LMFDB - Embedded newform 2005.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0100056053$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99940 q^{2} -2.40196 q^{3} +1.99760 q^{4} +1.00000 q^{5} +4.80247 q^{6} +1.00729 q^{7} +0.00479577 q^{8} +2.76940 q^{9} +O(q^{10})$	\(q-1.99940 q^{2} -2.40196 q^{3} +1.99760 q^{4} +1.00000 q^{5} +4.80247 q^{6} +1.00729 q^{7} +0.00479577 q^{8} +2.76940 q^{9} -1.99940 q^{10} -1.98097 q^{11} -4.79815 q^{12} +0.801632 q^{13} -2.01398 q^{14} -2.40196 q^{15} -4.00479 q^{16} +3.01591 q^{17} -5.53714 q^{18} -1.16632 q^{19} +1.99760 q^{20} -2.41947 q^{21} +3.96075 q^{22} +8.05679 q^{23} -0.0115192 q^{24} +1.00000 q^{25} -1.60278 q^{26} +0.553896 q^{27} +2.01217 q^{28} +1.41643 q^{29} +4.80247 q^{30} +7.64944 q^{31} +7.99759 q^{32} +4.75820 q^{33} -6.03002 q^{34} +1.00729 q^{35} +5.53215 q^{36} +3.14108 q^{37} +2.33193 q^{38} -1.92548 q^{39} +0.00479577 q^{40} -8.52297 q^{41} +4.83749 q^{42} +2.47825 q^{43} -3.95718 q^{44} +2.76940 q^{45} -16.1088 q^{46} -7.69300 q^{47} +9.61934 q^{48} -5.98537 q^{49} -1.99940 q^{50} -7.24409 q^{51} +1.60134 q^{52} -5.27664 q^{53} -1.10746 q^{54} -1.98097 q^{55} +0.00483073 q^{56} +2.80144 q^{57} -2.83202 q^{58} -7.69925 q^{59} -4.79815 q^{60} -9.96465 q^{61} -15.2943 q^{62} +2.78959 q^{63} -7.98080 q^{64} +0.801632 q^{65} -9.51354 q^{66} +14.0201 q^{67} +6.02459 q^{68} -19.3521 q^{69} -2.01398 q^{70} +12.6393 q^{71} +0.0132814 q^{72} -9.10885 q^{73} -6.28028 q^{74} -2.40196 q^{75} -2.32984 q^{76} -1.99541 q^{77} +3.84981 q^{78} -8.81676 q^{79} -4.00479 q^{80} -9.63863 q^{81} +17.0408 q^{82} +13.1284 q^{83} -4.83313 q^{84} +3.01591 q^{85} -4.95502 q^{86} -3.40221 q^{87} -0.00950025 q^{88} +15.8321 q^{89} -5.53714 q^{90} +0.807476 q^{91} +16.0943 q^{92} -18.3736 q^{93} +15.3814 q^{94} -1.16632 q^{95} -19.2099 q^{96} -15.8435 q^{97} +11.9671 q^{98} -5.48609 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.99940	−1.41379	−0.706895	−	0.707319i	$-0.749905\pi$
$2$	−1.99940	−1.41379	−0.706895	+	0.707319i	$0.749905\pi$
$3$	−2.40196	−1.38677	−0.693385	−	0.720567i	$-0.743882\pi$
$3$	−2.40196	−1.38677	−0.693385	+	0.720567i	$0.743882\pi$
$4$	1.99760	0.998801
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.80247	1.96060
$7$	1.00729	0.380720	0.190360	−	0.981714i	$-0.439034\pi$
$7$	1.00729	0.380720	0.190360	+	0.981714i	$0.439034\pi$
$8$	0.00479577	0.00169556
$9$	2.76940	0.923133
$10$	−1.99940	−0.632266
$11$	−1.98097	−0.597284	−0.298642	−	0.954365i	$-0.596534\pi$
$11$	−1.98097	−0.597284	−0.298642	+	0.954365i	$0.596534\pi$
$12$	−4.79815	−1.38511
$13$	0.801632	0.222333	0.111166	−	0.993802i	$-0.464541\pi$
$13$	0.801632	0.222333	0.111166	+	0.993802i	$0.464541\pi$
$14$	−2.01398	−0.538258
$15$	−2.40196	−0.620183
$16$	−4.00479	−1.00120
$17$	3.01591	0.731466	0.365733	−	0.930720i	$-0.380818\pi$
$17$	3.01591	0.731466	0.365733	+	0.930720i	$0.380818\pi$
$18$	−5.53714	−1.30512
$19$	−1.16632	−0.267571	−0.133786	−	0.991010i	$-0.542713\pi$
$19$	−1.16632	−0.267571	−0.133786	+	0.991010i	$0.542713\pi$
$20$	1.99760	0.446677
$21$	−2.41947	−0.527971
$22$	3.96075	0.844434
$23$	8.05679	1.67996	0.839979	−	0.542620i	$-0.182567\pi$
$23$	8.05679	1.67996	0.839979	+	0.542620i	$0.182567\pi$
$24$	−0.0115192	−0.00235135
$25$	1.00000	0.200000
$26$	−1.60278	−0.314331
$27$	0.553896	0.106597
$28$	2.01217	0.380263
$29$	1.41643	0.263025	0.131512	−	0.991315i	$-0.458017\pi$
$29$	1.41643	0.263025	0.131512	+	0.991315i	$0.458017\pi$
$30$	4.80247	0.876808
$31$	7.64944	1.37388	0.686940	−	0.726714i	$-0.258954\pi$
$31$	7.64944	1.37388	0.686940	+	0.726714i	$0.258954\pi$
$32$	7.99759	1.41379
$33$	4.75820	0.828296
$34$	−6.03002	−1.03414
$35$	1.00729	0.170263
$36$	5.53215	0.922026
$37$	3.14108	0.516391	0.258195	−	0.966093i	$-0.416872\pi$
$37$	3.14108	0.516391	0.258195	+	0.966093i	$0.416872\pi$
$38$	2.33193	0.378290
$39$	−1.92548	−0.308324
$40$	0.00479577	0.000758277 0
$41$	−8.52297	−1.33106	−0.665532	−	0.746369i	$-0.731795\pi$
$41$	−8.52297	−1.33106	−0.665532	+	0.746369i	$0.731795\pi$
$42$	4.83749	0.746440
$43$	2.47825	0.377930	0.188965	−	0.981984i	$-0.439487\pi$
$43$	2.47825	0.377930	0.188965	+	0.981984i	$0.439487\pi$
$44$	−3.95718	−0.596568
$45$	2.76940	0.412837
$46$	−16.1088	−2.37511
$47$	−7.69300	−1.12214	−0.561070	−	0.827768i	$-0.689610\pi$
$47$	−7.69300	−1.12214	−0.561070	+	0.827768i	$0.689610\pi$
$48$	9.61934	1.38843
$49$	−5.98537	−0.855052
$50$	−1.99940	−0.282758
$51$	−7.24409	−1.01438
$52$	1.60134	0.222066
$53$	−5.27664	−0.724802	−0.362401	−	0.932022i	$-0.618043\pi$
$53$	−5.27664	−0.724802	−0.362401	+	0.932022i	$0.618043\pi$
$54$	−1.10746	−0.150706
$55$	−1.98097	−0.267113
$56$	0.00483073	0.000645533 0
$57$	2.80144	0.371060
$58$	−2.83202	−0.371862
$59$	−7.69925	−1.00236	−0.501179	−	0.865344i	$-0.667100\pi$
$59$	−7.69925	−1.00236	−0.501179	+	0.865344i	$0.667100\pi$
$60$	−4.79815	−0.619439
$61$	−9.96465	−1.27584	−0.637922	−	0.770101i	$-0.720206\pi$
$61$	−9.96465	−1.27584	−0.637922	+	0.770101i	$0.720206\pi$
$62$	−15.2943	−1.94238
$63$	2.78959	0.351455
$64$	−7.98080	−0.997600
$65$	0.801632	0.0994302
$66$	−9.51354	−1.17104
$67$	14.0201	1.71283	0.856413	−	0.516291i	$-0.172688\pi$
$67$	14.0201	1.71283	0.856413	+	0.516291i	$0.172688\pi$
$68$	6.02459	0.730589
$69$	−19.3521	−2.32972
$70$	−2.01398	−0.240716
$71$	12.6393	1.50001	0.750006	−	0.661431i	$-0.230050\pi$
$71$	12.6393	1.50001	0.750006	+	0.661431i	$0.230050\pi$
$72$	0.0132814	0.00156523
$73$	−9.10885	−1.06611	−0.533055	−	0.846080i	$-0.678956\pi$
$73$	−9.10885	−1.06611	−0.533055	+	0.846080i	$0.678956\pi$
$74$	−6.28028	−0.730067
$75$	−2.40196	−0.277354
$76$	−2.32984	−0.267250
$77$	−1.99541	−0.227398
$78$	3.84981	0.435906
$79$	−8.81676	−0.991963	−0.495982	−	0.868333i	$-0.665192\pi$
$79$	−8.81676	−0.991963	−0.495982	+	0.868333i	$0.665192\pi$
$80$	−4.00479	−0.447749
$81$	−9.63863	−1.07096
$82$	17.0408	1.88184
$83$	13.1284	1.44103	0.720517	−	0.693437i	$-0.243905\pi$
$83$	13.1284	1.44103	0.720517	+	0.693437i	$0.243905\pi$
$84$	−4.83313	−0.527338
$85$	3.01591	0.327122
$86$	−4.95502	−0.534313
$87$	−3.40221	−0.364755
$88$	−0.00950025	−0.00101273
$89$	15.8321	1.67820	0.839102	−	0.543975i	$-0.183081\pi$
$89$	15.8321	1.67820	0.839102	+	0.543975i	$0.183081\pi$
$90$	−5.53714	−0.583665
$91$	0.807476	0.0846465
$92$	16.0943	1.67794
$93$	−18.3736	−1.90526
$94$	15.3814	1.58647
$95$	−1.16632	−0.119662
$96$	−19.2099	−1.96060
$97$	−15.8435	−1.60867	−0.804333	−	0.594178i	$-0.797477\pi$
$97$	−15.8435	−1.60867	−0.804333	+	0.594178i	$0.797477\pi$
$98$	11.9671	1.20886
$99$	−5.48609	−0.551372
$100$	1.99760	0.199760
$101$	16.3481	1.62669	0.813347	−	0.581779i	$-0.197643\pi$
$101$	16.3481	1.62669	0.813347	+	0.581779i	$0.197643\pi$
$102$	14.4838	1.43411
$103$	−14.4224	−1.42108	−0.710542	−	0.703655i	$-0.751550\pi$
$103$	−14.4224	−1.42108	−0.710542	+	0.703655i	$0.751550\pi$
$104$	0.00384444	0.000376978 0
$105$	−2.41947	−0.236116
$106$	10.5501	1.02472
$107$	17.4775	1.68962	0.844808	−	0.535069i	$-0.179714\pi$
$107$	17.4775	1.68962	0.844808	+	0.535069i	$0.179714\pi$
$108$	1.10646	0.106469
$109$	13.2690	1.27094	0.635470	−	0.772125i	$-0.280806\pi$
$109$	13.2690	1.27094	0.635470	+	0.772125i	$0.280806\pi$
$110$	3.96075	0.377642
$111$	−7.54474	−0.716115
$112$	−4.03399	−0.381176
$113$	−17.2917	−1.62667	−0.813334	−	0.581796i	$-0.802350\pi$
$113$	−17.2917	−1.62667	−0.813334	+	0.581796i	$0.802350\pi$
$114$	−5.60120	−0.524601
$115$	8.05679	0.751300
$116$	2.82947	0.262710
$117$	2.22004	0.205242
$118$	15.3939	1.41712
$119$	3.03790	0.278484
$120$	−0.0115192	−0.00105156
$121$	−7.07577	−0.643252
$122$	19.9233	1.80377
$123$	20.4718	1.84588
$124$	15.2805	1.37223
$125$	1.00000	0.0894427
$126$	−5.57750	−0.496884
$127$	3.20517	0.284413	0.142206	−	0.989837i	$-0.454580\pi$
$127$	3.20517	0.284413	0.142206	+	0.989837i	$0.454580\pi$
$128$	−0.0383661	−0.00339112
$129$	−5.95265	−0.524102
$130$	−1.60278	−0.140573
$131$	−8.82198	−0.770780	−0.385390	−	0.922754i	$-0.625933\pi$
$131$	−8.82198	−0.770780	−0.385390	+	0.922754i	$0.625933\pi$
$132$	9.50498	0.827302
$133$	−1.17482	−0.101870
$134$	−28.0318	−2.42158
$135$	0.553896	0.0476718
$136$	0.0144636	0.00124024
$137$	11.6201	0.992772	0.496386	−	0.868102i	$-0.334660\pi$
$137$	11.6201	0.992772	0.496386	+	0.868102i	$0.334660\pi$
$138$	38.6925	3.29373
$139$	10.1227	0.858594	0.429297	−	0.903163i	$-0.358761\pi$
$139$	10.1227	0.858594	0.429297	+	0.903163i	$0.358761\pi$
$140$	2.01217	0.170059
$141$	18.4783	1.55615
$142$	−25.2711	−2.12070
$143$	−1.58801	−0.132796
$144$	−11.0909	−0.924238
$145$	1.41643	0.117628
$146$	18.2122	1.50726
$147$	14.3766	1.18576
$148$	6.27463	0.515771
$149$	−18.5903	−1.52297	−0.761486	−	0.648181i	$-0.775530\pi$
$149$	−18.5903	−1.52297	−0.761486	+	0.648181i	$0.775530\pi$
$150$	4.80247	0.392120
$151$	−0.196687	−0.0160062	−0.00800309	−	0.999968i	$-0.502547\pi$
$151$	−0.196687	−0.0160062	−0.00800309	+	0.999968i	$0.502547\pi$
$152$	−0.00559338	−0.000453683 0
$153$	8.35226	0.675240
$154$	3.98962	0.321493
$155$	7.64944	0.614417
$156$	−3.84635	−0.307955
$157$	2.51921	0.201055	0.100528	−	0.994934i	$-0.467947\pi$
$157$	2.51921	0.201055	0.100528	+	0.994934i	$0.467947\pi$
$158$	17.6282	1.40243
$159$	12.6743	1.00513
$160$	7.99759	0.632265
$161$	8.11553	0.639593
$162$	19.2715	1.51411
$163$	4.38140	0.343178	0.171589	−	0.985169i	$-0.445110\pi$
$163$	4.38140	0.343178	0.171589	+	0.985169i	$0.445110\pi$
$164$	−17.0255	−1.32947
$165$	4.75820	0.370425
$166$	−26.2490	−2.03732
$167$	17.5990	1.36185	0.680927	−	0.732351i	$-0.261577\pi$
$167$	17.5990	1.36185	0.680927	+	0.732351i	$0.261577\pi$
$168$	−0.0116032	−0.000895207 0
$169$	−12.3574	−0.950568
$170$	−6.03002	−0.462481
$171$	−3.22999	−0.247004
$172$	4.95056	0.377476
$173$	3.87480	0.294596	0.147298	−	0.989092i	$-0.452942\pi$
$173$	3.87480	0.294596	0.147298	+	0.989092i	$0.452942\pi$
$174$	6.80238	0.515687
$175$	1.00729	0.0761440
$176$	7.93336	0.597999
$177$	18.4933	1.39004
$178$	−31.6548	−2.37263
$179$	13.0246	0.973503	0.486751	−	0.873541i	$-0.338182\pi$
$179$	13.0246	0.973503	0.486751	+	0.873541i	$0.338182\pi$
$180$	5.53215	0.412342
$181$	8.01529	0.595772	0.297886	−	0.954601i	$-0.403719\pi$
$181$	8.01529	0.595772	0.297886	+	0.954601i	$0.403719\pi$
$182$	−1.61447	−0.119672
$183$	23.9347	1.76930
$184$	0.0386385	0.00284847
$185$	3.14108	0.230937
$186$	36.7362	2.69363
$187$	−5.97442	−0.436893
$188$	−15.3676	−1.12079
$189$	0.557934	0.0405837
$190$	2.33193	0.169176
$191$	13.2893	0.961581	0.480791	−	0.876835i	$-0.340350\pi$
$191$	13.2893	0.961581	0.480791	+	0.876835i	$0.340350\pi$
$192$	19.1695	1.38344
$193$	−4.54938	−0.327472	−0.163736	−	0.986504i	$-0.552354\pi$
$193$	−4.54938	−0.327472	−0.163736	+	0.986504i	$0.552354\pi$
$194$	31.6776	2.27432
$195$	−1.92548	−0.137887
$196$	−11.9564	−0.854027
$197$	24.3984	1.73831	0.869156	−	0.494538i	$-0.164663\pi$
$197$	24.3984	1.73831	0.869156	+	0.494538i	$0.164663\pi$
$198$	10.9689	0.779524
$199$	−1.78615	−0.126617	−0.0633083	−	0.997994i	$-0.520165\pi$
$199$	−1.78615	−0.126617	−0.0633083	+	0.997994i	$0.520165\pi$
$200$	0.00479577	0.000339112 0
$201$	−33.6757	−2.37530
$202$	−32.6863	−2.29980
$203$	1.42676	0.100139
$204$	−14.4708	−1.01316
$205$	−8.52297	−0.595270
$206$	28.8362	2.00911
$207$	22.3125	1.55082
$208$	−3.21037	−0.222599
$209$	2.31043	0.159816
$210$	4.83749	0.333818
$211$	−7.40043	−0.509467	−0.254733	−	0.967011i	$-0.581988\pi$
$211$	−7.40043	−0.509467	−0.254733	+	0.967011i	$0.581988\pi$
$212$	−10.5406	−0.723933
$213$	−30.3591	−2.08017
$214$	−34.9446	−2.38876
$215$	2.47825	0.169015
$216$	0.00265636	0.000180742 0
$217$	7.70520	0.523063
$218$	−26.5301	−1.79684
$219$	21.8791	1.47845
$220$	−3.95718	−0.266793
$221$	2.41765	0.162629
$222$	15.0850	1.01244
$223$	−9.11960	−0.610694	−0.305347	−	0.952241i	$-0.598772\pi$
$223$	−9.11960	−0.610694	−0.305347	+	0.952241i	$0.598772\pi$
$224$	8.05590	0.538257
$225$	2.76940	0.184627
$226$	34.5731	2.29977
$227$	−21.6733	−1.43851	−0.719255	−	0.694746i	$-0.755517\pi$
$227$	−21.6733	−1.43851	−0.719255	+	0.694746i	$0.755517\pi$
$228$	5.59616	0.370615
$229$	15.5908	1.03027	0.515135	−	0.857109i	$-0.327742\pi$
$229$	15.5908	1.03027	0.515135	+	0.857109i	$0.327742\pi$
$230$	−16.1088	−1.06218
$231$	4.79289	0.315349
$232$	0.00679288	0.000445974 0
$233$	27.6671	1.81253	0.906266	−	0.422708i	$-0.138920\pi$
$233$	27.6671	1.81253	0.906266	+	0.422708i	$0.138920\pi$
$234$	−4.43874	−0.290170
$235$	−7.69300	−0.501836
$236$	−15.3800	−1.00116
$237$	21.1775	1.37563
$238$	−6.07398	−0.393718
$239$	12.6751	0.819887	0.409944	−	0.912111i	$-0.365548\pi$
$239$	12.6751	0.819887	0.409944	+	0.912111i	$0.365548\pi$
$240$	9.61934	0.620926
$241$	−5.95278	−0.383452	−0.191726	−	0.981448i	$-0.561409\pi$
$241$	−5.95278	−0.383452	−0.191726	+	0.981448i	$0.561409\pi$
$242$	14.1473	0.909423
$243$	21.4899	1.37858
$244$	−19.9054	−1.27431
$245$	−5.98537	−0.382391
$246$	−40.9313	−2.60969
$247$	−0.934956	−0.0594898
$248$	0.0366849	0.00232949
$249$	−31.5340	−1.99838
$250$	−1.99940	−0.126453
$251$	−3.49837	−0.220815	−0.110408	−	0.993886i	$-0.535216\pi$
$251$	−3.49837	−0.220815	−0.110408	+	0.993886i	$0.535216\pi$
$252$	5.57249	0.351034
$253$	−15.9602	−1.00341
$254$	−6.40841	−0.402100
$255$	−7.24409	−0.453643
$256$	16.0383	1.00239
$257$	0.879432	0.0548574	0.0274287	−	0.999624i	$-0.491268\pi$
$257$	0.879432	0.0548574	0.0274287	+	0.999624i	$0.491268\pi$
$258$	11.9017	0.740970
$259$	3.16398	0.196600
$260$	1.60134	0.0993109
$261$	3.92267	0.242807
$262$	17.6387	1.08972
$263$	0.946717	0.0583771	0.0291885	−	0.999574i	$-0.490708\pi$
$263$	0.946717	0.0583771	0.0291885	+	0.999574i	$0.490708\pi$
$264$	0.0228192	0.00140442
$265$	−5.27664	−0.324141
$266$	2.34893	0.144022
$267$	−38.0281	−2.32728
$268$	28.0066	1.71077
$269$	19.6098	1.19563	0.597815	−	0.801634i	$-0.296036\pi$
$269$	19.6098	1.19563	0.597815	+	0.801634i	$0.296036\pi$
$270$	−1.10746	−0.0673979
$271$	−7.14269	−0.433887	−0.216944	−	0.976184i	$-0.569609\pi$
$271$	−7.14269	−0.433887	−0.216944	+	0.976184i	$0.569609\pi$
$272$	−12.0781	−0.732342
$273$	−1.93952	−0.117385
$274$	−23.2332	−1.40357
$275$	−1.98097	−0.119457
$276$	−38.6577	−2.32692
$277$	21.1274	1.26942	0.634711	−	0.772750i	$-0.281119\pi$
$277$	21.1274	1.26942	0.634711	+	0.772750i	$0.281119\pi$
$278$	−20.2393	−1.21387
$279$	21.1843	1.26827
$280$	0.00483073	0.000288691 0
$281$	0.409597	0.0244345	0.0122173	−	0.999925i	$-0.496111\pi$
$281$	0.409597	0.0244345	0.0122173	+	0.999925i	$0.496111\pi$
$282$	−36.9454	−2.20007
$283$	12.6373	0.751209	0.375605	−	0.926780i	$-0.377435\pi$
$283$	12.6373	0.751209	0.375605	+	0.926780i	$0.377435\pi$
$284$	25.2483	1.49821
$285$	2.80144	0.165943
$286$	3.17506	0.187745
$287$	−8.58511	−0.506763
$288$	22.1485	1.30511
$289$	−7.90427	−0.464957
$290$	−2.83202	−0.166302
$291$	38.0555	2.23085
$292$	−18.1959	−1.06483
$293$	18.7504	1.09541	0.547705	−	0.836671i	$-0.315501\pi$
$293$	18.7504	1.09541	0.547705	+	0.836671i	$0.315501\pi$
$294$	−28.7446	−1.67642
$295$	−7.69925	−0.448268
$296$	0.0150639	0.000875571 0
$297$	−1.09725	−0.0636689
$298$	37.1694	2.15316
$299$	6.45858	0.373509
$300$	−4.79815	−0.277021
$301$	2.49632	0.143885
$302$	0.393257	0.0226294
$303$	−39.2674	−2.25585
$304$	4.67085	0.267892
$305$	−9.96465	−0.570574
$306$	−16.6995	−0.954648
$307$	31.4641	1.79575	0.897874	−	0.440252i	$-0.145111\pi$
$307$	31.4641	1.79575	0.897874	+	0.440252i	$0.145111\pi$
$308$	−3.98603	−0.227125
$309$	34.6421	1.97072
$310$	−15.2943	−0.868657
$311$	12.1449	0.688676	0.344338	−	0.938846i	$-0.388103\pi$
$311$	12.1449	0.688676	0.344338	+	0.938846i	$0.388103\pi$
$312$	−0.00923417	−0.000522782 0
$313$	−5.01857	−0.283667	−0.141833	−	0.989891i	$-0.545300\pi$
$313$	−5.01857	−0.283667	−0.141833	+	0.989891i	$0.545300\pi$
$314$	−5.03692	−0.284250
$315$	2.78959	0.157176
$316$	−17.6124	−0.990773
$317$	−19.0219	−1.06837	−0.534187	−	0.845366i	$-0.679382\pi$
$317$	−19.0219	−1.06837	−0.534187	+	0.845366i	$0.679382\pi$
$318$	−25.3409	−1.42105
$319$	−2.80591	−0.157101
$320$	−7.98080	−0.446140
$321$	−41.9803	−2.34311
$322$	−16.2262	−0.904250
$323$	−3.51751	−0.195719
$324$	−19.2541	−1.06967
$325$	0.801632	0.0444665
$326$	−8.76017	−0.485181
$327$	−31.8716	−1.76250
$328$	−0.0408742	−0.00225690
$329$	−7.74909	−0.427221
$330$	−9.51354	−0.523703
$331$	3.41105	0.187488	0.0937441	−	0.995596i	$-0.470116\pi$
$331$	3.41105	0.187488	0.0937441	+	0.995596i	$0.470116\pi$
$332$	26.2254	1.43931
$333$	8.69890	0.476697
$334$	−35.1875	−1.92538
$335$	14.0201	0.765999
$336$	9.68947	0.528604
$337$	4.30341	0.234422	0.117211	−	0.993107i	$-0.462605\pi$
$337$	4.30341	0.234422	0.117211	+	0.993107i	$0.462605\pi$
$338$	24.7074	1.34390
$339$	41.5340	2.25582
$340$	6.02459	0.326729
$341$	−15.1533	−0.820596
$342$	6.45805	0.349211
$343$	−13.0800	−0.706256
$344$	0.0118851	0.000640802 0
$345$	−19.3521	−1.04188
$346$	−7.74728	−0.416496
$347$	4.85708	0.260742	0.130371	−	0.991465i	$-0.458383\pi$
$347$	4.85708	0.260742	0.130371	+	0.991465i	$0.458383\pi$
$348$	−6.79626	−0.364318
$349$	28.9734	1.55091	0.775456	−	0.631402i	$-0.217520\pi$
$349$	28.9734	1.55091	0.775456	+	0.631402i	$0.217520\pi$
$350$	−2.01398	−0.107652
$351$	0.444021	0.0237001
$352$	−15.8430	−0.844433
$353$	−19.4286	−1.03408	−0.517039	−	0.855962i	$-0.672966\pi$
$353$	−19.4286	−1.03408	−0.517039	+	0.855962i	$0.672966\pi$
$354$	−36.9755	−1.96522
$355$	12.6393	0.670826
$356$	31.6263	1.67619
$357$	−7.29691	−0.386193
$358$	−26.0413	−1.37633
$359$	18.9650	1.00094	0.500468	−	0.865755i	$-0.333161\pi$
$359$	18.9650	1.00094	0.500468	+	0.865755i	$0.333161\pi$
$360$	0.0132814	0.000699990 0
$361$	−17.6397	−0.928406
$362$	−16.0258	−0.842296
$363$	16.9957	0.892043
$364$	1.61302	0.0845450
$365$	−9.10885	−0.476779
$366$	−47.8550	−2.50142
$367$	37.4488	1.95481	0.977405	−	0.211373i	$-0.0677935\pi$
$367$	37.4488	1.95481	0.977405	+	0.211373i	$0.0677935\pi$
$368$	−32.2658	−1.68197
$369$	−23.6035	−1.22875
$370$	−6.28028	−0.326496
$371$	−5.31511	−0.275947
$372$	−36.7032	−1.90297
$373$	−21.9008	−1.13398	−0.566991	−	0.823724i	$-0.691893\pi$
$373$	−21.9008	−1.13398	−0.566991	+	0.823724i	$0.691893\pi$
$374$	11.9453	0.617675
$375$	−2.40196	−0.124037
$376$	−0.0368938	−0.00190265
$377$	1.13546	0.0584790
$378$	−1.11553	−0.0573769
$379$	12.4414	0.639072	0.319536	−	0.947574i	$-0.396473\pi$
$379$	12.4414	0.639072	0.319536	+	0.947574i	$0.396473\pi$
$380$	−2.32984	−0.119518
$381$	−7.69868	−0.394415
$382$	−26.5707	−1.35947
$383$	−16.1283	−0.824117	−0.412058	−	0.911157i	$-0.635190\pi$
$383$	−16.1283	−0.824117	−0.412058	+	0.911157i	$0.635190\pi$
$384$	0.0921537	0.00470270
$385$	−1.99541	−0.101695
$386$	9.09604	0.462976
$387$	6.86326	0.348879
$388$	−31.6491	−1.60674
$389$	39.0403	1.97942	0.989711	−	0.143082i	$-0.0457014\pi$
$389$	39.0403	1.97942	0.989711	+	0.143082i	$0.0457014\pi$
$390$	3.84981	0.194943
$391$	24.2986	1.22883
$392$	−0.0287044	−0.00144979
$393$	21.1900	1.06889
$394$	−48.7821	−2.45761
$395$	−8.81676	−0.443619
$396$	−10.9590	−0.550711
$397$	27.8804	1.39928	0.699639	−	0.714496i	$-0.253344\pi$
$397$	27.8804	1.39928	0.699639	+	0.714496i	$0.253344\pi$
$398$	3.57122	0.179009
$399$	2.82187	0.141270
$400$	−4.00479	−0.200240
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	67.3311	3.35817
$403$	6.13203	0.305458
$404$	32.6569	1.62474
$405$	−9.63863	−0.478947
$406$	−2.85266	−0.141575
$407$	−6.22238	−0.308432
$408$	−0.0347410	−0.00171993
$409$	−27.1904	−1.34448	−0.672240	−	0.740333i	$-0.734668\pi$
$409$	−27.1904	−1.34448	−0.672240	+	0.740333i	$0.734668\pi$
$410$	17.0408	0.841586
$411$	−27.9110	−1.37675
$412$	−28.8103	−1.41938
$413$	−7.75538	−0.381617
$414$	−44.6115	−2.19254
$415$	13.1284	0.644450
$416$	6.41112	0.314331
$417$	−24.3142	−1.19067
$418$	−4.61948	−0.225946
$419$	32.1156	1.56895	0.784474	−	0.620161i	$-0.212933\pi$
$419$	32.1156	1.56895	0.784474	+	0.620161i	$0.212933\pi$
$420$	−4.83313	−0.235833
$421$	−5.81138	−0.283229	−0.141615	−	0.989922i	$-0.545229\pi$
$421$	−5.81138	−0.283229	−0.141615	+	0.989922i	$0.545229\pi$
$422$	14.7964	0.720279
$423$	−21.3050	−1.03588
$424$	−0.0253055	−0.00122894
$425$	3.01591	0.146293
$426$	60.7001	2.94093
$427$	−10.0373	−0.485739
$428$	34.9131	1.68759
$429$	3.81432	0.184157
$430$	−4.95502	−0.238952
$431$	−26.8171	−1.29174	−0.645868	−	0.763449i	$-0.723504\pi$
$431$	−26.8171	−1.29174	−0.645868	+	0.763449i	$0.723504\pi$
$432$	−2.21824	−0.106725
$433$	−3.86935	−0.185949	−0.0929746	−	0.995668i	$-0.529638\pi$
$433$	−3.86935	−0.185949	−0.0929746	+	0.995668i	$0.529638\pi$
$434$	−15.4058	−0.739502
$435$	−3.40221	−0.163124
$436$	26.5062	1.26942
$437$	−9.39677	−0.449508
$438$	−43.7450	−2.09022
$439$	−40.4974	−1.93284	−0.966418	−	0.256976i	$-0.917274\pi$
$439$	−40.4974	−1.93284	−0.966418	+	0.256976i	$0.917274\pi$
$440$	−0.00950025	−0.000452907 0
$441$	−16.5759	−0.789327
$442$	−4.83385	−0.229923
$443$	−29.3410	−1.39403	−0.697016	−	0.717055i	$-0.745489\pi$
$443$	−29.3410	−1.39403	−0.697016	+	0.717055i	$0.745489\pi$
$444$	−15.0714	−0.715256
$445$	15.8321	0.750515
$446$	18.2337	0.863392
$447$	44.6530	2.11201
$448$	−8.03898	−0.379806
$449$	9.21968	0.435104	0.217552	−	0.976049i	$-0.430193\pi$
$449$	9.21968	0.435104	0.217552	+	0.976049i	$0.430193\pi$
$450$	−5.53714	−0.261023
$451$	16.8837	0.795023
$452$	−34.5420	−1.62472
$453$	0.472434	0.0221969
$454$	43.3337	2.03375
$455$	0.807476	0.0378551
$456$	0.0134351	0.000629154 0
$457$	29.5120	1.38052	0.690258	−	0.723564i	$-0.257497\pi$
$457$	29.5120	1.38052	0.690258	+	0.723564i	$0.257497\pi$
$458$	−31.1723	−1.45659
$459$	1.67050	0.0779723
$460$	16.0943	0.750399
$461$	5.48217	0.255330	0.127665	−	0.991817i	$-0.459252\pi$
$461$	5.48217	0.255330	0.127665	+	0.991817i	$0.459252\pi$
$462$	−9.58290	−0.445837
$463$	22.4179	1.04185	0.520924	−	0.853603i	$-0.325588\pi$
$463$	22.4179	1.04185	0.520924	+	0.853603i	$0.325588\pi$
$464$	−5.67252	−0.263340
$465$	−18.3736	−0.852056
$466$	−55.3176	−2.56254
$467$	12.9655	0.599970	0.299985	−	0.953944i	$-0.403018\pi$
$467$	12.9655	0.599970	0.299985	+	0.953944i	$0.403018\pi$
$468$	4.43475	0.204996
$469$	14.1223	0.652107
$470$	15.3814	0.709491
$471$	−6.05105	−0.278817
$472$	−0.0369238	−0.00169956
$473$	−4.90933	−0.225731
$474$	−42.3423	−1.94484
$475$	−1.16632	−0.0535143
$476$	6.06851	0.278150
$477$	−14.6131	−0.669088
$478$	−25.3427	−1.15915
$479$	−9.13580	−0.417425	−0.208713	−	0.977977i	$-0.566927\pi$
$479$	−9.13580	−0.417425	−0.208713	+	0.977977i	$0.566927\pi$
$480$	−19.2099	−0.876806
$481$	2.51799	0.114810
$482$	11.9020	0.542121
$483$	−19.4932	−0.886969
$484$	−14.1346	−0.642480
$485$	−15.8435	−0.719418
$486$	−42.9669	−1.94902
$487$	35.3317	1.60103	0.800516	−	0.599312i	$-0.204559\pi$
$487$	35.3317	1.60103	0.800516	+	0.599312i	$0.204559\pi$
$488$	−0.0477881	−0.00216327
$489$	−10.5239	−0.475909
$490$	11.9671	0.540620
$491$	−1.23568	−0.0557654	−0.0278827	−	0.999611i	$-0.508876\pi$
$491$	−1.23568	−0.0557654	−0.0278827	+	0.999611i	$0.508876\pi$
$492$	40.8945	1.84367
$493$	4.27184	0.192394
$494$	1.86935	0.0841061
$495$	−5.48609	−0.246581
$496$	−30.6344	−1.37553
$497$	12.7315	0.571085
$498$	63.0490	2.82529
$499$	−20.8370	−0.932794	−0.466397	−	0.884575i	$-0.654448\pi$
$499$	−20.8370	−0.932794	−0.466397	+	0.884575i	$0.654448\pi$
$500$	1.99760	0.0893355
$501$	−42.2721	−1.88858
$502$	6.99465	0.312186
$503$	27.8103	1.24000	0.620000	−	0.784602i	$-0.287133\pi$
$503$	27.8103	1.24000	0.620000	+	0.784602i	$0.287133\pi$
$504$	0.0133782	0.000595913 0
$505$	16.3481	0.727479
$506$	31.9109	1.41861
$507$	29.6819	1.31822
$508$	6.40265	0.284072
$509$	−19.4500	−0.862104	−0.431052	−	0.902327i	$-0.641857\pi$
$509$	−19.4500	−0.862104	−0.431052	+	0.902327i	$0.641857\pi$
$510$	14.4838	0.641355
$511$	−9.17526	−0.405890
$512$	−31.9903	−1.41378
$513$	−0.646018	−0.0285224
$514$	−1.75834	−0.0775569
$515$	−14.4224	−0.635528
$516$	−11.8910	−0.523473
$517$	15.2396	0.670236
$518$	−6.32606	−0.277951
$519$	−9.30711	−0.408537
$520$	0.00384444	0.000168590 0
$521$	22.4509	0.983594	0.491797	−	0.870710i	$-0.336340\pi$
$521$	22.4509	0.983594	0.491797	+	0.870710i	$0.336340\pi$
$522$	−7.84298	−0.343278
$523$	−25.7720	−1.12693	−0.563465	−	0.826140i	$-0.690532\pi$
$523$	−25.7720	−1.12693	−0.563465	+	0.826140i	$0.690532\pi$
$524$	−17.6228	−0.769855
$525$	−2.41947	−0.105594
$526$	−1.89287	−0.0825329
$527$	23.0700	1.00495
$528$	−19.0556	−0.829288
$529$	41.9119	1.82226
$530$	10.5501	0.458268
$531$	−21.3223	−0.925309
$532$	−2.34682	−0.101748
$533$	−6.83228	−0.295939
$534$	76.0334	3.29029
$535$	17.4775	0.755619
$536$	0.0672371	0.00290420
$537$	−31.2845	−1.35003
$538$	−39.2078	−1.69037
$539$	11.8568	0.510709
$540$	1.10646	0.0476146
$541$	−33.7737	−1.45204	−0.726022	−	0.687672i	$-0.758633\pi$
$541$	−33.7737	−1.45204	−0.726022	+	0.687672i	$0.758633\pi$
$542$	14.2811	0.613425
$543$	−19.2524	−0.826199
$544$	24.1200	1.03414
$545$	13.2690	0.568382
$546$	3.87788	0.165958
$547$	−33.9016	−1.44953	−0.724764	−	0.688997i	$-0.758051\pi$
$547$	−33.9016	−1.44953	−0.724764	+	0.688997i	$0.758051\pi$
$548$	23.2123	0.991582
$549$	−27.5961	−1.17777
$550$	3.96075	0.168887
$551$	−1.65201	−0.0703779
$552$	−0.0928080	−0.00395017
$553$	−8.88104	−0.377660
$554$	−42.2421	−1.79470
$555$	−7.54474	−0.320256
$556$	20.2211	0.857564
$557$	12.4523	0.527623	0.263811	−	0.964574i	$-0.415020\pi$
$557$	12.4523	0.527623	0.263811	+	0.964574i	$0.415020\pi$
$558$	−42.3560	−1.79307
$559$	1.98664	0.0840261
$560$	−4.03399	−0.170467
$561$	14.3503	0.605870
$562$	−0.818948	−0.0345453
$563$	−8.98233	−0.378560	−0.189280	−	0.981923i	$-0.560615\pi$
$563$	−8.98233	−0.378560	−0.189280	+	0.981923i	$0.560615\pi$
$564$	36.9122	1.55428
$565$	−17.2917	−0.727468
$566$	−25.2670	−1.06205
$567$	−9.70890	−0.407735
$568$	0.0606153	0.00254336
$569$	3.76363	0.157779	0.0788897	−	0.996883i	$-0.474863\pi$
$569$	3.76363	0.157779	0.0788897	+	0.996883i	$0.474863\pi$
$570$	−5.60120	−0.234609
$571$	18.5918	0.778042	0.389021	−	0.921229i	$-0.372813\pi$
$571$	18.5918	0.778042	0.389021	+	0.921229i	$0.372813\pi$
$572$	−3.17220	−0.132636
$573$	−31.9204	−1.33349
$574$	17.1651	0.716456
$575$	8.05679	0.335991
$576$	−22.1020	−0.920917
$577$	−33.6640	−1.40145	−0.700726	−	0.713430i	$-0.747141\pi$
$577$	−33.6640	−1.40145	−0.700726	+	0.713430i	$0.747141\pi$
$578$	15.8038	0.657352
$579$	10.9274	0.454128
$580$	2.82947	0.117487
$581$	13.2242	0.548631
$582$	−76.0881	−3.15395
$583$	10.4528	0.432913
$584$	−0.0436839	−0.00180765
$585$	2.22004	0.0917872
$586$	−37.4896	−1.54868
$587$	5.52875	0.228196	0.114098	−	0.993470i	$-0.463602\pi$
$587$	5.52875	0.228196	0.114098	+	0.993470i	$0.463602\pi$
$588$	28.7187	1.18434
$589$	−8.92166	−0.367611
$590$	15.3939	0.633756
$591$	−58.6038	−2.41064
$592$	−12.5794	−0.517009
$593$	28.3311	1.16342	0.581710	−	0.813396i	$-0.302384\pi$
$593$	28.3311	1.16342	0.581710	+	0.813396i	$0.302384\pi$
$594$	2.19384	0.0900144
$595$	3.03790	0.124542
$596$	−37.1359	−1.52115
$597$	4.29025	0.175588
$598$	−12.9133	−0.528063
$599$	−39.4459	−1.61172	−0.805858	−	0.592109i	$-0.798296\pi$
$599$	−39.4459	−1.61172	−0.805858	+	0.592109i	$0.798296\pi$
$600$	−0.0115192	−0.000470270 0
$601$	9.10745	0.371500	0.185750	−	0.982597i	$-0.440528\pi$
$601$	9.10745	0.371500	0.185750	+	0.982597i	$0.440528\pi$
$602$	−4.99114	−0.203424
$603$	38.8272	1.58117
$604$	−0.392903	−0.0159870
$605$	−7.07577	−0.287671
$606$	78.5112	3.18930
$607$	4.76059	0.193226	0.0966132	−	0.995322i	$-0.469199\pi$
$607$	4.76059	0.193226	0.0966132	+	0.995322i	$0.469199\pi$
$608$	−9.32772	−0.378289
$609$	−3.42702	−0.138870
$610$	19.9233	0.806672
$611$	−6.16695	−0.249488
$612$	16.6845	0.674431
$613$	12.9284	0.522173	0.261086	−	0.965315i	$-0.415919\pi$
$613$	12.9284	0.522173	0.261086	+	0.965315i	$0.415919\pi$
$614$	−62.9092	−2.53881
$615$	20.4718	0.825503
$616$	−0.00956951	−0.000385567 0
$617$	1.32889	0.0534993	0.0267496	−	0.999642i	$-0.491484\pi$
$617$	1.32889	0.0534993	0.0267496	+	0.999642i	$0.491484\pi$
$618$	−69.2633	−2.78618
$619$	36.2929	1.45873	0.729367	−	0.684123i	$-0.239815\pi$
$619$	36.2929	1.45873	0.729367	+	0.684123i	$0.239815\pi$
$620$	15.2805	0.613681
$621$	4.46262	0.179079
$622$	−24.2826	−0.973643
$623$	15.9476	0.638926
$624$	7.71116	0.308694
$625$	1.00000	0.0400000
$626$	10.0341	0.401045
$627$	−5.54956	−0.221628
$628$	5.03239	0.200814
$629$	9.47323	0.377722
$630$	−5.57750	−0.222213
$631$	−12.2378	−0.487178	−0.243589	−	0.969878i	$-0.578325\pi$
$631$	−12.2378	−0.487178	−0.243589	+	0.969878i	$0.578325\pi$
$632$	−0.0422831	−0.00168193
$633$	17.7755	0.706514
$634$	38.0323	1.51046
$635$	3.20517	0.127193
$636$	25.3181	1.00393
$637$	−4.79806	−0.190106
$638$	5.61013	0.222107
$639$	35.0033	1.38471
$640$	−0.0383661	−0.00151655
$641$	27.4133	1.08276	0.541380	−	0.840778i	$-0.317902\pi$
$641$	27.4133	1.08276	0.541380	+	0.840778i	$0.317902\pi$
$642$	83.9354	3.31266
$643$	−44.7876	−1.76625	−0.883125	−	0.469137i	$-0.844565\pi$
$643$	−44.7876	−1.76625	−0.883125	+	0.469137i	$0.844565\pi$
$644$	16.2116	0.638826
$645$	−5.95265	−0.234385
$646$	7.03291	0.276706
$647$	45.9139	1.80506	0.902531	−	0.430624i	$-0.141707\pi$
$647$	45.9139	1.80506	0.902531	+	0.430624i	$0.141707\pi$
$648$	−0.0462246	−0.00181587
$649$	15.2520	0.598692
$650$	−1.60278	−0.0628663
$651$	−18.5076	−0.725369
$652$	8.75229	0.342766
$653$	16.7524	0.655574	0.327787	−	0.944752i	$-0.393697\pi$
$653$	16.7524	0.655574	0.327787	+	0.944752i	$0.393697\pi$
$654$	63.7241	2.49181
$655$	−8.82198	−0.344703
$656$	34.1327	1.33266
$657$	−25.2260	−0.984162
$658$	15.4935	0.604001
$659$	6.84760	0.266744	0.133372	−	0.991066i	$-0.457419\pi$
$659$	6.84760	0.266744	0.133372	+	0.991066i	$0.457419\pi$
$660$	9.50498	0.369981
$661$	36.4160	1.41642	0.708210	−	0.706002i	$-0.249503\pi$
$661$	36.4160	1.41642	0.708210	+	0.706002i	$0.249503\pi$
$662$	−6.82005	−0.265069
$663$	−5.80709	−0.225529
$664$	0.0629609	0.00244336
$665$	−1.17482	−0.0455575
$666$	−17.3926	−0.673949
$667$	11.4119	0.441871
$668$	35.1559	1.36022
$669$	21.9049	0.846892
$670$	−28.0318	−1.08296
$671$	19.7396	0.762041
$672$	−19.3499	−0.746439
$673$	15.3537	0.591843	0.295922	−	0.955212i	$-0.404373\pi$
$673$	15.3537	0.591843	0.295922	+	0.955212i	$0.404373\pi$
$674$	−8.60425	−0.331423
$675$	0.553896	0.0213195
$676$	−24.6851	−0.949428
$677$	−9.03864	−0.347383	−0.173692	−	0.984800i	$-0.555570\pi$
$677$	−9.03864	−0.347383	−0.173692	+	0.984800i	$0.555570\pi$
$678$	−83.0431	−3.18925
$679$	−15.9590	−0.612452
$680$	0.0144636	0.000554654 0
$681$	52.0584	1.99488
$682$	30.2975	1.16015
$683$	−15.1459	−0.579542	−0.289771	−	0.957096i	$-0.593579\pi$
$683$	−15.1459	−0.579542	−0.289771	+	0.957096i	$0.593579\pi$
$684$	−6.45224	−0.246708
$685$	11.6201	0.443981
$686$	26.1522	0.998497
$687$	−37.4485	−1.42875
$688$	−9.92488	−0.378382
$689$	−4.22992	−0.161147
$690$	38.6925	1.47300
$691$	−13.5621	−0.515927	−0.257964	−	0.966155i	$-0.583052\pi$
$691$	−13.5621	−0.515927	−0.257964	+	0.966155i	$0.583052\pi$
$692$	7.74031	0.294242
$693$	−5.52608	−0.209918
$694$	−9.71125	−0.368634
$695$	10.1227	0.383975
$696$	−0.0163162	−0.000618464 0
$697$	−25.7045	−0.973628
$698$	−57.9295	−2.19266
$699$	−66.4552	−2.51357
$700$	2.01217	0.0760527
$701$	−9.38319	−0.354398	−0.177199	−	0.984175i	$-0.556704\pi$
$701$	−9.38319	−0.354398	−0.177199	+	0.984175i	$0.556704\pi$
$702$	−0.887775	−0.0335069
$703$	−3.66349	−0.138171
$704$	15.8097	0.595850
$705$	18.4783	0.695932
$706$	38.8455	1.46197
$707$	16.4673	0.619315
$708$	36.9422	1.38837
$709$	−4.12847	−0.155048	−0.0775241	−	0.996990i	$-0.524701\pi$
$709$	−4.12847	−0.155048	−0.0775241	+	0.996990i	$0.524701\pi$
$710$	−25.2711	−0.948407
$711$	−24.4171	−0.915714
$712$	0.0759272	0.00284549
$713$	61.6299	2.30806
$714$	14.5894	0.545996
$715$	−1.58801	−0.0593880
$716$	26.0179	0.972335
$717$	−30.4452	−1.13700
$718$	−37.9187	−1.41511
$719$	−15.2565	−0.568970	−0.284485	−	0.958681i	$-0.591823\pi$
$719$	−15.2565	−0.568970	−0.284485	+	0.958681i	$0.591823\pi$
$720$	−11.0909	−0.413332
$721$	−14.5276	−0.541035
$722$	35.2688	1.31257
$723$	14.2983	0.531761
$724$	16.0114	0.595057
$725$	1.41643	0.0526050
$726$	−33.9812	−1.26116
$727$	8.32508	0.308760	0.154380	−	0.988012i	$-0.450662\pi$
$727$	8.32508	0.308760	0.154380	+	0.988012i	$0.450662\pi$
$728$	0.00387246	0.000143523 0
$729$	−22.7019	−0.840811
$730$	18.2122	0.674065
$731$	7.47419	0.276443
$732$	47.8119	1.76718
$733$	−35.5821	−1.31426	−0.657128	−	0.753779i	$-0.728229\pi$
$733$	−35.5821	−1.31426	−0.657128	+	0.753779i	$0.728229\pi$
$734$	−74.8751	−2.76369
$735$	14.3766	0.530289
$736$	64.4349	2.37510
$737$	−27.7733	−1.02304
$738$	47.1928	1.73719
$739$	−22.1218	−0.813763	−0.406882	−	0.913481i	$-0.633384\pi$
$739$	−22.1218	−0.813763	−0.406882	+	0.913481i	$0.633384\pi$
$740$	6.27463	0.230660
$741$	2.24572	0.0824987
$742$	10.6270	0.390131
$743$	−10.1423	−0.372083	−0.186042	−	0.982542i	$-0.559566\pi$
$743$	−10.1423	−0.372083	−0.186042	+	0.982542i	$0.559566\pi$
$744$	−0.0881156	−0.00323047
$745$	−18.5903	−0.681094
$746$	43.7886	1.60321
$747$	36.3579	1.33027
$748$	−11.9345	−0.436369
$749$	17.6049	0.643271
$750$	4.80247	0.175362
$751$	−43.9965	−1.60545	−0.802727	−	0.596347i	$-0.796618\pi$
$751$	−43.9965	−1.60545	−0.802727	+	0.596347i	$0.796618\pi$
$752$	30.8089	1.12348
$753$	8.40294	0.306220
$754$	−2.27023	−0.0826770
$755$	−0.196687	−0.00715818
$756$	1.11453	0.0405351
$757$	38.8373	1.41157	0.705783	−	0.708428i	$-0.250596\pi$
$757$	38.8373	1.41157	0.705783	+	0.708428i	$0.250596\pi$
$758$	−24.8754	−0.903513
$759$	38.3358	1.39150
$760$	−0.00559338	−0.000202893 0
$761$	11.7552	0.426125	0.213063	−	0.977039i	$-0.431656\pi$
$761$	11.7552	0.426125	0.213063	+	0.977039i	$0.431656\pi$
$762$	15.3927	0.557620
$763$	13.3657	0.483872
$764$	26.5468	0.960428
$765$	8.35226	0.301977
$766$	32.2469	1.16513
$767$	−6.17196	−0.222857
$768$	−38.5233	−1.39009
$769$	−12.5343	−0.451997	−0.225998	−	0.974128i	$-0.572564\pi$
$769$	−12.5343	−0.451997	−0.225998	+	0.974128i	$0.572564\pi$
$770$	3.98962	0.143776
$771$	−2.11236	−0.0760747
$772$	−9.08785	−0.327079
$773$	−26.9775	−0.970314	−0.485157	−	0.874427i	$-0.661238\pi$
$773$	−26.9775	−0.970314	−0.485157	+	0.874427i	$0.661238\pi$
$774$	−13.7224	−0.493242
$775$	7.64944	0.274776
$776$	−0.0759818	−0.00272759
$777$	−7.59975	−0.272639
$778$	−78.0572	−2.79849
$779$	9.94048	0.356155
$780$	−3.84635	−0.137721
$781$	−25.0381	−0.895934
$782$	−48.5826	−1.73731
$783$	0.784556	0.0280378
$784$	23.9701	0.856076
$785$	2.51921	0.0899146
$786$	−42.3673	−1.51119
$787$	−16.0933	−0.573666	−0.286833	−	0.957981i	$-0.592602\pi$
$787$	−16.0933	−0.573666	−0.286833	+	0.957981i	$0.592602\pi$
$788$	48.7382	1.73623
$789$	−2.27397	−0.0809556
$790$	17.6282	0.627184
$791$	−17.4178	−0.619305
$792$	−0.0263100	−0.000934884 0
$793$	−7.98798	−0.283662
$794$	−55.7441	−1.97828
$795$	12.6743	0.449510
$796$	−3.56801	−0.126465
$797$	−13.8723	−0.491382	−0.245691	−	0.969348i	$-0.579015\pi$
$797$	−13.8723	−0.491382	−0.245691	+	0.969348i	$0.579015\pi$
$798$	−5.64204	−0.199726
$799$	−23.2014	−0.820807
$800$	7.99759	0.282757
$801$	43.8455	1.54920
$802$	1.99940	0.0706013
$803$	18.0443	0.636771
$804$	−67.2705	−2.37245
$805$	8.11553	0.286035
$806$	−12.2604	−0.431854
$807$	−47.1019	−1.65806
$808$	0.0784015	0.00275815
$809$	−36.4080	−1.28004	−0.640019	−	0.768359i	$-0.721073\pi$
$809$	−36.4080	−1.28004	−0.640019	+	0.768359i	$0.721073\pi$
$810$	19.2715	0.677131
$811$	41.0826	1.44261	0.721303	−	0.692620i	$-0.243544\pi$
$811$	41.0826	1.44261	0.721303	+	0.692620i	$0.243544\pi$
$812$	2.85010	0.100019
$813$	17.1564	0.601702
$814$	12.4410	0.436058
$815$	4.38140	0.153474
$816$	29.0111	1.01559
$817$	−2.89042	−0.101123
$818$	54.3646	1.90081
$819$	2.23622	0.0781399
$820$	−17.0255	−0.594556
$821$	46.4897	1.62250	0.811251	−	0.584698i	$-0.198787\pi$
$821$	46.4897	1.62250	0.811251	+	0.584698i	$0.198787\pi$
$822$	55.8052	1.94643
$823$	8.86957	0.309174	0.154587	−	0.987979i	$-0.450595\pi$
$823$	8.86957	0.309174	0.154587	+	0.987979i	$0.450595\pi$
$824$	−0.0691666	−0.00240953
$825$	4.75820	0.165659
$826$	15.5061	0.539527
$827$	−33.6416	−1.16983	−0.584917	−	0.811093i	$-0.698873\pi$
$827$	−33.6416	−1.16983	−0.584917	+	0.811093i	$0.698873\pi$
$828$	44.5714	1.54896
$829$	−18.9354	−0.657654	−0.328827	−	0.944390i	$-0.606653\pi$
$829$	−18.9354	−0.657654	−0.328827	+	0.944390i	$0.606653\pi$
$830$	−26.2490	−0.911117
$831$	−50.7471	−1.76040
$832$	−6.39766	−0.221799
$833$	−18.0513	−0.625442
$834$	48.6139	1.68336
$835$	17.5990	0.609040
$836$	4.61533	0.159624
$837$	4.23699	0.146452
$838$	−64.2119	−2.21816
$839$	39.8363	1.37530	0.687650	−	0.726042i	$-0.258642\pi$
$839$	39.8363	1.37530	0.687650	+	0.726042i	$0.258642\pi$
$840$	−0.0116032	−0.000400349 0
$841$	−26.9937	−0.930818
$842$	11.6193	0.400426
$843$	−0.983835	−0.0338851
$844$	−14.7831	−0.508856
$845$	−12.3574	−0.425107
$846$	42.5972	1.46452
$847$	−7.12736	−0.244899
$848$	21.1318	0.725670
$849$	−30.3542	−1.04176
$850$	−6.03002	−0.206828
$851$	25.3070	0.867514
$852$	−60.6455	−2.07768
$853$	−12.4945	−0.427803	−0.213902	−	0.976855i	$-0.568617\pi$
$853$	−12.4945	−0.427803	−0.213902	+	0.976855i	$0.568617\pi$
$854$	20.0686	0.686733
$855$	−3.22999	−0.110463
$856$	0.0838181	0.00286484
$857$	−42.4184	−1.44898	−0.724492	−	0.689283i	$-0.757926\pi$
$857$	−42.4184	−1.44898	−0.724492	+	0.689283i	$0.757926\pi$
$858$	−7.62635	−0.260359
$859$	1.34892	0.0460247	0.0230123	−	0.999735i	$-0.492674\pi$
$859$	1.34892	0.0460247	0.0230123	+	0.999735i	$0.492674\pi$
$860$	4.95056	0.168813
$861$	20.6211	0.702764
$862$	53.6182	1.82624
$863$	32.8659	1.11877	0.559385	−	0.828908i	$-0.311037\pi$
$863$	32.8659	1.11877	0.559385	+	0.828908i	$0.311037\pi$
$864$	4.42983	0.150706
$865$	3.87480	0.131747
$866$	7.73638	0.262893
$867$	18.9857	0.644789
$868$	15.3919	0.522436
$869$	17.4657	0.592484
$870$	6.80238	0.230622
$871$	11.2389	0.380817
$872$	0.0636350	0.00215495
$873$	−43.8770	−1.48501
$874$	18.7879	0.635510
$875$	1.00729	0.0340526
$876$	43.7057	1.47668
$877$	3.76388	0.127097	0.0635486	−	0.997979i	$-0.479758\pi$
$877$	3.76388	0.127097	0.0635486	+	0.997979i	$0.479758\pi$
$878$	80.9705	2.73262
$879$	−45.0377	−1.51908
$880$	7.93336	0.267433
$881$	3.27917	0.110478	0.0552390	−	0.998473i	$-0.482408\pi$
$881$	3.27917	0.110478	0.0552390	+	0.998473i	$0.482408\pi$
$882$	33.1418	1.11594
$883$	9.93301	0.334272	0.167136	−	0.985934i	$-0.446548\pi$
$883$	9.93301	0.334272	0.167136	+	0.985934i	$0.446548\pi$
$884$	4.82950	0.162434
$885$	18.4933	0.621645
$886$	58.6644	1.97087
$887$	49.6829	1.66819	0.834095	−	0.551621i	$-0.185991\pi$
$887$	49.6829	1.66819	0.834095	+	0.551621i	$0.185991\pi$
$888$	−0.0361828	−0.00121422
$889$	3.22854	0.108282
$890$	−31.6548	−1.06107
$891$	19.0938	0.639666
$892$	−18.2173	−0.609961
$893$	8.97248	0.300252
$894$	−89.2792	−2.98594
$895$	13.0246	0.435364
$896$	−0.0386458	−0.00129107
$897$	−15.5132	−0.517972
$898$	−18.4338	−0.615145
$899$	10.8349	0.361365
$900$	5.53215	0.184405
$901$	−15.9139	−0.530168
$902$	−33.7573	−1.12400
$903$	−5.99605	−0.199536
$904$	−0.0829271	−0.00275811
$905$	8.01529	0.266437
$906$	−0.944585	−0.0313817
$907$	2.09792	0.0696604	0.0348302	−	0.999393i	$-0.488911\pi$
$907$	2.09792	0.0696604	0.0348302	+	0.999393i	$0.488911\pi$
$908$	−43.2947	−1.43678
$909$	45.2743	1.50165
$910$	−1.61447	−0.0535191
$911$	−17.7853	−0.589253	−0.294627	−	0.955612i	$-0.595195\pi$
$911$	−17.7853	−0.589253	−0.294627	+	0.955612i	$0.595195\pi$
$912$	−11.2192	−0.371505
$913$	−26.0070	−0.860707
$914$	−59.0064	−1.95176
$915$	23.9347	0.791256
$916$	31.1443	1.02904
$917$	−8.88629	−0.293451
$918$	−3.34000	−0.110236
$919$	3.52655	0.116330	0.0581651	−	0.998307i	$-0.481475\pi$
$919$	3.52655	0.116330	0.0581651	+	0.998307i	$0.481475\pi$
$920$	0.0386385	0.00127387
$921$	−75.5753	−2.49029
$922$	−10.9611	−0.360983
$923$	10.1321	0.333502
$924$	9.57428	0.314971
$925$	3.14108	0.103278
$926$	−44.8223	−1.47295
$927$	−39.9414	−1.31185
$928$	11.3280	0.371861
$929$	1.77899	0.0583667	0.0291833	−	0.999574i	$-0.490709\pi$
$929$	1.77899	0.0583667	0.0291833	+	0.999574i	$0.490709\pi$
$930$	36.7362	1.20463
$931$	6.98083	0.228787
$932$	55.2678	1.81036
$933$	−29.1716	−0.955036
$934$	−25.9232	−0.848232
$935$	−5.97442	−0.195384
$936$	0.0106468	0.000348001 0
$937$	44.4951	1.45359	0.726795	−	0.686854i	$-0.241009\pi$
$937$	44.4951	1.45359	0.726795	+	0.686854i	$0.241009\pi$
$938$	−28.2361	−0.921943
$939$	12.0544	0.393381
$940$	−15.3676	−0.501234
$941$	29.9758	0.977184	0.488592	−	0.872512i	$-0.337511\pi$
$941$	29.9758	0.977184	0.488592	+	0.872512i	$0.337511\pi$
$942$	12.0985	0.394189
$943$	−68.6678	−2.23613
$944$	30.8339	1.00356
$945$	0.557934	0.0181496
$946$	9.81572	0.319137
$947$	50.5703	1.64331	0.821657	−	0.569982i	$-0.193050\pi$
$947$	50.5703	1.64331	0.821657	+	0.569982i	$0.193050\pi$
$948$	42.3042	1.37398
$949$	−7.30195	−0.237031
$950$	2.33193	0.0756579
$951$	45.6897	1.48159
$952$	0.0145691	0.000472186 0
$953$	−37.0947	−1.20162	−0.600808	−	0.799393i	$-0.705154\pi$
$953$	−37.0947	−1.20162	−0.600808	+	0.799393i	$0.705154\pi$
$954$	29.2175	0.945950
$955$	13.2893	0.430032
$956$	25.3199	0.818904
$957$	6.73967	0.217862
$958$	18.2661	0.590151
$959$	11.7048	0.377968
$960$	19.1695	0.618694
$961$	27.5139	0.887544
$962$	−5.03447	−0.162318
$963$	48.4022	1.55974
$964$	−11.8913	−0.382993
$965$	−4.54938	−0.146450
$966$	38.9746	1.25399
$967$	44.4784	1.43033	0.715164	−	0.698957i	$-0.246352\pi$
$967$	44.4784	1.43033	0.715164	+	0.698957i	$0.246352\pi$
$968$	−0.0339337	−0.00109067
$969$	8.44890	0.271418
$970$	31.6776	1.01711
$971$	−54.1500	−1.73775	−0.868877	−	0.495027i	$-0.835158\pi$
$971$	−54.1500	−1.73775	−0.868877	+	0.495027i	$0.835158\pi$
$972$	42.9282	1.37692
$973$	10.1965	0.326884
$974$	−70.6422	−2.26352
$975$	−1.92548	−0.0616649
$976$	39.9064	1.27737
$977$	−9.58596	−0.306682	−0.153341	−	0.988173i	$-0.549003\pi$
$977$	−9.58596	−0.306682	−0.153341	+	0.988173i	$0.549003\pi$
$978$	21.0416	0.672835
$979$	−31.3629	−1.00236
$980$	−11.9564	−0.381932
$981$	36.7472	1.17325
$982$	2.47062	0.0788405
$983$	12.5775	0.401160	0.200580	−	0.979677i	$-0.435717\pi$
$983$	12.5775	0.401160	0.200580	+	0.979677i	$0.435717\pi$
$984$	0.0981780	0.00312980
$985$	24.3984	0.777397
$986$	−8.54111	−0.272004
$987$	18.6130	0.592458
$988$	−1.86767	−0.0594185
$989$	19.9668	0.634906
$990$	10.9689	0.348614
$991$	30.9249	0.982361	0.491180	−	0.871058i	$-0.336566\pi$
$991$	30.9249	0.982361	0.491180	+	0.871058i	$0.336566\pi$
$992$	61.1771	1.94237
$993$	−8.19319	−0.260003
$994$	−25.4553	−0.807394
$995$	−1.78615	−0.0566247
$996$	−62.9923	−1.99599
$997$	9.82906	0.311289	0.155645	−	0.987813i	$-0.450255\pi$
$997$	9.82906	0.311289	0.155645	+	0.987813i	$0.450255\pi$
$998$	41.6616	1.31877
$999$	1.73983	0.0550459

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.g.1.6	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.g.1.6	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-1.99940 q^{2} -2.40196 q^{3} +1.99760 q^{4} +1.00000 q^{5} +4.80247 q^{6} +1.00729 q^{7} +0.00479577 q^{8} +2.76940 q^{9} +O(q^{10})\)	\(q-1.99940 q^{2} -2.40196 q^{3} +1.99760 q^{4} +1.00000 q^{5} +4.80247 q^{6} +1.00729 q^{7} +0.00479577 q^{8} +2.76940 q^{9} -1.99940 q^{10} -1.98097 q^{11} -4.79815 q^{12} +0.801632 q^{13} -2.01398 q^{14} -2.40196 q^{15} -4.00479 q^{16} +3.01591 q^{17} -5.53714 q^{18} -1.16632 q^{19} +1.99760 q^{20} -2.41947 q^{21} +3.96075 q^{22} +8.05679 q^{23} -0.0115192 q^{24} +1.00000 q^{25} -1.60278 q^{26} +0.553896 q^{27} +2.01217 q^{28} +1.41643 q^{29} +4.80247 q^{30} +7.64944 q^{31} +7.99759 q^{32} +4.75820 q^{33} -6.03002 q^{34} +1.00729 q^{35} +5.53215 q^{36} +3.14108 q^{37} +2.33193 q^{38} -1.92548 q^{39} +0.00479577 q^{40} -8.52297 q^{41} +4.83749 q^{42} +2.47825 q^{43} -3.95718 q^{44} +2.76940 q^{45} -16.1088 q^{46} -7.69300 q^{47} +9.61934 q^{48} -5.98537 q^{49} -1.99940 q^{50} -7.24409 q^{51} +1.60134 q^{52} -5.27664 q^{53} -1.10746 q^{54} -1.98097 q^{55} +0.00483073 q^{56} +2.80144 q^{57} -2.83202 q^{58} -7.69925 q^{59} -4.79815 q^{60} -9.96465 q^{61} -15.2943 q^{62} +2.78959 q^{63} -7.98080 q^{64} +0.801632 q^{65} -9.51354 q^{66} +14.0201 q^{67} +6.02459 q^{68} -19.3521 q^{69} -2.01398 q^{70} +12.6393 q^{71} +0.0132814 q^{72} -9.10885 q^{73} -6.28028 q^{74} -2.40196 q^{75} -2.32984 q^{76} -1.99541 q^{77} +3.84981 q^{78} -8.81676 q^{79} -4.00479 q^{80} -9.63863 q^{81} +17.0408 q^{82} +13.1284 q^{83} -4.83313 q^{84} +3.01591 q^{85} -4.95502 q^{86} -3.40221 q^{87} -0.00950025 q^{88} +15.8321 q^{89} -5.53714 q^{90} +0.807476 q^{91} +16.0943 q^{92} -18.3736 q^{93} +15.3814 q^{94} -1.16632 q^{95} -19.2099 q^{96} -15.8435 q^{97} +11.9671 q^{98} -5.48609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

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