LMFDB - Embedded newform 6005.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78685 q^{2} -1.57697 q^{3} +5.76652 q^{4} -1.00000 q^{5} +4.39478 q^{6} -0.289151 q^{7} -10.4967 q^{8} -0.513163 q^{9} +O(q^{10})$	\(q-2.78685 q^{2} -1.57697 q^{3} +5.76652 q^{4} -1.00000 q^{5} +4.39478 q^{6} -0.289151 q^{7} -10.4967 q^{8} -0.513163 q^{9} +2.78685 q^{10} +6.20334 q^{11} -9.09363 q^{12} -3.17238 q^{13} +0.805821 q^{14} +1.57697 q^{15} +17.7197 q^{16} -5.52564 q^{17} +1.43011 q^{18} +0.271084 q^{19} -5.76652 q^{20} +0.455983 q^{21} -17.2877 q^{22} -6.15727 q^{23} +16.5530 q^{24} +1.00000 q^{25} +8.84093 q^{26} +5.54016 q^{27} -1.66740 q^{28} -9.39306 q^{29} -4.39478 q^{30} -5.73156 q^{31} -28.3886 q^{32} -9.78248 q^{33} +15.3991 q^{34} +0.289151 q^{35} -2.95916 q^{36} +8.15542 q^{37} -0.755471 q^{38} +5.00274 q^{39} +10.4967 q^{40} +7.19160 q^{41} -1.27076 q^{42} +1.26424 q^{43} +35.7716 q^{44} +0.513163 q^{45} +17.1594 q^{46} -11.5514 q^{47} -27.9434 q^{48} -6.91639 q^{49} -2.78685 q^{50} +8.71377 q^{51} -18.2936 q^{52} +2.12536 q^{53} -15.4396 q^{54} -6.20334 q^{55} +3.03514 q^{56} -0.427492 q^{57} +26.1770 q^{58} -6.76003 q^{59} +9.09363 q^{60} -11.7465 q^{61} +15.9730 q^{62} +0.148382 q^{63} +43.6753 q^{64} +3.17238 q^{65} +27.2623 q^{66} -1.75996 q^{67} -31.8637 q^{68} +9.70984 q^{69} -0.805821 q^{70} +7.24700 q^{71} +5.38651 q^{72} +14.6043 q^{73} -22.7279 q^{74} -1.57697 q^{75} +1.56321 q^{76} -1.79370 q^{77} -13.9419 q^{78} -10.5323 q^{79} -17.7197 q^{80} -7.19718 q^{81} -20.0419 q^{82} +6.35377 q^{83} +2.62943 q^{84} +5.52564 q^{85} -3.52323 q^{86} +14.8126 q^{87} -65.1146 q^{88} -0.905231 q^{89} -1.43011 q^{90} +0.917297 q^{91} -35.5060 q^{92} +9.03850 q^{93} +32.1919 q^{94} -0.271084 q^{95} +44.7680 q^{96} -15.3800 q^{97} +19.2749 q^{98} -3.18332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) $ 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * 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 $

$2$	−2.78685	−1.97060	−0.985299	−	0.170838i	$-0.945353\pi$
$2$	−2.78685	−1.97060	−0.985299	+	0.170838i	$0.945353\pi$
$3$	−1.57697	−0.910465	−0.455232	−	0.890373i	$-0.650444\pi$
$3$	−1.57697	−0.910465	−0.455232	+	0.890373i	$0.650444\pi$
$4$	5.76652	2.88326
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.39478	1.79416
$7$	−0.289151	−0.109289	−0.0546445	−	0.998506i	$-0.517403\pi$
$7$	−0.289151	−0.109289	−0.0546445	+	0.998506i	$0.517403\pi$
$8$	−10.4967	−3.71114
$9$	−0.513163	−0.171054
$10$	2.78685	0.881278
$11$	6.20334	1.87038	0.935188	−	0.354151i	$-0.115230\pi$
$11$	6.20334	1.87038	0.935188	+	0.354151i	$0.115230\pi$
$12$	−9.09363	−2.62510
$13$	−3.17238	−0.879859	−0.439929	−	0.898032i	$-0.644997\pi$
$13$	−3.17238	−0.879859	−0.439929	+	0.898032i	$0.644997\pi$
$14$	0.805821	0.215365
$15$	1.57697	0.407172
$16$	17.7197	4.42992
$17$	−5.52564	−1.34016	−0.670082	−	0.742287i	$-0.733741\pi$
$17$	−5.52564	−1.34016	−0.670082	+	0.742287i	$0.733741\pi$
$18$	1.43011	0.337079
$19$	0.271084	0.0621910	0.0310955	−	0.999516i	$-0.490100\pi$
$19$	0.271084	0.0621910	0.0310955	+	0.999516i	$0.490100\pi$
$20$	−5.76652	−1.28943
$21$	0.455983	0.0995037
$22$	−17.2877	−3.68576
$23$	−6.15727	−1.28388	−0.641940	−	0.766755i	$-0.721870\pi$
$23$	−6.15727	−1.28388	−0.641940	+	0.766755i	$0.721870\pi$
$24$	16.5530	3.37887
$25$	1.00000	0.200000
$26$	8.84093	1.73385
$27$	5.54016	1.06620
$28$	−1.66740	−0.315108
$29$	−9.39306	−1.74425	−0.872124	−	0.489286i	$-0.837258\pi$
$29$	−9.39306	−1.74425	−0.872124	+	0.489286i	$0.837258\pi$
$30$	−4.39478	−0.802373
$31$	−5.73156	−1.02942	−0.514709	−	0.857365i	$-0.672100\pi$
$31$	−5.73156	−1.02942	−0.514709	+	0.857365i	$0.672100\pi$
$32$	−28.3886	−5.01844
$33$	−9.78248	−1.70291
$34$	15.3991	2.64092
$35$	0.289151	0.0488755
$36$	−2.95916	−0.493193
$37$	8.15542	1.34074	0.670371	−	0.742026i	$-0.266135\pi$
$37$	8.15542	1.34074	0.670371	+	0.742026i	$0.266135\pi$
$38$	−0.755471	−0.122554
$39$	5.00274	0.801080
$40$	10.4967	1.65967
$41$	7.19160	1.12314	0.561570	−	0.827429i	$-0.310198\pi$
$41$	7.19160	1.12314	0.561570	+	0.827429i	$0.310198\pi$
$42$	−1.27076	−0.196082
$43$	1.26424	0.192794	0.0963970	−	0.995343i	$-0.469268\pi$
$43$	1.26424	0.192794	0.0963970	+	0.995343i	$0.469268\pi$
$44$	35.7716	5.39278
$45$	0.513163	0.0764978
$46$	17.1594	2.53001
$47$	−11.5514	−1.68494	−0.842471	−	0.538741i	$-0.818900\pi$
$47$	−11.5514	−1.68494	−0.842471	+	0.538741i	$0.818900\pi$
$48$	−27.9434	−4.03328
$49$	−6.91639	−0.988056
$50$	−2.78685	−0.394120
$51$	8.71377	1.22017
$52$	−18.2936	−2.53686
$53$	2.12536	0.291941	0.145971	−	0.989289i	$-0.453370\pi$
$53$	2.12536	0.291941	0.145971	+	0.989289i	$0.453370\pi$
$54$	−15.4396	−2.10106
$55$	−6.20334	−0.836458
$56$	3.03514	0.405587
$57$	−0.427492	−0.0566227
$58$	26.1770	3.43721
$59$	−6.76003	−0.880081	−0.440040	−	0.897978i	$-0.645036\pi$
$59$	−6.76003	−0.880081	−0.440040	+	0.897978i	$0.645036\pi$
$60$	9.09363	1.17398
$61$	−11.7465	−1.50398	−0.751992	−	0.659173i	$-0.770907\pi$
$61$	−11.7465	−1.50398	−0.751992	+	0.659173i	$0.770907\pi$
$62$	15.9730	2.02857
$63$	0.148382	0.0186943
$64$	43.6753	5.45942
$65$	3.17238	0.393485
$66$	27.2623	3.35575
$67$	−1.75996	−0.215013	−0.107507	−	0.994204i	$-0.534287\pi$
$67$	−1.75996	−0.215013	−0.107507	+	0.994204i	$0.534287\pi$
$68$	−31.8637	−3.86404
$69$	9.70984	1.16893
$70$	−0.805821	−0.0963140
$71$	7.24700	0.860060	0.430030	−	0.902815i	$-0.358503\pi$
$71$	7.24700	0.860060	0.430030	+	0.902815i	$0.358503\pi$
$72$	5.38651	0.634807
$73$	14.6043	1.70930	0.854652	−	0.519201i	$-0.173771\pi$
$73$	14.6043	1.70930	0.854652	+	0.519201i	$0.173771\pi$
$74$	−22.7279	−2.64207
$75$	−1.57697	−0.182093
$76$	1.56321	0.179313
$77$	−1.79370	−0.204411
$78$	−13.9419	−1.57861
$79$	−10.5323	−1.18497	−0.592486	−	0.805581i	$-0.701854\pi$
$79$	−10.5323	−1.18497	−0.592486	+	0.805581i	$0.701854\pi$
$80$	−17.7197	−1.98112
$81$	−7.19718	−0.799686
$82$	−20.0419	−2.21326
$83$	6.35377	0.697416	0.348708	−	0.937231i	$-0.386620\pi$
$83$	6.35377	0.697416	0.348708	+	0.937231i	$0.386620\pi$
$84$	2.62943	0.286895
$85$	5.52564	0.599340
$86$	−3.52323	−0.379920
$87$	14.8126	1.58808
$88$	−65.1146	−6.94124
$89$	−0.905231	−0.0959543	−0.0479771	−	0.998848i	$-0.515277\pi$
$89$	−0.905231	−0.0959543	−0.0479771	+	0.998848i	$0.515277\pi$
$90$	−1.43011	−0.150746
$91$	0.917297	0.0961588
$92$	−35.5060	−3.70176
$93$	9.03850	0.937249
$94$	32.1919	3.32034
$95$	−0.271084	−0.0278127
$96$	44.7680	4.56911
$97$	−15.3800	−1.56161	−0.780803	−	0.624777i	$-0.785190\pi$
$97$	−15.3800	−1.56161	−0.780803	+	0.624777i	$0.785190\pi$
$98$	19.2749	1.94706
$99$	−3.18332	−0.319936
$100$	5.76652	0.576652
$101$	−12.8707	−1.28068	−0.640339	−	0.768092i	$-0.721206\pi$
$101$	−12.8707	−1.28068	−0.640339	+	0.768092i	$0.721206\pi$
$102$	−24.2839	−2.40447
$103$	11.0093	1.08478	0.542392	−	0.840126i	$-0.317519\pi$
$103$	11.0093	1.08478	0.542392	+	0.840126i	$0.317519\pi$
$104$	33.2995	3.26528
$105$	−0.455983	−0.0444994
$106$	−5.92306	−0.575299
$107$	−12.6276	−1.22075	−0.610377	−	0.792111i	$-0.708982\pi$
$107$	−12.6276	−1.22075	−0.610377	+	0.792111i	$0.708982\pi$
$108$	31.9474	3.07414
$109$	8.53107	0.817128	0.408564	−	0.912730i	$-0.366030\pi$
$109$	8.53107	0.817128	0.408564	+	0.912730i	$0.366030\pi$
$110$	17.2877	1.64832
$111$	−12.8609	−1.22070
$112$	−5.12367	−0.484141
$113$	20.5045	1.92890	0.964452	−	0.264260i	$-0.0851276\pi$
$113$	20.5045	1.92890	0.964452	+	0.264260i	$0.0851276\pi$
$114$	1.19136	0.111581
$115$	6.15727	0.574169
$116$	−54.1652	−5.02911
$117$	1.62794	0.150504
$118$	18.8392	1.73429
$119$	1.59775	0.146465
$120$	−16.5530	−1.51107
$121$	27.4814	2.49831
$122$	32.7357	2.96375
$123$	−11.3409	−1.02258
$124$	−33.0511	−2.96808
$125$	−1.00000	−0.0894427
$126$	−0.413517	−0.0368390
$127$	5.73485	0.508886	0.254443	−	0.967088i	$-0.418108\pi$
$127$	5.73485	0.508886	0.254443	+	0.967088i	$0.418108\pi$
$128$	−64.9393	−5.73987
$129$	−1.99366	−0.175532
$130$	−8.84093	−0.775401
$131$	−15.3244	−1.33890	−0.669449	−	0.742858i	$-0.733470\pi$
$131$	−15.3244	−1.33890	−0.669449	+	0.742858i	$0.733470\pi$
$132$	−56.4108	−4.90993
$133$	−0.0783844	−0.00679679
$134$	4.90474	0.423705
$135$	−5.54016	−0.476821
$136$	58.0010	4.97354
$137$	3.40774	0.291143	0.145571	−	0.989348i	$-0.453498\pi$
$137$	3.40774	0.291143	0.145571	+	0.989348i	$0.453498\pi$
$138$	−27.0598	−2.30349
$139$	−9.67783	−0.820863	−0.410431	−	0.911891i	$-0.634622\pi$
$139$	−9.67783	−0.820863	−0.410431	+	0.911891i	$0.634622\pi$
$140$	1.66740	0.140921
$141$	18.2162	1.53408
$142$	−20.1963	−1.69483
$143$	−19.6793	−1.64567
$144$	−9.09307	−0.757756
$145$	9.39306	0.780051
$146$	−40.6999	−3.36835
$147$	10.9069	0.899590
$148$	47.0283	3.86571
$149$	−10.0219	−0.821025	−0.410513	−	0.911855i	$-0.634650\pi$
$149$	−10.0219	−0.821025	−0.410513	+	0.911855i	$0.634650\pi$
$150$	4.39478	0.358832
$151$	10.8787	0.885294	0.442647	−	0.896696i	$-0.354039\pi$
$151$	10.8787	0.885294	0.442647	+	0.896696i	$0.354039\pi$
$152$	−2.84549	−0.230800
$153$	2.83555	0.229241
$154$	4.99878	0.402813
$155$	5.73156	0.460370
$156$	28.8484	2.30972
$157$	−4.30900	−0.343896	−0.171948	−	0.985106i	$-0.555006\pi$
$157$	−4.30900	−0.343896	−0.171948	+	0.985106i	$0.555006\pi$
$158$	29.3518	2.33510
$159$	−3.35164	−0.265802
$160$	28.3886	2.24432
$161$	1.78038	0.140314
$162$	20.0574	1.57586
$163$	14.4533	1.13207	0.566035	−	0.824381i	$-0.308477\pi$
$163$	14.4533	1.13207	0.566035	+	0.824381i	$0.308477\pi$
$164$	41.4705	3.23830
$165$	9.78248	0.761565
$166$	−17.7070	−1.37433
$167$	−11.5667	−0.895057	−0.447529	−	0.894270i	$-0.647696\pi$
$167$	−11.5667	−0.895057	−0.447529	+	0.894270i	$0.647696\pi$
$168$	−4.78632	−0.369273
$169$	−2.93603	−0.225848
$170$	−15.3991	−1.18106
$171$	−0.139110	−0.0106380
$172$	7.29023	0.555875
$173$	20.6566	1.57049	0.785247	−	0.619182i	$-0.212536\pi$
$173$	20.6566	1.57049	0.785247	+	0.619182i	$0.212536\pi$
$174$	−41.2804	−3.12946
$175$	−0.289151	−0.0218578
$176$	109.921	8.28561
$177$	10.6604	0.801282
$178$	2.52274	0.189087
$179$	−8.69927	−0.650214	−0.325107	−	0.945677i	$-0.605400\pi$
$179$	−8.69927	−0.650214	−0.325107	+	0.945677i	$0.605400\pi$
$180$	2.95916	0.220563
$181$	−0.521741	−0.0387807	−0.0193904	−	0.999812i	$-0.506173\pi$
$181$	−0.521741	−0.0387807	−0.0193904	+	0.999812i	$0.506173\pi$
$182$	−2.55637	−0.189490
$183$	18.5239	1.36932
$184$	64.6310	4.76466
$185$	−8.15542	−0.599598
$186$	−25.1889	−1.84694
$187$	−34.2774	−2.50661
$188$	−66.6112	−4.85812
$189$	−1.60194	−0.116524
$190$	0.755471	0.0548076
$191$	−5.88622	−0.425912	−0.212956	−	0.977062i	$-0.568309\pi$
$191$	−5.88622	−0.425912	−0.212956	+	0.977062i	$0.568309\pi$
$192$	−68.8747	−4.97061
$193$	10.0964	0.726757	0.363378	−	0.931642i	$-0.381623\pi$
$193$	10.0964	0.726757	0.363378	+	0.931642i	$0.381623\pi$
$194$	42.8618	3.07730
$195$	−5.00274	−0.358254
$196$	−39.8835	−2.84882
$197$	16.6443	1.18586	0.592930	−	0.805254i	$-0.297971\pi$
$197$	16.6443	1.18586	0.592930	+	0.805254i	$0.297971\pi$
$198$	8.87143	0.630465
$199$	12.8417	0.910324	0.455162	−	0.890409i	$-0.349581\pi$
$199$	12.8417	0.910324	0.455162	+	0.890409i	$0.349581\pi$
$200$	−10.4967	−0.742229
$201$	2.77541	0.195762
$202$	35.8686	2.52370
$203$	2.71602	0.190627
$204$	50.2481	3.51807
$205$	−7.19160	−0.502283
$206$	−30.6814	−2.13767
$207$	3.15968	0.219613
$208$	−56.2134	−3.89770
$209$	1.68163	0.116321
$210$	1.27076	0.0876905
$211$	−17.0621	−1.17460	−0.587302	−	0.809368i	$-0.699810\pi$
$211$	−17.0621	−1.17460	−0.587302	+	0.809368i	$0.699810\pi$
$212$	12.2559	0.841742
$213$	−11.4283	−0.783054
$214$	35.1911	2.40562
$215$	−1.26424	−0.0862201
$216$	−58.1534	−3.95683
$217$	1.65729	0.112504
$218$	−23.7748	−1.61023
$219$	−23.0306	−1.55626
$220$	−35.7716	−2.41172
$221$	17.5294	1.17915
$222$	35.8412	2.40551
$223$	−14.8354	−0.993451	−0.496726	−	0.867908i	$-0.665464\pi$
$223$	−14.8354	−0.993451	−0.496726	+	0.867908i	$0.665464\pi$
$224$	8.20860	0.548460
$225$	−0.513163	−0.0342108
$226$	−57.1430	−3.80109
$227$	2.70436	0.179495	0.0897473	−	0.995965i	$-0.471394\pi$
$227$	2.70436	0.179495	0.0897473	+	0.995965i	$0.471394\pi$
$228$	−2.46514	−0.163258
$229$	6.22948	0.411656	0.205828	−	0.978588i	$-0.434011\pi$
$229$	6.22948	0.411656	0.205828	+	0.978588i	$0.434011\pi$
$230$	−17.1594	−1.13146
$231$	2.82862	0.186109
$232$	98.5961	6.47315
$233$	−22.9992	−1.50673	−0.753364	−	0.657604i	$-0.771570\pi$
$233$	−22.9992	−1.50673	−0.753364	+	0.657604i	$0.771570\pi$
$234$	−4.53683	−0.296582
$235$	11.5514	0.753529
$236$	−38.9818	−2.53750
$237$	16.6091	1.07888
$238$	−4.45267	−0.288624
$239$	−5.90067	−0.381683	−0.190841	−	0.981621i	$-0.561122\pi$
$239$	−5.90067	−0.381683	−0.190841	+	0.981621i	$0.561122\pi$
$240$	27.9434	1.80374
$241$	7.69386	0.495605	0.247802	−	0.968811i	$-0.420292\pi$
$241$	7.69386	0.495605	0.247802	+	0.968811i	$0.420292\pi$
$242$	−76.5864	−4.92316
$243$	−5.27073	−0.338117
$244$	−67.7363	−4.33637
$245$	6.91639	0.441872
$246$	31.6055	2.01509
$247$	−0.859982	−0.0547193
$248$	60.1625	3.82032
$249$	−10.0197	−0.634973
$250$	2.78685	0.176256
$251$	−14.2099	−0.896923	−0.448461	−	0.893802i	$-0.648028\pi$
$251$	−14.2099	−0.896923	−0.448461	+	0.893802i	$0.648028\pi$
$252$	0.855645	0.0539006
$253$	−38.1956	−2.40134
$254$	−15.9821	−1.00281
$255$	−8.71377	−0.545677
$256$	93.6251	5.85157
$257$	−26.1723	−1.63259	−0.816293	−	0.577638i	$-0.803975\pi$
$257$	−26.1723	−1.63259	−0.816293	+	0.577638i	$0.803975\pi$
$258$	5.55603	0.345903
$259$	−2.35815	−0.146528
$260$	18.2936	1.13452
$261$	4.82017	0.298361
$262$	42.7067	2.63843
$263$	4.29658	0.264938	0.132469	−	0.991187i	$-0.457709\pi$
$263$	4.29658	0.264938	0.132469	+	0.991187i	$0.457709\pi$
$264$	102.684	6.31975
$265$	−2.12536	−0.130560
$266$	0.218445	0.0133937
$267$	1.42752	0.0873630
$268$	−10.1488	−0.619939
$269$	−2.89355	−0.176423	−0.0882116	−	0.996102i	$-0.528115\pi$
$269$	−2.89355	−0.176423	−0.0882116	+	0.996102i	$0.528115\pi$
$270$	15.4396	0.939622
$271$	7.01650	0.426222	0.213111	−	0.977028i	$-0.431640\pi$
$271$	7.01650	0.426222	0.213111	+	0.977028i	$0.431640\pi$
$272$	−97.9124	−5.93681
$273$	−1.44655	−0.0875492
$274$	−9.49685	−0.573726
$275$	6.20334	0.374075
$276$	55.9919	3.37032
$277$	−20.3804	−1.22454	−0.612268	−	0.790650i	$-0.709743\pi$
$277$	−20.3804	−1.22454	−0.612268	+	0.790650i	$0.709743\pi$
$278$	26.9706	1.61759
$279$	2.94122	0.176086
$280$	−3.03514	−0.181384
$281$	−10.3104	−0.615069	−0.307535	−	0.951537i	$-0.599504\pi$
$281$	−10.3104	−0.615069	−0.307535	+	0.951537i	$0.599504\pi$
$282$	−50.7658	−3.02306
$283$	2.90449	0.172654	0.0863269	−	0.996267i	$-0.472487\pi$
$283$	2.90449	0.172654	0.0863269	+	0.996267i	$0.472487\pi$
$284$	41.7899	2.47977
$285$	0.427492	0.0253225
$286$	54.8432	3.24295
$287$	−2.07946	−0.122747
$288$	14.5680	0.858426
$289$	13.5327	0.796039
$290$	−26.1770	−1.53717
$291$	24.2539	1.42179
$292$	84.2159	4.92836
$293$	−26.9104	−1.57212	−0.786060	−	0.618150i	$-0.787883\pi$
$293$	−26.9104	−1.57212	−0.786060	+	0.618150i	$0.787883\pi$
$294$	−30.3960	−1.77273
$295$	6.76003	0.393584
$296$	−85.6050	−4.97569
$297$	34.3674	1.99420
$298$	27.9295	1.61791
$299$	19.5332	1.12963
$300$	−9.09363	−0.525021
$301$	−0.365555	−0.0210703
$302$	−30.3172	−1.74456
$303$	20.2967	1.16601
$304$	4.80353	0.275501
$305$	11.7465	0.672602
$306$	−7.90224	−0.451741
$307$	−1.23661	−0.0705769	−0.0352885	−	0.999377i	$-0.511235\pi$
$307$	−1.23661	−0.0705769	−0.0352885	+	0.999377i	$0.511235\pi$
$308$	−10.3434	−0.589371
$309$	−17.3614	−0.987657
$310$	−15.9730	−0.907204
$311$	8.66392	0.491286	0.245643	−	0.969360i	$-0.421001\pi$
$311$	8.66392	0.491286	0.245643	+	0.969360i	$0.421001\pi$
$312$	−52.5123	−2.97292
$313$	−4.27099	−0.241411	−0.120705	−	0.992688i	$-0.538516\pi$
$313$	−4.27099	−0.241411	−0.120705	+	0.992688i	$0.538516\pi$
$314$	12.0085	0.677680
$315$	−0.148382	−0.00836036
$316$	−60.7345	−3.41658
$317$	−16.5297	−0.928400	−0.464200	−	0.885730i	$-0.653658\pi$
$317$	−16.5297	−0.928400	−0.464200	+	0.885730i	$0.653658\pi$
$318$	9.34050	0.523789
$319$	−58.2683	−3.26240
$320$	−43.6753	−2.44153
$321$	19.9133	1.11145
$322$	−4.96166	−0.276502
$323$	−1.49791	−0.0833462
$324$	−41.5026	−2.30570
$325$	−3.17238	−0.175972
$326$	−40.2792	−2.23086
$327$	−13.4532	−0.743966
$328$	−75.4881	−4.16813
$329$	3.34010	0.184146
$330$	−27.2623	−1.50074
$331$	9.03528	0.496624	0.248312	−	0.968680i	$-0.420124\pi$
$331$	9.03528	0.496624	0.248312	+	0.968680i	$0.420124\pi$
$332$	36.6391	2.01083
$333$	−4.18506	−0.229340
$334$	32.2346	1.76380
$335$	1.75996	0.0961569
$336$	8.07987	0.440793
$337$	35.2035	1.91766	0.958828	−	0.283986i	$-0.0916570\pi$
$337$	35.2035	1.91766	0.958828	+	0.283986i	$0.0916570\pi$
$338$	8.18227	0.445057
$339$	−32.3350	−1.75620
$340$	31.8637	1.72805
$341$	−35.5548	−1.92540
$342$	0.387679	0.0209633
$343$	4.02394	0.217273
$344$	−13.2703	−0.715487
$345$	−9.70984	−0.522760
$346$	−57.5669	−3.09481
$347$	−2.48981	−0.133660	−0.0668300	−	0.997764i	$-0.521289\pi$
$347$	−2.48981	−0.133660	−0.0668300	+	0.997764i	$0.521289\pi$
$348$	85.4170	4.57883
$349$	−23.8723	−1.27785	−0.638927	−	0.769267i	$-0.720621\pi$
$349$	−23.8723	−1.27785	−0.638927	+	0.769267i	$0.720621\pi$
$350$	0.805821	0.0430729
$351$	−17.5755	−0.938108
$352$	−176.104	−9.38637
$353$	−10.8557	−0.577789	−0.288894	−	0.957361i	$-0.593288\pi$
$353$	−10.8557	−0.577789	−0.288894	+	0.957361i	$0.593288\pi$
$354$	−29.7088	−1.57901
$355$	−7.24700	−0.384631
$356$	−5.22003	−0.276661
$357$	−2.51960	−0.133351
$358$	24.2435	1.28131
$359$	−27.8390	−1.46928	−0.734642	−	0.678455i	$-0.762650\pi$
$359$	−27.8390	−1.46928	−0.734642	+	0.678455i	$0.762650\pi$
$360$	−5.38651	−0.283894
$361$	−18.9265	−0.996132
$362$	1.45401	0.0764212
$363$	−43.3373	−2.27462
$364$	5.28961	0.277251
$365$	−14.6043	−0.764424
$366$	−51.6232	−2.69839
$367$	−5.63829	−0.294316	−0.147158	−	0.989113i	$-0.547013\pi$
$367$	−5.63829	−0.294316	−0.147158	+	0.989113i	$0.547013\pi$
$368$	−109.105	−5.68748
$369$	−3.69046	−0.192118
$370$	22.7279	1.18157
$371$	−0.614552	−0.0319059
$372$	52.1207	2.70233
$373$	−5.73646	−0.297023	−0.148511	−	0.988911i	$-0.547448\pi$
$373$	−5.73646	−0.297023	−0.148511	+	0.988911i	$0.547448\pi$
$374$	95.5258	4.93952
$375$	1.57697	0.0814344
$376$	121.251	6.25306
$377$	29.7983	1.53469
$378$	4.46437	0.229622
$379$	12.8273	0.658894	0.329447	−	0.944174i	$-0.393138\pi$
$379$	12.8273	0.658894	0.329447	+	0.944174i	$0.393138\pi$
$380$	−1.56321	−0.0801911
$381$	−9.04369	−0.463322
$382$	16.4040	0.839301
$383$	5.98629	0.305885	0.152943	−	0.988235i	$-0.451125\pi$
$383$	5.98629	0.305885	0.152943	+	0.988235i	$0.451125\pi$
$384$	102.407	5.22595
$385$	1.79370	0.0914156
$386$	−28.1372	−1.43215
$387$	−0.648758	−0.0329782
$388$	−88.6893	−4.50252
$389$	2.02146	0.102492	0.0512462	−	0.998686i	$-0.483681\pi$
$389$	2.02146	0.102492	0.0512462	+	0.998686i	$0.483681\pi$
$390$	13.9419	0.705975
$391$	34.0228	1.72061
$392$	72.5993	3.66682
$393$	24.1661	1.21902
$394$	−46.3852	−2.33685
$395$	10.5323	0.529936
$396$	−18.3567	−0.922457
$397$	−16.4871	−0.827463	−0.413731	−	0.910399i	$-0.635775\pi$
$397$	−16.4871	−0.827463	−0.413731	+	0.910399i	$0.635775\pi$
$398$	−35.7879	−1.79388
$399$	0.123610	0.00618824
$400$	17.7197	0.885983
$401$	16.9201	0.844951	0.422475	−	0.906374i	$-0.361161\pi$
$401$	16.9201	0.844951	0.422475	+	0.906374i	$0.361161\pi$
$402$	−7.73463	−0.385768
$403$	18.1827	0.905743
$404$	−74.2189	−3.69253
$405$	7.19718	0.357631
$406$	−7.56912	−0.375649
$407$	50.5908	2.50769
$408$	−91.4658	−4.52823
$409$	21.9238	1.08406	0.542030	−	0.840359i	$-0.317656\pi$
$409$	21.9238	1.08406	0.542030	+	0.840359i	$0.317656\pi$
$410$	20.0419	0.989799
$411$	−5.37391	−0.265075
$412$	63.4856	3.12771
$413$	1.95467	0.0961831
$414$	−8.80555	−0.432769
$415$	−6.35377	−0.311894
$416$	90.0593	4.41552
$417$	15.2617	0.747367
$418$	−4.68644	−0.229221
$419$	39.0460	1.90752	0.953761	−	0.300566i	$-0.0971755\pi$
$419$	39.0460	1.90752	0.953761	+	0.300566i	$0.0971755\pi$
$420$	−2.62943	−0.128303
$421$	34.3310	1.67319	0.836596	−	0.547820i	$-0.184542\pi$
$421$	34.3310	1.67319	0.836596	+	0.547820i	$0.184542\pi$
$422$	47.5494	2.31467
$423$	5.92774	0.288217
$424$	−22.3093	−1.08344
$425$	−5.52564	−0.268033
$426$	31.8489	1.54309
$427$	3.39651	0.164369
$428$	−72.8171	−3.51975
$429$	31.0337	1.49832
$430$	3.52323	0.169905
$431$	26.5367	1.27823	0.639114	−	0.769112i	$-0.279301\pi$
$431$	26.5367	1.27823	0.639114	+	0.769112i	$0.279301\pi$
$432$	98.1697	4.72319
$433$	−7.01000	−0.336879	−0.168440	−	0.985712i	$-0.553873\pi$
$433$	−7.01000	−0.336879	−0.168440	+	0.985712i	$0.553873\pi$
$434$	−4.61861	−0.221700
$435$	−14.8126	−0.710209
$436$	49.1945	2.35599
$437$	−1.66914	−0.0798458
$438$	64.1826	3.06676
$439$	−14.9369	−0.712901	−0.356451	−	0.934314i	$-0.616013\pi$
$439$	−14.9369	−0.712901	−0.356451	+	0.934314i	$0.616013\pi$
$440$	65.1146	3.10421
$441$	3.54923	0.169011
$442$	−48.8517	−2.32364
$443$	−3.24619	−0.154231	−0.0771157	−	0.997022i	$-0.524571\pi$
$443$	−3.24619	−0.154231	−0.0771157	+	0.997022i	$0.524571\pi$
$444$	−74.1623	−3.51959
$445$	0.905231	0.0429121
$446$	41.3440	1.95769
$447$	15.8042	0.747515
$448$	−12.6288	−0.596654
$449$	32.5815	1.53761	0.768807	−	0.639481i	$-0.220851\pi$
$449$	32.5815	1.53761	0.768807	+	0.639481i	$0.220851\pi$
$450$	1.43011	0.0674158
$451$	44.6119	2.10069
$452$	118.240	5.56152
$453$	−17.1554	−0.806029
$454$	−7.53663	−0.353712
$455$	−0.917297	−0.0430035
$456$	4.48726	0.210135
$457$	−1.08807	−0.0508979	−0.0254490	−	0.999676i	$-0.508102\pi$
$457$	−1.08807	−0.0508979	−0.0254490	+	0.999676i	$0.508102\pi$
$458$	−17.3606	−0.811208
$459$	−30.6129	−1.42889
$460$	35.5060	1.65548
$461$	13.5156	0.629485	0.314743	−	0.949177i	$-0.398082\pi$
$461$	13.5156	0.629485	0.314743	+	0.949177i	$0.398082\pi$
$462$	−7.88292	−0.366747
$463$	−29.3337	−1.36325	−0.681627	−	0.731700i	$-0.738727\pi$
$463$	−29.3337	−1.36325	−0.681627	+	0.731700i	$0.738727\pi$
$464$	−166.442	−7.72687
$465$	−9.03850	−0.419151
$466$	64.0952	2.96915
$467$	−30.1023	−1.39297	−0.696484	−	0.717572i	$-0.745253\pi$
$467$	−30.1023	−1.39297	−0.696484	+	0.717572i	$0.745253\pi$
$468$	9.38757	0.433940
$469$	0.508895	0.0234986
$470$	−32.1919	−1.48490
$471$	6.79517	0.313105
$472$	70.9580	3.26611
$473$	7.84248	0.360597
$474$	−46.2870	−2.12603
$475$	0.271084	0.0124382
$476$	9.21342	0.422297
$477$	−1.09066	−0.0499378
$478$	16.4443	0.752144
$479$	10.2165	0.466805	0.233402	−	0.972380i	$-0.425014\pi$
$479$	10.2165	0.466805	0.233402	+	0.972380i	$0.425014\pi$
$480$	−44.7680	−2.04337
$481$	−25.8721	−1.17966
$482$	−21.4416	−0.976638
$483$	−2.80761	−0.127751
$484$	158.472	7.20326
$485$	15.3800	0.698372
$486$	14.6887	0.666293
$487$	14.1231	0.639978	0.319989	−	0.947421i	$-0.396321\pi$
$487$	14.1231	0.639978	0.319989	+	0.947421i	$0.396321\pi$
$488$	123.299	5.58150
$489$	−22.7925	−1.03071
$490$	−19.2749	−0.870752
$491$	−2.68705	−0.121265	−0.0606324	−	0.998160i	$-0.519312\pi$
$491$	−2.68705	−0.121265	−0.0606324	+	0.998160i	$0.519312\pi$
$492$	−65.3977	−2.94836
$493$	51.9026	2.33758
$494$	2.39664	0.107830
$495$	3.18332	0.143080
$496$	−101.561	−4.56024
$497$	−2.09548	−0.0939951
$498$	27.9234	1.25128
$499$	22.5704	1.01039	0.505195	−	0.863005i	$-0.331421\pi$
$499$	22.5704	1.01039	0.505195	+	0.863005i	$0.331421\pi$
$500$	−5.76652	−0.257886
$501$	18.2403	0.814918
$502$	39.6009	1.76747
$503$	−30.8245	−1.37440	−0.687198	−	0.726470i	$-0.741160\pi$
$503$	−30.8245	−1.37440	−0.687198	+	0.726470i	$0.741160\pi$
$504$	−1.55752	−0.0693774
$505$	12.8707	0.572737
$506$	106.445	4.73207
$507$	4.63003	0.205627
$508$	33.0701	1.46725
$509$	6.94130	0.307668	0.153834	−	0.988097i	$-0.450838\pi$
$509$	6.94130	0.307668	0.153834	+	0.988097i	$0.450838\pi$
$510$	24.2839	1.07531
$511$	−4.22285	−0.186808
$512$	−131.040	−5.79122
$513$	1.50185	0.0663083
$514$	72.9383	3.21717
$515$	−11.0093	−0.485130
$516$	−11.4965	−0.506104
$517$	−71.6571	−3.15148
$518$	6.57180	0.288748
$519$	−32.5749	−1.42988
$520$	−33.2995	−1.46028
$521$	19.2841	0.844854	0.422427	−	0.906397i	$-0.361178\pi$
$521$	19.2841	0.844854	0.422427	+	0.906397i	$0.361178\pi$
$522$	−13.4331	−0.587949
$523$	6.87498	0.300622	0.150311	−	0.988639i	$-0.451973\pi$
$523$	6.87498	0.300622	0.150311	+	0.988639i	$0.451973\pi$
$524$	−88.3684	−3.86039
$525$	0.455983	0.0199007
$526$	−11.9739	−0.522087
$527$	31.6705	1.37959
$528$	−173.342	−7.54375
$529$	14.9120	0.648347
$530$	5.92306	0.257281
$531$	3.46899	0.150542
$532$	−0.452005	−0.0195969
$533$	−22.8145	−0.988204
$534$	−3.97829	−0.172157
$535$	12.6276	0.545938
$536$	18.4738	0.797946
$537$	13.7185	0.591997
$538$	8.06389	0.347659
$539$	−42.9047	−1.84804
$540$	−31.9474	−1.37480
$541$	15.6516	0.672913	0.336457	−	0.941699i	$-0.390771\pi$
$541$	15.6516	0.672913	0.336457	+	0.941699i	$0.390771\pi$
$542$	−19.5539	−0.839913
$543$	0.822771	0.0353085
$544$	156.865	6.72553
$545$	−8.53107	−0.365431
$546$	4.03131	0.172524
$547$	−8.84809	−0.378317	−0.189159	−	0.981947i	$-0.560576\pi$
$547$	−8.84809	−0.378317	−0.189159	+	0.981947i	$0.560576\pi$
$548$	19.6508	0.839440
$549$	6.02786	0.257263
$550$	−17.2877	−0.737152
$551$	−2.54631	−0.108477
$552$	−101.921	−4.33806
$553$	3.04542	0.129504
$554$	56.7969	2.41307
$555$	12.8609	0.545913
$556$	−55.8074	−2.36676
$557$	39.1207	1.65760	0.828798	−	0.559547i	$-0.189025\pi$
$557$	39.1207	1.65760	0.828798	+	0.559547i	$0.189025\pi$
$558$	−8.19674	−0.346995
$559$	−4.01063	−0.169632
$560$	5.12367	0.216514
$561$	54.0544	2.28218
$562$	28.7336	1.21205
$563$	24.2741	1.02303	0.511516	−	0.859274i	$-0.329084\pi$
$563$	24.2741	1.02303	0.511516	+	0.859274i	$0.329084\pi$
$564$	105.044	4.42315
$565$	−20.5045	−0.862632
$566$	−8.09436	−0.340231
$567$	2.08107	0.0873969
$568$	−76.0695	−3.19181
$569$	1.65281	0.0692895	0.0346447	−	0.999400i	$-0.488970\pi$
$569$	1.65281	0.0692895	0.0346447	+	0.999400i	$0.488970\pi$
$570$	−1.19136	−0.0499004
$571$	11.6901	0.489214	0.244607	−	0.969622i	$-0.421341\pi$
$571$	11.6901	0.489214	0.244607	+	0.969622i	$0.421341\pi$
$572$	−113.481	−4.74488
$573$	9.28239	0.387778
$574$	5.79514	0.241884
$575$	−6.15727	−0.256776
$576$	−22.4125	−0.933856
$577$	13.3939	0.557596	0.278798	−	0.960350i	$-0.410064\pi$
$577$	13.3939	0.557596	0.278798	+	0.960350i	$0.410064\pi$
$578$	−37.7135	−1.56867
$579$	−15.9218	−0.661686
$580$	54.1652	2.24909
$581$	−1.83720	−0.0762199
$582$	−67.5919	−2.80177
$583$	13.1843	0.546040
$584$	−153.297	−6.34347
$585$	−1.62794	−0.0673072
$586$	74.9951	3.09802
$587$	25.5544	1.05474	0.527371	−	0.849635i	$-0.323178\pi$
$587$	25.5544	1.05474	0.527371	+	0.849635i	$0.323178\pi$
$588$	62.8951	2.59375
$589$	−1.55374	−0.0640206
$590$	−18.8392	−0.775596
$591$	−26.2476	−1.07968
$592$	144.511	5.93938
$593$	30.9129	1.26944	0.634720	−	0.772743i	$-0.281116\pi$
$593$	30.9129	1.26944	0.634720	+	0.772743i	$0.281116\pi$
$594$	−95.7768	−3.92977
$595$	−1.59775	−0.0655012
$596$	−57.7914	−2.36723
$597$	−20.2510	−0.828818
$598$	−54.4360	−2.22605
$599$	−4.67960	−0.191203	−0.0956016	−	0.995420i	$-0.530477\pi$
$599$	−4.67960	−0.191203	−0.0956016	+	0.995420i	$0.530477\pi$
$600$	16.5530	0.675773
$601$	22.9334	0.935472	0.467736	−	0.883868i	$-0.345070\pi$
$601$	22.9334	0.935472	0.467736	+	0.883868i	$0.345070\pi$
$602$	1.01875	0.0415210
$603$	0.903146	0.0367789
$604$	62.7321	2.55253
$605$	−27.4814	−1.11728
$606$	−56.5637	−2.29774
$607$	−37.2908	−1.51359	−0.756794	−	0.653654i	$-0.773235\pi$
$607$	−37.2908	−1.51359	−0.756794	+	0.653654i	$0.773235\pi$
$608$	−7.69571	−0.312102
$609$	−4.28308	−0.173559
$610$	−32.7357	−1.32543
$611$	36.6453	1.48251
$612$	16.3512	0.660960
$613$	10.1551	0.410161	0.205081	−	0.978745i	$-0.434254\pi$
$613$	10.1551	0.410161	0.205081	+	0.978745i	$0.434254\pi$
$614$	3.44624	0.139079
$615$	11.3409	0.457311
$616$	18.8280	0.758600
$617$	−2.04681	−0.0824014	−0.0412007	−	0.999151i	$-0.513118\pi$
$617$	−2.04681	−0.0824014	−0.0412007	+	0.999151i	$0.513118\pi$
$618$	48.3836	1.94627
$619$	14.1855	0.570161	0.285081	−	0.958504i	$-0.407980\pi$
$619$	14.1855	0.570161	0.285081	+	0.958504i	$0.407980\pi$
$620$	33.0511	1.32737
$621$	−34.1122	−1.36888
$622$	−24.1450	−0.968127
$623$	0.261749	0.0104867
$624$	88.6470	3.54872
$625$	1.00000	0.0400000
$626$	11.9026	0.475723
$627$	−2.65188	−0.105906
$628$	−24.8479	−0.991540
$629$	−45.0639	−1.79681
$630$	0.413517	0.0164749
$631$	32.0064	1.27416	0.637078	−	0.770799i	$-0.280143\pi$
$631$	32.0064	1.27416	0.637078	+	0.770799i	$0.280143\pi$
$632$	110.554	4.39760
$633$	26.9064	1.06943
$634$	46.0657	1.82950
$635$	−5.73485	−0.227581
$636$	−19.3273	−0.766376
$637$	21.9414	0.869350
$638$	162.385	6.42888
$639$	−3.71889	−0.147117
$640$	64.9393	2.56695
$641$	−18.6854	−0.738029	−0.369014	−	0.929424i	$-0.620305\pi$
$641$	−18.6854	−0.738029	−0.369014	+	0.929424i	$0.620305\pi$
$642$	−55.4954	−2.19023
$643$	40.2844	1.58866	0.794332	−	0.607484i	$-0.207821\pi$
$643$	40.2844	1.58866	0.794332	+	0.607484i	$0.207821\pi$
$644$	10.2666	0.404561
$645$	1.99366	0.0785004
$646$	4.17446	0.164242
$647$	8.28938	0.325889	0.162945	−	0.986635i	$-0.447901\pi$
$647$	8.28938	0.325889	0.162945	+	0.986635i	$0.447901\pi$
$648$	75.5466	2.96775
$649$	−41.9347	−1.64608
$650$	8.84093	0.346770
$651$	−2.61350	−0.102431
$652$	83.3452	3.26405
$653$	5.11815	0.200289	0.100144	−	0.994973i	$-0.468070\pi$
$653$	5.11815	0.200289	0.100144	+	0.994973i	$0.468070\pi$
$654$	37.4921	1.46606
$655$	15.3244	0.598774
$656$	127.433	4.97541
$657$	−7.49438	−0.292384
$658$	−9.30834	−0.362877
$659$	−34.9816	−1.36269	−0.681345	−	0.731962i	$-0.738605\pi$
$659$	−34.9816	−1.36269	−0.681345	+	0.731962i	$0.738605\pi$
$660$	56.4108	2.19579
$661$	33.5842	1.30628	0.653138	−	0.757239i	$-0.273452\pi$
$661$	33.5842	1.30628	0.653138	+	0.757239i	$0.273452\pi$
$662$	−25.1799	−0.978646
$663$	−27.6434	−1.07358
$664$	−66.6936	−2.58821
$665$	0.0783844	0.00303962
$666$	11.6631	0.451936
$667$	57.8356	2.23940
$668$	−66.6995	−2.58068
$669$	23.3950	0.904502
$670$	−4.90474	−0.189487
$671$	−72.8674	−2.81301
$672$	−12.9447	−0.499354
$673$	−27.9928	−1.07904	−0.539521	−	0.841972i	$-0.681395\pi$
$673$	−27.9928	−1.07904	−0.539521	+	0.841972i	$0.681395\pi$
$674$	−98.1068	−3.77893
$675$	5.54016	0.213241
$676$	−16.9307	−0.651179
$677$	40.5011	1.55658	0.778291	−	0.627904i	$-0.216087\pi$
$677$	40.5011	1.55658	0.778291	+	0.627904i	$0.216087\pi$
$678$	90.1128	3.46076
$679$	4.44716	0.170666
$680$	−58.0010	−2.22424
$681$	−4.26470	−0.163424
$682$	99.0858	3.79419
$683$	41.0054	1.56903	0.784513	−	0.620112i	$-0.212913\pi$
$683$	41.0054	1.56903	0.784513	+	0.620112i	$0.212913\pi$
$684$	−0.802182	−0.0306722
$685$	−3.40774	−0.130203
$686$	−11.2141	−0.428157
$687$	−9.82371	−0.374798
$688$	22.4018	0.854062
$689$	−6.74245	−0.256867
$690$	27.0598	1.03015
$691$	−32.0172	−1.21799	−0.608996	−	0.793173i	$-0.708427\pi$
$691$	−32.0172	−1.21799	−0.608996	+	0.793173i	$0.708427\pi$
$692$	119.117	4.52814
$693$	0.920461	0.0349654
$694$	6.93872	0.263390
$695$	9.67783	0.367101
$696$	−155.483	−5.89358
$697$	−39.7382	−1.50519
$698$	66.5284	2.51814
$699$	36.2691	1.37182
$700$	−1.66740	−0.0630216
$701$	−31.9330	−1.20609	−0.603047	−	0.797706i	$-0.706047\pi$
$701$	−31.9330	−1.20609	−0.603047	+	0.797706i	$0.706047\pi$
$702$	48.9801	1.84863
$703$	2.21081	0.0833822
$704$	270.933	10.2112
$705$	−18.2162	−0.686062
$706$	30.2531	1.13859
$707$	3.72157	0.139964
$708$	61.4732	2.31030
$709$	36.7431	1.37992	0.689958	−	0.723850i	$-0.257629\pi$
$709$	36.7431	1.37992	0.689958	+	0.723850i	$0.257629\pi$
$710$	20.1963	0.757952
$711$	5.40477	0.202695
$712$	9.50194	0.356100
$713$	35.2908	1.32165
$714$	7.02173	0.262782
$715$	19.6793	0.735965
$716$	−50.1645	−1.87473
$717$	9.30519	0.347509
$718$	77.5829	2.89537
$719$	16.3251	0.608822	0.304411	−	0.952541i	$-0.401540\pi$
$719$	16.3251	0.608822	0.304411	+	0.952541i	$0.401540\pi$
$720$	9.09307	0.338879
$721$	−3.18337	−0.118555
$722$	52.7453	1.96298
$723$	−12.1330	−0.451231
$724$	−3.00863	−0.111815
$725$	−9.39306	−0.348849
$726$	120.775	4.48236
$727$	−15.4980	−0.574788	−0.287394	−	0.957812i	$-0.592789\pi$
$727$	−15.4980	−0.574788	−0.287394	+	0.957812i	$0.592789\pi$
$728$	−9.62859	−0.356859
$729$	29.9033	1.10753
$730$	40.6999	1.50637
$731$	−6.98571	−0.258376
$732$	106.818	3.94811
$733$	8.30321	0.306686	0.153343	−	0.988173i	$-0.450996\pi$
$733$	8.30321	0.306686	0.153343	+	0.988173i	$0.450996\pi$
$734$	15.7130	0.579979
$735$	−10.9069	−0.402309
$736$	174.796	6.44308
$737$	−10.9176	−0.402156
$738$	10.2847	0.378587
$739$	−37.6402	−1.38462	−0.692309	−	0.721601i	$-0.743407\pi$
$739$	−37.6402	−1.38462	−0.692309	+	0.721601i	$0.743407\pi$
$740$	−47.0283	−1.72880
$741$	1.35617	0.0498200
$742$	1.71266	0.0628738
$743$	30.8158	1.13052	0.565261	−	0.824912i	$-0.308775\pi$
$743$	30.8158	1.13052	0.565261	+	0.824912i	$0.308775\pi$
$744$	−94.8745	−3.47827
$745$	10.0219	0.367174
$746$	15.9866	0.585312
$747$	−3.26052	−0.119296
$748$	−197.661	−7.22720
$749$	3.65128	0.133415
$750$	−4.39478	−0.160475
$751$	32.1420	1.17288	0.586439	−	0.809993i	$-0.300529\pi$
$751$	32.1420	1.17288	0.586439	+	0.809993i	$0.300529\pi$
$752$	−204.687	−7.46416
$753$	22.4086	0.816617
$754$	−83.0433	−3.02426
$755$	−10.8787	−0.395916
$756$	−9.23763	−0.335969
$757$	−21.4648	−0.780153	−0.390076	−	0.920783i	$-0.627551\pi$
$757$	−21.4648	−0.780153	−0.390076	+	0.920783i	$0.627551\pi$
$758$	−35.7477	−1.29842
$759$	60.2334	2.18633
$760$	2.84549	0.103217
$761$	10.4326	0.378183	0.189091	−	0.981960i	$-0.439446\pi$
$761$	10.4326	0.378183	0.189091	+	0.981960i	$0.439446\pi$
$762$	25.2034	0.913022
$763$	−2.46677	−0.0893031
$764$	−33.9430	−1.22801
$765$	−2.83555	−0.102520
$766$	−16.6829	−0.602777
$767$	21.4454	0.774347
$768$	−147.644	−5.32765
$769$	41.7251	1.50465	0.752323	−	0.658794i	$-0.228933\pi$
$769$	41.7251	1.50465	0.752323	+	0.658794i	$0.228933\pi$
$770$	−4.99878	−0.180143
$771$	41.2730	1.48641
$772$	58.2212	2.09543
$773$	−38.0631	−1.36904	−0.684518	−	0.728996i	$-0.739987\pi$
$773$	−38.0631	−1.36904	−0.684518	+	0.728996i	$0.739987\pi$
$774$	1.80799	0.0649869
$775$	−5.73156	−0.205884
$776$	161.440	5.79535
$777$	3.71873	0.133409
$778$	−5.63351	−0.201971
$779$	1.94953	0.0698492
$780$	−28.8484	−1.03294
$781$	44.9555	1.60864
$782$	−94.8165	−3.39063
$783$	−52.0390	−1.85972
$784$	−122.556	−4.37701
$785$	4.30900	0.153795
$786$	−67.3473	−2.40220
$787$	24.6254	0.877801	0.438900	−	0.898536i	$-0.355368\pi$
$787$	24.6254	0.877801	0.438900	+	0.898536i	$0.355368\pi$
$788$	95.9799	3.41914
$789$	−6.77557	−0.241217
$790$	−29.3518	−1.04429
$791$	−5.92891	−0.210808
$792$	33.4144	1.18733
$793$	37.2643	1.32329
$794$	45.9470	1.63060
$795$	3.35164	0.118870
$796$	74.0519	2.62470
$797$	−21.1526	−0.749262	−0.374631	−	0.927174i	$-0.622231\pi$
$797$	−21.1526	−0.749262	−0.374631	+	0.927174i	$0.622231\pi$
$798$	−0.344482	−0.0121945
$799$	63.8288	2.25810
$800$	−28.3886	−1.00369
$801$	0.464531	0.0164134
$802$	−47.1538	−1.66506
$803$	90.5954	3.19704
$804$	16.0044	0.564433
$805$	−1.78038	−0.0627503
$806$	−50.6723	−1.78486
$807$	4.56305	0.160627
$808$	135.100	4.75278
$809$	54.0496	1.90028	0.950141	−	0.311821i	$-0.100939\pi$
$809$	54.0496	1.90028	0.950141	+	0.311821i	$0.100939\pi$
$810$	−20.0574	−0.704746
$811$	−20.2890	−0.712442	−0.356221	−	0.934402i	$-0.615935\pi$
$811$	−20.2890	−0.712442	−0.356221	+	0.934402i	$0.615935\pi$
$812$	15.6619	0.549626
$813$	−11.0648	−0.388060
$814$	−140.989	−4.94166
$815$	−14.4533	−0.506277
$816$	154.405	5.40526
$817$	0.342714	0.0119901
$818$	−61.0982	−2.13625
$819$	−0.470722	−0.0164484
$820$	−41.4705	−1.44821
$821$	−14.4921	−0.505777	−0.252889	−	0.967495i	$-0.581381\pi$
$821$	−14.4921	−0.505777	−0.252889	+	0.967495i	$0.581381\pi$
$822$	14.9763	0.522357
$823$	5.62725	0.196153	0.0980767	−	0.995179i	$-0.468731\pi$
$823$	5.62725	0.196153	0.0980767	+	0.995179i	$0.468731\pi$
$824$	−115.562	−4.02579
$825$	−9.78248	−0.340582
$826$	−5.44737	−0.189538
$827$	18.3583	0.638381	0.319190	−	0.947691i	$-0.396589\pi$
$827$	18.3583	0.638381	0.319190	+	0.947691i	$0.396589\pi$
$828$	18.2204	0.633201
$829$	−5.96320	−0.207110	−0.103555	−	0.994624i	$-0.533022\pi$
$829$	−5.96320	−0.207110	−0.103555	+	0.994624i	$0.533022\pi$
$830$	17.7070	0.614618
$831$	32.1392	1.11490
$832$	−138.555	−4.80352
$833$	38.2175	1.32416
$834$	−42.5319	−1.47276
$835$	11.5667	0.400282
$836$	9.69713	0.335382
$837$	−31.7537	−1.09757
$838$	−108.815	−3.75896
$839$	36.8819	1.27330	0.636652	−	0.771151i	$-0.280319\pi$
$839$	36.8819	1.27330	0.636652	+	0.771151i	$0.280319\pi$
$840$	4.78632	0.165144
$841$	59.2295	2.04240
$842$	−95.6753	−3.29719
$843$	16.2593	0.559999
$844$	−98.3888	−3.38668
$845$	2.93603	0.101003
$846$	−16.5197	−0.567959
$847$	−7.94628	−0.273037
$848$	37.6607	1.29327
$849$	−4.58029	−0.157195
$850$	15.3991	0.528185
$851$	−50.2151	−1.72135
$852$	−65.9015	−2.25775
$853$	−32.0455	−1.09722	−0.548609	−	0.836079i	$-0.684842\pi$
$853$	−32.0455	−1.09722	−0.548609	+	0.836079i	$0.684842\pi$
$854$	−9.46556	−0.323905
$855$	0.139110	0.00475747
$856$	132.548	4.53039
$857$	31.7027	1.08294	0.541472	−	0.840719i	$-0.317867\pi$
$857$	31.7027	1.08294	0.541472	+	0.840719i	$0.317867\pi$
$858$	−86.4862	−2.95259
$859$	−13.5299	−0.461633	−0.230816	−	0.972997i	$-0.574140\pi$
$859$	−13.5299	−0.461633	−0.230816	+	0.972997i	$0.574140\pi$
$860$	−7.29023	−0.248595
$861$	3.27925	0.111757
$862$	−73.9538	−2.51888
$863$	4.90621	0.167009	0.0835046	−	0.996507i	$-0.473389\pi$
$863$	4.90621	0.167009	0.0835046	+	0.996507i	$0.473389\pi$
$864$	−157.277	−5.35068
$865$	−20.6566	−0.702347
$866$	19.5358	0.663854
$867$	−21.3406	−0.724766
$868$	9.55678	0.324378
$869$	−65.3352	−2.21634
$870$	41.2804	1.39954
$871$	5.58326	0.189181
$872$	−89.5481	−3.03248
$873$	7.89246	0.267119
$874$	4.65164	0.157344
$875$	0.289151	0.00977510
$876$	−132.806	−4.48710
$877$	−5.39663	−0.182231	−0.0911157	−	0.995840i	$-0.529043\pi$
$877$	−5.39663	−0.182231	−0.0911157	+	0.995840i	$0.529043\pi$
$878$	41.6270	1.40484
$879$	42.4369	1.43136
$880$	−109.921	−3.70544
$881$	−20.3549	−0.685775	−0.342888	−	0.939376i	$-0.611405\pi$
$881$	−20.3549	−0.685775	−0.342888	+	0.939376i	$0.611405\pi$
$882$	−9.89117	−0.333053
$883$	23.6214	0.794924	0.397462	−	0.917619i	$-0.369891\pi$
$883$	23.6214	0.794924	0.397462	+	0.917619i	$0.369891\pi$
$884$	101.084	3.39981
$885$	−10.6604	−0.358344
$886$	9.04665	0.303928
$887$	−9.62177	−0.323067	−0.161534	−	0.986867i	$-0.551644\pi$
$887$	−9.62177	−0.323067	−0.161534	+	0.986867i	$0.551644\pi$
$888$	134.997	4.53019
$889$	−1.65824	−0.0556156
$890$	−2.52274	−0.0845624
$891$	−44.6465	−1.49571
$892$	−85.5485	−2.86438
$893$	−3.13140	−0.104788
$894$	−44.0440	−1.47305
$895$	8.69927	0.290785
$896$	18.7773	0.627305
$897$	−30.8033	−1.02849
$898$	−90.7995	−3.03002
$899$	53.8369	1.79556
$900$	−2.95916	−0.0986387
$901$	−11.7440	−0.391249
$902$	−124.327	−4.13962
$903$	0.576470	0.0191837
$904$	−215.230	−7.15844
$905$	0.521741	0.0173433
$906$	47.8094	1.58836
$907$	5.84942	0.194227	0.0971134	−	0.995273i	$-0.469039\pi$
$907$	5.84942	0.194227	0.0971134	+	0.995273i	$0.469039\pi$
$908$	15.5947	0.517529
$909$	6.60474	0.219066
$910$	2.55637	0.0847427
$911$	−10.4377	−0.345815	−0.172907	−	0.984938i	$-0.555316\pi$
$911$	−10.4377	−0.345815	−0.172907	+	0.984938i	$0.555316\pi$
$912$	−7.57502	−0.250834
$913$	39.4145	1.30443
$914$	3.03229	0.100299
$915$	−18.5239	−0.612380
$916$	35.9224	1.18691
$917$	4.43107	0.146327
$918$	85.3134	2.81576
$919$	31.0621	1.02464	0.512322	−	0.858793i	$-0.328785\pi$
$919$	31.0621	1.02464	0.512322	+	0.858793i	$0.328785\pi$
$920$	−64.6310	−2.13082
$921$	1.95009	0.0642578
$922$	−37.6660	−1.24046
$923$	−22.9902	−0.756731
$924$	16.3113	0.536601
$925$	8.15542	0.268149
$926$	81.7486	2.68642
$927$	−5.64958	−0.185557
$928$	266.656	8.75340
$929$	−12.9142	−0.423701	−0.211851	−	0.977302i	$-0.567949\pi$
$929$	−12.9142	−0.423701	−0.211851	+	0.977302i	$0.567949\pi$
$930$	25.1889	0.825977
$931$	−1.87493	−0.0614482
$932$	−132.625	−4.34428
$933$	−13.6627	−0.447298
$934$	83.8905	2.74498
$935$	34.2774	1.12099
$936$	−17.0880	−0.558540
$937$	−18.4942	−0.604179	−0.302089	−	0.953280i	$-0.597684\pi$
$937$	−18.4942	−0.604179	−0.302089	+	0.953280i	$0.597684\pi$
$938$	−1.41821	−0.0463063
$939$	6.73523	0.219796
$940$	66.6112	2.17262
$941$	−22.9340	−0.747627	−0.373814	−	0.927504i	$-0.621950\pi$
$941$	−22.9340	−0.747627	−0.373814	+	0.927504i	$0.621950\pi$
$942$	−18.9371	−0.617004
$943$	−44.2806	−1.44198
$944$	−119.785	−3.89868
$945$	1.60194	0.0521112
$946$	−21.8558	−0.710593
$947$	33.0026	1.07244	0.536221	−	0.844078i	$-0.319851\pi$
$947$	33.0026	1.07244	0.536221	+	0.844078i	$0.319851\pi$
$948$	95.7765	3.11068
$949$	−46.3303	−1.50395
$950$	−0.755471	−0.0245107
$951$	26.0669	0.845276
$952$	−16.7711	−0.543553
$953$	−29.3998	−0.952353	−0.476177	−	0.879350i	$-0.657978\pi$
$953$	−29.3998	−0.952353	−0.476177	+	0.879350i	$0.657978\pi$
$954$	3.03949	0.0984073
$955$	5.88622	0.190474
$956$	−34.0263	−1.10049
$957$	91.8874	2.97030
$958$	−28.4719	−0.919885
$959$	−0.985353	−0.0318187
$960$	68.8747	2.22292
$961$	1.85078	0.0597024
$962$	72.1015	2.32464
$963$	6.48000	0.208815
$964$	44.3667	1.42896
$965$	−10.0964	−0.325015
$966$	7.82439	0.251746
$967$	61.0227	1.96236	0.981179	−	0.193099i	$-0.0618540\pi$
$967$	61.0227	1.96236	0.981179	+	0.193099i	$0.0618540\pi$
$968$	−288.464	−9.27158
$969$	2.36217	0.0758837
$970$	−42.8618	−1.37621
$971$	20.9261	0.671550	0.335775	−	0.941942i	$-0.391002\pi$
$971$	20.9261	0.671550	0.335775	+	0.941942i	$0.391002\pi$
$972$	−30.3937	−0.974879
$973$	2.79836	0.0897112
$974$	−39.3589	−1.26114
$975$	5.00274	0.160216
$976$	−208.144	−6.66252
$977$	2.06446	0.0660480	0.0330240	−	0.999455i	$-0.489486\pi$
$977$	2.06446	0.0660480	0.0330240	+	0.999455i	$0.489486\pi$
$978$	63.5191	2.03112
$979$	−5.61545	−0.179471
$980$	39.8835	1.27403
$981$	−4.37783	−0.139773
$982$	7.48839	0.238964
$983$	−3.85796	−0.123050	−0.0615249	−	0.998106i	$-0.519596\pi$
$983$	−3.85796	−0.123050	−0.0615249	+	0.998106i	$0.519596\pi$
$984$	119.043	3.79494
$985$	−16.6443	−0.530333
$986$	−144.645	−4.60643
$987$	−5.26724	−0.167658
$988$	−4.95910	−0.157770
$989$	−7.78424	−0.247524
$990$	−8.87143	−0.281952
$991$	52.9697	1.68264	0.841319	−	0.540539i	$-0.181780\pi$
$991$	52.9697	1.68264	0.841319	+	0.540539i	$0.181780\pi$
$992$	162.711	5.16608
$993$	−14.2484	−0.452159
$994$	5.83978	0.185226
$995$	−12.8417	−0.407109
$996$	−57.7788	−1.83079
$997$	−18.7873	−0.595000	−0.297500	−	0.954722i	$-0.596153\pi$
$997$	−18.7873	−0.595000	−0.297500	+	0.954722i	$0.596153\pi$
$998$	−62.9003	−1.99107
$999$	45.1823	1.42950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.g.1.3	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.g.1.3	✓	113	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78685 q^{2} -1.57697 q^{3} +5.76652 q^{4} -1.00000 q^{5} +4.39478 q^{6} -0.289151 q^{7} -10.4967 q^{8} -0.513163 q^{9} +O(q^{10})\)	\(q-2.78685 q^{2} -1.57697 q^{3} +5.76652 q^{4} -1.00000 q^{5} +4.39478 q^{6} -0.289151 q^{7} -10.4967 q^{8} -0.513163 q^{9} +2.78685 q^{10} +6.20334 q^{11} -9.09363 q^{12} -3.17238 q^{13} +0.805821 q^{14} +1.57697 q^{15} +17.7197 q^{16} -5.52564 q^{17} +1.43011 q^{18} +0.271084 q^{19} -5.76652 q^{20} +0.455983 q^{21} -17.2877 q^{22} -6.15727 q^{23} +16.5530 q^{24} +1.00000 q^{25} +8.84093 q^{26} +5.54016 q^{27} -1.66740 q^{28} -9.39306 q^{29} -4.39478 q^{30} -5.73156 q^{31} -28.3886 q^{32} -9.78248 q^{33} +15.3991 q^{34} +0.289151 q^{35} -2.95916 q^{36} +8.15542 q^{37} -0.755471 q^{38} +5.00274 q^{39} +10.4967 q^{40} +7.19160 q^{41} -1.27076 q^{42} +1.26424 q^{43} +35.7716 q^{44} +0.513163 q^{45} +17.1594 q^{46} -11.5514 q^{47} -27.9434 q^{48} -6.91639 q^{49} -2.78685 q^{50} +8.71377 q^{51} -18.2936 q^{52} +2.12536 q^{53} -15.4396 q^{54} -6.20334 q^{55} +3.03514 q^{56} -0.427492 q^{57} +26.1770 q^{58} -6.76003 q^{59} +9.09363 q^{60} -11.7465 q^{61} +15.9730 q^{62} +0.148382 q^{63} +43.6753 q^{64} +3.17238 q^{65} +27.2623 q^{66} -1.75996 q^{67} -31.8637 q^{68} +9.70984 q^{69} -0.805821 q^{70} +7.24700 q^{71} +5.38651 q^{72} +14.6043 q^{73} -22.7279 q^{74} -1.57697 q^{75} +1.56321 q^{76} -1.79370 q^{77} -13.9419 q^{78} -10.5323 q^{79} -17.7197 q^{80} -7.19718 q^{81} -20.0419 q^{82} +6.35377 q^{83} +2.62943 q^{84} +5.52564 q^{85} -3.52323 q^{86} +14.8126 q^{87} -65.1146 q^{88} -0.905231 q^{89} -1.43011 q^{90} +0.917297 q^{91} -35.5060 q^{92} +9.03850 q^{93} +32.1919 q^{94} -0.271084 q^{95} +44.7680 q^{96} -15.3800 q^{97} +19.2749 q^{98} -3.18332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

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