LMFDB - Embedded newform 6041.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41637 q^{2} -2.07802 q^{3} +3.83883 q^{4} +1.82876 q^{5} +5.02127 q^{6} -1.00000 q^{7} -4.44330 q^{8} +1.31818 q^{9} +O(q^{10})$	\(q-2.41637 q^{2} -2.07802 q^{3} +3.83883 q^{4} +1.82876 q^{5} +5.02127 q^{6} -1.00000 q^{7} -4.44330 q^{8} +1.31818 q^{9} -4.41896 q^{10} +3.57682 q^{11} -7.97719 q^{12} +4.09334 q^{13} +2.41637 q^{14} -3.80021 q^{15} +3.05898 q^{16} -5.00115 q^{17} -3.18521 q^{18} +1.07812 q^{19} +7.02031 q^{20} +2.07802 q^{21} -8.64290 q^{22} +3.88339 q^{23} +9.23328 q^{24} -1.65564 q^{25} -9.89101 q^{26} +3.49486 q^{27} -3.83883 q^{28} +4.54473 q^{29} +9.18270 q^{30} -7.39202 q^{31} +1.49498 q^{32} -7.43271 q^{33} +12.0846 q^{34} -1.82876 q^{35} +5.06028 q^{36} +2.14144 q^{37} -2.60512 q^{38} -8.50606 q^{39} -8.12573 q^{40} -10.0894 q^{41} -5.02127 q^{42} +10.7095 q^{43} +13.7308 q^{44} +2.41064 q^{45} -9.38370 q^{46} -5.67781 q^{47} -6.35664 q^{48} +1.00000 q^{49} +4.00063 q^{50} +10.3925 q^{51} +15.7137 q^{52} +4.80877 q^{53} -8.44486 q^{54} +6.54114 q^{55} +4.44330 q^{56} -2.24035 q^{57} -10.9817 q^{58} -11.8449 q^{59} -14.5884 q^{60} -13.9412 q^{61} +17.8618 q^{62} -1.31818 q^{63} -9.73038 q^{64} +7.48574 q^{65} +17.9602 q^{66} -7.17942 q^{67} -19.1986 q^{68} -8.06978 q^{69} +4.41896 q^{70} +5.72149 q^{71} -5.85708 q^{72} +12.8569 q^{73} -5.17451 q^{74} +3.44045 q^{75} +4.13871 q^{76} -3.57682 q^{77} +20.5538 q^{78} +10.0518 q^{79} +5.59414 q^{80} -11.2169 q^{81} +24.3797 q^{82} -10.9730 q^{83} +7.97719 q^{84} -9.14590 q^{85} -25.8781 q^{86} -9.44406 q^{87} -15.8929 q^{88} +1.18454 q^{89} -5.82499 q^{90} -4.09334 q^{91} +14.9077 q^{92} +15.3608 q^{93} +13.7197 q^{94} +1.97161 q^{95} -3.10660 q^{96} -4.74607 q^{97} -2.41637 q^{98} +4.71489 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) $ 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * 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 $

$2$	−2.41637	−1.70863	−0.854315	−	0.519755i	$-0.826023\pi$
$2$	−2.41637	−1.70863	−0.854315	+	0.519755i	$0.826023\pi$
$3$	−2.07802	−1.19975	−0.599874	−	0.800095i	$-0.704783\pi$
$3$	−2.07802	−1.19975	−0.599874	+	0.800095i	$0.704783\pi$
$4$	3.83883	1.91942
$5$	1.82876	0.817846	0.408923	−	0.912569i	$-0.365904\pi$
$5$	1.82876	0.817846	0.408923	+	0.912569i	$0.365904\pi$
$6$	5.02127	2.04992
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−4.44330	−1.57094
$9$	1.31818	0.439394
$10$	−4.41896	−1.39740
$11$	3.57682	1.07845	0.539225	−	0.842162i	$-0.318717\pi$
$11$	3.57682	1.07845	0.539225	+	0.842162i	$0.318717\pi$
$12$	−7.97719	−2.30282
$13$	4.09334	1.13529	0.567644	−	0.823274i	$-0.307855\pi$
$13$	4.09334	1.13529	0.567644	+	0.823274i	$0.307855\pi$
$14$	2.41637	0.645802
$15$	−3.80021	−0.981209
$16$	3.05898	0.764745
$17$	−5.00115	−1.21296	−0.606478	−	0.795100i	$-0.707418\pi$
$17$	−5.00115	−1.21296	−0.606478	+	0.795100i	$0.707418\pi$
$18$	−3.18521	−0.750762
$19$	1.07812	0.247337	0.123668	−	0.992324i	$-0.460534\pi$
$19$	1.07812	0.247337	0.123668	+	0.992324i	$0.460534\pi$
$20$	7.02031	1.56979
$21$	2.07802	0.453462
$22$	−8.64290	−1.84267
$23$	3.88339	0.809743	0.404872	−	0.914374i	$-0.367316\pi$
$23$	3.88339	0.809743	0.404872	+	0.914374i	$0.367316\pi$
$24$	9.23328	1.88474
$25$	−1.65564	−0.331127
$26$	−9.89101	−1.93979
$27$	3.49486	0.672586
$28$	−3.83883	−0.725472
$29$	4.54473	0.843936	0.421968	−	0.906611i	$-0.361340\pi$
$29$	4.54473	0.843936	0.421968	+	0.906611i	$0.361340\pi$
$30$	9.18270	1.67652
$31$	−7.39202	−1.32765	−0.663823	−	0.747889i	$-0.731067\pi$
$31$	−7.39202	−1.32765	−0.663823	+	0.747889i	$0.731067\pi$
$32$	1.49498	0.264277
$33$	−7.43271	−1.29387
$34$	12.0846	2.07249
$35$	−1.82876	−0.309117
$36$	5.06028	0.843380
$37$	2.14144	0.352051	0.176025	−	0.984386i	$-0.443676\pi$
$37$	2.14144	0.352051	0.176025	+	0.984386i	$0.443676\pi$
$38$	−2.60512	−0.422607
$39$	−8.50606	−1.36206
$40$	−8.12573	−1.28479
$41$	−10.0894	−1.57570	−0.787849	−	0.615868i	$-0.788805\pi$
$41$	−10.0894	−1.57570	−0.787849	+	0.615868i	$0.788805\pi$
$42$	−5.02127	−0.774799
$43$	10.7095	1.63318	0.816592	−	0.577215i	$-0.195861\pi$
$43$	10.7095	1.63318	0.816592	+	0.577215i	$0.195861\pi$
$44$	13.7308	2.07000
$45$	2.41064	0.359357
$46$	−9.38370	−1.38355
$47$	−5.67781	−0.828194	−0.414097	−	0.910233i	$-0.635902\pi$
$47$	−5.67781	−0.828194	−0.414097	+	0.910233i	$0.635902\pi$
$48$	−6.35664	−0.917501
$49$	1.00000	0.142857
$50$	4.00063	0.565774
$51$	10.3925	1.45524
$52$	15.7137	2.17909
$53$	4.80877	0.660535	0.330267	−	0.943887i	$-0.392861\pi$
$53$	4.80877	0.660535	0.330267	+	0.943887i	$0.392861\pi$
$54$	−8.44486	−1.14920
$55$	6.54114	0.882007
$56$	4.44330	0.593761
$57$	−2.24035	−0.296741
$58$	−10.9817	−1.44197
$59$	−11.8449	−1.54208	−0.771038	−	0.636789i	$-0.780262\pi$
$59$	−11.8449	−1.54208	−0.771038	+	0.636789i	$0.780262\pi$
$60$	−14.5884	−1.88335
$61$	−13.9412	−1.78499	−0.892496	−	0.451055i	$-0.851048\pi$
$61$	−13.9412	−1.78499	−0.892496	+	0.451055i	$0.851048\pi$
$62$	17.8618	2.26846
$63$	−1.31818	−0.166075
$64$	−9.73038	−1.21630
$65$	7.48574	0.928491
$66$	17.9602	2.21074
$67$	−7.17942	−0.877105	−0.438553	−	0.898705i	$-0.644509\pi$
$67$	−7.17942	−0.877105	−0.438553	+	0.898705i	$0.644509\pi$
$68$	−19.1986	−2.32817
$69$	−8.06978	−0.971487
$70$	4.41896	0.528166
$71$	5.72149	0.679016	0.339508	−	0.940603i	$-0.389739\pi$
$71$	5.72149	0.679016	0.339508	+	0.940603i	$0.389739\pi$
$72$	−5.85708	−0.690263
$73$	12.8569	1.50479	0.752393	−	0.658714i	$-0.228899\pi$
$73$	12.8569	1.50479	0.752393	+	0.658714i	$0.228899\pi$
$74$	−5.17451	−0.601525
$75$	3.44045	0.397269
$76$	4.13871	0.474742
$77$	−3.57682	−0.407616
$78$	20.5538	2.32726
$79$	10.0518	1.13092	0.565458	−	0.824777i	$-0.308699\pi$
$79$	10.0518	1.13092	0.565458	+	0.824777i	$0.308699\pi$
$80$	5.59414	0.625444
$81$	−11.2169	−1.24633
$82$	24.3797	2.69229
$83$	−10.9730	−1.20444	−0.602222	−	0.798329i	$-0.705718\pi$
$83$	−10.9730	−1.20444	−0.602222	+	0.798329i	$0.705718\pi$
$84$	7.97719	0.870383
$85$	−9.14590	−0.992012
$86$	−25.8781	−2.79051
$87$	−9.44406	−1.01251
$88$	−15.8929	−1.69419
$89$	1.18454	0.125561	0.0627803	−	0.998027i	$-0.480003\pi$
$89$	1.18454	0.125561	0.0627803	+	0.998027i	$0.480003\pi$
$90$	−5.82499	−0.614008
$91$	−4.09334	−0.429099
$92$	14.9077	1.55423
$93$	15.3608	1.59284
$94$	13.7197	1.41508
$95$	1.97161	0.202283
$96$	−3.10660	−0.317066
$97$	−4.74607	−0.481891	−0.240945	−	0.970539i	$-0.577457\pi$
$97$	−4.74607	−0.481891	−0.240945	+	0.970539i	$0.577457\pi$
$98$	−2.41637	−0.244090
$99$	4.71489	0.473864
$100$	−6.35572	−0.635572
$101$	−4.58271	−0.455997	−0.227998	−	0.973662i	$-0.573218\pi$
$101$	−4.58271	−0.455997	−0.227998	+	0.973662i	$0.573218\pi$
$102$	−25.1121	−2.48647
$103$	−15.2517	−1.50279	−0.751396	−	0.659852i	$-0.770619\pi$
$103$	−15.2517	−1.50279	−0.751396	+	0.659852i	$0.770619\pi$
$104$	−18.1879	−1.78347
$105$	3.80021	0.370862
$106$	−11.6197	−1.12861
$107$	−2.20680	−0.213339	−0.106670	−	0.994295i	$-0.534019\pi$
$107$	−2.20680	−0.213339	−0.106670	+	0.994295i	$0.534019\pi$
$108$	13.4162	1.29097
$109$	−4.59421	−0.440046	−0.220023	−	0.975495i	$-0.570613\pi$
$109$	−4.59421	−0.440046	−0.220023	+	0.975495i	$0.570613\pi$
$110$	−15.8058	−1.50702
$111$	−4.44997	−0.422372
$112$	−3.05898	−0.289047
$113$	7.60253	0.715186	0.357593	−	0.933878i	$-0.383598\pi$
$113$	7.60253	0.715186	0.357593	+	0.933878i	$0.383598\pi$
$114$	5.41351	0.507021
$115$	7.10179	0.662245
$116$	17.4465	1.61986
$117$	5.39576	0.498839
$118$	28.6217	2.63484
$119$	5.00115	0.458455
$120$	16.8855	1.54142
$121$	1.79361	0.163055
$122$	33.6872	3.04989
$123$	20.9660	1.89044
$124$	−28.3768	−2.54831
$125$	−12.1716	−1.08866
$126$	3.18521	0.283761
$127$	−19.0305	−1.68868	−0.844342	−	0.535805i	$-0.820008\pi$
$127$	−19.0305	−1.68868	−0.844342	+	0.535805i	$0.820008\pi$
$128$	20.5222	1.81393
$129$	−22.2546	−1.95941
$130$	−18.0883	−1.58645
$131$	−1.21906	−0.106510	−0.0532550	−	0.998581i	$-0.516960\pi$
$131$	−1.21906	−0.106510	−0.0532550	+	0.998581i	$0.516960\pi$
$132$	−28.5329	−2.48347
$133$	−1.07812	−0.0934844
$134$	17.3481	1.49865
$135$	6.39126	0.550072
$136$	22.2216	1.90549
$137$	−0.178747	−0.0152713	−0.00763567	−	0.999971i	$-0.502431\pi$
$137$	−0.178747	−0.0152713	−0.00763567	+	0.999971i	$0.502431\pi$
$138$	19.4996	1.65991
$139$	−21.8629	−1.85439	−0.927194	−	0.374582i	$-0.877786\pi$
$139$	−21.8629	−1.85439	−0.927194	+	0.374582i	$0.877786\pi$
$140$	−7.02031	−0.593324
$141$	11.7986	0.993623
$142$	−13.8252	−1.16019
$143$	14.6411	1.22435
$144$	4.03229	0.336024
$145$	8.31122	0.690210
$146$	−31.0670	−2.57112
$147$	−2.07802	−0.171392
$148$	8.22064	0.675733
$149$	−3.33889	−0.273533	−0.136766	−	0.990603i	$-0.543671\pi$
$149$	−3.33889	−0.273533	−0.136766	+	0.990603i	$0.543671\pi$
$150$	−8.31340	−0.678786
$151$	−15.4223	−1.25505	−0.627523	−	0.778598i	$-0.715931\pi$
$151$	−15.4223	−1.25505	−0.627523	+	0.778598i	$0.715931\pi$
$152$	−4.79039	−0.388552
$153$	−6.59242	−0.532966
$154$	8.64290	0.696465
$155$	−13.5182	−1.08581
$156$	−32.6533	−2.61436
$157$	−6.29366	−0.502289	−0.251144	−	0.967950i	$-0.580807\pi$
$157$	−6.29366	−0.502289	−0.251144	+	0.967950i	$0.580807\pi$
$158$	−24.2889	−1.93232
$159$	−9.99273	−0.792475
$160$	2.73395	0.216138
$161$	−3.88339	−0.306054
$162$	27.1043	2.12951
$163$	21.2791	1.66671	0.833353	−	0.552741i	$-0.186418\pi$
$163$	21.2791	1.66671	0.833353	+	0.552741i	$0.186418\pi$
$164$	−38.7315	−3.02442
$165$	−13.5926	−1.05819
$166$	26.5148	2.05795
$167$	8.49487	0.657353	0.328676	−	0.944443i	$-0.393397\pi$
$167$	8.49487	0.657353	0.328676	+	0.944443i	$0.393397\pi$
$168$	−9.23328	−0.712363
$169$	3.75543	0.288879
$170$	22.0999	1.69498
$171$	1.42115	0.108678
$172$	41.1120	3.13476
$173$	7.66999	0.583139	0.291569	−	0.956550i	$-0.405823\pi$
$173$	7.66999	0.583139	0.291569	+	0.956550i	$0.405823\pi$
$174$	22.8203	1.73000
$175$	1.65564	0.125154
$176$	10.9414	0.824740
$177$	24.6140	1.85010
$178$	−2.86228	−0.214537
$179$	−10.5611	−0.789373	−0.394687	−	0.918816i	$-0.629147\pi$
$179$	−10.5611	−0.789373	−0.394687	+	0.918816i	$0.629147\pi$
$180$	9.25404	0.689755
$181$	21.6112	1.60635	0.803175	−	0.595743i	$-0.203142\pi$
$181$	21.6112	1.60635	0.803175	+	0.595743i	$0.203142\pi$
$182$	9.89101	0.733171
$183$	28.9702	2.14154
$184$	−17.2551	−1.27206
$185$	3.91618	0.287924
$186$	−37.1173	−2.72158
$187$	−17.8882	−1.30811
$188$	−21.7962	−1.58965
$189$	−3.49486	−0.254214
$190$	−4.76414	−0.345627
$191$	9.63740	0.697338	0.348669	−	0.937246i	$-0.386634\pi$
$191$	9.63740	0.697338	0.348669	+	0.937246i	$0.386634\pi$
$192$	20.2200	1.45925
$193$	0.0526417	0.00378923	0.00189462	−	0.999998i	$-0.499397\pi$
$193$	0.0526417	0.00378923	0.00189462	+	0.999998i	$0.499397\pi$
$194$	11.4683	0.823373
$195$	−15.5555	−1.11395
$196$	3.83883	0.274202
$197$	8.55512	0.609527	0.304764	−	0.952428i	$-0.401423\pi$
$197$	8.55512	0.609527	0.304764	+	0.952428i	$0.401423\pi$
$198$	−11.3929	−0.809659
$199$	−2.65731	−0.188372	−0.0941859	−	0.995555i	$-0.530025\pi$
$199$	−2.65731	−0.188372	−0.0941859	+	0.995555i	$0.530025\pi$
$200$	7.35649	0.520183
$201$	14.9190	1.05231
$202$	11.0735	0.779130
$203$	−4.54473	−0.318978
$204$	39.8951	2.79322
$205$	−18.4511	−1.28868
$206$	36.8536	2.56772
$207$	5.11901	0.355796
$208$	12.5215	0.868206
$209$	3.85622	0.266740
$210$	−9.18270	−0.633666
$211$	−18.2906	−1.25918	−0.629589	−	0.776928i	$-0.716777\pi$
$211$	−18.2906	−1.25918	−0.629589	+	0.776928i	$0.716777\pi$
$212$	18.4601	1.26784
$213$	−11.8894	−0.814648
$214$	5.33244	0.364518
$215$	19.5851	1.33569
$216$	−15.5287	−1.05659
$217$	7.39202	0.501803
$218$	11.1013	0.751875
$219$	−26.7169	−1.80536
$220$	25.1103	1.69294
$221$	−20.4714	−1.37706
$222$	10.7528	0.721678
$223$	14.6737	0.982624	0.491312	−	0.870984i	$-0.336517\pi$
$223$	14.6737	0.982624	0.491312	+	0.870984i	$0.336517\pi$
$224$	−1.49498	−0.0998873
$225$	−2.18243	−0.145495
$226$	−18.3705	−1.22199
$227$	9.94050	0.659774	0.329887	−	0.944020i	$-0.392989\pi$
$227$	9.94050	0.659774	0.329887	+	0.944020i	$0.392989\pi$
$228$	−8.60033	−0.569571
$229$	8.78154	0.580301	0.290150	−	0.956981i	$-0.406295\pi$
$229$	8.78154	0.580301	0.290150	+	0.956981i	$0.406295\pi$
$230$	−17.1605	−1.13153
$231$	7.43271	0.489036
$232$	−20.1936	−1.32578
$233$	12.7183	0.833200	0.416600	−	0.909090i	$-0.363222\pi$
$233$	12.7183	0.833200	0.416600	+	0.909090i	$0.363222\pi$
$234$	−13.0382	−0.852331
$235$	−10.3833	−0.677335
$236$	−45.4707	−2.95989
$237$	−20.8879	−1.35681
$238$	−12.0846	−0.783329
$239$	−1.26166	−0.0816099	−0.0408049	−	0.999167i	$-0.512992\pi$
$239$	−1.26166	−0.0816099	−0.0408049	+	0.999167i	$0.512992\pi$
$240$	−11.6248	−0.750375
$241$	16.6916	1.07520	0.537600	−	0.843200i	$-0.319331\pi$
$241$	16.6916	1.07520	0.537600	+	0.843200i	$0.319331\pi$
$242$	−4.33402	−0.278601
$243$	12.8245	0.822692
$244$	−53.5181	−3.42615
$245$	1.82876	0.116835
$246$	−50.6616	−3.23006
$247$	4.41309	0.280798
$248$	32.8450	2.08566
$249$	22.8022	1.44503
$250$	29.4110	1.86011
$251$	22.8314	1.44110	0.720552	−	0.693401i	$-0.243889\pi$
$251$	22.8314	1.44110	0.720552	+	0.693401i	$0.243889\pi$
$252$	−5.06028	−0.318768
$253$	13.8902	0.873268
$254$	45.9847	2.88533
$255$	19.0054	1.19016
$256$	−30.1285	−1.88303
$257$	−8.97236	−0.559680	−0.279840	−	0.960047i	$-0.590281\pi$
$257$	−8.97236	−0.559680	−0.279840	+	0.960047i	$0.590281\pi$
$258$	53.7753	3.34790
$259$	−2.14144	−0.133063
$260$	28.7365	1.78216
$261$	5.99078	0.370820
$262$	2.94570	0.181986
$263$	−9.09861	−0.561044	−0.280522	−	0.959848i	$-0.590508\pi$
$263$	−9.09861	−0.561044	−0.280522	+	0.959848i	$0.590508\pi$
$264$	33.0258	2.03259
$265$	8.79408	0.540216
$266$	2.60512	0.159730
$267$	−2.46150	−0.150641
$268$	−27.5606	−1.68353
$269$	1.51142	0.0921528	0.0460764	−	0.998938i	$-0.485328\pi$
$269$	1.51142	0.0921528	0.0460764	+	0.998938i	$0.485328\pi$
$270$	−15.4436	−0.939869
$271$	−16.4829	−1.00127	−0.500634	−	0.865659i	$-0.666900\pi$
$271$	−16.4829	−1.00127	−0.500634	+	0.865659i	$0.666900\pi$
$272$	−15.2984	−0.927603
$273$	8.50606	0.514810
$274$	0.431917	0.0260931
$275$	−5.92191	−0.357104
$276$	−30.9785	−1.86469
$277$	7.72381	0.464079	0.232039	−	0.972706i	$-0.425460\pi$
$277$	7.72381	0.464079	0.232039	+	0.972706i	$0.425460\pi$
$278$	52.8288	3.16846
$279$	−9.74403	−0.583360
$280$	8.12573	0.485605
$281$	−3.43855	−0.205127	−0.102563	−	0.994726i	$-0.532704\pi$
$281$	−3.43855	−0.205127	−0.102563	+	0.994726i	$0.532704\pi$
$282$	−28.5098	−1.69773
$283$	−4.36725	−0.259606	−0.129803	−	0.991540i	$-0.541435\pi$
$283$	−4.36725	−0.259606	−0.129803	+	0.991540i	$0.541435\pi$
$284$	21.9639	1.30332
$285$	−4.09706	−0.242689
$286$	−35.3783	−2.09196
$287$	10.0894	0.595558
$288$	1.97065	0.116122
$289$	8.01149	0.471264
$290$	−20.0830	−1.17931
$291$	9.86245	0.578147
$292$	49.3555	2.88831
$293$	16.6610	0.973348	0.486674	−	0.873584i	$-0.338210\pi$
$293$	16.6610	0.973348	0.486674	+	0.873584i	$0.338210\pi$
$294$	5.02127	0.292846
$295$	−21.6615	−1.26118
$296$	−9.51507	−0.553052
$297$	12.5005	0.725350
$298$	8.06799	0.467366
$299$	15.8960	0.919292
$300$	13.2073	0.762525
$301$	−10.7095	−0.617285
$302$	37.2659	2.14441
$303$	9.52298	0.547081
$304$	3.29793	0.189150
$305$	−25.4952	−1.45985
$306$	15.9297	0.910641
$307$	−15.5696	−0.888603	−0.444301	−	0.895877i	$-0.646548\pi$
$307$	−15.5696	−0.888603	−0.444301	+	0.895877i	$0.646548\pi$
$308$	−13.7308	−0.782385
$309$	31.6933	1.80297
$310$	32.6650	1.85525
$311$	8.13920	0.461532	0.230766	−	0.973009i	$-0.425877\pi$
$311$	8.13920	0.461532	0.230766	+	0.973009i	$0.425877\pi$
$312$	37.7950	2.13972
$313$	25.9124	1.46465	0.732326	−	0.680954i	$-0.238435\pi$
$313$	25.9124	1.46465	0.732326	+	0.680954i	$0.238435\pi$
$314$	15.2078	0.858226
$315$	−2.41064	−0.135824
$316$	38.5872	2.17070
$317$	2.29369	0.128826	0.0644132	−	0.997923i	$-0.479482\pi$
$317$	2.29369	0.128826	0.0644132	+	0.997923i	$0.479482\pi$
$318$	24.1461	1.35405
$319$	16.2557	0.910143
$320$	−17.7945	−0.994744
$321$	4.58578	0.255953
$322$	9.38370	0.522933
$323$	−5.39181	−0.300009
$324$	−43.0600	−2.39222
$325$	−6.77708	−0.375925
$326$	−51.4181	−2.84778
$327$	9.54688	0.527944
$328$	44.8302	2.47533
$329$	5.67781	0.313028
$330$	32.8448	1.80805
$331$	3.24296	0.178249	0.0891247	−	0.996020i	$-0.471593\pi$
$331$	3.24296	0.178249	0.0891247	+	0.996020i	$0.471593\pi$
$332$	−42.1236	−2.31183
$333$	2.82281	0.154689
$334$	−20.5267	−1.12317
$335$	−13.1294	−0.717337
$336$	6.35664	0.346783
$337$	−16.4194	−0.894423	−0.447212	−	0.894428i	$-0.647583\pi$
$337$	−16.4194	−0.894423	−0.447212	+	0.894428i	$0.647583\pi$
$338$	−9.07450	−0.493588
$339$	−15.7982	−0.858042
$340$	−35.1096	−1.90409
$341$	−26.4399	−1.43180
$342$	−3.43402	−0.185691
$343$	−1.00000	−0.0539949
$344$	−47.5855	−2.56564
$345$	−14.7577	−0.794527
$346$	−18.5335	−0.996368
$347$	−12.2980	−0.660189	−0.330095	−	0.943948i	$-0.607081\pi$
$347$	−12.2980	−0.660189	−0.330095	+	0.943948i	$0.607081\pi$
$348$	−36.2542	−1.94343
$349$	17.0291	0.911548	0.455774	−	0.890096i	$-0.349363\pi$
$349$	17.0291	0.911548	0.455774	+	0.890096i	$0.349363\pi$
$350$	−4.00063	−0.213843
$351$	14.3056	0.763579
$352$	5.34725	0.285010
$353$	19.5985	1.04312	0.521562	−	0.853213i	$-0.325349\pi$
$353$	19.5985	1.04312	0.521562	+	0.853213i	$0.325349\pi$
$354$	−59.4765	−3.16114
$355$	10.4632	0.555331
$356$	4.54724	0.241003
$357$	−10.3925	−0.550030
$358$	25.5195	1.34875
$359$	−25.1710	−1.32847	−0.664237	−	0.747522i	$-0.731243\pi$
$359$	−25.1710	−1.32847	−0.664237	+	0.747522i	$0.731243\pi$
$360$	−10.7112	−0.564529
$361$	−17.8377	−0.938825
$362$	−52.2207	−2.74466
$363$	−3.72716	−0.195625
$364$	−15.7137	−0.823619
$365$	23.5122	1.23068
$366$	−70.0027	−3.65910
$367$	−27.9498	−1.45897	−0.729483	−	0.683999i	$-0.760239\pi$
$367$	−27.9498	−1.45897	−0.729483	+	0.683999i	$0.760239\pi$
$368$	11.8792	0.619247
$369$	−13.2997	−0.692352
$370$	−9.46294	−0.491955
$371$	−4.80877	−0.249659
$372$	58.9676	3.05733
$373$	4.91899	0.254696	0.127348	−	0.991858i	$-0.459354\pi$
$373$	4.91899	0.254696	0.127348	+	0.991858i	$0.459354\pi$
$374$	43.2244	2.23508
$375$	25.2928	1.30611
$376$	25.2282	1.30105
$377$	18.6031	0.958110
$378$	8.44486	0.434357
$379$	6.26741	0.321935	0.160968	−	0.986960i	$-0.448539\pi$
$379$	6.26741	0.321935	0.160968	+	0.986960i	$0.448539\pi$
$380$	7.56870	0.388266
$381$	39.5458	2.02599
$382$	−23.2875	−1.19149
$383$	2.40206	0.122739	0.0613697	−	0.998115i	$-0.480453\pi$
$383$	2.40206	0.122739	0.0613697	+	0.998115i	$0.480453\pi$
$384$	−42.6457	−2.17625
$385$	−6.54114	−0.333367
$386$	−0.127202	−0.00647440
$387$	14.1171	0.717611
$388$	−18.2194	−0.924949
$389$	7.46150	0.378313	0.189157	−	0.981947i	$-0.439425\pi$
$389$	7.46150	0.378313	0.189157	+	0.981947i	$0.439425\pi$
$390$	37.5879	1.90334
$391$	−19.4214	−0.982183
$392$	−4.44330	−0.224421
$393$	2.53324	0.127785
$394$	−20.6723	−1.04146
$395$	18.3823	0.924916
$396$	18.0997	0.909544
$397$	−36.5495	−1.83436	−0.917182	−	0.398467i	$-0.869542\pi$
$397$	−36.5495	−1.83436	−0.917182	+	0.398467i	$0.869542\pi$
$398$	6.42104	0.321858
$399$	2.24035	0.112158
$400$	−5.06456	−0.253228
$401$	28.3160	1.41403	0.707016	−	0.707197i	$-0.250041\pi$
$401$	28.3160	1.41403	0.707016	+	0.707197i	$0.250041\pi$
$402$	−36.0498	−1.79800
$403$	−30.2581	−1.50726
$404$	−17.5923	−0.875248
$405$	−20.5131	−1.01930
$406$	10.9817	0.545015
$407$	7.65954	0.379669
$408$	−46.1770	−2.28610
$409$	−14.6045	−0.722146	−0.361073	−	0.932538i	$-0.617590\pi$
$409$	−14.6045	−0.722146	−0.361073	+	0.932538i	$0.617590\pi$
$410$	44.5846	2.20188
$411$	0.371439	0.0183218
$412$	−58.5486	−2.88448
$413$	11.8449	0.582850
$414$	−12.3694	−0.607924
$415$	−20.0670	−0.985050
$416$	6.11945	0.300031
$417$	45.4316	2.22480
$418$	−9.31804	−0.455760
$419$	32.1144	1.56889	0.784445	−	0.620198i	$-0.212948\pi$
$419$	32.1144	1.56889	0.784445	+	0.620198i	$0.212948\pi$
$420$	14.5884	0.711839
$421$	−32.4989	−1.58390	−0.791950	−	0.610586i	$-0.790934\pi$
$421$	−32.4989	−1.58390	−0.791950	+	0.610586i	$0.790934\pi$
$422$	44.1969	2.15147
$423$	−7.48438	−0.363903
$424$	−21.3668	−1.03766
$425$	8.28009	0.401643
$426$	28.7292	1.39193
$427$	13.9412	0.674664
$428$	−8.47154	−0.409487
$429$	−30.4246	−1.46891
$430$	−47.3248	−2.28221
$431$	6.64321	0.319992	0.159996	−	0.987118i	$-0.448852\pi$
$431$	6.64321	0.319992	0.159996	+	0.987118i	$0.448852\pi$
$432$	10.6907	0.514357
$433$	6.59652	0.317008	0.158504	−	0.987358i	$-0.449333\pi$
$433$	6.59652	0.317008	0.158504	+	0.987358i	$0.449333\pi$
$434$	−17.8618	−0.857396
$435$	−17.2709	−0.828077
$436$	−17.6364	−0.844631
$437$	4.18674	0.200279
$438$	64.5580	3.08470
$439$	0.373588	0.0178304	0.00891518	−	0.999960i	$-0.497162\pi$
$439$	0.373588	0.0178304	0.00891518	+	0.999960i	$0.497162\pi$
$440$	−29.0642	−1.38558
$441$	1.31818	0.0627705
$442$	49.4664	2.35288
$443$	−8.98014	−0.426659	−0.213330	−	0.976980i	$-0.568431\pi$
$443$	−8.98014	−0.426659	−0.213330	+	0.976980i	$0.568431\pi$
$444$	−17.0827	−0.810708
$445$	2.16623	0.102689
$446$	−35.4571	−1.67894
$447$	6.93830	0.328170
$448$	9.73038	0.459717
$449$	−7.71156	−0.363931	−0.181966	−	0.983305i	$-0.558246\pi$
$449$	−7.71156	−0.363931	−0.181966	+	0.983305i	$0.558246\pi$
$450$	5.27355	0.248598
$451$	−36.0879	−1.69931
$452$	29.1848	1.37274
$453$	32.0478	1.50574
$454$	−24.0199	−1.12731
$455$	−7.48574	−0.350937
$456$	9.95454	0.466164
$457$	19.0573	0.891461	0.445731	−	0.895167i	$-0.352944\pi$
$457$	19.0573	0.891461	0.445731	+	0.895167i	$0.352944\pi$
$458$	−21.2194	−0.991519
$459$	−17.4783	−0.815817
$460$	27.2626	1.27113
$461$	−5.65766	−0.263504	−0.131752	−	0.991283i	$-0.542060\pi$
$461$	−5.65766	−0.263504	−0.131752	+	0.991283i	$0.542060\pi$
$462$	−17.9602	−0.835582
$463$	33.2581	1.54563	0.772817	−	0.634629i	$-0.218847\pi$
$463$	33.2581	1.54563	0.772817	+	0.634629i	$0.218847\pi$
$464$	13.9023	0.645396
$465$	28.0912	1.30270
$466$	−30.7320	−1.42363
$467$	−16.8660	−0.780467	−0.390234	−	0.920716i	$-0.627606\pi$
$467$	−16.8660	−0.780467	−0.390234	+	0.920716i	$0.627606\pi$
$468$	20.7134	0.957479
$469$	7.17942	0.331515
$470$	25.0900	1.15732
$471$	13.0784	0.602620
$472$	52.6305	2.42252
$473$	38.3059	1.76131
$474$	50.4728	2.31829
$475$	−1.78497	−0.0818999
$476$	19.1986	0.879966
$477$	6.33883	0.290235
$478$	3.04863	0.139441
$479$	0.645377	0.0294880	0.0147440	−	0.999891i	$-0.495307\pi$
$479$	0.645377	0.0294880	0.0147440	+	0.999891i	$0.495307\pi$
$480$	−5.68122	−0.259311
$481$	8.76565	0.399679
$482$	−40.3330	−1.83712
$483$	8.06978	0.367188
$484$	6.88536	0.312971
$485$	−8.67943	−0.394112
$486$	−30.9887	−1.40568
$487$	−36.0063	−1.63160	−0.815800	−	0.578334i	$-0.803703\pi$
$487$	−36.0063	−1.63160	−0.815800	+	0.578334i	$0.803703\pi$
$488$	61.9451	2.80412
$489$	−44.2184	−1.99963
$490$	−4.41896	−0.199628
$491$	−14.9227	−0.673454	−0.336727	−	0.941602i	$-0.609320\pi$
$491$	−14.9227	−0.673454	−0.336727	+	0.941602i	$0.609320\pi$
$492$	80.4850	3.62854
$493$	−22.7289	−1.02366
$494$	−10.6637	−0.479780
$495$	8.62241	0.387548
$496$	−22.6121	−1.01531
$497$	−5.72149	−0.256644
$498$	−55.0984	−2.46902
$499$	3.50914	0.157091	0.0785453	−	0.996911i	$-0.474972\pi$
$499$	3.50914	0.157091	0.0785453	+	0.996911i	$0.474972\pi$
$500$	−46.7246	−2.08959
$501$	−17.6525	−0.788658
$502$	−55.1690	−2.46231
$503$	−5.98439	−0.266831	−0.133415	−	0.991060i	$-0.542594\pi$
$503$	−5.98439	−0.266831	−0.133415	+	0.991060i	$0.542594\pi$
$504$	5.85708	0.260895
$505$	−8.38067	−0.372935
$506$	−33.5638	−1.49209
$507$	−7.80387	−0.346582
$508$	−73.0549	−3.24129
$509$	20.0372	0.888134	0.444067	−	0.895993i	$-0.353535\pi$
$509$	20.0372	0.888134	0.444067	+	0.895993i	$0.353535\pi$
$510$	−45.9240	−2.03355
$511$	−12.8569	−0.568756
$512$	31.7571	1.40348
$513$	3.76786	0.166355
$514$	21.6805	0.956287
$515$	−27.8916	−1.22905
$516$	−85.4317	−3.76092
$517$	−20.3085	−0.893166
$518$	5.17451	0.227355
$519$	−15.9384	−0.699619
$520$	−33.2614	−1.45861
$521$	19.9441	0.873768	0.436884	−	0.899518i	$-0.356082\pi$
$521$	19.9441	0.873768	0.436884	+	0.899518i	$0.356082\pi$
$522$	−14.4759	−0.633594
$523$	−35.9958	−1.57399	−0.786993	−	0.616962i	$-0.788363\pi$
$523$	−35.9958	−1.57399	−0.786993	+	0.616962i	$0.788363\pi$
$524$	−4.67978	−0.204437
$525$	−3.44045	−0.150154
$526$	21.9856	0.958617
$527$	36.9686	1.61038
$528$	−22.7365	−0.989480
$529$	−7.91927	−0.344316
$530$	−21.2497	−0.923029
$531$	−15.6137	−0.677579
$532$	−4.13871	−0.179436
$533$	−41.2993	−1.78887
$534$	5.94788	0.257390
$535$	−4.03571	−0.174479
$536$	31.9003	1.37788
$537$	21.9462	0.947048
$538$	−3.65214	−0.157455
$539$	3.57682	0.154064
$540$	24.5350	1.05582
$541$	−37.1597	−1.59762	−0.798811	−	0.601583i	$-0.794537\pi$
$541$	−37.1597	−1.59762	−0.798811	+	0.601583i	$0.794537\pi$
$542$	39.8289	1.71080
$543$	−44.9086	−1.92721
$544$	−7.47660	−0.320557
$545$	−8.40171	−0.359890
$546$	−20.5538	−0.879620
$547$	−13.9690	−0.597270	−0.298635	−	0.954367i	$-0.596531\pi$
$547$	−13.9690	−0.597270	−0.298635	+	0.954367i	$0.596531\pi$
$548$	−0.686178	−0.0293121
$549$	−18.3771	−0.784315
$550$	14.3095	0.610160
$551$	4.89974	0.208736
$552$	35.8565	1.52615
$553$	−10.0518	−0.427446
$554$	−18.6636	−0.792939
$555$	−8.13792	−0.345435
$556$	−83.9281	−3.55934
$557$	20.8438	0.883180	0.441590	−	0.897217i	$-0.354415\pi$
$557$	20.8438	0.883180	0.441590	+	0.897217i	$0.354415\pi$
$558$	23.5452	0.996746
$559$	43.8376	1.85413
$560$	−5.59414	−0.236396
$561$	37.1721	1.56941
$562$	8.30881	0.350486
$563$	−46.1988	−1.94705	−0.973524	−	0.228585i	$-0.926590\pi$
$563$	−46.1988	−1.94705	−0.973524	+	0.228585i	$0.926590\pi$
$564$	45.2930	1.90718
$565$	13.9032	0.584912
$566$	10.5529	0.443571
$567$	11.2169	0.471067
$568$	−25.4223	−1.06670
$569$	−27.4620	−1.15127	−0.575634	−	0.817707i	$-0.695245\pi$
$569$	−27.4620	−1.15127	−0.575634	+	0.817707i	$0.695245\pi$
$570$	9.90000	0.414666
$571$	19.7917	0.828258	0.414129	−	0.910218i	$-0.364086\pi$
$571$	19.7917	0.828258	0.414129	+	0.910218i	$0.364086\pi$
$572$	56.2048	2.35004
$573$	−20.0267	−0.836629
$574$	−24.3797	−1.01759
$575$	−6.42949	−0.268128
$576$	−12.8264	−0.534433
$577$	−20.5167	−0.854120	−0.427060	−	0.904223i	$-0.640451\pi$
$577$	−20.5167	−0.854120	−0.427060	+	0.904223i	$0.640451\pi$
$578$	−19.3587	−0.805216
$579$	−0.109391	−0.00454612
$580$	31.9054	1.32480
$581$	10.9730	0.455237
$582$	−23.8313	−0.987839
$583$	17.2001	0.712354
$584$	−57.1271	−2.36394
$585$	9.86756	0.407973
$586$	−40.2592	−1.66309
$587$	−10.0038	−0.412902	−0.206451	−	0.978457i	$-0.566191\pi$
$587$	−10.0038	−0.412902	−0.206451	+	0.978457i	$0.566191\pi$
$588$	−7.97719	−0.328974
$589$	−7.96945	−0.328376
$590$	52.3422	2.15489
$591$	−17.7777	−0.731279
$592$	6.55063	0.269229
$593$	−21.9442	−0.901142	−0.450571	−	0.892741i	$-0.648780\pi$
$593$	−21.9442	−0.901142	−0.450571	+	0.892741i	$0.648780\pi$
$594$	−30.2057	−1.23936
$595$	9.14590	0.374945
$596$	−12.8175	−0.525023
$597$	5.52196	0.225999
$598$	−38.4107	−1.57073
$599$	44.3277	1.81118	0.905591	−	0.424152i	$-0.139428\pi$
$599$	44.3277	1.81118	0.905591	+	0.424152i	$0.139428\pi$
$600$	−15.2870	−0.624088
$601$	39.0449	1.59268	0.796338	−	0.604852i	$-0.206768\pi$
$601$	39.0449	1.59268	0.796338	+	0.604852i	$0.206768\pi$
$602$	25.8781	1.05471
$603$	−9.46378	−0.385395
$604$	−59.2036	−2.40896
$605$	3.28008	0.133354
$606$	−23.0110	−0.934759
$607$	−9.98500	−0.405279	−0.202639	−	0.979253i	$-0.564952\pi$
$607$	−9.98500	−0.405279	−0.202639	+	0.979253i	$0.564952\pi$
$608$	1.61176	0.0653654
$609$	9.44406	0.382693
$610$	61.6057	2.49434
$611$	−23.2412	−0.940238
$612$	−25.3072	−1.02298
$613$	−27.3350	−1.10405	−0.552026	−	0.833827i	$-0.686145\pi$
$613$	−27.3350	−1.10405	−0.552026	+	0.833827i	$0.686145\pi$
$614$	37.6218	1.51829
$615$	38.3418	1.54609
$616$	15.8929	0.640342
$617$	35.2210	1.41794	0.708971	−	0.705238i	$-0.249160\pi$
$617$	35.2210	1.41794	0.708971	+	0.705238i	$0.249160\pi$
$618$	−76.5827	−3.08061
$619$	−34.7257	−1.39574	−0.697872	−	0.716223i	$-0.745869\pi$
$619$	−34.7257	−1.39574	−0.697872	+	0.716223i	$0.745869\pi$
$620$	−51.8943	−2.08412
$621$	13.5719	0.544622
$622$	−19.6673	−0.788587
$623$	−1.18454	−0.0474575
$624$	−26.0199	−1.04163
$625$	−13.9807	−0.559227
$626$	−62.6138	−2.50255
$627$	−8.01331	−0.320021
$628$	−24.1603	−0.964102
$629$	−10.7097	−0.427022
$630$	5.82499	0.232073
$631$	−33.2275	−1.32276	−0.661382	−	0.750049i	$-0.730030\pi$
$631$	−33.2275	−1.32276	−0.661382	+	0.750049i	$0.730030\pi$
$632$	−44.6632	−1.77661
$633$	38.0083	1.51070
$634$	−5.54240	−0.220117
$635$	−34.8022	−1.38108
$636$	−38.3604	−1.52109
$637$	4.09334	0.162184
$638$	−39.2797	−1.55510
$639$	7.54197	0.298356
$640$	37.5302	1.48351
$641$	−36.1210	−1.42670	−0.713348	−	0.700810i	$-0.752822\pi$
$641$	−36.1210	−1.42670	−0.713348	+	0.700810i	$0.752822\pi$
$642$	−11.0809	−0.437330
$643$	−47.7758	−1.88409	−0.942046	−	0.335484i	$-0.891100\pi$
$643$	−47.7758	−1.88409	−0.942046	+	0.335484i	$0.891100\pi$
$644$	−14.9077	−0.587446
$645$	−40.6983	−1.60249
$646$	13.0286	0.512604
$647$	−37.3263	−1.46745	−0.733724	−	0.679448i	$-0.762220\pi$
$647$	−37.3263	−1.46745	−0.733724	+	0.679448i	$0.762220\pi$
$648$	49.8403	1.95791
$649$	−42.3671	−1.66305
$650$	16.3759	0.642317
$651$	−15.3608	−0.602037
$652$	81.6869	3.19910
$653$	−37.5805	−1.47064	−0.735320	−	0.677720i	$-0.762968\pi$
$653$	−37.5805	−1.47064	−0.735320	+	0.677720i	$0.762968\pi$
$654$	−23.0688	−0.902060
$655$	−2.22937	−0.0871088
$656$	−30.8633	−1.20501
$657$	16.9477	0.661194
$658$	−13.7197	−0.534849
$659$	−0.791143	−0.0308185	−0.0154093	−	0.999881i	$-0.504905\pi$
$659$	−0.791143	−0.0308185	−0.0154093	+	0.999881i	$0.504905\pi$
$660$	−52.1799	−2.03110
$661$	−37.2950	−1.45061	−0.725303	−	0.688430i	$-0.758300\pi$
$661$	−37.2950	−1.45061	−0.725303	+	0.688430i	$0.758300\pi$
$662$	−7.83619	−0.304562
$663$	42.5400	1.65212
$664$	48.7564	1.89211
$665$	−1.97161	−0.0764559
$666$	−6.82095	−0.264306
$667$	17.6490	0.683371
$668$	32.6104	1.26173
$669$	−30.4923	−1.17890
$670$	31.7255	1.22566
$671$	−49.8652	−1.92503
$672$	3.10660	0.119840
$673$	28.7761	1.10924	0.554618	−	0.832105i	$-0.312864\pi$
$673$	28.7761	1.10924	0.554618	+	0.832105i	$0.312864\pi$
$674$	39.6754	1.52824
$675$	−5.78622	−0.222712
$676$	14.4165	0.554480
$677$	41.4126	1.59161	0.795807	−	0.605550i	$-0.207047\pi$
$677$	41.4126	1.59161	0.795807	+	0.605550i	$0.207047\pi$
$678$	38.1743	1.46608
$679$	4.74607	0.182138
$680$	40.6380	1.55840
$681$	−20.6566	−0.791562
$682$	63.8885	2.44642
$683$	−11.4579	−0.438423	−0.219212	−	0.975677i	$-0.570348\pi$
$683$	−11.4579	−0.438423	−0.219212	+	0.975677i	$0.570348\pi$
$684$	5.45557	0.208599
$685$	−0.326884	−0.0124896
$686$	2.41637	0.0922574
$687$	−18.2483	−0.696214
$688$	32.7602	1.24897
$689$	19.6839	0.749897
$690$	35.6600	1.35755
$691$	−34.0203	−1.29419	−0.647097	−	0.762408i	$-0.724017\pi$
$691$	−34.0203	−1.29419	−0.647097	+	0.762408i	$0.724017\pi$
$692$	29.4438	1.11929
$693$	−4.71489	−0.179104
$694$	29.7164	1.12802
$695$	−39.9820	−1.51660
$696$	41.9628	1.59060
$697$	50.4586	1.91125
$698$	−41.1486	−1.55750
$699$	−26.4288	−0.999630
$700$	6.35572	0.240224
$701$	−22.9716	−0.867627	−0.433814	−	0.901003i	$-0.642832\pi$
$701$	−22.9716	−0.867627	−0.433814	+	0.901003i	$0.642832\pi$
$702$	−34.5677	−1.30467
$703$	2.30872	0.0870751
$704$	−34.8038	−1.31172
$705$	21.5768	0.812631
$706$	−47.3573	−1.78231
$707$	4.58271	0.172351
$708$	94.4891	3.55112
$709$	8.21296	0.308444	0.154222	−	0.988036i	$-0.450713\pi$
$709$	8.21296	0.308444	0.154222	+	0.988036i	$0.450713\pi$
$710$	−25.2830	−0.948855
$711$	13.2501	0.496918
$712$	−5.26325	−0.197249
$713$	−28.7061	−1.07505
$714$	25.1121	0.939797
$715$	26.7751	1.00133
$716$	−40.5423	−1.51514
$717$	2.62175	0.0979112
$718$	60.8223	2.26987
$719$	−15.7706	−0.588143	−0.294072	−	0.955783i	$-0.595010\pi$
$719$	−15.7706	−0.588143	−0.294072	+	0.955783i	$0.595010\pi$
$720$	7.37410	0.274816
$721$	15.2517	0.568002
$722$	43.1024	1.60410
$723$	−34.6855	−1.28997
$724$	82.9619	3.08326
$725$	−7.52443	−0.279450
$726$	9.00619	0.334251
$727$	14.6487	0.543288	0.271644	−	0.962398i	$-0.412433\pi$
$727$	14.6487	0.543288	0.271644	+	0.962398i	$0.412433\pi$
$728$	18.1879	0.674090
$729$	7.00123	0.259305
$730$	−56.8141	−2.10278
$731$	−53.5598	−1.98098
$732$	111.212	4.11051
$733$	2.19023	0.0808978	0.0404489	−	0.999182i	$-0.487121\pi$
$733$	2.19023	0.0808978	0.0404489	+	0.999182i	$0.487121\pi$
$734$	67.5369	2.49283
$735$	−3.80021	−0.140173
$736$	5.80558	0.213996
$737$	−25.6795	−0.945915
$738$	32.1368	1.18297
$739$	−16.4894	−0.606574	−0.303287	−	0.952899i	$-0.598084\pi$
$739$	−16.4894	−0.606574	−0.303287	+	0.952899i	$0.598084\pi$
$740$	15.0336	0.552645
$741$	−9.17051	−0.336887
$742$	11.6197	0.426574
$743$	−10.3331	−0.379086	−0.189543	−	0.981872i	$-0.560701\pi$
$743$	−10.3331	−0.379086	−0.189543	+	0.981872i	$0.560701\pi$
$744$	−68.2526	−2.50226
$745$	−6.10603	−0.223708
$746$	−11.8861	−0.435181
$747$	−14.4644	−0.529225
$748$	−68.6698	−2.51082
$749$	2.20680	0.0806347
$750$	−61.1167	−2.23167
$751$	14.9198	0.544431	0.272215	−	0.962236i	$-0.412244\pi$
$751$	14.9198	0.544431	0.272215	+	0.962236i	$0.412244\pi$
$752$	−17.3683	−0.633357
$753$	−47.4441	−1.72896
$754$	−44.9520	−1.63706
$755$	−28.2036	−1.02644
$756$	−13.4162	−0.487942
$757$	21.0869	0.766417	0.383208	−	0.923662i	$-0.374819\pi$
$757$	21.0869	0.766417	0.383208	+	0.923662i	$0.374819\pi$
$758$	−15.1444	−0.550068
$759$	−28.8641	−1.04770
$760$	−8.76047	−0.317776
$761$	10.5388	0.382031	0.191015	−	0.981587i	$-0.438822\pi$
$761$	10.5388	0.382031	0.191015	+	0.981587i	$0.438822\pi$
$762$	−95.5572	−3.46167
$763$	4.59421	0.166322
$764$	36.9964	1.33848
$765$	−12.0560	−0.435884
$766$	−5.80425	−0.209716
$767$	−48.4853	−1.75070
$768$	62.6077	2.25916
$769$	−45.8073	−1.65185	−0.825927	−	0.563776i	$-0.809348\pi$
$769$	−45.8073	−1.65185	−0.825927	+	0.563776i	$0.809348\pi$
$770$	15.8058	0.569601
$771$	18.6448	0.671475
$772$	0.202083	0.00727312
$773$	−6.31200	−0.227027	−0.113513	−	0.993536i	$-0.536211\pi$
$773$	−6.31200	−0.227027	−0.113513	+	0.993536i	$0.536211\pi$
$774$	−34.1120	−1.22613
$775$	12.2385	0.439620
$776$	21.0882	0.757023
$777$	4.44997	0.159642
$778$	−18.0297	−0.646397
$779$	−10.8775	−0.389728
$780$	−59.7151	−2.13814
$781$	20.4647	0.732285
$782$	46.9293	1.67819
$783$	15.8832	0.567619
$784$	3.05898	0.109249
$785$	−11.5096	−0.410795
$786$	−6.12124	−0.218337
$787$	−53.0236	−1.89009	−0.945044	−	0.326943i	$-0.893981\pi$
$787$	−53.0236	−1.89009	−0.945044	+	0.326943i	$0.893981\pi$
$788$	32.8417	1.16994
$789$	18.9071	0.673112
$790$	−44.4185	−1.58034
$791$	−7.60253	−0.270315
$792$	−20.9497	−0.744415
$793$	−57.0662	−2.02648
$794$	88.3170	3.13425
$795$	−18.2743	−0.648123
$796$	−10.2010	−0.361564
$797$	19.8775	0.704096	0.352048	−	0.935982i	$-0.385485\pi$
$797$	19.8775	0.704096	0.352048	+	0.935982i	$0.385485\pi$
$798$	−5.41351	−0.191636
$799$	28.3956	1.00456
$800$	−2.47514	−0.0875094
$801$	1.56143	0.0551706
$802$	−68.4218	−2.41606
$803$	45.9868	1.62284
$804$	57.2716	2.01981
$805$	−7.10179	−0.250305
$806$	73.1146	2.57535
$807$	−3.14076	−0.110560
$808$	20.3624	0.716345
$809$	35.5303	1.24918	0.624590	−	0.780953i	$-0.285266\pi$
$809$	35.5303	1.24918	0.624590	+	0.780953i	$0.285266\pi$
$810$	49.5672	1.74161
$811$	22.6318	0.794711	0.397356	−	0.917665i	$-0.369928\pi$
$811$	22.6318	0.794711	0.397356	+	0.917665i	$0.369928\pi$
$812$	−17.4465	−0.612251
$813$	34.2519	1.20127
$814$	−18.5083	−0.648715
$815$	38.9143	1.36311
$816$	31.7905	1.11289
$817$	11.5461	0.403946
$818$	35.2899	1.23388
$819$	−5.39576	−0.188543
$820$	−70.8306	−2.47351
$821$	14.7289	0.514041	0.257020	−	0.966406i	$-0.417259\pi$
$821$	14.7289	0.514041	0.257020	+	0.966406i	$0.417259\pi$
$822$	−0.897534	−0.0313051
$823$	−17.8989	−0.623915	−0.311958	−	0.950096i	$-0.600985\pi$
$823$	−17.8989	−0.623915	−0.311958	+	0.950096i	$0.600985\pi$
$824$	67.7678	2.36080
$825$	12.3059	0.428435
$826$	−28.6217	−0.995875
$827$	44.0894	1.53314	0.766569	−	0.642162i	$-0.221962\pi$
$827$	44.0894	1.53314	0.766569	+	0.642162i	$0.221962\pi$
$828$	19.6510	0.682921
$829$	−44.3535	−1.54046	−0.770230	−	0.637767i	$-0.779858\pi$
$829$	−44.3535	−1.54046	−0.770230	+	0.637767i	$0.779858\pi$
$830$	48.4893	1.68309
$831$	−16.0503	−0.556777
$832$	−39.8297	−1.38085
$833$	−5.00115	−0.173280
$834$	−109.780	−3.80135
$835$	15.5351	0.537614
$836$	14.8034	0.511986
$837$	−25.8341	−0.892956
$838$	−77.6002	−2.68065
$839$	47.7556	1.64870	0.824352	−	0.566077i	$-0.191539\pi$
$839$	47.7556	1.64870	0.824352	+	0.566077i	$0.191539\pi$
$840$	−16.8855	−0.582604
$841$	−8.34541	−0.287773
$842$	78.5293	2.70630
$843$	7.14540	0.246101
$844$	−70.2146	−2.41689
$845$	6.86778	0.236259
$846$	18.0850	0.621776
$847$	−1.79361	−0.0616291
$848$	14.7099	0.505141
$849$	9.07525	0.311462
$850$	−20.0077	−0.686260
$851$	8.31606	0.285071
$852$	−45.6414	−1.56365
$853$	20.5305	0.702952	0.351476	−	0.936197i	$-0.385680\pi$
$853$	20.5305	0.702952	0.351476	+	0.936197i	$0.385680\pi$
$854$	−33.6872	−1.15275
$855$	2.59894	0.0888820
$856$	9.80548	0.335144
$857$	−46.6554	−1.59372	−0.796858	−	0.604166i	$-0.793506\pi$
$857$	−46.6554	−1.59372	−0.796858	+	0.604166i	$0.793506\pi$
$858$	73.5170	2.50983
$859$	10.9177	0.372506	0.186253	−	0.982502i	$-0.440366\pi$
$859$	10.9177	0.372506	0.186253	+	0.982502i	$0.440366\pi$
$860$	75.1840	2.56375
$861$	−20.9660	−0.714519
$862$	−16.0524	−0.546748
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	5.22473	0.177749
$865$	14.0266	0.476918
$866$	−15.9396	−0.541650
$867$	−16.6481	−0.565398
$868$	28.3768	0.963170
$869$	35.9535	1.21964
$870$	41.7329	1.41488
$871$	−29.3878	−0.995767
$872$	20.4135	0.691287
$873$	−6.25618	−0.211740
$874$	−10.1167	−0.342203
$875$	12.1716	0.411474
$876$	−102.562	−3.46525
$877$	3.20188	0.108120	0.0540599	−	0.998538i	$-0.482784\pi$
$877$	3.20188	0.108120	0.0540599	+	0.998538i	$0.482784\pi$
$878$	−0.902725	−0.0304655
$879$	−34.6220	−1.16777
$880$	20.0092	0.674511
$881$	−27.0279	−0.910592	−0.455296	−	0.890340i	$-0.650467\pi$
$881$	−27.0279	−0.910592	−0.455296	+	0.890340i	$0.650467\pi$
$882$	−3.18521	−0.107252
$883$	−9.44255	−0.317767	−0.158884	−	0.987297i	$-0.550789\pi$
$883$	−9.44255	−0.317767	−0.158884	+	0.987297i	$0.550789\pi$
$884$	−78.5863	−2.64314
$885$	45.0131	1.51310
$886$	21.6993	0.729003
$887$	35.6633	1.19746	0.598728	−	0.800952i	$-0.295673\pi$
$887$	35.6633	1.19746	0.598728	+	0.800952i	$0.295673\pi$
$888$	19.7725	0.663523
$889$	19.0305	0.638262
$890$	−5.23442	−0.175458
$891$	−40.1209	−1.34410
$892$	56.3299	1.88607
$893$	−6.12133	−0.204843
$894$	−16.7655	−0.560721
$895$	−19.3137	−0.645586
$896$	−20.5222	−0.685599
$897$	−33.0323	−1.10292
$898$	18.6340	0.621824
$899$	−33.5948	−1.12045
$900$	−8.37799	−0.279266
$901$	−24.0494	−0.801200
$902$	87.2016	2.90350
$903$	22.2546	0.740587
$904$	−33.7803	−1.12352
$905$	39.5218	1.31375
$906$	−77.4394	−2.57275
$907$	−14.7016	−0.488159	−0.244079	−	0.969755i	$-0.578486\pi$
$907$	−14.7016	−0.488159	−0.244079	+	0.969755i	$0.578486\pi$
$908$	38.1599	1.26638
$909$	−6.04084	−0.200362
$910$	18.0883	0.599621
$911$	−13.0679	−0.432959	−0.216479	−	0.976287i	$-0.569457\pi$
$911$	−13.0679	−0.432959	−0.216479	+	0.976287i	$0.569457\pi$
$912$	−6.85319	−0.226932
$913$	−39.2484	−1.29893
$914$	−46.0494	−1.52318
$915$	52.9796	1.75145
$916$	33.7109	1.11384
$917$	1.21906	0.0402570
$918$	42.2340	1.39393
$919$	28.2758	0.932731	0.466366	−	0.884592i	$-0.345563\pi$
$919$	28.2758	0.932731	0.466366	+	0.884592i	$0.345563\pi$
$920$	−31.5554	−1.04035
$921$	32.3539	1.06610
$922$	13.6710	0.450230
$923$	23.4200	0.770879
$924$	28.5329	0.938664
$925$	−3.54545	−0.116574
$926$	−80.3637	−2.64092
$927$	−20.1045	−0.660317
$928$	6.79427	0.223033
$929$	15.2495	0.500319	0.250160	−	0.968205i	$-0.419517\pi$
$929$	15.2495	0.500319	0.250160	+	0.968205i	$0.419517\pi$
$930$	−67.8787	−2.22583
$931$	1.07812	0.0353338
$932$	48.8233	1.59926
$933$	−16.9135	−0.553722
$934$	40.7545	1.33353
$935$	−32.7132	−1.06984
$936$	−23.9750	−0.783648
$937$	30.4668	0.995307	0.497654	−	0.867376i	$-0.334195\pi$
$937$	30.4668	0.995307	0.497654	+	0.867376i	$0.334195\pi$
$938$	−17.3481	−0.566436
$939$	−53.8465	−1.75721
$940$	−39.8600	−1.30009
$941$	48.3128	1.57495	0.787477	−	0.616344i	$-0.211387\pi$
$941$	48.3128	1.57495	0.787477	+	0.616344i	$0.211387\pi$
$942$	−31.6022	−1.02965
$943$	−39.1811	−1.27591
$944$	−36.2334	−1.17930
$945$	−6.39126	−0.207908
$946$	−92.5612	−3.00942
$947$	−29.9677	−0.973818	−0.486909	−	0.873453i	$-0.661876\pi$
$947$	−29.9677	−0.973818	−0.486909	+	0.873453i	$0.661876\pi$
$948$	−80.1852	−2.60429
$949$	52.6277	1.70837
$950$	4.31314	0.139937
$951$	−4.76634	−0.154559
$952$	−22.2216	−0.720206
$953$	−58.4596	−1.89369	−0.946846	−	0.321686i	$-0.895750\pi$
$953$	−58.4596	−1.89369	−0.946846	+	0.321686i	$0.895750\pi$
$954$	−15.3169	−0.495904
$955$	17.6245	0.570315
$956$	−4.84330	−0.156643
$957$	−33.7797	−1.09194
$958$	−1.55947	−0.0503842
$959$	0.178747	0.00577203
$960$	36.9774	1.19344
$961$	23.6420	0.762645
$962$	−21.1810	−0.682904
$963$	−2.90896	−0.0937400
$964$	64.0763	2.06376
$965$	0.0962691	0.00309901
$966$	−19.4996	−0.627388
$967$	23.3363	0.750446	0.375223	−	0.926935i	$-0.377566\pi$
$967$	23.3363	0.750446	0.375223	+	0.926935i	$0.377566\pi$
$968$	−7.96954	−0.256151
$969$	11.2043	0.359934
$970$	20.9727	0.673392
$971$	−12.9004	−0.413994	−0.206997	−	0.978342i	$-0.566369\pi$
$971$	−12.9004	−0.413994	−0.206997	+	0.978342i	$0.566369\pi$
$972$	49.2311	1.57909
$973$	21.8629	0.700893
$974$	87.0044	2.78780
$975$	14.0829	0.451015
$976$	−42.6460	−1.36506
$977$	37.5502	1.20134	0.600669	−	0.799498i	$-0.294901\pi$
$977$	37.5502	1.20134	0.600669	+	0.799498i	$0.294901\pi$
$978$	106.848	3.41662
$979$	4.23687	0.135411
$980$	7.02031	0.224255
$981$	−6.05600	−0.193353
$982$	36.0589	1.15068
$983$	31.1881	0.994746	0.497373	−	0.867537i	$-0.334298\pi$
$983$	31.1881	0.994746	0.497373	+	0.867537i	$0.334298\pi$
$984$	−93.1582	−2.96978
$985$	15.6453	0.498500
$986$	54.9213	1.74905
$987$	−11.7986	−0.375554
$988$	16.9411	0.538969
$989$	41.5892	1.32246
$990$	−20.8349	−0.662177
$991$	−54.9892	−1.74679	−0.873395	−	0.487013i	$-0.838087\pi$
$991$	−54.9892	−1.74679	−0.873395	+	0.487013i	$0.838087\pi$
$992$	−11.0509	−0.350866
$993$	−6.73895	−0.213854
$994$	13.8252	0.438510
$995$	−4.85959	−0.154059
$996$	87.5338	2.77361
$997$	34.3245	1.08707	0.543533	−	0.839388i	$-0.317086\pi$
$997$	34.3245	1.08707	0.543533	+	0.839388i	$0.317086\pi$
$998$	−8.47937	−0.268410
$999$	7.48404	0.236784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.d.1.8	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.d.1.8	✓	101	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41637 q^{2} -2.07802 q^{3} +3.83883 q^{4} +1.82876 q^{5} +5.02127 q^{6} -1.00000 q^{7} -4.44330 q^{8} +1.31818 q^{9} +O(q^{10})\)	\(q-2.41637 q^{2} -2.07802 q^{3} +3.83883 q^{4} +1.82876 q^{5} +5.02127 q^{6} -1.00000 q^{7} -4.44330 q^{8} +1.31818 q^{9} -4.41896 q^{10} +3.57682 q^{11} -7.97719 q^{12} +4.09334 q^{13} +2.41637 q^{14} -3.80021 q^{15} +3.05898 q^{16} -5.00115 q^{17} -3.18521 q^{18} +1.07812 q^{19} +7.02031 q^{20} +2.07802 q^{21} -8.64290 q^{22} +3.88339 q^{23} +9.23328 q^{24} -1.65564 q^{25} -9.89101 q^{26} +3.49486 q^{27} -3.83883 q^{28} +4.54473 q^{29} +9.18270 q^{30} -7.39202 q^{31} +1.49498 q^{32} -7.43271 q^{33} +12.0846 q^{34} -1.82876 q^{35} +5.06028 q^{36} +2.14144 q^{37} -2.60512 q^{38} -8.50606 q^{39} -8.12573 q^{40} -10.0894 q^{41} -5.02127 q^{42} +10.7095 q^{43} +13.7308 q^{44} +2.41064 q^{45} -9.38370 q^{46} -5.67781 q^{47} -6.35664 q^{48} +1.00000 q^{49} +4.00063 q^{50} +10.3925 q^{51} +15.7137 q^{52} +4.80877 q^{53} -8.44486 q^{54} +6.54114 q^{55} +4.44330 q^{56} -2.24035 q^{57} -10.9817 q^{58} -11.8449 q^{59} -14.5884 q^{60} -13.9412 q^{61} +17.8618 q^{62} -1.31818 q^{63} -9.73038 q^{64} +7.48574 q^{65} +17.9602 q^{66} -7.17942 q^{67} -19.1986 q^{68} -8.06978 q^{69} +4.41896 q^{70} +5.72149 q^{71} -5.85708 q^{72} +12.8569 q^{73} -5.17451 q^{74} +3.44045 q^{75} +4.13871 q^{76} -3.57682 q^{77} +20.5538 q^{78} +10.0518 q^{79} +5.59414 q^{80} -11.2169 q^{81} +24.3797 q^{82} -10.9730 q^{83} +7.97719 q^{84} -9.14590 q^{85} -25.8781 q^{86} -9.44406 q^{87} -15.8929 q^{88} +1.18454 q^{89} -5.82499 q^{90} -4.09334 q^{91} +14.9077 q^{92} +15.3608 q^{93} +13.7197 q^{94} +1.97161 q^{95} -3.10660 q^{96} -4.74607 q^{97} -2.41637 q^{98} +4.71489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * q^99

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