LMFDB - Embedded newform 8043.2.a.u.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$53$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.03619 q^{2} +1.00000 q^{3} +2.14608 q^{4} -0.995010 q^{5} -2.03619 q^{6} +1.00000 q^{7} -0.297449 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.03619 q^{2} +1.00000 q^{3} +2.14608 q^{4} -0.995010 q^{5} -2.03619 q^{6} +1.00000 q^{7} -0.297449 q^{8} +1.00000 q^{9} +2.02603 q^{10} +2.78629 q^{11} +2.14608 q^{12} -0.157376 q^{13} -2.03619 q^{14} -0.995010 q^{15} -3.68650 q^{16} -0.326958 q^{17} -2.03619 q^{18} +6.84798 q^{19} -2.13537 q^{20} +1.00000 q^{21} -5.67343 q^{22} +1.44776 q^{23} -0.297449 q^{24} -4.00995 q^{25} +0.320448 q^{26} +1.00000 q^{27} +2.14608 q^{28} -9.46932 q^{29} +2.02603 q^{30} -3.21266 q^{31} +8.10132 q^{32} +2.78629 q^{33} +0.665749 q^{34} -0.995010 q^{35} +2.14608 q^{36} -3.04633 q^{37} -13.9438 q^{38} -0.157376 q^{39} +0.295965 q^{40} +4.30718 q^{41} -2.03619 q^{42} -2.77766 q^{43} +5.97961 q^{44} -0.995010 q^{45} -2.94792 q^{46} +6.20824 q^{47} -3.68650 q^{48} +1.00000 q^{49} +8.16504 q^{50} -0.326958 q^{51} -0.337742 q^{52} +9.98353 q^{53} -2.03619 q^{54} -2.77239 q^{55} -0.297449 q^{56} +6.84798 q^{57} +19.2814 q^{58} +5.72936 q^{59} -2.13537 q^{60} +5.23993 q^{61} +6.54160 q^{62} +1.00000 q^{63} -9.12285 q^{64} +0.156591 q^{65} -5.67343 q^{66} -15.1152 q^{67} -0.701678 q^{68} +1.44776 q^{69} +2.02603 q^{70} +15.6778 q^{71} -0.297449 q^{72} +6.32909 q^{73} +6.20292 q^{74} -4.00995 q^{75} +14.6963 q^{76} +2.78629 q^{77} +0.320448 q^{78} -7.99402 q^{79} +3.66810 q^{80} +1.00000 q^{81} -8.77026 q^{82} -1.53152 q^{83} +2.14608 q^{84} +0.325326 q^{85} +5.65585 q^{86} -9.46932 q^{87} -0.828780 q^{88} +1.99136 q^{89} +2.02603 q^{90} -0.157376 q^{91} +3.10701 q^{92} -3.21266 q^{93} -12.6412 q^{94} -6.81381 q^{95} +8.10132 q^{96} +2.76785 q^{97} -2.03619 q^{98} +2.78629 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9}+O(q^{10}) $ 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9} + 2 q^{10} + 46 q^{11} + 63 q^{12} + 32 q^{13} + 11 q^{14} + 24 q^{15} + 67 q^{16} + 46 q^{17} + 11 q^{18} + 14 q^{19} + 53 q^{20} + 53 q^{21} + 13 q^{22} + 68 q^{23} + 30 q^{24} + 71 q^{25} + 11 q^{26} + 53 q^{27} + 63 q^{28} + 55 q^{29} + 2 q^{30} - 2 q^{31} + 51 q^{32} + 46 q^{33} - 7 q^{34} + 24 q^{35} + 63 q^{36} + 53 q^{37} + 16 q^{38} + 32 q^{39} - 20 q^{40} + 38 q^{41} + 11 q^{42} + 36 q^{43} + 70 q^{44} + 24 q^{45} + 4 q^{46} + 51 q^{47} + 67 q^{48} + 53 q^{49} + 32 q^{50} + 46 q^{51} + 10 q^{52} + 104 q^{53} + 11 q^{54} + 11 q^{55} + 30 q^{56} + 14 q^{57} + 4 q^{58} + 36 q^{59} + 53 q^{60} + 3 q^{61} + 25 q^{62} + 53 q^{63} + 82 q^{64} + 46 q^{65} + 13 q^{66} + 54 q^{67} + 88 q^{68} + 68 q^{69} + 2 q^{70} + 101 q^{71} + 30 q^{72} + q^{73} + 32 q^{74} + 71 q^{75} - 35 q^{76} + 46 q^{77} + 11 q^{78} + 14 q^{79} + 39 q^{80} + 53 q^{81} - 29 q^{82} + 38 q^{83} + 63 q^{84} + 16 q^{85} + 23 q^{86} + 55 q^{87} - 8 q^{88} + 52 q^{89} + 2 q^{90} + 32 q^{91} + 76 q^{92} - 2 q^{93} - 53 q^{94} + 46 q^{95} + 51 q^{96} - 3 q^{97} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9 + 2 * q^10 + 46 * q^11 + 63 * q^12 + 32 * q^13 + 11 * q^14 + 24 * q^15 + 67 * q^16 + 46 * q^17 + 11 * q^18 + 14 * q^19 + 53 * q^20 + 53 * q^21 + 13 * q^22 + 68 * q^23 + 30 * q^24 + 71 * q^25 + 11 * q^26 + 53 * q^27 + 63 * q^28 + 55 * q^29 + 2 * q^30 - 2 * q^31 + 51 * q^32 + 46 * q^33 - 7 * q^34 + 24 * q^35 + 63 * q^36 + 53 * q^37 + 16 * q^38 + 32 * q^39 - 20 * q^40 + 38 * q^41 + 11 * q^42 + 36 * q^43 + 70 * q^44 + 24 * q^45 + 4 * q^46 + 51 * q^47 + 67 * q^48 + 53 * q^49 + 32 * q^50 + 46 * q^51 + 10 * q^52 + 104 * q^53 + 11 * q^54 + 11 * q^55 + 30 * q^56 + 14 * q^57 + 4 * q^58 + 36 * q^59 + 53 * q^60 + 3 * q^61 + 25 * q^62 + 53 * q^63 + 82 * q^64 + 46 * q^65 + 13 * q^66 + 54 * q^67 + 88 * q^68 + 68 * q^69 + 2 * q^70 + 101 * q^71 + 30 * q^72 + q^73 + 32 * q^74 + 71 * q^75 - 35 * q^76 + 46 * q^77 + 11 * q^78 + 14 * q^79 + 39 * q^80 + 53 * q^81 - 29 * q^82 + 38 * q^83 + 63 * q^84 + 16 * q^85 + 23 * q^86 + 55 * q^87 - 8 * q^88 + 52 * q^89 + 2 * q^90 + 32 * q^91 + 76 * q^92 - 2 * q^93 - 53 * q^94 + 46 * q^95 + 51 * q^96 - 3 * q^97 + 11 * q^98 + 46 * 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 $

$2$	−2.03619	−1.43981	−0.719903	−	0.694075i	$-0.755814\pi$
$2$	−2.03619	−1.43981	−0.719903	+	0.694075i	$0.755814\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.14608	1.07304
$5$	−0.995010	−0.444982	−0.222491	−	0.974935i	$-0.571419\pi$
$5$	−0.995010	−0.444982	−0.222491	+	0.974935i	$0.571419\pi$
$6$	−2.03619	−0.831272
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.297449	−0.105164
$9$	1.00000	0.333333
$10$	2.02603	0.640688
$11$	2.78629	0.840099	0.420050	−	0.907501i	$-0.362013\pi$
$11$	2.78629	0.840099	0.420050	+	0.907501i	$0.362013\pi$
$12$	2.14608	0.619520
$13$	−0.157376	−0.0436483	−0.0218242	−	0.999762i	$-0.506947\pi$
$13$	−0.157376	−0.0436483	−0.0218242	+	0.999762i	$0.506947\pi$
$14$	−2.03619	−0.544195
$15$	−0.995010	−0.256911
$16$	−3.68650	−0.921625
$17$	−0.326958	−0.0792989	−0.0396495	−	0.999214i	$-0.512624\pi$
$17$	−0.326958	−0.0792989	−0.0396495	+	0.999214i	$0.512624\pi$
$18$	−2.03619	−0.479935
$19$	6.84798	1.57103	0.785517	−	0.618840i	$-0.212397\pi$
$19$	6.84798	1.57103	0.785517	+	0.618840i	$0.212397\pi$
$20$	−2.13537	−0.477484
$21$	1.00000	0.218218
$22$	−5.67343	−1.20958
$23$	1.44776	0.301879	0.150939	−	0.988543i	$-0.451770\pi$
$23$	1.44776	0.301879	0.150939	+	0.988543i	$0.451770\pi$
$24$	−0.297449	−0.0607165
$25$	−4.00995	−0.801991
$26$	0.320448	0.0628451
$27$	1.00000	0.192450
$28$	2.14608	0.405571
$29$	−9.46932	−1.75841	−0.879205	−	0.476445i	$-0.841925\pi$
$29$	−9.46932	−1.75841	−0.879205	+	0.476445i	$0.841925\pi$
$30$	2.02603	0.369901
$31$	−3.21266	−0.577011	−0.288506	−	0.957478i	$-0.593158\pi$
$31$	−3.21266	−0.577011	−0.288506	+	0.957478i	$0.593158\pi$
$32$	8.10132	1.43212
$33$	2.78629	0.485031
$34$	0.665749	0.114175
$35$	−0.995010	−0.168187
$36$	2.14608	0.357680
$37$	−3.04633	−0.500814	−0.250407	−	0.968141i	$-0.580564\pi$
$37$	−3.04633	−0.500814	−0.250407	+	0.968141i	$0.580564\pi$
$38$	−13.9438	−2.26198
$39$	−0.157376	−0.0252004
$40$	0.295965	0.0467962
$41$	4.30718	0.672669	0.336335	−	0.941743i	$-0.390813\pi$
$41$	4.30718	0.672669	0.336335	+	0.941743i	$0.390813\pi$
$42$	−2.03619	−0.314191
$43$	−2.77766	−0.423589	−0.211795	−	0.977314i	$-0.567931\pi$
$43$	−2.77766	−0.423589	−0.211795	+	0.977314i	$0.567931\pi$
$44$	5.97961	0.901460
$45$	−0.995010	−0.148327
$46$	−2.94792	−0.434647
$47$	6.20824	0.905564	0.452782	−	0.891621i	$-0.350432\pi$
$47$	6.20824	0.905564	0.452782	+	0.891621i	$0.350432\pi$
$48$	−3.68650	−0.532100
$49$	1.00000	0.142857
$50$	8.16504	1.15471
$51$	−0.326958	−0.0457833
$52$	−0.337742	−0.0468364
$53$	9.98353	1.37134	0.685672	−	0.727911i	$-0.259508\pi$
$53$	9.98353	1.37134	0.685672	+	0.727911i	$0.259508\pi$
$54$	−2.03619	−0.277091
$55$	−2.77239	−0.373829
$56$	−0.297449	−0.0397483
$57$	6.84798	0.907037
$58$	19.2814	2.53177
$59$	5.72936	0.745900	0.372950	−	0.927852i	$-0.378346\pi$
$59$	5.72936	0.745900	0.372950	+	0.927852i	$0.378346\pi$
$60$	−2.13537	−0.275675
$61$	5.23993	0.670904	0.335452	−	0.942057i	$-0.391111\pi$
$61$	5.23993	0.670904	0.335452	+	0.942057i	$0.391111\pi$
$62$	6.54160	0.830784
$63$	1.00000	0.125988
$64$	−9.12285	−1.14036
$65$	0.156591	0.0194227
$66$	−5.67343	−0.698351
$67$	−15.1152	−1.84662	−0.923310	−	0.384055i	$-0.874527\pi$
$67$	−15.1152	−1.84662	−0.923310	+	0.384055i	$0.874527\pi$
$68$	−0.701678	−0.0850910
$69$	1.44776	0.174290
$70$	2.02603	0.242157
$71$	15.6778	1.86061	0.930305	−	0.366787i	$-0.119542\pi$
$71$	15.6778	1.86061	0.930305	+	0.366787i	$0.119542\pi$
$72$	−0.297449	−0.0350547
$73$	6.32909	0.740764	0.370382	−	0.928880i	$-0.379227\pi$
$73$	6.32909	0.740764	0.370382	+	0.928880i	$0.379227\pi$
$74$	6.20292	0.721075
$75$	−4.00995	−0.463030
$76$	14.6963	1.68578
$77$	2.78629	0.317528
$78$	0.320448	0.0362836
$79$	−7.99402	−0.899398	−0.449699	−	0.893180i	$-0.648469\pi$
$79$	−7.99402	−0.899398	−0.449699	+	0.893180i	$0.648469\pi$
$80$	3.66810	0.410106
$81$	1.00000	0.111111
$82$	−8.77026	−0.968513
$83$	−1.53152	−0.168106	−0.0840530	−	0.996461i	$-0.526787\pi$
$83$	−1.53152	−0.168106	−0.0840530	+	0.996461i	$0.526787\pi$
$84$	2.14608	0.234157
$85$	0.325326	0.0352866
$86$	5.65585	0.609886
$87$	−9.46932	−1.01522
$88$	−0.828780	−0.0883483
$89$	1.99136	0.211084	0.105542	−	0.994415i	$-0.466342\pi$
$89$	1.99136	0.211084	0.105542	+	0.994415i	$0.466342\pi$
$90$	2.02603	0.213563
$91$	−0.157376	−0.0164975
$92$	3.10701	0.323928
$93$	−3.21266	−0.333138
$94$	−12.6412	−1.30384
$95$	−6.81381	−0.699082
$96$	8.10132	0.826837
$97$	2.76785	0.281032	0.140516	−	0.990078i	$-0.455124\pi$
$97$	2.76785	0.281032	0.140516	+	0.990078i	$0.455124\pi$
$98$	−2.03619	−0.205687
$99$	2.78629	0.280033
$100$	−8.60569	−0.860569
$101$	−1.38783	−0.138094	−0.0690472	−	0.997613i	$-0.521996\pi$
$101$	−1.38783	−0.138094	−0.0690472	+	0.997613i	$0.521996\pi$
$102$	0.665749	0.0659190
$103$	16.6206	1.63768	0.818839	−	0.574024i	$-0.194618\pi$
$103$	16.6206	1.63768	0.818839	+	0.574024i	$0.194618\pi$
$104$	0.0468114	0.00459024
$105$	−0.995010	−0.0971031
$106$	−20.3284	−1.97447
$107$	14.7973	1.43051	0.715257	−	0.698862i	$-0.246310\pi$
$107$	14.7973	1.43051	0.715257	+	0.698862i	$0.246310\pi$
$108$	2.14608	0.206507
$109$	16.4041	1.57123	0.785615	−	0.618716i	$-0.212347\pi$
$109$	16.4041	1.57123	0.785615	+	0.618716i	$0.212347\pi$
$110$	5.64512	0.538241
$111$	−3.04633	−0.289145
$112$	−3.68650	−0.348341
$113$	−4.14399	−0.389834	−0.194917	−	0.980820i	$-0.562444\pi$
$113$	−4.14399	−0.389834	−0.194917	+	0.980820i	$0.562444\pi$
$114$	−13.9438	−1.30596
$115$	−1.44054	−0.134331
$116$	−20.3219	−1.88684
$117$	−0.157376	−0.0145494
$118$	−11.6661	−1.07395
$119$	−0.326958	−0.0299722
$120$	0.295965	0.0270178
$121$	−3.23657	−0.294234
$122$	−10.6695	−0.965971
$123$	4.30718	0.388366
$124$	−6.89463	−0.619156
$125$	8.96500	0.801854
$126$	−2.03619	−0.181398
$127$	−7.95312	−0.705725	−0.352863	−	0.935675i	$-0.614792\pi$
$127$	−7.95312	−0.705725	−0.352863	+	0.935675i	$0.614792\pi$
$128$	2.37325	0.209767
$129$	−2.77766	−0.244559
$130$	−0.318849	−0.0279649
$131$	−13.7576	−1.20201	−0.601005	−	0.799245i	$-0.705233\pi$
$131$	−13.7576	−1.20201	−0.601005	+	0.799245i	$0.705233\pi$
$132$	5.97961	0.520458
$133$	6.84798	0.593795
$134$	30.7775	2.65877
$135$	−0.995010	−0.0856368
$136$	0.0972533	0.00833940
$137$	3.15882	0.269876	0.134938	−	0.990854i	$-0.456916\pi$
$137$	3.15882	0.269876	0.134938	+	0.990854i	$0.456916\pi$
$138$	−2.94792	−0.250943
$139$	14.3130	1.21401	0.607005	−	0.794698i	$-0.292371\pi$
$139$	14.3130	1.21401	0.607005	+	0.794698i	$0.292371\pi$
$140$	−2.13537	−0.180472
$141$	6.20824	0.522828
$142$	−31.9230	−2.67892
$143$	−0.438496	−0.0366689
$144$	−3.68650	−0.307208
$145$	9.42207	0.782461
$146$	−12.8872	−1.06656
$147$	1.00000	0.0824786
$148$	−6.53768	−0.537394
$149$	−7.10228	−0.581841	−0.290921	−	0.956747i	$-0.593962\pi$
$149$	−7.10228	−0.581841	−0.290921	+	0.956747i	$0.593962\pi$
$150$	8.16504	0.666673
$151$	−10.8816	−0.885530	−0.442765	−	0.896638i	$-0.646002\pi$
$151$	−10.8816	−0.885530	−0.442765	+	0.896638i	$0.646002\pi$
$152$	−2.03692	−0.165216
$153$	−0.326958	−0.0264330
$154$	−5.67343	−0.457178
$155$	3.19663	0.256760
$156$	−0.337742	−0.0270410
$157$	−17.2965	−1.38041	−0.690205	−	0.723614i	$-0.742480\pi$
$157$	−17.2965	−1.38041	−0.690205	+	0.723614i	$0.742480\pi$
$158$	16.2774	1.29496
$159$	9.98353	0.791746
$160$	−8.06090	−0.637270
$161$	1.44776	0.114099
$162$	−2.03619	−0.159978
$163$	11.7763	0.922390	0.461195	−	0.887299i	$-0.347421\pi$
$163$	11.7763	0.922390	0.461195	+	0.887299i	$0.347421\pi$
$164$	9.24357	0.721801
$165$	−2.77239	−0.215830
$166$	3.11847	0.242040
$167$	10.9214	0.845122	0.422561	−	0.906335i	$-0.361131\pi$
$167$	10.9214	0.845122	0.422561	+	0.906335i	$0.361131\pi$
$168$	−0.297449	−0.0229487
$169$	−12.9752	−0.998095
$170$	−0.662427	−0.0508058
$171$	6.84798	0.523678
$172$	−5.96109	−0.454529
$173$	−6.87123	−0.522410	−0.261205	−	0.965283i	$-0.584120\pi$
$173$	−6.87123	−0.522410	−0.261205	+	0.965283i	$0.584120\pi$
$174$	19.2814	1.46172
$175$	−4.00995	−0.303124
$176$	−10.2717	−0.774256
$177$	5.72936	0.430645
$178$	−4.05479	−0.303920
$179$	−20.1196	−1.50381	−0.751904	−	0.659272i	$-0.770864\pi$
$179$	−20.1196	−1.50381	−0.751904	+	0.659272i	$0.770864\pi$
$180$	−2.13537	−0.159161
$181$	7.19915	0.535109	0.267554	−	0.963543i	$-0.413785\pi$
$181$	7.19915	0.535109	0.267554	+	0.963543i	$0.413785\pi$
$182$	0.320448	0.0237532
$183$	5.23993	0.387347
$184$	−0.430635	−0.0317468
$185$	3.03113	0.222853
$186$	6.54160	0.479653
$187$	−0.911000	−0.0666189
$188$	13.3234	0.971707
$189$	1.00000	0.0727393
$190$	13.8742	1.00654
$191$	16.4111	1.18747	0.593734	−	0.804661i	$-0.297653\pi$
$191$	16.4111	1.18747	0.593734	+	0.804661i	$0.297653\pi$
$192$	−9.12285	−0.658385
$193$	0.121891	0.00877392	0.00438696	−	0.999990i	$-0.498604\pi$
$193$	0.121891	0.00877392	0.00438696	+	0.999990i	$0.498604\pi$
$194$	−5.63587	−0.404632
$195$	0.156591	0.0112137
$196$	2.14608	0.153292
$197$	−0.347314	−0.0247451	−0.0123725	−	0.999923i	$-0.503938\pi$
$197$	−0.347314	−0.0247451	−0.0123725	+	0.999923i	$0.503938\pi$
$198$	−5.67343	−0.403193
$199$	−11.9012	−0.843654	−0.421827	−	0.906676i	$-0.638611\pi$
$199$	−11.9012	−0.843654	−0.421827	+	0.906676i	$0.638611\pi$
$200$	1.19276	0.0843407
$201$	−15.1152	−1.06615
$202$	2.82589	0.198829
$203$	−9.46932	−0.664616
$204$	−0.701678	−0.0491273
$205$	−4.28569	−0.299326
$206$	−33.8428	−2.35794
$207$	1.44776	0.100626
$208$	0.580167	0.0402274
$209$	19.0805	1.31982
$210$	2.02603	0.139810
$211$	12.3195	0.848108	0.424054	−	0.905637i	$-0.360607\pi$
$211$	12.3195	0.848108	0.424054	+	0.905637i	$0.360607\pi$
$212$	21.4255	1.47151
$213$	15.6778	1.07422
$214$	−30.1303	−2.05966
$215$	2.76380	0.188490
$216$	−0.297449	−0.0202388
$217$	−3.21266	−0.218090
$218$	−33.4020	−2.26227
$219$	6.32909	0.427680
$220$	−5.94977	−0.401134
$221$	0.0514554	0.00346127
$222$	6.20292	0.416313
$223$	13.0718	0.875355	0.437677	−	0.899132i	$-0.355801\pi$
$223$	13.0718	0.875355	0.437677	+	0.899132i	$0.355801\pi$
$224$	8.10132	0.541292
$225$	−4.00995	−0.267330
$226$	8.43797	0.561285
$227$	21.0322	1.39596	0.697979	−	0.716119i	$-0.254083\pi$
$227$	21.0322	1.39596	0.697979	+	0.716119i	$0.254083\pi$
$228$	14.6963	0.973287
$229$	−14.8998	−0.984607	−0.492303	−	0.870424i	$-0.663845\pi$
$229$	−14.8998	−0.984607	−0.492303	+	0.870424i	$0.663845\pi$
$230$	2.93321	0.193410
$231$	2.78629	0.183325
$232$	2.81664	0.184922
$233$	−28.5367	−1.86950	−0.934751	−	0.355305i	$-0.884377\pi$
$233$	−28.5367	−1.86950	−0.934751	+	0.355305i	$0.884377\pi$
$234$	0.320448	0.0209484
$235$	−6.17726	−0.402960
$236$	12.2957	0.800380
$237$	−7.99402	−0.519268
$238$	0.665749	0.0431541
$239$	9.74386	0.630278	0.315139	−	0.949046i	$-0.397949\pi$
$239$	9.74386	0.630278	0.315139	+	0.949046i	$0.397949\pi$
$240$	3.66810	0.236775
$241$	10.0869	0.649752	0.324876	−	0.945757i	$-0.394677\pi$
$241$	10.0869	0.649752	0.324876	+	0.945757i	$0.394677\pi$
$242$	6.59028	0.423639
$243$	1.00000	0.0641500
$244$	11.2453	0.719907
$245$	−0.995010	−0.0635689
$246$	−8.77026	−0.559171
$247$	−1.07771	−0.0685730
$248$	0.955603	0.0606809
$249$	−1.53152	−0.0970560
$250$	−18.2545	−1.15451
$251$	29.7060	1.87502	0.937512	−	0.347954i	$-0.113123\pi$
$251$	29.7060	1.87502	0.937512	+	0.347954i	$0.113123\pi$
$252$	2.14608	0.135190
$253$	4.03388	0.253608
$254$	16.1941	1.01611
$255$	0.325326	0.0203727
$256$	13.4133	0.838332
$257$	−21.5338	−1.34324	−0.671621	−	0.740895i	$-0.734402\pi$
$257$	−21.5338	−1.34324	−0.671621	+	0.740895i	$0.734402\pi$
$258$	5.65585	0.352118
$259$	−3.04633	−0.189290
$260$	0.336057	0.0208414
$261$	−9.46932	−0.586136
$262$	28.0132	1.73066
$263$	4.95257	0.305389	0.152694	−	0.988273i	$-0.451205\pi$
$263$	4.95257	0.305389	0.152694	+	0.988273i	$0.451205\pi$
$264$	−0.828780	−0.0510079
$265$	−9.93372	−0.610223
$266$	−13.9438	−0.854949
$267$	1.99136	0.121869
$268$	−32.4385	−1.98150
$269$	−3.56354	−0.217273	−0.108637	−	0.994082i	$-0.534648\pi$
$269$	−3.56354	−0.217273	−0.108637	+	0.994082i	$0.534648\pi$
$270$	2.02603	0.123300
$271$	17.1157	1.03971	0.519853	−	0.854256i	$-0.325987\pi$
$271$	17.1157	1.03971	0.519853	+	0.854256i	$0.325987\pi$
$272$	1.20533	0.0730838
$273$	−0.157376	−0.00952485
$274$	−6.43197	−0.388569
$275$	−11.1729	−0.673752
$276$	3.10701	0.187020
$277$	−1.29888	−0.0780419	−0.0390210	−	0.999238i	$-0.512424\pi$
$277$	−1.29888	−0.0780419	−0.0390210	+	0.999238i	$0.512424\pi$
$278$	−29.1440	−1.74794
$279$	−3.21266	−0.192337
$280$	0.295965	0.0176873
$281$	−12.5232	−0.747070	−0.373535	−	0.927616i	$-0.621854\pi$
$281$	−12.5232	−0.747070	−0.373535	+	0.927616i	$0.621854\pi$
$282$	−12.6412	−0.752770
$283$	−1.27703	−0.0759118	−0.0379559	−	0.999279i	$-0.512085\pi$
$283$	−1.27703	−0.0759118	−0.0379559	+	0.999279i	$0.512085\pi$
$284$	33.6458	1.99651
$285$	−6.81381	−0.403615
$286$	0.892863	0.0527961
$287$	4.30718	0.254245
$288$	8.10132	0.477375
$289$	−16.8931	−0.993712
$290$	−19.1852	−1.12659
$291$	2.76785	0.162254
$292$	13.5827	0.794869
$293$	24.2581	1.41717	0.708585	−	0.705625i	$-0.249334\pi$
$293$	24.2581	1.41717	0.708585	+	0.705625i	$0.249334\pi$
$294$	−2.03619	−0.118753
$295$	−5.70077	−0.331912
$296$	0.906130	0.0526677
$297$	2.78629	0.161677
$298$	14.4616	0.837738
$299$	−0.227843	−0.0131765
$300$	−8.60569	−0.496850
$301$	−2.77766	−0.160102
$302$	22.1570	1.27499
$303$	−1.38783	−0.0797288
$304$	−25.2451	−1.44790
$305$	−5.21378	−0.298540
$306$	0.665749	0.0380583
$307$	−10.5773	−0.603680	−0.301840	−	0.953359i	$-0.597601\pi$
$307$	−10.5773	−0.603680	−0.301840	+	0.953359i	$0.597601\pi$
$308$	5.97961	0.340720
$309$	16.6206	0.945514
$310$	−6.50896	−0.369684
$311$	9.49808	0.538587	0.269293	−	0.963058i	$-0.413210\pi$
$311$	9.49808	0.538587	0.269293	+	0.963058i	$0.413210\pi$
$312$	0.0468114	0.00265018
$313$	−26.2628	−1.48446	−0.742230	−	0.670145i	$-0.766232\pi$
$313$	−26.2628	−1.48446	−0.742230	+	0.670145i	$0.766232\pi$
$314$	35.2190	1.98752
$315$	−0.995010	−0.0560625
$316$	−17.1558	−0.965090
$317$	27.5904	1.54963	0.774815	−	0.632188i	$-0.217843\pi$
$317$	27.5904	1.54963	0.774815	+	0.632188i	$0.217843\pi$
$318$	−20.3284	−1.13996
$319$	−26.3843	−1.47724
$320$	9.07733	0.507438
$321$	14.7973	0.825907
$322$	−2.94792	−0.164281
$323$	−2.23900	−0.124581
$324$	2.14608	0.119227
$325$	0.631072	0.0350056
$326$	−23.9788	−1.32806
$327$	16.4041	0.907150
$328$	−1.28117	−0.0707407
$329$	6.20824	0.342271
$330$	5.64512	0.310754
$331$	−10.9138	−0.599874	−0.299937	−	0.953959i	$-0.596966\pi$
$331$	−10.9138	−0.599874	−0.299937	+	0.953959i	$0.596966\pi$
$332$	−3.28676	−0.180385
$333$	−3.04633	−0.166938
$334$	−22.2380	−1.21681
$335$	15.0398	0.821713
$336$	−3.68650	−0.201115
$337$	9.99084	0.544236	0.272118	−	0.962264i	$-0.412276\pi$
$337$	9.99084	0.544236	0.272118	+	0.962264i	$0.412276\pi$
$338$	26.4201	1.43706
$339$	−4.14399	−0.225071
$340$	0.698177	0.0378639
$341$	−8.95142	−0.484747
$342$	−13.9438	−0.753994
$343$	1.00000	0.0539949
$344$	0.826213	0.0445464
$345$	−1.44054	−0.0775558
$346$	13.9912	0.752169
$347$	19.0456	1.02242	0.511211	−	0.859455i	$-0.329197\pi$
$347$	19.0456	1.02242	0.511211	+	0.859455i	$0.329197\pi$
$348$	−20.3219	−1.08937
$349$	−7.53014	−0.403079	−0.201540	−	0.979480i	$-0.564594\pi$
$349$	−7.53014	−0.403079	−0.201540	+	0.979480i	$0.564594\pi$
$350$	8.16504	0.436440
$351$	−0.157376	−0.00840012
$352$	22.5727	1.20313
$353$	11.2299	0.597710	0.298855	−	0.954299i	$-0.403395\pi$
$353$	11.2299	0.597710	0.298855	+	0.954299i	$0.403395\pi$
$354$	−11.6661	−0.620046
$355$	−15.5995	−0.827938
$356$	4.27362	0.226501
$357$	−0.326958	−0.0173044
$358$	40.9674	2.16519
$359$	29.0348	1.53240	0.766199	−	0.642603i	$-0.222146\pi$
$359$	29.0348	1.53240	0.766199	+	0.642603i	$0.222146\pi$
$360$	0.295965	0.0155987
$361$	27.8948	1.46815
$362$	−14.6589	−0.770453
$363$	−3.23657	−0.169876
$364$	−0.337742	−0.0177025
$365$	−6.29751	−0.329627
$366$	−10.6695	−0.557704
$367$	29.6214	1.54622	0.773112	−	0.634270i	$-0.218699\pi$
$367$	29.6214	1.54622	0.773112	+	0.634270i	$0.218699\pi$
$368$	−5.33716	−0.278219
$369$	4.30718	0.224223
$370$	−6.17197	−0.320866
$371$	9.98353	0.518319
$372$	−6.89463	−0.357470
$373$	−30.3758	−1.57280	−0.786400	−	0.617718i	$-0.788058\pi$
$373$	−30.3758	−1.57280	−0.786400	+	0.617718i	$0.788058\pi$
$374$	1.85497	0.0959183
$375$	8.96500	0.462950
$376$	−1.84663	−0.0952329
$377$	1.49025	0.0767516
$378$	−2.03619	−0.104730
$379$	8.51228	0.437247	0.218623	−	0.975809i	$-0.429843\pi$
$379$	8.51228	0.437247	0.218623	+	0.975809i	$0.429843\pi$
$380$	−14.6230	−0.750143
$381$	−7.95312	−0.407451
$382$	−33.4163	−1.70972
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	2.37325	0.121109
$385$	−2.77239	−0.141294
$386$	−0.248194	−0.0126327
$387$	−2.77766	−0.141196
$388$	5.94002	0.301559
$389$	−26.6502	−1.35122	−0.675609	−	0.737260i	$-0.736119\pi$
$389$	−26.6502	−1.35122	−0.675609	+	0.737260i	$0.736119\pi$
$390$	−0.318849	−0.0161456
$391$	−0.473356	−0.0239387
$392$	−0.297449	−0.0150234
$393$	−13.7576	−0.693981
$394$	0.707198	0.0356281
$395$	7.95413	0.400216
$396$	5.97961	0.300487
$397$	23.6444	1.18668	0.593339	−	0.804953i	$-0.297809\pi$
$397$	23.6444	1.18668	0.593339	+	0.804953i	$0.297809\pi$
$398$	24.2332	1.21470
$399$	6.84798	0.342828
$400$	14.7827	0.739135
$401$	−1.77329	−0.0885538	−0.0442769	−	0.999019i	$-0.514098\pi$
$401$	−1.77329	−0.0885538	−0.0442769	+	0.999019i	$0.514098\pi$
$402$	30.7775	1.53504
$403$	0.505597	0.0251856
$404$	−2.97840	−0.148181
$405$	−0.995010	−0.0494425
$406$	19.2814	0.956918
$407$	−8.48798	−0.420734
$408$	0.0972533	0.00481476
$409$	6.61705	0.327192	0.163596	−	0.986527i	$-0.447691\pi$
$409$	6.61705	0.327192	0.163596	+	0.986527i	$0.447691\pi$
$410$	8.72650	0.430971
$411$	3.15882	0.155813
$412$	35.6692	1.75729
$413$	5.72936	0.281924
$414$	−2.94792	−0.144882
$415$	1.52388	0.0748041
$416$	−1.27496	−0.0625098
$417$	14.3130	0.700909
$418$	−38.8515	−1.90029
$419$	9.53402	0.465767	0.232884	−	0.972505i	$-0.425184\pi$
$419$	9.53402	0.465767	0.232884	+	0.972505i	$0.425184\pi$
$420$	−2.13537	−0.104196
$421$	−37.0739	−1.80687	−0.903435	−	0.428725i	$-0.858963\pi$
$421$	−37.0739	−1.80687	−0.903435	+	0.428725i	$0.858963\pi$
$422$	−25.0848	−1.22111
$423$	6.20824	0.301855
$424$	−2.96959	−0.144216
$425$	1.31109	0.0635970
$426$	−31.9230	−1.54667
$427$	5.23993	0.253578
$428$	31.7563	1.53500
$429$	−0.438496	−0.0211708
$430$	−5.62763	−0.271389
$431$	41.0396	1.97681	0.988404	−	0.151844i	$-0.0485212\pi$
$431$	41.0396	1.97681	0.988404	+	0.151844i	$0.0485212\pi$
$432$	−3.68650	−0.177367
$433$	−19.1087	−0.918303	−0.459152	−	0.888358i	$-0.651847\pi$
$433$	−19.1087	−0.918303	−0.459152	+	0.888358i	$0.651847\pi$
$434$	6.54160	0.314007
$435$	9.42207	0.451754
$436$	35.2046	1.68599
$437$	9.91422	0.474262
$438$	−12.8872	−0.615776
$439$	4.33765	0.207025	0.103512	−	0.994628i	$-0.466992\pi$
$439$	4.33765	0.207025	0.103512	+	0.994628i	$0.466992\pi$
$440$	0.824645	0.0393134
$441$	1.00000	0.0476190
$442$	−0.104773	−0.00498355
$443$	32.0034	1.52053	0.760263	−	0.649615i	$-0.225070\pi$
$443$	32.0034	1.52053	0.760263	+	0.649615i	$0.225070\pi$
$444$	−6.53768	−0.310265
$445$	−1.98142	−0.0939285
$446$	−26.6168	−1.26034
$447$	−7.10228	−0.335926
$448$	−9.12285	−0.431014
$449$	4.56695	0.215528	0.107764	−	0.994177i	$-0.465631\pi$
$449$	4.56695	0.215528	0.107764	+	0.994177i	$0.465631\pi$
$450$	8.16504	0.384904
$451$	12.0011	0.565109
$452$	−8.89335	−0.418308
$453$	−10.8816	−0.511261
$454$	−42.8256	−2.00991
$455$	0.156591	0.00734110
$456$	−2.03692	−0.0953877
$457$	−3.76364	−0.176056	−0.0880278	−	0.996118i	$-0.528056\pi$
$457$	−3.76364	−0.176056	−0.0880278	+	0.996118i	$0.528056\pi$
$458$	30.3389	1.41764
$459$	−0.326958	−0.0152611
$460$	−3.09151	−0.144142
$461$	23.9428	1.11513	0.557563	−	0.830135i	$-0.311736\pi$
$461$	23.9428	1.11513	0.557563	+	0.830135i	$0.311736\pi$
$462$	−5.67343	−0.263952
$463$	34.2772	1.59300	0.796499	−	0.604640i	$-0.206683\pi$
$463$	34.2772	1.59300	0.796499	+	0.604640i	$0.206683\pi$
$464$	34.9086	1.62059
$465$	3.19663	0.148240
$466$	58.1062	2.69172
$467$	20.7147	0.958560	0.479280	−	0.877662i	$-0.340898\pi$
$467$	20.7147	0.958560	0.479280	+	0.877662i	$0.340898\pi$
$468$	−0.337742	−0.0156121
$469$	−15.1152	−0.697957
$470$	12.5781	0.580184
$471$	−17.2965	−0.796980
$472$	−1.70419	−0.0784419
$473$	−7.73938	−0.355857
$474$	16.2774	0.747644
$475$	−27.4601	−1.25995
$476$	−0.701678	−0.0321614
$477$	9.98353	0.457115
$478$	−19.8404	−0.907477
$479$	9.61948	0.439525	0.219763	−	0.975553i	$-0.429472\pi$
$479$	9.61948	0.439525	0.219763	+	0.975553i	$0.429472\pi$
$480$	−8.06090	−0.367928
$481$	0.479421	0.0218597
$482$	−20.5388	−0.935517
$483$	1.44776	0.0658753
$484$	−6.94594	−0.315725
$485$	−2.75403	−0.125054
$486$	−2.03619	−0.0923636
$487$	−2.16739	−0.0982140	−0.0491070	−	0.998794i	$-0.515638\pi$
$487$	−2.16739	−0.0982140	−0.0491070	+	0.998794i	$0.515638\pi$
$488$	−1.55861	−0.0705550
$489$	11.7763	0.532542
$490$	2.02603	0.0915268
$491$	39.5318	1.78404	0.892022	−	0.451992i	$-0.149287\pi$
$491$	39.5318	1.78404	0.892022	+	0.451992i	$0.149287\pi$
$492$	9.24357	0.416732
$493$	3.09607	0.139440
$494$	2.19442	0.0987318
$495$	−2.77239	−0.124610
$496$	11.8435	0.531788
$497$	15.6778	0.703244
$498$	3.11847	0.139742
$499$	−16.8256	−0.753218	−0.376609	−	0.926372i	$-0.622910\pi$
$499$	−16.8256	−0.753218	−0.376609	+	0.926372i	$0.622910\pi$
$500$	19.2396	0.860421
$501$	10.9214	0.487931
$502$	−60.4871	−2.69967
$503$	−18.9164	−0.843442	−0.421721	−	0.906726i	$-0.638574\pi$
$503$	−18.9164	−0.843442	−0.421721	+	0.906726i	$0.638574\pi$
$504$	−0.297449	−0.0132494
$505$	1.38091	0.0614495
$506$	−8.21376	−0.365146
$507$	−12.9752	−0.576250
$508$	−17.0680	−0.757272
$509$	10.6858	0.473640	0.236820	−	0.971554i	$-0.423895\pi$
$509$	10.6858	0.473640	0.236820	+	0.971554i	$0.423895\pi$
$510$	−0.662427	−0.0293328
$511$	6.32909	0.279982
$512$	−32.0586	−1.41680
$513$	6.84798	0.302346
$514$	43.8470	1.93401
$515$	−16.5377	−0.728737
$516$	−5.96109	−0.262422
$517$	17.2980	0.760764
$518$	6.20292	0.272541
$519$	−6.87123	−0.301614
$520$	−0.0465779	−0.00204257
$521$	−30.4780	−1.33527	−0.667633	−	0.744491i	$-0.732692\pi$
$521$	−30.4780	−1.33527	−0.667633	+	0.744491i	$0.732692\pi$
$522$	19.2814	0.843922
$523$	−19.8106	−0.866258	−0.433129	−	0.901332i	$-0.642591\pi$
$523$	−19.8106	−0.866258	−0.433129	+	0.901332i	$0.642591\pi$
$524$	−29.5250	−1.28981
$525$	−4.00995	−0.175009
$526$	−10.0844	−0.439701
$527$	1.05041	0.0457564
$528$	−10.2717	−0.447017
$529$	−20.9040	−0.908869
$530$	20.2270	0.878603
$531$	5.72936	0.248633
$532$	14.6963	0.637166
$533$	−0.677849	−0.0293609
$534$	−4.05479	−0.175468
$535$	−14.7235	−0.636553
$536$	4.49601	0.194198
$537$	−20.1196	−0.868224
$538$	7.25606	0.312831
$539$	2.78629	0.120014
$540$	−2.13537	−0.0918918
$541$	21.7588	0.935482	0.467741	−	0.883866i	$-0.345068\pi$
$541$	21.7588	0.935482	0.467741	+	0.883866i	$0.345068\pi$
$542$	−34.8509	−1.49697
$543$	7.19915	0.308945
$544$	−2.64879	−0.113566
$545$	−16.3223	−0.699169
$546$	0.320448	0.0137139
$547$	14.9901	0.640931	0.320466	−	0.947260i	$-0.396161\pi$
$547$	14.9901	0.640931	0.320466	+	0.947260i	$0.396161\pi$
$548$	6.77909	0.289588
$549$	5.23993	0.223635
$550$	22.7502	0.970072
$551$	−64.8457	−2.76252
$552$	−0.430635	−0.0183290
$553$	−7.99402	−0.339940
$554$	2.64476	0.112365
$555$	3.03113	0.128664
$556$	30.7168	1.30268
$557$	27.1064	1.14854	0.574268	−	0.818667i	$-0.305287\pi$
$557$	27.1064	1.14854	0.574268	+	0.818667i	$0.305287\pi$
$558$	6.54160	0.276928
$559$	0.437138	0.0184890
$560$	3.66810	0.155006
$561$	−0.911000	−0.0384625
$562$	25.4996	1.07563
$563$	−19.1348	−0.806435	−0.403218	−	0.915104i	$-0.632108\pi$
$563$	−19.1348	−0.806435	−0.403218	+	0.915104i	$0.632108\pi$
$564$	13.3234	0.561015
$565$	4.12332	0.173469
$566$	2.60029	0.109298
$567$	1.00000	0.0419961
$568$	−4.66334	−0.195669
$569$	−22.4324	−0.940416	−0.470208	−	0.882556i	$-0.655821\pi$
$569$	−22.4324	−0.940416	−0.470208	+	0.882556i	$0.655821\pi$
$570$	13.8742	0.581127
$571$	−30.3529	−1.27023	−0.635116	−	0.772417i	$-0.719048\pi$
$571$	−30.3529	−1.27023	−0.635116	+	0.772417i	$0.719048\pi$
$572$	−0.941049	−0.0393472
$573$	16.4111	0.685585
$574$	−8.77026	−0.366063
$575$	−5.80545	−0.242104
$576$	−9.12285	−0.380119
$577$	−32.3357	−1.34615	−0.673075	−	0.739574i	$-0.735027\pi$
$577$	−32.3357	−1.34615	−0.673075	+	0.739574i	$0.735027\pi$
$578$	34.3976	1.43075
$579$	0.121891	0.00506562
$580$	20.2205	0.839612
$581$	−1.53152	−0.0635381
$582$	−5.63587	−0.233614
$583$	27.8171	1.15206
$584$	−1.88258	−0.0779018
$585$	0.156591	0.00647424
$586$	−49.3941	−2.04045
$587$	19.2450	0.794325	0.397162	−	0.917748i	$-0.369995\pi$
$587$	19.2450	0.794325	0.397162	+	0.917748i	$0.369995\pi$
$588$	2.14608	0.0885029
$589$	−22.0002	−0.906504
$590$	11.6079	0.477889
$591$	−0.347314	−0.0142866
$592$	11.2303	0.461563
$593$	−31.2041	−1.28140	−0.640699	−	0.767792i	$-0.721355\pi$
$593$	−31.2041	−1.28140	−0.640699	+	0.767792i	$0.721355\pi$
$594$	−5.67343	−0.232784
$595$	0.325326	0.0133371
$596$	−15.2421	−0.624339
$597$	−11.9012	−0.487084
$598$	0.463932	0.0189716
$599$	20.6657	0.844377	0.422189	−	0.906508i	$-0.361262\pi$
$599$	20.6657	0.844377	0.422189	+	0.906508i	$0.361262\pi$
$600$	1.19276	0.0486941
$601$	9.83060	0.400998	0.200499	−	0.979694i	$-0.435744\pi$
$601$	9.83060	0.400998	0.200499	+	0.979694i	$0.435744\pi$
$602$	5.65585	0.230515
$603$	−15.1152	−0.615540
$604$	−23.3527	−0.950210
$605$	3.22042	0.130929
$606$	2.82589	0.114794
$607$	−26.3204	−1.06831	−0.534156	−	0.845386i	$-0.679370\pi$
$607$	−26.3204	−1.06831	−0.534156	+	0.845386i	$0.679370\pi$
$608$	55.4776	2.24992
$609$	−9.46932	−0.383716
$610$	10.6163	0.429840
$611$	−0.977029	−0.0395264
$612$	−0.701678	−0.0283637
$613$	23.9903	0.968959	0.484479	−	0.874803i	$-0.339009\pi$
$613$	23.9903	0.968959	0.484479	+	0.874803i	$0.339009\pi$
$614$	21.5375	0.869182
$615$	−4.28569	−0.172816
$616$	−0.828780	−0.0333925
$617$	11.4379	0.460473	0.230237	−	0.973135i	$-0.426050\pi$
$617$	11.4379	0.460473	0.230237	+	0.973135i	$0.426050\pi$
$618$	−33.8428	−1.36136
$619$	−40.9315	−1.64518	−0.822588	−	0.568638i	$-0.807471\pi$
$619$	−40.9315	−1.64518	−0.822588	+	0.568638i	$0.807471\pi$
$620$	6.86023	0.275513
$621$	1.44776	0.0580966
$622$	−19.3399	−0.775460
$623$	1.99136	0.0797822
$624$	0.580167	0.0232253
$625$	11.1295	0.445180
$626$	53.4761	2.13734
$627$	19.0805	0.762001
$628$	−37.1197	−1.48124
$629$	0.996023	0.0397140
$630$	2.02603	0.0807191
$631$	3.71368	0.147839	0.0739197	−	0.997264i	$-0.476449\pi$
$631$	3.71368	0.147839	0.0739197	+	0.997264i	$0.476449\pi$
$632$	2.37781	0.0945844
$633$	12.3195	0.489655
$634$	−56.1793	−2.23117
$635$	7.91344	0.314035
$636$	21.4255	0.849575
$637$	−0.157376	−0.00623548
$638$	53.7235	2.12694
$639$	15.6778	0.620203
$640$	−2.36140	−0.0933427
$641$	0.348285	0.0137564	0.00687822	−	0.999976i	$-0.497811\pi$
$641$	0.348285	0.0137564	0.00687822	+	0.999976i	$0.497811\pi$
$642$	−30.1303	−1.18915
$643$	47.0483	1.85541	0.927703	−	0.373320i	$-0.121781\pi$
$643$	47.0483	1.85541	0.927703	+	0.373320i	$0.121781\pi$
$644$	3.10701	0.122433
$645$	2.76380	0.108825
$646$	4.55903	0.179373
$647$	−41.9661	−1.64986	−0.824930	−	0.565235i	$-0.808785\pi$
$647$	−41.9661	−1.64986	−0.824930	+	0.565235i	$0.808785\pi$
$648$	−0.297449	−0.0116849
$649$	15.9637	0.626629
$650$	−1.28498	−0.0504012
$651$	−3.21266	−0.125914
$652$	25.2729	0.989762
$653$	−30.3310	−1.18694	−0.593472	−	0.804854i	$-0.702243\pi$
$653$	−30.3310	−1.18694	−0.593472	+	0.804854i	$0.702243\pi$
$654$	−33.4020	−1.30612
$655$	13.6890	0.534873
$656$	−15.8784	−0.619948
$657$	6.32909	0.246921
$658$	−12.6412	−0.492804
$659$	−27.2792	−1.06265	−0.531323	−	0.847169i	$-0.678305\pi$
$659$	−27.2792	−1.06265	−0.531323	+	0.847169i	$0.678305\pi$
$660$	−5.94977	−0.231595
$661$	−44.6687	−1.73741	−0.868705	−	0.495330i	$-0.835047\pi$
$661$	−44.6687	−1.73741	−0.868705	+	0.495330i	$0.835047\pi$
$662$	22.2225	0.863702
$663$	0.0514554	0.00199836
$664$	0.455549	0.0176787
$665$	−6.81381	−0.264228
$666$	6.20292	0.240358
$667$	−13.7093	−0.530826
$668$	23.4382	0.906850
$669$	13.0718	0.505386
$670$	−30.6240	−1.18311
$671$	14.6000	0.563626
$672$	8.10132	0.312515
$673$	10.5504	0.406687	0.203344	−	0.979107i	$-0.434819\pi$
$673$	10.5504	0.406687	0.203344	+	0.979107i	$0.434819\pi$
$674$	−20.3433	−0.783594
$675$	−4.00995	−0.154343
$676$	−27.8459	−1.07100
$677$	−18.8057	−0.722762	−0.361381	−	0.932418i	$-0.617695\pi$
$677$	−18.8057	−0.722762	−0.361381	+	0.932418i	$0.617695\pi$
$678$	8.43797	0.324058
$679$	2.76785	0.106220
$680$	−0.0967680	−0.00371088
$681$	21.0322	0.805956
$682$	18.2268	0.697941
$683$	−8.73641	−0.334290	−0.167145	−	0.985932i	$-0.553455\pi$
$683$	−8.73641	−0.334290	−0.167145	+	0.985932i	$0.553455\pi$
$684$	14.6963	0.561928
$685$	−3.14306	−0.120090
$686$	−2.03619	−0.0777422
$687$	−14.8998	−0.568463
$688$	10.2398	0.390390
$689$	−1.57117	−0.0598569
$690$	2.93321	0.111665
$691$	7.21348	0.274414	0.137207	−	0.990542i	$-0.456187\pi$
$691$	7.21348	0.274414	0.137207	+	0.990542i	$0.456187\pi$
$692$	−14.7462	−0.560567
$693$	2.78629	0.105843
$694$	−38.7805	−1.47209
$695$	−14.2415	−0.540213
$696$	2.81664	0.106765
$697$	−1.40827	−0.0533419
$698$	15.3328	0.580355
$699$	−28.5367	−1.07936
$700$	−8.60569	−0.325264
$701$	35.5691	1.34343	0.671714	−	0.740811i	$-0.265559\pi$
$701$	35.5691	1.34343	0.671714	+	0.740811i	$0.265559\pi$
$702$	0.320448	0.0120945
$703$	−20.8612	−0.786796
$704$	−25.4189	−0.958012
$705$	−6.17726	−0.232649
$706$	−22.8663	−0.860586
$707$	−1.38783	−0.0521947
$708$	12.2957	0.462100
$709$	30.4979	1.14537	0.572686	−	0.819775i	$-0.305902\pi$
$709$	30.4979	1.14537	0.572686	+	0.819775i	$0.305902\pi$
$710$	31.7637	1.19207
$711$	−7.99402	−0.299799
$712$	−0.592328	−0.0221984
$713$	−4.65116	−0.174187
$714$	0.665749	0.0249150
$715$	0.436308	0.0163170
$716$	−43.1783	−1.61365
$717$	9.74386	0.363891
$718$	−59.1205	−2.20636
$719$	21.0011	0.783208	0.391604	−	0.920134i	$-0.371920\pi$
$719$	21.0011	0.783208	0.391604	+	0.920134i	$0.371920\pi$
$720$	3.66810	0.136702
$721$	16.6206	0.618984
$722$	−56.7992	−2.11385
$723$	10.0869	0.375135
$724$	15.4500	0.574193
$725$	37.9716	1.41023
$726$	6.59028	0.244588
$727$	42.4387	1.57397	0.786983	−	0.616975i	$-0.211642\pi$
$727$	42.4387	1.57397	0.786983	+	0.616975i	$0.211642\pi$
$728$	0.0468114	0.00173495
$729$	1.00000	0.0370370
$730$	12.8229	0.474598
$731$	0.908178	0.0335902
$732$	11.2453	0.415639
$733$	26.9416	0.995111	0.497555	−	0.867432i	$-0.334231\pi$
$733$	26.9416	0.995111	0.497555	+	0.867432i	$0.334231\pi$
$734$	−60.3149	−2.22626
$735$	−0.995010	−0.0367015
$736$	11.7288	0.432328
$737$	−42.1155	−1.55134
$738$	−8.77026	−0.322838
$739$	37.9893	1.39746	0.698730	−	0.715385i	$-0.253749\pi$
$739$	37.9893	1.39746	0.698730	+	0.715385i	$0.253749\pi$
$740$	6.50506	0.239131
$741$	−1.07771	−0.0395906
$742$	−20.3284	−0.746279
$743$	47.6984	1.74989	0.874943	−	0.484226i	$-0.160899\pi$
$743$	47.6984	1.74989	0.874943	+	0.484226i	$0.160899\pi$
$744$	0.955603	0.0350341
$745$	7.06684	0.258909
$746$	61.8510	2.26453
$747$	−1.53152	−0.0560353
$748$	−1.95508	−0.0714848
$749$	14.7973	0.540683
$750$	−18.2545	−0.666559
$751$	−12.0848	−0.440980	−0.220490	−	0.975389i	$-0.570766\pi$
$751$	−12.0848	−0.440980	−0.220490	+	0.975389i	$0.570766\pi$
$752$	−22.8867	−0.834590
$753$	29.7060	1.08255
$754$	−3.03443	−0.110507
$755$	10.8273	0.394045
$756$	2.14608	0.0780522
$757$	−44.4803	−1.61666	−0.808332	−	0.588727i	$-0.799629\pi$
$757$	−44.4803	−1.61666	−0.808332	+	0.588727i	$0.799629\pi$
$758$	−17.3327	−0.629550
$759$	4.03388	0.146421
$760$	2.02676	0.0735183
$761$	−8.54431	−0.309731	−0.154865	−	0.987936i	$-0.549494\pi$
$761$	−8.54431	−0.309731	−0.154865	+	0.987936i	$0.549494\pi$
$762$	16.1941	0.586650
$763$	16.4041	0.593869
$764$	35.2196	1.27420
$765$	0.325326	0.0117622
$766$	−2.03619	−0.0735706
$767$	−0.901666	−0.0325573
$768$	13.4133	0.484011
$769$	28.9725	1.04478	0.522388	−	0.852708i	$-0.325041\pi$
$769$	28.9725	1.04478	0.522388	+	0.852708i	$0.325041\pi$
$770$	5.64512	0.203436
$771$	−21.5338	−0.775521
$772$	0.261588	0.00941477
$773$	−27.8396	−1.00132	−0.500661	−	0.865643i	$-0.666910\pi$
$773$	−27.8396	−1.00132	−0.500661	+	0.865643i	$0.666910\pi$
$774$	5.65585	0.203295
$775$	12.8826	0.462758
$776$	−0.823293	−0.0295545
$777$	−3.04633	−0.109287
$778$	54.2649	1.94549
$779$	29.4955	1.05679
$780$	0.336057	0.0120328
$781$	43.6829	1.56310
$782$	0.963845	0.0344670
$783$	−9.46932	−0.338406
$784$	−3.68650	−0.131661
$785$	17.2102	0.614258
$786$	28.0132	0.999198
$787$	35.5201	1.26616	0.633078	−	0.774088i	$-0.281791\pi$
$787$	35.5201	1.26616	0.633078	+	0.774088i	$0.281791\pi$
$788$	−0.745364	−0.0265525
$789$	4.95257	0.176316
$790$	−16.1961	−0.576233
$791$	−4.14399	−0.147343
$792$	−0.828780	−0.0294494
$793$	−0.824640	−0.0292838
$794$	−48.1445	−1.70859
$795$	−9.93372	−0.352313
$796$	−25.5410	−0.905275
$797$	47.1268	1.66932	0.834659	−	0.550767i	$-0.185665\pi$
$797$	47.1268	1.66932	0.834659	+	0.550767i	$0.185665\pi$
$798$	−13.9438	−0.493605
$799$	−2.02983	−0.0718103
$800$	−32.4859	−1.14855
$801$	1.99136	0.0703613
$802$	3.61076	0.127500
$803$	17.6347	0.622315
$804$	−32.4385	−1.14402
$805$	−1.44054	−0.0507722
$806$	−1.02949	−0.0362623
$807$	−3.56354	−0.125443
$808$	0.412809	0.0145226
$809$	−37.5469	−1.32008	−0.660040	−	0.751231i	$-0.729461\pi$
$809$	−37.5469	−1.32008	−0.660040	+	0.751231i	$0.729461\pi$
$810$	2.02603	0.0711875
$811$	11.1886	0.392884	0.196442	−	0.980515i	$-0.437061\pi$
$811$	11.1886	0.392884	0.196442	+	0.980515i	$0.437061\pi$
$812$	−20.3219	−0.713160
$813$	17.1157	0.600274
$814$	17.2832	0.605775
$815$	−11.7175	−0.410447
$816$	1.20533	0.0421950
$817$	−19.0214	−0.665473
$818$	−13.4736	−0.471093
$819$	−0.157376	−0.00549917
$820$	−9.19744	−0.321189
$821$	28.2821	0.987053	0.493526	−	0.869731i	$-0.335708\pi$
$821$	28.2821	0.987053	0.493526	+	0.869731i	$0.335708\pi$
$822$	−6.43197	−0.224341
$823$	21.9371	0.764680	0.382340	−	0.924022i	$-0.375118\pi$
$823$	21.9371	0.764680	0.382340	+	0.924022i	$0.375118\pi$
$824$	−4.94379	−0.172225
$825$	−11.1729	−0.388991
$826$	−11.6661	−0.405915
$827$	18.3897	0.639471	0.319736	−	0.947507i	$-0.396406\pi$
$827$	18.3897	0.639471	0.319736	+	0.947507i	$0.396406\pi$
$828$	3.10701	0.107976
$829$	−40.4971	−1.40652	−0.703261	−	0.710932i	$-0.748273\pi$
$829$	−40.4971	−1.40652	−0.703261	+	0.710932i	$0.748273\pi$
$830$	−3.10291	−0.107703
$831$	−1.29888	−0.0450575
$832$	1.43572	0.0497747
$833$	−0.326958	−0.0113284
$834$	−29.1440	−1.00917
$835$	−10.8669	−0.376064
$836$	40.9482	1.41622
$837$	−3.21266	−0.111046
$838$	−19.4131	−0.670615
$839$	8.79734	0.303718	0.151859	−	0.988402i	$-0.451474\pi$
$839$	8.79734	0.303718	0.151859	+	0.988402i	$0.451474\pi$
$840$	0.295965	0.0102118
$841$	60.6681	2.09200
$842$	75.4896	2.60154
$843$	−12.5232	−0.431321
$844$	26.4386	0.910054
$845$	12.9105	0.444134
$846$	−12.6412	−0.434612
$847$	−3.23657	−0.111210
$848$	−36.8043	−1.26386
$849$	−1.27703	−0.0438277
$850$	−2.66962	−0.0915673
$851$	−4.41036	−0.151185
$852$	33.6458	1.15269
$853$	25.2425	0.864287	0.432143	−	0.901805i	$-0.357757\pi$
$853$	25.2425	0.864287	0.432143	+	0.901805i	$0.357757\pi$
$854$	−10.6695	−0.365103
$855$	−6.81381	−0.233027
$856$	−4.40146	−0.150439
$857$	−2.22263	−0.0759236	−0.0379618	−	0.999279i	$-0.512087\pi$
$857$	−2.22263	−0.0759236	−0.0379618	+	0.999279i	$0.512087\pi$
$858$	0.892863	0.0304819
$859$	36.4219	1.24270	0.621350	−	0.783533i	$-0.286584\pi$
$859$	36.4219	1.24270	0.621350	+	0.783533i	$0.286584\pi$
$860$	5.93134	0.202257
$861$	4.30718	0.146788
$862$	−83.5646	−2.84622
$863$	3.60718	0.122790	0.0613949	−	0.998114i	$-0.480445\pi$
$863$	3.60718	0.122790	0.0613949	+	0.998114i	$0.480445\pi$
$864$	8.10132	0.275612
$865$	6.83694	0.232463
$866$	38.9089	1.32218
$867$	−16.8931	−0.573720
$868$	−6.89463	−0.234019
$869$	−22.2737	−0.755583
$870$	−19.1852	−0.650438
$871$	2.37878	0.0806019
$872$	−4.87939	−0.165237
$873$	2.76785	0.0936774
$874$	−20.1873	−0.682845
$875$	8.96500	0.303072
$876$	13.5827	0.458918
$877$	55.9741	1.89011	0.945055	−	0.326912i	$-0.106008\pi$
$877$	55.9741	1.89011	0.945055	+	0.326912i	$0.106008\pi$
$878$	−8.83229	−0.298075
$879$	24.2581	0.818204
$880$	10.2204	0.344530
$881$	−8.05031	−0.271222	−0.135611	−	0.990762i	$-0.543300\pi$
$881$	−8.05031	−0.271222	−0.135611	+	0.990762i	$0.543300\pi$
$882$	−2.03619	−0.0685622
$883$	−14.8216	−0.498788	−0.249394	−	0.968402i	$-0.580231\pi$
$883$	−14.8216	−0.498788	−0.249394	+	0.968402i	$0.580231\pi$
$884$	0.110427	0.00371408
$885$	−5.70077	−0.191629
$886$	−65.1651	−2.18926
$887$	−54.6214	−1.83401	−0.917004	−	0.398878i	$-0.869400\pi$
$887$	−54.6214	−1.83401	−0.917004	+	0.398878i	$0.869400\pi$
$888$	0.906130	0.0304077
$889$	−7.95312	−0.266739
$890$	4.03456	0.135239
$891$	2.78629	0.0933443
$892$	28.0532	0.939291
$893$	42.5139	1.42267
$894$	14.4616	0.483668
$895$	20.0192	0.669168
$896$	2.37325	0.0792846
$897$	−0.227843	−0.00760746
$898$	−9.29919	−0.310318
$899$	30.4217	1.01462
$900$	−8.60569	−0.286856
$901$	−3.26419	−0.108746
$902$	−24.4365	−0.813647
$903$	−2.77766	−0.0924348
$904$	1.23263	0.0409966
$905$	−7.16323	−0.238114
$906$	22.1570	0.736116
$907$	37.6767	1.25103	0.625516	−	0.780211i	$-0.284888\pi$
$907$	37.6767	1.25103	0.625516	+	0.780211i	$0.284888\pi$
$908$	45.1368	1.49792
$909$	−1.38783	−0.0460314
$910$	−0.318849	−0.0105698
$911$	22.3376	0.740079	0.370039	−	0.929016i	$-0.379344\pi$
$911$	22.3376	0.740079	0.370039	+	0.929016i	$0.379344\pi$
$912$	−25.2451	−0.835947
$913$	−4.26726	−0.141226
$914$	7.66349	0.253486
$915$	−5.21378	−0.172362
$916$	−31.9762	−1.05652
$917$	−13.7576	−0.454317
$918$	0.665749	0.0219730
$919$	13.2659	0.437600	0.218800	−	0.975770i	$-0.429786\pi$
$919$	13.2659	0.437600	0.218800	+	0.975770i	$0.429786\pi$
$920$	0.428486	0.0141268
$921$	−10.5773	−0.348535
$922$	−48.7521	−1.60556
$923$	−2.46731	−0.0812125
$924$	5.97961	0.196715
$925$	12.2157	0.401649
$926$	−69.7951	−2.29361
$927$	16.6206	0.545893
$928$	−76.7140	−2.51826
$929$	−26.8870	−0.882133	−0.441067	−	0.897474i	$-0.645400\pi$
$929$	−26.8870	−0.882133	−0.441067	+	0.897474i	$0.645400\pi$
$930$	−6.50896	−0.213437
$931$	6.84798	0.224433
$932$	−61.2421	−2.00605
$933$	9.49808	0.310953
$934$	−42.1790	−1.38014
$935$	0.906455	0.0296442
$936$	0.0468114	0.00153008
$937$	−3.58230	−0.117029	−0.0585144	−	0.998287i	$-0.518636\pi$
$937$	−3.58230	−0.117029	−0.0585144	+	0.998287i	$0.518636\pi$
$938$	30.7775	1.00492
$939$	−26.2628	−0.857054
$940$	−13.2569	−0.432392
$941$	−26.9381	−0.878157	−0.439079	−	0.898449i	$-0.644695\pi$
$941$	−26.9381	−0.878157	−0.439079	+	0.898449i	$0.644695\pi$
$942$	35.2190	1.14750
$943$	6.23577	0.203065
$944$	−21.1213	−0.687439
$945$	−0.995010	−0.0323677
$946$	15.7589	0.512365
$947$	−32.6349	−1.06049	−0.530246	−	0.847844i	$-0.677900\pi$
$947$	−32.6349	−1.06049	−0.530246	+	0.847844i	$0.677900\pi$
$948$	−17.1558	−0.557195
$949$	−0.996048	−0.0323331
$950$	55.9140	1.81409
$951$	27.5904	0.894679
$952$	0.0972533	0.00315200
$953$	14.8581	0.481301	0.240650	−	0.970612i	$-0.422639\pi$
$953$	14.8581	0.481301	0.240650	+	0.970612i	$0.422639\pi$
$954$	−20.3284	−0.658156
$955$	−16.3293	−0.528402
$956$	20.9111	0.676313
$957$	−26.3843	−0.852884
$958$	−19.5871	−0.632831
$959$	3.15882	0.102004
$960$	9.07733	0.292970
$961$	−20.6788	−0.667058
$962$	−0.976193	−0.0314737
$963$	14.7973	0.476838
$964$	21.6472	0.697210
$965$	−0.121283	−0.00390424
$966$	−2.94792	−0.0948477
$967$	−38.9138	−1.25138	−0.625691	−	0.780071i	$-0.715183\pi$
$967$	−38.9138	−1.25138	−0.625691	+	0.780071i	$0.715183\pi$
$968$	0.962715	0.0309428
$969$	−2.23900	−0.0719270
$970$	5.60774	0.180054
$971$	−43.4936	−1.39578	−0.697888	−	0.716206i	$-0.745877\pi$
$971$	−43.4936	−1.39578	−0.697888	+	0.716206i	$0.745877\pi$
$972$	2.14608	0.0688356
$973$	14.3130	0.458852
$974$	4.41323	0.141409
$975$	0.631072	0.0202105
$976$	−19.3170	−0.618322
$977$	51.8011	1.65727	0.828633	−	0.559793i	$-0.189119\pi$
$977$	51.8011	1.65727	0.828633	+	0.559793i	$0.189119\pi$
$978$	−23.9788	−0.766758
$979$	5.54851	0.177331
$980$	−2.13537	−0.0682120
$981$	16.4041	0.523743
$982$	−80.4943	−2.56868
$983$	17.0771	0.544675	0.272337	−	0.962202i	$-0.412203\pi$
$983$	17.0771	0.544675	0.272337	+	0.962202i	$0.412203\pi$
$984$	−1.28117	−0.0408421
$985$	0.345581	0.0110111
$986$	−6.30419	−0.200766
$987$	6.20824	0.197610
$988$	−2.31285	−0.0735816
$989$	−4.02139	−0.127873
$990$	5.64512	0.179414
$991$	43.0242	1.36671	0.683354	−	0.730087i	$-0.260521\pi$
$991$	43.0242	1.36671	0.683354	+	0.730087i	$0.260521\pi$
$992$	−26.0268	−0.826352
$993$	−10.9138	−0.346337
$994$	−31.9230	−1.01254
$995$	11.8418	0.375411
$996$	−3.28676	−0.104145
$997$	−25.9418	−0.821586	−0.410793	−	0.911729i	$-0.634748\pi$
$997$	−25.9418	−0.821586	−0.410793	+	0.911729i	$0.634748\pi$
$998$	34.2602	1.08449
$999$	−3.04633	−0.0963818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.u.1.9	✓	53

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.u.1.9	✓	53	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.03619 q^{2} +1.00000 q^{3} +2.14608 q^{4} -0.995010 q^{5} -2.03619 q^{6} +1.00000 q^{7} -0.297449 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.03619 q^{2} +1.00000 q^{3} +2.14608 q^{4} -0.995010 q^{5} -2.03619 q^{6} +1.00000 q^{7} -0.297449 q^{8} +1.00000 q^{9} +2.02603 q^{10} +2.78629 q^{11} +2.14608 q^{12} -0.157376 q^{13} -2.03619 q^{14} -0.995010 q^{15} -3.68650 q^{16} -0.326958 q^{17} -2.03619 q^{18} +6.84798 q^{19} -2.13537 q^{20} +1.00000 q^{21} -5.67343 q^{22} +1.44776 q^{23} -0.297449 q^{24} -4.00995 q^{25} +0.320448 q^{26} +1.00000 q^{27} +2.14608 q^{28} -9.46932 q^{29} +2.02603 q^{30} -3.21266 q^{31} +8.10132 q^{32} +2.78629 q^{33} +0.665749 q^{34} -0.995010 q^{35} +2.14608 q^{36} -3.04633 q^{37} -13.9438 q^{38} -0.157376 q^{39} +0.295965 q^{40} +4.30718 q^{41} -2.03619 q^{42} -2.77766 q^{43} +5.97961 q^{44} -0.995010 q^{45} -2.94792 q^{46} +6.20824 q^{47} -3.68650 q^{48} +1.00000 q^{49} +8.16504 q^{50} -0.326958 q^{51} -0.337742 q^{52} +9.98353 q^{53} -2.03619 q^{54} -2.77239 q^{55} -0.297449 q^{56} +6.84798 q^{57} +19.2814 q^{58} +5.72936 q^{59} -2.13537 q^{60} +5.23993 q^{61} +6.54160 q^{62} +1.00000 q^{63} -9.12285 q^{64} +0.156591 q^{65} -5.67343 q^{66} -15.1152 q^{67} -0.701678 q^{68} +1.44776 q^{69} +2.02603 q^{70} +15.6778 q^{71} -0.297449 q^{72} +6.32909 q^{73} +6.20292 q^{74} -4.00995 q^{75} +14.6963 q^{76} +2.78629 q^{77} +0.320448 q^{78} -7.99402 q^{79} +3.66810 q^{80} +1.00000 q^{81} -8.77026 q^{82} -1.53152 q^{83} +2.14608 q^{84} +0.325326 q^{85} +5.65585 q^{86} -9.46932 q^{87} -0.828780 q^{88} +1.99136 q^{89} +2.02603 q^{90} -0.157376 q^{91} +3.10701 q^{92} -3.21266 q^{93} -12.6412 q^{94} -6.81381 q^{95} +8.10132 q^{96} +2.76785 q^{97} -2.03619 q^{98} +2.78629 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9}+O(q^{10}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9} + 2 q^{10} + 46 q^{11} + 63 q^{12} + 32 q^{13} + 11 q^{14} + 24 q^{15} + 67 q^{16} + 46 q^{17} + 11 q^{18} + 14 q^{19} + 53 q^{20} + 53 q^{21} + 13 q^{22} + 68 q^{23} + 30 q^{24} + 71 q^{25} + 11 q^{26} + 53 q^{27} + 63 q^{28} + 55 q^{29} + 2 q^{30} - 2 q^{31} + 51 q^{32} + 46 q^{33} - 7 q^{34} + 24 q^{35} + 63 q^{36} + 53 q^{37} + 16 q^{38} + 32 q^{39} - 20 q^{40} + 38 q^{41} + 11 q^{42} + 36 q^{43} + 70 q^{44} + 24 q^{45} + 4 q^{46} + 51 q^{47} + 67 q^{48} + 53 q^{49} + 32 q^{50} + 46 q^{51} + 10 q^{52} + 104 q^{53} + 11 q^{54} + 11 q^{55} + 30 q^{56} + 14 q^{57} + 4 q^{58} + 36 q^{59} + 53 q^{60} + 3 q^{61} + 25 q^{62} + 53 q^{63} + 82 q^{64} + 46 q^{65} + 13 q^{66} + 54 q^{67} + 88 q^{68} + 68 q^{69} + 2 q^{70} + 101 q^{71} + 30 q^{72} + q^{73} + 32 q^{74} + 71 q^{75} - 35 q^{76} + 46 q^{77} + 11 q^{78} + 14 q^{79} + 39 q^{80} + 53 q^{81} - 29 q^{82} + 38 q^{83} + 63 q^{84} + 16 q^{85} + 23 q^{86} + 55 q^{87} - 8 q^{88} + 52 q^{89} + 2 q^{90} + 32 q^{91} + 76 q^{92} - 2 q^{93} - 53 q^{94} + 46 q^{95} + 51 q^{96} - 3 q^{97} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9 + 2 * q^10 + 46 * q^11 + 63 * q^12 + 32 * q^13 + 11 * q^14 + 24 * q^15 + 67 * q^16 + 46 * q^17 + 11 * q^18 + 14 * q^19 + 53 * q^20 + 53 * q^21 + 13 * q^22 + 68 * q^23 + 30 * q^24 + 71 * q^25 + 11 * q^26 + 53 * q^27 + 63 * q^28 + 55 * q^29 + 2 * q^30 - 2 * q^31 + 51 * q^32 + 46 * q^33 - 7 * q^34 + 24 * q^35 + 63 * q^36 + 53 * q^37 + 16 * q^38 + 32 * q^39 - 20 * q^40 + 38 * q^41 + 11 * q^42 + 36 * q^43 + 70 * q^44 + 24 * q^45 + 4 * q^46 + 51 * q^47 + 67 * q^48 + 53 * q^49 + 32 * q^50 + 46 * q^51 + 10 * q^52 + 104 * q^53 + 11 * q^54 + 11 * q^55 + 30 * q^56 + 14 * q^57 + 4 * q^58 + 36 * q^59 + 53 * q^60 + 3 * q^61 + 25 * q^62 + 53 * q^63 + 82 * q^64 + 46 * q^65 + 13 * q^66 + 54 * q^67 + 88 * q^68 + 68 * q^69 + 2 * q^70 + 101 * q^71 + 30 * q^72 + q^73 + 32 * q^74 + 71 * q^75 - 35 * q^76 + 46 * q^77 + 11 * q^78 + 14 * q^79 + 39 * q^80 + 53 * q^81 - 29 * q^82 + 38 * q^83 + 63 * q^84 + 16 * q^85 + 23 * q^86 + 55 * q^87 - 8 * q^88 + 52 * q^89 + 2 * q^90 + 32 * q^91 + 76 * q^92 - 2 * q^93 - 53 * q^94 + 46 * q^95 + 51 * q^96 - 3 * q^97 + 11 * q^98 + 46 * q^99

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