LMFDB - Embedded newform 8011.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8011,2,Mod(1,8011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, 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("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.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:	$63.9681570592$
Analytic rank:	$0$
Dimension:	$358$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81343 q^{2} +0.884173 q^{3} +5.91537 q^{4} +1.61259 q^{5} -2.48756 q^{6} -3.94545 q^{7} -11.0156 q^{8} -2.21824 q^{9} +O(q^{10})$	\(q-2.81343 q^{2} +0.884173 q^{3} +5.91537 q^{4} +1.61259 q^{5} -2.48756 q^{6} -3.94545 q^{7} -11.0156 q^{8} -2.21824 q^{9} -4.53689 q^{10} +0.390921 q^{11} +5.23021 q^{12} -0.126530 q^{13} +11.1002 q^{14} +1.42581 q^{15} +19.1609 q^{16} -1.86142 q^{17} +6.24085 q^{18} -1.54940 q^{19} +9.53904 q^{20} -3.48846 q^{21} -1.09983 q^{22} -3.99053 q^{23} -9.73970 q^{24} -2.39957 q^{25} +0.355983 q^{26} -4.61383 q^{27} -23.3388 q^{28} +1.53628 q^{29} -4.01140 q^{30} -4.00381 q^{31} -31.8765 q^{32} +0.345642 q^{33} +5.23698 q^{34} -6.36238 q^{35} -13.1217 q^{36} -4.51815 q^{37} +4.35913 q^{38} -0.111875 q^{39} -17.7636 q^{40} +7.57481 q^{41} +9.81454 q^{42} +0.336469 q^{43} +2.31244 q^{44} -3.57710 q^{45} +11.2271 q^{46} +9.11906 q^{47} +16.9415 q^{48} +8.56660 q^{49} +6.75100 q^{50} -1.64582 q^{51} -0.748472 q^{52} -9.02746 q^{53} +12.9807 q^{54} +0.630394 q^{55} +43.4615 q^{56} -1.36994 q^{57} -4.32222 q^{58} -10.7196 q^{59} +8.43417 q^{60} +14.9612 q^{61} +11.2644 q^{62} +8.75195 q^{63} +51.3604 q^{64} -0.204041 q^{65} -0.972439 q^{66} -10.2282 q^{67} -11.0110 q^{68} -3.52832 q^{69} +17.9001 q^{70} -8.96853 q^{71} +24.4352 q^{72} +4.69345 q^{73} +12.7115 q^{74} -2.12163 q^{75} -9.16528 q^{76} -1.54236 q^{77} +0.314751 q^{78} +3.20308 q^{79} +30.8985 q^{80} +2.57529 q^{81} -21.3112 q^{82} -2.42325 q^{83} -20.6355 q^{84} -3.00171 q^{85} -0.946630 q^{86} +1.35834 q^{87} -4.30624 q^{88} -0.0683005 q^{89} +10.0639 q^{90} +0.499219 q^{91} -23.6055 q^{92} -3.54007 q^{93} -25.6558 q^{94} -2.49854 q^{95} -28.1843 q^{96} +7.36358 q^{97} -24.1015 q^{98} -0.867157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) $ 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * 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 $

$2$	−2.81343	−1.98939	−0.994697	−	0.102853i	$-0.967203\pi$
$2$	−2.81343	−1.98939	−0.994697	+	0.102853i	$0.967203\pi$
$3$	0.884173	0.510478	0.255239	−	0.966878i	$-0.417846\pi$
$3$	0.884173	0.510478	0.255239	+	0.966878i	$0.417846\pi$
$4$	5.91537	2.95768
$5$	1.61259	0.721170	0.360585	−	0.932726i	$-0.382577\pi$
$5$	1.61259	0.721170	0.360585	+	0.932726i	$0.382577\pi$
$6$	−2.48756	−1.01554
$7$	−3.94545	−1.49124	−0.745620	−	0.666371i	$-0.767847\pi$
$7$	−3.94545	−1.49124	−0.745620	+	0.666371i	$0.767847\pi$
$8$	−11.0156	−3.89460
$9$	−2.21824	−0.739413
$10$	−4.53689	−1.43469
$11$	0.390921	0.117867	0.0589336	−	0.998262i	$-0.481230\pi$
$11$	0.390921	0.117867	0.0589336	+	0.998262i	$0.481230\pi$
$12$	5.23021	1.50983
$13$	−0.126530	−0.0350931	−0.0175466	−	0.999846i	$-0.505586\pi$
$13$	−0.126530	−0.0350931	−0.0175466	+	0.999846i	$0.505586\pi$
$14$	11.1002	2.96666
$15$	1.42581	0.368141
$16$	19.1609	4.79021
$17$	−1.86142	−0.451461	−0.225731	−	0.974190i	$-0.572477\pi$
$17$	−1.86142	−0.451461	−0.225731	+	0.974190i	$0.572477\pi$
$18$	6.24085	1.47098
$19$	−1.54940	−0.355457	−0.177729	−	0.984080i	$-0.556875\pi$
$19$	−1.54940	−0.355457	−0.177729	+	0.984080i	$0.556875\pi$
$20$	9.53904	2.13299
$21$	−3.48846	−0.761245
$22$	−1.09983	−0.234484
$23$	−3.99053	−0.832083	−0.416042	−	0.909346i	$-0.636583\pi$
$23$	−3.99053	−0.832083	−0.416042	+	0.909346i	$0.636583\pi$
$24$	−9.73970	−1.98811
$25$	−2.39957	−0.479913
$26$	0.355983	0.0698141
$27$	−4.61383	−0.887931
$28$	−23.3388	−4.41062
$29$	1.53628	0.285281	0.142640	−	0.989775i	$-0.454441\pi$
$29$	1.53628	0.285281	0.142640	+	0.989775i	$0.454441\pi$
$30$	−4.01140	−0.732378
$31$	−4.00381	−0.719106	−0.359553	−	0.933125i	$-0.617071\pi$
$31$	−4.00381	−0.719106	−0.359553	+	0.933125i	$0.617071\pi$
$32$	−31.8765	−5.63501
$33$	0.345642	0.0601686
$34$	5.23698	0.898134
$35$	−6.36238	−1.07544
$36$	−13.1217	−2.18695
$37$	−4.51815	−0.742779	−0.371389	−	0.928477i	$-0.621118\pi$
$37$	−4.51815	−0.742779	−0.371389	+	0.928477i	$0.621118\pi$
$38$	4.35913	0.707144
$39$	−0.111875	−0.0179143
$40$	−17.7636	−2.80867
$41$	7.57481	1.18299	0.591493	−	0.806310i	$-0.298539\pi$
$41$	7.57481	1.18299	0.591493	+	0.806310i	$0.298539\pi$
$42$	9.81454	1.51442
$43$	0.336469	0.0513110	0.0256555	−	0.999671i	$-0.491833\pi$
$43$	0.336469	0.0513110	0.0256555	+	0.999671i	$0.491833\pi$
$44$	2.31244	0.348614
$45$	−3.57710	−0.533243
$46$	11.2271	1.65534
$47$	9.11906	1.33015	0.665076	−	0.746776i	$-0.268399\pi$
$47$	9.11906	1.33015	0.665076	+	0.746776i	$0.268399\pi$
$48$	16.9415	2.44530
$49$	8.56660	1.22380
$50$	6.75100	0.954736
$51$	−1.64582	−0.230461
$52$	−0.748472	−0.103794
$53$	−9.02746	−1.24002	−0.620009	−	0.784595i	$-0.712871\pi$
$53$	−9.02746	−1.24002	−0.620009	+	0.784595i	$0.712871\pi$
$54$	12.9807	1.76644
$55$	0.630394	0.0850024
$56$	43.4615	5.80779
$57$	−1.36994	−0.181453
$58$	−4.32222	−0.567536
$59$	−10.7196	−1.39557	−0.697787	−	0.716305i	$-0.745832\pi$
$59$	−10.7196	−1.39557	−0.697787	+	0.716305i	$0.745832\pi$
$60$	8.43417	1.08885
$61$	14.9612	1.91559	0.957794	−	0.287456i	$-0.0928096\pi$
$61$	14.9612	1.91559	0.957794	+	0.287456i	$0.0928096\pi$
$62$	11.2644	1.43059
$63$	8.75195	1.10264
$64$	51.3604	6.42004
$65$	−0.204041	−0.0253081
$66$	−0.972439	−0.119699
$67$	−10.2282	−1.24958	−0.624790	−	0.780793i	$-0.714815\pi$
$67$	−10.2282	−1.24958	−0.624790	+	0.780793i	$0.714815\pi$
$68$	−11.0110	−1.33528
$69$	−3.52832	−0.424760
$70$	17.9001	2.13947
$71$	−8.96853	−1.06437	−0.532184	−	0.846629i	$-0.678629\pi$
$71$	−8.96853	−1.06437	−0.532184	+	0.846629i	$0.678629\pi$
$72$	24.4352	2.87972
$73$	4.69345	0.549327	0.274663	−	0.961540i	$-0.411434\pi$
$73$	4.69345	0.549327	0.274663	+	0.961540i	$0.411434\pi$
$74$	12.7115	1.47768
$75$	−2.12163	−0.244985
$76$	−9.16528	−1.05133
$77$	−1.54236	−0.175768
$78$	0.314751	0.0356385
$79$	3.20308	0.360374	0.180187	−	0.983632i	$-0.442330\pi$
$79$	3.20308	0.360374	0.180187	+	0.983632i	$0.442330\pi$
$80$	30.8985	3.45456
$81$	2.57529	0.286144
$82$	−21.3112	−2.35343
$83$	−2.42325	−0.265986	−0.132993	−	0.991117i	$-0.542459\pi$
$83$	−2.42325	−0.265986	−0.132993	+	0.991117i	$0.542459\pi$
$84$	−20.6355	−2.25152
$85$	−3.00171	−0.325581
$86$	−0.946630	−0.102078
$87$	1.35834	0.145629
$88$	−4.30624	−0.459046
$89$	−0.0683005	−0.00723983	−0.00361992	−	0.999993i	$-0.501152\pi$
$89$	−0.0683005	−0.00723983	−0.00361992	+	0.999993i	$0.501152\pi$
$90$	10.0639	1.06083
$91$	0.499219	0.0523323
$92$	−23.6055	−2.46104
$93$	−3.54007	−0.367088
$94$	−25.6558	−2.64619
$95$	−2.49854	−0.256345
$96$	−28.1843	−2.87655
$97$	7.36358	0.747658	0.373829	−	0.927498i	$-0.378045\pi$
$97$	7.36358	0.747658	0.373829	+	0.927498i	$0.378045\pi$
$98$	−24.1015	−2.43462
$99$	−0.867157	−0.0871525
$100$	−14.1943	−1.41943
$101$	2.03271	0.202263	0.101131	−	0.994873i	$-0.467754\pi$
$101$	2.03271	0.202263	0.101131	+	0.994873i	$0.467754\pi$
$102$	4.63040	0.458477
$103$	−17.2655	−1.70122	−0.850608	−	0.525800i	$-0.823766\pi$
$103$	−17.2655	−1.70122	−0.850608	+	0.525800i	$0.823766\pi$
$104$	1.39381	0.136674
$105$	−5.62545	−0.548987
$106$	25.3981	2.46688
$107$	8.01791	0.775121	0.387560	−	0.921844i	$-0.373318\pi$
$107$	8.01791	0.775121	0.387560	+	0.921844i	$0.373318\pi$
$108$	−27.2925	−2.62622
$109$	−4.07365	−0.390185	−0.195092	−	0.980785i	$-0.562501\pi$
$109$	−4.07365	−0.390185	−0.195092	+	0.980785i	$0.562501\pi$
$110$	−1.77357	−0.169103
$111$	−3.99482	−0.379172
$112$	−75.5983	−7.14336
$113$	9.55468	0.898829	0.449414	−	0.893323i	$-0.351633\pi$
$113$	9.55468	0.898829	0.449414	+	0.893323i	$0.351633\pi$
$114$	3.85422	0.360981
$115$	−6.43508	−0.600074
$116$	9.08769	0.843771
$117$	0.280674	0.0259483
$118$	30.1588	2.77635
$119$	7.34416	0.673238
$120$	−15.7061	−1.43376
$121$	−10.8472	−0.986107
$122$	−42.0923	−3.81086
$123$	6.69744	0.603888
$124$	−23.6840	−2.12689
$125$	−11.9324	−1.06727
$126$	−24.6230	−2.19359
$127$	−9.53618	−0.846199	−0.423099	−	0.906083i	$-0.639058\pi$
$127$	−9.53618	−0.846199	−0.423099	+	0.906083i	$0.639058\pi$
$128$	−80.7457	−7.13698
$129$	0.297497	0.0261931
$130$	0.574054	0.0503478
$131$	−2.40272	−0.209926	−0.104963	−	0.994476i	$-0.533472\pi$
$131$	−2.40272	−0.209926	−0.104963	+	0.994476i	$0.533472\pi$
$132$	2.04460	0.177960
$133$	6.11309	0.530072
$134$	28.7764	2.48590
$135$	−7.44019	−0.640350
$136$	20.5047	1.75826
$137$	18.9525	1.61922	0.809611	−	0.586967i	$-0.199678\pi$
$137$	18.9525	1.61922	0.809611	+	0.586967i	$0.199678\pi$
$138$	9.92667	0.845014
$139$	12.8476	1.08972	0.544858	−	0.838528i	$-0.316584\pi$
$139$	12.8476	1.08972	0.544858	+	0.838528i	$0.316584\pi$
$140$	−37.6358	−3.18081
$141$	8.06283	0.679013
$142$	25.2323	2.11745
$143$	−0.0494633	−0.00413633
$144$	−42.5033	−3.54194
$145$	2.47739	0.205736
$146$	−13.2047	−1.09283
$147$	7.57435	0.624722
$148$	−26.7265	−2.19690
$149$	−0.753234	−0.0617073	−0.0308537	−	0.999524i	$-0.509823\pi$
$149$	−0.753234	−0.0617073	−0.0308537	+	0.999524i	$0.509823\pi$
$150$	5.96906	0.487371
$151$	9.98767	0.812785	0.406393	−	0.913699i	$-0.366787\pi$
$151$	9.98767	0.812785	0.406393	+	0.913699i	$0.366787\pi$
$152$	17.0676	1.38436
$153$	4.12908	0.333816
$154$	4.33932	0.349673
$155$	−6.45650	−0.518598
$156$	−0.661779	−0.0529847
$157$	−2.82307	−0.225305	−0.112653	−	0.993634i	$-0.535935\pi$
$157$	−2.82307	−0.225305	−0.112653	+	0.993634i	$0.535935\pi$
$158$	−9.01162	−0.716926
$159$	−7.98184	−0.633001
$160$	−51.4035	−4.06381
$161$	15.7445	1.24084
$162$	−7.24540	−0.569252
$163$	−16.5065	−1.29289	−0.646446	−	0.762960i	$-0.723745\pi$
$163$	−16.5065	−1.29289	−0.646446	+	0.762960i	$0.723745\pi$
$164$	44.8078	3.49890
$165$	0.557378	0.0433918
$166$	6.81763	0.529151
$167$	−2.09423	−0.162056	−0.0810281	−	0.996712i	$-0.525820\pi$
$167$	−2.09423	−0.162056	−0.0810281	+	0.996712i	$0.525820\pi$
$168$	38.4275	2.96475
$169$	−12.9840	−0.998768
$170$	8.44508	0.647708
$171$	3.43694	0.262829
$172$	1.99034	0.151762
$173$	10.6545	0.810046	0.405023	−	0.914306i	$-0.367263\pi$
$173$	10.6545	0.810046	0.405023	+	0.914306i	$0.367263\pi$
$174$	−3.82159	−0.289714
$175$	9.46737	0.715666
$176$	7.49039	0.564609
$177$	−9.47799	−0.712409
$178$	0.192158	0.0144029
$179$	11.2140	0.838174	0.419087	−	0.907946i	$-0.362350\pi$
$179$	11.2140	0.838174	0.419087	+	0.907946i	$0.362350\pi$
$180$	−21.1599	−1.57716
$181$	−3.67663	−0.273282	−0.136641	−	0.990621i	$-0.543631\pi$
$181$	−3.67663	−0.273282	−0.136641	+	0.990621i	$0.543631\pi$
$182$	−1.40451	−0.104110
$183$	13.2283	0.977864
$184$	43.9581	3.24064
$185$	−7.28590	−0.535670
$186$	9.95971	0.730282
$187$	−0.727670	−0.0532125
$188$	53.9426	3.93417
$189$	18.2036	1.32412
$190$	7.02947	0.509971
$191$	9.67436	0.700012	0.350006	−	0.936747i	$-0.386180\pi$
$191$	9.67436	0.700012	0.350006	+	0.936747i	$0.386180\pi$
$192$	45.4114	3.27729
$193$	11.6414	0.837964	0.418982	−	0.907995i	$-0.362387\pi$
$193$	11.6414	0.837964	0.418982	+	0.907995i	$0.362387\pi$
$194$	−20.7169	−1.48739
$195$	−0.180407	−0.0129192
$196$	50.6746	3.61961
$197$	19.6763	1.40188	0.700941	−	0.713219i	$-0.252764\pi$
$197$	19.6763	1.40188	0.700941	+	0.713219i	$0.252764\pi$
$198$	2.43968	0.173381
$199$	3.20793	0.227404	0.113702	−	0.993515i	$-0.463729\pi$
$199$	3.20793	0.227404	0.113702	+	0.993515i	$0.463729\pi$
$200$	26.4327	1.86907
$201$	−9.04354	−0.637882
$202$	−5.71889	−0.402380
$203$	−6.06134	−0.425422
$204$	−9.73564	−0.681631
$205$	12.2150	0.853135
$206$	48.5751	3.38439
$207$	8.85195	0.615253
$208$	−2.42443	−0.168104
$209$	−0.605694	−0.0418967
$210$	15.8268	1.09215
$211$	−9.71904	−0.669086	−0.334543	−	0.942380i	$-0.608582\pi$
$211$	−9.71904	−0.669086	−0.334543	+	0.942380i	$0.608582\pi$
$212$	−53.4008	−3.66758
$213$	−7.92973	−0.543336
$214$	−22.5578	−1.54202
$215$	0.542585	0.0370040
$216$	50.8241	3.45814
$217$	15.7969	1.07236
$218$	11.4609	0.776231
$219$	4.14982	0.280419
$220$	3.72902	0.251410
$221$	0.235526	0.0158432
$222$	11.2391	0.754322
$223$	−18.4358	−1.23455	−0.617276	−	0.786747i	$-0.711764\pi$
$223$	−18.4358	−1.23455	−0.617276	+	0.786747i	$0.711764\pi$
$224$	125.767	8.40316
$225$	5.32281	0.354854
$226$	−26.8814	−1.78812
$227$	2.87943	0.191115	0.0955573	−	0.995424i	$-0.469537\pi$
$227$	2.87943	0.191115	0.0955573	+	0.995424i	$0.469537\pi$
$228$	−8.10369	−0.536680
$229$	17.2424	1.13941	0.569706	−	0.821848i	$-0.307057\pi$
$229$	17.2424	1.13941	0.569706	+	0.821848i	$0.307057\pi$
$230$	18.1046	1.19378
$231$	−1.36371	−0.0897259
$232$	−16.9231	−1.11106
$233$	−2.71881	−0.178115	−0.0890577	−	0.996026i	$-0.528386\pi$
$233$	−2.71881	−0.178115	−0.0890577	+	0.996026i	$0.528386\pi$
$234$	−0.789655	−0.0516214
$235$	14.7053	0.959266
$236$	−63.4104	−4.12767
$237$	2.83207	0.183963
$238$	−20.6622	−1.33933
$239$	14.4753	0.936331	0.468165	−	0.883641i	$-0.344915\pi$
$239$	14.4753	0.936331	0.468165	+	0.883641i	$0.344915\pi$
$240$	27.3197	1.76348
$241$	−27.6393	−1.78040	−0.890201	−	0.455568i	$-0.849436\pi$
$241$	−27.6393	−1.78040	−0.890201	+	0.455568i	$0.849436\pi$
$242$	30.5177	1.96176
$243$	16.1185	1.03400
$244$	88.5011	5.66570
$245$	13.8144	0.882568
$246$	−18.8428	−1.20137
$247$	0.196046	0.0124741
$248$	44.1044	2.80063
$249$	−2.14257	−0.135780
$250$	33.5710	2.12322
$251$	15.5819	0.983519	0.491760	−	0.870731i	$-0.336354\pi$
$251$	15.5819	0.983519	0.491760	+	0.870731i	$0.336354\pi$
$252$	51.7710	3.26127
$253$	−1.55998	−0.0980754
$254$	26.8293	1.68342
$255$	−2.65403	−0.166202
$256$	124.451	7.77821
$257$	−2.57588	−0.160679	−0.0803394	−	0.996768i	$-0.525600\pi$
$257$	−2.57588	−0.160679	−0.0803394	+	0.996768i	$0.525600\pi$
$258$	−0.836985	−0.0521084
$259$	17.8261	1.10766
$260$	−1.20698	−0.0748535
$261$	−3.40784	−0.210940
$262$	6.75987	0.417626
$263$	−20.9693	−1.29302	−0.646511	−	0.762904i	$-0.723773\pi$
$263$	−20.9693	−1.29302	−0.646511	+	0.762904i	$0.723773\pi$
$264$	−3.80746	−0.234333
$265$	−14.5576	−0.894264
$266$	−17.1987	−1.05452
$267$	−0.0603894	−0.00369577
$268$	−60.5039	−3.69586
$269$	−3.54376	−0.216067	−0.108034	−	0.994147i	$-0.534455\pi$
$269$	−3.54376	−0.216067	−0.108034	+	0.994147i	$0.534455\pi$
$270$	20.9324	1.27391
$271$	21.3475	1.29677	0.648384	−	0.761314i	$-0.275445\pi$
$271$	21.3475	1.29677	0.648384	+	0.761314i	$0.275445\pi$
$272$	−35.6665	−2.16260
$273$	0.441396	0.0267145
$274$	−53.3215	−3.22127
$275$	−0.938042	−0.0565660
$276$	−20.8713	−1.25631
$277$	7.28123	0.437487	0.218743	−	0.975782i	$-0.429804\pi$
$277$	7.28123	0.437487	0.218743	+	0.975782i	$0.429804\pi$
$278$	−36.1457	−2.16787
$279$	8.88141	0.531716
$280$	70.0855	4.18841
$281$	−6.66001	−0.397303	−0.198651	−	0.980070i	$-0.563656\pi$
$281$	−6.66001	−0.397303	−0.198651	+	0.980070i	$0.563656\pi$
$282$	−22.6842	−1.35082
$283$	22.0653	1.31165	0.655823	−	0.754914i	$-0.272322\pi$
$283$	22.0653	1.31165	0.655823	+	0.754914i	$0.272322\pi$
$284$	−53.0522	−3.14807
$285$	−2.20914	−0.130858
$286$	0.139161	0.00822879
$287$	−29.8861	−1.76412
$288$	70.7096	4.16660
$289$	−13.5351	−0.796183
$290$	−6.96996	−0.409290
$291$	6.51068	0.381663
$292$	27.7635	1.62473
$293$	20.1266	1.17581	0.587903	−	0.808931i	$-0.299954\pi$
$293$	20.1266	1.17581	0.587903	+	0.808931i	$0.299954\pi$
$294$	−21.3099	−1.24282
$295$	−17.2863	−1.00645
$296$	49.7701	2.89283
$297$	−1.80364	−0.104658
$298$	2.11917	0.122760
$299$	0.504922	0.0292004
$300$	−12.5502	−0.724588
$301$	−1.32752	−0.0765171
$302$	−28.0996	−1.61695
$303$	1.79727	0.103250
$304$	−29.6879	−1.70272
$305$	24.1263	1.38147
$306$	−11.6169	−0.664092
$307$	−29.2677	−1.67039	−0.835197	−	0.549950i	$-0.814647\pi$
$307$	−29.2677	−1.67039	−0.835197	+	0.549950i	$0.814647\pi$
$308$	−9.12364	−0.519868
$309$	−15.2657	−0.868433
$310$	18.1649	1.03170
$311$	31.4536	1.78357	0.891786	−	0.452457i	$-0.149452\pi$
$311$	31.4536	1.78357	0.891786	+	0.452457i	$0.149452\pi$
$312$	1.23237	0.0697690
$313$	4.26139	0.240868	0.120434	−	0.992721i	$-0.461571\pi$
$313$	4.26139	0.240868	0.120434	+	0.992721i	$0.461571\pi$
$314$	7.94250	0.448221
$315$	14.1133	0.795193
$316$	18.9474	1.06587
$317$	12.8686	0.722775	0.361387	−	0.932416i	$-0.382303\pi$
$317$	12.8686	0.722775	0.361387	+	0.932416i	$0.382303\pi$
$318$	22.4563	1.25929
$319$	0.600566	0.0336253
$320$	82.8230	4.62995
$321$	7.08922	0.395682
$322$	−44.2959	−2.46851
$323$	2.88409	0.160475
$324$	15.2338	0.846323
$325$	0.303617	0.0168417
$326$	46.4399	2.57207
$327$	−3.60181	−0.199181
$328$	−83.4411	−4.60726
$329$	−35.9788	−1.98358
$330$	−1.56814	−0.0863233
$331$	16.3653	0.899519	0.449759	−	0.893150i	$-0.351510\pi$
$331$	16.3653	0.899519	0.449759	+	0.893150i	$0.351510\pi$
$332$	−14.3344	−0.786703
$333$	10.0223	0.549220
$334$	5.89195	0.322393
$335$	−16.4939	−0.901160
$336$	−66.8419	−3.64653
$337$	−4.66200	−0.253956	−0.126978	−	0.991906i	$-0.540528\pi$
$337$	−4.66200	−0.253956	−0.126978	+	0.991906i	$0.540528\pi$
$338$	36.5295	1.98694
$339$	8.44799	0.458832
$340$	−17.7562	−0.962965
$341$	−1.56518	−0.0847591
$342$	−9.66958	−0.522871
$343$	−6.18093	−0.333739
$344$	−3.70641	−0.199836
$345$	−5.68972	−0.306324
$346$	−29.9756	−1.61150
$347$	29.8831	1.60421	0.802104	−	0.597184i	$-0.203714\pi$
$347$	29.8831	1.60421	0.802104	+	0.597184i	$0.203714\pi$
$348$	8.03509	0.430726
$349$	26.9773	1.44406	0.722030	−	0.691861i	$-0.243209\pi$
$349$	26.9773	1.44406	0.722030	+	0.691861i	$0.243209\pi$
$350$	−26.6358	−1.42374
$351$	0.583788	0.0311603
$352$	−12.4612	−0.664184
$353$	−7.73863	−0.411886	−0.205943	−	0.978564i	$-0.566026\pi$
$353$	−7.73863	−0.411886	−0.205943	+	0.978564i	$0.566026\pi$
$354$	26.6656	1.41726
$355$	−14.4625	−0.767591
$356$	−0.404022	−0.0214131
$357$	6.49351	0.343673
$358$	−31.5498	−1.66746
$359$	14.7919	0.780686	0.390343	−	0.920670i	$-0.372356\pi$
$359$	14.7919	0.780686	0.390343	+	0.920670i	$0.372356\pi$
$360$	39.4039	2.07677
$361$	−16.5994	−0.873650
$362$	10.3439	0.543665
$363$	−9.59079	−0.503386
$364$	2.95306	0.154783
$365$	7.56859	0.396158
$366$	−37.2169	−1.94536
$367$	−5.80421	−0.302977	−0.151489	−	0.988459i	$-0.548407\pi$
$367$	−5.80421	−0.302977	−0.151489	+	0.988459i	$0.548407\pi$
$368$	−76.4620	−3.98586
$369$	−16.8027	−0.874715
$370$	20.4983	1.06566
$371$	35.6174	1.84916
$372$	−20.9408	−1.08573
$373$	−7.20400	−0.373009	−0.186504	−	0.982454i	$-0.559716\pi$
$373$	−7.20400	−0.373009	−0.186504	+	0.982454i	$0.559716\pi$
$374$	2.04725	0.105861
$375$	−10.5503	−0.544817
$376$	−100.452	−5.18042
$377$	−0.194386	−0.0100114
$378$	−51.2146	−2.63419
$379$	7.80856	0.401099	0.200550	−	0.979684i	$-0.435727\pi$
$379$	7.80856	0.401099	0.200550	+	0.979684i	$0.435727\pi$
$380$	−14.7798	−0.758188
$381$	−8.43163	−0.431966
$382$	−27.2181	−1.39260
$383$	−16.6763	−0.852120	−0.426060	−	0.904695i	$-0.640099\pi$
$383$	−16.6763	−0.852120	−0.426060	+	0.904695i	$0.640099\pi$
$384$	−71.3932	−3.64327
$385$	−2.48719	−0.126759
$386$	−32.7521	−1.66704
$387$	−0.746368	−0.0379400
$388$	43.5583	2.21134
$389$	30.4984	1.54633	0.773164	−	0.634206i	$-0.218673\pi$
$389$	30.4984	1.54633	0.773164	+	0.634206i	$0.218673\pi$
$390$	0.507563	0.0257014
$391$	7.42807	0.375654
$392$	−94.3662	−4.76621
$393$	−2.12442	−0.107163
$394$	−55.3580	−2.78889
$395$	5.16523	0.259891
$396$	−5.12955	−0.257770
$397$	14.9238	0.749004	0.374502	−	0.927226i	$-0.377814\pi$
$397$	14.9238	0.749004	0.374502	+	0.927226i	$0.377814\pi$
$398$	−9.02528	−0.452397
$399$	5.40503	0.270590
$400$	−45.9777	−2.29889
$401$	8.16449	0.407715	0.203858	−	0.979001i	$-0.434652\pi$
$401$	8.16449	0.407715	0.203858	+	0.979001i	$0.434652\pi$
$402$	25.4433	1.26900
$403$	0.506603	0.0252357
$404$	12.0242	0.598229
$405$	4.15288	0.206358
$406$	17.0531	0.846332
$407$	−1.76624	−0.0875493
$408$	18.1297	0.897554
$409$	−13.5052	−0.667787	−0.333893	−	0.942611i	$-0.608363\pi$
$409$	−13.5052	−0.667787	−0.333893	+	0.942611i	$0.608363\pi$
$410$	−34.3661	−1.69722
$411$	16.7573	0.826577
$412$	−102.132	−5.03166
$413$	42.2937	2.08114
$414$	−24.9043	−1.22398
$415$	−3.90770	−0.191821
$416$	4.03333	0.197750
$417$	11.3595	0.556275
$418$	1.70408	0.0833491
$419$	−17.3975	−0.849925	−0.424963	−	0.905211i	$-0.639713\pi$
$419$	−17.3975	−0.849925	−0.424963	+	0.905211i	$0.639713\pi$
$420$	−33.2766	−1.62373
$421$	5.80649	0.282991	0.141495	−	0.989939i	$-0.454809\pi$
$421$	5.80649	0.282991	0.141495	+	0.989939i	$0.454809\pi$
$422$	27.3438	1.33108
$423$	−20.2282	−0.983531
$424$	99.4429	4.82938
$425$	4.46661	0.216662
$426$	22.3097	1.08091
$427$	−59.0288	−2.85660
$428$	47.4289	2.29256
$429$	−0.0437341	−0.00211150
$430$	−1.52652	−0.0736155
$431$	−22.1690	−1.06784	−0.533921	−	0.845534i	$-0.679282\pi$
$431$	−22.1690	−1.06784	−0.533921	+	0.845534i	$0.679282\pi$
$432$	−88.4049	−4.25338
$433$	37.3633	1.79556	0.897782	−	0.440440i	$-0.145178\pi$
$433$	37.3633	1.79556	0.897782	+	0.440440i	$0.145178\pi$
$434$	−44.4433	−2.13335
$435$	2.19044	0.105024
$436$	−24.0972	−1.15404
$437$	6.18293	0.295770
$438$	−11.6752	−0.557863
$439$	−18.5749	−0.886529	−0.443265	−	0.896391i	$-0.646180\pi$
$439$	−18.5749	−0.886529	−0.443265	+	0.896391i	$0.646180\pi$
$440$	−6.94418	−0.331051
$441$	−19.0027	−0.904893
$442$	−0.662636	−0.0315184
$443$	−5.64796	−0.268343	−0.134171	−	0.990958i	$-0.542837\pi$
$443$	−5.64796	−0.268343	−0.134171	+	0.990958i	$0.542837\pi$
$444$	−23.6309	−1.12147
$445$	−0.110140	−0.00522115
$446$	51.8677	2.45601
$447$	−0.665989	−0.0315002
$448$	−202.640	−9.57383
$449$	−6.81914	−0.321815	−0.160908	−	0.986969i	$-0.551442\pi$
$449$	−6.81914	−0.321815	−0.160908	+	0.986969i	$0.551442\pi$
$450$	−14.9753	−0.705944
$451$	2.96116	0.139435
$452$	56.5195	2.65845
$453$	8.83083	0.414909
$454$	−8.10107	−0.380202
$455$	0.805033	0.0377405
$456$	15.0907	0.706687
$457$	−36.9089	−1.72653	−0.863264	−	0.504754i	$-0.831583\pi$
$457$	−36.9089	−1.72653	−0.863264	+	0.504754i	$0.831583\pi$
$458$	−48.5103	−2.26674
$459$	8.58828	0.400867
$460$	−38.0658	−1.77483
$461$	1.85794	0.0865327	0.0432663	−	0.999064i	$-0.486224\pi$
$461$	1.85794	0.0865327	0.0432663	+	0.999064i	$0.486224\pi$
$462$	3.83671	0.178500
$463$	19.6895	0.915051	0.457525	−	0.889197i	$-0.348736\pi$
$463$	19.6895	0.915051	0.457525	+	0.889197i	$0.348736\pi$
$464$	29.4365	1.36656
$465$	−5.70866	−0.264733
$466$	7.64918	0.354342
$467$	31.2075	1.44411	0.722056	−	0.691834i	$-0.243197\pi$
$467$	31.2075	1.44411	0.722056	+	0.691834i	$0.243197\pi$
$468$	1.66029	0.0767469
$469$	40.3551	1.86342
$470$	−41.3722	−1.90836
$471$	−2.49608	−0.115013
$472$	118.083	5.43521
$473$	0.131533	0.00604789
$474$	−7.96783	−0.365975
$475$	3.71789	0.170589
$476$	43.4434	1.99123
$477$	20.0251	0.916884
$478$	−40.7253	−1.86273
$479$	13.6101	0.621861	0.310930	−	0.950433i	$-0.399359\pi$
$479$	13.6101	0.621861	0.310930	+	0.950433i	$0.399359\pi$
$480$	−45.4496	−2.07448
$481$	0.571682	0.0260664
$482$	77.7611	3.54192
$483$	13.9208	0.633419
$484$	−64.1651	−2.91659
$485$	11.8744	0.539189
$486$	−45.3482	−2.05703
$487$	24.8324	1.12526	0.562631	−	0.826708i	$-0.309789\pi$
$487$	24.8324	1.12526	0.562631	+	0.826708i	$0.309789\pi$
$488$	−164.807	−7.46046
$489$	−14.5946	−0.659992
$490$	−38.8657	−1.75577
$491$	26.1882	1.18186	0.590928	−	0.806725i	$-0.298762\pi$
$491$	26.1882	1.18186	0.590928	+	0.806725i	$0.298762\pi$
$492$	39.6179	1.78611
$493$	−2.85968	−0.128793
$494$	−0.551561	−0.0248159
$495$	−1.39836	−0.0628518
$496$	−76.7165	−3.44467
$497$	35.3849	1.58723
$498$	6.02797	0.270120
$499$	−29.6741	−1.32840	−0.664198	−	0.747557i	$-0.731227\pi$
$499$	−29.6741	−1.32840	−0.664198	+	0.747557i	$0.731227\pi$
$500$	−70.5848	−3.15665
$501$	−1.85166	−0.0827260
$502$	−43.8385	−1.95661
$503$	−18.2098	−0.811934	−0.405967	−	0.913888i	$-0.633065\pi$
$503$	−18.2098	−0.811934	−0.405967	+	0.913888i	$0.633065\pi$
$504$	−96.4080	−4.29436
$505$	3.27792	0.145866
$506$	4.38890	0.195110
$507$	−11.4801	−0.509849
$508$	−56.4100	−2.50279
$509$	−15.5052	−0.687254	−0.343627	−	0.939106i	$-0.611656\pi$
$509$	−15.5052	−0.687254	−0.343627	+	0.939106i	$0.611656\pi$
$510$	7.46691	0.330640
$511$	−18.5178	−0.819178
$512$	−188.643	−8.33694
$513$	7.14867	0.315621
$514$	7.24704	0.319653
$515$	−27.8420	−1.22687
$516$	1.75980	0.0774710
$517$	3.56484	0.156781
$518$	−50.1525	−2.20357
$519$	9.42042	0.413510
$520$	2.24763	0.0985652
$521$	24.4901	1.07293	0.536466	−	0.843922i	$-0.319759\pi$
$521$	24.4901	1.07293	0.536466	+	0.843922i	$0.319759\pi$
$522$	9.58772	0.419643
$523$	40.6091	1.77571	0.887855	−	0.460123i	$-0.152195\pi$
$523$	40.6091	1.77571	0.887855	+	0.460123i	$0.152195\pi$
$524$	−14.2130	−0.620896
$525$	8.37080	0.365332
$526$	58.9956	2.57233
$527$	7.45279	0.324649
$528$	6.62280	0.288220
$529$	−7.07566	−0.307637
$530$	40.9566	1.77904
$531$	23.7786	1.03191
$532$	36.1612	1.56779
$533$	−0.958442	−0.0415147
$534$	0.169901	0.00735234
$535$	12.9296	0.558994
$536$	112.670	4.86662
$537$	9.91512	0.427869
$538$	9.97012	0.429842
$539$	3.34887	0.144246
$540$	−44.0115	−1.89395
$541$	−41.0190	−1.76355	−0.881773	−	0.471674i	$-0.843650\pi$
$541$	−41.0190	−1.76355	−0.881773	+	0.471674i	$0.843650\pi$
$542$	−60.0596	−2.57978
$543$	−3.25078	−0.139504
$544$	59.3356	2.54399
$545$	−6.56911	−0.281390
$546$	−1.24183	−0.0531456
$547$	10.1663	0.434681	0.217340	−	0.976096i	$-0.430262\pi$
$547$	10.1663	0.434681	0.217340	+	0.976096i	$0.430262\pi$
$548$	112.111	4.78915
$549$	−33.1875	−1.41641
$550$	2.63911	0.112532
$551$	−2.38032	−0.101405
$552$	38.8666	1.65427
$553$	−12.6376	−0.537405
$554$	−20.4852	−0.870333
$555$	−6.44200	−0.273448
$556$	75.9981	3.22304
$557$	8.44343	0.357760	0.178880	−	0.983871i	$-0.442753\pi$
$557$	8.44343	0.357760	0.178880	+	0.983871i	$0.442753\pi$
$558$	−24.9872	−1.05779
$559$	−0.0425734	−0.00180066
$560$	−121.909	−5.15158
$561$	−0.643386	−0.0271638
$562$	18.7375	0.790392
$563$	−27.2697	−1.14928	−0.574641	−	0.818405i	$-0.694858\pi$
$563$	−27.2697	−1.14928	−0.574641	+	0.818405i	$0.694858\pi$
$564$	47.6946	2.00831
$565$	15.4077	0.648209
$566$	−62.0791	−2.60938
$567$	−10.1607	−0.426709
$568$	98.7938	4.14529
$569$	38.5614	1.61658	0.808288	−	0.588787i	$-0.200394\pi$
$569$	38.5614	1.61658	0.808288	+	0.588787i	$0.200394\pi$
$570$	6.21527	0.260329
$571$	−2.46267	−0.103060	−0.0515299	−	0.998671i	$-0.516410\pi$
$571$	−2.46267	−0.103060	−0.0515299	+	0.998671i	$0.516410\pi$
$572$	−0.292594	−0.0122340
$573$	8.55381	0.357340
$574$	84.0822	3.50952
$575$	9.57554	0.399328
$576$	−113.929	−4.74706
$577$	8.36280	0.348148	0.174074	−	0.984733i	$-0.444307\pi$
$577$	8.36280	0.348148	0.174074	+	0.984733i	$0.444307\pi$
$578$	38.0800	1.58392
$579$	10.2930	0.427762
$580$	14.6547	0.608502
$581$	9.56081	0.396649
$582$	−18.3173	−0.759277
$583$	−3.52903	−0.146157
$584$	−51.7012	−2.13941
$585$	0.452611	0.0187132
$586$	−56.6246	−2.33914
$587$	10.8802	0.449072	0.224536	−	0.974466i	$-0.427913\pi$
$587$	10.8802	0.449072	0.224536	+	0.974466i	$0.427913\pi$
$588$	44.8051	1.84773
$589$	6.20352	0.255611
$590$	48.6337	2.00222
$591$	17.3973	0.715629
$592$	−86.5715	−3.55807
$593$	−7.67066	−0.314996	−0.157498	−	0.987519i	$-0.550343\pi$
$593$	−7.67066	−0.314996	−0.157498	+	0.987519i	$0.550343\pi$
$594$	5.07442	0.208206
$595$	11.8431	0.485519
$596$	−4.45566	−0.182511
$597$	2.83637	0.116085
$598$	−1.42056	−0.0580911
$599$	41.9413	1.71368	0.856838	−	0.515585i	$-0.172425\pi$
$599$	41.9413	1.71368	0.856838	+	0.515585i	$0.172425\pi$
$600$	23.3711	0.954119
$601$	41.8772	1.70821	0.854103	−	0.520104i	$-0.174107\pi$
$601$	41.8772	1.70821	0.854103	+	0.520104i	$0.174107\pi$
$602$	3.73488	0.152223
$603$	22.6887	0.923955
$604$	59.0808	2.40396
$605$	−17.4920	−0.711151
$606$	−5.05649	−0.205406
$607$	20.3926	0.827711	0.413855	−	0.910343i	$-0.364182\pi$
$607$	20.3926	0.827711	0.413855	+	0.910343i	$0.364182\pi$
$608$	49.3894	2.00301
$609$	−5.35927	−0.217169
$610$	−67.8774	−2.74828
$611$	−1.15384	−0.0466792
$612$	24.4250	0.987323
$613$	−38.3502	−1.54895	−0.774475	−	0.632604i	$-0.781986\pi$
$613$	−38.3502	−1.54895	−0.774475	+	0.632604i	$0.781986\pi$
$614$	82.3425	3.32307
$615$	10.8002	0.435506
$616$	16.9900	0.684549
$617$	24.1188	0.970988	0.485494	−	0.874240i	$-0.338640\pi$
$617$	24.1188	0.970988	0.485494	+	0.874240i	$0.338640\pi$
$618$	42.9488	1.72765
$619$	20.7080	0.832324	0.416162	−	0.909291i	$-0.363375\pi$
$619$	20.7080	0.832324	0.416162	+	0.909291i	$0.363375\pi$
$620$	−38.1926	−1.53385
$621$	18.4116	0.738833
$622$	−88.4925	−3.54823
$623$	0.269476	0.0107963
$624$	−2.14361	−0.0858132
$625$	−7.24425	−0.289770
$626$	−11.9891	−0.479182
$627$	−0.535538	−0.0213873
$628$	−16.6995	−0.666382
$629$	8.41018	0.335336
$630$	−39.7067	−1.58195
$631$	−42.0281	−1.67311	−0.836556	−	0.547881i	$-0.815435\pi$
$631$	−42.0281	−1.67311	−0.836556	+	0.547881i	$0.815435\pi$
$632$	−35.2838	−1.40351
$633$	−8.59331	−0.341554
$634$	−36.2050	−1.43788
$635$	−15.3779	−0.610254
$636$	−47.2155	−1.87222
$637$	−1.08393	−0.0429470
$638$	−1.68965	−0.0668939
$639$	19.8943	0.787008
$640$	−130.209	−5.14698
$641$	−24.2811	−0.959046	−0.479523	−	0.877529i	$-0.659190\pi$
$641$	−24.2811	−0.959046	−0.479523	+	0.877529i	$0.659190\pi$
$642$	−19.9450	−0.787167
$643$	7.94360	0.313265	0.156633	−	0.987657i	$-0.449936\pi$
$643$	7.94360	0.313265	0.156633	+	0.987657i	$0.449936\pi$
$644$	93.1343	3.67000
$645$	0.479739	0.0188897
$646$	−8.11418	−0.319248
$647$	14.0235	0.551321	0.275660	−	0.961255i	$-0.411103\pi$
$647$	14.0235	0.551321	0.275660	+	0.961255i	$0.411103\pi$
$648$	−28.3684	−1.11442
$649$	−4.19052	−0.164492
$650$	−0.854205	−0.0335047
$651$	13.9672	0.547416
$652$	−97.6422	−3.82397
$653$	−12.6197	−0.493848	−0.246924	−	0.969035i	$-0.579420\pi$
$653$	−12.6197	−0.493848	−0.246924	+	0.969035i	$0.579420\pi$
$654$	10.1334	0.396249
$655$	−3.87459	−0.151393
$656$	145.140	5.66676
$657$	−10.4112	−0.406179
$658$	101.224	3.94611
$659$	−16.6361	−0.648051	−0.324026	−	0.946048i	$-0.605036\pi$
$659$	−16.6361	−0.648051	−0.324026	+	0.946048i	$0.605036\pi$
$660$	3.29710	0.128339
$661$	−48.2312	−1.87598	−0.937988	−	0.346667i	$-0.887313\pi$
$661$	−48.2312	−1.87598	−0.937988	+	0.346667i	$0.887313\pi$
$662$	−46.0426	−1.78950
$663$	0.208246	0.00808760
$664$	26.6935	1.03591
$665$	9.85788	0.382272
$666$	−28.1971	−1.09261
$667$	−6.13059	−0.237377
$668$	−12.3881	−0.479311
$669$	−16.3004	−0.630211
$670$	46.4045	1.79276
$671$	5.84866	0.225785
$672$	111.200	4.28963
$673$	−11.1206	−0.428669	−0.214335	−	0.976760i	$-0.568758\pi$
$673$	−11.1206	−0.428669	−0.214335	+	0.976760i	$0.568758\pi$
$674$	13.1162	0.505217
$675$	11.0712	0.426130
$676$	−76.8051	−2.95404
$677$	−7.69090	−0.295585	−0.147793	−	0.989018i	$-0.547217\pi$
$677$	−7.69090	−0.295585	−0.147793	+	0.989018i	$0.547217\pi$
$678$	−23.7678	−0.912797
$679$	−29.0526	−1.11494
$680$	33.0656	1.26801
$681$	2.54592	0.0975597
$682$	4.40351	0.168619
$683$	22.7599	0.870884	0.435442	−	0.900217i	$-0.356592\pi$
$683$	22.7599	0.870884	0.435442	+	0.900217i	$0.356592\pi$
$684$	20.3308	0.777366
$685$	30.5625	1.16774
$686$	17.3896	0.663938
$687$	15.2453	0.581645
$688$	6.44703	0.245791
$689$	1.14225	0.0435161
$690$	16.0076	0.609399
$691$	−28.5847	−1.08741	−0.543707	−	0.839275i	$-0.682980\pi$
$691$	−28.5847	−1.08741	−0.543707	+	0.839275i	$0.682980\pi$
$692$	63.0253	2.39586
$693$	3.42133	0.129965
$694$	−84.0739	−3.19140
$695$	20.7178	0.785871
$696$	−14.9629	−0.567169
$697$	−14.0999	−0.534073
$698$	−75.8986	−2.87280
$699$	−2.40390	−0.0909239
$700$	56.0030	2.11672
$701$	18.1689	0.686231	0.343116	−	0.939293i	$-0.388518\pi$
$701$	18.1689	0.686231	0.343116	+	0.939293i	$0.388518\pi$
$702$	−1.64244	−0.0619901
$703$	7.00042	0.264026
$704$	20.0779	0.756713
$705$	13.0020	0.489684
$706$	21.7721	0.819403
$707$	−8.01997	−0.301622
$708$	−56.0658	−2.10708
$709$	−3.28712	−0.123450	−0.0617252	−	0.998093i	$-0.519660\pi$
$709$	−3.28712	−0.123450	−0.0617252	+	0.998093i	$0.519660\pi$
$710$	40.6893	1.52704
$711$	−7.10518	−0.266465
$712$	0.752371	0.0281963
$713$	15.9773	0.598356
$714$	−18.2690	−0.683700
$715$	−0.0797639	−0.00298300
$716$	66.3350	2.47905
$717$	12.7987	0.477976
$718$	−41.6159	−1.55309
$719$	9.44679	0.352306	0.176153	−	0.984363i	$-0.443635\pi$
$719$	9.44679	0.352306	0.176153	+	0.984363i	$0.443635\pi$
$720$	−68.5403	−2.55435
$721$	68.1200	2.53692
$722$	46.7011	1.73803
$723$	−24.4379	−0.908855
$724$	−21.7486	−0.808282
$725$	−3.68641	−0.136910
$726$	26.9830	1.00143
$727$	19.4189	0.720206	0.360103	−	0.932913i	$-0.382742\pi$
$727$	19.4189	0.720206	0.360103	+	0.932913i	$0.382742\pi$
$728$	−5.49919	−0.203814
$729$	6.52565	0.241691
$730$	−21.2937	−0.788114
$731$	−0.626311	−0.0231649
$732$	78.2503	2.89221
$733$	4.74560	0.175283	0.0876414	−	0.996152i	$-0.472067\pi$
$733$	4.74560	0.175283	0.0876414	+	0.996152i	$0.472067\pi$
$734$	16.3297	0.602741
$735$	12.2143	0.450531
$736$	127.204	4.68880
$737$	−3.99844	−0.147284
$738$	47.2733	1.74015
$739$	−31.1655	−1.14644	−0.573221	−	0.819401i	$-0.694306\pi$
$739$	−31.1655	−1.14644	−0.573221	+	0.819401i	$0.694306\pi$
$740$	−43.0988	−1.58434
$741$	0.173339	0.00636775
$742$	−100.207	−3.67871
$743$	−10.9849	−0.402998	−0.201499	−	0.979489i	$-0.564581\pi$
$743$	−10.9849	−0.402998	−0.201499	+	0.979489i	$0.564581\pi$
$744$	38.9960	1.42966
$745$	−1.21465	−0.0445015
$746$	20.2679	0.742061
$747$	5.37534	0.196673
$748$	−4.30444	−0.157386
$749$	−31.6343	−1.15589
$750$	29.6826	1.08386
$751$	14.9883	0.546930	0.273465	−	0.961882i	$-0.411830\pi$
$751$	14.9883	0.546930	0.273465	+	0.961882i	$0.411830\pi$
$752$	174.729	6.37171
$753$	13.7771	0.502065
$754$	0.546891	0.0199166
$755$	16.1060	0.586157
$756$	107.681	3.91633
$757$	−38.0463	−1.38282	−0.691409	−	0.722464i	$-0.743010\pi$
$757$	−38.0463	−1.38282	−0.691409	+	0.722464i	$0.743010\pi$
$758$	−21.9688	−0.797944
$759$	−1.37930	−0.0500653
$760$	27.5230	0.998363
$761$	−11.6748	−0.423212	−0.211606	−	0.977355i	$-0.567869\pi$
$761$	−11.6748	−0.423212	−0.211606	+	0.977355i	$0.567869\pi$
$762$	23.7218	0.859349
$763$	16.0724	0.581860
$764$	57.2274	2.07041
$765$	6.65850	0.240738
$766$	46.9176	1.69520
$767$	1.35635	0.0489751
$768$	110.037	3.97060
$769$	−12.3601	−0.445716	−0.222858	−	0.974851i	$-0.571539\pi$
$769$	−12.3601	−0.445716	−0.222858	+	0.974851i	$0.571539\pi$
$770$	6.99753	0.252173
$771$	−2.27752	−0.0820229
$772$	68.8630	2.47843
$773$	−29.6115	−1.06505	−0.532525	−	0.846414i	$-0.678757\pi$
$773$	−29.6115	−1.06505	−0.532525	+	0.846414i	$0.678757\pi$
$774$	2.09985	0.0754776
$775$	9.60742	0.345109
$776$	−81.1143	−2.91183
$777$	15.7614	0.565437
$778$	−85.8049	−3.07626
$779$	−11.7364	−0.420501
$780$	−1.06718	−0.0382110
$781$	−3.50599	−0.125454
$782$	−20.8983	−0.747323
$783$	−7.08815	−0.253310
$784$	164.143	5.86226
$785$	−4.55244	−0.162484
$786$	5.97690	0.213189
$787$	35.1337	1.25238	0.626190	−	0.779671i	$-0.284614\pi$
$787$	35.1337	1.25238	0.626190	+	0.779671i	$0.284614\pi$
$788$	116.393	4.14632
$789$	−18.5405	−0.660059
$790$	−14.5320	−0.517026
$791$	−37.6975	−1.34037
$792$	9.55225	0.339425
$793$	−1.89304	−0.0672240
$794$	−41.9870	−1.49006
$795$	−12.8714	−0.456502
$796$	18.9761	0.672590
$797$	16.5353	0.585710	0.292855	−	0.956157i	$-0.405395\pi$
$797$	16.5353	0.585710	0.292855	+	0.956157i	$0.405395\pi$
$798$	−15.2067	−0.538310
$799$	−16.9744	−0.600512
$800$	76.4897	2.70432
$801$	0.151507	0.00535322
$802$	−22.9702	−0.811106
$803$	1.83477	0.0647476
$804$	−53.4959	−1.88665
$805$	25.3893	0.894855
$806$	−1.42529	−0.0502037
$807$	−3.13330	−0.110297
$808$	−22.3916	−0.787732
$809$	28.3862	0.998005	0.499002	−	0.866601i	$-0.333700\pi$
$809$	28.3862	0.998005	0.499002	+	0.866601i	$0.333700\pi$
$810$	−11.6838	−0.410528
$811$	−4.17265	−0.146522	−0.0732608	−	0.997313i	$-0.523341\pi$
$811$	−4.17265	−0.146522	−0.0732608	+	0.997313i	$0.523341\pi$
$812$	−35.8550	−1.25827
$813$	18.8749	0.661971
$814$	4.96919	0.174170
$815$	−26.6182	−0.932395
$816$	−31.5353	−1.10396
$817$	−0.521325	−0.0182389
$818$	37.9958	1.32849
$819$	−1.10739	−0.0386952
$820$	72.2564	2.52330
$821$	−11.6144	−0.405346	−0.202673	−	0.979246i	$-0.564963\pi$
$821$	−11.6144	−0.405346	−0.202673	+	0.979246i	$0.564963\pi$
$822$	−47.1454	−1.64439
$823$	−36.2902	−1.26500	−0.632498	−	0.774562i	$-0.717971\pi$
$823$	−36.2902	−1.26500	−0.632498	+	0.774562i	$0.717971\pi$
$824$	190.189	6.62556
$825$	−0.829391	−0.0288757
$826$	−118.990	−4.14020
$827$	−45.8109	−1.59300	−0.796501	−	0.604637i	$-0.793318\pi$
$827$	−45.8109	−1.59300	−0.796501	+	0.604637i	$0.793318\pi$
$828$	52.3625	1.81972
$829$	17.1152	0.594434	0.297217	−	0.954810i	$-0.403941\pi$
$829$	17.1152	0.594434	0.297217	+	0.954810i	$0.403941\pi$
$830$	10.9940	0.381608
$831$	6.43787	0.223327
$832$	−6.49863	−0.225300
$833$	−15.9461	−0.552498
$834$	−31.9590	−1.10665
$835$	−3.37712	−0.116870
$836$	−3.58290	−0.123917
$837$	18.4729	0.638517
$838$	48.9467	1.69084
$839$	12.3289	0.425642	0.212821	−	0.977091i	$-0.431735\pi$
$839$	12.3289	0.425642	0.212821	+	0.977091i	$0.431735\pi$
$840$	61.9677	2.13809
$841$	−26.6398	−0.918615
$842$	−16.3361	−0.562980
$843$	−5.88860	−0.202814
$844$	−57.4917	−1.97895
$845$	−20.9378	−0.720282
$846$	56.9107	1.95663
$847$	42.7970	1.47052
$848$	−172.974	−5.93995
$849$	19.5096	0.669566
$850$	−12.5665	−0.431027
$851$	18.0298	0.618054
$852$	−46.9073	−1.60702
$853$	46.1452	1.57998	0.789991	−	0.613119i	$-0.210085\pi$
$853$	46.1452	1.57998	0.789991	+	0.613119i	$0.210085\pi$
$854$	166.073	5.68291
$855$	5.54236	0.189545
$856$	−88.3221	−3.01879
$857$	50.0472	1.70958	0.854790	−	0.518974i	$-0.173686\pi$
$857$	50.0472	1.70958	0.854790	+	0.518974i	$0.173686\pi$
$858$	0.123043	0.00420061
$859$	−11.7176	−0.399798	−0.199899	−	0.979817i	$-0.564061\pi$
$859$	−11.7176	−0.399798	−0.199899	+	0.979817i	$0.564061\pi$
$860$	3.20959	0.109446
$861$	−26.4244	−0.900543
$862$	62.3708	2.12436
$863$	10.1759	0.346391	0.173196	−	0.984887i	$-0.444591\pi$
$863$	10.1759	0.346391	0.173196	+	0.984887i	$0.444591\pi$
$864$	147.072	5.00351
$865$	17.1813	0.584181
$866$	−105.119	−3.57208
$867$	−11.9674	−0.406433
$868$	93.4443	3.17171
$869$	1.25215	0.0424763
$870$	−6.16265	−0.208933
$871$	1.29418	0.0438517
$872$	44.8737	1.51962
$873$	−16.3342	−0.552828
$874$	−17.3952	−0.588402
$875$	47.0789	1.59156
$876$	24.5477	0.829391
$877$	42.1026	1.42170	0.710852	−	0.703342i	$-0.248310\pi$
$877$	42.1026	1.42170	0.710852	+	0.703342i	$0.248310\pi$
$878$	52.2590	1.76366
$879$	17.7954	0.600223
$880$	12.0789	0.407180
$881$	19.4872	0.656540	0.328270	−	0.944584i	$-0.393534\pi$
$881$	19.4872	0.656540	0.328270	+	0.944584i	$0.393534\pi$
$882$	53.4628	1.80019
$883$	−57.5957	−1.93825	−0.969125	−	0.246569i	$-0.920697\pi$
$883$	−57.5957	−1.93825	−0.969125	+	0.246569i	$0.920697\pi$
$884$	1.39322	0.0468592
$885$	−15.2841	−0.513768
$886$	15.8901	0.533839
$887$	−35.1840	−1.18136	−0.590682	−	0.806904i	$-0.701141\pi$
$887$	−35.1840	−1.18136	−0.590682	+	0.806904i	$0.701141\pi$
$888$	44.0054	1.47672
$889$	37.6245	1.26189
$890$	0.309872	0.0103869
$891$	1.00674	0.0337270
$892$	−109.054	−3.65141
$893$	−14.1291	−0.472812
$894$	1.87371	0.0626663
$895$	18.0835	0.604466
$896$	318.578	10.6430
$897$	0.446439	0.0149062
$898$	19.1851	0.640217
$899$	−6.15100	−0.205147
$900$	31.4864	1.04955
$901$	16.8039	0.559820
$902$	−8.33099	−0.277392
$903$	−1.17376	−0.0390603
$904$	−105.251	−3.50058
$905$	−5.92889	−0.197083
$906$	−24.8449	−0.825416
$907$	6.36743	0.211427	0.105713	−	0.994397i	$-0.466287\pi$
$907$	6.36743	0.211427	0.105713	+	0.994397i	$0.466287\pi$
$908$	17.0329	0.565257
$909$	−4.50904	−0.149555
$910$	−2.26490	−0.0750807
$911$	−19.5154	−0.646573	−0.323286	−	0.946301i	$-0.604788\pi$
$911$	−19.5154	−0.646573	−0.323286	+	0.946301i	$0.604788\pi$
$912$	−26.2492	−0.869198
$913$	−0.947300	−0.0313510
$914$	103.841	3.43474
$915$	21.3318	0.705207
$916$	101.995	3.37002
$917$	9.47981	0.313051
$918$	−24.1625	−0.797481
$919$	46.7587	1.54243	0.771213	−	0.636577i	$-0.219650\pi$
$919$	46.7587	1.54243	0.771213	+	0.636577i	$0.219650\pi$
$920$	70.8862	2.33705
$921$	−25.8777	−0.852699
$922$	−5.22717	−0.172148
$923$	1.13479	0.0373520
$924$	−8.06688	−0.265381
$925$	10.8416	0.356469
$926$	−55.3951	−1.82040
$927$	38.2989	1.25790
$928$	−48.9713	−1.60756
$929$	22.8271	0.748933	0.374467	−	0.927240i	$-0.377826\pi$
$929$	22.8271	0.748933	0.374467	+	0.927240i	$0.377826\pi$
$930$	16.0609	0.526658
$931$	−13.2731	−0.435008
$932$	−16.0828	−0.526809
$933$	27.8105	0.910474
$934$	−87.8001	−2.87291
$935$	−1.17343	−0.0383753
$936$	−3.09179	−0.101058
$937$	−9.50808	−0.310615	−0.155308	−	0.987866i	$-0.549637\pi$
$937$	−9.50808	−0.310615	−0.155308	+	0.987866i	$0.549637\pi$
$938$	−113.536	−3.70708
$939$	3.76781	0.122958
$940$	86.9871	2.83721
$941$	−33.6117	−1.09571	−0.547855	−	0.836573i	$-0.684555\pi$
$941$	−33.6117	−1.09571	−0.547855	+	0.836573i	$0.684555\pi$
$942$	7.02254	0.228807
$943$	−30.2275	−0.984343
$944$	−205.397	−6.68510
$945$	29.3549	0.954916
$946$	−0.370058	−0.0120316
$947$	−20.7879	−0.675516	−0.337758	−	0.941233i	$-0.609669\pi$
$947$	−20.7879	−0.675516	−0.337758	+	0.941233i	$0.609669\pi$
$948$	16.7528	0.544104
$949$	−0.593863	−0.0192776
$950$	−10.4600	−0.339368
$951$	11.3781	0.368960
$952$	−80.9003	−2.62200
$953$	−29.5520	−0.957284	−0.478642	−	0.878010i	$-0.658871\pi$
$953$	−29.5520	−0.957284	−0.478642	+	0.878010i	$0.658871\pi$
$954$	−56.3390	−1.82404
$955$	15.6007	0.504828
$956$	85.6269	2.76937
$957$	0.531005	0.0171649
$958$	−38.2910	−1.23713
$959$	−74.7762	−2.41465
$960$	73.2299	2.36348
$961$	−14.9695	−0.482886
$962$	−1.60838	−0.0518564
$963$	−17.7856	−0.573134
$964$	−163.497	−5.26587
$965$	18.7727	0.604315
$966$	−39.1652	−1.26012
$967$	13.1018	0.421326	0.210663	−	0.977559i	$-0.432438\pi$
$967$	13.1018	0.421326	0.210663	+	0.977559i	$0.432438\pi$
$968$	119.488	3.84050
$969$	2.55004	0.0819190
$970$	−33.4078	−1.07266
$971$	−17.8334	−0.572301	−0.286151	−	0.958185i	$-0.592376\pi$
$971$	−17.8334	−0.572301	−0.286151	+	0.958185i	$0.592376\pi$
$972$	95.3468	3.05825
$973$	−50.6894	−1.62503
$974$	−69.8640	−2.23859
$975$	0.268450	0.00859729
$976$	286.670	9.17607
$977$	−2.44557	−0.0782407	−0.0391204	−	0.999235i	$-0.512456\pi$
$977$	−2.44557	−0.0782407	−0.0391204	+	0.999235i	$0.512456\pi$
$978$	41.0609	1.31298
$979$	−0.0267001	−0.000853339 0
$980$	81.7171	2.61036
$981$	9.03633	0.288508
$982$	−73.6785	−2.35117
$983$	−33.0866	−1.05530	−0.527649	−	0.849462i	$-0.676927\pi$
$983$	−33.0866	−1.05530	−0.527649	+	0.849462i	$0.676927\pi$
$984$	−73.7764	−2.35191
$985$	31.7298	1.01100
$986$	8.04549	0.256220
$987$	−31.8115	−1.01257
$988$	1.15968	0.0368945
$989$	−1.34269	−0.0426950
$990$	3.93420	0.125037
$991$	−2.93415	−0.0932063	−0.0466032	−	0.998913i	$-0.514840\pi$
$991$	−2.93415	−0.0932063	−0.0466032	+	0.998913i	$0.514840\pi$
$992$	127.627	4.05217
$993$	14.4698	0.459184
$994$	−99.5528	−3.15762
$995$	5.17307	0.163997
$996$	−12.6741	−0.401594
$997$	12.1169	0.383747	0.191874	−	0.981420i	$-0.438544\pi$
$997$	12.1169	0.383747	0.191874	+	0.981420i	$0.438544\pi$
$998$	83.4859	2.64270
$999$	20.8459	0.659536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.1	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.1	✓	358	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:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.81343 q^{2} +0.884173 q^{3} +5.91537 q^{4} +1.61259 q^{5} -2.48756 q^{6} -3.94545 q^{7} -11.0156 q^{8} -2.21824 q^{9} +O(q^{10})\)	\(q-2.81343 q^{2} +0.884173 q^{3} +5.91537 q^{4} +1.61259 q^{5} -2.48756 q^{6} -3.94545 q^{7} -11.0156 q^{8} -2.21824 q^{9} -4.53689 q^{10} +0.390921 q^{11} +5.23021 q^{12} -0.126530 q^{13} +11.1002 q^{14} +1.42581 q^{15} +19.1609 q^{16} -1.86142 q^{17} +6.24085 q^{18} -1.54940 q^{19} +9.53904 q^{20} -3.48846 q^{21} -1.09983 q^{22} -3.99053 q^{23} -9.73970 q^{24} -2.39957 q^{25} +0.355983 q^{26} -4.61383 q^{27} -23.3388 q^{28} +1.53628 q^{29} -4.01140 q^{30} -4.00381 q^{31} -31.8765 q^{32} +0.345642 q^{33} +5.23698 q^{34} -6.36238 q^{35} -13.1217 q^{36} -4.51815 q^{37} +4.35913 q^{38} -0.111875 q^{39} -17.7636 q^{40} +7.57481 q^{41} +9.81454 q^{42} +0.336469 q^{43} +2.31244 q^{44} -3.57710 q^{45} +11.2271 q^{46} +9.11906 q^{47} +16.9415 q^{48} +8.56660 q^{49} +6.75100 q^{50} -1.64582 q^{51} -0.748472 q^{52} -9.02746 q^{53} +12.9807 q^{54} +0.630394 q^{55} +43.4615 q^{56} -1.36994 q^{57} -4.32222 q^{58} -10.7196 q^{59} +8.43417 q^{60} +14.9612 q^{61} +11.2644 q^{62} +8.75195 q^{63} +51.3604 q^{64} -0.204041 q^{65} -0.972439 q^{66} -10.2282 q^{67} -11.0110 q^{68} -3.52832 q^{69} +17.9001 q^{70} -8.96853 q^{71} +24.4352 q^{72} +4.69345 q^{73} +12.7115 q^{74} -2.12163 q^{75} -9.16528 q^{76} -1.54236 q^{77} +0.314751 q^{78} +3.20308 q^{79} +30.8985 q^{80} +2.57529 q^{81} -21.3112 q^{82} -2.42325 q^{83} -20.6355 q^{84} -3.00171 q^{85} -0.946630 q^{86} +1.35834 q^{87} -4.30624 q^{88} -0.0683005 q^{89} +10.0639 q^{90} +0.499219 q^{91} -23.6055 q^{92} -3.54007 q^{93} -25.6558 q^{94} -2.49854 q^{95} -28.1843 q^{96} +7.36358 q^{97} -24.1015 q^{98} -0.867157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * q^99

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