LMFDB - Embedded newform 4022.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.10960 q^{3} +1.00000 q^{4} +2.36799 q^{5} +1.10960 q^{6} +0.505980 q^{7} -1.00000 q^{8} -1.76879 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.10960 q^{3} +1.00000 q^{4} +2.36799 q^{5} +1.10960 q^{6} +0.505980 q^{7} -1.00000 q^{8} -1.76879 q^{9} -2.36799 q^{10} -3.96225 q^{11} -1.10960 q^{12} +2.83500 q^{13} -0.505980 q^{14} -2.62752 q^{15} +1.00000 q^{16} -4.17895 q^{17} +1.76879 q^{18} +2.34790 q^{19} +2.36799 q^{20} -0.561436 q^{21} +3.96225 q^{22} +0.120720 q^{23} +1.10960 q^{24} +0.607373 q^{25} -2.83500 q^{26} +5.29145 q^{27} +0.505980 q^{28} +5.49154 q^{29} +2.62752 q^{30} -2.86063 q^{31} -1.00000 q^{32} +4.39651 q^{33} +4.17895 q^{34} +1.19816 q^{35} -1.76879 q^{36} -0.733529 q^{37} -2.34790 q^{38} -3.14571 q^{39} -2.36799 q^{40} +2.42408 q^{41} +0.561436 q^{42} +5.41305 q^{43} -3.96225 q^{44} -4.18847 q^{45} -0.120720 q^{46} +4.21855 q^{47} -1.10960 q^{48} -6.74398 q^{49} -0.607373 q^{50} +4.63697 q^{51} +2.83500 q^{52} -4.78550 q^{53} -5.29145 q^{54} -9.38256 q^{55} -0.505980 q^{56} -2.60523 q^{57} -5.49154 q^{58} +9.35022 q^{59} -2.62752 q^{60} -10.8664 q^{61} +2.86063 q^{62} -0.894971 q^{63} +1.00000 q^{64} +6.71324 q^{65} -4.39651 q^{66} -5.28863 q^{67} -4.17895 q^{68} -0.133951 q^{69} -1.19816 q^{70} -5.68533 q^{71} +1.76879 q^{72} -8.62665 q^{73} +0.733529 q^{74} -0.673942 q^{75} +2.34790 q^{76} -2.00482 q^{77} +3.14571 q^{78} -14.7831 q^{79} +2.36799 q^{80} -0.565037 q^{81} -2.42408 q^{82} +11.1735 q^{83} -0.561436 q^{84} -9.89572 q^{85} -5.41305 q^{86} -6.09342 q^{87} +3.96225 q^{88} -5.14114 q^{89} +4.18847 q^{90} +1.43445 q^{91} +0.120720 q^{92} +3.17416 q^{93} -4.21855 q^{94} +5.55979 q^{95} +1.10960 q^{96} -14.2393 q^{97} +6.74398 q^{98} +7.00837 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) $ 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.10960	−0.640628	−0.320314	−	0.947311i	$-0.603788\pi$
$3$	−1.10960	−0.640628	−0.320314	+	0.947311i	$0.603788\pi$
$4$	1.00000	0.500000
$5$	2.36799	1.05900	0.529498	−	0.848311i	$-0.322380\pi$
$5$	2.36799	1.05900	0.529498	+	0.848311i	$0.322380\pi$
$6$	1.10960	0.452993
$7$	0.505980	0.191243	0.0956213	−	0.995418i	$-0.469516\pi$
$7$	0.505980	0.191243	0.0956213	+	0.995418i	$0.469516\pi$
$8$	−1.00000	−0.353553
$9$	−1.76879	−0.589595
$10$	−2.36799	−0.748824
$11$	−3.96225	−1.19466	−0.597331	−	0.801995i	$-0.703772\pi$
$11$	−3.96225	−1.19466	−0.597331	+	0.801995i	$0.703772\pi$
$12$	−1.10960	−0.320314
$13$	2.83500	0.786286	0.393143	−	0.919477i	$-0.371388\pi$
$13$	2.83500	0.786286	0.393143	+	0.919477i	$0.371388\pi$
$14$	−0.505980	−0.135229
$15$	−2.62752	−0.678423
$16$	1.00000	0.250000
$17$	−4.17895	−1.01355	−0.506773	−	0.862080i	$-0.669162\pi$
$17$	−4.17895	−1.01355	−0.506773	+	0.862080i	$0.669162\pi$
$18$	1.76879	0.416907
$19$	2.34790	0.538644	0.269322	−	0.963050i	$-0.413200\pi$
$19$	2.34790	0.538644	0.269322	+	0.963050i	$0.413200\pi$
$20$	2.36799	0.529498
$21$	−0.561436	−0.122515
$22$	3.96225	0.844754
$23$	0.120720	0.0251719	0.0125859	−	0.999921i	$-0.495994\pi$
$23$	0.120720	0.0251719	0.0125859	+	0.999921i	$0.495994\pi$
$24$	1.10960	0.226496
$25$	0.607373	0.121475
$26$	−2.83500	−0.555989
$27$	5.29145	1.01834
$28$	0.505980	0.0956213
$29$	5.49154	1.01975	0.509877	−	0.860248i	$-0.329691\pi$
$29$	5.49154	1.01975	0.509877	+	0.860248i	$0.329691\pi$
$30$	2.62752	0.479718
$31$	−2.86063	−0.513785	−0.256892	−	0.966440i	$-0.582699\pi$
$31$	−2.86063	−0.513785	−0.256892	+	0.966440i	$0.582699\pi$
$32$	−1.00000	−0.176777
$33$	4.39651	0.765335
$34$	4.17895	0.716685
$35$	1.19816	0.202525
$36$	−1.76879	−0.294798
$37$	−0.733529	−0.120591	−0.0602957	−	0.998181i	$-0.519204\pi$
$37$	−0.733529	−0.120591	−0.0602957	+	0.998181i	$0.519204\pi$
$38$	−2.34790	−0.380879
$39$	−3.14571	−0.503717
$40$	−2.36799	−0.374412
$41$	2.42408	0.378578	0.189289	−	0.981921i	$-0.439382\pi$
$41$	2.42408	0.378578	0.189289	+	0.981921i	$0.439382\pi$
$42$	0.561436	0.0866315
$43$	5.41305	0.825482	0.412741	−	0.910848i	$-0.364571\pi$
$43$	5.41305	0.825482	0.412741	+	0.910848i	$0.364571\pi$
$44$	−3.96225	−0.597331
$45$	−4.18847	−0.624380
$46$	−0.120720	−0.0177992
$47$	4.21855	0.615339	0.307670	−	0.951493i	$-0.400451\pi$
$47$	4.21855	0.615339	0.307670	+	0.951493i	$0.400451\pi$
$48$	−1.10960	−0.160157
$49$	−6.74398	−0.963426
$50$	−0.607373	−0.0858955
$51$	4.63697	0.649306
$52$	2.83500	0.393143
$53$	−4.78550	−0.657338	−0.328669	−	0.944445i	$-0.606600\pi$
$53$	−4.78550	−0.657338	−0.328669	+	0.944445i	$0.606600\pi$
$54$	−5.29145	−0.720075
$55$	−9.38256	−1.26514
$56$	−0.505980	−0.0676145
$57$	−2.60523	−0.345071
$58$	−5.49154	−0.721074
$59$	9.35022	1.21730	0.608648	−	0.793441i	$-0.291712\pi$
$59$	9.35022	1.21730	0.608648	+	0.793441i	$0.291712\pi$
$60$	−2.62752	−0.339212
$61$	−10.8664	−1.39130	−0.695652	−	0.718379i	$-0.744884\pi$
$61$	−10.8664	−1.39130	−0.695652	+	0.718379i	$0.744884\pi$
$62$	2.86063	0.363301
$63$	−0.894971	−0.112756
$64$	1.00000	0.125000
$65$	6.71324	0.832675
$66$	−4.39651	−0.541173
$67$	−5.28863	−0.646109	−0.323055	−	0.946380i	$-0.604710\pi$
$67$	−5.28863	−0.646109	−0.323055	+	0.946380i	$0.604710\pi$
$68$	−4.17895	−0.506773
$69$	−0.133951	−0.0161258
$70$	−1.19816	−0.143207
$71$	−5.68533	−0.674725	−0.337362	−	0.941375i	$-0.609535\pi$
$71$	−5.68533	−0.674725	−0.337362	+	0.941375i	$0.609535\pi$
$72$	1.76879	0.208453
$73$	−8.62665	−1.00967	−0.504836	−	0.863215i	$-0.668447\pi$
$73$	−8.62665	−1.00967	−0.504836	+	0.863215i	$0.668447\pi$
$74$	0.733529	0.0852710
$75$	−0.673942	−0.0778201
$76$	2.34790	0.269322
$77$	−2.00482	−0.228470
$78$	3.14571	0.356182
$79$	−14.7831	−1.66323	−0.831616	−	0.555352i	$-0.812584\pi$
$79$	−14.7831	−1.66323	−0.831616	+	0.555352i	$0.812584\pi$
$80$	2.36799	0.264749
$81$	−0.565037	−0.0627819
$82$	−2.42408	−0.267695
$83$	11.1735	1.22645	0.613227	−	0.789907i	$-0.289871\pi$
$83$	11.1735	1.22645	0.613227	+	0.789907i	$0.289871\pi$
$84$	−0.561436	−0.0612577
$85$	−9.89572	−1.07334
$86$	−5.41305	−0.583704
$87$	−6.09342	−0.653283
$88$	3.96225	0.422377
$89$	−5.14114	−0.544960	−0.272480	−	0.962161i	$-0.587844\pi$
$89$	−5.14114	−0.544960	−0.272480	+	0.962161i	$0.587844\pi$
$90$	4.18847	0.441503
$91$	1.43445	0.150371
$92$	0.120720	0.0125859
$93$	3.17416	0.329145
$94$	−4.21855	−0.435111
$95$	5.55979	0.570422
$96$	1.10960	0.113248
$97$	−14.2393	−1.44578	−0.722890	−	0.690963i	$-0.757187\pi$
$97$	−14.2393	−1.44578	−0.722890	+	0.690963i	$0.757187\pi$
$98$	6.74398	0.681245
$99$	7.00837	0.704368
$100$	0.607373	0.0607373
$101$	2.00402	0.199408	0.0997038	−	0.995017i	$-0.468210\pi$
$101$	2.00402	0.199408	0.0997038	+	0.995017i	$0.468210\pi$
$102$	−4.63697	−0.459128
$103$	−2.27215	−0.223881	−0.111941	−	0.993715i	$-0.535707\pi$
$103$	−2.27215	−0.223881	−0.111941	+	0.993715i	$0.535707\pi$
$104$	−2.83500	−0.277994
$105$	−1.32948	−0.129743
$106$	4.78550	0.464808
$107$	15.4805	1.49655	0.748276	−	0.663387i	$-0.230882\pi$
$107$	15.4805	1.49655	0.748276	+	0.663387i	$0.230882\pi$
$108$	5.29145	0.509170
$109$	−10.2893	−0.985540	−0.492770	−	0.870160i	$-0.664016\pi$
$109$	−10.2893	−0.985540	−0.492770	+	0.870160i	$0.664016\pi$
$110$	9.38256	0.894592
$111$	0.813924	0.0772542
$112$	0.505980	0.0478107
$113$	−9.85905	−0.927461	−0.463731	−	0.885976i	$-0.653489\pi$
$113$	−9.85905	−0.927461	−0.463731	+	0.885976i	$0.653489\pi$
$114$	2.60523	0.244002
$115$	0.285864	0.0266570
$116$	5.49154	0.509877
$117$	−5.01450	−0.463591
$118$	−9.35022	−0.860758
$119$	−2.11447	−0.193833
$120$	2.62752	0.239859
$121$	4.69941	0.427219
$122$	10.8664	0.983801
$123$	−2.68976	−0.242528
$124$	−2.86063	−0.256892
$125$	−10.4017	−0.930356
$126$	0.894971	0.0797304
$127$	−5.76105	−0.511211	−0.255605	−	0.966781i	$-0.582275\pi$
$127$	−5.76105	−0.511211	−0.255605	+	0.966781i	$0.582275\pi$
$128$	−1.00000	−0.0883883
$129$	−6.00632	−0.528827
$130$	−6.71324	−0.588790
$131$	13.6199	1.18997	0.594986	−	0.803736i	$-0.297158\pi$
$131$	13.6199	1.18997	0.594986	+	0.803736i	$0.297158\pi$
$132$	4.39651	0.382667
$133$	1.18799	0.103012
$134$	5.28863	0.456868
$135$	12.5301	1.07842
$136$	4.17895	0.358342
$137$	6.39040	0.545969	0.272984	−	0.962018i	$-0.411989\pi$
$137$	6.39040	0.545969	0.272984	+	0.962018i	$0.411989\pi$
$138$	0.133951	0.0114027
$139$	−15.8049	−1.34056	−0.670278	−	0.742110i	$-0.733825\pi$
$139$	−15.8049	−1.34056	−0.670278	+	0.742110i	$0.733825\pi$
$140$	1.19816	0.101263
$141$	−4.68091	−0.394204
$142$	5.68533	0.477103
$143$	−11.2330	−0.939347
$144$	−1.76879	−0.147399
$145$	13.0039	1.07992
$146$	8.62665	0.713946
$147$	7.48313	0.617198
$148$	−0.733529	−0.0602957
$149$	2.33898	0.191616	0.0958082	−	0.995400i	$-0.469456\pi$
$149$	2.33898	0.191616	0.0958082	+	0.995400i	$0.469456\pi$
$150$	0.673942	0.0550271
$151$	16.4745	1.34068	0.670339	−	0.742055i	$-0.266149\pi$
$151$	16.4745	1.34068	0.670339	+	0.742055i	$0.266149\pi$
$152$	−2.34790	−0.190439
$153$	7.39167	0.597581
$154$	2.00482	0.161553
$155$	−6.77395	−0.544096
$156$	−3.14571	−0.251859
$157$	0.700481	0.0559045	0.0279523	−	0.999609i	$-0.491101\pi$
$157$	0.700481	0.0559045	0.0279523	+	0.999609i	$0.491101\pi$
$158$	14.7831	1.17608
$159$	5.30999	0.421110
$160$	−2.36799	−0.187206
$161$	0.0610820	0.00481394
$162$	0.565037	0.0443935
$163$	5.98631	0.468884	0.234442	−	0.972130i	$-0.424674\pi$
$163$	5.98631	0.468884	0.234442	+	0.972130i	$0.424674\pi$
$164$	2.42408	0.189289
$165$	10.4109	0.810487
$166$	−11.1735	−0.867234
$167$	−18.4608	−1.42854	−0.714272	−	0.699869i	$-0.753242\pi$
$167$	−18.4608	−1.42854	−0.714272	+	0.699869i	$0.753242\pi$
$168$	0.561436	0.0433157
$169$	−4.96280	−0.381754
$170$	9.89572	0.758967
$171$	−4.15292	−0.317582
$172$	5.41305	0.412741
$173$	−0.558857	−0.0424891	−0.0212446	−	0.999774i	$-0.506763\pi$
$173$	−0.558857	−0.0424891	−0.0212446	+	0.999774i	$0.506763\pi$
$174$	6.09342	0.461941
$175$	0.307319	0.0232311
$176$	−3.96225	−0.298666
$177$	−10.3750	−0.779834
$178$	5.14114	0.385345
$179$	−8.40491	−0.628213	−0.314106	−	0.949388i	$-0.601705\pi$
$179$	−8.40491	−0.628213	−0.314106	+	0.949388i	$0.601705\pi$
$180$	−4.18847	−0.312190
$181$	14.8094	1.10077	0.550387	−	0.834910i	$-0.314480\pi$
$181$	14.8094	1.10077	0.550387	+	0.834910i	$0.314480\pi$
$182$	−1.43445	−0.106329
$183$	12.0574	0.891309
$184$	−0.120720	−0.00889961
$185$	−1.73699	−0.127706
$186$	−3.17416	−0.232741
$187$	16.5581	1.21084
$188$	4.21855	0.307670
$189$	2.67737	0.194750
$190$	−5.55979	−0.403350
$191$	8.56884	0.620019	0.310010	−	0.950733i	$-0.399668\pi$
$191$	8.56884	0.620019	0.310010	+	0.950733i	$0.399668\pi$
$192$	−1.10960	−0.0800785
$193$	0.617245	0.0444302	0.0222151	−	0.999753i	$-0.492928\pi$
$193$	0.617245	0.0444302	0.0222151	+	0.999753i	$0.492928\pi$
$194$	14.2393	1.02232
$195$	−7.44902	−0.533435
$196$	−6.74398	−0.481713
$197$	−19.3564	−1.37908	−0.689541	−	0.724246i	$-0.742188\pi$
$197$	−19.3564	−1.37908	−0.689541	+	0.724246i	$0.742188\pi$
$198$	−7.00837	−0.498063
$199$	−19.6696	−1.39434	−0.697171	−	0.716905i	$-0.745558\pi$
$199$	−19.6696	−1.39434	−0.697171	+	0.716905i	$0.745558\pi$
$200$	−0.607373	−0.0429478
$201$	5.86827	0.413916
$202$	−2.00402	−0.141002
$203$	2.77861	0.195020
$204$	4.63697	0.324653
$205$	5.74020	0.400913
$206$	2.27215	0.158308
$207$	−0.213528	−0.0148412
$208$	2.83500	0.196572
$209$	−9.30294	−0.643498
$210$	1.32948	0.0917425
$211$	−2.32532	−0.160082	−0.0800408	−	0.996792i	$-0.525505\pi$
$211$	−2.32532	−0.160082	−0.0800408	+	0.996792i	$0.525505\pi$
$212$	−4.78550	−0.328669
$213$	6.30845	0.432248
$214$	−15.4805	−1.05822
$215$	12.8180	0.874183
$216$	−5.29145	−0.360037
$217$	−1.44742	−0.0982575
$218$	10.2893	0.696882
$219$	9.57213	0.646825
$220$	−9.38256	−0.632572
$221$	−11.8473	−0.796937
$222$	−0.813924	−0.0546270
$223$	18.1934	1.21832	0.609160	−	0.793048i	$-0.291507\pi$
$223$	18.1934	1.21832	0.609160	+	0.793048i	$0.291507\pi$
$224$	−0.505980	−0.0338072
$225$	−1.07431	−0.0716209
$226$	9.85905	0.655814
$227$	−21.9420	−1.45634	−0.728170	−	0.685397i	$-0.759629\pi$
$227$	−21.9420	−1.45634	−0.728170	+	0.685397i	$0.759629\pi$
$228$	−2.60523	−0.172535
$229$	20.4771	1.35316	0.676581	−	0.736368i	$-0.263461\pi$
$229$	20.4771	1.35316	0.676581	+	0.736368i	$0.263461\pi$
$230$	−0.285864	−0.0188493
$231$	2.22455	0.146365
$232$	−5.49154	−0.360537
$233$	−17.1860	−1.12589	−0.562947	−	0.826493i	$-0.690332\pi$
$233$	−17.1860	−1.12589	−0.562947	+	0.826493i	$0.690332\pi$
$234$	5.01450	0.327808
$235$	9.98949	0.651642
$236$	9.35022	0.608648
$237$	16.4034	1.06551
$238$	2.11447	0.137061
$239$	2.26876	0.146754	0.0733770	−	0.997304i	$-0.476622\pi$
$239$	2.26876	0.146754	0.0733770	+	0.997304i	$0.476622\pi$
$240$	−2.62752	−0.169606
$241$	−18.2248	−1.17396	−0.586980	−	0.809602i	$-0.699683\pi$
$241$	−18.2248	−1.17396	−0.586980	+	0.809602i	$0.699683\pi$
$242$	−4.69941	−0.302090
$243$	−15.2474	−0.978120
$244$	−10.8664	−0.695652
$245$	−15.9697	−1.02027
$246$	2.68976	0.171493
$247$	6.65627	0.423529
$248$	2.86063	0.181650
$249$	−12.3982	−0.785701
$250$	10.4017	0.657861
$251$	15.5028	0.978528	0.489264	−	0.872136i	$-0.337265\pi$
$251$	15.5028	0.978528	0.489264	+	0.872136i	$0.337265\pi$
$252$	−0.894971	−0.0563779
$253$	−0.478323	−0.0300719
$254$	5.76105	0.361481
$255$	10.9803	0.687613
$256$	1.00000	0.0625000
$257$	10.2593	0.639961	0.319980	−	0.947424i	$-0.396324\pi$
$257$	10.2593	0.639961	0.319980	+	0.947424i	$0.396324\pi$
$258$	6.00632	0.373937
$259$	−0.371151	−0.0230622
$260$	6.71324	0.416338
$261$	−9.71336	−0.601242
$262$	−13.6199	−0.841437
$263$	−16.1425	−0.995391	−0.497696	−	0.867352i	$-0.665820\pi$
$263$	−16.1425	−0.995391	−0.497696	+	0.867352i	$0.665820\pi$
$264$	−4.39651	−0.270587
$265$	−11.3320	−0.696119
$266$	−1.18799	−0.0728403
$267$	5.70462	0.349117
$268$	−5.28863	−0.323055
$269$	8.58996	0.523739	0.261869	−	0.965103i	$-0.415661\pi$
$269$	8.58996	0.523739	0.261869	+	0.965103i	$0.415661\pi$
$270$	−12.5301	−0.762557
$271$	−14.8938	−0.904734	−0.452367	−	0.891832i	$-0.649420\pi$
$271$	−14.8938	−0.904734	−0.452367	+	0.891832i	$0.649420\pi$
$272$	−4.17895	−0.253386
$273$	−1.59167	−0.0963322
$274$	−6.39040	−0.386058
$275$	−2.40656	−0.145121
$276$	−0.133951	−0.00806292
$277$	−5.08889	−0.305762	−0.152881	−	0.988245i	$-0.548855\pi$
$277$	−5.08889	−0.305762	−0.152881	+	0.988245i	$0.548855\pi$
$278$	15.8049	0.947916
$279$	5.05985	0.302925
$280$	−1.19816	−0.0716035
$281$	−24.2002	−1.44366	−0.721830	−	0.692070i	$-0.756699\pi$
$281$	−24.2002	−1.44366	−0.721830	+	0.692070i	$0.756699\pi$
$282$	4.68091	0.278744
$283$	−11.9307	−0.709204	−0.354602	−	0.935017i	$-0.615384\pi$
$283$	−11.9307	−0.709204	−0.354602	+	0.935017i	$0.615384\pi$
$284$	−5.68533	−0.337362
$285$	−6.16915	−0.365429
$286$	11.2330	0.664219
$287$	1.22654	0.0724003
$288$	1.76879	0.104227
$289$	0.463652	0.0272737
$290$	−13.0039	−0.763616
$291$	15.7999	0.926208
$292$	−8.62665	−0.504836
$293$	2.61114	0.152544	0.0762722	−	0.997087i	$-0.475698\pi$
$293$	2.61114	0.152544	0.0762722	+	0.997087i	$0.475698\pi$
$294$	−7.48313	−0.436425
$295$	22.1412	1.28911
$296$	0.733529	0.0426355
$297$	−20.9660	−1.21657
$298$	−2.33898	−0.135493
$299$	0.342241	0.0197923
$300$	−0.673942	−0.0389100
$301$	2.73890	0.157867
$302$	−16.4745	−0.948003
$303$	−2.22366	−0.127746
$304$	2.34790	0.134661
$305$	−25.7316	−1.47339
$306$	−7.39167	−0.422554
$307$	−15.4650	−0.882633	−0.441317	−	0.897352i	$-0.645488\pi$
$307$	−15.4650	−0.882633	−0.441317	+	0.897352i	$0.645488\pi$
$308$	−2.00482	−0.114235
$309$	2.52118	0.143425
$310$	6.77395	0.384734
$311$	−0.914762	−0.0518714	−0.0259357	−	0.999664i	$-0.508257\pi$
$311$	−0.914762	−0.0518714	−0.0259357	+	0.999664i	$0.508257\pi$
$312$	3.14571	0.178091
$313$	−0.266075	−0.0150394	−0.00751972	−	0.999972i	$-0.502394\pi$
$313$	−0.266075	−0.0150394	−0.00751972	+	0.999972i	$0.502394\pi$
$314$	−0.700481	−0.0395305
$315$	−2.11928	−0.119408
$316$	−14.7831	−0.831616
$317$	27.3582	1.53659	0.768295	−	0.640096i	$-0.221105\pi$
$317$	27.3582	1.53659	0.768295	+	0.640096i	$0.221105\pi$
$318$	−5.30999	−0.297769
$319$	−21.7588	−1.21826
$320$	2.36799	0.132375
$321$	−17.1771	−0.958734
$322$	−0.0610820	−0.00340397
$323$	−9.81174	−0.545940
$324$	−0.565037	−0.0313910
$325$	1.72190	0.0955139
$326$	−5.98631	−0.331551
$327$	11.4171	0.631365
$328$	−2.42408	−0.133848
$329$	2.13451	0.117679
$330$	−10.4109	−0.573101
$331$	26.1106	1.43517	0.717583	−	0.696473i	$-0.245248\pi$
$331$	26.1106	1.43517	0.717583	+	0.696473i	$0.245248\pi$
$332$	11.1735	0.613227
$333$	1.29746	0.0711001
$334$	18.4608	1.01013
$335$	−12.5234	−0.684228
$336$	−0.561436	−0.0306289
$337$	−32.0851	−1.74779	−0.873894	−	0.486116i	$-0.838413\pi$
$337$	−32.0851	−1.74779	−0.873894	+	0.486116i	$0.838413\pi$
$338$	4.96280	0.269941
$339$	10.9396	0.594158
$340$	−9.89572	−0.536671
$341$	11.3345	0.613799
$342$	4.15292	0.224564
$343$	−6.95419	−0.375491
$344$	−5.41305	−0.291852
$345$	−0.317195	−0.0170772
$346$	0.558857	0.0300443
$347$	−31.8247	−1.70844	−0.854219	−	0.519913i	$-0.825964\pi$
$347$	−31.8247	−1.70844	−0.854219	+	0.519913i	$0.825964\pi$
$348$	−6.09342	−0.326641
$349$	−3.80622	−0.203742	−0.101871	−	0.994798i	$-0.532483\pi$
$349$	−3.80622	−0.203742	−0.101871	+	0.994798i	$0.532483\pi$
$350$	−0.307319	−0.0164269
$351$	15.0012	0.800707
$352$	3.96225	0.211189
$353$	14.2049	0.756049	0.378024	−	0.925796i	$-0.376604\pi$
$353$	14.2049	0.756049	0.378024	+	0.925796i	$0.376604\pi$
$354$	10.3750	0.551426
$355$	−13.4628	−0.714532
$356$	−5.14114	−0.272480
$357$	2.34622	0.124175
$358$	8.40491	0.444213
$359$	1.49472	0.0788883	0.0394441	−	0.999222i	$-0.487441\pi$
$359$	1.49472	0.0788883	0.0394441	+	0.999222i	$0.487441\pi$
$360$	4.18847	0.220752
$361$	−13.4874	−0.709863
$362$	−14.8094	−0.778365
$363$	−5.21447	−0.273689
$364$	1.43445	0.0751857
$365$	−20.4278	−1.06924
$366$	−12.0574	−0.630250
$367$	15.4713	0.807593	0.403796	−	0.914849i	$-0.367690\pi$
$367$	15.4713	0.807593	0.403796	+	0.914849i	$0.367690\pi$
$368$	0.120720	0.00629297
$369$	−4.28768	−0.223208
$370$	1.73699	0.0903017
$371$	−2.42137	−0.125711
$372$	3.17416	0.164572
$373$	−28.5630	−1.47894	−0.739469	−	0.673191i	$-0.764923\pi$
$373$	−28.5630	−1.47894	−0.739469	+	0.673191i	$0.764923\pi$
$374$	−16.5581	−0.856196
$375$	11.5417	0.596012
$376$	−4.21855	−0.217555
$377$	15.5685	0.801818
$378$	−2.67737	−0.137709
$379$	−14.2593	−0.732450	−0.366225	−	0.930526i	$-0.619350\pi$
$379$	−14.2593	−0.732450	−0.366225	+	0.930526i	$0.619350\pi$
$380$	5.55979	0.285211
$381$	6.39247	0.327496
$382$	−8.56884	−0.438420
$383$	−10.7443	−0.549007	−0.274503	−	0.961586i	$-0.588513\pi$
$383$	−10.7443	−0.549007	−0.274503	+	0.961586i	$0.588513\pi$
$384$	1.10960	0.0566241
$385$	−4.74739	−0.241950
$386$	−0.617245	−0.0314169
$387$	−9.57452	−0.486700
$388$	−14.2393	−0.722890
$389$	−9.80393	−0.497079	−0.248540	−	0.968622i	$-0.579951\pi$
$389$	−9.80393	−0.497079	−0.248540	+	0.968622i	$0.579951\pi$
$390$	7.44902	0.377196
$391$	−0.504484	−0.0255129
$392$	6.74398	0.340623
$393$	−15.1126	−0.762330
$394$	19.3564	0.975159
$395$	−35.0063	−1.76136
$396$	7.00837	0.352184
$397$	−26.2938	−1.31965	−0.659824	−	0.751420i	$-0.729369\pi$
$397$	−26.2938	−1.31965	−0.659824	+	0.751420i	$0.729369\pi$
$398$	19.6696	0.985949
$399$	−1.31819	−0.0659922
$400$	0.607373	0.0303687
$401$	−12.1558	−0.607029	−0.303515	−	0.952827i	$-0.598160\pi$
$401$	−12.1558	−0.607029	−0.303515	+	0.952827i	$0.598160\pi$
$402$	−5.86827	−0.292683
$403$	−8.10988	−0.403982
$404$	2.00402	0.0997038
$405$	−1.33800	−0.0664859
$406$	−2.77861	−0.137900
$407$	2.90642	0.144066
$408$	−4.63697	−0.229564
$409$	−13.6880	−0.676829	−0.338415	−	0.940997i	$-0.609891\pi$
$409$	−13.6880	−0.676829	−0.338415	+	0.940997i	$0.609891\pi$
$410$	−5.74020	−0.283488
$411$	−7.09079	−0.349763
$412$	−2.27215	−0.111941
$413$	4.73103	0.232799
$414$	0.213528	0.0104943
$415$	26.4588	1.29881
$416$	−2.83500	−0.138997
$417$	17.5372	0.858798
$418$	9.30294	0.455022
$419$	4.56121	0.222830	0.111415	−	0.993774i	$-0.464462\pi$
$419$	4.56121	0.222830	0.111415	+	0.993774i	$0.464462\pi$
$420$	−1.32948	−0.0648717
$421$	−31.3675	−1.52876	−0.764379	−	0.644768i	$-0.776954\pi$
$421$	−31.3675	−1.52876	−0.764379	+	0.644768i	$0.776954\pi$
$422$	2.32532	0.113195
$423$	−7.46172	−0.362801
$424$	4.78550	0.232404
$425$	−2.53818	−0.123120
$426$	−6.30845	−0.305645
$427$	−5.49820	−0.266077
$428$	15.4805	0.748276
$429$	12.4641	0.601772
$430$	−12.8180	−0.618141
$431$	−22.3875	−1.07837	−0.539184	−	0.842188i	$-0.681267\pi$
$431$	−22.3875	−1.07837	−0.539184	+	0.842188i	$0.681267\pi$
$432$	5.29145	0.254585
$433$	27.3176	1.31280	0.656399	−	0.754414i	$-0.272079\pi$
$433$	27.3176	1.31280	0.656399	+	0.754414i	$0.272079\pi$
$434$	1.44742	0.0694786
$435$	−14.4291	−0.691824
$436$	−10.2893	−0.492770
$437$	0.283438	0.0135587
$438$	−9.57213	−0.457374
$439$	12.6124	0.601957	0.300978	−	0.953631i	$-0.402687\pi$
$439$	12.6124	0.601957	0.300978	+	0.953631i	$0.402687\pi$
$440$	9.38256	0.447296
$441$	11.9287	0.568032
$442$	11.8473	0.563519
$443$	−24.2960	−1.15434	−0.577170	−	0.816624i	$-0.695843\pi$
$443$	−24.2960	−1.15434	−0.577170	+	0.816624i	$0.695843\pi$
$444$	0.813924	0.0386271
$445$	−12.1742	−0.577111
$446$	−18.1934	−0.861482
$447$	−2.59533	−0.122755
$448$	0.505980	0.0239053
$449$	2.16843	0.102335	0.0511673	−	0.998690i	$-0.483706\pi$
$449$	2.16843	0.102335	0.0511673	+	0.998690i	$0.483706\pi$
$450$	1.07431	0.0506436
$451$	−9.60482	−0.452273
$452$	−9.85905	−0.463731
$453$	−18.2802	−0.858877
$454$	21.9420	1.02979
$455$	3.39677	0.159243
$456$	2.60523	0.122001
$457$	15.0614	0.704543	0.352272	−	0.935898i	$-0.385409\pi$
$457$	15.0614	0.704543	0.352272	+	0.935898i	$0.385409\pi$
$458$	−20.4771	−0.956831
$459$	−22.1127	−1.03213
$460$	0.285864	0.0133285
$461$	32.7856	1.52698	0.763488	−	0.645822i	$-0.223485\pi$
$461$	32.7856	1.52698	0.763488	+	0.645822i	$0.223485\pi$
$462$	−2.22455	−0.103495
$463$	2.32484	0.108044	0.0540221	−	0.998540i	$-0.482796\pi$
$463$	2.32484	0.108044	0.0540221	+	0.998540i	$0.482796\pi$
$464$	5.49154	0.254938
$465$	7.51638	0.348564
$466$	17.1860	0.796127
$467$	−4.61341	−0.213483	−0.106742	−	0.994287i	$-0.534042\pi$
$467$	−4.61341	−0.213483	−0.106742	+	0.994287i	$0.534042\pi$
$468$	−5.01450	−0.231795
$469$	−2.67594	−0.123564
$470$	−9.98949	−0.460781
$471$	−0.777255	−0.0358140
$472$	−9.35022	−0.430379
$473$	−21.4478	−0.986173
$474$	−16.4034	−0.753432
$475$	1.42605	0.0654316
$476$	−2.11447	−0.0969165
$477$	8.46452	0.387564
$478$	−2.26876	−0.103771
$479$	41.3317	1.88849	0.944246	−	0.329241i	$-0.106793\pi$
$479$	41.3317	1.88849	0.944246	+	0.329241i	$0.106793\pi$
$480$	2.62752	0.119929
$481$	−2.07955	−0.0948194
$482$	18.2248	0.830115
$483$	−0.0677767	−0.00308395
$484$	4.69941	0.213610
$485$	−33.7185	−1.53108
$486$	15.2474	0.691635
$487$	−42.0692	−1.90634	−0.953168	−	0.302442i	$-0.902198\pi$
$487$	−42.0692	−1.90634	−0.953168	+	0.302442i	$0.902198\pi$
$488$	10.8664	0.491900
$489$	−6.64242	−0.300381
$490$	15.9697	0.721437
$491$	20.2271	0.912835	0.456417	−	0.889766i	$-0.349132\pi$
$491$	20.2271	0.912835	0.456417	+	0.889766i	$0.349132\pi$
$492$	−2.68976	−0.121264
$493$	−22.9489	−1.03357
$494$	−6.65627	−0.299480
$495$	16.5957	0.745923
$496$	−2.86063	−0.128446
$497$	−2.87667	−0.129036
$498$	12.3982	0.555575
$499$	15.2511	0.682733	0.341366	−	0.939930i	$-0.389110\pi$
$499$	15.2511	0.682733	0.341366	+	0.939930i	$0.389110\pi$
$500$	−10.4017	−0.465178
$501$	20.4842	0.915165
$502$	−15.5028	−0.691924
$503$	−2.04301	−0.0910931	−0.0455466	−	0.998962i	$-0.514503\pi$
$503$	−2.04301	−0.0910931	−0.0455466	+	0.998962i	$0.514503\pi$
$504$	0.894971	0.0398652
$505$	4.74550	0.211172
$506$	0.478323	0.0212641
$507$	5.50672	0.244562
$508$	−5.76105	−0.255605
$509$	6.89461	0.305598	0.152799	−	0.988257i	$-0.451171\pi$
$509$	6.89461	0.305598	0.152799	+	0.988257i	$0.451171\pi$
$510$	−10.9803	−0.486216
$511$	−4.36491	−0.193092
$512$	−1.00000	−0.0441942
$513$	12.4238	0.548523
$514$	−10.2593	−0.452520
$515$	−5.38042	−0.237090
$516$	−6.00632	−0.264414
$517$	−16.7150	−0.735123
$518$	0.371151	0.0163074
$519$	0.620108	0.0272197
$520$	−6.71324	−0.294395
$521$	−27.4679	−1.20339	−0.601696	−	0.798725i	$-0.705508\pi$
$521$	−27.4679	−1.20339	−0.601696	+	0.798725i	$0.705508\pi$
$522$	9.71336	0.425142
$523$	36.4456	1.59365	0.796827	−	0.604208i	$-0.206510\pi$
$523$	36.4456	1.59365	0.796827	+	0.604208i	$0.206510\pi$
$524$	13.6199	0.594986
$525$	−0.341001	−0.0148825
$526$	16.1425	0.703848
$527$	11.9544	0.520744
$528$	4.39651	0.191334
$529$	−22.9854	−0.999366
$530$	11.3320	0.492231
$531$	−16.5385	−0.717712
$532$	1.18799	0.0515059
$533$	6.87227	0.297671
$534$	−5.70462	−0.246863
$535$	36.6576	1.58484
$536$	5.28863	0.228434
$537$	9.32610	0.402451
$538$	−8.58996	−0.370339
$539$	26.7213	1.15097
$540$	12.5301	0.539209
$541$	18.6538	0.801991	0.400995	−	0.916080i	$-0.368664\pi$
$541$	18.6538	0.801991	0.400995	+	0.916080i	$0.368664\pi$
$542$	14.8938	0.639744
$543$	−16.4325	−0.705187
$544$	4.17895	0.179171
$545$	−24.3651	−1.04368
$546$	1.59167	0.0681172
$547$	−2.39691	−0.102485	−0.0512423	−	0.998686i	$-0.516318\pi$
$547$	−2.39691	−0.102485	−0.0512423	+	0.998686i	$0.516318\pi$
$548$	6.39040	0.272984
$549$	19.2204	0.820306
$550$	2.40656	0.102616
$551$	12.8936	0.549284
$552$	0.133951	0.00570134
$553$	−7.47997	−0.318081
$554$	5.08889	0.216206
$555$	1.92736	0.0818120
$556$	−15.8049	−0.670278
$557$	−2.40554	−0.101926	−0.0509630	−	0.998701i	$-0.516229\pi$
$557$	−2.40554	−0.101926	−0.0509630	+	0.998701i	$0.516229\pi$
$558$	−5.05985	−0.214200
$559$	15.3460	0.649065
$560$	1.19816	0.0506313
$561$	−18.3728	−0.775701
$562$	24.2002	1.02082
$563$	7.58035	0.319474	0.159737	−	0.987160i	$-0.448935\pi$
$563$	7.58035	0.319474	0.159737	+	0.987160i	$0.448935\pi$
$564$	−4.68091	−0.197102
$565$	−23.3461	−0.982179
$566$	11.9307	0.501483
$567$	−0.285898	−0.0120066
$568$	5.68533	0.238551
$569$	18.3180	0.767932	0.383966	−	0.923347i	$-0.374558\pi$
$569$	18.3180	0.767932	0.383966	+	0.923347i	$0.374558\pi$
$570$	6.16915	0.258397
$571$	−13.1435	−0.550039	−0.275019	−	0.961439i	$-0.588684\pi$
$571$	−13.1435	−0.550039	−0.275019	+	0.961439i	$0.588684\pi$
$572$	−11.2330	−0.469674
$573$	−9.50799	−0.397202
$574$	−1.22654	−0.0511947
$575$	0.0733222	0.00305775
$576$	−1.76879	−0.0736994
$577$	19.5987	0.815903	0.407951	−	0.913004i	$-0.366243\pi$
$577$	19.5987	0.815903	0.407951	+	0.913004i	$0.366243\pi$
$578$	−0.463652	−0.0192854
$579$	−0.684895	−0.0284633
$580$	13.0039	0.539958
$581$	5.65359	0.234550
$582$	−15.7999	−0.654928
$583$	18.9613	0.785298
$584$	8.62665	0.356973
$585$	−11.8743	−0.490941
$586$	−2.61114	−0.107865
$587$	−8.54827	−0.352825	−0.176412	−	0.984316i	$-0.556449\pi$
$587$	−8.54827	−0.352825	−0.176412	+	0.984316i	$0.556449\pi$
$588$	7.48313	0.308599
$589$	−6.71646	−0.276747
$590$	−22.1412	−0.911540
$591$	21.4778	0.883480
$592$	−0.733529	−0.0301478
$593$	−23.6134	−0.969686	−0.484843	−	0.874601i	$-0.661123\pi$
$593$	−23.6134	−0.969686	−0.484843	+	0.874601i	$0.661123\pi$
$594$	20.9660	0.860247
$595$	−5.00704	−0.205269
$596$	2.33898	0.0958082
$597$	21.8254	0.893255
$598$	−0.342241	−0.0139953
$599$	30.9579	1.26491	0.632453	−	0.774598i	$-0.282048\pi$
$599$	30.9579	1.26491	0.632453	+	0.774598i	$0.282048\pi$
$600$	0.673942	0.0275136
$601$	−9.84175	−0.401453	−0.200727	−	0.979647i	$-0.564330\pi$
$601$	−9.84175	−0.401453	−0.200727	+	0.979647i	$0.564330\pi$
$602$	−2.73890	−0.111629
$603$	9.35446	0.380943
$604$	16.4745	0.670339
$605$	11.1282	0.452424
$606$	2.22366	0.0903302
$607$	−41.4571	−1.68269	−0.841347	−	0.540496i	$-0.818237\pi$
$607$	−41.4571	−1.68269	−0.841347	+	0.540496i	$0.818237\pi$
$608$	−2.34790	−0.0952197
$609$	−3.08315	−0.124935
$610$	25.7316	1.04184
$611$	11.9596	0.483833
$612$	7.39167	0.298791
$613$	43.5252	1.75796	0.878982	−	0.476855i	$-0.158223\pi$
$613$	43.5252	1.75796	0.878982	+	0.476855i	$0.158223\pi$
$614$	15.4650	0.624116
$615$	−6.36933	−0.256836
$616$	2.00482	0.0807765
$617$	−10.7918	−0.434460	−0.217230	−	0.976120i	$-0.569702\pi$
$617$	−10.7918	−0.434460	−0.217230	+	0.976120i	$0.569702\pi$
$618$	−2.52118	−0.101417
$619$	−17.3065	−0.695606	−0.347803	−	0.937568i	$-0.613072\pi$
$619$	−17.3065	−0.695606	−0.347803	+	0.937568i	$0.613072\pi$
$620$	−6.77395	−0.272048
$621$	0.638785	0.0256335
$622$	0.914762	0.0366786
$623$	−2.60132	−0.104220
$624$	−3.14571	−0.125929
$625$	−27.6680	−1.10672
$626$	0.266075	0.0106345
$627$	10.3226	0.412243
$628$	0.700481	0.0279523
$629$	3.06538	0.122225
$630$	2.11928	0.0844342
$631$	−12.0597	−0.480090	−0.240045	−	0.970762i	$-0.577162\pi$
$631$	−12.0597	−0.480090	−0.240045	+	0.970762i	$0.577162\pi$
$632$	14.7831	0.588041
$633$	2.58017	0.102553
$634$	−27.3582	−1.08653
$635$	−13.6421	−0.541371
$636$	5.30999	0.210555
$637$	−19.1192	−0.757529
$638$	21.7588	0.861441
$639$	10.0561	0.397815
$640$	−2.36799	−0.0936030
$641$	−16.2644	−0.642406	−0.321203	−	0.947010i	$-0.604087\pi$
$641$	−16.2644	−0.642406	−0.321203	+	0.947010i	$0.604087\pi$
$642$	17.1771	0.677927
$643$	27.6821	1.09168	0.545838	−	0.837890i	$-0.316211\pi$
$643$	27.6821	1.09168	0.545838	+	0.837890i	$0.316211\pi$
$644$	0.0610820	0.00240697
$645$	−14.2229	−0.560026
$646$	9.81174	0.386038
$647$	6.42368	0.252541	0.126270	−	0.991996i	$-0.459699\pi$
$647$	6.42368	0.252541	0.126270	+	0.991996i	$0.459699\pi$
$648$	0.565037	0.0221968
$649$	−37.0479	−1.45426
$650$	−1.72190	−0.0675385
$651$	1.60606	0.0629466
$652$	5.98631	0.234442
$653$	30.6135	1.19800	0.598999	−	0.800750i	$-0.295565\pi$
$653$	30.6135	1.19800	0.598999	+	0.800750i	$0.295565\pi$
$654$	−11.4171	−0.446442
$655$	32.2517	1.26018
$656$	2.42408	0.0946445
$657$	15.2587	0.595298
$658$	−2.13451	−0.0832117
$659$	38.9654	1.51788	0.758938	−	0.651163i	$-0.225719\pi$
$659$	38.9654	1.51788	0.758938	+	0.651163i	$0.225719\pi$
$660$	10.4109	0.405244
$661$	48.4296	1.88369	0.941847	−	0.336041i	$-0.109088\pi$
$661$	48.4296	1.88369	0.941847	+	0.336041i	$0.109088\pi$
$662$	−26.1106	−1.01482
$663$	13.1458	0.510540
$664$	−11.1735	−0.433617
$665$	2.81315	0.109089
$666$	−1.29746	−0.0502754
$667$	0.662940	0.0256691
$668$	−18.4608	−0.714272
$669$	−20.1874	−0.780490
$670$	12.5234	0.483822
$671$	43.0555	1.66214
$672$	0.561436	0.0216579
$673$	−36.7074	−1.41497	−0.707483	−	0.706731i	$-0.750169\pi$
$673$	−36.7074	−1.41497	−0.707483	+	0.706731i	$0.750169\pi$
$674$	32.0851	1.23587
$675$	3.21388	0.123702
$676$	−4.96280	−0.190877
$677$	33.0718	1.27105	0.635526	−	0.772079i	$-0.280783\pi$
$677$	33.0718	1.27105	0.635526	+	0.772079i	$0.280783\pi$
$678$	−10.9396	−0.420133
$679$	−7.20480	−0.276495
$680$	9.89572	0.379483
$681$	24.3468	0.932972
$682$	−11.3345	−0.434022
$683$	−2.59345	−0.0992358	−0.0496179	−	0.998768i	$-0.515800\pi$
$683$	−2.59345	−0.0992358	−0.0496179	+	0.998768i	$0.515800\pi$
$684$	−4.15292	−0.158791
$685$	15.1324	0.578179
$686$	6.95419	0.265512
$687$	−22.7214	−0.866874
$688$	5.41305	0.206371
$689$	−13.5669	−0.516856
$690$	0.317195	0.0120754
$691$	11.6223	0.442134	0.221067	−	0.975259i	$-0.429046\pi$
$691$	11.6223	0.442134	0.221067	+	0.975259i	$0.429046\pi$
$692$	−0.558857	−0.0212446
$693$	3.54610	0.134705
$694$	31.8247	1.20805
$695$	−37.4259	−1.41965
$696$	6.09342	0.230970
$697$	−10.1301	−0.383706
$698$	3.80622	0.144068
$699$	19.0696	0.721279
$700$	0.307319	0.0116156
$701$	−5.52808	−0.208793	−0.104396	−	0.994536i	$-0.533291\pi$
$701$	−5.52808	−0.208793	−0.104396	+	0.994536i	$0.533291\pi$
$702$	−15.0012	−0.566185
$703$	−1.72225	−0.0649558
$704$	−3.96225	−0.149333
$705$	−11.0843	−0.417461
$706$	−14.2049	−0.534607
$707$	1.01400	0.0381352
$708$	−10.3750	−0.389917
$709$	−2.75459	−0.103451	−0.0517254	−	0.998661i	$-0.516472\pi$
$709$	−2.75459	−0.103451	−0.0517254	+	0.998661i	$0.516472\pi$
$710$	13.4628	0.505250
$711$	26.1482	0.980634
$712$	5.14114	0.192672
$713$	−0.345336	−0.0129329
$714$	−2.34622	−0.0878049
$715$	−26.5995	−0.994766
$716$	−8.40491	−0.314106
$717$	−2.51742	−0.0940147
$718$	−1.49472	−0.0557825
$719$	2.35597	0.0878627	0.0439314	−	0.999035i	$-0.486012\pi$
$719$	2.35597	0.0878627	0.0439314	+	0.999035i	$0.486012\pi$
$720$	−4.18847	−0.156095
$721$	−1.14966	−0.0428156
$722$	13.4874	0.501949
$723$	20.2222	0.752072
$724$	14.8094	0.550387
$725$	3.33541	0.123874
$726$	5.21447	0.193527
$727$	27.2745	1.01156	0.505778	−	0.862664i	$-0.331206\pi$
$727$	27.2745	1.01156	0.505778	+	0.862664i	$0.331206\pi$
$728$	−1.43445	−0.0531644
$729$	18.6136	0.689393
$730$	20.4278	0.756067
$731$	−22.6209	−0.836663
$732$	12.0574	0.445654
$733$	−8.35044	−0.308430	−0.154215	−	0.988037i	$-0.549285\pi$
$733$	−8.35044	−0.308430	−0.154215	+	0.988037i	$0.549285\pi$
$734$	−15.4713	−0.571054
$735$	17.7200	0.653611
$736$	−0.120720	−0.00444980
$737$	20.9549	0.771883
$738$	4.28768	0.157832
$739$	49.3602	1.81575	0.907873	−	0.419245i	$-0.137705\pi$
$739$	49.3602	1.81575	0.907873	+	0.419245i	$0.137705\pi$
$740$	−1.73699	−0.0638530
$741$	−7.38581	−0.271324
$742$	2.42137	0.0888912
$743$	4.56434	0.167449	0.0837246	−	0.996489i	$-0.473318\pi$
$743$	4.56434	0.167449	0.0837246	+	0.996489i	$0.473318\pi$
$744$	−3.17416	−0.116370
$745$	5.53867	0.202921
$746$	28.5630	1.04577
$747$	−19.7636	−0.723112
$748$	16.5581	0.605422
$749$	7.83281	0.286205
$750$	−11.5417	−0.421444
$751$	−18.0339	−0.658065	−0.329033	−	0.944319i	$-0.606723\pi$
$751$	−18.0339	−0.658065	−0.329033	+	0.944319i	$0.606723\pi$
$752$	4.21855	0.153835
$753$	−17.2019	−0.626873
$754$	−15.5685	−0.566971
$755$	39.0115	1.41977
$756$	2.67737	0.0973750
$757$	19.0559	0.692600	0.346300	−	0.938124i	$-0.387438\pi$
$757$	19.0559	0.692600	0.346300	+	0.938124i	$0.387438\pi$
$758$	14.2593	0.517920
$759$	0.530748	0.0192649
$760$	−5.55979	−0.201675
$761$	−5.95761	−0.215963	−0.107982	−	0.994153i	$-0.534439\pi$
$761$	−5.95761	−0.215963	−0.107982	+	0.994153i	$0.534439\pi$
$762$	−6.39247	−0.231575
$763$	−5.20621	−0.188477
$764$	8.56884	0.310010
$765$	17.5034	0.632837
$766$	10.7443	0.388206
$767$	26.5078	0.957143
$768$	−1.10960	−0.0400393
$769$	52.0098	1.87552	0.937761	−	0.347282i	$-0.112895\pi$
$769$	52.0098	1.87552	0.937761	+	0.347282i	$0.112895\pi$
$770$	4.74739	0.171084
$771$	−11.3838	−0.409977
$772$	0.617245	0.0222151
$773$	16.2797	0.585539	0.292770	−	0.956183i	$-0.405423\pi$
$773$	16.2797	0.585539	0.292770	+	0.956183i	$0.405423\pi$
$774$	9.57452	0.344149
$775$	−1.73747	−0.0624118
$776$	14.2393	0.511161
$777$	0.411830	0.0147743
$778$	9.80393	0.351488
$779$	5.69149	0.203919
$780$	−7.44902	−0.266718
$781$	22.5267	0.806069
$782$	0.504484	0.0180403
$783$	29.0582	1.03846
$784$	−6.74398	−0.240857
$785$	1.65873	0.0592027
$786$	15.1126	0.539049
$787$	3.34912	0.119383	0.0596916	−	0.998217i	$-0.480988\pi$
$787$	3.34912	0.119383	0.0596916	+	0.998217i	$0.480988\pi$
$788$	−19.3564	−0.689541
$789$	17.9118	0.637676
$790$	35.0063	1.24547
$791$	−4.98849	−0.177370
$792$	−7.00837	−0.249032
$793$	−30.8063	−1.09396
$794$	26.2938	0.933132
$795$	12.5740	0.445954
$796$	−19.6696	−0.697171
$797$	−52.6436	−1.86473	−0.932366	−	0.361516i	$-0.882259\pi$
$797$	−52.6436	−1.86473	−0.932366	+	0.361516i	$0.882259\pi$
$798$	1.31819	0.0466635
$799$	−17.6291	−0.623674
$800$	−0.607373	−0.0214739
$801$	9.09358	0.321306
$802$	12.1558	0.429235
$803$	34.1809	1.20622
$804$	5.86827	0.206958
$805$	0.144642	0.00509795
$806$	8.10988	0.285658
$807$	−9.53142	−0.335522
$808$	−2.00402	−0.0705012
$809$	29.3497	1.03188	0.515940	−	0.856625i	$-0.327443\pi$
$809$	29.3497	1.03188	0.515940	+	0.856625i	$0.327443\pi$
$810$	1.33800	0.0470126
$811$	−9.25285	−0.324912	−0.162456	−	0.986716i	$-0.551941\pi$
$811$	−9.25285	−0.324912	−0.162456	+	0.986716i	$0.551941\pi$
$812$	2.77861	0.0975101
$813$	16.5262	0.579598
$814$	−2.90642	−0.101870
$815$	14.1755	0.496547
$816$	4.63697	0.162326
$817$	12.7093	0.444641
$818$	13.6880	0.478591
$819$	−2.53724	−0.0886583
$820$	5.74020	0.200457
$821$	−46.3106	−1.61625	−0.808126	−	0.589010i	$-0.799518\pi$
$821$	−46.3106	−1.61625	−0.808126	+	0.589010i	$0.799518\pi$
$822$	7.09079	0.247320
$823$	−15.3413	−0.534766	−0.267383	−	0.963590i	$-0.586159\pi$
$823$	−15.3413	−0.534766	−0.267383	+	0.963590i	$0.586159\pi$
$824$	2.27215	0.0791540
$825$	2.67032	0.0929688
$826$	−4.73103	−0.164614
$827$	−42.7728	−1.48736	−0.743678	−	0.668538i	$-0.766921\pi$
$827$	−42.7728	−1.48736	−0.743678	+	0.668538i	$0.766921\pi$
$828$	−0.213528	−0.00742062
$829$	−11.5238	−0.400239	−0.200120	−	0.979771i	$-0.564133\pi$
$829$	−11.5238	−0.400239	−0.200120	+	0.979771i	$0.564133\pi$
$830$	−26.4588	−0.918398
$831$	5.64664	0.195880
$832$	2.83500	0.0982858
$833$	28.1828	0.976476
$834$	−17.5372	−0.607262
$835$	−43.7151	−1.51282
$836$	−9.30294	−0.321749
$837$	−15.1369	−0.523207
$838$	−4.56121	−0.157565
$839$	−19.7983	−0.683513	−0.341756	−	0.939789i	$-0.611022\pi$
$839$	−19.7983	−0.683513	−0.341756	+	0.939789i	$0.611022\pi$
$840$	1.32948	0.0458712
$841$	1.15700	0.0398964
$842$	31.3675	1.08099
$843$	26.8525	0.924850
$844$	−2.32532	−0.0800408
$845$	−11.7518	−0.404276
$846$	7.46172	0.256539
$847$	2.37781	0.0817025
$848$	−4.78550	−0.164335
$849$	13.2383	0.454336
$850$	2.53818	0.0870590
$851$	−0.0885517	−0.00303551
$852$	6.30845	0.216124
$853$	−7.59730	−0.260127	−0.130063	−	0.991506i	$-0.541518\pi$
$853$	−7.59730	−0.260127	−0.130063	+	0.991506i	$0.541518\pi$
$854$	5.49820	0.188145
$855$	−9.83408	−0.336318
$856$	−15.4805	−0.529111
$857$	3.08497	0.105381	0.0526903	−	0.998611i	$-0.483220\pi$
$857$	3.08497	0.105381	0.0526903	+	0.998611i	$0.483220\pi$
$858$	−12.4641	−0.425517
$859$	−24.3330	−0.830233	−0.415116	−	0.909768i	$-0.636259\pi$
$859$	−24.3330	−0.830233	−0.415116	+	0.909768i	$0.636259\pi$
$860$	12.8180	0.437092
$861$	−1.36097	−0.0463817
$862$	22.3875	0.762521
$863$	13.0693	0.444883	0.222441	−	0.974946i	$-0.428597\pi$
$863$	13.0693	0.444883	0.222441	+	0.974946i	$0.428597\pi$
$864$	−5.29145	−0.180019
$865$	−1.32337	−0.0449959
$866$	−27.3176	−0.928288
$867$	−0.514469	−0.0174723
$868$	−1.44742	−0.0491288
$869$	58.5744	1.98700
$870$	14.4291	0.489194
$871$	−14.9933	−0.508027
$872$	10.2893	0.348441
$873$	25.1863	0.852426
$874$	−0.283438	−0.00958744
$875$	−5.26305	−0.177924
$876$	9.57213	0.323412
$877$	23.9377	0.808318	0.404159	−	0.914689i	$-0.367564\pi$
$877$	23.9377	0.808318	0.404159	+	0.914689i	$0.367564\pi$
$878$	−12.6124	−0.425648
$879$	−2.89732	−0.0977243
$880$	−9.38256	−0.316286
$881$	33.9284	1.14308	0.571539	−	0.820575i	$-0.306347\pi$
$881$	33.9284	1.14308	0.571539	+	0.820575i	$0.306347\pi$
$882$	−11.9287	−0.401659
$883$	−33.6549	−1.13258	−0.566289	−	0.824207i	$-0.691621\pi$
$883$	−33.6549	−1.13258	−0.566289	+	0.824207i	$0.691621\pi$
$884$	−11.8473	−0.398468
$885$	−24.5679	−0.825842
$886$	24.2960	0.816241
$887$	−23.6876	−0.795352	−0.397676	−	0.917526i	$-0.630183\pi$
$887$	−23.6876	−0.795352	−0.397676	+	0.917526i	$0.630183\pi$
$888$	−0.813924	−0.0273135
$889$	−2.91498	−0.0977653
$890$	12.1742	0.408079
$891$	2.23882	0.0750032
$892$	18.1934	0.609160
$893$	9.90472	0.331449
$894$	2.59533	0.0868008
$895$	−19.9027	−0.665275
$896$	−0.505980	−0.0169036
$897$	−0.379751	−0.0126795
$898$	−2.16843	−0.0723614
$899$	−15.7093	−0.523933
$900$	−1.07431	−0.0358104
$901$	19.9984	0.666242
$902$	9.60482	0.319805
$903$	−3.03908	−0.101134
$904$	9.85905	0.327907
$905$	35.0685	1.16572
$906$	18.2802	0.607317
$907$	−10.5709	−0.351002	−0.175501	−	0.984479i	$-0.556154\pi$
$907$	−10.5709	−0.351002	−0.175501	+	0.984479i	$0.556154\pi$
$908$	−21.9420	−0.728170
$909$	−3.54469	−0.117570
$910$	−3.39677	−0.112602
$911$	−18.6259	−0.617105	−0.308552	−	0.951207i	$-0.599844\pi$
$911$	−18.6259	−0.617105	−0.308552	+	0.951207i	$0.599844\pi$
$912$	−2.60523	−0.0862677
$913$	−44.2723	−1.46520
$914$	−15.0614	−0.498187
$915$	28.5518	0.943893
$916$	20.4771	0.676581
$917$	6.89138	0.227573
$918$	22.1127	0.729828
$919$	14.1145	0.465593	0.232796	−	0.972525i	$-0.425212\pi$
$919$	14.1145	0.465593	0.232796	+	0.972525i	$0.425212\pi$
$920$	−0.285864	−0.00942466
$921$	17.1600	0.565440
$922$	−32.7856	−1.07973
$923$	−16.1179	−0.530527
$924$	2.22455	0.0731823
$925$	−0.445526	−0.0146488
$926$	−2.32484	−0.0763988
$927$	4.01894	0.131999
$928$	−5.49154	−0.180269
$929$	−36.0168	−1.18167	−0.590836	−	0.806792i	$-0.701202\pi$
$929$	−36.0168	−1.18167	−0.590836	+	0.806792i	$0.701202\pi$
$930$	−7.51638	−0.246472
$931$	−15.8342	−0.518944
$932$	−17.1860	−0.562947
$933$	1.01502	0.0332303
$934$	4.61341	0.150955
$935$	39.2093	1.28228
$936$	5.01450	0.163904
$937$	15.2733	0.498956	0.249478	−	0.968380i	$-0.419741\pi$
$937$	15.2733	0.498956	0.249478	+	0.968380i	$0.419741\pi$
$938$	2.67594	0.0873727
$939$	0.295237	0.00963469
$940$	9.98949	0.325821
$941$	−20.7243	−0.675593	−0.337796	−	0.941219i	$-0.609681\pi$
$941$	−20.7243	−0.675593	−0.337796	+	0.941219i	$0.609681\pi$
$942$	0.777255	0.0253243
$943$	0.292636	0.00952953
$944$	9.35022	0.304324
$945$	6.33998	0.206240
$946$	21.4478	0.697329
$947$	−29.5224	−0.959350	−0.479675	−	0.877446i	$-0.659245\pi$
$947$	−29.5224	−0.959350	−0.479675	+	0.877446i	$0.659245\pi$
$948$	16.4034	0.532757
$949$	−24.4565	−0.793892
$950$	−1.42605	−0.0462671
$951$	−30.3567	−0.984383
$952$	2.11447	0.0685303
$953$	−32.5431	−1.05417	−0.527087	−	0.849811i	$-0.676716\pi$
$953$	−32.5431	−1.05417	−0.527087	+	0.849811i	$0.676716\pi$
$954$	−8.46452	−0.274049
$955$	20.2909	0.656599
$956$	2.26876	0.0733770
$957$	24.1436	0.780453
$958$	−41.3317	−1.33537
$959$	3.23342	0.104413
$960$	−2.62752	−0.0848029
$961$	−22.8168	−0.736025
$962$	2.07955	0.0670474
$963$	−27.3816	−0.882360
$964$	−18.2248	−0.586980
$965$	1.46163	0.0470515
$966$	0.0677767	0.00218068
$967$	37.0839	1.19254	0.596269	−	0.802785i	$-0.296649\pi$
$967$	37.0839	1.19254	0.596269	+	0.802785i	$0.296649\pi$
$968$	−4.69941	−0.151045
$969$	10.8871	0.349745
$970$	33.7185	1.08264
$971$	22.2013	0.712474	0.356237	−	0.934396i	$-0.384060\pi$
$971$	22.2013	0.712474	0.356237	+	0.934396i	$0.384060\pi$
$972$	−15.2474	−0.489060
$973$	−7.99698	−0.256372
$974$	42.0692	1.34798
$975$	−1.91062	−0.0611889
$976$	−10.8664	−0.347826
$977$	−14.0666	−0.450031	−0.225015	−	0.974355i	$-0.572243\pi$
$977$	−14.0666	−0.450031	−0.225015	+	0.974355i	$0.572243\pi$
$978$	6.64242	0.212401
$979$	20.3705	0.651044
$980$	−15.9697	−0.510133
$981$	18.1996	0.581070
$982$	−20.2271	−0.645471
$983$	9.38920	0.299469	0.149735	−	0.988726i	$-0.452158\pi$
$983$	9.38920	0.299469	0.149735	+	0.988726i	$0.452158\pi$
$984$	2.68976	0.0857466
$985$	−45.8356	−1.46044
$986$	22.9489	0.730841
$987$	−2.36845	−0.0753886
$988$	6.65627	0.211764
$989$	0.653464	0.0207790
$990$	−16.5957	−0.527447
$991$	54.8285	1.74169	0.870843	−	0.491562i	$-0.163574\pi$
$991$	54.8285	1.74169	0.870843	+	0.491562i	$0.163574\pi$
$992$	2.86063	0.0908252
$993$	−28.9723	−0.919408
$994$	2.87667	0.0912423
$995$	−46.5775	−1.47660
$996$	−12.3982	−0.392851
$997$	22.6813	0.718325	0.359163	−	0.933275i	$-0.383062\pi$
$997$	22.6813	0.718325	0.359163	+	0.933275i	$0.383062\pi$
$998$	−15.2511	−0.482765
$999$	−3.88143	−0.122803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.d.1.16	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.d.1.16	✓	37	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.10960 q^{3} +1.00000 q^{4} +2.36799 q^{5} +1.10960 q^{6} +0.505980 q^{7} -1.00000 q^{8} -1.76879 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.10960 q^{3} +1.00000 q^{4} +2.36799 q^{5} +1.10960 q^{6} +0.505980 q^{7} -1.00000 q^{8} -1.76879 q^{9} -2.36799 q^{10} -3.96225 q^{11} -1.10960 q^{12} +2.83500 q^{13} -0.505980 q^{14} -2.62752 q^{15} +1.00000 q^{16} -4.17895 q^{17} +1.76879 q^{18} +2.34790 q^{19} +2.36799 q^{20} -0.561436 q^{21} +3.96225 q^{22} +0.120720 q^{23} +1.10960 q^{24} +0.607373 q^{25} -2.83500 q^{26} +5.29145 q^{27} +0.505980 q^{28} +5.49154 q^{29} +2.62752 q^{30} -2.86063 q^{31} -1.00000 q^{32} +4.39651 q^{33} +4.17895 q^{34} +1.19816 q^{35} -1.76879 q^{36} -0.733529 q^{37} -2.34790 q^{38} -3.14571 q^{39} -2.36799 q^{40} +2.42408 q^{41} +0.561436 q^{42} +5.41305 q^{43} -3.96225 q^{44} -4.18847 q^{45} -0.120720 q^{46} +4.21855 q^{47} -1.10960 q^{48} -6.74398 q^{49} -0.607373 q^{50} +4.63697 q^{51} +2.83500 q^{52} -4.78550 q^{53} -5.29145 q^{54} -9.38256 q^{55} -0.505980 q^{56} -2.60523 q^{57} -5.49154 q^{58} +9.35022 q^{59} -2.62752 q^{60} -10.8664 q^{61} +2.86063 q^{62} -0.894971 q^{63} +1.00000 q^{64} +6.71324 q^{65} -4.39651 q^{66} -5.28863 q^{67} -4.17895 q^{68} -0.133951 q^{69} -1.19816 q^{70} -5.68533 q^{71} +1.76879 q^{72} -8.62665 q^{73} +0.733529 q^{74} -0.673942 q^{75} +2.34790 q^{76} -2.00482 q^{77} +3.14571 q^{78} -14.7831 q^{79} +2.36799 q^{80} -0.565037 q^{81} -2.42408 q^{82} +11.1735 q^{83} -0.561436 q^{84} -9.89572 q^{85} -5.41305 q^{86} -6.09342 q^{87} +3.96225 q^{88} -5.14114 q^{89} +4.18847 q^{90} +1.43445 q^{91} +0.120720 q^{92} +3.17416 q^{93} -4.21855 q^{94} +5.55979 q^{95} +1.10960 q^{96} -14.2393 q^{97} +6.74398 q^{98} +7.00837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * q^99

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