LMFDB - Embedded newform 6005.2.a.f.1.15

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:	$111$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-2.23901 q^{2} +3.10819 q^{3} +3.01316 q^{4} +1.00000 q^{5} -6.95927 q^{6} +3.97064 q^{7} -2.26846 q^{8} +6.66087 q^{9} +O(q^{10})$	\(q-2.23901 q^{2} +3.10819 q^{3} +3.01316 q^{4} +1.00000 q^{5} -6.95927 q^{6} +3.97064 q^{7} -2.26846 q^{8} +6.66087 q^{9} -2.23901 q^{10} -4.60589 q^{11} +9.36547 q^{12} -2.90126 q^{13} -8.89030 q^{14} +3.10819 q^{15} -0.947204 q^{16} -0.996540 q^{17} -14.9137 q^{18} +1.05992 q^{19} +3.01316 q^{20} +12.3415 q^{21} +10.3126 q^{22} +3.82049 q^{23} -7.05082 q^{24} +1.00000 q^{25} +6.49595 q^{26} +11.3787 q^{27} +11.9642 q^{28} -0.973200 q^{29} -6.95927 q^{30} +7.95673 q^{31} +6.65772 q^{32} -14.3160 q^{33} +2.23126 q^{34} +3.97064 q^{35} +20.0702 q^{36} +11.7506 q^{37} -2.37318 q^{38} -9.01769 q^{39} -2.26846 q^{40} +2.05604 q^{41} -27.6328 q^{42} +0.400584 q^{43} -13.8783 q^{44} +6.66087 q^{45} -8.55410 q^{46} -8.34872 q^{47} -2.94410 q^{48} +8.76601 q^{49} -2.23901 q^{50} -3.09744 q^{51} -8.74195 q^{52} -9.27972 q^{53} -25.4770 q^{54} -4.60589 q^{55} -9.00726 q^{56} +3.29445 q^{57} +2.17900 q^{58} -3.46006 q^{59} +9.36547 q^{60} +0.760021 q^{61} -17.8152 q^{62} +26.4480 q^{63} -13.0123 q^{64} -2.90126 q^{65} +32.0537 q^{66} -6.78107 q^{67} -3.00273 q^{68} +11.8748 q^{69} -8.89030 q^{70} +4.94393 q^{71} -15.1099 q^{72} -3.62449 q^{73} -26.3096 q^{74} +3.10819 q^{75} +3.19372 q^{76} -18.2884 q^{77} +20.1907 q^{78} +12.4478 q^{79} -0.947204 q^{80} +15.3846 q^{81} -4.60349 q^{82} +5.06691 q^{83} +37.1870 q^{84} -0.996540 q^{85} -0.896911 q^{86} -3.02489 q^{87} +10.4483 q^{88} +3.85766 q^{89} -14.9137 q^{90} -11.5199 q^{91} +11.5117 q^{92} +24.7311 q^{93} +18.6928 q^{94} +1.05992 q^{95} +20.6935 q^{96} +5.98703 q^{97} -19.6272 q^{98} -30.6793 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) $ 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * 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 $

$2$	−2.23901	−1.58322	−0.791609	−	0.611028i	$-0.790756\pi$
$2$	−2.23901	−1.58322	−0.791609	+	0.611028i	$0.790756\pi$
$3$	3.10819	1.79452	0.897258	−	0.441506i	$-0.145556\pi$
$3$	3.10819	1.79452	0.897258	+	0.441506i	$0.145556\pi$
$4$	3.01316	1.50658
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.95927	−2.84111
$7$	3.97064	1.50076	0.750381	−	0.661005i	$-0.229870\pi$
$7$	3.97064	1.50076	0.750381	+	0.661005i	$0.229870\pi$
$8$	−2.26846	−0.802023
$9$	6.66087	2.22029
$10$	−2.23901	−0.708036
$11$	−4.60589	−1.38873	−0.694364	−	0.719624i	$-0.744314\pi$
$11$	−4.60589	−1.38873	−0.694364	+	0.719624i	$0.744314\pi$
$12$	9.36547	2.70358
$13$	−2.90126	−0.804665	−0.402333	−	0.915494i	$-0.631800\pi$
$13$	−2.90126	−0.804665	−0.402333	+	0.915494i	$0.631800\pi$
$14$	−8.89030	−2.37603
$15$	3.10819	0.802532
$16$	−0.947204	−0.236801
$17$	−0.996540	−0.241696	−0.120848	−	0.992671i	$-0.538561\pi$
$17$	−0.996540	−0.241696	−0.120848	+	0.992671i	$0.538561\pi$
$18$	−14.9137	−3.51520
$19$	1.05992	0.243163	0.121582	−	0.992581i	$-0.461203\pi$
$19$	1.05992	0.243163	0.121582	+	0.992581i	$0.461203\pi$
$20$	3.01316	0.673762
$21$	12.3415	2.69314
$22$	10.3126	2.19866
$23$	3.82049	0.796626	0.398313	−	0.917250i	$-0.369596\pi$
$23$	3.82049	0.796626	0.398313	+	0.917250i	$0.369596\pi$
$24$	−7.05082	−1.43924
$25$	1.00000	0.200000
$26$	6.49595	1.27396
$27$	11.3787	2.18983
$28$	11.9642	2.26102
$29$	−0.973200	−0.180719	−0.0903593	−	0.995909i	$-0.528802\pi$
$29$	−0.973200	−0.180719	−0.0903593	+	0.995909i	$0.528802\pi$
$30$	−6.95927	−1.27058
$31$	7.95673	1.42907	0.714536	−	0.699599i	$-0.246638\pi$
$31$	7.95673	1.42907	0.714536	+	0.699599i	$0.246638\pi$
$32$	6.65772	1.17693
$33$	−14.3160	−2.49210
$34$	2.23126	0.382658
$35$	3.97064	0.671161
$36$	20.0702	3.34504
$37$	11.7506	1.93178	0.965891	−	0.258949i	$-0.0833761\pi$
$37$	11.7506	1.93178	0.965891	+	0.258949i	$0.0833761\pi$
$38$	−2.37318	−0.384980
$39$	−9.01769	−1.44399
$40$	−2.26846	−0.358676
$41$	2.05604	0.321100	0.160550	−	0.987028i	$-0.448673\pi$
$41$	2.05604	0.321100	0.160550	+	0.987028i	$0.448673\pi$
$42$	−27.6328	−4.26383
$43$	0.400584	0.0610885	0.0305443	−	0.999533i	$-0.490276\pi$
$43$	0.400584	0.0610885	0.0305443	+	0.999533i	$0.490276\pi$
$44$	−13.8783	−2.09223
$45$	6.66087	0.992944
$46$	−8.55410	−1.26123
$47$	−8.34872	−1.21779	−0.608893	−	0.793253i	$-0.708386\pi$
$47$	−8.34872	−1.21779	−0.608893	+	0.793253i	$0.708386\pi$
$48$	−2.94410	−0.424944
$49$	8.76601	1.25229
$50$	−2.23901	−0.316644
$51$	−3.09744	−0.433728
$52$	−8.74195	−1.21229
$53$	−9.27972	−1.27467	−0.637334	−	0.770588i	$-0.719963\pi$
$53$	−9.27972	−1.27467	−0.637334	+	0.770588i	$0.719963\pi$
$54$	−25.4770	−3.46698
$55$	−4.60589	−0.621058
$56$	−9.00726	−1.20365
$57$	3.29445	0.436361
$58$	2.17900	0.286117
$59$	−3.46006	−0.450462	−0.225231	−	0.974305i	$-0.572314\pi$
$59$	−3.46006	−0.450462	−0.225231	+	0.974305i	$0.572314\pi$
$60$	9.36547	1.20908
$61$	0.760021	0.0973108	0.0486554	−	0.998816i	$-0.484506\pi$
$61$	0.760021	0.0973108	0.0486554	+	0.998816i	$0.484506\pi$
$62$	−17.8152	−2.26253
$63$	26.4480	3.33213
$64$	−13.0123	−1.62654
$65$	−2.90126	−0.359857
$66$	32.0537	3.94553
$67$	−6.78107	−0.828439	−0.414220	−	0.910177i	$-0.635945\pi$
$67$	−6.78107	−0.828439	−0.414220	+	0.910177i	$0.635945\pi$
$68$	−3.00273	−0.364134
$69$	11.8748	1.42956
$70$	−8.89030	−1.06259
$71$	4.94393	0.586737	0.293369	−	0.955999i	$-0.405224\pi$
$71$	4.94393	0.586737	0.293369	+	0.955999i	$0.405224\pi$
$72$	−15.1099	−1.78072
$73$	−3.62449	−0.424215	−0.212107	−	0.977246i	$-0.568033\pi$
$73$	−3.62449	−0.424215	−0.212107	+	0.977246i	$0.568033\pi$
$74$	−26.3096	−3.05843
$75$	3.10819	0.358903
$76$	3.19372	0.366344
$77$	−18.2884	−2.08415
$78$	20.1907	2.28614
$79$	12.4478	1.40049	0.700245	−	0.713903i	$-0.253074\pi$
$79$	12.4478	1.40049	0.700245	+	0.713903i	$0.253074\pi$
$80$	−0.947204	−0.105901
$81$	15.3846	1.70940
$82$	−4.60349	−0.508371
$83$	5.06691	0.556166	0.278083	−	0.960557i	$-0.410301\pi$
$83$	5.06691	0.556166	0.278083	+	0.960557i	$0.410301\pi$
$84$	37.1870	4.05743
$85$	−0.996540	−0.108090
$86$	−0.896911	−0.0967164
$87$	−3.02489	−0.324303
$88$	10.4483	1.11379
$89$	3.85766	0.408911	0.204456	−	0.978876i	$-0.434458\pi$
$89$	3.85766	0.408911	0.204456	+	0.978876i	$0.434458\pi$
$90$	−14.9137	−1.57205
$91$	−11.5199	−1.20761
$92$	11.5117	1.20018
$93$	24.7311	2.56449
$94$	18.6928	1.92802
$95$	1.05992	0.108746
$96$	20.6935	2.11202
$97$	5.98703	0.607891	0.303945	−	0.952689i	$-0.401696\pi$
$97$	5.98703	0.607891	0.303945	+	0.952689i	$0.401696\pi$
$98$	−19.6272	−1.98264
$99$	−30.6793	−3.08338
$100$	3.01316	0.301316
$101$	13.7933	1.37248	0.686240	−	0.727375i	$-0.259260\pi$
$101$	13.7933	1.37248	0.686240	+	0.727375i	$0.259260\pi$
$102$	6.93519	0.686686
$103$	10.8530	1.06938	0.534690	−	0.845048i	$-0.320428\pi$
$103$	10.8530	1.06938	0.534690	+	0.845048i	$0.320428\pi$
$104$	6.58141	0.645360
$105$	12.3415	1.20441
$106$	20.7774	2.01808
$107$	14.9961	1.44973	0.724863	−	0.688893i	$-0.241903\pi$
$107$	14.9961	1.44973	0.724863	+	0.688893i	$0.241903\pi$
$108$	34.2858	3.29915
$109$	4.34126	0.415817	0.207908	−	0.978148i	$-0.433334\pi$
$109$	4.34126	0.415817	0.207908	+	0.978148i	$0.433334\pi$
$110$	10.3126	0.983271
$111$	36.5231	3.46662
$112$	−3.76101	−0.355382
$113$	−6.51393	−0.612779	−0.306390	−	0.951906i	$-0.599121\pi$
$113$	−6.51393	−0.612779	−0.306390	+	0.951906i	$0.599121\pi$
$114$	−7.37630	−0.690854
$115$	3.82049	0.356262
$116$	−2.93240	−0.272267
$117$	−19.3249	−1.78659
$118$	7.74711	0.713179
$119$	−3.95690	−0.362729
$120$	−7.05082	−0.643649
$121$	10.2142	0.928568
$122$	−1.70169	−0.154064
$123$	6.39058	0.576219
$124$	23.9749	2.15301
$125$	1.00000	0.0894427
$126$	−59.2172	−5.27548
$127$	−11.6953	−1.03779	−0.518895	−	0.854838i	$-0.673657\pi$
$127$	−11.6953	−1.03779	−0.518895	+	0.854838i	$0.673657\pi$
$128$	15.8192	1.39823
$129$	1.24509	0.109624
$130$	6.49595	0.569732
$131$	9.66167	0.844144	0.422072	−	0.906562i	$-0.361303\pi$
$131$	9.66167	0.844144	0.422072	+	0.906562i	$0.361303\pi$
$132$	−43.1364	−3.75454
$133$	4.20858	0.364930
$134$	15.1829	1.31160
$135$	11.3787	0.979323
$136$	2.26061	0.193846
$137$	9.88886	0.844862	0.422431	−	0.906395i	$-0.361177\pi$
$137$	9.88886	0.844862	0.422431	+	0.906395i	$0.361177\pi$
$138$	−26.5878	−2.26330
$139$	−4.78660	−0.405994	−0.202997	−	0.979179i	$-0.565068\pi$
$139$	−4.78660	−0.405994	−0.202997	+	0.979179i	$0.565068\pi$
$140$	11.9642	1.01116
$141$	−25.9494	−2.18534
$142$	−11.0695	−0.928932
$143$	13.3629	1.11746
$144$	−6.30921	−0.525767
$145$	−0.973200	−0.0808198
$146$	8.11527	0.671624
$147$	27.2465	2.24725
$148$	35.4063	2.91038
$149$	2.18034	0.178621	0.0893103	−	0.996004i	$-0.471534\pi$
$149$	2.18034	0.178621	0.0893103	+	0.996004i	$0.471534\pi$
$150$	−6.95927	−0.568222
$151$	−8.66623	−0.705248	−0.352624	−	0.935765i	$-0.614711\pi$
$151$	−8.66623	−0.705248	−0.352624	+	0.935765i	$0.614711\pi$
$152$	−2.40440	−0.195023
$153$	−6.63782	−0.536636
$154$	40.9478	3.29967
$155$	7.95673	0.639100
$156$	−27.1717	−2.17548
$157$	−9.89605	−0.789791	−0.394895	−	0.918726i	$-0.629219\pi$
$157$	−9.89605	−0.789791	−0.394895	+	0.918726i	$0.629219\pi$
$158$	−27.8708	−2.21728
$159$	−28.8432	−2.28741
$160$	6.65772	0.526339
$161$	15.1698	1.19555
$162$	−34.4462	−2.70635
$163$	21.2919	1.66771	0.833854	−	0.551985i	$-0.186129\pi$
$163$	21.2919	1.66771	0.833854	+	0.551985i	$0.186129\pi$
$164$	6.19518	0.483762
$165$	−14.3160	−1.11450
$166$	−11.3449	−0.880531
$167$	−6.96417	−0.538904	−0.269452	−	0.963014i	$-0.586843\pi$
$167$	−6.96417	−0.538904	−0.269452	+	0.963014i	$0.586843\pi$
$168$	−27.9963	−2.15996
$169$	−4.58268	−0.352514
$170$	2.23126	0.171130
$171$	7.06002	0.539893
$172$	1.20702	0.0920346
$173$	0.0663312	0.00504307	0.00252154	−	0.999997i	$-0.499197\pi$
$173$	0.0663312	0.00504307	0.00252154	+	0.999997i	$0.499197\pi$
$174$	6.77276	0.513442
$175$	3.97064	0.300152
$176$	4.36272	0.328853
$177$	−10.7546	−0.808362
$178$	−8.63733	−0.647395
$179$	−6.84944	−0.511952	−0.255976	−	0.966683i	$-0.582397\pi$
$179$	−6.84944	−0.511952	−0.255976	+	0.966683i	$0.582397\pi$
$180$	20.0702	1.49595
$181$	18.7254	1.39185	0.695923	−	0.718116i	$-0.254995\pi$
$181$	18.7254	1.39185	0.695923	+	0.718116i	$0.254995\pi$
$182$	25.7931	1.91191
$183$	2.36229	0.174626
$184$	−8.66663	−0.638912
$185$	11.7506	0.863919
$186$	−55.3731	−4.06015
$187$	4.58995	0.335651
$188$	−25.1560	−1.83469
$189$	45.1808	3.28642
$190$	−2.37318	−0.172168
$191$	−15.4568	−1.11841	−0.559207	−	0.829028i	$-0.688894\pi$
$191$	−15.4568	−1.11841	−0.559207	+	0.829028i	$0.688894\pi$
$192$	−40.4447	−2.91885
$193$	−21.2218	−1.52758	−0.763789	−	0.645466i	$-0.776663\pi$
$193$	−21.2218	−1.52758	−0.763789	+	0.645466i	$0.776663\pi$
$194$	−13.4050	−0.962423
$195$	−9.01769	−0.645770
$196$	26.4134	1.88667
$197$	−7.13875	−0.508615	−0.254307	−	0.967123i	$-0.581847\pi$
$197$	−7.13875	−0.508615	−0.254307	+	0.967123i	$0.581847\pi$
$198$	68.6911	4.88166
$199$	9.59887	0.680446	0.340223	−	0.940345i	$-0.389497\pi$
$199$	9.59887	0.680446	0.340223	+	0.940345i	$0.389497\pi$
$200$	−2.26846	−0.160405
$201$	−21.0769	−1.48665
$202$	−30.8832	−2.17293
$203$	−3.86423	−0.271216
$204$	−9.33307	−0.653445
$205$	2.05604	0.143600
$206$	−24.3000	−1.69306
$207$	25.4478	1.76874
$208$	2.74809	0.190546
$209$	−4.88190	−0.337688
$210$	−27.6328	−1.90684
$211$	−15.4877	−1.06622	−0.533108	−	0.846047i	$-0.678976\pi$
$211$	−15.4877	−1.06622	−0.533108	+	0.846047i	$0.678976\pi$
$212$	−27.9612	−1.92039
$213$	15.3667	1.05291
$214$	−33.5763	−2.29523
$215$	0.400584	0.0273196
$216$	−25.8122	−1.75630
$217$	31.5934	2.14470
$218$	−9.72010	−0.658328
$219$	−11.2656	−0.761260
$220$	−13.8783	−0.935673
$221$	2.89122	0.194485
$222$	−81.7754	−5.48841
$223$	17.3631	1.16272	0.581358	−	0.813648i	$-0.302522\pi$
$223$	17.3631	1.16272	0.581358	+	0.813648i	$0.302522\pi$
$224$	26.4355	1.76629
$225$	6.66087	0.444058
$226$	14.5847	0.970163
$227$	−18.0129	−1.19556	−0.597780	−	0.801660i	$-0.703950\pi$
$227$	−18.0129	−1.19556	−0.597780	+	0.801660i	$0.703950\pi$
$228$	9.92669	0.657411
$229$	25.4345	1.68076	0.840380	−	0.541997i	$-0.182332\pi$
$229$	25.4345	1.68076	0.840380	+	0.541997i	$0.182332\pi$
$230$	−8.55410	−0.564040
$231$	−56.8438	−3.74005
$232$	2.20767	0.144940
$233$	−1.32180	−0.0865941	−0.0432970	−	0.999062i	$-0.513786\pi$
$233$	−1.32180	−0.0865941	−0.0432970	+	0.999062i	$0.513786\pi$
$234$	43.2687	2.82856
$235$	−8.34872	−0.544610
$236$	−10.4257	−0.678656
$237$	38.6903	2.51320
$238$	8.85954	0.574279
$239$	−2.27748	−0.147318	−0.0736591	−	0.997283i	$-0.523468\pi$
$239$	−2.27748	−0.147318	−0.0736591	+	0.997283i	$0.523468\pi$
$240$	−2.94410	−0.190041
$241$	−24.5088	−1.57875	−0.789375	−	0.613912i	$-0.789595\pi$
$241$	−24.5088	−1.57875	−0.789375	+	0.613912i	$0.789595\pi$
$242$	−22.8698	−1.47012
$243$	13.6822	0.877714
$244$	2.29006	0.146606
$245$	8.76601	0.560040
$246$	−14.3086	−0.912280
$247$	−3.07512	−0.195665
$248$	−18.0496	−1.14615
$249$	15.7489	0.998049
$250$	−2.23901	−0.141607
$251$	6.16627	0.389212	0.194606	−	0.980882i	$-0.437657\pi$
$251$	6.16627	0.389212	0.194606	+	0.980882i	$0.437657\pi$
$252$	79.6918	5.02011
$253$	−17.5967	−1.10630
$254$	26.1859	1.64305
$255$	−3.09744	−0.193969
$256$	−9.39466	−0.587166
$257$	19.3791	1.20884	0.604418	−	0.796668i	$-0.293406\pi$
$257$	19.3791	1.20884	0.604418	+	0.796668i	$0.293406\pi$
$258$	−2.78777	−0.173559
$259$	46.6573	2.89915
$260$	−8.74195	−0.542153
$261$	−6.48236	−0.401248
$262$	−21.6326	−1.33646
$263$	−11.2902	−0.696183	−0.348092	−	0.937461i	$-0.613170\pi$
$263$	−11.2902	−0.696183	−0.348092	+	0.937461i	$0.613170\pi$
$264$	32.4753	1.99872
$265$	−9.27972	−0.570048
$266$	−9.42305	−0.577764
$267$	11.9904	0.733798
$268$	−20.4324	−1.24811
$269$	25.6968	1.56676	0.783380	−	0.621543i	$-0.213494\pi$
$269$	25.6968	1.56676	0.783380	+	0.621543i	$0.213494\pi$
$270$	−25.4770	−1.55048
$271$	5.43462	0.330129	0.165065	−	0.986283i	$-0.447217\pi$
$271$	5.43462	0.330129	0.165065	+	0.986283i	$0.447217\pi$
$272$	0.943927	0.0572340
$273$	−35.8060	−2.16708
$274$	−22.1412	−1.33760
$275$	−4.60589	−0.277746
$276$	35.7807	2.15374
$277$	18.0307	1.08336	0.541679	−	0.840586i	$-0.317789\pi$
$277$	18.0307	1.08336	0.541679	+	0.840586i	$0.317789\pi$
$278$	10.7172	0.642777
$279$	52.9988	3.17295
$280$	−9.00726	−0.538287
$281$	−6.37692	−0.380415	−0.190207	−	0.981744i	$-0.560916\pi$
$281$	−6.37692	−0.380415	−0.190207	+	0.981744i	$0.560916\pi$
$282$	58.1010	3.45986
$283$	19.2645	1.14515	0.572577	−	0.819851i	$-0.305944\pi$
$283$	19.2645	1.14515	0.572577	+	0.819851i	$0.305944\pi$
$284$	14.8968	0.883965
$285$	3.29445	0.195146
$286$	−29.9196	−1.76919
$287$	8.16381	0.481895
$288$	44.3462	2.61313
$289$	−16.0069	−0.941583
$290$	2.17900	0.127955
$291$	18.6088	1.09087
$292$	−10.9212	−0.639113
$293$	−22.0317	−1.28711	−0.643554	−	0.765401i	$-0.722541\pi$
$293$	−22.0317	−1.28711	−0.643554	+	0.765401i	$0.722541\pi$
$294$	−61.0051	−3.55789
$295$	−3.46006	−0.201453
$296$	−26.6557	−1.54933
$297$	−52.4091	−3.04108
$298$	−4.88180	−0.282795
$299$	−11.0842	−0.641018
$300$	9.36547	0.540716
$301$	1.59058	0.0916793
$302$	19.4038	1.11656
$303$	42.8721	2.46294
$304$	−1.00396	−0.0575813
$305$	0.760021	0.0435187
$306$	14.8621	0.849612
$307$	−18.0427	−1.02975	−0.514875	−	0.857265i	$-0.672162\pi$
$307$	−18.0427	−1.02975	−0.514875	+	0.857265i	$0.672162\pi$
$308$	−55.1057	−3.13994
$309$	33.7333	1.91902
$310$	−17.8152	−1.01183
$311$	−22.7309	−1.28895	−0.644475	−	0.764626i	$-0.722924\pi$
$311$	−22.7309	−1.28895	−0.644475	+	0.764626i	$0.722924\pi$
$312$	20.4563	1.15811
$313$	24.2134	1.36862	0.684310	−	0.729191i	$-0.260104\pi$
$313$	24.2134	1.36862	0.684310	+	0.729191i	$0.260104\pi$
$314$	22.1573	1.25041
$315$	26.4480	1.49017
$316$	37.5072	2.10995
$317$	4.77699	0.268302	0.134151	−	0.990961i	$-0.457169\pi$
$317$	4.77699	0.268302	0.134151	+	0.990961i	$0.457169\pi$
$318$	64.5801	3.62147
$319$	4.48245	0.250969
$320$	−13.0123	−0.727409
$321$	46.6107	2.60156
$322$	−33.9653	−1.89281
$323$	−1.05626	−0.0587717
$324$	46.3562	2.57534
$325$	−2.90126	−0.160933
$326$	−47.6727	−2.64035
$327$	13.4935	0.746190
$328$	−4.66406	−0.257529
$329$	−33.1498	−1.82761
$330$	32.0537	1.76450
$331$	5.22916	0.287421	0.143710	−	0.989620i	$-0.454097\pi$
$331$	5.22916	0.287421	0.143710	+	0.989620i	$0.454097\pi$
$332$	15.2674	0.837907
$333$	78.2690	4.28912
$334$	15.5928	0.853202
$335$	−6.78107	−0.370489
$336$	−11.6900	−0.637739
$337$	−22.1085	−1.20433	−0.602163	−	0.798373i	$-0.705694\pi$
$337$	−22.1085	−1.20433	−0.602163	+	0.798373i	$0.705694\pi$
$338$	10.2606	0.558106
$339$	−20.2466	−1.09964
$340$	−3.00273	−0.162846
$341$	−36.6479	−1.98459
$342$	−15.8074	−0.854768
$343$	7.01221	0.378624
$344$	−0.908710	−0.0489944
$345$	11.8748	0.639318
$346$	−0.148516	−0.00798428
$347$	−4.18850	−0.224850	−0.112425	−	0.993660i	$-0.535862\pi$
$347$	−4.18850	−0.224850	−0.112425	+	0.993660i	$0.535862\pi$
$348$	−9.11448	−0.488587
$349$	28.3555	1.51784	0.758918	−	0.651186i	$-0.225728\pi$
$349$	28.3555	1.51784	0.758918	+	0.651186i	$0.225728\pi$
$350$	−8.89030	−0.475207
$351$	−33.0126	−1.76208
$352$	−30.6648	−1.63444
$353$	−32.1718	−1.71233	−0.856167	−	0.516699i	$-0.827160\pi$
$353$	−32.1718	−1.71233	−0.856167	+	0.516699i	$0.827160\pi$
$354$	24.0795	1.27981
$355$	4.94393	0.262397
$356$	11.6237	0.616056
$357$	−12.2988	−0.650923
$358$	15.3360	0.810531
$359$	−5.90949	−0.311891	−0.155945	−	0.987766i	$-0.549842\pi$
$359$	−5.90949	−0.311891	−0.155945	+	0.987766i	$0.549842\pi$
$360$	−15.1099	−0.796364
$361$	−17.8766	−0.940872
$362$	−41.9263	−2.20360
$363$	31.7479	1.66633
$364$	−34.7112	−1.81936
$365$	−3.62449	−0.189715
$366$	−5.28919	−0.276471
$367$	−11.0919	−0.578992	−0.289496	−	0.957179i	$-0.593488\pi$
$367$	−11.0919	−0.578992	−0.289496	+	0.957179i	$0.593488\pi$
$368$	−3.61878	−0.188642
$369$	13.6950	0.712935
$370$	−26.3096	−1.36777
$371$	−36.8465	−1.91297
$372$	74.5186	3.86361
$373$	−27.6642	−1.43240	−0.716198	−	0.697897i	$-0.754119\pi$
$373$	−27.6642	−1.43240	−0.716198	+	0.697897i	$0.754119\pi$
$374$	−10.2769	−0.531408
$375$	3.10819	0.160506
$376$	18.9388	0.976692
$377$	2.82351	0.145418
$378$	−101.160	−5.20311
$379$	−12.7689	−0.655893	−0.327946	−	0.944696i	$-0.606357\pi$
$379$	−12.7689	−0.655893	−0.327946	+	0.944696i	$0.606357\pi$
$380$	3.19372	0.163834
$381$	−36.3513	−1.86233
$382$	34.6079	1.77069
$383$	−5.99028	−0.306089	−0.153044	−	0.988219i	$-0.548908\pi$
$383$	−5.99028	−0.306089	−0.153044	+	0.988219i	$0.548908\pi$
$384$	49.1690	2.50915
$385$	−18.2884	−0.932061
$386$	47.5157	2.41849
$387$	2.66824	0.135634
$388$	18.0398	0.915834
$389$	−25.1095	−1.27310	−0.636550	−	0.771235i	$-0.719639\pi$
$389$	−25.1095	−1.27310	−0.636550	+	0.771235i	$0.719639\pi$
$390$	20.1907	1.02239
$391$	−3.80727	−0.192542
$392$	−19.8854	−1.00436
$393$	30.0303	1.51483
$394$	15.9837	0.805248
$395$	12.4478	0.626318
$396$	−92.4414	−4.64535
$397$	23.4647	1.17766	0.588831	−	0.808257i	$-0.299589\pi$
$397$	23.4647	1.17766	0.588831	+	0.808257i	$0.299589\pi$
$398$	−21.4919	−1.07729
$399$	13.0811	0.654874
$400$	−0.947204	−0.0473602
$401$	27.0239	1.34951	0.674755	−	0.738042i	$-0.264249\pi$
$401$	27.0239	1.34951	0.674755	+	0.738042i	$0.264249\pi$
$402$	47.1913	2.35369
$403$	−23.0846	−1.14992
$404$	41.5612	2.06775
$405$	15.3846	0.764467
$406$	8.65204	0.429394
$407$	−54.1219	−2.68272
$408$	7.02643	0.347860
$409$	0.389902	0.0192794	0.00963970	−	0.999954i	$-0.496932\pi$
$409$	0.389902	0.0192794	0.00963970	+	0.999954i	$0.496932\pi$
$410$	−4.60349	−0.227350
$411$	30.7365	1.51612
$412$	32.7019	1.61111
$413$	−13.7387	−0.676036
$414$	−56.9777	−2.80030
$415$	5.06691	0.248725
$416$	−19.3158	−0.947035
$417$	−14.8777	−0.728564
$418$	10.9306	0.534633
$419$	11.4592	0.559821	0.279910	−	0.960026i	$-0.409695\pi$
$419$	11.4592	0.559821	0.279910	+	0.960026i	$0.409695\pi$
$420$	37.1870	1.81454
$421$	34.4256	1.67780	0.838900	−	0.544285i	$-0.183199\pi$
$421$	34.4256	1.67780	0.838900	+	0.544285i	$0.183199\pi$
$422$	34.6771	1.68805
$423$	−55.6097	−2.70384
$424$	21.0507	1.02231
$425$	−0.996540	−0.0483393
$426$	−34.4062	−1.66698
$427$	3.01777	0.146040
$428$	45.1855	2.18413
$429$	41.5345	2.00530
$430$	−0.896911	−0.0432529
$431$	−9.74037	−0.469177	−0.234588	−	0.972095i	$-0.575374\pi$
$431$	−9.74037	−0.469177	−0.234588	+	0.972095i	$0.575374\pi$
$432$	−10.7780	−0.518555
$433$	22.0331	1.05884	0.529421	−	0.848359i	$-0.322409\pi$
$433$	22.0331	1.05884	0.529421	+	0.848359i	$0.322409\pi$
$434$	−70.7378	−3.39552
$435$	−3.02489	−0.145033
$436$	13.0809	0.626460
$437$	4.04943	0.193710
$438$	25.2238	1.20524
$439$	−31.5741	−1.50695	−0.753475	−	0.657476i	$-0.771624\pi$
$439$	−31.5741	−1.50695	−0.753475	+	0.657476i	$0.771624\pi$
$440$	10.4483	0.498103
$441$	58.3893	2.78044
$442$	−6.47347	−0.307912
$443$	1.75496	0.0833805	0.0416902	−	0.999131i	$-0.486726\pi$
$443$	1.75496	0.0833805	0.0416902	+	0.999131i	$0.486726\pi$
$444$	110.050	5.22273
$445$	3.85766	0.182871
$446$	−38.8760	−1.84083
$447$	6.77693	0.320538
$448$	−51.6672	−2.44104
$449$	−21.2993	−1.00517	−0.502587	−	0.864527i	$-0.667618\pi$
$449$	−21.2993	−1.00517	−0.502587	+	0.864527i	$0.667618\pi$
$450$	−14.9137	−0.703041
$451$	−9.46991	−0.445921
$452$	−19.6275	−0.923200
$453$	−26.9363	−1.26558
$454$	40.3311	1.89283
$455$	−11.5199	−0.540060
$456$	−7.47334	−0.349971
$457$	−22.0946	−1.03354	−0.516771	−	0.856124i	$-0.672866\pi$
$457$	−22.0946	−1.03354	−0.516771	+	0.856124i	$0.672866\pi$
$458$	−56.9481	−2.66101
$459$	−11.3393	−0.529274
$460$	11.5117	0.536737
$461$	−19.8120	−0.922738	−0.461369	−	0.887208i	$-0.652642\pi$
$461$	−19.8120	−0.922738	−0.461369	+	0.887208i	$0.652642\pi$
$462$	127.274	5.92131
$463$	38.0630	1.76894	0.884468	−	0.466600i	$-0.154521\pi$
$463$	38.0630	1.76894	0.884468	+	0.466600i	$0.154521\pi$
$464$	0.921819	0.0427944
$465$	24.7311	1.14688
$466$	2.95952	0.137097
$467$	−19.0322	−0.880706	−0.440353	−	0.897825i	$-0.645147\pi$
$467$	−19.0322	−0.880706	−0.440353	+	0.897825i	$0.645147\pi$
$468$	−58.2290	−2.69164
$469$	−26.9252	−1.24329
$470$	18.6928	0.862236
$471$	−30.7588	−1.41729
$472$	7.84903	0.361281
$473$	−1.84505	−0.0848354
$474$	−86.6278	−3.97895
$475$	1.05992	0.0486327
$476$	−11.9228	−0.546479
$477$	−61.8110	−2.83013
$478$	5.09930	0.233237
$479$	−8.46208	−0.386642	−0.193321	−	0.981136i	$-0.561926\pi$
$479$	−8.46208	−0.386642	−0.193321	+	0.981136i	$0.561926\pi$
$480$	20.6935	0.944525
$481$	−34.0915	−1.55444
$482$	54.8754	2.49950
$483$	47.1506	2.14543
$484$	30.7771	1.39896
$485$	5.98703	0.271857
$486$	−30.6346	−1.38961
$487$	16.6264	0.753414	0.376707	−	0.926333i	$-0.377056\pi$
$487$	16.6264	0.753414	0.376707	+	0.926333i	$0.377056\pi$
$488$	−1.72408	−0.0780455
$489$	66.1793	2.99273
$490$	−19.6272	−0.886665
$491$	−25.1140	−1.13338	−0.566689	−	0.823932i	$-0.691776\pi$
$491$	−25.1140	−1.13338	−0.566689	+	0.823932i	$0.691776\pi$
$492$	19.2558	0.868119
$493$	0.969832	0.0436790
$494$	6.88521	0.309780
$495$	−30.6793	−1.37893
$496$	−7.53665	−0.338406
$497$	19.6306	0.880553
$498$	−35.2620	−1.58013
$499$	−33.1575	−1.48433	−0.742167	−	0.670215i	$-0.766202\pi$
$499$	−33.1575	−1.48433	−0.742167	+	0.670215i	$0.766202\pi$
$500$	3.01316	0.134752
$501$	−21.6460	−0.967072
$502$	−13.8063	−0.616207
$503$	40.4093	1.80176	0.900882	−	0.434064i	$-0.142921\pi$
$503$	40.4093	1.80176	0.900882	+	0.434064i	$0.142921\pi$
$504$	−59.9962	−2.67244
$505$	13.7933	0.613792
$506$	39.3992	1.75151
$507$	−14.2439	−0.632592
$508$	−35.2398	−1.56351
$509$	10.1281	0.448920	0.224460	−	0.974483i	$-0.427938\pi$
$509$	10.1281	0.448920	0.224460	+	0.974483i	$0.427938\pi$
$510$	6.93519	0.307095
$511$	−14.3916	−0.636646
$512$	−10.6036	−0.468618
$513$	12.0606	0.532487
$514$	−43.3900	−1.91385
$515$	10.8530	0.478242
$516$	3.75166	0.165158
$517$	38.4533	1.69117
$518$	−104.466	−4.58998
$519$	0.206170	0.00904987
$520$	6.58141	0.288614
$521$	−7.77472	−0.340617	−0.170308	−	0.985391i	$-0.554476\pi$
$521$	−7.77472	−0.340617	−0.170308	+	0.985391i	$0.554476\pi$
$522$	14.5140	0.635263
$523$	8.54822	0.373787	0.186894	−	0.982380i	$-0.440158\pi$
$523$	8.54822	0.373787	0.186894	+	0.982380i	$0.440158\pi$
$524$	29.1121	1.27177
$525$	12.3415	0.538629
$526$	25.2788	1.10221
$527$	−7.92920	−0.345401
$528$	13.5602	0.590131
$529$	−8.40389	−0.365387
$530$	20.7774	0.902511
$531$	−23.0470	−1.00016
$532$	12.6811	0.549796
$533$	−5.96512	−0.258378
$534$	−26.8465	−1.16176
$535$	14.9961	0.648337
$536$	15.3826	0.664427
$537$	−21.2894	−0.918706
$538$	−57.5353	−2.48052
$539$	−40.3753	−1.73909
$540$	34.2858	1.47543
$541$	−14.3160	−0.615492	−0.307746	−	0.951468i	$-0.599575\pi$
$541$	−14.3160	−0.615492	−0.307746	+	0.951468i	$0.599575\pi$
$542$	−12.1681	−0.522667
$543$	58.2021	2.49769
$544$	−6.63469	−0.284460
$545$	4.34126	0.185959
$546$	80.1700	3.43096
$547$	23.9046	1.02209	0.511044	−	0.859554i	$-0.329259\pi$
$547$	23.9046	1.02209	0.511044	+	0.859554i	$0.329259\pi$
$548$	29.7967	1.27285
$549$	5.06241	0.216058
$550$	10.3126	0.439732
$551$	−1.03152	−0.0439441
$552$	−26.9376	−1.14654
$553$	49.4259	2.10180
$554$	−40.3708	−1.71519
$555$	36.5231	1.55032
$556$	−14.4228	−0.611662
$557$	−22.2514	−0.942821	−0.471410	−	0.881914i	$-0.656255\pi$
$557$	−22.2514	−0.942821	−0.471410	+	0.881914i	$0.656255\pi$
$558$	−118.665	−5.02348
$559$	−1.16220	−0.0491558
$560$	−3.76101	−0.158932
$561$	14.2665	0.602331
$562$	14.2780	0.602280
$563$	9.13817	0.385128	0.192564	−	0.981284i	$-0.438320\pi$
$563$	9.13817	0.385128	0.192564	+	0.981284i	$0.438320\pi$
$564$	−78.1897	−3.29238
$565$	−6.51393	−0.274043
$566$	−43.1333	−1.81303
$567$	61.0868	2.56540
$568$	−11.2151	−0.470577
$569$	−31.6807	−1.32812	−0.664062	−	0.747677i	$-0.731169\pi$
$569$	−31.6807	−1.32812	−0.664062	+	0.747677i	$0.731169\pi$
$570$	−7.37630	−0.308959
$571$	27.8663	1.16617	0.583084	−	0.812412i	$-0.301846\pi$
$571$	27.8663	1.16617	0.583084	+	0.812412i	$0.301846\pi$
$572$	40.2645	1.68354
$573$	−48.0427	−2.00701
$574$	−18.2788	−0.762944
$575$	3.82049	0.159325
$576$	−86.6732	−3.61138
$577$	−16.1204	−0.671103	−0.335551	−	0.942022i	$-0.608923\pi$
$577$	−16.1204	−0.671103	−0.335551	+	0.942022i	$0.608923\pi$
$578$	35.8396	1.49073
$579$	−65.9614	−2.74126
$580$	−2.93240	−0.121761
$581$	20.1189	0.834673
$582$	−41.6653	−1.72708
$583$	42.7414	1.77017
$584$	8.22203	0.340230
$585$	−19.3249	−0.798988
$586$	49.3292	2.03777
$587$	46.6733	1.92641	0.963207	−	0.268762i	$-0.0866145\pi$
$587$	46.6733	1.92641	0.963207	+	0.268762i	$0.0866145\pi$
$588$	82.0979	3.38566
$589$	8.43354	0.347498
$590$	7.74711	0.318943
$591$	−22.1886	−0.912718
$592$	−11.1302	−0.457448
$593$	45.8872	1.88436	0.942180	−	0.335107i	$-0.108773\pi$
$593$	45.8872	1.88436	0.942180	+	0.335107i	$0.108773\pi$
$594$	117.344	4.81470
$595$	−3.95690	−0.162217
$596$	6.56971	0.269106
$597$	29.8352	1.22107
$598$	24.8177	1.01487
$599$	34.0889	1.39283	0.696417	−	0.717637i	$-0.254776\pi$
$599$	34.0889	1.39283	0.696417	+	0.717637i	$0.254776\pi$
$600$	−7.05082	−0.287849
$601$	−34.7072	−1.41574	−0.707869	−	0.706344i	$-0.750343\pi$
$601$	−34.7072	−1.41574	−0.707869	+	0.706344i	$0.750343\pi$
$602$	−3.56131	−0.145148
$603$	−45.1678	−1.83938
$604$	−26.1127	−1.06251
$605$	10.2142	0.415268
$606$	−95.9910	−3.89937
$607$	19.7990	0.803616	0.401808	−	0.915724i	$-0.368382\pi$
$607$	19.7990	0.803616	0.401808	+	0.915724i	$0.368382\pi$
$608$	7.05668	0.286186
$609$	−12.0108	−0.486701
$610$	−1.70169	−0.0688996
$611$	24.2218	0.979910
$612$	−20.0008	−0.808484
$613$	3.39345	0.137060	0.0685301	−	0.997649i	$-0.478169\pi$
$613$	3.39345	0.137060	0.0685301	+	0.997649i	$0.478169\pi$
$614$	40.3977	1.63032
$615$	6.39058	0.257693
$616$	41.4865	1.67154
$617$	−20.3333	−0.818586	−0.409293	−	0.912403i	$-0.634225\pi$
$617$	−20.3333	−0.818586	−0.409293	+	0.912403i	$0.634225\pi$
$618$	−75.5292	−3.03823
$619$	−26.5409	−1.06677	−0.533385	−	0.845873i	$-0.679080\pi$
$619$	−26.5409	−1.06677	−0.533385	+	0.845873i	$0.679080\pi$
$620$	23.9749	0.962854
$621$	43.4722	1.74448
$622$	50.8946	2.04069
$623$	15.3174	0.613678
$624$	8.54159	0.341937
$625$	1.00000	0.0400000
$626$	−54.2139	−2.16682
$627$	−15.1739	−0.605987
$628$	−29.8183	−1.18988
$629$	−11.7099	−0.466905
$630$	−59.2172	−2.35927
$631$	−11.6629	−0.464293	−0.232146	−	0.972681i	$-0.574575\pi$
$631$	−11.6629	−0.464293	−0.232146	+	0.972681i	$0.574575\pi$
$632$	−28.2374	−1.12322
$633$	−48.1387	−1.91334
$634$	−10.6957	−0.424781
$635$	−11.6953	−0.464114
$636$	−86.9089	−3.44616
$637$	−25.4325	−1.00767
$638$	−10.0362	−0.397339
$639$	32.9309	1.30273
$640$	15.8192	0.625307
$641$	−47.1603	−1.86272	−0.931361	−	0.364098i	$-0.881377\pi$
$641$	−47.1603	−1.86272	−0.931361	+	0.364098i	$0.881377\pi$
$642$	−104.362	−4.11883
$643$	−41.1993	−1.62474	−0.812370	−	0.583142i	$-0.801823\pi$
$643$	−41.1993	−1.62474	−0.812370	+	0.583142i	$0.801823\pi$
$644$	45.7089	1.80118
$645$	1.24509	0.0490255
$646$	2.36497	0.0930484
$647$	7.99584	0.314349	0.157174	−	0.987571i	$-0.449762\pi$
$647$	7.99584	0.314349	0.157174	+	0.987571i	$0.449762\pi$
$648$	−34.8994	−1.37098
$649$	15.9367	0.625570
$650$	6.49595	0.254792
$651$	98.1983	3.84870
$652$	64.1557	2.51253
$653$	−13.8302	−0.541219	−0.270609	−	0.962689i	$-0.587225\pi$
$653$	−13.8302	−0.541219	−0.270609	+	0.962689i	$0.587225\pi$
$654$	−30.2120	−1.18138
$655$	9.66167	0.377513
$656$	−1.94749	−0.0760368
$657$	−24.1423	−0.941880
$658$	74.2226	2.89350
$659$	−20.2402	−0.788446	−0.394223	−	0.919015i	$-0.628986\pi$
$659$	−20.2402	−0.788446	−0.394223	+	0.919015i	$0.628986\pi$
$660$	−43.1364	−1.67908
$661$	−8.94220	−0.347811	−0.173906	−	0.984762i	$-0.555639\pi$
$661$	−8.94220	−0.347811	−0.173906	+	0.984762i	$0.555639\pi$
$662$	−11.7081	−0.455049
$663$	8.98648	0.349006
$664$	−11.4941	−0.446058
$665$	4.20858	0.163202
$666$	−175.245	−6.79061
$667$	−3.71809	−0.143965
$668$	−20.9841	−0.811900
$669$	53.9678	2.08651
$670$	15.1829	0.586565
$671$	−3.50058	−0.135138
$672$	82.1665	3.16964
$673$	25.7360	0.992051	0.496025	−	0.868308i	$-0.334792\pi$
$673$	25.7360	0.992051	0.496025	+	0.868308i	$0.334792\pi$
$674$	49.5011	1.90671
$675$	11.3787	0.437966
$676$	−13.8083	−0.531089
$677$	1.27142	0.0488645	0.0244322	−	0.999701i	$-0.492222\pi$
$677$	1.27142	0.0488645	0.0244322	+	0.999701i	$0.492222\pi$
$678$	45.3322	1.74097
$679$	23.7724	0.912299
$680$	2.26061	0.0866906
$681$	−55.9877	−2.14545
$682$	82.0549	3.14204
$683$	−31.5315	−1.20652	−0.603260	−	0.797545i	$-0.706132\pi$
$683$	−31.5315	−1.20652	−0.603260	+	0.797545i	$0.706132\pi$
$684$	21.2729	0.813391
$685$	9.88886	0.377834
$686$	−15.7004	−0.599444
$687$	79.0554	3.01615
$688$	−0.379435	−0.0144658
$689$	26.9229	1.02568
$690$	−26.5878	−1.01218
$691$	−26.2360	−0.998066	−0.499033	−	0.866583i	$-0.666311\pi$
$691$	−26.2360	−0.998066	−0.499033	+	0.866583i	$0.666311\pi$
$692$	0.199866	0.00759778
$693$	−121.816	−4.62742
$694$	9.37808	0.355987
$695$	−4.78660	−0.181566
$696$	6.86186	0.260098
$697$	−2.04893	−0.0776087
$698$	−63.4882	−2.40307
$699$	−4.10842	−0.155395
$700$	11.9642	0.452203
$701$	45.1333	1.70466	0.852330	−	0.523004i	$-0.175189\pi$
$701$	45.1333	1.70466	0.852330	+	0.523004i	$0.175189\pi$
$702$	73.9155	2.78976
$703$	12.4547	0.469739
$704$	59.9332	2.25882
$705$	−25.9494	−0.977312
$706$	72.0330	2.71100
$707$	54.7681	2.05977
$708$	−32.4051	−1.21786
$709$	−22.3138	−0.838011	−0.419005	−	0.907984i	$-0.637621\pi$
$709$	−22.3138	−0.838011	−0.419005	+	0.907984i	$0.637621\pi$
$710$	−11.0695	−0.415431
$711$	82.9134	3.10949
$712$	−8.75096	−0.327956
$713$	30.3986	1.13844
$714$	27.5372	1.03055
$715$	13.3629	0.499744
$716$	−20.6384	−0.771295
$717$	−7.07886	−0.264365
$718$	13.2314	0.493791
$719$	21.8948	0.816540	0.408270	−	0.912861i	$-0.366132\pi$
$719$	21.8948	0.816540	0.408270	+	0.912861i	$0.366132\pi$
$720$	−6.30921	−0.235130
$721$	43.0935	1.60489
$722$	40.0258	1.48960
$723$	−76.1781	−2.83309
$724$	56.4225	2.09692
$725$	−0.973200	−0.0361437
$726$	−71.0837	−2.63816
$727$	−3.09328	−0.114723	−0.0573616	−	0.998353i	$-0.518269\pi$
$727$	−3.09328	−0.114723	−0.0573616	+	0.998353i	$0.518269\pi$
$728$	26.1324	0.968532
$729$	−3.62681	−0.134326
$730$	8.11527	0.300359
$731$	−0.399198	−0.0147649
$732$	7.11796	0.263087
$733$	−20.5553	−0.759226	−0.379613	−	0.925145i	$-0.623943\pi$
$733$	−20.5553	−0.759226	−0.379613	+	0.925145i	$0.623943\pi$
$734$	24.8348	0.916671
$735$	27.2465	1.00500
$736$	25.4357	0.937574
$737$	31.2329	1.15048
$738$	−30.6633	−1.12873
$739$	53.9994	1.98640	0.993201	−	0.116413i	$-0.0371396\pi$
$739$	53.9994	1.98640	0.993201	+	0.116413i	$0.0371396\pi$
$740$	35.4063	1.30156
$741$	−9.55807	−0.351124
$742$	82.4995	3.02865
$743$	−41.8938	−1.53693	−0.768467	−	0.639889i	$-0.778980\pi$
$743$	−41.8938	−1.53693	−0.768467	+	0.639889i	$0.778980\pi$
$744$	−56.1015	−2.05678
$745$	2.18034	0.0798816
$746$	61.9403	2.26780
$747$	33.7500	1.23485
$748$	13.8302	0.505684
$749$	59.5441	2.17569
$750$	−6.95927	−0.254117
$751$	2.85333	0.104120	0.0520598	−	0.998644i	$-0.483421\pi$
$751$	2.85333	0.104120	0.0520598	+	0.998644i	$0.483421\pi$
$752$	7.90794	0.288373
$753$	19.1660	0.698447
$754$	−6.32186	−0.230228
$755$	−8.66623	−0.315396
$756$	136.137	4.95124
$757$	−24.8663	−0.903781	−0.451891	−	0.892073i	$-0.649250\pi$
$757$	−24.8663	−0.903781	−0.451891	+	0.892073i	$0.649250\pi$
$758$	28.5896	1.03842
$759$	−54.6941	−1.98527
$760$	−2.40440	−0.0872167
$761$	−41.2653	−1.49587	−0.747933	−	0.663774i	$-0.768954\pi$
$761$	−41.2653	−1.49587	−0.747933	+	0.663774i	$0.768954\pi$
$762$	81.3908	2.94848
$763$	17.2376	0.624042
$764$	−46.5737	−1.68498
$765$	−6.63782	−0.239991
$766$	13.4123	0.484605
$767$	10.0386	0.362471
$768$	−29.2004	−1.05368
$769$	−1.86395	−0.0672157	−0.0336078	−	0.999435i	$-0.510700\pi$
$769$	−1.86395	−0.0672157	−0.0336078	+	0.999435i	$0.510700\pi$
$770$	40.9478	1.47566
$771$	60.2340	2.16928
$772$	−63.9445	−2.30141
$773$	26.7868	0.963455	0.481727	−	0.876321i	$-0.340010\pi$
$773$	26.7868	0.963455	0.481727	+	0.876321i	$0.340010\pi$
$774$	−5.97421	−0.214739
$775$	7.95673	0.285814
$776$	−13.5814	−0.487542
$777$	145.020	5.20257
$778$	56.2203	2.01559
$779$	2.17925	0.0780797
$780$	−27.1717	−0.972903
$781$	−22.7712	−0.814819
$782$	8.52450	0.304835
$783$	−11.0737	−0.395743
$784$	−8.30321	−0.296543
$785$	−9.89605	−0.353205
$786$	−67.2382	−2.39831
$787$	−7.41340	−0.264259	−0.132130	−	0.991232i	$-0.542182\pi$
$787$	−7.41340	−0.264259	−0.132130	+	0.991232i	$0.542182\pi$
$788$	−21.5102	−0.766268
$789$	−35.0921	−1.24931
$790$	−27.8708	−0.991598
$791$	−25.8645	−0.919636
$792$	69.5948	2.47294
$793$	−2.20502	−0.0783026
$794$	−52.5377	−1.86449
$795$	−28.8432	−1.02296
$796$	28.9229	1.02514
$797$	12.2353	0.433396	0.216698	−	0.976239i	$-0.430471\pi$
$797$	12.2353	0.433396	0.216698	+	0.976239i	$0.430471\pi$
$798$	−29.2887	−1.03681
$799$	8.31983	0.294334
$800$	6.65772	0.235386
$801$	25.6954	0.907902
$802$	−60.5067	−2.13657
$803$	16.6940	0.589119
$804$	−63.5079	−2.23975
$805$	15.1698	0.534665
$806$	51.6865	1.82058
$807$	79.8706	2.81158
$808$	−31.2895	−1.10076
$809$	−9.39242	−0.330220	−0.165110	−	0.986275i	$-0.552798\pi$
$809$	−9.39242	−0.330220	−0.165110	+	0.986275i	$0.552798\pi$
$810$	−34.4462	−1.21032
$811$	−4.73026	−0.166102	−0.0830509	−	0.996545i	$-0.526466\pi$
$811$	−4.73026	−0.166102	−0.0830509	+	0.996545i	$0.526466\pi$
$812$	−11.6435	−0.408608
$813$	16.8918	0.592423
$814$	121.179	4.24733
$815$	21.2919	0.745822
$816$	2.93391	0.102707
$817$	0.424589	0.0148545
$818$	−0.872993	−0.0305235
$819$	−76.7324	−2.68125
$820$	6.19518	0.216345
$821$	5.24277	0.182974	0.0914870	−	0.995806i	$-0.470838\pi$
$821$	5.24277	0.182974	0.0914870	+	0.995806i	$0.470838\pi$
$822$	−68.8193	−2.40035
$823$	31.8341	1.10967	0.554833	−	0.831962i	$-0.312782\pi$
$823$	31.8341	1.10967	0.554833	+	0.831962i	$0.312782\pi$
$824$	−24.6197	−0.857668
$825$	−14.3160	−0.498419
$826$	30.7610	1.07031
$827$	−21.6758	−0.753741	−0.376871	−	0.926266i	$-0.623000\pi$
$827$	−21.6758	−0.753741	−0.376871	+	0.926266i	$0.623000\pi$
$828$	76.6781	2.66475
$829$	10.9544	0.380462	0.190231	−	0.981739i	$-0.439076\pi$
$829$	10.9544	0.380462	0.190231	+	0.981739i	$0.439076\pi$
$830$	−11.3449	−0.393786
$831$	56.0428	1.94410
$832$	37.7521	1.30882
$833$	−8.73568	−0.302673
$834$	33.3113	1.15347
$835$	−6.96417	−0.241005
$836$	−14.7099	−0.508753
$837$	90.5373	3.12943
$838$	−25.6573	−0.886318
$839$	−41.0153	−1.41601	−0.708003	−	0.706210i	$-0.750404\pi$
$839$	−41.0153	−1.41601	−0.708003	+	0.706210i	$0.750404\pi$
$840$	−27.9963	−0.965965
$841$	−28.0529	−0.967341
$842$	−77.0792	−2.65632
$843$	−19.8207	−0.682661
$844$	−46.6668	−1.60634
$845$	−4.58268	−0.157649
$846$	124.511	4.28076
$847$	40.5571	1.39356
$848$	8.78979	0.301843
$849$	59.8777	2.05500
$850$	2.23126	0.0765316
$851$	44.8929	1.53891
$852$	46.3023	1.58629
$853$	15.1289	0.518004	0.259002	−	0.965877i	$-0.416606\pi$
$853$	15.1289	0.518004	0.259002	+	0.965877i	$0.416606\pi$
$854$	−6.75682	−0.231214
$855$	7.06002	0.241448
$856$	−34.0181	−1.16271
$857$	29.4821	1.00709	0.503544	−	0.863969i	$-0.332029\pi$
$857$	29.4821	1.00709	0.503544	+	0.863969i	$0.332029\pi$
$858$	−92.9961	−3.17483
$859$	−23.2685	−0.793910	−0.396955	−	0.917838i	$-0.629933\pi$
$859$	−23.2685	−0.793910	−0.396955	+	0.917838i	$0.629933\pi$
$860$	1.20702	0.0411591
$861$	25.3747	0.864768
$862$	21.8088	0.742809
$863$	−44.7372	−1.52287	−0.761437	−	0.648239i	$-0.775506\pi$
$863$	−44.7372	−1.52287	−0.761437	+	0.648239i	$0.775506\pi$
$864$	75.7563	2.57728
$865$	0.0663312	0.00225533
$866$	−49.3322	−1.67638
$867$	−49.7526	−1.68969
$868$	95.1957	3.23115
$869$	−57.3334	−1.94490
$870$	6.77276	0.229618
$871$	19.6737	0.666616
$872$	−9.84798	−0.333495
$873$	39.8788	1.34969
$874$	−9.06669	−0.306686
$875$	3.97064	0.134232
$876$	−33.9451	−1.14690
$877$	−25.1324	−0.848661	−0.424331	−	0.905507i	$-0.639491\pi$
$877$	−25.1324	−0.848661	−0.424331	+	0.905507i	$0.639491\pi$
$878$	70.6947	2.38583
$879$	−68.4789	−2.30974
$880$	4.36272	0.147067
$881$	−7.50004	−0.252683	−0.126341	−	0.991987i	$-0.540323\pi$
$881$	−7.50004	−0.252683	−0.126341	+	0.991987i	$0.540323\pi$
$882$	−130.734	−4.40205
$883$	34.8175	1.17170	0.585852	−	0.810418i	$-0.300760\pi$
$883$	34.8175	1.17170	0.585852	+	0.810418i	$0.300760\pi$
$884$	8.71171	0.293006
$885$	−10.7546	−0.361510
$886$	−3.92936	−0.132009
$887$	1.29098	0.0433470	0.0216735	−	0.999765i	$-0.493101\pi$
$887$	1.29098	0.0433470	0.0216735	+	0.999765i	$0.493101\pi$
$888$	−82.8512	−2.78030
$889$	−46.4379	−1.55748
$890$	−8.63733	−0.289524
$891$	−70.8598	−2.37389
$892$	52.3176	1.75172
$893$	−8.84901	−0.296121
$894$	−15.1736	−0.507481
$895$	−6.84944	−0.228952
$896$	62.8123	2.09841
$897$	−34.4519	−1.15032
$898$	47.6892	1.59141
$899$	−7.74349	−0.258260
$900$	20.0702	0.669008
$901$	9.24761	0.308082
$902$	21.2032	0.705989
$903$	4.94382	0.164520
$904$	14.7766	0.491463
$905$	18.7254	0.622453
$906$	60.3107	2.00369
$907$	−26.5734	−0.882356	−0.441178	−	0.897420i	$-0.645439\pi$
$907$	−26.5734	−0.882356	−0.441178	+	0.897420i	$0.645439\pi$
$908$	−54.2758	−1.80121
$909$	91.8751	3.04731
$910$	25.7931	0.855033
$911$	−35.0222	−1.16034	−0.580169	−	0.814496i	$-0.697013\pi$
$911$	−35.0222	−1.16034	−0.580169	+	0.814496i	$0.697013\pi$
$912$	−3.12052	−0.103331
$913$	−23.3376	−0.772363
$914$	49.4700	1.63632
$915$	2.36229	0.0780950
$916$	76.6382	2.53220
$917$	38.3631	1.26686
$918$	25.3888	0.837957
$919$	−3.34163	−0.110230	−0.0551151	−	0.998480i	$-0.517553\pi$
$919$	−3.34163	−0.110230	−0.0551151	+	0.998480i	$0.517553\pi$
$920$	−8.66663	−0.285730
$921$	−56.0802	−1.84790
$922$	44.3593	1.46089
$923$	−14.3436	−0.472127
$924$	−171.279	−5.63467
$925$	11.7506	0.386356
$926$	−85.2233	−2.80061
$927$	72.2906	2.37434
$928$	−6.47930	−0.212693
$929$	−21.0885	−0.691891	−0.345946	−	0.938255i	$-0.612442\pi$
$929$	−21.0885	−0.691891	−0.345946	+	0.938255i	$0.612442\pi$
$930$	−55.3731	−1.81575
$931$	9.29131	0.304510
$932$	−3.98279	−0.130461
$933$	−70.6520	−2.31304
$934$	42.6133	1.39435
$935$	4.58995	0.150108
$936$	43.8379	1.43289
$937$	17.7478	0.579795	0.289898	−	0.957058i	$-0.406379\pi$
$937$	17.7478	0.579795	0.289898	+	0.957058i	$0.406379\pi$
$938$	60.2857	1.96840
$939$	75.2598	2.45601
$940$	−25.1560	−0.820498
$941$	0.659809	0.0215092	0.0107546	−	0.999942i	$-0.496577\pi$
$941$	0.659809	0.0215092	0.0107546	+	0.999942i	$0.496577\pi$
$942$	68.8693	2.24388
$943$	7.85508	0.255797
$944$	3.27739	0.106670
$945$	45.1808	1.46973
$946$	4.13108	0.134313
$947$	21.7416	0.706506	0.353253	−	0.935528i	$-0.385076\pi$
$947$	21.7416	0.706506	0.353253	+	0.935528i	$0.385076\pi$
$948$	116.580	3.78634
$949$	10.5156	0.341351
$950$	−2.37318	−0.0769961
$951$	14.8478	0.481473
$952$	8.97609	0.290917
$953$	44.2291	1.43272	0.716360	−	0.697731i	$-0.245807\pi$
$953$	44.2291	1.43272	0.716360	+	0.697731i	$0.245807\pi$
$954$	138.395	4.48071
$955$	−15.4568	−0.500170
$956$	−6.86241	−0.221946
$957$	13.9323	0.450368
$958$	18.9467	0.612139
$959$	39.2651	1.26794
$960$	−40.4447	−1.30535
$961$	32.3096	1.04225
$962$	76.3311	2.46101
$963$	99.8870	3.21881
$964$	−73.8488	−2.37851
$965$	−21.2218	−0.683153
$966$	−105.571	−3.39668
$967$	−55.7317	−1.79221	−0.896106	−	0.443841i	$-0.853616\pi$
$967$	−55.7317	−1.79221	−0.896106	+	0.443841i	$0.853616\pi$
$968$	−23.1706	−0.744733
$969$	−3.28305	−0.105467
$970$	−13.4050	−0.430409
$971$	57.3113	1.83921	0.919604	−	0.392846i	$-0.128510\pi$
$971$	57.3113	1.83921	0.919604	+	0.392846i	$0.128510\pi$
$972$	41.2266	1.32235
$973$	−19.0059	−0.609301
$974$	−37.2266	−1.19282
$975$	−9.01769	−0.288797
$976$	−0.719896	−0.0230433
$977$	32.0144	1.02423	0.512115	−	0.858917i	$-0.328862\pi$
$977$	32.0144	1.02423	0.512115	+	0.858917i	$0.328862\pi$
$978$	−148.176	−4.73814
$979$	−17.7680	−0.567867
$980$	26.4134	0.843744
$981$	28.9165	0.923234
$982$	56.2304	1.79438
$983$	−41.8018	−1.33327	−0.666635	−	0.745385i	$-0.732266\pi$
$983$	−41.8018	−1.33327	−0.666635	+	0.745385i	$0.732266\pi$
$984$	−14.4968	−0.462141
$985$	−7.13875	−0.227459
$986$	−2.17146	−0.0691534
$987$	−103.036	−3.27967
$988$	−9.26581	−0.294785
$989$	1.53043	0.0486647
$990$	68.6911	2.18315
$991$	−34.6520	−1.10076	−0.550379	−	0.834915i	$-0.685517\pi$
$991$	−34.6520	−1.10076	−0.550379	+	0.834915i	$0.685517\pi$
$992$	52.9737	1.68192
$993$	16.2532	0.515781
$994$	−43.9531	−1.39411
$995$	9.59887	0.304305
$996$	47.4540	1.50364
$997$	−10.6485	−0.337241	−0.168621	−	0.985681i	$-0.553931\pi$
$997$	−10.6485	−0.337241	−0.168621	+	0.985681i	$0.553931\pi$
$998$	74.2399	2.35002
$999$	133.706	4.23028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.f.1.15	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.f.1.15	✓	111	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)

\(f(q)\)	\(=\)	\(q-2.23901 q^{2} +3.10819 q^{3} +3.01316 q^{4} +1.00000 q^{5} -6.95927 q^{6} +3.97064 q^{7} -2.26846 q^{8} +6.66087 q^{9} +O(q^{10})\)	\(q-2.23901 q^{2} +3.10819 q^{3} +3.01316 q^{4} +1.00000 q^{5} -6.95927 q^{6} +3.97064 q^{7} -2.26846 q^{8} +6.66087 q^{9} -2.23901 q^{10} -4.60589 q^{11} +9.36547 q^{12} -2.90126 q^{13} -8.89030 q^{14} +3.10819 q^{15} -0.947204 q^{16} -0.996540 q^{17} -14.9137 q^{18} +1.05992 q^{19} +3.01316 q^{20} +12.3415 q^{21} +10.3126 q^{22} +3.82049 q^{23} -7.05082 q^{24} +1.00000 q^{25} +6.49595 q^{26} +11.3787 q^{27} +11.9642 q^{28} -0.973200 q^{29} -6.95927 q^{30} +7.95673 q^{31} +6.65772 q^{32} -14.3160 q^{33} +2.23126 q^{34} +3.97064 q^{35} +20.0702 q^{36} +11.7506 q^{37} -2.37318 q^{38} -9.01769 q^{39} -2.26846 q^{40} +2.05604 q^{41} -27.6328 q^{42} +0.400584 q^{43} -13.8783 q^{44} +6.66087 q^{45} -8.55410 q^{46} -8.34872 q^{47} -2.94410 q^{48} +8.76601 q^{49} -2.23901 q^{50} -3.09744 q^{51} -8.74195 q^{52} -9.27972 q^{53} -25.4770 q^{54} -4.60589 q^{55} -9.00726 q^{56} +3.29445 q^{57} +2.17900 q^{58} -3.46006 q^{59} +9.36547 q^{60} +0.760021 q^{61} -17.8152 q^{62} +26.4480 q^{63} -13.0123 q^{64} -2.90126 q^{65} +32.0537 q^{66} -6.78107 q^{67} -3.00273 q^{68} +11.8748 q^{69} -8.89030 q^{70} +4.94393 q^{71} -15.1099 q^{72} -3.62449 q^{73} -26.3096 q^{74} +3.10819 q^{75} +3.19372 q^{76} -18.2884 q^{77} +20.1907 q^{78} +12.4478 q^{79} -0.947204 q^{80} +15.3846 q^{81} -4.60349 q^{82} +5.06691 q^{83} +37.1870 q^{84} -0.996540 q^{85} -0.896911 q^{86} -3.02489 q^{87} +10.4483 q^{88} +3.85766 q^{89} -14.9137 q^{90} -11.5199 q^{91} +11.5117 q^{92} +24.7311 q^{93} +18.6928 q^{94} +1.05992 q^{95} +20.6935 q^{96} +5.98703 q^{97} -19.6272 q^{98} -30.6793 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

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