LMFDB - Embedded newform 6037.2.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, 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("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72852 q^{2} -2.79225 q^{3} +5.44481 q^{4} +1.20025 q^{5} +7.61871 q^{6} +1.91493 q^{7} -9.39922 q^{8} +4.79667 q^{9} +O(q^{10})$	\(q-2.72852 q^{2} -2.79225 q^{3} +5.44481 q^{4} +1.20025 q^{5} +7.61871 q^{6} +1.91493 q^{7} -9.39922 q^{8} +4.79667 q^{9} -3.27490 q^{10} +0.521857 q^{11} -15.2033 q^{12} +3.17959 q^{13} -5.22493 q^{14} -3.35139 q^{15} +14.7563 q^{16} -4.95996 q^{17} -13.0878 q^{18} +6.91410 q^{19} +6.53512 q^{20} -5.34698 q^{21} -1.42390 q^{22} -6.73892 q^{23} +26.2450 q^{24} -3.55940 q^{25} -8.67557 q^{26} -5.01674 q^{27} +10.4265 q^{28} +7.28495 q^{29} +9.14434 q^{30} +7.05583 q^{31} -21.4644 q^{32} -1.45716 q^{33} +13.5333 q^{34} +2.29840 q^{35} +26.1169 q^{36} -9.15605 q^{37} -18.8652 q^{38} -8.87822 q^{39} -11.2814 q^{40} +1.00282 q^{41} +14.5893 q^{42} +3.65698 q^{43} +2.84141 q^{44} +5.75719 q^{45} +18.3873 q^{46} +0.989020 q^{47} -41.2033 q^{48} -3.33302 q^{49} +9.71190 q^{50} +13.8495 q^{51} +17.3123 q^{52} +9.54968 q^{53} +13.6883 q^{54} +0.626358 q^{55} -17.9989 q^{56} -19.3059 q^{57} -19.8771 q^{58} -13.7900 q^{59} -18.2477 q^{60} +3.42434 q^{61} -19.2520 q^{62} +9.18530 q^{63} +29.0534 q^{64} +3.81630 q^{65} +3.97587 q^{66} -8.60500 q^{67} -27.0060 q^{68} +18.8168 q^{69} -6.27122 q^{70} -11.3459 q^{71} -45.0849 q^{72} +15.5383 q^{73} +24.9824 q^{74} +9.93875 q^{75} +37.6460 q^{76} +0.999322 q^{77} +24.2244 q^{78} +1.09554 q^{79} +17.7112 q^{80} -0.381988 q^{81} -2.73622 q^{82} -9.58358 q^{83} -29.1133 q^{84} -5.95318 q^{85} -9.97814 q^{86} -20.3414 q^{87} -4.90505 q^{88} -7.94134 q^{89} -15.7086 q^{90} +6.08871 q^{91} -36.6921 q^{92} -19.7017 q^{93} -2.69856 q^{94} +8.29864 q^{95} +59.9341 q^{96} -9.45839 q^{97} +9.09422 q^{98} +2.50317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) $ 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * 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 $

$2$	−2.72852	−1.92935	−0.964677	−	0.263437i	$-0.915144\pi$
$2$	−2.72852	−1.92935	−0.964677	+	0.263437i	$0.915144\pi$
$3$	−2.79225	−1.61211	−0.806053	−	0.591843i	$-0.798401\pi$
$3$	−2.79225	−1.61211	−0.806053	+	0.591843i	$0.798401\pi$
$4$	5.44481	2.72240
$5$	1.20025	0.536767	0.268384	−	0.963312i	$-0.413511\pi$
$5$	1.20025	0.536767	0.268384	+	0.963312i	$0.413511\pi$
$6$	7.61871	3.11032
$7$	1.91493	0.723777	0.361889	−	0.932221i	$-0.382132\pi$
$7$	1.91493	0.723777	0.361889	+	0.932221i	$0.382132\pi$
$8$	−9.39922	−3.32313
$9$	4.79667	1.59889
$10$	−3.27490	−1.03561
$11$	0.521857	0.157346	0.0786729	−	0.996900i	$-0.474932\pi$
$11$	0.521857	0.157346	0.0786729	+	0.996900i	$0.474932\pi$
$12$	−15.2033	−4.38881
$13$	3.17959	0.881860	0.440930	−	0.897541i	$-0.354649\pi$
$13$	3.17959	0.881860	0.440930	+	0.897541i	$0.354649\pi$
$14$	−5.22493	−1.39642
$15$	−3.35139	−0.865326
$16$	14.7563	3.68908
$17$	−4.95996	−1.20297	−0.601483	−	0.798885i	$-0.705423\pi$
$17$	−4.95996	−1.20297	−0.601483	+	0.798885i	$0.705423\pi$
$18$	−13.0878	−3.08482
$19$	6.91410	1.58620	0.793102	−	0.609089i	$-0.208465\pi$
$19$	6.91410	1.58620	0.793102	+	0.609089i	$0.208465\pi$
$20$	6.53512	1.46130
$21$	−5.34698	−1.16681
$22$	−1.42390	−0.303575
$23$	−6.73892	−1.40516	−0.702581	−	0.711604i	$-0.747969\pi$
$23$	−6.73892	−1.40516	−0.702581	+	0.711604i	$0.747969\pi$
$24$	26.2450	5.35723
$25$	−3.55940	−0.711881
$26$	−8.67557	−1.70142
$27$	−5.01674	−0.965473
$28$	10.4265	1.97041
$29$	7.28495	1.35278	0.676391	−	0.736543i	$-0.263543\pi$
$29$	7.28495	1.35278	0.676391	+	0.736543i	$0.263543\pi$
$30$	9.14434	1.66952
$31$	7.05583	1.26726	0.633632	−	0.773634i	$-0.281563\pi$
$31$	7.05583	1.26726	0.633632	+	0.773634i	$0.281563\pi$
$32$	−21.4644	−3.79441
$33$	−1.45716	−0.253658
$34$	13.5333	2.32095
$35$	2.29840	0.388500
$36$	26.1169	4.35282
$37$	−9.15605	−1.50525	−0.752623	−	0.658452i	$-0.771212\pi$
$37$	−9.15605	−1.50525	−0.752623	+	0.658452i	$0.771212\pi$
$38$	−18.8652	−3.06035
$39$	−8.87822	−1.42165
$40$	−11.2814	−1.78375
$41$	1.00282	0.156614	0.0783072	−	0.996929i	$-0.475048\pi$
$41$	1.00282	0.156614	0.0783072	+	0.996929i	$0.475048\pi$
$42$	14.5893	2.25118
$43$	3.65698	0.557684	0.278842	−	0.960337i	$-0.410049\pi$
$43$	3.65698	0.557684	0.278842	+	0.960337i	$0.410049\pi$
$44$	2.84141	0.428359
$45$	5.75719	0.858231
$46$	18.3873	2.71105
$47$	0.989020	0.144263	0.0721317	−	0.997395i	$-0.477020\pi$
$47$	0.989020	0.144263	0.0721317	+	0.997395i	$0.477020\pi$
$48$	−41.2033	−5.94719
$49$	−3.33302	−0.476146
$50$	9.71190	1.37347
$51$	13.8495	1.93931
$52$	17.3123	2.40078
$53$	9.54968	1.31175	0.655875	−	0.754870i	$-0.272300\pi$
$53$	9.54968	1.31175	0.655875	+	0.754870i	$0.272300\pi$
$54$	13.6883	1.86274
$55$	0.626358	0.0844580
$56$	−17.9989	−2.40520
$57$	−19.3059	−2.55713
$58$	−19.8771	−2.60999
$59$	−13.7900	−1.79530	−0.897652	−	0.440705i	$-0.854728\pi$
$59$	−13.7900	−1.79530	−0.897652	+	0.440705i	$0.854728\pi$
$60$	−18.2477	−2.35577
$61$	3.42434	0.438442	0.219221	−	0.975675i	$-0.429648\pi$
$61$	3.42434	0.438442	0.219221	+	0.975675i	$0.429648\pi$
$62$	−19.2520	−2.44500
$63$	9.18530	1.15724
$64$	29.0534	3.63168
$65$	3.81630	0.473354
$66$	3.97587	0.489396
$67$	−8.60500	−1.05127	−0.525634	−	0.850711i	$-0.676172\pi$
$67$	−8.60500	−1.05127	−0.525634	+	0.850711i	$0.676172\pi$
$68$	−27.0060	−3.27496
$69$	18.8168	2.26527
$70$	−6.27122	−0.749554
$71$	−11.3459	−1.34651	−0.673253	−	0.739412i	$-0.735104\pi$
$71$	−11.3459	−1.34651	−0.673253	+	0.739412i	$0.735104\pi$
$72$	−45.0849	−5.31331
$73$	15.5383	1.81862	0.909308	−	0.416123i	$-0.136611\pi$
$73$	15.5383	1.81862	0.909308	+	0.416123i	$0.136611\pi$
$74$	24.9824	2.90415
$75$	9.93875	1.14763
$76$	37.6460	4.31829
$77$	0.999322	0.113883
$78$	24.2244	2.74287
$79$	1.09554	0.123258	0.0616290	−	0.998099i	$-0.480370\pi$
$79$	1.09554	0.123258	0.0616290	+	0.998099i	$0.480370\pi$
$80$	17.7112	1.98018
$81$	−0.381988	−0.0424431
$82$	−2.73622	−0.302165
$83$	−9.58358	−1.05193	−0.525967	−	0.850505i	$-0.676297\pi$
$83$	−9.58358	−1.05193	−0.525967	+	0.850505i	$0.676297\pi$
$84$	−29.1133	−3.17652
$85$	−5.95318	−0.645713
$86$	−9.97814	−1.07597
$87$	−20.3414	−2.18083
$88$	−4.90505	−0.522880
$89$	−7.94134	−0.841780	−0.420890	−	0.907112i	$-0.638282\pi$
$89$	−7.94134	−0.841780	−0.420890	+	0.907112i	$0.638282\pi$
$90$	−15.7086	−1.65583
$91$	6.08871	0.638270
$92$	−36.6921	−3.82542
$93$	−19.7017	−2.04297
$94$	−2.69856	−0.278335
$95$	8.29864	0.851422
$96$	59.9341	6.11700
$97$	−9.45839	−0.960354	−0.480177	−	0.877172i	$-0.659428\pi$
$97$	−9.45839	−0.960354	−0.480177	+	0.877172i	$0.659428\pi$
$98$	9.09422	0.918654
$99$	2.50317	0.251578
$100$	−19.3803	−1.93803
$101$	−10.4086	−1.03569	−0.517845	−	0.855474i	$-0.673266\pi$
$101$	−10.4086	−1.03569	−0.517845	+	0.855474i	$0.673266\pi$
$102$	−37.7885	−3.74162
$103$	−15.7224	−1.54918	−0.774589	−	0.632465i	$-0.782043\pi$
$103$	−15.7224	−1.54918	−0.774589	+	0.632465i	$0.782043\pi$
$104$	−29.8857	−2.93053
$105$	−6.41770	−0.626304
$106$	−26.0565	−2.53083
$107$	17.9916	1.73931	0.869656	−	0.493658i	$-0.164340\pi$
$107$	17.9916	1.73931	0.869656	+	0.493658i	$0.164340\pi$
$108$	−27.3152	−2.62841
$109$	−9.06477	−0.868247	−0.434124	−	0.900853i	$-0.642942\pi$
$109$	−9.06477	−0.868247	−0.434124	+	0.900853i	$0.642942\pi$
$110$	−1.70903	−0.162949
$111$	25.5660	2.42662
$112$	28.2574	2.67007
$113$	−14.3513	−1.35006	−0.675030	−	0.737790i	$-0.735869\pi$
$113$	−14.3513	−1.35006	−0.675030	+	0.737790i	$0.735869\pi$
$114$	52.6765	4.93361
$115$	−8.08838	−0.754245
$116$	39.6652	3.68282
$117$	15.2514	1.41000
$118$	37.6262	3.46378
$119$	−9.49800	−0.870680
$120$	31.5005	2.87559
$121$	−10.7277	−0.975242
$122$	−9.34337	−0.845909
$123$	−2.80013	−0.252479
$124$	38.4177	3.45001
$125$	−10.2734	−0.918882
$126$	−25.0623	−2.23272
$127$	−6.01186	−0.533467	−0.266733	−	0.963770i	$-0.585944\pi$
$127$	−6.01186	−0.533467	−0.266733	+	0.963770i	$0.585944\pi$
$128$	−36.3440	−3.21238
$129$	−10.2112	−0.899047
$130$	−10.4128	−0.913266
$131$	−11.3081	−0.987993	−0.493997	−	0.869464i	$-0.664465\pi$
$131$	−11.3081	−0.987993	−0.493997	+	0.869464i	$0.664465\pi$
$132$	−7.93393	−0.690560
$133$	13.2401	1.14806
$134$	23.4789	2.02827
$135$	−6.02134	−0.518234
$136$	46.6197	3.99761
$137$	4.96490	0.424180	0.212090	−	0.977250i	$-0.431973\pi$
$137$	4.96490	0.424180	0.212090	+	0.977250i	$0.431973\pi$
$138$	−51.3419	−4.37051
$139$	−16.3922	−1.39037	−0.695183	−	0.718833i	$-0.744677\pi$
$139$	−16.3922	−1.39037	−0.695183	+	0.718833i	$0.744677\pi$
$140$	12.5143	1.05765
$141$	−2.76159	−0.232568
$142$	30.9574	2.59789
$143$	1.65929	0.138757
$144$	70.7811	5.89843
$145$	8.74375	0.726129
$146$	−42.3964	−3.50875
$147$	9.30664	0.767599
$148$	−49.8529	−4.09789
$149$	18.9882	1.55557	0.777786	−	0.628529i	$-0.216343\pi$
$149$	18.9882	1.55557	0.777786	+	0.628529i	$0.216343\pi$
$150$	−27.1181	−2.21418
$151$	8.95629	0.728853	0.364426	−	0.931232i	$-0.381265\pi$
$151$	8.95629	0.728853	0.364426	+	0.931232i	$0.381265\pi$
$152$	−64.9871	−5.27115
$153$	−23.7913	−1.92341
$154$	−2.72667	−0.219721
$155$	8.46875	0.680226
$156$	−48.3402	−3.87031
$157$	−16.2877	−1.29990	−0.649952	−	0.759975i	$-0.725211\pi$
$157$	−16.2877	−1.29990	−0.649952	+	0.759975i	$0.725211\pi$
$158$	−2.98920	−0.237808
$159$	−26.6651	−2.11468
$160$	−25.7626	−2.03672
$161$	−12.9046	−1.01702
$162$	1.04226	0.0818878
$163$	0.842344	0.0659775	0.0329887	−	0.999456i	$-0.489497\pi$
$163$	0.842344	0.0659775	0.0329887	+	0.999456i	$0.489497\pi$
$164$	5.46017	0.426368
$165$	−1.74895	−0.136155
$166$	26.1490	2.02955
$167$	−23.3048	−1.80338	−0.901688	−	0.432387i	$-0.857671\pi$
$167$	−23.3048	−1.80338	−0.901688	+	0.432387i	$0.857671\pi$
$168$	50.2574	3.87744
$169$	−2.89020	−0.222323
$170$	16.2434	1.24581
$171$	33.1646	2.53616
$172$	19.9116	1.51824
$173$	22.3173	1.69676	0.848378	−	0.529391i	$-0.177579\pi$
$173$	22.3173	1.69676	0.848378	+	0.529391i	$0.177579\pi$
$174$	55.5019	4.20759
$175$	−6.81603	−0.515243
$176$	7.70068	0.580461
$177$	38.5051	2.89422
$178$	21.6681	1.62409
$179$	9.38952	0.701806	0.350903	−	0.936412i	$-0.385875\pi$
$179$	9.38952	0.701806	0.350903	+	0.936412i	$0.385875\pi$
$180$	31.3468	2.33645
$181$	23.8184	1.77041	0.885205	−	0.465201i	$-0.154018\pi$
$181$	23.8184	1.77041	0.885205	+	0.465201i	$0.154018\pi$
$182$	−16.6132	−1.23145
$183$	−9.56162	−0.706815
$184$	63.3406	4.66953
$185$	−10.9895	−0.807967
$186$	53.7563	3.94160
$187$	−2.58839	−0.189282
$188$	5.38502	0.392743
$189$	−9.60674	−0.698787
$190$	−22.6430	−1.64269
$191$	6.07999	0.439933	0.219966	−	0.975507i	$-0.429405\pi$
$191$	6.07999	0.439933	0.219966	+	0.975507i	$0.429405\pi$
$192$	−81.1245	−5.85466
$193$	−6.87647	−0.494979	−0.247490	−	0.968891i	$-0.579606\pi$
$193$	−6.87647	−0.494979	−0.247490	+	0.968891i	$0.579606\pi$
$194$	25.8074	1.85286
$195$	−10.6561	−0.763097
$196$	−18.1477	−1.29626
$197$	−17.8644	−1.27278	−0.636391	−	0.771366i	$-0.719574\pi$
$197$	−17.8644	−1.27278	−0.636391	+	0.771366i	$0.719574\pi$
$198$	−6.82995	−0.485383
$199$	−15.1417	−1.07337	−0.536684	−	0.843783i	$-0.680323\pi$
$199$	−15.1417	−1.07337	−0.536684	+	0.843783i	$0.680323\pi$
$200$	33.4556	2.36567
$201$	24.0273	1.69476
$202$	28.3999	1.99821
$203$	13.9502	0.979113
$204$	75.4076	5.27959
$205$	1.20364	0.0840655
$206$	42.8990	2.98891
$207$	−32.3244	−2.24670
$208$	46.9191	3.25325
$209$	3.60817	0.249582
$210$	17.5108	1.20836
$211$	0.194521	0.0133914	0.00669568	−	0.999978i	$-0.497869\pi$
$211$	0.194521	0.0133914	0.00669568	+	0.999978i	$0.497869\pi$
$212$	51.9962	3.57111
$213$	31.6805	2.17071
$214$	−49.0904	−3.35575
$215$	4.38929	0.299347
$216$	47.1535	3.20839
$217$	13.5115	0.917218
$218$	24.7334	1.67516
$219$	−43.3868	−2.93181
$220$	3.41040	0.229929
$221$	−15.7706	−1.06085
$222$	−69.7573	−4.68180
$223$	5.60637	0.375430	0.187715	−	0.982223i	$-0.439892\pi$
$223$	5.60637	0.375430	0.187715	+	0.982223i	$0.439892\pi$
$224$	−41.1030	−2.74631
$225$	−17.0733	−1.13822
$226$	39.1579	2.60474
$227$	23.5120	1.56055	0.780274	−	0.625438i	$-0.215080\pi$
$227$	23.5120	1.56055	0.780274	+	0.625438i	$0.215080\pi$
$228$	−105.117	−6.96154
$229$	10.7375	0.709551	0.354775	−	0.934952i	$-0.384557\pi$
$229$	10.7375	0.709551	0.354775	+	0.934952i	$0.384557\pi$
$230$	22.0693	1.45521
$231$	−2.79036	−0.183592
$232$	−68.4729	−4.49546
$233$	4.63582	0.303703	0.151851	−	0.988403i	$-0.451476\pi$
$233$	4.63582	0.303703	0.151851	+	0.988403i	$0.451476\pi$
$234$	−41.6138	−2.72038
$235$	1.18707	0.0774359
$236$	−75.0839	−4.88754
$237$	−3.05903	−0.198705
$238$	25.9155	1.67985
$239$	−21.2353	−1.37360	−0.686798	−	0.726848i	$-0.740984\pi$
$239$	−21.2353	−1.37360	−0.686798	+	0.726848i	$0.740984\pi$
$240$	−49.4542	−3.19226
$241$	6.77187	0.436215	0.218107	−	0.975925i	$-0.430012\pi$
$241$	6.77187	0.436215	0.218107	+	0.975925i	$0.430012\pi$
$242$	29.2706	1.88159
$243$	16.1168	1.03390
$244$	18.6449	1.19362
$245$	−4.00046	−0.255580
$246$	7.64021	0.487122
$247$	21.9840	1.39881
$248$	−66.3193	−4.21128
$249$	26.7598	1.69583
$250$	28.0312	1.77285
$251$	−21.2802	−1.34320	−0.671598	−	0.740916i	$-0.734392\pi$
$251$	−21.2802	−1.34320	−0.671598	+	0.740916i	$0.734392\pi$
$252$	50.0122	3.15047
$253$	−3.51675	−0.221096
$254$	16.4035	1.02925
$255$	16.6228	1.04096
$256$	41.0583	2.56614
$257$	6.22380	0.388230	0.194115	−	0.980979i	$-0.437816\pi$
$257$	6.22380	0.388230	0.194115	+	0.980979i	$0.437816\pi$
$258$	27.8615	1.73458
$259$	−17.5332	−1.08946
$260$	20.7790	1.28866
$261$	34.9435	2.16295
$262$	30.8544	1.90619
$263$	19.3708	1.19446	0.597228	−	0.802072i	$-0.296269\pi$
$263$	19.3708	1.19446	0.597228	+	0.802072i	$0.296269\pi$
$264$	13.6961	0.842938
$265$	11.4620	0.704105
$266$	−36.1257	−2.21501
$267$	22.1742	1.35704
$268$	−46.8526	−2.86198
$269$	−22.4282	−1.36747	−0.683737	−	0.729729i	$-0.739646\pi$
$269$	−22.4282	−1.36747	−0.683737	+	0.729729i	$0.739646\pi$
$270$	16.4293	0.999857
$271$	−23.7523	−1.44285	−0.721426	−	0.692491i	$-0.756513\pi$
$271$	−23.7523	−1.44285	−0.721426	+	0.692491i	$0.756513\pi$
$272$	−73.1907	−4.43784
$273$	−17.0012	−1.02896
$274$	−13.5468	−0.818392
$275$	−1.85750	−0.112011
$276$	102.454	6.16699
$277$	16.1248	0.968842	0.484421	−	0.874835i	$-0.339030\pi$
$277$	16.1248	0.968842	0.484421	+	0.874835i	$0.339030\pi$
$278$	44.7263	2.68251
$279$	33.8445	2.02622
$280$	−21.6031	−1.29103
$281$	12.8080	0.764060	0.382030	−	0.924150i	$-0.375225\pi$
$281$	12.8080	0.764060	0.382030	+	0.924150i	$0.375225\pi$
$282$	7.53505	0.448706
$283$	−7.65087	−0.454797	−0.227399	−	0.973802i	$-0.573022\pi$
$283$	−7.65087	−0.454797	−0.227399	+	0.973802i	$0.573022\pi$
$284$	−61.7760	−3.66573
$285$	−23.1719	−1.37258
$286$	−4.52741	−0.267711
$287$	1.92034	0.113354
$288$	−102.958	−6.06684
$289$	7.60120	0.447129
$290$	−23.8575	−1.40096
$291$	26.4102	1.54819
$292$	84.6029	4.95101
$293$	32.6435	1.90705	0.953527	−	0.301309i	$-0.0974236\pi$
$293$	32.6435	1.90705	0.953527	+	0.301309i	$0.0974236\pi$
$294$	−25.3933	−1.48097
$295$	−16.5514	−0.963661
$296$	86.0597	5.00212
$297$	−2.61802	−0.151913
$298$	−51.8096	−3.00125
$299$	−21.4270	−1.23916
$300$	54.1146	3.12431
$301$	7.00288	0.403639
$302$	−24.4374	−1.40621
$303$	29.0633	1.66964
$304$	102.027	5.85163
$305$	4.11006	0.235341
$306$	64.9149	3.71094
$307$	25.9884	1.48323	0.741617	−	0.670824i	$-0.234059\pi$
$307$	25.9884	1.48323	0.741617	+	0.670824i	$0.234059\pi$
$308$	5.44111	0.310036
$309$	43.9010	2.49744
$310$	−23.1071	−1.31240
$311$	7.03372	0.398846	0.199423	−	0.979914i	$-0.436093\pi$
$311$	7.03372	0.398846	0.199423	+	0.979914i	$0.436093\pi$
$312$	83.4483	4.72433
$313$	−6.30855	−0.356580	−0.178290	−	0.983978i	$-0.557057\pi$
$313$	−6.30855	−0.356580	−0.178290	+	0.983978i	$0.557057\pi$
$314$	44.4414	2.50797
$315$	11.0246	0.621168
$316$	5.96501	0.335558
$317$	17.3976	0.977149	0.488575	−	0.872522i	$-0.337517\pi$
$317$	17.3976	0.977149	0.488575	+	0.872522i	$0.337517\pi$
$318$	72.7562	4.07997
$319$	3.80170	0.212854
$320$	34.8713	1.94937
$321$	−50.2370	−2.80396
$322$	35.2104	1.96220
$323$	−34.2937	−1.90815
$324$	−2.07985	−0.115547
$325$	−11.3175	−0.627779
$326$	−2.29835	−0.127294
$327$	25.3111	1.39971
$328$	−9.42574	−0.520450
$329$	1.89391	0.104415
$330$	4.77204	0.262692
$331$	−17.0353	−0.936345	−0.468172	−	0.883637i	$-0.655087\pi$
$331$	−17.0353	−0.936345	−0.468172	+	0.883637i	$0.655087\pi$
$332$	−52.1807	−2.86379
$333$	−43.9185	−2.40672
$334$	63.5874	3.47935
$335$	−10.3281	−0.564287
$336$	−78.9017	−4.30444
$337$	−28.3176	−1.54256	−0.771279	−	0.636497i	$-0.780383\pi$
$337$	−28.3176	−1.54256	−0.771279	+	0.636497i	$0.780383\pi$
$338$	7.88596	0.428939
$339$	40.0725	2.17644
$340$	−32.4139	−1.75789
$341$	3.68213	0.199399
$342$	−90.4903	−4.89315
$343$	−19.7871	−1.06840
$344$	−34.3728	−1.85326
$345$	22.5848	1.21592
$346$	−60.8933	−3.27364
$347$	2.43266	0.130592	0.0652960	−	0.997866i	$-0.479201\pi$
$347$	2.43266	0.130592	0.0652960	+	0.997866i	$0.479201\pi$
$348$	−110.755	−5.93710
$349$	−12.8290	−0.686723	−0.343361	−	0.939203i	$-0.611566\pi$
$349$	−12.8290	−0.686723	−0.343361	+	0.939203i	$0.611566\pi$
$350$	18.5976	0.994086
$351$	−15.9512	−0.851412
$352$	−11.2014	−0.597034
$353$	14.0560	0.748128	0.374064	−	0.927403i	$-0.377964\pi$
$353$	14.0560	0.748128	0.374064	+	0.927403i	$0.377964\pi$
$354$	−105.062	−5.58398
$355$	−13.6179	−0.722761
$356$	−43.2391	−2.29167
$357$	26.5208	1.40363
$358$	−25.6195	−1.35403
$359$	19.4546	1.02678	0.513388	−	0.858157i	$-0.328390\pi$
$359$	19.4546	1.02678	0.513388	+	0.858157i	$0.328390\pi$
$360$	−54.1131	−2.85201
$361$	28.8048	1.51604
$362$	−64.9890	−3.41575
$363$	29.9543	1.57219
$364$	33.1519	1.73763
$365$	18.6498	0.976174
$366$	26.0890	1.36370
$367$	−11.1557	−0.582320	−0.291160	−	0.956674i	$-0.594041\pi$
$367$	−11.1557	−0.582320	−0.291160	+	0.956674i	$0.594041\pi$
$368$	−99.4417	−5.18376
$369$	4.81020	0.250409
$370$	29.9851	1.55885
$371$	18.2870	0.949415
$372$	−107.272	−5.56178
$373$	32.5915	1.68752	0.843762	−	0.536717i	$-0.180336\pi$
$373$	32.5915	1.68752	0.843762	+	0.536717i	$0.180336\pi$
$374$	7.06246	0.365191
$375$	28.6859	1.48134
$376$	−9.29601	−0.479405
$377$	23.1632	1.19296
$378$	26.2122	1.34821
$379$	5.57354	0.286293	0.143147	−	0.989701i	$-0.454278\pi$
$379$	5.57354	0.286293	0.143147	+	0.989701i	$0.454278\pi$
$380$	45.1845	2.31792
$381$	16.7866	0.860005
$382$	−16.5894	−0.848785
$383$	−28.8295	−1.47312	−0.736561	−	0.676372i	$-0.763551\pi$
$383$	−28.8295	−1.47312	−0.736561	+	0.676372i	$0.763551\pi$
$384$	101.481	5.17871
$385$	1.19943	0.0611288
$386$	18.7626	0.954990
$387$	17.5413	0.891675
$388$	−51.4991	−2.61447
$389$	−22.1972	−1.12544	−0.562721	−	0.826647i	$-0.690246\pi$
$389$	−22.1972	−1.12544	−0.562721	+	0.826647i	$0.690246\pi$
$390$	29.0753	1.47228
$391$	33.4248	1.69036
$392$	31.3278	1.58229
$393$	31.5751	1.59275
$394$	48.7432	2.45565
$395$	1.31492	0.0661609
$396$	13.6293	0.684898
$397$	23.7623	1.19260	0.596299	−	0.802763i	$-0.296637\pi$
$397$	23.7623	1.19260	0.596299	+	0.802763i	$0.296637\pi$
$398$	41.3145	2.07091
$399$	−36.9696	−1.85079
$400$	−52.5237	−2.62618
$401$	−10.3969	−0.519198	−0.259599	−	0.965716i	$-0.583590\pi$
$401$	−10.3969	−0.519198	−0.259599	+	0.965716i	$0.583590\pi$
$402$	−65.5590	−3.26979
$403$	22.4347	1.11755
$404$	−56.6726	−2.81957
$405$	−0.458481	−0.0227821
$406$	−38.0634	−1.88905
$407$	−4.77815	−0.236844
$408$	−130.174	−6.44457
$409$	2.32961	0.115192	0.0575959	−	0.998340i	$-0.481656\pi$
$409$	2.32961	0.115192	0.0575959	+	0.998340i	$0.481656\pi$
$410$	−3.28414	−0.162192
$411$	−13.8632	−0.683823
$412$	−85.6057	−4.21749
$413$	−26.4069	−1.29940
$414$	88.1976	4.33468
$415$	−11.5027	−0.564644
$416$	−68.2481	−3.34614
$417$	45.7711	2.24142
$418$	−9.84496	−0.481533
$419$	−9.83398	−0.480421	−0.240211	−	0.970721i	$-0.577217\pi$
$419$	−9.83398	−0.480421	−0.240211	+	0.970721i	$0.577217\pi$
$420$	−34.9432	−1.70505
$421$	−11.4426	−0.557678	−0.278839	−	0.960338i	$-0.589950\pi$
$421$	−11.4426	−0.557678	−0.278839	+	0.960338i	$0.589950\pi$
$422$	−0.530754	−0.0258367
$423$	4.74400	0.230661
$424$	−89.7596	−4.35911
$425$	17.6545	0.856369
$426$	−86.4408	−4.18807
$427$	6.55739	0.317334
$428$	97.9608	4.73511
$429$	−4.63316	−0.223691
$430$	−11.9762	−0.577546
$431$	6.75566	0.325408	0.162704	−	0.986675i	$-0.447978\pi$
$431$	6.75566	0.325408	0.162704	+	0.986675i	$0.447978\pi$
$432$	−74.0287	−3.56171
$433$	−12.6310	−0.607007	−0.303503	−	0.952830i	$-0.598156\pi$
$433$	−12.6310	−0.607007	−0.303503	+	0.952830i	$0.598156\pi$
$434$	−36.8663	−1.76964
$435$	−24.4148	−1.17060
$436$	−49.3559	−2.36372
$437$	−46.5936	−2.22887
$438$	118.382	5.65649
$439$	−14.5544	−0.694643	−0.347321	−	0.937746i	$-0.612909\pi$
$439$	−14.5544	−0.694643	−0.347321	+	0.937746i	$0.612909\pi$
$440$	−5.88727	−0.280665
$441$	−15.9874	−0.761305
$442$	43.0305	2.04675
$443$	−17.2394	−0.819068	−0.409534	−	0.912295i	$-0.634309\pi$
$443$	−17.2394	−0.819068	−0.409534	+	0.912295i	$0.634309\pi$
$444$	139.202	6.60623
$445$	−9.53158	−0.451840
$446$	−15.2971	−0.724338
$447$	−53.0198	−2.50775
$448$	55.6355	2.62853
$449$	20.5235	0.968562	0.484281	−	0.874912i	$-0.339081\pi$
$449$	20.5235	0.968562	0.484281	+	0.874912i	$0.339081\pi$
$450$	46.5847	2.19603
$451$	0.523329	0.0246426
$452$	−78.1402	−3.67541
$453$	−25.0082	−1.17499
$454$	−64.1529	−3.01085
$455$	7.30796	0.342603
$456$	181.460	8.49766
$457$	−12.1083	−0.566402	−0.283201	−	0.959061i	$-0.591396\pi$
$457$	−12.1083	−0.566402	−0.283201	+	0.959061i	$0.591396\pi$
$458$	−29.2973	−1.36897
$459$	24.8829	1.16143
$460$	−44.0397	−2.05336
$461$	−1.05532	−0.0491511	−0.0245756	−	0.999698i	$-0.507823\pi$
$461$	−1.05532	−0.0491511	−0.0245756	+	0.999698i	$0.507823\pi$
$462$	7.61354	0.354214
$463$	2.66772	0.123979	0.0619897	−	0.998077i	$-0.480255\pi$
$463$	2.66772	0.123979	0.0619897	+	0.998077i	$0.480255\pi$
$464$	107.499	4.99052
$465$	−23.6469	−1.09660
$466$	−12.6489	−0.585950
$467$	11.4683	0.530692	0.265346	−	0.964153i	$-0.414514\pi$
$467$	11.4683	0.530692	0.265346	+	0.964153i	$0.414514\pi$
$468$	83.0412	3.83858
$469$	−16.4780	−0.760884
$470$	−3.23894	−0.149401
$471$	45.4795	2.09558
$472$	129.615	5.96602
$473$	1.90842	0.0877493
$474$	8.34661	0.383372
$475$	−24.6101	−1.12919
$476$	−51.7148	−2.37034
$477$	45.8066	2.09734
$478$	57.9409	2.65015
$479$	20.6453	0.943308	0.471654	−	0.881784i	$-0.343657\pi$
$479$	20.6453	0.943308	0.471654	+	0.881784i	$0.343657\pi$
$480$	71.9358	3.28340
$481$	−29.1125	−1.32742
$482$	−18.4772	−0.841612
$483$	36.0329	1.63955
$484$	−58.4101	−2.65500
$485$	−11.3524	−0.515487
$486$	−43.9751	−1.99475
$487$	−16.1911	−0.733688	−0.366844	−	0.930283i	$-0.619562\pi$
$487$	−16.1911	−0.733688	−0.366844	+	0.930283i	$0.619562\pi$
$488$	−32.1861	−1.45700
$489$	−2.35204	−0.106363
$490$	10.9153	0.493104
$491$	15.4046	0.695202	0.347601	−	0.937643i	$-0.386996\pi$
$491$	15.4046	0.695202	0.347601	+	0.937643i	$0.386996\pi$
$492$	−15.2462	−0.687351
$493$	−36.1331	−1.62735
$494$	−59.9838	−2.69880
$495$	3.00443	0.135039
$496$	104.118	4.67504
$497$	−21.7266	−0.974571
$498$	−73.0145	−3.27186
$499$	−3.30832	−0.148101	−0.0740504	−	0.997255i	$-0.523593\pi$
$499$	−3.30832	−0.148101	−0.0740504	+	0.997255i	$0.523593\pi$
$500$	−55.9367	−2.50157
$501$	65.0727	2.90724
$502$	58.0635	2.59150
$503$	−25.6732	−1.14471	−0.572355	−	0.820006i	$-0.693970\pi$
$503$	−25.6732	−1.14471	−0.572355	+	0.820006i	$0.693970\pi$
$504$	−86.3347	−3.84565
$505$	−12.4929	−0.555925
$506$	9.59552	0.426573
$507$	8.07016	0.358408
$508$	−32.7334	−1.45231
$509$	−39.1364	−1.73469	−0.867345	−	0.497707i	$-0.834176\pi$
$509$	−39.1364	−1.73469	−0.867345	+	0.497707i	$0.834176\pi$
$510$	−45.3556	−2.00838
$511$	29.7548	1.31627
$512$	−39.3403	−1.73861
$513$	−34.6863	−1.53144
$514$	−16.9818	−0.749033
$515$	−18.8708	−0.831548
$516$	−55.5981	−2.44757
$517$	0.516127	0.0226992
$518$	47.8398	2.10196
$519$	−62.3156	−2.73535
$520$	−35.8702	−1.57301
$521$	6.13752	0.268890	0.134445	−	0.990921i	$-0.457075\pi$
$521$	6.13752	0.268890	0.134445	+	0.990921i	$0.457075\pi$
$522$	−95.3440	−4.17309
$523$	−6.00999	−0.262798	−0.131399	−	0.991330i	$-0.541947\pi$
$523$	−6.00999	−0.262798	−0.131399	+	0.991330i	$0.541947\pi$
$524$	−61.5704	−2.68972
$525$	19.0321	0.830627
$526$	−52.8536	−2.30453
$527$	−34.9966	−1.52448
$528$	−21.5022	−0.935765
$529$	22.4131	0.974482
$530$	−31.2742	−1.35847
$531$	−66.1460	−2.87049
$532$	72.0895	3.12548
$533$	3.18856	0.138112
$534$	−60.5027	−2.61821
$535$	21.5944	0.933606
$536$	80.8803	3.49350
$537$	−26.2179	−1.13139
$538$	61.1958	2.63834
$539$	−1.73936	−0.0749196
$540$	−32.7850	−1.41084
$541$	9.90565	0.425877	0.212939	−	0.977066i	$-0.431697\pi$
$541$	9.90565	0.425877	0.212939	+	0.977066i	$0.431697\pi$
$542$	64.8087	2.78377
$543$	−66.5071	−2.85409
$544$	106.463	4.56455
$545$	−10.8800	−0.466047
$546$	46.3881	1.98523
$547$	−15.1039	−0.645797	−0.322898	−	0.946434i	$-0.604657\pi$
$547$	−15.1039	−0.645797	−0.322898	+	0.946434i	$0.604657\pi$
$548$	27.0329	1.15479
$549$	16.4254	0.701020
$550$	5.06822	0.216110
$551$	50.3689	2.14579
$552$	−176.863	−7.52778
$553$	2.09789	0.0892114
$554$	−43.9967	−1.86924
$555$	30.6855	1.30253
$556$	−89.2522	−3.78514
$557$	−46.9864	−1.99088	−0.995438	−	0.0954092i	$-0.969584\pi$
$557$	−46.9864	−1.99088	−0.995438	+	0.0954092i	$0.969584\pi$
$558$	−92.3452	−3.90929
$559$	11.6277	0.491800
$560$	33.9159	1.43321
$561$	7.22743	0.305142
$562$	−34.9468	−1.47414
$563$	41.4862	1.74843	0.874217	−	0.485536i	$-0.161376\pi$
$563$	41.4862	1.74843	0.874217	+	0.485536i	$0.161376\pi$
$564$	−15.0363	−0.633144
$565$	−17.2252	−0.724668
$566$	20.8755	0.877464
$567$	−0.731483	−0.0307194
$568$	106.642	4.47461
$569$	32.6057	1.36690	0.683452	−	0.729996i	$-0.260478\pi$
$569$	32.6057	1.36690	0.683452	+	0.729996i	$0.260478\pi$
$570$	63.2249	2.64820
$571$	−14.8640	−0.622039	−0.311019	−	0.950404i	$-0.600670\pi$
$571$	−14.8640	−0.622039	−0.311019	+	0.950404i	$0.600670\pi$
$572$	9.03452	0.377752
$573$	−16.9769	−0.709218
$574$	−5.23968	−0.218700
$575$	23.9865	1.00031
$576$	139.360	5.80665
$577$	29.1664	1.21422	0.607108	−	0.794620i	$-0.292330\pi$
$577$	29.1664	1.21422	0.607108	+	0.794620i	$0.292330\pi$
$578$	−20.7400	−0.862670
$579$	19.2008	0.797959
$580$	47.6081	1.97682
$581$	−18.3519	−0.761366
$582$	−72.0607	−2.98701
$583$	4.98357	0.206398
$584$	−146.048	−6.04349
$585$	18.3055	0.756840
$586$	−89.0683	−3.67938
$587$	−45.2383	−1.86718	−0.933592	−	0.358337i	$-0.883344\pi$
$587$	−45.2383	−1.86718	−0.933592	+	0.358337i	$0.883344\pi$
$588$	50.6729	2.08971
$589$	48.7847	2.01014
$590$	45.1608	1.85924
$591$	49.8818	2.05186
$592$	−135.110	−5.55297
$593$	−41.9530	−1.72280	−0.861401	−	0.507926i	$-0.830412\pi$
$593$	−41.9530	−1.72280	−0.861401	+	0.507926i	$0.830412\pi$
$594$	7.14332	0.293094
$595$	−11.4000	−0.467353
$596$	103.387	4.23490
$597$	42.2795	1.73038
$598$	58.4640	2.39077
$599$	−28.2263	−1.15329	−0.576647	−	0.816993i	$-0.695639\pi$
$599$	−28.2263	−1.15329	−0.576647	+	0.816993i	$0.695639\pi$
$600$	−93.4165	−3.81371
$601$	26.3111	1.07325	0.536625	−	0.843821i	$-0.319699\pi$
$601$	26.3111	1.07325	0.536625	+	0.843821i	$0.319699\pi$
$602$	−19.1075	−0.778763
$603$	−41.2753	−1.68086
$604$	48.7653	1.98423
$605$	−12.8759	−0.523478
$606$	−79.2997	−3.22133
$607$	−4.96374	−0.201472	−0.100736	−	0.994913i	$-0.532120\pi$
$607$	−4.96374	−0.201472	−0.100736	+	0.994913i	$0.532120\pi$
$608$	−148.407	−6.01871
$609$	−38.9525	−1.57844
$610$	−11.2144	−0.454056
$611$	3.14468	0.127220
$612$	−129.539	−5.23630
$613$	−6.22257	−0.251327	−0.125664	−	0.992073i	$-0.540106\pi$
$613$	−6.22257	−0.251327	−0.125664	+	0.992073i	$0.540106\pi$
$614$	−70.9097	−2.86168
$615$	−3.36085	−0.135523
$616$	−9.39284	−0.378448
$617$	1.00064	0.0402843	0.0201421	−	0.999797i	$-0.493588\pi$
$617$	1.00064	0.0402843	0.0201421	+	0.999797i	$0.493588\pi$
$618$	−119.785	−4.81845
$619$	8.65767	0.347981	0.173991	−	0.984747i	$-0.444334\pi$
$619$	8.65767	0.347981	0.173991	+	0.984747i	$0.444334\pi$
$620$	46.1107	1.85185
$621$	33.8075	1.35665
$622$	−19.1916	−0.769515
$623$	−15.2072	−0.609262
$624$	−131.010	−5.24459
$625$	5.46638	0.218655
$626$	17.2130	0.687969
$627$	−10.0749	−0.402353
$628$	−88.6837	−3.53886
$629$	45.4136	1.81076
$630$	−30.0809	−1.19845
$631$	6.89665	0.274551	0.137276	−	0.990533i	$-0.456165\pi$
$631$	6.89665	0.274551	0.137276	+	0.990533i	$0.456165\pi$
$632$	−10.2972	−0.409602
$633$	−0.543151	−0.0215883
$634$	−47.4698	−1.88527
$635$	−7.21573	−0.286347
$636$	−145.186	−5.75702
$637$	−10.5977	−0.419894
$638$	−10.3730	−0.410672
$639$	−54.4223	−2.15291
$640$	−43.6218	−1.72430
$641$	18.1454	0.716700	0.358350	−	0.933587i	$-0.383339\pi$
$641$	18.1454	0.716700	0.358350	+	0.933587i	$0.383339\pi$
$642$	137.073	5.40983
$643$	−6.58808	−0.259809	−0.129904	−	0.991527i	$-0.541467\pi$
$643$	−6.58808	−0.259809	−0.129904	+	0.991527i	$0.541467\pi$
$644$	−70.2631	−2.76875
$645$	−12.2560	−0.482579
$646$	93.5709	3.68150
$647$	−35.0058	−1.37622	−0.688109	−	0.725607i	$-0.741559\pi$
$647$	−35.0058	−1.37622	−0.688109	+	0.725607i	$0.741559\pi$
$648$	3.59039	0.141044
$649$	−7.19640	−0.282483
$650$	30.8799	1.21121
$651$	−37.7274	−1.47865
$652$	4.58640	0.179617
$653$	−6.32015	−0.247326	−0.123663	−	0.992324i	$-0.539464\pi$
$653$	−6.32015	−0.247326	−0.123663	+	0.992324i	$0.539464\pi$
$654$	−69.0618	−2.70053
$655$	−13.5725	−0.530323
$656$	14.7980	0.577763
$657$	74.5319	2.90777
$658$	−5.16756	−0.201453
$659$	28.7154	1.11859	0.559297	−	0.828967i	$-0.311071\pi$
$659$	28.7154	1.11859	0.559297	+	0.828967i	$0.311071\pi$
$660$	−9.52269	−0.370670
$661$	21.4168	0.833017	0.416508	−	0.909132i	$-0.363254\pi$
$661$	21.4168	0.833017	0.416508	+	0.909132i	$0.363254\pi$
$662$	46.4811	1.80654
$663$	44.0356	1.71020
$664$	90.0782	3.49571
$665$	15.8914	0.616240
$666$	119.832	4.64341
$667$	−49.0927	−1.90088
$668$	−126.890	−4.90952
$669$	−15.6544	−0.605234
$670$	28.1805	1.08871
$671$	1.78701	0.0689869
$672$	114.770	4.42734
$673$	−4.85368	−0.187095	−0.0935477	−	0.995615i	$-0.529821\pi$
$673$	−4.85368	−0.187095	−0.0935477	+	0.995615i	$0.529821\pi$
$674$	77.2651	2.97614
$675$	17.8566	0.687302
$676$	−15.7366	−0.605253
$677$	−20.2235	−0.777251	−0.388625	−	0.921396i	$-0.627050\pi$
$677$	−20.2235	−0.777251	−0.388625	+	0.921396i	$0.627050\pi$
$678$	−109.339	−4.19912
$679$	−18.1122	−0.695082
$680$	55.9553	2.14579
$681$	−65.6515	−2.51577
$682$	−10.0468	−0.384711
$683$	−37.0149	−1.41634	−0.708168	−	0.706044i	$-0.750478\pi$
$683$	−37.0149	−1.41634	−0.708168	+	0.706044i	$0.750478\pi$
$684$	180.575	6.90446
$685$	5.95911	0.227686
$686$	53.9894	2.06132
$687$	−29.9817	−1.14387
$688$	53.9636	2.05734
$689$	30.3641	1.15678
$690$	−61.6230	−2.34595
$691$	−39.2784	−1.49422	−0.747110	−	0.664701i	$-0.768559\pi$
$691$	−39.2784	−1.49422	−0.747110	+	0.664701i	$0.768559\pi$
$692$	121.514	4.61926
$693$	4.79341	0.182087
$694$	−6.63756	−0.251958
$695$	−19.6747	−0.746303
$696$	191.193	7.24717
$697$	−4.97396	−0.188402
$698$	35.0043	1.32493
$699$	−12.9444	−0.489602
$700$	−37.1120	−1.40270
$701$	−6.31198	−0.238400	−0.119200	−	0.992870i	$-0.538033\pi$
$701$	−6.31198	−0.238400	−0.119200	+	0.992870i	$0.538033\pi$
$702$	43.5231	1.64267
$703$	−63.3059	−2.38763
$704$	15.1617	0.571429
$705$	−3.31460	−0.124835
$706$	−38.3522	−1.44340
$707$	−19.9317	−0.749609
$708$	209.653	7.87924
$709$	−9.00728	−0.338275	−0.169138	−	0.985592i	$-0.554098\pi$
$709$	−9.00728	−0.338275	−0.169138	+	0.985592i	$0.554098\pi$
$710$	37.1565	1.39446
$711$	5.25495	0.197076
$712$	74.6424	2.79734
$713$	−47.5487	−1.78071
$714$	−72.3625	−2.70810
$715$	1.99156	0.0744802
$716$	51.1241	1.91060
$717$	59.2943	2.21438
$718$	−53.0823	−1.98101
$719$	35.2195	1.31347	0.656733	−	0.754123i	$-0.271938\pi$
$719$	35.2195	1.31347	0.656733	+	0.754123i	$0.271938\pi$
$720$	84.9549	3.16608
$721$	−30.1075	−1.12126
$722$	−78.5944	−2.92498
$723$	−18.9088	−0.703225
$724$	129.687	4.81977
$725$	−25.9301	−0.963020
$726$	−81.7309	−3.03332
$727$	22.4281	0.831813	0.415907	−	0.909407i	$-0.363464\pi$
$727$	22.4281	0.831813	0.415907	+	0.909407i	$0.363464\pi$
$728$	−57.2291	−2.12105
$729$	−43.8563	−1.62431
$730$	−50.8863	−1.88338
$731$	−18.1385	−0.670876
$732$	−52.0612	−1.92424
$733$	19.3402	0.714347	0.357173	−	0.934038i	$-0.383740\pi$
$733$	19.3402	0.714347	0.357173	+	0.934038i	$0.383740\pi$
$734$	30.4384	1.12350
$735$	11.1703	0.412022
$736$	144.647	5.33176
$737$	−4.49058	−0.165413
$738$	−13.1247	−0.483128
$739$	−2.65214	−0.0975607	−0.0487803	−	0.998810i	$-0.515533\pi$
$739$	−2.65214	−0.0975607	−0.0487803	+	0.998810i	$0.515533\pi$
$740$	−59.8359	−2.19961
$741$	−61.3849	−2.25503
$742$	−49.8965	−1.83176
$743$	31.5670	1.15808	0.579040	−	0.815299i	$-0.303428\pi$
$743$	31.5670	1.15808	0.579040	+	0.815299i	$0.303428\pi$
$744$	185.180	6.78903
$745$	22.7905	0.834981
$746$	−88.9265	−3.25583
$747$	−45.9692	−1.68193
$748$	−14.0933	−0.515301
$749$	34.4527	1.25888
$750$	−78.2701	−2.85802
$751$	−9.04620	−0.330100	−0.165050	−	0.986285i	$-0.552779\pi$
$751$	−9.04620	−0.330100	−0.165050	+	0.986285i	$0.552779\pi$
$752$	14.5943	0.532199
$753$	59.4197	2.16538
$754$	−63.2011	−2.30165
$755$	10.7498	0.391224
$756$	−52.3069	−1.90238
$757$	26.5744	0.965863	0.482931	−	0.875658i	$-0.339572\pi$
$757$	26.5744	0.965863	0.482931	+	0.875658i	$0.339572\pi$
$758$	−15.2075	−0.552361
$759$	9.81966	0.356431
$760$	−78.0007	−2.82938
$761$	−5.58089	−0.202307	−0.101154	−	0.994871i	$-0.532253\pi$
$761$	−5.58089	−0.202307	−0.101154	+	0.994871i	$0.532253\pi$
$762$	−45.8026	−1.65925
$763$	−17.3584	−0.628418
$764$	33.1044	1.19767
$765$	−28.5554	−1.03242
$766$	78.6619	2.84217
$767$	−43.8465	−1.58321
$768$	−114.645	−4.13689
$769$	31.8933	1.15010	0.575051	−	0.818118i	$-0.304982\pi$
$769$	31.8933	1.15010	0.575051	+	0.818118i	$0.304982\pi$
$770$	−3.27268	−0.117939
$771$	−17.3784	−0.625869
$772$	−37.4411	−1.34753
$773$	21.5138	0.773798	0.386899	−	0.922122i	$-0.373546\pi$
$773$	21.5138	0.773798	0.386899	+	0.922122i	$0.373546\pi$
$774$	−47.8618	−1.72036
$775$	−25.1146	−0.902142
$776$	88.9015	3.19138
$777$	48.9572	1.75633
$778$	60.5655	2.17138
$779$	6.93361	0.248422
$780$	−58.0202	−2.07746
$781$	−5.92092	−0.211867
$782$	−91.2001	−3.26131
$783$	−36.5468	−1.30607
$784$	−49.1832	−1.75654
$785$	−19.5493	−0.697746
$786$	−86.1531	−3.07298
$787$	−4.01352	−0.143066	−0.0715332	−	0.997438i	$-0.522789\pi$
$787$	−4.01352	−0.143066	−0.0715332	+	0.997438i	$0.522789\pi$
$788$	−97.2680	−3.46503
$789$	−54.0882	−1.92559
$790$	−3.58779	−0.127648
$791$	−27.4819	−0.977143
$792$	−23.5279	−0.836026
$793$	10.8880	0.386644
$794$	−64.8360	−2.30094
$795$	−32.0048	−1.13509
$796$	−82.4438	−2.92214
$797$	35.8758	1.27078	0.635392	−	0.772190i	$-0.280838\pi$
$797$	35.8758	1.27078	0.635392	+	0.772190i	$0.280838\pi$
$798$	100.872	3.57083
$799$	−4.90550	−0.173544
$800$	76.4006	2.70117
$801$	−38.0920	−1.34591
$802$	28.3682	1.00172
$803$	8.10875	0.286152
$804$	130.824	4.61381
$805$	−15.4887	−0.545906
$806$	−61.2134	−2.15615
$807$	62.6253	2.20451
$808$	97.8323	3.44173
$809$	−2.43945	−0.0857664	−0.0428832	−	0.999080i	$-0.513654\pi$
$809$	−2.43945	−0.0857664	−0.0428832	+	0.999080i	$0.513654\pi$
$810$	1.25097	0.0439547
$811$	−47.8783	−1.68123	−0.840617	−	0.541630i	$-0.817808\pi$
$811$	−47.8783	−1.68123	−0.840617	+	0.541630i	$0.817808\pi$
$812$	75.9562	2.66554
$813$	66.3225	2.32603
$814$	13.0373	0.456956
$815$	1.01102	0.0354145
$816$	204.367	7.15427
$817$	25.2847	0.884601
$818$	−6.35638	−0.222246
$819$	29.2055	1.02052
$820$	6.55356	0.228860
$821$	13.4895	0.470785	0.235393	−	0.971900i	$-0.424362\pi$
$821$	13.4895	0.470785	0.235393	+	0.971900i	$0.424362\pi$
$822$	37.8261	1.31934
$823$	−45.4075	−1.58280	−0.791402	−	0.611296i	$-0.790649\pi$
$823$	−45.4075	−1.58280	−0.791402	+	0.611296i	$0.790649\pi$
$824$	147.779	5.14811
$825$	5.18660	0.180574
$826$	72.0518	2.50700
$827$	−48.6976	−1.69338	−0.846690	−	0.532086i	$-0.821408\pi$
$827$	−48.6976	−1.69338	−0.846690	+	0.532086i	$0.821408\pi$
$828$	−176.000	−6.11642
$829$	−2.94544	−0.102300	−0.0511498	−	0.998691i	$-0.516289\pi$
$829$	−2.94544	−0.102300	−0.0511498	+	0.998691i	$0.516289\pi$
$830$	31.3852	1.08940
$831$	−45.0244	−1.56188
$832$	92.3781	3.20263
$833$	16.5317	0.572788
$834$	−124.887	−4.32449
$835$	−27.9715	−0.967994
$836$	19.6458	0.679464
$837$	−35.3973	−1.22351
$838$	26.8322	0.926902
$839$	19.1698	0.661816	0.330908	−	0.943663i	$-0.392645\pi$
$839$	19.1698	0.661816	0.330908	+	0.943663i	$0.392645\pi$
$840$	60.3214	2.08129
$841$	24.0706	0.830019
$842$	31.2213	1.07596
$843$	−35.7631	−1.23175
$844$	1.05913	0.0364567
$845$	−3.46895	−0.119336
$846$	−12.9441	−0.445027
$847$	−20.5428	−0.705858
$848$	140.918	4.83915
$849$	21.3632	0.733182
$850$	−48.1706	−1.65224
$851$	61.7019	2.11511
$852$	172.494	5.90955
$853$	−37.5247	−1.28482	−0.642411	−	0.766361i	$-0.722066\pi$
$853$	−37.5247	−1.28482	−0.642411	+	0.766361i	$0.722066\pi$
$854$	−17.8919	−0.612250
$855$	39.8058	1.36133
$856$	−169.107	−5.77995
$857$	49.1108	1.67759	0.838796	−	0.544446i	$-0.183260\pi$
$857$	49.1108	1.67759	0.838796	+	0.544446i	$0.183260\pi$
$858$	12.6417	0.431579
$859$	18.8388	0.642773	0.321387	−	0.946948i	$-0.395851\pi$
$859$	18.8388	0.642773	0.321387	+	0.946948i	$0.395851\pi$
$860$	23.8988	0.814943
$861$	−5.36207	−0.182739
$862$	−18.4329	−0.627828
$863$	35.5293	1.20943	0.604715	−	0.796442i	$-0.293287\pi$
$863$	35.5293	1.20943	0.604715	+	0.796442i	$0.293287\pi$
$864$	107.682	3.66340
$865$	26.7864	0.910763
$866$	34.4639	1.17113
$867$	−21.2245	−0.720820
$868$	73.5673	2.49704
$869$	0.571716	0.0193941
$870$	66.6161	2.25850
$871$	−27.3604	−0.927072
$872$	85.2017	2.88529
$873$	−45.3687	−1.53550
$874$	127.131	4.30028
$875$	−19.6729	−0.665066
$876$	−236.233	−7.98156
$877$	45.5226	1.53719	0.768595	−	0.639735i	$-0.220956\pi$
$877$	45.5226	1.53719	0.768595	+	0.639735i	$0.220956\pi$
$878$	39.7119	1.34021
$879$	−91.1488	−3.07437
$880$	9.24273	0.311572
$881$	−17.2496	−0.581153	−0.290576	−	0.956852i	$-0.593847\pi$
$881$	−17.2496	−0.581153	−0.290576	+	0.956852i	$0.593847\pi$
$882$	43.6219	1.46883
$883$	−9.23448	−0.310765	−0.155383	−	0.987854i	$-0.549661\pi$
$883$	−9.23448	−0.310765	−0.155383	+	0.987854i	$0.549661\pi$
$884$	−85.8681	−2.88806
$885$	46.2157	1.55352
$886$	47.0380	1.58027
$887$	−28.9628	−0.972476	−0.486238	−	0.873827i	$-0.661631\pi$
$887$	−28.9628	−0.972476	−0.486238	+	0.873827i	$0.661631\pi$
$888$	−240.300	−8.06395
$889$	−11.5123	−0.386111
$890$	26.0071	0.871759
$891$	−0.199343	−0.00667825
$892$	30.5256	1.02207
$893$	6.83818	0.228831
$894$	144.665	4.83833
$895$	11.2698	0.376706
$896$	−69.5963	−2.32505
$897$	59.8296	1.99765
$898$	−55.9987	−1.86870
$899$	51.4014	1.71433
$900$	−92.9607	−3.09869
$901$	−47.3660	−1.57799
$902$	−1.42791	−0.0475443
$903$	−19.5538	−0.650710
$904$	134.891	4.48642
$905$	28.5880	0.950298
$906$	68.2353	2.26697
$907$	36.1411	1.20005	0.600023	−	0.799983i	$-0.295158\pi$
$907$	36.1411	1.20005	0.600023	+	0.799983i	$0.295158\pi$
$908$	128.018	4.24844
$909$	−49.9264	−1.65595
$910$	−19.9399	−0.661002
$911$	−36.9688	−1.22483	−0.612416	−	0.790535i	$-0.709802\pi$
$911$	−36.9688	−1.22483	−0.612416	+	0.790535i	$0.709802\pi$
$912$	−284.884	−9.43345
$913$	−5.00126	−0.165517
$914$	33.0377	1.09279
$915$	−11.4763	−0.379395
$916$	58.4634	1.93168
$917$	−21.6543	−0.715087
$918$	−67.8933	−2.24081
$919$	−8.93223	−0.294647	−0.147323	−	0.989088i	$-0.547066\pi$
$919$	−8.93223	−0.294647	−0.147323	+	0.989088i	$0.547066\pi$
$920$	76.0245	2.50645
$921$	−72.5660	−2.39113
$922$	2.87946	0.0948298
$923$	−36.0752	−1.18743
$924$	−15.1930	−0.499812
$925$	32.5901	1.07156
$926$	−7.27892	−0.239200
$927$	−75.4153	−2.47696
$928$	−156.367	−5.13301
$929$	20.5228	0.673331	0.336665	−	0.941624i	$-0.390701\pi$
$929$	20.5228	0.673331	0.336665	+	0.941624i	$0.390701\pi$
$930$	64.5209	2.11572
$931$	−23.0449	−0.755265
$932$	25.2412	0.826802
$933$	−19.6399	−0.642982
$934$	−31.2916	−1.02389
$935$	−3.10671	−0.101600
$936$	−143.352	−4.68559
$937$	19.1460	0.625471	0.312735	−	0.949840i	$-0.398755\pi$
$937$	19.1460	0.625471	0.312735	+	0.949840i	$0.398755\pi$
$938$	44.9606	1.46801
$939$	17.6151	0.574845
$940$	6.46336	0.210812
$941$	−31.9168	−1.04046	−0.520229	−	0.854027i	$-0.674154\pi$
$941$	−31.9168	−1.04046	−0.520229	+	0.854027i	$0.674154\pi$
$942$	−124.092	−4.04312
$943$	−6.75794	−0.220069
$944$	−203.489	−6.62302
$945$	−11.5305	−0.375086
$946$	−5.20716	−0.169299
$947$	−19.0659	−0.619559	−0.309779	−	0.950808i	$-0.600255\pi$
$947$	−19.0659	−0.619559	−0.309779	+	0.950808i	$0.600255\pi$
$948$	−16.6558	−0.540956
$949$	49.4054	1.60377
$950$	67.1490	2.17860
$951$	−48.5786	−1.57527
$952$	89.2738	2.89338
$953$	−40.0067	−1.29594	−0.647972	−	0.761664i	$-0.724383\pi$
$953$	−40.0067	−1.29594	−0.647972	+	0.761664i	$0.724383\pi$
$954$	−124.984	−4.04651
$955$	7.29750	0.236141
$956$	−115.622	−3.73949
$957$	−10.6153	−0.343144
$958$	−56.3311	−1.81997
$959$	9.50745	0.307012
$960$	−97.3696	−3.14259
$961$	18.7848	0.605960
$962$	79.4340	2.56105
$963$	86.2997	2.78097
$964$	36.8716	1.18755
$965$	−8.25347	−0.265689
$966$	−98.3163	−3.16328
$967$	30.4150	0.978080	0.489040	−	0.872261i	$-0.337347\pi$
$967$	30.4150	0.978080	0.489040	+	0.872261i	$0.337347\pi$
$968$	100.832	3.24085
$969$	95.7565	3.07614
$970$	30.9753	0.994556
$971$	40.9686	1.31474	0.657372	−	0.753566i	$-0.271668\pi$
$971$	40.9686	1.31474	0.657372	+	0.753566i	$0.271668\pi$
$972$	87.7531	2.81468
$973$	−31.3899	−1.00632
$974$	44.1776	1.41554
$975$	31.6012	1.01205
$976$	50.5306	1.61745
$977$	−15.0145	−0.480356	−0.240178	−	0.970729i	$-0.577206\pi$
$977$	−15.0145	−0.480356	−0.240178	+	0.970729i	$0.577206\pi$
$978$	6.41757	0.205211
$979$	−4.14424	−0.132451
$980$	−21.7817	−0.695791
$981$	−43.4807	−1.38823
$982$	−42.0318	−1.34129
$983$	55.8072	1.77997	0.889986	−	0.455987i	$-0.150714\pi$
$983$	55.8072	1.77997	0.889986	+	0.455987i	$0.150714\pi$
$984$	26.3190	0.839020
$985$	−21.4417	−0.683188
$986$	98.5897	3.13974
$987$	−5.28827	−0.168327
$988$	119.699	3.80812
$989$	−24.6441	−0.783637
$990$	−8.19764	−0.260538
$991$	8.82893	0.280460	0.140230	−	0.990119i	$-0.455216\pi$
$991$	8.82893	0.280460	0.140230	+	0.990119i	$0.455216\pi$
$992$	−151.449	−4.80852
$993$	47.5668	1.50949
$994$	59.2814	1.88029
$995$	−18.1738	−0.576149
$996$	145.702	4.61674
$997$	−21.3124	−0.674971	−0.337485	−	0.941331i	$-0.609576\pi$
$997$	−21.3124	−0.674971	−0.337485	+	0.941331i	$0.609576\pi$
$998$	9.02681	0.285739
$999$	45.9336	1.45327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.9	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.9	✓	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72852 q^{2} -2.79225 q^{3} +5.44481 q^{4} +1.20025 q^{5} +7.61871 q^{6} +1.91493 q^{7} -9.39922 q^{8} +4.79667 q^{9} +O(q^{10})\)	\(q-2.72852 q^{2} -2.79225 q^{3} +5.44481 q^{4} +1.20025 q^{5} +7.61871 q^{6} +1.91493 q^{7} -9.39922 q^{8} +4.79667 q^{9} -3.27490 q^{10} +0.521857 q^{11} -15.2033 q^{12} +3.17959 q^{13} -5.22493 q^{14} -3.35139 q^{15} +14.7563 q^{16} -4.95996 q^{17} -13.0878 q^{18} +6.91410 q^{19} +6.53512 q^{20} -5.34698 q^{21} -1.42390 q^{22} -6.73892 q^{23} +26.2450 q^{24} -3.55940 q^{25} -8.67557 q^{26} -5.01674 q^{27} +10.4265 q^{28} +7.28495 q^{29} +9.14434 q^{30} +7.05583 q^{31} -21.4644 q^{32} -1.45716 q^{33} +13.5333 q^{34} +2.29840 q^{35} +26.1169 q^{36} -9.15605 q^{37} -18.8652 q^{38} -8.87822 q^{39} -11.2814 q^{40} +1.00282 q^{41} +14.5893 q^{42} +3.65698 q^{43} +2.84141 q^{44} +5.75719 q^{45} +18.3873 q^{46} +0.989020 q^{47} -41.2033 q^{48} -3.33302 q^{49} +9.71190 q^{50} +13.8495 q^{51} +17.3123 q^{52} +9.54968 q^{53} +13.6883 q^{54} +0.626358 q^{55} -17.9989 q^{56} -19.3059 q^{57} -19.8771 q^{58} -13.7900 q^{59} -18.2477 q^{60} +3.42434 q^{61} -19.2520 q^{62} +9.18530 q^{63} +29.0534 q^{64} +3.81630 q^{65} +3.97587 q^{66} -8.60500 q^{67} -27.0060 q^{68} +18.8168 q^{69} -6.27122 q^{70} -11.3459 q^{71} -45.0849 q^{72} +15.5383 q^{73} +24.9824 q^{74} +9.93875 q^{75} +37.6460 q^{76} +0.999322 q^{77} +24.2244 q^{78} +1.09554 q^{79} +17.7112 q^{80} -0.381988 q^{81} -2.73622 q^{82} -9.58358 q^{83} -29.1133 q^{84} -5.95318 q^{85} -9.97814 q^{86} -20.3414 q^{87} -4.90505 q^{88} -7.94134 q^{89} -15.7086 q^{90} +6.08871 q^{91} -36.6921 q^{92} -19.7017 q^{93} -2.69856 q^{94} +8.29864 q^{95} +59.9341 q^{96} -9.45839 q^{97} +9.09422 q^{98} +2.50317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

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