LMFDB - Embedded newform 6037.2.a.a.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.75691 q^{2} -3.25303 q^{3} +5.60054 q^{4} +1.79806 q^{5} +8.96830 q^{6} -3.80594 q^{7} -9.92635 q^{8} +7.58219 q^{9} +O(q^{10})$	\(q-2.75691 q^{2} -3.25303 q^{3} +5.60054 q^{4} +1.79806 q^{5} +8.96830 q^{6} -3.80594 q^{7} -9.92635 q^{8} +7.58219 q^{9} -4.95708 q^{10} -2.49038 q^{11} -18.2187 q^{12} -3.74920 q^{13} +10.4926 q^{14} -5.84913 q^{15} +16.1650 q^{16} +7.01748 q^{17} -20.9034 q^{18} -7.37522 q^{19} +10.0701 q^{20} +12.3808 q^{21} +6.86575 q^{22} -7.99585 q^{23} +32.2907 q^{24} -1.76699 q^{25} +10.3362 q^{26} -14.9060 q^{27} -21.3153 q^{28} -3.30028 q^{29} +16.1255 q^{30} +8.57601 q^{31} -24.7126 q^{32} +8.10128 q^{33} -19.3465 q^{34} -6.84329 q^{35} +42.4643 q^{36} -1.64652 q^{37} +20.3328 q^{38} +12.1963 q^{39} -17.8482 q^{40} +7.49158 q^{41} -34.1328 q^{42} -0.706248 q^{43} -13.9475 q^{44} +13.6332 q^{45} +22.0438 q^{46} +6.01634 q^{47} -52.5851 q^{48} +7.48516 q^{49} +4.87143 q^{50} -22.8280 q^{51} -20.9976 q^{52} +7.77088 q^{53} +41.0944 q^{54} -4.47785 q^{55} +37.7791 q^{56} +23.9918 q^{57} +9.09857 q^{58} +7.55279 q^{59} -32.7583 q^{60} -3.23030 q^{61} -23.6433 q^{62} -28.8573 q^{63} +35.8004 q^{64} -6.74128 q^{65} -22.3345 q^{66} +12.7529 q^{67} +39.3016 q^{68} +26.0107 q^{69} +18.8663 q^{70} +0.510338 q^{71} -75.2635 q^{72} -3.61194 q^{73} +4.53930 q^{74} +5.74807 q^{75} -41.3052 q^{76} +9.47824 q^{77} -33.6240 q^{78} -5.15244 q^{79} +29.0655 q^{80} +25.7430 q^{81} -20.6536 q^{82} -14.0763 q^{83} +69.3393 q^{84} +12.6178 q^{85} +1.94706 q^{86} +10.7359 q^{87} +24.7204 q^{88} -7.39389 q^{89} -37.5855 q^{90} +14.2692 q^{91} -44.7811 q^{92} -27.8980 q^{93} -16.5865 q^{94} -13.2611 q^{95} +80.3908 q^{96} +8.70729 q^{97} -20.6359 q^{98} -18.8825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.75691	−1.94943	−0.974714	−	0.223456i	$-0.928266\pi$
$2$	−2.75691	−1.94943	−0.974714	+	0.223456i	$0.928266\pi$
$3$	−3.25303	−1.87814	−0.939068	−	0.343731i	$-0.888309\pi$
$3$	−3.25303	−1.87814	−0.939068	+	0.343731i	$0.888309\pi$
$4$	5.60054	2.80027
$5$	1.79806	0.804116	0.402058	−	0.915614i	$-0.368295\pi$
$5$	1.79806	0.804116	0.402058	+	0.915614i	$0.368295\pi$
$6$	8.96830	3.66129
$7$	−3.80594	−1.43851	−0.719255	−	0.694747i	$-0.755517\pi$
$7$	−3.80594	−1.43851	−0.719255	+	0.694747i	$0.755517\pi$
$8$	−9.92635	−3.50950
$9$	7.58219	2.52740
$10$	−4.95708	−1.56757
$11$	−2.49038	−0.750878	−0.375439	−	0.926847i	$-0.622508\pi$
$11$	−2.49038	−0.750878	−0.375439	+	0.926847i	$0.622508\pi$
$12$	−18.2187	−5.25929
$13$	−3.74920	−1.03984	−0.519921	−	0.854214i	$-0.674039\pi$
$13$	−3.74920	−1.03984	−0.519921	+	0.854214i	$0.674039\pi$
$14$	10.4926	2.80427
$15$	−5.84913	−1.51024
$16$	16.1650	4.04124
$17$	7.01748	1.70199	0.850994	−	0.525176i	$-0.176000\pi$
$17$	7.01748	1.70199	0.850994	+	0.525176i	$0.176000\pi$
$18$	−20.9034	−4.92698
$19$	−7.37522	−1.69199	−0.845996	−	0.533190i	$-0.820993\pi$
$19$	−7.37522	−1.69199	−0.845996	+	0.533190i	$0.820993\pi$
$20$	10.0701	2.25174
$21$	12.3808	2.70172
$22$	6.86575	1.46378
$23$	−7.99585	−1.66725	−0.833625	−	0.552331i	$-0.813739\pi$
$23$	−7.99585	−1.66725	−0.833625	+	0.552331i	$0.813739\pi$
$24$	32.2907	6.59131
$25$	−1.76699	−0.353398
$26$	10.3362	2.02710
$27$	−14.9060	−2.86866
$28$	−21.3153	−4.02821
$29$	−3.30028	−0.612847	−0.306424	−	0.951895i	$-0.599132\pi$
$29$	−3.30028	−0.612847	−0.306424	+	0.951895i	$0.599132\pi$
$30$	16.1255	2.94410
$31$	8.57601	1.54030	0.770148	−	0.637865i	$-0.220182\pi$
$31$	8.57601	1.54030	0.770148	+	0.637865i	$0.220182\pi$
$32$	−24.7126	−4.36861
$33$	8.10128	1.41025
$34$	−19.3465	−3.31790
$35$	−6.84329	−1.15673
$36$	42.4643	7.07739
$37$	−1.64652	−0.270686	−0.135343	−	0.990799i	$-0.543214\pi$
$37$	−1.64652	−0.270686	−0.135343	+	0.990799i	$0.543214\pi$
$38$	20.3328	3.29842
$39$	12.1963	1.95296
$40$	−17.8482	−2.82204
$41$	7.49158	1.16999	0.584994	−	0.811037i	$-0.301097\pi$
$41$	7.49158	1.16999	0.584994	+	0.811037i	$0.301097\pi$
$42$	−34.1328	−5.26680
$43$	−0.706248	−0.107702	−0.0538509	−	0.998549i	$-0.517150\pi$
$43$	−0.706248	−0.107702	−0.0538509	+	0.998549i	$0.517150\pi$
$44$	−13.9475	−2.10266
$45$	13.6332	2.03232
$46$	22.0438	3.25018
$47$	6.01634	0.877574	0.438787	−	0.898591i	$-0.355408\pi$
$47$	6.01634	0.877574	0.438787	+	0.898591i	$0.355408\pi$
$48$	−52.5851	−7.59000
$49$	7.48516	1.06931
$50$	4.87143	0.688924
$51$	−22.8280	−3.19656
$52$	−20.9976	−2.91184
$53$	7.77088	1.06741	0.533707	−	0.845670i	$-0.320799\pi$
$53$	7.77088	1.06741	0.533707	+	0.845670i	$0.320799\pi$
$54$	41.0944	5.59224
$55$	−4.47785	−0.603793
$56$	37.7791	5.04844
$57$	23.9918	3.17779
$58$	9.09857	1.19470
$59$	7.55279	0.983290	0.491645	−	0.870796i	$-0.336396\pi$
$59$	7.55279	0.983290	0.491645	+	0.870796i	$0.336396\pi$
$60$	−32.7583	−4.22908
$61$	−3.23030	−0.413597	−0.206799	−	0.978384i	$-0.566305\pi$
$61$	−3.23030	−0.413597	−0.206799	+	0.978384i	$0.566305\pi$
$62$	−23.6433	−3.00270
$63$	−28.8573	−3.63568
$64$	35.8004	4.47505
$65$	−6.74128	−0.836153
$66$	−22.3345	−2.74918
$67$	12.7529	1.55802	0.779010	−	0.627012i	$-0.215722\pi$
$67$	12.7529	1.55802	0.779010	+	0.627012i	$0.215722\pi$
$68$	39.3016	4.76602
$69$	26.0107	3.13132
$70$	18.8663	2.25496
$71$	0.510338	0.0605659	0.0302830	−	0.999541i	$-0.490359\pi$
$71$	0.510338	0.0605659	0.0302830	+	0.999541i	$0.490359\pi$
$72$	−75.2635	−8.86989
$73$	−3.61194	−0.422746	−0.211373	−	0.977405i	$-0.567793\pi$
$73$	−3.61194	−0.422746	−0.211373	+	0.977405i	$0.567793\pi$
$74$	4.53930	0.527682
$75$	5.74807	0.663730
$76$	−41.3052	−4.73803
$77$	9.47824	1.08015
$78$	−33.6240	−3.80716
$79$	−5.15244	−0.579695	−0.289848	−	0.957073i	$-0.593605\pi$
$79$	−5.15244	−0.579695	−0.289848	+	0.957073i	$0.593605\pi$
$80$	29.0655	3.24963
$81$	25.7430	2.86033
$82$	−20.6536	−2.28081
$83$	−14.0763	−1.54508	−0.772539	−	0.634967i	$-0.781014\pi$
$83$	−14.0763	−1.54508	−0.772539	+	0.634967i	$0.781014\pi$
$84$	69.3393	7.56553
$85$	12.6178	1.36859
$86$	1.94706	0.209957
$87$	10.7359	1.15101
$88$	24.7204	2.63521
$89$	−7.39389	−0.783750	−0.391875	−	0.920018i	$-0.628174\pi$
$89$	−7.39389	−0.783750	−0.391875	+	0.920018i	$0.628174\pi$
$90$	−37.5855	−3.96186
$91$	14.2692	1.49582
$92$	−44.7811	−4.66875
$93$	−27.8980	−2.89289
$94$	−16.5865	−1.71077
$95$	−13.2611	−1.36056
$96$	80.3908	8.20485
$97$	8.70729	0.884091	0.442045	−	0.896993i	$-0.354253\pi$
$97$	8.70729	0.884091	0.442045	+	0.896993i	$0.354253\pi$
$98$	−20.6359	−2.08454
$99$	−18.8825	−1.89777
$100$	−9.89610	−0.989610
$101$	−12.6284	−1.25657	−0.628287	−	0.777982i	$-0.716244\pi$
$101$	−12.6284	−1.25657	−0.628287	+	0.777982i	$0.716244\pi$
$102$	62.9348	6.23147
$103$	−3.62814	−0.357491	−0.178746	−	0.983895i	$-0.557204\pi$
$103$	−3.62814	−0.357491	−0.178746	+	0.983895i	$0.557204\pi$
$104$	37.2159	3.64932
$105$	22.2614	2.17249
$106$	−21.4236	−2.08084
$107$	−0.0585757	−0.00566273	−0.00283137	−	0.999996i	$-0.500901\pi$
$107$	−0.0585757	−0.00566273	−0.00283137	+	0.999996i	$0.500901\pi$
$108$	−83.4815	−8.03301
$109$	17.3209	1.65904	0.829518	−	0.558479i	$-0.188615\pi$
$109$	17.3209	1.65904	0.829518	+	0.558479i	$0.188615\pi$
$110$	12.3450	1.17705
$111$	5.35617	0.508385
$112$	−61.5228	−5.81336
$113$	12.2456	1.15197	0.575983	−	0.817462i	$-0.304619\pi$
$113$	12.2456	1.15197	0.575983	+	0.817462i	$0.304619\pi$
$114$	−66.1431	−6.19487
$115$	−14.3770	−1.34066
$116$	−18.4834	−1.71614
$117$	−28.4272	−2.62809
$118$	−20.8223	−1.91685
$119$	−26.7081	−2.44833
$120$	58.0605	5.30018
$121$	−4.79800	−0.436182
$122$	8.90563	0.806278
$123$	−24.3703	−2.19740
$124$	48.0303	4.31325
$125$	−12.1674	−1.08829
$126$	79.5570	7.08750
$127$	13.8729	1.23102	0.615512	−	0.788127i	$-0.288949\pi$
$127$	13.8729	1.23102	0.615512	+	0.788127i	$0.288949\pi$
$128$	−49.2733	−4.35518
$129$	2.29744	0.202279
$130$	18.5851	1.63002
$131$	−16.0684	−1.40390	−0.701950	−	0.712226i	$-0.747687\pi$
$131$	−16.0684	−1.40390	−0.701950	+	0.712226i	$0.747687\pi$
$132$	45.3715	3.94909
$133$	28.0696	2.43395
$134$	−35.1587	−3.03725
$135$	−26.8018	−2.30673
$136$	−69.6579	−5.97312
$137$	−10.1798	−0.869722	−0.434861	−	0.900498i	$-0.643203\pi$
$137$	−10.1798	−0.869722	−0.434861	+	0.900498i	$0.643203\pi$
$138$	−71.7092	−6.10429
$139$	12.9963	1.10233	0.551165	−	0.834396i	$-0.314183\pi$
$139$	12.9963	1.10233	0.551165	+	0.834396i	$0.314183\pi$
$140$	−38.3261	−3.23915
$141$	−19.5713	−1.64820
$142$	−1.40695	−0.118069
$143$	9.33695	0.780795
$144$	122.566	10.2138
$145$	−5.93410	−0.492800
$146$	9.95779	0.824113
$147$	−24.3494	−2.00831
$148$	−9.22138	−0.757993
$149$	4.42574	0.362571	0.181285	−	0.983431i	$-0.441974\pi$
$149$	4.42574	0.362571	0.181285	+	0.983431i	$0.441974\pi$
$150$	−15.8469	−1.29389
$151$	7.32228	0.595878	0.297939	−	0.954585i	$-0.403701\pi$
$151$	7.32228	0.595878	0.297939	+	0.954585i	$0.403701\pi$
$152$	73.2090	5.93804
$153$	53.2078	4.30160
$154$	−26.1306	−2.10567
$155$	15.4202	1.23858
$156$	68.3056	5.46883
$157$	11.5458	0.921457	0.460728	−	0.887541i	$-0.347588\pi$
$157$	11.5458	0.921457	0.460728	+	0.887541i	$0.347588\pi$
$158$	14.2048	1.13007
$159$	−25.2789	−2.00475
$160$	−44.4347	−3.51287
$161$	30.4317	2.39835
$162$	−70.9711	−5.57601
$163$	9.41451	0.737402	0.368701	−	0.929548i	$-0.379803\pi$
$163$	9.41451	0.737402	0.368701	+	0.929548i	$0.379803\pi$
$164$	41.9569	3.27628
$165$	14.5666	1.13401
$166$	38.8072	3.01202
$167$	6.57335	0.508661	0.254331	−	0.967117i	$-0.418145\pi$
$167$	6.57335	0.508661	0.254331	+	0.967117i	$0.418145\pi$
$168$	−122.896	−9.48166
$169$	1.05653	0.0812713
$170$	−34.7862	−2.66798
$171$	−55.9203	−4.27633
$172$	−3.95537	−0.301594
$173$	−12.3020	−0.935306	−0.467653	−	0.883912i	$-0.654900\pi$
$173$	−12.3020	−0.935306	−0.467653	+	0.883912i	$0.654900\pi$
$174$	−29.5979	−2.24381
$175$	6.72505	0.508366
$176$	−40.2569	−3.03448
$177$	−24.5694	−1.84675
$178$	20.3843	1.52787
$179$	−0.101825	−0.00761077	−0.00380538	−	0.999993i	$-0.501211\pi$
$179$	−0.101825	−0.00761077	−0.00380538	+	0.999993i	$0.501211\pi$
$180$	76.3533	5.69104
$181$	−7.46934	−0.555192	−0.277596	−	0.960698i	$-0.589538\pi$
$181$	−7.46934	−0.555192	−0.277596	+	0.960698i	$0.589538\pi$
$182$	−39.3390	−2.91600
$183$	10.5082	0.776792
$184$	79.3696	5.85121
$185$	−2.96053	−0.217663
$186$	76.9122	5.63947
$187$	−17.4762	−1.27799
$188$	33.6948	2.45744
$189$	56.7312	4.12659
$190$	36.5595	2.65231
$191$	9.56732	0.692267	0.346133	−	0.938185i	$-0.387494\pi$
$191$	9.56732	0.692267	0.346133	+	0.938185i	$0.387494\pi$
$192$	−116.460	−8.40476
$193$	−6.68570	−0.481247	−0.240624	−	0.970618i	$-0.577352\pi$
$193$	−6.68570	−0.481247	−0.240624	+	0.970618i	$0.577352\pi$
$194$	−24.0052	−1.72347
$195$	21.9296	1.57041
$196$	41.9209	2.99435
$197$	−15.5028	−1.10453	−0.552265	−	0.833668i	$-0.686236\pi$
$197$	−15.5028	−1.10453	−0.552265	+	0.833668i	$0.686236\pi$
$198$	52.0574	3.69956
$199$	13.2417	0.938679	0.469339	−	0.883018i	$-0.344492\pi$
$199$	13.2417	0.938679	0.469339	+	0.883018i	$0.344492\pi$
$200$	17.5398	1.24025
$201$	−41.4857	−2.92617
$202$	34.8153	2.44960
$203$	12.5607	0.881586
$204$	−127.849	−8.95124
$205$	13.4703	0.940806
$206$	10.0025	0.696904
$207$	−60.6260	−4.21380
$208$	−60.6057	−4.20225
$209$	18.3671	1.27048
$210$	−61.3727	−4.23512
$211$	1.78065	0.122585	0.0612926	−	0.998120i	$-0.480478\pi$
$211$	1.78065	0.122585	0.0612926	+	0.998120i	$0.480478\pi$
$212$	43.5211	2.98904
$213$	−1.66014	−0.113751
$214$	0.161488	0.0110391
$215$	−1.26987	−0.0866047
$216$	147.962	10.0675
$217$	−32.6397	−2.21573
$218$	−47.7520	−3.23417
$219$	11.7498	0.793975
$220$	−25.0784	−1.69078
$221$	−26.3099	−1.76980
$222$	−14.7665	−0.991059
$223$	3.07804	0.206121	0.103060	−	0.994675i	$-0.467137\pi$
$223$	3.07804	0.206121	0.103060	+	0.994675i	$0.467137\pi$
$224$	94.0546	6.28429
$225$	−13.3976	−0.893177
$226$	−33.7599	−2.24567
$227$	2.80487	0.186166	0.0930829	−	0.995658i	$-0.470328\pi$
$227$	2.80487	0.186166	0.0930829	+	0.995658i	$0.470328\pi$
$228$	134.367	8.89867
$229$	11.6867	0.772276	0.386138	−	0.922441i	$-0.373809\pi$
$229$	11.6867	0.772276	0.386138	+	0.922441i	$0.373809\pi$
$230$	39.6361	2.61352
$231$	−30.8330	−2.02866
$232$	32.7598	2.15078
$233$	14.5461	0.952949	0.476474	−	0.879188i	$-0.341914\pi$
$233$	14.5461	0.952949	0.476474	+	0.879188i	$0.341914\pi$
$234$	78.3711	5.12328
$235$	10.8177	0.705671
$236$	42.2997	2.75348
$237$	16.7610	1.08875
$238$	73.6317	4.77283
$239$	−2.57658	−0.166665	−0.0833325	−	0.996522i	$-0.526556\pi$
$239$	−2.57658	−0.166665	−0.0833325	+	0.996522i	$0.526556\pi$
$240$	−94.5510	−6.10324
$241$	−5.40054	−0.347879	−0.173940	−	0.984756i	$-0.555650\pi$
$241$	−5.40054	−0.347879	−0.173940	+	0.984756i	$0.555650\pi$
$242$	13.2276	0.850305
$243$	−39.0248	−2.50344
$244$	−18.0914	−1.15818
$245$	13.4588	0.859848
$246$	67.1867	4.28367
$247$	27.6512	1.75940
$248$	−85.1285	−5.40566
$249$	45.7907	2.90187
$250$	33.5445	2.12154
$251$	25.2751	1.59535	0.797676	−	0.603086i	$-0.206062\pi$
$251$	25.2751	1.59535	0.797676	+	0.603086i	$0.206062\pi$
$252$	−161.617	−10.1809
$253$	19.9127	1.25190
$254$	−38.2464	−2.39979
$255$	−41.0461	−2.57041
$256$	64.2410	4.01506
$257$	2.80617	0.175044	0.0875220	−	0.996163i	$-0.472105\pi$
$257$	2.80617	0.175044	0.0875220	+	0.996163i	$0.472105\pi$
$258$	−6.33384	−0.394328
$259$	6.26654	0.389384
$260$	−37.7548	−2.34145
$261$	−25.0234	−1.54891
$262$	44.2990	2.73680
$263$	14.6623	0.904117	0.452059	−	0.891988i	$-0.350690\pi$
$263$	14.6623	0.904117	0.452059	+	0.891988i	$0.350690\pi$
$264$	−80.4162	−4.94927
$265$	13.9725	0.858324
$266$	−77.3854	−4.74480
$267$	24.0525	1.47199
$268$	71.4233	4.36287
$269$	28.1180	1.71439	0.857193	−	0.514995i	$-0.172206\pi$
$269$	28.1180	1.71439	0.857193	+	0.514995i	$0.172206\pi$
$270$	73.8901	4.49681
$271$	3.79653	0.230623	0.115311	−	0.993329i	$-0.463213\pi$
$271$	3.79653	0.230623	0.115311	+	0.993329i	$0.463213\pi$
$272$	113.437	6.87814
$273$	−46.4182	−2.80936
$274$	28.0649	1.69546
$275$	4.40048	0.265359
$276$	145.674	8.76855
$277$	17.1762	1.03202	0.516009	−	0.856583i	$-0.327417\pi$
$277$	17.1762	1.03202	0.516009	+	0.856583i	$0.327417\pi$
$278$	−35.8296	−2.14891
$279$	65.0249	3.89294
$280$	67.9290	4.05953
$281$	−18.3358	−1.09382	−0.546912	−	0.837190i	$-0.684197\pi$
$281$	−18.3358	−1.09382	−0.546912	+	0.837190i	$0.684197\pi$
$282$	53.9563	3.21305
$283$	−4.39088	−0.261010	−0.130505	−	0.991448i	$-0.541660\pi$
$283$	−4.39088	−0.261010	−0.130505	+	0.991448i	$0.541660\pi$
$284$	2.85817	0.169601
$285$	43.1386	2.55531
$286$	−25.7411	−1.52210
$287$	−28.5125	−1.68304
$288$	−187.376	−11.0412
$289$	32.2450	1.89676
$290$	16.3598	0.960678
$291$	−28.3250	−1.66044
$292$	−20.2288	−1.18380
$293$	−11.9366	−0.697343	−0.348672	−	0.937245i	$-0.613367\pi$
$293$	−11.9366	−0.697343	−0.348672	+	0.937245i	$0.613367\pi$
$294$	67.1292	3.91505
$295$	13.5804	0.790679
$296$	16.3439	0.949971
$297$	37.1216	2.15401
$298$	−12.2014	−0.706805
$299$	29.9781	1.73368
$300$	32.1923	1.85862
$301$	2.68793	0.154930
$302$	−20.1868	−1.16162
$303$	41.0806	2.36002
$304$	−119.220	−6.83774
$305$	−5.80826	−0.332580
$306$	−146.689	−8.38565
$307$	0.0903459	0.00515631	0.00257816	−	0.999997i	$-0.499179\pi$
$307$	0.0903459	0.00515631	0.00257816	+	0.999997i	$0.499179\pi$
$308$	53.0833	3.02470
$309$	11.8024	0.671418
$310$	−42.5119	−2.41452
$311$	9.06814	0.514207	0.257104	−	0.966384i	$-0.417232\pi$
$311$	9.06814	0.514207	0.257104	+	0.966384i	$0.417232\pi$
$312$	−121.064	−6.85392
$313$	11.7268	0.662839	0.331420	−	0.943483i	$-0.392472\pi$
$313$	11.7268	0.662839	0.331420	+	0.943483i	$0.392472\pi$
$314$	−31.8308	−1.79631
$315$	−51.8871	−2.92351
$316$	−28.8565	−1.62330
$317$	−17.5604	−0.986292	−0.493146	−	0.869947i	$-0.664153\pi$
$317$	−17.5604	−0.986292	−0.493146	+	0.869947i	$0.664153\pi$
$318$	69.6916	3.90811
$319$	8.21896	0.460174
$320$	64.3712	3.59846
$321$	0.190549	0.0106354
$322$	−83.8974	−4.67542
$323$	−51.7554	−2.87975
$324$	144.175	8.00971
$325$	6.62480	0.367478
$326$	−25.9549	−1.43751
$327$	−56.3452	−3.11590
$328$	−74.3641	−4.10607
$329$	−22.8978	−1.26240
$330$	−40.1587	−2.21066
$331$	−16.8606	−0.926741	−0.463370	−	0.886165i	$-0.653360\pi$
$331$	−16.8606	−0.926741	−0.463370	+	0.886165i	$0.653360\pi$
$332$	−78.8351	−4.32664
$333$	−12.4842	−0.684130
$334$	−18.1221	−0.991598
$335$	22.9305	1.25283
$336$	200.136	10.9183
$337$	18.6598	1.01646	0.508232	−	0.861220i	$-0.330299\pi$
$337$	18.6598	1.01646	0.508232	+	0.861220i	$0.330299\pi$
$338$	−2.91275	−0.158433
$339$	−39.8352	−2.16355
$340$	70.6666	3.83244
$341$	−21.3575	−1.15658
$342$	154.167	8.33640
$343$	−1.84650	−0.0997015
$344$	7.01047	0.377979
$345$	46.7688	2.51795
$346$	33.9156	1.82331
$347$	0.398374	0.0213859	0.0106929	−	0.999943i	$-0.496596\pi$
$347$	0.398374	0.0213859	0.0106929	+	0.999943i	$0.496596\pi$
$348$	60.1269	3.22314
$349$	−21.4289	−1.14706	−0.573530	−	0.819184i	$-0.694426\pi$
$349$	−21.4289	−1.14706	−0.573530	+	0.819184i	$0.694426\pi$
$350$	−18.5404	−0.991023
$351$	55.8856	2.98295
$352$	61.5438	3.28030
$353$	−24.4171	−1.29959	−0.649796	−	0.760108i	$-0.725146\pi$
$353$	−24.4171	−1.29959	−0.649796	+	0.760108i	$0.725146\pi$
$354$	67.7357	3.60011
$355$	0.917616	0.0487020
$356$	−41.4098	−2.19471
$357$	86.8821	4.59829
$358$	0.280722	0.0148366
$359$	19.5541	1.03203	0.516013	−	0.856581i	$-0.327415\pi$
$359$	19.5541	1.03203	0.516013	+	0.856581i	$0.327415\pi$
$360$	−135.328	−7.13241
$361$	35.3939	1.86283
$362$	20.5923	1.08231
$363$	15.6080	0.819208
$364$	79.9154	4.18871
$365$	−6.49448	−0.339937
$366$	−28.9703	−1.51430
$367$	−5.90639	−0.308311	−0.154156	−	0.988047i	$-0.549266\pi$
$367$	−5.90639	−0.308311	−0.154156	+	0.988047i	$0.549266\pi$
$368$	−129.253	−6.73776
$369$	56.8026	2.95703
$370$	8.16191	0.424318
$371$	−29.5755	−1.53548
$372$	−156.244	−8.10086
$373$	−10.5668	−0.547126	−0.273563	−	0.961854i	$-0.588202\pi$
$373$	−10.5668	−0.547126	−0.273563	+	0.961854i	$0.588202\pi$
$374$	48.1803	2.49134
$375$	39.5810	2.04395
$376$	−59.7204	−3.07984
$377$	12.3734	0.637264
$378$	−156.403	−8.04449
$379$	7.56953	0.388821	0.194410	−	0.980920i	$-0.437721\pi$
$379$	7.56953	0.388821	0.194410	+	0.980920i	$0.437721\pi$
$380$	−74.2691	−3.80993
$381$	−45.1290	−2.31203
$382$	−26.3762	−1.34952
$383$	17.9445	0.916922	0.458461	−	0.888715i	$-0.348401\pi$
$383$	17.9445	0.916922	0.458461	+	0.888715i	$0.348401\pi$
$384$	160.287	8.17963
$385$	17.0424	0.868562
$386$	18.4319	0.938157
$387$	−5.35490	−0.272205
$388$	48.7655	2.47569
$389$	6.65460	0.337402	0.168701	−	0.985667i	$-0.446043\pi$
$389$	6.65460	0.337402	0.168701	+	0.985667i	$0.446043\pi$
$390$	−60.4578	−3.06140
$391$	−56.1107	−2.83764
$392$	−74.3004	−3.75274
$393$	52.2708	2.63671
$394$	42.7399	2.15320
$395$	−9.26439	−0.466142
$396$	−105.752	−5.31426
$397$	−7.88802	−0.395888	−0.197944	−	0.980213i	$-0.563426\pi$
$397$	−7.88802	−0.395888	−0.197944	+	0.980213i	$0.563426\pi$
$398$	−36.5061	−1.82989
$399$	−91.3113	−4.57128
$400$	−28.5633	−1.42817
$401$	−10.6369	−0.531183	−0.265591	−	0.964086i	$-0.585567\pi$
$401$	−10.6369	−0.531183	−0.265591	+	0.964086i	$0.585567\pi$
$402$	114.372	5.70436
$403$	−32.1532	−1.60166
$404$	−70.7259	−3.51874
$405$	46.2874	2.30004
$406$	−34.6286	−1.71859
$407$	4.10046	0.203252
$408$	226.599	11.2183
$409$	14.3395	0.709043	0.354521	−	0.935048i	$-0.384644\pi$
$409$	14.3395	0.709043	0.354521	+	0.935048i	$0.384644\pi$
$410$	−37.1364	−1.83403
$411$	33.1153	1.63346
$412$	−20.3196	−1.00107
$413$	−28.7455	−1.41447
$414$	167.140	8.21450
$415$	−25.3101	−1.24242
$416$	92.6526	4.54267
$417$	−42.2773	−2.07033
$418$	−50.6364	−2.47671
$419$	−3.02610	−0.147835	−0.0739174	−	0.997264i	$-0.523550\pi$
$419$	−3.02610	−0.147835	−0.0739174	+	0.997264i	$0.523550\pi$
$420$	124.676	6.08357
$421$	−29.1758	−1.42194	−0.710970	−	0.703222i	$-0.751744\pi$
$421$	−29.1758	−1.42194	−0.710970	+	0.703222i	$0.751744\pi$
$422$	−4.90909	−0.238971
$423$	45.6170	2.21798
$424$	−77.1366	−3.74608
$425$	−12.3998	−0.601479
$426$	4.57686	0.221750
$427$	12.2943	0.594964
$428$	−0.328056	−0.0158572
$429$	−30.3734	−1.46644
$430$	3.50092	0.168830
$431$	8.61350	0.414898	0.207449	−	0.978246i	$-0.433484\pi$
$431$	8.61350	0.414898	0.207449	+	0.978246i	$0.433484\pi$
$432$	−240.955	−11.5929
$433$	−3.09369	−0.148673	−0.0743365	−	0.997233i	$-0.523684\pi$
$433$	−3.09369	−0.148673	−0.0743365	+	0.997233i	$0.523684\pi$
$434$	89.9848	4.31941
$435$	19.3038	0.925545
$436$	97.0061	4.64575
$437$	58.9711	2.82097
$438$	−32.3930	−1.54780
$439$	12.3698	0.590380	0.295190	−	0.955439i	$-0.404617\pi$
$439$	12.3698	0.590380	0.295190	+	0.955439i	$0.404617\pi$
$440$	44.4487	2.11901
$441$	56.7539	2.70257
$442$	72.5341	3.45009
$443$	−19.3522	−0.919450	−0.459725	−	0.888061i	$-0.652052\pi$
$443$	−19.3522	−0.919450	−0.459725	+	0.888061i	$0.652052\pi$
$444$	29.9974	1.42361
$445$	−13.2946	−0.630226
$446$	−8.48587	−0.401817
$447$	−14.3970	−0.680957
$448$	−136.254	−6.43741
$449$	17.6185	0.831467	0.415733	−	0.909487i	$-0.363525\pi$
$449$	17.6185	0.831467	0.415733	+	0.909487i	$0.363525\pi$
$450$	36.9361	1.74118
$451$	−18.6569	−0.878519
$452$	68.5818	3.22581
$453$	−23.8196	−1.11914
$454$	−7.73277	−0.362917
$455$	25.6569	1.20281
$456$	−238.151	−11.1524
$457$	−30.1173	−1.40883	−0.704414	−	0.709790i	$-0.748790\pi$
$457$	−30.1173	−1.40883	−0.704414	+	0.709790i	$0.748790\pi$
$458$	−32.2190	−1.50550
$459$	−104.602	−4.88242
$460$	−80.5189	−3.75422
$461$	−39.0856	−1.82040	−0.910198	−	0.414173i	$-0.864071\pi$
$461$	−39.0856	−1.82040	−0.910198	+	0.414173i	$0.864071\pi$
$462$	85.0037	3.95473
$463$	3.77824	0.175590	0.0877949	−	0.996139i	$-0.472018\pi$
$463$	3.77824	0.175590	0.0877949	+	0.996139i	$0.472018\pi$
$464$	−53.3489	−2.47666
$465$	−50.1622	−2.32622
$466$	−40.1023	−1.85771
$467$	−10.3711	−0.479919	−0.239960	−	0.970783i	$-0.577134\pi$
$467$	−10.3711	−0.479919	−0.239960	+	0.970783i	$0.577134\pi$
$468$	−159.207	−7.35937
$469$	−48.5369	−2.24123
$470$	−29.8235	−1.37565
$471$	−37.5589	−1.73062
$472$	−74.9717	−3.45085
$473$	1.75883	0.0808709
$474$	−46.2086	−2.12243
$475$	13.0319	0.597946
$476$	−149.580	−6.85597
$477$	58.9203	2.69778
$478$	7.10339	0.324902
$479$	−38.2741	−1.74879	−0.874393	−	0.485218i	$-0.838740\pi$
$479$	−38.2741	−1.74879	−0.874393	+	0.485218i	$0.838740\pi$
$480$	144.547	6.59765
$481$	6.17313	0.281470
$482$	14.8888	0.678165
$483$	−98.9952	−4.50444
$484$	−26.8714	−1.22143
$485$	15.6562	0.710911
$486$	107.588	4.88027
$487$	26.7520	1.21225	0.606124	−	0.795370i	$-0.292724\pi$
$487$	26.7520	1.21225	0.606124	+	0.795370i	$0.292724\pi$
$488$	32.0651	1.45152
$489$	−30.6257	−1.38494
$490$	−37.1045	−1.67621
$491$	37.4636	1.69071	0.845355	−	0.534205i	$-0.179389\pi$
$491$	37.4636	1.69071	0.845355	+	0.534205i	$0.179389\pi$
$492$	−136.487	−6.15331
$493$	−23.1596	−1.04306
$494$	−76.2318	−3.42983
$495$	−33.9519	−1.52602
$496$	138.631	6.22471
$497$	−1.94231	−0.0871247
$498$	−126.241	−5.65698
$499$	−18.1272	−0.811483	−0.405742	−	0.913988i	$-0.632987\pi$
$499$	−18.1272	−0.811483	−0.405742	+	0.913988i	$0.632987\pi$
$500$	−68.1442	−3.04750
$501$	−21.3833	−0.955335
$502$	−69.6812	−3.11002
$503$	−8.45159	−0.376838	−0.188419	−	0.982089i	$-0.560336\pi$
$503$	−8.45159	−0.376838	−0.188419	+	0.982089i	$0.560336\pi$
$504$	286.448	12.7594
$505$	−22.7066	−1.01043
$506$	−54.8975	−2.44049
$507$	−3.43691	−0.152639
$508$	77.6959	3.44720
$509$	1.95539	0.0866713	0.0433357	−	0.999061i	$-0.486202\pi$
$509$	1.95539	0.0866713	0.0433357	+	0.999061i	$0.486202\pi$
$510$	113.160	5.01083
$511$	13.7468	0.608124
$512$	−78.5600	−3.47189
$513$	109.935	4.85374
$514$	−7.73635	−0.341236
$515$	−6.52361	−0.287464
$516$	12.8669	0.566435
$517$	−14.9830	−0.658951
$518$	−17.2763	−0.759076
$519$	40.0188	1.75663
$520$	66.9164	2.93448
$521$	−39.1457	−1.71500	−0.857501	−	0.514482i	$-0.827984\pi$
$521$	−39.1457	−1.71500	−0.857501	+	0.514482i	$0.827984\pi$
$522$	68.9871	3.01948
$523$	32.8282	1.43548	0.717739	−	0.696313i	$-0.245177\pi$
$523$	32.8282	1.43548	0.717739	+	0.696313i	$0.245177\pi$
$524$	−89.9915	−3.93130
$525$	−21.8768	−0.954781
$526$	−40.4226	−1.76251
$527$	60.1819	2.62157
$528$	130.957	5.69917
$529$	40.9336	1.77972
$530$	−38.5209	−1.67324
$531$	57.2667	2.48516
$532$	157.205	6.81570
$533$	−28.0875	−1.21660
$534$	−66.3106	−2.86954
$535$	−0.105323	−0.00455349
$536$	−126.590	−5.46786
$537$	0.331240	0.0142941
$538$	−77.5188	−3.34207
$539$	−18.6409	−0.802921
$540$	−150.105	−6.45947
$541$	31.4410	1.35175	0.675877	−	0.737015i	$-0.263765\pi$
$541$	31.4410	1.35175	0.675877	+	0.737015i	$0.263765\pi$
$542$	−10.4667	−0.449582
$543$	24.2980	1.04273
$544$	−173.420	−7.43532
$545$	31.1439	1.33406
$546$	127.971	5.47664
$547$	−2.18087	−0.0932471	−0.0466236	−	0.998913i	$-0.514846\pi$
$547$	−2.18087	−0.0932471	−0.0466236	+	0.998913i	$0.514846\pi$
$548$	−57.0126	−2.43546
$549$	−24.4927	−1.04532
$550$	−12.1317	−0.517298
$551$	24.3403	1.03693
$552$	−258.192	−10.9894
$553$	19.6099	0.833897
$554$	−47.3532	−2.01184
$555$	9.63069	0.408800
$556$	72.7862	3.08682
$557$	30.5071	1.29263	0.646314	−	0.763071i	$-0.276310\pi$
$557$	30.5071	1.29263	0.646314	+	0.763071i	$0.276310\pi$
$558$	−179.268	−7.58900
$559$	2.64787	0.111993
$560$	−110.622	−4.67462
$561$	56.8505	2.40023
$562$	50.5502	2.13233
$563$	33.8418	1.42626	0.713131	−	0.701031i	$-0.247277\pi$
$563$	33.8418	1.42626	0.713131	+	0.701031i	$0.247277\pi$
$564$	−109.610	−4.61541
$565$	22.0182	0.926314
$566$	12.1052	0.508821
$567$	−97.9763	−4.11462
$568$	−5.06579	−0.212556
$569$	−11.2740	−0.472632	−0.236316	−	0.971676i	$-0.575940\pi$
$569$	−11.2740	−0.472632	−0.236316	+	0.971676i	$0.575940\pi$
$570$	−118.929	−4.98139
$571$	−17.7055	−0.740952	−0.370476	−	0.928842i	$-0.620805\pi$
$571$	−17.7055	−0.740952	−0.370476	+	0.928842i	$0.620805\pi$
$572$	52.2920	2.18644
$573$	−31.1227	−1.30017
$574$	78.6063	3.28097
$575$	14.1286	0.589203
$576$	271.446	11.3102
$577$	24.2712	1.01042	0.505211	−	0.862996i	$-0.331415\pi$
$577$	24.2712	1.01042	0.505211	+	0.862996i	$0.331415\pi$
$578$	−88.8964	−3.69760
$579$	21.7488	0.903848
$580$	−33.2341	−1.37997
$581$	53.5736	2.22261
$582$	78.0895	3.23691
$583$	−19.3525	−0.801497
$584$	35.8534	1.48363
$585$	−51.1137	−2.11329
$586$	32.9081	1.35942
$587$	−7.68768	−0.317305	−0.158652	−	0.987335i	$-0.550715\pi$
$587$	−7.68768	−0.317305	−0.158652	+	0.987335i	$0.550715\pi$
$588$	−136.370	−5.62380
$589$	−63.2499	−2.60617
$590$	−37.4398	−1.54137
$591$	50.4311	2.07446
$592$	−26.6159	−1.09391
$593$	45.1472	1.85397	0.926987	−	0.375093i	$-0.122389\pi$
$593$	45.1472	1.85397	0.926987	+	0.375093i	$0.122389\pi$
$594$	−102.341	−4.19909
$595$	−48.0226	−1.96874
$596$	24.7865	1.01530
$597$	−43.0756	−1.76297
$598$	−82.6468	−3.37968
$599$	−34.3422	−1.40318	−0.701592	−	0.712579i	$-0.747527\pi$
$599$	−34.3422	−1.40318	−0.701592	+	0.712579i	$0.747527\pi$
$600$	−57.0573	−2.32936
$601$	28.3016	1.15445	0.577223	−	0.816586i	$-0.304136\pi$
$601$	28.3016	1.15445	0.577223	+	0.816586i	$0.304136\pi$
$602$	−7.41039	−0.302025
$603$	96.6952	3.93773
$604$	41.0087	1.66862
$605$	−8.62707	−0.350740
$606$	−113.255	−4.60068
$607$	−1.92530	−0.0781456	−0.0390728	−	0.999236i	$-0.512440\pi$
$607$	−1.92530	−0.0781456	−0.0390728	+	0.999236i	$0.512440\pi$
$608$	182.261	7.39165
$609$	−40.8602	−1.65574
$610$	16.0128	0.648341
$611$	−22.5565	−0.912538
$612$	297.992	12.0456
$613$	−31.3471	−1.26610	−0.633048	−	0.774112i	$-0.718197\pi$
$613$	−31.3471	−1.26610	−0.633048	+	0.774112i	$0.718197\pi$
$614$	−0.249075	−0.0100519
$615$	−43.8192	−1.76696
$616$	−94.0844	−3.79077
$617$	47.3278	1.90535	0.952674	−	0.303995i	$-0.0983206\pi$
$617$	47.3278	1.90535	0.952674	+	0.303995i	$0.0983206\pi$
$618$	−32.5383	−1.30888
$619$	−23.2218	−0.933365	−0.466682	−	0.884425i	$-0.654551\pi$
$619$	−23.2218	−0.933365	−0.466682	+	0.884425i	$0.654551\pi$
$620$	86.3612	3.46835
$621$	119.186	4.78277
$622$	−25.0000	−1.00241
$623$	28.1407	1.12743
$624$	197.152	7.89240
$625$	−13.0428	−0.521712
$626$	−32.3298	−1.29216
$627$	−59.7487	−2.38613
$628$	64.6628	2.58033
$629$	−11.5544	−0.460704
$630$	143.048	5.69917
$631$	−31.6782	−1.26109	−0.630544	−	0.776154i	$-0.717168\pi$
$631$	−31.6782	−1.26109	−0.630544	+	0.776154i	$0.717168\pi$
$632$	51.1450	2.03444
$633$	−5.79251	−0.230232
$634$	48.4125	1.92271
$635$	24.9443	0.989886
$636$	−141.575	−5.61383
$637$	−28.0634	−1.11191
$638$	−22.6589	−0.897075
$639$	3.86948	0.153074
$640$	−88.5962	−3.50207
$641$	0.985742	0.0389345	0.0194672	−	0.999810i	$-0.493803\pi$
$641$	0.985742	0.0389345	0.0194672	+	0.999810i	$0.493803\pi$
$642$	−0.525325	−0.0207329
$643$	−20.1589	−0.794991	−0.397495	−	0.917604i	$-0.630121\pi$
$643$	−20.1589	−0.794991	−0.397495	+	0.917604i	$0.630121\pi$
$644$	170.434	6.71604
$645$	4.13093	0.162655
$646$	142.685	5.61386
$647$	−16.7382	−0.658045	−0.329022	−	0.944322i	$-0.606719\pi$
$647$	−16.7382	−0.658045	−0.329022	+	0.944322i	$0.606719\pi$
$648$	−255.534	−10.0383
$649$	−18.8093	−0.738331
$650$	−18.2640	−0.716372
$651$	106.178	4.16144
$652$	52.7264	2.06492
$653$	−39.3900	−1.54145	−0.770726	−	0.637167i	$-0.780106\pi$
$653$	−39.3900	−1.54145	−0.770726	+	0.637167i	$0.780106\pi$
$654$	155.339	6.07422
$655$	−28.8918	−1.12890
$656$	121.101	4.72821
$657$	−27.3864	−1.06845
$658$	63.1272	2.46095
$659$	−10.9746	−0.427508	−0.213754	−	0.976887i	$-0.568569\pi$
$659$	−10.9746	−0.427508	−0.213754	+	0.976887i	$0.568569\pi$
$660$	81.5806	3.17552
$661$	−2.39831	−0.0932835	−0.0466418	−	0.998912i	$-0.514852\pi$
$661$	−2.39831	−0.0932835	−0.0466418	+	0.998912i	$0.514852\pi$
$662$	46.4830	1.80661
$663$	85.5870	3.32392
$664$	139.727	5.42245
$665$	50.4708	1.95717
$666$	34.4178	1.33366
$667$	26.3886	1.02177
$668$	36.8143	1.42439
$669$	−10.0129	−0.387123
$670$	−63.2173	−2.44230
$671$	8.04468	0.310561
$672$	−305.962	−11.8028
$673$	15.3560	0.591931	0.295966	−	0.955199i	$-0.404359\pi$
$673$	15.3560	0.591931	0.295966	+	0.955199i	$0.404359\pi$
$674$	−51.4434	−1.98152
$675$	26.3387	1.01378
$676$	5.91712	0.227582
$677$	−20.5546	−0.789978	−0.394989	−	0.918686i	$-0.629252\pi$
$677$	−20.5546	−0.789978	−0.394989	+	0.918686i	$0.629252\pi$
$678$	109.822	4.21768
$679$	−33.1394	−1.27177
$680$	−125.249	−4.80308
$681$	−9.12432	−0.349645
$682$	58.8807	2.25466
$683$	−32.7145	−1.25179	−0.625893	−	0.779909i	$-0.715265\pi$
$683$	−32.7145	−1.25179	−0.625893	+	0.779909i	$0.715265\pi$
$684$	−313.184	−11.9749
$685$	−18.3039	−0.699357
$686$	5.09062	0.194361
$687$	−38.0170	−1.45044
$688$	−11.4165	−0.435249
$689$	−29.1346	−1.10994
$690$	−128.937	−4.90855
$691$	−36.9533	−1.40577	−0.702884	−	0.711304i	$-0.748105\pi$
$691$	−36.9533	−1.40577	−0.702884	+	0.711304i	$0.748105\pi$
$692$	−68.8980	−2.61911
$693$	71.8658	2.72996
$694$	−1.09828	−0.0416902
$695$	23.3681	0.886401
$696$	−106.568	−4.03947
$697$	52.5720	1.99131
$698$	59.0774	2.23611
$699$	−47.3190	−1.78977
$700$	37.6639	1.42356
$701$	−42.5056	−1.60541	−0.802707	−	0.596373i	$-0.796608\pi$
$701$	−42.5056	−1.60541	−0.802707	+	0.596373i	$0.796608\pi$
$702$	−154.071	−5.81505
$703$	12.1434	0.457998
$704$	−89.1568	−3.36022
$705$	−35.1904	−1.32535
$706$	67.3158	2.53346
$707$	48.0629	1.80759
$708$	−137.602	−5.17140
$709$	11.5810	0.434935	0.217468	−	0.976068i	$-0.430220\pi$
$709$	11.5810	0.434935	0.217468	+	0.976068i	$0.430220\pi$
$710$	−2.52978	−0.0949411
$711$	−39.0668	−1.46512
$712$	73.3943	2.75057
$713$	−68.5725	−2.56806
$714$	−239.526	−8.96403
$715$	16.7884	0.627849
$716$	−0.570276	−0.0213122
$717$	8.38168	0.313020
$718$	−53.9089	−2.01186
$719$	−43.5709	−1.62492	−0.812460	−	0.583017i	$-0.801872\pi$
$719$	−43.5709	−1.62492	−0.812460	+	0.583017i	$0.801872\pi$
$720$	220.380	8.21309
$721$	13.8085	0.514255
$722$	−97.5776	−3.63146
$723$	17.5681	0.653364
$724$	−41.8323	−1.55469
$725$	5.83157	0.216579
$726$	−43.0299	−1.59699
$727$	14.5406	0.539281	0.269641	−	0.962961i	$-0.413095\pi$
$727$	14.5406	0.539281	0.269641	+	0.962961i	$0.413095\pi$
$728$	−141.641	−5.24958
$729$	49.7196	1.84147
$730$	17.9047	0.662682
$731$	−4.95608	−0.183307
$732$	58.8519	2.17523
$733$	16.7695	0.619396	0.309698	−	0.950835i	$-0.399772\pi$
$733$	16.7695	0.619396	0.309698	+	0.950835i	$0.399772\pi$
$734$	16.2834	0.601031
$735$	−43.7817	−1.61491
$736$	197.598	7.28357
$737$	−31.7597	−1.16988
$738$	−156.600	−5.76451
$739$	−41.7571	−1.53606	−0.768029	−	0.640415i	$-0.778762\pi$
$739$	−41.7571	−1.53606	−0.768029	+	0.640415i	$0.778762\pi$
$740$	−16.5806	−0.609514
$741$	−89.9501	−3.30440
$742$	81.5369	2.99331
$743$	−8.79215	−0.322553	−0.161276	−	0.986909i	$-0.551561\pi$
$743$	−8.79215	−0.322553	−0.161276	+	0.986909i	$0.551561\pi$
$744$	276.925	10.1526
$745$	7.95773	0.291549
$746$	29.1316	1.06658
$747$	−106.729	−3.90502
$748$	−97.8761	−3.57871
$749$	0.222936	0.00814589
$750$	−109.121	−3.98454
$751$	29.9024	1.09116	0.545578	−	0.838060i	$-0.316310\pi$
$751$	29.9024	1.09116	0.545578	+	0.838060i	$0.316310\pi$
$752$	97.2540	3.54649
$753$	−82.2207	−2.99629
$754$	−34.1124	−1.24230
$755$	13.1659	0.479155
$756$	317.726	11.5556
$757$	23.6158	0.858330	0.429165	−	0.903226i	$-0.358808\pi$
$757$	23.6158	0.858330	0.429165	+	0.903226i	$0.358808\pi$
$758$	−20.8685	−0.757978
$759$	−64.7766	−2.35124
$760$	131.634	4.77487
$761$	−24.9825	−0.905613	−0.452807	−	0.891609i	$-0.649577\pi$
$761$	−24.9825	−0.905613	−0.452807	+	0.891609i	$0.649577\pi$
$762$	124.417	4.50714
$763$	−65.9221	−2.38654
$764$	53.5821	1.93853
$765$	95.6707	3.45898
$766$	−49.4714	−1.78747
$767$	−28.3170	−1.02247
$768$	−208.978	−7.54084
$769$	25.5392	0.920969	0.460484	−	0.887668i	$-0.347676\pi$
$769$	25.5392	0.920969	0.460484	+	0.887668i	$0.347676\pi$
$770$	−46.9844	−1.69320
$771$	−9.12854	−0.328756
$772$	−37.4435	−1.34762
$773$	31.3072	1.12604	0.563021	−	0.826443i	$-0.309639\pi$
$773$	31.3072	1.12604	0.563021	+	0.826443i	$0.309639\pi$
$774$	14.7630	0.530644
$775$	−15.1537	−0.544338
$776$	−86.4316	−3.10271
$777$	−20.3852	−0.731316
$778$	−18.3461	−0.657740
$779$	−55.2521	−1.97961
$780$	122.817	4.39757
$781$	−1.27094	−0.0454777
$782$	154.692	5.53177
$783$	49.1939	1.75805
$784$	120.997	4.32133
$785$	20.7600	0.740958
$786$	−144.106	−5.14009
$787$	31.0498	1.10681	0.553403	−	0.832913i	$-0.313329\pi$
$787$	31.0498	1.10681	0.553403	+	0.832913i	$0.313329\pi$
$788$	−86.8242	−3.09298
$789$	−47.6969	−1.69806
$790$	25.5411	0.908710
$791$	−46.6059	−1.65711
$792$	187.435	6.66021
$793$	12.1110	0.430076
$794$	21.7465	0.771756
$795$	−45.4529	−1.61205
$796$	74.1606	2.62855
$797$	6.16871	0.218507	0.109253	−	0.994014i	$-0.465154\pi$
$797$	6.16871	0.218507	0.109253	+	0.994014i	$0.465154\pi$
$798$	251.737	8.91138
$799$	42.2195	1.49362
$800$	43.6669	1.54386
$801$	−56.0618	−1.98085
$802$	29.3250	1.03550
$803$	8.99512	0.317431
$804$	−232.342	−8.19407
$805$	54.7180	1.92855
$806$	88.6434	3.12233
$807$	−91.4687	−3.21985
$808$	125.354	4.40994
$809$	−9.34320	−0.328489	−0.164245	−	0.986420i	$-0.552519\pi$
$809$	−9.34320	−0.328489	−0.164245	+	0.986420i	$0.552519\pi$
$810$	−127.610	−4.48376
$811$	−30.9477	−1.08672	−0.543361	−	0.839499i	$-0.682848\pi$
$811$	−30.9477	−1.08672	−0.543361	+	0.839499i	$0.682848\pi$
$812$	70.3465	2.46868
$813$	−12.3502	−0.433141
$814$	−11.3046	−0.396225
$815$	16.9278	0.592956
$816$	−369.014	−12.9181
$817$	5.20873	0.182230
$818$	−39.5327	−1.38223
$819$	108.192	3.78053
$820$	75.4409	2.63451
$821$	−47.8944	−1.67153	−0.835764	−	0.549089i	$-0.814975\pi$
$821$	−47.8944	−1.67153	−0.835764	+	0.549089i	$0.814975\pi$
$822$	−91.2958	−3.18431
$823$	42.2488	1.47270	0.736349	−	0.676601i	$-0.236548\pi$
$823$	42.2488	1.47270	0.736349	+	0.676601i	$0.236548\pi$
$824$	36.0142	1.25462
$825$	−14.3149	−0.498380
$826$	79.2486	2.75741
$827$	26.7842	0.931378	0.465689	−	0.884948i	$-0.345807\pi$
$827$	26.7842	0.931378	0.465689	+	0.884948i	$0.345807\pi$
$828$	−339.539	−11.7998
$829$	−41.3255	−1.43529	−0.717646	−	0.696408i	$-0.754780\pi$
$829$	−41.3255	−1.43529	−0.717646	+	0.696408i	$0.754780\pi$
$830$	69.7775	2.42201
$831$	−55.8746	−1.93827
$832$	−134.223	−4.65335
$833$	52.5269	1.81995
$834$	116.555	4.03595
$835$	11.8193	0.409022
$836$	102.866	3.55769
$837$	−127.834	−4.41858
$838$	8.34269	0.288193
$839$	−28.0086	−0.966963	−0.483481	−	0.875355i	$-0.660628\pi$
$839$	−28.0086	−0.966963	−0.483481	+	0.875355i	$0.660628\pi$
$840$	−220.975	−7.62435
$841$	−18.1081	−0.624418
$842$	80.4349	2.77197
$843$	59.6470	2.05435
$844$	9.97261	0.343272
$845$	1.89970	0.0653515
$846$	−125.762	−4.32379
$847$	18.2609	0.627451
$848$	125.616	4.31367
$849$	14.2836	0.490213
$850$	34.1851	1.17254
$851$	13.1653	0.451301
$852$	−9.29769	−0.318534
$853$	37.3733	1.27964	0.639818	−	0.768526i	$-0.279010\pi$
$853$	37.3733	1.27964	0.639818	+	0.768526i	$0.279010\pi$
$854$	−33.8943	−1.15984
$855$	−100.548	−3.43867
$856$	0.581444	0.0198733
$857$	−35.3987	−1.20920	−0.604598	−	0.796531i	$-0.706666\pi$
$857$	−35.3987	−1.20920	−0.604598	+	0.796531i	$0.706666\pi$
$858$	83.7365	2.85872
$859$	−3.01122	−0.102741	−0.0513707	−	0.998680i	$-0.516359\pi$
$859$	−3.01122	−0.102741	−0.0513707	+	0.998680i	$0.516359\pi$
$860$	−7.11198	−0.242516
$861$	92.7520	3.16098
$862$	−23.7466	−0.808813
$863$	−51.9625	−1.76882	−0.884411	−	0.466708i	$-0.845440\pi$
$863$	−51.9625	−1.76882	−0.884411	+	0.466708i	$0.845440\pi$
$864$	368.366	12.5321
$865$	−22.1198	−0.752094
$866$	8.52900	0.289827
$867$	−104.894	−3.56238
$868$	−182.800	−6.20464
$869$	12.8315	0.435281
$870$	−53.2187	−1.80428
$871$	−47.8134	−1.62009
$872$	−171.933	−5.82238
$873$	66.0203	2.23445
$874$	−162.578	−5.49928
$875$	46.3085	1.56551
$876$	65.8049	2.22334
$877$	31.5440	1.06517	0.532583	−	0.846378i	$-0.321222\pi$
$877$	31.5440	1.06517	0.532583	+	0.846378i	$0.321222\pi$
$878$	−34.1025	−1.15090
$879$	38.8301	1.30971
$880$	−72.3843	−2.44007
$881$	−39.1419	−1.31872	−0.659362	−	0.751826i	$-0.729174\pi$
$881$	−39.1419	−1.31872	−0.659362	+	0.751826i	$0.729174\pi$
$882$	−156.465	−5.26846
$883$	22.5504	0.758882	0.379441	−	0.925216i	$-0.376116\pi$
$883$	22.5504	0.758882	0.379441	+	0.925216i	$0.376116\pi$
$884$	−147.350	−4.95591
$885$	−44.1773	−1.48500
$886$	53.3522	1.79240
$887$	−27.8918	−0.936514	−0.468257	−	0.883592i	$-0.655118\pi$
$887$	−27.8918	−0.936514	−0.468257	+	0.883592i	$0.655118\pi$
$888$	−53.1672	−1.78417
$889$	−52.7995	−1.77084
$890$	36.6521	1.22858
$891$	−64.1099	−2.14776
$892$	17.2387	0.577194
$893$	−44.3719	−1.48485
$894$	39.6913	1.32748
$895$	−0.183087	−0.00611994
$896$	187.531	6.26497
$897$	−97.5195	−3.25608
$898$	−48.5725	−1.62088
$899$	−28.3032	−0.943966
$900$	−75.0341	−2.50114
$901$	54.5320	1.81672
$902$	51.4354	1.71261
$903$	−8.74393	−0.290980
$904$	−121.554	−4.04282
$905$	−13.4303	−0.446438
$906$	65.6683	2.18168
$907$	−30.0989	−0.999416	−0.499708	−	0.866194i	$-0.666559\pi$
$907$	−30.0989	−0.999416	−0.499708	+	0.866194i	$0.666559\pi$
$908$	15.7088	0.521314
$909$	−95.7509	−3.17586
$910$	−70.7337	−2.34480
$911$	−21.0655	−0.697931	−0.348966	−	0.937135i	$-0.613467\pi$
$911$	−21.0655	−0.697931	−0.348966	+	0.937135i	$0.613467\pi$
$912$	387.826	12.8422
$913$	35.0554	1.16017
$914$	83.0306	2.74641
$915$	18.8944	0.624631
$916$	65.4516	2.16258
$917$	61.1552	2.01952
$918$	288.379	9.51793
$919$	33.0883	1.09148	0.545741	−	0.837954i	$-0.316248\pi$
$919$	33.0883	1.09148	0.545741	+	0.837954i	$0.316248\pi$
$920$	142.711	4.70505
$921$	−0.293898	−0.00968426
$922$	107.755	3.54873
$923$	−1.91336	−0.0629790
$924$	−172.681	−5.68080
$925$	2.90938	0.0956598
$926$	−10.4163	−0.342300
$927$	−27.5093	−0.903522
$928$	81.5586	2.67729
$929$	3.42559	0.112390	0.0561949	−	0.998420i	$-0.482103\pi$
$929$	3.42559	0.112390	0.0561949	+	0.998420i	$0.482103\pi$
$930$	138.292	4.53479
$931$	−55.2047	−1.80926
$932$	81.4662	2.66851
$933$	−29.4989	−0.965751
$934$	28.5923	0.935568
$935$	−31.4232	−1.02765
$936$	282.178	9.22328
$937$	13.8708	0.453139	0.226570	−	0.973995i	$-0.427249\pi$
$937$	13.8708	0.453139	0.226570	+	0.973995i	$0.427249\pi$
$938$	133.812	4.36911
$939$	−38.1477	−1.24490
$940$	60.5851	1.97607
$941$	15.5257	0.506125	0.253062	−	0.967450i	$-0.418562\pi$
$941$	15.5257	0.506125	0.253062	+	0.967450i	$0.418562\pi$
$942$	103.546	3.37372
$943$	−59.9016	−1.95066
$944$	122.091	3.97371
$945$	102.006	3.31826
$946$	−4.84892	−0.157652
$947$	23.4713	0.762714	0.381357	−	0.924428i	$-0.375457\pi$
$947$	23.4713	0.762714	0.381357	+	0.924428i	$0.375457\pi$
$948$	93.8708	3.04878
$949$	13.5419	0.439589
$950$	−35.9278	−1.16565
$951$	57.1246	1.85239
$952$	265.114	8.59239
$953$	25.7524	0.834201	0.417100	−	0.908860i	$-0.363046\pi$
$953$	25.7524	0.834201	0.417100	+	0.908860i	$0.363046\pi$
$954$	−162.438	−5.25912
$955$	17.2026	0.556663
$956$	−14.4302	−0.466707
$957$	−26.7365	−0.864269
$958$	105.518	3.40913
$959$	38.7438	1.25110
$960$	−209.401	−6.75840
$961$	42.5479	1.37251
$962$	−17.0187	−0.548706
$963$	−0.444132	−0.0143120
$964$	−30.2459	−0.974156
$965$	−12.0213	−0.386978
$966$	272.921	8.78108
$967$	−40.0011	−1.28635	−0.643175	−	0.765719i	$-0.722383\pi$
$967$	−40.0011	−1.28635	−0.643175	+	0.765719i	$0.722383\pi$
$968$	47.6266	1.53078
$969$	168.362	5.40856
$970$	−43.1627	−1.38587
$971$	43.6514	1.40084	0.700421	−	0.713730i	$-0.252996\pi$
$971$	43.6514	1.40084	0.700421	+	0.713730i	$0.252996\pi$
$972$	−218.560	−7.01030
$973$	−49.4631	−1.58571
$974$	−73.7527	−2.36319
$975$	−21.5507	−0.690174
$976$	−52.2177	−1.67145
$977$	−57.2134	−1.83042	−0.915210	−	0.402978i	$-0.867975\pi$
$977$	−57.2134	−1.83042	−0.915210	+	0.402978i	$0.867975\pi$
$978$	84.4322	2.69984
$979$	18.4136	0.588501
$980$	75.3763	2.40781
$981$	131.330	4.19304
$982$	−103.284	−3.29592
$983$	−1.38910	−0.0443055	−0.0221528	−	0.999755i	$-0.507052\pi$
$983$	−1.38910	−0.0443055	−0.0221528	+	0.999755i	$0.507052\pi$
$984$	241.909	7.71176
$985$	−27.8750	−0.888170
$986$	63.8490	2.03337
$987$	74.4873	2.37096
$988$	154.862	4.92680
$989$	5.64705	0.179566
$990$	93.6022	2.97487
$991$	−2.21514	−0.0703663	−0.0351831	−	0.999381i	$-0.511201\pi$
$991$	−2.21514	−0.0703663	−0.0351831	+	0.999381i	$0.511201\pi$
$992$	−211.935	−6.72896
$993$	54.8479	1.74055
$994$	5.35478	0.169843
$995$	23.8093	0.754806
$996$	256.453	8.12601
$997$	−6.41302	−0.203102	−0.101551	−	0.994830i	$-0.532381\pi$
$997$	−6.41302	−0.203102	−0.101551	+	0.994830i	$0.532381\pi$
$998$	49.9749	1.58193
$999$	24.5430	0.776505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.6	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.75691 q^{2} -3.25303 q^{3} +5.60054 q^{4} +1.79806 q^{5} +8.96830 q^{6} -3.80594 q^{7} -9.92635 q^{8} +7.58219 q^{9} +O(q^{10})\)	\(q-2.75691 q^{2} -3.25303 q^{3} +5.60054 q^{4} +1.79806 q^{5} +8.96830 q^{6} -3.80594 q^{7} -9.92635 q^{8} +7.58219 q^{9} -4.95708 q^{10} -2.49038 q^{11} -18.2187 q^{12} -3.74920 q^{13} +10.4926 q^{14} -5.84913 q^{15} +16.1650 q^{16} +7.01748 q^{17} -20.9034 q^{18} -7.37522 q^{19} +10.0701 q^{20} +12.3808 q^{21} +6.86575 q^{22} -7.99585 q^{23} +32.2907 q^{24} -1.76699 q^{25} +10.3362 q^{26} -14.9060 q^{27} -21.3153 q^{28} -3.30028 q^{29} +16.1255 q^{30} +8.57601 q^{31} -24.7126 q^{32} +8.10128 q^{33} -19.3465 q^{34} -6.84329 q^{35} +42.4643 q^{36} -1.64652 q^{37} +20.3328 q^{38} +12.1963 q^{39} -17.8482 q^{40} +7.49158 q^{41} -34.1328 q^{42} -0.706248 q^{43} -13.9475 q^{44} +13.6332 q^{45} +22.0438 q^{46} +6.01634 q^{47} -52.5851 q^{48} +7.48516 q^{49} +4.87143 q^{50} -22.8280 q^{51} -20.9976 q^{52} +7.77088 q^{53} +41.0944 q^{54} -4.47785 q^{55} +37.7791 q^{56} +23.9918 q^{57} +9.09857 q^{58} +7.55279 q^{59} -32.7583 q^{60} -3.23030 q^{61} -23.6433 q^{62} -28.8573 q^{63} +35.8004 q^{64} -6.74128 q^{65} -22.3345 q^{66} +12.7529 q^{67} +39.3016 q^{68} +26.0107 q^{69} +18.8663 q^{70} +0.510338 q^{71} -75.2635 q^{72} -3.61194 q^{73} +4.53930 q^{74} +5.74807 q^{75} -41.3052 q^{76} +9.47824 q^{77} -33.6240 q^{78} -5.15244 q^{79} +29.0655 q^{80} +25.7430 q^{81} -20.6536 q^{82} -14.0763 q^{83} +69.3393 q^{84} +12.6178 q^{85} +1.94706 q^{86} +10.7359 q^{87} +24.7204 q^{88} -7.39389 q^{89} -37.5855 q^{90} +14.2692 q^{91} -44.7811 q^{92} -27.8980 q^{93} -16.5865 q^{94} -13.2611 q^{95} +80.3908 q^{96} +8.70729 q^{97} -20.6359 q^{98} -18.8825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 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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