LMFDB - Embedded newform 8049.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65190 q^{2} +1.00000 q^{3} +5.03256 q^{4} -2.74220 q^{5} -2.65190 q^{6} +0.184989 q^{7} -8.04204 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.65190 q^{2} +1.00000 q^{3} +5.03256 q^{4} -2.74220 q^{5} -2.65190 q^{6} +0.184989 q^{7} -8.04204 q^{8} +1.00000 q^{9} +7.27204 q^{10} -2.20250 q^{11} +5.03256 q^{12} -4.60348 q^{13} -0.490573 q^{14} -2.74220 q^{15} +11.2615 q^{16} -5.20245 q^{17} -2.65190 q^{18} -4.24372 q^{19} -13.8003 q^{20} +0.184989 q^{21} +5.84081 q^{22} -2.01906 q^{23} -8.04204 q^{24} +2.51967 q^{25} +12.2080 q^{26} +1.00000 q^{27} +0.930969 q^{28} -6.61867 q^{29} +7.27204 q^{30} -1.25856 q^{31} -13.7804 q^{32} -2.20250 q^{33} +13.7964 q^{34} -0.507278 q^{35} +5.03256 q^{36} +8.69948 q^{37} +11.2539 q^{38} -4.60348 q^{39} +22.0529 q^{40} -8.25186 q^{41} -0.490573 q^{42} -1.78980 q^{43} -11.0842 q^{44} -2.74220 q^{45} +5.35433 q^{46} -9.20382 q^{47} +11.2615 q^{48} -6.96578 q^{49} -6.68191 q^{50} -5.20245 q^{51} -23.1673 q^{52} -6.81997 q^{53} -2.65190 q^{54} +6.03970 q^{55} -1.48769 q^{56} -4.24372 q^{57} +17.5520 q^{58} +7.73150 q^{59} -13.8003 q^{60} -2.42620 q^{61} +3.33757 q^{62} +0.184989 q^{63} +14.0211 q^{64} +12.6237 q^{65} +5.84081 q^{66} -3.25245 q^{67} -26.1816 q^{68} -2.01906 q^{69} +1.34525 q^{70} +7.30897 q^{71} -8.04204 q^{72} -14.5923 q^{73} -23.0701 q^{74} +2.51967 q^{75} -21.3568 q^{76} -0.407439 q^{77} +12.2080 q^{78} +1.53972 q^{79} -30.8814 q^{80} +1.00000 q^{81} +21.8831 q^{82} -14.2180 q^{83} +0.930969 q^{84} +14.2662 q^{85} +4.74636 q^{86} -6.61867 q^{87} +17.7126 q^{88} -0.736460 q^{89} +7.27204 q^{90} -0.851594 q^{91} -10.1610 q^{92} -1.25856 q^{93} +24.4076 q^{94} +11.6371 q^{95} -13.7804 q^{96} +14.6149 q^{97} +18.4725 q^{98} -2.20250 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * 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 $

$2$	−2.65190	−1.87517	−0.937587	−	0.347750i	$-0.886946\pi$
$2$	−2.65190	−1.87517	−0.937587	+	0.347750i	$0.886946\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.03256	2.51628
$5$	−2.74220	−1.22635	−0.613175	−	0.789947i	$-0.710108\pi$
$5$	−2.74220	−1.22635	−0.613175	+	0.789947i	$0.710108\pi$
$6$	−2.65190	−1.08263
$7$	0.184989	0.0699194	0.0349597	−	0.999389i	$-0.488870\pi$
$7$	0.184989	0.0699194	0.0349597	+	0.999389i	$0.488870\pi$
$8$	−8.04204	−2.84329
$9$	1.00000	0.333333
$10$	7.27204	2.29962
$11$	−2.20250	−0.664079	−0.332039	−	0.943266i	$-0.607737\pi$
$11$	−2.20250	−0.664079	−0.332039	+	0.943266i	$0.607737\pi$
$12$	5.03256	1.45277
$13$	−4.60348	−1.27678	−0.638388	−	0.769715i	$-0.720398\pi$
$13$	−4.60348	−1.27678	−0.638388	+	0.769715i	$0.720398\pi$
$14$	−0.490573	−0.131111
$15$	−2.74220	−0.708033
$16$	11.2615	2.81538
$17$	−5.20245	−1.26178	−0.630890	−	0.775872i	$-0.717310\pi$
$17$	−5.20245	−1.26178	−0.630890	+	0.775872i	$0.717310\pi$
$18$	−2.65190	−0.625058
$19$	−4.24372	−0.973577	−0.486788	−	0.873520i	$-0.661832\pi$
$19$	−4.24372	−0.973577	−0.486788	+	0.873520i	$0.661832\pi$
$20$	−13.8003	−3.08584
$21$	0.184989	0.0403680
$22$	5.84081	1.24526
$23$	−2.01906	−0.421002	−0.210501	−	0.977594i	$-0.567510\pi$
$23$	−2.01906	−0.421002	−0.210501	+	0.977594i	$0.567510\pi$
$24$	−8.04204	−1.64157
$25$	2.51967	0.503934
$26$	12.2080	2.39418
$27$	1.00000	0.192450
$28$	0.930969	0.175937
$29$	−6.61867	−1.22906	−0.614529	−	0.788895i	$-0.710654\pi$
$29$	−6.61867	−1.22906	−0.614529	+	0.788895i	$0.710654\pi$
$30$	7.27204	1.32769
$31$	−1.25856	−0.226044	−0.113022	−	0.993592i	$-0.536053\pi$
$31$	−1.25856	−0.226044	−0.113022	+	0.993592i	$0.536053\pi$
$32$	−13.7804	−2.43605
$33$	−2.20250	−0.383406
$34$	13.7964	2.36606
$35$	−0.507278	−0.0857456
$36$	5.03256	0.838760
$37$	8.69948	1.43019	0.715093	−	0.699030i	$-0.246384\pi$
$37$	8.69948	1.43019	0.715093	+	0.699030i	$0.246384\pi$
$38$	11.2539	1.82563
$39$	−4.60348	−0.737147
$40$	22.0529	3.48687
$41$	−8.25186	−1.28872	−0.644362	−	0.764721i	$-0.722877\pi$
$41$	−8.25186	−1.28872	−0.644362	+	0.764721i	$0.722877\pi$
$42$	−0.490573	−0.0756970
$43$	−1.78980	−0.272942	−0.136471	−	0.990644i	$-0.543576\pi$
$43$	−1.78980	−0.272942	−0.136471	+	0.990644i	$0.543576\pi$
$44$	−11.0842	−1.67101
$45$	−2.74220	−0.408783
$46$	5.35433	0.789453
$47$	−9.20382	−1.34251	−0.671257	−	0.741224i	$-0.734246\pi$
$47$	−9.20382	−1.34251	−0.671257	+	0.741224i	$0.734246\pi$
$48$	11.2615	1.62546
$49$	−6.96578	−0.995111
$50$	−6.68191	−0.944965
$51$	−5.20245	−0.728489
$52$	−23.1673	−3.21273
$53$	−6.81997	−0.936796	−0.468398	−	0.883518i	$-0.655169\pi$
$53$	−6.81997	−0.936796	−0.468398	+	0.883518i	$0.655169\pi$
$54$	−2.65190	−0.360878
$55$	6.03970	0.814393
$56$	−1.48769	−0.198801
$57$	−4.24372	−0.562095
$58$	17.5520	2.30470
$59$	7.73150	1.00656	0.503278	−	0.864125i	$-0.332127\pi$
$59$	7.73150	1.00656	0.503278	+	0.864125i	$0.332127\pi$
$60$	−13.8003	−1.78161
$61$	−2.42620	−0.310643	−0.155322	−	0.987864i	$-0.549641\pi$
$61$	−2.42620	−0.310643	−0.155322	+	0.987864i	$0.549641\pi$
$62$	3.33757	0.423872
$63$	0.184989	0.0233065
$64$	14.0211	1.75263
$65$	12.6237	1.56577
$66$	5.84081	0.718953
$67$	−3.25245	−0.397350	−0.198675	−	0.980065i	$-0.563664\pi$
$67$	−3.25245	−0.397350	−0.198675	+	0.980065i	$0.563664\pi$
$68$	−26.1816	−3.17499
$69$	−2.01906	−0.243066
$70$	1.34525	0.160788
$71$	7.30897	0.867415	0.433707	−	0.901054i	$-0.357205\pi$
$71$	7.30897	0.867415	0.433707	+	0.901054i	$0.357205\pi$
$72$	−8.04204	−0.947763
$73$	−14.5923	−1.70790	−0.853951	−	0.520354i	$-0.825800\pi$
$73$	−14.5923	−1.70790	−0.853951	+	0.520354i	$0.825800\pi$
$74$	−23.0701	−2.68185
$75$	2.51967	0.290947
$76$	−21.3568	−2.44979
$77$	−0.407439	−0.0464320
$78$	12.2080	1.38228
$79$	1.53972	0.173233	0.0866163	−	0.996242i	$-0.472395\pi$
$79$	1.53972	0.173233	0.0866163	+	0.996242i	$0.472395\pi$
$80$	−30.8814	−3.45265
$81$	1.00000	0.111111
$82$	21.8831	2.41658
$83$	−14.2180	−1.56062	−0.780312	−	0.625391i	$-0.784939\pi$
$83$	−14.2180	−1.56062	−0.780312	+	0.625391i	$0.784939\pi$
$84$	0.930969	0.101577
$85$	14.2662	1.54738
$86$	4.74636	0.511813
$87$	−6.61867	−0.709596
$88$	17.7126	1.88817
$89$	−0.736460	−0.0780646	−0.0390323	−	0.999238i	$-0.512428\pi$
$89$	−0.736460	−0.0780646	−0.0390323	+	0.999238i	$0.512428\pi$
$90$	7.27204	0.766540
$91$	−0.851594	−0.0892714
$92$	−10.1610	−1.05936
$93$	−1.25856	−0.130506
$94$	24.4076	2.51745
$95$	11.6371	1.19395
$96$	−13.7804	−1.40645
$97$	14.6149	1.48392	0.741961	−	0.670443i	$-0.233896\pi$
$97$	14.6149	1.48392	0.741961	+	0.670443i	$0.233896\pi$
$98$	18.4725	1.86601
$99$	−2.20250	−0.221360
$100$	12.6804	1.26804
$101$	−5.78045	−0.575177	−0.287588	−	0.957754i	$-0.592853\pi$
$101$	−5.78045	−0.575177	−0.287588	+	0.957754i	$0.592853\pi$
$102$	13.7964	1.36604
$103$	−12.1958	−1.20169	−0.600846	−	0.799365i	$-0.705170\pi$
$103$	−12.1958	−1.20169	−0.600846	+	0.799365i	$0.705170\pi$
$104$	37.0214	3.63024
$105$	−0.507278	−0.0495053
$106$	18.0859	1.75666
$107$	13.4122	1.29661	0.648305	−	0.761381i	$-0.275478\pi$
$107$	13.4122	1.29661	0.648305	+	0.761381i	$0.275478\pi$
$108$	5.03256	0.484258
$109$	2.48675	0.238188	0.119094	−	0.992883i	$-0.462001\pi$
$109$	2.48675	0.238188	0.119094	+	0.992883i	$0.462001\pi$
$110$	−16.0167	−1.52713
$111$	8.69948	0.825718
$112$	2.08326	0.196850
$113$	9.16262	0.861947	0.430974	−	0.902365i	$-0.358170\pi$
$113$	9.16262	0.861947	0.430974	+	0.902365i	$0.358170\pi$
$114$	11.2539	1.05403
$115$	5.53666	0.516296
$116$	−33.3089	−3.09265
$117$	−4.60348	−0.425592
$118$	−20.5032	−1.88747
$119$	−0.962398	−0.0882228
$120$	22.0529	2.01314
$121$	−6.14899	−0.558999
$122$	6.43404	0.582510
$123$	−8.25186	−0.744045
$124$	−6.33377	−0.568790
$125$	6.80156	0.608350
$126$	−0.490573	−0.0437037
$127$	−3.59284	−0.318813	−0.159406	−	0.987213i	$-0.550958\pi$
$127$	−3.59284	−0.318813	−0.159406	+	0.987213i	$0.550958\pi$
$128$	−9.62165	−0.850441
$129$	−1.78980	−0.157583
$130$	−33.4767	−2.93610
$131$	−19.9931	−1.74680	−0.873401	−	0.487002i	$-0.838091\pi$
$131$	−19.9931	−1.74680	−0.873401	+	0.487002i	$0.838091\pi$
$132$	−11.0842	−0.964757
$133$	−0.785043	−0.0680719
$134$	8.62516	0.745100
$135$	−2.74220	−0.236011
$136$	41.8383	3.58761
$137$	−2.88865	−0.246794	−0.123397	−	0.992357i	$-0.539379\pi$
$137$	−2.88865	−0.246794	−0.123397	+	0.992357i	$0.539379\pi$
$138$	5.35433	0.455791
$139$	−7.65770	−0.649518	−0.324759	−	0.945797i	$-0.605283\pi$
$139$	−7.65770	−0.649518	−0.324759	+	0.945797i	$0.605283\pi$
$140$	−2.55291	−0.215760
$141$	−9.20382	−0.775101
$142$	−19.3826	−1.62655
$143$	10.1392	0.847880
$144$	11.2615	0.938462
$145$	18.1497	1.50725
$146$	38.6973	3.20261
$147$	−6.96578	−0.574528
$148$	43.7806	3.59875
$149$	16.7903	1.37551	0.687756	−	0.725942i	$-0.258596\pi$
$149$	16.7903	1.37551	0.687756	+	0.725942i	$0.258596\pi$
$150$	−6.68191	−0.545576
$151$	−12.5249	−1.01926	−0.509629	−	0.860394i	$-0.670217\pi$
$151$	−12.5249	−1.01926	−0.509629	+	0.860394i	$0.670217\pi$
$152$	34.1282	2.76816
$153$	−5.20245	−0.420593
$154$	1.08049	0.0870681
$155$	3.45122	0.277209
$156$	−23.1673	−1.85487
$157$	−12.7698	−1.01914	−0.509571	−	0.860429i	$-0.670196\pi$
$157$	−12.7698	−1.01914	−0.509571	+	0.860429i	$0.670196\pi$
$158$	−4.08319	−0.324841
$159$	−6.81997	−0.540859
$160$	37.7886	2.98745
$161$	−0.373504	−0.0294362
$162$	−2.65190	−0.208353
$163$	1.98925	0.155810	0.0779049	−	0.996961i	$-0.475177\pi$
$163$	1.98925	0.155810	0.0779049	+	0.996961i	$0.475177\pi$
$164$	−41.5280	−3.24279
$165$	6.03970	0.470190
$166$	37.7046	2.92644
$167$	4.95495	0.383425	0.191713	−	0.981451i	$-0.438596\pi$
$167$	4.95495	0.383425	0.191713	+	0.981451i	$0.438596\pi$
$168$	−1.48769	−0.114778
$169$	8.19204	0.630157
$170$	−37.8324	−2.90161
$171$	−4.24372	−0.324526
$172$	−9.00727	−0.686798
$173$	−14.9759	−1.13859	−0.569297	−	0.822132i	$-0.692784\pi$
$173$	−14.9759	−1.13859	−0.569297	+	0.822132i	$0.692784\pi$
$174$	17.5520	1.33062
$175$	0.466112	0.0352348
$176$	−24.8035	−1.86964
$177$	7.73150	0.581135
$178$	1.95302	0.146385
$179$	−2.15978	−0.161430	−0.0807148	−	0.996737i	$-0.525720\pi$
$179$	−2.15978	−0.161430	−0.0807148	+	0.996737i	$0.525720\pi$
$180$	−13.8003	−1.02861
$181$	11.5885	0.861365	0.430683	−	0.902503i	$-0.358273\pi$
$181$	11.5885	0.861365	0.430683	+	0.902503i	$0.358273\pi$
$182$	2.25834	0.167399
$183$	−2.42620	−0.179350
$184$	16.2373	1.19703
$185$	−23.8557	−1.75391
$186$	3.33757	0.244722
$187$	11.4584	0.837921
$188$	−46.3188	−3.37814
$189$	0.184989	0.0134560
$190$	−30.8605	−2.23886
$191$	−5.26055	−0.380640	−0.190320	−	0.981722i	$-0.560953\pi$
$191$	−5.26055	−0.380640	−0.190320	+	0.981722i	$0.560953\pi$
$192$	14.0211	1.01188
$193$	−0.328357	−0.0236357	−0.0118178	−	0.999930i	$-0.503762\pi$
$193$	−0.328357	−0.0236357	−0.0118178	+	0.999930i	$0.503762\pi$
$194$	−38.7573	−2.78261
$195$	12.6237	0.904000
$196$	−35.0557	−2.50398
$197$	−26.3493	−1.87731	−0.938655	−	0.344857i	$-0.887927\pi$
$197$	−26.3493	−1.87731	−0.938655	+	0.344857i	$0.887927\pi$
$198$	5.84081	0.415088
$199$	16.3358	1.15801	0.579007	−	0.815322i	$-0.303440\pi$
$199$	16.3358	1.15801	0.579007	+	0.815322i	$0.303440\pi$
$200$	−20.2633	−1.43283
$201$	−3.25245	−0.229410
$202$	15.3292	1.07856
$203$	−1.22438	−0.0859349
$204$	−26.1816	−1.83308
$205$	22.6283	1.58043
$206$	32.3421	2.25338
$207$	−2.01906	−0.140334
$208$	−51.8423	−3.59462
$209$	9.34680	0.646532
$210$	1.34525	0.0928310
$211$	9.80930	0.675300	0.337650	−	0.941272i	$-0.390368\pi$
$211$	9.80930	0.675300	0.337650	+	0.941272i	$0.390368\pi$
$212$	−34.3219	−2.35724
$213$	7.30897	0.500802
$214$	−35.5679	−2.43137
$215$	4.90799	0.334722
$216$	−8.04204	−0.547191
$217$	−0.232820	−0.0158048
$218$	−6.59461	−0.446643
$219$	−14.5923	−0.986057
$220$	30.3952	2.04924
$221$	23.9494	1.61101
$222$	−23.0701	−1.54837
$223$	3.42921	0.229637	0.114819	−	0.993386i	$-0.463371\pi$
$223$	3.42921	0.229637	0.114819	+	0.993386i	$0.463371\pi$
$224$	−2.54922	−0.170327
$225$	2.51967	0.167978
$226$	−24.2983	−1.61630
$227$	27.9642	1.85605	0.928025	−	0.372517i	$-0.121505\pi$
$227$	27.9642	1.85605	0.928025	+	0.372517i	$0.121505\pi$
$228$	−21.3568	−1.41439
$229$	20.5154	1.35570	0.677848	−	0.735202i	$-0.262913\pi$
$229$	20.5154	1.35570	0.677848	+	0.735202i	$0.262913\pi$
$230$	−14.6826	−0.968145
$231$	−0.407439	−0.0268075
$232$	53.2276	3.49457
$233$	−10.5108	−0.688586	−0.344293	−	0.938862i	$-0.611881\pi$
$233$	−10.5108	−0.688586	−0.344293	+	0.938862i	$0.611881\pi$
$234$	12.2080	0.798059
$235$	25.2387	1.64639
$236$	38.9093	2.53278
$237$	1.53972	0.100016
$238$	2.55218	0.165433
$239$	11.1214	0.719384	0.359692	−	0.933071i	$-0.382882\pi$
$239$	11.1214	0.719384	0.359692	+	0.933071i	$0.382882\pi$
$240$	−30.8814	−1.99339
$241$	26.7378	1.72233	0.861167	−	0.508321i	$-0.169734\pi$
$241$	26.7378	1.72233	0.861167	+	0.508321i	$0.169734\pi$
$242$	16.3065	1.04822
$243$	1.00000	0.0641500
$244$	−12.2100	−0.781665
$245$	19.1016	1.22035
$246$	21.8831	1.39521
$247$	19.5359	1.24304
$248$	10.1214	0.642708
$249$	−14.2180	−0.901026
$250$	−18.0370	−1.14076
$251$	−12.1440	−0.766520	−0.383260	−	0.923640i	$-0.625199\pi$
$251$	−12.1440	−0.766520	−0.383260	+	0.923640i	$0.625199\pi$
$252$	0.930969	0.0586456
$253$	4.44697	0.279579
$254$	9.52784	0.597830
$255$	14.2662	0.893382
$256$	−2.52648	−0.157905
$257$	9.18015	0.572642	0.286321	−	0.958134i	$-0.407568\pi$
$257$	9.18015	0.572642	0.286321	+	0.958134i	$0.407568\pi$
$258$	4.74636	0.295496
$259$	1.60931	0.0999977
$260$	63.5294	3.93993
$261$	−6.61867	−0.409686
$262$	53.0195	3.27556
$263$	−3.60302	−0.222172	−0.111086	−	0.993811i	$-0.535433\pi$
$263$	−3.60302	−0.222172	−0.111086	+	0.993811i	$0.535433\pi$
$264$	17.7126	1.09013
$265$	18.7017	1.14884
$266$	2.08185	0.127647
$267$	−0.736460	−0.0450706
$268$	−16.3681	−0.999843
$269$	−5.70200	−0.347657	−0.173829	−	0.984776i	$-0.555614\pi$
$269$	−5.70200	−0.347657	−0.173829	+	0.984776i	$0.555614\pi$
$270$	7.27204	0.442562
$271$	−16.0370	−0.974176	−0.487088	−	0.873353i	$-0.661941\pi$
$271$	−16.0370	−0.974176	−0.487088	+	0.873353i	$0.661941\pi$
$272$	−58.5876	−3.55240
$273$	−0.851594	−0.0515408
$274$	7.66041	0.462782
$275$	−5.54958	−0.334652
$276$	−10.1610	−0.611621
$277$	−13.8712	−0.833439	−0.416719	−	0.909035i	$-0.636820\pi$
$277$	−13.8712	−0.833439	−0.416719	+	0.909035i	$0.636820\pi$
$278$	20.3074	1.21796
$279$	−1.25856	−0.0753479
$280$	4.07955	0.243800
$281$	6.70728	0.400123	0.200061	−	0.979783i	$-0.435886\pi$
$281$	6.70728	0.400123	0.200061	+	0.979783i	$0.435886\pi$
$282$	24.4076	1.45345
$283$	−31.7643	−1.88819	−0.944095	−	0.329673i	$-0.893062\pi$
$283$	−31.7643	−1.88819	−0.944095	+	0.329673i	$0.893062\pi$
$284$	36.7828	2.18266
$285$	11.6371	0.689325
$286$	−26.8880	−1.58992
$287$	−1.52650	−0.0901067
$288$	−13.7804	−0.812016
$289$	10.0655	0.592088
$290$	−48.1313	−2.82636
$291$	14.6149	0.856743
$292$	−73.4367	−4.29756
$293$	−6.77053	−0.395539	−0.197769	−	0.980249i	$-0.563370\pi$
$293$	−6.77053	−0.395539	−0.197769	+	0.980249i	$0.563370\pi$
$294$	18.4725	1.07734
$295$	−21.2013	−1.23439
$296$	−69.9615	−4.06643
$297$	−2.20250	−0.127802
$298$	−44.5261	−2.57933
$299$	9.29468	0.537525
$300$	12.6804	0.732103
$301$	−0.331093	−0.0190839
$302$	33.2146	1.91129
$303$	−5.78045	−0.332078
$304$	−47.7909	−2.74099
$305$	6.65313	0.380957
$306$	13.7964	0.788686
$307$	0.859438	0.0490507	0.0245254	−	0.999699i	$-0.492193\pi$
$307$	0.859438	0.0490507	0.0245254	+	0.999699i	$0.492193\pi$
$308$	−2.05046	−0.116836
$309$	−12.1958	−0.693797
$310$	−9.15229	−0.519815
$311$	−12.8206	−0.726989	−0.363495	−	0.931596i	$-0.618417\pi$
$311$	−12.8206	−0.726989	−0.363495	+	0.931596i	$0.618417\pi$
$312$	37.0214	2.09592
$313$	5.42710	0.306758	0.153379	−	0.988167i	$-0.450985\pi$
$313$	5.42710	0.306758	0.153379	+	0.988167i	$0.450985\pi$
$314$	33.8642	1.91107
$315$	−0.507278	−0.0285819
$316$	7.74875	0.435902
$317$	−18.7466	−1.05291	−0.526456	−	0.850202i	$-0.676480\pi$
$317$	−18.7466	−1.05291	−0.526456	+	0.850202i	$0.676480\pi$
$318$	18.0859	1.01421
$319$	14.5776	0.816191
$320$	−38.4486	−2.14934
$321$	13.4122	0.748598
$322$	0.990493	0.0551980
$323$	22.0778	1.22844
$324$	5.03256	0.279587
$325$	−11.5993	−0.643411
$326$	−5.27528	−0.292171
$327$	2.48675	0.137518
$328$	66.3617	3.66421
$329$	−1.70261	−0.0938678
$330$	−16.0167	−0.881688
$331$	19.8045	1.08855	0.544276	−	0.838906i	$-0.316804\pi$
$331$	19.8045	1.08855	0.544276	+	0.838906i	$0.316804\pi$
$332$	−71.5527	−3.92696
$333$	8.69948	0.476728
$334$	−13.1400	−0.718989
$335$	8.91887	0.487290
$336$	2.08326	0.113651
$337$	21.2205	1.15595	0.577977	−	0.816053i	$-0.303843\pi$
$337$	21.2205	1.15595	0.577977	+	0.816053i	$0.303843\pi$
$338$	−21.7244	−1.18165
$339$	9.16262	0.497645
$340$	71.7954	3.89365
$341$	2.77198	0.150111
$342$	11.2539	0.608542
$343$	−2.58352	−0.139497
$344$	14.3936	0.776052
$345$	5.53666	0.298084
$346$	39.7144	2.13506
$347$	0.684040	0.0367212	0.0183606	−	0.999831i	$-0.494155\pi$
$347$	0.684040	0.0367212	0.0183606	+	0.999831i	$0.494155\pi$
$348$	−33.3089	−1.78554
$349$	21.9193	1.17331	0.586656	−	0.809836i	$-0.300444\pi$
$349$	21.9193	1.17331	0.586656	+	0.809836i	$0.300444\pi$
$350$	−1.23608	−0.0660713
$351$	−4.60348	−0.245716
$352$	30.3513	1.61773
$353$	−0.478235	−0.0254539	−0.0127269	−	0.999919i	$-0.504051\pi$
$353$	−0.478235	−0.0254539	−0.0127269	+	0.999919i	$0.504051\pi$
$354$	−20.5032	−1.08973
$355$	−20.0427	−1.06375
$356$	−3.70628	−0.196432
$357$	−0.962398	−0.0509355
$358$	5.72752	0.302709
$359$	10.7040	0.564937	0.282469	−	0.959277i	$-0.408847\pi$
$359$	10.7040	0.564937	0.282469	+	0.959277i	$0.408847\pi$
$360$	22.0529	1.16229
$361$	−0.990814	−0.0521481
$362$	−30.7315	−1.61521
$363$	−6.14899	−0.322738
$364$	−4.28570	−0.224632
$365$	40.0151	2.09448
$366$	6.43404	0.336313
$367$	−13.1953	−0.688790	−0.344395	−	0.938825i	$-0.611916\pi$
$367$	−13.1953	−0.688790	−0.344395	+	0.938825i	$0.611916\pi$
$368$	−22.7377	−1.18528
$369$	−8.25186	−0.429574
$370$	63.2629	3.28888
$371$	−1.26162	−0.0655001
$372$	−6.33377	−0.328391
$373$	−31.8911	−1.65126	−0.825628	−	0.564214i	$-0.809179\pi$
$373$	−31.8911	−1.65126	−0.825628	+	0.564214i	$0.809179\pi$
$374$	−30.3865	−1.57125
$375$	6.80156	0.351231
$376$	74.0175	3.81716
$377$	30.4689	1.56923
$378$	−0.490573	−0.0252323
$379$	−9.67624	−0.497035	−0.248518	−	0.968627i	$-0.579943\pi$
$379$	−9.67624	−0.497035	−0.248518	+	0.968627i	$0.579943\pi$
$380$	58.5646	3.00430
$381$	−3.59284	−0.184067
$382$	13.9505	0.713767
$383$	−15.2947	−0.781522	−0.390761	−	0.920492i	$-0.627788\pi$
$383$	−15.2947	−0.781522	−0.390761	+	0.920492i	$0.627788\pi$
$384$	−9.62165	−0.491003
$385$	1.11728	0.0569418
$386$	0.870770	0.0443210
$387$	−1.78980	−0.0909806
$388$	73.5506	3.73396
$389$	−5.80483	−0.294317	−0.147158	−	0.989113i	$-0.547013\pi$
$389$	−5.80483	−0.294317	−0.147158	+	0.989113i	$0.547013\pi$
$390$	−33.4767	−1.69516
$391$	10.5040	0.531212
$392$	56.0191	2.82939
$393$	−19.9931	−1.00852
$394$	69.8756	3.52028
$395$	−4.22223	−0.212444
$396$	−11.0842	−0.557003
$397$	−13.3026	−0.667637	−0.333818	−	0.942637i	$-0.608337\pi$
$397$	−13.3026	−0.667637	−0.333818	+	0.942637i	$0.608337\pi$
$398$	−43.3209	−2.17148
$399$	−0.785043	−0.0393013
$400$	28.3754	1.41877
$401$	30.3815	1.51718	0.758591	−	0.651567i	$-0.225888\pi$
$401$	30.3815	1.51718	0.758591	+	0.651567i	$0.225888\pi$
$402$	8.62516	0.430184
$403$	5.79375	0.288607
$404$	−29.0905	−1.44731
$405$	−2.74220	−0.136261
$406$	3.24694	0.161143
$407$	−19.1606	−0.949756
$408$	41.8383	2.07130
$409$	8.24583	0.407730	0.203865	−	0.978999i	$-0.434650\pi$
$409$	8.24583	0.407730	0.203865	+	0.978999i	$0.434650\pi$
$410$	−60.0078	−2.96357
$411$	−2.88865	−0.142487
$412$	−61.3763	−3.02379
$413$	1.43025	0.0703778
$414$	5.35433	0.263151
$415$	38.9885	1.91387
$416$	63.4377	3.11029
$417$	−7.65770	−0.374999
$418$	−24.7868	−1.21236
$419$	27.7055	1.35350	0.676750	−	0.736213i	$-0.263388\pi$
$419$	27.7055	1.35350	0.676750	+	0.736213i	$0.263388\pi$
$420$	−2.55291	−0.124569
$421$	−30.9957	−1.51064	−0.755318	−	0.655358i	$-0.772518\pi$
$421$	−30.9957	−1.51064	−0.755318	+	0.655358i	$0.772518\pi$
$422$	−26.0133	−1.26631
$423$	−9.20382	−0.447505
$424$	54.8465	2.66358
$425$	−13.1085	−0.635854
$426$	−19.3826	−0.939092
$427$	−0.448821	−0.0217200
$428$	67.4978	3.26263
$429$	10.1392	0.489524
$430$	−13.0155	−0.627662
$431$	35.5459	1.71219	0.856094	−	0.516821i	$-0.172885\pi$
$431$	35.5459	1.71219	0.856094	+	0.516821i	$0.172885\pi$
$432$	11.2615	0.541821
$433$	−25.9820	−1.24861	−0.624307	−	0.781179i	$-0.714619\pi$
$433$	−25.9820	−1.24861	−0.624307	+	0.781179i	$0.714619\pi$
$434$	0.617414	0.0296368
$435$	18.1497	0.870214
$436$	12.5147	0.599346
$437$	8.56831	0.409878
$438$	38.6973	1.84903
$439$	8.58215	0.409604	0.204802	−	0.978803i	$-0.434345\pi$
$439$	8.58215	0.409604	0.204802	+	0.978803i	$0.434345\pi$
$440$	−48.5715	−2.31556
$441$	−6.96578	−0.331704
$442$	−63.5113	−3.02093
$443$	−25.9923	−1.23493	−0.617466	−	0.786598i	$-0.711841\pi$
$443$	−25.9923	−1.23493	−0.617466	+	0.786598i	$0.711841\pi$
$444$	43.7806	2.07774
$445$	2.01952	0.0957346
$446$	−9.09392	−0.430610
$447$	16.7903	0.794152
$448$	2.59374	0.122543
$449$	−8.47245	−0.399840	−0.199920	−	0.979812i	$-0.564068\pi$
$449$	−8.47245	−0.399840	−0.199920	+	0.979812i	$0.564068\pi$
$450$	−6.68191	−0.314988
$451$	18.1747	0.855814
$452$	46.1114	2.16890
$453$	−12.5249	−0.588469
$454$	−74.1583	−3.48042
$455$	2.33524	0.109478
$456$	34.1282	1.59820
$457$	25.2185	1.17967	0.589835	−	0.807524i	$-0.299193\pi$
$457$	25.2185	1.17967	0.589835	+	0.807524i	$0.299193\pi$
$458$	−54.4048	−2.54217
$459$	−5.20245	−0.242830
$460$	27.8636	1.29915
$461$	15.3542	0.715115	0.357558	−	0.933891i	$-0.383610\pi$
$461$	15.3542	0.715115	0.357558	+	0.933891i	$0.383610\pi$
$462$	1.08049	0.0502688
$463$	−23.1482	−1.07579	−0.537895	−	0.843012i	$-0.680780\pi$
$463$	−23.1482	−1.07579	−0.537895	+	0.843012i	$0.680780\pi$
$464$	−74.5365	−3.46027
$465$	3.45122	0.160047
$466$	27.8736	1.29122
$467$	−4.57877	−0.211880	−0.105940	−	0.994373i	$-0.533785\pi$
$467$	−4.57877	−0.211880	−0.105940	+	0.994373i	$0.533785\pi$
$468$	−23.1673	−1.07091
$469$	−0.601668	−0.0277824
$470$	−66.9305	−3.08727
$471$	−12.7698	−0.588402
$472$	−62.1770	−2.86193
$473$	3.94203	0.181255
$474$	−4.08319	−0.187547
$475$	−10.6928	−0.490619
$476$	−4.84332	−0.221993
$477$	−6.81997	−0.312265
$478$	−29.4928	−1.34897
$479$	−38.4544	−1.75702	−0.878512	−	0.477720i	$-0.841463\pi$
$479$	−38.4544	−1.75702	−0.878512	+	0.477720i	$0.841463\pi$
$480$	37.7886	1.72480
$481$	−40.0479	−1.82603
$482$	−70.9060	−3.22968
$483$	−0.373504	−0.0169950
$484$	−30.9452	−1.40660
$485$	−40.0771	−1.81981
$486$	−2.65190	−0.120293
$487$	28.2134	1.27847	0.639235	−	0.769012i	$-0.279251\pi$
$487$	28.2134	1.27847	0.639235	+	0.769012i	$0.279251\pi$
$488$	19.5116	0.883249
$489$	1.98925	0.0899568
$490$	−50.6554	−2.28838
$491$	1.46198	0.0659781	0.0329890	−	0.999456i	$-0.489497\pi$
$491$	1.46198	0.0659781	0.0329890	+	0.999456i	$0.489497\pi$
$492$	−41.5280	−1.87222
$493$	34.4333	1.55080
$494$	−51.8072	−2.33092
$495$	6.03970	0.271464
$496$	−14.1733	−0.636400
$497$	1.35208	0.0606491
$498$	37.7046	1.68958
$499$	−38.2401	−1.71186	−0.855931	−	0.517090i	$-0.827015\pi$
$499$	−38.2401	−1.71186	−0.855931	+	0.517090i	$0.827015\pi$
$500$	34.2293	1.53078
$501$	4.95495	0.221371
$502$	32.2046	1.43736
$503$	−25.3255	−1.12921	−0.564604	−	0.825362i	$-0.690971\pi$
$503$	−25.3255	−1.12921	−0.564604	+	0.825362i	$0.690971\pi$
$504$	−1.48769	−0.0662670
$505$	15.8512	0.705368
$506$	−11.7929	−0.524259
$507$	8.19204	0.363821
$508$	−18.0812	−0.802222
$509$	−10.6268	−0.471024	−0.235512	−	0.971871i	$-0.575677\pi$
$509$	−10.6268	−0.471024	−0.235512	+	0.971871i	$0.575677\pi$
$510$	−37.8324	−1.67525
$511$	−2.69942	−0.119415
$512$	25.9433	1.14654
$513$	−4.24372	−0.187365
$514$	−24.3448	−1.07380
$515$	33.4435	1.47370
$516$	−9.00727	−0.396523
$517$	20.2714	0.891536
$518$	−4.26772	−0.187513
$519$	−14.9759	−0.657367
$520$	−101.520	−4.45195
$521$	3.53783	0.154995	0.0774976	−	0.996993i	$-0.475307\pi$
$521$	3.53783	0.154995	0.0774976	+	0.996993i	$0.475307\pi$
$522$	17.5520	0.768232
$523$	34.0564	1.48918	0.744590	−	0.667522i	$-0.232645\pi$
$523$	34.0564	1.48918	0.744590	+	0.667522i	$0.232645\pi$
$524$	−100.616	−4.39544
$525$	0.466112	0.0203428
$526$	9.55484	0.416611
$527$	6.54759	0.285218
$528$	−24.8035	−1.07944
$529$	−18.9234	−0.822757
$530$	−49.5951	−2.15427
$531$	7.73150	0.335519
$532$	−3.95078	−0.171288
$533$	37.9873	1.64541
$534$	1.95302	0.0845153
$535$	−36.7790	−1.59010
$536$	26.1563	1.12978
$537$	−2.15978	−0.0932014
$538$	15.1211	0.651918
$539$	15.3421	0.660832
$540$	−13.8003	−0.593870
$541$	−6.52188	−0.280397	−0.140199	−	0.990123i	$-0.544774\pi$
$541$	−6.52188	−0.280397	−0.140199	+	0.990123i	$0.544774\pi$
$542$	42.5284	1.82675
$543$	11.5885	0.497309
$544$	71.6917	3.07376
$545$	−6.81917	−0.292101
$546$	2.25834	0.0966481
$547$	−31.3083	−1.33865	−0.669324	−	0.742970i	$-0.733416\pi$
$547$	−31.3083	−1.33865	−0.669324	+	0.742970i	$0.733416\pi$
$548$	−14.5373	−0.621003
$549$	−2.42620	−0.103548
$550$	14.7169	0.627531
$551$	28.0878	1.19658
$552$	16.2373	0.691106
$553$	0.284832	0.0121123
$554$	36.7850	1.56284
$555$	−23.8557	−1.01262
$556$	−38.5378	−1.63437
$557$	45.2251	1.91625	0.958124	−	0.286354i	$-0.0924432\pi$
$557$	45.2251	1.91625	0.958124	+	0.286354i	$0.0924432\pi$
$558$	3.33757	0.141291
$559$	8.23930	0.348485
$560$	−5.71273	−0.241407
$561$	11.4584	0.483774
$562$	−17.7870	−0.750300
$563$	−36.6463	−1.54446	−0.772230	−	0.635343i	$-0.780859\pi$
$563$	−36.6463	−1.54446	−0.772230	+	0.635343i	$0.780859\pi$
$564$	−46.3188	−1.95037
$565$	−25.1258	−1.05705
$566$	84.2356	3.54069
$567$	0.184989	0.00776882
$568$	−58.7790	−2.46631
$569$	−39.1352	−1.64063	−0.820317	−	0.571910i	$-0.806203\pi$
$569$	−39.1352	−1.64063	−0.820317	+	0.571910i	$0.806203\pi$
$570$	−30.8605	−1.29260
$571$	2.36630	0.0990265	0.0495132	−	0.998773i	$-0.484233\pi$
$571$	2.36630	0.0990265	0.0495132	+	0.998773i	$0.484233\pi$
$572$	51.0260	2.13350
$573$	−5.26055	−0.219763
$574$	4.04813	0.168966
$575$	−5.08736	−0.212157
$576$	14.0211	0.584210
$577$	−14.9239	−0.621292	−0.310646	−	0.950526i	$-0.600545\pi$
$577$	−14.9239	−0.621292	−0.310646	+	0.950526i	$0.600545\pi$
$578$	−26.6927	−1.11027
$579$	−0.328357	−0.0136461
$580$	91.3397	3.79267
$581$	−2.63017	−0.109118
$582$	−38.7573	−1.60654
$583$	15.0210	0.622106
$584$	117.352	4.85606
$585$	12.6237	0.521925
$586$	17.9548	0.741704
$587$	−23.8468	−0.984261	−0.492131	−	0.870521i	$-0.663782\pi$
$587$	−23.8468	−0.984261	−0.492131	+	0.870521i	$0.663782\pi$
$588$	−35.0557	−1.44567
$589$	5.34098	0.220071
$590$	56.2238	2.31470
$591$	−26.3493	−1.08387
$592$	97.9695	4.02652
$593$	−33.3703	−1.37035	−0.685176	−	0.728377i	$-0.740275\pi$
$593$	−33.3703	−1.37035	−0.685176	+	0.728377i	$0.740275\pi$
$594$	5.84081	0.239651
$595$	2.63909	0.108192
$596$	84.4980	3.46117
$597$	16.3358	0.668580
$598$	−24.6485	−1.00795
$599$	−7.06556	−0.288691	−0.144346	−	0.989527i	$-0.546108\pi$
$599$	−7.06556	−0.288691	−0.144346	+	0.989527i	$0.546108\pi$
$600$	−20.2633	−0.827245
$601$	−13.8082	−0.563249	−0.281624	−	0.959525i	$-0.590873\pi$
$601$	−13.8082	−0.563249	−0.281624	+	0.959525i	$0.590873\pi$
$602$	0.878026	0.0357857
$603$	−3.25245	−0.132450
$604$	−63.0321	−2.56474
$605$	16.8618	0.685529
$606$	15.3292	0.622705
$607$	−28.7851	−1.16835	−0.584175	−	0.811628i	$-0.698582\pi$
$607$	−28.7851	−1.16835	−0.584175	+	0.811628i	$0.698582\pi$
$608$	58.4801	2.37168
$609$	−1.22438	−0.0496145
$610$	−17.6434	−0.714362
$611$	42.3696	1.71409
$612$	−26.1816	−1.05833
$613$	−32.5223	−1.31356	−0.656781	−	0.754081i	$-0.728083\pi$
$613$	−32.5223	−1.31356	−0.656781	+	0.754081i	$0.728083\pi$
$614$	−2.27914	−0.0919786
$615$	22.6283	0.912459
$616$	3.27664	0.132020
$617$	−17.6533	−0.710696	−0.355348	−	0.934734i	$-0.615638\pi$
$617$	−17.6533	−0.710696	−0.355348	+	0.934734i	$0.615638\pi$
$618$	32.3421	1.30099
$619$	6.88717	0.276819	0.138409	−	0.990375i	$-0.455801\pi$
$619$	6.88717	0.276819	0.138409	+	0.990375i	$0.455801\pi$
$620$	17.3685	0.697535
$621$	−2.01906	−0.0810219
$622$	33.9989	1.36323
$623$	−0.136237	−0.00545823
$624$	−51.8423	−2.07535
$625$	−31.2496	−1.24998
$626$	−14.3921	−0.575224
$627$	9.34680	0.373275
$628$	−64.2649	−2.56445
$629$	−45.2586	−1.80458
$630$	1.34525	0.0535960
$631$	7.78205	0.309798	0.154899	−	0.987930i	$-0.450495\pi$
$631$	7.78205	0.309798	0.154899	+	0.987930i	$0.450495\pi$
$632$	−12.3825	−0.492550
$633$	9.80930	0.389885
$634$	49.7140	1.97440
$635$	9.85229	0.390976
$636$	−34.3219	−1.36095
$637$	32.0668	1.27053
$638$	−38.6584	−1.53050
$639$	7.30897	0.289138
$640$	26.3845	1.04294
$641$	33.6202	1.32792	0.663959	−	0.747769i	$-0.268875\pi$
$641$	33.6202	1.32792	0.663959	+	0.747769i	$0.268875\pi$
$642$	−35.5679	−1.40375
$643$	−34.7156	−1.36905	−0.684525	−	0.728990i	$-0.739990\pi$
$643$	−34.7156	−1.36905	−0.684525	+	0.728990i	$0.739990\pi$
$644$	−1.87968	−0.0740697
$645$	4.90799	0.193252
$646$	−58.5480	−2.30354
$647$	31.7937	1.24994	0.624969	−	0.780649i	$-0.285111\pi$
$647$	31.7937	1.24994	0.624969	+	0.780649i	$0.285111\pi$
$648$	−8.04204	−0.315921
$649$	−17.0286	−0.668433
$650$	30.7600	1.20651
$651$	−0.232820	−0.00912493
$652$	10.0110	0.392061
$653$	50.0982	1.96050	0.980248	−	0.197774i	$-0.0633714\pi$
$653$	50.0982	1.96050	0.980248	+	0.197774i	$0.0633714\pi$
$654$	−6.59461	−0.257870
$655$	54.8250	2.14219
$656$	−92.9286	−3.62825
$657$	−14.5923	−0.569300
$658$	4.51514	0.176019
$659$	30.9420	1.20533	0.602665	−	0.797995i	$-0.294106\pi$
$659$	30.9420	1.20533	0.602665	+	0.797995i	$0.294106\pi$
$660$	30.3952	1.18313
$661$	−32.5963	−1.26785	−0.633925	−	0.773394i	$-0.718557\pi$
$661$	−32.5963	−1.26785	−0.633925	+	0.773394i	$0.718557\pi$
$662$	−52.5194	−2.04123
$663$	23.9494	0.930117
$664$	114.341	4.43730
$665$	2.15275	0.0834799
$666$	−23.0701	−0.893949
$667$	13.3635	0.517436
$668$	24.9361	0.964805
$669$	3.42921	0.132581
$670$	−23.6519	−0.913753
$671$	5.34371	0.206292
$672$	−2.54922	−0.0983383
$673$	47.9925	1.84998	0.924988	−	0.379997i	$-0.124075\pi$
$673$	47.9925	1.84998	0.924988	+	0.379997i	$0.124075\pi$
$674$	−56.2745	−2.16761
$675$	2.51967	0.0969822
$676$	41.2269	1.58565
$677$	−34.2773	−1.31738	−0.658692	−	0.752412i	$-0.728890\pi$
$677$	−34.2773	−1.31738	−0.658692	+	0.752412i	$0.728890\pi$
$678$	−24.2983	−0.933172
$679$	2.70361	0.103755
$680$	−114.729	−4.39966
$681$	27.9642	1.07159
$682$	−7.35100	−0.281484
$683$	38.4167	1.46997	0.734987	−	0.678081i	$-0.237188\pi$
$683$	38.4167	1.46997	0.734987	+	0.678081i	$0.237188\pi$
$684$	−21.3568	−0.816597
$685$	7.92126	0.302656
$686$	6.85123	0.261581
$687$	20.5154	0.782712
$688$	−20.1559	−0.768436
$689$	31.3956	1.19608
$690$	−14.6826	−0.558959
$691$	−1.72792	−0.0657333	−0.0328666	−	0.999460i	$-0.510464\pi$
$691$	−1.72792	−0.0657333	−0.0328666	+	0.999460i	$0.510464\pi$
$692$	−75.3669	−2.86502
$693$	−0.407439	−0.0154773
$694$	−1.81400	−0.0688586
$695$	20.9990	0.796536
$696$	53.2276	2.01759
$697$	42.9299	1.62609
$698$	−58.1277	−2.20016
$699$	−10.5108	−0.397555
$700$	2.34574	0.0886605
$701$	−5.07426	−0.191652	−0.0958261	−	0.995398i	$-0.530549\pi$
$701$	−5.07426	−0.191652	−0.0958261	+	0.995398i	$0.530549\pi$
$702$	12.2080	0.460760
$703$	−36.9182	−1.39240
$704$	−30.8814	−1.16389
$705$	25.2387	0.950546
$706$	1.26823	0.0477305
$707$	−1.06932	−0.0402160
$708$	38.9093	1.46230
$709$	27.6478	1.03834	0.519168	−	0.854673i	$-0.326242\pi$
$709$	27.6478	1.03834	0.519168	+	0.854673i	$0.326242\pi$
$710$	53.1511	1.99472
$711$	1.53972	0.0577442
$712$	5.92264	0.221960
$713$	2.54110	0.0951649
$714$	2.55218	0.0955129
$715$	−27.8036	−1.03980
$716$	−10.8692	−0.406202
$717$	11.1214	0.415337
$718$	−28.3860	−1.05936
$719$	−0.833177	−0.0310723	−0.0155361	−	0.999879i	$-0.504946\pi$
$719$	−0.833177	−0.0310723	−0.0155361	+	0.999879i	$0.504946\pi$
$720$	−30.8814	−1.15088
$721$	−2.25610	−0.0840216
$722$	2.62754	0.0977868
$723$	26.7378	0.994390
$724$	58.3197	2.16744
$725$	−16.6769	−0.619364
$726$	16.3065	0.605191
$727$	−12.6575	−0.469443	−0.234721	−	0.972063i	$-0.575418\pi$
$727$	−12.6575	−0.469443	−0.234721	+	0.972063i	$0.575418\pi$
$728$	6.84855	0.253824
$729$	1.00000	0.0370370
$730$	−106.116	−3.92752
$731$	9.31134	0.344392
$732$	−12.2100	−0.451295
$733$	23.8287	0.880134	0.440067	−	0.897965i	$-0.354955\pi$
$733$	23.8287	0.880134	0.440067	+	0.897965i	$0.354955\pi$
$734$	34.9926	1.29160
$735$	19.1016	0.704572
$736$	27.8233	1.02558
$737$	7.16352	0.263871
$738$	21.8831	0.805527
$739$	−38.0170	−1.39848	−0.699239	−	0.714888i	$-0.746478\pi$
$739$	−38.0170	−1.39848	−0.699239	+	0.714888i	$0.746478\pi$
$740$	−120.055	−4.41332
$741$	19.5359	0.717669
$742$	3.34569	0.122824
$743$	45.5065	1.66947	0.834735	−	0.550651i	$-0.185621\pi$
$743$	45.5065	1.66947	0.834735	+	0.550651i	$0.185621\pi$
$744$	10.1214	0.371068
$745$	−46.0423	−1.68686
$746$	84.5718	3.09640
$747$	−14.2180	−0.520208
$748$	57.6651	2.10844
$749$	2.48112	0.0906581
$750$	−18.0370	−0.658620
$751$	−1.35064	−0.0492854	−0.0246427	−	0.999696i	$-0.507845\pi$
$751$	−1.35064	−0.0492854	−0.0246427	+	0.999696i	$0.507845\pi$
$752$	−103.649	−3.77970
$753$	−12.1440	−0.442551
$754$	−80.8005	−2.94258
$755$	34.3457	1.24997
$756$	0.930969	0.0338590
$757$	−13.6870	−0.497461	−0.248731	−	0.968573i	$-0.580013\pi$
$757$	−13.6870	−0.497461	−0.248731	+	0.968573i	$0.580013\pi$
$758$	25.6604	0.932028
$759$	4.44697	0.161415
$760$	−93.5864	−3.39473
$761$	−30.1018	−1.09119	−0.545595	−	0.838049i	$-0.683696\pi$
$761$	−30.1018	−1.09119	−0.545595	+	0.838049i	$0.683696\pi$
$762$	9.52784	0.345157
$763$	0.460022	0.0166539
$764$	−26.4741	−0.957798
$765$	14.2662	0.515795
$766$	40.5599	1.46549
$767$	−35.5918	−1.28515
$768$	−2.52648	−0.0911665
$769$	19.8781	0.716821	0.358411	−	0.933564i	$-0.383319\pi$
$769$	19.8781	0.716821	0.358411	+	0.933564i	$0.383319\pi$
$770$	−2.96291	−0.106776
$771$	9.18015	0.330615
$772$	−1.65248	−0.0594740
$773$	23.0622	0.829488	0.414744	−	0.909938i	$-0.363871\pi$
$773$	23.0622	0.829488	0.414744	+	0.909938i	$0.363871\pi$
$774$	4.74636	0.170604
$775$	−3.17115	−0.113911
$776$	−117.534	−4.21922
$777$	1.60931	0.0577337
$778$	15.3938	0.551895
$779$	35.0186	1.25467
$780$	63.5294	2.27472
$781$	−16.0980	−0.576032
$782$	−27.8556	−0.996115
$783$	−6.61867	−0.236532
$784$	−78.4454	−2.80162
$785$	35.0174	1.24983
$786$	53.0195	1.89114
$787$	4.02189	0.143365	0.0716824	−	0.997428i	$-0.477163\pi$
$787$	4.02189	0.143365	0.0716824	+	0.997428i	$0.477163\pi$
$788$	−132.604	−4.72384
$789$	−3.60302	−0.128271
$790$	11.1969	0.398369
$791$	1.69499	0.0602668
$792$	17.7126	0.629389
$793$	11.1690	0.396622
$794$	35.2770	1.25194
$795$	18.7017	0.663283
$796$	82.2109	2.91389
$797$	42.6214	1.50973	0.754865	−	0.655881i	$-0.227703\pi$
$797$	42.6214	1.50973	0.754865	+	0.655881i	$0.227703\pi$
$798$	2.08185	0.0736968
$799$	47.8824	1.69396
$800$	−34.7220	−1.22761
$801$	−0.736460	−0.0260215
$802$	−80.5687	−2.84498
$803$	32.1396	1.13418
$804$	−16.3681	−0.577260
$805$	1.02422	0.0360991
$806$	−15.3644	−0.541189
$807$	−5.70200	−0.200720
$808$	46.4866	1.63539
$809$	36.2953	1.27607	0.638037	−	0.770005i	$-0.279747\pi$
$809$	36.2953	1.27607	0.638037	+	0.770005i	$0.279747\pi$
$810$	7.27204	0.255513
$811$	−23.1692	−0.813580	−0.406790	−	0.913522i	$-0.633352\pi$
$811$	−23.1692	−0.813580	−0.406790	+	0.913522i	$0.633352\pi$
$812$	−6.16178	−0.216236
$813$	−16.0370	−0.562441
$814$	50.8120	1.78096
$815$	−5.45492	−0.191077
$816$	−58.5876	−2.05098
$817$	7.59541	0.265730
$818$	−21.8671	−0.764565
$819$	−0.851594	−0.0297571
$820$	113.878	3.97679
$821$	19.9617	0.696668	0.348334	−	0.937371i	$-0.386748\pi$
$821$	19.9617	0.696668	0.348334	+	0.937371i	$0.386748\pi$
$822$	7.66041	0.267187
$823$	−8.47151	−0.295298	−0.147649	−	0.989040i	$-0.547171\pi$
$823$	−8.47151	−0.295298	−0.147649	+	0.989040i	$0.547171\pi$
$824$	98.0795	3.41676
$825$	−5.54958	−0.193211
$826$	−3.79286	−0.131971
$827$	−31.2908	−1.08809	−0.544044	−	0.839057i	$-0.683108\pi$
$827$	−31.2908	−1.08809	−0.544044	+	0.839057i	$0.683108\pi$
$828$	−10.1610	−0.353120
$829$	48.7035	1.69154	0.845771	−	0.533546i	$-0.179141\pi$
$829$	48.7035	1.69154	0.845771	+	0.533546i	$0.179141\pi$
$830$	−103.393	−3.58884
$831$	−13.8712	−0.481186
$832$	−64.5456	−2.23772
$833$	36.2391	1.25561
$834$	20.3074	0.703189
$835$	−13.5875	−0.470214
$836$	47.0383	1.62685
$837$	−1.25856	−0.0435022
$838$	−73.4721	−2.53805
$839$	8.98521	0.310204	0.155102	−	0.987898i	$-0.450429\pi$
$839$	8.98521	0.310204	0.155102	+	0.987898i	$0.450429\pi$
$840$	4.07955	0.140758
$841$	14.8069	0.510581
$842$	82.1973	2.83271
$843$	6.70728	0.231011
$844$	49.3659	1.69924
$845$	−22.4642	−0.772793
$846$	24.4076	0.839150
$847$	−1.13750	−0.0390849
$848$	−76.8034	−2.63744
$849$	−31.7643	−1.09015
$850$	34.7623	1.19234
$851$	−17.5647	−0.602111
$852$	36.7828	1.26016
$853$	−27.2817	−0.934108	−0.467054	−	0.884229i	$-0.654685\pi$
$853$	−27.2817	−0.934108	−0.467054	+	0.884229i	$0.654685\pi$
$854$	1.19023	0.0407288
$855$	11.6371	0.397982
$856$	−107.862	−3.68664
$857$	6.94451	0.237220	0.118610	−	0.992941i	$-0.462156\pi$
$857$	6.94451	0.237220	0.118610	+	0.992941i	$0.462156\pi$
$858$	−26.8880	−0.917942
$859$	26.2468	0.895530	0.447765	−	0.894151i	$-0.352220\pi$
$859$	26.2468	0.895530	0.447765	+	0.894151i	$0.352220\pi$
$860$	24.6997	0.842254
$861$	−1.52650	−0.0520231
$862$	−94.2642	−3.21065
$863$	11.7083	0.398554	0.199277	−	0.979943i	$-0.436141\pi$
$863$	11.7083	0.398554	0.199277	+	0.979943i	$0.436141\pi$
$864$	−13.7804	−0.468818
$865$	41.0668	1.39631
$866$	68.9015	2.34137
$867$	10.0655	0.341842
$868$	−1.17168	−0.0397694
$869$	−3.39124	−0.115040
$870$	−48.1313	−1.63180
$871$	14.9726	0.507326
$872$	−19.9985	−0.677236
$873$	14.6149	0.494641
$874$	−22.7223	−0.768593
$875$	1.25822	0.0425355
$876$	−73.4367	−2.48120
$877$	−0.978298	−0.0330348	−0.0165174	−	0.999864i	$-0.505258\pi$
$877$	−0.978298	−0.0330348	−0.0165174	+	0.999864i	$0.505258\pi$
$878$	−22.7590	−0.768078
$879$	−6.77053	−0.228364
$880$	68.0163	2.29283
$881$	−7.03261	−0.236935	−0.118467	−	0.992958i	$-0.537798\pi$
$881$	−7.03261	−0.236935	−0.118467	+	0.992958i	$0.537798\pi$
$882$	18.4725	0.622002
$883$	−23.8071	−0.801174	−0.400587	−	0.916259i	$-0.631194\pi$
$883$	−23.8071	−0.801174	−0.400587	+	0.916259i	$0.631194\pi$
$884$	120.527	4.05375
$885$	−21.2013	−0.712675
$886$	68.9289	2.31571
$887$	−6.20309	−0.208279	−0.104140	−	0.994563i	$-0.533209\pi$
$887$	−6.20309	−0.208279	−0.104140	+	0.994563i	$0.533209\pi$
$888$	−69.9615	−2.34776
$889$	−0.664636	−0.0222912
$890$	−5.35557	−0.179519
$891$	−2.20250	−0.0737865
$892$	17.2577	0.577831
$893$	39.0585	1.30704
$894$	−44.5261	−1.48917
$895$	5.92255	0.197969
$896$	−1.77990	−0.0594623
$897$	9.29468	0.310340
$898$	22.4681	0.749769
$899$	8.32999	0.277821
$900$	12.6804	0.422680
$901$	35.4806	1.18203
$902$	−48.1975	−1.60480
$903$	−0.331093	−0.0110181
$904$	−73.6862	−2.45077
$905$	−31.7780	−1.05634
$906$	33.2146	1.10348
$907$	−21.5982	−0.717156	−0.358578	−	0.933500i	$-0.616738\pi$
$907$	−21.5982	−0.717156	−0.358578	+	0.933500i	$0.616738\pi$
$908$	140.732	4.67034
$909$	−5.78045	−0.191726
$910$	−6.19283	−0.205290
$911$	32.5166	1.07732	0.538661	−	0.842523i	$-0.318930\pi$
$911$	32.5166	1.07732	0.538661	+	0.842523i	$0.318930\pi$
$912$	−47.7909	−1.58251
$913$	31.3150	1.03638
$914$	−66.8768	−2.21209
$915$	6.65313	0.219946
$916$	103.245	3.41131
$917$	−3.69850	−0.122135
$918$	13.7964	0.455348
$919$	−4.12843	−0.136184	−0.0680921	−	0.997679i	$-0.521691\pi$
$919$	−4.12843	−0.136184	−0.0680921	+	0.997679i	$0.521691\pi$
$920$	−44.5260	−1.46798
$921$	0.859438	0.0283194
$922$	−40.7177	−1.34097
$923$	−33.6467	−1.10749
$924$	−2.05046	−0.0674552
$925$	21.9198	0.720719
$926$	61.3868	2.01729
$927$	−12.1958	−0.400564
$928$	91.2078	2.99404
$929$	−5.90021	−0.193580	−0.0967898	−	0.995305i	$-0.530857\pi$
$929$	−5.90021	−0.193580	−0.0967898	+	0.995305i	$0.530857\pi$
$930$	−9.15229	−0.300115
$931$	29.5608	0.968817
$932$	−52.8963	−1.73268
$933$	−12.8206	−0.419727
$934$	12.1424	0.397313
$935$	−31.4212	−1.02758
$936$	37.0214	1.21008
$937$	−28.9021	−0.944190	−0.472095	−	0.881548i	$-0.656502\pi$
$937$	−28.9021	−0.944190	−0.472095	+	0.881548i	$0.656502\pi$
$938$	1.59556	0.0520969
$939$	5.42710	0.177107
$940$	127.015	4.14279
$941$	29.3301	0.956135	0.478067	−	0.878323i	$-0.341337\pi$
$941$	29.3301	0.956135	0.478067	+	0.878323i	$0.341337\pi$
$942$	33.8642	1.10336
$943$	16.6610	0.542555
$944$	87.0686	2.83384
$945$	−0.507278	−0.0165018
$946$	−10.4539	−0.339884
$947$	12.0502	0.391580	0.195790	−	0.980646i	$-0.437273\pi$
$947$	12.0502	0.391580	0.195790	+	0.980646i	$0.437273\pi$
$948$	7.74875	0.251668
$949$	67.1754	2.18061
$950$	28.3562	0.919996
$951$	−18.7466	−0.607899
$952$	7.73964	0.250843
$953$	41.3052	1.33801	0.669004	−	0.743259i	$-0.266721\pi$
$953$	41.3052	1.33801	0.669004	+	0.743259i	$0.266721\pi$
$954$	18.0859	0.585552
$955$	14.4255	0.466798
$956$	55.9691	1.81017
$957$	14.5776	0.471228
$958$	101.977	3.29473
$959$	−0.534369	−0.0172557
$960$	−38.4486	−1.24092
$961$	−29.4160	−0.948904
$962$	106.203	3.42412
$963$	13.4122	0.432203
$964$	134.560	4.33388
$965$	0.900422	0.0289856
$966$	0.990493	0.0318686
$967$	−32.1409	−1.03358	−0.516791	−	0.856111i	$-0.672874\pi$
$967$	−32.1409	−1.03358	−0.516791	+	0.856111i	$0.672874\pi$
$968$	49.4504	1.58940
$969$	22.0778	0.709240
$970$	106.280	3.41246
$971$	−47.6460	−1.52903	−0.764517	−	0.644604i	$-0.777022\pi$
$971$	−47.6460	−1.52903	−0.764517	+	0.644604i	$0.777022\pi$
$972$	5.03256	0.161419
$973$	−1.41659	−0.0454139
$974$	−74.8189	−2.39735
$975$	−11.5993	−0.371474
$976$	−27.3228	−0.874580
$977$	−44.5760	−1.42611	−0.713057	−	0.701106i	$-0.752690\pi$
$977$	−44.5760	−1.42611	−0.713057	+	0.701106i	$0.752690\pi$
$978$	−5.27528	−0.168685
$979$	1.62205	0.0518411
$980$	96.1298	3.07075
$981$	2.48675	0.0793958
$982$	−3.87701	−0.123720
$983$	52.3168	1.66865	0.834323	−	0.551276i	$-0.185859\pi$
$983$	52.3168	1.66865	0.834323	+	0.551276i	$0.185859\pi$
$984$	66.3617	2.11553
$985$	72.2551	2.30224
$986$	−91.3137	−2.90802
$987$	−1.70261	−0.0541946
$988$	98.3156	3.12784
$989$	3.61370	0.114909
$990$	−16.0167	−0.509043
$991$	−37.6517	−1.19605	−0.598023	−	0.801479i	$-0.704047\pi$
$991$	−37.6517	−1.19605	−0.598023	+	0.801479i	$0.704047\pi$
$992$	17.3434	0.550654
$993$	19.8045	0.628476
$994$	−3.58558	−0.113728
$995$	−44.7961	−1.42013
$996$	−71.5527	−2.26723
$997$	−0.700711	−0.0221917	−0.0110959	−	0.999938i	$-0.503532\pi$
$997$	−0.700711	−0.0221917	−0.0110959	+	0.999938i	$0.503532\pi$
$998$	101.409	3.21004
$999$	8.69948	0.275239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.d.1.8	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.d.1.8	✓	129	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65190 q^{2} +1.00000 q^{3} +5.03256 q^{4} -2.74220 q^{5} -2.65190 q^{6} +0.184989 q^{7} -8.04204 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.65190 q^{2} +1.00000 q^{3} +5.03256 q^{4} -2.74220 q^{5} -2.65190 q^{6} +0.184989 q^{7} -8.04204 q^{8} +1.00000 q^{9} +7.27204 q^{10} -2.20250 q^{11} +5.03256 q^{12} -4.60348 q^{13} -0.490573 q^{14} -2.74220 q^{15} +11.2615 q^{16} -5.20245 q^{17} -2.65190 q^{18} -4.24372 q^{19} -13.8003 q^{20} +0.184989 q^{21} +5.84081 q^{22} -2.01906 q^{23} -8.04204 q^{24} +2.51967 q^{25} +12.2080 q^{26} +1.00000 q^{27} +0.930969 q^{28} -6.61867 q^{29} +7.27204 q^{30} -1.25856 q^{31} -13.7804 q^{32} -2.20250 q^{33} +13.7964 q^{34} -0.507278 q^{35} +5.03256 q^{36} +8.69948 q^{37} +11.2539 q^{38} -4.60348 q^{39} +22.0529 q^{40} -8.25186 q^{41} -0.490573 q^{42} -1.78980 q^{43} -11.0842 q^{44} -2.74220 q^{45} +5.35433 q^{46} -9.20382 q^{47} +11.2615 q^{48} -6.96578 q^{49} -6.68191 q^{50} -5.20245 q^{51} -23.1673 q^{52} -6.81997 q^{53} -2.65190 q^{54} +6.03970 q^{55} -1.48769 q^{56} -4.24372 q^{57} +17.5520 q^{58} +7.73150 q^{59} -13.8003 q^{60} -2.42620 q^{61} +3.33757 q^{62} +0.184989 q^{63} +14.0211 q^{64} +12.6237 q^{65} +5.84081 q^{66} -3.25245 q^{67} -26.1816 q^{68} -2.01906 q^{69} +1.34525 q^{70} +7.30897 q^{71} -8.04204 q^{72} -14.5923 q^{73} -23.0701 q^{74} +2.51967 q^{75} -21.3568 q^{76} -0.407439 q^{77} +12.2080 q^{78} +1.53972 q^{79} -30.8814 q^{80} +1.00000 q^{81} +21.8831 q^{82} -14.2180 q^{83} +0.930969 q^{84} +14.2662 q^{85} +4.74636 q^{86} -6.61867 q^{87} +17.7126 q^{88} -0.736460 q^{89} +7.27204 q^{90} -0.851594 q^{91} -10.1610 q^{92} -1.25856 q^{93} +24.4076 q^{94} +11.6371 q^{95} -13.7804 q^{96} +14.6149 q^{97} +18.4725 q^{98} -2.20250 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * q^99

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