LMFDB - Embedded newform 6043.2.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.71243 q^{2} +2.12328 q^{3} +5.35728 q^{4} +1.35121 q^{5} -5.75926 q^{6} +0.0653501 q^{7} -9.10638 q^{8} +1.50834 q^{9} +O(q^{10})$	\(q-2.71243 q^{2} +2.12328 q^{3} +5.35728 q^{4} +1.35121 q^{5} -5.75926 q^{6} +0.0653501 q^{7} -9.10638 q^{8} +1.50834 q^{9} -3.66505 q^{10} +5.07548 q^{11} +11.3750 q^{12} -5.84180 q^{13} -0.177258 q^{14} +2.86899 q^{15} +13.9859 q^{16} -6.96155 q^{17} -4.09126 q^{18} +5.45646 q^{19} +7.23878 q^{20} +0.138757 q^{21} -13.7669 q^{22} +5.16462 q^{23} -19.3354 q^{24} -3.17424 q^{25} +15.8455 q^{26} -3.16722 q^{27} +0.350099 q^{28} -8.05040 q^{29} -7.78194 q^{30} -0.688348 q^{31} -19.7229 q^{32} +10.7767 q^{33} +18.8827 q^{34} +0.0883014 q^{35} +8.08059 q^{36} +6.36529 q^{37} -14.8003 q^{38} -12.4038 q^{39} -12.3046 q^{40} -6.91943 q^{41} -0.376368 q^{42} -5.67931 q^{43} +27.1907 q^{44} +2.03808 q^{45} -14.0087 q^{46} -1.10385 q^{47} +29.6960 q^{48} -6.99573 q^{49} +8.60992 q^{50} -14.7814 q^{51} -31.2961 q^{52} -11.7633 q^{53} +8.59087 q^{54} +6.85801 q^{55} -0.595103 q^{56} +11.5856 q^{57} +21.8361 q^{58} +9.25331 q^{59} +15.3700 q^{60} -4.59745 q^{61} +1.86710 q^{62} +0.0985701 q^{63} +25.5253 q^{64} -7.89347 q^{65} -29.2310 q^{66} -12.2666 q^{67} -37.2950 q^{68} +10.9660 q^{69} -0.239511 q^{70} -11.2719 q^{71} -13.7355 q^{72} +11.6703 q^{73} -17.2654 q^{74} -6.73983 q^{75} +29.2318 q^{76} +0.331683 q^{77} +33.6445 q^{78} -7.82241 q^{79} +18.8978 q^{80} -11.2499 q^{81} +18.7685 q^{82} +11.7203 q^{83} +0.743359 q^{84} -9.40649 q^{85} +15.4047 q^{86} -17.0933 q^{87} -46.2192 q^{88} +5.03357 q^{89} -5.52814 q^{90} -0.381762 q^{91} +27.6683 q^{92} -1.46156 q^{93} +2.99412 q^{94} +7.37280 q^{95} -41.8773 q^{96} +9.42436 q^{97} +18.9754 q^{98} +7.65555 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.71243	−1.91798	−0.958989	−	0.283444i	$-0.908523\pi$
$2$	−2.71243	−1.91798	−0.958989	+	0.283444i	$0.908523\pi$
$3$	2.12328	1.22588	0.612940	−	0.790130i	$-0.289987\pi$
$3$	2.12328	1.22588	0.612940	+	0.790130i	$0.289987\pi$
$4$	5.35728	2.67864
$5$	1.35121	0.604277	0.302139	−	0.953264i	$-0.402299\pi$
$5$	1.35121	0.604277	0.302139	+	0.953264i	$0.402299\pi$
$6$	−5.75926	−2.35121
$7$	0.0653501	0.0247000	0.0123500	−	0.999924i	$-0.496069\pi$
$7$	0.0653501	0.0247000	0.0123500	+	0.999924i	$0.496069\pi$
$8$	−9.10638	−3.21959
$9$	1.50834	0.502780
$10$	−3.66505	−1.15899
$11$	5.07548	1.53031	0.765157	−	0.643843i	$-0.222661\pi$
$11$	5.07548	1.53031	0.765157	+	0.643843i	$0.222661\pi$
$12$	11.3750	3.28369
$13$	−5.84180	−1.62022	−0.810112	−	0.586275i	$-0.800594\pi$
$13$	−5.84180	−1.62022	−0.810112	+	0.586275i	$0.800594\pi$
$14$	−0.177258	−0.0473741
$15$	2.86899	0.740771
$16$	13.9859	3.49646
$17$	−6.96155	−1.68842	−0.844212	−	0.536009i	$-0.819931\pi$
$17$	−6.96155	−1.68842	−0.844212	+	0.536009i	$0.819931\pi$
$18$	−4.09126	−0.964320
$19$	5.45646	1.25180	0.625899	−	0.779904i	$-0.284732\pi$
$19$	5.45646	1.25180	0.625899	+	0.779904i	$0.284732\pi$
$20$	7.23878	1.61864
$21$	0.138757	0.0302792
$22$	−13.7669	−2.93511
$23$	5.16462	1.07690	0.538449	−	0.842658i	$-0.319010\pi$
$23$	5.16462	1.07690	0.538449	+	0.842658i	$0.319010\pi$
$24$	−19.3354	−3.94683
$25$	−3.17424	−0.634849
$26$	15.8455	3.10755
$27$	−3.16722	−0.609532
$28$	0.350099	0.0661624
$29$	−8.05040	−1.49492	−0.747461	−	0.664306i	$-0.768727\pi$
$29$	−8.05040	−1.49492	−0.747461	+	0.664306i	$0.768727\pi$
$30$	−7.78194	−1.42078
$31$	−0.688348	−0.123631	−0.0618155	−	0.998088i	$-0.519689\pi$
$31$	−0.688348	−0.123631	−0.0618155	+	0.998088i	$0.519689\pi$
$32$	−19.7229	−3.48655
$33$	10.7767	1.87598
$34$	18.8827	3.23836
$35$	0.0883014	0.0149257
$36$	8.08059	1.34676
$37$	6.36529	1.04645	0.523224	−	0.852195i	$-0.324729\pi$
$37$	6.36529	1.04645	0.523224	+	0.852195i	$0.324729\pi$
$38$	−14.8003	−2.40092
$39$	−12.4038	−1.98620
$40$	−12.3046	−1.94553
$41$	−6.91943	−1.08063	−0.540317	−	0.841462i	$-0.681696\pi$
$41$	−6.91943	−1.08063	−0.540317	+	0.841462i	$0.681696\pi$
$42$	−0.376368	−0.0580749
$43$	−5.67931	−0.866087	−0.433044	−	0.901373i	$-0.642560\pi$
$43$	−5.67931	−0.866087	−0.433044	+	0.901373i	$0.642560\pi$
$44$	27.1907	4.09916
$45$	2.03808	0.303818
$46$	−14.0087	−2.06547
$47$	−1.10385	−0.161013	−0.0805067	−	0.996754i	$-0.525654\pi$
$47$	−1.10385	−0.161013	−0.0805067	+	0.996754i	$0.525654\pi$
$48$	29.6960	4.28624
$49$	−6.99573	−0.999390
$50$	8.60992	1.21763
$51$	−14.7814	−2.06980
$52$	−31.2961	−4.33999
$53$	−11.7633	−1.61581	−0.807906	−	0.589312i	$-0.799399\pi$
$53$	−11.7633	−1.61581	−0.807906	+	0.589312i	$0.799399\pi$
$54$	8.59087	1.16907
$55$	6.85801	0.924735
$56$	−0.595103	−0.0795239
$57$	11.5856	1.53455
$58$	21.8361	2.86723
$59$	9.25331	1.20468	0.602339	−	0.798240i	$-0.294235\pi$
$59$	9.25331	1.20468	0.602339	+	0.798240i	$0.294235\pi$
$60$	15.3700	1.98426
$61$	−4.59745	−0.588643	−0.294322	−	0.955706i	$-0.595094\pi$
$61$	−4.59745	−0.588643	−0.294322	+	0.955706i	$0.595094\pi$
$62$	1.86710	0.237121
$63$	0.0985701	0.0124187
$64$	25.5253	3.19066
$65$	−7.89347	−0.979065
$66$	−29.2310	−3.59809
$67$	−12.2666	−1.49861	−0.749305	−	0.662225i	$-0.769612\pi$
$67$	−12.2666	−1.49861	−0.749305	+	0.662225i	$0.769612\pi$
$68$	−37.2950	−4.52268
$69$	10.9660	1.32015
$70$	−0.239511	−0.0286271
$71$	−11.2719	−1.33772	−0.668862	−	0.743387i	$-0.733218\pi$
$71$	−11.2719	−1.33772	−0.668862	+	0.743387i	$0.733218\pi$
$72$	−13.7355	−1.61874
$73$	11.6703	1.36591	0.682953	−	0.730463i	$-0.260696\pi$
$73$	11.6703	1.36591	0.682953	+	0.730463i	$0.260696\pi$
$74$	−17.2654	−2.00706
$75$	−6.73983	−0.778248
$76$	29.2318	3.35312
$77$	0.331683	0.0377988
$78$	33.6445	3.80949
$79$	−7.82241	−0.880090	−0.440045	−	0.897976i	$-0.645038\pi$
$79$	−7.82241	−0.880090	−0.440045	+	0.897976i	$0.645038\pi$
$80$	18.8978	2.11283
$81$	−11.2499	−1.24999
$82$	18.7685	2.07263
$83$	11.7203	1.28647	0.643237	−	0.765667i	$-0.277591\pi$
$83$	11.7203	1.28647	0.643237	+	0.765667i	$0.277591\pi$
$84$	0.743359	0.0811071
$85$	−9.40649	−1.02028
$86$	15.4047	1.66114
$87$	−17.0933	−1.83259
$88$	−46.2192	−4.92699
$89$	5.03357	0.533558	0.266779	−	0.963758i	$-0.414041\pi$
$89$	5.03357	0.533558	0.266779	+	0.963758i	$0.414041\pi$
$90$	−5.52814	−0.582717
$91$	−0.381762	−0.0400196
$92$	27.6683	2.88462
$93$	−1.46156	−0.151557
$94$	2.99412	0.308820
$95$	7.37280	0.756433
$96$	−41.8773	−4.27409
$97$	9.42436	0.956899	0.478449	−	0.878115i	$-0.341199\pi$
$97$	9.42436	0.956899	0.478449	+	0.878115i	$0.341199\pi$
$98$	18.9754	1.91681
$99$	7.65555	0.769411
$100$	−17.0053	−1.70053
$101$	−1.14218	−0.113651	−0.0568255	−	0.998384i	$-0.518098\pi$
$101$	−1.14218	−0.113651	−0.0568255	+	0.998384i	$0.518098\pi$
$102$	40.0934	3.96984
$103$	−4.10892	−0.404864	−0.202432	−	0.979296i	$-0.564885\pi$
$103$	−4.10892	−0.404864	−0.202432	+	0.979296i	$0.564885\pi$
$104$	53.1976	5.21646
$105$	0.187489	0.0182971
$106$	31.9071	3.09909
$107$	−15.5058	−1.49900	−0.749501	−	0.662003i	$-0.769706\pi$
$107$	−15.5058	−1.49900	−0.749501	+	0.662003i	$0.769706\pi$
$108$	−16.9677	−1.63272
$109$	6.64765	0.636729	0.318364	−	0.947968i	$-0.396866\pi$
$109$	6.64765	0.636729	0.318364	+	0.947968i	$0.396866\pi$
$110$	−18.6019	−1.77362
$111$	13.5153	1.28282
$112$	0.913977	0.0863627
$113$	2.69515	0.253538	0.126769	−	0.991932i	$-0.459539\pi$
$113$	2.69515	0.253538	0.126769	+	0.991932i	$0.459539\pi$
$114$	−31.4252	−2.94324
$115$	6.97846	0.650745
$116$	−43.1282	−4.00435
$117$	−8.81142	−0.814616
$118$	−25.0990	−2.31055
$119$	−0.454938	−0.0417041
$120$	−26.1261	−2.38498
$121$	14.7605	1.34186
$122$	12.4703	1.12900
$123$	−14.6919	−1.32473
$124$	−3.68767	−0.331162
$125$	−11.0451	−0.987902
$126$	−0.267365	−0.0238187
$127$	10.2488	0.909437	0.454719	−	0.890635i	$-0.349740\pi$
$127$	10.2488	0.909437	0.454719	+	0.890635i	$0.349740\pi$
$128$	−29.7897	−2.63306
$129$	−12.0588	−1.06172
$130$	21.4105	1.87782
$131$	−11.5754	−1.01135	−0.505676	−	0.862724i	$-0.668757\pi$
$131$	−11.5754	−1.01135	−0.505676	+	0.862724i	$0.668757\pi$
$132$	57.7337	5.02507
$133$	0.356580	0.0309194
$134$	33.2724	2.87430
$135$	−4.27957	−0.368326
$136$	63.3945	5.43603
$137$	4.83319	0.412927	0.206463	−	0.978454i	$-0.433805\pi$
$137$	4.83319	0.412927	0.206463	+	0.978454i	$0.433805\pi$
$138$	−29.7444	−2.53201
$139$	8.55802	0.725882	0.362941	−	0.931812i	$-0.381773\pi$
$139$	8.55802	0.725882	0.362941	+	0.931812i	$0.381773\pi$
$140$	0.473055	0.0399804
$141$	−2.34379	−0.197383
$142$	30.5741	2.56572
$143$	−29.6500	−2.47945
$144$	21.0954	1.75795
$145$	−10.8777	−0.903347
$146$	−31.6549	−2.61978
$147$	−14.8539	−1.22513
$148$	34.1006	2.80305
$149$	−5.70276	−0.467188	−0.233594	−	0.972334i	$-0.575049\pi$
$149$	−5.70276	−0.467188	−0.233594	+	0.972334i	$0.575049\pi$
$150$	18.2813	1.49266
$151$	−1.86835	−0.152044	−0.0760220	−	0.997106i	$-0.524222\pi$
$151$	−1.86835	−0.152044	−0.0760220	+	0.997106i	$0.524222\pi$
$152$	−49.6886	−4.03028
$153$	−10.5004	−0.848906
$154$	−0.899667	−0.0724973
$155$	−0.930099	−0.0747074
$156$	−66.4506	−5.32031
$157$	4.08118	0.325714	0.162857	−	0.986650i	$-0.447929\pi$
$157$	4.08118	0.325714	0.162857	+	0.986650i	$0.447929\pi$
$158$	21.2177	1.68799
$159$	−24.9768	−1.98079
$160$	−26.6497	−2.10684
$161$	0.337508	0.0265994
$162$	30.5146	2.39746
$163$	−6.25620	−0.490024	−0.245012	−	0.969520i	$-0.578792\pi$
$163$	−6.25620	−0.490024	−0.245012	+	0.969520i	$0.578792\pi$
$164$	−37.0693	−2.89463
$165$	14.5615	1.13361
$166$	−31.7906	−2.46743
$167$	−2.13395	−0.165130	−0.0825649	−	0.996586i	$-0.526311\pi$
$167$	−2.13395	−0.165130	−0.0825649	+	0.996586i	$0.526311\pi$
$168$	−1.26357	−0.0974867
$169$	21.1267	1.62513
$170$	25.5144	1.95687
$171$	8.23020	0.629379
$172$	−30.4256	−2.31993
$173$	−16.1956	−1.23133	−0.615666	−	0.788007i	$-0.711113\pi$
$173$	−16.1956	−1.23133	−0.615666	+	0.788007i	$0.711113\pi$
$174$	46.3643	3.51487
$175$	−0.207437	−0.0156808
$176$	70.9849	5.35069
$177$	19.6474	1.47679
$178$	−13.6532	−1.02335
$179$	−1.45361	−0.108648	−0.0543241	−	0.998523i	$-0.517300\pi$
$179$	−1.45361	−0.108648	−0.0543241	+	0.998523i	$0.517300\pi$
$180$	10.9185	0.813819
$181$	−17.5173	−1.30205	−0.651027	−	0.759055i	$-0.725661\pi$
$181$	−17.5173	−1.30205	−0.651027	+	0.759055i	$0.725661\pi$
$182$	1.03550	0.0767566
$183$	−9.76170	−0.721605
$184$	−47.0310	−3.46717
$185$	8.60082	0.632345
$186$	3.96438	0.290682
$187$	−35.3332	−2.58382
$188$	−5.91364	−0.431297
$189$	−0.206978	−0.0150555
$190$	−19.9982	−1.45082
$191$	24.0721	1.74179	0.870897	−	0.491465i	$-0.163538\pi$
$191$	24.0721	1.74179	0.870897	+	0.491465i	$0.163538\pi$
$192$	54.1974	3.91136
$193$	−8.33539	−0.599995	−0.299997	−	0.953940i	$-0.596986\pi$
$193$	−8.33539	−0.599995	−0.299997	+	0.953940i	$0.596986\pi$
$194$	−25.5629	−1.83531
$195$	−16.7601	−1.20022
$196$	−37.4781	−2.67700
$197$	−26.8244	−1.91116	−0.955579	−	0.294736i	$-0.904768\pi$
$197$	−26.8244	−1.91116	−0.955579	+	0.294736i	$0.904768\pi$
$198$	−20.7651	−1.47571
$199$	−21.1741	−1.50099	−0.750496	−	0.660875i	$-0.770185\pi$
$199$	−21.1741	−1.50099	−0.750496	+	0.660875i	$0.770185\pi$
$200$	28.9059	2.04395
$201$	−26.0456	−1.83711
$202$	3.09808	0.217980
$203$	−0.526094	−0.0369246
$204$	−79.1878	−5.54426
$205$	−9.34957	−0.653002
$206$	11.1452	0.776521
$207$	7.79000	0.541442
$208$	−81.7026	−5.66506
$209$	27.6942	1.91565
$210$	−0.508551	−0.0350933
$211$	16.1784	1.11377	0.556884	−	0.830591i	$-0.311997\pi$
$211$	16.1784	1.11377	0.556884	+	0.830591i	$0.311997\pi$
$212$	−63.0192	−4.32817
$213$	−23.9334	−1.63989
$214$	42.0584	2.87505
$215$	−7.67392	−0.523357
$216$	28.8419	1.96244
$217$	−0.0449836	−0.00305369
$218$	−18.0313	−1.22123
$219$	24.7794	1.67443
$220$	36.7403	2.47703
$221$	40.6680	2.73563
$222$	−36.6594	−2.46042
$223$	−12.2944	−0.823296	−0.411648	−	0.911343i	$-0.635047\pi$
$223$	−12.2944	−0.823296	−0.411648	+	0.911343i	$0.635047\pi$
$224$	−1.28889	−0.0861178
$225$	−4.78784	−0.319189
$226$	−7.31040	−0.486280
$227$	−18.7428	−1.24400	−0.622002	−	0.783015i	$-0.713681\pi$
$227$	−18.7428	−1.24400	−0.622002	+	0.783015i	$0.713681\pi$
$228$	62.0674	4.11051
$229$	19.8191	1.30968	0.654841	−	0.755767i	$-0.272736\pi$
$229$	19.8191	1.30968	0.654841	+	0.755767i	$0.272736\pi$
$230$	−18.9286	−1.24811
$231$	0.704258	0.0463368
$232$	73.3099	4.81303
$233$	−1.02808	−0.0673515	−0.0336757	−	0.999433i	$-0.510721\pi$
$233$	−1.02808	−0.0673515	−0.0336757	+	0.999433i	$0.510721\pi$
$234$	23.9004	1.56242
$235$	−1.49153	−0.0972968
$236$	49.5726	3.22690
$237$	−16.6092	−1.07888
$238$	1.23399	0.0799875
$239$	−8.23413	−0.532621	−0.266311	−	0.963887i	$-0.585805\pi$
$239$	−8.23413	−0.532621	−0.266311	+	0.963887i	$0.585805\pi$
$240$	40.1253	2.59008
$241$	7.20130	0.463877	0.231938	−	0.972730i	$-0.425493\pi$
$241$	7.20130	0.463877	0.231938	+	0.972730i	$0.425493\pi$
$242$	−40.0368	−2.57366
$243$	−14.3851	−0.922807
$244$	−24.6298	−1.57676
$245$	−9.45267	−0.603909
$246$	39.8508	2.54079
$247$	−31.8756	−2.02819
$248$	6.26835	0.398041
$249$	24.8856	1.57706
$250$	29.9590	1.89477
$251$	2.67366	0.168760	0.0843798	−	0.996434i	$-0.473109\pi$
$251$	2.67366	0.168760	0.0843798	+	0.996434i	$0.473109\pi$
$252$	0.528067	0.0332651
$253$	26.2129	1.64799
$254$	−27.7993	−1.74428
$255$	−19.9726	−1.25074
$256$	29.7520	1.85950
$257$	−14.8666	−0.927352	−0.463676	−	0.886005i	$-0.653470\pi$
$257$	−14.8666	−0.927352	−0.463676	+	0.886005i	$0.653470\pi$
$258$	32.7086	2.03635
$259$	0.415972	0.0258473
$260$	−42.2875	−2.62256
$261$	−12.1427	−0.751616
$262$	31.3976	1.93975
$263$	−10.2856	−0.634238	−0.317119	−	0.948386i	$-0.602715\pi$
$263$	−10.2856	−0.634238	−0.317119	+	0.948386i	$0.602715\pi$
$264$	−98.1366	−6.03989
$265$	−15.8946	−0.976398
$266$	−0.967199	−0.0593028
$267$	10.6877	0.654077
$268$	−65.7158	−4.01423
$269$	18.1300	1.10541	0.552704	−	0.833378i	$-0.313596\pi$
$269$	18.1300	1.10541	0.552704	+	0.833378i	$0.313596\pi$
$270$	11.6080	0.706442
$271$	29.4667	1.78998	0.894988	−	0.446091i	$-0.147184\pi$
$271$	29.4667	1.78998	0.894988	+	0.446091i	$0.147184\pi$
$272$	−97.3633	−5.90351
$273$	−0.810590	−0.0490592
$274$	−13.1097	−0.791985
$275$	−16.1108	−0.971519
$276$	58.7477	3.53619
$277$	−5.77913	−0.347234	−0.173617	−	0.984813i	$-0.555546\pi$
$277$	−5.77913	−0.347234	−0.173617	+	0.984813i	$0.555546\pi$
$278$	−23.2130	−1.39223
$279$	−1.03826	−0.0621591
$280$	−0.804106	−0.0480545
$281$	11.2798	0.672894	0.336447	−	0.941702i	$-0.390775\pi$
$281$	11.2798	0.672894	0.336447	+	0.941702i	$0.390775\pi$
$282$	6.35738	0.378576
$283$	25.6648	1.52561	0.762807	−	0.646626i	$-0.223820\pi$
$283$	25.6648	1.52561	0.762807	+	0.646626i	$0.223820\pi$
$284$	−60.3864	−3.58328
$285$	15.6546	0.927296
$286$	80.4234	4.75554
$287$	−0.452185	−0.0266917
$288$	−29.7488	−1.75297
$289$	31.4632	1.85078
$290$	29.5051	1.73260
$291$	20.0106	1.17304
$292$	62.5210	3.65877
$293$	7.01305	0.409707	0.204853	−	0.978793i	$-0.434328\pi$
$293$	7.01305	0.409707	0.204853	+	0.978793i	$0.434328\pi$
$294$	40.2902	2.34977
$295$	12.5031	0.727960
$296$	−57.9647	−3.36913
$297$	−16.0752	−0.932776
$298$	15.4683	0.896057
$299$	−30.1707	−1.74482
$300$	−36.1071	−2.08464
$301$	−0.371144	−0.0213924
$302$	5.06777	0.291617
$303$	−2.42517	−0.139322
$304$	76.3133	4.37687
$305$	−6.21210	−0.355704
$306$	28.4815	1.62818
$307$	−15.4316	−0.880728	−0.440364	−	0.897819i	$-0.645151\pi$
$307$	−15.4316	−0.880728	−0.440364	+	0.897819i	$0.645151\pi$
$308$	1.77692	0.101249
$309$	−8.72442	−0.496315
$310$	2.52283	0.143287
$311$	−6.39161	−0.362435	−0.181217	−	0.983443i	$-0.558004\pi$
$311$	−6.39161	−0.362435	−0.181217	+	0.983443i	$0.558004\pi$
$312$	112.954	6.39475
$313$	28.1574	1.59155	0.795774	−	0.605594i	$-0.207064\pi$
$313$	28.1574	1.59155	0.795774	+	0.605594i	$0.207064\pi$
$314$	−11.0699	−0.624711
$315$	0.133188	0.00750432
$316$	−41.9068	−2.35744
$317$	−27.8961	−1.56680	−0.783401	−	0.621516i	$-0.786517\pi$
$317$	−27.8961	−1.56680	−0.783401	+	0.621516i	$0.786517\pi$
$318$	67.7478	3.79911
$319$	−40.8596	−2.28770
$320$	34.4899	1.92804
$321$	−32.9232	−1.83760
$322$	−0.915468	−0.0510170
$323$	−37.9855	−2.11357
$324$	−60.2690	−3.34828
$325$	18.5433	1.02860
$326$	16.9695	0.939855
$327$	14.1148	0.780553
$328$	63.0109	3.47920
$329$	−0.0721369	−0.00397704
$330$	−39.4971	−2.17424
$331$	26.3874	1.45039	0.725193	−	0.688546i	$-0.241751\pi$
$331$	26.3874	1.45039	0.725193	+	0.688546i	$0.241751\pi$
$332$	62.7891	3.44600
$333$	9.60102	0.526133
$334$	5.78819	0.316715
$335$	−16.5748	−0.905576
$336$	1.94063	0.105870
$337$	4.60665	0.250940	0.125470	−	0.992097i	$-0.459956\pi$
$337$	4.60665	0.250940	0.125470	+	0.992097i	$0.459956\pi$
$338$	−57.3046	−3.11696
$339$	5.72256	0.310807
$340$	−50.3931	−2.73295
$341$	−3.49370	−0.189194
$342$	−22.3238	−1.20713
$343$	−0.914622	−0.0493850
$344$	51.7180	2.78845
$345$	14.8173	0.797735
$346$	43.9296	2.36167
$347$	−34.1687	−1.83427	−0.917136	−	0.398575i	$-0.869505\pi$
$347$	−34.1687	−1.83427	−0.917136	+	0.398575i	$0.869505\pi$
$348$	−91.5735	−4.90885
$349$	−5.23155	−0.280039	−0.140019	−	0.990149i	$-0.544716\pi$
$349$	−5.23155	−0.280039	−0.140019	+	0.990149i	$0.544716\pi$
$350$	0.562659	0.0300754
$351$	18.5023	0.987579
$352$	−100.103	−5.33552
$353$	−8.07046	−0.429547	−0.214774	−	0.976664i	$-0.568901\pi$
$353$	−8.07046	−0.429547	−0.214774	+	0.976664i	$0.568901\pi$
$354$	−53.2923	−2.83245
$355$	−15.2306	−0.808356
$356$	26.9662	1.42921
$357$	−0.965963	−0.0511242
$358$	3.94282	0.208385
$359$	−4.63776	−0.244772	−0.122386	−	0.992483i	$-0.539055\pi$
$359$	−4.63776	−0.244772	−0.122386	+	0.992483i	$0.539055\pi$
$360$	−18.5595	−0.978171
$361$	10.7730	0.567000
$362$	47.5146	2.49731
$363$	31.3407	1.64496
$364$	−2.04521	−0.107198
$365$	15.7690	0.825385
$366$	26.4779	1.38402
$367$	5.65440	0.295157	0.147579	−	0.989050i	$-0.452852\pi$
$367$	5.65440	0.295157	0.147579	+	0.989050i	$0.452852\pi$
$368$	72.2316	3.76533
$369$	−10.4368	−0.543321
$370$	−23.3291	−1.21282
$371$	−0.768732	−0.0399106
$372$	−7.82997	−0.405965
$373$	23.1419	1.19824	0.599120	−	0.800659i	$-0.295517\pi$
$373$	23.1419	1.19824	0.599120	+	0.800659i	$0.295517\pi$
$374$	95.8389	4.95571
$375$	−23.4519	−1.21105
$376$	10.0521	0.518397
$377$	47.0288	2.42211
$378$	0.561414	0.0288760
$379$	−30.0336	−1.54272	−0.771362	−	0.636397i	$-0.780424\pi$
$379$	−30.0336	−1.54272	−0.771362	+	0.636397i	$0.780424\pi$
$380$	39.4981	2.02621
$381$	21.7612	1.11486
$382$	−65.2938	−3.34072
$383$	23.0495	1.17777	0.588886	−	0.808216i	$-0.299567\pi$
$383$	23.0495	1.17777	0.588886	+	0.808216i	$0.299567\pi$
$384$	−63.2520	−3.22782
$385$	0.448172	0.0228410
$386$	22.6092	1.15078
$387$	−8.56633	−0.435451
$388$	50.4889	2.56318
$389$	19.3609	0.981638	0.490819	−	0.871262i	$-0.336698\pi$
$389$	19.3609	0.981638	0.490819	+	0.871262i	$0.336698\pi$
$390$	45.4606	2.30199
$391$	−35.9538	−1.81826
$392$	63.7057	3.21763
$393$	−24.5780	−1.23979
$394$	72.7592	3.66556
$395$	−10.5697	−0.531818
$396$	41.0129	2.06097
$397$	4.14323	0.207943	0.103971	−	0.994580i	$-0.466845\pi$
$397$	4.14323	0.207943	0.103971	+	0.994580i	$0.466845\pi$
$398$	57.4332	2.87887
$399$	0.757122	0.0379035
$400$	−44.3945	−2.21973
$401$	−5.68547	−0.283919	−0.141959	−	0.989872i	$-0.545340\pi$
$401$	−5.68547	−0.283919	−0.141959	+	0.989872i	$0.545340\pi$
$402$	70.6468	3.52354
$403$	4.02119	0.200310
$404$	−6.11897	−0.304430
$405$	−15.2010	−0.755342
$406$	1.42699	0.0708205
$407$	32.3069	1.60139
$408$	134.605	6.66392
$409$	13.4218	0.663666	0.331833	−	0.943338i	$-0.392333\pi$
$409$	13.4218	0.663666	0.331833	+	0.943338i	$0.392333\pi$
$410$	25.3601	1.25244
$411$	10.2622	0.506199
$412$	−22.0126	−1.08448
$413$	0.604705	0.0297556
$414$	−21.1298	−1.03847
$415$	15.8366	0.777387
$416$	115.217	5.64899
$417$	18.1711	0.889844
$418$	−75.1185	−3.67417
$419$	13.4243	0.655819	0.327909	−	0.944709i	$-0.393656\pi$
$419$	13.4243	0.655819	0.327909	+	0.944709i	$0.393656\pi$
$420$	1.00443	0.0490112
$421$	40.1874	1.95861	0.979306	−	0.202384i	$-0.0648689\pi$
$421$	40.1874	1.95861	0.979306	+	0.202384i	$0.0648689\pi$
$422$	−43.8828	−2.13618
$423$	−1.66498	−0.0809543
$424$	107.121	5.20225
$425$	22.0977	1.07189
$426$	64.9176	3.14527
$427$	−0.300444	−0.0145395
$428$	−83.0688	−4.01528
$429$	−62.9553	−3.03951
$430$	20.8150	1.00379
$431$	−19.0433	−0.917284	−0.458642	−	0.888621i	$-0.651664\pi$
$431$	−19.0433	−0.917284	−0.458642	+	0.888621i	$0.651664\pi$
$432$	−44.2963	−2.13121
$433$	1.05078	0.0504972	0.0252486	−	0.999681i	$-0.491962\pi$
$433$	1.05078	0.0504972	0.0252486	+	0.999681i	$0.491962\pi$
$434$	0.122015	0.00585690
$435$	−23.0965	−1.10739
$436$	35.6133	1.70557
$437$	28.1806	1.34806
$438$	−67.2123	−3.21153
$439$	25.4647	1.21536	0.607682	−	0.794180i	$-0.292100\pi$
$439$	25.4647	1.21536	0.607682	+	0.794180i	$0.292100\pi$
$440$	−62.4517	−2.97727
$441$	−10.5519	−0.502473
$442$	−110.309	−5.24687
$443$	−21.3503	−1.01438	−0.507192	−	0.861833i	$-0.669316\pi$
$443$	−21.3503	−1.01438	−0.507192	+	0.861833i	$0.669316\pi$
$444$	72.4054	3.43621
$445$	6.80139	0.322417
$446$	33.3478	1.57906
$447$	−12.1086	−0.572716
$448$	1.66808	0.0788093
$449$	12.6856	0.598671	0.299335	−	0.954148i	$-0.403235\pi$
$449$	12.6856	0.598671	0.299335	+	0.954148i	$0.403235\pi$
$450$	12.9867	0.612198
$451$	−35.1194	−1.65371
$452$	14.4386	0.679137
$453$	−3.96704	−0.186388
$454$	50.8386	2.38597
$455$	−0.515839	−0.0241829
$456$	−105.503	−4.94063
$457$	−9.87105	−0.461748	−0.230874	−	0.972984i	$-0.574159\pi$
$457$	−9.87105	−0.461748	−0.230874	+	0.972984i	$0.574159\pi$
$458$	−53.7579	−2.51194
$459$	22.0488	1.02915
$460$	37.3855	1.74311
$461$	−23.6309	−1.10060	−0.550301	−	0.834966i	$-0.685487\pi$
$461$	−23.6309	−1.10060	−0.550301	+	0.834966i	$0.685487\pi$
$462$	−1.91025	−0.0888729
$463$	20.8384	0.968443	0.484222	−	0.874945i	$-0.339103\pi$
$463$	20.8384	0.968443	0.484222	+	0.874945i	$0.339103\pi$
$464$	−112.592	−5.22694
$465$	−1.97487	−0.0915822
$466$	2.78858	0.129179
$467$	28.5192	1.31971	0.659855	−	0.751393i	$-0.270618\pi$
$467$	28.5192	1.31971	0.659855	+	0.751393i	$0.270618\pi$
$468$	−47.2052	−2.18206
$469$	−0.801627	−0.0370157
$470$	4.04567	0.186613
$471$	8.66551	0.399285
$472$	−84.2642	−3.87857
$473$	−28.8252	−1.32539
$474$	45.0513	2.06928
$475$	−17.3201	−0.794703
$476$	−2.43723	−0.111710
$477$	−17.7430	−0.812397
$478$	22.3345	1.02156
$479$	39.7382	1.81568	0.907842	−	0.419311i	$-0.137728\pi$
$479$	39.7382	1.81568	0.907842	+	0.419311i	$0.137728\pi$
$480$	−56.5849	−2.58273
$481$	−37.1848	−1.69548
$482$	−19.5330	−0.889705
$483$	0.716627	0.0326076
$484$	79.0761	3.59437
$485$	12.7342	0.578232
$486$	39.0187	1.76992
$487$	−30.8941	−1.39995	−0.699974	−	0.714169i	$-0.746805\pi$
$487$	−30.8941	−1.39995	−0.699974	+	0.714169i	$0.746805\pi$
$488$	41.8661	1.89519
$489$	−13.2837	−0.600710
$490$	25.6397	1.15828
$491$	20.5332	0.926652	0.463326	−	0.886188i	$-0.346656\pi$
$491$	20.5332	0.926652	0.463326	+	0.886188i	$0.346656\pi$
$492$	−78.7087	−3.54846
$493$	56.0433	2.52406
$494$	86.4603	3.89003
$495$	10.3442	0.464938
$496$	−9.62713	−0.432271
$497$	−0.736617	−0.0330418
$498$	−67.5005	−3.02477
$499$	−13.4899	−0.603890	−0.301945	−	0.953325i	$-0.597636\pi$
$499$	−13.4899	−0.603890	−0.301945	+	0.953325i	$0.597636\pi$
$500$	−59.1715	−2.64623
$501$	−4.53098	−0.202429
$502$	−7.25210	−0.323677
$503$	9.88108	0.440576	0.220288	−	0.975435i	$-0.429300\pi$
$503$	9.88108	0.440576	0.220288	+	0.975435i	$0.429300\pi$
$504$	−0.897616	−0.0399830
$505$	−1.54332	−0.0686767
$506$	−71.1007	−3.16081
$507$	44.8579	1.99221
$508$	54.9059	2.43605
$509$	−19.2456	−0.853046	−0.426523	−	0.904477i	$-0.640262\pi$
$509$	−19.2456	−0.853046	−0.426523	+	0.904477i	$0.640262\pi$
$510$	54.1744	2.39888
$511$	0.762655	0.0337379
$512$	−21.1207	−0.933411
$513$	−17.2818	−0.763011
$514$	40.3246	1.77864
$515$	−5.55200	−0.244650
$516$	−64.6023	−2.84396
$517$	−5.60258	−0.246401
$518$	−1.12830	−0.0495745
$519$	−34.3880	−1.50946
$520$	71.8809	3.15219
$521$	0.568795	0.0249194	0.0124597	−	0.999922i	$-0.496034\pi$
$521$	0.568795	0.0249194	0.0124597	+	0.999922i	$0.496034\pi$
$522$	32.9363	1.44158
$523$	5.60631	0.245147	0.122573	−	0.992459i	$-0.460885\pi$
$523$	5.60631	0.245147	0.122573	+	0.992459i	$0.460885\pi$
$524$	−62.0129	−2.70904
$525$	−0.440448	−0.0192227
$526$	27.8990	1.21645
$527$	4.79197	0.208741
$528$	150.721	6.55930
$529$	3.67330	0.159709
$530$	43.1130	1.87271
$531$	13.9571	0.605688
$532$	1.91030	0.0828220
$533$	40.4219	1.75087
$534$	−28.9897	−1.25451
$535$	−20.9515	−0.905813
$536$	111.705	4.82491
$537$	−3.08643	−0.133189
$538$	−49.1765	−2.12015
$539$	−35.5067	−1.52938
$540$	−22.9268	−0.986613
$541$	10.8664	0.467183	0.233591	−	0.972335i	$-0.424952\pi$
$541$	10.8664	0.467183	0.233591	+	0.972335i	$0.424952\pi$
$542$	−79.9264	−3.43313
$543$	−37.1943	−1.59616
$544$	137.302	5.88677
$545$	8.98233	0.384761
$546$	2.19867	0.0940944
$547$	−6.31628	−0.270065	−0.135032	−	0.990841i	$-0.543114\pi$
$547$	−6.31628	−0.270065	−0.135032	+	0.990841i	$0.543114\pi$
$548$	25.8927	1.10608
$549$	−6.93451	−0.295958
$550$	43.6995	1.86335
$551$	−43.9267	−1.87134
$552$	−99.8602	−4.25033
$553$	−0.511195	−0.0217382
$554$	15.6755	0.665987
$555$	18.2620	0.775178
$556$	45.8477	1.94438
$557$	23.1902	0.982599	0.491299	−	0.870991i	$-0.336522\pi$
$557$	23.1902	0.982599	0.491299	+	0.870991i	$0.336522\pi$
$558$	2.81621	0.119220
$559$	33.1774	1.40326
$560$	1.23497	0.0521870
$561$	−75.0225	−3.16745
$562$	−30.5955	−1.29060
$563$	−1.85872	−0.0783356	−0.0391678	−	0.999233i	$-0.512471\pi$
$563$	−1.85872	−0.0783356	−0.0391678	+	0.999233i	$0.512471\pi$
$564$	−12.5564	−0.528718
$565$	3.64170	0.153207
$566$	−69.6140	−2.92609
$567$	−0.735184	−0.0308748
$568$	102.646	4.30692
$569$	−14.7591	−0.618734	−0.309367	−	0.950943i	$-0.600117\pi$
$569$	−14.7591	−0.618734	−0.309367	+	0.950943i	$0.600117\pi$
$570$	−42.4619	−1.77853
$571$	−18.2522	−0.763830	−0.381915	−	0.924197i	$-0.624735\pi$
$571$	−18.2522	−0.763830	−0.381915	+	0.924197i	$0.624735\pi$
$572$	−158.843	−6.64156
$573$	51.1119	2.13523
$574$	1.22652	0.0511940
$575$	−16.3938	−0.683667
$576$	38.5008	1.60420
$577$	36.6497	1.52575	0.762874	−	0.646547i	$-0.223787\pi$
$577$	36.6497	1.52575	0.762874	+	0.646547i	$0.223787\pi$
$578$	−85.3418	−3.54975
$579$	−17.6984	−0.735521
$580$	−58.2750	−2.41974
$581$	0.765925	0.0317759
$582$	−54.2773	−2.24987
$583$	−59.7043	−2.47270
$584$	−106.274	−4.39765
$585$	−11.9060	−0.492254
$586$	−19.0224	−0.785809
$587$	−1.27461	−0.0526087	−0.0263044	−	0.999654i	$-0.508374\pi$
$587$	−1.27461	−0.0526087	−0.0263044	+	0.999654i	$0.508374\pi$
$588$	−79.5766	−3.28168
$589$	−3.75594	−0.154761
$590$	−33.9139	−1.39621
$591$	−56.9558	−2.34285
$592$	89.0241	3.65887
$593$	−28.3082	−1.16248	−0.581240	−	0.813732i	$-0.697432\pi$
$593$	−28.3082	−1.16248	−0.581240	+	0.813732i	$0.697432\pi$
$594$	43.6028	1.78904
$595$	−0.614715	−0.0252008
$596$	−30.5513	−1.25143
$597$	−44.9586	−1.84003
$598$	81.8359	3.34652
$599$	−16.7347	−0.683762	−0.341881	−	0.939743i	$-0.611064\pi$
$599$	−16.7347	−0.683762	−0.341881	+	0.939743i	$0.611064\pi$
$600$	61.3754	2.50564
$601$	32.7784	1.33706	0.668530	−	0.743685i	$-0.266924\pi$
$601$	32.7784	1.33706	0.668530	+	0.743685i	$0.266924\pi$
$602$	1.00670	0.0410301
$603$	−18.5023	−0.753470
$604$	−10.0093	−0.407271
$605$	19.9445	0.810858
$606$	6.57810	0.267217
$607$	−46.3530	−1.88141	−0.940706	−	0.339223i	$-0.889836\pi$
$607$	−46.3530	−1.88141	−0.940706	+	0.339223i	$0.889836\pi$
$608$	−107.617	−4.36446
$609$	−1.11705	−0.0452651
$610$	16.8499	0.682232
$611$	6.44849	0.260878
$612$	−56.2534	−2.27391
$613$	−41.8067	−1.68856	−0.844279	−	0.535905i	$-0.819971\pi$
$613$	−41.8067	−1.68856	−0.844279	+	0.535905i	$0.819971\pi$
$614$	41.8571	1.68922
$615$	−19.8518	−0.800502
$616$	−3.02043	−0.121697
$617$	−20.2265	−0.814288	−0.407144	−	0.913364i	$-0.633475\pi$
$617$	−20.2265	−0.814288	−0.407144	+	0.913364i	$0.633475\pi$
$618$	23.6644	0.951921
$619$	−28.2189	−1.13421	−0.567107	−	0.823644i	$-0.691937\pi$
$619$	−28.2189	−1.13421	−0.567107	+	0.823644i	$0.691937\pi$
$620$	−4.98280	−0.200114
$621$	−16.3575	−0.656404
$622$	17.3368	0.695142
$623$	0.328945	0.0131789
$624$	−173.478	−6.94467
$625$	0.947052	0.0378821
$626$	−76.3749	−3.05255
$627$	58.8026	2.34835
$628$	21.8640	0.872469
$629$	−44.3123	−1.76685
$630$	−0.361264	−0.0143931
$631$	16.8114	0.669250	0.334625	−	0.942351i	$-0.391390\pi$
$631$	16.8114	0.669250	0.334625	+	0.942351i	$0.391390\pi$
$632$	71.2338	2.83353
$633$	34.3514	1.36534
$634$	75.6663	3.00509
$635$	13.8483	0.549552
$636$	−133.808	−5.30582
$637$	40.8677	1.61924
$638$	110.829	4.38776
$639$	−17.0018	−0.672580
$640$	−40.2520	−1.59110
$641$	−46.9607	−1.85484	−0.927418	−	0.374026i	$-0.877977\pi$
$641$	−46.9607	−1.85484	−0.927418	+	0.374026i	$0.877977\pi$
$642$	89.3019	3.52447
$643$	−10.9529	−0.431939	−0.215969	−	0.976400i	$-0.569291\pi$
$643$	−10.9529	−0.431939	−0.215969	+	0.976400i	$0.569291\pi$
$644$	1.80813	0.0712501
$645$	−16.2939	−0.641572
$646$	103.033	4.05377
$647$	7.84126	0.308272	0.154136	−	0.988050i	$-0.450741\pi$
$647$	7.84126	0.308272	0.154136	+	0.988050i	$0.450741\pi$
$648$	102.446	4.02446
$649$	46.9650	1.84354
$650$	−50.2974	−1.97283
$651$	−0.0955130	−0.00374345
$652$	−33.5162	−1.31260
$653$	−2.28684	−0.0894908	−0.0447454	−	0.998998i	$-0.514248\pi$
$653$	−2.28684	−0.0894908	−0.0447454	+	0.998998i	$0.514248\pi$
$654$	−38.2855	−1.49708
$655$	−15.6408	−0.611137
$656$	−96.7741	−3.77840
$657$	17.6028	0.686749
$658$	0.195666	0.00762786
$659$	−43.2735	−1.68570	−0.842848	−	0.538152i	$-0.819123\pi$
$659$	−43.2735	−1.68570	−0.842848	+	0.538152i	$0.819123\pi$
$660$	78.0101	3.03654
$661$	−16.3179	−0.634691	−0.317346	−	0.948310i	$-0.602792\pi$
$661$	−16.3179	−0.634691	−0.317346	+	0.948310i	$0.602792\pi$
$662$	−71.5741	−2.78181
$663$	86.3498	3.35355
$664$	−106.730	−4.14192
$665$	0.481813	0.0186839
$666$	−26.0421	−1.00911
$667$	−41.5772	−1.60988
$668$	−11.4322	−0.442323
$669$	−26.1046	−1.00926
$670$	44.9579	1.73687
$671$	−23.3343	−0.900809
$672$	−2.73669	−0.105570
$673$	−12.8563	−0.495575	−0.247787	−	0.968814i	$-0.579703\pi$
$673$	−12.8563	−0.495575	−0.247787	+	0.968814i	$0.579703\pi$
$674$	−12.4952	−0.481297
$675$	10.0535	0.386961
$676$	113.181	4.35313
$677$	4.87662	0.187424	0.0937119	−	0.995599i	$-0.470127\pi$
$677$	4.87662	0.187424	0.0937119	+	0.995599i	$0.470127\pi$
$678$	−15.5221	−0.596121
$679$	0.615883	0.0236354
$680$	85.6590	3.28487
$681$	−39.7964	−1.52500
$682$	9.47641	0.362870
$683$	11.1452	0.426458	0.213229	−	0.977002i	$-0.431602\pi$
$683$	11.1452	0.426458	0.213229	+	0.977002i	$0.431602\pi$
$684$	44.0914	1.68588
$685$	6.53063	0.249522
$686$	2.48085	0.0947193
$687$	42.0815	1.60551
$688$	−79.4300	−3.02824
$689$	68.7188	2.61798
$690$	−40.1908	−1.53004
$691$	25.6823	0.977001	0.488500	−	0.872564i	$-0.337544\pi$
$691$	25.6823	0.977001	0.488500	+	0.872564i	$0.337544\pi$
$692$	−86.7646	−3.29829
$693$	0.500291	0.0190045
$694$	92.6802	3.51809
$695$	11.5636	0.438634
$696$	155.658	5.90020
$697$	48.1700	1.82457
$698$	14.1902	0.537108
$699$	−2.18290	−0.0825648
$700$	−1.11130	−0.0420031
$701$	−36.8073	−1.39019	−0.695096	−	0.718917i	$-0.744638\pi$
$701$	−36.8073	−1.39019	−0.695096	+	0.718917i	$0.744638\pi$
$702$	−50.1861	−1.89415
$703$	34.7320	1.30994
$704$	129.553	4.88271
$705$	−3.16695	−0.119274
$706$	21.8906	0.823862
$707$	−0.0746415	−0.00280718
$708$	105.257	3.95579
$709$	3.53089	0.132605	0.0663026	−	0.997800i	$-0.478880\pi$
$709$	3.53089	0.132605	0.0663026	+	0.997800i	$0.478880\pi$
$710$	41.3119	1.55041
$711$	−11.7988	−0.442491
$712$	−45.8376	−1.71784
$713$	−3.55506	−0.133138
$714$	2.62011	0.0980551
$715$	−40.0632	−1.49828
$716$	−7.78741	−0.291029
$717$	−17.4834	−0.652929
$718$	12.5796	0.469467
$719$	15.7821	0.588572	0.294286	−	0.955717i	$-0.404918\pi$
$719$	15.7821	0.588572	0.294286	+	0.955717i	$0.404918\pi$
$720$	28.5042	1.06229
$721$	−0.268519	−0.0100002
$722$	−29.2210	−1.08749
$723$	15.2904	0.568657
$724$	−93.8452	−3.48773
$725$	25.5539	0.949049
$726$	−85.0096	−3.15500
$727$	−18.3558	−0.680780	−0.340390	−	0.940284i	$-0.610559\pi$
$727$	−18.3558	−0.680780	−0.340390	+	0.940284i	$0.610559\pi$
$728$	3.47647	0.128847
$729$	3.20603	0.118742
$730$	−42.7722	−1.58307
$731$	39.5368	1.46232
$732$	−52.2961	−1.93292
$733$	−36.7789	−1.35846	−0.679230	−	0.733926i	$-0.737686\pi$
$733$	−36.7789	−1.35846	−0.679230	+	0.733926i	$0.737686\pi$
$734$	−15.3372	−0.566105
$735$	−20.0707	−0.740319
$736$	−101.861	−3.75466
$737$	−62.2591	−2.29334
$738$	28.3092	1.04208
$739$	−30.5903	−1.12528	−0.562641	−	0.826701i	$-0.690215\pi$
$739$	−30.5903	−1.12528	−0.562641	+	0.826701i	$0.690215\pi$
$740$	46.0769	1.69382
$741$	−67.6809	−2.48632
$742$	2.08513	0.0765476
$743$	11.2083	0.411194	0.205597	−	0.978637i	$-0.434086\pi$
$743$	11.2083	0.411194	0.205597	+	0.978637i	$0.434086\pi$
$744$	13.3095	0.487950
$745$	−7.70560	−0.282311
$746$	−62.7707	−2.29820
$747$	17.6782	0.646813
$748$	−189.290	−6.92112
$749$	−1.01331	−0.0370254
$750$	63.6115	2.32276
$751$	32.4108	1.18269	0.591343	−	0.806420i	$-0.298598\pi$
$751$	32.4108	1.18269	0.591343	+	0.806420i	$0.298598\pi$
$752$	−15.4383	−0.562978
$753$	5.67693	0.206879
$754$	−127.562	−4.64555
$755$	−2.52452	−0.0918768
$756$	−1.10884	−0.0403281
$757$	51.6029	1.87554	0.937770	−	0.347258i	$-0.112887\pi$
$757$	51.6029	1.87554	0.937770	+	0.347258i	$0.112887\pi$
$758$	81.4641	2.95891
$759$	55.6575	2.02024
$760$	−67.1395	−2.43541
$761$	−29.2089	−1.05882	−0.529412	−	0.848365i	$-0.677587\pi$
$761$	−29.2089	−1.05882	−0.529412	+	0.848365i	$0.677587\pi$
$762$	−59.0257	−2.13828
$763$	0.434424	0.0157272
$764$	128.961	4.66564
$765$	−14.1882	−0.512974
$766$	−62.5200	−2.25894
$767$	−54.0560	−1.95185
$768$	63.1719	2.27952
$769$	4.93363	0.177911	0.0889557	−	0.996036i	$-0.471647\pi$
$769$	4.93363	0.177911	0.0889557	+	0.996036i	$0.471647\pi$
$770$	−1.21564	−0.0438084
$771$	−31.5660	−1.13682
$772$	−44.6550	−1.60717
$773$	−12.7814	−0.459716	−0.229858	−	0.973224i	$-0.573826\pi$
$773$	−12.7814	−0.459716	−0.229858	+	0.973224i	$0.573826\pi$
$774$	23.2356	0.835185
$775$	2.18498	0.0784870
$776$	−85.8217	−3.08082
$777$	0.883228	0.0316856
$778$	−52.5152	−1.88276
$779$	−37.7556	−1.35274
$780$	−89.7884	−3.21494
$781$	−57.2101	−2.04714
$782$	97.5221	3.48738
$783$	25.4974	0.911202
$784$	−97.8413	−3.49433
$785$	5.51451	0.196821
$786$	66.6660	2.37790
$787$	−30.7053	−1.09453	−0.547263	−	0.836961i	$-0.684330\pi$
$787$	−30.7053	−1.09453	−0.547263	+	0.836961i	$0.684330\pi$
$788$	−143.706	−5.11930
$789$	−21.8393	−0.777499
$790$	28.6695	1.02002
$791$	0.176128	0.00626239
$792$	−69.7143	−2.47719
$793$	26.8574	0.953734
$794$	−11.2382	−0.398829
$795$	−33.7488	−1.19695
$796$	−113.435	−4.02061
$797$	10.9344	0.387315	0.193657	−	0.981069i	$-0.437965\pi$
$797$	10.9344	0.387315	0.193657	+	0.981069i	$0.437965\pi$
$798$	−2.05364	−0.0726981
$799$	7.68453	0.271859
$800$	62.6053	2.21343
$801$	7.59234	0.268262
$802$	15.4214	0.544550
$803$	59.2324	2.09026
$804$	−139.533	−4.92096
$805$	0.456043	0.0160734
$806$	−10.9072	−0.384190
$807$	38.4952	1.35510
$808$	10.4011	0.365910
$809$	−25.0744	−0.881568	−0.440784	−	0.897613i	$-0.645300\pi$
$809$	−25.0744	−0.881568	−0.440784	+	0.897613i	$0.645300\pi$
$810$	41.2315	1.44873
$811$	47.8008	1.67851	0.839256	−	0.543736i	$-0.182991\pi$
$811$	47.8008	1.67851	0.839256	+	0.543736i	$0.182991\pi$
$812$	−2.81843	−0.0989076
$813$	62.5662	2.19429
$814$	−87.6302	−3.07144
$815$	−8.45342	−0.296110
$816$	−206.730	−7.23700
$817$	−30.9890	−1.08417
$818$	−36.4057	−1.27290
$819$	−0.575827	−0.0201210
$820$	−50.0882	−1.74916
$821$	−35.6049	−1.24262	−0.621310	−	0.783565i	$-0.713399\pi$
$821$	−35.6049	−1.24262	−0.621310	+	0.783565i	$0.713399\pi$
$822$	−27.8356	−0.970877
$823$	4.69184	0.163547	0.0817736	−	0.996651i	$-0.473942\pi$
$823$	4.69184	0.163547	0.0817736	+	0.996651i	$0.473942\pi$
$824$	37.4174	1.30350
$825$	−34.2079	−1.19096
$826$	−1.64022	−0.0570706
$827$	57.4033	1.99611	0.998055	−	0.0623407i	$-0.0198565\pi$
$827$	57.4033	1.99611	0.998055	+	0.0623407i	$0.0198565\pi$
$828$	41.7332	1.45033
$829$	22.9788	0.798085	0.399043	−	0.916932i	$-0.369343\pi$
$829$	22.9788	0.798085	0.399043	+	0.916932i	$0.369343\pi$
$830$	−42.9556	−1.49101
$831$	−12.2707	−0.425667
$832$	−149.114	−5.16958
$833$	48.7011	1.68739
$834$	−49.2879	−1.70670
$835$	−2.88340	−0.0997842
$836$	148.365	5.13132
$837$	2.18015	0.0753570
$838$	−36.4124	−1.25785
$839$	5.02847	0.173602	0.0868011	−	0.996226i	$-0.472336\pi$
$839$	5.02847	0.173602	0.0868011	+	0.996226i	$0.472336\pi$
$840$	−1.70735	−0.0589090
$841$	35.8089	1.23479
$842$	−109.005	−3.75657
$843$	23.9501	0.824887
$844$	86.6722	2.98338
$845$	28.5464	0.982027
$846$	4.51615	0.155269
$847$	0.964600	0.0331441
$848$	−164.520	−5.64963
$849$	54.4937	1.87022
$850$	−59.9384	−2.05587
$851$	32.8743	1.12692
$852$	−128.218	−4.39266
$853$	−22.3529	−0.765348	−0.382674	−	0.923884i	$-0.624997\pi$
$853$	−22.3529	−0.765348	−0.382674	+	0.923884i	$0.624997\pi$
$854$	0.814933	0.0278864
$855$	11.1207	0.380319
$856$	141.202	4.82617
$857$	−16.5729	−0.566118	−0.283059	−	0.959103i	$-0.591349\pi$
$857$	−16.5729	−0.566118	−0.283059	+	0.959103i	$0.591349\pi$
$858$	170.762	5.82971
$859$	1.28482	0.0438373	0.0219187	−	0.999760i	$-0.493023\pi$
$859$	1.28482	0.0438373	0.0219187	+	0.999760i	$0.493023\pi$
$860$	−41.1113	−1.40188
$861$	−0.960119	−0.0327208
$862$	51.6537	1.75933
$863$	−25.6120	−0.871842	−0.435921	−	0.899985i	$-0.643577\pi$
$863$	−25.6120	−0.871842	−0.435921	+	0.899985i	$0.643577\pi$
$864$	62.4668	2.12516
$865$	−21.8836	−0.744066
$866$	−2.85016	−0.0968525
$867$	66.8054	2.26883
$868$	−0.240990	−0.00817972
$869$	−39.7025	−1.34681
$870$	62.6477	2.12396
$871$	71.6593	2.42808
$872$	−60.5360	−2.05001
$873$	14.2151	0.481109
$874$	−76.4378	−2.58555
$875$	−0.721797	−0.0244012
$876$	132.750	4.48520
$877$	28.0473	0.947089	0.473545	−	0.880770i	$-0.342974\pi$
$877$	28.0473	0.947089	0.473545	+	0.880770i	$0.342974\pi$
$878$	−69.0712	−2.33104
$879$	14.8907	0.502251
$880$	95.9152	3.23330
$881$	−24.5931	−0.828563	−0.414282	−	0.910149i	$-0.635967\pi$
$881$	−24.5931	−0.828563	−0.414282	+	0.910149i	$0.635967\pi$
$882$	28.6214	0.963732
$883$	−21.3986	−0.720119	−0.360060	−	0.932929i	$-0.617244\pi$
$883$	−21.3986	−0.720119	−0.360060	+	0.932929i	$0.617244\pi$
$884$	217.870	7.32775
$885$	26.5477	0.892391
$886$	57.9112	1.94557
$887$	4.86180	0.163243	0.0816216	−	0.996663i	$-0.473990\pi$
$887$	4.86180	0.163243	0.0816216	+	0.996663i	$0.473990\pi$
$888$	−123.076	−4.13015
$889$	0.669763	0.0224631
$890$	−18.4483	−0.618388
$891$	−57.0988	−1.91288
$892$	−65.8646	−2.20531
$893$	−6.02313	−0.201556
$894$	32.8437	1.09846
$895$	−1.96413	−0.0656536
$896$	−1.94676	−0.0650367
$897$	−64.0610	−2.13893
$898$	−34.4088	−1.14824
$899$	5.54147	0.184818
$900$	−25.6498	−0.854992
$901$	81.8907	2.72818
$902$	95.2590	3.17178
$903$	−0.788044	−0.0262245
$904$	−24.5430	−0.816289
$905$	−23.6695	−0.786802
$906$	10.7603	0.357487
$907$	5.69128	0.188976	0.0944879	−	0.995526i	$-0.469879\pi$
$907$	5.69128	0.188976	0.0944879	+	0.995526i	$0.469879\pi$
$908$	−100.410	−3.33224
$909$	−1.72279	−0.0571414
$910$	1.39918	0.0463823
$911$	32.2914	1.06986	0.534930	−	0.844896i	$-0.320338\pi$
$911$	32.2914	1.06986	0.534930	+	0.844896i	$0.320338\pi$
$912$	162.035	5.36551
$913$	59.4863	1.96871
$914$	26.7745	0.885623
$915$	−13.1901	−0.436050
$916$	106.176	3.50816
$917$	−0.756457	−0.0249804
$918$	−59.8058	−1.97388
$919$	53.8803	1.77735	0.888673	−	0.458542i	$-0.151628\pi$
$919$	53.8803	1.77735	0.888673	+	0.458542i	$0.151628\pi$
$920$	−63.5485	−2.09513
$921$	−32.7657	−1.07967
$922$	64.0972	2.11093
$923$	65.8480	2.16741
$924$	3.77290	0.124119
$925$	−20.2050	−0.664336
$926$	−56.5227	−1.85745
$927$	−6.19765	−0.203558
$928$	158.777	5.21212
$929$	8.03593	0.263650	0.131825	−	0.991273i	$-0.457916\pi$
$929$	8.03593	0.263650	0.131825	+	0.991273i	$0.457916\pi$
$930$	5.35668	0.175653
$931$	−38.1719	−1.25103
$932$	−5.50769	−0.180410
$933$	−13.5712	−0.444301
$934$	−77.3563	−2.53118
$935$	−47.7424	−1.56134
$936$	80.2401	2.62273
$937$	−4.90054	−0.160094	−0.0800469	−	0.996791i	$-0.525507\pi$
$937$	−4.90054	−0.160094	−0.0800469	+	0.996791i	$0.525507\pi$
$938$	2.17436	0.0709952
$939$	59.7861	1.95105
$940$	−7.99055	−0.260623
$941$	13.9795	0.455717	0.227859	−	0.973694i	$-0.426828\pi$
$941$	13.9795	0.455717	0.227859	+	0.973694i	$0.426828\pi$
$942$	−23.5046	−0.765820
$943$	−35.7362	−1.16373
$944$	129.416	4.21212
$945$	−0.279670	−0.00909767
$946$	78.1864	2.54206
$947$	25.0025	0.812472	0.406236	−	0.913768i	$-0.366841\pi$
$947$	25.0025	0.812472	0.406236	+	0.913768i	$0.366841\pi$
$948$	−88.9801	−2.88994
$949$	−68.1756	−2.21307
$950$	46.9797	1.52422
$951$	−59.2314	−1.92071
$952$	4.14284	0.134270
$953$	15.6809	0.507953	0.253977	−	0.967210i	$-0.418261\pi$
$953$	15.6809	0.507953	0.253977	+	0.967210i	$0.418261\pi$
$954$	48.1267	1.55816
$955$	32.5263	1.05253
$956$	−44.1125	−1.42670
$957$	−86.7566	−2.80444
$958$	−107.787	−3.48244
$959$	0.315849	0.0101993
$960$	73.2318	2.36355
$961$	−30.5262	−0.984715
$962$	100.861	3.25189
$963$	−23.3880	−0.753668
$964$	38.5794	1.24256
$965$	−11.2628	−0.362563
$966$	−1.94380	−0.0625407
$967$	1.99695	0.0642176	0.0321088	−	0.999484i	$-0.489778\pi$
$967$	1.99695	0.0642176	0.0321088	+	0.999484i	$0.489778\pi$
$968$	−134.415	−4.32025
$969$	−80.6539	−2.59098
$970$	−34.5407	−1.10904
$971$	−39.9196	−1.28108	−0.640540	−	0.767925i	$-0.721289\pi$
$971$	−39.9196	−1.28108	−0.640540	+	0.767925i	$0.721289\pi$
$972$	−77.0652	−2.47187
$973$	0.559268	0.0179293
$974$	83.7982	2.68507
$975$	39.3727	1.26094
$976$	−64.2993	−2.05817
$977$	19.1945	0.614088	0.307044	−	0.951695i	$-0.400660\pi$
$977$	19.1945	0.614088	0.307044	+	0.951695i	$0.400660\pi$
$978$	36.0311	1.15215
$979$	25.5478	0.816511
$980$	−50.6405	−1.61765
$981$	10.0269	0.320134
$982$	−55.6950	−1.77730
$983$	−37.6242	−1.20003	−0.600013	−	0.799991i	$-0.704838\pi$
$983$	−37.6242	−1.20003	−0.600013	+	0.799991i	$0.704838\pi$
$984$	133.790	4.26507
$985$	−36.2452	−1.15487
$986$	−152.013	−4.84109
$987$	−0.153167	−0.00487536
$988$	−170.766	−5.43280
$989$	−29.3315	−0.932687
$990$	−28.0580	−0.891740
$991$	−58.0436	−1.84382	−0.921908	−	0.387409i	$-0.873370\pi$
$991$	−58.0436	−1.84382	−0.921908	+	0.387409i	$0.873370\pi$
$992$	13.5762	0.431045
$993$	56.0281	1.77800
$994$	1.99802	0.0633734
$995$	−28.6105	−0.907015
$996$	133.319	4.22438
$997$	−24.9105	−0.788922	−0.394461	−	0.918913i	$-0.629069\pi$
$997$	−24.9105	−0.788922	−0.394461	+	0.918913i	$0.629069\pi$
$998$	36.5903	1.15825
$999$	−20.1603	−0.637843

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.b.1.11	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.71243 q^{2} +2.12328 q^{3} +5.35728 q^{4} +1.35121 q^{5} -5.75926 q^{6} +0.0653501 q^{7} -9.10638 q^{8} +1.50834 q^{9} +O(q^{10})\)	\(q-2.71243 q^{2} +2.12328 q^{3} +5.35728 q^{4} +1.35121 q^{5} -5.75926 q^{6} +0.0653501 q^{7} -9.10638 q^{8} +1.50834 q^{9} -3.66505 q^{10} +5.07548 q^{11} +11.3750 q^{12} -5.84180 q^{13} -0.177258 q^{14} +2.86899 q^{15} +13.9859 q^{16} -6.96155 q^{17} -4.09126 q^{18} +5.45646 q^{19} +7.23878 q^{20} +0.138757 q^{21} -13.7669 q^{22} +5.16462 q^{23} -19.3354 q^{24} -3.17424 q^{25} +15.8455 q^{26} -3.16722 q^{27} +0.350099 q^{28} -8.05040 q^{29} -7.78194 q^{30} -0.688348 q^{31} -19.7229 q^{32} +10.7767 q^{33} +18.8827 q^{34} +0.0883014 q^{35} +8.08059 q^{36} +6.36529 q^{37} -14.8003 q^{38} -12.4038 q^{39} -12.3046 q^{40} -6.91943 q^{41} -0.376368 q^{42} -5.67931 q^{43} +27.1907 q^{44} +2.03808 q^{45} -14.0087 q^{46} -1.10385 q^{47} +29.6960 q^{48} -6.99573 q^{49} +8.60992 q^{50} -14.7814 q^{51} -31.2961 q^{52} -11.7633 q^{53} +8.59087 q^{54} +6.85801 q^{55} -0.595103 q^{56} +11.5856 q^{57} +21.8361 q^{58} +9.25331 q^{59} +15.3700 q^{60} -4.59745 q^{61} +1.86710 q^{62} +0.0985701 q^{63} +25.5253 q^{64} -7.89347 q^{65} -29.2310 q^{66} -12.2666 q^{67} -37.2950 q^{68} +10.9660 q^{69} -0.239511 q^{70} -11.2719 q^{71} -13.7355 q^{72} +11.6703 q^{73} -17.2654 q^{74} -6.73983 q^{75} +29.2318 q^{76} +0.331683 q^{77} +33.6445 q^{78} -7.82241 q^{79} +18.8978 q^{80} -11.2499 q^{81} +18.7685 q^{82} +11.7203 q^{83} +0.743359 q^{84} -9.40649 q^{85} +15.4047 q^{86} -17.0933 q^{87} -46.2192 q^{88} +5.03357 q^{89} -5.52814 q^{90} -0.381762 q^{91} +27.6683 q^{92} -1.46156 q^{93} +2.99412 q^{94} +7.37280 q^{95} -41.8773 q^{96} +9.42436 q^{97} +18.9754 q^{98} +7.65555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) \) 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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