LMFDB - Embedded newform 6011.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, 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("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$1$
Dimension:	$221$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51880 q^{2} +2.78779 q^{3} +4.34434 q^{4} +4.21455 q^{5} -7.02187 q^{6} -4.02027 q^{7} -5.90490 q^{8} +4.77177 q^{9} +O(q^{10})$	\(q-2.51880 q^{2} +2.78779 q^{3} +4.34434 q^{4} +4.21455 q^{5} -7.02187 q^{6} -4.02027 q^{7} -5.90490 q^{8} +4.77177 q^{9} -10.6156 q^{10} -2.68634 q^{11} +12.1111 q^{12} -2.76053 q^{13} +10.1263 q^{14} +11.7493 q^{15} +6.18458 q^{16} -1.33186 q^{17} -12.0191 q^{18} +1.94533 q^{19} +18.3094 q^{20} -11.2077 q^{21} +6.76634 q^{22} +3.31573 q^{23} -16.4616 q^{24} +12.7625 q^{25} +6.95321 q^{26} +4.93931 q^{27} -17.4654 q^{28} -4.33045 q^{29} -29.5941 q^{30} -5.45131 q^{31} -3.76789 q^{32} -7.48894 q^{33} +3.35469 q^{34} -16.9437 q^{35} +20.7302 q^{36} -9.83239 q^{37} -4.89988 q^{38} -7.69578 q^{39} -24.8865 q^{40} -4.52874 q^{41} +28.2299 q^{42} -7.21663 q^{43} -11.6704 q^{44} +20.1109 q^{45} -8.35164 q^{46} -4.04203 q^{47} +17.2413 q^{48} +9.16260 q^{49} -32.1460 q^{50} -3.71295 q^{51} -11.9927 q^{52} -12.8915 q^{53} -12.4411 q^{54} -11.3217 q^{55} +23.7393 q^{56} +5.42316 q^{57} +10.9075 q^{58} -9.97962 q^{59} +51.0428 q^{60} +2.89529 q^{61} +13.7307 q^{62} -19.1838 q^{63} -2.87861 q^{64} -11.6344 q^{65} +18.8631 q^{66} +11.4947 q^{67} -5.78606 q^{68} +9.24354 q^{69} +42.6776 q^{70} -8.94340 q^{71} -28.1768 q^{72} -3.92306 q^{73} +24.7658 q^{74} +35.5790 q^{75} +8.45115 q^{76} +10.7998 q^{77} +19.3841 q^{78} -2.96403 q^{79} +26.0652 q^{80} -0.545542 q^{81} +11.4070 q^{82} -6.78354 q^{83} -48.6899 q^{84} -5.61321 q^{85} +18.1772 q^{86} -12.0724 q^{87} +15.8626 q^{88} -14.7355 q^{89} -50.6552 q^{90} +11.0981 q^{91} +14.4046 q^{92} -15.1971 q^{93} +10.1811 q^{94} +8.19868 q^{95} -10.5041 q^{96} +6.62426 q^{97} -23.0787 q^{98} -12.8186 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) $ 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * 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 $

$2$	−2.51880	−1.78106	−0.890529	−	0.454926i	$-0.849666\pi$
$2$	−2.51880	−1.78106	−0.890529	+	0.454926i	$0.849666\pi$
$3$	2.78779	1.60953	0.804765	−	0.593593i	$-0.202291\pi$
$3$	2.78779	1.60953	0.804765	+	0.593593i	$0.202291\pi$
$4$	4.34434	2.17217
$5$	4.21455	1.88481	0.942403	−	0.334480i	$-0.108561\pi$
$5$	4.21455	1.88481	0.942403	+	0.334480i	$0.108561\pi$
$6$	−7.02187	−2.86667
$7$	−4.02027	−1.51952	−0.759760	−	0.650203i	$-0.774684\pi$
$7$	−4.02027	−1.51952	−0.759760	+	0.650203i	$0.774684\pi$
$8$	−5.90490	−2.08770
$9$	4.77177	1.59059
$10$	−10.6156	−3.35695
$11$	−2.68634	−0.809961	−0.404981	−	0.914325i	$-0.632722\pi$
$11$	−2.68634	−0.809961	−0.404981	+	0.914325i	$0.632722\pi$
$12$	12.1111	3.49617
$13$	−2.76053	−0.765633	−0.382817	−	0.923824i	$-0.625046\pi$
$13$	−2.76053	−0.765633	−0.382817	+	0.923824i	$0.625046\pi$
$14$	10.1263	2.70635
$15$	11.7493	3.03365
$16$	6.18458	1.54615
$17$	−1.33186	−0.323024	−0.161512	−	0.986871i	$-0.551637\pi$
$17$	−1.33186	−0.323024	−0.161512	+	0.986871i	$0.551637\pi$
$18$	−12.0191	−2.83293
$19$	1.94533	0.446288	0.223144	−	0.974785i	$-0.428368\pi$
$19$	1.94533	0.446288	0.223144	+	0.974785i	$0.428368\pi$
$20$	18.3094	4.09411
$21$	−11.2077	−2.44572
$22$	6.76634	1.44259
$23$	3.31573	0.691377	0.345688	−	0.938349i	$-0.387645\pi$
$23$	3.31573	0.691377	0.345688	+	0.938349i	$0.387645\pi$
$24$	−16.4616	−3.36022
$25$	12.7625	2.55249
$26$	6.95321	1.36364
$27$	4.93931	0.950571
$28$	−17.4654	−3.30065
$29$	−4.33045	−0.804144	−0.402072	−	0.915608i	$-0.631710\pi$
$29$	−4.33045	−0.804144	−0.402072	+	0.915608i	$0.631710\pi$
$30$	−29.5941	−5.40311
$31$	−5.45131	−0.979084	−0.489542	−	0.871980i	$-0.662836\pi$
$31$	−5.45131	−0.979084	−0.489542	+	0.871980i	$0.662836\pi$
$32$	−3.76789	−0.666075
$33$	−7.48894	−1.30366
$34$	3.35469	0.575325
$35$	−16.9437	−2.86400
$36$	20.7302	3.45503
$37$	−9.83239	−1.61643	−0.808217	−	0.588884i	$-0.799567\pi$
$37$	−9.83239	−1.61643	−0.808217	+	0.588884i	$0.799567\pi$
$38$	−4.89988	−0.794865
$39$	−7.69578	−1.23231
$40$	−24.8865	−3.93491
$41$	−4.52874	−0.707270	−0.353635	−	0.935383i	$-0.615055\pi$
$41$	−4.52874	−0.707270	−0.353635	+	0.935383i	$0.615055\pi$
$42$	28.2299	4.35596
$43$	−7.21663	−1.10053	−0.550263	−	0.834992i	$-0.685472\pi$
$43$	−7.21663	−1.10053	−0.550263	+	0.834992i	$0.685472\pi$
$44$	−11.6704	−1.75937
$45$	20.1109	2.99795
$46$	−8.35164	−1.23138
$47$	−4.04203	−0.589591	−0.294795	−	0.955560i	$-0.595252\pi$
$47$	−4.04203	−0.589591	−0.294795	+	0.955560i	$0.595252\pi$
$48$	17.2413	2.48857
$49$	9.16260	1.30894
$50$	−32.1460	−4.54614
$51$	−3.71295	−0.519917
$52$	−11.9927	−1.66308
$53$	−12.8915	−1.77079	−0.885393	−	0.464844i	$-0.846111\pi$
$53$	−12.8915	−1.77079	−0.885393	+	0.464844i	$0.846111\pi$
$54$	−12.4411	−1.69302
$55$	−11.3217	−1.52662
$56$	23.7393	3.17230
$57$	5.42316	0.718315
$58$	10.9075	1.43223
$59$	−9.97962	−1.29924	−0.649618	−	0.760261i	$-0.725071\pi$
$59$	−9.97962	−1.29924	−0.649618	+	0.760261i	$0.725071\pi$
$60$	51.0428	6.58960
$61$	2.89529	0.370704	0.185352	−	0.982672i	$-0.440657\pi$
$61$	2.89529	0.370704	0.185352	+	0.982672i	$0.440657\pi$
$62$	13.7307	1.74381
$63$	−19.1838	−2.41693
$64$	−2.87861	−0.359826
$65$	−11.6344	−1.44307
$66$	18.8631	2.32189
$67$	11.4947	1.40430	0.702149	−	0.712030i	$-0.252224\pi$
$67$	11.4947	1.40430	0.702149	+	0.712030i	$0.252224\pi$
$68$	−5.78606	−0.701663
$69$	9.24354	1.11279
$70$	42.6776	5.10095
$71$	−8.94340	−1.06139	−0.530693	−	0.847564i	$-0.678068\pi$
$71$	−8.94340	−1.06139	−0.530693	+	0.847564i	$0.678068\pi$
$72$	−28.1768	−3.32067
$73$	−3.92306	−0.459160	−0.229580	−	0.973290i	$-0.573735\pi$
$73$	−3.92306	−0.459160	−0.229580	+	0.973290i	$0.573735\pi$
$74$	24.7658	2.87896
$75$	35.5790	4.10831
$76$	8.45115	0.969413
$77$	10.7998	1.23075
$78$	19.3841	2.19482
$79$	−2.96403	−0.333480	−0.166740	−	0.986001i	$-0.553324\pi$
$79$	−2.96403	−0.333480	−0.166740	+	0.986001i	$0.553324\pi$
$80$	26.0652	2.91418
$81$	−0.545542	−0.0606158
$82$	11.4070	1.25969
$83$	−6.78354	−0.744590	−0.372295	−	0.928114i	$-0.621429\pi$
$83$	−6.78354	−0.744590	−0.372295	+	0.928114i	$0.621429\pi$
$84$	−48.6899	−5.31250
$85$	−5.61321	−0.608838
$86$	18.1772	1.96010
$87$	−12.0724	−1.29429
$88$	15.8626	1.69096
$89$	−14.7355	−1.56196	−0.780981	−	0.624555i	$-0.785280\pi$
$89$	−14.7355	−1.56196	−0.780981	+	0.624555i	$0.785280\pi$
$90$	−50.6552	−5.33952
$91$	11.0981	1.16340
$92$	14.4046	1.50179
$93$	−15.1971	−1.57587
$94$	10.1811	1.05010
$95$	8.19868	0.841167
$96$	−10.5041	−1.07207
$97$	6.62426	0.672592	0.336296	−	0.941756i	$-0.390826\pi$
$97$	6.62426	0.672592	0.336296	+	0.941756i	$0.390826\pi$
$98$	−23.0787	−2.33130
$99$	−12.8186	−1.28832
$100$	55.4444	5.54444
$101$	3.01020	0.299526	0.149763	−	0.988722i	$-0.452149\pi$
$101$	3.01020	0.299526	0.149763	+	0.988722i	$0.452149\pi$
$102$	9.35217	0.926003
$103$	15.8881	1.56550	0.782750	−	0.622336i	$-0.213816\pi$
$103$	15.8881	1.56550	0.782750	+	0.622336i	$0.213816\pi$
$104$	16.3007	1.59841
$105$	−47.2353	−4.60970
$106$	32.4711	3.15387
$107$	16.3541	1.58101	0.790507	−	0.612453i	$-0.209817\pi$
$107$	16.3541	1.58101	0.790507	+	0.612453i	$0.209817\pi$
$108$	21.4580	2.06480
$109$	−10.8277	−1.03711	−0.518554	−	0.855045i	$-0.673530\pi$
$109$	−10.8277	−1.03711	−0.518554	+	0.855045i	$0.673530\pi$
$110$	28.5171	2.71900
$111$	−27.4106	−2.60170
$112$	−24.8637	−2.34940
$113$	10.9976	1.03457	0.517284	−	0.855814i	$-0.326943\pi$
$113$	10.9976	1.03457	0.517284	+	0.855814i	$0.326943\pi$
$114$	−13.6598	−1.27936
$115$	13.9743	1.30311
$116$	−18.8129	−1.74674
$117$	−13.1726	−1.21781
$118$	25.1366	2.31401
$119$	5.35445	0.490842
$120$	−69.3784	−6.33335
$121$	−3.78359	−0.343962
$122$	−7.29264	−0.660245
$123$	−12.6252	−1.13837
$124$	−23.6823	−2.12674
$125$	32.7153	2.92614
$126$	48.3201	4.30470
$127$	−11.5528	−1.02515	−0.512574	−	0.858643i	$-0.671308\pi$
$127$	−11.5528	−1.02515	−0.512574	+	0.858643i	$0.671308\pi$
$128$	14.7864	1.30695
$129$	−20.1184	−1.77133
$130$	29.3047	2.57019
$131$	10.5472	0.921509	0.460754	−	0.887528i	$-0.347579\pi$
$131$	10.5472	0.921509	0.460754	+	0.887528i	$0.347579\pi$
$132$	−32.5345	−2.83176
$133$	−7.82074	−0.678144
$134$	−28.9528	−2.50114
$135$	20.8170	1.79164
$136$	7.86452	0.674377
$137$	−7.59697	−0.649053	−0.324526	−	0.945877i	$-0.605205\pi$
$137$	−7.59697	−0.649053	−0.324526	+	0.945877i	$0.605205\pi$
$138$	−23.2826	−1.98195
$139$	14.5353	1.23287	0.616433	−	0.787408i	$-0.288577\pi$
$139$	14.5353	1.23287	0.616433	+	0.787408i	$0.288577\pi$
$140$	−73.6089	−6.22109
$141$	−11.2683	−0.948965
$142$	22.5266	1.89039
$143$	7.41572	0.620134
$144$	29.5114	2.45928
$145$	−18.2509	−1.51565
$146$	9.88139	0.817790
$147$	25.5434	2.10678
$148$	−42.7152	−3.51117
$149$	1.61135	0.132007	0.0660036	−	0.997819i	$-0.478975\pi$
$149$	1.61135	0.132007	0.0660036	+	0.997819i	$0.478975\pi$
$150$	−89.6163	−7.31714
$151$	−21.7183	−1.76741	−0.883706	−	0.468042i	$-0.844960\pi$
$151$	−21.7183	−1.76741	−0.883706	+	0.468042i	$0.844960\pi$
$152$	−11.4870	−0.931716
$153$	−6.35534	−0.513799
$154$	−27.2025	−2.19204
$155$	−22.9748	−1.84538
$156$	−33.4330	−2.67678
$157$	5.62026	0.448546	0.224273	−	0.974526i	$-0.427999\pi$
$157$	5.62026	0.448546	0.224273	+	0.974526i	$0.427999\pi$
$158$	7.46580	0.593947
$159$	−35.9388	−2.85013
$160$	−15.8800	−1.25542
$161$	−13.3301	−1.05056
$162$	1.37411	0.107960
$163$	19.4348	1.52225	0.761125	−	0.648606i	$-0.224648\pi$
$163$	19.4348	1.52225	0.761125	+	0.648606i	$0.224648\pi$
$164$	−19.6744	−1.53631
$165$	−31.5626	−2.45714
$166$	17.0863	1.32616
$167$	19.1131	1.47902	0.739510	−	0.673146i	$-0.235057\pi$
$167$	19.1131	1.47902	0.739510	+	0.673146i	$0.235057\pi$
$168$	66.1802	5.10592
$169$	−5.37947	−0.413806
$170$	14.1385	1.08438
$171$	9.28264	0.709861
$172$	−31.3514	−2.39053
$173$	6.86180	0.521693	0.260846	−	0.965380i	$-0.415998\pi$
$173$	6.86180	0.521693	0.260846	+	0.965380i	$0.415998\pi$
$174$	30.4078	2.30521
$175$	−51.3086	−3.87856
$176$	−16.6139	−1.25232
$177$	−27.8211	−2.09116
$178$	37.1158	2.78194
$179$	17.7771	1.32872	0.664360	−	0.747413i	$-0.268704\pi$
$179$	17.7771	1.32872	0.664360	+	0.747413i	$0.268704\pi$
$180$	87.3683	6.51205
$181$	7.49699	0.557247	0.278623	−	0.960400i	$-0.410122\pi$
$181$	7.49699	0.557247	0.278623	+	0.960400i	$0.410122\pi$
$182$	−27.9538	−2.07208
$183$	8.07146	0.596659
$184$	−19.5790	−1.44339
$185$	−41.4391	−3.04666
$186$	38.2784	2.80671
$187$	3.57783	0.261637
$188$	−17.5599	−1.28069
$189$	−19.8574	−1.44441
$190$	−20.6508	−1.49817
$191$	15.2893	1.10629	0.553147	−	0.833084i	$-0.313427\pi$
$191$	15.2893	1.10629	0.553147	+	0.833084i	$0.313427\pi$
$192$	−8.02496	−0.579151
$193$	11.0256	0.793638	0.396819	−	0.917897i	$-0.370114\pi$
$193$	11.0256	0.793638	0.396819	+	0.917897i	$0.370114\pi$
$194$	−16.6852	−1.19793
$195$	−32.4343	−2.32267
$196$	39.8054	2.84324
$197$	−5.52038	−0.393311	−0.196655	−	0.980473i	$-0.563008\pi$
$197$	−5.52038	−0.393311	−0.196655	+	0.980473i	$0.563008\pi$
$198$	32.2874	2.29457
$199$	−14.5629	−1.03234	−0.516169	−	0.856487i	$-0.672642\pi$
$199$	−14.5629	−1.03234	−0.516169	+	0.856487i	$0.672642\pi$
$200$	−75.3611	−5.32883
$201$	32.0447	2.26026
$202$	−7.58207	−0.533473
$203$	17.4096	1.22191
$204$	−16.1303	−1.12935
$205$	−19.0866	−1.33307
$206$	−40.0189	−2.78825
$207$	15.8219	1.09970
$208$	−17.0727	−1.18378
$209$	−5.22580	−0.361476
$210$	118.976	8.21014
$211$	15.9504	1.09807	0.549036	−	0.835799i	$-0.314995\pi$
$211$	15.9504	1.09807	0.549036	+	0.835799i	$0.314995\pi$
$212$	−56.0051	−3.84644
$213$	−24.9323	−1.70833
$214$	−41.1927	−2.81588
$215$	−30.4149	−2.07428
$216$	−29.1662	−1.98451
$217$	21.9158	1.48774
$218$	27.2729	1.84715
$219$	−10.9367	−0.739031
$220$	−49.1853	−3.31607
$221$	3.67665	0.247318
$222$	69.0418	4.63378
$223$	−3.59800	−0.240940	−0.120470	−	0.992717i	$-0.538440\pi$
$223$	−3.59800	−0.240940	−0.120470	+	0.992717i	$0.538440\pi$
$224$	15.1480	1.01212
$225$	60.8995	4.05996
$226$	−27.7008	−1.84263
$227$	−1.78839	−0.118699	−0.0593497	−	0.998237i	$-0.518903\pi$
$227$	−1.78839	−0.118699	−0.0593497	+	0.998237i	$0.518903\pi$
$228$	23.5600	1.56030
$229$	4.84097	0.319900	0.159950	−	0.987125i	$-0.448867\pi$
$229$	4.84097	0.319900	0.159950	+	0.987125i	$0.448867\pi$
$230$	−35.1984	−2.32092
$231$	30.1076	1.98094
$232$	25.5709	1.67881
$233$	2.30675	0.151120	0.0755600	−	0.997141i	$-0.475926\pi$
$233$	2.30675	0.151120	0.0755600	+	0.997141i	$0.475926\pi$
$234$	33.1791	2.16899
$235$	−17.0354	−1.11126
$236$	−43.3548	−2.82216
$237$	−8.26310	−0.536746
$238$	−13.4868	−0.874218
$239$	−4.77072	−0.308592	−0.154296	−	0.988025i	$-0.549311\pi$
$239$	−4.77072	−0.308592	−0.154296	+	0.988025i	$0.549311\pi$
$240$	72.6644	4.69047
$241$	−19.1927	−1.23631	−0.618154	−	0.786057i	$-0.712119\pi$
$241$	−19.1927	−1.23631	−0.618154	+	0.786057i	$0.712119\pi$
$242$	9.53008	0.612617
$243$	−16.3388	−1.04813
$244$	12.5781	0.805231
$245$	38.6163	2.46710
$246$	31.8002	2.02751
$247$	−5.37013	−0.341693
$248$	32.1895	2.04403
$249$	−18.9111	−1.19844
$250$	−82.4031	−5.21163
$251$	5.74818	0.362822	0.181411	−	0.983407i	$-0.441934\pi$
$251$	5.74818	0.362822	0.181411	+	0.983407i	$0.441934\pi$
$252$	−83.3409	−5.24998
$253$	−8.90716	−0.559988
$254$	29.0992	1.82585
$255$	−15.6484	−0.979943
$256$	−31.4868	−1.96792
$257$	−22.3663	−1.39517	−0.697586	−	0.716501i	$-0.745743\pi$
$257$	−22.3663	−1.39517	−0.697586	+	0.716501i	$0.745743\pi$
$258$	50.6742	3.15484
$259$	39.5289	2.45621
$260$	−50.5437	−3.13459
$261$	−20.6639	−1.27906
$262$	−26.5661	−1.64126
$263$	−30.0858	−1.85517	−0.927585	−	0.373612i	$-0.878119\pi$
$263$	−30.0858	−1.85517	−0.927585	+	0.373612i	$0.878119\pi$
$264$	44.2215	2.72164
$265$	−54.3320	−3.33759
$266$	19.6989	1.20781
$267$	−41.0795	−2.51402
$268$	49.9368	3.05037
$269$	−26.2282	−1.59916	−0.799579	−	0.600560i	$-0.794944\pi$
$269$	−26.2282	−1.59916	−0.799579	+	0.600560i	$0.794944\pi$
$270$	−52.4338	−3.19102
$271$	−8.59707	−0.522235	−0.261117	−	0.965307i	$-0.584091\pi$
$271$	−8.59707	−0.522235	−0.261117	+	0.965307i	$0.584091\pi$
$272$	−8.23701	−0.499442
$273$	30.9391	1.87252
$274$	19.1352	1.15600
$275$	−34.2843	−2.06742
$276$	40.1571	2.41717
$277$	10.0264	0.602426	0.301213	−	0.953557i	$-0.402608\pi$
$277$	10.0264	0.602426	0.301213	+	0.953557i	$0.402608\pi$
$278$	−36.6114	−2.19580
$279$	−26.0124	−1.55732
$280$	100.051	5.97917
$281$	5.16993	0.308412	0.154206	−	0.988039i	$-0.450718\pi$
$281$	5.16993	0.308412	0.154206	+	0.988039i	$0.450718\pi$
$282$	28.3826	1.69016
$283$	21.2141	1.26105	0.630523	−	0.776171i	$-0.282841\pi$
$283$	21.2141	1.26105	0.630523	+	0.776171i	$0.282841\pi$
$284$	−38.8531	−2.30551
$285$	22.8562	1.35388
$286$	−18.6787	−1.10449
$287$	18.2068	1.07471
$288$	−17.9795	−1.05945
$289$	−15.2261	−0.895655
$290$	45.9703	2.69947
$291$	18.4670	1.08256
$292$	−17.0431	−0.997372
$293$	10.2117	0.596574	0.298287	−	0.954476i	$-0.403585\pi$
$293$	10.2117	0.596574	0.298287	+	0.954476i	$0.403585\pi$
$294$	−64.3386	−3.75231
$295$	−42.0596	−2.44881
$296$	58.0593	3.37463
$297$	−13.2687	−0.769926
$298$	−4.05867	−0.235112
$299$	−9.15316	−0.529341
$300$	154.567	8.92395
$301$	29.0128	1.67227
$302$	54.7041	3.14787
$303$	8.39179	0.482096
$304$	12.0310	0.690027
$305$	12.2024	0.698705
$306$	16.0078	0.915105
$307$	19.5879	1.11794	0.558971	−	0.829187i	$-0.311196\pi$
$307$	19.5879	1.11794	0.558971	+	0.829187i	$0.311196\pi$
$308$	46.9180	2.67340
$309$	44.2927	2.51972
$310$	57.8689	3.28673
$311$	20.7507	1.17666	0.588331	−	0.808620i	$-0.299785\pi$
$311$	20.7507	1.17666	0.588331	+	0.808620i	$0.299785\pi$
$312$	45.4428	2.57269
$313$	−2.06811	−0.116896	−0.0584482	−	0.998290i	$-0.518615\pi$
$313$	−2.06811	−0.116896	−0.0584482	+	0.998290i	$0.518615\pi$
$314$	−14.1563	−0.798886
$315$	−80.8512	−4.55545
$316$	−12.8768	−0.724374
$317$	28.8084	1.61804	0.809020	−	0.587781i	$-0.199998\pi$
$317$	28.8084	1.61804	0.809020	+	0.587781i	$0.199998\pi$
$318$	90.5226	5.07625
$319$	11.6330	0.651325
$320$	−12.1321	−0.678202
$321$	45.5919	2.54469
$322$	33.5759	1.87111
$323$	−2.59091	−0.144162
$324$	−2.37002	−0.131668
$325$	−35.2312	−1.95427
$326$	−48.9522	−2.71121
$327$	−30.1854	−1.66926
$328$	26.7418	1.47657
$329$	16.2501	0.895896
$330$	79.4996	4.37631
$331$	26.5256	1.45798	0.728991	−	0.684524i	$-0.239990\pi$
$331$	26.5256	1.45798	0.728991	+	0.684524i	$0.239990\pi$
$332$	−29.4700	−1.61737
$333$	−46.9179	−2.57108
$334$	−48.1421	−2.63422
$335$	48.4449	2.64683
$336$	−69.3148	−3.78143
$337$	7.37971	0.401998	0.200999	−	0.979591i	$-0.435581\pi$
$337$	7.37971	0.401998	0.200999	+	0.979591i	$0.435581\pi$
$338$	13.5498	0.737012
$339$	30.6590	1.66517
$340$	−24.3857	−1.32250
$341$	14.6441	0.793021
$342$	−23.3811	−1.26430
$343$	−8.69426	−0.469446
$344$	42.6135	2.29756
$345$	38.9574	2.09740
$346$	−17.2835	−0.929165
$347$	−1.54183	−0.0827700	−0.0413850	−	0.999143i	$-0.513177\pi$
$347$	−1.54183	−0.0827700	−0.0413850	+	0.999143i	$0.513177\pi$
$348$	−52.4464	−2.81142
$349$	17.0156	0.910823	0.455411	−	0.890281i	$-0.349492\pi$
$349$	17.0156	0.910823	0.455411	+	0.890281i	$0.349492\pi$
$350$	129.236	6.90795
$351$	−13.6351	−0.727789
$352$	10.1218	0.539495
$353$	19.8899	1.05863	0.529317	−	0.848424i	$-0.322448\pi$
$353$	19.8899	1.05863	0.529317	+	0.848424i	$0.322448\pi$
$354$	70.0756	3.72448
$355$	−37.6924	−2.00051
$356$	−64.0160	−3.39284
$357$	14.9271	0.790025
$358$	−44.7768	−2.36653
$359$	−10.5869	−0.558755	−0.279378	−	0.960181i	$-0.590128\pi$
$359$	−10.5869	−0.558755	−0.279378	+	0.960181i	$0.590128\pi$
$360$	−118.753	−6.25882
$361$	−15.2157	−0.800827
$362$	−18.8834	−0.992489
$363$	−10.5478	−0.553618
$364$	48.2138	2.52709
$365$	−16.5339	−0.865426
$366$	−20.3304	−1.06268
$367$	−10.7215	−0.559656	−0.279828	−	0.960050i	$-0.590277\pi$
$367$	−10.7215	−0.559656	−0.279828	+	0.960050i	$0.590277\pi$
$368$	20.5064	1.06897
$369$	−21.6101	−1.12498
$370$	104.377	5.42629
$371$	51.8274	2.69075
$372$	−66.0213	−3.42305
$373$	−19.4689	−1.00806	−0.504031	−	0.863686i	$-0.668150\pi$
$373$	−19.4689	−1.00806	−0.504031	+	0.863686i	$0.668150\pi$
$374$	−9.01184	−0.465991
$375$	91.2033	4.70972
$376$	23.8678	1.23089
$377$	11.9543	0.615679
$378$	50.0167	2.57258
$379$	−29.5183	−1.51626	−0.758128	−	0.652106i	$-0.773886\pi$
$379$	−29.5183	−1.51626	−0.758128	+	0.652106i	$0.773886\pi$
$380$	35.6178	1.82716
$381$	−32.2069	−1.65001
$382$	−38.5106	−1.97037
$383$	−6.21629	−0.317637	−0.158819	−	0.987308i	$-0.550769\pi$
$383$	−6.21629	−0.317637	−0.158819	+	0.987308i	$0.550769\pi$
$384$	41.2214	2.10357
$385$	45.5164	2.31973
$386$	−27.7712	−1.41352
$387$	−34.4361	−1.75048
$388$	28.7780	1.46098
$389$	8.57772	0.434908	0.217454	−	0.976071i	$-0.430225\pi$
$389$	8.57772	0.434908	0.217454	+	0.976071i	$0.430225\pi$
$390$	81.6953	4.13680
$391$	−4.41609	−0.223331
$392$	−54.1043	−2.73268
$393$	29.4032	1.48320
$394$	13.9047	0.700509
$395$	−12.4921	−0.628545
$396$	−55.6882	−2.79844
$397$	18.6324	0.935131	0.467566	−	0.883958i	$-0.345131\pi$
$397$	18.6324	0.935131	0.467566	+	0.883958i	$0.345131\pi$
$398$	36.6810	1.83865
$399$	−21.8026	−1.09149
$400$	78.9304	3.94652
$401$	25.6871	1.28275	0.641376	−	0.767227i	$-0.278364\pi$
$401$	25.6871	1.28275	0.641376	+	0.767227i	$0.278364\pi$
$402$	−80.7142	−4.02566
$403$	15.0485	0.749620
$404$	13.0773	0.650620
$405$	−2.29922	−0.114249
$406$	−43.8512	−2.17630
$407$	26.4131	1.30925
$408$	21.9246	1.08543
$409$	−38.8298	−1.92001	−0.960005	−	0.279983i	$-0.909671\pi$
$409$	−38.8298	−1.92001	−0.960005	+	0.279983i	$0.909671\pi$
$410$	48.0753	2.37427
$411$	−21.1787	−1.04467
$412$	69.0232	3.40053
$413$	40.1208	1.97421
$414$	−39.8521	−1.95862
$415$	−28.5896	−1.40341
$416$	10.4014	0.509970
$417$	40.5213	1.98433
$418$	13.1627	0.643810
$419$	18.6504	0.911132	0.455566	−	0.890202i	$-0.349437\pi$
$419$	18.6504	0.911132	0.455566	+	0.890202i	$0.349437\pi$
$420$	−205.206	−10.0130
$421$	16.7184	0.814805	0.407402	−	0.913249i	$-0.366435\pi$
$421$	16.7184	0.814805	0.407402	+	0.913249i	$0.366435\pi$
$422$	−40.1758	−1.95573
$423$	−19.2876	−0.937797
$424$	76.1232	3.69687
$425$	−16.9978	−0.824517
$426$	62.7994	3.04264
$427$	−11.6399	−0.563292
$428$	71.0478	3.43423
$429$	20.6735	0.998124
$430$	76.6088	3.69441
$431$	2.37883	0.114584	0.0572920	−	0.998357i	$-0.481753\pi$
$431$	2.37883	0.114584	0.0572920	+	0.998357i	$0.481753\pi$
$432$	30.5476	1.46972
$433$	−11.1366	−0.535193	−0.267596	−	0.963531i	$-0.586229\pi$
$433$	−11.1366	−0.535193	−0.267596	+	0.963531i	$0.586229\pi$
$434$	−55.2013	−2.64975
$435$	−50.8796	−2.43949
$436$	−47.0393	−2.25277
$437$	6.45017	0.308553
$438$	27.5472	1.31626
$439$	−40.0733	−1.91259	−0.956296	−	0.292400i	$-0.905546\pi$
$439$	−40.0733	−1.91259	−0.956296	+	0.292400i	$0.905546\pi$
$440$	66.8536	3.18712
$441$	43.7218	2.08199
$442$	−9.26073	−0.440488
$443$	−18.7771	−0.892125	−0.446063	−	0.895002i	$-0.647174\pi$
$443$	−18.7771	−0.892125	−0.446063	+	0.895002i	$0.647174\pi$
$444$	−119.081	−5.65133
$445$	−62.1036	−2.94399
$446$	9.06262	0.429128
$447$	4.49211	0.212470
$448$	11.5728	0.546763
$449$	−9.49073	−0.447895	−0.223948	−	0.974601i	$-0.571894\pi$
$449$	−9.49073	−0.447895	−0.223948	+	0.974601i	$0.571894\pi$
$450$	−153.393	−7.23103
$451$	12.1657	0.572862
$452$	47.7773	2.24726
$453$	−60.5461	−2.84471
$454$	4.50458	0.211411
$455$	46.7735	2.19277
$456$	−32.0232	−1.49962
$457$	−5.31625	−0.248684	−0.124342	−	0.992239i	$-0.539682\pi$
$457$	−5.31625	−0.248684	−0.124342	+	0.992239i	$0.539682\pi$
$458$	−12.1934	−0.569761
$459$	−6.57849	−0.307057
$460$	60.7091	2.83057
$461$	8.42228	0.392265	0.196132	−	0.980577i	$-0.437162\pi$
$461$	8.42228	0.392265	0.196132	+	0.980577i	$0.437162\pi$
$462$	−75.8349	−3.52816
$463$	14.8125	0.688397	0.344198	−	0.938897i	$-0.388151\pi$
$463$	14.8125	0.688397	0.344198	+	0.938897i	$0.388151\pi$
$464$	−26.7820	−1.24332
$465$	−64.0490	−2.97020
$466$	−5.81022	−0.269153
$467$	26.8661	1.24321	0.621607	−	0.783329i	$-0.286480\pi$
$467$	26.8661	1.24321	0.621607	+	0.783329i	$0.286480\pi$
$468$	−57.2262	−2.64528
$469$	−46.2118	−2.13386
$470$	42.9086	1.97923
$471$	15.6681	0.721948
$472$	58.9287	2.71241
$473$	19.3863	0.891383
$474$	20.8131	0.955976
$475$	24.8271	1.13915
$476$	23.2615	1.06619
$477$	−61.5153	−2.81659
$478$	12.0165	0.549621
$479$	23.5220	1.07475	0.537373	−	0.843344i	$-0.319417\pi$
$479$	23.5220	1.07475	0.537373	+	0.843344i	$0.319417\pi$
$480$	−44.2700	−2.02064
$481$	27.1426	1.23760
$482$	48.3424	2.20194
$483$	−37.1616	−1.69091
$484$	−16.4372	−0.747144
$485$	27.9183	1.26770
$486$	41.1541	1.86679
$487$	−16.0983	−0.729482	−0.364741	−	0.931109i	$-0.618842\pi$
$487$	−16.0983	−0.729482	−0.364741	+	0.931109i	$0.618842\pi$
$488$	−17.0964	−0.773918
$489$	54.1801	2.45011
$490$	−97.2665	−4.39405
$491$	2.08677	0.0941748	0.0470874	−	0.998891i	$-0.485006\pi$
$491$	2.08677	0.0941748	0.0470874	+	0.998891i	$0.485006\pi$
$492$	−54.8480	−2.47274
$493$	5.76756	0.259758
$494$	13.5263	0.608576
$495$	−54.0246	−2.42822
$496$	−33.7141	−1.51381
$497$	35.9549	1.61280
$498$	47.6331	2.13449
$499$	−29.4306	−1.31749	−0.658747	−	0.752364i	$-0.728913\pi$
$499$	−29.4306	−1.31749	−0.658747	+	0.752364i	$0.728913\pi$
$500$	142.126	6.35608
$501$	53.2834	2.38053
$502$	−14.4785	−0.646207
$503$	−31.4247	−1.40116	−0.700579	−	0.713574i	$-0.747075\pi$
$503$	−31.4247	−1.40116	−0.700579	+	0.713574i	$0.747075\pi$
$504$	113.279	5.04583
$505$	12.6866	0.564548
$506$	22.4353	0.997372
$507$	−14.9968	−0.666033
$508$	−50.1894	−2.22679
$509$	−26.2781	−1.16476	−0.582378	−	0.812918i	$-0.697878\pi$
$509$	−26.2781	−1.16476	−0.582378	+	0.812918i	$0.697878\pi$
$510$	39.4152	1.74534
$511$	15.7718	0.697702
$512$	49.7359	2.19804
$513$	9.60857	0.424229
$514$	56.3362	2.48488
$515$	66.9612	2.95066
$516$	−87.4012	−3.84762
$517$	10.8583	0.477546
$518$	−99.5652	−4.37465
$519$	19.1292	0.839681
$520$	68.7000	3.01270
$521$	−30.7579	−1.34753	−0.673764	−	0.738946i	$-0.735324\pi$
$521$	−30.7579	−1.34753	−0.673764	+	0.738946i	$0.735324\pi$
$522$	52.0481	2.27808
$523$	−15.5478	−0.679856	−0.339928	−	0.940451i	$-0.610403\pi$
$523$	−15.5478	−0.679856	−0.339928	+	0.940451i	$0.610403\pi$
$524$	45.8204	2.00167
$525$	−143.037	−6.24267
$526$	75.7800	3.30417
$527$	7.26040	0.316268
$528$	−46.3160	−2.01564
$529$	−12.0060	−0.521998
$530$	136.851	5.94443
$531$	−47.6204	−2.06655
$532$	−33.9759	−1.47304
$533$	12.5017	0.541510
$534$	103.471	4.47762
$535$	68.9253	2.97990
$536$	−67.8750	−2.93175
$537$	49.5587	2.13861
$538$	66.0634	2.84819
$539$	−24.6139	−1.06019
$540$	90.4360	3.89175
$541$	−32.9695	−1.41747	−0.708736	−	0.705474i	$-0.750734\pi$
$541$	−32.9695	−1.41747	−0.708736	+	0.705474i	$0.750734\pi$
$542$	21.6543	0.930130
$543$	20.9000	0.896906
$544$	5.01831	0.215158
$545$	−45.6340	−1.95475
$546$	−77.9294	−3.33507
$547$	−37.6596	−1.61021	−0.805104	−	0.593133i	$-0.797891\pi$
$547$	−37.6596	−1.61021	−0.805104	+	0.593133i	$0.797891\pi$
$548$	−33.0038	−1.40985
$549$	13.8156	0.589637
$550$	86.3551	3.68219
$551$	−8.42413	−0.358880
$552$	−54.5822	−2.32317
$553$	11.9162	0.506730
$554$	−25.2544	−1.07296
$555$	−115.524	−4.90370
$556$	63.1461	2.67799
$557$	−9.05867	−0.383828	−0.191914	−	0.981412i	$-0.561469\pi$
$557$	−9.05867	−0.383828	−0.191914	+	0.981412i	$0.561469\pi$
$558$	65.5199	2.77368
$559$	19.9217	0.842599
$560$	−104.789	−4.42816
$561$	9.97425	0.421113
$562$	−13.0220	−0.549300
$563$	−45.3976	−1.91328	−0.956640	−	0.291273i	$-0.905921\pi$
$563$	−45.3976	−1.91328	−0.956640	+	0.291273i	$0.905921\pi$
$564$	−48.9534	−2.06131
$565$	46.3500	1.94996
$566$	−53.4339	−2.24600
$567$	2.19323	0.0921069
$568$	52.8099	2.21586
$569$	−15.4543	−0.647877	−0.323939	−	0.946078i	$-0.605007\pi$
$569$	−15.4543	−0.647877	−0.323939	+	0.946078i	$0.605007\pi$
$570$	−57.5701	−2.41135
$571$	7.52483	0.314904	0.157452	−	0.987527i	$-0.449672\pi$
$571$	7.52483	0.314904	0.157452	+	0.987527i	$0.449672\pi$
$572$	32.2164	1.34703
$573$	42.6233	1.78061
$574$	−45.8592	−1.91412
$575$	42.3168	1.76473
$576$	−13.7361	−0.572336
$577$	−27.4861	−1.14426	−0.572130	−	0.820163i	$-0.693883\pi$
$577$	−27.4861	−1.14426	−0.572130	+	0.820163i	$0.693883\pi$
$578$	38.3516	1.59521
$579$	30.7370	1.27738
$580$	−79.2880	−3.29226
$581$	27.2717	1.13142
$582$	−46.5147	−1.92810
$583$	34.6310	1.43427
$584$	23.1653	0.958587
$585$	−55.5167	−2.29533
$586$	−25.7212	−1.06253
$587$	9.99659	0.412604	0.206302	−	0.978488i	$-0.433857\pi$
$587$	9.99659	0.412604	0.206302	+	0.978488i	$0.433857\pi$
$588$	110.969	4.57629
$589$	−10.6046	−0.436954
$590$	105.940	4.36146
$591$	−15.3897	−0.633046
$592$	−60.8092	−2.49924
$593$	4.32461	0.177591	0.0887953	−	0.996050i	$-0.471698\pi$
$593$	4.32461	0.177591	0.0887953	+	0.996050i	$0.471698\pi$
$594$	33.4211	1.37128
$595$	22.5666	0.925142
$596$	7.00026	0.286742
$597$	−40.5983	−1.66158
$598$	23.0550	0.942787
$599$	−0.587081	−0.0239875	−0.0119937	−	0.999928i	$-0.503818\pi$
$599$	−0.587081	−0.0239875	−0.0119937	+	0.999928i	$0.503818\pi$
$600$	−210.091	−8.57692
$601$	−16.7698	−0.684054	−0.342027	−	0.939690i	$-0.611113\pi$
$601$	−16.7698	−0.684054	−0.342027	+	0.939690i	$0.611113\pi$
$602$	−73.0774	−2.97841
$603$	54.8499	2.23366
$604$	−94.3517	−3.83912
$605$	−15.9461	−0.648302
$606$	−21.1372	−0.858641
$607$	−28.1552	−1.14278	−0.571391	−	0.820678i	$-0.693596\pi$
$607$	−28.1552	−1.14278	−0.571391	+	0.820678i	$0.693596\pi$
$608$	−7.32978	−0.297262
$609$	48.5342	1.96671
$610$	−30.7352	−1.24443
$611$	11.1581	0.451410
$612$	−27.6097	−1.11606
$613$	21.9282	0.885674	0.442837	−	0.896602i	$-0.353972\pi$
$613$	21.9282	0.885674	0.442837	+	0.896602i	$0.353972\pi$
$614$	−49.3380	−1.99112
$615$	−53.2094	−2.14561
$616$	−63.7719	−2.56944
$617$	−21.6364	−0.871049	−0.435524	−	0.900177i	$-0.643437\pi$
$617$	−21.6364	−0.871049	−0.435524	+	0.900177i	$0.643437\pi$
$618$	−111.564	−4.48777
$619$	−11.0305	−0.443355	−0.221678	−	0.975120i	$-0.571153\pi$
$619$	−11.0305	−0.443355	−0.221678	+	0.975120i	$0.571153\pi$
$620$	−99.8104	−4.00848
$621$	16.3774	0.657203
$622$	−52.2667	−2.09570
$623$	59.2408	2.37343
$624$	−47.5951	−1.90533
$625$	74.0680	2.96272
$626$	5.20915	0.208199
$627$	−14.5684	−0.581807
$628$	24.4163	0.974317
$629$	13.0954	0.522148
$630$	203.648	8.11352
$631$	−16.4022	−0.652959	−0.326480	−	0.945204i	$-0.605862\pi$
$631$	−16.4022	−0.652959	−0.326480	+	0.945204i	$0.605862\pi$
$632$	17.5023	0.696206
$633$	44.4664	1.76738
$634$	−72.5625	−2.88182
$635$	−48.6900	−1.93221
$636$	−156.130	−6.19097
$637$	−25.2936	−1.00217
$638$	−29.3013	−1.16005
$639$	−42.6758	−1.68823
$640$	62.3181	2.46334
$641$	−25.7071	−1.01537	−0.507684	−	0.861543i	$-0.669498\pi$
$641$	−25.7071	−1.01537	−0.507684	+	0.861543i	$0.669498\pi$
$642$	−114.837	−4.53224
$643$	17.9814	0.709119	0.354560	−	0.935033i	$-0.384631\pi$
$643$	17.9814	0.709119	0.354560	+	0.935033i	$0.384631\pi$
$644$	−57.9105	−2.28200
$645$	−84.7902	−3.33861
$646$	6.52597	0.256761
$647$	−4.48421	−0.176292	−0.0881462	−	0.996108i	$-0.528094\pi$
$647$	−4.48421	−0.176292	−0.0881462	+	0.996108i	$0.528094\pi$
$648$	3.22137	0.126547
$649$	26.8086	1.05233
$650$	88.7401	3.48067
$651$	61.0965	2.39456
$652$	84.4312	3.30658
$653$	−7.33819	−0.287166	−0.143583	−	0.989638i	$-0.545862\pi$
$653$	−7.33819	−0.287166	−0.143583	+	0.989638i	$0.545862\pi$
$654$	76.0310	2.97305
$655$	44.4515	1.73687
$656$	−28.0084	−1.09354
$657$	−18.7199	−0.730334
$658$	−40.9306	−1.59564
$659$	49.8291	1.94107	0.970534	−	0.240964i	$-0.0774637\pi$
$659$	49.8291	1.94107	0.970534	+	0.240964i	$0.0774637\pi$
$660$	−137.118	−5.33732
$661$	−33.3099	−1.29560	−0.647802	−	0.761808i	$-0.724312\pi$
$661$	−33.3099	−1.29560	−0.647802	+	0.761808i	$0.724312\pi$
$662$	−66.8127	−2.59675
$663$	10.2497	0.398066
$664$	40.0561	1.55448
$665$	−32.9609	−1.27817
$666$	118.177	4.57925
$667$	−14.3586	−0.555966
$668$	83.0339	3.21268
$669$	−10.0305	−0.387800
$670$	−122.023	−4.71416
$671$	−7.77773	−0.300256
$672$	42.2293	1.62903
$673$	−3.55980	−0.137220	−0.0686102	−	0.997644i	$-0.521856\pi$
$673$	−3.55980	−0.137220	−0.0686102	+	0.997644i	$0.521856\pi$
$674$	−18.5880	−0.715982
$675$	63.0378	2.42632
$676$	−23.3702	−0.898855
$677$	8.35821	0.321232	0.160616	−	0.987017i	$-0.448652\pi$
$677$	8.35821	0.321232	0.160616	+	0.987017i	$0.448652\pi$
$678$	−77.2238	−2.96576
$679$	−26.6313	−1.02202
$680$	33.1454	1.27107
$681$	−4.98564	−0.191050
$682$	−36.8854	−1.41242
$683$	28.0504	1.07332	0.536660	−	0.843799i	$-0.319686\pi$
$683$	28.0504	1.07332	0.536660	+	0.843799i	$0.319686\pi$
$684$	40.3269	1.54194
$685$	−32.0178	−1.22334
$686$	21.8991	0.836110
$687$	13.4956	0.514890
$688$	−44.6318	−1.70157
$689$	35.5874	1.35577
$690$	−98.1258	−3.73558
$691$	−23.6734	−0.900577	−0.450289	−	0.892883i	$-0.648679\pi$
$691$	−23.6734	−0.900577	−0.450289	+	0.892883i	$0.648679\pi$
$692$	29.8100	1.13320
$693$	51.5342	1.95762
$694$	3.88357	0.147418
$695$	61.2597	2.32371
$696$	71.2862	2.70210
$697$	6.03166	0.228465
$698$	−42.8588	−1.62223
$699$	6.43072	0.243232
$700$	−222.902	−8.42489
$701$	45.1795	1.70641	0.853203	−	0.521579i	$-0.174657\pi$
$701$	45.1795	1.70641	0.853203	+	0.521579i	$0.174657\pi$
$702$	34.3441	1.29623
$703$	−19.1272	−0.721396
$704$	7.73292	0.291445
$705$	−47.4910	−1.78861
$706$	−50.0986	−1.88549
$707$	−12.1018	−0.455136
$708$	−120.864	−4.54235
$709$	−38.9053	−1.46112	−0.730559	−	0.682850i	$-0.760740\pi$
$709$	−38.9053	−1.46112	−0.730559	+	0.682850i	$0.760740\pi$
$710$	94.9396	3.56302
$711$	−14.1437	−0.530430
$712$	87.0118	3.26090
$713$	−18.0751	−0.676916
$714$	−37.5983	−1.40708
$715$	31.2539	1.16883
$716$	77.2295	2.88620
$717$	−13.2998	−0.496689
$718$	26.6662	0.995175
$719$	−21.3396	−0.795833	−0.397917	−	0.917422i	$-0.630267\pi$
$719$	−21.3396	−0.795833	−0.397917	+	0.917422i	$0.630267\pi$
$720$	124.377	4.63527
$721$	−63.8745	−2.37881
$722$	38.3253	1.42632
$723$	−53.5051	−1.98988
$724$	32.5694	1.21043
$725$	−55.2671	−2.05257
$726$	26.5679	0.986026
$727$	−35.4584	−1.31508	−0.657539	−	0.753420i	$-0.728403\pi$
$727$	−35.4584	−1.31508	−0.657539	+	0.753420i	$0.728403\pi$
$728$	−65.5332	−2.42882
$729$	−43.9125	−1.62639
$730$	41.6456	1.54137
$731$	9.61156	0.355496
$732$	35.0651	1.29604
$733$	22.9125	0.846291	0.423145	−	0.906062i	$-0.360926\pi$
$733$	22.9125	0.846291	0.423145	+	0.906062i	$0.360926\pi$
$734$	27.0052	0.996780
$735$	107.654	3.97088
$736$	−12.4933	−0.460509
$737$	−30.8786	−1.13743
$738$	54.4314	2.00365
$739$	33.3145	1.22549	0.612747	−	0.790279i	$-0.290065\pi$
$739$	33.3145	1.22549	0.612747	+	0.790279i	$0.290065\pi$
$740$	−180.025	−6.61787
$741$	−14.9708	−0.549966
$742$	−130.543	−4.79237
$743$	−36.5095	−1.33940	−0.669701	−	0.742631i	$-0.733578\pi$
$743$	−36.5095	−1.33940	−0.669701	+	0.742631i	$0.733578\pi$
$744$	89.7374	3.28993
$745$	6.79113	0.248808
$746$	49.0382	1.79542
$747$	−32.3695	−1.18434
$748$	15.5433	0.568320
$749$	−65.7481	−2.40238
$750$	−229.723	−8.38828
$751$	30.4123	1.10976	0.554881	−	0.831930i	$-0.312764\pi$
$751$	30.4123	1.10976	0.554881	+	0.831930i	$0.312764\pi$
$752$	−24.9983	−0.911593
$753$	16.0247	0.583973
$754$	−30.1105	−1.09656
$755$	−91.5331	−3.33123
$756$	−86.2672	−3.13751
$757$	7.34395	0.266920	0.133460	−	0.991054i	$-0.457391\pi$
$757$	7.34395	0.266920	0.133460	+	0.991054i	$0.457391\pi$
$758$	74.3507	2.70054
$759$	−24.8313	−0.901319
$760$	−48.4124	−1.75610
$761$	6.68433	0.242307	0.121153	−	0.992634i	$-0.461341\pi$
$761$	6.68433	0.242307	0.121153	+	0.992634i	$0.461341\pi$
$762$	81.1226	2.93876
$763$	43.5304	1.57591
$764$	66.4218	2.40306
$765$	−26.7849	−0.968411
$766$	15.6576	0.565731
$767$	27.5490	0.994738
$768$	−87.7784	−3.16743
$769$	−29.0270	−1.04674	−0.523369	−	0.852106i	$-0.675325\pi$
$769$	−29.0270	−1.04674	−0.523369	+	0.852106i	$0.675325\pi$
$770$	−114.647	−4.13157
$771$	−62.3526	−2.24557
$772$	47.8988	1.72391
$773$	32.6405	1.17400	0.586999	−	0.809588i	$-0.300309\pi$
$773$	32.6405	1.17400	0.586999	+	0.809588i	$0.300309\pi$
$774$	86.7374	3.11771
$775$	−69.5721	−2.49910
$776$	−39.1156	−1.40417
$777$	110.198	3.95334
$778$	−21.6055	−0.774596
$779$	−8.80987	−0.315646
$780$	−140.905	−5.04522
$781$	24.0250	0.859682
$782$	11.1232	0.397766
$783$	−21.3894	−0.764396
$784$	56.6669	2.02382
$785$	23.6869	0.845422
$786$	−74.0608	−2.64166
$787$	31.3732	1.11833	0.559167	−	0.829055i	$-0.311121\pi$
$787$	31.3732	1.11833	0.559167	+	0.829055i	$0.311121\pi$
$788$	−23.9824	−0.854337
$789$	−83.8729	−2.98595
$790$	31.4650	1.11947
$791$	−44.2134	−1.57205
$792$	75.6925	2.68962
$793$	−7.99253	−0.283823
$794$	−46.9311	−1.66552
$795$	−151.466	−5.37195
$796$	−63.2662	−2.24241
$797$	−26.9845	−0.955838	−0.477919	−	0.878404i	$-0.658609\pi$
$797$	−26.9845	−0.955838	−0.477919	+	0.878404i	$0.658609\pi$
$798$	54.9163	1.94401
$799$	5.38343	0.190452
$800$	−48.0875	−1.70015
$801$	−70.3144	−2.48444
$802$	−64.7005	−2.28466
$803$	10.5387	0.371902
$804$	139.213	4.90967
$805$	−56.1805	−1.98010
$806$	−37.9041	−1.33512
$807$	−73.1186	−2.57390
$808$	−17.7749	−0.625319
$809$	22.6824	0.797471	0.398736	−	0.917066i	$-0.369449\pi$
$809$	22.6824	0.797471	0.398736	+	0.917066i	$0.369449\pi$
$810$	5.79126	0.203484
$811$	11.9772	0.420578	0.210289	−	0.977639i	$-0.432560\pi$
$811$	11.9772	0.420578	0.210289	+	0.977639i	$0.432560\pi$
$812$	75.6331	2.65420
$813$	−23.9668	−0.840552
$814$	−66.5293	−2.33185
$815$	81.9089	2.86914
$816$	−22.9631	−0.803868
$817$	−14.0387	−0.491151
$818$	97.8044	3.41965
$819$	52.9575	1.85048
$820$	−82.9186	−2.89564
$821$	−19.8979	−0.694441	−0.347221	−	0.937783i	$-0.612875\pi$
$821$	−19.8979	−0.694441	−0.347221	+	0.937783i	$0.612875\pi$
$822$	53.3450	1.86062
$823$	4.68467	0.163297	0.0816487	−	0.996661i	$-0.473981\pi$
$823$	4.68467	0.163297	0.0816487	+	0.996661i	$0.473981\pi$
$824$	−93.8177	−3.26829
$825$	−95.5773	−3.32758
$826$	−101.056	−3.51619
$827$	55.7532	1.93873	0.969365	−	0.245626i	$-0.0789935\pi$
$827$	55.7532	1.93873	0.969365	+	0.245626i	$0.0789935\pi$
$828$	68.7355	2.38872
$829$	−2.98518	−0.103680	−0.0518398	−	0.998655i	$-0.516509\pi$
$829$	−2.98518	−0.103680	−0.0518398	+	0.998655i	$0.516509\pi$
$830$	72.0113	2.49955
$831$	27.9514	0.969623
$832$	7.94649	0.275495
$833$	−12.2033	−0.422820
$834$	−102.065	−3.53421
$835$	80.5534	2.78766
$836$	−22.7026	−0.785187
$837$	−26.9257	−0.930689
$838$	−46.9766	−1.62278
$839$	−26.9335	−0.929846	−0.464923	−	0.885351i	$-0.653918\pi$
$839$	−26.9335	−0.929846	−0.464923	+	0.885351i	$0.653918\pi$
$840$	278.920	9.62366
$841$	−10.2472	−0.353353
$842$	−42.1102	−1.45121
$843$	14.4127	0.496399
$844$	69.2940	2.38520
$845$	−22.6721	−0.779943
$846$	48.5816	1.67027
$847$	15.2111	0.522658
$848$	−79.7286	−2.73789
$849$	59.1404	2.02969
$850$	42.8141	1.46851
$851$	−32.6015	−1.11757
$852$	−108.314	−3.71079
$853$	−18.5553	−0.635320	−0.317660	−	0.948205i	$-0.602897\pi$
$853$	−18.5553	−0.635320	−0.317660	+	0.948205i	$0.602897\pi$
$854$	29.3184	1.00326
$855$	39.1222	1.33795
$856$	−96.5696	−3.30068
$857$	−33.7307	−1.15222	−0.576109	−	0.817373i	$-0.695430\pi$
$857$	−33.7307	−1.15222	−0.576109	+	0.817373i	$0.695430\pi$
$858$	−52.0722	−1.77772
$859$	38.6481	1.31866	0.659328	−	0.751856i	$-0.270841\pi$
$859$	38.6481	1.31866	0.659328	+	0.751856i	$0.270841\pi$
$860$	−132.132	−4.50567
$861$	50.7566	1.72978
$862$	−5.99178	−0.204081
$863$	12.8820	0.438510	0.219255	−	0.975668i	$-0.429637\pi$
$863$	12.8820	0.438510	0.219255	+	0.975668i	$0.429637\pi$
$864$	−18.6108	−0.633152
$865$	28.9194	0.983290
$866$	28.0509	0.953209
$867$	−42.4473	−1.44158
$868$	95.2094	3.23162
$869$	7.96240	0.270106
$870$	128.155	4.34488
$871$	−31.7314	−1.07518
$872$	63.9367	2.16517
$873$	31.6094	1.06982
$874$	−16.2467	−0.549551
$875$	−131.524	−4.44634
$876$	−47.5125	−1.60530
$877$	−5.17283	−0.174674	−0.0873370	−	0.996179i	$-0.527836\pi$
$877$	−5.17283	−0.174674	−0.0873370	+	0.996179i	$0.527836\pi$
$878$	100.936	3.40644
$879$	28.4681	0.960204
$880$	−70.0201	−2.36038
$881$	−23.7442	−0.799961	−0.399981	−	0.916524i	$-0.630983\pi$
$881$	−23.7442	−0.799961	−0.399981	+	0.916524i	$0.630983\pi$
$882$	−110.126	−3.70815
$883$	32.0184	1.07751	0.538753	−	0.842464i	$-0.318896\pi$
$883$	32.0184	1.07751	0.538753	+	0.842464i	$0.318896\pi$
$884$	15.9726	0.537216
$885$	−117.253	−3.94143
$886$	47.2956	1.58893
$887$	35.8694	1.20438	0.602188	−	0.798354i	$-0.294296\pi$
$887$	35.8694	1.20438	0.602188	+	0.798354i	$0.294296\pi$
$888$	161.857	5.43157
$889$	46.4456	1.55773
$890$	156.426	5.24342
$891$	1.46551	0.0490964
$892$	−15.6309	−0.523362
$893$	−7.86307	−0.263128
$894$	−11.3147	−0.378421
$895$	74.9223	2.50438
$896$	−59.4454	−1.98593
$897$	−25.5171	−0.851991
$898$	23.9052	0.797727
$899$	23.6066	0.787324
$900$	264.568	8.81892
$901$	17.1697	0.572007
$902$	−30.6430	−1.02030
$903$	80.8816	2.69157
$904$	−64.9399	−2.15987
$905$	31.5965	1.05030
$906$	152.503	5.06659
$907$	−25.1528	−0.835187	−0.417593	−	0.908634i	$-0.637126\pi$
$907$	−25.1528	−0.835187	−0.417593	+	0.908634i	$0.637126\pi$
$908$	−7.76935	−0.257835
$909$	14.3640	0.476422
$910$	−117.813	−3.90546
$911$	23.4121	0.775678	0.387839	−	0.921727i	$-0.373222\pi$
$911$	23.4121	0.775678	0.387839	+	0.921727i	$0.373222\pi$
$912$	33.5400	1.11062
$913$	18.2229	0.603089
$914$	13.3906	0.442920
$915$	34.0176	1.12459
$916$	21.0308	0.694878
$917$	−42.4024	−1.40025
$918$	16.5699	0.546887
$919$	−25.3881	−0.837478	−0.418739	−	0.908107i	$-0.637528\pi$
$919$	−25.3881	−0.837478	−0.418739	+	0.908107i	$0.637528\pi$
$920$	−82.5169	−2.72050
$921$	54.6070	1.79936
$922$	−21.2140	−0.698646
$923$	24.6885	0.812633
$924$	130.798	4.30292
$925$	−125.485	−4.12594
$926$	−37.3098	−1.22607
$927$	75.8143	2.49007
$928$	16.3167	0.535620
$929$	−3.80194	−0.124738	−0.0623688	−	0.998053i	$-0.519866\pi$
$929$	−3.80194	−0.124738	−0.0623688	+	0.998053i	$0.519866\pi$
$930$	161.326	5.29010
$931$	17.8242	0.584166
$932$	10.0213	0.328258
$933$	57.8485	1.89387
$934$	−67.6702	−2.21424
$935$	15.0790	0.493135
$936$	77.7830	2.54242
$937$	31.8962	1.04200	0.521001	−	0.853556i	$-0.325559\pi$
$937$	31.8962	1.04200	0.521001	+	0.853556i	$0.325559\pi$
$938$	116.398	3.80053
$939$	−5.76545	−0.188148
$940$	−74.0073	−2.41385
$941$	−14.1314	−0.460670	−0.230335	−	0.973111i	$-0.573982\pi$
$941$	−14.1314	−0.460670	−0.230335	+	0.973111i	$0.573982\pi$
$942$	−39.4648	−1.28583
$943$	−15.0161	−0.488990
$944$	−61.7197	−2.00881
$945$	−83.6900	−2.72244
$946$	−48.8301	−1.58760
$947$	7.36481	0.239324	0.119662	−	0.992815i	$-0.461819\pi$
$947$	7.36481	0.239324	0.119662	+	0.992815i	$0.461819\pi$
$948$	−35.8977	−1.16590
$949$	10.8297	0.351548
$950$	−62.5345	−2.02889
$951$	80.3117	2.60429
$952$	−31.6175	−1.02473
$953$	34.4731	1.11669	0.558346	−	0.829608i	$-0.311436\pi$
$953$	34.4731	1.11669	0.558346	+	0.829608i	$0.311436\pi$
$954$	154.945	5.01651
$955$	64.4375	2.08515
$956$	−20.7256	−0.670314
$957$	32.4305	1.04833
$958$	−59.2471	−1.91419
$959$	30.5419	0.986249
$960$	−33.8216	−1.09159
$961$	−1.28322	−0.0413941
$962$	−68.3667	−2.20423
$963$	78.0381	2.51474
$964$	−83.3794	−2.68547
$965$	46.4679	1.49585
$966$	93.6025	3.01161
$967$	21.1144	0.678992	0.339496	−	0.940608i	$-0.389744\pi$
$967$	21.1144	0.678992	0.339496	+	0.940608i	$0.389744\pi$
$968$	22.3417	0.718090
$969$	−7.22290	−0.232033
$970$	−70.3205	−2.25786
$971$	13.5521	0.434909	0.217455	−	0.976070i	$-0.430225\pi$
$971$	13.5521	0.434909	0.217455	+	0.976070i	$0.430225\pi$
$972$	−70.9812	−2.27672
$973$	−58.4358	−1.87336
$974$	40.5483	1.29925
$975$	−98.2170	−3.14546
$976$	17.9062	0.573162
$977$	24.7117	0.790597	0.395299	−	0.918553i	$-0.370641\pi$
$977$	24.7117	0.790597	0.395299	+	0.918553i	$0.370641\pi$
$978$	−136.469	−4.36378
$979$	39.5846	1.26513
$980$	167.762	5.35896
$981$	−51.6674	−1.64961
$982$	−5.25616	−0.167731
$983$	−40.6694	−1.29715	−0.648576	−	0.761150i	$-0.724635\pi$
$983$	−40.6694	−1.29715	−0.648576	+	0.761150i	$0.724635\pi$
$984$	74.5504	2.37658
$985$	−23.2659	−0.741314
$986$	−14.5273	−0.462644
$987$	45.3018	1.44197
$988$	−23.3297	−0.742215
$989$	−23.9284	−0.760877
$990$	136.077	4.32481
$991$	40.3852	1.28288	0.641439	−	0.767174i	$-0.278338\pi$
$991$	40.3852	1.28288	0.641439	+	0.767174i	$0.278338\pi$
$992$	20.5399	0.652144
$993$	73.9479	2.34667
$994$	−90.5631	−2.87249
$995$	−61.3761	−1.94575
$996$	−82.1560	−2.60321
$997$	20.8298	0.659685	0.329843	−	0.944036i	$-0.393004\pi$
$997$	20.8298	0.659685	0.329843	+	0.944036i	$0.393004\pi$
$998$	74.1297	2.34653
$999$	−48.5652	−1.53654

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.e.1.15	✓	221

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.e.1.15	✓	221	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51880 q^{2} +2.78779 q^{3} +4.34434 q^{4} +4.21455 q^{5} -7.02187 q^{6} -4.02027 q^{7} -5.90490 q^{8} +4.77177 q^{9} +O(q^{10})\)	\(q-2.51880 q^{2} +2.78779 q^{3} +4.34434 q^{4} +4.21455 q^{5} -7.02187 q^{6} -4.02027 q^{7} -5.90490 q^{8} +4.77177 q^{9} -10.6156 q^{10} -2.68634 q^{11} +12.1111 q^{12} -2.76053 q^{13} +10.1263 q^{14} +11.7493 q^{15} +6.18458 q^{16} -1.33186 q^{17} -12.0191 q^{18} +1.94533 q^{19} +18.3094 q^{20} -11.2077 q^{21} +6.76634 q^{22} +3.31573 q^{23} -16.4616 q^{24} +12.7625 q^{25} +6.95321 q^{26} +4.93931 q^{27} -17.4654 q^{28} -4.33045 q^{29} -29.5941 q^{30} -5.45131 q^{31} -3.76789 q^{32} -7.48894 q^{33} +3.35469 q^{34} -16.9437 q^{35} +20.7302 q^{36} -9.83239 q^{37} -4.89988 q^{38} -7.69578 q^{39} -24.8865 q^{40} -4.52874 q^{41} +28.2299 q^{42} -7.21663 q^{43} -11.6704 q^{44} +20.1109 q^{45} -8.35164 q^{46} -4.04203 q^{47} +17.2413 q^{48} +9.16260 q^{49} -32.1460 q^{50} -3.71295 q^{51} -11.9927 q^{52} -12.8915 q^{53} -12.4411 q^{54} -11.3217 q^{55} +23.7393 q^{56} +5.42316 q^{57} +10.9075 q^{58} -9.97962 q^{59} +51.0428 q^{60} +2.89529 q^{61} +13.7307 q^{62} -19.1838 q^{63} -2.87861 q^{64} -11.6344 q^{65} +18.8631 q^{66} +11.4947 q^{67} -5.78606 q^{68} +9.24354 q^{69} +42.6776 q^{70} -8.94340 q^{71} -28.1768 q^{72} -3.92306 q^{73} +24.7658 q^{74} +35.5790 q^{75} +8.45115 q^{76} +10.7998 q^{77} +19.3841 q^{78} -2.96403 q^{79} +26.0652 q^{80} -0.545542 q^{81} +11.4070 q^{82} -6.78354 q^{83} -48.6899 q^{84} -5.61321 q^{85} +18.1772 q^{86} -12.0724 q^{87} +15.8626 q^{88} -14.7355 q^{89} -50.6552 q^{90} +11.0981 q^{91} +14.4046 q^{92} -15.1971 q^{93} +10.1811 q^{94} +8.19868 q^{95} -10.5041 q^{96} +6.62426 q^{97} -23.0787 q^{98} -12.8186 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * q^99

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