LMFDB - Embedded newform 6043.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2535979415$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-2.51764 q^{2} -0.610944 q^{3} +4.33849 q^{4} +0.176769 q^{5} +1.53813 q^{6} -3.05611 q^{7} -5.88747 q^{8} -2.62675 q^{9} +O(q^{10})$	\(q-2.51764 q^{2} -0.610944 q^{3} +4.33849 q^{4} +0.176769 q^{5} +1.53813 q^{6} -3.05611 q^{7} -5.88747 q^{8} -2.62675 q^{9} -0.445041 q^{10} -0.477457 q^{11} -2.65057 q^{12} +2.10903 q^{13} +7.69418 q^{14} -0.107996 q^{15} +6.14552 q^{16} -1.24698 q^{17} +6.61319 q^{18} -0.222634 q^{19} +0.766912 q^{20} +1.86711 q^{21} +1.20206 q^{22} +6.18733 q^{23} +3.59691 q^{24} -4.96875 q^{25} -5.30976 q^{26} +3.43763 q^{27} -13.2589 q^{28} -5.02202 q^{29} +0.271895 q^{30} +9.51600 q^{31} -3.69724 q^{32} +0.291699 q^{33} +3.13944 q^{34} -0.540228 q^{35} -11.3961 q^{36} +2.48700 q^{37} +0.560511 q^{38} -1.28850 q^{39} -1.04072 q^{40} +1.93310 q^{41} -4.70071 q^{42} -2.62042 q^{43} -2.07144 q^{44} -0.464329 q^{45} -15.5774 q^{46} +5.21089 q^{47} -3.75457 q^{48} +2.33984 q^{49} +12.5095 q^{50} +0.761835 q^{51} +9.15000 q^{52} -2.89062 q^{53} -8.65469 q^{54} -0.0843997 q^{55} +17.9928 q^{56} +0.136017 q^{57} +12.6436 q^{58} +3.56995 q^{59} -0.468540 q^{60} -7.59163 q^{61} -23.9578 q^{62} +8.02764 q^{63} -2.98273 q^{64} +0.372812 q^{65} -0.734392 q^{66} -15.6915 q^{67} -5.41001 q^{68} -3.78011 q^{69} +1.36010 q^{70} -10.7796 q^{71} +15.4649 q^{72} -3.65630 q^{73} -6.26135 q^{74} +3.03563 q^{75} -0.965896 q^{76} +1.45916 q^{77} +3.24397 q^{78} -3.15880 q^{79} +1.08634 q^{80} +5.78005 q^{81} -4.86683 q^{82} -9.82213 q^{83} +8.10046 q^{84} -0.220428 q^{85} +6.59726 q^{86} +3.06817 q^{87} +2.81101 q^{88} -17.9718 q^{89} +1.16901 q^{90} -6.44543 q^{91} +26.8437 q^{92} -5.81374 q^{93} -13.1191 q^{94} -0.0393549 q^{95} +2.25881 q^{96} -1.65104 q^{97} -5.89086 q^{98} +1.25416 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.51764	−1.78024	−0.890119	−	0.455729i	$-0.849379\pi$
$2$	−2.51764	−1.78024	−0.890119	+	0.455729i	$0.849379\pi$
$3$	−0.610944	−0.352728	−0.176364	−	0.984325i	$-0.556434\pi$
$3$	−0.610944	−0.352728	−0.176364	+	0.984325i	$0.556434\pi$
$4$	4.33849	2.16925
$5$	0.176769	0.0790537	0.0395268	−	0.999219i	$-0.487415\pi$
$5$	0.176769	0.0790537	0.0395268	+	0.999219i	$0.487415\pi$
$6$	1.53813	0.627940
$7$	−3.05611	−1.15510	−0.577551	−	0.816354i	$-0.695992\pi$
$7$	−3.05611	−1.15510	−0.577551	+	0.816354i	$0.695992\pi$
$8$	−5.88747	−2.08153
$9$	−2.62675	−0.875583
$10$	−0.445041	−0.140734
$11$	−0.477457	−0.143959	−0.0719793	−	0.997406i	$-0.522932\pi$
$11$	−0.477457	−0.143959	−0.0719793	+	0.997406i	$0.522932\pi$
$12$	−2.65057	−0.765155
$13$	2.10903	0.584939	0.292470	−	0.956275i	$-0.405523\pi$
$13$	2.10903	0.584939	0.292470	+	0.956275i	$0.405523\pi$
$14$	7.69418	2.05636
$15$	−0.107996	−0.0278845
$16$	6.14552	1.53638
$17$	−1.24698	−0.302437	−0.151219	−	0.988500i	$-0.548320\pi$
$17$	−1.24698	−0.302437	−0.151219	+	0.988500i	$0.548320\pi$
$18$	6.61319	1.55874
$19$	−0.222634	−0.0510757	−0.0255379	−	0.999674i	$-0.508130\pi$
$19$	−0.222634	−0.0510757	−0.0255379	+	0.999674i	$0.508130\pi$
$20$	0.766912	0.171487
$21$	1.86711	0.407438
$22$	1.20206	0.256281
$23$	6.18733	1.29015	0.645074	−	0.764120i	$-0.276827\pi$
$23$	6.18733	1.29015	0.645074	+	0.764120i	$0.276827\pi$
$24$	3.59691	0.734216
$25$	−4.96875	−0.993751
$26$	−5.30976	−1.04133
$27$	3.43763	0.661571
$28$	−13.2589	−2.50570
$29$	−5.02202	−0.932566	−0.466283	−	0.884636i	$-0.654407\pi$
$29$	−5.02202	−0.932566	−0.466283	+	0.884636i	$0.654407\pi$
$30$	0.271895	0.0496410
$31$	9.51600	1.70912	0.854562	−	0.519349i	$-0.173826\pi$
$31$	9.51600	1.70912	0.854562	+	0.519349i	$0.173826\pi$
$32$	−3.69724	−0.653586
$33$	0.291699	0.0507783
$34$	3.13944	0.538410
$35$	−0.540228	−0.0913151
$36$	−11.3961	−1.89935
$37$	2.48700	0.408860	0.204430	−	0.978881i	$-0.434466\pi$
$37$	2.48700	0.408860	0.204430	+	0.978881i	$0.434466\pi$
$38$	0.560511	0.0909270
$39$	−1.28850	−0.206325
$40$	−1.04072	−0.164553
$41$	1.93310	0.301899	0.150949	−	0.988541i	$-0.451767\pi$
$41$	1.93310	0.301899	0.150949	+	0.988541i	$0.451767\pi$
$42$	−4.70071	−0.725336
$43$	−2.62042	−0.399610	−0.199805	−	0.979836i	$-0.564031\pi$
$43$	−2.62042	−0.399610	−0.199805	+	0.979836i	$0.564031\pi$
$44$	−2.07144	−0.312282
$45$	−0.464329	−0.0692180
$46$	−15.5774	−2.29677
$47$	5.21089	0.760086	0.380043	−	0.924969i	$-0.375909\pi$
$47$	5.21089	0.760086	0.380043	+	0.924969i	$0.375909\pi$
$48$	−3.75457	−0.541925
$49$	2.33984	0.334263
$50$	12.5095	1.76911
$51$	0.761835	0.106678
$52$	9.15000	1.26888
$53$	−2.89062	−0.397058	−0.198529	−	0.980095i	$-0.563616\pi$
$53$	−2.89062	−0.397058	−0.198529	+	0.980095i	$0.563616\pi$
$54$	−8.65469	−1.17775
$55$	−0.0843997	−0.0113805
$56$	17.9928	2.40439
$57$	0.136017	0.0180159
$58$	12.6436	1.66019
$59$	3.56995	0.464768	0.232384	−	0.972624i	$-0.425347\pi$
$59$	3.56995	0.464768	0.232384	+	0.972624i	$0.425347\pi$
$60$	−0.468540	−0.0604883
$61$	−7.59163	−0.972009	−0.486004	−	0.873956i	$-0.661546\pi$
$61$	−7.59163	−0.972009	−0.486004	+	0.873956i	$0.661546\pi$
$62$	−23.9578	−3.04265
$63$	8.02764	1.01139
$64$	−2.98273	−0.372841
$65$	0.372812	0.0462416
$66$	−0.734392	−0.0903974
$67$	−15.6915	−1.91702	−0.958512	−	0.285052i	$-0.907989\pi$
$67$	−15.6915	−1.91702	−0.958512	+	0.285052i	$0.907989\pi$
$68$	−5.41001	−0.656060
$69$	−3.78011	−0.455072
$70$	1.36010	0.162563
$71$	−10.7796	−1.27930	−0.639649	−	0.768667i	$-0.720920\pi$
$71$	−10.7796	−1.27930	−0.639649	+	0.768667i	$0.720920\pi$
$72$	15.4649	1.82256
$73$	−3.65630	−0.427938	−0.213969	−	0.976840i	$-0.568639\pi$
$73$	−3.65630	−0.427938	−0.213969	+	0.976840i	$0.568639\pi$
$74$	−6.26135	−0.727867
$75$	3.03563	0.350524
$76$	−0.965896	−0.110796
$77$	1.45916	0.166287
$78$	3.24397	0.367307
$79$	−3.15880	−0.355393	−0.177696	−	0.984085i	$-0.556865\pi$
$79$	−3.15880	−0.355393	−0.177696	+	0.984085i	$0.556865\pi$
$80$	1.08634	0.121456
$81$	5.78005	0.642228
$82$	−4.86683	−0.537452
$83$	−9.82213	−1.07812	−0.539060	−	0.842268i	$-0.681220\pi$
$83$	−9.82213	−1.07812	−0.539060	+	0.842268i	$0.681220\pi$
$84$	8.10046	0.883832
$85$	−0.220428	−0.0239088
$86$	6.59726	0.711400
$87$	3.06817	0.328943
$88$	2.81101	0.299655
$89$	−17.9718	−1.90501	−0.952506	−	0.304520i	$-0.901504\pi$
$89$	−17.9718	−1.90501	−0.952506	+	0.304520i	$0.901504\pi$
$90$	1.16901	0.123225
$91$	−6.44543	−0.675665
$92$	26.8437	2.79865
$93$	−5.81374	−0.602857
$94$	−13.1191	−1.35313
$95$	−0.0393549	−0.00403773
$96$	2.25881	0.230539
$97$	−1.65104	−0.167638	−0.0838189	−	0.996481i	$-0.526712\pi$
$97$	−1.65104	−0.167638	−0.0838189	+	0.996481i	$0.526712\pi$
$98$	−5.89086	−0.595067
$99$	1.25416	0.126048
$100$	−21.5569	−2.15569
$101$	−2.74978	−0.273613	−0.136807	−	0.990598i	$-0.543684\pi$
$101$	−2.74978	−0.273613	−0.136807	+	0.990598i	$0.543684\pi$
$102$	−1.91802	−0.189913
$103$	−6.42671	−0.633242	−0.316621	−	0.948552i	$-0.602548\pi$
$103$	−6.42671	−0.633242	−0.316621	+	0.948552i	$0.602548\pi$
$104$	−12.4168	−1.21757
$105$	0.330049	0.0322094
$106$	7.27754	0.706857
$107$	0.0720207	0.00696250	0.00348125	−	0.999994i	$-0.498892\pi$
$107$	0.0720207	0.00696250	0.00348125	+	0.999994i	$0.498892\pi$
$108$	14.9141	1.43511
$109$	−2.22458	−0.213076	−0.106538	−	0.994309i	$-0.533977\pi$
$109$	−2.22458	−0.213076	−0.106538	+	0.994309i	$0.533977\pi$
$110$	0.212488	0.0202599
$111$	−1.51941	−0.144216
$112$	−18.7814	−1.77468
$113$	16.2713	1.53067	0.765336	−	0.643631i	$-0.222573\pi$
$113$	16.2713	1.53067	0.765336	+	0.643631i	$0.222573\pi$
$114$	−0.342441	−0.0320725
$115$	1.09373	0.101991
$116$	−21.7880	−2.02296
$117$	−5.53988	−0.512162
$118$	−8.98785	−0.827398
$119$	3.81092	0.349346
$120$	0.635824	0.0580425
$121$	−10.7720	−0.979276
$122$	19.1130	1.73041
$123$	−1.18101	−0.106488
$124$	41.2851	3.70751
$125$	−1.76217	−0.157613
$126$	−20.2107	−1.80051
$127$	2.89812	0.257167	0.128583	−	0.991699i	$-0.458957\pi$
$127$	2.89812	0.257167	0.128583	+	0.991699i	$0.458957\pi$
$128$	14.9039	1.31733
$129$	1.60093	0.140954
$130$	−0.938604	−0.0823210
$131$	17.7986	1.55507	0.777534	−	0.628841i	$-0.216471\pi$
$131$	17.7986	1.55507	0.777534	+	0.628841i	$0.216471\pi$
$132$	1.26553	0.110151
$133$	0.680395	0.0589977
$134$	39.5055	3.41276
$135$	0.607667	0.0522997
$136$	7.34156	0.629533
$137$	−4.26882	−0.364709	−0.182355	−	0.983233i	$-0.558372\pi$
$137$	−4.26882	−0.364709	−0.182355	+	0.983233i	$0.558372\pi$
$138$	9.51694	0.810136
$139$	16.8136	1.42611	0.713055	−	0.701109i	$-0.247311\pi$
$139$	16.8136	1.42611	0.713055	+	0.701109i	$0.247311\pi$
$140$	−2.34377	−0.198085
$141$	−3.18356	−0.268104
$142$	27.1390	2.27745
$143$	−1.00697	−0.0842070
$144$	−16.1427	−1.34523
$145$	−0.887740	−0.0737228
$146$	9.20523	0.761831
$147$	−1.42951	−0.117904
$148$	10.7898	0.886917
$149$	7.58518	0.621402	0.310701	−	0.950508i	$-0.399436\pi$
$149$	7.58518	0.621402	0.310701	+	0.950508i	$0.399436\pi$
$150$	−7.64261	−0.624016
$151$	17.9402	1.45995	0.729975	−	0.683474i	$-0.239532\pi$
$151$	17.9402	1.45995	0.729975	+	0.683474i	$0.239532\pi$
$152$	1.31075	0.106316
$153$	3.27550	0.264809
$154$	−3.67364	−0.296030
$155$	1.68214	0.135113
$156$	−5.59013	−0.447569
$157$	2.54437	0.203062	0.101531	−	0.994832i	$-0.467626\pi$
$157$	2.54437	0.203062	0.101531	+	0.994832i	$0.467626\pi$
$158$	7.95271	0.632684
$159$	1.76601	0.140054
$160$	−0.653559	−0.0516684
$161$	−18.9092	−1.49025
$162$	−14.5521	−1.14332
$163$	−12.7193	−0.996253	−0.498127	−	0.867104i	$-0.665979\pi$
$163$	−12.7193	−0.996253	−0.498127	+	0.867104i	$0.665979\pi$
$164$	8.38672	0.654893
$165$	0.0515635	0.00401421
$166$	24.7286	1.91931
$167$	−17.9523	−1.38919	−0.694595	−	0.719401i	$-0.744416\pi$
$167$	−17.9523	−1.38919	−0.694595	+	0.719401i	$0.744416\pi$
$168$	−10.9926	−0.848095
$169$	−8.55200	−0.657846
$170$	0.554957	0.0425633
$171$	0.584803	0.0447210
$172$	−11.3687	−0.866852
$173$	5.27995	0.401427	0.200714	−	0.979650i	$-0.435674\pi$
$173$	5.27995	0.401427	0.200714	+	0.979650i	$0.435674\pi$
$174$	−7.72454	−0.585596
$175$	15.1851	1.14788
$176$	−2.93422	−0.221175
$177$	−2.18104	−0.163937
$178$	45.2466	3.39137
$179$	3.18079	0.237743	0.118872	−	0.992910i	$-0.462072\pi$
$179$	3.18079	0.237743	0.118872	+	0.992910i	$0.462072\pi$
$180$	−2.01449	−0.150151
$181$	11.6984	0.869538	0.434769	−	0.900542i	$-0.356830\pi$
$181$	11.6984	0.869538	0.434769	+	0.900542i	$0.356830\pi$
$182$	16.2272	1.20284
$183$	4.63806	0.342855
$184$	−36.4277	−2.68549
$185$	0.439625	0.0323219
$186$	14.6369	1.07323
$187$	0.595379	0.0435384
$188$	22.6074	1.64881
$189$	−10.5058	−0.764183
$190$	0.0990813	0.00718811
$191$	−14.8778	−1.07652	−0.538260	−	0.842779i	$-0.680918\pi$
$191$	−14.8778	−1.07652	−0.538260	+	0.842779i	$0.680918\pi$
$192$	1.82228	0.131512
$193$	11.8026	0.849570	0.424785	−	0.905294i	$-0.360350\pi$
$193$	11.8026	0.849570	0.424785	+	0.905294i	$0.360350\pi$
$194$	4.15672	0.298435
$195$	−0.227767	−0.0163107
$196$	10.1514	0.725098
$197$	24.9960	1.78089	0.890447	−	0.455088i	$-0.150392\pi$
$197$	24.9960	1.78089	0.890447	+	0.455088i	$0.150392\pi$
$198$	−3.15751	−0.224395
$199$	−25.6949	−1.82146	−0.910731	−	0.412999i	$-0.864481\pi$
$199$	−25.6949	−1.82146	−0.910731	+	0.412999i	$0.864481\pi$
$200$	29.2534	2.06853
$201$	9.58663	0.676189
$202$	6.92294	0.487096
$203$	15.3479	1.07721
$204$	3.30521	0.231411
$205$	0.341712	0.0238662
$206$	16.1801	1.12732
$207$	−16.2526	−1.12963
$208$	12.9611	0.898688
$209$	0.106298	0.00735279
$210$	−0.830942	−0.0573405
$211$	2.96575	0.204171	0.102085	−	0.994776i	$-0.467449\pi$
$211$	2.96575	0.204171	0.102085	+	0.994776i	$0.467449\pi$
$212$	−12.5409	−0.861316
$213$	6.58570	0.451245
$214$	−0.181322	−0.0123949
$215$	−0.463210	−0.0315906
$216$	−20.2389	−1.37708
$217$	−29.0820	−1.97421
$218$	5.60068	0.379326
$219$	2.23379	0.150946
$220$	−0.366167	−0.0246870
$221$	−2.62992	−0.176907
$222$	3.82533	0.256739
$223$	−10.4819	−0.701922	−0.350961	−	0.936390i	$-0.614145\pi$
$223$	−10.4819	−0.701922	−0.350961	+	0.936390i	$0.614145\pi$
$224$	11.2992	0.754959
$225$	13.0517	0.870111
$226$	−40.9651	−2.72496
$227$	18.8163	1.24888	0.624440	−	0.781073i	$-0.285327\pi$
$227$	18.8163	1.24888	0.624440	+	0.781073i	$0.285327\pi$
$228$	0.590108	0.0390808
$229$	−11.3267	−0.748490	−0.374245	−	0.927330i	$-0.622098\pi$
$229$	−11.3267	−0.748490	−0.374245	+	0.927330i	$0.622098\pi$
$230$	−2.75361	−0.181568
$231$	−0.891466	−0.0586542
$232$	29.5670	1.94117
$233$	27.8410	1.82392	0.911961	−	0.410278i	$-0.134568\pi$
$233$	27.8410	1.82392	0.911961	+	0.410278i	$0.134568\pi$
$234$	13.9474	0.911771
$235$	0.921126	0.0600876
$236$	15.4882	1.00820
$237$	1.92985	0.125357
$238$	−9.59450	−0.621919
$239$	−3.81586	−0.246827	−0.123414	−	0.992355i	$-0.539384\pi$
$239$	−3.81586	−0.246827	−0.123414	+	0.992355i	$0.539384\pi$
$240$	−0.663692	−0.0428412
$241$	−11.9373	−0.768947	−0.384473	−	0.923136i	$-0.625617\pi$
$241$	−11.9373	−0.768947	−0.384473	+	0.923136i	$0.625617\pi$
$242$	27.1201	1.74334
$243$	−13.8442	−0.888103
$244$	−32.9362	−2.10852
$245$	0.413612	0.0264247
$246$	2.97336	0.189575
$247$	−0.469541	−0.0298762
$248$	−56.0251	−3.55760
$249$	6.00077	0.380283
$250$	4.43650	0.280589
$251$	20.8524	1.31619	0.658096	−	0.752934i	$-0.271362\pi$
$251$	20.8524	1.31619	0.658096	+	0.752934i	$0.271362\pi$
$252$	34.8279	2.19395
$253$	−2.95418	−0.185728
$254$	−7.29642	−0.457818
$255$	0.134669	0.00843330
$256$	−31.5571	−1.97232
$257$	10.8336	0.675781	0.337891	−	0.941185i	$-0.390287\pi$
$257$	10.8336	0.675781	0.337891	+	0.941185i	$0.390287\pi$
$258$	−4.03055	−0.250931
$259$	−7.60054	−0.472275
$260$	1.61744	0.100309
$261$	13.1916	0.816539
$262$	−44.8103	−2.76839
$263$	8.39252	0.517505	0.258753	−	0.965944i	$-0.416689\pi$
$263$	8.39252	0.517505	0.258753	+	0.965944i	$0.416689\pi$
$264$	−1.71737	−0.105697
$265$	−0.510974	−0.0313889
$266$	−1.71299	−0.105030
$267$	10.9798	0.671952
$268$	−68.0775	−4.15849
$269$	−13.9904	−0.853013	−0.426506	−	0.904485i	$-0.640256\pi$
$269$	−13.9904	−0.853013	−0.426506	+	0.904485i	$0.640256\pi$
$270$	−1.52988	−0.0931058
$271$	4.63936	0.281821	0.140911	−	0.990022i	$-0.454997\pi$
$271$	4.63936	0.281821	0.140911	+	0.990022i	$0.454997\pi$
$272$	−7.66334	−0.464658
$273$	3.93780	0.238326
$274$	10.7473	0.649269
$275$	2.37236	0.143059
$276$	−16.4000	−0.987162
$277$	−15.5739	−0.935745	−0.467873	−	0.883796i	$-0.654979\pi$
$277$	−15.5739	−0.935745	−0.467873	+	0.883796i	$0.654979\pi$
$278$	−42.3305	−2.53881
$279$	−24.9961	−1.49648
$280$	3.18057	0.190076
$281$	28.0544	1.67358	0.836792	−	0.547521i	$-0.184428\pi$
$281$	28.0544	1.67358	0.836792	+	0.547521i	$0.184428\pi$
$282$	8.01504	0.477289
$283$	−3.22478	−0.191694	−0.0958468	−	0.995396i	$-0.530556\pi$
$283$	−3.22478	−0.191694	−0.0958468	+	0.995396i	$0.530556\pi$
$284$	−46.7670	−2.77511
$285$	0.0240436	0.00142422
$286$	2.53518	0.149908
$287$	−5.90777	−0.348724
$288$	9.71172	0.572269
$289$	−15.4450	−0.908532
$290$	2.23501	0.131244
$291$	1.00869	0.0591306
$292$	−15.8628	−0.928302
$293$	−32.5814	−1.90343	−0.951714	−	0.306987i	$-0.900679\pi$
$293$	−32.5814	−1.90343	−0.951714	+	0.306987i	$0.900679\pi$
$294$	3.59898	0.209897
$295$	0.631059	0.0367417
$296$	−14.6421	−0.851055
$297$	−1.64132	−0.0952389
$298$	−19.0967	−1.10624
$299$	13.0492	0.754657
$300$	13.1700	0.760373
$301$	8.00830	0.461590
$302$	−45.1668	−2.59906
$303$	1.67996	0.0965112
$304$	−1.36820	−0.0784717
$305$	−1.34197	−0.0768409
$306$	−8.24652	−0.471422
$307$	9.77170	0.557700	0.278850	−	0.960335i	$-0.410047\pi$
$307$	9.77170	0.557700	0.278850	+	0.960335i	$0.410047\pi$
$308$	6.33056	0.360717
$309$	3.92635	0.223363
$310$	−4.23501	−0.240532
$311$	−19.4096	−1.10062	−0.550308	−	0.834962i	$-0.685490\pi$
$311$	−19.4096	−1.10062	−0.550308	+	0.834962i	$0.685490\pi$
$312$	7.58598	0.429472
$313$	27.0515	1.52904	0.764520	−	0.644600i	$-0.222976\pi$
$313$	27.0515	1.52904	0.764520	+	0.644600i	$0.222976\pi$
$314$	−6.40579	−0.361499
$315$	1.41904	0.0799539
$316$	−13.7044	−0.770934
$317$	17.4793	0.981734	0.490867	−	0.871235i	$-0.336680\pi$
$317$	17.4793	0.981734	0.490867	+	0.871235i	$0.336680\pi$
$318$	−4.44617	−0.249329
$319$	2.39780	0.134251
$320$	−0.527255	−0.0294744
$321$	−0.0440006	−0.00245587
$322$	47.6064	2.65300
$323$	0.277620	0.0154472
$324$	25.0767	1.39315
$325$	−10.4792	−0.581283
$326$	32.0226	1.77357
$327$	1.35909	0.0751579
$328$	−11.3810	−0.628413
$329$	−15.9251	−0.877978
$330$	−0.129818	−0.00714625
$331$	−21.8443	−1.20067	−0.600335	−	0.799748i	$-0.704966\pi$
$331$	−21.8443	−1.20067	−0.600335	+	0.799748i	$0.704966\pi$
$332$	−42.6132	−2.33870
$333$	−6.53271	−0.357990
$334$	45.1973	2.47309
$335$	−2.77378	−0.151548
$336$	11.4744	0.625979
$337$	22.1634	1.20732	0.603658	−	0.797243i	$-0.293709\pi$
$337$	22.1634	1.20732	0.603658	+	0.797243i	$0.293709\pi$
$338$	21.5308	1.17112
$339$	−9.94082	−0.539911
$340$	−0.956325	−0.0518640
$341$	−4.54348	−0.246043
$342$	−1.47232	−0.0796141
$343$	14.2420	0.768995
$344$	15.4276	0.831802
$345$	−0.668208	−0.0359751
$346$	−13.2930	−0.714636
$347$	30.6379	1.64473	0.822364	−	0.568962i	$-0.192655\pi$
$347$	30.6379	1.64473	0.822364	+	0.568962i	$0.192655\pi$
$348$	13.3112	0.713557
$349$	28.6853	1.53549	0.767745	−	0.640755i	$-0.221379\pi$
$349$	28.6853	1.53549	0.767745	+	0.640755i	$0.221379\pi$
$350$	−38.2305	−2.04351
$351$	7.25005	0.386979
$352$	1.76527	0.0940894
$353$	20.9841	1.11687	0.558434	−	0.829549i	$-0.311402\pi$
$353$	20.9841	1.11687	0.558434	+	0.829549i	$0.311402\pi$
$354$	5.49107	0.291847
$355$	−1.90550	−0.101133
$356$	−77.9707	−4.13244
$357$	−2.32825	−0.123224
$358$	−8.00806	−0.423239
$359$	−17.8834	−0.943852	−0.471926	−	0.881638i	$-0.656441\pi$
$359$	−17.8834	−0.943852	−0.471926	+	0.881638i	$0.656441\pi$
$360$	2.73372	0.144080
$361$	−18.9504	−0.997391
$362$	−29.4524	−1.54798
$363$	6.58111	0.345419
$364$	−27.9634	−1.46568
$365$	−0.646322	−0.0338300
$366$	−11.6769	−0.610363
$367$	34.8042	1.81676	0.908382	−	0.418142i	$-0.137319\pi$
$367$	34.8042	1.81676	0.908382	+	0.418142i	$0.137319\pi$
$368$	38.0243	1.98216
$369$	−5.07776	−0.264337
$370$	−1.10681	−0.0575406
$371$	8.83408	0.458643
$372$	−25.2229	−1.30774
$373$	9.84750	0.509884	0.254942	−	0.966956i	$-0.417944\pi$
$373$	9.84750	0.509884	0.254942	+	0.966956i	$0.417944\pi$
$374$	−1.49895	−0.0775088
$375$	1.07659	0.0555947
$376$	−30.6789	−1.58215
$377$	−10.5916	−0.545494
$378$	26.4497	1.36043
$379$	−30.3498	−1.55897	−0.779483	−	0.626423i	$-0.784518\pi$
$379$	−30.3498	−1.55897	−0.779483	+	0.626423i	$0.784518\pi$
$380$	−0.170741	−0.00875882
$381$	−1.77059	−0.0907101
$382$	37.4569	1.91646
$383$	19.6521	1.00417	0.502087	−	0.864817i	$-0.332566\pi$
$383$	19.6521	1.00417	0.502087	+	0.864817i	$0.332566\pi$
$384$	−9.10544	−0.464660
$385$	0.257935	0.0131456
$386$	−29.7147	−1.51244
$387$	6.88317	0.349891
$388$	−7.16303	−0.363648
$389$	−18.6555	−0.945871	−0.472935	−	0.881097i	$-0.656806\pi$
$389$	−18.6555	−0.945871	−0.472935	+	0.881097i	$0.656806\pi$
$390$	0.573434	0.0290370
$391$	−7.71548	−0.390188
$392$	−13.7757	−0.695779
$393$	−10.8739	−0.548516
$394$	−62.9309	−3.17041
$395$	−0.558379	−0.0280951
$396$	5.44115	0.273428
$397$	−17.7899	−0.892851	−0.446425	−	0.894821i	$-0.647303\pi$
$397$	−17.7899	−0.892851	−0.446425	+	0.894821i	$0.647303\pi$
$398$	64.6904	3.24264
$399$	−0.415683	−0.0208102
$400$	−30.5356	−1.52678
$401$	−25.3371	−1.26528	−0.632638	−	0.774448i	$-0.718028\pi$
$401$	−25.3371	−1.26528	−0.632638	+	0.774448i	$0.718028\pi$
$402$	−24.1356	−1.20378
$403$	20.0695	0.999733
$404$	−11.9299	−0.593534
$405$	1.02174	0.0507705
$406$	−38.6404	−1.91769
$407$	−1.18743	−0.0588589
$408$	−4.48528	−0.222054
$409$	14.2878	0.706485	0.353243	−	0.935532i	$-0.385079\pi$
$409$	14.2878	0.706485	0.353243	+	0.935532i	$0.385079\pi$
$410$	−0.860307	−0.0424875
$411$	2.60801	0.128643
$412$	−27.8822	−1.37366
$413$	−10.9102	−0.536855
$414$	40.9180	2.01101
$415$	−1.73625	−0.0852293
$416$	−7.79759	−0.382308
$417$	−10.2721	−0.503029
$418$	−0.267620	−0.0130897
$419$	33.3520	1.62935	0.814675	−	0.579918i	$-0.196915\pi$
$419$	33.3520	1.62935	0.814675	+	0.579918i	$0.196915\pi$
$420$	1.43191	0.0698702
$421$	−33.1173	−1.61404	−0.807019	−	0.590526i	$-0.798920\pi$
$421$	−33.1173	−1.61404	−0.807019	+	0.590526i	$0.798920\pi$
$422$	−7.46667	−0.363472
$423$	−13.6877	−0.665518
$424$	17.0185	0.826489
$425$	6.19594	0.300547
$426$	−16.5804	−0.803323
$427$	23.2009	1.12277
$428$	0.312461	0.0151034
$429$	0.615202	0.0297022
$430$	1.16619	0.0562388
$431$	−30.0194	−1.44598	−0.722992	−	0.690856i	$-0.757234\pi$
$431$	−30.0194	−1.44598	−0.722992	+	0.690856i	$0.757234\pi$
$432$	21.1260	1.01642
$433$	7.90812	0.380040	0.190020	−	0.981780i	$-0.439145\pi$
$433$	7.90812	0.380040	0.190020	+	0.981780i	$0.439145\pi$
$434$	73.2179	3.51457
$435$	0.542359	0.0260041
$436$	−9.65131	−0.462214
$437$	−1.37751	−0.0658952
$438$	−5.62388	−0.268719
$439$	−17.6298	−0.841423	−0.420711	−	0.907195i	$-0.638219\pi$
$439$	−17.6298	−0.841423	−0.420711	+	0.907195i	$0.638219\pi$
$440$	0.496901	0.0236888
$441$	−6.14617	−0.292675
$442$	6.62117	0.314937
$443$	−12.4815	−0.593015	−0.296508	−	0.955030i	$-0.595822\pi$
$443$	−12.4815	−0.593015	−0.296508	+	0.955030i	$0.595822\pi$
$444$	−6.59196	−0.312841
$445$	−3.17687	−0.150598
$446$	26.3897	1.24959
$447$	−4.63412	−0.219186
$448$	9.11555	0.430669
$449$	36.5846	1.72653	0.863267	−	0.504748i	$-0.168415\pi$
$449$	36.5846	1.72653	0.863267	+	0.504748i	$0.168415\pi$
$450$	−32.8593	−1.54900
$451$	−0.922970	−0.0434610
$452$	70.5927	3.32040
$453$	−10.9604	−0.514966
$454$	−47.3726	−2.22330
$455$	−1.13935	−0.0534138
$456$	−0.800795	−0.0375006
$457$	8.57821	0.401272	0.200636	−	0.979666i	$-0.435699\pi$
$457$	8.57821	0.401272	0.200636	+	0.979666i	$0.435699\pi$
$458$	28.5165	1.33249
$459$	−4.28665	−0.200084
$460$	4.74514	0.221243
$461$	36.5500	1.70231	0.851153	−	0.524918i	$-0.175904\pi$
$461$	36.5500	1.70231	0.851153	+	0.524918i	$0.175904\pi$
$462$	2.24439	0.104418
$463$	28.4027	1.31999	0.659993	−	0.751272i	$-0.270559\pi$
$463$	28.4027	1.31999	0.659993	+	0.751272i	$0.270559\pi$
$464$	−30.8629	−1.43278
$465$	−1.02769	−0.0476580
$466$	−70.0934	−3.24701
$467$	3.46082	0.160148	0.0800738	−	0.996789i	$-0.474484\pi$
$467$	3.46082	0.160148	0.0800738	+	0.996789i	$0.474484\pi$
$468$	−24.0347	−1.11101
$469$	47.9551	2.21436
$470$	−2.31906	−0.106970
$471$	−1.55446	−0.0716259
$472$	−21.0180	−0.967431
$473$	1.25114	0.0575273
$474$	−4.85866	−0.223166
$475$	1.10621	0.0507565
$476$	16.5336	0.757817
$477$	7.59294	0.347657
$478$	9.60694	0.439411
$479$	−29.6044	−1.35266	−0.676329	−	0.736600i	$-0.736430\pi$
$479$	−29.6044	−1.35266	−0.676329	+	0.736600i	$0.736430\pi$
$480$	0.399288	0.0182249
$481$	5.24514	0.239158
$482$	30.0537	1.36891
$483$	11.5524	0.525655
$484$	−46.7344	−2.12429
$485$	−0.291854	−0.0132524
$486$	34.8546	1.58103
$487$	7.94844	0.360178	0.180089	−	0.983650i	$-0.442361\pi$
$487$	7.94844	0.360178	0.180089	+	0.983650i	$0.442361\pi$
$488$	44.6955	2.02327
$489$	7.77078	0.351407
$490$	−1.04132	−0.0470422
$491$	0.776247	0.0350315	0.0175158	−	0.999847i	$-0.494424\pi$
$491$	0.776247	0.0350315	0.0175158	+	0.999847i	$0.494424\pi$
$492$	−5.12381	−0.230999
$493$	6.26236	0.282043
$494$	1.18213	0.0531867
$495$	0.221697	0.00996453
$496$	58.4807	2.62586
$497$	32.9436	1.47772
$498$	−15.1078	−0.676995
$499$	8.32713	0.372773	0.186387	−	0.982476i	$-0.440322\pi$
$499$	8.32713	0.372773	0.186387	+	0.982476i	$0.440322\pi$
$500$	−7.64516	−0.341902
$501$	10.9678	0.490007
$502$	−52.4988	−2.34314
$503$	17.1212	0.763397	0.381698	−	0.924287i	$-0.375339\pi$
$503$	17.1212	0.763397	0.381698	+	0.924287i	$0.375339\pi$
$504$	−47.2625	−2.10524
$505$	−0.486077	−0.0216301
$506$	7.43755	0.330640
$507$	5.22479	0.232041
$508$	12.5735	0.557858
$509$	13.1186	0.581473	0.290736	−	0.956803i	$-0.406100\pi$
$509$	13.1186	0.581473	0.290736	+	0.956803i	$0.406100\pi$
$510$	−0.339048	−0.0150133
$511$	11.1741	0.494312
$512$	49.6416	2.19387
$513$	−0.765332	−0.0337903
$514$	−27.2751	−1.20305
$515$	−1.13604	−0.0500601
$516$	6.94561	0.305763
$517$	−2.48797	−0.109421
$518$	19.1354	0.840761
$519$	−3.22575	−0.141595
$520$	−2.19492	−0.0962534
$521$	29.7063	1.30145	0.650727	−	0.759311i	$-0.274464\pi$
$521$	29.7063	1.30145	0.650727	+	0.759311i	$0.274464\pi$
$522$	−33.2116	−1.45363
$523$	2.66144	0.116377	0.0581883	−	0.998306i	$-0.481468\pi$
$523$	2.66144	0.116377	0.0581883	+	0.998306i	$0.481468\pi$
$524$	77.2189	3.37332
$525$	−9.27723	−0.404891
$526$	−21.1293	−0.921282
$527$	−11.8663	−0.516903
$528$	1.79264	0.0780147
$529$	15.2830	0.664480
$530$	1.28645	0.0558797
$531$	−9.37737	−0.406943
$532$	2.95189	0.127981
$533$	4.07695	0.176592
$534$	−27.6431	−1.19623
$535$	0.0127311	0.000550411 0
$536$	92.3833	3.99035
$537$	−1.94328	−0.0838588
$538$	35.2229	1.51856
$539$	−1.11717	−0.0481200
$540$	2.63636	0.113451
$541$	31.8091	1.36758	0.683790	−	0.729679i	$-0.260330\pi$
$541$	31.8091	1.36758	0.683790	+	0.729679i	$0.260330\pi$
$542$	−11.6802	−0.501709
$543$	−7.14708	−0.306711
$544$	4.61039	0.197669
$545$	−0.393237	−0.0168444
$546$	−9.91393	−0.424277
$547$	14.7285	0.629747	0.314873	−	0.949134i	$-0.398038\pi$
$547$	14.7285	0.629747	0.314873	+	0.949134i	$0.398038\pi$
$548$	−18.5202	−0.791144
$549$	19.9413	0.851074
$550$	−5.97275	−0.254679
$551$	1.11807	0.0476315
$552$	22.2553	0.947247
$553$	9.65366	0.410515
$554$	39.2094	1.66585
$555$	−0.268586	−0.0114008
$556$	72.9455	3.09358
$557$	44.9500	1.90459	0.952297	−	0.305172i	$-0.0987141\pi$
$557$	44.9500	1.90459	0.952297	+	0.305172i	$0.0987141\pi$
$558$	62.9312	2.66409
$559$	−5.52653	−0.233747
$560$	−3.31998	−0.140295
$561$	−0.363743	−0.0153572
$562$	−70.6307	−2.97938
$563$	8.30505	0.350016	0.175008	−	0.984567i	$-0.444005\pi$
$563$	8.30505	0.350016	0.175008	+	0.984567i	$0.444005\pi$
$564$	−13.8118	−0.581583
$565$	2.87626	0.121005
$566$	8.11883	0.341260
$567$	−17.6645	−0.741839
$568$	63.4643	2.66290
$569$	−25.0832	−1.05154	−0.525772	−	0.850626i	$-0.676223\pi$
$569$	−25.0832	−1.05154	−0.525772	+	0.850626i	$0.676223\pi$
$570$	−0.0605331	−0.00253545
$571$	−25.8100	−1.08011	−0.540057	−	0.841628i	$-0.681597\pi$
$571$	−25.8100	−1.08011	−0.540057	+	0.841628i	$0.681597\pi$
$572$	−4.36873	−0.182666
$573$	9.08949	0.379719
$574$	14.8736	0.620812
$575$	−30.7433	−1.28208
$576$	7.83487	0.326453
$577$	−12.2635	−0.510537	−0.255268	−	0.966870i	$-0.582164\pi$
$577$	−12.2635	−0.510537	−0.255268	+	0.966870i	$0.582164\pi$
$578$	38.8850	1.61740
$579$	−7.21073	−0.299668
$580$	−3.85145	−0.159923
$581$	30.0176	1.24534
$582$	−2.53952	−0.105267
$583$	1.38015	0.0571599
$584$	21.5264	0.890767
$585$	−0.979282	−0.0404883
$586$	82.0282	3.38855
$587$	−24.7181	−1.02023	−0.510113	−	0.860107i	$-0.670396\pi$
$587$	−24.7181	−1.02023	−0.510113	+	0.860107i	$0.670396\pi$
$588$	−6.20191	−0.255763
$589$	−2.11859	−0.0872948
$590$	−1.58878	−0.0654089
$591$	−15.2712	−0.628172
$592$	15.2839	0.628163
$593$	35.4218	1.45460	0.727299	−	0.686321i	$-0.240775\pi$
$593$	35.4218	1.45460	0.727299	+	0.686321i	$0.240775\pi$
$594$	4.13224	0.169548
$595$	0.673653	0.0276171
$596$	32.9082	1.34797
$597$	15.6981	0.642482
$598$	−32.8533	−1.34347
$599$	30.8890	1.26209	0.631045	−	0.775746i	$-0.282626\pi$
$599$	30.8890	1.26209	0.631045	+	0.775746i	$0.282626\pi$
$600$	−17.8722	−0.729628
$601$	−44.6254	−1.82031	−0.910154	−	0.414270i	$-0.864037\pi$
$601$	−44.6254	−1.82031	−0.910154	+	0.414270i	$0.864037\pi$
$602$	−20.1620	−0.821741
$603$	41.2177	1.67851
$604$	77.8332	3.16699
$605$	−1.90417	−0.0774154
$606$	−4.22953	−0.171813
$607$	−17.7420	−0.720126	−0.360063	−	0.932928i	$-0.617245\pi$
$607$	−17.7420	−0.720126	−0.360063	+	0.932928i	$0.617245\pi$
$608$	0.823132	0.0333824
$609$	−9.37669	−0.379963
$610$	3.37859	0.136795
$611$	10.9899	0.444604
$612$	14.2107	0.574435
$613$	17.5552	0.709049	0.354524	−	0.935047i	$-0.384643\pi$
$613$	17.5552	0.709049	0.354524	+	0.935047i	$0.384643\pi$
$614$	−24.6016	−0.992839
$615$	−0.208767	−0.00841830
$616$	−8.59077	−0.346132
$617$	−20.3795	−0.820449	−0.410225	−	0.911985i	$-0.634550\pi$
$617$	−20.3795	−0.820449	−0.410225	+	0.911985i	$0.634550\pi$
$618$	−9.88513	−0.397638
$619$	−26.3845	−1.06048	−0.530241	−	0.847847i	$-0.677899\pi$
$619$	−26.3845	−1.06048	−0.530241	+	0.847847i	$0.677899\pi$
$620$	7.29794	0.293092
$621$	21.2697	0.853524
$622$	48.8662	1.95936
$623$	54.9240	2.20048
$624$	−7.91848	−0.316993
$625$	24.5323	0.981291
$626$	−68.1058	−2.72206
$627$	−0.0649422	−0.00259354
$628$	11.0387	0.440492
$629$	−3.10123	−0.123654
$630$	−3.57263	−0.142337
$631$	−2.93189	−0.116717	−0.0583583	−	0.998296i	$-0.518587\pi$
$631$	−2.93189	−0.116717	−0.0583583	+	0.998296i	$0.518587\pi$
$632$	18.5973	0.739762
$633$	−1.81190	−0.0720168
$634$	−44.0064	−1.74772
$635$	0.512300	0.0203300
$636$	7.66181	0.303811
$637$	4.93478	0.195523
$638$	−6.03678	−0.238999
$639$	28.3152	1.12013
$640$	2.63455	0.104140
$641$	42.5123	1.67914	0.839568	−	0.543254i	$-0.182808\pi$
$641$	42.5123	1.67914	0.839568	+	0.543254i	$0.182808\pi$
$642$	0.110777	0.00437204
$643$	−11.3905	−0.449197	−0.224598	−	0.974451i	$-0.572107\pi$
$643$	−11.3905	−0.449197	−0.224598	+	0.974451i	$0.572107\pi$
$644$	−82.0373	−3.23272
$645$	0.282995	0.0111429
$646$	−0.698947	−0.0274997
$647$	−20.0268	−0.787336	−0.393668	−	0.919253i	$-0.628794\pi$
$647$	−20.0268	−0.787336	−0.393668	+	0.919253i	$0.628794\pi$
$648$	−34.0298	−1.33682
$649$	−1.70450	−0.0669074
$650$	26.3829	1.03482
$651$	17.7675	0.696362
$652$	−55.1826	−2.16112
$653$	27.8257	1.08890	0.544452	−	0.838792i	$-0.316738\pi$
$653$	27.8257	1.08890	0.544452	+	0.838792i	$0.316738\pi$
$654$	−3.42170	−0.133799
$655$	3.14624	0.122934
$656$	11.8799	0.463831
$657$	9.60418	0.374695
$658$	40.0935	1.56301
$659$	−7.29751	−0.284270	−0.142135	−	0.989847i	$-0.545397\pi$
$659$	−7.29751	−0.284270	−0.142135	+	0.989847i	$0.545397\pi$
$660$	0.223708	0.00870781
$661$	18.1236	0.704926	0.352463	−	0.935826i	$-0.385344\pi$
$661$	18.1236	0.704926	0.352463	+	0.935826i	$0.385344\pi$
$662$	54.9960	2.13748
$663$	1.60673	0.0624002
$664$	57.8275	2.24414
$665$	0.120273	0.00466399
$666$	16.4470	0.637308
$667$	−31.0729	−1.20315
$668$	−77.8859	−3.01349
$669$	6.40387	0.247588
$670$	6.98337	0.269791
$671$	3.62467	0.139929
$672$	−6.90317	−0.266296
$673$	26.0321	1.00346	0.501732	−	0.865023i	$-0.332696\pi$
$673$	26.0321	1.00346	0.501732	+	0.865023i	$0.332696\pi$
$674$	−55.7993	−2.14931
$675$	−17.0807	−0.657437
$676$	−37.1028	−1.42703
$677$	−3.19335	−0.122730	−0.0613652	−	0.998115i	$-0.519545\pi$
$677$	−3.19335	−0.122730	−0.0613652	+	0.998115i	$0.519545\pi$
$678$	25.0274	0.961170
$679$	5.04577	0.193639
$680$	1.29776	0.0497669
$681$	−11.4957	−0.440516
$682$	11.4388	0.438015
$683$	29.1000	1.11348	0.556741	−	0.830686i	$-0.312052\pi$
$683$	29.1000	1.11348	0.556741	+	0.830686i	$0.312052\pi$
$684$	2.53716	0.0970109
$685$	−0.754596	−0.0288316
$686$	−35.8561	−1.36899
$687$	6.91999	0.264014
$688$	−16.1038	−0.613952
$689$	−6.09641	−0.232255
$690$	1.68230	0.0640442
$691$	7.06910	0.268921	0.134461	−	0.990919i	$-0.457070\pi$
$691$	7.06910	0.268921	0.134461	+	0.990919i	$0.457070\pi$
$692$	22.9070	0.870794
$693$	−3.83285	−0.145598
$694$	−77.1350	−2.92800
$695$	2.97213	0.112739
$696$	−18.0638	−0.684705
$697$	−2.41053	−0.0913055
$698$	−72.2192	−2.73354
$699$	−17.0093	−0.643349
$700$	65.8803	2.49004
$701$	29.3587	1.10886	0.554431	−	0.832229i	$-0.312936\pi$
$701$	29.3587	1.10886	0.554431	+	0.832229i	$0.312936\pi$
$702$	−18.2530	−0.688914
$703$	−0.553690	−0.0208828
$704$	1.42412	0.0536736
$705$	−0.562756	−0.0211946
$706$	−52.8302	−1.98829
$707$	8.40364	0.316051
$708$	−9.46243	−0.355620
$709$	36.9475	1.38759	0.693796	−	0.720171i	$-0.255937\pi$
$709$	36.9475	1.38759	0.693796	+	0.720171i	$0.255937\pi$
$710$	4.79735	0.180041
$711$	8.29737	0.311176
$712$	105.809	3.96535
$713$	58.8786	2.20502
$714$	5.86170	0.219369
$715$	−0.178001	−0.00665687
$716$	13.7998	0.515723
$717$	2.33127	0.0870630
$718$	45.0240	1.68028
$719$	−37.7682	−1.40851	−0.704257	−	0.709945i	$-0.748720\pi$
$719$	−37.7682	−1.40851	−0.704257	+	0.709945i	$0.748720\pi$
$720$	−2.85354	−0.106345
$721$	19.6407	0.731460
$722$	47.7103	1.77559
$723$	7.29300	0.271229
$724$	50.7535	1.88624
$725$	24.9532	0.926738
$726$	−16.5688	−0.614927
$727$	−26.6690	−0.989097	−0.494549	−	0.869150i	$-0.664667\pi$
$727$	−26.6690	−0.989097	−0.494549	+	0.869150i	$0.664667\pi$
$728$	37.9473	1.40642
$729$	−8.88214	−0.328968
$730$	1.62720	0.0602255
$731$	3.26761	0.120857
$732$	20.1222	0.743737
$733$	−39.9196	−1.47447	−0.737233	−	0.675639i	$-0.763868\pi$
$733$	−39.9196	−1.47447	−0.737233	+	0.675639i	$0.763868\pi$
$734$	−87.6243	−3.23427
$735$	−0.252694	−0.00932074
$736$	−22.8761	−0.843223
$737$	7.49202	0.275972
$738$	12.7839	0.470583
$739$	−26.5621	−0.977102	−0.488551	−	0.872535i	$-0.662474\pi$
$739$	−26.5621	−0.977102	−0.488551	+	0.872535i	$0.662474\pi$
$740$	1.90731	0.0701140
$741$	0.286863	0.0105382
$742$	−22.2410	−0.816493
$743$	8.18188	0.300164	0.150082	−	0.988674i	$-0.452046\pi$
$743$	8.18188	0.300164	0.150082	+	0.988674i	$0.452046\pi$
$744$	34.2282	1.25487
$745$	1.34083	0.0491241
$746$	−24.7924	−0.907715
$747$	25.8003	0.943982
$748$	2.58305	0.0944455
$749$	−0.220103	−0.00804241
$750$	−2.71045	−0.0989718
$751$	42.9890	1.56869	0.784345	−	0.620325i	$-0.212999\pi$
$751$	42.9890	1.56869	0.784345	+	0.620325i	$0.212999\pi$
$752$	32.0236	1.16778
$753$	−12.7396	−0.464259
$754$	26.6657	0.971109
$755$	3.17127	0.115414
$756$	−45.5792	−1.65770
$757$	−45.1172	−1.63981	−0.819906	−	0.572498i	$-0.805975\pi$
$757$	−45.1172	−1.63981	−0.819906	+	0.572498i	$0.805975\pi$
$758$	76.4098	2.77533
$759$	1.80484	0.0655115
$760$	0.231701	0.00840466
$761$	−27.0706	−0.981310	−0.490655	−	0.871354i	$-0.663242\pi$
$761$	−27.0706	−0.981310	−0.490655	+	0.871354i	$0.663242\pi$
$762$	4.45770	0.161486
$763$	6.79856	0.246125
$764$	−64.5471	−2.33523
$765$	0.579009	0.0209341
$766$	−49.4768	−1.78767
$767$	7.52913	0.271861
$768$	19.2796	0.695694
$769$	38.3379	1.38250	0.691251	−	0.722615i	$-0.257060\pi$
$769$	38.3379	1.38250	0.691251	+	0.722615i	$0.257060\pi$
$770$	−0.649387	−0.0234023
$771$	−6.61872	−0.238367
$772$	51.2055	1.84293
$773$	42.6980	1.53574	0.767869	−	0.640607i	$-0.221317\pi$
$773$	42.6980	1.53574	0.767869	+	0.640607i	$0.221317\pi$
$774$	−17.3293	−0.622890
$775$	−47.2826	−1.69844
$776$	9.72045	0.348944
$777$	4.64350	0.166585
$778$	46.9677	1.68387
$779$	−0.430373	−0.0154197
$780$	−0.988164	−0.0353820
$781$	5.14677	0.184166
$782$	19.4248	0.694628
$783$	−17.2638	−0.616959
$784$	14.3795	0.513554
$785$	0.449766	0.0160528
$786$	27.3766	0.976490
$787$	−19.5768	−0.697836	−0.348918	−	0.937153i	$-0.613451\pi$
$787$	−19.5768	−0.697836	−0.348918	+	0.937153i	$0.613451\pi$
$788$	108.445	3.86319
$789$	−5.12736	−0.182539
$790$	1.40580	0.0500160
$791$	−49.7268	−1.76808
$792$	−7.38382	−0.262372
$793$	−16.0110	−0.568566
$794$	44.7886	1.58949
$795$	0.312176	0.0110718
$796$	−111.477	−3.95120
$797$	−23.7971	−0.842936	−0.421468	−	0.906843i	$-0.638485\pi$
$797$	−23.7971	−0.842936	−0.421468	+	0.906843i	$0.638485\pi$
$798$	1.04654	0.0370471
$799$	−6.49788	−0.229878
$800$	18.3707	0.649502
$801$	47.2075	1.66800
$802$	63.7897	2.25249
$803$	1.74573	0.0616053
$804$	41.5915	1.46682
$805$	−3.34257	−0.117810
$806$	−50.5277	−1.77976
$807$	8.54737	0.300882
$808$	16.1892	0.569535
$809$	35.6869	1.25468	0.627341	−	0.778744i	$-0.284143\pi$
$809$	35.6869	1.25468	0.627341	+	0.778744i	$0.284143\pi$
$810$	−2.57236	−0.0903835
$811$	16.7169	0.587009	0.293504	−	0.955958i	$-0.405178\pi$
$811$	16.7169	0.587009	0.293504	+	0.955958i	$0.405178\pi$
$812$	66.5866	2.33673
$813$	−2.83439	−0.0994064
$814$	2.98952	0.104783
$815$	−2.24839	−0.0787575
$816$	4.68187	0.163898
$817$	0.583394	0.0204104
$818$	−35.9714	−1.25771
$819$	16.9305	0.591600
$820$	1.48252	0.0517717
$821$	−25.1902	−0.879143	−0.439571	−	0.898208i	$-0.644870\pi$
$821$	−25.1902	−0.879143	−0.439571	+	0.898208i	$0.644870\pi$
$822$	−6.56601	−0.229016
$823$	56.2753	1.96164	0.980818	−	0.194928i	$-0.0624472\pi$
$823$	56.2753	1.96164	0.980818	+	0.194928i	$0.0624472\pi$
$824$	37.8370	1.31811
$825$	−1.44938	−0.0504610
$826$	27.4679	0.955730
$827$	9.94051	0.345666	0.172833	−	0.984951i	$-0.444708\pi$
$827$	9.94051	0.345666	0.172833	+	0.984951i	$0.444708\pi$
$828$	−70.5115	−2.45045
$829$	11.8848	0.412775	0.206387	−	0.978470i	$-0.433829\pi$
$829$	11.8848	0.412775	0.206387	+	0.978470i	$0.433829\pi$
$830$	4.37125	0.151728
$831$	9.51478	0.330064
$832$	−6.29065	−0.218089
$833$	−2.91773	−0.101093
$834$	25.8615	0.895512
$835$	−3.17342	−0.109821
$836$	0.461173	0.0159500
$837$	32.7124	1.13071
$838$	−83.9681	−2.90063
$839$	−13.3753	−0.461768	−0.230884	−	0.972981i	$-0.574162\pi$
$839$	−13.3753	−0.461768	−0.230884	+	0.972981i	$0.574162\pi$
$840$	−1.94315	−0.0670451
$841$	−3.77930	−0.130321
$842$	83.3773	2.87337
$843$	−17.1396	−0.590321
$844$	12.8669	0.442896
$845$	−1.51173	−0.0520052
$846$	34.4606	1.18478
$847$	32.9206	1.13116
$848$	−17.7644	−0.610032
$849$	1.97016	0.0676158
$850$	−15.5991	−0.535045
$851$	15.3879	0.527489
$852$	28.5720	0.978861
$853$	15.2822	0.523254	0.261627	−	0.965169i	$-0.415741\pi$
$853$	15.2822	0.523254	0.261627	+	0.965169i	$0.415741\pi$
$854$	−58.4114	−1.99880
$855$	0.103375	0.00353536
$856$	−0.424019	−0.0144927
$857$	25.4349	0.868839	0.434420	−	0.900711i	$-0.356954\pi$
$857$	25.4349	0.868839	0.434420	+	0.900711i	$0.356954\pi$
$858$	−1.54885	−0.0528770
$859$	−8.61083	−0.293798	−0.146899	−	0.989152i	$-0.546929\pi$
$859$	−8.61083	−0.293798	−0.146899	+	0.989152i	$0.546929\pi$
$860$	−2.00963	−0.0685278
$861$	3.60931	0.123005
$862$	75.5779	2.57419
$863$	28.3484	0.964991	0.482495	−	0.875899i	$-0.339731\pi$
$863$	28.3484	0.964991	0.482495	+	0.875899i	$0.339731\pi$
$864$	−12.7097	−0.432394
$865$	0.933334	0.0317343
$866$	−19.9098	−0.676562
$867$	9.43605	0.320465
$868$	−126.172	−4.28255
$869$	1.50819	0.0511619
$870$	−1.36546	−0.0462935
$871$	−33.0938	−1.12134
$872$	13.0971	0.443525
$873$	4.33687	0.146781
$874$	3.46807	0.117309
$875$	5.38540	0.182060
$876$	9.69129	0.327438
$877$	18.6939	0.631248	0.315624	−	0.948884i	$-0.397786\pi$
$877$	18.6939	0.631248	0.315624	+	0.948884i	$0.397786\pi$
$878$	44.3853	1.49793
$879$	19.9054	0.671393
$880$	−0.518680	−0.0174847
$881$	20.8840	0.703600	0.351800	−	0.936075i	$-0.385570\pi$
$881$	20.8840	0.703600	0.351800	+	0.936075i	$0.385570\pi$
$882$	15.4738	0.521030
$883$	−42.2999	−1.42350	−0.711752	−	0.702431i	$-0.752098\pi$
$883$	−42.2999	−1.42350	−0.711752	+	0.702431i	$0.752098\pi$
$884$	−11.4099	−0.383755
$885$	−0.385541	−0.0129598
$886$	31.4239	1.05571
$887$	−30.7519	−1.03255	−0.516273	−	0.856424i	$-0.672681\pi$
$887$	−30.7519	−1.03255	−0.516273	+	0.856424i	$0.672681\pi$
$888$	8.94550	0.300191
$889$	−8.85700	−0.297054
$890$	7.99821	0.268101
$891$	−2.75972	−0.0924542
$892$	−45.4757	−1.52264
$893$	−1.16012	−0.0388220
$894$	11.6670	0.390204
$895$	0.562266	0.0187945
$896$	−45.5480	−1.52165
$897$	−7.97235	−0.266189
$898$	−92.1067	−3.07364
$899$	−47.7896	−1.59387
$900$	56.6245	1.88748
$901$	3.60455	0.120085
$902$	2.32370	0.0773708
$903$	−4.89262	−0.162816
$904$	−95.7965	−3.18614
$905$	2.06793	0.0687402
$906$	27.5944	0.916762
$907$	−12.1538	−0.403562	−0.201781	−	0.979431i	$-0.564673\pi$
$907$	−12.1538	−0.403562	−0.201781	+	0.979431i	$0.564673\pi$
$908$	81.6343	2.70913
$909$	7.22298	0.239571
$910$	2.86848	0.0950892
$911$	17.3699	0.575490	0.287745	−	0.957707i	$-0.407095\pi$
$911$	17.3699	0.575490	0.287745	+	0.957707i	$0.407095\pi$
$912$	0.835894	0.0276792
$913$	4.68964	0.155205
$914$	−21.5968	−0.714359
$915$	0.819867	0.0271040
$916$	−49.1408	−1.62366
$917$	−54.3944	−1.79626
$918$	10.7922	0.356197
$919$	−20.2934	−0.669419	−0.334710	−	0.942321i	$-0.608638\pi$
$919$	−20.2934	−0.669419	−0.334710	+	0.942321i	$0.608638\pi$
$920$	−6.43930	−0.212297
$921$	−5.96996	−0.196717
$922$	−92.0197	−3.03051
$923$	−22.7344	−0.748312
$924$	−3.86762	−0.127235
$925$	−12.3573	−0.406304
$926$	−71.5077	−2.34989
$927$	16.8813	0.554456
$928$	18.5676	0.609512
$929$	54.3304	1.78252	0.891261	−	0.453490i	$-0.149821\pi$
$929$	54.3304	1.78252	0.891261	+	0.453490i	$0.149821\pi$
$930$	2.58735	0.0848426
$931$	−0.520928	−0.0170727
$932$	120.788	3.95653
$933$	11.8582	0.388218
$934$	−8.71308	−0.285101
$935$	0.105245	0.00344187
$936$	32.6159	1.06608
$937$	23.1490	0.756243	0.378122	−	0.925756i	$-0.376570\pi$
$937$	23.1490	0.756243	0.378122	+	0.925756i	$0.376570\pi$
$938$	−120.733	−3.94209
$939$	−16.5269	−0.539336
$940$	3.99629	0.130345
$941$	−0.993515	−0.0323877	−0.0161938	−	0.999869i	$-0.505155\pi$
$941$	−0.993515	−0.0323877	−0.0161938	+	0.999869i	$0.505155\pi$
$942$	3.91357	0.127511
$943$	11.9607	0.389494
$944$	21.9392	0.714061
$945$	−1.85710	−0.0604115
$946$	−3.14990	−0.102412
$947$	31.1490	1.01221	0.506103	−	0.862473i	$-0.331086\pi$
$947$	31.1490	1.01221	0.506103	+	0.862473i	$0.331086\pi$
$948$	8.37263	0.271930
$949$	−7.71124	−0.250317
$950$	−2.78504	−0.0903587
$951$	−10.6788	−0.346285
$952$	−22.4366	−0.727176
$953$	−1.49833	−0.0485358	−0.0242679	−	0.999705i	$-0.507725\pi$
$953$	−1.49833	−0.0485358	−0.0242679	+	0.999705i	$0.507725\pi$
$954$	−19.1163	−0.618912
$955$	−2.62994	−0.0851028
$956$	−16.5551	−0.535429
$957$	−1.46492	−0.0473541
$958$	74.5330	2.40805
$959$	13.0460	0.421277
$960$	0.322123	0.0103965
$961$	59.5542	1.92110
$962$	−13.2054	−0.425758
$963$	−0.189180	−0.00609625
$964$	−51.7897	−1.66803
$965$	2.08634	0.0671617
$966$	−29.0849	−0.935790
$967$	36.2681	1.16630	0.583151	−	0.812364i	$-0.301820\pi$
$967$	36.2681	1.16630	0.583151	+	0.812364i	$0.301820\pi$
$968$	63.4200	2.03840
$969$	−0.169610	−0.00544867
$970$	0.734781	0.0235924
$971$	−45.5074	−1.46040	−0.730201	−	0.683232i	$-0.760574\pi$
$971$	−45.5074	−1.46040	−0.730201	+	0.683232i	$0.760574\pi$
$972$	−60.0628	−1.92651
$973$	−51.3842	−1.64730
$974$	−20.0113	−0.641202
$975$	6.40222	0.205035
$976$	−46.6545	−1.49337
$977$	11.8164	0.378040	0.189020	−	0.981973i	$-0.439469\pi$
$977$	11.8164	0.378040	0.189020	+	0.981973i	$0.439469\pi$
$978$	−19.5640	−0.625588
$979$	8.58078	0.274243
$980$	1.79445	0.0573216
$981$	5.84340	0.186566
$982$	−1.95431	−0.0623644
$983$	−42.4026	−1.35243	−0.676216	−	0.736703i	$-0.736381\pi$
$983$	−42.4026	−1.35243	−0.676216	+	0.736703i	$0.736381\pi$
$984$	6.95318	0.221659
$985$	4.41853	0.140786
$986$	−15.7663	−0.502103
$987$	9.72932	0.309688
$988$	−2.03710	−0.0648088
$989$	−16.2134	−0.515555
$990$	−0.558152	−0.0177392
$991$	−2.93834	−0.0933396	−0.0466698	−	0.998910i	$-0.514861\pi$
$991$	−2.93834	−0.0933396	−0.0466698	+	0.998910i	$0.514861\pi$
$992$	−35.1830	−1.11706
$993$	13.3456	0.423511
$994$	−82.9399	−2.63069
$995$	−4.54207	−0.143993
$996$	26.0343	0.824928
$997$	−0.890048	−0.0281881	−0.0140940	−	0.999901i	$-0.504486\pi$
$997$	−0.890048	−0.0281881	−0.0140940	+	0.999901i	$0.504486\pi$
$998$	−20.9647	−0.663625
$999$	8.54936	0.270490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.13	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.13	✓	259	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.51764 q^{2} -0.610944 q^{3} +4.33849 q^{4} +0.176769 q^{5} +1.53813 q^{6} -3.05611 q^{7} -5.88747 q^{8} -2.62675 q^{9} +O(q^{10})\)	\(q-2.51764 q^{2} -0.610944 q^{3} +4.33849 q^{4} +0.176769 q^{5} +1.53813 q^{6} -3.05611 q^{7} -5.88747 q^{8} -2.62675 q^{9} -0.445041 q^{10} -0.477457 q^{11} -2.65057 q^{12} +2.10903 q^{13} +7.69418 q^{14} -0.107996 q^{15} +6.14552 q^{16} -1.24698 q^{17} +6.61319 q^{18} -0.222634 q^{19} +0.766912 q^{20} +1.86711 q^{21} +1.20206 q^{22} +6.18733 q^{23} +3.59691 q^{24} -4.96875 q^{25} -5.30976 q^{26} +3.43763 q^{27} -13.2589 q^{28} -5.02202 q^{29} +0.271895 q^{30} +9.51600 q^{31} -3.69724 q^{32} +0.291699 q^{33} +3.13944 q^{34} -0.540228 q^{35} -11.3961 q^{36} +2.48700 q^{37} +0.560511 q^{38} -1.28850 q^{39} -1.04072 q^{40} +1.93310 q^{41} -4.70071 q^{42} -2.62042 q^{43} -2.07144 q^{44} -0.464329 q^{45} -15.5774 q^{46} +5.21089 q^{47} -3.75457 q^{48} +2.33984 q^{49} +12.5095 q^{50} +0.761835 q^{51} +9.15000 q^{52} -2.89062 q^{53} -8.65469 q^{54} -0.0843997 q^{55} +17.9928 q^{56} +0.136017 q^{57} +12.6436 q^{58} +3.56995 q^{59} -0.468540 q^{60} -7.59163 q^{61} -23.9578 q^{62} +8.02764 q^{63} -2.98273 q^{64} +0.372812 q^{65} -0.734392 q^{66} -15.6915 q^{67} -5.41001 q^{68} -3.78011 q^{69} +1.36010 q^{70} -10.7796 q^{71} +15.4649 q^{72} -3.65630 q^{73} -6.26135 q^{74} +3.03563 q^{75} -0.965896 q^{76} +1.45916 q^{77} +3.24397 q^{78} -3.15880 q^{79} +1.08634 q^{80} +5.78005 q^{81} -4.86683 q^{82} -9.82213 q^{83} +8.10046 q^{84} -0.220428 q^{85} +6.59726 q^{86} +3.06817 q^{87} +2.81101 q^{88} -17.9718 q^{89} +1.16901 q^{90} -6.44543 q^{91} +26.8437 q^{92} -5.81374 q^{93} -13.1191 q^{94} -0.0393549 q^{95} +2.25881 q^{96} -1.65104 q^{97} -5.89086 q^{98} +1.25416 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

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