LMFDB - Embedded newform 6001.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51719 q^{2} +0.226046 q^{3} +4.33623 q^{4} -1.31460 q^{5} -0.569001 q^{6} -1.40872 q^{7} -5.88074 q^{8} -2.94890 q^{9} +O(q^{10})$	\(q-2.51719 q^{2} +0.226046 q^{3} +4.33623 q^{4} -1.31460 q^{5} -0.569001 q^{6} -1.40872 q^{7} -5.88074 q^{8} -2.94890 q^{9} +3.30910 q^{10} -1.02148 q^{11} +0.980189 q^{12} -5.01297 q^{13} +3.54602 q^{14} -0.297161 q^{15} +6.13046 q^{16} +1.00000 q^{17} +7.42294 q^{18} -0.951166 q^{19} -5.70043 q^{20} -0.318436 q^{21} +2.57126 q^{22} -1.09105 q^{23} -1.32932 q^{24} -3.27182 q^{25} +12.6186 q^{26} -1.34473 q^{27} -6.10856 q^{28} -6.92080 q^{29} +0.748010 q^{30} +1.56426 q^{31} -3.67004 q^{32} -0.230902 q^{33} -2.51719 q^{34} +1.85191 q^{35} -12.7871 q^{36} -4.13201 q^{37} +2.39426 q^{38} -1.13316 q^{39} +7.73085 q^{40} +5.99367 q^{41} +0.801564 q^{42} +2.31457 q^{43} -4.42939 q^{44} +3.87664 q^{45} +2.74639 q^{46} -3.40367 q^{47} +1.38577 q^{48} -5.01550 q^{49} +8.23578 q^{50} +0.226046 q^{51} -21.7374 q^{52} -7.12979 q^{53} +3.38493 q^{54} +1.34284 q^{55} +8.28434 q^{56} -0.215007 q^{57} +17.4209 q^{58} -8.87087 q^{59} -1.28856 q^{60} +5.70622 q^{61} -3.93753 q^{62} +4.15419 q^{63} -3.02274 q^{64} +6.59006 q^{65} +0.581224 q^{66} -4.65124 q^{67} +4.33623 q^{68} -0.246629 q^{69} -4.66161 q^{70} -7.50941 q^{71} +17.3417 q^{72} -16.3112 q^{73} +10.4010 q^{74} -0.739582 q^{75} -4.12448 q^{76} +1.43899 q^{77} +2.85238 q^{78} -12.2566 q^{79} -8.05913 q^{80} +8.54274 q^{81} -15.0872 q^{82} -0.783044 q^{83} -1.38082 q^{84} -1.31460 q^{85} -5.82621 q^{86} -1.56442 q^{87} +6.00707 q^{88} -6.64570 q^{89} -9.75823 q^{90} +7.06188 q^{91} -4.73107 q^{92} +0.353594 q^{93} +8.56767 q^{94} +1.25041 q^{95} -0.829599 q^{96} -1.92941 q^{97} +12.6250 q^{98} +3.01225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * 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 $

$2$	−2.51719	−1.77992	−0.889960	−	0.456038i	$-0.849268\pi$
$2$	−2.51719	−1.77992	−0.889960	+	0.456038i	$0.849268\pi$
$3$	0.226046	0.130508	0.0652539	−	0.997869i	$-0.479214\pi$
$3$	0.226046	0.130508	0.0652539	+	0.997869i	$0.479214\pi$
$4$	4.33623	2.16812
$5$	−1.31460	−0.587909	−0.293954	−	0.955819i	$-0.594971\pi$
$5$	−1.31460	−0.587909	−0.293954	+	0.955819i	$0.594971\pi$
$6$	−0.569001	−0.232293
$7$	−1.40872	−0.532447	−0.266224	−	0.963911i	$-0.585776\pi$
$7$	−1.40872	−0.532447	−0.266224	+	0.963911i	$0.585776\pi$
$8$	−5.88074	−2.07916
$9$	−2.94890	−0.982968
$10$	3.30910	1.04643
$11$	−1.02148	−0.307988	−0.153994	−	0.988072i	$-0.549214\pi$
$11$	−1.02148	−0.307988	−0.153994	+	0.988072i	$0.549214\pi$
$12$	0.980189	0.282956
$13$	−5.01297	−1.39035	−0.695173	−	0.718842i	$-0.744672\pi$
$13$	−5.01297	−1.39035	−0.695173	+	0.718842i	$0.744672\pi$
$14$	3.54602	0.947714
$15$	−0.297161	−0.0767267
$16$	6.13046	1.53262
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	7.42294	1.74960
$19$	−0.951166	−0.218212	−0.109106	−	0.994030i	$-0.534799\pi$
$19$	−0.951166	−0.218212	−0.109106	+	0.994030i	$0.534799\pi$
$20$	−5.70043	−1.27466
$21$	−0.318436	−0.0694885
$22$	2.57126	0.548195
$23$	−1.09105	−0.227501	−0.113750	−	0.993509i	$-0.536286\pi$
$23$	−1.09105	−0.227501	−0.113750	+	0.993509i	$0.536286\pi$
$24$	−1.32932	−0.271346
$25$	−3.27182	−0.654363
$26$	12.6186	2.47471
$27$	−1.34473	−0.258793
$28$	−6.10856	−1.15441
$29$	−6.92080	−1.28516	−0.642580	−	0.766219i	$-0.722136\pi$
$29$	−6.92080	−1.28516	−0.642580	+	0.766219i	$0.722136\pi$
$30$	0.748010	0.136567
$31$	1.56426	0.280949	0.140474	−	0.990084i	$-0.455137\pi$
$31$	1.56426	0.280949	0.140474	+	0.990084i	$0.455137\pi$
$32$	−3.67004	−0.648778
$33$	−0.230902	−0.0401949
$34$	−2.51719	−0.431694
$35$	1.85191	0.313030
$36$	−12.7871	−2.13119
$37$	−4.13201	−0.679298	−0.339649	−	0.940552i	$-0.610308\pi$
$37$	−4.13201	−0.679298	−0.339649	+	0.940552i	$0.610308\pi$
$38$	2.39426	0.388401
$39$	−1.13316	−0.181451
$40$	7.73085	1.22235
$41$	5.99367	0.936053	0.468027	−	0.883714i	$-0.344965\pi$
$41$	5.99367	0.936053	0.468027	+	0.883714i	$0.344965\pi$
$42$	0.801564	0.123684
$43$	2.31457	0.352969	0.176484	−	0.984303i	$-0.443528\pi$
$43$	2.31457	0.352969	0.176484	+	0.984303i	$0.443528\pi$
$44$	−4.42939	−0.667755
$45$	3.87664	0.577895
$46$	2.74639	0.404933
$47$	−3.40367	−0.496476	−0.248238	−	0.968699i	$-0.579851\pi$
$47$	−3.40367	−0.496476	−0.248238	+	0.968699i	$0.579851\pi$
$48$	1.38577	0.200018
$49$	−5.01550	−0.716500
$50$	8.23578	1.16471
$51$	0.226046	0.0316528
$52$	−21.7374	−3.01443
$53$	−7.12979	−0.979352	−0.489676	−	0.871904i	$-0.662885\pi$
$53$	−7.12979	−0.979352	−0.489676	+	0.871904i	$0.662885\pi$
$54$	3.38493	0.460631
$55$	1.34284	0.181069
$56$	8.28434	1.10704
$57$	−0.215007	−0.0284784
$58$	17.4209	2.28748
$59$	−8.87087	−1.15489	−0.577444	−	0.816430i	$-0.695950\pi$
$59$	−8.87087	−1.15489	−0.577444	+	0.816430i	$0.695950\pi$
$60$	−1.28856	−0.166352
$61$	5.70622	0.730606	0.365303	−	0.930889i	$-0.380965\pi$
$61$	5.70622	0.730606	0.365303	+	0.930889i	$0.380965\pi$
$62$	−3.93753	−0.500067
$63$	4.15419	0.523379
$64$	−3.02274	−0.377842
$65$	6.59006	0.817397
$66$	0.581224	0.0715437
$67$	−4.65124	−0.568239	−0.284119	−	0.958789i	$-0.591701\pi$
$67$	−4.65124	−0.568239	−0.284119	+	0.958789i	$0.591701\pi$
$68$	4.33623	0.525846
$69$	−0.246629	−0.0296906
$70$	−4.66161	−0.557169
$71$	−7.50941	−0.891203	−0.445601	−	0.895232i	$-0.647010\pi$
$71$	−7.50941	−0.891203	−0.445601	+	0.895232i	$0.647010\pi$
$72$	17.3417	2.04374
$73$	−16.3112	−1.90908	−0.954541	−	0.298079i	$-0.903654\pi$
$73$	−16.3112	−1.90908	−0.954541	+	0.298079i	$0.903654\pi$
$74$	10.4010	1.20910
$75$	−0.739582	−0.0853995
$76$	−4.12448	−0.473110
$77$	1.43899	0.163988
$78$	2.85238	0.322968
$79$	−12.2566	−1.37898	−0.689489	−	0.724296i	$-0.742165\pi$
$79$	−12.2566	−1.37898	−0.689489	+	0.724296i	$0.742165\pi$
$80$	−8.05913	−0.901038
$81$	8.54274	0.949193
$82$	−15.0872	−1.66610
$83$	−0.783044	−0.0859503	−0.0429751	−	0.999076i	$-0.513684\pi$
$83$	−0.783044	−0.0859503	−0.0429751	+	0.999076i	$0.513684\pi$
$84$	−1.38082	−0.150659
$85$	−1.31460	−0.142589
$86$	−5.82621	−0.628256
$87$	−1.56442	−0.167723
$88$	6.00707	0.640356
$89$	−6.64570	−0.704443	−0.352221	−	0.935917i	$-0.614574\pi$
$89$	−6.64570	−0.704443	−0.352221	+	0.935917i	$0.614574\pi$
$90$	−9.75823	−1.02861
$91$	7.06188	0.740286
$92$	−4.73107	−0.493248
$93$	0.353594	0.0366660
$94$	8.56767	0.883687
$95$	1.25041	0.128289
$96$	−0.829599	−0.0846706
$97$	−1.92941	−0.195902	−0.0979510	−	0.995191i	$-0.531229\pi$
$97$	−1.92941	−0.195902	−0.0979510	+	0.995191i	$0.531229\pi$
$98$	12.6250	1.27531
$99$	3.01225	0.302743
$100$	−14.1874	−1.41874
$101$	−4.24603	−0.422495	−0.211248	−	0.977433i	$-0.567753\pi$
$101$	−4.24603	−0.422495	−0.211248	+	0.977433i	$0.567753\pi$
$102$	−0.569001	−0.0563394
$103$	−18.4570	−1.81862	−0.909311	−	0.416117i	$-0.863391\pi$
$103$	−18.4570	−1.81862	−0.909311	+	0.416117i	$0.863391\pi$
$104$	29.4800	2.89075
$105$	0.418618	0.0408529
$106$	17.9470	1.74317
$107$	5.69734	0.550783	0.275391	−	0.961332i	$-0.411193\pi$
$107$	5.69734	0.550783	0.275391	+	0.961332i	$0.411193\pi$
$108$	−5.83105	−0.561093
$109$	2.42033	0.231826	0.115913	−	0.993259i	$-0.463021\pi$
$109$	2.42033	0.231826	0.115913	+	0.993259i	$0.463021\pi$
$110$	−3.38019	−0.322289
$111$	−0.934025	−0.0886537
$112$	−8.63613	−0.816037
$113$	5.43135	0.510939	0.255469	−	0.966817i	$-0.417770\pi$
$113$	5.43135	0.510939	0.255469	+	0.966817i	$0.417770\pi$
$114$	0.541214	0.0506893
$115$	1.43430	0.133750
$116$	−30.0102	−2.78638
$117$	14.7828	1.36667
$118$	22.3296	2.05561
$119$	−1.40872	−0.129137
$120$	1.74753	0.159527
$121$	−9.95657	−0.905143
$122$	−14.3636	−1.30042
$123$	1.35485	0.122162
$124$	6.78299	0.609130
$125$	10.8742	0.972615
$126$	−10.4569	−0.931572
$127$	7.45605	0.661617	0.330809	−	0.943698i	$-0.392679\pi$
$127$	7.45605	0.661617	0.330809	+	0.943698i	$0.392679\pi$
$128$	14.9489	1.32131
$129$	0.523200	0.0460652
$130$	−16.5884	−1.45490
$131$	−0.160797	−0.0140489	−0.00702445	−	0.999975i	$-0.502236\pi$
$131$	−0.160797	−0.0140489	−0.00702445	+	0.999975i	$0.502236\pi$
$132$	−1.00125	−0.0871472
$133$	1.33993	0.116187
$134$	11.7080	1.01142
$135$	1.76778	0.152146
$136$	−5.88074	−0.504269
$137$	−8.37661	−0.715662	−0.357831	−	0.933786i	$-0.616484\pi$
$137$	−8.37661	−0.715662	−0.357831	+	0.933786i	$0.616484\pi$
$138$	0.620810	0.0528469
$139$	−15.5989	−1.32308	−0.661541	−	0.749909i	$-0.730097\pi$
$139$	−15.5989	−1.32308	−0.661541	+	0.749909i	$0.730097\pi$
$140$	8.03033	0.678687
$141$	−0.769385	−0.0647939
$142$	18.9026	1.58627
$143$	5.12066	0.428211
$144$	−18.0781	−1.50651
$145$	9.09811	0.755557
$146$	41.0584	3.39802
$147$	−1.13373	−0.0935088
$148$	−17.9174	−1.47280
$149$	13.5055	1.10641	0.553207	−	0.833044i	$-0.313404\pi$
$149$	13.5055	1.10641	0.553207	+	0.833044i	$0.313404\pi$
$150$	1.86167	0.152004
$151$	10.1311	0.824459	0.412229	−	0.911080i	$-0.364750\pi$
$151$	10.1311	0.824459	0.412229	+	0.911080i	$0.364750\pi$
$152$	5.59356	0.453698
$153$	−2.94890	−0.238405
$154$	−3.62220	−0.291885
$155$	−2.05638	−0.165172
$156$	−4.91365	−0.393407
$157$	−1.25996	−0.100556	−0.0502778	−	0.998735i	$-0.516011\pi$
$157$	−1.25996	−0.100556	−0.0502778	+	0.998735i	$0.516011\pi$
$158$	30.8522	2.45447
$159$	−1.61166	−0.127813
$160$	4.82465	0.381422
$161$	1.53699	0.121132
$162$	−21.5037	−1.68949
$163$	−11.5435	−0.904159	−0.452079	−	0.891978i	$-0.649318\pi$
$163$	−11.5435	−0.904159	−0.452079	+	0.891978i	$0.649318\pi$
$164$	25.9899	2.02947
$165$	0.303545	0.0236309
$166$	1.97107	0.152985
$167$	−22.9962	−1.77950	−0.889750	−	0.456448i	$-0.849121\pi$
$167$	−22.9962	−1.77950	−0.889750	+	0.456448i	$0.849121\pi$
$168$	1.87264	0.144478
$169$	12.1298	0.933064
$170$	3.30910	0.253797
$171$	2.80490	0.214496
$172$	10.0365	0.765278
$173$	21.1518	1.60814	0.804071	−	0.594533i	$-0.202663\pi$
$173$	21.1518	1.60814	0.804071	+	0.594533i	$0.202663\pi$
$174$	3.93794	0.298534
$175$	4.60909	0.348414
$176$	−6.26216	−0.472028
$177$	−2.00523	−0.150722
$178$	16.7285	1.25385
$179$	22.2942	1.66635	0.833174	−	0.553011i	$-0.186521\pi$
$179$	22.2942	1.66635	0.833174	+	0.553011i	$0.186521\pi$
$180$	16.8100	1.25294
$181$	21.4779	1.59644	0.798220	−	0.602366i	$-0.205775\pi$
$181$	21.4779	1.59644	0.798220	+	0.602366i	$0.205775\pi$
$182$	−17.7761	−1.31765
$183$	1.28987	0.0953498
$184$	6.41621	0.473009
$185$	5.43196	0.399365
$186$	−0.890063	−0.0652626
$187$	−1.02148	−0.0746982
$188$	−14.7591	−1.07642
$189$	1.89435	0.137794
$190$	−3.14751	−0.228344
$191$	15.4949	1.12117	0.560585	−	0.828097i	$-0.310576\pi$
$191$	15.4949	1.12117	0.560585	+	0.828097i	$0.310576\pi$
$192$	−0.683278	−0.0493113
$193$	−1.53595	−0.110560	−0.0552802	−	0.998471i	$-0.517605\pi$
$193$	−1.53595	−0.110560	−0.0552802	+	0.998471i	$0.517605\pi$
$194$	4.85669	0.348690
$195$	1.48966	0.106677
$196$	−21.7484	−1.55346
$197$	−13.3486	−0.951051	−0.475525	−	0.879702i	$-0.657742\pi$
$197$	−13.3486	−0.951051	−0.475525	+	0.879702i	$0.657742\pi$
$198$	−7.58240	−0.538858
$199$	−15.4734	−1.09688	−0.548439	−	0.836190i	$-0.684778\pi$
$199$	−15.4734	−1.09688	−0.548439	+	0.836190i	$0.684778\pi$
$200$	19.2407	1.36052
$201$	−1.05139	−0.0741596
$202$	10.6880	0.752008
$203$	9.74949	0.684280
$204$	0.980189	0.0686270
$205$	−7.87930	−0.550314
$206$	46.4597	3.23700
$207$	3.21741	0.223626
$208$	−30.7318	−2.13087
$209$	0.971599	0.0672069
$210$	−1.05374	−0.0727149
$211$	−11.1948	−0.770684	−0.385342	−	0.922774i	$-0.625917\pi$
$211$	−11.1948	−0.770684	−0.385342	+	0.922774i	$0.625917\pi$
$212$	−30.9165	−2.12335
$213$	−1.69747	−0.116309
$214$	−14.3413	−0.980350
$215$	−3.04274	−0.207513
$216$	7.90799	0.538071
$217$	−2.20361	−0.149591
$218$	−6.09243	−0.412632
$219$	−3.68709	−0.249150
$220$	5.82289	0.392579
$221$	−5.01297	−0.337209
$222$	2.35112	0.157797
$223$	−4.05908	−0.271816	−0.135908	−	0.990721i	$-0.543395\pi$
$223$	−4.05908	−0.271816	−0.135908	+	0.990721i	$0.543395\pi$
$224$	5.17008	0.345440
$225$	9.64827	0.643218
$226$	−13.6717	−0.909430
$227$	−16.0124	−1.06278	−0.531390	−	0.847127i	$-0.678330\pi$
$227$	−16.0124	−1.06278	−0.531390	+	0.847127i	$0.678330\pi$
$228$	−0.932323	−0.0617446
$229$	11.8656	0.784099	0.392050	−	0.919944i	$-0.371766\pi$
$229$	11.8656	0.784099	0.392050	+	0.919944i	$0.371766\pi$
$230$	−3.61041	−0.238064
$231$	0.325277	0.0214017
$232$	40.6994	2.67205
$233$	12.3850	0.811369	0.405685	−	0.914013i	$-0.367033\pi$
$233$	12.3850	0.811369	0.405685	+	0.914013i	$0.367033\pi$
$234$	−37.2110	−2.43256
$235$	4.47447	0.291882
$236$	−38.4662	−2.50393
$237$	−2.77056	−0.179967
$238$	3.54602	0.229854
$239$	7.73043	0.500040	0.250020	−	0.968241i	$-0.419563\pi$
$239$	7.73043	0.500040	0.250020	+	0.968241i	$0.419563\pi$
$240$	−1.82174	−0.117592
$241$	−7.99939	−0.515286	−0.257643	−	0.966240i	$-0.582946\pi$
$241$	−7.99939	−0.515286	−0.257643	+	0.966240i	$0.582946\pi$
$242$	25.0626	1.61108
$243$	5.96523	0.382670
$244$	24.7435	1.58404
$245$	6.59339	0.421236
$246$	−3.41040	−0.217439
$247$	4.76816	0.303391
$248$	−9.19900	−0.584137
$249$	−0.177004	−0.0112172
$250$	−27.3723	−1.73118
$251$	12.2332	0.772154	0.386077	−	0.922467i	$-0.373830\pi$
$251$	12.2332	0.772154	0.386077	+	0.922467i	$0.373830\pi$
$252$	18.0135	1.13475
$253$	1.11449	0.0700675
$254$	−18.7683	−1.17763
$255$	−0.297161	−0.0186089
$256$	−31.5837	−1.97398
$257$	4.04582	0.252371	0.126186	−	0.992007i	$-0.459727\pi$
$257$	4.04582	0.252371	0.126186	+	0.992007i	$0.459727\pi$
$258$	−1.31699	−0.0819923
$259$	5.82086	0.361691
$260$	28.5761	1.77221
$261$	20.4088	1.26327
$262$	0.404756	0.0250059
$263$	−8.36439	−0.515770	−0.257885	−	0.966176i	$-0.583026\pi$
$263$	−8.36439	−0.515770	−0.257885	+	0.966176i	$0.583026\pi$
$264$	1.35788	0.0835715
$265$	9.37285	0.575770
$266$	−3.37286	−0.206803
$267$	−1.50223	−0.0919352
$268$	−20.1689	−1.23201
$269$	−7.96237	−0.485474	−0.242737	−	0.970092i	$-0.578045\pi$
$269$	−7.96237	−0.485474	−0.242737	+	0.970092i	$0.578045\pi$
$270$	−4.44984	−0.270809
$271$	13.6117	0.826851	0.413426	−	0.910538i	$-0.364332\pi$
$271$	13.6117	0.826851	0.413426	+	0.910538i	$0.364332\pi$
$272$	6.13046	0.371714
$273$	1.59631	0.0966131
$274$	21.0855	1.27382
$275$	3.34210	0.201536
$276$	−1.06944	−0.0643727
$277$	−32.6275	−1.96039	−0.980197	−	0.198023i	$-0.936548\pi$
$277$	−32.6275	−1.96039	−0.980197	+	0.198023i	$0.936548\pi$
$278$	39.2654	2.35498
$279$	−4.61284	−0.276164
$280$	−10.8906	−0.650839
$281$	6.39414	0.381442	0.190721	−	0.981644i	$-0.438917\pi$
$281$	6.39414	0.381442	0.190721	+	0.981644i	$0.438917\pi$
$282$	1.93669	0.115328
$283$	−14.4517	−0.859062	−0.429531	−	0.903052i	$-0.641321\pi$
$283$	−14.4517	−0.859062	−0.429531	+	0.903052i	$0.641321\pi$
$284$	−32.5626	−1.93223
$285$	0.282650	0.0167427
$286$	−12.8897	−0.762181
$287$	−8.44342	−0.498399
$288$	10.8226	0.637728
$289$	1.00000	0.0588235
$290$	−22.9016	−1.34483
$291$	−0.436136	−0.0255667
$292$	−70.7292	−4.13912
$293$	31.1633	1.82058	0.910290	−	0.413971i	$-0.135858\pi$
$293$	31.1633	1.82058	0.910290	+	0.413971i	$0.135858\pi$
$294$	2.85382	0.166438
$295$	11.6617	0.678969
$296$	24.2993	1.41237
$297$	1.37361	0.0797052
$298$	−33.9959	−1.96933
$299$	5.46942	0.316305
$300$	−3.20700	−0.185156
$301$	−3.26059	−0.187937
$302$	−25.5019	−1.46747
$303$	−0.959798	−0.0551389
$304$	−5.83109	−0.334436
$305$	−7.50141	−0.429530
$306$	7.42294	0.424341
$307$	9.06668	0.517463	0.258731	−	0.965949i	$-0.416696\pi$
$307$	9.06668	0.517463	0.258731	+	0.965949i	$0.416696\pi$
$308$	6.23978	0.355544
$309$	−4.17213	−0.237344
$310$	5.17629	0.293994
$311$	2.45790	0.139375	0.0696874	−	0.997569i	$-0.477800\pi$
$311$	2.45790	0.139375	0.0696874	+	0.997569i	$0.477800\pi$
$312$	6.66383	0.377265
$313$	−13.7705	−0.778355	−0.389178	−	0.921163i	$-0.627241\pi$
$313$	−13.7705	−0.778355	−0.389178	+	0.921163i	$0.627241\pi$
$314$	3.17155	0.178981
$315$	−5.46111	−0.307699
$316$	−53.1476	−2.98979
$317$	−12.0510	−0.676851	−0.338425	−	0.940993i	$-0.609894\pi$
$317$	−12.0510	−0.676851	−0.338425	+	0.940993i	$0.609894\pi$
$318$	4.05686	0.227497
$319$	7.06947	0.395814
$320$	3.97370	0.222137
$321$	1.28786	0.0718814
$322$	−3.86890	−0.215605
$323$	−0.951166	−0.0529243
$324$	37.0433	2.05796
$325$	16.4015	0.909792
$326$	29.0572	1.60933
$327$	0.547107	0.0302551
$328$	−35.2472	−1.94620
$329$	4.79482	0.264347
$330$	−0.764079	−0.0420612
$331$	−28.7869	−1.58227	−0.791135	−	0.611642i	$-0.790509\pi$
$331$	−28.7869	−1.58227	−0.791135	+	0.611642i	$0.790509\pi$
$332$	−3.39546	−0.186350
$333$	12.1849	0.667728
$334$	57.8858	3.16737
$335$	6.11453	0.334073
$336$	−1.95216	−0.106499
$337$	3.11784	0.169840	0.0849199	−	0.996388i	$-0.472937\pi$
$337$	3.11784	0.169840	0.0849199	+	0.996388i	$0.472937\pi$
$338$	−30.5331	−1.66078
$339$	1.22774	0.0666815
$340$	−5.70043	−0.309149
$341$	−1.59786	−0.0865290
$342$	−7.06045	−0.381786
$343$	16.9265	0.913946
$344$	−13.6114	−0.733877
$345$	0.324219	0.0174554
$346$	−53.2431	−2.86237
$347$	−8.66605	−0.465218	−0.232609	−	0.972570i	$-0.574726\pi$
$347$	−8.66605	−0.465218	−0.232609	+	0.972570i	$0.574726\pi$
$348$	−6.78369	−0.363644
$349$	15.1240	0.809568	0.404784	−	0.914412i	$-0.367347\pi$
$349$	15.1240	0.809568	0.404784	+	0.914412i	$0.367347\pi$
$350$	−11.6019	−0.620149
$351$	6.74107	0.359812
$352$	3.74888	0.199816
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	5.04753	0.268273
$355$	9.87189	0.523946
$356$	−28.8173	−1.52731
$357$	−0.318436	−0.0168534
$358$	−56.1187	−2.96597
$359$	14.4053	0.760285	0.380142	−	0.924928i	$-0.375875\pi$
$359$	14.4053	0.760285	0.380142	+	0.924928i	$0.375875\pi$
$360$	−22.7975	−1.20153
$361$	−18.0953	−0.952383
$362$	−54.0639	−2.84154
$363$	−2.25064	−0.118128
$364$	30.6220	1.60503
$365$	21.4428	1.12237
$366$	−3.24684	−0.169715
$367$	18.8529	0.984112	0.492056	−	0.870563i	$-0.336245\pi$
$367$	18.8529	0.984112	0.492056	+	0.870563i	$0.336245\pi$
$368$	−6.68867	−0.348671
$369$	−17.6747	−0.920110
$370$	−13.6733	−0.710839
$371$	10.0439	0.521454
$372$	1.53327	0.0794963
$373$	−29.4885	−1.52685	−0.763427	−	0.645894i	$-0.776485\pi$
$373$	−29.4885	−1.52685	−0.763427	+	0.645894i	$0.776485\pi$
$374$	2.57126	0.132957
$375$	2.45806	0.126934
$376$	20.0161	1.03225
$377$	34.6937	1.78682
$378$	−4.76843	−0.245261
$379$	−7.47070	−0.383744	−0.191872	−	0.981420i	$-0.561456\pi$
$379$	−7.47070	−0.383744	−0.191872	+	0.981420i	$0.561456\pi$
$380$	5.42206	0.278146
$381$	1.68541	0.0863462
$382$	−39.0035	−1.99559
$383$	−9.42889	−0.481794	−0.240897	−	0.970551i	$-0.577442\pi$
$383$	−9.42889	−0.481794	−0.240897	+	0.970551i	$0.577442\pi$
$384$	3.37914	0.172441
$385$	−1.89170	−0.0964097
$386$	3.86628	0.196789
$387$	−6.82544	−0.346957
$388$	−8.36638	−0.424739
$389$	−25.6280	−1.29939	−0.649696	−	0.760194i	$-0.725104\pi$
$389$	−25.6280	−1.29939	−0.649696	+	0.760194i	$0.725104\pi$
$390$	−3.74975	−0.189876
$391$	−1.09105	−0.0551770
$392$	29.4949	1.48972
$393$	−0.0363475	−0.00183349
$394$	33.6010	1.69279
$395$	16.1126	0.810713
$396$	13.0618	0.656382
$397$	5.64709	0.283419	0.141710	−	0.989908i	$-0.454740\pi$
$397$	5.64709	0.283419	0.141710	+	0.989908i	$0.454740\pi$
$398$	38.9494	1.95236
$399$	0.302886	0.0151633
$400$	−20.0578	−1.00289
$401$	16.0817	0.803084	0.401542	−	0.915841i	$-0.368474\pi$
$401$	16.0817	0.803084	0.401542	+	0.915841i	$0.368474\pi$
$402$	2.64656	0.131998
$403$	−7.84157	−0.390616
$404$	−18.4118	−0.916020
$405$	−11.2303	−0.558039
$406$	−24.5413	−1.21796
$407$	4.22077	0.209216
$408$	−1.32932	−0.0658111
$409$	−25.8404	−1.27773	−0.638864	−	0.769320i	$-0.720595\pi$
$409$	−25.8404	−1.27773	−0.638864	+	0.769320i	$0.720595\pi$
$410$	19.8337	0.979515
$411$	−1.89350	−0.0933995
$412$	−80.0339	−3.94299
$413$	12.4966	0.614917
$414$	−8.09883	−0.398036
$415$	1.02939	0.0505309
$416$	18.3978	0.902027
$417$	−3.52607	−0.172673
$418$	−2.44570	−0.119623
$419$	15.6134	0.762764	0.381382	−	0.924418i	$-0.375448\pi$
$419$	15.6134	0.762764	0.381382	+	0.924418i	$0.375448\pi$
$420$	1.81522	0.0885739
$421$	27.8087	1.35531	0.677657	−	0.735378i	$-0.262996\pi$
$421$	27.8087	1.35531	0.677657	+	0.735378i	$0.262996\pi$
$422$	28.1795	1.37176
$423$	10.0371	0.488020
$424$	41.9285	2.03623
$425$	−3.27182	−0.158706
$426$	4.27286	0.207021
$427$	−8.03848	−0.389009
$428$	24.7050	1.19416
$429$	1.15750	0.0558848
$430$	7.65916	0.369357
$431$	10.1001	0.486503	0.243251	−	0.969963i	$-0.421786\pi$
$431$	10.1001	0.486503	0.243251	+	0.969963i	$0.421786\pi$
$432$	−8.24380	−0.396630
$433$	9.55758	0.459308	0.229654	−	0.973272i	$-0.426241\pi$
$433$	9.55758	0.459308	0.229654	+	0.973272i	$0.426241\pi$
$434$	5.54689	0.266259
$435$	2.05659	0.0986060
$436$	10.4951	0.502626
$437$	1.03777	0.0496435
$438$	9.28109	0.443467
$439$	−35.8363	−1.71037	−0.855186	−	0.518321i	$-0.826557\pi$
$439$	−35.8363	−1.71037	−0.855186	+	0.518321i	$0.826557\pi$
$440$	−7.89692	−0.376471
$441$	14.7902	0.704296
$442$	12.6186	0.600205
$443$	−18.8100	−0.893689	−0.446844	−	0.894612i	$-0.647452\pi$
$443$	−18.8100	−0.893689	−0.446844	+	0.894612i	$0.647452\pi$
$444$	−4.05015	−0.192212
$445$	8.73646	0.414148
$446$	10.2175	0.483811
$447$	3.05286	0.144396
$448$	4.25820	0.201181
$449$	6.28119	0.296428	0.148214	−	0.988955i	$-0.452648\pi$
$449$	6.28119	0.296428	0.148214	+	0.988955i	$0.452648\pi$
$450$	−24.2865	−1.14488
$451$	−6.12242	−0.288294
$452$	23.5516	1.10778
$453$	2.29010	0.107598
$454$	40.3062	1.89167
$455$	−9.28358	−0.435221
$456$	1.26440	0.0592111
$457$	−2.01982	−0.0944831	−0.0472415	−	0.998883i	$-0.515043\pi$
$457$	−2.01982	−0.0944831	−0.0472415	+	0.998883i	$0.515043\pi$
$458$	−29.8679	−1.39563
$459$	−1.34473	−0.0627665
$460$	6.21948	0.289985
$461$	12.4472	0.579725	0.289862	−	0.957068i	$-0.406390\pi$
$461$	12.4472	0.579725	0.289862	+	0.957068i	$0.406390\pi$
$462$	−0.818784	−0.0380933
$463$	26.2053	1.21786	0.608931	−	0.793223i	$-0.291598\pi$
$463$	26.2053	1.21786	0.608931	+	0.793223i	$0.291598\pi$
$464$	−42.4277	−1.96966
$465$	−0.464836	−0.0215563
$466$	−31.1754	−1.44417
$467$	−17.0538	−0.789156	−0.394578	−	0.918862i	$-0.629109\pi$
$467$	−17.0538	−0.789156	−0.394578	+	0.918862i	$0.629109\pi$
$468$	64.1015	2.96309
$469$	6.55231	0.302557
$470$	−11.2631	−0.519527
$471$	−0.284809	−0.0131233
$472$	52.1673	2.40119
$473$	−2.36429	−0.108710
$474$	6.97403	0.320328
$475$	3.11204	0.142790
$476$	−6.10856	−0.279985
$477$	21.0251	0.962672
$478$	−19.4590	−0.890032
$479$	6.48745	0.296419	0.148210	−	0.988956i	$-0.452649\pi$
$479$	6.48745	0.296419	0.148210	+	0.988956i	$0.452649\pi$
$480$	1.09059	0.0497786
$481$	20.7136	0.944460
$482$	20.1360	0.917168
$483$	0.347431	0.0158087
$484$	−43.1740	−1.96246
$485$	2.53641	0.115173
$486$	−15.0156	−0.681122
$487$	10.4743	0.474634	0.237317	−	0.971432i	$-0.423732\pi$
$487$	10.4743	0.474634	0.237317	+	0.971432i	$0.423732\pi$
$488$	−33.5568	−1.51904
$489$	−2.60937	−0.118000
$490$	−16.5968	−0.749767
$491$	−33.8748	−1.52875	−0.764375	−	0.644772i	$-0.776952\pi$
$491$	−33.8748	−1.52875	−0.764375	+	0.644772i	$0.776952\pi$
$492$	5.87493	0.264862
$493$	−6.92080	−0.311697
$494$	−12.0024	−0.540012
$495$	−3.95992	−0.177985
$496$	9.58963	0.430587
$497$	10.5787	0.474519
$498$	0.445553	0.0199657
$499$	15.7015	0.702896	0.351448	−	0.936207i	$-0.385689\pi$
$499$	15.7015	0.702896	0.351448	+	0.936207i	$0.385689\pi$
$500$	47.1529	2.10874
$501$	−5.19820	−0.232239
$502$	−30.7933	−1.37437
$503$	3.86430	0.172300	0.0861502	−	0.996282i	$-0.472543\pi$
$503$	3.86430	0.172300	0.0861502	+	0.996282i	$0.472543\pi$
$504$	−24.4297	−1.08819
$505$	5.58184	0.248389
$506$	−2.80539	−0.124715
$507$	2.74190	0.121772
$508$	32.3312	1.43446
$509$	34.2055	1.51613	0.758065	−	0.652179i	$-0.226145\pi$
$509$	34.2055	1.51613	0.758065	+	0.652179i	$0.226145\pi$
$510$	0.748010	0.0331224
$511$	22.9780	1.01649
$512$	49.6043	2.19222
$513$	1.27906	0.0564718
$514$	−10.1841	−0.449201
$515$	24.2636	1.06918
$516$	2.26872	0.0998747
$517$	3.47678	0.152909
$518$	−14.6522	−0.643780
$519$	4.78129	0.209875
$520$	−38.7545	−1.69950
$521$	33.6971	1.47629	0.738147	−	0.674640i	$-0.235701\pi$
$521$	33.6971	1.47629	0.738147	+	0.674640i	$0.235701\pi$
$522$	−51.3727	−2.24852
$523$	−25.8606	−1.13080	−0.565402	−	0.824815i	$-0.691279\pi$
$523$	−25.8606	−1.13080	−0.565402	+	0.824815i	$0.691279\pi$
$524$	−0.697253	−0.0304597
$525$	1.04187	0.0454707
$526$	21.0547	0.918030
$527$	1.56426	0.0681401
$528$	−1.41554	−0.0616033
$529$	−21.8096	−0.948244
$530$	−23.5932	−1.02482
$531$	26.1593	1.13522
$532$	5.81025	0.251906
$533$	−30.0460	−1.30144
$534$	3.78141	0.163637
$535$	−7.48975	−0.323810
$536$	27.3527	1.18146
$537$	5.03952	0.217471
$538$	20.0428	0.864105
$539$	5.12324	0.220674
$540$	7.66552	0.329871
$541$	−3.66888	−0.157737	−0.0788686	−	0.996885i	$-0.525131\pi$
$541$	−3.66888	−0.157737	−0.0788686	+	0.996885i	$0.525131\pi$
$542$	−34.2632	−1.47173
$543$	4.85500	0.208348
$544$	−3.67004	−0.157352
$545$	−3.18178	−0.136292
$546$	−4.01821	−0.171964
$547$	−23.6004	−1.00908	−0.504539	−	0.863389i	$-0.668338\pi$
$547$	−23.6004	−1.00908	−0.504539	+	0.863389i	$0.668338\pi$
$548$	−36.3230	−1.55164
$549$	−16.8271	−0.718162
$550$	−8.41270	−0.358719
$551$	6.58283	0.280438
$552$	1.45036	0.0617314
$553$	17.2662	0.734233
$554$	82.1295	3.48935
$555$	1.22787	0.0521203
$556$	−67.6405	−2.86860
$557$	−43.4823	−1.84241	−0.921203	−	0.389083i	$-0.872792\pi$
$557$	−43.4823	−1.84241	−0.921203	+	0.389083i	$0.872792\pi$
$558$	11.6114	0.491550
$559$	−11.6029	−0.490749
$560$	11.3531	0.479755
$561$	−0.230902	−0.00974869
$562$	−16.0953	−0.678937
$563$	−9.00718	−0.379607	−0.189804	−	0.981822i	$-0.560785\pi$
$563$	−9.00718	−0.379607	−0.189804	+	0.981822i	$0.560785\pi$
$564$	−3.33624	−0.140481
$565$	−7.14008	−0.300385
$566$	36.3776	1.52906
$567$	−12.0344	−0.505395
$568$	44.1609	1.85295
$569$	−0.164297	−0.00688770	−0.00344385	−	0.999994i	$-0.501096\pi$
$569$	−0.164297	−0.00688770	−0.00344385	+	0.999994i	$0.501096\pi$
$570$	−0.711482	−0.0298007
$571$	19.3848	0.811227	0.405614	−	0.914045i	$-0.367058\pi$
$571$	19.3848	0.811227	0.405614	+	0.914045i	$0.367058\pi$
$572$	22.2044	0.928411
$573$	3.50256	0.146321
$574$	21.2537	0.887111
$575$	3.56973	0.148868
$576$	8.91376	0.371407
$577$	6.27380	0.261182	0.130591	−	0.991436i	$-0.458313\pi$
$577$	6.27380	0.261182	0.130591	+	0.991436i	$0.458313\pi$
$578$	−2.51719	−0.104701
$579$	−0.347196	−0.0144290
$580$	39.4515	1.63814
$581$	1.10309	0.0457640
$582$	1.09784	0.0455068
$583$	7.28295	0.301629
$584$	95.9220	3.96928
$585$	−19.4335	−0.803475
$586$	−78.4439	−3.24049
$587$	11.9381	0.492738	0.246369	−	0.969176i	$-0.420762\pi$
$587$	11.9381	0.492738	0.246369	+	0.969176i	$0.420762\pi$
$588$	−4.91614	−0.202738
$589$	−1.48787	−0.0613066
$590$	−29.3546	−1.20851
$591$	−3.01741	−0.124120
$592$	−25.3311	−1.04110
$593$	−8.12303	−0.333573	−0.166786	−	0.985993i	$-0.553339\pi$
$593$	−8.12303	−0.333573	−0.166786	+	0.985993i	$0.553339\pi$
$594$	−3.45764	−0.141869
$595$	1.85191	0.0759210
$596$	58.5630	2.39883
$597$	−3.49770	−0.143151
$598$	−13.7676	−0.562997
$599$	−5.04744	−0.206233	−0.103116	−	0.994669i	$-0.532881\pi$
$599$	−5.04744	−0.206233	−0.103116	+	0.994669i	$0.532881\pi$
$600$	4.34929	0.177559
$601$	−5.72672	−0.233598	−0.116799	−	0.993156i	$-0.537263\pi$
$601$	−5.72672	−0.233598	−0.116799	+	0.993156i	$0.537263\pi$
$602$	8.20752	0.334513
$603$	13.7160	0.558561
$604$	43.9309	1.78752
$605$	13.0889	0.532141
$606$	2.41599	0.0981429
$607$	24.9072	1.01095	0.505476	−	0.862841i	$-0.331317\pi$
$607$	24.9072	1.01095	0.505476	+	0.862841i	$0.331317\pi$
$608$	3.49082	0.141572
$609$	2.20383	0.0893039
$610$	18.8825	0.764529
$611$	17.0625	0.690273
$612$	−12.7871	−0.516889
$613$	−7.54483	−0.304733	−0.152366	−	0.988324i	$-0.548689\pi$
$613$	−7.54483	−0.304733	−0.152366	+	0.988324i	$0.548689\pi$
$614$	−22.8225	−0.921042
$615$	−1.78108	−0.0718202
$616$	−8.46230	−0.340956
$617$	19.3009	0.777024	0.388512	−	0.921444i	$-0.372989\pi$
$617$	19.3009	0.777024	0.388512	+	0.921444i	$0.372989\pi$
$618$	10.5020	0.422454
$619$	29.1962	1.17350	0.586748	−	0.809770i	$-0.300408\pi$
$619$	29.1962	1.17350	0.586748	+	0.809770i	$0.300408\pi$
$620$	−8.91694	−0.358113
$621$	1.46717	0.0588755
$622$	−6.18700	−0.248076
$623$	9.36195	0.375079
$624$	−6.94681	−0.278095
$625$	2.06387	0.0825549
$626$	34.6630	1.38541
$627$	0.219626	0.00877103
$628$	−5.46348	−0.218016
$629$	−4.13201	−0.164754
$630$	13.7466	0.547679
$631$	30.3443	1.20799	0.603993	−	0.796990i	$-0.293575\pi$
$631$	30.3443	1.20799	0.603993	+	0.796990i	$0.293575\pi$
$632$	72.0781	2.86711
$633$	−2.53055	−0.100580
$634$	30.3346	1.20474
$635$	−9.80175	−0.388970
$636$	−6.98854	−0.277114
$637$	25.1425	0.996183
$638$	−17.7952	−0.704518
$639$	22.1445	0.876023
$640$	−19.6519	−0.776808
$641$	4.53817	0.179247	0.0896235	−	0.995976i	$-0.471434\pi$
$641$	4.53817	0.179247	0.0896235	+	0.995976i	$0.471434\pi$
$642$	−3.24179	−0.127943
$643$	−41.7656	−1.64707	−0.823536	−	0.567263i	$-0.808002\pi$
$643$	−41.7656	−1.64707	−0.823536	+	0.567263i	$0.808002\pi$
$644$	6.66477	0.262629
$645$	−0.687800	−0.0270821
$646$	2.39426	0.0942010
$647$	45.1787	1.77616	0.888079	−	0.459692i	$-0.152040\pi$
$647$	45.1787	1.77616	0.888079	+	0.459692i	$0.152040\pi$
$648$	−50.2376	−1.97352
$649$	9.06143	0.355692
$650$	−41.2857	−1.61936
$651$	−0.498117	−0.0195227
$652$	−50.0554	−1.96032
$653$	2.04722	0.0801138	0.0400569	−	0.999197i	$-0.487246\pi$
$653$	2.04722	0.0801138	0.0400569	+	0.999197i	$0.487246\pi$
$654$	−1.37717	−0.0538516
$655$	0.211384	0.00825947
$656$	36.7440	1.43461
$657$	48.1002	1.87657
$658$	−12.0695	−0.470517
$659$	27.6716	1.07793	0.538966	−	0.842328i	$-0.318815\pi$
$659$	27.6716	1.07793	0.538966	+	0.842328i	$0.318815\pi$
$660$	1.31624	0.0512346
$661$	−19.2316	−0.748022	−0.374011	−	0.927424i	$-0.622018\pi$
$661$	−19.2316	−0.748022	−0.374011	+	0.927424i	$0.622018\pi$
$662$	72.4620	2.81631
$663$	−1.13316	−0.0440083
$664$	4.60488	0.178704
$665$	−1.76148	−0.0683071
$666$	−30.6717	−1.18850
$667$	7.55097	0.292375
$668$	−99.7169	−3.85816
$669$	−0.917539	−0.0354741
$670$	−15.3914	−0.594623
$671$	−5.82880	−0.225018
$672$	1.16868	0.0450826
$673$	2.10297	0.0810635	0.0405317	−	0.999178i	$-0.487095\pi$
$673$	2.10297	0.0810635	0.0405317	+	0.999178i	$0.487095\pi$
$674$	−7.84820	−0.302301
$675$	4.39970	0.169344
$676$	52.5978	2.02299
$677$	−5.72501	−0.220030	−0.110015	−	0.993930i	$-0.535090\pi$
$677$	−5.72501	−0.220030	−0.110015	+	0.993930i	$0.535090\pi$
$678$	−3.09044	−0.118688
$679$	2.71801	0.104308
$680$	7.73085	0.296464
$681$	−3.61954	−0.138701
$682$	4.02212	0.154015
$683$	20.2773	0.775891	0.387945	−	0.921682i	$-0.373185\pi$
$683$	20.2773	0.775891	0.387945	+	0.921682i	$0.373185\pi$
$684$	12.1627	0.465052
$685$	11.0119	0.420744
$686$	−42.6072	−1.62675
$687$	2.68217	0.102331
$688$	14.1894	0.540965
$689$	35.7414	1.36164
$690$	−0.816120	−0.0310691
$691$	12.8820	0.490053	0.245027	−	0.969516i	$-0.421203\pi$
$691$	12.8820	0.490053	0.245027	+	0.969516i	$0.421203\pi$
$692$	91.7193	3.48664
$693$	−4.24343	−0.161195
$694$	21.8141	0.828051
$695$	20.5064	0.777852
$696$	9.19995	0.348723
$697$	5.99367	0.227026
$698$	−38.0699	−1.44097
$699$	2.79958	0.105890
$700$	19.9861	0.755403
$701$	4.33328	0.163666	0.0818328	−	0.996646i	$-0.473923\pi$
$701$	4.33328	0.163666	0.0818328	+	0.996646i	$0.473923\pi$
$702$	−16.9685	−0.640436
$703$	3.93023	0.148231
$704$	3.08767	0.116371
$705$	1.01144	0.0380929
$706$	2.51719	0.0947356
$707$	5.98148	0.224957
$708$	−8.69513	−0.326783
$709$	15.3229	0.575465	0.287733	−	0.957711i	$-0.407099\pi$
$709$	15.3229	0.575465	0.287733	+	0.957711i	$0.407099\pi$
$710$	−24.8494	−0.932582
$711$	36.1436	1.35549
$712$	39.0816	1.46465
$713$	−1.70669	−0.0639160
$714$	0.801564	0.0299978
$715$	−6.73163	−0.251749
$716$	96.6729	3.61284
$717$	1.74743	0.0652591
$718$	−36.2610	−1.35325
$719$	−42.0079	−1.56663	−0.783316	−	0.621624i	$-0.786473\pi$
$719$	−42.0079	−1.56663	−0.783316	+	0.621624i	$0.786473\pi$
$720$	23.7656	0.885691
$721$	26.0008	0.968320
$722$	45.5492	1.69517
$723$	−1.80823	−0.0672488
$724$	93.1332	3.46127
$725$	22.6436	0.840962
$726$	5.66530	0.210259
$727$	17.7469	0.658197	0.329099	−	0.944296i	$-0.393255\pi$
$727$	17.7469	0.658197	0.329099	+	0.944296i	$0.393255\pi$
$728$	−41.5291	−1.53917
$729$	−24.2798	−0.899252
$730$	−53.9755	−1.99772
$731$	2.31457	0.0856075
$732$	5.59317	0.206730
$733$	5.27157	0.194710	0.0973549	−	0.995250i	$-0.468962\pi$
$733$	5.27157	0.194710	0.0973549	+	0.995250i	$0.468962\pi$
$734$	−47.4562	−1.75164
$735$	1.49041	0.0549746
$736$	4.00422	0.147597
$737$	4.75115	0.175011
$738$	44.4906	1.63772
$739$	−10.9566	−0.403044	−0.201522	−	0.979484i	$-0.564589\pi$
$739$	−10.9566	−0.403044	−0.201522	+	0.979484i	$0.564589\pi$
$740$	23.5542	0.865871
$741$	1.07782	0.0395949
$742$	−25.2824	−0.928146
$743$	−18.5926	−0.682097	−0.341049	−	0.940046i	$-0.610782\pi$
$743$	−18.5926	−0.682097	−0.341049	+	0.940046i	$0.610782\pi$
$744$	−2.07940	−0.0762344
$745$	−17.7544	−0.650470
$746$	74.2280	2.71768
$747$	2.30912	0.0844863
$748$	−4.42939	−0.161954
$749$	−8.02598	−0.293263
$750$	−6.18740	−0.225932
$751$	−4.73229	−0.172684	−0.0863418	−	0.996266i	$-0.527518\pi$
$751$	−4.73229	−0.172684	−0.0863418	+	0.996266i	$0.527518\pi$
$752$	−20.8660	−0.760907
$753$	2.76527	0.100772
$754$	−87.3306	−3.18039
$755$	−13.3184	−0.484706
$756$	8.21434	0.298753
$757$	17.0694	0.620400	0.310200	−	0.950671i	$-0.399604\pi$
$757$	17.0694	0.620400	0.310200	+	0.950671i	$0.399604\pi$
$758$	18.8051	0.683034
$759$	0.251927	0.00914436
$760$	−7.35332	−0.266733
$761$	16.6592	0.603896	0.301948	−	0.953324i	$-0.402363\pi$
$761$	16.6592	0.603896	0.301948	+	0.953324i	$0.402363\pi$
$762$	−4.24249	−0.153689
$763$	−3.40958	−0.123435
$764$	67.1894	2.43083
$765$	3.87664	0.140160
$766$	23.7343	0.857555
$767$	44.4694	1.60570
$768$	−7.13937	−0.257620
$769$	1.59039	0.0573508	0.0286754	−	0.999589i	$-0.490871\pi$
$769$	1.59039	0.0573508	0.0286754	+	0.999589i	$0.490871\pi$
$770$	4.76175	0.171602
$771$	0.914541	0.0329364
$772$	−6.66026	−0.239708
$773$	−25.4927	−0.916907	−0.458454	−	0.888718i	$-0.651596\pi$
$773$	−25.4927	−0.916907	−0.458454	+	0.888718i	$0.651596\pi$
$774$	17.1809	0.617556
$775$	−5.11797	−0.183843
$776$	11.3464	0.407311
$777$	1.31578	0.0472034
$778$	64.5105	2.31281
$779$	−5.70097	−0.204259
$780$	6.45951	0.231288
$781$	7.67073	0.274480
$782$	2.74639	0.0982107
$783$	9.30658	0.332590
$784$	−30.7473	−1.09812
$785$	1.65635	0.0591175
$786$	0.0914936	0.00326347
$787$	−22.2458	−0.792979	−0.396489	−	0.918039i	$-0.629772\pi$
$787$	−22.2458	−0.792979	−0.396489	+	0.918039i	$0.629772\pi$
$788$	−57.8828	−2.06199
$789$	−1.89074	−0.0673121
$790$	−40.5585	−1.44301
$791$	−7.65127	−0.272048
$792$	−17.7143	−0.629449
$793$	−28.6051	−1.01580
$794$	−14.2148	−0.504464
$795$	2.11870	0.0751424
$796$	−67.0962	−2.37816
$797$	19.2321	0.681237	0.340618	−	0.940202i	$-0.389364\pi$
$797$	19.2321	0.681237	0.340618	+	0.940202i	$0.389364\pi$
$798$	−0.762421	−0.0269894
$799$	−3.40367	−0.120413
$800$	12.0077	0.424537
$801$	19.5975	0.692444
$802$	−40.4808	−1.42943
$803$	16.6616	0.587975
$804$	−4.55909	−0.160787
$805$	−2.02054	−0.0712146
$806$	19.7387	0.695266
$807$	−1.79986	−0.0633582
$808$	24.9698	0.878434
$809$	−3.99308	−0.140389	−0.0701946	−	0.997533i	$-0.522362\pi$
$809$	−3.99308	−0.140389	−0.0701946	+	0.997533i	$0.522362\pi$
$810$	28.2688	0.993265
$811$	−7.55121	−0.265159	−0.132579	−	0.991172i	$-0.542326\pi$
$811$	−7.55121	−0.265159	−0.132579	+	0.991172i	$0.542326\pi$
$812$	42.2761	1.48360
$813$	3.07687	0.107911
$814$	−10.6245	−0.372388
$815$	15.1752	0.531563
$816$	1.38577	0.0485116
$817$	−2.20154	−0.0770222
$818$	65.0452	2.27425
$819$	−20.8248	−0.727678
$820$	−34.1665	−1.19315
$821$	−32.7376	−1.14255	−0.571275	−	0.820759i	$-0.693551\pi$
$821$	−32.7376	−1.14255	−0.571275	+	0.820759i	$0.693551\pi$
$822$	4.76630	0.166244
$823$	28.0235	0.976837	0.488419	−	0.872609i	$-0.337574\pi$
$823$	28.0235	0.976837	0.488419	+	0.872609i	$0.337574\pi$
$824$	108.541	3.78120
$825$	0.755469	0.0263021
$826$	−31.4563	−1.09450
$827$	−8.65602	−0.300999	−0.150500	−	0.988610i	$-0.548088\pi$
$827$	−8.65602	−0.300999	−0.150500	+	0.988610i	$0.548088\pi$
$828$	13.9515	0.484847
$829$	10.5150	0.365201	0.182600	−	0.983187i	$-0.441549\pi$
$829$	10.5150	0.365201	0.182600	+	0.983187i	$0.441549\pi$
$830$	−2.59118	−0.0899410
$831$	−7.37531	−0.255847
$832$	15.1529	0.525331
$833$	−5.01550	−0.173777
$834$	8.87579	0.307343
$835$	30.2309	1.04618
$836$	4.21308	0.145712
$837$	−2.10350	−0.0727076
$838$	−39.3018	−1.35766
$839$	25.7370	0.888538	0.444269	−	0.895893i	$-0.353463\pi$
$839$	25.7370	0.888538	0.444269	+	0.895893i	$0.353463\pi$
$840$	−2.46178	−0.0849396
$841$	18.8974	0.651636
$842$	−69.9997	−2.41235
$843$	1.44537	0.0497812
$844$	−48.5435	−1.67093
$845$	−15.9459	−0.548556
$846$	−25.2652	−0.868636
$847$	14.0261	0.481941
$848$	−43.7089	−1.50097
$849$	−3.26674	−0.112114
$850$	8.23578	0.282485
$851$	4.50825	0.154541
$852$	−7.36064	−0.252171
$853$	−25.9860	−0.889744	−0.444872	−	0.895594i	$-0.646751\pi$
$853$	−25.9860	−0.889744	−0.444872	+	0.895594i	$0.646751\pi$
$854$	20.2344	0.692406
$855$	−3.68733	−0.126104
$856$	−33.5046	−1.14516
$857$	36.3072	1.24023	0.620114	−	0.784511i	$-0.287086\pi$
$857$	36.3072	1.24023	0.620114	+	0.784511i	$0.287086\pi$
$858$	−2.91366	−0.0994706
$859$	−44.1007	−1.50470	−0.752349	−	0.658765i	$-0.771079\pi$
$859$	−44.1007	−1.50470	−0.752349	+	0.658765i	$0.771079\pi$
$860$	−13.1940	−0.449913
$861$	−1.90860	−0.0650450
$862$	−25.4238	−0.865937
$863$	−9.87300	−0.336081	−0.168040	−	0.985780i	$-0.553744\pi$
$863$	−9.87300	−0.336081	−0.168040	+	0.985780i	$0.553744\pi$
$864$	4.93521	0.167899
$865$	−27.8063	−0.945441
$866$	−24.0582	−0.817532
$867$	0.226046	0.00767693
$868$	−9.55535	−0.324330
$869$	12.5199	0.424709
$870$	−5.17683	−0.175511
$871$	23.3165	0.790049
$872$	−14.2334	−0.482002
$873$	5.68965	0.192565
$874$	−2.61227	−0.0883614
$875$	−15.3187	−0.517866
$876$	−15.9881	−0.540187
$877$	47.9676	1.61975	0.809875	−	0.586603i	$-0.199535\pi$
$877$	47.9676	1.61975	0.809875	+	0.586603i	$0.199535\pi$
$878$	90.2067	3.04433
$879$	7.04435	0.237600
$880$	8.23226	0.277509
$881$	17.3149	0.583353	0.291677	−	0.956517i	$-0.405787\pi$
$881$	17.3149	0.583353	0.291677	+	0.956517i	$0.405787\pi$
$882$	−37.2298	−1.25359
$883$	37.5856	1.26486	0.632428	−	0.774619i	$-0.282058\pi$
$883$	37.5856	1.26486	0.632428	+	0.774619i	$0.282058\pi$
$884$	−21.7374	−0.731108
$885$	2.63608	0.0886107
$886$	47.3482	1.59069
$887$	−37.8419	−1.27061	−0.635303	−	0.772263i	$-0.719125\pi$
$887$	−37.8419	−1.27061	−0.635303	+	0.772263i	$0.719125\pi$
$888$	5.49276	0.184325
$889$	−10.5035	−0.352276
$890$	−21.9913	−0.737150
$891$	−8.72626	−0.292341
$892$	−17.6011	−0.589329
$893$	3.23745	0.108337
$894$	−7.68463	−0.257013
$895$	−29.3080	−0.979660
$896$	−21.0588	−0.703527
$897$	1.23634	0.0412802
$898$	−15.8109	−0.527618
$899$	−10.8259	−0.361064
$900$	41.8372	1.39457
$901$	−7.12979	−0.237528
$902$	15.4113	0.513140
$903$	−0.737044	−0.0245273
$904$	−31.9404	−1.06232
$905$	−28.2349	−0.938561
$906$	−5.76461	−0.191516
$907$	24.0021	0.796977	0.398488	−	0.917173i	$-0.369535\pi$
$907$	24.0021	0.796977	0.398488	+	0.917173i	$0.369535\pi$
$908$	−69.4336	−2.30423
$909$	12.5211	0.415299
$910$	23.3685	0.774658
$911$	45.7637	1.51622	0.758110	−	0.652127i	$-0.226123\pi$
$911$	45.7637	1.51622	0.758110	+	0.652127i	$0.226123\pi$
$912$	−1.31810	−0.0436465
$913$	0.799866	0.0264717
$914$	5.08426	0.168172
$915$	−1.69567	−0.0560570
$916$	51.4519	1.70002
$917$	0.226518	0.00748030
$918$	3.38493	0.111719
$919$	57.9941	1.91305	0.956524	−	0.291654i	$-0.0942054\pi$
$919$	57.9941	1.91305	0.956524	+	0.291654i	$0.0942054\pi$
$920$	−8.43477	−0.278086
$921$	2.04949	0.0675329
$922$	−31.3320	−1.03186
$923$	37.6444	1.23908
$924$	1.41048	0.0464013
$925$	13.5192	0.444508
$926$	−65.9636	−2.16770
$927$	54.4279	1.78765
$928$	25.3996	0.833784
$929$	−37.6625	−1.23567	−0.617833	−	0.786309i	$-0.711989\pi$
$929$	−37.6625	−1.23567	−0.617833	+	0.786309i	$0.711989\pi$
$930$	1.17008	0.0383685
$931$	4.77057	0.156349
$932$	53.7043	1.75914
$933$	0.555599	0.0181895
$934$	42.9276	1.40464
$935$	1.34284	0.0439157
$936$	−86.9336	−2.84151
$937$	−28.4965	−0.930940	−0.465470	−	0.885064i	$-0.654115\pi$
$937$	−28.4965	−0.930940	−0.465470	+	0.885064i	$0.654115\pi$
$938$	−16.4934	−0.538528
$939$	−3.11277	−0.101581
$940$	19.4024	0.632835
$941$	−7.13056	−0.232450	−0.116225	−	0.993223i	$-0.537079\pi$
$941$	−7.13056	−0.232450	−0.116225	+	0.993223i	$0.537079\pi$
$942$	0.716917	0.0233584
$943$	−6.53942	−0.212953
$944$	−54.3825	−1.77000
$945$	−2.49032	−0.0810100
$946$	5.95137	0.193496
$947$	−25.2752	−0.821333	−0.410667	−	0.911786i	$-0.634704\pi$
$947$	−25.2752	−0.821333	−0.410667	+	0.911786i	$0.634704\pi$
$948$	−12.0138	−0.390190
$949$	81.7675	2.65429
$950$	−7.83359	−0.254155
$951$	−2.72408	−0.0883343
$952$	8.28434	0.268497
$953$	−54.8068	−1.77537	−0.887684	−	0.460454i	$-0.847687\pi$
$953$	−54.8068	−1.77537	−0.887684	+	0.460454i	$0.847687\pi$
$954$	−52.9240	−1.71348
$955$	−20.3696	−0.659145
$956$	33.5210	1.08415
$957$	1.59803	0.0516569
$958$	−16.3301	−0.527602
$959$	11.8003	0.381053
$960$	0.898239	0.0289906
$961$	−28.5531	−0.921068
$962$	−52.1401	−1.68106
$963$	−16.8009	−0.541402
$964$	−34.6872	−1.11720
$965$	2.01917	0.0649994
$966$	−0.874550	−0.0281382
$967$	14.3275	0.460743	0.230371	−	0.973103i	$-0.426006\pi$
$967$	14.3275	0.460743	0.230371	+	0.973103i	$0.426006\pi$
$968$	58.5520	1.88193
$969$	−0.215007	−0.00690703
$970$	−6.38463	−0.204998
$971$	−45.7927	−1.46956	−0.734779	−	0.678306i	$-0.762714\pi$
$971$	−45.7927	−1.46956	−0.734779	+	0.678306i	$0.762714\pi$
$972$	25.8666	0.829673
$973$	21.9746	0.704472
$974$	−26.3657	−0.844811
$975$	3.70750	0.118735
$976$	34.9817	1.11974
$977$	46.5848	1.49038	0.745190	−	0.666852i	$-0.232359\pi$
$977$	46.5848	1.49038	0.745190	+	0.666852i	$0.232359\pi$
$978$	6.56827	0.210030
$979$	6.78846	0.216960
$980$	28.5905	0.913290
$981$	−7.13733	−0.227877
$982$	85.2693	2.72105
$983$	−5.91694	−0.188721	−0.0943605	−	0.995538i	$-0.530081\pi$
$983$	−5.91694	−0.188721	−0.0943605	+	0.995538i	$0.530081\pi$
$984$	−7.96749	−0.253994
$985$	17.5482	0.559131
$986$	17.4209	0.554796
$987$	1.08385	0.0344994
$988$	20.6759	0.657787
$989$	−2.52532	−0.0803006
$990$	9.96786	0.316799
$991$	62.2444	1.97726	0.988630	−	0.150369i	$-0.0480463\pi$
$991$	62.2444	1.97726	0.988630	+	0.150369i	$0.0480463\pi$
$992$	−5.74090	−0.182274
$993$	−6.50716	−0.206499
$994$	−26.6285	−0.844605
$995$	20.3414	0.644865
$996$	−0.767531	−0.0243202
$997$	−44.5025	−1.40941	−0.704704	−	0.709501i	$-0.748920\pi$
$997$	−44.5025	−1.40941	−0.704704	+	0.709501i	$0.748920\pi$
$998$	−39.5236	−1.25110
$999$	5.55642	0.175797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.8	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.8	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51719 q^{2} +0.226046 q^{3} +4.33623 q^{4} -1.31460 q^{5} -0.569001 q^{6} -1.40872 q^{7} -5.88074 q^{8} -2.94890 q^{9} +O(q^{10})\)	\(q-2.51719 q^{2} +0.226046 q^{3} +4.33623 q^{4} -1.31460 q^{5} -0.569001 q^{6} -1.40872 q^{7} -5.88074 q^{8} -2.94890 q^{9} +3.30910 q^{10} -1.02148 q^{11} +0.980189 q^{12} -5.01297 q^{13} +3.54602 q^{14} -0.297161 q^{15} +6.13046 q^{16} +1.00000 q^{17} +7.42294 q^{18} -0.951166 q^{19} -5.70043 q^{20} -0.318436 q^{21} +2.57126 q^{22} -1.09105 q^{23} -1.32932 q^{24} -3.27182 q^{25} +12.6186 q^{26} -1.34473 q^{27} -6.10856 q^{28} -6.92080 q^{29} +0.748010 q^{30} +1.56426 q^{31} -3.67004 q^{32} -0.230902 q^{33} -2.51719 q^{34} +1.85191 q^{35} -12.7871 q^{36} -4.13201 q^{37} +2.39426 q^{38} -1.13316 q^{39} +7.73085 q^{40} +5.99367 q^{41} +0.801564 q^{42} +2.31457 q^{43} -4.42939 q^{44} +3.87664 q^{45} +2.74639 q^{46} -3.40367 q^{47} +1.38577 q^{48} -5.01550 q^{49} +8.23578 q^{50} +0.226046 q^{51} -21.7374 q^{52} -7.12979 q^{53} +3.38493 q^{54} +1.34284 q^{55} +8.28434 q^{56} -0.215007 q^{57} +17.4209 q^{58} -8.87087 q^{59} -1.28856 q^{60} +5.70622 q^{61} -3.93753 q^{62} +4.15419 q^{63} -3.02274 q^{64} +6.59006 q^{65} +0.581224 q^{66} -4.65124 q^{67} +4.33623 q^{68} -0.246629 q^{69} -4.66161 q^{70} -7.50941 q^{71} +17.3417 q^{72} -16.3112 q^{73} +10.4010 q^{74} -0.739582 q^{75} -4.12448 q^{76} +1.43899 q^{77} +2.85238 q^{78} -12.2566 q^{79} -8.05913 q^{80} +8.54274 q^{81} -15.0872 q^{82} -0.783044 q^{83} -1.38082 q^{84} -1.31460 q^{85} -5.82621 q^{86} -1.56442 q^{87} +6.00707 q^{88} -6.64570 q^{89} -9.75823 q^{90} +7.06188 q^{91} -4.73107 q^{92} +0.353594 q^{93} +8.56767 q^{94} +1.25041 q^{95} -0.829599 q^{96} -1.92941 q^{97} +12.6250 q^{98} +3.01225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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