LMFDB - Embedded newform 2005.2.a.e.1.27

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			1.27
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)

$f(q)$	$=$	$q+2.06684 q^{2} -0.262672 q^{3} +2.27184 q^{4} -1.00000 q^{5} -0.542902 q^{6} +0.878786 q^{7} +0.561843 q^{8} -2.93100 q^{9} +O(q^{10})$	\(q+2.06684 q^{2} -0.262672 q^{3} +2.27184 q^{4} -1.00000 q^{5} -0.542902 q^{6} +0.878786 q^{7} +0.561843 q^{8} -2.93100 q^{9} -2.06684 q^{10} -1.12505 q^{11} -0.596749 q^{12} -1.02946 q^{13} +1.81631 q^{14} +0.262672 q^{15} -3.38243 q^{16} -6.09313 q^{17} -6.05792 q^{18} +3.06690 q^{19} -2.27184 q^{20} -0.230833 q^{21} -2.32530 q^{22} -1.49839 q^{23} -0.147581 q^{24} +1.00000 q^{25} -2.12774 q^{26} +1.55791 q^{27} +1.99646 q^{28} -3.98049 q^{29} +0.542902 q^{30} +0.991875 q^{31} -8.11464 q^{32} +0.295519 q^{33} -12.5935 q^{34} -0.878786 q^{35} -6.65876 q^{36} -5.54076 q^{37} +6.33880 q^{38} +0.270412 q^{39} -0.561843 q^{40} -5.20053 q^{41} -0.477095 q^{42} +8.75520 q^{43} -2.55593 q^{44} +2.93100 q^{45} -3.09694 q^{46} -4.69010 q^{47} +0.888472 q^{48} -6.22773 q^{49} +2.06684 q^{50} +1.60050 q^{51} -2.33877 q^{52} +0.906734 q^{53} +3.21996 q^{54} +1.12505 q^{55} +0.493740 q^{56} -0.805590 q^{57} -8.22704 q^{58} -7.88387 q^{59} +0.596749 q^{60} +2.41969 q^{61} +2.05005 q^{62} -2.57573 q^{63} -10.0068 q^{64} +1.02946 q^{65} +0.610792 q^{66} +7.11502 q^{67} -13.8426 q^{68} +0.393586 q^{69} -1.81631 q^{70} -1.32186 q^{71} -1.64676 q^{72} +0.935253 q^{73} -11.4519 q^{74} -0.262672 q^{75} +6.96750 q^{76} -0.988677 q^{77} +0.558899 q^{78} +5.24913 q^{79} +3.38243 q^{80} +8.38379 q^{81} -10.7487 q^{82} +10.8117 q^{83} -0.524415 q^{84} +6.09313 q^{85} +18.0956 q^{86} +1.04556 q^{87} -0.632101 q^{88} -5.35414 q^{89} +6.05792 q^{90} -0.904679 q^{91} -3.40410 q^{92} -0.260538 q^{93} -9.69369 q^{94} -3.06690 q^{95} +2.13149 q^{96} -7.29246 q^{97} -12.8717 q^{98} +3.29752 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.06684	1.46148	0.730739	−	0.682657i	$-0.239176\pi$
$2$	2.06684	1.46148	0.730739	+	0.682657i	$0.239176\pi$
$3$	−0.262672	−0.151654	−0.0758270	−	0.997121i	$-0.524160\pi$
$3$	−0.262672	−0.151654	−0.0758270	+	0.997121i	$0.524160\pi$
$4$	2.27184	1.13592
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.542902	−0.221639
$7$	0.878786	0.332150	0.166075	−	0.986113i	$-0.446891\pi$
$7$	0.878786	0.332150	0.166075	+	0.986113i	$0.446891\pi$
$8$	0.561843	0.198641
$9$	−2.93100	−0.977001
$10$	−2.06684	−0.653593
$11$	−1.12505	−0.339215	−0.169608	−	0.985512i	$-0.554250\pi$
$11$	−1.12505	−0.339215	−0.169608	+	0.985512i	$0.554250\pi$
$12$	−0.596749	−0.172267
$13$	−1.02946	−0.285522	−0.142761	−	0.989757i	$-0.545598\pi$
$13$	−1.02946	−0.285522	−0.142761	+	0.989757i	$0.545598\pi$
$14$	1.81631	0.485430
$15$	0.262672	0.0678217
$16$	−3.38243	−0.845608
$17$	−6.09313	−1.47780	−0.738901	−	0.673814i	$-0.764655\pi$
$17$	−6.09313	−1.47780	−0.738901	+	0.673814i	$0.764655\pi$
$18$	−6.05792	−1.42787
$19$	3.06690	0.703596	0.351798	−	0.936076i	$-0.385570\pi$
$19$	3.06690	0.703596	0.351798	+	0.936076i	$0.385570\pi$
$20$	−2.27184	−0.507998
$21$	−0.230833	−0.0503719
$22$	−2.32530	−0.495755
$23$	−1.49839	−0.312436	−0.156218	−	0.987723i	$-0.549930\pi$
$23$	−1.49839	−0.312436	−0.156218	+	0.987723i	$0.549930\pi$
$24$	−0.147581	−0.0301248
$25$	1.00000	0.200000
$26$	−2.12774	−0.417284
$27$	1.55791	0.299820
$28$	1.99646	0.377295
$29$	−3.98049	−0.739158	−0.369579	−	0.929199i	$-0.620498\pi$
$29$	−3.98049	−0.739158	−0.369579	+	0.929199i	$0.620498\pi$
$30$	0.542902	0.0991200
$31$	0.991875	0.178146	0.0890730	−	0.996025i	$-0.471610\pi$
$31$	0.991875	0.178146	0.0890730	+	0.996025i	$0.471610\pi$
$32$	−8.11464	−1.43448
$33$	0.295519	0.0514433
$34$	−12.5935	−2.15978
$35$	−0.878786	−0.148542
$36$	−6.65876	−1.10979
$37$	−5.54076	−0.910896	−0.455448	−	0.890262i	$-0.650521\pi$
$37$	−5.54076	−0.910896	−0.455448	+	0.890262i	$0.650521\pi$
$38$	6.33880	1.02829
$39$	0.270412	0.0433006
$40$	−0.561843	−0.0888352
$41$	−5.20053	−0.812186	−0.406093	−	0.913832i	$-0.633109\pi$
$41$	−5.20053	−0.812186	−0.406093	+	0.913832i	$0.633109\pi$
$42$	−0.477095	−0.0736174
$43$	8.75520	1.33516	0.667578	−	0.744540i	$-0.267331\pi$
$43$	8.75520	1.33516	0.667578	+	0.744540i	$0.267331\pi$
$44$	−2.55593	−0.385320
$45$	2.93100	0.436928
$46$	−3.09694	−0.456618
$47$	−4.69010	−0.684121	−0.342060	−	0.939678i	$-0.611125\pi$
$47$	−4.69010	−0.684121	−0.342060	+	0.939678i	$0.611125\pi$
$48$	0.888472	0.128240
$49$	−6.22773	−0.889676
$50$	2.06684	0.292296
$51$	1.60050	0.224115
$52$	−2.33877	−0.324330
$53$	0.906734	0.124550	0.0622748	−	0.998059i	$-0.480164\pi$
$53$	0.906734	0.124550	0.0622748	+	0.998059i	$0.480164\pi$
$54$	3.21996	0.438180
$55$	1.12505	0.151702
$56$	0.493740	0.0659788
$57$	−0.805590	−0.106703
$58$	−8.22704	−1.08026
$59$	−7.88387	−1.02639	−0.513196	−	0.858271i	$-0.671539\pi$
$59$	−7.88387	−1.02639	−0.513196	+	0.858271i	$0.671539\pi$
$60$	0.596749	0.0770399
$61$	2.41969	0.309810	0.154905	−	0.987929i	$-0.450493\pi$
$61$	2.41969	0.309810	0.154905	+	0.987929i	$0.450493\pi$
$62$	2.05005	0.260356
$63$	−2.57573	−0.324511
$64$	−10.0068	−1.25085
$65$	1.02946	0.127689
$66$	0.610792	0.0751833
$67$	7.11502	0.869238	0.434619	−	0.900614i	$-0.356883\pi$
$67$	7.11502	0.869238	0.434619	+	0.900614i	$0.356883\pi$
$68$	−13.8426	−1.67866
$69$	0.393586	0.0473822
$70$	−1.81631	−0.217091
$71$	−1.32186	−0.156875	−0.0784377	−	0.996919i	$-0.524993\pi$
$71$	−1.32186	−0.156875	−0.0784377	+	0.996919i	$0.524993\pi$
$72$	−1.64676	−0.194073
$73$	0.935253	0.109463	0.0547315	−	0.998501i	$-0.482570\pi$
$73$	0.935253	0.109463	0.0547315	+	0.998501i	$0.482570\pi$
$74$	−11.4519	−1.33125
$75$	−0.262672	−0.0303308
$76$	6.96750	0.799227
$77$	−0.988677	−0.112670
$78$	0.558899	0.0632828
$79$	5.24913	0.590573	0.295287	−	0.955409i	$-0.404585\pi$
$79$	5.24913	0.590573	0.295287	+	0.955409i	$0.404585\pi$
$80$	3.38243	0.378167
$81$	8.38379	0.931532
$82$	−10.7487	−1.18699
$83$	10.8117	1.18674	0.593368	−	0.804931i	$-0.297798\pi$
$83$	10.8117	1.18674	0.593368	+	0.804931i	$0.297798\pi$
$84$	−0.524415	−0.0572183
$85$	6.09313	0.660893
$86$	18.0956	1.95130
$87$	1.04556	0.112096
$88$	−0.632101	−0.0673822
$89$	−5.35414	−0.567538	−0.283769	−	0.958893i	$-0.591585\pi$
$89$	−5.35414	−0.567538	−0.283769	+	0.958893i	$0.591585\pi$
$90$	6.05792	0.638561
$91$	−0.904679	−0.0948361
$92$	−3.40410	−0.354902
$93$	−0.260538	−0.0270165
$94$	−9.69369	−0.999828
$95$	−3.06690	−0.314657
$96$	2.13149	0.217544
$97$	−7.29246	−0.740437	−0.370218	−	0.928945i	$-0.620717\pi$
$97$	−7.29246	−0.740437	−0.370218	+	0.928945i	$0.620717\pi$
$98$	−12.8717	−1.30024
$99$	3.29752	0.331413
$100$	2.27184	0.227184
$101$	−7.65072	−0.761276	−0.380638	−	0.924724i	$-0.624296\pi$
$101$	−7.65072	−0.761276	−0.380638	+	0.924724i	$0.624296\pi$
$102$	3.30798	0.327539
$103$	7.47299	0.736335	0.368168	−	0.929759i	$-0.379985\pi$
$103$	7.47299	0.736335	0.368168	+	0.929759i	$0.379985\pi$
$104$	−0.578397	−0.0567165
$105$	0.230833	0.0225270
$106$	1.87408	0.182026
$107$	1.84793	0.178646	0.0893230	−	0.996003i	$-0.471530\pi$
$107$	1.84793	0.178646	0.0893230	+	0.996003i	$0.471530\pi$
$108$	3.53932	0.340571
$109$	13.3646	1.28010	0.640048	−	0.768335i	$-0.278915\pi$
$109$	13.3646	1.28010	0.640048	+	0.768335i	$0.278915\pi$
$110$	2.32530	0.221709
$111$	1.45541	0.138141
$112$	−2.97243	−0.280869
$113$	−6.84209	−0.643649	−0.321825	−	0.946799i	$-0.604296\pi$
$113$	−6.84209	−0.643649	−0.321825	+	0.946799i	$0.604296\pi$
$114$	−1.66503	−0.155944
$115$	1.49839	0.139726
$116$	−9.04302	−0.839623
$117$	3.01736	0.278955
$118$	−16.2947	−1.50005
$119$	−5.35456	−0.490852
$120$	0.147581	0.0134722
$121$	−9.73427	−0.884933
$122$	5.00112	0.452781
$123$	1.36604	0.123171
$124$	2.25338	0.202359
$125$	−1.00000	−0.0894427
$126$	−5.32362	−0.474266
$127$	−20.4159	−1.81162	−0.905811	−	0.423682i	$-0.860737\pi$
$127$	−20.4159	−1.81162	−0.905811	+	0.423682i	$0.860737\pi$
$128$	−4.45323	−0.393613
$129$	−2.29975	−0.202482
$130$	2.12774	0.186615
$131$	13.7051	1.19742	0.598709	−	0.800966i	$-0.295681\pi$
$131$	13.7051	1.19742	0.598709	+	0.800966i	$0.295681\pi$
$132$	0.671371	0.0584354
$133$	2.69515	0.233699
$134$	14.7056	1.27037
$135$	−1.55791	−0.134084
$136$	−3.42338	−0.293553
$137$	−16.9037	−1.44418	−0.722092	−	0.691797i	$-0.756819\pi$
$137$	−16.9037	−1.44418	−0.722092	+	0.691797i	$0.756819\pi$
$138$	0.813480	0.0692480
$139$	11.0804	0.939825	0.469912	−	0.882713i	$-0.344286\pi$
$139$	11.0804	0.939825	0.469912	+	0.882713i	$0.344286\pi$
$140$	−1.99646	−0.168732
$141$	1.23196	0.103750
$142$	−2.73207	−0.229270
$143$	1.15820	0.0968534
$144$	9.91392	0.826160
$145$	3.98049	0.330561
$146$	1.93302	0.159978
$147$	1.63585	0.134923
$148$	−12.5877	−1.03470
$149$	5.49235	0.449951	0.224975	−	0.974364i	$-0.427770\pi$
$149$	5.49235	0.449951	0.224975	+	0.974364i	$0.427770\pi$
$150$	−0.542902	−0.0443278
$151$	10.0565	0.818390	0.409195	−	0.912447i	$-0.365810\pi$
$151$	10.0565	0.818390	0.409195	+	0.912447i	$0.365810\pi$
$152$	1.72312	0.139763
$153$	17.8590	1.44381
$154$	−2.04344	−0.164665
$155$	−0.991875	−0.0796693
$156$	0.614332	0.0491859
$157$	4.76723	0.380466	0.190233	−	0.981739i	$-0.439076\pi$
$157$	4.76723	0.380466	0.190233	+	0.981739i	$0.439076\pi$
$158$	10.8491	0.863110
$159$	−0.238174	−0.0188884
$160$	8.11464	0.641519
$161$	−1.31676	−0.103776
$162$	17.3280	1.36141
$163$	−13.0994	−1.02603	−0.513013	−	0.858381i	$-0.671471\pi$
$163$	−13.0994	−1.02603	−0.513013	+	0.858381i	$0.671471\pi$
$164$	−11.8148	−0.922577
$165$	−0.295519	−0.0230061
$166$	22.3460	1.73439
$167$	10.1839	0.788054	0.394027	−	0.919099i	$-0.371082\pi$
$167$	10.1839	0.788054	0.394027	+	0.919099i	$0.371082\pi$
$168$	−0.129692	−0.0100059
$169$	−11.9402	−0.918477
$170$	12.5935	0.965881
$171$	−8.98910	−0.687414
$172$	19.8904	1.51663
$173$	−16.6465	−1.26561	−0.632804	−	0.774312i	$-0.718096\pi$
$173$	−16.6465	−1.26561	−0.632804	+	0.774312i	$0.718096\pi$
$174$	2.16102	0.163826
$175$	0.878786	0.0664300
$176$	3.80540	0.286843
$177$	2.07088	0.155657
$178$	−11.0662	−0.829445
$179$	−13.7933	−1.03096	−0.515478	−	0.856903i	$-0.672386\pi$
$179$	−13.7933	−1.03096	−0.515478	+	0.856903i	$0.672386\pi$
$180$	6.65876	0.496315
$181$	10.9366	0.812907	0.406454	−	0.913671i	$-0.366765\pi$
$181$	10.9366	0.812907	0.406454	+	0.913671i	$0.366765\pi$
$182$	−1.86983	−0.138601
$183$	−0.635587	−0.0469839
$184$	−0.841860	−0.0620627
$185$	5.54076	0.407365
$186$	−0.538491	−0.0394841
$187$	6.85507	0.501293
$188$	−10.6551	−0.777105
$189$	1.36907	0.0995852
$190$	−6.33880	−0.459865
$191$	21.3637	1.54582	0.772911	−	0.634515i	$-0.218800\pi$
$191$	21.3637	1.54582	0.772911	+	0.634515i	$0.218800\pi$
$192$	2.62851	0.189697
$193$	14.8156	1.06645	0.533227	−	0.845972i	$-0.320979\pi$
$193$	14.8156	1.06645	0.533227	+	0.845972i	$0.320979\pi$
$194$	−15.0724	−1.08213
$195$	−0.270412	−0.0193646
$196$	−14.1484	−1.01060
$197$	−3.54684	−0.252702	−0.126351	−	0.991986i	$-0.540327\pi$
$197$	−3.54684	−0.252702	−0.126351	+	0.991986i	$0.540327\pi$
$198$	6.81546	0.484353
$199$	−14.7387	−1.04480	−0.522398	−	0.852702i	$-0.674962\pi$
$199$	−14.7387	−1.04480	−0.522398	+	0.852702i	$0.674962\pi$
$200$	0.561843	0.0397283
$201$	−1.86892	−0.131823
$202$	−15.8128	−1.11259
$203$	−3.49800	−0.245511
$204$	3.63607	0.254576
$205$	5.20053	0.363221
$206$	15.4455	1.07614
$207$	4.39179	0.305250
$208$	3.48209	0.241440
$209$	−3.45041	−0.238670
$210$	0.477095	0.0329227
$211$	−18.6015	−1.28058	−0.640290	−	0.768133i	$-0.721186\pi$
$211$	−18.6015	−1.28058	−0.640290	+	0.768133i	$0.721186\pi$
$212$	2.05995	0.141478
$213$	0.347215	0.0237908
$214$	3.81938	0.261087
$215$	−8.75520	−0.597100
$216$	0.875301	0.0595567
$217$	0.871646	0.0591712
$218$	27.6225	1.87083
$219$	−0.245665	−0.0166005
$220$	2.55593	0.172321
$221$	6.27266	0.421945
$222$	3.00809	0.201890
$223$	19.4010	1.29919	0.649594	−	0.760282i	$-0.274939\pi$
$223$	19.4010	1.29919	0.649594	+	0.760282i	$0.274939\pi$
$224$	−7.13103	−0.476462
$225$	−2.93100	−0.195400
$226$	−14.1415	−0.940680
$227$	3.11109	0.206490	0.103245	−	0.994656i	$-0.467077\pi$
$227$	3.11109	0.206490	0.103245	+	0.994656i	$0.467077\pi$
$228$	−1.83017	−0.121206
$229$	−24.4337	−1.61462	−0.807312	−	0.590125i	$-0.799078\pi$
$229$	−24.4337	−1.61462	−0.807312	+	0.590125i	$0.799078\pi$
$230$	3.09694	0.204206
$231$	0.259698	0.0170869
$232$	−2.23641	−0.146827
$233$	25.4903	1.66992	0.834962	−	0.550308i	$-0.185490\pi$
$233$	25.4903	1.66992	0.834962	+	0.550308i	$0.185490\pi$
$234$	6.23641	0.407687
$235$	4.69010	0.305948
$236$	−17.9109	−1.16590
$237$	−1.37880	−0.0895628
$238$	−11.0670	−0.717369
$239$	−5.16808	−0.334296	−0.167148	−	0.985932i	$-0.553456\pi$
$239$	−5.16808	−0.334296	−0.167148	+	0.985932i	$0.553456\pi$
$240$	−0.888472	−0.0573506
$241$	−1.15022	−0.0740922	−0.0370461	−	0.999314i	$-0.511795\pi$
$241$	−1.15022	−0.0740922	−0.0370461	+	0.999314i	$0.511795\pi$
$242$	−20.1192	−1.29331
$243$	−6.87592	−0.441091
$244$	5.49715	0.351919
$245$	6.22773	0.397875
$246$	2.82338	0.180012
$247$	−3.15727	−0.200892
$248$	0.557278	0.0353872
$249$	−2.83993	−0.179973
$250$	−2.06684	−0.130719
$251$	−4.39021	−0.277107	−0.138554	−	0.990355i	$-0.544245\pi$
$251$	−4.39021	−0.277107	−0.138554	+	0.990355i	$0.544245\pi$
$252$	−5.85163	−0.368618
$253$	1.68576	0.105983
$254$	−42.1965	−2.64765
$255$	−1.60050	−0.100227
$256$	10.8095	0.675595
$257$	−9.43332	−0.588434	−0.294217	−	0.955739i	$-0.595059\pi$
$257$	−9.43332	−0.588434	−0.294217	+	0.955739i	$0.595059\pi$
$258$	−4.75322	−0.295922
$259$	−4.86915	−0.302554
$260$	2.33877	0.145045
$261$	11.6668	0.722158
$262$	28.3262	1.75000
$263$	−7.04626	−0.434491	−0.217245	−	0.976117i	$-0.569707\pi$
$263$	−7.04626	−0.434491	−0.217245	+	0.976117i	$0.569707\pi$
$264$	0.166035	0.0102188
$265$	−0.906734	−0.0557002
$266$	5.57045	0.341546
$267$	1.40639	0.0860694
$268$	16.1642	0.987383
$269$	12.8317	0.782361	0.391180	−	0.920314i	$-0.372067\pi$
$269$	12.8317	0.782361	0.391180	+	0.920314i	$0.372067\pi$
$270$	−3.21996	−0.195960
$271$	19.4883	1.18383	0.591915	−	0.806000i	$-0.298372\pi$
$271$	19.4883	1.18383	0.591915	+	0.806000i	$0.298372\pi$
$272$	20.6096	1.24964
$273$	0.237634	0.0143823
$274$	−34.9374	−2.11064
$275$	−1.12505	−0.0678430
$276$	0.894162	0.0538222
$277$	−15.6496	−0.940296	−0.470148	−	0.882588i	$-0.655799\pi$
$277$	−15.6496	−0.940296	−0.470148	+	0.882588i	$0.655799\pi$
$278$	22.9014	1.37353
$279$	−2.90719	−0.174049
$280$	−0.493740	−0.0295066
$281$	20.6504	1.23190	0.615951	−	0.787785i	$-0.288772\pi$
$281$	20.6504	1.23190	0.615951	+	0.787785i	$0.288772\pi$
$282$	2.54626	0.151628
$283$	−0.756752	−0.0449843	−0.0224921	−	0.999747i	$-0.507160\pi$
$283$	−0.756752	−0.0449843	−0.0224921	+	0.999747i	$0.507160\pi$
$284$	−3.00304	−0.178198
$285$	0.805590	0.0477191
$286$	2.39381	0.141549
$287$	−4.57015	−0.269768
$288$	23.7840	1.40149
$289$	20.1263	1.18390
$290$	8.22704	0.483108
$291$	1.91553	0.112290
$292$	2.12474	0.124341
$293$	7.63195	0.445863	0.222932	−	0.974834i	$-0.428437\pi$
$293$	7.63195	0.445863	0.222932	+	0.974834i	$0.428437\pi$
$294$	3.38105	0.197187
$295$	7.88387	0.459017
$296$	−3.11304	−0.180942
$297$	−1.75273	−0.101703
$298$	11.3518	0.657593
$299$	1.54254	0.0892074
$300$	−0.596749	−0.0344533
$301$	7.69395	0.443472
$302$	20.7853	1.19606
$303$	2.00963	0.115450
$304$	−10.3736	−0.594966
$305$	−2.41969	−0.138551
$306$	36.9117	2.11010
$307$	25.5357	1.45740	0.728699	−	0.684834i	$-0.240125\pi$
$307$	25.5357	1.45740	0.728699	+	0.684834i	$0.240125\pi$
$308$	−2.24611	−0.127984
$309$	−1.96295	−0.111668
$310$	−2.05005	−0.116435
$311$	−31.6667	−1.79565	−0.897827	−	0.440348i	$-0.854855\pi$
$311$	−31.6667	−1.79565	−0.897827	+	0.440348i	$0.854855\pi$
$312$	0.151929	0.00860129
$313$	22.4422	1.26851	0.634254	−	0.773124i	$-0.281307\pi$
$313$	22.4422	1.26851	0.634254	+	0.773124i	$0.281307\pi$
$314$	9.85311	0.556043
$315$	2.57573	0.145126
$316$	11.9252	0.670843
$317$	−32.6878	−1.83593	−0.917966	−	0.396659i	$-0.870170\pi$
$317$	−32.6878	−1.83593	−0.917966	+	0.396659i	$0.870170\pi$
$318$	−0.492268	−0.0276050
$319$	4.47824	0.250733
$320$	10.0068	0.559398
$321$	−0.485400	−0.0270924
$322$	−2.72154	−0.151666
$323$	−18.6870	−1.03977
$324$	19.0466	1.05814
$325$	−1.02946	−0.0571044
$326$	−27.0744	−1.49951
$327$	−3.51051	−0.194132
$328$	−2.92188	−0.161334
$329$	−4.12159	−0.227231
$330$	−0.610792	−0.0336230
$331$	−22.5974	−1.24207	−0.621033	−	0.783784i	$-0.713287\pi$
$331$	−22.5974	−1.24207	−0.621033	+	0.783784i	$0.713287\pi$
$332$	24.5624	1.34804
$333$	16.2400	0.889946
$334$	21.0485	1.15172
$335$	−7.11502	−0.388735
$336$	0.780777	0.0425949
$337$	10.0204	0.545845	0.272922	−	0.962036i	$-0.412010\pi$
$337$	10.0204	0.545845	0.272922	+	0.962036i	$0.412010\pi$
$338$	−24.6785	−1.34233
$339$	1.79723	0.0976120
$340$	13.8426	0.750721
$341$	−1.11591	−0.0604298
$342$	−18.5790	−1.00464
$343$	−11.6244	−0.627656
$344$	4.91905	0.265217
$345$	−0.393586	−0.0211899
$346$	−34.4056	−1.84966
$347$	8.45091	0.453669	0.226834	−	0.973933i	$-0.427162\pi$
$347$	8.45091	0.453669	0.226834	+	0.973933i	$0.427162\pi$
$348$	2.37535	0.127332
$349$	0.401461	0.0214897	0.0107449	−	0.999942i	$-0.496580\pi$
$349$	0.401461	0.0214897	0.0107449	+	0.999942i	$0.496580\pi$
$350$	1.81631	0.0970860
$351$	−1.60381	−0.0856052
$352$	9.12937	0.486597
$353$	−10.6096	−0.564691	−0.282346	−	0.959313i	$-0.591112\pi$
$353$	−10.6096	−0.564691	−0.282346	+	0.959313i	$0.591112\pi$
$354$	4.28017	0.227489
$355$	1.32186	0.0701568
$356$	−12.1637	−0.644677
$357$	1.40650	0.0744396
$358$	−28.5085	−1.50672
$359$	−0.312602	−0.0164985	−0.00824926	−	0.999966i	$-0.502626\pi$
$359$	−0.312602	−0.0164985	−0.00824926	+	0.999966i	$0.502626\pi$
$360$	1.64676	0.0867920
$361$	−9.59411	−0.504953
$362$	22.6041	1.18805
$363$	2.55692	0.134204
$364$	−2.05528	−0.107726
$365$	−0.935253	−0.0489534
$366$	−1.31366	−0.0686660
$367$	10.6649	0.556701	0.278350	−	0.960480i	$-0.410212\pi$
$367$	10.6649	0.556701	0.278350	+	0.960480i	$0.410212\pi$
$368$	5.06820	0.264198
$369$	15.2428	0.793507
$370$	11.4519	0.595355
$371$	0.796826	0.0413691
$372$	−0.591900	−0.0306886
$373$	8.60583	0.445593	0.222796	−	0.974865i	$-0.428481\pi$
$373$	8.60583	0.445593	0.222796	+	0.974865i	$0.428481\pi$
$374$	14.1684	0.732628
$375$	0.262672	0.0135643
$376$	−2.63510	−0.135895
$377$	4.09777	0.211046
$378$	2.82965	0.145542
$379$	−0.807909	−0.0414995	−0.0207497	−	0.999785i	$-0.506605\pi$
$379$	−0.807909	−0.0414995	−0.0207497	+	0.999785i	$0.506605\pi$
$380$	−6.96750	−0.357425
$381$	5.36270	0.274740
$382$	44.1554	2.25918
$383$	14.1937	0.725265	0.362632	−	0.931932i	$-0.381878\pi$
$383$	14.1937	0.725265	0.362632	+	0.931932i	$0.381878\pi$
$384$	1.16974	0.0596930
$385$	0.988677	0.0503877
$386$	30.6216	1.55860
$387$	−25.6615	−1.30445
$388$	−16.5673	−0.841076
$389$	−21.5364	−1.09194	−0.545968	−	0.837806i	$-0.683838\pi$
$389$	−21.5364	−1.09194	−0.545968	+	0.837806i	$0.683838\pi$
$390$	−0.558899	−0.0283009
$391$	9.12989	0.461718
$392$	−3.49901	−0.176727
$393$	−3.59995	−0.181593
$394$	−7.33076	−0.369318
$395$	−5.24913	−0.264112
$396$	7.49143	0.376459
$397$	−7.58822	−0.380842	−0.190421	−	0.981703i	$-0.560985\pi$
$397$	−7.58822	−0.380842	−0.190421	+	0.981703i	$0.560985\pi$
$398$	−30.4625	−1.52695
$399$	−0.707942	−0.0354414
$400$	−3.38243	−0.169122
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−3.86276	−0.192657
$403$	−1.02110	−0.0508646
$404$	−17.3812	−0.864747
$405$	−8.38379	−0.416594
$406$	−7.22981	−0.358809
$407$	6.23363	0.308990
$408$	0.899228	0.0445184
$409$	−33.7750	−1.67006	−0.835032	−	0.550202i	$-0.814551\pi$
$409$	−33.7750	−1.67006	−0.835032	+	0.550202i	$0.814551\pi$
$410$	10.7487	0.530839
$411$	4.44014	0.219016
$412$	16.9774	0.836417
$413$	−6.92824	−0.340916
$414$	9.07713	0.446117
$415$	−10.8117	−0.530725
$416$	8.35373	0.409575
$417$	−2.91051	−0.142528
$418$	−7.13146	−0.348811
$419$	21.0064	1.02623	0.513116	−	0.858320i	$-0.328491\pi$
$419$	21.0064	1.02623	0.513116	+	0.858320i	$0.328491\pi$
$420$	0.524415	0.0255888
$421$	−1.30664	−0.0636815	−0.0318408	−	0.999493i	$-0.510137\pi$
$421$	−1.30664	−0.0636815	−0.0318408	+	0.999493i	$0.510137\pi$
$422$	−38.4464	−1.87154
$423$	13.7467	0.668387
$424$	0.509442	0.0247407
$425$	−6.09313	−0.295560
$426$	0.717638	0.0347697
$427$	2.12639	0.102903
$428$	4.19819	0.202927
$429$	−0.304227	−0.0146882
$430$	−18.0956	−0.872648
$431$	−8.64315	−0.416326	−0.208163	−	0.978094i	$-0.566748\pi$
$431$	−8.64315	−0.416326	−0.208163	+	0.978094i	$0.566748\pi$
$432$	−5.26953	−0.253530
$433$	3.85270	0.185149	0.0925744	−	0.995706i	$-0.470490\pi$
$433$	3.85270	0.185149	0.0925744	+	0.995706i	$0.470490\pi$
$434$	1.80155	0.0864774
$435$	−1.04556	−0.0501310
$436$	30.3622	1.45408
$437$	−4.59542	−0.219829
$438$	−0.507751	−0.0242613
$439$	−23.0287	−1.09910	−0.549551	−	0.835460i	$-0.685201\pi$
$439$	−23.0287	−1.09910	−0.549551	+	0.835460i	$0.685201\pi$
$440$	0.632101	0.0301342
$441$	18.2535	0.869215
$442$	12.9646	0.616664
$443$	−13.6140	−0.646820	−0.323410	−	0.946259i	$-0.604829\pi$
$443$	−13.6140	−0.646820	−0.323410	+	0.946259i	$0.604829\pi$
$444$	3.30644	0.156917
$445$	5.35414	0.253811
$446$	40.0988	1.89873
$447$	−1.44269	−0.0682368
$448$	−8.79385	−0.415470
$449$	2.35577	0.111176	0.0555878	−	0.998454i	$-0.482297\pi$
$449$	2.35577	0.111176	0.0555878	+	0.998454i	$0.482297\pi$
$450$	−6.05792	−0.285573
$451$	5.85085	0.275506
$452$	−15.5441	−0.731133
$453$	−2.64158	−0.124112
$454$	6.43013	0.301781
$455$	0.904679	0.0424120
$456$	−0.452615	−0.0211957
$457$	36.7977	1.72132	0.860662	−	0.509178i	$-0.170050\pi$
$457$	36.7977	1.72132	0.860662	+	0.509178i	$0.170050\pi$
$458$	−50.5006	−2.35974
$459$	−9.49256	−0.443075
$460$	3.40410	0.158717
$461$	−7.44784	−0.346881	−0.173440	−	0.984844i	$-0.555488\pi$
$461$	−7.44784	−0.346881	−0.173440	+	0.984844i	$0.555488\pi$
$462$	0.536755	0.0249721
$463$	−13.2116	−0.613994	−0.306997	−	0.951710i	$-0.599324\pi$
$463$	−13.2116	−0.613994	−0.306997	+	0.951710i	$0.599324\pi$
$464$	13.4637	0.625038
$465$	0.260538	0.0120822
$466$	52.6844	2.44056
$467$	8.58967	0.397482	0.198741	−	0.980052i	$-0.436315\pi$
$467$	8.58967	0.397482	0.198741	+	0.980052i	$0.436315\pi$
$468$	6.85496	0.316870
$469$	6.25258	0.288717
$470$	9.69369	0.447137
$471$	−1.25222	−0.0576993
$472$	−4.42950	−0.203884
$473$	−9.85003	−0.452905
$474$	−2.84976	−0.130894
$475$	3.06690	0.140719
$476$	−12.1647	−0.557568
$477$	−2.65764	−0.121685
$478$	−10.6816	−0.488566
$479$	27.7678	1.26874	0.634372	−	0.773028i	$-0.281259\pi$
$479$	27.7678	1.26874	0.634372	+	0.773028i	$0.281259\pi$
$480$	−2.13149	−0.0972888
$481$	5.70402	0.260081
$482$	−2.37732	−0.108284
$483$	0.345878	0.0157380
$484$	−22.1147	−1.00521
$485$	7.29246	0.331133
$486$	−14.2114	−0.644644
$487$	−30.4651	−1.38051	−0.690253	−	0.723568i	$-0.742501\pi$
$487$	−30.4651	−1.38051	−0.690253	+	0.723568i	$0.742501\pi$
$488$	1.35949	0.0615411
$489$	3.44086	0.155601
$490$	12.8717	0.581486
$491$	21.1590	0.954894	0.477447	−	0.878661i	$-0.341562\pi$
$491$	21.1590	0.954894	0.477447	+	0.878661i	$0.341562\pi$
$492$	3.10341	0.139913
$493$	24.2536	1.09233
$494$	−6.52557	−0.293599
$495$	−3.29752	−0.148213
$496$	−3.35495	−0.150642
$497$	−1.16163	−0.0521061
$498$	−5.86969	−0.263027
$499$	−36.9284	−1.65314	−0.826571	−	0.562832i	$-0.809712\pi$
$499$	−36.9284	−1.65314	−0.826571	+	0.562832i	$0.809712\pi$
$500$	−2.27184	−0.101600
$501$	−2.67503	−0.119512
$502$	−9.07387	−0.404986
$503$	−25.7051	−1.14613	−0.573066	−	0.819509i	$-0.694246\pi$
$503$	−25.7051	−1.14613	−0.573066	+	0.819509i	$0.694246\pi$
$504$	−1.44715	−0.0644613
$505$	7.65072	0.340453
$506$	3.48420	0.154892
$507$	3.13636	0.139291
$508$	−46.3817	−2.05785
$509$	−18.5699	−0.823096	−0.411548	−	0.911388i	$-0.635012\pi$
$509$	−18.5699	−0.823096	−0.411548	+	0.911388i	$0.635012\pi$
$510$	−3.30798	−0.146480
$511$	0.821887	0.0363581
$512$	31.2480	1.38098
$513$	4.77796	0.210952
$514$	−19.4972	−0.859984
$515$	−7.47299	−0.329299
$516$	−5.22465	−0.230003
$517$	5.27659	0.232064
$518$	−10.0638	−0.442176
$519$	4.37257	0.191934
$520$	0.578397	0.0253644
$521$	−31.5135	−1.38063	−0.690317	−	0.723507i	$-0.742529\pi$
$521$	−31.5135	−1.38063	−0.690317	+	0.723507i	$0.742529\pi$
$522$	24.1135	1.05542
$523$	−14.2124	−0.621466	−0.310733	−	0.950497i	$-0.600575\pi$
$523$	−14.2124	−0.621466	−0.310733	+	0.950497i	$0.600575\pi$
$524$	31.1357	1.36017
$525$	−0.230833	−0.0100744
$526$	−14.5635	−0.634999
$527$	−6.04363	−0.263264
$528$	−0.999574	−0.0435009
$529$	−20.7548	−0.902384
$530$	−1.87408	−0.0814047
$531$	23.1077	1.00279
$532$	6.12294	0.265463
$533$	5.35376	0.231897
$534$	2.90678	0.125789
$535$	−1.84793	−0.0798929
$536$	3.99752	0.172667
$537$	3.62311	0.156349
$538$	26.5210	1.14340
$539$	7.00651	0.301792
$540$	−3.53932	−0.152308
$541$	4.84551	0.208325	0.104162	−	0.994560i	$-0.466784\pi$
$541$	4.84551	0.208325	0.104162	+	0.994560i	$0.466784\pi$
$542$	40.2793	1.73014
$543$	−2.87273	−0.123281
$544$	49.4436	2.11988
$545$	−13.3646	−0.572476
$546$	0.491152	0.0210194
$547$	1.66957	0.0713855	0.0356927	−	0.999363i	$-0.488636\pi$
$547$	1.66957	0.0713855	0.0356927	+	0.999363i	$0.488636\pi$
$548$	−38.4025	−1.64047
$549$	−7.09213	−0.302685
$550$	−2.32530	−0.0991511
$551$	−12.2078	−0.520068
$552$	0.221133	0.00941206
$553$	4.61286	0.196159
$554$	−32.3453	−1.37422
$555$	−1.45541	−0.0617785
$556$	25.1728	1.06756
$557$	−14.0436	−0.595045	−0.297523	−	0.954715i	$-0.596160\pi$
$557$	−14.0436	−0.595045	−0.297523	+	0.954715i	$0.596160\pi$
$558$	−6.00870	−0.254368
$559$	−9.01317	−0.381216
$560$	2.97243	0.125608
$561$	−1.80064	−0.0760230
$562$	42.6812	1.80040
$563$	−2.22510	−0.0937767	−0.0468884	−	0.998900i	$-0.514931\pi$
$563$	−2.22510	−0.0937767	−0.0468884	+	0.998900i	$0.514931\pi$
$564$	2.79881	0.117851
$565$	6.84209	0.287849
$566$	−1.56409	−0.0657435
$567$	7.36756	0.309408
$568$	−0.742675	−0.0311620
$569$	3.57484	0.149865	0.0749325	−	0.997189i	$-0.476126\pi$
$569$	3.57484	0.149865	0.0749325	+	0.997189i	$0.476126\pi$
$570$	1.66503	0.0697404
$571$	−24.9372	−1.04359	−0.521794	−	0.853071i	$-0.674737\pi$
$571$	−24.9372	−1.04359	−0.521794	+	0.853071i	$0.674737\pi$
$572$	2.63124	0.110018
$573$	−5.61165	−0.234430
$574$	−9.44579	−0.394260
$575$	−1.49839	−0.0624872
$576$	29.3300	1.22208
$577$	30.8545	1.28449	0.642245	−	0.766500i	$-0.278003\pi$
$577$	30.8545	1.28449	0.642245	+	0.766500i	$0.278003\pi$
$578$	41.5978	1.73024
$579$	−3.89166	−0.161732
$580$	9.04302	0.375491
$581$	9.50116	0.394174
$582$	3.95909	0.164110
$583$	−1.02012	−0.0422491
$584$	0.525465	0.0217439
$585$	−3.01736	−0.124753
$586$	15.7740	0.651619
$587$	6.34468	0.261873	0.130936	−	0.991391i	$-0.458202\pi$
$587$	6.34468	0.261873	0.130936	+	0.991391i	$0.458202\pi$
$588$	3.71639	0.153261
$589$	3.04198	0.125343
$590$	16.2947	0.670843
$591$	0.931657	0.0383233
$592$	18.7413	0.770261
$593$	4.03339	0.165632	0.0828158	−	0.996565i	$-0.473609\pi$
$593$	4.03339	0.165632	0.0828158	+	0.996565i	$0.473609\pi$
$594$	−3.62261	−0.148637
$595$	5.35456	0.219516
$596$	12.4777	0.511107
$597$	3.87144	0.158447
$598$	3.18819	0.130375
$599$	−16.2199	−0.662728	−0.331364	−	0.943503i	$-0.607509\pi$
$599$	−16.2199	−0.662728	−0.331364	+	0.943503i	$0.607509\pi$
$600$	−0.147581	−0.00602495
$601$	−5.82904	−0.237771	−0.118886	−	0.992908i	$-0.537932\pi$
$601$	−5.82904	−0.237771	−0.118886	+	0.992908i	$0.537932\pi$
$602$	15.9022	0.648124
$603$	−20.8541	−0.849246
$604$	22.8468	0.929624
$605$	9.73427	0.395754
$606$	4.15360	0.168728
$607$	2.93440	0.119104	0.0595519	−	0.998225i	$-0.481033\pi$
$607$	2.93440	0.119104	0.0595519	+	0.998225i	$0.481033\pi$
$608$	−24.8868	−1.00929
$609$	0.918827	0.0372328
$610$	−5.00112	−0.202490
$611$	4.82829	0.195332
$612$	40.5727	1.64005
$613$	−46.5854	−1.88157	−0.940784	−	0.339007i	$-0.889909\pi$
$613$	−46.5854	−1.88157	−0.940784	+	0.339007i	$0.889909\pi$
$614$	52.7782	2.12996
$615$	−1.36604	−0.0550839
$616$	−0.555481	−0.0223810
$617$	−24.8119	−0.998891	−0.499445	−	0.866345i	$-0.666463\pi$
$617$	−24.8119	−0.998891	−0.499445	+	0.866345i	$0.666463\pi$
$618$	−4.05710	−0.163201
$619$	9.26565	0.372418	0.186209	−	0.982510i	$-0.440380\pi$
$619$	9.26565	0.372418	0.186209	+	0.982510i	$0.440380\pi$
$620$	−2.25338	−0.0904978
$621$	−2.33436	−0.0936746
$622$	−65.4501	−2.62431
$623$	−4.70515	−0.188508
$624$	−0.914650	−0.0366153
$625$	1.00000	0.0400000
$626$	46.3845	1.85390
$627$	0.906329	0.0361953
$628$	10.8304	0.432179
$629$	33.7606	1.34612
$630$	5.32362	0.212098
$631$	−30.1268	−1.19933	−0.599665	−	0.800251i	$-0.704699\pi$
$631$	−30.1268	−1.19933	−0.599665	+	0.800251i	$0.704699\pi$
$632$	2.94919	0.117312
$633$	4.88610	0.194205
$634$	−67.5606	−2.68317
$635$	20.4159	0.810182
$636$	−0.541093	−0.0214557
$637$	6.41123	0.254022
$638$	9.25582	0.366441
$639$	3.87436	0.153267
$640$	4.45323	0.176029
$641$	−1.91092	−0.0754769	−0.0377384	−	0.999288i	$-0.512015\pi$
$641$	−1.91092	−0.0754769	−0.0377384	+	0.999288i	$0.512015\pi$
$642$	−1.00324	−0.0395949
$643$	−8.05299	−0.317579	−0.158789	−	0.987312i	$-0.550759\pi$
$643$	−8.05299	−0.317579	−0.158789	+	0.987312i	$0.550759\pi$
$644$	−2.99147	−0.117881
$645$	2.29975	0.0905525
$646$	−38.6232	−1.51961
$647$	14.2108	0.558684	0.279342	−	0.960192i	$-0.409884\pi$
$647$	14.2108	0.558684	0.279342	+	0.960192i	$0.409884\pi$
$648$	4.71037	0.185041
$649$	8.86974	0.348168
$650$	−2.12774	−0.0834568
$651$	−0.228957	−0.00897354
$652$	−29.7597	−1.16548
$653$	19.5488	0.765005	0.382502	−	0.923955i	$-0.375062\pi$
$653$	19.5488	0.765005	0.382502	+	0.923955i	$0.375062\pi$
$654$	−7.25567	−0.283719
$655$	−13.7051	−0.535502
$656$	17.5904	0.686791
$657$	−2.74123	−0.106946
$658$	−8.51868	−0.332093
$659$	−4.73052	−0.184275	−0.0921374	−	0.995746i	$-0.529370\pi$
$659$	−4.73052	−0.184275	−0.0921374	+	0.995746i	$0.529370\pi$
$660$	−0.671371	−0.0261331
$661$	9.49404	0.369276	0.184638	−	0.982807i	$-0.440889\pi$
$661$	9.49404	0.369276	0.184638	+	0.982807i	$0.440889\pi$
$662$	−46.7053	−1.81525
$663$	−1.64766	−0.0639897
$664$	6.07447	0.235735
$665$	−2.69515	−0.104513
$666$	33.5655	1.30064
$667$	5.96432	0.230939
$668$	23.1362	0.895165
$669$	−5.09611	−0.197027
$670$	−14.7056	−0.568128
$671$	−2.72227	−0.105092
$672$	1.87313	0.0722574
$673$	−38.6525	−1.48994	−0.744972	−	0.667096i	$-0.767537\pi$
$673$	−38.6525	−1.48994	−0.744972	+	0.667096i	$0.767537\pi$
$674$	20.7105	0.797740
$675$	1.55791	0.0599640
$676$	−27.1262	−1.04331
$677$	28.1678	1.08258	0.541288	−	0.840837i	$-0.317937\pi$
$677$	28.1678	1.08258	0.541288	+	0.840837i	$0.317937\pi$
$678$	3.71459	0.142658
$679$	−6.40851	−0.245936
$680$	3.42338	0.131281
$681$	−0.817197	−0.0313151
$682$	−2.30640	−0.0883168
$683$	−29.7519	−1.13843	−0.569213	−	0.822190i	$-0.692752\pi$
$683$	−29.7519	−1.13843	−0.569213	+	0.822190i	$0.692752\pi$
$684$	−20.4218	−0.780846
$685$	16.9037	0.645859
$686$	−24.0257	−0.917305
$687$	6.41806	0.244864
$688$	−29.6139	−1.12902
$689$	−0.933451	−0.0355616
$690$	−0.813480	−0.0309686
$691$	13.1513	0.500297	0.250149	−	0.968207i	$-0.419521\pi$
$691$	13.1513	0.500297	0.250149	+	0.968207i	$0.419521\pi$
$692$	−37.8180	−1.43763
$693$	2.89782	0.110079
$694$	17.4667	0.663027
$695$	−11.0804	−0.420302
$696$	0.587443	0.0222670
$697$	31.6875	1.20025
$698$	0.829756	0.0314067
$699$	−6.69559	−0.253251
$700$	1.99646	0.0754590
$701$	−26.0600	−0.984273	−0.492137	−	0.870518i	$-0.663784\pi$
$701$	−26.0600	−0.984273	−0.492137	+	0.870518i	$0.663784\pi$
$702$	−3.31483	−0.125110
$703$	−16.9930	−0.640902
$704$	11.2582	0.424308
$705$	−1.23196	−0.0463983
$706$	−21.9283	−0.825284
$707$	−6.72335	−0.252858
$708$	4.70469	0.176813
$709$	−22.6119	−0.849207	−0.424604	−	0.905379i	$-0.639587\pi$
$709$	−22.6119	−0.849207	−0.424604	+	0.905379i	$0.639587\pi$
$710$	2.73207	0.102533
$711$	−15.3852	−0.576991
$712$	−3.00819	−0.112737
$713$	−1.48622	−0.0556592
$714$	2.90700	0.108792
$715$	−1.15820	−0.0433141
$716$	−31.3360	−1.17108
$717$	1.35751	0.0506972
$718$	−0.646099	−0.0241122
$719$	−42.3990	−1.58122	−0.790609	−	0.612322i	$-0.790236\pi$
$719$	−42.3990	−1.58122	−0.790609	+	0.612322i	$0.790236\pi$
$720$	−9.91392	−0.369470
$721$	6.56716	0.244574
$722$	−19.8295	−0.737978
$723$	0.302131	0.0112364
$724$	24.8461	0.923396
$725$	−3.98049	−0.147832
$726$	5.28476	0.196136
$727$	18.1300	0.672406	0.336203	−	0.941790i	$-0.390857\pi$
$727$	18.1300	0.672406	0.336203	+	0.941790i	$0.390857\pi$
$728$	−0.508288	−0.0188384
$729$	−23.3453	−0.864639
$730$	−1.93302	−0.0715443
$731$	−53.3466	−1.97310
$732$	−1.44395	−0.0533699
$733$	28.6342	1.05763	0.528815	−	0.848737i	$-0.322637\pi$
$733$	28.6342	1.05763	0.528815	+	0.848737i	$0.322637\pi$
$734$	22.0426	0.813606
$735$	−1.63585	−0.0603394
$736$	12.1589	0.448183
$737$	−8.00474	−0.294859
$738$	31.5044	1.15969
$739$	−51.4384	−1.89219	−0.946097	−	0.323885i	$-0.895011\pi$
$739$	−51.4384	−1.89219	−0.946097	+	0.323885i	$0.895011\pi$
$740$	12.5877	0.462733
$741$	0.829327	0.0304661
$742$	1.64691	0.0604601
$743$	−4.16154	−0.152672	−0.0763361	−	0.997082i	$-0.524322\pi$
$743$	−4.16154	−0.152672	−0.0763361	+	0.997082i	$0.524322\pi$
$744$	−0.146381	−0.00536661
$745$	−5.49235	−0.201224
$746$	17.7869	0.651224
$747$	−31.6891	−1.15944
$748$	15.5736	0.569427
$749$	1.62393	0.0593373
$750$	0.542902	0.0198240
$751$	−36.4732	−1.33093	−0.665464	−	0.746430i	$-0.731766\pi$
$751$	−36.4732	−1.33093	−0.665464	+	0.746430i	$0.731766\pi$
$752$	15.8639	0.578498
$753$	1.15319	0.0420244
$754$	8.46944	0.308439
$755$	−10.0565	−0.365995
$756$	3.11030	0.113121
$757$	−54.0392	−1.96409	−0.982043	−	0.188655i	$-0.939587\pi$
$757$	−54.0392	−1.96409	−0.982043	+	0.188655i	$0.939587\pi$
$758$	−1.66982	−0.0606506
$759$	−0.442803	−0.0160727
$760$	−1.72312	−0.0625040
$761$	−3.55049	−0.128705	−0.0643526	−	0.997927i	$-0.520498\pi$
$761$	−3.55049	−0.128705	−0.0643526	+	0.997927i	$0.520498\pi$
$762$	11.0839	0.401526
$763$	11.7446	0.425184
$764$	48.5348	1.75593
$765$	−17.8590	−0.645693
$766$	29.3362	1.05996
$767$	8.11617	0.293058
$768$	−2.83936	−0.102457
$769$	3.57412	0.128886	0.0644431	−	0.997921i	$-0.479473\pi$
$769$	3.57412	0.128886	0.0644431	+	0.997921i	$0.479473\pi$
$770$	2.04344	0.0736405
$771$	2.47787	0.0892384
$772$	33.6587	1.21140
$773$	18.2249	0.655503	0.327751	−	0.944764i	$-0.393709\pi$
$773$	18.2249	0.655503	0.327751	+	0.944764i	$0.393709\pi$
$774$	−53.0383	−1.90642
$775$	0.991875	0.0356292
$776$	−4.09722	−0.147081
$777$	1.27899	0.0458835
$778$	−44.5123	−1.59584
$779$	−15.9495	−0.571451
$780$	−0.614332	−0.0219966
$781$	1.48715	0.0532145
$782$	18.8700	0.674791
$783$	−6.20124	−0.221614
$784$	21.0649	0.752318
$785$	−4.76723	−0.170150
$786$	−7.44052	−0.265395
$787$	12.4282	0.443016	0.221508	−	0.975159i	$-0.428902\pi$
$787$	12.4282	0.443016	0.221508	+	0.975159i	$0.428902\pi$
$788$	−8.05784	−0.287049
$789$	1.85086	0.0658923
$790$	−10.8491	−0.385994
$791$	−6.01273	−0.213788
$792$	1.85269	0.0658324
$793$	−2.49099	−0.0884576
$794$	−15.6837	−0.556592
$795$	0.238174	0.00844716
$796$	−33.4838	−1.18680
$797$	−8.99847	−0.318742	−0.159371	−	0.987219i	$-0.550947\pi$
$797$	−8.99847	−0.318742	−0.159371	+	0.987219i	$0.550947\pi$
$798$	−1.46320	−0.0517969
$799$	28.5774	1.01100
$800$	−8.11464	−0.286896
$801$	15.6930	0.554485
$802$	−2.06684	−0.0729827
$803$	−1.05220	−0.0371315
$804$	−4.24588	−0.149741
$805$	1.31676	0.0464098
$806$	−2.11045	−0.0743375
$807$	−3.37053	−0.118648
$808$	−4.29851	−0.151221
$809$	32.2984	1.13555	0.567776	−	0.823183i	$-0.307804\pi$
$809$	32.2984	1.13555	0.567776	+	0.823183i	$0.307804\pi$
$810$	−17.3280	−0.608843
$811$	−12.0847	−0.424352	−0.212176	−	0.977231i	$-0.568055\pi$
$811$	−12.0847	−0.424352	−0.212176	+	0.977231i	$0.568055\pi$
$812$	−7.94688	−0.278881
$813$	−5.11904	−0.179533
$814$	12.8839	0.451581
$815$	13.0994	0.458853
$816$	−5.41358	−0.189513
$817$	26.8513	0.939409
$818$	−69.8075	−2.44076
$819$	2.65162	0.0926550
$820$	11.8148	0.412589
$821$	0.314207	0.0109659	0.00548294	−	0.999985i	$-0.498255\pi$
$821$	0.314207	0.0109659	0.00548294	+	0.999985i	$0.498255\pi$
$822$	9.17708	0.320087
$823$	44.0175	1.53435	0.767177	−	0.641435i	$-0.221661\pi$
$823$	44.0175	1.53435	0.767177	+	0.641435i	$0.221661\pi$
$824$	4.19865	0.146267
$825$	0.295519	0.0102887
$826$	−14.3196	−0.498242
$827$	18.7586	0.652299	0.326149	−	0.945318i	$-0.394249\pi$
$827$	18.7586	0.652299	0.326149	+	0.945318i	$0.394249\pi$
$828$	9.97742	0.346739
$829$	−17.3352	−0.602076	−0.301038	−	0.953612i	$-0.597333\pi$
$829$	−17.3352	−0.602076	−0.301038	+	0.953612i	$0.597333\pi$
$830$	−22.3460	−0.775642
$831$	4.11073	0.142600
$832$	10.3017	0.357146
$833$	37.9464	1.31477
$834$	−6.01556	−0.208302
$835$	−10.1839	−0.352429
$836$	−7.83878	−0.271110
$837$	1.54525	0.0534117
$838$	43.4170	1.49981
$839$	−11.1794	−0.385956	−0.192978	−	0.981203i	$-0.561815\pi$
$839$	−11.1794	−0.385956	−0.192978	+	0.981203i	$0.561815\pi$
$840$	0.129692	0.00447479
$841$	−13.1557	−0.453646
$842$	−2.70061	−0.0930692
$843$	−5.42430	−0.186823
$844$	−42.2596	−1.45463
$845$	11.9402	0.410755
$846$	28.4122	0.976833
$847$	−8.55434	−0.293931
$848$	−3.06697	−0.105320
$849$	0.198778	0.00682204
$850$	−12.5935	−0.431955
$851$	8.30222	0.284597
$852$	0.788815	0.0270244
$853$	13.9401	0.477299	0.238650	−	0.971106i	$-0.423295\pi$
$853$	13.9401	0.477299	0.238650	+	0.971106i	$0.423295\pi$
$854$	4.39492	0.150391
$855$	8.98910	0.307421
$856$	1.03825	0.0354865
$857$	27.6629	0.944948	0.472474	−	0.881345i	$-0.343361\pi$
$857$	27.6629	0.944948	0.472474	+	0.881345i	$0.343361\pi$
$858$	−0.628788	−0.0214665
$859$	−3.78329	−0.129084	−0.0645421	−	0.997915i	$-0.520559\pi$
$859$	−3.78329	−0.129084	−0.0645421	+	0.997915i	$0.520559\pi$
$860$	−19.8904	−0.678256
$861$	1.20045	0.0409113
$862$	−17.8640	−0.608451
$863$	−33.6095	−1.14408	−0.572041	−	0.820225i	$-0.693848\pi$
$863$	−33.6095	−1.14408	−0.572041	+	0.820225i	$0.693848\pi$
$864$	−12.6419	−0.430086
$865$	16.6465	0.565997
$866$	7.96292	0.270591
$867$	−5.28662	−0.179543
$868$	1.98024	0.0672136
$869$	−5.90553	−0.200331
$870$	−2.16102	−0.0732653
$871$	−7.32466	−0.248187
$872$	7.50880	0.254280
$873$	21.3742	0.723408
$874$	−9.49800	−0.321275
$875$	−0.878786	−0.0297084
$876$	−0.558111	−0.0188568
$877$	−21.5199	−0.726675	−0.363337	−	0.931658i	$-0.618363\pi$
$877$	−21.5199	−0.726675	−0.363337	+	0.931658i	$0.618363\pi$
$878$	−47.5968	−1.60631
$879$	−2.00470	−0.0676169
$880$	−3.80540	−0.128280
$881$	21.6830	0.730519	0.365260	−	0.930906i	$-0.380980\pi$
$881$	21.6830	0.730519	0.365260	+	0.930906i	$0.380980\pi$
$882$	37.7271	1.27034
$883$	31.4890	1.05969	0.529844	−	0.848095i	$-0.322250\pi$
$883$	31.4890	1.05969	0.529844	+	0.848095i	$0.322250\pi$
$884$	14.2505	0.479295
$885$	−2.07088	−0.0696117
$886$	−28.1380	−0.945313
$887$	41.0909	1.37970	0.689849	−	0.723953i	$-0.257677\pi$
$887$	41.0909	1.37970	0.689849	+	0.723953i	$0.257677\pi$
$888$	0.817709	0.0274405
$889$	−17.9412	−0.601730
$890$	11.0662	0.370939
$891$	−9.43217	−0.315990
$892$	44.0759	1.47577
$893$	−14.3841	−0.481344
$894$	−2.98181	−0.0997266
$895$	13.7933	0.461058
$896$	−3.91343	−0.130739
$897$	−0.405182	−0.0135286
$898$	4.86900	0.162481
$899$	−3.94814	−0.131678
$900$	−6.65876	−0.221959
$901$	−5.52485	−0.184060
$902$	12.0928	0.402646
$903$	−2.02099	−0.0672543
$904$	−3.84418	−0.127855
$905$	−10.9366	−0.363543
$906$	−5.45972	−0.181387
$907$	25.4881	0.846319	0.423160	−	0.906055i	$-0.360921\pi$
$907$	25.4881	0.846319	0.423160	+	0.906055i	$0.360921\pi$
$908$	7.06788	0.234556
$909$	22.4243	0.743767
$910$	1.86983	0.0619842
$911$	−12.5084	−0.414422	−0.207211	−	0.978296i	$-0.566439\pi$
$911$	−12.5084	−0.414422	−0.207211	+	0.978296i	$0.566439\pi$
$912$	2.72486	0.0902290
$913$	−12.1637	−0.402559
$914$	76.0550	2.51568
$915$	0.635587	0.0210118
$916$	−55.5093	−1.83408
$917$	12.0438	0.397722
$918$	−19.6196	−0.647544
$919$	9.72317	0.320738	0.160369	−	0.987057i	$-0.448732\pi$
$919$	9.72317	0.320738	0.160369	+	0.987057i	$0.448732\pi$
$920$	0.841860	0.0277553
$921$	−6.70752	−0.221020
$922$	−15.3935	−0.506958
$923$	1.36080	0.0447914
$924$	0.589992	0.0194093
$925$	−5.54076	−0.182179
$926$	−27.3063	−0.897339
$927$	−21.9034	−0.719401
$928$	32.3002	1.06031
$929$	51.9286	1.70372	0.851862	−	0.523767i	$-0.175474\pi$
$929$	51.9286	1.70372	0.851862	+	0.523767i	$0.175474\pi$
$930$	0.538491	0.0176578
$931$	−19.0999	−0.625972
$932$	57.9098	1.89690
$933$	8.31797	0.272318
$934$	17.7535	0.580912
$935$	−6.85507	−0.224185
$936$	1.69528	0.0554121
$937$	−20.2924	−0.662924	−0.331462	−	0.943468i	$-0.607542\pi$
$937$	−20.2924	−0.662924	−0.331462	+	0.943468i	$0.607542\pi$
$938$	12.9231	0.421954
$939$	−5.89495	−0.192374
$940$	10.6551	0.347532
$941$	21.2507	0.692755	0.346377	−	0.938095i	$-0.387412\pi$
$941$	21.2507	0.692755	0.346377	+	0.938095i	$0.387412\pi$
$942$	−2.58814	−0.0843262
$943$	7.79242	0.253756
$944$	26.6667	0.867926
$945$	−1.36907	−0.0445359
$946$	−20.3585	−0.661910
$947$	−29.6835	−0.964586	−0.482293	−	0.876010i	$-0.660196\pi$
$947$	−29.6835	−0.964586	−0.482293	+	0.876010i	$0.660196\pi$
$948$	−3.13241	−0.101736
$949$	−0.962809	−0.0312541
$950$	6.33880	0.205658
$951$	8.58619	0.278426
$952$	−3.00842	−0.0975035
$953$	52.1849	1.69044	0.845218	−	0.534422i	$-0.179471\pi$
$953$	52.1849	1.69044	0.845218	+	0.534422i	$0.179471\pi$
$954$	−5.49292	−0.177840
$955$	−21.3637	−0.691312
$956$	−11.7410	−0.379732
$957$	−1.17631	−0.0380247
$958$	57.3917	1.85424
$959$	−14.8548	−0.479686
$960$	−2.62851	−0.0848349
$961$	−30.0162	−0.968264
$962$	11.7893	0.380102
$963$	−5.41628	−0.174537
$964$	−2.61311	−0.0841626
$965$	−14.8156	−0.476933
$966$	0.714875	0.0230007
$967$	16.0184	0.515118	0.257559	−	0.966263i	$-0.417082\pi$
$967$	16.0184	0.515118	0.257559	+	0.966263i	$0.417082\pi$
$968$	−5.46913	−0.175784
$969$	4.90857	0.157686
$970$	15.0724	0.483944
$971$	−17.2150	−0.552457	−0.276228	−	0.961092i	$-0.589085\pi$
$971$	−17.2150	−0.552457	−0.276228	+	0.961092i	$0.589085\pi$
$972$	−15.6210	−0.501043
$973$	9.73728	0.312163
$974$	−62.9666	−2.01758
$975$	0.270412	0.00866011
$976$	−8.18445	−0.261978
$977$	8.46114	0.270696	0.135348	−	0.990798i	$-0.456785\pi$
$977$	8.46114	0.270696	0.135348	+	0.990798i	$0.456785\pi$
$978$	7.11171	0.227407
$979$	6.02367	0.192517
$980$	14.1484	0.451954
$981$	−39.1717	−1.25065
$982$	43.7324	1.39556
$983$	31.8135	1.01469	0.507346	−	0.861743i	$-0.330627\pi$
$983$	31.8135	1.01469	0.507346	+	0.861743i	$0.330627\pi$
$984$	0.767498	0.0244669
$985$	3.54684	0.113012
$986$	50.1284	1.59641
$987$	1.08263	0.0344604
$988$	−7.17279	−0.228197
$989$	−13.1187	−0.417151
$990$	−6.81546	−0.216609
$991$	−4.72788	−0.150186	−0.0750931	−	0.997177i	$-0.523925\pi$
$991$	−4.72788	−0.150186	−0.0750931	+	0.997177i	$0.523925\pi$
$992$	−8.04871	−0.255547
$993$	5.93572	0.188364
$994$	−2.40090	−0.0761520
$995$	14.7387	0.467247
$996$	−6.45186	−0.204435
$997$	−8.33890	−0.264095	−0.132048	−	0.991243i	$-0.542155\pi$
$997$	−8.33890	−0.264095	−0.132048	+	0.991243i	$0.542155\pi$
$998$	−76.3252	−2.41603
$999$	−8.63201	−0.273105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.e.1.27	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.e.1.27	✓	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)

\(f(q)\)	\(=\)	\(q+2.06684 q^{2} -0.262672 q^{3} +2.27184 q^{4} -1.00000 q^{5} -0.542902 q^{6} +0.878786 q^{7} +0.561843 q^{8} -2.93100 q^{9} +O(q^{10})\)	\(q+2.06684 q^{2} -0.262672 q^{3} +2.27184 q^{4} -1.00000 q^{5} -0.542902 q^{6} +0.878786 q^{7} +0.561843 q^{8} -2.93100 q^{9} -2.06684 q^{10} -1.12505 q^{11} -0.596749 q^{12} -1.02946 q^{13} +1.81631 q^{14} +0.262672 q^{15} -3.38243 q^{16} -6.09313 q^{17} -6.05792 q^{18} +3.06690 q^{19} -2.27184 q^{20} -0.230833 q^{21} -2.32530 q^{22} -1.49839 q^{23} -0.147581 q^{24} +1.00000 q^{25} -2.12774 q^{26} +1.55791 q^{27} +1.99646 q^{28} -3.98049 q^{29} +0.542902 q^{30} +0.991875 q^{31} -8.11464 q^{32} +0.295519 q^{33} -12.5935 q^{34} -0.878786 q^{35} -6.65876 q^{36} -5.54076 q^{37} +6.33880 q^{38} +0.270412 q^{39} -0.561843 q^{40} -5.20053 q^{41} -0.477095 q^{42} +8.75520 q^{43} -2.55593 q^{44} +2.93100 q^{45} -3.09694 q^{46} -4.69010 q^{47} +0.888472 q^{48} -6.22773 q^{49} +2.06684 q^{50} +1.60050 q^{51} -2.33877 q^{52} +0.906734 q^{53} +3.21996 q^{54} +1.12505 q^{55} +0.493740 q^{56} -0.805590 q^{57} -8.22704 q^{58} -7.88387 q^{59} +0.596749 q^{60} +2.41969 q^{61} +2.05005 q^{62} -2.57573 q^{63} -10.0068 q^{64} +1.02946 q^{65} +0.610792 q^{66} +7.11502 q^{67} -13.8426 q^{68} +0.393586 q^{69} -1.81631 q^{70} -1.32186 q^{71} -1.64676 q^{72} +0.935253 q^{73} -11.4519 q^{74} -0.262672 q^{75} +6.96750 q^{76} -0.988677 q^{77} +0.558899 q^{78} +5.24913 q^{79} +3.38243 q^{80} +8.38379 q^{81} -10.7487 q^{82} +10.8117 q^{83} -0.524415 q^{84} +6.09313 q^{85} +18.0956 q^{86} +1.04556 q^{87} -0.632101 q^{88} -5.35414 q^{89} +6.05792 q^{90} -0.904679 q^{91} -3.40410 q^{92} -0.260538 q^{93} -9.69369 q^{94} -3.06690 q^{95} +2.13149 q^{96} -7.29246 q^{97} -12.8717 q^{98} +3.29752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) \) 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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