LMFDB - Embedded newform 6001.2.a.b.1.4

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:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.73023 q^{2} -3.10574 q^{3} +5.45415 q^{4} -3.71411 q^{5} +8.47938 q^{6} +1.88828 q^{7} -9.43061 q^{8} +6.64562 q^{9} +O(q^{10})$	\(q-2.73023 q^{2} -3.10574 q^{3} +5.45415 q^{4} -3.71411 q^{5} +8.47938 q^{6} +1.88828 q^{7} -9.43061 q^{8} +6.64562 q^{9} +10.1404 q^{10} +0.489363 q^{11} -16.9392 q^{12} +5.48712 q^{13} -5.15543 q^{14} +11.5351 q^{15} +14.8394 q^{16} +1.00000 q^{17} -18.1441 q^{18} -0.332704 q^{19} -20.2573 q^{20} -5.86450 q^{21} -1.33607 q^{22} +8.82357 q^{23} +29.2890 q^{24} +8.79459 q^{25} -14.9811 q^{26} -11.3223 q^{27} +10.2989 q^{28} +0.482276 q^{29} -31.4933 q^{30} -5.74916 q^{31} -21.6538 q^{32} -1.51984 q^{33} -2.73023 q^{34} -7.01326 q^{35} +36.2462 q^{36} +8.83875 q^{37} +0.908359 q^{38} -17.0416 q^{39} +35.0263 q^{40} -4.82872 q^{41} +16.0114 q^{42} +4.70608 q^{43} +2.66906 q^{44} -24.6825 q^{45} -24.0904 q^{46} -9.37780 q^{47} -46.0874 q^{48} -3.43441 q^{49} -24.0112 q^{50} -3.10574 q^{51} +29.9276 q^{52} +6.17027 q^{53} +30.9126 q^{54} -1.81755 q^{55} -17.8076 q^{56} +1.03329 q^{57} -1.31672 q^{58} +1.46121 q^{59} +62.9139 q^{60} -6.01970 q^{61} +15.6965 q^{62} +12.5488 q^{63} +29.4409 q^{64} -20.3798 q^{65} +4.14950 q^{66} +6.95743 q^{67} +5.45415 q^{68} -27.4037 q^{69} +19.1478 q^{70} -10.4009 q^{71} -62.6722 q^{72} -14.5071 q^{73} -24.1318 q^{74} -27.3137 q^{75} -1.81462 q^{76} +0.924054 q^{77} +46.5274 q^{78} +3.18488 q^{79} -55.1152 q^{80} +15.2274 q^{81} +13.1835 q^{82} -7.61897 q^{83} -31.9858 q^{84} -3.71411 q^{85} -12.8487 q^{86} -1.49782 q^{87} -4.61500 q^{88} -10.6162 q^{89} +67.3890 q^{90} +10.3612 q^{91} +48.1250 q^{92} +17.8554 q^{93} +25.6035 q^{94} +1.23570 q^{95} +67.2510 q^{96} -13.5666 q^{97} +9.37672 q^{98} +3.25212 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) $ 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * 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 $

$2$	−2.73023	−1.93056	−0.965281	−	0.261212i	$-0.915878\pi$
$2$	−2.73023	−1.93056	−0.965281	+	0.261212i	$0.915878\pi$
$3$	−3.10574	−1.79310	−0.896550	−	0.442943i	$-0.853934\pi$
$3$	−3.10574	−1.79310	−0.896550	+	0.442943i	$0.853934\pi$
$4$	5.45415	2.72707
$5$	−3.71411	−1.66100	−0.830500	−	0.557019i	$-0.811945\pi$
$5$	−3.71411	−1.66100	−0.830500	+	0.557019i	$0.811945\pi$
$6$	8.47938	3.46169
$7$	1.88828	0.713702	0.356851	−	0.934161i	$-0.383850\pi$
$7$	1.88828	0.713702	0.356851	+	0.934161i	$0.383850\pi$
$8$	−9.43061	−3.33422
$9$	6.64562	2.21521
$10$	10.1404	3.20666
$11$	0.489363	0.147549	0.0737743	−	0.997275i	$-0.476496\pi$
$11$	0.489363	0.147549	0.0737743	+	0.997275i	$0.476496\pi$
$12$	−16.9392	−4.88991
$13$	5.48712	1.52185	0.760927	−	0.648838i	$-0.224745\pi$
$13$	5.48712	1.52185	0.760927	+	0.648838i	$0.224745\pi$
$14$	−5.15543	−1.37785
$15$	11.5351	2.97834
$16$	14.8394	3.70986
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−18.1441	−4.27660
$19$	−0.332704	−0.0763276	−0.0381638	−	0.999271i	$-0.512151\pi$
$19$	−0.332704	−0.0763276	−0.0381638	+	0.999271i	$0.512151\pi$
$20$	−20.2573	−4.52967
$21$	−5.86450	−1.27974
$22$	−1.33607	−0.284852
$23$	8.82357	1.83984	0.919921	−	0.392104i	$-0.128253\pi$
$23$	8.82357	1.83984	0.919921	+	0.392104i	$0.128253\pi$
$24$	29.2890	5.97860
$25$	8.79459	1.75892
$26$	−14.9811	−2.93803
$27$	−11.3223	−2.17899
$28$	10.2989	1.94632
$29$	0.482276	0.0895564	0.0447782	−	0.998997i	$-0.485742\pi$
$29$	0.482276	0.0895564	0.0447782	+	0.998997i	$0.485742\pi$
$30$	−31.4933	−5.74987
$31$	−5.74916	−1.03258	−0.516290	−	0.856414i	$-0.672687\pi$
$31$	−5.74916	−1.03258	−0.516290	+	0.856414i	$0.672687\pi$
$32$	−21.6538	−3.82789
$33$	−1.51984	−0.264569
$34$	−2.73023	−0.468230
$35$	−7.01326	−1.18546
$36$	36.2462	6.04103
$37$	8.83875	1.45308	0.726541	−	0.687124i	$-0.241127\pi$
$37$	8.83875	1.45308	0.726541	+	0.687124i	$0.241127\pi$
$38$	0.908359	0.147355
$39$	−17.0416	−2.72883
$40$	35.0263	5.53814
$41$	−4.82872	−0.754120	−0.377060	−	0.926189i	$-0.623065\pi$
$41$	−4.82872	−0.754120	−0.377060	+	0.926189i	$0.623065\pi$
$42$	16.0114	2.47061
$43$	4.70608	0.717671	0.358836	−	0.933401i	$-0.383174\pi$
$43$	4.70608	0.717671	0.358836	+	0.933401i	$0.383174\pi$
$44$	2.66906	0.402376
$45$	−24.6825	−3.67946
$46$	−24.0904	−3.55193
$47$	−9.37780	−1.36789	−0.683947	−	0.729532i	$-0.739738\pi$
$47$	−9.37780	−1.36789	−0.683947	+	0.729532i	$0.739738\pi$
$48$	−46.0874	−6.65214
$49$	−3.43441	−0.490630
$50$	−24.0112	−3.39570
$51$	−3.10574	−0.434891
$52$	29.9276	4.15021
$53$	6.17027	0.847552	0.423776	−	0.905767i	$-0.360704\pi$
$53$	6.17027	0.847552	0.423776	+	0.905767i	$0.360704\pi$
$54$	30.9126	4.20667
$55$	−1.81755	−0.245078
$56$	−17.8076	−2.37964
$57$	1.03329	0.136863
$58$	−1.31672	−0.172894
$59$	1.46121	0.190234	0.0951170	−	0.995466i	$-0.469677\pi$
$59$	1.46121	0.190234	0.0951170	+	0.995466i	$0.469677\pi$
$60$	62.9139	8.12214
$61$	−6.01970	−0.770744	−0.385372	−	0.922761i	$-0.625927\pi$
$61$	−6.01970	−0.770744	−0.385372	+	0.922761i	$0.625927\pi$
$62$	15.6965	1.99346
$63$	12.5488	1.58100
$64$	29.4409	3.68012
$65$	−20.3798	−2.52780
$66$	4.14950	0.510768
$67$	6.95743	0.849986	0.424993	−	0.905197i	$-0.360277\pi$
$67$	6.95743	0.849986	0.424993	+	0.905197i	$0.360277\pi$
$68$	5.45415	0.661412
$69$	−27.4037	−3.29902
$70$	19.1478	2.28860
$71$	−10.4009	−1.23436	−0.617181	−	0.786821i	$-0.711726\pi$
$71$	−10.4009	−1.23436	−0.617181	+	0.786821i	$0.711726\pi$
$72$	−62.6722	−7.38599
$73$	−14.5071	−1.69793	−0.848963	−	0.528452i	$-0.822773\pi$
$73$	−14.5071	−1.69793	−0.848963	+	0.528452i	$0.822773\pi$
$74$	−24.1318	−2.80526
$75$	−27.3137	−3.15392
$76$	−1.81462	−0.208151
$77$	0.924054	0.105306
$78$	46.5274	5.26819
$79$	3.18488	0.358327	0.179163	−	0.983819i	$-0.442661\pi$
$79$	3.18488	0.358327	0.179163	+	0.983819i	$0.442661\pi$
$80$	−55.1152	−6.16207
$81$	15.2274	1.69193
$82$	13.1835	1.45588
$83$	−7.61897	−0.836290	−0.418145	−	0.908380i	$-0.637320\pi$
$83$	−7.61897	−0.836290	−0.418145	+	0.908380i	$0.637320\pi$
$84$	−31.9858	−3.48994
$85$	−3.71411	−0.402852
$86$	−12.8487	−1.38551
$87$	−1.49782	−0.160583
$88$	−4.61500	−0.491960
$89$	−10.6162	−1.12531	−0.562657	−	0.826690i	$-0.690221\pi$
$89$	−10.6162	−1.12531	−0.562657	+	0.826690i	$0.690221\pi$
$90$	67.3890	7.10342
$91$	10.3612	1.08615
$92$	48.1250	5.01738
$93$	17.8554	1.85152
$94$	25.6035	2.64080
$95$	1.23570	0.126780
$96$	67.2510	6.86378
$97$	−13.5666	−1.37747	−0.688737	−	0.725011i	$-0.741835\pi$
$97$	−13.5666	−1.37747	−0.688737	+	0.725011i	$0.741835\pi$
$98$	9.37672	0.947192
$99$	3.25212	0.326851
$100$	47.9670	4.79670
$101$	17.6559	1.75682	0.878412	−	0.477905i	$-0.158604\pi$
$101$	17.6559	1.75682	0.878412	+	0.477905i	$0.158604\pi$
$102$	8.47938	0.839584
$103$	5.54877	0.546737	0.273368	−	0.961909i	$-0.411862\pi$
$103$	5.54877	0.546737	0.273368	+	0.961909i	$0.411862\pi$
$104$	−51.7469	−5.07420
$105$	21.7814	2.12564
$106$	−16.8462	−1.63625
$107$	−6.62995	−0.640942	−0.320471	−	0.947258i	$-0.603841\pi$
$107$	−6.62995	−0.640942	−0.320471	+	0.947258i	$0.603841\pi$
$108$	−61.7537	−5.94225
$109$	3.56639	0.341598	0.170799	−	0.985306i	$-0.445365\pi$
$109$	3.56639	0.341598	0.170799	+	0.985306i	$0.445365\pi$
$110$	4.96232	0.473139
$111$	−27.4508	−2.60552
$112$	28.0209	2.64773
$113$	12.7847	1.20268	0.601341	−	0.798993i	$-0.294633\pi$
$113$	12.7847	1.20268	0.601341	+	0.798993i	$0.294633\pi$
$114$	−2.82113	−0.264223
$115$	−32.7717	−3.05598
$116$	2.63040	0.244227
$117$	36.4653	3.37122
$118$	−3.98945	−0.367259
$119$	1.88828	0.173098
$120$	−108.783	−9.93044
$121$	−10.7605	−0.978229
$122$	16.4352	1.48797
$123$	14.9968	1.35221
$124$	−31.3568	−2.81592
$125$	−14.0935	−1.26056
$126$	−34.2610	−3.05221
$127$	4.13427	0.366857	0.183428	−	0.983033i	$-0.441280\pi$
$127$	4.13427	0.366857	0.183428	+	0.983033i	$0.441280\pi$
$128$	−37.0729	−3.27682
$129$	−14.6159	−1.28686
$130$	55.6414	4.88007
$131$	−2.51700	−0.219911	−0.109956	−	0.993937i	$-0.535071\pi$
$131$	−2.51700	−0.219911	−0.109956	+	0.993937i	$0.535071\pi$
$132$	−8.28941	−0.721500
$133$	−0.628238	−0.0544751
$134$	−18.9954	−1.64095
$135$	42.0524	3.61929
$136$	−9.43061	−0.808668
$137$	−4.34490	−0.371210	−0.185605	−	0.982624i	$-0.559424\pi$
$137$	−4.34490	−0.371210	−0.185605	+	0.982624i	$0.559424\pi$
$138$	74.8184	6.36896
$139$	−14.4175	−1.22287	−0.611437	−	0.791293i	$-0.709408\pi$
$139$	−14.4175	−1.22287	−0.611437	+	0.791293i	$0.709408\pi$
$140$	−38.2514	−3.23283
$141$	29.1250	2.45277
$142$	28.3969	2.38302
$143$	2.68520	0.224547
$144$	98.6171	8.21810
$145$	−1.79122	−0.148753
$146$	39.6077	3.27795
$147$	10.6664	0.879748
$148$	48.2078	3.96266
$149$	8.91601	0.730428	0.365214	−	0.930924i	$-0.380996\pi$
$149$	8.91601	0.730428	0.365214	+	0.930924i	$0.380996\pi$
$150$	74.5727	6.08883
$151$	−23.3970	−1.90402	−0.952012	−	0.306062i	$-0.900988\pi$
$151$	−23.3970	−1.90402	−0.952012	+	0.306062i	$0.900988\pi$
$152$	3.13760	0.254493
$153$	6.64562	0.537266
$154$	−2.52288	−0.203299
$155$	21.3530	1.71511
$156$	−92.9472	−7.44173
$157$	−7.57057	−0.604197	−0.302098	−	0.953277i	$-0.597687\pi$
$157$	−7.57057	−0.604197	−0.302098	+	0.953277i	$0.597687\pi$
$158$	−8.69545	−0.691773
$159$	−19.1633	−1.51974
$160$	80.4245	6.35812
$161$	16.6613	1.31310
$162$	−41.5743	−3.26638
$163$	−22.9019	−1.79381	−0.896907	−	0.442219i	$-0.854192\pi$
$163$	−22.9019	−1.79381	−0.896907	+	0.442219i	$0.854192\pi$
$164$	−26.3366	−2.05654
$165$	5.64483	0.439450
$166$	20.8015	1.61451
$167$	−5.06068	−0.391607	−0.195803	−	0.980643i	$-0.562731\pi$
$167$	−5.06068	−0.391607	−0.195803	+	0.980643i	$0.562731\pi$
$168$	55.3058	4.26693
$169$	17.1085	1.31604
$170$	10.1404	0.777730
$171$	−2.21103	−0.169081
$172$	25.6677	1.95714
$173$	14.9806	1.13895	0.569477	−	0.822007i	$-0.307146\pi$
$173$	14.9806	1.13895	0.569477	+	0.822007i	$0.307146\pi$
$174$	4.08940	0.310017
$175$	16.6066	1.25534
$176$	7.26187	0.547384
$177$	−4.53815	−0.341108
$178$	28.9846	2.17249
$179$	−2.28495	−0.170785	−0.0853924	−	0.996347i	$-0.527214\pi$
$179$	−2.28495	−0.170785	−0.0853924	+	0.996347i	$0.527214\pi$
$180$	−134.622	−10.0341
$181$	−9.98093	−0.741877	−0.370938	−	0.928657i	$-0.620964\pi$
$181$	−9.98093	−0.741877	−0.370938	+	0.928657i	$0.620964\pi$
$182$	−28.2885	−2.09688
$183$	18.6956	1.38202
$184$	−83.2116	−6.13444
$185$	−32.8281	−2.41357
$186$	−48.7493	−3.57447
$187$	0.489363	0.0357858
$188$	−51.1479	−3.73035
$189$	−21.3797	−1.55515
$190$	−3.37374	−0.244757
$191$	9.37472	0.678331	0.339166	−	0.940727i	$-0.389855\pi$
$191$	9.37472	0.678331	0.339166	+	0.940727i	$0.389855\pi$
$192$	−91.4359	−6.59882
$193$	−3.57459	−0.257305	−0.128652	−	0.991690i	$-0.541065\pi$
$193$	−3.57459	−0.257305	−0.128652	+	0.991690i	$0.541065\pi$
$194$	37.0398	2.65930
$195$	63.2942	4.53259
$196$	−18.7318	−1.33798
$197$	−3.72825	−0.265627	−0.132814	−	0.991141i	$-0.542401\pi$
$197$	−3.72825	−0.265627	−0.132814	+	0.991141i	$0.542401\pi$
$198$	−8.87904	−0.631006
$199$	16.2589	1.15257	0.576283	−	0.817250i	$-0.304503\pi$
$199$	16.2589	1.15257	0.576283	+	0.817250i	$0.304503\pi$
$200$	−82.9384	−5.86463
$201$	−21.6080	−1.52411
$202$	−48.2045	−3.39166
$203$	0.910670	0.0639165
$204$	−16.9392	−1.18598
$205$	17.9344	1.25259
$206$	−15.1494	−1.05551
$207$	58.6381	4.07563
$208$	81.4257	5.64586
$209$	−0.162813	−0.0112620
$210$	−59.4681	−4.10369
$211$	−17.6162	−1.21275	−0.606375	−	0.795179i	$-0.707377\pi$
$211$	−17.6162	−1.21275	−0.606375	+	0.795179i	$0.707377\pi$
$212$	33.6536	2.31134
$213$	32.3026	2.21334
$214$	18.1013	1.23738
$215$	−17.4789	−1.19205
$216$	106.777	7.26523
$217$	−10.8560	−0.736954
$218$	−9.73705	−0.659476
$219$	45.0552	3.04455
$220$	−9.91318	−0.668346
$221$	5.48712	0.369104
$222$	74.9471	5.03012
$223$	21.3039	1.42662	0.713308	−	0.700851i	$-0.247196\pi$
$223$	21.3039	1.42662	0.713308	+	0.700851i	$0.247196\pi$
$224$	−40.8884	−2.73197
$225$	58.4455	3.89637
$226$	−34.9051	−2.32185
$227$	−23.3592	−1.55040	−0.775201	−	0.631715i	$-0.782351\pi$
$227$	−23.3592	−1.55040	−0.775201	+	0.631715i	$0.782351\pi$
$228$	5.63573	0.373236
$229$	24.0406	1.58865	0.794324	−	0.607494i	$-0.207825\pi$
$229$	24.0406	1.58865	0.794324	+	0.607494i	$0.207825\pi$
$230$	89.4742	5.89975
$231$	−2.86987	−0.188824
$232$	−4.54815	−0.298601
$233$	24.7168	1.61925	0.809626	−	0.586946i	$-0.199670\pi$
$233$	24.7168	1.61925	0.809626	+	0.586946i	$0.199670\pi$
$234$	−99.5586	−6.50835
$235$	34.8302	2.27207
$236$	7.96968	0.518782
$237$	−9.89141	−0.642516
$238$	−5.15543	−0.334177
$239$	15.3728	0.994386	0.497193	−	0.867640i	$-0.334364\pi$
$239$	15.3728	0.994386	0.497193	+	0.867640i	$0.334364\pi$
$240$	171.173	11.0492
$241$	−2.36423	−0.152294	−0.0761468	−	0.997097i	$-0.524262\pi$
$241$	−2.36423	−0.152294	−0.0761468	+	0.997097i	$0.524262\pi$
$242$	29.3787	1.88853
$243$	−13.3253	−0.854818
$244$	−32.8323	−2.10187
$245$	12.7558	0.814936
$246$	−40.9446	−2.61053
$247$	−1.82559	−0.116159
$248$	54.2181	3.44285
$249$	23.6625	1.49955
$250$	38.4785	2.43360
$251$	−4.03403	−0.254626	−0.127313	−	0.991863i	$-0.540635\pi$
$251$	−4.03403	−0.254626	−0.127313	+	0.991863i	$0.540635\pi$
$252$	68.4428	4.31149
$253$	4.31793	0.271466
$254$	−11.2875	−0.708240
$255$	11.5351	0.722353
$256$	42.3357	2.64598
$257$	−20.6869	−1.29041	−0.645207	−	0.764008i	$-0.723229\pi$
$257$	−20.6869	−1.29041	−0.645207	+	0.764008i	$0.723229\pi$
$258$	39.9047	2.48436
$259$	16.6900	1.03707
$260$	−111.154	−6.89349
$261$	3.20502	0.198386
$262$	6.87198	0.424552
$263$	4.81240	0.296745	0.148373	−	0.988932i	$-0.452597\pi$
$263$	4.81240	0.296745	0.148373	+	0.988932i	$0.452597\pi$
$264$	14.3330	0.882134
$265$	−22.9170	−1.40778
$266$	1.71523	0.105168
$267$	32.9711	2.01780
$268$	37.9469	2.31797
$269$	−21.4166	−1.30579	−0.652896	−	0.757448i	$-0.726446\pi$
$269$	−21.4166	−1.30579	−0.652896	+	0.757448i	$0.726446\pi$
$270$	−114.813	−6.98728
$271$	9.59117	0.582622	0.291311	−	0.956628i	$-0.405908\pi$
$271$	9.59117	0.582622	0.291311	+	0.956628i	$0.405908\pi$
$272$	14.8394	0.899772
$273$	−32.1792	−1.94757
$274$	11.8626	0.716644
$275$	4.30375	0.259526
$276$	−149.464	−8.99667
$277$	25.2227	1.51549	0.757744	−	0.652552i	$-0.226302\pi$
$277$	25.2227	1.51549	0.757744	+	0.652552i	$0.226302\pi$
$278$	39.3630	2.36084
$279$	−38.2067	−2.28738
$280$	66.1393	3.95258
$281$	−28.2834	−1.68725	−0.843623	−	0.536935i	$-0.819582\pi$
$281$	−28.2834	−1.68725	−0.843623	+	0.536935i	$0.819582\pi$
$282$	−79.5179	−4.73523
$283$	−6.79798	−0.404098	−0.202049	−	0.979375i	$-0.564760\pi$
$283$	−6.79798	−0.404098	−0.202049	+	0.979375i	$0.564760\pi$
$284$	−56.7282	−3.36620
$285$	−3.83776	−0.227329
$286$	−7.33120	−0.433503
$287$	−9.11797	−0.538217
$288$	−143.903	−8.47956
$289$	1.00000	0.0588235
$290$	4.89045	0.287177
$291$	42.1342	2.46995
$292$	−79.1238	−4.63037
$293$	25.8654	1.51107	0.755536	−	0.655107i	$-0.227376\pi$
$293$	25.8654	1.51107	0.755536	+	0.655107i	$0.227376\pi$
$294$	−29.1217	−1.69841
$295$	−5.42711	−0.315978
$296$	−83.3548	−4.84490
$297$	−5.54074	−0.321506
$298$	−24.3427	−1.41014
$299$	48.4160	2.79997
$300$	−148.973	−8.60096
$301$	8.88639	0.512203
$302$	63.8792	3.67584
$303$	−54.8345	−3.15016
$304$	−4.93714	−0.283164
$305$	22.3578	1.28020
$306$	−18.1441	−1.03723
$307$	−2.79061	−0.159268	−0.0796342	−	0.996824i	$-0.525375\pi$
$307$	−2.79061	−0.159268	−0.0796342	+	0.996824i	$0.525375\pi$
$308$	5.03992	0.287176
$309$	−17.2330	−0.980353
$310$	−58.2986	−3.31114
$311$	15.4616	0.876749	0.438375	−	0.898792i	$-0.355554\pi$
$311$	15.4616	0.876749	0.438375	+	0.898792i	$0.355554\pi$
$312$	160.712	9.09855
$313$	−15.3716	−0.868851	−0.434426	−	0.900708i	$-0.643049\pi$
$313$	−15.3716	−0.868851	−0.434426	+	0.900708i	$0.643049\pi$
$314$	20.6694	1.16644
$315$	−46.6075	−2.62603
$316$	17.3708	0.977184
$317$	8.42410	0.473145	0.236572	−	0.971614i	$-0.423976\pi$
$317$	8.42410	0.473145	0.236572	+	0.971614i	$0.423976\pi$
$318$	52.3201	2.93396
$319$	0.236008	0.0132139
$320$	−109.347	−6.11267
$321$	20.5909	1.14927
$322$	−45.4893	−2.53502
$323$	−0.332704	−0.0185122
$324$	83.0524	4.61402
$325$	48.2570	2.67682
$326$	62.5274	3.46307
$327$	−11.0763	−0.612519
$328$	45.5378	2.51440
$329$	−17.7079	−0.976268
$330$	−15.4117	−0.848385
$331$	−0.912109	−0.0501341	−0.0250670	−	0.999686i	$-0.507980\pi$
$331$	−0.912109	−0.0501341	−0.0250670	+	0.999686i	$0.507980\pi$
$332$	−41.5550	−2.28062
$333$	58.7390	3.21887
$334$	13.8168	0.756022
$335$	−25.8407	−1.41183
$336$	−87.0257	−4.74764
$337$	4.59478	0.250294	0.125147	−	0.992138i	$-0.460060\pi$
$337$	4.59478	0.250294	0.125147	+	0.992138i	$0.460060\pi$
$338$	−46.7101	−2.54069
$339$	−39.7059	−2.15653
$340$	−20.2573	−1.09861
$341$	−2.81343	−0.152356
$342$	6.03661	0.326422
$343$	−19.7031	−1.06387
$344$	−44.3812	−2.39288
$345$	101.780	5.47967
$346$	−40.9004	−2.19882
$347$	−25.7120	−1.38029	−0.690147	−	0.723669i	$-0.742454\pi$
$347$	−25.7120	−1.38029	−0.690147	+	0.723669i	$0.742454\pi$
$348$	−8.16935	−0.437923
$349$	−17.9258	−0.959544	−0.479772	−	0.877393i	$-0.659281\pi$
$349$	−17.9258	−0.959544	−0.479772	+	0.877393i	$0.659281\pi$
$350$	−45.3399	−2.42352
$351$	−62.1271	−3.31610
$352$	−10.5966	−0.564799
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	12.3902	0.658531
$355$	38.6302	2.05028
$356$	−57.9023	−3.06881
$357$	−5.86450	−0.310382
$358$	6.23842	0.329711
$359$	−1.81147	−0.0956059	−0.0478029	−	0.998857i	$-0.515222\pi$
$359$	−1.81147	−0.0956059	−0.0478029	+	0.998857i	$0.515222\pi$
$360$	232.771	12.2681
$361$	−18.8893	−0.994174
$362$	27.2502	1.43224
$363$	33.4194	1.75406
$364$	56.5115	2.96201
$365$	53.8809	2.82025
$366$	−51.0433	−2.66808
$367$	−16.0234	−0.836416	−0.418208	−	0.908351i	$-0.637342\pi$
$367$	−16.0234	−0.836416	−0.418208	+	0.908351i	$0.637342\pi$
$368$	130.937	6.82555
$369$	−32.0899	−1.67053
$370$	89.6281	4.65954
$371$	11.6512	0.604899
$372$	97.3860	5.04923
$373$	26.3507	1.36439	0.682194	−	0.731171i	$-0.261026\pi$
$373$	26.3507	1.36439	0.682194	+	0.731171i	$0.261026\pi$
$374$	−1.33607	−0.0690867
$375$	43.7708	2.26032
$376$	88.4384	4.56086
$377$	2.64631	0.136292
$378$	58.3715	3.00231
$379$	17.1585	0.881374	0.440687	−	0.897661i	$-0.354735\pi$
$379$	17.1585	0.881374	0.440687	+	0.897661i	$0.354735\pi$
$380$	6.73969	0.345739
$381$	−12.8400	−0.657811
$382$	−25.5951	−1.30956
$383$	−24.1693	−1.23499	−0.617497	−	0.786574i	$-0.711853\pi$
$383$	−24.1693	−1.23499	−0.617497	+	0.786574i	$0.711853\pi$
$384$	115.139	5.87566
$385$	−3.43203	−0.174913
$386$	9.75946	0.496743
$387$	31.2748	1.58979
$388$	−73.9940	−3.75647
$389$	−38.4853	−1.95128	−0.975640	−	0.219378i	$-0.929597\pi$
$389$	−38.4853	−1.95128	−0.975640	+	0.219378i	$0.929597\pi$
$390$	−172.808	−8.75046
$391$	8.82357	0.446227
$392$	32.3886	1.63587
$393$	7.81714	0.394323
$394$	10.1790	0.512810
$395$	−11.8290	−0.595181
$396$	17.7376	0.891346
$397$	18.6066	0.933839	0.466919	−	0.884300i	$-0.345364\pi$
$397$	18.6066	0.933839	0.466919	+	0.884300i	$0.345364\pi$
$398$	−44.3906	−2.22510
$399$	1.95114	0.0976794
$400$	130.507	6.52533
$401$	−34.1431	−1.70503	−0.852513	−	0.522706i	$-0.824922\pi$
$401$	−34.1431	−1.70503	−0.852513	+	0.522706i	$0.824922\pi$
$402$	58.9947	2.94239
$403$	−31.5464	−1.57144
$404$	96.2976	4.79099
$405$	−56.5562	−2.81030
$406$	−2.48634	−0.123395
$407$	4.32536	0.214400
$408$	29.2890	1.45002
$409$	−17.0858	−0.844838	−0.422419	−	0.906401i	$-0.638819\pi$
$409$	−17.0858	−0.844838	−0.422419	+	0.906401i	$0.638819\pi$
$410$	−48.9650	−2.41821
$411$	13.4941	0.665616
$412$	30.2638	1.49099
$413$	2.75918	0.135770
$414$	−160.095	−7.86826
$415$	28.2977	1.38908
$416$	−118.817	−5.82548
$417$	44.7769	2.19274
$418$	0.444518	0.0217421
$419$	18.4805	0.902831	0.451415	−	0.892314i	$-0.350919\pi$
$419$	18.4805	0.902831	0.451415	+	0.892314i	$0.350919\pi$
$420$	118.799	5.79679
$421$	−33.3756	−1.62663	−0.813314	−	0.581825i	$-0.802339\pi$
$421$	−33.3756	−1.62663	−0.813314	+	0.581825i	$0.802339\pi$
$422$	48.0963	2.34129
$423$	−62.3213	−3.03017
$424$	−58.1894	−2.82593
$425$	8.79459	0.426600
$426$	−88.1934	−4.27298
$427$	−11.3669	−0.550081
$428$	−36.1607	−1.74789
$429$	−8.33952	−0.402636
$430$	47.7214	2.30133
$431$	31.4371	1.51427	0.757135	−	0.653259i	$-0.226599\pi$
$431$	31.4371	1.51427	0.757135	+	0.653259i	$0.226599\pi$
$432$	−168.017	−8.08372
$433$	39.5437	1.90035	0.950175	−	0.311716i	$-0.100904\pi$
$433$	39.5437	1.90035	0.950175	+	0.311716i	$0.100904\pi$
$434$	29.6394	1.42274
$435$	5.56308	0.266729
$436$	19.4516	0.931562
$437$	−2.93564	−0.140431
$438$	−123.011	−5.87770
$439$	−12.6570	−0.604084	−0.302042	−	0.953295i	$-0.597668\pi$
$439$	−12.6570	−0.604084	−0.302042	+	0.953295i	$0.597668\pi$
$440$	17.1406	0.817145
$441$	−22.8238	−1.08685
$442$	−14.9811	−0.712578
$443$	−7.99741	−0.379968	−0.189984	−	0.981787i	$-0.560844\pi$
$443$	−7.99741	−0.379968	−0.189984	+	0.981787i	$0.560844\pi$
$444$	−149.721	−7.10544
$445$	39.4297	1.86915
$446$	−58.1646	−2.75417
$447$	−27.6908	−1.30973
$448$	55.5927	2.62651
$449$	−2.48995	−0.117508	−0.0587541	−	0.998272i	$-0.518713\pi$
$449$	−2.48995	−0.117508	−0.0587541	+	0.998272i	$0.518713\pi$
$450$	−159.570	−7.52218
$451$	−2.36300	−0.111269
$452$	69.7295	3.27980
$453$	72.6651	3.41410
$454$	63.7758	2.99315
$455$	−38.4826	−1.80409
$456$	−9.74458	−0.456332
$457$	1.67177	0.0782022	0.0391011	−	0.999235i	$-0.487551\pi$
$457$	1.67177	0.0782022	0.0391011	+	0.999235i	$0.487551\pi$
$458$	−65.6364	−3.06699
$459$	−11.3223	−0.528482
$460$	−178.742	−8.33387
$461$	−7.96759	−0.371088	−0.185544	−	0.982636i	$-0.559405\pi$
$461$	−7.96759	−0.371088	−0.185544	+	0.982636i	$0.559405\pi$
$462$	7.83540	0.364536
$463$	−3.44446	−0.160078	−0.0800389	−	0.996792i	$-0.525504\pi$
$463$	−3.44446	−0.160078	−0.0800389	+	0.996792i	$0.525504\pi$
$464$	7.15669	0.332241
$465$	−66.3169	−3.07537
$466$	−67.4825	−3.12607
$467$	−19.0809	−0.882960	−0.441480	−	0.897271i	$-0.645546\pi$
$467$	−19.0809	−0.882960	−0.441480	+	0.897271i	$0.645546\pi$
$468$	198.887	9.19356
$469$	13.1376	0.606636
$470$	−95.0943	−4.38637
$471$	23.5122	1.08339
$472$	−13.7801	−0.634283
$473$	2.30299	0.105891
$474$	27.0058	1.24042
$475$	−2.92600	−0.134254
$476$	10.2989	0.472051
$477$	41.0053	1.87750
$478$	−41.9714	−1.91973
$479$	−0.317062	−0.0144869	−0.00724346	−	0.999974i	$-0.502306\pi$
$479$	−0.317062	−0.0144869	−0.00724346	+	0.999974i	$0.502306\pi$
$480$	−249.778	−11.4007
$481$	48.4993	2.21138
$482$	6.45490	0.294013
$483$	−51.7458	−2.35452
$484$	−58.6895	−2.66770
$485$	50.3876	2.28798
$486$	36.3811	1.65028
$487$	−36.3431	−1.64686	−0.823431	−	0.567416i	$-0.807943\pi$
$487$	−36.3431	−1.64686	−0.823431	+	0.567416i	$0.807943\pi$
$488$	56.7694	2.56983
$489$	71.1273	3.21649
$490$	−34.8262	−1.57329
$491$	23.0676	1.04103	0.520514	−	0.853853i	$-0.325740\pi$
$491$	23.0676	1.04103	0.520514	+	0.853853i	$0.325740\pi$
$492$	81.7945	3.68758
$493$	0.482276	0.0217206
$494$	4.98427	0.224253
$495$	−12.0787	−0.542899
$496$	−85.3143	−3.83072
$497$	−19.6398	−0.880967
$498$	−64.6041	−2.89498
$499$	35.8699	1.60576	0.802879	−	0.596142i	$-0.203300\pi$
$499$	35.8699	1.60576	0.802879	+	0.596142i	$0.203300\pi$
$500$	−76.8682	−3.43765
$501$	15.7171	0.702190
$502$	11.0138	0.491571
$503$	−12.3750	−0.551776	−0.275888	−	0.961190i	$-0.588972\pi$
$503$	−12.3750	−0.551776	−0.275888	+	0.961190i	$0.588972\pi$
$504$	−118.343	−5.27140
$505$	−65.5758	−2.91808
$506$	−11.7889	−0.524082
$507$	−53.1345	−2.35979
$508$	22.5489	1.00045
$509$	−22.9858	−1.01883	−0.509414	−	0.860522i	$-0.670138\pi$
$509$	−22.9858	−1.01883	−0.509414	+	0.860522i	$0.670138\pi$
$510$	−31.4933	−1.39455
$511$	−27.3934	−1.21181
$512$	−41.4402	−1.83141
$513$	3.76699	0.166317
$514$	56.4800	2.49123
$515$	−20.6087	−0.908129
$516$	−79.7171	−3.50935
$517$	−4.58915	−0.201831
$518$	−45.5675	−2.00212
$519$	−46.5258	−2.04226
$520$	192.193	8.42824
$521$	−2.92055	−0.127952	−0.0639758	−	0.997951i	$-0.520378\pi$
$521$	−2.92055	−0.127952	−0.0639758	+	0.997951i	$0.520378\pi$
$522$	−8.75044	−0.382996
$523$	−9.77817	−0.427569	−0.213785	−	0.976881i	$-0.568579\pi$
$523$	−9.77817	−0.427569	−0.213785	+	0.976881i	$0.568579\pi$
$524$	−13.7281	−0.599714
$525$	−51.5759	−2.25096
$526$	−13.1389	−0.572885
$527$	−5.74916	−0.250437
$528$	−22.5535	−0.981514
$529$	54.8554	2.38502
$530$	62.5688	2.71781
$531$	9.71068	0.421408
$532$	−3.42650	−0.148558
$533$	−26.4958	−1.14766
$534$	−90.0187	−3.89549
$535$	24.6244	1.06460
$536$	−65.6128	−2.83404
$537$	7.09645	0.306234
$538$	58.4721	2.52091
$539$	−1.68067	−0.0723918
$540$	229.360	9.87008
$541$	−5.62524	−0.241848	−0.120924	−	0.992662i	$-0.538586\pi$
$541$	−5.62524	−0.241848	−0.120924	+	0.992662i	$0.538586\pi$
$542$	−26.1861	−1.12479
$543$	30.9982	1.33026
$544$	−21.6538	−0.928399
$545$	−13.2459	−0.567394
$546$	87.8566	3.75991
$547$	−19.7322	−0.843686	−0.421843	−	0.906669i	$-0.638617\pi$
$547$	−19.7322	−0.843686	−0.421843	+	0.906669i	$0.638617\pi$
$548$	−23.6977	−1.01232
$549$	−40.0046	−1.70736
$550$	−11.7502	−0.501031
$551$	−0.160455	−0.00683562
$552$	258.434	10.9997
$553$	6.01393	0.255739
$554$	−68.8638	−2.92574
$555$	101.955	4.32777
$556$	−78.6350	−3.33487
$557$	27.0923	1.14794	0.573970	−	0.818877i	$-0.305403\pi$
$557$	27.0923	1.14794	0.573970	+	0.818877i	$0.305403\pi$
$558$	104.313	4.41593
$559$	25.8229	1.09219
$560$	−104.073	−4.39788
$561$	−1.51984	−0.0641675
$562$	77.2202	3.25734
$563$	−7.40450	−0.312063	−0.156031	−	0.987752i	$-0.549870\pi$
$563$	−7.40450	−0.312063	−0.156031	+	0.987752i	$0.549870\pi$
$564$	158.852	6.68888
$565$	−47.4837	−1.99765
$566$	18.5600	0.780137
$567$	28.7535	1.20754
$568$	98.0871	4.11564
$569$	−27.7703	−1.16419	−0.582096	−	0.813120i	$-0.697767\pi$
$569$	−27.7703	−1.16419	−0.582096	+	0.813120i	$0.697767\pi$
$570$	10.4780	0.438874
$571$	−11.5386	−0.482876	−0.241438	−	0.970416i	$-0.577619\pi$
$571$	−11.5386	−0.482876	−0.241438	+	0.970416i	$0.577619\pi$
$572$	14.6455	0.612357
$573$	−29.1154	−1.21632
$574$	24.8941	1.03906
$575$	77.5997	3.23613
$576$	195.653	8.15222
$577$	−32.1425	−1.33811	−0.669055	−	0.743213i	$-0.733301\pi$
$577$	−32.1425	−1.33811	−0.669055	+	0.743213i	$0.733301\pi$
$578$	−2.73023	−0.113563
$579$	11.1018	0.461373
$580$	−9.76960	−0.405660
$581$	−14.3867	−0.596862
$582$	−115.036	−4.76839
$583$	3.01950	0.125055
$584$	136.811	5.66127
$585$	−135.436	−5.59959
$586$	−70.6185	−2.91722
$587$	7.24354	0.298973	0.149486	−	0.988764i	$-0.452238\pi$
$587$	7.24354	0.298973	0.149486	+	0.988764i	$0.452238\pi$
$588$	58.1760	2.39914
$589$	1.91277	0.0788144
$590$	14.8172	0.610016
$591$	11.5790	0.476296
$592$	131.162	5.39072
$593$	14.1958	0.582951	0.291476	−	0.956578i	$-0.405854\pi$
$593$	14.1958	0.582951	0.291476	+	0.956578i	$0.405854\pi$
$594$	15.1275	0.620688
$595$	−7.01326	−0.287516
$596$	48.6292	1.99193
$597$	−50.4960	−2.06666
$598$	−132.187	−5.40552
$599$	−41.0042	−1.67539	−0.837693	−	0.546142i	$-0.816096\pi$
$599$	−41.0042	−1.67539	−0.837693	+	0.546142i	$0.816096\pi$
$600$	257.585	10.5159
$601$	−19.2506	−0.785250	−0.392625	−	0.919699i	$-0.628433\pi$
$601$	−19.2506	−0.785250	−0.392625	+	0.919699i	$0.628433\pi$
$602$	−24.2619	−0.988840
$603$	46.2364	1.88289
$604$	−127.611	−5.19241
$605$	39.9657	1.62484
$606$	149.711	6.08158
$607$	−22.0815	−0.896259	−0.448130	−	0.893969i	$-0.647910\pi$
$607$	−22.0815	−0.896259	−0.448130	+	0.893969i	$0.647910\pi$
$608$	7.20431	0.292173
$609$	−2.82830	−0.114609
$610$	−61.0419	−2.47152
$611$	−51.4571	−2.08173
$612$	36.2462	1.46516
$613$	−22.8577	−0.923214	−0.461607	−	0.887085i	$-0.652727\pi$
$613$	−22.8577	−0.923214	−0.461607	+	0.887085i	$0.652727\pi$
$614$	7.61900	0.307478
$615$	−55.6996	−2.24602
$616$	−8.71439	−0.351113
$617$	−26.1765	−1.05383	−0.526913	−	0.849919i	$-0.676651\pi$
$617$	−26.1765	−1.05383	−0.526913	+	0.849919i	$0.676651\pi$
$618$	47.0501	1.89263
$619$	17.5333	0.704724	0.352362	−	0.935864i	$-0.385379\pi$
$619$	17.5333	0.704724	0.352362	+	0.935864i	$0.385379\pi$
$620$	116.462	4.67724
$621$	−99.9035	−4.00899
$622$	−42.2138	−1.69262
$623$	−20.0463	−0.803139
$624$	−252.887	−10.1236
$625$	8.37191	0.334876
$626$	41.9678	1.67737
$627$	0.505656	0.0201940
$628$	−41.2910	−1.64769
$629$	8.83875	0.352424
$630$	127.249	5.06972
$631$	0.116003	0.00461802	0.00230901	−	0.999997i	$-0.499265\pi$
$631$	0.116003	0.00461802	0.00230901	+	0.999997i	$0.499265\pi$
$632$	−30.0354	−1.19474
$633$	54.7114	2.17458
$634$	−22.9997	−0.913435
$635$	−15.3551	−0.609349
$636$	−104.519	−4.14446
$637$	−18.8450	−0.746667
$638$	−0.644356	−0.0255103
$639$	−69.1206	−2.73437
$640$	137.693	5.44279
$641$	31.7091	1.25243	0.626216	−	0.779649i	$-0.284603\pi$
$641$	31.7091	1.25243	0.626216	+	0.779649i	$0.284603\pi$
$642$	−56.2179	−2.21874
$643$	4.04807	0.159640	0.0798202	−	0.996809i	$-0.474565\pi$
$643$	4.04807	0.159640	0.0798202	+	0.996809i	$0.474565\pi$
$644$	90.8734	3.58091
$645$	54.2849	2.13747
$646$	0.908359	0.0357389
$647$	39.8631	1.56718	0.783590	−	0.621279i	$-0.213386\pi$
$647$	39.8631	1.56718	0.783590	+	0.621279i	$0.213386\pi$
$648$	−143.604	−5.64128
$649$	0.715065	0.0280688
$650$	−131.753	−5.16776
$651$	33.7159	1.32143
$652$	−124.910	−4.89186
$653$	−17.4076	−0.681212	−0.340606	−	0.940206i	$-0.610632\pi$
$653$	−17.4076	−0.681212	−0.340606	+	0.940206i	$0.610632\pi$
$654$	30.2407	1.18251
$655$	9.34840	0.365272
$656$	−71.6555	−2.79768
$657$	−96.4086	−3.76126
$658$	48.3466	1.88475
$659$	−18.7947	−0.732138	−0.366069	−	0.930588i	$-0.619297\pi$
$659$	−18.7947	−0.732138	−0.366069	+	0.930588i	$0.619297\pi$
$660$	30.7877	1.19841
$661$	−4.61400	−0.179464	−0.0897320	−	0.995966i	$-0.528601\pi$
$661$	−4.61400	−0.179464	−0.0897320	+	0.995966i	$0.528601\pi$
$662$	2.49027	0.0967870
$663$	−17.0416	−0.661840
$664$	71.8515	2.78838
$665$	2.33334	0.0904832
$666$	−160.371	−6.21424
$667$	4.25539	0.164770
$668$	−27.6017	−1.06794
$669$	−66.1644	−2.55807
$670$	70.5509	2.72562
$671$	−2.94582	−0.113722
$672$	126.989	4.89869
$673$	−18.9647	−0.731037	−0.365518	−	0.930804i	$-0.619108\pi$
$673$	−18.9647	−0.731037	−0.365518	+	0.930804i	$0.619108\pi$
$674$	−12.5448	−0.483208
$675$	−99.5754	−3.83266
$676$	93.3122	3.58893
$677$	12.8848	0.495203	0.247601	−	0.968862i	$-0.420358\pi$
$677$	12.8848	0.495203	0.247601	+	0.968862i	$0.420358\pi$
$678$	108.406	4.16331
$679$	−25.6174	−0.983106
$680$	35.0263	1.34320
$681$	72.5474	2.78002
$682$	7.68131	0.294132
$683$	−13.3476	−0.510731	−0.255366	−	0.966845i	$-0.582196\pi$
$683$	−13.3476	−0.510731	−0.255366	+	0.966845i	$0.582196\pi$
$684$	−12.0593	−0.461097
$685$	16.1374	0.616579
$686$	53.7938	2.05386
$687$	−74.6639	−2.84861
$688$	69.8356	2.66246
$689$	33.8570	1.28985
$690$	−277.884	−10.5788
$691$	26.1747	0.995734	0.497867	−	0.867253i	$-0.334117\pi$
$691$	26.1747	0.995734	0.497867	+	0.867253i	$0.334117\pi$
$692$	81.7064	3.10601
$693$	6.14091	0.233274
$694$	70.1997	2.66474
$695$	53.5480	2.03119
$696$	14.1254	0.535421
$697$	−4.82872	−0.182901
$698$	48.9414	1.85246
$699$	−76.7640	−2.90348
$700$	90.5750	3.42341
$701$	9.87840	0.373102	0.186551	−	0.982445i	$-0.440269\pi$
$701$	9.87840	0.373102	0.186551	+	0.982445i	$0.440269\pi$
$702$	169.621	6.40193
$703$	−2.94069	−0.110910
$704$	14.4073	0.542996
$705$	−108.173	−4.07405
$706$	−2.73023	−0.102753
$707$	33.3391	1.25385
$708$	−24.7518	−0.930228
$709$	−33.9452	−1.27484	−0.637419	−	0.770518i	$-0.719998\pi$
$709$	−33.9452	−1.27484	−0.637419	+	0.770518i	$0.719998\pi$
$710$	−105.469	−3.95819
$711$	21.1655	0.793768
$712$	100.117	3.75205
$713$	−50.7281	−1.89978
$714$	16.0114	0.599212
$715$	−9.97311	−0.372973
$716$	−12.4624	−0.465743
$717$	−47.7440	−1.78303
$718$	4.94573	0.184573
$719$	−32.9145	−1.22750	−0.613752	−	0.789499i	$-0.710340\pi$
$719$	−32.9145	−1.22750	−0.613752	+	0.789499i	$0.710340\pi$
$720$	−366.275	−13.6503
$721$	10.4776	0.390207
$722$	51.5721	1.91932
$723$	7.34269	0.273078
$724$	−54.4375	−2.02315
$725$	4.24142	0.157522
$726$	−91.2425	−3.38633
$727$	11.4999	0.426508	0.213254	−	0.976997i	$-0.431594\pi$
$727$	11.4999	0.426508	0.213254	+	0.976997i	$0.431594\pi$
$728$	−97.7125	−3.62146
$729$	−4.29729	−0.159159
$730$	−147.107	−5.44468
$731$	4.70608	0.174061
$732$	101.969	3.76887
$733$	8.26852	0.305405	0.152702	−	0.988272i	$-0.451202\pi$
$733$	8.26852	0.305405	0.152702	+	0.988272i	$0.451202\pi$
$734$	43.7476	1.61475
$735$	−39.6161	−1.46126
$736$	−191.064	−7.04270
$737$	3.40471	0.125414
$738$	87.6126	3.22507
$739$	−41.6012	−1.53032	−0.765162	−	0.643837i	$-0.777341\pi$
$739$	−41.6012	−1.53032	−0.765162	+	0.643837i	$0.777341\pi$
$740$	−179.049	−6.58197
$741$	5.66980	0.208285
$742$	−31.8104	−1.16780
$743$	−13.8321	−0.507450	−0.253725	−	0.967276i	$-0.581656\pi$
$743$	−13.8321	−0.507450	−0.253725	+	0.967276i	$0.581656\pi$
$744$	−168.387	−6.17338
$745$	−33.1150	−1.21324
$746$	−71.9435	−2.63404
$747$	−50.6327	−1.85256
$748$	2.66906	0.0975905
$749$	−12.5192	−0.457441
$750$	−119.504	−4.36368
$751$	−16.5109	−0.602491	−0.301245	−	0.953547i	$-0.597402\pi$
$751$	−16.5109	−0.602491	−0.301245	+	0.953547i	$0.597402\pi$
$752$	−139.161	−5.07469
$753$	12.5287	0.456570
$754$	−7.22502	−0.263120
$755$	86.8991	3.16258
$756$	−116.608	−4.24100
$757$	−16.7520	−0.608863	−0.304432	−	0.952534i	$-0.598467\pi$
$757$	−16.7520	−0.608863	−0.304432	+	0.952534i	$0.598467\pi$
$758$	−46.8467	−1.70155
$759$	−13.4104	−0.486766
$760$	−11.6534	−0.422713
$761$	43.9955	1.59483	0.797417	−	0.603429i	$-0.206199\pi$
$761$	43.9955	1.59483	0.797417	+	0.603429i	$0.206199\pi$
$762$	35.0560	1.26995
$763$	6.73433	0.243799
$764$	51.1311	1.84986
$765$	−24.6825	−0.892399
$766$	65.9877	2.38423
$767$	8.01786	0.289508
$768$	−131.484	−4.74450
$769$	33.2541	1.19917	0.599587	−	0.800309i	$-0.295331\pi$
$769$	33.2541	1.19917	0.599587	+	0.800309i	$0.295331\pi$
$770$	9.37024	0.337680
$771$	64.2482	2.31384
$772$	−19.4964	−0.701689
$773$	−18.5456	−0.667039	−0.333520	−	0.942743i	$-0.608236\pi$
$773$	−18.5456	−0.667039	−0.333520	+	0.942743i	$0.608236\pi$
$774$	−85.3875	−3.06919
$775$	−50.5616	−1.81622
$776$	127.941	4.59281
$777$	−51.8348	−1.85956
$778$	105.074	3.76707
$779$	1.60654	0.0575602
$780$	345.216	12.3607
$781$	−5.08983	−0.182129
$782$	−24.0904	−0.861470
$783$	−5.46049	−0.195142
$784$	−50.9647	−1.82017
$785$	28.1179	1.00357
$786$	−21.3426	−0.761265
$787$	−13.0023	−0.463482	−0.231741	−	0.972778i	$-0.574442\pi$
$787$	−13.0023	−0.463482	−0.231741	+	0.972778i	$0.574442\pi$
$788$	−20.3344	−0.724385
$789$	−14.9461	−0.532094
$790$	32.2958	1.14903
$791$	24.1410	0.858356
$792$	−30.6695	−1.08979
$793$	−33.0308	−1.17296
$794$	−50.8003	−1.80283
$795$	71.1744	2.52430
$796$	88.6786	3.14313
$797$	10.8613	0.384729	0.192364	−	0.981324i	$-0.438384\pi$
$797$	10.8613	0.384729	0.192364	+	0.981324i	$0.438384\pi$
$798$	−5.32707	−0.188576
$799$	−9.37780	−0.331763
$800$	−190.436	−6.73294
$801$	−70.5512	−2.49280
$802$	93.2185	3.29166
$803$	−7.09924	−0.250527
$804$	−117.853	−4.15636
$805$	−61.8820	−2.18105
$806$	86.1287	3.03376
$807$	66.5143	2.34141
$808$	−166.505	−5.85764
$809$	−12.1153	−0.425953	−0.212976	−	0.977057i	$-0.568316\pi$
$809$	−12.1153	−0.425953	−0.212976	+	0.977057i	$0.568316\pi$
$810$	154.411	5.42546
$811$	−1.56410	−0.0549230	−0.0274615	−	0.999623i	$-0.508742\pi$
$811$	−1.56410	−0.0549230	−0.0274615	+	0.999623i	$0.508742\pi$
$812$	4.96693	0.174305
$813$	−29.7877	−1.04470
$814$	−11.8092	−0.413913
$815$	85.0601	2.97952
$816$	−46.0874	−1.61338
$817$	−1.56573	−0.0547781
$818$	46.6481	1.63101
$819$	68.8566	2.40604
$820$	97.8168	3.41591
$821$	37.1552	1.29672	0.648362	−	0.761332i	$-0.275454\pi$
$821$	37.1552	1.29672	0.648362	+	0.761332i	$0.275454\pi$
$822$	−36.8420	−1.28501
$823$	−34.0078	−1.18544	−0.592719	−	0.805409i	$-0.701945\pi$
$823$	−34.0078	−1.18544	−0.592719	+	0.805409i	$0.701945\pi$
$824$	−52.3283	−1.82294
$825$	−13.3663	−0.465356
$826$	−7.53319	−0.262113
$827$	−39.5015	−1.37360	−0.686801	−	0.726845i	$-0.740986\pi$
$827$	−39.5015	−1.37360	−0.686801	+	0.726845i	$0.740986\pi$
$828$	319.821	11.1145
$829$	−55.2152	−1.91770	−0.958852	−	0.283906i	$-0.908370\pi$
$829$	−55.2152	−1.91770	−0.958852	+	0.283906i	$0.908370\pi$
$830$	−77.2591	−2.68170
$831$	−78.3353	−2.71742
$832$	161.546	5.60060
$833$	−3.43441	−0.118995
$834$	−122.251	−4.23321
$835$	18.7959	0.650459
$836$	−0.888008	−0.0307124
$837$	65.0940	2.24998
$838$	−50.4560	−1.74297
$839$	16.5066	0.569871	0.284935	−	0.958547i	$-0.408028\pi$
$839$	16.5066	0.569871	0.284935	+	0.958547i	$0.408028\pi$
$840$	−205.412	−7.08737
$841$	−28.7674	−0.991980
$842$	91.1230	3.14031
$843$	87.8409	3.02540
$844$	−96.0814	−3.30726
$845$	−63.5428	−2.18594
$846$	170.151	5.84993
$847$	−20.3188	−0.698164
$848$	91.5632	3.14429
$849$	21.1128	0.724588
$850$	−24.0112	−0.823579
$851$	77.9893	2.67344
$852$	176.183	6.03593
$853$	45.0347	1.54196	0.770979	−	0.636860i	$-0.219767\pi$
$853$	45.0347	1.54196	0.770979	+	0.636860i	$0.219767\pi$
$854$	31.0341	1.06197
$855$	8.21199	0.280844
$856$	62.5245	2.13704
$857$	29.9362	1.02260	0.511301	−	0.859402i	$-0.329164\pi$
$857$	29.9362	1.02260	0.511301	+	0.859402i	$0.329164\pi$
$858$	22.7688	0.777314
$859$	45.5819	1.55523	0.777617	−	0.628738i	$-0.216428\pi$
$859$	45.5819	1.55523	0.777617	+	0.628738i	$0.216428\pi$
$860$	−95.3325	−3.25081
$861$	28.3180	0.965076
$862$	−85.8303	−2.92339
$863$	23.0996	0.786320	0.393160	−	0.919470i	$-0.371382\pi$
$863$	23.0996	0.786320	0.393160	+	0.919470i	$0.371382\pi$
$864$	245.172	8.34091
$865$	−55.6395	−1.89180
$866$	−107.963	−3.66875
$867$	−3.10574	−0.105476
$868$	−59.2103	−2.00973
$869$	1.55856	0.0528706
$870$	−15.1885	−0.514937
$871$	38.1763	1.29355
$872$	−33.6332	−1.13896
$873$	−90.1581	−3.05139
$874$	8.01497	0.271110
$875$	−26.6125	−0.899666
$876$	245.738	8.30271
$877$	6.42386	0.216918	0.108459	−	0.994101i	$-0.465408\pi$
$877$	6.42386	0.216918	0.108459	+	0.994101i	$0.465408\pi$
$878$	34.5564	1.16622
$879$	−80.3312	−2.70950
$880$	−26.9714	−0.909205
$881$	32.9297	1.10943	0.554715	−	0.832040i	$-0.312827\pi$
$881$	32.9297	1.10943	0.554715	+	0.832040i	$0.312827\pi$
$882$	62.3141	2.09823
$883$	20.2052	0.679960	0.339980	−	0.940433i	$-0.389580\pi$
$883$	20.2052	0.679960	0.339980	+	0.940433i	$0.389580\pi$
$884$	29.9276	1.00657
$885$	16.8552	0.566581
$886$	21.8348	0.733553
$887$	10.2533	0.344271	0.172135	−	0.985073i	$-0.444933\pi$
$887$	10.2533	0.344271	0.172135	+	0.985073i	$0.444933\pi$
$888$	258.878	8.68738
$889$	7.80664	0.261826
$890$	−107.652	−3.60850
$891$	7.45173	0.249642
$892$	116.195	3.89049
$893$	3.12004	0.104408
$894$	75.6022	2.52852
$895$	8.48653	0.283673
$896$	−70.0040	−2.33867
$897$	−150.367	−5.02062
$898$	6.79814	0.226857
$899$	−2.77268	−0.0924741
$900$	318.770	10.6257
$901$	6.17027	0.205562
$902$	6.45153	0.214812
$903$	−27.5988	−0.918431
$904$	−120.567	−4.01001
$905$	37.0703	1.23226
$906$	−198.392	−6.59114
$907$	−20.5685	−0.682966	−0.341483	−	0.939888i	$-0.610929\pi$
$907$	−20.5685	−0.682966	−0.341483	+	0.939888i	$0.610929\pi$
$908$	−127.404	−4.22806
$909$	117.334	3.89173
$910$	105.066	3.48292
$911$	−45.9796	−1.52337	−0.761685	−	0.647947i	$-0.775628\pi$
$911$	−45.9796	−1.52337	−0.761685	+	0.647947i	$0.775628\pi$
$912$	15.3335	0.507742
$913$	−3.72844	−0.123393
$914$	−4.56432	−0.150974
$915$	−69.4375	−2.29553
$916$	131.121	4.33236
$917$	−4.75279	−0.156951
$918$	30.9126	1.02027
$919$	14.9234	0.492278	0.246139	−	0.969235i	$-0.420838\pi$
$919$	14.9234	0.492278	0.246139	+	0.969235i	$0.420838\pi$
$920$	309.057	10.1893
$921$	8.66690	0.285584
$922$	21.7533	0.716408
$923$	−57.0711	−1.87852
$924$	−15.6527	−0.514936
$925$	77.7332	2.55585
$926$	9.40417	0.309040
$927$	36.8750	1.21113
$928$	−10.4431	−0.342812
$929$	53.1100	1.74248	0.871241	−	0.490855i	$-0.163315\pi$
$929$	53.1100	1.74248	0.871241	+	0.490855i	$0.163315\pi$
$930$	181.060	5.93720
$931$	1.14264	0.0374486
$932$	134.809	4.41582
$933$	−48.0198	−1.57210
$934$	52.0953	1.70461
$935$	−1.81755	−0.0594402
$936$	−343.890	−11.2404
$937$	26.7036	0.872369	0.436184	−	0.899857i	$-0.356330\pi$
$937$	26.7036	0.872369	0.436184	+	0.899857i	$0.356330\pi$
$938$	−35.8685	−1.17115
$939$	47.7400	1.55794
$940$	189.969	6.19610
$941$	−0.757355	−0.0246891	−0.0123445	−	0.999924i	$-0.503929\pi$
$941$	−0.757355	−0.0246891	−0.0123445	+	0.999924i	$0.503929\pi$
$942$	−64.1937	−2.09154
$943$	−42.6066	−1.38746
$944$	21.6836	0.705741
$945$	79.4066	2.58310
$946$	−6.28768	−0.204430
$947$	13.5317	0.439722	0.219861	−	0.975531i	$-0.429440\pi$
$947$	13.5317	0.439722	0.219861	+	0.975531i	$0.429440\pi$
$948$	−53.9492	−1.75219
$949$	−79.6021	−2.58399
$950$	7.98865	0.259186
$951$	−26.1631	−0.848395
$952$	−17.8076	−0.577148
$953$	−50.2605	−1.62810	−0.814048	−	0.580798i	$-0.802741\pi$
$953$	−50.2605	−1.62810	−0.814048	+	0.580798i	$0.802741\pi$
$954$	−111.954	−3.62464
$955$	−34.8187	−1.12671
$956$	83.8457	2.71176
$957$	−0.732980	−0.0236939
$958$	0.865651	0.0279679
$959$	−8.20437	−0.264933
$960$	339.603	10.9606
$961$	2.05288	0.0662218
$962$	−132.414	−4.26920
$963$	−44.0601	−1.41982
$964$	−12.8949	−0.415316
$965$	13.2764	0.427383
$966$	141.278	4.54554
$967$	60.4776	1.94483	0.972414	−	0.233262i	$-0.0749401\pi$
$967$	60.4776	1.94483	0.972414	+	0.233262i	$0.0749401\pi$
$968$	101.478	3.26164
$969$	1.03329	0.0331942
$970$	−137.570	−4.41710
$971$	23.4587	0.752825	0.376413	−	0.926452i	$-0.377157\pi$
$971$	23.4587	0.752825	0.376413	+	0.926452i	$0.377157\pi$
$972$	−72.6781	−2.33115
$973$	−27.2242	−0.872767
$974$	99.2249	3.17937
$975$	−149.874	−4.79980
$976$	−89.3289	−2.85935
$977$	−24.5612	−0.785784	−0.392892	−	0.919585i	$-0.628525\pi$
$977$	−24.5612	−0.785784	−0.392892	+	0.919585i	$0.628525\pi$
$978$	−194.194	−6.20963
$979$	−5.19518	−0.166039
$980$	69.5718	2.22239
$981$	23.7008	0.756710
$982$	−62.9799	−2.00977
$983$	−19.2821	−0.615003	−0.307502	−	0.951548i	$-0.599493\pi$
$983$	−19.2821	−0.615003	−0.307502	+	0.951548i	$0.599493\pi$
$984$	−141.429	−4.50858
$985$	13.8471	0.441207
$986$	−1.31672	−0.0419330
$987$	54.9961	1.75055
$988$	−9.95703	−0.316775
$989$	41.5245	1.32040
$990$	32.9777	1.04810
$991$	27.2784	0.866528	0.433264	−	0.901267i	$-0.357362\pi$
$991$	27.2784	0.866528	0.433264	+	0.901267i	$0.357362\pi$
$992$	124.491	3.95260
$993$	2.83277	0.0898954
$994$	53.6212	1.70076
$995$	−60.3874	−1.91441
$996$	129.059	4.08939
$997$	40.6600	1.28771	0.643857	−	0.765146i	$-0.277333\pi$
$997$	40.6600	1.28771	0.643857	+	0.765146i	$0.277333\pi$
$998$	−97.9331	−3.10002
$999$	−100.075	−3.16624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.4	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.4	✓	114	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)

\(f(q)\)	\(=\)	\(q-2.73023 q^{2} -3.10574 q^{3} +5.45415 q^{4} -3.71411 q^{5} +8.47938 q^{6} +1.88828 q^{7} -9.43061 q^{8} +6.64562 q^{9} +O(q^{10})\)	\(q-2.73023 q^{2} -3.10574 q^{3} +5.45415 q^{4} -3.71411 q^{5} +8.47938 q^{6} +1.88828 q^{7} -9.43061 q^{8} +6.64562 q^{9} +10.1404 q^{10} +0.489363 q^{11} -16.9392 q^{12} +5.48712 q^{13} -5.15543 q^{14} +11.5351 q^{15} +14.8394 q^{16} +1.00000 q^{17} -18.1441 q^{18} -0.332704 q^{19} -20.2573 q^{20} -5.86450 q^{21} -1.33607 q^{22} +8.82357 q^{23} +29.2890 q^{24} +8.79459 q^{25} -14.9811 q^{26} -11.3223 q^{27} +10.2989 q^{28} +0.482276 q^{29} -31.4933 q^{30} -5.74916 q^{31} -21.6538 q^{32} -1.51984 q^{33} -2.73023 q^{34} -7.01326 q^{35} +36.2462 q^{36} +8.83875 q^{37} +0.908359 q^{38} -17.0416 q^{39} +35.0263 q^{40} -4.82872 q^{41} +16.0114 q^{42} +4.70608 q^{43} +2.66906 q^{44} -24.6825 q^{45} -24.0904 q^{46} -9.37780 q^{47} -46.0874 q^{48} -3.43441 q^{49} -24.0112 q^{50} -3.10574 q^{51} +29.9276 q^{52} +6.17027 q^{53} +30.9126 q^{54} -1.81755 q^{55} -17.8076 q^{56} +1.03329 q^{57} -1.31672 q^{58} +1.46121 q^{59} +62.9139 q^{60} -6.01970 q^{61} +15.6965 q^{62} +12.5488 q^{63} +29.4409 q^{64} -20.3798 q^{65} +4.14950 q^{66} +6.95743 q^{67} +5.45415 q^{68} -27.4037 q^{69} +19.1478 q^{70} -10.4009 q^{71} -62.6722 q^{72} -14.5071 q^{73} -24.1318 q^{74} -27.3137 q^{75} -1.81462 q^{76} +0.924054 q^{77} +46.5274 q^{78} +3.18488 q^{79} -55.1152 q^{80} +15.2274 q^{81} +13.1835 q^{82} -7.61897 q^{83} -31.9858 q^{84} -3.71411 q^{85} -12.8487 q^{86} -1.49782 q^{87} -4.61500 q^{88} -10.6162 q^{89} +67.3890 q^{90} +10.3612 q^{91} +48.1250 q^{92} +17.8554 q^{93} +25.6035 q^{94} +1.23570 q^{95} +67.2510 q^{96} -13.5666 q^{97} +9.37672 q^{98} +3.25212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * q^99

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