LMFDB - Embedded newform 4011.2.a.l.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.786373 q^{2} -1.00000 q^{3} -1.38162 q^{4} +2.33863 q^{5} +0.786373 q^{6} +1.00000 q^{7} +2.65921 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.786373 q^{2} -1.00000 q^{3} -1.38162 q^{4} +2.33863 q^{5} +0.786373 q^{6} +1.00000 q^{7} +2.65921 q^{8} +1.00000 q^{9} -1.83903 q^{10} -3.89883 q^{11} +1.38162 q^{12} -0.530472 q^{13} -0.786373 q^{14} -2.33863 q^{15} +0.672103 q^{16} +7.72460 q^{17} -0.786373 q^{18} +5.30907 q^{19} -3.23109 q^{20} -1.00000 q^{21} +3.06593 q^{22} -4.99190 q^{23} -2.65921 q^{24} +0.469176 q^{25} +0.417149 q^{26} -1.00000 q^{27} -1.38162 q^{28} +1.84363 q^{29} +1.83903 q^{30} -3.08226 q^{31} -5.84695 q^{32} +3.89883 q^{33} -6.07441 q^{34} +2.33863 q^{35} -1.38162 q^{36} +8.94240 q^{37} -4.17491 q^{38} +0.530472 q^{39} +6.21891 q^{40} -3.77674 q^{41} +0.786373 q^{42} +0.235909 q^{43} +5.38669 q^{44} +2.33863 q^{45} +3.92549 q^{46} +11.5066 q^{47} -0.672103 q^{48} +1.00000 q^{49} -0.368948 q^{50} -7.72460 q^{51} +0.732910 q^{52} +9.25430 q^{53} +0.786373 q^{54} -9.11791 q^{55} +2.65921 q^{56} -5.30907 q^{57} -1.44978 q^{58} +3.64745 q^{59} +3.23109 q^{60} -11.5437 q^{61} +2.42380 q^{62} +1.00000 q^{63} +3.25367 q^{64} -1.24058 q^{65} -3.06593 q^{66} +9.20905 q^{67} -10.6724 q^{68} +4.99190 q^{69} -1.83903 q^{70} -5.81566 q^{71} +2.65921 q^{72} -9.66677 q^{73} -7.03206 q^{74} -0.469176 q^{75} -7.33511 q^{76} -3.89883 q^{77} -0.417149 q^{78} -0.986882 q^{79} +1.57180 q^{80} +1.00000 q^{81} +2.96993 q^{82} -13.1086 q^{83} +1.38162 q^{84} +18.0650 q^{85} -0.185513 q^{86} -1.84363 q^{87} -10.3678 q^{88} +14.4964 q^{89} -1.83903 q^{90} -0.530472 q^{91} +6.89690 q^{92} +3.08226 q^{93} -9.04850 q^{94} +12.4159 q^{95} +5.84695 q^{96} +0.239447 q^{97} -0.786373 q^{98} -3.89883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.786373	−0.556050	−0.278025	−	0.960574i	$-0.589680\pi$
$2$	−0.786373	−0.556050	−0.278025	+	0.960574i	$0.589680\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.38162	−0.690809
$5$	2.33863	1.04587	0.522933	−	0.852374i	$-0.324838\pi$
$5$	2.33863	1.04587	0.522933	+	0.852374i	$0.324838\pi$
$6$	0.786373	0.321035
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.65921	0.940174
$9$	1.00000	0.333333
$10$	−1.83903	−0.581553
$11$	−3.89883	−1.17554	−0.587771	−	0.809028i	$-0.699994\pi$
$11$	−3.89883	−1.17554	−0.587771	+	0.809028i	$0.699994\pi$
$12$	1.38162	0.398839
$13$	−0.530472	−0.147127	−0.0735633	−	0.997291i	$-0.523437\pi$
$13$	−0.530472	−0.147127	−0.0735633	+	0.997291i	$0.523437\pi$
$14$	−0.786373	−0.210167
$15$	−2.33863	−0.603831
$16$	0.672103	0.168026
$17$	7.72460	1.87349	0.936745	−	0.350012i	$-0.113823\pi$
$17$	7.72460	1.87349	0.936745	+	0.350012i	$0.113823\pi$
$18$	−0.786373	−0.185350
$19$	5.30907	1.21798	0.608992	−	0.793176i	$-0.291574\pi$
$19$	5.30907	1.21798	0.608992	+	0.793176i	$0.291574\pi$
$20$	−3.23109	−0.722493
$21$	−1.00000	−0.218218
$22$	3.06593	0.653659
$23$	−4.99190	−1.04088	−0.520442	−	0.853897i	$-0.674233\pi$
$23$	−4.99190	−1.04088	−0.520442	+	0.853897i	$0.674233\pi$
$24$	−2.65921	−0.542809
$25$	0.469176	0.0938353
$26$	0.417149	0.0818097
$27$	−1.00000	−0.192450
$28$	−1.38162	−0.261101
$29$	1.84363	0.342354	0.171177	−	0.985240i	$-0.445243\pi$
$29$	1.84363	0.342354	0.171177	+	0.985240i	$0.445243\pi$
$30$	1.83903	0.335760
$31$	−3.08226	−0.553590	−0.276795	−	0.960929i	$-0.589272\pi$
$31$	−3.08226	−0.553590	−0.276795	+	0.960929i	$0.589272\pi$
$32$	−5.84695	−1.03360
$33$	3.89883	0.678699
$34$	−6.07441	−1.04175
$35$	2.33863	0.395300
$36$	−1.38162	−0.230270
$37$	8.94240	1.47012	0.735061	−	0.678001i	$-0.237153\pi$
$37$	8.94240	1.47012	0.735061	+	0.678001i	$0.237153\pi$
$38$	−4.17491	−0.677260
$39$	0.530472	0.0849436
$40$	6.21891	0.983295
$41$	−3.77674	−0.589828	−0.294914	−	0.955524i	$-0.595291\pi$
$41$	−3.77674	−0.589828	−0.294914	+	0.955524i	$0.595291\pi$
$42$	0.786373	0.121340
$43$	0.235909	0.0359758	0.0179879	−	0.999838i	$-0.494274\pi$
$43$	0.235909	0.0359758	0.0179879	+	0.999838i	$0.494274\pi$
$44$	5.38669	0.812074
$45$	2.33863	0.348622
$46$	3.92549	0.578783
$47$	11.5066	1.67841	0.839207	−	0.543812i	$-0.183019\pi$
$47$	11.5066	1.67841	0.839207	+	0.543812i	$0.183019\pi$
$48$	−0.672103	−0.0970098
$49$	1.00000	0.142857
$50$	−0.368948	−0.0521771
$51$	−7.72460	−1.08166
$52$	0.732910	0.101636
$53$	9.25430	1.27118	0.635588	−	0.772029i	$-0.280758\pi$
$53$	9.25430	1.27118	0.635588	+	0.772029i	$0.280758\pi$
$54$	0.786373	0.107012
$55$	−9.11791	−1.22946
$56$	2.65921	0.355352
$57$	−5.30907	−0.703204
$58$	−1.44978	−0.190366
$59$	3.64745	0.474857	0.237428	−	0.971405i	$-0.423695\pi$
$59$	3.64745	0.474857	0.237428	+	0.971405i	$0.423695\pi$
$60$	3.23109	0.417132
$61$	−11.5437	−1.47802	−0.739011	−	0.673693i	$-0.764707\pi$
$61$	−11.5437	−1.47802	−0.739011	+	0.673693i	$0.764707\pi$
$62$	2.42380	0.307823
$63$	1.00000	0.125988
$64$	3.25367	0.406709
$65$	−1.24058	−0.153875
$66$	−3.06593	−0.377390
$67$	9.20905	1.12506	0.562532	−	0.826775i	$-0.309827\pi$
$67$	9.20905	1.12506	0.562532	+	0.826775i	$0.309827\pi$
$68$	−10.6724	−1.29422
$69$	4.99190	0.600954
$70$	−1.83903	−0.219806
$71$	−5.81566	−0.690191	−0.345096	−	0.938568i	$-0.612154\pi$
$71$	−5.81566	−0.690191	−0.345096	+	0.938568i	$0.612154\pi$
$72$	2.65921	0.313391
$73$	−9.66677	−1.13141	−0.565705	−	0.824608i	$-0.691396\pi$
$73$	−9.66677	−1.13141	−0.565705	+	0.824608i	$0.691396\pi$
$74$	−7.03206	−0.817461
$75$	−0.469176	−0.0541758
$76$	−7.33511	−0.841395
$77$	−3.89883	−0.444313
$78$	−0.417149	−0.0472328
$79$	−0.986882	−0.111033	−0.0555164	−	0.998458i	$-0.517681\pi$
$79$	−0.986882	−0.111033	−0.0555164	+	0.998458i	$0.517681\pi$
$80$	1.57180	0.175732
$81$	1.00000	0.111111
$82$	2.96993	0.327974
$83$	−13.1086	−1.43886	−0.719430	−	0.694565i	$-0.755597\pi$
$83$	−13.1086	−1.43886	−0.719430	+	0.694565i	$0.755597\pi$
$84$	1.38162	0.150747
$85$	18.0650	1.95942
$86$	−0.185513	−0.0200043
$87$	−1.84363	−0.197658
$88$	−10.3678	−1.10521
$89$	14.4964	1.53661	0.768306	−	0.640083i	$-0.221100\pi$
$89$	14.4964	1.53661	0.768306	+	0.640083i	$0.221100\pi$
$90$	−1.83903	−0.193851
$91$	−0.530472	−0.0556086
$92$	6.89690	0.719051
$93$	3.08226	0.319615
$94$	−9.04850	−0.933282
$95$	12.4159	1.27385
$96$	5.84695	0.596752
$97$	0.239447	0.0243122	0.0121561	−	0.999926i	$-0.496131\pi$
$97$	0.239447	0.0243122	0.0121561	+	0.999926i	$0.496131\pi$
$98$	−0.786373	−0.0794356
$99$	−3.89883	−0.391847
$100$	−0.648222	−0.0648222
$101$	−9.67723	−0.962921	−0.481460	−	0.876468i	$-0.659893\pi$
$101$	−9.67723	−0.962921	−0.481460	+	0.876468i	$0.659893\pi$
$102$	6.07441	0.601457
$103$	−14.9235	−1.47045	−0.735226	−	0.677822i	$-0.762924\pi$
$103$	−14.9235	−1.47045	−0.735226	+	0.677822i	$0.762924\pi$
$104$	−1.41064	−0.138325
$105$	−2.33863	−0.228227
$106$	−7.27733	−0.706837
$107$	−7.94249	−0.767830	−0.383915	−	0.923369i	$-0.625424\pi$
$107$	−7.94249	−0.767830	−0.383915	+	0.923369i	$0.625424\pi$
$108$	1.38162	0.132946
$109$	8.76774	0.839797	0.419899	−	0.907571i	$-0.362066\pi$
$109$	8.76774	0.839797	0.419899	+	0.907571i	$0.362066\pi$
$110$	7.17008	0.683640
$111$	−8.94240	−0.848775
$112$	0.672103	0.0635078
$113$	5.57800	0.524734	0.262367	−	0.964968i	$-0.415497\pi$
$113$	5.57800	0.524734	0.262367	+	0.964968i	$0.415497\pi$
$114$	4.17491	0.391016
$115$	−11.6742	−1.08862
$116$	−2.54720	−0.236501
$117$	−0.530472	−0.0490422
$118$	−2.86825	−0.264044
$119$	7.72460	0.708113
$120$	−6.21891	−0.567706
$121$	4.20087	0.381898
$122$	9.07767	0.821853
$123$	3.77674	0.340538
$124$	4.25850	0.382425
$125$	−10.5959	−0.947727
$126$	−0.786373	−0.0700557
$127$	16.2300	1.44018	0.720091	−	0.693880i	$-0.244100\pi$
$127$	16.2300	1.44018	0.720091	+	0.693880i	$0.244100\pi$
$128$	9.13530	0.807454
$129$	−0.235909	−0.0207707
$130$	0.975556	0.0855619
$131$	18.9013	1.65141	0.825707	−	0.564099i	$-0.190777\pi$
$131$	18.9013	1.65141	0.825707	+	0.564099i	$0.190777\pi$
$132$	−5.38669	−0.468851
$133$	5.30907	0.460355
$134$	−7.24175	−0.625592
$135$	−2.33863	−0.201277
$136$	20.5413	1.76141
$137$	15.6720	1.33895	0.669474	−	0.742836i	$-0.266520\pi$
$137$	15.6720	1.33895	0.669474	+	0.742836i	$0.266520\pi$
$138$	−3.92549	−0.334160
$139$	−1.72393	−0.146222	−0.0731108	−	0.997324i	$-0.523293\pi$
$139$	−1.72393	−0.146222	−0.0731108	+	0.997324i	$0.523293\pi$
$140$	−3.23109	−0.273077
$141$	−11.5066	−0.969033
$142$	4.57327	0.383781
$143$	2.06822	0.172953
$144$	0.672103	0.0560086
$145$	4.31157	0.358056
$146$	7.60168	0.629120
$147$	−1.00000	−0.0824786
$148$	−12.3550	−1.01557
$149$	−8.64016	−0.707829	−0.353915	−	0.935278i	$-0.615150\pi$
$149$	−8.64016	−0.707829	−0.353915	+	0.935278i	$0.615150\pi$
$150$	0.368948	0.0301244
$151$	−16.9084	−1.37598	−0.687991	−	0.725719i	$-0.741507\pi$
$151$	−16.9084	−1.37598	−0.687991	+	0.725719i	$0.741507\pi$
$152$	14.1179	1.14512
$153$	7.72460	0.624497
$154$	3.06593	0.247060
$155$	−7.20825	−0.578981
$156$	−0.732910	−0.0586798
$157$	19.0723	1.52213	0.761066	−	0.648674i	$-0.224676\pi$
$157$	19.0723	1.52213	0.761066	+	0.648674i	$0.224676\pi$
$158$	0.776057	0.0617398
$159$	−9.25430	−0.733913
$160$	−13.6738	−1.08101
$161$	−4.99190	−0.393417
$162$	−0.786373	−0.0617833
$163$	14.8192	1.16073	0.580363	−	0.814358i	$-0.302911\pi$
$163$	14.8192	1.16073	0.580363	+	0.814358i	$0.302911\pi$
$164$	5.21802	0.407459
$165$	9.11791	0.709828
$166$	10.3083	0.800077
$167$	−11.6787	−0.903722	−0.451861	−	0.892088i	$-0.649240\pi$
$167$	−11.6787	−0.903722	−0.451861	+	0.892088i	$0.649240\pi$
$168$	−2.65921	−0.205163
$169$	−12.7186	−0.978354
$170$	−14.2058	−1.08953
$171$	5.30907	0.405995
$172$	−0.325936	−0.0248524
$173$	−12.9644	−0.985666	−0.492833	−	0.870124i	$-0.664039\pi$
$173$	−12.9644	−0.985666	−0.492833	+	0.870124i	$0.664039\pi$
$174$	1.44978	0.109908
$175$	0.469176	0.0354664
$176$	−2.62042	−0.197521
$177$	−3.64745	−0.274159
$178$	−11.3995	−0.854432
$179$	−15.8596	−1.18540	−0.592699	−	0.805424i	$-0.701938\pi$
$179$	−15.8596	−1.18540	−0.592699	+	0.805424i	$0.701938\pi$
$180$	−3.23109	−0.240831
$181$	4.09049	0.304044	0.152022	−	0.988377i	$-0.451422\pi$
$181$	4.09049	0.304044	0.152022	+	0.988377i	$0.451422\pi$
$182$	0.417149	0.0309212
$183$	11.5437	0.853336
$184$	−13.2745	−0.978611
$185$	20.9129	1.53755
$186$	−2.42380	−0.177722
$187$	−30.1169	−2.20237
$188$	−15.8978	−1.15946
$189$	−1.00000	−0.0727393
$190$	−9.76356	−0.708323
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−3.25367	−0.234814
$193$	22.5417	1.62258	0.811292	−	0.584641i	$-0.198765\pi$
$193$	22.5417	1.62258	0.811292	+	0.584641i	$0.198765\pi$
$194$	−0.188295	−0.0135188
$195$	1.24058	0.0888396
$196$	−1.38162	−0.0986870
$197$	16.8534	1.20076	0.600378	−	0.799717i	$-0.295017\pi$
$197$	16.8534	1.20076	0.600378	+	0.799717i	$0.295017\pi$
$198$	3.06593	0.217886
$199$	6.71267	0.475849	0.237924	−	0.971284i	$-0.423533\pi$
$199$	6.71267	0.475849	0.237924	+	0.971284i	$0.423533\pi$
$200$	1.24764	0.0882214
$201$	−9.20905	−0.649557
$202$	7.60991	0.535432
$203$	1.84363	0.129398
$204$	10.6724	0.747220
$205$	−8.83240	−0.616881
$206$	11.7354	0.817644
$207$	−4.99190	−0.346961
$208$	−0.356532	−0.0247211
$209$	−20.6992	−1.43179
$210$	1.83903	0.126905
$211$	3.85459	0.265361	0.132680	−	0.991159i	$-0.457642\pi$
$211$	3.85459	0.265361	0.132680	+	0.991159i	$0.457642\pi$
$212$	−12.7859	−0.878139
$213$	5.81566	0.398482
$214$	6.24576	0.426951
$215$	0.551704	0.0376259
$216$	−2.65921	−0.180936
$217$	−3.08226	−0.209237
$218$	−6.89471	−0.466969
$219$	9.66677	0.653219
$220$	12.5975	0.849321
$221$	−4.09769	−0.275640
$222$	7.03206	0.471961
$223$	19.9666	1.33706	0.668532	−	0.743684i	$-0.266923\pi$
$223$	19.9666	1.33706	0.668532	+	0.743684i	$0.266923\pi$
$224$	−5.84695	−0.390666
$225$	0.469176	0.0312784
$226$	−4.38638	−0.291778
$227$	−20.0058	−1.32783	−0.663915	−	0.747808i	$-0.731106\pi$
$227$	−20.0058	−1.32783	−0.663915	+	0.747808i	$0.731106\pi$
$228$	7.33511	0.485779
$229$	3.97267	0.262521	0.131261	−	0.991348i	$-0.458098\pi$
$229$	3.97267	0.262521	0.131261	+	0.991348i	$0.458098\pi$
$230$	9.18027	0.605329
$231$	3.89883	0.256524
$232$	4.90261	0.321872
$233$	14.5875	0.955657	0.477828	−	0.878453i	$-0.341424\pi$
$233$	14.5875	0.955657	0.477828	+	0.878453i	$0.341424\pi$
$234$	0.417149	0.0272699
$235$	26.9097	1.75540
$236$	−5.03938	−0.328035
$237$	0.986882	0.0641049
$238$	−6.07441	−0.393746
$239$	−9.60732	−0.621446	−0.310723	−	0.950501i	$-0.600571\pi$
$239$	−9.60732	−0.621446	−0.310723	+	0.950501i	$0.600571\pi$
$240$	−1.57180	−0.101459
$241$	24.5114	1.57891	0.789457	−	0.613805i	$-0.210362\pi$
$241$	24.5114	1.57891	0.789457	+	0.613805i	$0.210362\pi$
$242$	−3.30345	−0.212354
$243$	−1.00000	−0.0641500
$244$	15.9490	1.02103
$245$	2.33863	0.149409
$246$	−2.96993	−0.189356
$247$	−2.81632	−0.179198
$248$	−8.19638	−0.520471
$249$	13.1086	0.830726
$250$	8.33233	0.526983
$251$	−10.2297	−0.645690	−0.322845	−	0.946452i	$-0.604639\pi$
$251$	−10.2297	−0.645690	−0.322845	+	0.946452i	$0.604639\pi$
$252$	−1.38162	−0.0870337
$253$	19.4626	1.22360
$254$	−12.7628	−0.800812
$255$	−18.0650	−1.13127
$256$	−13.6911	−0.855694
$257$	5.13894	0.320558	0.160279	−	0.987072i	$-0.448761\pi$
$257$	5.13894	0.320558	0.160279	+	0.987072i	$0.448761\pi$
$258$	0.185513	0.0115495
$259$	8.94240	0.555654
$260$	1.71400	0.106298
$261$	1.84363	0.114118
$262$	−14.8635	−0.918268
$263$	25.0158	1.54254	0.771269	−	0.636509i	$-0.219622\pi$
$263$	25.0158	1.54254	0.771269	+	0.636509i	$0.219622\pi$
$264$	10.3678	0.638095
$265$	21.6423	1.32948
$266$	−4.17491	−0.255980
$267$	−14.4964	−0.887163
$268$	−12.7234	−0.777205
$269$	20.0921	1.22504	0.612519	−	0.790456i	$-0.290156\pi$
$269$	20.0921	1.22504	0.612519	+	0.790456i	$0.290156\pi$
$270$	1.83903	0.111920
$271$	20.8138	1.26435	0.632174	−	0.774826i	$-0.282163\pi$
$271$	20.8138	1.26435	0.632174	+	0.774826i	$0.282163\pi$
$272$	5.19173	0.314795
$273$	0.530472	0.0321057
$274$	−12.3240	−0.744521
$275$	−1.82924	−0.110307
$276$	−6.89690	−0.415144
$277$	0.524027	0.0314857	0.0157429	−	0.999876i	$-0.494989\pi$
$277$	0.524027	0.0314857	0.0157429	+	0.999876i	$0.494989\pi$
$278$	1.35565	0.0813065
$279$	−3.08226	−0.184530
$280$	6.21891	0.371651
$281$	−11.1028	−0.662340	−0.331170	−	0.943571i	$-0.607443\pi$
$281$	−11.1028	−0.662340	−0.331170	+	0.943571i	$0.607443\pi$
$282$	9.04850	0.538830
$283$	−5.39068	−0.320443	−0.160221	−	0.987081i	$-0.551221\pi$
$283$	−5.39068	−0.320443	−0.160221	+	0.987081i	$0.551221\pi$
$284$	8.03501	0.476790
$285$	−12.4159	−0.735457
$286$	−1.62639	−0.0961707
$287$	−3.77674	−0.222934
$288$	−5.84695	−0.344535
$289$	42.6694	2.50997
$290$	−3.39050	−0.199097
$291$	−0.239447	−0.0140366
$292$	13.3558	0.781588
$293$	−0.691269	−0.0403844	−0.0201922	−	0.999796i	$-0.506428\pi$
$293$	−0.691269	−0.0403844	−0.0201922	+	0.999796i	$0.506428\pi$
$294$	0.786373	0.0458622
$295$	8.53001	0.496637
$296$	23.7798	1.38217
$297$	3.89883	0.226233
$298$	6.79439	0.393588
$299$	2.64807	0.153142
$300$	0.648222	0.0374251
$301$	0.235909	0.0135976
$302$	13.2963	0.765114
$303$	9.67723	0.555943
$304$	3.56824	0.204653
$305$	−26.9965	−1.54581
$306$	−6.07441	−0.347251
$307$	−3.94910	−0.225387	−0.112694	−	0.993630i	$-0.535948\pi$
$307$	−3.94910	−0.225387	−0.112694	+	0.993630i	$0.535948\pi$
$308$	5.38669	0.306935
$309$	14.9235	0.848966
$310$	5.66837	0.321942
$311$	30.5173	1.73048	0.865239	−	0.501360i	$-0.167167\pi$
$311$	30.5173	1.73048	0.865239	+	0.501360i	$0.167167\pi$
$312$	1.41064	0.0798617
$313$	−7.42984	−0.419959	−0.209980	−	0.977706i	$-0.567340\pi$
$313$	−7.42984	−0.419959	−0.209980	+	0.977706i	$0.567340\pi$
$314$	−14.9979	−0.846381
$315$	2.33863	0.131767
$316$	1.36349	0.0767025
$317$	14.4974	0.814256	0.407128	−	0.913371i	$-0.366530\pi$
$317$	14.4974	0.814256	0.407128	+	0.913371i	$0.366530\pi$
$318$	7.27733	0.408092
$319$	−7.18801	−0.402451
$320$	7.60913	0.425363
$321$	7.94249	0.443307
$322$	3.92549	0.218759
$323$	41.0104	2.28188
$324$	−1.38162	−0.0767565
$325$	−0.248885	−0.0138057
$326$	−11.6534	−0.645422
$327$	−8.76774	−0.484857
$328$	−10.0432	−0.554541
$329$	11.5066	0.634381
$330$	−7.17008	−0.394700
$331$	6.70773	0.368690	0.184345	−	0.982862i	$-0.440984\pi$
$331$	6.70773	0.368690	0.184345	+	0.982862i	$0.440984\pi$
$332$	18.1111	0.993977
$333$	8.94240	0.490041
$334$	9.18379	0.502514
$335$	21.5365	1.17667
$336$	−0.672103	−0.0366662
$337$	25.3756	1.38230	0.691150	−	0.722712i	$-0.257105\pi$
$337$	25.3756	1.38230	0.691150	+	0.722712i	$0.257105\pi$
$338$	10.0016	0.544013
$339$	−5.57800	−0.302955
$340$	−24.9589	−1.35358
$341$	12.0172	0.650768
$342$	−4.17491	−0.225753
$343$	1.00000	0.0539949
$344$	0.627333	0.0338235
$345$	11.6742	0.628517
$346$	10.1949	0.548079
$347$	−26.4246	−1.41855	−0.709275	−	0.704932i	$-0.750977\pi$
$347$	−26.4246	−1.41855	−0.709275	+	0.704932i	$0.750977\pi$
$348$	2.54720	0.136544
$349$	10.0311	0.536954	0.268477	−	0.963286i	$-0.413480\pi$
$349$	10.0311	0.536954	0.268477	+	0.963286i	$0.413480\pi$
$350$	−0.368948	−0.0197211
$351$	0.530472	0.0283145
$352$	22.7963	1.21504
$353$	20.4005	1.08581	0.542904	−	0.839795i	$-0.317325\pi$
$353$	20.4005	1.08581	0.542904	+	0.839795i	$0.317325\pi$
$354$	2.86825	0.152446
$355$	−13.6006	−0.721847
$356$	−20.0284	−1.06150
$357$	−7.72460	−0.408829
$358$	12.4715	0.659141
$359$	−29.6490	−1.56482	−0.782408	−	0.622766i	$-0.786009\pi$
$359$	−29.6490	−1.56482	−0.782408	+	0.622766i	$0.786009\pi$
$360$	6.21891	0.327765
$361$	9.18624	0.483486
$362$	−3.21665	−0.169063
$363$	−4.20087	−0.220489
$364$	0.732910	0.0384149
$365$	−22.6070	−1.18330
$366$	−9.07767	−0.474497
$367$	28.4310	1.48408	0.742042	−	0.670353i	$-0.233857\pi$
$367$	28.4310	1.48408	0.742042	+	0.670353i	$0.233857\pi$
$368$	−3.35507	−0.174895
$369$	−3.77674	−0.196609
$370$	−16.4454	−0.854954
$371$	9.25430	0.480459
$372$	−4.25850	−0.220793
$373$	27.8841	1.44379	0.721893	−	0.692005i	$-0.243272\pi$
$373$	27.8841	1.44379	0.721893	+	0.692005i	$0.243272\pi$
$374$	23.6831	1.22462
$375$	10.5959	0.547170
$376$	30.5986	1.57800
$377$	−0.977997	−0.0503694
$378$	0.786373	0.0404467
$379$	−3.78128	−0.194231	−0.0971156	−	0.995273i	$-0.530962\pi$
$379$	−3.78128	−0.194231	−0.0971156	+	0.995273i	$0.530962\pi$
$380$	−17.1541	−0.879986
$381$	−16.2300	−0.831489
$382$	0.786373	0.0402343
$383$	28.0501	1.43329	0.716646	−	0.697437i	$-0.245676\pi$
$383$	28.0501	1.43329	0.716646	+	0.697437i	$0.245676\pi$
$384$	−9.13530	−0.466184
$385$	−9.11791	−0.464692
$386$	−17.7261	−0.902237
$387$	0.235909	0.0119919
$388$	−0.330824	−0.0167951
$389$	−16.0754	−0.815055	−0.407527	−	0.913193i	$-0.633609\pi$
$389$	−16.0754	−0.815055	−0.407527	+	0.913193i	$0.633609\pi$
$390$	−0.975556	−0.0493992
$391$	−38.5604	−1.95008
$392$	2.65921	0.134311
$393$	−18.9013	−0.953444
$394$	−13.2531	−0.667679
$395$	−2.30795	−0.116125
$396$	5.38669	0.270691
$397$	22.5701	1.13276	0.566381	−	0.824144i	$-0.308343\pi$
$397$	22.5701	1.13276	0.566381	+	0.824144i	$0.308343\pi$
$398$	−5.27866	−0.264595
$399$	−5.30907	−0.265786
$400$	0.315335	0.0157668
$401$	2.07213	0.103477	0.0517386	−	0.998661i	$-0.483524\pi$
$401$	2.07213	0.103477	0.0517386	+	0.998661i	$0.483524\pi$
$402$	7.24175	0.361186
$403$	1.63505	0.0814478
$404$	13.3702	0.665194
$405$	2.33863	0.116207
$406$	−1.44978	−0.0719515
$407$	−34.8649	−1.72819
$408$	−20.5413	−1.01695
$409$	−18.2052	−0.900188	−0.450094	−	0.892981i	$-0.648609\pi$
$409$	−18.2052	−0.900188	−0.450094	+	0.892981i	$0.648609\pi$
$410$	6.94556	0.343017
$411$	−15.6720	−0.773042
$412$	20.6185	1.01580
$413$	3.64745	0.179479
$414$	3.92549	0.192928
$415$	−30.6562	−1.50485
$416$	3.10165	0.152071
$417$	1.72393	0.0844211
$418$	16.2773	0.796147
$419$	16.7628	0.818919	0.409459	−	0.912328i	$-0.365717\pi$
$419$	16.7628	0.818919	0.409459	+	0.912328i	$0.365717\pi$
$420$	3.23109	0.157661
$421$	21.2022	1.03333	0.516665	−	0.856188i	$-0.327173\pi$
$421$	21.2022	1.03333	0.516665	+	0.856188i	$0.327173\pi$
$422$	−3.03115	−0.147554
$423$	11.5066	0.559472
$424$	24.6091	1.19513
$425$	3.62420	0.175799
$426$	−4.57327	−0.221576
$427$	−11.5437	−0.558640
$428$	10.9735	0.530424
$429$	−2.06822	−0.0998547
$430$	−0.433845	−0.0209219
$431$	17.4357	0.839847	0.419923	−	0.907560i	$-0.362057\pi$
$431$	17.4357	0.839847	0.419923	+	0.907560i	$0.362057\pi$
$432$	−0.672103	−0.0323366
$433$	3.27595	0.157432	0.0787161	−	0.996897i	$-0.474918\pi$
$433$	3.27595	0.157432	0.0787161	+	0.996897i	$0.474918\pi$
$434$	2.42380	0.116346
$435$	−4.31157	−0.206724
$436$	−12.1137	−0.580139
$437$	−26.5024	−1.26778
$438$	−7.60168	−0.363222
$439$	35.3517	1.68724	0.843622	−	0.536937i	$-0.180419\pi$
$439$	35.3517	1.68724	0.843622	+	0.536937i	$0.180419\pi$
$440$	−24.2465	−1.15590
$441$	1.00000	0.0476190
$442$	3.22231	0.153270
$443$	−10.1698	−0.483183	−0.241591	−	0.970378i	$-0.577669\pi$
$443$	−10.1698	−0.483183	−0.241591	+	0.970378i	$0.577669\pi$
$444$	12.3550	0.586342
$445$	33.9016	1.60709
$446$	−15.7012	−0.743473
$447$	8.64016	0.408665
$448$	3.25367	0.153722
$449$	0.0851872	0.00402023	0.00201012	−	0.999998i	$-0.499360\pi$
$449$	0.0851872	0.00402023	0.00201012	+	0.999998i	$0.499360\pi$
$450$	−0.368948	−0.0173924
$451$	14.7249	0.693368
$452$	−7.70666	−0.362491
$453$	16.9084	0.794424
$454$	15.7320	0.738339
$455$	−1.24058	−0.0581592
$456$	−14.1179	−0.661134
$457$	9.85072	0.460797	0.230399	−	0.973096i	$-0.425997\pi$
$457$	9.85072	0.460797	0.230399	+	0.973096i	$0.425997\pi$
$458$	−3.12400	−0.145975
$459$	−7.72460	−0.360553
$460$	16.1293	0.752031
$461$	−35.8231	−1.66845	−0.834224	−	0.551426i	$-0.814084\pi$
$461$	−35.8231	−1.66845	−0.834224	+	0.551426i	$0.814084\pi$
$462$	−3.06593	−0.142640
$463$	−20.4661	−0.951140	−0.475570	−	0.879678i	$-0.657758\pi$
$463$	−20.4661	−0.951140	−0.475570	+	0.879678i	$0.657758\pi$
$464$	1.23911	0.0575243
$465$	7.20825	0.334275
$466$	−11.4712	−0.531393
$467$	12.0497	0.557593	0.278797	−	0.960350i	$-0.410064\pi$
$467$	12.0497	0.557593	0.278797	+	0.960350i	$0.410064\pi$
$468$	0.732910	0.0338788
$469$	9.20905	0.425235
$470$	−21.1611	−0.976087
$471$	−19.0723	−0.878803
$472$	9.69933	0.446448
$473$	−0.919770	−0.0422911
$474$	−0.776057	−0.0356455
$475$	2.49089	0.114290
$476$	−10.6724	−0.489171
$477$	9.25430	0.423725
$478$	7.55493	0.345555
$479$	30.1805	1.37898	0.689492	−	0.724293i	$-0.257834\pi$
$479$	30.1805	1.37898	0.689492	+	0.724293i	$0.257834\pi$
$480$	13.6738	0.624122
$481$	−4.74370	−0.216294
$482$	−19.2751	−0.877955
$483$	4.99190	0.227139
$484$	−5.80400	−0.263818
$485$	0.559977	0.0254272
$486$	0.786373	0.0356706
$487$	−41.7523	−1.89198	−0.945988	−	0.324200i	$-0.894905\pi$
$487$	−41.7523	−1.89198	−0.945988	+	0.324200i	$0.894905\pi$
$488$	−30.6972	−1.38960
$489$	−14.8192	−0.670146
$490$	−1.83903	−0.0830790
$491$	18.5657	0.837857	0.418928	−	0.908019i	$-0.362406\pi$
$491$	18.5657	0.837857	0.418928	+	0.908019i	$0.362406\pi$
$492$	−5.21802	−0.235246
$493$	14.2413	0.641397
$494$	2.21467	0.0996429
$495$	−9.11791	−0.409820
$496$	−2.07160	−0.0930174
$497$	−5.81566	−0.260868
$498$	−10.3083	−0.461925
$499$	27.3816	1.22577	0.612885	−	0.790172i	$-0.290009\pi$
$499$	27.3816	1.22577	0.612885	+	0.790172i	$0.290009\pi$
$500$	14.6395	0.654698
$501$	11.6787	0.521764
$502$	8.04432	0.359036
$503$	−32.1280	−1.43252	−0.716258	−	0.697836i	$-0.754147\pi$
$503$	−32.1280	−1.43252	−0.716258	+	0.697836i	$0.754147\pi$
$504$	2.65921	0.118451
$505$	−22.6314	−1.00709
$506$	−15.3048	−0.680383
$507$	12.7186	0.564853
$508$	−22.4237	−0.994890
$509$	−40.4840	−1.79442	−0.897210	−	0.441604i	$-0.854410\pi$
$509$	−40.4840	−1.79442	−0.897210	+	0.441604i	$0.854410\pi$
$510$	14.2058	0.629043
$511$	−9.66677	−0.427633
$512$	−7.50428	−0.331646
$513$	−5.30907	−0.234401
$514$	−4.04112	−0.178246
$515$	−34.9004	−1.53790
$516$	0.325936	0.0143486
$517$	−44.8624	−1.97305
$518$	−7.03206	−0.308971
$519$	12.9644	0.569075
$520$	−3.29896	−0.144669
$521$	−25.9235	−1.13573	−0.567865	−	0.823122i	$-0.692230\pi$
$521$	−25.9235	−1.13573	−0.567865	+	0.823122i	$0.692230\pi$
$522$	−1.44978	−0.0634553
$523$	14.9458	0.653533	0.326766	−	0.945105i	$-0.394041\pi$
$523$	14.9458	0.653533	0.326766	+	0.945105i	$0.394041\pi$
$524$	−26.1144	−1.14081
$525$	−0.469176	−0.0204765
$526$	−19.6717	−0.857728
$527$	−23.8092	−1.03715
$528$	2.62042	0.114039
$529$	1.91907	0.0834377
$530$	−17.0190	−0.739256
$531$	3.64745	0.158286
$532$	−7.33511	−0.318017
$533$	2.00346	0.0867795
$534$	11.3995	0.493307
$535$	−18.5745	−0.803047
$536$	24.4888	1.05776
$537$	15.8596	0.684390
$538$	−15.7999	−0.681182
$539$	−3.89883	−0.167934
$540$	3.23109	0.139044
$541$	35.5658	1.52909	0.764546	−	0.644570i	$-0.222963\pi$
$541$	35.5658	1.52909	0.764546	+	0.644570i	$0.222963\pi$
$542$	−16.3674	−0.703041
$543$	−4.09049	−0.175540
$544$	−45.1653	−1.93645
$545$	20.5045	0.878315
$546$	−0.417149	−0.0178523
$547$	9.24058	0.395099	0.197549	−	0.980293i	$-0.436702\pi$
$547$	9.24058	0.395099	0.197549	+	0.980293i	$0.436702\pi$
$548$	−21.6527	−0.924957
$549$	−11.5437	−0.492674
$550$	1.43846	0.0613363
$551$	9.78798	0.416982
$552$	13.2745	0.565001
$553$	−0.986882	−0.0419665
$554$	−0.412080	−0.0175076
$555$	−20.9129	−0.887705
$556$	2.38181	0.101011
$557$	−11.3985	−0.482970	−0.241485	−	0.970405i	$-0.577634\pi$
$557$	−11.3985	−0.482970	−0.241485	+	0.970405i	$0.577634\pi$
$558$	2.42380	0.102608
$559$	−0.125143	−0.00529300
$560$	1.57180	0.0664206
$561$	30.1169	1.27154
$562$	8.73097	0.368294
$563$	0.657243	0.0276995	0.0138497	−	0.999904i	$-0.495591\pi$
$563$	0.657243	0.0276995	0.0138497	+	0.999904i	$0.495591\pi$
$564$	15.8978	0.669417
$565$	13.0449	0.548801
$566$	4.23909	0.178182
$567$	1.00000	0.0419961
$568$	−15.4651	−0.648900
$569$	−8.63433	−0.361970	−0.180985	−	0.983486i	$-0.557929\pi$
$569$	−8.63433	−0.361970	−0.180985	+	0.983486i	$0.557929\pi$
$570$	9.76356	0.408950
$571$	6.17806	0.258544	0.129272	−	0.991609i	$-0.458736\pi$
$571$	6.17806	0.258544	0.129272	+	0.991609i	$0.458736\pi$
$572$	−2.85749	−0.119478
$573$	1.00000	0.0417756
$574$	2.96993	0.123962
$575$	−2.34208	−0.0976716
$576$	3.25367	0.135570
$577$	1.27825	0.0532144	0.0266072	−	0.999646i	$-0.491530\pi$
$577$	1.27825	0.0532144	0.0266072	+	0.999646i	$0.491530\pi$
$578$	−33.5541	−1.39567
$579$	−22.5417	−0.936799
$580$	−5.95694	−0.247349
$581$	−13.1086	−0.543838
$582$	0.188295	0.00780506
$583$	−36.0809	−1.49432
$584$	−25.7060	−1.06372
$585$	−1.24058	−0.0512916
$586$	0.543595	0.0224557
$587$	1.30333	0.0537940	0.0268970	−	0.999638i	$-0.491437\pi$
$587$	1.30333	0.0537940	0.0268970	+	0.999638i	$0.491437\pi$
$588$	1.38162	0.0569770
$589$	−16.3639	−0.674264
$590$	−6.70777	−0.276155
$591$	−16.8534	−0.693256
$592$	6.01022	0.247019
$593$	−39.6965	−1.63014	−0.815069	−	0.579364i	$-0.803301\pi$
$593$	−39.6965	−1.63014	−0.815069	+	0.579364i	$0.803301\pi$
$594$	−3.06593	−0.125797
$595$	18.0650	0.740591
$596$	11.9374	0.488975
$597$	−6.71267	−0.274731
$598$	−2.08237	−0.0851543
$599$	45.1957	1.84665	0.923324	−	0.384023i	$-0.125462\pi$
$599$	45.1957	1.84665	0.923324	+	0.384023i	$0.125462\pi$
$600$	−1.24764	−0.0509347
$601$	−10.7129	−0.436989	−0.218494	−	0.975838i	$-0.570115\pi$
$601$	−10.7129	−0.436989	−0.218494	+	0.975838i	$0.570115\pi$
$602$	−0.185513	−0.00756093
$603$	9.20905	0.375022
$604$	23.3609	0.950541
$605$	9.82428	0.399414
$606$	−7.60991	−0.309132
$607$	−1.35966	−0.0551871	−0.0275935	−	0.999619i	$-0.508784\pi$
$607$	−1.35966	−0.0551871	−0.0275935	+	0.999619i	$0.508784\pi$
$608$	−31.0419	−1.25891
$609$	−1.84363	−0.0747078
$610$	21.2293	0.859548
$611$	−6.10395	−0.246939
$612$	−10.6724	−0.431408
$613$	8.18587	0.330624	0.165312	−	0.986241i	$-0.447137\pi$
$613$	8.18587	0.330624	0.165312	+	0.986241i	$0.447137\pi$
$614$	3.10547	0.125327
$615$	8.83240	0.356157
$616$	−10.3678	−0.417731
$617$	−5.53280	−0.222742	−0.111371	−	0.993779i	$-0.535524\pi$
$617$	−5.53280	−0.222742	−0.111371	+	0.993779i	$0.535524\pi$
$618$	−11.7354	−0.472067
$619$	−20.7432	−0.833738	−0.416869	−	0.908966i	$-0.636873\pi$
$619$	−20.7432	−0.833738	−0.416869	+	0.908966i	$0.636873\pi$
$620$	9.95905	0.399965
$621$	4.99190	0.200318
$622$	−23.9980	−0.962232
$623$	14.4964	0.580785
$624$	0.356532	0.0142727
$625$	−27.1258	−1.08503
$626$	5.84262	0.233518
$627$	20.6992	0.826645
$628$	−26.3506	−1.05150
$629$	69.0765	2.75426
$630$	−1.83903	−0.0732688
$631$	−9.20913	−0.366609	−0.183305	−	0.983056i	$-0.558680\pi$
$631$	−9.20913	−0.366609	−0.183305	+	0.983056i	$0.558680\pi$
$632$	−2.62433	−0.104390
$633$	−3.85459	−0.153206
$634$	−11.4004	−0.452767
$635$	37.9560	1.50624
$636$	12.7859	0.506994
$637$	−0.530472	−0.0210181
$638$	5.65246	0.223783
$639$	−5.81566	−0.230064
$640$	21.3640	0.844488
$641$	22.0104	0.869360	0.434680	−	0.900585i	$-0.356861\pi$
$641$	22.0104	0.869360	0.434680	+	0.900585i	$0.356861\pi$
$642$	−6.24576	−0.246500
$643$	8.25780	0.325656	0.162828	−	0.986654i	$-0.447938\pi$
$643$	8.25780	0.325656	0.162828	+	0.986654i	$0.447938\pi$
$644$	6.89690	0.271776
$645$	−0.551704	−0.0217233
$646$	−32.2495	−1.26884
$647$	14.2059	0.558490	0.279245	−	0.960220i	$-0.409916\pi$
$647$	14.2059	0.558490	0.279245	+	0.960220i	$0.409916\pi$
$648$	2.65921	0.104464
$649$	−14.2208	−0.558214
$650$	0.195717	0.00767663
$651$	3.08226	0.120803
$652$	−20.4744	−0.801840
$653$	−25.8767	−1.01263	−0.506317	−	0.862347i	$-0.668993\pi$
$653$	−25.8767	−1.01263	−0.506317	+	0.862347i	$0.668993\pi$
$654$	6.89471	0.269605
$655$	44.2031	1.72716
$656$	−2.53836	−0.0991064
$657$	−9.66677	−0.377136
$658$	−9.04850	−0.352747
$659$	2.77671	0.108165	0.0540827	−	0.998536i	$-0.482777\pi$
$659$	2.77671	0.108165	0.0540827	+	0.998536i	$0.482777\pi$
$660$	−12.5975	−0.490356
$661$	32.7572	1.27411	0.637055	−	0.770819i	$-0.280153\pi$
$661$	32.7572	1.27411	0.637055	+	0.770819i	$0.280153\pi$
$662$	−5.27477	−0.205010
$663$	4.09769	0.159141
$664$	−34.8587	−1.35278
$665$	12.4159	0.481469
$666$	−7.03206	−0.272487
$667$	−9.20323	−0.356351
$668$	16.1355	0.624299
$669$	−19.9666	−0.771954
$670$	−16.9358	−0.654285
$671$	45.0070	1.73748
$672$	5.84695	0.225551
$673$	31.8684	1.22843	0.614217	−	0.789137i	$-0.289472\pi$
$673$	31.8684	1.22843	0.614217	+	0.789137i	$0.289472\pi$
$674$	−19.9547	−0.768627
$675$	−0.469176	−0.0180586
$676$	17.5722	0.675855
$677$	14.0474	0.539885	0.269942	−	0.962876i	$-0.412995\pi$
$677$	14.0474	0.539885	0.269942	+	0.962876i	$0.412995\pi$
$678$	4.38638	0.168458
$679$	0.239447	0.00918913
$680$	48.0386	1.84219
$681$	20.0058	0.766623
$682$	−9.45000	−0.361859
$683$	−49.0345	−1.87625	−0.938126	−	0.346293i	$-0.887440\pi$
$683$	−49.0345	−1.87625	−0.938126	+	0.346293i	$0.887440\pi$
$684$	−7.33511	−0.280465
$685$	36.6509	1.40036
$686$	−0.786373	−0.0300239
$687$	−3.97267	−0.151567
$688$	0.158555	0.00604487
$689$	−4.90915	−0.187024
$690$	−9.18027	−0.349487
$691$	−7.91758	−0.301199	−0.150599	−	0.988595i	$-0.548120\pi$
$691$	−7.91758	−0.301199	−0.150599	+	0.988595i	$0.548120\pi$
$692$	17.9119	0.680907
$693$	−3.89883	−0.148104
$694$	20.7796	0.788784
$695$	−4.03163	−0.152928
$696$	−4.90261	−0.185833
$697$	−29.1738	−1.10504
$698$	−7.88821	−0.298573
$699$	−14.5875	−0.551749
$700$	−0.648222	−0.0245005
$701$	−32.4023	−1.22382	−0.611909	−	0.790928i	$-0.709598\pi$
$701$	−32.4023	−1.22382	−0.611909	+	0.790928i	$0.709598\pi$
$702$	−0.417149	−0.0157443
$703$	47.4759	1.79059
$704$	−12.6855	−0.478104
$705$	−26.9097	−1.01348
$706$	−16.0424	−0.603763
$707$	−9.67723	−0.363950
$708$	5.03938	0.189391
$709$	−35.0502	−1.31634	−0.658170	−	0.752870i	$-0.728669\pi$
$709$	−35.0502	−1.31634	−0.658170	+	0.752870i	$0.728669\pi$
$710$	10.6952	0.401383
$711$	−0.986882	−0.0370110
$712$	38.5489	1.44468
$713$	15.3863	0.576222
$714$	6.07441	0.227329
$715$	4.83680	0.180886
$716$	21.9118	0.818884
$717$	9.60732	0.358792
$718$	23.3152	0.870115
$719$	−46.5119	−1.73460	−0.867301	−	0.497783i	$-0.834148\pi$
$719$	−46.5119	−1.73460	−0.867301	+	0.497783i	$0.834148\pi$
$720$	1.57180	0.0585775
$721$	−14.9235	−0.555779
$722$	−7.22381	−0.268842
$723$	−24.5114	−0.911587
$724$	−5.65149	−0.210036
$725$	0.864989	0.0321249
$726$	3.30345	0.122603
$727$	5.40428	0.200434	0.100217	−	0.994966i	$-0.468046\pi$
$727$	5.40428	0.200434	0.100217	+	0.994966i	$0.468046\pi$
$728$	−1.41064	−0.0522818
$729$	1.00000	0.0370370
$730$	17.7775	0.657975
$731$	1.82230	0.0674004
$732$	−15.9490	−0.589492
$733$	−15.3248	−0.566033	−0.283016	−	0.959115i	$-0.591335\pi$
$733$	−15.3248	−0.566033	−0.283016	+	0.959115i	$0.591335\pi$
$734$	−22.3573	−0.825224
$735$	−2.33863	−0.0862616
$736$	29.1874	1.07586
$737$	−35.9045	−1.32256
$738$	2.96993	0.109325
$739$	3.55701	0.130847	0.0654234	−	0.997858i	$-0.479160\pi$
$739$	3.55701	0.130847	0.0654234	+	0.997858i	$0.479160\pi$
$740$	−28.8937	−1.06215
$741$	2.81632	0.103460
$742$	−7.27733	−0.267159
$743$	−20.9046	−0.766914	−0.383457	−	0.923559i	$-0.625267\pi$
$743$	−20.9046	−0.766914	−0.383457	+	0.923559i	$0.625267\pi$
$744$	8.19638	0.300494
$745$	−20.2061	−0.740295
$746$	−21.9273	−0.802817
$747$	−13.1086	−0.479620
$748$	41.6100	1.52141
$749$	−7.94249	−0.290212
$750$	−8.33233	−0.304254
$751$	−33.0813	−1.20715	−0.603577	−	0.797304i	$-0.706259\pi$
$751$	−33.0813	−1.20715	−0.603577	+	0.797304i	$0.706259\pi$
$752$	7.73365	0.282017
$753$	10.2297	0.372789
$754$	0.769070	0.0280079
$755$	−39.5423	−1.43909
$756$	1.38162	0.0502490
$757$	26.3647	0.958242	0.479121	−	0.877749i	$-0.340955\pi$
$757$	26.3647	0.958242	0.479121	+	0.877749i	$0.340955\pi$
$758$	2.97349	0.108002
$759$	−19.4626	−0.706447
$760$	33.0166	1.19764
$761$	−30.6401	−1.11070	−0.555351	−	0.831616i	$-0.687416\pi$
$761$	−30.6401	−1.11070	−0.555351	+	0.831616i	$0.687416\pi$
$762$	12.7628	0.462349
$763$	8.76774	0.317413
$764$	1.38162	0.0499852
$765$	18.0650	0.653140
$766$	−22.0578	−0.796982
$767$	−1.93487	−0.0698641
$768$	13.6911	0.494035
$769$	19.4375	0.700934	0.350467	−	0.936575i	$-0.386023\pi$
$769$	19.4375	0.700934	0.350467	+	0.936575i	$0.386023\pi$
$770$	7.17008	0.258392
$771$	−5.13894	−0.185074
$772$	−31.1440	−1.12090
$773$	−18.0006	−0.647438	−0.323719	−	0.946153i	$-0.604933\pi$
$773$	−18.0006	−0.647438	−0.323719	+	0.946153i	$0.604933\pi$
$774$	−0.185513	−0.00666811
$775$	−1.44612	−0.0519463
$776$	0.636740	0.0228576
$777$	−8.94240	−0.320807
$778$	12.6412	0.453211
$779$	−20.0510	−0.718402
$780$	−1.71400	−0.0613712
$781$	22.6743	0.811348
$782$	30.3229	1.08434
$783$	−1.84363	−0.0658861
$784$	0.672103	0.0240037
$785$	44.6029	1.59195
$786$	14.8635	0.530162
$787$	−17.4986	−0.623759	−0.311879	−	0.950122i	$-0.600958\pi$
$787$	−17.4986	−0.623759	−0.311879	+	0.950122i	$0.600958\pi$
$788$	−23.2850	−0.829492
$789$	−25.0158	−0.890585
$790$	1.81491	0.0645715
$791$	5.57800	0.198331
$792$	−10.3678	−0.368404
$793$	6.12363	0.217456
$794$	−17.7485	−0.629871
$795$	−21.6423	−0.767575
$796$	−9.27434	−0.328720
$797$	−6.96917	−0.246861	−0.123430	−	0.992353i	$-0.539390\pi$
$797$	−6.96917	−0.246861	−0.123430	+	0.992353i	$0.539390\pi$
$798$	4.17491	0.147790
$799$	88.8841	3.14449
$800$	−2.74325	−0.0969885
$801$	14.4964	0.512204
$802$	−1.62947	−0.0575385
$803$	37.6891	1.33002
$804$	12.7234	0.448719
$805$	−11.6742	−0.411461
$806$	−1.28576	−0.0452890
$807$	−20.0921	−0.707276
$808$	−25.7338	−0.905313
$809$	−26.4025	−0.928263	−0.464132	−	0.885766i	$-0.653633\pi$
$809$	−26.4025	−0.928263	−0.464132	+	0.885766i	$0.653633\pi$
$810$	−1.83903	−0.0646170
$811$	−28.6295	−1.00532	−0.502660	−	0.864484i	$-0.667645\pi$
$811$	−28.6295	−1.00532	−0.502660	+	0.864484i	$0.667645\pi$
$812$	−2.54720	−0.0893891
$813$	−20.8138	−0.729972
$814$	27.4168	0.960959
$815$	34.6565	1.21396
$816$	−5.19173	−0.181747
$817$	1.25246	0.0438180
$818$	14.3160	0.500549
$819$	−0.530472	−0.0185362
$820$	12.2030	0.426147
$821$	10.3898	0.362605	0.181302	−	0.983427i	$-0.441969\pi$
$821$	10.3898	0.362605	0.181302	+	0.983427i	$0.441969\pi$
$822$	12.3240	0.429849
$823$	−25.3250	−0.882775	−0.441388	−	0.897316i	$-0.645514\pi$
$823$	−25.3250	−0.882775	−0.441388	+	0.897316i	$0.645514\pi$
$824$	−39.6846	−1.38248
$825$	1.82924	0.0636859
$826$	−2.86825	−0.0997992
$827$	21.2947	0.740491	0.370245	−	0.928934i	$-0.379274\pi$
$827$	21.2947	0.740491	0.370245	+	0.928934i	$0.379274\pi$
$828$	6.89690	0.239684
$829$	34.3346	1.19249	0.596244	−	0.802803i	$-0.296659\pi$
$829$	34.3346	1.19249	0.596244	+	0.802803i	$0.296659\pi$
$830$	24.1072	0.836774
$831$	−0.524027	−0.0181783
$832$	−1.72598	−0.0598378
$833$	7.72460	0.267641
$834$	−1.35565	−0.0469423
$835$	−27.3120	−0.945172
$836$	28.5983	0.989094
$837$	3.08226	0.106538
$838$	−13.1818	−0.455359
$839$	7.92611	0.273640	0.136820	−	0.990596i	$-0.456312\pi$
$839$	7.92611	0.273640	0.136820	+	0.990596i	$0.456312\pi$
$840$	−6.21891	−0.214573
$841$	−25.6010	−0.882794
$842$	−16.6728	−0.574583
$843$	11.1028	0.382402
$844$	−5.32557	−0.183314
$845$	−29.7441	−1.02323
$846$	−9.04850	−0.311094
$847$	4.20087	0.144344
$848$	6.21984	0.213590
$849$	5.39068	0.185008
$850$	−2.84997	−0.0977532
$851$	−44.6396	−1.53023
$852$	−8.03501	−0.275275
$853$	9.77786	0.334788	0.167394	−	0.985890i	$-0.446465\pi$
$853$	9.77786	0.334788	0.167394	+	0.985890i	$0.446465\pi$
$854$	9.07767	0.310631
$855$	12.4159	0.424616
$856$	−21.1208	−0.721893
$857$	−51.7224	−1.76680	−0.883402	−	0.468616i	$-0.844753\pi$
$857$	−51.7224	−1.76680	−0.883402	+	0.468616i	$0.844753\pi$
$858$	1.62639	0.0555242
$859$	2.14996	0.0733558	0.0366779	−	0.999327i	$-0.488322\pi$
$859$	2.14996	0.0733558	0.0366779	+	0.999327i	$0.488322\pi$
$860$	−0.762244	−0.0259923
$861$	3.77674	0.128711
$862$	−13.7109	−0.466996
$863$	15.5719	0.530074	0.265037	−	0.964238i	$-0.414616\pi$
$863$	15.5719	0.530074	0.265037	+	0.964238i	$0.414616\pi$
$864$	5.84695	0.198917
$865$	−30.3189	−1.03087
$866$	−2.57612	−0.0875402
$867$	−42.6694	−1.44913
$868$	4.25850	0.144543
$869$	3.84768	0.130524
$870$	3.39050	0.114949
$871$	−4.88515	−0.165527
$872$	23.3153	0.789555
$873$	0.239447	0.00810405
$874$	20.8407	0.704948
$875$	−10.5959	−0.358207
$876$	−13.3558	−0.451250
$877$	−5.63492	−0.190278	−0.0951389	−	0.995464i	$-0.530330\pi$
$877$	−5.63492	−0.190278	−0.0951389	+	0.995464i	$0.530330\pi$
$878$	−27.7996	−0.938191
$879$	0.691269	0.0233159
$880$	−6.12818	−0.206581
$881$	−22.3390	−0.752620	−0.376310	−	0.926494i	$-0.622807\pi$
$881$	−22.3390	−0.752620	−0.376310	+	0.926494i	$0.622807\pi$
$882$	−0.786373	−0.0264785
$883$	24.3537	0.819568	0.409784	−	0.912183i	$-0.365604\pi$
$883$	24.3537	0.819568	0.409784	+	0.912183i	$0.365604\pi$
$884$	5.66144	0.190415
$885$	−8.53001	−0.286733
$886$	7.99727	0.268673
$887$	−47.6244	−1.59907	−0.799535	−	0.600620i	$-0.794920\pi$
$887$	−47.6244	−1.59907	−0.799535	+	0.600620i	$0.794920\pi$
$888$	−23.7798	−0.797996
$889$	16.2300	0.544337
$890$	−26.6593	−0.893621
$891$	−3.89883	−0.130616
$892$	−27.5862	−0.923655
$893$	61.0895	2.04428
$894$	−6.79439	−0.227238
$895$	−37.0896	−1.23977
$896$	9.13530	0.305189
$897$	−2.64807	−0.0884163
$898$	−0.0669889	−0.00223545
$899$	−5.68255	−0.189524
$900$	−0.648222	−0.0216074
$901$	71.4857	2.38153
$902$	−11.5792	−0.385547
$903$	−0.235909	−0.00785057
$904$	14.8331	0.493341
$905$	9.56612	0.317989
$906$	−13.2963	−0.441739
$907$	40.0240	1.32897	0.664487	−	0.747300i	$-0.268650\pi$
$907$	40.0240	1.32897	0.664487	+	0.747300i	$0.268650\pi$
$908$	27.6403	0.917277
$909$	−9.67723	−0.320974
$910$	0.975556	0.0323394
$911$	−27.0880	−0.897464	−0.448732	−	0.893666i	$-0.648124\pi$
$911$	−27.0880	−0.897464	−0.448732	+	0.893666i	$0.648124\pi$
$912$	−3.56824	−0.118156
$913$	51.1084	1.69144
$914$	−7.74634	−0.256226
$915$	26.9965	0.892475
$916$	−5.48871	−0.181352
$917$	18.9013	0.624176
$918$	6.07441	0.200486
$919$	2.45888	0.0811109	0.0405554	−	0.999177i	$-0.487087\pi$
$919$	2.45888	0.0811109	0.0405554	+	0.999177i	$0.487087\pi$
$920$	−31.0442	−1.02350
$921$	3.94910	0.130127
$922$	28.1703	0.927740
$923$	3.08505	0.101545
$924$	−5.38669	−0.177209
$925$	4.19556	0.137949
$926$	16.0940	0.528881
$927$	−14.9235	−0.490151
$928$	−10.7796	−0.353859
$929$	−47.7686	−1.56724	−0.783619	−	0.621241i	$-0.786629\pi$
$929$	−47.7686	−1.56724	−0.783619	+	0.621241i	$0.786629\pi$
$930$	−5.66837	−0.185873
$931$	5.30907	0.173998
$932$	−20.1543	−0.660176
$933$	−30.5173	−0.999092
$934$	−9.47555	−0.310050
$935$	−70.4322	−2.30338
$936$	−1.41064	−0.0461082
$937$	−6.57797	−0.214893	−0.107446	−	0.994211i	$-0.534267\pi$
$937$	−6.57797	−0.214893	−0.107446	+	0.994211i	$0.534267\pi$
$938$	−7.24175	−0.236452
$939$	7.42984	0.242464
$940$	−37.1789	−1.21264
$941$	−15.3289	−0.499707	−0.249854	−	0.968284i	$-0.580383\pi$
$941$	−15.3289	−0.499707	−0.249854	+	0.968284i	$0.580383\pi$
$942$	14.9979	0.488658
$943$	18.8531	0.613942
$944$	2.45146	0.0797882
$945$	−2.33863	−0.0760755
$946$	0.723282	0.0235159
$947$	24.4393	0.794170	0.397085	−	0.917782i	$-0.370022\pi$
$947$	24.4393	0.794170	0.397085	+	0.917782i	$0.370022\pi$
$948$	−1.36349	−0.0442842
$949$	5.12795	0.166460
$950$	−1.95877	−0.0635509
$951$	−14.4974	−0.470111
$952$	20.5413	0.665749
$953$	15.1538	0.490878	0.245439	−	0.969412i	$-0.421068\pi$
$953$	15.1538	0.490878	0.245439	+	0.969412i	$0.421068\pi$
$954$	−7.27733	−0.235612
$955$	−2.33863	−0.0756762
$956$	13.2736	0.429300
$957$	7.18801	0.232355
$958$	−23.7332	−0.766783
$959$	15.6720	0.506074
$960$	−7.60913	−0.245584
$961$	−21.4997	−0.693538
$962$	3.73032	0.120270
$963$	−7.94249	−0.255943
$964$	−33.8653	−1.09073
$965$	52.7165	1.69701
$966$	−3.92549	−0.126301
$967$	−28.5076	−0.916744	−0.458372	−	0.888760i	$-0.651567\pi$
$967$	−28.5076	−0.916744	−0.458372	+	0.888760i	$0.651567\pi$
$968$	11.1710	0.359050
$969$	−41.0104	−1.31745
$970$	−0.440351	−0.0141388
$971$	−4.20614	−0.134981	−0.0674907	−	0.997720i	$-0.521499\pi$
$971$	−4.20614	−0.134981	−0.0674907	+	0.997720i	$0.521499\pi$
$972$	1.38162	0.0443154
$973$	−1.72393	−0.0552666
$974$	32.8329	1.05203
$975$	0.248885	0.00797070
$976$	−7.75857	−0.248346
$977$	13.9289	0.445624	0.222812	−	0.974861i	$-0.428476\pi$
$977$	13.9289	0.445624	0.222812	+	0.974861i	$0.428476\pi$
$978$	11.6534	0.372634
$979$	−56.5189	−1.80635
$980$	−3.23109	−0.103213
$981$	8.76774	0.279932
$982$	−14.5995	−0.465890
$983$	−26.4694	−0.844244	−0.422122	−	0.906539i	$-0.638715\pi$
$983$	−26.4694	−0.844244	−0.422122	+	0.906539i	$0.638715\pi$
$984$	10.0432	0.320164
$985$	39.4138	1.25583
$986$	−11.1990	−0.356649
$987$	−11.5066	−0.366260
$988$	3.89107	0.123792
$989$	−1.17764	−0.0374466
$990$	7.17008	0.227880
$991$	−28.1557	−0.894394	−0.447197	−	0.894435i	$-0.647578\pi$
$991$	−28.1557	−0.894394	−0.447197	+	0.894435i	$0.647578\pi$
$992$	18.0218	0.572193
$993$	−6.70773	−0.212863
$994$	4.57327	0.145055
$995$	15.6984	0.497674
$996$	−18.1111	−0.573873
$997$	2.14751	0.0680122	0.0340061	−	0.999422i	$-0.489173\pi$
$997$	2.14751	0.0680122	0.0340061	+	0.999422i	$0.489173\pi$
$998$	−21.5322	−0.681589
$999$	−8.94240	−0.282925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.l.1.12	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.l.1.12	✓	28	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-0.786373 q^{2} -1.00000 q^{3} -1.38162 q^{4} +2.33863 q^{5} +0.786373 q^{6} +1.00000 q^{7} +2.65921 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.786373 q^{2} -1.00000 q^{3} -1.38162 q^{4} +2.33863 q^{5} +0.786373 q^{6} +1.00000 q^{7} +2.65921 q^{8} +1.00000 q^{9} -1.83903 q^{10} -3.89883 q^{11} +1.38162 q^{12} -0.530472 q^{13} -0.786373 q^{14} -2.33863 q^{15} +0.672103 q^{16} +7.72460 q^{17} -0.786373 q^{18} +5.30907 q^{19} -3.23109 q^{20} -1.00000 q^{21} +3.06593 q^{22} -4.99190 q^{23} -2.65921 q^{24} +0.469176 q^{25} +0.417149 q^{26} -1.00000 q^{27} -1.38162 q^{28} +1.84363 q^{29} +1.83903 q^{30} -3.08226 q^{31} -5.84695 q^{32} +3.89883 q^{33} -6.07441 q^{34} +2.33863 q^{35} -1.38162 q^{36} +8.94240 q^{37} -4.17491 q^{38} +0.530472 q^{39} +6.21891 q^{40} -3.77674 q^{41} +0.786373 q^{42} +0.235909 q^{43} +5.38669 q^{44} +2.33863 q^{45} +3.92549 q^{46} +11.5066 q^{47} -0.672103 q^{48} +1.00000 q^{49} -0.368948 q^{50} -7.72460 q^{51} +0.732910 q^{52} +9.25430 q^{53} +0.786373 q^{54} -9.11791 q^{55} +2.65921 q^{56} -5.30907 q^{57} -1.44978 q^{58} +3.64745 q^{59} +3.23109 q^{60} -11.5437 q^{61} +2.42380 q^{62} +1.00000 q^{63} +3.25367 q^{64} -1.24058 q^{65} -3.06593 q^{66} +9.20905 q^{67} -10.6724 q^{68} +4.99190 q^{69} -1.83903 q^{70} -5.81566 q^{71} +2.65921 q^{72} -9.66677 q^{73} -7.03206 q^{74} -0.469176 q^{75} -7.33511 q^{76} -3.89883 q^{77} -0.417149 q^{78} -0.986882 q^{79} +1.57180 q^{80} +1.00000 q^{81} +2.96993 q^{82} -13.1086 q^{83} +1.38162 q^{84} +18.0650 q^{85} -0.185513 q^{86} -1.84363 q^{87} -10.3678 q^{88} +14.4964 q^{89} -1.83903 q^{90} -0.530472 q^{91} +6.89690 q^{92} +3.08226 q^{93} -9.04850 q^{94} +12.4159 q^{95} +5.84695 q^{96} +0.239447 q^{97} -0.786373 q^{98} -3.89883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

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