LMFDB - Embedded newform 6017.2.a.f.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.32206 q^{2} +0.535084 q^{3} +3.39196 q^{4} -0.511363 q^{5} -1.24250 q^{6} +3.83500 q^{7} -3.23221 q^{8} -2.71368 q^{9} +O(q^{10})$	\(q-2.32206 q^{2} +0.535084 q^{3} +3.39196 q^{4} -0.511363 q^{5} -1.24250 q^{6} +3.83500 q^{7} -3.23221 q^{8} -2.71368 q^{9} +1.18742 q^{10} -1.00000 q^{11} +1.81498 q^{12} +1.58554 q^{13} -8.90510 q^{14} -0.273622 q^{15} +0.721461 q^{16} +5.58922 q^{17} +6.30134 q^{18} +6.53126 q^{19} -1.73452 q^{20} +2.05205 q^{21} +2.32206 q^{22} -3.91383 q^{23} -1.72950 q^{24} -4.73851 q^{25} -3.68173 q^{26} -3.05730 q^{27} +13.0082 q^{28} +0.712066 q^{29} +0.635367 q^{30} +4.98368 q^{31} +4.78914 q^{32} -0.535084 q^{33} -12.9785 q^{34} -1.96108 q^{35} -9.20470 q^{36} +3.92575 q^{37} -15.1660 q^{38} +0.848400 q^{39} +1.65283 q^{40} -2.55719 q^{41} -4.76498 q^{42} +7.01225 q^{43} -3.39196 q^{44} +1.38768 q^{45} +9.08815 q^{46} +1.87117 q^{47} +0.386043 q^{48} +7.70725 q^{49} +11.0031 q^{50} +2.99071 q^{51} +5.37810 q^{52} -8.57947 q^{53} +7.09924 q^{54} +0.511363 q^{55} -12.3955 q^{56} +3.49478 q^{57} -1.65346 q^{58} +6.46824 q^{59} -0.928116 q^{60} +10.8232 q^{61} -11.5724 q^{62} -10.4070 q^{63} -12.5636 q^{64} -0.810789 q^{65} +1.24250 q^{66} +4.01160 q^{67} +18.9584 q^{68} -2.09423 q^{69} +4.55374 q^{70} -15.2159 q^{71} +8.77119 q^{72} +1.42979 q^{73} -9.11582 q^{74} -2.53550 q^{75} +22.1538 q^{76} -3.83500 q^{77} -1.97003 q^{78} -7.90726 q^{79} -0.368928 q^{80} +6.50514 q^{81} +5.93794 q^{82} +3.88440 q^{83} +6.96047 q^{84} -2.85812 q^{85} -16.2828 q^{86} +0.381015 q^{87} +3.23221 q^{88} -4.21218 q^{89} -3.22227 q^{90} +6.08057 q^{91} -13.2756 q^{92} +2.66669 q^{93} -4.34497 q^{94} -3.33985 q^{95} +2.56259 q^{96} -13.1317 q^{97} -17.8967 q^{98} +2.71368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.32206	−1.64194	−0.820972	−	0.570969i	$-0.806568\pi$
$2$	−2.32206	−1.64194	−0.820972	+	0.570969i	$0.806568\pi$
$3$	0.535084	0.308931	0.154466	−	0.987998i	$-0.450634\pi$
$3$	0.535084	0.308931	0.154466	+	0.987998i	$0.450634\pi$
$4$	3.39196	1.69598
$5$	−0.511363	−0.228689	−0.114344	−	0.993441i	$-0.536477\pi$
$5$	−0.511363	−0.228689	−0.114344	+	0.993441i	$0.536477\pi$
$6$	−1.24250	−0.507248
$7$	3.83500	1.44950	0.724748	−	0.689014i	$-0.241956\pi$
$7$	3.83500	1.44950	0.724748	+	0.689014i	$0.241956\pi$
$8$	−3.23221	−1.14276
$9$	−2.71368	−0.904562
$10$	1.18742	0.375494
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.81498	0.523941
$13$	1.58554	0.439751	0.219875	−	0.975528i	$-0.429435\pi$
$13$	1.58554	0.439751	0.219875	+	0.975528i	$0.429435\pi$
$14$	−8.90510	−2.37999
$15$	−0.273622	−0.0706490
$16$	0.721461	0.180365
$17$	5.58922	1.35559	0.677793	−	0.735253i	$-0.262937\pi$
$17$	5.58922	1.35559	0.677793	+	0.735253i	$0.262937\pi$
$18$	6.30134	1.48524
$19$	6.53126	1.49837	0.749187	−	0.662359i	$-0.230444\pi$
$19$	6.53126	1.49837	0.749187	+	0.662359i	$0.230444\pi$
$20$	−1.73452	−0.387851
$21$	2.05205	0.447794
$22$	2.32206	0.495065
$23$	−3.91383	−0.816091	−0.408045	−	0.912962i	$-0.633789\pi$
$23$	−3.91383	−0.816091	−0.408045	+	0.912962i	$0.633789\pi$
$24$	−1.72950	−0.353034
$25$	−4.73851	−0.947702
$26$	−3.68173	−0.722046
$27$	−3.05730	−0.588378
$28$	13.0082	2.45831
$29$	0.712066	0.132227	0.0661137	−	0.997812i	$-0.478940\pi$
$29$	0.712066	0.132227	0.0661137	+	0.997812i	$0.478940\pi$
$30$	0.635367	0.116002
$31$	4.98368	0.895095	0.447548	−	0.894260i	$-0.352297\pi$
$31$	4.98368	0.895095	0.447548	+	0.894260i	$0.352297\pi$
$32$	4.78914	0.846608
$33$	−0.535084	−0.0931463
$34$	−12.9785	−2.22579
$35$	−1.96108	−0.331483
$36$	−9.20470	−1.53412
$37$	3.92575	0.645389	0.322695	−	0.946503i	$-0.395411\pi$
$37$	3.92575	0.645389	0.322695	+	0.946503i	$0.395411\pi$
$38$	−15.1660	−2.46025
$39$	0.848400	0.135853
$40$	1.65283	0.261336
$41$	−2.55719	−0.399365	−0.199683	−	0.979861i	$-0.563991\pi$
$41$	−2.55719	−0.399365	−0.199683	+	0.979861i	$0.563991\pi$
$42$	−4.76498	−0.735253
$43$	7.01225	1.06936	0.534679	−	0.845055i	$-0.320433\pi$
$43$	7.01225	1.06936	0.534679	+	0.845055i	$0.320433\pi$
$44$	−3.39196	−0.511357
$45$	1.38768	0.206863
$46$	9.08815	1.33997
$47$	1.87117	0.272938	0.136469	−	0.990644i	$-0.456425\pi$
$47$	1.87117	0.272938	0.136469	+	0.990644i	$0.456425\pi$
$48$	0.386043	0.0557204
$49$	7.70725	1.10104
$50$	11.0031	1.55607
$51$	2.99071	0.418783
$52$	5.37810	0.745808
$53$	−8.57947	−1.17848	−0.589240	−	0.807958i	$-0.700573\pi$
$53$	−8.57947	−1.17848	−0.589240	+	0.807958i	$0.700573\pi$
$54$	7.09924	0.966084
$55$	0.511363	0.0689522
$56$	−12.3955	−1.65642
$57$	3.49478	0.462894
$58$	−1.65346	−0.217110
$59$	6.46824	0.842093	0.421046	−	0.907039i	$-0.361663\pi$
$59$	6.46824	0.842093	0.421046	+	0.907039i	$0.361663\pi$
$60$	−0.928116	−0.119819
$61$	10.8232	1.38577	0.692886	−	0.721047i	$-0.256339\pi$
$61$	10.8232	1.38577	0.692886	+	0.721047i	$0.256339\pi$
$62$	−11.5724	−1.46970
$63$	−10.4070	−1.31116
$64$	−12.5636	−1.57045
$65$	−0.810789	−0.100566
$66$	1.24250	0.152941
$67$	4.01160	0.490095	0.245048	−	0.969511i	$-0.421196\pi$
$67$	4.01160	0.490095	0.245048	+	0.969511i	$0.421196\pi$
$68$	18.9584	2.29904
$69$	−2.09423	−0.252116
$70$	4.55374	0.544276
$71$	−15.2159	−1.80579	−0.902896	−	0.429859i	$-0.858563\pi$
$71$	−15.2159	−1.80579	−0.902896	+	0.429859i	$0.858563\pi$
$72$	8.77119	1.03369
$73$	1.42979	0.167345	0.0836723	−	0.996493i	$-0.473335\pi$
$73$	1.42979	0.167345	0.0836723	+	0.996493i	$0.473335\pi$
$74$	−9.11582	−1.05969
$75$	−2.53550	−0.292775
$76$	22.1538	2.54121
$77$	−3.83500	−0.437039
$78$	−1.97003	−0.223062
$79$	−7.90726	−0.889636	−0.444818	−	0.895621i	$-0.646732\pi$
$79$	−7.90726	−0.889636	−0.444818	+	0.895621i	$0.646732\pi$
$80$	−0.368928	−0.0412475
$81$	6.50514	0.722793
$82$	5.93794	0.655735
$83$	3.88440	0.426368	0.213184	−	0.977012i	$-0.431617\pi$
$83$	3.88440	0.426368	0.213184	+	0.977012i	$0.431617\pi$
$84$	6.96047	0.759450
$85$	−2.85812	−0.310007
$86$	−16.2828	−1.75582
$87$	0.381015	0.0408491
$88$	3.23221	0.344554
$89$	−4.21218	−0.446491	−0.223245	−	0.974762i	$-0.571665\pi$
$89$	−4.21218	−0.446491	−0.223245	+	0.974762i	$0.571665\pi$
$90$	−3.22227	−0.339657
$91$	6.08057	0.637417
$92$	−13.2756	−1.38407
$93$	2.66669	0.276523
$94$	−4.34497	−0.448149
$95$	−3.33985	−0.342661
$96$	2.56259	0.261544
$97$	−13.1317	−1.33332	−0.666662	−	0.745361i	$-0.732277\pi$
$97$	−13.1317	−1.33332	−0.666662	+	0.745361i	$0.732277\pi$
$98$	−17.8967	−1.80784
$99$	2.71368	0.272736
$100$	−16.0728	−1.60728
$101$	6.69632	0.666309	0.333154	−	0.942872i	$-0.391887\pi$
$101$	6.69632	0.666309	0.333154	+	0.942872i	$0.391887\pi$
$102$	−6.94459	−0.687617
$103$	2.57956	0.254172	0.127086	−	0.991892i	$-0.459438\pi$
$103$	2.57956	0.254172	0.127086	+	0.991892i	$0.459438\pi$
$104$	−5.12481	−0.502529
$105$	−1.04934	−0.102405
$106$	19.9220	1.93500
$107$	−5.09966	−0.493003	−0.246501	−	0.969142i	$-0.579281\pi$
$107$	−5.09966	−0.493003	−0.246501	+	0.969142i	$0.579281\pi$
$108$	−10.3702	−0.997877
$109$	0.985401	0.0943843	0.0471921	−	0.998886i	$-0.484973\pi$
$109$	0.985401	0.0943843	0.0471921	+	0.998886i	$0.484973\pi$
$110$	−1.18742	−0.113216
$111$	2.10061	0.199381
$112$	2.76681	0.261439
$113$	12.0717	1.13561	0.567803	−	0.823164i	$-0.307793\pi$
$113$	12.0717	1.13561	0.567803	+	0.823164i	$0.307793\pi$
$114$	−8.11508	−0.760047
$115$	2.00139	0.186631
$116$	2.41530	0.224255
$117$	−4.30267	−0.397782
$118$	−15.0196	−1.38267
$119$	21.4347	1.96491
$120$	0.884404	0.0807347
$121$	1.00000	0.0909091
$122$	−25.1322	−2.27536
$123$	−1.36831	−0.123376
$124$	16.9044	1.51806
$125$	4.97991	0.445417
$126$	24.1656	2.15285
$127$	−6.01434	−0.533687	−0.266843	−	0.963740i	$-0.585981\pi$
$127$	−6.01434	−0.533687	−0.266843	+	0.963740i	$0.585981\pi$
$128$	19.5951	1.73198
$129$	3.75214	0.330358
$130$	1.88270	0.165124
$131$	12.1508	1.06162	0.530812	−	0.847490i	$-0.321887\pi$
$131$	12.1508	1.06162	0.530812	+	0.847490i	$0.321887\pi$
$132$	−1.81498	−0.157974
$133$	25.0474	2.17189
$134$	−9.31518	−0.804709
$135$	1.56339	0.134555
$136$	−18.0655	−1.54911
$137$	5.39118	0.460600	0.230300	−	0.973120i	$-0.426029\pi$
$137$	5.39118	0.460600	0.230300	+	0.973120i	$0.426029\pi$
$138$	4.86293	0.413960
$139$	17.2878	1.46633	0.733167	−	0.680048i	$-0.238041\pi$
$139$	17.2878	1.46633	0.733167	+	0.680048i	$0.238041\pi$
$140$	−6.65190	−0.562188
$141$	1.00123	0.0843191
$142$	35.3322	2.96501
$143$	−1.58554	−0.132590
$144$	−1.95782	−0.163151
$145$	−0.364124	−0.0302389
$146$	−3.32006	−0.274770
$147$	4.12403	0.340144
$148$	13.3160	1.09457
$149$	17.8974	1.46621	0.733107	−	0.680114i	$-0.238070\pi$
$149$	17.8974	1.46621	0.733107	+	0.680114i	$0.238070\pi$
$150$	5.88758	0.480719
$151$	19.5040	1.58722	0.793608	−	0.608429i	$-0.208200\pi$
$151$	19.5040	1.58722	0.793608	+	0.608429i	$0.208200\pi$
$152$	−21.1104	−1.71228
$153$	−15.1674	−1.22621
$154$	8.90510	0.717594
$155$	−2.54847	−0.204698
$156$	2.87774	0.230403
$157$	−8.23540	−0.657257	−0.328628	−	0.944459i	$-0.606586\pi$
$157$	−8.23540	−0.657257	−0.328628	+	0.944459i	$0.606586\pi$
$158$	18.3611	1.46073
$159$	−4.59074	−0.364069
$160$	−2.44899	−0.193610
$161$	−15.0096	−1.18292
$162$	−15.1053	−1.18679
$163$	−10.1968	−0.798677	−0.399338	−	0.916804i	$-0.630760\pi$
$163$	−10.1968	−0.798677	−0.399338	+	0.916804i	$0.630760\pi$
$164$	−8.67386	−0.677315
$165$	0.273622	0.0213015
$166$	−9.01980	−0.700072
$167$	8.31389	0.643348	0.321674	−	0.946850i	$-0.395754\pi$
$167$	8.31389	0.643348	0.321674	+	0.946850i	$0.395754\pi$
$168$	−6.63265	−0.511720
$169$	−10.4861	−0.806619
$170$	6.63673	0.509014
$171$	−17.7238	−1.35537
$172$	23.7852	1.81361
$173$	6.30465	0.479334	0.239667	−	0.970855i	$-0.422962\pi$
$173$	6.30465	0.479334	0.239667	+	0.970855i	$0.422962\pi$
$174$	−0.884740	−0.0670720
$175$	−18.1722	−1.37369
$176$	−0.721461	−0.0543822
$177$	3.46105	0.260149
$178$	9.78094	0.733112
$179$	−17.2773	−1.29136	−0.645682	−	0.763606i	$-0.723427\pi$
$179$	−17.2773	−1.29136	−0.645682	+	0.763606i	$0.723427\pi$
$180$	4.70694	0.350835
$181$	22.7089	1.68794	0.843969	−	0.536392i	$-0.180213\pi$
$181$	22.7089	1.68794	0.843969	+	0.536392i	$0.180213\pi$
$182$	−14.1194	−1.04660
$183$	5.79134	0.428108
$184$	12.6503	0.932594
$185$	−2.00748	−0.147593
$186$	−6.19221	−0.454035
$187$	−5.58922	−0.408724
$188$	6.34693	0.462897
$189$	−11.7248	−0.852852
$190$	7.75532	0.562630
$191$	10.8194	0.782862	0.391431	−	0.920208i	$-0.371980\pi$
$191$	10.8194	0.782862	0.391431	+	0.920208i	$0.371980\pi$
$192$	−6.72258	−0.485160
$193$	−23.0050	−1.65594	−0.827968	−	0.560775i	$-0.810503\pi$
$193$	−23.0050	−1.65594	−0.827968	+	0.560775i	$0.810503\pi$
$194$	30.4926	2.18924
$195$	−0.433840	−0.0310680
$196$	26.1427	1.86733
$197$	−13.2646	−0.945061	−0.472531	−	0.881314i	$-0.656659\pi$
$197$	−13.2646	−0.945061	−0.472531	+	0.881314i	$0.656659\pi$
$198$	−6.30134	−0.447816
$199$	−15.9498	−1.13065	−0.565327	−	0.824867i	$-0.691250\pi$
$199$	−15.9498	−1.13065	−0.565327	+	0.824867i	$0.691250\pi$
$200$	15.3158	1.08299
$201$	2.14655	0.151406
$202$	−15.5493	−1.09404
$203$	2.73078	0.191663
$204$	10.1443	0.710246
$205$	1.30765	0.0913302
$206$	−5.98990	−0.417336
$207$	10.6209	0.738204
$208$	1.14391	0.0793157
$209$	−6.53126	−0.451777
$210$	2.43664	0.168144
$211$	3.34523	0.230295	0.115148	−	0.993348i	$-0.463266\pi$
$211$	3.34523	0.230295	0.115148	+	0.993348i	$0.463266\pi$
$212$	−29.1012	−1.99868
$213$	−8.14178	−0.557865
$214$	11.8417	0.809482
$215$	−3.58580	−0.244550
$216$	9.88184	0.672374
$217$	19.1124	1.29744
$218$	−2.28816	−0.154974
$219$	0.765060	0.0516980
$220$	1.73452	0.116941
$221$	8.86195	0.596120
$222$	−4.87773	−0.327372
$223$	7.75735	0.519470	0.259735	−	0.965680i	$-0.416365\pi$
$223$	7.75735	0.519470	0.259735	+	0.965680i	$0.416365\pi$
$224$	18.3664	1.22715
$225$	12.8588	0.857254
$226$	−28.0311	−1.86460
$227$	−9.32991	−0.619248	−0.309624	−	0.950859i	$-0.600203\pi$
$227$	−9.32991	−0.619248	−0.309624	+	0.950859i	$0.600203\pi$
$228$	11.8541	0.785059
$229$	4.62785	0.305817	0.152909	−	0.988240i	$-0.451136\pi$
$229$	4.62785	0.305817	0.152909	+	0.988240i	$0.451136\pi$
$230$	−4.64734	−0.306437
$231$	−2.05205	−0.135015
$232$	−2.30154	−0.151104
$233$	−4.93453	−0.323272	−0.161636	−	0.986850i	$-0.551677\pi$
$233$	−4.93453	−0.323272	−0.161636	+	0.986850i	$0.551677\pi$
$234$	9.99104	0.653135
$235$	−0.956847	−0.0624178
$236$	21.9400	1.42817
$237$	−4.23105	−0.274836
$238$	−49.7726	−3.22628
$239$	−25.9547	−1.67887	−0.839434	−	0.543462i	$-0.817113\pi$
$239$	−25.9547	−1.67887	−0.839434	+	0.543462i	$0.817113\pi$
$240$	−0.197408	−0.0127426
$241$	−10.0236	−0.645675	−0.322838	−	0.946454i	$-0.604637\pi$
$241$	−10.0236	−0.645675	−0.322838	+	0.946454i	$0.604637\pi$
$242$	−2.32206	−0.149268
$243$	12.6527	0.811672
$244$	36.7119	2.35024
$245$	−3.94120	−0.251794
$246$	3.17730	0.202577
$247$	10.3556	0.658911
$248$	−16.1083	−1.02288
$249$	2.07848	0.131718
$250$	−11.5637	−0.731350
$251$	1.46742	0.0926226	0.0463113	−	0.998927i	$-0.485253\pi$
$251$	1.46742	0.0926226	0.0463113	+	0.998927i	$0.485253\pi$
$252$	−35.3001	−2.22370
$253$	3.91383	0.246061
$254$	13.9657	0.876283
$255$	−1.52934	−0.0957707
$256$	−20.3738	−1.27336
$257$	−6.41556	−0.400192	−0.200096	−	0.979776i	$-0.564125\pi$
$257$	−6.41556	−0.400192	−0.200096	+	0.979776i	$0.564125\pi$
$258$	−8.71270	−0.542429
$259$	15.0553	0.935489
$260$	−2.75016	−0.170558
$261$	−1.93232	−0.119608
$262$	−28.2150	−1.74313
$263$	0.626901	0.0386564	0.0193282	−	0.999813i	$-0.493847\pi$
$263$	0.626901	0.0386564	0.0193282	+	0.999813i	$0.493847\pi$
$264$	1.72950	0.106444
$265$	4.38722	0.269505
$266$	−58.1616	−3.56611
$267$	−2.25387	−0.137935
$268$	13.6072	0.831192
$269$	15.8922	0.968963	0.484482	−	0.874801i	$-0.339008\pi$
$269$	15.8922	0.968963	0.484482	+	0.874801i	$0.339008\pi$
$270$	−3.63029	−0.220932
$271$	14.0706	0.854726	0.427363	−	0.904080i	$-0.359443\pi$
$271$	14.0706	0.854726	0.427363	+	0.904080i	$0.359443\pi$
$272$	4.03240	0.244500
$273$	3.25362	0.196918
$274$	−12.5186	−0.756279
$275$	4.73851	0.285743
$276$	−7.10354	−0.427583
$277$	29.5429	1.77506	0.887529	−	0.460752i	$-0.152420\pi$
$277$	29.5429	1.77506	0.887529	+	0.460752i	$0.152420\pi$
$278$	−40.1434	−2.40764
$279$	−13.5241	−0.809669
$280$	6.33861	0.378805
$281$	4.46193	0.266176	0.133088	−	0.991104i	$-0.457511\pi$
$281$	4.46193	0.266176	0.133088	+	0.991104i	$0.457511\pi$
$282$	−2.32492	−0.138447
$283$	0.471128	0.0280057	0.0140028	−	0.999902i	$-0.495543\pi$
$283$	0.471128	0.0280057	0.0140028	+	0.999902i	$0.495543\pi$
$284$	−51.6116	−3.06258
$285$	−1.78710	−0.105859
$286$	3.68173	0.217705
$287$	−9.80682	−0.578878
$288$	−12.9962	−0.765809
$289$	14.2394	0.837611
$290$	0.845518	0.0496505
$291$	−7.02657	−0.411905
$292$	4.84980	0.283813
$293$	−8.91018	−0.520538	−0.260269	−	0.965536i	$-0.583811\pi$
$293$	−8.91018	−0.520538	−0.260269	+	0.965536i	$0.583811\pi$
$294$	−9.57624	−0.558498
$295$	−3.30762	−0.192577
$296$	−12.6888	−0.737524
$297$	3.05730	0.177403
$298$	−41.5589	−2.40744
$299$	−6.20555	−0.358876
$300$	−8.60032	−0.496539
$301$	26.8920	1.55003
$302$	−45.2895	−2.60612
$303$	3.58310	0.205844
$304$	4.71205	0.270255
$305$	−5.53460	−0.316910
$306$	35.2196	2.01337
$307$	−6.28255	−0.358564	−0.179282	−	0.983798i	$-0.557377\pi$
$307$	−6.28255	−0.358564	−0.179282	+	0.983798i	$0.557377\pi$
$308$	−13.0082	−0.741209
$309$	1.38028	0.0785217
$310$	5.91770	0.336103
$311$	−21.1922	−1.20170	−0.600850	−	0.799362i	$-0.705171\pi$
$311$	−21.1922	−1.20170	−0.600850	+	0.799362i	$0.705171\pi$
$312$	−2.74220	−0.155247
$313$	27.3794	1.54757	0.773787	−	0.633446i	$-0.218360\pi$
$313$	27.3794	1.54757	0.773787	+	0.633446i	$0.218360\pi$
$314$	19.1231	1.07918
$315$	5.32175	0.299847
$316$	−26.8211	−1.50880
$317$	−20.0952	−1.12866	−0.564331	−	0.825549i	$-0.690866\pi$
$317$	−20.0952	−1.12866	−0.564331	+	0.825549i	$0.690866\pi$
$318$	10.6600	0.597781
$319$	−0.712066	−0.0398680
$320$	6.42455	0.359143
$321$	−2.72875	−0.152304
$322$	34.8531	1.94229
$323$	36.5047	2.03117
$324$	22.0652	1.22584
$325$	−7.51311	−0.416752
$326$	23.6776	1.31138
$327$	0.527273	0.0291582
$328$	8.26535	0.456378
$329$	7.17594	0.395622
$330$	−0.635367	−0.0349758
$331$	−12.6702	−0.696415	−0.348207	−	0.937418i	$-0.613209\pi$
$331$	−12.6702	−0.696415	−0.348207	+	0.937418i	$0.613209\pi$
$332$	13.1757	0.723111
$333$	−10.6532	−0.583794
$334$	−19.3053	−1.05634
$335$	−2.05139	−0.112079
$336$	1.48047	0.0807665
$337$	3.25249	0.177175	0.0885873	−	0.996068i	$-0.471765\pi$
$337$	3.25249	0.177175	0.0885873	+	0.996068i	$0.471765\pi$
$338$	24.3492	1.32442
$339$	6.45936	0.350824
$340$	−9.69463	−0.525765
$341$	−4.98368	−0.269881
$342$	41.1557	2.22544
$343$	2.71232	0.146452
$344$	−22.6650	−1.22202
$345$	1.07091	0.0576560
$346$	−14.6398	−0.787039
$347$	5.52353	0.296518	0.148259	−	0.988949i	$-0.452633\pi$
$347$	5.52353	0.296518	0.148259	+	0.988949i	$0.452633\pi$
$348$	1.29239	0.0692793
$349$	−2.62547	−0.140538	−0.0702691	−	0.997528i	$-0.522386\pi$
$349$	−2.62547	−0.140538	−0.0702691	+	0.997528i	$0.522386\pi$
$350$	42.1969	2.25552
$351$	−4.84749	−0.258740
$352$	−4.78914	−0.255262
$353$	−20.2212	−1.07627	−0.538134	−	0.842859i	$-0.680871\pi$
$353$	−20.2212	−1.07627	−0.538134	+	0.842859i	$0.680871\pi$
$354$	−8.03677	−0.427150
$355$	7.78084	0.412964
$356$	−14.2876	−0.757239
$357$	11.4694	0.607023
$358$	40.1189	2.12035
$359$	7.67286	0.404958	0.202479	−	0.979287i	$-0.435100\pi$
$359$	7.67286	0.404958	0.202479	+	0.979287i	$0.435100\pi$
$360$	−4.48526	−0.236394
$361$	23.6574	1.24512
$362$	−52.7313	−2.77150
$363$	0.535084	0.0280847
$364$	20.6250	1.08104
$365$	−0.731143	−0.0382698
$366$	−13.4478	−0.702930
$367$	2.20396	0.115046	0.0575228	−	0.998344i	$-0.481680\pi$
$367$	2.20396	0.115046	0.0575228	+	0.998344i	$0.481680\pi$
$368$	−2.82368	−0.147194
$369$	6.93939	0.361250
$370$	4.66149	0.242340
$371$	−32.9023	−1.70820
$372$	9.04530	0.468977
$373$	−13.2353	−0.685297	−0.342648	−	0.939464i	$-0.611324\pi$
$373$	−13.2353	−0.685297	−0.342648	+	0.939464i	$0.611324\pi$
$374$	12.9785	0.671102
$375$	2.66467	0.137603
$376$	−6.04801	−0.311902
$377$	1.12901	0.0581471
$378$	27.2256	1.40033
$379$	20.0253	1.02863	0.514315	−	0.857601i	$-0.328046\pi$
$379$	20.0253	1.02863	0.514315	+	0.857601i	$0.328046\pi$
$380$	−11.3286	−0.581146
$381$	−3.21818	−0.164872
$382$	−25.1232	−1.28541
$383$	−2.22060	−0.113467	−0.0567336	−	0.998389i	$-0.518069\pi$
$383$	−2.22060	−0.113467	−0.0567336	+	0.998389i	$0.518069\pi$
$384$	10.4850	0.535062
$385$	1.96108	0.0999458
$386$	53.4190	2.71895
$387$	−19.0290	−0.967300
$388$	−44.5422	−2.26129
$389$	12.2727	0.622249	0.311124	−	0.950369i	$-0.399294\pi$
$389$	12.2727	0.622249	0.311124	+	0.950369i	$0.399294\pi$
$390$	1.00740	0.0510118
$391$	−21.8753	−1.10628
$392$	−24.9114	−1.25822
$393$	6.50173	0.327969
$394$	30.8011	1.55174
$395$	4.04348	0.203450
$396$	9.20470	0.462554
$397$	−0.0859503	−0.00431372	−0.00215686	−	0.999998i	$-0.500687\pi$
$397$	−0.0859503	−0.00431372	−0.00215686	+	0.999998i	$0.500687\pi$
$398$	37.0365	1.85647
$399$	13.4025	0.670963
$400$	−3.41865	−0.170932
$401$	28.2346	1.40997	0.704984	−	0.709224i	$-0.250954\pi$
$401$	28.2346	1.40997	0.704984	+	0.709224i	$0.250954\pi$
$402$	−4.98441	−0.248600
$403$	7.90184	0.393619
$404$	22.7136	1.13005
$405$	−3.32649	−0.165294
$406$	−6.34102	−0.314700
$407$	−3.92575	−0.194592
$408$	−9.66658	−0.478567
$409$	−0.718707	−0.0355378	−0.0177689	−	0.999842i	$-0.505656\pi$
$409$	−0.718707	−0.0355378	−0.0177689	+	0.999842i	$0.505656\pi$
$410$	−3.03644	−0.149959
$411$	2.88474	0.142294
$412$	8.74977	0.431070
$413$	24.8057	1.22061
$414$	−24.6624	−1.21209
$415$	−1.98634	−0.0975054
$416$	7.59339	0.372297
$417$	9.25045	0.452996
$418$	15.1660	0.741792
$419$	−37.5851	−1.83615	−0.918075	−	0.396406i	$-0.870257\pi$
$419$	−37.5851	−1.83615	−0.918075	+	0.396406i	$0.870257\pi$
$420$	−3.55933	−0.173677
$421$	13.8651	0.675746	0.337873	−	0.941192i	$-0.390293\pi$
$421$	13.8651	0.675746	0.337873	+	0.941192i	$0.390293\pi$
$422$	−7.76782	−0.378131
$423$	−5.07776	−0.246889
$424$	27.7306	1.34672
$425$	−26.4846	−1.28469
$426$	18.9057	0.915984
$427$	41.5071	2.00867
$428$	−17.2978	−0.836122
$429$	−0.848400	−0.0409611
$430$	8.32645	0.401537
$431$	22.7350	1.09511	0.547553	−	0.836771i	$-0.315559\pi$
$431$	22.7350	1.09511	0.547553	+	0.836771i	$0.315559\pi$
$432$	−2.20573	−0.106123
$433$	5.10427	0.245296	0.122648	−	0.992450i	$-0.460861\pi$
$433$	5.10427	0.245296	0.122648	+	0.992450i	$0.460861\pi$
$434$	−44.3802	−2.13032
$435$	−0.194837	−0.00934173
$436$	3.34244	0.160074
$437$	−25.5623	−1.22281
$438$	−1.77651	−0.0848852
$439$	3.12851	0.149316	0.0746579	−	0.997209i	$-0.476214\pi$
$439$	3.12851	0.149316	0.0746579	+	0.997209i	$0.476214\pi$
$440$	−1.65283	−0.0787956
$441$	−20.9151	−0.995955
$442$	−20.5780	−0.978795
$443$	23.8040	1.13096	0.565481	−	0.824762i	$-0.308691\pi$
$443$	23.8040	1.13096	0.565481	+	0.824762i	$0.308691\pi$
$444$	7.12517	0.338146
$445$	2.15396	0.102107
$446$	−18.0130	−0.852941
$447$	9.57663	0.452959
$448$	−48.1814	−2.27636
$449$	−21.0284	−0.992391	−0.496196	−	0.868211i	$-0.665270\pi$
$449$	−21.0284	−0.992391	−0.496196	+	0.868211i	$0.665270\pi$
$450$	−29.8589	−1.40756
$451$	2.55719	0.120413
$452$	40.9466	1.92596
$453$	10.4363	0.490340
$454$	21.6646	1.01677
$455$	−3.10938	−0.145770
$456$	−11.2958	−0.528976
$457$	17.4770	0.817539	0.408769	−	0.912638i	$-0.365958\pi$
$457$	17.4770	0.817539	0.408769	+	0.912638i	$0.365958\pi$
$458$	−10.7461	−0.502134
$459$	−17.0879	−0.797597
$460$	6.78863	0.316521
$461$	−20.4826	−0.953969	−0.476985	−	0.878912i	$-0.658270\pi$
$461$	−20.4826	−0.953969	−0.476985	+	0.878912i	$0.658270\pi$
$462$	4.76498	0.221687
$463$	−3.52212	−0.163687	−0.0818435	−	0.996645i	$-0.526081\pi$
$463$	−3.52212	−0.163687	−0.0818435	+	0.996645i	$0.526081\pi$
$464$	0.513728	0.0238492
$465$	−1.36365	−0.0632376
$466$	11.4583	0.530794
$467$	−21.9680	−1.01656	−0.508280	−	0.861192i	$-0.669718\pi$
$467$	−21.9680	−1.01656	−0.508280	+	0.861192i	$0.669718\pi$
$468$	−14.5945	−0.674629
$469$	15.3845	0.710391
$470$	2.22185	0.102487
$471$	−4.40664	−0.203047
$472$	−20.9067	−0.962308
$473$	−7.01225	−0.322423
$474$	9.82475	0.451266
$475$	−30.9484	−1.42001
$476$	72.7055	3.33245
$477$	23.2820	1.06601
$478$	60.2683	2.75661
$479$	−23.9165	−1.09277	−0.546386	−	0.837534i	$-0.683997\pi$
$479$	−23.9165	−1.09277	−0.546386	+	0.837534i	$0.683997\pi$
$480$	−1.31042	−0.0598120
$481$	6.22445	0.283810
$482$	23.2753	1.06016
$483$	−8.03139	−0.365441
$484$	3.39196	0.154180
$485$	6.71507	0.304916
$486$	−29.3803	−1.33272
$487$	23.5503	1.06717	0.533584	−	0.845747i	$-0.320845\pi$
$487$	23.5503	1.06717	0.533584	+	0.845747i	$0.320845\pi$
$488$	−34.9829	−1.58360
$489$	−5.45616	−0.246736
$490$	9.15171	0.413432
$491$	14.7853	0.667253	0.333627	−	0.942705i	$-0.391727\pi$
$491$	14.7853	0.667253	0.333627	+	0.942705i	$0.391727\pi$
$492$	−4.64125	−0.209244
$493$	3.97989	0.179245
$494$	−24.0463	−1.08189
$495$	−1.38768	−0.0623715
$496$	3.59553	0.161444
$497$	−58.3529	−2.61749
$498$	−4.82635	−0.216274
$499$	−34.8161	−1.55858	−0.779292	−	0.626661i	$-0.784421\pi$
$499$	−34.8161	−1.55858	−0.779292	+	0.626661i	$0.784421\pi$
$500$	16.8917	0.755418
$501$	4.44863	0.198750
$502$	−3.40743	−0.152081
$503$	7.20245	0.321141	0.160571	−	0.987024i	$-0.448667\pi$
$503$	7.20245	0.321141	0.160571	+	0.987024i	$0.448667\pi$
$504$	33.6376	1.49834
$505$	−3.42425	−0.152377
$506$	−9.08815	−0.404018
$507$	−5.61092	−0.249190
$508$	−20.4004	−0.905121
$509$	32.9017	1.45834	0.729171	−	0.684332i	$-0.239906\pi$
$509$	32.9017	1.45834	0.729171	+	0.684332i	$0.239906\pi$
$510$	3.55121	0.157250
$511$	5.48326	0.242565
$512$	8.11900	0.358812
$513$	−19.9680	−0.881611
$514$	14.8973	0.657092
$515$	−1.31909	−0.0581262
$516$	12.7271	0.560280
$517$	−1.87117	−0.0822939
$518$	−34.9592	−1.53602
$519$	3.37352	0.148081
$520$	2.62064	0.114923
$521$	−0.603507	−0.0264401	−0.0132201	−	0.999913i	$-0.504208\pi$
$521$	−0.603507	−0.0264401	−0.0132201	+	0.999913i	$0.504208\pi$
$522$	4.48697	0.196389
$523$	40.4316	1.76795	0.883975	−	0.467534i	$-0.154858\pi$
$523$	40.4316	1.76795	0.883975	+	0.467534i	$0.154858\pi$
$524$	41.2151	1.80049
$525$	−9.72366	−0.424375
$526$	−1.45570	−0.0634716
$527$	27.8549	1.21338
$528$	−0.386043	−0.0168003
$529$	−7.68191	−0.333996
$530$	−10.1874	−0.442512
$531$	−17.5528	−0.761725
$532$	84.9598	3.68347
$533$	−4.05453	−0.175621
$534$	5.23363	0.226481
$535$	2.60778	0.112744
$536$	−12.9663	−0.560060
$537$	−9.24481	−0.398943
$538$	−36.9026	−1.59098
$539$	−7.70725	−0.331975
$540$	5.30296	0.228203
$541$	13.8931	0.597311	0.298655	−	0.954361i	$-0.403462\pi$
$541$	13.8931	0.597311	0.298655	+	0.954361i	$0.403462\pi$
$542$	−32.6727	−1.40341
$543$	12.1512	0.521456
$544$	26.7676	1.14765
$545$	−0.503898	−0.0215846
$546$	−7.55509	−0.323328
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	18.2867	0.781168
$549$	−29.3708	−1.25352
$550$	−11.0031	−0.469174
$551$	4.65069	0.198126
$552$	6.76899	0.288107
$553$	−30.3244	−1.28952
$554$	−68.6003	−2.91455
$555$	−1.07417	−0.0455961
$556$	58.6396	2.48687
$557$	38.5965	1.63539	0.817693	−	0.575654i	$-0.195253\pi$
$557$	38.5965	1.63539	0.817693	+	0.575654i	$0.195253\pi$
$558$	31.4038	1.32943
$559$	11.1182	0.470251
$560$	−1.41484	−0.0597880
$561$	−2.99071	−0.126268
$562$	−10.3609	−0.437047
$563$	15.3573	0.647234	0.323617	−	0.946188i	$-0.395101\pi$
$563$	15.3573	0.647234	0.323617	+	0.946188i	$0.395101\pi$
$564$	3.39614	0.143003
$565$	−6.17300	−0.259700
$566$	−1.09399	−0.0459837
$567$	24.9472	1.04769
$568$	49.1809	2.06358
$569$	29.8962	1.25331	0.626657	−	0.779296i	$-0.284423\pi$
$569$	29.8962	1.25331	0.626657	+	0.779296i	$0.284423\pi$
$570$	4.14975	0.173814
$571$	−1.28845	−0.0539200	−0.0269600	−	0.999637i	$-0.508583\pi$
$571$	−1.28845	−0.0539200	−0.0269600	+	0.999637i	$0.508583\pi$
$572$	−5.37810	−0.224870
$573$	5.78927	0.241850
$574$	22.7720	0.950485
$575$	18.5457	0.773410
$576$	34.0936	1.42057
$577$	28.2462	1.17590	0.587952	−	0.808896i	$-0.299934\pi$
$577$	28.2462	1.17590	0.587952	+	0.808896i	$0.299934\pi$
$578$	−33.0647	−1.37531
$579$	−12.3096	−0.511570
$580$	−1.23509	−0.0512845
$581$	14.8967	0.618018
$582$	16.3161	0.676325
$583$	8.57947	0.355325
$584$	−4.62139	−0.191234
$585$	2.20022	0.0909681
$586$	20.6900	0.854694
$587$	43.5216	1.79633	0.898164	−	0.439661i	$-0.144901\pi$
$587$	43.5216	1.79633	0.898164	+	0.439661i	$0.144901\pi$
$588$	13.9885	0.576878
$589$	32.5497	1.34119
$590$	7.68048	0.316201
$591$	−7.09766	−0.291959
$592$	2.83227	0.116406
$593$	24.0740	0.988600	0.494300	−	0.869291i	$-0.335424\pi$
$593$	24.0740	0.988600	0.494300	+	0.869291i	$0.335424\pi$
$594$	−7.09924	−0.291285
$595$	−10.9609	−0.449353
$596$	60.7073	2.48667
$597$	−8.53451	−0.349294
$598$	14.4097	0.589255
$599$	−24.0120	−0.981104	−0.490552	−	0.871412i	$-0.663205\pi$
$599$	−24.0120	−0.981104	−0.490552	+	0.871412i	$0.663205\pi$
$600$	8.19527	0.334570
$601$	11.8849	0.484797	0.242398	−	0.970177i	$-0.422066\pi$
$601$	11.8849	0.484797	0.242398	+	0.970177i	$0.422066\pi$
$602$	−62.4448	−2.54506
$603$	−10.8862	−0.443322
$604$	66.1569	2.69188
$605$	−0.511363	−0.0207899
$606$	−8.32016	−0.337984
$607$	−23.9979	−0.974047	−0.487023	−	0.873389i	$-0.661917\pi$
$607$	−23.9979	−0.974047	−0.487023	+	0.873389i	$0.661917\pi$
$608$	31.2791	1.26854
$609$	1.46120	0.0592106
$610$	12.8517	0.520349
$611$	2.96682	0.120025
$612$	−51.4471	−2.07963
$613$	20.5271	0.829081	0.414540	−	0.910031i	$-0.363942\pi$
$613$	20.5271	0.829081	0.414540	+	0.910031i	$0.363942\pi$
$614$	14.5885	0.588742
$615$	0.699703	0.0282148
$616$	12.3955	0.499430
$617$	20.5495	0.827293	0.413647	−	0.910438i	$-0.364255\pi$
$617$	20.5495	0.827293	0.413647	+	0.910438i	$0.364255\pi$
$618$	−3.20510	−0.128928
$619$	2.72676	0.109598	0.0547989	−	0.998497i	$-0.482548\pi$
$619$	2.72676	0.109598	0.0547989	+	0.998497i	$0.482548\pi$
$620$	−8.64430	−0.347163
$621$	11.9658	0.480170
$622$	49.2095	1.97312
$623$	−16.1537	−0.647186
$624$	0.612087	0.0245031
$625$	21.1460	0.845840
$626$	−63.5765	−2.54103
$627$	−3.49478	−0.139568
$628$	−27.9341	−1.11469
$629$	21.9419	0.874880
$630$	−12.3574	−0.492331
$631$	47.0291	1.87220	0.936100	−	0.351735i	$-0.114408\pi$
$631$	47.0291	1.87220	0.936100	+	0.351735i	$0.114408\pi$
$632$	25.5579	1.01664
$633$	1.78998	0.0711453
$634$	46.6623	1.85320
$635$	3.07551	0.122048
$636$	−15.5716	−0.617454
$637$	12.2202	0.484182
$638$	1.65346	0.0654611
$639$	41.2911	1.63345
$640$	−10.0202	−0.396084
$641$	9.34444	0.369083	0.184542	−	0.982825i	$-0.440920\pi$
$641$	9.34444	0.369083	0.184542	+	0.982825i	$0.440920\pi$
$642$	6.33631	0.250074
$643$	−20.3819	−0.803785	−0.401892	−	0.915687i	$-0.631647\pi$
$643$	−20.3819	−0.803785	−0.401892	+	0.915687i	$0.631647\pi$
$644$	−50.9118	−2.00621
$645$	−1.91871	−0.0755490
$646$	−84.7660	−3.33507
$647$	11.5584	0.454409	0.227204	−	0.973847i	$-0.427041\pi$
$647$	11.5584	0.454409	0.227204	+	0.973847i	$0.427041\pi$
$648$	−21.0260	−0.825978
$649$	−6.46824	−0.253901
$650$	17.4459	0.684284
$651$	10.2268	0.400819
$652$	−34.5872	−1.35454
$653$	19.1569	0.749666	0.374833	−	0.927092i	$-0.377700\pi$
$653$	19.1569	0.749666	0.374833	+	0.927092i	$0.377700\pi$
$654$	−1.22436	−0.0478762
$655$	−6.21349	−0.242781
$656$	−1.84491	−0.0720316
$657$	−3.88001	−0.151374
$658$	−16.6630	−0.649590
$659$	−17.7388	−0.691005	−0.345503	−	0.938418i	$-0.612292\pi$
$659$	−17.7388	−0.691005	−0.345503	+	0.938418i	$0.612292\pi$
$660$	0.928116	0.0361269
$661$	−18.8366	−0.732660	−0.366330	−	0.930485i	$-0.619386\pi$
$661$	−18.8366	−0.732660	−0.366330	+	0.930485i	$0.619386\pi$
$662$	29.4208	1.14347
$663$	4.74189	0.184160
$664$	−12.5552	−0.487235
$665$	−12.8083	−0.496685
$666$	24.7375	0.958557
$667$	−2.78691	−0.107909
$668$	28.2004	1.09110
$669$	4.15084	0.160481
$670$	4.76344	0.184028
$671$	−10.8232	−0.417826
$672$	9.82756	0.379106
$673$	47.0527	1.81375	0.906874	−	0.421403i	$-0.138462\pi$
$673$	47.0527	1.81375	0.906874	+	0.421403i	$0.138462\pi$
$674$	−7.55248	−0.290911
$675$	14.4871	0.557607
$676$	−35.5682	−1.36801
$677$	−15.4235	−0.592774	−0.296387	−	0.955068i	$-0.595782\pi$
$677$	−15.4235	−0.592774	−0.296387	+	0.955068i	$0.595782\pi$
$678$	−14.9990	−0.576034
$679$	−50.3602	−1.93265
$680$	9.23804	0.354263
$681$	−4.99229	−0.191305
$682$	11.5724	0.443130
$683$	5.77772	0.221078	0.110539	−	0.993872i	$-0.464742\pi$
$683$	5.77772	0.221078	0.110539	+	0.993872i	$0.464742\pi$
$684$	−60.1183	−2.29868
$685$	−2.75685	−0.105334
$686$	−6.29817	−0.240465
$687$	2.47629	0.0944764
$688$	5.05906	0.192875
$689$	−13.6031	−0.518238
$690$	−2.48672	−0.0946679
$691$	25.6592	0.976120	0.488060	−	0.872810i	$-0.337705\pi$
$691$	25.6592	0.976120	0.488060	+	0.872810i	$0.337705\pi$
$692$	21.3851	0.812940
$693$	10.4070	0.395329
$694$	−12.8260	−0.486867
$695$	−8.84036	−0.335334
$696$	−1.23152	−0.0466807
$697$	−14.2927	−0.541374
$698$	6.09649	0.230756
$699$	−2.64039	−0.0998688
$700$	−61.6393	−2.32975
$701$	10.6531	0.402361	0.201181	−	0.979554i	$-0.435522\pi$
$701$	10.6531	0.402361	0.201181	+	0.979554i	$0.435522\pi$
$702$	11.2562	0.424836
$703$	25.6401	0.967035
$704$	12.5636	0.473508
$705$	−0.511994	−0.0192828
$706$	46.9549	1.76717
$707$	25.6804	0.965812
$708$	11.7397	0.441207
$709$	−28.0448	−1.05324	−0.526622	−	0.850100i	$-0.676542\pi$
$709$	−28.0448	−1.05324	−0.526622	+	0.850100i	$0.676542\pi$
$710$	−18.0676	−0.678063
$711$	21.4578	0.804731
$712$	13.6147	0.510231
$713$	−19.5053	−0.730479
$714$	−26.6325	−0.996698
$715$	0.810789	0.0303218
$716$	−58.6038	−2.19013
$717$	−13.8879	−0.518655
$718$	−17.8168	−0.664918
$719$	41.2641	1.53889	0.769445	−	0.638713i	$-0.220533\pi$
$719$	41.2641	1.53889	0.769445	+	0.638713i	$0.220533\pi$
$720$	1.00116	0.0373109
$721$	9.89264	0.368421
$722$	−54.9338	−2.04442
$723$	−5.36346	−0.199469
$724$	77.0275	2.86271
$725$	−3.37413	−0.125312
$726$	−1.24250	−0.0461134
$727$	−5.13660	−0.190506	−0.0952530	−	0.995453i	$-0.530366\pi$
$727$	−5.13660	−0.190506	−0.0952530	+	0.995453i	$0.530366\pi$
$728$	−19.6537	−0.728413
$729$	−12.7451	−0.472042
$730$	1.69776	0.0628368
$731$	39.1930	1.44961
$732$	19.6440	0.726063
$733$	−22.6014	−0.834802	−0.417401	−	0.908722i	$-0.637059\pi$
$733$	−22.6014	−0.834802	−0.417401	+	0.908722i	$0.637059\pi$
$734$	−5.11772	−0.188898
$735$	−2.10888	−0.0777871
$736$	−18.7439	−0.690909
$737$	−4.01160	−0.147769
$738$	−16.1137	−0.593153
$739$	−31.3649	−1.15378	−0.576888	−	0.816823i	$-0.695733\pi$
$739$	−31.3649	−1.15378	−0.576888	+	0.816823i	$0.695733\pi$
$740$	−6.80930	−0.250315
$741$	5.54112	0.203558
$742$	76.4011	2.80477
$743$	8.10292	0.297267	0.148634	−	0.988892i	$-0.452512\pi$
$743$	8.10292	0.297267	0.148634	+	0.988892i	$0.452512\pi$
$744$	−8.61929	−0.315999
$745$	−9.15208	−0.335306
$746$	30.7331	1.12522
$747$	−10.5410	−0.385676
$748$	−18.9584	−0.693188
$749$	−19.5572	−0.714605
$750$	−6.18753	−0.225937
$751$	−9.94714	−0.362976	−0.181488	−	0.983393i	$-0.558091\pi$
$751$	−9.94714	−0.362976	−0.181488	+	0.983393i	$0.558091\pi$
$752$	1.34998	0.0492285
$753$	0.785193	0.0286140
$754$	−2.62163	−0.0954742
$755$	−9.97364	−0.362978
$756$	−39.7699	−1.44642
$757$	19.9049	0.723457	0.361728	−	0.932284i	$-0.382187\pi$
$757$	19.9049	0.723457	0.361728	+	0.932284i	$0.382187\pi$
$758$	−46.4999	−1.68895
$759$	2.09423	0.0760158
$760$	10.7951	0.391578
$761$	16.8165	0.609599	0.304800	−	0.952417i	$-0.401411\pi$
$761$	16.8165	0.609599	0.304800	+	0.952417i	$0.401411\pi$
$762$	7.47281	0.270711
$763$	3.77902	0.136810
$764$	36.6988	1.32772
$765$	7.75604	0.280420
$766$	5.15636	0.186307
$767$	10.2557	0.370311
$768$	−10.9017	−0.393382
$769$	−11.6024	−0.418394	−0.209197	−	0.977874i	$-0.567085\pi$
$769$	−11.6024	−0.418394	−0.209197	+	0.977874i	$0.567085\pi$
$770$	−4.55374	−0.164105
$771$	−3.43287	−0.123632
$772$	−78.0320	−2.80843
$773$	−3.08532	−0.110971	−0.0554856	−	0.998459i	$-0.517671\pi$
$773$	−3.08532	−0.110971	−0.0554856	+	0.998459i	$0.517671\pi$
$774$	44.1865	1.58825
$775$	−23.6152	−0.848283
$776$	42.4444	1.52367
$777$	8.05584	0.289002
$778$	−28.4979	−1.02170
$779$	−16.7016	−0.598399
$780$	−1.47157	−0.0526906
$781$	15.2159	0.544467
$782$	50.7957	1.81645
$783$	−2.17700	−0.0777997
$784$	5.56048	0.198589
$785$	4.21128	0.150307
$786$	−15.0974	−0.538506
$787$	−27.8226	−0.991770	−0.495885	−	0.868388i	$-0.665156\pi$
$787$	−27.8226	−0.991770	−0.495885	+	0.868388i	$0.665156\pi$
$788$	−44.9929	−1.60280
$789$	0.335445	0.0119422
$790$	−9.38920	−0.334053
$791$	46.2949	1.64606
$792$	−8.77119	−0.311671
$793$	17.1607	0.609394
$794$	0.199582	0.00708289
$795$	2.34754	0.0832585
$796$	−54.1012	−1.91757
$797$	−34.8594	−1.23478	−0.617391	−	0.786656i	$-0.711810\pi$
$797$	−34.8594	−1.23478	−0.617391	+	0.786656i	$0.711810\pi$
$798$	−31.1213	−1.10168
$799$	10.4584	0.369991
$800$	−22.6934	−0.802332
$801$	11.4305	0.403878
$802$	−65.5623	−2.31509
$803$	−1.42979	−0.0504563
$804$	7.28100	0.256781
$805$	7.67534	0.270520
$806$	−18.3485	−0.646300
$807$	8.50366	0.299343
$808$	−21.6439	−0.761430
$809$	−5.69898	−0.200365	−0.100183	−	0.994969i	$-0.531943\pi$
$809$	−5.69898	−0.200365	−0.100183	+	0.994969i	$0.531943\pi$
$810$	7.72430	0.271404
$811$	17.4954	0.614346	0.307173	−	0.951654i	$-0.400617\pi$
$811$	17.4954	0.614346	0.307173	+	0.951654i	$0.400617\pi$
$812$	9.26267	0.325056
$813$	7.52894	0.264051
$814$	9.11582	0.319509
$815$	5.21428	0.182648
$816$	2.15768	0.0755338
$817$	45.7988	1.60230
$818$	1.66888	0.0583510
$819$	−16.5007	−0.576583
$820$	4.43549	0.154894
$821$	−7.87520	−0.274846	−0.137423	−	0.990512i	$-0.543882\pi$
$821$	−7.87520	−0.274846	−0.137423	+	0.990512i	$0.543882\pi$
$822$	−6.69853	−0.233638
$823$	−30.5507	−1.06493	−0.532466	−	0.846451i	$-0.678735\pi$
$823$	−30.5507	−1.06493	−0.532466	+	0.846451i	$0.678735\pi$
$824$	−8.33769	−0.290457
$825$	2.53550	0.0882748
$826$	−57.6003	−2.00417
$827$	−9.64557	−0.335409	−0.167705	−	0.985837i	$-0.553635\pi$
$827$	−9.64557	−0.335409	−0.167705	+	0.985837i	$0.553635\pi$
$828$	36.0257	1.25198
$829$	16.0498	0.557433	0.278717	−	0.960373i	$-0.410091\pi$
$829$	16.0498	0.557433	0.278717	+	0.960373i	$0.410091\pi$
$830$	4.61239	0.160098
$831$	15.8079	0.548371
$832$	−19.9201	−0.690606
$833$	43.0775	1.49255
$834$	−21.4801	−0.743795
$835$	−4.25142	−0.147126
$836$	−22.1538	−0.766204
$837$	−15.2366	−0.526655
$838$	87.2748	3.01486
$839$	−0.0291175	−0.00100525	−0.000502624	−	1.00000i	$-0.500160\pi$
$839$	−0.0291175	−0.00100525	−0.000502624		1.00000i	$0.500160\pi$
$840$	3.39169	0.117025
$841$	−28.4930	−0.982516
$842$	−32.1957	−1.10954
$843$	2.38751	0.0822302
$844$	11.3469	0.390575
$845$	5.36218	0.184465
$846$	11.7909	0.405378
$847$	3.83500	0.131772
$848$	−6.18975	−0.212557
$849$	0.252093	0.00865182
$850$	61.4987	2.10939
$851$	−15.3647	−0.526696
$852$	−27.6166	−0.946128
$853$	0.807124	0.0276354	0.0138177	−	0.999905i	$-0.495602\pi$
$853$	0.807124	0.0276354	0.0138177	+	0.999905i	$0.495602\pi$
$854$	−96.3820	−3.29812
$855$	9.06329	0.309958
$856$	16.4832	0.563383
$857$	33.9410	1.15940	0.579701	−	0.814829i	$-0.303169\pi$
$857$	33.9410	1.15940	0.579701	+	0.814829i	$0.303169\pi$
$858$	1.97003	0.0672559
$859$	50.7405	1.73124	0.865621	−	0.500700i	$-0.166924\pi$
$859$	50.7405	1.73124	0.865621	+	0.500700i	$0.166924\pi$
$860$	−12.1629	−0.414751
$861$	−5.24747	−0.178833
$862$	−52.7920	−1.79810
$863$	19.7754	0.673162	0.336581	−	0.941655i	$-0.390729\pi$
$863$	19.7754	0.673162	0.336581	+	0.941655i	$0.390729\pi$
$864$	−14.6419	−0.498126
$865$	−3.22397	−0.109618
$866$	−11.8524	−0.402761
$867$	7.61928	0.258764
$868$	64.8286	2.20042
$869$	7.90726	0.268235
$870$	0.452423	0.0153386
$871$	6.36057	0.215520
$872$	−3.18502	−0.107858
$873$	35.6353	1.20607
$874$	59.3571	2.00778
$875$	19.0980	0.645630
$876$	2.59505	0.0876787
$877$	44.5437	1.50413	0.752067	−	0.659086i	$-0.229057\pi$
$877$	44.5437	1.50413	0.752067	+	0.659086i	$0.229057\pi$
$878$	−7.26459	−0.245168
$879$	−4.76770	−0.160810
$880$	0.368928	0.0124366
$881$	7.80297	0.262889	0.131444	−	0.991324i	$-0.458039\pi$
$881$	7.80297	0.262889	0.131444	+	0.991324i	$0.458039\pi$
$882$	48.5660	1.63530
$883$	24.0304	0.808687	0.404343	−	0.914607i	$-0.367500\pi$
$883$	24.0304	0.808687	0.404343	+	0.914607i	$0.367500\pi$
$884$	30.0594	1.01101
$885$	−1.76986	−0.0594930
$886$	−55.2742	−1.85697
$887$	15.1318	0.508076	0.254038	−	0.967194i	$-0.418241\pi$
$887$	15.1318	0.508076	0.254038	+	0.967194i	$0.418241\pi$
$888$	−6.78960	−0.227844
$889$	−23.0650	−0.773576
$890$	−5.00161	−0.167654
$891$	−6.50514	−0.217930
$892$	26.3126	0.881011
$893$	12.2211	0.408963
$894$	−22.2375	−0.743733
$895$	8.83496	0.295320
$896$	75.1473	2.51050
$897$	−3.32050	−0.110868
$898$	48.8292	1.62945
$899$	3.54871	0.118356
$900$	43.6166	1.45389
$901$	−47.9525	−1.59753
$902$	−5.93794	−0.197712
$903$	14.3895	0.478852
$904$	−39.0181	−1.29772
$905$	−11.6125	−0.386012
$906$	−24.2337	−0.805111
$907$	12.5128	0.415480	0.207740	−	0.978184i	$-0.433389\pi$
$907$	12.5128	0.415480	0.207740	+	0.978184i	$0.433389\pi$
$908$	−31.6467	−1.05023
$909$	−18.1717	−0.602717
$910$	7.22016	0.239346
$911$	−33.1250	−1.09748	−0.548741	−	0.835992i	$-0.684893\pi$
$911$	−33.1250	−1.09748	−0.548741	+	0.835992i	$0.684893\pi$
$912$	2.52134	0.0834901
$913$	−3.88440	−0.128555
$914$	−40.5826	−1.34235
$915$	−2.96148	−0.0979034
$916$	15.6975	0.518659
$917$	46.5985	1.53882
$918$	39.6792	1.30961
$919$	−31.2214	−1.02990	−0.514950	−	0.857220i	$-0.672190\pi$
$919$	−31.2214	−1.02990	−0.514950	+	0.857220i	$0.672190\pi$
$920$	−6.46891	−0.213274
$921$	−3.36170	−0.110772
$922$	47.5618	1.56636
$923$	−24.1254	−0.794098
$924$	−6.96047	−0.228983
$925$	−18.6022	−0.611636
$926$	8.17858	0.268765
$927$	−7.00012	−0.229914
$928$	3.41018	0.111945
$929$	58.6317	1.92364	0.961822	−	0.273674i	$-0.0882390\pi$
$929$	58.6317	1.92364	0.961822	+	0.273674i	$0.0882390\pi$
$930$	3.16647	0.103833
$931$	50.3381	1.64976
$932$	−16.7377	−0.548262
$933$	−11.3396	−0.371242
$934$	51.0111	1.66913
$935$	2.85812	0.0934706
$936$	13.9071	0.454568
$937$	53.2436	1.73939	0.869697	−	0.493587i	$-0.164314\pi$
$937$	53.2436	1.73939	0.869697	+	0.493587i	$0.164314\pi$
$938$	−35.7238	−1.16642
$939$	14.6503	0.478094
$940$	−3.24558	−0.105859
$941$	−4.02381	−0.131172	−0.0655862	−	0.997847i	$-0.520892\pi$
$941$	−4.02381	−0.131172	−0.0655862	+	0.997847i	$0.520892\pi$
$942$	10.2325	0.333392
$943$	10.0084	0.325918
$944$	4.66658	0.151884
$945$	5.99562	0.195037
$946$	16.2828	0.529401
$947$	−8.98501	−0.291974	−0.145987	−	0.989287i	$-0.546636\pi$
$947$	−8.98501	−0.291974	−0.145987	+	0.989287i	$0.546636\pi$
$948$	−14.3516	−0.466117
$949$	2.26700	0.0735899
$950$	71.8641	2.33158
$951$	−10.7527	−0.348679
$952$	−69.2813	−2.24542
$953$	46.9602	1.52119	0.760595	−	0.649226i	$-0.224907\pi$
$953$	46.9602	1.52119	0.760595	+	0.649226i	$0.224907\pi$
$954$	−54.0621	−1.75033
$955$	−5.53262	−0.179031
$956$	−88.0371	−2.84732
$957$	−0.381015	−0.0123165
$958$	55.5354	1.79427
$959$	20.6752	0.667637
$960$	3.43768	0.110951
$961$	−6.16293	−0.198804
$962$	−14.4535	−0.466001
$963$	13.8389	0.445951
$964$	−33.9995	−1.09505
$965$	11.7639	0.378694
$966$	18.6493	0.600033
$967$	46.4368	1.49331	0.746654	−	0.665213i	$-0.231659\pi$
$967$	46.4368	1.49331	0.746654	+	0.665213i	$0.231659\pi$
$968$	−3.23221	−0.103887
$969$	19.5331	0.627493
$970$	−15.5928	−0.500654
$971$	58.5314	1.87836	0.939180	−	0.343424i	$-0.111587\pi$
$971$	58.5314	1.87836	0.939180	+	0.343424i	$0.111587\pi$
$972$	42.9175	1.37658
$973$	66.2989	2.12544
$974$	−54.6853	−1.75223
$975$	−4.02015	−0.128748
$976$	7.80854	0.249945
$977$	12.5090	0.400198	0.200099	−	0.979776i	$-0.435874\pi$
$977$	12.5090	0.400198	0.200099	+	0.979776i	$0.435874\pi$
$978$	12.6695	0.405127
$979$	4.21218	0.134622
$980$	−13.3684	−0.427038
$981$	−2.67407	−0.0853764
$982$	−34.3325	−1.09559
$983$	10.5568	0.336708	0.168354	−	0.985727i	$-0.446155\pi$
$983$	10.5568	0.336708	0.168354	+	0.985727i	$0.446155\pi$
$984$	4.42266	0.140989
$985$	6.78301	0.216125
$986$	−9.24155	−0.294311
$987$	3.83974	0.122220
$988$	35.1258	1.11750
$989$	−27.4448	−0.872693
$990$	3.22227	0.102410
$991$	7.16396	0.227571	0.113785	−	0.993505i	$-0.463702\pi$
$991$	7.16396	0.227571	0.113785	+	0.993505i	$0.463702\pi$
$992$	23.8675	0.757795
$993$	−6.77960	−0.215144
$994$	135.499	4.29777
$995$	8.15616	0.258568
$996$	7.05012	0.223391
$997$	20.2829	0.642367	0.321183	−	0.947017i	$-0.395919\pi$
$997$	20.2829	0.642367	0.321183	+	0.947017i	$0.395919\pi$
$998$	80.8451	2.55911
$999$	−12.0022	−0.379733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.13	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.32206 q^{2} +0.535084 q^{3} +3.39196 q^{4} -0.511363 q^{5} -1.24250 q^{6} +3.83500 q^{7} -3.23221 q^{8} -2.71368 q^{9} +O(q^{10})\)	\(q-2.32206 q^{2} +0.535084 q^{3} +3.39196 q^{4} -0.511363 q^{5} -1.24250 q^{6} +3.83500 q^{7} -3.23221 q^{8} -2.71368 q^{9} +1.18742 q^{10} -1.00000 q^{11} +1.81498 q^{12} +1.58554 q^{13} -8.90510 q^{14} -0.273622 q^{15} +0.721461 q^{16} +5.58922 q^{17} +6.30134 q^{18} +6.53126 q^{19} -1.73452 q^{20} +2.05205 q^{21} +2.32206 q^{22} -3.91383 q^{23} -1.72950 q^{24} -4.73851 q^{25} -3.68173 q^{26} -3.05730 q^{27} +13.0082 q^{28} +0.712066 q^{29} +0.635367 q^{30} +4.98368 q^{31} +4.78914 q^{32} -0.535084 q^{33} -12.9785 q^{34} -1.96108 q^{35} -9.20470 q^{36} +3.92575 q^{37} -15.1660 q^{38} +0.848400 q^{39} +1.65283 q^{40} -2.55719 q^{41} -4.76498 q^{42} +7.01225 q^{43} -3.39196 q^{44} +1.38768 q^{45} +9.08815 q^{46} +1.87117 q^{47} +0.386043 q^{48} +7.70725 q^{49} +11.0031 q^{50} +2.99071 q^{51} +5.37810 q^{52} -8.57947 q^{53} +7.09924 q^{54} +0.511363 q^{55} -12.3955 q^{56} +3.49478 q^{57} -1.65346 q^{58} +6.46824 q^{59} -0.928116 q^{60} +10.8232 q^{61} -11.5724 q^{62} -10.4070 q^{63} -12.5636 q^{64} -0.810789 q^{65} +1.24250 q^{66} +4.01160 q^{67} +18.9584 q^{68} -2.09423 q^{69} +4.55374 q^{70} -15.2159 q^{71} +8.77119 q^{72} +1.42979 q^{73} -9.11582 q^{74} -2.53550 q^{75} +22.1538 q^{76} -3.83500 q^{77} -1.97003 q^{78} -7.90726 q^{79} -0.368928 q^{80} +6.50514 q^{81} +5.93794 q^{82} +3.88440 q^{83} +6.96047 q^{84} -2.85812 q^{85} -16.2828 q^{86} +0.381015 q^{87} +3.23221 q^{88} -4.21218 q^{89} -3.22227 q^{90} +6.08057 q^{91} -13.2756 q^{92} +2.66669 q^{93} -4.34497 q^{94} -3.33985 q^{95} +2.56259 q^{96} -13.1317 q^{97} -17.8967 q^{98} +2.71368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 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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