LMFDB - Embedded newform 8049.2.a.c.1.20

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:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-2.08408 q^{2} -1.00000 q^{3} +2.34338 q^{4} -1.55135 q^{5} +2.08408 q^{6} +4.26949 q^{7} -0.715634 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.08408 q^{2} -1.00000 q^{3} +2.34338 q^{4} -1.55135 q^{5} +2.08408 q^{6} +4.26949 q^{7} -0.715634 q^{8} +1.00000 q^{9} +3.23314 q^{10} +6.28932 q^{11} -2.34338 q^{12} +4.09016 q^{13} -8.89796 q^{14} +1.55135 q^{15} -3.19533 q^{16} +7.58053 q^{17} -2.08408 q^{18} -5.75863 q^{19} -3.63541 q^{20} -4.26949 q^{21} -13.1074 q^{22} -7.25232 q^{23} +0.715634 q^{24} -2.59331 q^{25} -8.52421 q^{26} -1.00000 q^{27} +10.0051 q^{28} +1.10700 q^{29} -3.23314 q^{30} +8.24881 q^{31} +8.09058 q^{32} -6.28932 q^{33} -15.7984 q^{34} -6.62348 q^{35} +2.34338 q^{36} +0.601076 q^{37} +12.0014 q^{38} -4.09016 q^{39} +1.11020 q^{40} +8.36448 q^{41} +8.89796 q^{42} -10.1879 q^{43} +14.7383 q^{44} -1.55135 q^{45} +15.1144 q^{46} +5.77677 q^{47} +3.19533 q^{48} +11.2286 q^{49} +5.40466 q^{50} -7.58053 q^{51} +9.58480 q^{52} +3.15944 q^{53} +2.08408 q^{54} -9.75693 q^{55} -3.05539 q^{56} +5.75863 q^{57} -2.30708 q^{58} -0.961238 q^{59} +3.63541 q^{60} -11.7284 q^{61} -17.1912 q^{62} +4.26949 q^{63} -10.4707 q^{64} -6.34527 q^{65} +13.1074 q^{66} +11.9310 q^{67} +17.7641 q^{68} +7.25232 q^{69} +13.8038 q^{70} +4.46975 q^{71} -0.715634 q^{72} +4.82196 q^{73} -1.25269 q^{74} +2.59331 q^{75} -13.4947 q^{76} +26.8522 q^{77} +8.52421 q^{78} +12.9955 q^{79} +4.95707 q^{80} +1.00000 q^{81} -17.4322 q^{82} +11.5788 q^{83} -10.0051 q^{84} -11.7601 q^{85} +21.2323 q^{86} -1.10700 q^{87} -4.50085 q^{88} +12.6036 q^{89} +3.23314 q^{90} +17.4629 q^{91} -16.9949 q^{92} -8.24881 q^{93} -12.0392 q^{94} +8.93366 q^{95} -8.09058 q^{96} -4.56228 q^{97} -23.4012 q^{98} +6.28932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * 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 $

$2$	−2.08408	−1.47367	−0.736833	−	0.676075i	$-0.763680\pi$
$2$	−2.08408	−1.47367	−0.736833	+	0.676075i	$0.763680\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.34338	1.17169
$5$	−1.55135	−0.693785	−0.346893	−	0.937905i	$-0.612763\pi$
$5$	−1.55135	−0.693785	−0.346893	+	0.937905i	$0.612763\pi$
$6$	2.08408	0.850821
$7$	4.26949	1.61372	0.806858	−	0.590745i	$-0.201166\pi$
$7$	4.26949	1.61372	0.806858	+	0.590745i	$0.201166\pi$
$8$	−0.715634	−0.253015
$9$	1.00000	0.333333
$10$	3.23314	1.02241
$11$	6.28932	1.89630	0.948150	−	0.317823i	$-0.102952\pi$
$11$	6.28932	1.89630	0.948150	+	0.317823i	$0.102952\pi$
$12$	−2.34338	−0.676476
$13$	4.09016	1.13441	0.567203	−	0.823578i	$-0.308026\pi$
$13$	4.09016	1.13441	0.567203	+	0.823578i	$0.308026\pi$
$14$	−8.89796	−2.37808
$15$	1.55135	0.400557
$16$	−3.19533	−0.798832
$17$	7.58053	1.83855	0.919274	−	0.393619i	$-0.128777\pi$
$17$	7.58053	1.83855	0.919274	+	0.393619i	$0.128777\pi$
$18$	−2.08408	−0.491222
$19$	−5.75863	−1.32112	−0.660561	−	0.750773i	$-0.729681\pi$
$19$	−5.75863	−1.32112	−0.660561	+	0.750773i	$0.729681\pi$
$20$	−3.63541	−0.812902
$21$	−4.26949	−0.931680
$22$	−13.1074	−2.79451
$23$	−7.25232	−1.51221	−0.756106	−	0.654449i	$-0.772901\pi$
$23$	−7.25232	−1.51221	−0.756106	+	0.654449i	$0.772901\pi$
$24$	0.715634	0.146078
$25$	−2.59331	−0.518662
$26$	−8.52421	−1.67173
$27$	−1.00000	−0.192450
$28$	10.0051	1.89078
$29$	1.10700	0.205565	0.102783	−	0.994704i	$-0.467225\pi$
$29$	1.10700	0.205565	0.102783	+	0.994704i	$0.467225\pi$
$30$	−3.23314	−0.590287
$31$	8.24881	1.48153	0.740765	−	0.671764i	$-0.234463\pi$
$31$	8.24881	1.48153	0.740765	+	0.671764i	$0.234463\pi$
$32$	8.09058	1.43023
$33$	−6.28932	−1.09483
$34$	−15.7984	−2.70940
$35$	−6.62348	−1.11957
$36$	2.34338	0.390564
$37$	0.601076	0.0988162	0.0494081	−	0.998779i	$-0.484267\pi$
$37$	0.601076	0.0988162	0.0494081	+	0.998779i	$0.484267\pi$
$38$	12.0014	1.94689
$39$	−4.09016	−0.654949
$40$	1.11020	0.175538
$41$	8.36448	1.30631	0.653156	−	0.757223i	$-0.273445\pi$
$41$	8.36448	1.30631	0.653156	+	0.757223i	$0.273445\pi$
$42$	8.89796	1.37298
$43$	−10.1879	−1.55364	−0.776818	−	0.629725i	$-0.783168\pi$
$43$	−10.1879	−1.55364	−0.776818	+	0.629725i	$0.783168\pi$
$44$	14.7383	2.22188
$45$	−1.55135	−0.231262
$46$	15.1144	2.22850
$47$	5.77677	0.842629	0.421314	−	0.906915i	$-0.361569\pi$
$47$	5.77677	0.842629	0.421314	+	0.906915i	$0.361569\pi$
$48$	3.19533	0.461206
$49$	11.2286	1.60408
$50$	5.40466	0.764335
$51$	−7.58053	−1.06149
$52$	9.58480	1.32917
$53$	3.15944	0.433983	0.216991	−	0.976174i	$-0.430376\pi$
$53$	3.15944	0.433983	0.216991	+	0.976174i	$0.430376\pi$
$54$	2.08408	0.283607
$55$	−9.75693	−1.31562
$56$	−3.05539	−0.408294
$57$	5.75863	0.762750
$58$	−2.30708	−0.302935
$59$	−0.961238	−0.125142	−0.0625712	−	0.998040i	$-0.519930\pi$
$59$	−0.961238	−0.125142	−0.0625712	+	0.998040i	$0.519930\pi$
$60$	3.63541	0.469329
$61$	−11.7284	−1.50166	−0.750831	−	0.660494i	$-0.770347\pi$
$61$	−11.7284	−1.50166	−0.750831	+	0.660494i	$0.770347\pi$
$62$	−17.1912	−2.18328
$63$	4.26949	0.537906
$64$	−10.4707	−1.30884
$65$	−6.34527	−0.787034
$66$	13.1074	1.61341
$67$	11.9310	1.45761	0.728804	−	0.684723i	$-0.240077\pi$
$67$	11.9310	1.45761	0.728804	+	0.684723i	$0.240077\pi$
$68$	17.7641	2.15421
$69$	7.25232	0.873076
$70$	13.8038	1.64988
$71$	4.46975	0.530462	0.265231	−	0.964185i	$-0.414552\pi$
$71$	4.46975	0.530462	0.265231	+	0.964185i	$0.414552\pi$
$72$	−0.715634	−0.0843382
$73$	4.82196	0.564368	0.282184	−	0.959360i	$-0.408941\pi$
$73$	4.82196	0.564368	0.282184	+	0.959360i	$0.408941\pi$
$74$	−1.25269	−0.145622
$75$	2.59331	0.299450
$76$	−13.4947	−1.54795
$77$	26.8522	3.06009
$78$	8.52421	0.965176
$79$	12.9955	1.46210	0.731052	−	0.682321i	$-0.239030\pi$
$79$	12.9955	1.46210	0.731052	+	0.682321i	$0.239030\pi$
$80$	4.95707	0.554217
$81$	1.00000	0.111111
$82$	−17.4322	−1.92507
$83$	11.5788	1.27094	0.635472	−	0.772124i	$-0.280806\pi$
$83$	11.5788	1.27094	0.635472	+	0.772124i	$0.280806\pi$
$84$	−10.0051	−1.09164
$85$	−11.7601	−1.27556
$86$	21.2323	2.28954
$87$	−1.10700	−0.118683
$88$	−4.50085	−0.479792
$89$	12.6036	1.33598	0.667991	−	0.744169i	$-0.267154\pi$
$89$	12.6036	1.33598	0.667991	+	0.744169i	$0.267154\pi$
$90$	3.23314	0.340802
$91$	17.4629	1.83061
$92$	−16.9949	−1.77185
$93$	−8.24881	−0.855362
$94$	−12.0392	−1.24175
$95$	8.93366	0.916574
$96$	−8.09058	−0.825741
$97$	−4.56228	−0.463230	−0.231615	−	0.972808i	$-0.574401\pi$
$97$	−4.56228	−0.463230	−0.231615	+	0.972808i	$0.574401\pi$
$98$	−23.4012	−2.36388
$99$	6.28932	0.632100
$100$	−6.07712	−0.607712
$101$	−16.3872	−1.63058	−0.815291	−	0.579051i	$-0.803423\pi$
$101$	−16.3872	−1.63058	−0.815291	+	0.579051i	$0.803423\pi$
$102$	15.7984	1.56428
$103$	6.78140	0.668191	0.334096	−	0.942539i	$-0.391569\pi$
$103$	6.78140	0.668191	0.334096	+	0.942539i	$0.391569\pi$
$104$	−2.92705	−0.287021
$105$	6.62348	0.646385
$106$	−6.58453	−0.639546
$107$	3.02943	0.292866	0.146433	−	0.989221i	$-0.453221\pi$
$107$	3.02943	0.292866	0.146433	+	0.989221i	$0.453221\pi$
$108$	−2.34338	−0.225492
$109$	−6.03258	−0.577816	−0.288908	−	0.957357i	$-0.593292\pi$
$109$	−6.03258	−0.577816	−0.288908	+	0.957357i	$0.593292\pi$
$110$	20.3342	1.93879
$111$	−0.601076	−0.0570516
$112$	−13.6424	−1.28909
$113$	5.05759	0.475778	0.237889	−	0.971292i	$-0.423544\pi$
$113$	5.05759	0.475778	0.237889	+	0.971292i	$0.423544\pi$
$114$	−12.0014	−1.12404
$115$	11.2509	1.04915
$116$	2.59413	0.240859
$117$	4.09016	0.378135
$118$	2.00329	0.184418
$119$	32.3650	2.96690
$120$	−1.11020	−0.101347
$121$	28.5555	2.59595
$122$	24.4428	2.21295
$123$	−8.36448	−0.754200
$124$	19.3301	1.73590
$125$	11.7799	1.05363
$126$	−8.89796	−0.792693
$127$	−7.44218	−0.660387	−0.330193	−	0.943913i	$-0.607114\pi$
$127$	−7.44218	−0.660387	−0.330193	+	0.943913i	$0.607114\pi$
$128$	5.64069	0.498571
$129$	10.1879	0.896992
$130$	13.2240	1.15982
$131$	−3.56522	−0.311495	−0.155747	−	0.987797i	$-0.549779\pi$
$131$	−3.56522	−0.311495	−0.155747	+	0.987797i	$0.549779\pi$
$132$	−14.7383	−1.28280
$133$	−24.5864	−2.13192
$134$	−24.8652	−2.14803
$135$	1.55135	0.133519
$136$	−5.42488	−0.465180
$137$	−11.8896	−1.01580	−0.507898	−	0.861417i	$-0.669577\pi$
$137$	−11.8896	−1.01580	−0.507898	+	0.861417i	$0.669577\pi$
$138$	−15.1144	−1.28662
$139$	−15.6106	−1.32408	−0.662039	−	0.749470i	$-0.730309\pi$
$139$	−15.6106	−1.32408	−0.662039	+	0.749470i	$0.730309\pi$
$140$	−15.5213	−1.31179
$141$	−5.77677	−0.486492
$142$	−9.31532	−0.781724
$143$	25.7243	2.15117
$144$	−3.19533	−0.266277
$145$	−1.71735	−0.142618
$146$	−10.0493	−0.831690
$147$	−11.2286	−0.926117
$148$	1.40855	0.115782
$149$	−20.6859	−1.69465	−0.847327	−	0.531071i	$-0.821790\pi$
$149$	−20.6859	−1.69465	−0.847327	+	0.531071i	$0.821790\pi$
$150$	−5.40466	−0.441289
$151$	−8.27601	−0.673492	−0.336746	−	0.941596i	$-0.609326\pi$
$151$	−8.27601	−0.673492	−0.336746	+	0.941596i	$0.609326\pi$
$152$	4.12107	0.334263
$153$	7.58053	0.612849
$154$	−55.9621	−4.50955
$155$	−12.7968	−1.02786
$156$	−9.58480	−0.767398
$157$	7.25935	0.579359	0.289680	−	0.957124i	$-0.406451\pi$
$157$	7.25935	0.579359	0.289680	+	0.957124i	$0.406451\pi$
$158$	−27.0836	−2.15465
$159$	−3.15944	−0.250560
$160$	−12.5513	−0.992269
$161$	−30.9637	−2.44028
$162$	−2.08408	−0.163741
$163$	−12.7021	−0.994907	−0.497453	−	0.867491i	$-0.665731\pi$
$163$	−12.7021	−0.994907	−0.497453	+	0.867491i	$0.665731\pi$
$164$	19.6012	1.53059
$165$	9.75693	0.759576
$166$	−24.1312	−1.87295
$167$	4.08054	0.315761	0.157881	−	0.987458i	$-0.449534\pi$
$167$	4.08054	0.315761	0.157881	+	0.987458i	$0.449534\pi$
$168$	3.05539	0.235729
$169$	3.72938	0.286876
$170$	24.5089	1.87974
$171$	−5.75863	−0.440374
$172$	−23.8741	−1.82038
$173$	18.1940	1.38326	0.691631	−	0.722251i	$-0.256892\pi$
$173$	18.1940	1.38326	0.691631	+	0.722251i	$0.256892\pi$
$174$	2.30708	0.174899
$175$	−11.0721	−0.836974
$176$	−20.0964	−1.51482
$177$	0.961238	0.0722511
$178$	−26.2670	−1.96879
$179$	−4.70481	−0.351654	−0.175827	−	0.984421i	$-0.556260\pi$
$179$	−4.70481	−0.351654	−0.175827	+	0.984421i	$0.556260\pi$
$180$	−3.63541	−0.270967
$181$	−13.4808	−1.00202	−0.501010	−	0.865442i	$-0.667038\pi$
$181$	−13.4808	−1.00202	−0.501010	+	0.865442i	$0.667038\pi$
$182$	−36.3940	−2.69771
$183$	11.7284	0.866985
$184$	5.19000	0.382612
$185$	−0.932479	−0.0685572
$186$	17.1912	1.26052
$187$	47.6763	3.48644
$188$	13.5372	0.987300
$189$	−4.26949	−0.310560
$190$	−18.6184	−1.35072
$191$	23.1275	1.67345	0.836723	−	0.547626i	$-0.184468\pi$
$191$	23.1275	1.67345	0.836723	+	0.547626i	$0.184468\pi$
$192$	10.4707	0.755661
$193$	−15.8005	−1.13735	−0.568674	−	0.822563i	$-0.692543\pi$
$193$	−15.8005	−1.13735	−0.568674	+	0.822563i	$0.692543\pi$
$194$	9.50816	0.682646
$195$	6.34527	0.454394
$196$	26.3128	1.87949
$197$	8.05578	0.573951	0.286975	−	0.957938i	$-0.407350\pi$
$197$	8.05578	0.573951	0.286975	+	0.957938i	$0.407350\pi$
$198$	−13.1074	−0.931504
$199$	−3.99296	−0.283054	−0.141527	−	0.989934i	$-0.545201\pi$
$199$	−3.99296	−0.283054	−0.141527	+	0.989934i	$0.545201\pi$
$200$	1.85586	0.131229
$201$	−11.9310	−0.841550
$202$	34.1521	2.40293
$203$	4.72634	0.331724
$204$	−17.7641	−1.24373
$205$	−12.9762	−0.906300
$206$	−14.1330	−0.984690
$207$	−7.25232	−0.504071
$208$	−13.0694	−0.906199
$209$	−36.2179	−2.50524
$210$	−13.8038	−0.952556
$211$	−1.26264	−0.0869236	−0.0434618	−	0.999055i	$-0.513839\pi$
$211$	−1.26264	−0.0869236	−0.0434618	+	0.999055i	$0.513839\pi$
$212$	7.40378	0.508494
$213$	−4.46975	−0.306263
$214$	−6.31357	−0.431587
$215$	15.8050	1.07789
$216$	0.715634	0.0486927
$217$	35.2182	2.39077
$218$	12.5724	0.851508
$219$	−4.82196	−0.325838
$220$	−22.8642	−1.54151
$221$	31.0055	2.08566
$222$	1.25269	0.0840750
$223$	9.74718	0.652719	0.326360	−	0.945246i	$-0.394178\pi$
$223$	9.74718	0.652719	0.326360	+	0.945246i	$0.394178\pi$
$224$	34.5427	2.30798
$225$	−2.59331	−0.172887
$226$	−10.5404	−0.701138
$227$	15.9114	1.05607	0.528037	−	0.849221i	$-0.322928\pi$
$227$	15.9114	1.05607	0.528037	+	0.849221i	$0.322928\pi$
$228$	13.4947	0.893707
$229$	−0.710034	−0.0469204	−0.0234602	−	0.999725i	$-0.507468\pi$
$229$	−0.710034	−0.0469204	−0.0234602	+	0.999725i	$0.507468\pi$
$230$	−23.4477	−1.54610
$231$	−26.8522	−1.76674
$232$	−0.792209	−0.0520110
$233$	−10.7010	−0.701048	−0.350524	−	0.936554i	$-0.613996\pi$
$233$	−10.7010	−0.701048	−0.350524	+	0.936554i	$0.613996\pi$
$234$	−8.52421	−0.557245
$235$	−8.96180	−0.584603
$236$	−2.25255	−0.146628
$237$	−12.9955	−0.844146
$238$	−67.4512	−4.37221
$239$	4.04005	0.261329	0.130664	−	0.991427i	$-0.458289\pi$
$239$	4.04005	0.261329	0.130664	+	0.991427i	$0.458289\pi$
$240$	−4.95707	−0.319978
$241$	13.0799	0.842551	0.421275	−	0.906933i	$-0.361583\pi$
$241$	13.0799	0.842551	0.421275	+	0.906933i	$0.361583\pi$
$242$	−59.5119	−3.82557
$243$	−1.00000	−0.0641500
$244$	−27.4840	−1.75948
$245$	−17.4194	−1.11289
$246$	17.4322	1.11144
$247$	−23.5537	−1.49869
$248$	−5.90313	−0.374849
$249$	−11.5788	−0.733780
$250$	−24.5502	−1.55269
$251$	13.3066	0.839903	0.419951	−	0.907547i	$-0.362047\pi$
$251$	13.3066	0.839903	0.419951	+	0.907547i	$0.362047\pi$
$252$	10.0051	0.630259
$253$	−45.6121	−2.86761
$254$	15.5101	0.973189
$255$	11.7601	0.736443
$256$	9.18585	0.574115
$257$	8.31418	0.518624	0.259312	−	0.965794i	$-0.416504\pi$
$257$	8.31418	0.518624	0.259312	+	0.965794i	$0.416504\pi$
$258$	−21.2323	−1.32187
$259$	2.56629	0.159461
$260$	−14.8694	−0.922160
$261$	1.10700	0.0685218
$262$	7.43020	0.459039
$263$	−10.8964	−0.671901	−0.335951	−	0.941880i	$-0.609058\pi$
$263$	−10.8964	−0.671901	−0.335951	+	0.941880i	$0.609058\pi$
$264$	4.50085	0.277008
$265$	−4.90140	−0.301091
$266$	51.2401	3.14173
$267$	−12.6036	−0.771330
$268$	27.9590	1.70787
$269$	21.3144	1.29956	0.649782	−	0.760120i	$-0.274860\pi$
$269$	21.3144	1.29956	0.649782	+	0.760120i	$0.274860\pi$
$270$	−3.23314	−0.196762
$271$	−1.88072	−0.114246	−0.0571228	−	0.998367i	$-0.518193\pi$
$271$	−1.88072	−0.114246	−0.0571228	+	0.998367i	$0.518193\pi$
$272$	−24.2223	−1.46869
$273$	−17.4629	−1.05690
$274$	24.7788	1.49694
$275$	−16.3102	−0.983539
$276$	16.9949	1.02298
$277$	21.7402	1.30624	0.653122	−	0.757252i	$-0.273459\pi$
$277$	21.7402	1.30624	0.653122	+	0.757252i	$0.273459\pi$
$278$	32.5338	1.95125
$279$	8.24881	0.493843
$280$	4.73999	0.283268
$281$	−12.7106	−0.758250	−0.379125	−	0.925346i	$-0.623775\pi$
$281$	−12.7106	−0.758250	−0.379125	+	0.925346i	$0.623775\pi$
$282$	12.0392	0.716926
$283$	−27.5688	−1.63880	−0.819398	−	0.573224i	$-0.805692\pi$
$283$	−27.5688	−1.63880	−0.819398	+	0.573224i	$0.805692\pi$
$284$	10.4743	0.621538
$285$	−8.93366	−0.529184
$286$	−53.6114	−3.17011
$287$	35.7121	2.10802
$288$	8.09058	0.476742
$289$	40.4644	2.38026
$290$	3.57909	0.210171
$291$	4.56228	0.267446
$292$	11.2997	0.661265
$293$	5.71950	0.334136	0.167068	−	0.985945i	$-0.446570\pi$
$293$	5.71950	0.334136	0.167068	+	0.985945i	$0.446570\pi$
$294$	23.4012	1.36479
$295$	1.49122	0.0868220
$296$	−0.430150	−0.0250020
$297$	−6.28932	−0.364943
$298$	43.1110	2.49735
$299$	−29.6631	−1.71546
$300$	6.07712	0.350863
$301$	−43.4971	−2.50713
$302$	17.2478	0.992502
$303$	16.3872	0.941417
$304$	18.4007	1.05535
$305$	18.1948	1.04183
$306$	−15.7984	−0.903135
$307$	2.44777	0.139702	0.0698508	−	0.997557i	$-0.477748\pi$
$307$	2.44777	0.139702	0.0698508	+	0.997557i	$0.477748\pi$
$308$	62.9249	3.58548
$309$	−6.78140	−0.385780
$310$	26.6695	1.51473
$311$	27.4773	1.55809	0.779047	−	0.626965i	$-0.215703\pi$
$311$	27.4773	1.55809	0.779047	+	0.626965i	$0.215703\pi$
$312$	2.92705	0.165712
$313$	16.0937	0.909667	0.454834	−	0.890576i	$-0.349699\pi$
$313$	16.0937	0.909667	0.454834	+	0.890576i	$0.349699\pi$
$314$	−15.1291	−0.853782
$315$	−6.62348	−0.373191
$316$	30.4533	1.71313
$317$	−16.4476	−0.923791	−0.461895	−	0.886934i	$-0.652830\pi$
$317$	−16.4476	−0.923791	−0.461895	+	0.886934i	$0.652830\pi$
$318$	6.58453	0.369242
$319$	6.96229	0.389813
$320$	16.2438	0.908055
$321$	−3.02943	−0.169086
$322$	64.5308	3.59616
$323$	−43.6535	−2.42894
$324$	2.34338	0.130188
$325$	−10.6071	−0.588373
$326$	26.4722	1.46616
$327$	6.03258	0.333602
$328$	−5.98590	−0.330516
$329$	24.6639	1.35976
$330$	−20.3342	−1.11936
$331$	6.48203	0.356285	0.178142	−	0.984005i	$-0.442991\pi$
$331$	6.48203	0.356285	0.178142	+	0.984005i	$0.442991\pi$
$332$	27.1337	1.48915
$333$	0.601076	0.0329387
$334$	−8.50416	−0.465327
$335$	−18.5092	−1.01127
$336$	13.6424	0.744255
$337$	−16.8161	−0.916029	−0.458015	−	0.888945i	$-0.651439\pi$
$337$	−16.8161	−0.916029	−0.458015	+	0.888945i	$0.651439\pi$
$338$	−7.77233	−0.422759
$339$	−5.05759	−0.274691
$340$	−27.5583	−1.49456
$341$	51.8794	2.80943
$342$	12.0014	0.648964
$343$	18.0538	0.974816
$344$	7.29079	0.393093
$345$	−11.2509	−0.605727
$346$	−37.9177	−2.03847
$347$	7.19276	0.386128	0.193064	−	0.981186i	$-0.438158\pi$
$347$	7.19276	0.386128	0.193064	+	0.981186i	$0.438158\pi$
$348$	−2.59413	−0.139060
$349$	5.20803	0.278779	0.139390	−	0.990238i	$-0.455486\pi$
$349$	5.20803	0.278779	0.139390	+	0.990238i	$0.455486\pi$
$350$	23.0752	1.23342
$351$	−4.09016	−0.218316
$352$	50.8842	2.71214
$353$	5.75261	0.306181	0.153090	−	0.988212i	$-0.451077\pi$
$353$	5.75261	0.306181	0.153090	+	0.988212i	$0.451077\pi$
$354$	−2.00329	−0.106474
$355$	−6.93416	−0.368027
$356$	29.5351	1.56536
$357$	−32.3650	−1.71294
$358$	9.80520	0.518221
$359$	−5.42164	−0.286143	−0.143072	−	0.989712i	$-0.545698\pi$
$359$	−5.42164	−0.286143	−0.143072	+	0.989712i	$0.545698\pi$
$360$	1.11020	0.0585126
$361$	14.1619	0.745361
$362$	28.0950	1.47664
$363$	−28.5555	−1.49877
$364$	40.9222	2.14491
$365$	−7.48055	−0.391550
$366$	−24.4428	−1.27765
$367$	19.9833	1.04312	0.521559	−	0.853215i	$-0.325351\pi$
$367$	19.9833	1.04312	0.521559	+	0.853215i	$0.325351\pi$
$368$	23.1735	1.20800
$369$	8.36448	0.435437
$370$	1.94336	0.101030
$371$	13.4892	0.700325
$372$	−19.3301	−1.00222
$373$	−11.6539	−0.603415	−0.301708	−	0.953400i	$-0.597557\pi$
$373$	−11.6539	−0.603415	−0.301708	+	0.953400i	$0.597557\pi$
$374$	−99.3612	−5.13784
$375$	−11.7799	−0.608311
$376$	−4.13405	−0.213197
$377$	4.52782	0.233194
$378$	8.89796	0.457661
$379$	−9.93686	−0.510422	−0.255211	−	0.966885i	$-0.582145\pi$
$379$	−9.93686	−0.510422	−0.255211	+	0.966885i	$0.582145\pi$
$380$	20.9350	1.07394
$381$	7.44218	0.381274
$382$	−48.1995	−2.46610
$383$	−19.6831	−1.00576	−0.502880	−	0.864356i	$-0.667726\pi$
$383$	−19.6831	−1.00576	−0.502880	+	0.864356i	$0.667726\pi$
$384$	−5.64069	−0.287850
$385$	−41.6572	−2.12305
$386$	32.9296	1.67607
$387$	−10.1879	−0.517879
$388$	−10.6912	−0.542762
$389$	−3.52493	−0.178721	−0.0893605	−	0.995999i	$-0.528482\pi$
$389$	−3.52493	−0.178721	−0.0893605	+	0.995999i	$0.528482\pi$
$390$	−13.2240	−0.669625
$391$	−54.9764	−2.78027
$392$	−8.03554	−0.405856
$393$	3.56522	0.179842
$394$	−16.7889	−0.845811
$395$	−20.1605	−1.01439
$396$	14.7383	0.740626
$397$	−30.1787	−1.51462	−0.757312	−	0.653053i	$-0.773488\pi$
$397$	−30.1787	−1.51462	−0.757312	+	0.653053i	$0.773488\pi$
$398$	8.32164	0.417126
$399$	24.5864	1.23086
$400$	8.28648	0.414324
$401$	−23.8483	−1.19093	−0.595464	−	0.803382i	$-0.703032\pi$
$401$	−23.8483	−1.19093	−0.595464	+	0.803382i	$0.703032\pi$
$402$	24.8652	1.24016
$403$	33.7389	1.68066
$404$	−38.4013	−1.91054
$405$	−1.55135	−0.0770872
$406$	−9.85006	−0.488850
$407$	3.78035	0.187385
$408$	5.42488	0.268572
$409$	11.7437	0.580691	0.290345	−	0.956922i	$-0.406230\pi$
$409$	11.7437	0.580691	0.290345	+	0.956922i	$0.406230\pi$
$410$	27.0435	1.33558
$411$	11.8896	0.586470
$412$	15.8914	0.782913
$413$	−4.10400	−0.201945
$414$	15.1144	0.742832
$415$	−17.9629	−0.881762
$416$	33.0917	1.62246
$417$	15.6106	0.764457
$418$	75.4808	3.69189
$419$	−31.7062	−1.54895	−0.774475	−	0.632604i	$-0.781986\pi$
$419$	−31.7062	−1.54895	−0.774475	+	0.632604i	$0.781986\pi$
$420$	15.5213	0.757364
$421$	14.4735	0.705396	0.352698	−	0.935737i	$-0.385264\pi$
$421$	14.4735	0.705396	0.352698	+	0.935737i	$0.385264\pi$
$422$	2.63144	0.128096
$423$	5.77677	0.280876
$424$	−2.26100	−0.109804
$425$	−19.6587	−0.953585
$426$	9.31532	0.451329
$427$	−50.0742	−2.42326
$428$	7.09911	0.343149
$429$	−25.7243	−1.24198
$430$	−32.9388	−1.58845
$431$	−26.4588	−1.27447	−0.637237	−	0.770668i	$-0.719923\pi$
$431$	−26.4588	−1.27447	−0.637237	+	0.770668i	$0.719923\pi$
$432$	3.19533	0.153735
$433$	−1.57446	−0.0756639	−0.0378319	−	0.999284i	$-0.512045\pi$
$433$	−1.57446	−0.0756639	−0.0378319	+	0.999284i	$0.512045\pi$
$434$	−73.3976	−3.52320
$435$	1.71735	0.0823406
$436$	−14.1366	−0.677022
$437$	41.7634	1.99782
$438$	10.0493	0.480176
$439$	23.7935	1.13560	0.567800	−	0.823167i	$-0.307795\pi$
$439$	23.7935	1.13560	0.567800	+	0.823167i	$0.307795\pi$
$440$	6.98239	0.332872
$441$	11.2286	0.534694
$442$	−64.6180	−3.07356
$443$	30.3654	1.44270	0.721351	−	0.692569i	$-0.243521\pi$
$443$	30.3654	1.44270	0.721351	+	0.692569i	$0.243521\pi$
$444$	−1.40855	−0.0668468
$445$	−19.5527	−0.926885
$446$	−20.3139	−0.961890
$447$	20.6859	0.978409
$448$	−44.7048	−2.11210
$449$	−6.92900	−0.327000	−0.163500	−	0.986543i	$-0.552278\pi$
$449$	−6.92900	−0.327000	−0.163500	+	0.986543i	$0.552278\pi$
$450$	5.40466	0.254778
$451$	52.6069	2.47716
$452$	11.8519	0.557465
$453$	8.27601	0.388841
$454$	−33.1605	−1.55630
$455$	−27.0911	−1.27005
$456$	−4.12107	−0.192987
$457$	31.8598	1.49034	0.745170	−	0.666874i	$-0.232368\pi$
$457$	31.8598	1.49034	0.745170	+	0.666874i	$0.232368\pi$
$458$	1.47977	0.0691450
$459$	−7.58053	−0.353829
$460$	26.3651	1.22928
$461$	−37.0262	−1.72448	−0.862241	−	0.506498i	$-0.830940\pi$
$461$	−37.0262	−1.72448	−0.862241	+	0.506498i	$0.830940\pi$
$462$	55.9621	2.60359
$463$	−41.3898	−1.92355	−0.961773	−	0.273847i	$-0.911704\pi$
$463$	−41.3898	−1.92355	−0.961773	+	0.273847i	$0.911704\pi$
$464$	−3.53724	−0.164212
$465$	12.7968	0.593437
$466$	22.3018	1.03311
$467$	4.59472	0.212618	0.106309	−	0.994333i	$-0.466097\pi$
$467$	4.59472	0.212618	0.106309	+	0.994333i	$0.466097\pi$
$468$	9.58480	0.443057
$469$	50.9395	2.35217
$470$	18.6771	0.861510
$471$	−7.25935	−0.334493
$472$	0.687894	0.0316629
$473$	−64.0748	−2.94616
$474$	27.0836	1.24399
$475$	14.9339	0.685216
$476$	75.8435	3.47628
$477$	3.15944	0.144661
$478$	−8.41977	−0.385111
$479$	−15.8461	−0.724025	−0.362012	−	0.932173i	$-0.617910\pi$
$479$	−15.8461	−0.724025	−0.362012	+	0.932173i	$0.617910\pi$
$480$	12.5513	0.572887
$481$	2.45849	0.112098
$482$	−27.2595	−1.24164
$483$	30.9637	1.40890
$484$	66.9164	3.04165
$485$	7.07770	0.321382
$486$	2.08408	0.0945357
$487$	−33.2135	−1.50505	−0.752524	−	0.658565i	$-0.771164\pi$
$487$	−33.2135	−1.50505	−0.752524	+	0.658565i	$0.771164\pi$
$488$	8.39321	0.379943
$489$	12.7021	0.574410
$490$	36.3035	1.64002
$491$	3.31945	0.149804	0.0749022	−	0.997191i	$-0.476136\pi$
$491$	3.31945	0.149804	0.0749022	+	0.997191i	$0.476136\pi$
$492$	−19.6012	−0.883689
$493$	8.39167	0.377942
$494$	49.0878	2.20856
$495$	−9.75693	−0.438542
$496$	−26.3576	−1.18349
$497$	19.0836	0.856016
$498$	24.1312	1.08135
$499$	26.9180	1.20501	0.602507	−	0.798114i	$-0.294169\pi$
$499$	26.9180	1.20501	0.602507	+	0.798114i	$0.294169\pi$
$500$	27.6048	1.23452
$501$	−4.08054	−0.182305
$502$	−27.7319	−1.23774
$503$	3.37915	0.150669	0.0753343	−	0.997158i	$-0.475998\pi$
$503$	3.37915	0.150669	0.0753343	+	0.997158i	$0.475998\pi$
$504$	−3.05539	−0.136098
$505$	25.4222	1.13127
$506$	95.0592	4.22590
$507$	−3.72938	−0.165628
$508$	−17.4399	−0.773769
$509$	−2.41018	−0.106829	−0.0534147	−	0.998572i	$-0.517011\pi$
$509$	−2.41018	−0.106829	−0.0534147	+	0.998572i	$0.517011\pi$
$510$	−24.5089	−1.08527
$511$	20.5873	0.910730
$512$	−30.4254	−1.34463
$513$	5.75863	0.254250
$514$	−17.3274	−0.764279
$515$	−10.5203	−0.463581
$516$	23.8741	1.05100
$517$	36.3319	1.59788
$518$	−5.34835	−0.234993
$519$	−18.1940	−0.798627
$520$	4.54089	0.199131
$521$	−16.8061	−0.736290	−0.368145	−	0.929768i	$-0.620007\pi$
$521$	−16.8061	−0.736290	−0.368145	+	0.929768i	$0.620007\pi$
$522$	−2.30708	−0.100978
$523$	−12.9053	−0.564308	−0.282154	−	0.959369i	$-0.591049\pi$
$523$	−12.9053	−0.564308	−0.282154	+	0.959369i	$0.591049\pi$
$524$	−8.35468	−0.364976
$525$	11.0721	0.483227
$526$	22.7090	0.990158
$527$	62.5303	2.72386
$528$	20.0964	0.874584
$529$	29.5961	1.28679
$530$	10.2149	0.443707
$531$	−0.961238	−0.0417142
$532$	−57.6154	−2.49795
$533$	34.2120	1.48189
$534$	26.2670	1.13668
$535$	−4.69971	−0.203186
$536$	−8.53825	−0.368796
$537$	4.70481	0.203028
$538$	−44.4210	−1.91512
$539$	70.6200	3.04182
$540$	3.63541	0.156443
$541$	25.7160	1.10562	0.552809	−	0.833308i	$-0.313556\pi$
$541$	25.7160	1.10562	0.552809	+	0.833308i	$0.313556\pi$
$542$	3.91957	0.168360
$543$	13.4808	0.578516
$544$	61.3308	2.62954
$545$	9.35864	0.400880
$546$	36.3940	1.55752
$547$	−22.9358	−0.980664	−0.490332	−	0.871536i	$-0.663125\pi$
$547$	−22.9358	−0.980664	−0.490332	+	0.871536i	$0.663125\pi$
$548$	−27.8618	−1.19020
$549$	−11.7284	−0.500554
$550$	33.9916	1.44941
$551$	−6.37482	−0.271577
$552$	−5.19000	−0.220901
$553$	55.4841	2.35942
$554$	−45.3084	−1.92497
$555$	0.932479	0.0395815
$556$	−36.5817	−1.55141
$557$	−19.9520	−0.845393	−0.422697	−	0.906271i	$-0.638916\pi$
$557$	−19.9520	−0.845393	−0.422697	+	0.906271i	$0.638916\pi$
$558$	−17.1912	−0.727760
$559$	−41.6700	−1.76245
$560$	21.1642	0.894350
$561$	−47.6763	−2.01290
$562$	26.4898	1.11741
$563$	−25.9207	−1.09243	−0.546213	−	0.837646i	$-0.683931\pi$
$563$	−25.9207	−1.09243	−0.546213	+	0.837646i	$0.683931\pi$
$564$	−13.5372	−0.570018
$565$	−7.84610	−0.330088
$566$	57.4556	2.41504
$567$	4.26949	0.179302
$568$	−3.19871	−0.134215
$569$	−15.5962	−0.653829	−0.326914	−	0.945054i	$-0.606009\pi$
$569$	−15.5962	−0.653829	−0.326914	+	0.945054i	$0.606009\pi$
$570$	18.6184	0.779841
$571$	−31.7862	−1.33021	−0.665105	−	0.746750i	$-0.731613\pi$
$571$	−31.7862	−1.33021	−0.665105	+	0.746750i	$0.731613\pi$
$572$	60.2818	2.52051
$573$	−23.1275	−0.966164
$574$	−74.4268	−3.10651
$575$	18.8075	0.784328
$576$	−10.4707	−0.436281
$577$	−7.02842	−0.292597	−0.146298	−	0.989240i	$-0.546736\pi$
$577$	−7.02842	−0.292597	−0.146298	+	0.989240i	$0.546736\pi$
$578$	−84.3309	−3.50770
$579$	15.8005	0.656648
$580$	−4.02441	−0.167104
$581$	49.4358	2.05094
$582$	−9.50816	−0.394126
$583$	19.8707	0.822962
$584$	−3.45076	−0.142793
$585$	−6.34527	−0.262345
$586$	−11.9199	−0.492405
$587$	8.30189	0.342656	0.171328	−	0.985214i	$-0.445194\pi$
$587$	8.30189	0.342656	0.171328	+	0.985214i	$0.445194\pi$
$588$	−26.3128	−1.08512
$589$	−47.5019	−1.95728
$590$	−3.10781	−0.127947
$591$	−8.05578	−0.331371
$592$	−1.92063	−0.0789375
$593$	−37.3165	−1.53240	−0.766202	−	0.642600i	$-0.777856\pi$
$593$	−37.3165	−1.53240	−0.766202	+	0.642600i	$0.777856\pi$
$594$	13.1074	0.537804
$595$	−50.2095	−2.05839
$596$	−48.4749	−1.98561
$597$	3.99296	0.163421
$598$	61.8202	2.52802
$599$	9.88805	0.404015	0.202007	−	0.979384i	$-0.435253\pi$
$599$	9.88805	0.404015	0.202007	+	0.979384i	$0.435253\pi$
$600$	−1.85586	−0.0757652
$601$	−27.1416	−1.10713	−0.553565	−	0.832806i	$-0.686733\pi$
$601$	−27.1416	−1.10713	−0.553565	+	0.832806i	$0.686733\pi$
$602$	90.6513	3.69467
$603$	11.9310	0.485869
$604$	−19.3938	−0.789124
$605$	−44.2996	−1.80103
$606$	−34.1521	−1.38733
$607$	−35.1256	−1.42571	−0.712853	−	0.701314i	$-0.752597\pi$
$607$	−35.1256	−1.42571	−0.712853	+	0.701314i	$0.752597\pi$
$608$	−46.5907	−1.88950
$609$	−4.72634	−0.191521
$610$	−37.9194	−1.53531
$611$	23.6279	0.955883
$612$	17.7641	0.718070
$613$	−5.42319	−0.219040	−0.109520	−	0.993985i	$-0.534931\pi$
$613$	−5.42319	−0.219040	−0.109520	+	0.993985i	$0.534931\pi$
$614$	−5.10134	−0.205873
$615$	12.9762	0.523253
$616$	−19.2163	−0.774248
$617$	6.26023	0.252028	0.126014	−	0.992028i	$-0.459782\pi$
$617$	6.26023	0.252028	0.126014	+	0.992028i	$0.459782\pi$
$618$	14.1330	0.568511
$619$	−41.5418	−1.66970	−0.834852	−	0.550474i	$-0.814447\pi$
$619$	−41.5418	−1.66970	−0.834852	+	0.550474i	$0.814447\pi$
$620$	−29.9878	−1.20434
$621$	7.25232	0.291025
$622$	−57.2648	−2.29611
$623$	53.8111	2.15590
$624$	13.0694	0.523194
$625$	−5.30818	−0.212327
$626$	−33.5404	−1.34055
$627$	36.2179	1.44640
$628$	17.0114	0.678830
$629$	4.55647	0.181678
$630$	13.8038	0.549959
$631$	36.2383	1.44262	0.721311	−	0.692611i	$-0.243540\pi$
$631$	36.2383	1.44262	0.721311	+	0.692611i	$0.243540\pi$
$632$	−9.30000	−0.369934
$633$	1.26264	0.0501853
$634$	34.2781	1.36136
$635$	11.5454	0.458166
$636$	−7.40378	−0.293579
$637$	45.9266	1.81968
$638$	−14.5100	−0.574455
$639$	4.46975	0.176821
$640$	−8.75069	−0.345901
$641$	21.2250	0.838337	0.419168	−	0.907909i	$-0.362322\pi$
$641$	21.2250	0.838337	0.419168	+	0.907909i	$0.362322\pi$
$642$	6.31357	0.249177
$643$	−3.91688	−0.154467	−0.0772333	−	0.997013i	$-0.524609\pi$
$643$	−3.91688	−0.154467	−0.0772333	+	0.997013i	$0.524609\pi$
$644$	−72.5598	−2.85926
$645$	−15.8050	−0.622320
$646$	90.9772	3.57945
$647$	27.4719	1.08003	0.540016	−	0.841655i	$-0.318418\pi$
$647$	27.4719	1.08003	0.540016	+	0.841655i	$0.318418\pi$
$648$	−0.715634	−0.0281127
$649$	−6.04553	−0.237308
$650$	22.1059	0.867066
$651$	−35.2182	−1.38031
$652$	−29.7659	−1.16572
$653$	31.5249	1.23367	0.616833	−	0.787094i	$-0.288416\pi$
$653$	31.5249	1.23367	0.616833	+	0.787094i	$0.288416\pi$
$654$	−12.5724	−0.491618
$655$	5.53091	0.216111
$656$	−26.7272	−1.04352
$657$	4.82196	0.188123
$658$	−51.4015	−2.00384
$659$	15.4681	0.602550	0.301275	−	0.953537i	$-0.402588\pi$
$659$	15.4681	0.602550	0.301275	+	0.953537i	$0.402588\pi$
$660$	22.8642	0.889988
$661$	48.2494	1.87669	0.938343	−	0.345706i	$-0.112361\pi$
$661$	48.2494	1.87669	0.938343	+	0.345706i	$0.112361\pi$
$662$	−13.5091	−0.525044
$663$	−31.0055	−1.20416
$664$	−8.28621	−0.321567
$665$	38.1422	1.47909
$666$	−1.25269	−0.0485407
$667$	−8.02833	−0.310858
$668$	9.56226	0.369975
$669$	−9.74718	−0.376848
$670$	38.5746	1.49027
$671$	−73.7634	−2.84760
$672$	−34.5427	−1.33251
$673$	−26.0703	−1.00494	−0.502468	−	0.864596i	$-0.667575\pi$
$673$	−26.0703	−1.00494	−0.502468	+	0.864596i	$0.667575\pi$
$674$	35.0460	1.34992
$675$	2.59331	0.0998166
$676$	8.73937	0.336130
$677$	42.7282	1.64218	0.821089	−	0.570800i	$-0.193367\pi$
$677$	42.7282	1.64218	0.821089	+	0.570800i	$0.193367\pi$
$678$	10.5404	0.404802
$679$	−19.4786	−0.747522
$680$	8.41589	0.322735
$681$	−15.9114	−0.609724
$682$	−108.121	−4.14015
$683$	−11.5371	−0.441454	−0.220727	−	0.975336i	$-0.570843\pi$
$683$	−11.5371	−0.441454	−0.220727	+	0.975336i	$0.570843\pi$
$684$	−13.4947	−0.515982
$685$	18.4449	0.704744
$686$	−37.6256	−1.43655
$687$	0.710034	0.0270895
$688$	32.5536	1.24109
$689$	12.9226	0.492312
$690$	23.4477	0.892639
$691$	8.27492	0.314793	0.157396	−	0.987536i	$-0.449690\pi$
$691$	8.27492	0.314793	0.157396	+	0.987536i	$0.449690\pi$
$692$	42.6354	1.62076
$693$	26.8522	1.02003
$694$	−14.9903	−0.569023
$695$	24.2176	0.918625
$696$	0.792209	0.0300286
$697$	63.4072	2.40172
$698$	−10.8539	−0.410828
$699$	10.7010	0.404750
$700$	−25.9462	−0.980675
$701$	35.4171	1.33769	0.668843	−	0.743403i	$-0.266790\pi$
$701$	35.4171	1.33769	0.668843	+	0.743403i	$0.266790\pi$
$702$	8.52421	0.321725
$703$	−3.46137	−0.130548
$704$	−65.8538	−2.48196
$705$	8.96180	0.337521
$706$	−11.9889	−0.451208
$707$	−69.9648	−2.63130
$708$	2.25255	0.0846559
$709$	20.4767	0.769020	0.384510	−	0.923121i	$-0.374370\pi$
$709$	20.4767	0.769020	0.384510	+	0.923121i	$0.374370\pi$
$710$	14.4513	0.542348
$711$	12.9955	0.487368
$712$	−9.01958	−0.338023
$713$	−59.8230	−2.24039
$714$	67.4512	2.52430
$715$	−39.9074	−1.49245
$716$	−11.0252	−0.412030
$717$	−4.04005	−0.150878
$718$	11.2991	0.421680
$719$	11.9642	0.446189	0.223095	−	0.974797i	$-0.428384\pi$
$719$	11.9642	0.446189	0.223095	+	0.974797i	$0.428384\pi$
$720$	4.95707	0.184739
$721$	28.9531	1.07827
$722$	−29.5144	−1.09841
$723$	−13.0799	−0.486447
$724$	−31.5907	−1.17406
$725$	−2.87080	−0.106619
$726$	59.5119	2.20869
$727$	−10.2973	−0.381904	−0.190952	−	0.981599i	$-0.561158\pi$
$727$	−10.2973	−0.381904	−0.190952	+	0.981599i	$0.561158\pi$
$728$	−12.4970	−0.463171
$729$	1.00000	0.0370370
$730$	15.5901	0.577014
$731$	−77.2295	−2.85643
$732$	27.4840	1.01584
$733$	−5.81126	−0.214644	−0.107322	−	0.994224i	$-0.534228\pi$
$733$	−5.81126	−0.214644	−0.107322	+	0.994224i	$0.534228\pi$
$734$	−41.6467	−1.53721
$735$	17.4194	0.642526
$736$	−58.6754	−2.16280
$737$	75.0380	2.76406
$738$	−17.4322	−0.641689
$739$	49.6724	1.82723	0.913614	−	0.406582i	$-0.133279\pi$
$739$	49.6724	1.82723	0.913614	+	0.406582i	$0.133279\pi$
$740$	−2.18515	−0.0803279
$741$	23.5537	0.865267
$742$	−28.1126	−1.03205
$743$	−45.0350	−1.65217	−0.826087	−	0.563543i	$-0.809438\pi$
$743$	−45.0350	−1.65217	−0.826087	+	0.563543i	$0.809438\pi$
$744$	5.90313	0.216419
$745$	32.0911	1.17573
$746$	24.2876	0.889232
$747$	11.5788	0.423648
$748$	111.724	4.08503
$749$	12.9341	0.472603
$750$	24.5502	0.896447
$751$	2.00422	0.0731351	0.0365676	−	0.999331i	$-0.488358\pi$
$751$	2.00422	0.0731351	0.0365676	+	0.999331i	$0.488358\pi$
$752$	−18.4587	−0.673118
$753$	−13.3066	−0.484918
$754$	−9.43632	−0.343651
$755$	12.8390	0.467259
$756$	−10.0051	−0.363880
$757$	18.4710	0.671339	0.335669	−	0.941980i	$-0.391038\pi$
$757$	18.4710	0.671339	0.335669	+	0.941980i	$0.391038\pi$
$758$	20.7092	0.752192
$759$	45.6121	1.65561
$760$	−6.39323	−0.231907
$761$	−31.8949	−1.15619	−0.578096	−	0.815969i	$-0.696204\pi$
$761$	−31.8949	−1.15619	−0.578096	+	0.815969i	$0.696204\pi$
$762$	−15.5101	−0.561871
$763$	−25.7560	−0.932432
$764$	54.1965	1.96076
$765$	−11.7601	−0.425186
$766$	41.0211	1.48215
$767$	−3.93161	−0.141962
$768$	−9.18585	−0.331466
$769$	22.8611	0.824394	0.412197	−	0.911095i	$-0.364762\pi$
$769$	22.8611	0.824394	0.412197	+	0.911095i	$0.364762\pi$
$770$	86.8168	3.12866
$771$	−8.31418	−0.299428
$772$	−37.0267	−1.33262
$773$	−48.3575	−1.73930	−0.869650	−	0.493669i	$-0.835655\pi$
$773$	−48.3575	−1.73930	−0.869650	+	0.493669i	$0.835655\pi$
$774$	21.2323	0.763180
$775$	−21.3917	−0.768414
$776$	3.26492	0.117204
$777$	−2.56629	−0.0920651
$778$	7.34622	0.263375
$779$	−48.1680	−1.72580
$780$	14.8694	0.532409
$781$	28.1117	1.00592
$782$	114.575	4.09720
$783$	−1.10700	−0.0395611
$784$	−35.8789	−1.28139
$785$	−11.2618	−0.401951
$786$	−7.43020	−0.265027
$787$	30.0890	1.07256	0.536279	−	0.844041i	$-0.319829\pi$
$787$	30.0890	1.07256	0.536279	+	0.844041i	$0.319829\pi$
$788$	18.8778	0.672493
$789$	10.8964	0.387922
$790$	42.0161	1.49487
$791$	21.5934	0.767772
$792$	−4.50085	−0.159931
$793$	−47.9708	−1.70349
$794$	62.8947	2.23205
$795$	4.90140	0.173835
$796$	−9.35703	−0.331651
$797$	−19.7042	−0.697958	−0.348979	−	0.937131i	$-0.613472\pi$
$797$	−19.7042	−0.697958	−0.348979	+	0.937131i	$0.613472\pi$
$798$	−51.2401	−1.81388
$799$	43.7910	1.54921
$800$	−20.9814	−0.741804
$801$	12.6036	0.445327
$802$	49.7017	1.75503
$803$	30.3268	1.07021
$804$	−27.9590	−0.986036
$805$	48.0356	1.69303
$806$	−70.3146	−2.47673
$807$	−21.3144	−0.750304
$808$	11.7272	0.412561
$809$	−6.32294	−0.222303	−0.111151	−	0.993803i	$-0.535454\pi$
$809$	−6.32294	−0.222303	−0.111151	+	0.993803i	$0.535454\pi$
$810$	3.23314	0.113601
$811$	6.52826	0.229238	0.114619	−	0.993410i	$-0.463435\pi$
$811$	6.52826	0.229238	0.114619	+	0.993410i	$0.463435\pi$
$812$	11.0756	0.388678
$813$	1.88072	0.0659598
$814$	−7.87855	−0.276143
$815$	19.7054	0.690251
$816$	24.2223	0.847949
$817$	58.6682	2.05254
$818$	−24.4749	−0.855744
$819$	17.4629	0.610203
$820$	−30.4083	−1.06190
$821$	−55.8790	−1.95019	−0.975096	−	0.221783i	$-0.928812\pi$
$821$	−55.8790	−1.95019	−0.975096	+	0.221783i	$0.928812\pi$
$822$	−24.7788	−0.864261
$823$	6.30251	0.219692	0.109846	−	0.993949i	$-0.464964\pi$
$823$	6.30251	0.219692	0.109846	+	0.993949i	$0.464964\pi$
$824$	−4.85300	−0.169062
$825$	16.3102	0.567847
$826$	8.55305	0.297599
$827$	−0.359881	−0.0125143	−0.00625715	−	0.999980i	$-0.501992\pi$
$827$	−0.359881	−0.0125143	−0.00625715	+	0.999980i	$0.501992\pi$
$828$	−16.9949	−0.590615
$829$	−41.6611	−1.44695	−0.723474	−	0.690351i	$-0.757456\pi$
$829$	−41.6611	−1.44695	−0.723474	+	0.690351i	$0.757456\pi$
$830$	37.4360	1.29942
$831$	−21.7402	−0.754161
$832$	−42.8270	−1.48476
$833$	85.1185	2.94918
$834$	−32.5338	−1.12655
$835$	−6.33034	−0.219071
$836$	−84.8723	−2.93537
$837$	−8.24881	−0.285121
$838$	66.0782	2.28264
$839$	−38.4795	−1.32846	−0.664230	−	0.747528i	$-0.731241\pi$
$839$	−38.4795	−1.32846	−0.664230	+	0.747528i	$0.731241\pi$
$840$	−4.73999	−0.163545
$841$	−27.7745	−0.957743
$842$	−30.1639	−1.03952
$843$	12.7106	0.437776
$844$	−2.95884	−0.101848
$845$	−5.78558	−0.199030
$846$	−12.0392	−0.413918
$847$	121.917	4.18913
$848$	−10.0955	−0.346679
$849$	27.5688	0.946160
$850$	40.9702	1.40527
$851$	−4.35919	−0.149431
$852$	−10.4743	−0.358845
$853$	32.8504	1.12478	0.562388	−	0.826874i	$-0.309883\pi$
$853$	32.8504	1.12478	0.562388	+	0.826874i	$0.309883\pi$
$854$	104.358	3.57107
$855$	8.93366	0.305525
$856$	−2.16796	−0.0740995
$857$	32.5651	1.11240	0.556202	−	0.831047i	$-0.312258\pi$
$857$	32.5651	1.11240	0.556202	+	0.831047i	$0.312258\pi$
$858$	53.6114	1.83026
$859$	19.7725	0.674629	0.337314	−	0.941392i	$-0.390481\pi$
$859$	19.7725	0.674629	0.337314	+	0.941392i	$0.390481\pi$
$860$	37.0371	1.26295
$861$	−35.7121	−1.21706
$862$	55.1422	1.87815
$863$	−27.1260	−0.923380	−0.461690	−	0.887041i	$-0.652757\pi$
$863$	−27.1260	−0.923380	−0.461690	+	0.887041i	$0.652757\pi$
$864$	−8.09058	−0.275247
$865$	−28.2252	−0.959687
$866$	3.28130	0.111503
$867$	−40.4644	−1.37424
$868$	82.5298	2.80124
$869$	81.7326	2.77259
$870$	−3.57909	−0.121343
$871$	48.7998	1.65352
$872$	4.31712	0.146196
$873$	−4.56228	−0.154410
$874$	−87.0382	−2.94411
$875$	50.2941	1.70025
$876$	−11.2997	−0.381781
$877$	−44.2928	−1.49566	−0.747831	−	0.663889i	$-0.768905\pi$
$877$	−44.2928	−1.49566	−0.747831	+	0.663889i	$0.768905\pi$
$878$	−49.5874	−1.67349
$879$	−5.71950	−0.192914
$880$	31.1766	1.05096
$881$	42.3425	1.42656	0.713278	−	0.700881i	$-0.247210\pi$
$881$	42.3425	1.42656	0.713278	+	0.700881i	$0.247210\pi$
$882$	−23.4012	−0.787960
$883$	−13.2455	−0.445745	−0.222873	−	0.974848i	$-0.571543\pi$
$883$	−13.2455	−0.445745	−0.222873	+	0.974848i	$0.571543\pi$
$884$	72.6578	2.44375
$885$	−1.49122	−0.0501267
$886$	−63.2838	−2.12606
$887$	8.01212	0.269021	0.134510	−	0.990912i	$-0.457054\pi$
$887$	8.01212	0.269021	0.134510	+	0.990912i	$0.457054\pi$
$888$	0.430150	0.0144349
$889$	−31.7743	−1.06568
$890$	40.7493	1.36592
$891$	6.28932	0.210700
$892$	22.8414	0.764785
$893$	−33.2663	−1.11321
$894$	−43.1110	−1.44185
$895$	7.29881	0.243972
$896$	24.0829	0.804553
$897$	29.6631	0.990422
$898$	14.4406	0.481888
$899$	9.13146	0.304551
$900$	−6.07712	−0.202571
$901$	23.9502	0.797898
$902$	−109.637	−3.65051
$903$	43.4971	1.44749
$904$	−3.61938	−0.120379
$905$	20.9134	0.695186
$906$	−17.2478	−0.573021
$907$	−14.3983	−0.478086	−0.239043	−	0.971009i	$-0.576834\pi$
$907$	−14.3983	−0.478086	−0.239043	+	0.971009i	$0.576834\pi$
$908$	37.2864	1.23739
$909$	−16.3872	−0.543527
$910$	56.4599	1.87163
$911$	28.9830	0.960249	0.480124	−	0.877200i	$-0.340592\pi$
$911$	28.9830	0.960249	0.480124	+	0.877200i	$0.340592\pi$
$912$	−18.4007	−0.609308
$913$	72.8230	2.41009
$914$	−66.3984	−2.19626
$915$	−18.1948	−0.601502
$916$	−1.66388	−0.0549762
$917$	−15.2217	−0.502665
$918$	15.7984	0.521425
$919$	24.1540	0.796766	0.398383	−	0.917219i	$-0.369572\pi$
$919$	24.1540	0.796766	0.398383	+	0.917219i	$0.369572\pi$
$920$	−8.05151	−0.265450
$921$	−2.44777	−0.0806568
$922$	77.1655	2.54131
$923$	18.2820	0.601759
$924$	−62.9249	−2.07008
$925$	−1.55878	−0.0512523
$926$	86.2595	2.83466
$927$	6.78140	0.222730
$928$	8.95629	0.294005
$929$	−13.7923	−0.452512	−0.226256	−	0.974068i	$-0.572649\pi$
$929$	−13.7923	−0.452512	−0.226256	+	0.974068i	$0.572649\pi$
$930$	−26.6695	−0.874528
$931$	−64.6612	−2.11919
$932$	−25.0766	−0.821411
$933$	−27.4773	−0.899567
$934$	−9.57575	−0.313328
$935$	−73.9627	−2.41884
$936$	−2.92705	−0.0956738
$937$	−45.1008	−1.47338	−0.736689	−	0.676232i	$-0.763612\pi$
$937$	−45.1008	−1.47338	−0.736689	+	0.676232i	$0.763612\pi$
$938$	−106.162	−3.46631
$939$	−16.0937	−0.525197
$940$	−21.0009	−0.684974
$941$	−19.0445	−0.620833	−0.310417	−	0.950601i	$-0.600469\pi$
$941$	−19.0445	−0.620833	−0.310417	+	0.950601i	$0.600469\pi$
$942$	15.1291	0.492931
$943$	−60.6618	−1.97542
$944$	3.07147	0.0999678
$945$	6.62348	0.215462
$946$	133.537	4.34166
$947$	−17.3848	−0.564931	−0.282465	−	0.959277i	$-0.591152\pi$
$947$	−17.3848	−0.564931	−0.282465	+	0.959277i	$0.591152\pi$
$948$	−30.4533	−0.989079
$949$	19.7226	0.640222
$950$	−31.1235	−1.00978
$951$	16.4476	0.533351
$952$	−23.1615	−0.750668
$953$	52.1004	1.68770	0.843848	−	0.536582i	$-0.180285\pi$
$953$	52.1004	1.68770	0.843848	+	0.536582i	$0.180285\pi$
$954$	−6.58453	−0.213182
$955$	−35.8788	−1.16101
$956$	9.46737	0.306197
$957$	−6.96229	−0.225059
$958$	33.0244	1.06697
$959$	−50.7625	−1.63921
$960$	−16.2438	−0.524266
$961$	37.0429	1.19493
$962$	−5.12369	−0.165195
$963$	3.02943	0.0976221
$964$	30.6512	0.987209
$965$	24.5122	0.789075
$966$	−64.5308	−2.07624
$967$	38.9047	1.25109	0.625545	−	0.780188i	$-0.284877\pi$
$967$	38.9047	1.25109	0.625545	+	0.780188i	$0.284877\pi$
$968$	−20.4353	−0.656814
$969$	43.6535	1.40235
$970$	−14.7505	−0.473610
$971$	34.3596	1.10265	0.551326	−	0.834290i	$-0.314122\pi$
$971$	34.3596	1.10265	0.551326	+	0.834290i	$0.314122\pi$
$972$	−2.34338	−0.0751640
$973$	−66.6495	−2.13669
$974$	69.2195	2.21794
$975$	10.6071	0.339697
$976$	37.4759	1.19958
$977$	40.7160	1.30262	0.651310	−	0.758811i	$-0.274220\pi$
$977$	40.7160	1.30262	0.651310	+	0.758811i	$0.274220\pi$
$978$	−26.4722	−0.846488
$979$	79.2682	2.53342
$980$	−40.8204	−1.30396
$981$	−6.03258	−0.192605
$982$	−6.91798	−0.220762
$983$	40.0980	1.27893	0.639464	−	0.768821i	$-0.279156\pi$
$983$	40.0980	1.27893	0.639464	+	0.768821i	$0.279156\pi$
$984$	5.98590	0.190824
$985$	−12.4973	−0.398198
$986$	−17.4889	−0.556960
$987$	−24.6639	−0.785060
$988$	−55.1953	−1.75600
$989$	73.8857	2.34943
$990$	20.3342	0.646264
$991$	26.2835	0.834923	0.417461	−	0.908695i	$-0.362920\pi$
$991$	26.2835	0.834923	0.417461	+	0.908695i	$0.362920\pi$
$992$	66.7376	2.11892
$993$	−6.48203	−0.205701
$994$	−39.7717	−1.26148
$995$	6.19448	0.196378
$996$	−27.1337	−0.859763
$997$	11.3002	0.357880	0.178940	−	0.983860i	$-0.442733\pi$
$997$	11.3002	0.357880	0.178940	+	0.983860i	$0.442733\pi$
$998$	−56.0991	−1.77579
$999$	−0.601076	−0.0190172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.20	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.20	✓	119	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)

\(f(q)\)	\(=\)	\(q-2.08408 q^{2} -1.00000 q^{3} +2.34338 q^{4} -1.55135 q^{5} +2.08408 q^{6} +4.26949 q^{7} -0.715634 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.08408 q^{2} -1.00000 q^{3} +2.34338 q^{4} -1.55135 q^{5} +2.08408 q^{6} +4.26949 q^{7} -0.715634 q^{8} +1.00000 q^{9} +3.23314 q^{10} +6.28932 q^{11} -2.34338 q^{12} +4.09016 q^{13} -8.89796 q^{14} +1.55135 q^{15} -3.19533 q^{16} +7.58053 q^{17} -2.08408 q^{18} -5.75863 q^{19} -3.63541 q^{20} -4.26949 q^{21} -13.1074 q^{22} -7.25232 q^{23} +0.715634 q^{24} -2.59331 q^{25} -8.52421 q^{26} -1.00000 q^{27} +10.0051 q^{28} +1.10700 q^{29} -3.23314 q^{30} +8.24881 q^{31} +8.09058 q^{32} -6.28932 q^{33} -15.7984 q^{34} -6.62348 q^{35} +2.34338 q^{36} +0.601076 q^{37} +12.0014 q^{38} -4.09016 q^{39} +1.11020 q^{40} +8.36448 q^{41} +8.89796 q^{42} -10.1879 q^{43} +14.7383 q^{44} -1.55135 q^{45} +15.1144 q^{46} +5.77677 q^{47} +3.19533 q^{48} +11.2286 q^{49} +5.40466 q^{50} -7.58053 q^{51} +9.58480 q^{52} +3.15944 q^{53} +2.08408 q^{54} -9.75693 q^{55} -3.05539 q^{56} +5.75863 q^{57} -2.30708 q^{58} -0.961238 q^{59} +3.63541 q^{60} -11.7284 q^{61} -17.1912 q^{62} +4.26949 q^{63} -10.4707 q^{64} -6.34527 q^{65} +13.1074 q^{66} +11.9310 q^{67} +17.7641 q^{68} +7.25232 q^{69} +13.8038 q^{70} +4.46975 q^{71} -0.715634 q^{72} +4.82196 q^{73} -1.25269 q^{74} +2.59331 q^{75} -13.4947 q^{76} +26.8522 q^{77} +8.52421 q^{78} +12.9955 q^{79} +4.95707 q^{80} +1.00000 q^{81} -17.4322 q^{82} +11.5788 q^{83} -10.0051 q^{84} -11.7601 q^{85} +21.2323 q^{86} -1.10700 q^{87} -4.50085 q^{88} +12.6036 q^{89} +3.23314 q^{90} +17.4629 q^{91} -16.9949 q^{92} -8.24881 q^{93} -12.0392 q^{94} +8.93366 q^{95} -8.09058 q^{96} -4.56228 q^{97} -23.4012 q^{98} +6.28932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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