LMFDB - Embedded newform 8041.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70186 q^{2} -1.87988 q^{3} +0.896329 q^{4} -0.570066 q^{5} +3.19929 q^{6} -0.204447 q^{7} +1.87829 q^{8} +0.533941 q^{9} +O(q^{10})$	\(q-1.70186 q^{2} -1.87988 q^{3} +0.896329 q^{4} -0.570066 q^{5} +3.19929 q^{6} -0.204447 q^{7} +1.87829 q^{8} +0.533941 q^{9} +0.970172 q^{10} +1.00000 q^{11} -1.68499 q^{12} -5.82314 q^{13} +0.347940 q^{14} +1.07165 q^{15} -4.98925 q^{16} -1.00000 q^{17} -0.908693 q^{18} -2.98710 q^{19} -0.510966 q^{20} +0.384335 q^{21} -1.70186 q^{22} -0.439002 q^{23} -3.53096 q^{24} -4.67503 q^{25} +9.91017 q^{26} +4.63589 q^{27} -0.183251 q^{28} +7.25373 q^{29} -1.82380 q^{30} -1.81649 q^{31} +4.73442 q^{32} -1.87988 q^{33} +1.70186 q^{34} +0.116548 q^{35} +0.478587 q^{36} -4.36893 q^{37} +5.08363 q^{38} +10.9468 q^{39} -1.07075 q^{40} +10.0418 q^{41} -0.654084 q^{42} +1.00000 q^{43} +0.896329 q^{44} -0.304381 q^{45} +0.747120 q^{46} +12.6898 q^{47} +9.37919 q^{48} -6.95820 q^{49} +7.95624 q^{50} +1.87988 q^{51} -5.21945 q^{52} +10.0454 q^{53} -7.88964 q^{54} -0.570066 q^{55} -0.384011 q^{56} +5.61538 q^{57} -12.3448 q^{58} -3.91248 q^{59} +0.960554 q^{60} -8.89855 q^{61} +3.09142 q^{62} -0.109162 q^{63} +1.92118 q^{64} +3.31957 q^{65} +3.19929 q^{66} -3.58339 q^{67} -0.896329 q^{68} +0.825270 q^{69} -0.198348 q^{70} +6.77001 q^{71} +1.00290 q^{72} -10.9667 q^{73} +7.43531 q^{74} +8.78848 q^{75} -2.67742 q^{76} -0.204447 q^{77} -18.6299 q^{78} -1.67653 q^{79} +2.84420 q^{80} -10.3167 q^{81} -17.0898 q^{82} -9.44566 q^{83} +0.344490 q^{84} +0.570066 q^{85} -1.70186 q^{86} -13.6361 q^{87} +1.87829 q^{88} -11.3340 q^{89} +0.518015 q^{90} +1.19052 q^{91} -0.393490 q^{92} +3.41479 q^{93} -21.5963 q^{94} +1.70284 q^{95} -8.90014 q^{96} +9.48312 q^{97} +11.8419 q^{98} +0.533941 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) $ 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.70186	−1.20340	−0.601699	−	0.798723i	$-0.705509\pi$
$2$	−1.70186	−1.20340	−0.601699	+	0.798723i	$0.705509\pi$
$3$	−1.87988	−1.08535	−0.542674	−	0.839943i	$-0.682588\pi$
$3$	−1.87988	−1.08535	−0.542674	+	0.839943i	$0.682588\pi$
$4$	0.896329	0.448165
$5$	−0.570066	−0.254941	−0.127471	−	0.991842i	$-0.540686\pi$
$5$	−0.570066	−0.254941	−0.127471	+	0.991842i	$0.540686\pi$
$6$	3.19929	1.30610
$7$	−0.204447	−0.0772736	−0.0386368	−	0.999253i	$-0.512302\pi$
$7$	−0.204447	−0.0772736	−0.0386368	+	0.999253i	$0.512302\pi$
$8$	1.87829	0.664077
$9$	0.533941	0.177980
$10$	0.970172	0.306795
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.68499	−0.486415
$13$	−5.82314	−1.61505	−0.807524	−	0.589835i	$-0.799193\pi$
$13$	−5.82314	−1.61505	−0.807524	+	0.589835i	$0.799193\pi$
$14$	0.347940	0.0929908
$15$	1.07165	0.276700
$16$	−4.98925	−1.24731
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.908693	−0.214181
$19$	−2.98710	−0.685287	−0.342644	−	0.939465i	$-0.611322\pi$
$19$	−2.98710	−0.685287	−0.342644	+	0.939465i	$0.611322\pi$
$20$	−0.510966	−0.114256
$21$	0.384335	0.0838687
$22$	−1.70186	−0.362838
$23$	−0.439002	−0.0915382	−0.0457691	−	0.998952i	$-0.514574\pi$
$23$	−0.439002	−0.0915382	−0.0457691	+	0.998952i	$0.514574\pi$
$24$	−3.53096	−0.720755
$25$	−4.67503	−0.935005
$26$	9.91017	1.94354
$27$	4.63589	0.892177
$28$	−0.183251	−0.0346313
$29$	7.25373	1.34698	0.673492	−	0.739195i	$-0.264794\pi$
$29$	7.25373	1.34698	0.673492	+	0.739195i	$0.264794\pi$
$30$	−1.82380	−0.332980
$31$	−1.81649	−0.326252	−0.163126	−	0.986605i	$-0.552158\pi$
$31$	−1.81649	−0.326252	−0.163126	+	0.986605i	$0.552158\pi$
$32$	4.73442	0.836936
$33$	−1.87988	−0.327245
$34$	1.70186	0.291867
$35$	0.116548	0.0197002
$36$	0.478587	0.0797645
$37$	−4.36893	−0.718247	−0.359124	−	0.933290i	$-0.616924\pi$
$37$	−4.36893	−0.718247	−0.359124	+	0.933290i	$0.616924\pi$
$38$	5.08363	0.824673
$39$	10.9468	1.75289
$40$	−1.07075	−0.169301
$41$	10.0418	1.56827	0.784135	−	0.620591i	$-0.213107\pi$
$41$	10.0418	1.56827	0.784135	+	0.620591i	$0.213107\pi$
$42$	−0.654084	−0.100927
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.896329	0.135127
$45$	−0.304381	−0.0453745
$46$	0.747120	0.110157
$47$	12.6898	1.85100	0.925500	−	0.378748i	$-0.123645\pi$
$47$	12.6898	1.85100	0.925500	+	0.378748i	$0.123645\pi$
$48$	9.37919	1.35377
$49$	−6.95820	−0.994029
$50$	7.95624	1.12518
$51$	1.87988	0.263236
$52$	−5.21945	−0.723807
$53$	10.0454	1.37984	0.689921	−	0.723885i	$-0.257645\pi$
$53$	10.0454	1.37984	0.689921	+	0.723885i	$0.257645\pi$
$54$	−7.88964	−1.07364
$55$	−0.570066	−0.0768676
$56$	−0.384011	−0.0513156
$57$	5.61538	0.743775
$58$	−12.3448	−1.62096
$59$	−3.91248	−0.509361	−0.254681	−	0.967025i	$-0.581970\pi$
$59$	−3.91248	−0.509361	−0.254681	+	0.967025i	$0.581970\pi$
$60$	0.960554	0.124007
$61$	−8.89855	−1.13934	−0.569671	−	0.821873i	$-0.692930\pi$
$61$	−8.89855	−1.13934	−0.569671	+	0.821873i	$0.692930\pi$
$62$	3.09142	0.392610
$63$	−0.109162	−0.0137532
$64$	1.92118	0.240147
$65$	3.31957	0.411742
$66$	3.19929	0.393805
$67$	−3.58339	−0.437780	−0.218890	−	0.975749i	$-0.570244\pi$
$67$	−3.58339	−0.437780	−0.218890	+	0.975749i	$0.570244\pi$
$68$	−0.896329	−0.108696
$69$	0.825270	0.0993508
$70$	−0.198348	−0.0237072
$71$	6.77001	0.803452	0.401726	−	0.915760i	$-0.368410\pi$
$71$	6.77001	0.803452	0.401726	+	0.915760i	$0.368410\pi$
$72$	1.00290	0.118193
$73$	−10.9667	−1.28356	−0.641780	−	0.766889i	$-0.721804\pi$
$73$	−10.9667	−1.28356	−0.641780	+	0.766889i	$0.721804\pi$
$74$	7.43531	0.864337
$75$	8.78848	1.01481
$76$	−2.67742	−0.307122
$77$	−0.204447	−0.0232989
$78$	−18.6299	−2.10942
$79$	−1.67653	−0.188624	−0.0943119	−	0.995543i	$-0.530065\pi$
$79$	−1.67653	−0.188624	−0.0943119	+	0.995543i	$0.530065\pi$
$80$	2.84420	0.317991
$81$	−10.3167	−1.14630
$82$	−17.0898	−1.88725
$83$	−9.44566	−1.03680	−0.518398	−	0.855139i	$-0.673471\pi$
$83$	−9.44566	−1.03680	−0.518398	+	0.855139i	$0.673471\pi$
$84$	0.344490	0.0375870
$85$	0.570066	0.0618323
$86$	−1.70186	−0.183516
$87$	−13.6361	−1.46195
$88$	1.87829	0.200227
$89$	−11.3340	−1.20140	−0.600701	−	0.799474i	$-0.705112\pi$
$89$	−11.3340	−1.20140	−0.600701	+	0.799474i	$0.705112\pi$
$90$	0.518015	0.0546035
$91$	1.19052	0.124801
$92$	−0.393490	−0.0410242
$93$	3.41479	0.354097
$94$	−21.5963	−2.22749
$95$	1.70284	0.174708
$96$	−8.90014	−0.908367
$97$	9.48312	0.962865	0.481433	−	0.876483i	$-0.340117\pi$
$97$	9.48312	0.962865	0.481433	+	0.876483i	$0.340117\pi$
$98$	11.8419	1.19621
$99$	0.533941	0.0536631
$100$	−4.19036	−0.419036
$101$	−12.4349	−1.23731	−0.618657	−	0.785661i	$-0.712323\pi$
$101$	−12.4349	−1.23731	−0.618657	+	0.785661i	$0.712323\pi$
$102$	−3.19929	−0.316777
$103$	2.78260	0.274178	0.137089	−	0.990559i	$-0.456225\pi$
$103$	2.78260	0.274178	0.137089	+	0.990559i	$0.456225\pi$
$104$	−10.9376	−1.07252
$105$	−0.219096	−0.0213816
$106$	−17.0959	−1.66050
$107$	11.4403	1.10598	0.552989	−	0.833188i	$-0.313487\pi$
$107$	11.4403	1.10598	0.552989	+	0.833188i	$0.313487\pi$
$108$	4.15528	0.399842
$109$	10.2642	0.983131	0.491566	−	0.870840i	$-0.336425\pi$
$109$	10.2642	0.983131	0.491566	+	0.870840i	$0.336425\pi$
$110$	0.970172	0.0925023
$111$	8.21305	0.779548
$112$	1.02004	0.0963843
$113$	11.1989	1.05351	0.526753	−	0.850019i	$-0.323409\pi$
$113$	11.1989	1.05351	0.526753	+	0.850019i	$0.323409\pi$
$114$	−9.55660	−0.895057
$115$	0.250260	0.0233369
$116$	6.50173	0.603670
$117$	−3.10921	−0.287447
$118$	6.65849	0.612964
$119$	0.204447	0.0187416
$120$	2.01288	0.183750
$121$	1.00000	0.0909091
$122$	15.1441	1.37108
$123$	−18.8774	−1.70212
$124$	−1.62818	−0.146214
$125$	5.51540	0.493312
$126$	0.185779	0.0165505
$127$	4.36631	0.387447	0.193724	−	0.981056i	$-0.437944\pi$
$127$	4.36631	0.387447	0.193724	+	0.981056i	$0.437944\pi$
$128$	−12.7384	−1.12593
$129$	−1.87988	−0.165514
$130$	−5.64945	−0.495489
$131$	15.4691	1.35154	0.675770	−	0.737113i	$-0.263811\pi$
$131$	15.4691	1.35154	0.675770	+	0.737113i	$0.263811\pi$
$132$	−1.68499	−0.146660
$133$	0.610702	0.0529546
$134$	6.09842	0.526824
$135$	−2.64276	−0.227453
$136$	−1.87829	−0.161062
$137$	−17.8498	−1.52501	−0.762507	−	0.646980i	$-0.776032\pi$
$137$	−17.8498	−1.52501	−0.762507	+	0.646980i	$0.776032\pi$
$138$	−1.40449	−0.119559
$139$	−0.349177	−0.0296168	−0.0148084	−	0.999890i	$-0.504714\pi$
$139$	−0.349177	−0.0296168	−0.0148084	+	0.999890i	$0.504714\pi$
$140$	0.104465	0.00882893
$141$	−23.8553	−2.00898
$142$	−11.5216	−0.966872
$143$	−5.82314	−0.486955
$144$	−2.66397	−0.221997
$145$	−4.13510	−0.343401
$146$	18.6639	1.54463
$147$	13.0806	1.07887
$148$	−3.91600	−0.321893
$149$	1.98431	0.162561	0.0812804	−	0.996691i	$-0.474099\pi$
$149$	1.98431	0.162561	0.0812804	+	0.996691i	$0.474099\pi$
$150$	−14.9568	−1.22121
$151$	17.6520	1.43650	0.718248	−	0.695787i	$-0.244944\pi$
$151$	17.6520	1.43650	0.718248	+	0.695787i	$0.244944\pi$
$152$	−5.61065	−0.455084
$153$	−0.533941	−0.0431666
$154$	0.347940	0.0280378
$155$	1.03552	0.0831750
$156$	9.81193	0.785583
$157$	−2.82594	−0.225534	−0.112767	−	0.993621i	$-0.535971\pi$
$157$	−2.82594	−0.225534	−0.112767	+	0.993621i	$0.535971\pi$
$158$	2.85321	0.226989
$159$	−18.8841	−1.49761
$160$	−2.69893	−0.213369
$161$	0.0897525	0.00707349
$162$	17.5576	1.37946
$163$	9.51047	0.744917	0.372459	−	0.928049i	$-0.378515\pi$
$163$	9.51047	0.744917	0.372459	+	0.928049i	$0.378515\pi$
$164$	9.00078	0.702843
$165$	1.07165	0.0834281
$166$	16.0752	1.24768
$167$	21.7698	1.68460	0.842299	−	0.539010i	$-0.181202\pi$
$167$	21.7698	1.68460	0.842299	+	0.539010i	$0.181202\pi$
$168$	0.721894	0.0556953
$169$	20.9090	1.60838
$170$	−0.970172	−0.0744088
$171$	−1.59493	−0.121968
$172$	0.896329	0.0683445
$173$	23.7970	1.80925	0.904627	−	0.426205i	$-0.140150\pi$
$173$	23.7970	1.80925	0.904627	+	0.426205i	$0.140150\pi$
$174$	23.2068	1.75930
$175$	0.955793	0.0722512
$176$	−4.98925	−0.376079
$177$	7.35498	0.552834
$178$	19.2889	1.44576
$179$	−18.1933	−1.35983	−0.679917	−	0.733289i	$-0.737984\pi$
$179$	−18.1933	−1.35983	−0.679917	+	0.733289i	$0.737984\pi$
$180$	−0.272826	−0.0203352
$181$	25.9428	1.92832	0.964158	−	0.265331i	$-0.0854811\pi$
$181$	25.9428	1.92832	0.964158	+	0.265331i	$0.0854811\pi$
$182$	−2.02610	−0.150185
$183$	16.7282	1.23658
$184$	−0.824575	−0.0607885
$185$	2.49058	0.183111
$186$	−5.81149	−0.426119
$187$	−1.00000	−0.0731272
$188$	11.3743	0.829553
$189$	−0.947792	−0.0689417
$190$	−2.89800	−0.210243
$191$	−8.36623	−0.605359	−0.302680	−	0.953092i	$-0.597881\pi$
$191$	−8.36623	−0.605359	−0.302680	+	0.953092i	$0.597881\pi$
$192$	−3.61158	−0.260643
$193$	−10.3627	−0.745922	−0.372961	−	0.927847i	$-0.621657\pi$
$193$	−10.3627	−0.745922	−0.372961	+	0.927847i	$0.621657\pi$
$194$	−16.1389	−1.15871
$195$	−6.24039	−0.446884
$196$	−6.23684	−0.445489
$197$	−14.9216	−1.06312	−0.531561	−	0.847020i	$-0.678394\pi$
$197$	−14.9216	−1.06312	−0.531561	+	0.847020i	$0.678394\pi$
$198$	−0.908693	−0.0645780
$199$	11.1045	0.787175	0.393588	−	0.919287i	$-0.371234\pi$
$199$	11.1045	0.787175	0.393588	+	0.919287i	$0.371234\pi$
$200$	−8.78107	−0.620915
$201$	6.73633	0.475144
$202$	21.1624	1.48898
$203$	−1.48300	−0.104086
$204$	1.68499	0.117973
$205$	−5.72450	−0.399816
$206$	−4.73559	−0.329945
$207$	−0.234401	−0.0162920
$208$	29.0531	2.01447
$209$	−2.98710	−0.206622
$210$	0.372871	0.0257305
$211$	−22.9867	−1.58247	−0.791234	−	0.611514i	$-0.790561\pi$
$211$	−22.9867	−1.58247	−0.791234	+	0.611514i	$0.790561\pi$
$212$	9.00398	0.618396
$213$	−12.7268	−0.872025
$214$	−19.4698	−1.33093
$215$	−0.570066	−0.0388781
$216$	8.70756	0.592475
$217$	0.371376	0.0252106
$218$	−17.4682	−1.18310
$219$	20.6161	1.39311
$220$	−0.510966	−0.0344493
$221$	5.82314	0.391707
$222$	−13.9775	−0.938106
$223$	0.721638	0.0483245	0.0241622	−	0.999708i	$-0.492308\pi$
$223$	0.721638	0.0483245	0.0241622	+	0.999708i	$0.492308\pi$
$224$	−0.967937	−0.0646730
$225$	−2.49619	−0.166412
$226$	−19.0590	−1.26778
$227$	21.7583	1.44415	0.722073	−	0.691817i	$-0.243189\pi$
$227$	21.7583	1.44415	0.722073	+	0.691817i	$0.243189\pi$
$228$	5.03323	0.333334
$229$	19.2987	1.27529	0.637645	−	0.770330i	$-0.279909\pi$
$229$	19.2987	1.27529	0.637645	+	0.770330i	$0.279909\pi$
$230$	−0.425907	−0.0280835
$231$	0.384335	0.0252874
$232$	13.6246	0.894501
$233$	−15.1006	−0.989272	−0.494636	−	0.869100i	$-0.664699\pi$
$233$	−15.1006	−0.989272	−0.494636	+	0.869100i	$0.664699\pi$
$234$	5.29145	0.345913
$235$	−7.23403	−0.471896
$236$	−3.50687	−0.228278
$237$	3.15166	0.204723
$238$	−0.347940	−0.0225536
$239$	−15.5903	−1.00845	−0.504226	−	0.863572i	$-0.668222\pi$
$239$	−15.5903	−1.00845	−0.504226	+	0.863572i	$0.668222\pi$
$240$	−5.34675	−0.345131
$241$	7.90132	0.508969	0.254484	−	0.967077i	$-0.418094\pi$
$241$	7.90132	0.508969	0.254484	+	0.967077i	$0.418094\pi$
$242$	−1.70186	−0.109400
$243$	5.48652	0.351961
$244$	−7.97603	−0.510613
$245$	3.96663	0.253419
$246$	32.1267	2.04832
$247$	17.3943	1.10677
$248$	−3.41191	−0.216656
$249$	17.7567	1.12528
$250$	−9.38644	−0.593651
$251$	4.65133	0.293590	0.146795	−	0.989167i	$-0.453104\pi$
$251$	4.65133	0.293590	0.146795	+	0.989167i	$0.453104\pi$
$252$	−0.0978455	−0.00616369
$253$	−0.439002	−0.0275998
$254$	−7.43085	−0.466253
$255$	−1.07165	−0.0671096
$256$	17.8367	1.11479
$257$	13.3112	0.830329	0.415165	−	0.909746i	$-0.363724\pi$
$257$	13.3112	0.830329	0.415165	+	0.909746i	$0.363724\pi$
$258$	3.19929	0.199179
$259$	0.893213	0.0555015
$260$	2.97543	0.184528
$261$	3.87306	0.239737
$262$	−26.3262	−1.62644
$263$	12.1424	0.748735	0.374368	−	0.927280i	$-0.377860\pi$
$263$	12.1424	0.748735	0.374368	+	0.927280i	$0.377860\pi$
$264$	−3.53096	−0.217316
$265$	−5.72653	−0.351778
$266$	−1.03933	−0.0637254
$267$	21.3065	1.30394
$268$	−3.21189	−0.196198
$269$	−25.7854	−1.57216	−0.786082	−	0.618123i	$-0.787894\pi$
$269$	−25.7854	−1.57216	−0.786082	+	0.618123i	$0.787894\pi$
$270$	4.49761	0.273716
$271$	−24.1083	−1.46448	−0.732238	−	0.681049i	$-0.761524\pi$
$271$	−24.1083	−1.46448	−0.732238	+	0.681049i	$0.761524\pi$
$272$	4.98925	0.302518
$273$	−2.23803	−0.135452
$274$	30.3779	1.83520
$275$	−4.67503	−0.281915
$276$	0.739714	0.0445255
$277$	31.5869	1.89787	0.948937	−	0.315466i	$-0.102161\pi$
$277$	31.5869	1.89787	0.948937	+	0.315466i	$0.102161\pi$
$278$	0.594250	0.0356407
$279$	−0.969900	−0.0580664
$280$	0.218911	0.0130825
$281$	6.99823	0.417479	0.208740	−	0.977971i	$-0.433064\pi$
$281$	6.99823	0.417479	0.208740	+	0.977971i	$0.433064\pi$
$282$	40.5984	2.41760
$283$	6.64768	0.395164	0.197582	−	0.980286i	$-0.436691\pi$
$283$	6.64768	0.395164	0.197582	+	0.980286i	$0.436691\pi$
$284$	6.06816	0.360079
$285$	−3.20114	−0.189619
$286$	9.91017	0.586001
$287$	−2.05302	−0.121186
$288$	2.52790	0.148958
$289$	1.00000	0.0588235
$290$	7.03736	0.413248
$291$	−17.8271	−1.04504
$292$	−9.82982	−0.575246
$293$	5.86067	0.342384	0.171192	−	0.985238i	$-0.445238\pi$
$293$	5.86067	0.342384	0.171192	+	0.985238i	$0.445238\pi$
$294$	−22.2613	−1.29831
$295$	2.23037	0.129857
$296$	−8.20613	−0.476972
$297$	4.63589	0.269002
$298$	−3.37702	−0.195625
$299$	2.55637	0.147839
$300$	7.87737	0.454800
$301$	−0.204447	−0.0117841
$302$	−30.0412	−1.72867
$303$	23.3760	1.34292
$304$	14.9034	0.854768
$305$	5.07276	0.290465
$306$	0.908693	0.0519465
$307$	22.0264	1.25711	0.628556	−	0.777765i	$-0.283646\pi$
$307$	22.0264	1.25711	0.628556	+	0.777765i	$0.283646\pi$
$308$	−0.183251	−0.0104417
$309$	−5.23095	−0.297578
$310$	−1.76231	−0.100093
$311$	−0.463125	−0.0262614	−0.0131307	−	0.999914i	$-0.504180\pi$
$311$	−0.463125	−0.0262614	−0.0131307	+	0.999914i	$0.504180\pi$
$312$	20.5613	1.16405
$313$	−27.6307	−1.56178	−0.780891	−	0.624667i	$-0.785235\pi$
$313$	−27.6307	−1.56178	−0.780891	+	0.624667i	$0.785235\pi$
$314$	4.80935	0.271407
$315$	0.0622297	0.00350625
$316$	−1.50272	−0.0845345
$317$	31.1582	1.75002	0.875010	−	0.484106i	$-0.160855\pi$
$317$	31.1582	1.75002	0.875010	+	0.484106i	$0.160855\pi$
$318$	32.1381	1.80222
$319$	7.25373	0.406131
$320$	−1.09520	−0.0612233
$321$	−21.5064	−1.20037
$322$	−0.152746	−0.00851221
$323$	2.98710	0.166207
$324$	−9.24719	−0.513733
$325$	27.2233	1.51008
$326$	−16.1855	−0.896431
$327$	−19.2954	−1.06704
$328$	18.8615	1.04145
$329$	−2.59439	−0.143033
$330$	−1.82380	−0.100397
$331$	4.43739	0.243901	0.121951	−	0.992536i	$-0.461085\pi$
$331$	4.43739	0.243901	0.121951	+	0.992536i	$0.461085\pi$
$332$	−8.46642	−0.464655
$333$	−2.33275	−0.127834
$334$	−37.0492	−2.02724
$335$	2.04277	0.111608
$336$	−1.91754	−0.104611
$337$	−18.6812	−1.01763	−0.508814	−	0.860877i	$-0.669916\pi$
$337$	−18.6812	−1.01763	−0.508814	+	0.860877i	$0.669916\pi$
$338$	−35.5841	−1.93552
$339$	−21.0526	−1.14342
$340$	0.510966	0.0277110
$341$	−1.81649	−0.0983686
$342$	2.71436	0.146776
$343$	2.85371	0.154086
$344$	1.87829	0.101271
$345$	−0.470458	−0.0253286
$346$	−40.4992	−2.17725
$347$	−26.3895	−1.41666	−0.708332	−	0.705879i	$-0.750552\pi$
$347$	−26.3895	−1.41666	−0.708332	+	0.705879i	$0.750552\pi$
$348$	−12.2225	−0.655192
$349$	13.4867	0.721928	0.360964	−	0.932580i	$-0.382448\pi$
$349$	13.4867	0.721928	0.360964	+	0.932580i	$0.382448\pi$
$350$	−1.62663	−0.0869469
$351$	−26.9954	−1.44091
$352$	4.73442	0.252346
$353$	10.6953	0.569252	0.284626	−	0.958639i	$-0.408131\pi$
$353$	10.6953	0.569252	0.284626	+	0.958639i	$0.408131\pi$
$354$	−12.5172	−0.665279
$355$	−3.85935	−0.204833
$356$	−10.1590	−0.538425
$357$	−0.384335	−0.0203412
$358$	30.9625	1.63642
$359$	−26.3688	−1.39169	−0.695846	−	0.718191i	$-0.744971\pi$
$359$	−26.3688	−1.39169	−0.695846	+	0.718191i	$0.744971\pi$
$360$	−0.571718	−0.0301322
$361$	−10.0772	−0.530381
$362$	−44.1511	−2.32053
$363$	−1.87988	−0.0986680
$364$	1.06710	0.0559312
$365$	6.25176	0.327232
$366$	−28.4690	−1.48810
$367$	−21.9190	−1.14416	−0.572081	−	0.820197i	$-0.693864\pi$
$367$	−21.9190	−1.14416	−0.572081	+	0.820197i	$0.693864\pi$
$368$	2.19029	0.114177
$369$	5.36174	0.279121
$370$	−4.23861	−0.220355
$371$	−2.05375	−0.106625
$372$	3.06077	0.158694
$373$	2.91761	0.151068	0.0755342	−	0.997143i	$-0.475934\pi$
$373$	2.91761	0.151068	0.0755342	+	0.997143i	$0.475934\pi$
$374$	1.70186	0.0880011
$375$	−10.3683	−0.535415
$376$	23.8352	1.22921
$377$	−42.2395	−2.17544
$378$	1.61301	0.0829643
$379$	−20.2175	−1.03850	−0.519251	−	0.854622i	$-0.673789\pi$
$379$	−20.2175	−1.03850	−0.519251	+	0.854622i	$0.673789\pi$
$380$	1.52631	0.0782979
$381$	−8.20813	−0.420515
$382$	14.2382	0.728488
$383$	34.7212	1.77417	0.887086	−	0.461604i	$-0.152726\pi$
$383$	34.7212	1.77417	0.887086	+	0.461604i	$0.152726\pi$
$384$	23.9467	1.22202
$385$	0.116548	0.00593984
$386$	17.6358	0.897640
$387$	0.533941	0.0271417
$388$	8.50000	0.431522
$389$	15.3813	0.779863	0.389932	−	0.920844i	$-0.372499\pi$
$389$	15.3813	0.779863	0.389932	+	0.920844i	$0.372499\pi$
$390$	10.6203	0.537778
$391$	0.439002	0.0222013
$392$	−13.0695	−0.660112
$393$	−29.0800	−1.46689
$394$	25.3945	1.27936
$395$	0.955730	0.0480880
$396$	0.478587	0.0240499
$397$	−7.03346	−0.352999	−0.176500	−	0.984301i	$-0.556477\pi$
$397$	−7.03346	−0.352999	−0.176500	+	0.984301i	$0.556477\pi$
$398$	−18.8983	−0.947284
$399$	−1.14805	−0.0574742
$400$	23.3249	1.16624
$401$	23.9442	1.19571	0.597857	−	0.801602i	$-0.296019\pi$
$401$	23.9442	1.19571	0.597857	+	0.801602i	$0.296019\pi$
$402$	−11.4643	−0.571787
$403$	10.5777	0.526912
$404$	−11.1457	−0.554520
$405$	5.88121	0.292240
$406$	2.52386	0.125257
$407$	−4.36893	−0.216560
$408$	3.53096	0.174809
$409$	−6.85370	−0.338894	−0.169447	−	0.985539i	$-0.554198\pi$
$409$	−6.85370	−0.338894	−0.169447	+	0.985539i	$0.554198\pi$
$410$	9.74230	0.481138
$411$	33.5555	1.65517
$412$	2.49412	0.122877
$413$	0.799893	0.0393602
$414$	0.398918	0.0196058
$415$	5.38465	0.264322
$416$	−27.5692	−1.35169
$417$	0.656409	0.0321445
$418$	5.08363	0.248648
$419$	10.9732	0.536075	0.268037	−	0.963409i	$-0.413625\pi$
$419$	10.9732	0.536075	0.268037	+	0.963409i	$0.413625\pi$
$420$	−0.196382	−0.00958247
$421$	−12.3361	−0.601227	−0.300614	−	0.953746i	$-0.597191\pi$
$421$	−12.3361	−0.601227	−0.300614	+	0.953746i	$0.597191\pi$
$422$	39.1201	1.90434
$423$	6.77561	0.329442
$424$	18.8682	0.916321
$425$	4.67503	0.226772
$426$	21.6592	1.04939
$427$	1.81928	0.0880411
$428$	10.2543	0.495660
$429$	10.9468	0.528516
$430$	0.970172	0.0467859
$431$	−19.6211	−0.945116	−0.472558	−	0.881300i	$-0.656669\pi$
$431$	−19.6211	−0.945116	−0.472558	+	0.881300i	$0.656669\pi$
$432$	−23.1296	−1.11282
$433$	−12.8732	−0.618646	−0.309323	−	0.950957i	$-0.600102\pi$
$433$	−12.8732	−0.618646	−0.309323	+	0.950957i	$0.600102\pi$
$434$	−0.632030	−0.0303384
$435$	7.77348	0.372710
$436$	9.20010	0.440605
$437$	1.31134	0.0627300
$438$	−35.0858	−1.67646
$439$	10.5332	0.502721	0.251360	−	0.967894i	$-0.419122\pi$
$439$	10.5332	0.502721	0.251360	+	0.967894i	$0.419122\pi$
$440$	−1.07075	−0.0510460
$441$	−3.71527	−0.176918
$442$	−9.91017	−0.471379
$443$	−4.00801	−0.190426	−0.0952131	−	0.995457i	$-0.530353\pi$
$443$	−4.00801	−0.190426	−0.0952131	+	0.995457i	$0.530353\pi$
$444$	7.36160	0.349366
$445$	6.46112	0.306286
$446$	−1.22813	−0.0581535
$447$	−3.73026	−0.176435
$448$	−0.392778	−0.0185570
$449$	−10.6790	−0.503974	−0.251987	−	0.967731i	$-0.581084\pi$
$449$	−10.6790	−0.503974	−0.251987	+	0.967731i	$0.581084\pi$
$450$	4.24816	0.200260
$451$	10.0418	0.472851
$452$	10.0379	0.472144
$453$	−33.1835	−1.55910
$454$	−37.0295	−1.73788
$455$	−0.678675	−0.0318168
$456$	10.5473	0.493924
$457$	−33.3162	−1.55847	−0.779233	−	0.626734i	$-0.784391\pi$
$457$	−33.3162	−1.55847	−0.779233	+	0.626734i	$0.784391\pi$
$458$	−32.8436	−1.53468
$459$	−4.63589	−0.216385
$460$	0.224315	0.0104588
$461$	−29.9706	−1.39587	−0.697934	−	0.716162i	$-0.745897\pi$
$461$	−29.9706	−1.39587	−0.697934	+	0.716162i	$0.745897\pi$
$462$	−0.654084	−0.0304307
$463$	−39.5191	−1.83661	−0.918304	−	0.395877i	$-0.870441\pi$
$463$	−39.5191	−1.83661	−0.918304	+	0.395877i	$0.870441\pi$
$464$	−36.1907	−1.68011
$465$	−1.94665	−0.0902738
$466$	25.6991	1.19049
$467$	18.7050	0.865565	0.432782	−	0.901498i	$-0.357532\pi$
$467$	18.7050	0.865565	0.432782	+	0.901498i	$0.357532\pi$
$468$	−2.78688	−0.128823
$469$	0.732611	0.0338289
$470$	12.3113	0.567878
$471$	5.31242	0.244783
$472$	−7.34878	−0.338255
$473$	1.00000	0.0459800
$474$	−5.36369	−0.246363
$475$	13.9648	0.640747
$476$	0.183251	0.00839932
$477$	5.36365	0.245585
$478$	26.5325	1.21357
$479$	4.07059	0.185990	0.0929950	−	0.995667i	$-0.470356\pi$
$479$	4.07059	0.185990	0.0929950	+	0.995667i	$0.470356\pi$
$480$	5.07366	0.231580
$481$	25.4409	1.16000
$482$	−13.4469	−0.612491
$483$	−0.168724	−0.00767719
$484$	0.896329	0.0407422
$485$	−5.40600	−0.245474
$486$	−9.33730	−0.423548
$487$	−30.4152	−1.37825	−0.689123	−	0.724644i	$-0.742004\pi$
$487$	−30.4152	−1.37825	−0.689123	+	0.724644i	$0.742004\pi$
$488$	−16.7141	−0.756611
$489$	−17.8785	−0.808494
$490$	−6.75065	−0.304963
$491$	−13.3686	−0.603315	−0.301658	−	0.953416i	$-0.597540\pi$
$491$	−13.3686	−0.603315	−0.301658	+	0.953416i	$0.597540\pi$
$492$	−16.9204	−0.762829
$493$	−7.25373	−0.326692
$494$	−29.6027	−1.33189
$495$	−0.304381	−0.0136809
$496$	9.06294	0.406938
$497$	−1.38411	−0.0620856
$498$	−30.2194	−1.35416
$499$	−5.53668	−0.247856	−0.123928	−	0.992291i	$-0.539549\pi$
$499$	−5.53668	−0.247856	−0.123928	+	0.992291i	$0.539549\pi$
$500$	4.94361	0.221085
$501$	−40.9246	−1.82838
$502$	−7.91592	−0.353305
$503$	44.4740	1.98300	0.991499	−	0.130111i	$-0.0415335\pi$
$503$	44.4740	1.98300	0.991499	+	0.130111i	$0.0415335\pi$
$504$	−0.205039	−0.00913317
$505$	7.08868	0.315442
$506$	0.747120	0.0332135
$507$	−39.3063	−1.74565
$508$	3.91365	0.173640
$509$	21.6505	0.959641	0.479821	−	0.877367i	$-0.340702\pi$
$509$	21.6505	0.959641	0.479821	+	0.877367i	$0.340702\pi$
$510$	1.82380	0.0807594
$511$	2.24211	0.0991853
$512$	−4.87867	−0.215609
$513$	−13.8479	−0.611398
$514$	−22.6538	−0.999216
$515$	−1.58626	−0.0698991
$516$	−1.68499	−0.0741775
$517$	12.6898	0.558097
$518$	−1.52012	−0.0667904
$519$	−44.7355	−1.96367
$520$	6.23513	0.273429
$521$	0.696293	0.0305052	0.0152526	−	0.999884i	$-0.495145\pi$
$521$	0.696293	0.0305052	0.0152526	+	0.999884i	$0.495145\pi$
$522$	−6.59141	−0.288498
$523$	3.89054	0.170121	0.0850607	−	0.996376i	$-0.472892\pi$
$523$	3.89054	0.170121	0.0850607	+	0.996376i	$0.472892\pi$
$524$	13.8654	0.605712
$525$	−1.79677	−0.0784177
$526$	−20.6648	−0.901026
$527$	1.81649	0.0791277
$528$	9.37919	0.408177
$529$	−22.8073	−0.991621
$530$	9.74576	0.423329
$531$	−2.08903	−0.0906563
$532$	0.547390	0.0237324
$533$	−58.4749	−2.53283
$534$	−36.2607	−1.56916
$535$	−6.52174	−0.281959
$536$	−6.73065	−0.290720
$537$	34.2013	1.47589
$538$	43.8831	1.89194
$539$	−6.95820	−0.299711
$540$	−2.36878	−0.101936
$541$	24.6293	1.05890	0.529448	−	0.848342i	$-0.322399\pi$
$541$	24.6293	1.05890	0.529448	+	0.848342i	$0.322399\pi$
$542$	41.0290	1.76235
$543$	−48.7693	−2.09289
$544$	−4.73442	−0.202987
$545$	−5.85126	−0.250641
$546$	3.80882	0.163003
$547$	−19.6011	−0.838082	−0.419041	−	0.907967i	$-0.637634\pi$
$547$	−19.6011	−0.838082	−0.419041	+	0.907967i	$0.637634\pi$
$548$	−15.9993	−0.683457
$549$	−4.75130	−0.202781
$550$	7.95624	0.339255
$551$	−21.6676	−0.923071
$552$	1.55010	0.0659766
$553$	0.342760	0.0145756
$554$	−53.7565	−2.28390
$555$	−4.68198	−0.198739
$556$	−0.312977	−0.0132732
$557$	−16.4492	−0.696975	−0.348487	−	0.937313i	$-0.613305\pi$
$557$	−16.4492	−0.696975	−0.348487	+	0.937313i	$0.613305\pi$
$558$	1.65063	0.0698769
$559$	−5.82314	−0.246293
$560$	−0.581487	−0.0245723
$561$	1.87988	0.0793685
$562$	−11.9100	−0.502394
$563$	−23.3405	−0.983684	−0.491842	−	0.870685i	$-0.663676\pi$
$563$	−23.3405	−0.983684	−0.491842	+	0.870685i	$0.663676\pi$
$564$	−21.3822	−0.900353
$565$	−6.38411	−0.268582
$566$	−11.3134	−0.475539
$567$	2.10922	0.0885789
$568$	12.7161	0.533554
$569$	4.44155	0.186200	0.0930998	−	0.995657i	$-0.470322\pi$
$569$	4.44155	0.186200	0.0930998	+	0.995657i	$0.470322\pi$
$570$	5.44789	0.228187
$571$	−6.65578	−0.278536	−0.139268	−	0.990255i	$-0.544475\pi$
$571$	−6.65578	−0.278536	−0.139268	+	0.990255i	$0.544475\pi$
$572$	−5.21945	−0.218236
$573$	15.7275	0.657026
$574$	3.49395	0.145835
$575$	2.05235	0.0855887
$576$	1.02579	0.0427414
$577$	8.97052	0.373448	0.186724	−	0.982412i	$-0.440213\pi$
$577$	8.97052	0.373448	0.186724	+	0.982412i	$0.440213\pi$
$578$	−1.70186	−0.0707881
$579$	19.4806	0.809585
$580$	−3.70641	−0.153900
$581$	1.93113	0.0801169
$582$	30.3393	1.25760
$583$	10.0454	0.416038
$584$	−20.5988	−0.852383
$585$	1.77246	0.0732820
$586$	−9.97404	−0.412024
$587$	40.9226	1.68906	0.844528	−	0.535512i	$-0.179881\pi$
$587$	40.9226	1.68906	0.844528	+	0.535512i	$0.179881\pi$
$588$	11.7245	0.483510
$589$	5.42604	0.223576
$590$	−3.79578	−0.156270
$591$	28.0508	1.15386
$592$	21.7977	0.895879
$593$	−28.3171	−1.16285	−0.581423	−	0.813602i	$-0.697504\pi$
$593$	−28.3171	−1.16285	−0.581423	+	0.813602i	$0.697504\pi$
$594$	−7.88964	−0.323716
$595$	−0.116548	−0.00477800
$596$	1.77859	0.0728540
$597$	−20.8751	−0.854359
$598$	−4.35058	−0.177909
$599$	−29.2842	−1.19652	−0.598260	−	0.801302i	$-0.704141\pi$
$599$	−29.2842	−1.19652	−0.598260	+	0.801302i	$0.704141\pi$
$600$	16.5073	0.673909
$601$	46.0798	1.87963	0.939816	−	0.341681i	$-0.110996\pi$
$601$	46.0798	1.87963	0.939816	+	0.341681i	$0.110996\pi$
$602$	0.347940	0.0141810
$603$	−1.91332	−0.0779163
$604$	15.8220	0.643787
$605$	−0.570066	−0.0231765
$606$	−39.7827	−1.61606
$607$	7.54581	0.306275	0.153138	−	0.988205i	$-0.451062\pi$
$607$	7.54581	0.306275	0.153138	+	0.988205i	$0.451062\pi$
$608$	−14.1422	−0.573542
$609$	2.78786	0.112970
$610$	−8.63313	−0.349545
$611$	−73.8946	−2.98945
$612$	−0.478587	−0.0193457
$613$	−30.8444	−1.24579	−0.622897	−	0.782304i	$-0.714045\pi$
$613$	−30.8444	−1.24579	−0.622897	+	0.782304i	$0.714045\pi$
$614$	−37.4858	−1.51280
$615$	10.7614	0.433940
$616$	−0.384011	−0.0154722
$617$	8.49825	0.342127	0.171063	−	0.985260i	$-0.445280\pi$
$617$	8.49825	0.342127	0.171063	+	0.985260i	$0.445280\pi$
$618$	8.90234	0.358105
$619$	13.0842	0.525898	0.262949	−	0.964810i	$-0.415305\pi$
$619$	13.0842	0.525898	0.262949	+	0.964810i	$0.415305\pi$
$620$	0.928167	0.0372761
$621$	−2.03516	−0.0816684
$622$	0.788174	0.0316029
$623$	2.31720	0.0928365
$624$	−54.6163	−2.18640
$625$	20.2310	0.809240
$626$	47.0237	1.87944
$627$	5.61538	0.224257
$628$	−2.53297	−0.101076
$629$	4.36893	0.174201
$630$	−0.105906	−0.00421941
$631$	−14.5380	−0.578750	−0.289375	−	0.957216i	$-0.593447\pi$
$631$	−14.5380	−0.578750	−0.289375	+	0.957216i	$0.593447\pi$
$632$	−3.14901	−0.125261
$633$	43.2121	1.71753
$634$	−53.0269	−2.10597
$635$	−2.48908	−0.0987762
$636$	−16.9264	−0.671175
$637$	40.5186	1.60540
$638$	−12.3448	−0.488737
$639$	3.61479	0.142999
$640$	7.26173	0.287045
$641$	24.2260	0.956871	0.478435	−	0.878123i	$-0.341204\pi$
$641$	24.2260	0.956871	0.478435	+	0.878123i	$0.341204\pi$
$642$	36.6009	1.44452
$643$	26.3606	1.03956	0.519779	−	0.854301i	$-0.326014\pi$
$643$	26.3606	1.03956	0.519779	+	0.854301i	$0.326014\pi$
$644$	0.0804478	0.00317009
$645$	1.07165	0.0421963
$646$	−5.08363	−0.200013
$647$	24.5599	0.965551	0.482775	−	0.875744i	$-0.339629\pi$
$647$	24.5599	0.965551	0.482775	+	0.875744i	$0.339629\pi$
$648$	−19.3778	−0.761234
$649$	−3.91248	−0.153578
$650$	−46.3303	−1.81722
$651$	−0.698141	−0.0273623
$652$	8.52451	0.333846
$653$	19.8011	0.774875	0.387438	−	0.921896i	$-0.373360\pi$
$653$	19.8011	0.774875	0.387438	+	0.921896i	$0.373360\pi$
$654$	32.8381	1.28407
$655$	−8.81839	−0.344563
$656$	−50.1012	−1.95612
$657$	−5.85560	−0.228449
$658$	4.41529	0.172126
$659$	−6.31617	−0.246043	−0.123022	−	0.992404i	$-0.539258\pi$
$659$	−6.31617	−0.246043	−0.123022	+	0.992404i	$0.539258\pi$
$660$	0.960554	0.0373895
$661$	−33.7686	−1.31345	−0.656723	−	0.754132i	$-0.728058\pi$
$661$	−33.7686	−1.31345	−0.656723	+	0.754132i	$0.728058\pi$
$662$	−7.55182	−0.293510
$663$	−10.9468	−0.425138
$664$	−17.7417	−0.688513
$665$	−0.348140	−0.0135003
$666$	3.97001	0.153835
$667$	−3.18440	−0.123301
$668$	19.5129	0.754977
$669$	−1.35659	−0.0524489
$670$	−3.47650	−0.134309
$671$	−8.89855	−0.343525
$672$	1.81960	0.0701927
$673$	−0.0663216	−0.00255651	−0.00127825	−	0.999999i	$-0.500407\pi$
$673$	−0.0663216	−0.00255651	−0.00127825	+	0.999999i	$0.500407\pi$
$674$	31.7927	1.22461
$675$	−21.6729	−0.834190
$676$	18.7413	0.720819
$677$	34.2919	1.31794	0.658972	−	0.752167i	$-0.270992\pi$
$677$	34.2919	1.31794	0.658972	+	0.752167i	$0.270992\pi$
$678$	35.8286	1.37599
$679$	−1.93879	−0.0744040
$680$	1.07075	0.0410614
$681$	−40.9029	−1.56740
$682$	3.09142	0.118377
$683$	−8.29352	−0.317343	−0.158671	−	0.987331i	$-0.550721\pi$
$683$	−8.29352	−0.317343	−0.158671	+	0.987331i	$0.550721\pi$
$684$	−1.42959	−0.0546616
$685$	10.1756	0.388789
$686$	−4.85661	−0.185426
$687$	−36.2791	−1.38413
$688$	−4.98925	−0.190213
$689$	−58.4957	−2.22851
$690$	0.800654	0.0304804
$691$	−39.0621	−1.48599	−0.742997	−	0.669295i	$-0.766596\pi$
$691$	−39.0621	−1.48599	−0.742997	+	0.669295i	$0.766596\pi$
$692$	21.3300	0.810843
$693$	−0.109162	−0.00414674
$694$	44.9113	1.70481
$695$	0.199054	0.00755053
$696$	−25.6126	−0.970845
$697$	−10.0418	−0.380361
$698$	−22.9525	−0.868766
$699$	28.3872	1.07370
$700$	0.856705	0.0323804
$701$	21.1530	0.798937	0.399469	−	0.916747i	$-0.369195\pi$
$701$	21.1530	0.798937	0.399469	+	0.916747i	$0.369195\pi$
$702$	45.9425	1.73399
$703$	13.0504	0.492206
$704$	1.92118	0.0724070
$705$	13.5991	0.512171
$706$	−18.2019	−0.685036
$707$	2.54226	0.0956117
$708$	6.59249	0.247761
$709$	−20.2939	−0.762154	−0.381077	−	0.924543i	$-0.624447\pi$
$709$	−20.2939	−0.762154	−0.381077	+	0.924543i	$0.624447\pi$
$710$	6.56807	0.246495
$711$	−0.895166	−0.0335713
$712$	−21.2886	−0.797823
$713$	0.797444	0.0298645
$714$	0.654084	0.0244785
$715$	3.31957	0.124145
$716$	−16.3072	−0.609430
$717$	29.3078	1.09452
$718$	44.8760	1.67476
$719$	34.7525	1.29605	0.648024	−	0.761620i	$-0.275595\pi$
$719$	34.7525	1.29605	0.648024	+	0.761620i	$0.275595\pi$
$720$	1.51864	0.0565962
$721$	−0.568893	−0.0211867
$722$	17.1501	0.638259
$723$	−14.8535	−0.552408
$724$	23.2533	0.864203
$725$	−33.9114	−1.25944
$726$	3.19929	0.118737
$727$	2.22035	0.0823482	0.0411741	−	0.999152i	$-0.486890\pi$
$727$	2.22035	0.0823482	0.0411741	+	0.999152i	$0.486890\pi$
$728$	2.23615	0.0828772
$729$	20.6362	0.764304
$730$	−10.6396	−0.393790
$731$	−1.00000	−0.0369863
$732$	14.9940	0.554193
$733$	−44.0476	−1.62693	−0.813467	−	0.581611i	$-0.802423\pi$
$733$	−44.0476	−1.62693	−0.813467	+	0.581611i	$0.802423\pi$
$734$	37.3031	1.37688
$735$	−7.45678	−0.275048
$736$	−2.07842	−0.0766116
$737$	−3.58339	−0.131996
$738$	−9.12493	−0.335893
$739$	−3.25882	−0.119878	−0.0599389	−	0.998202i	$-0.519091\pi$
$739$	−3.25882	−0.119878	−0.0599389	+	0.998202i	$0.519091\pi$
$740$	2.23238	0.0820638
$741$	−32.6991	−1.20123
$742$	3.49519	0.128313
$743$	38.5123	1.41288	0.706439	−	0.707774i	$-0.250300\pi$
$743$	38.5123	1.41288	0.706439	+	0.707774i	$0.250300\pi$
$744$	6.41397	0.235148
$745$	−1.13119	−0.0414434
$746$	−4.96537	−0.181795
$747$	−5.04343	−0.184529
$748$	−0.896329	−0.0327730
$749$	−2.33894	−0.0854629
$750$	17.6454	0.644317
$751$	−31.2507	−1.14036	−0.570178	−	0.821521i	$-0.693126\pi$
$751$	−31.2507	−1.14036	−0.570178	+	0.821521i	$0.693126\pi$
$752$	−63.3127	−2.30878
$753$	−8.74394	−0.318647
$754$	71.8857	2.61792
$755$	−10.0628	−0.366222
$756$	−0.849534	−0.0308972
$757$	22.6310	0.822537	0.411268	−	0.911514i	$-0.365086\pi$
$757$	22.6310	0.822537	0.411268	+	0.911514i	$0.365086\pi$
$758$	34.4074	1.24973
$759$	0.825270	0.0299554
$760$	3.19844	0.116020
$761$	37.1889	1.34810	0.674049	−	0.738687i	$-0.264554\pi$
$761$	37.1889	1.34810	0.674049	+	0.738687i	$0.264554\pi$
$762$	13.9691	0.506047
$763$	−2.09848	−0.0759701
$764$	−7.49890	−0.271301
$765$	0.304381	0.0110049
$766$	−59.0907	−2.13503
$767$	22.7829	0.822643
$768$	−33.5308	−1.20994
$769$	−48.8909	−1.76305	−0.881526	−	0.472135i	$-0.843483\pi$
$769$	−48.8909	−1.76305	−0.881526	+	0.472135i	$0.843483\pi$
$770$	−0.198348	−0.00714798
$771$	−25.0234	−0.901196
$772$	−9.28837	−0.334296
$773$	5.96032	0.214378	0.107189	−	0.994239i	$-0.465815\pi$
$773$	5.96032	0.214378	0.107189	+	0.994239i	$0.465815\pi$
$774$	−0.908693	−0.0326623
$775$	8.49215	0.305047
$776$	17.8121	0.639417
$777$	−1.67913	−0.0602385
$778$	−26.1768	−0.938485
$779$	−29.9959	−1.07472
$780$	−5.59344	−0.200277
$781$	6.77001	0.242250
$782$	−0.747120	−0.0267170
$783$	33.6275	1.20175
$784$	34.7162	1.23987
$785$	1.61097	0.0574980
$786$	49.4901	1.76525
$787$	9.18881	0.327546	0.163773	−	0.986498i	$-0.447634\pi$
$787$	9.18881	0.327546	0.163773	+	0.986498i	$0.447634\pi$
$788$	−13.3747	−0.476453
$789$	−22.8263	−0.812639
$790$	−1.62652	−0.0578689
$791$	−2.28958	−0.0814081
$792$	1.00290	0.0356364
$793$	51.8175	1.84009
$794$	11.9700	0.424798
$795$	10.7652	0.381802
$796$	9.95326	0.352784
$797$	8.06429	0.285652	0.142826	−	0.989748i	$-0.454381\pi$
$797$	8.06429	0.285652	0.142826	+	0.989748i	$0.454381\pi$
$798$	1.95381	0.0691643
$799$	−12.6898	−0.448933
$800$	−22.1336	−0.782539
$801$	−6.05168	−0.213826
$802$	−40.7496	−1.43892
$803$	−10.9667	−0.387008
$804$	6.03797	0.212943
$805$	−0.0511648	−0.00180332
$806$	−18.0018	−0.634085
$807$	48.4734	1.70634
$808$	−23.3563	−0.821672
$809$	−45.3003	−1.59267	−0.796337	−	0.604853i	$-0.793232\pi$
$809$	−45.3003	−1.59267	−0.796337	+	0.604853i	$0.793232\pi$
$810$	−10.0090	−0.351681
$811$	−45.7462	−1.60637	−0.803183	−	0.595732i	$-0.796862\pi$
$811$	−45.7462	−1.60637	−0.803183	+	0.595732i	$0.796862\pi$
$812$	−1.32926	−0.0466478
$813$	45.3207	1.58947
$814$	7.43531	0.260607
$815$	−5.42159	−0.189910
$816$	−9.37919	−0.328337
$817$	−2.98710	−0.104505
$818$	11.6640	0.407824
$819$	0.635668	0.0222120
$820$	−5.13103	−0.179183
$821$	−5.47068	−0.190928	−0.0954640	−	0.995433i	$-0.530433\pi$
$821$	−5.47068	−0.190928	−0.0954640	+	0.995433i	$0.530433\pi$
$822$	−57.1068	−1.99183
$823$	40.4700	1.41069	0.705347	−	0.708862i	$-0.250791\pi$
$823$	40.4700	1.41069	0.705347	+	0.708862i	$0.250791\pi$
$824$	5.22654	0.182075
$825$	8.78848	0.305975
$826$	−1.36131	−0.0473659
$827$	−47.6984	−1.65864	−0.829318	−	0.558777i	$-0.811271\pi$
$827$	−47.6984	−1.65864	−0.829318	+	0.558777i	$0.811271\pi$
$828$	−0.210101	−0.00730150
$829$	−20.0338	−0.695803	−0.347901	−	0.937531i	$-0.613106\pi$
$829$	−20.0338	−0.695803	−0.347901	+	0.937531i	$0.613106\pi$
$830$	−9.16392	−0.318084
$831$	−59.3795	−2.05985
$832$	−11.1873	−0.387849
$833$	6.95820	0.241087
$834$	−1.11712	−0.0386826
$835$	−12.4102	−0.429473
$836$	−2.67742	−0.0926006
$837$	−8.42106	−0.291074
$838$	−18.6748	−0.645111
$839$	−27.4593	−0.948001	−0.474001	−	0.880525i	$-0.657191\pi$
$839$	−27.4593	−0.948001	−0.474001	+	0.880525i	$0.657191\pi$
$840$	−0.411527	−0.0141990
$841$	23.6166	0.814365
$842$	20.9944	0.723515
$843$	−13.1558	−0.453110
$844$	−20.6036	−0.709206
$845$	−11.9195	−0.410042
$846$	−11.5311	−0.396449
$847$	−0.204447	−0.00702487
$848$	−50.1190	−1.72109
$849$	−12.4968	−0.428890
$850$	−7.95624	−0.272897
$851$	1.91797	0.0657471
$852$	−11.4074	−0.390811
$853$	−30.2331	−1.03516	−0.517581	−	0.855634i	$-0.673167\pi$
$853$	−30.2331	−1.03516	−0.517581	+	0.855634i	$0.673167\pi$
$854$	−3.09616	−0.105948
$855$	0.909217	0.0310946
$856$	21.4883	0.734455
$857$	−6.19740	−0.211699	−0.105850	−	0.994382i	$-0.533756\pi$
$857$	−6.19740	−0.211699	−0.105850	+	0.994382i	$0.533756\pi$
$858$	−18.6299	−0.636015
$859$	6.64983	0.226889	0.113445	−	0.993544i	$-0.463812\pi$
$859$	6.64983	0.226889	0.113445	+	0.993544i	$0.463812\pi$
$860$	−0.510966	−0.0174238
$861$	3.85942	0.131529
$862$	33.3924	1.13735
$863$	20.8325	0.709146	0.354573	−	0.935028i	$-0.384626\pi$
$863$	20.8325	0.709146	0.354573	+	0.935028i	$0.384626\pi$
$864$	21.9483	0.746695
$865$	−13.5659	−0.461253
$866$	21.9084	0.744477
$867$	−1.87988	−0.0638440
$868$	0.332875	0.0112985
$869$	−1.67653	−0.0568722
$870$	−13.2294	−0.448518
$871$	20.8666	0.707037
$872$	19.2792	0.652875
$873$	5.06343	0.171371
$874$	−2.23172	−0.0754891
$875$	−1.12760	−0.0381200
$876$	18.4789	0.624343
$877$	−32.5827	−1.10024	−0.550120	−	0.835086i	$-0.685418\pi$
$877$	−32.5827	−1.10024	−0.550120	+	0.835086i	$0.685418\pi$
$878$	−17.9260	−0.604973
$879$	−11.0173	−0.371606
$880$	2.84420	0.0958780
$881$	−4.33305	−0.145984	−0.0729920	−	0.997333i	$-0.523255\pi$
$881$	−4.33305	−0.145984	−0.0729920	+	0.997333i	$0.523255\pi$
$882$	6.32287	0.212902
$883$	−39.5274	−1.33020	−0.665101	−	0.746754i	$-0.731611\pi$
$883$	−39.5274	−1.33020	−0.665101	+	0.746754i	$0.731611\pi$
$884$	5.21945	0.175549
$885$	−4.19282	−0.140940
$886$	6.82107	0.229158
$887$	0.592889	0.0199073	0.00995364	−	0.999950i	$-0.496832\pi$
$887$	0.592889	0.0199073	0.00995364	+	0.999950i	$0.496832\pi$
$888$	15.4265	0.517680
$889$	−0.892677	−0.0299394
$890$	−10.9959	−0.368584
$891$	−10.3167	−0.345623
$892$	0.646826	0.0216573
$893$	−37.9057	−1.26847
$894$	6.34838	0.212322
$895$	10.3714	0.346678
$896$	2.60433	0.0870045
$897$	−4.80566	−0.160456
$898$	18.1742	0.606481
$899$	−13.1763	−0.439456
$900$	−2.23741	−0.0745802
$901$	−10.0454	−0.334661
$902$	−17.0898	−0.569027
$903$	0.384335	0.0127899
$904$	21.0348	0.699609
$905$	−14.7891	−0.491607
$906$	56.4737	1.87621
$907$	−48.7254	−1.61790	−0.808950	−	0.587877i	$-0.799964\pi$
$907$	−48.7254	−1.61790	−0.808950	+	0.587877i	$0.799964\pi$
$908$	19.5026	0.647215
$909$	−6.63948	−0.220218
$910$	1.15501	0.0382882
$911$	−14.6354	−0.484893	−0.242446	−	0.970165i	$-0.577950\pi$
$911$	−14.6354	−0.484893	−0.242446	+	0.970165i	$0.577950\pi$
$912$	−28.0166	−0.927721
$913$	−9.44566	−0.312606
$914$	56.6995	1.87545
$915$	−9.53617	−0.315256
$916$	17.2979	0.571540
$917$	−3.16260	−0.104438
$918$	7.88964	0.260397
$919$	−6.61830	−0.218317	−0.109159	−	0.994024i	$-0.534816\pi$
$919$	−6.61830	−0.218317	−0.109159	+	0.994024i	$0.534816\pi$
$920$	0.470062	0.0154975
$921$	−41.4069	−1.36440
$922$	51.0057	1.67978
$923$	−39.4227	−1.29761
$924$	0.344490	0.0113329
$925$	20.4249	0.671565
$926$	67.2559	2.21017
$927$	1.48574	0.0487982
$928$	34.3422	1.12734
$929$	−45.3425	−1.48764	−0.743819	−	0.668381i	$-0.766988\pi$
$929$	−45.3425	−1.48764	−0.743819	+	0.668381i	$0.766988\pi$
$930$	3.31293	0.108635
$931$	20.7848	0.681195
$932$	−13.5351	−0.443357
$933$	0.870619	0.0285028
$934$	−31.8333	−1.04162
$935$	0.570066	0.0186431
$936$	−5.84001	−0.190887
$937$	0.847806	0.0276966	0.0138483	−	0.999904i	$-0.495592\pi$
$937$	0.847806	0.0276966	0.0138483	+	0.999904i	$0.495592\pi$
$938$	−1.24680	−0.0407095
$939$	51.9424	1.69508
$940$	−6.48407	−0.211487
$941$	23.2567	0.758148	0.379074	−	0.925366i	$-0.376243\pi$
$941$	23.2567	0.758148	0.379074	+	0.925366i	$0.376243\pi$
$942$	−9.04099	−0.294571
$943$	−4.40838	−0.143557
$944$	19.5203	0.635333
$945$	0.540304	0.0175761
$946$	−1.70186	−0.0553323
$947$	39.4880	1.28319	0.641594	−	0.767044i	$-0.278273\pi$
$947$	39.4880	1.28319	0.641594	+	0.767044i	$0.278273\pi$
$948$	2.82493	0.0917494
$949$	63.8609	2.07301
$950$	−23.7661	−0.771073
$951$	−58.5736	−1.89938
$952$	0.384011	0.0124459
$953$	−15.4323	−0.499900	−0.249950	−	0.968259i	$-0.580414\pi$
$953$	−15.4323	−0.499900	−0.249950	+	0.968259i	$0.580414\pi$
$954$	−9.12818	−0.295536
$955$	4.76930	0.154331
$956$	−13.9740	−0.451952
$957$	−13.6361	−0.440793
$958$	−6.92757	−0.223820
$959$	3.64934	0.117843
$960$	2.05883	0.0664486
$961$	−27.7004	−0.893560
$962$	−43.2968	−1.39595
$963$	6.10846	0.196842
$964$	7.08218	0.228102
$965$	5.90740	0.190166
$966$	0.287144	0.00923871
$967$	−9.25024	−0.297468	−0.148734	−	0.988877i	$-0.547520\pi$
$967$	−9.25024	−0.297468	−0.148734	+	0.988877i	$0.547520\pi$
$968$	1.87829	0.0603706
$969$	−5.61538	−0.180392
$970$	9.20026	0.295403
$971$	−15.1316	−0.485597	−0.242799	−	0.970077i	$-0.578065\pi$
$971$	−15.1316	−0.485597	−0.242799	+	0.970077i	$0.578065\pi$
$972$	4.91773	0.157736
$973$	0.0713880	0.00228859
$974$	51.7625	1.65858
$975$	−51.1765	−1.63896
$976$	44.3971	1.42112
$977$	−4.48783	−0.143578	−0.0717892	−	0.997420i	$-0.522871\pi$
$977$	−4.48783	−0.143578	−0.0717892	+	0.997420i	$0.522871\pi$
$978$	30.4267	0.972940
$979$	−11.3340	−0.362236
$980$	3.55541	0.113573
$981$	5.48047	0.174978
$982$	22.7514	0.726028
$983$	−33.0862	−1.05529	−0.527643	−	0.849466i	$-0.676924\pi$
$983$	−33.0862	−1.05529	−0.527643	+	0.849466i	$0.676924\pi$
$984$	−35.4573	−1.13034
$985$	8.50630	0.271033
$986$	12.3448	0.393140
$987$	4.87714	0.155241
$988$	15.5910	0.496016
$989$	−0.439002	−0.0139595
$990$	0.518015	0.0164636
$991$	46.2789	1.47010	0.735048	−	0.678015i	$-0.237160\pi$
$991$	46.2789	1.47010	0.735048	+	0.678015i	$0.237160\pi$
$992$	−8.60005	−0.273052
$993$	−8.34175	−0.264717
$994$	2.35555	0.0747137
$995$	−6.33028	−0.200683
$996$	15.9158	0.504313
$997$	38.5839	1.22196	0.610982	−	0.791644i	$-0.290775\pi$
$997$	38.5839	1.22196	0.610982	+	0.791644i	$0.290775\pi$
$998$	9.42266	0.298269
$999$	−20.2539	−0.640804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.16	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.16	✓	62	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.70186 q^{2} -1.87988 q^{3} +0.896329 q^{4} -0.570066 q^{5} +3.19929 q^{6} -0.204447 q^{7} +1.87829 q^{8} +0.533941 q^{9} +O(q^{10})\)	\(q-1.70186 q^{2} -1.87988 q^{3} +0.896329 q^{4} -0.570066 q^{5} +3.19929 q^{6} -0.204447 q^{7} +1.87829 q^{8} +0.533941 q^{9} +0.970172 q^{10} +1.00000 q^{11} -1.68499 q^{12} -5.82314 q^{13} +0.347940 q^{14} +1.07165 q^{15} -4.98925 q^{16} -1.00000 q^{17} -0.908693 q^{18} -2.98710 q^{19} -0.510966 q^{20} +0.384335 q^{21} -1.70186 q^{22} -0.439002 q^{23} -3.53096 q^{24} -4.67503 q^{25} +9.91017 q^{26} +4.63589 q^{27} -0.183251 q^{28} +7.25373 q^{29} -1.82380 q^{30} -1.81649 q^{31} +4.73442 q^{32} -1.87988 q^{33} +1.70186 q^{34} +0.116548 q^{35} +0.478587 q^{36} -4.36893 q^{37} +5.08363 q^{38} +10.9468 q^{39} -1.07075 q^{40} +10.0418 q^{41} -0.654084 q^{42} +1.00000 q^{43} +0.896329 q^{44} -0.304381 q^{45} +0.747120 q^{46} +12.6898 q^{47} +9.37919 q^{48} -6.95820 q^{49} +7.95624 q^{50} +1.87988 q^{51} -5.21945 q^{52} +10.0454 q^{53} -7.88964 q^{54} -0.570066 q^{55} -0.384011 q^{56} +5.61538 q^{57} -12.3448 q^{58} -3.91248 q^{59} +0.960554 q^{60} -8.89855 q^{61} +3.09142 q^{62} -0.109162 q^{63} +1.92118 q^{64} +3.31957 q^{65} +3.19929 q^{66} -3.58339 q^{67} -0.896329 q^{68} +0.825270 q^{69} -0.198348 q^{70} +6.77001 q^{71} +1.00290 q^{72} -10.9667 q^{73} +7.43531 q^{74} +8.78848 q^{75} -2.67742 q^{76} -0.204447 q^{77} -18.6299 q^{78} -1.67653 q^{79} +2.84420 q^{80} -10.3167 q^{81} -17.0898 q^{82} -9.44566 q^{83} +0.344490 q^{84} +0.570066 q^{85} -1.70186 q^{86} -13.6361 q^{87} +1.87829 q^{88} -11.3340 q^{89} +0.518015 q^{90} +1.19052 q^{91} -0.393490 q^{92} +3.41479 q^{93} -21.5963 q^{94} +1.70284 q^{95} -8.90014 q^{96} +9.48312 q^{97} +11.8419 q^{98} +0.533941 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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