LMFDB - Embedded newform 6043.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2535979415$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72028 q^{2} -2.17990 q^{3} +5.39995 q^{4} -3.45469 q^{5} +5.92994 q^{6} +1.90963 q^{7} -9.24882 q^{8} +1.75196 q^{9} +O(q^{10})$	\(q-2.72028 q^{2} -2.17990 q^{3} +5.39995 q^{4} -3.45469 q^{5} +5.92994 q^{6} +1.90963 q^{7} -9.24882 q^{8} +1.75196 q^{9} +9.39775 q^{10} -5.43569 q^{11} -11.7713 q^{12} +3.65319 q^{13} -5.19472 q^{14} +7.53088 q^{15} +14.3595 q^{16} +3.35588 q^{17} -4.76582 q^{18} -4.57662 q^{19} -18.6552 q^{20} -4.16279 q^{21} +14.7866 q^{22} +1.03181 q^{23} +20.1615 q^{24} +6.93490 q^{25} -9.93772 q^{26} +2.72061 q^{27} +10.3119 q^{28} -9.16833 q^{29} -20.4861 q^{30} -1.11101 q^{31} -20.5643 q^{32} +11.8492 q^{33} -9.12896 q^{34} -6.59717 q^{35} +9.46047 q^{36} -1.94956 q^{37} +12.4497 q^{38} -7.96359 q^{39} +31.9518 q^{40} +6.85297 q^{41} +11.3240 q^{42} -6.48425 q^{43} -29.3524 q^{44} -6.05247 q^{45} -2.80681 q^{46} -4.35006 q^{47} -31.3023 q^{48} -3.35333 q^{49} -18.8649 q^{50} -7.31548 q^{51} +19.7270 q^{52} +5.85263 q^{53} -7.40083 q^{54} +18.7786 q^{55} -17.6618 q^{56} +9.97658 q^{57} +24.9405 q^{58} +10.9158 q^{59} +40.6663 q^{60} +8.19204 q^{61} +3.02227 q^{62} +3.34558 q^{63} +27.2218 q^{64} -12.6207 q^{65} -32.2333 q^{66} -13.0688 q^{67} +18.1216 q^{68} -2.24924 q^{69} +17.9462 q^{70} +9.48379 q^{71} -16.2035 q^{72} -12.9678 q^{73} +5.30336 q^{74} -15.1174 q^{75} -24.7135 q^{76} -10.3801 q^{77} +21.6632 q^{78} +17.3335 q^{79} -49.6077 q^{80} -11.1865 q^{81} -18.6420 q^{82} -13.4116 q^{83} -22.4788 q^{84} -11.5935 q^{85} +17.6390 q^{86} +19.9860 q^{87} +50.2737 q^{88} +2.95652 q^{89} +16.4644 q^{90} +6.97623 q^{91} +5.57172 q^{92} +2.42190 q^{93} +11.8334 q^{94} +15.8108 q^{95} +44.8282 q^{96} -5.99193 q^{97} +9.12201 q^{98} -9.52308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) $ 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9} - 24 q^{10} - 37 q^{11} - 74 q^{12} - 113 q^{13} - 35 q^{14} - 34 q^{15} + 218 q^{16} - 125 q^{17} - 108 q^{18} - 46 q^{19} - 157 q^{20} - 113 q^{21} - 16 q^{22} - 60 q^{23} - 49 q^{24} + 208 q^{25} - 52 q^{26} - 90 q^{27} - 70 q^{28} - 137 q^{29} - 26 q^{30} - 36 q^{31} - 258 q^{32} - 153 q^{33} - 23 q^{34} - 77 q^{35} + 180 q^{36} - 108 q^{37} - 122 q^{38} - 32 q^{39} - 57 q^{40} - 186 q^{41} - 28 q^{42} - 54 q^{43} - 90 q^{44} - 233 q^{45} - 42 q^{46} - 188 q^{47} - 149 q^{48} + 189 q^{49} - 146 q^{50} - 34 q^{51} - 195 q^{52} - 196 q^{53} - 36 q^{54} - 57 q^{55} - 63 q^{56} - 76 q^{57} - 24 q^{58} - 137 q^{59} - 73 q^{60} - 96 q^{61} - 167 q^{62} - 113 q^{63} + 224 q^{64} - 131 q^{65} - 11 q^{66} - 71 q^{67} - 260 q^{68} - 162 q^{69} - 48 q^{70} - 77 q^{71} - 290 q^{72} - 160 q^{73} - 34 q^{74} - 100 q^{75} - 84 q^{76} - 416 q^{77} - 59 q^{78} - 17 q^{79} - 268 q^{80} + 147 q^{81} - 28 q^{82} - 238 q^{83} - 184 q^{84} - 108 q^{85} - 61 q^{86} - 127 q^{87} - 47 q^{88} - 183 q^{89} - 56 q^{90} - 14 q^{91} - 109 q^{92} - 206 q^{93} + q^{94} - 84 q^{95} - 54 q^{96} - 127 q^{97} - 294 q^{98} - 66 q^{99}+O(q^{100}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9 - 24 * q^10 - 37 * q^11 - 74 * q^12 - 113 * q^13 - 35 * q^14 - 34 * q^15 + 218 * q^16 - 125 * q^17 - 108 * q^18 - 46 * q^19 - 157 * q^20 - 113 * q^21 - 16 * q^22 - 60 * q^23 - 49 * q^24 + 208 * q^25 - 52 * q^26 - 90 * q^27 - 70 * q^28 - 137 * q^29 - 26 * q^30 - 36 * q^31 - 258 * q^32 - 153 * q^33 - 23 * q^34 - 77 * q^35 + 180 * q^36 - 108 * q^37 - 122 * q^38 - 32 * q^39 - 57 * q^40 - 186 * q^41 - 28 * q^42 - 54 * q^43 - 90 * q^44 - 233 * q^45 - 42 * q^46 - 188 * q^47 - 149 * q^48 + 189 * q^49 - 146 * q^50 - 34 * q^51 - 195 * q^52 - 196 * q^53 - 36 * q^54 - 57 * q^55 - 63 * q^56 - 76 * q^57 - 24 * q^58 - 137 * q^59 - 73 * q^60 - 96 * q^61 - 167 * q^62 - 113 * q^63 + 224 * q^64 - 131 * q^65 - 11 * q^66 - 71 * q^67 - 260 * q^68 - 162 * q^69 - 48 * q^70 - 77 * q^71 - 290 * q^72 - 160 * q^73 - 34 * q^74 - 100 * q^75 - 84 * q^76 - 416 * q^77 - 59 * q^78 - 17 * q^79 - 268 * q^80 + 147 * q^81 - 28 * q^82 - 238 * q^83 - 184 * q^84 - 108 * q^85 - 61 * q^86 - 127 * q^87 - 47 * q^88 - 183 * q^89 - 56 * q^90 - 14 * q^91 - 109 * q^92 - 206 * q^93 + q^94 - 84 * q^95 - 54 * q^96 - 127 * q^97 - 294 * q^98 - 66 * 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 $

$2$	−2.72028	−1.92353	−0.961766	−	0.273874i	$-0.911695\pi$
$2$	−2.72028	−1.92353	−0.961766	+	0.273874i	$0.911695\pi$
$3$	−2.17990	−1.25856	−0.629282	−	0.777177i	$-0.716651\pi$
$3$	−2.17990	−1.25856	−0.629282	+	0.777177i	$0.716651\pi$
$4$	5.39995	2.69997
$5$	−3.45469	−1.54499	−0.772493	−	0.635023i	$-0.780990\pi$
$5$	−3.45469	−1.54499	−0.772493	+	0.635023i	$0.780990\pi$
$6$	5.92994	2.42089
$7$	1.90963	0.721771	0.360885	−	0.932610i	$-0.382475\pi$
$7$	1.90963	0.721771	0.360885	+	0.932610i	$0.382475\pi$
$8$	−9.24882	−3.26995
$9$	1.75196	0.583985
$10$	9.39775	2.97183
$11$	−5.43569	−1.63892	−0.819460	−	0.573136i	$-0.805727\pi$
$11$	−5.43569	−1.63892	−0.819460	+	0.573136i	$0.805727\pi$
$12$	−11.7713	−3.39809
$13$	3.65319	1.01321	0.506607	−	0.862177i	$-0.330900\pi$
$13$	3.65319	1.01321	0.506607	+	0.862177i	$0.330900\pi$
$14$	−5.19472	−1.38835
$15$	7.53088	1.94446
$16$	14.3595	3.58988
$17$	3.35588	0.813921	0.406961	−	0.913446i	$-0.366589\pi$
$17$	3.35588	0.813921	0.406961	+	0.913446i	$0.366589\pi$
$18$	−4.76582	−1.12331
$19$	−4.57662	−1.04995	−0.524975	−	0.851118i	$-0.675925\pi$
$19$	−4.57662	−1.04995	−0.524975	+	0.851118i	$0.675925\pi$
$20$	−18.6552	−4.17142
$21$	−4.16279	−0.908395
$22$	14.7866	3.15252
$23$	1.03181	0.215147	0.107574	−	0.994197i	$-0.465692\pi$
$23$	1.03181	0.215147	0.107574	+	0.994197i	$0.465692\pi$
$24$	20.1615	4.11545
$25$	6.93490	1.38698
$26$	−9.93772	−1.94895
$27$	2.72061	0.523582
$28$	10.3119	1.94876
$29$	−9.16833	−1.70252	−0.851258	−	0.524747i	$-0.824160\pi$
$29$	−9.16833	−1.70252	−0.851258	+	0.524747i	$0.824160\pi$
$30$	−20.4861	−3.74024
$31$	−1.11101	−0.199544	−0.0997719	−	0.995010i	$-0.531811\pi$
$31$	−1.11101	−0.199544	−0.0997719	+	0.995010i	$0.531811\pi$
$32$	−20.5643	−3.63530
$33$	11.8492	2.06269
$34$	−9.12896	−1.56560
$35$	−6.59717	−1.11513
$36$	9.46047	1.57674
$37$	−1.94956	−0.320506	−0.160253	−	0.987076i	$-0.551231\pi$
$37$	−1.94956	−0.320506	−0.160253	+	0.987076i	$0.551231\pi$
$38$	12.4497	2.01961
$39$	−7.96359	−1.27519
$40$	31.9518	5.05203
$41$	6.85297	1.07025	0.535127	−	0.844772i	$-0.320264\pi$
$41$	6.85297	1.07025	0.535127	+	0.844772i	$0.320264\pi$
$42$	11.3240	1.74733
$43$	−6.48425	−0.988839	−0.494420	−	0.869223i	$-0.664619\pi$
$43$	−6.48425	−0.988839	−0.494420	+	0.869223i	$0.664619\pi$
$44$	−29.3524	−4.42504
$45$	−6.05247	−0.902249
$46$	−2.80681	−0.413842
$47$	−4.35006	−0.634522	−0.317261	−	0.948338i	$-0.602763\pi$
$47$	−4.35006	−0.634522	−0.317261	+	0.948338i	$0.602763\pi$
$48$	−31.3023	−4.51810
$49$	−3.35333	−0.479047
$50$	−18.8649	−2.66790
$51$	−7.31548	−1.02437
$52$	19.7270	2.73565
$53$	5.85263	0.803920	0.401960	−	0.915657i	$-0.368329\pi$
$53$	5.85263	0.803920	0.401960	+	0.915657i	$0.368329\pi$
$54$	−7.40083	−1.00713
$55$	18.7786	2.53211
$56$	−17.6618	−2.36015
$57$	9.97658	1.32143
$58$	24.9405	3.27484
$59$	10.9158	1.42112	0.710560	−	0.703636i	$-0.248441\pi$
$59$	10.9158	1.42112	0.710560	+	0.703636i	$0.248441\pi$
$60$	40.6663	5.25000
$61$	8.19204	1.04888	0.524442	−	0.851446i	$-0.324274\pi$
$61$	8.19204	1.04888	0.524442	+	0.851446i	$0.324274\pi$
$62$	3.02227	0.383829
$63$	3.34558	0.421503
$64$	27.2218	3.40273
$65$	−12.6207	−1.56540
$66$	−32.2333	−3.96764
$67$	−13.0688	−1.59661	−0.798304	−	0.602255i	$-0.794269\pi$
$67$	−13.0688	−1.59661	−0.798304	+	0.602255i	$0.794269\pi$
$68$	18.1216	2.19757
$69$	−2.24924	−0.270777
$70$	17.9462	2.14498
$71$	9.48379	1.12552	0.562759	−	0.826621i	$-0.309740\pi$
$71$	9.48379	1.12552	0.562759	+	0.826621i	$0.309740\pi$
$72$	−16.2035	−1.90960
$73$	−12.9678	−1.51777	−0.758885	−	0.651224i	$-0.774256\pi$
$73$	−12.9678	−1.51777	−0.758885	+	0.651224i	$0.774256\pi$
$74$	5.30336	0.616503
$75$	−15.1174	−1.74561
$76$	−24.7135	−2.83484
$77$	−10.3801	−1.18292
$78$	21.6632	2.45288
$79$	17.3335	1.95017	0.975086	−	0.221827i	$-0.0712020\pi$
$79$	17.3335	1.95017	0.975086	+	0.221827i	$0.0712020\pi$
$80$	−49.6077	−5.54631
$81$	−11.1865	−1.24295
$82$	−18.6420	−2.05867
$83$	−13.4116	−1.47212	−0.736058	−	0.676919i	$-0.763315\pi$
$83$	−13.4116	−1.47212	−0.736058	+	0.676919i	$0.763315\pi$
$84$	−22.4788	−2.45264
$85$	−11.5935	−1.25750
$86$	17.6390	1.90206
$87$	19.9860	2.14273
$88$	50.2737	5.35919
$89$	2.95652	0.313390	0.156695	−	0.987647i	$-0.449916\pi$
$89$	2.95652	0.313390	0.156695	+	0.987647i	$0.449916\pi$
$90$	16.4644	1.73550
$91$	6.97623	0.731308
$92$	5.57172	0.580891
$93$	2.42190	0.251139
$94$	11.8334	1.22052
$95$	15.8108	1.62216
$96$	44.8282	4.57526
$97$	−5.99193	−0.608389	−0.304194	−	0.952610i	$-0.598387\pi$
$97$	−5.99193	−0.608389	−0.304194	+	0.952610i	$0.598387\pi$
$98$	9.12201	0.921462
$99$	−9.52308	−0.957106
$100$	37.4481	3.74481
$101$	−7.04069	−0.700575	−0.350287	−	0.936642i	$-0.613916\pi$
$101$	−7.04069	−0.700575	−0.350287	+	0.936642i	$0.613916\pi$
$102$	19.9002	1.97041
$103$	13.1109	1.29185	0.645926	−	0.763400i	$-0.276471\pi$
$103$	13.1109	1.29185	0.645926	+	0.763400i	$0.276471\pi$
$104$	−33.7877	−3.31316
$105$	14.3812	1.40346
$106$	−15.9208	−1.54637
$107$	14.2761	1.38012	0.690062	−	0.723750i	$-0.257583\pi$
$107$	14.2761	1.38012	0.690062	+	0.723750i	$0.257583\pi$
$108$	14.6911	1.41366
$109$	−2.32604	−0.222794	−0.111397	−	0.993776i	$-0.535533\pi$
$109$	−2.32604	−0.222794	−0.111397	+	0.993776i	$0.535533\pi$
$110$	−51.0832	−4.87059
$111$	4.24984	0.403377
$112$	27.4213	2.59107
$113$	−18.5846	−1.74829	−0.874146	−	0.485663i	$-0.838578\pi$
$113$	−18.5846	−1.74829	−0.874146	+	0.485663i	$0.838578\pi$
$114$	−27.1391	−2.54181
$115$	−3.56459	−0.332399
$116$	−49.5085	−4.59675
$117$	6.40023	0.591702
$118$	−29.6942	−2.73357
$119$	6.40848	0.587464
$120$	−69.6517	−6.35830
$121$	18.5467	1.68606
$122$	−22.2847	−2.01756
$123$	−14.9388	−1.34698
$124$	−5.99941	−0.538763
$125$	−6.68450	−0.597880
$126$	−9.10093	−0.810775
$127$	0.976570	0.0866566	0.0433283	−	0.999061i	$-0.486204\pi$
$127$	0.976570	0.0866566	0.0433283	+	0.999061i	$0.486204\pi$
$128$	−32.9224	−2.90995
$129$	14.1350	1.24452
$130$	34.3318	3.01110
$131$	18.2347	1.59318	0.796588	−	0.604522i	$-0.206636\pi$
$131$	18.2347	1.59318	0.796588	+	0.604522i	$0.206636\pi$
$132$	63.9853	5.56920
$133$	−8.73964	−0.757823
$134$	35.5508	3.07113
$135$	−9.39887	−0.808926
$136$	−31.0380	−2.66148
$137$	−2.27512	−0.194377	−0.0971883	−	0.995266i	$-0.530985\pi$
$137$	−2.27512	−0.194377	−0.0971883	+	0.995266i	$0.530985\pi$
$138$	6.11857	0.520847
$139$	−16.8510	−1.42928	−0.714640	−	0.699493i	$-0.753409\pi$
$139$	−16.8510	−1.42928	−0.714640	+	0.699493i	$0.753409\pi$
$140$	−35.6244	−3.01081
$141$	9.48269	0.798587
$142$	−25.7986	−2.16497
$143$	−19.8576	−1.66058
$144$	25.1572	2.09644
$145$	31.6738	2.63036
$146$	35.2762	2.91948
$147$	7.30992	0.602912
$148$	−10.5275	−0.865357
$149$	−16.6055	−1.36037	−0.680186	−	0.733040i	$-0.738101\pi$
$149$	−16.6055	−1.36037	−0.680186	+	0.733040i	$0.738101\pi$
$150$	41.1236	3.35773
$151$	12.9833	1.05656	0.528281	−	0.849070i	$-0.322837\pi$
$151$	12.9833	1.05656	0.528281	+	0.849070i	$0.322837\pi$
$152$	42.3284	3.43328
$153$	5.87936	0.475318
$154$	28.2369	2.27539
$155$	3.83821	0.308292
$156$	−43.0030	−3.44299
$157$	16.1681	1.29035	0.645177	−	0.764033i	$-0.276784\pi$
$157$	16.1681	1.29035	0.645177	+	0.764033i	$0.276784\pi$
$158$	−47.1521	−3.75122
$159$	−12.7581	−1.01179
$160$	71.0435	5.61648
$161$	1.97037	0.155287
$162$	30.4305	2.39085
$163$	−14.3646	−1.12512	−0.562561	−	0.826756i	$-0.690184\pi$
$163$	−14.3646	−1.12512	−0.562561	+	0.826756i	$0.690184\pi$
$164$	37.0057	2.88966
$165$	−40.9355	−3.18682
$166$	36.4834	2.83166
$167$	0.412198	0.0318968	0.0159484	−	0.999873i	$-0.494923\pi$
$167$	0.412198	0.0318968	0.0159484	+	0.999873i	$0.494923\pi$
$168$	38.5009	2.97041
$169$	0.345824	0.0266018
$170$	31.5377	2.41883
$171$	−8.01804	−0.613155
$172$	−35.0146	−2.66984
$173$	−5.72094	−0.434955	−0.217478	−	0.976065i	$-0.569783\pi$
$173$	−5.72094	−0.434955	−0.217478	+	0.976065i	$0.569783\pi$
$174$	−54.3677	−4.12160
$175$	13.2431	1.00108
$176$	−78.0538	−5.88353
$177$	−23.7954	−1.78857
$178$	−8.04257	−0.602816
$179$	16.9841	1.26945	0.634726	−	0.772737i	$-0.281113\pi$
$179$	16.9841	1.26945	0.634726	+	0.772737i	$0.281113\pi$
$180$	−32.6830	−2.43605
$181$	14.5969	1.08498	0.542490	−	0.840063i	$-0.317482\pi$
$181$	14.5969	1.08498	0.542490	+	0.840063i	$0.317482\pi$
$182$	−18.9773	−1.40669
$183$	−17.8578	−1.32009
$184$	−9.54302	−0.703521
$185$	6.73513	0.495177
$186$	−6.58824	−0.483074
$187$	−18.2415	−1.33395
$188$	−23.4901	−1.71319
$189$	5.19534	0.377906
$190$	−43.0100	−3.12027
$191$	11.0674	0.800809	0.400405	−	0.916338i	$-0.368870\pi$
$191$	11.0674	0.800809	0.400405	+	0.916338i	$0.368870\pi$
$192$	−59.3408	−4.28255
$193$	−4.64451	−0.334319	−0.167159	−	0.985930i	$-0.553459\pi$
$193$	−4.64451	−0.334319	−0.167159	+	0.985930i	$0.553459\pi$
$194$	16.2998	1.17025
$195$	27.5118	1.97016
$196$	−18.1078	−1.29341
$197$	22.7989	1.62435	0.812177	−	0.583410i	$-0.198282\pi$
$197$	22.7989	1.62435	0.812177	+	0.583410i	$0.198282\pi$
$198$	25.9055	1.84102
$199$	14.3134	1.01465	0.507326	−	0.861754i	$-0.330634\pi$
$199$	14.3134	1.01465	0.507326	+	0.861754i	$0.330634\pi$
$200$	−64.1397	−4.53536
$201$	28.4887	2.00943
$202$	19.1527	1.34758
$203$	−17.5081	−1.22883
$204$	−39.5032	−2.76578
$205$	−23.6749	−1.65353
$206$	−35.6653	−2.48492
$207$	1.80768	0.125643
$208$	52.4581	3.63732
$209$	24.8771	1.72078
$210$	−39.1208	−2.69959
$211$	7.51438	0.517311	0.258656	−	0.965970i	$-0.416721\pi$
$211$	7.51438	0.517311	0.258656	+	0.965970i	$0.416721\pi$
$212$	31.6039	2.17056
$213$	−20.6737	−1.41654
$214$	−38.8351	−2.65471
$215$	22.4011	1.52774
$216$	−25.1624	−1.71209
$217$	−2.12162	−0.144025
$218$	6.32749	0.428552
$219$	28.2686	1.91021
$220$	101.404	6.83663
$221$	12.2597	0.824676
$222$	−11.5608	−0.775909
$223$	26.7573	1.79180	0.895902	−	0.444252i	$-0.146531\pi$
$223$	26.7573	1.79180	0.895902	+	0.444252i	$0.146531\pi$
$224$	−39.2702	−2.62385
$225$	12.1496	0.809976
$226$	50.5554	3.36290
$227$	−4.37606	−0.290449	−0.145225	−	0.989399i	$-0.546390\pi$
$227$	−4.37606	−0.290449	−0.145225	+	0.989399i	$0.546390\pi$
$228$	53.8730	3.56782
$229$	25.6425	1.69450	0.847252	−	0.531191i	$-0.178255\pi$
$229$	25.6425	1.69450	0.847252	+	0.531191i	$0.178255\pi$
$230$	9.69668	0.639380
$231$	22.6276	1.48879
$232$	84.7962	5.56715
$233$	17.6398	1.15562	0.577812	−	0.816170i	$-0.303906\pi$
$233$	17.6398	1.15562	0.577812	+	0.816170i	$0.303906\pi$
$234$	−17.4105	−1.13816
$235$	15.0281	0.980327
$236$	58.9449	3.83699
$237$	−37.7853	−2.45442
$238$	−17.4329	−1.13001
$239$	−21.2067	−1.37175	−0.685873	−	0.727721i	$-0.740579\pi$
$239$	−21.2067	−1.37175	−0.685873	+	0.727721i	$0.740579\pi$
$240$	108.140	6.98040
$241$	−12.9854	−0.836464	−0.418232	−	0.908340i	$-0.637350\pi$
$241$	−12.9854	−0.836464	−0.418232	+	0.908340i	$0.637350\pi$
$242$	−50.4522	−3.24319
$243$	16.2236	1.04075
$244$	44.2366	2.83196
$245$	11.5847	0.740121
$246$	40.6377	2.59097
$247$	−16.7193	−1.06382
$248$	10.2756	0.652499
$249$	29.2359	1.85275
$250$	18.1837	1.15004
$251$	17.5519	1.10787	0.553933	−	0.832561i	$-0.313126\pi$
$251$	17.5519	1.10787	0.553933	+	0.832561i	$0.313126\pi$
$252$	18.0659	1.13805
$253$	−5.60859	−0.352609
$254$	−2.65655	−0.166687
$255$	25.2727	1.58264
$256$	35.1146	2.19466
$257$	27.5608	1.71920	0.859598	−	0.510971i	$-0.170714\pi$
$257$	27.5608	1.71920	0.859598	+	0.510971i	$0.170714\pi$
$258$	−38.4512	−2.39387
$259$	−3.72293	−0.231332
$260$	−68.1509	−4.22654
$261$	−16.0625	−0.994245
$262$	−49.6037	−3.06452
$263$	16.7080	1.03026	0.515131	−	0.857112i	$-0.327743\pi$
$263$	16.7080	1.03026	0.515131	+	0.857112i	$0.327743\pi$
$264$	−109.591	−6.74489
$265$	−20.2190	−1.24204
$266$	23.7743	1.45770
$267$	−6.44491	−0.394422
$268$	−70.5708	−4.31080
$269$	−5.40426	−0.329503	−0.164752	−	0.986335i	$-0.552682\pi$
$269$	−5.40426	−0.329503	−0.164752	+	0.986335i	$0.552682\pi$
$270$	25.5676	1.55599
$271$	19.2193	1.16749	0.583746	−	0.811936i	$-0.301586\pi$
$271$	19.2193	1.16749	0.583746	+	0.811936i	$0.301586\pi$
$272$	48.1889	2.92188
$273$	−15.2075	−0.920398
$274$	6.18897	0.373889
$275$	−37.6960	−2.27315
$276$	−12.1458	−0.731090
$277$	−16.3222	−0.980707	−0.490354	−	0.871524i	$-0.663132\pi$
$277$	−16.3222	−0.980707	−0.490354	+	0.871524i	$0.663132\pi$
$278$	45.8394	2.74926
$279$	−1.94645	−0.116531
$280$	61.0160	3.64640
$281$	−23.6098	−1.40844	−0.704221	−	0.709981i	$-0.748704\pi$
$281$	−23.6098	−1.40844	−0.704221	+	0.709981i	$0.748704\pi$
$282$	−25.7956	−1.53611
$283$	8.43369	0.501331	0.250666	−	0.968074i	$-0.419351\pi$
$283$	8.43369	0.501331	0.250666	+	0.968074i	$0.419351\pi$
$284$	51.2119	3.03887
$285$	−34.4660	−2.04159
$286$	54.0183	3.19417
$287$	13.0866	0.772478
$288$	−36.0278	−2.12296
$289$	−5.73805	−0.337532
$290$	−86.1617	−5.05959
$291$	13.0618	0.765697
$292$	−70.0256	−4.09794
$293$	11.7915	0.688867	0.344433	−	0.938811i	$-0.388071\pi$
$293$	11.7915	0.688867	0.344433	+	0.938811i	$0.388071\pi$
$294$	−19.8851	−1.15972
$295$	−37.7109	−2.19561
$296$	18.0311	1.04804
$297$	−14.7884	−0.858109
$298$	45.1716	2.61672
$299$	3.76940	0.217990
$300$	−81.6331	−4.71309
$301$	−12.3825	−0.713715
$302$	−35.3181	−2.03233
$303$	15.3480	0.881719
$304$	−65.7181	−3.76919
$305$	−28.3010	−1.62051
$306$	−15.9935	−0.914289
$307$	−2.91446	−0.166337	−0.0831685	−	0.996535i	$-0.526504\pi$
$307$	−2.91446	−0.166337	−0.0831685	+	0.996535i	$0.526504\pi$
$308$	−56.0521	−3.19386
$309$	−28.5804	−1.62588
$310$	−10.4410	−0.593010
$311$	−1.21953	−0.0691530	−0.0345765	−	0.999402i	$-0.511008\pi$
$311$	−1.21953	−0.0691530	−0.0345765	+	0.999402i	$0.511008\pi$
$312$	73.6538	4.16983
$313$	17.8807	1.01068	0.505339	−	0.862921i	$-0.331367\pi$
$313$	17.8807	1.01068	0.505339	+	0.862921i	$0.331367\pi$
$314$	−43.9818	−2.48204
$315$	−11.5579	−0.651217
$316$	93.6000	5.26541
$317$	−8.96874	−0.503735	−0.251867	−	0.967762i	$-0.581045\pi$
$317$	−8.96874	−0.503735	−0.251867	+	0.967762i	$0.581045\pi$
$318$	34.7057	1.94620
$319$	49.8362	2.79029
$320$	−94.0430	−5.25716
$321$	−31.1205	−1.73698
$322$	−5.35997	−0.298699
$323$	−15.3586	−0.854576
$324$	−60.4066	−3.35592
$325$	25.3346	1.40531
$326$	39.0758	2.16421
$327$	5.07053	0.280401
$328$	−63.3819	−3.49968
$329$	−8.30699	−0.457979
$330$	111.356	6.12995
$331$	20.4206	1.12242	0.561208	−	0.827675i	$-0.310337\pi$
$331$	20.4206	1.12242	0.561208	+	0.827675i	$0.310337\pi$
$332$	−72.4220	−3.97467
$333$	−3.41554	−0.187171
$334$	−1.12129	−0.0613545
$335$	45.1487	2.46674
$336$	−59.7757	−3.26103
$337$	1.62850	0.0887101	0.0443551	−	0.999016i	$-0.485877\pi$
$337$	1.62850	0.0887101	0.0443551	+	0.999016i	$0.485877\pi$
$338$	−0.940740	−0.0511695
$339$	40.5125	2.20034
$340$	−62.6045	−3.39521
$341$	6.03912	0.327037
$342$	21.8114	1.17942
$343$	−19.7710	−1.06753
$344$	59.9717	3.23346
$345$	7.77043	0.418346
$346$	15.5626	0.836650
$347$	−7.74019	−0.415515	−0.207758	−	0.978180i	$-0.566617\pi$
$347$	−7.74019	−0.415515	−0.207758	+	0.978180i	$0.566617\pi$
$348$	107.923	5.78531
$349$	0.800704	0.0428607	0.0214304	−	0.999770i	$-0.493178\pi$
$349$	0.800704	0.0428607	0.0214304	+	0.999770i	$0.493178\pi$
$350$	−36.0249	−1.92561
$351$	9.93891	0.530500
$352$	111.781	5.95796
$353$	5.72293	0.304601	0.152300	−	0.988334i	$-0.451332\pi$
$353$	5.72293	0.304601	0.152300	+	0.988334i	$0.451332\pi$
$354$	64.7303	3.44038
$355$	−32.7636	−1.73891
$356$	15.9650	0.846146
$357$	−13.9698	−0.739362
$358$	−46.2016	−2.44183
$359$	4.95482	0.261505	0.130753	−	0.991415i	$-0.458261\pi$
$359$	4.95482	0.261505	0.130753	+	0.991415i	$0.458261\pi$
$360$	55.9782	2.95031
$361$	1.94550	0.102395
$362$	−39.7077	−2.08699
$363$	−40.4299	−2.12202
$364$	37.6713	1.97451
$365$	44.7999	2.34493
$366$	48.5784	2.53923
$367$	−22.2599	−1.16196	−0.580978	−	0.813919i	$-0.697330\pi$
$367$	−22.2599	−1.16196	−0.580978	+	0.813919i	$0.697330\pi$
$368$	14.8163	0.772353
$369$	12.0061	0.625013
$370$	−18.3215	−0.952488
$371$	11.1763	0.580246
$372$	13.0781	0.678068
$373$	−20.1099	−1.04125	−0.520627	−	0.853784i	$-0.674302\pi$
$373$	−20.1099	−1.04125	−0.520627	+	0.853784i	$0.674302\pi$
$374$	49.6221	2.56590
$375$	14.5715	0.752471
$376$	40.2329	2.07486
$377$	−33.4937	−1.72501
$378$	−14.1328	−0.726914
$379$	−6.00408	−0.308409	−0.154204	−	0.988039i	$-0.549281\pi$
$379$	−6.00408	−0.308409	−0.154204	+	0.988039i	$0.549281\pi$
$380$	85.3776	4.37978
$381$	−2.12882	−0.109063
$382$	−30.1065	−1.54038
$383$	2.71909	0.138939	0.0694696	−	0.997584i	$-0.477869\pi$
$383$	2.71909	0.138939	0.0694696	+	0.997584i	$0.477869\pi$
$384$	71.7674	3.66237
$385$	35.8601	1.82760
$386$	12.6344	0.643073
$387$	−11.3601	−0.577468
$388$	−32.3561	−1.64263
$389$	−17.2434	−0.874277	−0.437139	−	0.899394i	$-0.644008\pi$
$389$	−17.2434	−0.874277	−0.437139	+	0.899394i	$0.644008\pi$
$390$	−74.8398	−3.78966
$391$	3.46263	0.175113
$392$	31.0143	1.56646
$393$	−39.7499	−2.00512
$394$	−62.0195	−3.12450
$395$	−59.8820	−3.01299
$396$	−51.4241	−2.58416
$397$	35.2847	1.77089	0.885444	−	0.464747i	$-0.153855\pi$
$397$	35.2847	1.77089	0.885444	+	0.464747i	$0.153855\pi$
$398$	−38.9366	−1.95172
$399$	19.0515	0.953769
$400$	99.5819	4.97910
$401$	3.98090	0.198797	0.0993984	−	0.995048i	$-0.468308\pi$
$401$	3.98090	0.198797	0.0993984	+	0.995048i	$0.468308\pi$
$402$	−77.4972	−3.86521
$403$	−4.05875	−0.202181
$404$	−38.0193	−1.89153
$405$	38.6460	1.92033
$406$	47.6270	2.36369
$407$	10.5972	0.525284
$408$	67.6596	3.34965
$409$	−17.0387	−0.842509	−0.421255	−	0.906942i	$-0.638410\pi$
$409$	−17.0387	−0.842509	−0.421255	+	0.906942i	$0.638410\pi$
$410$	64.4025	3.18061
$411$	4.95953	0.244636
$412$	70.7980	3.48797
$413$	20.8452	1.02572
$414$	−4.91742	−0.241678
$415$	46.3330	2.27440
$416$	−75.1255	−3.68333
$417$	36.7334	1.79884
$418$	−67.6728	−3.30998
$419$	9.84253	0.480839	0.240420	−	0.970669i	$-0.422715\pi$
$419$	9.84253	0.480839	0.240420	+	0.970669i	$0.422715\pi$
$420$	77.6575	3.78930
$421$	−33.1842	−1.61730	−0.808649	−	0.588291i	$-0.799801\pi$
$421$	−33.1842	−1.61730	−0.808649	+	0.588291i	$0.799801\pi$
$422$	−20.4412	−0.995064
$423$	−7.62112	−0.370551
$424$	−54.1299	−2.62878
$425$	23.2727	1.12889
$426$	56.2383	2.72476
$427$	15.6437	0.757053
$428$	77.0903	3.72630
$429$	43.2876	2.08994
$430$	−60.9374	−2.93866
$431$	34.5365	1.66356	0.831781	−	0.555104i	$-0.187321\pi$
$431$	34.5365	1.66356	0.831781	+	0.555104i	$0.187321\pi$
$432$	39.0666	1.87960
$433$	−13.1238	−0.630692	−0.315346	−	0.948977i	$-0.602120\pi$
$433$	−13.1238	−0.630692	−0.315346	+	0.948977i	$0.602120\pi$
$434$	5.77141	0.277036
$435$	−69.0456	−3.31048
$436$	−12.5605	−0.601538
$437$	−4.72221	−0.225894
$438$	−76.8985	−3.67435
$439$	16.9176	0.807435	0.403717	−	0.914884i	$-0.367718\pi$
$439$	16.9176	0.807435	0.403717	+	0.914884i	$0.367718\pi$
$440$	−173.680	−8.27987
$441$	−5.87489	−0.279757
$442$	−33.3498	−1.58629
$443$	10.8257	0.514347	0.257173	−	0.966365i	$-0.417209\pi$
$443$	10.8257	0.514347	0.257173	+	0.966365i	$0.417209\pi$
$444$	22.9489	1.08911
$445$	−10.2139	−0.484184
$446$	−72.7875	−3.44659
$447$	36.1982	1.71212
$448$	51.9835	2.45599
$449$	22.8348	1.07764	0.538821	−	0.842421i	$-0.318870\pi$
$449$	22.8348	1.07764	0.538821	+	0.842421i	$0.318870\pi$
$450$	−33.0505	−1.55801
$451$	−37.2506	−1.75406
$452$	−100.356	−4.72034
$453$	−28.3022	−1.32975
$454$	11.9041	0.558688
$455$	−24.1007	−1.12986
$456$	−92.2715	−4.32101
$457$	12.5156	0.585456	0.292728	−	0.956196i	$-0.405437\pi$
$457$	12.5156	0.585456	0.292728	+	0.956196i	$0.405437\pi$
$458$	−69.7549	−3.25943
$459$	9.13005	0.426154
$460$	−19.2486	−0.897469
$461$	−21.6962	−1.01049	−0.505245	−	0.862976i	$-0.668598\pi$
$461$	−21.6962	−1.01049	−0.505245	+	0.862976i	$0.668598\pi$
$462$	−61.5535	−2.86373
$463$	12.4322	0.577774	0.288887	−	0.957363i	$-0.406715\pi$
$463$	12.4322	0.577774	0.288887	+	0.957363i	$0.406715\pi$
$464$	−131.653	−6.11183
$465$	−8.36691	−0.388006
$466$	−47.9854	−2.22288
$467$	−23.0649	−1.06732	−0.533659	−	0.845700i	$-0.679183\pi$
$467$	−23.0649	−1.06732	−0.533659	+	0.845700i	$0.679183\pi$
$468$	34.5609	1.59758
$469$	−24.9565	−1.15238
$470$	−40.8808	−1.88569
$471$	−35.2448	−1.62399
$472$	−100.959	−4.64700
$473$	35.2464	1.62063
$474$	102.787	4.72115
$475$	−31.7385	−1.45626
$476$	34.6054	1.58614
$477$	10.2535	0.469477
$478$	57.6882	2.63860
$479$	8.86415	0.405013	0.202507	−	0.979281i	$-0.435091\pi$
$479$	8.86415	0.405013	0.202507	+	0.979281i	$0.435091\pi$
$480$	−154.868	−7.06871
$481$	−7.12212	−0.324741
$482$	35.3240	1.60896
$483$	−4.29521	−0.195439
$484$	100.151	4.55232
$485$	20.7003	0.939952
$486$	−44.1329	−2.00191
$487$	−27.3654	−1.24005	−0.620023	−	0.784583i	$-0.712877\pi$
$487$	−27.3654	−1.24005	−0.620023	+	0.784583i	$0.712877\pi$
$488$	−75.7667	−3.42980
$489$	31.3134	1.41604
$490$	−31.5138	−1.42365
$491$	26.5414	1.19780	0.598899	−	0.800825i	$-0.295605\pi$
$491$	26.5414	1.19780	0.598899	+	0.800825i	$0.295605\pi$
$492$	−80.6686	−3.63682
$493$	−30.7679	−1.38571
$494$	45.4812	2.04630
$495$	32.8993	1.47871
$496$	−15.9536	−0.716339
$497$	18.1105	0.812366
$498$	−79.5301	−3.56383
$499$	−17.7185	−0.793187	−0.396593	−	0.917994i	$-0.629808\pi$
$499$	−17.7185	−0.793187	−0.396593	+	0.917994i	$0.629808\pi$
$500$	−36.0959	−1.61426
$501$	−0.898549	−0.0401442
$502$	−47.7461	−2.13101
$503$	−9.06375	−0.404132	−0.202066	−	0.979372i	$-0.564766\pi$
$503$	−9.06375	−0.404132	−0.202066	+	0.979372i	$0.564766\pi$
$504$	−30.9427	−1.37830
$505$	24.3234	1.08238
$506$	15.2570	0.678255
$507$	−0.753861	−0.0334801
$508$	5.27343	0.233971
$509$	−6.99548	−0.310069	−0.155035	−	0.987909i	$-0.549549\pi$
$509$	−6.99548	−0.310069	−0.155035	+	0.987909i	$0.549549\pi$
$510$	−68.7491	−3.04426
$511$	−24.7637	−1.09548
$512$	−29.6769	−1.31155
$513$	−12.4512	−0.549734
$514$	−74.9732	−3.30693
$515$	−45.2940	−1.99589
$516$	76.3283	3.36017
$517$	23.6456	1.03993
$518$	10.1274	0.444974
$519$	12.4711	0.547419
$520$	116.726	5.11878
$521$	−6.17104	−0.270358	−0.135179	−	0.990821i	$-0.543161\pi$
$521$	−6.17104	−0.270358	−0.135179	+	0.990821i	$0.543161\pi$
$522$	43.6946	1.91246
$523$	−12.2388	−0.535167	−0.267584	−	0.963535i	$-0.586225\pi$
$523$	−12.2388	−0.535167	−0.267584	+	0.963535i	$0.586225\pi$
$524$	98.4666	4.30153
$525$	−28.8685	−1.25993
$526$	−45.4506	−1.98174
$527$	−3.72843	−0.162413
$528$	170.149	7.40480
$529$	−21.9354	−0.953712
$530$	55.0015	2.38911
$531$	19.1241	0.829914
$532$	−47.1936	−2.04610
$533$	25.0352	1.08440
$534$	17.5320	0.758684
$535$	−49.3196	−2.13227
$536$	120.871	5.22083
$537$	−37.0236	−1.59769
$538$	14.7011	0.633810
$539$	18.2277	0.785120
$540$	−50.7534	−2.18408
$541$	20.8770	0.897573	0.448786	−	0.893639i	$-0.351856\pi$
$541$	20.8770	0.897573	0.448786	+	0.893639i	$0.351856\pi$
$542$	−52.2821	−2.24571
$543$	−31.8198	−1.36552
$544$	−69.0115	−2.95884
$545$	8.03575	0.344214
$546$	41.3686	1.77041
$547$	−21.9355	−0.937895	−0.468947	−	0.883226i	$-0.655367\pi$
$547$	−21.9355	−0.937895	−0.468947	+	0.883226i	$0.655367\pi$
$548$	−12.2855	−0.524812
$549$	14.3521	0.612533
$550$	102.544	4.37248
$551$	41.9600	1.78756
$552$	20.8028	0.885426
$553$	33.1005	1.40758
$554$	44.4011	1.88642
$555$	−14.6819	−0.623212
$556$	−90.9943	−3.85902
$557$	12.7573	0.540545	0.270272	−	0.962784i	$-0.412886\pi$
$557$	12.7573	0.540545	0.270272	+	0.962784i	$0.412886\pi$
$558$	5.29489	0.224150
$559$	−23.6882	−1.00191
$560$	−94.7322	−4.00317
$561$	39.7647	1.67887
$562$	64.2254	2.70918
$563$	−25.0994	−1.05781	−0.528907	−	0.848680i	$-0.677398\pi$
$563$	−25.0994	−1.05781	−0.528907	+	0.848680i	$0.677398\pi$
$564$	51.2060	2.15616
$565$	64.2041	2.70109
$566$	−22.9420	−0.964326
$567$	−21.3621	−0.897122
$568$	−87.7138	−3.68039
$569$	−26.9084	−1.12806	−0.564029	−	0.825755i	$-0.690749\pi$
$569$	−26.9084	−1.12806	−0.564029	+	0.825755i	$0.690749\pi$
$570$	93.7573	3.92706
$571$	−1.98504	−0.0830714	−0.0415357	−	0.999137i	$-0.513225\pi$
$571$	−1.98504	−0.0830714	−0.0415357	+	0.999137i	$0.513225\pi$
$572$	−107.230	−4.48351
$573$	−24.1258	−1.00787
$574$	−35.5993	−1.48589
$575$	7.15550	0.298405
$576$	47.6914	1.98714
$577$	22.4339	0.933935	0.466967	−	0.884275i	$-0.345347\pi$
$577$	22.4339	0.933935	0.466967	+	0.884275i	$0.345347\pi$
$578$	15.6091	0.649254
$579$	10.1246	0.420762
$580$	171.037	7.10191
$581$	−25.6112	−1.06253
$582$	−35.5318	−1.47284
$583$	−31.8130	−1.31756
$584$	119.937	4.96304
$585$	−22.1108	−0.914171
$586$	−32.0762	−1.32506
$587$	−31.4174	−1.29673	−0.648367	−	0.761328i	$-0.724548\pi$
$587$	−31.4174	−1.29673	−0.648367	+	0.761328i	$0.724548\pi$
$588$	39.4732	1.62785
$589$	5.08469	0.209511
$590$	102.584	4.22333
$591$	−49.6993	−2.04436
$592$	−27.9948	−1.15058
$593$	−5.62879	−0.231147	−0.115573	−	0.993299i	$-0.536871\pi$
$593$	−5.62879	−0.231147	−0.115573	+	0.993299i	$0.536871\pi$
$594$	40.2286	1.65060
$595$	−22.1393	−0.907624
$596$	−89.6686	−3.67297
$597$	−31.2018	−1.27701
$598$	−10.2538	−0.419311
$599$	35.7543	1.46088	0.730441	−	0.682976i	$-0.239314\pi$
$599$	35.7543	1.46088	0.730441	+	0.682976i	$0.239314\pi$
$600$	139.818	5.70804
$601$	−23.6754	−0.965741	−0.482871	−	0.875692i	$-0.660406\pi$
$601$	−23.6754	−0.965741	−0.482871	+	0.875692i	$0.660406\pi$
$602$	33.6839	1.37285
$603$	−22.8960	−0.932396
$604$	70.1089	2.85269
$605$	−64.0731	−2.60494
$606$	−41.7509	−1.69601
$607$	−14.5738	−0.591533	−0.295767	−	0.955260i	$-0.595575\pi$
$607$	−14.5738	−0.591533	−0.295767	+	0.955260i	$0.595575\pi$
$608$	94.1153	3.81688
$609$	38.1658	1.54656
$610$	76.9868	3.11710
$611$	−15.8916	−0.642906
$612$	31.7482	1.28335
$613$	26.3632	1.06480	0.532399	−	0.846494i	$-0.321291\pi$
$613$	26.3632	1.06480	0.532399	+	0.846494i	$0.321291\pi$
$614$	7.92816	0.319955
$615$	51.6089	2.08107
$616$	96.0039	3.86811
$617$	−4.75528	−0.191440	−0.0957202	−	0.995408i	$-0.530515\pi$
$617$	−4.75528	−0.191440	−0.0957202	+	0.995408i	$0.530515\pi$
$618$	77.7467	3.12743
$619$	−18.7492	−0.753596	−0.376798	−	0.926295i	$-0.622975\pi$
$619$	−18.7492	−0.753596	−0.376798	+	0.926295i	$0.622975\pi$
$620$	20.7261	0.832381
$621$	2.80715	0.112647
$622$	3.31746	0.133018
$623$	5.64585	0.226196
$624$	−114.353	−4.57780
$625$	−11.5816	−0.463265
$626$	−48.6407	−1.94407
$627$	−54.2295	−2.16572
$628$	87.3068	3.48392
$629$	−6.54250	−0.260866
$630$	31.4409	1.25264
$631$	−21.7467	−0.865724	−0.432862	−	0.901460i	$-0.642496\pi$
$631$	−21.7467	−0.865724	−0.432862	+	0.901460i	$0.642496\pi$
$632$	−160.314	−6.37697
$633$	−16.3806	−0.651070
$634$	24.3975	0.968949
$635$	−3.37375	−0.133883
$636$	−68.8932	−2.73179
$637$	−12.2504	−0.485377
$638$	−135.569	−5.36721
$639$	16.6152	0.657286
$640$	113.737	4.49584
$641$	−23.2249	−0.917327	−0.458663	−	0.888610i	$-0.651672\pi$
$641$	−23.2249	−0.917327	−0.458663	+	0.888610i	$0.651672\pi$
$642$	84.6566	3.34113
$643$	44.8521	1.76879	0.884397	−	0.466735i	$-0.154570\pi$
$643$	44.8521	1.76879	0.884397	+	0.466735i	$0.154570\pi$
$644$	10.6399	0.419270
$645$	−48.8321	−1.92276
$646$	41.7798	1.64380
$647$	−33.0119	−1.29783	−0.648917	−	0.760860i	$-0.724778\pi$
$647$	−33.0119	−1.29783	−0.648917	+	0.760860i	$0.724778\pi$
$648$	103.462	4.06437
$649$	−59.3351	−2.32910
$650$	−68.9172	−2.70315
$651$	4.62491	0.181265
$652$	−77.5681	−3.03780
$653$	−4.03285	−0.157817	−0.0789087	−	0.996882i	$-0.525144\pi$
$653$	−4.03285	−0.157817	−0.0789087	+	0.996882i	$0.525144\pi$
$654$	−13.7933	−0.539360
$655$	−62.9954	−2.46143
$656$	98.4054	3.84208
$657$	−22.7191	−0.886356
$658$	22.5974	0.880937
$659$	−15.8076	−0.615777	−0.307889	−	0.951422i	$-0.599622\pi$
$659$	−15.8076	−0.615777	−0.307889	+	0.951422i	$0.599622\pi$
$660$	−221.049	−8.60434
$661$	37.9191	1.47488	0.737440	−	0.675412i	$-0.236034\pi$
$661$	37.9191	1.47488	0.737440	+	0.675412i	$0.236034\pi$
$662$	−55.5498	−2.15900
$663$	−26.7249	−1.03791
$664$	124.042	4.81375
$665$	30.1928	1.17083
$666$	9.29125	0.360029
$667$	−9.45997	−0.366292
$668$	2.22584	0.0861205
$669$	−58.3283	−2.25510
$670$	−122.817	−4.74485
$671$	−44.5294	−1.71904
$672$	85.6050	3.30229
$673$	−43.1863	−1.66471	−0.832355	−	0.554244i	$-0.813008\pi$
$673$	−43.1863	−1.66471	−0.832355	+	0.554244i	$0.813008\pi$
$674$	−4.42999	−0.170637
$675$	18.8672	0.726198
$676$	1.86743	0.0718243
$677$	−12.1720	−0.467810	−0.233905	−	0.972259i	$-0.575150\pi$
$677$	−12.1720	−0.467810	−0.233905	+	0.972259i	$0.575150\pi$
$678$	−110.206	−4.23242
$679$	−11.4424	−0.439117
$680$	107.227	4.11195
$681$	9.53936	0.365549
$682$	−16.4281	−0.629065
$683$	−2.88376	−0.110344	−0.0551719	−	0.998477i	$-0.517571\pi$
$683$	−2.88376	−0.110344	−0.0551719	+	0.998477i	$0.517571\pi$
$684$	−43.2970	−1.65550
$685$	7.85984	0.300309
$686$	53.7827	2.05343
$687$	−55.8981	−2.13264
$688$	−93.1108	−3.54981
$689$	21.3808	0.814543
$690$	−21.1378	−0.804702
$691$	−32.2196	−1.22569	−0.612846	−	0.790202i	$-0.709976\pi$
$691$	−32.2196	−1.22569	−0.612846	+	0.790202i	$0.709976\pi$
$692$	−30.8928	−1.17437
$693$	−18.1855	−0.690811
$694$	21.0555	0.799257
$695$	58.2149	2.20822
$696$	−184.847	−7.00661
$697$	22.9978	0.871103
$698$	−2.17814	−0.0824439
$699$	−38.4531	−1.45443
$700$	71.5119	2.70289
$701$	−8.16281	−0.308305	−0.154152	−	0.988047i	$-0.549265\pi$
$701$	−8.16281	−0.308305	−0.154152	+	0.988047i	$0.549265\pi$
$702$	−27.0367	−1.02043
$703$	8.92241	0.336515
$704$	−147.969	−5.57680
$705$	−32.7598	−1.23381
$706$	−15.5680	−0.585909
$707$	−13.4451	−0.505654
$708$	−128.494	−4.82910
$709$	10.2899	0.386445	0.193223	−	0.981155i	$-0.438106\pi$
$709$	10.2899	0.386445	0.193223	+	0.981155i	$0.438106\pi$
$710$	89.1262	3.34485
$711$	30.3675	1.13887
$712$	−27.3443	−1.02477
$713$	−1.14635	−0.0429313
$714$	38.0019	1.42219
$715$	68.6020	2.56557
$716$	91.7133	3.42749
$717$	46.2284	1.72643
$718$	−13.4785	−0.503014
$719$	14.6125	0.544953	0.272477	−	0.962162i	$-0.412157\pi$
$719$	14.6125	0.544953	0.272477	+	0.962162i	$0.412157\pi$
$720$	−86.9106	−3.23897
$721$	25.0369	0.932421
$722$	−5.29230	−0.196959
$723$	28.3069	1.05274
$724$	78.8225	2.92941
$725$	−63.5815	−2.36136
$726$	109.981	4.08177
$727$	−6.44215	−0.238926	−0.119463	−	0.992839i	$-0.538117\pi$
$727$	−6.44215	−0.238926	−0.119463	+	0.992839i	$0.538117\pi$
$728$	−64.5219	−2.39134
$729$	−1.80633	−0.0669012
$730$	−121.868	−4.51055
$731$	−21.7604	−0.804837
$732$	−96.4313	−3.56420
$733$	5.62289	0.207686	0.103843	−	0.994594i	$-0.466886\pi$
$733$	5.62289	0.207686	0.103843	+	0.994594i	$0.466886\pi$
$734$	60.5532	2.23506
$735$	−25.2535	−0.931490
$736$	−21.2185	−0.782124
$737$	71.0379	2.61671
$738$	−32.6600	−1.20223
$739$	−10.4189	−0.383266	−0.191633	−	0.981467i	$-0.561378\pi$
$739$	−10.4189	−0.383266	−0.191633	+	0.981467i	$0.561378\pi$
$740$	36.3694	1.33696
$741$	36.4464	1.33889
$742$	−30.4028	−1.11612
$743$	−30.0844	−1.10369	−0.551845	−	0.833947i	$-0.686076\pi$
$743$	−30.0844	−1.10369	−0.551845	+	0.833947i	$0.686076\pi$
$744$	−22.3997	−0.821212
$745$	57.3667	2.10176
$746$	54.7048	2.00288
$747$	−23.4965	−0.859694
$748$	−98.5032	−3.60164
$749$	27.2620	0.996133
$750$	−39.6387	−1.44740
$751$	13.4593	0.491136	0.245568	−	0.969379i	$-0.421026\pi$
$751$	13.4593	0.491136	0.245568	+	0.969379i	$0.421026\pi$
$752$	−62.4648	−2.27786
$753$	−38.2613	−1.39432
$754$	91.1124	3.31812
$755$	−44.8532	−1.63237
$756$	28.0546	1.02034
$757$	−24.4017	−0.886896	−0.443448	−	0.896300i	$-0.646245\pi$
$757$	−24.4017	−0.886896	−0.443448	+	0.896300i	$0.646245\pi$
$758$	16.3328	0.593234
$759$	12.2262	0.443781
$760$	−146.232	−5.30438
$761$	−18.9193	−0.685823	−0.342912	−	0.939368i	$-0.611413\pi$
$761$	−18.9193	−0.685823	−0.342912	+	0.939368i	$0.611413\pi$
$762$	5.79101	0.209786
$763$	−4.44186	−0.160806
$764$	59.7634	2.16216
$765$	−20.3114	−0.734359
$766$	−7.39670	−0.267254
$767$	39.8777	1.43990
$768$	−76.5462	−2.76212
$769$	−8.25170	−0.297564	−0.148782	−	0.988870i	$-0.547535\pi$
$769$	−8.25170	−0.297564	−0.148782	+	0.988870i	$0.547535\pi$
$770$	−97.5498	−3.51545
$771$	−60.0798	−2.16372
$772$	−25.0801	−0.902652
$773$	−39.1544	−1.40829	−0.704143	−	0.710058i	$-0.748668\pi$
$773$	−39.1544	−1.40829	−0.704143	+	0.710058i	$0.748668\pi$
$774$	30.9028	1.11078
$775$	−7.70477	−0.276764
$776$	55.4183	1.98940
$777$	8.11561	0.291146
$778$	46.9071	1.68170
$779$	−31.3635	−1.12371
$780$	148.562	5.31937
$781$	−51.5509	−1.84464
$782$	−9.41934	−0.336835
$783$	−24.9435	−0.891406
$784$	−48.1522	−1.71972
$785$	−55.8558	−1.99358
$786$	108.131	3.85690
$787$	11.6153	0.414042	0.207021	−	0.978336i	$-0.433623\pi$
$787$	11.6153	0.414042	0.207021	+	0.978336i	$0.433623\pi$
$788$	123.113	4.38571
$789$	−36.4218	−1.29665
$790$	162.896	5.79558
$791$	−35.4896	−1.26187
$792$	88.0772	3.12969
$793$	29.9271	1.06274
$794$	−95.9844	−3.40636
$795$	44.0754	1.56319
$796$	77.2918	2.73953
$797$	−53.3132	−1.88845	−0.944225	−	0.329301i	$-0.893187\pi$
$797$	−53.3132	−1.88845	−0.944225	+	0.329301i	$0.893187\pi$
$798$	−51.8256	−1.83460
$799$	−14.5983	−0.516451
$800$	−142.612	−5.04209
$801$	5.17969	0.183015
$802$	−10.8292	−0.382392
$803$	70.4891	2.48751
$804$	153.837	5.42542
$805$	−6.80702	−0.239916
$806$	11.0409	0.388901
$807$	11.7807	0.414701
$808$	65.1181	2.29085
$809$	5.81970	0.204610	0.102305	−	0.994753i	$-0.467378\pi$
$809$	5.81970	0.204610	0.102305	+	0.994753i	$0.467378\pi$
$810$	−105.128	−3.69382
$811$	4.60268	0.161622	0.0808109	−	0.996729i	$-0.474249\pi$
$811$	4.60268	0.161622	0.0808109	+	0.996729i	$0.474249\pi$
$812$	−94.5427	−3.31780
$813$	−41.8962	−1.46936
$814$	−28.8274	−1.01040
$815$	49.6253	1.73830
$816$	−105.047	−3.67737
$817$	29.6760	1.03823
$818$	46.3501	1.62059
$819$	12.2220	0.427073
$820$	−127.843	−4.46448
$821$	46.1777	1.61161	0.805806	−	0.592180i	$-0.201732\pi$
$821$	46.1777	1.61161	0.805806	+	0.592180i	$0.201732\pi$
$822$	−13.4913	−0.470564
$823$	−6.24898	−0.217826	−0.108913	−	0.994051i	$-0.534737\pi$
$823$	−6.24898	−0.217826	−0.108913	+	0.994051i	$0.534737\pi$
$824$	−121.260	−4.22430
$825$	82.1734	2.86091
$826$	−56.7048	−1.97301
$827$	−31.6381	−1.10016	−0.550082	−	0.835111i	$-0.685404\pi$
$827$	−31.6381	−1.10016	−0.550082	+	0.835111i	$0.685404\pi$
$828$	9.76140	0.339232
$829$	−4.11550	−0.142937	−0.0714687	−	0.997443i	$-0.522769\pi$
$829$	−4.11550	−0.142937	−0.0714687	+	0.997443i	$0.522769\pi$
$830$	−126.039	−4.37487
$831$	35.5808	1.23428
$832$	99.4465	3.44769
$833$	−11.2534	−0.389907
$834$	−99.9252	−3.46013
$835$	−1.42402	−0.0492801
$836$	134.335	4.64607
$837$	−3.02263	−0.104477
$838$	−26.7745	−0.924909
$839$	−21.0486	−0.726680	−0.363340	−	0.931657i	$-0.618364\pi$
$839$	−21.0486	−0.726680	−0.363340	+	0.931657i	$0.618364\pi$
$840$	−133.009	−4.58924
$841$	55.0583	1.89856
$842$	90.2705	3.11093
$843$	51.4670	1.77262
$844$	40.5772	1.39673
$845$	−1.19472	−0.0410995
$846$	20.7316	0.712767
$847$	35.4172	1.21695
$848$	84.0409	2.88598
$849$	−18.3846	−0.630958
$850$	−63.3084	−2.17146
$851$	−2.01158	−0.0689559
$852$	−111.637	−3.82461
$853$	4.96594	0.170030	0.0850152	−	0.996380i	$-0.472906\pi$
$853$	4.96594	0.170030	0.0850152	+	0.996380i	$0.472906\pi$
$854$	−42.5554	−1.45622
$855$	27.6999	0.947316
$856$	−132.037	−4.51294
$857$	−26.2759	−0.897567	−0.448784	−	0.893640i	$-0.648143\pi$
$857$	−26.2759	−0.897567	−0.448784	+	0.893640i	$0.648143\pi$
$858$	−117.754	−4.02007
$859$	−41.1147	−1.40282	−0.701408	−	0.712760i	$-0.747445\pi$
$859$	−41.1147	−1.40282	−0.701408	+	0.712760i	$0.747445\pi$
$860$	120.965	4.12486
$861$	−28.5275	−0.972214
$862$	−93.9490	−3.19991
$863$	19.5371	0.665051	0.332525	−	0.943094i	$-0.392099\pi$
$863$	19.5371	0.665051	0.332525	+	0.943094i	$0.392099\pi$
$864$	−55.9475	−1.90337
$865$	19.7641	0.672000
$866$	35.7006	1.21315
$867$	12.5084	0.424806
$868$	−11.4566	−0.388863
$869$	−94.2195	−3.19618
$870$	187.824	6.36782
$871$	−47.7429	−1.61771
$872$	21.5131	0.728526
$873$	−10.4976	−0.355290
$874$	12.8457	0.434514
$875$	−12.7649	−0.431532
$876$	152.649	5.15752
$877$	−22.2330	−0.750755	−0.375377	−	0.926872i	$-0.622487\pi$
$877$	−22.2330	−0.750755	−0.375377	+	0.926872i	$0.622487\pi$
$878$	−46.0208	−1.55313
$879$	−25.7043	−0.866983
$880$	269.652	9.08997
$881$	7.57763	0.255297	0.127648	−	0.991819i	$-0.459257\pi$
$881$	7.57763	0.255297	0.127648	+	0.991819i	$0.459257\pi$
$882$	15.9814	0.538120
$883$	26.2406	0.883068	0.441534	−	0.897245i	$-0.354434\pi$
$883$	26.2406	0.883068	0.441534	+	0.897245i	$0.354434\pi$
$884$	66.2017	2.22660
$885$	82.2058	2.76332
$886$	−29.4491	−0.989362
$887$	−34.0453	−1.14313	−0.571565	−	0.820557i	$-0.693663\pi$
$887$	−34.0453	−1.14313	−0.571565	+	0.820557i	$0.693663\pi$
$888$	−39.3060	−1.31902
$889$	1.86488	0.0625462
$890$	27.7846	0.931343
$891$	60.8064	2.03709
$892$	144.488	4.83782
$893$	19.9086	0.666216
$894$	−98.4694	−3.29331
$895$	−58.6749	−1.96129
$896$	−62.8694	−2.10032
$897$	−8.21691	−0.274355
$898$	−62.1172	−2.07288
$899$	10.1861	0.339727
$900$	65.6074	2.18691
$901$	19.6407	0.654328
$902$	101.332	3.37399
$903$	26.9926	0.898257
$904$	171.886	5.71683
$905$	−50.4278	−1.67628
$906$	76.9899	2.55782
$907$	−1.69564	−0.0563029	−0.0281515	−	0.999604i	$-0.508962\pi$
$907$	−1.69564	−0.0563029	−0.0281515	+	0.999604i	$0.508962\pi$
$908$	−23.6305	−0.784205
$909$	−12.3350	−0.409125
$910$	65.5609	2.17332
$911$	−24.4284	−0.809349	−0.404674	−	0.914461i	$-0.632615\pi$
$911$	−24.4284	−0.809349	−0.404674	+	0.914461i	$0.632615\pi$
$912$	143.259	4.74377
$913$	72.9013	2.41268
$914$	−34.0461	−1.12614
$915$	61.6933	2.03952
$916$	138.468	4.57512
$917$	34.8215	1.14991
$918$	−24.8363	−0.819721
$919$	17.0572	0.562666	0.281333	−	0.959610i	$-0.409223\pi$
$919$	17.0572	0.562666	0.281333	+	0.959610i	$0.409223\pi$
$920$	32.9682	1.08693
$921$	6.35323	0.209346
$922$	59.0197	1.94371
$923$	34.6461	1.14039
$924$	122.188	4.01969
$925$	−13.5200	−0.444535
$926$	−33.8192	−1.11137
$927$	22.9697	0.754423
$928$	188.541	6.18915
$929$	−2.89145	−0.0948653	−0.0474327	−	0.998874i	$-0.515104\pi$
$929$	−2.89145	−0.0948653	−0.0474327	+	0.998874i	$0.515104\pi$
$930$	22.7604	0.746342
$931$	15.3469	0.502976
$932$	95.2542	3.12016
$933$	2.65844	0.0870335
$934$	62.7432	2.05302
$935$	63.0189	2.06094
$936$	−59.1946	−1.93484
$937$	49.8120	1.62729	0.813644	−	0.581364i	$-0.197481\pi$
$937$	49.8120	1.62729	0.813644	+	0.581364i	$0.197481\pi$
$938$	67.8888	2.21665
$939$	−38.9782	−1.27200
$940$	81.1511	2.64686
$941$	43.9267	1.43197	0.715984	−	0.698117i	$-0.245978\pi$
$941$	43.9267	1.43197	0.715984	+	0.698117i	$0.245978\pi$
$942$	95.8759	3.12380
$943$	7.07096	0.230262
$944$	156.746	5.10165
$945$	−17.9483	−0.583859
$946$	−95.8801	−3.11733
$947$	1.13382	0.0368441	0.0184220	−	0.999830i	$-0.494136\pi$
$947$	1.13382	0.0368441	0.0184220	+	0.999830i	$0.494136\pi$
$948$	−204.038	−6.62686
$949$	−47.3740	−1.53783
$950$	86.3376	2.80116
$951$	19.5509	0.633983
$952$	−59.2709	−1.92098
$953$	−21.9242	−0.710195	−0.355097	−	0.934829i	$-0.615552\pi$
$953$	−21.9242	−0.710195	−0.355097	+	0.934829i	$0.615552\pi$
$954$	−27.8925	−0.903054
$955$	−38.2345	−1.23724
$956$	−114.515	−3.70368
$957$	−108.638	−3.51176
$958$	−24.1130	−0.779056
$959$	−4.34463	−0.140295
$960$	205.004	6.61648
$961$	−29.7656	−0.960182
$962$	19.3742	0.624649
$963$	25.0111	0.805972
$964$	−70.1205	−2.25843
$965$	16.0453	0.516518
$966$	11.6842	0.375932
$967$	−59.0555	−1.89910	−0.949548	−	0.313623i	$-0.898457\pi$
$967$	−59.0555	−1.89910	−0.949548	+	0.313623i	$0.898457\pi$
$968$	−171.535	−5.51334
$969$	33.4802	1.07554
$970$	−56.3107	−1.80803
$971$	20.2359	0.649400	0.324700	−	0.945817i	$-0.394737\pi$
$971$	20.2359	0.649400	0.324700	+	0.945817i	$0.394737\pi$
$972$	87.6068	2.80999
$973$	−32.1790	−1.03161
$974$	74.4418	2.38527
$975$	−55.2267	−1.76867
$976$	117.634	3.76537
$977$	5.50841	0.176230	0.0881148	−	0.996110i	$-0.471916\pi$
$977$	5.50841	0.176230	0.0881148	+	0.996110i	$0.471916\pi$
$978$	−85.1813	−2.72380
$979$	−16.0707	−0.513622
$980$	62.5569	1.99831
$981$	−4.07512	−0.130109
$982$	−72.2002	−2.30400
$983$	27.1313	0.865353	0.432677	−	0.901549i	$-0.357569\pi$
$983$	27.1313	0.865353	0.432677	+	0.901549i	$0.357569\pi$
$984$	138.166	4.40457
$985$	−78.7632	−2.50961
$986$	83.6973	2.66547
$987$	18.1084	0.576396
$988$	−90.2833	−2.87229
$989$	−6.69051	−0.212746
$990$	−89.4955	−2.84435
$991$	34.6690	1.10130	0.550648	−	0.834737i	$-0.314381\pi$
$991$	34.6690	1.10130	0.550648	+	0.834737i	$0.314381\pi$
$992$	22.8473	0.725401
$993$	−44.5148	−1.41263
$994$	−49.2657	−1.56261
$995$	−49.4485	−1.56762
$996$	157.873	5.00238
$997$	−39.8374	−1.26166	−0.630831	−	0.775920i	$-0.717286\pi$
$997$	−39.8374	−1.26166	−0.630831	+	0.775920i	$0.717286\pi$
$998$	48.1992	1.52572
$999$	−5.30399	−0.167811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.b.1.9	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.b.1.9	✓	243	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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72028 q^{2} -2.17990 q^{3} +5.39995 q^{4} -3.45469 q^{5} +5.92994 q^{6} +1.90963 q^{7} -9.24882 q^{8} +1.75196 q^{9} +O(q^{10})\)	\(q-2.72028 q^{2} -2.17990 q^{3} +5.39995 q^{4} -3.45469 q^{5} +5.92994 q^{6} +1.90963 q^{7} -9.24882 q^{8} +1.75196 q^{9} +9.39775 q^{10} -5.43569 q^{11} -11.7713 q^{12} +3.65319 q^{13} -5.19472 q^{14} +7.53088 q^{15} +14.3595 q^{16} +3.35588 q^{17} -4.76582 q^{18} -4.57662 q^{19} -18.6552 q^{20} -4.16279 q^{21} +14.7866 q^{22} +1.03181 q^{23} +20.1615 q^{24} +6.93490 q^{25} -9.93772 q^{26} +2.72061 q^{27} +10.3119 q^{28} -9.16833 q^{29} -20.4861 q^{30} -1.11101 q^{31} -20.5643 q^{32} +11.8492 q^{33} -9.12896 q^{34} -6.59717 q^{35} +9.46047 q^{36} -1.94956 q^{37} +12.4497 q^{38} -7.96359 q^{39} +31.9518 q^{40} +6.85297 q^{41} +11.3240 q^{42} -6.48425 q^{43} -29.3524 q^{44} -6.05247 q^{45} -2.80681 q^{46} -4.35006 q^{47} -31.3023 q^{48} -3.35333 q^{49} -18.8649 q^{50} -7.31548 q^{51} +19.7270 q^{52} +5.85263 q^{53} -7.40083 q^{54} +18.7786 q^{55} -17.6618 q^{56} +9.97658 q^{57} +24.9405 q^{58} +10.9158 q^{59} +40.6663 q^{60} +8.19204 q^{61} +3.02227 q^{62} +3.34558 q^{63} +27.2218 q^{64} -12.6207 q^{65} -32.2333 q^{66} -13.0688 q^{67} +18.1216 q^{68} -2.24924 q^{69} +17.9462 q^{70} +9.48379 q^{71} -16.2035 q^{72} -12.9678 q^{73} +5.30336 q^{74} -15.1174 q^{75} -24.7135 q^{76} -10.3801 q^{77} +21.6632 q^{78} +17.3335 q^{79} -49.6077 q^{80} -11.1865 q^{81} -18.6420 q^{82} -13.4116 q^{83} -22.4788 q^{84} -11.5935 q^{85} +17.6390 q^{86} +19.9860 q^{87} +50.2737 q^{88} +2.95652 q^{89} +16.4644 q^{90} +6.97623 q^{91} +5.57172 q^{92} +2.42190 q^{93} +11.8334 q^{94} +15.8108 q^{95} +44.8282 q^{96} -5.99193 q^{97} +9.12201 q^{98} -9.52308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9} - 24 q^{10} - 37 q^{11} - 74 q^{12} - 113 q^{13} - 35 q^{14} - 34 q^{15} + 218 q^{16} - 125 q^{17} - 108 q^{18} - 46 q^{19} - 157 q^{20} - 113 q^{21} - 16 q^{22} - 60 q^{23} - 49 q^{24} + 208 q^{25} - 52 q^{26} - 90 q^{27} - 70 q^{28} - 137 q^{29} - 26 q^{30} - 36 q^{31} - 258 q^{32} - 153 q^{33} - 23 q^{34} - 77 q^{35} + 180 q^{36} - 108 q^{37} - 122 q^{38} - 32 q^{39} - 57 q^{40} - 186 q^{41} - 28 q^{42} - 54 q^{43} - 90 q^{44} - 233 q^{45} - 42 q^{46} - 188 q^{47} - 149 q^{48} + 189 q^{49} - 146 q^{50} - 34 q^{51} - 195 q^{52} - 196 q^{53} - 36 q^{54} - 57 q^{55} - 63 q^{56} - 76 q^{57} - 24 q^{58} - 137 q^{59} - 73 q^{60} - 96 q^{61} - 167 q^{62} - 113 q^{63} + 224 q^{64} - 131 q^{65} - 11 q^{66} - 71 q^{67} - 260 q^{68} - 162 q^{69} - 48 q^{70} - 77 q^{71} - 290 q^{72} - 160 q^{73} - 34 q^{74} - 100 q^{75} - 84 q^{76} - 416 q^{77} - 59 q^{78} - 17 q^{79} - 268 q^{80} + 147 q^{81} - 28 q^{82} - 238 q^{83} - 184 q^{84} - 108 q^{85} - 61 q^{86} - 127 q^{87} - 47 q^{88} - 183 q^{89} - 56 q^{90} - 14 q^{91} - 109 q^{92} - 206 q^{93} + q^{94} - 84 q^{95} - 54 q^{96} - 127 q^{97} - 294 q^{98} - 66 q^{99}+O(q^{100}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9 - 24 * q^10 - 37 * q^11 - 74 * q^12 - 113 * q^13 - 35 * q^14 - 34 * q^15 + 218 * q^16 - 125 * q^17 - 108 * q^18 - 46 * q^19 - 157 * q^20 - 113 * q^21 - 16 * q^22 - 60 * q^23 - 49 * q^24 + 208 * q^25 - 52 * q^26 - 90 * q^27 - 70 * q^28 - 137 * q^29 - 26 * q^30 - 36 * q^31 - 258 * q^32 - 153 * q^33 - 23 * q^34 - 77 * q^35 + 180 * q^36 - 108 * q^37 - 122 * q^38 - 32 * q^39 - 57 * q^40 - 186 * q^41 - 28 * q^42 - 54 * q^43 - 90 * q^44 - 233 * q^45 - 42 * q^46 - 188 * q^47 - 149 * q^48 + 189 * q^49 - 146 * q^50 - 34 * q^51 - 195 * q^52 - 196 * q^53 - 36 * q^54 - 57 * q^55 - 63 * q^56 - 76 * q^57 - 24 * q^58 - 137 * q^59 - 73 * q^60 - 96 * q^61 - 167 * q^62 - 113 * q^63 + 224 * q^64 - 131 * q^65 - 11 * q^66 - 71 * q^67 - 260 * q^68 - 162 * q^69 - 48 * q^70 - 77 * q^71 - 290 * q^72 - 160 * q^73 - 34 * q^74 - 100 * q^75 - 84 * q^76 - 416 * q^77 - 59 * q^78 - 17 * q^79 - 268 * q^80 + 147 * q^81 - 28 * q^82 - 238 * q^83 - 184 * q^84 - 108 * q^85 - 61 * q^86 - 127 * q^87 - 47 * q^88 - 183 * q^89 - 56 * q^90 - 14 * q^91 - 109 * q^92 - 206 * q^93 + q^94 - 84 * q^95 - 54 * q^96 - 127 * q^97 - 294 * q^98 - 66 * q^99

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