LMFDB - Embedded newform 6037.2.a.a.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.79753 q^{2} -2.64112 q^{3} +5.82619 q^{4} -2.23668 q^{5} +7.38863 q^{6} -3.27355 q^{7} -10.7039 q^{8} +3.97554 q^{9} +O(q^{10})$	\(q-2.79753 q^{2} -2.64112 q^{3} +5.82619 q^{4} -2.23668 q^{5} +7.38863 q^{6} -3.27355 q^{7} -10.7039 q^{8} +3.97554 q^{9} +6.25720 q^{10} +2.82619 q^{11} -15.3877 q^{12} +0.422688 q^{13} +9.15785 q^{14} +5.90736 q^{15} +18.2921 q^{16} -1.15037 q^{17} -11.1217 q^{18} +6.14718 q^{19} -13.0313 q^{20} +8.64584 q^{21} -7.90636 q^{22} +5.61831 q^{23} +28.2703 q^{24} +0.00275197 q^{25} -1.18248 q^{26} -2.57651 q^{27} -19.0723 q^{28} -5.43869 q^{29} -16.5260 q^{30} -9.76944 q^{31} -29.7650 q^{32} -7.46432 q^{33} +3.21820 q^{34} +7.32188 q^{35} +23.1622 q^{36} -4.78322 q^{37} -17.1969 q^{38} -1.11637 q^{39} +23.9412 q^{40} -3.27748 q^{41} -24.1870 q^{42} -1.13266 q^{43} +16.4659 q^{44} -8.89202 q^{45} -15.7174 q^{46} -9.62890 q^{47} -48.3117 q^{48} +3.71610 q^{49} -0.00769871 q^{50} +3.03827 q^{51} +2.46266 q^{52} +5.77106 q^{53} +7.20788 q^{54} -6.32130 q^{55} +35.0397 q^{56} -16.2355 q^{57} +15.2149 q^{58} -2.67824 q^{59} +34.4174 q^{60} +13.5696 q^{61} +27.3303 q^{62} -13.0141 q^{63} +46.6843 q^{64} -0.945418 q^{65} +20.8817 q^{66} +12.9183 q^{67} -6.70227 q^{68} -14.8387 q^{69} -20.4832 q^{70} -7.11005 q^{71} -42.5537 q^{72} -14.5251 q^{73} +13.3812 q^{74} -0.00726828 q^{75} +35.8146 q^{76} -9.25167 q^{77} +3.12308 q^{78} +7.07259 q^{79} -40.9137 q^{80} -5.12172 q^{81} +9.16887 q^{82} -9.72765 q^{83} +50.3723 q^{84} +2.57301 q^{85} +3.16865 q^{86} +14.3643 q^{87} -30.2513 q^{88} -7.16245 q^{89} +24.8757 q^{90} -1.38369 q^{91} +32.7333 q^{92} +25.8023 q^{93} +26.9372 q^{94} -13.7493 q^{95} +78.6131 q^{96} +13.9886 q^{97} -10.3959 q^{98} +11.2356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.79753	−1.97815	−0.989077	−	0.147398i	$-0.952910\pi$
$2$	−2.79753	−1.97815	−0.989077	+	0.147398i	$0.952910\pi$
$3$	−2.64112	−1.52485	−0.762427	−	0.647074i	$-0.775992\pi$
$3$	−2.64112	−1.52485	−0.762427	+	0.647074i	$0.775992\pi$
$4$	5.82619	2.91310
$5$	−2.23668	−1.00028	−0.500138	−	0.865946i	$-0.666717\pi$
$5$	−2.23668	−1.00028	−0.500138	+	0.865946i	$0.666717\pi$
$6$	7.38863	3.01640
$7$	−3.27355	−1.23728	−0.618642	−	0.785673i	$-0.712317\pi$
$7$	−3.27355	−1.23728	−0.618642	+	0.785673i	$0.712317\pi$
$8$	−10.7039	−3.78440
$9$	3.97554	1.32518
$10$	6.25720	1.97870
$11$	2.82619	0.852129	0.426064	−	0.904693i	$-0.359900\pi$
$11$	2.82619	0.852129	0.426064	+	0.904693i	$0.359900\pi$
$12$	−15.3877	−4.44204
$13$	0.422688	0.117232	0.0586162	−	0.998281i	$-0.481331\pi$
$13$	0.422688	0.117232	0.0586162	+	0.998281i	$0.481331\pi$
$14$	9.15785	2.44754
$15$	5.90736	1.52527
$16$	18.2921	4.57303
$17$	−1.15037	−0.279006	−0.139503	−	0.990222i	$-0.544550\pi$
$17$	−1.15037	−0.279006	−0.139503	+	0.990222i	$0.544550\pi$
$18$	−11.1217	−2.62141
$19$	6.14718	1.41026	0.705130	−	0.709078i	$-0.250889\pi$
$19$	6.14718	1.41026	0.705130	+	0.709078i	$0.250889\pi$
$20$	−13.0313	−2.91390
$21$	8.64584	1.88668
$22$	−7.90636	−1.68564
$23$	5.61831	1.17150	0.585749	−	0.810492i	$-0.300800\pi$
$23$	5.61831	1.17150	0.585749	+	0.810492i	$0.300800\pi$
$24$	28.2703	5.77065
$25$	0.00275197	0.000550393 0
$26$	−1.18248	−0.231904
$27$	−2.57651	−0.495850
$28$	−19.0723	−3.60433
$29$	−5.43869	−1.00994	−0.504970	−	0.863137i	$-0.668497\pi$
$29$	−5.43869	−1.00994	−0.504970	+	0.863137i	$0.668497\pi$
$30$	−16.5260	−3.01723
$31$	−9.76944	−1.75464	−0.877321	−	0.479904i	$-0.840672\pi$
$31$	−9.76944	−1.75464	−0.877321	+	0.479904i	$0.840672\pi$
$32$	−29.7650	−5.26176
$33$	−7.46432	−1.29937
$34$	3.21820	0.551916
$35$	7.32188	1.23762
$36$	23.1622	3.86037
$37$	−4.78322	−0.786357	−0.393179	−	0.919462i	$-0.628625\pi$
$37$	−4.78322	−0.786357	−0.393179	+	0.919462i	$0.628625\pi$
$38$	−17.1969	−2.78971
$39$	−1.11637	−0.178762
$40$	23.9412	3.78544
$41$	−3.27748	−0.511857	−0.255929	−	0.966696i	$-0.582381\pi$
$41$	−3.27748	−0.511857	−0.255929	+	0.966696i	$0.582381\pi$
$42$	−24.1870	−3.73214
$43$	−1.13266	−0.172729	−0.0863644	−	0.996264i	$-0.527525\pi$
$43$	−1.13266	−0.172729	−0.0863644	+	0.996264i	$0.527525\pi$
$44$	16.4659	2.48233
$45$	−8.89202	−1.32554
$46$	−15.7174	−2.31740
$47$	−9.62890	−1.40452	−0.702260	−	0.711921i	$-0.747826\pi$
$47$	−9.62890	−1.40452	−0.702260	+	0.711921i	$0.747826\pi$
$48$	−48.3117	−6.97320
$49$	3.71610	0.530871
$50$	−0.00769871	−0.00108876
$51$	3.03827	0.425443
$52$	2.46266	0.341509
$53$	5.77106	0.792716	0.396358	−	0.918096i	$-0.370274\pi$
$53$	5.77106	0.792716	0.396358	+	0.918096i	$0.370274\pi$
$54$	7.20788	0.980868
$55$	−6.32130	−0.852363
$56$	35.0397	4.68237
$57$	−16.2355	−2.15044
$58$	15.2149	1.99782
$59$	−2.67824	−0.348677	−0.174338	−	0.984686i	$-0.555779\pi$
$59$	−2.67824	−0.348677	−0.174338	+	0.984686i	$0.555779\pi$
$60$	34.4174	4.44327
$61$	13.5696	1.73741	0.868705	−	0.495330i	$-0.164953\pi$
$61$	13.5696	1.73741	0.868705	+	0.495330i	$0.164953\pi$
$62$	27.3303	3.47095
$63$	−13.0141	−1.63962
$64$	46.6843	5.83554
$65$	−0.945418	−0.117265
$66$	20.8817	2.57036
$67$	12.9183	1.57822	0.789112	−	0.614249i	$-0.210541\pi$
$67$	12.9183	1.57822	0.789112	+	0.614249i	$0.210541\pi$
$68$	−6.70227	−0.812770
$69$	−14.8387	−1.78636
$70$	−20.4832	−2.44821
$71$	−7.11005	−0.843808	−0.421904	−	0.906640i	$-0.638638\pi$
$71$	−7.11005	−0.843808	−0.421904	+	0.906640i	$0.638638\pi$
$72$	−42.5537	−5.01500
$73$	−14.5251	−1.70003	−0.850017	−	0.526755i	$-0.823409\pi$
$73$	−14.5251	−1.70003	−0.850017	+	0.526755i	$0.823409\pi$
$74$	13.3812	1.55554
$75$	−0.00726828	−0.000839269 0
$76$	35.8146	4.10822
$77$	−9.25167	−1.05433
$78$	3.12308	0.353620
$79$	7.07259	0.795729	0.397864	−	0.917444i	$-0.369751\pi$
$79$	7.07259	0.795729	0.397864	+	0.917444i	$0.369751\pi$
$80$	−40.9137	−4.57429
$81$	−5.12172	−0.569080
$82$	9.16887	1.01253
$83$	−9.72765	−1.06775	−0.533874	−	0.845564i	$-0.679264\pi$
$83$	−9.72765	−1.06775	−0.533874	+	0.845564i	$0.679264\pi$
$84$	50.3723	5.49607
$85$	2.57301	0.279082
$86$	3.16865	0.341684
$87$	14.3643	1.54001
$88$	−30.2513	−3.22479
$89$	−7.16245	−0.759218	−0.379609	−	0.925147i	$-0.623942\pi$
$89$	−7.16245	−0.759218	−0.379609	+	0.925147i	$0.623942\pi$
$90$	24.8757	2.62213
$91$	−1.38369	−0.145050
$92$	32.7333	3.41269
$93$	25.8023	2.67557
$94$	26.9372	2.77836
$95$	−13.7493	−1.41065
$96$	78.6131	8.02341
$97$	13.9886	1.42032	0.710162	−	0.704038i	$-0.248622\pi$
$97$	13.9886	1.42032	0.710162	+	0.704038i	$0.248622\pi$
$98$	−10.3959	−1.05015
$99$	11.2356	1.12922
$100$	0.0160335	0.00160335
$101$	8.80707	0.876337	0.438168	−	0.898893i	$-0.355627\pi$
$101$	8.80707	0.876337	0.438168	+	0.898893i	$0.355627\pi$
$102$	−8.49965	−0.841591
$103$	16.3924	1.61519	0.807595	−	0.589738i	$-0.200769\pi$
$103$	16.3924	1.61519	0.807595	+	0.589738i	$0.200769\pi$
$104$	−4.52440	−0.443654
$105$	−19.3380	−1.88720
$106$	−16.1447	−1.56811
$107$	−12.9633	−1.25321	−0.626603	−	0.779339i	$-0.715555\pi$
$107$	−12.9633	−1.25321	−0.626603	+	0.779339i	$0.715555\pi$
$108$	−15.0113	−1.44446
$109$	10.4638	1.00225	0.501124	−	0.865376i	$-0.332920\pi$
$109$	10.4638	1.00225	0.501124	+	0.865376i	$0.332920\pi$
$110$	17.6840	1.68611
$111$	12.6331	1.19908
$112$	−59.8801	−5.65813
$113$	3.38229	0.318179	0.159089	−	0.987264i	$-0.449144\pi$
$113$	3.38229	0.318179	0.159089	+	0.987264i	$0.449144\pi$
$114$	45.4192	4.25390
$115$	−12.5664	−1.17182
$116$	−31.6869	−2.94205
$117$	1.68041	0.155354
$118$	7.49245	0.689736
$119$	3.76579	0.345209
$120$	−63.2317	−5.77224
$121$	−3.01264	−0.273877
$122$	−37.9614	−3.43687
$123$	8.65624	0.780507
$124$	−56.9186	−5.11144
$125$	11.1773	0.999725
$126$	36.4074	3.24343
$127$	2.21220	0.196301	0.0981504	−	0.995172i	$-0.468707\pi$
$127$	2.21220	0.196301	0.0981504	+	0.995172i	$0.468707\pi$
$128$	−71.0710	−6.28185
$129$	2.99149	0.263386
$130$	2.64484	0.231968
$131$	14.6174	1.27712	0.638562	−	0.769570i	$-0.279530\pi$
$131$	14.6174	1.27712	0.638562	+	0.769570i	$0.279530\pi$
$132$	−43.4886	−3.78519
$133$	−20.1231	−1.74489
$134$	−36.1394	−3.12197
$135$	5.76284	0.495987
$136$	12.3134	1.05587
$137$	0.779217	0.0665730	0.0332865	−	0.999446i	$-0.489403\pi$
$137$	0.779217	0.0665730	0.0332865	+	0.999446i	$0.489403\pi$
$138$	41.5116	3.53370
$139$	4.40686	0.373785	0.186892	−	0.982380i	$-0.440158\pi$
$139$	4.40686	0.373785	0.186892	+	0.982380i	$0.440158\pi$
$140$	42.6587	3.60532
$141$	25.4311	2.14169
$142$	19.8906	1.66918
$143$	1.19460	0.0998972
$144$	72.7210	6.06008
$145$	12.1646	1.01022
$146$	40.6345	3.36293
$147$	−9.81468	−0.809501
$148$	−27.8680	−2.29073
$149$	−18.6521	−1.52804	−0.764019	−	0.645194i	$-0.776776\pi$
$149$	−18.6521	−1.52804	−0.764019	+	0.645194i	$0.776776\pi$
$150$	0.0203333	0.00166020
$151$	−14.9523	−1.21680	−0.608401	−	0.793630i	$-0.708189\pi$
$151$	−14.9523	−1.21680	−0.608401	+	0.793630i	$0.708189\pi$
$152$	−65.7987	−5.33698
$153$	−4.57333	−0.369732
$154$	25.8818	2.08562
$155$	21.8511	1.75513
$156$	−6.50419	−0.520752
$157$	2.70182	0.215629	0.107814	−	0.994171i	$-0.465615\pi$
$157$	2.70182	0.215629	0.107814	+	0.994171i	$0.465615\pi$
$158$	−19.7858	−1.57407
$159$	−15.2421	−1.20878
$160$	66.5749	5.26321
$161$	−18.3918	−1.44948
$162$	14.3282	1.12573
$163$	−1.44916	−0.113507	−0.0567535	−	0.998388i	$-0.518075\pi$
$163$	−1.44916	−0.113507	−0.0567535	+	0.998388i	$0.518075\pi$
$164$	−19.0952	−1.49109
$165$	16.6953	1.29973
$166$	27.2134	2.11217
$167$	18.2220	1.41006	0.705029	−	0.709179i	$-0.250934\pi$
$167$	18.2220	1.41006	0.705029	+	0.709179i	$0.250934\pi$
$168$	−92.5441	−7.13994
$169$	−12.8213	−0.986257
$170$	−7.19808	−0.552068
$171$	24.4383	1.86885
$172$	−6.59908	−0.503175
$173$	12.3339	0.937731	0.468866	−	0.883270i	$-0.344663\pi$
$173$	12.3339	0.937731	0.468866	+	0.883270i	$0.344663\pi$
$174$	−40.1845	−3.04638
$175$	−0.00900868	−0.000680992 0
$176$	51.6970	3.89681
$177$	7.07355	0.531681
$178$	20.0372	1.50185
$179$	−5.34467	−0.399480	−0.199740	−	0.979849i	$-0.564010\pi$
$179$	−5.34467	−0.399480	−0.199740	+	0.979849i	$0.564010\pi$
$180$	−51.8066	−3.86143
$181$	25.4686	1.89307	0.946534	−	0.322603i	$-0.104558\pi$
$181$	25.4686	1.89307	0.946534	+	0.322603i	$0.104558\pi$
$182$	3.87091	0.286931
$183$	−35.8390	−2.64930
$184$	−60.1378	−4.43342
$185$	10.6986	0.786574
$186$	−72.1828	−5.29270
$187$	−3.25116	−0.237749
$188$	−56.0998	−4.09150
$189$	8.43433	0.613507
$190$	38.4641	2.79048
$191$	−17.1770	−1.24288	−0.621441	−	0.783461i	$-0.713452\pi$
$191$	−17.1770	−1.24288	−0.621441	+	0.783461i	$0.713452\pi$
$192$	−123.299	−8.89835
$193$	6.72782	0.484279	0.242140	−	0.970241i	$-0.422151\pi$
$193$	6.72782	0.484279	0.242140	+	0.970241i	$0.422151\pi$
$194$	−39.1335	−2.80962
$195$	2.49697	0.178812
$196$	21.6507	1.54648
$197$	−0.563334	−0.0401359	−0.0200679	−	0.999799i	$-0.506388\pi$
$197$	−0.563334	−0.0401359	−0.0200679	+	0.999799i	$0.506388\pi$
$198$	−31.4320	−2.23378
$199$	11.0840	0.785720	0.392860	−	0.919598i	$-0.371486\pi$
$199$	11.0840	0.785720	0.392860	+	0.919598i	$0.371486\pi$
$200$	−0.0294567	−0.00208291
$201$	−34.1189	−2.40656
$202$	−24.6381	−1.73353
$203$	17.8038	1.24958
$204$	17.7015	1.23935
$205$	7.33069	0.511998
$206$	−45.8582	−3.19510
$207$	22.3358	1.55244
$208$	7.73185	0.536107
$209$	17.3731	1.20172
$210$	54.0987	3.73317
$211$	14.7909	1.01824	0.509122	−	0.860694i	$-0.329970\pi$
$211$	14.7909	1.01824	0.509122	+	0.860694i	$0.329970\pi$
$212$	33.6233	2.30926
$213$	18.7785	1.28668
$214$	36.2652	2.47903
$215$	2.53340	0.172776
$216$	27.5787	1.87649
$217$	31.9807	2.17099
$218$	−29.2727	−1.98260
$219$	38.3626	2.59230
$220$	−36.8291	−2.48302
$221$	−0.486247	−0.0327085
$222$	−35.3415	−2.37196
$223$	13.2955	0.890335	0.445168	−	0.895447i	$-0.353144\pi$
$223$	13.2955	0.890335	0.445168	+	0.895447i	$0.353144\pi$
$224$	97.4371	6.51029
$225$	0.0109405	0.000729369 0
$226$	−9.46206	−0.629407
$227$	−16.1507	−1.07196	−0.535978	−	0.844232i	$-0.680057\pi$
$227$	−16.1507	−1.07196	−0.535978	+	0.844232i	$0.680057\pi$
$228$	−94.5909	−6.26443
$229$	8.61353	0.569198	0.284599	−	0.958647i	$-0.408140\pi$
$229$	8.61353	0.569198	0.284599	+	0.958647i	$0.408140\pi$
$230$	35.1549	2.31804
$231$	24.4348	1.60769
$232$	58.2152	3.82202
$233$	−8.99808	−0.589484	−0.294742	−	0.955577i	$-0.595234\pi$
$233$	−8.99808	−0.589484	−0.294742	+	0.955577i	$0.595234\pi$
$234$	−4.70100	−0.307314
$235$	21.5368	1.40491
$236$	−15.6039	−1.01573
$237$	−18.6796	−1.21337
$238$	−10.5349	−0.682877
$239$	−23.5695	−1.52459	−0.762293	−	0.647232i	$-0.775926\pi$
$239$	−23.5695	−1.52459	−0.762293	+	0.647232i	$0.775926\pi$
$240$	108.058	6.97512
$241$	17.2330	1.11007	0.555036	−	0.831826i	$-0.312704\pi$
$241$	17.2330	1.11007	0.555036	+	0.831826i	$0.312704\pi$
$242$	8.42797	0.541770
$243$	21.2566	1.36361
$244$	79.0591	5.06124
$245$	−8.31174	−0.531017
$246$	−24.2161	−1.54396
$247$	2.59834	0.165328
$248$	104.571	6.64026
$249$	25.6919	1.62816
$250$	−31.2688	−1.97761
$251$	11.9339	0.753260	0.376630	−	0.926364i	$-0.377083\pi$
$251$	11.9339	0.753260	0.376630	+	0.926364i	$0.377083\pi$
$252$	−75.8226	−4.77638
$253$	15.8784	0.998267
$254$	−6.18870	−0.388313
$255$	−6.79564	−0.425560
$256$	105.455	6.59092
$257$	0.0265183	0.00165416	0.000827082	−	1.00000i	$-0.499737\pi$
$257$	0.0265183	0.00165416	0.000827082		1.00000i	$0.499737\pi$
$258$	−8.36880	−0.521019
$259$	15.6581	0.972947
$260$	−5.50819	−0.341603
$261$	−21.6217	−1.33835
$262$	−40.8925	−2.52635
$263$	12.1668	0.750236	0.375118	−	0.926977i	$-0.377602\pi$
$263$	12.1668	0.750236	0.375118	+	0.926977i	$0.377602\pi$
$264$	79.8973	4.91734
$265$	−12.9080	−0.792934
$266$	56.2949	3.45166
$267$	18.9169	1.15770
$268$	75.2646	4.59752
$269$	10.7221	0.653736	0.326868	−	0.945070i	$-0.394007\pi$
$269$	10.7221	0.653736	0.326868	+	0.945070i	$0.394007\pi$
$270$	−16.1217	−0.981138
$271$	−15.7125	−0.954466	−0.477233	−	0.878777i	$-0.658360\pi$
$271$	−15.7125	−0.954466	−0.477233	+	0.878777i	$0.658360\pi$
$272$	−21.0427	−1.27590
$273$	3.65449	0.221180
$274$	−2.17988	−0.131692
$275$	0.00777758	0.000469006 0
$276$	−86.4528	−5.20385
$277$	−22.9353	−1.37805	−0.689025	−	0.724738i	$-0.741961\pi$
$277$	−22.9353	−1.37805	−0.689025	+	0.724738i	$0.741961\pi$
$278$	−12.3283	−0.739404
$279$	−38.8387	−2.32522
$280$	−78.3727	−4.68366
$281$	11.0329	0.658169	0.329084	−	0.944301i	$-0.393260\pi$
$281$	11.0329	0.658169	0.329084	+	0.944301i	$0.393260\pi$
$282$	−71.1444	−4.23659
$283$	−6.44214	−0.382946	−0.191473	−	0.981498i	$-0.561326\pi$
$283$	−6.44214	−0.382946	−0.191473	+	0.981498i	$0.561326\pi$
$284$	−41.4245	−2.45809
$285$	36.3136	2.15103
$286$	−3.34192	−0.197612
$287$	10.7290	0.633312
$288$	−118.332	−6.97277
$289$	−15.6767	−0.922156
$290$	−34.0310	−1.99837
$291$	−36.9455	−2.16579
$292$	−84.6260	−4.95236
$293$	7.89948	0.461492	0.230746	−	0.973014i	$-0.425883\pi$
$293$	7.89948	0.461492	0.230746	+	0.973014i	$0.425883\pi$
$294$	27.4569	1.60132
$295$	5.99036	0.348772
$296$	51.1991	2.97589
$297$	−7.28172	−0.422528
$298$	52.1798	3.02269
$299$	2.37479	0.137338
$300$	−0.0423464	−0.00244487
$301$	3.70781	0.213715
$302$	41.8296	2.40702
$303$	−23.2606	−1.33628
$304$	112.445	6.44916
$305$	−30.3509	−1.73789
$306$	12.7941	0.731387
$307$	18.9821	1.08336	0.541682	−	0.840584i	$-0.317788\pi$
$307$	18.9821	1.08336	0.541682	+	0.840584i	$0.317788\pi$
$308$	−53.9020	−3.07135
$309$	−43.2943	−2.46293
$310$	−61.1293	−3.47191
$311$	0.972350	0.0551369	0.0275685	−	0.999620i	$-0.491224\pi$
$311$	0.972350	0.0551369	0.0275685	+	0.999620i	$0.491224\pi$
$312$	11.9495	0.676508
$313$	−2.76853	−0.156487	−0.0782434	−	0.996934i	$-0.524931\pi$
$313$	−2.76853	−0.156487	−0.0782434	+	0.996934i	$0.524931\pi$
$314$	−7.55843	−0.426547
$315$	29.1084	1.64007
$316$	41.2063	2.31803
$317$	27.5905	1.54963	0.774817	−	0.632185i	$-0.217842\pi$
$317$	27.5905	1.54963	0.774817	+	0.632185i	$0.217842\pi$
$318$	42.6402	2.39114
$319$	−15.3708	−0.860599
$320$	−104.418	−5.83715
$321$	34.2376	1.91096
$322$	51.4516	2.86729
$323$	−7.07152	−0.393470
$324$	−29.8401	−1.65778
$325$	0.00116322	6.45239e−5 0
$326$	4.05407	0.224534
$327$	−27.6361	−1.52828
$328$	35.0818	1.93707
$329$	31.5206	1.73779
$330$	−46.7057	−2.57107
$331$	18.2967	1.00568	0.502838	−	0.864381i	$-0.332289\pi$
$331$	18.2967	1.00568	0.502838	+	0.864381i	$0.332289\pi$
$332$	−56.6751	−3.11045
$333$	−19.0159	−1.04206
$334$	−50.9765	−2.78931
$335$	−28.8942	−1.57866
$336$	158.151	8.62783
$337$	−10.1901	−0.555091	−0.277546	−	0.960712i	$-0.589521\pi$
$337$	−10.1901	−0.555091	−0.277546	+	0.960712i	$0.589521\pi$
$338$	35.8681	1.95097
$339$	−8.93304	−0.485176
$340$	14.9909	0.812993
$341$	−27.6103	−1.49518
$342$	−68.3670	−3.69687
$343$	10.7500	0.580445
$344$	12.1239	0.653675
$345$	33.1894	1.78686
$346$	−34.5046	−1.85498
$347$	−15.3601	−0.824572	−0.412286	−	0.911054i	$-0.635270\pi$
$347$	−15.3601	−0.824572	−0.412286	+	0.911054i	$0.635270\pi$
$348$	83.6890	4.48620
$349$	−23.8658	−1.27751	−0.638754	−	0.769411i	$-0.720550\pi$
$349$	−23.8658	−1.27751	−0.638754	+	0.769411i	$0.720550\pi$
$350$	0.0252021	0.00134711
$351$	−1.08906	−0.0581297
$352$	−84.1216	−4.48370
$353$	1.38749	0.0738485	0.0369242	−	0.999318i	$-0.488244\pi$
$353$	1.38749	0.0738485	0.0369242	+	0.999318i	$0.488244\pi$
$354$	−19.7885	−1.05175
$355$	15.9029	0.844040
$356$	−41.7298	−2.21168
$357$	−9.94591	−0.526393
$358$	14.9519	0.790233
$359$	19.3823	1.02296	0.511479	−	0.859296i	$-0.329098\pi$
$359$	19.3823	1.02296	0.511479	+	0.859296i	$0.329098\pi$
$360$	95.1792	5.01638
$361$	18.7878	0.988831
$362$	−71.2493	−3.74478
$363$	7.95676	0.417622
$364$	−8.06163	−0.422544
$365$	32.4881	1.70050
$366$	100.261	5.24072
$367$	−3.77179	−0.196886	−0.0984429	−	0.995143i	$-0.531386\pi$
$367$	−3.77179	−0.196886	−0.0984429	+	0.995143i	$0.531386\pi$
$368$	102.771	5.35730
$369$	−13.0298	−0.678302
$370$	−29.9296	−1.55596
$371$	−18.8918	−0.980814
$372$	150.329	7.79420
$373$	21.1980	1.09759	0.548797	−	0.835956i	$-0.315086\pi$
$373$	21.1980	1.09759	0.548797	+	0.835956i	$0.315086\pi$
$374$	9.09524	0.470304
$375$	−29.5205	−1.52443
$376$	103.067	5.31526
$377$	−2.29887	−0.118398
$378$	−23.5953	−1.21361
$379$	−34.5944	−1.77700	−0.888498	−	0.458881i	$-0.848251\pi$
$379$	−34.5944	−1.77700	−0.888498	+	0.458881i	$0.848251\pi$
$380$	−80.1060	−4.10935
$381$	−5.84269	−0.299330
$382$	48.0531	2.45861
$383$	21.7843	1.11312	0.556562	−	0.830806i	$-0.312120\pi$
$383$	21.7843	1.11312	0.556562	+	0.830806i	$0.312120\pi$
$384$	187.707	9.57890
$385$	20.6930	1.05462
$386$	−18.8213	−0.957979
$387$	−4.50293	−0.228897
$388$	81.5000	4.13754
$389$	9.60999	0.487246	0.243623	−	0.969870i	$-0.421664\pi$
$389$	9.60999	0.487246	0.243623	+	0.969870i	$0.421664\pi$
$390$	−6.98535	−0.353717
$391$	−6.46313	−0.326854
$392$	−39.7767	−2.00903
$393$	−38.6063	−1.94743
$394$	1.57594	0.0793949
$395$	−15.8191	−0.795948
$396$	65.4609	3.28953
$397$	−26.2362	−1.31676	−0.658378	−	0.752687i	$-0.728757\pi$
$397$	−26.2362	−1.31676	−0.658378	+	0.752687i	$0.728757\pi$
$398$	−31.0077	−1.55428
$399$	53.1475	2.66070
$400$	0.0503393	0.00251696
$401$	23.7476	1.18590	0.592948	−	0.805240i	$-0.297964\pi$
$401$	23.7476	1.18590	0.592948	+	0.805240i	$0.297964\pi$
$402$	95.4487	4.76055
$403$	−4.12942	−0.205701
$404$	51.3117	2.55285
$405$	11.4557	0.569236
$406$	−49.8068	−2.47187
$407$	−13.5183	−0.670078
$408$	−32.5213	−1.61004
$409$	34.6401	1.71284	0.856421	−	0.516278i	$-0.172683\pi$
$409$	34.6401	1.71284	0.856421	+	0.516278i	$0.172683\pi$
$410$	−20.5079	−1.01281
$411$	−2.05801	−0.101514
$412$	95.5052	4.70520
$413$	8.76732	0.431412
$414$	−62.4851	−3.07098
$415$	21.7577	1.06804
$416$	−12.5813	−0.616849
$417$	−11.6391	−0.569967
$418$	−48.6018	−2.37719
$419$	−36.0734	−1.76230	−0.881150	−	0.472836i	$-0.843230\pi$
$419$	−36.0734	−1.76230	−0.881150	+	0.472836i	$0.843230\pi$
$420$	−112.667	−5.49758
$421$	−13.6957	−0.667486	−0.333743	−	0.942664i	$-0.608312\pi$
$421$	−13.6957	−0.667486	−0.333743	+	0.942664i	$0.608312\pi$
$422$	−41.3779	−2.01424
$423$	−38.2801	−1.86124
$424$	−61.7728	−2.99995
$425$	−0.00316578	−0.000153563 0
$426$	−52.5336	−2.54526
$427$	−44.4207	−2.14967
$428$	−75.5264	−3.65071
$429$	−3.15508	−0.152329
$430$	−7.08727	−0.341778
$431$	30.8116	1.48414	0.742072	−	0.670320i	$-0.233843\pi$
$431$	30.8116	1.48414	0.742072	+	0.670320i	$0.233843\pi$
$432$	−47.1299	−2.26754
$433$	2.14577	0.103119	0.0515596	−	0.998670i	$-0.483581\pi$
$433$	2.14577	0.103119	0.0515596	+	0.998670i	$0.483581\pi$
$434$	−89.4670	−4.29455
$435$	−32.1283	−1.54043
$436$	60.9639	2.91964
$437$	34.5367	1.65212
$438$	−107.321	−5.12798
$439$	−6.08630	−0.290483	−0.145242	−	0.989396i	$-0.546396\pi$
$439$	−6.08630	−0.290483	−0.145242	+	0.989396i	$0.546396\pi$
$440$	67.6625	3.22568
$441$	14.7735	0.703499
$442$	1.36029	0.0647025
$443$	−32.8131	−1.55900	−0.779499	−	0.626404i	$-0.784526\pi$
$443$	−32.8131	−1.55900	−0.779499	+	0.626404i	$0.784526\pi$
$444$	73.6028	3.49303
$445$	16.0201	0.759427
$446$	−37.1947	−1.76122
$447$	49.2624	2.33003
$448$	−152.823	−7.22022
$449$	−0.0255115	−0.00120396	−0.000601980	−	1.00000i	$-0.500192\pi$
$449$	−0.0255115	−0.00120396	−0.000601980		1.00000i	$0.500192\pi$
$450$	−0.0306065	−0.00144281
$451$	−9.26280	−0.436168
$452$	19.7058	0.926885
$453$	39.4909	1.85544
$454$	45.1820	2.12050
$455$	3.09487	0.145090
$456$	173.783	8.13812
$457$	9.36383	0.438021	0.219011	−	0.975722i	$-0.429717\pi$
$457$	9.36383	0.438021	0.219011	+	0.975722i	$0.429717\pi$
$458$	−24.0966	−1.12596
$459$	2.96394	0.138345
$460$	−73.2141	−3.41363
$461$	−2.49901	−0.116390	−0.0581952	−	0.998305i	$-0.518535\pi$
$461$	−2.49901	−0.116390	−0.0581952	+	0.998305i	$0.518535\pi$
$462$	−68.3571	−3.18026
$463$	−4.08859	−0.190013	−0.0950065	−	0.995477i	$-0.530287\pi$
$463$	−4.08859	−0.190013	−0.0950065	+	0.995477i	$0.530287\pi$
$464$	−99.4852	−4.61849
$465$	−57.7116	−2.67631
$466$	25.1724	1.16609
$467$	−9.92113	−0.459095	−0.229547	−	0.973297i	$-0.573725\pi$
$467$	−9.92113	−0.459095	−0.229547	+	0.973297i	$0.573725\pi$
$468$	9.79039	0.452561
$469$	−42.2887	−1.95271
$470$	−60.2499	−2.77912
$471$	−7.13584	−0.328802
$472$	28.6675	1.31953
$473$	−3.20111	−0.147187
$474$	52.2568	2.40023
$475$	0.0169168	0.000776197 0
$476$	21.9402	1.00563
$477$	22.9430	1.05049
$478$	65.9365	3.01587
$479$	0.0492393	0.00224980	0.00112490	−	0.999999i	$-0.499642\pi$
$479$	0.0492393	0.00224980	0.00112490	+	0.999999i	$0.499642\pi$
$480$	−175.833	−8.02562
$481$	−2.02181	−0.0921866
$482$	−48.2097	−2.19589
$483$	48.5750	2.21024
$484$	−17.5522	−0.797828
$485$	−31.2880	−1.42071
$486$	−59.4661	−2.69744
$487$	11.4807	0.520239	0.260120	−	0.965576i	$-0.416238\pi$
$487$	11.4807	0.520239	0.260120	+	0.965576i	$0.416238\pi$
$488$	−145.248	−6.57505
$489$	3.82741	0.173082
$490$	23.2524	1.05043
$491$	−6.08443	−0.274586	−0.137293	−	0.990530i	$-0.543840\pi$
$491$	−6.08443	−0.274586	−0.137293	+	0.990530i	$0.543840\pi$
$492$	50.4329	2.27369
$493$	6.25651	0.281779
$494$	−7.26893	−0.327045
$495$	−25.1305	−1.12953
$496$	−178.704	−8.02403
$497$	23.2751	1.04403
$498$	−71.8740	−3.22075
$499$	15.5579	0.696467	0.348233	−	0.937408i	$-0.386782\pi$
$499$	15.5579	0.696467	0.348233	+	0.937408i	$0.386782\pi$
$500$	65.1209	2.91229
$501$	−48.1265	−2.15013
$502$	−33.3854	−1.49006
$503$	30.9593	1.38041	0.690204	−	0.723615i	$-0.257521\pi$
$503$	30.9593	1.38041	0.690204	+	0.723615i	$0.257521\pi$
$504$	139.302	6.20498
$505$	−19.6986	−0.876578
$506$	−44.4204	−1.97473
$507$	33.8627	1.50390
$508$	12.8887	0.571843
$509$	−29.8788	−1.32435	−0.662177	−	0.749348i	$-0.730367\pi$
$509$	−29.8788	−1.32435	−0.662177	+	0.749348i	$0.730367\pi$
$510$	19.0110	0.841823
$511$	47.5486	2.10343
$512$	−152.871	−6.75601
$513$	−15.8383	−0.699277
$514$	−0.0741857	−0.00327219
$515$	−36.6646	−1.61563
$516$	17.4290	0.767269
$517$	−27.2131	−1.19683
$518$	−43.8040	−1.92464
$519$	−32.5754	−1.42990
$520$	10.1197	0.443776
$521$	19.5999	0.858689	0.429344	−	0.903141i	$-0.358745\pi$
$521$	19.5999	0.858689	0.429344	+	0.903141i	$0.358745\pi$
$522$	60.4875	2.64747
$523$	11.0580	0.483532	0.241766	−	0.970335i	$-0.422273\pi$
$523$	11.0580	0.483532	0.241766	+	0.970335i	$0.422273\pi$
$524$	85.1635	3.72038
$525$	0.0237931	0.00103841
$526$	−34.0370	−1.48408
$527$	11.2385	0.489555
$528$	−136.538	−5.94206
$529$	8.56539	0.372408
$530$	36.1106	1.56855
$531$	−10.6474	−0.462059
$532$	−117.241	−5.08303
$533$	−1.38535	−0.0600063
$534$	−52.9207	−2.29010
$535$	28.9947	1.25355
$536$	−138.276	−5.97263
$537$	14.1159	0.609148
$538$	−29.9953	−1.29319
$539$	10.5024	0.452371
$540$	33.5754	1.44486
$541$	15.7541	0.677320	0.338660	−	0.940909i	$-0.390026\pi$
$541$	15.7541	0.677320	0.338660	+	0.940909i	$0.390026\pi$
$542$	43.9562	1.88808
$543$	−67.2658	−2.88665
$544$	34.2407	1.46806
$545$	−23.4041	−1.00252
$546$	−10.2236	−0.437528
$547$	−32.8539	−1.40473	−0.702366	−	0.711816i	$-0.747873\pi$
$547$	−32.8539	−1.40473	−0.702366	+	0.711816i	$0.747873\pi$
$548$	4.53986	0.193933
$549$	53.9465	2.30238
$550$	−0.0217580	−0.000927766 0
$551$	−33.4326	−1.42428
$552$	158.831	6.76031
$553$	−23.1525	−0.984542
$554$	64.1623	2.72599
$555$	−28.2562	−1.19941
$556$	25.6752	1.08887
$557$	−8.96768	−0.379973	−0.189986	−	0.981787i	$-0.560844\pi$
$557$	−8.96768	−0.379973	−0.189986	+	0.981787i	$0.560844\pi$
$558$	108.653	4.59963
$559$	−0.478761	−0.0202494
$560$	133.933	5.65969
$561$	8.58673	0.362532
$562$	−30.8650	−1.30196
$563$	−41.0777	−1.73122	−0.865610	−	0.500719i	$-0.833069\pi$
$563$	−41.0777	−1.73122	−0.865610	+	0.500719i	$0.833069\pi$
$564$	148.167	6.23894
$565$	−7.56510	−0.318266
$566$	18.0221	0.757526
$567$	16.7662	0.704113
$568$	76.1053	3.19331
$569$	−21.9102	−0.918524	−0.459262	−	0.888301i	$-0.651886\pi$
$569$	−21.9102	−0.918524	−0.459262	+	0.888301i	$0.651886\pi$
$570$	−101.588	−4.25507
$571$	−19.4488	−0.813905	−0.406952	−	0.913449i	$-0.633409\pi$
$571$	−19.4488	−0.813905	−0.406952	+	0.913449i	$0.633409\pi$
$572$	6.95995	0.291010
$573$	45.3665	1.89521
$574$	−30.0147	−1.25279
$575$	0.0154614	0.000644785 0
$576$	185.595	7.73314
$577$	44.3100	1.84465	0.922325	−	0.386415i	$-0.126287\pi$
$577$	44.3100	1.84465	0.922325	+	0.386415i	$0.126287\pi$
$578$	43.8559	1.82417
$579$	−17.7690	−0.738455
$580$	70.8735	2.94286
$581$	31.8439	1.32111
$582$	103.356	4.28426
$583$	16.3101	0.675496
$584$	155.475	6.43361
$585$	−3.75855	−0.155397
$586$	−22.0991	−0.912903
$587$	−0.695373	−0.0287011	−0.0143506	−	0.999897i	$-0.504568\pi$
$587$	−0.695373	−0.0287011	−0.0143506	+	0.999897i	$0.504568\pi$
$588$	−57.1822	−2.35815
$589$	−60.0545	−2.47450
$590$	−16.7582	−0.689926
$591$	1.48783	0.0612013
$592$	−87.4953	−3.59603
$593$	−25.7659	−1.05808	−0.529040	−	0.848597i	$-0.677448\pi$
$593$	−25.7659	−1.05808	−0.529040	+	0.848597i	$0.677448\pi$
$594$	20.3709	0.835826
$595$	−8.42287	−0.345304
$596$	−108.671	−4.45132
$597$	−29.2741	−1.19811
$598$	−6.64355	−0.271675
$599$	15.7179	0.642217	0.321109	−	0.947042i	$-0.395945\pi$
$599$	15.7179	0.642217	0.321109	+	0.947042i	$0.395945\pi$
$600$	0.0777989	0.00317613
$601$	11.4825	0.468380	0.234190	−	0.972191i	$-0.424756\pi$
$601$	11.4825	0.468380	0.234190	+	0.972191i	$0.424756\pi$
$602$	−10.3727	−0.422760
$603$	51.3572	2.09143
$604$	−87.1150	−3.54466
$605$	6.73833	0.273952
$606$	65.0722	2.64338
$607$	−1.25150	−0.0507969	−0.0253985	−	0.999677i	$-0.508085\pi$
$607$	−1.25150	−0.0507969	−0.0253985	+	0.999677i	$0.508085\pi$
$608$	−182.971	−7.42044
$609$	−47.0221	−1.90543
$610$	84.9077	3.43781
$611$	−4.07002	−0.164655
$612$	−26.6451	−1.07707
$613$	10.9114	0.440709	0.220355	−	0.975420i	$-0.429279\pi$
$613$	10.9114	0.440709	0.220355	+	0.975420i	$0.429279\pi$
$614$	−53.1029	−2.14306
$615$	−19.3613	−0.780722
$616$	99.0288	3.98999
$617$	−0.774334	−0.0311735	−0.0155867	−	0.999879i	$-0.504962\pi$
$617$	−0.774334	−0.0311735	−0.0155867	+	0.999879i	$0.504962\pi$
$618$	121.117	4.87205
$619$	21.4067	0.860407	0.430203	−	0.902732i	$-0.358442\pi$
$619$	21.4067	0.860407	0.430203	+	0.902732i	$0.358442\pi$
$620$	127.309	5.11285
$621$	−14.4756	−0.580888
$622$	−2.72018	−0.109069
$623$	23.4466	0.939369
$624$	−20.4208	−0.817485
$625$	−25.0138	−1.00055
$626$	7.74506	0.309555
$627$	−45.8845	−1.83245
$628$	15.7413	0.628147
$629$	5.50247	0.219398
$630$	−81.4318	−3.24432
$631$	−28.2046	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$631$	−28.2046	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$632$	−75.7043	−3.01135
$633$	−39.0645	−1.55267
$634$	−77.1852	−3.06542
$635$	−4.94799	−0.196355
$636$	−88.8032	−3.52128
$637$	1.57075	0.0622354
$638$	43.0003	1.70240
$639$	−28.2663	−1.11820
$640$	158.963	6.28358
$641$	39.9342	1.57731	0.788653	−	0.614838i	$-0.210779\pi$
$641$	39.9342	1.57731	0.788653	+	0.614838i	$0.210779\pi$
$642$	−95.7808	−3.78017
$643$	23.2143	0.915483	0.457742	−	0.889085i	$-0.348658\pi$
$643$	23.2143	0.915483	0.457742	+	0.889085i	$0.348658\pi$
$644$	−107.154	−4.22246
$645$	−6.69102	−0.263459
$646$	19.7828	0.778345
$647$	7.65966	0.301132	0.150566	−	0.988600i	$-0.451890\pi$
$647$	7.65966	0.301132	0.150566	+	0.988600i	$0.451890\pi$
$648$	54.8223	2.15362
$649$	−7.56920	−0.297117
$650$	−0.00325415	−0.000127638 0
$651$	−84.4650	−3.31044
$652$	−8.44308	−0.330657
$653$	36.0850	1.41211	0.706057	−	0.708155i	$-0.250472\pi$
$653$	36.0850	1.41211	0.706057	+	0.708155i	$0.250472\pi$
$654$	77.3129	3.02318
$655$	−32.6944	−1.27748
$656$	−59.9521	−2.34074
$657$	−57.7451	−2.25285
$658$	−88.1801	−3.43762
$659$	29.8589	1.16314	0.581569	−	0.813497i	$-0.302439\pi$
$659$	29.8589	1.16314	0.581569	+	0.813497i	$0.302439\pi$
$660$	97.2701	3.78624
$661$	−24.8293	−0.965749	−0.482875	−	0.875689i	$-0.660407\pi$
$661$	−24.8293	−0.965749	−0.482875	+	0.875689i	$0.660407\pi$
$662$	−51.1856	−1.98938
$663$	1.28424	0.0498757
$664$	104.124	4.04078
$665$	45.0089	1.74537
$666$	53.1976	2.06136
$667$	−30.5563	−1.18314
$668$	106.165	4.10763
$669$	−35.1152	−1.35763
$670$	80.8324	3.12283
$671$	38.3503	1.48050
$672$	−257.343	−9.92724
$673$	−39.9498	−1.53995	−0.769975	−	0.638074i	$-0.779732\pi$
$673$	−39.9498	−1.53995	−0.769975	+	0.638074i	$0.779732\pi$
$674$	28.5072	1.09806
$675$	−0.00709048	−0.000272913 0
$676$	−74.6995	−2.87306
$677$	28.6722	1.10196	0.550981	−	0.834518i	$-0.314254\pi$
$677$	28.6722	1.10196	0.550981	+	0.834518i	$0.314254\pi$
$678$	24.9905	0.959753
$679$	−45.7922	−1.75734
$680$	−27.5412	−1.05616
$681$	42.6559	1.63458
$682$	77.2407	2.95770
$683$	2.91588	0.111573	0.0557865	−	0.998443i	$-0.482233\pi$
$683$	2.91588	0.111573	0.0557865	+	0.998443i	$0.482233\pi$
$684$	142.382	5.44413
$685$	−1.74286	−0.0665913
$686$	−30.0735	−1.14821
$687$	−22.7494	−0.867944
$688$	−20.7187	−0.789894
$689$	2.43935	0.0929320
$690$	−92.8483	−3.53468
$691$	−39.1964	−1.49110	−0.745550	−	0.666449i	$-0.767813\pi$
$691$	−39.1964	−1.49110	−0.745550	+	0.666449i	$0.767813\pi$
$692$	71.8598	2.73170
$693$	−36.7803	−1.39717
$694$	42.9703	1.63113
$695$	−9.85674	−0.373888
$696$	−153.754	−5.82802
$697$	3.77032	0.142811
$698$	66.7655	2.52711
$699$	23.7651	0.898877
$700$	−0.0524863	−0.00198380
$701$	9.94840	0.375746	0.187873	−	0.982193i	$-0.439841\pi$
$701$	9.94840	0.375746	0.187873	+	0.982193i	$0.439841\pi$
$702$	3.04668	0.114990
$703$	−29.4033	−1.10897
$704$	131.939	4.97263
$705$	−56.8814	−2.14228
$706$	−3.88154	−0.146084
$707$	−28.8304	−1.08428
$708$	41.2119	1.54884
$709$	0.345603	0.0129794	0.00648970	−	0.999979i	$-0.497934\pi$
$709$	0.345603	0.0129794	0.00648970	+	0.999979i	$0.497934\pi$
$710$	−44.4890	−1.66964
$711$	28.1173	1.05448
$712$	76.6661	2.87318
$713$	−54.8877	−2.05556
$714$	27.8240	1.04129
$715$	−2.67193	−0.0999247
$716$	−31.1391	−1.16372
$717$	62.2500	2.32477
$718$	−54.2226	−2.02357
$719$	−16.5347	−0.616641	−0.308320	−	0.951283i	$-0.599767\pi$
$719$	−16.5347	−0.616641	−0.308320	+	0.951283i	$0.599767\pi$
$720$	−162.654	−6.06175
$721$	−53.6612	−1.99845
$722$	−52.5595	−1.95606
$723$	−45.5144	−1.69270
$724$	148.385	5.51469
$725$	−0.0149671	−0.000555864 0
$726$	−22.2593	−0.826120
$727$	−4.24350	−0.157383	−0.0786914	−	0.996899i	$-0.525074\pi$
$727$	−4.24350	−0.157383	−0.0786914	+	0.996899i	$0.525074\pi$
$728$	14.8108	0.548926
$729$	−40.7763	−1.51023
$730$	−90.8864	−3.36386
$731$	1.30298	0.0481923
$732$	−208.805	−7.71765
$733$	44.2526	1.63451	0.817254	−	0.576277i	$-0.195495\pi$
$733$	44.2526	1.63451	0.817254	+	0.576277i	$0.195495\pi$
$734$	10.5517	0.389471
$735$	21.9523	0.809724
$736$	−167.229	−6.16414
$737$	36.5096	1.34485
$738$	36.4512	1.34179
$739$	−33.8978	−1.24695	−0.623474	−	0.781844i	$-0.714279\pi$
$739$	−33.8978	−1.24695	−0.623474	+	0.781844i	$0.714279\pi$
$740$	62.3318	2.29136
$741$	−6.86253	−0.252101
$742$	52.8505	1.94020
$743$	−41.5621	−1.52476	−0.762382	−	0.647127i	$-0.775970\pi$
$743$	−41.5621	−1.52476	−0.762382	+	0.647127i	$0.775970\pi$
$744$	−276.185	−10.1254
$745$	41.7188	1.52846
$746$	−59.3022	−2.17121
$747$	−38.6726	−1.41496
$748$	−18.9419	−0.692584
$749$	42.4358	1.55057
$750$	82.5847	3.01557
$751$	−27.6375	−1.00851	−0.504253	−	0.863556i	$-0.668232\pi$
$751$	−27.6375	−1.00851	−0.504253	+	0.863556i	$0.668232\pi$
$752$	−176.133	−6.42291
$753$	−31.5189	−1.14861
$754$	6.43116	0.234209
$755$	33.4436	1.21714
$756$	49.1400	1.78721
$757$	−45.0284	−1.63658	−0.818292	−	0.574803i	$-0.805079\pi$
$757$	−45.0284	−1.63658	−0.818292	+	0.574803i	$0.805079\pi$
$758$	96.7790	3.51517
$759$	−41.9369	−1.52221
$760$	147.171	5.33845
$761$	26.9088	0.975444	0.487722	−	0.872999i	$-0.337828\pi$
$761$	26.9088	0.975444	0.487722	+	0.872999i	$0.337828\pi$
$762$	16.3451	0.592121
$763$	−34.2536	−1.24006
$764$	−100.076	−3.62063
$765$	10.2291	0.369834
$766$	−60.9422	−2.20193
$767$	−1.13206	−0.0408762
$768$	−278.519	−10.0502
$769$	−23.1620	−0.835243	−0.417622	−	0.908621i	$-0.637136\pi$
$769$	−23.1620	−0.835243	−0.417622	+	0.908621i	$0.637136\pi$
$770$	−57.8895	−2.08619
$771$	−0.0700380	−0.00252236
$772$	39.1976	1.41075
$773$	−37.8677	−1.36201	−0.681003	−	0.732281i	$-0.738456\pi$
$773$	−37.8677	−1.36201	−0.681003	+	0.732281i	$0.738456\pi$
$774$	12.5971	0.452793
$775$	−0.0268851	−0.000965743 0
$776$	−149.732	−5.37507
$777$	−41.3550	−1.48360
$778$	−26.8843	−0.963847
$779$	−20.1473	−0.721851
$780$	14.5478	0.520895
$781$	−20.0944	−0.719033
$782$	18.0808	0.646569
$783$	14.0129	0.500779
$784$	67.9753	2.42769
$785$	−6.04311	−0.215688
$786$	108.002	3.85231
$787$	−31.8704	−1.13606	−0.568029	−	0.823009i	$-0.692294\pi$
$787$	−31.8704	−1.13606	−0.568029	+	0.823009i	$0.692294\pi$
$788$	−3.28209	−0.116920
$789$	−32.1340	−1.14400
$790$	44.2546	1.57451
$791$	−11.0721	−0.393677
$792$	−120.265	−4.27343
$793$	5.73571	0.203681
$794$	73.3966	2.60475
$795$	34.0917	1.20911
$796$	64.5772	2.28888
$797$	47.5733	1.68513	0.842567	−	0.538592i	$-0.181043\pi$
$797$	47.5733	1.68513	0.842567	+	0.538592i	$0.181043\pi$
$798$	−148.682	−5.26328
$799$	11.0768	0.391869
$800$	−0.0819123	−0.00289604
$801$	−28.4746	−1.00610
$802$	−66.4346	−2.34589
$803$	−41.0507	−1.44865
$804$	−198.783	−7.01054
$805$	41.1366	1.44987
$806$	11.5522	0.406908
$807$	−28.3183	−0.996852
$808$	−94.2700	−3.31641
$809$	−16.3622	−0.575263	−0.287631	−	0.957741i	$-0.592868\pi$
$809$	−16.3622	−0.575263	−0.287631	+	0.957741i	$0.592868\pi$
$810$	−32.0476	−1.12604
$811$	−9.85742	−0.346141	−0.173070	−	0.984909i	$-0.555369\pi$
$811$	−9.85742	−0.346141	−0.173070	+	0.984909i	$0.555369\pi$
$812$	103.728	3.64015
$813$	41.4986	1.45542
$814$	37.8179	1.32552
$815$	3.24131	0.113538
$816$	55.5763	1.94556
$817$	−6.96265	−0.243592
$818$	−96.9068	−3.38827
$819$	−5.50090	−0.192217
$820$	42.7100	1.49150
$821$	4.40351	0.153684	0.0768418	−	0.997043i	$-0.475516\pi$
$821$	4.40351	0.153684	0.0768418	+	0.997043i	$0.475516\pi$
$822$	5.75734	0.200810
$823$	−9.28162	−0.323537	−0.161768	−	0.986829i	$-0.551720\pi$
$823$	−9.28162	−0.323537	−0.161768	+	0.986829i	$0.551720\pi$
$824$	−175.462	−6.11252
$825$	−0.0205416	−0.000715165 0
$826$	−24.5269	−0.853399
$827$	−14.3120	−0.497677	−0.248839	−	0.968545i	$-0.580049\pi$
$827$	−14.3120	−0.497677	−0.248839	+	0.968545i	$0.580049\pi$
$828$	130.133	4.52242
$829$	13.4431	0.466899	0.233450	−	0.972369i	$-0.424999\pi$
$829$	13.4431	0.466899	0.233450	+	0.972369i	$0.424999\pi$
$830$	−60.8678	−2.11275
$831$	60.5750	2.10132
$832$	19.7329	0.684115
$833$	−4.27489	−0.148116
$834$	32.5606	1.12748
$835$	−40.7568	−1.41045
$836$	101.219	3.50073
$837$	25.1711	0.870040
$838$	100.917	3.48610
$839$	27.4806	0.948735	0.474367	−	0.880327i	$-0.342677\pi$
$839$	27.4806	0.948735	0.474367	+	0.880327i	$0.342677\pi$
$840$	206.992	7.14190
$841$	0.579402	0.0199794
$842$	38.3141	1.32039
$843$	−29.1393	−1.00361
$844$	86.1743	2.96624
$845$	28.6773	0.986528
$846$	107.090	3.68182
$847$	9.86202	0.338863
$848$	105.565	3.62511
$849$	17.0145	0.583936
$850$	0.00885636	0.000303771 0
$851$	−26.8736	−0.921216
$852$	109.407	3.74823
$853$	29.0153	0.993466	0.496733	−	0.867903i	$-0.334533\pi$
$853$	29.0153	0.993466	0.496733	+	0.867903i	$0.334533\pi$
$854$	124.268	4.25238
$855$	−54.6608	−1.86936
$856$	138.757	4.74263
$857$	36.9710	1.26291	0.631453	−	0.775414i	$-0.282459\pi$
$857$	36.9710	1.26291	0.631453	+	0.775414i	$0.282459\pi$
$858$	8.82643	0.301329
$859$	−32.4394	−1.10682	−0.553408	−	0.832910i	$-0.686673\pi$
$859$	−32.4394	−1.10682	−0.553408	+	0.832910i	$0.686673\pi$
$860$	14.7601	0.503314
$861$	−28.3366	−0.965709
$862$	−86.1965	−2.93587
$863$	42.9190	1.46098	0.730491	−	0.682923i	$-0.239291\pi$
$863$	42.9190	1.46098	0.730491	+	0.682923i	$0.239291\pi$
$864$	76.6899	2.60904
$865$	−27.5871	−0.937989
$866$	−6.00287	−0.203986
$867$	41.4040	1.40615
$868$	186.326	6.32430
$869$	19.9885	0.678063
$870$	89.8800	3.04722
$871$	5.46041	0.185019
$872$	−112.003	−3.79290
$873$	55.6121	1.88218
$874$	−96.6177	−3.26814
$875$	−36.5893	−1.23694
$876$	223.508	7.55163
$877$	18.1102	0.611538	0.305769	−	0.952106i	$-0.401086\pi$
$877$	18.1102	0.611538	0.305769	+	0.952106i	$0.401086\pi$
$878$	17.0266	0.574621
$879$	−20.8635	−0.703708
$880$	−115.630	−3.89788
$881$	4.31254	0.145293	0.0726466	−	0.997358i	$-0.476855\pi$
$881$	4.31254	0.145293	0.0726466	+	0.997358i	$0.476855\pi$
$882$	−41.3293	−1.39163
$883$	15.1311	0.509202	0.254601	−	0.967046i	$-0.418056\pi$
$883$	15.1311	0.509202	0.254601	+	0.967046i	$0.418056\pi$
$884$	−2.83297	−0.0952830
$885$	−15.8213	−0.531827
$886$	91.7957	3.08394
$887$	12.9405	0.434500	0.217250	−	0.976116i	$-0.430291\pi$
$887$	12.9405	0.434500	0.217250	+	0.976116i	$0.430291\pi$
$888$	−135.223	−4.53779
$889$	−7.24173	−0.242880
$890$	−44.8169	−1.50226
$891$	−14.4750	−0.484929
$892$	77.4623	2.59363
$893$	−59.1906	−1.98074
$894$	−137.813	−4.60917
$895$	11.9543	0.399590
$896$	232.654	7.77243
$897$	−6.27211	−0.209420
$898$	0.0713692	0.00238162
$899$	53.1330	1.77208
$900$	0.0637417	0.00212472
$901$	−6.63885	−0.221172
$902$	25.9130	0.862808
$903$	−9.79278	−0.325883
$904$	−36.2036	−1.20412
$905$	−56.9653	−1.89359
$906$	−110.477	−3.67035
$907$	−45.0235	−1.49498	−0.747490	−	0.664273i	$-0.768741\pi$
$907$	−45.0235	−1.49498	−0.747490	+	0.664273i	$0.768741\pi$
$908$	−94.0968	−3.12271
$909$	35.0128	1.16130
$910$	−8.65800	−0.287010
$911$	−48.4297	−1.60455	−0.802274	−	0.596956i	$-0.796377\pi$
$911$	−48.4297	−1.60455	−0.802274	+	0.596956i	$0.796377\pi$
$912$	−296.981	−9.83402
$913$	−27.4922	−0.909859
$914$	−26.1956	−0.866474
$915$	80.1605	2.65003
$916$	50.1841	1.65813
$917$	−47.8506	−1.58017
$918$	−8.29172	−0.273668
$919$	2.26181	0.0746101	0.0373050	−	0.999304i	$-0.488123\pi$
$919$	2.26181	0.0746101	0.0373050	+	0.999304i	$0.488123\pi$
$920$	134.509	4.43464
$921$	−50.1340	−1.65197
$922$	6.99105	0.230238
$923$	−3.00533	−0.0989217
$924$	142.362	4.68336
$925$	−0.0131633	−0.000432806 0
$926$	11.4380	0.375875
$927$	65.1685	2.14042
$928$	161.883	5.31406
$929$	46.4296	1.52331	0.761653	−	0.647985i	$-0.224388\pi$
$929$	46.4296	1.52331	0.761653	+	0.647985i	$0.224388\pi$
$930$	161.450	5.29415
$931$	22.8435	0.748666
$932$	−52.4246	−1.71722
$933$	−2.56810	−0.0840758
$934$	27.7547	0.908161
$935$	7.27182	0.237814
$936$	−17.9869	−0.587921
$937$	−25.9335	−0.847210	−0.423605	−	0.905847i	$-0.639236\pi$
$937$	−25.9335	−0.847210	−0.423605	+	0.905847i	$0.639236\pi$
$938$	118.304	3.86276
$939$	7.31204	0.238619
$940$	125.478	4.09263
$941$	22.6401	0.738046	0.369023	−	0.929420i	$-0.379692\pi$
$941$	22.6401	0.738046	0.369023	+	0.929420i	$0.379692\pi$
$942$	19.9628	0.650422
$943$	−18.4139	−0.599640
$944$	−48.9906	−1.59451
$945$	−18.8649	−0.613676
$946$	8.95521	0.291159
$947$	13.5891	0.441587	0.220793	−	0.975321i	$-0.429135\pi$
$947$	13.5891	0.441587	0.220793	+	0.975321i	$0.429135\pi$
$948$	−108.831	−3.53466
$949$	−6.13958	−0.199299
$950$	−0.0473254	−0.00153544
$951$	−72.8698	−2.36297
$952$	−40.3086	−1.30641
$953$	27.6601	0.895997	0.447999	−	0.894034i	$-0.352137\pi$
$953$	27.6601	0.895997	0.447999	+	0.894034i	$0.352137\pi$
$954$	−64.1839	−2.07803
$955$	38.4194	1.24322
$956$	−137.321	−4.44126
$957$	40.5962	1.31229
$958$	−0.137749	−0.00445046
$959$	−2.55080	−0.0823697
$960$	275.781	8.90080
$961$	64.4419	2.07877
$962$	5.65608	0.182359
$963$	−51.5359	−1.66072
$964$	100.402	3.23375
$965$	−15.0480	−0.484413
$966$	−135.890	−4.37219
$967$	−55.9798	−1.80019	−0.900094	−	0.435695i	$-0.856503\pi$
$967$	−55.9798	−1.80019	−0.900094	+	0.435695i	$0.856503\pi$
$968$	32.2470	1.03646
$969$	18.6768	0.599984
$970$	87.5292	2.81039
$971$	5.85159	0.187786	0.0938932	−	0.995582i	$-0.470069\pi$
$971$	5.85159	0.187786	0.0938932	+	0.995582i	$0.470069\pi$
$972$	123.845	3.97234
$973$	−14.4260	−0.462478
$974$	−32.1176	−1.02911
$975$	−0.00307221	−9.83896e−5 0
$976$	248.217	7.94523
$977$	−3.14161	−0.100509	−0.0502545	−	0.998736i	$-0.516003\pi$
$977$	−3.14161	−0.100509	−0.0502545	+	0.998736i	$0.516003\pi$
$978$	−10.7073	−0.342382
$979$	−20.2425	−0.646952
$980$	−48.4258	−1.54690
$981$	41.5991	1.32816
$982$	17.0214	0.543174
$983$	−41.9970	−1.33950	−0.669748	−	0.742588i	$-0.733598\pi$
$983$	−41.9970	−1.33950	−0.669748	+	0.742588i	$0.733598\pi$
$984$	−92.6555	−2.95375
$985$	1.26000	0.0401469
$986$	−17.5028	−0.557402
$987$	−83.2499	−2.64987
$988$	15.1384	0.481617
$989$	−6.36363	−0.202352
$990$	70.3035	2.23439
$991$	−23.2422	−0.738312	−0.369156	−	0.929367i	$-0.620353\pi$
$991$	−23.2422	−0.738312	−0.369156	+	0.929367i	$0.620353\pi$
$992$	290.787	9.23251
$993$	−48.3238	−1.53351
$994$	−65.1128	−2.06525
$995$	−24.7913	−0.785937
$996$	149.686	4.74298
$997$	13.0472	0.413210	0.206605	−	0.978424i	$-0.433758\pi$
$997$	13.0472	0.413210	0.206605	+	0.978424i	$0.433758\pi$
$998$	−43.5237	−1.37772
$999$	12.3240	0.389915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.3	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.79753 q^{2} -2.64112 q^{3} +5.82619 q^{4} -2.23668 q^{5} +7.38863 q^{6} -3.27355 q^{7} -10.7039 q^{8} +3.97554 q^{9} +O(q^{10})\)	\(q-2.79753 q^{2} -2.64112 q^{3} +5.82619 q^{4} -2.23668 q^{5} +7.38863 q^{6} -3.27355 q^{7} -10.7039 q^{8} +3.97554 q^{9} +6.25720 q^{10} +2.82619 q^{11} -15.3877 q^{12} +0.422688 q^{13} +9.15785 q^{14} +5.90736 q^{15} +18.2921 q^{16} -1.15037 q^{17} -11.1217 q^{18} +6.14718 q^{19} -13.0313 q^{20} +8.64584 q^{21} -7.90636 q^{22} +5.61831 q^{23} +28.2703 q^{24} +0.00275197 q^{25} -1.18248 q^{26} -2.57651 q^{27} -19.0723 q^{28} -5.43869 q^{29} -16.5260 q^{30} -9.76944 q^{31} -29.7650 q^{32} -7.46432 q^{33} +3.21820 q^{34} +7.32188 q^{35} +23.1622 q^{36} -4.78322 q^{37} -17.1969 q^{38} -1.11637 q^{39} +23.9412 q^{40} -3.27748 q^{41} -24.1870 q^{42} -1.13266 q^{43} +16.4659 q^{44} -8.89202 q^{45} -15.7174 q^{46} -9.62890 q^{47} -48.3117 q^{48} +3.71610 q^{49} -0.00769871 q^{50} +3.03827 q^{51} +2.46266 q^{52} +5.77106 q^{53} +7.20788 q^{54} -6.32130 q^{55} +35.0397 q^{56} -16.2355 q^{57} +15.2149 q^{58} -2.67824 q^{59} +34.4174 q^{60} +13.5696 q^{61} +27.3303 q^{62} -13.0141 q^{63} +46.6843 q^{64} -0.945418 q^{65} +20.8817 q^{66} +12.9183 q^{67} -6.70227 q^{68} -14.8387 q^{69} -20.4832 q^{70} -7.11005 q^{71} -42.5537 q^{72} -14.5251 q^{73} +13.3812 q^{74} -0.00726828 q^{75} +35.8146 q^{76} -9.25167 q^{77} +3.12308 q^{78} +7.07259 q^{79} -40.9137 q^{80} -5.12172 q^{81} +9.16887 q^{82} -9.72765 q^{83} +50.3723 q^{84} +2.57301 q^{85} +3.16865 q^{86} +14.3643 q^{87} -30.2513 q^{88} -7.16245 q^{89} +24.8757 q^{90} -1.38369 q^{91} +32.7333 q^{92} +25.8023 q^{93} +26.9372 q^{94} -13.7493 q^{95} +78.6131 q^{96} +13.9886 q^{97} -10.3959 q^{98} +11.2356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 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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