LMFDB - Embedded newform 6017.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74533 q^{2} -1.76027 q^{3} +5.53683 q^{4} -2.91942 q^{5} +4.83253 q^{6} +1.39362 q^{7} -9.70977 q^{8} +0.0985659 q^{9} +O(q^{10})$	\(q-2.74533 q^{2} -1.76027 q^{3} +5.53683 q^{4} -2.91942 q^{5} +4.83253 q^{6} +1.39362 q^{7} -9.70977 q^{8} +0.0985659 q^{9} +8.01478 q^{10} -1.00000 q^{11} -9.74634 q^{12} +4.17660 q^{13} -3.82595 q^{14} +5.13898 q^{15} +15.5828 q^{16} -4.04082 q^{17} -0.270596 q^{18} +4.18485 q^{19} -16.1644 q^{20} -2.45316 q^{21} +2.74533 q^{22} +0.233100 q^{23} +17.0919 q^{24} +3.52303 q^{25} -11.4661 q^{26} +5.10732 q^{27} +7.71625 q^{28} +6.60665 q^{29} -14.1082 q^{30} -10.0639 q^{31} -23.3605 q^{32} +1.76027 q^{33} +11.0934 q^{34} -4.06857 q^{35} +0.545743 q^{36} +0.0900760 q^{37} -11.4888 q^{38} -7.35196 q^{39} +28.3469 q^{40} +5.18704 q^{41} +6.73472 q^{42} +10.6096 q^{43} -5.53683 q^{44} -0.287756 q^{45} -0.639936 q^{46} +10.2834 q^{47} -27.4301 q^{48} -5.05782 q^{49} -9.67187 q^{50} +7.11296 q^{51} +23.1251 q^{52} +2.66520 q^{53} -14.0213 q^{54} +2.91942 q^{55} -13.5317 q^{56} -7.36649 q^{57} -18.1374 q^{58} +7.50326 q^{59} +28.4537 q^{60} -2.25827 q^{61} +27.6288 q^{62} +0.137364 q^{63} +32.9666 q^{64} -12.1933 q^{65} -4.83253 q^{66} -8.19712 q^{67} -22.3734 q^{68} -0.410320 q^{69} +11.1696 q^{70} -14.1572 q^{71} -0.957052 q^{72} +10.4395 q^{73} -0.247288 q^{74} -6.20150 q^{75} +23.1708 q^{76} -1.39362 q^{77} +20.1836 q^{78} -7.55634 q^{79} -45.4929 q^{80} -9.28598 q^{81} -14.2401 q^{82} -0.344433 q^{83} -13.5827 q^{84} +11.7969 q^{85} -29.1267 q^{86} -11.6295 q^{87} +9.70977 q^{88} +0.821841 q^{89} +0.789984 q^{90} +5.82060 q^{91} +1.29063 q^{92} +17.7153 q^{93} -28.2314 q^{94} -12.2174 q^{95} +41.1209 q^{96} +1.35371 q^{97} +13.8854 q^{98} -0.0985659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) $ 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * 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 $

$2$	−2.74533	−1.94124	−0.970620	−	0.240616i	$-0.922651\pi$
$2$	−2.74533	−1.94124	−0.970620	+	0.240616i	$0.922651\pi$
$3$	−1.76027	−1.01629	−0.508147	−	0.861270i	$-0.669670\pi$
$3$	−1.76027	−1.01629	−0.508147	+	0.861270i	$0.669670\pi$
$4$	5.53683	2.76842
$5$	−2.91942	−1.30561	−0.652803	−	0.757528i	$-0.726407\pi$
$5$	−2.91942	−1.30561	−0.652803	+	0.757528i	$0.726407\pi$
$6$	4.83253	1.97287
$7$	1.39362	0.526740	0.263370	−	0.964695i	$-0.415166\pi$
$7$	1.39362	0.526740	0.263370	+	0.964695i	$0.415166\pi$
$8$	−9.70977	−3.43292
$9$	0.0985659	0.0328553
$10$	8.01478	2.53449
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−9.74634	−2.81353
$13$	4.17660	1.15838	0.579190	−	0.815192i	$-0.303369\pi$
$13$	4.17660	1.15838	0.579190	+	0.815192i	$0.303369\pi$
$14$	−3.82595	−1.02253
$15$	5.13898	1.32688
$16$	15.5828	3.89571
$17$	−4.04082	−0.980044	−0.490022	−	0.871710i	$-0.663011\pi$
$17$	−4.04082	−0.980044	−0.490022	+	0.871710i	$0.663011\pi$
$18$	−0.270596	−0.0637801
$19$	4.18485	0.960071	0.480036	−	0.877249i	$-0.340624\pi$
$19$	4.18485	0.960071	0.480036	+	0.877249i	$0.340624\pi$
$20$	−16.1644	−3.61446
$21$	−2.45316	−0.535323
$22$	2.74533	0.585306
$23$	0.233100	0.0486047	0.0243023	−	0.999705i	$-0.492264\pi$
$23$	0.233100	0.0486047	0.0243023	+	0.999705i	$0.492264\pi$
$24$	17.0919	3.48886
$25$	3.52303	0.704606
$26$	−11.4661	−2.24870
$27$	5.10732	0.982904
$28$	7.71625	1.45823
$29$	6.60665	1.22682	0.613412	−	0.789763i	$-0.289796\pi$
$29$	6.60665	1.22682	0.613412	+	0.789763i	$0.289796\pi$
$30$	−14.1082	−2.57579
$31$	−10.0639	−1.80753	−0.903766	−	0.428026i	$-0.859209\pi$
$31$	−10.0639	−1.80753	−0.903766	+	0.428026i	$0.859209\pi$
$32$	−23.3605	−4.12959
$33$	1.76027	0.306424
$34$	11.0934	1.90250
$35$	−4.06857	−0.687714
$36$	0.545743	0.0909572
$37$	0.0900760	0.0148084	0.00740420	−	0.999973i	$-0.497643\pi$
$37$	0.0900760	0.0148084	0.00740420	+	0.999973i	$0.497643\pi$
$38$	−11.4888	−1.86373
$39$	−7.35196	−1.17726
$40$	28.3469	4.48204
$41$	5.18704	0.810080	0.405040	−	0.914299i	$-0.367258\pi$
$41$	5.18704	0.810080	0.405040	+	0.914299i	$0.367258\pi$
$42$	6.73472	1.03919
$43$	10.6096	1.61794	0.808971	−	0.587848i	$-0.200025\pi$
$43$	10.6096	1.61794	0.808971	+	0.587848i	$0.200025\pi$
$44$	−5.53683	−0.834709
$45$	−0.287756	−0.0428961
$46$	−0.639936	−0.0943534
$47$	10.2834	1.49999	0.749995	−	0.661443i	$-0.230056\pi$
$47$	10.2834	1.49999	0.749995	+	0.661443i	$0.230056\pi$
$48$	−27.4301	−3.95919
$49$	−5.05782	−0.722545
$50$	−9.67187	−1.36781
$51$	7.11296	0.996013
$52$	23.1251	3.20688
$53$	2.66520	0.366094	0.183047	−	0.983104i	$-0.441404\pi$
$53$	2.66520	0.366094	0.183047	+	0.983104i	$0.441404\pi$
$54$	−14.0213	−1.90805
$55$	2.91942	0.393655
$56$	−13.5317	−1.80826
$57$	−7.36649	−0.975716
$58$	−18.1374	−2.38156
$59$	7.50326	0.976842	0.488421	−	0.872608i	$-0.337573\pi$
$59$	7.50326	0.976842	0.488421	+	0.872608i	$0.337573\pi$
$60$	28.4537	3.67336
$61$	−2.25827	−0.289141	−0.144571	−	0.989494i	$-0.546180\pi$
$61$	−2.25827	−0.289141	−0.144571	+	0.989494i	$0.546180\pi$
$62$	27.6288	3.50886
$63$	0.137364	0.0173062
$64$	32.9666	4.12082
$65$	−12.1933	−1.51239
$66$	−4.83253	−0.594844
$67$	−8.19712	−1.00144	−0.500719	−	0.865610i	$-0.666931\pi$
$67$	−8.19712	−1.00144	−0.500719	+	0.865610i	$0.666931\pi$
$68$	−22.3734	−2.71317
$69$	−0.410320	−0.0493967
$70$	11.1696	1.33502
$71$	−14.1572	−1.68015	−0.840075	−	0.542470i	$-0.817489\pi$
$71$	−14.1572	−1.68015	−0.840075	+	0.542470i	$0.817489\pi$
$72$	−0.957052	−0.112790
$73$	10.4395	1.22185	0.610926	−	0.791687i	$-0.290797\pi$
$73$	10.4395	1.22185	0.610926	+	0.791687i	$0.290797\pi$
$74$	−0.247288	−0.0287467
$75$	−6.20150	−0.716087
$76$	23.1708	2.65788
$77$	−1.39362	−0.158818
$78$	20.1836	2.28534
$79$	−7.55634	−0.850155	−0.425078	−	0.905157i	$-0.639753\pi$
$79$	−7.55634	−0.850155	−0.425078	+	0.905157i	$0.639753\pi$
$80$	−45.4929	−5.08626
$81$	−9.28598	−1.03178
$82$	−14.2401	−1.57256
$83$	−0.344433	−0.0378064	−0.0189032	−	0.999821i	$-0.506017\pi$
$83$	−0.344433	−0.0378064	−0.0189032	+	0.999821i	$0.506017\pi$
$84$	−13.5827	−1.48200
$85$	11.7969	1.27955
$86$	−29.1267	−3.14082
$87$	−11.6295	−1.24682
$88$	9.70977	1.03506
$89$	0.821841	0.0871149	0.0435575	−	0.999051i	$-0.486131\pi$
$89$	0.821841	0.0871149	0.0435575	+	0.999051i	$0.486131\pi$
$90$	0.789984	0.0832716
$91$	5.82060	0.610165
$92$	1.29063	0.134558
$93$	17.7153	1.83699
$94$	−28.2314	−2.91184
$95$	−12.2174	−1.25347
$96$	41.1209	4.19688
$97$	1.35371	0.137449	0.0687243	−	0.997636i	$-0.478107\pi$
$97$	1.35371	0.137449	0.0687243	+	0.997636i	$0.478107\pi$
$98$	13.8854	1.40263
$99$	−0.0985659	−0.00990625
$100$	19.5064	1.95064
$101$	−14.6047	−1.45322	−0.726609	−	0.687051i	$-0.758905\pi$
$101$	−14.6047	−1.45322	−0.726609	+	0.687051i	$0.758905\pi$
$102$	−19.5274	−1.93350
$103$	14.6073	1.43930	0.719651	−	0.694336i	$-0.244302\pi$
$103$	14.6073	1.43930	0.719651	+	0.694336i	$0.244302\pi$
$104$	−40.5538	−3.97663
$105$	7.16180	0.698920
$106$	−7.31686	−0.710677
$107$	9.63702	0.931646	0.465823	−	0.884878i	$-0.345758\pi$
$107$	9.63702	0.931646	0.465823	+	0.884878i	$0.345758\pi$
$108$	28.2784	2.72109
$109$	9.25588	0.886553	0.443276	−	0.896385i	$-0.353816\pi$
$109$	9.25588	0.886553	0.443276	+	0.896385i	$0.353816\pi$
$110$	−8.01478	−0.764179
$111$	−0.158558	−0.0150497
$112$	21.7166	2.05202
$113$	3.96690	0.373175	0.186587	−	0.982438i	$-0.440257\pi$
$113$	3.96690	0.373175	0.186587	+	0.982438i	$0.440257\pi$
$114$	20.2234	1.89410
$115$	−0.680517	−0.0634585
$116$	36.5799	3.39636
$117$	0.411671	0.0380590
$118$	−20.5989	−1.89629
$119$	−5.63138	−0.516228
$120$	−49.8983	−4.55507
$121$	1.00000	0.0909091
$122$	6.19968	0.561293
$123$	−9.13061	−0.823280
$124$	−55.7222	−5.00400
$125$	4.31191	0.385669
$126$	−0.377108	−0.0335955
$127$	6.06002	0.537739	0.268870	−	0.963177i	$-0.413350\pi$
$127$	6.06002	0.537739	0.268870	+	0.963177i	$0.413350\pi$
$128$	−43.7831	−3.86991
$129$	−18.6757	−1.64431
$130$	33.4745	2.93591
$131$	−6.79270	−0.593481	−0.296741	−	0.954958i	$-0.595900\pi$
$131$	−6.79270	−0.593481	−0.296741	+	0.954958i	$0.595900\pi$
$132$	9.74634	0.848310
$133$	5.83210	0.505708
$134$	22.5038	1.94403
$135$	−14.9104	−1.28329
$136$	39.2355	3.36441
$137$	−8.44497	−0.721503	−0.360751	−	0.932662i	$-0.617480\pi$
$137$	−8.44497	−0.721503	−0.360751	+	0.932662i	$0.617480\pi$
$138$	1.12646	0.0958908
$139$	−6.39878	−0.542737	−0.271369	−	0.962475i	$-0.587476\pi$
$139$	−6.39878	−0.542737	−0.271369	+	0.962475i	$0.587476\pi$
$140$	−22.5270	−1.90388
$141$	−18.1016	−1.52443
$142$	38.8662	3.26158
$143$	−4.17660	−0.349265
$144$	1.53594	0.127995
$145$	−19.2876	−1.60175
$146$	−28.6599	−2.37191
$147$	8.90315	0.734319
$148$	0.498735	0.0409958
$149$	18.1623	1.48792	0.743959	−	0.668225i	$-0.232946\pi$
$149$	18.1623	1.48792	0.743959	+	0.668225i	$0.232946\pi$
$150$	17.0251	1.39010
$151$	0.662890	0.0539452	0.0269726	−	0.999636i	$-0.491413\pi$
$151$	0.662890	0.0539452	0.0269726	+	0.999636i	$0.491413\pi$
$152$	−40.6340	−3.29585
$153$	−0.398288	−0.0321996
$154$	3.82595	0.308304
$155$	29.3808	2.35992
$156$	−40.7066	−3.25914
$157$	−9.77593	−0.780204	−0.390102	−	0.920772i	$-0.627560\pi$
$157$	−9.77593	−0.780204	−0.390102	+	0.920772i	$0.627560\pi$
$158$	20.7446	1.65036
$159$	−4.69149	−0.372059
$160$	68.1992	5.39162
$161$	0.324853	0.0256020
$162$	25.4931	2.00293
$163$	1.01986	0.0798812	0.0399406	−	0.999202i	$-0.487283\pi$
$163$	1.01986	0.0798812	0.0399406	+	0.999202i	$0.487283\pi$
$164$	28.7198	2.24264
$165$	−5.13898	−0.400069
$166$	0.945582	0.0733914
$167$	−1.92166	−0.148703	−0.0743513	−	0.997232i	$-0.523689\pi$
$167$	−1.92166	−0.148703	−0.0743513	+	0.997232i	$0.523689\pi$
$168$	23.8196	1.83772
$169$	4.44399	0.341846
$170$	−32.3863	−2.48392
$171$	0.412484	0.0315434
$172$	58.7433	4.47914
$173$	−0.598043	−0.0454684	−0.0227342	−	0.999742i	$-0.507237\pi$
$173$	−0.598043	−0.0454684	−0.0227342	+	0.999742i	$0.507237\pi$
$174$	31.9269	2.42037
$175$	4.90977	0.371144
$176$	−15.5828	−1.17460
$177$	−13.2078	−0.992759
$178$	−2.25622	−0.169111
$179$	11.0169	0.823439	0.411719	−	0.911311i	$-0.364928\pi$
$179$	11.0169	0.823439	0.411719	+	0.911311i	$0.364928\pi$
$180$	−1.59325	−0.118754
$181$	−6.65971	−0.495012	−0.247506	−	0.968886i	$-0.579611\pi$
$181$	−6.65971	−0.495012	−0.247506	+	0.968886i	$0.579611\pi$
$182$	−15.9795	−1.18448
$183$	3.97517	0.293853
$184$	−2.26334	−0.166856
$185$	−0.262970	−0.0193339
$186$	−48.6342	−3.56603
$187$	4.04082	0.295494
$188$	56.9376	4.15260
$189$	7.11767	0.517735
$190$	33.5407	2.43330
$191$	−24.1186	−1.74516	−0.872581	−	0.488470i	$-0.837555\pi$
$191$	−24.1186	−1.74516	−0.872581	+	0.488470i	$0.837555\pi$
$192$	−58.0302	−4.18797
$193$	−2.73543	−0.196900	−0.0984502	−	0.995142i	$-0.531389\pi$
$193$	−2.73543	−0.196900	−0.0984502	+	0.995142i	$0.531389\pi$
$194$	−3.71638	−0.266821
$195$	21.4635	1.53703
$196$	−28.0043	−2.00031
$197$	4.14743	0.295492	0.147746	−	0.989025i	$-0.452798\pi$
$197$	4.14743	0.295492	0.147746	+	0.989025i	$0.452798\pi$
$198$	0.270596	0.0192304
$199$	2.20216	0.156107	0.0780536	−	0.996949i	$-0.475129\pi$
$199$	2.20216	0.156107	0.0780536	+	0.996949i	$0.475129\pi$
$200$	−34.2078	−2.41886
$201$	14.4292	1.01776
$202$	40.0946	2.82105
$203$	9.20717	0.646217
$204$	39.3833	2.75738
$205$	−15.1432	−1.05764
$206$	−40.1019	−2.79403
$207$	0.0229757	0.00159692
$208$	65.0833	4.51272
$209$	−4.18485	−0.289472
$210$	−19.6615	−1.35677
$211$	−3.00306	−0.206739	−0.103370	−	0.994643i	$-0.532962\pi$
$211$	−3.00306	−0.206739	−0.103370	+	0.994643i	$0.532962\pi$
$212$	14.7568	1.01350
$213$	24.9206	1.70753
$214$	−26.4568	−1.80855
$215$	−30.9738	−2.11239
$216$	−49.5909	−3.37423
$217$	−14.0253	−0.952099
$218$	−25.4104	−1.72101
$219$	−18.3764	−1.24176
$220$	16.1644	1.08980
$221$	−16.8769	−1.13526
$222$	0.435295	0.0292151
$223$	−16.2916	−1.09097	−0.545485	−	0.838121i	$-0.683654\pi$
$223$	−16.2916	−1.09097	−0.545485	+	0.838121i	$0.683654\pi$
$224$	−32.5557	−2.17522
$225$	0.347251	0.0231500
$226$	−10.8904	−0.724422
$227$	−16.4083	−1.08905	−0.544527	−	0.838743i	$-0.683291\pi$
$227$	−16.4083	−1.08905	−0.544527	+	0.838743i	$0.683291\pi$
$228$	−40.7870	−2.70119
$229$	23.3002	1.53972	0.769862	−	0.638211i	$-0.220325\pi$
$229$	23.3002	1.53972	0.769862	+	0.638211i	$0.220325\pi$
$230$	1.86824	0.123188
$231$	2.45316	0.161406
$232$	−64.1490	−4.21159
$233$	1.59536	0.104515	0.0522577	−	0.998634i	$-0.483358\pi$
$233$	1.59536	0.104515	0.0522577	+	0.998634i	$0.483358\pi$
$234$	−1.13017	−0.0738816
$235$	−30.0216	−1.95840
$236$	41.5443	2.70430
$237$	13.3012	0.864008
$238$	15.4600	1.00212
$239$	−2.96461	−0.191765	−0.0958824	−	0.995393i	$-0.530567\pi$
$239$	−2.96461	−0.191765	−0.0958824	+	0.995393i	$0.530567\pi$
$240$	80.0800	5.16914
$241$	−29.0139	−1.86895	−0.934473	−	0.356033i	$-0.884129\pi$
$241$	−29.0139	−1.86895	−0.934473	+	0.356033i	$0.884129\pi$
$242$	−2.74533	−0.176476
$243$	1.02392	0.0656843
$244$	−12.5036	−0.800463
$245$	14.7659	0.943359
$246$	25.0665	1.59818
$247$	17.4785	1.11213
$248$	97.7183	6.20512
$249$	0.606296	0.0384225
$250$	−11.8376	−0.748676
$251$	−28.6112	−1.80592	−0.902961	−	0.429723i	$-0.858611\pi$
$251$	−28.6112	−1.80592	−0.902961	+	0.429723i	$0.858611\pi$
$252$	0.760559	0.0479107
$253$	−0.233100	−0.0146549
$254$	−16.6367	−1.04388
$255$	−20.7657	−1.30040
$256$	54.2658	3.39161
$257$	−20.4485	−1.27555	−0.637773	−	0.770225i	$-0.720144\pi$
$257$	−20.4485	−1.27555	−0.637773	+	0.770225i	$0.720144\pi$
$258$	51.2710	3.19199
$259$	0.125532	0.00780017
$260$	−67.5120	−4.18692
$261$	0.651191	0.0403077
$262$	18.6482	1.15209
$263$	−0.931131	−0.0574160	−0.0287080	−	0.999588i	$-0.509139\pi$
$263$	−0.931131	−0.0574160	−0.0287080	+	0.999588i	$0.509139\pi$
$264$	−17.0919	−1.05193
$265$	−7.78086	−0.477974
$266$	−16.0110	−0.981700
$267$	−1.44667	−0.0885345
$268$	−45.3861	−2.77240
$269$	−16.5950	−1.01181	−0.505907	−	0.862588i	$-0.668842\pi$
$269$	−16.5950	−1.01181	−0.505907	+	0.862588i	$0.668842\pi$
$270$	40.9340	2.49117
$271$	13.7921	0.837813	0.418907	−	0.908029i	$-0.362413\pi$
$271$	13.7921	0.837813	0.418907	+	0.908029i	$0.362413\pi$
$272$	−62.9675	−3.81797
$273$	−10.2459	−0.620107
$274$	23.1842	1.40061
$275$	−3.52303	−0.212447
$276$	−2.27187	−0.136751
$277$	1.31718	0.0791414	0.0395707	−	0.999217i	$-0.487401\pi$
$277$	1.31718	0.0791414	0.0395707	+	0.999217i	$0.487401\pi$
$278$	17.5667	1.05358
$279$	−0.991959	−0.0593871
$280$	39.5049	2.36087
$281$	−0.103367	−0.00616633	−0.00308317	−	0.999995i	$-0.500981\pi$
$281$	−0.103367	−0.00616633	−0.00308317	+	0.999995i	$0.500981\pi$
$282$	49.6950	2.95929
$283$	−22.1311	−1.31556	−0.657780	−	0.753210i	$-0.728504\pi$
$283$	−22.1311	−1.31556	−0.657780	+	0.753210i	$0.728504\pi$
$284$	−78.3860	−4.65136
$285$	21.5059	1.27390
$286$	11.4661	0.678007
$287$	7.22877	0.426701
$288$	−2.30255	−0.135679
$289$	−0.671742	−0.0395143
$290$	52.9508	3.10938
$291$	−2.38290	−0.139688
$292$	57.8018	3.38260
$293$	24.0575	1.40545	0.702726	−	0.711461i	$-0.251966\pi$
$293$	24.0575	1.40545	0.702726	+	0.711461i	$0.251966\pi$
$294$	−24.4421	−1.42549
$295$	−21.9052	−1.27537
$296$	−0.874617	−0.0508361
$297$	−5.10732	−0.296357
$298$	−49.8616	−2.88841
$299$	0.973565	0.0563027
$300$	−34.3366	−1.98243
$301$	14.7857	0.852234
$302$	−1.81985	−0.104721
$303$	25.7082	1.47690
$304$	65.2119	3.74016
$305$	6.59283	0.377504
$306$	1.09343	0.0625073
$307$	−4.83792	−0.276115	−0.138057	−	0.990424i	$-0.544086\pi$
$307$	−4.83792	−0.276115	−0.138057	+	0.990424i	$0.544086\pi$
$308$	−7.71625	−0.439674
$309$	−25.7129	−1.46276
$310$	−80.6600	−4.58118
$311$	23.4273	1.32844	0.664220	−	0.747538i	$-0.268764\pi$
$311$	23.4273	1.32844	0.664220	+	0.747538i	$0.268764\pi$
$312$	71.3859	4.04143
$313$	21.9358	1.23988	0.619941	−	0.784648i	$-0.287156\pi$
$313$	21.9358	1.23988	0.619941	+	0.784648i	$0.287156\pi$
$314$	26.8381	1.51456
$315$	−0.401023	−0.0225951
$316$	−41.8382	−2.35358
$317$	15.1930	0.853324	0.426662	−	0.904411i	$-0.359689\pi$
$317$	15.1930	0.853324	0.426662	+	0.904411i	$0.359689\pi$
$318$	12.8797	0.722257
$319$	−6.60665	−0.369901
$320$	−96.2433	−5.38017
$321$	−16.9638	−0.946827
$322$	−0.891828	−0.0496996
$323$	−16.9103	−0.940912
$324$	−51.4149	−2.85638
$325$	14.7143	0.816201
$326$	−2.79984	−0.155069
$327$	−16.2929	−0.900999
$328$	−50.3650	−2.78094
$329$	14.3312	0.790104
$330$	14.1082	0.776631
$331$	23.1349	1.27161	0.635804	−	0.771850i	$-0.280668\pi$
$331$	23.1349	1.27161	0.635804	+	0.771850i	$0.280668\pi$
$332$	−1.90707	−0.104664
$333$	0.00887842	0.000486534 0
$334$	5.27559	0.288667
$335$	23.9309	1.30748
$336$	−38.2272	−2.08546
$337$	−18.8948	−1.02927	−0.514634	−	0.857410i	$-0.672072\pi$
$337$	−18.8948	−1.02927	−0.514634	+	0.857410i	$0.672072\pi$
$338$	−12.2002	−0.663605
$339$	−6.98283	−0.379255
$340$	65.3173	3.54233
$341$	10.0639	0.544992
$342$	−1.13240	−0.0612334
$343$	−16.8040	−0.907333
$344$	−103.016	−5.55427
$345$	1.19790	0.0644926
$346$	1.64182	0.0882650
$347$	−8.54255	−0.458588	−0.229294	−	0.973357i	$-0.573642\pi$
$347$	−8.54255	−0.458588	−0.229294	+	0.973357i	$0.573642\pi$
$348$	−64.3907	−3.45170
$349$	−32.2973	−1.72883	−0.864417	−	0.502775i	$-0.832313\pi$
$349$	−32.2973	−1.72883	−0.864417	+	0.502775i	$0.832313\pi$
$350$	−13.4789	−0.720479
$351$	21.3312	1.13858
$352$	23.3605	1.24512
$353$	−11.2333	−0.597887	−0.298943	−	0.954271i	$-0.596634\pi$
$353$	−11.2333	−0.597887	−0.298943	+	0.954271i	$0.596634\pi$
$354$	36.2598	1.92718
$355$	41.3308	2.19361
$356$	4.55039	0.241170
$357$	9.91278	0.524640
$358$	−30.2449	−1.59849
$359$	27.8100	1.46776	0.733878	−	0.679282i	$-0.237708\pi$
$359$	27.8100	1.46776	0.733878	+	0.679282i	$0.237708\pi$
$360$	2.79404	0.147259
$361$	−1.48700	−0.0782630
$362$	18.2831	0.960938
$363$	−1.76027	−0.0923904
$364$	32.2277	1.68919
$365$	−30.4774	−1.59526
$366$	−10.9131	−0.570439
$367$	13.4579	0.702499	0.351250	−	0.936282i	$-0.385757\pi$
$367$	13.4579	0.702499	0.351250	+	0.936282i	$0.385757\pi$
$368$	3.63236	0.189350
$369$	0.511266	0.0266154
$370$	0.721939	0.0375318
$371$	3.71429	0.192836
$372$	98.0864	5.08554
$373$	0.687232	0.0355835	0.0177918	−	0.999842i	$-0.494336\pi$
$373$	0.687232	0.0355835	0.0177918	+	0.999842i	$0.494336\pi$
$374$	−11.0934	−0.573626
$375$	−7.59014	−0.391953
$376$	−99.8496	−5.14935
$377$	27.5933	1.42113
$378$	−19.5404	−1.00505
$379$	−23.8203	−1.22357	−0.611785	−	0.791024i	$-0.709548\pi$
$379$	−23.8203	−1.22357	−0.611785	+	0.791024i	$0.709548\pi$
$380$	−67.6454	−3.47014
$381$	−10.6673	−0.546502
$382$	66.2135	3.38778
$383$	0.114211	0.00583593	0.00291797	−	0.999996i	$-0.499071\pi$
$383$	0.114211	0.00583593	0.00291797	+	0.999996i	$0.499071\pi$
$384$	77.0702	3.93297
$385$	4.06857	0.207354
$386$	7.50965	0.382231
$387$	1.04574	0.0531580
$388$	7.49528	0.380515
$389$	−20.2010	−1.02423	−0.512115	−	0.858917i	$-0.671138\pi$
$389$	−20.2010	−1.02423	−0.512115	+	0.858917i	$0.671138\pi$
$390$	−58.9243	−2.98375
$391$	−0.941915	−0.0476347
$392$	49.1102	2.48044
$393$	11.9570	0.603152
$394$	−11.3861	−0.573621
$395$	22.0602	1.10997
$396$	−0.545743	−0.0274246
$397$	−2.84104	−0.142588	−0.0712938	−	0.997455i	$-0.522713\pi$
$397$	−2.84104	−0.142588	−0.0712938	+	0.997455i	$0.522713\pi$
$398$	−6.04566	−0.303042
$399$	−10.2661	−0.513948
$400$	54.8988	2.74494
$401$	30.2521	1.51072	0.755359	−	0.655311i	$-0.227462\pi$
$401$	30.2521	1.51072	0.755359	+	0.655311i	$0.227462\pi$
$402$	−39.6128	−1.97571
$403$	−42.0330	−2.09381
$404$	−80.8635	−4.02311
$405$	27.1097	1.34709
$406$	−25.2767	−1.25446
$407$	−0.0900760	−0.00446490
$408$	−69.0652	−3.41924
$409$	31.3126	1.54831	0.774155	−	0.632997i	$-0.218175\pi$
$409$	31.3126	1.54831	0.774155	+	0.632997i	$0.218175\pi$
$410$	41.5730	2.05314
$411$	14.8655	0.733259
$412$	80.8783	3.98459
$413$	10.4567	0.514541
$414$	−0.0630758	−0.00310001
$415$	1.00555	0.0493603
$416$	−97.5675	−4.78364
$417$	11.2636	0.551581
$418$	11.4888	0.561936
$419$	31.7629	1.55172	0.775859	−	0.630906i	$-0.217317\pi$
$419$	31.7629	1.55172	0.775859	+	0.630906i	$0.217317\pi$
$420$	39.6537	1.93490
$421$	7.42962	0.362097	0.181049	−	0.983474i	$-0.442051\pi$
$421$	7.42962	0.362097	0.181049	+	0.983474i	$0.442051\pi$
$422$	8.24438	0.401330
$423$	1.01359	0.0492827
$424$	−25.8785	−1.25677
$425$	−14.2359	−0.690544
$426$	−68.4151	−3.31472
$427$	−3.14717	−0.152302
$428$	53.3586	2.57918
$429$	7.35196	0.354956
$430$	85.0332	4.10067
$431$	−16.9035	−0.814214	−0.407107	−	0.913381i	$-0.633462\pi$
$431$	−16.9035	−0.814214	−0.407107	+	0.913381i	$0.633462\pi$
$432$	79.5866	3.82911
$433$	−0.933000	−0.0448371	−0.0224186	−	0.999749i	$-0.507137\pi$
$433$	−0.933000	−0.0448371	−0.0224186	+	0.999749i	$0.507137\pi$
$434$	38.5040	1.84825
$435$	33.9515	1.62785
$436$	51.2483	2.45435
$437$	0.975488	0.0466639
$438$	50.4493	2.41056
$439$	−11.4733	−0.547592	−0.273796	−	0.961788i	$-0.588279\pi$
$439$	−11.4733	−0.547592	−0.273796	+	0.961788i	$0.588279\pi$
$440$	−28.3469	−1.35139
$441$	−0.498529	−0.0237395
$442$	46.3327	2.20382
$443$	4.79990	0.228050	0.114025	−	0.993478i	$-0.463626\pi$
$443$	4.79990	0.228050	0.114025	+	0.993478i	$0.463626\pi$
$444$	−0.877911	−0.0416638
$445$	−2.39930	−0.113738
$446$	44.7259	2.11783
$447$	−31.9707	−1.51216
$448$	45.9429	2.17060
$449$	13.3768	0.631290	0.315645	−	0.948877i	$-0.397779\pi$
$449$	13.3768	0.631290	0.315645	+	0.948877i	$0.397779\pi$
$450$	−0.953317	−0.0449398
$451$	−5.18704	−0.244248
$452$	21.9641	1.03310
$453$	−1.16687	−0.0548243
$454$	45.0461	2.11412
$455$	−16.9928	−0.796635
$456$	71.5269	3.34955
$457$	32.8355	1.53598	0.767991	−	0.640461i	$-0.221257\pi$
$457$	32.8355	1.53598	0.767991	+	0.640461i	$0.221257\pi$
$458$	−63.9668	−2.98897
$459$	−20.6378	−0.963289
$460$	−3.76791	−0.175680
$461$	11.1740	0.520427	0.260213	−	0.965551i	$-0.416207\pi$
$461$	11.1740	0.520427	0.260213	+	0.965551i	$0.416207\pi$
$462$	−6.73472	−0.313328
$463$	−35.5155	−1.65054	−0.825272	−	0.564735i	$-0.808978\pi$
$463$	−35.5155	−1.65054	−0.825272	+	0.564735i	$0.808978\pi$
$464$	102.950	4.77935
$465$	−51.7183	−2.39838
$466$	−4.37978	−0.202889
$467$	−25.7390	−1.19106	−0.595530	−	0.803333i	$-0.703058\pi$
$467$	−25.7390	−1.19106	−0.595530	+	0.803333i	$0.703058\pi$
$468$	2.27935	0.105363
$469$	−11.4237	−0.527497
$470$	82.4193	3.80172
$471$	17.2083	0.792917
$472$	−72.8549	−3.35342
$473$	−10.6096	−0.487828
$474$	−36.5163	−1.67725
$475$	14.7434	0.676472
$476$	−31.1800	−1.42913
$477$	0.262698	0.0120281
$478$	8.13884	0.372262
$479$	35.0553	1.60172	0.800858	−	0.598854i	$-0.204377\pi$
$479$	35.0553	1.60172	0.800858	+	0.598854i	$0.204377\pi$
$480$	−120.049	−5.47947
$481$	0.376211	0.0171538
$482$	79.6526	3.62808
$483$	−0.571830	−0.0260192
$484$	5.53683	0.251674
$485$	−3.95206	−0.179454
$486$	−2.81099	−0.127509
$487$	21.2177	0.961464	0.480732	−	0.876867i	$-0.340371\pi$
$487$	21.2177	0.961464	0.480732	+	0.876867i	$0.340371\pi$
$488$	21.9272	0.992599
$489$	−1.79522	−0.0811829
$490$	−40.5373	−1.83129
$491$	−14.9938	−0.676662	−0.338331	−	0.941027i	$-0.609862\pi$
$491$	−14.9938	−0.676662	−0.338331	+	0.941027i	$0.609862\pi$
$492$	−50.5547	−2.27918
$493$	−26.6963	−1.20234
$494$	−47.9841	−2.15891
$495$	0.287756	0.0129337
$496$	−156.824	−7.04162
$497$	−19.7298	−0.885002
$498$	−1.66448	−0.0745873
$499$	11.5706	0.517969	0.258985	−	0.965881i	$-0.416612\pi$
$499$	11.5706	0.517969	0.258985	+	0.965881i	$0.416612\pi$
$500$	23.8743	1.06769
$501$	3.38265	0.151126
$502$	78.5471	3.50573
$503$	7.10798	0.316929	0.158465	−	0.987365i	$-0.449346\pi$
$503$	7.10798	0.316929	0.158465	+	0.987365i	$0.449346\pi$
$504$	−1.33377	−0.0594108
$505$	42.6372	1.89733
$506$	0.639936	0.0284486
$507$	−7.82265	−0.347416
$508$	33.5533	1.48869
$509$	−15.1023	−0.669399	−0.334700	−	0.942325i	$-0.608635\pi$
$509$	−15.1023	−0.669399	−0.334700	+	0.942325i	$0.608635\pi$
$510$	57.0088	2.52439
$511$	14.5487	0.643598
$512$	−61.4114	−2.71403
$513$	21.3734	0.943658
$514$	56.1380	2.47614
$515$	−42.6450	−1.87916
$516$	−103.404	−4.55212
$517$	−10.2834	−0.452264
$518$	−0.344626	−0.0151420
$519$	1.05272	0.0462093
$520$	118.394	5.19191
$521$	26.4312	1.15797	0.578987	−	0.815337i	$-0.303448\pi$
$521$	26.4312	1.15797	0.578987	+	0.815337i	$0.303448\pi$
$522$	−1.78773	−0.0782469
$523$	2.91773	0.127584	0.0637918	−	0.997963i	$-0.479681\pi$
$523$	2.91773	0.127584	0.0637918	+	0.997963i	$0.479681\pi$
$524$	−37.6100	−1.64300
$525$	−8.64254	−0.377191
$526$	2.55626	0.111458
$527$	40.6665	1.77146
$528$	27.4301	1.19374
$529$	−22.9457	−0.997638
$530$	21.3610	0.927863
$531$	0.739566	0.0320944
$532$	32.2914	1.40001
$533$	21.6642	0.938381
$534$	3.97157	0.171867
$535$	−28.1345	−1.21636
$536$	79.5921	3.43786
$537$	−19.3927	−0.836857
$538$	45.5586	1.96417
$539$	5.05782	0.217856
$540$	−82.5565	−3.55267
$541$	−17.4476	−0.750132	−0.375066	−	0.926998i	$-0.622380\pi$
$541$	−17.4476	−0.750132	−0.375066	+	0.926998i	$0.622380\pi$
$542$	−37.8640	−1.62640
$543$	11.7229	0.503078
$544$	94.3957	4.04718
$545$	−27.0218	−1.15749
$546$	28.1282	1.20378
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−46.7584	−1.99742
$549$	−0.222588	−0.00949983
$550$	9.67187	0.412410
$551$	27.6479	1.17784
$552$	3.98411	0.169575
$553$	−10.5307	−0.447810
$554$	−3.61608	−0.153632
$555$	0.462899	0.0196490
$556$	−35.4290	−1.50252
$557$	−40.0753	−1.69804	−0.849022	−	0.528358i	$-0.822808\pi$
$557$	−40.0753	−1.69804	−0.849022	+	0.528358i	$0.822808\pi$
$558$	2.72325	0.115285
$559$	44.3119	1.87419
$560$	−63.3999	−2.67913
$561$	−7.11296	−0.300309
$562$	0.283775	0.0119703
$563$	36.6473	1.54450	0.772249	−	0.635320i	$-0.219132\pi$
$563$	36.6473	1.54450	0.772249	+	0.635320i	$0.219132\pi$
$564$	−100.226	−4.22026
$565$	−11.5811	−0.487219
$566$	60.7573	2.55382
$567$	−12.9411	−0.543477
$568$	137.463	5.76782
$569$	7.94421	0.333038	0.166519	−	0.986038i	$-0.446747\pi$
$569$	7.94421	0.333038	0.166519	+	0.986038i	$0.446747\pi$
$570$	−59.0408	−2.47295
$571$	−28.5304	−1.19396	−0.596981	−	0.802256i	$-0.703633\pi$
$571$	−28.5304	−1.19396	−0.596981	+	0.802256i	$0.703633\pi$
$572$	−23.1251	−0.966911
$573$	42.4554	1.77360
$574$	−19.8454	−0.828329
$575$	0.821217	0.0342471
$576$	3.24938	0.135391
$577$	3.12857	0.130244	0.0651221	−	0.997877i	$-0.479256\pi$
$577$	3.12857	0.130244	0.0651221	+	0.997877i	$0.479256\pi$
$578$	1.84415	0.0767067
$579$	4.81510	0.200109
$580$	−106.792	−4.43431
$581$	−0.480009	−0.0199141
$582$	6.54186	0.271169
$583$	−2.66520	−0.110381
$584$	−101.365	−4.19452
$585$	−1.20184	−0.0496900
$586$	−66.0456	−2.72832
$587$	24.8519	1.02575	0.512873	−	0.858464i	$-0.328581\pi$
$587$	24.8519	1.02575	0.512873	+	0.858464i	$0.328581\pi$
$588$	49.2952	2.03290
$589$	−42.1160	−1.73536
$590$	60.1370	2.47580
$591$	−7.30061	−0.300307
$592$	1.40364	0.0576892
$593$	14.8903	0.611471	0.305736	−	0.952116i	$-0.401098\pi$
$593$	14.8903	0.611471	0.305736	+	0.952116i	$0.401098\pi$
$594$	14.0213	0.575300
$595$	16.4404	0.673990
$596$	100.562	4.11917
$597$	−3.87641	−0.158651
$598$	−2.67276	−0.109297
$599$	20.4039	0.833680	0.416840	−	0.908980i	$-0.363137\pi$
$599$	20.4039	0.833680	0.416840	+	0.908980i	$0.363137\pi$
$600$	60.2151	2.45827
$601$	−35.8147	−1.46091	−0.730457	−	0.682959i	$-0.760693\pi$
$601$	−35.8147	−1.46091	−0.730457	+	0.682959i	$0.760693\pi$
$602$	−40.5916	−1.65439
$603$	−0.807957	−0.0329025
$604$	3.67031	0.149343
$605$	−2.91942	−0.118691
$606$	−70.5775	−2.86701
$607$	5.20724	0.211355	0.105678	−	0.994400i	$-0.466299\pi$
$607$	5.20724	0.211355	0.105678	+	0.994400i	$0.466299\pi$
$608$	−97.7603	−3.96470
$609$	−16.2072	−0.656747
$610$	−18.0995	−0.732827
$611$	42.9497	1.73756
$612$	−2.20525	−0.0891420
$613$	43.1599	1.74321	0.871607	−	0.490206i	$-0.163078\pi$
$613$	43.1599	1.74321	0.871607	+	0.490206i	$0.163078\pi$
$614$	13.2817	0.536005
$615$	26.6561	1.07488
$616$	13.5317	0.545210
$617$	30.2381	1.21734	0.608671	−	0.793423i	$-0.291703\pi$
$617$	30.2381	1.21734	0.608671	+	0.793423i	$0.291703\pi$
$618$	70.5904	2.83956
$619$	26.6695	1.07194	0.535970	−	0.844237i	$-0.319946\pi$
$619$	26.6695	1.07194	0.535970	+	0.844237i	$0.319946\pi$
$620$	162.677	6.53325
$621$	1.19052	0.0477737
$622$	−64.3156	−2.57882
$623$	1.14534	0.0458869
$624$	−114.564	−4.58625
$625$	−30.2034	−1.20814
$626$	−60.2209	−2.40691
$627$	7.36649	0.294189
$628$	−54.1277	−2.15993
$629$	−0.363981	−0.0145129
$630$	1.10094	0.0438625
$631$	15.2518	0.607164	0.303582	−	0.952805i	$-0.401817\pi$
$631$	15.2518	0.607164	0.303582	+	0.952805i	$0.401817\pi$
$632$	73.3703	2.91852
$633$	5.28621	0.210108
$634$	−41.7098	−1.65651
$635$	−17.6917	−0.702075
$636$	−25.9760	−1.03002
$637$	−21.1245	−0.836983
$638$	18.1374	0.718068
$639$	−1.39542	−0.0552019
$640$	127.821	5.05258
$641$	46.1642	1.82338	0.911689	−	0.410881i	$-0.134779\pi$
$641$	46.1642	1.82338	0.911689	+	0.410881i	$0.134779\pi$
$642$	46.5712	1.83802
$643$	−21.0821	−0.831396	−0.415698	−	0.909503i	$-0.636463\pi$
$643$	−21.0821	−0.831396	−0.415698	+	0.909503i	$0.636463\pi$
$644$	1.79866	0.0708770
$645$	54.5223	2.14682
$646$	46.4242	1.82654
$647$	46.6933	1.83570	0.917852	−	0.396924i	$-0.129922\pi$
$647$	46.6933	1.83570	0.917852	+	0.396924i	$0.129922\pi$
$648$	90.1647	3.54201
$649$	−7.50326	−0.294529
$650$	−40.3955	−1.58444
$651$	24.6884	0.967613
$652$	5.64677	0.221144
$653$	21.8463	0.854911	0.427456	−	0.904036i	$-0.359410\pi$
$653$	21.8463	0.854911	0.427456	+	0.904036i	$0.359410\pi$
$654$	44.7294	1.74906
$655$	19.8308	0.774852
$656$	80.8288	3.15584
$657$	1.02898	0.0401444
$658$	−39.3439	−1.53378
$659$	19.3462	0.753620	0.376810	−	0.926291i	$-0.377021\pi$
$659$	19.3462	0.753620	0.376810	+	0.926291i	$0.377021\pi$
$660$	−28.4537	−1.10756
$661$	3.66906	0.142710	0.0713550	−	0.997451i	$-0.477268\pi$
$661$	3.66906	0.142710	0.0713550	+	0.997451i	$0.477268\pi$
$662$	−63.5129	−2.46850
$663$	29.7080	1.15376
$664$	3.34436	0.129786
$665$	−17.0264	−0.660255
$666$	−0.0243742	−0.000944481 0
$667$	1.54001	0.0596294
$668$	−10.6399	−0.411671
$669$	28.6778	1.10875
$670$	−65.6981	−2.53814
$671$	2.25827	0.0871794
$672$	57.3070	2.21066
$673$	36.4040	1.40327	0.701636	−	0.712536i	$-0.252453\pi$
$673$	36.4040	1.40327	0.701636	+	0.712536i	$0.252453\pi$
$674$	51.8725	1.99806
$675$	17.9932	0.692560
$676$	24.6056	0.946371
$677$	18.5883	0.714407	0.357203	−	0.934027i	$-0.383730\pi$
$677$	18.5883	0.714407	0.357203	+	0.934027i	$0.383730\pi$
$678$	19.1702	0.736226
$679$	1.88656	0.0723996
$680$	−114.545	−4.39260
$681$	28.8830	1.10680
$682$	−27.6288	−1.05796
$683$	−6.28731	−0.240577	−0.120289	−	0.992739i	$-0.538382\pi$
$683$	−6.28731	−0.240577	−0.120289	+	0.992739i	$0.538382\pi$
$684$	2.28385	0.0873254
$685$	24.6544	0.941998
$686$	46.1326	1.76135
$687$	−41.0148	−1.56481
$688$	165.327	6.30303
$689$	11.1315	0.424076
$690$	−3.28862	−0.125196
$691$	31.4679	1.19710	0.598548	−	0.801087i	$-0.295745\pi$
$691$	31.4679	1.19710	0.598548	+	0.801087i	$0.295745\pi$
$692$	−3.31126	−0.125875
$693$	−0.137364	−0.00521801
$694$	23.4521	0.890230
$695$	18.6807	0.708601
$696$	112.920	4.28022
$697$	−20.9599	−0.793913
$698$	88.6667	3.35609
$699$	−2.80827	−0.106218
$700$	27.1846	1.02748
$701$	−44.8385	−1.69353	−0.846763	−	0.531971i	$-0.821452\pi$
$701$	−44.8385	−1.69353	−0.846763	+	0.531971i	$0.821452\pi$
$702$	−58.5613	−2.21025
$703$	0.376955	0.0142171
$704$	−32.9666	−1.24247
$705$	52.8463	1.99031
$706$	30.8390	1.16064
$707$	−20.3534	−0.765467
$708$	−73.1294	−2.74837
$709$	−16.7550	−0.629246	−0.314623	−	0.949217i	$-0.601878\pi$
$709$	−16.7550	−0.629246	−0.314623	+	0.949217i	$0.601878\pi$
$710$	−113.467	−4.25833
$711$	−0.744798	−0.0279321
$712$	−7.97988	−0.299059
$713$	−2.34590	−0.0878545
$714$	−27.2138	−1.01845
$715$	12.1933	0.456002
$716$	60.9985	2.27962
$717$	5.21853	0.194890
$718$	−76.3476	−2.84927
$719$	15.1433	0.564751	0.282375	−	0.959304i	$-0.408878\pi$
$719$	15.1433	0.564751	0.282375	+	0.959304i	$0.408878\pi$
$720$	−4.48405	−0.167111
$721$	20.3571	0.758138
$722$	4.08230	0.151927
$723$	51.0723	1.89940
$724$	−36.8737	−1.37040
$725$	23.2754	0.864427
$726$	4.83253	0.179352
$727$	32.3389	1.19938	0.599691	−	0.800232i	$-0.295290\pi$
$727$	32.3389	1.19938	0.599691	+	0.800232i	$0.295290\pi$
$728$	−56.5167	−2.09465
$729$	26.0556	0.965021
$730$	83.6704	3.09678
$731$	−42.8713	−1.58565
$732$	22.0098	0.813507
$733$	−4.80015	−0.177298	−0.0886488	−	0.996063i	$-0.528255\pi$
$733$	−4.80015	−0.177298	−0.0886488	+	0.996063i	$0.528255\pi$
$734$	−36.9465	−1.36372
$735$	−25.9920	−0.958731
$736$	−5.44533	−0.200717
$737$	8.19712	0.301945
$738$	−1.40359	−0.0516669
$739$	−18.2578	−0.671625	−0.335813	−	0.941929i	$-0.609011\pi$
$739$	−18.2578	−0.671625	−0.335813	+	0.941929i	$0.609011\pi$
$740$	−1.45602	−0.0535243
$741$	−30.7669	−1.13025
$742$	−10.1969	−0.374341
$743$	23.7385	0.870880	0.435440	−	0.900218i	$-0.356593\pi$
$743$	23.7385	0.870880	0.435440	+	0.900218i	$0.356593\pi$
$744$	−172.011	−6.30623
$745$	−53.0236	−1.94263
$746$	−1.88668	−0.0690762
$747$	−0.0339493	−0.00124214
$748$	22.3734	0.818051
$749$	13.4304	0.490735
$750$	20.8374	0.760875
$751$	−19.0061	−0.693542	−0.346771	−	0.937950i	$-0.612722\pi$
$751$	−19.0061	−0.693542	−0.346771	+	0.937950i	$0.612722\pi$
$752$	160.245	5.84353
$753$	50.3635	1.83535
$754$	−75.7528	−2.75875
$755$	−1.93526	−0.0704312
$756$	39.4094	1.43330
$757$	11.4560	0.416375	0.208188	−	0.978089i	$-0.433244\pi$
$757$	11.4560	0.416375	0.208188	+	0.978089i	$0.433244\pi$
$758$	65.3947	2.37524
$759$	0.410320	0.0148937
$760$	118.628	4.30308
$761$	5.45779	0.197845	0.0989224	−	0.995095i	$-0.468460\pi$
$761$	5.45779	0.197845	0.0989224	+	0.995095i	$0.468460\pi$
$762$	29.2852	1.06089
$763$	12.8992	0.466982
$764$	−133.541	−4.83133
$765$	1.16277	0.0420400
$766$	−0.313548	−0.0113290
$767$	31.3381	1.13155
$768$	−95.5228	−3.44688
$769$	22.1372	0.798288	0.399144	−	0.916888i	$-0.369307\pi$
$769$	22.1372	0.798288	0.399144	+	0.916888i	$0.369307\pi$
$770$	−11.1696	−0.402523
$771$	35.9951	1.29633
$772$	−15.1456	−0.545102
$773$	49.7206	1.78833	0.894164	−	0.447740i	$-0.147771\pi$
$773$	49.7206	1.78833	0.894164	+	0.447740i	$0.147771\pi$
$774$	−2.87090	−0.103192
$775$	−35.4555	−1.27360
$776$	−13.1442	−0.471850
$777$	−0.220970	−0.00792727
$778$	55.4583	1.98828
$779$	21.7070	0.777734
$780$	118.840	4.25514
$781$	14.1572	0.506584
$782$	2.58587	0.0924704
$783$	33.7423	1.20585
$784$	−78.8152	−2.81483
$785$	28.5401	1.01864
$786$	−32.8260	−1.17086
$787$	48.9531	1.74499	0.872496	−	0.488622i	$-0.162500\pi$
$787$	48.9531	1.74499	0.872496	+	0.488622i	$0.162500\pi$
$788$	22.9636	0.818045
$789$	1.63905	0.0583516
$790$	−60.5624	−2.15471
$791$	5.52836	0.196566
$792$	0.957052	0.0340074
$793$	−9.43188	−0.334936
$794$	7.79958	0.276797
$795$	13.6964	0.485763
$796$	12.1930	0.432170
$797$	44.3730	1.57177	0.785886	−	0.618371i	$-0.212207\pi$
$797$	44.3730	1.57177	0.785886	+	0.618371i	$0.212207\pi$
$798$	28.1838	0.997697
$799$	−41.5535	−1.47006
$800$	−82.2997	−2.90973
$801$	0.0810055	0.00286219
$802$	−83.0520	−2.93267
$803$	−10.4395	−0.368402
$804$	79.8919	2.81757
$805$	−0.948383	−0.0334261
$806$	115.394	4.06459
$807$	29.2117	1.02830
$808$	141.808	4.98878
$809$	17.3397	0.609633	0.304816	−	0.952411i	$-0.401405\pi$
$809$	17.3397	0.609633	0.304816	+	0.952411i	$0.401405\pi$
$810$	−74.4251	−2.61503
$811$	−1.03704	−0.0364154	−0.0182077	−	0.999834i	$-0.505796\pi$
$811$	−1.03704	−0.0364154	−0.0182077	+	0.999834i	$0.505796\pi$
$812$	50.9786	1.78900
$813$	−24.2780	−0.851465
$814$	0.247288	0.00866744
$815$	−2.97739	−0.104293
$816$	110.840	3.88018
$817$	44.3994	1.55334
$818$	−85.9634	−3.00564
$819$	0.573713	0.0200472
$820$	−83.8451	−2.92800
$821$	48.7330	1.70079	0.850397	−	0.526141i	$-0.176362\pi$
$821$	48.7330	1.70079	0.850397	+	0.526141i	$0.176362\pi$
$822$	−40.8106	−1.42343
$823$	20.5954	0.717911	0.358956	−	0.933355i	$-0.383133\pi$
$823$	20.5954	0.717911	0.358956	+	0.933355i	$0.383133\pi$
$824$	−141.834	−4.94101
$825$	6.20150	0.215908
$826$	−28.7071	−0.998848
$827$	−17.0096	−0.591481	−0.295741	−	0.955268i	$-0.595566\pi$
$827$	−17.0096	−0.591481	−0.295741	+	0.955268i	$0.595566\pi$
$828$	0.127213	0.00442094
$829$	21.1487	0.734524	0.367262	−	0.930117i	$-0.380295\pi$
$829$	21.1487	0.734524	0.367262	+	0.930117i	$0.380295\pi$
$830$	−2.76055	−0.0958202
$831$	−2.31859	−0.0804310
$832$	137.688	4.77348
$833$	20.4378	0.708126
$834$	−30.9223	−1.07075
$835$	5.61014	0.194147
$836$	−23.1708	−0.801380
$837$	−51.3996	−1.77663
$838$	−87.1995	−3.01226
$839$	−44.5242	−1.53715	−0.768573	−	0.639762i	$-0.779033\pi$
$839$	−44.5242	−1.53715	−0.768573	+	0.639762i	$0.779033\pi$
$840$	−69.5394	−2.39934
$841$	14.6478	0.505098
$842$	−20.3967	−0.702918
$843$	0.181954	0.00626681
$844$	−16.6274	−0.572340
$845$	−12.9739	−0.446316
$846$	−2.78265	−0.0956695
$847$	1.39362	0.0478854
$848$	41.5315	1.42620
$849$	38.9569	1.33700
$850$	39.0823	1.34051
$851$	0.0209967	0.000719757 0
$852$	137.981	4.72715
$853$	−20.2031	−0.691741	−0.345871	−	0.938282i	$-0.612416\pi$
$853$	−20.2031	−0.691741	−0.345871	+	0.938282i	$0.612416\pi$
$854$	8.64001	0.295655
$855$	−1.20422	−0.0411833
$856$	−93.5733	−3.19827
$857$	−55.0124	−1.87919	−0.939595	−	0.342289i	$-0.888798\pi$
$857$	−55.0124	−1.87919	−0.939595	+	0.342289i	$0.888798\pi$
$858$	−20.1836	−0.689055
$859$	−17.9952	−0.613987	−0.306993	−	0.951712i	$-0.599323\pi$
$859$	−17.9952	−0.613987	−0.306993	+	0.951712i	$0.599323\pi$
$860$	−171.497	−5.84799
$861$	−12.7246	−0.433654
$862$	46.4057	1.58058
$863$	−31.0200	−1.05593	−0.527966	−	0.849266i	$-0.677045\pi$
$863$	−31.0200	−1.05593	−0.527966	+	0.849266i	$0.677045\pi$
$864$	−119.310	−4.05899
$865$	1.74594	0.0593637
$866$	2.56139	0.0870397
$867$	1.18245	0.0401581
$868$	−77.6557	−2.63581
$869$	7.55634	0.256331
$870$	−93.2080	−3.16005
$871$	−34.2361	−1.16005
$872$	−89.8725	−3.04347
$873$	0.133430	0.00451592
$874$	−2.67804	−0.0905859
$875$	6.00917	0.203147
$876$	−101.747	−3.43772
$877$	−22.4479	−0.758012	−0.379006	−	0.925394i	$-0.623734\pi$
$877$	−22.4479	−0.758012	−0.379006	+	0.925394i	$0.623734\pi$
$878$	31.4980	1.06301
$879$	−42.3477	−1.42835
$880$	45.4929	1.53357
$881$	25.3401	0.853730	0.426865	−	0.904315i	$-0.359618\pi$
$881$	25.3401	0.853730	0.426865	+	0.904315i	$0.359618\pi$
$882$	1.36863	0.0460840
$883$	19.4402	0.654214	0.327107	−	0.944987i	$-0.393926\pi$
$883$	19.4402	0.654214	0.327107	+	0.944987i	$0.393926\pi$
$884$	−93.4446	−3.14288
$885$	38.5592	1.29615
$886$	−13.1773	−0.442700
$887$	−19.9544	−0.670002	−0.335001	−	0.942218i	$-0.608737\pi$
$887$	−19.9544	−0.670002	−0.335001	+	0.942218i	$0.608737\pi$
$888$	1.53957	0.0516644
$889$	8.44537	0.283249
$890$	6.58687	0.220792
$891$	9.28598	0.311092
$892$	−90.2041	−3.02026
$893$	43.0346	1.44010
$894$	87.7701	2.93547
$895$	−32.1629	−1.07509
$896$	−61.0171	−2.03844
$897$	−1.71374	−0.0572201
$898$	−36.7237	−1.22549
$899$	−66.4888	−2.21752
$900$	1.92267	0.0640889
$901$	−10.7696	−0.358788
$902$	14.2401	0.474145
$903$	−26.0269	−0.866121
$904$	−38.5177	−1.28108
$905$	19.4425	0.646291
$906$	3.20344	0.106427
$907$	21.7942	0.723663	0.361832	−	0.932243i	$-0.382152\pi$
$907$	21.7942	0.723663	0.361832	+	0.932243i	$0.382152\pi$
$908$	−90.8498	−3.01496
$909$	−1.43952	−0.0477459
$910$	46.6508	1.54646
$911$	−43.9366	−1.45569	−0.727843	−	0.685744i	$-0.759477\pi$
$911$	−43.9366	−1.45569	−0.727843	+	0.685744i	$0.759477\pi$
$912$	−114.791	−3.80111
$913$	0.344433	0.0113991
$914$	−90.1444	−2.98171
$915$	−11.6052	−0.383656
$916$	129.010	4.26260
$917$	−9.46646	−0.312610
$918$	56.6575	1.86998
$919$	44.0816	1.45412	0.727058	−	0.686576i	$-0.240887\pi$
$919$	44.0816	1.45412	0.727058	+	0.686576i	$0.240887\pi$
$920$	6.60766	0.217848
$921$	8.51606	0.280614
$922$	−30.6764	−1.01027
$923$	−59.1290	−1.94625
$924$	13.5827	0.446839
$925$	0.317340	0.0104341
$926$	97.5017	3.20410
$927$	1.43978	0.0472887
$928$	−154.335	−5.06628
$929$	−39.3871	−1.29225	−0.646124	−	0.763232i	$-0.723611\pi$
$929$	−39.3871	−1.29225	−0.646124	+	0.763232i	$0.723611\pi$
$930$	141.984	4.65583
$931$	−21.1662	−0.693695
$932$	8.83323	0.289342
$933$	−41.2384	−1.35009
$934$	70.6621	2.31214
$935$	−11.7969	−0.385799
$936$	−3.99723	−0.130653
$937$	46.4279	1.51673	0.758367	−	0.651828i	$-0.225998\pi$
$937$	46.4279	1.51673	0.758367	+	0.651828i	$0.225998\pi$
$938$	31.3618	1.02400
$939$	−38.6130	−1.26009
$940$	−166.225	−5.42165
$941$	6.78771	0.221273	0.110637	−	0.993861i	$-0.464711\pi$
$941$	6.78771	0.221273	0.110637	+	0.993861i	$0.464711\pi$
$942$	−47.2425	−1.53924
$943$	1.20910	0.0393736
$944$	116.922	3.80549
$945$	−20.7795	−0.675957
$946$	29.1267	0.946991
$947$	−11.8387	−0.384705	−0.192353	−	0.981326i	$-0.561612\pi$
$947$	−11.8387	−0.384705	−0.192353	+	0.981326i	$0.561612\pi$
$948$	73.6467	2.39193
$949$	43.6017	1.41537
$950$	−40.4754	−1.31319
$951$	−26.7438	−0.867229
$952$	54.6794	1.77217
$953$	7.88246	0.255338	0.127669	−	0.991817i	$-0.459251\pi$
$953$	7.88246	0.255338	0.127669	+	0.991817i	$0.459251\pi$
$954$	−0.721193	−0.0233495
$955$	70.4124	2.27849
$956$	−16.4146	−0.530885
$957$	11.6295	0.375929
$958$	−96.2382	−3.10932
$959$	−11.7691	−0.380044
$960$	169.415	5.46784
$961$	70.2824	2.26717
$962$	−1.03282	−0.0332996
$963$	0.949882	0.0306095
$964$	−160.645	−5.17402
$965$	7.98587	0.257074
$966$	1.56986	0.0505095
$967$	−41.2742	−1.32729	−0.663644	−	0.748048i	$-0.730991\pi$
$967$	−41.2742	−1.32729	−0.663644	+	0.748048i	$0.730991\pi$
$968$	−9.70977	−0.312084
$969$	29.7667	0.956244
$970$	10.8497	0.348363
$971$	4.74863	0.152391	0.0761954	−	0.997093i	$-0.475723\pi$
$971$	4.74863	0.152391	0.0761954	+	0.997093i	$0.475723\pi$
$972$	5.66926	0.181841
$973$	−8.91748	−0.285881
$974$	−58.2495	−1.86643
$975$	−25.9012	−0.829501
$976$	−35.1902	−1.12641
$977$	−55.4754	−1.77481	−0.887407	−	0.460986i	$-0.847496\pi$
$977$	−55.4754	−1.77481	−0.887407	+	0.460986i	$0.847496\pi$
$978$	4.92848	0.157596
$979$	−0.821841	−0.0262661
$980$	81.7563	2.61161
$981$	0.912315	0.0291280
$982$	41.1630	1.31356
$983$	36.5224	1.16488	0.582442	−	0.812872i	$-0.302097\pi$
$983$	36.5224	1.16488	0.582442	+	0.812872i	$0.302097\pi$
$984$	88.6561	2.82625
$985$	−12.1081	−0.385796
$986$	73.2902	2.33403
$987$	−25.2268	−0.802979
$988$	96.7753	3.07883
$989$	2.47309	0.0786395
$990$	−0.789984	−0.0251073
$991$	39.0820	1.24148	0.620740	−	0.784017i	$-0.286832\pi$
$991$	39.0820	1.24148	0.620740	+	0.784017i	$0.286832\pi$
$992$	235.098	7.46437
$993$	−40.7238	−1.29233
$994$	54.1648	1.71800
$995$	−6.42904	−0.203814
$996$	3.35696	0.106369
$997$	−39.9497	−1.26522	−0.632609	−	0.774471i	$-0.718016\pi$
$997$	−39.9497	−1.26522	−0.632609	+	0.774471i	$0.718016\pi$
$998$	−31.7650	−1.00550
$999$	0.460047	0.0145552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.2	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.2	✓	121	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74533 q^{2} -1.76027 q^{3} +5.53683 q^{4} -2.91942 q^{5} +4.83253 q^{6} +1.39362 q^{7} -9.70977 q^{8} +0.0985659 q^{9} +O(q^{10})\)	\(q-2.74533 q^{2} -1.76027 q^{3} +5.53683 q^{4} -2.91942 q^{5} +4.83253 q^{6} +1.39362 q^{7} -9.70977 q^{8} +0.0985659 q^{9} +8.01478 q^{10} -1.00000 q^{11} -9.74634 q^{12} +4.17660 q^{13} -3.82595 q^{14} +5.13898 q^{15} +15.5828 q^{16} -4.04082 q^{17} -0.270596 q^{18} +4.18485 q^{19} -16.1644 q^{20} -2.45316 q^{21} +2.74533 q^{22} +0.233100 q^{23} +17.0919 q^{24} +3.52303 q^{25} -11.4661 q^{26} +5.10732 q^{27} +7.71625 q^{28} +6.60665 q^{29} -14.1082 q^{30} -10.0639 q^{31} -23.3605 q^{32} +1.76027 q^{33} +11.0934 q^{34} -4.06857 q^{35} +0.545743 q^{36} +0.0900760 q^{37} -11.4888 q^{38} -7.35196 q^{39} +28.3469 q^{40} +5.18704 q^{41} +6.73472 q^{42} +10.6096 q^{43} -5.53683 q^{44} -0.287756 q^{45} -0.639936 q^{46} +10.2834 q^{47} -27.4301 q^{48} -5.05782 q^{49} -9.67187 q^{50} +7.11296 q^{51} +23.1251 q^{52} +2.66520 q^{53} -14.0213 q^{54} +2.91942 q^{55} -13.5317 q^{56} -7.36649 q^{57} -18.1374 q^{58} +7.50326 q^{59} +28.4537 q^{60} -2.25827 q^{61} +27.6288 q^{62} +0.137364 q^{63} +32.9666 q^{64} -12.1933 q^{65} -4.83253 q^{66} -8.19712 q^{67} -22.3734 q^{68} -0.410320 q^{69} +11.1696 q^{70} -14.1572 q^{71} -0.957052 q^{72} +10.4395 q^{73} -0.247288 q^{74} -6.20150 q^{75} +23.1708 q^{76} -1.39362 q^{77} +20.1836 q^{78} -7.55634 q^{79} -45.4929 q^{80} -9.28598 q^{81} -14.2401 q^{82} -0.344433 q^{83} -13.5827 q^{84} +11.7969 q^{85} -29.1267 q^{86} -11.6295 q^{87} +9.70977 q^{88} +0.821841 q^{89} +0.789984 q^{90} +5.82060 q^{91} +1.29063 q^{92} +17.7153 q^{93} -28.2314 q^{94} -12.2174 q^{95} +41.1209 q^{96} +1.35371 q^{97} +13.8854 q^{98} -0.0985659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

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