LMFDB - Embedded newform 6043.2.a.c.1.20

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:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-2.43000 q^{2} -2.97934 q^{3} +3.90490 q^{4} +2.39158 q^{5} +7.23980 q^{6} -4.31478 q^{7} -4.62892 q^{8} +5.87647 q^{9} +O(q^{10})$	\(q-2.43000 q^{2} -2.97934 q^{3} +3.90490 q^{4} +2.39158 q^{5} +7.23980 q^{6} -4.31478 q^{7} -4.62892 q^{8} +5.87647 q^{9} -5.81153 q^{10} -5.44754 q^{11} -11.6340 q^{12} -0.235452 q^{13} +10.4849 q^{14} -7.12532 q^{15} +3.43847 q^{16} +4.43064 q^{17} -14.2798 q^{18} -2.63284 q^{19} +9.33888 q^{20} +12.8552 q^{21} +13.2375 q^{22} +4.49112 q^{23} +13.7911 q^{24} +0.719641 q^{25} +0.572148 q^{26} -8.56998 q^{27} -16.8488 q^{28} -8.50593 q^{29} +17.3145 q^{30} -2.66272 q^{31} +0.902352 q^{32} +16.2301 q^{33} -10.7665 q^{34} -10.3191 q^{35} +22.9471 q^{36} +7.18619 q^{37} +6.39781 q^{38} +0.701491 q^{39} -11.0704 q^{40} +0.00669624 q^{41} -31.2382 q^{42} -0.412958 q^{43} -21.2721 q^{44} +14.0540 q^{45} -10.9134 q^{46} -8.76513 q^{47} -10.2444 q^{48} +11.6173 q^{49} -1.74873 q^{50} -13.2004 q^{51} -0.919417 q^{52} -11.7809 q^{53} +20.8251 q^{54} -13.0282 q^{55} +19.9728 q^{56} +7.84413 q^{57} +20.6694 q^{58} -6.58295 q^{59} -27.8237 q^{60} -1.95665 q^{61} +6.47040 q^{62} -25.3557 q^{63} -9.06966 q^{64} -0.563101 q^{65} -39.4391 q^{66} +4.07697 q^{67} +17.3012 q^{68} -13.3806 q^{69} +25.0755 q^{70} -14.9096 q^{71} -27.2017 q^{72} -7.52581 q^{73} -17.4625 q^{74} -2.14406 q^{75} -10.2810 q^{76} +23.5049 q^{77} -1.70462 q^{78} +10.8880 q^{79} +8.22337 q^{80} +7.90349 q^{81} -0.0162719 q^{82} +17.0869 q^{83} +50.1983 q^{84} +10.5962 q^{85} +1.00349 q^{86} +25.3421 q^{87} +25.2162 q^{88} +9.00022 q^{89} -34.1513 q^{90} +1.01592 q^{91} +17.5374 q^{92} +7.93314 q^{93} +21.2993 q^{94} -6.29665 q^{95} -2.68841 q^{96} +17.8253 q^{97} -28.2301 q^{98} -32.0123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * 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 $

$2$	−2.43000	−1.71827	−0.859135	−	0.511749i	$-0.828998\pi$
$2$	−2.43000	−1.71827	−0.859135	+	0.511749i	$0.828998\pi$
$3$	−2.97934	−1.72012	−0.860062	−	0.510190i	$-0.829575\pi$
$3$	−2.97934	−1.72012	−0.860062	+	0.510190i	$0.829575\pi$
$4$	3.90490	1.95245
$5$	2.39158	1.06955	0.534773	−	0.844996i	$-0.320397\pi$
$5$	2.39158	1.06955	0.534773	+	0.844996i	$0.320397\pi$
$6$	7.23980	2.95564
$7$	−4.31478	−1.63083	−0.815417	−	0.578874i	$-0.803492\pi$
$7$	−4.31478	−1.63083	−0.815417	+	0.578874i	$0.803492\pi$
$8$	−4.62892	−1.63657
$9$	5.87647	1.95882
$10$	−5.81153	−1.83777
$11$	−5.44754	−1.64249	−0.821247	−	0.570572i	$-0.806721\pi$
$11$	−5.44754	−1.64249	−0.821247	+	0.570572i	$0.806721\pi$
$12$	−11.6340	−3.35846
$13$	−0.235452	−0.0653026	−0.0326513	−	0.999467i	$-0.510395\pi$
$13$	−0.235452	−0.0653026	−0.0326513	+	0.999467i	$0.510395\pi$
$14$	10.4849	2.80221
$15$	−7.12532	−1.83975
$16$	3.43847	0.859618
$17$	4.43064	1.07459	0.537294	−	0.843395i	$-0.319447\pi$
$17$	4.43064	1.07459	0.537294	+	0.843395i	$0.319447\pi$
$18$	−14.2798	−3.36579
$19$	−2.63284	−0.604015	−0.302008	−	0.953305i	$-0.597657\pi$
$19$	−2.63284	−0.604015	−0.302008	+	0.953305i	$0.597657\pi$
$20$	9.33888	2.08824
$21$	12.8552	2.80524
$22$	13.2375	2.82225
$23$	4.49112	0.936463	0.468232	−	0.883606i	$-0.344891\pi$
$23$	4.49112	0.936463	0.468232	+	0.883606i	$0.344891\pi$
$24$	13.7911	2.81510
$25$	0.719641	0.143928
$26$	0.572148	0.112207
$27$	−8.56998	−1.64929
$28$	−16.8488	−3.18413
$29$	−8.50593	−1.57951	−0.789756	−	0.613422i	$-0.789793\pi$
$29$	−8.50593	−1.57951	−0.789756	+	0.613422i	$0.789793\pi$
$30$	17.3145	3.16119
$31$	−2.66272	−0.478238	−0.239119	−	0.970990i	$-0.576859\pi$
$31$	−2.66272	−0.478238	−0.239119	+	0.970990i	$0.576859\pi$
$32$	0.902352	0.159515
$33$	16.2301	2.82529
$34$	−10.7665	−1.84643
$35$	−10.3191	−1.74425
$36$	22.9471	3.82451
$37$	7.18619	1.18140	0.590701	−	0.806890i	$-0.298851\pi$
$37$	7.18619	1.18140	0.590701	+	0.806890i	$0.298851\pi$
$38$	6.39781	1.03786
$39$	0.701491	0.112328
$40$	−11.0704	−1.75039
$41$	0.00669624	0.00104578	0.000522889	−	1.00000i	$-0.499834\pi$
$41$	0.00669624	0.00104578	0.000522889		1.00000i	$0.499834\pi$
$42$	−31.2382	−4.82015
$43$	−0.412958	−0.0629756	−0.0314878	−	0.999504i	$-0.510025\pi$
$43$	−0.412958	−0.0629756	−0.0314878	+	0.999504i	$0.510025\pi$
$44$	−21.2721	−3.20689
$45$	14.0540	2.09505
$46$	−10.9134	−1.60910
$47$	−8.76513	−1.27853	−0.639263	−	0.768989i	$-0.720760\pi$
$47$	−8.76513	−1.27853	−0.639263	+	0.768989i	$0.720760\pi$
$48$	−10.2444	−1.47865
$49$	11.6173	1.65962
$50$	−1.74873	−0.247308
$51$	−13.2004	−1.84842
$52$	−0.919417	−0.127500
$53$	−11.7809	−1.61823	−0.809117	−	0.587647i	$-0.800054\pi$
$53$	−11.7809	−1.61823	−0.809117	+	0.587647i	$0.800054\pi$
$54$	20.8251	2.83393
$55$	−13.0282	−1.75672
$56$	19.9728	2.66897
$57$	7.84413	1.03898
$58$	20.6694	2.71403
$59$	−6.58295	−0.857027	−0.428514	−	0.903535i	$-0.640963\pi$
$59$	−6.58295	−0.857027	−0.428514	+	0.903535i	$0.640963\pi$
$60$	−27.8237	−3.59202
$61$	−1.95665	−0.250523	−0.125262	−	0.992124i	$-0.539977\pi$
$61$	−1.95665	−0.250523	−0.125262	+	0.992124i	$0.539977\pi$
$62$	6.47040	0.821742
$63$	−25.3557	−3.19452
$64$	−9.06966	−1.13371
$65$	−0.563101	−0.0698441
$66$	−39.4391	−4.85462
$67$	4.07697	0.498081	0.249041	−	0.968493i	$-0.419885\pi$
$67$	4.07697	0.498081	0.249041	+	0.968493i	$0.419885\pi$
$68$	17.3012	2.09808
$69$	−13.3806	−1.61083
$70$	25.0755	2.99710
$71$	−14.9096	−1.76944	−0.884720	−	0.466123i	$-0.845651\pi$
$71$	−14.9096	−1.76944	−0.884720	+	0.466123i	$0.845651\pi$
$72$	−27.2017	−3.20575
$73$	−7.52581	−0.880829	−0.440415	−	0.897794i	$-0.645169\pi$
$73$	−7.52581	−0.880829	−0.440415	+	0.897794i	$0.645169\pi$
$74$	−17.4625	−2.02997
$75$	−2.14406	−0.247574
$76$	−10.2810	−1.17931
$77$	23.5049	2.67864
$78$	−1.70462	−0.193011
$79$	10.8880	1.22499	0.612496	−	0.790474i	$-0.290166\pi$
$79$	10.8880	1.22499	0.612496	+	0.790474i	$0.290166\pi$
$80$	8.22337	0.919401
$81$	7.90349	0.878165
$82$	−0.0162719	−0.00179693
$83$	17.0869	1.87553	0.937763	−	0.347276i	$-0.112893\pi$
$83$	17.0869	1.87553	0.937763	+	0.347276i	$0.112893\pi$
$84$	50.1983	5.47709
$85$	10.5962	1.14932
$86$	1.00349	0.108209
$87$	25.3421	2.71695
$88$	25.2162	2.68806
$89$	9.00022	0.954022	0.477011	−	0.878897i	$-0.341720\pi$
$89$	9.00022	0.954022	0.477011	+	0.878897i	$0.341720\pi$
$90$	−34.1513	−3.59986
$91$	1.01592	0.106498
$92$	17.5374	1.82840
$93$	7.93314	0.822628
$94$	21.2993	2.19685
$95$	−6.29665	−0.646022
$96$	−2.68841	−0.274385
$97$	17.8253	1.80989	0.904944	−	0.425532i	$-0.139913\pi$
$97$	17.8253	1.80989	0.904944	+	0.425532i	$0.139913\pi$
$98$	−28.2301	−2.85168
$99$	−32.0123	−3.21736
$100$	2.81013	0.281013
$101$	−13.0929	−1.30279	−0.651396	−	0.758738i	$-0.725816\pi$
$101$	−13.0929	−1.30279	−0.651396	+	0.758738i	$0.725816\pi$
$102$	32.0769	3.17609
$103$	−11.2950	−1.11293	−0.556464	−	0.830871i	$-0.687842\pi$
$103$	−11.2950	−1.11293	−0.556464	+	0.830871i	$0.687842\pi$
$104$	1.08989	0.106872
$105$	30.7442	3.00033
$106$	28.6277	2.78056
$107$	12.1090	1.17062	0.585311	−	0.810809i	$-0.300972\pi$
$107$	12.1090	1.17062	0.585311	+	0.810809i	$0.300972\pi$
$108$	−33.4650	−3.22017
$109$	−11.2234	−1.07501	−0.537504	−	0.843261i	$-0.680633\pi$
$109$	−11.2234	−1.07501	−0.537504	+	0.843261i	$0.680633\pi$
$110$	31.6586	3.01853
$111$	−21.4101	−2.03216
$112$	−14.8363	−1.40189
$113$	−7.43288	−0.699226	−0.349613	−	0.936894i	$-0.613687\pi$
$113$	−7.43288	−0.699226	−0.349613	+	0.936894i	$0.613687\pi$
$114$	−19.0613	−1.78525
$115$	10.7409	1.00159
$116$	−33.2148	−3.08392
$117$	−1.38363	−0.127916
$118$	15.9966	1.47260
$119$	−19.1172	−1.75247
$120$	32.9825	3.01088
$121$	18.6757	1.69779
$122$	4.75466	0.430467
$123$	−0.0199504	−0.00179887
$124$	−10.3976	−0.933737
$125$	−10.2368	−0.915608
$126$	61.6143	5.48904
$127$	−7.91311	−0.702175	−0.351087	−	0.936343i	$-0.614188\pi$
$127$	−7.91311	−0.702175	−0.351087	+	0.936343i	$0.614188\pi$
$128$	20.2346	1.78850
$129$	1.23034	0.108326
$130$	1.36834	0.120011
$131$	7.04241	0.615298	0.307649	−	0.951500i	$-0.400458\pi$
$131$	7.04241	0.615298	0.307649	+	0.951500i	$0.400458\pi$
$132$	63.3769	5.51625
$133$	11.3601	0.985049
$134$	−9.90704	−0.855838
$135$	−20.4958	−1.76400
$136$	−20.5091	−1.75864
$137$	−19.5719	−1.67214	−0.836072	−	0.548620i	$-0.815153\pi$
$137$	−19.5719	−1.67214	−0.836072	+	0.548620i	$0.815153\pi$
$138$	32.5148	2.76784
$139$	−22.2898	−1.89060	−0.945299	−	0.326205i	$-0.894230\pi$
$139$	−22.2898	−1.89060	−0.945299	+	0.326205i	$0.894230\pi$
$140$	−40.2952	−3.40557
$141$	26.1143	2.19922
$142$	36.2303	3.04038
$143$	1.28263	0.107259
$144$	20.2061	1.68384
$145$	−20.3426	−1.68936
$146$	18.2877	1.51350
$147$	−34.6120	−2.85475
$148$	28.0614	2.30663
$149$	17.1746	1.40700	0.703501	−	0.710694i	$-0.251619\pi$
$149$	17.1746	1.40700	0.703501	+	0.710694i	$0.251619\pi$
$150$	5.21006	0.425400
$151$	−0.739691	−0.0601952	−0.0300976	−	0.999547i	$-0.509582\pi$
$151$	−0.739691	−0.0601952	−0.0300976	+	0.999547i	$0.509582\pi$
$152$	12.1872	0.988514
$153$	26.0365	2.10493
$154$	−57.1170	−4.60262
$155$	−6.36809	−0.511497
$156$	2.73926	0.219316
$157$	−2.54444	−0.203069	−0.101534	−	0.994832i	$-0.532375\pi$
$157$	−2.54444	−0.203069	−0.101534	+	0.994832i	$0.532375\pi$
$158$	−26.4578	−2.10487
$159$	35.0994	2.78356
$160$	2.15805	0.170608
$161$	−19.3782	−1.52722
$162$	−19.2055	−1.50893
$163$	3.16273	0.247724	0.123862	−	0.992299i	$-0.460472\pi$
$163$	3.16273	0.247724	0.123862	+	0.992299i	$0.460472\pi$
$164$	0.0261482	0.00204183
$165$	38.8155	3.02178
$166$	−41.5211	−3.22266
$167$	9.74286	0.753925	0.376962	−	0.926229i	$-0.376969\pi$
$167$	9.74286	0.753925	0.376962	+	0.926229i	$0.376969\pi$
$168$	−59.5057	−4.59096
$169$	−12.9446	−0.995736
$170$	−25.7488	−1.97484
$171$	−15.4718	−1.18316
$172$	−1.61256	−0.122957
$173$	7.99063	0.607517	0.303758	−	0.952749i	$-0.401758\pi$
$173$	7.99063	0.607517	0.303758	+	0.952749i	$0.401758\pi$
$174$	−61.5812	−4.66846
$175$	−3.10510	−0.234723
$176$	−18.7312	−1.41192
$177$	19.6129	1.47419
$178$	−21.8706	−1.63927
$179$	9.35508	0.699232	0.349616	−	0.936893i	$-0.386312\pi$
$179$	9.35508	0.699232	0.349616	+	0.936893i	$0.386312\pi$
$180$	54.8797	4.09049
$181$	−16.4730	−1.22443	−0.612216	−	0.790691i	$-0.709722\pi$
$181$	−16.4730	−1.22443	−0.612216	+	0.790691i	$0.709722\pi$
$182$	−2.46869	−0.182992
$183$	5.82952	0.430931
$184$	−20.7890	−1.53259
$185$	17.1863	1.26356
$186$	−19.2775	−1.41350
$187$	−24.1361	−1.76500
$188$	−34.2270	−2.49626
$189$	36.9776	2.68972
$190$	15.3009	1.11004
$191$	−21.9098	−1.58534	−0.792670	−	0.609652i	$-0.791309\pi$
$191$	−21.9098	−1.58534	−0.792670	+	0.609652i	$0.791309\pi$
$192$	27.0216	1.95012
$193$	−26.1872	−1.88499	−0.942497	−	0.334215i	$-0.891529\pi$
$193$	−26.1872	−1.88499	−0.942497	+	0.334215i	$0.891529\pi$
$194$	−43.3155	−3.10987
$195$	1.67767	0.120140
$196$	45.3646	3.24033
$197$	17.2980	1.23243	0.616216	−	0.787578i	$-0.288665\pi$
$197$	17.2980	1.23243	0.616216	+	0.787578i	$0.288665\pi$
$198$	77.7899	5.52829
$199$	−16.4449	−1.16575	−0.582874	−	0.812562i	$-0.698072\pi$
$199$	−16.4449	−1.16575	−0.582874	+	0.812562i	$0.698072\pi$
$200$	−3.33116	−0.235549
$201$	−12.1467	−0.856761
$202$	31.8158	2.23855
$203$	36.7012	2.57592
$204$	−51.5462	−3.60896
$205$	0.0160146	0.00111851
$206$	27.4468	1.91231
$207$	26.3919	1.83437
$208$	−0.809594	−0.0561353
$209$	14.3425	0.992092
$210$	−74.7085	−5.15537
$211$	11.2611	0.775249	0.387625	−	0.921817i	$-0.373296\pi$
$211$	11.2611	0.775249	0.387625	+	0.921817i	$0.373296\pi$
$212$	−46.0034	−3.15953
$213$	44.4207	3.04365
$214$	−29.4249	−2.01145
$215$	−0.987622	−0.0673553
$216$	39.6698	2.69919
$217$	11.4890	0.779927
$218$	27.2729	1.84715
$219$	22.4219	1.51513
$220$	−50.8739	−3.42992
$221$	−1.04320	−0.0701733
$222$	52.0266	3.49180
$223$	4.04040	0.270565	0.135283	−	0.990807i	$-0.456806\pi$
$223$	4.04040	0.270565	0.135283	+	0.990807i	$0.456806\pi$
$224$	−3.89345	−0.260142
$225$	4.22895	0.281930
$226$	18.0619	1.20146
$227$	−15.0505	−0.998936	−0.499468	−	0.866332i	$-0.666471\pi$
$227$	−15.0505	−0.998936	−0.499468	+	0.866332i	$0.666471\pi$
$228$	30.6306	2.02856
$229$	−10.9920	−0.726371	−0.363186	−	0.931717i	$-0.618311\pi$
$229$	−10.9920	−0.726371	−0.363186	+	0.931717i	$0.618311\pi$
$230$	−26.1003	−1.72100
$231$	−70.0292	−4.60758
$232$	39.3733	2.58498
$233$	−26.7825	−1.75458	−0.877290	−	0.479960i	$-0.840651\pi$
$233$	−26.7825	−1.75458	−0.877290	+	0.479960i	$0.840651\pi$
$234$	3.36221	0.219795
$235$	−20.9625	−1.36744
$236$	−25.7058	−1.67330
$237$	−32.4389	−2.10714
$238$	46.4549	3.01122
$239$	−4.16983	−0.269724	−0.134862	−	0.990864i	$-0.543059\pi$
$239$	−4.16983	−0.269724	−0.134862	+	0.990864i	$0.543059\pi$
$240$	−24.5002	−1.58148
$241$	12.2472	0.788914	0.394457	−	0.918914i	$-0.370933\pi$
$241$	12.2472	0.788914	0.394457	+	0.918914i	$0.370933\pi$
$242$	−45.3819	−2.91726
$243$	2.16277	0.138742
$244$	−7.64053	−0.489135
$245$	27.7838	1.77504
$246$	0.0484795	0.00309094
$247$	0.619907	0.0394438
$248$	12.3255	0.782670
$249$	−50.9076	−3.22614
$250$	24.8755	1.57326
$251$	−0.892836	−0.0563553	−0.0281777	−	0.999603i	$-0.508970\pi$
$251$	−0.892836	−0.0563553	−0.0281777	+	0.999603i	$0.508970\pi$
$252$	−99.0115	−6.23714
$253$	−24.4656	−1.53814
$254$	19.2289	1.20653
$255$	−31.5697	−1.97697
$256$	−31.0307	−1.93942
$257$	−8.30236	−0.517887	−0.258943	−	0.965893i	$-0.583374\pi$
$257$	−8.30236	−0.517887	−0.258943	+	0.965893i	$0.583374\pi$
$258$	−2.98974	−0.186133
$259$	−31.0069	−1.92667
$260$	−2.19886	−0.136367
$261$	−49.9848	−3.09398
$262$	−17.1131	−1.05725
$263$	22.5465	1.39028	0.695139	−	0.718875i	$-0.255343\pi$
$263$	22.5465	1.39028	0.695139	+	0.718875i	$0.255343\pi$
$264$	−75.1277	−4.62379
$265$	−28.1750	−1.73078
$266$	−27.6052	−1.69258
$267$	−26.8147	−1.64104
$268$	15.9202	0.972480
$269$	−7.75810	−0.473020	−0.236510	−	0.971629i	$-0.576004\pi$
$269$	−7.75810	−0.473020	−0.236510	+	0.971629i	$0.576004\pi$
$270$	49.8048	3.03102
$271$	−12.4122	−0.753987	−0.376994	−	0.926216i	$-0.623042\pi$
$271$	−12.4122	−0.753987	−0.376994	+	0.926216i	$0.623042\pi$
$272$	15.2346	0.923734
$273$	−3.02678	−0.183189
$274$	47.5598	2.87319
$275$	−3.92027	−0.236401
$276$	−52.2499	−3.14507
$277$	−8.36693	−0.502720	−0.251360	−	0.967894i	$-0.580878\pi$
$277$	−8.36693	−0.502720	−0.251360	+	0.967894i	$0.580878\pi$
$278$	54.1643	3.24856
$279$	−15.6474	−0.936783
$280$	47.7664	2.85459
$281$	−2.79514	−0.166744	−0.0833720	−	0.996518i	$-0.526569\pi$
$281$	−2.79514	−0.166744	−0.0833720	+	0.996518i	$0.526569\pi$
$282$	−63.4578	−3.77885
$283$	−24.5800	−1.46113	−0.730565	−	0.682843i	$-0.760743\pi$
$283$	−24.5800	−1.46113	−0.730565	+	0.682843i	$0.760743\pi$
$284$	−58.2204	−3.45475
$285$	18.7599	1.11124
$286$	−3.11680	−0.184300
$287$	−0.0288928	−0.00170549
$288$	5.30265	0.312461
$289$	2.63055	0.154738
$290$	49.4325	2.90278
$291$	−53.1077	−3.11323
$292$	−29.3876	−1.71978
$293$	17.0496	0.996049	0.498024	−	0.867163i	$-0.334059\pi$
$293$	17.0496	0.996049	0.498024	+	0.867163i	$0.334059\pi$
$294$	84.1072	4.90523
$295$	−15.7436	−0.916630
$296$	−33.2643	−1.93345
$297$	46.6853	2.70896
$298$	−41.7344	−2.41761
$299$	−1.05744	−0.0611535
$300$	−8.37234	−0.483377
$301$	1.78183	0.102703
$302$	1.79745	0.103432
$303$	39.0082	2.24096
$304$	−9.05295	−0.519222
$305$	−4.67948	−0.267946
$306$	−63.2687	−3.61683
$307$	−8.56523	−0.488844	−0.244422	−	0.969669i	$-0.578598\pi$
$307$	−8.56523	−0.488844	−0.244422	+	0.969669i	$0.578598\pi$
$308$	91.7845	5.22991
$309$	33.6516	1.91437
$310$	15.4745	0.878890
$311$	7.41889	0.420687	0.210343	−	0.977628i	$-0.432542\pi$
$311$	7.41889	0.420687	0.210343	+	0.977628i	$0.432542\pi$
$312$	−3.24715	−0.183833
$313$	−4.07177	−0.230150	−0.115075	−	0.993357i	$-0.536711\pi$
$313$	−4.07177	−0.230150	−0.115075	+	0.993357i	$0.536711\pi$
$314$	6.18300	0.348927
$315$	−60.6401	−3.41668
$316$	42.5164	2.39174
$317$	28.6127	1.60705	0.803524	−	0.595273i	$-0.202956\pi$
$317$	28.6127	1.60705	0.803524	+	0.595273i	$0.202956\pi$
$318$	−85.2915	−4.78291
$319$	46.3364	2.59434
$320$	−21.6908	−1.21255
$321$	−36.0769	−2.01361
$322$	47.0891	2.62417
$323$	−11.6652	−0.649067
$324$	30.8624	1.71458
$325$	−0.169441	−0.00939889
$326$	−7.68544	−0.425657
$327$	33.4384	1.84915
$328$	−0.0309964	−0.00171149
$329$	37.8196	2.08506
$330$	−94.3216	−5.19223
$331$	1.16207	0.0638733	0.0319366	−	0.999490i	$-0.489833\pi$
$331$	1.16207	0.0638733	0.0319366	+	0.999490i	$0.489833\pi$
$332$	66.7225	3.66187
$333$	42.2294	2.31416
$334$	−23.6751	−1.29545
$335$	9.75039	0.532721
$336$	44.2022	2.41143
$337$	−36.2000	−1.97194	−0.985969	−	0.166928i	$-0.946615\pi$
$337$	−36.2000	−1.97194	−0.985969	+	0.166928i	$0.946615\pi$
$338$	31.4553	1.71094
$339$	22.1451	1.20276
$340$	41.3772	2.24399
$341$	14.5052	0.785503
$342$	37.5965	2.03299
$343$	−19.9228	−1.07573
$344$	1.91155	0.103064
$345$	−32.0007	−1.72286
$346$	−19.4172	−1.04388
$347$	−4.08963	−0.219543	−0.109771	−	0.993957i	$-0.535012\pi$
$347$	−4.08963	−0.219543	−0.109771	+	0.993957i	$0.535012\pi$
$348$	98.9583	5.30472
$349$	16.3207	0.873626	0.436813	−	0.899552i	$-0.356107\pi$
$349$	16.3207	0.873626	0.436813	+	0.899552i	$0.356107\pi$
$350$	7.54539	0.403318
$351$	2.01782	0.107703
$352$	−4.91560	−0.262002
$353$	−19.4945	−1.03759	−0.518793	−	0.854900i	$-0.673618\pi$
$353$	−19.4945	−1.03759	−0.518793	+	0.854900i	$0.673618\pi$
$354$	−47.6592	−2.53306
$355$	−35.6574	−1.89250
$356$	35.1450	1.86268
$357$	56.9567	3.01447
$358$	−22.7329	−1.20147
$359$	−25.7263	−1.35778	−0.678892	−	0.734238i	$-0.737540\pi$
$359$	−25.7263	−1.35778	−0.678892	+	0.734238i	$0.737540\pi$
$360$	−65.0550	−3.42870
$361$	−12.0681	−0.635165
$362$	40.0295	2.10390
$363$	−55.6412	−2.92040
$364$	3.96708	0.207932
$365$	−17.9986	−0.942087
$366$	−14.1657	−0.740455
$367$	17.1734	0.896443	0.448221	−	0.893923i	$-0.352058\pi$
$367$	17.1734	0.896443	0.448221	+	0.893923i	$0.352058\pi$
$368$	15.4426	0.805001
$369$	0.0393503	0.00204849
$370$	−41.7628	−2.17115
$371$	50.8321	2.63907
$372$	30.9781	1.60614
$373$	13.3830	0.692946	0.346473	−	0.938060i	$-0.387379\pi$
$373$	13.3830	0.692946	0.346473	+	0.938060i	$0.387379\pi$
$374$	58.6507	3.03275
$375$	30.4989	1.57496
$376$	40.5731	2.09240
$377$	2.00274	0.103146
$378$	−89.8556	−4.62167
$379$	24.1906	1.24259	0.621295	−	0.783577i	$-0.286607\pi$
$379$	24.1906	1.24259	0.621295	+	0.783577i	$0.286607\pi$
$380$	−24.5878	−1.26133
$381$	23.5758	1.20783
$382$	53.2409	2.72404
$383$	−19.6083	−1.00194	−0.500970	−	0.865465i	$-0.667023\pi$
$383$	−19.6083	−1.00194	−0.500970	+	0.865465i	$0.667023\pi$
$384$	−60.2857	−3.07644
$385$	56.2139	2.86492
$386$	63.6348	3.23893
$387$	−2.42674	−0.123358
$388$	69.6062	3.53372
$389$	10.8224	0.548718	0.274359	−	0.961627i	$-0.411534\pi$
$389$	10.8224	0.548718	0.274359	+	0.961627i	$0.411534\pi$
$390$	−4.07674	−0.206434
$391$	19.8985	1.00631
$392$	−53.7757	−2.71608
$393$	−20.9817	−1.05839
$394$	−42.0341	−2.11765
$395$	26.0394	1.31018
$396$	−125.005	−6.28174
$397$	−33.3047	−1.67151	−0.835757	−	0.549099i	$-0.814971\pi$
$397$	−33.3047	−1.67151	−0.835757	+	0.549099i	$0.814971\pi$
$398$	39.9611	2.00307
$399$	−33.8457	−1.69441
$400$	2.47447	0.123723
$401$	9.47566	0.473192	0.236596	−	0.971608i	$-0.423968\pi$
$401$	9.47566	0.473192	0.236596	+	0.971608i	$0.423968\pi$
$402$	29.5165	1.47215
$403$	0.626941	0.0312302
$404$	−51.1265	−2.54364
$405$	18.9018	0.939238
$406$	−89.1840	−4.42613
$407$	−39.1471	−1.94045
$408$	61.1035	3.02507
$409$	11.2416	0.555862	0.277931	−	0.960601i	$-0.410351\pi$
$409$	11.2416	0.555862	0.277931	+	0.960601i	$0.410351\pi$
$410$	−0.0389154	−0.00192190
$411$	58.3115	2.87629
$412$	−44.1059	−2.17294
$413$	28.4040	1.39767
$414$	−64.1324	−3.15194
$415$	40.8645	2.00596
$416$	−0.212460	−0.0104167
$417$	66.4090	3.25206
$418$	−34.8523	−1.70468
$419$	−5.51488	−0.269420	−0.134710	−	0.990885i	$-0.543010\pi$
$419$	−5.51488	−0.269420	−0.134710	+	0.990885i	$0.543010\pi$
$420$	120.053	5.85800
$421$	10.8727	0.529905	0.264952	−	0.964262i	$-0.414644\pi$
$421$	10.8727	0.529905	0.264952	+	0.964262i	$0.414644\pi$
$422$	−27.3646	−1.33209
$423$	−51.5080	−2.50440
$424$	54.5330	2.64835
$425$	3.18847	0.154664
$426$	−107.942	−5.22982
$427$	8.44251	0.408562
$428$	47.2845	2.28558
$429$	−3.82140	−0.184499
$430$	2.39992	0.115735
$431$	1.63985	0.0789887	0.0394944	−	0.999220i	$-0.487425\pi$
$431$	1.63985	0.0789887	0.0394944	+	0.999220i	$0.487425\pi$
$432$	−29.4676	−1.41776
$433$	−27.2784	−1.31092	−0.655458	−	0.755232i	$-0.727524\pi$
$433$	−27.2784	−1.31092	−0.655458	+	0.755232i	$0.727524\pi$
$434$	−27.9184	−1.34012
$435$	60.6075	2.90591
$436$	−43.8264	−2.09890
$437$	−11.8244	−0.565638
$438$	−54.4853	−2.60341
$439$	16.0533	0.766180	0.383090	−	0.923711i	$-0.374860\pi$
$439$	16.0533	0.766180	0.383090	+	0.923711i	$0.374860\pi$
$440$	60.3065	2.87500
$441$	68.2689	3.25090
$442$	2.53498	0.120577
$443$	−13.5840	−0.645397	−0.322698	−	0.946502i	$-0.604590\pi$
$443$	−13.5840	−0.645397	−0.322698	+	0.946502i	$0.604590\pi$
$444$	−83.6045	−3.96769
$445$	21.5247	1.02037
$446$	−9.81817	−0.464904
$447$	−51.1691	−2.42022
$448$	39.1336	1.84889
$449$	24.2850	1.14608	0.573041	−	0.819527i	$-0.305764\pi$
$449$	24.2850	1.14608	0.573041	+	0.819527i	$0.305764\pi$
$450$	−10.2764	−0.484432
$451$	−0.0364780	−0.00171768
$452$	−29.0247	−1.36521
$453$	2.20379	0.103543
$454$	36.5727	1.71644
$455$	2.42966	0.113904
$456$	−36.3099	−1.70037
$457$	−29.0457	−1.35870	−0.679351	−	0.733814i	$-0.737739\pi$
$457$	−29.0457	−1.35870	−0.679351	+	0.733814i	$0.737739\pi$
$458$	26.7106	1.24810
$459$	−37.9705	−1.77231
$460$	41.9420	1.95556
$461$	21.1184	0.983581	0.491790	−	0.870714i	$-0.336343\pi$
$461$	21.1184	0.983581	0.491790	+	0.870714i	$0.336343\pi$
$462$	170.171	7.91707
$463$	19.4268	0.902840	0.451420	−	0.892312i	$-0.350918\pi$
$463$	19.4268	0.902840	0.451420	+	0.892312i	$0.350918\pi$
$464$	−29.2474	−1.35778
$465$	18.9727	0.879838
$466$	65.0815	3.01484
$467$	17.1700	0.794535	0.397267	−	0.917703i	$-0.369959\pi$
$467$	17.1700	0.794535	0.397267	+	0.917703i	$0.369959\pi$
$468$	−5.40292	−0.249750
$469$	−17.5912	−0.812288
$470$	50.9388	2.34963
$471$	7.58076	0.349303
$472$	30.4720	1.40259
$473$	2.24961	0.103437
$474$	78.8267	3.62063
$475$	−1.89470	−0.0869349
$476$	−74.6510	−3.42162
$477$	−69.2302	−3.16983
$478$	10.1327	0.463459
$479$	−15.8462	−0.724032	−0.362016	−	0.932172i	$-0.617911\pi$
$479$	−15.8462	−0.724032	−0.362016	+	0.932172i	$0.617911\pi$
$480$	−6.42955	−0.293468
$481$	−1.69200	−0.0771486
$482$	−29.7608	−1.35557
$483$	57.7343	2.62700
$484$	72.9267	3.31485
$485$	42.6306	1.93576
$486$	−5.25553	−0.238396
$487$	4.17774	0.189312	0.0946558	−	0.995510i	$-0.469825\pi$
$487$	4.17774	0.189312	0.0946558	+	0.995510i	$0.469825\pi$
$488$	9.05717	0.409999
$489$	−9.42286	−0.426116
$490$	−67.5146	−3.05000
$491$	29.3993	1.32677	0.663385	−	0.748278i	$-0.269119\pi$
$491$	29.3993	1.32677	0.663385	+	0.748278i	$0.269119\pi$
$492$	−0.0779044	−0.00351220
$493$	−37.6867	−1.69732
$494$	−1.50638	−0.0677751
$495$	−76.5599	−3.44111
$496$	−9.15567	−0.411102
$497$	64.3315	2.88566
$498$	123.705	5.54337
$499$	0.101733	0.00455420	0.00227710	−	0.999997i	$-0.499275\pi$
$499$	0.101733	0.00455420	0.00227710	+	0.999997i	$0.499275\pi$
$500$	−39.9738	−1.78768
$501$	−29.0273	−1.29684
$502$	2.16959	0.0968336
$503$	−26.3639	−1.17551	−0.587755	−	0.809039i	$-0.699988\pi$
$503$	−26.3639	−1.17551	−0.587755	+	0.809039i	$0.699988\pi$
$504$	117.369	5.22805
$505$	−31.3127	−1.39340
$506$	59.4513	2.64293
$507$	38.5663	1.71279
$508$	−30.8999	−1.37096
$509$	−3.78791	−0.167896	−0.0839480	−	0.996470i	$-0.526753\pi$
$509$	−3.78791	−0.167896	−0.0839480	+	0.996470i	$0.526753\pi$
$510$	76.7145	3.39697
$511$	32.4722	1.43649
$512$	34.9355	1.54395
$513$	22.5634	0.996199
$514$	20.1747	0.889869
$515$	−27.0128	−1.19033
$516$	4.80437	0.211501
$517$	47.7484	2.09997
$518$	75.3467	3.31054
$519$	−23.8068	−1.04500
$520$	2.60655	0.114305
$521$	8.06185	0.353196	0.176598	−	0.984283i	$-0.443491\pi$
$521$	8.06185	0.353196	0.176598	+	0.984283i	$0.443491\pi$
$522$	121.463	5.31630
$523$	18.6317	0.814706	0.407353	−	0.913271i	$-0.366452\pi$
$523$	18.6317	0.814706	0.407353	+	0.913271i	$0.366452\pi$
$524$	27.4999	1.20134
$525$	9.25114	0.403753
$526$	−54.7881	−2.38887
$527$	−11.7975	−0.513908
$528$	55.8066	2.42867
$529$	−2.82984	−0.123036
$530$	68.4652	2.97394
$531$	−38.6845	−1.67876
$532$	44.3603	1.92326
$533$	−0.00157664	−6.82920e−5 0
$534$	65.1598	2.81974
$535$	28.9596	1.25203
$536$	−18.8720	−0.815145
$537$	−27.8720	−1.20276
$538$	18.8522	0.812775
$539$	−63.2859	−2.72592
$540$	−80.0340	−3.44412
$541$	23.0274	0.990025	0.495012	−	0.868886i	$-0.335163\pi$
$541$	23.0274	0.990025	0.495012	+	0.868886i	$0.335163\pi$
$542$	30.1616	1.29555
$543$	49.0788	2.10617
$544$	3.99800	0.171413
$545$	−26.8417	−1.14977
$546$	7.35508	0.314768
$547$	−14.5246	−0.621028	−0.310514	−	0.950569i	$-0.600501\pi$
$547$	−14.5246	−0.621028	−0.310514	+	0.950569i	$0.600501\pi$
$548$	−76.4265	−3.26478
$549$	−11.4982	−0.490731
$550$	9.52627	0.406202
$551$	22.3948	0.954049
$552$	61.9376	2.63624
$553$	−46.9792	−1.99776
$554$	20.3316	0.863809
$555$	−51.2039	−2.17349
$556$	−87.0396	−3.69130
$557$	36.2578	1.53629	0.768145	−	0.640276i	$-0.221180\pi$
$557$	36.2578	1.53629	0.768145	+	0.640276i	$0.221180\pi$
$558$	38.0231	1.60965
$559$	0.0972318	0.00411247
$560$	−35.4820	−1.49939
$561$	71.9096	3.03602
$562$	6.79219	0.286511
$563$	22.2584	0.938080	0.469040	−	0.883177i	$-0.344600\pi$
$563$	22.2584	0.938080	0.469040	+	0.883177i	$0.344600\pi$
$564$	101.974	4.29387
$565$	−17.7763	−0.747854
$566$	59.7295	2.51062
$567$	−34.1018	−1.43214
$568$	69.0152	2.89581
$569$	−23.0463	−0.966149	−0.483075	−	0.875579i	$-0.660480\pi$
$569$	−23.0463	−0.966149	−0.483075	+	0.875579i	$0.660480\pi$
$570$	−45.5865	−1.90941
$571$	46.6206	1.95101	0.975506	−	0.219975i	$-0.0705975\pi$
$571$	46.6206	1.95101	0.975506	+	0.219975i	$0.0705975\pi$
$572$	5.00856	0.209418
$573$	65.2768	2.72698
$574$	0.0702096	0.00293049
$575$	3.23200	0.134784
$576$	−53.2976	−2.22073
$577$	24.7314	1.02958	0.514792	−	0.857315i	$-0.327869\pi$
$577$	24.7314	1.02958	0.514792	+	0.857315i	$0.327869\pi$
$578$	−6.39224	−0.265882
$579$	78.0205	3.24242
$580$	−79.4358	−3.29839
$581$	−73.7260	−3.05867
$582$	129.052	5.34937
$583$	64.1770	2.65794
$584$	34.8364	1.44154
$585$	−3.30905	−0.136812
$586$	−41.4306	−1.71148
$587$	18.1101	0.747482	0.373741	−	0.927533i	$-0.378075\pi$
$587$	18.1101	0.747482	0.373741	+	0.927533i	$0.378075\pi$
$588$	−135.157	−5.57376
$589$	7.01051	0.288863
$590$	38.2570	1.57502
$591$	−51.5366	−2.11993
$592$	24.7095	1.01555
$593$	−2.14826	−0.0882183	−0.0441092	−	0.999027i	$-0.514045\pi$
$593$	−2.14826	−0.0882183	−0.0441092	+	0.999027i	$0.514045\pi$
$594$	−113.445	−4.65472
$595$	−45.7203	−1.87435
$596$	67.0654	2.74710
$597$	48.9950	2.00523
$598$	2.56959	0.105078
$599$	10.7775	0.440356	0.220178	−	0.975460i	$-0.429336\pi$
$599$	10.7775	0.440356	0.220178	+	0.975460i	$0.429336\pi$
$600$	9.92467	0.405173
$601$	−7.32492	−0.298790	−0.149395	−	0.988778i	$-0.547733\pi$
$601$	−7.32492	−0.298790	−0.149395	+	0.988778i	$0.547733\pi$
$602$	−4.32984	−0.176471
$603$	23.9582	0.975653
$604$	−2.88842	−0.117528
$605$	44.6643	1.81586
$606$	−94.7900	−3.85058
$607$	20.6381	0.837677	0.418838	−	0.908061i	$-0.362437\pi$
$607$	20.6381	0.837677	0.418838	+	0.908061i	$0.362437\pi$
$608$	−2.37575	−0.0963494
$609$	−109.345	−4.43090
$610$	11.3711	0.460404
$611$	2.06376	0.0834910
$612$	101.670	4.10977
$613$	−13.7150	−0.553943	−0.276971	−	0.960878i	$-0.589331\pi$
$613$	−13.7150	−0.553943	−0.276971	+	0.960878i	$0.589331\pi$
$614$	20.8135	0.839966
$615$	−0.0477129	−0.00192397
$616$	−108.802	−4.38378
$617$	−16.7796	−0.675521	−0.337760	−	0.941232i	$-0.609669\pi$
$617$	−16.7796	−0.675521	−0.337760	+	0.941232i	$0.609669\pi$
$618$	−81.7735	−3.28941
$619$	0.583040	0.0234344	0.0117172	−	0.999931i	$-0.496270\pi$
$619$	0.583040	0.0234344	0.0117172	+	0.999931i	$0.496270\pi$
$620$	−24.8668	−0.998674
$621$	−38.4888	−1.54450
$622$	−18.0279	−0.722854
$623$	−38.8340	−1.55585
$624$	2.41206	0.0965595
$625$	−28.0803	−1.12321
$626$	9.89441	0.395460
$627$	−42.7312	−1.70652
$628$	−9.93580	−0.396482
$629$	31.8394	1.26952
$630$	147.355	5.87078
$631$	11.9530	0.475840	0.237920	−	0.971285i	$-0.423534\pi$
$631$	11.9530	0.475840	0.237920	+	0.971285i	$0.423534\pi$
$632$	−50.3995	−2.00478
$633$	−33.5508	−1.33352
$634$	−69.5288	−2.76134
$635$	−18.9248	−0.751008
$636$	137.060	5.43477
$637$	−2.73532	−0.108377
$638$	−112.597	−4.45777
$639$	−87.6156	−3.46602
$640$	48.3925	1.91288
$641$	−29.5676	−1.16785	−0.583925	−	0.811808i	$-0.698484\pi$
$641$	−29.5676	−1.16785	−0.583925	+	0.811808i	$0.698484\pi$
$642$	87.6668	3.45993
$643$	−24.4534	−0.964348	−0.482174	−	0.876075i	$-0.660153\pi$
$643$	−24.4534	−0.964348	−0.482174	+	0.876075i	$0.660153\pi$
$644$	−75.6700	−2.98182
$645$	2.94246	0.115859
$646$	28.3464	1.11527
$647$	33.6879	1.32441	0.662204	−	0.749324i	$-0.269621\pi$
$647$	33.6879	1.32441	0.662204	+	0.749324i	$0.269621\pi$
$648$	−36.5846	−1.43718
$649$	35.8609	1.40766
$650$	0.411741	0.0161498
$651$	−34.2297	−1.34157
$652$	12.3502	0.483670
$653$	42.3086	1.65566	0.827831	−	0.560977i	$-0.189574\pi$
$653$	42.3086	1.65566	0.827831	+	0.560977i	$0.189574\pi$
$654$	−81.2553	−3.17733
$655$	16.8425	0.658090
$656$	0.0230248	0.000898969 0
$657$	−44.2252	−1.72539
$658$	−91.9017	−3.58270
$659$	17.9296	0.698438	0.349219	−	0.937041i	$-0.386447\pi$
$659$	17.9296	0.698438	0.349219	+	0.937041i	$0.386447\pi$
$660$	151.571	5.89988
$661$	−47.4860	−1.84699	−0.923495	−	0.383611i	$-0.874680\pi$
$661$	−47.4860	−1.84699	−0.923495	+	0.383611i	$0.874680\pi$
$662$	−2.82384	−0.109752
$663$	3.10805	0.120707
$664$	−79.0937	−3.06943
$665$	27.1687	1.05356
$666$	−102.618	−3.97635
$667$	−38.2011	−1.47915
$668$	38.0449	1.47200
$669$	−12.0377	−0.465405
$670$	−23.6935	−0.915358
$671$	10.6589	0.411483
$672$	11.5999	0.447477
$673$	−9.98601	−0.384932	−0.192466	−	0.981304i	$-0.561649\pi$
$673$	−9.98601	−0.384932	−0.192466	+	0.981304i	$0.561649\pi$
$674$	87.9660	3.38832
$675$	−6.16731	−0.237380
$676$	−50.5473	−1.94413
$677$	13.7095	0.526899	0.263450	−	0.964673i	$-0.415140\pi$
$677$	13.7095	0.526899	0.263450	+	0.964673i	$0.415140\pi$
$678$	−53.8125	−2.06666
$679$	−76.9124	−2.95163
$680$	−49.0490	−1.88094
$681$	44.8405	1.71829
$682$	−35.2478	−1.34971
$683$	−0.976330	−0.0373582	−0.0186791	−	0.999826i	$-0.505946\pi$
$683$	−0.976330	−0.0373582	−0.0186791	+	0.999826i	$0.505946\pi$
$684$	−60.4160	−2.31006
$685$	−46.8078	−1.78843
$686$	48.4124	1.84840
$687$	32.7489	1.24945
$688$	−1.41995	−0.0541349
$689$	2.77384	0.105675
$690$	77.7617	2.96034
$691$	15.2042	0.578396	0.289198	−	0.957269i	$-0.406611\pi$
$691$	15.2042	0.578396	0.289198	+	0.957269i	$0.406611\pi$
$692$	31.2027	1.18615
$693$	138.126	5.24697
$694$	9.93781	0.377234
$695$	−53.3078	−2.02208
$696$	−117.306	−4.44649
$697$	0.0296686	0.00112378
$698$	−39.6593	−1.50113
$699$	79.7942	3.01809
$700$	−12.1251	−0.458286
$701$	4.23399	0.159916	0.0799579	−	0.996798i	$-0.474521\pi$
$701$	4.23399	0.159916	0.0799579	+	0.996798i	$0.474521\pi$
$702$	−4.90330	−0.185063
$703$	−18.9201	−0.713586
$704$	49.4073	1.86211
$705$	62.4544	2.35217
$706$	47.3715	1.78285
$707$	56.4930	2.12464
$708$	76.5863	2.87829
$709$	−37.3790	−1.40380	−0.701900	−	0.712276i	$-0.747665\pi$
$709$	−37.3790	−1.40380	−0.701900	+	0.712276i	$0.747665\pi$
$710$	86.6475	3.25182
$711$	63.9828	2.39954
$712$	−41.6613	−1.56132
$713$	−11.9586	−0.447852
$714$	−138.405	−5.17967
$715$	3.06751	0.114719
$716$	36.5307	1.36522
$717$	12.4233	0.463958
$718$	62.5150	2.33304
$719$	38.5152	1.43638	0.718188	−	0.695849i	$-0.244972\pi$
$719$	38.5152	1.43638	0.718188	+	0.695849i	$0.244972\pi$
$720$	48.3244	1.80094
$721$	48.7354	1.81500
$722$	29.3256	1.09139
$723$	−36.4887	−1.35703
$724$	−64.3257	−2.39064
$725$	−6.12122	−0.227336
$726$	135.208	5.01804
$727$	−15.5571	−0.576983	−0.288491	−	0.957483i	$-0.593154\pi$
$727$	−15.5571	−0.576983	−0.288491	+	0.957483i	$0.593154\pi$
$728$	−4.70263	−0.174291
$729$	−30.1541	−1.11682
$730$	43.7365	1.61876
$731$	−1.82967	−0.0676728
$732$	22.7637	0.841372
$733$	23.7742	0.878122	0.439061	−	0.898457i	$-0.355311\pi$
$733$	23.7742	0.878122	0.439061	+	0.898457i	$0.355311\pi$
$734$	−41.7313	−1.54033
$735$	−82.7773	−3.05329
$736$	4.05257	0.149380
$737$	−22.2095	−0.818096
$738$	−0.0956212	−0.00351986
$739$	−18.3679	−0.675675	−0.337837	−	0.941204i	$-0.609695\pi$
$739$	−18.3679	−0.675675	−0.337837	+	0.941204i	$0.609695\pi$
$740$	67.1110	2.46705
$741$	−1.84692	−0.0678481
$742$	−123.522	−4.53464
$743$	21.7521	0.798006	0.399003	−	0.916950i	$-0.369356\pi$
$743$	21.7521	0.798006	0.399003	+	0.916950i	$0.369356\pi$
$744$	−36.7219	−1.34629
$745$	41.0745	1.50485
$746$	−32.5207	−1.19067
$747$	100.410	3.67382
$748$	−94.2490	−3.44609
$749$	−52.2477	−1.90909
$750$	−74.1124	−2.70620
$751$	8.53079	0.311293	0.155647	−	0.987813i	$-0.450254\pi$
$751$	8.53079	0.311293	0.155647	+	0.987813i	$0.450254\pi$
$752$	−30.1386	−1.09904
$753$	2.66006	0.0969381
$754$	−4.86665	−0.177233
$755$	−1.76903	−0.0643815
$756$	144.394	5.25156
$757$	43.4711	1.57998	0.789991	−	0.613118i	$-0.210085\pi$
$757$	43.4711	1.57998	0.789991	+	0.613118i	$0.210085\pi$
$758$	−58.7833	−2.13510
$759$	72.8912	2.64578
$760$	29.1467	1.05726
$761$	14.4300	0.523086	0.261543	−	0.965192i	$-0.415769\pi$
$761$	14.4300	0.523086	0.261543	+	0.965192i	$0.415769\pi$
$762$	−57.2893	−2.07537
$763$	48.4266	1.75316
$764$	−85.5558	−3.09530
$765$	62.2683	2.25132
$766$	47.6483	1.72160
$767$	1.54997	0.0559661
$768$	92.4511	3.33604
$769$	−20.2990	−0.732002	−0.366001	−	0.930614i	$-0.619273\pi$
$769$	−20.2990	−0.732002	−0.366001	+	0.930614i	$0.619273\pi$
$770$	−136.600	−4.92271
$771$	24.7355	0.890829
$772$	−102.258	−3.68036
$773$	8.25496	0.296910	0.148455	−	0.988919i	$-0.452570\pi$
$773$	8.25496	0.296910	0.148455	+	0.988919i	$0.452570\pi$
$774$	5.89697	0.211962
$775$	−1.91620	−0.0688320
$776$	−82.5120	−2.96201
$777$	92.3800	3.31411
$778$	−26.2984	−0.942845
$779$	−0.0176302	−0.000631666 0
$780$	6.55114	0.234568
$781$	81.2204	2.90630
$782$	−48.3534	−1.72912
$783$	72.8957	2.60508
$784$	39.9459	1.42664
$785$	−6.08523	−0.217191
$786$	50.9857	1.81860
$787$	−29.6274	−1.05610	−0.528052	−	0.849212i	$-0.677077\pi$
$787$	−29.6274	−1.05610	−0.528052	+	0.849212i	$0.677077\pi$
$788$	67.5470	2.40626
$789$	−67.1738	−2.39145
$790$	−63.2758	−2.25125
$791$	32.0712	1.14032
$792$	148.182	5.26543
$793$	0.460696	0.0163598
$794$	80.9304	2.87211
$795$	83.9429	2.97715
$796$	−64.2158	−2.27607
$797$	8.44684	0.299203	0.149601	−	0.988746i	$-0.452201\pi$
$797$	8.44684	0.299203	0.149601	+	0.988746i	$0.452201\pi$
$798$	82.2451	2.91145
$799$	−38.8351	−1.37389
$800$	0.649370	0.0229587
$801$	52.8895	1.86876
$802$	−23.0259	−0.813071
$803$	40.9971	1.44676
$804$	−47.4316	−1.67279
$805$	−46.3445	−1.63343
$806$	−1.52347	−0.0536619
$807$	23.1140	0.813652
$808$	60.6060	2.13211
$809$	30.7671	1.08171	0.540857	−	0.841114i	$-0.318100\pi$
$809$	30.7671	1.08171	0.540857	+	0.841114i	$0.318100\pi$
$810$	−45.9314	−1.61386
$811$	−5.23801	−0.183931	−0.0919657	−	0.995762i	$-0.529315\pi$
$811$	−5.23801	−0.183931	−0.0919657	+	0.995762i	$0.529315\pi$
$812$	143.315	5.02936
$813$	36.9801	1.29695
$814$	95.1274	3.33421
$815$	7.56392	0.264952
$816$	−45.3891	−1.58894
$817$	1.08725	0.0380382
$818$	−27.3171	−0.955122
$819$	5.97004	0.208610
$820$	0.0625354	0.00218383
$821$	53.3641	1.86242	0.931209	−	0.364485i	$-0.118755\pi$
$821$	53.3641	1.86242	0.931209	+	0.364485i	$0.118755\pi$
$822$	−141.697	−4.94225
$823$	−2.87375	−0.100173	−0.0500863	−	0.998745i	$-0.515950\pi$
$823$	−2.87375	−0.100173	−0.0500863	+	0.998745i	$0.515950\pi$
$824$	52.2836	1.82139
$825$	11.6798	0.406640
$826$	−69.0217	−2.40157
$827$	−10.1099	−0.351555	−0.175777	−	0.984430i	$-0.556244\pi$
$827$	−10.1099	−0.351555	−0.175777	+	0.984430i	$0.556244\pi$
$828$	103.058	3.58151
$829$	5.38282	0.186953	0.0934766	−	0.995621i	$-0.470202\pi$
$829$	5.38282	0.186953	0.0934766	+	0.995621i	$0.470202\pi$
$830$	−99.3008	−3.44678
$831$	24.9279	0.864740
$832$	2.13547	0.0740340
$833$	51.4722	1.78341
$834$	−161.374	−5.58792
$835$	23.3008	0.806357
$836$	56.0061	1.93701
$837$	22.8194	0.788755
$838$	13.4012	0.462936
$839$	−37.3146	−1.28824	−0.644122	−	0.764923i	$-0.722777\pi$
$839$	−37.3146	−1.28824	−0.644122	+	0.764923i	$0.722777\pi$
$840$	−142.312	−4.91025
$841$	43.3508	1.49486
$842$	−26.4208	−0.910519
$843$	8.32767	0.286820
$844$	43.9737	1.51364
$845$	−30.9579	−1.06498
$846$	125.164	4.30324
$847$	−80.5814	−2.76881
$848$	−40.5084	−1.39106
$849$	73.2323	2.51332
$850$	−7.74799	−0.265754
$851$	32.2741	1.10634
$852$	173.459	5.94259
$853$	12.4504	0.426294	0.213147	−	0.977020i	$-0.431629\pi$
$853$	12.4504	0.426294	0.213147	+	0.977020i	$0.431629\pi$
$854$	−20.5153	−0.702020
$855$	−37.0020	−1.26544
$856$	−56.0516	−1.91581
$857$	1.43085	0.0488769	0.0244384	−	0.999701i	$-0.492220\pi$
$857$	1.43085	0.0488769	0.0244384	+	0.999701i	$0.492220\pi$
$858$	9.28600	0.317019
$859$	−31.2960	−1.06781	−0.533903	−	0.845546i	$-0.679275\pi$
$859$	−31.2960	−1.06781	−0.533903	+	0.845546i	$0.679275\pi$
$860$	−3.85657	−0.131508
$861$	0.0860816	0.00293365
$862$	−3.98483	−0.135724
$863$	−9.84338	−0.335073	−0.167536	−	0.985866i	$-0.553581\pi$
$863$	−9.84338	−0.335073	−0.167536	+	0.985866i	$0.553581\pi$
$864$	−7.73314	−0.263087
$865$	19.1102	0.649767
$866$	66.2865	2.25251
$867$	−7.83730	−0.266169
$868$	44.8636	1.52277
$869$	−59.3126	−2.01204
$870$	−147.276	−4.99313
$871$	−0.959930	−0.0325260
$872$	51.9523	1.75933
$873$	104.750	3.54525
$874$	28.7333	0.971920
$875$	44.1696	1.49320
$876$	87.5556	2.95823
$877$	19.6212	0.662561	0.331281	−	0.943532i	$-0.392519\pi$
$877$	19.6212	0.662561	0.331281	+	0.943532i	$0.392519\pi$
$878$	−39.0094	−1.31650
$879$	−50.7966	−1.71333
$880$	−44.7971	−1.51011
$881$	−21.9581	−0.739788	−0.369894	−	0.929074i	$-0.620606\pi$
$881$	−21.9581	−0.739788	−0.369894	+	0.929074i	$0.620606\pi$
$882$	−165.894	−5.58593
$883$	23.0545	0.775846	0.387923	−	0.921692i	$-0.373193\pi$
$883$	23.0545	0.775846	0.387923	+	0.921692i	$0.373193\pi$
$884$	−4.07360	−0.137010
$885$	46.9056	1.57672
$886$	33.0092	1.10897
$887$	7.35094	0.246820	0.123410	−	0.992356i	$-0.460617\pi$
$887$	7.35094	0.246820	0.123410	+	0.992356i	$0.460617\pi$
$888$	99.1057	3.32577
$889$	34.1433	1.14513
$890$	−52.3051	−1.75327
$891$	−43.0545	−1.44238
$892$	15.7774	0.528266
$893$	23.0772	0.772249
$894$	124.341	4.15859
$895$	22.3734	0.747860
$896$	−87.3078	−2.91675
$897$	3.15048	0.105191
$898$	−59.0127	−1.96928
$899$	22.6489	0.755382
$900$	16.5137	0.550455
$901$	−52.1970	−1.73893
$902$	0.0886417	0.00295144
$903$	−5.30866	−0.176661
$904$	34.4062	1.14433
$905$	−39.3966	−1.30959
$906$	−5.35521	−0.177915
$907$	36.4572	1.21054	0.605271	−	0.796019i	$-0.293065\pi$
$907$	36.4572	1.21054	0.605271	+	0.796019i	$0.293065\pi$
$908$	−58.7707	−1.95038
$909$	−76.9400	−2.55194
$910$	−5.90407	−0.195718
$911$	22.3737	0.741275	0.370638	−	0.928778i	$-0.379139\pi$
$911$	22.3737	0.741275	0.370638	+	0.928778i	$0.379139\pi$
$912$	26.9718	0.893127
$913$	−93.0813	−3.08054
$914$	70.5811	2.33462
$915$	13.9418	0.460900
$916$	−42.9227	−1.41821
$917$	−30.3865	−1.00345
$918$	92.2683	3.04531
$919$	13.3384	0.439994	0.219997	−	0.975501i	$-0.429395\pi$
$919$	13.3384	0.439994	0.219997	+	0.975501i	$0.429395\pi$
$920$	−49.7186	−1.63917
$921$	25.5188	0.840871
$922$	−51.3177	−1.69006
$923$	3.51048	0.115549
$924$	−273.457	−8.99609
$925$	5.17148	0.170037
$926$	−47.2071	−1.55132
$927$	−66.3747	−2.18003
$928$	−7.67534	−0.251955
$929$	−36.8530	−1.20911	−0.604554	−	0.796564i	$-0.706649\pi$
$929$	−36.8530	−1.20911	−0.604554	+	0.796564i	$0.706649\pi$
$930$	−46.1037	−1.51180
$931$	−30.5866	−1.00244
$932$	−104.583	−3.42573
$933$	−22.1034	−0.723633
$934$	−41.7232	−1.36523
$935$	−57.7233	−1.88775
$936$	6.40469	0.209344
$937$	41.5886	1.35864	0.679321	−	0.733841i	$-0.262274\pi$
$937$	41.5886	1.35864	0.679321	+	0.733841i	$0.262274\pi$
$938$	42.7467	1.39573
$939$	12.1312	0.395887
$940$	−81.8565	−2.66986
$941$	36.4948	1.18970	0.594848	−	0.803839i	$-0.297212\pi$
$941$	36.4948	1.18970	0.594848	+	0.803839i	$0.297212\pi$
$942$	−18.4212	−0.600197
$943$	0.0300736	0.000979332 0
$944$	−22.6353	−0.736716
$945$	88.4348	2.87678
$946$	−5.46655	−0.177733
$947$	0.831007	0.0270041	0.0135021	−	0.999909i	$-0.495702\pi$
$947$	0.831007	0.0270041	0.0135021	+	0.999909i	$0.495702\pi$
$948$	−126.671	−4.11408
$949$	1.77197	0.0575204
$950$	4.60413	0.149378
$951$	−85.2469	−2.76432
$952$	88.4921	2.86805
$953$	30.0385	0.973043	0.486522	−	0.873669i	$-0.338265\pi$
$953$	30.0385	0.973043	0.486522	+	0.873669i	$0.338265\pi$
$954$	168.230	5.44663
$955$	−52.3990	−1.69559
$956$	−16.2828	−0.526623
$957$	−138.052	−4.46258
$958$	38.5063	1.24408
$959$	84.4486	2.72699
$960$	64.6242	2.08574
$961$	−23.9099	−0.771289
$962$	4.11157	0.132562
$963$	71.1582	2.29304
$964$	47.8243	1.54032
$965$	−62.6286	−2.01609
$966$	−140.294	−4.51390
$967$	−41.5740	−1.33693	−0.668465	−	0.743743i	$-0.733048\pi$
$967$	−41.5740	−1.33693	−0.668465	+	0.743743i	$0.733048\pi$
$968$	−86.4482	−2.77855
$969$	34.7545	1.11648
$970$	−103.592	−3.32615
$971$	21.6681	0.695361	0.347681	−	0.937613i	$-0.386969\pi$
$971$	21.6681	0.695361	0.347681	+	0.937613i	$0.386969\pi$
$972$	8.44541	0.270887
$973$	96.1757	3.08325
$974$	−10.1519	−0.325288
$975$	0.504822	0.0161672
$976$	−6.72788	−0.215354
$977$	12.9510	0.414340	0.207170	−	0.978305i	$-0.433575\pi$
$977$	12.9510	0.414340	0.207170	+	0.978305i	$0.433575\pi$
$978$	22.8975	0.732183
$979$	−49.0291	−1.56698
$980$	108.493	3.46568
$981$	−65.9541	−2.10575
$982$	−71.4402	−2.27975
$983$	−30.6009	−0.976016	−0.488008	−	0.872839i	$-0.662276\pi$
$983$	−30.6009	−0.976016	−0.488008	+	0.872839i	$0.662276\pi$
$984$	0.0923487	0.00294397
$985$	41.3695	1.31814
$986$	91.5787	2.91646
$987$	−112.677	−3.58656
$988$	2.42068	0.0770121
$989$	−1.85465	−0.0589743
$990$	186.041	5.91276
$991$	−33.5228	−1.06489	−0.532443	−	0.846466i	$-0.678726\pi$
$991$	−33.5228	−1.06489	−0.532443	+	0.846466i	$0.678726\pi$
$992$	−2.40271	−0.0762860
$993$	−3.46221	−0.109870
$994$	−156.326	−4.95835
$995$	−39.3293	−1.24682
$996$	−198.789	−6.29887
$997$	−32.8027	−1.03887	−0.519436	−	0.854509i	$-0.673858\pi$
$997$	−32.8027	−1.03887	−0.519436	+	0.854509i	$0.673858\pi$
$998$	−0.247212	−0.00782535
$999$	−61.5855	−1.94848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.20	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.20	✓	259	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)

\(f(q)\)	\(=\)	\(q-2.43000 q^{2} -2.97934 q^{3} +3.90490 q^{4} +2.39158 q^{5} +7.23980 q^{6} -4.31478 q^{7} -4.62892 q^{8} +5.87647 q^{9} +O(q^{10})\)	\(q-2.43000 q^{2} -2.97934 q^{3} +3.90490 q^{4} +2.39158 q^{5} +7.23980 q^{6} -4.31478 q^{7} -4.62892 q^{8} +5.87647 q^{9} -5.81153 q^{10} -5.44754 q^{11} -11.6340 q^{12} -0.235452 q^{13} +10.4849 q^{14} -7.12532 q^{15} +3.43847 q^{16} +4.43064 q^{17} -14.2798 q^{18} -2.63284 q^{19} +9.33888 q^{20} +12.8552 q^{21} +13.2375 q^{22} +4.49112 q^{23} +13.7911 q^{24} +0.719641 q^{25} +0.572148 q^{26} -8.56998 q^{27} -16.8488 q^{28} -8.50593 q^{29} +17.3145 q^{30} -2.66272 q^{31} +0.902352 q^{32} +16.2301 q^{33} -10.7665 q^{34} -10.3191 q^{35} +22.9471 q^{36} +7.18619 q^{37} +6.39781 q^{38} +0.701491 q^{39} -11.0704 q^{40} +0.00669624 q^{41} -31.2382 q^{42} -0.412958 q^{43} -21.2721 q^{44} +14.0540 q^{45} -10.9134 q^{46} -8.76513 q^{47} -10.2444 q^{48} +11.6173 q^{49} -1.74873 q^{50} -13.2004 q^{51} -0.919417 q^{52} -11.7809 q^{53} +20.8251 q^{54} -13.0282 q^{55} +19.9728 q^{56} +7.84413 q^{57} +20.6694 q^{58} -6.58295 q^{59} -27.8237 q^{60} -1.95665 q^{61} +6.47040 q^{62} -25.3557 q^{63} -9.06966 q^{64} -0.563101 q^{65} -39.4391 q^{66} +4.07697 q^{67} +17.3012 q^{68} -13.3806 q^{69} +25.0755 q^{70} -14.9096 q^{71} -27.2017 q^{72} -7.52581 q^{73} -17.4625 q^{74} -2.14406 q^{75} -10.2810 q^{76} +23.5049 q^{77} -1.70462 q^{78} +10.8880 q^{79} +8.22337 q^{80} +7.90349 q^{81} -0.0162719 q^{82} +17.0869 q^{83} +50.1983 q^{84} +10.5962 q^{85} +1.00349 q^{86} +25.3421 q^{87} +25.2162 q^{88} +9.00022 q^{89} -34.1513 q^{90} +1.01592 q^{91} +17.5374 q^{92} +7.93314 q^{93} +21.2993 q^{94} -6.29665 q^{95} -2.68841 q^{96} +17.8253 q^{97} -28.2301 q^{98} -32.0123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

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