LMFDB - Embedded newform 2005.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.154915 q^{2} +0.533773 q^{3} -1.97600 q^{4} -1.00000 q^{5} +0.0826896 q^{6} +2.26312 q^{7} -0.615943 q^{8} -2.71509 q^{9} +O(q^{10})$	\(q+0.154915 q^{2} +0.533773 q^{3} -1.97600 q^{4} -1.00000 q^{5} +0.0826896 q^{6} +2.26312 q^{7} -0.615943 q^{8} -2.71509 q^{9} -0.154915 q^{10} -3.52597 q^{11} -1.05474 q^{12} +1.90318 q^{13} +0.350591 q^{14} -0.533773 q^{15} +3.85658 q^{16} +6.24946 q^{17} -0.420608 q^{18} +3.99364 q^{19} +1.97600 q^{20} +1.20799 q^{21} -0.546226 q^{22} -2.76020 q^{23} -0.328774 q^{24} +1.00000 q^{25} +0.294831 q^{26} -3.05056 q^{27} -4.47193 q^{28} -8.23445 q^{29} -0.0826896 q^{30} +8.66728 q^{31} +1.82933 q^{32} -1.88207 q^{33} +0.968136 q^{34} -2.26312 q^{35} +5.36501 q^{36} -7.40134 q^{37} +0.618675 q^{38} +1.01587 q^{39} +0.615943 q^{40} -5.38142 q^{41} +0.187136 q^{42} -9.62542 q^{43} +6.96732 q^{44} +2.71509 q^{45} -0.427596 q^{46} -10.8259 q^{47} +2.05854 q^{48} -1.87829 q^{49} +0.154915 q^{50} +3.33580 q^{51} -3.76069 q^{52} -5.84009 q^{53} -0.472578 q^{54} +3.52597 q^{55} -1.39395 q^{56} +2.13170 q^{57} -1.27564 q^{58} -9.55607 q^{59} +1.05474 q^{60} -8.52946 q^{61} +1.34269 q^{62} -6.14456 q^{63} -7.42978 q^{64} -1.90318 q^{65} -0.291561 q^{66} -6.38838 q^{67} -12.3489 q^{68} -1.47332 q^{69} -0.350591 q^{70} +5.92587 q^{71} +1.67234 q^{72} +10.8690 q^{73} -1.14658 q^{74} +0.533773 q^{75} -7.89143 q^{76} -7.97969 q^{77} +0.157373 q^{78} +14.8381 q^{79} -3.85658 q^{80} +6.51695 q^{81} -0.833663 q^{82} -13.7492 q^{83} -2.38700 q^{84} -6.24946 q^{85} -1.49112 q^{86} -4.39533 q^{87} +2.17179 q^{88} +9.87374 q^{89} +0.420608 q^{90} +4.30713 q^{91} +5.45416 q^{92} +4.62637 q^{93} -1.67710 q^{94} -3.99364 q^{95} +0.976447 q^{96} +9.69814 q^{97} -0.290975 q^{98} +9.57330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) $ 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9} + 5 q^{10} - 38 q^{11} - 6 q^{12} + 5 q^{13} - 18 q^{14} + 3 q^{15} + 7 q^{16} - 16 q^{17} - 2 q^{18} - 18 q^{19} - 19 q^{20} - 20 q^{21} - 2 q^{22} - 19 q^{23} - 19 q^{24} + 29 q^{25} - 21 q^{26} - 21 q^{27} + 26 q^{28} - 31 q^{29} + 6 q^{30} - 13 q^{31} - 30 q^{32} + 2 q^{33} - 14 q^{34} - 12 q^{35} - 29 q^{36} - q^{37} - 23 q^{38} - 39 q^{39} + 15 q^{40} - 24 q^{41} - 20 q^{42} - 27 q^{43} - 76 q^{44} - 14 q^{45} - 11 q^{46} - 5 q^{47} - 2 q^{48} - 11 q^{49} - 5 q^{50} - 58 q^{51} + 11 q^{52} - 37 q^{53} - 18 q^{54} + 38 q^{55} - 50 q^{56} - 6 q^{57} + 31 q^{58} - 67 q^{59} + 6 q^{60} - 31 q^{61} - 19 q^{62} - 2 q^{63} - 13 q^{64} - 5 q^{65} + 6 q^{66} - 17 q^{67} - 16 q^{68} - 48 q^{69} + 18 q^{70} - 53 q^{71} + 9 q^{72} + 29 q^{73} - 59 q^{74} - 3 q^{75} - 21 q^{76} - 62 q^{77} - 12 q^{78} - 13 q^{79} - 7 q^{80} - 11 q^{81} + 32 q^{82} - 72 q^{83} - 58 q^{84} + 16 q^{85} - 43 q^{86} + 4 q^{87} + 12 q^{88} - 38 q^{89} + 2 q^{90} - 45 q^{91} - 37 q^{92} - 27 q^{93} - 44 q^{94} + 18 q^{95} - 21 q^{96} + 32 q^{97} - 32 q^{98} - 107 q^{99}+O(q^{100}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9 + 5 * q^10 - 38 * q^11 - 6 * q^12 + 5 * q^13 - 18 * q^14 + 3 * q^15 + 7 * q^16 - 16 * q^17 - 2 * q^18 - 18 * q^19 - 19 * q^20 - 20 * q^21 - 2 * q^22 - 19 * q^23 - 19 * q^24 + 29 * q^25 - 21 * q^26 - 21 * q^27 + 26 * q^28 - 31 * q^29 + 6 * q^30 - 13 * q^31 - 30 * q^32 + 2 * q^33 - 14 * q^34 - 12 * q^35 - 29 * q^36 - q^37 - 23 * q^38 - 39 * q^39 + 15 * q^40 - 24 * q^41 - 20 * q^42 - 27 * q^43 - 76 * q^44 - 14 * q^45 - 11 * q^46 - 5 * q^47 - 2 * q^48 - 11 * q^49 - 5 * q^50 - 58 * q^51 + 11 * q^52 - 37 * q^53 - 18 * q^54 + 38 * q^55 - 50 * q^56 - 6 * q^57 + 31 * q^58 - 67 * q^59 + 6 * q^60 - 31 * q^61 - 19 * q^62 - 2 * q^63 - 13 * q^64 - 5 * q^65 + 6 * q^66 - 17 * q^67 - 16 * q^68 - 48 * q^69 + 18 * q^70 - 53 * q^71 + 9 * q^72 + 29 * q^73 - 59 * q^74 - 3 * q^75 - 21 * q^76 - 62 * q^77 - 12 * q^78 - 13 * q^79 - 7 * q^80 - 11 * q^81 + 32 * q^82 - 72 * q^83 - 58 * q^84 + 16 * q^85 - 43 * q^86 + 4 * q^87 + 12 * q^88 - 38 * q^89 + 2 * q^90 - 45 * q^91 - 37 * q^92 - 27 * q^93 - 44 * q^94 + 18 * q^95 - 21 * q^96 + 32 * q^97 - 32 * q^98 - 107 * 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 $

$2$	0.154915	0.109542	0.0547708	−	0.998499i	$-0.482557\pi$
$2$	0.154915	0.109542	0.0547708	+	0.998499i	$0.482557\pi$
$3$	0.533773	0.308174	0.154087	−	0.988057i	$-0.450756\pi$
$3$	0.533773	0.308174	0.154087	+	0.988057i	$0.450756\pi$
$4$	−1.97600	−0.988001
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.0826896	0.0337579
$7$	2.26312	0.855379	0.427689	−	0.903926i	$-0.359328\pi$
$7$	2.26312	0.855379	0.427689	+	0.903926i	$0.359328\pi$
$8$	−0.615943	−0.217769
$9$	−2.71509	−0.905029
$10$	−0.154915	−0.0489885
$11$	−3.52597	−1.06312	−0.531560	−	0.847021i	$-0.678394\pi$
$11$	−3.52597	−1.06312	−0.531560	+	0.847021i	$0.678394\pi$
$12$	−1.05474	−0.304476
$13$	1.90318	0.527847	0.263924	−	0.964544i	$-0.414983\pi$
$13$	1.90318	0.527847	0.263924	+	0.964544i	$0.414983\pi$
$14$	0.350591	0.0936995
$15$	−0.533773	−0.137820
$16$	3.85658	0.964146
$17$	6.24946	1.51572	0.757858	−	0.652419i	$-0.226246\pi$
$17$	6.24946	1.51572	0.757858	+	0.652419i	$0.226246\pi$
$18$	−0.420608	−0.0991382
$19$	3.99364	0.916203	0.458102	−	0.888900i	$-0.348530\pi$
$19$	3.99364	0.916203	0.458102	+	0.888900i	$0.348530\pi$
$20$	1.97600	0.441847
$21$	1.20799	0.263606
$22$	−0.546226	−0.116456
$23$	−2.76020	−0.575541	−0.287771	−	0.957699i	$-0.592914\pi$
$23$	−2.76020	−0.575541	−0.287771	+	0.957699i	$0.592914\pi$
$24$	−0.328774	−0.0671107
$25$	1.00000	0.200000
$26$	0.294831	0.0578212
$27$	−3.05056	−0.587081
$28$	−4.47193	−0.845115
$29$	−8.23445	−1.52910	−0.764550	−	0.644565i	$-0.777039\pi$
$29$	−8.23445	−1.52910	−0.764550	+	0.644565i	$0.777039\pi$
$30$	−0.0826896	−0.0150970
$31$	8.66728	1.55669	0.778345	−	0.627837i	$-0.216059\pi$
$31$	8.66728	1.55669	0.778345	+	0.627837i	$0.216059\pi$
$32$	1.82933	0.323383
$33$	−1.88207	−0.327626
$34$	0.968136	0.166034
$35$	−2.26312	−0.382537
$36$	5.36501	0.894169
$37$	−7.40134	−1.21677	−0.608386	−	0.793641i	$-0.708183\pi$
$37$	−7.40134	−1.21677	−0.608386	+	0.793641i	$0.708183\pi$
$38$	0.618675	0.100362
$39$	1.01587	0.162669
$40$	0.615943	0.0973891
$41$	−5.38142	−0.840437	−0.420218	−	0.907423i	$-0.638047\pi$
$41$	−5.38142	−0.840437	−0.420218	+	0.907423i	$0.638047\pi$
$42$	0.187136	0.0288758
$43$	−9.62542	−1.46786	−0.733931	−	0.679224i	$-0.762317\pi$
$43$	−9.62542	−1.46786	−0.733931	+	0.679224i	$0.762317\pi$
$44$	6.96732	1.05036
$45$	2.71509	0.404741
$46$	−0.427596	−0.0630457
$47$	−10.8259	−1.57913	−0.789563	−	0.613669i	$-0.789693\pi$
$47$	−10.8259	−1.57913	−0.789563	+	0.613669i	$0.789693\pi$
$48$	2.05854	0.297125
$49$	−1.87829	−0.268327
$50$	0.154915	0.0219083
$51$	3.33580	0.467105
$52$	−3.76069	−0.521514
$53$	−5.84009	−0.802199	−0.401099	−	0.916035i	$-0.631372\pi$
$53$	−5.84009	−0.802199	−0.401099	+	0.916035i	$0.631372\pi$
$54$	−0.472578	−0.0643097
$55$	3.52597	0.475441
$56$	−1.39395	−0.186275
$57$	2.13170	0.282350
$58$	−1.27564	−0.167500
$59$	−9.55607	−1.24409	−0.622047	−	0.782980i	$-0.713699\pi$
$59$	−9.55607	−1.24409	−0.622047	+	0.782980i	$0.713699\pi$
$60$	1.05474	0.136166
$61$	−8.52946	−1.09208	−0.546042	−	0.837757i	$-0.683866\pi$
$61$	−8.52946	−1.09208	−0.546042	+	0.837757i	$0.683866\pi$
$62$	1.34269	0.170522
$63$	−6.14456	−0.774142
$64$	−7.42978	−0.928722
$65$	−1.90318	−0.236061
$66$	−0.291561	−0.0358886
$67$	−6.38838	−0.780465	−0.390233	−	0.920716i	$-0.627605\pi$
$67$	−6.38838	−0.780465	−0.390233	+	0.920716i	$0.627605\pi$
$68$	−12.3489	−1.49753
$69$	−1.47332	−0.177367
$70$	−0.350591	−0.0419037
$71$	5.92587	0.703272	0.351636	−	0.936137i	$-0.385626\pi$
$71$	5.92587	0.703272	0.351636	+	0.936137i	$0.385626\pi$
$72$	1.67234	0.197087
$73$	10.8690	1.27211	0.636057	−	0.771642i	$-0.280564\pi$
$73$	10.8690	1.27211	0.636057	+	0.771642i	$0.280564\pi$
$74$	−1.14658	−0.133287
$75$	0.533773	0.0616349
$76$	−7.89143	−0.905209
$77$	−7.97969	−0.909370
$78$	0.157373	0.0178190
$79$	14.8381	1.66941	0.834706	−	0.550696i	$-0.185638\pi$
$79$	14.8381	1.66941	0.834706	+	0.550696i	$0.185638\pi$
$80$	−3.85658	−0.431179
$81$	6.51695	0.724105
$82$	−0.833663	−0.0920627
$83$	−13.7492	−1.50917	−0.754586	−	0.656201i	$-0.772162\pi$
$83$	−13.7492	−1.50917	−0.754586	+	0.656201i	$0.772162\pi$
$84$	−2.38700	−0.260443
$85$	−6.24946	−0.677849
$86$	−1.49112	−0.160792
$87$	−4.39533	−0.471229
$88$	2.17179	0.231514
$89$	9.87374	1.04661	0.523307	−	0.852144i	$-0.324698\pi$
$89$	9.87374	1.04661	0.523307	+	0.852144i	$0.324698\pi$
$90$	0.420608	0.0443360
$91$	4.30713	0.451509
$92$	5.45416	0.568635
$93$	4.62637	0.479732
$94$	−1.67710	−0.172980
$95$	−3.99364	−0.409739
$96$	0.976447	0.0996582
$97$	9.69814	0.984697	0.492348	−	0.870398i	$-0.336139\pi$
$97$	9.69814	0.984697	0.492348	+	0.870398i	$0.336139\pi$
$98$	−0.290975	−0.0293930
$99$	9.57330	0.962153
$100$	−1.97600	−0.197600
$101$	0.659390	0.0656118	0.0328059	−	0.999462i	$-0.489556\pi$
$101$	0.659390	0.0656118	0.0328059	+	0.999462i	$0.489556\pi$
$102$	0.516765	0.0511674
$103$	−5.77645	−0.569170	−0.284585	−	0.958651i	$-0.591856\pi$
$103$	−5.77645	−0.569170	−0.284585	+	0.958651i	$0.591856\pi$
$104$	−1.17225	−0.114949
$105$	−1.20799	−0.117888
$106$	−0.904719	−0.0878741
$107$	4.65899	0.450401	0.225201	−	0.974312i	$-0.427696\pi$
$107$	4.65899	0.450401	0.225201	+	0.974312i	$0.427696\pi$
$108$	6.02791	0.580036
$109$	−8.46360	−0.810666	−0.405333	−	0.914169i	$-0.632844\pi$
$109$	−8.46360	−0.810666	−0.405333	+	0.914169i	$0.632844\pi$
$110$	0.546226	0.0520806
$111$	−3.95064	−0.374978
$112$	8.72791	0.824710
$113$	−13.5414	−1.27386	−0.636932	−	0.770920i	$-0.719797\pi$
$113$	−13.5414	−1.27386	−0.636932	+	0.770920i	$0.719797\pi$
$114$	0.330232	0.0309291
$115$	2.76020	0.257390
$116$	16.2713	1.51075
$117$	−5.16730	−0.477717
$118$	−1.48038	−0.136280
$119$	14.1433	1.29651
$120$	0.328774	0.0300128
$121$	1.43244	0.130222
$122$	−1.32134	−0.119629
$123$	−2.87246	−0.259001
$124$	−17.1266	−1.53801
$125$	−1.00000	−0.0894427
$126$	−0.951886	−0.0848007
$127$	15.9726	1.41734	0.708670	−	0.705540i	$-0.249295\pi$
$127$	15.9726	1.41734	0.708670	+	0.705540i	$0.249295\pi$
$128$	−4.80964	−0.425116
$129$	−5.13779	−0.452358
$130$	−0.294831	−0.0258584
$131$	−6.25620	−0.546607	−0.273304	−	0.961928i	$-0.588116\pi$
$131$	−6.25620	−0.546607	−0.273304	+	0.961928i	$0.588116\pi$
$132$	3.71897	0.323695
$133$	9.03808	0.783701
$134$	−0.989657	−0.0854933
$135$	3.05056	0.262551
$136$	−3.84931	−0.330075
$137$	−4.66215	−0.398315	−0.199157	−	0.979968i	$-0.563820\pi$
$137$	−4.66215	−0.398315	−0.199157	+	0.979968i	$0.563820\pi$
$138$	−0.228240	−0.0194290
$139$	−14.0347	−1.19040	−0.595202	−	0.803576i	$-0.702928\pi$
$139$	−14.0347	−1.19040	−0.595202	+	0.803576i	$0.702928\pi$
$140$	4.47193	0.377947
$141$	−5.77860	−0.486646
$142$	0.918007	0.0770375
$143$	−6.71055	−0.561165
$144$	−10.4710	−0.872580
$145$	8.23445	0.683834
$146$	1.68376	0.139349
$147$	−1.00258	−0.0826915
$148$	14.6251	1.20217
$149$	−2.62110	−0.214729	−0.107365	−	0.994220i	$-0.534241\pi$
$149$	−2.62110	−0.214729	−0.107365	+	0.994220i	$0.534241\pi$
$150$	0.0826896	0.00675157
$151$	−5.46157	−0.444457	−0.222228	−	0.974995i	$-0.571333\pi$
$151$	−5.46157	−0.444457	−0.222228	+	0.974995i	$0.571333\pi$
$152$	−2.45985	−0.199520
$153$	−16.9678	−1.37177
$154$	−1.23617	−0.0996137
$155$	−8.66728	−0.696173
$156$	−2.00736	−0.160717
$157$	13.3376	1.06445	0.532227	−	0.846602i	$-0.321355\pi$
$157$	13.3376	1.06445	0.532227	+	0.846602i	$0.321355\pi$
$158$	2.29864	0.182870
$159$	−3.11729	−0.247217
$160$	−1.82933	−0.144621
$161$	−6.24666	−0.492306
$162$	1.00957	0.0793196
$163$	−16.9643	−1.32875	−0.664375	−	0.747399i	$-0.731302\pi$
$163$	−16.9643	−1.32875	−0.664375	+	0.747399i	$0.731302\pi$
$164$	10.6337	0.830352
$165$	1.88207	0.146519
$166$	−2.12996	−0.165317
$167$	2.06154	0.159527	0.0797634	−	0.996814i	$-0.474584\pi$
$167$	2.06154	0.159527	0.0797634	+	0.996814i	$0.474584\pi$
$168$	−0.744055	−0.0574051
$169$	−9.37790	−0.721377
$170$	−0.968136	−0.0742526
$171$	−10.8431	−0.829190
$172$	19.0198	1.45025
$173$	−18.1996	−1.38369	−0.691843	−	0.722048i	$-0.743201\pi$
$173$	−18.1996	−1.38369	−0.691843	+	0.722048i	$0.743201\pi$
$174$	−0.680903	−0.0516192
$175$	2.26312	0.171076
$176$	−13.5982	−1.02500
$177$	−5.10078	−0.383398
$178$	1.52959	0.114648
$179$	−5.77028	−0.431291	−0.215645	−	0.976472i	$-0.569186\pi$
$179$	−5.77028	−0.431291	−0.215645	+	0.976472i	$0.569186\pi$
$180$	−5.36501	−0.399884
$181$	−13.3376	−0.991373	−0.495686	−	0.868502i	$-0.665083\pi$
$181$	−13.3376	−0.991373	−0.495686	+	0.868502i	$0.665083\pi$
$182$	0.667239	0.0494590
$183$	−4.55280	−0.336552
$184$	1.70012	0.125335
$185$	7.40134	0.544157
$186$	0.716694	0.0525506
$187$	−22.0354	−1.61139
$188$	21.3921	1.56018
$189$	−6.90379	−0.502176
$190$	−0.618675	−0.0448834
$191$	21.1610	1.53115	0.765577	−	0.643344i	$-0.222454\pi$
$191$	21.1610	1.53115	0.765577	+	0.643344i	$0.222454\pi$
$192$	−3.96582	−0.286208
$193$	9.59074	0.690356	0.345178	−	0.938537i	$-0.387818\pi$
$193$	9.59074	0.690356	0.345178	+	0.938537i	$0.387818\pi$
$194$	1.50239	0.107865
$195$	−1.01587	−0.0727478
$196$	3.71150	0.265107
$197$	4.73503	0.337357	0.168678	−	0.985671i	$-0.446050\pi$
$197$	4.73503	0.337357	0.168678	+	0.985671i	$0.446050\pi$
$198$	1.48305	0.105396
$199$	−23.7154	−1.68114	−0.840571	−	0.541701i	$-0.817781\pi$
$199$	−23.7154	−1.68114	−0.840571	+	0.541701i	$0.817781\pi$
$200$	−0.615943	−0.0435537
$201$	−3.40995	−0.240519
$202$	0.102149	0.00718721
$203$	−18.6356	−1.30796
$204$	−6.59154	−0.461500
$205$	5.38142	0.375855
$206$	−0.894859	−0.0623478
$207$	7.49418	0.520881
$208$	7.33978	0.508922
$209$	−14.0814	−0.974033
$210$	−0.187136	−0.0129136
$211$	20.5590	1.41534	0.707669	−	0.706544i	$-0.249747\pi$
$211$	20.5590	1.41534	0.707669	+	0.706544i	$0.249747\pi$
$212$	11.5400	0.792573
$213$	3.16307	0.216730
$214$	0.721748	0.0493377
$215$	9.62542	0.656448
$216$	1.87897	0.127848
$217$	19.6151	1.33156
$218$	−1.31114	−0.0888016
$219$	5.80156	0.392033
$220$	−6.96732	−0.469736
$221$	11.8939	0.800067
$222$	−0.612013	−0.0410756
$223$	−13.4228	−0.898857	−0.449428	−	0.893316i	$-0.648372\pi$
$223$	−13.4228	−0.898857	−0.449428	+	0.893316i	$0.648372\pi$
$224$	4.13999	0.276615
$225$	−2.71509	−0.181006
$226$	−2.09776	−0.139541
$227$	10.6452	0.706545	0.353272	−	0.935521i	$-0.385069\pi$
$227$	10.6452	0.706545	0.353272	+	0.935521i	$0.385069\pi$
$228$	−4.21224	−0.278962
$229$	17.2720	1.14137	0.570684	−	0.821169i	$-0.306678\pi$
$229$	17.2720	1.14137	0.570684	+	0.821169i	$0.306678\pi$
$230$	0.427596	0.0281949
$231$	−4.25934	−0.280244
$232$	5.07195	0.332990
$233$	0.702842	0.0460447	0.0230223	−	0.999735i	$-0.492671\pi$
$233$	0.702842	0.0460447	0.0230223	+	0.999735i	$0.492671\pi$
$234$	−0.800493	−0.0523298
$235$	10.8259	0.706207
$236$	18.8828	1.22917
$237$	7.92016	0.514470
$238$	2.19101	0.142022
$239$	25.3198	1.63780	0.818900	−	0.573936i	$-0.194584\pi$
$239$	25.3198	1.63780	0.818900	+	0.573936i	$0.194584\pi$
$240$	−2.05854	−0.132878
$241$	−19.9912	−1.28775	−0.643873	−	0.765132i	$-0.722674\pi$
$241$	−19.9912	−1.28775	−0.643873	+	0.765132i	$0.722674\pi$
$242$	0.221907	0.0142647
$243$	12.6303	0.810231
$244$	16.8542	1.07898
$245$	1.87829	0.120000
$246$	−0.444987	−0.0283714
$247$	7.60061	0.483615
$248$	−5.33855	−0.338998
$249$	−7.33897	−0.465088
$250$	−0.154915	−0.00979769
$251$	16.2111	1.02323	0.511616	−	0.859214i	$-0.329047\pi$
$251$	16.2111	1.02323	0.511616	+	0.859214i	$0.329047\pi$
$252$	12.1417	0.764853
$253$	9.73237	0.611869
$254$	2.47440	0.155258
$255$	−3.33580	−0.208896
$256$	14.1145	0.882154
$257$	3.96583	0.247382	0.123691	−	0.992321i	$-0.460527\pi$
$257$	3.96583	0.247382	0.123691	+	0.992321i	$0.460527\pi$
$258$	−0.795922	−0.0495519
$259$	−16.7501	−1.04080
$260$	3.76069	0.233228
$261$	22.3573	1.38388
$262$	−0.969180	−0.0598762
$263$	−3.76832	−0.232365	−0.116182	−	0.993228i	$-0.537066\pi$
$263$	−3.76832	−0.232365	−0.116182	+	0.993228i	$0.537066\pi$
$264$	1.15925	0.0713466
$265$	5.84009	0.358754
$266$	1.40013	0.0858478
$267$	5.27034	0.322540
$268$	12.6235	0.771100
$269$	−5.99220	−0.365351	−0.182675	−	0.983173i	$-0.558476\pi$
$269$	−5.99220	−0.365351	−0.182675	+	0.983173i	$0.558476\pi$
$270$	0.472578	0.0287602
$271$	−21.5486	−1.30899	−0.654493	−	0.756068i	$-0.727118\pi$
$271$	−21.5486	−1.30899	−0.654493	+	0.756068i	$0.727118\pi$
$272$	24.1016	1.46137
$273$	2.29903	0.139144
$274$	−0.722238	−0.0436320
$275$	−3.52597	−0.212624
$276$	2.91128	0.175239
$277$	−9.49032	−0.570218	−0.285109	−	0.958495i	$-0.592030\pi$
$277$	−9.49032	−0.570218	−0.285109	+	0.958495i	$0.592030\pi$
$278$	−2.17418	−0.130399
$279$	−23.5324	−1.40885
$280$	1.39395	0.0833046
$281$	3.03281	0.180922	0.0904612	−	0.995900i	$-0.471166\pi$
$281$	3.03281	0.180922	0.0904612	+	0.995900i	$0.471166\pi$
$282$	−0.895193	−0.0533080
$283$	16.2013	0.963067	0.481534	−	0.876428i	$-0.340080\pi$
$283$	16.2013	0.963067	0.481534	+	0.876428i	$0.340080\pi$
$284$	−11.7095	−0.694833
$285$	−2.13170	−0.126271
$286$	−1.03957	−0.0614708
$287$	−12.1788	−0.718892
$288$	−4.96678	−0.292671
$289$	22.0557	1.29740
$290$	1.27564	0.0749082
$291$	5.17661	0.303458
$292$	−21.4771	−1.25685
$293$	−11.4719	−0.670195	−0.335097	−	0.942183i	$-0.608769\pi$
$293$	−11.4719	−0.670195	−0.335097	+	0.942183i	$0.608769\pi$
$294$	−0.155315	−0.00905815
$295$	9.55607	0.556376
$296$	4.55880	0.264975
$297$	10.7562	0.624137
$298$	−0.406048	−0.0235218
$299$	−5.25316	−0.303798
$300$	−1.05474	−0.0608953
$301$	−21.7835	−1.25558
$302$	−0.846080	−0.0486865
$303$	0.351965	0.0202199
$304$	15.4018	0.883354
$305$	8.52946	0.488395
$306$	−2.62857	−0.150265
$307$	−14.9149	−0.851237	−0.425618	−	0.904903i	$-0.639943\pi$
$307$	−14.9149	−0.851237	−0.425618	+	0.904903i	$0.639943\pi$
$308$	15.7679	0.898458
$309$	−3.08331	−0.175404
$310$	−1.34269	−0.0762598
$311$	−13.3468	−0.756829	−0.378415	−	0.925636i	$-0.623531\pi$
$311$	−13.3468	−0.756829	−0.378415	+	0.925636i	$0.623531\pi$
$312$	−0.625716	−0.0354242
$313$	33.6209	1.90037	0.950184	−	0.311690i	$-0.100895\pi$
$313$	33.6209	1.90037	0.950184	+	0.311690i	$0.100895\pi$
$314$	2.06619	0.116602
$315$	6.14456	0.346207
$316$	−29.3200	−1.64938
$317$	−10.5030	−0.589905	−0.294953	−	0.955512i	$-0.595304\pi$
$317$	−10.5030	−0.589905	−0.294953	+	0.955512i	$0.595304\pi$
$318$	−0.482915	−0.0270805
$319$	29.0344	1.62562
$320$	7.42978	0.415337
$321$	2.48684	0.138802
$322$	−0.967702	−0.0539279
$323$	24.9581	1.38870
$324$	−12.8775	−0.715417
$325$	1.90318	0.105569
$326$	−2.62803	−0.145553
$327$	−4.51764	−0.249826
$328$	3.31465	0.183021
$329$	−24.5004	−1.35075
$330$	0.291561	0.0160499
$331$	25.1597	1.38290	0.691452	−	0.722423i	$-0.256971\pi$
$331$	25.1597	1.38290	0.691452	+	0.722423i	$0.256971\pi$
$332$	27.1685	1.49106
$333$	20.0953	1.10121
$334$	0.319364	0.0174748
$335$	6.38838	0.349035
$336$	4.65873	0.254154
$337$	−4.66612	−0.254180	−0.127090	−	0.991891i	$-0.540564\pi$
$337$	−4.66612	−0.254180	−0.127090	+	0.991891i	$0.540564\pi$
$338$	−1.45278	−0.0790207
$339$	−7.22801	−0.392572
$340$	12.3489	0.669715
$341$	−30.5606	−1.65495
$342$	−1.67975	−0.0908307
$343$	−20.0926	−1.08490
$344$	5.92871	0.319654
$345$	1.47332	0.0793209
$346$	−2.81939	−0.151571
$347$	24.0434	1.29072	0.645358	−	0.763880i	$-0.276708\pi$
$347$	24.0434	1.29072	0.645358	+	0.763880i	$0.276708\pi$
$348$	8.68518	0.465575
$349$	22.8086	1.22092	0.610458	−	0.792049i	$-0.290985\pi$
$349$	22.8086	1.22092	0.610458	+	0.792049i	$0.290985\pi$
$350$	0.350591	0.0187399
$351$	−5.80577	−0.309889
$352$	−6.45015	−0.343794
$353$	−20.5374	−1.09310	−0.546548	−	0.837428i	$-0.684059\pi$
$353$	−20.5374	−1.09310	−0.546548	+	0.837428i	$0.684059\pi$
$354$	−0.790188	−0.0419980
$355$	−5.92587	−0.314513
$356$	−19.5105	−1.03406
$357$	7.54930	0.399552
$358$	−0.893903	−0.0472443
$359$	5.70509	0.301103	0.150552	−	0.988602i	$-0.451895\pi$
$359$	5.70509	0.301103	0.150552	+	0.988602i	$0.451895\pi$
$360$	−1.67234	−0.0881399
$361$	−3.05086	−0.160572
$362$	−2.06619	−0.108596
$363$	0.764600	0.0401311
$364$	−8.51089	−0.446092
$365$	−10.8690	−0.568907
$366$	−0.705297	−0.0368665
$367$	12.1119	0.632234	0.316117	−	0.948720i	$-0.397621\pi$
$367$	12.1119	0.632234	0.316117	+	0.948720i	$0.397621\pi$
$368$	−10.6449	−0.554906
$369$	14.6110	0.760619
$370$	1.14658	0.0596078
$371$	−13.2168	−0.686184
$372$	−9.14171	−0.473975
$373$	4.23567	0.219315	0.109657	−	0.993969i	$-0.465025\pi$
$373$	4.23567	0.219315	0.109657	+	0.993969i	$0.465025\pi$
$374$	−3.41361	−0.176514
$375$	−0.533773	−0.0275639
$376$	6.66816	0.343884
$377$	−15.6717	−0.807131
$378$	−1.06950	−0.0550092
$379$	−9.51719	−0.488865	−0.244433	−	0.969666i	$-0.578602\pi$
$379$	−9.51719	−0.488865	−0.244433	+	0.969666i	$0.578602\pi$
$380$	7.89143	0.404822
$381$	8.52576	0.436788
$382$	3.27815	0.167725
$383$	−4.18038	−0.213608	−0.106804	−	0.994280i	$-0.534062\pi$
$383$	−4.18038	−0.213608	−0.106804	+	0.994280i	$0.534062\pi$
$384$	−2.56726	−0.131010
$385$	7.97969	0.406682
$386$	1.48575	0.0756227
$387$	26.1338	1.32846
$388$	−19.1635	−0.972881
$389$	−7.85354	−0.398190	−0.199095	−	0.979980i	$-0.563800\pi$
$389$	−7.85354	−0.398190	−0.199095	+	0.979980i	$0.563800\pi$
$390$	−0.157373	−0.00796890
$391$	−17.2497	−0.872357
$392$	1.15692	0.0584332
$393$	−3.33940	−0.168450
$394$	0.733527	0.0369546
$395$	−14.8381	−0.746583
$396$	−18.9169	−0.950608
$397$	2.58902	0.129939	0.0649696	−	0.997887i	$-0.479305\pi$
$397$	2.58902	0.129939	0.0649696	+	0.997887i	$0.479305\pi$
$398$	−3.67388	−0.184155
$399$	4.82429	0.241516
$400$	3.85658	0.192829
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−0.528253	−0.0263468
$403$	16.4954	0.821695
$404$	−1.30296	−0.0648245
$405$	−6.51695	−0.323830
$406$	−2.88693	−0.143276
$407$	26.0969	1.29357
$408$	−2.05466	−0.101721
$409$	−26.9443	−1.33231	−0.666155	−	0.745813i	$-0.732061\pi$
$409$	−26.9443	−1.33231	−0.666155	+	0.745813i	$0.732061\pi$
$410$	0.833663	0.0411717
$411$	−2.48853	−0.122750
$412$	11.4143	0.562341
$413$	−21.6265	−1.06417
$414$	1.16096	0.0570581
$415$	13.7492	0.674922
$416$	3.48154	0.170697
$417$	−7.49133	−0.366852
$418$	−2.18143	−0.106697
$419$	17.8957	0.874261	0.437130	−	0.899398i	$-0.355995\pi$
$419$	17.8957	0.874261	0.437130	+	0.899398i	$0.355995\pi$
$420$	2.38700	0.116473
$421$	−23.3810	−1.13952	−0.569760	−	0.821811i	$-0.692964\pi$
$421$	−23.3810	−1.13952	−0.569760	+	0.821811i	$0.692964\pi$
$422$	3.18490	0.155038
$423$	29.3934	1.42915
$424$	3.59716	0.174694
$425$	6.24946	0.303143
$426$	0.490008	0.0237410
$427$	−19.3032	−0.934146
$428$	−9.20617	−0.444997
$429$	−3.58192	−0.172936
$430$	1.49112	0.0719083
$431$	14.3609	0.691742	0.345871	−	0.938282i	$-0.387584\pi$
$431$	14.3609	0.691742	0.345871	+	0.938282i	$0.387584\pi$
$432$	−11.7647	−0.566032
$433$	17.8671	0.858636	0.429318	−	0.903153i	$-0.358754\pi$
$433$	17.8671	0.858636	0.429318	+	0.903153i	$0.358754\pi$
$434$	3.03868	0.145861
$435$	4.39533	0.210740
$436$	16.7241	0.800938
$437$	−11.0232	−0.527313
$438$	0.898749	0.0429439
$439$	−2.14329	−0.102294	−0.0511468	−	0.998691i	$-0.516288\pi$
$439$	−2.14329	−0.102294	−0.0511468	+	0.998691i	$0.516288\pi$
$440$	−2.17179	−0.103536
$441$	5.09972	0.242844
$442$	1.84254	0.0876406
$443$	0.874206	0.0415348	0.0207674	−	0.999784i	$-0.493389\pi$
$443$	0.874206	0.0415348	0.0207674	+	0.999784i	$0.493389\pi$
$444$	7.80646	0.370478
$445$	−9.87374	−0.468060
$446$	−2.07939	−0.0984621
$447$	−1.39908	−0.0661740
$448$	−16.8145	−0.794409
$449$	7.07420	0.333852	0.166926	−	0.985969i	$-0.446616\pi$
$449$	7.07420	0.333852	0.166926	+	0.985969i	$0.446616\pi$
$450$	−0.420608	−0.0198276
$451$	18.9747	0.893484
$452$	26.7577	1.25858
$453$	−2.91524	−0.136970
$454$	1.64910	0.0773960
$455$	−4.30713	−0.201921
$456$	−1.31300	−0.0614870
$457$	−13.6228	−0.637247	−0.318624	−	0.947881i	$-0.603221\pi$
$457$	−13.6228	−0.637247	−0.318624	+	0.947881i	$0.603221\pi$
$458$	2.67570	0.125027
$459$	−19.0644	−0.889848
$460$	−5.45416	−0.254301
$461$	6.38888	0.297560	0.148780	−	0.988870i	$-0.452465\pi$
$461$	6.38888	0.297560	0.148780	+	0.988870i	$0.452465\pi$
$462$	−0.659837	−0.0306984
$463$	−31.1592	−1.44809	−0.724045	−	0.689753i	$-0.757719\pi$
$463$	−31.1592	−1.44809	−0.724045	+	0.689753i	$0.757719\pi$
$464$	−31.7569	−1.47428
$465$	−4.62637	−0.214543
$466$	0.108881	0.00504380
$467$	−15.0806	−0.697846	−0.348923	−	0.937151i	$-0.613452\pi$
$467$	−15.0806	−0.697846	−0.348923	+	0.937151i	$0.613452\pi$
$468$	10.2106	0.471985
$469$	−14.4577	−0.667593
$470$	1.67710	0.0773590
$471$	7.11924	0.328037
$472$	5.88599	0.270925
$473$	33.9389	1.56051
$474$	1.22695	0.0563558
$475$	3.99364	0.183241
$476$	−27.9471	−1.28095
$477$	15.8564	0.726013
$478$	3.92242	0.179407
$479$	−19.0723	−0.871438	−0.435719	−	0.900083i	$-0.643506\pi$
$479$	−19.0723	−0.871438	−0.435719	+	0.900083i	$0.643506\pi$
$480$	−0.976447	−0.0445685
$481$	−14.0861	−0.642270
$482$	−3.09694	−0.141062
$483$	−3.33430	−0.151716
$484$	−2.83051	−0.128660
$485$	−9.69814	−0.440370
$486$	1.95662	0.0887540
$487$	−19.8770	−0.900711	−0.450356	−	0.892849i	$-0.648703\pi$
$487$	−19.8770	−0.900711	−0.450356	+	0.892849i	$0.648703\pi$
$488$	5.25366	0.237822
$489$	−9.05512	−0.409487
$490$	0.290975	0.0131449
$491$	19.9780	0.901593	0.450796	−	0.892627i	$-0.351140\pi$
$491$	19.9780	0.901593	0.450796	+	0.892627i	$0.351140\pi$
$492$	5.67598	0.255893
$493$	−51.4609	−2.31768
$494$	1.17745	0.0529760
$495$	−9.57330	−0.430288
$496$	33.4261	1.50088
$497$	13.4110	0.601564
$498$	−1.13692	−0.0509465
$499$	21.1758	0.947960	0.473980	−	0.880536i	$-0.342817\pi$
$499$	21.1758	0.947960	0.473980	+	0.880536i	$0.342817\pi$
$500$	1.97600	0.0883695
$501$	1.10040	0.0491620
$502$	2.51134	0.112086
$503$	−13.1478	−0.586231	−0.293116	−	0.956077i	$-0.594692\pi$
$503$	−13.1478	−0.586231	−0.293116	+	0.956077i	$0.594692\pi$
$504$	3.78470	0.168584
$505$	−0.659390	−0.0293425
$506$	1.50769	0.0670250
$507$	−5.00568	−0.222310
$508$	−31.5619	−1.40033
$509$	18.0425	0.799721	0.399860	−	0.916576i	$-0.369059\pi$
$509$	18.0425	0.799721	0.399860	+	0.916576i	$0.369059\pi$
$510$	−0.516765	−0.0228827
$511$	24.5977	1.08814
$512$	11.8058	0.521749
$513$	−12.1828	−0.537885
$514$	0.614367	0.0270985
$515$	5.77645	0.254541
$516$	10.1523	0.446930
$517$	38.1719	1.67880
$518$	−2.59485	−0.114011
$519$	−9.71444	−0.426417
$520$	1.17225	0.0514066
$521$	−0.634090	−0.0277800	−0.0138900	−	0.999904i	$-0.504421\pi$
$521$	−0.634090	−0.0277800	−0.0138900	+	0.999904i	$0.504421\pi$
$522$	3.46348	0.151592
$523$	19.0394	0.832534	0.416267	−	0.909243i	$-0.363338\pi$
$523$	19.0394	0.832534	0.416267	+	0.909243i	$0.363338\pi$
$524$	12.3623	0.540048
$525$	1.20799	0.0527211
$526$	−0.583770	−0.0254536
$527$	54.1658	2.35950
$528$	−7.25835	−0.315879
$529$	−15.3813	−0.668752
$530$	0.904719	0.0392985
$531$	25.9456	1.12594
$532$	−17.8593	−0.774297
$533$	−10.2418	−0.443622
$534$	0.816455	0.0353315
$535$	−4.65899	−0.201426
$536$	3.93488	0.169961
$537$	−3.08002	−0.132913
$538$	−0.928282	−0.0400211
$539$	6.62279	0.285264
$540$	−6.02791	−0.259400
$541$	10.5103	0.451872	0.225936	−	0.974142i	$-0.427456\pi$
$541$	10.5103	0.451872	0.225936	+	0.974142i	$0.427456\pi$
$542$	−3.33821	−0.143388
$543$	−7.11923	−0.305516
$544$	11.4323	0.490156
$545$	8.46360	0.362541
$546$	0.356154	0.0152420
$547$	9.78448	0.418354	0.209177	−	0.977878i	$-0.432921\pi$
$547$	9.78448	0.418354	0.209177	+	0.977878i	$0.432921\pi$
$548$	9.21242	0.393535
$549$	23.1582	0.988368
$550$	−0.546226	−0.0232911
$551$	−32.8854	−1.40097
$552$	0.907481	0.0386250
$553$	33.5803	1.42798
$554$	−1.47019	−0.0624625
$555$	3.95064	0.167695
$556$	27.7325	1.17612
$557$	−17.9955	−0.762494	−0.381247	−	0.924473i	$-0.624505\pi$
$557$	−17.9955	−0.762494	−0.381247	+	0.924473i	$0.624505\pi$
$558$	−3.64553	−0.154327
$559$	−18.3189	−0.774808
$560$	−8.72791	−0.368822
$561$	−11.7619	−0.496588
$562$	0.469828	0.0198185
$563$	−31.4543	−1.32564	−0.662821	−	0.748778i	$-0.730641\pi$
$563$	−31.4543	−1.32564	−0.662821	+	0.748778i	$0.730641\pi$
$564$	11.4185	0.480807
$565$	13.5414	0.569689
$566$	2.50983	0.105496
$567$	14.7486	0.619384
$568$	−3.65000	−0.153151
$569$	30.3485	1.27227	0.636137	−	0.771576i	$-0.280531\pi$
$569$	30.3485	1.27227	0.636137	+	0.771576i	$0.280531\pi$
$570$	−0.330232	−0.0138319
$571$	−40.1854	−1.68171	−0.840853	−	0.541264i	$-0.817946\pi$
$571$	−40.1854	−1.68171	−0.840853	+	0.541264i	$0.817946\pi$
$572$	13.2601	0.554431
$573$	11.2952	0.471862
$574$	−1.88668	−0.0787485
$575$	−2.76020	−0.115108
$576$	20.1725	0.840520
$577$	−18.5591	−0.772626	−0.386313	−	0.922368i	$-0.626251\pi$
$577$	−18.5591	−0.772626	−0.386313	+	0.922368i	$0.626251\pi$
$578$	3.41677	0.142119
$579$	5.11928	0.212750
$580$	−16.2713	−0.675629
$581$	−31.1161	−1.29091
$582$	0.801935	0.0332413
$583$	20.5920	0.852833
$584$	−6.69465	−0.277027
$585$	5.16730	0.213642
$586$	−1.77717	−0.0734141
$587$	29.0928	1.20079	0.600393	−	0.799705i	$-0.295011\pi$
$587$	29.0928	1.20079	0.600393	+	0.799705i	$0.295011\pi$
$588$	1.98110	0.0816992
$589$	34.6140	1.42624
$590$	1.48038	0.0609463
$591$	2.52743	0.103965
$592$	−28.5439	−1.17315
$593$	46.4708	1.90833	0.954164	−	0.299285i	$-0.0967480\pi$
$593$	46.4708	1.90833	0.954164	+	0.299285i	$0.0967480\pi$
$594$	1.66629	0.0683689
$595$	−14.1433	−0.579818
$596$	5.17930	0.212153
$597$	−12.6587	−0.518085
$598$	−0.813793	−0.0332785
$599$	−34.6221	−1.41462	−0.707311	−	0.706903i	$-0.750092\pi$
$599$	−34.6221	−1.41462	−0.707311	+	0.706903i	$0.750092\pi$
$600$	−0.328774	−0.0134221
$601$	−8.78546	−0.358366	−0.179183	−	0.983816i	$-0.557345\pi$
$601$	−8.78546	−0.358366	−0.179183	+	0.983816i	$0.557345\pi$
$602$	−3.37459	−0.137538
$603$	17.3450	0.706343
$604$	10.7921	0.439123
$605$	−1.43244	−0.0582371
$606$	0.0545247	0.00221491
$607$	23.1530	0.939751	0.469875	−	0.882733i	$-0.344299\pi$
$607$	23.1530	0.939751	0.469875	+	0.882733i	$0.344299\pi$
$608$	7.30567	0.296284
$609$	−9.94717	−0.403079
$610$	1.32134	0.0534996
$611$	−20.6037	−0.833538
$612$	33.5284	1.35531
$613$	29.6788	1.19872	0.599359	−	0.800481i	$-0.295422\pi$
$613$	29.6788	1.19872	0.599359	+	0.800481i	$0.295422\pi$
$614$	−2.31054	−0.0932457
$615$	2.87246	0.115829
$616$	4.91503	0.198032
$617$	−33.8674	−1.36345	−0.681726	−	0.731608i	$-0.738770\pi$
$617$	−33.8674	−1.36345	−0.681726	+	0.731608i	$0.738770\pi$
$618$	−0.477652	−0.0192140
$619$	−49.0038	−1.96963	−0.984814	−	0.173611i	$-0.944456\pi$
$619$	−49.0038	−1.96963	−0.984814	+	0.173611i	$0.944456\pi$
$620$	17.1266	0.687819
$621$	8.42015	0.337889
$622$	−2.06763	−0.0829042
$623$	22.3455	0.895252
$624$	3.91778	0.156837
$625$	1.00000	0.0400000
$626$	5.20839	0.208169
$627$	−7.51630	−0.300172
$628$	−26.3550	−1.05168
$629$	−46.2544	−1.84428
$630$	0.951886	0.0379240
$631$	−3.08886	−0.122965	−0.0614827	−	0.998108i	$-0.519583\pi$
$631$	−3.08886	−0.122965	−0.0614827	+	0.998108i	$0.519583\pi$
$632$	−9.13939	−0.363545
$633$	10.9738	0.436171
$634$	−1.62707	−0.0646191
$635$	−15.9726	−0.633854
$636$	6.15976	0.244251
$637$	−3.57472	−0.141636
$638$	4.49787	0.178072
$639$	−16.0893	−0.636481
$640$	4.80964	0.190118
$641$	−27.3504	−1.08027	−0.540137	−	0.841577i	$-0.681628\pi$
$641$	−27.3504	−1.08027	−0.540137	+	0.841577i	$0.681628\pi$
$642$	0.385250	0.0152046
$643$	38.1242	1.50347	0.751735	−	0.659465i	$-0.229217\pi$
$643$	38.1242	1.50347	0.751735	+	0.659465i	$0.229217\pi$
$644$	12.3434	0.486398
$645$	5.13779	0.202300
$646$	3.86638	0.152121
$647$	14.6584	0.576280	0.288140	−	0.957588i	$-0.406963\pi$
$647$	14.6584	0.576280	0.288140	+	0.957588i	$0.406963\pi$
$648$	−4.01407	−0.157687
$649$	33.6944	1.32262
$650$	0.294831	0.0115642
$651$	10.4700	0.410352
$652$	33.5216	1.31281
$653$	21.5707	0.844129	0.422064	−	0.906566i	$-0.361306\pi$
$653$	21.5707	0.844129	0.422064	+	0.906566i	$0.361306\pi$
$654$	−0.699851	−0.0273664
$655$	6.25620	0.244450
$656$	−20.7539	−0.810304
$657$	−29.5101	−1.15130
$658$	−3.79548	−0.147963
$659$	−46.4264	−1.80852	−0.904259	−	0.426985i	$-0.859576\pi$
$659$	−46.4264	−1.80852	−0.904259	+	0.426985i	$0.859576\pi$
$660$	−3.71897	−0.144761
$661$	21.4865	0.835729	0.417864	−	0.908509i	$-0.362779\pi$
$661$	21.4865	0.835729	0.417864	+	0.908509i	$0.362779\pi$
$662$	3.89762	0.151485
$663$	6.34862	0.246560
$664$	8.46873	0.328650
$665$	−9.03808	−0.350482
$666$	3.11306	0.120629
$667$	22.7287	0.880060
$668$	−4.07360	−0.157612
$669$	−7.16473	−0.277005
$670$	0.989657	0.0382338
$671$	30.0746	1.16102
$672$	2.20982	0.0852455
$673$	19.5685	0.754310	0.377155	−	0.926150i	$-0.376902\pi$
$673$	19.5685	0.754310	0.377155	+	0.926150i	$0.376902\pi$
$674$	−0.722853	−0.0278433
$675$	−3.05056	−0.117416
$676$	18.5307	0.712721
$677$	−8.30995	−0.319377	−0.159689	−	0.987167i	$-0.551049\pi$
$677$	−8.30995	−0.319377	−0.159689	+	0.987167i	$0.551049\pi$
$678$	−1.11973	−0.0430029
$679$	21.9480	0.842289
$680$	3.84931	0.147614
$681$	5.68211	0.217739
$682$	−4.73429	−0.181285
$683$	−4.36593	−0.167058	−0.0835289	−	0.996505i	$-0.526619\pi$
$683$	−4.36593	−0.167058	−0.0835289	+	0.996505i	$0.526619\pi$
$684$	21.4259	0.819240
$685$	4.66215	0.178132
$686$	−3.11265	−0.118842
$687$	9.21936	0.351741
$688$	−37.1212	−1.41523
$689$	−11.1148	−0.423438
$690$	0.228240	0.00868893
$691$	−23.6104	−0.898180	−0.449090	−	0.893486i	$-0.648252\pi$
$691$	−23.6104	−0.898180	−0.449090	+	0.893486i	$0.648252\pi$
$692$	35.9623	1.36708
$693$	21.6655	0.823005
$694$	3.72468	0.141387
$695$	14.0347	0.532365
$696$	2.70727	0.102619
$697$	−33.6310	−1.27386
$698$	3.53339	0.133741
$699$	0.375158	0.0141898
$700$	−4.47193	−0.169023
$701$	48.5228	1.83268	0.916340	−	0.400400i	$-0.131129\pi$
$701$	48.5228	1.83268	0.916340	+	0.400400i	$0.131129\pi$
$702$	−0.899401	−0.0339457
$703$	−29.5583	−1.11481
$704$	26.1971	0.987342
$705$	5.77860	0.217635
$706$	−3.18156	−0.119739
$707$	1.49228	0.0561229
$708$	10.0791	0.378798
$709$	−35.3980	−1.32940	−0.664700	−	0.747110i	$-0.731441\pi$
$709$	−35.3980	−1.32940	−0.664700	+	0.747110i	$0.731441\pi$
$710$	−0.918007	−0.0344522
$711$	−40.2866	−1.51086
$712$	−6.08166	−0.227920
$713$	−23.9234	−0.895939
$714$	1.16950	0.0437675
$715$	6.71055	0.250960
$716$	11.4021	0.426116
$717$	13.5150	0.504728
$718$	0.883805	0.0329833
$719$	16.7741	0.625567	0.312783	−	0.949824i	$-0.398739\pi$
$719$	16.7741	0.625567	0.312783	+	0.949824i	$0.398739\pi$
$720$	10.4710	0.390230
$721$	−13.0728	−0.486856
$722$	−0.472625	−0.0175893
$723$	−10.6708	−0.396850
$724$	26.3550	0.979477
$725$	−8.23445	−0.305820
$726$	0.118448	0.00439602
$727$	−12.3805	−0.459169	−0.229584	−	0.973289i	$-0.573737\pi$
$727$	−12.3805	−0.459169	−0.229584	+	0.973289i	$0.573737\pi$
$728$	−2.65294	−0.0983246
$729$	−12.8092	−0.474413
$730$	−1.68376	−0.0623189
$731$	−60.1537	−2.22486
$732$	8.99633	0.332514
$733$	36.5546	1.35017	0.675087	−	0.737738i	$-0.264106\pi$
$733$	36.5546	1.35017	0.675087	+	0.737738i	$0.264106\pi$
$734$	1.87631	0.0692559
$735$	1.00258	0.0369808
$736$	−5.04931	−0.186120
$737$	22.5252	0.829727
$738$	2.26347	0.0833194
$739$	15.2198	0.559868	0.279934	−	0.960019i	$-0.409687\pi$
$739$	15.2198	0.559868	0.279934	+	0.960019i	$0.409687\pi$
$740$	−14.6251	−0.537628
$741$	4.05701	0.149038
$742$	−2.04749	−0.0751656
$743$	1.73756	0.0637450	0.0318725	−	0.999492i	$-0.489853\pi$
$743$	1.73756	0.0637450	0.0318725	+	0.999492i	$0.489853\pi$
$744$	−2.84958	−0.104471
$745$	2.62110	0.0960298
$746$	0.656169	0.0240241
$747$	37.3303	1.36584
$748$	43.5420	1.59205
$749$	10.5438	0.385264
$750$	−0.0826896	−0.00301940
$751$	35.3330	1.28932	0.644660	−	0.764469i	$-0.276999\pi$
$751$	35.3330	1.28932	0.644660	+	0.764469i	$0.276999\pi$
$752$	−41.7512	−1.52251
$753$	8.65303	0.315334
$754$	−2.42778	−0.0884144
$755$	5.46157	0.198767
$756$	13.6419	0.496151
$757$	−17.2573	−0.627228	−0.313614	−	0.949550i	$-0.601540\pi$
$757$	−17.2573	−0.627228	−0.313614	+	0.949550i	$0.601540\pi$
$758$	−1.47436	−0.0535510
$759$	5.19488	0.188562
$760$	2.45985	0.0892282
$761$	22.2402	0.806207	0.403103	−	0.915154i	$-0.367932\pi$
$761$	22.2402	0.806207	0.403103	+	0.915154i	$0.367932\pi$
$762$	1.32077	0.0478464
$763$	−19.1541	−0.693426
$764$	−41.8141	−1.51278
$765$	16.9678	0.613473
$766$	−0.647605	−0.0233989
$767$	−18.1869	−0.656692
$768$	7.53393	0.271857
$769$	6.99679	0.252311	0.126155	−	0.992010i	$-0.459736\pi$
$769$	6.99679	0.252311	0.126155	+	0.992010i	$0.459736\pi$
$770$	1.23617	0.0445486
$771$	2.11685	0.0762366
$772$	−18.9513	−0.682073
$773$	36.4145	1.30974	0.654869	−	0.755742i	$-0.272724\pi$
$773$	36.4145	1.30974	0.654869	+	0.755742i	$0.272724\pi$
$774$	4.04853	0.145521
$775$	8.66728	0.311338
$776$	−5.97350	−0.214436
$777$	−8.94077	−0.320748
$778$	−1.21663	−0.0436184
$779$	−21.4914	−0.770011
$780$	2.00736	0.0718749
$781$	−20.8944	−0.747662
$782$	−2.67225	−0.0955593
$783$	25.1197	0.897705
$784$	−7.24378	−0.258706
$785$	−13.3376	−0.476038
$786$	−0.517323	−0.0184523
$787$	7.31801	0.260859	0.130429	−	0.991458i	$-0.458364\pi$
$787$	7.31801	0.260859	0.130429	+	0.991458i	$0.458364\pi$
$788$	−9.35642	−0.333309
$789$	−2.01143	−0.0716088
$790$	−2.29864	−0.0817819
$791$	−30.6457	−1.08964
$792$	−5.89661	−0.209527
$793$	−16.2331	−0.576454
$794$	0.401078	0.0142337
$795$	3.11729	0.110559
$796$	46.8617	1.66097
$797$	−51.2167	−1.81419	−0.907094	−	0.420927i	$-0.861705\pi$
$797$	−51.2167	−1.81419	−0.907094	+	0.420927i	$0.861705\pi$
$798$	0.747355	0.0264561
$799$	−67.6563	−2.39351
$800$	1.82933	0.0646765
$801$	−26.8080	−0.947216
$802$	−0.154915	−0.00547024
$803$	−38.3236	−1.35241
$804$	6.73806	0.237633
$805$	6.24666	0.220166
$806$	2.55539	0.0900097
$807$	−3.19848	−0.112592
$808$	−0.406146	−0.0142882
$809$	−25.8754	−0.909731	−0.454866	−	0.890560i	$-0.650313\pi$
$809$	−25.8754	−0.909731	−0.454866	+	0.890560i	$0.650313\pi$
$810$	−1.00957	−0.0354728
$811$	7.95834	0.279455	0.139728	−	0.990190i	$-0.455377\pi$
$811$	7.95834	0.279455	0.139728	+	0.990190i	$0.455377\pi$
$812$	36.8239	1.29226
$813$	−11.5021	−0.403396
$814$	4.04280	0.141700
$815$	16.9643	0.594235
$816$	12.8648	0.450357
$817$	−38.4404	−1.34486
$818$	−4.17408	−0.145943
$819$	−11.6942	−0.408629
$820$	−10.6337	−0.371345
$821$	39.7299	1.38658	0.693292	−	0.720657i	$-0.256160\pi$
$821$	39.7299	1.38658	0.693292	+	0.720657i	$0.256160\pi$
$822$	−0.385511	−0.0134463
$823$	−17.1238	−0.596899	−0.298449	−	0.954425i	$-0.596469\pi$
$823$	−17.1238	−0.596899	−0.298449	+	0.954425i	$0.596469\pi$
$824$	3.55796	0.123947
$825$	−1.88207	−0.0655252
$826$	−3.35028	−0.116571
$827$	−5.90627	−0.205381	−0.102691	−	0.994713i	$-0.532745\pi$
$827$	−5.90627	−0.205381	−0.102691	+	0.994713i	$0.532745\pi$
$828$	−14.8085	−0.514631
$829$	38.5433	1.33867	0.669333	−	0.742963i	$-0.266580\pi$
$829$	38.5433	1.33867	0.669333	+	0.742963i	$0.266580\pi$
$830$	2.12996	0.0739320
$831$	−5.06568	−0.175726
$832$	−14.1402	−0.490224
$833$	−11.7383	−0.406708
$834$	−1.16052	−0.0401855
$835$	−2.06154	−0.0713425
$836$	27.8249	0.962345
$837$	−26.4401	−0.913903
$838$	2.77231	0.0957678
$839$	−31.0508	−1.07199	−0.535996	−	0.844220i	$-0.680064\pi$
$839$	−31.0508	−1.07199	−0.535996	+	0.844220i	$0.680064\pi$
$840$	0.744055	0.0256723
$841$	38.8062	1.33815
$842$	−3.62207	−0.124825
$843$	1.61883	0.0557556
$844$	−40.6246	−1.39835
$845$	9.37790	0.322610
$846$	4.55348	0.156552
$847$	3.24179	0.111389
$848$	−22.5228	−0.773437
$849$	8.64782	0.296793
$850$	0.968136	0.0332068
$851$	20.4292	0.700303
$852$	−6.25024	−0.214130
$853$	29.2934	1.00299	0.501494	−	0.865161i	$-0.332784\pi$
$853$	29.2934	1.00299	0.501494	+	0.865161i	$0.332784\pi$
$854$	−2.99035	−0.102328
$855$	10.8431	0.370825
$856$	−2.86967	−0.0980833
$857$	38.0513	1.29981	0.649903	−	0.760017i	$-0.274809\pi$
$857$	38.0513	1.29981	0.649903	+	0.760017i	$0.274809\pi$
$858$	−0.554893	−0.0189437
$859$	−57.2040	−1.95178	−0.975888	−	0.218271i	$-0.929958\pi$
$859$	−57.2040	−1.95178	−0.975888	+	0.218271i	$0.929958\pi$
$860$	−19.0198	−0.648571
$861$	−6.50072	−0.221544
$862$	2.22472	0.0757744
$863$	−17.8332	−0.607050	−0.303525	−	0.952823i	$-0.598164\pi$
$863$	−17.8332	−0.607050	−0.303525	+	0.952823i	$0.598164\pi$
$864$	−5.58048	−0.189852
$865$	18.1996	0.618803
$866$	2.76788	0.0940563
$867$	11.7728	0.399824
$868$	−38.7595	−1.31558
$869$	−52.3185	−1.77478
$870$	0.680903	0.0230848
$871$	−12.1582	−0.411966
$872$	5.21309	0.176538
$873$	−26.3313	−0.891179
$874$	−1.70766	−0.0577626
$875$	−2.26312	−0.0765074
$876$	−11.4639	−0.387329
$877$	45.2555	1.52817	0.764085	−	0.645116i	$-0.223191\pi$
$877$	45.2555	1.52817	0.764085	+	0.645116i	$0.223191\pi$
$878$	−0.332028	−0.0112054
$879$	−6.12339	−0.206537
$880$	13.5982	0.458395
$881$	−19.4363	−0.654826	−0.327413	−	0.944881i	$-0.606177\pi$
$881$	−19.4363	−0.654826	−0.327413	+	0.944881i	$0.606177\pi$
$882$	0.790023	0.0266015
$883$	28.9251	0.973406	0.486703	−	0.873568i	$-0.338199\pi$
$883$	28.9251	0.973406	0.486703	+	0.873568i	$0.338199\pi$
$884$	−23.5023	−0.790467
$885$	5.10078	0.171461
$886$	0.135428	0.00454978
$887$	−45.8066	−1.53803	−0.769017	−	0.639228i	$-0.779254\pi$
$887$	−45.8066	−1.53803	−0.769017	+	0.639228i	$0.779254\pi$
$888$	2.43337	0.0816584
$889$	36.1480	1.21236
$890$	−1.52959	−0.0512720
$891$	−22.9785	−0.769810
$892$	26.5235	0.888071
$893$	−43.2349	−1.44680
$894$	−0.216738	−0.00724880
$895$	5.77028	0.192879
$896$	−10.8848	−0.363635
$897$	−2.80400	−0.0936227
$898$	1.09590	0.0365707
$899$	−71.3704	−2.38033
$900$	5.36501	0.178834
$901$	−36.4974	−1.21591
$902$	2.93947	0.0978736
$903$	−11.6274	−0.386937
$904$	8.34069	0.277407
$905$	13.3376	0.443355
$906$	−0.451615	−0.0150039
$907$	−9.57597	−0.317965	−0.158982	−	0.987281i	$-0.550821\pi$
$907$	−9.57597	−0.317965	−0.158982	+	0.987281i	$0.550821\pi$
$908$	−21.0349	−0.698066
$909$	−1.79030	−0.0593805
$910$	−0.667239	−0.0221188
$911$	−27.1526	−0.899607	−0.449803	−	0.893128i	$-0.648506\pi$
$911$	−27.1526	−0.899607	−0.449803	+	0.893128i	$0.648506\pi$
$912$	8.22107	0.272227
$913$	48.4793	1.60443
$914$	−2.11038	−0.0698050
$915$	4.55280	0.150511
$916$	−34.1296	−1.12767
$917$	−14.1585	−0.467556
$918$	−2.95336	−0.0974753
$919$	34.4279	1.13567	0.567835	−	0.823142i	$-0.307781\pi$
$919$	34.4279	1.13567	0.567835	+	0.823142i	$0.307781\pi$
$920$	−1.70012	−0.0560514
$921$	−7.96116	−0.262329
$922$	0.989734	0.0325952
$923$	11.2780	0.371220
$924$	8.41647	0.276882
$925$	−7.40134	−0.243354
$926$	−4.82702	−0.158626
$927$	15.6836	0.515115
$928$	−15.0635	−0.494484
$929$	−15.2737	−0.501115	−0.250558	−	0.968102i	$-0.580614\pi$
$929$	−15.2737	−0.501115	−0.250558	+	0.968102i	$0.580614\pi$
$930$	−0.716694	−0.0235013
$931$	−7.50121	−0.245842
$932$	−1.38882	−0.0454922
$933$	−7.12418	−0.233235
$934$	−2.33621	−0.0764431
$935$	22.0354	0.720634
$936$	3.18276	0.104032
$937$	34.4960	1.12694	0.563468	−	0.826138i	$-0.309467\pi$
$937$	34.4960	1.12694	0.563468	+	0.826138i	$0.309467\pi$
$938$	−2.23971	−0.0731292
$939$	17.9460	0.585644
$940$	−21.3921	−0.697733
$941$	47.4939	1.54826	0.774129	−	0.633028i	$-0.218188\pi$
$941$	47.4939	1.54826	0.774129	+	0.633028i	$0.218188\pi$
$942$	1.10288	0.0359337
$943$	14.8538	0.483706
$944$	−36.8538	−1.19949
$945$	6.90379	0.224580
$946$	5.25765	0.170941
$947$	17.5784	0.571221	0.285610	−	0.958346i	$-0.407804\pi$
$947$	17.5784	0.571221	0.285610	+	0.958346i	$0.407804\pi$
$948$	−15.6502	−0.508296
$949$	20.6856	0.671482
$950$	0.618675	0.0200725
$951$	−5.60620	−0.181794
$952$	−8.71145	−0.282340
$953$	46.4904	1.50597	0.752985	−	0.658037i	$-0.228613\pi$
$953$	46.4904	1.50597	0.752985	+	0.658037i	$0.228613\pi$
$954$	2.45639	0.0795285
$955$	−21.1610	−0.684753
$956$	−50.0319	−1.61815
$957$	15.4978	0.500973
$958$	−2.95459	−0.0954586
$959$	−10.5510	−0.340710
$960$	3.96582	0.127996
$961$	44.1218	1.42328
$962$	−2.18215	−0.0703552
$963$	−12.6496	−0.407626
$964$	39.5026	1.27229
$965$	−9.59074	−0.308737
$966$	−0.516534	−0.0166192
$967$	−14.9840	−0.481852	−0.240926	−	0.970544i	$-0.577451\pi$
$967$	−14.9840	−0.481852	−0.240926	+	0.970544i	$0.577451\pi$
$968$	−0.882303	−0.0283583
$969$	13.3220	0.427963
$970$	−1.50239	−0.0482388
$971$	10.1173	0.324680	0.162340	−	0.986735i	$-0.448096\pi$
$971$	10.1173	0.324680	0.162340	+	0.986735i	$0.448096\pi$
$972$	−24.9574	−0.800509
$973$	−31.7621	−1.01825
$974$	−3.07924	−0.0986653
$975$	1.01587	0.0325338
$976$	−32.8946	−1.05293
$977$	40.7039	1.30223	0.651117	−	0.758978i	$-0.274301\pi$
$977$	40.7039	1.30223	0.651117	+	0.758978i	$0.274301\pi$
$978$	−1.40277	−0.0448558
$979$	−34.8145	−1.11268
$980$	−3.71150	−0.118560
$981$	22.9794	0.733676
$982$	3.09489	0.0987618
$983$	−56.4744	−1.80125	−0.900626	−	0.434594i	$-0.856892\pi$
$983$	−56.4744	−1.80125	−0.900626	+	0.434594i	$0.856892\pi$
$984$	1.76927	0.0564023
$985$	−4.73503	−0.150871
$986$	−7.97207	−0.253882
$987$	−13.0777	−0.416267
$988$	−15.0188	−0.477812
$989$	26.5681	0.844816
$990$	−1.48305	−0.0471344
$991$	12.3767	0.393159	0.196580	−	0.980488i	$-0.437017\pi$
$991$	12.3767	0.393159	0.196580	+	0.980488i	$0.437017\pi$
$992$	15.8553	0.503407
$993$	13.4296	0.426175
$994$	2.07756	0.0658962
$995$	23.7154	0.751830
$996$	14.5018	0.459507
$997$	10.2213	0.323711	0.161856	−	0.986814i	$-0.448252\pi$
$997$	10.2213	0.323711	0.161856	+	0.986814i	$0.448252\pi$
$998$	3.28046	0.103841
$999$	22.5782	0.714344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.e.1.16	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.e.1.16	✓	29	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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q+0.154915 q^{2} +0.533773 q^{3} -1.97600 q^{4} -1.00000 q^{5} +0.0826896 q^{6} +2.26312 q^{7} -0.615943 q^{8} -2.71509 q^{9} +O(q^{10})\)	\(q+0.154915 q^{2} +0.533773 q^{3} -1.97600 q^{4} -1.00000 q^{5} +0.0826896 q^{6} +2.26312 q^{7} -0.615943 q^{8} -2.71509 q^{9} -0.154915 q^{10} -3.52597 q^{11} -1.05474 q^{12} +1.90318 q^{13} +0.350591 q^{14} -0.533773 q^{15} +3.85658 q^{16} +6.24946 q^{17} -0.420608 q^{18} +3.99364 q^{19} +1.97600 q^{20} +1.20799 q^{21} -0.546226 q^{22} -2.76020 q^{23} -0.328774 q^{24} +1.00000 q^{25} +0.294831 q^{26} -3.05056 q^{27} -4.47193 q^{28} -8.23445 q^{29} -0.0826896 q^{30} +8.66728 q^{31} +1.82933 q^{32} -1.88207 q^{33} +0.968136 q^{34} -2.26312 q^{35} +5.36501 q^{36} -7.40134 q^{37} +0.618675 q^{38} +1.01587 q^{39} +0.615943 q^{40} -5.38142 q^{41} +0.187136 q^{42} -9.62542 q^{43} +6.96732 q^{44} +2.71509 q^{45} -0.427596 q^{46} -10.8259 q^{47} +2.05854 q^{48} -1.87829 q^{49} +0.154915 q^{50} +3.33580 q^{51} -3.76069 q^{52} -5.84009 q^{53} -0.472578 q^{54} +3.52597 q^{55} -1.39395 q^{56} +2.13170 q^{57} -1.27564 q^{58} -9.55607 q^{59} +1.05474 q^{60} -8.52946 q^{61} +1.34269 q^{62} -6.14456 q^{63} -7.42978 q^{64} -1.90318 q^{65} -0.291561 q^{66} -6.38838 q^{67} -12.3489 q^{68} -1.47332 q^{69} -0.350591 q^{70} +5.92587 q^{71} +1.67234 q^{72} +10.8690 q^{73} -1.14658 q^{74} +0.533773 q^{75} -7.89143 q^{76} -7.97969 q^{77} +0.157373 q^{78} +14.8381 q^{79} -3.85658 q^{80} +6.51695 q^{81} -0.833663 q^{82} -13.7492 q^{83} -2.38700 q^{84} -6.24946 q^{85} -1.49112 q^{86} -4.39533 q^{87} +2.17179 q^{88} +9.87374 q^{89} +0.420608 q^{90} +4.30713 q^{91} +5.45416 q^{92} +4.62637 q^{93} -1.67710 q^{94} -3.99364 q^{95} +0.976447 q^{96} +9.69814 q^{97} -0.290975 q^{98} +9.57330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9} + 5 q^{10} - 38 q^{11} - 6 q^{12} + 5 q^{13} - 18 q^{14} + 3 q^{15} + 7 q^{16} - 16 q^{17} - 2 q^{18} - 18 q^{19} - 19 q^{20} - 20 q^{21} - 2 q^{22} - 19 q^{23} - 19 q^{24} + 29 q^{25} - 21 q^{26} - 21 q^{27} + 26 q^{28} - 31 q^{29} + 6 q^{30} - 13 q^{31} - 30 q^{32} + 2 q^{33} - 14 q^{34} - 12 q^{35} - 29 q^{36} - q^{37} - 23 q^{38} - 39 q^{39} + 15 q^{40} - 24 q^{41} - 20 q^{42} - 27 q^{43} - 76 q^{44} - 14 q^{45} - 11 q^{46} - 5 q^{47} - 2 q^{48} - 11 q^{49} - 5 q^{50} - 58 q^{51} + 11 q^{52} - 37 q^{53} - 18 q^{54} + 38 q^{55} - 50 q^{56} - 6 q^{57} + 31 q^{58} - 67 q^{59} + 6 q^{60} - 31 q^{61} - 19 q^{62} - 2 q^{63} - 13 q^{64} - 5 q^{65} + 6 q^{66} - 17 q^{67} - 16 q^{68} - 48 q^{69} + 18 q^{70} - 53 q^{71} + 9 q^{72} + 29 q^{73} - 59 q^{74} - 3 q^{75} - 21 q^{76} - 62 q^{77} - 12 q^{78} - 13 q^{79} - 7 q^{80} - 11 q^{81} + 32 q^{82} - 72 q^{83} - 58 q^{84} + 16 q^{85} - 43 q^{86} + 4 q^{87} + 12 q^{88} - 38 q^{89} + 2 q^{90} - 45 q^{91} - 37 q^{92} - 27 q^{93} - 44 q^{94} + 18 q^{95} - 21 q^{96} + 32 q^{97} - 32 q^{98} - 107 q^{99}+O(q^{100}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9 + 5 * q^10 - 38 * q^11 - 6 * q^12 + 5 * q^13 - 18 * q^14 + 3 * q^15 + 7 * q^16 - 16 * q^17 - 2 * q^18 - 18 * q^19 - 19 * q^20 - 20 * q^21 - 2 * q^22 - 19 * q^23 - 19 * q^24 + 29 * q^25 - 21 * q^26 - 21 * q^27 + 26 * q^28 - 31 * q^29 + 6 * q^30 - 13 * q^31 - 30 * q^32 + 2 * q^33 - 14 * q^34 - 12 * q^35 - 29 * q^36 - q^37 - 23 * q^38 - 39 * q^39 + 15 * q^40 - 24 * q^41 - 20 * q^42 - 27 * q^43 - 76 * q^44 - 14 * q^45 - 11 * q^46 - 5 * q^47 - 2 * q^48 - 11 * q^49 - 5 * q^50 - 58 * q^51 + 11 * q^52 - 37 * q^53 - 18 * q^54 + 38 * q^55 - 50 * q^56 - 6 * q^57 + 31 * q^58 - 67 * q^59 + 6 * q^60 - 31 * q^61 - 19 * q^62 - 2 * q^63 - 13 * q^64 - 5 * q^65 + 6 * q^66 - 17 * q^67 - 16 * q^68 - 48 * q^69 + 18 * q^70 - 53 * q^71 + 9 * q^72 + 29 * q^73 - 59 * q^74 - 3 * q^75 - 21 * q^76 - 62 * q^77 - 12 * q^78 - 13 * q^79 - 7 * q^80 - 11 * q^81 + 32 * q^82 - 72 * q^83 - 58 * q^84 + 16 * q^85 - 43 * q^86 + 4 * q^87 + 12 * q^88 - 38 * q^89 + 2 * q^90 - 45 * q^91 - 37 * q^92 - 27 * q^93 - 44 * q^94 + 18 * q^95 - 21 * q^96 + 32 * q^97 - 32 * q^98 - 107 * q^99

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