	1.35422	0.0810750
$280$	−0.262444	−0.0156840
$281$	16.9628	1.01192	0.505958	−	0.862558i	$-0.331139\pi$
$281$	16.9628	1.01192	0.505958	+	0.862558i	$0.331139\pi$
$282$	25.0091	1.48927
$283$	13.3769	0.795177	0.397588	−	0.917564i	$-0.369847\pi$
$283$	13.3769	0.795177	0.397588	+	0.917564i	$0.369847\pi$
$284$	−0.898306	−0.0533047
$285$	4.50455	0.266826
$286$	−12.9458	−0.765502
$287$	−0.500997	−0.0295729
$288$	−0.247614	−0.0145908
$289$	−5.66070	−0.332982
$290$	3.52093	0.206756
$291$	0.0369450	0.00216575
$292$	3.35730	0.196471
$293$	11.6607	0.681227	0.340614	−	0.940203i	$-0.389365\pi$
$293$	11.6607	0.681227	0.340614	+	0.940203i	$0.389365\pi$
$294$	15.4509	0.901116
$295$	−9.78089	−0.569465
$296$	−3.40748	−0.198056
$297$	−7.36283	−0.427235
$298$	−3.13474	−0.181591
$299$	−50.5929	−2.92586
$300$	0.477733	0.0275819
$301$	−0.695122	−0.0400662
$302$	−20.0624	−1.15446
$303$	22.4178	1.28787
$304$	8.95631	0.513680
$305$	2.48430	0.142251
$306$	−0.687213	−0.0392853
$307$	−3.31655	−0.189286	−0.0946428	−	0.995511i	$-0.530171\pi$
$307$	−3.31655	−0.189286	−0.0946428	+	0.995511i	$0.530171\pi$
$308$	0.0343786	0.00195890
$309$	−6.82295	−0.388144
$310$	−11.3918	−0.647012
$311$	−6.86809	−0.389454	−0.194727	−	0.980858i	$-0.562382\pi$
$311$	−6.86809	−0.389454	−0.194727	+	0.980858i	$0.562382\pi$
$312$	36.0340	2.04002
$313$	32.4521	1.83430	0.917150	−	0.398541i	$-0.130483\pi$
$313$	32.4521	1.83430	0.917150	+	0.398541i	$0.130483\pi$
$314$	10.0126	0.565043
$315$	−0.0136639	−0.000769875 0
$316$	1.76039	0.0990297
$317$	21.7340	1.22070	0.610351	−	0.792131i	$-0.291028\pi$
$317$	21.7340	1.22070	0.610351	+	0.792131i	$0.291028\pi$
$318$	−5.56976	−0.312337
$319$	−3.71762	−0.208147
$320$	8.78938	0.491341
$321$	12.8085	0.714903
$322$	−0.814232	−0.0453754
$323$	−8.99416	−0.500449
$324$	2.41020	0.133900
$325$	7.14201	0.396168
$326$	9.04659	0.501044
$327$	−8.82451	−0.487996
$328$	17.0850	0.943362
$329$	−0.992871	−0.0547387
$330$	3.05698	0.168281
$331$	−21.2653	−1.16885	−0.584424	−	0.811449i	$-0.698679\pi$
$331$	−21.2653	−1.16885	−0.584424	+	0.811449i	$0.698679\pi$
$332$	3.23681	0.177643
$333$	−0.177407	−0.00972187
$334$	−19.6234	−1.07374
$335$	11.1066	0.606818
$336$	0.496105	0.0270647
$337$	11.4814	0.625431	0.312715	−	0.949847i	$-0.398761\pi$
$337$	11.4814	0.625431	0.312715	+	0.949847i	$0.398761\pi$
$338$	49.8000	2.70877
$339$	3.66891	0.199268
$340$	−0.953883	−0.0517316
$341$	12.0282	0.651362
$342$	0.545087	0.0294749
$343$	−1.22749	−0.0662782
$344$	23.7050	1.27809
$345$	11.9468	0.643195
$346$	−30.8530	−1.65867
$347$	8.52502	0.457647	0.228823	−	0.973468i	$-0.426512\pi$
$347$	8.52502	0.457647	0.228823	+	0.973468i	$0.426512\pi$
$348$	1.28378	0.0688181
$349$	16.6587	0.891719	0.445860	−	0.895103i	$-0.352898\pi$
$349$	16.6587	0.891719	0.445860	+	0.895103i	$0.352898\pi$
$350$	0.114942	0.00614392
$351$	38.0108	2.02887
$352$	−2.19931	−0.117224
$353$	−23.1070	−1.22986	−0.614931	−	0.788581i	$-0.710816\pi$
$353$	−23.1070	−1.22986	−0.614931	+	0.788581i	$0.710816\pi$
$354$	21.6129	1.14871
$355$	3.17119	0.168309
$356$	−1.56063	−0.0827133
$357$	−0.498202	−0.0263676
$358$	28.0148	1.48063
$359$	−29.9559	−1.58101	−0.790505	−	0.612455i	$-0.790182\pi$
$359$	−29.9559	−1.58101	−0.790505	+	0.612455i	$0.790182\pi$
$360$	0.465967	0.0245586
$361$	−11.8660	−0.624525
$362$	−16.8570	−0.885984
$363$	15.3236	0.804282
$364$	−0.177481	−0.00930251
$365$	−11.8519	−0.620357
$366$	−5.48958	−0.286945
$367$	7.89567	0.412151	0.206075	−	0.978536i	$-0.433931\pi$
$367$	7.89567	0.412151	0.206075	+	0.978536i	$0.433931\pi$
$368$	23.7537	1.23825
$369$	0.889517	0.0463064
$370$	1.49237	0.0775845
$371$	0.221122	0.0114801
$372$	−4.15362	−0.215355
$373$	−20.3432	−1.05333	−0.526667	−	0.850072i	$-0.676558\pi$
$373$	−20.3432	−1.05333	−0.526667	+	0.850072i	$0.676558\pi$
$374$	−6.10382	−0.315621
$375$	−1.68649	−0.0870899
$376$	33.8589	1.74614
$377$	19.1923	0.988455
$378$	0.611739	0.0314645
$379$	33.5090	1.72124	0.860621	−	0.509246i	$-0.170076\pi$
$379$	33.5090	1.72124	0.860621	+	0.509246i	$0.170076\pi$
$380$	0.756605	0.0388130
$381$	−14.3890	−0.737171
$382$	7.49122	0.383284
$383$	11.7700	0.601417	0.300709	−	0.953716i	$-0.402777\pi$
$383$	11.7700	0.601417	0.300709	+	0.953716i	$0.402777\pi$
$384$	−14.0598	−0.717484
$385$	−0.121363	−0.00618523
$386$	3.20215	0.162985
$387$	1.23418	0.0627371
$388$	0.00620546	0.000315035 0
$389$	−16.9732	−0.860575	−0.430288	−	0.902692i	$-0.641588\pi$
$389$	−16.9732	−0.860575	−0.430288	+	0.902692i	$0.641588\pi$
$390$	−15.7817	−0.799139
$391$	−23.8541	−1.20635
$392$	20.9184	1.05654
$393$	−33.8470	−1.70735
$394$	0.809146	0.0407642
$395$	−6.21451	−0.312686
$396$	−0.0610389	−0.00306732
$397$	−10.0005	−0.501913	−0.250956	−	0.967998i	$-0.580745\pi$
$397$	−10.0005	−0.501913	−0.250956	+	0.967998i	$0.580745\pi$
$398$	27.6265	1.38479
$399$	0.395166	0.0197830
$400$	−3.35322	−0.167661
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−24.5423	−1.22406
$403$	−62.0958	−3.09321
$404$	3.76540	0.187336
$405$	−8.50847	−0.422789
$406$	0.308878	0.0153293
$407$	−1.57573	−0.0781062
$408$	16.9897	0.841114
$409$	−22.2165	−1.09854	−0.549269	−	0.835646i	$-0.685094\pi$
$409$	−22.2165	−1.09854	−0.549269	+	0.835646i	$0.685094\pi$
$410$	−7.48269	−0.369544
$411$	25.6743	1.26642
$412$	−1.14602	−0.0564601
$413$	−0.858039	−0.0422213
$414$	1.44566	0.0710505
$415$	−11.4266	−0.560907
$416$	11.3540	0.556676
$417$	−8.72265	−0.427150
$418$	4.84146	0.236804
$419$	18.6594	0.911574	0.455787	−	0.890089i	$-0.349358\pi$
$419$	18.6594	0.911574	0.455787	+	0.890089i	$0.349358\pi$
$420$	0.0419096	0.00204498
$421$	7.60102	0.370451	0.185225	−	0.982696i	$-0.440698\pi$
$421$	7.60102	0.370451	0.185225	+	0.982696i	$0.440698\pi$
$422$	−29.3628	−1.42936
$423$	1.76283	0.0857119
$424$	−7.54069	−0.366208
$425$	3.36739	0.163342
$426$	−7.00740	−0.339510
$427$	0.217938	0.0105468
$428$	2.15138	0.103991
$429$	16.6633	0.804513
$430$	−10.3821	−0.500667
$431$	25.9586	1.25038	0.625190	−	0.780472i	$-0.285021\pi$
$431$	25.9586	1.25038	0.625190	+	0.780472i	$0.285021\pi$
$432$	−17.8463	−0.858631
$433$	−30.3678	−1.45938	−0.729691	−	0.683777i	$-0.760336\pi$
$433$	−30.3678	−1.45938	−0.729691	+	0.683777i	$0.760336\pi$
$434$	−0.999359	−0.0479708
$435$	−4.53200	−0.217293
$436$	−1.48221	−0.0709849
$437$	18.9207	0.905099
$438$	26.1892	1.25137
$439$	19.8796	0.948804	0.474402	−	0.880308i	$-0.342664\pi$
$439$	19.8796	0.948804	0.474402	+	0.880308i	$0.342664\pi$
$440$	4.13872	0.197306
$441$	1.08910	0.0518619
$442$	31.5112	1.49883
$443$	16.2349	0.771343	0.385671	−	0.922636i	$-0.373970\pi$
$443$	16.2349	0.771343	0.385671	+	0.922636i	$0.373970\pi$
$444$	0.544139	0.0258237
$445$	5.50933	0.261167
$446$	−14.3658	−0.680239
$447$	4.03491	0.190845
$448$	0.771058	0.0364291
$449$	25.3045	1.19419	0.597097	−	0.802169i	$-0.296321\pi$
$449$	25.3045	1.19419	0.597097	+	0.802169i	$0.296321\pi$
$450$	−0.204079	−0.00962037
$451$	7.90069	0.372029
$452$	0.616249	0.0289859
$453$	25.8235	1.21329
$454$	14.0590	0.659822
$455$	0.626540	0.0293727
$456$	−13.4759	−0.631069
$457$	16.2650	0.760846	0.380423	−	0.924813i	$-0.375778\pi$
$457$	16.2650	0.760846	0.380423	+	0.924813i	$0.375778\pi$
$458$	24.6262	1.15070
$459$	17.9217	0.836515
$460$	2.00665	0.0935604
$461$	12.2560	0.570818	0.285409	−	0.958406i	$-0.407871\pi$
$461$	12.2560	0.570818	0.285409	+	0.958406i	$0.407871\pi$
$462$	0.268177	0.0124767
$463$	−17.5631	−0.816225	−0.408112	−	0.912932i	$-0.633813\pi$
$463$	−17.5631	−0.816225	−0.408112	+	0.912932i	$0.633813\pi$
$464$	−9.01091	−0.418321
$465$	14.6631	0.679984
$466$	−32.5494	−1.50782
$467$	−9.54882	−0.441867	−0.220933	−	0.975289i	$-0.570910\pi$
$467$	−9.54882	−0.441867	−0.220933	+	0.975289i	$0.570910\pi$
$468$	0.315115	0.0145662
$469$	0.974338	0.0449907
$470$	−14.8291	−0.684016
$471$	−12.8878	−0.593839
$472$	29.2608	1.34684
$473$	10.9620	0.504034
$474$	13.7322	0.630743
$475$	−2.67096	−0.122552
$476$	−0.0836804	−0.00383548
$477$	−0.392599	−0.0179759
$478$	−3.84262	−0.175757
$479$	−19.0724	−0.871441	−0.435720	−	0.900082i	$-0.643506\pi$
$479$	−19.0724	−0.871441	−0.435720	+	0.900082i	$0.643506\pi$
$480$	−2.68109	−0.122375
$481$	8.13477	0.370914
$482$	−21.6533	−0.986283
$483$	1.04805	0.0476878
$484$	2.57383	0.116992
$485$	−0.0219065	−0.000994722 0
$486$	−2.11867	−0.0961047
$487$	12.2823	0.556562	0.278281	−	0.960500i	$-0.410235\pi$
$487$	12.2823	0.556562	0.278281	+	0.960500i	$0.410235\pi$
$488$	−7.43213	−0.336437
$489$	−11.6444	−0.526578
$490$	−9.16160	−0.413879
$491$	−31.6932	−1.43029	−0.715146	−	0.698975i	$-0.753640\pi$
$491$	−31.6932	−1.43029	−0.715146	+	0.698975i	$0.753640\pi$
$492$	−2.72830	−0.123001
$493$	9.04899	0.407546
$494$	−24.9942	−1.12454
$495$	0.215479	0.00968506
$496$	29.1544	1.30907
$497$	0.278196	0.0124788
$498$	25.2493	1.13145
$499$	−27.8432	−1.24643	−0.623216	−	0.782050i	$-0.714174\pi$
$499$	−27.8432	−1.24643	−0.623216	+	0.782050i	$0.714174\pi$
$500$	−0.283271	−0.0126683
$501$	25.2584	1.12846
$502$	25.4015	1.13372
$503$	17.9325	0.799569	0.399784	−	0.916609i	$-0.369085\pi$
$503$	17.9325	0.799569	0.399784	+	0.916609i	$0.369085\pi$
$504$	0.0408775	0.00182083
$505$	−13.2926	−0.591512
$506$	12.8404	0.570824
$507$	−64.1006	−2.84681
$508$	−2.41685	−0.107230
$509$	−31.6247	−1.40174	−0.700870	−	0.713289i	$-0.747205\pi$
$509$	−31.6247	−1.40174	−0.700870	+	0.713289i	$0.747205\pi$
$510$	−7.44093	−0.329490
$511$	−1.03972	−0.0459946
$512$	−25.3940	−1.12226
$513$	−14.2152	−0.627619
$514$	−28.0758	−1.23837
$515$	4.04565	0.178273
$516$	−3.78545	−0.166645
$517$	15.6575	0.688616
$518$	0.130919	0.00575227
$519$	39.7127	1.74319
$520$	−21.3663	−0.936973
$521$	11.0387	0.483616	0.241808	−	0.970324i	$-0.422260\pi$
$521$	11.0387	0.483616	0.241808	+	0.970324i	$0.422260\pi$
$522$	−0.548410	−0.0240032
$523$	8.54859	0.373804	0.186902	−	0.982379i	$-0.440155\pi$
$523$	8.54859	0.373804	0.186902	+	0.982379i	$0.440155\pi$
$524$	−5.68510	−0.248355
$525$	−0.147949	−0.00645702
$526$	26.6679	1.16278
$527$	−29.2776	−1.27535
$528$	−7.82353	−0.340476
$529$	27.1808	1.18178
$530$	3.30258	0.143455
$531$	1.52344	0.0661117
$532$	0.0663740	0.00287768
$533$	−40.7875	−1.76670
$534$	−12.1740	−0.526820
$535$	−7.59480	−0.328352
$536$	−33.2269	−1.43518
$537$	−36.0595	−1.55608
$538$	13.1174	0.565533
$539$	9.67338	0.416662
$540$	−1.50761	−0.0648772
$541$	19.1445	0.823087	0.411544	−	0.911390i	$-0.364990\pi$
$541$	19.1445	0.823087	0.411544	+	0.911390i	$0.364990\pi$
$542$	27.2733	1.17149
$543$	21.6976	0.931135
$544$	5.35330	0.229521
$545$	5.23248	0.224135
$546$	−1.38447	−0.0592498
$547$	−14.9017	−0.637149	−0.318574	−	0.947898i	$-0.603204\pi$
$547$	−14.9017	−0.637149	−0.318574	+	0.947898i	$0.603204\pi$
$548$	4.31238	0.184216
$549$	−0.386948	−0.0165145
$550$	−1.81263	−0.0772907
$551$	−7.17752	−0.305773
$552$	−35.7405	−1.52122
$553$	−0.545175	−0.0231832
$554$	−13.5214	−0.574468
$555$	−1.92091	−0.0815383
$556$	−1.46510	−0.0621340
$557$	−14.3157	−0.606574	−0.303287	−	0.952899i	$-0.598084\pi$
$557$	−14.3157	−0.606574	−0.303287	+	0.952899i	$0.598084\pi$
$558$	1.77435	0.0751144
$559$	−56.5917	−2.39358
$560$	−0.294164	−0.0124307
$561$	7.85660	0.331706
$562$	22.2254	0.937520
$563$	31.8501	1.34232	0.671161	−	0.741311i	$-0.265796\pi$
$563$	31.8501	1.34232	0.671161	+	0.741311i	$0.265796\pi$
$564$	−5.40691	−0.227672
$565$	−2.17548	−0.0915230
$566$	17.5270	0.736715
$567$	−0.746414	−0.0313465
$568$	−9.48704	−0.398068
$569$	36.3429	1.52357	0.761786	−	0.647828i	$-0.224323\pi$
$569$	36.3429	1.52357	0.761786	+	0.647828i	$0.224323\pi$
$570$	5.90204	0.247209
$571$	17.7675	0.743547	0.371774	−	0.928323i	$-0.378750\pi$
$571$	17.7675	0.743547	0.371774	+	0.928323i	$0.378750\pi$
$572$	2.79885	0.117026
$573$	−9.64240	−0.402817
$574$	−0.656427	−0.0273987
$575$	−7.08384	−0.295417
$576$	−1.36901	−0.0570419
$577$	7.32537	0.304959	0.152480	−	0.988307i	$-0.451274\pi$
$577$	7.32537	0.304959	0.152480	+	0.988307i	$0.451274\pi$
$578$	−7.41687	−0.308501
$579$	−4.12168	−0.171291
$580$	−0.761217	−0.0316078
$581$	−1.00241	−0.0415868
$582$	0.0484068	0.00200653
$583$	−3.48707	−0.144420
$584$	35.4566	1.46720
$585$	−1.11242	−0.0459928
$586$	15.2784	0.631143
$587$	−2.39693	−0.0989320	−0.0494660	−	0.998776i	$-0.515752\pi$
$587$	−2.39693	−0.0989320	−0.0494660	+	0.998776i	$0.515752\pi$
$588$	−3.34045	−0.137758
$589$	23.2225	0.956868
$590$	−12.8153	−0.527598
$591$	−1.04150	−0.0428416
$592$	−3.81932	−0.156973
$593$	−34.4851	−1.41613	−0.708066	−	0.706146i	$-0.750432\pi$
$593$	−34.4851	−1.41613	−0.708066	+	0.706146i	$0.750432\pi$
$594$	−9.64708	−0.395824
$595$	0.295408	0.0121105
$596$	0.677724	0.0277606
$597$	−35.5597	−1.45536
$598$	−66.2888	−2.71075
$599$	−27.7210	−1.13265	−0.566324	−	0.824183i	$-0.691635\pi$
$599$	−27.7210	−1.13265	−0.566324	+	0.824183i	$0.691635\pi$
$600$	5.04535	0.205976
$601$	−10.0382	−0.409469	−0.204734	−	0.978818i	$-0.565633\pi$
$601$	−10.0382	−0.409469	−0.204734	+	0.978818i	$0.565633\pi$
$602$	−0.910777	−0.0371205
$603$	−1.72993	−0.0704482
$604$	4.33743	0.176488
$605$	−9.08611	−0.369403
$606$	29.3727	1.19318
$607$	−22.9437	−0.931254	−0.465627	−	0.884981i	$-0.654171\pi$
$607$	−22.9437	−0.931254	−0.465627	+	0.884981i	$0.654171\pi$
$608$	−4.24615	−0.172204
$609$	−0.397575	−0.0161105
$610$	3.25504	0.131793
$611$	−80.8323	−3.27012
$612$	0.148574	0.00600574
$613$	−38.6700	−1.56187	−0.780934	−	0.624614i	$-0.785257\pi$
$613$	−38.6700	−1.56187	−0.780934	+	0.624614i	$0.785257\pi$
$614$	−4.34548	−0.175369
$615$	9.63142	0.388376
$616$	0.363074	0.0146287
$617$	25.6667	1.03330	0.516652	−	0.856196i	$-0.327178\pi$
$617$	25.6667	1.03330	0.516652	+	0.856196i	$0.327178\pi$
$618$	−8.93970	−0.359607
$619$	13.6779	0.549760	0.274880	−	0.961479i	$-0.411362\pi$
$619$	13.6779	0.549760	0.274880	+	0.961479i	$0.411362\pi$
$620$	2.46288	0.0989118
$621$	−37.7013	−1.51290
$622$	−8.99885	−0.360821
$623$	0.483312	0.0193635
$624$	40.3892	1.61686
$625$	1.00000	0.0400000
$626$	42.5200	1.69944
$627$	−6.23173	−0.248871
$628$	−2.16470	−0.0863808
$629$	3.83546	0.152930
$630$	−0.0179030	−0.000713274 0
$631$	45.8513	1.82531	0.912655	−	0.408730i	$-0.134028\pi$
$631$	45.8513	1.82531	0.912655	+	0.408730i	$0.134028\pi$
$632$	18.5915	0.739532
$633$	37.7946	1.50220
$634$	28.4767	1.13096
$635$	8.53193	0.338579
$636$	1.20417	0.0477484
$637$	−49.9391	−1.97866
$638$	−4.87097	−0.192844
$639$	−0.493935	−0.0195398
$640$	8.33671	0.329537
$641$	−8.29708	−0.327715	−0.163858	−	0.986484i	$-0.552394\pi$
$641$	−8.29708	−0.327715	−0.163858	+	0.986484i	$0.552394\pi$
$642$	16.7823	0.662343
$643$	−17.0408	−0.672023	−0.336011	−	0.941858i	$-0.609078\pi$
$643$	−17.0408	−0.672023	−0.336011	+	0.941858i	$0.609078\pi$
$644$	0.176035	0.00693675
$645$	13.3634	0.526182
$646$	−11.7845	−0.463656
$647$	13.4083	0.527136	0.263568	−	0.964641i	$-0.415101\pi$
$647$	13.4083	0.527136	0.263568	+	0.964641i	$0.415101\pi$
$648$	25.4542	0.999936
$649$	13.5312	0.531146
$650$	9.35775	0.367041
$651$	1.28633	0.0504154
$652$	−1.95585	−0.0765970
$653$	−19.2110	−0.751784	−0.375892	−	0.926663i	$-0.622664\pi$
$653$	−19.2110	−0.751784	−0.375892	+	0.926663i	$0.622664\pi$
$654$	−11.5622	−0.452119
$655$	20.0695	0.784180
$656$	19.1500	0.747681
$657$	1.84602	0.0720200
$658$	−1.30090	−0.0507143
$659$	−10.3512	−0.403224	−0.201612	−	0.979465i	$-0.564618\pi$
$659$	−10.3512	−0.403224	−0.201612	+	0.979465i	$0.564618\pi$
$660$	−0.660911	−0.0257259
$661$	−27.5682	−1.07228	−0.536139	−	0.844130i	$-0.680118\pi$
$661$	−27.5682	−1.07228	−0.536139	+	0.844130i	$0.680118\pi$
$662$	−27.8627	−1.08291
$663$	−40.5599	−1.57522
$664$	34.1841	1.32660
$665$	−0.234313	−0.00908626
$666$	−0.232446	−0.00900711
$667$	−19.0360	−0.737077
$668$	4.24253	0.164148
$669$	18.4911	0.714905
$670$	14.5523	0.562205
$671$	−3.43687	−0.132679
$672$	−0.235202	−0.00907310
$673$	−8.55198	−0.329655	−0.164827	−	0.986322i	$-0.552707\pi$
$673$	−8.55198	−0.329655	−0.164827	+	0.986322i	$0.552707\pi$
$674$	15.0434	0.579449
$675$	5.32215	0.204850
$676$	−10.7667	−0.414102
$677$	−11.5175	−0.442654	−0.221327	−	0.975200i	$-0.571039\pi$
$677$	−11.5175	−0.442654	−0.221327	+	0.975200i	$0.571039\pi$
$678$	4.80716	0.184618
$679$	−0.00192177	−7.37507e−5 0
$680$	−10.0740	−0.386320
$681$	−18.0962	−0.693447
$682$	15.7598	0.603474
$683$	−22.1915	−0.849134	−0.424567	−	0.905397i	$-0.639574\pi$
$683$	−22.1915	−0.849134	−0.424567	+	0.905397i	$0.639574\pi$
$684$	−0.117846	−0.00450597
$685$	−15.2235	−0.581661
$686$	−1.60831	−0.0614054
$687$	−31.6978	−1.20935
$688$	26.5702	1.01298
$689$	18.0021	0.685825
$690$	15.6532	0.595907
$691$	39.6378	1.50789	0.753947	−	0.656936i	$-0.228148\pi$
$691$	39.6378	1.50789	0.753947	+	0.656936i	$0.228148\pi$
$692$	6.67034	0.253568
$693$	0.0189031	0.000718070 0
$694$	11.1698	0.424000
$695$	5.17208	0.196188
$696$	13.5581	0.513918
$697$	−19.2309	−0.728423
$698$	21.8269	0.826160
$699$	41.8963	1.58466
$700$	−0.0248502	−0.000939250 0
$701$	−14.3987	−0.543833	−0.271916	−	0.962321i	$-0.587657\pi$
$701$	−14.3987	−0.543833	−0.271916	+	0.962321i	$0.587657\pi$
$702$	49.8033	1.87971
$703$	−3.04223	−0.114740
$704$	−12.1595	−0.458279
$705$	19.0874	0.718874
$706$	−30.2757	−1.13944
$707$	−1.16610	−0.0438559
$708$	−4.67265	−0.175609
$709$	−22.5409	−0.846543	−0.423272	−	0.906003i	$-0.639118\pi$
$709$	−22.5409	−0.846543	−0.423272	+	0.906003i	$0.639118\pi$
$710$	4.15502	0.155935
$711$	0.967953	0.0363011
$712$	−16.4819	−0.617685
$713$	61.5901	2.30657
$714$	−0.652764	−0.0244291
$715$	−9.88049	−0.369509
$716$	−6.05673	−0.226350
$717$	4.94606	0.184714
$718$	−39.2494	−1.46477
$719$	−50.3366	−1.87724	−0.938618	−	0.344957i	$-0.887893\pi$
$719$	−50.3366	−1.87724	−0.938618	+	0.344957i	$0.887893\pi$
$720$	0.522286	0.0194645
$721$	0.354909	0.0132175
$722$	−15.5473	−0.578609
$723$	27.8713	1.03655
$724$	3.64444	0.135445
$725$	2.68724	0.0998017
$726$	20.0776	0.745151
$727$	5.62855	0.208751	0.104376	−	0.994538i	$-0.466716\pi$
$727$	5.62855	0.208751	0.104376	+	0.994538i	$0.466716\pi$
$728$	−1.87438	−0.0694691
$729$	28.2525	1.04639
$730$	−15.5288	−0.574749
$731$	−26.6824	−0.986886
$732$	1.18683	0.0438667
$733$	11.2154	0.414252	0.207126	−	0.978314i	$-0.433589\pi$
$733$	11.2154	0.414252	0.207126	+	0.978314i	$0.433589\pi$
$734$	10.3452	0.381849
$735$	11.7924	0.434971
$736$	−11.2615	−0.415105
$737$	−15.3652	−0.565986
$738$	1.16548	0.0429019
$739$	14.3976	0.529626	0.264813	−	0.964300i	$-0.414690\pi$
$739$	14.3976	0.529626	0.264813	+	0.964300i	$0.414690\pi$
$740$	−0.322646	−0.0118607
$741$	32.1715	1.18185
$742$	0.289722	0.0106360
$743$	−42.0502	−1.54267	−0.771336	−	0.636428i	$-0.780411\pi$
$743$	−42.0502	−1.54267	−0.771336	+	0.636428i	$0.780411\pi$
$744$	−43.8666	−1.60823
$745$	−2.39249	−0.0876542
$746$	−26.6545	−0.975892
$747$	1.77976	0.0651182
$748$	1.31963	0.0482505
$749$	−0.666262	−0.0243447
$750$	−2.20970	−0.0806870
$751$	−2.69472	−0.0983318	−0.0491659	−	0.998791i	$-0.515656\pi$
$751$	−2.69472	−0.0983318	−0.0491659	+	0.998791i	$0.515656\pi$
$752$	37.9512	1.38394
$753$	−32.6958	−1.19150
$754$	25.1466	0.915783
$755$	−15.3120	−0.557260
$756$	−0.132257	−0.00481012
$757$	−8.55113	−0.310796	−0.155398	−	0.987852i	$-0.549666\pi$
$757$	−8.55113	−0.310796	−0.155398	+	0.987852i	$0.549666\pi$
$758$	43.9048	1.59470
$759$	−16.5276	−0.599915
$760$	7.99054	0.289847
$761$	33.4703	1.21330	0.606649	−	0.794970i	$-0.292513\pi$
$761$	33.4703	1.21330	0.606649	+	0.794970i	$0.292513\pi$
$762$	−18.8531	−0.682974
$763$	0.459024	0.0166178
$764$	−1.61958	−0.0585945
$765$	−0.524494	−0.0189631
$766$	15.4215	0.557201
$767$	−69.8552	−2.52233
$768$	11.2247	0.405037
$769$	26.6247	0.960112	0.480056	−	0.877238i	$-0.340616\pi$
$769$	26.6247	0.960112	0.480056	+	0.877238i	$0.340616\pi$
$770$	−0.159015	−0.00573049
$771$	36.1380	1.30148
$772$	−0.692297	−0.0249163
$773$	−38.5542	−1.38670	−0.693349	−	0.720602i	$-0.743865\pi$
$773$	−38.5542	−1.38670	−0.693349	+	0.720602i	$0.743865\pi$
$774$	1.61708	0.0581246
$775$	−8.69445	−0.312314
$776$	0.0655361	0.00235261
$777$	−0.168514	−0.00604541
$778$	−22.2390	−0.797305
$779$	15.2537	0.546520
$780$	3.41197	0.122168
$781$	−4.38713	−0.156984
$782$	−31.2545	−1.11766
$783$	14.3019	0.511108
$784$	23.4467	0.837382
$785$	7.64180	0.272747
$786$	−44.3477	−1.58183
$787$	−2.88297	−0.102767	−0.0513835	−	0.998679i	$-0.516363\pi$
$787$	−2.88297	−0.102767	−0.0513835	+	0.998679i	$0.516363\pi$
$788$	−0.174936	−0.00623182
$789$	−34.3258	−1.22203
$790$	−8.14250	−0.289697
$791$	−0.190846	−0.00678570
$792$	−0.644634	−0.0229061
$793$	17.7429	0.630070
$794$	−13.1031	−0.465012
$795$	−4.25095	−0.150766
$796$	−5.97278	−0.211700
$797$	−39.1001	−1.38500	−0.692498	−	0.721420i	$-0.743490\pi$
$797$	−39.1001	−1.38500	−0.692498	+	0.721420i	$0.743490\pi$
$798$	0.517762	0.0183286
$799$	−38.1116	−1.34829
$800$	1.58975	0.0562061
$801$	−0.858116	−0.0303200
$802$	1.31024	0.0462662
$803$	16.3963	0.578614
$804$	5.30599	0.187128
$805$	−0.621438	−0.0219028
$806$	−81.3605	−2.86580
$807$	−16.8842	−0.594353
$808$	39.7665	1.39898
$809$	−30.3751	−1.06793	−0.533967	−	0.845506i	$-0.679299\pi$
$809$	−30.3751	−1.06793	−0.533967	+	0.845506i	$0.679299\pi$
$810$	−11.1481	−0.391706
$811$	8.33138	0.292554	0.146277	−	0.989244i	$-0.453271\pi$
$811$	8.33138	0.292554	0.146277	+	0.989244i	$0.453271\pi$
$812$	−0.0667786	−0.00234347
$813$	−35.1051	−1.23119
$814$	−2.06459	−0.0723638
$815$	6.90452	0.241855
$816$	19.0431	0.666643
$817$	21.1641	0.740439
$818$	−29.1090	−1.01777
$819$	−0.0975880	−0.00341000
$820$	1.61774	0.0564939
$821$	−24.1038	−0.841227	−0.420613	−	0.907240i	$-0.638185\pi$
$821$	−24.1038	−0.841227	−0.420613	+	0.907240i	$0.638185\pi$
$822$	33.6395	1.17331
$823$	−15.5561	−0.542252	−0.271126	−	0.962544i	$-0.587396\pi$
$823$	−15.5561	−0.542252	−0.271126	+	0.962544i	$0.587396\pi$
$824$	−12.1031	−0.421632
$825$	2.33314	0.0812296
$826$	−1.12424	−0.0391172
$827$	27.6585	0.961782	0.480891	−	0.876781i	$-0.340313\pi$
$827$	27.6585	0.961782	0.480891	+	0.876781i	$0.340313\pi$
$828$	−0.312549	−0.0108618
$829$	−39.0800	−1.35730	−0.678652	−	0.734460i	$-0.737435\pi$
$829$	−39.0800	−1.35730	−0.678652	+	0.734460i	$0.737435\pi$
$830$	−14.9715	−0.519669
$831$	17.4042	0.603744
$832$	62.7739	2.17629
$833$	−23.5458	−0.815814
$834$	−11.4288	−0.395746
$835$	−14.9769	−0.518298
$836$	−1.04671	−0.0362013
$837$	−46.2731	−1.59943
$838$	24.4484	0.844554
$839$	−32.8989	−1.13580	−0.567898	−	0.823099i	$-0.692243\pi$
$839$	−32.8989	−1.13580	−0.567898	+	0.823099i	$0.692243\pi$
$840$	0.442609	0.0152715
$841$	−21.7787	−0.750991
$842$	9.95916	0.343215
$843$	−28.6076	−0.985298
$844$	6.34816	0.218513
$845$	38.0083	1.30753
$846$	2.30974	0.0794103
$847$	−0.797089	−0.0273883
$848$	−8.45209	−0.290246
$849$	−22.5601	−0.774259
$850$	4.41209	0.151333
$851$	−8.06852	−0.276585
$852$	1.51498	0.0519025
$853$	53.9014	1.84555	0.922775	−	0.385340i	$-0.125916\pi$
$853$	53.9014	1.84555	0.922775	+	0.385340i	$0.125916\pi$
$854$	0.285551	0.00977137
$855$	0.416021	0.0142276
$856$	22.7209	0.776583
$857$	−5.88202	−0.200926	−0.100463	−	0.994941i	$-0.532032\pi$
$857$	−5.88202	−0.200926	−0.100463	+	0.994941i	$0.532032\pi$
$858$	21.8330	0.745365
$859$	−24.3526	−0.830899	−0.415450	−	0.909616i	$-0.636376\pi$
$859$	−24.3526	−0.830899	−0.415450	+	0.909616i	$0.636376\pi$
$860$	2.24458	0.0765394
$861$	0.844926	0.0287950
$862$	34.0120	1.15845
$863$	−42.9382	−1.46163	−0.730817	−	0.682573i	$-0.760861\pi$
$863$	−42.9382	−1.46163	−0.730817	+	0.682573i	$0.760861\pi$
$864$	8.46087	0.287845
$865$	−23.5476	−0.800641
$866$	−39.7891	−1.35209
$867$	9.54670	0.324223
$868$	0.216059	0.00733352
$869$	8.59736	0.291645
$870$	−5.93801	−0.201318
$871$	79.3235	2.68777
$872$	−15.6536	−0.530099
$873$	0.00341208	0.000115482 0
$874$	24.7906	0.838555
$875$	0.0877260	0.00296568
$876$	−5.66205	−0.191303
$877$	7.82308	0.264167	0.132083	−	0.991239i	$-0.457833\pi$
$877$	7.82308	0.264167	0.132083	+	0.991239i	$0.457833\pi$
$878$	26.0471	0.879048
$879$	−19.6657	−0.663307
$880$	4.63895	0.156379
$881$	43.0066	1.44893	0.724465	−	0.689311i	$-0.242087\pi$
$881$	43.0066	1.44893	0.724465	+	0.689311i	$0.242087\pi$
$882$	1.42698	0.0480490
$883$	33.6751	1.13326	0.566629	−	0.823973i	$-0.308247\pi$
$883$	33.6751	1.13326	0.566629	+	0.823973i	$0.308247\pi$
$884$	−6.81264	−0.229134
$885$	16.4954	0.554485
$886$	21.2716	0.714633
$887$	27.8258	0.934300	0.467150	−	0.884178i	$-0.345281\pi$
$887$	27.8258	0.934300	0.467150	+	0.884178i	$0.345281\pi$
$888$	5.74667	0.192846
$889$	0.748473	0.0251030
$890$	7.21854	0.241966
$891$	11.7709	0.394340
$892$	3.10585	0.103991
$893$	30.2296	1.01159
$894$	5.28671	0.176814
$895$	21.3814	0.714701
$896$	0.731346	0.0244326
$897$	85.3243	2.84890
$898$	33.1550	1.10640
$899$	−23.3641	−0.779236
$900$	0.0441214	0.00147071
$901$	8.48781	0.282770
$902$	10.3518	0.344677
$903$	1.17232	0.0390122
$904$	6.50823	0.216460
$905$	−12.8656	−0.427666
$906$	33.8349	1.12409
$907$	−8.16844	−0.271229	−0.135614	−	0.990762i	$-0.543301\pi$
$907$	−8.16844	−0.271229	−0.135614	+	0.990762i	$0.543301\pi$
$908$	−3.03952	−0.100870
$909$	2.07041	0.0686711
$910$	0.820918	0.0272132
$911$	−15.8082	−0.523748	−0.261874	−	0.965102i	$-0.584341\pi$
$911$	−15.8082	−0.523748	−0.261874	+	0.965102i	$0.584341\pi$
$912$	−15.1047	−0.500167
$913$	15.8079	0.523164
$914$	21.3111	0.704908
$915$	−4.18975	−0.138509
$916$	−5.32412	−0.175914
$917$	1.76062	0.0581407
$918$	23.4818	0.775014
$919$	36.3723	1.19981	0.599905	−	0.800071i	$-0.295205\pi$
$919$	36.3723	1.19981	0.599905	+	0.800071i	$0.295205\pi$
$920$	21.1923	0.698688
$921$	5.59333	0.184306
$922$	16.0583	0.528851
$923$	22.6487	0.745491
$924$	−0.0579791	−0.00190737
$925$	1.13900	0.0374502
$926$	−23.0118	−0.756215
$927$	−0.630138	−0.0206965
$928$	4.27204	0.140237
$929$	8.62936	0.283120	0.141560	−	0.989930i	$-0.454788\pi$
$929$	8.62936	0.283120	0.141560	+	0.989930i	$0.454788\pi$
$930$	19.2122	0.629992
$931$	18.6762	0.612087
$932$	7.03711	0.230508
$933$	11.5830	0.379209
$934$	−12.5112	−0.409381
$935$	−4.65855	−0.152351
$936$	3.32794	0.108777
$937$	0.714403	0.0233385	0.0116693	−	0.999932i	$-0.496285\pi$
$937$	0.714403	0.0233385	0.0116693	+	0.999932i	$0.496285\pi$
$938$	1.27662	0.0416830
$939$	−54.7301	−1.78605
$940$	3.20602	0.104569
$941$	51.5688	1.68109	0.840547	−	0.541739i	$-0.182234\pi$
$941$	51.5688	1.68109	0.840547	+	0.541739i	$0.182234\pi$
$942$	−16.8861	−0.550179
$943$	40.4553	1.31741
$944$	32.7974	1.06747
$945$	0.466891	0.0151880
$946$	14.3629	0.466977
$947$	−9.80112	−0.318494	−0.159247	−	0.987239i	$-0.550907\pi$
$947$	−9.80112	−0.318494	−0.159247	+	0.987239i	$0.550907\pi$
$948$	−2.96888	−0.0964247
$949$	−84.6465	−2.74774
$950$	−3.49960	−0.113542
$951$	−36.6541	−1.18859
$952$	−0.883751	−0.0286425
$953$	−21.8079	−0.706426	−0.353213	−	0.935543i	$-0.614911\pi$
$953$	−21.8079	−0.706426	−0.353213	+	0.935543i	$0.614911\pi$
$954$	−0.514400	−0.0166543
$955$	5.71744	0.185012
$956$	0.830765	0.0268689
$957$	6.26972	0.202671
$958$	−24.9894	−0.807372
$959$	−1.33550	−0.0431256
$960$	−14.8232	−0.478417
$961$	44.5934	1.43850
$962$	10.6585	0.343644
$963$	1.18294	0.0381198
$964$	4.68140	0.150778
$965$	2.44394	0.0786733
$966$	1.37319	0.0441818
$967$	39.1861	1.26014	0.630069	−	0.776539i	$-0.283026\pi$
$967$	39.1861	1.26014	0.630069	+	0.776539i	$0.283026\pi$
$968$	27.1823	0.873673
$969$	15.1686	0.487284
$970$	−0.0287027	−0.000921589 0
$971$	−31.3755	−1.00689	−0.503444	−	0.864028i	$-0.667934\pi$
$971$	−31.3755	−1.00689	−0.503444	+	0.864028i	$0.667934\pi$
$972$	0.458051	0.0146920
$973$	0.453726	0.0145458
$974$	16.0927	0.515644
$975$	−12.0449	−0.385746
$976$	−8.33041	−0.266650
$977$	61.7668	1.97609	0.988047	−	0.154153i	$-0.0492650\pi$
$977$	61.7668	1.97609	0.988047	+	0.154153i	$0.0492650\pi$
$978$	−15.2570	−0.487864
$979$	−7.62178	−0.243593
$980$	1.98072	0.0632716
$981$	−0.814994	−0.0260208
$982$	−41.5257	−1.32514
$983$	−54.6181	−1.74205	−0.871024	−	0.491241i	$-0.836543\pi$
$983$	−54.6181	−1.74205	−0.871024	+	0.491241i	$0.836543\pi$
$984$	−28.8137	−0.918546
$985$	0.617556	0.0196770
$986$	11.8564	0.377583
$987$	1.67446	0.0532988
$988$	5.40368	0.171914
$989$	56.1308	1.78486
$990$	0.282329	0.00897302
$991$	3.54343	0.112561	0.0562804	−	0.998415i	$-0.482076\pi$
$991$	3.54343	0.112561	0.0562804	+	0.998415i	$0.482076\pi$
$992$	−13.8220	−0.438848
$993$	35.8637	1.13810
$994$	0.364504	0.0115614
$995$	21.0851	0.668442
$996$	−5.45884	−0.172970
$997$	3.50337	0.110953	0.0554765	−	0.998460i	$-0.482332\pi$
$997$	3.50337	0.110953	0.0554765	+	0.998460i	$0.482332\pi$
$998$	−36.4813	−1.15479
$999$	6.06194	0.191791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.d.1.19	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.d.1.19	✓	25	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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q+1.31024 q^{2} -1.68649 q^{3} -0.283271 q^{4} +1.00000 q^{5} -2.20970 q^{6} +0.0877260 q^{7} -2.99163 q^{8} -0.155757 q^{9} +O(q^{10})\)	\(q+1.31024 q^{2} -1.68649 q^{3} -0.283271 q^{4} +1.00000 q^{5} -2.20970 q^{6} +0.0877260 q^{7} -2.99163 q^{8} -0.155757 q^{9} +1.31024 q^{10} -1.38343 q^{11} +0.477733 q^{12} +7.14201 q^{13} +0.114942 q^{14} -1.68649 q^{15} -3.35322 q^{16} +3.36739 q^{17} -0.204079 q^{18} -2.67096 q^{19} -0.283271 q^{20} -0.147949 q^{21} -1.81263 q^{22} -7.08384 q^{23} +5.04535 q^{24} +1.00000 q^{25} +9.35775 q^{26} +5.32215 q^{27} -0.0248502 q^{28} +2.68724 q^{29} -2.20970 q^{30} -8.69445 q^{31} +1.58975 q^{32} +2.33314 q^{33} +4.41209 q^{34} +0.0877260 q^{35} +0.0441214 q^{36} +1.13900 q^{37} -3.49960 q^{38} -12.0449 q^{39} -2.99163 q^{40} -5.71093 q^{41} -0.193849 q^{42} -7.92378 q^{43} +0.391886 q^{44} -0.155757 q^{45} -9.28154 q^{46} -11.3179 q^{47} +5.65516 q^{48} -6.99230 q^{49} +1.31024 q^{50} -5.67906 q^{51} -2.02312 q^{52} +2.52059 q^{53} +6.97329 q^{54} -1.38343 q^{55} -0.262444 q^{56} +4.50455 q^{57} +3.52093 q^{58} -9.78089 q^{59} +0.477733 q^{60} +2.48430 q^{61} -11.3918 q^{62} -0.0136639 q^{63} +8.78938 q^{64} +7.14201 q^{65} +3.05698 q^{66} +11.1066 q^{67} -0.953883 q^{68} +11.9468 q^{69} +0.114942 q^{70} +3.17119 q^{71} +0.465967 q^{72} -11.8519 q^{73} +1.49237 q^{74} -1.68649 q^{75} +0.756605 q^{76} -0.121363 q^{77} -15.7817 q^{78} -6.21451 q^{79} -3.35322 q^{80} -8.50847 q^{81} -7.48269 q^{82} -11.4266 q^{83} +0.0419096 q^{84} +3.36739 q^{85} -10.3821 q^{86} -4.53200 q^{87} +4.13872 q^{88} +5.50933 q^{89} -0.204079 q^{90} +0.626540 q^{91} +2.00665 q^{92} +14.6631 q^{93} -14.8291 q^{94} -2.67096 q^{95} -2.68109 q^{96} -0.0219065 q^{97} -9.16160 q^{98} +0.215479 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9}+O(q^{10}) \) 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9	\( 25 q - 5 q^{2} - 10 q^{3} + 25 q^{4} + 25 q^{5} + 2 q^{6} - 31 q^{7} - 30 q^{8} + 17 q^{9} - 5 q^{10} - 30 q^{11} - 29 q^{12} - 18 q^{13} + 6 q^{14} - 10 q^{15} + 21 q^{16} - 18 q^{17} - 30 q^{18} - 17 q^{19} + 25 q^{20} + 6 q^{21} - 2 q^{22} - 44 q^{23} + 11 q^{24} + 25 q^{25} - 14 q^{26} - 25 q^{27} - 50 q^{28} - 9 q^{29} + 2 q^{30} - 13 q^{31} - 45 q^{32} - 21 q^{33} - 21 q^{34} - 31 q^{35} + 5 q^{36} - 28 q^{37} - 32 q^{38} + 9 q^{39} - 30 q^{40} + 28 q^{41} - 67 q^{42} - 61 q^{43} - 49 q^{44} + 17 q^{45} + 18 q^{46} - 53 q^{47} - 44 q^{48} + 28 q^{49} - 5 q^{50} - 30 q^{51} - 3 q^{52} - 36 q^{53} + 17 q^{54} - 30 q^{55} - 3 q^{56} - 13 q^{57} + 2 q^{58} - 39 q^{59} - 29 q^{60} + 10 q^{61} - 30 q^{62} - 44 q^{63} - 4 q^{64} - 18 q^{65} + 33 q^{66} - 10 q^{67} - 18 q^{68} - 6 q^{69} + 6 q^{70} - 7 q^{71} - q^{72} - 26 q^{73} - 3 q^{74} - 10 q^{75} + 12 q^{76} + 29 q^{77} - 5 q^{78} - 6 q^{79} + 21 q^{80} + 13 q^{81} - 30 q^{82} - 35 q^{83} + 117 q^{84} - 18 q^{85} + 14 q^{86} - 104 q^{87} + 53 q^{88} + 7 q^{89} - 30 q^{90} - 25 q^{91} - 31 q^{92} + 2 q^{93} + 68 q^{94} - 17 q^{95} + 92 q^{96} + 6 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 25 * q - 5 * q^2 - 10 * q^3 + 25 * q^4 + 25 * q^5 + 2 * q^6 - 31 * q^7 - 30 * q^8 + 17 * q^9 - 5 * q^10 - 30 * q^11 - 29 * q^12 - 18 * q^13 + 6 * q^14 - 10 * q^15 + 21 * q^16 - 18 * q^17 - 30 * q^18 - 17 * q^19 + 25 * q^20 + 6 * q^21 - 2 * q^22 - 44 * q^23 + 11 * q^24 + 25 * q^25 - 14 * q^26 - 25 * q^27 - 50 * q^28 - 9 * q^29 + 2 * q^30 - 13 * q^31 - 45 * q^32 - 21 * q^33 - 21 * q^34 - 31 * q^35 + 5 * q^36 - 28 * q^37 - 32 * q^38 + 9 * q^39 - 30 * q^40 + 28 * q^41 - 67 * q^42 - 61 * q^43 - 49 * q^44 + 17 * q^45 + 18 * q^46 - 53 * q^47 - 44 * q^48 + 28 * q^49 - 5 * q^50 - 30 * q^51 - 3 * q^52 - 36 * q^53 + 17 * q^54 - 30 * q^55 - 3 * q^56 - 13 * q^57 + 2 * q^58 - 39 * q^59 - 29 * q^60 + 10 * q^61 - 30 * q^62 - 44 * q^63 - 4 * q^64 - 18 * q^65 + 33 * q^66 - 10 * q^67 - 18 * q^68 - 6 * q^69 + 6 * q^70 - 7 * q^71 - q^72 - 26 * q^73 - 3 * q^74 - 10 * q^75 + 12 * q^76 + 29 * q^77 - 5 * q^78 - 6 * q^79 + 21 * q^80 + 13 * q^81 - 30 * q^82 - 35 * q^83 + 117 * q^84 - 18 * q^85 + 14 * q^86 - 104 * q^87 + 53 * q^88 + 7 * q^89 - 30 * q^90 - 25 * q^91 - 31 * q^92 + 2 * q^93 + 68 * q^94 - 17 * q^95 + 92 * q^96 + 6 * q^97 + 15 * q^98 - 36 * q^99

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