LMFDB - Embedded newform 8049.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2715885869$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36016 q^{2} -1.00000 q^{3} +3.57036 q^{4} +3.05076 q^{5} +2.36016 q^{6} -4.76162 q^{7} -3.70631 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.36016 q^{2} -1.00000 q^{3} +3.57036 q^{4} +3.05076 q^{5} +2.36016 q^{6} -4.76162 q^{7} -3.70631 q^{8} +1.00000 q^{9} -7.20028 q^{10} -1.81795 q^{11} -3.57036 q^{12} -0.0708824 q^{13} +11.2382 q^{14} -3.05076 q^{15} +1.60677 q^{16} +3.98773 q^{17} -2.36016 q^{18} -6.66253 q^{19} +10.8923 q^{20} +4.76162 q^{21} +4.29066 q^{22} +5.70129 q^{23} +3.70631 q^{24} +4.30712 q^{25} +0.167294 q^{26} -1.00000 q^{27} -17.0007 q^{28} +6.44490 q^{29} +7.20028 q^{30} -5.57126 q^{31} +3.62039 q^{32} +1.81795 q^{33} -9.41170 q^{34} -14.5265 q^{35} +3.57036 q^{36} -5.77987 q^{37} +15.7247 q^{38} +0.0708824 q^{39} -11.3071 q^{40} -6.04279 q^{41} -11.2382 q^{42} -0.204505 q^{43} -6.49075 q^{44} +3.05076 q^{45} -13.4560 q^{46} +0.870317 q^{47} -1.60677 q^{48} +15.6730 q^{49} -10.1655 q^{50} -3.98773 q^{51} -0.253076 q^{52} -4.22884 q^{53} +2.36016 q^{54} -5.54613 q^{55} +17.6480 q^{56} +6.66253 q^{57} -15.2110 q^{58} +12.2472 q^{59} -10.8923 q^{60} +11.0715 q^{61} +13.1491 q^{62} -4.76162 q^{63} -11.7582 q^{64} -0.216245 q^{65} -4.29066 q^{66} -5.39399 q^{67} +14.2377 q^{68} -5.70129 q^{69} +34.2850 q^{70} -7.31279 q^{71} -3.70631 q^{72} +9.23453 q^{73} +13.6414 q^{74} -4.30712 q^{75} -23.7877 q^{76} +8.65640 q^{77} -0.167294 q^{78} +13.7293 q^{79} +4.90186 q^{80} +1.00000 q^{81} +14.2620 q^{82} -3.94626 q^{83} +17.0007 q^{84} +12.1656 q^{85} +0.482665 q^{86} -6.44490 q^{87} +6.73790 q^{88} +1.02561 q^{89} -7.20028 q^{90} +0.337515 q^{91} +20.3557 q^{92} +5.57126 q^{93} -2.05409 q^{94} -20.3258 q^{95} -3.62039 q^{96} -2.83484 q^{97} -36.9908 q^{98} -1.81795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9}+O(q^{10}) $ 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9} + 8 q^{10} - 52 q^{11} - 87 q^{12} + 35 q^{13} - 23 q^{14} + 15 q^{15} + 53 q^{16} - 19 q^{17} - 9 q^{18} - 22 q^{19} - 35 q^{20} + 10 q^{21} - q^{22} - 70 q^{23} + 27 q^{24} + 79 q^{25} - 39 q^{26} - 104 q^{27} - 9 q^{28} - 37 q^{29} - 8 q^{30} - 47 q^{31} - 53 q^{32} + 52 q^{33} - 17 q^{34} - 54 q^{35} + 87 q^{36} + 65 q^{37} - 33 q^{38} - 35 q^{39} + 14 q^{40} - 47 q^{41} + 23 q^{42} - 30 q^{43} - 122 q^{44} - 15 q^{45} - 6 q^{46} - 101 q^{47} - 53 q^{48} + 78 q^{49} - 64 q^{50} + 19 q^{51} + 41 q^{52} - 48 q^{53} + 9 q^{54} - 29 q^{55} - 71 q^{56} + 22 q^{57} - 2 q^{58} - 86 q^{59} + 35 q^{60} + 34 q^{61} - 36 q^{62} - 10 q^{63} - 15 q^{64} - 64 q^{65} + q^{66} - 38 q^{67} - 33 q^{68} + 70 q^{69} - 29 q^{70} - 176 q^{71} - 27 q^{72} + 69 q^{73} - 86 q^{74} - 79 q^{75} - 54 q^{76} - 45 q^{77} + 39 q^{78} - 101 q^{79} - 76 q^{80} + 104 q^{81} + 38 q^{82} - 67 q^{83} + 9 q^{84} + 3 q^{85} - 90 q^{86} + 37 q^{87} + 7 q^{88} - 91 q^{89} + 8 q^{90} - 47 q^{91} - 136 q^{92} + 47 q^{93} - 20 q^{94} - 130 q^{95} + 53 q^{96} + 86 q^{97} - 44 q^{98} - 52 q^{99}+O(q^{100}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9 + 8 * q^10 - 52 * q^11 - 87 * q^12 + 35 * q^13 - 23 * q^14 + 15 * q^15 + 53 * q^16 - 19 * q^17 - 9 * q^18 - 22 * q^19 - 35 * q^20 + 10 * q^21 - q^22 - 70 * q^23 + 27 * q^24 + 79 * q^25 - 39 * q^26 - 104 * q^27 - 9 * q^28 - 37 * q^29 - 8 * q^30 - 47 * q^31 - 53 * q^32 + 52 * q^33 - 17 * q^34 - 54 * q^35 + 87 * q^36 + 65 * q^37 - 33 * q^38 - 35 * q^39 + 14 * q^40 - 47 * q^41 + 23 * q^42 - 30 * q^43 - 122 * q^44 - 15 * q^45 - 6 * q^46 - 101 * q^47 - 53 * q^48 + 78 * q^49 - 64 * q^50 + 19 * q^51 + 41 * q^52 - 48 * q^53 + 9 * q^54 - 29 * q^55 - 71 * q^56 + 22 * q^57 - 2 * q^58 - 86 * q^59 + 35 * q^60 + 34 * q^61 - 36 * q^62 - 10 * q^63 - 15 * q^64 - 64 * q^65 + q^66 - 38 * q^67 - 33 * q^68 + 70 * q^69 - 29 * q^70 - 176 * q^71 - 27 * q^72 + 69 * q^73 - 86 * q^74 - 79 * q^75 - 54 * q^76 - 45 * q^77 + 39 * q^78 - 101 * q^79 - 76 * q^80 + 104 * q^81 + 38 * q^82 - 67 * q^83 + 9 * q^84 + 3 * q^85 - 90 * q^86 + 37 * q^87 + 7 * q^88 - 91 * q^89 + 8 * q^90 - 47 * q^91 - 136 * q^92 + 47 * q^93 - 20 * q^94 - 130 * q^95 + 53 * q^96 + 86 * q^97 - 44 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.36016	−1.66889	−0.834443	−	0.551094i	$-0.814211\pi$
$2$	−2.36016	−1.66889	−0.834443	+	0.551094i	$0.814211\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.57036	1.78518
$5$	3.05076	1.36434	0.682170	−	0.731194i	$-0.261036\pi$
$5$	3.05076	1.36434	0.682170	+	0.731194i	$0.261036\pi$
$6$	2.36016	0.963532
$7$	−4.76162	−1.79972	−0.899861	−	0.436176i	$-0.856332\pi$
$7$	−4.76162	−1.79972	−0.899861	+	0.436176i	$0.856332\pi$
$8$	−3.70631	−1.31038
$9$	1.00000	0.333333
$10$	−7.20028	−2.27693
$11$	−1.81795	−0.548133	−0.274067	−	0.961711i	$-0.588369\pi$
$11$	−1.81795	−0.548133	−0.274067	+	0.961711i	$0.588369\pi$
$12$	−3.57036	−1.03068
$13$	−0.0708824	−0.0196592	−0.00982962	−	0.999952i	$-0.503129\pi$
$13$	−0.0708824	−0.0196592	−0.00982962	+	0.999952i	$0.503129\pi$
$14$	11.2382	3.00353
$15$	−3.05076	−0.787702
$16$	1.60677	0.401692
$17$	3.98773	0.967167	0.483584	−	0.875298i	$-0.339335\pi$
$17$	3.98773	0.967167	0.483584	+	0.875298i	$0.339335\pi$
$18$	−2.36016	−0.556295
$19$	−6.66253	−1.52849	−0.764245	−	0.644926i	$-0.776888\pi$
$19$	−6.66253	−1.52849	−0.764245	+	0.644926i	$0.776888\pi$
$20$	10.8923	2.43559
$21$	4.76162	1.03907
$22$	4.29066	0.914772
$23$	5.70129	1.18880	0.594401	−	0.804169i	$-0.297389\pi$
$23$	5.70129	1.18880	0.594401	+	0.804169i	$0.297389\pi$
$24$	3.70631	0.756548
$25$	4.30712	0.861424
$26$	0.167294	0.0328090
$27$	−1.00000	−0.192450
$28$	−17.0007	−3.21283
$29$	6.44490	1.19679	0.598394	−	0.801202i	$-0.295806\pi$
$29$	6.44490	1.19679	0.598394	+	0.801202i	$0.295806\pi$
$30$	7.20028	1.31459
$31$	−5.57126	−1.00063	−0.500314	−	0.865844i	$-0.666782\pi$
$31$	−5.57126	−1.00063	−0.500314	+	0.865844i	$0.666782\pi$
$32$	3.62039	0.640000
$33$	1.81795	0.316465
$34$	−9.41170	−1.61409
$35$	−14.5265	−2.45543
$36$	3.57036	0.595061
$37$	−5.77987	−0.950205	−0.475102	−	0.879931i	$-0.657589\pi$
$37$	−5.77987	−0.950205	−0.475102	+	0.879931i	$0.657589\pi$
$38$	15.7247	2.55088
$39$	0.0708824	0.0113503
$40$	−11.3071	−1.78780
$41$	−6.04279	−0.943725	−0.471863	−	0.881672i	$-0.656418\pi$
$41$	−6.04279	−0.943725	−0.471863	+	0.881672i	$0.656418\pi$
$42$	−11.2382	−1.73409
$43$	−0.204505	−0.0311867	−0.0155934	−	0.999878i	$-0.504964\pi$
$43$	−0.204505	−0.0311867	−0.0155934	+	0.999878i	$0.504964\pi$
$44$	−6.49075	−0.978518
$45$	3.05076	0.454780
$46$	−13.4560	−1.98398
$47$	0.870317	0.126949	0.0634744	−	0.997983i	$-0.479782\pi$
$47$	0.870317	0.126949	0.0634744	+	0.997983i	$0.479782\pi$
$48$	−1.60677	−0.231917
$49$	15.6730	2.23900
$50$	−10.1655	−1.43762
$51$	−3.98773	−0.558394
$52$	−0.253076	−0.0350953
$53$	−4.22884	−0.580876	−0.290438	−	0.956894i	$-0.593801\pi$
$53$	−4.22884	−0.580876	−0.290438	+	0.956894i	$0.593801\pi$
$54$	2.36016	0.321177
$55$	−5.54613	−0.747840
$56$	17.6480	2.35832
$57$	6.66253	0.882474
$58$	−15.2110	−1.99730
$59$	12.2472	1.59445	0.797225	−	0.603683i	$-0.206301\pi$
$59$	12.2472	1.59445	0.797225	+	0.603683i	$0.206301\pi$
$60$	−10.8923	−1.40619
$61$	11.0715	1.41756	0.708778	−	0.705432i	$-0.249247\pi$
$61$	11.0715	1.41756	0.708778	+	0.705432i	$0.249247\pi$
$62$	13.1491	1.66993
$63$	−4.76162	−0.599907
$64$	−11.7582	−1.46978
$65$	−0.216245	−0.0268219
$66$	−4.29066	−0.528144
$67$	−5.39399	−0.658981	−0.329490	−	0.944159i	$-0.606877\pi$
$67$	−5.39399	−0.658981	−0.329490	+	0.944159i	$0.606877\pi$
$68$	14.2377	1.72657
$69$	−5.70129	−0.686355
$70$	34.2850	4.09784
$71$	−7.31279	−0.867869	−0.433934	−	0.900944i	$-0.642875\pi$
$71$	−7.31279	−0.867869	−0.433934	+	0.900944i	$0.642875\pi$
$72$	−3.70631	−0.436793
$73$	9.23453	1.08082	0.540410	−	0.841402i	$-0.318269\pi$
$73$	9.23453	1.08082	0.540410	+	0.841402i	$0.318269\pi$
$74$	13.6414	1.58578
$75$	−4.30712	−0.497343
$76$	−23.7877	−2.72863
$77$	8.65640	0.986488
$78$	−0.167294	−0.0189423
$79$	13.7293	1.54467	0.772335	−	0.635215i	$-0.219089\pi$
$79$	13.7293	1.54467	0.772335	+	0.635215i	$0.219089\pi$
$80$	4.90186	0.548045
$81$	1.00000	0.111111
$82$	14.2620	1.57497
$83$	−3.94626	−0.433158	−0.216579	−	0.976265i	$-0.569490\pi$
$83$	−3.94626	−0.433158	−0.216579	+	0.976265i	$0.569490\pi$
$84$	17.0007	1.85493
$85$	12.1656	1.31955
$86$	0.482665	0.0520471
$87$	−6.44490	−0.690966
$88$	6.73790	0.718263
$89$	1.02561	0.108714	0.0543570	−	0.998522i	$-0.482689\pi$
$89$	1.02561	0.108714	0.0543570	+	0.998522i	$0.482689\pi$
$90$	−7.20028	−0.758976
$91$	0.337515	0.0353812
$92$	20.3557	2.12223
$93$	5.57126	0.577712
$94$	−2.05409	−0.211863
$95$	−20.3258	−2.08538
$96$	−3.62039	−0.369504
$97$	−2.83484	−0.287835	−0.143917	−	0.989590i	$-0.545970\pi$
$97$	−2.83484	−0.287835	−0.143917	+	0.989590i	$0.545970\pi$
$98$	−36.9908	−3.73664
$99$	−1.81795	−0.182711
$100$	15.3780	1.53780
$101$	−2.54104	−0.252843	−0.126421	−	0.991977i	$-0.540349\pi$
$101$	−2.54104	−0.252843	−0.126421	+	0.991977i	$0.540349\pi$
$102$	9.41170	0.931897
$103$	7.60992	0.749828	0.374914	−	0.927060i	$-0.377672\pi$
$103$	7.60992	0.749828	0.374914	+	0.927060i	$0.377672\pi$
$104$	0.262712	0.0257611
$105$	14.5265	1.41765
$106$	9.98074	0.969415
$107$	15.7542	1.52302	0.761508	−	0.648156i	$-0.224459\pi$
$107$	15.7542	1.52302	0.761508	+	0.648156i	$0.224459\pi$
$108$	−3.57036	−0.343558
$109$	−2.30382	−0.220666	−0.110333	−	0.993895i	$-0.535192\pi$
$109$	−2.30382	−0.220666	−0.110333	+	0.993895i	$0.535192\pi$
$110$	13.0898	1.24806
$111$	5.77987	0.548601
$112$	−7.65082	−0.722935
$113$	−3.42778	−0.322458	−0.161229	−	0.986917i	$-0.551546\pi$
$113$	−3.42778	−0.322458	−0.161229	+	0.986917i	$0.551546\pi$
$114$	−15.7247	−1.47275
$115$	17.3933	1.62193
$116$	23.0106	2.13649
$117$	−0.0708824	−0.00655308
$118$	−28.9054	−2.66096
$119$	−18.9881	−1.74063
$120$	11.3071	1.03219
$121$	−7.69505	−0.699550
$122$	−26.1304	−2.36574
$123$	6.04279	0.544860
$124$	−19.8914	−1.78630
$125$	−2.11382	−0.189065
$126$	11.2382	1.00118
$127$	5.09403	0.452022	0.226011	−	0.974125i	$-0.427431\pi$
$127$	5.09403	0.452022	0.226011	+	0.974125i	$0.427431\pi$
$128$	20.5106	1.81290
$129$	0.204505	0.0180057
$130$	0.510373	0.0447627
$131$	−7.43967	−0.650007	−0.325003	−	0.945713i	$-0.605365\pi$
$131$	−7.43967	−0.650007	−0.325003	+	0.945713i	$0.605365\pi$
$132$	6.49075	0.564947
$133$	31.7244	2.75086
$134$	12.7307	1.09976
$135$	−3.05076	−0.262567
$136$	−14.7798	−1.26736
$137$	10.2638	0.876896	0.438448	−	0.898756i	$-0.355528\pi$
$137$	10.2638	0.876896	0.438448	+	0.898756i	$0.355528\pi$
$138$	13.4560	1.14545
$139$	−16.0837	−1.36420	−0.682100	−	0.731258i	$-0.738933\pi$
$139$	−16.0837	−1.36420	−0.682100	+	0.731258i	$0.738933\pi$
$140$	−51.8650	−4.38340
$141$	−0.870317	−0.0732940
$142$	17.2594	1.44837
$143$	0.128861	0.0107759
$144$	1.60677	0.133897
$145$	19.6618	1.63283
$146$	−21.7950	−1.80377
$147$	−15.6730	−1.29269
$148$	−20.6362	−1.69629
$149$	18.1251	1.48487	0.742433	−	0.669921i	$-0.233672\pi$
$149$	18.1251	1.48487	0.742433	+	0.669921i	$0.233672\pi$
$150$	10.1655	0.830009
$151$	−11.4018	−0.927867	−0.463934	−	0.885870i	$-0.653562\pi$
$151$	−11.4018	−0.927867	−0.463934	+	0.885870i	$0.653562\pi$
$152$	24.6934	2.00290
$153$	3.98773	0.322389
$154$	−20.4305	−1.64634
$155$	−16.9965	−1.36520
$156$	0.253076	0.0202623
$157$	2.86574	0.228711	0.114356	−	0.993440i	$-0.463520\pi$
$157$	2.86574	0.228711	0.114356	+	0.993440i	$0.463520\pi$
$158$	−32.4034	−2.57788
$159$	4.22884	0.335369
$160$	11.0449	0.873178
$161$	−27.1474	−2.13951
$162$	−2.36016	−0.185432
$163$	−5.15364	−0.403664	−0.201832	−	0.979420i	$-0.564690\pi$
$163$	−5.15364	−0.403664	−0.201832	+	0.979420i	$0.564690\pi$
$164$	−21.5750	−1.68472
$165$	5.54613	0.431766
$166$	9.31381	0.722892
$167$	11.1208	0.860553	0.430277	−	0.902697i	$-0.358416\pi$
$167$	11.1208	0.860553	0.430277	+	0.902697i	$0.358416\pi$
$168$	−17.6480	−1.36158
$169$	−12.9950	−0.999614
$170$	−28.7128	−2.20217
$171$	−6.66253	−0.509497
$172$	−0.730157	−0.0556740
$173$	−16.0098	−1.21720	−0.608600	−	0.793477i	$-0.708269\pi$
$173$	−16.0098	−1.21720	−0.608600	+	0.793477i	$0.708269\pi$
$174$	15.2110	1.15314
$175$	−20.5088	−1.55032
$176$	−2.92103	−0.220181
$177$	−12.2472	−0.920556
$178$	−2.42059	−0.181431
$179$	−15.7497	−1.17719	−0.588594	−	0.808429i	$-0.700318\pi$
$179$	−15.7497	−1.17719	−0.588594	+	0.808429i	$0.700318\pi$
$180$	10.8923	0.811865
$181$	−10.5809	−0.786471	−0.393235	−	0.919438i	$-0.628644\pi$
$181$	−10.5809	−0.786471	−0.393235	+	0.919438i	$0.628644\pi$
$182$	−0.796590	−0.0590472
$183$	−11.0715	−0.818426
$184$	−21.1308	−1.55778
$185$	−17.6330	−1.29640
$186$	−13.1491	−0.964136
$187$	−7.24951	−0.530137
$188$	3.10735	0.226627
$189$	4.76162	0.346357
$190$	47.9721	3.48026
$191$	6.04355	0.437296	0.218648	−	0.975804i	$-0.429835\pi$
$191$	6.04355	0.437296	0.218648	+	0.975804i	$0.429835\pi$
$192$	11.7582	0.848578
$193$	3.30634	0.237996	0.118998	−	0.992895i	$-0.462032\pi$
$193$	3.30634	0.237996	0.118998	+	0.992895i	$0.462032\pi$
$194$	6.69069	0.480363
$195$	0.216245	0.0154856
$196$	55.9583	3.99702
$197$	−5.01820	−0.357532	−0.178766	−	0.983892i	$-0.557211\pi$
$197$	−5.01820	−0.357532	−0.178766	+	0.983892i	$0.557211\pi$
$198$	4.29066	0.304924
$199$	−25.8697	−1.83385	−0.916926	−	0.399057i	$-0.869337\pi$
$199$	−25.8697	−1.83385	−0.916926	+	0.399057i	$0.869337\pi$
$200$	−15.9635	−1.12879
$201$	5.39399	0.380463
$202$	5.99726	0.421966
$203$	−30.6882	−2.15389
$204$	−14.2377	−0.996835
$205$	−18.4351	−1.28756
$206$	−17.9606	−1.25138
$207$	5.70129	0.396267
$208$	−0.113892	−0.00789697
$209$	12.1122	0.837816
$210$	−34.2850	−2.36589
$211$	−2.31429	−0.159322	−0.0796611	−	0.996822i	$-0.525384\pi$
$211$	−2.31429	−0.159322	−0.0796611	+	0.996822i	$0.525384\pi$
$212$	−15.0985	−1.03697
$213$	7.31279	0.501064
$214$	−37.1824	−2.54174
$215$	−0.623895	−0.0425493
$216$	3.70631	0.252183
$217$	26.5282	1.80085
$218$	5.43739	0.368266
$219$	−9.23453	−0.624011
$220$	−19.8017	−1.33503
$221$	−0.282660	−0.0190138
$222$	−13.6414	−0.915553
$223$	22.9304	1.53553	0.767767	−	0.640729i	$-0.221368\pi$
$223$	22.9304	1.53553	0.767767	+	0.640729i	$0.221368\pi$
$224$	−17.2389	−1.15182
$225$	4.30712	0.287141
$226$	8.09012	0.538147
$227$	2.88389	0.191410	0.0957052	−	0.995410i	$-0.469489\pi$
$227$	2.88389	0.191410	0.0957052	+	0.995410i	$0.469489\pi$
$228$	23.7877	1.57538
$229$	−13.5809	−0.897448	−0.448724	−	0.893670i	$-0.648121\pi$
$229$	−13.5809	−0.897448	−0.448724	+	0.893670i	$0.648121\pi$
$230$	−41.0509	−2.70682
$231$	−8.65640	−0.569549
$232$	−23.8868	−1.56825
$233$	−2.38106	−0.155988	−0.0779941	−	0.996954i	$-0.524852\pi$
$233$	−2.38106	−0.155988	−0.0779941	+	0.996954i	$0.524852\pi$
$234$	0.167294	0.0109363
$235$	2.65513	0.173201
$236$	43.7270	2.84638
$237$	−13.7293	−0.891816
$238$	44.8149	2.90492
$239$	6.72695	0.435130	0.217565	−	0.976046i	$-0.430189\pi$
$239$	6.72695	0.435130	0.217565	+	0.976046i	$0.430189\pi$
$240$	−4.90186	−0.316414
$241$	26.0456	1.67774	0.838872	−	0.544328i	$-0.183215\pi$
$241$	26.0456	1.67774	0.838872	+	0.544328i	$0.183215\pi$
$242$	18.1616	1.16747
$243$	−1.00000	−0.0641500
$244$	39.5291	2.53059
$245$	47.8145	3.05476
$246$	−14.2620	−0.909309
$247$	0.472256	0.0300490
$248$	20.6488	1.31120
$249$	3.94626	0.250084
$250$	4.98895	0.315529
$251$	−3.30532	−0.208630	−0.104315	−	0.994544i	$-0.533265\pi$
$251$	−3.30532	−0.208630	−0.104315	+	0.994544i	$0.533265\pi$
$252$	−17.0007	−1.07094
$253$	−10.3647	−0.651622
$254$	−12.0227	−0.754373
$255$	−12.1656	−0.761840
$256$	−24.8918	−1.55574
$257$	3.58963	0.223915	0.111958	−	0.993713i	$-0.464288\pi$
$257$	3.58963	0.223915	0.111958	+	0.993713i	$0.464288\pi$
$258$	−0.482665	−0.0300494
$259$	27.5215	1.71010
$260$	−0.772073	−0.0478820
$261$	6.44490	0.398930
$262$	17.5588	1.08479
$263$	13.1787	0.812633	0.406316	−	0.913732i	$-0.366813\pi$
$263$	13.1787	0.812633	0.406316	+	0.913732i	$0.366813\pi$
$264$	−6.73790	−0.414689
$265$	−12.9012	−0.792512
$266$	−74.8748	−4.59087
$267$	−1.02561	−0.0627660
$268$	−19.2585	−1.17640
$269$	1.60177	0.0976619	0.0488309	−	0.998807i	$-0.484450\pi$
$269$	1.60177	0.0976619	0.0488309	+	0.998807i	$0.484450\pi$
$270$	7.20028	0.438195
$271$	−16.8143	−1.02140	−0.510699	−	0.859759i	$-0.670613\pi$
$271$	−16.8143	−1.02140	−0.510699	+	0.859759i	$0.670613\pi$
$272$	6.40737	0.388504
$273$	−0.337515	−0.0204273
$274$	−24.2242	−1.46344
$275$	−7.83014	−0.472175
$276$	−20.3557	−1.22527
$277$	12.6390	0.759405	0.379702	−	0.925109i	$-0.376026\pi$
$277$	12.6390	0.759405	0.379702	+	0.925109i	$0.376026\pi$
$278$	37.9601	2.27670
$279$	−5.57126	−0.333542
$280$	53.8399	3.21755
$281$	7.67751	0.458002	0.229001	−	0.973426i	$-0.426454\pi$
$281$	7.67751	0.458002	0.229001	+	0.973426i	$0.426454\pi$
$282$	2.05409	0.122319
$283$	−6.89707	−0.409988	−0.204994	−	0.978763i	$-0.565718\pi$
$283$	−6.89707	−0.409988	−0.204994	+	0.978763i	$0.565718\pi$
$284$	−26.1093	−1.54930
$285$	20.3258	1.20399
$286$	−0.304132	−0.0179837
$287$	28.7735	1.69844
$288$	3.62039	0.213333
$289$	−1.09798	−0.0645873
$290$	−46.4051	−2.72500
$291$	2.83484	0.166181
$292$	32.9706	1.92946
$293$	−5.79072	−0.338298	−0.169149	−	0.985591i	$-0.554102\pi$
$293$	−5.79072	−0.338298	−0.169149	+	0.985591i	$0.554102\pi$
$294$	36.9908	2.15735
$295$	37.3632	2.17537
$296$	21.4220	1.24513
$297$	1.81795	0.105488
$298$	−42.7781	−2.47807
$299$	−0.404121	−0.0233709
$300$	−15.3780	−0.887848
$301$	0.973775	0.0561274
$302$	26.9102	1.54851
$303$	2.54104	0.145979
$304$	−10.7052	−0.613983
$305$	33.7763	1.93403
$306$	−9.41170	−0.538031
$307$	30.2251	1.72504	0.862518	−	0.506026i	$-0.168886\pi$
$307$	30.2251	1.72504	0.862518	+	0.506026i	$0.168886\pi$
$308$	30.9065	1.76106
$309$	−7.60992	−0.432913
$310$	40.1146	2.27836
$311$	−28.0693	−1.59167	−0.795833	−	0.605516i	$-0.792967\pi$
$311$	−28.0693	−1.59167	−0.795833	+	0.605516i	$0.792967\pi$
$312$	−0.262712	−0.0148732
$313$	−27.5121	−1.55508	−0.777538	−	0.628836i	$-0.783532\pi$
$313$	−27.5121	−1.55508	−0.777538	+	0.628836i	$0.783532\pi$
$314$	−6.76362	−0.381693
$315$	−14.5265	−0.818478
$316$	49.0187	2.75752
$317$	−11.4280	−0.641859	−0.320930	−	0.947103i	$-0.603995\pi$
$317$	−11.4280	−0.641859	−0.320930	+	0.947103i	$0.603995\pi$
$318$	−9.98074	−0.559692
$319$	−11.7165	−0.656000
$320$	−35.8715	−2.00528
$321$	−15.7542	−0.879313
$322$	64.0722	3.57061
$323$	−26.5684	−1.47831
$324$	3.57036	0.198354
$325$	−0.305299	−0.0169349
$326$	12.1634	0.673669
$327$	2.30382	0.127402
$328$	22.3965	1.23664
$329$	−4.14412	−0.228473
$330$	−13.0898	−0.720568
$331$	−29.9513	−1.64627	−0.823136	−	0.567844i	$-0.807778\pi$
$331$	−29.9513	−1.64627	−0.823136	+	0.567844i	$0.807778\pi$
$332$	−14.0896	−0.773266
$333$	−5.77987	−0.316735
$334$	−26.2469	−1.43617
$335$	−16.4558	−0.899074
$336$	7.65082	0.417387
$337$	−21.3339	−1.16213	−0.581067	−	0.813856i	$-0.697364\pi$
$337$	−21.3339	−1.16213	−0.581067	+	0.813856i	$0.697364\pi$
$338$	30.6702	1.66824
$339$	3.42778	0.186171
$340$	43.4356	2.35563
$341$	10.1283	0.548477
$342$	15.7247	0.850292
$343$	−41.2975	−2.22986
$344$	0.757959	0.0408664
$345$	−17.3933	−0.936422
$346$	37.7856	2.03137
$347$	21.3326	1.14520	0.572598	−	0.819837i	$-0.305936\pi$
$347$	21.3326	1.14520	0.572598	+	0.819837i	$0.305936\pi$
$348$	−23.0106	−1.23350
$349$	34.8012	1.86287	0.931434	−	0.363911i	$-0.118559\pi$
$349$	34.8012	1.86287	0.931434	+	0.363911i	$0.118559\pi$
$350$	48.4042	2.58731
$351$	0.0708824	0.00378342
$352$	−6.58169	−0.350806
$353$	−25.6064	−1.36289	−0.681446	−	0.731869i	$-0.738648\pi$
$353$	−25.6064	−1.36289	−0.681446	+	0.731869i	$0.738648\pi$
$354$	28.9054	1.53630
$355$	−22.3096	−1.18407
$356$	3.66178	0.194074
$357$	18.9881	1.00495
$358$	37.1718	1.96459
$359$	−26.8041	−1.41467	−0.707334	−	0.706879i	$-0.750103\pi$
$359$	−26.8041	−1.41467	−0.707334	+	0.706879i	$0.750103\pi$
$360$	−11.3071	−0.595934
$361$	25.3894	1.33628
$362$	24.9726	1.31253
$363$	7.69505	0.403885
$364$	1.20505	0.0631618
$365$	28.1723	1.47461
$366$	26.1304	1.36586
$367$	−15.3131	−0.799337	−0.399668	−	0.916660i	$-0.630875\pi$
$367$	−15.3131	−0.799337	−0.399668	+	0.916660i	$0.630875\pi$
$368$	9.16067	0.477533
$369$	−6.04279	−0.314575
$370$	41.6167	2.16355
$371$	20.1361	1.04541
$372$	19.8914	1.03132
$373$	32.1645	1.66542	0.832708	−	0.553712i	$-0.186789\pi$
$373$	32.1645	1.66542	0.832708	+	0.553712i	$0.186789\pi$
$374$	17.1100	0.884738
$375$	2.11382	0.109157
$376$	−3.22567	−0.166351
$377$	−0.456830	−0.0235280
$378$	−11.2382	−0.578030
$379$	10.4171	0.535088	0.267544	−	0.963546i	$-0.413788\pi$
$379$	10.4171	0.535088	0.267544	+	0.963546i	$0.413788\pi$
$380$	−72.5704	−3.72278
$381$	−5.09403	−0.260975
$382$	−14.2638	−0.729798
$383$	−11.4074	−0.582892	−0.291446	−	0.956587i	$-0.594136\pi$
$383$	−11.4074	−0.582892	−0.291446	+	0.956587i	$0.594136\pi$
$384$	−20.5106	−1.04668
$385$	26.4086	1.34590
$386$	−7.80350	−0.397188
$387$	−0.204505	−0.0103956
$388$	−10.1214	−0.513837
$389$	−26.3674	−1.33688	−0.668440	−	0.743766i	$-0.733038\pi$
$389$	−26.3674	−1.33688	−0.668440	+	0.743766i	$0.733038\pi$
$390$	−0.510373	−0.0258438
$391$	22.7352	1.14977
$392$	−58.0891	−2.93394
$393$	7.43967	0.375282
$394$	11.8438	0.596681
$395$	41.8848	2.10745
$396$	−6.49075	−0.326173
$397$	29.3960	1.47534	0.737671	−	0.675160i	$-0.235926\pi$
$397$	29.3960	1.47534	0.737671	+	0.675160i	$0.235926\pi$
$398$	61.0566	3.06049
$399$	−31.7244	−1.58821
$400$	6.92055	0.346027
$401$	−21.2818	−1.06276	−0.531381	−	0.847133i	$-0.678327\pi$
$401$	−21.2818	−1.06276	−0.531381	+	0.847133i	$0.678327\pi$
$402$	−12.7307	−0.634949
$403$	0.394904	0.0196716
$404$	−9.07243	−0.451370
$405$	3.05076	0.151593
$406$	72.4290	3.59459
$407$	10.5075	0.520839
$408$	14.7798	0.731708
$409$	1.77553	0.0877942	0.0438971	−	0.999036i	$-0.486023\pi$
$409$	1.77553	0.0877942	0.0438971	+	0.999036i	$0.486023\pi$
$410$	43.5098	2.14879
$411$	−10.2638	−0.506276
$412$	27.1702	1.33858
$413$	−58.3165	−2.86957
$414$	−13.4560	−0.661325
$415$	−12.0391	−0.590975
$416$	−0.256622	−0.0125819
$417$	16.0837	0.787622
$418$	−28.5867	−1.39822
$419$	−25.2330	−1.23271	−0.616357	−	0.787467i	$-0.711392\pi$
$419$	−25.2330	−1.23271	−0.616357	+	0.787467i	$0.711392\pi$
$420$	51.8650	2.53075
$421$	−2.05479	−0.100144	−0.0500721	−	0.998746i	$-0.515945\pi$
$421$	−2.05479	−0.100144	−0.0500721	+	0.998746i	$0.515945\pi$
$422$	5.46210	0.265891
$423$	0.870317	0.0423163
$424$	15.6734	0.761167
$425$	17.1756	0.833141
$426$	−17.2594	−0.836219
$427$	−52.7181	−2.55121
$428$	56.2482	2.71886
$429$	−0.128861	−0.00622146
$430$	1.47249	0.0710099
$431$	−31.2100	−1.50333	−0.751667	−	0.659543i	$-0.770750\pi$
$431$	−31.2100	−1.50333	−0.751667	+	0.659543i	$0.770750\pi$
$432$	−1.60677	−0.0773058
$433$	34.7379	1.66940	0.834698	−	0.550708i	$-0.185642\pi$
$433$	34.7379	1.66940	0.834698	+	0.550708i	$0.185642\pi$
$434$	−62.6108	−3.00542
$435$	−19.6618	−0.942713
$436$	−8.22548	−0.393929
$437$	−37.9851	−1.81707
$438$	21.7950	1.04140
$439$	6.87893	0.328313	0.164157	−	0.986434i	$-0.447510\pi$
$439$	6.87893	0.328313	0.164157	+	0.986434i	$0.447510\pi$
$440$	20.5557	0.979954
$441$	15.6730	0.746334
$442$	0.667124	0.0317318
$443$	34.9560	1.66081	0.830405	−	0.557160i	$-0.188109\pi$
$443$	34.9560	1.66081	0.830405	+	0.557160i	$0.188109\pi$
$444$	20.6362	0.979353
$445$	3.12887	0.148323
$446$	−54.1195	−2.56263
$447$	−18.1251	−0.857287
$448$	55.9883	2.64520
$449$	12.2849	0.579762	0.289881	−	0.957063i	$-0.406384\pi$
$449$	12.2849	0.579762	0.289881	+	0.957063i	$0.406384\pi$
$450$	−10.1655	−0.479206
$451$	10.9855	0.517287
$452$	−12.2384	−0.575647
$453$	11.4018	0.535704
$454$	−6.80644	−0.319442
$455$	1.02968	0.0482720
$456$	−24.6934	−1.15638
$457$	−31.8263	−1.48877	−0.744386	−	0.667750i	$-0.767258\pi$
$457$	−31.8263	−1.48877	−0.744386	+	0.667750i	$0.767258\pi$
$458$	32.0530	1.49774
$459$	−3.98773	−0.186131
$460$	62.1003	2.89544
$461$	7.10430	0.330880	0.165440	−	0.986220i	$-0.447096\pi$
$461$	7.10430	0.330880	0.165440	+	0.986220i	$0.447096\pi$
$462$	20.4305	0.950513
$463$	−26.8265	−1.24673	−0.623366	−	0.781930i	$-0.714235\pi$
$463$	−26.8265	−1.24673	−0.623366	+	0.781930i	$0.714235\pi$
$464$	10.3555	0.480741
$465$	16.9965	0.788196
$466$	5.61968	0.260327
$467$	16.0699	0.743628	0.371814	−	0.928307i	$-0.378736\pi$
$467$	16.0699	0.743628	0.371814	+	0.928307i	$0.378736\pi$
$468$	−0.253076	−0.0116984
$469$	25.6841	1.18598
$470$	−6.26653	−0.289053
$471$	−2.86574	−0.132047
$472$	−45.3919	−2.08933
$473$	0.371780	0.0170945
$474$	32.4034	1.48834
$475$	−28.6963	−1.31668
$476$	−67.7943	−3.10735
$477$	−4.22884	−0.193625
$478$	−15.8767	−0.726183
$479$	28.3736	1.29642	0.648212	−	0.761460i	$-0.275517\pi$
$479$	28.3736	1.29642	0.648212	+	0.761460i	$0.275517\pi$
$480$	−11.0449	−0.504130
$481$	0.409691	0.0186803
$482$	−61.4718	−2.79997
$483$	27.1474	1.23525
$484$	−27.4741	−1.24882
$485$	−8.64841	−0.392704
$486$	2.36016	0.107059
$487$	2.96871	0.134525	0.0672625	−	0.997735i	$-0.478574\pi$
$487$	2.96871	0.134525	0.0672625	+	0.997735i	$0.478574\pi$
$488$	−41.0343	−1.85754
$489$	5.15364	0.233056
$490$	−112.850	−5.09804
$491$	23.4314	1.05744	0.528722	−	0.848795i	$-0.322671\pi$
$491$	23.4314	1.05744	0.528722	+	0.848795i	$0.322671\pi$
$492$	21.5750	0.972674
$493$	25.7006	1.15749
$494$	−1.11460	−0.0501483
$495$	−5.54613	−0.249280
$496$	−8.95173	−0.401944
$497$	34.8207	1.56192
$498$	−9.31381	−0.417362
$499$	27.2540	1.22006	0.610029	−	0.792379i	$-0.291158\pi$
$499$	27.2540	1.22006	0.610029	+	0.792379i	$0.291158\pi$
$500$	−7.54709	−0.337516
$501$	−11.1208	−0.496841
$502$	7.80108	0.348179
$503$	11.2439	0.501342	0.250671	−	0.968072i	$-0.419349\pi$
$503$	11.2439	0.501342	0.250671	+	0.968072i	$0.419349\pi$
$504$	17.6480	0.786106
$505$	−7.75209	−0.344964
$506$	24.4623	1.08748
$507$	12.9950	0.577127
$508$	18.1875	0.806941
$509$	2.64560	0.117264	0.0586321	−	0.998280i	$-0.481326\pi$
$509$	2.64560	0.117264	0.0586321	+	0.998280i	$0.481326\pi$
$510$	28.7128	1.27142
$511$	−43.9713	−1.94518
$512$	17.7275	0.783453
$513$	6.66253	0.294158
$514$	−8.47211	−0.373689
$515$	23.2160	1.02302
$516$	0.730157	0.0321434
$517$	−1.58220	−0.0695849
$518$	−64.9553	−2.85397
$519$	16.0098	0.702751
$520$	0.801472	0.0351469
$521$	45.3176	1.98540	0.992701	−	0.120601i	$-0.0384822\pi$
$521$	45.3176	1.98540	0.992701	+	0.120601i	$0.0384822\pi$
$522$	−15.2110	−0.665768
$523$	8.66370	0.378837	0.189418	−	0.981896i	$-0.439340\pi$
$523$	8.66370	0.378837	0.189418	+	0.981896i	$0.439340\pi$
$524$	−26.5623	−1.16038
$525$	20.5088	0.895080
$526$	−31.1038	−1.35619
$527$	−22.2167	−0.967774
$528$	2.92103	0.127122
$529$	9.50475	0.413250
$530$	30.4488	1.32261
$531$	12.2472	0.531483
$532$	113.268	4.91078
$533$	0.428327	0.0185529
$534$	2.42059	0.104749
$535$	48.0622	2.07791
$536$	19.9918	0.863515
$537$	15.7497	0.679650
$538$	−3.78045	−0.162987
$539$	−28.4928	−1.22727
$540$	−10.8923	−0.468730
$541$	−2.17364	−0.0934520	−0.0467260	−	0.998908i	$-0.514879\pi$
$541$	−2.17364	−0.0934520	−0.0467260	+	0.998908i	$0.514879\pi$
$542$	39.6846	1.70460
$543$	10.5809	0.454069
$544$	14.4371	0.618987
$545$	−7.02839	−0.301063
$546$	0.796590	0.0340909
$547$	−32.4437	−1.38719	−0.693596	−	0.720364i	$-0.743975\pi$
$547$	−32.4437	−1.38719	−0.693596	+	0.720364i	$0.743975\pi$
$548$	36.6455	1.56542
$549$	11.0715	0.472518
$550$	18.4804	0.788006
$551$	−42.9394	−1.82928
$552$	21.1308	0.899386
$553$	−65.3738	−2.77998
$554$	−29.8301	−1.26736
$555$	17.6330	0.748478
$556$	−57.4246	−2.43535
$557$	−17.8650	−0.756963	−0.378482	−	0.925609i	$-0.623554\pi$
$557$	−17.8650	−0.756963	−0.378482	+	0.925609i	$0.623554\pi$
$558$	13.1491	0.556644
$559$	0.0144958	0.000613107 0
$560$	−23.3408	−0.986329
$561$	7.24951	0.306075
$562$	−18.1202	−0.764353
$563$	6.40334	0.269869	0.134934	−	0.990855i	$-0.456918\pi$
$563$	6.40334	0.269869	0.134934	+	0.990855i	$0.456918\pi$
$564$	−3.10735	−0.130843
$565$	−10.4573	−0.439943
$566$	16.2782	0.684224
$567$	−4.76162	−0.199969
$568$	27.1035	1.13724
$569$	12.7202	0.533259	0.266629	−	0.963799i	$-0.414090\pi$
$569$	12.7202	0.533259	0.266629	+	0.963799i	$0.414090\pi$
$570$	−47.9721	−2.00933
$571$	−13.8337	−0.578920	−0.289460	−	0.957190i	$-0.593476\pi$
$571$	−13.8337	−0.578920	−0.289460	+	0.957190i	$0.593476\pi$
$572$	0.460080	0.0192369
$573$	−6.04355	−0.252473
$574$	−67.9100	−2.83451
$575$	24.5561	1.02406
$576$	−11.7582	−0.489927
$577$	−23.8208	−0.991673	−0.495836	−	0.868416i	$-0.665138\pi$
$577$	−23.8208	−0.991673	−0.495836	+	0.868416i	$0.665138\pi$
$578$	2.59142	0.107789
$579$	−3.30634	−0.137407
$580$	70.1999	2.91489
$581$	18.7906	0.779565
$582$	−6.69069	−0.277338
$583$	7.68783	0.318397
$584$	−34.2260	−1.41628
$585$	−0.216245	−0.00894063
$586$	13.6670	0.564580
$587$	−45.6695	−1.88498	−0.942491	−	0.334232i	$-0.891523\pi$
$587$	−45.6695	−1.88498	−0.942491	+	0.334232i	$0.891523\pi$
$588$	−55.9583	−2.30768
$589$	37.1187	1.52945
$590$	−88.1833	−3.63045
$591$	5.01820	0.206421
$592$	−9.28692	−0.381690
$593$	−29.6439	−1.21733	−0.608664	−	0.793428i	$-0.708294\pi$
$593$	−29.6439	−1.21733	−0.608664	+	0.793428i	$0.708294\pi$
$594$	−4.29066	−0.176048
$595$	−57.9280	−2.37481
$596$	64.7132	2.65075
$597$	25.8697	1.05877
$598$	0.953792	0.0390035
$599$	29.7256	1.21455	0.607277	−	0.794490i	$-0.292262\pi$
$599$	29.7256	1.21455	0.607277	+	0.794490i	$0.292262\pi$
$600$	15.9635	0.651708
$601$	−33.6572	−1.37291	−0.686453	−	0.727174i	$-0.740833\pi$
$601$	−33.6572	−1.37291	−0.686453	+	0.727174i	$0.740833\pi$
$602$	−2.29827	−0.0936703
$603$	−5.39399	−0.219660
$604$	−40.7087	−1.65641
$605$	−23.4757	−0.954424
$606$	−5.99726	−0.243622
$607$	10.0791	0.409098	0.204549	−	0.978856i	$-0.434427\pi$
$607$	10.0791	0.409098	0.204549	+	0.978856i	$0.434427\pi$
$608$	−24.1210	−0.978234
$609$	30.6882	1.24355
$610$	−79.7176	−3.22767
$611$	−0.0616902	−0.00249572
$612$	14.2377	0.575523
$613$	28.7150	1.15979	0.579893	−	0.814692i	$-0.303094\pi$
$613$	28.7150	1.15979	0.579893	+	0.814692i	$0.303094\pi$
$614$	−71.3361	−2.87889
$615$	18.4351	0.743374
$616$	−32.0833	−1.29267
$617$	20.3425	0.818958	0.409479	−	0.912319i	$-0.365710\pi$
$617$	20.3425	0.818958	0.409479	+	0.912319i	$0.365710\pi$
$618$	17.9606	0.722483
$619$	−45.7568	−1.83912	−0.919561	−	0.392948i	$-0.871455\pi$
$619$	−45.7568	−1.83912	−0.919561	+	0.392948i	$0.871455\pi$
$620$	−60.6839	−2.43712
$621$	−5.70129	−0.228785
$622$	66.2482	2.65631
$623$	−4.88354	−0.195655
$624$	0.113892	0.00455932
$625$	−27.9843	−1.11937
$626$	64.9330	2.59524
$627$	−12.1122	−0.483714
$628$	10.2317	0.408291
$629$	−23.0486	−0.919007
$630$	34.2850	1.36595
$631$	−30.2263	−1.20329	−0.601644	−	0.798764i	$-0.705488\pi$
$631$	−30.2263	−1.20329	−0.601644	+	0.798764i	$0.705488\pi$
$632$	−50.8852	−2.02410
$633$	2.31429	0.0919848
$634$	26.9719	1.07119
$635$	15.5406	0.616712
$636$	15.0985	0.598694
$637$	−1.11094	−0.0440171
$638$	27.6529	1.09479
$639$	−7.31279	−0.289290
$640$	62.5728	2.47341
$641$	−46.4742	−1.83562	−0.917811	−	0.397017i	$-0.870045\pi$
$641$	−46.4742	−1.83562	−0.917811	+	0.397017i	$0.870045\pi$
$642$	37.1824	1.46747
$643$	33.3333	1.31454	0.657269	−	0.753656i	$-0.271712\pi$
$643$	33.3333	1.31454	0.657269	+	0.753656i	$0.271712\pi$
$644$	−96.9260	−3.81942
$645$	0.623895	0.0245658
$646$	62.7057	2.46712
$647$	−7.34123	−0.288613	−0.144307	−	0.989533i	$-0.546095\pi$
$647$	−7.34123	−0.288613	−0.144307	+	0.989533i	$0.546095\pi$
$648$	−3.70631	−0.145598
$649$	−22.2648	−0.873971
$650$	0.720555	0.0282625
$651$	−26.5282	−1.03972
$652$	−18.4004	−0.720614
$653$	7.22526	0.282746	0.141373	−	0.989956i	$-0.454848\pi$
$653$	7.22526	0.282746	0.141373	+	0.989956i	$0.454848\pi$
$654$	−5.43739	−0.212619
$655$	−22.6966	−0.886830
$656$	−9.70937	−0.379087
$657$	9.23453	0.360273
$658$	9.78079	0.381295
$659$	−7.80415	−0.304006	−0.152003	−	0.988380i	$-0.548572\pi$
$659$	−7.80415	−0.304006	−0.152003	+	0.988380i	$0.548572\pi$
$660$	19.8017	0.770780
$661$	−12.6361	−0.491489	−0.245744	−	0.969335i	$-0.579032\pi$
$661$	−12.6361	−0.491489	−0.245744	+	0.969335i	$0.579032\pi$
$662$	70.6899	2.74744
$663$	0.282660	0.0109776
$664$	14.6261	0.567602
$665$	96.7836	3.75311
$666$	13.6414	0.528595
$667$	36.7443	1.42274
$668$	39.7053	1.53624
$669$	−22.9304	−0.886541
$670$	38.8382	1.50045
$671$	−20.1274	−0.777009
$672$	17.2389	0.665005
$673$	12.7508	0.491506	0.245753	−	0.969333i	$-0.420965\pi$
$673$	12.7508	0.491506	0.245753	+	0.969333i	$0.420965\pi$
$674$	50.3515	1.93947
$675$	−4.30712	−0.165781
$676$	−46.3968	−1.78449
$677$	5.08822	0.195556	0.0977780	−	0.995208i	$-0.468826\pi$
$677$	5.08822	0.195556	0.0977780	+	0.995208i	$0.468826\pi$
$678$	−8.09012	−0.310699
$679$	13.4984	0.518022
$680$	−45.0895	−1.72910
$681$	−2.88389	−0.110511
$682$	−23.9044	−0.915346
$683$	−19.0720	−0.729769	−0.364885	−	0.931053i	$-0.618892\pi$
$683$	−19.0720	−0.729769	−0.364885	+	0.931053i	$0.618892\pi$
$684$	−23.7877	−0.909544
$685$	31.3124	1.19638
$686$	97.4689	3.72138
$687$	13.5809	0.518142
$688$	−0.328592	−0.0125275
$689$	0.299750	0.0114196
$690$	41.0509	1.56278
$691$	−38.0977	−1.44930	−0.724652	−	0.689115i	$-0.757999\pi$
$691$	−38.0977	−1.44930	−0.724652	+	0.689115i	$0.757999\pi$
$692$	−57.1607	−2.17292
$693$	8.65640	0.328829
$694$	−50.3484	−1.91120
$695$	−49.0674	−1.86123
$696$	23.8868	0.905428
$697$	−24.0970	−0.912740
$698$	−82.1365	−3.10891
$699$	2.38106	0.0900599
$700$	−73.2241	−2.76761
$701$	−45.8454	−1.73156	−0.865779	−	0.500427i	$-0.833176\pi$
$701$	−45.8454	−1.73156	−0.865779	+	0.500427i	$0.833176\pi$
$702$	−0.167294	−0.00631410
$703$	38.5086	1.45238
$704$	21.3759	0.805636
$705$	−2.65513	−0.0999979
$706$	60.4352	2.27451
$707$	12.0995	0.455047
$708$	−43.7270	−1.64336
$709$	13.8889	0.521609	0.260804	−	0.965392i	$-0.416012\pi$
$709$	13.8889	0.521609	0.260804	+	0.965392i	$0.416012\pi$
$710$	52.6542	1.97608
$711$	13.7293	0.514890
$712$	−3.80121	−0.142457
$713$	−31.7634	−1.18955
$714$	−44.8149	−1.67716
$715$	0.393123	0.0147020
$716$	−56.2321	−2.10149
$717$	−6.72695	−0.251222
$718$	63.2621	2.36092
$719$	−19.9209	−0.742923	−0.371461	−	0.928448i	$-0.621143\pi$
$719$	−19.9209	−0.742923	−0.371461	+	0.928448i	$0.621143\pi$
$720$	4.90186	0.182682
$721$	−36.2355	−1.34948
$722$	−59.9230	−2.23010
$723$	−26.0456	−0.968646
$724$	−37.7776	−1.40399
$725$	27.7590	1.03094
$726$	−18.1616	−0.674039
$727$	0.311874	0.0115668	0.00578338	−	0.999983i	$-0.498159\pi$
$727$	0.311874	0.0115668	0.00578338	+	0.999983i	$0.498159\pi$
$728$	−1.25094	−0.0463628
$729$	1.00000	0.0370370
$730$	−66.4912	−2.46095
$731$	−0.815511	−0.0301628
$732$	−39.5291	−1.46104
$733$	−31.2355	−1.15371	−0.576854	−	0.816847i	$-0.695720\pi$
$733$	−31.2355	−1.15371	−0.576854	+	0.816847i	$0.695720\pi$
$734$	36.1414	1.33400
$735$	−47.8145	−1.76367
$736$	20.6409	0.760834
$737$	9.80602	0.361209
$738$	14.2620	0.524990
$739$	−29.9399	−1.10136	−0.550678	−	0.834717i	$-0.685631\pi$
$739$	−29.9399	−1.10136	−0.550678	+	0.834717i	$0.685631\pi$
$740$	−62.9561	−2.31431
$741$	−0.472256	−0.0173488
$742$	−47.5245	−1.74468
$743$	−9.45816	−0.346986	−0.173493	−	0.984835i	$-0.555505\pi$
$743$	−9.45816	−0.346986	−0.173493	+	0.984835i	$0.555505\pi$
$744$	−20.6488	−0.757022
$745$	55.2952	2.02586
$746$	−75.9135	−2.77939
$747$	−3.94626	−0.144386
$748$	−25.8834	−0.946390
$749$	−75.0155	−2.74100
$750$	−4.98895	−0.182171
$751$	−17.5032	−0.638703	−0.319351	−	0.947636i	$-0.603465\pi$
$751$	−17.5032	−0.638703	−0.319351	+	0.947636i	$0.603465\pi$
$752$	1.39840	0.0509944
$753$	3.30532	0.120452
$754$	1.07819	0.0392655
$755$	−34.7842	−1.26593
$756$	17.0007	0.618310
$757$	−47.9669	−1.74339	−0.871693	−	0.490052i	$-0.836978\pi$
$757$	−47.9669	−1.74339	−0.871693	+	0.490052i	$0.836978\pi$
$758$	−24.5859	−0.893001
$759$	10.3647	0.376214
$760$	75.3337	2.73264
$761$	−36.6623	−1.32901	−0.664504	−	0.747285i	$-0.731357\pi$
$761$	−36.6623	−1.32901	−0.664504	+	0.747285i	$0.731357\pi$
$762$	12.0227	0.435538
$763$	10.9699	0.397137
$764$	21.5777	0.780653
$765$	12.1656	0.439848
$766$	26.9234	0.972781
$767$	−0.868111	−0.0313457
$768$	24.8918	0.898205
$769$	0.0820171	0.00295761	0.00147881	−	0.999999i	$-0.499529\pi$
$769$	0.0820171	0.00295761	0.00147881	+	0.999999i	$0.499529\pi$
$770$	−62.3285	−2.24616
$771$	−3.58963	−0.129277
$772$	11.8048	0.424866
$773$	−38.6347	−1.38959	−0.694797	−	0.719206i	$-0.744506\pi$
$773$	−38.6347	−1.38959	−0.694797	+	0.719206i	$0.744506\pi$
$774$	0.482665	0.0173490
$775$	−23.9961	−0.861964
$776$	10.5068	0.377172
$777$	−27.5215	−0.987330
$778$	62.2314	2.23110
$779$	40.2603	1.44247
$780$	0.772073	0.0276447
$781$	13.2943	0.475708
$782$	−53.6588	−1.91884
$783$	−6.44490	−0.230322
$784$	25.1829	0.899390
$785$	8.74269	0.312040
$786$	−17.5588	−0.626302
$787$	−30.4340	−1.08485	−0.542427	−	0.840103i	$-0.682495\pi$
$787$	−30.4340	−1.08485	−0.542427	+	0.840103i	$0.682495\pi$
$788$	−17.9168	−0.638260
$789$	−13.1787	−0.469174
$790$	−98.8550	−3.51710
$791$	16.3218	0.580336
$792$	6.73790	0.239421
$793$	−0.784772	−0.0278681
$794$	−69.3793	−2.46218
$795$	12.9012	0.457557
$796$	−92.3641	−3.27376
$797$	39.0404	1.38288	0.691440	−	0.722434i	$-0.256977\pi$
$797$	39.0404	1.38288	0.691440	+	0.722434i	$0.256977\pi$
$798$	74.8748	2.65054
$799$	3.47059	0.122781
$800$	15.5934	0.551311
$801$	1.02561	0.0362380
$802$	50.2285	1.77363
$803$	−16.7879	−0.592433
$804$	19.2585	0.679195
$805$	−82.8201	−2.91902
$806$	−0.932038	−0.0328296
$807$	−1.60177	−0.0563851
$808$	9.41788	0.331320
$809$	13.5241	0.475483	0.237742	−	0.971328i	$-0.423593\pi$
$809$	13.5241	0.475483	0.237742	+	0.971328i	$0.423593\pi$
$810$	−7.20028	−0.252992
$811$	39.6958	1.39391	0.696953	−	0.717117i	$-0.254539\pi$
$811$	39.6958	1.39391	0.696953	+	0.717117i	$0.254539\pi$
$812$	−109.568	−3.84508
$813$	16.8143	0.589705
$814$	−24.7995	−0.869221
$815$	−15.7225	−0.550735
$816$	−6.40737	−0.224303
$817$	1.36252	0.0476686
$818$	−4.19053	−0.146519
$819$	0.337515	0.0117937
$820$	−65.8199	−2.29853
$821$	−5.64050	−0.196855	−0.0984275	−	0.995144i	$-0.531381\pi$
$821$	−5.64050	−0.196855	−0.0984275	+	0.995144i	$0.531381\pi$
$822$	24.2242	0.844918
$823$	53.3035	1.85804	0.929022	−	0.370024i	$-0.120650\pi$
$823$	53.3035	1.85804	0.929022	+	0.370024i	$0.120650\pi$
$824$	−28.2047	−0.982559
$825$	7.83014	0.272610
$826$	137.636	4.78898
$827$	45.2706	1.57421	0.787107	−	0.616817i	$-0.211578\pi$
$827$	45.2706	1.57421	0.787107	+	0.616817i	$0.211578\pi$
$828$	20.3557	0.707409
$829$	12.9465	0.449652	0.224826	−	0.974399i	$-0.427819\pi$
$829$	12.9465	0.449652	0.224826	+	0.974399i	$0.427819\pi$
$830$	28.4142	0.986271
$831$	−12.6390	−0.438443
$832$	0.833452	0.0288948
$833$	62.4998	2.16549
$834$	−37.9601	−1.31445
$835$	33.9268	1.17409
$836$	43.2449	1.49565
$837$	5.57126	0.192571
$838$	59.5540	2.05726
$839$	−24.4128	−0.842823	−0.421412	−	0.906869i	$-0.638465\pi$
$839$	−24.4128	−0.842823	−0.421412	+	0.906869i	$0.638465\pi$
$840$	−53.8399	−1.85765
$841$	12.5368	0.432303
$842$	4.84963	0.167129
$843$	−7.67751	−0.264427
$844$	−8.26286	−0.284419
$845$	−39.6445	−1.36381
$846$	−2.05409	−0.0706211
$847$	36.6409	1.25900
$848$	−6.79477	−0.233333
$849$	6.89707	0.236707
$850$	−40.5373	−1.39042
$851$	−32.9527	−1.12961
$852$	26.1093	0.894491
$853$	0.362628	0.0124162	0.00620808	−	0.999981i	$-0.498024\pi$
$853$	0.362628	0.0124162	0.00620808	+	0.999981i	$0.498024\pi$
$854$	124.423	4.25767
$855$	−20.3258	−0.695127
$856$	−58.3900	−1.99573
$857$	−11.6414	−0.397661	−0.198831	−	0.980034i	$-0.563714\pi$
$857$	−11.6414	−0.397661	−0.198831	+	0.980034i	$0.563714\pi$
$858$	0.304132	0.0103829
$859$	−20.4958	−0.699309	−0.349655	−	0.936879i	$-0.613701\pi$
$859$	−20.4958	−0.699309	−0.349655	+	0.936879i	$0.613701\pi$
$860$	−2.22753	−0.0759582
$861$	−28.7735	−0.980597
$862$	73.6607	2.50889
$863$	−15.9068	−0.541475	−0.270737	−	0.962653i	$-0.587267\pi$
$863$	−15.9068	−0.541475	−0.270737	+	0.962653i	$0.587267\pi$
$864$	−3.62039	−0.123168
$865$	−48.8419	−1.66067
$866$	−81.9870	−2.78603
$867$	1.09798	0.0372895
$868$	94.7153	3.21485
$869$	−24.9593	−0.846685
$870$	46.4051	1.57328
$871$	0.382339	0.0129551
$872$	8.53868	0.289156
$873$	−2.83484	−0.0959449
$874$	89.6509	3.03249
$875$	10.0652	0.340265
$876$	−32.9706	−1.11397
$877$	10.1217	0.341785	0.170893	−	0.985290i	$-0.445335\pi$
$877$	10.1217	0.341785	0.170893	+	0.985290i	$0.445335\pi$
$878$	−16.2354	−0.547918
$879$	5.79072	0.195316
$880$	−8.91136	−0.300402
$881$	20.1759	0.679745	0.339872	−	0.940472i	$-0.389616\pi$
$881$	20.1759	0.679745	0.339872	+	0.940472i	$0.389616\pi$
$882$	−36.9908	−1.24555
$883$	−51.1747	−1.72217	−0.861083	−	0.508464i	$-0.830213\pi$
$883$	−51.1747	−1.72217	−0.861083	+	0.508464i	$0.830213\pi$
$884$	−1.00920	−0.0339431
$885$	−37.3632	−1.25595
$886$	−82.5018	−2.77170
$887$	−54.5861	−1.83282	−0.916410	−	0.400240i	$-0.868927\pi$
$887$	−54.5861	−1.83282	−0.916410	+	0.400240i	$0.868927\pi$
$888$	−21.4220	−0.718875
$889$	−24.2558	−0.813514
$890$	−7.38465	−0.247534
$891$	−1.81795	−0.0609037
$892$	81.8699	2.74121
$893$	−5.79852	−0.194040
$894$	42.7781	1.43072
$895$	−48.0485	−1.60608
$896$	−97.6635	−3.26271
$897$	0.404121	0.0134932
$898$	−28.9944	−0.967556
$899$	−35.9062	−1.19754
$900$	15.3780	0.512599
$901$	−16.8635	−0.561804
$902$	−25.9276	−0.863294
$903$	−0.973775	−0.0324052
$904$	12.7044	0.422543
$905$	−32.2797	−1.07301
$906$	−26.9102	−0.894030
$907$	35.8674	1.19096	0.595478	−	0.803371i	$-0.296962\pi$
$907$	35.8674	1.19096	0.595478	+	0.803371i	$0.296962\pi$
$908$	10.2965	0.341702
$909$	−2.54104	−0.0842809
$910$	−2.43020	−0.0805604
$911$	17.0441	0.564695	0.282347	−	0.959312i	$-0.408887\pi$
$911$	17.0441	0.564695	0.282347	+	0.959312i	$0.408887\pi$
$912$	10.7052	0.354483
$913$	7.17412	0.237429
$914$	75.1152	2.48459
$915$	−33.7763	−1.11661
$916$	−48.4886	−1.60211
$917$	35.4249	1.16983
$918$	9.41170	0.310632
$919$	−24.7291	−0.815738	−0.407869	−	0.913040i	$-0.633728\pi$
$919$	−24.7291	−0.815738	−0.407869	+	0.913040i	$0.633728\pi$
$920$	−64.4649	−2.12534
$921$	−30.2251	−0.995951
$922$	−16.7673	−0.552202
$923$	0.518348	0.0170616
$924$	−30.9065	−1.01675
$925$	−24.8946	−0.818529
$926$	63.3149	2.08066
$927$	7.60992	0.249943
$928$	23.3331	0.765945
$929$	27.3056	0.895869	0.447935	−	0.894066i	$-0.352160\pi$
$929$	27.3056	0.895869	0.447935	+	0.894066i	$0.352160\pi$
$930$	−40.1146	−1.31541
$931$	−104.422	−3.42229
$932$	−8.50124	−0.278467
$933$	28.0693	0.918949
$934$	−37.9277	−1.24103
$935$	−22.1165	−0.723287
$936$	0.262712	0.00858702
$937$	−42.0960	−1.37522	−0.687608	−	0.726083i	$-0.741339\pi$
$937$	−42.0960	−1.37522	−0.687608	+	0.726083i	$0.741339\pi$
$938$	−60.6187	−1.97927
$939$	27.5121	0.897823
$940$	9.47977	0.309196
$941$	36.5347	1.19100	0.595498	−	0.803357i	$-0.296955\pi$
$941$	36.5347	1.19100	0.595498	+	0.803357i	$0.296955\pi$
$942$	6.76362	0.220371
$943$	−34.4517	−1.12190
$944$	19.6784	0.640478
$945$	14.5265	0.472548
$946$	−0.877462	−0.0285287
$947$	2.34820	0.0763063	0.0381532	−	0.999272i	$-0.487853\pi$
$947$	2.34820	0.0763063	0.0381532	+	0.999272i	$0.487853\pi$
$948$	−49.0187	−1.59205
$949$	−0.654565	−0.0212481
$950$	67.7280	2.19738
$951$	11.4280	0.370578
$952$	70.3757	2.28089
$953$	2.72792	0.0883661	0.0441830	−	0.999023i	$-0.485932\pi$
$953$	2.72792	0.0883661	0.0441830	+	0.999023i	$0.485932\pi$
$954$	9.98074	0.323138
$955$	18.4374	0.596621
$956$	24.0176	0.776786
$957$	11.7165	0.378742
$958$	−66.9664	−2.16359
$959$	−48.8723	−1.57817
$960$	35.8715	1.15775
$961$	0.0388992	0.00125481
$962$	−0.966937	−0.0311753
$963$	15.7542	0.507672
$964$	92.9923	2.99508
$965$	10.0868	0.324707
$966$	−64.0722	−2.06149
$967$	−15.8235	−0.508851	−0.254425	−	0.967092i	$-0.581886\pi$
$967$	−15.8235	−0.508851	−0.254425	+	0.967092i	$0.581886\pi$
$968$	28.5203	0.916676
$969$	26.5684	0.853500
$970$	20.4117	0.655379
$971$	20.4857	0.657416	0.328708	−	0.944432i	$-0.393387\pi$
$971$	20.4857	0.657416	0.328708	+	0.944432i	$0.393387\pi$
$972$	−3.57036	−0.114519
$973$	76.5844	2.45518
$974$	−7.00663	−0.224507
$975$	0.305299	0.00977739
$976$	17.7893	0.569421
$977$	−34.6683	−1.10914	−0.554569	−	0.832138i	$-0.687117\pi$
$977$	−34.6683	−1.10914	−0.554569	+	0.832138i	$0.687117\pi$
$978$	−12.1634	−0.388943
$979$	−1.86450	−0.0595897
$980$	170.715	5.45330
$981$	−2.30382	−0.0735553
$982$	−55.3019	−1.76475
$983$	−9.50794	−0.303256	−0.151628	−	0.988438i	$-0.548452\pi$
$983$	−9.50794	−0.303256	−0.151628	+	0.988438i	$0.548452\pi$
$984$	−22.3965	−0.713973
$985$	−15.3093	−0.487795
$986$	−60.6575	−1.93173
$987$	4.14412	0.131909
$988$	1.68613	0.0536429
$989$	−1.16594	−0.0370748
$990$	13.0898	0.416020
$991$	−39.5167	−1.25529	−0.627645	−	0.778500i	$-0.715981\pi$
$991$	−39.5167	−1.25529	−0.627645	+	0.778500i	$0.715981\pi$
$992$	−20.1701	−0.640402
$993$	29.9513	0.950476
$994$	−82.1825	−2.60667
$995$	−78.9221	−2.50200
$996$	14.0896	0.446446
$997$	13.9963	0.443267	0.221634	−	0.975130i	$-0.428861\pi$
$997$	13.9963	0.443267	0.221634	+	0.975130i	$0.428861\pi$
$998$	−64.3239	−2.03614
$999$	5.77987	0.182867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.b.1.11	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.b.1.11	✓	104	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.36016 q^{2} -1.00000 q^{3} +3.57036 q^{4} +3.05076 q^{5} +2.36016 q^{6} -4.76162 q^{7} -3.70631 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.36016 q^{2} -1.00000 q^{3} +3.57036 q^{4} +3.05076 q^{5} +2.36016 q^{6} -4.76162 q^{7} -3.70631 q^{8} +1.00000 q^{9} -7.20028 q^{10} -1.81795 q^{11} -3.57036 q^{12} -0.0708824 q^{13} +11.2382 q^{14} -3.05076 q^{15} +1.60677 q^{16} +3.98773 q^{17} -2.36016 q^{18} -6.66253 q^{19} +10.8923 q^{20} +4.76162 q^{21} +4.29066 q^{22} +5.70129 q^{23} +3.70631 q^{24} +4.30712 q^{25} +0.167294 q^{26} -1.00000 q^{27} -17.0007 q^{28} +6.44490 q^{29} +7.20028 q^{30} -5.57126 q^{31} +3.62039 q^{32} +1.81795 q^{33} -9.41170 q^{34} -14.5265 q^{35} +3.57036 q^{36} -5.77987 q^{37} +15.7247 q^{38} +0.0708824 q^{39} -11.3071 q^{40} -6.04279 q^{41} -11.2382 q^{42} -0.204505 q^{43} -6.49075 q^{44} +3.05076 q^{45} -13.4560 q^{46} +0.870317 q^{47} -1.60677 q^{48} +15.6730 q^{49} -10.1655 q^{50} -3.98773 q^{51} -0.253076 q^{52} -4.22884 q^{53} +2.36016 q^{54} -5.54613 q^{55} +17.6480 q^{56} +6.66253 q^{57} -15.2110 q^{58} +12.2472 q^{59} -10.8923 q^{60} +11.0715 q^{61} +13.1491 q^{62} -4.76162 q^{63} -11.7582 q^{64} -0.216245 q^{65} -4.29066 q^{66} -5.39399 q^{67} +14.2377 q^{68} -5.70129 q^{69} +34.2850 q^{70} -7.31279 q^{71} -3.70631 q^{72} +9.23453 q^{73} +13.6414 q^{74} -4.30712 q^{75} -23.7877 q^{76} +8.65640 q^{77} -0.167294 q^{78} +13.7293 q^{79} +4.90186 q^{80} +1.00000 q^{81} +14.2620 q^{82} -3.94626 q^{83} +17.0007 q^{84} +12.1656 q^{85} +0.482665 q^{86} -6.44490 q^{87} +6.73790 q^{88} +1.02561 q^{89} -7.20028 q^{90} +0.337515 q^{91} +20.3557 q^{92} +5.57126 q^{93} -2.05409 q^{94} -20.3258 q^{95} -3.62039 q^{96} -2.83484 q^{97} -36.9908 q^{98} -1.81795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9}+O(q^{10}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9} + 8 q^{10} - 52 q^{11} - 87 q^{12} + 35 q^{13} - 23 q^{14} + 15 q^{15} + 53 q^{16} - 19 q^{17} - 9 q^{18} - 22 q^{19} - 35 q^{20} + 10 q^{21} - q^{22} - 70 q^{23} + 27 q^{24} + 79 q^{25} - 39 q^{26} - 104 q^{27} - 9 q^{28} - 37 q^{29} - 8 q^{30} - 47 q^{31} - 53 q^{32} + 52 q^{33} - 17 q^{34} - 54 q^{35} + 87 q^{36} + 65 q^{37} - 33 q^{38} - 35 q^{39} + 14 q^{40} - 47 q^{41} + 23 q^{42} - 30 q^{43} - 122 q^{44} - 15 q^{45} - 6 q^{46} - 101 q^{47} - 53 q^{48} + 78 q^{49} - 64 q^{50} + 19 q^{51} + 41 q^{52} - 48 q^{53} + 9 q^{54} - 29 q^{55} - 71 q^{56} + 22 q^{57} - 2 q^{58} - 86 q^{59} + 35 q^{60} + 34 q^{61} - 36 q^{62} - 10 q^{63} - 15 q^{64} - 64 q^{65} + q^{66} - 38 q^{67} - 33 q^{68} + 70 q^{69} - 29 q^{70} - 176 q^{71} - 27 q^{72} + 69 q^{73} - 86 q^{74} - 79 q^{75} - 54 q^{76} - 45 q^{77} + 39 q^{78} - 101 q^{79} - 76 q^{80} + 104 q^{81} + 38 q^{82} - 67 q^{83} + 9 q^{84} + 3 q^{85} - 90 q^{86} + 37 q^{87} + 7 q^{88} - 91 q^{89} + 8 q^{90} - 47 q^{91} - 136 q^{92} + 47 q^{93} - 20 q^{94} - 130 q^{95} + 53 q^{96} + 86 q^{97} - 44 q^{98} - 52 q^{99}+O(q^{100}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9 + 8 * q^10 - 52 * q^11 - 87 * q^12 + 35 * q^13 - 23 * q^14 + 15 * q^15 + 53 * q^16 - 19 * q^17 - 9 * q^18 - 22 * q^19 - 35 * q^20 + 10 * q^21 - q^22 - 70 * q^23 + 27 * q^24 + 79 * q^25 - 39 * q^26 - 104 * q^27 - 9 * q^28 - 37 * q^29 - 8 * q^30 - 47 * q^31 - 53 * q^32 + 52 * q^33 - 17 * q^34 - 54 * q^35 + 87 * q^36 + 65 * q^37 - 33 * q^38 - 35 * q^39 + 14 * q^40 - 47 * q^41 + 23 * q^42 - 30 * q^43 - 122 * q^44 - 15 * q^45 - 6 * q^46 - 101 * q^47 - 53 * q^48 + 78 * q^49 - 64 * q^50 + 19 * q^51 + 41 * q^52 - 48 * q^53 + 9 * q^54 - 29 * q^55 - 71 * q^56 + 22 * q^57 - 2 * q^58 - 86 * q^59 + 35 * q^60 + 34 * q^61 - 36 * q^62 - 10 * q^63 - 15 * q^64 - 64 * q^65 + q^66 - 38 * q^67 - 33 * q^68 + 70 * q^69 - 29 * q^70 - 176 * q^71 - 27 * q^72 + 69 * q^73 - 86 * q^74 - 79 * q^75 - 54 * q^76 - 45 * q^77 + 39 * q^78 - 101 * q^79 - 76 * q^80 + 104 * q^81 + 38 * q^82 - 67 * q^83 + 9 * q^84 + 3 * q^85 - 90 * q^86 + 37 * q^87 + 7 * q^88 - 91 * q^89 + 8 * q^90 - 47 * q^91 - 136 * q^92 + 47 * q^93 - 20 * q^94 - 130 * q^95 + 53 * q^96 + 86 * q^97 - 44 * q^98 - 52 * q^99

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