LMFDB - Embedded newform 6043.2.a.b.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.76265 q^{2} +1.82603 q^{3} +5.63224 q^{4} -3.05466 q^{5} -5.04467 q^{6} +4.94747 q^{7} -10.0346 q^{8} +0.334370 q^{9} +O(q^{10})$	\(q-2.76265 q^{2} +1.82603 q^{3} +5.63224 q^{4} -3.05466 q^{5} -5.04467 q^{6} +4.94747 q^{7} -10.0346 q^{8} +0.334370 q^{9} +8.43896 q^{10} -1.87612 q^{11} +10.2846 q^{12} -2.03886 q^{13} -13.6681 q^{14} -5.57789 q^{15} +16.4576 q^{16} +1.81744 q^{17} -0.923747 q^{18} +7.48249 q^{19} -17.2046 q^{20} +9.03421 q^{21} +5.18307 q^{22} +2.52811 q^{23} -18.3234 q^{24} +4.33096 q^{25} +5.63266 q^{26} -4.86751 q^{27} +27.8653 q^{28} +1.78616 q^{29} +15.4098 q^{30} -9.33875 q^{31} -25.3974 q^{32} -3.42585 q^{33} -5.02094 q^{34} -15.1129 q^{35} +1.88325 q^{36} -11.6546 q^{37} -20.6715 q^{38} -3.72302 q^{39} +30.6523 q^{40} -5.33311 q^{41} -24.9584 q^{42} +8.34593 q^{43} -10.5668 q^{44} -1.02139 q^{45} -6.98427 q^{46} -7.08890 q^{47} +30.0520 q^{48} +17.4775 q^{49} -11.9649 q^{50} +3.31868 q^{51} -11.4834 q^{52} -6.31941 q^{53} +13.4472 q^{54} +5.73092 q^{55} -49.6459 q^{56} +13.6632 q^{57} -4.93453 q^{58} +0.365127 q^{59} -31.4160 q^{60} -8.42183 q^{61} +25.7997 q^{62} +1.65429 q^{63} +37.2490 q^{64} +6.22803 q^{65} +9.46442 q^{66} -6.30411 q^{67} +10.2362 q^{68} +4.61639 q^{69} +41.7515 q^{70} +11.6511 q^{71} -3.35527 q^{72} -6.25574 q^{73} +32.1976 q^{74} +7.90844 q^{75} +42.1431 q^{76} -9.28207 q^{77} +10.2854 q^{78} -5.31828 q^{79} -50.2724 q^{80} -9.89131 q^{81} +14.7335 q^{82} -0.910604 q^{83} +50.8828 q^{84} -5.55165 q^{85} -23.0569 q^{86} +3.26157 q^{87} +18.8261 q^{88} -8.19459 q^{89} +2.82173 q^{90} -10.0872 q^{91} +14.2389 q^{92} -17.0528 q^{93} +19.5841 q^{94} -22.8565 q^{95} -46.3763 q^{96} -15.0315 q^{97} -48.2842 q^{98} -0.627319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76265	−1.95349	−0.976744	−	0.214407i	$-0.931218\pi$
$2$	−2.76265	−1.95349	−0.976744	+	0.214407i	$0.931218\pi$
$3$	1.82603	1.05426	0.527128	−	0.849786i	$-0.323269\pi$
$3$	1.82603	1.05426	0.527128	+	0.849786i	$0.323269\pi$
$4$	5.63224	2.81612
$5$	−3.05466	−1.36609	−0.683043	−	0.730378i	$-0.739344\pi$
$5$	−3.05466	−1.36609	−0.683043	+	0.730378i	$0.739344\pi$
$6$	−5.04467	−2.05948
$7$	4.94747	1.86997	0.934985	−	0.354688i	$-0.115413\pi$
$7$	4.94747	1.86997	0.934985	+	0.354688i	$0.115413\pi$
$8$	−10.0346	−3.54777
$9$	0.334370	0.111457
$10$	8.43896	2.66863
$11$	−1.87612	−0.565672	−0.282836	−	0.959168i	$-0.591275\pi$
$11$	−1.87612	−0.565672	−0.282836	+	0.959168i	$0.591275\pi$
$12$	10.2846	2.96891
$13$	−2.03886	−0.565479	−0.282739	−	0.959197i	$-0.591243\pi$
$13$	−2.03886	−0.565479	−0.282739	+	0.959197i	$0.591243\pi$
$14$	−13.6681	−3.65296
$15$	−5.57789	−1.44021
$16$	16.4576	4.11440
$17$	1.81744	0.440793	0.220396	−	0.975410i	$-0.429265\pi$
$17$	1.81744	0.440793	0.220396	+	0.975410i	$0.429265\pi$
$18$	−0.923747	−0.217729
$19$	7.48249	1.71660	0.858300	−	0.513147i	$-0.171521\pi$
$19$	7.48249	1.71660	0.858300	+	0.513147i	$0.171521\pi$
$20$	−17.2046	−3.84706
$21$	9.03421	1.97143
$22$	5.18307	1.10503
$23$	2.52811	0.527147	0.263573	−	0.964639i	$-0.415099\pi$
$23$	2.52811	0.527147	0.263573	+	0.964639i	$0.415099\pi$
$24$	−18.3234	−3.74025
$25$	4.33096	0.866191
$26$	5.63266	1.10466
$27$	−4.86751	−0.936753
$28$	27.8653	5.26605
$29$	1.78616	0.331681	0.165840	−	0.986153i	$-0.446966\pi$
$29$	1.78616	0.331681	0.165840	+	0.986153i	$0.446966\pi$
$30$	15.4098	2.81342
$31$	−9.33875	−1.67729	−0.838644	−	0.544680i	$-0.816651\pi$
$31$	−9.33875	−1.67729	−0.838644	+	0.544680i	$0.816651\pi$
$32$	−25.3974	−4.48967
$33$	−3.42585	−0.596364
$34$	−5.02094	−0.861084
$35$	−15.1129	−2.55454
$36$	1.88325	0.313875
$37$	−11.6546	−1.91600	−0.958002	−	0.286763i	$-0.907421\pi$
$37$	−11.6546	−1.91600	−0.958002	+	0.286763i	$0.907421\pi$
$38$	−20.6715	−3.35336
$39$	−3.72302	−0.596160
$40$	30.6523	4.84655
$41$	−5.33311	−0.832892	−0.416446	−	0.909160i	$-0.636725\pi$
$41$	−5.33311	−0.832892	−0.416446	+	0.909160i	$0.636725\pi$
$42$	−24.9584	−3.85116
$43$	8.34593	1.27274	0.636372	−	0.771383i	$-0.280435\pi$
$43$	8.34593	1.27274	0.636372	+	0.771383i	$0.280435\pi$
$44$	−10.5668	−1.59300
$45$	−1.02139	−0.152259
$46$	−6.98427	−1.02977
$47$	−7.08890	−1.03402	−0.517011	−	0.855979i	$-0.672955\pi$
$47$	−7.08890	−1.03402	−0.517011	+	0.855979i	$0.672955\pi$
$48$	30.0520	4.33763
$49$	17.4775	2.49678
$50$	−11.9649	−1.69209
$51$	3.31868	0.464709
$52$	−11.4834	−1.59245
$53$	−6.31941	−0.868038	−0.434019	−	0.900904i	$-0.642905\pi$
$53$	−6.31941	−0.868038	−0.434019	+	0.900904i	$0.642905\pi$
$54$	13.4472	1.82994
$55$	5.73092	0.772757
$56$	−49.6459	−6.63421
$57$	13.6632	1.80974
$58$	−4.93453	−0.647935
$59$	0.365127	0.0475355	0.0237677	−	0.999718i	$-0.492434\pi$
$59$	0.365127	0.0475355	0.0237677	+	0.999718i	$0.492434\pi$
$60$	−31.4160	−4.05579
$61$	−8.42183	−1.07831	−0.539153	−	0.842208i	$-0.681255\pi$
$61$	−8.42183	−1.07831	−0.539153	+	0.842208i	$0.681255\pi$
$62$	25.7997	3.27656
$63$	1.65429	0.208420
$64$	37.2490	4.65612
$65$	6.22803	0.772493
$66$	9.46442	1.16499
$67$	−6.30411	−0.770169	−0.385085	−	0.922881i	$-0.625828\pi$
$67$	−6.30411	−0.770169	−0.385085	+	0.922881i	$0.625828\pi$
$68$	10.2362	1.24132
$69$	4.61639	0.555748
$70$	41.7515	4.99026
$71$	11.6511	1.38273	0.691367	−	0.722504i	$-0.257009\pi$
$71$	11.6511	1.38273	0.691367	+	0.722504i	$0.257009\pi$
$72$	−3.35527	−0.395422
$73$	−6.25574	−0.732179	−0.366090	−	0.930580i	$-0.619304\pi$
$73$	−6.25574	−0.732179	−0.366090	+	0.930580i	$0.619304\pi$
$74$	32.1976	3.74289
$75$	7.90844	0.913188
$76$	42.1431	4.83415
$77$	−9.28207	−1.05779
$78$	10.2854	1.16459
$79$	−5.31828	−0.598353	−0.299176	−	0.954198i	$-0.596712\pi$
$79$	−5.31828	−0.598353	−0.299176	+	0.954198i	$0.596712\pi$
$80$	−50.2724	−5.62063
$81$	−9.89131	−1.09903
$82$	14.7335	1.62705
$83$	−0.910604	−0.0999518	−0.0499759	−	0.998750i	$-0.515914\pi$
$83$	−0.910604	−0.0999518	−0.0499759	+	0.998750i	$0.515914\pi$
$84$	50.8828	5.55177
$85$	−5.55165	−0.602161
$86$	−23.0569	−2.48629
$87$	3.26157	0.349677
$88$	18.8261	2.00687
$89$	−8.19459	−0.868625	−0.434312	−	0.900762i	$-0.643009\pi$
$89$	−8.19459	−0.868625	−0.434312	+	0.900762i	$0.643009\pi$
$90$	2.82173	0.297437
$91$	−10.0872	−1.05743
$92$	14.2389	1.48451
$93$	−17.0528	−1.76829
$94$	19.5841	2.01995
$95$	−22.8565	−2.34502
$96$	−46.3763	−4.73326
$97$	−15.0315	−1.52622	−0.763111	−	0.646268i	$-0.776329\pi$
$97$	−15.0315	−1.52622	−0.763111	+	0.646268i	$0.776329\pi$
$98$	−48.2842	−4.87744
$99$	−0.627319	−0.0630479
$100$	24.3930	2.43930
$101$	1.14251	0.113684	0.0568421	−	0.998383i	$-0.481897\pi$
$101$	1.14251	0.113684	0.0568421	+	0.998383i	$0.481897\pi$
$102$	−9.16836	−0.907803
$103$	15.0973	1.48759	0.743793	−	0.668410i	$-0.233025\pi$
$103$	15.0973	1.48759	0.743793	+	0.668410i	$0.233025\pi$
$104$	20.4592	2.00619
$105$	−27.5965	−2.69314
$106$	17.4583	1.69570
$107$	10.5402	1.01896	0.509481	−	0.860482i	$-0.329838\pi$
$107$	10.5402	1.01896	0.509481	+	0.860482i	$0.329838\pi$
$108$	−27.4150	−2.63801
$109$	8.06665	0.772645	0.386323	−	0.922364i	$-0.373745\pi$
$109$	8.06665	0.772645	0.386323	+	0.922364i	$0.373745\pi$
$110$	−15.8325	−1.50957
$111$	−21.2816	−2.01996
$112$	81.4236	7.69380
$113$	11.2401	1.05738	0.528689	−	0.848816i	$-0.322684\pi$
$113$	11.2401	1.05738	0.528689	+	0.848816i	$0.322684\pi$
$114$	−37.7467	−3.53530
$115$	−7.72251	−0.720128
$116$	10.0601	0.934053
$117$	−0.681734	−0.0630263
$118$	−1.00872	−0.0928600
$119$	8.99171	0.824269
$120$	55.9719	5.10951
$121$	−7.48016	−0.680015
$122$	23.2666	2.10646
$123$	−9.73840	−0.878082
$124$	−52.5980	−4.72344
$125$	2.04370	0.182794
$126$	−4.57021	−0.407147
$127$	−0.294295	−0.0261145	−0.0130572	−	0.999915i	$-0.504156\pi$
$127$	−0.294295	−0.0261145	−0.0130572	+	0.999915i	$0.504156\pi$
$128$	−52.1110	−4.60601
$129$	15.2399	1.34180
$130$	−17.2059	−1.50906
$131$	6.52342	0.569954	0.284977	−	0.958534i	$-0.408014\pi$
$131$	6.52342	0.569954	0.284977	+	0.958534i	$0.408014\pi$
$132$	−19.2952	−1.67943
$133$	37.0194	3.20999
$134$	17.4160	1.50452
$135$	14.8686	1.27968
$136$	−18.2372	−1.56383
$137$	5.13961	0.439106	0.219553	−	0.975601i	$-0.429540\pi$
$137$	5.13961	0.439106	0.219553	+	0.975601i	$0.429540\pi$
$138$	−12.7535	−1.08565
$139$	−11.5357	−0.978444	−0.489222	−	0.872159i	$-0.662719\pi$
$139$	−11.5357	−0.978444	−0.489222	+	0.872159i	$0.662719\pi$
$140$	−85.1192	−7.19388
$141$	−12.9445	−1.09012
$142$	−32.1880	−2.70115
$143$	3.82516	0.319876
$144$	5.50293	0.458577
$145$	−5.45610	−0.453105
$146$	17.2824	1.43030
$147$	31.9143	2.63225
$148$	−65.6414	−5.39569
$149$	9.51536	0.779529	0.389764	−	0.920915i	$-0.372556\pi$
$149$	9.51536	0.779529	0.389764	+	0.920915i	$0.372556\pi$
$150$	−21.8482	−1.78390
$151$	0.794585	0.0646624	0.0323312	−	0.999477i	$-0.489707\pi$
$151$	0.794585	0.0646624	0.0323312	+	0.999477i	$0.489707\pi$
$152$	−75.0838	−6.09010
$153$	0.607696	0.0491293
$154$	25.6431	2.06638
$155$	28.5267	2.29132
$156$	−20.9689	−1.67886
$157$	−21.7059	−1.73232	−0.866159	−	0.499768i	$-0.833418\pi$
$157$	−21.7059	−1.73232	−0.866159	+	0.499768i	$0.833418\pi$
$158$	14.6925	1.16888
$159$	−11.5394	−0.915135
$160$	77.5805	6.13328
$161$	12.5077	0.985748
$162$	27.3262	2.14695
$163$	−7.42806	−0.581811	−0.290905	−	0.956752i	$-0.593956\pi$
$163$	−7.42806	−0.581811	−0.290905	+	0.956752i	$0.593956\pi$
$164$	−30.0373	−2.34552
$165$	10.4648	0.814684
$166$	2.51568	0.195255
$167$	−2.41267	−0.186698	−0.0933489	−	0.995633i	$-0.529757\pi$
$167$	−2.41267	−0.186698	−0.0933489	+	0.995633i	$0.529757\pi$
$168$	−90.6547	−6.99416
$169$	−8.84304	−0.680234
$170$	15.3373	1.17631
$171$	2.50192	0.191327
$172$	47.0063	3.58419
$173$	−16.4595	−1.25139	−0.625696	−	0.780067i	$-0.715185\pi$
$173$	−16.4595	−1.25139	−0.625696	+	0.780067i	$0.715185\pi$
$174$	−9.01057	−0.683090
$175$	21.4273	1.61975
$176$	−30.8765	−2.32740
$177$	0.666731	0.0501146
$178$	22.6388	1.69685
$179$	6.57100	0.491140	0.245570	−	0.969379i	$-0.421025\pi$
$179$	6.57100	0.491140	0.245570	+	0.969379i	$0.421025\pi$
$180$	−5.75269	−0.428780
$181$	−22.3114	−1.65839	−0.829195	−	0.558959i	$-0.811201\pi$
$181$	−22.3114	−1.65839	−0.829195	+	0.558959i	$0.811201\pi$
$182$	27.8675	2.06567
$183$	−15.3785	−1.13681
$184$	−25.3685	−1.87019
$185$	35.6008	2.61743
$186$	47.1109	3.45434
$187$	−3.40973	−0.249344
$188$	−39.9263	−2.91193
$189$	−24.0819	−1.75170
$190$	63.1444	4.58098
$191$	−9.14692	−0.661848	−0.330924	−	0.943657i	$-0.607360\pi$
$191$	−9.14692	−0.661848	−0.330924	+	0.943657i	$0.607360\pi$
$192$	68.0176	4.90874
$193$	14.5350	1.04625	0.523127	−	0.852255i	$-0.324765\pi$
$193$	14.5350	1.04625	0.523127	+	0.852255i	$0.324765\pi$
$194$	41.5269	2.98146
$195$	11.3726	0.814405
$196$	98.4373	7.03124
$197$	7.55912	0.538565	0.269283	−	0.963061i	$-0.413213\pi$
$197$	7.55912	0.538565	0.269283	+	0.963061i	$0.413213\pi$
$198$	1.73306	0.123163
$199$	−5.15972	−0.365763	−0.182881	−	0.983135i	$-0.558542\pi$
$199$	−5.15972	−0.365763	−0.182881	+	0.983135i	$0.558542\pi$
$200$	−43.4594	−3.07304
$201$	−11.5115	−0.811956
$202$	−3.15636	−0.222081
$203$	8.83696	0.620233
$204$	18.6916	1.30867
$205$	16.2909	1.13780
$206$	−41.7087	−2.90598
$207$	0.845322	0.0587540
$208$	−33.5548	−2.32661
$209$	−14.0381	−0.971034
$210$	76.2394	5.26102
$211$	27.6018	1.90019	0.950093	−	0.311966i	$-0.100987\pi$
$211$	27.6018	1.90019	0.950093	+	0.311966i	$0.100987\pi$
$212$	−35.5924	−2.44450
$213$	21.2752	1.45776
$214$	−29.1189	−1.99053
$215$	−25.4940	−1.73868
$216$	48.8435	3.32338
$217$	−46.2032	−3.13648
$218$	−22.2853	−1.50935
$219$	−11.4231	−0.771905
$220$	32.2779	2.17617
$221$	−3.70550	−0.249259
$222$	58.7936	3.94597
$223$	−17.6489	−1.18186	−0.590930	−	0.806723i	$-0.701239\pi$
$223$	−17.6489	−1.18186	−0.590930	+	0.806723i	$0.701239\pi$
$224$	−125.653	−8.39555
$225$	1.44814	0.0965427
$226$	−31.0524	−2.06557
$227$	7.33648	0.486939	0.243470	−	0.969909i	$-0.421714\pi$
$227$	7.33648	0.486939	0.243470	+	0.969909i	$0.421714\pi$
$228$	76.9545	5.09643
$229$	−15.1006	−0.997877	−0.498939	−	0.866637i	$-0.666277\pi$
$229$	−15.1006	−0.997877	−0.498939	+	0.866637i	$0.666277\pi$
$230$	21.3346	1.40676
$231$	−16.9493	−1.11518
$232$	−17.9234	−1.17673
$233$	12.7924	0.838058	0.419029	−	0.907973i	$-0.362371\pi$
$233$	12.7924	0.838058	0.419029	+	0.907973i	$0.362371\pi$
$234$	1.88339	0.123121
$235$	21.6542	1.41256
$236$	2.05648	0.133865
$237$	−9.71131	−0.630817
$238$	−24.8410	−1.61020
$239$	−10.7988	−0.698518	−0.349259	−	0.937026i	$-0.613567\pi$
$239$	−10.7988	−0.698518	−0.349259	+	0.937026i	$0.613567\pi$
$240$	−91.7987	−5.92558
$241$	2.79069	0.179764	0.0898821	−	0.995952i	$-0.471351\pi$
$241$	2.79069	0.179764	0.0898821	+	0.995952i	$0.471351\pi$
$242$	20.6651	1.32840
$243$	−3.45925	−0.221911
$244$	−47.4337	−3.03663
$245$	−53.3878	−3.41082
$246$	26.9038	1.71532
$247$	−15.2558	−0.970701
$248$	93.7105	5.95063
$249$	−1.66279	−0.105375
$250$	−5.64603	−0.357086
$251$	−6.39270	−0.403504	−0.201752	−	0.979437i	$-0.564663\pi$
$251$	−6.39270	−0.403504	−0.201752	+	0.979437i	$0.564663\pi$
$252$	9.31733	0.586936
$253$	−4.74304	−0.298192
$254$	0.813035	0.0510144
$255$	−10.1375	−0.634832
$256$	69.4666	4.34166
$257$	−18.1908	−1.13471	−0.567356	−	0.823473i	$-0.692033\pi$
$257$	−18.1908	−1.13471	−0.567356	+	0.823473i	$0.692033\pi$
$258$	−42.1025	−2.62119
$259$	−57.6608	−3.58287
$260$	35.0778	2.17543
$261$	0.597237	0.0369680
$262$	−18.0219	−1.11340
$263$	8.97182	0.553226	0.276613	−	0.960981i	$-0.410788\pi$
$263$	8.97182	0.553226	0.276613	+	0.960981i	$0.410788\pi$
$264$	34.3770	2.11576
$265$	19.3037	1.18581
$266$	−102.272	−6.27068
$267$	−14.9635	−0.915753
$268$	−35.5062	−2.16889
$269$	−11.7045	−0.713637	−0.356818	−	0.934174i	$-0.616139\pi$
$269$	−11.7045	−0.713637	−0.356818	+	0.934174i	$0.616139\pi$
$270$	−41.0767	−2.49985
$271$	4.30094	0.261264	0.130632	−	0.991431i	$-0.458299\pi$
$271$	4.30094	0.261264	0.130632	+	0.991431i	$0.458299\pi$
$272$	29.9106	1.81360
$273$	−18.4195	−1.11480
$274$	−14.1989	−0.857789
$275$	−8.12541	−0.489980
$276$	26.0006	1.56505
$277$	3.61473	0.217188	0.108594	−	0.994086i	$-0.465365\pi$
$277$	3.61473	0.217188	0.108594	+	0.994086i	$0.465365\pi$
$278$	31.8691	1.91138
$279$	−3.12259	−0.186945
$280$	151.651	9.06290
$281$	10.2212	0.609744	0.304872	−	0.952393i	$-0.401386\pi$
$281$	10.2212	0.609744	0.304872	+	0.952393i	$0.401386\pi$
$282$	35.7612	2.12955
$283$	19.3836	1.15224	0.576118	−	0.817367i	$-0.304567\pi$
$283$	19.3836	1.15224	0.576118	+	0.817367i	$0.304567\pi$
$284$	65.6218	3.89394
$285$	−41.7365	−2.47226
$286$	−10.5676	−0.624873
$287$	−26.3854	−1.55748
$288$	−8.49213	−0.500403
$289$	−13.6969	−0.805702
$290$	15.0733	0.885135
$291$	−27.4480	−1.60903
$292$	−35.2338	−2.06190
$293$	−22.7532	−1.32926	−0.664629	−	0.747174i	$-0.731410\pi$
$293$	−22.7532	−1.32926	−0.664629	+	0.747174i	$0.731410\pi$
$294$	−88.1682	−5.14207
$295$	−1.11534	−0.0649375
$296$	116.949	6.79753
$297$	9.13204	0.529895
$298$	−26.2876	−1.52280
$299$	−5.15446	−0.298090
$300$	44.5422	2.57164
$301$	41.2913	2.37999
$302$	−2.19516	−0.126317
$303$	2.08626	0.119852
$304$	123.144	7.06279
$305$	25.7258	1.47306
$306$	−1.67885	−0.0959735
$307$	−25.9515	−1.48113	−0.740565	−	0.671985i	$-0.765442\pi$
$307$	−25.9515	−1.48113	−0.740565	+	0.671985i	$0.765442\pi$
$308$	−52.2788	−2.97886
$309$	27.5681	1.56830
$310$	−78.8093	−4.47607
$311$	−10.5706	−0.599401	−0.299701	−	0.954033i	$-0.596887\pi$
$311$	−10.5706	−0.599401	−0.299701	+	0.954033i	$0.596887\pi$
$312$	37.3590	2.11503
$313$	14.3664	0.812038	0.406019	−	0.913865i	$-0.366917\pi$
$313$	14.3664	0.812038	0.406019	+	0.913865i	$0.366917\pi$
$314$	59.9658	3.38406
$315$	−5.05328	−0.284720
$316$	−29.9538	−1.68503
$317$	−22.8109	−1.28119	−0.640594	−	0.767880i	$-0.721312\pi$
$317$	−22.8109	−1.28119	−0.640594	+	0.767880i	$0.721312\pi$
$318$	31.8793	1.78770
$319$	−3.35105	−0.187623
$320$	−113.783	−6.36066
$321$	19.2467	1.07425
$322$	−34.5545	−1.92565
$323$	13.5989	0.756665
$324$	−55.7102	−3.09501
$325$	−8.83022	−0.489813
$326$	20.5211	1.13656
$327$	14.7299	0.814566
$328$	53.5156	2.95491
$329$	−35.0721	−1.93359
$330$	−28.9106	−1.59148
$331$	16.5740	0.910991	0.455496	−	0.890238i	$-0.349462\pi$
$331$	16.5740	0.910991	0.455496	+	0.890238i	$0.349462\pi$
$332$	−5.12874	−0.281476
$333$	−3.89694	−0.213551
$334$	6.66536	0.364712
$335$	19.2569	1.05212
$336$	148.682	8.11124
$337$	6.25410	0.340683	0.170341	−	0.985385i	$-0.445513\pi$
$337$	6.25410	0.340683	0.170341	+	0.985385i	$0.445513\pi$
$338$	24.4302	1.32883
$339$	20.5247	1.11475
$340$	−31.2682	−1.69576
$341$	17.5206	0.948795
$342$	−6.91193	−0.373754
$343$	51.8371	2.79894
$344$	−83.7481	−4.51539
$345$	−14.1015	−0.759199
$346$	45.4718	2.44458
$347$	23.6172	1.26784	0.633919	−	0.773400i	$-0.281445\pi$
$347$	23.6172	1.26784	0.633919	+	0.773400i	$0.281445\pi$
$348$	18.3699	0.984731
$349$	−15.4070	−0.824716	−0.412358	−	0.911022i	$-0.635295\pi$
$349$	−15.4070	−0.824716	−0.412358	+	0.911022i	$0.635295\pi$
$350$	−59.1961	−3.16416
$351$	9.92418	0.529714
$352$	47.6487	2.53968
$353$	−10.1992	−0.542849	−0.271424	−	0.962460i	$-0.587495\pi$
$353$	−10.1992	−0.542849	−0.271424	+	0.962460i	$0.587495\pi$
$354$	−1.84194	−0.0978982
$355$	−35.5902	−1.88893
$356$	−46.1539	−2.44615
$357$	16.4191	0.868991
$358$	−18.1534	−0.959436
$359$	−0.0289095	−0.00152578	−0.000762892	−	1.00000i	$-0.500243\pi$
$359$	−0.0289095	−0.00152578	−0.000762892		1.00000i	$0.500243\pi$
$360$	10.2492	0.540180
$361$	36.9877	1.94672
$362$	61.6385	3.23965
$363$	−13.6590	−0.716910
$364$	−56.8136	−2.97784
$365$	19.1092	1.00022
$366$	42.4854	2.22075
$367$	−23.6590	−1.23499	−0.617495	−	0.786575i	$-0.711852\pi$
$367$	−23.6590	−1.23499	−0.617495	+	0.786575i	$0.711852\pi$
$368$	41.6066	2.16889
$369$	−1.78323	−0.0928313
$370$	−98.3527	−5.11311
$371$	−31.2651	−1.62320
$372$	−96.0453	−4.97972
$373$	21.1988	1.09763	0.548816	−	0.835943i	$-0.315079\pi$
$373$	21.1988	1.09763	0.548816	+	0.835943i	$0.315079\pi$
$374$	9.41990	0.487091
$375$	3.73185	0.192712
$376$	71.1342	3.66847
$377$	−3.64173	−0.187559
$378$	66.5298	3.42192
$379$	2.98818	0.153492	0.0767461	−	0.997051i	$-0.475547\pi$
$379$	2.98818	0.153492	0.0767461	+	0.997051i	$0.475547\pi$
$380$	−128.733	−6.60387
$381$	−0.537391	−0.0275314
$382$	25.2697	1.29291
$383$	−3.33822	−0.170575	−0.0852876	−	0.996356i	$-0.527181\pi$
$383$	−3.33822	−0.170575	−0.0852876	+	0.996356i	$0.527181\pi$
$384$	−95.1560	−4.85591
$385$	28.3536	1.44503
$386$	−40.1552	−2.04384
$387$	2.79063	0.141856
$388$	−84.6612	−4.29802
$389$	−6.68535	−0.338961	−0.169480	−	0.985534i	$-0.554209\pi$
$389$	−6.68535	−0.338961	−0.169480	+	0.985534i	$0.554209\pi$
$390$	−31.4184	−1.59093
$391$	4.59467	0.232362
$392$	−175.380	−8.85801
$393$	11.9119	0.600877
$394$	−20.8832	−1.05208
$395$	16.2455	0.817402
$396$	−3.53321	−0.177550
$397$	−22.1102	−1.10968	−0.554839	−	0.831958i	$-0.687220\pi$
$397$	−22.1102	−1.10968	−0.554839	+	0.831958i	$0.687220\pi$
$398$	14.2545	0.714513
$399$	67.5984	3.38415
$400$	71.2772	3.56386
$401$	8.23992	0.411482	0.205741	−	0.978606i	$-0.434040\pi$
$401$	8.23992	0.411482	0.205741	+	0.978606i	$0.434040\pi$
$402$	31.8021	1.58615
$403$	19.0404	0.948471
$404$	6.43490	0.320148
$405$	30.2146	1.50138
$406$	−24.4134	−1.21162
$407$	21.8654	1.08383
$408$	−33.3017	−1.64868
$409$	−7.39817	−0.365816	−0.182908	−	0.983130i	$-0.558551\pi$
$409$	−7.39817	−0.365816	−0.182908	+	0.983130i	$0.558551\pi$
$410$	−45.0059	−2.22268
$411$	9.38505	0.462931
$412$	85.0318	4.18922
$413$	1.80645	0.0888898
$414$	−2.33533	−0.114775
$415$	2.78159	0.136543
$416$	51.7818	2.53881
$417$	−21.0645	−1.03153
$418$	38.7823	1.89690
$419$	−20.0772	−0.980834	−0.490417	−	0.871488i	$-0.663156\pi$
$419$	−20.0772	−0.980834	−0.490417	+	0.871488i	$0.663156\pi$
$420$	−155.430	−7.58420
$421$	−4.88107	−0.237889	−0.118944	−	0.992901i	$-0.537951\pi$
$421$	−4.88107	−0.237889	−0.118944	+	0.992901i	$0.537951\pi$
$422$	−76.2541	−3.71199
$423$	−2.37031	−0.115249
$424$	63.4127	3.07959
$425$	7.87123	0.381811
$426$	−58.7760	−2.84771
$427$	−41.6668	−2.01640
$428$	59.3650	2.86951
$429$	6.98483	0.337231
$430$	70.4310	3.39649
$431$	−35.8615	−1.72739	−0.863695	−	0.504016i	$-0.831855\pi$
$431$	−35.8615	−1.72739	−0.863695	+	0.504016i	$0.831855\pi$
$432$	−80.1075	−3.85418
$433$	8.10578	0.389539	0.194769	−	0.980849i	$-0.437604\pi$
$433$	8.10578	0.389539	0.194769	+	0.980849i	$0.437604\pi$
$434$	127.643	6.12707
$435$	−9.96298	−0.477689
$436$	45.4333	2.17586
$437$	18.9165	0.904900
$438$	31.5582	1.50791
$439$	6.27874	0.299668	0.149834	−	0.988711i	$-0.452126\pi$
$439$	6.27874	0.299668	0.149834	+	0.988711i	$0.452126\pi$
$440$	−57.5075	−2.74156
$441$	5.84395	0.278283
$442$	10.2370	0.486925
$443$	−32.3306	−1.53607	−0.768037	−	0.640405i	$-0.778766\pi$
$443$	−32.3306	−1.53607	−0.768037	+	0.640405i	$0.778766\pi$
$444$	−119.863	−5.68844
$445$	25.0317	1.18662
$446$	48.7578	2.30875
$447$	17.3753	0.821823
$448$	184.288	8.70680
$449$	−28.3696	−1.33884	−0.669422	−	0.742882i	$-0.733458\pi$
$449$	−28.3696	−1.33884	−0.669422	+	0.742882i	$0.733458\pi$
$450$	−4.00071	−0.188595
$451$	10.0056	0.471144
$452$	63.3067	2.97770
$453$	1.45093	0.0681707
$454$	−20.2681	−0.951230
$455$	30.8130	1.44454
$456$	−137.105	−6.42052
$457$	24.3423	1.13869	0.569343	−	0.822100i	$-0.307198\pi$
$457$	24.3423	1.13869	0.569343	+	0.822100i	$0.307198\pi$
$458$	41.7177	1.94934
$459$	−8.84638	−0.412914
$460$	−43.4950	−2.02796
$461$	16.3350	0.760799	0.380399	−	0.924822i	$-0.375787\pi$
$461$	16.3350	0.760799	0.380399	+	0.924822i	$0.375787\pi$
$462$	46.8250	2.17849
$463$	32.1850	1.49576	0.747882	−	0.663832i	$-0.231071\pi$
$463$	32.1850	1.49576	0.747882	+	0.663832i	$0.231071\pi$
$464$	29.3959	1.36467
$465$	52.0905	2.41564
$466$	−35.3409	−1.63714
$467$	−41.9673	−1.94202	−0.971008	−	0.239048i	$-0.923165\pi$
$467$	−41.9673	−1.94202	−0.971008	+	0.239048i	$0.923165\pi$
$468$	−3.83969	−0.177490
$469$	−31.1894	−1.44019
$470$	−59.8229	−2.75943
$471$	−39.6355	−1.82631
$472$	−3.66390	−0.168645
$473$	−15.6580	−0.719955
$474$	26.8290	1.23229
$475$	32.4063	1.48690
$476$	50.6434	2.32124
$477$	−2.11302	−0.0967486
$478$	29.8334	1.36455
$479$	25.8715	1.18210	0.591049	−	0.806636i	$-0.298714\pi$
$479$	25.8715	1.18210	0.591049	+	0.806636i	$0.298714\pi$
$480$	141.664	6.46605
$481$	23.7621	1.08346
$482$	−7.70970	−0.351167
$483$	22.8394	1.03923
$484$	−42.1300	−1.91500
$485$	45.9163	2.08495
$486$	9.55670	0.433501
$487$	−9.05871	−0.410489	−0.205245	−	0.978711i	$-0.565799\pi$
$487$	−9.05871	−0.410489	−0.205245	+	0.978711i	$0.565799\pi$
$488$	84.5097	3.82557
$489$	−13.5638	−0.613378
$490$	147.492	6.66300
$491$	−21.2860	−0.960622	−0.480311	−	0.877098i	$-0.659476\pi$
$491$	−21.2860	−0.960622	−0.480311	+	0.877098i	$0.659476\pi$
$492$	−54.8490	−2.47278
$493$	3.24622	0.146203
$494$	42.1464	1.89625
$495$	1.91625	0.0861289
$496$	−153.693	−6.90104
$497$	57.6436	2.58567
$498$	4.59370	0.205849
$499$	41.1047	1.84010	0.920050	−	0.391801i	$-0.128148\pi$
$499$	41.1047	1.84010	0.920050	+	0.391801i	$0.128148\pi$
$500$	11.5106	0.514770
$501$	−4.40559	−0.196827
$502$	17.6608	0.788240
$503$	19.4727	0.868243	0.434122	−	0.900854i	$-0.357059\pi$
$503$	19.4727	0.868243	0.434122	+	0.900854i	$0.357059\pi$
$504$	−16.6001	−0.739427
$505$	−3.48999	−0.155303
$506$	13.1034	0.582515
$507$	−16.1476	−0.717141
$508$	−1.65754	−0.0735415
$509$	36.1895	1.60407	0.802036	−	0.597276i	$-0.203750\pi$
$509$	36.1895	1.60407	0.802036	+	0.597276i	$0.203750\pi$
$510$	28.0062	1.24014
$511$	−30.9501	−1.36915
$512$	−87.6898	−3.87538
$513$	−36.4211	−1.60803
$514$	50.2548	2.21665
$515$	−46.1173	−2.03217
$516$	85.8347	3.77866
$517$	13.2996	0.584918
$518$	159.297	6.99909
$519$	−30.0555	−1.31929
$520$	−62.4958	−2.74062
$521$	9.39578	0.411637	0.205818	−	0.978590i	$-0.434014\pi$
$521$	9.39578	0.411637	0.205818	+	0.978590i	$0.434014\pi$
$522$	−1.64996	−0.0722166
$523$	−34.2986	−1.49977	−0.749887	−	0.661565i	$-0.769892\pi$
$523$	−34.2986	−1.49977	−0.749887	+	0.661565i	$0.769892\pi$
$524$	36.7414	1.60506
$525$	39.1268	1.70763
$526$	−24.7860	−1.08072
$527$	−16.9726	−0.739337
$528$	−56.3813	−2.45368
$529$	−16.6087	−0.722117
$530$	−53.3293	−2.31648
$531$	0.122087	0.00529814
$532$	208.502	9.03971
$533$	10.8735	0.470983
$534$	41.3390	1.78891
$535$	−32.1968	−1.39199
$536$	63.2592	2.73238
$537$	11.9988	0.517787
$538$	32.3355	1.39408
$539$	−32.7899	−1.41236
$540$	83.7434	3.60374
$541$	−31.0218	−1.33373	−0.666866	−	0.745177i	$-0.732365\pi$
$541$	−31.0218	−1.33373	−0.666866	+	0.745177i	$0.732365\pi$
$542$	−11.8820	−0.510376
$543$	−40.7411	−1.74837
$544$	−46.1582	−1.97901
$545$	−24.6409	−1.05550
$546$	50.8867	2.17775
$547$	−2.02065	−0.0863967	−0.0431984	−	0.999067i	$-0.513755\pi$
$547$	−2.02065	−0.0863967	−0.0431984	+	0.999067i	$0.513755\pi$
$548$	28.9475	1.23657
$549$	−2.81601	−0.120184
$550$	22.4477	0.957171
$551$	13.3649	0.569364
$552$	−46.3236	−1.97166
$553$	−26.3120	−1.11890
$554$	−9.98624	−0.424275
$555$	65.0080	2.75944
$556$	−64.9717	−2.75541
$557$	−12.2901	−0.520748	−0.260374	−	0.965508i	$-0.583846\pi$
$557$	−12.2901	−0.520748	−0.260374	+	0.965508i	$0.583846\pi$
$558$	8.62664	0.365195
$559$	−17.0162	−0.719709
$560$	−248.721	−10.5104
$561$	−6.22626	−0.262873
$562$	−28.2375	−1.19113
$563$	−37.1349	−1.56505	−0.782525	−	0.622619i	$-0.786068\pi$
$563$	−37.1349	−1.56505	−0.782525	+	0.622619i	$0.786068\pi$
$564$	−72.9065	−3.06992
$565$	−34.3346	−1.44447
$566$	−53.5501	−2.25088
$567$	−48.9370	−2.05516
$568$	−116.914	−4.90561
$569$	12.1167	0.507960	0.253980	−	0.967210i	$-0.418260\pi$
$569$	12.1167	0.507960	0.253980	+	0.967210i	$0.418260\pi$
$570$	115.303	4.82953
$571$	−12.3746	−0.517860	−0.258930	−	0.965896i	$-0.583370\pi$
$571$	−12.3746	−0.517860	−0.258930	+	0.965896i	$0.583370\pi$
$572$	21.5442	0.900807
$573$	−16.7025	−0.697757
$574$	72.8937	3.04253
$575$	10.9491	0.456610
$576$	12.4549	0.518955
$577$	−42.9904	−1.78972	−0.894858	−	0.446351i	$-0.852723\pi$
$577$	−42.9904	−1.78972	−0.894858	+	0.446351i	$0.852723\pi$
$578$	37.8398	1.57393
$579$	26.5413	1.10302
$580$	−30.7301	−1.27600
$581$	−4.50519	−0.186907
$582$	75.8292	3.14322
$583$	11.8560	0.491025
$584$	62.7739	2.59760
$585$	2.08247	0.0860994
$586$	62.8592	2.59669
$587$	14.9019	0.615067	0.307534	−	0.951537i	$-0.400496\pi$
$587$	14.9019	0.615067	0.307534	+	0.951537i	$0.400496\pi$
$588$	179.749	7.41273
$589$	−69.8771	−2.87923
$590$	3.08129	0.126855
$591$	13.8031	0.567786
$592$	−191.807	−7.88321
$593$	19.1821	0.787713	0.393856	−	0.919172i	$-0.371141\pi$
$593$	19.1821	0.787713	0.393856	+	0.919172i	$0.371141\pi$
$594$	−25.2286	−1.03514
$595$	−27.4666	−1.12602
$596$	53.5928	2.19525
$597$	−9.42178	−0.385608
$598$	14.2400	0.582316
$599$	23.1618	0.946367	0.473183	−	0.880964i	$-0.343105\pi$
$599$	23.1618	0.946367	0.473183	+	0.880964i	$0.343105\pi$
$600$	−79.3580	−3.23978
$601$	32.4611	1.32411	0.662057	−	0.749453i	$-0.269684\pi$
$601$	32.4611	1.32411	0.662057	+	0.749453i	$0.269684\pi$
$602$	−114.073	−4.64928
$603$	−2.10790	−0.0858405
$604$	4.47529	0.182097
$605$	22.8494	0.928959
$606$	−5.76360	−0.234130
$607$	32.8895	1.33494	0.667472	−	0.744635i	$-0.267377\pi$
$607$	32.8895	1.33494	0.667472	+	0.744635i	$0.267377\pi$
$608$	−190.036	−7.70697
$609$	16.1365	0.653885
$610$	−71.0715	−2.87760
$611$	14.4533	0.584718
$612$	3.42268	0.138354
$613$	14.2840	0.576927	0.288464	−	0.957491i	$-0.406856\pi$
$613$	14.2840	0.576927	0.288464	+	0.957491i	$0.406856\pi$
$614$	71.6949	2.89337
$615$	29.7475	1.19954
$616$	93.1418	3.75279
$617$	28.0574	1.12955	0.564774	−	0.825246i	$-0.308963\pi$
$617$	28.0574	1.12955	0.564774	+	0.825246i	$0.308963\pi$
$618$	−76.1611	−3.06365
$619$	−17.6065	−0.707666	−0.353833	−	0.935309i	$-0.615122\pi$
$619$	−17.6065	−0.707666	−0.353833	+	0.935309i	$0.615122\pi$
$620$	160.669	6.45263
$621$	−12.3056	−0.493806
$622$	29.2027	1.17092
$623$	−40.5425	−1.62430
$624$	−61.2719	−2.45284
$625$	−27.8976	−1.11590
$626$	−39.6894	−1.58631
$627$	−25.6339	−1.02372
$628$	−122.253	−4.87841
$629$	−21.1815	−0.844561
$630$	13.9605	0.556198
$631$	5.51593	0.219586	0.109793	−	0.993954i	$-0.464981\pi$
$631$	5.51593	0.219586	0.109793	+	0.993954i	$0.464981\pi$
$632$	53.3668	2.12282
$633$	50.4016	2.00328
$634$	63.0185	2.50279
$635$	0.898973	0.0356746
$636$	−64.9927	−2.57713
$637$	−35.6342	−1.41188
$638$	9.25777	0.366519
$639$	3.89578	0.154115
$640$	159.181	6.29220
$641$	50.2684	1.98548	0.992742	−	0.120265i	$-0.0383743\pi$
$641$	50.2684	1.98548	0.992742	+	0.120265i	$0.0383743\pi$
$642$	−53.1719	−2.09853
$643$	−13.4316	−0.529692	−0.264846	−	0.964291i	$-0.585321\pi$
$643$	−13.4316	−0.529692	−0.264846	+	0.964291i	$0.585321\pi$
$644$	70.4465	2.77598
$645$	−46.5527	−1.83301
$646$	−37.5691	−1.47814
$647$	−18.3384	−0.720956	−0.360478	−	0.932768i	$-0.617386\pi$
$647$	−18.3384	−0.720956	−0.360478	+	0.932768i	$0.617386\pi$
$648$	99.2553	3.89911
$649$	−0.685023	−0.0268895
$650$	24.3948	0.956844
$651$	−84.3682	−3.30665
$652$	−41.8366	−1.63845
$653$	−44.1433	−1.72746	−0.863730	−	0.503955i	$-0.831878\pi$
$653$	−44.1433	−1.72746	−0.863730	+	0.503955i	$0.831878\pi$
$654$	−40.6936	−1.59125
$655$	−19.9268	−0.778606
$656$	−87.7703	−3.42685
$657$	−2.09173	−0.0816062
$658$	96.8920	3.77724
$659$	−47.7483	−1.86001	−0.930005	−	0.367547i	$-0.880198\pi$
$659$	−47.7483	−1.86001	−0.930005	+	0.367547i	$0.880198\pi$
$660$	58.9403	2.29425
$661$	19.0562	0.741199	0.370599	−	0.928793i	$-0.379152\pi$
$661$	19.0562	0.741199	0.370599	+	0.928793i	$0.379152\pi$
$662$	−45.7882	−1.77961
$663$	−6.76634	−0.262783
$664$	9.13754	0.354605
$665$	−113.082	−4.38512
$666$	10.7659	0.417170
$667$	4.51559	0.174844
$668$	−13.5887	−0.525763
$669$	−32.2274	−1.24598
$670$	−53.2001	−2.05530
$671$	15.8004	0.609967
$672$	−229.446	−8.85106
$673$	−19.6149	−0.756097	−0.378049	−	0.925786i	$-0.623405\pi$
$673$	−19.6149	−0.756097	−0.378049	+	0.925786i	$0.623405\pi$
$674$	−17.2779	−0.665520
$675$	−21.0810	−0.811407
$676$	−49.8061	−1.91562
$677$	15.2093	0.584542	0.292271	−	0.956336i	$-0.405589\pi$
$677$	15.2093	0.584542	0.292271	+	0.956336i	$0.405589\pi$
$678$	−56.7025	−2.17764
$679$	−74.3681	−2.85399
$680$	55.7086	2.13633
$681$	13.3966	0.513359
$682$	−48.4034	−1.85346
$683$	−49.6193	−1.89863	−0.949315	−	0.314325i	$-0.898222\pi$
$683$	−49.6193	−1.89863	−0.949315	+	0.314325i	$0.898222\pi$
$684$	14.0914	0.538798
$685$	−15.6998	−0.599857
$686$	−143.208	−5.46770
$687$	−27.5741	−1.05202
$688$	137.354	5.23658
$689$	12.8844	0.490857
$690$	38.9575	1.48309
$691$	16.0594	0.610929	0.305464	−	0.952204i	$-0.401188\pi$
$691$	16.0594	0.610929	0.305464	+	0.952204i	$0.401188\pi$
$692$	−92.7038	−3.52407
$693$	−3.10364	−0.117898
$694$	−65.2460	−2.47671
$695$	35.2376	1.33664
$696$	−32.7285	−1.24057
$697$	−9.69259	−0.367133
$698$	42.5641	1.61107
$699$	23.3593	0.883528
$700$	120.684	4.56141
$701$	1.34507	0.0508026	0.0254013	−	0.999677i	$-0.491914\pi$
$701$	1.34507	0.0508026	0.0254013	+	0.999677i	$0.491914\pi$
$702$	−27.4170	−1.03479
$703$	−87.2054	−3.28901
$704$	−69.8836	−2.63384
$705$	39.5411	1.48920
$706$	28.1768	1.06045
$707$	5.65255	0.212586
$708$	3.75519	0.141128
$709$	29.7900	1.11879	0.559393	−	0.828903i	$-0.311034\pi$
$709$	29.7900	1.11879	0.559393	+	0.828903i	$0.311034\pi$
$710$	98.3233	3.69001
$711$	−1.77827	−0.0666904
$712$	82.2294	3.08168
$713$	−23.6093	−0.884177
$714$	−45.3602	−1.69756
$715$	−11.6846	−0.436978
$716$	37.0094	1.38311
$717$	−19.7189	−0.736417
$718$	0.0798668	0.00298060
$719$	−43.5662	−1.62475	−0.812373	−	0.583138i	$-0.801825\pi$
$719$	−43.5662	−1.62475	−0.812373	+	0.583138i	$0.801825\pi$
$720$	−16.8096	−0.626456
$721$	74.6937	2.78174
$722$	−102.184	−3.80289
$723$	5.09587	0.189518
$724$	−125.663	−4.67022
$725$	7.73577	0.287299
$726$	37.7350	1.40048
$727$	35.1624	1.30410	0.652050	−	0.758176i	$-0.273909\pi$
$727$	35.1624	1.30410	0.652050	+	0.758176i	$0.273909\pi$
$728$	101.221	3.75151
$729$	23.3572	0.865083
$730$	−52.7920	−1.95392
$731$	15.1682	0.561016
$732$	−86.6152	−3.20139
$733$	−5.19448	−0.191862	−0.0959312	−	0.995388i	$-0.530583\pi$
$733$	−5.19448	−0.191862	−0.0959312	+	0.995388i	$0.530583\pi$
$734$	65.3616	2.41254
$735$	−97.4875	−3.59588
$736$	−64.2074	−2.36671
$737$	11.8273	0.435663
$738$	4.92645	0.181345
$739$	−1.71292	−0.0630109	−0.0315054	−	0.999504i	$-0.510030\pi$
$739$	−1.71292	−0.0630109	−0.0315054	+	0.999504i	$0.510030\pi$
$740$	200.512	7.37098
$741$	−27.8574	−1.02337
$742$	86.3746	3.17091
$743$	−35.1797	−1.29062	−0.645308	−	0.763922i	$-0.723271\pi$
$743$	−35.1797	−1.29062	−0.645308	+	0.763922i	$0.723271\pi$
$744$	171.118	6.27348
$745$	−29.0662	−1.06490
$746$	−58.5649	−2.14421
$747$	−0.304479	−0.0111403
$748$	−19.2044	−0.702183
$749$	52.1474	1.90543
$750$	−10.3098	−0.376461
$751$	−46.4538	−1.69512	−0.847561	−	0.530697i	$-0.821930\pi$
$751$	−46.4538	−1.69512	−0.847561	+	0.530697i	$0.821930\pi$
$752$	−116.666	−4.25438
$753$	−11.6732	−0.425397
$754$	10.0608	0.366393
$755$	−2.42719	−0.0883344
$756$	−135.635	−4.93299
$757$	−20.6189	−0.749407	−0.374704	−	0.927145i	$-0.622256\pi$
$757$	−20.6189	−0.749407	−0.374704	+	0.927145i	$0.622256\pi$
$758$	−8.25528	−0.299845
$759$	−8.66091	−0.314371
$760$	229.355	8.31960
$761$	−24.2187	−0.877929	−0.438964	−	0.898504i	$-0.644655\pi$
$761$	−24.2187	−0.877929	−0.438964	+	0.898504i	$0.644655\pi$
$762$	1.48462	0.0537822
$763$	39.9095	1.44482
$764$	−51.5176	−1.86384
$765$	−1.85630	−0.0671148
$766$	9.22234	0.333217
$767$	−0.744443	−0.0268803
$768$	126.848	4.57722
$769$	22.9523	0.827680	0.413840	−	0.910350i	$-0.364187\pi$
$769$	22.9523	0.827680	0.413840	+	0.910350i	$0.364187\pi$
$770$	−78.3310	−2.82285
$771$	−33.2169	−1.19628
$772$	81.8646	2.94637
$773$	54.1606	1.94802	0.974010	−	0.226505i	$-0.0727301\pi$
$773$	54.1606	1.94802	0.974010	+	0.226505i	$0.0727301\pi$
$774$	−7.70953	−0.277113
$775$	−40.4457	−1.45285
$776$	150.835	5.41468
$777$	−105.290	−3.77726
$778$	18.4693	0.662156
$779$	−39.9050	−1.42974
$780$	64.0529	2.29346
$781$	−21.8589	−0.782174
$782$	−12.6935	−0.453917
$783$	−8.69413	−0.310703
$784$	287.638	10.2728
$785$	66.3041	2.36650
$786$	−32.9085	−1.17381
$787$	−39.2059	−1.39754	−0.698769	−	0.715347i	$-0.746269\pi$
$787$	−39.2059	−1.39754	−0.698769	+	0.715347i	$0.746269\pi$
$788$	42.5748	1.51666
$789$	16.3828	0.583242
$790$	−44.8807	−1.59678
$791$	55.6100	1.97726
$792$	6.29489	0.223679
$793$	17.1710	0.609759
$794$	61.0827	2.16774
$795$	35.2490	1.25015
$796$	−29.0607	−1.03003
$797$	−12.4095	−0.439567	−0.219783	−	0.975549i	$-0.570535\pi$
$797$	−12.4095	−0.439567	−0.219783	+	0.975549i	$0.570535\pi$
$798$	−186.751	−6.61090
$799$	−12.8836	−0.455790
$800$	−109.995	−3.88891
$801$	−2.74002	−0.0968140
$802$	−22.7640	−0.803825
$803$	11.7365	0.414174
$804$	−64.8353	−2.28656
$805$	−38.2069	−1.34662
$806$	−52.6020	−1.85283
$807$	−21.3727	−0.752356
$808$	−11.4647	−0.403325
$809$	32.7768	1.15237	0.576185	−	0.817319i	$-0.304541\pi$
$809$	32.7768	1.15237	0.576185	+	0.817319i	$0.304541\pi$
$810$	−83.4723	−2.93292
$811$	−31.1350	−1.09330	−0.546650	−	0.837361i	$-0.684097\pi$
$811$	−31.1350	−1.09330	−0.546650	+	0.837361i	$0.684097\pi$
$812$	49.7718	1.74665
$813$	7.85363	0.275439
$814$	−60.4066	−2.11725
$815$	22.6902	0.794804
$816$	54.6176	1.91200
$817$	62.4484	2.18479
$818$	20.4386	0.714618
$819$	−3.37286	−0.117857
$820$	91.7539	3.20419
$821$	14.5591	0.508116	0.254058	−	0.967189i	$-0.418235\pi$
$821$	14.5591	0.508116	0.254058	+	0.967189i	$0.418235\pi$
$822$	−25.9276	−0.904329
$823$	5.77896	0.201442	0.100721	−	0.994915i	$-0.467885\pi$
$823$	5.77896	0.201442	0.100721	+	0.994915i	$0.467885\pi$
$824$	−151.496	−5.27760
$825$	−14.8372	−0.516565
$826$	−4.99060	−0.173645
$827$	−52.0259	−1.80912	−0.904558	−	0.426350i	$-0.859799\pi$
$827$	−52.0259	−1.80912	−0.904558	+	0.426350i	$0.859799\pi$
$828$	4.76105	0.165458
$829$	32.1868	1.11789	0.558946	−	0.829204i	$-0.311206\pi$
$829$	32.1868	1.11789	0.558946	+	0.829204i	$0.311206\pi$
$830$	−7.68455	−0.266735
$831$	6.60059	0.228972
$832$	−75.9455	−2.63294
$833$	31.7642	1.10056
$834$	58.1937	2.01508
$835$	7.36988	0.255045
$836$	−79.0657	−2.73454
$837$	45.4564	1.57120
$838$	55.4662	1.91605
$839$	−39.4989	−1.36365	−0.681826	−	0.731514i	$-0.738814\pi$
$839$	−39.4989	−1.36365	−0.681826	+	0.731514i	$0.738814\pi$
$840$	276.919	9.55462
$841$	−25.8096	−0.889988
$842$	13.4847	0.464713
$843$	18.6641	0.642827
$844$	155.460	5.35115
$845$	27.0125	0.929258
$846$	6.54835	0.225137
$847$	−37.0079	−1.27161
$848$	−104.002	−3.57146
$849$	35.3950	1.21475
$850$	−21.7455	−0.745863
$851$	−29.4640	−1.01001
$852$	119.827	4.10521
$853$	−19.8638	−0.680124	−0.340062	−	0.940403i	$-0.610448\pi$
$853$	−19.8638	−0.680124	−0.340062	+	0.940403i	$0.610448\pi$
$854$	115.111	3.93901
$855$	−7.64252	−0.261368
$856$	−105.767	−3.61504
$857$	−31.8334	−1.08741	−0.543705	−	0.839277i	$-0.682979\pi$
$857$	−31.8334	−1.08741	−0.543705	+	0.839277i	$0.682979\pi$
$858$	−19.2967	−0.658777
$859$	−34.7976	−1.18728	−0.593640	−	0.804731i	$-0.702310\pi$
$859$	−34.7976	−1.18728	−0.593640	+	0.804731i	$0.702310\pi$
$860$	−143.588	−4.89632
$861$	−48.1805	−1.64199
$862$	99.0729	3.37444
$863$	−18.4724	−0.628808	−0.314404	−	0.949289i	$-0.601805\pi$
$863$	−18.4724	−0.628808	−0.314404	+	0.949289i	$0.601805\pi$
$864$	123.622	4.20571
$865$	50.2782	1.70951
$866$	−22.3934	−0.760960
$867$	−25.0109	−0.849416
$868$	−260.227	−8.83269
$869$	9.97774	0.338472
$870$	27.5242	0.933159
$871$	12.8532	0.435514
$872$	−80.9456	−2.74116
$873$	−5.02609	−0.170107
$874$	−52.2597	−1.76771
$875$	10.1112	0.341820
$876$	−64.3379	−2.17377
$877$	−47.6281	−1.60829	−0.804144	−	0.594435i	$-0.797376\pi$
$877$	−47.6281	−1.60829	−0.804144	+	0.594435i	$0.797376\pi$
$878$	−17.3460	−0.585398
$879$	−41.5480	−1.40138
$880$	94.3172	3.17943
$881$	−45.5641	−1.53509	−0.767546	−	0.640993i	$-0.778523\pi$
$881$	−45.5641	−1.53509	−0.767546	+	0.640993i	$0.778523\pi$
$882$	−16.1448	−0.543623
$883$	40.1160	1.35001	0.675006	−	0.737813i	$-0.264141\pi$
$883$	40.1160	1.35001	0.675006	+	0.737813i	$0.264141\pi$
$884$	−20.8703	−0.701943
$885$	−2.03664	−0.0684608
$886$	89.3182	3.00070
$887$	−34.5585	−1.16036	−0.580180	−	0.814488i	$-0.697018\pi$
$887$	−34.5585	−1.16036	−0.580180	+	0.814488i	$0.697018\pi$
$888$	213.552	7.16634
$889$	−1.45602	−0.0488333
$890$	−69.1538	−2.31804
$891$	18.5573	0.621693
$892$	−99.4030	−3.32826
$893$	−53.0426	−1.77500
$894$	−48.0019	−1.60542
$895$	−20.0722	−0.670939
$896$	−257.818	−8.61309
$897$	−9.41218	−0.314263
$898$	78.3753	2.61542
$899$	−16.6805	−0.556325
$900$	8.15627	0.271876
$901$	−11.4851	−0.382625
$902$	−27.6419	−0.920375
$903$	75.3990	2.50912
$904$	−112.790	−3.75133
$905$	68.1537	2.26550
$906$	−4.00842	−0.133171
$907$	−4.98268	−0.165447	−0.0827235	−	0.996573i	$-0.526362\pi$
$907$	−4.98268	−0.165447	−0.0827235	+	0.996573i	$0.526362\pi$
$908$	41.3208	1.37128
$909$	0.382022	0.0126709
$910$	−85.1256	−2.82189
$911$	6.77017	0.224306	0.112153	−	0.993691i	$-0.464225\pi$
$911$	6.77017	0.224306	0.112153	+	0.993691i	$0.464225\pi$
$912$	224.864	7.44599
$913$	1.70841	0.0565400
$914$	−67.2494	−2.22441
$915$	46.9761	1.55298
$916$	−85.0503	−2.81014
$917$	32.2744	1.06580
$918$	24.4395	0.806622
$919$	8.54128	0.281751	0.140875	−	0.990027i	$-0.455008\pi$
$919$	8.54128	0.281751	0.140875	+	0.990027i	$0.455008\pi$
$920$	77.4922	2.55484
$921$	−47.3881	−1.56149
$922$	−45.1280	−1.48621
$923$	−23.7550	−0.781906
$924$	−95.4624	−3.14048
$925$	−50.4755	−1.65963
$926$	−88.9159	−2.92196
$927$	5.04810	0.165801
$928$	−45.3638	−1.48914
$929$	23.4436	0.769161	0.384580	−	0.923092i	$-0.374346\pi$
$929$	23.4436	0.769161	0.384580	+	0.923092i	$0.374346\pi$
$930$	−143.908	−4.71892
$931$	130.775	4.28598
$932$	72.0498	2.36007
$933$	−19.3021	−0.631923
$934$	115.941	3.79371
$935$	10.4156	0.340626
$936$	6.84093	0.223603
$937$	−23.4208	−0.765124	−0.382562	−	0.923930i	$-0.624958\pi$
$937$	−23.4208	−0.765124	−0.382562	+	0.923930i	$0.624958\pi$
$938$	86.1654	2.81340
$939$	26.2334	0.856096
$940$	121.961	3.97794
$941$	−44.1472	−1.43916	−0.719578	−	0.694411i	$-0.755665\pi$
$941$	−44.1472	−1.43916	−0.719578	+	0.694411i	$0.755665\pi$
$942$	109.499	3.56767
$943$	−13.4827	−0.439056
$944$	6.00911	0.195580
$945$	73.5620	2.39297
$946$	43.2576	1.40642
$947$	15.2925	0.496939	0.248469	−	0.968640i	$-0.420072\pi$
$947$	15.2925	0.496939	0.248469	+	0.968640i	$0.420072\pi$
$948$	−54.6964	−1.77646
$949$	12.7546	0.414032
$950$	−89.5274	−2.90465
$951$	−41.6533	−1.35070
$952$	−90.2282	−2.92431
$953$	−27.7578	−0.899163	−0.449582	−	0.893239i	$-0.648427\pi$
$953$	−27.7578	−0.899163	−0.449582	+	0.893239i	$0.648427\pi$
$954$	5.83754	0.188997
$955$	27.9407	0.904141
$956$	−60.8215	−1.96711
$957$	−6.11910	−0.197802
$958$	−71.4739	−2.30922
$959$	25.4281	0.821115
$960$	−207.771	−6.70577
$961$	56.2122	1.81330
$962$	−65.6464	−2.11653
$963$	3.52433	0.113570
$964$	15.7178	0.506237
$965$	−44.3996	−1.42927
$966$	−63.0974	−2.03013
$967$	42.1471	1.35536	0.677680	−	0.735357i	$-0.262985\pi$
$967$	42.1471	1.35536	0.677680	+	0.735357i	$0.262985\pi$
$968$	75.0604	2.41253
$969$	24.8320	0.797719
$970$	−126.851	−4.07293
$971$	−7.02831	−0.225549	−0.112775	−	0.993621i	$-0.535974\pi$
$971$	−7.02831	−0.225549	−0.112775	+	0.993621i	$0.535974\pi$
$972$	−19.4833	−0.624928
$973$	−57.0725	−1.82966
$974$	25.0260	0.801886
$975$	−16.1242	−0.516388
$976$	−138.603	−4.43658
$977$	16.1945	0.518109	0.259054	−	0.965863i	$-0.416589\pi$
$977$	16.1945	0.518109	0.259054	+	0.965863i	$0.416589\pi$
$978$	37.4721	1.19823
$979$	15.3741	0.491357
$980$	−300.693	−9.60528
$981$	2.69724	0.0861164
$982$	58.8057	1.87656
$983$	47.5364	1.51618	0.758088	−	0.652153i	$-0.226134\pi$
$983$	47.5364	1.51618	0.758088	+	0.652153i	$0.226134\pi$
$984$	97.7209	3.11523
$985$	−23.0906	−0.735726
$986$	−8.96818	−0.285605
$987$	−64.0426	−2.03850
$988$	−85.9241	−2.73361
$989$	21.0994	0.670922
$990$	−5.29392	−0.168252
$991$	0.0767518	0.00243810	0.00121905	−	0.999999i	$-0.499612\pi$
$991$	0.0767518	0.00243810	0.00121905	+	0.999999i	$0.499612\pi$
$992$	237.180	7.53047
$993$	30.2646	0.960418
$994$	−159.249	−5.05107
$995$	15.7612	0.499663
$996$	−9.36521	−0.296748
$997$	31.6309	1.00176	0.500880	−	0.865517i	$-0.333010\pi$
$997$	31.6309	1.00176	0.500880	+	0.865517i	$0.333010\pi$
$998$	−113.558	−3.59462
$999$	56.7288	1.79482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.b.1.7	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.b.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.76265 q^{2} +1.82603 q^{3} +5.63224 q^{4} -3.05466 q^{5} -5.04467 q^{6} +4.94747 q^{7} -10.0346 q^{8} +0.334370 q^{9} +O(q^{10})\)	\(q-2.76265 q^{2} +1.82603 q^{3} +5.63224 q^{4} -3.05466 q^{5} -5.04467 q^{6} +4.94747 q^{7} -10.0346 q^{8} +0.334370 q^{9} +8.43896 q^{10} -1.87612 q^{11} +10.2846 q^{12} -2.03886 q^{13} -13.6681 q^{14} -5.57789 q^{15} +16.4576 q^{16} +1.81744 q^{17} -0.923747 q^{18} +7.48249 q^{19} -17.2046 q^{20} +9.03421 q^{21} +5.18307 q^{22} +2.52811 q^{23} -18.3234 q^{24} +4.33096 q^{25} +5.63266 q^{26} -4.86751 q^{27} +27.8653 q^{28} +1.78616 q^{29} +15.4098 q^{30} -9.33875 q^{31} -25.3974 q^{32} -3.42585 q^{33} -5.02094 q^{34} -15.1129 q^{35} +1.88325 q^{36} -11.6546 q^{37} -20.6715 q^{38} -3.72302 q^{39} +30.6523 q^{40} -5.33311 q^{41} -24.9584 q^{42} +8.34593 q^{43} -10.5668 q^{44} -1.02139 q^{45} -6.98427 q^{46} -7.08890 q^{47} +30.0520 q^{48} +17.4775 q^{49} -11.9649 q^{50} +3.31868 q^{51} -11.4834 q^{52} -6.31941 q^{53} +13.4472 q^{54} +5.73092 q^{55} -49.6459 q^{56} +13.6632 q^{57} -4.93453 q^{58} +0.365127 q^{59} -31.4160 q^{60} -8.42183 q^{61} +25.7997 q^{62} +1.65429 q^{63} +37.2490 q^{64} +6.22803 q^{65} +9.46442 q^{66} -6.30411 q^{67} +10.2362 q^{68} +4.61639 q^{69} +41.7515 q^{70} +11.6511 q^{71} -3.35527 q^{72} -6.25574 q^{73} +32.1976 q^{74} +7.90844 q^{75} +42.1431 q^{76} -9.28207 q^{77} +10.2854 q^{78} -5.31828 q^{79} -50.2724 q^{80} -9.89131 q^{81} +14.7335 q^{82} -0.910604 q^{83} +50.8828 q^{84} -5.55165 q^{85} -23.0569 q^{86} +3.26157 q^{87} +18.8261 q^{88} -8.19459 q^{89} +2.82173 q^{90} -10.0872 q^{91} +14.2389 q^{92} -17.0528 q^{93} +19.5841 q^{94} -22.8565 q^{95} -46.3763 q^{96} -15.0315 q^{97} -48.2842 q^{98} -0.627319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) \) 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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