LMFDB - Embedded newform 8011.2.a.a.1.14

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:	$1$
Dimension:	$309$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-2.64340 q^{2} +2.84192 q^{3} +4.98759 q^{4} +0.696294 q^{5} -7.51235 q^{6} -3.08264 q^{7} -7.89741 q^{8} +5.07651 q^{9} +O(q^{10})$	\(q-2.64340 q^{2} +2.84192 q^{3} +4.98759 q^{4} +0.696294 q^{5} -7.51235 q^{6} -3.08264 q^{7} -7.89741 q^{8} +5.07651 q^{9} -1.84059 q^{10} -3.36093 q^{11} +14.1743 q^{12} +2.41392 q^{13} +8.14867 q^{14} +1.97881 q^{15} +10.9009 q^{16} -5.44350 q^{17} -13.4193 q^{18} +1.90377 q^{19} +3.47283 q^{20} -8.76063 q^{21} +8.88430 q^{22} -1.39423 q^{23} -22.4438 q^{24} -4.51517 q^{25} -6.38098 q^{26} +5.90128 q^{27} -15.3750 q^{28} +4.63295 q^{29} -5.23080 q^{30} +2.87055 q^{31} -13.0206 q^{32} -9.55150 q^{33} +14.3894 q^{34} -2.14643 q^{35} +25.3195 q^{36} +10.5785 q^{37} -5.03243 q^{38} +6.86018 q^{39} -5.49892 q^{40} +0.220309 q^{41} +23.1579 q^{42} +2.30716 q^{43} -16.7629 q^{44} +3.53475 q^{45} +3.68550 q^{46} +3.34993 q^{47} +30.9794 q^{48} +2.50269 q^{49} +11.9354 q^{50} -15.4700 q^{51} +12.0397 q^{52} -2.42818 q^{53} -15.5995 q^{54} -2.34020 q^{55} +24.3449 q^{56} +5.41036 q^{57} -12.2468 q^{58} -3.33182 q^{59} +9.86951 q^{60} -14.0250 q^{61} -7.58804 q^{62} -15.6491 q^{63} +12.6169 q^{64} +1.68080 q^{65} +25.2485 q^{66} +13.1042 q^{67} -27.1500 q^{68} -3.96228 q^{69} +5.67388 q^{70} -5.78569 q^{71} -40.0913 q^{72} -4.01998 q^{73} -27.9632 q^{74} -12.8318 q^{75} +9.49521 q^{76} +10.3605 q^{77} -18.1342 q^{78} -0.525363 q^{79} +7.59021 q^{80} +1.54143 q^{81} -0.582366 q^{82} -10.2848 q^{83} -43.6944 q^{84} -3.79028 q^{85} -6.09876 q^{86} +13.1665 q^{87} +26.5426 q^{88} +3.27972 q^{89} -9.34377 q^{90} -7.44126 q^{91} -6.95382 q^{92} +8.15789 q^{93} -8.85521 q^{94} +1.32558 q^{95} -37.0035 q^{96} +1.92704 q^{97} -6.61561 q^{98} -17.0618 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) $ 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * 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 $

$2$	−2.64340	−1.86917	−0.934585	−	0.355741i	$-0.884229\pi$
$2$	−2.64340	−1.86917	−0.934585	+	0.355741i	$0.884229\pi$
$3$	2.84192	1.64078	0.820392	−	0.571802i	$-0.193755\pi$
$3$	2.84192	1.64078	0.820392	+	0.571802i	$0.193755\pi$
$4$	4.98759	2.49379
$5$	0.696294	0.311392	0.155696	−	0.987805i	$-0.450238\pi$
$5$	0.696294	0.311392	0.155696	+	0.987805i	$0.450238\pi$
$6$	−7.51235	−3.06690
$7$	−3.08264	−1.16513	−0.582565	−	0.812784i	$-0.697951\pi$
$7$	−3.08264	−1.16513	−0.582565	+	0.812784i	$0.697951\pi$
$8$	−7.89741	−2.79215
$9$	5.07651	1.69217
$10$	−1.84059	−0.582045
$11$	−3.36093	−1.01336	−0.506679	−	0.862135i	$-0.669127\pi$
$11$	−3.36093	−1.01336	−0.506679	+	0.862135i	$0.669127\pi$
$12$	14.1743	4.09178
$13$	2.41392	0.669502	0.334751	−	0.942307i	$-0.391348\pi$
$13$	2.41392	0.669502	0.334751	+	0.942307i	$0.391348\pi$
$14$	8.14867	2.17782
$15$	1.97881	0.510927
$16$	10.9009	2.72522
$17$	−5.44350	−1.32024	−0.660122	−	0.751159i	$-0.729495\pi$
$17$	−5.44350	−1.32024	−0.660122	+	0.751159i	$0.729495\pi$
$18$	−13.4193	−3.16295
$19$	1.90377	0.436754	0.218377	−	0.975864i	$-0.429924\pi$
$19$	1.90377	0.436754	0.218377	+	0.975864i	$0.429924\pi$
$20$	3.47283	0.776548
$21$	−8.76063	−1.91173
$22$	8.88430	1.89414
$23$	−1.39423	−0.290716	−0.145358	−	0.989379i	$-0.546433\pi$
$23$	−1.39423	−0.290716	−0.145358	+	0.989379i	$0.546433\pi$
$24$	−22.4438	−4.58132
$25$	−4.51517	−0.903035
$26$	−6.38098	−1.25141
$27$	5.90128	1.13570
$28$	−15.3750	−2.90559
$29$	4.63295	0.860317	0.430159	−	0.902753i	$-0.358458\pi$
$29$	4.63295	0.860317	0.430159	+	0.902753i	$0.358458\pi$
$30$	−5.23080	−0.955010
$31$	2.87055	0.515567	0.257783	−	0.966203i	$-0.417008\pi$
$31$	2.87055	0.515567	0.257783	+	0.966203i	$0.417008\pi$
$32$	−13.0206	−2.30174
$33$	−9.55150	−1.66270
$34$	14.3894	2.46776
$35$	−2.14643	−0.362812
$36$	25.3195	4.21992
$37$	10.5785	1.73909	0.869545	−	0.493854i	$-0.164412\pi$
$37$	10.5785	1.73909	0.869545	+	0.493854i	$0.164412\pi$
$38$	−5.03243	−0.816368
$39$	6.86018	1.09851
$40$	−5.49892	−0.869456
$41$	0.220309	0.0344065	0.0172033	−	0.999852i	$-0.494524\pi$
$41$	0.220309	0.0344065	0.0172033	+	0.999852i	$0.494524\pi$
$42$	23.1579	3.57334
$43$	2.30716	0.351839	0.175920	−	0.984405i	$-0.443710\pi$
$43$	2.30716	0.351839	0.175920	+	0.984405i	$0.443710\pi$
$44$	−16.7629	−2.52711
$45$	3.53475	0.526929
$46$	3.68550	0.543398
$47$	3.34993	0.488637	0.244318	−	0.969695i	$-0.421436\pi$
$47$	3.34993	0.488637	0.244318	+	0.969695i	$0.421436\pi$
$48$	30.9794	4.47149
$49$	2.50269	0.357527
$50$	11.9354	1.68793
$51$	−15.4700	−2.16623
$52$	12.0397	1.66960
$53$	−2.42818	−0.333536	−0.166768	−	0.985996i	$-0.553333\pi$
$53$	−2.42818	−0.333536	−0.166768	+	0.985996i	$0.553333\pi$
$54$	−15.5995	−2.12282
$55$	−2.34020	−0.315552
$56$	24.3449	3.25322
$57$	5.41036	0.716619
$58$	−12.2468	−1.60808
$59$	−3.33182	−0.433766	−0.216883	−	0.976198i	$-0.569589\pi$
$59$	−3.33182	−0.433766	−0.216883	+	0.976198i	$0.569589\pi$
$60$	9.86951	1.27415
$61$	−14.0250	−1.79571	−0.897857	−	0.440287i	$-0.854877\pi$
$61$	−14.0250	−1.79571	−0.897857	+	0.440287i	$0.854877\pi$
$62$	−7.58804	−0.963682
$63$	−15.6491	−1.97160
$64$	12.6169	1.57712
$65$	1.68080	0.208478
$66$	25.2485	3.10787
$67$	13.1042	1.60093	0.800465	−	0.599380i	$-0.204586\pi$
$67$	13.1042	1.60093	0.800465	+	0.599380i	$0.204586\pi$
$68$	−27.1500	−3.29242
$69$	−3.96228	−0.477002
$70$	5.67388	0.678158
$71$	−5.78569	−0.686635	−0.343317	−	0.939219i	$-0.611551\pi$
$71$	−5.78569	−0.686635	−0.343317	+	0.939219i	$0.611551\pi$
$72$	−40.0913	−4.72480
$73$	−4.01998	−0.470503	−0.235252	−	0.971934i	$-0.575591\pi$
$73$	−4.01998	−0.470503	−0.235252	+	0.971934i	$0.575591\pi$
$74$	−27.9632	−3.25065
$75$	−12.8318	−1.48168
$76$	9.49521	1.08918
$77$	10.3605	1.18069
$78$	−18.1342	−2.05330
$79$	−0.525363	−0.0591080	−0.0295540	−	0.999563i	$-0.509409\pi$
$79$	−0.525363	−0.0591080	−0.0295540	+	0.999563i	$0.509409\pi$
$80$	7.59021	0.848611
$81$	1.54143	0.171270
$82$	−0.582366	−0.0643116
$83$	−10.2848	−1.12891	−0.564453	−	0.825465i	$-0.690913\pi$
$83$	−10.2848	−1.12891	−0.564453	+	0.825465i	$0.690913\pi$
$84$	−43.6944	−4.76745
$85$	−3.79028	−0.411114
$86$	−6.09876	−0.657647
$87$	13.1665	1.41159
$88$	26.5426	2.82945
$89$	3.27972	0.347650	0.173825	−	0.984777i	$-0.444387\pi$
$89$	3.27972	0.347650	0.173825	+	0.984777i	$0.444387\pi$
$90$	−9.34377	−0.984919
$91$	−7.44126	−0.780056
$92$	−6.95382	−0.724986
$93$	8.15789	0.845934
$94$	−8.85521	−0.913345
$95$	1.32558	0.136002
$96$	−37.0035	−3.77665
$97$	1.92704	0.195662	0.0978308	−	0.995203i	$-0.468810\pi$
$97$	1.92704	0.195662	0.0978308	+	0.995203i	$0.468810\pi$
$98$	−6.61561	−0.668278
$99$	−17.0618	−1.71478
$100$	−22.5198	−2.25198
$101$	7.20165	0.716591	0.358296	−	0.933608i	$-0.383358\pi$
$101$	7.20165	0.716591	0.358296	+	0.933608i	$0.383358\pi$
$102$	40.8935	4.04906
$103$	11.0788	1.09163	0.545814	−	0.837906i	$-0.316221\pi$
$103$	11.0788	1.09163	0.545814	+	0.837906i	$0.316221\pi$
$104$	−19.0637	−1.86935
$105$	−6.09997	−0.595297
$106$	6.41867	0.623436
$107$	−6.85840	−0.663027	−0.331514	−	0.943450i	$-0.607559\pi$
$107$	−6.85840	−0.663027	−0.331514	+	0.943450i	$0.607559\pi$
$108$	29.4331	2.83221
$109$	−7.58316	−0.726335	−0.363168	−	0.931724i	$-0.618305\pi$
$109$	−7.58316	−0.726335	−0.363168	+	0.931724i	$0.618305\pi$
$110$	6.18609	0.589820
$111$	30.0632	2.85347
$112$	−33.6035	−3.17523
$113$	−13.6494	−1.28403	−0.642014	−	0.766693i	$-0.721901\pi$
$113$	−13.6494	−1.28403	−0.642014	+	0.766693i	$0.721901\pi$
$114$	−14.3018	−1.33948
$115$	−0.970792	−0.0905268
$116$	23.1072	2.14545
$117$	12.2543	1.13291
$118$	8.80736	0.810783
$119$	16.7804	1.53825
$120$	−15.6275	−1.42659
$121$	0.295856	0.0268960
$122$	37.0737	3.35649
$123$	0.626101	0.0564536
$124$	14.3171	1.28572
$125$	−6.62536	−0.592590
$126$	41.3668	3.68525
$127$	−12.3491	−1.09580	−0.547901	−	0.836543i	$-0.684573\pi$
$127$	−12.3491	−1.09580	−0.547901	+	0.836543i	$0.684573\pi$
$128$	−7.31052	−0.646164
$129$	6.55677	0.577292
$130$	−4.44304	−0.389680
$131$	−9.89639	−0.864651	−0.432326	−	0.901718i	$-0.642307\pi$
$131$	−9.89639	−0.864651	−0.432326	+	0.901718i	$0.642307\pi$
$132$	−47.6389	−4.14644
$133$	−5.86864	−0.508876
$134$	−34.6396	−2.99241
$135$	4.10903	0.353649
$136$	42.9895	3.68632
$137$	−3.87336	−0.330923	−0.165462	−	0.986216i	$-0.552911\pi$
$137$	−3.87336	−0.330923	−0.165462	+	0.986216i	$0.552911\pi$
$138$	10.4739	0.891598
$139$	−2.20164	−0.186741	−0.0933703	−	0.995631i	$-0.529764\pi$
$139$	−2.20164	−0.186741	−0.0933703	+	0.995631i	$0.529764\pi$
$140$	−10.7055	−0.904780
$141$	9.52022	0.801747
$142$	15.2939	1.28344
$143$	−8.11303	−0.678446
$144$	55.3383	4.61153
$145$	3.22590	0.267896
$146$	10.6264	0.879450
$147$	7.11244	0.586624
$148$	52.7610	4.33693
$149$	1.37316	0.112494	0.0562469	−	0.998417i	$-0.482087\pi$
$149$	1.37316	0.112494	0.0562469	+	0.998417i	$0.482087\pi$
$150$	33.9195	2.76952
$151$	16.6233	1.35279	0.676394	−	0.736540i	$-0.263542\pi$
$151$	16.6233	1.35279	0.676394	+	0.736540i	$0.263542\pi$
$152$	−15.0348	−1.21949
$153$	−27.6340	−2.23408
$154$	−27.3871	−2.20692
$155$	1.99875	0.160544
$156$	34.2157	2.73945
$157$	1.54777	0.123525	0.0617627	−	0.998091i	$-0.480328\pi$
$157$	1.54777	0.123525	0.0617627	+	0.998091i	$0.480328\pi$
$158$	1.38875	0.110483
$159$	−6.90070	−0.547261
$160$	−9.06616	−0.716743
$161$	4.29790	0.338722
$162$	−4.07462	−0.320133
$163$	−2.87032	−0.224821	−0.112410	−	0.993662i	$-0.535857\pi$
$163$	−2.87032	−0.224821	−0.112410	+	0.993662i	$0.535857\pi$
$164$	1.09881	0.0858027
$165$	−6.65065	−0.517753
$166$	27.1869	2.11012
$167$	−5.43124	−0.420282	−0.210141	−	0.977671i	$-0.567392\pi$
$167$	−5.43124	−0.420282	−0.210141	+	0.977671i	$0.567392\pi$
$168$	69.1862	5.33783
$169$	−7.17297	−0.551767
$170$	10.0192	0.768441
$171$	9.66450	0.739063
$172$	11.5072	0.877414
$173$	−3.65035	−0.277531	−0.138766	−	0.990325i	$-0.544313\pi$
$173$	−3.65035	−0.277531	−0.138766	+	0.990325i	$0.544313\pi$
$174$	−34.8043	−2.63851
$175$	13.9187	1.05215
$176$	−36.6370	−2.76162
$177$	−9.46877	−0.711717
$178$	−8.66964	−0.649817
$179$	11.8902	0.888718	0.444359	−	0.895849i	$-0.353431\pi$
$179$	11.8902	0.888718	0.444359	+	0.895849i	$0.353431\pi$
$180$	17.6299	1.31405
$181$	−0.880575	−0.0654526	−0.0327263	−	0.999464i	$-0.510419\pi$
$181$	−0.880575	−0.0654526	−0.0327263	+	0.999464i	$0.510419\pi$
$182$	19.6703	1.45806
$183$	−39.8579	−2.94638
$184$	11.0108	0.811725
$185$	7.36573	0.541539
$186$	−21.5646	−1.58119
$187$	18.2952	1.33788
$188$	16.7081	1.21856
$189$	−18.1915	−1.32324
$190$	−3.50405	−0.254211
$191$	−7.92009	−0.573078	−0.286539	−	0.958069i	$-0.592505\pi$
$191$	−7.92009	−0.573078	−0.286539	+	0.958069i	$0.592505\pi$
$192$	35.8563	2.58771
$193$	−7.87881	−0.567129	−0.283565	−	0.958953i	$-0.591517\pi$
$193$	−7.87881	−0.567129	−0.283565	+	0.958953i	$0.591517\pi$
$194$	−5.09395	−0.365725
$195$	4.77670	0.342067
$196$	12.4824	0.891598
$197$	−6.19166	−0.441137	−0.220569	−	0.975371i	$-0.570791\pi$
$197$	−6.19166	−0.441137	−0.220569	+	0.975371i	$0.570791\pi$
$198$	45.1012	3.20521
$199$	−10.4292	−0.739309	−0.369655	−	0.929169i	$-0.620524\pi$
$199$	−10.4292	−0.739309	−0.369655	+	0.929169i	$0.620524\pi$
$200$	35.6582	2.52141
$201$	37.2410	2.62678
$202$	−19.0369	−1.33943
$203$	−14.2817	−1.00238
$204$	−77.1580	−5.40214
$205$	0.153400	0.0107139
$206$	−29.2858	−2.04044
$207$	−7.07780	−0.491941
$208$	26.3138	1.82454
$209$	−6.39843	−0.442589
$210$	16.1247	1.11271
$211$	−7.95825	−0.547868	−0.273934	−	0.961748i	$-0.588325\pi$
$211$	−7.95825	−0.547868	−0.273934	+	0.961748i	$0.588325\pi$
$212$	−12.1108	−0.831771
$213$	−16.4425	−1.12662
$214$	18.1295	1.23931
$215$	1.60646	0.109560
$216$	−46.6048	−3.17105
$217$	−8.84890	−0.600702
$218$	20.0454	1.35764
$219$	−11.4245	−0.771994
$220$	−11.6719	−0.786922
$221$	−13.1402	−0.883905
$222$	−79.4691	−5.33362
$223$	−5.80984	−0.389056	−0.194528	−	0.980897i	$-0.562317\pi$
$223$	−5.80984	−0.389056	−0.194528	+	0.980897i	$0.562317\pi$
$224$	40.1378	2.68182
$225$	−22.9213	−1.52809
$226$	36.0809	2.40007
$227$	−0.879219	−0.0583558	−0.0291779	−	0.999574i	$-0.509289\pi$
$227$	−0.879219	−0.0583558	−0.0291779	+	0.999574i	$0.509289\pi$
$228$	26.9846	1.78710
$229$	−15.9651	−1.05500	−0.527502	−	0.849554i	$-0.676871\pi$
$229$	−15.9651	−1.05500	−0.527502	+	0.849554i	$0.676871\pi$
$230$	2.56620	0.169210
$231$	29.4439	1.93726
$232$	−36.5883	−2.40214
$233$	−11.3654	−0.744571	−0.372285	−	0.928118i	$-0.621426\pi$
$233$	−11.3654	−0.744571	−0.372285	+	0.928118i	$0.621426\pi$
$234$	−32.3931	−2.11760
$235$	2.33253	0.152158
$236$	−16.6178	−1.08172
$237$	−1.49304	−0.0969834
$238$	−44.3573	−2.87526
$239$	−18.1748	−1.17563	−0.587815	−	0.808996i	$-0.700012\pi$
$239$	−18.1748	−1.17563	−0.587815	+	0.808996i	$0.700012\pi$
$240$	21.5708	1.39239
$241$	−2.77449	−0.178721	−0.0893603	−	0.995999i	$-0.528482\pi$
$241$	−2.77449	−0.178721	−0.0893603	+	0.995999i	$0.528482\pi$
$242$	−0.782067	−0.0502731
$243$	−13.3232	−0.854685
$244$	−69.9508	−4.47814
$245$	1.74261	0.111331
$246$	−1.65504	−0.105521
$247$	4.59555	0.292408
$248$	−22.6699	−1.43954
$249$	−29.2286	−1.85229
$250$	17.5135	1.10765
$251$	−26.9972	−1.70405	−0.852023	−	0.523504i	$-0.824625\pi$
$251$	−26.9972	−1.70405	−0.852023	+	0.523504i	$0.824625\pi$
$252$	−78.0511	−4.91676
$253$	4.68590	0.294600
$254$	32.6436	2.04824
$255$	−10.7717	−0.674549
$256$	−5.90923	−0.369327
$257$	24.0897	1.50267	0.751336	−	0.659920i	$-0.229410\pi$
$257$	24.0897	1.50267	0.751336	+	0.659920i	$0.229410\pi$
$258$	−17.3322	−1.07906
$259$	−32.6096	−2.02626
$260$	8.38315	0.519901
$261$	23.5192	1.45580
$262$	26.1602	1.61618
$263$	−6.17187	−0.380574	−0.190287	−	0.981729i	$-0.560942\pi$
$263$	−6.17187	−0.380574	−0.190287	+	0.981729i	$0.560942\pi$
$264$	75.4321	4.64252
$265$	−1.69073	−0.103861
$266$	15.5132	0.951175
$267$	9.32071	0.570418
$268$	65.3582	3.99239
$269$	−25.5086	−1.55529	−0.777644	−	0.628705i	$-0.783585\pi$
$269$	−25.5086	−1.55529	−0.777644	+	0.628705i	$0.783585\pi$
$270$	−10.8618	−0.661029
$271$	−20.0051	−1.21523	−0.607613	−	0.794233i	$-0.707873\pi$
$271$	−20.0051	−1.21523	−0.607613	+	0.794233i	$0.707873\pi$
$272$	−59.3389	−3.59795
$273$	−21.1475	−1.27990
$274$	10.2389	0.618552
$275$	15.1752	0.915098
$276$	−19.7622	−1.18955
$277$	−1.69060	−0.101579	−0.0507893	−	0.998709i	$-0.516174\pi$
$277$	−1.69060	−0.101579	−0.0507893	+	0.998709i	$0.516174\pi$
$278$	5.81982	0.349050
$279$	14.5724	0.872427
$280$	16.9512	1.01303
$281$	−17.0055	−1.01447	−0.507233	−	0.861809i	$-0.669331\pi$
$281$	−17.0055	−1.01447	−0.507233	+	0.861809i	$0.669331\pi$
$282$	−25.1658	−1.49860
$283$	−20.9919	−1.24784	−0.623920	−	0.781488i	$-0.714461\pi$
$283$	−20.9919	−1.24784	−0.623920	+	0.781488i	$0.714461\pi$
$284$	−28.8566	−1.71233
$285$	3.76720	0.223150
$286$	21.4460	1.26813
$287$	−0.679134	−0.0400880
$288$	−66.0991	−3.89493
$289$	12.6317	0.743042
$290$	−8.52735	−0.500743
$291$	5.47650	0.321038
$292$	−20.0500	−1.17334
$293$	5.67633	0.331615	0.165808	−	0.986158i	$-0.446977\pi$
$293$	5.67633	0.331615	0.165808	+	0.986158i	$0.446977\pi$
$294$	−18.8010	−1.09650
$295$	−2.31993	−0.135072
$296$	−83.5425	−4.85581
$297$	−19.8338	−1.15087
$298$	−3.62982	−0.210270
$299$	−3.36555	−0.194635
$300$	−63.9996	−3.69502
$301$	−7.11216	−0.409938
$302$	−43.9422	−2.52859
$303$	20.4665	1.17577
$304$	20.7527	1.19025
$305$	−9.76551	−0.559172
$306$	73.0478	4.17587
$307$	−2.09147	−0.119367	−0.0596833	−	0.998217i	$-0.519009\pi$
$307$	−2.09147	−0.119367	−0.0596833	+	0.998217i	$0.519009\pi$
$308$	51.6742	2.94441
$309$	31.4851	1.79112
$310$	−5.28351	−0.300083
$311$	−18.7308	−1.06212	−0.531062	−	0.847333i	$-0.678207\pi$
$311$	−18.7308	−1.06212	−0.531062	+	0.847333i	$0.678207\pi$
$312$	−54.1776	−3.06720
$313$	12.2457	0.692169	0.346084	−	0.938203i	$-0.387511\pi$
$313$	12.2457	0.692169	0.346084	+	0.938203i	$0.387511\pi$
$314$	−4.09138	−0.230890
$315$	−10.8964	−0.613940
$316$	−2.62030	−0.147403
$317$	−6.19987	−0.348220	−0.174110	−	0.984726i	$-0.555705\pi$
$317$	−6.19987	−0.348220	−0.174110	+	0.984726i	$0.555705\pi$
$318$	18.2413	1.02292
$319$	−15.5710	−0.871810
$320$	8.78511	0.491102
$321$	−19.4910	−1.08788
$322$	−11.3611	−0.633129
$323$	−10.3632	−0.576622
$324$	7.68802	0.427112
$325$	−10.8993	−0.604584
$326$	7.58742	0.420228
$327$	−21.5507	−1.19176
$328$	−1.73987	−0.0960683
$329$	−10.3266	−0.569325
$330$	17.5804	0.967768
$331$	−14.6976	−0.807853	−0.403926	−	0.914791i	$-0.632355\pi$
$331$	−14.6976	−0.807853	−0.403926	+	0.914791i	$0.632355\pi$
$332$	−51.2965	−2.81526
$333$	53.7017	2.94284
$334$	14.3570	0.785579
$335$	9.12436	0.498517
$336$	−95.4984	−5.20986
$337$	23.9124	1.30259	0.651296	−	0.758824i	$-0.274226\pi$
$337$	23.9124	1.30259	0.651296	+	0.758824i	$0.274226\pi$
$338$	18.9611	1.03135
$339$	−38.7905	−2.10681
$340$	−18.9044	−1.02523
$341$	−9.64774	−0.522454
$342$	−25.5472	−1.38143
$343$	13.8636	0.748565
$344$	−18.2206	−0.982389
$345$	−2.75891	−0.148535
$346$	9.64936	0.518753
$347$	−1.90030	−0.102013	−0.0510067	−	0.998698i	$-0.516243\pi$
$347$	−1.90030	−0.102013	−0.0510067	+	0.998698i	$0.516243\pi$
$348$	65.6690	3.52023
$349$	10.2951	0.551084	0.275542	−	0.961289i	$-0.411143\pi$
$349$	10.2951	0.551084	0.275542	+	0.961289i	$0.411143\pi$
$350$	−36.7927	−1.96665
$351$	14.2452	0.760354
$352$	43.7613	2.33248
$353$	26.9018	1.43184	0.715919	−	0.698183i	$-0.246008\pi$
$353$	26.9018	1.43184	0.715919	+	0.698183i	$0.246008\pi$
$354$	25.0298	1.33032
$355$	−4.02854	−0.213813
$356$	16.3579	0.866967
$357$	47.6885	2.52394
$358$	−31.4307	−1.66116
$359$	32.7162	1.72670	0.863348	−	0.504608i	$-0.168363\pi$
$359$	32.7162	1.72670	0.863348	+	0.504608i	$0.168363\pi$
$360$	−27.9153	−1.47127
$361$	−15.3757	−0.809246
$362$	2.32772	0.122342
$363$	0.840799	0.0441305
$364$	−37.1140	−1.94530
$365$	−2.79909	−0.146511
$366$	105.360	5.50728
$367$	20.1953	1.05419	0.527093	−	0.849807i	$-0.323282\pi$
$367$	20.1953	1.05419	0.527093	+	0.849807i	$0.323282\pi$
$368$	−15.1983	−0.792264
$369$	1.11840	0.0582217
$370$	−19.4706	−1.01223
$371$	7.48522	0.388613
$372$	40.6882	2.10958
$373$	3.85497	0.199603	0.0998013	−	0.995007i	$-0.468179\pi$
$373$	3.85497	0.199603	0.0998013	+	0.995007i	$0.468179\pi$
$374$	−48.3617	−2.50072
$375$	−18.8288	−0.972313
$376$	−26.4557	−1.36435
$377$	11.1836	0.575984
$378$	48.0876	2.47336
$379$	−10.3584	−0.532077	−0.266039	−	0.963962i	$-0.585715\pi$
$379$	−10.3584	−0.532077	−0.266039	+	0.963962i	$0.585715\pi$
$380$	6.61147	0.339161
$381$	−35.0951	−1.79798
$382$	20.9360	1.07118
$383$	−20.6194	−1.05360	−0.526801	−	0.849989i	$-0.676609\pi$
$383$	−20.6194	−1.05360	−0.526801	+	0.849989i	$0.676609\pi$
$384$	−20.7759	−1.06022
$385$	7.21399	0.367659
$386$	20.8269	1.06006
$387$	11.7123	0.595371
$388$	9.61130	0.487940
$389$	20.2951	1.02900	0.514500	−	0.857490i	$-0.327977\pi$
$389$	20.2951	1.02900	0.514500	+	0.857490i	$0.327977\pi$
$390$	−12.6268	−0.639381
$391$	7.58947	0.383816
$392$	−19.7647	−0.998270
$393$	−28.1247	−1.41871
$394$	16.3671	0.824560
$395$	−0.365808	−0.0184058
$396$	−85.0972	−4.27630
$397$	−10.0823	−0.506015	−0.253008	−	0.967464i	$-0.581420\pi$
$397$	−10.0823	−0.506015	−0.253008	+	0.967464i	$0.581420\pi$
$398$	27.5687	1.38189
$399$	−16.6782	−0.834954
$400$	−49.2193	−2.46096
$401$	13.7540	0.686843	0.343421	−	0.939181i	$-0.388414\pi$
$401$	13.7540	0.686843	0.343421	+	0.939181i	$0.388414\pi$
$402$	−98.4431	−4.90989
$403$	6.92930	0.345173
$404$	35.9189	1.78703
$405$	1.07329	0.0533322
$406$	37.7524	1.87362
$407$	−35.5535	−1.76232
$408$	122.173	6.04846
$409$	3.56347	0.176202	0.0881012	−	0.996112i	$-0.471920\pi$
$409$	3.56347	0.176202	0.0881012	+	0.996112i	$0.471920\pi$
$410$	−0.405498	−0.0200261
$411$	−11.0078	−0.542973
$412$	55.2566	2.72230
$413$	10.2708	0.505394
$414$	18.7095	0.919522
$415$	−7.16126	−0.351533
$416$	−31.4307	−1.54102
$417$	−6.25688	−0.306401
$418$	16.9137	0.827274
$419$	−9.70532	−0.474136	−0.237068	−	0.971493i	$-0.576186\pi$
$419$	−9.70532	−0.474136	−0.237068	+	0.971493i	$0.576186\pi$
$420$	−30.4242	−1.48455
$421$	0.0721222	0.00351502	0.00175751	−	0.999998i	$-0.499441\pi$
$421$	0.0721222	0.00351502	0.00175751	+	0.999998i	$0.499441\pi$
$422$	21.0369	1.02406
$423$	17.0059	0.826857
$424$	19.1763	0.931285
$425$	24.5784	1.19223
$426$	43.4641	2.10584
$427$	43.2340	2.09224
$428$	−34.2069	−1.65345
$429$	−23.0566	−1.11318
$430$	−4.24654	−0.204786
$431$	−15.0675	−0.725775	−0.362887	−	0.931833i	$-0.618209\pi$
$431$	−15.0675	−0.725775	−0.362887	+	0.931833i	$0.618209\pi$
$432$	64.3290	3.09503
$433$	−29.1862	−1.40260	−0.701300	−	0.712866i	$-0.747397\pi$
$433$	−29.1862	−1.40260	−0.701300	+	0.712866i	$0.747397\pi$
$434$	23.3912	1.12281
$435$	9.16774	0.439560
$436$	−37.8217	−1.81133
$437$	−2.65428	−0.126972
$438$	30.1995	1.44299
$439$	−31.2848	−1.49314	−0.746570	−	0.665307i	$-0.768301\pi$
$439$	−31.2848	−1.49314	−0.746570	+	0.665307i	$0.768301\pi$
$440$	18.4815	0.881070
$441$	12.7049	0.604996
$442$	34.7349	1.65217
$443$	−21.9826	−1.04442	−0.522212	−	0.852815i	$-0.674893\pi$
$443$	−21.9826	−1.04442	−0.522212	+	0.852815i	$0.674893\pi$
$444$	149.943	7.11597
$445$	2.28365	0.108256
$446$	15.3578	0.727211
$447$	3.90242	0.184578
$448$	−38.8935	−1.83755
$449$	−5.11815	−0.241540	−0.120770	−	0.992680i	$-0.538536\pi$
$449$	−5.11815	−0.241540	−0.120770	+	0.992680i	$0.538536\pi$
$450$	60.5904	2.85626
$451$	−0.740444	−0.0348661
$452$	−68.0776	−3.20210
$453$	47.2422	2.21963
$454$	2.32413	0.109077
$455$	−5.18131	−0.242904
$456$	−42.7278	−2.00091
$457$	7.29501	0.341246	0.170623	−	0.985336i	$-0.445422\pi$
$457$	7.29501	0.341246	0.170623	+	0.985336i	$0.445422\pi$
$458$	42.2023	1.97198
$459$	−32.1236	−1.49940
$460$	−4.84191	−0.225755
$461$	−25.5056	−1.18791	−0.593957	−	0.804497i	$-0.702435\pi$
$461$	−25.5056	−1.18791	−0.593957	+	0.804497i	$0.702435\pi$
$462$	−77.8320	−3.62107
$463$	37.3956	1.73792	0.868962	−	0.494880i	$-0.164788\pi$
$463$	37.3956	1.73792	0.868962	+	0.494880i	$0.164788\pi$
$464$	50.5032	2.34455
$465$	5.68029	0.263417
$466$	30.0433	1.39173
$467$	10.4007	0.481287	0.240644	−	0.970614i	$-0.422641\pi$
$467$	10.4007	0.481287	0.240644	+	0.970614i	$0.422641\pi$
$468$	61.1194	2.82525
$469$	−40.3955	−1.86529
$470$	−6.16583	−0.284409
$471$	4.39863	0.202678
$472$	26.3128	1.21114
$473$	−7.75421	−0.356539
$474$	3.94671	0.181278
$475$	−8.59585	−0.394404
$476$	83.6936	3.83609
$477$	−12.3267	−0.564400
$478$	48.0433	2.19745
$479$	12.7409	0.582149	0.291074	−	0.956700i	$-0.405987\pi$
$479$	12.7409	0.582149	0.291074	+	0.956700i	$0.405987\pi$
$480$	−25.7653	−1.17602
$481$	25.5356	1.16432
$482$	7.33410	0.334059
$483$	12.2143	0.555769
$484$	1.47561	0.0670730
$485$	1.34179	0.0609275
$486$	35.2186	1.59755
$487$	30.2602	1.37122	0.685610	−	0.727969i	$-0.259536\pi$
$487$	30.2602	1.37122	0.685610	+	0.727969i	$0.259536\pi$
$488$	110.761	5.01391
$489$	−8.15722	−0.368882
$490$	−4.60642	−0.208097
$491$	12.4558	0.562123	0.281061	−	0.959690i	$-0.409314\pi$
$491$	12.4558	0.562123	0.281061	+	0.959690i	$0.409314\pi$
$492$	3.12273	0.140784
$493$	−25.2195	−1.13583
$494$	−12.1479	−0.546560
$495$	−11.8800	−0.533968
$496$	31.2915	1.40503
$497$	17.8352	0.800018
$498$	77.2631	3.46224
$499$	−35.9649	−1.61001	−0.805004	−	0.593269i	$-0.797837\pi$
$499$	−35.9649	−1.61001	−0.805004	+	0.593269i	$0.797837\pi$
$500$	−33.0446	−1.47780
$501$	−15.4352	−0.689592
$502$	71.3645	3.18515
$503$	0.762675	0.0340060	0.0170030	−	0.999855i	$-0.494588\pi$
$503$	0.762675	0.0340060	0.0170030	+	0.999855i	$0.494588\pi$
$504$	123.587	5.50501
$505$	5.01447	0.223141
$506$	−12.3867	−0.550657
$507$	−20.3850	−0.905330
$508$	−61.5921	−2.73271
$509$	−19.7593	−0.875815	−0.437908	−	0.899020i	$-0.644280\pi$
$509$	−19.7593	−0.875815	−0.437908	+	0.899020i	$0.644280\pi$
$510$	28.4739	1.26085
$511$	12.3922	0.548197
$512$	30.2415	1.33650
$513$	11.2347	0.496023
$514$	−63.6787	−2.80875
$515$	7.71412	0.339925
$516$	32.7025	1.43965
$517$	−11.2589	−0.495165
$518$	86.2005	3.78743
$519$	−10.3740	−0.455369
$520$	−13.2740	−0.582102
$521$	13.9698	0.612028	0.306014	−	0.952027i	$-0.401005\pi$
$521$	13.9698	0.612028	0.306014	+	0.952027i	$0.401005\pi$
$522$	−62.1708	−2.72114
$523$	8.53493	0.373207	0.186603	−	0.982435i	$-0.440252\pi$
$523$	8.53493	0.373207	0.186603	+	0.982435i	$0.440252\pi$
$524$	−49.3591	−2.15626
$525$	39.5557	1.72635
$526$	16.3147	0.711356
$527$	−15.6259	−0.680674
$528$	−104.120	−4.53122
$529$	−21.0561	−0.915484
$530$	4.46928	0.194133
$531$	−16.9140	−0.734007
$532$	−29.2704	−1.26903
$533$	0.531809	0.0230352
$534$	−24.6384	−1.06621
$535$	−4.77547	−0.206462
$536$	−103.489	−4.47004
$537$	33.7911	1.45819
$538$	67.4296	2.90710
$539$	−8.41136	−0.362303
$540$	20.4941	0.881927
$541$	−1.43725	−0.0617920	−0.0308960	−	0.999523i	$-0.509836\pi$
$541$	−1.43725	−0.0617920	−0.0308960	+	0.999523i	$0.509836\pi$
$542$	52.8817	2.27146
$543$	−2.50252	−0.107394
$544$	70.8776	3.03885
$545$	−5.28012	−0.226175
$546$	55.9013	2.39236
$547$	7.47156	0.319461	0.159730	−	0.987161i	$-0.448938\pi$
$547$	7.47156	0.319461	0.159730	+	0.987161i	$0.448938\pi$
$548$	−19.3187	−0.825255
$549$	−71.1979	−3.03865
$550$	−40.1142	−1.71047
$551$	8.82007	0.375747
$552$	31.2917	1.33186
$553$	1.61951	0.0688685
$554$	4.46895	0.189867
$555$	20.9328	0.888549
$556$	−10.9809	−0.465692
$557$	19.4527	0.824239	0.412119	−	0.911130i	$-0.364789\pi$
$557$	19.4527	0.824239	0.412119	+	0.911130i	$0.364789\pi$
$558$	−38.5208	−1.63071
$559$	5.56931	0.235557
$560$	−23.3979	−0.988742
$561$	51.9936	2.19517
$562$	44.9525	1.89621
$563$	4.37335	0.184315	0.0921574	−	0.995744i	$-0.470624\pi$
$563$	4.37335	0.184315	0.0921574	+	0.995744i	$0.470624\pi$
$564$	47.4830	1.99939
$565$	−9.50401	−0.399837
$566$	55.4901	2.33242
$567$	−4.75168	−0.199552
$568$	45.6919	1.91719
$569$	−43.3082	−1.81557	−0.907787	−	0.419432i	$-0.862229\pi$
$569$	−43.3082	−1.81557	−0.907787	+	0.419432i	$0.862229\pi$
$570$	−9.95824	−0.417105
$571$	24.3069	1.01721	0.508607	−	0.860999i	$-0.330161\pi$
$571$	24.3069	1.01721	0.508607	+	0.860999i	$0.330161\pi$
$572$	−40.4645	−1.69190
$573$	−22.5083	−0.940296
$574$	1.79523	0.0749313
$575$	6.29517	0.262527
$576$	64.0500	2.66875
$577$	−20.8127	−0.866444	−0.433222	−	0.901287i	$-0.642623\pi$
$577$	−20.8127	−0.866444	−0.433222	+	0.901287i	$0.642623\pi$
$578$	−33.3908	−1.38887
$579$	−22.3910	−0.930537
$580$	16.0895	0.668078
$581$	31.7044	1.31532
$582$	−14.4766	−0.600075
$583$	8.16095	0.337992
$584$	31.7474	1.31372
$585$	8.53261	0.352780
$586$	−15.0049	−0.619845
$587$	21.0280	0.867919	0.433959	−	0.900932i	$-0.357116\pi$
$587$	21.0280	0.867919	0.433959	+	0.900932i	$0.357116\pi$
$588$	35.4739	1.46292
$589$	5.46487	0.225176
$590$	6.13251	0.252472
$591$	−17.5962	−0.723811
$592$	115.314	4.73939
$593$	−39.1469	−1.60757	−0.803784	−	0.594921i	$-0.797183\pi$
$593$	−39.1469	−1.60757	−0.803784	+	0.594921i	$0.797183\pi$
$594$	52.4287	2.15118
$595$	11.6841	0.479001
$596$	6.84877	0.280537
$597$	−29.6391	−1.21305
$598$	8.89652	0.363806
$599$	5.47924	0.223876	0.111938	−	0.993715i	$-0.464294\pi$
$599$	5.47924	0.223876	0.111938	+	0.993715i	$0.464294\pi$
$600$	101.338	4.13709
$601$	−25.2952	−1.03181	−0.515906	−	0.856645i	$-0.672545\pi$
$601$	−25.2952	−1.03181	−0.515906	+	0.856645i	$0.672545\pi$
$602$	18.8003	0.766244
$603$	66.5235	2.70905
$604$	82.9103	3.37357
$605$	0.206003	0.00837520
$606$	−54.1013	−2.19771
$607$	−27.7267	−1.12539	−0.562695	−	0.826664i	$-0.690236\pi$
$607$	−27.7267	−1.12539	−0.562695	+	0.826664i	$0.690236\pi$
$608$	−24.7882	−1.00529
$609$	−40.5875	−1.64469
$610$	25.8142	1.04519
$611$	8.08646	0.327143
$612$	−137.827	−5.57133
$613$	−2.78068	−0.112310	−0.0561552	−	0.998422i	$-0.517884\pi$
$613$	−2.78068	−0.112310	−0.0561552	+	0.998422i	$0.517884\pi$
$614$	5.52860	0.223116
$615$	0.435951	0.0175792
$616$	−81.8215	−3.29668
$617$	−15.6695	−0.630829	−0.315414	−	0.948954i	$-0.602144\pi$
$617$	−15.6695	−0.630829	−0.315414	+	0.948954i	$0.602144\pi$
$618$	−83.2279	−3.34792
$619$	34.9761	1.40581	0.702904	−	0.711284i	$-0.251886\pi$
$619$	34.9761	1.40581	0.702904	+	0.711284i	$0.251886\pi$
$620$	9.96895	0.400363
$621$	−8.22771	−0.330167
$622$	49.5130	1.98529
$623$	−10.1102	−0.405057
$624$	74.7819	2.99367
$625$	17.9627	0.718507
$626$	−32.3704	−1.29378
$627$	−18.1838	−0.726193
$628$	7.71963	0.308047
$629$	−57.5839	−2.29602
$630$	28.8035	1.14756
$631$	22.2056	0.883990	0.441995	−	0.897018i	$-0.354271\pi$
$631$	22.2056	0.883990	0.441995	+	0.897018i	$0.354271\pi$
$632$	4.14901	0.165039
$633$	−22.6167	−0.898933
$634$	16.3888	0.650881
$635$	−8.59859	−0.341225
$636$	−34.4178	−1.36476
$637$	6.04129	0.239365
$638$	41.1605	1.62956
$639$	−29.3711	−1.16190
$640$	−5.09027	−0.201211
$641$	39.3663	1.55488	0.777438	−	0.628959i	$-0.216519\pi$
$641$	39.3663	1.55488	0.777438	+	0.628959i	$0.216519\pi$
$642$	51.5227	2.03344
$643$	22.7498	0.897163	0.448581	−	0.893742i	$-0.351929\pi$
$643$	22.7498	0.897163	0.448581	+	0.893742i	$0.351929\pi$
$644$	21.4362	0.844703
$645$	4.56544	0.179764
$646$	27.3941	1.07780
$647$	−44.2195	−1.73845	−0.869223	−	0.494420i	$-0.835381\pi$
$647$	−44.2195	−1.73845	−0.869223	+	0.494420i	$0.835381\pi$
$648$	−12.1733	−0.478212
$649$	11.1980	0.439561
$650$	28.8112	1.13007
$651$	−25.1479	−0.985622
$652$	−14.3160	−0.560657
$653$	30.3588	1.18803	0.594017	−	0.804453i	$-0.297541\pi$
$653$	30.3588	1.18803	0.594017	+	0.804453i	$0.297541\pi$
$654$	56.9673	2.22760
$655$	−6.89080	−0.269246
$656$	2.40156	0.0937652
$657$	−20.4075	−0.796172
$658$	27.2975	1.06417
$659$	−36.4799	−1.42106	−0.710528	−	0.703669i	$-0.751544\pi$
$659$	−36.4799	−1.42106	−0.710528	+	0.703669i	$0.751544\pi$
$660$	−33.1707	−1.29117
$661$	12.4613	0.484687	0.242344	−	0.970190i	$-0.422084\pi$
$661$	12.4613	0.484687	0.242344	+	0.970190i	$0.422084\pi$
$662$	38.8517	1.51001
$663$	−37.3434	−1.45030
$664$	81.2234	3.15208
$665$	−4.08630	−0.158460
$666$	−141.955	−5.50066
$667$	−6.45938	−0.250108
$668$	−27.0888	−1.04810
$669$	−16.5111	−0.638356
$670$	−24.1194	−0.931813
$671$	47.1370	1.81970
$672$	114.068	4.40029
$673$	28.9919	1.11756	0.558778	−	0.829318i	$-0.311271\pi$
$673$	28.9919	1.11756	0.558778	+	0.829318i	$0.311271\pi$
$674$	−63.2102	−2.43476
$675$	−26.6453	−1.02558
$676$	−35.7758	−1.37599
$677$	−16.2722	−0.625391	−0.312696	−	0.949853i	$-0.601232\pi$
$677$	−16.2722	−0.625391	−0.312696	+	0.949853i	$0.601232\pi$
$678$	102.539	3.93799
$679$	−5.94038	−0.227971
$680$	29.9334	1.14789
$681$	−2.49867	−0.0957492
$682$	25.5029	0.976555
$683$	14.7008	0.562509	0.281254	−	0.959633i	$-0.409250\pi$
$683$	14.7008	0.562509	0.281254	+	0.959633i	$0.409250\pi$
$684$	48.2026	1.84307
$685$	−2.69700	−0.103047
$686$	−36.6471	−1.39919
$687$	−45.3716	−1.73103
$688$	25.1501	0.958837
$689$	−5.86144	−0.223303
$690$	7.29292	0.277637
$691$	27.6859	1.05322	0.526610	−	0.850107i	$-0.323463\pi$
$691$	27.6859	1.05322	0.526610	+	0.850107i	$0.323463\pi$
$692$	−18.2065	−0.692106
$693$	52.5954	1.99794
$694$	5.02326	0.190680
$695$	−1.53299	−0.0581496
$696$	−103.981	−3.94139
$697$	−1.19925	−0.0454250
$698$	−27.2141	−1.03007
$699$	−32.2995	−1.22168
$700$	69.4206	2.62385
$701$	5.68261	0.214629	0.107315	−	0.994225i	$-0.465775\pi$
$701$	5.68261	0.214629	0.107315	+	0.994225i	$0.465775\pi$
$702$	−37.6559	−1.42123
$703$	20.1390	0.759555
$704$	−42.4047	−1.59819
$705$	6.62888	0.249658
$706$	−71.1124	−2.67635
$707$	−22.2001	−0.834921
$708$	−47.2263	−1.77487
$709$	22.2577	0.835904	0.417952	−	0.908469i	$-0.362748\pi$
$709$	22.2577	0.835904	0.417952	+	0.908469i	$0.362748\pi$
$710$	10.6491	0.399652
$711$	−2.66701	−0.100021
$712$	−25.9013	−0.970692
$713$	−4.00220	−0.149884
$714$	−126.060	−4.71768
$715$	−5.64906	−0.211263
$716$	59.3036	2.21628
$717$	−51.6513	−1.92895
$718$	−86.4822	−3.22749
$719$	34.4961	1.28649	0.643243	−	0.765662i	$-0.277588\pi$
$719$	34.4961	1.28649	0.643243	+	0.765662i	$0.277588\pi$
$720$	38.5318	1.43599
$721$	−34.1520	−1.27189
$722$	40.6441	1.51262
$723$	−7.88488	−0.293242
$724$	−4.39195	−0.163225
$725$	−20.9186	−0.776896
$726$	−2.22257	−0.0824873
$727$	37.3564	1.38547	0.692736	−	0.721191i	$-0.256405\pi$
$727$	37.3564	1.38547	0.692736	+	0.721191i	$0.256405\pi$
$728$	58.7667	2.17804
$729$	−42.4878	−1.57362
$730$	7.39913	0.273854
$731$	−12.5590	−0.464513
$732$	−198.795	−7.34766
$733$	43.1969	1.59551	0.797757	−	0.602979i	$-0.206020\pi$
$733$	43.1969	1.59551	0.797757	+	0.602979i	$0.206020\pi$
$734$	−53.3844	−1.97045
$735$	4.95235	0.182670
$736$	18.1536	0.669152
$737$	−44.0422	−1.62232
$738$	−2.95639	−0.108826
$739$	27.9443	1.02795	0.513974	−	0.857806i	$-0.328173\pi$
$739$	27.9443	1.02795	0.513974	+	0.857806i	$0.328173\pi$
$740$	36.7372	1.35049
$741$	13.0602	0.479778
$742$	−19.7865	−0.726384
$743$	12.8173	0.470221	0.235111	−	0.971969i	$-0.424455\pi$
$743$	12.8173	0.470221	0.235111	+	0.971969i	$0.424455\pi$
$744$	−64.4262	−2.36198
$745$	0.956125	0.0350297
$746$	−10.1902	−0.373091
$747$	−52.2110	−1.91030
$748$	91.2491	3.33640
$749$	21.1420	0.772512
$750$	49.7720	1.81742
$751$	39.0194	1.42384	0.711919	−	0.702261i	$-0.247826\pi$
$751$	39.0194	1.42384	0.711919	+	0.702261i	$0.247826\pi$
$752$	36.5171	1.33164
$753$	−76.7238	−2.79597
$754$	−29.5627	−1.07661
$755$	11.5747	0.421248
$756$	−90.7319	−3.29989
$757$	24.3019	0.883268	0.441634	−	0.897195i	$-0.354399\pi$
$757$	24.3019	0.883268	0.441634	+	0.897195i	$0.354399\pi$
$758$	27.3815	0.994542
$759$	13.3169	0.483374
$760$	−10.4687	−0.379739
$761$	35.1313	1.27351	0.636755	−	0.771066i	$-0.280276\pi$
$761$	35.1313	1.27351	0.636755	+	0.771066i	$0.280276\pi$
$762$	92.7705	3.36072
$763$	23.3762	0.846275
$764$	−39.5022	−1.42914
$765$	−19.2414	−0.695674
$766$	54.5054	1.96936
$767$	−8.04276	−0.290407
$768$	−16.7936	−0.605985
$769$	26.7996	0.966420	0.483210	−	0.875505i	$-0.339471\pi$
$769$	26.7996	0.966420	0.483210	+	0.875505i	$0.339471\pi$
$770$	−19.0695	−0.687217
$771$	68.4609	2.46556
$772$	−39.2963	−1.41430
$773$	−2.58420	−0.0929473	−0.0464736	−	0.998920i	$-0.514798\pi$
$773$	−2.58420	−0.0929473	−0.0464736	+	0.998920i	$0.514798\pi$
$774$	−30.9604	−1.11285
$775$	−12.9611	−0.465575
$776$	−15.2186	−0.546317
$777$	−92.6740	−3.32466
$778$	−53.6481	−1.92338
$779$	0.419418	0.0150272
$780$	23.8242	0.853044
$781$	19.4453	0.695807
$782$	−20.0620	−0.717417
$783$	27.3403	0.977064
$784$	27.2814	0.974337
$785$	1.07770	0.0384648
$786$	74.3451	2.65180
$787$	−3.20231	−0.114150	−0.0570750	−	0.998370i	$-0.518177\pi$
$787$	−3.20231	−0.114150	−0.0570750	+	0.998370i	$0.518177\pi$
$788$	−30.8814	−1.10011
$789$	−17.5400	−0.624439
$790$	0.966978	0.0344035
$791$	42.0763	1.49606
$792$	134.744	4.78792
$793$	−33.8552	−1.20223
$794$	26.6515	0.945828
$795$	−4.80492	−0.170413
$796$	−52.0168	−1.84369
$797$	−7.79036	−0.275949	−0.137974	−	0.990436i	$-0.544059\pi$
$797$	−7.79036	−0.275949	−0.137974	+	0.990436i	$0.544059\pi$
$798$	44.0872	1.56067
$799$	−18.2353	−0.645120
$800$	58.7902	2.07855
$801$	16.6495	0.588283
$802$	−36.3574	−1.28383
$803$	13.5109	0.476789
$804$	185.743	6.55065
$805$	2.99260	0.105475
$806$	−18.3169	−0.645187
$807$	−72.4935	−2.55189
$808$	−56.8744	−2.00083
$809$	−4.01161	−0.141041	−0.0705204	−	0.997510i	$-0.522466\pi$
$809$	−4.01161	−0.141041	−0.0705204	+	0.997510i	$0.522466\pi$
$810$	−2.83714	−0.0996868
$811$	−12.0912	−0.424578	−0.212289	−	0.977207i	$-0.568092\pi$
$811$	−12.0912	−0.424578	−0.212289	+	0.977207i	$0.568092\pi$
$812$	−71.2314	−2.49973
$813$	−56.8530	−1.99392
$814$	93.9823	3.29408
$815$	−1.99859	−0.0700075
$816$	−168.636	−5.90345
$817$	4.39230	0.153667
$818$	−9.41970	−0.329352
$819$	−37.7757	−1.31999
$820$	0.765096	0.0267183
$821$	−39.9823	−1.39539	−0.697696	−	0.716393i	$-0.745792\pi$
$821$	−39.9823	−1.39539	−0.697696	+	0.716393i	$0.745792\pi$
$822$	29.0980	1.01491
$823$	0.922454	0.0321547	0.0160774	−	0.999871i	$-0.494882\pi$
$823$	0.922454	0.0321547	0.0160774	+	0.999871i	$0.494882\pi$
$824$	−87.4939	−3.04799
$825$	43.1267	1.50148
$826$	−27.1499	−0.944667
$827$	30.4331	1.05826	0.529130	−	0.848541i	$-0.322518\pi$
$827$	30.4331	1.05826	0.529130	+	0.848541i	$0.322518\pi$
$828$	−35.3012	−1.22680
$829$	33.2102	1.15344	0.576719	−	0.816943i	$-0.304333\pi$
$829$	33.2102	1.15344	0.576719	+	0.816943i	$0.304333\pi$
$830$	18.9301	0.657074
$831$	−4.80456	−0.166668
$832$	30.4563	1.05588
$833$	−13.6234	−0.472022
$834$	16.5395	0.572715
$835$	−3.78174	−0.130873
$836$	−31.9128	−1.10373
$837$	16.9399	0.585530
$838$	25.6551	0.886241
$839$	17.9771	0.620638	0.310319	−	0.950632i	$-0.399564\pi$
$839$	17.9771	0.620638	0.310319	+	0.950632i	$0.399564\pi$
$840$	48.1740	1.66216
$841$	−7.53577	−0.259854
$842$	−0.190648	−0.00657017
$843$	−48.3284	−1.66452
$844$	−39.6925	−1.36627
$845$	−4.99450	−0.171816
$846$	−44.9536	−1.54554
$847$	−0.912018	−0.0313373
$848$	−26.4693	−0.908958
$849$	−59.6573	−2.04743
$850$	−64.9706	−2.22847
$851$	−14.7488	−0.505581
$852$	−82.0082	−2.80956
$853$	56.5864	1.93748	0.968742	−	0.248072i	$-0.0797971\pi$
$853$	56.5864	1.93748	0.968742	+	0.248072i	$0.0797971\pi$
$854$	−114.285	−3.91075
$855$	6.72934	0.230139
$856$	54.1636	1.85127
$857$	35.2983	1.20577	0.602884	−	0.797829i	$-0.294018\pi$
$857$	35.2983	1.20577	0.602884	+	0.797829i	$0.294018\pi$
$858$	60.9479	2.08073
$859$	37.8022	1.28980	0.644898	−	0.764269i	$-0.276900\pi$
$859$	37.8022	1.28980	0.644898	+	0.764269i	$0.276900\pi$
$860$	8.01238	0.273220
$861$	−1.93005	−0.0657758
$862$	39.8294	1.35660
$863$	21.4074	0.728716	0.364358	−	0.931259i	$-0.381288\pi$
$863$	21.4074	0.728716	0.364358	+	0.931259i	$0.381288\pi$
$864$	−76.8381	−2.61408
$865$	−2.54172	−0.0864211
$866$	77.1510	2.62170
$867$	35.8983	1.21917
$868$	−44.1346	−1.49803
$869$	1.76571	0.0598976
$870$	−24.2341	−0.821611
$871$	31.6325	1.07183
$872$	59.8873	2.02804
$873$	9.78265	0.331093
$874$	7.01635	0.237331
$875$	20.4236	0.690445
$876$	−56.9805	−1.92519
$877$	−52.4738	−1.77192	−0.885958	−	0.463766i	$-0.846498\pi$
$877$	−52.4738	−1.77192	−0.885958	+	0.463766i	$0.846498\pi$
$878$	82.6983	2.79093
$879$	16.1317	0.544108
$880$	−25.5102	−0.859948
$881$	33.9490	1.14377	0.571886	−	0.820333i	$-0.306212\pi$
$881$	33.9490	1.14377	0.571886	+	0.820333i	$0.306212\pi$
$882$	−33.5842	−1.13084
$883$	13.2873	0.447154	0.223577	−	0.974686i	$-0.428227\pi$
$883$	13.2873	0.447154	0.223577	+	0.974686i	$0.428227\pi$
$884$	−65.5379	−2.20428
$885$	−6.59305	−0.221623
$886$	58.1089	1.95221
$887$	−2.92617	−0.0982511	−0.0491256	−	0.998793i	$-0.515643\pi$
$887$	−2.92617	−0.0982511	−0.0491256	+	0.998793i	$0.515643\pi$
$888$	−237.421	−7.96733
$889$	38.0678	1.27675
$890$	−6.03662	−0.202348
$891$	−5.18064	−0.173558
$892$	−28.9771	−0.970224
$893$	6.37748	0.213414
$894$	−10.3157	−0.345008
$895$	8.27911	0.276740
$896$	22.5357	0.752865
$897$	−9.56464	−0.319354
$898$	13.5293	0.451480
$899$	13.2991	0.443551
$900$	−114.322	−3.81074
$901$	13.2178	0.440349
$902$	1.95729	0.0651707
$903$	−20.2122	−0.672619
$904$	107.795	3.58521
$905$	−0.613140	−0.0203815
$906$	−124.880	−4.14887
$907$	36.5644	1.21410	0.607051	−	0.794663i	$-0.292352\pi$
$907$	36.5644	1.21410	0.607051	+	0.794663i	$0.292352\pi$
$908$	−4.38518	−0.145527
$909$	36.5593	1.21259
$910$	13.6963	0.454028
$911$	−21.9242	−0.726380	−0.363190	−	0.931715i	$-0.618312\pi$
$911$	−21.9242	−0.726380	−0.363190	+	0.931715i	$0.618312\pi$
$912$	58.9776	1.95294
$913$	34.5666	1.14399
$914$	−19.2837	−0.637847
$915$	−27.7528	−0.917480
$916$	−79.6274	−2.63096
$917$	30.5070	1.00743
$918$	84.9157	2.80264
$919$	−32.5496	−1.07371	−0.536856	−	0.843674i	$-0.680388\pi$
$919$	−32.5496	−1.07371	−0.536856	+	0.843674i	$0.680388\pi$
$920$	7.66674	0.252765
$921$	−5.94379	−0.195855
$922$	67.4216	2.22041
$923$	−13.9662	−0.459703
$924$	146.854	4.83114
$925$	−47.7636	−1.57046
$926$	−98.8518	−3.24847
$927$	56.2417	1.84722
$928$	−60.3237	−1.98022
$929$	55.9196	1.83466	0.917331	−	0.398125i	$-0.130339\pi$
$929$	55.9196	1.83466	0.917331	+	0.398125i	$0.130339\pi$
$930$	−15.0153	−0.492371
$931$	4.76454	0.156151
$932$	−56.6858	−1.85681
$933$	−53.2313	−1.74272
$934$	−27.4933	−0.899608
$935$	12.7389	0.416606
$936$	−96.7772	−3.16326
$937$	−50.4904	−1.64945	−0.824725	−	0.565534i	$-0.808670\pi$
$937$	−50.4904	−1.64945	−0.824725	+	0.565534i	$0.808670\pi$
$938$	106.782	3.48654
$939$	34.8013	1.13570
$940$	11.6337	0.379450
$941$	−36.9055	−1.20308	−0.601542	−	0.798841i	$-0.705447\pi$
$941$	−36.9055	−1.20308	−0.601542	+	0.798841i	$0.705447\pi$
$942$	−11.6274	−0.378840
$943$	−0.307161	−0.0100025
$944$	−36.3197	−1.18211
$945$	−12.6667	−0.412047
$946$	20.4975	0.666432
$947$	14.5908	0.474137	0.237068	−	0.971493i	$-0.423813\pi$
$947$	14.5908	0.474137	0.237068	+	0.971493i	$0.423813\pi$
$948$	−7.44667	−0.241857
$949$	−9.70393	−0.315003
$950$	22.7223	0.737209
$951$	−17.6195	−0.571353
$952$	−132.521	−4.29504
$953$	−32.1632	−1.04187	−0.520934	−	0.853597i	$-0.674416\pi$
$953$	−32.1632	−1.04187	−0.520934	+	0.853597i	$0.674416\pi$
$954$	32.5844	1.05496
$955$	−5.51472	−0.178452
$956$	−90.6484	−2.93178
$957$	−44.2516	−1.43045
$958$	−33.6795	−1.08813
$959$	11.9402	0.385568
$960$	24.9666	0.805793
$961$	−22.7599	−0.734191
$962$	−67.5010	−2.17632
$963$	−34.8168	−1.12195
$964$	−13.8380	−0.445692
$965$	−5.48597	−0.176600
$966$	−32.2873	−1.03883
$967$	−19.7216	−0.634204	−0.317102	−	0.948391i	$-0.602710\pi$
$967$	−19.7216	−0.634204	−0.317102	+	0.948391i	$0.602710\pi$
$968$	−2.33649	−0.0750977
$969$	−29.4513	−0.946112
$970$	−3.54689	−0.113884
$971$	30.4178	0.976152	0.488076	−	0.872801i	$-0.337699\pi$
$971$	30.4178	0.976152	0.488076	+	0.872801i	$0.337699\pi$
$972$	−66.4507	−2.13141
$973$	6.78686	0.217577
$974$	−79.9899	−2.56304
$975$	−30.9749	−0.991991
$976$	−152.884	−4.89371
$977$	−54.1222	−1.73152	−0.865761	−	0.500457i	$-0.833165\pi$
$977$	−54.1222	−1.73152	−0.865761	+	0.500457i	$0.833165\pi$
$978$	21.5628	0.689504
$979$	−11.0229	−0.352294
$980$	8.69141	0.277637
$981$	−38.4960	−1.22908
$982$	−32.9258	−1.05070
$983$	−7.93700	−0.253151	−0.126575	−	0.991957i	$-0.540399\pi$
$983$	−7.93700	−0.253151	−0.126575	+	0.991957i	$0.540399\pi$
$984$	−4.94457	−0.157627
$985$	−4.31122	−0.137367
$986$	66.6653	2.12306
$987$	−29.3474	−0.934140
$988$	22.9207	0.729205
$989$	−3.21671	−0.102285
$990$	31.4037	0.998077
$991$	−56.0145	−1.77936	−0.889680	−	0.456585i	$-0.849073\pi$
$991$	−56.0145	−1.77936	−0.889680	+	0.456585i	$0.849073\pi$
$992$	−37.3763	−1.18670
$993$	−41.7694	−1.32551
$994$	−47.1457	−1.49537
$995$	−7.26182	−0.230215
$996$	−145.780	−4.61923
$997$	−33.3936	−1.05759	−0.528794	−	0.848750i	$-0.677355\pi$
$997$	−33.3936	−1.05759	−0.528794	+	0.848750i	$0.677355\pi$
$998$	95.0697	3.00938
$999$	62.4265	1.97509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.a.1.14	✓	309

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.a.1.14	✓	309	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)

\(f(q)\)	\(=\)	\(q-2.64340 q^{2} +2.84192 q^{3} +4.98759 q^{4} +0.696294 q^{5} -7.51235 q^{6} -3.08264 q^{7} -7.89741 q^{8} +5.07651 q^{9} +O(q^{10})\)	\(q-2.64340 q^{2} +2.84192 q^{3} +4.98759 q^{4} +0.696294 q^{5} -7.51235 q^{6} -3.08264 q^{7} -7.89741 q^{8} +5.07651 q^{9} -1.84059 q^{10} -3.36093 q^{11} +14.1743 q^{12} +2.41392 q^{13} +8.14867 q^{14} +1.97881 q^{15} +10.9009 q^{16} -5.44350 q^{17} -13.4193 q^{18} +1.90377 q^{19} +3.47283 q^{20} -8.76063 q^{21} +8.88430 q^{22} -1.39423 q^{23} -22.4438 q^{24} -4.51517 q^{25} -6.38098 q^{26} +5.90128 q^{27} -15.3750 q^{28} +4.63295 q^{29} -5.23080 q^{30} +2.87055 q^{31} -13.0206 q^{32} -9.55150 q^{33} +14.3894 q^{34} -2.14643 q^{35} +25.3195 q^{36} +10.5785 q^{37} -5.03243 q^{38} +6.86018 q^{39} -5.49892 q^{40} +0.220309 q^{41} +23.1579 q^{42} +2.30716 q^{43} -16.7629 q^{44} +3.53475 q^{45} +3.68550 q^{46} +3.34993 q^{47} +30.9794 q^{48} +2.50269 q^{49} +11.9354 q^{50} -15.4700 q^{51} +12.0397 q^{52} -2.42818 q^{53} -15.5995 q^{54} -2.34020 q^{55} +24.3449 q^{56} +5.41036 q^{57} -12.2468 q^{58} -3.33182 q^{59} +9.86951 q^{60} -14.0250 q^{61} -7.58804 q^{62} -15.6491 q^{63} +12.6169 q^{64} +1.68080 q^{65} +25.2485 q^{66} +13.1042 q^{67} -27.1500 q^{68} -3.96228 q^{69} +5.67388 q^{70} -5.78569 q^{71} -40.0913 q^{72} -4.01998 q^{73} -27.9632 q^{74} -12.8318 q^{75} +9.49521 q^{76} +10.3605 q^{77} -18.1342 q^{78} -0.525363 q^{79} +7.59021 q^{80} +1.54143 q^{81} -0.582366 q^{82} -10.2848 q^{83} -43.6944 q^{84} -3.79028 q^{85} -6.09876 q^{86} +13.1665 q^{87} +26.5426 q^{88} +3.27972 q^{89} -9.34377 q^{90} -7.44126 q^{91} -6.95382 q^{92} +8.15789 q^{93} -8.85521 q^{94} +1.32558 q^{95} -37.0035 q^{96} +1.92704 q^{97} -6.61561 q^{98} -17.0618 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * q^99

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