LMFDB - Embedded newform 6037.2.a.a.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.63608 q^{2} +3.35251 q^{3} +4.94891 q^{4} +0.139412 q^{5} -8.83747 q^{6} -3.57933 q^{7} -7.77355 q^{8} +8.23930 q^{9} +O(q^{10})$	\(q-2.63608 q^{2} +3.35251 q^{3} +4.94891 q^{4} +0.139412 q^{5} -8.83747 q^{6} -3.57933 q^{7} -7.77355 q^{8} +8.23930 q^{9} -0.367500 q^{10} +4.81078 q^{11} +16.5912 q^{12} -2.83799 q^{13} +9.43540 q^{14} +0.467378 q^{15} +10.5939 q^{16} -1.12339 q^{17} -21.7194 q^{18} -8.30787 q^{19} +0.689935 q^{20} -11.9997 q^{21} -12.6816 q^{22} +0.306756 q^{23} -26.0609 q^{24} -4.98056 q^{25} +7.48115 q^{26} +17.5648 q^{27} -17.7138 q^{28} +5.36970 q^{29} -1.23205 q^{30} +5.08515 q^{31} -12.3792 q^{32} +16.1282 q^{33} +2.96134 q^{34} -0.499000 q^{35} +40.7755 q^{36} -6.89507 q^{37} +21.9002 q^{38} -9.51436 q^{39} -1.08372 q^{40} -8.43061 q^{41} +31.6322 q^{42} -10.7462 q^{43} +23.8081 q^{44} +1.14865 q^{45} -0.808633 q^{46} -11.2986 q^{47} +35.5160 q^{48} +5.81162 q^{49} +13.1292 q^{50} -3.76617 q^{51} -14.0449 q^{52} +6.72691 q^{53} -46.3021 q^{54} +0.670679 q^{55} +27.8241 q^{56} -27.8522 q^{57} -14.1550 q^{58} -9.34685 q^{59} +2.31301 q^{60} +14.9682 q^{61} -13.4049 q^{62} -29.4912 q^{63} +11.4448 q^{64} -0.395648 q^{65} -42.5151 q^{66} -5.20538 q^{67} -5.55955 q^{68} +1.02840 q^{69} +1.31540 q^{70} -6.81801 q^{71} -64.0486 q^{72} +0.738860 q^{73} +18.1759 q^{74} -16.6974 q^{75} -41.1149 q^{76} -17.2194 q^{77} +25.0806 q^{78} -6.31651 q^{79} +1.47691 q^{80} +34.1681 q^{81} +22.2237 q^{82} -15.7446 q^{83} -59.3856 q^{84} -0.156614 q^{85} +28.3278 q^{86} +18.0020 q^{87} -37.3969 q^{88} +2.65035 q^{89} -3.02794 q^{90} +10.1581 q^{91} +1.51811 q^{92} +17.0480 q^{93} +29.7840 q^{94} -1.15821 q^{95} -41.5013 q^{96} +12.9368 q^{97} -15.3199 q^{98} +39.6375 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.63608	−1.86399	−0.931994	−	0.362473i	$-0.881933\pi$
$2$	−2.63608	−1.86399	−0.931994	+	0.362473i	$0.881933\pi$
$3$	3.35251	1.93557	0.967785	−	0.251777i	$-0.0810151\pi$
$3$	3.35251	1.93557	0.967785	+	0.251777i	$0.0810151\pi$
$4$	4.94891	2.47445
$5$	0.139412	0.0623467	0.0311734	−	0.999514i	$-0.490076\pi$
$5$	0.139412	0.0623467	0.0311734	+	0.999514i	$0.490076\pi$
$6$	−8.83747	−3.60788
$7$	−3.57933	−1.35286	−0.676430	−	0.736507i	$-0.736474\pi$
$7$	−3.57933	−1.35286	−0.676430	+	0.736507i	$0.736474\pi$
$8$	−7.77355	−2.74837
$9$	8.23930	2.74643
$10$	−0.367500	−0.116214
$11$	4.81078	1.45051	0.725253	−	0.688483i	$-0.241723\pi$
$11$	4.81078	1.45051	0.725253	+	0.688483i	$0.241723\pi$
$12$	16.5912	4.78948
$13$	−2.83799	−0.787116	−0.393558	−	0.919300i	$-0.628756\pi$
$13$	−2.83799	−0.787116	−0.393558	+	0.919300i	$0.628756\pi$
$14$	9.43540	2.52172
$15$	0.467378	0.120677
$16$	10.5939	2.64847
$17$	−1.12339	−0.272462	−0.136231	−	0.990677i	$-0.543499\pi$
$17$	−1.12339	−0.272462	−0.136231	+	0.990677i	$0.543499\pi$
$18$	−21.7194	−5.11932
$19$	−8.30787	−1.90596	−0.952979	−	0.303038i	$-0.901999\pi$
$19$	−8.30787	−1.90596	−0.952979	+	0.303038i	$0.901999\pi$
$20$	0.689935	0.154274
$21$	−11.9997	−2.61856
$22$	−12.6816	−2.70373
$23$	0.306756	0.0639630	0.0319815	−	0.999488i	$-0.489818\pi$
$23$	0.306756	0.0639630	0.0319815	+	0.999488i	$0.489818\pi$
$24$	−26.0609	−5.31966
$25$	−4.98056	−0.996113
$26$	7.48115	1.46717
$27$	17.5648	3.38034
$28$	−17.7138	−3.34759
$29$	5.36970	0.997128	0.498564	−	0.866853i	$-0.333861\pi$
$29$	5.36970	0.997128	0.498564	+	0.866853i	$0.333861\pi$
$30$	−1.23205	−0.224940
$31$	5.08515	0.913321	0.456660	−	0.889641i	$-0.349045\pi$
$31$	5.08515	0.913321	0.456660	+	0.889641i	$0.349045\pi$
$32$	−12.3792	−2.18835
$33$	16.1282	2.80755
$34$	2.96134	0.507866
$35$	−0.499000	−0.0843464
$36$	40.7755	6.79592
$37$	−6.89507	−1.13354	−0.566771	−	0.823875i	$-0.691808\pi$
$37$	−6.89507	−1.13354	−0.566771	+	0.823875i	$0.691808\pi$
$38$	21.9002	3.55268
$39$	−9.51436	−1.52352
$40$	−1.08372	−0.171352
$41$	−8.43061	−1.31664	−0.658320	−	0.752738i	$-0.728733\pi$
$41$	−8.43061	−1.31664	−0.658320	+	0.752738i	$0.728733\pi$
$42$	31.6322	4.88096
$43$	−10.7462	−1.63878	−0.819389	−	0.573238i	$-0.805687\pi$
$43$	−10.7462	−1.63878	−0.819389	+	0.573238i	$0.805687\pi$
$44$	23.8081	3.58921
$45$	1.14865	0.171231
$46$	−0.808633	−0.119226
$47$	−11.2986	−1.64807	−0.824036	−	0.566538i	$-0.808282\pi$
$47$	−11.2986	−1.64807	−0.824036	+	0.566538i	$0.808282\pi$
$48$	35.5160	5.12630
$49$	5.81162	0.830231
$50$	13.1292	1.85674
$51$	−3.76617	−0.527369
$52$	−14.0449	−1.94768
$53$	6.72691	0.924012	0.462006	−	0.886877i	$-0.347130\pi$
$53$	6.72691	0.924012	0.462006	+	0.886877i	$0.347130\pi$
$54$	−46.3021	−6.30092
$55$	0.670679	0.0904343
$56$	27.8241	3.71816
$57$	−27.8522	−3.68911
$58$	−14.1550	−1.85864
$59$	−9.34685	−1.21686	−0.608428	−	0.793609i	$-0.708200\pi$
$59$	−9.34685	−1.21686	−0.608428	+	0.793609i	$0.708200\pi$
$60$	2.31301	0.298609
$61$	14.9682	1.91648	0.958239	−	0.285968i	$-0.0923150\pi$
$61$	14.9682	1.91648	0.958239	+	0.285968i	$0.0923150\pi$
$62$	−13.4049	−1.70242
$63$	−29.4912	−3.71554
$64$	11.4448	1.43059
$65$	−0.395648	−0.0490741
$66$	−42.5151	−5.23325
$67$	−5.20538	−0.635938	−0.317969	−	0.948101i	$-0.603001\pi$
$67$	−5.20538	−0.635938	−0.317969	+	0.948101i	$0.603001\pi$
$68$	−5.55955	−0.674195
$69$	1.02840	0.123805
$70$	1.31540	0.157221
$71$	−6.81801	−0.809149	−0.404574	−	0.914505i	$-0.632580\pi$
$71$	−6.81801	−0.809149	−0.404574	+	0.914505i	$0.632580\pi$
$72$	−64.0486	−7.54820
$73$	0.738860	0.0864770	0.0432385	−	0.999065i	$-0.486232\pi$
$73$	0.738860	0.0864770	0.0432385	+	0.999065i	$0.486232\pi$
$74$	18.1759	2.11291
$75$	−16.6974	−1.92805
$76$	−41.1149	−4.71620
$77$	−17.2194	−1.96233
$78$	25.0806	2.83982
$79$	−6.31651	−0.710663	−0.355332	−	0.934740i	$-0.615632\pi$
$79$	−6.31651	−0.710663	−0.355332	+	0.934740i	$0.615632\pi$
$80$	1.47691	0.165123
$81$	34.1681	3.79646
$82$	22.2237	2.45420
$83$	−15.7446	−1.72820	−0.864098	−	0.503324i	$-0.832110\pi$
$83$	−15.7446	−1.72820	−0.864098	+	0.503324i	$0.832110\pi$
$84$	−59.3856	−6.47950
$85$	−0.156614	−0.0169871
$86$	28.3278	3.05466
$87$	18.0020	1.93001
$88$	−37.3969	−3.98652
$89$	2.65035	0.280937	0.140468	−	0.990085i	$-0.455139\pi$
$89$	2.65035	0.280937	0.140468	+	0.990085i	$0.455139\pi$
$90$	−3.02794	−0.319173
$91$	10.1581	1.06486
$92$	1.51811	0.158274
$93$	17.0480	1.76780
$94$	29.7840	3.07199
$95$	−1.15821	−0.118830
$96$	−41.5013	−4.23571
$97$	12.9368	1.31354	0.656768	−	0.754093i	$-0.271923\pi$
$97$	12.9368	1.31354	0.656768	+	0.754093i	$0.271923\pi$
$98$	−15.3199	−1.54754
$99$	39.6375	3.98371
$100$	−24.6484	−2.46484
$101$	−0.754208	−0.0750465	−0.0375232	−	0.999296i	$-0.511947\pi$
$101$	−0.754208	−0.0750465	−0.0375232	+	0.999296i	$0.511947\pi$
$102$	9.92792	0.983011
$103$	−18.2521	−1.79843	−0.899215	−	0.437506i	$-0.855862\pi$
$103$	−18.2521	−1.79843	−0.899215	+	0.437506i	$0.855862\pi$
$104$	22.0612	2.16328
$105$	−1.67290	−0.163258
$106$	−17.7327	−1.72235
$107$	1.46622	0.141745	0.0708726	−	0.997485i	$-0.477422\pi$
$107$	1.46622	0.141745	0.0708726	+	0.997485i	$0.477422\pi$
$108$	86.9265	8.36450
$109$	12.9936	1.24456	0.622279	−	0.782795i	$-0.286207\pi$
$109$	12.9936	1.24456	0.622279	+	0.782795i	$0.286207\pi$
$110$	−1.76796	−0.168568
$111$	−23.1158	−2.19405
$112$	−37.9190	−3.58301
$113$	−4.63346	−0.435879	−0.217940	−	0.975962i	$-0.569934\pi$
$113$	−4.63346	−0.435879	−0.217940	+	0.975962i	$0.569934\pi$
$114$	73.4206	6.87647
$115$	0.0427653	0.00398789
$116$	26.5742	2.46735
$117$	−23.3830	−2.16176
$118$	24.6390	2.26821
$119$	4.02098	0.368603
$120$	−3.63319	−0.331663
$121$	12.1436	1.10397
$122$	−39.4573	−3.57229
$123$	−28.2637	−2.54845
$124$	25.1660	2.25997
$125$	−1.39141	−0.124451
$126$	77.7411	6.92572
$127$	0.259836	0.0230567	0.0115284	−	0.999934i	$-0.496330\pi$
$127$	0.259836	0.0230567	0.0115284	+	0.999934i	$0.496330\pi$
$128$	−5.41088	−0.478259
$129$	−36.0267	−3.17197
$130$	1.04296	0.0914736
$131$	−13.9513	−1.21893	−0.609466	−	0.792812i	$-0.708616\pi$
$131$	−13.9513	−1.21893	−0.609466	+	0.792812i	$0.708616\pi$
$132$	79.8169	6.94717
$133$	29.7366	2.57849
$134$	13.7218	1.18538
$135$	2.44873	0.210753
$136$	8.73273	0.748826
$137$	0.742861	0.0634669	0.0317334	−	0.999496i	$-0.489897\pi$
$137$	0.742861	0.0634669	0.0317334	+	0.999496i	$0.489897\pi$
$138$	−2.71095	−0.230771
$139$	11.3508	0.962762	0.481381	−	0.876512i	$-0.340135\pi$
$139$	11.3508	0.962762	0.481381	+	0.876512i	$0.340135\pi$
$140$	−2.46951	−0.208711
$141$	−37.8786	−3.18996
$142$	17.9728	1.50824
$143$	−13.6529	−1.14172
$144$	87.2861	7.27384
$145$	0.748598	0.0621677
$146$	−1.94769	−0.161192
$147$	19.4835	1.60697
$148$	−34.1231	−2.80490
$149$	11.2077	0.918174	0.459087	−	0.888391i	$-0.348177\pi$
$149$	11.2077	0.918174	0.459087	+	0.888391i	$0.348177\pi$
$150$	44.0156	3.59386
$151$	−14.1989	−1.15549	−0.577745	−	0.816217i	$-0.696067\pi$
$151$	−14.1989	−1.15549	−0.577745	+	0.816217i	$0.696067\pi$
$152$	64.5817	5.23827
$153$	−9.25594	−0.748299
$154$	45.3916	3.65776
$155$	0.708929	0.0569426
$156$	−47.0857	−3.76987
$157$	15.1118	1.20605	0.603027	−	0.797721i	$-0.293961\pi$
$157$	15.1118	1.20605	0.603027	+	0.797721i	$0.293961\pi$
$158$	16.6508	1.32467
$159$	22.5520	1.78849
$160$	−1.72580	−0.136437
$161$	−1.09798	−0.0865330
$162$	−90.0699	−7.07656
$163$	1.08748	0.0851777	0.0425889	−	0.999093i	$-0.486439\pi$
$163$	1.08748	0.0851777	0.0425889	+	0.999093i	$0.486439\pi$
$164$	−41.7223	−3.25797
$165$	2.24845	0.175042
$166$	41.5040	3.22134
$167$	10.8876	0.842509	0.421254	−	0.906943i	$-0.361590\pi$
$167$	10.8876	0.842509	0.421254	+	0.906943i	$0.361590\pi$
$168$	93.2806	7.19675
$169$	−4.94584	−0.380449
$170$	0.412845	0.0316638
$171$	−68.4511	−5.23458
$172$	−53.1819	−4.05508
$173$	9.57587	0.728040	0.364020	−	0.931391i	$-0.381404\pi$
$173$	9.57587	0.728040	0.364020	+	0.931391i	$0.381404\pi$
$174$	−47.4546	−3.59752
$175$	17.8271	1.34760
$176$	50.9648	3.84162
$177$	−31.3354	−2.35531
$178$	−6.98654	−0.523663
$179$	−21.5821	−1.61312	−0.806560	−	0.591152i	$-0.798673\pi$
$179$	−21.5821	−1.61312	−0.806560	+	0.591152i	$0.798673\pi$
$180$	5.68458	0.423704
$181$	8.50292	0.632017	0.316008	−	0.948756i	$-0.397657\pi$
$181$	8.50292	0.632017	0.316008	+	0.948756i	$0.397657\pi$
$182$	−26.7775	−1.98488
$183$	50.1809	3.70948
$184$	−2.38458	−0.175794
$185$	−0.961252	−0.0706727
$186$	−44.9399	−3.29515
$187$	−5.40438	−0.395208
$188$	−55.9158	−4.07808
$189$	−62.8702	−4.57313
$190$	3.05314	0.221498
$191$	5.37393	0.388844	0.194422	−	0.980918i	$-0.437717\pi$
$191$	5.37393	0.388844	0.194422	+	0.980918i	$0.437717\pi$
$192$	38.3686	2.76902
$193$	−10.2351	−0.736735	−0.368368	−	0.929680i	$-0.620083\pi$
$193$	−10.2351	−0.736735	−0.368368	+	0.929680i	$0.620083\pi$
$194$	−34.1025	−2.44842
$195$	−1.32641	−0.0949864
$196$	28.7612	2.05437
$197$	−0.0219384	−0.00156304	−0.000781522	−	1.00000i	$-0.500249\pi$
$197$	−0.0219384	−0.00156304	−0.000781522		1.00000i	$0.500249\pi$
$198$	−104.487	−7.42560
$199$	−2.90175	−0.205700	−0.102850	−	0.994697i	$-0.532796\pi$
$199$	−2.90175	−0.205700	−0.102850	+	0.994697i	$0.532796\pi$
$200$	38.7167	2.73768
$201$	−17.4511	−1.23090
$202$	1.98815	0.139886
$203$	−19.2199	−1.34898
$204$	−18.6384	−1.30495
$205$	−1.17532	−0.0820882
$206$	48.1139	3.35225
$207$	2.52745	0.175670
$208$	−30.0653	−2.08465
$209$	−39.9674	−2.76460
$210$	4.40990	0.304312
$211$	6.28676	0.432798	0.216399	−	0.976305i	$-0.430569\pi$
$211$	6.28676	0.432798	0.216399	+	0.976305i	$0.430569\pi$
$212$	33.2909	2.28643
$213$	−22.8574	−1.56616
$214$	−3.86508	−0.264212
$215$	−1.49814	−0.102172
$216$	−136.541	−9.29042
$217$	−18.2015	−1.23560
$218$	−34.2521	−2.31984
$219$	2.47703	0.167382
$220$	3.31913	0.223775
$221$	3.18816	0.214459
$222$	60.9350	4.08969
$223$	−16.3336	−1.09378	−0.546888	−	0.837206i	$-0.684188\pi$
$223$	−16.3336	−1.09378	−0.546888	+	0.837206i	$0.684188\pi$
$224$	44.3092	2.96053
$225$	−41.0364	−2.73576
$226$	12.2142	0.812474
$227$	7.80791	0.518229	0.259115	−	0.965847i	$-0.416569\pi$
$227$	7.80791	0.518229	0.259115	+	0.965847i	$0.416569\pi$
$228$	−137.838	−9.12854
$229$	5.26693	0.348048	0.174024	−	0.984741i	$-0.444323\pi$
$229$	5.26693	0.348048	0.174024	+	0.984741i	$0.444323\pi$
$230$	−0.112733	−0.00743338
$231$	−57.7281	−3.79823
$232$	−41.7417	−2.74047
$233$	−13.3979	−0.877723	−0.438862	−	0.898555i	$-0.644618\pi$
$233$	−13.3979	−0.877723	−0.438862	+	0.898555i	$0.644618\pi$
$234$	61.6394	4.02950
$235$	−1.57516	−0.102752
$236$	−46.2567	−3.01106
$237$	−21.1761	−1.37554
$238$	−10.5996	−0.687072
$239$	22.5570	1.45909	0.729547	−	0.683931i	$-0.239731\pi$
$239$	22.5570	1.45909	0.729547	+	0.683931i	$0.239731\pi$
$240$	4.95135	0.319608
$241$	−12.2303	−0.787823	−0.393911	−	0.919148i	$-0.628878\pi$
$241$	−12.2303	−0.787823	−0.393911	+	0.919148i	$0.628878\pi$
$242$	−32.0115	−2.05778
$243$	61.8545	3.96797
$244$	74.0761	4.74224
$245$	0.810206	0.0517622
$246$	74.5053	4.75028
$247$	23.5776	1.50021
$248$	−39.5297	−2.51014
$249$	−52.7839	−3.34504
$250$	3.66786	0.231976
$251$	−27.6848	−1.74745	−0.873725	−	0.486420i	$-0.838302\pi$
$251$	−27.6848	−1.74745	−0.873725	+	0.486420i	$0.838302\pi$
$252$	−145.949	−9.19393
$253$	1.47574	0.0927787
$254$	−0.684949	−0.0429775
$255$	−0.525048	−0.0328798
$256$	−8.62599	−0.539124
$257$	8.42207	0.525354	0.262677	−	0.964884i	$-0.415395\pi$
$257$	8.42207	0.525354	0.262677	+	0.964884i	$0.415395\pi$
$258$	94.9691	5.91252
$259$	24.6797	1.53352
$260$	−1.95803	−0.121432
$261$	44.2426	2.73855
$262$	36.7767	2.27207
$263$	−23.8654	−1.47160	−0.735801	−	0.677198i	$-0.763194\pi$
$263$	−23.8654	−1.47160	−0.735801	+	0.677198i	$0.763194\pi$
$264$	−125.373	−7.71619
$265$	0.937809	0.0576092
$266$	−78.3881	−4.80628
$267$	8.88533	0.543773
$268$	−25.7609	−1.57360
$269$	−3.64723	−0.222376	−0.111188	−	0.993799i	$-0.535466\pi$
$269$	−3.64723	−0.222376	−0.111188	+	0.993799i	$0.535466\pi$
$270$	−6.45505	−0.392842
$271$	25.5288	1.55077	0.775383	−	0.631491i	$-0.217557\pi$
$271$	25.5288	1.55077	0.775383	+	0.631491i	$0.217557\pi$
$272$	−11.9011	−0.721608
$273$	34.0551	2.06111
$274$	−1.95824	−0.118302
$275$	−23.9604	−1.44487
$276$	5.08946	0.306350
$277$	−3.55251	−0.213450	−0.106725	−	0.994289i	$-0.534036\pi$
$277$	−3.55251	−0.213450	−0.106725	+	0.994289i	$0.534036\pi$
$278$	−29.9216	−1.79458
$279$	41.8981	2.50837
$280$	3.87901	0.231815
$281$	−19.3231	−1.15272	−0.576359	−	0.817196i	$-0.695527\pi$
$281$	−19.3231	−1.15272	−0.576359	+	0.817196i	$0.695527\pi$
$282$	99.8511	5.94604
$283$	1.06295	0.0631856	0.0315928	−	0.999501i	$-0.489942\pi$
$283$	1.06295	0.0631856	0.0315928	+	0.999501i	$0.489942\pi$
$284$	−33.7417	−2.00220
$285$	−3.88292	−0.230004
$286$	35.9902	2.12814
$287$	30.1760	1.78123
$288$	−101.996	−6.01016
$289$	−15.7380	−0.925764
$290$	−1.97336	−0.115880
$291$	43.3708	2.54244
$292$	3.65655	0.213983
$293$	17.6674	1.03214	0.516071	−	0.856546i	$-0.327394\pi$
$293$	17.6674	1.03214	0.516071	+	0.856546i	$0.327394\pi$
$294$	−51.3600	−2.99537
$295$	−1.30306	−0.0758670
$296$	53.5992	3.11539
$297$	84.5003	4.90320
$298$	−29.5445	−1.71147
$299$	−0.870569	−0.0503463
$300$	−82.6338	−4.77086
$301$	38.4642	2.21704
$302$	37.4294	2.15382
$303$	−2.52849	−0.145258
$304$	−88.0126	−5.04787
$305$	2.08674	0.119486
$306$	24.3994	1.39482
$307$	10.5569	0.602513	0.301257	−	0.953543i	$-0.402594\pi$
$307$	10.5569	0.602513	0.301257	+	0.953543i	$0.402594\pi$
$308$	−85.2172	−4.85570
$309$	−61.1902	−3.48099
$310$	−1.86879	−0.106140
$311$	−19.1163	−1.08399	−0.541993	−	0.840383i	$-0.682330\pi$
$311$	−19.1163	−1.08399	−0.541993	+	0.840383i	$0.682330\pi$
$312$	73.9604	4.18718
$313$	−4.73044	−0.267380	−0.133690	−	0.991023i	$-0.542683\pi$
$313$	−4.73044	−0.267380	−0.133690	+	0.991023i	$0.542683\pi$
$314$	−39.8359	−2.24807
$315$	−4.11141	−0.231652
$316$	−31.2598	−1.75850
$317$	7.93205	0.445508	0.222754	−	0.974875i	$-0.428495\pi$
$317$	7.93205	0.445508	0.222754	+	0.974875i	$0.428495\pi$
$318$	−59.4489	−3.33373
$319$	25.8325	1.44634
$320$	1.59553	0.0891929
$321$	4.91553	0.274358
$322$	2.89436	0.161297
$323$	9.33298	0.519301
$324$	169.095	9.39416
$325$	14.1348	0.784056
$326$	−2.86667	−0.158770
$327$	43.5610	2.40893
$328$	65.5358	3.61861
$329$	40.4415	2.22961
$330$	−5.92710	−0.326276
$331$	11.4119	0.627255	0.313628	−	0.949546i	$-0.398456\pi$
$331$	11.4119	0.627255	0.313628	+	0.949546i	$0.398456\pi$
$332$	−77.9187	−4.27634
$333$	−56.8105	−3.11320
$334$	−28.7006	−1.57043
$335$	−0.725689	−0.0396486
$336$	−127.124	−6.93517
$337$	−18.7172	−1.01959	−0.509796	−	0.860296i	$-0.670279\pi$
$337$	−18.7172	−1.01959	−0.509796	+	0.860296i	$0.670279\pi$
$338$	13.0376	0.709153
$339$	−15.5337	−0.843675
$340$	−0.775066	−0.0420339
$341$	24.4636	1.32478
$342$	180.442	9.75720
$343$	4.25362	0.229674
$344$	83.5361	4.50396
$345$	0.143371	0.00771883
$346$	−25.2428	−1.35706
$347$	−3.08754	−0.165748	−0.0828738	−	0.996560i	$-0.526410\pi$
$347$	−3.08754	−0.165748	−0.0828738	+	0.996560i	$0.526410\pi$
$348$	89.0900	4.77573
$349$	19.1872	1.02707	0.513533	−	0.858070i	$-0.328337\pi$
$349$	19.1872	1.02707	0.513533	+	0.858070i	$0.328337\pi$
$350$	−46.9936	−2.51191
$351$	−49.8486	−2.66072
$352$	−59.5536	−3.17422
$353$	−18.2073	−0.969078	−0.484539	−	0.874770i	$-0.661013\pi$
$353$	−18.2073	−0.969078	−0.484539	+	0.874770i	$0.661013\pi$
$354$	82.6025	4.39027
$355$	−0.950509	−0.0504478
$356$	13.1164	0.695166
$357$	13.4804	0.713457
$358$	56.8921	3.00684
$359$	−8.01675	−0.423108	−0.211554	−	0.977366i	$-0.567852\pi$
$359$	−8.01675	−0.423108	−0.211554	+	0.977366i	$0.567852\pi$
$360$	−8.92912	−0.470606
$361$	50.0208	2.63267
$362$	−22.4144	−1.17807
$363$	40.7116	2.13680
$364$	50.2715	2.63494
$365$	0.103006	0.00539156
$366$	−132.281	−6.91443
$367$	13.9264	0.726952	0.363476	−	0.931604i	$-0.381590\pi$
$367$	13.9264	0.726952	0.363476	+	0.931604i	$0.381590\pi$
$368$	3.24974	0.169404
$369$	−69.4623	−3.61606
$370$	2.53394	0.131733
$371$	−24.0778	−1.25006
$372$	84.3691	4.37433
$373$	−22.8261	−1.18189	−0.590946	−	0.806711i	$-0.701245\pi$
$373$	−22.8261	−1.18189	−0.590946	+	0.806711i	$0.701245\pi$
$374$	14.2464	0.736663
$375$	−4.66470	−0.240884
$376$	87.8303	4.52950
$377$	−15.2391	−0.784855
$378$	165.731	8.52427
$379$	6.42048	0.329798	0.164899	−	0.986310i	$-0.447270\pi$
$379$	6.42048	0.329798	0.164899	+	0.986310i	$0.447270\pi$
$380$	−5.73189	−0.294040
$381$	0.871103	0.0446280
$382$	−14.1661	−0.724801
$383$	−1.73010	−0.0884042	−0.0442021	−	0.999023i	$-0.514075\pi$
$383$	−1.73010	−0.0884042	−0.0442021	+	0.999023i	$0.514075\pi$
$384$	−18.1400	−0.925704
$385$	−2.40058	−0.122345
$386$	26.9804	1.37327
$387$	−88.5410	−4.50079
$388$	64.0232	3.25029
$389$	−17.8275	−0.903890	−0.451945	−	0.892046i	$-0.649270\pi$
$389$	−17.8275	−0.903890	−0.451945	+	0.892046i	$0.649270\pi$
$390$	3.49653	0.177054
$391$	−0.344606	−0.0174275
$392$	−45.1769	−2.28178
$393$	−46.7718	−2.35933
$394$	0.0578312	0.00291350
$395$	−0.880595	−0.0443075
$396$	196.162	9.85752
$397$	38.7545	1.94503	0.972516	−	0.232836i	$-0.0748005\pi$
$397$	38.7545	1.94503	0.972516	+	0.232836i	$0.0748005\pi$
$398$	7.64924	0.383422
$399$	99.6923	4.99086
$400$	−52.7635	−2.63818
$401$	24.1276	1.20487	0.602437	−	0.798167i	$-0.294197\pi$
$401$	24.1276	1.20487	0.602437	+	0.798167i	$0.294197\pi$
$402$	46.0023	2.29439
$403$	−14.4316	−0.718889
$404$	−3.73251	−0.185699
$405$	4.76343	0.236697
$406$	50.6653	2.51448
$407$	−33.1707	−1.64421
$408$	29.2765	1.44940
$409$	−29.5050	−1.45893	−0.729464	−	0.684019i	$-0.760230\pi$
$409$	−29.5050	−1.45893	−0.729464	+	0.684019i	$0.760230\pi$
$410$	3.09825	0.153012
$411$	2.49044	0.122845
$412$	−90.3279	−4.45013
$413$	33.4555	1.64624
$414$	−6.66256	−0.327447
$415$	−2.19498	−0.107747
$416$	35.1320	1.72249
$417$	38.0536	1.86349
$418$	105.357	5.15318
$419$	25.8919	1.26490	0.632452	−	0.774600i	$-0.282049\pi$
$419$	25.8919	1.26490	0.632452	+	0.774600i	$0.282049\pi$
$420$	−8.27904	−0.403976
$421$	−34.5058	−1.68171	−0.840854	−	0.541262i	$-0.817947\pi$
$421$	−34.5058	−1.68171	−0.840854	+	0.541262i	$0.817947\pi$
$422$	−16.5724	−0.806731
$423$	−93.0926	−4.52632
$424$	−52.2920	−2.53952
$425$	5.59512	0.271403
$426$	60.2539	2.91931
$427$	−53.5761	−2.59273
$428$	7.25621	0.350742
$429$	−45.7715	−2.20987
$430$	3.94922	0.190448
$431$	−11.1239	−0.535820	−0.267910	−	0.963444i	$-0.586333\pi$
$431$	−11.1239	−0.535820	−0.267910	+	0.963444i	$0.586333\pi$
$432$	186.079	8.95274
$433$	11.8858	0.571193	0.285596	−	0.958350i	$-0.407808\pi$
$433$	11.8858	0.571193	0.285596	+	0.958350i	$0.407808\pi$
$434$	47.9805	2.30314
$435$	2.50968	0.120330
$436$	64.3040	3.07960
$437$	−2.54849	−0.121911
$438$	−6.52965	−0.311999
$439$	−38.0852	−1.81771	−0.908854	−	0.417115i	$-0.863041\pi$
$439$	−38.0852	−1.81771	−0.908854	+	0.417115i	$0.863041\pi$
$440$	−5.21356	−0.248547
$441$	47.8836	2.28017
$442$	−8.40425	−0.399749
$443$	−28.4597	−1.35216	−0.676080	−	0.736828i	$-0.736323\pi$
$443$	−28.4597	−1.35216	−0.676080	+	0.736828i	$0.736323\pi$
$444$	−114.398	−5.42908
$445$	0.369490	0.0175155
$446$	43.0566	2.03879
$447$	37.5740	1.77719
$448$	−40.9646	−1.93539
$449$	0.138562	0.00653916	0.00326958	−	0.999995i	$-0.498959\pi$
$449$	0.138562	0.00653916	0.00326958	+	0.999995i	$0.498959\pi$
$450$	108.175	5.09942
$451$	−40.5578	−1.90979
$452$	−22.9306	−1.07856
$453$	−47.6019	−2.23653
$454$	−20.5823	−0.965973
$455$	1.41616	0.0663904
$456$	216.511	10.1390
$457$	−4.45155	−0.208235	−0.104117	−	0.994565i	$-0.533202\pi$
$457$	−4.45155	−0.208235	−0.104117	+	0.994565i	$0.533202\pi$
$458$	−13.8840	−0.648758
$459$	−19.7321	−0.921015
$460$	0.211642	0.00986784
$461$	2.69593	0.125562	0.0627809	−	0.998027i	$-0.480003\pi$
$461$	2.69593	0.125562	0.0627809	+	0.998027i	$0.480003\pi$
$462$	152.176	7.07986
$463$	−18.2721	−0.849177	−0.424588	−	0.905387i	$-0.639581\pi$
$463$	−18.2721	−0.849177	−0.424588	+	0.905387i	$0.639581\pi$
$464$	56.8860	2.64086
$465$	2.37669	0.110216
$466$	35.3178	1.63607
$467$	−1.79558	−0.0830896	−0.0415448	−	0.999137i	$-0.513228\pi$
$467$	−1.79558	−0.0830896	−0.0415448	+	0.999137i	$0.513228\pi$
$468$	−115.720	−5.34918
$469$	18.6318	0.860335
$470$	4.15224	0.191528
$471$	50.6625	2.33440
$472$	72.6583	3.34437
$473$	−51.6976	−2.37706
$474$	55.8220	2.56399
$475$	41.3779	1.89855
$476$	19.8995	0.912092
$477$	55.4250	2.53774
$478$	−59.4621	−2.71973
$479$	20.6996	0.945788	0.472894	−	0.881119i	$-0.343209\pi$
$479$	20.6996	0.945788	0.472894	+	0.881119i	$0.343209\pi$
$480$	−5.78576	−0.264083
$481$	19.5681	0.892229
$482$	32.2400	1.46849
$483$	−3.68099	−0.167491
$484$	60.0977	2.73171
$485$	1.80354	0.0818947
$486$	−163.053	−7.39625
$487$	14.5620	0.659867	0.329934	−	0.944004i	$-0.392974\pi$
$487$	14.5620	0.659867	0.329934	+	0.944004i	$0.392974\pi$
$488$	−116.356	−5.26719
$489$	3.64577	0.164868
$490$	−2.13577	−0.0964842
$491$	−7.58912	−0.342492	−0.171246	−	0.985228i	$-0.554779\pi$
$491$	−7.58912	−0.342492	−0.171246	+	0.985228i	$0.554779\pi$
$492$	−139.874	−6.30602
$493$	−6.03227	−0.271680
$494$	−62.1525	−2.79637
$495$	5.52592	0.248372
$496$	53.8715	2.41890
$497$	24.4039	1.09467
$498$	139.143	6.23513
$499$	17.6846	0.791672	0.395836	−	0.918321i	$-0.370455\pi$
$499$	17.6846	0.791672	0.395836	+	0.918321i	$0.370455\pi$
$500$	−6.88594	−0.307949
$501$	36.5008	1.63073
$502$	72.9793	3.25723
$503$	2.66705	0.118918	0.0594590	−	0.998231i	$-0.481062\pi$
$503$	2.66705	0.118918	0.0594590	+	0.998231i	$0.481062\pi$
$504$	229.251	10.2117
$505$	−0.105145	−0.00467890
$506$	−3.89015	−0.172938
$507$	−16.5809	−0.736386
$508$	1.28591	0.0570529
$509$	38.3965	1.70190	0.850948	−	0.525249i	$-0.176028\pi$
$509$	38.3965	1.70190	0.850948	+	0.525249i	$0.176028\pi$
$510$	1.38407	0.0612875
$511$	−2.64462	−0.116991
$512$	33.5606	1.48318
$513$	−145.926	−6.44279
$514$	−22.2012	−0.979255
$515$	−2.54455	−0.112126
$516$	−178.293	−7.84890
$517$	−54.3551	−2.39054
$518$	−65.0577	−2.85847
$519$	32.1032	1.40917
$520$	3.07559	0.134874
$521$	11.9662	0.524248	0.262124	−	0.965034i	$-0.415577\pi$
$521$	11.9662	0.524248	0.262124	+	0.965034i	$0.415577\pi$
$522$	−116.627	−5.10462
$523$	4.19719	0.183530	0.0917651	−	0.995781i	$-0.470749\pi$
$523$	4.19719	0.183530	0.0917651	+	0.995781i	$0.470749\pi$
$524$	−69.0438	−3.01619
$525$	59.7654	2.60838
$526$	62.9110	2.74305
$527$	−5.71261	−0.248845
$528$	170.860	7.43572
$529$	−22.9059	−0.995909
$530$	−2.47214	−0.107383
$531$	−77.0115	−3.34201
$532$	147.164	6.38037
$533$	23.9260	1.03635
$534$	−23.4224	−1.01359
$535$	0.204409	0.00883735
$536$	40.4643	1.74779
$537$	−72.3541	−3.12231
$538$	9.61438	0.414506
$539$	27.9584	1.20425
$540$	12.1186	0.521500
$541$	−10.2809	−0.442012	−0.221006	−	0.975272i	$-0.570934\pi$
$541$	−10.2809	−0.442012	−0.221006	+	0.975272i	$0.570934\pi$
$542$	−67.2960	−2.89061
$543$	28.5061	1.22331
$544$	13.9067	0.596243
$545$	1.81145	0.0775942
$546$	−89.7718	−3.84188
$547$	33.5065	1.43264	0.716318	−	0.697774i	$-0.245826\pi$
$547$	33.5065	1.43264	0.716318	+	0.697774i	$0.245826\pi$
$548$	3.67635	0.157046
$549$	123.327	5.26348
$550$	63.1615	2.69322
$551$	−44.6108	−1.90048
$552$	−7.99433	−0.340261
$553$	22.6089	0.961428
$554$	9.36469	0.397868
$555$	−3.22260	−0.136792
$556$	56.1740	2.38231
$557$	−30.4177	−1.28884	−0.644420	−	0.764672i	$-0.722901\pi$
$557$	−30.4177	−1.28884	−0.644420	+	0.764672i	$0.722901\pi$
$558$	−110.447	−4.67558
$559$	30.4975	1.28991
$560$	−5.28635	−0.223389
$561$	−18.1182	−0.764952
$562$	50.9372	2.14865
$563$	−1.36250	−0.0574224	−0.0287112	−	0.999588i	$-0.509140\pi$
$563$	−1.36250	−0.0574224	−0.0287112	+	0.999588i	$0.509140\pi$
$564$	−187.458	−7.89340
$565$	−0.645958	−0.0271757
$566$	−2.80201	−0.117777
$567$	−122.299	−5.13608
$568$	53.0002	2.22384
$569$	−15.0923	−0.632704	−0.316352	−	0.948642i	$-0.602458\pi$
$569$	−15.0923	−0.632704	−0.316352	+	0.948642i	$0.602458\pi$
$570$	10.2357	0.428725
$571$	19.7143	0.825018	0.412509	−	0.910953i	$-0.364652\pi$
$571$	19.7143	0.825018	0.412509	+	0.910953i	$0.364652\pi$
$572$	−67.5671	−2.82512
$573$	18.0161	0.752635
$574$	−79.5462	−3.32019
$575$	−1.52782	−0.0637144
$576$	94.2967	3.92903
$577$	−47.3307	−1.97040	−0.985202	−	0.171395i	$-0.945173\pi$
$577$	−47.3307	−1.97040	−0.985202	+	0.171395i	$0.945173\pi$
$578$	41.4866	1.72561
$579$	−34.3131	−1.42600
$580$	3.70474	0.153831
$581$	56.3552	2.33801
$582$	−114.329	−4.73908
$583$	32.3617	1.34028
$584$	−5.74357	−0.237670
$585$	−3.25986	−0.134779
$586$	−46.5728	−1.92390
$587$	7.16607	0.295775	0.147888	−	0.989004i	$-0.452753\pi$
$587$	7.16607	0.295775	0.147888	+	0.989004i	$0.452753\pi$
$588$	96.4220	3.97637
$589$	−42.2468	−1.74075
$590$	3.43497	0.141415
$591$	−0.0735485	−0.00302538
$592$	−73.0455	−3.00215
$593$	−28.9805	−1.19009	−0.595044	−	0.803693i	$-0.702865\pi$
$593$	−28.9805	−1.19009	−0.595044	+	0.803693i	$0.702865\pi$
$594$	−222.749	−9.13952
$595$	0.560572	0.0229812
$596$	55.4661	2.27198
$597$	−9.72813	−0.398146
$598$	2.29489	0.0938449
$599$	8.27781	0.338222	0.169111	−	0.985597i	$-0.445910\pi$
$599$	8.27781	0.338222	0.169111	+	0.985597i	$0.445910\pi$
$600$	129.798	5.29898
$601$	−3.40703	−0.138976	−0.0694879	−	0.997583i	$-0.522137\pi$
$601$	−3.40703	−0.138976	−0.0694879	+	0.997583i	$0.522137\pi$
$602$	−101.395	−4.13253
$603$	−42.8886	−1.74656
$604$	−70.2691	−2.85921
$605$	1.69296	0.0688286
$606$	6.66529	0.270759
$607$	−13.1561	−0.533990	−0.266995	−	0.963698i	$-0.586031\pi$
$607$	−13.1561	−0.533990	−0.266995	+	0.963698i	$0.586031\pi$
$608$	102.845	4.17091
$609$	−64.4350	−2.61104
$610$	−5.50080	−0.222721
$611$	32.0653	1.29722
$612$	−45.8068	−1.85163
$613$	4.38339	0.177043	0.0885216	−	0.996074i	$-0.471786\pi$
$613$	4.38339	0.177043	0.0885216	+	0.996074i	$0.471786\pi$
$614$	−27.8288	−1.12308
$615$	−3.94028	−0.158888
$616$	133.856	5.39320
$617$	8.25915	0.332501	0.166250	−	0.986084i	$-0.446834\pi$
$617$	8.25915	0.332501	0.166250	+	0.986084i	$0.446834\pi$
$618$	161.302	6.48853
$619$	17.1887	0.690872	0.345436	−	0.938442i	$-0.387731\pi$
$619$	17.1887	0.690872	0.345436	+	0.938442i	$0.387731\pi$
$620$	3.50843	0.140902
$621$	5.38810	0.216217
$622$	50.3920	2.02054
$623$	−9.48650	−0.380068
$624$	−100.794	−4.03499
$625$	24.7088	0.988354
$626$	12.4698	0.498394
$627$	−133.991	−5.35108
$628$	74.7870	2.98433
$629$	7.74585	0.308847
$630$	10.8380	0.431796
$631$	37.8587	1.50713	0.753565	−	0.657374i	$-0.228333\pi$
$631$	37.8587	1.50713	0.753565	+	0.657374i	$0.228333\pi$
$632$	49.1017	1.95316
$633$	21.0764	0.837712
$634$	−20.9095	−0.830422
$635$	0.0362242	0.00143751
$636$	111.608	4.42554
$637$	−16.4933	−0.653488
$638$	−68.0964	−2.69596
$639$	−56.1756	−2.22227
$640$	−0.754340	−0.0298179
$641$	48.5206	1.91645	0.958225	−	0.286017i	$-0.0923313\pi$
$641$	48.5206	1.91645	0.958225	+	0.286017i	$0.0923313\pi$
$642$	−12.9577	−0.511400
$643$	5.98554	0.236046	0.118023	−	0.993011i	$-0.462344\pi$
$643$	5.98554	0.236046	0.118023	+	0.993011i	$0.462344\pi$
$644$	−5.43381	−0.214122
$645$	−5.02253	−0.197762
$646$	−24.6025	−0.967971
$647$	−7.48530	−0.294278	−0.147139	−	0.989116i	$-0.547006\pi$
$647$	−7.48530	−0.294278	−0.147139	+	0.989116i	$0.547006\pi$
$648$	−265.608	−10.4341
$649$	−44.9657	−1.76506
$650$	−37.2604	−1.46147
$651$	−61.0205	−2.39158
$652$	5.38182	0.210768
$653$	32.7362	1.28107	0.640534	−	0.767930i	$-0.278713\pi$
$653$	32.7362	1.28107	0.640534	+	0.767930i	$0.278713\pi$
$654$	−114.830	−4.49022
$655$	−1.94497	−0.0759964
$656$	−89.3129	−3.48708
$657$	6.08768	0.237503
$658$	−106.607	−4.15597
$659$	35.4245	1.37994	0.689970	−	0.723838i	$-0.257624\pi$
$659$	35.4245	1.37994	0.689970	+	0.723838i	$0.257624\pi$
$660$	11.1274	0.433133
$661$	−27.8943	−1.08496	−0.542482	−	0.840067i	$-0.682515\pi$
$661$	−27.8943	−1.08496	−0.542482	+	0.840067i	$0.682515\pi$
$662$	−30.0827	−1.16920
$663$	10.6883	0.415101
$664$	122.392	4.74972
$665$	4.14563	0.160761
$666$	149.757	5.80297
$667$	1.64719	0.0637794
$668$	53.8818	2.08475
$669$	−54.7584	−2.11708
$670$	1.91297	0.0739046
$671$	72.0086	2.77986
$672$	148.547	5.73032
$673$	26.3114	1.01423	0.507116	−	0.861878i	$-0.330712\pi$
$673$	26.3114	1.01423	0.507116	+	0.861878i	$0.330712\pi$
$674$	49.3400	1.90051
$675$	−87.4825	−3.36720
$676$	−24.4765	−0.941404
$677$	−17.9553	−0.690078	−0.345039	−	0.938588i	$-0.612134\pi$
$677$	−17.9553	−0.690078	−0.345039	+	0.938588i	$0.612134\pi$
$678$	40.9481	1.57260
$679$	−46.3052	−1.77703
$680$	1.21744	0.0466868
$681$	26.1761	1.00307
$682$	−64.4879	−2.46937
$683$	−8.68515	−0.332328	−0.166164	−	0.986098i	$-0.553138\pi$
$683$	−8.68515	−0.332328	−0.166164	+	0.986098i	$0.553138\pi$
$684$	−338.758	−12.9527
$685$	0.103563	0.00395695
$686$	−11.2129	−0.428109
$687$	17.6574	0.673672
$688$	−113.844	−4.34026
$689$	−19.0909	−0.727305
$690$	−0.377937	−0.0143878
$691$	15.2203	0.579008	0.289504	−	0.957177i	$-0.406510\pi$
$691$	15.2203	0.579008	0.289504	+	0.957177i	$0.406510\pi$
$692$	47.3901	1.80150
$693$	−141.876	−5.38941
$694$	8.13899	0.308952
$695$	1.58243	0.0600251
$696$	−139.939	−5.30438
$697$	9.47086	0.358734
$698$	−50.5789	−1.91444
$699$	−44.9164	−1.69889
$700$	88.2247	3.33458
$701$	9.59192	0.362282	0.181141	−	0.983457i	$-0.442021\pi$
$701$	9.59192	0.362282	0.181141	+	0.983457i	$0.442021\pi$
$702$	131.405	4.95955
$703$	57.2834	2.16048
$704$	55.0582	2.07508
$705$	−5.28072	−0.198883
$706$	47.9959	1.80635
$707$	2.69956	0.101527
$708$	−155.076	−5.82811
$709$	−41.4943	−1.55835	−0.779176	−	0.626806i	$-0.784362\pi$
$709$	−41.4943	−1.55835	−0.779176	+	0.626806i	$0.784362\pi$
$710$	2.50562	0.0940341
$711$	−52.0436	−1.95179
$712$	−20.6027	−0.772118
$713$	1.55990	0.0584188
$714$	−35.5353	−1.32988
$715$	−1.90338	−0.0711822
$716$	−106.808	−3.99159
$717$	75.6226	2.82418
$718$	21.1328	0.788668
$719$	−13.4634	−0.502101	−0.251051	−	0.967974i	$-0.580776\pi$
$719$	−13.4634	−0.502101	−0.251051	+	0.967974i	$0.580776\pi$
$720$	12.1687	0.453500
$721$	65.3302	2.43303
$722$	−131.859	−4.90727
$723$	−41.0022	−1.52489
$724$	42.0802	1.56390
$725$	−26.7441	−0.993252
$726$	−107.319	−3.98298
$727$	25.1887	0.934198	0.467099	−	0.884205i	$-0.345299\pi$
$727$	25.1887	0.934198	0.467099	+	0.884205i	$0.345299\pi$
$728$	−78.9645	−2.92662
$729$	104.863	3.88383
$730$	−0.271531	−0.0100498
$731$	12.0722	0.446505
$732$	248.341	9.17894
$733$	37.3749	1.38047	0.690237	−	0.723583i	$-0.257506\pi$
$733$	37.3749	1.38047	0.690237	+	0.723583i	$0.257506\pi$
$734$	−36.7111	−1.35503
$735$	2.71622	0.100189
$736$	−3.79739	−0.139974
$737$	−25.0419	−0.922431
$738$	183.108	6.74030
$739$	−44.6535	−1.64261	−0.821303	−	0.570493i	$-0.806752\pi$
$739$	−44.6535	−1.64261	−0.821303	+	0.570493i	$0.806752\pi$
$740$	−4.75715	−0.174876
$741$	79.0441	2.90376
$742$	63.4711	2.33010
$743$	−14.2477	−0.522697	−0.261349	−	0.965244i	$-0.584167\pi$
$743$	−14.2477	−0.522697	−0.261349	+	0.965244i	$0.584167\pi$
$744$	−132.524	−4.85855
$745$	1.56249	0.0572451
$746$	60.1715	2.20303
$747$	−129.725	−4.74637
$748$	−26.7458	−0.977923
$749$	−5.24810	−0.191762
$750$	12.2965	0.449005
$751$	2.48116	0.0905389	0.0452694	−	0.998975i	$-0.485585\pi$
$751$	2.48116	0.0905389	0.0452694	+	0.998975i	$0.485585\pi$
$752$	−119.696	−4.36487
$753$	−92.8135	−3.38231
$754$	40.1716	1.46296
$755$	−1.97949	−0.0720411
$756$	−311.139	−11.3160
$757$	−2.10294	−0.0764327	−0.0382163	−	0.999269i	$-0.512168\pi$
$757$	−2.10294	−0.0764327	−0.0382163	+	0.999269i	$0.512168\pi$
$758$	−16.9249	−0.614739
$759$	4.94741	0.179580
$760$	9.00344	0.326589
$761$	29.4533	1.06768	0.533840	−	0.845586i	$-0.320748\pi$
$761$	29.4533	1.06768	0.533840	+	0.845586i	$0.320748\pi$
$762$	−2.29630	−0.0831860
$763$	−46.5083	−1.68371
$764$	26.5951	0.962177
$765$	−1.29039	−0.0466540
$766$	4.56069	0.164784
$767$	26.5262	0.957807
$768$	−28.9187	−1.04351
$769$	−34.9026	−1.25862	−0.629309	−	0.777155i	$-0.716662\pi$
$769$	−34.9026	−1.25862	−0.629309	+	0.777155i	$0.716662\pi$
$770$	6.32812	0.228050
$771$	28.2350	1.01686
$772$	−50.6524	−1.82302
$773$	−9.82220	−0.353280	−0.176640	−	0.984276i	$-0.556523\pi$
$773$	−9.82220	−0.353280	−0.176640	+	0.984276i	$0.556523\pi$
$774$	233.401	8.38943
$775$	−25.3269	−0.909771
$776$	−100.565	−3.61008
$777$	82.7390	2.96824
$778$	46.9947	1.68484
$779$	70.0405	2.50946
$780$	−6.56429	−0.235039
$781$	−32.7999	−1.17367
$782$	0.908410	0.0324847
$783$	94.3176	3.37064
$784$	61.5676	2.19884
$785$	2.10676	0.0751936
$786$	123.294	4.39776
$787$	−0.186320	−0.00664158	−0.00332079	−	0.999994i	$-0.501057\pi$
$787$	−0.186320	−0.00664158	−0.00332079	+	0.999994i	$0.501057\pi$
$788$	−0.108571	−0.00386768
$789$	−80.0088	−2.84839
$790$	2.32132	0.0825887
$791$	16.5847	0.589684
$792$	−308.124	−10.9487
$793$	−42.4795	−1.50849
$794$	−102.160	−3.62552
$795$	3.14401	0.111507
$796$	−14.3605	−0.508994
$797$	4.07205	0.144240	0.0721198	−	0.997396i	$-0.477024\pi$
$797$	4.07205	0.144240	0.0721198	+	0.997396i	$0.477024\pi$
$798$	−262.797	−9.30290
$799$	12.6927	0.449037
$800$	61.6554	2.17985
$801$	21.8371	0.771574
$802$	−63.6022	−2.24587
$803$	3.55449	0.125435
$804$	−86.3637	−3.04581
$805$	−0.153071	−0.00539505
$806$	38.0428	1.34000
$807$	−12.2274	−0.430424
$808$	5.86288	0.206255
$809$	25.7700	0.906024	0.453012	−	0.891504i	$-0.350349\pi$
$809$	25.7700	0.906024	0.453012	+	0.891504i	$0.350349\pi$
$810$	−12.5568	−0.441200
$811$	53.7952	1.88901	0.944503	−	0.328504i	$-0.106544\pi$
$811$	53.7952	1.88901	0.944503	+	0.328504i	$0.106544\pi$
$812$	−95.1177	−3.33798
$813$	85.5856	3.00162
$814$	87.4405	3.06479
$815$	0.151607	0.00531055
$816$	−39.8984	−1.39672
$817$	89.2780	3.12344
$818$	77.7774	2.71942
$819$	83.6955	2.92456
$820$	−5.81657	−0.203124
$821$	−22.1644	−0.773542	−0.386771	−	0.922176i	$-0.626410\pi$
$821$	−22.1644	−0.773542	−0.386771	+	0.922176i	$0.626410\pi$
$822$	−6.56501	−0.228981
$823$	−36.3151	−1.26587	−0.632933	−	0.774206i	$-0.718149\pi$
$823$	−36.3151	−1.26587	−0.632933	+	0.774206i	$0.718149\pi$
$824$	141.884	4.94275
$825$	−80.3274	−2.79664
$826$	−88.1913	−3.06857
$827$	−12.2211	−0.424969	−0.212484	−	0.977164i	$-0.568155\pi$
$827$	−12.2211	−0.424969	−0.212484	+	0.977164i	$0.568155\pi$
$828$	12.5081	0.434688
$829$	23.2033	0.805883	0.402942	−	0.915226i	$-0.367988\pi$
$829$	23.2033	0.805883	0.402942	+	0.915226i	$0.367988\pi$
$830$	5.78614	0.200840
$831$	−11.9098	−0.413147
$832$	−32.4800	−1.12604
$833$	−6.52871	−0.226206
$834$	−100.312	−3.47353
$835$	1.51786	0.0525277
$836$	−197.795	−6.84088
$837$	89.3196	3.08734
$838$	−68.2531	−2.35777
$839$	−15.2314	−0.525847	−0.262923	−	0.964817i	$-0.584687\pi$
$839$	−15.2314	−0.525847	−0.262923	+	0.964817i	$0.584687\pi$
$840$	13.0044	0.448694
$841$	−0.166313	−0.00573491
$842$	90.9599	3.13468
$843$	−64.7808	−2.23117
$844$	31.1126	1.07094
$845$	−0.689507	−0.0237198
$846$	245.399	8.43700
$847$	−43.4660	−1.49351
$848$	71.2641	2.44722
$849$	3.56353	0.122300
$850$	−14.7492	−0.505892
$851$	−2.11510	−0.0725048
$852$	−113.119	−3.87540
$853$	−51.7745	−1.77273	−0.886363	−	0.462991i	$-0.846776\pi$
$853$	−51.7745	−1.77273	−0.886363	+	0.462991i	$0.846776\pi$
$854$	141.231	4.83282
$855$	−9.54287	−0.326359
$856$	−11.3978	−0.389568
$857$	−27.3382	−0.933856	−0.466928	−	0.884295i	$-0.654639\pi$
$857$	−27.3382	−0.933856	−0.466928	+	0.884295i	$0.654639\pi$
$858$	120.657	4.11917
$859$	−42.9870	−1.46670	−0.733348	−	0.679853i	$-0.762043\pi$
$859$	−42.9870	−1.46670	−0.733348	+	0.679853i	$0.762043\pi$
$860$	−7.41417	−0.252821
$861$	101.165	3.44770
$862$	29.3235	0.998762
$863$	−12.2192	−0.415947	−0.207973	−	0.978134i	$-0.566687\pi$
$863$	−12.2192	−0.415947	−0.207973	+	0.978134i	$0.566687\pi$
$864$	−217.438	−7.39738
$865$	1.33499	0.0453909
$866$	−31.3318	−1.06470
$867$	−52.7617	−1.79188
$868$	−90.0773	−3.05742
$869$	−30.3874	−1.03082
$870$	−6.61571	−0.224294
$871$	14.7728	0.500557
$872$	−101.006	−3.42050
$873$	106.590	3.60754
$874$	6.71802	0.227240
$875$	4.98030	0.168365
$876$	12.2586	0.414180
$877$	52.9115	1.78669	0.893346	−	0.449369i	$-0.148351\pi$
$877$	52.9115	1.78669	0.893346	+	0.449369i	$0.148351\pi$
$878$	100.396	3.38819
$879$	59.2302	1.99779
$880$	7.10509	0.239512
$881$	32.2056	1.08503	0.542517	−	0.840045i	$-0.317472\pi$
$881$	32.2056	1.08503	0.542517	+	0.840045i	$0.317472\pi$
$882$	−126.225	−4.25022
$883$	−25.0284	−0.842274	−0.421137	−	0.906997i	$-0.638369\pi$
$883$	−25.0284	−0.842274	−0.421137	+	0.906997i	$0.638369\pi$
$884$	15.7779	0.530669
$885$	−4.36851	−0.146846
$886$	75.0219	2.52041
$887$	−14.6914	−0.493290	−0.246645	−	0.969106i	$-0.579328\pi$
$887$	−14.6914	−0.493290	−0.246645	+	0.969106i	$0.579328\pi$
$888$	179.692	6.03006
$889$	−0.930040	−0.0311926
$890$	−0.974004	−0.0326487
$891$	164.375	5.50678
$892$	−80.8333	−2.70650
$893$	93.8674	3.14115
$894$	−99.0480	−3.31266
$895$	−3.00879	−0.100573
$896$	19.3673	0.647018
$897$	−2.91859	−0.0974488
$898$	−0.365261	−0.0121889
$899$	27.3058	0.910698
$900$	−203.085	−6.76951
$901$	−7.55694	−0.251758
$902$	106.914	3.55983
$903$	128.951	4.29123
$904$	36.0185	1.19796
$905$	1.18540	0.0394042
$906$	125.482	4.16887
$907$	50.5278	1.67775	0.838874	−	0.544326i	$-0.183215\pi$
$907$	50.5278	1.67775	0.838874	+	0.544326i	$0.183215\pi$
$908$	38.6406	1.28233
$909$	−6.21414	−0.206110
$910$	−3.73310	−0.123751
$911$	46.1538	1.52915	0.764573	−	0.644538i	$-0.222950\pi$
$911$	46.1538	1.52915	0.764573	+	0.644538i	$0.222950\pi$
$912$	−295.063	−9.77051
$913$	−75.7439	−2.50676
$914$	11.7346	0.388147
$915$	6.99580	0.231274
$916$	26.0655	0.861230
$917$	49.9364	1.64904
$918$	52.0153	1.71676
$919$	−42.1230	−1.38951	−0.694754	−	0.719247i	$-0.744487\pi$
$919$	−42.1230	−1.38951	−0.694754	+	0.719247i	$0.744487\pi$
$920$	−0.332439	−0.0109602
$921$	35.3920	1.16621
$922$	−7.10668	−0.234046
$923$	19.3494	0.636894
$924$	−285.691	−9.39855
$925$	34.3413	1.12914
$926$	48.1667	1.58286
$927$	−150.384	−4.93927
$928$	−66.4725	−2.18207
$929$	−9.19451	−0.301662	−0.150831	−	0.988560i	$-0.548195\pi$
$929$	−9.19451	−0.301662	−0.150831	+	0.988560i	$0.548195\pi$
$930$	−6.26514	−0.205442
$931$	−48.2822	−1.58238
$932$	−66.3048	−2.17189
$933$	−64.0875	−2.09813
$934$	4.73329	0.154878
$935$	−0.753433	−0.0246399
$936$	181.769	5.94131
$937$	16.5211	0.539719	0.269860	−	0.962900i	$-0.413023\pi$
$937$	16.5211	0.539719	0.269860	+	0.962900i	$0.413023\pi$
$938$	−49.1148	−1.60365
$939$	−15.8588	−0.517534
$940$	−7.79530	−0.254255
$941$	−5.26419	−0.171608	−0.0858038	−	0.996312i	$-0.527346\pi$
$941$	−5.26419	−0.171608	−0.0858038	+	0.996312i	$0.527346\pi$
$942$	−133.550	−4.35130
$943$	−2.58614	−0.0842163
$944$	−99.0194	−3.22281
$945$	−8.76483	−0.285120
$946$	136.279	4.43081
$947$	12.0656	0.392079	0.196039	−	0.980596i	$-0.437192\pi$
$947$	12.0656	0.392079	0.196039	+	0.980596i	$0.437192\pi$
$948$	−104.799	−3.40371
$949$	−2.09687	−0.0680674
$950$	−109.075	−3.53887
$951$	26.5922	0.862312
$952$	−31.2573	−1.01306
$953$	−17.7126	−0.573768	−0.286884	−	0.957965i	$-0.592619\pi$
$953$	−17.7126	−0.573768	−0.286884	+	0.957965i	$0.592619\pi$
$954$	−146.105	−4.73031
$955$	0.749188	0.0242432
$956$	111.633	3.61046
$957$	86.6035	2.79949
$958$	−54.5657	−1.76294
$959$	−2.65894	−0.0858618
$960$	5.34903	0.172639
$961$	−5.14120	−0.165845
$962$	−51.5831	−1.66310
$963$	12.0807	0.389294
$964$	−60.5266	−1.94943
$965$	−1.42689	−0.0459331
$966$	9.70337	0.312201
$967$	32.5963	1.04823	0.524113	−	0.851649i	$-0.324397\pi$
$967$	32.5963	1.04823	0.524113	+	0.851649i	$0.324397\pi$
$968$	−94.3991	−3.03410
$969$	31.2889	1.00514
$970$	−4.75428	−0.152651
$971$	−41.5923	−1.33476	−0.667380	−	0.744718i	$-0.732584\pi$
$971$	−41.5923	−1.33476	−0.667380	+	0.744718i	$0.732584\pi$
$972$	306.112	9.81856
$973$	−40.6283	−1.30248
$974$	−38.3866	−1.22998
$975$	47.3869	1.51760
$976$	158.571	5.07574
$977$	−21.1307	−0.676031	−0.338015	−	0.941141i	$-0.609756\pi$
$977$	−21.1307	−0.676031	−0.338015	+	0.941141i	$0.609756\pi$
$978$	−9.61054	−0.307311
$979$	12.7503	0.407500
$980$	4.00964	0.128083
$981$	107.058	3.41810
$982$	20.0055	0.638402
$983$	−32.8278	−1.04704	−0.523522	−	0.852012i	$-0.675382\pi$
$983$	−32.8278	−1.04704	−0.523522	+	0.852012i	$0.675382\pi$
$984$	219.709	7.00407
$985$	−0.00305846	−9.74507e−5 0
$986$	15.9015	0.506408
$987$	135.580	4.31557
$988$	116.684	3.71220
$989$	−3.29646	−0.104821
$990$	−14.5668	−0.462962
$991$	−36.6951	−1.16566	−0.582829	−	0.812595i	$-0.698054\pi$
$991$	−36.6951	−1.16566	−0.582829	+	0.812595i	$0.698054\pi$
$992$	−62.9501	−1.99867
$993$	38.2585	1.21410
$994$	−64.3306	−2.04044
$995$	−0.404537	−0.0128247
$996$	−261.223	−8.27716
$997$	18.4524	0.584392	0.292196	−	0.956358i	$-0.405614\pi$
$997$	18.4524	0.584392	0.292196	+	0.956358i	$0.405614\pi$
$998$	−46.6180	−1.47567
$999$	−121.110	−3.83176

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.16	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.63608 q^{2} +3.35251 q^{3} +4.94891 q^{4} +0.139412 q^{5} -8.83747 q^{6} -3.57933 q^{7} -7.77355 q^{8} +8.23930 q^{9} +O(q^{10})\)	\(q-2.63608 q^{2} +3.35251 q^{3} +4.94891 q^{4} +0.139412 q^{5} -8.83747 q^{6} -3.57933 q^{7} -7.77355 q^{8} +8.23930 q^{9} -0.367500 q^{10} +4.81078 q^{11} +16.5912 q^{12} -2.83799 q^{13} +9.43540 q^{14} +0.467378 q^{15} +10.5939 q^{16} -1.12339 q^{17} -21.7194 q^{18} -8.30787 q^{19} +0.689935 q^{20} -11.9997 q^{21} -12.6816 q^{22} +0.306756 q^{23} -26.0609 q^{24} -4.98056 q^{25} +7.48115 q^{26} +17.5648 q^{27} -17.7138 q^{28} +5.36970 q^{29} -1.23205 q^{30} +5.08515 q^{31} -12.3792 q^{32} +16.1282 q^{33} +2.96134 q^{34} -0.499000 q^{35} +40.7755 q^{36} -6.89507 q^{37} +21.9002 q^{38} -9.51436 q^{39} -1.08372 q^{40} -8.43061 q^{41} +31.6322 q^{42} -10.7462 q^{43} +23.8081 q^{44} +1.14865 q^{45} -0.808633 q^{46} -11.2986 q^{47} +35.5160 q^{48} +5.81162 q^{49} +13.1292 q^{50} -3.76617 q^{51} -14.0449 q^{52} +6.72691 q^{53} -46.3021 q^{54} +0.670679 q^{55} +27.8241 q^{56} -27.8522 q^{57} -14.1550 q^{58} -9.34685 q^{59} +2.31301 q^{60} +14.9682 q^{61} -13.4049 q^{62} -29.4912 q^{63} +11.4448 q^{64} -0.395648 q^{65} -42.5151 q^{66} -5.20538 q^{67} -5.55955 q^{68} +1.02840 q^{69} +1.31540 q^{70} -6.81801 q^{71} -64.0486 q^{72} +0.738860 q^{73} +18.1759 q^{74} -16.6974 q^{75} -41.1149 q^{76} -17.2194 q^{77} +25.0806 q^{78} -6.31651 q^{79} +1.47691 q^{80} +34.1681 q^{81} +22.2237 q^{82} -15.7446 q^{83} -59.3856 q^{84} -0.156614 q^{85} +28.3278 q^{86} +18.0020 q^{87} -37.3969 q^{88} +2.65035 q^{89} -3.02794 q^{90} +10.1581 q^{91} +1.51811 q^{92} +17.0480 q^{93} +29.7840 q^{94} -1.15821 q^{95} -41.5013 q^{96} +12.9368 q^{97} -15.3199 q^{98} +39.6375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 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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