LMFDB - Embedded newform 4034.2.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.42842 q^{3} +1.00000 q^{4} +2.01766 q^{5} -1.42842 q^{6} +0.289927 q^{7} +1.00000 q^{8} -0.959611 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.42842 q^{3} +1.00000 q^{4} +2.01766 q^{5} -1.42842 q^{6} +0.289927 q^{7} +1.00000 q^{8} -0.959611 q^{9} +2.01766 q^{10} +2.02642 q^{11} -1.42842 q^{12} +0.335567 q^{13} +0.289927 q^{14} -2.88207 q^{15} +1.00000 q^{16} -5.48365 q^{17} -0.959611 q^{18} -7.61667 q^{19} +2.01766 q^{20} -0.414139 q^{21} +2.02642 q^{22} -2.63257 q^{23} -1.42842 q^{24} -0.929048 q^{25} +0.335567 q^{26} +5.65599 q^{27} +0.289927 q^{28} +0.540826 q^{29} -2.88207 q^{30} -1.62265 q^{31} +1.00000 q^{32} -2.89458 q^{33} -5.48365 q^{34} +0.584975 q^{35} -0.959611 q^{36} +6.32341 q^{37} -7.61667 q^{38} -0.479332 q^{39} +2.01766 q^{40} -9.54198 q^{41} -0.414139 q^{42} -3.83115 q^{43} +2.02642 q^{44} -1.93617 q^{45} -2.63257 q^{46} -10.0082 q^{47} -1.42842 q^{48} -6.91594 q^{49} -0.929048 q^{50} +7.83297 q^{51} +0.335567 q^{52} -1.55552 q^{53} +5.65599 q^{54} +4.08862 q^{55} +0.289927 q^{56} +10.8798 q^{57} +0.540826 q^{58} -0.0777539 q^{59} -2.88207 q^{60} -6.36457 q^{61} -1.62265 q^{62} -0.278217 q^{63} +1.00000 q^{64} +0.677061 q^{65} -2.89458 q^{66} +7.92116 q^{67} -5.48365 q^{68} +3.76042 q^{69} +0.584975 q^{70} +3.20788 q^{71} -0.959611 q^{72} -9.17117 q^{73} +6.32341 q^{74} +1.32707 q^{75} -7.61667 q^{76} +0.587514 q^{77} -0.479332 q^{78} +8.16424 q^{79} +2.01766 q^{80} -5.20031 q^{81} -9.54198 q^{82} +1.94693 q^{83} -0.414139 q^{84} -11.0641 q^{85} -3.83115 q^{86} -0.772528 q^{87} +2.02642 q^{88} +13.0797 q^{89} -1.93617 q^{90} +0.0972901 q^{91} -2.63257 q^{92} +2.31783 q^{93} -10.0082 q^{94} -15.3679 q^{95} -1.42842 q^{96} -17.7702 q^{97} -6.91594 q^{98} -1.94457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * 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
$3$	−1.42842	−0.824700	−0.412350	−	0.911026i	$-0.635292\pi$
$3$	−1.42842	−0.824700	−0.412350	+	0.911026i	$0.635292\pi$
$4$	1.00000	0.500000
$5$	2.01766	0.902325	0.451162	−	0.892442i	$-0.351009\pi$
$5$	2.01766	0.902325	0.451162	+	0.892442i	$0.351009\pi$
$6$	−1.42842	−0.583151
$7$	0.289927	0.109582	0.0547911	−	0.998498i	$-0.482551\pi$
$7$	0.289927	0.109582	0.0547911	+	0.998498i	$0.482551\pi$
$8$	1.00000	0.353553
$9$	−0.959611	−0.319870
$10$	2.01766	0.638040
$11$	2.02642	0.610988	0.305494	−	0.952194i	$-0.401178\pi$
$11$	2.02642	0.610988	0.305494	+	0.952194i	$0.401178\pi$
$12$	−1.42842	−0.412350
$13$	0.335567	0.0930696	0.0465348	−	0.998917i	$-0.485182\pi$
$13$	0.335567	0.0930696	0.0465348	+	0.998917i	$0.485182\pi$
$14$	0.289927	0.0774863
$15$	−2.88207	−0.744147
$16$	1.00000	0.250000
$17$	−5.48365	−1.32998	−0.664991	−	0.746852i	$-0.731564\pi$
$17$	−5.48365	−1.32998	−0.664991	+	0.746852i	$0.731564\pi$
$18$	−0.959611	−0.226182
$19$	−7.61667	−1.74738	−0.873692	−	0.486479i	$-0.838281\pi$
$19$	−7.61667	−1.74738	−0.873692	+	0.486479i	$0.838281\pi$
$20$	2.01766	0.451162
$21$	−0.414139	−0.0903724
$22$	2.02642	0.432033
$23$	−2.63257	−0.548929	−0.274465	−	0.961597i	$-0.588501\pi$
$23$	−2.63257	−0.548929	−0.274465	+	0.961597i	$0.588501\pi$
$24$	−1.42842	−0.291575
$25$	−0.929048	−0.185810
$26$	0.335567	0.0658102
$27$	5.65599	1.08850
$28$	0.289927	0.0547911
$29$	0.540826	0.100429	0.0502145	−	0.998738i	$-0.484010\pi$
$29$	0.540826	0.100429	0.0502145	+	0.998738i	$0.484010\pi$
$30$	−2.88207	−0.526192
$31$	−1.62265	−0.291436	−0.145718	−	0.989326i	$-0.546549\pi$
$31$	−1.62265	−0.291436	−0.145718	+	0.989326i	$0.546549\pi$
$32$	1.00000	0.176777
$33$	−2.89458	−0.503881
$34$	−5.48365	−0.940439
$35$	0.584975	0.0988788
$36$	−0.959611	−0.159935
$37$	6.32341	1.03956	0.519781	−	0.854299i	$-0.326013\pi$
$37$	6.32341	1.03956	0.519781	+	0.854299i	$0.326013\pi$
$38$	−7.61667	−1.23559
$39$	−0.479332	−0.0767545
$40$	2.01766	0.319020
$41$	−9.54198	−1.49021	−0.745104	−	0.666949i	$-0.767600\pi$
$41$	−9.54198	−1.49021	−0.745104	+	0.666949i	$0.767600\pi$
$42$	−0.414139	−0.0639030
$43$	−3.83115	−0.584245	−0.292123	−	0.956381i	$-0.594362\pi$
$43$	−3.83115	−0.584245	−0.292123	+	0.956381i	$0.594362\pi$
$44$	2.02642	0.305494
$45$	−1.93617	−0.288627
$46$	−2.63257	−0.388151
$47$	−10.0082	−1.45985	−0.729925	−	0.683527i	$-0.760445\pi$
$47$	−10.0082	−1.45985	−0.729925	+	0.683527i	$0.760445\pi$
$48$	−1.42842	−0.206175
$49$	−6.91594	−0.987992
$50$	−0.929048	−0.131387
$51$	7.83297	1.09684
$52$	0.335567	0.0465348
$53$	−1.55552	−0.213668	−0.106834	−	0.994277i	$-0.534071\pi$
$53$	−1.55552	−0.213668	−0.106834	+	0.994277i	$0.534071\pi$
$54$	5.65599	0.769683
$55$	4.08862	0.551309
$56$	0.289927	0.0387432
$57$	10.8798	1.44107
$58$	0.540826	0.0710140
$59$	−0.0777539	−0.0101227	−0.00506135	−	0.999987i	$-0.501611\pi$
$59$	−0.0777539	−0.0101227	−0.00506135	+	0.999987i	$0.501611\pi$
$60$	−2.88207	−0.372074
$61$	−6.36457	−0.814900	−0.407450	−	0.913228i	$-0.633582\pi$
$61$	−6.36457	−0.814900	−0.407450	+	0.913228i	$0.633582\pi$
$62$	−1.62265	−0.206076
$63$	−0.278217	−0.0350521
$64$	1.00000	0.125000
$65$	0.677061	0.0839791
$66$	−2.89458	−0.356298
$67$	7.92116	0.967724	0.483862	−	0.875144i	$-0.339234\pi$
$67$	7.92116	0.967724	0.483862	+	0.875144i	$0.339234\pi$
$68$	−5.48365	−0.664991
$69$	3.76042	0.452702
$70$	0.584975	0.0699179
$71$	3.20788	0.380706	0.190353	−	0.981716i	$-0.439037\pi$
$71$	3.20788	0.380706	0.190353	+	0.981716i	$0.439037\pi$
$72$	−0.959611	−0.113091
$73$	−9.17117	−1.07340	−0.536702	−	0.843772i	$-0.680330\pi$
$73$	−9.17117	−1.07340	−0.536702	+	0.843772i	$0.680330\pi$
$74$	6.32341	0.735082
$75$	1.32707	0.153237
$76$	−7.61667	−0.873692
$77$	0.587514	0.0669534
$78$	−0.479332	−0.0542736
$79$	8.16424	0.918549	0.459275	−	0.888294i	$-0.348109\pi$
$79$	8.16424	0.918549	0.459275	+	0.888294i	$0.348109\pi$
$80$	2.01766	0.225581
$81$	−5.20031	−0.577813
$82$	−9.54198	−1.05374
$83$	1.94693	0.213703	0.106851	−	0.994275i	$-0.465923\pi$
$83$	1.94693	0.213703	0.106851	+	0.994275i	$0.465923\pi$
$84$	−0.414139	−0.0451862
$85$	−11.0641	−1.20008
$86$	−3.83115	−0.413124
$87$	−0.772528	−0.0828237
$88$	2.02642	0.216017
$89$	13.0797	1.38645	0.693224	−	0.720722i	$-0.256190\pi$
$89$	13.0797	1.38645	0.693224	+	0.720722i	$0.256190\pi$
$90$	−1.93617	−0.204090
$91$	0.0972901	0.0101988
$92$	−2.63257	−0.274465
$93$	2.31783	0.240347
$94$	−10.0082	−1.03227
$95$	−15.3679	−1.57671
$96$	−1.42842	−0.145788
$97$	−17.7702	−1.80430	−0.902148	−	0.431428i	$-0.858010\pi$
$97$	−17.7702	−1.80430	−0.902148	+	0.431428i	$0.858010\pi$
$98$	−6.91594	−0.698616
$99$	−1.94457	−0.195437
$100$	−0.929048	−0.0929048
$101$	15.5425	1.54654	0.773270	−	0.634077i	$-0.218620\pi$
$101$	15.5425	1.54654	0.773270	+	0.634077i	$0.218620\pi$
$102$	7.83297	0.775580
$103$	−10.0832	−0.993530	−0.496765	−	0.867885i	$-0.665479\pi$
$103$	−10.0832	−0.993530	−0.496765	+	0.867885i	$0.665479\pi$
$104$	0.335567	0.0329051
$105$	−0.835591	−0.0815453
$106$	−1.55552	−0.151086
$107$	8.64489	0.835733	0.417866	−	0.908508i	$-0.362778\pi$
$107$	8.64489	0.835733	0.417866	+	0.908508i	$0.362778\pi$
$108$	5.65599	0.544248
$109$	16.2632	1.55773	0.778866	−	0.627191i	$-0.215795\pi$
$109$	16.2632	1.55773	0.778866	+	0.627191i	$0.215795\pi$
$110$	4.08862	0.389835
$111$	−9.03250	−0.857327
$112$	0.289927	0.0273956
$113$	2.78080	0.261596	0.130798	−	0.991409i	$-0.458246\pi$
$113$	2.78080	0.261596	0.130798	+	0.991409i	$0.458246\pi$
$114$	10.8798	1.01899
$115$	−5.31163	−0.495312
$116$	0.540826	0.0502145
$117$	−0.322014	−0.0297702
$118$	−0.0777539	−0.00715782
$119$	−1.58986	−0.145742
$120$	−2.88207	−0.263096
$121$	−6.89364	−0.626694
$122$	−6.36457	−0.576221
$123$	13.6300	1.22897
$124$	−1.62265	−0.145718
$125$	−11.9628	−1.06999
$126$	−0.278217	−0.0247856
$127$	17.9745	1.59498	0.797488	−	0.603335i	$-0.206162\pi$
$127$	17.9745	1.59498	0.797488	+	0.603335i	$0.206162\pi$
$128$	1.00000	0.0883883
$129$	5.47250	0.481827
$130$	0.677061	0.0593822
$131$	−12.3553	−1.07949	−0.539743	−	0.841830i	$-0.681479\pi$
$131$	−12.3553	−1.07949	−0.539743	+	0.841830i	$0.681479\pi$
$132$	−2.89458	−0.251941
$133$	−2.20828	−0.191482
$134$	7.92116	0.684284
$135$	11.4119	0.982178
$136$	−5.48365	−0.470219
$137$	2.46612	0.210695	0.105347	−	0.994435i	$-0.466405\pi$
$137$	2.46612	0.210695	0.105347	+	0.994435i	$0.466405\pi$
$138$	3.76042	0.320108
$139$	17.5749	1.49069	0.745343	−	0.666681i	$-0.232286\pi$
$139$	17.5749	1.49069	0.745343	+	0.666681i	$0.232286\pi$
$140$	0.584975	0.0494394
$141$	14.2960	1.20394
$142$	3.20788	0.269200
$143$	0.679999	0.0568644
$144$	−0.959611	−0.0799676
$145$	1.09120	0.0906196
$146$	−9.17117	−0.759011
$147$	9.87888	0.814797
$148$	6.32341	0.519781
$149$	−17.6654	−1.44720	−0.723601	−	0.690218i	$-0.757514\pi$
$149$	−17.6654	−1.44720	−0.723601	+	0.690218i	$0.757514\pi$
$150$	1.32707	0.108355
$151$	−14.5702	−1.18571	−0.592855	−	0.805310i	$-0.701999\pi$
$151$	−14.5702	−1.18571	−0.592855	+	0.805310i	$0.701999\pi$
$152$	−7.61667	−0.617794
$153$	5.26217	0.425421
$154$	0.587514	0.0473432
$155$	−3.27395	−0.262970
$156$	−0.479332	−0.0383773
$157$	−15.5966	−1.24474	−0.622372	−	0.782721i	$-0.713831\pi$
$157$	−15.5966	−1.24474	−0.622372	+	0.782721i	$0.713831\pi$
$158$	8.16424	0.649512
$159$	2.22195	0.176212
$160$	2.01766	0.159510
$161$	−0.763254	−0.0601529
$162$	−5.20031	−0.408575
$163$	17.1691	1.34478	0.672392	−	0.740195i	$-0.265267\pi$
$163$	17.1691	1.34478	0.672392	+	0.740195i	$0.265267\pi$
$164$	−9.54198	−0.745104
$165$	−5.84027	−0.454665
$166$	1.94693	0.151111
$167$	9.88046	0.764573	0.382286	−	0.924044i	$-0.375137\pi$
$167$	9.88046	0.764573	0.382286	+	0.924044i	$0.375137\pi$
$168$	−0.414139	−0.0319515
$169$	−12.8874	−0.991338
$170$	−11.0641	−0.848581
$171$	7.30904	0.558936
$172$	−3.83115	−0.292123
$173$	−15.6736	−1.19164	−0.595819	−	0.803119i	$-0.703172\pi$
$173$	−15.6736	−1.19164	−0.595819	+	0.803119i	$0.703172\pi$
$174$	−0.772528	−0.0585652
$175$	−0.269356	−0.0203614
$176$	2.02642	0.152747
$177$	0.111065	0.00834818
$178$	13.0797	0.980367
$179$	−0.220786	−0.0165023	−0.00825116	−	0.999966i	$-0.502626\pi$
$179$	−0.220786	−0.0165023	−0.00825116	+	0.999966i	$0.502626\pi$
$180$	−1.93617	−0.144313
$181$	5.97336	0.443996	0.221998	−	0.975047i	$-0.428742\pi$
$181$	5.97336	0.443996	0.221998	+	0.975047i	$0.428742\pi$
$182$	0.0972901	0.00721163
$183$	9.09129	0.672048
$184$	−2.63257	−0.194076
$185$	12.7585	0.938023
$186$	2.31783	0.169951
$187$	−11.1122	−0.812602
$188$	−10.0082	−0.729925
$189$	1.63983	0.119280
$190$	−15.3679	−1.11490
$191$	−27.5960	−1.99678	−0.998388	−	0.0567641i	$-0.981922\pi$
$191$	−27.5960	−1.99678	−0.998388	+	0.0567641i	$0.981922\pi$
$192$	−1.42842	−0.103087
$193$	−15.4616	−1.11295	−0.556474	−	0.830865i	$-0.687846\pi$
$193$	−15.4616	−1.11295	−0.556474	+	0.830865i	$0.687846\pi$
$194$	−17.7702	−1.27583
$195$	−0.967128	−0.0692575
$196$	−6.91594	−0.493996
$197$	−9.46075	−0.674050	−0.337025	−	0.941496i	$-0.609421\pi$
$197$	−9.46075	−0.674050	−0.337025	+	0.941496i	$0.609421\pi$
$198$	−1.94457	−0.138195
$199$	−10.1978	−0.722902	−0.361451	−	0.932391i	$-0.617719\pi$
$199$	−10.1978	−0.722902	−0.361451	+	0.932391i	$0.617719\pi$
$200$	−0.929048	−0.0656936
$201$	−11.3148	−0.798082
$202$	15.5425	1.09357
$203$	0.156800	0.0110052
$204$	7.83297	0.548418
$205$	−19.2525	−1.34465
$206$	−10.0832	−0.702532
$207$	2.52624	0.175586
$208$	0.335567	0.0232674
$209$	−15.4345	−1.06763
$210$	−0.835591	−0.0576612
$211$	13.1498	0.905271	0.452636	−	0.891696i	$-0.350484\pi$
$211$	13.1498	0.905271	0.452636	+	0.891696i	$0.350484\pi$
$212$	−1.55552	−0.106834
$213$	−4.58221	−0.313968
$214$	8.64489	0.590952
$215$	−7.72996	−0.527179
$216$	5.65599	0.384842
$217$	−0.470450	−0.0319362
$218$	16.2632	1.10148
$219$	13.1003	0.885236
$220$	4.08862	0.275655
$221$	−1.84013	−0.123781
$222$	−9.03250	−0.606222
$223$	−1.07855	−0.0722248	−0.0361124	−	0.999348i	$-0.511497\pi$
$223$	−1.07855	−0.0722248	−0.0361124	+	0.999348i	$0.511497\pi$
$224$	0.289927	0.0193716
$225$	0.891525	0.0594350
$226$	2.78080	0.184976
$227$	−3.24743	−0.215540	−0.107770	−	0.994176i	$-0.534371\pi$
$227$	−3.24743	−0.215540	−0.107770	+	0.994176i	$0.534371\pi$
$228$	10.8798	0.720534
$229$	20.9208	1.38248	0.691241	−	0.722624i	$-0.257064\pi$
$229$	20.9208	1.38248	0.691241	+	0.722624i	$0.257064\pi$
$230$	−5.31163	−0.350239
$231$	−0.839217	−0.0552164
$232$	0.540826	0.0355070
$233$	−11.6641	−0.764140	−0.382070	−	0.924133i	$-0.624789\pi$
$233$	−11.6641	−0.764140	−0.382070	+	0.924133i	$0.624789\pi$
$234$	−0.322014	−0.0210507
$235$	−20.1932	−1.31726
$236$	−0.0777539	−0.00506135
$237$	−11.6620	−0.757527
$238$	−1.58986	−0.103055
$239$	−9.98397	−0.645809	−0.322905	−	0.946432i	$-0.604659\pi$
$239$	−9.98397	−0.645809	−0.322905	+	0.946432i	$0.604659\pi$
$240$	−2.88207	−0.186037
$241$	9.61128	0.619117	0.309559	−	0.950880i	$-0.399819\pi$
$241$	9.61128	0.619117	0.309559	+	0.950880i	$0.399819\pi$
$242$	−6.89364	−0.443140
$243$	−9.53974	−0.611975
$244$	−6.36457	−0.407450
$245$	−13.9540	−0.891490
$246$	13.6300	0.869016
$247$	−2.55591	−0.162628
$248$	−1.62265	−0.103038
$249$	−2.78103	−0.176241
$250$	−11.9628	−0.756594
$251$	−25.2696	−1.59501	−0.797503	−	0.603315i	$-0.793846\pi$
$251$	−25.2696	−1.59501	−0.797503	+	0.603315i	$0.793846\pi$
$252$	−0.278217	−0.0175260
$253$	−5.33469	−0.335389
$254$	17.9745	1.12782
$255$	15.8043	0.989702
$256$	1.00000	0.0625000
$257$	−7.87728	−0.491371	−0.245686	−	0.969350i	$-0.579013\pi$
$257$	−7.87728	−0.491371	−0.245686	+	0.969350i	$0.579013\pi$
$258$	5.47250	0.340703
$259$	1.83333	0.113918
$260$	0.677061	0.0419895
$261$	−0.518983	−0.0321242
$262$	−12.3553	−0.763312
$263$	−0.376764	−0.0232323	−0.0116161	−	0.999933i	$-0.503698\pi$
$263$	−0.376764	−0.0232323	−0.0116161	+	0.999933i	$0.503698\pi$
$264$	−2.89458	−0.178149
$265$	−3.13852	−0.192798
$266$	−2.20828	−0.135398
$267$	−18.6834	−1.14340
$268$	7.92116	0.483862
$269$	30.3144	1.84830	0.924151	−	0.382027i	$-0.124774\pi$
$269$	30.3144	1.84830	0.924151	+	0.382027i	$0.124774\pi$
$270$	11.4119	0.694505
$271$	−16.3263	−0.991751	−0.495876	−	0.868394i	$-0.665153\pi$
$271$	−16.3263	−0.991751	−0.495876	+	0.868394i	$0.665153\pi$
$272$	−5.48365	−0.332495
$273$	−0.138971	−0.00841093
$274$	2.46612	0.148984
$275$	−1.88264	−0.113527
$276$	3.76042	0.226351
$277$	1.26665	0.0761056	0.0380528	−	0.999276i	$-0.487884\pi$
$277$	1.26665	0.0761056	0.0380528	+	0.999276i	$0.487884\pi$
$278$	17.5749	1.05407
$279$	1.55711	0.0932218
$280$	0.584975	0.0349589
$281$	−10.4098	−0.620997	−0.310498	−	0.950574i	$-0.600496\pi$
$281$	−10.4098	−0.620997	−0.310498	+	0.950574i	$0.600496\pi$
$282$	14.2960	0.851313
$283$	10.3421	0.614773	0.307387	−	0.951585i	$-0.400546\pi$
$283$	10.3421	0.614773	0.307387	+	0.951585i	$0.400546\pi$
$284$	3.20788	0.190353
$285$	21.9518	1.30031
$286$	0.679999	0.0402092
$287$	−2.76648	−0.163300
$288$	−0.959611	−0.0565456
$289$	13.0704	0.768850
$290$	1.09120	0.0640777
$291$	25.3834	1.48800
$292$	−9.17117	−0.536702
$293$	8.19655	0.478848	0.239424	−	0.970915i	$-0.423041\pi$
$293$	8.19655	0.478848	0.239424	+	0.970915i	$0.423041\pi$
$294$	9.87888	0.576148
$295$	−0.156881	−0.00913396
$296$	6.32341	0.367541
$297$	11.4614	0.665058
$298$	−17.6654	−1.02333
$299$	−0.883405	−0.0510886
$300$	1.32707	0.0766186
$301$	−1.11076	−0.0640229
$302$	−14.5702	−0.838423
$303$	−22.2013	−1.27543
$304$	−7.61667	−0.436846
$305$	−12.8415	−0.735304
$306$	5.26217	0.300818
$307$	−12.8227	−0.731831	−0.365915	−	0.930648i	$-0.619244\pi$
$307$	−12.8227	−0.731831	−0.365915	+	0.930648i	$0.619244\pi$
$308$	0.587514	0.0334767
$309$	14.4031	0.819364
$310$	−3.27395	−0.185948
$311$	14.5061	0.822568	0.411284	−	0.911507i	$-0.365080\pi$
$311$	14.5061	0.822568	0.411284	+	0.911507i	$0.365080\pi$
$312$	−0.479332	−0.0271368
$313$	12.3691	0.699145	0.349572	−	0.936909i	$-0.386327\pi$
$313$	12.3691	0.699145	0.349572	+	0.936909i	$0.386327\pi$
$314$	−15.5966	−0.880167
$315$	−0.561348	−0.0316284
$316$	8.16424	0.459275
$317$	−12.6462	−0.710282	−0.355141	−	0.934813i	$-0.615567\pi$
$317$	−12.6462	−0.710282	−0.355141	+	0.934813i	$0.615567\pi$
$318$	2.22195	0.124601
$319$	1.09594	0.0613608
$320$	2.01766	0.112791
$321$	−12.3485	−0.689229
$322$	−0.763254	−0.0425345
$323$	41.7672	2.32399
$324$	−5.20031	−0.288906
$325$	−0.311758	−0.0172932
$326$	17.1691	0.950906
$327$	−23.2307	−1.28466
$328$	−9.54198	−0.526868
$329$	−2.90166	−0.159974
$330$	−5.84027	−0.321496
$331$	17.3941	0.956066	0.478033	−	0.878342i	$-0.341350\pi$
$331$	17.3941	0.956066	0.478033	+	0.878342i	$0.341350\pi$
$332$	1.94693	0.106851
$333$	−6.06801	−0.332525
$334$	9.88046	0.540635
$335$	15.9822	0.873202
$336$	−0.414139	−0.0225931
$337$	−6.33911	−0.345313	−0.172657	−	0.984982i	$-0.555235\pi$
$337$	−6.33911	−0.345313	−0.172657	+	0.984982i	$0.555235\pi$
$338$	−12.8874	−0.700982
$339$	−3.97216	−0.215738
$340$	−11.0641	−0.600038
$341$	−3.28816	−0.178064
$342$	7.30904	0.395228
$343$	−4.03461	−0.217849
$344$	−3.83115	−0.206562
$345$	7.58725	0.408484
$346$	−15.6736	−0.842615
$347$	18.4769	0.991892	0.495946	−	0.868353i	$-0.334821\pi$
$347$	18.4769	0.991892	0.495946	+	0.868353i	$0.334821\pi$
$348$	−0.772528	−0.0414119
$349$	−10.7756	−0.576802	−0.288401	−	0.957510i	$-0.593124\pi$
$349$	−10.7756	−0.576802	−0.288401	+	0.957510i	$0.593124\pi$
$350$	−0.269356	−0.0143977
$351$	1.89797	0.101306
$352$	2.02642	0.108008
$353$	14.5832	0.776184	0.388092	−	0.921621i	$-0.373134\pi$
$353$	14.5832	0.776184	0.388092	+	0.921621i	$0.373134\pi$
$354$	0.111065	0.00590306
$355$	6.47242	0.343520
$356$	13.0797	0.693224
$357$	2.27099	0.120194
$358$	−0.220786	−0.0116689
$359$	28.1487	1.48563	0.742816	−	0.669496i	$-0.233490\pi$
$359$	28.1487	1.48563	0.742816	+	0.669496i	$0.233490\pi$
$360$	−1.93617	−0.102045
$361$	39.0137	2.05335
$362$	5.97336	0.313953
$363$	9.84702	0.516835
$364$	0.0972901	0.00509939
$365$	−18.5043	−0.968559
$366$	9.09129	0.475209
$367$	−14.3674	−0.749972	−0.374986	−	0.927030i	$-0.622353\pi$
$367$	−14.3674	−0.749972	−0.374986	+	0.927030i	$0.622353\pi$
$368$	−2.63257	−0.137232
$369$	9.15659	0.476673
$370$	12.7585	0.663283
$371$	−0.450989	−0.0234142
$372$	2.31783	0.120174
$373$	−17.6289	−0.912792	−0.456396	−	0.889777i	$-0.650860\pi$
$373$	−17.6289	−0.912792	−0.456396	+	0.889777i	$0.650860\pi$
$374$	−11.1122	−0.574596
$375$	17.0879	0.882417
$376$	−10.0082	−0.516135
$377$	0.181484	0.00934689
$378$	1.63983	0.0843436
$379$	13.7633	0.706975	0.353487	−	0.935439i	$-0.384996\pi$
$379$	13.7633	0.706975	0.353487	+	0.935439i	$0.384996\pi$
$380$	−15.3679	−0.788354
$381$	−25.6751	−1.31538
$382$	−27.5960	−1.41193
$383$	−19.0487	−0.973342	−0.486671	−	0.873585i	$-0.661789\pi$
$383$	−19.0487	−0.973342	−0.486671	+	0.873585i	$0.661789\pi$
$384$	−1.42842	−0.0728939
$385$	1.18540	0.0604137
$386$	−15.4616	−0.786973
$387$	3.67641	0.186883
$388$	−17.7702	−0.902148
$389$	−8.76115	−0.444208	−0.222104	−	0.975023i	$-0.571292\pi$
$389$	−8.76115	−0.444208	−0.222104	+	0.975023i	$0.571292\pi$
$390$	−0.967128	−0.0489725
$391$	14.4361	0.730065
$392$	−6.91594	−0.349308
$393$	17.6486	0.890252
$394$	−9.46075	−0.476626
$395$	16.4727	0.828830
$396$	−1.94457	−0.0977184
$397$	16.1362	0.809852	0.404926	−	0.914349i	$-0.367297\pi$
$397$	16.1362	0.809852	0.404926	+	0.914349i	$0.367297\pi$
$398$	−10.1978	−0.511169
$399$	3.15436	0.157915
$400$	−0.929048	−0.0464524
$401$	4.04403	0.201949	0.100975	−	0.994889i	$-0.467804\pi$
$401$	4.04403	0.201949	0.100975	+	0.994889i	$0.467804\pi$
$402$	−11.3148	−0.564329
$403$	−0.544508	−0.0271239
$404$	15.5425	0.773270
$405$	−10.4925	−0.521375
$406$	0.156800	0.00778187
$407$	12.8139	0.635160
$408$	7.83297	0.387790
$409$	−18.2878	−0.904272	−0.452136	−	0.891949i	$-0.649338\pi$
$409$	−18.2878	−0.904272	−0.452136	+	0.891949i	$0.649338\pi$
$410$	−19.2525	−0.950812
$411$	−3.52266	−0.173760
$412$	−10.0832	−0.496765
$413$	−0.0225430	−0.00110927
$414$	2.52624	0.124158
$415$	3.92824	0.192830
$416$	0.335567	0.0164525
$417$	−25.1044	−1.22937
$418$	−15.4345	−0.754928
$419$	0.278123	0.0135872	0.00679359	−	0.999977i	$-0.497838\pi$
$419$	0.278123	0.0135872	0.00679359	+	0.999977i	$0.497838\pi$
$420$	−0.835591	−0.0407727
$421$	−29.8431	−1.45446	−0.727232	−	0.686392i	$-0.759193\pi$
$421$	−29.8431	−1.45446	−0.727232	+	0.686392i	$0.759193\pi$
$422$	13.1498	0.640124
$423$	9.60400	0.466963
$424$	−1.55552	−0.0755430
$425$	5.09458	0.247123
$426$	−4.58221	−0.222009
$427$	−1.84526	−0.0892985
$428$	8.64489	0.417866
$429$	−0.971326	−0.0468960
$430$	−7.72996	−0.372772
$431$	4.27950	0.206136	0.103068	−	0.994674i	$-0.467134\pi$
$431$	4.27950	0.206136	0.103068	+	0.994674i	$0.467134\pi$
$432$	5.65599	0.272124
$433$	14.3669	0.690430	0.345215	−	0.938524i	$-0.387806\pi$
$433$	14.3669	0.690430	0.345215	+	0.938524i	$0.387806\pi$
$434$	−0.470450	−0.0225823
$435$	−1.55870	−0.0747339
$436$	16.2632	0.778866
$437$	20.0514	0.959190
$438$	13.1003	0.625956
$439$	7.50778	0.358327	0.179163	−	0.983819i	$-0.442661\pi$
$439$	7.50778	0.358327	0.179163	+	0.983819i	$0.442661\pi$
$440$	4.08862	0.194917
$441$	6.63661	0.316029
$442$	−1.84013	−0.0875263
$443$	29.3459	1.39427	0.697134	−	0.716941i	$-0.254458\pi$
$443$	29.3459	1.39427	0.697134	+	0.716941i	$0.254458\pi$
$444$	−9.03250	−0.428663
$445$	26.3904	1.25103
$446$	−1.07855	−0.0510707
$447$	25.2336	1.19351
$448$	0.289927	0.0136978
$449$	−13.9390	−0.657823	−0.328911	−	0.944361i	$-0.606682\pi$
$449$	−13.9390	−0.657823	−0.328911	+	0.944361i	$0.606682\pi$
$450$	0.891525	0.0420269
$451$	−19.3360	−0.910498
$452$	2.78080	0.130798
$453$	20.8124	0.977854
$454$	−3.24743	−0.152409
$455$	0.196298	0.00920261
$456$	10.8798	0.509494
$457$	−1.96136	−0.0917487	−0.0458744	−	0.998947i	$-0.514607\pi$
$457$	−1.96136	−0.0917487	−0.0458744	+	0.998947i	$0.514607\pi$
$458$	20.9208	0.977563
$459$	−31.0155	−1.44768
$460$	−5.31163	−0.247656
$461$	14.7108	0.685150	0.342575	−	0.939490i	$-0.388701\pi$
$461$	14.7108	0.685150	0.342575	+	0.939490i	$0.388701\pi$
$462$	−0.839217	−0.0390439
$463$	12.9161	0.600260	0.300130	−	0.953898i	$-0.402970\pi$
$463$	12.9161	0.600260	0.300130	+	0.953898i	$0.402970\pi$
$464$	0.540826	0.0251072
$465$	4.67658	0.216871
$466$	−11.6641	−0.540328
$467$	40.7389	1.88517	0.942585	−	0.333966i	$-0.108387\pi$
$467$	40.7389	1.88517	0.942585	+	0.333966i	$0.108387\pi$
$468$	−0.322014	−0.0148851
$469$	2.29656	0.106045
$470$	−20.1932	−0.931443
$471$	22.2785	1.02654
$472$	−0.0777539	−0.00357891
$473$	−7.76351	−0.356966
$474$	−11.6620	−0.535653
$475$	7.07625	0.324681
$476$	−1.58986	−0.0728711
$477$	1.49270	0.0683460
$478$	−9.98397	−0.456656
$479$	4.22532	0.193060	0.0965299	−	0.995330i	$-0.469226\pi$
$479$	4.22532	0.193060	0.0965299	+	0.995330i	$0.469226\pi$
$480$	−2.88207	−0.131548
$481$	2.12193	0.0967517
$482$	9.61128	0.437782
$483$	1.09025	0.0496081
$484$	−6.89364	−0.313347
$485$	−35.8543	−1.62806
$486$	−9.53974	−0.432731
$487$	4.81635	0.218250	0.109125	−	0.994028i	$-0.465195\pi$
$487$	4.81635	0.218250	0.109125	+	0.994028i	$0.465195\pi$
$488$	−6.36457	−0.288111
$489$	−24.5247	−1.10904
$490$	−13.9540	−0.630378
$491$	−1.90654	−0.0860409	−0.0430205	−	0.999074i	$-0.513698\pi$
$491$	−1.90654	−0.0860409	−0.0430205	+	0.999074i	$0.513698\pi$
$492$	13.6300	0.614487
$493$	−2.96570	−0.133569
$494$	−2.55591	−0.114996
$495$	−3.92348	−0.176347
$496$	−1.62265	−0.0728590
$497$	0.930053	0.0417186
$498$	−2.78103	−0.124621
$499$	−16.1743	−0.724060	−0.362030	−	0.932166i	$-0.617916\pi$
$499$	−16.1743	−0.724060	−0.362030	+	0.932166i	$0.617916\pi$
$500$	−11.9628	−0.534993
$501$	−14.1135	−0.630543
$502$	−25.2696	−1.12784
$503$	−5.74301	−0.256068	−0.128034	−	0.991770i	$-0.540867\pi$
$503$	−5.74301	−0.256068	−0.128034	+	0.991770i	$0.540867\pi$
$504$	−0.278217	−0.0123928
$505$	31.3595	1.39548
$506$	−5.33469	−0.237156
$507$	18.4086	0.817556
$508$	17.9745	0.797488
$509$	−2.54818	−0.112946	−0.0564731	−	0.998404i	$-0.517986\pi$
$509$	−2.54818	−0.112946	−0.0564731	+	0.998404i	$0.517986\pi$
$510$	15.8043	0.699825
$511$	−2.65897	−0.117626
$512$	1.00000	0.0441942
$513$	−43.0798	−1.90202
$514$	−7.87728	−0.347452
$515$	−20.3445	−0.896487
$516$	5.47250	0.240913
$517$	−20.2808	−0.891950
$518$	1.83333	0.0805519
$519$	22.3884	0.982744
$520$	0.677061	0.0296911
$521$	−45.4821	−1.99261	−0.996303	−	0.0859109i	$-0.972620\pi$
$521$	−45.4821	−1.99261	−0.996303	+	0.0859109i	$0.972620\pi$
$522$	−0.518983	−0.0227153
$523$	−32.3360	−1.41396	−0.706978	−	0.707236i	$-0.749942\pi$
$523$	−32.3360	−1.41396	−0.706978	+	0.707236i	$0.749942\pi$
$524$	−12.3553	−0.539743
$525$	0.384755	0.0167921
$526$	−0.376764	−0.0164277
$527$	8.89804	0.387605
$528$	−2.89458	−0.125970
$529$	−16.0696	−0.698677
$530$	−3.13852	−0.136329
$531$	0.0746135	0.00323795
$532$	−2.20828	−0.0957411
$533$	−3.20198	−0.138693
$534$	−18.6834	−0.808508
$535$	17.4424	0.754103
$536$	7.92116	0.342142
$537$	0.315376	0.0136095
$538$	30.3144	1.30695
$539$	−14.0146	−0.603651
$540$	11.4119	0.491089
$541$	−0.0830455	−0.00357041	−0.00178520	−	0.999998i	$-0.500568\pi$
$541$	−0.0830455	−0.00357041	−0.00178520	+	0.999998i	$0.500568\pi$
$542$	−16.3263	−0.701274
$543$	−8.53248	−0.366164
$544$	−5.48365	−0.235110
$545$	32.8136	1.40558
$546$	−0.138971	−0.00594743
$547$	22.9537	0.981430	0.490715	−	0.871320i	$-0.336736\pi$
$547$	22.9537	0.981430	0.490715	+	0.871320i	$0.336736\pi$
$548$	2.46612	0.105347
$549$	6.10751	0.260662
$550$	−1.88264	−0.0802760
$551$	−4.11930	−0.175488
$552$	3.76042	0.160054
$553$	2.36704	0.100657
$554$	1.26665	0.0538148
$555$	−18.2245	−0.773588
$556$	17.5749	0.745343
$557$	−35.4188	−1.50074	−0.750372	−	0.661016i	$-0.770126\pi$
$557$	−35.4188	−1.50074	−0.750372	+	0.661016i	$0.770126\pi$
$558$	1.55711	0.0659177
$559$	−1.28561	−0.0543755
$560$	0.584975	0.0247197
$561$	15.8729	0.670153
$562$	−10.4098	−0.439111
$563$	27.7368	1.16897	0.584483	−	0.811406i	$-0.301297\pi$
$563$	27.7368	1.16897	0.584483	+	0.811406i	$0.301297\pi$
$564$	14.2960	0.601969
$565$	5.61071	0.236044
$566$	10.3421	0.434710
$567$	−1.50771	−0.0633180
$568$	3.20788	0.134600
$569$	5.35206	0.224370	0.112185	−	0.993687i	$-0.464215\pi$
$569$	5.35206	0.224370	0.112185	+	0.993687i	$0.464215\pi$
$570$	21.9518	0.919459
$571$	−22.0447	−0.922540	−0.461270	−	0.887260i	$-0.652606\pi$
$571$	−22.0447	−0.922540	−0.461270	+	0.887260i	$0.652606\pi$
$572$	0.679999	0.0284322
$573$	39.4187	1.64674
$574$	−2.76648	−0.115471
$575$	2.44579	0.101996
$576$	−0.959611	−0.0399838
$577$	−19.9025	−0.828550	−0.414275	−	0.910152i	$-0.635965\pi$
$577$	−19.9025	−0.828550	−0.414275	+	0.910152i	$0.635965\pi$
$578$	13.0704	0.543659
$579$	22.0856	0.917848
$580$	1.09120	0.0453098
$581$	0.564467	0.0234181
$582$	25.3834	1.05218
$583$	−3.15214	−0.130548
$584$	−9.17117	−0.379506
$585$	−0.649715	−0.0268624
$586$	8.19655	0.338597
$587$	11.5293	0.475865	0.237932	−	0.971282i	$-0.423530\pi$
$587$	11.5293	0.475865	0.237932	+	0.971282i	$0.423530\pi$
$588$	9.87888	0.407398
$589$	12.3592	0.509251
$590$	−0.156881	−0.00645868
$591$	13.5139	0.555889
$592$	6.32341	0.259891
$593$	−24.6873	−1.01379	−0.506893	−	0.862009i	$-0.669206\pi$
$593$	−24.6873	−1.01379	−0.506893	+	0.862009i	$0.669206\pi$
$594$	11.4614	0.470267
$595$	−3.20780	−0.131507
$596$	−17.6654	−0.723601
$597$	14.5667	0.596177
$598$	−0.883405	−0.0361251
$599$	−41.8645	−1.71054	−0.855268	−	0.518187i	$-0.826607\pi$
$599$	−41.8645	−1.71054	−0.855268	+	0.518187i	$0.826607\pi$
$600$	1.32707	0.0541775
$601$	21.5726	0.879966	0.439983	−	0.898006i	$-0.354985\pi$
$601$	21.5726	0.879966	0.439983	+	0.898006i	$0.354985\pi$
$602$	−1.11076	−0.0452710
$603$	−7.60123	−0.309546
$604$	−14.5702	−0.592855
$605$	−13.9090	−0.565482
$606$	−22.2013	−0.901866
$607$	24.8470	1.00851	0.504254	−	0.863555i	$-0.331768\pi$
$607$	24.8470	1.00851	0.504254	+	0.863555i	$0.331768\pi$
$608$	−7.61667	−0.308897
$609$	−0.223977	−0.00907601
$610$	−12.8415	−0.519939
$611$	−3.35843	−0.135868
$612$	5.26217	0.212711
$613$	48.0882	1.94226	0.971131	−	0.238546i	$-0.0766708\pi$
$613$	48.0882	1.94226	0.971131	+	0.238546i	$0.0766708\pi$
$614$	−12.8227	−0.517482
$615$	27.5007	1.10893
$616$	0.587514	0.0236716
$617$	26.6342	1.07225	0.536127	−	0.844137i	$-0.319887\pi$
$617$	26.6342	1.07225	0.536127	+	0.844137i	$0.319887\pi$
$618$	14.4031	0.579378
$619$	34.8345	1.40012	0.700058	−	0.714086i	$-0.253158\pi$
$619$	34.8345	1.40012	0.700058	+	0.714086i	$0.253158\pi$
$620$	−3.27395	−0.131485
$621$	−14.8898	−0.597508
$622$	14.5061	0.581643
$623$	3.79217	0.151930
$624$	−0.479332	−0.0191886
$625$	−19.4916	−0.779665
$626$	12.3691	0.494370
$627$	22.0470	0.880474
$628$	−15.5966	−0.622372
$629$	−34.6754	−1.38260
$630$	−0.561348	−0.0223646
$631$	13.8740	0.552316	0.276158	−	0.961112i	$-0.410939\pi$
$631$	13.8740	0.552316	0.276158	+	0.961112i	$0.410939\pi$
$632$	8.16424	0.324756
$633$	−18.7835	−0.746577
$634$	−12.6462	−0.502245
$635$	36.2664	1.43919
$636$	2.22195	0.0881059
$637$	−2.32076	−0.0919520
$638$	1.09594	0.0433887
$639$	−3.07832	−0.121776
$640$	2.01766	0.0797550
$641$	4.61127	0.182134	0.0910670	−	0.995845i	$-0.470972\pi$
$641$	4.61127	0.182134	0.0910670	+	0.995845i	$0.470972\pi$
$642$	−12.3485	−0.487358
$643$	−14.2145	−0.560566	−0.280283	−	0.959917i	$-0.590428\pi$
$643$	−14.2145	−0.560566	−0.280283	+	0.959917i	$0.590428\pi$
$644$	−0.763254	−0.0300764
$645$	11.0416	0.434764
$646$	41.7672	1.64331
$647$	−3.21041	−0.126214	−0.0631072	−	0.998007i	$-0.520101\pi$
$647$	−3.21041	−0.126214	−0.0631072	+	0.998007i	$0.520101\pi$
$648$	−5.20031	−0.204288
$649$	−0.157562	−0.00618484
$650$	−0.311758	−0.0122282
$651$	0.672001	0.0263378
$652$	17.1691	0.672392
$653$	−12.3401	−0.482904	−0.241452	−	0.970413i	$-0.577624\pi$
$653$	−12.3401	−0.482904	−0.241452	+	0.970413i	$0.577624\pi$
$654$	−23.2307	−0.908393
$655$	−24.9288	−0.974047
$656$	−9.54198	−0.372552
$657$	8.80075	0.343350
$658$	−2.90166	−0.113118
$659$	48.5600	1.89163	0.945815	−	0.324707i	$-0.105266\pi$
$659$	48.5600	1.89163	0.945815	+	0.324707i	$0.105266\pi$
$660$	−5.84027	−0.227332
$661$	48.3750	1.88157	0.940785	−	0.339005i	$-0.110090\pi$
$661$	48.3750	1.88157	0.940785	+	0.339005i	$0.110090\pi$
$662$	17.3941	0.676041
$663$	2.62849	0.102082
$664$	1.94693	0.0755554
$665$	−4.45556	−0.172779
$666$	−6.06801	−0.235131
$667$	−1.42376	−0.0551284
$668$	9.88046	0.382286
$669$	1.54062	0.0595638
$670$	15.9822	0.617447
$671$	−12.8973	−0.497894
$672$	−0.414139	−0.0159757
$673$	16.9900	0.654917	0.327459	−	0.944865i	$-0.393808\pi$
$673$	16.9900	0.654917	0.327459	+	0.944865i	$0.393808\pi$
$674$	−6.33911	−0.244173
$675$	−5.25469	−0.202253
$676$	−12.8874	−0.495669
$677$	26.3649	1.01329	0.506643	−	0.862156i	$-0.330886\pi$
$677$	26.3649	1.01329	0.506643	+	0.862156i	$0.330886\pi$
$678$	−3.97216	−0.152550
$679$	−5.15208	−0.197719
$680$	−11.0641	−0.424291
$681$	4.63870	0.177755
$682$	−3.28816	−0.125910
$683$	26.0655	0.997367	0.498684	−	0.866784i	$-0.333817\pi$
$683$	26.0655	0.997367	0.498684	+	0.866784i	$0.333817\pi$
$684$	7.30904	0.279468
$685$	4.97579	0.190115
$686$	−4.03461	−0.154042
$687$	−29.8837	−1.14013
$688$	−3.83115	−0.146061
$689$	−0.521983	−0.0198860
$690$	7.58725	0.288842
$691$	1.59755	0.0607738	0.0303869	−	0.999538i	$-0.490326\pi$
$691$	1.59755	0.0607738	0.0303869	+	0.999538i	$0.490326\pi$
$692$	−15.6736	−0.595819
$693$	−0.563784	−0.0214164
$694$	18.4769	0.701373
$695$	35.4602	1.34508
$696$	−0.772528	−0.0292826
$697$	52.3249	1.98195
$698$	−10.7756	−0.407861
$699$	16.6612	0.630186
$700$	−0.269356	−0.0101807
$701$	−45.4862	−1.71799	−0.858994	−	0.511985i	$-0.828910\pi$
$701$	−45.4862	−1.71799	−0.858994	+	0.511985i	$0.828910\pi$
$702$	1.89797	0.0716342
$703$	−48.1633	−1.81651
$704$	2.02642	0.0763734
$705$	28.8444	1.08634
$706$	14.5832	0.548845
$707$	4.50620	0.169473
$708$	0.111065	0.00417409
$709$	17.7573	0.666890	0.333445	−	0.942770i	$-0.391789\pi$
$709$	17.7573	0.666890	0.333445	+	0.942770i	$0.391789\pi$
$710$	6.47242	0.242905
$711$	−7.83450	−0.293817
$712$	13.0797	0.490183
$713$	4.27174	0.159978
$714$	2.27099	0.0849897
$715$	1.37201	0.0513102
$716$	−0.220786	−0.00825116
$717$	14.2613	0.532599
$718$	28.1487	1.05050
$719$	−12.9686	−0.483647	−0.241823	−	0.970320i	$-0.577745\pi$
$719$	−12.9686	−0.483647	−0.241823	+	0.970320i	$0.577745\pi$
$720$	−1.93617	−0.0721567
$721$	−2.92340	−0.108873
$722$	39.0137	1.45194
$723$	−13.7290	−0.510586
$724$	5.97336	0.221998
$725$	−0.502454	−0.0186607
$726$	9.84702	0.365457
$727$	−8.64458	−0.320610	−0.160305	−	0.987068i	$-0.551248\pi$
$727$	−8.64458	−0.320610	−0.160305	+	0.987068i	$0.551248\pi$
$728$	0.0972901	0.00360581
$729$	29.2277	1.08251
$730$	−18.5043	−0.684875
$731$	21.0087	0.777035
$732$	9.09129	0.336024
$733$	−23.2037	−0.857047	−0.428524	−	0.903531i	$-0.640966\pi$
$733$	−23.2037	−0.857047	−0.428524	+	0.903531i	$0.640966\pi$
$734$	−14.3674	−0.530311
$735$	19.9322	0.735211
$736$	−2.63257	−0.0970379
$737$	16.0516	0.591267
$738$	9.15659	0.337059
$739$	−35.1364	−1.29251	−0.646256	−	0.763120i	$-0.723666\pi$
$739$	−35.1364	−1.29251	−0.646256	+	0.763120i	$0.723666\pi$
$740$	12.7585	0.469012
$741$	3.65091	0.134120
$742$	−0.450989	−0.0165563
$743$	28.9361	1.06156	0.530780	−	0.847509i	$-0.321899\pi$
$743$	28.9361	1.06156	0.530780	+	0.847509i	$0.321899\pi$
$744$	2.31783	0.0849756
$745$	−35.6427	−1.30585
$746$	−17.6289	−0.645442
$747$	−1.86829	−0.0683572
$748$	−11.1122	−0.406301
$749$	2.50639	0.0915815
$750$	17.0879	0.623963
$751$	−0.675360	−0.0246443	−0.0123221	−	0.999924i	$-0.503922\pi$
$751$	−0.675360	−0.0246443	−0.0123221	+	0.999924i	$0.503922\pi$
$752$	−10.0082	−0.364963
$753$	36.0957	1.31540
$754$	0.181484	0.00660925
$755$	−29.3978	−1.06989
$756$	1.63983	0.0596400
$757$	−52.1789	−1.89648	−0.948238	−	0.317561i	$-0.897136\pi$
$757$	−52.1789	−1.89648	−0.948238	+	0.317561i	$0.897136\pi$
$758$	13.7633	0.499907
$759$	7.62018	0.276595
$760$	−15.3679	−0.557451
$761$	16.6707	0.604312	0.302156	−	0.953258i	$-0.402294\pi$
$761$	16.6707	0.604312	0.302156	+	0.953258i	$0.402294\pi$
$762$	−25.6751	−0.930112
$763$	4.71515	0.170700
$764$	−27.5960	−0.998388
$765$	10.6173	0.383868
$766$	−19.0487	−0.688257
$767$	−0.0260917	−0.000942115 0
$768$	−1.42842	−0.0515437
$769$	8.58938	0.309741	0.154870	−	0.987935i	$-0.450504\pi$
$769$	8.58938	0.309741	0.154870	+	0.987935i	$0.450504\pi$
$770$	1.18540	0.0427189
$771$	11.2521	0.405234
$772$	−15.4616	−0.556474
$773$	16.9871	0.610985	0.305493	−	0.952194i	$-0.401179\pi$
$773$	16.9871	0.610985	0.305493	+	0.952194i	$0.401179\pi$
$774$	3.67641	0.132146
$775$	1.50752	0.0541516
$776$	−17.7702	−0.637915
$777$	−2.61877	−0.0939478
$778$	−8.76115	−0.314103
$779$	72.6781	2.60396
$780$	−0.967128	−0.0346288
$781$	6.50051	0.232606
$782$	14.4361	0.516234
$783$	3.05891	0.109317
$784$	−6.91594	−0.246998
$785$	−31.4686	−1.12316
$786$	17.6486	0.629503
$787$	53.9185	1.92199	0.960994	−	0.276571i	$-0.0891981\pi$
$787$	53.9185	1.92199	0.960994	+	0.276571i	$0.0891981\pi$
$788$	−9.46075	−0.337025
$789$	0.538178	0.0191597
$790$	16.4727	0.586071
$791$	0.806230	0.0286662
$792$	−1.94457	−0.0690973
$793$	−2.13574	−0.0758424
$794$	16.1362	0.572652
$795$	4.48313	0.159000
$796$	−10.1978	−0.361451
$797$	−46.0193	−1.63009	−0.815044	−	0.579399i	$-0.803287\pi$
$797$	−46.0193	−1.63009	−0.815044	+	0.579399i	$0.803287\pi$
$798$	3.15436	0.111663
$799$	54.8816	1.94157
$800$	−0.929048	−0.0328468
$801$	−12.5514	−0.443483
$802$	4.04403	0.142800
$803$	−18.5846	−0.655836
$804$	−11.3148	−0.399041
$805$	−1.53999	−0.0542774
$806$	−0.544508	−0.0191795
$807$	−43.3018	−1.52429
$808$	15.5425	0.546784
$809$	2.48123	0.0872354	0.0436177	−	0.999048i	$-0.486112\pi$
$809$	2.48123	0.0872354	0.0436177	+	0.999048i	$0.486112\pi$
$810$	−10.4925	−0.368668
$811$	−24.4423	−0.858284	−0.429142	−	0.903237i	$-0.641184\pi$
$811$	−24.4423	−0.858284	−0.429142	+	0.903237i	$0.641184\pi$
$812$	0.156800	0.00550261
$813$	23.3208	0.817897
$814$	12.8139	0.449126
$815$	34.6413	1.21343
$816$	7.83297	0.274209
$817$	29.1806	1.02090
$818$	−18.2878	−0.639417
$819$	−0.0933607	−0.00326229
$820$	−19.2525	−0.672326
$821$	−52.6140	−1.83624	−0.918121	−	0.396300i	$-0.870294\pi$
$821$	−52.6140	−1.83624	−0.918121	+	0.396300i	$0.870294\pi$
$822$	−3.52266	−0.122867
$823$	−3.36404	−0.117263	−0.0586316	−	0.998280i	$-0.518674\pi$
$823$	−3.36404	−0.117263	−0.0586316	+	0.998280i	$0.518674\pi$
$824$	−10.0832	−0.351266
$825$	2.68920	0.0936260
$826$	−0.0225430	−0.000784370 0
$827$	52.8402	1.83743	0.918716	−	0.394919i	$-0.129227\pi$
$827$	52.8402	1.83743	0.918716	+	0.394919i	$0.129227\pi$
$828$	2.52624	0.0877930
$829$	−47.1855	−1.63882	−0.819411	−	0.573207i	$-0.805699\pi$
$829$	−47.1855	−1.63882	−0.819411	+	0.573207i	$0.805699\pi$
$830$	3.92824	0.136351
$831$	−1.80931	−0.0627642
$832$	0.335567	0.0116337
$833$	37.9246	1.31401
$834$	−25.1044	−0.869295
$835$	19.9354	0.689893
$836$	−15.4345	−0.533815
$837$	−9.17769	−0.317227
$838$	0.278123	0.00960759
$839$	46.6373	1.61010	0.805049	−	0.593208i	$-0.202139\pi$
$839$	46.6373	1.61010	0.805049	+	0.593208i	$0.202139\pi$
$840$	−0.835591	−0.0288306
$841$	−28.7075	−0.989914
$842$	−29.8431	−1.02846
$843$	14.8696	0.512136
$844$	13.1498	0.452636
$845$	−26.0024	−0.894509
$846$	9.60400	0.330192
$847$	−1.99865	−0.0686746
$848$	−1.55552	−0.0534169
$849$	−14.7729	−0.507003
$850$	5.09458	0.174743
$851$	−16.6468	−0.570646
$852$	−4.58221	−0.156984
$853$	−44.2870	−1.51636	−0.758179	−	0.652047i	$-0.773911\pi$
$853$	−44.2870	−1.51636	−0.758179	+	0.652047i	$0.773911\pi$
$854$	−1.84526	−0.0631436
$855$	14.7472	0.504342
$856$	8.64489	0.295476
$857$	−0.753496	−0.0257389	−0.0128695	−	0.999917i	$-0.504097\pi$
$857$	−0.753496	−0.0257389	−0.0128695	+	0.999917i	$0.504097\pi$
$858$	−0.971326	−0.0331605
$859$	−33.3121	−1.13659	−0.568296	−	0.822824i	$-0.692397\pi$
$859$	−33.3121	−1.13659	−0.568296	+	0.822824i	$0.692397\pi$
$860$	−7.72996	−0.263589
$861$	3.95170	0.134674
$862$	4.27950	0.145760
$863$	0.252486	0.00859474	0.00429737	−	0.999991i	$-0.498632\pi$
$863$	0.252486	0.00859474	0.00429737	+	0.999991i	$0.498632\pi$
$864$	5.65599	0.192421
$865$	−31.6239	−1.07524
$866$	14.3669	0.488208
$867$	−18.6701	−0.634070
$868$	−0.470450	−0.0159681
$869$	16.5442	0.561222
$870$	−1.55870	−0.0528449
$871$	2.65808	0.0900657
$872$	16.2632	0.550741
$873$	17.0525	0.577140
$874$	20.0514	0.678250
$875$	−3.46834	−0.117251
$876$	13.1003	0.442618
$877$	50.2276	1.69607	0.848033	−	0.529944i	$-0.177787\pi$
$877$	50.2276	1.69607	0.848033	+	0.529944i	$0.177787\pi$
$878$	7.50778	0.253375
$879$	−11.7081	−0.394906
$880$	4.08862	0.137827
$881$	37.7537	1.27195	0.635977	−	0.771708i	$-0.280597\pi$
$881$	37.7537	1.27195	0.635977	+	0.771708i	$0.280597\pi$
$882$	6.63661	0.223466
$883$	4.81831	0.162149	0.0810746	−	0.996708i	$-0.474165\pi$
$883$	4.81831	0.162149	0.0810746	+	0.996708i	$0.474165\pi$
$884$	−1.84013	−0.0618904
$885$	0.224092	0.00753277
$886$	29.3459	0.985896
$887$	48.6994	1.63516	0.817582	−	0.575812i	$-0.195314\pi$
$887$	48.6994	1.63516	0.817582	+	0.575812i	$0.195314\pi$
$888$	−9.03250	−0.303111
$889$	5.21129	0.174781
$890$	26.3904	0.884609
$891$	−10.5380	−0.353036
$892$	−1.07855	−0.0361124
$893$	76.2294	2.55092
$894$	25.2336	0.843937
$895$	−0.445471	−0.0148905
$896$	0.289927	0.00968579
$897$	1.26188	0.0421328
$898$	−13.9390	−0.465151
$899$	−0.877571	−0.0292686
$900$	0.891525	0.0297175
$901$	8.52996	0.284174
$902$	−19.3360	−0.643819
$903$	1.58663	0.0527997
$904$	2.78080	0.0924880
$905$	12.0522	0.400629
$906$	20.8124	0.691447
$907$	32.8968	1.09232	0.546159	−	0.837681i	$-0.316089\pi$
$907$	32.8968	1.09232	0.546159	+	0.837681i	$0.316089\pi$
$908$	−3.24743	−0.107770
$909$	−14.9148	−0.494692
$910$	0.196298	0.00650723
$911$	0.0911827	0.00302102	0.00151051	−	0.999999i	$-0.499519\pi$
$911$	0.0911827	0.00302102	0.00151051	+	0.999999i	$0.499519\pi$
$912$	10.8798	0.360267
$913$	3.94528	0.130570
$914$	−1.96136	−0.0648761
$915$	18.3431	0.606405
$916$	20.9208	0.691241
$917$	−3.58213	−0.118293
$918$	−31.0155	−1.02366
$919$	39.0187	1.28711	0.643554	−	0.765401i	$-0.277459\pi$
$919$	39.0187	1.28711	0.643554	+	0.765401i	$0.277459\pi$
$920$	−5.31163	−0.175119
$921$	18.3162	0.603541
$922$	14.7108	0.484474
$923$	1.07646	0.0354321
$924$	−0.839217	−0.0276082
$925$	−5.87475	−0.193161
$926$	12.9161	0.424448
$927$	9.67597	0.317801
$928$	0.540826	0.0177535
$929$	−20.5000	−0.672582	−0.336291	−	0.941758i	$-0.609173\pi$
$929$	−20.5000	−0.672582	−0.336291	+	0.941758i	$0.609173\pi$
$930$	4.67658	0.153351
$931$	52.6765	1.72640
$932$	−11.6641	−0.382070
$933$	−20.7209	−0.678372
$934$	40.7389	1.33302
$935$	−22.4206	−0.733231
$936$	−0.322014	−0.0105254
$937$	−38.7070	−1.26450	−0.632252	−	0.774763i	$-0.717869\pi$
$937$	−38.7070	−1.26450	−0.632252	+	0.774763i	$0.717869\pi$
$938$	2.29656	0.0749854
$939$	−17.6683	−0.576584
$940$	−20.1932	−0.658630
$941$	−8.35455	−0.272351	−0.136175	−	0.990685i	$-0.543481\pi$
$941$	−8.35455	−0.272351	−0.136175	+	0.990685i	$0.543481\pi$
$942$	22.2785	0.725874
$943$	25.1200	0.818018
$944$	−0.0777539	−0.00253067
$945$	3.30861	0.107629
$946$	−7.76351	−0.252413
$947$	4.30184	0.139791	0.0698955	−	0.997554i	$-0.477733\pi$
$947$	4.30184	0.139791	0.0698955	+	0.997554i	$0.477733\pi$
$948$	−11.6620	−0.378764
$949$	−3.07754	−0.0999013
$950$	7.07625	0.229584
$951$	18.0641	0.585769
$952$	−1.58986	−0.0515277
$953$	59.2871	1.92050	0.960250	−	0.279143i	$-0.0900504\pi$
$953$	59.2871	1.92050	0.960250	+	0.279143i	$0.0900504\pi$
$954$	1.49270	0.0483279
$955$	−55.6793	−1.80174
$956$	−9.98397	−0.322905
$957$	−1.56546	−0.0506043
$958$	4.22532	0.136514
$959$	0.714996	0.0230884
$960$	−2.88207	−0.0930184
$961$	−28.3670	−0.915065
$962$	2.12193	0.0684138
$963$	−8.29573	−0.267326
$964$	9.61128	0.309559
$965$	−31.1962	−1.00424
$966$	1.09025	0.0350782
$967$	−15.4689	−0.497445	−0.248723	−	0.968575i	$-0.580011\pi$
$967$	−15.4689	−0.497445	−0.248723	+	0.968575i	$0.580011\pi$
$968$	−6.89364	−0.221570
$969$	−59.6611	−1.91659
$970$	−35.8543	−1.15121
$971$	−6.64684	−0.213307	−0.106654	−	0.994296i	$-0.534014\pi$
$971$	−6.64684	−0.213307	−0.106654	+	0.994296i	$0.534014\pi$
$972$	−9.53974	−0.305987
$973$	5.09545	0.163353
$974$	4.81635	0.154326
$975$	0.445322	0.0142617
$976$	−6.36457	−0.203725
$977$	−15.7342	−0.503381	−0.251690	−	0.967808i	$-0.580986\pi$
$977$	−15.7342	−0.503381	−0.251690	+	0.967808i	$0.580986\pi$
$978$	−24.5247	−0.784212
$979$	26.5050	0.847102
$980$	−13.9540	−0.445745
$981$	−15.6063	−0.498272
$982$	−1.90654	−0.0608401
$983$	35.2131	1.12312	0.561561	−	0.827435i	$-0.310201\pi$
$983$	35.2131	1.12312	0.561561	+	0.827435i	$0.310201\pi$
$984$	13.6300	0.434508
$985$	−19.0886	−0.608212
$986$	−2.96570	−0.0944473
$987$	4.14479	0.131930
$988$	−2.55591	−0.0813142
$989$	10.0858	0.320709
$990$	−3.92348	−0.124696
$991$	35.8132	1.13765	0.568823	−	0.822460i	$-0.307399\pi$
$991$	35.8132	1.13765	0.568823	+	0.822460i	$0.307399\pi$
$992$	−1.62265	−0.0515191
$993$	−24.8461	−0.788467
$994$	0.930053	0.0294995
$995$	−20.5757	−0.652293
$996$	−2.78103	−0.0881204
$997$	51.9203	1.64433	0.822165	−	0.569249i	$-0.192766\pi$
$997$	51.9203	1.64433	0.822165	+	0.569249i	$0.192766\pi$
$998$	−16.1743	−0.511988
$999$	35.7652	1.13156

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.13	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.13	✓	33	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.42842 q^{3} +1.00000 q^{4} +2.01766 q^{5} -1.42842 q^{6} +0.289927 q^{7} +1.00000 q^{8} -0.959611 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.42842 q^{3} +1.00000 q^{4} +2.01766 q^{5} -1.42842 q^{6} +0.289927 q^{7} +1.00000 q^{8} -0.959611 q^{9} +2.01766 q^{10} +2.02642 q^{11} -1.42842 q^{12} +0.335567 q^{13} +0.289927 q^{14} -2.88207 q^{15} +1.00000 q^{16} -5.48365 q^{17} -0.959611 q^{18} -7.61667 q^{19} +2.01766 q^{20} -0.414139 q^{21} +2.02642 q^{22} -2.63257 q^{23} -1.42842 q^{24} -0.929048 q^{25} +0.335567 q^{26} +5.65599 q^{27} +0.289927 q^{28} +0.540826 q^{29} -2.88207 q^{30} -1.62265 q^{31} +1.00000 q^{32} -2.89458 q^{33} -5.48365 q^{34} +0.584975 q^{35} -0.959611 q^{36} +6.32341 q^{37} -7.61667 q^{38} -0.479332 q^{39} +2.01766 q^{40} -9.54198 q^{41} -0.414139 q^{42} -3.83115 q^{43} +2.02642 q^{44} -1.93617 q^{45} -2.63257 q^{46} -10.0082 q^{47} -1.42842 q^{48} -6.91594 q^{49} -0.929048 q^{50} +7.83297 q^{51} +0.335567 q^{52} -1.55552 q^{53} +5.65599 q^{54} +4.08862 q^{55} +0.289927 q^{56} +10.8798 q^{57} +0.540826 q^{58} -0.0777539 q^{59} -2.88207 q^{60} -6.36457 q^{61} -1.62265 q^{62} -0.278217 q^{63} +1.00000 q^{64} +0.677061 q^{65} -2.89458 q^{66} +7.92116 q^{67} -5.48365 q^{68} +3.76042 q^{69} +0.584975 q^{70} +3.20788 q^{71} -0.959611 q^{72} -9.17117 q^{73} +6.32341 q^{74} +1.32707 q^{75} -7.61667 q^{76} +0.587514 q^{77} -0.479332 q^{78} +8.16424 q^{79} +2.01766 q^{80} -5.20031 q^{81} -9.54198 q^{82} +1.94693 q^{83} -0.414139 q^{84} -11.0641 q^{85} -3.83115 q^{86} -0.772528 q^{87} +2.02642 q^{88} +13.0797 q^{89} -1.93617 q^{90} +0.0972901 q^{91} -2.63257 q^{92} +2.31783 q^{93} -10.0082 q^{94} -15.3679 q^{95} -1.42842 q^{96} -17.7702 q^{97} -6.91594 q^{98} -1.94457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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