LMFDB - Embedded newform 6037.2.a.a.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.76337 q^{2} -0.302967 q^{3} +5.63621 q^{4} +1.94141 q^{5} +0.837209 q^{6} -2.44102 q^{7} -10.0482 q^{8} -2.90821 q^{9} +O(q^{10})$	\(q-2.76337 q^{2} -0.302967 q^{3} +5.63621 q^{4} +1.94141 q^{5} +0.837209 q^{6} -2.44102 q^{7} -10.0482 q^{8} -2.90821 q^{9} -5.36484 q^{10} +4.45893 q^{11} -1.70758 q^{12} -4.69126 q^{13} +6.74545 q^{14} -0.588183 q^{15} +16.4945 q^{16} -5.40561 q^{17} +8.03646 q^{18} -0.558271 q^{19} +10.9422 q^{20} +0.739548 q^{21} -12.3217 q^{22} +3.42333 q^{23} +3.04427 q^{24} -1.23092 q^{25} +12.9637 q^{26} +1.78999 q^{27} -13.7581 q^{28} -1.19090 q^{29} +1.62537 q^{30} +5.51641 q^{31} -25.4839 q^{32} -1.35091 q^{33} +14.9377 q^{34} -4.73903 q^{35} -16.3913 q^{36} +2.38518 q^{37} +1.54271 q^{38} +1.42130 q^{39} -19.5077 q^{40} +1.18864 q^{41} -2.04364 q^{42} -0.116366 q^{43} +25.1315 q^{44} -5.64604 q^{45} -9.45994 q^{46} +6.93007 q^{47} -4.99728 q^{48} -1.04141 q^{49} +3.40148 q^{50} +1.63772 q^{51} -26.4410 q^{52} -0.703676 q^{53} -4.94641 q^{54} +8.65662 q^{55} +24.5279 q^{56} +0.169137 q^{57} +3.29090 q^{58} +8.97331 q^{59} -3.31513 q^{60} +1.53741 q^{61} -15.2439 q^{62} +7.09901 q^{63} +37.4326 q^{64} -9.10767 q^{65} +3.73306 q^{66} +9.31048 q^{67} -30.4672 q^{68} -1.03716 q^{69} +13.0957 q^{70} +9.19066 q^{71} +29.2223 q^{72} +7.00506 q^{73} -6.59113 q^{74} +0.372927 q^{75} -3.14653 q^{76} -10.8843 q^{77} -3.92757 q^{78} +9.33269 q^{79} +32.0226 q^{80} +8.18233 q^{81} -3.28466 q^{82} +8.96439 q^{83} +4.16825 q^{84} -10.4945 q^{85} +0.321562 q^{86} +0.360803 q^{87} -44.8042 q^{88} -5.81065 q^{89} +15.6021 q^{90} +11.4515 q^{91} +19.2946 q^{92} -1.67129 q^{93} -19.1503 q^{94} -1.08383 q^{95} +7.72078 q^{96} -6.81041 q^{97} +2.87781 q^{98} -12.9675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76337	−1.95400	−0.976999	−	0.213245i	$-0.931597\pi$
$2$	−2.76337	−1.95400	−0.976999	+	0.213245i	$0.931597\pi$
$3$	−0.302967	−0.174918	−0.0874589	−	0.996168i	$-0.527875\pi$
$3$	−0.302967	−0.174918	−0.0874589	+	0.996168i	$0.527875\pi$
$4$	5.63621	2.81811
$5$	1.94141	0.868226	0.434113	−	0.900858i	$-0.357062\pi$
$5$	1.94141	0.868226	0.434113	+	0.900858i	$0.357062\pi$
$6$	0.837209	0.341789
$7$	−2.44102	−0.922619	−0.461310	−	0.887239i	$-0.652620\pi$
$7$	−2.44102	−0.922619	−0.461310	+	0.887239i	$0.652620\pi$
$8$	−10.0482	−3.55258
$9$	−2.90821	−0.969404
$10$	−5.36484	−1.69651
$11$	4.45893	1.34442	0.672209	−	0.740361i	$-0.265346\pi$
$11$	4.45893	1.34442	0.672209	+	0.740361i	$0.265346\pi$
$12$	−1.70758	−0.492937
$13$	−4.69126	−1.30112	−0.650561	−	0.759454i	$-0.725466\pi$
$13$	−4.69126	−1.30112	−0.650561	+	0.759454i	$0.725466\pi$
$14$	6.74545	1.80280
$15$	−0.588183	−0.151868
$16$	16.4945	4.12362
$17$	−5.40561	−1.31105	−0.655526	−	0.755172i	$-0.727553\pi$
$17$	−5.40561	−1.31105	−0.655526	+	0.755172i	$0.727553\pi$
$18$	8.03646	1.89421
$19$	−0.558271	−0.128076	−0.0640380	−	0.997947i	$-0.520398\pi$
$19$	−0.558271	−0.128076	−0.0640380	+	0.997947i	$0.520398\pi$
$20$	10.9422	2.44675
$21$	0.739548	0.161383
$22$	−12.3217	−2.62699
$23$	3.42333	0.713815	0.356907	−	0.934140i	$-0.383831\pi$
$23$	3.42333	0.713815	0.356907	+	0.934140i	$0.383831\pi$
$24$	3.04427	0.621409
$25$	−1.23092	−0.246183
$26$	12.9637	2.54239
$27$	1.78999	0.344484
$28$	−13.7581	−2.60004
$29$	−1.19090	−0.221144	−0.110572	−	0.993868i	$-0.535268\pi$
$29$	−1.19090	−0.221144	−0.110572	+	0.993868i	$0.535268\pi$
$30$	1.62537	0.296750
$31$	5.51641	0.990777	0.495388	−	0.868672i	$-0.335026\pi$
$31$	5.51641	0.990777	0.495388	+	0.868672i	$0.335026\pi$
$32$	−25.4839	−4.50497
$33$	−1.35091	−0.235163
$34$	14.9377	2.56179
$35$	−4.73903	−0.801042
$36$	−16.3913	−2.73188
$37$	2.38518	0.392121	0.196060	−	0.980592i	$-0.437185\pi$
$37$	2.38518	0.392121	0.196060	+	0.980592i	$0.437185\pi$
$38$	1.54271	0.250260
$39$	1.42130	0.227589
$40$	−19.5077	−3.08444
$41$	1.18864	0.185635	0.0928175	−	0.995683i	$-0.470413\pi$
$41$	1.18864	0.185635	0.0928175	+	0.995683i	$0.470413\pi$
$42$	−2.04364	−0.315341
$43$	−0.116366	−0.0177456	−0.00887282	−	0.999961i	$-0.502824\pi$
$43$	−0.116366	−0.0177456	−0.00887282	+	0.999961i	$0.502824\pi$
$44$	25.1315	3.78871
$45$	−5.64604	−0.841662
$46$	−9.45994	−1.39479
$47$	6.93007	1.01085	0.505427	−	0.862869i	$-0.331335\pi$
$47$	6.93007	1.01085	0.505427	+	0.862869i	$0.331335\pi$
$48$	−4.99728	−0.721295
$49$	−1.04141	−0.148773
$50$	3.40148	0.481042
$51$	1.63772	0.229327
$52$	−26.4410	−3.66670
$53$	−0.703676	−0.0966573	−0.0483287	−	0.998831i	$-0.515389\pi$
$53$	−0.703676	−0.0966573	−0.0483287	+	0.998831i	$0.515389\pi$
$54$	−4.94641	−0.673121
$55$	8.65662	1.16726
$56$	24.5279	3.27768
$57$	0.169137	0.0224028
$58$	3.29090	0.432116
$59$	8.97331	1.16823	0.584113	−	0.811672i	$-0.301443\pi$
$59$	8.97331	1.16823	0.584113	+	0.811672i	$0.301443\pi$
$60$	−3.31513	−0.427981
$61$	1.53741	0.196846	0.0984228	−	0.995145i	$-0.468620\pi$
$61$	1.53741	0.196846	0.0984228	+	0.995145i	$0.468620\pi$
$62$	−15.2439	−1.93598
$63$	7.09901	0.894391
$64$	37.4326	4.67907
$65$	−9.10767	−1.12967
$66$	3.73306	0.459507
$67$	9.31048	1.13746	0.568728	−	0.822526i	$-0.307436\pi$
$67$	9.31048	1.13746	0.568728	+	0.822526i	$0.307436\pi$
$68$	−30.4672	−3.69469
$69$	−1.03716	−0.124859
$70$	13.0957	1.56523
$71$	9.19066	1.09073	0.545365	−	0.838199i	$-0.316391\pi$
$71$	9.19066	1.09073	0.545365	+	0.838199i	$0.316391\pi$
$72$	29.2223	3.44388
$73$	7.00506	0.819880	0.409940	−	0.912113i	$-0.365550\pi$
$73$	7.00506	0.819880	0.409940	+	0.912113i	$0.365550\pi$
$74$	−6.59113	−0.766203
$75$	0.372927	0.0430619
$76$	−3.14653	−0.360932
$77$	−10.8843	−1.24039
$78$	−3.92757	−0.444709
$79$	9.33269	1.05001	0.525005	−	0.851099i	$-0.324063\pi$
$79$	9.33269	1.05001	0.525005	+	0.851099i	$0.324063\pi$
$80$	32.0226	3.58023
$81$	8.18233	0.909147
$82$	−3.28466	−0.362730
$83$	8.96439	0.983969	0.491985	−	0.870604i	$-0.336272\pi$
$83$	8.96439	0.983969	0.491985	+	0.870604i	$0.336272\pi$
$84$	4.16825	0.454793
$85$	−10.4945	−1.13829
$86$	0.321562	0.0346749
$87$	0.360803	0.0386821
$88$	−44.8042	−4.77615
$89$	−5.81065	−0.615928	−0.307964	−	0.951398i	$-0.599648\pi$
$89$	−5.81065	−0.615928	−0.307964	+	0.951398i	$0.599648\pi$
$90$	15.6021	1.64460
$91$	11.4515	1.20044
$92$	19.2946	2.01161
$93$	−1.67129	−0.173305
$94$	−19.1503	−1.97521
$95$	−1.08383	−0.111199
$96$	7.72078	0.787999
$97$	−6.81041	−0.691493	−0.345746	−	0.938328i	$-0.612374\pi$
$97$	−6.81041	−0.691493	−0.345746	+	0.938328i	$0.612374\pi$
$98$	2.87781	0.290703
$99$	−12.9675	−1.30328
$100$	−6.93771	−0.693771
$101$	0.218012	0.0216930	0.0108465	−	0.999941i	$-0.496547\pi$
$101$	0.218012	0.0216930	0.0108465	+	0.999941i	$0.496547\pi$
$102$	−4.52562	−0.448104
$103$	−4.71971	−0.465047	−0.232524	−	0.972591i	$-0.574698\pi$
$103$	−4.71971	−0.465047	−0.232524	+	0.972591i	$0.574698\pi$
$104$	47.1387	4.62233
$105$	1.43577	0.140117
$106$	1.94452	0.188868
$107$	12.2322	1.18253	0.591267	−	0.806476i	$-0.298628\pi$
$107$	12.2322	1.18253	0.591267	+	0.806476i	$0.298628\pi$
$108$	10.0888	0.970792
$109$	−11.7288	−1.12341	−0.561706	−	0.827337i	$-0.689855\pi$
$109$	−11.7288	−1.12341	−0.561706	+	0.827337i	$0.689855\pi$
$110$	−23.9215	−2.28082
$111$	−0.722629	−0.0685890
$112$	−40.2634	−3.80453
$113$	−19.5330	−1.83751	−0.918754	−	0.394829i	$-0.870804\pi$
$113$	−19.5330	−1.83751	−0.918754	+	0.394829i	$0.870804\pi$
$114$	−0.467389	−0.0437750
$115$	6.64611	0.619752
$116$	−6.71216	−0.623209
$117$	13.6432	1.26131
$118$	−24.7966	−2.28271
$119$	13.1952	1.20960
$120$	5.91019	0.539524
$121$	8.88206	0.807460
$122$	−4.24844	−0.384636
$123$	−0.360119	−0.0324709
$124$	31.0917	2.79212
$125$	−12.0968	−1.08197
$126$	−19.6172	−1.74764
$127$	0.723391	0.0641906	0.0320953	−	0.999485i	$-0.489782\pi$
$127$	0.723391	0.0641906	0.0320953	+	0.999485i	$0.489782\pi$
$128$	−52.4722	−4.63793
$129$	0.0352550	0.00310403
$130$	25.1679	2.20737
$131$	−9.54215	−0.833702	−0.416851	−	0.908975i	$-0.636866\pi$
$131$	−9.54215	−0.833702	−0.416851	+	0.908975i	$0.636866\pi$
$132$	−7.61400	−0.662714
$133$	1.36275	0.118165
$134$	−25.7283	−2.22259
$135$	3.47511	0.299090
$136$	54.3167	4.65761
$137$	−16.3943	−1.40066	−0.700331	−	0.713818i	$-0.746964\pi$
$137$	−16.3943	−1.40066	−0.700331	+	0.713818i	$0.746964\pi$
$138$	2.86605	0.243974
$139$	7.91434	0.671286	0.335643	−	0.941989i	$-0.391046\pi$
$139$	7.91434	0.671286	0.335643	+	0.941989i	$0.391046\pi$
$140$	−26.7102	−2.25742
$141$	−2.09958	−0.176817
$142$	−25.3972	−2.13128
$143$	−20.9180	−1.74925
$144$	−47.9694	−3.99745
$145$	−2.31203	−0.192003
$146$	−19.3576	−1.60204
$147$	0.315514	0.0260231
$148$	13.4434	1.10504
$149$	−13.0931	−1.07263	−0.536314	−	0.844019i	$-0.680184\pi$
$149$	−13.0931	−1.07263	−0.536314	+	0.844019i	$0.680184\pi$
$150$	−1.03053	−0.0841428
$151$	−8.05783	−0.655737	−0.327868	−	0.944723i	$-0.606330\pi$
$151$	−8.05783	−0.655737	−0.327868	+	0.944723i	$0.606330\pi$
$152$	5.60962	0.455000
$153$	15.7207	1.27094
$154$	30.0775	2.42371
$155$	10.7096	0.860218
$156$	8.01073	0.641371
$157$	−11.6095	−0.926543	−0.463271	−	0.886217i	$-0.653324\pi$
$157$	−11.6095	−0.926543	−0.463271	+	0.886217i	$0.653324\pi$
$158$	−25.7897	−2.05172
$159$	0.213190	0.0169071
$160$	−49.4748	−3.91133
$161$	−8.35643	−0.658579
$162$	−22.6108	−1.77647
$163$	3.39906	0.266235	0.133118	−	0.991100i	$-0.457501\pi$
$163$	3.39906	0.266235	0.133118	+	0.991100i	$0.457501\pi$
$164$	6.69945	0.523139
$165$	−2.62267	−0.204174
$166$	−24.7719	−1.92267
$167$	−22.0891	−1.70931	−0.854653	−	0.519200i	$-0.826230\pi$
$167$	−22.0891	−1.70931	−0.854653	+	0.519200i	$0.826230\pi$
$168$	−7.43113	−0.573324
$169$	9.00793	0.692918
$170$	29.0002	2.22422
$171$	1.62357	0.124157
$172$	−0.655863	−0.0500091
$173$	0.932074	0.0708642	0.0354321	−	0.999372i	$-0.488719\pi$
$173$	0.932074	0.0708642	0.0354321	+	0.999372i	$0.488719\pi$
$174$	−0.997032	−0.0755848
$175$	3.00469	0.227133
$176$	73.5477	5.54387
$177$	−2.71861	−0.204344
$178$	16.0570	1.20352
$179$	−25.0984	−1.87595	−0.937973	−	0.346709i	$-0.887299\pi$
$179$	−25.0984	−1.87595	−0.937973	+	0.346709i	$0.887299\pi$
$180$	−31.8223	−2.37189
$181$	10.9747	0.815743	0.407871	−	0.913039i	$-0.366271\pi$
$181$	10.9747	0.815743	0.407871	+	0.913039i	$0.366271\pi$
$182$	−31.6446	−2.34566
$183$	−0.465785	−0.0344318
$184$	−34.3984	−2.53588
$185$	4.63062	0.340450
$186$	4.61839	0.338637
$187$	−24.1032	−1.76260
$188$	39.0593	2.84870
$189$	−4.36941	−0.317828
$190$	2.99503	0.217283
$191$	−15.3209	−1.10858	−0.554290	−	0.832323i	$-0.687010\pi$
$191$	−15.3209	−1.10858	−0.554290	+	0.832323i	$0.687010\pi$
$192$	−11.3408	−0.818454
$193$	18.7566	1.35013	0.675065	−	0.737758i	$-0.264116\pi$
$193$	18.7566	1.35013	0.675065	+	0.737758i	$0.264116\pi$
$194$	18.8197	1.35117
$195$	2.75932	0.197599
$196$	−5.86963	−0.419260
$197$	−18.0316	−1.28470	−0.642350	−	0.766412i	$-0.722040\pi$
$197$	−18.0316	−1.28470	−0.642350	+	0.766412i	$0.722040\pi$
$198$	35.8340	2.54661
$199$	5.79134	0.410538	0.205269	−	0.978706i	$-0.434193\pi$
$199$	5.79134	0.410538	0.205269	+	0.978706i	$0.434193\pi$
$200$	12.3685	0.874585
$201$	−2.82076	−0.198961
$202$	−0.602449	−0.0423882
$203$	2.90701	0.204032
$204$	9.23053	0.646267
$205$	2.30765	0.161173
$206$	13.0423	0.908701
$207$	−9.95578	−0.691975
$208$	−77.3799	−5.36533
$209$	−2.48929	−0.172188
$210$	−3.96756	−0.273788
$211$	−22.1472	−1.52467	−0.762337	−	0.647181i	$-0.775948\pi$
$211$	−22.1472	−1.52467	−0.762337	+	0.647181i	$0.775948\pi$
$212$	−3.96607	−0.272391
$213$	−2.78446	−0.190788
$214$	−33.8022	−2.31067
$215$	−0.225914	−0.0154072
$216$	−17.9862	−1.22381
$217$	−13.4657	−0.914110
$218$	32.4109	2.19514
$219$	−2.12230	−0.143412
$220$	48.7906	3.28946
$221$	25.3591	1.70584
$222$	1.99689	0.134023
$223$	10.6336	0.712076	0.356038	−	0.934472i	$-0.384127\pi$
$223$	10.6336	0.712076	0.356038	+	0.934472i	$0.384127\pi$
$224$	62.2068	4.15637
$225$	3.57977	0.238651
$226$	53.9769	3.59049
$227$	−25.5834	−1.69803	−0.849016	−	0.528368i	$-0.822804\pi$
$227$	−25.5834	−1.69803	−0.849016	+	0.528368i	$0.822804\pi$
$228$	0.953294	0.0631335
$229$	8.72817	0.576774	0.288387	−	0.957514i	$-0.406881\pi$
$229$	8.72817	0.576774	0.288387	+	0.957514i	$0.406881\pi$
$230$	−18.3656	−1.21099
$231$	3.29759	0.216966
$232$	11.9664	0.785633
$233$	4.14812	0.271752	0.135876	−	0.990726i	$-0.456615\pi$
$233$	4.14812	0.271752	0.135876	+	0.990726i	$0.456615\pi$
$234$	−37.7011	−2.46460
$235$	13.4541	0.877650
$236$	50.5755	3.29219
$237$	−2.82750	−0.183666
$238$	−36.4632	−2.36356
$239$	16.2166	1.04896	0.524482	−	0.851421i	$-0.324259\pi$
$239$	16.2166	1.04896	0.524482	+	0.851421i	$0.324259\pi$
$240$	−9.70178	−0.626247
$241$	−6.83375	−0.440200	−0.220100	−	0.975477i	$-0.570638\pi$
$241$	−6.83375	−0.440200	−0.220100	+	0.975477i	$0.570638\pi$
$242$	−24.5444	−1.57777
$243$	−7.84894	−0.503510
$244$	8.66519	0.554732
$245$	−2.02182	−0.129169
$246$	0.995143	0.0634480
$247$	2.61899	0.166643
$248$	−55.4300	−3.51981
$249$	−2.71591	−0.172114
$250$	33.4279	2.11416
$251$	−15.5245	−0.979898	−0.489949	−	0.871751i	$-0.662985\pi$
$251$	−15.5245	−0.979898	−0.489949	+	0.871751i	$0.662985\pi$
$252$	40.0115	2.52049
$253$	15.2644	0.959665
$254$	−1.99900	−0.125428
$255$	3.17949	0.199107
$256$	70.1350	4.38344
$257$	0.472289	0.0294606	0.0147303	−	0.999892i	$-0.495311\pi$
$257$	0.472289	0.0294606	0.0147303	+	0.999892i	$0.495311\pi$
$258$	−0.0974226	−0.00606527
$259$	−5.82227	−0.361778
$260$	−51.3328	−3.18352
$261$	3.46339	0.214378
$262$	26.3685	1.62905
$263$	−26.5889	−1.63954	−0.819772	−	0.572690i	$-0.805900\pi$
$263$	−26.5889	−1.63954	−0.819772	+	0.572690i	$0.805900\pi$
$264$	13.5742	0.835434
$265$	−1.36613	−0.0839204
$266$	−3.76578	−0.230895
$267$	1.76043	0.107737
$268$	52.4758	3.20547
$269$	5.47992	0.334117	0.167058	−	0.985947i	$-0.446573\pi$
$269$	5.47992	0.334117	0.167058	+	0.985947i	$0.446573\pi$
$270$	−9.60302	−0.584421
$271$	−13.6717	−0.830494	−0.415247	−	0.909709i	$-0.636305\pi$
$271$	−13.6717	−0.830494	−0.415247	+	0.909709i	$0.636305\pi$
$272$	−89.1627	−5.40628
$273$	−3.46941	−0.209978
$274$	45.3036	2.73689
$275$	−5.48857	−0.330973
$276$	−5.84563	−0.351866
$277$	−30.6030	−1.83876	−0.919379	−	0.393373i	$-0.871308\pi$
$277$	−30.6030	−1.83876	−0.919379	+	0.393373i	$0.871308\pi$
$278$	−21.8703	−1.31169
$279$	−16.0429	−0.960463
$280$	47.6187	2.84576
$281$	−4.85315	−0.289514	−0.144757	−	0.989467i	$-0.546240\pi$
$281$	−4.85315	−0.289514	−0.144757	+	0.989467i	$0.546240\pi$
$282$	5.80192	0.345499
$283$	−4.05080	−0.240795	−0.120397	−	0.992726i	$-0.538417\pi$
$283$	−4.05080	−0.240795	−0.120397	+	0.992726i	$0.538417\pi$
$284$	51.8005	3.07379
$285$	0.328365	0.0194507
$286$	57.8042	3.41803
$287$	−2.90150	−0.171270
$288$	74.1127	4.36713
$289$	12.2206	0.718859
$290$	6.38899	0.375174
$291$	2.06333	0.120954
$292$	39.4820	2.31051
$293$	14.3252	0.836885	0.418443	−	0.908243i	$-0.362576\pi$
$293$	14.3252	0.836885	0.418443	+	0.908243i	$0.362576\pi$
$294$	−0.871881	−0.0508492
$295$	17.4209	1.01428
$296$	−23.9668	−1.39304
$297$	7.98144	0.463130
$298$	36.1811	2.09591
$299$	−16.0598	−0.928760
$300$	2.10189	0.121353
$301$	0.284052	0.0163725
$302$	22.2668	1.28131
$303$	−0.0660505	−0.00379450
$304$	−9.20838	−0.528137
$305$	2.98475	0.170907
$306$	−43.4420	−2.48341
$307$	17.5174	0.999773	0.499887	−	0.866091i	$-0.333375\pi$
$307$	17.5174	0.999773	0.499887	+	0.866091i	$0.333375\pi$
$308$	−61.3465	−3.49554
$309$	1.42992	0.0813451
$310$	−29.5947	−1.68086
$311$	7.62504	0.432376	0.216188	−	0.976352i	$-0.430638\pi$
$311$	7.62504	0.432376	0.216188	+	0.976352i	$0.430638\pi$
$312$	−14.2815	−0.808529
$313$	−29.3527	−1.65911	−0.829556	−	0.558424i	$-0.811406\pi$
$313$	−29.3527	−1.65911	−0.829556	+	0.558424i	$0.811406\pi$
$314$	32.0815	1.81046
$315$	13.7821	0.776533
$316$	52.6011	2.95904
$317$	17.5135	0.983654	0.491827	−	0.870693i	$-0.336329\pi$
$317$	17.5135	0.983654	0.491827	+	0.870693i	$0.336329\pi$
$318$	−0.589124	−0.0330364
$319$	−5.31014	−0.297311
$320$	72.6721	4.06249
$321$	−3.70596	−0.206846
$322$	23.0919	1.28686
$323$	3.01779	0.167914
$324$	46.1173	2.56207
$325$	5.77455	0.320314
$326$	−9.39287	−0.520223
$327$	3.55342	0.196505
$328$	−11.9437	−0.659482
$329$	−16.9164	−0.932634
$330$	7.24740	0.398956
$331$	−16.5824	−0.911453	−0.455727	−	0.890120i	$-0.650620\pi$
$331$	−16.5824	−0.911453	−0.455727	+	0.890120i	$0.650620\pi$
$332$	50.5252	2.77293
$333$	−6.93660	−0.380123
$334$	61.0404	3.33998
$335$	18.0755	0.987569
$336$	12.1985	0.665480
$337$	31.6732	1.72535	0.862674	−	0.505760i	$-0.168788\pi$
$337$	31.6732	1.72535	0.862674	+	0.505760i	$0.168788\pi$
$338$	−24.8922	−1.35396
$339$	5.91784	0.321413
$340$	−59.1493	−3.20782
$341$	24.5973	1.33202
$342$	−4.48652	−0.242603
$343$	19.6293	1.05988
$344$	1.16927	0.0630427
$345$	−2.01355	−0.108406
$346$	−2.57566	−0.138469
$347$	−20.2391	−1.08649	−0.543246	−	0.839573i	$-0.682805\pi$
$347$	−20.2391	−1.08649	−0.543246	+	0.839573i	$0.682805\pi$
$348$	2.03356	0.109010
$349$	−8.71296	−0.466394	−0.233197	−	0.972429i	$-0.574919\pi$
$349$	−8.71296	−0.466394	−0.233197	+	0.972429i	$0.574919\pi$
$350$	−8.30308	−0.443818
$351$	−8.39732	−0.448216
$352$	−113.631	−6.05656
$353$	13.5501	0.721199	0.360600	−	0.932721i	$-0.382572\pi$
$353$	13.5501	0.721199	0.360600	+	0.932721i	$0.382572\pi$
$354$	7.51254	0.399287
$355$	17.8429	0.947001
$356$	−32.7501	−1.73575
$357$	−3.99771	−0.211581
$358$	69.3563	3.66559
$359$	22.0090	1.16159	0.580796	−	0.814049i	$-0.302741\pi$
$359$	22.0090	1.16159	0.580796	+	0.814049i	$0.302741\pi$
$360$	56.7325	2.99007
$361$	−18.6883	−0.983597
$362$	−30.3271	−1.59396
$363$	−2.69097	−0.141239
$364$	64.5429	3.38297
$365$	13.5997	0.711841
$366$	1.28714	0.0672797
$367$	−30.9766	−1.61697	−0.808484	−	0.588519i	$-0.799711\pi$
$367$	−30.9766	−1.61697	−0.808484	+	0.588519i	$0.799711\pi$
$368$	56.4661	2.94350
$369$	−3.45683	−0.179955
$370$	−12.7961	−0.665238
$371$	1.71769	0.0891779
$372$	−9.41974	−0.488391
$373$	−6.84198	−0.354264	−0.177132	−	0.984187i	$-0.556682\pi$
$373$	−6.84198	−0.354264	−0.177132	+	0.984187i	$0.556682\pi$
$374$	66.6061	3.44412
$375$	3.66492	0.189256
$376$	−69.6347	−3.59114
$377$	5.58682	0.287736
$378$	12.0743	0.621034
$379$	33.1580	1.70321	0.851605	−	0.524184i	$-0.175630\pi$
$379$	33.1580	1.70321	0.851605	+	0.524184i	$0.175630\pi$
$380$	−6.10872	−0.313371
$381$	−0.219163	−0.0112281
$382$	42.3373	2.16616
$383$	−27.1982	−1.38976	−0.694881	−	0.719125i	$-0.744543\pi$
$383$	−27.1982	−1.38976	−0.694881	+	0.719125i	$0.744543\pi$
$384$	15.8973	0.811257
$385$	−21.1310	−1.07694
$386$	−51.8315	−2.63815
$387$	0.338417	0.0172027
$388$	−38.3849	−1.94870
$389$	6.20393	0.314552	0.157276	−	0.987555i	$-0.449729\pi$
$389$	6.20393	0.314552	0.157276	+	0.987555i	$0.449729\pi$
$390$	−7.62503	−0.386108
$391$	−18.5052	−0.935848
$392$	10.4643	0.528529
$393$	2.89095	0.145829
$394$	49.8280	2.51030
$395$	18.1186	0.911646
$396$	−73.0877	−3.67279
$397$	−7.85219	−0.394090	−0.197045	−	0.980394i	$-0.563135\pi$
$397$	−7.85219	−0.394090	−0.197045	+	0.980394i	$0.563135\pi$
$398$	−16.0036	−0.802189
$399$	−0.412868	−0.0206692
$400$	−20.3033	−1.01517
$401$	19.7704	0.987288	0.493644	−	0.869664i	$-0.335665\pi$
$401$	19.7704	0.987288	0.493644	+	0.869664i	$0.335665\pi$
$402$	7.79481	0.388770
$403$	−25.8789	−1.28912
$404$	1.22876	0.0611333
$405$	15.8853	0.789346
$406$	−8.03315	−0.398678
$407$	10.6353	0.527174
$408$	−16.4561	−0.814700
$409$	2.02629	0.100194	0.0500968	−	0.998744i	$-0.484047\pi$
$409$	2.02629	0.100194	0.0500968	+	0.998744i	$0.484047\pi$
$410$	−6.37688	−0.314932
$411$	4.96694	0.245001
$412$	−26.6013	−1.31055
$413$	−21.9040	−1.07783
$414$	27.5115	1.35212
$415$	17.4036	0.854308
$416$	119.552	5.86151
$417$	−2.39778	−0.117420
$418$	6.87883	0.336454
$419$	−12.5822	−0.614683	−0.307341	−	0.951599i	$-0.599439\pi$
$419$	−12.5822	−0.614683	−0.307341	+	0.951599i	$0.599439\pi$
$420$	8.09230	0.394864
$421$	4.32247	0.210665	0.105332	−	0.994437i	$-0.466409\pi$
$421$	4.32247	0.210665	0.105332	+	0.994437i	$0.466409\pi$
$422$	61.2008	2.97921
$423$	−20.1541	−0.979926
$424$	7.07068	0.343383
$425$	6.65385	0.322759
$426$	7.69450	0.372800
$427$	−3.75286	−0.181614
$428$	68.9434	3.33251
$429$	6.33746	0.305975
$430$	0.624285	0.0301057
$431$	−0.217470	−0.0104752	−0.00523758	−	0.999986i	$-0.501667\pi$
$431$	−0.217470	−0.0104752	−0.00523758	+	0.999986i	$0.501667\pi$
$432$	29.5250	1.42052
$433$	14.9294	0.717459	0.358729	−	0.933442i	$-0.383210\pi$
$433$	14.9294	0.717459	0.358729	+	0.933442i	$0.383210\pi$
$434$	37.2107	1.78617
$435$	0.700467	0.0335848
$436$	−66.1058	−3.16589
$437$	−1.91115	−0.0914225
$438$	5.86469	0.280226
$439$	11.5816	0.552759	0.276379	−	0.961049i	$-0.410865\pi$
$439$	11.5816	0.552759	0.276379	+	0.961049i	$0.410865\pi$
$440$	−86.9835	−4.14678
$441$	3.02865	0.144222
$442$	−70.0766	−3.33321
$443$	8.56325	0.406852	0.203426	−	0.979090i	$-0.434792\pi$
$443$	8.56325	0.406852	0.203426	+	0.979090i	$0.434792\pi$
$444$	−4.07289	−0.193291
$445$	−11.2809	−0.534764
$446$	−29.3844	−1.39139
$447$	3.96677	0.187622
$448$	−91.3737	−4.31700
$449$	−11.2729	−0.532002	−0.266001	−	0.963973i	$-0.585702\pi$
$449$	−11.2729	−0.532002	−0.266001	+	0.963973i	$0.585702\pi$
$450$	−9.89222	−0.466324
$451$	5.30008	0.249571
$452$	−110.092	−5.17830
$453$	2.44125	0.114700
$454$	70.6965	3.31795
$455$	22.2320	1.04225
$456$	−1.69953	−0.0795876
$457$	4.88010	0.228282	0.114141	−	0.993465i	$-0.463589\pi$
$457$	4.88010	0.228282	0.114141	+	0.993465i	$0.463589\pi$
$458$	−24.1192	−1.12701
$459$	−9.67599	−0.451637
$460$	37.4589	1.74653
$461$	−34.4445	−1.60424	−0.802119	−	0.597164i	$-0.796294\pi$
$461$	−34.4445	−1.60424	−0.802119	+	0.597164i	$0.796294\pi$
$462$	−9.11247	−0.423950
$463$	29.6890	1.37976	0.689882	−	0.723921i	$-0.257662\pi$
$463$	29.6890	1.37976	0.689882	+	0.723921i	$0.257662\pi$
$464$	−19.6433	−0.911916
$465$	−3.24466	−0.150468
$466$	−11.4628	−0.531004
$467$	0.692086	0.0320259	0.0160130	−	0.999872i	$-0.494903\pi$
$467$	0.692086	0.0320259	0.0160130	+	0.999872i	$0.494903\pi$
$468$	76.8959	3.55451
$469$	−22.7271	−1.04944
$470$	−37.1787	−1.71493
$471$	3.51731	0.162069
$472$	−90.1657	−4.15021
$473$	−0.518868	−0.0238576
$474$	7.81341	0.358882
$475$	0.687184	0.0315302
$476$	74.3710	3.40879
$477$	2.04644	0.0937000
$478$	−44.8125	−2.04967
$479$	−20.5244	−0.937783	−0.468892	−	0.883256i	$-0.655347\pi$
$479$	−20.5244	−0.937783	−0.468892	+	0.883256i	$0.655347\pi$
$480$	14.9892	0.684161
$481$	−11.1895	−0.510197
$482$	18.8842	0.860150
$483$	2.53172	0.115197
$484$	50.0612	2.27551
$485$	−13.2218	−0.600372
$486$	21.6895	0.983857
$487$	−14.4713	−0.655756	−0.327878	−	0.944720i	$-0.606333\pi$
$487$	−14.4713	−0.655756	−0.327878	+	0.944720i	$0.606333\pi$
$488$	−15.4482	−0.699309
$489$	−1.02980	−0.0465693
$490$	5.58702	0.252396
$491$	−36.4653	−1.64566	−0.822828	−	0.568290i	$-0.807605\pi$
$491$	−36.4653	−1.64566	−0.822828	+	0.568290i	$0.807605\pi$
$492$	−2.02971	−0.0915064
$493$	6.43754	0.289932
$494$	−7.23725	−0.325619
$495$	−25.1753	−1.13155
$496$	90.9903	4.08559
$497$	−22.4346	−1.00633
$498$	7.50507	0.336310
$499$	14.1476	0.633336	0.316668	−	0.948537i	$-0.397436\pi$
$499$	14.1476	0.633336	0.316668	+	0.948537i	$0.397436\pi$
$500$	−68.1800	−3.04910
$501$	6.69226	0.298988
$502$	42.8999	1.91472
$503$	4.91616	0.219201	0.109600	−	0.993976i	$-0.465043\pi$
$503$	4.91616	0.219201	0.109600	+	0.993976i	$0.465043\pi$
$504$	−71.3323	−3.17739
$505$	0.423252	0.0188345
$506$	−42.1812	−1.87518
$507$	−2.72910	−0.121204
$508$	4.07719	0.180896
$509$	−16.7715	−0.743384	−0.371692	−	0.928356i	$-0.621222\pi$
$509$	−16.7715	−0.743384	−0.371692	+	0.928356i	$0.621222\pi$
$510$	−8.78610	−0.389055
$511$	−17.0995	−0.756437
$512$	−88.8644	−3.92729
$513$	−0.999299	−0.0441201
$514$	−1.30511	−0.0575659
$515$	−9.16291	−0.403766
$516$	0.198705	0.00874749
$517$	30.9007	1.35901
$518$	16.0891	0.706914
$519$	−0.282387	−0.0123954
$520$	91.5158	4.01323
$521$	20.5983	0.902426	0.451213	−	0.892416i	$-0.350991\pi$
$521$	20.5983	0.902426	0.451213	+	0.892416i	$0.350991\pi$
$522$	−9.57062	−0.418895
$523$	13.5391	0.592023	0.296011	−	0.955184i	$-0.404343\pi$
$523$	13.5391	0.592023	0.296011	+	0.955184i	$0.404343\pi$
$524$	−53.7816	−2.34946
$525$	−0.910322	−0.0397297
$526$	73.4750	3.20366
$527$	−29.8196	−1.29896
$528$	−22.2825	−0.969722
$529$	−11.2808	−0.490469
$530$	3.77511	0.163980
$531$	−26.0963	−1.13248
$532$	7.68075	0.333003
$533$	−5.57624	−0.241534
$534$	−4.86473	−0.210517
$535$	23.7478	1.02671
$536$	−93.5536	−4.04090
$537$	7.60399	0.328136
$538$	−15.1431	−0.652863
$539$	−4.64359	−0.200014
$540$	19.5865	0.842867
$541$	−24.9197	−1.07138	−0.535690	−	0.844415i	$-0.679949\pi$
$541$	−24.9197	−1.07138	−0.535690	+	0.844415i	$0.679949\pi$
$542$	37.7798	1.62278
$543$	−3.32497	−0.142688
$544$	137.756	5.90625
$545$	−22.7704	−0.975375
$546$	9.58727	0.410297
$547$	42.0450	1.79772	0.898858	−	0.438240i	$-0.144398\pi$
$547$	42.0450	1.79772	0.898858	+	0.438240i	$0.144398\pi$
$548$	−92.4020	−3.94722
$549$	−4.47112	−0.190823
$550$	15.1670	0.646721
$551$	0.664844	0.0283233
$552$	10.4216	0.443571
$553$	−22.7813	−0.968760
$554$	84.5675	3.59293
$555$	−1.40292	−0.0595507
$556$	44.6069	1.89176
$557$	−28.8980	−1.22445	−0.612224	−	0.790684i	$-0.709725\pi$
$557$	−28.8980	−1.22445	−0.612224	+	0.790684i	$0.709725\pi$
$558$	44.3324	1.87674
$559$	0.545903	0.0230892
$560$	−78.1678	−3.30319
$561$	7.30247	0.308311
$562$	13.4110	0.565710
$563$	1.17927	0.0497003	0.0248501	−	0.999691i	$-0.492089\pi$
$563$	1.17927	0.0497003	0.0248501	+	0.999691i	$0.492089\pi$
$564$	−11.8337	−0.498288
$565$	−37.9216	−1.59537
$566$	11.1939	0.470513
$567$	−19.9732	−0.838797
$568$	−92.3496	−3.87490
$569$	−40.8569	−1.71281	−0.856406	−	0.516303i	$-0.827308\pi$
$569$	−40.8569	−1.71281	−0.856406	+	0.516303i	$0.827308\pi$
$570$	−0.907395	−0.0380066
$571$	37.2498	1.55886	0.779428	−	0.626492i	$-0.215510\pi$
$571$	37.2498	1.55886	0.779428	+	0.626492i	$0.215510\pi$
$572$	−117.898	−4.92958
$573$	4.64172	0.193911
$574$	8.01793	0.334662
$575$	−4.21384	−0.175729
$576$	−108.862	−4.53591
$577$	−17.7121	−0.737366	−0.368683	−	0.929555i	$-0.620191\pi$
$577$	−17.7121	−0.737366	−0.368683	+	0.929555i	$0.620191\pi$
$578$	−33.7700	−1.40465
$579$	−5.68263	−0.236162
$580$	−13.0311	−0.541086
$581$	−21.8823	−0.907829
$582$	−5.70174	−0.236345
$583$	−3.13764	−0.129948
$584$	−70.3882	−2.91269
$585$	26.4870	1.09510
$586$	−39.5858	−1.63527
$587$	23.7710	0.981133	0.490567	−	0.871404i	$-0.336790\pi$
$587$	23.7710	0.981133	0.490567	+	0.871404i	$0.336790\pi$
$588$	1.77830	0.0733360
$589$	−3.07965	−0.126895
$590$	−48.1404	−1.98191
$591$	5.46298	0.224717
$592$	39.3423	1.61696
$593$	15.7539	0.646935	0.323468	−	0.946239i	$-0.395151\pi$
$593$	15.7539	0.646935	0.323468	+	0.946239i	$0.395151\pi$
$594$	−22.0557	−0.904956
$595$	25.6173	1.05021
$596$	−73.7954	−3.02278
$597$	−1.75458	−0.0718104
$598$	44.3790	1.81479
$599$	−15.4822	−0.632585	−0.316293	−	0.948662i	$-0.602438\pi$
$599$	−15.4822	−0.632585	−0.316293	+	0.948662i	$0.602438\pi$
$600$	−3.74724	−0.152981
$601$	27.3579	1.11595	0.557976	−	0.829857i	$-0.311578\pi$
$601$	27.3579	1.11595	0.557976	+	0.829857i	$0.311578\pi$
$602$	−0.784940	−0.0319918
$603$	−27.0768	−1.10265
$604$	−45.4156	−1.84794
$605$	17.2437	0.701058
$606$	0.182522	0.00741445
$607$	−33.9208	−1.37680	−0.688401	−	0.725330i	$-0.741687\pi$
$607$	−33.9208	−1.37680	−0.688401	+	0.725330i	$0.741687\pi$
$608$	14.2269	0.576978
$609$	−0.880727	−0.0356889
$610$	−8.24798	−0.333951
$611$	−32.5108	−1.31524
$612$	88.6049	3.58164
$613$	−14.6912	−0.593371	−0.296686	−	0.954975i	$-0.595881\pi$
$613$	−14.6912	−0.593371	−0.296686	+	0.954975i	$0.595881\pi$
$614$	−48.4072	−1.95355
$615$	−0.699140	−0.0281921
$616$	109.368	4.40657
$617$	4.58005	0.184386	0.0921929	−	0.995741i	$-0.470612\pi$
$617$	4.58005	0.184386	0.0921929	+	0.995741i	$0.470612\pi$
$618$	−3.95139	−0.158948
$619$	1.86395	0.0749184	0.0374592	−	0.999298i	$-0.488074\pi$
$619$	1.86395	0.0749184	0.0374592	+	0.999298i	$0.488074\pi$
$620$	60.3618	2.42419
$621$	6.12774	0.245898
$622$	−21.0708	−0.844862
$623$	14.1839	0.568267
$624$	23.4435	0.938492
$625$	−17.3303	−0.693210
$626$	81.1123	3.24190
$627$	0.754172	0.0301187
$628$	−65.4339	−2.61110
$629$	−12.8933	−0.514091
$630$	−38.0850	−1.51734
$631$	26.9971	1.07474	0.537369	−	0.843348i	$-0.319418\pi$
$631$	26.9971	1.07474	0.537369	+	0.843348i	$0.319418\pi$
$632$	−93.7768	−3.73024
$633$	6.70985	0.266693
$634$	−48.3962	−1.92206
$635$	1.40440	0.0557319
$636$	1.20159	0.0476460
$637$	4.88555	0.193572
$638$	14.6739	0.580944
$639$	−26.7284	−1.05736
$640$	−101.870	−4.02677
$641$	14.3137	0.565359	0.282679	−	0.959214i	$-0.408777\pi$
$641$	14.3137	0.565359	0.282679	+	0.959214i	$0.408777\pi$
$642$	10.2409	0.404177
$643$	−4.04305	−0.159442	−0.0797212	−	0.996817i	$-0.525403\pi$
$643$	−4.04305	−0.159442	−0.0797212	+	0.996817i	$0.525403\pi$
$644$	−47.0986	−1.85595
$645$	0.0684445	0.00269500
$646$	−8.33928	−0.328104
$647$	−39.2054	−1.54132	−0.770661	−	0.637245i	$-0.780074\pi$
$647$	−39.2054	−1.54132	−0.770661	+	0.637245i	$0.780074\pi$
$648$	−82.2177	−3.22982
$649$	40.0114	1.57058
$650$	−15.9572	−0.625894
$651$	4.07965	0.159894
$652$	19.1578	0.750279
$653$	−34.6595	−1.35633	−0.678165	−	0.734909i	$-0.737225\pi$
$653$	−34.6595	−1.35633	−0.678165	+	0.734909i	$0.737225\pi$
$654$	−9.81942	−0.383970
$655$	−18.5253	−0.723841
$656$	19.6061	0.765488
$657$	−20.3722	−0.794794
$658$	46.7464	1.82236
$659$	−39.2724	−1.52983	−0.764917	−	0.644129i	$-0.777220\pi$
$659$	−39.2724	−1.52983	−0.764917	+	0.644129i	$0.777220\pi$
$660$	−14.7819	−0.575385
$661$	26.0407	1.01286	0.506432	−	0.862280i	$-0.330964\pi$
$661$	26.0407	1.01286	0.506432	+	0.862280i	$0.330964\pi$
$662$	45.8234	1.78098
$663$	−7.68297	−0.298382
$664$	−90.0760	−3.49563
$665$	2.64566	0.102594
$666$	19.1684	0.742760
$667$	−4.07685	−0.157856
$668$	−124.499	−4.81701
$669$	−3.22161	−0.124555
$670$	−49.9492	−1.92971
$671$	6.85522	0.264643
$672$	−18.8466	−0.727023
$673$	30.7418	1.18501	0.592505	−	0.805567i	$-0.298139\pi$
$673$	30.7418	1.18501	0.592505	+	0.805567i	$0.298139\pi$
$674$	−87.5247	−3.37133
$675$	−2.20333	−0.0848062
$676$	50.7706	1.95272
$677$	30.5236	1.17312	0.586559	−	0.809906i	$-0.300482\pi$
$677$	30.5236	1.17312	0.586559	+	0.809906i	$0.300482\pi$
$678$	−16.3532	−0.628041
$679$	16.6244	0.637985
$680$	105.451	4.04386
$681$	7.75092	0.297016
$682$	−67.9714	−2.60276
$683$	28.6561	1.09650	0.548249	−	0.836315i	$-0.315295\pi$
$683$	28.6561	1.09650	0.548249	+	0.836315i	$0.315295\pi$
$684$	9.15078	0.349889
$685$	−31.8282	−1.21609
$686$	−54.2429	−2.07100
$687$	−2.64434	−0.100888
$688$	−1.91940	−0.0731763
$689$	3.30113	0.125763
$690$	5.56418	0.211825
$691$	0.991560	0.0377207	0.0188604	−	0.999822i	$-0.493996\pi$
$691$	0.991560	0.0377207	0.0188604	+	0.999822i	$0.493996\pi$
$692$	5.25337	0.199703
$693$	31.6540	1.20243
$694$	55.9281	2.12300
$695$	15.3650	0.582828
$696$	−3.62542	−0.137421
$697$	−6.42534	−0.243377
$698$	24.0771	0.911333
$699$	−1.25674	−0.0475344
$700$	16.9351	0.640086
$701$	−30.7651	−1.16198	−0.580991	−	0.813910i	$-0.697335\pi$
$701$	−30.7651	−1.16198	−0.580991	+	0.813910i	$0.697335\pi$
$702$	23.2049	0.875812
$703$	−1.33157	−0.0502213
$704$	166.909	6.29063
$705$	−4.07615	−0.153517
$706$	−37.4439	−1.40922
$707$	−0.532173	−0.0200144
$708$	−15.3227	−0.575862
$709$	−5.05456	−0.189828	−0.0949140	−	0.995485i	$-0.530258\pi$
$709$	−5.05456	−0.189828	−0.0949140	+	0.995485i	$0.530258\pi$
$710$	−49.3064	−1.85044
$711$	−27.1414	−1.01788
$712$	58.3866	2.18813
$713$	18.8845	0.707231
$714$	11.0471	0.413429
$715$	−40.6105	−1.51875
$716$	−141.460	−5.28662
$717$	−4.91309	−0.183483
$718$	−60.8191	−2.26975
$719$	−19.5549	−0.729276	−0.364638	−	0.931149i	$-0.618807\pi$
$719$	−19.5549	−0.729276	−0.364638	+	0.931149i	$0.618807\pi$
$720$	−93.1284	−3.47069
$721$	11.5209	0.429062
$722$	51.6428	1.92195
$723$	2.07040	0.0769989
$724$	61.8557	2.29885
$725$	1.46590	0.0544421
$726$	7.43614	0.275981
$727$	−42.1320	−1.56259	−0.781294	−	0.624163i	$-0.785440\pi$
$727$	−42.1320	−1.56259	−0.781294	+	0.624163i	$0.785440\pi$
$728$	−115.067	−4.26466
$729$	−22.1690	−0.821074
$730$	−37.5810	−1.39094
$731$	0.629029	0.0232655
$732$	−2.62526	−0.0970326
$733$	3.14151	0.116034	0.0580171	−	0.998316i	$-0.481522\pi$
$733$	3.14151	0.116034	0.0580171	+	0.998316i	$0.481522\pi$
$734$	85.5999	3.15955
$735$	0.612543	0.0225940
$736$	−87.2400	−3.21571
$737$	41.5148	1.52922
$738$	9.55249	0.351632
$739$	40.8134	1.50135	0.750673	−	0.660674i	$-0.229730\pi$
$739$	40.8134	1.50135	0.750673	+	0.660674i	$0.229730\pi$
$740$	26.0991	0.959423
$741$	−0.793467	−0.0291488
$742$	−4.74661	−0.174253
$743$	4.81200	0.176535	0.0882675	−	0.996097i	$-0.471867\pi$
$743$	4.81200	0.176535	0.0882675	+	0.996097i	$0.471867\pi$
$744$	16.7935	0.615678
$745$	−25.4191	−0.931283
$746$	18.9069	0.692232
$747$	−26.0703	−0.953864
$748$	−135.851	−4.96720
$749$	−29.8591	−1.09103
$750$	−10.1275	−0.369805
$751$	−32.9085	−1.20085	−0.600424	−	0.799682i	$-0.705002\pi$
$751$	−32.9085	−1.20085	−0.600424	+	0.799682i	$0.705002\pi$
$752$	114.308	4.16838
$753$	4.70341	0.171402
$754$	−15.4385	−0.562235
$755$	−15.6436	−0.569328
$756$	−24.6269	−0.895672
$757$	−34.5848	−1.25701	−0.628503	−	0.777808i	$-0.716332\pi$
$757$	−34.5848	−1.25701	−0.628503	+	0.777808i	$0.716332\pi$
$758$	−91.6277	−3.32807
$759$	−4.62461	−0.167863
$760$	10.8906	0.395043
$761$	−50.8984	−1.84507	−0.922533	−	0.385917i	$-0.873885\pi$
$761$	−50.8984	−1.84507	−0.922533	+	0.385917i	$0.873885\pi$
$762$	0.605629	0.0219396
$763$	28.6302	1.03648
$764$	−86.3518	−3.12410
$765$	30.5203	1.10346
$766$	75.1586	2.71559
$767$	−42.0962	−1.52000
$768$	−21.2486	−0.766741
$769$	−38.8943	−1.40257	−0.701283	−	0.712883i	$-0.747389\pi$
$769$	−38.8943	−1.40257	−0.701283	+	0.712883i	$0.747389\pi$
$770$	58.3928	2.10433
$771$	−0.143088	−0.00515318
$772$	105.716	3.80481
$773$	36.8636	1.32589	0.662946	−	0.748668i	$-0.269306\pi$
$773$	36.8636	1.32589	0.662946	+	0.748668i	$0.269306\pi$
$774$	−0.935171	−0.0336140
$775$	−6.79024	−0.243913
$776$	68.4324	2.45658
$777$	1.76395	0.0632815
$778$	−17.1438	−0.614634
$779$	−0.663585	−0.0237754
$780$	15.5521	0.556855
$781$	40.9805	1.46640
$782$	51.1367	1.82865
$783$	−2.13170	−0.0761807
$784$	−17.1776	−0.613485
$785$	−22.5389	−0.804449
$786$	−7.98877	−0.284950
$787$	23.4994	0.837664	0.418832	−	0.908064i	$-0.362440\pi$
$787$	23.4994	0.837664	0.418832	+	0.908064i	$0.362440\pi$
$788$	−101.630	−3.62042
$789$	8.05556	0.286785
$790$	−50.0684	−1.78135
$791$	47.6804	1.69532
$792$	130.300	4.63002
$793$	−7.21241	−0.256120
$794$	21.6985	0.770051
$795$	0.413890	0.0146792
$796$	32.6413	1.15694
$797$	−17.1675	−0.608103	−0.304051	−	0.952656i	$-0.598339\pi$
$797$	−17.1675	−0.608103	−0.304051	+	0.952656i	$0.598339\pi$
$798$	1.14091	0.0403877
$799$	−37.4612	−1.32528
$800$	31.3686	1.10905
$801$	16.8986	0.597082
$802$	−54.6330	−1.92916
$803$	31.2351	1.10226
$804$	−15.8984	−0.560694
$805$	−16.2233	−0.571796
$806$	71.5131	2.51894
$807$	−1.66023	−0.0584430
$808$	−2.19063	−0.0770662
$809$	55.2013	1.94078	0.970388	−	0.241553i	$-0.0776566\pi$
$809$	55.2013	1.94078	0.970388	+	0.241553i	$0.0776566\pi$
$810$	−43.8969	−1.54238
$811$	19.3573	0.679727	0.339863	−	0.940475i	$-0.389619\pi$
$811$	19.3573	0.679727	0.339863	+	0.940475i	$0.389619\pi$
$812$	16.3845	0.574984
$813$	4.14206	0.145268
$814$	−29.3894	−1.03010
$815$	6.59898	0.231152
$816$	27.0133	0.945655
$817$	0.0649637	0.00227279
$818$	−5.59939	−0.195778
$819$	−33.3033	−1.16371
$820$	13.0064	0.454203
$821$	24.6520	0.860360	0.430180	−	0.902743i	$-0.358450\pi$
$821$	24.6520	0.860360	0.430180	+	0.902743i	$0.358450\pi$
$822$	−13.7255	−0.478731
$823$	9.68908	0.337740	0.168870	−	0.985638i	$-0.445988\pi$
$823$	9.68908	0.337740	0.168870	+	0.985638i	$0.445988\pi$
$824$	47.4247	1.65212
$825$	1.66285	0.0578931
$826$	60.5290	2.10607
$827$	5.91555	0.205704	0.102852	−	0.994697i	$-0.467203\pi$
$827$	5.91555	0.205704	0.102852	+	0.994697i	$0.467203\pi$
$828$	−56.1129	−1.95006
$829$	−25.9328	−0.900683	−0.450342	−	0.892856i	$-0.648698\pi$
$829$	−25.9328	−0.900683	−0.450342	+	0.892856i	$0.648698\pi$
$830$	−48.0925	−1.66932
$831$	9.27170	0.321632
$832$	−175.606	−6.08804
$833$	5.62948	0.195050
$834$	6.62596	0.229438
$835$	−42.8841	−1.48406
$836$	−14.0302	−0.485243
$837$	9.87433	0.341307
$838$	34.7694	1.20109
$839$	−16.6607	−0.575190	−0.287595	−	0.957752i	$-0.592856\pi$
$839$	−16.6607	−0.575190	−0.287595	+	0.957752i	$0.592856\pi$
$840$	−14.4269	−0.497775
$841$	−27.5818	−0.951095
$842$	−11.9446	−0.411638
$843$	1.47034	0.0506412
$844$	−124.826	−4.29669
$845$	17.4881	0.601609
$846$	55.6932	1.91477
$847$	−21.6813	−0.744978
$848$	−11.6068	−0.398578
$849$	1.22726	0.0421193
$850$	−18.3871	−0.630671
$851$	8.16526	0.279902
$852$	−15.6938	−0.537662
$853$	36.0748	1.23518	0.617589	−	0.786501i	$-0.288110\pi$
$853$	36.0748	1.23518	0.617589	+	0.786501i	$0.288110\pi$
$854$	10.3705	0.354873
$855$	3.15202	0.107797
$856$	−122.912	−4.20104
$857$	−17.1441	−0.585631	−0.292815	−	0.956169i	$-0.594592\pi$
$857$	−17.1441	−0.585631	−0.292815	+	0.956169i	$0.594592\pi$
$858$	−17.5127	−0.597875
$859$	55.9335	1.90843	0.954214	−	0.299126i	$-0.0966952\pi$
$859$	55.9335	1.90843	0.954214	+	0.299126i	$0.0966952\pi$
$860$	−1.27330	−0.0434192
$861$	0.879059	0.0299583
$862$	0.600950	0.0204684
$863$	11.1895	0.380895	0.190447	−	0.981697i	$-0.439006\pi$
$863$	11.1895	0.380895	0.190447	+	0.981697i	$0.439006\pi$
$864$	−45.6160	−1.55189
$865$	1.80954	0.0615262
$866$	−41.2553	−1.40191
$867$	−3.70243	−0.125741
$868$	−75.8955	−2.57606
$869$	41.6138	1.41165
$870$	−1.93565	−0.0656247
$871$	−43.6779	−1.47997
$872$	117.853	3.99101
$873$	19.8061	0.670336
$874$	5.28121	0.178639
$875$	29.5285	0.998246
$876$	−11.9617	−0.404149
$877$	−9.16469	−0.309470	−0.154735	−	0.987956i	$-0.549452\pi$
$877$	−9.16469	−0.309470	−0.154735	+	0.987956i	$0.549452\pi$
$878$	−32.0042	−1.08009
$879$	−4.34005	−0.146386
$880$	142.786	4.81333
$881$	−5.91002	−0.199114	−0.0995569	−	0.995032i	$-0.531743\pi$
$881$	−5.91002	−0.199114	−0.0995569	+	0.995032i	$0.531743\pi$
$882$	−8.36929	−0.281809
$883$	31.3893	1.05633	0.528167	−	0.849141i	$-0.322880\pi$
$883$	31.3893	1.05633	0.528167	+	0.849141i	$0.322880\pi$
$884$	142.929	4.80724
$885$	−5.27795	−0.177416
$886$	−23.6634	−0.794988
$887$	39.7132	1.33344	0.666720	−	0.745309i	$-0.267698\pi$
$887$	39.7132	1.33344	0.666720	+	0.745309i	$0.267698\pi$
$888$	7.26113	0.243667
$889$	−1.76581	−0.0592235
$890$	31.1732	1.04493
$891$	36.4844	1.22227
$892$	59.9330	2.00670
$893$	−3.86885	−0.129466
$894$	−10.9617	−0.366612
$895$	−48.7264	−1.62875
$896$	128.086	4.27905
$897$	4.86557	0.162457
$898$	31.1512	1.03953
$899$	−6.56949	−0.219105
$900$	20.1763	0.672544
$901$	3.80380	0.126723
$902$	−14.6461	−0.487661
$903$	−0.0860582	−0.00286384
$904$	196.271	6.52789
$905$	21.3064	0.708249
$906$	−6.74608	−0.224124
$907$	7.38580	0.245241	0.122621	−	0.992454i	$-0.460870\pi$
$907$	7.38580	0.245241	0.122621	+	0.992454i	$0.460870\pi$
$908$	−144.194	−4.78523
$909$	−0.634026	−0.0210293
$910$	−61.4353	−2.03656
$911$	23.0109	0.762387	0.381193	−	0.924495i	$-0.375513\pi$
$911$	23.0109	0.762387	0.381193	+	0.924495i	$0.375513\pi$
$912$	2.78983	0.0923806
$913$	39.9716	1.32287
$914$	−13.4855	−0.446062
$915$	−0.904281	−0.0298946
$916$	49.1938	1.62541
$917$	23.2926	0.769189
$918$	26.7383	0.882497
$919$	20.1740	0.665478	0.332739	−	0.943019i	$-0.392027\pi$
$919$	20.1740	0.665478	0.332739	+	0.943019i	$0.392027\pi$
$920$	−66.7814	−2.20172
$921$	−5.30720	−0.174878
$922$	95.1828	3.13468
$923$	−43.1158	−1.41917
$924$	18.5859	0.611433
$925$	−2.93596	−0.0965336
$926$	−82.0417	−2.69606
$927$	13.7259	0.450819
$928$	30.3488	0.996248
$929$	3.83185	0.125719	0.0628594	−	0.998022i	$-0.479978\pi$
$929$	3.83185	0.125719	0.0628594	+	0.998022i	$0.479978\pi$
$930$	8.96620	0.294013
$931$	0.581391	0.0190543
$932$	23.3797	0.765827
$933$	−2.31013	−0.0756303
$934$	−1.91249	−0.0625786
$935$	−46.7943	−1.53034
$936$	−137.089	−4.48091
$937$	−31.9238	−1.04291	−0.521453	−	0.853280i	$-0.674610\pi$
$937$	−31.9238	−1.04291	−0.521453	+	0.853280i	$0.674610\pi$
$938$	62.8033	2.05060
$939$	8.89288	0.290208
$940$	75.8303	2.47331
$941$	13.8288	0.450804	0.225402	−	0.974266i	$-0.427630\pi$
$941$	13.8288	0.450804	0.225402	+	0.974266i	$0.427630\pi$
$942$	−9.71962	−0.316682
$943$	4.06912	0.132509
$944$	148.010	4.81732
$945$	−8.48282	−0.275946
$946$	1.43382	0.0466176
$947$	−4.09153	−0.132957	−0.0664785	−	0.997788i	$-0.521176\pi$
$947$	−4.09153	−0.132957	−0.0664785	+	0.997788i	$0.521176\pi$
$948$	−15.9364	−0.517589
$949$	−32.8625	−1.06676
$950$	−1.89894	−0.0616099
$951$	−5.30600	−0.172059
$952$	−132.588	−4.29721
$953$	−17.1275	−0.554814	−0.277407	−	0.960753i	$-0.589475\pi$
$953$	−17.1275	−0.554814	−0.277407	+	0.960753i	$0.589475\pi$
$954$	−5.65507	−0.183090
$955$	−29.7442	−0.962498
$956$	91.4002	2.95609
$957$	1.60879	0.0520049
$958$	56.7165	1.83243
$959$	40.0189	1.29228
$960$	−22.0172	−0.710603
$961$	−0.569196	−0.0183612
$962$	30.9207	0.996924
$963$	−35.5739	−1.14635
$964$	−38.5165	−1.24053
$965$	36.4143	1.17222
$966$	−6.99608	−0.225095
$967$	60.8299	1.95616	0.978078	−	0.208239i	$-0.0667730\pi$
$967$	60.8299	1.95616	0.978078	+	0.208239i	$0.0667730\pi$
$968$	−89.2487	−2.86856
$969$	−0.914290	−0.0293712
$970$	36.5368	1.17313
$971$	−14.5826	−0.467978	−0.233989	−	0.972239i	$-0.575178\pi$
$971$	−14.5826	−0.467978	−0.233989	+	0.972239i	$0.575178\pi$
$972$	−44.2383	−1.41895
$973$	−19.3191	−0.619341
$974$	39.9895	1.28135
$975$	−1.74950	−0.0560287
$976$	25.3588	0.811717
$977$	−12.2949	−0.393349	−0.196675	−	0.980469i	$-0.563014\pi$
$977$	−12.2949	−0.393349	−0.196675	+	0.980469i	$0.563014\pi$
$978$	2.84573	0.0909963
$979$	−25.9093	−0.828064
$980$	−11.3954	−0.364012
$981$	34.1097	1.08904
$982$	100.767	3.21561
$983$	−13.6613	−0.435728	−0.217864	−	0.975979i	$-0.569909\pi$
$983$	−13.6613	−0.435728	−0.217864	+	0.975979i	$0.569909\pi$
$984$	3.61855	0.115355
$985$	−35.0068	−1.11541
$986$	−17.7893	−0.566527
$987$	5.12512	0.163134
$988$	14.7612	0.469616
$989$	−0.398360	−0.0126671
$990$	69.5686	2.21104
$991$	10.2787	0.326514	0.163257	−	0.986584i	$-0.447800\pi$
$991$	10.2787	0.326514	0.163257	+	0.986584i	$0.447800\pi$
$992$	−140.580	−4.46342
$993$	5.02392	0.159429
$994$	61.9951	1.96636
$995$	11.2434	0.356439
$996$	−15.3075	−0.485035
$997$	16.4771	0.521835	0.260917	−	0.965361i	$-0.415975\pi$
$997$	16.4771	0.521835	0.260917	+	0.965361i	$0.415975\pi$
$998$	−39.0952	−1.23754
$999$	4.26945	0.135079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.5	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.76337 q^{2} -0.302967 q^{3} +5.63621 q^{4} +1.94141 q^{5} +0.837209 q^{6} -2.44102 q^{7} -10.0482 q^{8} -2.90821 q^{9} +O(q^{10})\)	\(q-2.76337 q^{2} -0.302967 q^{3} +5.63621 q^{4} +1.94141 q^{5} +0.837209 q^{6} -2.44102 q^{7} -10.0482 q^{8} -2.90821 q^{9} -5.36484 q^{10} +4.45893 q^{11} -1.70758 q^{12} -4.69126 q^{13} +6.74545 q^{14} -0.588183 q^{15} +16.4945 q^{16} -5.40561 q^{17} +8.03646 q^{18} -0.558271 q^{19} +10.9422 q^{20} +0.739548 q^{21} -12.3217 q^{22} +3.42333 q^{23} +3.04427 q^{24} -1.23092 q^{25} +12.9637 q^{26} +1.78999 q^{27} -13.7581 q^{28} -1.19090 q^{29} +1.62537 q^{30} +5.51641 q^{31} -25.4839 q^{32} -1.35091 q^{33} +14.9377 q^{34} -4.73903 q^{35} -16.3913 q^{36} +2.38518 q^{37} +1.54271 q^{38} +1.42130 q^{39} -19.5077 q^{40} +1.18864 q^{41} -2.04364 q^{42} -0.116366 q^{43} +25.1315 q^{44} -5.64604 q^{45} -9.45994 q^{46} +6.93007 q^{47} -4.99728 q^{48} -1.04141 q^{49} +3.40148 q^{50} +1.63772 q^{51} -26.4410 q^{52} -0.703676 q^{53} -4.94641 q^{54} +8.65662 q^{55} +24.5279 q^{56} +0.169137 q^{57} +3.29090 q^{58} +8.97331 q^{59} -3.31513 q^{60} +1.53741 q^{61} -15.2439 q^{62} +7.09901 q^{63} +37.4326 q^{64} -9.10767 q^{65} +3.73306 q^{66} +9.31048 q^{67} -30.4672 q^{68} -1.03716 q^{69} +13.0957 q^{70} +9.19066 q^{71} +29.2223 q^{72} +7.00506 q^{73} -6.59113 q^{74} +0.372927 q^{75} -3.14653 q^{76} -10.8843 q^{77} -3.92757 q^{78} +9.33269 q^{79} +32.0226 q^{80} +8.18233 q^{81} -3.28466 q^{82} +8.96439 q^{83} +4.16825 q^{84} -10.4945 q^{85} +0.321562 q^{86} +0.360803 q^{87} -44.8042 q^{88} -5.81065 q^{89} +15.6021 q^{90} +11.4515 q^{91} +19.2946 q^{92} -1.67129 q^{93} -19.1503 q^{94} -1.08383 q^{95} +7.72078 q^{96} -6.81041 q^{97} +2.87781 q^{98} -12.9675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 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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