LMFDB - Embedded newform 6033.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$97$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.11811 q^{2} +1.00000 q^{3} +2.48641 q^{4} +0.996414 q^{5} -2.11811 q^{6} -4.64745 q^{7} -1.03027 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.11811 q^{2} +1.00000 q^{3} +2.48641 q^{4} +0.996414 q^{5} -2.11811 q^{6} -4.64745 q^{7} -1.03027 q^{8} +1.00000 q^{9} -2.11052 q^{10} -2.11706 q^{11} +2.48641 q^{12} -4.22626 q^{13} +9.84384 q^{14} +0.996414 q^{15} -2.79059 q^{16} -0.208878 q^{17} -2.11811 q^{18} +0.542144 q^{19} +2.47749 q^{20} -4.64745 q^{21} +4.48418 q^{22} +5.01547 q^{23} -1.03027 q^{24} -4.00716 q^{25} +8.95171 q^{26} +1.00000 q^{27} -11.5555 q^{28} +3.85837 q^{29} -2.11052 q^{30} -9.59784 q^{31} +7.97133 q^{32} -2.11706 q^{33} +0.442426 q^{34} -4.63079 q^{35} +2.48641 q^{36} +8.67873 q^{37} -1.14832 q^{38} -4.22626 q^{39} -1.02657 q^{40} -1.93238 q^{41} +9.84384 q^{42} -2.13189 q^{43} -5.26389 q^{44} +0.996414 q^{45} -10.6233 q^{46} +1.17897 q^{47} -2.79059 q^{48} +14.5988 q^{49} +8.48762 q^{50} -0.208878 q^{51} -10.5082 q^{52} -12.3121 q^{53} -2.11811 q^{54} -2.10947 q^{55} +4.78812 q^{56} +0.542144 q^{57} -8.17246 q^{58} -11.0863 q^{59} +2.47749 q^{60} +6.98684 q^{61} +20.3293 q^{62} -4.64745 q^{63} -11.3030 q^{64} -4.21110 q^{65} +4.48418 q^{66} -0.434606 q^{67} -0.519355 q^{68} +5.01547 q^{69} +9.80854 q^{70} -8.13955 q^{71} -1.03027 q^{72} -3.03509 q^{73} -18.3825 q^{74} -4.00716 q^{75} +1.34799 q^{76} +9.83896 q^{77} +8.95171 q^{78} -3.11865 q^{79} -2.78058 q^{80} +1.00000 q^{81} +4.09300 q^{82} +10.3799 q^{83} -11.5555 q^{84} -0.208128 q^{85} +4.51558 q^{86} +3.85837 q^{87} +2.18114 q^{88} +11.8329 q^{89} -2.11052 q^{90} +19.6414 q^{91} +12.4705 q^{92} -9.59784 q^{93} -2.49719 q^{94} +0.540200 q^{95} +7.97133 q^{96} -8.01986 q^{97} -30.9220 q^{98} -2.11706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) $ 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * 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 $

$2$	−2.11811	−1.49773	−0.748866	−	0.662721i	$-0.769402\pi$
$2$	−2.11811	−1.49773	−0.748866	+	0.662721i	$0.769402\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.48641	1.24320
$5$	0.996414	0.445610	0.222805	−	0.974863i	$-0.428479\pi$
$5$	0.996414	0.445610	0.222805	+	0.974863i	$0.428479\pi$
$6$	−2.11811	−0.864717
$7$	−4.64745	−1.75657	−0.878286	−	0.478135i	$-0.841313\pi$
$7$	−4.64745	−1.75657	−0.878286	+	0.478135i	$0.841313\pi$
$8$	−1.03027	−0.364255
$9$	1.00000	0.333333
$10$	−2.11052	−0.667404
$11$	−2.11706	−0.638319	−0.319159	−	0.947701i	$-0.603401\pi$
$11$	−2.11706	−0.638319	−0.319159	+	0.947701i	$0.603401\pi$
$12$	2.48641	0.717764
$13$	−4.22626	−1.17215	−0.586077	−	0.810255i	$-0.699328\pi$
$13$	−4.22626	−1.17215	−0.586077	+	0.810255i	$0.699328\pi$
$14$	9.84384	2.63088
$15$	0.996414	0.257273
$16$	−2.79059	−0.697648
$17$	−0.208878	−0.0506602	−0.0253301	−	0.999679i	$-0.508064\pi$
$17$	−0.208878	−0.0506602	−0.0253301	+	0.999679i	$0.508064\pi$
$18$	−2.11811	−0.499244
$19$	0.542144	0.124376	0.0621882	−	0.998064i	$-0.480192\pi$
$19$	0.542144	0.124376	0.0621882	+	0.998064i	$0.480192\pi$
$20$	2.47749	0.553984
$21$	−4.64745	−1.01416
$22$	4.48418	0.956031
$23$	5.01547	1.04580	0.522899	−	0.852394i	$-0.324850\pi$
$23$	5.01547	1.04580	0.522899	+	0.852394i	$0.324850\pi$
$24$	−1.03027	−0.210303
$25$	−4.00716	−0.801432
$26$	8.95171	1.75557
$27$	1.00000	0.192450
$28$	−11.5555	−2.18378
$29$	3.85837	0.716481	0.358240	−	0.933629i	$-0.383377\pi$
$29$	3.85837	0.716481	0.358240	+	0.933629i	$0.383377\pi$
$30$	−2.11052	−0.385326
$31$	−9.59784	−1.72382	−0.861912	−	0.507058i	$-0.830733\pi$
$31$	−9.59784	−1.72382	−0.861912	+	0.507058i	$0.830733\pi$
$32$	7.97133	1.40914
$33$	−2.11706	−0.368534
$34$	0.442426	0.0758755
$35$	−4.63079	−0.782746
$36$	2.48641	0.414401
$37$	8.67873	1.42677	0.713387	−	0.700770i	$-0.247160\pi$
$37$	8.67873	1.42677	0.713387	+	0.700770i	$0.247160\pi$
$38$	−1.14832	−0.186283
$39$	−4.22626	−0.676743
$40$	−1.02657	−0.162316
$41$	−1.93238	−0.301787	−0.150893	−	0.988550i	$-0.548215\pi$
$41$	−1.93238	−0.301787	−0.150893	+	0.988550i	$0.548215\pi$
$42$	9.84384	1.51894
$43$	−2.13189	−0.325110	−0.162555	−	0.986700i	$-0.551973\pi$
$43$	−2.13189	−0.325110	−0.162555	+	0.986700i	$0.551973\pi$
$44$	−5.26389	−0.793561
$45$	0.996414	0.148537
$46$	−10.6233	−1.56633
$47$	1.17897	0.171970	0.0859850	−	0.996296i	$-0.472596\pi$
$47$	1.17897	0.171970	0.0859850	+	0.996296i	$0.472596\pi$
$48$	−2.79059	−0.402787
$49$	14.5988	2.08555
$50$	8.48762	1.20033
$51$	−0.208878	−0.0292487
$52$	−10.5082	−1.45723
$53$	−12.3121	−1.69119	−0.845596	−	0.533824i	$-0.820755\pi$
$53$	−12.3121	−1.69119	−0.845596	+	0.533824i	$0.820755\pi$
$54$	−2.11811	−0.288239
$55$	−2.10947	−0.284441
$56$	4.78812	0.639840
$57$	0.542144	0.0718088
$58$	−8.17246	−1.07310
$59$	−11.0863	−1.44332	−0.721658	−	0.692250i	$-0.756620\pi$
$59$	−11.0863	−1.44332	−0.721658	+	0.692250i	$0.756620\pi$
$60$	2.47749	0.319843
$61$	6.98684	0.894573	0.447287	−	0.894391i	$-0.352390\pi$
$61$	6.98684	0.894573	0.447287	+	0.894391i	$0.352390\pi$
$62$	20.3293	2.58183
$63$	−4.64745	−0.585524
$64$	−11.3030	−1.41287
$65$	−4.21110	−0.522323
$66$	4.48418	0.551965
$67$	−0.434606	−0.0530956	−0.0265478	−	0.999648i	$-0.508451\pi$
$67$	−0.434606	−0.0530956	−0.0265478	+	0.999648i	$0.508451\pi$
$68$	−0.519355	−0.0629810
$69$	5.01547	0.603792
$70$	9.80854	1.17234
$71$	−8.13955	−0.965987	−0.482993	−	0.875624i	$-0.660450\pi$
$71$	−8.13955	−0.965987	−0.482993	+	0.875624i	$0.660450\pi$
$72$	−1.03027	−0.121418
$73$	−3.03509	−0.355230	−0.177615	−	0.984100i	$-0.556838\pi$
$73$	−3.03509	−0.355230	−0.177615	+	0.984100i	$0.556838\pi$
$74$	−18.3825	−2.13693
$75$	−4.00716	−0.462707
$76$	1.34799	0.154625
$77$	9.83896	1.12125
$78$	8.95171	1.01358
$79$	−3.11865	−0.350876	−0.175438	−	0.984490i	$-0.556134\pi$
$79$	−3.11865	−0.350876	−0.175438	+	0.984490i	$0.556134\pi$
$80$	−2.78058	−0.310879
$81$	1.00000	0.111111
$82$	4.09300	0.451996
$83$	10.3799	1.13934	0.569668	−	0.821875i	$-0.307072\pi$
$83$	10.3799	1.13934	0.569668	+	0.821875i	$0.307072\pi$
$84$	−11.5555	−1.26080
$85$	−0.208128	−0.0225747
$86$	4.51558	0.486927
$87$	3.85837	0.413660
$88$	2.18114	0.232511
$89$	11.8329	1.25428	0.627141	−	0.778906i	$-0.284225\pi$
$89$	11.8329	1.25428	0.627141	+	0.778906i	$0.284225\pi$
$90$	−2.11052	−0.222468
$91$	19.6414	2.05897
$92$	12.4705	1.30014
$93$	−9.59784	−0.995250
$94$	−2.49719	−0.257565
$95$	0.540200	0.0554234
$96$	7.97133	0.813570
$97$	−8.01986	−0.814293	−0.407147	−	0.913363i	$-0.633476\pi$
$97$	−8.01986	−0.814293	−0.407147	+	0.913363i	$0.633476\pi$
$98$	−30.9220	−3.12359
$99$	−2.11706	−0.212773
$100$	−9.96344	−0.996344
$101$	−18.4102	−1.83189	−0.915944	−	0.401307i	$-0.868556\pi$
$101$	−18.4102	−1.83189	−0.915944	+	0.401307i	$0.868556\pi$
$102$	0.442426	0.0438067
$103$	−6.85324	−0.675269	−0.337635	−	0.941277i	$-0.609627\pi$
$103$	−6.85324	−0.675269	−0.337635	+	0.941277i	$0.609627\pi$
$104$	4.35418	0.426963
$105$	−4.63079	−0.451918
$106$	26.0783	2.53295
$107$	17.2503	1.66765	0.833824	−	0.552031i	$-0.186147\pi$
$107$	17.2503	1.66765	0.833824	+	0.552031i	$0.186147\pi$
$108$	2.48641	0.239255
$109$	−5.45244	−0.522249	−0.261125	−	0.965305i	$-0.584093\pi$
$109$	−5.45244	−0.522249	−0.261125	+	0.965305i	$0.584093\pi$
$110$	4.46810	0.426017
$111$	8.67873	0.823749
$112$	12.9691	1.22547
$113$	−19.5368	−1.83787	−0.918934	−	0.394411i	$-0.870949\pi$
$113$	−19.5368	−1.83787	−0.918934	+	0.394411i	$0.870949\pi$
$114$	−1.14832	−0.107550
$115$	4.99749	0.466018
$116$	9.59347	0.890732
$117$	−4.22626	−0.390718
$118$	23.4821	2.16170
$119$	0.970749	0.0889884
$120$	−1.02657	−0.0937129
$121$	−6.51804	−0.592549
$122$	−14.7989	−1.33983
$123$	−1.93238	−0.174237
$124$	−23.8642	−2.14306
$125$	−8.97486	−0.802736
$126$	9.84384	0.876959
$127$	17.7746	1.57724	0.788622	−	0.614879i	$-0.210795\pi$
$127$	17.7746	1.57724	0.788622	+	0.614879i	$0.210795\pi$
$128$	7.99839	0.706965
$129$	−2.13189	−0.187702
$130$	8.91960	0.782301
$131$	18.0464	1.57672	0.788360	−	0.615214i	$-0.210930\pi$
$131$	18.0464	1.57672	0.788360	+	0.615214i	$0.210930\pi$
$132$	−5.26389	−0.458162
$133$	−2.51959	−0.218476
$134$	0.920546	0.0795230
$135$	0.996414	0.0857576
$136$	0.215200	0.0184532
$137$	−14.5707	−1.24486	−0.622430	−	0.782676i	$-0.713854\pi$
$137$	−14.5707	−1.24486	−0.622430	+	0.782676i	$0.713854\pi$
$138$	−10.6233	−0.904320
$139$	18.8121	1.59562	0.797812	−	0.602906i	$-0.205990\pi$
$139$	18.8121	1.59562	0.797812	+	0.602906i	$0.205990\pi$
$140$	−11.5140	−0.973113
$141$	1.17897	0.0992869
$142$	17.2405	1.44679
$143$	8.94727	0.748208
$144$	−2.79059	−0.232549
$145$	3.84453	0.319271
$146$	6.42866	0.532040
$147$	14.5988	1.20409
$148$	21.5789	1.77377
$149$	13.4216	1.09954	0.549771	−	0.835315i	$-0.314715\pi$
$149$	13.4216	1.09954	0.549771	+	0.835315i	$0.314715\pi$
$150$	8.48762	0.693011
$151$	10.0886	0.821002	0.410501	−	0.911860i	$-0.365354\pi$
$151$	10.0886	0.821002	0.410501	+	0.911860i	$0.365354\pi$
$152$	−0.558554	−0.0453047
$153$	−0.208878	−0.0168867
$154$	−20.8400	−1.67934
$155$	−9.56342	−0.768153
$156$	−10.5082	−0.841330
$157$	11.4415	0.913128	0.456564	−	0.889690i	$-0.349080\pi$
$157$	11.4415	0.913128	0.456564	+	0.889690i	$0.349080\pi$
$158$	6.60566	0.525518
$159$	−12.3121	−0.976410
$160$	7.94274	0.627929
$161$	−23.3092	−1.83702
$162$	−2.11811	−0.166415
$163$	−0.283544	−0.0222089	−0.0111044	−	0.999938i	$-0.503535\pi$
$163$	−0.283544	−0.0222089	−0.0111044	+	0.999938i	$0.503535\pi$
$164$	−4.80468	−0.375182
$165$	−2.10947	−0.164222
$166$	−21.9857	−1.70642
$167$	10.3871	0.803777	0.401888	−	0.915689i	$-0.368354\pi$
$167$	10.3871	0.803777	0.401888	+	0.915689i	$0.368354\pi$
$168$	4.78812	0.369412
$169$	4.86129	0.373945
$170$	0.440840	0.0338109
$171$	0.542144	0.0414588
$172$	−5.30074	−0.404178
$173$	−11.3396	−0.862135	−0.431068	−	0.902320i	$-0.641863\pi$
$173$	−11.3396	−0.862135	−0.431068	+	0.902320i	$0.641863\pi$
$174$	−8.17246	−0.619553
$175$	18.6231	1.40777
$176$	5.90786	0.445322
$177$	−11.0863	−0.833299
$178$	−25.0634	−1.87858
$179$	16.9769	1.26891	0.634456	−	0.772959i	$-0.281224\pi$
$179$	16.9769	1.26891	0.634456	+	0.772959i	$0.281224\pi$
$180$	2.47749	0.184661
$181$	13.5741	1.00895	0.504476	−	0.863426i	$-0.331686\pi$
$181$	13.5741	1.00895	0.504476	+	0.863426i	$0.331686\pi$
$182$	−41.6026	−3.08379
$183$	6.98684	0.516482
$184$	−5.16728	−0.380937
$185$	8.64761	0.635785
$186$	20.3293	1.49062
$187$	0.442207	0.0323374
$188$	2.93139	0.213794
$189$	−4.64745	−0.338053
$190$	−1.14421	−0.0830094
$191$	8.34039	0.603489	0.301745	−	0.953389i	$-0.402431\pi$
$191$	8.34039	0.603489	0.301745	+	0.953389i	$0.402431\pi$
$192$	−11.3030	−0.815724
$193$	−1.66958	−0.120179	−0.0600895	−	0.998193i	$-0.519139\pi$
$193$	−1.66958	−0.120179	−0.0600895	+	0.998193i	$0.519139\pi$
$194$	16.9870	1.21959
$195$	−4.21110	−0.301563
$196$	36.2986	2.59276
$197$	−0.624044	−0.0444613	−0.0222307	−	0.999753i	$-0.507077\pi$
$197$	−0.624044	−0.0444613	−0.0222307	+	0.999753i	$0.507077\pi$
$198$	4.48418	0.318677
$199$	22.7130	1.61008	0.805041	−	0.593220i	$-0.202143\pi$
$199$	22.7130	1.61008	0.805041	+	0.593220i	$0.202143\pi$
$200$	4.12845	0.291925
$201$	−0.434606	−0.0306548
$202$	38.9950	2.74368
$203$	−17.9316	−1.25855
$204$	−0.519355	−0.0363621
$205$	−1.92545	−0.134479
$206$	14.5159	1.01137
$207$	5.01547	0.348600
$208$	11.7938	0.817751
$209$	−1.14775	−0.0793918
$210$	9.80854	0.676853
$211$	−10.1803	−0.700838	−0.350419	−	0.936593i	$-0.613961\pi$
$211$	−10.1803	−0.700838	−0.350419	+	0.936593i	$0.613961\pi$
$212$	−30.6128	−2.10250
$213$	−8.13955	−0.557713
$214$	−36.5381	−2.49769
$215$	−2.12424	−0.144872
$216$	−1.03027	−0.0701009
$217$	44.6055	3.02802
$218$	11.5489	0.782190
$219$	−3.03509	−0.205092
$220$	−5.24501	−0.353618
$221$	0.882771	0.0593816
$222$	−18.3825	−1.23376
$223$	29.2306	1.95743	0.978714	−	0.205230i	$-0.0657942\pi$
$223$	29.2306	1.95743	0.978714	+	0.205230i	$0.0657942\pi$
$224$	−37.0464	−2.47526
$225$	−4.00716	−0.267144
$226$	41.3812	2.75264
$227$	−17.1454	−1.13798	−0.568991	−	0.822344i	$-0.692666\pi$
$227$	−17.1454	−1.13798	−0.568991	+	0.822344i	$0.692666\pi$
$228$	1.34799	0.0892730
$229$	4.06524	0.268639	0.134319	−	0.990938i	$-0.457115\pi$
$229$	4.06524	0.268639	0.134319	+	0.990938i	$0.457115\pi$
$230$	−10.5852	−0.697971
$231$	9.83896	0.647356
$232$	−3.97515	−0.260982
$233$	9.93587	0.650921	0.325460	−	0.945556i	$-0.394481\pi$
$233$	9.93587	0.650921	0.325460	+	0.945556i	$0.394481\pi$
$234$	8.95171	0.585191
$235$	1.17474	0.0766315
$236$	−27.5651	−1.79434
$237$	−3.11865	−0.202578
$238$	−2.05616	−0.133281
$239$	27.0525	1.74988	0.874941	−	0.484230i	$-0.160900\pi$
$239$	27.0525	1.74988	0.874941	+	0.484230i	$0.160900\pi$
$240$	−2.78058	−0.179486
$241$	−17.6106	−1.13440	−0.567199	−	0.823581i	$-0.691973\pi$
$241$	−17.6106	−1.13440	−0.567199	+	0.823581i	$0.691973\pi$
$242$	13.8060	0.887480
$243$	1.00000	0.0641500
$244$	17.3721	1.11214
$245$	14.5465	0.929340
$246$	4.09300	0.260960
$247$	−2.29124	−0.145788
$248$	9.88835	0.627911
$249$	10.3799	0.657796
$250$	19.0098	1.20228
$251$	9.82228	0.619977	0.309989	−	0.950740i	$-0.399675\pi$
$251$	9.82228	0.619977	0.309989	+	0.950740i	$0.399675\pi$
$252$	−11.5555	−0.727926
$253$	−10.6181	−0.667553
$254$	−37.6487	−2.36229
$255$	−0.208128	−0.0130335
$256$	5.66449	0.354031
$257$	11.7680	0.734071	0.367035	−	0.930207i	$-0.380373\pi$
$257$	11.7680	0.734071	0.367035	+	0.930207i	$0.380373\pi$
$258$	4.51558	0.281128
$259$	−40.3340	−2.50623
$260$	−10.4705	−0.649354
$261$	3.85837	0.238827
$262$	−38.2243	−2.36151
$263$	−13.4208	−0.827562	−0.413781	−	0.910376i	$-0.635792\pi$
$263$	−13.4208	−0.827562	−0.413781	+	0.910376i	$0.635792\pi$
$264$	2.18114	0.134240
$265$	−12.2679	−0.753611
$266$	5.33678	0.327219
$267$	11.8329	0.724160
$268$	−1.08061	−0.0660087
$269$	−18.7218	−1.14149	−0.570745	−	0.821128i	$-0.693345\pi$
$269$	−18.7218	−1.14149	−0.570745	+	0.821128i	$0.693345\pi$
$270$	−2.11052	−0.128442
$271$	−7.66641	−0.465701	−0.232851	−	0.972512i	$-0.574805\pi$
$271$	−7.66641	−0.465701	−0.232851	+	0.972512i	$0.574805\pi$
$272$	0.582892	0.0353430
$273$	19.6414	1.18875
$274$	30.8624	1.86447
$275$	8.48341	0.511569
$276$	12.4705	0.750637
$277$	29.3020	1.76059	0.880294	−	0.474428i	$-0.157345\pi$
$277$	29.3020	1.76059	0.880294	+	0.474428i	$0.157345\pi$
$278$	−39.8463	−2.38982
$279$	−9.59784	−0.574608
$280$	4.77095	0.285119
$281$	−7.25564	−0.432835	−0.216418	−	0.976301i	$-0.569437\pi$
$281$	−7.25564	−0.432835	−0.216418	+	0.976301i	$0.569437\pi$
$282$	−2.49719	−0.148705
$283$	24.6072	1.46274	0.731372	−	0.681978i	$-0.238880\pi$
$283$	24.6072	1.46274	0.731372	+	0.681978i	$0.238880\pi$
$284$	−20.2382	−1.20092
$285$	0.540200	0.0319987
$286$	−18.9513	−1.12062
$287$	8.98064	0.530110
$288$	7.97133	0.469715
$289$	−16.9564	−0.997434
$290$	−8.14315	−0.478182
$291$	−8.01986	−0.470132
$292$	−7.54646	−0.441623
$293$	25.3617	1.48165	0.740823	−	0.671700i	$-0.234436\pi$
$293$	25.3617	1.48165	0.740823	+	0.671700i	$0.234436\pi$
$294$	−30.9220	−1.80341
$295$	−11.0466	−0.643156
$296$	−8.94142	−0.519710
$297$	−2.11706	−0.122845
$298$	−28.4285	−1.64682
$299$	−21.1967	−1.22584
$300$	−9.96344	−0.575239
$301$	9.90784	0.571078
$302$	−21.3689	−1.22964
$303$	−18.4102	−1.05764
$304$	−1.51290	−0.0867709
$305$	6.96178	0.398631
$306$	0.442426	0.0252918
$307$	21.2392	1.21219	0.606093	−	0.795394i	$-0.292736\pi$
$307$	21.2392	1.21219	0.606093	+	0.795394i	$0.292736\pi$
$308$	24.4637	1.39395
$309$	−6.85324	−0.389867
$310$	20.2564	1.15049
$311$	−10.6658	−0.604799	−0.302400	−	0.953181i	$-0.597788\pi$
$311$	−10.6658	−0.604799	−0.302400	+	0.953181i	$0.597788\pi$
$312$	4.35418	0.246507
$313$	27.0548	1.52923	0.764615	−	0.644488i	$-0.222929\pi$
$313$	27.0548	1.52923	0.764615	+	0.644488i	$0.222929\pi$
$314$	−24.2343	−1.36762
$315$	−4.63079	−0.260915
$316$	−7.75424	−0.436210
$317$	21.1480	1.18779	0.593895	−	0.804543i	$-0.297590\pi$
$317$	21.1480	1.18779	0.593895	+	0.804543i	$0.297590\pi$
$318$	26.0783	1.46240
$319$	−8.16841	−0.457343
$320$	−11.2625	−0.629591
$321$	17.2503	0.962817
$322$	49.3715	2.75137
$323$	−0.113242	−0.00630094
$324$	2.48641	0.138134
$325$	16.9353	0.939402
$326$	0.600579	0.0332630
$327$	−5.45244	−0.301521
$328$	1.99087	0.109927
$329$	−5.47919	−0.302078
$330$	4.46810	0.245961
$331$	−31.2903	−1.71987	−0.859935	−	0.510404i	$-0.829496\pi$
$331$	−31.2903	−1.71987	−0.859935	+	0.510404i	$0.829496\pi$
$332$	25.8085	1.41643
$333$	8.67873	0.475592
$334$	−22.0010	−1.20384
$335$	−0.433048	−0.0236599
$336$	12.9691	0.707525
$337$	−28.7562	−1.56645	−0.783226	−	0.621737i	$-0.786427\pi$
$337$	−28.7562	−1.56645	−0.783226	+	0.621737i	$0.786427\pi$
$338$	−10.2968	−0.560070
$339$	−19.5368	−1.06109
$340$	−0.517492	−0.0280650
$341$	20.3192	1.10035
$342$	−1.14832	−0.0620942
$343$	−35.3152	−1.90684
$344$	2.19641	0.118423
$345$	4.99749	0.269056
$346$	24.0186	1.29125
$347$	−8.84937	−0.475059	−0.237530	−	0.971380i	$-0.576338\pi$
$347$	−8.84937	−0.475059	−0.237530	+	0.971380i	$0.576338\pi$
$348$	9.59347	0.514264
$349$	20.5655	1.10085	0.550424	−	0.834885i	$-0.314466\pi$
$349$	20.5655	1.10085	0.550424	+	0.834885i	$0.314466\pi$
$350$	−39.4458	−2.10847
$351$	−4.22626	−0.225581
$352$	−16.8758	−0.899484
$353$	−3.11229	−0.165650	−0.0828252	−	0.996564i	$-0.526394\pi$
$353$	−3.11229	−0.165650	−0.0828252	+	0.996564i	$0.526394\pi$
$354$	23.4821	1.24806
$355$	−8.11036	−0.430453
$356$	29.4214	1.55933
$357$	0.970749	0.0513775
$358$	−35.9590	−1.90049
$359$	−25.6240	−1.35238	−0.676190	−	0.736727i	$-0.736370\pi$
$359$	−25.6240	−1.35238	−0.676190	+	0.736727i	$0.736370\pi$
$360$	−1.02657	−0.0541052
$361$	−18.7061	−0.984530
$362$	−28.7514	−1.51114
$363$	−6.51804	−0.342108
$364$	48.8364	2.55972
$365$	−3.02420	−0.158294
$366$	−14.7989	−0.773553
$367$	−28.2555	−1.47492	−0.737462	−	0.675388i	$-0.763976\pi$
$367$	−28.2555	−1.47492	−0.737462	+	0.675388i	$0.763976\pi$
$368$	−13.9961	−0.729599
$369$	−1.93238	−0.100596
$370$	−18.3166	−0.952236
$371$	57.2197	2.97070
$372$	−23.8642	−1.23730
$373$	6.96163	0.360459	0.180230	−	0.983625i	$-0.442316\pi$
$373$	6.96163	0.360459	0.180230	+	0.983625i	$0.442316\pi$
$374$	−0.936645	−0.0484328
$375$	−8.97486	−0.463460
$376$	−1.21465	−0.0626409
$377$	−16.3065	−0.839826
$378$	9.84384	0.506312
$379$	−10.1087	−0.519248	−0.259624	−	0.965710i	$-0.583599\pi$
$379$	−10.1087	−0.519248	−0.259624	+	0.965710i	$0.583599\pi$
$380$	1.34316	0.0689026
$381$	17.7746	0.910622
$382$	−17.6659	−0.903866
$383$	32.5167	1.66153	0.830763	−	0.556626i	$-0.187904\pi$
$383$	32.5167	1.66153	0.830763	+	0.556626i	$0.187904\pi$
$384$	7.99839	0.408166
$385$	9.80367	0.499641
$386$	3.53636	0.179996
$387$	−2.13189	−0.108370
$388$	−19.9406	−1.01233
$389$	5.64859	0.286395	0.143197	−	0.989694i	$-0.454262\pi$
$389$	5.64859	0.286395	0.143197	+	0.989694i	$0.454262\pi$
$390$	8.91960	0.451662
$391$	−1.04762	−0.0529804
$392$	−15.0407	−0.759671
$393$	18.0464	0.910320
$394$	1.32180	0.0665912
$395$	−3.10747	−0.156354
$396$	−5.26389	−0.264520
$397$	−21.2630	−1.06716	−0.533580	−	0.845750i	$-0.679154\pi$
$397$	−21.2630	−1.06716	−0.533580	+	0.845750i	$0.679154\pi$
$398$	−48.1087	−2.41147
$399$	−2.51959	−0.126137
$400$	11.1823	0.559117
$401$	−5.81398	−0.290336	−0.145168	−	0.989407i	$-0.546372\pi$
$401$	−5.81398	−0.290336	−0.145168	+	0.989407i	$0.546372\pi$
$402$	0.920546	0.0459126
$403$	40.5630	2.02059
$404$	−45.7754	−2.27741
$405$	0.996414	0.0495122
$406$	37.9811	1.88497
$407$	−18.3734	−0.910737
$408$	0.215200	0.0106540
$409$	13.9094	0.687775	0.343888	−	0.939011i	$-0.388256\pi$
$409$	13.9094	0.687775	0.343888	+	0.939011i	$0.388256\pi$
$410$	4.07832	0.201414
$411$	−14.5707	−0.718720
$412$	−17.0399	−0.839498
$413$	51.5232	2.53529
$414$	−10.6233	−0.522109
$415$	10.3426	0.507699
$416$	−33.6889	−1.65173
$417$	18.8121	0.921234
$418$	2.43108	0.118908
$419$	14.9833	0.731983	0.365991	−	0.930618i	$-0.380730\pi$
$419$	14.9833	0.731983	0.365991	+	0.930618i	$0.380730\pi$
$420$	−11.5140	−0.561827
$421$	3.21319	0.156601	0.0783005	−	0.996930i	$-0.475051\pi$
$421$	3.21319	0.156601	0.0783005	+	0.996930i	$0.475051\pi$
$422$	21.5630	1.04967
$423$	1.17897	0.0573233
$424$	12.6847	0.616025
$425$	0.837006	0.0406007
$426$	17.2405	0.835305
$427$	−32.4710	−1.57138
$428$	42.8912	2.07323
$429$	8.94727	0.431978
$430$	4.49938	0.216980
$431$	−7.72536	−0.372118	−0.186059	−	0.982539i	$-0.559571\pi$
$431$	−7.72536	−0.372118	−0.186059	+	0.982539i	$0.559571\pi$
$432$	−2.79059	−0.134262
$433$	12.3044	0.591311	0.295656	−	0.955295i	$-0.404462\pi$
$433$	12.3044	0.591311	0.295656	+	0.955295i	$0.404462\pi$
$434$	−94.4796	−4.53517
$435$	3.84453	0.184331
$436$	−13.5570	−0.649262
$437$	2.71911	0.130073
$438$	6.42866	0.307173
$439$	33.6506	1.60605	0.803027	−	0.595943i	$-0.203222\pi$
$439$	33.6506	1.60605	0.803027	+	0.595943i	$0.203222\pi$
$440$	2.17332	0.103609
$441$	14.5988	0.695182
$442$	−1.86981	−0.0889378
$443$	38.4312	1.82592	0.912960	−	0.408049i	$-0.133791\pi$
$443$	38.4312	1.82592	0.912960	+	0.408049i	$0.133791\pi$
$444$	21.5789	1.02409
$445$	11.7904	0.558920
$446$	−61.9138	−2.93170
$447$	13.4216	0.634821
$448$	52.5302	2.48182
$449$	−35.2320	−1.66270	−0.831351	−	0.555748i	$-0.812432\pi$
$449$	−35.2320	−1.66270	−0.831351	+	0.555748i	$0.812432\pi$
$450$	8.48762	0.400110
$451$	4.09097	0.192636
$452$	−48.5765	−2.28485
$453$	10.0886	0.474006
$454$	36.3160	1.70439
$455$	19.5709	0.917499
$456$	−0.558554	−0.0261567
$457$	4.39077	0.205392	0.102696	−	0.994713i	$-0.467253\pi$
$457$	4.39077	0.205392	0.102696	+	0.994713i	$0.467253\pi$
$458$	−8.61064	−0.402349
$459$	−0.208878	−0.00974957
$460$	12.4258	0.579356
$461$	−33.6325	−1.56642	−0.783212	−	0.621755i	$-0.786420\pi$
$461$	−33.6325	−1.56642	−0.783212	+	0.621755i	$0.786420\pi$
$462$	−20.8400	−0.969566
$463$	8.98157	0.417409	0.208704	−	0.977979i	$-0.433075\pi$
$463$	8.98157	0.417409	0.208704	+	0.977979i	$0.433075\pi$
$464$	−10.7671	−0.499851
$465$	−9.56342	−0.443493
$466$	−21.0453	−0.974905
$467$	5.66611	0.262196	0.131098	−	0.991369i	$-0.458150\pi$
$467$	5.66611	0.262196	0.131098	+	0.991369i	$0.458150\pi$
$468$	−10.5082	−0.485742
$469$	2.01981	0.0932663
$470$	−2.48823	−0.114773
$471$	11.4415	0.527195
$472$	11.4219	0.525735
$473$	4.51334	0.207524
$474$	6.60566	0.303408
$475$	−2.17246	−0.0996793
$476$	2.41368	0.110631
$477$	−12.3121	−0.563730
$478$	−57.3003	−2.62086
$479$	−2.66551	−0.121790	−0.0608951	−	0.998144i	$-0.519396\pi$
$479$	−2.66551	−0.121790	−0.0608951	+	0.998144i	$0.519396\pi$
$480$	7.94274	0.362535
$481$	−36.6786	−1.67240
$482$	37.3012	1.69902
$483$	−23.3092	−1.06060
$484$	−16.2065	−0.736660
$485$	−7.99109	−0.362857
$486$	−2.11811	−0.0960796
$487$	−12.6509	−0.573269	−0.286634	−	0.958040i	$-0.592536\pi$
$487$	−12.6509	−0.573269	−0.286634	+	0.958040i	$0.592536\pi$
$488$	−7.19832	−0.325853
$489$	−0.283544	−0.0128223
$490$	−30.8111	−1.39190
$491$	36.1406	1.63100	0.815502	−	0.578754i	$-0.196461\pi$
$491$	36.1406	1.63100	0.815502	+	0.578754i	$0.196461\pi$
$492$	−4.80468	−0.216612
$493$	−0.805926	−0.0362971
$494$	4.85312	0.218352
$495$	−2.10947	−0.0948137
$496$	26.7837	1.20262
$497$	37.8282	1.69683
$498$	−21.9857	−0.985203
$499$	−36.3042	−1.62520	−0.812599	−	0.582823i	$-0.801948\pi$
$499$	−36.3042	−1.62520	−0.812599	+	0.582823i	$0.801948\pi$
$500$	−22.3152	−0.997964
$501$	10.3871	0.464061
$502$	−20.8047	−0.928560
$503$	−6.15299	−0.274348	−0.137174	−	0.990547i	$-0.543802\pi$
$503$	−6.15299	−0.274348	−0.137174	+	0.990547i	$0.543802\pi$
$504$	4.78812	0.213280
$505$	−18.3442	−0.816307
$506$	22.4903	0.999816
$507$	4.86129	0.215897
$508$	44.1950	1.96084
$509$	2.96066	0.131229	0.0656145	−	0.997845i	$-0.479099\pi$
$509$	2.96066	0.131229	0.0656145	+	0.997845i	$0.479099\pi$
$510$	0.440840	0.0195207
$511$	14.1054	0.623987
$512$	−27.9948	−1.23721
$513$	0.542144	0.0239363
$514$	−24.9261	−1.09944
$515$	−6.82866	−0.300907
$516$	−5.30074	−0.233352
$517$	−2.49595	−0.109772
$518$	85.4320	3.75367
$519$	−11.3396	−0.497754
$520$	4.33857	0.190259
$521$	−15.9630	−0.699351	−0.349675	−	0.936871i	$-0.613708\pi$
$521$	−15.9630	−0.699351	−0.349675	+	0.936871i	$0.613708\pi$
$522$	−8.17246	−0.357699
$523$	−2.90723	−0.127124	−0.0635620	−	0.997978i	$-0.520246\pi$
$523$	−2.90723	−0.127124	−0.0635620	+	0.997978i	$0.520246\pi$
$524$	44.8707	1.96019
$525$	18.6231	0.812778
$526$	28.4268	1.23947
$527$	2.00477	0.0873293
$528$	5.90786	0.257107
$529$	2.15499	0.0936952
$530$	25.9848	1.12871
$531$	−11.0863	−0.481105
$532$	−6.26473	−0.271611
$533$	8.16673	0.353741
$534$	−25.0634	−1.08460
$535$	17.1884	0.743120
$536$	0.447761	0.0193403
$537$	16.9769	0.732607
$538$	39.6549	1.70965
$539$	−30.9067	−1.33124
$540$	2.47749	0.106614
$541$	44.3921	1.90857	0.954284	−	0.298903i	$-0.0966206\pi$
$541$	44.3921	1.90857	0.954284	+	0.298903i	$0.0966206\pi$
$542$	16.2383	0.697496
$543$	13.5741	0.582519
$544$	−1.66503	−0.0713876
$545$	−5.43289	−0.232719
$546$	−41.6026	−1.78043
$547$	21.2015	0.906510	0.453255	−	0.891381i	$-0.350263\pi$
$547$	21.2015	0.906510	0.453255	+	0.891381i	$0.350263\pi$
$548$	−36.2287	−1.54761
$549$	6.98684	0.298191
$550$	−17.9688	−0.766194
$551$	2.09179	0.0891133
$552$	−5.16728	−0.219934
$553$	14.4938	0.616339
$554$	−62.0651	−2.63689
$555$	8.64761	0.367070
$556$	46.7747	1.98369
$557$	10.7625	0.456020	0.228010	−	0.973659i	$-0.426778\pi$
$557$	10.7625	0.456020	0.228010	+	0.973659i	$0.426778\pi$
$558$	20.3293	0.860609
$559$	9.00991	0.381078
$560$	12.9226	0.546081
$561$	0.442207	0.0186700
$562$	15.3683	0.648272
$563$	−2.56348	−0.108038	−0.0540189	−	0.998540i	$-0.517203\pi$
$563$	−2.56348	−0.108038	−0.0540189	+	0.998540i	$0.517203\pi$
$564$	2.93139	0.123434
$565$	−19.4667	−0.818972
$566$	−52.1208	−2.19080
$567$	−4.64745	−0.195175
$568$	8.38592	0.351865
$569$	−23.7175	−0.994287	−0.497144	−	0.867668i	$-0.665618\pi$
$569$	−23.7175	−0.994287	−0.497144	+	0.867668i	$0.665618\pi$
$570$	−1.14421	−0.0479255
$571$	18.7301	0.783830	0.391915	−	0.920001i	$-0.371813\pi$
$571$	18.7301	0.783830	0.391915	+	0.920001i	$0.371813\pi$
$572$	22.2466	0.930175
$573$	8.34039	0.348425
$574$	−19.0220	−0.793964
$575$	−20.0978	−0.838137
$576$	−11.3030	−0.470958
$577$	−0.370525	−0.0154251	−0.00771257	−	0.999970i	$-0.502455\pi$
$577$	−0.370525	−0.0154251	−0.00771257	+	0.999970i	$0.502455\pi$
$578$	35.9155	1.49389
$579$	−1.66958	−0.0693854
$580$	9.55907	0.396919
$581$	−48.2399	−2.00133
$582$	16.9870	0.704133
$583$	26.0654	1.07952
$584$	3.12695	0.129394
$585$	−4.21110	−0.174108
$586$	−53.7190	−2.21911
$587$	3.59501	0.148382	0.0741909	−	0.997244i	$-0.476363\pi$
$587$	3.59501	0.148382	0.0741909	+	0.997244i	$0.476363\pi$
$588$	36.2986	1.49693
$589$	−5.20342	−0.214403
$590$	23.3979	0.963276
$591$	−0.624044	−0.0256698
$592$	−24.2188	−0.995386
$593$	19.2514	0.790560	0.395280	−	0.918561i	$-0.370648\pi$
$593$	19.2514	0.790560	0.395280	+	0.918561i	$0.370648\pi$
$594$	4.48418	0.183988
$595$	0.967267	0.0396541
$596$	33.3716	1.36696
$597$	22.7130	0.929581
$598$	44.8971	1.83598
$599$	1.00742	0.0411622	0.0205811	−	0.999788i	$-0.493448\pi$
$599$	1.00742	0.0411622	0.0205811	+	0.999788i	$0.493448\pi$
$600$	4.12845	0.168543
$601$	6.07450	0.247784	0.123892	−	0.992296i	$-0.460462\pi$
$601$	6.07450	0.247784	0.123892	+	0.992296i	$0.460462\pi$
$602$	−20.9859	−0.855323
$603$	−0.434606	−0.0176985
$604$	25.0845	1.02067
$605$	−6.49466	−0.264046
$606$	38.9950	1.58406
$607$	15.5504	0.631172	0.315586	−	0.948897i	$-0.397799\pi$
$607$	15.5504	0.631172	0.315586	+	0.948897i	$0.397799\pi$
$608$	4.32161	0.175264
$609$	−17.9316	−0.726624
$610$	−14.7459	−0.597042
$611$	−4.98262	−0.201575
$612$	−0.519355	−0.0209937
$613$	12.0233	0.485616	0.242808	−	0.970074i	$-0.421932\pi$
$613$	12.0233	0.485616	0.242808	+	0.970074i	$0.421932\pi$
$614$	−44.9871	−1.81553
$615$	−1.92545	−0.0776415
$616$	−10.1368	−0.408422
$617$	43.0069	1.73139	0.865695	−	0.500571i	$-0.166877\pi$
$617$	43.0069	1.73139	0.865695	+	0.500571i	$0.166877\pi$
$618$	14.5159	0.583917
$619$	−18.9774	−0.762766	−0.381383	−	0.924417i	$-0.624552\pi$
$619$	−18.9774	−0.762766	−0.381383	+	0.924417i	$0.624552\pi$
$620$	−23.7786	−0.954970
$621$	5.01547	0.201264
$622$	22.5913	0.905828
$623$	−54.9927	−2.20324
$624$	11.7938	0.472128
$625$	11.0931	0.443725
$626$	−57.3052	−2.29038
$627$	−1.14775	−0.0458369
$628$	28.4482	1.13520
$629$	−1.81279	−0.0722808
$630$	9.80854	0.390781
$631$	20.3046	0.808315	0.404157	−	0.914690i	$-0.367565\pi$
$631$	20.3046	0.808315	0.404157	+	0.914690i	$0.367565\pi$
$632$	3.21305	0.127808
$633$	−10.1803	−0.404629
$634$	−44.7939	−1.77899
$635$	17.7109	0.702835
$636$	−30.6128	−1.21388
$637$	−61.6985	−2.44458
$638$	17.3016	0.684978
$639$	−8.13955	−0.321996
$640$	7.96971	0.315030
$641$	−38.7451	−1.53034	−0.765170	−	0.643829i	$-0.777345\pi$
$641$	−38.7451	−1.53034	−0.765170	+	0.643829i	$0.777345\pi$
$642$	−36.5381	−1.44204
$643$	47.5593	1.87556	0.937779	−	0.347234i	$-0.112879\pi$
$643$	47.5593	1.87556	0.937779	+	0.347234i	$0.112879\pi$
$644$	−57.9562	−2.28379
$645$	−2.12424	−0.0836419
$646$	0.239859	0.00943713
$647$	−8.14859	−0.320354	−0.160177	−	0.987088i	$-0.551206\pi$
$647$	−8.14859	−0.320354	−0.160177	+	0.987088i	$0.551206\pi$
$648$	−1.03027	−0.0404728
$649$	23.4705	0.921296
$650$	−35.8709	−1.40697
$651$	44.6055	1.74823
$652$	−0.705006	−0.0276102
$653$	−17.5333	−0.686129	−0.343065	−	0.939312i	$-0.611465\pi$
$653$	−17.5333	−0.686129	−0.343065	+	0.939312i	$0.611465\pi$
$654$	11.5489	0.451597
$655$	17.9817	0.702602
$656$	5.39248	0.210541
$657$	−3.03509	−0.118410
$658$	11.6056	0.452432
$659$	−40.2430	−1.56764	−0.783822	−	0.620986i	$-0.786732\pi$
$659$	−40.2430	−1.56764	−0.783822	+	0.620986i	$0.786732\pi$
$660$	−5.24501	−0.204162
$661$	26.4116	1.02729	0.513646	−	0.858002i	$-0.328295\pi$
$661$	26.4116	1.02729	0.513646	+	0.858002i	$0.328295\pi$
$662$	66.2764	2.57591
$663$	0.882771	0.0342840
$664$	−10.6940	−0.415009
$665$	−2.51056	−0.0973552
$666$	−18.3825	−0.712309
$667$	19.3515	0.749295
$668$	25.8265	0.999258
$669$	29.2306	1.13012
$670$	0.917244	0.0354362
$671$	−14.7916	−0.571023
$672$	−37.0464	−1.42909
$673$	−2.40167	−0.0925777	−0.0462888	−	0.998928i	$-0.514739\pi$
$673$	−2.40167	−0.0925777	−0.0462888	+	0.998928i	$0.514739\pi$
$674$	60.9090	2.34613
$675$	−4.00716	−0.154236
$676$	12.0871	0.464890
$677$	2.84038	0.109165	0.0545824	−	0.998509i	$-0.482617\pi$
$677$	2.84038	0.109165	0.0545824	+	0.998509i	$0.482617\pi$
$678$	41.3812	1.58923
$679$	37.2719	1.43036
$680$	0.214428	0.00822294
$681$	−17.1454	−0.657014
$682$	−43.0385	−1.64803
$683$	15.2038	0.581757	0.290879	−	0.956760i	$-0.406052\pi$
$683$	15.2038	0.581757	0.290879	+	0.956760i	$0.406052\pi$
$684$	1.34799	0.0515418
$685$	−14.5185	−0.554722
$686$	74.8016	2.85594
$687$	4.06524	0.155099
$688$	5.94922	0.226812
$689$	52.0340	1.98234
$690$	−10.5852	−0.402974
$691$	−40.7015	−1.54836	−0.774179	−	0.632967i	$-0.781837\pi$
$691$	−40.7015	−1.54836	−0.774179	+	0.632967i	$0.781837\pi$
$692$	−28.1949	−1.07181
$693$	9.83896	0.373751
$694$	18.7440	0.711512
$695$	18.7447	0.711026
$696$	−3.97515	−0.150678
$697$	0.403630	0.0152886
$698$	−43.5602	−1.64878
$699$	9.93587	0.375809
$700$	46.3046	1.75015
$701$	9.03109	0.341100	0.170550	−	0.985349i	$-0.445446\pi$
$701$	9.03109	0.341100	0.170550	+	0.985349i	$0.445446\pi$
$702$	8.95171	0.337860
$703$	4.70513	0.177457
$704$	23.9292	0.901865
$705$	1.17474	0.0442432
$706$	6.59219	0.248100
$707$	85.5607	3.21784
$708$	−27.5651	−1.03596
$709$	33.2641	1.24926	0.624630	−	0.780921i	$-0.285250\pi$
$709$	33.2641	1.24926	0.624630	+	0.780921i	$0.285250\pi$
$710$	17.1787	0.644704
$711$	−3.11865	−0.116959
$712$	−12.1910	−0.456878
$713$	−48.1377	−1.80277
$714$	−2.05616	−0.0769497
$715$	8.91518	0.333409
$716$	42.2115	1.57752
$717$	27.0525	1.01029
$718$	54.2745	2.02551
$719$	12.6356	0.471229	0.235615	−	0.971847i	$-0.424290\pi$
$719$	12.6356	0.471229	0.235615	+	0.971847i	$0.424290\pi$
$720$	−2.78058	−0.103626
$721$	31.8501	1.18616
$722$	39.6216	1.47456
$723$	−17.6106	−0.654945
$724$	33.7506	1.25433
$725$	−15.4611	−0.574211
$726$	13.8060	0.512387
$727$	44.4246	1.64762	0.823809	−	0.566868i	$-0.191845\pi$
$727$	44.4246	1.64762	0.823809	+	0.566868i	$0.191845\pi$
$728$	−20.2359	−0.749991
$729$	1.00000	0.0370370
$730$	6.40560	0.237082
$731$	0.445303	0.0164701
$732$	17.3721	0.642093
$733$	−14.2905	−0.527833	−0.263917	−	0.964545i	$-0.585014\pi$
$733$	−14.2905	−0.527833	−0.263917	+	0.964545i	$0.585014\pi$
$734$	59.8484	2.20904
$735$	14.5465	0.536555
$736$	39.9800	1.47368
$737$	0.920089	0.0338919
$738$	4.09300	0.150665
$739$	20.7592	0.763640	0.381820	−	0.924237i	$-0.375297\pi$
$739$	20.7592	0.763640	0.381820	+	0.924237i	$0.375297\pi$
$740$	21.5015	0.790410
$741$	−2.29124	−0.0841710
$742$	−121.198	−4.44932
$743$	2.42495	0.0889630	0.0444815	−	0.999010i	$-0.485836\pi$
$743$	2.42495	0.0889630	0.0444815	+	0.999010i	$0.485836\pi$
$744$	9.88835	0.362525
$745$	13.3735	0.489967
$746$	−14.7455	−0.539872
$747$	10.3799	0.379779
$748$	1.09951	0.0402020
$749$	−80.1699	−2.92934
$750$	19.0098	0.694139
$751$	44.3722	1.61917	0.809583	−	0.587005i	$-0.199693\pi$
$751$	44.3722	1.61917	0.809583	+	0.587005i	$0.199693\pi$
$752$	−3.29001	−0.119974
$753$	9.82228	0.357944
$754$	34.5390	1.25783
$755$	10.0525	0.365846
$756$	−11.5555	−0.420268
$757$	23.1251	0.840496	0.420248	−	0.907409i	$-0.361943\pi$
$757$	23.1251	0.840496	0.420248	+	0.907409i	$0.361943\pi$
$758$	21.4113	0.777695
$759$	−10.6181	−0.385412
$760$	−0.556551	−0.0201882
$761$	−22.4054	−0.812195	−0.406097	−	0.913830i	$-0.633111\pi$
$761$	−22.4054	−0.812195	−0.406097	+	0.913830i	$0.633111\pi$
$762$	−37.6487	−1.36387
$763$	25.3400	0.917368
$764$	20.7376	0.750260
$765$	−0.208128	−0.00752490
$766$	−68.8741	−2.48852
$767$	46.8537	1.69179
$768$	5.66449	0.204400
$769$	38.9236	1.40362	0.701811	−	0.712363i	$-0.252375\pi$
$769$	38.9236	1.40362	0.701811	+	0.712363i	$0.252375\pi$
$770$	−20.7653	−0.748329
$771$	11.7680	0.423816
$772$	−4.15126	−0.149407
$773$	−18.7719	−0.675179	−0.337589	−	0.941294i	$-0.609611\pi$
$773$	−18.7719	−0.675179	−0.337589	+	0.941294i	$0.609611\pi$
$774$	4.51558	0.162309
$775$	38.4601	1.38153
$776$	8.26260	0.296610
$777$	−40.3340	−1.44697
$778$	−11.9644	−0.428943
$779$	−1.04763	−0.0375352
$780$	−10.4705	−0.374905
$781$	17.2319	0.616607
$782$	2.21898	0.0793505
$783$	3.85837	0.137887
$784$	−40.7394	−1.45498
$785$	11.4004	0.406899
$786$	−38.2243	−1.36342
$787$	−15.1015	−0.538309	−0.269155	−	0.963097i	$-0.586744\pi$
$787$	−15.1015	−0.538309	−0.269155	+	0.963097i	$0.586744\pi$
$788$	−1.55163	−0.0552745
$789$	−13.4208	−0.477793
$790$	6.58197	0.234176
$791$	90.7964	3.22835
$792$	2.18114	0.0775036
$793$	−29.5282	−1.04858
$794$	45.0375	1.59832
$795$	−12.2679	−0.435098
$796$	56.4738	2.00166
$797$	18.4943	0.655101	0.327551	−	0.944834i	$-0.393777\pi$
$797$	18.4943	0.655101	0.327551	+	0.944834i	$0.393777\pi$
$798$	5.33678	0.188920
$799$	−0.246260	−0.00871204
$800$	−31.9424	−1.12933
$801$	11.8329	0.418094
$802$	12.3147	0.434846
$803$	6.42547	0.226750
$804$	−1.08061	−0.0381101
$805$	−23.2256	−0.818595
$806$	−85.9171	−3.02630
$807$	−18.7218	−0.659039
$808$	18.9675	0.667274
$809$	43.2680	1.52122	0.760610	−	0.649209i	$-0.224900\pi$
$809$	43.2680	1.52122	0.760610	+	0.649209i	$0.224900\pi$
$810$	−2.11052	−0.0741560
$811$	−24.4145	−0.857309	−0.428654	−	0.903469i	$-0.641012\pi$
$811$	−24.4145	−0.857309	−0.428654	+	0.903469i	$0.641012\pi$
$812$	−44.5852	−1.56463
$813$	−7.66641	−0.268873
$814$	38.9170	1.36404
$815$	−0.282527	−0.00989650
$816$	0.582892	0.0204053
$817$	−1.15579	−0.0404360
$818$	−29.4617	−1.03010
$819$	19.6414	0.686325
$820$	−4.78745	−0.167185
$821$	43.4813	1.51751	0.758753	−	0.651378i	$-0.225809\pi$
$821$	43.4813	1.51751	0.758753	+	0.651378i	$0.225809\pi$
$822$	30.8624	1.07645
$823$	−4.57015	−0.159305	−0.0796527	−	0.996823i	$-0.525381\pi$
$823$	−4.57015	−0.159305	−0.0796527	+	0.996823i	$0.525381\pi$
$824$	7.06067	0.245970
$825$	8.48341	0.295355
$826$	−109.132	−3.79719
$827$	23.1647	0.805515	0.402757	−	0.915307i	$-0.368052\pi$
$827$	23.1647	0.805515	0.402757	+	0.915307i	$0.368052\pi$
$828$	12.4705	0.433380
$829$	−19.6810	−0.683549	−0.341775	−	0.939782i	$-0.611028\pi$
$829$	−19.6810	−0.683549	−0.341775	+	0.939782i	$0.611028\pi$
$830$	−21.9069	−0.760398
$831$	29.3020	1.01648
$832$	47.7694	1.65611
$833$	−3.04937	−0.105654
$834$	−39.8463	−1.37976
$835$	10.3498	0.358171
$836$	−2.85379	−0.0987003
$837$	−9.59784	−0.331750
$838$	−31.7364	−1.09631
$839$	−46.5999	−1.60881	−0.804403	−	0.594084i	$-0.797515\pi$
$839$	−46.5999	−1.60881	−0.804403	+	0.594084i	$0.797515\pi$
$840$	4.77095	0.164614
$841$	−14.1130	−0.486655
$842$	−6.80589	−0.234547
$843$	−7.25564	−0.249897
$844$	−25.3123	−0.871285
$845$	4.84385	0.166634
$846$	−2.49719	−0.0858550
$847$	30.2923	1.04086
$848$	34.3579	1.17986
$849$	24.6072	0.844516
$850$	−1.77287	−0.0608091
$851$	43.5280	1.49212
$852$	−20.2382	−0.693351
$853$	−31.1325	−1.06596	−0.532978	−	0.846129i	$-0.678927\pi$
$853$	−31.1325	−1.06596	−0.532978	+	0.846129i	$0.678927\pi$
$854$	68.7774	2.35351
$855$	0.540200	0.0184745
$856$	−17.7724	−0.607449
$857$	16.6606	0.569114	0.284557	−	0.958659i	$-0.408154\pi$
$857$	16.6606	0.569114	0.284557	+	0.958659i	$0.408154\pi$
$858$	−18.9513	−0.646988
$859$	9.15873	0.312492	0.156246	−	0.987718i	$-0.450061\pi$
$859$	9.15873	0.312492	0.156246	+	0.987718i	$0.450061\pi$
$860$	−5.28173	−0.180105
$861$	8.98064	0.306059
$862$	16.3632	0.557333
$863$	8.38564	0.285451	0.142725	−	0.989762i	$-0.454413\pi$
$863$	8.38564	0.285451	0.142725	+	0.989762i	$0.454413\pi$
$864$	7.97133	0.271190
$865$	−11.2989	−0.384176
$866$	−26.0621	−0.885626
$867$	−16.9564	−0.575869
$868$	110.908	3.76445
$869$	6.60239	0.223971
$870$	−8.14315	−0.276079
$871$	1.83676	0.0622362
$872$	5.61748	0.190232
$873$	−8.01986	−0.271431
$874$	−5.75939	−0.194814
$875$	41.7102	1.41006
$876$	−7.54646	−0.254971
$877$	−37.4490	−1.26456	−0.632282	−	0.774739i	$-0.717881\pi$
$877$	−37.4490	−1.26456	−0.632282	+	0.774739i	$0.717881\pi$
$878$	−71.2757	−2.40544
$879$	25.3617	0.855429
$880$	5.88667	0.198440
$881$	12.4514	0.419498	0.209749	−	0.977755i	$-0.432735\pi$
$881$	12.4514	0.419498	0.209749	+	0.977755i	$0.432735\pi$
$882$	−30.9220	−1.04120
$883$	57.6072	1.93864	0.969319	−	0.245806i	$-0.0790525\pi$
$883$	57.6072	1.93864	0.969319	+	0.245806i	$0.0790525\pi$
$884$	2.19493	0.0738235
$885$	−11.0466	−0.371326
$886$	−81.4016	−2.73474
$887$	41.3660	1.38893	0.694467	−	0.719525i	$-0.255640\pi$
$887$	41.3660	1.38893	0.694467	+	0.719525i	$0.255640\pi$
$888$	−8.94142	−0.300054
$889$	−82.6068	−2.77054
$890$	−24.9735	−0.837114
$891$	−2.11706	−0.0709243
$892$	72.6793	2.43348
$893$	0.639170	0.0213890
$894$	−28.4285	−0.950793
$895$	16.9160	0.565440
$896$	−37.1722	−1.24183
$897$	−21.1967	−0.707738
$898$	74.6255	2.49028
$899$	−37.0320	−1.23509
$900$	−9.96344	−0.332115
$901$	2.57171	0.0856762
$902$	−8.66514	−0.288517
$903$	9.90784	0.329712
$904$	20.1282	0.669452
$905$	13.5254	0.449599
$906$	−21.3689	−0.709934
$907$	−39.7114	−1.31860	−0.659298	−	0.751882i	$-0.729146\pi$
$907$	−39.7114	−1.31860	−0.659298	+	0.751882i	$0.729146\pi$
$908$	−42.6305	−1.41474
$909$	−18.4102	−0.610629
$910$	−41.4534	−1.37417
$911$	−31.9343	−1.05803	−0.529015	−	0.848613i	$-0.677438\pi$
$911$	−31.9343	−1.05803	−0.529015	+	0.848613i	$0.677438\pi$
$912$	−1.51290	−0.0500972
$913$	−21.9748	−0.727260
$914$	−9.30016	−0.307622
$915$	6.96178	0.230150
$916$	10.1078	0.333973
$917$	−83.8698	−2.76962
$918$	0.442426	0.0146022
$919$	−38.9348	−1.28434	−0.642170	−	0.766563i	$-0.721966\pi$
$919$	−38.9348	−1.28434	−0.642170	+	0.766563i	$0.721966\pi$
$920$	−5.14875	−0.169749
$921$	21.2392	0.699856
$922$	71.2376	2.34608
$923$	34.3999	1.13229
$924$	24.4637	0.804795
$925$	−34.7771	−1.14346
$926$	−19.0240	−0.625167
$927$	−6.85324	−0.225090
$928$	30.7563	1.00962
$929$	−5.51819	−0.181046	−0.0905230	−	0.995894i	$-0.528854\pi$
$929$	−5.51819	−0.181046	−0.0905230	+	0.995894i	$0.528854\pi$
$930$	20.2564	0.664234
$931$	7.91467	0.259393
$932$	24.7046	0.809227
$933$	−10.6658	−0.349181
$934$	−12.0015	−0.392700
$935$	0.440621	0.0144099
$936$	4.35418	0.142321
$937$	22.4452	0.733253	0.366627	−	0.930368i	$-0.380513\pi$
$937$	22.4452	0.733253	0.366627	+	0.930368i	$0.380513\pi$
$938$	−4.27819	−0.139688
$939$	27.0548	0.882901
$940$	2.92088	0.0952686
$941$	13.0504	0.425432	0.212716	−	0.977114i	$-0.431769\pi$
$941$	13.0504	0.425432	0.212716	+	0.977114i	$0.431769\pi$
$942$	−24.2343	−0.789597
$943$	−9.69179	−0.315608
$944$	30.9374	1.00693
$945$	−4.63079	−0.150639
$946$	−9.55977	−0.310815
$947$	−6.99279	−0.227235	−0.113618	−	0.993525i	$-0.536244\pi$
$947$	−6.99279	−0.227235	−0.113618	+	0.993525i	$0.536244\pi$
$948$	−7.75424	−0.251846
$949$	12.8271	0.416384
$950$	4.60152	0.149293
$951$	21.1480	0.685771
$952$	−1.00013	−0.0324145
$953$	15.7171	0.509128	0.254564	−	0.967056i	$-0.418068\pi$
$953$	15.7171	0.509128	0.254564	+	0.967056i	$0.418068\pi$
$954$	26.0783	0.844318
$955$	8.31048	0.268921
$956$	67.2636	2.17546
$957$	−8.16841	−0.264047
$958$	5.64586	0.182409
$959$	67.7167	2.18669
$960$	−11.2625	−0.363494
$961$	61.1186	1.97157
$962$	77.6895	2.50481
$963$	17.2503	0.555882
$964$	−43.7871	−1.41029
$965$	−1.66359	−0.0535529
$966$	49.3715	1.58850
$967$	−11.9878	−0.385503	−0.192751	−	0.981248i	$-0.561741\pi$
$967$	−11.9878	−0.385503	−0.192751	+	0.981248i	$0.561741\pi$
$968$	6.71533	0.215839
$969$	−0.113242	−0.00363785
$970$	16.9261	0.543463
$971$	−2.66856	−0.0856383	−0.0428191	−	0.999083i	$-0.513634\pi$
$971$	−2.66856	−0.0856383	−0.0428191	+	0.999083i	$0.513634\pi$
$972$	2.48641	0.0797516
$973$	−87.4286	−2.80283
$974$	26.7961	0.858603
$975$	16.9353	0.542364
$976$	−19.4974	−0.624097
$977$	43.5995	1.39487	0.697436	−	0.716647i	$-0.254324\pi$
$977$	43.5995	1.39487	0.697436	+	0.716647i	$0.254324\pi$
$978$	0.600579	0.0192044
$979$	−25.0510	−0.800632
$980$	36.1685	1.15536
$981$	−5.45244	−0.174083
$982$	−76.5500	−2.44281
$983$	55.6759	1.77579	0.887893	−	0.460050i	$-0.152168\pi$
$983$	55.6759	1.77579	0.887893	+	0.460050i	$0.152168\pi$
$984$	1.99087	0.0634665
$985$	−0.621806	−0.0198124
$986$	1.70704	0.0543633
$987$	−5.47919	−0.174405
$988$	−5.69697	−0.181245
$989$	−10.6924	−0.339999
$990$	4.46810	0.142006
$991$	−13.9510	−0.443168	−0.221584	−	0.975141i	$-0.571123\pi$
$991$	−13.9510	−0.443168	−0.221584	+	0.975141i	$0.571123\pi$
$992$	−76.5075	−2.42912
$993$	−31.2903	−0.992967
$994$	−80.1244	−2.54139
$995$	22.6315	0.717468
$996$	25.8085	0.817775
$997$	20.6927	0.655343	0.327671	−	0.944792i	$-0.393736\pi$
$997$	20.6927	0.655343	0.327671	+	0.944792i	$0.393736\pi$
$998$	76.8964	2.43411
$999$	8.67873	0.274583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.e.1.14	✓	97

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.e.1.14	✓	97	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.11811 q^{2} +1.00000 q^{3} +2.48641 q^{4} +0.996414 q^{5} -2.11811 q^{6} -4.64745 q^{7} -1.03027 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.11811 q^{2} +1.00000 q^{3} +2.48641 q^{4} +0.996414 q^{5} -2.11811 q^{6} -4.64745 q^{7} -1.03027 q^{8} +1.00000 q^{9} -2.11052 q^{10} -2.11706 q^{11} +2.48641 q^{12} -4.22626 q^{13} +9.84384 q^{14} +0.996414 q^{15} -2.79059 q^{16} -0.208878 q^{17} -2.11811 q^{18} +0.542144 q^{19} +2.47749 q^{20} -4.64745 q^{21} +4.48418 q^{22} +5.01547 q^{23} -1.03027 q^{24} -4.00716 q^{25} +8.95171 q^{26} +1.00000 q^{27} -11.5555 q^{28} +3.85837 q^{29} -2.11052 q^{30} -9.59784 q^{31} +7.97133 q^{32} -2.11706 q^{33} +0.442426 q^{34} -4.63079 q^{35} +2.48641 q^{36} +8.67873 q^{37} -1.14832 q^{38} -4.22626 q^{39} -1.02657 q^{40} -1.93238 q^{41} +9.84384 q^{42} -2.13189 q^{43} -5.26389 q^{44} +0.996414 q^{45} -10.6233 q^{46} +1.17897 q^{47} -2.79059 q^{48} +14.5988 q^{49} +8.48762 q^{50} -0.208878 q^{51} -10.5082 q^{52} -12.3121 q^{53} -2.11811 q^{54} -2.10947 q^{55} +4.78812 q^{56} +0.542144 q^{57} -8.17246 q^{58} -11.0863 q^{59} +2.47749 q^{60} +6.98684 q^{61} +20.3293 q^{62} -4.64745 q^{63} -11.3030 q^{64} -4.21110 q^{65} +4.48418 q^{66} -0.434606 q^{67} -0.519355 q^{68} +5.01547 q^{69} +9.80854 q^{70} -8.13955 q^{71} -1.03027 q^{72} -3.03509 q^{73} -18.3825 q^{74} -4.00716 q^{75} +1.34799 q^{76} +9.83896 q^{77} +8.95171 q^{78} -3.11865 q^{79} -2.78058 q^{80} +1.00000 q^{81} +4.09300 q^{82} +10.3799 q^{83} -11.5555 q^{84} -0.208128 q^{85} +4.51558 q^{86} +3.85837 q^{87} +2.18114 q^{88} +11.8329 q^{89} -2.11052 q^{90} +19.6414 q^{91} +12.4705 q^{92} -9.59784 q^{93} -2.49719 q^{94} +0.540200 q^{95} +7.97133 q^{96} -8.01986 q^{97} -30.9220 q^{98} -2.11706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * q^99

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