LMFDB - Embedded newform 8043.2.a.r.1.12

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:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.59029 q^{2} -1.00000 q^{3} +0.529036 q^{4} +3.24933 q^{5} +1.59029 q^{6} -1.00000 q^{7} +2.33927 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.59029 q^{2} -1.00000 q^{3} +0.529036 q^{4} +3.24933 q^{5} +1.59029 q^{6} -1.00000 q^{7} +2.33927 q^{8} +1.00000 q^{9} -5.16740 q^{10} +1.62287 q^{11} -0.529036 q^{12} -0.895940 q^{13} +1.59029 q^{14} -3.24933 q^{15} -4.77819 q^{16} -1.17570 q^{17} -1.59029 q^{18} -3.87144 q^{19} +1.71902 q^{20} +1.00000 q^{21} -2.58084 q^{22} -0.189919 q^{23} -2.33927 q^{24} +5.55817 q^{25} +1.42481 q^{26} -1.00000 q^{27} -0.529036 q^{28} -5.15534 q^{29} +5.16740 q^{30} +5.55873 q^{31} +2.92020 q^{32} -1.62287 q^{33} +1.86971 q^{34} -3.24933 q^{35} +0.529036 q^{36} +3.72581 q^{37} +6.15672 q^{38} +0.895940 q^{39} +7.60105 q^{40} -5.04904 q^{41} -1.59029 q^{42} +4.17425 q^{43} +0.858555 q^{44} +3.24933 q^{45} +0.302027 q^{46} +7.08044 q^{47} +4.77819 q^{48} +1.00000 q^{49} -8.83913 q^{50} +1.17570 q^{51} -0.473985 q^{52} -3.53771 q^{53} +1.59029 q^{54} +5.27324 q^{55} -2.33927 q^{56} +3.87144 q^{57} +8.19851 q^{58} +2.34950 q^{59} -1.71902 q^{60} +15.3304 q^{61} -8.84002 q^{62} -1.00000 q^{63} +4.91240 q^{64} -2.91121 q^{65} +2.58084 q^{66} -15.0902 q^{67} -0.621989 q^{68} +0.189919 q^{69} +5.16740 q^{70} -14.2494 q^{71} +2.33927 q^{72} -13.4497 q^{73} -5.92514 q^{74} -5.55817 q^{75} -2.04813 q^{76} -1.62287 q^{77} -1.42481 q^{78} -10.8863 q^{79} -15.5259 q^{80} +1.00000 q^{81} +8.02946 q^{82} -1.36072 q^{83} +0.529036 q^{84} -3.82025 q^{85} -6.63829 q^{86} +5.15534 q^{87} +3.79631 q^{88} -18.4356 q^{89} -5.16740 q^{90} +0.895940 q^{91} -0.100474 q^{92} -5.55873 q^{93} -11.2600 q^{94} -12.5796 q^{95} -2.92020 q^{96} +4.60697 q^{97} -1.59029 q^{98} +1.62287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * 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 $

$2$	−1.59029	−1.12451	−0.562254	−	0.826965i	$-0.690066\pi$
$2$	−1.59029	−1.12451	−0.562254	+	0.826965i	$0.690066\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.529036	0.264518
$5$	3.24933	1.45315	0.726573	−	0.687089i	$-0.241112\pi$
$5$	3.24933	1.45315	0.726573	+	0.687089i	$0.241112\pi$
$6$	1.59029	0.649235
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.33927	0.827055
$9$	1.00000	0.333333
$10$	−5.16740	−1.63407
$11$	1.62287	0.489313	0.244656	−	0.969610i	$-0.421325\pi$
$11$	1.62287	0.489313	0.244656	+	0.969610i	$0.421325\pi$
$12$	−0.529036	−0.152720
$13$	−0.895940	−0.248489	−0.124245	−	0.992252i	$-0.539651\pi$
$13$	−0.895940	−0.248489	−0.124245	+	0.992252i	$0.539651\pi$
$14$	1.59029	0.425024
$15$	−3.24933	−0.838974
$16$	−4.77819	−1.19455
$17$	−1.17570	−0.285150	−0.142575	−	0.989784i	$-0.545538\pi$
$17$	−1.17570	−0.285150	−0.142575	+	0.989784i	$0.545538\pi$
$18$	−1.59029	−0.374836
$19$	−3.87144	−0.888169	−0.444084	−	0.895985i	$-0.646471\pi$
$19$	−3.87144	−0.888169	−0.444084	+	0.895985i	$0.646471\pi$
$20$	1.71902	0.384384
$21$	1.00000	0.218218
$22$	−2.58084	−0.550236
$23$	−0.189919	−0.0396008	−0.0198004	−	0.999804i	$-0.506303\pi$
$23$	−0.189919	−0.0396008	−0.0198004	+	0.999804i	$0.506303\pi$
$24$	−2.33927	−0.477501
$25$	5.55817	1.11163
$26$	1.42481	0.279428
$27$	−1.00000	−0.192450
$28$	−0.529036	−0.0999785
$29$	−5.15534	−0.957323	−0.478661	−	0.878000i	$-0.658878\pi$
$29$	−5.15534	−0.957323	−0.478661	+	0.878000i	$0.658878\pi$
$30$	5.16740	0.943433
$31$	5.55873	0.998378	0.499189	−	0.866493i	$-0.333631\pi$
$31$	5.55873	0.998378	0.499189	+	0.866493i	$0.333631\pi$
$32$	2.92020	0.516224
$33$	−1.62287	−0.282505
$34$	1.86971	0.320653
$35$	−3.24933	−0.549238
$36$	0.529036	0.0881727
$37$	3.72581	0.612520	0.306260	−	0.951948i	$-0.400922\pi$
$37$	3.72581	0.612520	0.306260	+	0.951948i	$0.400922\pi$
$38$	6.15672	0.998753
$39$	0.895940	0.143465
$40$	7.60105	1.20183
$41$	−5.04904	−0.788528	−0.394264	−	0.918997i	$-0.629000\pi$
$41$	−5.04904	−0.788528	−0.394264	+	0.918997i	$0.629000\pi$
$42$	−1.59029	−0.245388
$43$	4.17425	0.636567	0.318284	−	0.947996i	$-0.396894\pi$
$43$	4.17425	0.636567	0.318284	+	0.947996i	$0.396894\pi$
$44$	0.858555	0.129432
$45$	3.24933	0.484382
$46$	0.302027	0.0445314
$47$	7.08044	1.03279	0.516394	−	0.856351i	$-0.327274\pi$
$47$	7.08044	1.03279	0.516394	+	0.856351i	$0.327274\pi$
$48$	4.77819	0.689673
$49$	1.00000	0.142857
$50$	−8.83913	−1.25004
$51$	1.17570	0.164631
$52$	−0.473985	−0.0657299
$53$	−3.53771	−0.485942	−0.242971	−	0.970034i	$-0.578122\pi$
$53$	−3.53771	−0.485942	−0.242971	+	0.970034i	$0.578122\pi$
$54$	1.59029	0.216412
$55$	5.27324	0.711043
$56$	−2.33927	−0.312597
$57$	3.87144	0.512784
$58$	8.19851	1.07652
$59$	2.34950	0.305879	0.152940	−	0.988236i	$-0.451126\pi$
$59$	2.34950	0.305879	0.152940	+	0.988236i	$0.451126\pi$
$60$	−1.71902	−0.221924
$61$	15.3304	1.96286	0.981428	−	0.191830i	$-0.0614423\pi$
$61$	15.3304	1.96286	0.981428	+	0.191830i	$0.0614423\pi$
$62$	−8.84002	−1.12268
$63$	−1.00000	−0.125988
$64$	4.91240	0.614050
$65$	−2.91121	−0.361091
$66$	2.58084	0.317679
$67$	−15.0902	−1.84356	−0.921781	−	0.387710i	$-0.873266\pi$
$67$	−15.0902	−1.84356	−0.921781	+	0.387710i	$0.873266\pi$
$68$	−0.621989	−0.0754273
$69$	0.189919	0.0228635
$70$	5.16740	0.617622
$71$	−14.2494	−1.69109	−0.845547	−	0.533901i	$-0.820725\pi$
$71$	−14.2494	−1.69109	−0.845547	+	0.533901i	$0.820725\pi$
$72$	2.33927	0.275685
$73$	−13.4497	−1.57417	−0.787085	−	0.616844i	$-0.788411\pi$
$73$	−13.4497	−1.57417	−0.787085	+	0.616844i	$0.788411\pi$
$74$	−5.92514	−0.688784
$75$	−5.55817	−0.641802
$76$	−2.04813	−0.234937
$77$	−1.62287	−0.184943
$78$	−1.42481	−0.161328
$79$	−10.8863	−1.22481	−0.612403	−	0.790545i	$-0.709797\pi$
$79$	−10.8863	−1.22481	−0.612403	+	0.790545i	$0.709797\pi$
$80$	−15.5259	−1.73585
$81$	1.00000	0.111111
$82$	8.02946	0.886706
$83$	−1.36072	−0.149358	−0.0746790	−	0.997208i	$-0.523793\pi$
$83$	−1.36072	−0.149358	−0.0746790	+	0.997208i	$0.523793\pi$
$84$	0.529036	0.0577226
$85$	−3.82025	−0.414364
$86$	−6.63829	−0.715825
$87$	5.15534	0.552710
$88$	3.79631	0.404689
$89$	−18.4356	−1.95417	−0.977083	−	0.212860i	$-0.931722\pi$
$89$	−18.4356	−1.95417	−0.977083	+	0.212860i	$0.931722\pi$
$90$	−5.16740	−0.544692
$91$	0.895940	0.0939200
$92$	−0.100474	−0.0104751
$93$	−5.55873	−0.576414
$94$	−11.2600	−1.16138
$95$	−12.5796	−1.29064
$96$	−2.92020	−0.298042
$97$	4.60697	0.467767	0.233884	−	0.972265i	$-0.424857\pi$
$97$	4.60697	0.467767	0.233884	+	0.972265i	$0.424857\pi$
$98$	−1.59029	−0.160644
$99$	1.62287	0.163104
$100$	2.94048	0.294048
$101$	3.03257	0.301752	0.150876	−	0.988553i	$-0.451791\pi$
$101$	3.03257	0.301752	0.150876	+	0.988553i	$0.451791\pi$
$102$	−1.86971	−0.185129
$103$	5.42293	0.534337	0.267169	−	0.963650i	$-0.413912\pi$
$103$	5.42293	0.534337	0.267169	+	0.963650i	$0.413912\pi$
$104$	−2.09584	−0.205514
$105$	3.24933	0.317103
$106$	5.62601	0.546446
$107$	4.08820	0.395221	0.197611	−	0.980281i	$-0.436682\pi$
$107$	4.08820	0.395221	0.197611	+	0.980281i	$0.436682\pi$
$108$	−0.529036	−0.0509066
$109$	−3.92179	−0.375639	−0.187820	−	0.982204i	$-0.560142\pi$
$109$	−3.92179	−0.375639	−0.187820	+	0.982204i	$0.560142\pi$
$110$	−8.38600	−0.799573
$111$	−3.72581	−0.353639
$112$	4.77819	0.451497
$113$	−6.56482	−0.617566	−0.308783	−	0.951133i	$-0.599922\pi$
$113$	−6.56482	−0.617566	−0.308783	+	0.951133i	$0.599922\pi$
$114$	−6.15672	−0.576630
$115$	−0.617109	−0.0575457
$116$	−2.72736	−0.253229
$117$	−0.895940	−0.0828297
$118$	−3.73640	−0.343964
$119$	1.17570	0.107776
$120$	−7.60105	−0.693878
$121$	−8.36630	−0.760573
$122$	−24.3798	−2.20725
$123$	5.04904	0.455257
$124$	2.94077	0.264089
$125$	1.81369	0.162221
$126$	1.59029	0.141675
$127$	1.76252	0.156399	0.0781994	−	0.996938i	$-0.475083\pi$
$127$	1.76252	0.156399	0.0781994	+	0.996938i	$0.475083\pi$
$128$	−13.6526	−1.20673
$129$	−4.17425	−0.367522
$130$	4.62968	0.406050
$131$	15.4948	1.35379	0.676893	−	0.736081i	$-0.263326\pi$
$131$	15.4948	1.35379	0.676893	+	0.736081i	$0.263326\pi$
$132$	−0.858555	−0.0747277
$133$	3.87144	0.335696
$134$	23.9979	2.07310
$135$	−3.24933	−0.279658
$136$	−2.75028	−0.235835
$137$	22.2205	1.89843	0.949214	−	0.314630i	$-0.101881\pi$
$137$	22.2205	1.89843	0.949214	+	0.314630i	$0.101881\pi$
$138$	−0.302027	−0.0257102
$139$	21.1078	1.79034	0.895169	−	0.445726i	$-0.147054\pi$
$139$	21.1078	1.79034	0.895169	+	0.445726i	$0.147054\pi$
$140$	−1.71902	−0.145283
$141$	−7.08044	−0.596281
$142$	22.6608	1.90165
$143$	−1.45399	−0.121589
$144$	−4.77819	−0.398183
$145$	−16.7514	−1.39113
$146$	21.3890	1.77017
$147$	−1.00000	−0.0824786
$148$	1.97109	0.162023
$149$	−16.5693	−1.35741	−0.678705	−	0.734411i	$-0.737459\pi$
$149$	−16.5693	−1.35741	−0.678705	+	0.734411i	$0.737459\pi$
$150$	8.83913	0.721712
$151$	5.09157	0.414346	0.207173	−	0.978304i	$-0.433574\pi$
$151$	5.09157	0.414346	0.207173	+	0.978304i	$0.433574\pi$
$152$	−9.05632	−0.734564
$153$	−1.17570	−0.0950499
$154$	2.58084	0.207970
$155$	18.0622	1.45079
$156$	0.473985	0.0379492
$157$	−17.2704	−1.37833	−0.689163	−	0.724606i	$-0.742022\pi$
$157$	−17.2704	−1.37833	−0.689163	+	0.724606i	$0.742022\pi$
$158$	17.3125	1.37731
$159$	3.53771	0.280559
$160$	9.48872	0.750149
$161$	0.189919	0.0149677
$162$	−1.59029	−0.124945
$163$	−6.44788	−0.505037	−0.252519	−	0.967592i	$-0.581259\pi$
$163$	−6.44788	−0.505037	−0.252519	+	0.967592i	$0.581259\pi$
$164$	−2.67113	−0.208580
$165$	−5.27324	−0.410521
$166$	2.16394	0.167954
$167$	−16.0138	−1.23919	−0.619593	−	0.784923i	$-0.712702\pi$
$167$	−16.0138	−1.23919	−0.619593	+	0.784923i	$0.712702\pi$
$168$	2.33927	0.180478
$169$	−12.1973	−0.938253
$170$	6.07532	0.465956
$171$	−3.87144	−0.296056
$172$	2.20833	0.168384
$173$	−24.2213	−1.84151	−0.920757	−	0.390136i	$-0.872428\pi$
$173$	−24.2213	−1.84151	−0.920757	+	0.390136i	$0.872428\pi$
$174$	−8.19851	−0.621527
$175$	−5.55817	−0.420158
$176$	−7.75437	−0.584508
$177$	−2.34950	−0.176600
$178$	29.3180	2.19747
$179$	22.4133	1.67525	0.837626	−	0.546244i	$-0.183943\pi$
$179$	22.4133	1.67525	0.837626	+	0.546244i	$0.183943\pi$
$180$	1.71902	0.128128
$181$	−10.9539	−0.814199	−0.407099	−	0.913384i	$-0.633460\pi$
$181$	−10.9539	−0.814199	−0.407099	+	0.913384i	$0.633460\pi$
$182$	−1.42481	−0.105614
$183$	−15.3304	−1.13326
$184$	−0.444270	−0.0327520
$185$	12.1064	0.890081
$186$	8.84002	0.648182
$187$	−1.90801	−0.139527
$188$	3.74581	0.273191
$189$	1.00000	0.0727393
$190$	20.0053	1.45133
$191$	3.99674	0.289194	0.144597	−	0.989491i	$-0.453811\pi$
$191$	3.99674	0.289194	0.144597	+	0.989491i	$0.453811\pi$
$192$	−4.91240	−0.354522
$193$	16.7762	1.20757	0.603787	−	0.797146i	$-0.293658\pi$
$193$	16.7762	1.20757	0.603787	+	0.797146i	$0.293658\pi$
$194$	−7.32644	−0.526008
$195$	2.91121	0.208476
$196$	0.529036	0.0377883
$197$	7.83521	0.558236	0.279118	−	0.960257i	$-0.409958\pi$
$197$	7.83521	0.558236	0.279118	+	0.960257i	$0.409958\pi$
$198$	−2.58084	−0.183412
$199$	−5.35138	−0.379349	−0.189675	−	0.981847i	$-0.560743\pi$
$199$	−5.35138	−0.379349	−0.189675	+	0.981847i	$0.560743\pi$
$200$	13.0020	0.919383
$201$	15.0902	1.06438
$202$	−4.82268	−0.339322
$203$	5.15534	0.361834
$204$	0.621989	0.0435480
$205$	−16.4060	−1.14585
$206$	−8.62406	−0.600867
$207$	−0.189919	−0.0132003
$208$	4.28097	0.296832
$209$	−6.28283	−0.434592
$210$	−5.16740	−0.356584
$211$	−16.6817	−1.14842	−0.574209	−	0.818709i	$-0.694690\pi$
$211$	−16.6817	−1.14842	−0.574209	+	0.818709i	$0.694690\pi$
$212$	−1.87158	−0.128541
$213$	14.2494	0.976353
$214$	−6.50144	−0.444429
$215$	13.5635	0.925025
$216$	−2.33927	−0.159167
$217$	−5.55873	−0.377351
$218$	6.23680	0.422409
$219$	13.4497	0.908848
$220$	2.78973	0.188084
$221$	1.05336	0.0708566
$222$	5.92514	0.397669
$223$	−16.5649	−1.10927	−0.554635	−	0.832094i	$-0.687142\pi$
$223$	−16.5649	−1.10927	−0.554635	+	0.832094i	$0.687142\pi$
$224$	−2.92020	−0.195114
$225$	5.55817	0.370545
$226$	10.4400	0.694458
$227$	−2.35366	−0.156218	−0.0781089	−	0.996945i	$-0.524888\pi$
$227$	−2.35366	−0.156218	−0.0781089	+	0.996945i	$0.524888\pi$
$228$	2.04813	0.135641
$229$	12.3863	0.818510	0.409255	−	0.912420i	$-0.365789\pi$
$229$	12.3863	0.818510	0.409255	+	0.912420i	$0.365789\pi$
$230$	0.981386	0.0647106
$231$	1.62287	0.106777
$232$	−12.0597	−0.791759
$233$	−18.1192	−1.18703	−0.593515	−	0.804823i	$-0.702260\pi$
$233$	−18.1192	−1.18703	−0.593515	+	0.804823i	$0.702260\pi$
$234$	1.42481	0.0931426
$235$	23.0067	1.50079
$236$	1.24297	0.0809107
$237$	10.8863	0.707143
$238$	−1.86971	−0.121195
$239$	6.05420	0.391614	0.195807	−	0.980642i	$-0.437267\pi$
$239$	6.05420	0.391614	0.195807	+	0.980642i	$0.437267\pi$
$240$	15.5259	1.00220
$241$	−2.12467	−0.136862	−0.0684311	−	0.997656i	$-0.521799\pi$
$241$	−2.12467	−0.136862	−0.0684311	+	0.997656i	$0.521799\pi$
$242$	13.3049	0.855271
$243$	−1.00000	−0.0641500
$244$	8.11034	0.519211
$245$	3.24933	0.207592
$246$	−8.02946	−0.511940
$247$	3.46858	0.220700
$248$	13.0033	0.825713
$249$	1.36072	0.0862318
$250$	−2.88430	−0.182419
$251$	5.81890	0.367285	0.183643	−	0.982993i	$-0.441211\pi$
$251$	5.81890	0.367285	0.183643	+	0.982993i	$0.441211\pi$
$252$	−0.529036	−0.0333262
$253$	−0.308213	−0.0193772
$254$	−2.80293	−0.175872
$255$	3.82025	0.239233
$256$	11.8868	0.742925
$257$	−8.55334	−0.533543	−0.266771	−	0.963760i	$-0.585957\pi$
$257$	−8.55334	−0.533543	−0.266771	+	0.963760i	$0.585957\pi$
$258$	6.63829	0.413282
$259$	−3.72581	−0.231511
$260$	−1.54014	−0.0955151
$261$	−5.15534	−0.319108
$262$	−24.6413	−1.52234
$263$	5.75266	0.354724	0.177362	−	0.984146i	$-0.443244\pi$
$263$	5.75266	0.354724	0.177362	+	0.984146i	$0.443244\pi$
$264$	−3.79631	−0.233647
$265$	−11.4952	−0.706145
$266$	−6.15672	−0.377493
$267$	18.4356	1.12824
$268$	−7.98327	−0.487656
$269$	−21.9930	−1.34093	−0.670467	−	0.741939i	$-0.733906\pi$
$269$	−21.9930	−1.34093	−0.670467	+	0.741939i	$0.733906\pi$
$270$	5.16740	0.314478
$271$	19.5375	1.18682	0.593411	−	0.804900i	$-0.297781\pi$
$271$	19.5375	1.18682	0.593411	+	0.804900i	$0.297781\pi$
$272$	5.61773	0.340625
$273$	−0.895940	−0.0542248
$274$	−35.3372	−2.13480
$275$	9.02017	0.543937
$276$	0.100474	0.00604782
$277$	24.4011	1.46612	0.733060	−	0.680164i	$-0.238092\pi$
$277$	24.4011	1.46612	0.733060	+	0.680164i	$0.238092\pi$
$278$	−33.5676	−2.01325
$279$	5.55873	0.332793
$280$	−7.60105	−0.454250
$281$	−6.17758	−0.368524	−0.184262	−	0.982877i	$-0.558989\pi$
$281$	−6.17758	−0.368524	−0.184262	+	0.982877i	$0.558989\pi$
$282$	11.2600	0.670522
$283$	−13.0900	−0.778120	−0.389060	−	0.921212i	$-0.627200\pi$
$283$	−13.0900	−0.778120	−0.389060	+	0.921212i	$0.627200\pi$
$284$	−7.53846	−0.447325
$285$	12.5796	0.745151
$286$	2.31227	0.136728
$287$	5.04904	0.298036
$288$	2.92020	0.172075
$289$	−15.6177	−0.918690
$290$	26.6397	1.56434
$291$	−4.60697	−0.270065
$292$	−7.11539	−0.416397
$293$	23.0911	1.34899	0.674497	−	0.738278i	$-0.264361\pi$
$293$	23.0911	1.34899	0.674497	+	0.738278i	$0.264361\pi$
$294$	1.59029	0.0927479
$295$	7.63433	0.444488
$296$	8.71567	0.506588
$297$	−1.62287	−0.0941683
$298$	26.3501	1.52642
$299$	0.170156	0.00984036
$300$	−2.94048	−0.169768
$301$	−4.17425	−0.240600
$302$	−8.09709	−0.465935
$303$	−3.03257	−0.174217
$304$	18.4985	1.06096
$305$	49.8136	2.85232
$306$	1.86971	0.106884
$307$	−1.51258	−0.0863274	−0.0431637	−	0.999068i	$-0.513744\pi$
$307$	−1.51258	−0.0863274	−0.0431637	+	0.999068i	$0.513744\pi$
$308$	−0.858555	−0.0489207
$309$	−5.42293	−0.308500
$310$	−28.7242	−1.63142
$311$	20.8216	1.18069	0.590343	−	0.807153i	$-0.298993\pi$
$311$	20.8216	1.18069	0.590343	+	0.807153i	$0.298993\pi$
$312$	2.09584	0.118654
$313$	−14.4740	−0.818119	−0.409059	−	0.912508i	$-0.634143\pi$
$313$	−14.4740	−0.818119	−0.409059	+	0.912508i	$0.634143\pi$
$314$	27.4650	1.54994
$315$	−3.24933	−0.183079
$316$	−5.75926	−0.323984
$317$	9.65168	0.542092	0.271046	−	0.962566i	$-0.412630\pi$
$317$	9.65168	0.542092	0.271046	+	0.962566i	$0.412630\pi$
$318$	−5.62601	−0.315491
$319$	−8.36643	−0.468430
$320$	15.9620	0.892305
$321$	−4.08820	−0.228181
$322$	−0.302027	−0.0168313
$323$	4.55166	0.253261
$324$	0.529036	0.0293909
$325$	−4.97979	−0.276229
$326$	10.2540	0.567918
$327$	3.92179	0.216875
$328$	−11.8111	−0.652156
$329$	−7.08044	−0.390357
$330$	8.38600	0.461634
$331$	−12.0048	−0.659846	−0.329923	−	0.944008i	$-0.607023\pi$
$331$	−12.0048	−0.659846	−0.329923	+	0.944008i	$0.607023\pi$
$332$	−0.719868	−0.0395079
$333$	3.72581	0.204173
$334$	25.4667	1.39348
$335$	−49.0331	−2.67897
$336$	−4.77819	−0.260672
$337$	−17.5254	−0.954672	−0.477336	−	0.878721i	$-0.658397\pi$
$337$	−17.5254	−0.954672	−0.477336	+	0.878721i	$0.658397\pi$
$338$	19.3973	1.05507
$339$	6.56482	0.356552
$340$	−2.02105	−0.109607
$341$	9.02108	0.488519
$342$	6.15672	0.332918
$343$	−1.00000	−0.0539949
$344$	9.76468	0.526476
$345$	0.617109	0.0332240
$346$	38.5191	2.07080
$347$	18.7585	1.00701	0.503504	−	0.863993i	$-0.332044\pi$
$347$	18.7585	1.00701	0.503504	+	0.863993i	$0.332044\pi$
$348$	2.72736	0.146202
$349$	−1.08226	−0.0579321	−0.0289661	−	0.999580i	$-0.509221\pi$
$349$	−1.08226	−0.0579321	−0.0289661	+	0.999580i	$0.509221\pi$
$350$	8.83913	0.472471
$351$	0.895940	0.0478217
$352$	4.73910	0.252595
$353$	−0.715603	−0.0380877	−0.0190438	−	0.999819i	$-0.506062\pi$
$353$	−0.715603	−0.0380877	−0.0190438	+	0.999819i	$0.506062\pi$
$354$	3.73640	0.198588
$355$	−46.3011	−2.45741
$356$	−9.75308	−0.516912
$357$	−1.17570	−0.0622248
$358$	−35.6438	−1.88383
$359$	23.9066	1.26174	0.630872	−	0.775887i	$-0.282697\pi$
$359$	23.9066	1.26174	0.630872	+	0.775887i	$0.282697\pi$
$360$	7.60105	0.400611
$361$	−4.01197	−0.211157
$362$	17.4200	0.915573
$363$	8.36630	0.439117
$364$	0.473985	0.0248436
$365$	−43.7026	−2.28750
$366$	24.3798	1.27435
$367$	−23.0393	−1.20264	−0.601320	−	0.799008i	$-0.705358\pi$
$367$	−23.0393	−1.20264	−0.601320	+	0.799008i	$0.705358\pi$
$368$	0.907468	0.0473051
$369$	−5.04904	−0.262843
$370$	−19.2528	−1.00090
$371$	3.53771	0.183669
$372$	−2.94077	−0.152472
$373$	34.7390	1.79872	0.899359	−	0.437211i	$-0.144034\pi$
$373$	34.7390	1.79872	0.899359	+	0.437211i	$0.144034\pi$
$374$	3.03429	0.156900
$375$	−1.81369	−0.0936584
$376$	16.5630	0.854173
$377$	4.61888	0.237884
$378$	−1.59029	−0.0817959
$379$	8.63307	0.443451	0.221725	−	0.975109i	$-0.428831\pi$
$379$	8.63307	0.443451	0.221725	+	0.975109i	$0.428831\pi$
$380$	−6.65506	−0.341397
$381$	−1.76252	−0.0902969
$382$	−6.35599	−0.325201
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	13.6526	0.696705
$385$	−5.27324	−0.268749
$386$	−26.6790	−1.35793
$387$	4.17425	0.212189
$388$	2.43726	0.123733
$389$	−27.5144	−1.39503	−0.697517	−	0.716569i	$-0.745712\pi$
$389$	−27.5144	−1.39503	−0.697517	+	0.716569i	$0.745712\pi$
$390$	−4.62968	−0.234433
$391$	0.223288	0.0112922
$392$	2.33927	0.118151
$393$	−15.4948	−0.781609
$394$	−12.4603	−0.627741
$395$	−35.3733	−1.77982
$396$	0.858555	0.0431440
$397$	19.9785	1.00269	0.501345	−	0.865248i	$-0.332839\pi$
$397$	19.9785	1.00269	0.501345	+	0.865248i	$0.332839\pi$
$398$	8.51027	0.426581
$399$	−3.87144	−0.193814
$400$	−26.5580	−1.32790
$401$	−4.89984	−0.244686	−0.122343	−	0.992488i	$-0.539041\pi$
$401$	−4.89984	−0.244686	−0.122343	+	0.992488i	$0.539041\pi$
$402$	−23.9979	−1.19691
$403$	−4.98029	−0.248086
$404$	1.60434	0.0798189
$405$	3.24933	0.161461
$406$	−8.19851	−0.406885
$407$	6.04650	0.299714
$408$	2.75028	0.136159
$409$	26.3243	1.30165	0.650826	−	0.759227i	$-0.274423\pi$
$409$	26.3243	1.30165	0.650826	+	0.759227i	$0.274423\pi$
$410$	26.0904	1.28851
$411$	−22.2205	−1.09606
$412$	2.86893	0.141342
$413$	−2.34950	−0.115612
$414$	0.302027	0.0148438
$415$	−4.42142	−0.217039
$416$	−2.61633	−0.128276
$417$	−21.1078	−1.03365
$418$	9.99154	0.488702
$419$	5.64274	0.275666	0.137833	−	0.990455i	$-0.455986\pi$
$419$	5.64274	0.275666	0.137833	+	0.990455i	$0.455986\pi$
$420$	1.71902	0.0838794
$421$	−30.6285	−1.49274	−0.746371	−	0.665531i	$-0.768205\pi$
$421$	−30.6285	−1.49274	−0.746371	+	0.665531i	$0.768205\pi$
$422$	26.5289	1.29140
$423$	7.08044	0.344263
$424$	−8.27565	−0.401901
$425$	−6.53475	−0.316982
$426$	−22.6608	−1.09792
$427$	−15.3304	−0.741890
$428$	2.16281	0.104543
$429$	1.45399	0.0701993
$430$	−21.5700	−1.04020
$431$	21.7751	1.04887	0.524434	−	0.851451i	$-0.324277\pi$
$431$	21.7751	1.04887	0.524434	+	0.851451i	$0.324277\pi$
$432$	4.77819	0.229891
$433$	−13.0831	−0.628735	−0.314368	−	0.949301i	$-0.601792\pi$
$433$	−13.0831	−0.628735	−0.314368	+	0.949301i	$0.601792\pi$
$434$	8.84002	0.424335
$435$	16.7514	0.803169
$436$	−2.07477	−0.0993634
$437$	0.735258	0.0351722
$438$	−21.3890	−1.02201
$439$	−26.2659	−1.25360	−0.626802	−	0.779178i	$-0.715637\pi$
$439$	−26.2659	−1.25360	−0.626802	+	0.779178i	$0.715637\pi$
$440$	12.3355	0.588072
$441$	1.00000	0.0476190
$442$	−1.67515	−0.0796788
$443$	−35.8780	−1.70462	−0.852309	−	0.523039i	$-0.824798\pi$
$443$	−35.8780	−1.70462	−0.852309	+	0.523039i	$0.824798\pi$
$444$	−1.97109	−0.0935439
$445$	−59.9033	−2.83969
$446$	26.3431	1.24738
$447$	16.5693	0.783702
$448$	−4.91240	−0.232089
$449$	−8.70712	−0.410915	−0.205457	−	0.978666i	$-0.565868\pi$
$449$	−8.70712	−0.410915	−0.205457	+	0.978666i	$0.565868\pi$
$450$	−8.83913	−0.416681
$451$	−8.19392	−0.385837
$452$	−3.47303	−0.163357
$453$	−5.09157	−0.239223
$454$	3.74301	0.175668
$455$	2.91121	0.136480
$456$	9.05632	0.424101
$457$	−15.1374	−0.708097	−0.354048	−	0.935227i	$-0.615195\pi$
$457$	−15.1374	−0.708097	−0.354048	+	0.935227i	$0.615195\pi$
$458$	−19.6979	−0.920421
$459$	1.17570	0.0548771
$460$	−0.326473	−0.0152219
$461$	27.7885	1.29424	0.647121	−	0.762388i	$-0.275973\pi$
$461$	27.7885	1.29424	0.647121	+	0.762388i	$0.275973\pi$
$462$	−2.58084	−0.120071
$463$	−20.8057	−0.966924	−0.483462	−	0.875365i	$-0.660621\pi$
$463$	−20.8057	−0.966924	−0.483462	+	0.875365i	$0.660621\pi$
$464$	24.6332	1.14357
$465$	−18.0622	−0.837613
$466$	28.8149	1.33483
$467$	−0.519669	−0.0240474	−0.0120237	−	0.999928i	$-0.503827\pi$
$467$	−0.519669	−0.0240474	−0.0120237	+	0.999928i	$0.503827\pi$
$468$	−0.473985	−0.0219100
$469$	15.0902	0.696801
$470$	−36.5875	−1.68765
$471$	17.2704	0.795777
$472$	5.49612	0.252979
$473$	6.77425	0.311480
$474$	−17.3125	−0.795188
$475$	−21.5181	−0.987319
$476$	0.621989	0.0285088
$477$	−3.53771	−0.161981
$478$	−9.62796	−0.440373
$479$	4.11167	0.187867	0.0939336	−	0.995578i	$-0.470056\pi$
$479$	4.11167	0.187867	0.0939336	+	0.995578i	$0.470056\pi$
$480$	−9.48872	−0.433099
$481$	−3.33811	−0.152205
$482$	3.37885	0.153903
$483$	−0.189919	−0.00864160
$484$	−4.42608	−0.201185
$485$	14.9696	0.679734
$486$	1.59029	0.0721372
$487$	12.1880	0.552293	0.276147	−	0.961116i	$-0.410942\pi$
$487$	12.1880	0.552293	0.276147	+	0.961116i	$0.410942\pi$
$488$	35.8619	1.62339
$489$	6.44788	0.291583
$490$	−5.16740	−0.233439
$491$	7.58317	0.342224	0.171112	−	0.985252i	$-0.445264\pi$
$491$	7.58317	0.342224	0.171112	+	0.985252i	$0.445264\pi$
$492$	2.67113	0.120424
$493$	6.06114	0.272980
$494$	−5.51606	−0.248179
$495$	5.27324	0.237014
$496$	−26.5607	−1.19261
$497$	14.2494	0.639173
$498$	−2.16394	−0.0969684
$499$	22.5763	1.01065	0.505327	−	0.862928i	$-0.331372\pi$
$499$	22.5763	1.01065	0.505327	+	0.862928i	$0.331372\pi$
$500$	0.959506	0.0429104
$501$	16.0138	0.715445
$502$	−9.25376	−0.413015
$503$	−8.39812	−0.374454	−0.187227	−	0.982317i	$-0.559950\pi$
$503$	−8.39812	−0.374454	−0.187227	+	0.982317i	$0.559950\pi$
$504$	−2.33927	−0.104199
$505$	9.85383	0.438490
$506$	0.490149	0.0217898
$507$	12.1973	0.541701
$508$	0.932440	0.0413703
$509$	−23.4135	−1.03779	−0.518893	−	0.854839i	$-0.673656\pi$
$509$	−23.4135	−1.03779	−0.518893	+	0.854839i	$0.673656\pi$
$510$	−6.07532	−0.269020
$511$	13.4497	0.594981
$512$	8.40163	0.371303
$513$	3.87144	0.170928
$514$	13.6023	0.599973
$515$	17.6209	0.776471
$516$	−2.20833	−0.0972163
$517$	11.4906	0.505356
$518$	5.92514	0.260336
$519$	24.2213	1.06320
$520$	−6.81009	−0.298642
$521$	25.6683	1.12455	0.562275	−	0.826950i	$-0.309926\pi$
$521$	25.6683	1.12455	0.562275	+	0.826950i	$0.309926\pi$
$522$	8.19851	0.358839
$523$	−36.9208	−1.61443	−0.807216	−	0.590256i	$-0.799027\pi$
$523$	−36.9208	−1.61443	−0.807216	+	0.590256i	$0.799027\pi$
$524$	8.19731	0.358101
$525$	5.55817	0.242579
$526$	−9.14842	−0.398890
$527$	−6.53541	−0.284687
$528$	7.75437	0.337466
$529$	−22.9639	−0.998432
$530$	18.2808	0.794066
$531$	2.34950	0.101960
$532$	2.04813	0.0887977
$533$	4.52364	0.195941
$534$	−29.3180	−1.26871
$535$	13.2839	0.574314
$536$	−35.3000	−1.52473
$537$	−22.4133	−0.967207
$538$	34.9753	1.50789
$539$	1.62287	0.0699018
$540$	−1.71902	−0.0739747
$541$	14.1408	0.607961	0.303981	−	0.952678i	$-0.401684\pi$
$541$	14.1408	0.607961	0.303981	+	0.952678i	$0.401684\pi$
$542$	−31.0705	−1.33459
$543$	10.9539	0.470078
$544$	−3.43329	−0.147201
$545$	−12.7432	−0.545859
$546$	1.42481	0.0609762
$547$	3.31618	0.141790	0.0708949	−	0.997484i	$-0.477415\pi$
$547$	3.31618	0.141790	0.0708949	+	0.997484i	$0.477415\pi$
$548$	11.7555	0.502169
$549$	15.3304	0.654285
$550$	−14.3447	−0.611661
$551$	19.9586	0.850264
$552$	0.444270	0.0189094
$553$	10.8863	0.462934
$554$	−38.8049	−1.64866
$555$	−12.1064	−0.513889
$556$	11.1668	0.473577
$557$	13.1984	0.559235	0.279618	−	0.960111i	$-0.409792\pi$
$557$	13.1984	0.559235	0.279618	+	0.960111i	$0.409792\pi$
$558$	−8.84002	−0.374228
$559$	−3.73988	−0.158180
$560$	15.5259	0.656091
$561$	1.90801	0.0805561
$562$	9.82418	0.414408
$563$	−41.4416	−1.74656	−0.873278	−	0.487222i	$-0.838010\pi$
$563$	−41.4416	−1.74656	−0.873278	+	0.487222i	$0.838010\pi$
$564$	−3.74581	−0.157727
$565$	−21.3313	−0.897414
$566$	20.8170	0.875003
$567$	−1.00000	−0.0419961
$568$	−33.3331	−1.39863
$569$	−19.8121	−0.830566	−0.415283	−	0.909692i	$-0.636317\pi$
$569$	−19.8121	−0.830566	−0.415283	+	0.909692i	$0.636317\pi$
$570$	−20.0053	−0.837928
$571$	8.08561	0.338372	0.169186	−	0.985584i	$-0.445886\pi$
$571$	8.08561	0.338372	0.169186	+	0.985584i	$0.445886\pi$
$572$	−0.769214	−0.0321625
$573$	−3.99674	−0.166966
$574$	−8.02946	−0.335143
$575$	−1.05560	−0.0440216
$576$	4.91240	0.204683
$577$	29.1220	1.21236	0.606182	−	0.795326i	$-0.292700\pi$
$577$	29.1220	1.21236	0.606182	+	0.795326i	$0.292700\pi$
$578$	24.8368	1.03307
$579$	−16.7762	−0.697193
$580$	−8.86211	−0.367979
$581$	1.36072	0.0564520
$582$	7.32644	0.303691
$583$	−5.74124	−0.237778
$584$	−31.4625	−1.30193
$585$	−2.91121	−0.120364
$586$	−36.7216	−1.51695
$587$	−25.5434	−1.05429	−0.527144	−	0.849776i	$-0.676737\pi$
$587$	−25.5434	−1.05429	−0.527144	+	0.849776i	$0.676737\pi$
$588$	−0.529036	−0.0218171
$589$	−21.5203	−0.886728
$590$	−12.1408	−0.499830
$591$	−7.83521	−0.322298
$592$	−17.8027	−0.731685
$593$	3.12801	0.128452	0.0642261	−	0.997935i	$-0.479542\pi$
$593$	3.12801	0.128452	0.0642261	+	0.997935i	$0.479542\pi$
$594$	2.58084	0.105893
$595$	3.82025	0.156615
$596$	−8.76577	−0.359060
$597$	5.35138	0.219017
$598$	−0.270598	−0.0110656
$599$	8.35214	0.341259	0.170630	−	0.985335i	$-0.445420\pi$
$599$	8.35214	0.341259	0.170630	+	0.985335i	$0.445420\pi$
$600$	−13.0020	−0.530806
$601$	−21.3950	−0.872719	−0.436360	−	0.899772i	$-0.643732\pi$
$601$	−21.3950	−0.872719	−0.436360	+	0.899772i	$0.643732\pi$
$602$	6.63829	0.270556
$603$	−15.0902	−0.614521
$604$	2.69362	0.109602
$605$	−27.1849	−1.10522
$606$	4.82268	0.195908
$607$	20.7611	0.842666	0.421333	−	0.906906i	$-0.361562\pi$
$607$	20.7611	0.842666	0.421333	+	0.906906i	$0.361562\pi$
$608$	−11.3054	−0.458494
$609$	−5.15534	−0.208905
$610$	−79.2183	−3.20745
$611$	−6.34365	−0.256637
$612$	−0.621989	−0.0251424
$613$	−20.0351	−0.809210	−0.404605	−	0.914492i	$-0.632591\pi$
$613$	−20.0351	−0.809210	−0.404605	+	0.914492i	$0.632591\pi$
$614$	2.40544	0.0970759
$615$	16.4060	0.661555
$616$	−3.79631	−0.152958
$617$	−30.1590	−1.21416	−0.607078	−	0.794642i	$-0.707658\pi$
$617$	−30.1590	−1.21416	−0.607078	+	0.794642i	$0.707658\pi$
$618$	8.62406	0.346911
$619$	15.5566	0.625271	0.312635	−	0.949873i	$-0.398788\pi$
$619$	15.5566	0.625271	0.312635	+	0.949873i	$0.398788\pi$
$620$	9.55555	0.383760
$621$	0.189919	0.00762118
$622$	−33.1125	−1.32769
$623$	18.4356	0.738605
$624$	−4.28097	−0.171376
$625$	−21.8976	−0.875903
$626$	23.0179	0.919981
$627$	6.28283	0.250912
$628$	−9.13666	−0.364592
$629$	−4.38045	−0.174660
$630$	5.16740	0.205874
$631$	−14.8103	−0.589587	−0.294793	−	0.955561i	$-0.595251\pi$
$631$	−14.8103	−0.589587	−0.294793	+	0.955561i	$0.595251\pi$
$632$	−25.4660	−1.01298
$633$	16.6817	0.663039
$634$	−15.3490	−0.609587
$635$	5.72703	0.227270
$636$	1.87158	0.0742129
$637$	−0.895940	−0.0354984
$638$	13.3051	0.526753
$639$	−14.2494	−0.563698
$640$	−44.3618	−1.75355
$641$	29.4158	1.16185	0.580927	−	0.813956i	$-0.302690\pi$
$641$	29.4158	1.16185	0.580927	+	0.813956i	$0.302690\pi$
$642$	6.50144	0.256591
$643$	−32.8561	−1.29572	−0.647858	−	0.761761i	$-0.724335\pi$
$643$	−32.8561	−1.29572	−0.647858	+	0.761761i	$0.724335\pi$
$644$	0.100474	0.00395923
$645$	−13.5635	−0.534064
$646$	−7.23848	−0.284794
$647$	20.3245	0.799040	0.399520	−	0.916724i	$-0.369177\pi$
$647$	20.3245	0.799040	0.399520	+	0.916724i	$0.369177\pi$
$648$	2.33927	0.0918950
$649$	3.81293	0.149671
$650$	7.91933	0.310622
$651$	5.55873	0.217864
$652$	−3.41117	−0.133592
$653$	−42.6510	−1.66906	−0.834532	−	0.550959i	$-0.814262\pi$
$653$	−42.6510	−1.66906	−0.834532	+	0.550959i	$0.814262\pi$
$654$	−6.23680	−0.243878
$655$	50.3478	1.96725
$656$	24.1253	0.941935
$657$	−13.4497	−0.524724
$658$	11.2600	0.438960
$659$	36.9998	1.44131	0.720654	−	0.693295i	$-0.243842\pi$
$659$	36.9998	1.44131	0.720654	+	0.693295i	$0.243842\pi$
$660$	−2.78973	−0.108590
$661$	−7.74066	−0.301077	−0.150538	−	0.988604i	$-0.548101\pi$
$661$	−7.74066	−0.301077	−0.150538	+	0.988604i	$0.548101\pi$
$662$	19.0912	0.742002
$663$	−1.05336	−0.0409091
$664$	−3.18307	−0.123527
$665$	12.5796	0.487816
$666$	−5.92514	−0.229595
$667$	0.979095	0.0379107
$668$	−8.47189	−0.327787
$669$	16.5649	0.640437
$670$	77.9771	3.01252
$671$	24.8792	0.960450
$672$	2.92020	0.112649
$673$	0.132756	0.00511736	0.00255868	−	0.999997i	$-0.499186\pi$
$673$	0.132756	0.00511736	0.00255868	+	0.999997i	$0.499186\pi$
$674$	27.8706	1.07354
$675$	−5.55817	−0.213934
$676$	−6.45281	−0.248185
$677$	−31.3469	−1.20476	−0.602380	−	0.798209i	$-0.705781\pi$
$677$	−31.3469	−1.20476	−0.602380	+	0.798209i	$0.705781\pi$
$678$	−10.4400	−0.400945
$679$	−4.60697	−0.176799
$680$	−8.93658	−0.342702
$681$	2.35366	0.0901924
$682$	−14.3462	−0.549343
$683$	−36.5168	−1.39728	−0.698638	−	0.715475i	$-0.746210\pi$
$683$	−36.5168	−1.39728	−0.698638	+	0.715475i	$0.746210\pi$
$684$	−2.04813	−0.0783123
$685$	72.2019	2.75869
$686$	1.59029	0.0607177
$687$	−12.3863	−0.472567
$688$	−19.9454	−0.760410
$689$	3.16958	0.120751
$690$	−0.981386	−0.0373607
$691$	−30.8578	−1.17388	−0.586942	−	0.809629i	$-0.699669\pi$
$691$	−30.8578	−1.17388	−0.586942	+	0.809629i	$0.699669\pi$
$692$	−12.8140	−0.487114
$693$	−1.62287	−0.0616476
$694$	−29.8315	−1.13239
$695$	68.5862	2.60162
$696$	12.0597	0.457122
$697$	5.93617	0.224849
$698$	1.72111	0.0651452
$699$	18.1192	0.685332
$700$	−2.94048	−0.111140
$701$	−13.7214	−0.518249	−0.259124	−	0.965844i	$-0.583434\pi$
$701$	−13.7214	−0.518249	−0.259124	+	0.965844i	$0.583434\pi$
$702$	−1.42481	−0.0537759
$703$	−14.4243	−0.544021
$704$	7.97217	0.300463
$705$	−23.0067	−0.866483
$706$	1.13802	0.0428299
$707$	−3.03257	−0.114051
$708$	−1.24297	−0.0467138
$709$	−14.6288	−0.549398	−0.274699	−	0.961530i	$-0.588578\pi$
$709$	−14.6288	−0.549398	−0.274699	+	0.961530i	$0.588578\pi$
$710$	73.6324	2.76337
$711$	−10.8863	−0.408269
$712$	−43.1257	−1.61620
$713$	−1.05571	−0.0395365
$714$	1.86971	0.0699722
$715$	−4.72450	−0.176686
$716$	11.8575	0.443135
$717$	−6.05420	−0.226098
$718$	−38.0186	−1.41884
$719$	25.5534	0.952982	0.476491	−	0.879179i	$-0.341908\pi$
$719$	25.5534	0.952982	0.476491	+	0.879179i	$0.341908\pi$
$720$	−15.5259	−0.578618
$721$	−5.42293	−0.201961
$722$	6.38022	0.237447
$723$	2.12467	0.0790174
$724$	−5.79503	−0.215370
$725$	−28.6543	−1.06419
$726$	−13.3049	−0.493791
$727$	−49.0189	−1.81801	−0.909006	−	0.416784i	$-0.863157\pi$
$727$	−49.0189	−1.81801	−0.909006	+	0.416784i	$0.863157\pi$
$728$	2.09584	0.0776771
$729$	1.00000	0.0370370
$730$	69.5001	2.57231
$731$	−4.90768	−0.181517
$732$	−8.11034	−0.299767
$733$	24.4687	0.903772	0.451886	−	0.892076i	$-0.350751\pi$
$733$	24.4687	0.903772	0.451886	+	0.892076i	$0.350751\pi$
$734$	36.6392	1.35238
$735$	−3.24933	−0.119853
$736$	−0.554601	−0.0204429
$737$	−24.4894	−0.902079
$738$	8.02946	0.295569
$739$	14.0534	0.516964	0.258482	−	0.966016i	$-0.416778\pi$
$739$	14.0534	0.516964	0.258482	+	0.966016i	$0.416778\pi$
$740$	6.40473	0.235443
$741$	−3.46858	−0.127421
$742$	−5.62601	−0.206537
$743$	−48.6742	−1.78568	−0.892841	−	0.450372i	$-0.851291\pi$
$743$	−48.6742	−1.78568	−0.892841	+	0.450372i	$0.851291\pi$
$744$	−13.0033	−0.476726
$745$	−53.8392	−1.97252
$746$	−55.2453	−2.02267
$747$	−1.36072	−0.0497860
$748$	−1.00941	−0.0369075
$749$	−4.08820	−0.149380
$750$	2.88430	0.105320
$751$	−24.2195	−0.883783	−0.441892	−	0.897068i	$-0.645692\pi$
$751$	−24.2195	−0.883783	−0.441892	+	0.897068i	$0.645692\pi$
$752$	−33.8317	−1.23372
$753$	−5.81890	−0.212052
$754$	−7.34537	−0.267503
$755$	16.5442	0.602105
$756$	0.529036	0.0192409
$757$	39.0924	1.42084	0.710419	−	0.703779i	$-0.248505\pi$
$757$	39.0924	1.42084	0.710419	+	0.703779i	$0.248505\pi$
$758$	−13.7291	−0.498664
$759$	0.308213	0.0111874
$760$	−29.4270	−1.06743
$761$	−34.5200	−1.25135	−0.625675	−	0.780084i	$-0.715176\pi$
$761$	−34.5200	−1.25135	−0.625675	+	0.780084i	$0.715176\pi$
$762$	2.80293	0.101540
$763$	3.92179	0.141978
$764$	2.11442	0.0764970
$765$	−3.82025	−0.138121
$766$	1.59029	0.0574597
$767$	−2.10502	−0.0760077
$768$	−11.8868	−0.428928
$769$	−47.3281	−1.70669	−0.853347	−	0.521344i	$-0.825431\pi$
$769$	−47.3281	−1.70669	−0.853347	+	0.521344i	$0.825431\pi$
$770$	8.38600	0.302210
$771$	8.55334	0.308041
$772$	8.87520	0.319425
$773$	−32.2432	−1.15971	−0.579853	−	0.814721i	$-0.696890\pi$
$773$	−32.2432	−1.15971	−0.579853	+	0.814721i	$0.696890\pi$
$774$	−6.63829	−0.238608
$775$	30.8964	1.10983
$776$	10.7769	0.386869
$777$	3.72581	0.133663
$778$	43.7559	1.56873
$779$	19.5471	0.700346
$780$	1.54014	0.0551457
$781$	−23.1249	−0.827473
$782$	−0.355093	−0.0126981
$783$	5.15534	0.184237
$784$	−4.77819	−0.170650
$785$	−56.1172	−2.00291
$786$	24.6413	0.878926
$787$	23.3356	0.831826	0.415913	−	0.909404i	$-0.363462\pi$
$787$	23.3356	0.831826	0.415913	+	0.909404i	$0.363462\pi$
$788$	4.14511	0.147664
$789$	−5.75266	−0.204800
$790$	56.2540	2.00143
$791$	6.56482	0.233418
$792$	3.79631	0.134896
$793$	−13.7351	−0.487748
$794$	−31.7716	−1.12753
$795$	11.4952	0.407693
$796$	−2.83107	−0.100345
$797$	−8.68479	−0.307631	−0.153816	−	0.988100i	$-0.549156\pi$
$797$	−8.68479	−0.307631	−0.153816	+	0.988100i	$0.549156\pi$
$798$	6.15672	0.217946
$799$	−8.32449	−0.294499
$800$	16.2310	0.573852
$801$	−18.4356	−0.651388
$802$	7.79219	0.275152
$803$	−21.8271	−0.770262
$804$	7.98327	0.281548
$805$	0.617109	0.0217502
$806$	7.92013	0.278975
$807$	21.9930	0.774189
$808$	7.09398	0.249565
$809$	43.8217	1.54069	0.770345	−	0.637628i	$-0.220084\pi$
$809$	43.8217	1.54069	0.770345	+	0.637628i	$0.220084\pi$
$810$	−5.16740	−0.181564
$811$	−10.5752	−0.371345	−0.185673	−	0.982612i	$-0.559446\pi$
$811$	−10.5752	−0.371345	−0.185673	+	0.982612i	$0.559446\pi$
$812$	2.72736	0.0957116
$813$	−19.5375	−0.685212
$814$	−9.61571	−0.337031
$815$	−20.9513	−0.733893
$816$	−5.61773	−0.196660
$817$	−16.1603	−0.565379
$818$	−41.8633	−1.46372
$819$	0.895940	0.0313067
$820$	−8.67939	−0.303097
$821$	30.5500	1.06620	0.533102	−	0.846051i	$-0.321026\pi$
$821$	30.5500	1.06620	0.533102	+	0.846051i	$0.321026\pi$
$822$	35.3372	1.23253
$823$	−9.75881	−0.340171	−0.170085	−	0.985429i	$-0.554404\pi$
$823$	−9.75881	−0.340171	−0.170085	+	0.985429i	$0.554404\pi$
$824$	12.6857	0.441927
$825$	−9.02017	−0.314042
$826$	3.73640	0.130006
$827$	−24.0363	−0.835825	−0.417913	−	0.908487i	$-0.637238\pi$
$827$	−24.0363	−0.835825	−0.417913	+	0.908487i	$0.637238\pi$
$828$	−0.100474	−0.00349171
$829$	44.7315	1.55359	0.776795	−	0.629754i	$-0.216844\pi$
$829$	44.7315	1.55359	0.776795	+	0.629754i	$0.216844\pi$
$830$	7.03136	0.244062
$831$	−24.4011	−0.846464
$832$	−4.40122	−0.152585
$833$	−1.17570	−0.0407357
$834$	33.5676	1.16235
$835$	−52.0342	−1.80072
$836$	−3.32384	−0.114958
$837$	−5.55873	−0.192138
$838$	−8.97362	−0.309988
$839$	44.2402	1.52734	0.763670	−	0.645607i	$-0.223396\pi$
$839$	44.2402	1.52734	0.763670	+	0.645607i	$0.223396\pi$
$840$	7.60105	0.262261
$841$	−2.42247	−0.0835336
$842$	48.7083	1.67860
$843$	6.17758	0.212767
$844$	−8.82524	−0.303777
$845$	−39.6331	−1.36342
$846$	−11.2600	−0.387126
$847$	8.36630	0.287470
$848$	16.9039	0.580481
$849$	13.0900	0.449248
$850$	10.3922	0.356449
$851$	−0.707602	−0.0242563
$852$	7.53846	0.258263
$853$	33.0275	1.13084	0.565419	−	0.824804i	$-0.308714\pi$
$853$	33.0275	1.13084	0.565419	+	0.824804i	$0.308714\pi$
$854$	24.3798	0.834261
$855$	−12.5796	−0.430213
$856$	9.56338	0.326870
$857$	−24.3033	−0.830186	−0.415093	−	0.909779i	$-0.636251\pi$
$857$	−24.3033	−0.830186	−0.415093	+	0.909779i	$0.636251\pi$
$858$	−2.31227	−0.0789397
$859$	−6.17356	−0.210639	−0.105320	−	0.994438i	$-0.533587\pi$
$859$	−6.17356	−0.210639	−0.105320	+	0.994438i	$0.533587\pi$
$860$	7.17560	0.244686
$861$	−5.04904	−0.172071
$862$	−34.6288	−1.17946
$863$	−27.1239	−0.923308	−0.461654	−	0.887060i	$-0.652744\pi$
$863$	−27.1239	−0.923308	−0.461654	+	0.887060i	$0.652744\pi$
$864$	−2.92020	−0.0993473
$865$	−78.7032	−2.67599
$866$	20.8060	0.707018
$867$	15.6177	0.530406
$868$	−2.94077	−0.0998163
$869$	−17.6670	−0.599314
$870$	−26.6397	−0.903170
$871$	13.5199	0.458105
$872$	−9.17411	−0.310674
$873$	4.60697	0.155922
$874$	−1.16928	−0.0395514
$875$	−1.81369	−0.0613138
$876$	7.11539	0.240407
$877$	−40.3743	−1.36334	−0.681672	−	0.731658i	$-0.738747\pi$
$877$	−40.3743	−1.36334	−0.681672	+	0.731658i	$0.738747\pi$
$878$	41.7706	1.40969
$879$	−23.0911	−0.778842
$880$	−25.1965	−0.849375
$881$	−20.4841	−0.690126	−0.345063	−	0.938580i	$-0.612142\pi$
$881$	−20.4841	−0.690126	−0.345063	+	0.938580i	$0.612142\pi$
$882$	−1.59029	−0.0535480
$883$	3.95833	0.133208	0.0666041	−	0.997779i	$-0.478784\pi$
$883$	3.95833	0.133208	0.0666041	+	0.997779i	$0.478784\pi$
$884$	0.557265	0.0187429
$885$	−7.63433	−0.256625
$886$	57.0567	1.91686
$887$	−36.0922	−1.21186	−0.605928	−	0.795519i	$-0.707198\pi$
$887$	−36.0922	−1.21186	−0.605928	+	0.795519i	$0.707198\pi$
$888$	−8.71567	−0.292479
$889$	−1.76252	−0.0591132
$890$	95.2639	3.19325
$891$	1.62287	0.0543681
$892$	−8.76345	−0.293422
$893$	−27.4115	−0.917290
$894$	−26.3501	−0.881279
$895$	72.8284	2.43439
$896$	13.6526	0.456100
$897$	−0.170156	−0.00568134
$898$	13.8469	0.462077
$899$	−28.6571	−0.955769
$900$	2.94048	0.0980158
$901$	4.15930	0.138566
$902$	13.0307	0.433876
$903$	4.17425	0.138910
$904$	−15.3568	−0.510761
$905$	−35.5930	−1.18315
$906$	8.09709	0.269008
$907$	45.3097	1.50448	0.752242	−	0.658887i	$-0.228972\pi$
$907$	45.3097	1.50448	0.752242	+	0.658887i	$0.228972\pi$
$908$	−1.24517	−0.0413224
$909$	3.03257	0.100584
$910$	−4.62968	−0.153472
$911$	10.3012	0.341295	0.170648	−	0.985332i	$-0.445414\pi$
$911$	10.3012	0.341295	0.170648	+	0.985332i	$0.445414\pi$
$912$	−18.4985	−0.612546
$913$	−2.20826	−0.0730827
$914$	24.0729	0.796261
$915$	−49.8136	−1.64679
$916$	6.55280	0.216511
$917$	−15.4948	−0.511683
$918$	−1.86971	−0.0617097
$919$	−24.2081	−0.798551	−0.399276	−	0.916831i	$-0.630738\pi$
$919$	−24.2081	−0.798551	−0.399276	+	0.916831i	$0.630738\pi$
$920$	−1.44358	−0.0475935
$921$	1.51258	0.0498411
$922$	−44.1920	−1.45538
$923$	12.7666	0.420218
$924$	0.858555	0.0282444
$925$	20.7087	0.680898
$926$	33.0872	1.08731
$927$	5.42293	0.178112
$928$	−15.0546	−0.494193
$929$	−43.3906	−1.42360	−0.711799	−	0.702383i	$-0.752119\pi$
$929$	−43.3906	−1.42360	−0.711799	+	0.702383i	$0.752119\pi$
$930$	28.7242	0.941903
$931$	−3.87144	−0.126881
$932$	−9.58573	−0.313991
$933$	−20.8216	−0.681669
$934$	0.826426	0.0270415
$935$	−6.19975	−0.202754
$936$	−2.09584	−0.0685047
$937$	7.47776	0.244288	0.122144	−	0.992512i	$-0.461023\pi$
$937$	7.47776	0.244288	0.122144	+	0.992512i	$0.461023\pi$
$938$	−23.9979	−0.783559
$939$	14.4740	0.472341
$940$	12.1714	0.396987
$941$	−40.3009	−1.31377	−0.656886	−	0.753989i	$-0.728127\pi$
$941$	−40.3009	−1.31377	−0.656886	+	0.753989i	$0.728127\pi$
$942$	−27.4650	−0.894858
$943$	0.958908	0.0312263
$944$	−11.2264	−0.365388
$945$	3.24933	0.105701
$946$	−10.7731	−0.350262
$947$	−23.7154	−0.770646	−0.385323	−	0.922782i	$-0.625910\pi$
$947$	−23.7154	−0.770646	−0.385323	+	0.922782i	$0.625910\pi$
$948$	5.75926	0.187052
$949$	12.0501	0.391164
$950$	34.2201	1.11025
$951$	−9.65168	−0.312977
$952$	2.75028	0.0891371
$953$	53.6529	1.73799	0.868994	−	0.494822i	$-0.164767\pi$
$953$	53.6529	1.73799	0.868994	+	0.494822i	$0.164767\pi$
$954$	5.62601	0.182149
$955$	12.9867	0.420241
$956$	3.20289	0.103589
$957$	8.36643	0.270448
$958$	−6.53877	−0.211258
$959$	−22.2205	−0.717539
$960$	−15.9620	−0.515173
$961$	−0.100508	−0.00324219
$962$	5.30857	0.171155
$963$	4.08820	0.131740
$964$	−1.12403	−0.0362025
$965$	54.5114	1.75478
$966$	0.302027	0.00971755
$967$	35.0754	1.12795	0.563975	−	0.825792i	$-0.309272\pi$
$967$	35.0754	1.12795	0.563975	+	0.825792i	$0.309272\pi$
$968$	−19.5710	−0.629036
$969$	−4.55166	−0.146220
$970$	−23.8061	−0.764366
$971$	18.4287	0.591407	0.295703	−	0.955280i	$-0.404446\pi$
$971$	18.4287	0.591407	0.295703	+	0.955280i	$0.404446\pi$
$972$	−0.529036	−0.0169689
$973$	−21.1078	−0.676684
$974$	−19.3826	−0.621058
$975$	4.97979	0.159481
$976$	−73.2516	−2.34473
$977$	−4.29165	−0.137302	−0.0686510	−	0.997641i	$-0.521869\pi$
$977$	−4.29165	−0.137302	−0.0686510	+	0.997641i	$0.521869\pi$
$978$	−10.2540	−0.327888
$979$	−29.9185	−0.956198
$980$	1.71902	0.0549120
$981$	−3.92179	−0.125213
$982$	−12.0595	−0.384833
$983$	29.2127	0.931742	0.465871	−	0.884853i	$-0.345741\pi$
$983$	29.2127	0.931742	0.465871	+	0.884853i	$0.345741\pi$
$984$	11.8111	0.376523
$985$	25.4592	0.811198
$986$	−9.63900	−0.306968
$987$	7.08044	0.225373
$988$	1.83500	0.0583792
$989$	−0.792768	−0.0252086
$990$	−8.38600	−0.266524
$991$	38.4239	1.22057	0.610287	−	0.792180i	$-0.291054\pi$
$991$	38.4239	1.22057	0.610287	+	0.792180i	$0.291054\pi$
$992$	16.2326	0.515386
$993$	12.0048	0.380962
$994$	−22.6608	−0.718755
$995$	−17.3884	−0.551250
$996$	0.719868	0.0228099
$997$	−50.6313	−1.60351	−0.801754	−	0.597654i	$-0.796100\pi$
$997$	−50.6313	−1.60351	−0.801754	+	0.597654i	$0.796100\pi$
$998$	−35.9030	−1.13649
$999$	−3.72581	−0.117880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.r.1.12	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.r.1.12	✓	46	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)

\(f(q)\)	\(=\)	\(q-1.59029 q^{2} -1.00000 q^{3} +0.529036 q^{4} +3.24933 q^{5} +1.59029 q^{6} -1.00000 q^{7} +2.33927 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.59029 q^{2} -1.00000 q^{3} +0.529036 q^{4} +3.24933 q^{5} +1.59029 q^{6} -1.00000 q^{7} +2.33927 q^{8} +1.00000 q^{9} -5.16740 q^{10} +1.62287 q^{11} -0.529036 q^{12} -0.895940 q^{13} +1.59029 q^{14} -3.24933 q^{15} -4.77819 q^{16} -1.17570 q^{17} -1.59029 q^{18} -3.87144 q^{19} +1.71902 q^{20} +1.00000 q^{21} -2.58084 q^{22} -0.189919 q^{23} -2.33927 q^{24} +5.55817 q^{25} +1.42481 q^{26} -1.00000 q^{27} -0.529036 q^{28} -5.15534 q^{29} +5.16740 q^{30} +5.55873 q^{31} +2.92020 q^{32} -1.62287 q^{33} +1.86971 q^{34} -3.24933 q^{35} +0.529036 q^{36} +3.72581 q^{37} +6.15672 q^{38} +0.895940 q^{39} +7.60105 q^{40} -5.04904 q^{41} -1.59029 q^{42} +4.17425 q^{43} +0.858555 q^{44} +3.24933 q^{45} +0.302027 q^{46} +7.08044 q^{47} +4.77819 q^{48} +1.00000 q^{49} -8.83913 q^{50} +1.17570 q^{51} -0.473985 q^{52} -3.53771 q^{53} +1.59029 q^{54} +5.27324 q^{55} -2.33927 q^{56} +3.87144 q^{57} +8.19851 q^{58} +2.34950 q^{59} -1.71902 q^{60} +15.3304 q^{61} -8.84002 q^{62} -1.00000 q^{63} +4.91240 q^{64} -2.91121 q^{65} +2.58084 q^{66} -15.0902 q^{67} -0.621989 q^{68} +0.189919 q^{69} +5.16740 q^{70} -14.2494 q^{71} +2.33927 q^{72} -13.4497 q^{73} -5.92514 q^{74} -5.55817 q^{75} -2.04813 q^{76} -1.62287 q^{77} -1.42481 q^{78} -10.8863 q^{79} -15.5259 q^{80} +1.00000 q^{81} +8.02946 q^{82} -1.36072 q^{83} +0.529036 q^{84} -3.82025 q^{85} -6.63829 q^{86} +5.15534 q^{87} +3.79631 q^{88} -18.4356 q^{89} -5.16740 q^{90} +0.895940 q^{91} -0.100474 q^{92} -5.55873 q^{93} -11.2600 q^{94} -12.5796 q^{95} -2.92020 q^{96} +4.60697 q^{97} -1.59029 q^{98} +1.62287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * q^99

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