LMFDB - Embedded newform 6043.2.a.b.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.78744 q^{2} +0.620034 q^{3} +5.76982 q^{4} +0.534830 q^{5} -1.72831 q^{6} -0.323304 q^{7} -10.5081 q^{8} -2.61556 q^{9} +O(q^{10})$	\(q-2.78744 q^{2} +0.620034 q^{3} +5.76982 q^{4} +0.534830 q^{5} -1.72831 q^{6} -0.323304 q^{7} -10.5081 q^{8} -2.61556 q^{9} -1.49081 q^{10} -3.05404 q^{11} +3.57749 q^{12} +0.0721059 q^{13} +0.901189 q^{14} +0.331613 q^{15} +17.7512 q^{16} +0.928589 q^{17} +7.29071 q^{18} +7.46525 q^{19} +3.08587 q^{20} -0.200459 q^{21} +8.51295 q^{22} -3.06617 q^{23} -6.51541 q^{24} -4.71396 q^{25} -0.200991 q^{26} -3.48184 q^{27} -1.86540 q^{28} +1.93189 q^{29} -0.924351 q^{30} +2.44108 q^{31} -28.4640 q^{32} -1.89361 q^{33} -2.58839 q^{34} -0.172912 q^{35} -15.0913 q^{36} +5.97032 q^{37} -20.8089 q^{38} +0.0447081 q^{39} -5.62007 q^{40} +10.8098 q^{41} +0.558768 q^{42} -7.67694 q^{43} -17.6213 q^{44} -1.39888 q^{45} +8.54677 q^{46} +1.10341 q^{47} +11.0063 q^{48} -6.89547 q^{49} +13.1399 q^{50} +0.575757 q^{51} +0.416038 q^{52} -7.27242 q^{53} +9.70541 q^{54} -1.63339 q^{55} +3.39732 q^{56} +4.62871 q^{57} -5.38502 q^{58} -12.0281 q^{59} +1.91335 q^{60} +5.27823 q^{61} -6.80437 q^{62} +0.845619 q^{63} +43.8394 q^{64} +0.0385644 q^{65} +5.27832 q^{66} +5.90627 q^{67} +5.35779 q^{68} -1.90113 q^{69} +0.481983 q^{70} +12.8779 q^{71} +27.4846 q^{72} -1.09610 q^{73} -16.6419 q^{74} -2.92281 q^{75} +43.0731 q^{76} +0.987382 q^{77} -0.124621 q^{78} +15.7379 q^{79} +9.49386 q^{80} +5.68781 q^{81} -30.1318 q^{82} -6.80665 q^{83} -1.15661 q^{84} +0.496637 q^{85} +21.3990 q^{86} +1.19784 q^{87} +32.0923 q^{88} -0.418360 q^{89} +3.89929 q^{90} -0.0233121 q^{91} -17.6913 q^{92} +1.51355 q^{93} -3.07570 q^{94} +3.99264 q^{95} -17.6487 q^{96} +8.49658 q^{97} +19.2207 q^{98} +7.98801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.78744	−1.97102	−0.985509	−	0.169625i	$-0.945744\pi$
$2$	−2.78744	−1.97102	−0.985509	+	0.169625i	$0.945744\pi$
$3$	0.620034	0.357977	0.178988	−	0.983851i	$-0.442718\pi$
$3$	0.620034	0.357977	0.178988	+	0.983851i	$0.442718\pi$
$4$	5.76982	2.88491
$5$	0.534830	0.239183	0.119592	−	0.992823i	$-0.461841\pi$
$5$	0.534830	0.239183	0.119592	+	0.992823i	$0.461841\pi$
$6$	−1.72831	−0.705579
$7$	−0.323304	−0.122197	−0.0610986	−	0.998132i	$-0.519460\pi$
$7$	−0.323304	−0.122197	−0.0610986	+	0.998132i	$0.519460\pi$
$8$	−10.5081	−3.71519
$9$	−2.61556	−0.871852
$10$	−1.49081	−0.471434
$11$	−3.05404	−0.920827	−0.460414	−	0.887704i	$-0.652299\pi$
$11$	−3.05404	−0.920827	−0.460414	+	0.887704i	$0.652299\pi$
$12$	3.57749	1.03273
$13$	0.0721059	0.0199986	0.00999929	−	0.999950i	$-0.496817\pi$
$13$	0.0721059	0.0199986	0.00999929	+	0.999950i	$0.496817\pi$
$14$	0.901189	0.240853
$15$	0.331613	0.0856221
$16$	17.7512	4.43779
$17$	0.928589	0.225216	0.112608	−	0.993639i	$-0.464080\pi$
$17$	0.928589	0.225216	0.112608	+	0.993639i	$0.464080\pi$
$18$	7.29071	1.71844
$19$	7.46525	1.71265	0.856323	−	0.516441i	$-0.172743\pi$
$19$	7.46525	1.71265	0.856323	+	0.516441i	$0.172743\pi$
$20$	3.08587	0.690022
$21$	−0.200459	−0.0437438
$22$	8.51295	1.81497
$23$	−3.06617	−0.639341	−0.319671	−	0.947529i	$-0.603572\pi$
$23$	−3.06617	−0.639341	−0.319671	+	0.947529i	$0.603572\pi$
$24$	−6.51541	−1.32995
$25$	−4.71396	−0.942791
$26$	−0.200991	−0.0394175
$27$	−3.48184	−0.670080
$28$	−1.86540	−0.352528
$29$	1.93189	0.358743	0.179371	−	0.983781i	$-0.442594\pi$
$29$	1.93189	0.358743	0.179371	+	0.983781i	$0.442594\pi$
$30$	−0.924351	−0.168763
$31$	2.44108	0.438431	0.219216	−	0.975676i	$-0.429650\pi$
$31$	2.44108	0.438431	0.219216	+	0.975676i	$0.429650\pi$
$32$	−28.4640	−5.03178
$33$	−1.89361	−0.329635
$34$	−2.58839	−0.443905
$35$	−0.172912	−0.0292275
$36$	−15.0913	−2.51522
$37$	5.97032	0.981515	0.490757	−	0.871296i	$-0.336720\pi$
$37$	5.97032	0.981515	0.490757	+	0.871296i	$0.336720\pi$
$38$	−20.8089	−3.37565
$39$	0.0447081	0.00715903
$40$	−5.62007	−0.888611
$41$	10.8098	1.68821	0.844106	−	0.536176i	$-0.180132\pi$
$41$	10.8098	1.68821	0.844106	+	0.536176i	$0.180132\pi$
$42$	0.558768	0.0862198
$43$	−7.67694	−1.17072	−0.585361	−	0.810773i	$-0.699047\pi$
$43$	−7.67694	−1.17072	−0.585361	+	0.810773i	$0.699047\pi$
$44$	−17.6213	−2.65650
$45$	−1.39888	−0.208532
$46$	8.54677	1.26015
$47$	1.10341	0.160949	0.0804747	−	0.996757i	$-0.474356\pi$
$47$	1.10341	0.160949	0.0804747	+	0.996757i	$0.474356\pi$
$48$	11.0063	1.58863
$49$	−6.89547	−0.985068
$50$	13.1399	1.85826
$51$	0.575757	0.0806221
$52$	0.416038	0.0576941
$53$	−7.27242	−0.998943	−0.499472	−	0.866330i	$-0.666472\pi$
$53$	−7.27242	−0.998943	−0.499472	+	0.866330i	$0.666472\pi$
$54$	9.70541	1.32074
$55$	−1.63339	−0.220246
$56$	3.39732	0.453986
$57$	4.62871	0.613088
$58$	−5.38502	−0.707088
$59$	−12.0281	−1.56592	−0.782962	−	0.622070i	$-0.786292\pi$
$59$	−12.0281	−1.56592	−0.782962	+	0.622070i	$0.786292\pi$
$60$	1.91335	0.247012
$61$	5.27823	0.675808	0.337904	−	0.941181i	$-0.390282\pi$
$61$	5.27823	0.675808	0.337904	+	0.941181i	$0.390282\pi$
$62$	−6.80437	−0.864155
$63$	0.845619	0.106538
$64$	43.8394	5.47993
$65$	0.0385644	0.00478332
$66$	5.27832	0.649716
$67$	5.90627	0.721566	0.360783	−	0.932650i	$-0.382510\pi$
$67$	5.90627	0.721566	0.360783	+	0.932650i	$0.382510\pi$
$68$	5.35779	0.649728
$69$	−1.90113	−0.228869
$70$	0.481983	0.0576080
$71$	12.8779	1.52832	0.764161	−	0.645025i	$-0.223153\pi$
$71$	12.8779	1.52832	0.764161	+	0.645025i	$0.223153\pi$
$72$	27.4846	3.23910
$73$	−1.09610	−0.128289	−0.0641444	−	0.997941i	$-0.520432\pi$
$73$	−1.09610	−0.128289	−0.0641444	+	0.997941i	$0.520432\pi$
$74$	−16.6419	−1.93458
$75$	−2.92281	−0.337498
$76$	43.0731	4.94083
$77$	0.987382	0.112523
$78$	−0.124621	−0.0141106
$79$	15.7379	1.77065	0.885325	−	0.464974i	$-0.153936\pi$
$79$	15.7379	1.77065	0.885325	+	0.464974i	$0.153936\pi$
$80$	9.49386	1.06145
$81$	5.68781	0.631979
$82$	−30.1318	−3.32750
$83$	−6.80665	−0.747127	−0.373563	−	0.927605i	$-0.621864\pi$
$83$	−6.80665	−0.747127	−0.373563	+	0.927605i	$0.621864\pi$
$84$	−1.15661	−0.126197
$85$	0.496637	0.0538679
$86$	21.3990	2.30751
$87$	1.19784	0.128422
$88$	32.0923	3.42105
$89$	−0.418360	−0.0443461	−0.0221731	−	0.999754i	$-0.507058\pi$
$89$	−0.418360	−0.0443461	−0.0221731	+	0.999754i	$0.507058\pi$
$90$	3.89929	0.411021
$91$	−0.0233121	−0.00244377
$92$	−17.6913	−1.84444
$93$	1.51355	0.156948
$94$	−3.07570	−0.317234
$95$	3.99264	0.409636
$96$	−17.6487	−1.80126
$97$	8.49658	0.862697	0.431348	−	0.902185i	$-0.358038\pi$
$97$	8.49658	0.862697	0.431348	+	0.902185i	$0.358038\pi$
$98$	19.2207	1.94159
$99$	7.98801	0.802826
$100$	−27.1987	−2.71987
$101$	−13.2560	−1.31902	−0.659512	−	0.751694i	$-0.729237\pi$
$101$	−13.2560	−1.31902	−0.659512	+	0.751694i	$0.729237\pi$
$102$	−1.60489	−0.158908
$103$	−14.3448	−1.41344	−0.706718	−	0.707495i	$-0.749825\pi$
$103$	−14.3448	−1.41344	−0.706718	+	0.707495i	$0.749825\pi$
$104$	−0.757699	−0.0742985
$105$	−0.107212	−0.0104628
$106$	20.2714	1.96893
$107$	7.05792	0.682314	0.341157	−	0.940006i	$-0.389181\pi$
$107$	7.05792	0.682314	0.341157	+	0.940006i	$0.389181\pi$
$108$	−20.0896	−1.93312
$109$	−9.63063	−0.922447	−0.461224	−	0.887284i	$-0.652589\pi$
$109$	−9.63063	−0.922447	−0.461224	+	0.887284i	$0.652589\pi$
$110$	4.55298	0.434110
$111$	3.70180	0.351360
$112$	−5.73902	−0.542286
$113$	10.6144	0.998523	0.499262	−	0.866451i	$-0.333605\pi$
$113$	10.6144	0.998523	0.499262	+	0.866451i	$0.333605\pi$
$114$	−12.9023	−1.20841
$115$	−1.63988	−0.152920
$116$	11.1466	1.03494
$117$	−0.188597	−0.0174358
$118$	33.5276	3.08646
$119$	−0.300216	−0.0275208
$120$	−3.48464	−0.318102
$121$	−1.67285	−0.152077
$122$	−14.7127	−1.33203
$123$	6.70247	0.604341
$124$	14.0846	1.26483
$125$	−5.19532	−0.464683
$126$	−2.35711	−0.209988
$127$	20.8290	1.84828	0.924138	−	0.382058i	$-0.124785\pi$
$127$	20.8290	1.84828	0.924138	+	0.382058i	$0.124785\pi$
$128$	−65.2717	−5.76925
$129$	−4.75996	−0.419091
$130$	−0.107496	−0.00942801
$131$	−10.2135	−0.892358	−0.446179	−	0.894944i	$-0.647216\pi$
$131$	−10.2135	−0.892358	−0.446179	+	0.894944i	$0.647216\pi$
$132$	−10.9258	−0.950967
$133$	−2.41354	−0.209281
$134$	−16.4634	−1.42222
$135$	−1.86219	−0.160272
$136$	−9.75775	−0.836720
$137$	−20.5560	−1.75622	−0.878109	−	0.478460i	$-0.841195\pi$
$137$	−20.5560	−1.75622	−0.878109	+	0.478460i	$0.841195\pi$
$138$	5.29929	0.451106
$139$	−8.45653	−0.717273	−0.358637	−	0.933477i	$-0.616758\pi$
$139$	−8.45653	−0.717273	−0.358637	+	0.933477i	$0.616758\pi$
$140$	−0.997673	−0.0843188
$141$	0.684154	0.0576162
$142$	−35.8963	−3.01235
$143$	−0.220214	−0.0184152
$144$	−46.4292	−3.86910
$145$	1.03323	0.0858052
$146$	3.05531	0.252859
$147$	−4.27543	−0.352632
$148$	34.4477	2.83158
$149$	3.57129	0.292572	0.146286	−	0.989242i	$-0.453268\pi$
$149$	3.57129	0.292572	0.146286	+	0.989242i	$0.453268\pi$
$150$	8.14717	0.665214
$151$	−2.23484	−0.181868	−0.0909342	−	0.995857i	$-0.528985\pi$
$151$	−2.23484	−0.181868	−0.0909342	+	0.995857i	$0.528985\pi$
$152$	−78.4459	−6.36280
$153$	−2.42878	−0.196355
$154$	−2.75227	−0.221784
$155$	1.30556	0.104865
$156$	0.257958	0.0206531
$157$	9.46726	0.755570	0.377785	−	0.925893i	$-0.376686\pi$
$157$	9.46726	0.755570	0.377785	+	0.925893i	$0.376686\pi$
$158$	−43.8684	−3.48998
$159$	−4.50915	−0.357599
$160$	−15.2234	−1.20352
$161$	0.991305	0.0781257
$162$	−15.8544	−1.24564
$163$	−17.5323	−1.37323	−0.686616	−	0.727020i	$-0.740905\pi$
$163$	−17.5323	−1.37323	−0.686616	+	0.727020i	$0.740905\pi$
$164$	62.3708	4.87034
$165$	−1.01276	−0.0788432
$166$	18.9731	1.47260
$167$	−6.24642	−0.483363	−0.241681	−	0.970356i	$-0.577699\pi$
$167$	−6.24642	−0.483363	−0.241681	+	0.970356i	$0.577699\pi$
$168$	2.10645	0.162517
$169$	−12.9948	−0.999600
$170$	−1.38435	−0.106175
$171$	−19.5258	−1.49317
$172$	−44.2945	−3.37743
$173$	3.38507	0.257362	0.128681	−	0.991686i	$-0.458926\pi$
$173$	3.38507	0.257362	0.128681	+	0.991686i	$0.458926\pi$
$174$	−3.33890	−0.253121
$175$	1.52404	0.115207
$176$	−54.2128	−4.08644
$177$	−7.45783	−0.560565
$178$	1.16615	0.0874069
$179$	−14.9495	−1.11738	−0.558690	−	0.829377i	$-0.688696\pi$
$179$	−14.9495	−1.11738	−0.558690	+	0.829377i	$0.688696\pi$
$180$	−8.07128	−0.601597
$181$	3.71466	0.276108	0.138054	−	0.990425i	$-0.455915\pi$
$181$	3.71466	0.276108	0.138054	+	0.990425i	$0.455915\pi$
$182$	0.0649810	0.00481672
$183$	3.27268	0.241924
$184$	32.2198	2.37527
$185$	3.19311	0.234762
$186$	−4.21894	−0.309348
$187$	−2.83595	−0.207385
$188$	6.36650	0.464325
$189$	1.12569	0.0818820
$190$	−11.1292	−0.807400
$191$	16.0293	1.15984	0.579918	−	0.814675i	$-0.303084\pi$
$191$	16.0293	1.15984	0.579918	+	0.814675i	$0.303084\pi$
$192$	27.1819	1.96169
$193$	2.16694	0.155980	0.0779899	−	0.996954i	$-0.475150\pi$
$193$	2.16694	0.155980	0.0779899	+	0.996954i	$0.475150\pi$
$194$	−23.6837	−1.70039
$195$	0.0239112	0.00171232
$196$	−39.7856	−2.84183
$197$	−22.0414	−1.57039	−0.785193	−	0.619251i	$-0.787437\pi$
$197$	−22.0414	−1.57039	−0.785193	+	0.619251i	$0.787437\pi$
$198$	−22.2661	−1.58238
$199$	23.0245	1.63216	0.816080	−	0.577939i	$-0.196143\pi$
$199$	23.0245	1.63216	0.816080	+	0.577939i	$0.196143\pi$
$200$	49.5349	3.50265
$201$	3.66209	0.258304
$202$	36.9504	2.59982
$203$	−0.624587	−0.0438374
$204$	3.32201	0.232588
$205$	5.78142	0.403792
$206$	39.9853	2.78591
$207$	8.01975	0.557411
$208$	1.27996	0.0887495
$209$	−22.7992	−1.57705
$210$	0.298846	0.0206223
$211$	−23.4109	−1.61168	−0.805838	−	0.592136i	$-0.798285\pi$
$211$	−23.4109	−1.61168	−0.805838	+	0.592136i	$0.798285\pi$
$212$	−41.9605	−2.88186
$213$	7.98472	0.547104
$214$	−19.6735	−1.34485
$215$	−4.10586	−0.280017
$216$	36.5876	2.48947
$217$	−0.789210	−0.0535751
$218$	26.8448	1.81816
$219$	−0.679619	−0.0459244
$220$	−9.42437	−0.635391
$221$	0.0669568	0.00450400
$222$	−10.3186	−0.692536
$223$	−22.7848	−1.52578	−0.762891	−	0.646527i	$-0.776221\pi$
$223$	−22.7848	−1.52578	−0.762891	+	0.646527i	$0.776221\pi$
$224$	9.20252	0.614869
$225$	12.3296	0.821975
$226$	−29.5871	−1.96811
$227$	−10.4820	−0.695713	−0.347856	−	0.937548i	$-0.613090\pi$
$227$	−10.4820	−0.695713	−0.347856	+	0.937548i	$0.613090\pi$
$228$	26.7068	1.76870
$229$	−2.31850	−0.153211	−0.0766054	−	0.997061i	$-0.524408\pi$
$229$	−2.31850	−0.153211	−0.0766054	+	0.997061i	$0.524408\pi$
$230$	4.57107	0.301407
$231$	0.612211	0.0402805
$232$	−20.3006	−1.33280
$233$	−1.42166	−0.0931359	−0.0465680	−	0.998915i	$-0.514828\pi$
$233$	−1.42166	−0.0931359	−0.0465680	+	0.998915i	$0.514828\pi$
$234$	0.525703	0.0343663
$235$	0.590139	0.0384964
$236$	−69.3999	−4.51755
$237$	9.75802	0.633852
$238$	0.836835	0.0542439
$239$	1.11810	0.0723239	0.0361619	−	0.999346i	$-0.488487\pi$
$239$	1.11810	0.0723239	0.0361619	+	0.999346i	$0.488487\pi$
$240$	5.88652	0.379973
$241$	2.51934	0.162285	0.0811424	−	0.996703i	$-0.474143\pi$
$241$	2.51934	0.162285	0.0811424	+	0.996703i	$0.474143\pi$
$242$	4.66296	0.299746
$243$	13.9722	0.896314
$244$	30.4544	1.94964
$245$	−3.68791	−0.235612
$246$	−18.6827	−1.19117
$247$	0.538289	0.0342505
$248$	−25.6512	−1.62885
$249$	−4.22036	−0.267454
$250$	14.4816	0.915898
$251$	−2.34417	−0.147963	−0.0739813	−	0.997260i	$-0.523570\pi$
$251$	−2.34417	−0.147963	−0.0739813	+	0.997260i	$0.523570\pi$
$252$	4.87907	0.307352
$253$	9.36421	0.588723
$254$	−58.0596	−3.64299
$255$	0.307932	0.0192835
$256$	94.2620	5.89137
$257$	6.25255	0.390024	0.195012	−	0.980801i	$-0.437525\pi$
$257$	6.25255	0.390024	0.195012	+	0.980801i	$0.437525\pi$
$258$	13.2681	0.826036
$259$	−1.93023	−0.119938
$260$	0.222510	0.0137995
$261$	−5.05297	−0.312771
$262$	28.4695	1.75885
$263$	18.7096	1.15368	0.576842	−	0.816856i	$-0.304285\pi$
$263$	18.7096	1.15368	0.576842	+	0.816856i	$0.304285\pi$
$264$	19.8983	1.22466
$265$	−3.88951	−0.238930
$266$	6.72760	0.412496
$267$	−0.259398	−0.0158749
$268$	34.0781	2.08165
$269$	−16.0077	−0.976004	−0.488002	−	0.872842i	$-0.662274\pi$
$269$	−16.0077	−0.976004	−0.488002	+	0.872842i	$0.662274\pi$
$270$	5.19075	0.315899
$271$	7.23812	0.439685	0.219842	−	0.975535i	$-0.429446\pi$
$271$	7.23812	0.439685	0.219842	+	0.975535i	$0.429446\pi$
$272$	16.4835	0.999462
$273$	−0.0144543	−0.000874814 0
$274$	57.2986	3.46154
$275$	14.3966	0.868148
$276$	−10.9692	−0.660267
$277$	−17.7085	−1.06400	−0.531999	−	0.846745i	$-0.678559\pi$
$277$	−17.7085	−1.06400	−0.531999	+	0.846745i	$0.678559\pi$
$278$	23.5721	1.41376
$279$	−6.38479	−0.382247
$280$	1.81699	0.108586
$281$	−10.8654	−0.648178	−0.324089	−	0.946027i	$-0.605058\pi$
$281$	−10.8654	−0.648178	−0.324089	+	0.946027i	$0.605058\pi$
$282$	−1.90704	−0.113563
$283$	−16.9462	−1.00735	−0.503674	−	0.863894i	$-0.668019\pi$
$283$	−16.9462	−1.00735	−0.503674	+	0.863894i	$0.668019\pi$
$284$	74.3030	4.40907
$285$	2.47557	0.146640
$286$	0.613834	0.0362967
$287$	−3.49486	−0.206295
$288$	74.4493	4.38697
$289$	−16.1377	−0.949278
$290$	−2.88007	−0.169124
$291$	5.26817	0.308826
$292$	−6.32430	−0.370101
$293$	−15.2241	−0.889402	−0.444701	−	0.895679i	$-0.646690\pi$
$293$	−15.2241	−0.889402	−0.444701	+	0.895679i	$0.646690\pi$
$294$	11.9175	0.695043
$295$	−6.43298	−0.374543
$296$	−62.7370	−3.64651
$297$	10.6337	0.617028
$298$	−9.95477	−0.576664
$299$	−0.221089	−0.0127859
$300$	−16.8641	−0.973650
$301$	2.48198	0.143059
$302$	6.22947	0.358466
$303$	−8.21919	−0.472180
$304$	132.517	7.60037
$305$	2.82296	0.161642
$306$	6.77007	0.387019
$307$	17.5570	1.00203	0.501015	−	0.865439i	$-0.332960\pi$
$307$	17.5570	1.00203	0.501015	+	0.865439i	$0.332960\pi$
$308$	5.69701	0.324617
$309$	−8.89428	−0.505978
$310$	−3.63918	−0.206691
$311$	11.4011	0.646497	0.323248	−	0.946314i	$-0.395225\pi$
$311$	11.4011	0.646497	0.323248	+	0.946314i	$0.395225\pi$
$312$	−0.469799	−0.0265971
$313$	−14.6990	−0.830838	−0.415419	−	0.909630i	$-0.636365\pi$
$313$	−14.6990	−0.830838	−0.415419	+	0.909630i	$0.636365\pi$
$314$	−26.3894	−1.48924
$315$	0.452262	0.0254821
$316$	90.8047	5.10816
$317$	32.6442	1.83348	0.916740	−	0.399484i	$-0.130811\pi$
$317$	32.6442	1.83348	0.916740	+	0.399484i	$0.130811\pi$
$318$	12.5690	0.704833
$319$	−5.90006	−0.330340
$320$	23.4466	1.31071
$321$	4.37615	0.244253
$322$	−2.76320	−0.153987
$323$	6.93215	0.385715
$324$	32.8177	1.82320
$325$	−0.339904	−0.0188545
$326$	48.8701	2.70667
$327$	−5.97132	−0.330215
$328$	−113.591	−6.27203
$329$	−0.356738	−0.0196676
$330$	2.82300	0.155401
$331$	15.7869	0.867728	0.433864	−	0.900978i	$-0.357150\pi$
$331$	15.7869	0.867728	0.433864	+	0.900978i	$0.357150\pi$
$332$	−39.2731	−2.15539
$333$	−15.6157	−0.855736
$334$	17.4115	0.952716
$335$	3.15885	0.172586
$336$	−3.55839	−0.194126
$337$	−2.85647	−0.155602	−0.0778009	−	0.996969i	$-0.524790\pi$
$337$	−2.85647	−0.155602	−0.0778009	+	0.996969i	$0.524790\pi$
$338$	36.2222	1.97023
$339$	6.58132	0.357448
$340$	2.86551	0.155404
$341$	−7.45516	−0.403719
$342$	54.4270	2.94307
$343$	4.49246	0.242570
$344$	80.6703	4.34945
$345$	−1.01678	−0.0547417
$346$	−9.43568	−0.507265
$347$	−20.1368	−1.08100	−0.540501	−	0.841343i	$-0.681765\pi$
$347$	−20.1368	−1.08100	−0.540501	+	0.841343i	$0.681765\pi$
$348$	6.91130	0.370485
$349$	−29.0125	−1.55300	−0.776501	−	0.630116i	$-0.783007\pi$
$349$	−29.0125	−1.55300	−0.776501	+	0.630116i	$0.783007\pi$
$350$	−4.24817	−0.227074
$351$	−0.251061	−0.0134006
$352$	86.9302	4.63340
$353$	6.74295	0.358891	0.179445	−	0.983768i	$-0.442570\pi$
$353$	6.74295	0.358891	0.179445	+	0.983768i	$0.442570\pi$
$354$	20.7882	1.10488
$355$	6.88747	0.365549
$356$	−2.41386	−0.127934
$357$	−0.186144	−0.00985181
$358$	41.6709	2.20238
$359$	−20.7505	−1.09517	−0.547585	−	0.836750i	$-0.684453\pi$
$359$	−20.7505	−1.09517	−0.547585	+	0.836750i	$0.684453\pi$
$360$	14.6996	0.774738
$361$	36.7300	1.93316
$362$	−10.3544	−0.544215
$363$	−1.03722	−0.0544400
$364$	−0.134507	−0.00705006
$365$	−0.586227	−0.0306845
$366$	−9.12241	−0.476836
$367$	−22.1365	−1.15551	−0.577757	−	0.816209i	$-0.696072\pi$
$367$	−22.1365	−1.15551	−0.577757	+	0.816209i	$0.696072\pi$
$368$	−54.4281	−2.83726
$369$	−28.2737	−1.47187
$370$	−8.90059	−0.462720
$371$	2.35120	0.122068
$372$	8.73293	0.452781
$373$	−6.81483	−0.352858	−0.176429	−	0.984313i	$-0.556455\pi$
$373$	−6.81483	−0.352858	−0.176429	+	0.984313i	$0.556455\pi$
$374$	7.90503	0.408760
$375$	−3.22127	−0.166346
$376$	−11.5948	−0.597958
$377$	0.139301	0.00717434
$378$	−3.13779	−0.161391
$379$	−7.50844	−0.385683	−0.192841	−	0.981230i	$-0.561770\pi$
$379$	−7.50844	−0.385683	−0.192841	+	0.981230i	$0.561770\pi$
$380$	23.0368	1.18176
$381$	12.9147	0.661640
$382$	−44.6806	−2.28606
$383$	−6.93330	−0.354275	−0.177138	−	0.984186i	$-0.556684\pi$
$383$	−6.93330	−0.354275	−0.177138	+	0.984186i	$0.556684\pi$
$384$	−40.4707	−2.06526
$385$	0.528081	0.0269135
$386$	−6.04021	−0.307439
$387$	20.0795	1.02070
$388$	49.0237	2.48880
$389$	20.5834	1.04362	0.521810	−	0.853061i	$-0.325257\pi$
$389$	20.5834	1.04362	0.521810	+	0.853061i	$0.325257\pi$
$390$	−0.0666511	−0.00337501
$391$	−2.84722	−0.143990
$392$	72.4586	3.65971
$393$	−6.33272	−0.319444
$394$	61.4392	3.09526
$395$	8.41709	0.423510
$396$	46.0894	2.31608
$397$	−8.17168	−0.410125	−0.205062	−	0.978749i	$-0.565740\pi$
$397$	−8.17168	−0.410125	−0.205062	+	0.978749i	$0.565740\pi$
$398$	−64.1793	−3.21702
$399$	−1.49648	−0.0749177
$400$	−83.6782	−4.18391
$401$	−2.49175	−0.124432	−0.0622159	−	0.998063i	$-0.519817\pi$
$401$	−2.49175	−0.124432	−0.0622159	+	0.998063i	$0.519817\pi$
$402$	−10.2079	−0.509121
$403$	0.176016	0.00876800
$404$	−76.4849	−3.80526
$405$	3.04201	0.151159
$406$	1.74100	0.0864042
$407$	−18.2336	−0.903806
$408$	−6.05014	−0.299526
$409$	−37.7086	−1.86457	−0.932285	−	0.361725i	$-0.882188\pi$
$409$	−37.7086	−1.86457	−0.932285	+	0.361725i	$0.882188\pi$
$410$	−16.1154	−0.795881
$411$	−12.7454	−0.628686
$412$	−82.7670	−4.07764
$413$	3.88872	0.191352
$414$	−22.3546	−1.09867
$415$	−3.64040	−0.178700
$416$	−2.05242	−0.100628
$417$	−5.24334	−0.256767
$418$	63.5513	3.10840
$419$	9.79537	0.478535	0.239268	−	0.970954i	$-0.423093\pi$
$419$	9.79537	0.478535	0.239268	+	0.970954i	$0.423093\pi$
$420$	−0.618592	−0.0301842
$421$	1.90104	0.0926510	0.0463255	−	0.998926i	$-0.485249\pi$
$421$	1.90104	0.0926510	0.0463255	+	0.998926i	$0.485249\pi$
$422$	65.2566	3.17664
$423$	−2.88604	−0.140324
$424$	76.4196	3.71126
$425$	−4.37733	−0.212332
$426$	−22.2569	−1.07835
$427$	−1.70647	−0.0825819
$428$	40.7229	1.96842
$429$	−0.136540	−0.00659223
$430$	11.4448	0.551918
$431$	−19.1380	−0.921847	−0.460924	−	0.887440i	$-0.652482\pi$
$431$	−19.1380	−0.921847	−0.460924	+	0.887440i	$0.652482\pi$
$432$	−61.8067	−2.97368
$433$	23.9001	1.14857	0.574283	−	0.818657i	$-0.305281\pi$
$433$	23.9001	1.14857	0.574283	+	0.818657i	$0.305281\pi$
$434$	2.19988	0.105597
$435$	0.640639	0.0307163
$436$	−55.5670	−2.66118
$437$	−22.8897	−1.09497
$438$	1.89440	0.0905178
$439$	−10.7513	−0.513133	−0.256567	−	0.966527i	$-0.582591\pi$
$439$	−10.7513	−0.513133	−0.256567	+	0.966527i	$0.582591\pi$
$440$	17.1639	0.818257
$441$	18.0355	0.858834
$442$	−0.186638	−0.00887746
$443$	−13.4271	−0.637940	−0.318970	−	0.947765i	$-0.603337\pi$
$443$	−13.4271	−0.637940	−0.318970	+	0.947765i	$0.603337\pi$
$444$	21.3587	1.01364
$445$	−0.223752	−0.0106068
$446$	63.5112	3.00734
$447$	2.21432	0.104734
$448$	−14.1734	−0.669632
$449$	21.1967	1.00034	0.500168	−	0.865928i	$-0.333272\pi$
$449$	21.1967	1.00034	0.500168	+	0.865928i	$0.333272\pi$
$450$	−34.3681	−1.62013
$451$	−33.0137	−1.55455
$452$	61.2434	2.88065
$453$	−1.38567	−0.0651047
$454$	29.2178	1.37126
$455$	−0.0124680	−0.000584509 0
$456$	−48.6392	−2.27774
$457$	19.0779	0.892425	0.446212	−	0.894927i	$-0.352773\pi$
$457$	19.0779	0.892425	0.446212	+	0.894927i	$0.352773\pi$
$458$	6.46268	0.301981
$459$	−3.23320	−0.150913
$460$	−9.46182	−0.441159
$461$	0.201006	0.00936179	0.00468090	−	0.999989i	$-0.498510\pi$
$461$	0.201006	0.00936179	0.00468090	+	0.999989i	$0.498510\pi$
$462$	−1.70650	−0.0793936
$463$	−6.69928	−0.311342	−0.155671	−	0.987809i	$-0.549754\pi$
$463$	−6.69928	−0.311342	−0.155671	+	0.987809i	$0.549754\pi$
$464$	34.2933	1.59203
$465$	0.809494	0.0375394
$466$	3.96279	0.183572
$467$	−14.6078	−0.675966	−0.337983	−	0.941152i	$-0.609745\pi$
$467$	−14.6078	−0.675966	−0.337983	+	0.941152i	$0.609745\pi$
$468$	−1.08817	−0.0503007
$469$	−1.90952	−0.0881734
$470$	−1.64498	−0.0758771
$471$	5.87003	0.270477
$472$	126.393	5.81770
$473$	23.4457	1.07803
$474$	−27.1999	−1.24933
$475$	−35.1909	−1.61467
$476$	−1.73219	−0.0793950
$477$	19.0214	0.870931
$478$	−3.11664	−0.142552
$479$	−17.2137	−0.786515	−0.393258	−	0.919428i	$-0.628652\pi$
$479$	−17.2137	−0.786515	−0.393258	+	0.919428i	$0.628652\pi$
$480$	−9.43904	−0.430831
$481$	0.430495	0.0196289
$482$	−7.02250	−0.319866
$483$	0.614643	0.0279672
$484$	−9.65202	−0.438728
$485$	4.54422	0.206343
$486$	−38.9465	−1.76665
$487$	−27.1178	−1.22882	−0.614412	−	0.788986i	$-0.710607\pi$
$487$	−27.1178	−1.22882	−0.614412	+	0.788986i	$0.710607\pi$
$488$	−55.4644	−2.51075
$489$	−10.8706	−0.491586
$490$	10.2798	0.464395
$491$	−33.4414	−1.50919	−0.754594	−	0.656192i	$-0.772166\pi$
$491$	−33.4414	−1.50919	−0.754594	+	0.656192i	$0.772166\pi$
$492$	38.6720	1.74347
$493$	1.79393	0.0807946
$494$	−1.50045	−0.0675083
$495$	4.27223	0.192022
$496$	43.3320	1.94567
$497$	−4.16346	−0.186757
$498$	11.7640	0.527157
$499$	22.4779	1.00625	0.503125	−	0.864213i	$-0.332183\pi$
$499$	22.4779	1.00625	0.503125	+	0.864213i	$0.332183\pi$
$500$	−29.9760	−1.34057
$501$	−3.87299	−0.173033
$502$	6.53422	0.291637
$503$	−40.7356	−1.81631	−0.908155	−	0.418634i	$-0.862509\pi$
$503$	−40.7356	−1.81631	−0.908155	+	0.418634i	$0.862509\pi$
$504$	−8.88589	−0.395809
$505$	−7.08972	−0.315488
$506$	−26.1022	−1.16038
$507$	−8.05722	−0.357834
$508$	120.180	5.33211
$509$	27.9648	1.23952	0.619759	−	0.784792i	$-0.287230\pi$
$509$	27.9648	1.23952	0.619759	+	0.784792i	$0.287230\pi$
$510$	−0.858342	−0.0380080
$511$	0.354373	0.0156765
$512$	−132.206	−5.84274
$513$	−25.9928	−1.14761
$514$	−17.4286	−0.768743
$515$	−7.67204	−0.338070
$516$	−27.4641	−1.20904
$517$	−3.36987	−0.148207
$518$	5.38039	0.236401
$519$	2.09886	0.0921297
$520$	−0.405240	−0.0177710
$521$	34.4637	1.50988	0.754940	−	0.655794i	$-0.227666\pi$
$521$	34.4637	1.50988	0.754940	+	0.655794i	$0.227666\pi$
$522$	14.0848	0.616477
$523$	−15.8566	−0.693359	−0.346680	−	0.937984i	$-0.612691\pi$
$523$	−15.8566	−0.693359	−0.346680	+	0.937984i	$0.612691\pi$
$524$	−58.9301	−2.57437
$525$	0.944957	0.0412413
$526$	−52.1519	−2.27393
$527$	2.26676	0.0987417
$528$	−33.6138	−1.46285
$529$	−13.5986	−0.591243
$530$	10.8418	0.470936
$531$	31.4602	1.36525
$532$	−13.9257	−0.603756
$533$	0.779453	0.0337618
$534$	0.723055	0.0312897
$535$	3.77478	0.163198
$536$	−62.0639	−2.68075
$537$	−9.26922	−0.399996
$538$	44.6204	1.92372
$539$	21.0590	0.907077
$540$	−10.7445	−0.462370
$541$	−22.8851	−0.983908	−0.491954	−	0.870621i	$-0.663717\pi$
$541$	−22.8851	−0.983908	−0.491954	+	0.870621i	$0.663717\pi$
$542$	−20.1758	−0.866626
$543$	2.30322	0.0988405
$544$	−26.4314	−1.13324
$545$	−5.15075	−0.220634
$546$	0.0402905	0.00172427
$547$	15.3626	0.656858	0.328429	−	0.944529i	$-0.393481\pi$
$547$	15.3626	0.656858	0.328429	+	0.944529i	$0.393481\pi$
$548$	−118.604	−5.06653
$549$	−13.8055	−0.589205
$550$	−40.1297	−1.71113
$551$	14.4220	0.614399
$552$	19.9774	0.850293
$553$	−5.08811	−0.216368
$554$	49.3613	2.09716
$555$	1.97984	0.0840393
$556$	−48.7926	−2.06927
$557$	−28.8962	−1.22437	−0.612185	−	0.790715i	$-0.709709\pi$
$557$	−28.8962	−1.22437	−0.612185	+	0.790715i	$0.709709\pi$
$558$	17.7972	0.753416
$559$	−0.553552	−0.0234128
$560$	−3.06940	−0.129706
$561$	−1.75838	−0.0742391
$562$	30.2868	1.27757
$563$	−23.8583	−1.00551	−0.502754	−	0.864430i	$-0.667680\pi$
$563$	−23.8583	−1.00551	−0.502754	+	0.864430i	$0.667680\pi$
$564$	3.94745	0.166217
$565$	5.67692	0.238830
$566$	47.2366	1.98550
$567$	−1.83889	−0.0772261
$568$	−135.323	−5.67801
$569$	−27.2281	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$569$	−27.2281	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$570$	−6.90051	−0.289031
$571$	23.1669	0.969504	0.484752	−	0.874652i	$-0.338910\pi$
$571$	23.1669	0.969504	0.484752	+	0.874652i	$0.338910\pi$
$572$	−1.27060	−0.0531263
$573$	9.93869	0.415195
$574$	9.74171	0.406611
$575$	14.4538	0.602765
$576$	−114.665	−4.77769
$577$	34.0941	1.41935	0.709677	−	0.704527i	$-0.248841\pi$
$577$	34.0941	1.41935	0.709677	+	0.704527i	$0.248841\pi$
$578$	44.9829	1.87104
$579$	1.34358	0.0558372
$580$	5.96156	0.247540
$581$	2.20061	0.0912968
$582$	−14.6847	−0.608700
$583$	22.2102	0.919854
$584$	11.5180	0.476617
$585$	−0.100867	−0.00417035
$586$	42.4363	1.75303
$587$	−13.0568	−0.538912	−0.269456	−	0.963013i	$-0.586844\pi$
$587$	−13.0568	−0.538912	−0.269456	+	0.963013i	$0.586844\pi$
$588$	−24.6685	−1.01731
$589$	18.2233	0.750877
$590$	17.9315	0.738230
$591$	−13.6664	−0.562162
$592$	105.980	4.35576
$593$	−8.87137	−0.364304	−0.182152	−	0.983270i	$-0.558306\pi$
$593$	−8.87137	−0.364304	−0.182152	+	0.983270i	$0.558306\pi$
$594$	−29.6407	−1.21617
$595$	−0.160565	−0.00658251
$596$	20.6057	0.844043
$597$	14.2759	0.584276
$598$	0.616272	0.0252013
$599$	6.29963	0.257396	0.128698	−	0.991684i	$-0.458920\pi$
$599$	6.29963	0.257396	0.128698	+	0.991684i	$0.458920\pi$
$600$	30.7134	1.25387
$601$	24.1039	0.983217	0.491608	−	0.870816i	$-0.336409\pi$
$601$	24.1039	0.983217	0.491608	+	0.870816i	$0.336409\pi$
$602$	−6.91837	−0.281972
$603$	−15.4482	−0.629099
$604$	−12.8946	−0.524674
$605$	−0.894688	−0.0363743
$606$	22.9105	0.930675
$607$	−18.3996	−0.746818	−0.373409	−	0.927667i	$-0.621811\pi$
$607$	−18.3996	−0.746818	−0.373409	+	0.927667i	$0.621811\pi$
$608$	−212.491	−8.61765
$609$	−0.387265	−0.0156928
$610$	−7.86882	−0.318599
$611$	0.0795626	0.00321876
$612$	−14.0136	−0.566467
$613$	−34.6947	−1.40131	−0.700653	−	0.713503i	$-0.747108\pi$
$613$	−34.6947	−1.40131	−0.700653	+	0.713503i	$0.747108\pi$
$614$	−48.9390	−1.97502
$615$	3.58468	0.144548
$616$	−10.3755	−0.418043
$617$	−42.9141	−1.72766	−0.863828	−	0.503787i	$-0.831940\pi$
$617$	−42.9141	−1.72766	−0.863828	+	0.503787i	$0.831940\pi$
$618$	24.7923	0.997291
$619$	34.9273	1.40385	0.701923	−	0.712253i	$-0.252325\pi$
$619$	34.9273	1.40385	0.701923	+	0.712253i	$0.252325\pi$
$620$	7.53286	0.302527
$621$	10.6759	0.428410
$622$	−31.7798	−1.27426
$623$	0.135257	0.00541897
$624$	0.793621	0.0317703
$625$	20.7912	0.831647
$626$	40.9726	1.63760
$627$	−14.1363	−0.564548
$628$	54.6244	2.17975
$629$	5.54398	0.221053
$630$	−1.26065	−0.0502257
$631$	30.8459	1.22795	0.613977	−	0.789324i	$-0.289569\pi$
$631$	30.8459	1.22795	0.613977	+	0.789324i	$0.289569\pi$
$632$	−165.376	−6.57830
$633$	−14.5156	−0.576943
$634$	−90.9937	−3.61382
$635$	11.1400	0.442077
$636$	−26.0170	−1.03164
$637$	−0.497204	−0.0197000
$638$	16.4461	0.651106
$639$	−33.6828	−1.33247
$640$	−34.9092	−1.37991
$641$	−10.5145	−0.415297	−0.207649	−	0.978203i	$-0.566581\pi$
$641$	−10.5145	−0.415297	−0.207649	+	0.978203i	$0.566581\pi$
$642$	−12.1983	−0.481427
$643$	18.7021	0.737540	0.368770	−	0.929521i	$-0.379779\pi$
$643$	18.7021	0.737540	0.368770	+	0.929521i	$0.379779\pi$
$644$	5.71965	0.225386
$645$	−2.54577	−0.100240
$646$	−19.3230	−0.760251
$647$	14.5184	0.570775	0.285388	−	0.958412i	$-0.407878\pi$
$647$	14.5184	0.570775	0.285388	+	0.958412i	$0.407878\pi$
$648$	−59.7683	−2.34792
$649$	36.7343	1.44195
$650$	0.947462	0.0371625
$651$	−0.489337	−0.0191786
$652$	−101.158	−3.96165
$653$	44.8898	1.75667	0.878336	−	0.478043i	$-0.158654\pi$
$653$	44.8898	1.75667	0.878336	+	0.478043i	$0.158654\pi$
$654$	16.6447	0.650859
$655$	−5.46249	−0.213437
$656$	191.887	7.49194
$657$	2.86691	0.111849
$658$	0.994385	0.0387651
$659$	30.4249	1.18519	0.592593	−	0.805502i	$-0.298104\pi$
$659$	30.4249	1.18519	0.592593	+	0.805502i	$0.298104\pi$
$660$	−5.84343	−0.227455
$661$	−28.5794	−1.11161	−0.555805	−	0.831312i	$-0.687590\pi$
$661$	−28.5794	−1.11161	−0.555805	+	0.831312i	$0.687590\pi$
$662$	−44.0051	−1.71031
$663$	0.0415155	0.00161233
$664$	71.5252	2.77572
$665$	−1.29083	−0.0500564
$666$	43.5279	1.68667
$667$	−5.92350	−0.229359
$668$	−36.0407	−1.39446
$669$	−14.1274	−0.546195
$670$	−8.80510	−0.340171
$671$	−16.1199	−0.622303
$672$	5.70588	0.220109
$673$	−49.8844	−1.92290	−0.961452	−	0.274973i	$-0.911331\pi$
$673$	−49.8844	−1.92290	−0.961452	+	0.274973i	$0.911331\pi$
$674$	7.96223	0.306694
$675$	16.4132	0.631746
$676$	−74.9776	−2.88376
$677$	9.08634	0.349217	0.174608	−	0.984638i	$-0.444134\pi$
$677$	9.08634	0.349217	0.174608	+	0.984638i	$0.444134\pi$
$678$	−18.3450	−0.704537
$679$	−2.74697	−0.105419
$680$	−5.21874	−0.200129
$681$	−6.49918	−0.249049
$682$	20.7808	0.795738
$683$	−4.97962	−0.190540	−0.0952698	−	0.995451i	$-0.530371\pi$
$683$	−4.97962	−0.190540	−0.0952698	+	0.995451i	$0.530371\pi$
$684$	−112.660	−4.30767
$685$	−10.9940	−0.420058
$686$	−12.5225	−0.478109
$687$	−1.43755	−0.0548459
$688$	−136.275	−5.19542
$689$	−0.524384	−0.0199774
$690$	2.83422	0.107897
$691$	−27.5939	−1.04972	−0.524861	−	0.851188i	$-0.675883\pi$
$691$	−27.5939	−1.04972	−0.524861	+	0.851188i	$0.675883\pi$
$692$	19.5312	0.742466
$693$	−2.58255	−0.0981031
$694$	56.1302	2.13067
$695$	−4.52281	−0.171560
$696$	−12.5870	−0.477111
$697$	10.0379	0.380212
$698$	80.8705	3.06100
$699$	−0.881477	−0.0333405
$700$	8.79343	0.332360
$701$	35.0543	1.32398	0.661991	−	0.749511i	$-0.269711\pi$
$701$	35.0543	1.32398	0.661991	+	0.749511i	$0.269711\pi$
$702$	0.699817	0.0264129
$703$	44.5699	1.68099
$704$	−133.887	−5.04607
$705$	0.365906	0.0137808
$706$	−18.7956	−0.707380
$707$	4.28572	0.161181
$708$	−43.0303	−1.61718
$709$	15.7732	0.592374	0.296187	−	0.955130i	$-0.404285\pi$
$709$	15.7732	0.592374	0.296187	+	0.955130i	$0.404285\pi$
$710$	−19.1984	−0.720504
$711$	−41.1633	−1.54374
$712$	4.39619	0.164754
$713$	−7.48478	−0.280307
$714$	0.518866	0.0194181
$715$	−0.117777	−0.00440462
$716$	−86.2560	−3.22354
$717$	0.693260	0.0258903
$718$	57.8408	2.15860
$719$	−19.7226	−0.735528	−0.367764	−	0.929919i	$-0.619877\pi$
$719$	−19.7226	−0.735528	−0.367764	+	0.929919i	$0.619877\pi$
$720$	−24.8317	−0.925424
$721$	4.63773	0.172718
$722$	−102.383	−3.81028
$723$	1.56208	0.0580942
$724$	21.4329	0.796548
$725$	−9.10684	−0.338220
$726$	2.89119	0.107302
$727$	1.31344	0.0487128	0.0243564	−	0.999703i	$-0.492246\pi$
$727$	1.31344	0.0487128	0.0243564	+	0.999703i	$0.492246\pi$
$728$	0.244967	0.00907907
$729$	−8.40023	−0.311119
$730$	1.63407	0.0604797
$731$	−7.12872	−0.263665
$732$	18.8828	0.697928
$733$	1.34708	0.0497555	0.0248778	−	0.999691i	$-0.492080\pi$
$733$	1.34708	0.0497555	0.0248778	+	0.999691i	$0.492080\pi$
$734$	61.7040	2.27754
$735$	−2.28663	−0.0843436
$736$	87.2756	3.21702
$737$	−18.0380	−0.664437
$738$	78.8113	2.90109
$739$	51.2242	1.88431	0.942157	−	0.335173i	$-0.108795\pi$
$739$	51.2242	1.88431	0.942157	+	0.335173i	$0.108795\pi$
$740$	18.4236	0.677267
$741$	0.333757	0.0122609
$742$	−6.55382	−0.240598
$743$	7.52319	0.275999	0.138000	−	0.990432i	$-0.455933\pi$
$743$	7.52319	0.275999	0.138000	+	0.990432i	$0.455933\pi$
$744$	−15.9046	−0.583092
$745$	1.91004	0.0699783
$746$	18.9959	0.695490
$747$	17.8032	0.651384
$748$	−16.3629	−0.598287
$749$	−2.28185	−0.0833770
$750$	8.97910	0.327871
$751$	−3.06255	−0.111754	−0.0558770	−	0.998438i	$-0.517795\pi$
$751$	−3.06255	−0.111754	−0.0558770	+	0.998438i	$0.517795\pi$
$752$	19.5869	0.714260
$753$	−1.45346	−0.0529672
$754$	−0.388292	−0.0141408
$755$	−1.19526	−0.0434999
$756$	6.49503	0.236222
$757$	−16.6430	−0.604899	−0.302450	−	0.953165i	$-0.597804\pi$
$757$	−16.6430	−0.604899	−0.302450	+	0.953165i	$0.597804\pi$
$758$	20.9293	0.760187
$759$	5.80613	0.210749
$760$	−41.9552	−1.52188
$761$	−4.94454	−0.179239	−0.0896197	−	0.995976i	$-0.528565\pi$
$761$	−4.94454	−0.179239	−0.0896197	+	0.995976i	$0.528565\pi$
$762$	−35.9990	−1.30410
$763$	3.11362	0.112721
$764$	92.4859	3.34602
$765$	−1.29898	−0.0469649
$766$	19.3262	0.698282
$767$	−0.867296	−0.0313162
$768$	58.4456	2.10898
$769$	−46.1602	−1.66458	−0.832289	−	0.554341i	$-0.812970\pi$
$769$	−46.1602	−1.66458	−0.832289	+	0.554341i	$0.812970\pi$
$770$	−1.47199	−0.0530470
$771$	3.87680	0.139619
$772$	12.5029	0.449987
$773$	16.2734	0.585313	0.292657	−	0.956218i	$-0.405461\pi$
$773$	16.2734	0.585313	0.292657	+	0.956218i	$0.405461\pi$
$774$	−55.9703	−2.01181
$775$	−11.5072	−0.413349
$776$	−89.2832	−3.20508
$777$	−1.19681	−0.0429352
$778$	−57.3750	−2.05699
$779$	80.6981	2.89131
$780$	0.137964	0.00493989
$781$	−39.3295	−1.40732
$782$	7.93644	0.283806
$783$	−6.72652	−0.240386
$784$	−122.403	−4.37153
$785$	5.06337	0.180720
$786$	17.6521	0.629629
$787$	−28.5299	−1.01698	−0.508490	−	0.861068i	$-0.669796\pi$
$787$	−28.5299	−1.01698	−0.508490	+	0.861068i	$0.669796\pi$
$788$	−127.175	−4.53042
$789$	11.6006	0.412992
$790$	−23.4621	−0.834745
$791$	−3.43169	−0.122017
$792$	−83.9392	−2.98265
$793$	0.380591	0.0135152
$794$	22.7781	0.808363
$795$	−2.41163	−0.0855316
$796$	132.847	4.70863
$797$	25.8453	0.915488	0.457744	−	0.889084i	$-0.348658\pi$
$797$	25.8453	0.915488	0.457744	+	0.889084i	$0.348658\pi$
$798$	4.17134	0.147664
$799$	1.02462	0.0362484
$800$	134.178	4.74392
$801$	1.09425	0.0386633
$802$	6.94559	0.245257
$803$	3.34753	0.118132
$804$	21.1296	0.745183
$805$	0.530179	0.0186864
$806$	−0.490635	−0.0172819
$807$	−9.92530	−0.349387
$808$	139.296	4.90042
$809$	4.21148	0.148068	0.0740339	−	0.997256i	$-0.476413\pi$
$809$	4.21148	0.148068	0.0740339	+	0.997256i	$0.476413\pi$
$810$	−8.47943	−0.297937
$811$	17.5178	0.615134	0.307567	−	0.951526i	$-0.400485\pi$
$811$	17.5178	0.615134	0.307567	+	0.951526i	$0.400485\pi$
$812$	−3.60375	−0.126467
$813$	4.48788	0.157397
$814$	50.8250	1.78142
$815$	−9.37678	−0.328454
$816$	10.2204	0.357784
$817$	−57.3103	−2.00503
$818$	105.110	3.67510
$819$	0.0609741	0.00213061
$820$	33.3578	1.16490
$821$	6.72521	0.234711	0.117356	−	0.993090i	$-0.462558\pi$
$821$	6.72521	0.234711	0.117356	+	0.993090i	$0.462558\pi$
$822$	35.5271	1.23915
$823$	−7.07847	−0.246740	−0.123370	−	0.992361i	$-0.539370\pi$
$823$	−7.07847	−0.246740	−0.123370	+	0.992361i	$0.539370\pi$
$824$	150.737	5.25119
$825$	8.92639	0.310777
$826$	−10.8396	−0.377157
$827$	−39.5158	−1.37410	−0.687050	−	0.726610i	$-0.741095\pi$
$827$	−39.5158	−1.37410	−0.687050	+	0.726610i	$0.741095\pi$
$828$	46.2725	1.60808
$829$	32.1968	1.11824	0.559120	−	0.829087i	$-0.311139\pi$
$829$	32.1968	1.11824	0.559120	+	0.829087i	$0.311139\pi$
$830$	10.1474	0.352221
$831$	−10.9799	−0.380887
$832$	3.16108	0.109591
$833$	−6.40306	−0.221853
$834$	14.6155	0.506093
$835$	−3.34077	−0.115612
$836$	−131.547	−4.54965
$837$	−8.49945	−0.293784
$838$	−27.3040	−0.943201
$839$	−42.5135	−1.46773	−0.733865	−	0.679295i	$-0.762285\pi$
$839$	−42.5135	−1.46773	−0.733865	+	0.679295i	$0.762285\pi$
$840$	1.12660	0.0388712
$841$	−25.2678	−0.871304
$842$	−5.29903	−0.182617
$843$	−6.73695	−0.232033
$844$	−135.077	−4.64954
$845$	−6.95001	−0.239088
$846$	8.04467	0.276581
$847$	0.540837	0.0185834
$848$	−129.094	−4.43310
$849$	−10.5072	−0.360607
$850$	12.2015	0.418509
$851$	−18.3060	−0.627523
$852$	46.0704	1.57835
$853$	−36.3690	−1.24525	−0.622626	−	0.782519i	$-0.713934\pi$
$853$	−36.3690	−1.24525	−0.622626	+	0.782519i	$0.713934\pi$
$854$	4.75668	0.162770
$855$	−10.4430	−0.357142
$856$	−74.1656	−2.53493
$857$	51.3585	1.75437	0.877187	−	0.480149i	$-0.159417\pi$
$857$	51.3585	1.75437	0.877187	+	0.480149i	$0.159417\pi$
$858$	0.380598	0.0129934
$859$	9.10073	0.310513	0.155257	−	0.987874i	$-0.450380\pi$
$859$	9.10073	0.310513	0.155257	+	0.987874i	$0.450380\pi$
$860$	−23.6900	−0.807824
$861$	−2.16693	−0.0738488
$862$	53.3461	1.81698
$863$	48.8350	1.66236	0.831181	−	0.556001i	$-0.187665\pi$
$863$	48.8350	1.66236	0.831181	+	0.556001i	$0.187665\pi$
$864$	99.1071	3.37169
$865$	1.81044	0.0615567
$866$	−66.6201	−2.26384
$867$	−10.0059	−0.339820
$868$	−4.55360	−0.154559
$869$	−48.0641	−1.63046
$870$	−1.78574	−0.0605424
$871$	0.425877	0.0144303
$872$	101.200	3.42706
$873$	−22.2233	−0.752144
$874$	63.8038	2.15820
$875$	1.67966	0.0567830
$876$	−3.92128	−0.132488
$877$	−13.8809	−0.468726	−0.234363	−	0.972149i	$-0.575300\pi$
$877$	−13.8809	−0.468726	−0.234363	+	0.972149i	$0.575300\pi$
$878$	29.9687	1.01139
$879$	−9.43947	−0.318385
$880$	−28.9946	−0.977408
$881$	−1.11113	−0.0374350	−0.0187175	−	0.999825i	$-0.505958\pi$
$881$	−1.11113	−0.0374350	−0.0187175	+	0.999825i	$0.505958\pi$
$882$	−50.2729	−1.69278
$883$	−47.6544	−1.60370	−0.801849	−	0.597526i	$-0.796150\pi$
$883$	−47.6544	−1.60370	−0.801849	+	0.597526i	$0.796150\pi$
$884$	0.386328	0.0129936
$885$	−3.98867	−0.134078
$886$	37.4272	1.25739
$887$	−38.6840	−1.29888	−0.649441	−	0.760412i	$-0.724997\pi$
$887$	−38.6840	−1.29888	−0.649441	+	0.760412i	$0.724997\pi$
$888$	−38.8991	−1.30537
$889$	−6.73410	−0.225854
$890$	0.623694	0.0209063
$891$	−17.3708	−0.581944
$892$	−131.464	−4.40175
$893$	8.23726	0.275649
$894$	−6.17230	−0.206432
$895$	−7.99545	−0.267259
$896$	21.1026	0.704987
$897$	−0.137083	−0.00457706
$898$	−59.0846	−1.97168
$899$	4.71590	0.157284
$900$	71.1397	2.37132
$901$	−6.75309	−0.224978
$902$	92.0236	3.06405
$903$	1.53891	0.0512118
$904$	−111.538	−3.70970
$905$	1.98671	0.0660405
$906$	3.86248	0.128322
$907$	34.9311	1.15987	0.579935	−	0.814663i	$-0.303078\pi$
$907$	34.9311	1.15987	0.579935	+	0.814663i	$0.303078\pi$
$908$	−60.4790	−2.00707
$909$	34.6719	1.14999
$910$	0.0347538	0.00115208
$911$	−1.59165	−0.0527337	−0.0263669	−	0.999652i	$-0.508394\pi$
$911$	−1.59165	−0.0527337	−0.0263669	+	0.999652i	$0.508394\pi$
$912$	82.1650	2.72076
$913$	20.7878	0.687975
$914$	−53.1784	−1.75898
$915$	1.75033	0.0578641
$916$	−13.3773	−0.441999
$917$	3.30206	0.109044
$918$	9.01234	0.297452
$919$	47.8091	1.57708	0.788538	−	0.614987i	$-0.210839\pi$
$919$	47.8091	1.57708	0.788538	+	0.614987i	$0.210839\pi$
$920$	17.2321	0.568125
$921$	10.8859	0.358704
$922$	−0.560293	−0.0184523
$923$	0.928571	0.0305643
$924$	3.53234	0.116206
$925$	−28.1438	−0.925364
$926$	18.6738	0.613660
$927$	37.5197	1.23231
$928$	−54.9893	−1.80511
$929$	−8.03348	−0.263570	−0.131785	−	0.991278i	$-0.542071\pi$
$929$	−8.03348	−0.263570	−0.131785	+	0.991278i	$0.542071\pi$
$930$	−2.25642	−0.0739908
$931$	−51.4764	−1.68707
$932$	−8.20271	−0.268689
$933$	7.06907	0.231431
$934$	40.7182	1.33234
$935$	−1.51675	−0.0496030
$936$	1.98180	0.0647773
$937$	−54.6900	−1.78664	−0.893322	−	0.449417i	$-0.851632\pi$
$937$	−54.6900	−1.78664	−0.893322	+	0.449417i	$0.851632\pi$
$938$	5.32267	0.173791
$939$	−9.11390	−0.297421
$940$	3.40499	0.111059
$941$	−27.2089	−0.886984	−0.443492	−	0.896278i	$-0.646261\pi$
$941$	−27.2089	−0.886984	−0.443492	+	0.896278i	$0.646261\pi$
$942$	−16.3623	−0.533114
$943$	−33.1448	−1.07934
$944$	−213.513	−6.94924
$945$	0.602053	0.0195848
$946$	−65.3534	−2.12482
$947$	−2.69271	−0.0875013	−0.0437507	−	0.999042i	$-0.513931\pi$
$947$	−2.69271	−0.0875013	−0.0437507	+	0.999042i	$0.513931\pi$
$948$	56.3020	1.82860
$949$	−0.0790352	−0.00256559
$950$	98.0924	3.18254
$951$	20.2405	0.656344
$952$	3.15471	0.102245
$953$	−14.5803	−0.472304	−0.236152	−	0.971716i	$-0.575886\pi$
$953$	−14.5803	−0.472304	−0.236152	+	0.971716i	$0.575886\pi$
$954$	−53.0211	−1.71662
$955$	8.57293	0.277413
$956$	6.45123	0.208648
$957$	−3.65824	−0.118254
$958$	47.9822	1.55023
$959$	6.64583	0.214605
$960$	14.5377	0.469203
$961$	−25.0411	−0.807778
$962$	−1.19998	−0.0386889
$963$	−18.4604	−0.594878
$964$	14.5361	0.468177
$965$	1.15894	0.0373077
$966$	−1.71328	−0.0551239
$967$	36.1805	1.16349	0.581744	−	0.813372i	$-0.302371\pi$
$967$	36.1805	1.16349	0.581744	+	0.813372i	$0.302371\pi$
$968$	17.5785	0.564995
$969$	4.29817	0.138077
$970$	−12.6667	−0.406705
$971$	−16.2152	−0.520372	−0.260186	−	0.965559i	$-0.583784\pi$
$971$	−16.2152	−0.520372	−0.260186	+	0.965559i	$0.583784\pi$
$972$	80.6168	2.58578
$973$	2.73403	0.0876489
$974$	75.5891	2.42203
$975$	−0.210752	−0.00674947
$976$	93.6947	2.99910
$977$	−47.4077	−1.51671	−0.758353	−	0.651844i	$-0.773996\pi$
$977$	−47.4077	−1.51671	−0.758353	+	0.651844i	$0.773996\pi$
$978$	30.3011	0.968924
$979$	1.27769	0.0408351
$980$	−21.2786	−0.679718
$981$	25.1895	0.804238
$982$	93.2158	2.97464
$983$	−6.85909	−0.218771	−0.109385	−	0.993999i	$-0.534888\pi$
$983$	−6.85909	−0.218771	−0.109385	+	0.993999i	$0.534888\pi$
$984$	−70.4305	−2.24524
$985$	−11.7884	−0.375610
$986$	−5.00047	−0.159248
$987$	−0.221190	−0.00704054
$988$	3.10583	0.0988095
$989$	23.5388	0.748491
$990$	−11.9086	−0.378480
$991$	17.5468	0.557393	0.278696	−	0.960379i	$-0.410098\pi$
$991$	17.5468	0.557393	0.278696	+	0.960379i	$0.410098\pi$
$992$	−69.4830	−2.20609
$993$	9.78844	0.310627
$994$	11.6054	0.368101
$995$	12.3142	0.390385
$996$	−24.3507	−0.771581
$997$	9.24864	0.292907	0.146454	−	0.989218i	$-0.453214\pi$
$997$	9.24864	0.292907	0.146454	+	0.989218i	$0.453214\pi$
$998$	−62.6559	−1.98334
$999$	−20.7877	−0.657693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.b.1.4	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.b.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.78744 q^{2} +0.620034 q^{3} +5.76982 q^{4} +0.534830 q^{5} -1.72831 q^{6} -0.323304 q^{7} -10.5081 q^{8} -2.61556 q^{9} +O(q^{10})\)	\(q-2.78744 q^{2} +0.620034 q^{3} +5.76982 q^{4} +0.534830 q^{5} -1.72831 q^{6} -0.323304 q^{7} -10.5081 q^{8} -2.61556 q^{9} -1.49081 q^{10} -3.05404 q^{11} +3.57749 q^{12} +0.0721059 q^{13} +0.901189 q^{14} +0.331613 q^{15} +17.7512 q^{16} +0.928589 q^{17} +7.29071 q^{18} +7.46525 q^{19} +3.08587 q^{20} -0.200459 q^{21} +8.51295 q^{22} -3.06617 q^{23} -6.51541 q^{24} -4.71396 q^{25} -0.200991 q^{26} -3.48184 q^{27} -1.86540 q^{28} +1.93189 q^{29} -0.924351 q^{30} +2.44108 q^{31} -28.4640 q^{32} -1.89361 q^{33} -2.58839 q^{34} -0.172912 q^{35} -15.0913 q^{36} +5.97032 q^{37} -20.8089 q^{38} +0.0447081 q^{39} -5.62007 q^{40} +10.8098 q^{41} +0.558768 q^{42} -7.67694 q^{43} -17.6213 q^{44} -1.39888 q^{45} +8.54677 q^{46} +1.10341 q^{47} +11.0063 q^{48} -6.89547 q^{49} +13.1399 q^{50} +0.575757 q^{51} +0.416038 q^{52} -7.27242 q^{53} +9.70541 q^{54} -1.63339 q^{55} +3.39732 q^{56} +4.62871 q^{57} -5.38502 q^{58} -12.0281 q^{59} +1.91335 q^{60} +5.27823 q^{61} -6.80437 q^{62} +0.845619 q^{63} +43.8394 q^{64} +0.0385644 q^{65} +5.27832 q^{66} +5.90627 q^{67} +5.35779 q^{68} -1.90113 q^{69} +0.481983 q^{70} +12.8779 q^{71} +27.4846 q^{72} -1.09610 q^{73} -16.6419 q^{74} -2.92281 q^{75} +43.0731 q^{76} +0.987382 q^{77} -0.124621 q^{78} +15.7379 q^{79} +9.49386 q^{80} +5.68781 q^{81} -30.1318 q^{82} -6.80665 q^{83} -1.15661 q^{84} +0.496637 q^{85} +21.3990 q^{86} +1.19784 q^{87} +32.0923 q^{88} -0.418360 q^{89} +3.89929 q^{90} -0.0233121 q^{91} -17.6913 q^{92} +1.51355 q^{93} -3.07570 q^{94} +3.99264 q^{95} -17.6487 q^{96} +8.49658 q^{97} +19.2207 q^{98} +7.98801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) \) 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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