LMFDB - Embedded newform 2005.2.a.g.1.8

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:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-1.72190 q^{2} +2.28979 q^{3} +0.964945 q^{4} +1.00000 q^{5} -3.94280 q^{6} +2.06448 q^{7} +1.78226 q^{8} +2.24315 q^{9} +O(q^{10})$	\(q-1.72190 q^{2} +2.28979 q^{3} +0.964945 q^{4} +1.00000 q^{5} -3.94280 q^{6} +2.06448 q^{7} +1.78226 q^{8} +2.24315 q^{9} -1.72190 q^{10} -1.10189 q^{11} +2.20952 q^{12} -1.06506 q^{13} -3.55484 q^{14} +2.28979 q^{15} -4.99877 q^{16} -4.78702 q^{17} -3.86249 q^{18} -1.29997 q^{19} +0.964945 q^{20} +4.72724 q^{21} +1.89734 q^{22} +4.56689 q^{23} +4.08101 q^{24} +1.00000 q^{25} +1.83393 q^{26} -1.73302 q^{27} +1.99211 q^{28} +9.49134 q^{29} -3.94280 q^{30} +7.58659 q^{31} +5.04287 q^{32} -2.52309 q^{33} +8.24277 q^{34} +2.06448 q^{35} +2.16452 q^{36} +3.69187 q^{37} +2.23842 q^{38} -2.43876 q^{39} +1.78226 q^{40} +4.40075 q^{41} -8.13984 q^{42} +9.72491 q^{43} -1.06326 q^{44} +2.24315 q^{45} -7.86374 q^{46} -1.42748 q^{47} -11.4462 q^{48} -2.73791 q^{49} -1.72190 q^{50} -10.9613 q^{51} -1.02772 q^{52} +9.03818 q^{53} +2.98409 q^{54} -1.10189 q^{55} +3.67945 q^{56} -2.97666 q^{57} -16.3432 q^{58} +1.33695 q^{59} +2.20952 q^{60} +2.17445 q^{61} -13.0634 q^{62} +4.63095 q^{63} +1.31422 q^{64} -1.06506 q^{65} +4.34452 q^{66} -9.94458 q^{67} -4.61921 q^{68} +10.4572 q^{69} -3.55484 q^{70} +0.544890 q^{71} +3.99789 q^{72} -12.3036 q^{73} -6.35704 q^{74} +2.28979 q^{75} -1.25440 q^{76} -2.27483 q^{77} +4.19931 q^{78} +15.3520 q^{79} -4.99877 q^{80} -10.6977 q^{81} -7.57766 q^{82} +4.61979 q^{83} +4.56152 q^{84} -4.78702 q^{85} -16.7453 q^{86} +21.7332 q^{87} -1.96385 q^{88} +2.91864 q^{89} -3.86249 q^{90} -2.19880 q^{91} +4.40680 q^{92} +17.3717 q^{93} +2.45798 q^{94} -1.29997 q^{95} +11.5471 q^{96} +8.46681 q^{97} +4.71441 q^{98} -2.47170 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.72190	−1.21757	−0.608784	−	0.793336i	$-0.708342\pi$
$2$	−1.72190	−1.21757	−0.608784	+	0.793336i	$0.708342\pi$
$3$	2.28979	1.32201	0.661006	−	0.750380i	$-0.270130\pi$
$3$	2.28979	1.32201	0.661006	+	0.750380i	$0.270130\pi$
$4$	0.964945	0.482472
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.94280	−1.60964
$7$	2.06448	0.780301	0.390151	−	0.920751i	$-0.372423\pi$
$7$	2.06448	0.780301	0.390151	+	0.920751i	$0.372423\pi$
$8$	1.78226	0.630125
$9$	2.24315	0.747718
$10$	−1.72190	−0.544513
$11$	−1.10189	−0.332231	−0.166116	−	0.986106i	$-0.553123\pi$
$11$	−1.10189	−0.332231	−0.166116	+	0.986106i	$0.553123\pi$
$12$	2.20952	0.637835
$13$	−1.06506	−0.295394	−0.147697	−	0.989033i	$-0.547186\pi$
$13$	−1.06506	−0.295394	−0.147697	+	0.989033i	$0.547186\pi$
$14$	−3.55484	−0.950070
$15$	2.28979	0.591222
$16$	−4.99877	−1.24969
$17$	−4.78702	−1.16102	−0.580511	−	0.814252i	$-0.697147\pi$
$17$	−4.78702	−1.16102	−0.580511	+	0.814252i	$0.697147\pi$
$18$	−3.86249	−0.910397
$19$	−1.29997	−0.298233	−0.149117	−	0.988820i	$-0.547643\pi$
$19$	−1.29997	−0.298233	−0.149117	+	0.988820i	$0.547643\pi$
$20$	0.964945	0.215768
$21$	4.72724	1.03157
$22$	1.89734	0.404514
$23$	4.56689	0.952263	0.476132	−	0.879374i	$-0.342039\pi$
$23$	4.56689	0.952263	0.476132	+	0.879374i	$0.342039\pi$
$24$	4.08101	0.833034
$25$	1.00000	0.200000
$26$	1.83393	0.359663
$27$	−1.73302	−0.333520
$28$	1.99211	0.376474
$29$	9.49134	1.76250	0.881249	−	0.472653i	$-0.156703\pi$
$29$	9.49134	1.76250	0.881249	+	0.472653i	$0.156703\pi$
$30$	−3.94280	−0.719853
$31$	7.58659	1.36259	0.681295	−	0.732008i	$-0.261417\pi$
$31$	7.58659	1.36259	0.681295	+	0.732008i	$0.261417\pi$
$32$	5.04287	0.891461
$33$	−2.52309	−0.439214
$34$	8.24277	1.41362
$35$	2.06448	0.348961
$36$	2.16452	0.360753
$37$	3.69187	0.606940	0.303470	−	0.952841i	$-0.401855\pi$
$37$	3.69187	0.606940	0.303470	+	0.952841i	$0.401855\pi$
$38$	2.23842	0.363119
$39$	−2.43876	−0.390515
$40$	1.78226	0.281801
$41$	4.40075	0.687282	0.343641	−	0.939101i	$-0.388340\pi$
$41$	4.40075	0.687282	0.343641	+	0.939101i	$0.388340\pi$
$42$	−8.13984	−1.25600
$43$	9.72491	1.48303	0.741517	−	0.670934i	$-0.234107\pi$
$43$	9.72491	1.48303	0.741517	+	0.670934i	$0.234107\pi$
$44$	−1.06326	−0.160292
$45$	2.24315	0.334390
$46$	−7.86374	−1.15945
$47$	−1.42748	−0.208220	−0.104110	−	0.994566i	$-0.533199\pi$
$47$	−1.42748	−0.208220	−0.104110	+	0.994566i	$0.533199\pi$
$48$	−11.4462	−1.65211
$49$	−2.73791	−0.391130
$50$	−1.72190	−0.243514
$51$	−10.9613	−1.53489
$52$	−1.02772	−0.142520
$53$	9.03818	1.24149	0.620745	−	0.784013i	$-0.286830\pi$
$53$	9.03818	1.24149	0.620745	+	0.784013i	$0.286830\pi$
$54$	2.98409	0.406084
$55$	−1.10189	−0.148578
$56$	3.67945	0.491687
$57$	−2.97666	−0.394268
$58$	−16.3432	−2.14596
$59$	1.33695	0.174056	0.0870280	−	0.996206i	$-0.472263\pi$
$59$	1.33695	0.174056	0.0870280	+	0.996206i	$0.472263\pi$
$60$	2.20952	0.285248
$61$	2.17445	0.278409	0.139205	−	0.990264i	$-0.455545\pi$
$61$	2.17445	0.278409	0.139205	+	0.990264i	$0.455545\pi$
$62$	−13.0634	−1.65905
$63$	4.63095	0.583445
$64$	1.31422	0.164278
$65$	−1.06506	−0.132104
$66$	4.34452	0.534773
$67$	−9.94458	−1.21492	−0.607462	−	0.794349i	$-0.707812\pi$
$67$	−9.94458	−1.21492	−0.607462	+	0.794349i	$0.707812\pi$
$68$	−4.61921	−0.560161
$69$	10.4572	1.25890
$70$	−3.55484	−0.424884
$71$	0.544890	0.0646665	0.0323332	−	0.999477i	$-0.489706\pi$
$71$	0.544890	0.0646665	0.0323332	+	0.999477i	$0.489706\pi$
$72$	3.99789	0.471156
$73$	−12.3036	−1.44003	−0.720015	−	0.693958i	$-0.755865\pi$
$73$	−12.3036	−1.44003	−0.720015	+	0.693958i	$0.755865\pi$
$74$	−6.35704	−0.738991
$75$	2.28979	0.264403
$76$	−1.25440	−0.143889
$77$	−2.27483	−0.259240
$78$	4.19931	0.475479
$79$	15.3520	1.72723	0.863615	−	0.504152i	$-0.168195\pi$
$79$	15.3520	1.72723	0.863615	+	0.504152i	$0.168195\pi$
$80$	−4.99877	−0.558880
$81$	−10.6977	−1.18864
$82$	−7.57766	−0.836813
$83$	4.61979	0.507088	0.253544	−	0.967324i	$-0.418404\pi$
$83$	4.61979	0.507088	0.253544	+	0.967324i	$0.418404\pi$
$84$	4.56152	0.497703
$85$	−4.78702	−0.519225
$86$	−16.7453	−1.80570
$87$	21.7332	2.33004
$88$	−1.96385	−0.209347
$89$	2.91864	0.309376	0.154688	−	0.987963i	$-0.450563\pi$
$89$	2.91864	0.309376	0.154688	+	0.987963i	$0.450563\pi$
$90$	−3.86249	−0.407142
$91$	−2.19880	−0.230496
$92$	4.40680	0.459441
$93$	17.3717	1.80136
$94$	2.45798	0.253522
$95$	−1.29997	−0.133374
$96$	11.5471	1.17852
$97$	8.46681	0.859675	0.429837	−	0.902906i	$-0.358571\pi$
$97$	8.46681	0.859675	0.429837	+	0.902906i	$0.358571\pi$
$98$	4.71441	0.476228
$99$	−2.47170	−0.248415
$100$	0.964945	0.0964945
$101$	9.02602	0.898123	0.449061	−	0.893501i	$-0.351758\pi$
$101$	9.02602	0.898123	0.449061	+	0.893501i	$0.351758\pi$
$102$	18.8742	1.86883
$103$	−4.46974	−0.440416	−0.220208	−	0.975453i	$-0.570674\pi$
$103$	−4.46974	−0.440416	−0.220208	+	0.975453i	$0.570674\pi$
$104$	−1.89822	−0.186135
$105$	4.72724	0.461331
$106$	−15.5629	−1.51160
$107$	−8.11981	−0.784972	−0.392486	−	0.919758i	$-0.628385\pi$
$107$	−8.11981	−0.784972	−0.392486	+	0.919758i	$0.628385\pi$
$108$	−1.67227	−0.160914
$109$	−4.55290	−0.436089	−0.218045	−	0.975939i	$-0.569968\pi$
$109$	−4.55290	−0.436089	−0.218045	+	0.975939i	$0.569968\pi$
$110$	1.89734	0.180904
$111$	8.45362	0.802382
$112$	−10.3199	−0.975137
$113$	7.33462	0.689983	0.344992	−	0.938606i	$-0.387882\pi$
$113$	7.33462	0.689983	0.344992	+	0.938606i	$0.387882\pi$
$114$	5.12551	0.480048
$115$	4.56689	0.425865
$116$	9.15862	0.850356
$117$	−2.38909	−0.220871
$118$	−2.30210	−0.211925
$119$	−9.88271	−0.905947
$120$	4.08101	0.372544
$121$	−9.78585	−0.889622
$122$	−3.74418	−0.338983
$123$	10.0768	0.908596
$124$	7.32064	0.657413
$125$	1.00000	0.0894427
$126$	−7.97404	−0.710384
$127$	15.0670	1.33698	0.668490	−	0.743721i	$-0.266941\pi$
$127$	15.0670	1.33698	0.668490	+	0.743721i	$0.266941\pi$
$128$	−12.3487	−1.09148
$129$	22.2680	1.96059
$130$	1.83393	0.160846
$131$	−12.7805	−1.11663	−0.558317	−	0.829628i	$-0.688553\pi$
$131$	−12.7805	−1.11663	−0.558317	+	0.829628i	$0.688553\pi$
$132$	−2.43465	−0.211909
$133$	−2.68376	−0.232712
$134$	17.1236	1.47925
$135$	−1.73302	−0.149155
$136$	−8.53172	−0.731589
$137$	9.58501	0.818903	0.409451	−	0.912332i	$-0.365720\pi$
$137$	9.58501	0.818903	0.409451	+	0.912332i	$0.365720\pi$
$138$	−18.0063	−1.53280
$139$	−15.4961	−1.31436	−0.657181	−	0.753732i	$-0.728251\pi$
$139$	−15.4961	−1.31436	−0.657181	+	0.753732i	$0.728251\pi$
$140$	1.99211	0.168364
$141$	−3.26864	−0.275269
$142$	−0.938246	−0.0787359
$143$	1.17357	0.0981392
$144$	−11.2130	−0.934417
$145$	9.49134	0.788213
$146$	21.1856	1.75334
$147$	−6.26925	−0.517079
$148$	3.56245	0.292832
$149$	19.3776	1.58748	0.793739	−	0.608258i	$-0.208131\pi$
$149$	19.3776	1.58748	0.793739	+	0.608258i	$0.208131\pi$
$150$	−3.94280	−0.321928
$151$	−14.3225	−1.16555	−0.582775	−	0.812633i	$-0.698033\pi$
$151$	−14.3225	−1.16555	−0.582775	+	0.812633i	$0.698033\pi$
$152$	−2.31689	−0.187924
$153$	−10.7380	−0.868117
$154$	3.91703	0.315643
$155$	7.58659	0.609369
$156$	−2.35327	−0.188413
$157$	−8.38308	−0.669043	−0.334521	−	0.942388i	$-0.608575\pi$
$157$	−8.38308	−0.669043	−0.334521	+	0.942388i	$0.608575\pi$
$158$	−26.4345	−2.10302
$159$	20.6956	1.64126
$160$	5.04287	0.398674
$161$	9.42827	0.743052
$162$	18.4204	1.44725
$163$	12.8665	1.00778	0.503892	−	0.863766i	$-0.331901\pi$
$163$	12.8665	1.00778	0.503892	+	0.863766i	$0.331901\pi$
$164$	4.24648	0.331595
$165$	−2.52309	−0.196422
$166$	−7.95482	−0.617414
$167$	5.40751	0.418446	0.209223	−	0.977868i	$-0.432907\pi$
$167$	5.40751	0.418446	0.209223	+	0.977868i	$0.432907\pi$
$168$	8.42518	0.650017
$169$	−11.8656	−0.912742
$170$	8.24277	0.632192
$171$	−2.91603	−0.222994
$172$	9.38400	0.715523
$173$	−8.00548	−0.608645	−0.304323	−	0.952569i	$-0.598430\pi$
$173$	−8.00548	−0.608645	−0.304323	+	0.952569i	$0.598430\pi$
$174$	−37.4224	−2.83699
$175$	2.06448	0.156060
$176$	5.50808	0.415187
$177$	3.06134	0.230104
$178$	−5.02562	−0.376686
$179$	−19.6144	−1.46605	−0.733025	−	0.680202i	$-0.761892\pi$
$179$	−19.6144	−1.46605	−0.733025	+	0.680202i	$0.761892\pi$
$180$	2.16452	0.161334
$181$	0.797186	0.0592544	0.0296272	−	0.999561i	$-0.490568\pi$
$181$	0.797186	0.0592544	0.0296272	+	0.999561i	$0.490568\pi$
$182$	3.78611	0.280645
$183$	4.97904	0.368061
$184$	8.13941	0.600045
$185$	3.69187	0.271432
$186$	−29.9124	−2.19328
$187$	5.27475	0.385728
$188$	−1.37744	−0.100460
$189$	−3.57779	−0.260246
$190$	2.23842	0.162392
$191$	−17.4324	−1.26137	−0.630684	−	0.776040i	$-0.717225\pi$
$191$	−17.4324	−1.26137	−0.630684	+	0.776040i	$0.717225\pi$
$192$	3.00930	0.217178
$193$	−3.87217	−0.278725	−0.139362	−	0.990241i	$-0.544505\pi$
$193$	−3.87217	−0.278725	−0.139362	+	0.990241i	$0.544505\pi$
$194$	−14.5790	−1.04671
$195$	−2.43876	−0.174644
$196$	−2.64193	−0.188710
$197$	−6.18348	−0.440555	−0.220277	−	0.975437i	$-0.570696\pi$
$197$	−6.18348	−0.440555	−0.220277	+	0.975437i	$0.570696\pi$
$198$	4.25602	0.302463
$199$	7.06767	0.501014	0.250507	−	0.968115i	$-0.419403\pi$
$199$	7.06767	0.501014	0.250507	+	0.968115i	$0.419403\pi$
$200$	1.78226	0.126025
$201$	−22.7710	−1.60615
$202$	−15.5419	−1.09353
$203$	19.5947	1.37528
$204$	−10.5770	−0.740540
$205$	4.40075	0.307362
$206$	7.69645	0.536237
$207$	10.2442	0.712024
$208$	5.32399	0.369152
$209$	1.43242	0.0990824
$210$	−8.13984	−0.561702
$211$	−1.43809	−0.0990019	−0.0495010	−	0.998774i	$-0.515763\pi$
$211$	−1.43809	−0.0990019	−0.0495010	+	0.998774i	$0.515763\pi$
$212$	8.72134	0.598984
$213$	1.24768	0.0854899
$214$	13.9815	0.955757
$215$	9.72491	0.663233
$216$	−3.08870	−0.210160
$217$	15.6624	1.06323
$218$	7.83965	0.530968
$219$	−28.1728	−1.90374
$220$	−1.06326	−0.0716850
$221$	5.09846	0.342959
$222$	−14.5563	−0.976955
$223$	−13.1058	−0.877631	−0.438815	−	0.898577i	$-0.644602\pi$
$223$	−13.1058	−0.877631	−0.438815	+	0.898577i	$0.644602\pi$
$224$	10.4109	0.695608
$225$	2.24315	0.149544
$226$	−12.6295	−0.840101
$227$	18.4554	1.22493	0.612466	−	0.790497i	$-0.290178\pi$
$227$	18.4554	1.22493	0.612466	+	0.790497i	$0.290178\pi$
$228$	−2.87231	−0.190223
$229$	3.74257	0.247316	0.123658	−	0.992325i	$-0.460537\pi$
$229$	3.74257	0.247316	0.123658	+	0.992325i	$0.460537\pi$
$230$	−7.86374	−0.518520
$231$	−5.20888	−0.342719
$232$	16.9161	1.11059
$233$	18.6524	1.22196	0.610978	−	0.791647i	$-0.290776\pi$
$233$	18.6524	1.22196	0.610978	+	0.791647i	$0.290776\pi$
$234$	4.11378	0.268926
$235$	−1.42748	−0.0931186
$236$	1.29008	0.0839772
$237$	35.1528	2.28342
$238$	17.0171	1.10305
$239$	11.4174	0.738531	0.369266	−	0.929324i	$-0.379609\pi$
$239$	11.4174	0.738531	0.369266	+	0.929324i	$0.379609\pi$
$240$	−11.4462	−0.738846
$241$	−21.8905	−1.41009	−0.705047	−	0.709161i	$-0.749074\pi$
$241$	−21.8905	−1.41009	−0.705047	+	0.709161i	$0.749074\pi$
$242$	16.8503	1.08318
$243$	−19.2965	−1.23787
$244$	2.09822	0.134325
$245$	−2.73791	−0.174919
$246$	−17.3513	−1.10628
$247$	1.38454	0.0880964
$248$	13.5213	0.858603
$249$	10.5784	0.670376
$250$	−1.72190	−0.108903
$251$	−21.6837	−1.36866	−0.684332	−	0.729170i	$-0.739906\pi$
$251$	−21.6837	−1.36866	−0.684332	+	0.729170i	$0.739906\pi$
$252$	4.46861	0.281496
$253$	−5.03220	−0.316372
$254$	−25.9439	−1.62787
$255$	−10.9613	−0.686422
$256$	18.6348	1.16467
$257$	26.6929	1.66506	0.832529	−	0.553981i	$-0.186892\pi$
$257$	26.6929	1.66506	0.832529	+	0.553981i	$0.186892\pi$
$258$	−38.3433	−2.38715
$259$	7.62180	0.473596
$260$	−1.02772	−0.0637367
$261$	21.2905	1.31785
$262$	22.0067	1.35958
$263$	18.7057	1.15344	0.576722	−	0.816941i	$-0.304332\pi$
$263$	18.7057	1.15344	0.576722	+	0.816941i	$0.304332\pi$
$264$	−4.49681	−0.276760
$265$	9.03818	0.555211
$266$	4.62117	0.283342
$267$	6.68309	0.408999
$268$	−9.59597	−0.586167
$269$	19.0183	1.15956	0.579782	−	0.814771i	$-0.303138\pi$
$269$	19.0183	1.15956	0.579782	+	0.814771i	$0.303138\pi$
$270$	2.98409	0.181606
$271$	10.1369	0.615775	0.307887	−	0.951423i	$-0.400378\pi$
$271$	10.1369	0.615775	0.307887	+	0.951423i	$0.400378\pi$
$272$	23.9292	1.45092
$273$	−5.03479	−0.304719
$274$	−16.5044	−0.997070
$275$	−1.10189	−0.0664463
$276$	10.0907	0.607386
$277$	−1.95845	−0.117672	−0.0588359	−	0.998268i	$-0.518739\pi$
$277$	−1.95845	−0.117672	−0.0588359	+	0.998268i	$0.518739\pi$
$278$	26.6828	1.60033
$279$	17.0179	1.01883
$280$	3.67945	0.219889
$281$	1.91641	0.114324	0.0571618	−	0.998365i	$-0.481795\pi$
$281$	1.91641	0.114324	0.0571618	+	0.998365i	$0.481795\pi$
$282$	5.62827	0.335159
$283$	−29.9244	−1.77882	−0.889410	−	0.457111i	$-0.848884\pi$
$283$	−29.9244	−1.77882	−0.889410	+	0.457111i	$0.848884\pi$
$284$	0.525788	0.0311998
$285$	−2.97666	−0.176322
$286$	−2.02078	−0.119491
$287$	9.08528	0.536287
$288$	11.3119	0.666561
$289$	5.91553	0.347972
$290$	−16.3432	−0.959703
$291$	19.3873	1.13650
$292$	−11.8723	−0.694775
$293$	−8.79382	−0.513741	−0.256870	−	0.966446i	$-0.582691\pi$
$293$	−8.79382	−0.513741	−0.256870	+	0.966446i	$0.582691\pi$
$294$	10.7950	0.629579
$295$	1.33695	0.0778402
$296$	6.57989	0.382448
$297$	1.90959	0.110806
$298$	−33.3664	−1.93286
$299$	−4.86401	−0.281293
$300$	2.20952	0.127567
$301$	20.0769	1.15721
$302$	24.6620	1.41914
$303$	20.6677	1.18733
$304$	6.49824	0.372700
$305$	2.17445	0.124509
$306$	18.4898	1.05699
$307$	14.3667	0.819950	0.409975	−	0.912097i	$-0.365537\pi$
$307$	14.3667	0.819950	0.409975	+	0.912097i	$0.365537\pi$
$308$	−2.19508	−0.125076
$309$	−10.2348	−0.582236
$310$	−13.0634	−0.741949
$311$	−11.0165	−0.624688	−0.312344	−	0.949969i	$-0.601114\pi$
$311$	−11.0165	−0.624688	−0.312344	+	0.949969i	$0.601114\pi$
$312$	−4.34652	−0.246073
$313$	−24.0511	−1.35945	−0.679725	−	0.733467i	$-0.737901\pi$
$313$	−24.0511	−1.35945	−0.679725	+	0.733467i	$0.737901\pi$
$314$	14.4348	0.814605
$315$	4.63095	0.260925
$316$	14.8138	0.833341
$317$	−9.02231	−0.506743	−0.253372	−	0.967369i	$-0.581540\pi$
$317$	−9.02231	−0.506743	−0.253372	+	0.967369i	$0.581540\pi$
$318$	−35.6357	−1.99835
$319$	−10.4584	−0.585557
$320$	1.31422	0.0734674
$321$	−18.5927	−1.03774
$322$	−16.2346	−0.904716
$323$	6.22297	0.346255
$324$	−10.3227	−0.573484
$325$	−1.06506	−0.0590788
$326$	−22.1549	−1.22705
$327$	−10.4252	−0.576515
$328$	7.84330	0.433074
$329$	−2.94701	−0.162474
$330$	4.34452	0.239158
$331$	9.87694	0.542886	0.271443	−	0.962455i	$-0.412499\pi$
$331$	9.87694	0.542886	0.271443	+	0.962455i	$0.412499\pi$
$332$	4.45784	0.244656
$333$	8.28143	0.453820
$334$	−9.31120	−0.509486
$335$	−9.94458	−0.543331
$336$	−23.6304	−1.28914
$337$	0.730553	0.0397958	0.0198979	−	0.999802i	$-0.493666\pi$
$337$	0.730553	0.0397958	0.0198979	+	0.999802i	$0.493666\pi$
$338$	20.4315	1.11133
$339$	16.7948	0.912166
$340$	−4.61921	−0.250512
$341$	−8.35956	−0.452695
$342$	5.02111	0.271511
$343$	−20.1037	−1.08550
$344$	17.3323	0.934497
$345$	10.4572	0.562999
$346$	13.7846	0.741067
$347$	28.5535	1.53283	0.766415	−	0.642346i	$-0.222039\pi$
$347$	28.5535	1.53283	0.766415	+	0.642346i	$0.222039\pi$
$348$	20.9713	1.12418
$349$	−24.4903	−1.31094	−0.655468	−	0.755223i	$-0.727529\pi$
$349$	−24.4903	−1.31094	−0.655468	+	0.755223i	$0.727529\pi$
$350$	−3.55484	−0.190014
$351$	1.84577	0.0985200
$352$	−5.55667	−0.296171
$353$	−10.9231	−0.581377	−0.290688	−	0.956818i	$-0.593884\pi$
$353$	−10.9231	−0.581377	−0.290688	+	0.956818i	$0.593884\pi$
$354$	−5.27132	−0.280168
$355$	0.544890	0.0289197
$356$	2.81633	0.149265
$357$	−22.6294	−1.19767
$358$	33.7741	1.78501
$359$	−5.86087	−0.309325	−0.154663	−	0.987967i	$-0.549429\pi$
$359$	−5.86087	−0.309325	−0.154663	+	0.987967i	$0.549429\pi$
$360$	3.99789	0.210707
$361$	−17.3101	−0.911057
$362$	−1.37268	−0.0721463
$363$	−22.4076	−1.17609
$364$	−2.12172	−0.111208
$365$	−12.3036	−0.644001
$366$	−8.57341	−0.448139
$367$	−20.5409	−1.07222	−0.536112	−	0.844147i	$-0.680108\pi$
$367$	−20.5409	−1.07222	−0.536112	+	0.844147i	$0.680108\pi$
$368$	−22.8289	−1.19004
$369$	9.87156	0.513893
$370$	−6.35704	−0.330487
$371$	18.6592	0.968736
$372$	16.7627	0.869108
$373$	−0.435049	−0.0225260	−0.0112630	−	0.999937i	$-0.503585\pi$
$373$	−0.435049	−0.0225260	−0.0112630	+	0.999937i	$0.503585\pi$
$374$	−9.08260	−0.469650
$375$	2.28979	0.118244
$376$	−2.54415	−0.131204
$377$	−10.1088	−0.520632
$378$	6.16061	0.316868
$379$	8.32001	0.427370	0.213685	−	0.976903i	$-0.431453\pi$
$379$	8.32001	0.427370	0.213685	+	0.976903i	$0.431453\pi$
$380$	−1.25440	−0.0643492
$381$	34.5003	1.76751
$382$	30.0170	1.53580
$383$	25.1228	1.28372	0.641858	−	0.766824i	$-0.278164\pi$
$383$	25.1228	1.28372	0.641858	+	0.766824i	$0.278164\pi$
$384$	−28.2760	−1.44295
$385$	−2.27483	−0.115936
$386$	6.66749	0.339366
$387$	21.8145	1.10889
$388$	8.17001	0.414769
$389$	−9.63659	−0.488594	−0.244297	−	0.969700i	$-0.578557\pi$
$389$	−9.63659	−0.488594	−0.244297	+	0.969700i	$0.578557\pi$
$390$	4.19931	0.212640
$391$	−21.8618	−1.10560
$392$	−4.87968	−0.246461
$393$	−29.2646	−1.47621
$394$	10.6473	0.536406
$395$	15.3520	0.772441
$396$	−2.38505	−0.119854
$397$	−9.74657	−0.489166	−0.244583	−	0.969628i	$-0.578651\pi$
$397$	−9.74657	−0.489166	−0.244583	+	0.969628i	$0.578651\pi$
$398$	−12.1698	−0.610019
$399$	−6.14526	−0.307648
$400$	−4.99877	−0.249939
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	39.2095	1.95559
$403$	−8.08016	−0.402501
$404$	8.70961	0.433319
$405$	−10.6977	−0.531574
$406$	−33.7402	−1.67450
$407$	−4.06802	−0.201644
$408$	−19.5359	−0.967170
$409$	23.7571	1.17471	0.587357	−	0.809328i	$-0.300169\pi$
$409$	23.7571	1.17471	0.587357	+	0.809328i	$0.300169\pi$
$410$	−7.57766	−0.374234
$411$	21.9477	1.08260
$412$	−4.31305	−0.212489
$413$	2.76011	0.135816
$414$	−17.6396	−0.866938
$415$	4.61979	0.226776
$416$	−5.37095	−0.263332
$417$	−35.4829	−1.73760
$418$	−2.46648	−0.120640
$419$	−39.6721	−1.93811	−0.969054	−	0.246848i	$-0.920605\pi$
$419$	−39.6721	−1.93811	−0.969054	+	0.246848i	$0.920605\pi$
$420$	4.56152	0.222580
$421$	−24.9481	−1.21590	−0.607948	−	0.793977i	$-0.708007\pi$
$421$	−24.9481	−1.21590	−0.607948	+	0.793977i	$0.708007\pi$
$422$	2.47624	0.120542
$423$	−3.20206	−0.155689
$424$	16.1084	0.782294
$425$	−4.78702	−0.232204
$426$	−2.14839	−0.104090
$427$	4.48911	0.217243
$428$	−7.83517	−0.378727
$429$	2.68724	0.129741
$430$	−16.7453	−0.807532
$431$	9.88377	0.476084	0.238042	−	0.971255i	$-0.423494\pi$
$431$	9.88377	0.476084	0.238042	+	0.971255i	$0.423494\pi$
$432$	8.66298	0.416798
$433$	2.49508	0.119906	0.0599530	−	0.998201i	$-0.480905\pi$
$433$	2.49508	0.119906	0.0599530	+	0.998201i	$0.480905\pi$
$434$	−26.9691	−1.29456
$435$	21.7332	1.04203
$436$	−4.39330	−0.210401
$437$	−5.93682	−0.283996
$438$	48.5107	2.31793
$439$	−27.5724	−1.31596	−0.657978	−	0.753037i	$-0.728588\pi$
$439$	−27.5724	−1.31596	−0.657978	+	0.753037i	$0.728588\pi$
$440$	−1.96385	−0.0936230
$441$	−6.14156	−0.292455
$442$	−8.77904	−0.417576
$443$	3.64462	0.173161	0.0865807	−	0.996245i	$-0.472406\pi$
$443$	3.64462	0.173161	0.0865807	+	0.996245i	$0.472406\pi$
$444$	8.15728	0.387127
$445$	2.91864	0.138357
$446$	22.5669	1.06858
$447$	44.3708	2.09867
$448$	2.71319	0.128186
$449$	3.87430	0.182840	0.0914198	−	0.995812i	$-0.470859\pi$
$449$	3.87430	0.182840	0.0914198	+	0.995812i	$0.470859\pi$
$450$	−3.86249	−0.182079
$451$	−4.84913	−0.228337
$452$	7.07750	0.332898
$453$	−32.7956	−1.54087
$454$	−31.7785	−1.49144
$455$	−2.19880	−0.103081
$456$	−5.30519	−0.248438
$457$	23.7087	1.10905	0.554524	−	0.832168i	$-0.312900\pi$
$457$	23.7087	1.10905	0.554524	+	0.832168i	$0.312900\pi$
$458$	−6.44433	−0.301124
$459$	8.29601	0.387224
$460$	4.40680	0.205468
$461$	35.5535	1.65589	0.827945	−	0.560809i	$-0.189510\pi$
$461$	35.5535	1.65589	0.827945	+	0.560809i	$0.189510\pi$
$462$	8.96918	0.417284
$463$	21.6869	1.00788	0.503938	−	0.863740i	$-0.331884\pi$
$463$	21.6869	1.00788	0.503938	+	0.863740i	$0.331884\pi$
$464$	−47.4450	−2.20258
$465$	17.3717	0.805594
$466$	−32.1175	−1.48782
$467$	−23.3410	−1.08009	−0.540047	−	0.841635i	$-0.681594\pi$
$467$	−23.3410	−1.08009	−0.540047	+	0.841635i	$0.681594\pi$
$468$	−2.30534	−0.106564
$469$	−20.5304	−0.948007
$470$	2.45798	0.113378
$471$	−19.1955	−0.884483
$472$	2.38280	0.109677
$473$	−10.7157	−0.492710
$474$	−60.5297	−2.78022
$475$	−1.29997	−0.0596466
$476$	−9.53627	−0.437094
$477$	20.2740	0.928284
$478$	−19.6597	−0.899212
$479$	−30.3864	−1.38839	−0.694194	−	0.719788i	$-0.744239\pi$
$479$	−30.3864	−1.38839	−0.694194	+	0.719788i	$0.744239\pi$
$480$	11.5471	0.527051
$481$	−3.93206	−0.179287
$482$	37.6933	1.71688
$483$	21.5888	0.982324
$484$	−9.44280	−0.429218
$485$	8.46681	0.384458
$486$	33.2267	1.50719
$487$	−13.9456	−0.631937	−0.315969	−	0.948770i	$-0.602329\pi$
$487$	−13.9456	−0.631937	−0.315969	+	0.948770i	$0.602329\pi$
$488$	3.87544	0.175433
$489$	29.4617	1.33230
$490$	4.71441	0.212976
$491$	−28.0258	−1.26479	−0.632393	−	0.774648i	$-0.717927\pi$
$491$	−28.0258	−1.26479	−0.632393	+	0.774648i	$0.717927\pi$
$492$	9.72357	0.438372
$493$	−45.4352	−2.04630
$494$	−2.38405	−0.107263
$495$	−2.47170	−0.111095
$496$	−37.9236	−1.70282
$497$	1.12492	0.0504593
$498$	−18.2149	−0.816229
$499$	9.07727	0.406355	0.203177	−	0.979142i	$-0.434873\pi$
$499$	9.07727	0.406355	0.203177	+	0.979142i	$0.434873\pi$
$500$	0.964945	0.0431536
$501$	12.3821	0.553191
$502$	37.3372	1.66644
$503$	−7.98861	−0.356195	−0.178097	−	0.984013i	$-0.556994\pi$
$503$	−7.98861	−0.356195	−0.178097	+	0.984013i	$0.556994\pi$
$504$	8.25357	0.367643
$505$	9.02602	0.401653
$506$	8.66495	0.385204
$507$	−27.1699	−1.20666
$508$	14.5388	0.645056
$509$	19.2374	0.852683	0.426341	−	0.904562i	$-0.359802\pi$
$509$	19.2374	0.852683	0.426341	+	0.904562i	$0.359802\pi$
$510$	18.8742	0.835766
$511$	−25.4006	−1.12366
$512$	−7.38988	−0.326590
$513$	2.25287	0.0994668
$514$	−45.9626	−2.02732
$515$	−4.46974	−0.196960
$516$	21.4874	0.945931
$517$	1.57292	0.0691771
$518$	−13.1240	−0.576635
$519$	−18.3309	−0.804637
$520$	−1.89822	−0.0832422
$521$	−28.4872	−1.24805	−0.624024	−	0.781405i	$-0.714503\pi$
$521$	−28.4872	−1.24805	−0.624024	+	0.781405i	$0.714503\pi$
$522$	−36.6602	−1.60457
$523$	15.3540	0.671383	0.335691	−	0.941972i	$-0.391030\pi$
$523$	15.3540	0.671383	0.335691	+	0.941972i	$0.391030\pi$
$524$	−12.3324	−0.538745
$525$	4.72724	0.206314
$526$	−32.2094	−1.40440
$527$	−36.3171	−1.58200
$528$	12.6124	0.548883
$529$	−2.14348	−0.0931949
$530$	−15.5629	−0.676007
$531$	2.99898	0.130145
$532$	−2.58968	−0.112277
$533$	−4.68706	−0.203019
$534$	−11.5076	−0.497984
$535$	−8.11981	−0.351050
$536$	−17.7239	−0.765554
$537$	−44.9129	−1.93814
$538$	−32.7476	−1.41185
$539$	3.01687	0.129946
$540$	−1.67227	−0.0719631
$541$	23.7006	1.01897	0.509485	−	0.860480i	$-0.329836\pi$
$541$	23.7006	1.01897	0.509485	+	0.860480i	$0.329836\pi$
$542$	−17.4548	−0.749748
$543$	1.82539	0.0783351
$544$	−24.1403	−1.03501
$545$	−4.55290	−0.195025
$546$	8.66941	0.371016
$547$	−17.3084	−0.740052	−0.370026	−	0.929021i	$-0.620651\pi$
$547$	−17.3084	−0.740052	−0.370026	+	0.929021i	$0.620651\pi$
$548$	9.24901	0.395098
$549$	4.87762	0.208172
$550$	1.89734	0.0809029
$551$	−12.3384	−0.525635
$552$	18.6376	0.793267
$553$	31.6938	1.34776
$554$	3.37225	0.143273
$555$	8.45362	0.358836
$556$	−14.9529	−0.634144
$557$	−43.6282	−1.84859	−0.924294	−	0.381682i	$-0.875345\pi$
$557$	−43.6282	−1.84859	−0.924294	+	0.381682i	$0.875345\pi$
$558$	−29.3031	−1.24050
$559$	−10.3576	−0.438080
$560$	−10.3199	−0.436094
$561$	12.0781	0.509937
$562$	−3.29988	−0.139197
$563$	35.3162	1.48840	0.744201	−	0.667956i	$-0.232830\pi$
$563$	35.3162	1.48840	0.744201	+	0.667956i	$0.232830\pi$
$564$	−3.15405	−0.132810
$565$	7.33462	0.308570
$566$	51.5268	2.16583
$567$	−22.0853	−0.927494
$568$	0.971137	0.0407480
$569$	19.6082	0.822018	0.411009	−	0.911631i	$-0.365176\pi$
$569$	19.6082	0.822018	0.411009	+	0.911631i	$0.365176\pi$
$570$	5.12551	0.214684
$571$	−31.6719	−1.32543	−0.662713	−	0.748874i	$-0.730595\pi$
$571$	−31.6719	−1.32543	−0.662713	+	0.748874i	$0.730595\pi$
$572$	1.13243	0.0473495
$573$	−39.9167	−1.66754
$574$	−15.6440	−0.652966
$575$	4.56689	0.190453
$576$	2.94801	0.122834
$577$	−13.5704	−0.564944	−0.282472	−	0.959276i	$-0.591154\pi$
$577$	−13.5704	−0.564944	−0.282472	+	0.959276i	$0.591154\pi$
$578$	−10.1860	−0.423680
$579$	−8.86647	−0.368478
$580$	9.15862	0.380291
$581$	9.53747	0.395681
$582$	−33.3829	−1.38377
$583$	−9.95905	−0.412462
$584$	−21.9283	−0.907400
$585$	−2.38909	−0.0987767
$586$	15.1421	0.625514
$587$	−19.1917	−0.792128	−0.396064	−	0.918223i	$-0.629624\pi$
$587$	−19.1917	−0.792128	−0.396064	+	0.918223i	$0.629624\pi$
$588$	−6.04948	−0.249476
$589$	−9.86232	−0.406370
$590$	−2.30210	−0.0947758
$591$	−14.1589	−0.582419
$592$	−18.4548	−0.758488
$593$	−18.4177	−0.756322	−0.378161	−	0.925740i	$-0.623443\pi$
$593$	−18.4177	−0.756322	−0.378161	+	0.925740i	$0.623443\pi$
$594$	−3.28813	−0.134914
$595$	−9.88271	−0.405152
$596$	18.6984	0.765915
$597$	16.1835	0.662347
$598$	8.37535	0.342493
$599$	−2.81114	−0.114860	−0.0574301	−	0.998350i	$-0.518291\pi$
$599$	−2.81114	−0.114860	−0.0574301	+	0.998350i	$0.518291\pi$
$600$	4.08101	0.166607
$601$	−12.3795	−0.504970	−0.252485	−	0.967601i	$-0.581248\pi$
$601$	−12.3795	−0.504970	−0.252485	+	0.967601i	$0.581248\pi$
$602$	−34.5704	−1.40899
$603$	−22.3072	−0.908420
$604$	−13.8204	−0.562346
$605$	−9.78585	−0.397851
$606$	−35.5878	−1.44565
$607$	5.31870	0.215879	0.107940	−	0.994157i	$-0.465575\pi$
$607$	5.31870	0.215879	0.107940	+	0.994157i	$0.465575\pi$
$608$	−6.55557	−0.265863
$609$	44.8678	1.81814
$610$	−3.74418	−0.151598
$611$	1.52035	0.0615068
$612$	−10.3616	−0.418842
$613$	7.88709	0.318557	0.159278	−	0.987234i	$-0.449083\pi$
$613$	7.88709	0.318557	0.159278	+	0.987234i	$0.449083\pi$
$614$	−24.7380	−0.998346
$615$	10.0768	0.406336
$616$	−4.05434	−0.163354
$617$	−30.1760	−1.21484	−0.607420	−	0.794381i	$-0.707795\pi$
$617$	−30.1760	−1.21484	−0.607420	+	0.794381i	$0.707795\pi$
$618$	17.6233	0.708912
$619$	4.37305	0.175768	0.0878839	−	0.996131i	$-0.471990\pi$
$619$	4.37305	0.175768	0.0878839	+	0.996131i	$0.471990\pi$
$620$	7.32064	0.294004
$621$	−7.91453	−0.317599
$622$	18.9693	0.760600
$623$	6.02549	0.241406
$624$	12.1908	0.488024
$625$	1.00000	0.0400000
$626$	41.4137	1.65522
$627$	3.27994	0.130988
$628$	−8.08921	−0.322795
$629$	−17.6730	−0.704671
$630$	−7.97404	−0.317693
$631$	−44.9045	−1.78762	−0.893811	−	0.448444i	$-0.851978\pi$
$631$	−44.9045	−1.78762	−0.893811	+	0.448444i	$0.851978\pi$
$632$	27.3612	1.08837
$633$	−3.29292	−0.130882
$634$	15.5355	0.616995
$635$	15.0670	0.597916
$636$	19.9701	0.791865
$637$	2.91604	0.115538
$638$	18.0083	0.712955
$639$	1.22227	0.0483523
$640$	−12.3487	−0.488125
$641$	−14.2727	−0.563736	−0.281868	−	0.959453i	$-0.590954\pi$
$641$	−14.2727	−0.563736	−0.281868	+	0.959453i	$0.590954\pi$
$642$	32.0148	1.26352
$643$	−20.7658	−0.818925	−0.409462	−	0.912327i	$-0.634284\pi$
$643$	−20.7658	−0.818925	−0.409462	+	0.912327i	$0.634284\pi$
$644$	9.09776	0.358502
$645$	22.2680	0.876803
$646$	−10.7153	−0.421590
$647$	20.1849	0.793550	0.396775	−	0.917916i	$-0.370129\pi$
$647$	20.1849	0.793550	0.396775	+	0.917916i	$0.370129\pi$
$648$	−19.0662	−0.748989
$649$	−1.47317	−0.0578269
$650$	1.83393	0.0719325
$651$	35.8636	1.40561
$652$	12.4155	0.486228
$653$	43.8685	1.71671	0.858353	−	0.513060i	$-0.171488\pi$
$653$	43.8685	1.71671	0.858353	+	0.513060i	$0.171488\pi$
$654$	17.9512	0.701947
$655$	−12.7805	−0.499374
$656$	−21.9984	−0.858892
$657$	−27.5989	−1.07674
$658$	5.07446	0.197823
$659$	41.4161	1.61334	0.806672	−	0.591000i	$-0.201267\pi$
$659$	41.4161	1.61334	0.806672	+	0.591000i	$0.201267\pi$
$660$	−2.43465	−0.0947684
$661$	−4.38603	−0.170597	−0.0852985	−	0.996355i	$-0.527184\pi$
$661$	−4.38603	−0.170597	−0.0852985	+	0.996355i	$0.527184\pi$
$662$	−17.0071	−0.661000
$663$	11.6744	0.453396
$664$	8.23368	0.319529
$665$	−2.68376	−0.104072
$666$	−14.2598	−0.552556
$667$	43.3459	1.67836
$668$	5.21795	0.201889
$669$	−30.0096	−1.16024
$670$	17.1236	0.661542
$671$	−2.39599	−0.0924964
$672$	23.8388	0.919603
$673$	23.6033	0.909841	0.454920	−	0.890532i	$-0.349668\pi$
$673$	23.6033	0.909841	0.454920	+	0.890532i	$0.349668\pi$
$674$	−1.25794	−0.0484541
$675$	−1.73302	−0.0667041
$676$	−11.4497	−0.440373
$677$	23.7110	0.911290	0.455645	−	0.890162i	$-0.349409\pi$
$677$	23.7110	0.911290	0.455645	+	0.890162i	$0.349409\pi$
$678$	−28.9189	−1.11062
$679$	17.4796	0.670805
$680$	−8.53172	−0.327177
$681$	42.2592	1.61937
$682$	14.3943	0.551188
$683$	47.3006	1.80991	0.904954	−	0.425509i	$-0.139905\pi$
$683$	47.3006	1.80991	0.904954	+	0.425509i	$0.139905\pi$
$684$	−2.81381	−0.107589
$685$	9.58501	0.366224
$686$	34.6167	1.32167
$687$	8.56971	0.326955
$688$	−48.6126	−1.85334
$689$	−9.62619	−0.366729
$690$	−18.0063	−0.685490
$691$	−34.3330	−1.30609	−0.653044	−	0.757320i	$-0.726508\pi$
$691$	−34.3330	−1.30609	−0.653044	+	0.757320i	$0.726508\pi$
$692$	−7.72485	−0.293655
$693$	−5.10278	−0.193839
$694$	−49.1662	−1.86633
$695$	−15.4961	−0.587801
$696$	38.7343	1.46822
$697$	−21.0665	−0.797950
$698$	42.1699	1.59616
$699$	42.7101	1.61544
$700$	1.99211	0.0752947
$701$	17.8539	0.674332	0.337166	−	0.941445i	$-0.390532\pi$
$701$	17.8539	0.674332	0.337166	+	0.941445i	$0.390532\pi$
$702$	−3.17824	−0.119955
$703$	−4.79932	−0.181010
$704$	−1.44813	−0.0545783
$705$	−3.26864	−0.123104
$706$	18.8085	0.707866
$707$	18.6341	0.700806
$708$	2.95402	0.111019
$709$	−42.4446	−1.59404	−0.797020	−	0.603952i	$-0.793592\pi$
$709$	−42.4446	−1.59404	−0.797020	+	0.603952i	$0.793592\pi$
$710$	−0.938246	−0.0352118
$711$	34.4368	1.29148
$712$	5.20179	0.194945
$713$	34.6471	1.29755
$714$	38.9655	1.45825
$715$	1.17357	0.0438892
$716$	−18.9268	−0.707328
$717$	26.1435	0.976348
$718$	10.0918	0.376624
$719$	6.45684	0.240800	0.120400	−	0.992725i	$-0.461582\pi$
$719$	6.45684	0.240800	0.120400	+	0.992725i	$0.461582\pi$
$720$	−11.2130	−0.417884
$721$	−9.22769	−0.343657
$722$	29.8063	1.10927
$723$	−50.1248	−1.86416
$724$	0.769241	0.0285886
$725$	9.49134	0.352500
$726$	38.5836	1.43197
$727$	23.8908	0.886062	0.443031	−	0.896506i	$-0.353903\pi$
$727$	23.8908	0.886062	0.443031	+	0.896506i	$0.353903\pi$
$728$	−3.91883	−0.145242
$729$	−12.0918	−0.447846
$730$	21.1856	0.784116
$731$	−46.5533	−1.72184
$732$	4.80449	0.177579
$733$	1.57981	0.0583515	0.0291758	−	0.999574i	$-0.490712\pi$
$733$	1.57981	0.0583515	0.0291758	+	0.999574i	$0.490712\pi$
$734$	35.3693	1.30551
$735$	−6.26925	−0.231245
$736$	23.0302	0.848906
$737$	10.9578	0.403636
$738$	−16.9979	−0.625700
$739$	−35.2520	−1.29677	−0.648383	−	0.761314i	$-0.724555\pi$
$739$	−35.2520	−1.29677	−0.648383	+	0.761314i	$0.724555\pi$
$740$	3.56245	0.130958
$741$	3.17032	0.116465
$742$	−32.1292	−1.17950
$743$	16.6927	0.612396	0.306198	−	0.951968i	$-0.400943\pi$
$743$	16.6927	0.612396	0.306198	+	0.951968i	$0.400943\pi$
$744$	30.9610	1.13508
$745$	19.3776	0.709942
$746$	0.749111	0.0274269
$747$	10.3629	0.379158
$748$	5.08984	0.186103
$749$	−16.7632	−0.612514
$750$	−3.94280	−0.143971
$751$	8.39121	0.306200	0.153100	−	0.988211i	$-0.451074\pi$
$751$	8.39121	0.306200	0.153100	+	0.988211i	$0.451074\pi$
$752$	7.13565	0.260210
$753$	−49.6513	−1.80939
$754$	17.4064	0.633904
$755$	−14.3225	−0.521250
$756$	−3.45237	−0.125562
$757$	−3.00516	−0.109224	−0.0546122	−	0.998508i	$-0.517392\pi$
$757$	−3.00516	−0.109224	−0.0546122	+	0.998508i	$0.517392\pi$
$758$	−14.3262	−0.520353
$759$	−11.5227	−0.418247
$760$	−2.31689	−0.0840423
$761$	−0.580364	−0.0210382	−0.0105191	−	0.999945i	$-0.503348\pi$
$761$	−0.580364	−0.0210382	−0.0105191	+	0.999945i	$0.503348\pi$
$762$	−59.4062	−2.15206
$763$	−9.39939	−0.340281
$764$	−16.8213	−0.608575
$765$	−10.7380	−0.388234
$766$	−43.2590	−1.56301
$767$	−1.42393	−0.0514151
$768$	42.6698	1.53971
$769$	−52.4078	−1.88987	−0.944937	−	0.327253i	$-0.893877\pi$
$769$	−52.4078	−1.88987	−0.944937	+	0.327253i	$0.893877\pi$
$770$	3.91703	0.141160
$771$	61.1213	2.20123
$772$	−3.73643	−0.134477
$773$	20.6908	0.744195	0.372098	−	0.928194i	$-0.378639\pi$
$773$	20.6908	0.744195	0.372098	+	0.928194i	$0.378639\pi$
$774$	−37.5623	−1.35015
$775$	7.58659	0.272518
$776$	15.0901	0.541703
$777$	17.4524	0.626100
$778$	16.5933	0.594897
$779$	−5.72084	−0.204970
$780$	−2.35327	−0.0842607
$781$	−0.600407	−0.0214842
$782$	37.6439	1.34614
$783$	−16.4487	−0.587829
$784$	13.6862	0.488793
$785$	−8.38308	−0.299205
$786$	50.3908	1.79738
$787$	−39.9278	−1.42327	−0.711636	−	0.702549i	$-0.752045\pi$
$787$	−39.9278	−1.42327	−0.711636	+	0.702549i	$0.752045\pi$
$788$	−5.96672	−0.212556
$789$	42.8322	1.52487
$790$	−26.4345	−0.940499
$791$	15.1422	0.538395
$792$	−4.40522	−0.156533
$793$	−2.31591	−0.0822406
$794$	16.7826	0.595593
$795$	20.6956	0.733996
$796$	6.81991	0.241725
$797$	5.76857	0.204333	0.102167	−	0.994767i	$-0.467423\pi$
$797$	5.76857	0.204333	0.102167	+	0.994767i	$0.467423\pi$
$798$	10.5815	0.374582
$799$	6.83338	0.241748
$800$	5.04287	0.178292
$801$	6.54697	0.231326
$802$	1.72190	0.0608025
$803$	13.5572	0.478423
$804$	−21.9728	−0.774921
$805$	9.42827	0.332303
$806$	13.9132	0.490073
$807$	43.5479	1.53296
$808$	16.0867	0.565930
$809$	30.6751	1.07848	0.539239	−	0.842153i	$-0.318712\pi$
$809$	30.6751	1.07848	0.539239	+	0.842153i	$0.318712\pi$
$810$	18.4204	0.647228
$811$	−15.1705	−0.532709	−0.266354	−	0.963875i	$-0.585819\pi$
$811$	−15.1705	−0.532709	−0.266354	+	0.963875i	$0.585819\pi$
$812$	18.9078	0.663534
$813$	23.2115	0.814062
$814$	7.00474	0.245516
$815$	12.8665	0.450695
$816$	54.7929	1.91814
$817$	−12.6421	−0.442290
$818$	−40.9074	−1.43029
$819$	−4.93224	−0.172346
$820$	4.24648	0.148294
$821$	−1.16866	−0.0407867	−0.0203933	−	0.999792i	$-0.506492\pi$
$821$	−1.16866	−0.0407867	−0.0203933	+	0.999792i	$0.506492\pi$
$822$	−37.7918	−1.31814
$823$	35.1019	1.22357	0.611787	−	0.791022i	$-0.290451\pi$
$823$	35.1019	1.22357	0.611787	+	0.791022i	$0.290451\pi$
$824$	−7.96625	−0.277517
$825$	−2.52309	−0.0878428
$826$	−4.75264	−0.165365
$827$	−15.0564	−0.523563	−0.261781	−	0.965127i	$-0.584310\pi$
$827$	−15.0564	−0.523563	−0.261781	+	0.965127i	$0.584310\pi$
$828$	9.88513	0.343532
$829$	36.2338	1.25845	0.629226	−	0.777222i	$-0.283372\pi$
$829$	36.2338	1.25845	0.629226	+	0.777222i	$0.283372\pi$
$830$	−7.95482	−0.276116
$831$	−4.48444	−0.155564
$832$	−1.39973	−0.0485268
$833$	13.1064	0.454111
$834$	61.0980	2.11565
$835$	5.40751	0.187135
$836$	1.38220	0.0478045
$837$	−13.1477	−0.454452
$838$	68.3114	2.35978
$839$	−50.1352	−1.73086	−0.865429	−	0.501031i	$-0.832954\pi$
$839$	−50.1352	−1.73086	−0.865429	+	0.501031i	$0.832954\pi$
$840$	8.42518	0.290696
$841$	61.0855	2.10640
$842$	42.9582	1.48044
$843$	4.38819	0.151137
$844$	−1.38767	−0.0477657
$845$	−11.8656	−0.408191
$846$	5.51363	0.189563
$847$	−20.2027	−0.694173
$848$	−45.1798	−1.55148
$849$	−68.5206	−2.35162
$850$	8.24277	0.282725
$851$	16.8604	0.577966
$852$	1.20395	0.0412465
$853$	−29.3919	−1.00636	−0.503180	−	0.864182i	$-0.667837\pi$
$853$	−29.3919	−1.00636	−0.503180	+	0.864182i	$0.667837\pi$
$854$	−7.72980	−0.264508
$855$	−2.91603	−0.0997261
$856$	−14.4716	−0.494631
$857$	−2.34312	−0.0800396	−0.0400198	−	0.999199i	$-0.512742\pi$
$857$	−2.34312	−0.0800396	−0.0400198	+	0.999199i	$0.512742\pi$
$858$	−4.62717	−0.157969
$859$	36.5834	1.24821	0.624105	−	0.781340i	$-0.285464\pi$
$859$	36.5834	1.24821	0.624105	+	0.781340i	$0.285464\pi$
$860$	9.38400	0.319992
$861$	20.8034	0.708978
$862$	−17.0189	−0.579665
$863$	−38.6151	−1.31447	−0.657237	−	0.753684i	$-0.728275\pi$
$863$	−38.6151	−1.31447	−0.657237	+	0.753684i	$0.728275\pi$
$864$	−8.73940	−0.297320
$865$	−8.00548	−0.272195
$866$	−4.29629	−0.145994
$867$	13.5453	0.460024
$868$	15.1133	0.512980
$869$	−16.9161	−0.573840
$870$	−37.4224	−1.26874
$871$	10.5916	0.358882
$872$	−8.11447	−0.274791
$873$	18.9924	0.642794
$874$	10.2226	0.345785
$875$	2.06448	0.0697923
$876$	−27.1852	−0.918502
$877$	18.4949	0.624528	0.312264	−	0.949995i	$-0.398913\pi$
$877$	18.4949	0.624528	0.312264	+	0.949995i	$0.398913\pi$
$878$	47.4769	1.60227
$879$	−20.1360	−0.679172
$880$	5.50808	0.185677
$881$	−55.3749	−1.86563	−0.932814	−	0.360358i	$-0.882655\pi$
$881$	−55.3749	−1.86563	−0.932814	+	0.360358i	$0.882655\pi$
$882$	10.5752	0.356084
$883$	27.2930	0.918483	0.459241	−	0.888312i	$-0.348121\pi$
$883$	27.2930	0.918483	0.459241	+	0.888312i	$0.348121\pi$
$884$	4.91973	0.165468
$885$	3.06134	0.102906
$886$	−6.27568	−0.210836
$887$	−43.2236	−1.45131	−0.725654	−	0.688060i	$-0.758463\pi$
$887$	−43.2236	−1.45131	−0.725654	+	0.688060i	$0.758463\pi$
$888$	15.0666	0.505601
$889$	31.1056	1.04325
$890$	−5.02562	−0.168459
$891$	11.7877	0.394902
$892$	−12.6464	−0.423433
$893$	1.85568	0.0620980
$894$	−76.4021	−2.55527
$895$	−19.6144	−0.655637
$896$	−25.4937	−0.851684
$897$	−11.1376	−0.371873
$898$	−6.67117	−0.222620
$899$	72.0069	2.40156
$900$	2.16452	0.0721506
$901$	−43.2659	−1.44140
$902$	8.34973	0.278015
$903$	45.9720	1.52985
$904$	13.0722	0.434776
$905$	0.797186	0.0264994
$906$	56.4708	1.87612
$907$	29.0453	0.964435	0.482217	−	0.876052i	$-0.339832\pi$
$907$	29.0453	0.964435	0.482217	+	0.876052i	$0.339832\pi$
$908$	17.8085	0.590995
$909$	20.2468	0.671542
$910$	3.78611	0.125508
$911$	36.3485	1.20428	0.602140	−	0.798391i	$-0.294315\pi$
$911$	36.3485	1.20428	0.602140	+	0.798391i	$0.294315\pi$
$912$	14.8796	0.492714
$913$	−5.09048	−0.168470
$914$	−40.8241	−1.35034
$915$	4.97904	0.164602
$916$	3.61137	0.119323
$917$	−26.3850	−0.871311
$918$	−14.2849	−0.471472
$919$	54.1928	1.78765	0.893827	−	0.448411i	$-0.148010\pi$
$919$	54.1928	1.78765	0.893827	+	0.448411i	$0.148010\pi$
$920$	8.13941	0.268348
$921$	32.8968	1.08398
$922$	−61.2196	−2.01616
$923$	−0.580340	−0.0191021
$924$	−5.02628	−0.165353
$925$	3.69187	0.121388
$926$	−37.3427	−1.22716
$927$	−10.0263	−0.329307
$928$	47.8635	1.57120
$929$	−14.0316	−0.460360	−0.230180	−	0.973148i	$-0.573932\pi$
$929$	−14.0316	−0.460360	−0.230180	+	0.973148i	$0.573932\pi$
$930$	−29.9124	−0.980866
$931$	3.55920	0.116648
$932$	17.9985	0.589560
$933$	−25.2255	−0.825845
$934$	40.1910	1.31509
$935$	5.27475	0.172503
$936$	−4.25799	−0.139177
$937$	−37.6042	−1.22848	−0.614238	−	0.789121i	$-0.710536\pi$
$937$	−37.6042	−1.22848	−0.614238	+	0.789121i	$0.710536\pi$
$938$	35.3514	1.15426
$939$	−55.0721	−1.79721
$940$	−1.37744	−0.0449272
$941$	36.8214	1.20034	0.600172	−	0.799871i	$-0.295099\pi$
$941$	36.8214	1.20034	0.600172	+	0.799871i	$0.295099\pi$
$942$	33.0528	1.07692
$943$	20.0978	0.654473
$944$	−6.68310	−0.217517
$945$	−3.57779	−0.116386
$946$	18.4515	0.599909
$947$	−16.9989	−0.552391	−0.276196	−	0.961101i	$-0.589074\pi$
$947$	−16.9989	−0.552391	−0.276196	+	0.961101i	$0.589074\pi$
$948$	33.9205	1.10169
$949$	13.1041	0.425377
$950$	2.23842	0.0726239
$951$	−20.6592	−0.669921
$952$	−17.6136	−0.570860
$953$	14.8447	0.480868	0.240434	−	0.970665i	$-0.422710\pi$
$953$	14.8447	0.480868	0.240434	+	0.970665i	$0.422710\pi$
$954$	−34.9099	−1.13025
$955$	−17.4324	−0.564101
$956$	11.0172	0.356321
$957$	−23.9475	−0.774114
$958$	52.3223	1.69046
$959$	19.7881	0.638991
$960$	3.00930	0.0971248
$961$	26.5563	0.856654
$962$	6.77062	0.218294
$963$	−18.2140	−0.586937
$964$	−21.1232	−0.680331
$965$	−3.87217	−0.124650
$966$	−37.1738	−1.19605
$967$	22.1559	0.712487	0.356244	−	0.934393i	$-0.384057\pi$
$967$	22.1559	0.712487	0.356244	+	0.934393i	$0.384057\pi$
$968$	−17.4410	−0.560573
$969$	14.2493	0.457754
$970$	−14.5790	−0.468104
$971$	0.375750	0.0120584	0.00602919	−	0.999982i	$-0.498081\pi$
$971$	0.375750	0.0120584	0.00602919	+	0.999982i	$0.498081\pi$
$972$	−18.6201	−0.597239
$973$	−31.9914	−1.02560
$974$	24.0130	0.769427
$975$	−2.43876	−0.0781030
$976$	−10.8696	−0.347926
$977$	−54.5051	−1.74377	−0.871887	−	0.489707i	$-0.837104\pi$
$977$	−54.5051	−1.74377	−0.871887	+	0.489707i	$0.837104\pi$
$978$	−50.7302	−1.62217
$979$	−3.21602	−0.102784
$980$	−2.64193	−0.0843935
$981$	−10.2129	−0.326072
$982$	48.2577	1.53996
$983$	18.6303	0.594214	0.297107	−	0.954844i	$-0.403978\pi$
$983$	18.6303	0.594214	0.297107	+	0.954844i	$0.403978\pi$
$984$	17.9595	0.572529
$985$	−6.18348	−0.197022
$986$	78.2349	2.49151
$987$	−6.74804	−0.214793
$988$	1.33601	0.0425041
$989$	44.4126	1.41224
$990$	4.25602	0.135265
$991$	56.8464	1.80578	0.902892	−	0.429867i	$-0.141440\pi$
$991$	56.8464	1.80578	0.902892	+	0.429867i	$0.141440\pi$
$992$	38.2581	1.21470
$993$	22.6161	0.717702
$994$	−1.93699	−0.0614377
$995$	7.06767	0.224060
$996$	10.2075	0.323438
$997$	−24.3698	−0.771801	−0.385900	−	0.922540i	$-0.626109\pi$
$997$	−24.3698	−0.771801	−0.385900	+	0.922540i	$0.626109\pi$
$998$	−15.6302	−0.494764
$999$	−6.39810	−0.202427

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.g.1.8	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.g.1.8	✓	37	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)

\(f(q)\)	\(=\)	\(q-1.72190 q^{2} +2.28979 q^{3} +0.964945 q^{4} +1.00000 q^{5} -3.94280 q^{6} +2.06448 q^{7} +1.78226 q^{8} +2.24315 q^{9} +O(q^{10})\)	\(q-1.72190 q^{2} +2.28979 q^{3} +0.964945 q^{4} +1.00000 q^{5} -3.94280 q^{6} +2.06448 q^{7} +1.78226 q^{8} +2.24315 q^{9} -1.72190 q^{10} -1.10189 q^{11} +2.20952 q^{12} -1.06506 q^{13} -3.55484 q^{14} +2.28979 q^{15} -4.99877 q^{16} -4.78702 q^{17} -3.86249 q^{18} -1.29997 q^{19} +0.964945 q^{20} +4.72724 q^{21} +1.89734 q^{22} +4.56689 q^{23} +4.08101 q^{24} +1.00000 q^{25} +1.83393 q^{26} -1.73302 q^{27} +1.99211 q^{28} +9.49134 q^{29} -3.94280 q^{30} +7.58659 q^{31} +5.04287 q^{32} -2.52309 q^{33} +8.24277 q^{34} +2.06448 q^{35} +2.16452 q^{36} +3.69187 q^{37} +2.23842 q^{38} -2.43876 q^{39} +1.78226 q^{40} +4.40075 q^{41} -8.13984 q^{42} +9.72491 q^{43} -1.06326 q^{44} +2.24315 q^{45} -7.86374 q^{46} -1.42748 q^{47} -11.4462 q^{48} -2.73791 q^{49} -1.72190 q^{50} -10.9613 q^{51} -1.02772 q^{52} +9.03818 q^{53} +2.98409 q^{54} -1.10189 q^{55} +3.67945 q^{56} -2.97666 q^{57} -16.3432 q^{58} +1.33695 q^{59} +2.20952 q^{60} +2.17445 q^{61} -13.0634 q^{62} +4.63095 q^{63} +1.31422 q^{64} -1.06506 q^{65} +4.34452 q^{66} -9.94458 q^{67} -4.61921 q^{68} +10.4572 q^{69} -3.55484 q^{70} +0.544890 q^{71} +3.99789 q^{72} -12.3036 q^{73} -6.35704 q^{74} +2.28979 q^{75} -1.25440 q^{76} -2.27483 q^{77} +4.19931 q^{78} +15.3520 q^{79} -4.99877 q^{80} -10.6977 q^{81} -7.57766 q^{82} +4.61979 q^{83} +4.56152 q^{84} -4.78702 q^{85} -16.7453 q^{86} +21.7332 q^{87} -1.96385 q^{88} +2.91864 q^{89} -3.86249 q^{90} -2.19880 q^{91} +4.40680 q^{92} +17.3717 q^{93} +2.45798 q^{94} -1.29997 q^{95} +11.5471 q^{96} +8.46681 q^{97} +4.71441 q^{98} -2.47170 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

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