LMFDB - Embedded newform 6043.2.a.b.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.63490 q^{2} +3.27029 q^{3} +4.94268 q^{4} -2.75610 q^{5} -8.61687 q^{6} -4.50836 q^{7} -7.75365 q^{8} +7.69478 q^{9} +O(q^{10})$	\(q-2.63490 q^{2} +3.27029 q^{3} +4.94268 q^{4} -2.75610 q^{5} -8.61687 q^{6} -4.50836 q^{7} -7.75365 q^{8} +7.69478 q^{9} +7.26204 q^{10} +2.45473 q^{11} +16.1640 q^{12} -4.76555 q^{13} +11.8791 q^{14} -9.01325 q^{15} +10.5447 q^{16} -1.28615 q^{17} -20.2750 q^{18} +5.79354 q^{19} -13.6225 q^{20} -14.7436 q^{21} -6.46797 q^{22} -6.53388 q^{23} -25.3567 q^{24} +2.59610 q^{25} +12.5567 q^{26} +15.3533 q^{27} -22.2834 q^{28} +3.50245 q^{29} +23.7490 q^{30} +8.47265 q^{31} -12.2769 q^{32} +8.02769 q^{33} +3.38887 q^{34} +12.4255 q^{35} +38.0328 q^{36} -6.16149 q^{37} -15.2654 q^{38} -15.5847 q^{39} +21.3699 q^{40} -1.42945 q^{41} +38.8480 q^{42} +10.9739 q^{43} +12.1330 q^{44} -21.2076 q^{45} +17.2161 q^{46} +9.11502 q^{47} +34.4842 q^{48} +13.3253 q^{49} -6.84046 q^{50} -4.20608 q^{51} -23.5546 q^{52} -0.189783 q^{53} -40.4543 q^{54} -6.76550 q^{55} +34.9563 q^{56} +18.9466 q^{57} -9.22860 q^{58} -5.66167 q^{59} -44.5496 q^{60} -3.91141 q^{61} -22.3246 q^{62} -34.6909 q^{63} +11.2590 q^{64} +13.1344 q^{65} -21.1521 q^{66} -0.0699318 q^{67} -6.35702 q^{68} -21.3677 q^{69} -32.7399 q^{70} -2.40852 q^{71} -59.6627 q^{72} -12.3594 q^{73} +16.2349 q^{74} +8.49000 q^{75} +28.6356 q^{76} -11.0668 q^{77} +41.0642 q^{78} -0.523650 q^{79} -29.0623 q^{80} +27.1253 q^{81} +3.76646 q^{82} -7.35347 q^{83} -72.8731 q^{84} +3.54476 q^{85} -28.9152 q^{86} +11.4540 q^{87} -19.0332 q^{88} -6.09051 q^{89} +55.8799 q^{90} +21.4848 q^{91} -32.2949 q^{92} +27.7080 q^{93} -24.0171 q^{94} -15.9676 q^{95} -40.1491 q^{96} -0.621559 q^{97} -35.1109 q^{98} +18.8886 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.63490	−1.86315	−0.931577	−	0.363545i	$-0.881566\pi$
$2$	−2.63490	−1.86315	−0.931577	+	0.363545i	$0.881566\pi$
$3$	3.27029	1.88810	0.944051	−	0.329800i	$-0.106981\pi$
$3$	3.27029	1.88810	0.944051	+	0.329800i	$0.106981\pi$
$4$	4.94268	2.47134
$5$	−2.75610	−1.23257	−0.616283	−	0.787525i	$-0.711362\pi$
$5$	−2.75610	−1.23257	−0.616283	+	0.787525i	$0.711362\pi$
$6$	−8.61687	−3.51782
$7$	−4.50836	−1.70400	−0.852000	−	0.523541i	$-0.824611\pi$
$7$	−4.50836	−1.70400	−0.852000	+	0.523541i	$0.824611\pi$
$8$	−7.75365	−2.74133
$9$	7.69478	2.56493
$10$	7.26204	2.29646
$11$	2.45473	0.740130	0.370065	−	0.929006i	$-0.379335\pi$
$11$	2.45473	0.740130	0.370065	+	0.929006i	$0.379335\pi$
$12$	16.1640	4.66614
$13$	−4.76555	−1.32173	−0.660863	−	0.750506i	$-0.729810\pi$
$13$	−4.76555	−1.32173	−0.660863	+	0.750506i	$0.729810\pi$
$14$	11.8791	3.17481
$15$	−9.01325	−2.32721
$16$	10.5447	2.63618
$17$	−1.28615	−0.311937	−0.155969	−	0.987762i	$-0.549850\pi$
$17$	−1.28615	−0.311937	−0.155969	+	0.987762i	$0.549850\pi$
$18$	−20.2750	−4.77885
$19$	5.79354	1.32913	0.664565	−	0.747231i	$-0.268617\pi$
$19$	5.79354	1.32913	0.664565	+	0.747231i	$0.268617\pi$
$20$	−13.6225	−3.04609
$21$	−14.7436	−3.21733
$22$	−6.46797	−1.37898
$23$	−6.53388	−1.36241	−0.681205	−	0.732093i	$-0.738544\pi$
$23$	−6.53388	−1.36241	−0.681205	+	0.732093i	$0.738544\pi$
$24$	−25.3567	−5.17591
$25$	2.59610	0.519220
$26$	12.5567	2.46258
$27$	15.3533	2.95474
$28$	−22.2834	−4.21116
$29$	3.50245	0.650389	0.325195	−	0.945647i	$-0.394570\pi$
$29$	3.50245	0.650389	0.325195	+	0.945647i	$0.394570\pi$
$30$	23.7490	4.33595
$31$	8.47265	1.52173	0.760867	−	0.648908i	$-0.224774\pi$
$31$	8.47265	1.52173	0.760867	+	0.648908i	$0.224774\pi$
$32$	−12.2769	−2.17027
$33$	8.02769	1.39744
$34$	3.38887	0.581186
$35$	12.4255	2.10029
$36$	38.0328	6.33881
$37$	−6.16149	−1.01294	−0.506472	−	0.862257i	$-0.669051\pi$
$37$	−6.16149	−1.01294	−0.506472	+	0.862257i	$0.669051\pi$
$38$	−15.2654	−2.47637
$39$	−15.5847	−2.49555
$40$	21.3699	3.37887
$41$	−1.42945	−0.223243	−0.111622	−	0.993751i	$-0.535604\pi$
$41$	−1.42945	−0.223243	−0.111622	+	0.993751i	$0.535604\pi$
$42$	38.8480	5.99437
$43$	10.9739	1.67351	0.836756	−	0.547576i	$-0.184449\pi$
$43$	10.9739	1.67351	0.836756	+	0.547576i	$0.184449\pi$
$44$	12.1330	1.82911
$45$	−21.2076	−3.16144
$46$	17.2161	2.53838
$47$	9.11502	1.32956	0.664781	−	0.747038i	$-0.268525\pi$
$47$	9.11502	1.32956	0.664781	+	0.747038i	$0.268525\pi$
$48$	34.4842	4.97737
$49$	13.3253	1.90362
$50$	−6.84046	−0.967387
$51$	−4.20608	−0.588969
$52$	−23.5546	−3.26644
$53$	−0.189783	−0.0260686	−0.0130343	−	0.999915i	$-0.504149\pi$
$53$	−0.189783	−0.0260686	−0.0130343	+	0.999915i	$0.504149\pi$
$54$	−40.4543	−5.50514
$55$	−6.76550	−0.912260
$56$	34.9563	4.67123
$57$	18.9466	2.50953
$58$	−9.22860	−1.21177
$59$	−5.66167	−0.737087	−0.368543	−	0.929611i	$-0.620143\pi$
$59$	−5.66167	−0.737087	−0.368543	+	0.929611i	$0.620143\pi$
$60$	−44.5496	−5.75133
$61$	−3.91141	−0.500804	−0.250402	−	0.968142i	$-0.580563\pi$
$61$	−3.91141	−0.500804	−0.250402	+	0.968142i	$0.580563\pi$
$62$	−22.3246	−2.83522
$63$	−34.6909	−4.37064
$64$	11.2590	1.40737
$65$	13.1344	1.62912
$66$	−21.1521	−2.60365
$67$	−0.0699318	−0.00854353	−0.00427177	−	0.999991i	$-0.501360\pi$
$67$	−0.0699318	−0.00854353	−0.00427177	+	0.999991i	$0.501360\pi$
$68$	−6.35702	−0.770902
$69$	−21.3677	−2.57237
$70$	−32.7399	−3.91317
$71$	−2.40852	−0.285839	−0.142920	−	0.989734i	$-0.545649\pi$
$71$	−2.40852	−0.285839	−0.142920	+	0.989734i	$0.545649\pi$
$72$	−59.6627	−7.03131
$73$	−12.3594	−1.44656	−0.723281	−	0.690554i	$-0.757367\pi$
$73$	−12.3594	−1.44656	−0.723281	+	0.690554i	$0.757367\pi$
$74$	16.2349	1.88727
$75$	8.49000	0.980341
$76$	28.6356	3.28473
$77$	−11.0668	−1.26118
$78$	41.0642	4.64960
$79$	−0.523650	−0.0589152	−0.0294576	−	0.999566i	$-0.509378\pi$
$79$	−0.523650	−0.0589152	−0.0294576	+	0.999566i	$0.509378\pi$
$80$	−29.0623	−3.24927
$81$	27.1253	3.01393
$82$	3.76646	0.415936
$83$	−7.35347	−0.807149	−0.403574	−	0.914947i	$-0.632232\pi$
$83$	−7.35347	−0.807149	−0.403574	+	0.914947i	$0.632232\pi$
$84$	−72.8731	−7.95110
$85$	3.54476	0.384483
$86$	−28.9152	−3.11801
$87$	11.4540	1.22800
$88$	−19.0332	−2.02894
$89$	−6.09051	−0.645593	−0.322797	−	0.946468i	$-0.604623\pi$
$89$	−6.09051	−0.645593	−0.322797	+	0.946468i	$0.604623\pi$
$90$	55.8799	5.89025
$91$	21.4848	2.25222
$92$	−32.2949	−3.36697
$93$	27.7080	2.87319
$94$	−24.0171	−2.47718
$95$	−15.9676	−1.63824
$96$	−40.1491	−4.09770
$97$	−0.621559	−0.0631097	−0.0315549	−	0.999502i	$-0.510046\pi$
$97$	−0.621559	−0.0631097	−0.0315549	+	0.999502i	$0.510046\pi$
$98$	−35.1109	−3.54673
$99$	18.8886	1.89838
$100$	12.8317	1.28317
$101$	−0.949417	−0.0944705	−0.0472353	−	0.998884i	$-0.515041\pi$
$101$	−0.949417	−0.0944705	−0.0472353	+	0.998884i	$0.515041\pi$
$102$	11.0826	1.09734
$103$	14.1204	1.39132	0.695660	−	0.718371i	$-0.255112\pi$
$103$	14.1204	1.39132	0.695660	+	0.718371i	$0.255112\pi$
$104$	36.9504	3.62329
$105$	40.6350	3.96557
$106$	0.500057	0.0485698
$107$	−12.6803	−1.22585	−0.612926	−	0.790140i	$-0.710008\pi$
$107$	−12.6803	−1.22585	−0.612926	+	0.790140i	$0.710008\pi$
$108$	75.8864	7.30217
$109$	−5.78826	−0.554415	−0.277208	−	0.960810i	$-0.589409\pi$
$109$	−5.78826	−0.554415	−0.277208	+	0.960810i	$0.589409\pi$
$110$	17.8264	1.69968
$111$	−20.1499	−1.91254
$112$	−47.5394	−4.49205
$113$	14.8132	1.39351	0.696755	−	0.717309i	$-0.254626\pi$
$113$	14.8132	1.39351	0.696755	+	0.717309i	$0.254626\pi$
$114$	−49.9222	−4.67564
$115$	18.0081	1.67926
$116$	17.3115	1.60733
$117$	−36.6699	−3.39013
$118$	14.9179	1.37331
$119$	5.79843	0.531541
$120$	69.8856	6.37965
$121$	−4.97428	−0.452207
$122$	10.3061	0.933075
$123$	−4.67473	−0.421506
$124$	41.8776	3.76072
$125$	6.62539	0.592593
$126$	91.4068	8.14317
$127$	6.52912	0.579366	0.289683	−	0.957123i	$-0.406450\pi$
$127$	6.52912	0.579366	0.289683	+	0.957123i	$0.406450\pi$
$128$	−5.11242	−0.451878
$129$	35.8880	3.15976
$130$	−34.6077	−3.03529
$131$	−6.43887	−0.562567	−0.281283	−	0.959625i	$-0.590760\pi$
$131$	−6.43887	−0.562567	−0.281283	+	0.959625i	$0.590760\pi$
$132$	39.6783	3.45355
$133$	−26.1194	−2.26484
$134$	0.184263	0.0159179
$135$	−42.3152	−3.64192
$136$	9.97236	0.855122
$137$	−21.5389	−1.84019	−0.920097	−	0.391691i	$-0.871890\pi$
$137$	−21.5389	−1.84019	−0.920097	+	0.391691i	$0.871890\pi$
$138$	56.3016	4.79271
$139$	−11.0055	−0.933475	−0.466737	−	0.884396i	$-0.654571\pi$
$139$	−11.0055	−0.933475	−0.466737	+	0.884396i	$0.654571\pi$
$140$	61.4153	5.19054
$141$	29.8087	2.51035
$142$	6.34621	0.532562
$143$	−11.6982	−0.978250
$144$	81.1393	6.76161
$145$	−9.65312	−0.801648
$146$	32.5658	2.69517
$147$	43.5777	3.59422
$148$	−30.4543	−2.50333
$149$	−22.9820	−1.88276	−0.941378	−	0.337354i	$-0.890468\pi$
$149$	−22.9820	−1.88276	−0.941378	+	0.337354i	$0.890468\pi$
$150$	−22.3703	−1.82653
$151$	−17.1973	−1.39950	−0.699749	−	0.714389i	$-0.746705\pi$
$151$	−17.1973	−1.39950	−0.699749	+	0.714389i	$0.746705\pi$
$152$	−44.9211	−3.64358
$153$	−9.89664	−0.800096
$154$	29.1600	2.34978
$155$	−23.3515	−1.87564
$156$	−77.0303	−6.16736
$157$	4.32227	0.344955	0.172477	−	0.985013i	$-0.444823\pi$
$157$	4.32227	0.344955	0.172477	+	0.985013i	$0.444823\pi$
$158$	1.37976	0.109768
$159$	−0.620643	−0.0492202
$160$	33.8365	2.67501
$161$	29.4571	2.32155
$162$	−71.4724	−5.61541
$163$	−17.4676	−1.36817	−0.684083	−	0.729405i	$-0.739797\pi$
$163$	−17.4676	−1.36817	−0.684083	+	0.729405i	$0.739797\pi$
$164$	−7.06533	−0.551710
$165$	−22.1251	−1.72244
$166$	19.3756	1.50384
$167$	−2.72377	−0.210772	−0.105386	−	0.994431i	$-0.533608\pi$
$167$	−2.72377	−0.210772	−0.105386	+	0.994431i	$0.533608\pi$
$168$	114.317	8.81975
$169$	9.71050	0.746962
$170$	−9.34007	−0.716351
$171$	44.5800	3.40912
$172$	54.2407	4.13581
$173$	0.0768987	0.00584650	0.00292325	−	0.999996i	$-0.499069\pi$
$173$	0.0768987	0.00584650	0.00292325	+	0.999996i	$0.499069\pi$
$174$	−30.1802	−2.28795
$175$	−11.7042	−0.884752
$176$	25.8845	1.95112
$177$	−18.5153	−1.39169
$178$	16.0479	1.20284
$179$	−11.3331	−0.847072	−0.423536	−	0.905879i	$-0.639211\pi$
$179$	−11.3331	−0.847072	−0.423536	+	0.905879i	$0.639211\pi$
$180$	−104.822	−7.81300
$181$	26.2434	1.95065	0.975327	−	0.220766i	$-0.0708558\pi$
$181$	26.2434	1.95065	0.975327	+	0.220766i	$0.0708558\pi$
$182$	−56.6103	−4.19624
$183$	−12.7914	−0.945569
$184$	50.6615	3.73481
$185$	16.9817	1.24852
$186$	−73.0077	−5.35319
$187$	−3.15716	−0.230874
$188$	45.0526	3.28580
$189$	−69.2182	−5.03488
$190$	42.0730	3.05229
$191$	−24.5562	−1.77683	−0.888414	−	0.459044i	$-0.848192\pi$
$191$	−24.5562	−1.77683	−0.888414	+	0.459044i	$0.848192\pi$
$192$	36.8201	2.65726
$193$	19.1899	1.38132	0.690660	−	0.723180i	$-0.257320\pi$
$193$	19.1899	1.38132	0.690660	+	0.723180i	$0.257320\pi$
$194$	1.63774	0.117583
$195$	42.9531	3.07594
$196$	65.8628	4.70449
$197$	−26.0541	−1.85628	−0.928139	−	0.372234i	$-0.878592\pi$
$197$	−26.0541	−1.85628	−0.928139	+	0.372234i	$0.878592\pi$
$198$	−49.7696	−3.53697
$199$	−2.04709	−0.145115	−0.0725573	−	0.997364i	$-0.523116\pi$
$199$	−2.04709	−0.145115	−0.0725573	+	0.997364i	$0.523116\pi$
$200$	−20.1293	−1.42335
$201$	−0.228697	−0.0161311
$202$	2.50162	0.176013
$203$	−15.7903	−1.10826
$204$	−20.7893	−1.45554
$205$	3.93972	0.275162
$206$	−37.2057	−2.59224
$207$	−50.2768	−3.49448
$208$	−50.2514	−3.48431
$209$	14.2216	0.983729
$210$	−107.069	−7.38846
$211$	−7.47089	−0.514317	−0.257159	−	0.966369i	$-0.582786\pi$
$211$	−7.47089	−0.514317	−0.257159	+	0.966369i	$0.582786\pi$
$212$	−0.938034	−0.0644244
$213$	−7.87657	−0.539694
$214$	33.4113	2.28395
$215$	−30.2453	−2.06271
$216$	−119.044	−8.09992
$217$	−38.1978	−2.59303
$218$	15.2515	1.03296
$219$	−40.4189	−2.73126
$220$	−33.4397	−2.25450
$221$	6.12921	0.412296
$222$	53.0928	3.56335
$223$	15.2816	1.02333	0.511665	−	0.859185i	$-0.329029\pi$
$223$	15.2816	1.02333	0.511665	+	0.859185i	$0.329029\pi$
$224$	55.3488	3.69815
$225$	19.9764	1.33176
$226$	−39.0313	−2.59632
$227$	−25.4474	−1.68900	−0.844500	−	0.535555i	$-0.820103\pi$
$227$	−25.4474	−1.68900	−0.844500	+	0.535555i	$0.820103\pi$
$228$	93.6467	6.20190
$229$	6.22667	0.411470	0.205735	−	0.978608i	$-0.434042\pi$
$229$	6.22667	0.411470	0.205735	+	0.978608i	$0.434042\pi$
$230$	−47.4494	−3.12872
$231$	−36.1917	−2.38124
$232$	−27.1568	−1.78293
$233$	7.88635	0.516652	0.258326	−	0.966058i	$-0.416829\pi$
$233$	7.88635	0.516652	0.258326	+	0.966058i	$0.416829\pi$
$234$	96.6214	6.31634
$235$	−25.1219	−1.63877
$236$	−27.9838	−1.82159
$237$	−1.71249	−0.111238
$238$	−15.2783	−0.990342
$239$	−17.1519	−1.10947	−0.554733	−	0.832029i	$-0.687179\pi$
$239$	−17.1519	−1.10947	−0.554733	+	0.832029i	$0.687179\pi$
$240$	−95.0421	−6.13494
$241$	23.7521	1.53001	0.765004	−	0.644026i	$-0.222737\pi$
$241$	23.7521	1.53001	0.765004	+	0.644026i	$0.222737\pi$
$242$	13.1067	0.842531
$243$	42.6478	2.73586
$244$	−19.3328	−1.23766
$245$	−36.7260	−2.34634
$246$	12.3174	0.785330
$247$	−27.6094	−1.75675
$248$	−65.6940	−4.17157
$249$	−24.0480	−1.52398
$250$	−17.4572	−1.10409
$251$	−4.23346	−0.267214	−0.133607	−	0.991034i	$-0.542656\pi$
$251$	−4.23346	−0.267214	−0.133607	+	0.991034i	$0.542656\pi$
$252$	−171.466	−10.8013
$253$	−16.0390	−1.00836
$254$	−17.2035	−1.07945
$255$	11.5924	0.725943
$256$	−9.04728	−0.565455
$257$	26.1162	1.62908	0.814541	−	0.580106i	$-0.196989\pi$
$257$	26.1162	1.62908	0.814541	+	0.580106i	$0.196989\pi$
$258$	−94.5611	−5.88712
$259$	27.7782	1.72606
$260$	64.9189	4.02610
$261$	26.9506	1.66820
$262$	16.9658	1.04815
$263$	−7.77038	−0.479142	−0.239571	−	0.970879i	$-0.577007\pi$
$263$	−7.77038	−0.479142	−0.239571	+	0.970879i	$0.577007\pi$
$264$	−62.2439	−3.83085
$265$	0.523060	0.0321313
$266$	68.8219	4.21974
$267$	−19.9177	−1.21895
$268$	−0.345651	−0.0211140
$269$	−15.9945	−0.975201	−0.487601	−	0.873067i	$-0.662128\pi$
$269$	−15.9945	−0.975201	−0.487601	+	0.873067i	$0.662128\pi$
$270$	111.496	6.78545
$271$	8.52797	0.518037	0.259019	−	0.965872i	$-0.416601\pi$
$271$	8.52797	0.518037	0.259019	+	0.965872i	$0.416601\pi$
$272$	−13.5621	−0.822322
$273$	70.2616	4.25243
$274$	56.7528	3.42856
$275$	6.37274	0.384291
$276$	−105.614	−6.35719
$277$	14.4583	0.868716	0.434358	−	0.900740i	$-0.356975\pi$
$277$	14.4583	0.868716	0.434358	+	0.900740i	$0.356975\pi$
$278$	28.9984	1.73921
$279$	65.1952	3.90314
$280$	−96.3431	−5.75760
$281$	−4.77857	−0.285066	−0.142533	−	0.989790i	$-0.545525\pi$
$281$	−4.77857	−0.285066	−0.142533	+	0.989790i	$0.545525\pi$
$282$	−78.5429	−4.67716
$283$	11.4791	0.682361	0.341181	−	0.939998i	$-0.389173\pi$
$283$	11.4791	0.682361	0.341181	+	0.939998i	$0.389173\pi$
$284$	−11.9046	−0.706406
$285$	−52.2186	−3.09317
$286$	30.8235	1.82263
$287$	6.44450	0.380407
$288$	−94.4682	−5.56659
$289$	−15.3458	−0.902695
$290$	25.4350	1.49359
$291$	−2.03268	−0.119158
$292$	−61.0887	−3.57494
$293$	1.57800	0.0921877	0.0460939	−	0.998937i	$-0.485323\pi$
$293$	1.57800	0.0921877	0.0460939	+	0.998937i	$0.485323\pi$
$294$	−114.823	−6.69659
$295$	15.6041	0.908509
$296$	47.7741	2.77681
$297$	37.6882	2.18689
$298$	60.5551	3.50786
$299$	31.1376	1.80073
$300$	41.9633	2.42276
$301$	−49.4745	−2.85166
$302$	45.3132	2.60748
$303$	−3.10487	−0.178370
$304$	61.0912	3.50382
$305$	10.7802	0.617275
$306$	26.0766	1.49070
$307$	−24.9662	−1.42490	−0.712448	−	0.701725i	$-0.752414\pi$
$307$	−24.9662	−1.42490	−0.712448	+	0.701725i	$0.752414\pi$
$308$	−54.6998	−3.11681
$309$	46.1776	2.62695
$310$	61.5288	3.49460
$311$	14.8169	0.840188	0.420094	−	0.907481i	$-0.361997\pi$
$311$	14.8169	0.840188	0.420094	+	0.907481i	$0.361997\pi$
$312$	120.839	6.84114
$313$	−21.6193	−1.22200	−0.610998	−	0.791632i	$-0.709232\pi$
$313$	−21.6193	−1.22200	−0.610998	+	0.791632i	$0.709232\pi$
$314$	−11.3887	−0.642704
$315$	95.6116	5.38710
$316$	−2.58823	−0.145599
$317$	−4.53633	−0.254786	−0.127393	−	0.991852i	$-0.540661\pi$
$317$	−4.53633	−0.254786	−0.127393	+	0.991852i	$0.540661\pi$
$318$	1.63533	0.0917048
$319$	8.59759	0.481373
$320$	−31.0309	−1.73468
$321$	−41.4683	−2.31453
$322$	−77.6164	−4.32540
$323$	−7.45136	−0.414605
$324$	134.072	7.44843
$325$	−12.3719	−0.686268
$326$	46.0252	2.54910
$327$	−18.9293	−1.04679
$328$	11.0835	0.611984
$329$	−41.0938	−2.26557
$330$	58.2974	3.20917
$331$	−27.1811	−1.49401	−0.747005	−	0.664819i	$-0.768509\pi$
$331$	−27.1811	−1.49401	−0.747005	+	0.664819i	$0.768509\pi$
$332$	−36.3459	−1.99474
$333$	−47.4114	−2.59813
$334$	7.17685	0.392700
$335$	0.192739	0.0105305
$336$	−155.467	−8.48145
$337$	−27.3209	−1.48827	−0.744133	−	0.668032i	$-0.767137\pi$
$337$	−27.3209	−1.48827	−0.744133	+	0.668032i	$0.767137\pi$
$338$	−25.5862	−1.39170
$339$	48.4435	2.63109
$340$	17.5206	0.950188
$341$	20.7981	1.12628
$342$	−117.464	−6.35171
$343$	−28.5169	−1.53977
$344$	−85.0882	−4.58765
$345$	58.8915	3.17061
$346$	−0.202620	−0.0108929
$347$	−24.9979	−1.34196	−0.670980	−	0.741476i	$-0.734126\pi$
$347$	−24.9979	−1.34196	−0.670980	+	0.741476i	$0.734126\pi$
$348$	56.6136	3.03481
$349$	−7.15553	−0.383027	−0.191513	−	0.981490i	$-0.561340\pi$
$349$	−7.15553	−0.383027	−0.191513	+	0.981490i	$0.561340\pi$
$350$	30.8393	1.64843
$351$	−73.1669	−3.90536
$352$	−30.1366	−1.60628
$353$	−12.6684	−0.674270	−0.337135	−	0.941456i	$-0.609458\pi$
$353$	−12.6684	−0.674270	−0.337135	+	0.941456i	$0.609458\pi$
$354$	48.7859	2.59294
$355$	6.63814	0.352316
$356$	−30.1034	−1.59548
$357$	18.9625	1.00360
$358$	29.8614	1.57823
$359$	−16.1659	−0.853201	−0.426601	−	0.904440i	$-0.640289\pi$
$359$	−16.1659	−0.853201	−0.426601	+	0.904440i	$0.640289\pi$
$360$	164.436	8.66656
$361$	14.5651	0.766586
$362$	−69.1485	−3.63437
$363$	−16.2673	−0.853813
$364$	106.193	5.56601
$365$	34.0639	1.78298
$366$	33.7041	1.76174
$367$	−9.39574	−0.490454	−0.245227	−	0.969466i	$-0.578862\pi$
$367$	−9.39574	−0.490454	−0.245227	+	0.969466i	$0.578862\pi$
$368$	−68.8979	−3.59155
$369$	−10.9993	−0.572603
$370$	−44.7450	−2.32618
$371$	0.855608	0.0444210
$372$	136.952	7.10062
$373$	14.5402	0.752863	0.376431	−	0.926445i	$-0.377151\pi$
$373$	14.5402	0.752863	0.376431	+	0.926445i	$0.377151\pi$
$374$	8.31878	0.430154
$375$	21.6669	1.11888
$376$	−70.6747	−3.64477
$377$	−16.6911	−0.859637
$378$	182.383	9.38076
$379$	6.98852	0.358976	0.179488	−	0.983760i	$-0.442556\pi$
$379$	6.98852	0.358976	0.179488	+	0.983760i	$0.442556\pi$
$380$	−78.9227	−4.04865
$381$	21.3521	1.09390
$382$	64.7031	3.31050
$383$	−16.8664	−0.861833	−0.430917	−	0.902392i	$-0.641810\pi$
$383$	−16.8664	−0.861833	−0.430917	+	0.902392i	$0.641810\pi$
$384$	−16.7191	−0.853192
$385$	30.5013	1.55449
$386$	−50.5634	−2.57361
$387$	84.4422	4.29244
$388$	−3.07217	−0.155966
$389$	1.34866	0.0683800	0.0341900	−	0.999415i	$-0.489115\pi$
$389$	1.34866	0.0683800	0.0341900	+	0.999415i	$0.489115\pi$
$390$	−113.177	−5.73094
$391$	8.40355	0.424986
$392$	−103.320	−5.21845
$393$	−21.0570	−1.06218
$394$	68.6498	3.45853
$395$	1.44323	0.0726169
$396$	93.3605	4.69154
$397$	−13.4489	−0.674982	−0.337491	−	0.941329i	$-0.609578\pi$
$397$	−13.4489	−0.674982	−0.337491	+	0.941329i	$0.609578\pi$
$398$	5.39388	0.270371
$399$	−85.4179	−4.27624
$400$	27.3752	1.36876
$401$	7.45498	0.372284	0.186142	−	0.982523i	$-0.440402\pi$
$401$	7.45498	0.372284	0.186142	+	0.982523i	$0.440402\pi$
$402$	0.602593	0.0300546
$403$	−40.3769	−2.01132
$404$	−4.69266	−0.233469
$405$	−74.7602	−3.71486
$406$	41.6059	2.06486
$407$	−15.1248	−0.749710
$408$	32.6125	1.61456
$409$	26.5662	1.31362	0.656808	−	0.754058i	$-0.271906\pi$
$409$	26.5662	1.31362	0.656808	+	0.754058i	$0.271906\pi$
$410$	−10.3808	−0.512669
$411$	−70.4385	−3.47447
$412$	69.7924	3.43842
$413$	25.5249	1.25600
$414$	132.474	6.51075
$415$	20.2669	0.994864
$416$	58.5063	2.86851
$417$	−35.9912	−1.76249
$418$	−37.4725	−1.83284
$419$	35.4269	1.73072	0.865358	−	0.501154i	$-0.167091\pi$
$419$	35.4269	1.73072	0.865358	+	0.501154i	$0.167091\pi$
$420$	200.846	9.80027
$421$	12.1034	0.589883	0.294942	−	0.955515i	$-0.404700\pi$
$421$	12.1034	0.589883	0.294942	+	0.955515i	$0.404700\pi$
$422$	19.6850	0.958252
$423$	70.1381	3.41023
$424$	1.47151	0.0714627
$425$	−3.33898	−0.161964
$426$	20.7539	1.00553
$427$	17.6340	0.853371
$428$	−62.6747	−3.02950
$429$	−38.2564	−1.84704
$430$	79.6933	3.84315
$431$	37.0838	1.78627	0.893133	−	0.449793i	$-0.148502\pi$
$431$	37.0838	1.78627	0.893133	+	0.449793i	$0.148502\pi$
$432$	161.896	7.78923
$433$	13.9273	0.669301	0.334651	−	0.942342i	$-0.391382\pi$
$433$	13.9273	0.669301	0.334651	+	0.942342i	$0.391382\pi$
$434$	100.647	4.83122
$435$	−31.5685	−1.51359
$436$	−28.6095	−1.37015
$437$	−37.8543	−1.81082
$438$	106.500	5.08875
$439$	−25.6537	−1.22439	−0.612193	−	0.790708i	$-0.709712\pi$
$439$	−25.6537	−1.22439	−0.612193	+	0.790708i	$0.709712\pi$
$440$	52.4573	2.50081
$441$	102.536	4.88264
$442$	−16.1498	−0.768170
$443$	−36.1426	−1.71719	−0.858593	−	0.512658i	$-0.828661\pi$
$443$	−36.1426	−1.71719	−0.858593	+	0.512658i	$0.828661\pi$
$444$	−99.5943	−4.72654
$445$	16.7861	0.795736
$446$	−40.2654	−1.90662
$447$	−75.1576	−3.55483
$448$	−50.7596	−2.39816
$449$	32.8243	1.54908	0.774538	−	0.632528i	$-0.217983\pi$
$449$	32.8243	1.54908	0.774538	+	0.632528i	$0.217983\pi$
$450$	−52.6359	−2.48128
$451$	−3.50893	−0.165229
$452$	73.2170	3.44384
$453$	−56.2402	−2.64240
$454$	67.0512	3.14687
$455$	−59.2144	−2.77602
$456$	−146.905	−6.87946
$457$	2.30410	0.107781	0.0538907	−	0.998547i	$-0.482838\pi$
$457$	2.30410	0.107781	0.0538907	+	0.998547i	$0.482838\pi$
$458$	−16.4066	−0.766631
$459$	−19.7466	−0.921694
$460$	89.0080	4.15002
$461$	17.7306	0.825796	0.412898	−	0.910777i	$-0.364517\pi$
$461$	17.7306	0.825796	0.412898	+	0.910777i	$0.364517\pi$
$462$	95.3614	4.43662
$463$	−5.38158	−0.250103	−0.125052	−	0.992150i	$-0.539910\pi$
$463$	−5.38158	−0.250103	−0.125052	+	0.992150i	$0.539910\pi$
$464$	36.9324	1.71454
$465$	−76.3661	−3.54139
$466$	−20.7797	−0.962601
$467$	−8.18433	−0.378726	−0.189363	−	0.981907i	$-0.560642\pi$
$467$	−8.18433	−0.378726	−0.189363	+	0.981907i	$0.560642\pi$
$468$	−181.248	−8.37817
$469$	0.315278	0.0145582
$470$	66.1937	3.05329
$471$	14.1351	0.651310
$472$	43.8986	2.02060
$473$	26.9381	1.23862
$474$	4.51222	0.207253
$475$	15.0406	0.690111
$476$	28.6598	1.31362
$477$	−1.46034	−0.0668642
$478$	45.1935	2.06710
$479$	11.0229	0.503651	0.251825	−	0.967773i	$-0.418969\pi$
$479$	11.0229	0.503651	0.251825	+	0.967773i	$0.418969\pi$
$480$	110.655	5.05068
$481$	29.3629	1.33883
$482$	−62.5843	−2.85064
$483$	96.3333	4.38331
$484$	−24.5863	−1.11756
$485$	1.71308	0.0777870
$486$	−112.372	−5.09732
$487$	24.5450	1.11224	0.556120	−	0.831102i	$-0.312289\pi$
$487$	24.5450	1.11224	0.556120	+	0.831102i	$0.312289\pi$
$488$	30.3277	1.37287
$489$	−57.1240	−2.58323
$490$	96.7691	4.37158
$491$	−32.9452	−1.48680	−0.743399	−	0.668848i	$-0.766788\pi$
$491$	−32.9452	−1.48680	−0.743399	+	0.668848i	$0.766788\pi$
$492$	−23.1057	−1.04168
$493$	−4.50468	−0.202880
$494$	72.7480	3.27309
$495$	−52.0591	−2.33988
$496$	89.3417	4.01156
$497$	10.8585	0.487070
$498$	63.3639	2.83941
$499$	12.5258	0.560731	0.280365	−	0.959893i	$-0.409544\pi$
$499$	12.5258	0.560731	0.280365	+	0.959893i	$0.409544\pi$
$500$	32.7472	1.46450
$501$	−8.90751	−0.397958
$502$	11.1547	0.497860
$503$	28.6156	1.27591	0.637953	−	0.770075i	$-0.279781\pi$
$503$	28.6156	1.27591	0.637953	+	0.770075i	$0.279781\pi$
$504$	268.981	11.9814
$505$	2.61669	0.116441
$506$	42.2610	1.87873
$507$	31.7561	1.41034
$508$	32.2713	1.43181
$509$	−25.7647	−1.14200	−0.570999	−	0.820950i	$-0.693444\pi$
$509$	−25.7647	−1.14200	−0.570999	+	0.820950i	$0.693444\pi$
$510$	−30.5447	−1.35254
$511$	55.7208	2.46494
$512$	34.0635	1.50541
$513$	88.9499	3.92724
$514$	−68.8134	−3.03523
$515$	−38.9172	−1.71489
$516$	177.383	7.80884
$517$	22.3749	0.984049
$518$	−73.1928	−3.21591
$519$	0.251481	0.0110388
$520$	−101.839	−4.46595
$521$	−3.29855	−0.144512	−0.0722560	−	0.997386i	$-0.523020\pi$
$521$	−3.29855	−0.144512	−0.0722560	+	0.997386i	$0.523020\pi$
$522$	−71.0121	−3.10811
$523$	33.9813	1.48590	0.742949	−	0.669348i	$-0.233426\pi$
$523$	33.9813	1.48590	0.742949	+	0.669348i	$0.233426\pi$
$524$	−31.8253	−1.39029
$525$	−38.2760	−1.67050
$526$	20.4741	0.892715
$527$	−10.8971	−0.474685
$528$	84.6497	3.68390
$529$	19.6916	0.856159
$530$	−1.37821	−0.0598656
$531$	−43.5653	−1.89057
$532$	−129.100	−5.59718
$533$	6.81214	0.295067
$534$	52.4812	2.27108
$535$	34.9483	1.51094
$536$	0.542227	0.0234206
$537$	−37.0624	−1.59936
$538$	42.1438	1.81695
$539$	32.7101	1.40893
$540$	−209.151	−9.00041
$541$	−13.4864	−0.579826	−0.289913	−	0.957053i	$-0.593626\pi$
$541$	−13.4864	−0.579826	−0.289913	+	0.957053i	$0.593626\pi$
$542$	−22.4703	−0.965183
$543$	85.8233	3.68303
$544$	15.7900	0.676989
$545$	15.9530	0.683354
$546$	−185.132	−7.92292
$547$	−7.11317	−0.304137	−0.152069	−	0.988370i	$-0.548593\pi$
$547$	−7.11317	−0.304137	−0.152069	+	0.988370i	$0.548593\pi$
$548$	−106.460	−4.54774
$549$	−30.0974	−1.28453
$550$	−16.7915	−0.715993
$551$	20.2916	0.864452
$552$	165.678	7.05171
$553$	2.36080	0.100392
$554$	−38.0962	−1.61855
$555$	55.5351	2.35733
$556$	−54.3967	−2.30693
$557$	31.0046	1.31371	0.656853	−	0.754019i	$-0.271887\pi$
$557$	31.0046	1.31371	0.656853	+	0.754019i	$0.271887\pi$
$558$	−171.783	−7.27214
$559$	−52.2969	−2.21193
$560$	131.023	5.53675
$561$	−10.3248	−0.435914
$562$	12.5910	0.531121
$563$	18.8559	0.794681	0.397341	−	0.917671i	$-0.369933\pi$
$563$	18.8559	0.794681	0.397341	+	0.917671i	$0.369933\pi$
$564$	147.335	6.20392
$565$	−40.8268	−1.71759
$566$	−30.2462	−1.27134
$567$	−122.291	−5.13573
$568$	18.6749	0.783580
$569$	−42.7071	−1.79037	−0.895187	−	0.445690i	$-0.852958\pi$
$569$	−42.7071	−1.79037	−0.895187	+	0.445690i	$0.852958\pi$
$570$	137.591	5.76304
$571$	−21.2316	−0.888513	−0.444257	−	0.895900i	$-0.646532\pi$
$571$	−21.2316	−0.888513	−0.444257	+	0.895900i	$0.646532\pi$
$572$	−57.8203	−2.41759
$573$	−80.3060	−3.35483
$574$	−16.9806	−0.708756
$575$	−16.9626	−0.707391
$576$	86.6354	3.60981
$577$	5.08196	0.211565	0.105782	−	0.994389i	$-0.466265\pi$
$577$	5.08196	0.211565	0.105782	+	0.994389i	$0.466265\pi$
$578$	40.4346	1.68186
$579$	62.7565	2.60807
$580$	−47.7123	−1.98114
$581$	33.1521	1.37538
$582$	5.35589	0.222009
$583$	−0.465866	−0.0192942
$584$	95.8307	3.96550
$585$	101.066	4.17857
$586$	−4.15787	−0.171760
$587$	3.65071	0.150681	0.0753405	−	0.997158i	$-0.475996\pi$
$587$	3.65071	0.150681	0.0753405	+	0.997158i	$0.475996\pi$
$588$	215.390	8.88255
$589$	49.0867	2.02258
$590$	−41.1153	−1.69269
$591$	−85.2044	−3.50484
$592$	−64.9712	−2.67030
$593$	−24.1504	−0.991737	−0.495869	−	0.868397i	$-0.665150\pi$
$593$	−24.1504	−0.991737	−0.495869	+	0.868397i	$0.665150\pi$
$594$	−99.3046	−4.07452
$595$	−15.9811	−0.655160
$596$	−113.592	−4.65293
$597$	−6.69459	−0.273991
$598$	−82.0443	−3.35504
$599$	26.6366	1.08834	0.544171	−	0.838974i	$-0.316844\pi$
$599$	26.6366	1.08834	0.544171	+	0.838974i	$0.316844\pi$
$600$	−65.8285	−2.68744
$601$	−16.3409	−0.666557	−0.333279	−	0.942828i	$-0.608155\pi$
$601$	−16.3409	−0.666557	−0.333279	+	0.942828i	$0.608155\pi$
$602$	130.360	5.31309
$603$	−0.538110	−0.0219135
$604$	−85.0009	−3.45864
$605$	13.7096	0.557376
$606$	8.18100	0.332331
$607$	−19.8220	−0.804550	−0.402275	−	0.915519i	$-0.631780\pi$
$607$	−19.8220	−0.804550	−0.402275	+	0.915519i	$0.631780\pi$
$608$	−71.1269	−2.88457
$609$	−51.6389	−2.09251
$610$	−28.4048	−1.15008
$611$	−43.4381	−1.75732
$612$	−48.9159	−1.97731
$613$	4.91179	0.198385	0.0991927	−	0.995068i	$-0.468374\pi$
$613$	4.91179	0.198385	0.0991927	+	0.995068i	$0.468374\pi$
$614$	65.7834	2.65480
$615$	12.8840	0.519534
$616$	85.8084	3.45732
$617$	−40.8699	−1.64536	−0.822680	−	0.568505i	$-0.807522\pi$
$617$	−40.8699	−1.64536	−0.822680	+	0.568505i	$0.807522\pi$
$618$	−121.673	−4.89442
$619$	−18.3751	−0.738559	−0.369279	−	0.929318i	$-0.620395\pi$
$619$	−18.3751	−0.738559	−0.369279	+	0.929318i	$0.620395\pi$
$620$	−115.419	−4.63534
$621$	−100.317	−4.02557
$622$	−39.0409	−1.56540
$623$	27.4582	1.10009
$624$	−164.337	−6.57873
$625$	−31.2408	−1.24963
$626$	56.9647	2.27677
$627$	46.5087	1.85738
$628$	21.3636	0.852500
$629$	7.92460	0.315975
$630$	−251.927	−10.0370
$631$	5.31243	0.211484	0.105742	−	0.994394i	$-0.466278\pi$
$631$	5.31243	0.211484	0.105742	+	0.994394i	$0.466278\pi$
$632$	4.06020	0.161506
$633$	−24.4320	−0.971084
$634$	11.9528	0.474705
$635$	−17.9949	−0.714107
$636$	−3.06764	−0.121640
$637$	−63.5026	−2.51606
$638$	−22.6538	−0.896871
$639$	−18.5331	−0.733157
$640$	14.0903	0.556970
$641$	14.2387	0.562397	0.281198	−	0.959650i	$-0.409268\pi$
$641$	14.2387	0.562397	0.281198	+	0.959650i	$0.409268\pi$
$642$	109.265	4.31233
$643$	14.0553	0.554288	0.277144	−	0.960828i	$-0.410612\pi$
$643$	14.0553	0.554288	0.277144	+	0.960828i	$0.410612\pi$
$644$	145.597	5.73733
$645$	−98.9109	−3.89461
$646$	19.6336	0.772472
$647$	−33.7530	−1.32697	−0.663484	−	0.748191i	$-0.730923\pi$
$647$	−33.7530	−1.32697	−0.663484	+	0.748191i	$0.730923\pi$
$648$	−210.320	−8.26217
$649$	−13.8979	−0.545540
$650$	32.5986	1.27862
$651$	−124.918	−4.89591
$652$	−86.3365	−3.38120
$653$	2.02516	0.0792507	0.0396253	−	0.999215i	$-0.487384\pi$
$653$	2.02516	0.0792507	0.0396253	+	0.999215i	$0.487384\pi$
$654$	49.8767	1.95033
$655$	17.7462	0.693401
$656$	−15.0732	−0.588509
$657$	−95.1031	−3.71033
$658$	108.278	4.22111
$659$	10.6936	0.416562	0.208281	−	0.978069i	$-0.433213\pi$
$659$	10.6936	0.416562	0.208281	+	0.978069i	$0.433213\pi$
$660$	−109.357	−4.25673
$661$	18.2251	0.708873	0.354437	−	0.935080i	$-0.384673\pi$
$661$	18.2251	0.708873	0.354437	+	0.935080i	$0.384673\pi$
$662$	71.6194	2.78357
$663$	20.0443	0.778456
$664$	57.0163	2.21266
$665$	71.9877	2.79156
$666$	124.924	4.84071
$667$	−22.8846	−0.886096
$668$	−13.4627	−0.520888
$669$	49.9752	1.93215
$670$	−0.507848	−0.0196199
$671$	−9.60146	−0.370660
$672$	181.007	6.98248
$673$	−19.6552	−0.757654	−0.378827	−	0.925467i	$-0.623672\pi$
$673$	−19.6552	−0.757654	−0.378827	+	0.925467i	$0.623672\pi$
$674$	71.9878	2.77287
$675$	39.8587	1.53416
$676$	47.9959	1.84600
$677$	24.0369	0.923814	0.461907	−	0.886928i	$-0.347165\pi$
$677$	24.0369	0.923814	0.461907	+	0.886928i	$0.347165\pi$
$678$	−127.644	−4.90212
$679$	2.80221	0.107539
$680$	−27.4848	−1.05400
$681$	−83.2202	−3.18901
$682$	−54.8009	−2.09843
$683$	22.7294	0.869717	0.434858	−	0.900499i	$-0.356798\pi$
$683$	22.7294	0.869717	0.434858	+	0.900499i	$0.356798\pi$
$684$	220.345	8.42510
$685$	59.3635	2.26816
$686$	75.1390	2.86882
$687$	20.3630	0.776896
$688$	115.717	4.41167
$689$	0.904419	0.0344556
$690$	−155.173	−5.90734
$691$	2.34511	0.0892121	0.0446060	−	0.999005i	$-0.485797\pi$
$691$	2.34511	0.0892121	0.0446060	+	0.999005i	$0.485797\pi$
$692$	0.380085	0.0144487
$693$	−85.1569	−3.23484
$694$	65.8670	2.50028
$695$	30.3323	1.15057
$696$	−88.8106	−3.36636
$697$	1.83849	0.0696379
$698$	18.8541	0.713637
$699$	25.7906	0.975491
$700$	−57.8499	−2.18652
$701$	−2.35496	−0.0889458	−0.0444729	−	0.999011i	$-0.514161\pi$
$701$	−2.35496	−0.0889458	−0.0444729	+	0.999011i	$0.514161\pi$
$702$	192.787	7.27629
$703$	−35.6969	−1.34633
$704$	27.6378	1.04164
$705$	−82.1559	−3.09417
$706$	33.3799	1.25627
$707$	4.28032	0.160978
$708$	−91.5151	−3.43935
$709$	−29.0525	−1.09109	−0.545546	−	0.838081i	$-0.683678\pi$
$709$	−29.0525	−1.09109	−0.545546	+	0.838081i	$0.683678\pi$
$710$	−17.4908	−0.656418
$711$	−4.02937	−0.151113
$712$	47.2237	1.76978
$713$	−55.3593	−2.07322
$714$	−49.9643	−1.86987
$715$	32.2414	1.20576
$716$	−56.0156	−2.09340
$717$	−56.0917	−2.09478
$718$	42.5953	1.58964
$719$	−23.3604	−0.871195	−0.435597	−	0.900142i	$-0.643463\pi$
$719$	−23.3604	−0.871195	−0.435597	+	0.900142i	$0.643463\pi$
$720$	−223.628	−8.33413
$721$	−63.6597	−2.37081
$722$	−38.3776	−1.42827
$723$	77.6762	2.88881
$724$	129.712	4.82073
$725$	9.09273	0.337695
$726$	42.8627	1.59078
$727$	23.1192	0.857442	0.428721	−	0.903437i	$-0.358964\pi$
$727$	23.1192	0.857442	0.428721	+	0.903437i	$0.358964\pi$
$728$	−166.586	−6.17409
$729$	58.0945	2.15165
$730$	−89.7547	−3.32197
$731$	−14.1141	−0.522030
$732$	−63.2239	−2.33682
$733$	−28.7868	−1.06327	−0.531633	−	0.846975i	$-0.678421\pi$
$733$	−28.7868	−1.06327	−0.531633	+	0.846975i	$0.678421\pi$
$734$	24.7568	0.913790
$735$	−120.105	−4.43012
$736$	80.2160	2.95680
$737$	−0.171664	−0.00632333
$738$	28.9821	1.06685
$739$	−35.2732	−1.29754	−0.648772	−	0.760983i	$-0.724717\pi$
$739$	−35.2732	−1.29754	−0.648772	+	0.760983i	$0.724717\pi$
$740$	83.9351	3.08552
$741$	−90.2908	−3.31692
$742$	−2.25444	−0.0827631
$743$	−33.8956	−1.24351	−0.621755	−	0.783212i	$-0.713580\pi$
$743$	−33.8956	−1.24351	−0.621755	+	0.783212i	$0.713580\pi$
$744$	−214.838	−7.87635
$745$	63.3406	2.32062
$746$	−38.3119	−1.40270
$747$	−56.5834	−2.07028
$748$	−15.6048	−0.570568
$749$	57.1675	2.08885
$750$	−57.0901	−2.08464
$751$	49.0853	1.79115	0.895574	−	0.444912i	$-0.146765\pi$
$751$	49.0853	1.79115	0.895574	+	0.444912i	$0.146765\pi$
$752$	96.1152	3.50496
$753$	−13.8446	−0.504527
$754$	43.9794	1.60163
$755$	47.3976	1.72498
$756$	−342.123	−12.4429
$757$	−29.2948	−1.06474	−0.532369	−	0.846512i	$-0.678698\pi$
$757$	−29.2948	−1.06474	−0.532369	+	0.846512i	$0.678698\pi$
$758$	−18.4140	−0.668827
$759$	−52.4520	−1.90389
$760$	123.807	4.49096
$761$	42.0318	1.52365	0.761826	−	0.647782i	$-0.224303\pi$
$761$	42.0318	1.52365	0.761826	+	0.647782i	$0.224303\pi$
$762$	−56.2606	−2.03810
$763$	26.0956	0.944724
$764$	−121.374	−4.39114
$765$	27.2762	0.986172
$766$	44.4412	1.60573
$767$	26.9810	0.974227
$768$	−29.5872	−1.06764
$769$	25.8810	0.933292	0.466646	−	0.884444i	$-0.345462\pi$
$769$	25.8810	0.933292	0.466646	+	0.884444i	$0.345462\pi$
$770$	−80.3678	−2.89626
$771$	85.4074	3.07587
$772$	94.8495	3.41371
$773$	−41.9999	−1.51063	−0.755315	−	0.655362i	$-0.772516\pi$
$773$	−41.9999	−1.51063	−0.755315	+	0.655362i	$0.772516\pi$
$774$	−222.496	−7.99747
$775$	21.9959	0.790115
$776$	4.81935	0.173005
$777$	90.8429	3.25897
$778$	−3.55359	−0.127402
$779$	−8.28161	−0.296719
$780$	212.303	7.60168
$781$	−5.91229	−0.211558
$782$	−22.1425	−0.791814
$783$	53.7742	1.92173
$784$	140.512	5.01828
$785$	−11.9126	−0.425180
$786$	55.4829	1.97901
$787$	15.6216	0.556851	0.278425	−	0.960458i	$-0.410188\pi$
$787$	15.6216	0.556851	0.278425	+	0.960458i	$0.410188\pi$
$788$	−128.777	−4.58749
$789$	−25.4114	−0.904669
$790$	−3.80277	−0.135296
$791$	−66.7834	−2.37454
$792$	−146.456	−5.20409
$793$	18.6400	0.661926
$794$	35.4365	1.25759
$795$	1.71056	0.0606672
$796$	−10.1181	−0.358627
$797$	−12.2427	−0.433660	−0.216830	−	0.976209i	$-0.569572\pi$
$797$	−12.2427	−0.433660	−0.216830	+	0.976209i	$0.569572\pi$
$798$	225.067	7.96730
$799$	−11.7233	−0.414740
$800$	−31.8721	−1.12685
$801$	−46.8652	−1.65590
$802$	−19.6431	−0.693622
$803$	−30.3391	−1.07064
$804$	−1.13038	−0.0398653
$805$	−81.1868	−2.86146
$806$	106.389	3.74739
$807$	−52.3066	−1.84128
$808$	7.36145	0.258975
$809$	−33.0454	−1.16182	−0.580908	−	0.813969i	$-0.697302\pi$
$809$	−33.0454	−1.16182	−0.580908	+	0.813969i	$0.697302\pi$
$810$	196.985	6.92136
$811$	5.45827	0.191666	0.0958330	−	0.995397i	$-0.469449\pi$
$811$	5.45827	0.191666	0.0958330	+	0.995397i	$0.469449\pi$
$812$	−78.0465	−2.73890
$813$	27.8889	0.978107
$814$	39.8524	1.39682
$815$	48.1424	1.68635
$816$	−44.3519	−1.55263
$817$	63.5780	2.22431
$818$	−69.9993	−2.44747
$819$	165.321	5.77679
$820$	19.4728	0.680019
$821$	15.2755	0.533119	0.266559	−	0.963819i	$-0.414113\pi$
$821$	15.2755	0.533119	0.266559	+	0.963819i	$0.414113\pi$
$822$	185.598	6.47347
$823$	16.9428	0.590588	0.295294	−	0.955406i	$-0.404582\pi$
$823$	16.9428	0.590588	0.295294	+	0.955406i	$0.404582\pi$
$824$	−109.484	−3.81407
$825$	20.8407	0.725580
$826$	−67.2554	−2.34011
$827$	30.6325	1.06520	0.532598	−	0.846368i	$-0.321216\pi$
$827$	30.6325	1.06520	0.532598	+	0.846368i	$0.321216\pi$
$828$	−248.502	−8.63605
$829$	−50.2522	−1.74533	−0.872665	−	0.488320i	$-0.837610\pi$
$829$	−50.2522	−1.74533	−0.872665	+	0.488320i	$0.837610\pi$
$830$	−53.4013	−1.85358
$831$	47.2829	1.64022
$832$	−53.6553	−1.86016
$833$	−17.1384	−0.593809
$834$	94.8330	3.28380
$835$	7.50699	0.259790
$836$	70.2928	2.43113
$837$	130.083	4.49633
$838$	−93.3462	−3.22459
$839$	50.5373	1.74474	0.872371	−	0.488844i	$-0.162581\pi$
$839$	50.5373	1.74474	0.872371	+	0.488844i	$0.162581\pi$
$840$	−315.070	−10.8709
$841$	−16.7328	−0.576994
$842$	−31.8912	−1.09904
$843$	−15.6273	−0.538233
$844$	−36.9262	−1.27105
$845$	−26.7631	−0.920680
$846$	−184.807	−6.35378
$847$	22.4259	0.770561
$848$	−2.00120	−0.0687216
$849$	37.5399	1.28837
$850$	8.79785	0.301764
$851$	40.2585	1.38004
$852$	−38.9313	−1.33377
$853$	30.8989	1.05796	0.528979	−	0.848635i	$-0.322575\pi$
$853$	30.8989	1.05796	0.528979	+	0.848635i	$0.322575\pi$
$854$	−46.4638	−1.58996
$855$	−122.867	−4.20197
$856$	98.3188	3.36047
$857$	−39.7231	−1.35691	−0.678457	−	0.734640i	$-0.737351\pi$
$857$	−39.7231	−1.35691	−0.678457	+	0.734640i	$0.737351\pi$
$858$	100.802	3.44131
$859$	−28.0469	−0.956949	−0.478475	−	0.878101i	$-0.658810\pi$
$859$	−28.0469	−0.956949	−0.478475	+	0.878101i	$0.658810\pi$
$860$	−149.493	−5.09767
$861$	21.0754	0.718247
$862$	−97.7121	−3.32809
$863$	9.80514	0.333771	0.166885	−	0.985976i	$-0.446629\pi$
$863$	9.80514	0.333771	0.166885	+	0.985976i	$0.446629\pi$
$864$	−188.491	−6.41260
$865$	−0.211941	−0.00720620
$866$	−36.6969	−1.24701
$867$	−50.1852	−1.70438
$868$	−188.799	−6.40827
$869$	−1.28542	−0.0436049
$870$	83.1797	2.82006
$871$	0.333264	0.0112922
$872$	44.8802	1.51983
$873$	−4.78276	−0.161872
$874$	99.7422	3.37383
$875$	−29.8697	−1.00978
$876$	−199.778	−6.74986
$877$	39.9402	1.34868	0.674342	−	0.738420i	$-0.264428\pi$
$877$	39.9402	1.34868	0.674342	+	0.738420i	$0.264428\pi$
$878$	67.5949	2.28122
$879$	5.16051	0.174060
$880$	−71.3403	−2.40488
$881$	13.0550	0.439835	0.219917	−	0.975518i	$-0.429421\pi$
$881$	13.0550	0.439835	0.219917	+	0.975518i	$0.429421\pi$
$882$	−270.170	−9.09711
$883$	6.83155	0.229900	0.114950	−	0.993371i	$-0.463329\pi$
$883$	6.83155	0.229900	0.114950	+	0.993371i	$0.463329\pi$
$884$	30.2947	1.01892
$885$	51.0301	1.71536
$886$	95.2319	3.19938
$887$	20.1447	0.676392	0.338196	−	0.941076i	$-0.390183\pi$
$887$	20.1447	0.676392	0.338196	+	0.941076i	$0.390183\pi$
$888$	156.235	5.24290
$889$	−29.4356	−0.987239
$890$	−44.2296	−1.48258
$891$	66.5855	2.23070
$892$	75.5320	2.52900
$893$	52.8082	1.76716
$894$	198.033	6.62320
$895$	31.2351	1.04407
$896$	23.0486	0.770001
$897$	101.829	3.39997
$898$	−86.4887	−2.88616
$899$	29.6751	0.989719
$900$	98.7371	3.29124
$901$	0.244089	0.00813177
$902$	9.24567	0.307847
$903$	−161.796	−5.38423
$904$	−114.857	−3.82007
$905$	−72.3294	−2.40431
$906$	148.187	4.92319
$907$	27.0891	0.899478	0.449739	−	0.893160i	$-0.351517\pi$
$907$	27.0891	0.899478	0.449739	+	0.893160i	$0.351517\pi$
$908$	−125.778	−4.17409
$909$	−7.30556	−0.242310
$910$	156.024	5.17214
$911$	−26.0624	−0.863486	−0.431743	−	0.901997i	$-0.642101\pi$
$911$	−26.0624	−0.863486	−0.431743	+	0.901997i	$0.642101\pi$
$912$	199.786	6.61557
$913$	−18.0508	−0.597395
$914$	−6.07108	−0.200813
$915$	35.2545	1.16548
$916$	30.7764	1.01688
$917$	29.0288	0.958614
$918$	52.0303	1.71726
$919$	−39.0089	−1.28678	−0.643392	−	0.765537i	$-0.722474\pi$
$919$	−39.0089	−1.28678	−0.643392	+	0.765537i	$0.722474\pi$
$920$	−139.628	−4.60341
$921$	−81.6467	−2.69035
$922$	−46.7183	−1.53858
$923$	11.4780	0.377801
$924$	−178.884	−5.88485
$925$	−15.9959	−0.525941
$926$	14.1799	0.465981
$927$	108.653	3.56863
$928$	−42.9993	−1.41152
$929$	48.6493	1.59613	0.798066	−	0.602569i	$-0.205856\pi$
$929$	48.6493	1.59613	0.798066	+	0.602569i	$0.205856\pi$
$930$	201.217	6.59816
$931$	77.2009	2.53016
$932$	38.9797	1.27682
$933$	48.4555	1.58636
$934$	21.5649	0.705624
$935$	8.70144	0.284568
$936$	284.326	9.29347
$937$	33.7778	1.10347	0.551737	−	0.834018i	$-0.313965\pi$
$937$	33.7778	1.10347	0.551737	+	0.834018i	$0.313965\pi$
$938$	−0.830725	−0.0271241
$939$	−70.7014	−2.30725
$940$	−124.170	−4.04997
$941$	20.7870	0.677636	0.338818	−	0.940852i	$-0.389973\pi$
$941$	20.7870	0.677636	0.338818	+	0.940852i	$0.389973\pi$
$942$	−37.2445	−1.21349
$943$	9.33989	0.304149
$944$	−59.7007	−1.94309
$945$	190.772	6.20583
$946$	−70.9792	−2.30773
$947$	21.4128	0.695823	0.347911	−	0.937527i	$-0.386891\pi$
$947$	21.4128	0.695823	0.347911	+	0.937527i	$0.386891\pi$
$948$	−8.46427	−0.274907
$949$	58.8995	1.91196
$950$	−39.6305	−1.28578
$951$	−14.8351	−0.481061
$952$	−44.9590	−1.45713
$953$	56.6223	1.83418	0.917088	−	0.398684i	$-0.130533\pi$
$953$	56.6223	1.83418	0.917088	+	0.398684i	$0.130533\pi$
$954$	3.84783	0.124578
$955$	67.6795	2.19006
$956$	−84.7764	−2.74186
$957$	28.1166	0.908881
$958$	−29.0443	−0.938378
$959$	97.1052	3.13569
$960$	−101.480	−3.27525
$961$	40.7858	1.31567
$962$	−77.3683	−2.49445
$963$	−97.5723	−3.14422
$964$	117.399	3.78117
$965$	−52.8894	−1.70257
$966$	−253.828	−8.16679
$967$	49.8071	1.60169	0.800843	−	0.598874i	$-0.204385\pi$
$967$	49.8071	1.60169	0.800843	+	0.598874i	$0.204385\pi$
$968$	38.5688	1.23965
$969$	−24.3681	−0.782816
$970$	−4.51379	−0.144929
$971$	22.4336	0.719930	0.359965	−	0.932966i	$-0.382789\pi$
$971$	22.4336	0.719930	0.359965	+	0.932966i	$0.382789\pi$
$972$	210.794	6.76123
$973$	49.6168	1.59064
$974$	−64.6735	−2.07227
$975$	−40.4596	−1.29574
$976$	−41.2446	−1.32021
$977$	−50.1566	−1.60465	−0.802325	−	0.596887i	$-0.796404\pi$
$977$	−50.1566	−1.60465	−0.802325	+	0.596887i	$0.796404\pi$
$978$	150.516	4.81296
$979$	−14.9506	−0.477823
$980$	−181.525	−5.79859
$981$	−44.5394	−1.42203
$982$	86.8073	2.77013
$983$	−42.8592	−1.36700	−0.683499	−	0.729952i	$-0.739543\pi$
$983$	−42.8592	−1.36700	−0.683499	+	0.729952i	$0.739543\pi$
$984$	36.2462	1.15549
$985$	71.8078	2.28799
$986$	11.8694	0.377997
$987$	−134.389	−4.27763
$988$	−136.465	−4.34152
$989$	−71.7025	−2.28001
$990$	137.170	4.35956
$991$	−57.7038	−1.83302	−0.916510	−	0.400011i	$-0.869006\pi$
$991$	−57.7038	−1.83302	−0.916510	+	0.400011i	$0.869006\pi$
$992$	−104.018	−3.30258
$993$	−88.8901	−2.82084
$994$	−28.6110	−0.907486
$995$	5.64200	0.178863
$996$	−118.861	−3.76627
$997$	−9.66839	−0.306201	−0.153100	−	0.988211i	$-0.548926\pi$
$997$	−9.66839	−0.306201	−0.153100	+	0.988211i	$0.548926\pi$
$998$	−33.0041	−1.04473
$999$	−94.5992	−2.99299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.b.1.15	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.63490 q^{2} +3.27029 q^{3} +4.94268 q^{4} -2.75610 q^{5} -8.61687 q^{6} -4.50836 q^{7} -7.75365 q^{8} +7.69478 q^{9} +O(q^{10})\)	\(q-2.63490 q^{2} +3.27029 q^{3} +4.94268 q^{4} -2.75610 q^{5} -8.61687 q^{6} -4.50836 q^{7} -7.75365 q^{8} +7.69478 q^{9} +7.26204 q^{10} +2.45473 q^{11} +16.1640 q^{12} -4.76555 q^{13} +11.8791 q^{14} -9.01325 q^{15} +10.5447 q^{16} -1.28615 q^{17} -20.2750 q^{18} +5.79354 q^{19} -13.6225 q^{20} -14.7436 q^{21} -6.46797 q^{22} -6.53388 q^{23} -25.3567 q^{24} +2.59610 q^{25} +12.5567 q^{26} +15.3533 q^{27} -22.2834 q^{28} +3.50245 q^{29} +23.7490 q^{30} +8.47265 q^{31} -12.2769 q^{32} +8.02769 q^{33} +3.38887 q^{34} +12.4255 q^{35} +38.0328 q^{36} -6.16149 q^{37} -15.2654 q^{38} -15.5847 q^{39} +21.3699 q^{40} -1.42945 q^{41} +38.8480 q^{42} +10.9739 q^{43} +12.1330 q^{44} -21.2076 q^{45} +17.2161 q^{46} +9.11502 q^{47} +34.4842 q^{48} +13.3253 q^{49} -6.84046 q^{50} -4.20608 q^{51} -23.5546 q^{52} -0.189783 q^{53} -40.4543 q^{54} -6.76550 q^{55} +34.9563 q^{56} +18.9466 q^{57} -9.22860 q^{58} -5.66167 q^{59} -44.5496 q^{60} -3.91141 q^{61} -22.3246 q^{62} -34.6909 q^{63} +11.2590 q^{64} +13.1344 q^{65} -21.1521 q^{66} -0.0699318 q^{67} -6.35702 q^{68} -21.3677 q^{69} -32.7399 q^{70} -2.40852 q^{71} -59.6627 q^{72} -12.3594 q^{73} +16.2349 q^{74} +8.49000 q^{75} +28.6356 q^{76} -11.0668 q^{77} +41.0642 q^{78} -0.523650 q^{79} -29.0623 q^{80} +27.1253 q^{81} +3.76646 q^{82} -7.35347 q^{83} -72.8731 q^{84} +3.54476 q^{85} -28.9152 q^{86} +11.4540 q^{87} -19.0332 q^{88} -6.09051 q^{89} +55.8799 q^{90} +21.4848 q^{91} -32.2949 q^{92} +27.7080 q^{93} -24.0171 q^{94} -15.9676 q^{95} -40.1491 q^{96} -0.621559 q^{97} -35.1109 q^{98} +18.8886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) \) 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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